{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Load the pickle data object for sep=5 and do a scatter plot (code in the NA-2 writeup)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Ring Data - sep = 5')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd \n", "import matplotlib.pyplot as plt\n", "\n", "filename = \"data/ring_data_5.pkl\"\n", "#filename = \"data/ring_data_-5.pkl\"\n", "df = pd.read_pickle(filename)\n", "data = df.to_numpy()\n", "ndat,n1 = np.shape(data)\n", "ndim = n1-1\n", "\n", "X = np.transpose(data[:,0:ndim])\n", "Y = np.reshape(data[:,ndim],(ndat,1))\n", "\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "plt.legend(('class +1','class -1'))\n", "plt.title('Ring Data - sep = 5')\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Fixed Increment Perceptron Learning Algorithm (PLA) using sep=5 dataset" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "normal termination: iter = 26\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'perceptron error = 0.0, MSE = 0.0')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#perceptron learning algorithm\n", "def perceptron(X,Y,eta,w0,maxiter):\n", " Jup = 1\n", " iter = 0\n", " w = np.reshape(w0,(1,len(w0)))\n", " errors = []\n", " while Jup!=0:\n", " Jup = 0\n", " for k in range(len(Y)):\n", " x = np.array(X[:,k])\n", " y = Y[k]\n", " z = y*x\n", " u = np.sum(z*w)\n", " error = np.sign(u)\n", " errors.append(error)\n", " if u<0:\n", " w += eta*z\n", " iter += 1\n", " Jup=1\n", " if iter > maxiter:\n", " Jup = 0\n", " if (iter>maxiter):\n", " print(\"terminate on maxiter\", maxiter)\n", " else:\n", " print(\"normal termination: iter = \",iter)\n", " \n", " _,ndim = np.shape(w)\n", " w = np.reshape(w,(ndim,1))\n", " #print(w)\n", " return w\n", "\n", "eta = 1\n", "maxiter = 1000\n", "w0 = np.random.rand(ndim,1) #random initial weight\n", "w = perceptron(X,Y,eta,w0,maxiter)\n", "#print(w) #perceptron weights\n", "\n", "x0 = np.arange(-20,30,.5) #points for hyperplane\n", "x1 = -w[0]/w[2]-x0*w[1]/w[2]\n", "\n", "Yhat = np.sign((X.T)@w) #prediction\n", "diff = (Yhat!=Y)\n", "accuracy = np.sum(diff.astype('int'))/len(diff) #accuracy\n", "MSE = (1/ndat)*np.sum((Yhat-Y)**2) #MSE\n", "\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "plt.plot(x0,x1,'b-')\n", "plt.legend(('data +1','data -1','hyperplane'))\n", "tstring = \"perceptron error = {}, MSE = {}\".format(accuracy,MSE)\n", "plt.title(tstring)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We now do this using the pseudo inverse. That optimal weight vector is $w = {\\rm inv}(XX^T)XY$ where $X$ is the input data matrix and $Y$ is the target data matrix. The predicted output on the dataset is then given as $\\hat{y} = {\\rm sign}(X^T w)$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy = 0.0, MSE = 0.0\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'pseudoinverse error = 0.0, MSE = 0.0')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Xdag = np.linalg.inv(X@X.T)@X\n", "w = Xdag@Y\n", "\n", "x0 = np.arange(-20,30,.5) #points for hyperplane\n", "x1 = -w[0]/w[2]-x0*w[1]/w[2]\n", "\n", "Yhat = np.sign((X.T)@w) #prediction\n", "diff = (Yhat!=Y)\n", "accuracy = np.sum(diff.astype('int'))/len(diff) #accuracy\n", "MSE = (1/ndat)*np.sum((Yhat-Y)**2) #MSE\n", "print(\"accuracy = {}, MSE = {}\".format(accuracy,MSE))\n", "\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "plt.plot(x0,x1,'b-')\n", "plt.legend(('data +1','data -1','hyperplane'))\n", "tstring = \"pseudoinverse error = {}, MSE = {}\".format(accuracy,MSE)\n", "plt.title(tstring)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "For the linearly separable dataset, we see the PLA and pseudoinverse classifiers achieve the same error rate of 0. \n", "\n", "We now redo this example for the nonseparable dataset where sep = -5. Let us first try the PLA. Note that the PLA does not converge and terminates on the maxiter=1000 condition. The accuracy at the end is 0.09 (classfication error) and a MSE of 0.386. Note that these numbers will change depending on how we initialize the weights. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "terminate on maxiter 1000\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'perceptron error = 0.121, MSE = 0.484')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#filename = \"data/ring_data_5.pkl\"\n", "filename = \"data/ring_data_-5.pkl\"\n", "df = pd.read_pickle(filename)\n", "data = df.to_numpy()\n", "ndat,n1 = np.shape(data)\n", "ndim = n1-1\n", "\n", "X = np.transpose(data[:,0:ndim])\n", "Y = np.reshape(data[:,ndim],(ndat,1))\n", "\n", "eta = 1\n", "maxiter = 1000\n", "w0 = np.random.rand(ndim,1) #random initial weight\n", "w = perceptron(X,Y,eta,w0,maxiter)\n", "#print(w) #perceptron weights\n", "\n", "x0 = np.arange(-20,30,.5) #points for hyperplane\n", "x1 = -w[0]/w[2]-x0*w[1]/w[2]\n", "\n", "Yhat = np.sign((X.T)@w) #prediction\n", "diff = (Yhat!=Y)\n", "accuracy = np.sum(diff.astype('int'))/len(diff) #accuracy\n", "MSE = (1/ndat)*np.sum((Yhat-Y)**2) #MSE\n", "\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "plt.plot(x0,x1,'b-')\n", "plt.legend(('data +1','data -1','hyperplane'))\n", "tstring = \"perceptron error = {}, MSE = {}\".format(accuracy,MSE)\n", "plt.title(tstring)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Now let us repeat this for the pseudoinverse method on the nonseparable dataset. We get an answer that is very similar to what was obtained using the PLA. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy = 0.0995, MSE = 0.398\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'pseudoinverse error = 0.0995, MSE = 0.398')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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RoFWrVggKCsKxY8cA8GGPf//733juuecwceJEJCcnIy0tDQMGDDAYLYcOHcIff/wBjUZjdR/nzp1zqk2lpaWorKys0zYAaNu2rZmhcvz4cQQFBdW5iRMTE9GoUSMcP37c4f5MjSHA+KC7dOmSYV56ejrmzZuHL774AoMHD0ZFRQU2bNiAf/zjH4YxZWG8WTDQLDGNZwCAevXqQavVms1r0aIFxowZg/feew/Lly9H165d0bdvXwwZMsRgxBw6dAiMMavHB+Cub1uUlpbi8uXLWLhwodVMEqDu+bKWoWGr/cePH0fjxo3ruM1vueUWw/ditm2Ndu3aiTZq7CEYXZYxTAAMQwv2YgIcrW+67gsvvICTJ09i9uzZWLp0KQDgnnvuwYQJEzB9+nSD0dugQQOsX78egwYNQv/+/QHwjnTWrFlmy9midevWSE1NRWFhIfR6vaiO3xb169fHwIEDsWLFCtx33304efIkBg8ebHP5kJAQTJo0CZMmTcLp06fx7bffYv78+cjLy0P9+vXrpDvfd999Lg1RKeX8CwQHB6Nnz54AgN69eyM5ORkPPPAA4uPj0bt3bwDAI488ggULFmDixIm46667APBzNX36dEyYMMHsvA4cOBD16tXDl19+aZiXmpqKNm3aYNKkSTbjlIi6kKHi51iKqYWGhmLbtm0oKirC+vXr8fXXX2PlypV46KGHsGnTJqjVatTW1qJDhw547733rG5Tp9NZ3baAaSCqVO12BlsPdWYS/NmxY0c0b94ceXl5GDx4ML788ktUVlYiPT3dsExtbS0AHqeSmJhYZ3uW4/chISFWPVTvvvsuhg0bhrVr12LTpk145ZVXDDFEWq0WtbW1UKlU+Oqrr6y23V6nJrRxyJAhGDp0qNVlbrvtNrPPth7attrvDM4ECZaVlYl60w0ODkZMTIzN72NiYhASEmLwapgizGvcuLHN9ZOSksyWtVzfct3p06dj3Lhx2LdvH6KiotChQweDx8vUs9C+fXv8/vvv2L9/Py5duoR27dohNDQUo0ePRrdu3ez8Yo5Op0N1dTWuXr1axyh2lsGDB+Pjjz/G1KlTcfvtt4s2EJKSkpCRkYH+/fujffv2yMvLw5IlS0TFrjhCKeffFp07d0ZSUhKWL19uMFQAHoz/9NNP49dffzXEMX366acAjOf/r7/+wtdff13n5SEmJgZdunQxiwkkHEOGip9x6NAhs7faw4cPo7a21iyoMSgoCMnJyUhOTsZ7772Ht99+G5MmTUJRURF69uyJVq1aYe/evUhOTrZrMAieCtOoeKDuW7ZGo0FoaKhZRLzAwYMHzT43a9YMtbW1OHTokOGtHeABo5cvXzYE+0nBoEGDMH/+fJSXl2PlypVo3rw5OnbsaPi+VatWAID4+HjDm5ardOjQAR06dMDkyZOxY8cOPPDAA/j4448xbdo0tGrVCowxtGjRoo4L3REajQYRERHQ6/Vut9EazZo1w5YtW+oEIwrCX+6cj1GjRhm8Evbo1q0biouLbX4fFBSEDh06GNzvpuzatQstW7a0G0h56623ol69evjpp58waNAgw/zq6mrs2bPHbJ5AdHS0YYgQALZs2QKtVltHY0SlUqF9+/aGzxs2bEBtba2oc/XXX3+hQYMGDr0vYujSpQuaNm2K4uJivPPOO06vX79+fdx22204dOgQzp8/b9VwdxalnH97XL9+vU52HgA0bNgQnTp1MnzesmULQkNDDUOsZ8+eBWD9pe3GjRuSZnYFApSe7Gd88MEHZp8XLFgAgLssAeDixYt11rnjjjsAGF2ngwYNQklJCRYtWlRn2crKSly9ehUAH/qIi4vDtm3bzJb58MMPzT6r1WqkpKRgzZo1OHHihGH+H3/8gY0bN5ot++ijjwIA5s2bZzZf8O489thjddrkKunp6aiqqsLSpUvx9ddf1+mQUlJSEBkZibfffhs3btyos7411UpLysvL6zyUOnTogKCgIMPxTktLg1qtRnZ2dp2UX/a/TARbqNVq9O/fHwUFBfj9999daqM9Hn30Uej1evzrX/8ymz937lyoVCrDdeUKEyZMwObNmx1O7777rsNtDRgwAD/++KNZZ3Xw4EF88803ZpldADeyTK/DqKgo9OzZE8uWLcOVK1cM8z///HNUVFTUWd+SlStX4scff0RWVpZdj1RlZSVef/11JCUlITMz0zDf2jnau3cvvvjiC/Tq1cttLxfADab3338fU6ZMwZNPPmlzuUOHDpkdG4HLly9j586diI6Otjkk7CxKOf9Xr161KlVQUFCAS5cuORzW2rFjBwoLC/Hss88ahnNbt26NoKAgrFy50uyePnXqlCHFmRAPeVT8jKNHj6Jv3754+OGHsXPnTixbtgyDBw/G7bffDoCrSG7btg2PPfYYmjVrhnPnzuHDDz+EVqs1vCE++eSTyMvLwwsvvICioiI88MAD0Ov1OHDgAPLy8rBx40bDzfvcc89h5syZeO6553DPPfdg27Zt+PPPP+u0Kzs7G19//TW6du2Kl156CTU1NViwYAHat29vliJ5++23Y+jQoVi4cCEuX75sUPxcunQp+vXr5zCQ1hnuuusutG7dGpMmTUJVVZXZsA/ADbGPPvoITz75JO666y5kZGRAo9HgxIkTWL9+PR544IE6Hbgl33zzDUaOHImBAwfipptuQk1NDT7//HODgQFwz820adPw6quv4tixY+jXrx8iIiJw9OhRrF69GsOHD8e4ceNs7mPmzJkoKirC/fffj+effx7t2rXDxYsX8fPPP2PLli1WjVOx9OnTBz169MCkSZNw7Ngx3H777di0aRPWrl2LrKwsg9fJFaSKUQB4kOuiRYvw2GOPYdy4cahfvz7ee+89JCQkYOzYsWbL3nLLLXXe0qdPn47OnTujW7duGD58OE6dOoV3330XvXr1wsMPP2xYbtu2bXjzzTfRq1cvxMbG4vvvv8fixYvx8MMP10k5HTRoEBo3box27dqhvLwcn332Gf766y+sX7/e7A0/PT0doaGh6Ny5M+Lj47F//34sXLgQYWFhmDlzptk2p06diuzsbBQVFTld5yo1NRWpqal2l9m7dy8GDx6MRx55BF27dkVMTAxKSkqwdOlS/P3335g3b16d4cmvvvrKTFpfoHPnzmjZsqXNfSnl/B86dAg9e/ZEeno6br75ZgQFBeGnn37CsmXL0Lx5c7Pzevz4cQwaNAh9+/ZFYmIi9u3bh48//hi33XYb3n77bcNyGo0GzzzzDP79738b4gCvXLmCDz/8EJWVlXj11Vcl+d0Bg3wJR4SUCOnJ+/fvZwMGDGAREREsOjqajRw50kwddOvWrSw1NZU1btyYBQcHs8aNG7PMzEz2559/mm2vurqavfPOO6x9+/YsJCSERUdHs7vvvptlZ2ebqXdeu3aNPfvssywqKopFRESwQYMGsXPnztVJT2aMsW+//ZbdfffdLDg4mLVs2ZJ9/PHHVpVpb9y4wbKzs1mLFi1Y/fr1mU6nY6+++iq7fv262XK20pMtU4HtpVFPmjSJAWCtW7e2eWyLiopYSkoKi4qKYg0aNGCtWrViw4YNYz/99JNhmaFDh7KGDRvWWfevv/5izzzzDGvVqhVr0KABi4mJYT169GBbtmyps2xBQQHr0qULa9iwIWvYsCG7+eab2YgRI9jBgwdttk3g7NmzbMSIEUyn07H69euzxMRElpyczBYuXOjw+NhrP2M8TXv06NGscePGrH79+qxNmzZs9uzZZoqbjPH05BEjRjhsq6c4efIkGzBgAIuMjGTh4eGsd+/e7NChQ3WWg42U1+3bt7POnTuzBg0aMI1Gw0aMGFEnDfXw4cOsV69eLC4ujoWEhLCbb76ZzZgxwywdXuCdd95hN998M2vQoAGLjo5mffv2Zb/88kud5ebPn8/uu+8+FhMTw+rVq8eSkpLYkCFDrLZdULb9448/7B4LsWq3lunJZ8+eZTNnzmTdunVjSUlJrF69eiw6Opo99NBDhtRrAXvpybbuN0/i6vkvLS1lw4cPZzfffDNr2LAhCw4OZm3atGFZWVl1ZBwuXrzIUlNTWWJiIgsODmYtWrRg//znP+tcJ4zx59iCBQvYHXfcwcLDw1l4eDjr0aOHmcQCIQ4VYxa+ZsInEd60SktLERcXJ3dzCILwAPfddx+aNWtWR2mWIPwZGvohCILwAcrLy7F3715RAagE4U+QoUIQBOEDREZGWtUKIQh/h7J+CIIgCIJQLBSjQhAEQRCEYiGPCkEQBEEQioUMFYIgCIIgFIvPB9PW1tbi77//RkREhFv1YQiCIAiC8B6MMVy5cgWNGze2q8Ds84bK33//bSiSRxAEQRCEb3Hy5Mk6ldtN8XlDRZCiPnnypNsVRgmCIAiC8A7l5eXQ6XQOi0b6vKEiDPdERkaSoUIQBEEQPoajsA0KpiUIgiAIQrGQoUIQBEEQhGIhQ4UgCIIgCMXi8zEqBEEQhLJhjKGmpgZ6vV7uphBeRK1Wo169em5Lh5ChQhAEQXiM6upqnD59GteuXZO7KYQMhIWFISkpCcHBwS5vgwwVgiAIwiPU1tbi6NGjUKvVaNy4MYKDg0mYM0BgjKG6uhqlpaU4evQo2rRpY1fUzR5kqBAEQRAeobq6GrW1tdDpdAgLC5O7OYSXCQ0NRf369XH8+HFUV1ejQYMGLm2HgmkJgiAIj+LqmzTh+0hx7smjQhD+gF4PbN8OnD4NJCUBXbsCarXcrSIIgnAbj5q527ZtQ58+fdC4cWOoVCqsWbPG7Pthw4ZBpVKZTQ8//LAnm0QQ/kd+PpCYCPToAQwezP/GxwNvvskNGGvo9UBxMZCTw/9WV/O/y5cD8+bxv8XFttcnCILwEh71qFy9ehW33347nnnmGaSlpVld5uGHH8bixYsNn0NCQjzZJILwLyZMAGbPrjv/4kVgyhTg3XeBZ54BUlONXpbCQmDUKODUKePyarV1o0SrBebPB2zcvwQRSHTv3h133HEH5s2bJ3dTAgqPelQeeeQRTJs2DY8//rjNZUJCQpCYmGiYoqOjPdkkgvAfVq2ybqSYUl7OPSQ9egDNmwPjxgH9+5sbKYBtz8mpU8CAAdy4IQjCKYqLi6FSqXD58mWv73v69Ono3LkzwsLC0KhRI6/vX0pkj3AqLi5GfHw82rZtixdffBEXLlywu3xVVRXKy8vNJoLwe6wN1bz0knPbOHWKe1ichTHghRf4PsW2k4aQCKmxvAcC/Jrq3r07lixZYvP76upqDBw4EC+++KL3GuUhZDVUHn74YfznP//B1q1b8c477+Dbb7/FI488Yle9cMaMGYiKijJMOp3Oiy0mCBkoLOTeENMYFK0WKC31XhtKS4EmTex7VkzbOWQIMHo0/yt4c8grQ7iKtXvAw9fU1atX8dRTTyE8PBxJSUl414qR//nnn+Oee+5BREQEEhMTMXjwYJw7dw4AcOzYMfTo0QMAEB0dDZVKhWHDhgEAvv76a3Tp0gWNGjVCbGwsevfujSNHjkja/uzsbIwePRodOnSQdLtyIKuhkpGRgb59+6JDhw7o168f1q1bhx9//BHFxcU213n11VdRVlZmmE6ePOm9BhOEtyks5EMvlkM13jRSBM6f58NG+fl1v7PVTgEaQiJcxda1VVLi0Wtq/Pjx+Pbbb7F27Vps2rQJxcXF+Pnnn82WuXHjBt566y3s3bsXa9aswbFjxwzGiE6nQ0FBAQDg4MGDOH36NObPnw+AG0FjxozBTz/9hK1btyIoKAiPP/44amtrPfJbfB1FpSe3bNkScXFxOHz4MJKTk60uExISQgG3RGCg1/OgV8bkbok5mZmASsU7CUB8OxkDsrJ4YC+lThNisHdtMcavQw9cUxUVFfj000+xbNkyQ1+0dOlSaLVas+WeeeYZw/8tW7bE+++/j3vvvRcVFRUIDw9HTEwMACA+Pt4sTqR///5m2/nss8+g0Wiwf/9+3HrrrZL9Dn9B9hgVU06dOoULFy4gKSlJ7qYQhPxs327bQyEnej0wcKDxTdaZdp48yZcnCDE4urYY88g1deTIEVRXV+P+++83zIuJiUHbtm3Nltu9ezf69OmDpk2bIiIiAt26dQMAnDhxwu72Dx06hMzMTLRs2RKRkZFo3ry5w/XefvtthIeHG6bt27fjhRdeMJvnaL++ikc9KhUVFTh8+LDh89GjR7Fnzx7ExMQgJiYG2dnZ6N+/PxITE3HkyBFMmDABrVu3RkpKiiebRRC+wenTcrfAPsKbrLPtXLsW6N7dEy0i/A2x15YM98rVq1eRkpKClJQULF++HBqNBidOnEBKSgqqHQSe9+nTB82aNcOiRYvQuHFj1NbW4tZbb7W73gsvvIBBgwYZPj/xxBPo37+/mfRH48aN3f9hCsSjhspPP/1kCCYCgDFjxgAAhg4dio8++gi//vorli5disuXL6Nx48bo1asX3nrrLRraIQiAK8wqGeFN9tAh59ZbvhyYM4eGfwjHiL0HJL5XWrVqhfr162PXrl1o2rQpAODSpUv4888/DV6TAwcO4MKFC5g5c6YhqeOnn34y245QMdg0QeTChQs4ePAgFi1ahK5duwIA/vvf/zpsk/CCLxAaGor4+Hi0bt3ajV/qG3jUUOnevTuYnXHrjRs3enL3BOHbdO3Ks3tKSpQXpyLwwQdcz8UZSkt5emn37iT7T9jH0T2gUvHv/9fhS0V4eDieffZZjB8/HrGxsYiPj8ekSZPM6tY0bdoUwcHBWLBgAV544QX8/vvveOutt8y206xZM6hUKqxbtw6PPvooQkNDER0djdjYWCxcuBBJSUk4ceIEJk6cKGn7AT6MdPHiRZw4cQJ6vR579uwBALRu3Rrh4eGS78+jMB+nrKyMAWBlZWVyN4UgzKmpYayoiLEVK/jfmhrn18nPZ0yl4hN/VPvHFB7OWGys+TytlrGCAs+eE8KrVFZWsv3797PKykrXN1JQYP0eEOZ56Jq5cuUKGzJkCAsLC2MJCQls1qxZrFu3bmzUqFGGZVasWMGaN2/OQkJCWKdOndgXX3zBALBffvnFsMybb77JEhMTmUqlYkOHDmWMMbZ582Z2yy23sJCQEHbbbbex4uJiBoCtXr1adPu6devGFi9ebPP7oUOHMgB1pqKiIqeOg7vYuwbE9t8qxpT6qiaO8vJyREVFoaysDJGRkXI3hyA41mTqHcnR21onM5OLXJnOj40FLlzgb5S+fQsbUan435UrAY2GPC1+wPXr13H06FG0aNECDRo0cH1D1u4NnY6LClJ5B0Vj7xoQ23+ToUIQ7mCtavHatTx11/LWEjriVavqPlwFrQhr6zDG6/YI49zdu/Np7dq6D+8mTXhbfFmPwbLuENUb8lkkM1QAqhDuo5ChAjJUCBmx9pYXF8cNC1ulIIQx9aNHjQ9ZvZ6rbIpN8dVogA8/5IZNdTX//8gRoFUroF07wN+y5uwZeISikdRQIXwSKQwVRQm+EYTPYMsDcv68/fUE3YennwaGDjUGlDqjl1JaynVMUlOB3bvN1zXJCvAbPCjsRRCE8lGU4BtB+ARSKMZ+/jnQsyeQkMCHcFxh7dq6Bs7Fi663Scl4SNiLIAjlQ4YKQTiLlIqxFy7wgEAlIQy1KBGli+ARBCE5NPRDELYQysoLRTKF4L01a2RslBcICjIPZlUSShfBIwhCcshQIQhrFBYCw4fbDor1Z5RopHhI2IsgCOVDhgpBWFJYCFhUN/V7VCple1IYAzIy+P/FxZSiShABBBkqBGGKXg+88orcrfA+jCnXSBGYPRv47DNzLxdprBCE30PBtERgIsSf5OTwv0InPX06rysSSKhUwOOPy90KcVgOxZWU8DTxwkJ52kMEFN27d0dWVpbczQg4yFAhAo/CQi6w1qMHMHgw/9u8OTBhAleA9QV0OmD8eGl0UxgDVq92fztyIKSIv/ACr8psanQSfoWtdwslU1xcDJVKhcuXL3tk+4WFhejVqxdiY2OhUqkMhQf9DTJUiMBCEGqzTC8+dYoPLXibiAjnlh85Eigq4sq2s2YBeXmeaZcvwRgXwRsyxGh0kofFr7D1bhHop/nq1avo0qUL3nnnHbmb4lHIUCECBymE2pzFkWz4p58CBQVcel8M/ftzNVshgLRrV4BKR5hDw0F+ha13C0+f5qtXr+Kpp55CeHg4kpKS8O6779ZZ5vPPP8c999yDiIgIJCYmYvDgwTh37hwA4NixY+jRowcAIDo6GiqVCsOGDQMAfP311+jSpQsaNWqE2NhY9O7dG0eOHHG6jU8++STeeOMN9OzZ0/Uf6gOQoUIEDlIKtYnl+nXb36lUwNixXBb+X//iWTf2ltXpzNNzCwt5fZ/ycuna6w8IhmhWlm+MDxA2sfdu4enTPH78eHz77bdYu3YtNm3ahOLiYvz8889my9y4cQNvvfUW9u7dizVr1uDYsWMGY0Sn06GgoAAAcPDgQZw+fRrz588HwI2gMWPG4KeffsLWrVsRFBSExx9/HLW+XEzUg1DWDxE4KE3VVJCFnz5dXGzMvHlGT4qtWkNKJS6OV3S+dMk7bTaV3O/e3fw7qsLrMzh6t7B3mt2hoqICn376KZYtW4bk5GQAwNKlS6HVas2We+aZZwz/t2zZEu+//z7uvfdeVFRUIDw8HDH/iyGLj49Ho0aNDMv2t5A/+Oyzz6DRaLB//37ceuut0v0QP4E8KkTgoFRVU0exMWo1j0VJS+Od7NatwPPP+46RAvBsnYsXvd9mS+OUgh18CrHvFlK/gxw5cgTV1dW4//77DfNiYmLQtm1bs+V2796NPn36oGnTpoiIiEC3bt0AACdOnLC7/UOHDiEzMxMtW7ZEZGQkmjdvbne95cuXIzw83DBtD7CaV+RRIQKHrl2BJk2Ul35cUWH/e72eeyQKC7kf3NvDV1LgroGiUvEMpwYNnDt/psbpqlW86rQlQrDDqlWkx6IwxL5byPEOcvXqVaSkpCAlJQXLly+HRqPBiRMnkJKSgurqarvr9unTB82aNcOiRYvQuHFj1NbW4tZbb7W5Xt++fc2MpiZNmkj6W5QOeVSIwEGt5rL4SkJsAcDVq61HFAYCKhU3dJ58Eli6FNiyBVi2zH4AsmVMT34+kJ5ufVmKaVEsXbtyTT9bt4m10C0paNWqFerXr49du3YZ5l26dAl//vmn4fOBAwdw4cIFzJw5E127dsXNN99sCKQVCA4