Machine Learning/unsupervised  learning/K-mean-clustering.ipynb

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   "source": [
    "# Chapter 10 Unsupervised  learning \n",
    "## Introduction to K-Means Algorithm\n",
    "K-means clustering algorithm computes the centroids and iterates until we it finds optimal centroid. It assumes that the number of clusters are already known. It is also called flat clustering algorithm. The number of clusters identified from data by algorithm is represented by ‘K’ in K-means.\n",
    "\n",
    "In this algorithm, the data points are assigned to a cluster in such a manner that the sum of the squared distance between the data points and centroid would be minimum. It is to be understood that less variation within the clusters will lead to more similar data points within same cluster.\n",
    "\n",
    "## Working of K-Means Algorithm\n",
    "We can understand the working of K-Means clustering algorithm with the help of following steps −\n",
    "\n",
    "**Step 1** − First, we need to specify the number of clusters, K, need to be generated by this algorithm.\n",
    "\n",
    "**Step 2** − Next, randomly select K data points and assign each data point to a cluster. In simple words, classify the data based on the number of data points.\n",
    "\n",
    "**Step 3** − Now it will compute the cluster centroids.\n",
    "\n",
    "**Step 4 **− Next, keep iterating the following until we find optimal centroid which is the assignment of data points to the clusters that are not changing any more\n",
    "\n",
    "- 4.1 − First, the sum of squared distance between data points and centroids would be computed.\n",
    "\n",
    "- 4.2 − Now, we have to assign each data point to the cluster that is closer than other cluster (centroid).\n",
    "\n",
    "- 4.3 − At last compute the centroids for the clusters by taking the average of all data points of that cluster.\n",
    "\n",
    "K-means follows **Expectation-Maximization** approach to solve the problem. The Expectation-step is used for assigning the data points to the closest cluster and the Maximization-step is used for computing the centroid of each cluster.\n",
    "\n",
    "While working with K-means algorithm we need to take care of the following things −\n",
    "\n",
    "- hile working with clustering algorithms including K-Means, it is recommended to standardize the data because such algorithms use distance-based measurement to determine the similarity between data points.\n",
    "\n",
    "- Due to the iterative nature of K-Means and random initialization of centroids, K-Means may stick in a local optimum and may not converge to global optimum. That is why it is recommended to use different initializations of centroids.\n",
    "\n",
    "## Implementation in Python\n",
    "\n",
    "It is a simple example to understand how k-means works. In this example, we are going to first generate 2D dataset containing 4 different blobs and after that will apply k-means algorithm to see the result.\n",
    "\n",
    "First, we will start by importing the necessary packages −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np\n",
    "from sklearn.cluster import KMeans\n",
    "import sklearn.datasets._samples_generator  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code will generate the 2D, containing four blobs −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets._samples_generator  import make_blobs\n",
    "X, y_true = make_blobs(n_samples = 400, centers = 4, cluster_std = 0.60, random_state = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, the following code will help us to visualize the dataset −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s = 20);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, make an object of KMeans along with providing number of clusters, train the model and do the prediction as follows −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans = KMeans(n_clusters = 4)\n",
    "kmeans.fit(X)\n",
    "y_kmeans = kmeans.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, with the help of following code we can plot and visualize the cluster’s centers picked by k-means Python estimator −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets._samples_generator  import make_blobs\n",
