15_autoencoders.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 15 – Autoencoders**\n",
    "\n",
    "autoencoders are capable of randomly generating new data that looks very similar to the training data, this is called a generative model.\n",
    "\n",
    "internal representation has a lower dimensionality than the input data, so that it's forced to learn the most important features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 15._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "import sys\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "def reset_graph(seed=42):\n",
    "    tf.reset_default_graph()\n",
    "    tf.set_random_seed(seed)\n",
    "    np.random.seed(seed)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"autoencoders\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A couple utility functions to plot grayscale 28x28 image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_image(image, shape=[28, 28]):\n",
    "    plt.imshow(image.reshape(shape), cmap=\"Greys\", interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_multiple_images(images, n_rows, n_cols, pad=2):\n",
    "    images = images - images.min()  # make the minimum == 0, so the padding looks white\n",
    "    w,h = images.shape[1:]\n",
    "    image = np.zeros(((w+pad)*n_rows+pad, (h+pad)*n_cols+pad))\n",
    "    for y in range(n_rows):\n",
    "        for x in range(n_cols):\n",
    "            image[(y*(h+pad)+pad):(y*(h+pad)+pad+h),(x*(w+pad)+pad):(x*(w+pad)+pad+w)] = images[y*n_cols+x]\n",
    "    plt.imshow(image, cmap=\"Greys\", interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA with a linear Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build 3D dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "rnd = np.random\n",
    "\n",
    "rnd.seed(4)\n",
    "m = 200\n",
    "w1, w2 = 0.1, 0.3\n",
    "noise = 0.1\n",
    "\n",
    "angles = rnd.rand(m) * 3 * np.pi / 2 - 0.5\n",
    "data = np.empty((m, 3))\n",
    "data[:, 0] = np.cos(angles) + np.sin(angles)/2 + noise * rnd.randn(m) / 2\n",
    "data[:, 1] = np.sin(angles) * 0.7 + noise * rnd.randn(m) / 2\n",
    "data[:, 2] = data[:, 0] * w1 + data[:, 1] * w2 + noise * rnd.randn(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(data[:100])\n",
    "X_test = scaler.transform(data[100:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the Autoencoder..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "reset_graph()\n",
    "\n",
    "n_inputs = 3\n",
    "n_hidden = 2  # codings\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "hidden = tf.layers.dense(X, n_hidden)\n",
    "outputs = tf.layers.dense(hidden, n_outputs)\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X))\n",
    "\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(reconstruction_loss)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iterations = 1000\n",
    "codings = hidden\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for iteration in range(n_iterations):\n",
    "        training_op.run(feed_dict={X: X_train})\n",
    "    codings_val = codings.eval(feed_dict={X: X_test})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_autoencoder_pca_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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otfQ/W+PS+jhPPbWwTujAgYXeixlcdx1s3Nj/687aXma4QMKAcfcjnL7h9w/N7CVgFfBy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\nEs3/AQcsVH7eWduMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa5eed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4,3))\n",
    "plt.plot(codings_val[:,0], codings_val[:, 1], \"b.\")\n",
    "plt.xlabel(\"$z_1$\", fontsize=18)\n",
    "plt.ylabel(\"$z_2$\", fontsize=18, rotation=0)\n",
    "save_fig(\"linear_autoencoder_pca_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacked Autoencoders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use MNIST:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting /tmp/data/train-images-idx3-ubyte.gz\n",
      "Extracting /tmp/data/train-labels-idx1-ubyte.gz\n",
      "Extracting /tmp/data/t10k-images-idx3-ubyte.gz\n",
      "Extracting /tmp/data/t10k-labels-idx1-ubyte.gz\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"/tmp/data/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train all layers at once"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's build a stacked Autoencoder with 3 hidden layers and 1 output layer (ie. 2 stacked Autoencoders). We will use ELU activation, He initialization and L2 regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "from functools import partial\n",
    "\n",
    "# symmatrical layers\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150  # codings\n",
    "n_hidden3 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01\n",
    "l2_reg = 0.0001\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "\n",
    "he_init = tf.contrib.layers.variance_scaling_initializer() # He initialization\n",
    "#Equivalent to:\n",
    "#he_init = lambda shape, dtype=tf.float32: tf.truncated_normal(shape, 0., stddev=np.sqrt(2/shape[0]))\n",
    "l2_regularizer = tf.contrib.layers.l2_regularizer(l2_reg)\n",
    "my_dense_layer = partial(tf.layers.dense,\n",