OBgDoTa6rCxcu4ODBg5g8eTKSk5Nxyy234NKlS3bbExERgdatWxum0NBQKX6mz0CGChFYtGkjdws4wpNXrKfhX//yraEeKRGCjOfNA3r25FL6wcHAJ5/w42jZiwmfharUb74JDBrEY2RsYRrsQCgGtZoLDwP2T7PUIUbh4eF49tlnMX78eHzzzTf4/fffMWzYMASZBLw3bdoUwcHBWLBgAf766y988cUXeOutt8y206xZM6hUKqxbtw6lpaWoqKhAdHQ0YmNjsXDhQhw+fBjffPMNxowZ41I7L168iD179mD//v0AeNDunj17cObMGdd/vAIhQ4UILJQSp6LV8jd4sciRDSDW2+NpLL0c589zw+P77/lwjaUbXKvl8wGgWTPnRPyUFnBNIC3N/mn21Gjd7Nmz0bVrV/Tp0wc9e/ZEly5dcPfddxu+12g0WLJkCfLz89GuXTvMnDkTc+bMMdtGkyZNkJ2djYkTJyIhIQEjR45EUFAQcnNzsXv3btx6660YPXo0Zruo4fTFF1/gzjvvxGOPPQYAyMjIwJ133omPP/7Y9R+uQFSM+fZrWnl5OaKiolBWVoZI0pMgHKHX8+BJuYZQJk8GkpO5r3r7dh7MqVSmTgUuXwY+/9x+FWmVivcir7wCZGcDV696q4V8SOfxx7lUaXExn9e9Ow/cTU933gtVVGQ8N5QV5DbXr1/H0aNH0aJFCzRwpCnkAErW8k3sXQNi+28KpiUCC8GXLFdqb7t2xjxKYQC+pMQ7bYmMFKe5EhvL/06dapwXEQFcuVJ3WSF+pLKSlyDwNi+9xPc/ZozR+Jw2jZ9nZ49pbCxXuLU0ZKnwoSJQq6VNQSZ8Bxr6IQIPwZdsoYngFUyHnuwNwEuNRgOcOWM0QmwRGcm9J5YeFMFIsVxfqDVkz+NiC5WKnwN3SheUlvJhIEsPmStBsT17ci+MtyVQCYKwCxkqhP8hVC9bvpxH2lkrVpeWBhw5Il663hYqFTcC/vMf57JQTNuxapU0xQXt8fHHwK5djg0KRx4XxnjWzYoV/K8jd76t7wXDbP78usEHctCwIfDf/8ojgUoQhF3IUCH8C1NBryFDgNGjbRer27GDB2a6y8cf89RZW1koAO/snnvO+vqpqY47fHfIyuIGkRSBohcv8sDe+HieKuxI0+T6de6lsPRemUZCKiHAuWtX+79FyApasICMFYLwMmSoEP6DreplAqdOmbvw3e24NRouwBYTwzsvW+kJAlOmWFdB3b7dsyJ0qan8r1QGQWoqHyb5/HNxy2/ezL1XRUXcEyNUfxZiPhyJZXgDsfEso0eTki1BeBkyVAjfQRjSycmpO5TjTGVkwYXvSsc9bBjfj0bD4yPmzTP31qSlAXPn2q5obC3ewZMpsbGx3BDQ6/kkxRBTZaVzy1+8yL1X3bsDmZnm1Z8B78bq2GLjRvHLUswKQXgVMlQI38BRjRaxlZFNhb3OnhW/f50OKCgA+vQB3n+fGymmCJ3XhAk8uNNWrIe1eAdPDn3cuMG9PM2bcy/IxYvWl/O0gWBqjFkzOL0VqyMFFLNCEF6F0pMJ5WOrUrBpjZaqKue2uWYNV3t1xKhRQL9+xiDY5s3tB1y+955jr45lyVdh6MMT2i7l5VzJ1RHR0cDLL/MYDFvGjDvEx/O/1uoVCem/gGvZQ3JgGrOSkEDCHgThQcijQigbe0M6jPEpK8vYEYpl/nxxb8P9+hmHKsR4bZx5w968mS+vVvMhETkQJMEvXuRibdeueWY/27fbjiE6dQro3x94+mnP7NuTjB5NVZgJwsOQoUIom+Jix8bByZP8rxhdFJXKubde0yELqWNJ3n6bv41PmABYSG97DUtp/uvXPbOfBQu4cq09b5MYMTolQ7ErfkX37t2R5UyZC4Xh6+03hQwVQrkUFnKPhhjWreNeEkexFow55/UwjR/xRCzJhQtc8My3K1k45uJFz2Y2KQGKXSEIj0CGCqFMCgv5cEBFhbjlP/sMiIoCVq607VnR6ZwrBGgp0KaENFpC2VAVZsKD6PV61MpRoFRmyFAhlIcQl+IM5eU8q2XMGJ4eXFQELFvG/1+2zKjdIWiKiMGyfryYmvMEAVAVZjswxutWyjE567isra3FhAkTEBMTg8TEREz9X/2rZ555Br179zZb9saNG4iPj8enn34KgA+9jBw5EiNHjkRUVBTi4uLw+uuvw7QOcFVVFcaNG4cmTZqgYcOGuP/++1EsFNcEsGTJEjRq1AhffPEF2rVrh5CQEJw4cQLDhg1Dv379kJ2dDY1Gg8jISLzwwguorq62+Vs+//xz3HPPPYiIiEBiYiIGDx6Mc+fOGb4vLi6GSqXC1q1bcc899yAsLAydO3fGwYMHzbazdu1a3HXXXWjQoAFatmyJ7Oxs1NTUOHdgnYX5OGVlZQwAKysrk7sphFQUFQlhss5PKhWfCgoYq6nh21qxgv+tqWFs5Upx28nNtd2+/HzGNBrz5XU6Pl+rdb3t/jxptYw1aSJ/O7w1FRV5515ROJWVlWz//v2ssrLSMK+iQr7TUlEhvu3dunVjkZGRbOrUqezPP/9kS5cuZSqVim3atIl99913TK1Ws7///tuwfGFhIWvYsCG7cuWKYf3w8HA2atQoduDAAbZs2TIWFhbGFi5caFjnueeeY507d2bbtm1jhw8fZrNnz2YhISHszz//ZIwxtnjxYla/fn3WuXNn9t1337EDBw6wq1evsqFDh7Lw8HCWnp7Ofv/9d7Zu3Tqm0WjYa6+9Ztb+UaNGGT5/+umnbMOGDezIkSNs586drFOnTuyRRx4xfF9UVMQAsPvvv58VFxezffv2sa5du7LOnTsbltm2bRuLjIxkS5YsYUeOHGGbNm1izZs3Z1OnTnXqGhAQ23/D7rc+ABkqfsiKFe49jVQqxiIjGYuJMZ/fpAmf705HU1BQ1xiJjDQaNgUFfP9yd5RKm7KzGRs/Xv52eGPS6bhRTPi8odKlSxezeffeey/75z//yRhjrF27duydd94xfNenTx82bNgws/VvueUWVltba5j3z3/+k91yyy2MMcaOHz/O1Go1KykpMdtHcnIye/XVVxlj3FABwPbs2WO2zNChQ1lMTAy7evWqYd5HH33EwsPDmV6vN+zf1FCx5Mcff2QADIaVYKhs2bLFsMz69esZAMP5S05OZm+//bbZdj7//HOWlJRkcz9SGCqko0IoD3eDVhmznkHiTDCnNde9EDdjiaBVsns3MGsW13UZPtx3NEG8waVLxmEzqdBqeVq3kDHFmLTbdxXLIUPCjLAw8aFnnti3M9x2221mn5OSkgzDJc899xwWLlyICRMm4OzZs/jqq6/wzTffmC3fsWNHqEyGhTt16oR3330Xer0ev/32G/R6PW666SazdaqqqhBrUqU8ODi4TjsA4Pbbb0eYyQ/q1KkTKioqcPLkSTRr1qzO8rt378bUqVOxd+9eXLp0yRDrcuLECbRr187qb07637P43LlzaNq0Kfbu3YvvvvsO06dPNyyj1+tx/fp1XLt2zaw9UkKGCqE8unbl0u9ydvSHDpl/1uu58WGP2bN5Fd7Ll8lIsWTxYmkNiQcf5Do0wcFAx451ReTcRSgu6WzgYnY2j4MqLubGLgnB1UGl4reJL1C/fn2zzyqVytDBP/XUU5g4cSJ27tyJHTt2oEWLFuhqWR3dDhUVFVCr1di9ezfUFtdHeHi44f/Q0FAzY8cVrl69ipSUFKSkpGD58uXQaDQ4ceIEUlJS6sS1mP5mYb/Cb66oqEB2djbShDpdJjTwYGFVMlQIwhqLFgGTJhk7mOnTxRkf/wu280n69eOKvZ6grEza7W3bBrRqxb00aWlG42DQIGmUdceN439nzxa/jlYLtGvHhd9MjabwcGDgQF5lOzjY/bYRiiA2Nhb9+vXD4sWLsXPnTjxtRbBw165dZp+///57tGnTBmq1GnfeeSf0ej3OnTvnlIEjsHfvXlRWViI0NNSw7fDwcOh0ujrLHjhwABcuXMDMmTMN3//0009O7/Ouu+7CwYMH0bp1a6fXdQfK+iGUx/bt8nskTp0yppjq9dIPWyiRbt3kboFzmAqsqdV8kkr+PzcXmDEDGD9evDfk7ru5oWTp2amo4B6l0FAu7kf4Dc899xyWLl2KP/74A0OHDq3z/YkTJzBmzBgcPHgQOTk5WLBgAUb9L6PxpptuwhNPPIGnnnoKhYWFOHr0KH744QfMmDED69evd7jv6upqPPvss9i/fz82bNiAKVOmYOTIkQgKqtutN23aFMHBwViwYAH++usvfPHFF3jrrbec/r1vvPEG/vOf/yA7Oxv79u3DH3/8gdzcXEyePNnpbTkDGSqE8lBKaufWrbxw3rx5nql/40ksi/vZcx2rVFwz5qWXfEsnRhhKEgTWpLxuBC2UWbOAK1e4Ro8j1q2zP7xVW8s9NGSs+A09e/ZEUlISUlJS0Lhx4zrfP/XUU6isrMR9992HESNGYNSoURhuMoS8ePFiPPXUUxg7dizatm2Lfv364ccff0TTpk0d7js5ORlt2rTBgw8+iPT0dPTt29eQPm2JRqPBkiVLkJ+fj3bt2mHmzJmY44IadkpKCtatW4dNmzbh3nvvRceOHTF37lyrMTGSYjfU1gegrB8/xJ305ECbLDOMdDrz1OysrLqp1Na2UVDAj72QteRrmUtFRdJfNytWeOZ6VKsZq6qS5dbyNvYyPvyBK1eusMjISFYg3D8mOMq6cYehQ4ey1NRUj2xbaqTI+iGPCqE8SAFWPOHhPIBzxQqjqF1amnEYZP58oLTU/jbGjePrAPxvXh4QF2e+jFbLA5yVek5OnzZeN1IhZJ+tXSvdNgHu/fnwQ2m3SXiV2tpanDt3Dm+99RYaNWqEvn37yt0kv4YMFUKZPP88f/8k7FNRwQN4Q0KMVZ4B+1WnTVGpeDyGUJumsJBXBDY1buLigPfeAxYuNK6jNJKSjMrBUrRPo+GGT2EhH/qTmiNHpN8m4TVOnDiBhIQErFixAp999hnq1aO8FE+iYsy3e4Py8nJERUWhrKwMkZGRcjeHcJfCQulTTQMBjYYfMyGrpLgY6NFD/PpFRdwDM2BAXeNG6PhXrgT++IMbA0qJ2VGpuBfl6FGjkVZY6L6OTVYW12exzOCRijlzgLFjpd+uwrh+/TqOHj2KFi1aeDR9lVAu9q4Bsf03eVQI5VBYyDtKMlKcp7SUd9iFhfyzs4GlJSW2PTBCdEVmJjBlirKMFKCuwFpaGnD2LB8SswwqFktqKk9J99S1+N57xnNFEIRdyFAhlIHYoQpHxMW53jn5OqWlxnRdZ9V9t2xx3CkLw0NKoUkTrgJsRXwKajXwxhvAuXPGApViPa46HXD+PDfKPMXp08ZzFQD4uOOecAMpzj0ZKoQy2L5dmrfXIUOcr7zsb2RlAZ07OxdYumSJp1ojD3o9H/7Ky+Of4+Otl1WwxuzZwIsveqxpAIwGuZBa7acIKqfXrl2TuSWEXAjn3lLl1xkoRoVQBjk5wODB7m9nyxYeVJqQIL9onJTExPB6OWJvVyHmxFptIn9BGPqx9KpYi3OKiOB6KI7o2BE4fJh7VLxFURG/Zv2U06dP4/Lly4iPj0dYWJjbcvCEb8AYw7Vr13Du3Dk0atTIUDfIFLH9N4UqE95Dr+eeE2s1UNwtRChw4wbf5sKF/tVJjxrlnDz/6dM8E8ifYYwbK1lZPKZErTbGOVkadGKMFAD4/nvJm+mQrVv9uh5QYmIiABiK+RGBRaNGjQzXgKuQR4XwDtbecrVaY60WvZ5nWJSUuBenEhHBhzHS0vg+n3uOeyJ8FdOslrVrgX/8Q9zb/uDBwJdfiu+gfZ0tW/hfqWr9eJuYGH5/mNaX8jP0ej1u3LghdzMIL1K/fv06BRdNEdt/k6FCeB5bb7mWrntbyzmLSmXc5tatQM+e7m1PbgoKjEMblZXc+yR1kT9fJzratw1SgdhY7g20FiBMEH4GpScTysBeNo9lQGFaGjcwNBr39ytss3t3adVK5aSwELjpJjJSrOEPRgrA46r69w+YbCCCEAMZKoRncZTNw5ixABzAjZUFC9zbp+k2pVQrlQOVCnjhBW549e/vXxoz/fsDkyfzNGBLYzI2FggLk6ddSsDPs4EIwhk8aqhs27YNffr0QePGjaFSqbBmzRqz7xljeOONN5CUlITQ0FD07NkThw4d8mSTCG8jVnjs9Gn+YN66lceVSLlvwVPji54Vxrg+yvz5crdEegoKgGnTuDAbY+Y1i86eBYYNk7uFziOVQWxqvBNEgONRQ+Xq1au4/fbb8cEHH1j9ftasWXj//ffx8ccfY9euXWjYsCFSUlJw/fp1TzaL8CZiC7odOsSDaXv25PVrpMA0kygtDTh2DJg7V5ptE9JSUlK3ZlGbNnK3SjwqFTB+PNC4sXTbdFZdmCD8FSnLOdsDAFu9erXhc21tLUtMTGSzZ882zLt8+TILCQlhOTk5orcrtkw0IQP5+eLK3sfGMqZSiVtW7NSkCWM1NXXbtGKFNNvPzmYsL4+3Xcp2B/qk0/HzVlPD2IYN0l8Xnpi0WsYKCvj1tWWLdNstKvLq7UoQ3kZs/y1bjMrRo0dx5swZ9DTJyIiKisL999+PnTt32lyvqqoK5eXlZhOhQPR64KWXxC174wZ/NEvJlStGb46gUrp8OfDdd+5tNyoKeOUV4MEHuXYHFVqTlpMneY2dhATg0Uelvy6kJjube+qELB2ptEJiY7m2CkEQ8gm+nTlzBgCQkJBgNj8hIcHwnTVmzJiB7Oxsj7aNkIDt23lshRg8YWyWl/NgzYEDgZ07pQtCLSsD3n+fTxqN+N9IiMeTNXakQqcD3n2XXwN5eUYBQymFC/V6v9VUIQhn8Lmsn1dffRVlZWWG6eTJk3I3ibCGUsbX8/M9lykTCEaKSmU/QLRhQ++1RSloNLwe0JgxQI8eXFyvRw8eYyVUsXY3qLa8nBddpDRlgpDPUBEkdc+ePWs2/+zZs3bldkNCQhAZGWk2EQpEqjdLwjnCw80/u9thjhtnfTuCATNhgnvb90VKS4GMjLoGcEkJkJ4OZGbyz+4e+/PnuVcwP9+97RCEjyObodKiRQskJiZi69athnnl5eXYtWsXOnXqJFezCKno2hWIi5O7FYGDSsWHIy5c4Om9QppvXp51r4gwb/x4Hg9hSWwsTx+eNYundjdpYv69VsvnT5qk/LTv11/3zhCKEE+Tm8uPu+Uxc5XMTH6sCSJA8WiMSkVFBQ4fPmz4fPToUezZswcxMTFo2rQpsrKyMG3aNLRp0wYtWrTA66+/jsaNG6Nfv36ebBbhaYTig/fcA3z9tdyt8X8EI2TePCA4uG4l3lWrrNdZmjePB4HOmMGDjYuL+XfduxtThAG+TGqq7YKS8+crvwCkt8TTGOMBwXFxPMi2uNj9+kN6PY+1Mi2lQBCBhCdTj4qKihiAOtPQoUMZYzxF+fXXX2cJCQksJCSEJScns4MHDzq1D0pPVhgFBTxdU+6UUV+Y1Gpp0m91OmN6rC1qani664oV/K+11G13yM4W19apU/nvdvc3x8Qwlp4ublk5UpxXrDC/J1Qq99shpG4ThJ8gtv+mooSEdEhVVNDfETwg48YBc+bw/505Zlot8PzzXBDN0rshF0L1a1uBy6ZVoAsLuZfBXVQqvp2VK93fltQUFZl7tqxVD5diuwThw4jtv2VLTyb8DHvFB11FpXK8vfHjgXvv5cGNtbXS7duTmA67dOxYtwPT6YD33uPDB6dPA/HxfP65c8oxTCwRaioNGMA/m54306EptZoPY2Rnu5+GzBiwfr172/AEWq1RA0UYBq2qApYsMX7+4w9gwwZeDdsZlJJNRxBehAwVQhocFR90BaFDB+p25g0bAv/+NzdQAN4ZDhwo7f6lRKPh8v1NmpgbGo7iP3wJoaaSvXgYgVtukWafUpVbkJLKSqPYoOWxUKvdi5ehbDoiAKGhH0Iali8HhgyRbnvZ2TyjROiwx43jHb2p10St5loWs2bxh39CAs96sUVMDPDaa0BiIq8t5E3hwEAKhBS8BrYML0fDRL6OGE+gK8TEcK+aLxqxBGEFGvohvEdhIS9LLxUqFfeWTJrEP0+YwFVALdHrufAWwOXW7RkpAM+8uOMOIDmZf752zbi+pwgK4umqgWKkALwjtRdH4Qnvm5Lw1LvfxYvA6tXG4TWCCBB8TpmWUBhCAO3589JtkzFjmfvqah6vYY85c7jHQgyDBhnVPmfN4noXntR7yclR9pCUHIiNs5g40b1aSkF++HjLyCABOCLg8MM7mfAangigNeX0aeDDDx2P6TMG/Otf4rZ58SI3rPLzga1bgV9/BZ57DvDEsOH48dJkt/gbYuMsPv0UuH7dtX1ERooviulL6PXmxjZBBAAUo0K4TnExr3HiKYqKuKdErBHiDEFBnssSCgvjGR7kSbGOEKNSUkKp7K6i0/FUb4pXIXwYsf03eVQI1/FkqqRGw4MwW7XyzPY9mcocHR1YMSnOIqQyA+7XwwlUhKFRgggAyFAhnEev596U/fs9t48HH+R/Gzf23D48RUkJdSKOEFKZLevhaDSe22dUFPDyy/x/fzCQSFOFCBAo64dwDqkUNh1RUMCHB5wVxFIK1Ik4xpqGTEmJtGnuppSV8Qys8eN5kLPpNSwUZnSUOSaGhg25IeRpjRfSVCECBDJUCPF4WyLfl1NYqRMRh2Uqs1AY0VOUlvIssZUruffGVOsFABYsAEaPdn37nTsDO3d6/h6JjOSeTb2e4lQIv4eGfghxeDrDx5/Q6YwdH+EcXbtyJVtPD82MHcv3lZlpNJS2b+eeFVfTmrOygBMnvHOPlJcDPXtyryNlABF+DhkqhDjEinRNngxs2cIVYAMVoaYN4TzeCLQ11ekBeEffvDnPYHvqKdcDrZs1874XsKSEeznJWCH8GDJUCHEItUsc0a4dV379v//zbHuUSGRkYEnlewp7gbbh4dLt5/Rp43CmFAbGkSPub8NZBO9NVpZ7NYQIQsGQoUI4Rq/ntXzEIMRmeMuFrxQiI3n8Axkp0pCWBhw7xrV0Vqzgf0+fBpYu5deUFNdVfLy0w5meSqV3hKWHiCD8DDJUCMds3847YUcI2idA4GllLF4MBAfL3Qr/Qgi0FeJI1Grb3hZXti1lzSGNhse3OOPxkbp0A2WaEX4KGSqEY8Q+AJ94wjw2IzUVmDqVC6D5OioV74gsO0idjoZ7vI3gbZk71/Vt6PXSVs8uLeXxLWJTknU68V7KESPELUeZZoSfQoYK4RixD8DUVOP/QoDilCm8vg4gbXyBt2EMWLgQOH7cfDji6FEyUuRArebibVqt3C1xjXnzgK++Erdsp072h1FVKso0I/waMlQIxziKN7F8UNoKUPS0AJYnCQ/nhpi14QhCHtRq4Pnn5dl3aqrrKrpZWXx9sR6VJk1sD6MKnynTjPBjyFAhHGMv3sTyQemveisVFRSsqETatJFnvw8+KC5uyxqCGq+Y9YOCuIicrdgcrZbPJ68e4ceQoUKIQ+yDUsoARaVBwYrKQ664jBMnXFtP8DyKvZZqa4EdO/j/1jKhaOiRCABIQp8Qj7XaLF27mruc/bkzp2BF5SEMS5aUeNeLt3ixa+sJnkdnriXTe8qy5ABBBABkqBDO4ehB6Y+duUrFO0MKVlQewrDkgAH8PHnLWCkvd36dmBj+V6jRExEBXLnieD1/vKcIn+LMGV58PDRUnv3T0A9hnepq/vb38sv8b3W1uPU6d/avoD4KVlQ+UmmreJqLF4H+/YGEBF6nR4yRQtk8hExcvAj8+99caLxJE+DLL+VrCxkqRF0mTADCwngV2X/9i/8NC+PzHbFjh29LeVtmclCwom9gGr8xebLcrbHPhQvillOpyEAmvEpFBQ9/6tMHSEzkSXXffMNDpXbvlq9dNPRDmDNhAjB7dt35ej2fzxgwcyZQXMwngA8FCam6vhqjIgzvHD7MjS1bMTiEchGGJX31GjRFp+NGSmoqv88sr0e93n6sGEGI5Pp1LumTm8u9JpWVxu9uu40rMaSnAy1ayNdGFWO+nUdaXl6OqKgolJWVITIyUu7m+DbV1dxz4sgj0rAhcPWq+bzYWC6IFhPDq9D6GioVeU78heJi37wGAe4NSk7mhsfatTzV3zSLTqvlPUdOTt358+fT9UuI4sYN7inJyQFWrzYPuWrdml9iGRm8xqwnEdt/k0eFMPLhh+KGbSyNFIC7s/v3B/LzuTiar4m7TZ1KD3l/QcgE8sU0+Ztv5l6hVauAgQPrfn/qlHWPZ0kJDygmY5uwQW0t8N//cs9Jfj5w/rzxO62We00yM4G77lJeeTYyVAgjUpSpf/pp3zNSAPmEwwjpMc0E8jWHcWkp70UyM51bjzHeuwiqtzQMRIBfFrt3c+Nk5Upz2z0ujtvCmZnAAw9wbUGlQoYKYUSKMvW+aKQAlALqbwiZQE8/7VoqsVz89RcPXncFxoCTJ3nsCmmtBDT79nHjJDeXh90JREUBjz/OjZOHHgLq+YgFQDEqhBGxMSr+hBBEe/QovYX6I9XVvHr3tWtyt0QcQUHcR+8OK1Y475EhfJ6//jIaJ7/9ZpwfGgr07csviYcfBkJC5GujJWL7bwU7ewivExwMjBkjdyu8B2mk+D/BwcDw4d7bn04HjB/Pry1XBvrdNVIA8g4GEH//zR9f99/PHeKTJnEjpX59nmK8YgVw7hw3XlJTlWWkOIOPOH4IrzFrFnchz5kjd0ukY+5c4PhxYNmyuhFk8+ZR8KG/k5rKz7OnmDyZp0eYpgl37Fg3Yyc2lgede1JBlwTi/J4LF/ioZm4u8O23xkspKIgP52Rk8EdadLS87ZQSMlSIunTqJHcLpEOtBl56ib9Zz5lD2hOBiJgsoMhI12NZ6tevO9Riqy7W2rXACy+4XnnZEe+9R9e0H1Jezi+dnBxg82agpsb43QMPcONk4EAueuyPUIwKYY5eDzRv7pupnbYoKqLgwkCnsJBnAQHOeTPExowUFIj3zC1fDgwZIr4NzkDXut9QWQmsX889J+vXc2E2gTvv5MZJejrQrJl8bXQX0lEhXGP7dv8yUgD/UCol3EPIArIcjnGEGCPF2bRgT9YkWruWDBUf5sYN7jHJyQHWrDFPomzb1ijE1ratbE2UBQqmJczxx06dggsJwLwe0LJldes6uYppWrAYhKEoe8G2lgaP2LYuXx5YWXt+gF7PxZT/8Q9eX+exx/jlWVHBvSX//Cfwyy/AH38AU6YEnpECkEeFsMTVTt2TAYKuIqQeU3AhISDUAyoulj5OxNTIt1eLx1SQzvK+EYyX3FyuyCWs37kz0Lix44KGpaXAggW86jnFqigWxoAffuCnOS+PZ+8IxMcDgwZx70mnTspTiZUDMlQIc4S3vZIS5wwPYdnwcB7VtXixZ9onFko9JuzhCc+hYOQXFlqv0WNai8fWUJStTLTCQqCqSlw7Ro8G3n2Xav8oDMaA33/nwzq5uVy6SaBRI16BJDMT6NbNd4TYvAUF0xJ1cTXwUECl4sUJxZaz9wRC9Vl6UBPWkLpwoUbDjZ+1a61L9wuGs2UtHjFVkIX70Zl70db+CK9z+DA3THJygP37jfMbNuRhTRkZQEoKT0wMNMT232SoENax9lboDIJmhLfp3RsYO5ZSjwn7CNltznoObZGVxdPf7WXMuaKC7G4WnkbDdYSaNKF7woucPMmHdHJzgZ9+Ms4PDgYefZR7Th57jBsrgQwZKoT7CG97W7cC06Y5v/6wYcCSJVK3yj46HcnhE+Jw13NoSlER/yvGS+NMCrGUnh/L4SdCUoR6krm55nHVajWQnMyNk8cf5/V2CA5J6BPiEcLOc3L4XyFrQAg8nDqVP+ScpWdPz6ZiWsOZ7AsisBHiRNy9RjUaHuwqNu7FmfgYKWNpSkq4YVZYKN02A5zLl/m7WEoKH7kbMcL4+OnaFfjwQx4ou3Ejf28jI8U1KGQn0BET+KdW89eB2bOd23ZpKXc7p6fzz95y3vljijXhGSwVZA8dAhYtMr8fwsPtVwUvLeXGTrdu4vbpKLPONG7l7Flx2xQDY85rvhB1uHYN+PJL7jnZsIHXvRS45x4eczJoEHfuEtJAQz+BjK0gPctAPFeC+QS0Wm7k5OR4T0iO1DkJdxA8jMXFXPBt4ULzGlHu4ChmxNqLg1otvTYK3SNOUV3NvSK5uTxe+upV43ft2vFHXHo60KaNfG30RShGhbCPoyA9IfDv8GFeltNVI0MwesaMAZYule6Bb2tfzgYrEoQl7gaSiyUmhu9n0iR+vbrzQuAsK1bUrU9EmGE6Il5QwId5BFq04J6TzEzg1ltJ68RVSEKfsI8jqXxBbfPDD917YAsP3XffdX0bzkC6KYQ7eNNYuHiRS42+/z7w0UfcmHdmvxqN66J1pNZsFcaAnTuNQmymI29JSdxrkpEB3HcfGSfehAyVQEVsHMeRI55th1RoNMDHH1NGA+E6ej33cHjbyXzhAg9qEMvDD/PozX/8A7jpJtdSrD1VvdkHYQzYu5cbJ7m5wPHjxu9iYrjdmplJ2d1yQoZKoCL2jap5c482QzIGDyYjhXAPXynI+fXXfHr3Xd6DzpnjfAmLsWP5/RLAPe+ffxpVYg8cMM4PD+dpxBkZwP/9H1C/vnxtJDhkqAQqYqTydTqgQwfvtstV5s8HHnyQjBXCdXwtW6ykhBsprsR/CWn8ARZQe+IEsHIlN1B++cU4PySEa0VmZnJBttBQ+dpI1IUMlUBFrebZBwMH2l4mIwP46ivvtcldKO2ScAdfi9sQXjDee8/8ZSMiArhyxfH6vmaYucjZs1yILScH2LHDOL9ePaBXL/6YS00FKBdDuZChEqgUFvLiZfaYM4f7QX2FAH1LJCSia1eeNlxSIndLnMPSIyrGSAG4ZoyfcukSsHo1N06++YZnmQN8hOzBB7nnpH9/XqCaUD5kqAQihYX8LnUEY+IfekohQN4SCQ+gVgPDh/NMHDkICjL2qN5g6lSeW+snw6VXrwJffMGNk6+/Bm7cMH53333cOBk40Pti2YT7kKESaOj1/GGsVIYM4QUN5893bX1fc98TykJOxS5vGikCPj5cWlXFjZKcHK4We+2a8bsOHfiwTkYG0LKlfG0k3IcMlUCjuFieqsZiWbaMB/mOH19XzdaeQqcg9ta1q3faSfgnchi6nlCeFYOgleRjw6U1NXw4JyeHD++UlRm/a9WKe04yMoD27eVrIyEtZKgEGsXFcrfAMUI2w8qVXB/l9GkgPp4/ULOz6y4vKC+R2BvhLkI2nCfTlJs04Xmv4eHcWPjgA8/tSww+MFxaWwt89x1PJc7PN5eBadLE6Dm5+24SYvNHyFAhlIdQPG3sWC6Hv3YtLz1qq/PQarmR4idj7aYI9elKSvjDWaOxXSaGkAC1mg87Sq1OGxEBPPssEB3Nix4uWSLdtm0hVrlWocOljAE//8yNk5UrufNHIC6Ox5tkZgIPPMDDe7yJad3IpCTX7kcptiHHtmWBycyUKVMYALOpbdu2otcvKytjAFhZWZkHW+lHbNnCGH8GuDdpNNJsx9GUnc2YSmX/+5oauY+qRygoYEyrtf6ztVr+vTVqahgrKmJsxQr+19HhcXZ5qdZVNAUFjMXGeuca99Rk774xvZAUdtL272fs9dcZa9PGvKmRkYwNHcrY118zVl0tX/us3Zf27keptiH2XpOifd5CbP+tCEOlffv27PTp04aptLRU9PpkqDhJTY37D+DXXmNs2TLvPGxjYnzuQSsFBQXi+pm8vLrriXlICQ+9rCzG4uJce6j50gPRJWpquCHs6Br05Sk2VhEn7K+/GJsxg7HbbjNvXmgoY4MGMVZYyFhlpdyttH1fqlR8EnvfOLsNsfeaFO3zJj5lqNx+++0ur0+Gigvk5bn3cJs7l/dycj9khSk7W+4jKik1NbY9KZaTWs1Yfj5fT+xDqqCAsSZNbG9TzEPN1x6IbmH6KjtnjvzXu5STjCfs778ZmzePsY4dzZtUvz5jvXsztnw5Y+XlXm+WTcTclzqd/femqir7zmiVqu42xN5rjtpnbdty41OGSlhYGEtKSmItWrRggwcPZsePH7e5/PXr11lZWZlhOnnypKgfSvwPe+MJ0dHiHm7LlhnvCjGv/d6Y/KhndMUGzM8X95DKzxe/TVvOKl98IErGihXyX+tST148YefPM7ZwIWM9epg/OoKCGEtOZmzRIsYuXPB4M1xC7H25ZYv1IZqCgrreS1tTURFfx5l7LTvbuW0rAZ8xVDZs2MDy8vLY3r172ddff806derEmjZtysptmNLWYlrIUBGJo/GEoUPFXemCB0Ps+IQ3Jj/qGV3pC8WGDEVGOrddS2dVTQ13qPnaA1Ey5PAkWhuby87mF8rkydLtx0MnrLycsc8/Z+zRRxmrV898l506Mfb++9y7onTEjnZbvu9ptYyNH+/co3LFCr5PsZebWCPFdNtKwGcMFUsuXbrEIiMj2b///W+r35NHxUWcGU8Q8+Bctsz2+H1oqDyBiH7SMyppVA3gXhghnsWZGOqsLLmPpAeoqWEsIsK7J2DZMttRlFJeLBL2YNeu8feYAQMYa9DAfDe3387YzJmMHT0q2e68gtj3OMvJlXc54QVB7EuLM2FUSnpMijVUFJee3KhRI9x00004fPiw1e9DQkIQEhLi5Vb5AVKWsD9/nivI2qKyEmjQALjjDmDPHmn2KQYf0IMQgzekPJwhI8M1PbJ58/hv8bus8eBg7+6vSRPbgmxiqqCLxc005Rs3gC1beDrx6tXm1TduuskoxHbzze41Uw4mTOAFql3BldMiVDcQe0ouXhS3nE7nm5qYXs4+d0xFRQWOHDmCJIXm9vss3u7EL12SxkiJjQVef13csn5yzQhSHs4KV3lKS8Id0dRRo+QRXfUY27d7V9lZozHvWfR6LtqYk2MUb3