    "X, y_true = make_blobs(n_samples = 400, centers = 4, cluster_std = 0.60, random_state = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, the following code will help us to visualize the dataset −"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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exrljp+S9b51lf/12DgS92XZw7D8QtCvY8+fPZ+bMmZSVpfyqc+fO5dFHH+2wYNfWhrHtjhUXgtRNa6vE577gx83/LvsOW0P1FLpSkRNx02BzbS0vf74cIeD6CUdz1oCJPPXpIr74+kM0JuIMKSzlkTnXZxoOGJbFBS/8haU121DScczPnHtLm+VJK7wBdseyv/MInRF3fx9dUTEsi0vHHcHc0VM5qt8wLnnxb1SFg1n7uxSVXx47N+ccb39cw+4HLwJLAS01a01aNvXSotzrJ5mEKy4XPPn8N/j39pdYXrODyRUD+e5RZ1BbE+HJ5fnDCDfUVFNdHeLcp+5jY31Npqzqz99/mbGBvhS6PPzk3ZeQEiQ2X375Mb788mMMDpTyj9OvYlxZP0b6KlCFAqREW5BaWL16zCzuPf6yzLlau2/r6ndTG48wvrQvhW5v3n0y93g//nb2N73ZdnDs70oURbQ60W1XsMeOHctvfvMbotEoXq+Xt956i4kTJ3a5kQcKTVEZ1ixBw6PpPHDaVVi2jRCgCIWd4UaufuVfmdf4zcFaLnjhz3x65fdRFYXH1yxkSfXWrJofX5r3KGsP+2mr5314znWc++y9mfKko0v78O62dVk1Pf614iMeX7OQ26adzKJdW3Jm5ReOmcbxg0bnjP3ggy4w1YxYN2FLiWnb6LpCIgFPP+bnzu/PzTm+jy//zOK1jSuwpc3Kmh0ZsYbUA2vJ7q08v34JESO3WNWGxmrOf/5+Fl35f8waMIJvTT+FX378Kqa0kUBDIsqFL/6Fh868jtkDR+U9t5SSb777FE+v/TRVa0RKfjTrLEaVVDKtz5BOJes4OBwstOswPOaYY5gzZw5z587lnHPOwTRNbrzxxgNh2wFFVZSML3hpzbYsX6oE6uMxdqdrSG8N1eUUaKoKN7KxvobPdm8jYiRoyZTKQSy48v/4+2lX8cQ5N/KdI0/LKzox0+A3C16n3Jf9hPWqOpMqBmZtq49H+d/Ojax/byiouYWlJNAUZq5p8Mwz+WuJfHfGGXi13O8sJIZtU1lQmLXdpWoMDJRQ3cpCJqREfW3dLgC+MvVEzhye/ZCPmQa//uS1Vo9/c/Mqnlm7mJhpEErGCRkJvv3u01z+339wwhO/J5juruPgcCjRoRWeG2+8kVdffZUXX3yRX/ziF702SqSjVHgDOR1cbGlTlH4ln9ZnCL5mAqci8LvcjL/vx8x9/n6mPfRzVuVpWFDpC3Dm8AkcM2Ako0v6YFj5Q9sUIfjBUWfi1934dTcFuptxZX2z2on9b8fnTHvo51z+3wcIhQSIXLeTriioQkkVbJIGdQ02H2xfT00sW2gHF5byzDk3owml2bEq0yoH41Y1/m/GGXhUnQLdRYHm4ugBIzhv5GSOHjgy72IpQNK2KGkWopcvMiRhmTnbmtjQWJPj+5ak4s43N9byy49fbfVYB4eDFWdJPg+HVw5izvAJFOguvJqOV9P58ayz8aUz/k4dOp6bJs9GUxRciko/fxENiRhx0yBkJFJZe68+2OY5BgZKuHzckXn/AUzb5tSh4/nwstu564QL+fupV/DS3C9nxFFKydWv/IuwkSCUjIM7DjI3Y9O0bYLJOPXxKMF4gqjayGX/fYAjHv4F87evz+wnpeTPn72Xtbg6KFDCQ3Ou49efvMY33nkSVVEwLIubJs/m4TOvQxEKvznuCxw9YASKSFUk0RUVTSj4NBcXj5meiScHuGr8jKxZvFfTufqwma3en7GlfdFE/rKrSdtibf2uVo91cDhYcRyBeRBCcM9Jl/LO1rVsC9czsXwAUyoHZe3z3Rln8LWpJxE1kzy+egG/aDHj2xysbXX8qJFkzjN/YnOwDlVRsVvMPv26G01R6VtQxLkjpwDw4vrP+OOnbyGB6ybMojHZzCUw8RP49Jgct4iUkpiZTE1NLRUO/yTjyrnmlX+x7vqfIoRgye6tvLF5VZabZ2uoni2Ntdyz+J2sjMz7lrzDV6aeQEF69v+fs76YSqJB8I/lH7K8ZgdHDxjBBaOzQz9PGjKOP514Cb9f9AamLblh4tFc3uyNoSXHDxrN9RNn8Zel85G2jdEsld6j6hyRJ0XfweFgxxHsVhBCcMLgMW3u49Nd+HQXo0v6pCI9mgnvkMLSVo/7y2fvsb6hOq9LwKWozBowImvbM+sW87W3Hs/s/735z1GguQg1+cqnvwefzUyJspot/gKBtBTQLJj2fmZ7xEgSMRL4XR5q45Gc+GdNUVhbX42uqlmCrQiF6miYgqI9bjFVKNz29pM8u34xuqLy/IYlDAwUM7N/9nWcM3Iy54yc3Op9ackPZp7FjZNmsyPSwA/mv8Bn6d6WRw8YzjemndzhcRwcDhYcwe4CTh4yjovHTOexNQsyboEHTr+61f0/b8wv1qoQTOszhLtPvDiz7bcL3uA3C17LKW06oaw/W8P1WLZNsryR0769kBd/Mx1MDRQbhA0oSEsF1YS5D0DJnll/qceX6dY+qWIgdrMZrEBQ4vYxo99QjBZ2aopCP39R1rZ3tq7lufVLUs0O0mVTr3v1QVZd95N271179CkopE9BIS+efytVkSCKEFT6Ak5bModDEkewuwAhBL86bi4/OGkO63fsZlRJZUYM83FUv+G8uGEp0bQLwqWonDFsAn866RI8zfy8b21Zw92fzstT4Rq8us5nV/2ATcFayr1+Kn0BfjtyEb/9cxx76ZGQ8FBWpDD9lN28Xfk3zKJqbJnyHbtVnUfn3JARvUpfgMfO+iI3v/kwVeEgo4or+feZ19LXX0SFL8DWZunwt045PmehcXOwNic9vi4ewbLtLstcFELkPCgcHA41DmnBbi2LsQkpJR9XbaI2FubwykH09xe3Od6wknL8ZvsRNHOGT+StLWt4ZeNyhBBMrBjA746/IEusF1Zt5upX/tlqJMXS6u18Vr01y+3wrVOmcdnMBraGtjG8qJwKXwAowbC+SUMiihBQF4syuLA061wAR/UbxvZv/Jrdu4MZIX989UJqY5Gs/f689D1um57tjphQPiCr6aQAhhSWOWnmDg5dzCEp2B/t2MB1rz5IXTzKgEAxD595HePL+mXtY0ub6159kHe2rkUVAktKHp5zHccMGLlP537l8+Xc/OYjqCIVcveLY8/jivEzsl7xbWlz+X8faDPsLZHuVvPR5d/JbGsK1zuy79Cs8XRVTYs3lHvbTr9tflxdPJITWhdO5saYT+87hG9PP5VffvIquqJSoLt46Mxr2zyPg4ND5znkpkA1sTCX/fcBauMRJJJtoXq+8Pyfs8qKAry6cSXvbltL1EwSMhJEzSQ3vf7IPp27MRHj5jcfIWYahI0ECdvk/+Y/T3WLuOj6eCxv8k2+a4FUXZNb3niEKf/+KTMeuZNTn/ojjenEkqRl0hCP5rgsOkIqZC87NvuofsPy7nv2yEkMDBQTM5OEkwnW1e/u9PkcHBza5pAT7JW1O9O1LfYQt4wsPy3A9nA9Zovkmdp4uF3hW7J7Ky9u+IwNDdU5320J1eWcW1dVNjVmhwAWu715/dYtaWoU8K/lH/LyxuUkbYuEZbKqdie3v/c0f1g0j6F/+x6H/esnnPD479kVDbYzYjaTKgZyz4mXpFuFiUzj3s8ba3L2vfjFv7E5WIckVUf71nmPOaLt4NDFHHKCXekL5GTdGbaV07BgcsUglGbuAUUIxpT0YeGuzfxuwes8sGw+4Raz4G++9iTnPncfX3vrCU544vc8vnph1vcD/SU5DwHDshhcWJK1LWom8zbTbY4iBHcceRoAn+zalBVDnbQtPti+gbsWvYlpp+pPr63fxU2vP9zmmPk4Z+RkZvUfgVtViZpJPtixgdOf+mNWtmTESLA5WJvVzEARCp/uyq026ODgsPcccoI9trQvF4+Zjk9z4UtnMd5xxGmUeHyYtsVLG5bx0Mr/UeLx8b0ZZ6ArKm5VY6C/hCvGz+CCF/7Cbxa8wU8+/C8nPXFXxnWxrGY7f170XsbdETcNvtWsVvTquioufOEvqCIltn7djUfV+OWx59G3IDv6oTYWwaW0vbzQ11fI5HRtkVHFlVmRG4oQeDU9q5mAKe1MHHN77Ag38N33nuXG1x/m+XWLeW3TCuJpl5EtJYZt8e7WtZn9vZqemX03IaWkT4saJA4ODvvGIbno+KvZczlrxCQ2NdYyvqwf0/sOwbAsznv+flY2a3Dw91OvZMMNPyOUjFPu9TP+nz/OCHDcMqiKNPLU2k+5+rCZ7Ag3oLWIilCEoDYWpkB3c/az9xJMxJCkao+UeHy8cN6XGBAoaWkeA/zFeDU9q+h/S+rj0cwbwJemHM+rm1awIl1VT0pJXTSCW9Wzkl4q21lwBNgVDXLCE7+nMR7FBp5bvyTvfs2vVREKfzjhIm5750kEAiFg9sBRHNdKJT4HB4e945AUbCEEsweOyirt+fyGz1hRsyNLJL/29uOsvPYnmRC4lguBhmVlekSOL+uX4+7wai76FhTy3rZ12HKPk8NCsjsaajXsTVdVnjznJi7779+pjoZwKRoSssTXkBbhZIJCtxef7uKKcTP4/gfPY1kWEoiYCQpcHlRFpLIdkdxz8qXt3pun135KOBEnt/Zf2jZFpdjt46QWrbzmjp7K+PL+fLprC30LCjlh0Jic5JYm/7+T9OLgsHcckoKdj+poKKf+dEOLEp4nDh7LvC2r97S2UlWOH5iqTz0oUMpD51/LFc/8A0tKArqbx8/+Ipqi4tPdWZmEkHIt+DRXq/ZMKO/P0qt/SMRIsDVYz2lP/zHr+3KPP6u7+5r6XSSbVf+zScVDf33qyVT4/JwwaEyHEk+SlpVV+7oJt6oxoaw/U/sM5hvTT8Gfp33Z2NK+jC3tm7M9aiS5+Y1HeGPzKlyqyh1HnMaXDj++XVscHByycQQ7zYx+w1Iz3rRoa0LJ6YN4z8mX8rV5j/P21jUUujz86ri5TKwYkPl+7ripbLhhOPXxKGXpbuUAR/QZwqTygSyu3krcNPBpLi4bd0S7HVQg1Z1lbFlf7jx2Lre/9zQCQcCVehg0n6lOLB+Q1YVdkIqZvnvxWwjg2XNv6ZBgnzlsAnctfJOYlV3vWxUKPz/2PPr7i6iPRyhye1KNBTrAHe89zdtb12BJm5hp86sFrzGipILThh7WoePbI2ok+fGHL7KoegsDfcX84tjzGRAo7pKxHRx6EkLuTYBuJ+hJLcLa4z+rF3DHe8+QsEymVAzioTOvzSScdIS2bDcsi4dXfcznDTVM6zOYc0dO7rRrIG4aNCSiVHgDOe4UW9rc+PrDvL5pJZJU/HXzuz6yuIIPL7ujQ/YvrNrM9a/9m6pIKgzQq7k4buAoij0+nlm3GFUolHsLeOH8W9vN/gSY+K+fsCuafV+umzCLO2fndr/ZGy544S98vHMjCctEFYIyr5+PLrsj6w2kp9OTWlTtDY79Xcc+tQg7lLhk7BFcPGZ6qq1Wi5T1t7es4Rcfv0LMNLhs3BHcMvm4TgmurqpcO2HWXttmS5tHV33C/O3rGVJYxtennZRpqACphb+/nXolm4N13P/Zu/xz+YdZx2/vRCf46X2H8NnVP+TtLWtYVrOdIYWlJC2Lb7/7dMYdtD1scssbj/L8+V9qd7wyrz9LsF2KSt8uiiBpiEf5aMfnmVBNS0piRpL/7ficU4aO75JzODj0FBzBboEQIkesF1Rt4ppX/5VxN/z6k9ewpOQrh5+wX2ywbJsn1y5ibd0uxpX144LRU7nj3Wd4Yu0iYqaBS1F5eeNy3rn4m1lNAYQQDC0q46TBY3l89cLMAqoqBONK+7V2ulY5YfCYTInZH3/4YtaCrCVtVtXldtXJx2+O+wIXvvBXbClRhKDC5+e6CUd32p58qIqSE7MuAbWD7hoHh96EI9gd4Mk1i7ISU6KmwYMr/rdfBFtKyfWvPcg7W9cQNQ18ms68zat5fsNnWOmFy6RtUR0N8e7WtZw+LNcPfOrQ8Vw3YRZ/Wfo+mqJQ4Q3wt9Ou2Ce7RhVXtvCRC4YWlrdzVIoj+g7lnYu/ydtb1+DTXJw1YmKb1Qw7Q8Dl4ewRk3h144rMw6yPr5BZ/Yd3yfgODj0JR7A7gFvVEJA1j3O1UeVvX1hTv4u3t67JCGPUNHjp86Utzp7CsFsvDvXDWWfx1aknEjLi9C8o3ufKeZeMPYKXNy7ng+0bUNOt0e7rQJhgE0OLyri2aO9dQm1x30mX8efP3mVhzRYG+kr41vRTcqoROjgcDDiC3QGunTCLh1d9QtRIICGTHbk/CCcTWc1wIeX/nlw2kKXV20lYJopI1fU4up3KgcUeH8UeX5fYpSoKD595HctrdhAxEkwo7583tK87UBWFWw8/oUctHDk47A8cwe4Aw4sreOOCr3H/Z+8RNRJcNGZ6u+3D9pZxZX1xazoRM4ktJaoQFLt9PHrm9fzs45f5YPvnDAwUc+fsuTn1T/Y3TbW7eztbgnVsCtYyvKicgXkyTR0ceiqOYHeQkSWV/O74C/b7eQp0Ny/N/TK3vPEInzfWMLqkkj+fcjlFHh+/Oa5rzm9Lm3e2rqU6GuaIvkMYXlzRJeP2Bv69/CN+8MHzuFSNpGVx5+zzuayNZsAODj0JR7B7IMOLynntgq/tl7Et2+ay//6dT6o2gQQbyd9PvfKQCIHbFQny/Q+eJ2GZmWJW33nvGU4dOp5yb/64VweHnsQhV63vUOeVjSv4pGpTqmu6mSRmGtw67z/dbdYBYWuoHleLfpS6orE91NA9Bjk4dBJHsA8xdkWDWC2KVDUmYjm1Tg5GhhWV59SLsaTNkMLSbrLIwaFzOIJ9iDG9z5CsDE1VCA4r75fVCuxgpcxbwP0nX4ZX0ynQ3Xg1nb+eekWXRdI4OOxvHB/2IcbkyoHceez5fPu9Z7Bsm5HFFTx0xnXdbdYB48zhE1lx7Y/ZGW6kn78Ifxcl8Dg4HAgcwe4hSClZWr2d6liIieUD9mu3lkvHHcnFY6cTM40uyzjsTfh1N6NKKrvbDAeHTuMIdg9ASsnX3n6cF9Z/hqaomLbNQ2dey7H7sWOLIpRDUqwdHHozHXJcvvXWW8ydO5czzjiDn/3sZ/vbpkOOd7et44X1S4maBsFknKiZ5IbXHupusxwcHHoY7Qr21q1b+dGPfsR9993HCy+8wMqVK3n33XcPhG2HDFuCdTkV5xoSMQzLauUIBweHQ5F2XSJvvPEGZ555Jn37plo/3XXXXbjdzqt0VzKxvH/WZwEMCpTklHl1cHA4tGl3hr1582Ysy+Lmm2/m3HPP5dFHH6WoqP1WUw4d5/A+g/nejDNwKSpeTafSF+DROdd3t1kODg49jHZbhH3/+99n8eLFPPTQQ/h8Pm655RbOPvts5s7tmvZODnsIJ+PUxaL0DxR1uF+ig4PDoUO7LpHy8nJmzpxJaWkqG+zkk09m6dKlHRbs3tTTcV/pCtu96NTXRrvIos7Rm+899G77e7Pt4NjflbTV07Fdl8gJJ5zA/PnzCQaDWJbF+++/z2GHdU23awcHBweHjtPuDHvy5MnccMMNXHbZZRiGwdFHH80XvvCFA2Gbg4ODg0MzOpQ4c8EFF3DBBfu/FrSDg4ODQ+sc/BV/HBwcHA4SHMF2cHBw6CU4gu3Qa1HVHej6GoTo/Oq+EDE0bTtCRLrIGgs4+GuKO3QvTvEnh16IxO9/Co/nU6RUAZtg8HpgSoeOdrlWUVj4EFIKhLAIheaSSGT3dRQiSCDwNKq6C9PsTzj8BaTM1/Q4QWHhv3G51gGCSOQ4YrHTgYMpjl7i8fwPXV+HZZUSi52IlE4N8e7AEWyHXoeur8PtXowQBkIYABQW/puOCXaCQOAhhEjS1MchEHgWwxiFbTd1UDcpKfkTitKIEDaqWo+m7aK+/hu0FOJA4Glcrg0IIQFJQcHbFBS8Syh0EYnE9Hat0bStKEo9MBLomSJYUPAcHs8nKIqBlCoez1Lq6r4JOCUqDjSOYDv0OlS1DloUyxIiRsot0d6xjTnbpFRR1ZqMYKdcJVGEsNNjWyhKPapag2X1yTpW19cjxJ7zph4CNoHA05jmQCyrb875hIjhdi/G7V6Mrm/NvCW43ReQSExr9xoOLCZe70dZ90KICC7XWpLJid1s26GHI9gOvQ7T7EezLmdICbZdjNqBYlmWVZSeDe9BCAvLKms2npZnH5kW1mxsO4CqBnO2S6mgadtzBFuIKCUlv0OICEKYCAFCpDq4BwJPkkhMAvR2r+PAkS9LWWZsdjiwOIuODr0O0xxCJHIaUqpI6UJKP42NHS2W5SYYvAwpdWzbg5Qa4fBZ2PaeRryW1Q/DGICUqfmMbesYxmBcrlV4PB9kLXKGwxdi2y5yK/JIbDu3SJrX+wGKEkZRzKyHTgqBonTVImhXoZNMjsncCykFoJJM7r/mGg6t48ywHXolsdjxxOMzECKSdmV0fJEvmZxIbe3/ZdwgucKq0Nh4I17vu2jaDmy7OL3othkpBQUFr1Ff/w1suxjTHEh9/e14vW/h9X6cFjZJIjEBwxiRc24hwlkulOZIqaNpG1GUBIYxAsuq6PgN2Y8Eg1fh97+Ay7UKkCSTo1CUGJaVv94FgKZtpKDgTcAgHp9FIjHlQJl7UOMItkOvRUovUnr38lg/ptm64IBOLHYyAEVFf80sUgoBUpr4fK8TDl8EpNwxkchcYrHZ6Po2LKsI0xxKqrJ5NsnkeLzeTzKLpamZuUCIAmzbRyDwJCmXAzQ2XothjN6r6+tadBKJSXg8CxHCwONZiNu9jIaGr+b49AE0bQvFxX/NXKOubwXMFouwTSGQzkt+Z3AE28GhHVKz4uafJYqSG/tt2+UkEuVtjmUYYwiHz6Gg4GWEMEkkDiMcnkN5+SYU5QkUxcjsGwj8B9Psh65vwbYLCYUuxTQHdtl1dYaCglcyApy6F0m83ncIhy/O2dfj+Sizb2p/A5/vnbRgWwQCj+N2LwEgFptFJHIOjnB3DEewHRzaIZmcgKZVN5sV6ySTE/LsaeL1vo2ub8KyKolGT0NKT85e8fhM4vGZLbYuy1nIU5QQLlckHaUSo6jofurq7kDKwi66suZYuN3LECKMYQzHslp0QRLJFp8lQiQ6fRaf7zVcrmWZqBOP52Msq5x4/Ji9N/0QwhFsB4cWCBHG7V4BCBKJ8USjJ6MoYTyeBUgpiMWOIx4/ssVRksLCB3G51iGEgZQbcLnWUl9/Gx37MxuV3q/poaAAdo6/W9c374dwOovi4vtR1R1pIRUEg5eQTE7O7BGLHUlBwSuZNwApdRKJI/KOFo/PwuNZkvWAi0ZPBMDlWp31FqEoBi7XKkewO4gj2A6HOAkKCl5H03ZgGAOJx6dTUnIvTcJZUPAS9fVfJxyeSzjcetOO1Gx4bWaWLISJojSg65vzLj7mMppw+Gz8/hcBE8MYjK5vJjusTiJl1yeruN3LUNUdKMqeWXQg8CS1tXsEOx4/FiEsvN7/IaVCNHoqyeS4vOOZ5iAaGm7C55uHEAax2CySyUkA2HYRUu7MhE1KqWDbxV1+TQcrjmA7HCJI3O5PcLuXYtsFRKOnYdslFBffj6ZVIYSJrm9MLwhGMz5rKU0KCl4mFLqinfFbqyPS8W5L8fgs4vGZuFwr8fnewrb9KEoUsJBST4cb5hN/G0UJYts+wNXh8zWR8tHbLbYl0rY3Oe8FsdgJxGIndGhM0xyaLheQTTh8LiUlm5Cy6c3BTTR6Wvq/LVyuNQgRxTCGYtttrwccijiC7XBI4PW+ic/3Vjq9GjyeJUipI0QiI86p2bGVZ4ExNzuyJbZdhGkORNO2IYSJlApS+jCMwZ2yU9fXU1j4cDN3gkoiMRbDGJ92w2SHL6rqToqL/5IWWJtw+Lw8/vG2MYzhNI9okVLBNAeRL8qlPVS1mkDgoXTIZBnB4JVYVmXme9sup67udlyu1YBCMjk+HeljUVT0ZzRtO5C67z0nSqbn4Ai2wyGBz/duxneaCs2zUZR8i2ZKuihUyrWRWmDM/+qfjaCh4Yv4/S+h65swzUoikVPx+19EVXdhGIPTM8m2sxhzIywsVDVMKDQr7/5FRX/PimLx+19AiBA+33yEMEgkDiMUurjN81pWf4LBSwgEnkSIBKY5iMbGazpwzS0xKC6+N53FKRGiiuLi+6it/R7NZ/5SBnL83273EnR9e9biZiDwGHV1P9oLOw5eHMF2OERo+cq/57+lbBJxBdMswzSH4/F8AkA8Pp1Y7PgWY1mo6i5ATSe3NIWkuQmHm9rnmZSU/B5VrUUIC13fgq5vo7HxJtqeueYLb5N4vW+iqkGSyTEkk009VRMoSqjFtUgKCuZlFivd7uVIqRIOX9rGOSGZnJz2WTd3g3QOTdsFGBn/dCqd30DTdqVn7K2jKEFa1oJJuYMcmuMItsN+weN5n4KC1wGLRGIq4fD5dGfJUcMYgcu1Kk86eIqmBBZNqyMen0VNza/S32QfIESY4uJ7UZQgQtgYxmAaG79Iyz+lVBW+xoxwpnzkm1CUxjYW2SSmWZGe4TctymkoSpCCgjcQwsLtXkA0emral+zKuHX22GfT/OEkhInbvZpwOPtMqlpNYeG/UdVqbLuYYPDKdIz33ok1gG178/jCbWy7/eQmwxhK6mGVul9SKhhG2yJ/KOJEqzt0OS7XMvz+l1GUGIqSxO1eREHBK91qUzKZ3xfaVAMklcVoIYSJ3/9S2m+dEi9FqaGg4Hn8/qcpLHwIVa1DURIIYaDrW/B638kZt2XxqI7g8XxIQcE7zcRaEI8fnvazW2lbDAoKXqNpJhwKXdGsLoqOaQ6g5YMxVzBNioruQ1V3pV0utRQV/Tld8XDvse0y4vEp6fouIKWLeHxShxYPTXMY4fDZSKkhpcA0+xEMXrVP9hyMODNshy4nlYDRMtZ2OZHIWfvhbAkKCl5D03YAw4Hj0fXNqGoNptkvnSKeEoTUz73JNw2pyIfpeDyfZflOU7Pa+nQFwGqKi/+QWZxscp80IYSRWShrjmEMxrYD6Yp8FratYZqD03VLUoubqlqLooQxzX5AAJ/v3az7BhJVrSc30sSiSbCTyXHU1d2Bpm3HtguxrGJKSu5GUcKkZtpKTjiiqtalryd73FRoY0dCEFsnHL6IZHIsmlaFZfUhkZjc/kFpUlEyR6WvrydVLOw5OILt0OXYth8plazX4/3TocTOCsuDzZSWfoQQcSAlrJHIicRip2CaAwmFLiQQeAowMM3KtCvDi8fzWdaoqXjjt9C0WlJRI80jSbJFe8+stiUaDQ1foaDgJTRtF4YxhEjkDHy+V/D53qZJcKV0pf/7xrQfNxvLKkHXt+y5YlvDNIciRAQpA+ltxcBmioruRwgDyyojEjkJ0Egmx2BZ/bLvmu3NSchJPVS64t9IkExOzkq66RwKzot/6ziC7dDlxGLH4/EsAppieVXC4XO7/DyquhNV3d0spdtAUYysGXBBwTzi8ZlI6UZKN6HQhSSTw5CyJLNPMHh1umNNypVh2x7c7rUIYeXMqNNnxrZVhJAYxuA8i5IppCzIqrXhcn2G1/s+mzeX8uc/z+bRR48kGPRQWBjnsss+4aabihg2rDZ9bOqYWOxY4vGj8PufQlVDQBJd30xZ2c+IxY4iEjkPVd1FYeF/MrNzVa3F4/mU+vrbAdC0zRQWPoiiBLGsCoLBa4nFjsXj+TB97wRgUVLyR+Lx6d2+3uDQOo5gO3Q5tl1IXd238XgWAybJ5IT9Uiq0tQXE5kipoij1FBY+lvZLS0ChoeFLmXoZhjGG2tofo6qNCBFOh8o1LRbmzqgjkVNIJseQihKpJP+M0CLl+tiTmajrG3jnneFcfvn1JJMqqmrj9SaJxzX+9rdj+Pe/Z/LIIw9w4olrMlErQliY5hAaGr5JcfHdaNrWjCvD41mAYYxEiFh6obLpvkhUtZpUxEaSoqK/ZkIYVbU6XZPk/0gmR+HxfILbvSJ9vTZu9yJs20c0embn/jEcDgjOu8cBQEpJbWIV26LzaUhu7G5zDghS+onFjiUWO2G/1XU2zb7YdkmzTjAq2QkgqW0u16rMQqGiJBEini5j2hwXllWBlLmRDqBimiVYVimRyCnpaxqQ7ibT8k9I4vO9Qnn5dykv/wFFRfdmFvM2bhzA5Zdfj2kquN0mmmYjBGiajdttYpoKl19+PZs2laXtV2juv04tEu75LEQSTduRcY20tKOw8B+4XCuy7kkqESiGojRgGGNI1SvZU3RKUYx0HRWHnogzw97PSClZHXqM6vhyUotAgiEFpzCk4MTuNu0gQKWh4da0n3gHuj6MhoZxFBU9ihBhbLuExsZr8Xo/yBIlIUiH5YUIBJ5A03Zimn0Ihy/EsioxzXI0bWdmlmsYQ2lsvBkQ6Ppa/P6nsG0f8fgxmeYHQsRwuZaj61vSdaNToq/rGykuvov6+tv5y1+OJpmUuN1GvotB1y0SCY2//OVYfvGL59INEvZUzbPtEoSoajbbd2FZ5SSTYzCMEej62nSkS+oaXa516PrniJxXEQNFacC2y5AykLXekGq3lq87vENPQEiZ29yoK6mtDWPbHT9FRUWA6urcWsO9gXy2h4xtLK6/F5tm2WuoHF3+YzRl74rv7y96872HlvZbNPlh3e7F+P17ak1LqZFITEDTtqUjJmykFNh2EcHgZeni+03RJArR6LFEo2fjdi8kEHiaVDU+BSk91Nd/CykFJSV3IUScVCf37N+7lBCPz2DUqGtIJEDTTFKFnNS0wMZpmkmbpoLXa7J69ZNEIudlLdam0tDvS+9rYxijCAavJjXLtykp+TWaVpNzbssqSrt7mm8ro77+uyhKIyUlvwcSmQdUY+OtrSykdvTe9z56kv2KIigry99cw5lh72eSdhghVJDNBVvBkDE0epZgH1zsWTRLJKagqjvw+d4FwDCGEIsdS1HRX9jTDVwiRAyv9yOaQv9S2208nsVEo2enmw4Yme0Qx+1egKKEUJRIxu+dG/oHbvdSQiGBxyMz/RFT+6aiIoRIIiUoiouGBo1w+LKcK7KsftTVfQ9N246UHmzbne7kXk4qpT5/lEcqPDFI00NBCFDVhvR3RdTVfQu3eyFCQCIxCdsuyzuOQ/fjCPZ+JqAPoGVatKZ4cSu5DVod9g6XayUezweAC02bnY65bo4gGp1DNHo6qX8LHUWpyZkJp7Ly3DTNWPeQqlOd22XGRohkVkZjapxc0ZbSRSAgSSSgeXP31Aw7SqotmIJpCgoLW38jldKLYQylqOgBdH0jYKfdNmOJxWami081t10lkZiULtXaNAZYVmH6/CGKi/+WTrVPNSVI3afs6/R638bj+RQpPYTDZ+W5xw4HAmfRcT/jUgJMLLoBXUktDHnVCqYU34wiui5sKmmHWN7wLz6uvZPljf8maYfbP+ggweVaTmHhQ7jda4BlFBf/FU3b1MreKk0JGbZdRjI5CttOfZZSxzCGEoudlA4BFJntkcgZeDyfkr9H40SSybFIuSfRo8nJmMr2axrjbObONTCzmsrIjFinsLHtBHPnZnd3aUmqq83GdFKOjaKYuFzLKSh4jWDwCgyjEtt2Yxh9aWy8kdQDZ8+fesrHnbqWwsJHUdWq9IPDxud7N71QuQef7zV8vjfRtF3o+maKi/+Kqu5s00aH/YMzwz4AFLuGc3T5j5DSRoiufUba0mRx/b3ErXokFnGrnsVmFUeUfqtLHwo9FZ/vLVr2D/R63yMUGtrOkYJg8Co8nvnprLx+xGLHACr19d/A652PEDESiSkYxmi83rfyjqLra4nFjkdVd+PzvUdTA90mpBSEQl8gkZjC1VcbPP64jmGArpOTvGIYKi6XyY03foDXm0wnvfTNc86ttGwnlhLhGFJ6aGi4vcX+a8gtfpUqrJQKE2z+nYGmbWlWYAq83o+zusSAgdu9hGg0OyHHYf/TYcH+1a9+RX19PXfeeef+tOegpqvFGiBi7iJphZBNRXOwSNqNRK1d+LX+7Rx9MJDPfdDS1RHB738eTavCMAYSiZyNy7WCQOBpwMSy+hKNnkGT39u2S4hEzs4awzBG5pxFCCgoeDX90EiQ6n7e0h6RKfY0eLDk/vvj3HKLJ734KNA0sCwFy1JwuSwefvgBxo/fAEgKCl6lsfE6DGNU1oim2S9d6N8il9y3gJT7QmdP+zEVwxiWvtZCFCW+585JPac41Z6wySYUnMSa7qFDCvLRRx/x7LPP7m9bHPaChN2ARXaYmJQS0U0vT1GzmkZjE6Ydb3/nrjhf9PgW7gi9RX9Ak+Lie3C7P0PTduDxLKKo6O5MtEcqyaSKwsJ/tBjZwuVaidv9KYrSgGkOztueK+WSiKcXLfN1nZHpWiEpjj3W4uWXo1x1lYHHoxKLefB6U7PqDz/8DSeeuDZTf0QIA7//6TzXfDKmOQApRTP3i4ptF2aEuDnJ5DgikVPTkS0C0xxEKJQqtxoKXYptu9P/c2FZA4jHs2tVR6OnZO5x6pyunH0cDgzt/lU3NDRw1113cfPNN7N69eoDYZNDBwkaW1jZ+AhZ5TTRKNSH4lP3T7JKa0gpWRt6ml3xRQihIhBMLr45vei6/0gmJxMMKni97+NyuWhsPC6rgJGm7UjHXDdlLlpoWh0tk0lSxaNSxZJSIn8vqrq76epobLwWyypBUbIr2uUuLjbPioRo9ESkbB7XbDNixDp++tMwP/zhEGy7DJdrHUVFLuLxgUB11vjZNaEtFCWEbRfQ0PBlNG0rHs8nqGodptkn3SAh+0/a5VqBpm3Btkupqfl5euueB5xpDqKu7g50fRNSetJvEtnzuHj8KGzbj9u9GCm9RKMnYNslOBx42o3D/upXv8qll17Kzp07+eSTTxyXSA/i7Y2/oSa6PmtbiWcoJw77NopyYGfYO0PL+Gjr37DkntrMBXo5Z47+eRtHHQi2AL8lVdekCTX9v+aLez7grvR/vwc82eJ7gEFAFZA/8SWFAAoBD3A60LxTjA3cAzT9m5nAEen/TQBWA/c2O68OHA5cD2wG/tjsuyuBGW3YAfAM8FbaXg0YBnwDJ9ag99LmX/WTTz5Jv379mDlzJs8888xeneBQT5xpDyltNkVeoyq+CEVoDC84kwrPpA4dG03kRoOoMkBt7d7VNd6Xe78zugVbZi+ERYzaA/pvmd/+IoqLKzIV/VLRIIMABU1LVcETQhIMXkwymTrW59uFz5fMqVUi5XYMow+GMQZVrcY0ByBEAp/vw5QbSlikKvDFECJKY6OOYeyxx+VaRiCwLqs7uZT/Q8pPUZRTqK4+AY/nXAoKXkQIk2RyLMHgeQixk9LSP2TNtqV8iLq6yjZqTScoL3+jmZvGRMr1NDYuwjDGdv7mtkNv/ruFnmX/XifOvPzyy1RXV3PuuefS2NhINBrlF7/4Bd/73vf2i6GHIpsib7A1+l4mE3JV8DE0xUeJK3eRqyWVnklsidRmjlXQqXDtXVlLw4qwYve71AS34dP6MMh3HKroeE3iArUPAjWz+AngVXtCAoZCQ8Mt+HxvoOs7MIxBRKMnk6oxshpFCWMYQ7Maxaa6n+xZpGtCCBtd34miWNTXf42mwk7J5CQ8noXplPRUwSWAwsLHqK39yR5L0l1qssckvf+rCDGTeHwG8XjTzNkiEHgUt3s5LdtnSamiaVUkk/kFu6kpbzYSt3vpfhFshwNDm4L9z3/+M/PfzzzzDJ988skhI9a2tAgaW5CYBLTBaEruglNrxK064lY9Pq0Sl5KvMM8edsUXZaWt2xjsji/pkGAP8Z2Macepii9AoDC44GT6eKd02M4mdsQ+YW3oSTLRFQmVmsRyppZ8hZhVg2FHKND6obeRSl/qHkN/70y2xz5AESoKGhOKrum0LfsHN9FobvOEZHJ83r0NYyyRyCnpLjnZYXqpLMF6PJ4FmcVN0xyCZW0hNzqlKcZapPcbTL4ojhQKQiSQ0pPZ4vW+i8u1Mm80SKp+det+5FRBKJFjU1PcuUPvxInDzoMlEyyuv4+YVQ0IVOFmaslX8ajF7R67JfI2myKvIYSGlBbjCq+gwnNYq/urwtViS+p8HUEIhZGBcxgZOKdD++cjatawPvQM2X/YFhGziuUN/6TB2JBeRCS9iDiw1bFGBs5mkG82hozgVSs6NUPvacRiJxKLHUVJyZ9Q1eoW7hEj3dGl2RZjCNmVAkW6HseebanojPMIBJ4h1Rhhz75CFGPb2Q93Xf+8RfzzngqEsdisdup9CBKJcbjdK5vZrmEYzX+LFm73MhQlhGEMST9QHHoyHV59mDt37iGz4Lgl8jZRcxeWTGLJBEk7zNpQbnhVS4KJKjZFXsfGxJJxbAxWBR/Gkq0vUg33n4mSWbUXKLgI6AOpS67NWsDbX0StXYi8MbWSBmM9NgaWjGPKOCsaH2x3PLdahF/r36vFeg8+6uu/gWEMTtf8aELPistWlAaEMNKhcxpSKlhWH4LBa3NGTCRmUFPzSxobr8ay/EippoU3dzHQsiqzYqD3hAfYWVX8WiMcvoxkchxSKti2i3D4HAyjqbelTVHRX/H7n6Cg4L8UF9+P272gQ3fFoftwZth5iFi7sWm+gGanZ9vtHJeszin0BGDYIVS1NO8xZe7xTC65id3xxYBCXXIVa4NPgQBVeJhW8lXcaufrjtjSJGhsRmJTqA/OO2s37ThupQiZ4+sEUHK2x+2GTtvR+9EJBm8kEHgYl2ttOs38nIxgu90fEwg8l6m8FwrNTfcxbP0tSVEaKCx8ktRCoJouxJQ7d4pGT0nX8k799vbMlCWBwOMkEhPaPI+UHoLB62nulmnC5VqJpm3JmsEHAk+TSEzP2deh5+AIdh6KtCHUJVZlfMsClUK9/dfFgLsvUrbslafgUgrbPp8+lCJ9KBtCLxK3GpCYIMGSButCzzGh+OpO2W/acRbX30Pcqs8r/KYdY2njPwgZqYJAAW0wYXMbEhuJjU/py+CC41kbeqZLFhFtabI5Mo+QuQ2/1o8hBSfncQX1XFLCdwMthU+IIIHAs+lEl9RvJRB4Jj2rbV1I/f4XESLGnu7oJvAc8IUW5/VSX/8NSkt/jKrmvm0pSjhdrKo9cgU4VV3QbLHVBGKkQhz3hVQ3eSmVtJvFyYrsKnqkYBt2FImNLgryFF/f/wz0HUvQ3EJNYjkCQYHWj1H+89s9zu+qYKT/XNaFn8vU8ZhQdC2K6Nhtjli7U2KdoWMz+5Zsjr5J1KpOiW1G+J9lQvE1AKwJPUnI2JKZQYfN7QwrOIOB5SNJhgO41dQDJmJWsS02P72IqO/VIqKUkqUNfydobMLGpCG5jvrkOqaWfGW/pOrvDULEcblWIIRBMjmmjcW87N+iqtYjpZYlfFKq+P0vZDq9xGLHpKvf7Tk25UJp3jnGBupaOaeOZfVDUTa18KMrmeYJe0MqEiY3jd7tXksiMWWvxxUiREnJ3ZkFV9suo6Hh1qzF1Fya3uR6xu+hJ9OjBNuWFh9u+TM7QkuB1MxzYvH1+2021mhsJm7VUqD1zaq7IYTCYUVXkrRDxMx6FDR2xz+j0dyIRyljkG82mpL/B9jfdxQVnokk7CAepbRT0SVF+lAakuubzew1CvUhnb6uqLk7a2YMNtFmwt9obMz63sYgalVT6T+L6tieWNQRgbMY6JuNKaN41fIOP3iaE7NqCRqbMy4mG5OItYuwuXO/Z0F2BCGi6eYDEVL1OwSNjV/CNFtfXG3CsspzIjiEMHG5lqEoqev1+d7HtguJx4/O7JNMjkFVq5o1VNARYkKr5wmFrkg3GWiKw1ZoaLiGffnzTdXQzo4iSdXpbjnr7hx+/3PpcrNNdcZ34/W+QTR6dp69bfz+Z/B4PgEgHj+CcPgLOMLdOj1KsLdG36EqujwjJkFjMxvCLzE6MLfLz7U+9AI7Yv9L1y6WDPfPYaBvTw0KKSUbw69RFV+Ynommf4CoVCeWMK30tlYX1nSlAF3pfJulQb7jCRlbqU2uQiAI6IMY5j+DFY0PUpNYgSJUhhacziDf7DbHKdKHUp9c16rwu5VikvYeYRZoeFvxsbvVQty07dJpC5lui9YcgWjxQOk+vN73slLXpYTi4nuor78Ny+rT5rFSFhAMXkph4WOZNluWVZTV9UWIJG73sizBjkZPQVEa0iVbIR6fjtd7MhDJex7bLqa29odo2jY0bQMFBfMoLn4A2y6ksfEGLKsCTduMEIm0b70jExyVZHIcLtfadEJRalvLQlOdRdN2Z8Wap0oBVOXd1+t9B49nUWZ/j+dTLKuEWOzkfbLhYKZHCXaD8XlWRIWNSdDY1OXniZhV7Ih9lBK09ARjQ/gl+nqmZdp21SSWsSv+aQsXRaoaXsJqpD65jnJ3/jjevUURKhOKryFph5HSxqUEWBN6gprESiQWlrTYGH4Fr1qec24pU7NogcIA72yCxpaM8Pu1AYz07wn9G1N4EYvr700XvgCPUsoA3zEtzekSfGo5ulJAwt6T3acJX4+pJJi/+YBJcfF91Nb+H+2JXzI5idra0ekeicUEAo+gqrXN/NMiJ1wPVMLhSwiHL2qyAq+3vVmlhm2X4PfPyyTmKEojxcV/RkqlWXMFQUPDzZjmiNaHShMMXpF236zDsgoJh+fuk5sFwDAGpcMgm1qs6Wn3Sy4u16qc0rhu92pHsNugRwm2T62gQaxvtnCn4FVbS73dexJ2MCeaQ6CQtCMZwQ6bO7FzaknswW4jVG9fcSl70lLrkmuyHho2BnWJVVmCbdhRltTfT8yqBSSF+mAmFX8RU8bSwl+YtRbg1/oxo+wOGpKfowoXJa5RJOwg729+lGBsN0X6MEYGzulwPHhzO6oTy5DSosw9Do9aQtyux2jRUEER6l65V/YHyeRYPJ7FtGzSK6WJplWh6+vweBYhpZtI5My8M1ApPZm61ZHIWej656RcCyIdVdKyg0sTnXv1T3VIVzK+7NT/R9OVAjPWUFz8t3Shp/YW+1yEwxd0yob2iETOQdOq0LSdgCSZHEEslr/htG0Xp2PQ9zzcLMvpxNQWPeOvJs3QgtMIWuuIGg1AKrphpP/cLj9PgdoXKbND1hShZSXG+LQKFFx5RVsIhWJX+zOYzmDJJHGrHpdSmMkotKWFZbeMDsiNOlkffp6otTvLlbQ5Mo9h/tOwpYkhI+hkL+C6lACVnlQau2nH+LTubkyZWuyNWXXErBqmlNxCXWJNOrbcYoB3Fv28R+a1P2mHWFD7eyyZaij7eeS/HF5yKxGzKrW42Gx9K27VYdrxVtcBDiTJ5GSi0c34fO+1yGi0cLs/xePZU7y/qOgfNDTc2qZ/27L6UF//LdzuZaSSVybt86x1z9iFebIeszMx03umq/oVd8l5O0OqgcJXUJQGUgujhbQWJhiJnJkOlTTSD0mNSGTOgTS319GjBFtXvJwy4ges37kUpCSgDaE2uZyaxHJ0xc+QgpM7lG3YGnGrnjXBJ4ha1RRofYmYVUhMNOFjUvENWbO+SvcUatwrqE2sJBWTbKIrBXjUUsYELsyaBe8rDcmNLGt8gFQnbYuRgfPo7z2KrdG3sVv4ehU0BviOztoWNra3WEQ0CZlb2RlbwNrQU4BAVwqYXHwTBVolLWkwPsfGyESNSEwajU3UxFeyMvhQxhe+LpSqiZ5PtDdH5mHICJkVf2myLvQcQwpObp7xkUb0qLC+aPQcFCWO272EVEd0nUTicNzupXk6rXza7oKkbZcQi7W9zrA3pGpVT8ftXgSkilYZRiW6vj1HtG2782soXYfoUPlV2y6hru52XK6VQKpUQHYpWoeW9CjBBlAVnVJXKhtrc+QtNkfeSAuGoCaxjCPKvtVufY58WNLg0/p70ottNgk7iFctY2rxrWhKbvigEArjC68gau3CtGMUaP3QFA8hYztbo+8isenvPYoifWib55XSTs1wRUHeMDZbWixrfCA9M02xPvQ8xfrIdDRHtg/do5agK9lxsi6liIiVvbAjpMLa0NMZIU/ajSxt+Bszy/8vj40y540DJFXxhTl1TrZF388r2Am7kZbFhgw7TIk+kiLXMBqMjSBTC5Aj/Of0mJC+JsLhC0kmx6FpuzHNMnR9c076ecrF0b1/MuFwqt2YotRhmv2xrHJKS3+FogQzNoZCF9C85nVPRsoCEgmnGUJH6XGC3UTI2M7GSKr4TgqJKRPsjn+WFc3RUcLm9rQoNomKTcJqJCmj6CL/bFkIQYG2p6deyNjG4vp7MyK2K76IMYELMwJmS4uQsT11nNqXRmMTyxr/gS1NFKFyWNHVlOgjsbEyESZJO5Q32aYh+TlmHndIgZYbuZC0gznbao1VtIyzTdqNWDKR5ZsOGltYE3o8K7NTQafCMznn+Cbb8lHuGk9dYnVW5cAy1ziEUJhYdD01iRUk7EYK9cEdSkI68Ih0Q10IBB7B7V6OEHamIUGqma6bePyo7jY03aBhj0uuru4H6SJRjZjmyKzKgw4HFz1SsBNWkCUN95ErGBJTxtgdX4IiNEpcYzpcs0JBJ7dXg43aicWvzdF5WTNOkKwJPUmxawSa8PL6ht8SSdSm3RjZs01LmixreACJBCR+rT+Tim/I61qxZJK14SdyrsCtFDLSf156HyNz7SlXREvyiC0aSrOoByklyxoewJSxrL36e2cxwj+HsLmT6vjSLBEeWnBK3nvTxzOdmFXP1ujbSGwqPJMZ5j8zNaJQqPBMzHtcz0Pidn/WLI44tRhmGMMIhS7CtvOHP3YvIqtprsPBS48U7Lrkqjzimork2Bp5J/PZpQaYVvK1TGRHW/i1fhTqgwgaW7AxUNApdY3BrXS81VH+yBDJ7vgSotYuIonqHJ9z9p57vgubO1nR+CCHl9zKuMIrWBV8mN3by3ntiaOY/98jiYU9eP1xjpnzCadc9B6VA+qZWHw9cbuOhXW/w5BRdFHAxOLrKNKGU51c0oblAgWN8UWXZ1w/lkyyJvh0jtirQsev90cIhYA+gMNLbmVr9F1saeBVK9kZ+4TqxFKG+E7Bp+1pQyaEYJj/VIb5T00X8+/N9SgUmj9wU30ij8C2yxEiSiDwKLq+ESkLCIUu3OfYZQeHjtKjHIlSSpbsfIK1oafzRmf4tEosklgksEgQt+rZEn27Q2MLoTCp+IsMKzidPp4jGOE/i8OKruqUsPT3zmz1u7Cxs02xzsUmaKQ6nlR4DsNc9SN+cMUdzHvqGIykhsuTxEhqzHvqGL5/+R2s+Hh8qgZIw9/TIisxZJjPGv6S7lCT/zoECkXaUI4o+xbl7j2zsJWNj7A7sThnfyklvmahlAF9IOOLLqfYNYrtsfepTa5kV3wxi+r/kA4jzHPOToq1lJK65FqqYouImrvbP6AD2NLK45fvCIJo9LhmTWdVpPSQTKYyEQsL/4XLtQ5FSaCqdRQV/QNFqWlrQAeHLqNHzbBrksv5PPh+TpU4BRcDfcewO/4ZWam0WMSt1mow5KIIjUEFx+2VbUk7xJZI7sNBFW7K3RPYHV9KvoLx6TOns/skzWduTdmQW7YIvnJrCYYRR3ft8SWrqo2q2piGyh/vuJrZ47fRMunQkgl2xRejoLaoMAgCHa9awoTia7MWKqW0qU2uyHud/TxH5k2H3xJ9q5k7SGLJJFWxhQzzn5Z3nI4ipc3yxn9Rn1yPEAIpbcYVXU6Fu/VU7bawpMHKxoepTa5EIBjkO55hBWd06iESjZ6OZZXhcq3GtguJRk9CSi9goesbs+qASAku13ri8a7PF3BwaEmPmmGHjG1YMntmLVAZV3gJw/1nUuwagdLsGaOgU6y335mlK1jW8ABBc0vWNgUXla7DWR18nKi1i5ZiraCjCR+j/OdzeMmXKVD7oKAh0FHQGRO4mMbkJn7156XEEnFUPX8dB12XYBbw9KMDcvomAtQmV+SINcAg73FML/1mTlRJ6sGSX8B2xZdkpa0bdjRVQVDmxv/mL8vaOeqSa6hPrscmVXvcxmB18LG8LrGOsD70AvXJNRn7tkXfZ1d8USdHESQSRxIKXUUkcl66ewuk/lxaJqOIdgobOTh0HT1qhu1Vy1CFK0u0fWpFpintqMC5JKwGGoz1SFLxwP287XWO3ndsaREyt5PTbokkVYkF5IqXYFjB6ehKARXuiWjCx5rQU8SsGlJCaTPUdwabIq8RMrfw1ku/RFHziZ9AV3wIVCwNXng2wMVfm8Ku+MKsvVShp+9Zc/sUdNWbqRqYNaoQlLsmUJNclvOdSYTFdfcyoehatsXmUxX/BIFAFR4EOjKzAOmij+fwDty9tknkiXCxZBKJhdiLn2d9cm3Ww8vGoC65hr7e6ftkZwpBOHw2fv9LpPo96lhWeboutYPD/qdHCXZfz3Qa7BVUR9ch0m6EcUWXZ75XhZvJJTdiySQC5YClN6dsUXNioiF7IbEJBY0+nmmZJJ/G5EZ2xxdnRZh8Hv0vIj3LjYU9uDwt3yyUVHx4eh9FgWBQMNJ/DrvjS7JskVKm47Y/z9ijoFLiGoWUkt2JxdQl1+FRihnkOw5N8TCu8HIW1P2GuJ3rh47ZNSyq/0M6nsVK/b+M4VXLUISOJjwM95+ZFfK4txTqg8h+0Ah8asVe/9u61MKsaxKouPch2aol8fjRWFYfdH0Dth0gHj+CHvZn5HAQ06N+aUIoHDvkK3y+cyWmjBPQBuZ5nc/XB3H/YsoYCipWm6UnU/5rgYpXrcCt7GkWUJ1YTr4O1jItVF5/HCOpoWZm2am+jqKZ28K2obBQois+JhZdy4rgv1NuAyGYUHg1hfoQVgUfoyG5DlXxMDpwAX6tPxtC/2V7bD42BgKV3YnFTC/9Bqri4siyb7Os4QEajA057o3ULDV7vcCwoxxd8eO9uYWt4tf6MzrwBdaGnkJi41HLmFh8w16PNzowl8X192RcKi6lgMG+E7rKXAAMY2RWizAHhwNFjxJsSL2udySxImmHqYotwJIJyt0T2mwOu6/UJ9e1s4fAr/XHIkqBMpAifQgL6n6DxCZhhUgVGW1d7I+Z8wnznjomLdgCTXhQWsSXmybMnZuaoZe6x3B0+f8jaQdxKYWZ2ejE4uwegra02BZ7t1nKuUXSDlKXWE2FZxKK0JhYfAPrwy+wI/ZBiytK+bn3CLnA00oJ1n2lr3c6fTxTsaTRqfrh+fBr/Tiy9