Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.io import loadmat\n",
    "import random\n",
    "import math\n",
    "\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import linear_model as lm\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.model_selection import train_test_split\n",
    " \n",
    "from sklearn.model_selection import cross_validate\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.datasets import make_circles, load_boston, load_iris, load_digits\n",
    "\n",
    "import warnings\n",
    "warnings.simplefilter(action = \"ignore\", category = FutureWarning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "sns.set(color_codes=True)\n",
    "sns.set_style('whitegrid')\n",
    "sns.set_context('paper',font_scale=2)\n",
    "from mpl_toolkits import mplot3d\n",
    "%config InlineBackend.print_figure_kwargs = {'bbox_inches':None}\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa1feeb0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = .02  # step size in the mesh\n",
    "\n",
    "\n",
    "ds = make_circles(noise=0.3, factor=0.6, random_state=1)\n",
    "\n",
    "# preprocess dataset, split into training and test part\n",
    "X, y = ds\n",
    "X = StandardScaler().fit_transform(X)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)\n",
    "\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "\n",
    "# just plot the dataset first\n",
    "cm = plt.cm.RdBu\n",
    "cm_bright = ListedColormap(['#FF0000', '#0000FF'])\n",
    "# Plot the training points\n",
    "plt.scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], c='r',marker='^',s=48)\n",
    "plt.scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], c='b',marker='o',s=48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = .02  # step size in the mesh\n",
    "\n",
    "\n",
    "ds = make_circles(noise=0.3, factor=0.6, random_state=1)\n",
    "\n",
    "# preprocess dataset, split into training and test part\n",
    "X, y = ds\n",
    "X = StandardScaler().fit_transform(X)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)\n",
    "\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "\n",
    "# just plot the dataset first\n",
    "cm = plt.cm.RdBu\n",
    "cm_bright = ListedColormap(['#FF0000', '#0000FF'])\n",
    "# Plot the training points\n",
    "plt.scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], c='r',marker='^',s=48)\n",
    "plt.scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], c='b',marker='o',s=48)\n",
    "\n",
    "\n",
    "clf = LogisticRegression(C=1e5)\n",
    "clf.fit(X_train, y_train)\n",
    "score = clf.score(X_test, y_test)\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.contourf(xx, yy, Z, cmap=cm, alpha=.8)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], c='r',marker='^',s=48)\n",
    "plt.scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], c='b',marker='o',s=48)    \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# non-linear (polynomial) expansion\n",
    "p = 50\n",
    "pf = PolynomialFeatures(degree=p,include_bias=False)\n",
    "\n",
    "pf = pf.fit(X_train)\n",
    "X_train_p = pf.transform(X_train)\n",
    "\n",
    "X_test = np.c_[xx.ravel(), yy.ravel()]\n",
    "pf = pf.fit(X_test)\n",
    "X_test_p = pf.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = LogisticRegression()\n",
    "clf.fit(X_train_p, y_train)\n",
    "mZ = clf.predict(X_test_p)\n",
    "mZ = mZ.reshape(xx.shape)\n",
    "plt.contourf(xx, yy, mZ, cmap=cm, alpha=.8)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], c='r',marker='^',s=48)\n",
    "plt.scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], c='b',marker='o',s=48)    \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa24fb30>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = np.array([[0.2,0],[0,0.2]])\n",
    "n = 8\n",
    "mu1 = np.array([1,1])\n",
    "mu2 = np.array([1,5])\n",
    "mu3 = np.array([5,1])\n",
    "mu4 = np.array([5,5])\n",
    "x11 = np.random.multivariate_normal(mu1,sigma,n)\n",
    "x15 = np.random.multivariate_normal(mu2,sigma,n)\n",
    "x51 = np.random.multivariate_normal(mu3,sigma,n)\n",
    "x55 = np.random.multivariate_normal(mu4,sigma,n)\n",
    "\n",
    "X = np.vstack([x11,x15,x51,x55])\n",
    "y = np.ones([4*n,1])\n",
    "y[n:3*n] = 2\n",
    "plt.scatter(X[np.where(y == 1)[0],0],X[np.where(y == 1)[0],1],c='r',marker='+')\n",
    "plt.scatter(X[np.where(y == 2)[0],0],X[np.where(y == 2)[0],1],c='b',marker='o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xa5b3f10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use logistic regression with basis function expansion\n",
    "p = 3\n",
    "mX = np.zeros((X.shape[0],p))\n",
    "for i in range(p):\n",
    "    mX[:,i] = np.sum(X**(i+1),axis=1)\n",
    "\n",
    "# Learn logistic regression\n",
    "lr = lm.LogisticRegression()\n",
    "w = lr.fit(mX,y.ravel())\n",
    "\n",
    "# evaluate on a grid\n",
    "x1 = np.linspace(-2,7,100)\n",
    "x2 = np.linspace(-2,7,100)\n",
    "xx1,xx2 = np.meshgrid(x1,x2)\n",
    "Xstar = np.zeros((x1.shape[0]*x2.shape[0],2))\n",
    "Xstar[:,0] = xx1.ravel()\n",
    "Xstar[:,1] = xx2.ravel()\n",
    "mXstar = np.zeros((Xstar.shape[0],p))\n",
    "for i in range(p):\n",
    "    mXstar[:,i] = np.sum(Xstar**(i+1),axis=1)\n",
    "ystar = lr.predict(mXstar)\n",
    "\n",
    "# visualize the result\n",
    "plt.contourf(x1,x2,ystar.reshape((x1.shape[0],x2.shape[0])),alpha=0.2)\n",
    "plt.scatter(X[np.where(y == 1)[0],0],X[np.where(y == 1)[0],1],c='r',marker='+')\n",
    "plt.scatter(X[np.where(y == 2)[0],0],X[np.where(y == 2)[0],1],c='b',marker='o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "###DEaling with radial data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0xa5db9b0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_circles\n",
    "X, y = make_circles(100, factor=.1, noise=.1)\n",