S13IQpLvZgtbXAt98CL7zAb79HHwX+8x9upOh0XGB6927gwAHe+fqikZKfD8ye7f39ZmUBnTtzO9TWs0ClAmJixG/TZzUxveThscnYsWNZcXExO3r0KPvuu+9Yz549WVxcHDt37pyo9SnrRyRKG08QO0VEMNa4sWPfqh/FqAjYi3v2pUlJrma38XYwrZDSxZj9HFVnIjWtTU4Eo9fWMrZrF2OjR9e9NePjGRsxgrHt2xnT6z1w/L1MTY17h1WKe0cIBbQcQhLmTZkibltKTI70mRiV9PR0lpSUxIKDg1mTJk1Yeno6O3z4sOj1yVARidKydKSa/DIf1oiQGTtqlPyH2tVJScF7buNNg3/sWON+xeSoVlU5Hy0N8EASEUb+r79yCaWWLc1Xj4pi7JlnGNu0ibEbNzx25GVB7ve7yZP5qbFmo+p0PEhXzMuMUuWmfMZQcRcyVJzAlmnuy5NfKYzZp6DAe4LAUk5+5VHxlsFvaqSIzVGtqnI9iN3GfXToEGNvvcVY+/bmi4eFMZaRwdjatYxdv+7F4+9llJCNLpyaqiqecTdyJP+bm+v4MlT6exwZKoR1/GU8QZi2bJH7iHoVdwSBVSp+6r2ZkBUXp8w3ObfwpMEfF8fTS4TeqKpK/Gu92LxxWxfH/3q0U6cYe/ddxu6913yR4GDGUlMZy8lhrKJC1jPgNeT2qAinBqh736rVjtdV+nucz2b9EB4mLQ1ITTVWrDp0CJgyRe5Wuc65c3K3wKs0aeLaekIw3vPPe/d0f/ihjwbv2SMtDVi1ikcKm6ZmRUYC5eWubzc4mKdvmKaXjBsHPPKIuPXdqIxeymKxCgORO7gxtlczMMYvmKAgIDmZZ+w8/jjQqJHLu/BJlJCBxxj/axnDLSZIfckSfv58HRVjwmHwTcrLyxEVFYWysjJERkbK3RzfQ68HEhK8m8kgJUVFtlM3/RC9Hmje3HY2qpAF0KABX0ZAp+MR/1VVwODB3mlrjx7AN994Z1+yIJSoXbsWWLaMp+37EGWIxBr0Qy4ysBn/Bz2M760PPMCNkwED+OMhkCkslL6YtrdYsYKfR6Uitv8mj0qg4+10S6lQqfirji+KAriBkLrcv3/d7wSvycKF5k4z0zLvbrx0GwgK4mmp9lCpgK+/dn9fikat5h6Q+fN9phe7hlCsx2PIQSY24FFUoYHhu7vxEzKQi0Hvd0XTl1NlbKWyEBxozz8vXq/EWdx1xtnCTxQbyFAJeHxVJI0xHxYFcA3hBX77dusPtogI4JlnjLoK1hxNnTsDcXHuvfzX1gLp6cDKlbaXYQxYt84Pxd5M0ev58I/CjZRq1Mcm9EIuMrAWqahAhOG7W7AfmchBOlbiJhziMzv0lqmlyiUtDYiKAnr2lH7bc+cCHTpIu21/e48jQ8XfEXo3y1drAV81ubOz/bwXNKewsG5IhCXl5dx2mzePP6Tmzzc/RIWFwPDh0jjQEhKA8HCgosL69yoVF6xKTfVjW1JKtWeJ0SMI36IbcpCJAvTHJRhVwZrjKDKQiwzk4jb8CjMtMUuBOcLwCD1zxr6RLwy7Mibe86JWAy+9xP9KGQvjd+9xXgnt9SCU9WMHewJRAjU1zhWKUMrkV+Ic9nGl9qNlWmJBgTynya9Sky1xJwXLA1MtwHbifvYK5rFE/G32dSL+ZqMwl+3E/azW3nb8skCT6ziTJKlScX2+Jk1cu0ekvEfDw7nAm9Iz7sT234qT0CckQogAszTRS0r4/MJC/lmt5q/qvoaveoKcxNXRBWH5rCygulq+U+yrI4uiKC2VuwVgAPbiNryKt9ESf6ETvsf7GIUzSEI0LuJ5LMRWPIRT0GIeRqMjdsFuZYbUVC+1XPnYeoTaIiKCD4eaBrGLQbhH0tK4o1gKKip4dl9CgvFR78tQ1o8/IqSG2LrDhAHMo0e5oaLXc5+lJ6K5PIFGw+9uv/Fr2qa4mGfPuMPcucDo0ZI0x2n8Oilr+XL7xTk9yJ9o87/Bmwz8gXaG+Q1RgX5Yg0zk4P+wGcG4IX6jOp3xmRDgOHqESonpPaLXA82aOW/sOKKgQJkj5WL7b/Ko+COOxs4ZA06e5MsB/MH06afO7SMykgcpyMEHHwTMw1QKj8TGje5vwxX8KZjPKq6K2jiDWg307QsAOAkt5mAs7sZPaIs/MQVv4g+0QwiuIw0FyMNAnEM8luFJPIYNzhkpKpWfBTW4hzfCj1QqYy1IodZkXh6PIxO+l4qsLN8uDkrBtP6I2N7NdLkBA3ipU0dlQnv3Bnbtks/tnZ4ODBwoz75lQIoRLrnShJ9/3s/7va5d3U+hcsC5uHbI39oWudiG/8Jo9alRg57YgkzkoB/WIApueEMFkR0lvnLLhKeHLAUjZN48LsNjGSgfG8v/SqUcIbyX+qp3kwwVf0Rs72a53IwZwEcf2U7lAHjOqZwE2Bi6oIxpS+BNLMIInzdp08a7+/M6ajUf+pk3T9LNXkYUVuNx5CATW88moxbc2lOhFg9iGzKQiwFYhTiY9GIREcDYsUCXLlytef9+YNo0xzsbMADIzfVzi9J5PB0Cp9UaLxtrYnIXL7p3v1vDl+PFaOjHHxF6N1u+Q1Ofo4Bez1+B7RkpniDIyUswPt4z7VAogsCbu8jh9g2IeGeJDOerCEMu0pGKNUjAWTyDxdiMXqiFGvfiB7yLMTiBpihGD7yAT8yNFAC4coVHYpaVcSlSsbrpmzbxMQdfHhfwAI4eoe7w+us8FCg11XagvCciR336fvRKDpIHofRkG9gqnGatnGZBgfM5dVJN48c7l3sbYEUIBcaPt12ErEED909Derq0p1Wj4fX0/J6aGpfvnesIZmvRh2VgBQtDhdnX7fEbm4bX2CG0cm67sbH8Hqmq4gUOxa4XF8dYXp7cR1NReDKlv6DAewUPheLaSkxVpurJhHURAJ2urpHi6ZL1th6opiIfYrVcAkg/RcAbp0irld5WVXrlVslwoke7ATXbhJ7saXzKonDJ7OuWOMxewzT2G9pLc/B793Z+vfHj5T6aikJqA16YdDrvyfBYvpcqCbH9N6Un+zNCKLlQ4KV7dz4J49HezMF74gmedxcUZGwHYFTNPX2aj7E7wq/zXc0RTt+gQZ6rMWJKdra0lZUFt/mqVQEQp2lH9rcWKuxAZ+QiA/kYiHMwVvlrjBKkYyUykIt78aN9jRNnUKl4P+UK+fk8cCLAKSy0XlNLKkaM4AmMnsSaQrWSEN1/e8Vs8iDkUbGBGFVab/kegbpDNtbaZ89toGT/pQeQYzQuK4uxUaOkf5sLmNNWU8PYu+8yBq4Suxt3svF4h+lw3OyYxKKUvYAPWTEeZHp42FWmVjvvjtNoAuSE2aamRrwirbunx1Pb9idlWsr68Uds1SUXVGmFV1y5wsBtvapYtlfANJcvALIT3HmTc+dF+rPP+KUhRfCuAGO+nxopGrUaB2pvQg6mIhcZ+BNtDV9FoByPYzUykYNkbEV91HinTUKQrDMXRmlpgJww23irjJOtGGZ37mOle1FcgbJ+/A17muvCPEH9x5th4OfO8b96vVHRSCwxMQEyfuDa4THF1YcbwIWJly1zfX17+HJqpCOOHQPeeQe44w7glvG98Sam4E+0RQNUYiDyUIA0nEM8lmIYHsZG7xkpAllZzovTrV3rkab4Ct6+Xi3fv7RanjUeGur8tpYs8b9HJXlU/A2xqrQLFvCynVKW7LTH77/zgIsbN5xXMZJK9cgHKC6W9+cWFHhmuz6dGmmFM2d4KEdODrBzp3F+vXoMKTUbkIkV6IsvEAEvp/tbIzWVW1ILFgCTJwPXrzteZ948nqPrbz2eSLx9ver1vNRFQgLf9/nzvOxFZaXz2xLeCf0KLw1FeQyKUbFgxQrxg5harfPpwe5OERHOrxNAgQ6TJ3vvVHhrio31j1N34QJjixYxlpzMWFCQ+eXZowdjCxcydn7NdvkPuOXUubPzARcBdM9ZIy/Ps/Ej1iYhodHdLD9fUnCg6smBijOvAiUlwJw5wLhxfHjFG1y54vw6jJnXJiJ8ilde8d3QoooKXnuwTx8gMZFrIm7dCtTWAh07csdDSQnwzTf8u9hrJ+Vucl127HDeaxrA91xhIa/U4W0NvKQk16ulmzJokH9UTDaFDBV/wxlJReFuyM3lPmyl48+BDv/D3+IXY2OBSZPkboVzXL8OrF7NH/jx8Vwlf906Pmp5++280sRff/Ehn1GjLN4N/G2MKwDuOVOkMBRcISaG73vqVPdH4i9e5MH4/mSsUIyKvyForg8YIC50XHhzUqu9F6/iKv7WCVihe3feucsRp6JSGWMupboMFi70DW/KjRvcU5Kby42UcpMaf23acFX69HSgXTsHGxJeFJR8HzlDANxzpngr28eSmhqgZ09ptzlqFA9P8oX7zxHkUfFH0tJ4lowzkf7nzkmblyol1moT+SlqNe/cpcDSqWbPySZ8N38+n9ytcaLT8cBcJcdi1tYC27YBL74ING4MPPIIsHQpN1K0Wj4iuns3cPAgF8NzaKQAxhcFTxSJ8SYBdM+ZIpcDqdyN4te2OHXKf0buyFDxV9LSeN7k3Lnilk9K4uvk5SnTBA8QDRWAn4aCAt5Zukp4eN2wo+ho3uHm5dXdtlYLrFzJ16mq4i5oodS8GLRavu0VK4AtW4DFi/l2lFbvjjHgp5+4CHLTpkC3bsDHH/MsC42GJ8Jt3w4cPw7Mng3cdZcLNofwouDOCZSTANMtMsXfHEh+M3LnpeBej0FZPw6oquJKk85E9+fnez7EXWwlvYgI5Raq8DA1NVxd0p3DnJ5et4ySVstPcVERzzQoKuKfLRNDTDNbrE0aDa9XUlRkvHzECCLLwe+/84yq1q3N2xYVxdjTTzO2cSNjN25ItLOaGn5Qli3jG4+O9m76iLuTZT2wAEJQpJWj/JknpqIiuY+ofagoIWG917CcbFWsErOuO9Prr4tbbuNG7x83hVBTw1N7pT70lgW03UmHNH0Q2tqOtYLd3uDIEcamT2esQwfz9oSGcgNuzRrGrl+XeKeevm88MWm1PKdVsFoDNCVZQK46rVJPTZoo/1SSoRLoiLnb1GquoyK8AVo+qGpqGJs713N3kaP2BQVxj1CA4q43xd4kONKqqtzrVwXtB0e1Ubwly1FSwi/Z++4z33/9+oz17cvbe+WKh3buqz1cgHpP7DF+vPynxd3JtEC9UqHqyYGM2KrIQlaQZZqJabGI6mogLEy+QIMAqpZsil7PU2M9XTV57lyugOkqkycDycm8vWKyFjxxOs+f5zE9ubnAt9/ySxrghbofegjIyOCXcnS0tPs1w5uVyKVk2DCgVy8enNG1a8DFpFjDV0+lJb5QvVxs/03pyf6I2Bw74YlumQtrWrxQSPCXC7+JBnOO7ds9b6QAwMaN7q0/bRqfxOoFSnU6y8uBNWu4cbJ5M0/vFHjgAW6cDBzIJcm9glx5re6yZAmfAP+sZucCvnoqLWGMGytZWb6fpkyGij/ibm9geoXPmCFJk1zG38LwReIt+8xdQ0VArFHlzumsrATWr+fahOvX86wigTvv5FongwYBzZq5vg+X8QeD2rK6eoDiD6dSgDH/qF5Ohoo/Eh/v/jaEK7y01P1tuYJKxd/wAkzHQcBb9pm3Bn5dPZ03bnCPSU4O96BUmNT4a9uWGycZGfx/WfEHg9qfXsHdwB9OpSW+bnyRoeJvFBby4ipSERsLxMXxQABvEcA6DgKCwGlJifeMCU/h7OnU67kQW24uf7k39dY0a8YNk4wMLmevGF21rl35+Jc3xus8ib+8gruIXs/D8sSIevsSvm58keCbP1FYyIs8lJRIt80xY4ChQ6XbnjUslcW02oB3PwsCp4CCOmORWMariDmdjAG7dvGXeZ2OB8EuXMj7/YQE4OWXge++A44eBWbOBO64Q2HHRa3mmuX+gq+/grtAYSEPok1J8S8jxR8Ehinrx1/Q6/kT3RNFYlQq7ls/cED6bQO8J1uyhMv4U/aBGYWFvP/zpeC+LVv46Tt92v7pZAz47TfuOcnN5UaIQKNG3ObOzOTqsfV8wffryXvQ2wRYtl1hIQ/P8e3e0DpKLmVBWT+BRnGx5x6QjAF//umZbQO8F/7tN/7aTAaKGWlpPFxg+3Zg7Vo+fOIp3HV3C3Eo3bvz06jX83bn5ZkbLIcOGY2T/fuN6zdsyH9rRgZ/qw0OdvsneRehUFP//nK3xH3WrQsYQ0WuisneIDtbuUaKU3hB08WjkODb/5g8WX6FIXcnJWitK5yCAsbi4qQ97CoVY+Hh0mwrO5uLuhUUcE0/0+8iIxlr1cp8XnAwY/36MZaby1hFhdxHVyIKCqQ7oHJOeXlyH0mvUFQk/6H2xKTV+o8yLcWo+Au1tXK3wH2E9MjCQrlbolhSU4Hhw6XdJmPm2TTuMGUKH/2wFipVXg4cOcKF2Hr14oULz54FVq8G0tO5R8UvSEvjKUq+zogRyqoo6SGkDOlzhtBQz25//nz/cVCToeIv+FIQgy0Y43+zsgLiAeksQrDf22/L3RL7OBqBjIoCNmzgoqiNGnmjRTJw6ZLv9xKlpXzszs+RS4GBEA8ZKv6AXg98+aXcrZAGxozpkYQBIdjPH+zRS5d4SJXfUljIlef8wdgOgOwfjUae/VZWem7bghyOP1yCABkq/sH27fzp708EwANSLEoJ9ouLk25bfmuoKOVkSYWvC3CIoEkTuVsgPf72vkeGij/gj516ADwgxeJO7ZGICGnaoNEAJ04Ac+bwZJAGDaTZrt/hL4ViAP8Q4BCBIK7oLC+9BDz9NBAeLn2bpMJfugZKT/YHPNWpR0UBZWWe2bY91Gqgc2fv71ehuPqw0emA997joxDuvuA3bw60aMGDX6XAbzNf/aVnUKkCRhlaEFd0Vkdl2TIeIK5k/OV9jzwq/kDXrtK9Ogs8+STwySfSblMsej2wY4c8+1Ygrj5s5s0z1phzdxz+xx+5kRIeDvTuzbN6XFWGjY31Y0PFH3qG2NiAU4ZOS+M/2RnPilxGikrFh2HtVSxXqfzLIUaGij+gVnOpeynR6YBx41xbN0iCy8pf3kwlQHBNizUMIiN5IF1MDLf50tL4aIQUMSYVFVwLrKDAdS/NwoV+/KIu5mQpSvvfhJgYnoo1f77x4gkg0tKAY8e4srKShzYZ49qYH3/MLyXLy8kfS6WRoeIvvP66tIOlsbGuj7WPGOH+/v3hzVQiTOv+2CM8nBsp5eX8IdWjBz+NeXlc5fWTT6w/2LyFWs3b4tcv6mJOllyBtpYvEFotly5dsYL/DQ3lpSyGDOEXT/PmAadppFbzmlLXr8vbhtxcfkpseU2mTOHvpuPG1Q0G9stSaV4SoPMYpExrQl6eNJKGMTGMLVvm+vruSKeqVIzpdMqXVJSB8eMZU6vND1dQEGO9e3NFWHuHtW9fvo2CAsaSkuRTyywqkvUQeo/UVPmlSa1N6emMrVjBT4RwjxUU8PvO2r2oUgWUWnRNDX/8yXmK8vPN22Pr3hZOT34+P52Wp9UXENt/UzCtPyGVIIBKxSVEXeX8edfXZcy/fJYSUVjIM24YM5/PGLB+PbBzp/31v/iCVxzWaMwDYlUqoF07YN8+yZtslYAY0auu5uNjSmTlSh5gJAQJ2UunZswoyJGaGhD35PbtvGK3XAwbBty4wdP3hfiSRYusLyucnjFjeEFPfz49NPTjT4jtBcLDuW/RVgDuxYvctyhFrImzxMZ6f58Kx1Ffwpi4epR79/Lx99pa4L77gLlzudbC77/zmBNXUjSdJSBG9D78UNnxHabS+I7SqRnzL0EOB3jSkI6JsT/sqlbzkbfBg40jb9On0+kByFDxL8T2Ano9MHYscOWK9e+FHlGK+kEhIc4tf/Ei1fuxQEppDrUa+OMPYNcu/qIsjG8LgYSvvSbNfqyh1fpPFoJdDh2SuwX2MZXGF9szB4QrzLOG9EMPGb0g1rC0bUtK+PuiGPz99JCh4k907SoutaOy0nuVuJ5+2rnlBSPJn/Sf3UTKh5Bezy8TUztQr+eu5rw8z8qJV1YCa9d6bvuKwRcKhG7dyk+82J45IFxhnlF6EFi1iv+1dFTbGrKx5kG1hb+fHjJU/Am1mkfsK4m2bZ1fJ1D8mSKR+iF0/jwPUxg9GnjzTaBZM+5qHjyYz/PUiF/AOMt8odLitGl8bKG01H46tb8Jcjhg7Vqgqsqz+xDev7Ky+PCru+9jGo3/nx4yVPyN1FS5W2BEp+M60/aUiezh7/5Mkbgq8e2IefO4a9nSueYph0DAOMvq+UiOQkkJkJ4OZGbyz4EgyGEDvR6YOpUb8NXVnt+fSsXjwqTwYA4e7PenhwwVv8NZdTBP8u67XMBj1CjX1vd3f6ZIDh4EOnaUuxXSEBDOMl+R3RUsx9xcPu4XEIIcdSksBOLjuW6JtxDug9JS97fVvLn721A6PmL6E6IxLVyhUjk30Ck1wuvCpEnA7Nlc1lQMKlUARV5a5+hRnkmakwP8+qvcrZGezZu5wywpiZ9mv3oj7N6dZ6+JScWyhzfuX6HHjIvj0dTFxcbS1t27+47R5QR6PTeUT5/mcc9iA1Y9gUbDH3XuBMt7Mq5MMXhJ18Uu//rXv1izZs1YSEgIu++++9iuXbtEr0uCbzYoKGBMqzVXCIqIcF2FKCXF+XWysnhbamoYi40Vt04AikwJ/P03Y/PmMdaxo/khqV+fi7otW8bY+fPu6ekpcdJq/fB0jx8v/4F1Zlqxwvozw89OjrWfKOdUVMTb5O42fBWx/Te81B6b5ObmsuDgYPbZZ5+xffv2seeff541atSInT17VtT6ZKjYoabGXLLwtddcvxuio11br6CA71vs8jqdXz0YHXH+PGOffMJYjx7m4qBBQYwlJzO2aBFjFy6YryMIiVqKiQrzxo9nrEkT+R/CYie/s01tKb0qecrO9nt1WqWdFo2Gsaoq/piOjHRtG1qtbynRWuIzhsp9993HRowYYfis1+tZ48aN2YwZM0StT4aKE2zZ4v0eSKcTL8c/ebJv33UiKS9n7PPPGXv0Ucbq1TM/BJ06Mfb++4ydPm1/G9beDE1tvJoaxrp3l/9h7Oyl4vOnv6ZGWa/sYqaYGPtt9oOTo9TTotU6Ln9hb8rOlvvIuodPSOhXV1dj9+7dePXVVw3zgoKC0LNnT+y0oQleVVWFKpP8sXK5am37Iq6Onbs63s6YcxFjycl+FqxgpLIS2LCBxy2uW2de9OyOO4CMDJ6AITYwLi2NJ3gJY+2WsR6vvmoMNfAFhEtl+3YfD4uQUp3PW/TtyyVRbeEHJ0epp8UZUTdrtGkjXVuUjKxZP+fPn4der0dCQoLZ/ISEBJw5c8bqOjNmzEBUVJRh0ul03miqf6BWAwsXOreOSgW88op7+xUixgJMq+HGDeCrr4CnngISEnh886pV3Ei56Sb+gPrjD+CXX4B//tP56H21mvcbmZn8r2Ck5Ofz2GVfxOcz0n3tB8TGAj17ilvW136bCZ5uuqvaQ4y5t99ASYz0ufTkV199FWVlZYbp5MmTcjfJt0hL4wn8lqmIsbF16+zodLxnnTTJvZTnJk14JhLg91oNgsrrCy/wh8ijjwKff86rFTRtCkyYAPz8M3DgANdtuPlm6ff/0kvSbtObxMfL3QI3caXnkEtKQKXiLy6WzwJb+HCv6GlF5Jdf5ofTm6dSrZYmvdkn8NJQlFWqqqqYWq1mq1evNpv/1FNPsb5CXXoHUIyKi1gG2tbUWJ8nYCuC05nAA0eBFT5KbS1ju3bxJKfGjc1/Xnw8YyNHMvbf/zKm13u+Lc7ELStxatLExy8HIRhCzH2i0zGWn1/3nhAy5DwZ+WkZ0GSvzT4eo1JVxYPTPXndbtkiT0aRr8c5+1Qw7ciRIw2f9Xo9a9KkCQXTKhFrd6Kth6qtbAF7xpCP8dtvPJGqZUvznx4VxdgzzzC2eTNjN254py3CYR050vvGhdQPXl9/+IpKLzH9kdbuCU/0eunptu87R6lkPnxC5s71/HW7ZQvfl+mp3LKFT506iT89rtwvPmxD+o6hkpuby0JCQtiSJUvY/v372fDhw1mjRo3YmTNnRK1PhoqXEftQ9QNPiTUOHWLsrbcYa9/e/OeGhTGWkcHY2rWMXb/u3TYpTRvC3cnXH76MMfsnRey9IdxrWVl1xXN0Osby8nhPOHkyn7Zs4fMs96vRcM+NK232g/vYG8b7ihXW9+2MnE54uOv791UtFbH9t4oxxuQcegKAf/3rX5g9ezbOnDmDO+64A++//z7uv/9+UeuWl5cjKioKZWVliIyM9HBLCZuYyj36mdzoqVNcYTw3F/jxR+P84GDg4Yd5MGufPkDDht5vW34+MGiQtNscN44r4nqrwLYtiop8NsmEI9wTJSU8mECj4fEgrtwbztxf7tyLfngfv/ceMHasZ/dh7VqtrgbCwrxT12rFCmPJJl9CbP+tCEPFHchQITxBaSmPI87N5c9t4S4JCuJZ1JmZwOOPy1sod9UqntYs9YOwqIg/ZFNSpN2us/jqw5dQDqtWAS++yCuGewq1Grh2jb+4mDJvHq9G7g181agX239TrR+C+B9lZcCaNdw42bzZ3ADo0oXrnAwcyFON5aawkLfFE6xdC/znP57ZtjP4cJIJoQAmTPBOmr7ghFKrzR1RGzd6ft8Ad9T5mbJDHchQIQKaa9eA9ev5UMeGDYCJliDuussoxNa0qXxttESvd70gtRjmzfPctsVANSkJd/G2ltCgQcDFi8bPERHmzxJP8sQTPj865xAyVIiAo7oa2LSJe07WrjUv6nzzzXy4ISODi7IpEaWqbDpDgwZc+M6yQLCfyeoQMiCHlpCpkQJw3SRvkZrqvX3JBRkqRECg1wPffsuNk4IC8wdLs2bcMMnMBG67TT79LbH4sECogTFjgJAQYNEic6NLq+VGSlqabE0jfJzt2z0bk6IUAsnzSIYK4bcwBuzaxYd18vIA06oMiYncXZuRAXTsqHzjxBR/iN14+23+t0kTIDub1yzxkyQTQmb8wZB3RKB5HslQIfwKxoBff+Wek9xc4Ngx43fR0bzeTkYG0K2b797gXbvyN6mSEvNhE1/k7795KYFVq3wza4FQHv5gyDsi0DyPlJ5M+AWHDnHPSW4uL/QnEB7Ox3AzM4H/+7+6KYS+SmEhN7oA68ZKRIR3x8ndQXBhHz3qu8YjoRz0el7gU0wcl07HO/zvv1duIU+djmvBxMX5lbwNAEpPJgKAkyeBlSu5gfLzz8b5ISHAY49xz8ljj3HRJX8jLY17IUaNMn8gCw9evV56IThPwRg/l9u3k1eFcB+1mtdAHTDAtsexd28uAid0+Hp93cBuJTBnDnDHHcC5c/zzoEH+YaA4CxkqhE9x7hxPPczNBf77X+N8tZp7TDIzuQclKkq+NnqLtDT+W60JiRYWurZNsZ6YqCiuOyMlgRBbQHgHwZAfPhy4cMH8u5gY4OmnjUZxYaHyjHqVirdz7lxzhWitlhthgTLkI0CGCqF4Ll8GVq/mnpOtW4HaWj5fpQIefJB7TgYM4K7RQEOtruuFcEdnZcwY4NNPbbvNhWGagwe5toyU2RWBEFtAeBbTCgCHDtVNGwb4vAEDeIB9dDTw/PPeb6cjGKtrYAH8vhwwgBthgWSsUIwKoUiuXgW+/JIbJ19/zbVPBO69lxsngwbxTpMwp7gY6NHDtXVXrOBDZ9biX4RMA+Eh6ShORiwUo0K4i14PTJ/OvQ3WjBNrCEM+SiMujr+M2fsdOp1/3C9i++8gL7aJIOxSVQV88QUfvomP53+/+IIbKe3bA9Om8bekH37gb/5kpFjHnWKCSUlGt3mTJubfabX8LTQmhhuQMTE8Rsjacq+/7lzKd6CkWRLSU1jIy1pMmSLeSAHcN1LCw4HYWPe2YY3z5x3/DiGmK1CgoR9CVmpqeEGt3Fz+wLl82fhdy5ZGIbZbb5WtiT5FYSGQleXaulot0Lkz98hUVQFLlvD5585xA6a0lBdZsxRomzvXmJFw8CDwwQfAW2+J26dGA3z8sX03th8W9CUkQvDqyTEucPUqV7WWK8NO7urm3oQMFcLr1NYCO3fyt/L8fGNEOwA0bsxr62RmAvfc41tCbHLj7kP7gQeAVq3qGiKCOz09ve62S0r4ENyqVcAvvzif4jl4sH0jpbCwbmZToAYUEuYIsVhyBS8I+5VLBqC0VJ79ygHFqBBegTHekQlCbCdPGr+LjeUdbGYmr1JMb8vO44x2hLMIGQjWgvuE76OjnXO7m1JQYN3osGV4WcbKEIGJO7FY/sCyZbwgoS9DOiqEIjhwwCjE9uefxvkREcDjj3PjJDkZqF9fvjb6A54sVGgrA8H0e1eNFICnkKammhuo9t6WGePGSlZW3fWIwCHQ09ktY8P8GTJUCMk5dszoOdm71zi/QQOgTx8ed/LII0BoqGxN9Dt8+aF94QJ/O05ONs5zZHiRSBwRyOnsOl1gFCMUIEOFkIQzZ3hGSE4Ol6MWqFcPSEnhnpO+fbknhZAeX39oWxoqYg0vXzbQCPfwpZpX4eE88NZdAq0YoQAZKoTLXLzI4whycnhHYyrE1r07N07S0jyTwkeYI+ahHRnJH5h//+3dtonh6FEu5nfuHE9NF9tGXzfQCNcQMsEGDOCdttJZupQ/H196yb0g2EArRihAwbSEU1RUcG2TnBxg40bgxg3jdx078mGdgQN59g7hXcQIsGm1QM+extRjqYiMBMrLpd2mI/xF9IpwDmuZYEoVbwN4W/v1496/+HhusGRkOBfXNXky9zj6W2o+BdMSknH9OvDVVzzm5MsvgcpK43e3385vuvR0oEUL+dpI2C5UaEpJifRGCgA884z332wzMvzroU04xlYmmODNbd6cx8gpieXLeTq9QFyc88Hn7doFdiwWeVQIq9y4wV3xubm8zo7p23Lr1nxYJyOD30CEsqiu5p4Tb+osbNnCjVV72UFSExsLnD1Lxkqg4CgFX6XiRoA/6osUFfmnoUIeFcJpamt5ReKcHP5mblpwTqvlhklGBnDXXSTEpmR27PDew1qo0wN410gR9jd9OvDGG97dLyEP06c7zgQrLfVMZW85Uau5YnQgQ7V+AhzGgJ9+AsaO5dVwu3Xjkubnz3N58xdfBLZtA44f56qjd99NRorS8VYmjGkGgqm6sD0aNJC2DfPnKzc2gZCOwkJey0cMw4Z5tCleR6/nLx+BDHlUApR9+4xaJ4cPG+dHRvJYh8xM4KGHeHox4Vt4KxMmLs5Yp6e4WNw6169L24aLF0lLxd8RxP/E0q8fEBzsfDkHJRPoafjUDQUQf/1lNE5++804PzSUa5xkZnLNE6nfegnv4oq+hErlvBbF3LnGNElH+1SpgIYNpdGSsETwqnTvTvEq/ogzqstqNfcGz5oF3HsvTwe2HMJ+7jng/ffdU1P2NoGehk+Gip9TUsKF2HJzgR9+MM6vX5+rw2ZkcLXY8HD52khIi1rNO+8BA8QbIK6E1B85Im6fwmdPGCkAsGYNnyIjgU8/NaZoE/6BM1WC9XoujyCUVygp4cMmlpW3r171DY+LEAMWSCq01qCsHz/k/Hle6C0nh8eXCGc4KIgP52Rm8jo70dHytpPwLNb0JqREq+WpoKZeDFvVjisrvRdsm57OOynTjonwXebNA0aPdm1d00rbej0fovzmG2DBAvmqHjuDSuXfxTfF9t9kqPgJ5eX8rTI3F9i8GaipMX73wANGIbaEBNmaSMiAXs8fyq4+6B2xZYu59L2wz+3bjW+xej0XmZMD046K8E2WLweGDHFtXSHge9w44LPPvJ+Z5g4ajTEGzF8hQyUAqKwE1q/nnpP164GqKuN3d97JPSeDBgHNmsnXRkJ+9HogMdF8rF4qYmKARYvMH6aWhkpJiesdjbsIHZU/v5X6O8XFQI8ecrfCnIYNeaKBp9KgIyN5qnVwsGe2rxRIR8VPuXGDe0xycrgHxXTcv21boxBb27ayNZFQGGo1NxQ8oRx78SKPCREMAWtDP3LWehJew4YP5/oaFHDre3TuzDPMPGFou0pQEPDJJ9xDvXUrMG2atNsvLwfWrSPjWoA8Kj6AXs9jTXJzeYdgGq3etCk3TDIzuZw9aZwQ1vD0W6lOx4MTMzI8tw8poKEg38LTcVbuMn48MGOGfcVcVxCCaP29lhUN/fg4jPEsnZwcnrVjmkefkMCHdDIzeSFAMk4IRwjy486kLDtLUJCx5oqS8fcARX8hP58/55TOypU8eSEvT/pt+6t0vgAN/fggjHF9E0Hr5OhR43fR0UD//vyNldzXhLO4krLsLL5gpAD8twvpq3QfKZNVq/iLmC+Qnu65bQe60JsAGSoK4PBh7jnJzQX27zfOb9iQP0wzM4Fevfw/sIrwLGKqKwcKJ0+Soq3SEIKw1671fiVupRLoQm8CZKjIxMmT3FWYkwPs3m2cHxICPPoo95z07g2EhcnXRsL/SEvjxq8nU5Z9hYIC/pe0VuRH6bEo3oaE3syhGBUvUlrKx11zc/mbg4BazXUmMjN5nYqoKNmaSAQIej1Qr54egHJ6aMvMDq2Wa7QsXerZ/VKArbwUFvIhSU/2RGPHAkuW+IaOSiCl1FMwrUIoKwNWr+bGyZYt5pVeu3blxsmAAVzchyC8iUqVD0DQm5c/InvjRj68aSp3DkifUWFJIHUMSkMI8va0J0Wj4RXgd+wwFtA8edLzRrAr6HR86CsQrkUyVGTk2jWeA5+TA2zYAFRXG7+75x4+rJOezt/kCEIulCaktWwZ8MQTdecXFvJAck8SKOmgSsOb12BUFPD003zoUzCCExLk9bIIRvLUqUCbNoFX9kFs/x3kxTb5NdXVwJdfAoMHA/Hx3BBZs4bPb9cOeOst4M8/gR9/5G5IMlIIuZEqo0DoaNxNk8/K4kaJJWlpQHa2e9t2BGPGAFvCe3gzq6WsjHsqevTgXpy1a4Enn/Te/q2h1XJP3htvcO86ZXRahwwVN9Dr+XDOc89xy7xvX+5FuXoVaNECePVV4Ndfgd9/ByZP5hYzQSgFqTIKioq4+mxMjPl8nY7XWBHL+fN8GNSasTJpEtCkiXvtFAOlg3qX+Hh59ltSwq81OQuzajQ84zMQhnjchbJ+nKS2Fvj+e26Q5OcDZ88av0tK4p6UjAzgvvtIiI1QNufPSyfSJqglZ2cbXdidOwOtWjm/LWsaJ2o18P77nh8ConRQ71FYCLzyijz7Zow/nxct4gbw3397NpjXGqWlPGaGUuQdQ4aKCBgD9u41ap2cOGH8LiaGW+aZmYE1tkj4NoWFXPVTqoezsJ1//9sY51Fc7HyQpOkQjOUDPC2NpxQPHWpe40oqdDpKB/UW3sj0cQRj/PrMzgamTJGnDeTBEwcZKnY4eNCoEnvggHF+eDjw+OPcc/J//wfUry9fGwnCWfR6rlnhiU7C1Mhw5yFcUsINHdMMILWae1rWrOGF4AoKeNyXVDz3HNc2EoYjzp0LvOBGb+DJ688VWrXiQ5dyBNWSB08cZKjY4IUXeHVMgZAQLsCWkQE89hgQGipf2wjCHbZv92w66MmT3MgwVVl2ltGjuWtcQKvlXsucHM+0XaWy/VZNOivS4unrz1lKS71vpJCgm3OQoWKDu+4C6tXjHpPMTP4mp5DsZ4JwC0+7m19+mWdYuIOpkQLwjm32bPe2aQ97b/dC4CXprDiPIItv6hlbu1buVnEEY0EuDat588hTJxYyVGwweDB/KMXFyd0SgpAWT7ub3TVSlIYQeEmFDO1jaZScPQuMHGmuNuyNIZbYWK70vXmzMcjbEiHRYd68utlqniYmhgfxktErHhJ8I4gAQ1ADLSlRTpyAr1BURFka1lByrZ7wcJ7dVl5unGeq/urt+2HLFl4agiDBN4IgbKBW85gLgFLonYWyNMzR64E33+Rp40o0UgCeIVZezrN7VqzgxubRo0aPhjfvB62WDF1XIEOFIAKQtDQec2EpotaggTzt8RXi43mgcE4O/2tauyvQKCwEmjWTL7XXWd5/n6fkW1N/tXU/SM3zz9PQoSuQoUIQAUpaGnDsGH/DFN40Kyp4ii7FZtUlPJxruPTowWPYBCl2a0q6/o6gg1JSIndLxHPhAjB9uu3vTe+H3r090wZSJ3cNilEhCKIOQmDk2rXA8uXmWTgaTd2snEAlECsve6visSeIjeVBvva8Gp78fRTjZA5VTyYIQhIsszlOngSeekruVimHQKu8rLSq287iyFjwxO8LtGtELBRMSxCEJKjV/MEuVHeVQ8FTyQRa5WUpAoobNnR/G67iqP1SB0ybpkKTkeIaZKgQBGEXvd48gDQ2Vu4WKZOtW30juNbyfDrbZnd1eMaP51o7W7bwqvIDBvD53spAO3TI/vdS6wxptYE1NOgJaOiHIAibWNPHiIszF/EijChdbt/W+RwyhIvZWdY1sqYsq9cDYWGuGWWjRnHPguV2S0uBMWO8E/ei1fKgWVveDaliVPr354J3VCvKNhSjQhCEWyihwq09YmJ43a3PP/fsPj7+mHeiYgTBpAqutWYgiOnsLNfr3BnYsYN/PnQImDrV/m8wNbSsGTVaLU+xdTUluaiIq8Va2+7cudxoEtq6cKF5VpFaLZ3HylGcyoQJ0pRsKChQrtGqBHzCUGnevDmOHz9uNm/GjBmYOHGi6G2QoUIQ0uPLmR1SolJxowMwDlGIMVYcBU46MigWLarbkc+fz70ewnqWVZ7Pn+fFHE3Xc7ZzFwytceOAOXPq/laVyj3DdcwYbpBY2y5gbuCZHqP4eOC//+WGlhQsWwY88YT176S69imA1jE+Y6g8++yzeP755w3zIiIi0NCJSCsyVAhCetzNfFCp+Nuxr6cxm3Y2a9c6JxNfVMQ9IZaGxbp1dVO+HRkUgoHgjVo5KhWXnJcj3kaj4cc3ONg4zxPy/HFxwCefWPd2TJ3KVWylglKSbSO2/5a9KGFERAQSExPlbgZBECa4k/kgdKoPPshd376MkNGzYAGvCp2ayjuyadMcr7t2LfDkk+I6WEdGgfA66Y2MK8bkCwouLeXqsIIR4Wj48eGHga+/dn4/58/zGJIBA4xqsefO8XO2cqV7v8ESKrvgPrJ7VK5fv44bN26gadOmGDx4MEaPHo169WzbT1VVVaiqqjJ8Li8vh06nI48KQUiIOx6V8HD+t6JCsuYoAmH4JSbGt3VEfAGVihsM3gqw9STkUbGNT+iovPLKK8jNzUVRURH+8Y9/4O2338aECRPsrjNjxgxERUUZJp1O56XWEkTg0LUr75hdSRmtqFCekSJF6mtJCX8DLy21n6KtUlFMghSMGOHbRopKxas0d+0qd0t8H8k9KhMnTsQ777xjd5k//vgDN998c535n332Gf7xj3+goqICISEhVtcljwpBeAfB7Q4oN/NHLEFBQG2t+9tRqbhHhUTvlE9MDM8w8iRCzJBlkHEgllZwBdmCaUtLS3HBwV3csmVLBJtGS/2Pffv24dZbb8WBAwfQtm1bUfujYFqC8ByeCGT0d0JCAJN3KUIG5s4FOnQAevaUftthYcDw4UbdGWtB1jod14shI8U+sgXTajQaaDQal9bds2cPgoKCEC+ExxMEIStpaeYpsWfP8hRYd3E3zVXJkJEiHa4WwNRoeFyIVitO/8YZKit5rJKgbWN5jzije0OIQ7Zg2p07d2LXrl3o0aMHIiIisHPnTowePRqPPPIIli5dKno75FEhCO8haEy4+/C/917gxx8laxbhh+h0QHo613NxltBQrpUCeEa0kDRSpEHxwbQhISHIzc1Ft27d0L59e0yfPh2jR4/GwoUL5WoSQRAOUKv526S7kJFCOGLQIGDxYtfWrazk6ccA0LevdG0SCLRClHJDEvoEQThNYSHXn/B0sKI3mDuXDxW8+CJw5YrcrSEEXB32MSU83LMZaCtW8KrihGv4jOAbQRC+R1oaEBXlmWBFbyG4719+mXuKjhxxvYYNIT1SqBp7Ok2ewim9g6w6KgRB+C5CsKIUGiVyMW+eMcZg0iT7+igEQcgDGSoEQbiEabyKrxkrQUFc+dQ0fVSt5hV7fe23yMGgQVzqPtA5d07uFgQGZKgQBOEyaWlc1MrXOq3aWh4DYYnwe7Ra77fJl8jL83wNm5gYwIn6tLKQlCR3CwIDMlQIgnCLtDTg2DHX0kjlxLSj1et5faOcHN5BHjkCTJ4sW9N8AimUfu1x++3A1aue3YerkDy+dyFDhSAIt1Grge+/l7sVziG8DRcWcm2YHj2AwYP531atADu1Uf2S0FDgkUfkboWRoiK5W2Af0/gmwrNQejJBEG5TWGjUrfAFmjQBjh/n8ueeEAQjlI1GAwwZwlPTnUWook3y+O6jeME3giD8A72e1zrxJU6fBiZO5O1WmpESESF3C/yXAQO4p+b0aeC994CCAufikbKz+TAnGSnehTwqBEG4RXExHy4hpGHTJiAjwz/E9JSGNYE2vd68Tk9pKTBmDBUZ9AYk+EYQhFfwdPaHI1Qqnm6s18vXhuhoLtt+/br72zp/nnt6SHxOes6e5deJaWyJWs01gUxJS6Mig0qCDBWCINxCzhRNoQqznEZK587Ajh3SbY9SXj3H6NHAu+/y8g9t2tg2QqwZL4R8UIwKQRBu0bWrfAq1Wi2QleX9/ZoilZFimvJKxornOHWKe6uEDK/mzXkwOKFcyFAhCMItpKqoDACRkUCDBuKWnTsXOHoUSE11f79KUKNlzJjy2rmzdUE6QnpKSnjG2ptvch2d4mJ5PXREXchQIQjCbQRF17g497ZTXi4+ziMhgXfqgkfHFYKCgNxcZSjrCnWGCgu5josURfl8HW/UXhLSScjLolzIUCEIQhLS0rhHwFvEx/O337w8HnPgCgMHAunpPOW0qAgYOVLKFjrHxYv8zb5/f/OMk0AlO5sHvxYUAOHh3t13SQlPZSZjRRlQejJBEJLhjVRllYrL3IeEAH//bZwfHQ2UlYmXdg8PBy5fNg+kpFRr+VGr+RDMwIHGeVu3Aj17ercdKhX31B09Shk/noIE3wiC8DruDMOIhTHgwgVzIwUALl1yrv7M0qXGDkio9VNS4v7wlS+hRHG5/v3r6pV07+58wLa7cUeMASdP8jRlQl7IUCEIQjKkDKy1hkbjeBggNNR+zIlOx4cThM7QtNbPkCFcx0RK7rlH2u1JiRKCiC3Jy+PxR6bDLq5cV1KNFcitE0TQ0A9BEB4gP58rgEqZPaHRcC/Io486XjYigquLtm3LY1kA4Ny5uroZhYXia/2EhwMVFa63n3AOlYoHaJt6VwoLgRde8G6gcVERaap4CrH9NxkqBEF4hFWrzOMMLBHb8Qtv/atWAb/8AkybJr4N48cDs2ZZ/06v554UW4GrKhUfBpo7l3to9Hrvx0kEOjpd3RiR6mp+PqT2fFlCMSqeh2JUCIKQlQEDrBd9E4Zeli7lnYGj4Qettu6btVhmz+brWqO42H52DWP8zb1JE/5G3b2799KYlTgkA/AOe+xYcedNCqzFiAQHA5984p02CLo2hLyQoUIQhMdISzOm/q5Ywf8ePcrnC9orlp2/VstTUy2XB1xzwb/0Ut0hqMJCYNAgcesXFHCjZvVqaWr52CMigsdoWB4TseJvQ4fyGB1PkZMDzJlj/byJxVnHt7UYEVvXjlQiee4Yx4T00NAPQRCyYlm9tmtXPt9aUTi9nqcml5c7tw/TOANn4lLkIDsbmDTJ+Pvj43k2k6OKyuHhwNWrnvtdw4YBvXqZn6OMDNseK1vExfHzeOmSuOXtxYhYXjudO3OxvJIS14+DcPzJk+J5RPffzMcpKytjAFhZWZncTSEIQgIKChjTahnjXQ2ftFo+nzHGsrLMvxMzrVjB162pqbttpU0xMbydto6FEiatlrHx4z27D5WKMZ3OeCycuX5UKuf3p9MZrzHCO4jtv8mjQhCEYrDl7TANqI2JcV6UbcoU7gVYsgRYtkySpnqUoiLuPVGy58eTmJ5vV4ZfxGSdxcYCK1dazwYjvIPY/rueF9tEEARhE70eGDXKesfMGO+8srKAw4e5sWJvGMSS7GzJmukVSkqAiROlN1JCQ4HKSmm3KQUqlflvbdKE66bYMlKsDReaGhkajePU+AsX+DqZme63n/AsFExLEIQi2L7dcRbOyZPAjh3coPFnSks9U+9HiUYKUNcgs2egmQr02SoiKFakjcTcfAMyVAiCUATOdC6TJnGvij+i1UqXveKr/P239aKAwtCgpRFnWUQwKUncfsQuR8gLGSoEQSgCsZ1GfDz3vrRt69n2yEVlJXDkiNytkBfBo5KVZRzCcTQ0aLq8UHPKls6KSsX1fITsJULZkKFCEIQiENO5xMZyrZAePYCdO73bPm9x8SIP/o2Nlbsl8iIM9QmCb2KHBrdvN68NZHk9CZ9JzM13IEOFIAhF4KhzYYwHQJaUeLYdDz/Mg2+9pUJriRA4XFXl/rYeeMD9bTiLs1WOHVFSwgX3CgrELS8MIdoTFCQxN9+C0pMJglAUhYXcxW/69qzV8iGRCxc8v39BYEyvBxYsAEaPdrzO0KFcudZZITp/QaMx1kQqLpY2yyouzrm6PpYCcY4yhAj5oKKEBEH4LJadizcKAlorQicULrSldKpS8aBebxhQSsRS76SwEOjfX762UBFB34KKEhIE4bOo1fytODOT/z13zrP7sxW3ICbWIZCJi+NGSmoqsHUr8Pzz8rSD4k78GzJUCIJQPK6kkYaHi1/WXtyCvViHqVMD15sC8OEegHudevZ0ToRPSijuxL8hQ4UgCMXjKCPIkuxsYM0accvOnWteodkatqpAt2kjbh/OIPxGX8j6OXLEuq6Jtxg5sm6FbcL/IAl9giAUjzAEM2BAXbl1U3Q67v5PS+PxJVqt/Uq6Gg3w0kvGysz2gi6F4SiAL1tcDGzYIOGP/B9aLf8NgPdq/dg7prbQaoFFi6RvnzNt6d/fdmVlwn8gjwpBED6BrSEYjYYLfVm+WavVwHvv2e/0SkuBli2BCRMcy7ILFBYCCQl8qEPqAoeTJxt/g/B7lZoj8PzznvGkaLVAXh4JthFGKOuHIAifQmy6qbU0Z2ewVsHX01ktlqm1AFBdDURHA9eueW6/zpKdzYe9Bg+WdruTJ/O4H7XaKJcPmBub7lZWJpQDZf0QBOGXWGYE2TJS3I2dYIxPo0Zx40ivB155xfXtOcKWhyA4GBg+3L1tx8ZK55nRanmtpUOHpNmeKabnkwTbCAEyVAiC8Cvs1YRxhVOngOnTuRfHk6q4GRm2U2tTU13f7ogRvMjfhx+6vg1TMjL430WLpNmePWwFMZOREliQoUIQhF/hqCaMK0yZAqxdK+02LZkzx3pMDGDMenKFDz4AWrWSrtDhnDlAly6eiU85c6buPDEeNMK/IUOFIAi/Qqj1IjWffeaZ7ZpiWi1YQIjJEeI1XKGkxFjoUAqhuu+/d38b1igt9cx2Cd+G0pMJgvArXBGHE4On6/gI1X+Li4HkZD5v1SqePu1uBy4UOhRwJR3ZG2g0creAUCLkUSEIwq9wZ5hECQwaxIeAJkwABg6UzssgVJ+eOrVugKpSxOXkqlhNKBvyqBAE4VcI4nByFcdzl4sXPdv2Nm14gKq3iz46gnRRCFuQR4UgCL8jLQ3Iz6fAS2skJXm/6KMjVCoqKEjYhgwVgiD8kgEDgJwcuVuhHOypuUoR1+NMEUhTdDrSRSHsQ4YKQRB+y8CBQEFB3ZiVuDg+vCImk8af3vJteS2cLfpoimAALV7M/3dmG2IKQhIEGSoEQfg11kTDzpzhb/H5+dYNGY0G6N2b/2+ZLuyrjBtn2yAQ4noA14yVefO40WdNSdYagnHz8sv+ZQgSnoFq/RAEEfBY1g/q3JmLpHlC1EwudDruvbBnGDhbH0mr5QaOqQEkHMu1a41VoE2hWj2EANX6IQiCEIllcOmOHf5lpABco2X7dvvLCN6nuXPFbfPZZ+saG8KxnDvXureKavUQzkLpyQRBEBZ4St1WbrZudVx1Wq0WL7yWnQ3cdpttoyMtjdcpElPtmiBsQYYKQRCEBZ5St5WbadOM/8fF8UKFAwfWXc4ZkbmsLG6M2DI+BA8LQbgKDf0QBEFY4E4WDMDXU4raqy3On+cquBMm1P3OGSl7MUNKBOEOZKgQBEFY4E4WjLD8woU8RkPpBsvs2TxmxBRnpez9daiMUAZkqBAEQVghLc16uq3lEIflZ9Ng0bQ04OxZHssRE+PZ9rrDSy+Zp2E7Wy/JX4fKCGXgMUNl+vTp6Ny5M8LCwtCoUSOry5w4cQKPPfYYwsLCEB8fj/Hjx6OmpsZTTSIIgnAKaxos167Z/2wpYKZWA2+8wWXqt2xx3WCZPJnvQ2xGjjOUlpoP3wgeJUfeJHtqtwQhFR4Lpq2ursbAgQPRqVMnfPrpp3W+1+v1eOyxx5CYmIgdO3bg9OnTeOqpp1