HbqkmtRhEaZa/w+j+ng0FPocYLdEVKFhn6XqkaHxdbou4wrvKzTyRkJq5GVwYcJG9txqUVUuqewPfY+lkxS4hrN+MIr0BRPKruvtQAQACSlrrHMGHYRS7e8xbrQMy0SbNrmlIve493nZyJND25X7tuDYYDLBVddtWfMVLGq9gR0zyy+ORbNx1EZHTgfTbjZHpuf9oWnZvhetTy9mKoAkhLXKGoTKyl1jevyOGshFLROVgdsDbdaRD+vk+7scPDRo6JEOsq26AfpynIpf62NwYrgv1ne8C/snGiG/Ehps6ThzzQam7BIErOq2Rx9A1PGkdjUJ9exKvgYACX6aDTha6W7eMpPqolUpMDOpjrbrSDy3PLKAbX88Pfvous6iQRYVipczLIgkQBNg/vvjzN4cOciJ1LZoKNbLN4plOi5iR7DCs5gUp+5FOsjqXRPYVrp15la8hUmFn2RCtek1Gw9+i4rGh9mVfDRvY7icHBw2Ht6pWCbdixvSFldcg2bI290aIykHSZh1dPatFli0WCsB0BT3Ewr/Tr9PDMo0ccQUAdl9kuJtY++6XoiShv+dQWdQm1o3u8GTn2Z//fwzzj/0o243BbxuMDjSc2qX345yrHH7l2HlglFV1HpmYJbKaFQG8LhJbdmejY2RwjByLITmFJyM+OLLserliGEgl/rx67EIiQmNiY2SWoSKwiZ2/bKHgcHh72nV7pEKjwTqIp/kjOTtTFoMDZkbYua1TQam3ApBZS6xmaKF6nClddd0BxN7El5dykFjAycy6f1f0q7CVKz5WJ9BOOKLseVToIZWnAqSxs2N7Mt5QsWQLl7AmMDF/NR7S8wZMtwNklZ/x2ccetvmXOrypCCk1KlSdsgdW0b0RU/Zc2urTmqcDOu8JI2x2kLU0YRKFnRMEIo1CVW0ZBcj0+rpMw1vpenojs49A56pWCXuEalIwuezhLtpgiNJmoTq1jR+CBNSSKF+iAmF9+U8pcqHgb5jkuXSs0XmqczOpDdjaMuuZqYuTtzTolNg7EevZmwF7uGM6XkFnbGPgYEA3yz0EUBjcam1ENCWEwqvo4lDfflJAmlsLGx2Rx5kz6e6a3W/65NrGRF40OAQAgIaHuuLWJWUZNYiSJS4YWuvegv2YRbKUZTvCTtPVEjtkyyOfo2EgsFjUrPZMYWXrzX53BwcOgYvVKwIRVZUOIazaf1f8S0U7WkNcXH8HSFOIBVwceyBD1obKU6sSzTaWW4/0wsmWB77COah90JNKaWfhW/1i/rnKaM5yw+plJmLNRm3qXmJUSTdohFdXdj2tG0jV6mlX6NI0pvZ13omXQLsNwHhhAqSbuxVcFeFfzPnmuTe67NpQRY2vA3bCwEClsib3FE2Tf3qoZ4yg6FKcW3sKzxH8SsanRRgCHjkD63TZLd8SUM9p2YVQzKwcGh6+m1gg2pjt5HlN5Oo7EBEBS7hmdqPUspW5QNTc2IW9aOHlZwJrWJ1STsRiQmCjoj/efliDVAsT48q3mKQMWvDmBX7FNqkksJJEroq52Y1YH88/DLJO3gngVS22Rd6HmG+E5kTOAi1oafoiaxPOdcUtpZbwvZ3+VeG+lra17zQ2JjyChbo+8xwr/3rZd8WgUzyu5ASpuItYvF9fdgyeYuEjVdkMoR7EOFJdXLeH3LW0gpOXnQ8ZxecWx3m3RI0KsFG1ILgmV5upcLIQhoA9OLYymVFYicwkaa4mZ66W3sjH9M0g5T6hpNiSt/uUyPWsLkkhtZHXycpB2iSB+KX+vH+vDz2CSpSwq2i884ovTbmYW9mFWTNYOWWFQnPkuXkLUZ4juFGnIFe0zg4rxJQ03X5lUriFnNK9sJCvWhbIu+12JvG8POVy+78wiRaoqsoGOxp7mCINWwweHQYFnNSv616lEMOzUxeHjN4xQX+RjhGd3Nlh389MookY4yoegaCtR+NNWDHhU4P29STpM/e4R/Tqti3USRPpQZZXdwbMXPmFR8A9tjHzUrBSuxpEF14rNm+w9DyWnXJDOFjjZFX88JF1TQ8aitN26tTawi0aJK4ZCCkynUB1HunpB1PgV9ryvf5UMVOlNKvoRP7ZNeMyhnSvEtPaKhbk/EljYLdy3m5U2v81n18oMiHPLd7R9kxBogaRu8sv6tbrTo0KHXz7Dbwq0WcUTZN7CkkaqSt18iGXK74jQPORxacCoRsyrtq7ZzjmkZgdH0vasNwd4YfiUnczJhNQAw3H8WlkyyO7EEBY2hBaflfQPZFwq0So4s+3aXjnkwIqXkHysfZkXtapJ2EpfiYmbfI7ho9Pndbdo+oSm5+QiqclBLSY+hQzPse+65hzlz5jBnzhx+/etf72+buhxV6Pst7KyfZ0b2jFZolLsnZn2eWHwdo/1fSCfN5LYpG+w7CQUdFTcKOoMLsv3gLcmX5m6lZ/mKUBlTeCHHVvycoyt+wgDfrH26Poe9Z0dkJytqV5G0U/82STvJBzs/pjGRW6GwN3HK4BPQlT2/eV3RmTvujG606NCh3cfihx9+yPz583n22WcRQnDDDTfwxhtvcMop+Xv79UQsaaTKbkqDYteIvY6YyMcI/1noSgHViWX43UUMdJ+eI7YJq5F14WdzZtIKGqMDF9DXO50KzwSi5m68agUBfUCb5+znOZKNkdczrhgFnb4eJxW7pxE1Y+nytnvcB6pQiFtxilp2ouhFjCgaxlcn38Tb295HIjl+wDFMqBxLdXWo/YMd9ol2BbuiooLvfOc7uNI1LkaMGMGOHTv2u2FdhWnH+bT+bhJWI5BaODu85NYuKQ3aNF4qyeUkKioCeX+0UasaIVRo1hNSQWdi8Q2UuFLdr/1af/xafyAVChgxd+FWivKGyg30HYcEdsb/h4LGMP/plLic6nE9jYH+ASjN3uwEAq/mpdxT1o1WdQ3Di4YyvGhod5txyNGuYI8atWcRbtOmTbzyyis89thj+9WormRr9D1iVu2e2a2ENaGnmFry5QNmg0ctQeZ0ipEE0gLdnLrkWpY3/AshFKS0GOA9hhGB7JA8IQSDC45ncMHx+89oh33Gq3m4bcqX+MfKh6mN19HX14frD7sSNY8PuDPsiFTx8sbXiVkxjuwzjRl99645w/Lalby97X0UoXDKoBMYXeI89Hs6HV4pWLduHTfddBO33347Q4cO7fAJysr8nTaqoqLrXBYbE6EcV4RJsEvP0Zz84waIaeeyYvcLKELDlibT+l9Bv+LKrL2ktJm/+sGUqyPt6t4R/4DRfWdQ6huW2S+UqGLhjoeIJGsp941gWv8r0NU92ZaGFaM+vgWX6qPIPbBT/vv9dV8OFD3N/oqKAH8c9v86vG977Azt4nfz/0TcTIVVbgxuRvVIzhh1YqfsWrjjMx5Y+RBJK/XWt75xI9879iuMr9j70Lyedu87S2+wv0OCvWjRIr761a/yve99jzlzOpeAUVsbxrY7HsrUmlthb/HYg1FYmEkmEWgE1KH7xd/Wlu2lzGRayUjiVh0+rQKPUZqzr2FHseyWlf4EO2q3YEXK0/tE+Lj2V+nEGcm24GIao9UcXvJlhBCEzR0sqb8/VVhVWpS6xnJY0ZV564x0xv7eQG+2v6O2v/z5uyTMPSUNElaSZ1e9yvTizq1hPLLkuYxYAyStJM8se5WKibkJYx2hN9976Fn2K4podaLbrmDv3LmTW2+9lbvuuouZM2d2uXH7m76e6UTMHWyLfYAACvUhjPLPzdpHSsmu+CLqkqtxK8UMLjgh09G8K/FpFW2mb2vCiyY86azBJtvsLH97o7Ex/caQeghKLELmNkwZQxc+VjY+nJUFWZdcw+7EZ13Sf9GhJ5Bb43xvYrt3RXflbAsme4ZgObROu4L9wAMPkEgkuPPOOzPbLrnkEi699NL9alhXIYRgZOBchvvnYEsrb/eRTZHX2Bp9N6uN1hGl3z7gySBCCCYWX8/Shr8hsbGlxXD/mZnFSCBPEg6AzDTbjVv1Wd/YGMSs3L6NDr2TI/pM5e1t8zOhgi5F54SBnU8Lt2RueeJBgbajkw4kSctgwa5FRMwoY4pHMqSw/S5UhwLtCvb3v/99vv/97x8IW/YritDyNnaVUrIlXXkOmnoXxqhJLO+iTtudo1AfzMzyHxK36nEp/pz09GLXCDxKKTGrGjtd+6Sv54hMDRWf1odwsw7vCnreuigOvZN+BX257fAv8eLnrxCz4hzZZxrH9s9+890a2s7m0FZK3EWMLx2bdw2j0lvOrlh15rMmNKaUd65j0/4iaRn8etEfqI3XYdoWLysqV465mGl9pnS3ad2Ok56U7g3ecpudp4LevhAxq1gdfJy4VU9AH8TYwktaLXuqCp0CrTLvd4rQmFr6ZbZG3ydm1VCsD8+KwT6s6EqW1N+HYafap/XzHkmZq2szHR26l8GBgdw6+Yt5v/tgx/94cv3zmSrs40rHcMNhV+WI9o0TruEPS+4naRtYtskJA49lbGnnFhyX1azg88ZNlHhKOKe0c4uebbFw92Jq43Uk0+s5tm3z+LpnGBQYwPwd/8OSFjP6TmdwYP/1ce2pHPKCLYRCuXsitYkVmQxCIRRKXWO67ByGHWFx/b0Z33J9ci1LG/7CtJLb9ioDUxVuhrbS3MCrljGj7HvErTo0xdOlSUIOPRvLtnhi3bOYzSoprqpbw/rGzxlVPCJr374FffjpzO9TE6uhQC+g0NW538kLG17mja3vYKfLLXxQ9RG3H/71fQ5ZBIia0RyXTdxKcOeiP5CwUtExH+z8mFsn3ZB1XXXxeh5a/Ti7orvpX9CXK8deQpG79yYo5eOgLv7UUcYWXkJf7wy8ajmF+jAOL7611TrUe0OjsTlroUhiETF3Y8hwl52jOYpQ8WkVjlgfYsStRG4PJSFaXUwMJoLpbMzOyYBpm7y29a2MWANsC+3ktc3zOmlxfsYUj8qySRMqfr2ApLUnOsawDV7c+Grmc9Iy+N2n97C+YQONySBr6tfz+8X3Ytld+6bc3RzyM2xIuSBGB/ZfQR5VuCBnkcduZQHRwWHv8GleStxF1MbrMxMEKW2GBAbl7PvKpjd4bcs8VKFhS5ubJlzTYZfI0prccsAAr215izOGnrLPdXsGBQZw7bjLeWztU8StBKOLRyAQLK9blbVf02wbYHtkB3Erjt3UFQmbkBFid6yafgXZWc0xM05jopFidzEeLTcIoSfjCPYBoEgfRoHWl7C5ExsDBZ1+3hk9uiSplDbbYx/SYGzAq5Yx2HcSuuJt/0CHbmF7eCfVsRouGX0BT65/jt3Rajyqm2vGX065NzsVfmtoO69teQvDNjHSbsC/rfg3vznmp+3Otv+78XXe2PJ23u8saRExo/j1fQ+JnVwxgckVe8oCL61ZwZqG9Zmyri5FZ2bfIzPfuxQXdotJkS1tXEp2U+xFu5fw0OrHUYSClJIvTria8aVd5/7c3ziCfQBQhMqUki+xI/YRMauGQn0ole4p3W0WkBLm6sRSotZuku7h6HIEQgjWhp5mV/zTTKhjTWI500u/iSqct4Kexiub3kzPlhUsafOFEWczq9+MVv3Ju2PVqELJamFt2hYRI0rA1XpmctJK8tqWN/OGBALoioZP6/hDXUpJxIji0dxoLcqzSinZGt5OMBlikH8Ak8oP49LRX+CVTW9gYTO7/yyOG3B0Zv/+BX0ZWTScdY2fY9gGLkVnfOlYSj0lmX0aE0EeWv14Vi3vv6/4N7+Y+UOgd7gPHcE+QChCY6CvZ7VRklKyMvgItYlV2CTZEtXxKX2o9EyhKr4gU79bYpG0QtQn11HexbW1ezL18QZq4rVUeMspdrden7yrkVKyKbSFiBFlcGBgmwuCNbFaXtvyZnq2nOKp9S8wtXIKBa10LOrn65MjurqqU6Cn9t8drWZNw3q8qofJ5RPQ1dRDOm4l0iWCs48VCHRF44bDrmpzhh5KhtgW3oFf9+NR3dyz9K/UJ1JF2S4YcQ6zBx6duf6HVv+HxdXL0jNhm5snXseMvtNbrZsihODmidfx/o6P2BGpYnBgILP6HZnlnkk9qFSMrEeVoC5ez6Be0t7OEexDmKi1i9rEykzavi0NwtY2wpEdtPyjRJC3WfDByvwd/+Op9c+jChVLWlw6+gt7XWSpM9jS5oEVD7Gybk1KrJB8edIXW62MV59oQBVaxrUBoCoqjclgRoBb0t/fj3OGncHzn7+cbkYguGXidShCYW39eu5f9gASUBC8uvlNbp/2NVyqi4Dup8xTwu5YTcZH7lJcXDHmImaMmIQZTon18tpVPLT6P0TNGEP8A/nihGuojtVy37K/IVCwpYWqqMTMeMamZz9/iUGFAxlWOIRV9WtZXL0skxwE8MDKh/jV0T9p896pisrxA49p9ftSTwlWiyJstrQodhe3OW5PwhHsQxjTjuWUfU1hk5o3ifQsO9VirVgfkWeUg4+GRCNPrX8uPWtN3ZvH1j7NYaXj8Lu6tmSBLW2W1azEDiapUPpSE6tlZd2aHLH6+cwf5D2+r68SW2Y/SAVQ1swVkI8TB83miD6HE0yGKPOUZRbfHl79RCb+GaAqupv5O/7HiYNmI4Tgq1Nu5oEVD7ItvIMiVyHXjL+coYWDKfEG2BVq5NE1T/JR1YLM8ZtD27h/2QM0JoMkmkV50KJmjkSyJbSNYYVDqI3V5qTfh40ItrQ7HdHSnDJPKecNP4vnPn8JVWhY0uKyMRfg03vP2owj2IcwBVq/9CtufvzaACyZwK2UMLpwbqtNgQ826uL1ubNWoVCXqO9SwbalzZ8++wsbGzdjI7GkRYm7GNPOngW2VeMj4Apww2FX8fcVDyGx0YTGzROvx622H/0QcAUIpN0ttrR5Yt1z1Caye4VKJG9ufYeJ5eMzrqFvTv1Kzlg7Qru4e/E/2BjcnH2N2GwNb2/XFgWFYlcROyJVuFQXtKiPUugqpC5en1lAjZsJDNvArxd0Kirl+IHHMLFsPDXxWiq9FZR4ijt0XMyM8cLnr7AzuoshgUHMGXoaLvXAr+c4gn2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    "plt.scatter(X[:, 0], X[:, 1], c = y_kmeans, s = 20, cmap = 'summer')\n",
    "centers = kmeans.cluster_centers_\n",
    "plt.scatter(centers[:, 0], centers[:, 1], c = 'blue', s = 100, alpha = 0.9);\n",
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    "## Advantages and Disadvantages\n",
    "### Advantages\n",
    "The following are some advantages of K-Means clustering algorithms −\n",
    "\n",
    "- It is very easy to understand and implement.\n",
    "\n",
    "- If we have large number of variables then, K-means would be faster than Hierarchical clustering.\n",
    "\n",
    "- On re-computation of centroids, an instance can change the cluster.\n",
    "\n",
    "- Tighter clusters are formed with K-means as compared to Hierarchical clustering.\n",
    "\n",
    "### Disadvantages\n",
    "The following are some disadvantages of K-Means clustering algorithms −\n",
    "\n",
    "- It is a bit difficult to predict the number of clusters i.e. the value of k.\n",
    "\n",
    "- Output is strongly impacted by initial inputs like number of clusters (value of k)\n",
    "\n",
    "- Order of data will have strong impact on the final output.\n",
    "\n",
    "- It is very sensitive to rescaling. If we will rescale our data by means of normalization or standardization, then the output will completely change.\n",
    "\n",
    "- It is not good in doing clustering job if the clusters have a complicated geometric shape.\n",
    "\n",
    "## Applications of K-Means Clustering Algorithm\n",
    "The main goals of cluster analysis are −\n",
    "\n",
    "- To get a meaningful intuition from the data we are working with.\n",
    "\n",
    "- Cluster-then-predict where different models will be built for different subgroups.\n",
    "\n",
    "To fulfill the above-mentioned goals, K-means clustering is performing well enough. It can be used in following applications −\n",
    "\n",
    "- Market segmentation\n",
    "- Document Clustering\n",
    "- Image segmentation\n",
    "- Image compression\n",
    "- Customer segmentation\n",
    "- Analyzing the trend on dynamic data"
   ]
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