    "lr = lm.LogisticRegression()\n",
    "w = lr.fit(X,y.ravel())\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')\n",
    "# evaluate on a grid\n",
    "x1 = np.linspace(-2,2,100)\n",
    "x2 = np.linspace(-2,2,100)\n",
    "xx1,xx2 = np.meshgrid(x1,x2)\n",
    "Xstar = np.zeros((x1.shape[0]*x2.shape[0],2))\n",
    "Xstar[:,0] = xx1.ravel()\n",
    "Xstar[:,1] = xx2.ravel()\n",
    "ystar = lr.predict(Xstar)\n",
    "\n",
    "# visualize the result\n",
    "plt.contourf(x1,x2,ystar.reshape((x1.shape[0],x2.shape[0])),cmap='autumn',alpha=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = np.exp(-(X ** 2).sum(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0xab728f0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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R1jlwqy0CA0iEtBIhArbC0DQNhUIBmUwGXq+3bIBkM6ztnurtDTm5+HQrAutEuCqP1Qt0XcePnpvDE0+fgKoCTp+1ICj4xJefx+f//LfL9suceH0sy4Jl2apWWlZhi8fj5o0Uz/OmmQQodZPo1cLezwisF1zIr61bEAFbIViLjyVJQiaTKdu0b4S13VOjBd9pZ1436sDS6TSKxWLbwmWlVwL2jR8dwfeePQnFuWC0inhaxPs/tRs6KAx5Odzwmgm89brprpzLahyp1Uprbm4OsixjeXnZLJav3F/rRseRfkdg3YR0om8PImB9plbxMcdxtoRBlmUkk0kUi8W67Z6sGE5EpxYBpyIwI3LM5/MYGhpypHNGKxFYO6L+m0NL+PaPjyGZEZHIitC07otlXigpZFFQ8PQzs3juwCL+4C2TXT+vgeFwZFkWkUjEdLBa092VjWxrdRzppN6vX6nLC+EcFyJEwPpEo+LjZl0zrO2eQqEQotGorS92N1J+nURglR3uA4GAmTZ14tq6tSj85Dfz+PcfHYGq6lBUrSfiVYmkaFhKFPH1n5zGXVwIl6wLgaF7s7hXCj5FUXUb2VqnIMfjcSiKYhpNrOJmp5VWvyKwXnXhIBFY6xAB6yF2i4/rfZBFUUQikYCiKAiHw7baPVlpJoyt0q4gWoXL2uE+Ho87dn3dWAxOx/L41u6jePbls9Chg2cZ0D0SDSv6uf8jyhpePZXHp77yAkZDHjz4nisxOeJr9vTOz28zYrXTSss6g41l2aqIzSoc/arF6mf9GaExRMB6hK7rOHLkCEZHR1tyFALn2z3pum4KVzt0q27LLvWEy3o8p6ImpyOw2TNZ/M2/vYhcUYam6dABiJLquGGjHWRZw+lYHn/zry/ib//0t+pa7p2i033Udlppud1us5yk18NFeyGcJIXYHkTAekg2m8X4+LitL78xwyuZTIKm6bbbPVnpVwTWTLgMnBYdJ4/1xNMHIMoqOIaGQBnHd+zwHaPrQCon4aXDMVx9qXO1frXP1R0bfbMZbMlkEvF4vGwGm7XjSLdaaZEU4sqFCFiPMPa5mqUjDOGSZRmZTAbRaNQcudApTgtYswjMrnBZj7cSI7CiqCCWEs7vMVEU9D7se9XDSCkKsor55VzXBQzoneXbOoONZVlMT5ecl9Z5Wt2ewdaLLhyE9iAC1kNomjbHZlRitHtKJpPmXWU0Gm17TlS983ej+W4lqqoimUwin88jGAxi7dq1tvdMnCqMdnKB1Speo8/NIlvorEgZACjK2SiOoymMh9tLL7fCSugaUTlPy6AbM9hIH8SVCxGwHsIwTNUCres6MpkMUqkUvF4vpqamwLIszpw543iNVTcEzEqlcM3MzLS00K3UCMzn5jA85MJiogCGpsCxNGiKqhI2u/AsDVXToDo8zDrg43HVJd2PvlYy3ZjB1m0Tx0q4IRhUiID1EIZhTAGxtnvy+/1muycDJ6ORbh4TKBcuI1XYzhey13tgxt8gm82aRgHjv8r9lPe9dTMe/uZeSLIKhqHBMhQkpfVr9XtYXHXJKJ7ZewaVPTt4joabYyBIKhRNA0NRUDQdlA4007ohL4cH33tlwwbAq5lGxhFD2FKplNks2zqDTRRFRzMhBOcgf5UeQtM0EokEisUicrkcAoFA3anBTkdL3TimqqpQFAXz8/MdCZdBryIwXdeRTqeRSqUQCASwbt06s9mtYe2uLMSdirhx/12vwZM/Po7Ty3kMeYF4Rmx8DQBYhobXzSISdGEs7MU7dlyER765F2qNPTRN0/Hm62YwMuzGYryIjWuCmBjx4icvLmDf0ThOns2aKUcK5+VvetSHz97XffdhP+mWS69RKy1r82PjJo3n+bKOI04ZR0gE1h5EwHrE8ePH8eijj+JXv/oVHnvsMWzatKlhXt0arTmFUwJmjbgoiupYuAyctPnXEjBrutbv95s3DzRNg2VZ8DyPQCBgPt5aiJvNZsEoAu78rSAYJoyCROMz3ziMglg7omVoCsN+F3ZcMYE73rARPFe6ScnkJeQFpeZzFFXHcwcW8Xd/ekPZz9/7ls04eSaLf/rOfpyO5yHLGiiq9Br9HgYff/81F7R4Ab1Ns1XOYFNVFR6PB0NDQ6aVXxCEns5gI9SGCFgPOHDgAH7/938fb3vb2/DlL38Z69evb/qcbqUQO+2cUZkqPHXqlGPX160IzGqQ8Xq9Venaeuest5+iKAoKhSJcHA1BKv8bldymwO/sWI87br64xriTxs4NpuKmZn4ph89+bQ9yBRmyqkHXdPg8HMbCHly1OYLLpzmEAp2VVwwCK2Eas9U4Unmj0+kMNiJ27UEErAds2bIFv/jFL7CwsABJkmw9h6ZpKErtO/V2aTfCUVUViUQChUKhKlVo1II5FYE5KWCqqiKXyyEej8Pj8ZgGmU5hWRaBwBB+902b8G//dQhFUTEthbquw+/hsHWGxbFjx8rmc7ndbnhcLoQCbmRquBgpAGfjeXziiefx7ls2YWLEi0888TxSWdF8f3VdhwZgPOLFW6+bxvLycsevZxDo9yywRiaORjPYrBF8vRlsRokAoXVW9bumKAre8573YNOmTfjEJz7R9PHf+c538Pjjj+PkyZMIh8N45zvfiQ9/+MNmU9NGGGkqQRBsXdtK2AOzdrmv1yx4JToHjeay2WwWPp8Pk5OTjkygruSN10yDpih868dHISsaFEXF2okA/uT2bYiGSlGb0axZFEXTJHDb9iCe+GHBbM5rXjdKM8X2HY3j+MLzuPKSKHJFuarvoCyr2HMohtzN61fNnftKiMBapZEj0vhMpNNpCIKAjRs3OnW5q4pVK2CFQgEPPPAA9uzZg02bNjV9/JNPPomPfexjuPPOO3H//fdj7969+Kd/+icsLy/jU5/6lK1zsixrW0D6uQdmR7gMjKjOCZuxE82GC4UC4vE4AMDv9zs6gboWb7h6DW66cgqZvITT86dwyeYNZYsdwzDw+XxlJoH163WsnZnCv//wCA7NZZAvKlUtqXJFBc/uOwtV1av6LVLnLPxnYgWEPFgV9DsCc1I8Kz8TpM6sfValgP30pz/FX//1XyOZTNp6vCiKeOihh/DmN78Zn/zkJwEAN910E3w+H/72b/8W73//+7Fhw4amx2lFlLqxB9YswmlFuKzXuRIisGKxiHg8DpqmMTo6ClmWbUe7nULTFIaHXEi47Ik4RVFYNxnCX96zHf/8n/vxg1/P1X6gZQ8PFEDh/N+CpigEfBygdV5Q3Qr96tnXzwis2504SBup9ll1sp/JZPChD30ImzdvxlNPPWXrOfv27UMymcStt95a9vO3v/3t0HUdu3fvtnUclmVti1I3Uoj1viSKomB5eRkLCwtwuVyYmZlBIBCw9aXqtnOwGaIoYmFhAYlEAtFoFJOTkz2dEtwpklL/veM4Bu5zokiBgg5Ahw5N0+FzAZqYNt1wRn/AbtOvotsLKQKrhDTybZ9VF4G53W5873vfsxUxGRw9ehQAqp4zNjYGr9dr/r4ZraQQuyFglbQTcVXSrwhMFEVz/EokEqnaZ+jmPLBGtHrOG7ZN4Ln9izWt9RxL47Yb1+M/f3YCBUEBdB08x8Dv4fD/3HsNPKxi1hUmk0nT+WbtLGE435yinwLWzzRbN1/zoNxsrURWnYDxPN+SeAGlLvIAMDQ0VPU7v99v/r4ZraYQuyVginJ+4WtXuAycjsCaHcsY5inLMiKRSMPRMr0WsHbew60bIpgY8WH2TAaKev56PS4Wb7luLd654yK87vJx/PDXpxBPi9i6MYIbXjMBF8egUCiA53mMjY2Zz6uctbW4uFg2ksTqfuvkb95r+plC7AVExNpj1QlYOxiLar0Pmd0vFsdxthf7bnygFUWBoihYWFhoaZJzI5yOwOohyzISiQREUTSFq9Hj+xWBtQpNU/h//2A7/vX7h/DLl89C13W4XCz+900X4Y3XlDqvj4W9eO9bL6n5/Mr3oFbLJOtIEsPSbRTg1mpw2+h9XY0pxG4zCJ/TlQoRMBsYRYvZbLbsbhcAcrlczcisFsYXsNfpEGvERdO0Y/VQgPNDMiuxXnskEsHo6KjtvblBWRhcHIMP3LYFH7htC1RNPz+2xSGsI0msn1VrnVI+n0c8HjfrlKy1ay6Xy/y89kvA+hWB9eIzREwc7UMEzAZGynF2drasXmNxcRGFQsF2DYcxE6wVV1MnC4Z18Q+Hw4hGozh9+rSjX0onIzAr1uJp49pb7Wxvl5U0RNNp8WpEo04jRl/IRCIBQRDMAZIcx0FRFEiS1NN2Sf2KwPq990ZoDBEwG1xxxRUIBoN4+umn8cY3vtH8+Xe/+11QFIUdO3bYPpYhYHYKa9vtciHLMpLJZJlwWTtnOD2V2Um7v67riMfjyOVyGB4ebnt/rh8RWK8X2F5PRpYkCdlsFpqm4ezZs5AkqWzOVjdMI9bzd3OkST26PUqF0BlEwGpw+vRpnD59Gps3b8bQ0BB4nscf//Ef46/+6q/gdrvxlre8Bfv27cNjjz2Gd73rXbYKoQ3aqQWzewfYSLisx+zFUMtW0TQNqVQKsiyDYRhHGgQPSgpxEDD2y3RdhyAIWLNmDYDGphGrsHVa2nChRmBkFlhnEAGrwc6dO/EP//AP+OpXv4prr70WAPC+970PHMfhq1/9Kp5++mmMjo7iD//wD/HhD3+4pWPXGmpZD7tiYzU4NDNnOJ3y63QPzDoXLRgMguM4DA8PO3Jdg2CjH5RzWc9p/WzVM41Y05DZbNbsAVrZ3LaZacR6zH6k8rpdxEzojFUvYIcOHar62X333Yf77ruv6ufvfve78e53v7uj8zlppa8ULjsGh26kENtZSCtncs3MzICmaWQyGUfuSvtxV7sa7qTt/G0qx5EYWLu21zKNWIWtUjQu1AgMWB2fm26x6gWs17QSgdUTO6twhcNh2848wHnXYKvHs4428fl8VQM9jcjJCQFbDSnEQdp3q9e13To8MplMlplGjMcrinLBChihfYiA9RiWZW2PSak0SHQiXNZj9iMC03UduVwOiUSi5kwuAyeF50JPIfaDbry+RqYRIw1ZKBQgCELVeBqXy9XVUSS9MHGQCKx9iID1GJZlIcv2GrAaYuOEcFmP6eScsWYRmK7ryOfzSCQScLvdTWvQnBKw1eJC7DW9Mh1Yh0cCgCAIGBsbA8dxpqhlMhkIggBVVcGybJmw8TzvSOREUogrGyJgPaaVFKKu68hkMshkMh0Ll0GvIjBd183ptDzPY2JiwlbpwCALWD8YpBRip+elaRo0TbdkGrGmIVsxjRjYLXlpl9XwGe0mRMB6jJ2GvrIsIx6PQxAEc/F3atHoho2+8njFYhGxWAwsy2JsbMzWwE/r9TklYHbQNA3JZLKs+0QnKanVsCCttFZS9UwjxmDTStNIZRqylmnEel4Sga1ciID1mEYuRKNRrSRJCIfDCAQCyGazjn7AnbbRW48nCAJisZg5k8tI/7RCryInqwsyGAyCYRhks1ksLy/XTEnZqWMiKcTunrdVIaEoqqZpxJiILAgCkskkRFGEpmngeb7MCcnzfNcFjLSR6gwiYD2m1kwwq3BZG9UaXywn6UYEpqoqFhYWAAAjIyNVC0arx+tmb0WrC9Lv92NmZgYMw5SliWqlpIzmt5V37qutS8OF0My31pRso+Gx8TdPp9OQJAmyLEOSJIiiWNbw2ClWQ8TeTYiA9RhrCtE6GiQcDld1WO/WUEunjilJkpmWGR8fr+qp1w7disCMPbl4PN7UTNKojsm6wFWOKpFlGbIsg+f5ni3yq2UPDOj+TC6j4bHRvBsATp06hWAwCE3TGkbo7ZpGSPTVGUTAegzLsti/fz9+9rOf4eabb64pXAatFD3bxQlRNPbojJlckiQ5Il5AdwSsWCwiHo+DYRjbZpJa1DMQGHfumUwGy8vLOHv2bEv7LIPEamt9pGkavF5v3QhdFEXEYjGIonhuFI6rZdPIano/nYYIWA85cOAA/uZv/gZHjx7Fn/zJn2DNmjVNZ1qtJAFrdSZXOzgpYJqmmd33o9FoW3tyzbDeuWcyGTOFWrnPYhTntrPA1aNfe2AXghDbpdYemF3TiJFdqVW7ZqSeSQqxM4iA9ZBXXnkFb3vb27B27Qn9R/wAACAASURBVFpcfPHFfbkza+eYlWNZnLDz18MJk4kRISqKgrGxsYZTm7tFvX2WZvO3PB5PS+mo1ZRC7AetmDhaNY0YfT872TNe7axaAduzZw8eeugh7N+/HxzHYceOHXjwwQcRjUbrPkeSJPzzP/8znnrqKSwuLmJiYgJ33HEH7r77blsbu3feeScAYO/evVBVdcUbAFRVRTKZRD6fb9gk2Kn2T9ZjtYN1hlgkEoEgCD0Xr0bXXm+BsxpGlpeXq6YlO2Hvd4rVJmBA5zcJjUwjq/H9dJL+fyP6wMGDB3Hvvfdi69at+MxnPoN4PI6HH34YBw4cwK5du+rWLX3iE5/Azp078cEPfhBXX301XnjhBXz2s5/F0tISPvrRj9o+fyvFzEDvFw1VVZFKpcyZXM1GmxipTicEuR0BM0axZLPZshli8Xi84+tphXb/RrVaKVmnJVvNA4ZhxO12Q5Kknqeg+rHgXoiLvJF6JinEzliVAvbII48gGAziS1/6krkvsmXLFtxxxx3YuXMn7rrrrqrniKKIXbt24Z3vfCc+8pGPAABuvPFGnDlzBl/72tdw//332zYHtNOR3ulordaiYAhBJpOxJVzWa3Tqi9iKgFXWck1PT1ele+wsfitxEak1LbnS6p3NZiHLMrLZbFkK0rrH4jT9EJN+daLvNheiMPeaVSdgkiTh2Wefxe233162qb9t2zasW7cOu3fvrilgsixDVdUyiy0A04VXKBQQDAZtXUM7M8GcXJAqJz1XzuQyRpvYxUmziVFX1ghrY+BaHe2tx7qQqLR68zwPRVEQCoXMaC2VSkEQBLMw15qC5DhuIIeE9ss4QgRm5bPqBGxubg6iKGLDhg1Vv1u/fj1effXVms/z+/2488478e1vfxvXX389rrrqKuzZswdPPvkk3vzmN9sWL8CZkSqdYAgORVHIZDJIpVJmUW87C0UvI7BCoYBYLAaXy2W7MXAva7L6MdCy3lBJo5t7sVhEMpk0HXEej6fMEdfK33w1RWCkjdTKZ9UJWDabBYCy/QYDn89n/r4WH/nIR3DixAl88IMfNH+2fft2fPrTn27pGroxlbkVDOHKZrPw+Xx1R5u0cjwnI7BaImC0qWIYBuPj47b7K67E9KCTNOoPaHRzt95cWQ0j8Xi8Zv2Sx+Ope2PQLwHrRwRGZoGtfFadgBkLbb0vYb0PbCKRwB133IF8Po+Pfexj2Lx5M44cOYLPf/7zeN/73ocnnniirCakESzLQhRFW4+tnAnWCUbqrVgsgqbpphGMXboZgRndPlRVbblN1WrpSN8K9WZvWe39sVgMiqKUGUaMaA1YPdZ9VVVJBLbCWXUCZtyN1oq08vl8XRH69re/jfn5eXzlK1/BddddBwC45pprcOWVV+Id73gH/uVf/gX33XefrWtox8TRCdaZXC6XC36/H4FAwDFbtpMRmCGGiqKYEcLIyEhbdni7i4Ou600XSV3XsZwqoiiq8Hs4RILVQtqKYGqajqVkAXOLOdAMhfUTAYQDrdUDOXnTUGnvr9cP0miX5ff7e9YP8kKOwIiAdcaqE7Dp6WlwHIfZ2dmq3504cQIbN26s+bz5+XlQFIWrr7667OeXXHIJhoeH6+6d1cLOSBWDTvfAjP5/HMeZbZRisVhfpjLbQdd1FItFLCwsdFw0bVdQmh0/k5ew+4V55IsSNB2gKQrDQy7cfPUaeFytf4VSWRH/+fMTWE4WERpyIeDjcPhkChdNBbB9y9iKWNTqdZuYm5vD0NCQafyp7Adp7Q3o1Ovol4mj2wJGsgOds+oEjOd5XH/99di9ezfuv/9+865z3759mJ2dxd13313zeRs3boSu63j++efxute9zvz5q6++ilQqhZmZGdvX0IqA0TRte4KzFWv/v8qZXE6PVHEiAjMs/Ol0GgzDYHp62pEF0O7rzBdlHFvIIJUTER32YMNUEC6egarp+NFzcwAFDA+dj1AKgoIf/2Ye/+v6dS1dz/GFNJ7+xSwSGQE+N4+lZAHxDI3NMyEcX8hgYsSHmTF7qWigXHxVTcexhTQOzSYhqxoiATe2XTyC0JCzLbQMq75BvU7uTvWD7KeJo9vR5Uq4WRlkVp2AAcB9992Hu+66C/fccw/uvfdepNNpPPTQQ9i4cSNuv/12AMDs7CxisRi2bdsGnudx++234xvf+Ab+7M/+DH/0R3+EzZs34/jx4/jCF76AaDSKe++91/b5WzVxtLIHZmzOUxRVt/9fr6Yy28GYOp1MJhEIBDAxMYFkMtnTrh5zi1n84uVl0DQNF0/j1GIWLx2J4S3XzaAoKiiISpUIeN0skhkRyYyAUKA89VaPvCDj+YNLKAgKgr7SfDGOpaGoGo4vpLFpehivziZtCVhl2lPTdPz8pQWcjRcQ8LnAcQySORH/9cuTeP1VazAecaYjSa1Ua71O7vX6QRr2fsMN2awf5IUagZFZYJ2zKgVs69atePzxx/G5z30ODzzwAHw+H3bs2IEHHnjAXPAfe+wx7Nq1C7t378aaNWvg9Xrx9a9/HY8++iieeOIJJBIJTExM4Oabb8af/umfIhKJ2D5/qxGYnceKooh4PA5d1xGJRBqaHZw0hgD2arcqMfbl4vE4vF6vWcsly7KjjsZmiJKKZ/YtIuh3g2FKj3fzDGRFw+4X5rFlXQgMXfs4uq6jICgIBeyd7+SZLBiagq6XP5ZlaBRFBYqmQxEbv4/JrIC9R+JIZgUUCgVMhD143WsDSOdEnIkVy8TUzbNgGRq/3r+I225c51hEa/c49VooSZKEYrFYtx9kpb2/XxFYt00cJIXYOatSwADg2muvxTe+8Y26v//0pz9dZY8fHh7Gxz/+cXz84x/v6NxO7oFZXXqRSMTWWBOnu9y3GoEZ+3I8z2NycrKsg4mTzkE7x5pfykHXAbpCpDiWRi4rQtN0qFrtY1AUBY/b/leoKCpgGRpunoGqaWDKFkcduYKMi6YCdZ+fzAr48QsL8LpZBHwuMLqM5bSI3S/MI+Dj4XZVp7tYhka+KCJXlDHktVd6ICsaRFmFm2fAMq13NmmE1d5vpdLeLwiC+Vhjj01RlJ72gzTOS1i5rFoB6yfGVGY7i0G9CKxyJlcrLr1uTGW2GyXGYjFQFFW1L2c9lpN3ps2OVZRU0DSF2n+GklnDzTOQZBU8d14giqKC4SFXlXOw0flGQ14cW8hgzZgfh06m4HOfTyGVNFLHZReF6z5/75E4vG627Dq8bhaKomIpXgDDVkcLuq5DEFWkcxK8bq5uNAmUhOuFg0s4cSZz7tUDm9YO47UXR83ndcvS3qgfZCwWgyAImJubKxsmaaQguzVAlKQQVz5EwPoATdO2u0RUpvus9vJwOAyfz9fyl6DXe2CyLCMWi9mq5ep1BBYd9kDV4ufSehXPh45wwI1btk/jR8/NIZkRzGMGfC68/qqpqvM1YnLEC6+bhapquGgqgLnFHBRVhSipmBzx4U3bpxHw1Y6SNE1HIiMi6D//ex0lkfF5eSQzAmRJKXNFpvMSTp7OQFZVPHdgESxDY9vGEaybqL3H9j8vziOWFhA8dw26ruPV2SREUcX12ybMn/Vq0TW6hrhcLgQCAQSDQdPeXywWywwj1lIAp+z93TZxkBRi5xAB6xOGMDW7wzMWTEVRkEwmUSgUOraX9yoCM+aICYJgewBmrwVsJMjDxag4vRhDwFcyFHAch7ygYN1EAD5PKYX0OzdtwFKygFxBRtDPIzrsafn9ZxgaN1+9Br98+SxEWcP6ySFIsoYNa4LYfukoGKbxZ6FW8ESh9BqH/S6wDI2lVBEBLw9RUnH4VMkMs2V9GMN+FzRdx/MHF+HhGYxVmDriaQGLiWKZWYWiKAz7XThxJoPXbBqBz831rRu98T2x2vuthhFN08pckIa9v5N+kL2IwAidQQSsTxhOxGY5dk3ToCgKFhYWEAqFzFEhndDtCEzTNCQSiaZzxGpR63EFQUE8LYBlaYyFPFX7VVaSGRF7jsQRTwuQxCIuXRfCazZ5qsTBcD+mUincuDWKA/Mi5pcyUIpFqHIWE2EeE0M8zpw5Y6arxsNeUJHO3nuPi8Ubrl6DoqhAkjV43Sy4Gqm/SmiawkTEi6WUAG/Fvlu2IOPKTVHMjPlxeC6FQ6dSOHEmgyEvh4umgvCfE2GaohDw8XjlRKJKwJaShbrvq6bpSGVEU8B6jR0TB03TLfWDrOzeX0uoSCeOlQ8RsD7RTEQ0TUMymUQulwNFUbZHm9g9dzfqwKxd7VsZx1IPTdPx871n8OrJFAwfhYdncMv2NZiM+qoefzZewO7fLMDjYuHzsNBUGi8fTyOR0/CGq6bMBdpwv3k8HrMP5JopDoKkQpBU+M7tM9UbNGld/Cprm+y+rx4XC0+L5VnbLh7B7ufnkC1I8Hs4qKqGXFHB5OgwZsb8YBgal64L49J1YXzvF7M1DSYcSyObl6p+7uJZaA3MKqxFZPsZgbVCvX6QqqqaKch6/SDdbjfphTgAEAHrE/VqwSpFYHp6GnNzc46euxspRFmWMTc311FX+0peeHUZB06kEPSfT/soqobv/uIU3n3LRgx5y6PXX+9fwpCXA8vQ0DQdmbyMbFHFYkpCJOjGJTN+xM81BDa6klgpicr5r0Q9Y0Gt2iaXywVFUQAAXq+3K245j4vFm7bP4OhCCnNncwAFbL0ohMs2TlRFmG6ehaJqVS5CTdfB1UhVTkV9525E9LJITFE18ByDkeHm7tZu4bSNnmGYpv0g4/E48vk85ufnq7r397ocgVAfImB9olLArMMZA4FAmQg4PRPMqX0may2XqqpYt26dY9eoqhr2HUuUiReAcwuygpePJ3D95WPmz/NFGUVJQcDHQ1F1HJlPo1AQwPMsNE3F939xHAunfXjDtRfBa6PUoB61UlWapmEpkcXZ00vgCxnk8nnolvZKxgLoxDwuF8/gsvURXLY+guXlZfA8X3PvbNPaYTy3fxGhQHmYl83JVU5HQVJw+FQKqqpi75EMIkE3oiEPZFWFpgE3X72moXux2/SikLlWP8ijR49iamqqbDK2EYVXdu/vdscOQm2IgPUJoxbMuhdTL3oxasFW0pekWCwiFouZPRbPnDnj6PUVRRWaVvsu1etisRgv1H3umVgBqqrBzTNQVAWyrCEU9KCoeZDIqvBa9MtIfeq6XiUwdsRGkBS8eGgZBUFFLieDZVgEA25csXkEPIOq/Rdrwa6x/9KuqDW6CVkT9WF5cggnTmfBcTQoAJKsYXLEiw1rzqfTTpxO48cvlNyHLp6B20VjOVWAKCu4bus4tm6IwOfurBZK03TEMwJUVUc44CorA7D3/P5NZDY6jFj7QRr2/mKxiEwmg6Wlpbb6QZIIrHOIgPUJURTx3e9+F1u3bsXmzZsbzuTqxkywdjHqcgBgdHS0ZquqdjgbL+CXrywhli5CEgq44Qo/NK12l3hR0bDGX24393k4eHgWsqIhmRPBQIN0TjBYnsfkyBD8Xg5H5jJYM+ovEy6apuu+x8Z+odUFZ6DrOl46HIOuAcN+HpTKgeVK3S/2HIrht7ZNIBAob69k7KsVi0Xb+2rtQFEUrtw8ig1TQcwv5aDppTShtW4tlRXx/MElZItyWYrQ7ZIx7HdBUfSOxev0ch4/fO4UBKmUbaApClddEsWVm+0be1baXpRh77c2Deh2P0hCbYiA9Rhd1/G1r30N//iP/4jNmzfjXe96F0ZGRho+x+nWT+1gLZweGRmx1fHDLscX0vjeL+fg4Vm4eRbFoo6f7T1T2scqwKxL0jQdRVFBJi9hy/rq5snXXh7F/312FrncuX6ALAdRVhEK8mb9lCirUFXVXBQ5jqu7oOi6boqctfegsfDmBQW5gozhij6JHEsjL8hIZgVEguXvU6N9NSNSs+6rVfYMrKSZCAT9LgT9tW8yjp/OIF+U4aqIiNw8i3ROQjIrQJRUuPjmEZOu6zi9nEemIGMs7EE44EY6J+GpZ07A5+EQ9LPm4361fxEunsHlF9lrv9avXoit0E4/yMnJSduDWQm1IQLWY4rFIg4dOoTPfvazGB0dxejoaNPndGsqs507W1VVkUgkUCgUEIlE2iqcboSm6dj9mzMY8vLmPgtL0/D7eCRzIjwuBqmchEJRxlJKAKBjetSPn710Fq+9OIyLp4cBlFJ1SiGJ37o0gHxRQ15QAF3DeMSDdRPDoCgKmbyE9RM+M13YLOVpvE7rv1YxKxQlaLoGVVXN91PXSwsuQ1MoNulraFDPAm6kqbLZLJaXl82yC0PUFEXpaC8zV5BAU1SVfZ6iKOgAdB1QNA0uNH6fllNFPLbrFSSzIlS11CJr45phXLJ2GAxNlRlJjNqyFw4u4bL1YVufpX7Vnjlxznr9IEVRJG2qHGDVC9iePXvw0EMPYf/+/eA4Djt27MCDDz6IaDTa8Hn/8R//ga9+9as4fvw4AoEAbrzxRtx///1Noymv14tPfvKTiMfjWFpasnWNnc4Eq0UzK73Vxu9U/Vkt4mkB0rm+ewal0+hwsQzWjQ8hEnDjh8/PY/NMACPDHrg4pjTa5mAMLpYChwJUVUU0GsUalwuh0Ah++tJp8KwOStcACigIEgAdm9eGO0p7WsXM4+IAlBoZZ7IZyLIMr9cLTdMgKwrcHFVVS9RKPVytIZNGmqpYLCKXyyGbzSKRSJRFanb31UIBN87ES1GTVWR0XQcNwMXR8PCNlwhZ0fDwN/YiW5QgKxoUVQeg4sVDSzgyl8LVl1bfoNE0BVHWzOiu2bX2Q8C6mbY0orWVHlUOAqtawA4ePIh7770XW7duxWc+8xnE43E8/PDDOHDgAHbt2lU3vP/iF7+Iv/u7v8Ndd92FP//zP8fJkyfx6KOP4uDBg9i5c6ctM0OrHemdTiHWczZa3ZDBYBDT09O2v2jtLDQ6UOqHVEapY7vx86VkERevCYDnSl3iZ8/mIIoKXKyGZ17K4x07Npbd4Y6GPbjxNRP45csLyBUkiCqNkaAH12wZg9/r3Gwsr5sBpQlYOJNDNDKM0HAIFEWda4TLIuDjzb02q/DViuzsUCtN5fV64fF4TFGzOuWsolZr7+WiyQBmT2fA0mJZr8d8UUHQz+PS9eGGReMAsPfIMjJ5CYKsgAJlRtEaVYrMYukiRkPlRdOZnIjjp9P48v89CJYuzUK79rIxW6nKXkGKmAeDVS1gjzzyCILBIL70pS+Zd+VbtmzBHXfcgZ07d+Kuu+6qes7S0hIeffRRvP/978df/MVfAABuuOEGhEIhfPrTn8ahQ4ewZcuWpuduJaqiadqsMXKKyrSkruvIZrNIJpPw+Xwt13IZEV2rX8pIwAXuXN2WsVgaEZii6Ng0PYxf7V+C181gfimP5w8uQ1ZUqJoOnmXg87J41xvKRUnTNIwEebx5+xQWziyBgg6fl4YsZJGDXHc/yS7GexWLxXDJzBDmE37kigqkggQKgMfF4cpNIzXt7Ub60fr/W0WtllmkGa3uq1lF7brLx/H8wUWcPJNDPC2AAjAW9uL1V01humIuWa2/7/HTWYiyCgrlqUiaosAwwNxirqztVjon4sDxUieQYb+71G/xZAKnY3n879dvsNWVpBeQRr6DwaoVMEmS8Oyzz+L2228vSylt27YN69atw+7du2sK2A9+8APIslw1wPLWW2/Frbfeavv83ZgJ1grn92x0c7yJ2+3G1NRUW4t7u7VlDENjx2sn8MPn5uHzsOBZBpoGpHIS1k8GMB7xwM3TSOdE/PrAEjRVK+2rsKU0YiYv4yvfP4IPvfNSACgzaPh8PlyyaUNZ6q1QKCCRSEBRlCrbc7PBikBpD3NpaQk8z2NmZgYsy2JyHMgVZAiSAp5jMOStX+9V+fPKfbVKyzhFUXVFrdH73cq+2qWTLDaOD4NhOYQCfgwHPDUX71oCNhJ0Q1a0mtGTi2UQDbqRyopgGBoMBRyeSyHod2Ht+JD5moZ8LiSzIo4vpLF5bajua+olK835SKjNqhWwubk5iKKIDRs2VP1u/fr1ePXVV2s+78CBA4hEIlhcXMQDDzyAF198ETzP45ZbbsFHP/rRspY1jTBGqtihW3tgRiudep0pWj1eu7Vql6wdhs/N4tmXF5HKSdB04LotI7hmywQoisLGSS8ef3oeiqKV7tCp81OI3RyNw3MpZAsi3BxtNnu1Xket1JvRINlwiKVSKciyDJZly4pUjVoeWZaxvLwMRVEwNjZW1VHf7+Xg97b3/tVKJRriVCsFCbQXqTXaVzNaK2XTMSRi5+vVrPtqtQRs+2Vj+PcfHa7q4KFqOrxuFpeuD2PHaydxeC6FTEHCcqoIRdNx4EQSQR+P8REveI6B183i8FxqRQkY6US/8lm1ApbNZgGgLO1i4PP5zN9XEovFIIoiPvCBD+C9730vPvzhD+PgwYP4+7//exw6dAjf/OY3bQkBwzBVY+Hr4XQEJkkS8vk8KIrC+Pi4I7VcnXb3mB7z43fHSn+LxcVFBAIBKEppDIuH0cDzLCiqJG7Qdego2dU5joGul5r4zowHbC861q7m1iJVq6gZ+0lGpBoIBBCNRh2rfWt2fdZ/AZRFatlsFtlsFkNDQ6YLstUibONxhrhbb76sI0us+2qyLJumEbfbDb+Hwzt2XITv/PQ4VE03tzPdPINrLh3D+skAhodc2L5lDC8cXMKxhcy5+WsUltNFzJ7N4DUXj4DnGKRzIp7ZexqhITc2zQyDY53t2dkKJIU4GKxaATMEod6HqN6HV5Zl5HI5/OVf/iXuueceAKXpzuFwGA888AC+//3v47bbbmt6fiM1ZAzoa4RTJg5j8ZEkqezO2gmaiWyuIEPVdAR89topJZNJKIqCkZEReL1evPZiGcvpBXOkCMvQoKlzd7I0hWjI58gds7Gf5PP5kMlkIEkSQqEQ3G43RFE03z8AZenHeh3NnYSiKEiSZLpXp6enwbKsmXo0HmP8265ZBCi9D0NDQ2XiLooiFhYWoOt62b7a5VM8CleP4djpPDRQiA57EQq4EPTx2DxTKnMoCAqe+vkJuHjm3Oy181H03iMxqJoGTQMY+gwAIDjkwofeeRnWTwz1JZXXCxMHoXNWrYAZd5u1Iq18Pl/2xbViRGw333xz2c9vuukmAMArr7xiS8CA8/0Q7QhYJxFYZS3X6OgoMplMVzrSV7KYKOKpZ2aRyooAKLhdDN509RQuWVedKtI0DalUCrlcDoFAABMTE+ZCd9OVk3hm31momn5+LhZFQVV1bN0Yht/rXEFooVDA0tIS3G63uc8FoGFTX1EUAaAs/ehyuRxLQ2mahng8jlwuh9HR0TLXJVB7f8xpswhFUWAYBpHI+QJkY1/t9X4fLhpP4/jpNFRVxESAwUVTfgjFPKC7se9oArKqYSToxmKiCEAHw5QmYSfSAliWwUjQBeqcGShXkPDok3vx/31we18iFbIHNhisWgGbnp4Gx3GYnZ2t+t2JEyewcePGms9bv349AJgLloFxV95Khwq7wtTu+BNDEDKZTFUtF03TkGW55WO2co3LySIe+sY+5Iql81AUEA64sOtns7iDpbHxXE8+IyUWjyfg9vgQCATg8ZQPjAwHXHjfrRfjX//rCCS5VG/kdrHYuCaIe27d7MhrkGXZ7Gs3MTHRMDptZJIQBAGZTAaCIEDTtCpRa8UkY3U8Dg8PY926dbYWdCfNItZrqXVc47VFRyK4elv5vprhgjw+W0q9czSH6DCPXFGFKGvQdA0agCEvC4qmAV2HrGiQZA3ZgoydPzmGHZdVj87pNkZvw25CUoids2oFjOd5XH/99di9ezfuv/9+c2N73759mJ2dxd13313zeW94wxvwxS9+Ebt27cIDDzxg/vwHP/gBgFI60S71Rqp0SqPO9gbdnsqsaTq+sOtgKfKiAEUtLZrpXKn7w2e/vg83bBvDjVtHoAgZ/PSVDI6eLgIUBRoabrpiDG/c7jOPq6oqLls3jL/60HYcmssgX1SwbmIIUzXmgrWKqqrm+IxoNFpzX9Tue1DLJGEMVczlcojFYmUdNRo5IAVBwOLiYpnjsRM6NYvYLZOota8m0UG8MncQDEND01T43RS8PIVssbRvxtClv3O2oEBWNNB06TP0q/1LEIpD+P3pmZ5a7Fda82xCbVatgAHAfffdh7vuugv33HMP7r33XqTTaTz00EPYuHEjbr/9dgDA7OwsYrEYtm3bBp7nccUVV+C2227D448/DlVVccMNN+CVV17B5z//eezYsQOve93rbJ/faXehruvI5XJIJBLw+XyYnp6u+yWsl/Jrl8oI7NhCBovJAhiGgihpoGhA1QBNP9fTUJCx7+gy9h+Pwe3ikCuULOgURUFWNHz/12eg6gxuvqqURmRZ1my6+9qLG3c7sYsh9IlEAqFQyHZ00woUVT1UsbKjhrHfx7Ks6XzM5/N1HY9OX5/1X+P6rJGa8XtBEKrMOnbfrw1TQURDHsTTAjwu3jxPQRLAMgpomkJRkCFKKhga0DUAuo4hN4t4VsJz+xfxW6+ZcOhVN6ebKUTiQHQO6gJ+M229sF//+tf43Oc+hwMHDsDn8+HGG2/EAw88YLaS+uhHP4pdu3Zh9+7dWLNmDYDSHfuXv/xlfOtb38LCwgIikQje/va347777mvJFHHs2DFwHIdQqLl1+OTJkw0nHBcKBcRiMbhcLkQikaZ364Z1fHx83Pb1NiKVSgEo7S3Ons3i3390DEfn0lA1HRxLQ9V1SLJmLoAMBYyFS3OUlpIFjIe95mtTVQWaroOhGXz8/VfC63a+7U4+n8fS0hK8Xi9GRkb6frdtiFo8Hkc2mzXNGYao2R3R0Q1UVcXS0hIkScLY2FjZNbRiFskXZXz9h4dxajFn/mzLutC5cTQK8oKR0j4XdWs6XnPREBhKg6JR+D+vnyorwnZivlo95ufnEYlEHG1abWBEsr1ws7bJwOQ2V72A9ZOTJ0+WukY06Z8IlL5QExMTVQutIAiInZsyHIlE/7VY7AAAIABJREFUbHe3liQJsVgMk5OTbV17JZlMBoqi4IUjBbx8PIFkVsByUkBOUEBTpc16VdVBUaU/jNfFwu/loGo60jkR42EvWKbURNZINeYFFcN+DhNhD95+wwy2bhztWMgkScLi4iIoisLo6OiK6QZeKBSwuLgIn8+HkZER83Vabf2iKEIUxaoRHU5NCa7EGqFGIhEEAoG6xdTGomzHLJLOScgVJAwHXPC5OZw4ncYjT+7DcrJ4rsSv9HnZMBXAZMQDSZagUzw+eNtm870oFotQFAUMw3RlYvKpU6cwNjbWFZExuuuvlM9eDQZGwFZ1CrHfMAxju0WUYaU3BEySJHMS8sjISMtppm7sgZ1NCHj5RALDfh48SyOZEcHQFFRNB7Tyx7pdDFiGhq6rKH1fdOg6BVBAPCNBPDc/iqJonE0I+OJ/voq3XL2Ey9cNlY0ZsWtfV1UVsVgMxWIR0Wi0ysXXL6zGkampqapFrVabKFVVTbNIIpGockC28r7Uw9h/c7lcWLt2bcNUdOW/zcwiAR9XVk6xfjKIT/zBtfj8zpcxt5SDz81ieqw0v02WJMiKjomouyoVC5TXqxllDxRFlYlaOzO4yB7YYEAErI+wLItisWjrsYbgKIqCeDwOURTNGql2aNfZWA+KovDKbBqucxvtHheD4SEeoqRApgBVLUVeNF1awHQd8HtYKAqNdE4CRZWOIcoqJKmkdjRFgWdpc1H8+YE83nzDFqiKbKZABUEAUG5fty5YRs1SKpVCOBzG6OjoinB/aZqGRCKBbDbbsnGEYZgqB6QxJdj6vlhnihn/NVuUVVU1B222u//WjllkyMvhA7dtwb/94DC8btY0bCiKDkFSseO1tTMFterVrDO4DIGv7APp8XgavhfERj8YEAHrI62YOCiKQjKZhCRJjizE3TBxiJIKmqagaiqKRQFjQRZBXxCzZwsoijI4ljHbQAX9XOkOXdex/dIojp/OQtc15IoyNL20wAUtd+mGueN0rIh1E0NV03Ctk3CXlpbMNI0kSWZz4k5dfE5gtcUHg0HHjCP1pgQbomb0PtQ0DTzPVzkgdV1HJpNBPB5HOBzG2NiYo0JvxywS9LH4nRvX4b9fWEAmJwEUwEDDLddMYDLamsBXzuCyCnw2mzWjXo7jykTNcINWRo5OsxJuoi4E+v+NXsXYaeiraRrS6TRyuRz8fn9DI0crdMNtNxN149kDSXhdNDzn7vZ9AEIBD3JFBa+/cgIvHY5h9mwO0IFI0I3/9boZbJwexoETSex+YR6vnkqBZxkE/XzZjKpm57Yu3qIoYnFxEQAQDochyzLm5+erarLsRCROYlwXy7I9EdRmtv58Pm9O2TYW80gk0nZU3871Wf8FAIoGGBrI5Eu9Lbeu5XHRZMBsl2WdztzKZ7iewBvvRbFYRCKRMPthyrKMdDoNj8fjuHGmH/PNLlSIgPWRRg19jTviZDKJQCCAUCgEhmk+/K8fqKqKdDqNsYCO0JAbknJ+817VdGQLMt549SQuWz+My9YFQdO0aYs3uOyiMC67KIzDcyn84879YCvmUOl6yc24ZrT+3pWiKIjFYhAEAWNjY1UOsnoRSbdFzbr/Vuu6eonV1u/3+xGLxaDrOiKRiPn+ZDIZcyG3vi/1XH+apmMxWQDL0BgJutv+jB44kcC3fnwcLEOBgop0TsDP90soqHHcduNQWcTmVGeRWvtqsizj+PHjkGXZ3FezGmec2GNcid/jQYQIWB+pFYHpum7eGXu9XrOWK51OO96RvlOsBdNDQ0MY8ntx963r8d/Pz+PEmSwACm6expu3T2HzTMnBxnFcwy/+xWuC2DgVwOG51Ll+hxQUtfS67/zti2pGZbquI5FIIJ1OIxKJ1E1/tVJoXCvN1s77k0qlkEwmV9T+mzWNGQqF6l6X1QFpLOQMw5QJ/p4jKXzn57OQldLfyO/h8N63bMLF0/amMhioqoannjkJngVkWQTHcQgM+aDrwEtH47j28rGyUgsnOovUw5hmYJ3Kbt1XM/agdV0v+4w021ezXhvBGYiNvo9IkoQDBw6YI12MuVxGKsfayiabzUKSpLI+dJ3SrLasHlaR9fl8CIfD0DQNi4uLmJqaAlAaNS/KCngGZsRlN7JRVQ27f7OAn+45A1lREQ648c4b11X1TzQKt5eXlxEIBBAOhx3ZeLeKmvFfq6Jm9FP0eDwros7MwEhjchyHaDTasjBbF/I9h2PY+fPTYGgKDE2DoiloOgWWpvAX770CY2H7qcjZ02l86T9fgdvFwO0q9UQ0yBVlXH/5GN60fbrpcay2fqA6TWlH1HRdx/Hjx2uOWrJi3VcznJCVe4zWfTXr8Xne+dpGBxkYhSURWB9hWdZMexnjKoxC0Uq6NROsVbuwIAhYXl4Gx3FVwy+N69M0DdBVuNjyDhp2YRgat2yfxi0NFixBELC0tASWZc2+lk7RrHtGLpfDkdmzgK5hZPi8AcDtLk0YXlpagqqqTfsp9hJN0xCLxVAoFDpKY1oNEs/sPw4Xz4OmKei6Bl3TAV1DQVDx7//1Mu68abqpld2IUhdOnwXDsvB4ql2PFEqpaDu00lnE+p/1+XYdiNZ9NaMZgfXmxxieaqRjrdb+FVwDNlAQAesj+/btw6c+9Sm43W488sgjDRcVp0aqVB7TroDJcmk2l6ZpGB0drVqYKYqCoqhYjOfAsTSGh0p7SU7fZSqKguXlZUiShNHR0Z7tJxn9/fYcSeLrPzwKSdago1QK8HtvWovJkIazZ89CURRzf8nYO+l2U9hGVKYL165d60gKS9N0ZAoyGNoQDBpgAAYAyzBYygChUKjMGVq530hRlBmlXrV1I/7nlZfrGhy2rA+3fa3NRK0SWZbLWmY5ta9mRGqSJJmDVQmdQQSsT3zta1/DF7/4Rdx22234vd/7vaYLsdOFx8Yxm6WQjVEsxWIRkUikbgHwb15dwtPPnIGmL4KmaUTDHvzuzRe3lEZqhFE3lclkMDIygvHx8Z7vJew7Gsfj3z0IUVbNcxdEGV/4zhG8/5ZxXLw2iuHhYWiaVtaJ3ehzaL0Dr9W812mMriMMwzjueizV7QG6Vi04mg543Wxd15+RXjX21GRZRi6bxvWXh/GTPUvweTiwDA1N15EvyFg/GcB0A/NOe9df/d5bSwmi0ShUVXXELAKgbHjqBbxt03OIgPWJd7zjHbj99ttx+PBhWxFQN1OItTDs+7VGsVhRVRUvHYnhqV/Mwef2AJRe6p0Xy+HRb76I99w8iciwv+5+QDNq1U31a+/g6z86AkFWQZ+7fl0HoJeGNf7ysIDrriztTzIMUzIhnLvL1nW9zBBR2by33femHtbZYWNjY12xxVMUhddsjOC5A0twceWfX1XTcfNVUzWfI8sykskkhoeHzbSbEZ1cNuMFlAB+eSCJrKTBxbHYfkkEN121xvHrr0SWZZw9exYMw5R1HummWYTQOUTAzrFnzx489NBD2L9/PziOw44dO/Dggw+WOZEaoaoq3vOe92BxcRE//vGPmz7e6LzQykywXgiYtaP90NAQpqenawqGMeIEAP5nzyKGPBzoc+kklmHg4nnkBRmzMRprJjxmKslqzzYiknoLd7FYxNLSkmPjRDpB13WksqVRMNABzZJeYhjgxJlc3eca7kvjDtzAWLhrvTftNqw1ygNamR3WLre/fgNmz2SxnBLMXX+KAi5dO4xrLxsre6wsy2ZtXuWepTF6JRAIYHR0FDddW9pvNAwS8dgyZFkGwzCONza2OkXHxsZqZhja6Sxi/c7Uc8QSOocIGICDBw/i3nvvxdatW/GZz3wG8XgcDz/8MA4cOIBdu3bZ2nD9whe+gBdffNF04dmlUS2YFWtO3ikqu3EUi0XEYjHwPF9l0DCwChfLshAkDUVJhYevjiI9PIujp7N46/Xr6i7cldFILKuhIOpw0yICXrrr40TsUkojocoEAJQiMb6NWVW1RM2I1IrFoilqxsJtCH4tUTPShTRNO25qqYfXzeIv774SLx5axguvLoNjadywbRyXrA2ZNzNWgRgdHbXVMsvYb+R5vuZ7Y9TxVdZntdrMVxRFnD17Fm63u+XI3o5ZxPqYWo8ndA4RMACPPPIIgsEgvvSlL5nmhC1btuCOO+7Azp07cddddzV8/p49e/DYY49hbGys4eNq0a2hlnYwIjCjMz2Aui5Iq3AxDGMaNFzQ6npuFVWDz1W9kFYu3LquY2Epi0f+Yz/SORGKqoNlKEyNuPHeN/EIBnxmiq38mnT89/Pz+O8X5iHJGvxeDrfdsA7bt4x28K7UplgsYuOECy8dO2dcsLxomqJx8zXOpLlqNe+tV49lLNiG4I2Ojva8STHH0rj2srGqiAsoOUXPnj0Lr9frSOq3XmNjo1O/tbFxpahZz63rujm2Znx83DEjUDNRMwraBUHAli1bHDnnamfVC5gkSXj22Wf///bOPDyq+t7/71mzTDLZ90ASiAlbwiJKymXTWsFy1cIPnsoVg8hTq5VIFRK916d9wKUIvYArCsJtK0otsmi1VrhGsSDoLUJBkjCCJhAgM5NMlsnsM+ec3x/J93hm5sxkMpkt8H09Tx70zJw531nO+ZzP9v5g0aJFbpV1lZWVKC4uRn19vV8DZjKZUFtbiwceeAANDQ1obm4e1PGjacAAoKenh28A9pUrcblcvISPp4KGQi5FSb4a318xIiHO3QtzuFhMrxjYqDucDF589xuYLQ4oFXLE9XtzVzud2PP5VSy9rZD31ITadX/6uBlnvuuEtF8IuKPLhT/87Rzau62YP71oCJ+K+3vX6/VwuVxY/u/j8btd38BgtIFhWYADFHIZRuYm4SdTw5enEV64O402XLhgAMuyKMpkYDS2QyaTgeM4dHR0wGQyRXV2GNB3s9Pe3g6r1Yrc3NywetAD6R56Cj7LZDKYTCYkJyeHPcQK/GDMzGYz2trakJCQgNLS0rAe83riujdgra2tsNvtok2LJSUlOHfunN/9161bB7VajZqaGjz00EODPj7RXQsEEkYc6knHsiy6u7vR3d2NhIQEnxV9DMPwoRB/jZc/m1WMbe81wWi2I04hA8NycDEsJozOQHlRqt+1WCwWfPLld7BYnYiPj3Pz5pRyGS532CCLU2NkdrZbL9aFVgO++a4DHMuBEfTzcByHg1+24tYbC5AQF/zPW6juQdTiJRIJfvfQzXj/H8343xNX4HAyGJGjwrI7yiEP87h7juPw1sFvcewbHSxWJzhwiFPIMHtKPu69vRQSicStyZj0FkZqdhiB5OD8KXyEGzHdQ4ZhoNPpeANvsVjQ3NwcEsUVfxB1f6PRiBEjRoRUiIBCDRh6e3sBQDQ2r1Kp+MfF+PDDD3Ho0CHs378/6JyDTCbjwx4DQXrBgj3JSEUf0VfMysriG6iFkHAhKT4YqEoyOVGJRxdPwL++7UBDcxfi42SYNi4HJfnJPi9gDoeDV43vsSsglcpEQ5EMw0LXaUFGv8YeyY20/MsAFwMoFHL+vZE/q43BFycvYNINmby3NphmbaLuQe7ShYb7+Dc6fHLiCqx2BlIJ8N0VI9a/eRJL55VhZhhH3v/jX228MgkkgEwihYvh8PnJNozOT8GPKnJFvRFPCSQyLyvURo0UaUgkkqgX3HhiNpuh0+mQmpqKvLw8Qe7SW9iYYRgoFAovoxbM50O8rsTERIwfPz6q/YDXKrHzK4sSwqS8GL68jsuXL2Pt2rWoq6sbUHLGH4Eo0gvXEmwlosViQUdHBxISElBYWAiZTAaLxeJWGOJZoDEYBQ2lQoabx+fgZpFciBCGYWAwGGA2m/mcTZ72MjhJu+jzZVIpUpK81Swknv/2NyaxHAeLw4W9R3Q48IUemWoFfjIlDfnpfYZP2IvladSEhRCFhYVeFxyLzYk/f3IBNgfDN/DKJBLYHAx2HzqPqWOyhuT1+eOvR5rhcLr6vhPBb9XJsHj/SAt+VJErup8vo+Y5EJM04Aov3IFctIXz1gIt0ogUDMNAr9fD6XSKFrYMpLji2ccXaHUo8bp6e3tRWFhIva4wct0bMPLDFfO0zGazWxUUgWEY1NbWYuLEifj5z3/uNVXZ5XIFfPEfTA4sGANmt9vR0dEBqVSKvLw8t5OYvJ6vAo1QIqxGS0tLc8s/VI3PwUfHL4FlOb56DejTU8xKi0d+pnduburYbPzvPy+DYVi3O2qj2QmW4xDfLz101WDHnw+345H/Nx4FWSpRJXqlUgmHwwGHw+G3b+rrc+2wOVxeFy5JvxH717cdPg1JsJCJzWZrX+GG5yVTKpHAZA0sBE3wNRBTWBkaSDFEqIs0Qgn5jjMyMqBWqwP2oIRevlAtgxg1otYvLKSJj48Hy7L80My2tjaoVCqMGzeOel1h5ro3YOTOrKWlxeux5uZm0YRrW1sbTp48CQAYP3681+Pjx4/HggUL8Pzzzw94/MF4YINpZiYai06nE5mZmaKVVlKpFC6XCwzDiBZohAqz2Qy9Xg+VSiU6nj4pUYH7f1qOP36kgd3J9K9NgmSVAg8vGC968SnIUmFSWSZONOnB9Rs+q50By3FIUMp5QyiTSeB0MXjr4Hn87qFpbnfbLMuiq6sLnZ2dfOWlVqt1m9wr1PCz2F18haQnLhcLi93ltT1YhDm47OxsJKniYe+28gNBCSzHISlh6BfJ9m4bWnUmqFVKlBbmQSqV8MUQxBMhRk2pVPK/m7y8vJDKeWkNFnx28graDBbkpidizpR85GcGXlnpcrn4frNQhjLFWh6E4dn33nsPO3fu5A3XpEmTUF1dTQ1YmLnuDZhSqcT06dNRX1+P1atX8xVTZ86cQUtLC6qrq732yc7Oxt69e722P/fcc7h8+TJee+01XmVgIAZjlALRQySSS2azmZd+8lWgQUp7r1696vOiPRTsdjv0ej0kEgkKCgr89tNVlmbgmV/chH826dHebcOofDUm3pDhd6jlA/PH4IbCFBz6v1ZYbK6+frQ4OeIU7vtIpRL0WpzotTiQnNi3BpvNBp1Oh7i4OIwaNYo3qsKZYUajkc/TxcXFoSBNBlW8DHYnC0/BblWCAmOKAvvOB8JisUCn0yEpKYn3bOZPH4m3D5738jgVcimqJmTjhb+cQavOhIzUePz79CJUlgYWtrI5GLy67yyarxrhdLGQy6RIjJdj5aIJGJmThIt6Gw6fbIPDyWDq2GyUF8Sjq7MvFK1QKKDVagHAK/wYzO/n63Pt2Hf4+77XU8jQ0d2Js993YuHsEkwd6781goz26ezsRFZWlmjkJNSQ8CzHcZg9ezbmzZsHqVQKjUaD8+fPw2azRWQd1zN0nAqAb775BkuWLMGECROwfPly9PT0YPPmzcjIyMD+/fsRFxeHlpYWdHR0oLKy0ueFeMWKFWhubg5IiYNgs9mg0WgwatSoAZ/b1dUFqVTqJhJKEM7mSk1NRUpKiqjhEhZokBEnwou21WrlZx15GrVAwzDCAY7Z2dkRm/D7zB9OoFVncgtDEuRyKZ5/uArxCgkvBhxokzT5fKxWK17cew7NWjNYFv0q7H3tBeOK01C3dPKQ1k9K9hmG8erH4zgOuz7uq0K02l2QAIiPk2NUgRrfX+mB3cH0eU1cX2vD7TcVYtGtA+dmX9xzBg3fd0Em8CoZlkNCnAyjC9TQXOyBi2H5Ju7UJAWeWnYjUpJ/8LqEZeskzEZ+P4EaNZuDwXN/+pqfAce/NsfB5WLxX8um+MwvOp1OtLW1QaFQIDs7O2Kja0iOzWQyYeTIkQHftA4Dhk23NTVg/Xz11VfYsmULGhsboVKpMHPmTNTW1vJSUk8++SQOHDiA+vp6FBaK9/wEY8AYhsHp06dxww03DPhco9EIhmHcThTP2VxkcrMngy3QEIaPyEVJWL0mNmpdmNBPT0/3aUTDxWcnr2D3oQvwdNoYlkNuRiIe+3+l6O7uRmZmJpKTfVdI+sPhZPDm37/F15p2gOPAchwqipMx98Y0yGUSN6Mf6NRe4ec2kPdg6LHh9AUDJOibYv30/5zoM2ge34NSIcPTv7gJWam+w3vdvXb85o1/8gNDhdjsDCDhoIpX8HlSmUwGF8PhxjFZePBu/424wpsi8udv+vWZ7wzYffBbqBK8bw5NVieW3FaKSWWZop8bCbNGsonbZDJBq9UiKSkpYsonEYQasBhgWLwxjuNw8uRJ3HDDDQNeUE0mE+x2O1/VRPp95HK51wBMQigLNEiiX2jUyIReiUQCs9mMpKQkZGZmRiWh73AyePaPJ9HWYQY5PMNyUMplWDI7C2NKMpGRkRGStTmcDExWJ5ISFFD2i9l6DjgUK4Tw9GRJuFClUg36cztzwYBX9n4DsVFZLobFwjmjcNeMYp/7ay5146U93/C6jkJ6THbIpFKo4qWQSKWQ9a+L4zjIZVJsWfVvop6uP/wZtW+v2PDhl1qkJHmX9PdaHFg4uwRVE34okLHb7XyJeiR/b2SczzXodQkZNgbsus+BRRuiZh1Ifxd5HpnNxTAMMjMzfYbB/CloBINUKvWqXiMXYI7jeJUDm83mpd0XCZQKGf5r2RT8/fhFfHFGBxfDIDdNgZ9MyURF+YiQDhFUKmRI91BhFxtw6K8QgjSw5+fnBzX40uFkRI0XwTZAUUlaclxfTYjIa7AcoJD0faee6utAX4VonIj+pT+EHjyB9GLZ2R7IpG2w223guB/OC5lMBoVcilEFP5S5d3R0wGw2h13lwxOTyYS2tjYkJyfTCsMYgRqwGICU0gdSMWWxWGC1WpGZmYnExMQB81zhGl0uHCzpqSfncrl4L00oAeWpQB8O4pUy3D2zGDPGJcNkMkVFH1CI5lIP9h/+HvouK9LUcbjr34pRnC1DZ2cnEhMTwXEcrl69GlRzcdnIVCjlUrf5ZISEODmmlPufpJCdloCctARc0pv4YhmO5eBiXIiTS6FUyLxel2U5JCUqoFSE5jdFerFGjcjGhNFdaGzu4iXJGIaByWLHyOx4mLraYDXK4HA4oFKpUFBQEDEDQnKTZrMZRUVFSE31ry5DiRw0hBgDnD171u90YdJD1dPTwysdBFqgEWpI6XlPT0/AuSRhcygJrzEMM2Bj8WARzg4j86aiqf596KtW7P3se9idfQUWDMtCLgVmVmRi2b9XuN1YCPuwyNTegXKOAPCnjzQ4eqYNbP9gSXI+jypQ47+qpwz4/rt67djw1in0mBywOZyQSiRIiFNgwewS/PVICxwulm/a7nttCe6bV4aqCYMXrh4IF8Pio+OX8PW5dv79TB2TiXlVI9Bp6OCr+oi4MVHN8BwUGkqEXlesKYyEkWETQqQGLAZoampCamqql4qBcDZXUlIS1Go1dDqdVxFJpBqRiXFQq9VIT08f0jGEMj7EWxts5ZoQUhavVCqRlZUV9QuNxebC6peP9VcMSsBy/YovAOLjFPjdQzcjXe0//CXsMyI5R6Jt+IMnq8BHxy/hk39ehovhAAkwbVw2lvzkBigC0GfkOA4dhk6caLyKLoscOZnJqBqfA1WCAhcu9+B/PjwHs9UJDoBcJsHdM4oxe8rgRgYNFhfDwmp3ISFODrvNCp1Oh7S0NKSmpnoVqwhvjGw2m5u3L1TNGPQarm+vixqwGGDYvLFvv/0WiYmJbuXxwtlcGRkZkMvl4DgOly5dQlFRn9J6JAwXEDnjICxXJxckAG5eiGdojcj22O12JCal4aumTmhau5GREo+f3DQCBVnRCR9+1aDDtvcawfbrMwpnQrEshyU/KcW8qpGDfl0xo0YKaaQyJZKTEvtEkQPwPK3WPuPgrxCC4zi0d9vgcDLIy0iEzE9fXigh4rsMwyA3NzdgIxSoUfOnb9jb2wutVgu1Wo0RI0ZE/WYoCgwbA3bdfTOxiLCZmczm4jgO2dnZbsl94QkX6gINMZxOJ9rb2+FyuSIyWFIsyS8sgvDU7SNht4yMDNihwrNvnobF5urTRGS78X+N7fjZzGLcPm1EWNcthtVmh4thIJVIIJVI3S4JHMf1eUtB4E+w12q1wmDo8JI5Ik3H5PcjNPp5eXl+C0gkEgmy00KntBEIRqMRHR0dQbU7iElBcRznNijUU98wLi4OWq0W+fn56O3thcViuR69rmEJNWAxgFwuh1arhclkAsdxfIGGL8gk2nAVaBA1D6PR6DZKJBqIjcbo7e2FXq+HXC5HXFwcDAYDXvngCsxWF2QyKSSSPhFgpl/odnJ5pt9+qFBCjENGohOJcQrYnIzX/WxivAKTPXqahoKYURObXky8dKvVyo87iSX9QqJoL5VKQ5pvIlMVPIeoks/IaDTit7/9LVpaWpCXl4eJEydi7ty5uO2220JyfDE2btyITz/9FB9//HFAzz916hQ2b96MhoYGKBQKzJo1C3V1dXyf6vUKNWBRprOzE6+99ho++eQTbNq0CZMnT/ZboBEXF4erV6/yyetQVvVxHAej0QiDwYCUlBSUlJTE1Ah0ImzLsixGjPihLP6ithcO1xXIZFJwHJkw0FdwYHUx+N+vWrD41tKwVq0JpYwyMjIwIScH075z4oszWjgZBn1WrK+HakxRathDm57Ti4laBcMwSElJgdVqRUtLi5vKOpl6HenvXCj0HClFe2LUJBIJjEYjnnvuOeTl5UGv16OhoQFWqzVsx962bRt27tyJkpKSgJ7f1NSE5cuXo6KiAhs2bIDBYMALL7yAxsZGHDhwIKTtIcMNasCiiMPhwF133YUZM2bgtddew5gxY7ye45nnIvOMSKm6xWLh5xiRAghi1AZzd03yIfHx8TFXbUU8wt7eXt4jFGK2ufrMlUTqoXXLgeUYdPZY0dbW5jXROVSGX6irKBQr/vlPStHY0onLenO/OQWSEhS4b17ZkI8ZKEJR4JycHK+WAmHLQ09PD5xOJ2/UhDdH4TJqDocDWq0WSqUy4or2wlzXuHHjIJfLkZWVJSrQHQrOnz+PDRs24NixY4PSSHzxxReRkpKCHTt28OHeceMyc58kAAAgAElEQVTGYfHixdi3b5/fifHXOrFzlboOUSqVqK+vh9FoRGdnp9tjAxVokJCIMM7vcDhgtVrdRGj9FUAA7l7NQPmQSEOqMNvb25GSkuJzBHxhlgpSiQQMx3o8LoFCJsPUcfkYOTLXLcEvHGAYbDk/0Xy02WyiOcKX9pxBe7cN8XFyvpDDZHXh+V2nsOFXVYNWshgs5KZEpVL5NA5yuRzJycluF1RhEYQwXyT8jIbqzRLDajQa/Y6wCQdEsd5qtaK4uFhUWzQcrFmzBnK5HLt378amTZvQ3i4+A0+Iw+HAsWPHsGjRIrdzs7KyEsXFxaivr6cGjPIDwcSaTSYTtm3bhkOHDkGr1SInJwe33HILVq5cOeCdVlxcHORyuZvKPMMwYFl2UAUawuF8BM8CCJvNxueUlEol/5iYVxNt7HY7dDod5HL5gB6hWqXElPIsfNmgA/oNBdA3zTlNHY+pY/qUzH0l+InhJzOkhOX8xPALvwNhqDU9PR3Z2dlehlVrsKBFa+K3k3+lUgm6TQ6cvtCByWXhyV8MpkhDDH/5ImERhKGXRVOrBRKZHFUT8lBamBqQp0bmiJHxOpH0uoxGI3Q6HR8ij2SkYcOGDaJRFn+0trbCbreLDs0tKSnBuXPnQrW8YQk1YAKCiTUzDINHHnkEZ8+exUMPPYSxY8fi3LlzeO2113D8+HHs3bt3wBg1mQkWagUNsQIIl8sFg8GA9vZ2vjS/s7MTVqvVLQ8SLYRK9jk5OQHPmlp2RxnkMgn+2dQODhzAASNz1Hh44XjI/fRDiRl+YTl/d3e3Wzm/XC6HyWRCfHy86GwzwkVtL+wO8dE3docLmks9ITdgwl699PR05OTkhCT051kEwbIc/vC3c/jX+Y7+98jh+Fk9CjPi8B8/LoAqUTw3y7Is9Pp2nP2+A1e6pUhKYFE1ITEirQ4ulwtarRY2mw0lJSVuwyqHQnl5ud/HX331Vb4YZLDGC/hh0K7YDaZKpRIdxHs9QQ2YgGBizV999RW+/PJLbNy4EXfffTcAYMaMGcjKykJdXR0+/fRTzJs3z+9xZTIZnE4njEYjVCqVqOJCKLBYLNDr9UhISMDo0aP5i69whHpnZ6dbWC2YfFowCIsgfHk1/pDJpKi+oxyLbx2N9m4b1IkKpCYHFw4VK+cnYaeenh4olUrYbDa0tra65YqE35tapYRCLoXT5a30LpNKkB7k2nzhdDqh1Wohk8nCnsM8flaLk5oOyKRwG3FyudOJM5dcmDMxzi03q1QqIZPJ0Nndi33HOtFt6tNw5DgOX3yjxY8m5GDRLaPClmczGo3QarVIS0tz+92Hgrq6Or+PBzJlwh+kvcbXZxNLVaTRgBqwfoKNNUulUixcuBAzZ850207uzMjAP3/Ex8dDrVbzJz0A/qIYiipDh8MBvV4PoE841tMjFAsZieXTyKgQX/m0YBEaVn9eTSAkxMkxMid04VChV5OWlob8/Hy3fiqSKyK6kKT/Ki81HvEKWZ+MlId6RLxSjukVub4OOej1kVxSpHQfD/3fZUgl3hdVuVSCY9/ocdfMUbyHI8w3HWkwQddphUIuhUQi6Wt5AIcvzmgxrjgN40elh3SdpCzfbrdj1KhRIfO6hKxYsSLkrymE5OfEPC2z2XzdD8ykBqyfYGPNVVVVqKqq8tp+8OBBAMDYsWMHPLZUKuWPS8JXJpMJZrOZLxIQKgkkJiYGNGCShOMsFsugLm6B5NNIQ7HQ0AqbZQNB2CgdawUkwMB5uIH6r5bMycEfD12GzcH26QhKJEiIl2P5/HIkJQ69pN9qtfIzqSKZS7LYXKIFKBKJBA7nD2FTk8kEvV7fH87Mxfd/10GVEN83HLNfoaQvbM7i/cPnkKIcGTJtzJ6eHl6CKtReVyQhs8ZaWlq8HmtubkZpaWnkFxVDUAPWTyhjzcePH8eOHTswffp0TJs2bVDrEIavMjP7ml05joPFYuGNWltbGxwOh9vwRKHYq7CvJphwnBhi+TShAgRplhVWq/nKpwkFgaPdKC0Gy7K84R9MHg5w77/KzMxExdhifHqiFRdau5GeLMeNpSqo4sxobW11+5wGc4EVFmkEO4plKGSlJuCi1sgr2PPrYjmkJsfxXhfHcbzht9j6RrvwxSwSCSABZFIZ5DIOTk6BrKwsvvG6vb3d7wBMX0TC64okSqUS06dPR319PVavXs2Htc+cOYOWlhZUV1dHeYXRhRqwfkIVaz506BBqa2tRVFSETZs2hWRtEolE9E7fbDbzRq29vR0Mw+CLL77A7t278fTTT+Omm24Ka5OjmAcizKeRajVhmTrxCtVqdcT7fgZCWLafmpqKoqKiIRvWpAQF7po5yus4YuX8A/XxhatIY7DcPbMIr+xr4FsDyNoA4MeTs3Dp0iVkZma6GY94Zd9cL4eD9fLe7E4WFaVq3usnYTOxClGhUfP8nIjXlZ6ePmy9rt7eXmg0GuTn5yM/Px8AUFNTgyVLluD+++/H8uXL0dPTg82bN6O0tBSLFi2K8oqjCzVg/Qw11sxxHF5++WVs3boVkyZNwtatW5GeHtqYvhC5XI6UlBR+3TabDffccw8UCgXWrl2LwsJCNDc38zkZYe4qnCe2r3waGUvBsizkcjkcDgd6enpEpxRHA4fDAZ1OF5EiiIHK+T3zjiQH2t3dHVBbQbgpL0rDPbeNxr7DzXyRikwqwb+NVeOG/DhkZ2d7/cakUgnm3jwC+z9vhlIi/SGPyHJQyCWYK6JX6a9ClEhAXbx4EY899hiys7MxevRoVFVVoaCgICy/cZ1Oh40bN+LYsWOwWq2orKzEmjVrUFlZ6Xc/juNw0003iV5b3n33XSxevJj//8bGRlRXV2PlypWoqakBAFRUVGDnzp3YsmULamtroVKpMGvWLNTW1sZc2D3SUDX6fhwOB6ZMmYIlS5bgqaeecnts7ty5KCoqwvbt233uu2bNGhw8eBDz58/H+vXrI/7D4jgOp0+fxsSJE93uiq1WK++lWSwW2O12N48o1AUZnjAMA4PBwOfhyBBH4RgVkk8TGtrB5tOChWVZGAwGmEymiDfUDgT5/jo7O2GxWPgJxQM1p0cKp4vFd5d7YOzthTrOgREFeX7zrBzH4eMvL+Gzk1fBMBwkEiBOKUP1vHKUFw1eOJdUrn777bdob2+HTqdDQ0MDcnJysHbt2iG8M28sFgsWLFgAu92OVatWIT4+Hm+88Qaam5uxd+9e0dw54eLFi7j99tuxatUq3HzzzW6PFRcX86mCGCJ24vkDQD2wfoKNNXMch8ceewyffPIJampqsHLlykgum0cikWDSpEle2xITE90uygzDwGw2838kfCW8KBIDMhSEzb5paWlu4ThS/BFIPk24pnAMK9Tr9X5VPqIJkahKSkpCfn4+pFKp2+BLg8EgOiMsXG0YnrCMEwkSI9Ky45GVVThgOFgikeCOHxXh1hsL0ao3QSmXojA7KShFEtI24HQ6ceONN4a9Gu+dd95BS0sLPvjgA5SV9UmBzZw5E/PmzcMrr7yCLVu2+Ny3oaEBADBv3jyMGjXK5/Mog4caMAGBxJpbWlrQ0dGByspKKJVK7N27F5988glmzJiBqqoqnDhxwu01CwsLkZsbmpLpUCCTyaBWq93yEw6Hg8+n9fT0QKvVenlEg6kKE+oqBloWH0w+LdhKNXLxk0qlfJVXLEGKNBwOh1eRhlQqFb0pESvn95R+CpVR4zgOBoMBvb29yM3NHVSRC9DndZUWBiffRLwuUt1YWloakVzX4cOHccMNN/DGC+gr+Lrlllvw4Ycf8so5YjQ0NEClUgUs3ksJHGrABAQSa3799ddx4MAB1NfXo7CwEH//+98BAEePHsXRo0e9XnP16tV48MEHI/o+BgvJx6SlpQEAH+IjRq29vZ0v5ffsT/OcUabX60NWFu8rnyasVBP2pw2UTxOKAkeqZ2owCIs0MjIyAi7S8FfOb7Va3UR6B6oQHQhSup+cnBxxr1XodZWWlkZU/uy7777DjTfe6LW9pKQEFosFV65cwYgR4nPnGhoakJqail//+tc4fvw4LBYLJk+ejNWrV3tFTSiDg+bAKAHBsiwsFgtv1CwWC5xOJ19Z+PbbbyM3Nxf33HPPoIcQDgVibMnF2lc+jVRqqtVqpKenx1y4kKiyy+VyZGdnhzxcSvQMhdOuiUcrDB/78mZYluVvZHJzcyOa4yVtIe3t7cjIyEB+fn7IvK5ApaAqKipw11134bnnnnN7fM+ePfjNb36DAwcOYNy4caKvMW3aNJhMJjz88MOoqqqCVqvFtm3b0NzcjF27dmHy5MkheS8hJLZODj9QD4wSEFKplO9vysnJAdB3R/zBBx/g97//PaZMmYI77rgDWq0W3d3dIZ9V5gthPo14kMKQmlarhdVqhUQiQXJyMpRKJRiGiZlxMZFSZRfqGQorH51OJ6xWq99yfhISTk1NDUlP4WAght3lcoXF6wpUCkrYMiCGr/Ahy7J4+eWXkZCQgIqKCn779OnTcccdd2DLli148803g1g5BaAGjDIEFAoFpFIp3njjDUyYMMGtZN5kMsFgMMBms3kNTQy3tqJMJkNiYiJsNhsYhkFBQQF/IfbMpwnXFOm+IYvFAp1OF5VwHOBezi/We9Xd3c1PCSfhSZvN5qXOHw7C6XUJCVQKSq1Wi5bBm0wmAOICCECfYfOsPASA9PR0TJkyxStnThkc1IBRhsTPfvYz/r+FfTsZGRkAflARERaJEBURoTRWKCvnzGYz9Ho9kpOT3SSWhHOvhN5HMPm0ocAwDPR6PZxOJwoKCmJqoi75DkmuMScnB8nJyXzvVVdXF+x2OwC4Gf9QlvOH2+sKhtGjR/uUc1KpVMjLyxPdT6/Xo76+HlOnTvUS9rXZbGHtFb0eoAaMElaEKiLZ2X1zuVwul5s0VkdHB1iW9ap6HGx1oHA450CGwZf3IRzk6JlPG2qJumeRhlqtjrlcHBk7IpFI3BqmPcO04SjnF3pdmZmZyMvLixk1jdmzZ+O///u/cf78ed4QmUwmfPrpp5gxY4bPdUokEqxbtw7z5893U+ZpbW3FyZMnsWDBgois/1qFFnFQYgJhKb/ZbIbVavVq2vUV5uM4Dl1dXeju7kZWVlZIe4KE+TSr1erVnxaooSVehUKhEFWqiDbCcTbBfobCXj6bzeZVzk8qH8WMGvl8GIZBUVFRTHhdQkwmE+688044nU78+te/RlJSErZv347m5ma8++67vKiuwWBAc3MzSkpK+CjEc889hzfffBNLlizBrbfeira2NmzduhUMw+D999/nnxdDxNZdlR+oAaPEJMQbIvk0oYqI0Hh8/vnnSE1NxejRo5GRkRERbUVhNZ/VavWbTxP2TMWa0gchnMZVWM5vs9ncyvmJtmF2dja6u7uRmZnJN2zHIpcvX8bGjRvxxRdfgOM4VFZW4vHHH3eTktq/fz/+8z//E+vXr8fChQsB9Bn2P//5z/jLX/7Cz5CbOXMmHnvsMV7vMMagBiwGuGbf2PUKwzB86LGpqQmvvvoqent78eSTT6KkpMQtdBVJhPk0crHmOA4ymQx2ux1JSUkx63WRqQCRMq7Ccv59+/Zh37596OjoQFlZGSZNmoSHH344JB7JqVOnsHnzZjQ0NEChUGDWrFmoq6tDVpbvKdgcx+EPf/gD3nnnHbS1tSEvLw//8R//gWXLlsVcqDfMDJs3Sw3YMGLjxo349NNP8fHHHwf0/GBO4uHCAw88gDlz5mDx4sVu89NIybxn6DGSZfOkSMNut0OlUsHpdIY8nzZU7HY72trakJiYiMzMzIh6PcRwdnR0ICsrC2q1Gk1NTWhqasL8+fOHrA3Y1NSEJUuWoKKiAtXV1TAYDHjhhReQkZGBAwcO+LzB2bJlC7Zv344VK1Zg6tSpOHLkCN566y2sWrUKv/rVr4a0pmEGNWAxwDX1xrZt24bNmzejpKQkIAMW7Ek83BEOBCWhR+FAUGGRSKiNh1D/UaxIgxQ+kHJ+YY4o2MKVYNbY0dEBs9mM3NxcXvMzUjgcDn4qQUlJSVi8voceeghNTU04dOgQ33B95swZLF68GGvXrhWdrK7T6fDjH/8Y9913H5544gl++7p167Bv3z4cPXp02M8WGwTDxoDRKsQY5/z589iwYQOOHTs2qMT6iy++iJSUFOzYsYM/iceNG4fFixdj3759oifxtcBAA0FNJhO6urrgdDp9DgQNBmEeyZf+o5iOoTCfRvrTiGRXqPvTiAyUWq0OyayzweDpdeXl5YXF63M4HDh27BgWLVrkphZSWVmJ4uJi1NfXi/72jx8/DqfTiZ/+9Kdu2++8807s3r0bR48e9XqMEn2oAYtx1qxZA7lcjt27d2PTpk1ob28fcJ9gT+JrFWEpP1ERERsIynGclyr/QKHHoRZpyOVyn/1pRIeStBgIR6gM5uIvlIGKRt+Z3W6HVqsFx3EoKysLa66ttbUVdrtddLxJSUkJzp07J7rfhQsXAMBrPyLAe/78+RCvlBIKqAGLcTZs2IAxY8YMap9gT+LrCc+BoADccmmdnZ2w2Wx+B4IKG6ZDpaThqz/Nbrfz6hg2m80rz+fLeyQjY9LS0iIuA0VksgwGQ1i9LiFELUOsDF+lUomqaQCA0WjkFVyEkNfxtR8lulADFgUCFRAFMGjjBQR/El/viKmICAeC6nQ62O12dHV1Yfv27SgsLERdXR2SkpLCahiExoogzKd1dHTAbre79VwplUp0dnaCYZiojIwhRSJA3+99sCNXgoVl+yZE+/o+fBlQX1qHZFuslvZf71ADFgUCFRANlmBPYkI4Rqc/++yzbqPThwNiA0E//PBDPP300/j5z3+On/70p9DpdLh69WrIB4IOhL98Wk9PD8xmM6RSKeLi4tDT0xMxvUeh15WdnY28vLyIen3EaxX7DZrNZp95ZLVazX9+QmNLXifcAzMpwUENWBQIVEA0WII9iYE+gdnq6mrY7XbU1dXxo9OXLVs24Oj0S5cuobe31+fo9GuBsWPHYv/+/SgsLOS3eQ4EbWtrc5NViqTx6O7uhkwmQ2lpKaRSKT8UNFT5NH9Ey+sSQrxNX7qFRDHDE/K7bmlpwdixY932AeBzP0p0oQbsGiTYkxigo9MHQsyA+xoIKiwQsdlsXrO3QlXKTwxXV1cXsrOz3ULHZG3CESrB5tP8HZ94XTk5OcjNzY1af5tSqcT06dNRX1+P1atX82HXM2fOoKWlBdXV1aL7zZw5EzKZDB9++KGbAfvggw8QHx+PadOmRWT9lMFBDdg1SLAnMUBHp4cC4Ywy0jTOsizMZjP/R0r5xUKPg7n4k76q+Ph4FBcXD+hNBZNP86dhSLwuiUQSNa/Lk5qaGixZsgT3338/li9fjp6eHmzevBmlpaVYtGgRgD5Pq6OjA5WVlVAqlcjKysLSpUuxc+dOMAyDqqoqHDlyBLt378ajjz5KVeNjFGrArgF6e3uh0WiQn5/Pa6sFchKLQUenhwepVOpWLg/0qeeT0GNvby90Oh0AuBkOXyoiwkGYubm5QzIcvvJpxKh1d3e79addvnwZiYmJSElJ4WWoQul1BaMg09DQwGsPCl/n1KlTSElJwZw5c1BbW8u3lbz++us4cOAA6uvr+XDwE088gZSUFOzbtw9vv/028vPz8dRTT/m94aNEF2rArgEaGxtRXV2NlStXoqamBgBQUVGBnTt3YsuWLaitreVnOHV1dYkWY5DKR6PRKJojC6ScuKmpCSaTCQsXLsR9993Hj05funRprI5OjyoKhQKpqalITU0F8EN4jxg1g8EAq9XKq4gQo3bixAkwDIMJEya4zTsLJXK5nJ/ATdZG8mmfffYZDh48CKPRiAkTJmDy5Mn45S9/GRIF+aamJixfvhwVFRXYsGEDryDT2NjoV0GmsbERQJ9ijec6Kioq3PohAeD555/H888/77ZNJpPhkUcewSOPPDLk90GJDNSADSN27dolun3atGnQaDSi29955x0AwM6dO/2+Nh2dHn2E4T2xgaBXrlzB1q1b0dTUhLq6OrhcLhiNxiGriAS6NoVCAaPRiPnz52PFihVQKpU4e/Yszp07B5fLFZLjBKsgc/bsWWRlZWHOnDkhWQdleEAN2HVCLI5Op4rhAyNUEdm6dStGjRqFTZs2geM4tyIRlmW9Qo+hLOW32Wx8deWYMWP4HNqsWbMwa9askBxjKAoyjY2NGD9+fEjWQRk+UANGcSNSo9ODDRW98MILXorh69evh8ViueYVw9euXev2/0IVEYfD4ab1OJiBoP5gWRYGgwFdXV3Izc1FTk5O2G4UglWQcblc0Gg0mDhxIu69916cPXsWCoUCs2fPRl1dHS8fRrn2oAaM4kakRqcHEyrS6XTYuXMn7r//fqxZswYAMGfOHLAsi9dffx1Lly69nhTD3VAqlUhPT+dvFIiKCMmnkfEuwsGbpA/Ml0EiXpdMJnPzusJFsAoyFy5cgN1ux/fff4/HH38cjz32GBobG/Hqq6/i1KlT2L9/P59npFxbUANGceOee+7B22+/jeXLl7uNTrdYLHj00Uf553mOTs/KysJ9992HN998E8nJyW6j05OTk/niEoAqhkcCoYoICckKB4KazWYYDAYwDCM6O414XXl5eRHTUAxWQaawsBA7duzAqFGjUFBQAACYOnUqysvLUV1djbfeegsrV64Mz6IpUYUaMIobSUlJ2LVrFzZu3Ij169fzo9P/9Kc/uTVAf/75516j05988kkUFRXhL3/5C9577z230enCKbtUMTw6yGQy0VJ+Enrs6emBVqvl82mR8LqEBKsgk5SUhJkzZ3ptnzZtGpKTk9HU1BTahVJiBmrAKF4UFhbipZde8vuchQsXevXdyGQyLF26FEuXLvW7L1UMjx0UCgXS0tK8VERCKTEVKMEqyDQ2NuLrr7/GggUL3H5TLMvC4XDQJuRrGCqxTIk40VYMP3XqFO677z5MmTIF06ZNQ21t7YBz1hoaGlBeXi76d/HixYCOOxwgKiLRUF8XKsjYbDZ+O1GQmT17tuh+LS0tePbZZ/HRRx+5bf/oo49gt9vxox/9KKzrpkQP6oFRIk40FcPD0Sibm5s74HEpgRGMDNRtt92GyspKrF+/Ht3d3Rg7dixOnz6NN954A9OnT6d50WsYasAoESeaiuG0UTa28VSQUalUmDVrll8ZKKVSiR07dmDr1q3Ys2cPtFotsrOzsWzZMjz88MNRfkeUsMJx3LX6R4lhfvGLX3C33HILZ7Va+W2nT5/mysrKuLfeekt0H71ez40dO5bbuHGj2/a1a9dylZWVnMFg8HtMu93OVVRUcOvWrfN67Pbbb+dWrFjhc99FixZxDz74oN/Xp1CuEaJ97Q74j+bAKFGhpqYGer0e999/Pw4ePIg9e/bgwQcf9AoVnThxAg6HAwDcFMOff/55HD58GM888wx2796NBx98cMBk/UDVj6TK0RPSKGuxWHDvvfdi4sSJmDp1KlavXs0L8FJ+wOVy4Z577sFvf/vbgJ7/3nvv4c4770RlZSXmzJmDF154gf/OKRR/UANGiQokVAQAtbW12LJlC2bNmoU//vGPbqGie++9F3q9nt/viSeeQE1NDQ4dOoSamhocPXoUTz31VEACrKFolF24cCF27tyJRx99FEePHsWSJUvQ3d096Pd/rWKxWLBq1SqcOnUqoOfv2bMHTzzxBCZNmoSXXnoJCxYswPbt27Fu3bowr5RyTRBtFzCMfxSKG19//TVXVlbGvf/++16PPf7449zUqVNF9+vt7eX+8Y9/cJcvX3bb/uWXX3JlZWXcyy+/HJb1DjcOHz7MzZ07l7v55pu5srIy7je/+Y3f59tsNm7atGlcTU2N2/Y33niDKy8v5y5cuBDO5VJ8E+1rNw0hUiieDLVRlqg8EIbSKHuthdmMRiN++ctfory8HH/9618D2ufMmTPo6uoSVVbhOA719fXhWCrlGoIaMMp1w1AaZXft2sUr8hOCbZS9FsNs8fHx+Nvf/oYXX3wxYPFcX8oqOTk5SExM9JmTpFAI1IBRrhtioVH2888/x8KFC0XHy4hht9uxefNmzJ07F8888wzmzJmDVatW4fHHH8e+ffvw3XffBXzscKJUKkWLY/zhr38vKSmJKqtQBoQaMMp1RTDVj8JG2e3bt+PIkSN45ZVX8NRTTw2qUZaG2dwJVpGFQiHQRmbKdUU0G2VJmG0wnsq1HGYjo296e3u9wo4mkykgZRXK9Y2E47hor4FCuS4pLy/nAGzTaDQP+XnOkwDWAxih0Wguezx2BcAJjUZzd3hXOngCfG9zAHwGYIFGo3lPsD0fwBUAdRqN5vfhXitl+EJ9dAoltiHnqK87TTZSCwkDxwB0AfDU77oXfe/37xFfEWVYQUOIFEps09X/bwr6vBIhagA9kV1O8JSXl48EMBLANxqNpkej0TjKy8vXAXihvLzcCuBdADcDeArAHzQazdkoLpcyDKAeGIUS25AmszLhxv4wWxKAhoivKHgeAHAEwGSyQaPRvAjgVwCqAOwHsAzAcwB+GY0FUoYX1AOjUGIbYZjtPcH2mA6zaTQar9JCjUazFsBake2vAXgt/KuiXGtQA0ahxBA0zEahBA4NIVIosQUNs1EoAULL6CkUCoUyLKEeGIVCoVCGJdSAUSgUCmVYQg0YhUKhUIYl1IBRKBQKZVhCDRiFQqFQhiXUgFEoFAplWEINGIVCoVCGJdSAUSgUCmVYQg0YhUKhUIYl1IBRKBQKZVhCDRiFQqFQhiXUgFEoFAplWEINGIVCoVCGJdSAUSgUCmVYQg0YhUKhUIYl1IBRKBQKZVhCDRiFQqFQhiXUgFEoFAplWEINGIVCoVCGJdSAUSgUCmVYQg0YhUKhUIYl1IBRKBQKZVhCDRiFQqFQhiXUgFEoFAplWEINGIVCoVCGJdSAUSgUCmVYQg0YhUKhUIYl1IBRKBQKZXtTrSgAAAAISURBVFjy/wHd8rphBC/NfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot(projection='3d')\n",
    "ax.view_init(elev=30, azim=30)\n",
    "ax.scatter3D(X[:, 0], X[:, 1], r,  s=50, cmap='autumn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "def plot_3D(elev=30, azim=30, X=X, y=y,r=r):\n",
    "    \n",
    "    ax.view_init(elev=elev, azim=azim)\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "    ax.set_zlabel('r')\n",
    "plot_3D(X=X,y=y,r=r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1,4,2,3,8])\n",
    "x = x[:,np.newaxis]\n",
    "y = np.array([4,7,6,3,8])\n",
    "y = y[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.linalg.inv(np.matmul(x.T,x))*np.matmul(x.T,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.24468085]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.382114204883213"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.mean(np.square(np.matmul(x,w) - y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting mpl_toolkits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  ERROR: Could not find a version that satisfies the requirement mpl_toolkits (from versions: none)\n",
      "ERROR: No matching distribution found for mpl_toolkits\n"
     ]
    }
   ],
   "source": [
    "!pip install mpl_toolkits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}