C/fn28/fbbnmoWQRCEU1gLBnX02dZ2kpOBRYtcKzqYnMz3o9cD774rffq05fCN4FEaPpxXXbZEMGKoRg/haTzmUcnOzsbo0aPRoUMHq99v2rQJ+/fvx7Jly3DHHXfgkUcewVtvvYUPPvgA1dXVNrdbVVWF8vJys4kgCMJXSEvjQ0FisfRaiPV2OIu14Rt7Q1ekh0J4C9liVHbu3IkOHTogISHBMC8lJQXl5eXYt2+fzfVmzJiBqKgow6TT6bzRXIIgCMmYNEm81DxQ12sheDss40h0OmD8eOfiS4T1bA3fmA5d2RviIghPIZuhcubMGTMjBYDh85kzZ2yu9+qrr6KsrMwwnTx50qPtJAiCkBq1Gnj/fcdF/Ox5LazFzxw9CsyaxeeLjYdRqcQN31iq99JwD+EtnDJUJk6cCJVKZXc6cOCAp9oKAAgJCUFkZKTZRBAE4WvYyirSaLiImhivhS3jwTQexp4xFBtLwzeE8nEqmHbs2LEYNmyY3WVatmwpaluJiYn44YcfzOadPXvW8B1BEIS/42mJecEYsiw0GBPD502aRJ4RQvk4ZahoNBponJEstEOnTp0wffp0nDt3DvHx8QCAzZs3IzIyEu3atZNkHwRBEErH0xLzVG+H8HU8lp584sQJXLx4ESdOnIBer8eePXsAAK1bt0Z4eDh69eqFdu3a4cknn8SsWbNw5swZTJ48GSNGjEBISIinmkUQBBFwUL0dwpdRMcaYJzY8bNgwLF26tM78oqIidP/fHXP8+HG8+OKLKC4uRsOGDTF06FDMnDkT9eqJt5/Ky8sRFRWFsrIyilchCIIgCB9BbP/tMUPFW5ChQhAEQRC+h9j+m2r9EARBEAShWMhQIQiCIAhCsZChQhAEQRCEYiFDhSAIgiAIxUKGCkEQBEEQioUMFYIgCIIgFAsZKgRBEARBKBaPKdN6C0EGpry8XOaWEARBEAQhFqHfdiTn5vOGypUrVwAAOp1O5pYQBEEQBOEsV65cQVRUlM3vfV6Ztra2Fn///TciIiKgslXL3EXKy8uh0+lw8uRJUr31MHSsvQcda+9Bx9p70LH2HlIda8YYrly5gsaNGyMoyHYkis97VIKCgqDVaj26j8jISLrwvQQda+9Bx9p70LH2HnSsvYcUx9qeJ0WAgmkJgiAIglAsZKgQBEEQBKFYyFCxQ0hICKZMmYKQkBC5m+L30LH2HnSsvQcda+9Bx9p7ePtY+3wwLUEQBEEQ/gt5VAiCIAiCUCxkqBAEQRAEoVjIUCEIgiAIQrGQoUIQBEEQhGIhQ4UgCIIgCMVChooFx44dw7PPPosWLVogNDQUrVq1wpQpU1BdXW223K+//oquXbuiQYMG0Ol0mDVrlkwt9m2mT5+Ozp07IywsDI0aNbK6zIkTJ/DYY48hLCwM8fHxGD9+PGpqarzbUD/hgw8+QPPmzdGgQQPcf//9+OGHH+Rukl+wbds29OnTB40bN4ZKpcKaNWvMvmeM4Y033kBSUhJCQ0PRs2dPHDp0SJ7G+jAzZszAvffei4iICMTHx6Nfv344ePCg2TLXr1/HiBEjEBsbi/DwcPTv3x9nz56VqcW+y0cffYTbbrvNoD7bqVMnfPXVV4bvvXmcyVCx4MCBA6itrcUnn3yCffv2Ye7cufj444/x2muvGZYpLy9Hr1690KxZM+zevRuzZ8/G1KlTsXDhQhlb7ptUV1dj4MCBePHFF61+r9fr8dhjj6G6uho7duzA0qVLsWTJErzxxhtebqnvs3LlSowZMwZTpkzBzz//jNtvvx0pKSk4d+6c3E3zea5evYrbb78dH3zwgdXvZ82ahffffx8ff/wxdu3ahYYNGyIlJQXXr1/3ckt9m2+//RYjRozA999/j82bN+PGjRvo1asXrl69alhm9OjR+PLLL5Gfn49vv/0Wf//9N9LS0mRstW+i1Woxc+ZM7N69Gz/99BMeeughpKamYt++fQC8fJwZ4ZBZs2axFi1aGD5/+OGHLDo6mlVVVRnm/fOf/2Rt27aVo3l+weLFi1lUVFSd+Rs2bGBBQUHszJkzhnkfffQRi4yMNDv+hGPuu+8+NmLECMNnvV7PGjduzGbMmCFjq/wPAGz16tWGz7W1tSwxMZHNnj3bMO/y5cssJCSE5eTkyNBC/+HcuXMMAPv2228ZY/y41q9fn+Xn5xuW+eOPPxgAtnPnTrma6TdER0ezf//7314/zuRREUFZWRliYmIMn3fu3IkHH3wQwcHBhnkpKSk4ePAgLl26JEcT/ZadO3eiQ4cOSEhIMMxLSUlBeXm5wbInHFNdXY3du3ejZ8+ehnlBQUHo2bMndu7cKWPL/J+jR4/izJkzZsc+KioK999/Px17NykrKwMAw/N59+7duHHjhtmxvvnmm9G0aVM61m6g1+uRm5uLq1evolOnTl4/zmSoOODw4cNYsGAB/vGPfxjmnTlzxqzjBGD4fObMGa+2z9+hYy0N58+fh16vt3os6Th6FuH40rGXltraWmRlZeGBBx7ArbfeCoAf6+Dg4DrxbnSsXeO3335DeHg4QkJC8MILL2D16tVo166d149zwBgqEydOhEqlsjsdOHDAbJ2SkhI8/PDDGDhwIJ5//nmZWu57uHKsCYIgnGHEiBH4/fffkZubK3dT/Ja2bdtiz5492LVrF1588UUMHToU+/fv93o76nl9jzIxduxYDBs2zO4yLVu2NPz/999/o0ePHujcuXOdINnExMQ60c3C58TERGka7MM4e6ztkZiYWCczhY6188TFxUGtVlu9buk4ehbh+J49exZJSUmG+WfPnsUdd9whU6t8m5EjR2LdunXYtm0btFqtYX5iYiKqq6tx+fJls7d9us5dIzg4GK1btwYA3H333fjxxx8xf/58pKene/U4B4yhotFooNFoRC1bUlKCHj164O6778bixYsRFGTueOrUqRMmTZqEGzduoH79+gCAzZs3o23btoiOjpa87b6GM8faEZ06dcL06dNx7tw5xMfHA+DHOjIyEu3atZNkH4FAcHAw7r77bmzduhX9+vUDwF3nW7duxciRI+VtnJ/TokULJCYmYuvWrQbDpLy83PCWSoiHMYaXX34Zq1evRnFxMVq0aGH2/d1334369etj69at6N+/PwDg4MGDOHHiBDp16iRHk/2K2tpaVFVVef84Sx6e6+OcOnWKtW7dmiUnJ7NTp06x06dPGyaBy5cvs4SEBPbkk0+y33//neXm5rKwsDD2ySefyNhy3+T48ePsl19+YdnZ2Sw8PJz98ssv7JdffmFXrlxhjDFWU1PDbr31VtarVy+2Z88e9vXXXzONRsNeffVVmVvue+Tm5rKQkBC2ZMkStn//fjZ8+HDWqFEjs4wqwjWuXLliuHYBsPfee4/98ssv7Pjx44wxxmbOnMkaNWrE1q5dy3799VeWmprKWrRowSorK2VuuW/x4osvsqioKFZcXGz2bL527ZphmRdeeIE1bdqUffPNN+ynn35inTp1Yp06dZKx1b7JxIkT2bfffsuOHj3Kfv31VzZx4kSmUqnYpk2bGGPePc5kqFiwePFiBsDqZMrevXtZly5dWEhICGvSpAmbOXOmTC32bYYOHWr1WBcVFRmWOXbsGHvkkUdYaGgoi4uLY2PHjmU3btyQr9E+zIIFC1jTpk1ZcHAwu++++9j3338vd5P8gqKiIqvX8dChQxljPEX59ddfZwkJCSwkJIQlJyezgwcPyttoH8TWs3nx4sWGZSorK9lLL73EoqOjWVhYGHv88cfNXjQJcTzzzDOsWbNmLDg4mGk0GpacnGwwUhjz7nFWMcaY9H4agiAIgiAI9wmYrB+CIAiCIHwPMlQIgiAIglAsZKgQBEEQBKFYyFAhCIIgCEKxkKFCEARBEIRiIUOFIAiCIAjFQoYKQRAEQRCKhQwVgiAIgiAUCxkqBEEQBEEoFjJUCIIgCIJQLGSoEARBEAShWP4fA0XHy9dmD7wAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Xdag = np.linalg.inv(X@X.T)@X\n", "w = Xdag@Y\n", "\n", "x0 = np.arange(-20,30,.5) #points for hyperplane\n", "x1 = -w[0]/w[2]-x0*w[1]/w[2]\n", "\n", "Yhat = np.sign((X.T)@w) #prediction\n", "diff = (Yhat!=Y)\n", "accuracy = np.sum(diff.astype('int'))/len(diff) #accuracy\n", "MSE = (1/ndat)*np.sum((Yhat-Y)**2) #MSE\n", "print(\"accuracy = {}, MSE = {}\".format(accuracy,MSE))\n", "\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "plt.plot(x0,x1,'b-')\n", "plt.legend(('data +1','data -1','hyperplane'))\n", "tstring = \"pseudoinverse error = {}, MSE = {}\".format(accuracy,MSE)\n", "plt.title(tstring)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "To use the 3rd order polynomials as features, we first construct a 3rd order polynomial feature data matrix" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. 1. 1. ]\n", " [ 0.71281562 19.4392373 17.36007128]\n", " [-3.08217326 -5.58074237 -8.63890169]]\n", "(10, 2000)\n" ] } ], "source": [ "Xr = X[:,0:3]\n", "print(Xr)\n", "\n", "def poly3feature(X):\n", " Xnew = X\n", " ndim,ndat = np.shape(Xnew)\n", " x1row = Xnew[1,:]\n", " x2row = Xnew[2,:]\n", " for n in [2,3]:\n", " for k in np.arange(n+1):\n", " xnewrow = (x1row**(n-k))*(x2row**k)\n", " xnewrow = np.reshape(xnewrow,(1,ndat))\n", " #print(np.shape(xnewrow))\n", " Xnew = np.vstack((Xnew,xnewrow))\n", " return Xnew\n", " \n", "Xnew = poly3feature(X)\n", "print(np.shape(Xnew))\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "and then use the pseudo inverse algorithm " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " accuracy = 0.0105, MSE = 0.042\n" ] } ], "source": [ "Xdag = np.linalg.inv(Xnew@Xnew.T)@Xnew\n", "w = Xdag@Y\n", "\n", " \n", "Yhat = np.sign((Xnew.T)@w) #prediction\n", "diff = (Yhat!=Y)\n", "accuracy = np.sum(diff.astype('int'))/len(diff) #accuracy\n", "MSE = (1/ndat)*np.sum((Yhat-Y)**2) #MSE\n", "\n", "print(\" accuracy = {}, MSE = {}\".format(accuracy,MSE))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "and then plot the hyper-surface and data points\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/n5/97z323y53hdfh34j_jcw52dr0000gn/T/ipykernel_86074/2912857681.py:16: ComplexWarning: Casting complex values to real discards the imaginary part\n", " x2pp = x2pp.astype(\"float64\")\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'polynomial features: error = 0.0105, MSE = 0.042')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0 = np.arange(-20,30,.05) #points for hyperplane\n", "indx = np.where(Y==1)\n", "plt.scatter(X[1,indx],X[2,indx],c='r')\n", "indx = np.where(Y==-1)\n", "plt.scatter(X[1,indx],X[2,indx],c='b')\n", "\n", "for x1 in np.nditer(x0):\n", " #print(x1)\n", " coeff = np.array([w[9], w[5]+w[8]*x1, w[2]+w[4]*x1+w[7]*x1**2, w[0]+w[1]*x1+w[3]*x1**2+w[6]*x1**3])\n", " coeff = np.reshape(coeff,4)\n", " #print(coeff)\n", " x2p = np.roots(coeff)\n", " #print(x2p)\n", " indx = np.where(np.isreal(x2p))\n", " x2pp = x2p[indx]\n", " x2pp = x2pp.astype(\"float64\")\n", " #print(x2pp)\n", " x1pp = x1*np.ones(np.shape(x2pp))\n", " #print(x1pp)\n", " plt.scatter(x1pp,x2pp)\n", "\n", "plt.legend(('data +1','data -1','classifier manifold'))\n", "tstring = \"polynomial features: error = {}, MSE = {}\".format(accuracy,MSE)\n", "plt.title(tstring)\n" ] } ], "metadata": { "kernelspec": { "display_name": "tf", "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": "3.11.9" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }