01b_MachineLearning_Basics_NeuralNetworksPython_MoreVisualization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Networks with Pure Python / Tutorials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code for the lecture series \"Machine Learning for Physicists\" by Florian Marquardt\n",
    "\n",
    "Lecture 1, Homework\n",
    "\n",
    "See https://machine-learning-for-physicists.org and the current course website linked there!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to:\n",
    "- visualize how the result of a NN changes when cutting away the higher layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports: only numpy and matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from numpy import array, zeros, exp, random, dot, shape, reshape, meshgrid, linspace\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt # for plotting\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.dpi']=300 # highres display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For fun: a network with MANY hidden layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_layer(y_in,w,b): # a function that applies a layer    \n",
    "    \"\"\"\n",
    "    Go from one layer to the next, given a \n",
    "    weight matrix w (shape [n_neurons_in,n_neurons_out])\n",
    "    a bias vector b (length n_neurons_out)\n",
    "    and the values of input neurons y_in (shape [batchsize,n_neurons_in])\n",
    "    \n",
    "    returns the values of the output neurons (shape [batchsize, n_neurons_out])\n",
    "    \"\"\"\n",
    "    z=np.dot(y_in,w)+b # batch processing: y_in is of shape [batchsize,num_neurons_in]\n",
    "    return(1/(1+np.exp(-z))) # output is of shape [batchsize,num_neurons_out]\n",
    "\n",
    "def apply_multi_net(y_in):\n",
    "    \"\"\"\n",
    "    Apply a whole network of multiple layers\n",
    "    \"\"\"\n",
    "    global Weights, Biases, WeightsFinal, BiasesFinal, WeightsFirst, BiasesFirst, Nlayers\n",
    "    \n",
    "    # MODIFIED HERE FOR VISUALIZATION:\n",
    "    global y_stored # for storing intermediate results\n",
    "    \n",
    "    y=apply_layer(y_in,WeightsFirst,BiasesFirst)\n",
    "\n",
    "    # MODIFIED HERE FOR VISUALIZATION:\n",
    "    y_stored[0,:]=apply_layer(y,WeightsFinal,BiasesFinal)[:,0] # storing output value when final layer is evaluated right here\n",
    "\n",
    "    for j in range(Nlayers):\n",
    "        y=apply_layer(y,Weights[j,:,:],Biases[j,:])\n",
    "\n",
    "        # MODIFIED HERE FOR VISUALIZATION:\n",
    "        y_stored[j,:]=apply_layer(y,WeightsFinal,BiasesFinal)[:,0] # storing output value when final layer is evaluated right here \n",
    "\n",
    "    output=apply_layer(y,WeightsFinal,BiasesFinal)\n",
    "    return(output)\n",
    "\n",
    "# initialize random weights and biases\n",
    "\n",
    "def init_random_network(num_layers=20,layer_size=100):\n",
    "    \"\"\"\n",
    "    Initialize a random network\n",
    "    num_layers counts only hidden layers\n",
    "    layer_size is number of neurons in hidden layer\n",
    "    Input layer is of size 2\n",
    "    Output of size 1\n",
    "    \"\"\"\n",
    "    global Weights, Biases, WeightsFinal, BiasesFinal\n",
    "    global Nlayers, LayerSize\n",
    "    \n",
    "    Nlayers=num_layers\n",
    "    LayerSize=layer_size\n",
    "    \n",
    "    Weights=np.random.uniform(low=-3,high=3,size=[Nlayers,LayerSize,LayerSize])\n",
    "    Biases=np.random.uniform(low=-1,high=1,size=[Nlayers,LayerSize])\n",
    "\n",
    "    # for the first hidden layer (coming in from the input layer)\n",
    "    WeightsFirst=np.random.uniform(low=-1,high=1,size=[2,LayerSize])\n",
    "    BiasesFirst=np.random.uniform(low=-1,high=1,size=LayerSize)\n",
    "\n",
    "    # for the final layer (i.e. the output neuron)\n",
    "    WeightsFinal=np.random.uniform(low=-1,high=1,size=[LayerSize,1])\n",
    "    BiasesFinal=np.random.uniform(low=-1,high=1,size=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize network\n",
    "\n",
    "init_random_network(num_layers=20,layer_size=100)\n",
    "\n",
    "# Generate a MxM 'mesh grid', i.e. x,y values in an image\n",
    "# as input to the network\n",
    "\n",
    "M=40\n",
    "v0,v1=np.meshgrid(np.linspace(-0.5,0.5,M),np.linspace(-0.5,0.5,M))\n",
    "batchsize=M**2 # number of samples = number of pixels = M^2\n",
    "y_in=np.zeros([batchsize,2])\n",
    "y_in[:,0]=v0.flatten() # fill first component (index 0)\n",
    "y_in[:,1]=v1.flatten() # fill second component\n",
    "\n",
    "# MODIFIED HERE FOR VISUALIZATION:\n",
    "# prepare array to hold results for intermediate\n",
    "# layers\n",
    "\n",
    "y_stored=np.zeros([Nlayers+1,batchsize])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the MxM input grid that we generated above \n",
    "y_out=apply_multi_net(y_in) # apply net to all these samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2D=np.reshape(y_out[:,0],[M,M]) # back to 2D image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
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Jrpv4p6vXH0P+MMmrq+pzPXPbrv30nKx5uoH1O329I+cWTj+f5H1J\nfi1rP9jJavilSW5srf3FDikdyHDhtJJ8bD2nX0ny75LcNrXNatYWRH57a03RHAAAAJbQXq9nutXH\nIqqq+6vqNUlembVRkedzd5KfT/LsqnrPLuX28axNc//7ObemM+nW9W2+vqpu2Y3ctmu/PCdFtI29\nOcm3T7RPZW3q/vR6GM/K2l8uzkzpP5zk3a21/67XsO4ko6wVS385yW8OLRXQWnt+kp9J8pcmul+e\ntYWSf6xTXgAAAAALq6rembU1Ty/P2jT9y7I2c/ezWZuW/ruTdZ8Z4u6oarw+U/jNSd68XtN5+npu\nSfLnST5eVX+wg/g3JLlhJzlu45hdn9NuUDw9j9baFUl+cKr7lVV14/S2VfUnrbVvTfKb+UoB9XFZ\nu7vY/zLn1B7JWqH2zZst0FtVf9Ba+5Yk/yrJX534px9urf1CVd0+59wAAAAAlkJVfSLJJ/Y6jyHr\nBcWFLirOalmfk2n75/eGnH0jprcNFU7PqKqHsla9n/zLxOvWi7Dz8nCSq6rq+7dwZ7MzeY2SvC7J\npye6DyV51RzzAgAAAHbBOG0pHrBfKJ4OaK0dTfKKqe6f3Gy/9bUc3j3RdSDJd88rr6o6vdWi6dR+\nDyV561T3N88nKwAAAADYnxRPh12f5NhE+0NV9bEt7jtdpHz5fFLasZum2pcNbgUAAAAAJFE8PZ8X\nT7XfP8O+H0hyeqJ9XWvt0h1ntHOnp9qH9iQLAAAAAFgSbhg17NlT7Q9tdceqeqC19uEk1010X5vk\nc/NIbAeummrfsSdZAAAAANtW1TLe2U3du9vhTedhoRh5OuyaqfYtM+5/61T7WTvIZV6m13D9/T3J\nAgAAAACWhOLplNbaxUkunur+1Ixhpre/evsZ7Vxr7WuTfMNU97v2IhcAAAAAWBam7Z/roqn2g1X1\nwIwx7pxqX7iDfHaktXYwyT+f6v5AVRl5CgAAAEtmvATT9hc9P5iF4um5Tky1H9pGjOl9LthmLvPw\nj3L2+qunkvydeR6gtXZJkifMuNuV88wBAAAAAOZN8fRc08XTh7cRY7p4Oh1zV7TWvjfJD051v7Gq\n/mjOh/pbSd4w55gAAAAAsKcUTzdXu7TPXLXWXpzkn011//sk/3AP0tnUv/2NF+bwHz9xrjHf/pm5\nhvuyS2/7Qp/ASdL6TW1ohw93iXvft07fX21+Djw07hJ39aFRl7hJcuTDn+4We3zf/d1iL6Na6bNs\nd9cJRqN+516v60d7TL/JE/XAg/1iX3C8T9x7O37EnzrVLfRKp5/j+Ev3dYmbpOv7pU6f7hK3dfwc\nT6drXsZ9PmuTZHz/rCtfbV3rdf04eLBP3CTtUL/YWVntFLfjOd3zM3HU6byufu+XjPt9vlSn17od\nmf/vF+30oe3N/QToSPH0XNPViaPbiDG9z65WPFpr35Dk3yaZ/Ib2O0leXVV7XtgFAAAAtmdci7+m\naMe/B8CuUzw911IXT1trz0/yH5Icm+j+/STfUVW9hvj8XJJfm3GfK5Pc2CEXAAAAAJgLxdNz3TvV\nPtZaO15Vs8w7umSqfc8Oc9qS1tpzkrwvyYUT3Tclub6qvtTruFV1Z5I7Z9mn67Q2AAAAAJgDxdMp\nVfWF1toXkzx2ovupSf50hjBfPdW+eceJbaK19qwk/ynJxRPdH0nyV6pqV4q3AAAAQF+VtvDT9qvv\nnQRgV3VaeX7pTRdKr5px/ys2iTdXrbVnJPnNJE+Y6P5Ykm+rqrt6HhsAAAAA9ivF02EfmWq/YKs7\nttaOJ3nOJvHmprV2VZLfSjJ5q/qbk3xLVX2u13EBAAAAYL9TPB32nqn2i2bY9xtz9nIIN/UqYrbW\nLs9a4fSyie7bslY4vaPHMQEAAADg0cKap8Pem+ShJEfX2y9orT2zqj62hX1vmGq/a56JndFae2rW\nCqdPmei+PWuF0z/rcUwAAABgb1W11KKvebrg+cEsjDwdUFUPJnnnVPePbLZfa+3pSV420XU6ya/M\nMbUzx7ksa2ucPm2i+zNZK5zePu/jAQAAAMCjkeLp+b0xyamJ9g2tte8838attSNJ3prk0ET3L1XV\nrRsdpLVWU48XbbL9JVkrnE7exOqOJN9cVbdttC8AAAAAsHWm7Z9HVd3WWntLkh+a6H5na+31Sf5F\nVZ0809lauybJLyZ54cS2X0jypnnm1Fq7KMlvJHnmRPcDSV6X5FRr7WmzxKuqT84rNwAAAKC/cVrG\nWexp8YueH8xC8XRjP5rk2iQvWW8fTPKzSX68tfaHSe5LckWS5yVnXRlOJnlZh5s2PTfJc6b6jif5\nj9uM52oGAAAAAOeheLqBqhq11l6VtVGlr574p0uSvPg8u92Z5LVV9YHe+QEAAAAA/VjzdBNVdX9V\nvSbJK5P83gab3p3k55M8u6resyvJAQAAAADdGHm6RVX1zqyteXp51qbpX5a1KfOfTXJ7kt+dXAd1\nhrhbnjpfVe+PqfYAAADwqFXVMt56KWFPzFDqgIWneDqjqvpEkk/sdR4AAAAAQF+m7QMAAAAADFA8\nBQAAAAAYYNo+AAAAwJKoagu/puii5wezMPIUAAAAAGCA4ikAAAAAwADT9lkIT/zgwzlx/KG5xqyD\nnf42UNUnbpLxzZ/sFnvlxPEucdu43+tx9I4H+wT+rx/vEzfJaDTqFrutdJr60jr+Ha3j+2Xl/vle\nM86otpxTjGo07hP3gU7vwyR18mS32O3e+/sEvvIpfeImqZtv7xY7nc7rdrDfV8la6XdtaqdOdYlb\nHa956fT50jpe83rG7qbTuZEkHc+OtAM9o3dSfT63kiQdv5/20vP60Y4d6xO4x3fTUqLYinEl4wWf\nFr+Eb0M4LyNPAQAAAAAGKJ4CAAAAAAxQPAUAAAAAGGBBEQAAAIAlUdVSC77m6aLnB7Mw8hQAAAAA\nYIDiKQAAAADAANP2AQAAAJZEpWW84NPiK4udH8zCyFMAAAAAgAGKpwAAAAAAAxRPAQAAAAAGWPMU\nAAAAYElUrT0W2aLnB7Mw8hQAAAAAYIDiKQAAAADAANP2AQAAAJbEOC3jtL1OY0OLnh/MwshTAAAA\nAIABiqcAAAAAAAMUTwEAAAAABljzFAAAAGBJVLVULfaaooueH8zCyFMAAAAAgAGKpwAAAAAAA0zb\nBwAAAFgSVS3jBZ8Wb9o++4mRpwAAAAAAA4w8ZSF89oVHcvjSo3ONedl/PjnXeF82rj5xk7Qjh7vF\n/tyrntkl7gWfOt0lbpLkwzf3i91JW13tGLvP37tqNO4St7f20CNd4vZ7hyfV8fqRjLpErZOdrqVJ\n2gUXdItdDz7YJe7KXfd2iZsk4yuf0i123frpLnFXLjjRJW6S5JF+516vd2I7dapT5H7X6uo4lKK1\njqOOOn7edjPu+Hk76vMZwO5phw/1i33oYJe4deLY/IM+8kjyhfmHBdgJI08BAAAAAAYYeQoAAACw\nJKrWHots0fODWRh5CgAAAAAwQPEUAAAAAGCAafsAAAAAS6KSVHW8Kd8cmLXPfmLkKQAAAADAAMVT\nAAAAAIABiqcAAAAAAAOseQoAAACwJKra4q95uuD5wSyMPAUAAAAAGKB4CgAAAAAwwLR9AAAAgCUx\nrpbxgk+LX/T8YBZGngIAAAAADFA8BQAAAAAYoHgKAAAAADDAmqcAAAAAy6KSqr1OYhOLnh/MwMhT\nAAAAAIABiqcAAAAAAAMUTwEAAAAABljzFAAAAGBJVLVUtb1OY0OLnh/MwshTAAAAAIABiqcAAAAA\nAANM22chHL3mnhz96oNzjXn4Jz8z13hnjE+f7hI3SUZfe0232Ace6hP32H+5rU/gJHWgzyWqOv4M\nW6ec8/+zd+dxllbloe9/T1X13A09MMNhbpHBJEAUIXjURIPk5kQxGjxqDPeamGPiSQx6E0xUJBcV\nTKLxxpNEPxqHOHHkXuUkOSJe7zFBGeJRciM4MGOAlqmx6aan6qrn/rHfsne9/VbV3rv2qt67+H0/\nn/35sN79rmc99bKH6qfWWi8Qo6Nl4haJ2pK7d5eLPT5eJvCIf1dsV/L9ws6d5WJnlgn7xNYicQFG\noty7MY89qkjcyR88WCQuwMjqVcVis7vQtR4t+Pmxc1eRsDkxWSQuQBa8HFHoPU7B92GpzyWAnJgo\nE7jgd2KUvNaFfmei4O95rF1TLPTEgSuLxI3x/r/uMi1RdMJl+9LC8l+IkiRJkiRJktTA4qkkSZIk\nSZIkNbB4KkmSJEmSJEkN3FBEkiRJkiRpSGT1GGSDnp/UDWeeSpIkSZIkSVIDi6eSJEmSJEmS1MBl\n+5IkSZIkSUMiCTJjf6cxq2Sw85O64cxTSZIkSZIkSWpg8VSSJEmSJEmSGlg8lSRJkiRJkqQG7nkq\nSZIkSZI0LLJ6DLJBz0/qgjNPJUmSJEmSJKmBxVNJkiRJkiRJauCyfUmSJEmSpCGRCZmxv9OYVbps\nX4uIM08lSZIkSZIkqYHFU0mSJEmSJElqYPFUkiRJkiRJkhq456kkSZIkSdKwyCHYU3TQ85O64MxT\nSZIkSZIkSWpg8VSSJEmSJEmSGrhsX5IkSZIkaUhkBpmxv9OY1aDnJ3XD4qkGwvY71rLniQ19jbnu\nmav7Gm/K0lvvKxIX4NGnrygWe/13tpcJXHCznRgdLRN36dIicQEYK/ixmpNl4k4UigswUnCBw549\nZeJOFrwemm58vFjoWFHm8zR37CgSF4AtTxQLHYU+q/O4I4vEBcgHHykWO5YsKRI3R8p8b0G578Tc\n9mSRuMUN42d1ye/EUrFLXudCr2mAWL2qSNzxow8qEhdgdNuucrF/+HiRuJPr1xSJKy2kiDgO+Cng\nCGA1sAm4D7ghM8v9stpZbmcAG4GpX7geAG7PzFv6PM5a4JxqnIOAR6uxbsjMH/VxnPXATwPHAWuB\nALYA9wPfyMwf9musfrN4KkmSJEmSpKeMiHgZcDFw9gynbI6Iq4C3Z+ajC5jXEuBNwK8DJ8xwzp3A\nh4H3zqfAGxGnA28HfgFommG0KyK+CFyWmf/S4xgBXAj8NnDuHOfeAvw18DeZWWimTG/c81SSJEmS\nJEmLXkSsjojPAJ9j5sIpwHrg9cCtEXHeAuW2EbgJeDczFE4rJwJXADdGxIk9jnUJcDPwEpoLpwDL\nqudvjojf72GMw4CvAJ9hjsJp5XTgg8BNvf5cpTjzVJIkSZIkaVhktB6DbADzi4hR4CpaMy3bPQLc\nQmsJ+Qm0inhTP8ChwDUR8YLM/FrB3A4DvgwcU3vqTuC2Kp9TmV5UPRO4LiKenZkPdzHWHwLvrB3e\nAXyD1rYFRwDPBJZXzy0FroyIzMw/6XCMg4H/ATy99tQ4rWt9HzAJHFX9HMvbzjkT+B8RcW5mlts3\nsQvOPJUkSZIkSdJidwXTC6fjwH8GjsrM8zLzVzLzTOA04Ma285YBX4iIw0skFREjwBeYXjjdBJyX\nmRsz8yWZ+eLMPBE4H2jfG/Q44PPV8vhOxvpF4PLa4Q8BR2fmczPzFZn574GjaW0N0O7KiHhRhz/W\nn7Nv4fSvaV3rs6pr/YrMPBc4nNb/m/aNto+iNQt1IFg8lSRJkiRJ0qIVEccDv1s7/PLM/EBm7m4/\nmJnfAX6O6QXUDcClhdJ7FXBWW3szcE5mXlc/MTOvpXVzp/Y7wZ1Da1/RWVUzb/+UvbNqAd6Xmb9Z\n39c1Mx/JzN+gVQT9cQjgz6o4s41zLPDK2uF3Z+brm2bIZuaPMvMt7Pv/57yIOKt+/v5g8VSSJEmS\nJGlIJJA54I/9fZH2dSmwpK39scy8ZqaTM3MHcBHQXlh9bVWE7ZuqEHlZ7fDFmXnvLLndQ+tmV+0u\nr2awzuY1wElt7e8Db5mjzyXVeVNOoVXsnc1/qLUfYt+fscl/Af51jlj7hcVTSZIkSZIkLUoRsQJ4\nWe3wlXP1y8zbaS2nnzLGvjMq5+tcWkvvpzwAfLKDfn9bnTvlBFozUGfzmlr7fZm5a7YO1fPvnyNO\nXb3AfN1c41RjJfB3tcMb5+q3ECyeSpIkSZIkabE6D1jZ1r4xM7/XYd+P1tov7U9KP3ZBrf2JzJyY\nq1N1Tr3IOmNuEbEBeE7bod3ApzvM8VO09oed8tyIWD/L+atq7fs7HAfg32rtdV30LcbiqSRJkiRJ\nkhar+k2OvtpF3+uBPW3t0yPi0HlntNd8cqufe/4s574QaN+r9JuZubWTQTLzCeBbbYfGqngz+WGt\nvbyTcWY4d3MXfYuxeCpJkiRJkjQsckgeg+O0WvvGxrMaZOaTwLdrh0+dd0ZARCwDTqwdvqmLEDfU\n2hsjYukM5/Z8DWYYa7ZrcH2tfUYX45xZa3+ji77FWDyVJEmSJEnSYnVyrX1nl/3vqrVPmUcu7U5i\n+mzQh6tZnh2pzn207dAo8LQZTq/nXPIafIXpN5l6TkT8xFwDRMSRwC+3HRoHPtNxhgVZPJUkSZIk\nSdKiU+3NWd+f8wddhqmf36+bGNVnnXabV1OfmXKb71gdX4PMnAT+N2DqJlEjwNURcexMfaqtEL7A\n9L1pL8/MB7vMs4ix/Z2AJEmSJEmSOpMZZMb+TmNWDfmdENF1zo9k5sPzTGVtrb29WorfjXoOB84j\nn3b13Hr5WTvNbb5jdXUNMvOGiPhFWjelOphWsfVfI+IjwLXAfbQ2dzgK+DngdcCGthAfBP6PLnMs\nxuKpJEmSJEmSSrqmhz6XAe+Y57ira+0dPcSo91nTYy51C5nbfMfq+hpk5v8TEScDbwReBRxX/fcb\nZ+n2PeDtmfm5LvMrymX7kiRJkiRJWozqRcOdPcSoFw7rMXu1kLnNd6xer8HUpM1ds57VcgPwO8DV\nnSa1UCyeSpIkSZIk6akgF6hPLxYyt277dT1ORPwGrRtNvRV4egddzgGuo7W8/2e6Ha8kl+1LkiRJ\nkiQNi2Thynm92je/F7PvHdvn8kgfMtlWa6/oIUa9Tz1mrxYyt23AunmM1dU1iIg/Ai6vHf6fwF8C\n1wMPApPAYcCzae15+vzqvNOAf4yI12bmx7vMswiLp5IkSZIkSSrprsy8bT+Ma/F07/EFKZ5GxM+y\n782e3gH8cWbWy+r3Vo/PRsTrgL8GAhgFPhIRd2bm17vMte9cti9JkiRJkqTFaEutvTIiVnUZ45Ba\n+0fzyKddPbeDe4jRaW7zHauba/BOWgXQKR/PzMsaCqfTZOaHqr5TRoH3d5VlIRZPJUmSJEmStOhk\n5mPA47XDR3cZ5pha+47eM5o1Tn2cTnSa23zH6miciDiS1jL8dpd1Mc4VTL851ZkR8RNd9C/C4qkk\nSZIkSdKQyIyheAyQ79baJ3bZ//g54vXq+8BEW/uQiFjTaeeIOAA4qO3QBDMXTxfqGvxUrX13Zt7T\n6SCZ+SRwU+3wWZ32L8XiqSRJkiRJkharW2vtszvtWC3xr898rMfrSWbuYt+baHWcG62707e7o4rZ\npOdrUPmZOeJNWVtr/3VtIVgAACAASURBVLDLcZr6HNR41gLyhlEaCEf/zV2sHt3c15g5vqev8aZM\nnnxckbgAKx+ZmPukHo099mSZwJMFb/M4UuivlUuXlIkLRa9HrO52a57O5LZCrw0gxgp+zRS61rGk\nYM475j6lV1Hq/RLl/s6aE5PFYrNrpt8b5ydW9LKPf2dyR7kXSG55okjc2LW7SFyAPKyXbb86E1vL\nfO7F7vEicQFyvMz7JUZHi8SFcr+LAeQwTgGZKPd7XqnYI2tWF4kLsPsZvaxO7UxGme/E5Xc9XCQu\nwPhRG4rF3n70kUXiLn+o/99bk5OWKFTEtbTu5j7leV30fQ7Ta2e3ZOZD/Uiqci3wtLb284DrOuz7\nvFr7i7Oc+2VaM1OnvvjPjIg1mbl1rkGq2bBntB3aU8VrUt8LtZd/xNa/fPp1g66eDeOvHZIkSZIk\nSU9NOSSPwfElpk9jODsint5h34tq7c/3JaOZ4/1qRMz5l83qnFfPEevHMvNR4Gtth5YCr+wwx1cB\n7TOQ/ikzZ5r99mCtfVJErOxwnCln1Nq9zF7tK4unkiRJkiRJWpQycztwde3wH8zVLyKeBlzQdmgP\n8Ok+pgZwPdC+J+hR7FsUbfJqoH1a+V3A1+fo84la+/ciYtlsHarn31g7/PFZuvwr02/QtRz41Tny\nah/vF5n+c8H0ou9+YfFUkiRJkiRJi9k7gPb9dS6KiF+a6eSIWA58lNYMzSkfycz6HqX1fll7PG+2\n8zNzAri0dvi9EXHsLGMcC7yvdvitmTnXHj8fp3WTqiknAe+ao8+7q/OmfAf41EwnVz9PvVB9RUSc\nNsc4RMTRwF/XDn89MzfN1bc0i6eSJEmSJElatDLzbuD9tcNXR8QbIqK9QEpEnAx8hek3ZHoMuKxQ\nep8Cbm5rrwduiIifr58YEecBNwLr2g7fAFw11yBVYfPNTN9U4eKI+GBETNt4OSIOiogPAb/XHgJ4\nUxVnNn/M9G0S1lY/zxualvBHxNKI+DXgm+w76/Qtc4y1INyNWZIkSZIkaWhE9RhkA5nfJcCpwPlV\newnwF8DbIuJbwFbgeFp7brb/ALuBC0rNgMzMyYi4ALgJOLo6fDjwpYi4A7ityudU4MRa93uBl2Zm\nR7vMZubfR8RbgXe2HX4drb1Wb6a1v+jhwLOA+p1SL8nMazsY4/6IeBXwOfbeoGoNrWv9noj4Jq29\nUSeBw4CfZt+bRAH8UWZe38nPVZrFU0mSJEmSJC1qmTkREb8CfBi4sO2pQ4AXzdDtYeDXShfxMnNT\nRLwQ+CxwettTG6tHk28BF2bmQ12O9a6ISFozaaduBLUCeN4MXcaBt2Xme7oY4/MR8WLgI8ChbU+t\nAM6do/uTtAq1H+h0vNJcti9JkiRJkqRFLzO3ZeYrgJfTmuk5k83AXwGndTLbsk+53Q6cRWup+t2z\nnHpXdc6zM/POHsd6dzXWNbRm1jbZXT3/rMy8socx/gE4BfjDKue5PAT8KXDqIBVOwZmnkiRJkiRJ\nw6WjRdqaSWZeTWvP0+NoLdM/AlhFa9n6fbRuVDRTUXG2uPParyAzx4EraN1k6UzgaVVu0Frqfntm\nfnM+Y7SNdQvwkohYR2t/1yOBDbT2d30AuCEzH5/nGJtp3XTq3RFxFHAmrW0B1tLaimAL8AhwS6+F\n4IVg8VSSJEmSJElPOZl5D3DP/s6jSVUk7UuhdI5xHgf+YQHGuR+4v/Q4JbhsX5IkSZIkSZIaWDyV\nJEmSJEmSpAYu25ckSZIkSRoWyeDveTro+UldcOapJEmSJEmSJDWweCpJkiRJkiRJDVy2L0mSJEmS\nNCwSyNjfWczOZftaRJx5KkmSJEmSJEkNLJ5KkiRJkiRJUgOLp5IkSZIkSZLUwD1PJUmSJEmShkRm\n6zHIBj0/qRvOPJUkSZIkSZKkBhZPJUmSJEmSJKmBy/YlSZIkSZKGRVaPQTbo+UldsHiqwbByFbF0\nTV9D5oYD+hpvyuTS0SJxAVbdu7VY7Lx/U5nAI+UmsMfKFWXirlheJC5ArlhWLPb2ow8sEnf5pm1F\n4gKMPPx4sdi5c2eRuBNPP6ZIXAD++bZysaPQe3EkysQFYrTc52kpuXt3sdixvNznR05Mlom7fXuR\nuABxf7lrzapV5WKXsmdPkbA5MVEkbnGThf5VXvAzb/Tgg4rFnlzf39+jf2z7rjJxgaXfvLNY7Dzu\nyCJxx49YXyQuwOi2ctd61eOFPquj/++X0Z3jfY8pSfPlsn1JkiRJkiRJamDxVJIkSZIkSZIauGxf\nkiRJkiRpWGS0HoNs0POTuuDMU0mSJEmSJElqYPFUkiRJkiRJkhq4bF+SJEmSJGlIBBC5v7OYnYv2\ntZg481SSJEmSJEmSGlg8lSRJkiRJkqQGFk8lSZIkSZIkqYF7nkqSJEmSJA2LrB6DbNDzk7rgzFNJ\nkiRJkiRJamDxVJIkSZIkSZIauGxfkiRJkiRpWGS0HoNs0POTuuDMU0mSJEmSJElqYPFUkiRJkiRJ\nkhpYPJUkSZIkSZKkBu55KkmSJEmSNCyyegyyQc9P6oIzTyVJkiRJkiSpgcVTSZIkSZIkSWpg8VSS\nJEmSJEmSGrjnqSRJkiRJ0rBwz1NpQVk81WDYvp3cvbyvIScPX9fXeFNGdu0pEhcg7nuwWGyWLysS\nNlauLBIXgJEoEnbywFVF4gKMr1tRLPbK7z9cJG6OjRaJC5B7yr1fcmKySNzdBy4tEhegXORyIsq8\nDwEYLffai9Eyi2tyfPhe0yXFiv5+d7fLHTvLxX5ia5G4sXRJkbgAceABReKOLCvz+wFAbt9RLDbj\n40XClnwfTm5+vFhsHn2sSNjJgtcjlpT7p2g8UOZ3prH1a4vEBZhcU+7zdHJZmWsdBYpjk5T7HJWk\nXrlsX5IkSZIkSZIaOPNUkiRJkiRpWLhsX1pQzjyVJEmSJEmSpAYWTyVJkiRJkiSpgcVTSZIkSZIk\nSWrgnqeSJEmSJElDIyBjfycxh0HPT+qcM08lSZIkSZIkqYEzT7sUEccBPwUcAawGNgH3ATdk5vh+\nzu0MYCNwZHXoAeD2zLxl/2UlSZIkSZIkDSeLpx2KiJcBFwNnz3DK5oi4Cnh7Zj66gHktAd4E/Dpw\nwgzn3Al8GHjv/i7wSpIkSZKk3kW2HoNs0POTuuGy/TlExOqI+AzwOWYunAKsB14P3BoR5y1QbhuB\nm4B3M0PhtHIicAVwY0ScuBC5SZIkSZIkScPOmaeziIhR4CrgF2pPPQLcAmyhVbQ8nb27IR8KXBMR\nL8jMrxXM7TDgy8AxtafuBG6r8jmV6UXVM4HrIuLZmflwqdwkSZIkSZKkxcCZp7O7gumF03HgPwNH\nZeZ5mfkrmXkmcBpwY9t5y4AvRMThJZKKiBHgC0wvnG4CzsvMjZn5ksx8cWaeCJwP/LDtvOOAz0eE\nt76TJEmSJEmSZmHxdAYRcTzwu7XDL8/MD2Tm7vaDmfkd4OeYXkDdAFxaKL1XAWe1tTcD52TmdfUT\nM/Na4Bzg8bbD5wAXFspNkiRJkiSVkkPykBYJi6czuxRY0tb+WGZeM9PJmbkDuAhoL6y+tirC9k21\nlcBltcMXZ+a9s+R2D62bXbW7vJrBKkmSJEmSJKmBxbMGEbECeFnt8JVz9cvM22ktp58yBryyj6kB\nnEtr6f2UB4BPdtDvb6tzp5xAawaqJEmSJEmSpAYWT5udB6xsa9+Ymd/rsO9Ha+2X9ielH7ug1v5E\nZk7M1ak6p15k7XdukiRJkiRJ0qJh8bTZi2rtr3bR93pgT1v79Ig4dN4Z7TWf3Ornnj+vTCRJkiRJ\nkqRFzOJps9Nq7Rsbz2qQmU8C364dPnXeGQERsQw4sXb4pi5C3FBrb4yIpfPLSpIkSZIkSVqcLJ42\nO7nWvrPL/nfV2qfMI5d2JwGjbe2HM/OJTjtX5z7admgUeFqfcpMkSZIkSZIWlbH9ncCgiYj1wPra\n4R90GaZ+/sbeM5qmPuu027ym+hzU1t4I3NpzRpIkSZIkacFEth6DbNDzk7ph8XRfa2vt7dVS/G48\nXGsfOI982tVzq4/Tib7nFhGHAAd32e2E+Y4rSZIkSZIklWTxdF+ra+0dPcSo91nTYy51g5rbbwGX\n9iGOJEmSJEmSNDAsnu6rXqDc2UOMeoGyHrNXg5zb/IyNtR59NLmizMt7yYNbisQFYLLg2oYlo3Of\n04uRKBMX2HNofbJ1f+xet6xIXICVdzw690k9ymVl7u82uWZ5kbgAsbLcteaeB4qEXfLEeJG4xZV6\nL46U2x49Rgtuvb6kzPsllhV8Te/o5Wu9M5llvl+yYM6xvOC1Hin0nZiTZeICub3MtY5C3y0AeUx9\nJ6z+ifs3FYmbT/YyN6HD2BMTxWKXUvJzOvr8u/80aw8oEnbygBVF4gJMlvpdvaSJ/n/mZbl/Wiwu\nGYN/sQY9P6kL3jBqbr38a2OhdvcY5NwkSZIkSZKkoebM031tq7V7+fNivU89Zq8GNbe/BD7XZZ8T\ngGv6MLYkSZIkSZJUhMXTfQ1qgbIpzkDklpkP0+XNqyKcwi9JkiRJkqTBZvF0X/UNLVdGxKrMfLKL\nGIfU2j+aZ05T6rl1e4d7KJebJEmSJEkqLRn8DfkGPT+pC+55WpOZjwGP1w4f3WWYY2rtO3rPaNY4\n9XE6USo3SZIkSZIkaVGxeNrsu7X2iV32P36OeL36PtB+m85DImJNp50j4gDgoLZDE1g8lSRJkiRJ\nkhpZPG12a619dqcdI2IV8BNzxOtJZu4C7qod7jg34Jxa+44qpiRJkiRJGhY54A9pEbF42uzaWvt5\nXfR9DtP3kr0lMx+ad0Z7zSe3+rlfnFcmkiRJkiRJ0iJm8bTZl4Adbe2zI+LpHfa9qNb+fF8ymjne\nr0bE6FydqnNePUcsSZIkSZIkSRWLpw0ycztwde3wH8zVLyKeBlzQdmgP8Ok+pgZwPXBPW/so9i2K\nNnk1cGRb+y7g633MS5IkSZIkSVpULJ7O7B3AeFv7ooj4pZlOjojlwEeBpW2HP5KZ9T1K6/2y9nje\nbOdn5gRwae3weyPi2FnGOBZ4X+3wWzNzcraxJEmSJEnSYIkcjoe0WFg8nUFm3g28v3b46oh4Q0S0\nF0iJiJOBrzD9hkyPAZcVSu9TwM1t7fXADRHx8/UTI+I84EZgXdvhG4CrCuUmSZIkSZIkLQpjc5/y\nlHYJcCpwftVeAvwF8LaI+BawFTgeOAOItn67gQsyc1OJpDJzMiIuAG4Cjq4OHw58KSLuAG6r8jkV\nOLHW/V7gpZnp34EkSZIkSZKkWVg8nUVmTkTErwAfBi5se+oQ4EUzdHsY+LXMvL5wbpsi4oXAZ4HT\n257aWD2afAu4MDMfKpmbJEmSJEkqJKvHIBv0/KQuuGx/Dpm5LTNfAbyc1kzPmWwG/go4LTOvXaDc\nbgfOAt4C3D3LqXdV5zw7M+9ciNwkSZIkSZKkYefM0w5l5tW09jw9jtYy/SOAVcAPgfuAr2fm7h7i\nxtxnzdp/HLgCuCIizgSeVuUG8CBwe2Z+cz5jSJIkSZIkSU9FFk+7lJn3APfs7zyaVEVSC6WSJEmS\nJElSH1g8lSRJkiRJGhbueSotKPc8lSRJkiRJkqQGFk8lSZIkSZIkqYHFU0mSJEmSJElq4J6nkiRJ\nkiRJQyKy9Rhkg56f1A2LpxoMq1fCstV9DTmyY09f402JnbuLxAXggDXlYo+NFgk7uXplkbgAT/67\nMrHX3LGlSFyAyTUrisVmYvh+A9l1WH/f1+1WPLKqSNzYsqNIXIDJ0TLvw6IiysVesrRY6FhWKPbE\nRJm4UPY74MntZeIWvB65e7xY7Bgr9Hk6OoSLugr+PxzZsq1Y7IkTjioSN757T5G4ALF0SbnY69cV\niZvLCua8Y1ex2Owq8/kxsnVnkbgAIyU/P3J4focc3VnwdSFJPRrC3/AkSZIkSZIkqTxnnkqSJEmS\nJA2LjNZjkA16flIXnHkqSZIkSZIkSQ0snkqSJEmSJElSA4unkiRJkiRJktTAPU8lSZIkSZKGSe7v\nBKSnDmeeSpIkSZIkSVIDi6eSJEmSJEmS1MBl+5IkSZIkScMiIQZ92f6g5yd1wZmnkiRJkiRJktTA\n4qkkSZIkSZIkNbB4KkmSJEmSJEkN3PNUkiRJkiRpWCSDv6fooOcndcGZp5IkSZIkSZLUwOKpJEmS\nJEmSJDVw2b4kSZIkSdKQiGw9Btmg5yd1w5mnkiRJkiRJktTA4qkkSZIkSZIkNXDZviRJkiRJkp5y\nIuI44KeAI4DVwCbgPuCGzBzfz7mdAWwEjqwOPQDcnpm39HmctcA51TgHAY9WY92QmT/q51jVeGPA\nGcCpwMHAUmBbNebtwG2Zuaff486HxVNJkiRJkqRhkdVjkA14fhHxMuBi4OwZTtkcEVcBb8/MRxcw\nryXAm4BfB06Y4Zw7gQ8D751PgTciTgfeDvwCrQJm3a6I+CJwWWb+S6/jtI23EXgzcCFw4Cyn7oiI\nrwF/lZmfn++4/eCyfUmSJEmSJC16EbE6Ij4DfI6ZC6cA64HXA7dGxHkLlNtG4Cbg3cxQOK2cCFwB\n3BgRJ/Y41iXAzcBLaC6cAiyrnr85In6/l3GqscYi4o+B7wCvY/bCKcAK4IW0iqwDwZmnGggTB65k\nYuXqvsbMJaN9jffjuCuWFYkLELt2F4udy2b6PJyfXUf09/9bu5WbdhaJO7myzLUAyIhisUe37ioS\nd2RHudUoMVHu/cJYoa+wPRNl4pY2USbvWFPuPR6rVhSLzUihvw9PlvluAWBisljoWL2qSNzcvr1I\nXAB2F1wpN1LoszrKzUuIpUvKBB4r+Jou+P9wfO3yInGXFvwej7Vz/Vuxdzla5rUXWwu+x/eUW5GZ\npWLv2FEmLhClfq8BWF7m97Es8fkxrL+HaShExChwFa2Zlu0eAW4BttAqWp4OTH0hHApcExEvyMyv\nFcztMODLwDG1p+4EbqvyOZXpRdUzgesi4tmZ+XAXY/0h8M7a4R3AN2htW3AE8Exg6st2KXBlRGRm\n/kmn41RjrQCuZt9rnrR+rh8AP6K1ZcLxwNMZwFrlwCUkSZIkSZKkGbhsv1dXML2IN05r6f6HMvPH\nM5ki4hRay+KnZqYuA74QEc/IzE39TioiRoAvML1wugm4KDOvq537IuCjwGHVoeOAz0fEuZk551WP\niF8ELq8d/hDwR+3bE0TEwcC7aG0fMOXKiPh2Zl7b4c8VwGeZfs13Au+hdc0faOizktas01cA5WaX\ndcll+5IkSZIkSVq0IuJ44Hdrh1+emR9oL5wCZOZ3gJ8Dbmw7vAG4tFB6rwLOamtvBs6pF06r3K6l\ndXOnx9sOn0MHS9yrmbd/yt5ZtQDvy8zfrO/rmpmPZOZvAH/eHgL4sypOJ34L+KW29ibgjMy8tKlw\nWo27PTOvycz/CLy2w3GKs3gqSZIkSZKkxexSoH0PnI9l5jUznZyZO4CLmD778bVVEbZvqkLkZbXD\nF2fmvbPkdg+tGbPtLq9msM7mNcBJbe3vA2+Zo88l1XlTTqFV7J1VRBxNa6bvlJ3ACzLzu3P1nZKZ\n5fZ36ZLFU0mSJEmSJC1K1b6bL6sdvnKufpl5O63l9FPGgFf2MTWAc2ktvZ/yAPDJDvr9bXXulBNo\nzUCdzWtq7fdl5qw31qief/8ccZr8Ea19TKe8s5rRO5QsnkqSJEmSJA2JACIH/LG/L9J05wEr29o3\nZub3Ouz70Vr7pf1J6ccuqLU/kZlz3jmtOqdeZJ0xt4jYADyn7dBu4NMd5vgpWvvDTnluRKyfZaw1\nTC8yP8m+BdihYvFUkiRJkiRJi9WLau2vdtH3eqB9+fjpEXHovDPaaz651c89f5ZzXwi071X6zczc\n2skgmfkE8K22Q2NVvJlcyPRZp/9Xp2MNKounkiRJkiRJWqxOq7VvbDyrQWY+CXy7dvjUeWcERMQy\n4MTa4Zu6CHFDrb0xIpbOcG7P12CGsWa7Bs+vtb/c5VgDx+KpJEmSJEmSFquTa+07u+x/V619yjxy\naXcS02eDPlzN8uxIde6jbYdGgafNcHo955LX4Fm19o3Q2ns2Il4ZEf8tIu6KiB0R8aOIuDMiPhcR\nr6uW/A8ci6eSJEmSJEladKq9Oev7c/6gyzD18zf2ntE09Vmn3ebV1Gem3OY7VkfjRMTa2li7gbsj\n4rnAbbT2T/0PwPHAcuBAWje7ehnwQeCeiPidLnMrbmx/JyBJkiRJkqRF7YSIrm8j9UhmPjzPcdfW\n2turpfjdqOdw4DzyaVfPrZeftdPc5jtWp+McVms/SOtGVv+VziZwbgDeHxHPBP7XzNwzV4eFYPFU\nkiRJkiRJJV3TQ5/LgHfMc9zVtfaOHmLU+/RraflC5jbfsTodp16kXQ18kr2F0/uA/wJ8DXiM1qzg\nc4HfBo5t6/dq4CHgzV3mWYTFU0mSJEmSpGGR1WOQDU5+9aLhzh5i1AuH9Zi9Wsjc5jtWp+PUi6cH\ntf3354Bfy8x6rJsi4gPAJ4CXtx1/U0Rck5nXd5lr37nnqSRJkiRJkp4KeinrLlQpeCFz67Zfp+fP\nVGf8BvDKhsJpK3jmTuCV1Xnt3trhuEU581SSJEmSJEklvZh979g+l0f6MO62WntFDzHqfeoxe7WQ\nuW0D1s1jrG7GafLmufYvzcw9EXEx0D7T9Ocj4pA+7H07LxZPJUmSJEmShkRk6zHIGvK7KzNv2w+p\nWDzde3x/FU/vy8x/6mSQzPxaRNwNHN92+Lm0lvzvNy7blyRJkiRJ0mK0pdZeGRGruoxxSK39o3nk\n066e28E9xOg0t/mO1ek4Tcdv6nKsm2vtk7vs33cWTyVJkiRJkrToZOZjwOO1w0d3GeaYWvuO3jOa\nNU59nE50mtt8x+p0nPuAXbVjm7oc68Fae0OX/fvO4qkkSZIkSZIWq+/W2id22f/4Wrser1ffByba\n2odExJpOO0fEAUy/m/0EMxc1F+QaZOYErZ+rXb2YOpf6+cu77N93Fk8lSZIkSZKGRQ7JY3DcWmuf\n3WnHaon/T8wRryeZuYt9b6LVcW7AObX2HVXMJj1fg8rPzBGv3b/W2mu7HKt+/mNd9u87i6eSJEmS\nJElarK6ttZ/XRd/nMP1m67dk5kPzzmiv+eRWP/eLs5z7ZabPcj2z01mu1XlntB3aU8WbyX+vtU/t\nZJw2p9Xa93fZv+8snkqSJEmSJGmx+hKwo619dkQ8vcO+F9Xan+9LRjPH+9WIGJ2rU3XOq+eI9WOZ\n+SjwtbZDS4FXdpjjq4Albe1/yszNs5z/90xfev/MiFjfyUARsQ54Vu3w9R1lWZDFU0mSJEmSJC1K\nmbkduLp2+A/m6hcRTwMuaDu0B/h0H1ODVmHwnrb2UexbFG3yauDItvZdwNfn6POJWvv3ImLZbB2q\n599YO/zx2fpk5lamX+9lwBvmyG3KG5i+x+l99GmbhPkYm/sUqbwcC3Ksv7X8iWVz/rGmJ5NHHlgk\nLsCyO/o5+3+63UccUCTunpXl/gYzuj2KxI09k0XiAuw5YMncJ/VodGu3+2x3aM/E3Of0aMmPdhaL\nzWSZ/4+xvWDOI2Ve0wBMlnkvxooVReIC5JIh/DWk5P/DsTLfWwBR6n0+Vu7/YUyU+2yKpUuLxM2C\nn6fFXh9R7jWdazu+50XXxp4cLxJ3ZF2327J1Lku+x3eXuR5kwU0LC772Ykmh38eG9HoUM1Lgd4+S\n37OLyeDtKbqvwcvvHcAr2DuD8qKI+Hxm/remkyNiOfBRWjM0p3wkM+t7lNb71X/y52fmV2c6PzMn\nIuJSphc23xsR/5iZ984wxrHA+2qH35qZc/0D6ePA7wMnVe2TgHcBb5qlz7vbzgf4DvCpOcYBeBvw\ncvZevz+MiC9n5o0zdYiIs4G31sfPLPnh2xlnnkqSJEmSJGnRysy7gffXDl8dEW+IiGl/VY2Ik4Gv\nMP2GTI8BlxVK71PAzW3t9cANEfHz9RMj4jzgRmBd2+EbgKvmGiQzJ4A3M720fXFEfDAiNtTGOSgi\nPgT8XnsI4E1VnLnGugd4T9uhZcB1EfH6iJj2F66IGIuI3wSuY3qx+p9pFbD3uyGc8iFJkiRJkiR1\n5RJaNy86v2ovAf4CeFtEfAvYChxP6+ZI7dOgdwMXZOamEkll5mREXADcBBxdHT4c+FJE3AHcVuVz\nKnBirfu9wEs7nZ2ZmX8fEW8F3tl2+HW09lq9GfhhNfazgPoStEsys36Dq9m8ndas1ZdX7dXAXwLv\nioibgM20CsXPBupLPx4Afjkzd3cxXjEWTyVJkiRJkoZEZOsxyAYxv2qJ/K8AHwYubHvqEOBFM3R7\nGPi1zCx606LM3BQRLwQ+C5ze9tTG6tHkW8CFmdnV/n+Z+a5qe4HL2LuNwQrgeTN0GQfelpnvmeH5\nmcbJiPhVWkXS32x7ai0zX29ozTi9IDMf7Ga8kly2L0mSJEmSpEUvM7dl5itozYa8aZZTNwN/BZzW\n5WzL+eR2O3AW8Bbg7llOvas659mZeWePY727GusaWjNrm+yunn9WZl7Z4zi7MvM/AS8AvgzMtuT/\nVuAi4JxBKpyCM08lSZIkSZL0FJKZV9Pa8/Q4Wsv0jwBW0Vq2fh/w9V6WjGfmvO56lpnjwBXAFRFx\nJvC0KjeAB4HbM/Ob8xmjbaxbgJdExDpa+7seCWygtb/rA8ANmfl4n8b6CvCViDiY1jL9w4GDaG2V\n8FA11v39GKsEi6eSJEmSJEl6yqlubHTP/s6jSVUk7UuhdI5xHgf+ofQ41ViPAH+3EGP1k8VTSZIk\nSZKkYTKAe4pKi5V7nkqSJEmSJElSA4unkiRJkiRJktTAZfuSJEmSJElDIrL1GGSDnp/UDWeeSpIk\nSZIkSVIDi6eSJEmSJEmS1MDiqSRJkiRJkiQ1cM9TSZIkSZKkYZHVY5ANen5SF5x5KkmSJEmSJEkN\nLJ5KkiRJkiRJUgOX7UuSJEmSJA0Ll+1LC8qZp5IkSZIkSZLUwOKpJEmSJEmSJDWweCpJkiRJkiRJ\nDdzzVJIkSZIkjjdl5QAAIABJREFUaVgkxKDvKTro+UldcOapJEmSJEmSJDVw5qkGwti/PcqSJf39\n09T4T/67vsabsmTrniJxASYOX18s9tKHnywT9/7xInEBnjzpoDJxDx8tEhdgzb8VfH0csKxI3NEn\nioQFYOSJHcVi586dReLG0qVF4gJERLnYB64uE3is3PulqFLXuuD/w5Kxc6TQ38t3lHkfAjBa7rWX\n44W+u0rmvHJ5mcDj5b63tjxjQ7HYa6+/t0jcXLOqSFyA2LGrWOzcWSj25ESZuFD0My/GCv0zt+B7\nvOj37TB9J5b8npWkHlk8lSRJkiRJGhbJ4C+LH/T8pC64bF+SJEmSJEmSGlg8lSRJkiRJkqQGFk8l\nSZIkSZIkqYF7nkqSJEmSJA0T9xSVFowzTyVJkiRJkiSpgcVTSZIkSZIkSWrgsn1JkiRJkqQhEdl6\nDLJBz0/qhjNPJUmSJEmSJKmBxVNJkiRJkiRJamDxVJIkSZIkSZIauOepJEmSJEnSsMjqMcgGPT+p\nC848lSRJkiRJkqQGFk8lSZIkSZIkqYHFU0mSJEmSJElq4J6nkiRJkiRJQyKy9Rhkg56f1A1nnkqS\nJEmSJElSA4unkiRJkiRJktTAZfuSJEmSJEnDIqvHIBv0/KQuOPNUkiRJkiRJkhpYPJUkSZIkSZKk\nBi7b10DIDQcyuXxdX2OuuHtzX+NN2Xnc+iJxAca2jReLzcqlRcLGWLm/way894kicZdtXlYkLsCu\n9eVijz2+vUjcXFruqyC2lckZYPLJQrEjysQFGB0tFjpWrSwUuOD1KKlU3iMFr0fJa51l1s5FwZyL\nrvabmCwSNpaV+w7IyTJXZM+hBxaJC7D6BwW/AzasLRJ3ZMu2InEBcuvWcrHH9xSLXUosKfhP0bFC\nsUcKzj0axu+AEq+7PRP9jylJ82TxVJIkSZIkaVi456m0oFy2L0mSJEmSJEkNLJ5KkiRJkiRJUgOX\n7UuSJEmSJA2JqB6DbNDzk7rhzFNJkiRJkiRJamDxVJIkSZIkSZIaWDyVJEmSJEmSpAbueSpJkiRJ\nkjRMcn8nID11OPNUkiRJkiRJkhpYPJUkSZIkSZKkBi7blyRJkiRJGhKRrccgG/T8pG4481SSJEmS\nJEmSGlg8lSRJkiRJkqQGFk8lSZIkSZIkqYF7nkqSJEmSJA2LrB6DbNDzk7rgzFNJkiRJkiRJamDx\nVJIkSZIkSZIauGxfkiRJkiRpWLhsX1pQzjyVJEmSJEmSpAYWTyVJkiRJkiSpgcVTSZIkSZIkSWrg\nnqeSJEmSJElDIrL1GGSDnp/UDYunGgg/OvkAdq1b19eYG771eF/jTVnx/YeKxAXYc3h/r0G72DVe\nKHCUiQvE5GSRuGOPbisSF2B0265isXceeUCRuMse2V4kLkDuLHc9GB0tEja37ygSt7hS12O04CKV\nkYKxS+Vd8DMvRwt+no5PFImbWfBfRpND+K+ugq+PUq/pHYcuKxIXYPnD5b4DRgt9v+T2gt+JE2V+\nr1GDJUvKxC35nTi+p1zsZUuLhM3Ht/Q/6J6t/Y8pSfPksn1JkiRJkiRJauDMU0mSJEmSpGGR1WOQ\nDXp+UheceSpJkiRJkiRJDSyeSpIkSZIkSVIDi6eSJEmSJEmS1MA9TyVJkiRJkoZIuKeotGCceSpJ\nkiRJkiRJDSyeSpIkSZIkSVIDl+1LkiRJkiQNi6weg2zQ85O64MxTSZIkSZIkSWpg8VSSJEmSJEmS\nGlg8lSRJkiRJkqQG7nkqSZIkSZI0JCJbj0E26PlJ3XDmqSRJkiRJkiQ1sHgqSZIkSZIkSQ0snkqS\nJEmSJElSA/c8lSRJkiRJGhZZPQbZoOcndcGZp5IkSZIkSZLUwOKpJEmSJEmSJDVw2b4kSZIkSdKw\ncNm+tKCceSpJkiRJkiRJDSyeSpIkSZIkSVIDl+1rIKy7dQurly/ta8zHf3JdX+NNGd11YJG4AAfc\n+lix2HvWryoSd/TJXUXilhTje8rF3vpksdjLH3ykTODR0TJxgVi1sljs3DV8r72cmCgXeyTKBB4p\n+HfWsXKvvRwtdD2iUNzS9hR67RV8TRdV6v1S8PWx6/A1ReIu3VLuO3HJ4zuKxY5d40Xi5uSQrjMt\n+Vldyli5f4rmsiVF4saQvj5yyxOFAk+WCFogpiTNj8VTSZIkSZKkIRHZegyyQc9P6sYQ/olSkiRJ\nkiRJksqzeCpJkiRJkiRJDVy2L0mSJEmSNExcFi8tGGeeSpIkSZIkSVIDi6eSJEmSJEmS1MBl+12I\niJOBU4EjgaXAg8DdwM2ZObmfcloDnAKcBGwAVgJPAI8B/wJ8NzOd0C9JkiRJkiR1yeLpHCIigN8A\nfhv4iRlOezAiPgFcnplPFs5nBPgZ4JeA5wOnM/sM4s1Vbn+RmXeXzE2SJEmSJJUVmcSAz5Ea9Pyk\nbrhsfxYRcShwHfBBZi6cAhwBXAL8fxHx0wXzOQa4H/gn4M3Amcz9/3A98Ebgtoi4uFRukiRJkiRJ\n0mLjzNMZRMQq4L8DZ9Seuh/4V2AnraXyp7Y9dwJwXUScnZnfL5DWGuDwhuMTwG20thHYDBxIa0bq\nEW3nLAf+LCKOyczfLZCbJEmSJEmStKhYPJ3Zx5heON0K/CZwVfv+phFxFvBxWoVUgHXAP0TEMzJz\nR8H8dgHXAJ8E/jEzn6ifEBE/C/w58Iy2w78TEd/OzA8XzE2SJEmSJJWQ1WOQDXp+Uhdctt8gIs4F\nXtZ2aDfws5n5mfqNoTLzZlp7kN7VdvgEoNTszq3A5cARmXlhZv5dU+G0yu3/Bc4C/rH21BURsbpQ\nfpIkSZIkSdKiYPG02Ttr7Xdl5v+c6eTMfAz49drhP4iIA/qc133AsZn5tszc3EmHavbrfwS2tR3e\nAJzf59wkSZIkSZKkRcXiaU11U6Z/33ZoB/B/ztUvM78K/HPbobXAL/Uzt8zc2mnRtNZvE/B/1w4/\nvz9ZSZIkSZIkSYuTxdN9XVBrfyEzH++w70dr7Zf2IZ9+uaXWPqLxLEmSJEmSNLAih+MhLRbeMGpf\nL6q1v9pF3/q5Px8RI/V9UveTPbX20v2ShSRJkiRJ0gCIiOOAn6I1wWw1sInWlok3ZOb4fs7tDGAj\ncGR16AHg9sysT46b7zhrgXOqcQ4CHq3GuiEzf9TPsYaVxdN9nVZr39hpx8z8XkRsBtZXh1YBxwJ3\n9ye1eTmx1t60X7KQJEmSJEnajyLiZcDFwNkznLI5Iq4C3p6Zjy5gXkuAN9G6r84JM5xzJ/Bh4L3z\nKfBGxOnA24FfoHmC3a6I+CJwWWb+S6/jzDL+SuDbwPG1pz6emRf1e7z5cNl+m+oGT0fWDt/VZZh6\nofSU3jPqj4gYYd/tCP656VxJkiRJkjTAckgeAygiVkfEZ4DPMXPhFFqT4l4P3BoR5y1QbhuBm4B3\nM0PhtHIicAVwY0TUJ8p1OtYlwM3AS5h5ZfKy6vmbI+L3exlnDu9k38LpQHLm6XT1F92jmbm9yxg/\nAH66rb1xfin1xS8DR7e1J4C/20+5SJIkSZIkLaiIGAWuojXTst0jtO4Ts4VW0fJ0IKrnDgWuiYgX\nZObXCuZ2GPBl4JjaU3cCt1X5nMr0ouqZwHUR8ezMfLiLsf6QVuGy3Q7gG7RWKR8BPBNYXj23FLgy\nIjIz/6TTcebI4dnA7/Qj1kKweDrd2lq74xffLH0O7DGXvoiIA4H31g5/KjMf7OMYhwAHd9lttr+i\nSJIkSZIk9dMVTC+cjtNauv+hzNw9dTAiTqG1LH5qZuoy4AsR8YzM7PsWiNVq4S8wvXC6CbgoM6+r\nnfsiWjcrP6w6dBzw+Yg4NzPnnO8bEb8IXF47/CHgj9q3J4iIg4F30do+YMqVEfHtzLy2s59sxhyW\nAh9h72r4rcCa+cQszeLpdKtr7R09xKj32W8vgIgI4GPAUW2HtwBv6fNQvwVc2ueYkiRJkiRJ8xYR\nxwO/Wzv88sy8pn5uZn4nIn4O+Ap7C6gbaNU9/lOB9F4FnNXW3gyck5n3NuR2bUScA3wTWFcdPge4\nEPjsbINUM2//lL2zagHel5kXN4zzCPAbEbENeONUCODPIuLLmTnRyQ82g7ezd4vL+2htofDmecQr\nzuLpdPXi6c4eYtSLp/WYC+kyWvtTtPutfs467ZeJFUuYWDnTNhu9WXNvL7Xvue04dPncJ/Vo/LBy\ntfaxx8pcj9hd7gaEuaK/r4kpsTPmPumpZNeuYqGz4Osjjjxs7pN6kA/8sEhcgJGVK4vFZsu2MnEP\nqi/K6J+Mgu/FUrFL5jz3ZIGelfqs7mCCw2AaGS0SNlevKBIXYPeBZX5tX/P9cjfRjR3lvl/Ys6dc\n7EKi5OdHKSPlco7l5X6nLvb9snv33Of0aumScrFL/a43VuJzqczn82IT2XoMsgHM71Kg/Y32sabC\n6ZTM3BERF9G6odHUP0xfGxHvycy+3RS8KmheVjt8cVPhtC23eyLiYlozUKdcHhH/NTMnZxnuNcBJ\nbe3vM/fkukuA89v6nUKr2PuJOfo1ioifBP6g7dDrmV44HkgDdcOoiPhAROQCPN7RYUq9vN0H4iMi\nIl4LvK12+C8z89P7Ix9JkiRJkqSFFhErgJfVDl85V7/MvJ3WcvopY8Ar+5gawLm0lt5PeQD4ZAf9\n/rY6d8oJtGagzuY1tfb7MnPWv65Uz79/jjgdiYgx4G/YO5HzM5n5xV5iLbSBKp4OgPq0nV6mD9T7\nFJoKNLOI+GXgg7XDn6PcZrx/CZzW5ePFhXKRJEmSJEmach7QvgTsxsz8Xod9P1prv7Q/Kf3YBbX2\nJzpZEl+dUy+yzphbRGwAntN2aDfQ6eS6T9HaH3bKcyNifYd92/3vwBnVf29m73YAA89l+9MNffE0\nIv4XWm+A9vUOfwe8ap57UsyouqtbVzfXGsplS5IkSZIkDYKBWPM6NF5Ua3+1i77XA3vYWz87PSIO\nzcyH+pEY88vtq0xfAn8+rRtgNXkh0+tE38zMrZ0MkplPRMS32Lu8fqyKd1WniUbESUy/V86bqlrS\nUBi04uk1wP0LMM7XZji+pdbu9g7yAIfU2uU2kqqJiBcAV7N3Pw6AL9HaBLncxoOSJEmSJEmD6bRa\n+8ZOO2bmkxHxbfj/2bv/MMmq+sD/70/3/B5+/xIBBQREgWiQRARMgsYg0ayCMWJidsMTY7LJutGY\n5KvJagQfgxoTEzWbjYm/N8aQmFUSWUVXYyIBNFFUEEUYEMMPQWCAYWaYme76fP+oauf2ndvdVdV1\num/1vF/PU88z99S9n/OZmlPV1Z8551xOrTSfDCy6eBoRa4Hja83XDBDiqtrxCRGxJjObNmge+jWo\n9FXdm/Tkfi+MiAngPcDaXtNnM/P9A/a/rFpVPM3MTwOfXsYUbqodHxoRGzJz2wAxjl4gZhER8WN0\ni8/Vndf/CTh/oT0sJEmSJEmSVqgn1o5vHvD6Tcwunp4EfHZRGXWdyOzZoPdk5kP9XtybEXovcEiv\naRJ4PHB9w+kn1Y6HeQ3mizeflwNn9f68HfiVAftedu55WtEbpPU70R83YJhja8ffGD6j/kTEWcDH\nmb2Hx5XAf8rMMrdYlyRJkiRJarHe3pz1/Tm/M2CY+vknDJ/RLPVZp4Pm1XTNXLkttq+hXoOIOAa4\npNJ0cWYOWrhddq2aedoS1wNHVI7PAK7r58KIeAJwcKVpG3Dr6FJr7PN04BPAPpXma4DnZObWkn1L\nkiRJkqQllhBt3/N0z/yOG+LeJ98bwb6YB9SOtw1RK6nnsP8i8qmq5zbM37Xf3Bbb17CvwV8CG3t/\n/irwRwP22woWT/f0SeCcyvHZwF/0ee3ZteMrMrMzgpwaRcRpdPc03bfS/O/Auf1u/CtJkiRJklTY\nZUNcczFw0SL73ad2PMzq3Po1+zaeNbilzG2xfQ38GkTES4Fn9Q47wMsyc2rAflvBZft7+mjt+LyI\nqFfo53LhArFGJiKeDHyK2dX+rwDnZGb9xleSJEmSJEl7m3rR8JEhYtQLh/WYw1rK3Bbb10CvQUQc\nAfxhpekdmflvA/bZGhZPazLz28DnK03rgVcsdF3vhk3VO489APzDSJPb3ddJdG+sVd234zrgWZm5\nuUSfkiRJkiSpBXJMHu00TGZL9bdZytwGvW7Q8/+M3VsF3Aa8dsDrW8Vl+81+l9kF1N+NiMsz89+b\nTu5tQPyeWvNbFpoB2ts4t74n6rG9Au5c15wAfAY4tNL8DbqF0/vm60+SJEmSJGkZPJ8979i+kO+N\noN+Ha8frh4hRv6Yec1hLmdvDwIGL6Kvv1yAiXkz333vGr477PXksnjbIzCsj4iPAC3tNa4DPRMSv\nAH9b3ce0d8OmDwDHVUJsAt4x6rwi4rF0C6eHV5rvBn4R2NArxvZrKjNvH112kiRJkiRJjTZl5teX\noV+Lp7vbixdPI+IQZtfDPpyZnxiwr9axeDq3C+kWRE/tHe8HfBj4g4j4KrATeDxwSu26zcBzM3Nb\ngZyeCTym1vYo4OohYt0GHLPYhCRJkiRJklqqviJ4Q0RsHHAm5GG14wcWmdOMem6HNp41v35ze5DZ\n9aRB++q3n3dUYt8PvHLAflrJ4ukcMnNrRDwH+CvgxytPPYY9C5gzNgE/m5k3ls5PkiRJkiTtfSK7\njzZrS36ZeV9EbGb2rMvH0t3+sF9H145vWnRizXHq/fSj39xuYvbkv0H7WrCfiDgR+NlK05/Q3yrp\n+k3a96ld08nM7/SVZSHeMGoemfld4CeA/0r3hkxzuQt4C/Dkcb57mCRJkiRJ0gpTL5QeP+D1j1sg\n3rBuBKYrx4dFxL79XhwR+wGHVJqmmbt4uhSvQX1p/xvo3udnoUf9Ju0/XXv+awPmOnLOPF1AZibw\nLuBdvbvcnwIcQXcf1DuBW4BrqvugDhD720AMcP77gfcP2o8kSZIkSdJe6nrgzMrxGcA/9nNhRGwE\nntQQb9Eyc0dEbKK7JWQ1t0/1GeLM2vFNmbljjnPrOZ/RZx8zzlog3opm8XQAmXkDcMNy5yFJkiRJ\nkqS+fBL45crx2QNc+yPMrp1dm5l3jyKpnk8yu3h6Nv0XT8+uHc93Y6ZP052ZOtk7Pi0i9s3MLQt1\n0psN+5RK01Qv3l7DZfuSJEmSJEnjInM8Hu1xBbC9cnxGRDyhz2svrB1/dCQZzR3vP0fEZOOZFb1z\nfn6BWN+XmfcCV1aa1gA/12eOLwFWV47/JTPvb+jjK5kZgz6Ai2uhPlA7p74n6pKzeCpJkiRJkqQV\nKTO3AR+pNb96oesi4vHA+ZWmKeCvR5gawOfp7us54yj2LIo2+XngyMrxJuBfF7jmg7Xj34iItfNd\n0Hv+lbXmD/SR34pi8VSSJEmSJEkr2UXArsrxhRHxvLlOjoh1wPvoztCc8Z7M3DRfJxGRtcfZ852f\nmdPA62vNb5vvDvW95/641vzaPu7F8wG6N6macSJwyQLXvKl33owbgA8tcM2KY/FUkiRJkiRpTAQQ\n2fLHcr9INZl5C/D2WvNHIuLlEVEtkBIRTwQ+w+wbMt3HnsvLR+VDwBcqxwcBV0XEOfUTI+LZwNXA\ngZXmq4BLF+qkV6j9LaC6p8KrIuJdEXFwrZ9DIuIvgN+ohgB+sxdnr+INoyRJkiRJkrTSvQY4GfjJ\n3vFq4J3A6yLiy8AW4HF0b45Urf/uBM7PzLtKJJWZnYg4H7gGeGyv+dHAFRFxE/D1Xj4nA8fXLv82\n8ILM/jaZzcyPR8Rrgd+vNP8y3b1WvwB8t9f3U4H1tctfk5mf7PsvtoJYPFUr5GSQk6OdCL36zs0j\njTdj1be2FokLwPRCs+wXYVWZt3uM+N+tKtccuPBJQ+jss65IXICJTrl/w1L/e5tRcBHCrp3lYt9b\n5j0eGzcWiQuQWwt+fuws81rHxEFF4gLEdLn/tM7JQl9xCt78IHYV/E/8HQXfi6VMlJuzEqsWvA/D\nUHYetk+RuAD7fv2+MoEL/tyi5Hu8VN4Fxx3ZtnlYfZgs814ByHVrFj5pSDFVaOyVHNNbtxWLXcq2\nM+s1nMXbvmUD/PPIw0pAd+ZlRLwIeDdwQeWpw4Bz57jsHuAXMvPzhXO7KyJ+Avgb4NTKUyf0Hk2+\nDFyQmXcP2NclEZF0Z9LO3AhqPXD2HJfsAl6XmX8wSD8ricv2JUmSJEmStOJl5sOZ+WLgZ+jO9JzL\n/cD/Ak5ZqtmWmfkt4HTgd4Bb5jl1U++cp2XmzUP29aZeX5fRnVnbZGfv+adm5luG6WelcOapJEmS\nJEnSuEhm71rZRi3PLzM/QnfP02PpLtM/AthId9n6bcC/ZubAS3cyF7fMIDN3AW8G3hwRpwGP7+UG\ncCfwrcz80mL6qPR1LXBeRBxId3/XI4GD6e7vegdwVWaWWe43O4+L6N7Qq7UsnkqSJEmSJGmvk5m3\nArcudx5NekXSkRRKF+hnM3B56X7Gmcv2JUmSJEmSJKmBM08lSZIkSZLGRHS6jzZre37SIJx5KkmS\nJEmSJEkNLJ5KkiRJkiRJUgOLp5IkSZIkSZLUwD1PJUmSJEmSxkX2Hm3W9vykATjzVJIkSZIkSZIa\nWDyVJEmSJEmSpAYu25ckSZIkSRoTkd1Hm7U9P2kQzjyVJEmSJEmSpAYWTyVJkiRJkiSpgcVTSZIk\nSZIkSWrgnqeSJEmSJEljIyHbvqlo2/OT+ufMU0mSJEmSJElqYPFUkiRJkiRJkhq4bF+SJEmSJGlM\nRHYfbdb2/KRBOPNUkiRJkiRJkhpYPJUkSZIkSZKkBhZPJUmSJEmSJKmBe56qFVZt3saqbVtGG3Rq\nerTxZkS5/3PIqZ3FYkehuJ0t2wtFhokok3Xn4AOKxAWYPnDfYrEndk4ViRvbdxSJC8CO1eVidzpl\n4q5bWyYuwI6Cr3Uhcf+DxWLnxvXFYk88UubzNCfL/QyIHbuKxc6pMp8fRRX6GQDA+nVFwmbJnLPM\n5nFR6vsSlPsuVtLE5HJn0CqxutzP8Zws91qX2moxVhX89Xmi3O8B7CrzM+DhR4/+9di+1hJFX5Jy\nA31U2p6fNABnnkqSJEmSJElSA4unkiRJkiRJktTAOfGSJEmSJEnjIiHaviy+7flJA3DmqSRJkiRJ\nkiQ1sHgqSZIkSZIkSQ0snkqSJEmSJElSA/c8lSRJkiRJGheZ3UebtT0/aQDOPJUkSZIkSZKkBhZP\nJUmSJEmSJKmBy/YlSZIkSZLGRGT30WZtz08ahDNPJUmSJEmSJKmBxVNJkiRJkiRJamDxVJIkSZIk\nSZIauOepJEmSJEnSOHFPUWnJOPNUkiRJkiRJkhpYPJUkSZIkSZKkBhZPJUmSJEmSJKmBe55KkiRJ\nkiSNicjuo83anp80CGeeSpIkSZIkSVIDi6eSJEmSJEmS1MBl+5IkSZIkSeOik91Hm7U9P2kAFk/V\nDlu2wva1o425bsTxenLLliJxATo7dxWLPbFmdZnAk5Nl4gL5yI4icaPTKRIXYOL+rcViTx+6f5nA\nG9aUiQswVfC13vpImcAFx0ccdECx2Lm9zOtR6n0IEMUiU+6z6eGdZeICmeXGHlnoF5iSvxitKvfz\npbNhXZG4qwqOj9hRLnYx09PFQkcU+gSZLPfJNJZlhLUFvyOU+lwCYtdUmcCTBRduTpT7zOPRBxUJ\nO1HgZZ4o97EhSUNz2b4kSZIkSZIkNbB4KkmSJEmSJEkNXLYvSZIkSZI0LpL27wXS9vykATjzVJIk\nSZIkSZIaWDyVJEmSJEmSpAYu25ckSZIkSRoTkd1Hm7U9P2kQzjyVJEmSJEmSpAYWTyVJkiRJkiSp\ngcVTSZIkSZIkSWrgnqeSJEmSJEnjJN1UVFoqzjyVJEmSJEmSpAYWTyVJkiRJkiSpgcv2JUmSJEmS\nxkRk99Fmbc9PGoQzTyVJkiRJkiSpgcVTSZIkSZIkSWpg8VSSJEmSJEmSGrjnqSRJkiRJ0rjI3qPN\n2p6fNABnnkqSJEmSJElSA4unkiRJkiRJktTAZfuSJEmSJEljIjKJbPe6+LbnJw3CmaeSJEmSJEmS\n1MDiqSRJkiRJkiQ1cNm+2mH9WmLN+tHG3DU12ng9Od0pEheAznS52BNri4SNfTYWiQuQjz6kSNyJ\nh7YViQuQG0c8jismNt1RJO72px5XJC7Ams07isWePmBDkbgTOwu+D3eW+VwCYMvDRcLGxjKvM0Bu\n314sNp1CS8Wy4M+AVX4tWyq5rsxrPfHA1iJxiyr1XiktYrkzGFhMjuG8lcnJYqFjquDP21Kxp8vl\nXHJ8PHTywUXiTuwa/efHxNSYfiZJWtH8li5JkiRJkjQuOr1Hm7U9P2kAY/jfn5IkSZIkSZJUnsVT\nSZIkSZIkSWrgsn1JkiRJkqSxkUS2fX/Ytucn9c+Zp5IkSZIkSZLUwOKpJEmSJEmSJDWweCpJkiRJ\nkiRJDdzzVJIkSZIkaVwk7d9StO35SQNw5qkkSZIkSZIkNbB4KkmSJEmSJEkNXLYvSZIkSZI0LjK7\njzZre37SAJx5KkmSJEmSJEkNLJ5KkiRJkiRJUgOLp5IkSZIkSZLUwD1PJUmSJEmSxkRk99Fmbc9P\nGoQzTyVJkiRJkiSpgcVTSZIkSZIkSWpg8VSSJEmSJEmSGrjnqSRJkiRJ0rjI7D7arO35SQNw5qkk\nSZIkSZIkNbB4KkmSJEmSJEkNXLavdtiylVy1drQxJ2K08WbC7r9vkbildY55dJnAU50ycYGJ+x4q\nEvfucx5TJC7Awdc9XCz2qo0bisRdvWVXkbgA244skzPAvjduLhJ3av/1ReICTKyeLBZ7cv/9ygTe\nsbNMXIBVBb+GTE0VClzu3zDWjvjnYEWWej12lvv8KKmzpsy/4+TUdJG4YyvKfBcDYGIM54B0yn1n\n8vWoKfV6FBzTuavc5+nDh5f5zFv7YMF/Q80rEqLlL3+4al8ryBj+lJUkSZIkSZKk8iyeSpI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ruPNmt7ftIAXLZfExFPB15YadoJPDMzP1y/MVRmfgE4C9hUaT4OeEXxRJu9HTis9+cvAh9bpjwk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\nwlMAAAAAgA7hKQAAAABAx/8BTAmgS/SFp2gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113541e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot output of network as a function of 2D input values\n",
    "plt.imshow(y_2D,origin='lower',extent=[-0.5,0.5,-0.5,0.5],interpolation='nearest')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hGKNTxQLXkzlUHrFCCQXJuH23CI3DSvZDPsbfjOsq7h0se7fksm765TfD33lQ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\nNltxQzPAftuj+e94W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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a15320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# MODIFIED HERE FOR VISUALIZATION:\n",
    "# plot all the intermediate results\n",
    "# lay them out nicely in a grid of images\n",
    "ncols=5\n",
    "nrows=4\n",
    "fig,ax=plt.subplots(ncols=ncols,nrows=nrows,figsize=(ncols,nrows))\n",
    "for j in range(ncols*nrows):\n",
    "    # actually drawing the image:\n",
    "    ax[int(j/ncols),j%ncols].imshow(np.reshape(y_stored[j,],[M,M]),origin='lower')\n",
    "    ax[int(j/ncols),j%ncols].axis('off')\n",
    "plt.subplots_adjust(wspace=-0.15,hspace=0)\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}