    "                         activation=tf.nn.elu,\n",
    "                         kernel_initializer=he_init,\n",
    "                         kernel_regularizer=l2_regularizer)\n",
    "\n",
    "hidden1 = my_dense_layer(X, n_hidden1)\n",
    "hidden2 = my_dense_layer(hidden1, n_hidden2)\n",
    "hidden3 = my_dense_layer(hidden2, n_hidden3)\n",
    "outputs = my_dense_layer(hidden3, n_outputs, activation=None)\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X))\n",
    "\n",
    "reg_losses = tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)\n",
    "loss = tf.add_n([reconstruction_loss] + reg_losses)\n",
    "\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(loss)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver() # not shown in the book"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's train it! Note that we don't feed target values (`y_batch` is not used). This is unsupervised training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train MSE: 0.0204011\n",
      "19% Train MSE: 0.0114192\n",
      "2 Train MSE: 0.0102221\n",
      "3 Train MSE: 0.00989991\n",
      "4 Train MSE: 0.0103724\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 5\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\") # not shown in the book\n",
    "            sys.stdout.flush()                                          # not shown\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch})\n",
    "        loss_train = reconstruction_loss.eval(feed_dict={X: X_batch})   # not shown\n",
    "        print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)           # not shown\n",
    "        saver.save(sess, \"./my_model_all_layers.ckpt\")                  # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function loads the model, evaluates it on the test set (it measures the reconstruction error), then it displays the original image and its reconstruction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_reconstructed_digits(X, outputs, model_path = None, n_test_digits = 2):\n",
    "    with tf.Session() as sess:\n",
    "        if model_path:\n",
    "            saver.restore(sess, model_path)\n",
    "        X_test = mnist.test.images[:n_test_digits]\n",
    "        outputs_val = outputs.eval(feed_dict={X: X_test})\n",
    "\n",
    "    fig = plt.figure(figsize=(8, 3 * n_test_digits))\n",
    "    for digit_index in range(n_test_digits):\n",
    "        plt.subplot(n_test_digits, 2, digit_index * 2 + 1)\n",
    "        plot_image(X_test[digit_index])\n",
    "        plt.subplot(n_test_digits, 2, digit_index * 2 + 2)\n",
    "        plot_image(outputs_val[digit_index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_all_layers.ckpt\n",
      "Saving figure reconstruction_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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EBDIAJCCQASABgQwACQhkAEhAIANAAgIZABIQyACQgEAGgAQEMgAkIJABIAGBDAAJCGQA\nSEAgA0ACAhkAEhDIAJCAQAaABBbN0bxvztG8MFMWzPUNHCqGh4d9XxyCFiyI/8TefHN+/ZcYHBzc\nr+8Lb8gAkIBABoAEBDIAJCCQASCBuWrqAuD/iBqYas1LtaanNjppkJrJpqrDDvNe+H95EgCQgEAG\ngAQEMgAkIJABIAGBDAAJCGQASMCyJ+CQN5PLi2pjRUt8omtqY+3bt69VPZp70aI4Bvbu3VusR89k\namoqHCuaP5qjthwq+hnbzp3N/LhLADjICWQASEAgA0ACAhkAEhDIAJCALutZ9rOf/Sz8bPfu3cX6\n+vXri/Uf/vCHref/+te/Xqx/6EMfKtY/8IEPtJ4D5ptaJ3XbDuioa7hp4i7kiYmJYn18fDwca+fO\nneFnJVGncTR30zTNwoULi/Wurq5ifWBgIByrr6+vWO/t7Q2vaSvqGO/kMIyZOryjDW/IAJCAQAaA\nBAQyACQgkAEgAYEMAAks6KT7bAbMyaSz6Ytf/GKx/oMf/GCW72T/vOtd7yrW//znP4fXLFu27EDd\nznww+y2Yh6jh4eED/n1R+x6MuqajDujR0dFwrOHh4WL92WefLdYfffTRcKx//vOfxfqWLVuK9cHB\nwWK99rP39/cX62vWrCnWo9UaTdM0p512WrF+1FFHFeu1/aqje446xjvpoo+u6SQzBwcH9+v7whsy\nACQgkAEgAYEMAAkIZABIQCADQAICGQAScLjENM3G8qZTTz21WP/EJz5RrG/YsCEc66abbirW//GP\nfxTrv/71r8OxPv/5z4efQUbRUpraEptoeVNU37ZtWzjWQw89VKzfe++9xfoTTzwRjjU5OVmsr169\nulhfvnx5sb506dJwjueee65Y37p1a7G+ffv2cKzocItODoSIljdF1+zZsyccq7u7O/ys7X1N90AK\nb8gAkIBABoAEBDIAJCCQASABgQwACeiy3g8vv/xy+NmPfvSjVmOdccYZ4Wd33nlnsR5t8B51B0ab\n4TdN0/zrX/8q1v/yl78U66+99lo4Fsw3nXTBRl3AUZfzwoULw7GizuzomgsuuCAc68wzzyzWzzvv\nvGL98MMPL9affPLJcI6f//znxfobb7xRrL/++uvhWFGn88jISHhNJOqKr3VTR8bGxor1vr6+1mNN\nlzdkAEhAIANAAgIZABIQyACQgEAGgAR0We+HWqdxtK9p1E199913h2MtXry43Y0FbrzxxvCzRx55\npNVYl1xyyTTvBvKI9lOu7U8cdVlHHdvRPstN0zRDQ0PF+llnnVWsf/jDHw7Hiva4j1Zl7Nq1q1h/\n9dVXwzk2btxYrEed0bUVHl1dXcV6Jx3T0TPu6elpNXdtrGj+6P9D09jLGgAOCgIZABIQyACQgEAG\ngAQEMgAkIJABIAHLnvbDaaedFn4WLYmKDn6YjQ3LawdedLL5Osw30fKTaPlL7UCIqampYn3lypXF\nerTsqHZfp5xySqt608T3HC1Jevrpp4v1O+64I5wjuiZapnXCCSeEYx155JHFevS8tm/fHo4VLVOL\nvl9ry5GiQ0Kia6a7tKnGGzIAJCCQASABgQwACQhkAEhAIANAArqsp2nZsmVzNvfNN99crD/xxBOt\nx7rggguK9dWrV7ceC+ZadIhE2+7r//ZZSW9vb+uxOjn0YnR0tFjfunVrsf7www8X6y+88EI4R9RJ\n/p73vKdYP/HEE8Oxoq7wsbGxYn18fDwcKzrEIuqYHhgYaH1f0aEXtd/JdHlDBoAEBDIAJCCQASAB\ngQwACQhkAEhAl/U88NhjjxXrX/jCF4r1iYmJcKyjjz66WL/uuuuK9bYdpjBbansKt+2ErY0VdeFG\nnb61sRYtKn/lRh29tT22d+/eXaxv2bKlWH/++efDsSLR3tRnnnlmsV7bx3vz5s2t5q51q7d9XrWO\n7U463A8Ub8gAkIBABoAEBDIAJCCQASABgQwACQhkAEjAsqd54IEHHijWa8ubIldeeWWx/s53vrP1\nWJBVtGSlk6VK0bKYaOnN1NRUOFa07Kmnp6f1WNEhEvfee2+xfscddxTrS5cuDeeIljedfPLJxXpt\nmWT0fRUtlaqNFf1+a7/HSPQ76UQn8/8nb8gAkIBABoAEBDIAJCCQASABgQwACeiyTuTyyy8v1n/5\ny1+2GufLX/5y+NlXv/rVVmNBVrXN/9t2u9a6maN5oi7rqJO7aeIDE/bs2VOsR53UTdM0d911V7F+\n++23F+vRoRPr1q0L5zj33HOL9VWrVhXro6Oj4VgjIyPF+rJly4r12nPs5NlHaodYlNT+3033QApv\nyACQgEAGgAQEMgAkIJABIAGBDAAJ6LKeZbt27Qo/i/aaHR8fL9ZXrlxZrF977bXhHN3d3ZW7g4ND\n272sa92xUQd09Le0cOHC/3J3/1v0vbB+/frwmnvuuadYj7qp3//+9xfrF198cTjHaaedVqxHz6v2\nHKP9uiOTk5PhZ233n65970X/J6LO+1oHv72sAeAgIJABIAGBDAAJCGQASEAgA0ACuqxn2aWXXhp+\nNjw83Gqsq666qlhfsWJFq3HgUBHtgXzYYfG7SdTt29XVVazXOm2jju2dO3cW6xs3bgzHeuaZZ4r1\no48+uli/6KKLivXTTz89nGNgYKBYj+63tpd01IEd7X8dzdE0TbN06dJWc9T2Km/bGT2Te6j//7wh\nA0ACAhkAEhDIAJCAQAaABAQyACQgkAEgAcueDpBoU/j77ruv9Vgf//jHi/Wrr7669VhwKIuWrNQO\nMogOi4jqtYMPNm3aVKw/9NBDxfrdd98djrVt27Zi/ZxzzinWTz755GK9tozntddeK9Z37NhRrNcO\ncYiecbRUqJNDOqLla7XlSG0Pl4iWu80Eb8gAkIBABoAEBDIAJCCQASABgQwACeiynqaxsbFi/Zpr\nrinWo83la6LN32sdjcD/FnXb1jqjo67a3t7eYr32Nz4yMlKsP/LII8X63/72t3CsoaGhYv1973tf\nsT44OFis17qZo07jww8/vFivdSBHndlRl3M0R9PE9xwdHhLN3TRxZ/aB7KaOeEMGgAQEMgAkIJAB\nIAGBDAAJCGQASECX9TRdf/31xfo999zTeqzLL7+8WLdnNbQTdVO3rTdN3NEbdQfXOnr//ve/t6rX\nOo0/9alPFesXXnhhsR51Zde6wkdHR4v1aIVHbeVH9Byj+ZcsWdL6vqK9t8fHx8Ox+vv7i/XoZ6n9\nX5kub8gAkIBABoAEBDIAJCCQASABgQwACQhkAEjAsqdpuvbaa2dsrO985zvFukMkoJ3okIHoIIGa\naJlLtPRm69at4Vjr168v1rdv316sH3nkkeFYZ599drF+xBFHFOvRz97JYRgDAwPFeu2QjmjpUbQc\natu2beFY0fKmF198sVivLR9bunRpsR793t98881wrOkuifKGDAAJCGQASEAgA0ACAhkAEhDIAJCA\nLutEdu3aVax30hnaVk9PT7EedUA2Tby5/sTEROv5x8bGivXrrruu9ViR6Gepdcp3dXXN2PzMrE66\nXaN67W+s7eESte7g5557rljfsGFDsR4dCNE0TfPoo48W61GXddTlvHv37nCOTZs2FevRwQ+1AyEW\nL15crEe/k6effjoc65lnnmk1//nnnx+OFf0ea/+/DhRvyACQgEAGgAQEMgAkIJABIAGBDAAJ6LJO\n5Nhjj52zua+88spi/Zhjjgmv2bJlS7H+/e9/f0buabbUnvsVV1wxi3dCG53sGxztcR2tMmiauNu2\ntgIhEnXtR3st11Ys3HrrrcX6Pffc0+qeBgcHw89ef/31Yj3q/u7v7w/HWrZsWbH+yiuvFOvPP/98\nONaKFSuK9TPPPLNYj1aw1ESd9/ayBoCDnEAGgAQEMgAkIJABIAGBDAAJCGQASMCyp2m67LLLivUb\nbrhhlu9keq6//voDPseiRfF/t7ZLSD73uc+Fn5111lmtxjrnnHNa/Xvmr2hZSrQcqiY6lCBaktM0\nTXPyyScX6zt27CjWR0dHw7FGRkaK9egAi6mpqWJ9+fLl4RwDAwPF+ubNm4v1VatWhWNFf+PR0q7a\nEqoTTzyxWH/7299erNeWdrX97pnu0qYab8gAkIBABoAEBDIAJCCQASABgQwACSyobZR9AM3JpLPp\nJz/5SbG+Z8+eGZvjiSeeKNZn8nCHr3zlK+FnUUdj5OKLLw4/q3VBJnXgWi35fwwPD7f+vog6YaN6\ndJBA0zRNd3d3sT4+Pl6sRx3TTdM0r776arG+cePGYr3WZR11Uw8PD4fXlEQHSDRNfChD1Jm9evXq\ncKwlS5YU61EGRYdRNE383bNy5cpi/cgjjwzH6u3tLdajg0Bqq0Uig4OD+/V94Q0ZABIQyACQgEAG\ngAQEMgAkIJABIAFd1tAZXdazpJMu60jUZR11Uteuib47a3sdT05OFuvRXtq1jt5oL+2oa3r37t3F\nerQvde2aqGt5aGgoHKvtfuG1bIqeS09PT7Fe2xc7eo6ddFNHdFkDwDwikAEgAYEMAAkIZABIQCAD\nQAICGQASsOwJOmPZ0yyZjWVPCxcuDK+JDp6oLW9qO//U1FSxXlt6Ex1+EC39iURz1z6Lfo5oCVFt\nrGg5VG2saPlYJ0uYOjlwpC3LngBgHhHIAJCAQAaABAQyACQgkAEggZnbPRsguWhVSa2jN/osGqu2\nciXqKJ7Jju2JiYliPeoart3v2NhYsR51LXdyGEYn2na+155vJ8/+QPGGDAAJCGQASEAgA0ACAhkA\nEhDIAJCALmvgkNfJnv7RNbWu3WjP7OiaaM/m2vzRntFRl3NtL+uZ7EBu22Ee/fummdl9pjM5OH8q\nAJhnBDIAJCCQASABgQwACQhkAEhAIANAApY9AXQgWq5TW0LV9prasqNoWVDbQyS6u7vDOTo5rKHt\nWJ3o5HnNB96QASABgQwACQhkAEhAIANAAgIZABJY0Mmm6gDAzPKGDAAJCGQASEAgA0ACAhkAEhDI\nAJCAQAaABAQyACQgkAEgAYEMAAkIZABIQCADQAICGQASEMgAkIBABoAEBDIAJCCQASABgQwACQhk\nAEhAIANAAgIZABIQyACQgEAGgAQEMgAkIJABIAGBDAAJCGQASOB/AJrX8D+McXeHAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103380e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_reconstructed_digits(X, outputs, \"./my_model_all_layers.ckpt\")\n",
    "save_fig(\"reconstruction_plot\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tying weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is common to tie the weights of the encoder and the decoder (`weights_decoder = tf.transpose(weights_encoder)`). Unfortunately this makes it impossible (or very tricky) to use the `tf.layers.dense()` function, so we need to build the Autoencoder manually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150  # codings\n",
    "n_hidden3 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01\n",
    "l2_reg = 0.0005"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "activation = tf.nn.elu\n",
    "regularizer = tf.contrib.layers.l2_regularizer(l2_reg)\n",
    "initializer = tf.contrib.layers.variance_scaling_initializer()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "\n",
    "weights1_init = initializer([n_inputs, n_hidden1])\n",
    "weights2_init = initializer([n_hidden1, n_hidden2])\n",
    "\n",
    "weights1 = tf.Variable(weights1_init, dtype=tf.float32, name=\"weights1\")\n",
    "weights2 = tf.Variable(weights2_init, dtype=tf.float32, name=\"weights2\")\n",
    "weights3 = tf.transpose(weights2, name=\"weights3\")  # tied weights\n",
    "weights4 = tf.transpose(weights1, name=\"weights4\")  # tied weights\n",
    "\n",
    "biases1 = tf.Variable(tf.zeros(n_hidden1), name=\"biases1\")\n",
    "biases2 = tf.Variable(tf.zeros(n_hidden2), name=\"biases2\")\n",
    "biases3 = tf.Variable(tf.zeros(n_hidden3), name=\"biases3\")\n",
    "biases4 = tf.Variable(tf.zeros(n_outputs), name=\"biases4\")\n",
    "\n",
    "hidden1 = activation(tf.matmul(X, weights1) + biases1)\n",
    "hidden2 = activation(tf.matmul(hidden1, weights2) + biases2)\n",
    "hidden3 = activation(tf.matmul(hidden2, weights3) + biases3)\n",
    "outputs = tf.matmul(hidden3, weights4) + biases4\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X))\n",
    "reg_loss = regularizer(weights1) + regularizer(weights2)\n",
    "loss = reconstruction_loss + reg_loss\n",
    "\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(loss)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train MSE: 0.0150667\n",
      "1 Train MSE: 0.0164884\n",
      "2 Train MSE: 0.0173757\n",
      "3 Train MSE: 0.0168781\n",
      "4 Train MSE: 0.0155875\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 5\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch})\n",
    "        loss_train = reconstruction_loss.eval(feed_dict={X: X_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)\n",
    "        saver.save(sess, \"./my_model_tying_weights.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_tying_weights.ckpt\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ip1LPvACgsNxnSd5zoNxnbqU+XypyzlxFnm0VOVZd11g8myz3sznuvAAA4dC8AADh0LwA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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdd1cecb9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_reconstructed_digits(X, outputs, \"./my_model_tying_weights.ckpt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training one Autoencoder at a time in multiple graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many ways to train one Autoencoder at a time. The first approach it to train each Autoencoder using a different graph, then we create the Stacked Autoencoder by simply initializing it with the weights and biases copied from these Autoencoders."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a function that will train one autoencoder and return the transformed training set (i.e., the output of the hidden layer) and the model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "from functools import partial\n",
    "\n",
    "def train_autoencoder(X_train, n_neurons, n_epochs, batch_size,\n",
    "                      learning_rate = 0.01, l2_reg = 0.0005,\n",
    "                      activation=tf.nn.elu, seed=42):\n",
    "    graph = tf.Graph()\n",
    "    with graph.as_default():\n",
    "        tf.set_random_seed(seed)\n",
    "\n",
    "        n_inputs = X_train.shape[1]\n",
    "\n",
    "        X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "        \n",
    "        my_dense_layer = partial(\n",
    "            tf.layers.dense,\n",
    "            activation=activation,\n",
    "            kernel_initializer=tf.contrib.layers.variance_scaling_initializer(),\n",
    "            kernel_regularizer=tf.contrib.layers.l2_regularizer(l2_reg))\n",
    "\n",
    "        hidden = my_dense_layer(X, n_neurons, name=\"hidden\")\n",
    "        outputs = my_dense_layer(hidden, n_inputs, activation=None, name=\"outputs\")\n",
    "\n",
    "        reconstruction_loss = tf.reduce_mean(tf.square(outputs - X))\n",
    "\n",
    "        reg_losses = tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)\n",
    "        loss = tf.add_n([reconstruction_loss] + reg_losses)\n",
    "\n",
    "        optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "        training_op = optimizer.minimize(loss)\n",
    "\n",
    "        init = tf.global_variables_initializer()\n",
    "\n",
    "    with tf.Session(graph=graph) as sess:\n",
    "        init.run()\n",
    "        for epoch in range(n_epochs):\n",
    "            n_batches = len(X_train) // batch_size\n",
    "            for iteration in range(n_batches):\n",
    "                print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "                sys.stdout.flush()\n",
    "                indices = rnd.permutation(len(X_train))[:batch_size]\n",
    "                X_batch = X_train[indices]\n",
    "                sess.run(training_op, feed_dict={X: X_batch})\n",
    "            loss_train = reconstruction_loss.eval(feed_dict={X: X_batch})\n",
    "            print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)\n",
    "        params = dict([(var.name, var.eval()) for var in tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES)])\n",
    "        hidden_val = hidden.eval(feed_dict={X: X_train})\n",
    "        return hidden_val, params[\"hidden/kernel:0\"], params[\"hidden/bias:0\"], params[\"outputs/kernel:0\"], params[\"outputs/bias:0\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's train two Autoencoders. The first one is trained on the training data, and the second is trained on the previous Autoencoder's hidden layer output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train MSE: 0.0185175\n",
      "1 Train MSE: 0.0186825\n",
      "2 Train MSE: 0.0184675\n",
      "3 Train MSE: 0.0192315\n",
      "0 Train MSE: 0.00411001\n",
      "1 Train MSE: 0.00461448\n",
      "2 Train MSE: 0.00455272\n",
      "39% Train MSE: 0.00431477\n"
     ]
    }
   ],
   "source": [
    "hidden_output, W1, b1, W4, b4 = train_autoencoder(mnist.train.images, n_neurons=300, n_epochs=4, batch_size=150)\n",
    "_, W2, b2, W3, b3 = train_autoencoder(hidden_output, n_neurons=150, n_epochs=4, batch_size=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can create a Stacked Autoencoder by simply reusing the weights and biases from the Autoencoders we just trained:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28*28\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "hidden1 = tf.nn.elu(tf.matmul(X, W1) + b1)\n",
    "hidden2 = tf.nn.elu(tf.matmul(hidden1, W2) + b2)\n",
    "hidden3 = tf.nn.elu(tf.matmul(hidden2, W3) + b3)\n",
    "outputs = tf.matmul(hidden3, W4) + b4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116362b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_reconstructed_digits(X, outputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training one Autoencoder at a time in a single graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another approach is to use a single graph. To do this, we create the graph for the full Stacked Autoencoder, but then we also add operations to train each Autoencoder independently: phase 1 trains the bottom and top layer (ie. the first Autoencoder) and phase 2 trains the two middle layers (ie. the second Autoencoder)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150  # codings\n",
    "n_hidden3 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01\n",
    "l2_reg = 0.0001\n",
    "\n",
    "activation = tf.nn.elu\n",
    "regularizer = tf.contrib.layers.l2_regularizer(l2_reg)\n",
    "initializer = tf.contrib.layers.variance_scaling_initializer()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "\n",
    "weights1_init = initializer([n_inputs, n_hidden1])\n",
    "weights2_init = initializer([n_hidden1, n_hidden2])\n",
    "weights3_init = initializer([n_hidden2, n_hidden3])\n",
    "weights4_init = initializer([n_hidden3, n_outputs])\n",
    "\n",
    "weights1 = tf.Variable(weights1_init, dtype=tf.float32, name=\"weights1\")\n",
    "weights2 = tf.Variable(weights2_init, dtype=tf.float32, name=\"weights2\")\n",
    "weights3 = tf.Variable(weights3_init, dtype=tf.float32, name=\"weights3\")\n",
    "weights4 = tf.Variable(weights4_init, dtype=tf.float32, name=\"weights4\")\n",
    "\n",
    "biases1 = tf.Variable(tf.zeros(n_hidden1), name=\"biases1\")\n",
    "biases2 = tf.Variable(tf.zeros(n_hidden2), name=\"biases2\")\n",
    "biases3 = tf.Variable(tf.zeros(n_hidden3), name=\"biases3\")\n",
    "biases4 = tf.Variable(tf.zeros(n_outputs), name=\"biases4\")\n",
    "\n",
    "hidden1 = activation(tf.matmul(X, weights1) + biases1)\n",
    "hidden2 = activation(tf.matmul(hidden1, weights2) + biases2)\n",
    "hidden3 = activation(tf.matmul(hidden2, weights3) + biases3)\n",
    "outputs = tf.matmul(hidden3, weights4) + biases4\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "\n",
    "with tf.name_scope(\"phase1\"):\n",
    "    phase1_outputs = tf.matmul(hidden1, weights4) + biases4  # bypass hidden2 and hidden3\n",
    "    phase1_reconstruction_loss = tf.reduce_mean(tf.square(phase1_outputs - X))\n",
    "    phase1_reg_loss = regularizer(weights1) + regularizer(weights4)\n",
    "    phase1_loss = phase1_reconstruction_loss + phase1_reg_loss\n",
    "    phase1_training_op = optimizer.minimize(phase1_loss)\n",
    "\n",
    "with tf.name_scope(\"phase2\"):\n",
    "    phase2_reconstruction_loss = tf.reduce_mean(tf.square(hidden3 - hidden1))\n",
    "    phase2_reg_loss = regularizer(weights2) + regularizer(weights3)\n",
    "    phase2_loss = phase2_reconstruction_loss + phase2_reg_loss\n",
    "    train_vars = [weights2, biases2, weights3, biases3]\n",
    "    phase2_training_op = optimizer.minimize(phase2_loss, var_list=train_vars) # freeze hidden1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cache the frozen layer outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training phase #1\n",
      "0 Train MSE: 0.00753817\n",
      "1 Train MSE: 0.00775457\n",
      "2 Train MSE: 0.00734359\n",
      "3 Train MSE: 0.00783768\n",
      "Training phase #2\n",
      "0 Train MSE: 0.252959\n",
      "19% Train MSE: 0.0046542\n",
      "29% Train MSE: 0.00249056\n",
      "39% Train MSE: 0.00205957\n",
      "Test MSE: 0.0097731\n"
     ]
    }
   ],
   "source": [
    "training_ops = [phase1_training_op, phase2_training_op]\n",
    "reconstruction_losses = [phase1_reconstruction_loss, phase2_reconstruction_loss]\n",
    "n_epochs = [4, 4]\n",
    "batch_sizes = [150, 150]\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for phase in range(2):\n",
    "        print(\"Training phase #{}\".format(phase + 1))\n",
    "        if phase == 1:\n",
    "            hidden1_cache = hidden1.eval(feed_dict={X: mnist.train.images})\n",
    "        for epoch in range(n_epochs[phase]):\n",
    "            n_batches = mnist.train.num_examples // batch_sizes[phase]\n",
    "            for iteration in range(n_batches):\n",
    "                print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "                sys.stdout.flush()\n",
    "                if phase == 1:\n",
    "                    indices = rnd.permutation(mnist.train.num_examples)\n",
    "                    hidden1_batch = hidden1_cache[indices[:batch_sizes[phase]]]\n",
    "                    feed_dict = {hidden1: hidden1_batch}\n",
    "                    sess.run(training_ops[phase], feed_dict=feed_dict)\n",
    "                else:\n",
    "                    X_batch, y_batch = mnist.train.next_batch(batch_sizes[phase])\n",
    "                    feed_dict = {X: X_batch}\n",
    "                    sess.run(training_ops[phase], feed_dict=feed_dict)\n",
    "            loss_train = reconstruction_losses[phase].eval(feed_dict=feed_dict)\n",
    "            print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)\n",
    "            saver.save(sess, \"./my_model_cache_frozen.ckpt\")\n",
    "    loss_test = reconstruction_loss.eval(feed_dict={X: mnist.test.images})\n",
    "    print(\"Test MSE:\", loss_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Reconstructions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_one_at_a_time.ckpt\n"
     ]
    },
    {
     "data": {
      "image/png": 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111yjYjNmzIhjuXQzhBBuuummOL7uuutUbP/+/XFcX1+vYnV1depYxm0bTO/evePY/luS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\nggBcYxIE4BqTIADXmAQBuMYkCMC1/wBFeVZKJWQkbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdd169fe6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_test_digits = 2\n",
    "X_test = mnist.test.images[:n_test_digits]\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"./my_model_one_at_a_time.ckpt\") # not shown in the book\n",
    "    outputs_val = outputs.eval(feed_dict={X: X_test})\n",
    "\n",
    "def plot_image(image, shape=[28, 28]):\n",
    "    plt.imshow(image.reshape(shape), cmap=\"Greys\", interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")\n",
    "\n",
    "for digit_index in range(n_test_digits):\n",
    "    plt.subplot(n_test_digits, 2, digit_index * 2 + 1)\n",
    "    plot_image(X_test[digit_index])\n",
    "    plt.subplot(n_test_digits, 2, digit_index * 2 + 2)\n",
    "    plot_image(outputs_val[digit_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the extracted features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784, 300)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights1_val.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised pretraining"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a small neural network for MNIST classification:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150\n",
    "n_outputs = 10\n",
    "\n",
    "learning_rate = 0.01\n",
    "l2_reg = 0.0005\n",
    "\n",
    "activation = tf.nn.elu\n",
    "regularizer = tf.contrib.layers.l2_regularizer(l2_reg)\n",
    "initializer = tf.contrib.layers.variance_scaling_initializer()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "y = tf.placeholder(tf.int32, shape=[None])\n",
    "\n",
    "weights1_init = initializer([n_inputs, n_hidden1])\n",
    "weights2_init = initializer([n_hidden1, n_hidden2])\n",
    "weights3_init = initializer([n_hidden2, n_outputs])\n",
    "\n",
    "weights1 = tf.Variable(weights1_init, dtype=tf.float32, name=\"weights1\")\n",
    "weights2 = tf.Variable(weights2_init, dtype=tf.float32, name=\"weights2\")\n",
    "weights3 = tf.Variable(weights3_init, dtype=tf.float32, name=\"weights3\")\n",
    "\n",
    "biases1 = tf.Variable(tf.zeros(n_hidden1), name=\"biases1\")\n",
    "biases2 = tf.Variable(tf.zeros(n_hidden2), name=\"biases2\")\n",
    "biases3 = tf.Variable(tf.zeros(n_outputs), name=\"biases3\")\n",
    "\n",
    "hidden1 = activation(tf.matmul(X, weights1) + biases1)\n",
    "hidden2 = activation(tf.matmul(hidden1, weights2) + biases2)\n",
    "logits = tf.matmul(hidden2, weights3) + biases3\n",
    "\n",
    "cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "reg_loss = regularizer(weights1) + regularizer(weights2) + regularizer(weights3)\n",
    "loss = cross_entropy + reg_loss\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(loss)\n",
    "\n",
    "correct = tf.nn.in_top_k(logits, y, 1)\n",
    "accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "pretrain_saver = tf.train.Saver([weights1, weights2, biases1, biases2])\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regular training (without pretraining):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "09% Train accuracy: 0.973333 Test accuracy: 0.9334\n",
      "1 Train accuracy: 0.98 Test accuracy: 0.936\n",
      "29% Train accuracy: 0.973333 Test accuracy: 0.9382\n",
      "39% Train accuracy: 0.986667 Test accuracy: 0.9491\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 4\n",
    "batch_size = 150\n",
    "n_labeled_instances = 20000\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = n_labeled_instances // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            indices = rnd.permutation(n_labeled_instances)[:batch_size]\n",
    "            X_batch, y_batch = mnist.train.images[indices], mnist.train.labels[indices]\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        accuracy_val = accuracy.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train accuracy:\", accuracy_val, end=\" \")\n",
    "        saver.save(sess, \"./my_model_supervised.ckpt\")\n",
    "        accuracy_val = accuracy.eval(feed_dict={X: mnist.test.images, y: mnist.test.labels})\n",
    "        print(\"Test accuracy:\", accuracy_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now reusing the first two layers of the autoencoder we pretrained:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_cache_frozen.ckpt\n",
      "0 Train accuracy: 0.94\tTest accuracy: 0.9348\n",
      "1 Train accuracy: 0.993333\tTest accuracy: 0.942\n",
      "2 Train accuracy: 0.986667\tTest accuracy: 0.9455\n",
      "3 Train accuracy: 0.98\tTest accuracy: 0.9487\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 4\n",
    "batch_size = 150\n",
    "n_labeled_instances = 20000\n",
    "\n",
    "#training_op = optimizer.minimize(loss, var_list=[weights3, biases3])  # Freeze layers 1 and 2 (optional)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    pretrain_saver.restore(sess, \"./my_model_cache_frozen.ckpt\")\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = n_labeled_instances // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            indices = rnd.permutation(n_labeled_instances)[:batch_size]\n",
    "            X_batch, y_batch = mnist.train.images[indices], mnist.train.labels[indices]\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        accuracy_val = accuracy.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train accuracy:\", accuracy_val, end=\"\\t\")\n",
    "        saver.save(sess, \"./my_model_supervised_pretrained.ckpt\")\n",
    "        accuracy_val = accuracy.eval(feed_dict={X: mnist.test.images, y: mnist.test.labels})\n",
    "        print(\"Test accuracy:\", accuracy_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacked denoising Autoencoder\n",
    "\n",
    "Another way to force the autoencoder to learn useful features is to add noise to its inputs, training it to recover the original, noise-free inputs. This prevents the autoencoder from trivially copying its inputs to its outputs.\n",
    "\n",
    "The noise can be pure Gaussian noise added to the inputs, or it can be randomly switched off inputs, just like in dropout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: the book uses `tf.contrib.layers.dropout()` rather than `tf.layers.dropout()` (which did not exist when this chapter was written). It is now preferable to use `tf.layers.dropout()`, because anything in the contrib module may change or be deleted without notice. The `tf.layers.dropout()` function is almost identical to the `tf.contrib.layers.dropout()` function, except for a few minor differences. Most importantly:\n",
    "* you must specify the dropout rate (`rate`) rather than the keep probability (`keep_prob`), where `rate` is simply equal to `1 - keep_prob`,\n",
    "* the `is_training` parameter is renamed to `training`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Gaussian noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150  # codings\n",
    "n_hidden3 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_level = 1.0\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "# add Gaussian noise\n",
    "X_noisy = X + noise_level * tf.random_normal(tf.shape(X))\n",
    "\n",
    "hidden1 = tf.layers.dense(X_noisy, n_hidden1, activation=tf.nn.relu,\n",
    "                          name=\"hidden1\")\n",
    "hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=tf.nn.relu, # not shown in the book\n",
    "                          name=\"hidden2\")                            # not shown\n",
    "hidden3 = tf.layers.dense(hidden2, n_hidden3, activation=tf.nn.relu, # not shown\n",
    "                          name=\"hidden3\")                            # not shown\n",
    "outputs = tf.layers.dense(hidden3, n_outputs, name=\"outputs\")        # not shown\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X)) # MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(reconstruction_loss)\n",
    "    \n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train MSE: 0.0440489\n",
      "1 Train MSE: 0.0432517\n",
      "2 Train MSE: 0.042057\n",
      "3 Train MSE: 0.0409477\n",
      "4 Train MSE: 0.0402107\n",
      "5 Train MSE: 0.0388787\n",
      "6 Train MSE: 0.0391096\n",
      "7 Train MSE: 0.0421885\n",
      "8 Train MSE: 0.0398648\n",
      "9 Train MSE: 0.0408181\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch})\n",
    "        loss_train = reconstruction_loss.eval(feed_dict={X: X_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)\n",
    "        saver.save(sess, \"./my_model_stacked_denoising_gaussian.ckpt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using dropout:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 150  # codings\n",
    "n_hidden3 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "\n",
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "dropout_rate = 0.3\n",
    "\n",
    "training = tf.placeholder_with_default(False, shape=(), name='training')\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])\n",
    "X_drop = tf.layers.dropout(X, dropout_rate, training=training)\n",
    "\n",
    "hidden1 = tf.layers.dense(X_drop, n_hidden1, activation=tf.nn.relu,\n",
    "                          name=\"hidden1\")\n",
    "hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=tf.nn.relu, # not shown in the book\n",
    "                          name=\"hidden2\")                            # not shown\n",
    "hidden3 = tf.layers.dense(hidden2, n_hidden3, activation=tf.nn.relu, # not shown\n",
    "                          name=\"hidden3\")                            # not shown\n",
    "outputs = tf.layers.dense(hidden3, n_outputs, name=\"outputs\")        # not shown\n",
    "\n",
    "reconstruction_loss = tf.reduce_mean(tf.square(outputs - X)) # MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(reconstruction_loss)\n",
    "    \n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train MSE: 0.0302958\n",
      "1 Train MSE: 0.0292939\n",
      "2 Train MSE: 0.027049\n",
      "3 Train MSE: 0.0253021\n",
      "49% Train MSE: 0.0243453\n",
      "5 Train MSE: 0.0247929\n",
      "6 Train MSE: 0.0237942\n",
      "7 Train MSE: 0.0252127\n",
      "8 Train MSE: 0.0237634\n",
      "9 Train MSE: 0.0247091\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, training: True})\n",
    "        loss_train = reconstruction_loss.eval(feed_dict={X: X_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train MSE:\", loss_train)\n",
    "        saver.save(sess, \"./my_model_stacked_denoising_dropout.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_stacked_denoising_dropout.ckpt\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fe39a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_reconstructed_digits(X, outputs, \"./my_model_stacked_denoising_dropout.ckpt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sparse Autoencoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sparsity_loss_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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xceRKVh6lfPnyFClSJPH5+vXrOXHiBHXq1EncVqhQIS677LLE5ytWrCA+Pp5L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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1163e6a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.1\n",
    "q = np.linspace(0.001, 0.999, 500)\n",
    "kl_div = p * np.log(p / q) + (1 - p) * np.log((1 - p) / (1 - q))\n",
    "mse = (p - q)**2\n",
    "plt.plot([p, p], [0, 0.3], \"k:\")\n",
    "plt.text(0.05, 0.32, \"Target\\nsparsity\", fontsize=14)\n",
    "plt.plot(q, kl_div, \"b-\", label=\"KL divergence\")\n",
    "plt.plot(q, mse, \"r--\", label=\"MSE\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"Actual sparsity\")\n",
    "plt.ylabel(\"Cost\", rotation=0)\n",
    "plt.axis([0, 1, 0, 0.95])\n",
    "save_fig(\"sparsity_loss_plot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 1000  # sparse codings\n",
    "n_outputs = n_inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kl_divergence(p, q):\n",
    "    # Kullback Leibler divergence\n",
    "    return p * tf.log(p / q) + (1 - p) * tf.log((1 - p) / (1 - q))\n",
    "\n",
    "learning_rate = 0.01\n",
    "sparsity_target = 0.1\n",
    "sparsity_weight = 0.2\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=[None, n_inputs])            # not shown in the book\n",
    "\n",
    "# Note that the coding layer must output values from 0 to 1, which is why we use the sigmoid activation function:\n",
    "hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.sigmoid) # not shown\n",
    "#outputs = tf.layers.dense(hidden1, n_outputs)                     # not shown\n",
    "logits = tf.layers.dense(hidden1, n_outputs)\n",
    "outputs = tf.nn.sigmoid(logits)\n",
    "\n",
    "xentropy = tf.nn.sigmoid_cross_entropy_with_logits(labels=X, logits=outputs)\n",
    "reconstruction_loss = tf.reduce_mean(xentropy)\n",
    "\n",
    "hidden1_mean = tf.reduce_mean(hidden1, axis=0) # batch mean\n",
    "sparsity_loss = tf.reduce_sum(kl_divergence(sparsity_target, hidden1_mean))\n",
    "#reconstruction_loss = tf.reduce_mean(tf.square(outputs - X)) # MSE\n",
    "loss = reconstruction_loss + sparsity_weight * sparsity_loss\n",
    "\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate)\n",
    "training_op = optimizer.minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train loss: 0.715603 \tSparsity loss: 0.333232 \tTotal loss: 0.78225\n",
      "1 Train loss: 0.708853 \tSparsity loss: 0.0746283 \tTotal loss: 0.723779\n",
      "2 Train loss: 0.703599 \tSparsity loss: 0.0109317 \tTotal loss: 0.705785\n",
      "3 Train loss: 0.698804 \tSparsity loss: 0.627469 \tTotal loss: 0.824298\n",
      "4 Train loss: 0.696388 \tSparsity loss: 0.0724939 \tTotal loss: 0.710886\n",
      "5 Train loss: 0.695163 \tSparsity loss: 0.0227809 \tTotal loss: 0.69972\n",
      "6 Train loss: 0.692975 \tSparsity loss: 0.00796508 \tTotal loss: 0.694568\n",
      "7 Train loss: 0.691804 \tSparsity loss: 0.0855785 \tTotal loss: 0.708919\n",
      "8 Train loss: 0.690664 \tSparsity loss: 0.0993482 \tTotal loss: 0.710533\n",
      "9 Train loss: 0.689972 \tSparsity loss: 0.192672 \tTotal loss: 0.728506\n",
      "10 Train loss: 0.689334 \tSparsity loss: 0.172671 \tTotal loss: 0.723869\n",
      "11 Train loss: 0.688208 \tSparsity loss: 0.0431758 \tTotal loss: 0.696843\n",
      "12 Train loss: 0.687773 \tSparsity loss: 0.0242359 \tTotal loss: 0.69262\n",
      "13 Train loss: 0.686685 \tSparsity loss: 0.28806 \tTotal loss: 0.744297\n",
      "14 Train loss: 0.685716 \tSparsity loss: 0.0581899 \tTotal loss: 0.697354\n",
      "15 Train loss: 0.684483 \tSparsity loss: 0.0232808 \tTotal loss: 0.689139\n",
      "16 Train loss: 0.683949 \tSparsity loss: 0.236464 \tTotal loss: 0.731242\n",
      "17 Train loss: 0.682309 \tSparsity loss: 0.0483435 \tTotal loss: 0.691978\n",
      "18 Train loss: 0.681268 \tSparsity loss: 0.0621521 \tTotal loss: 0.693698\n",
      "19 Train loss: 0.681262 \tSparsity loss: 0.0828823 \tTotal loss: 0.697839\n",
      "20 Train loss: 0.680072 \tSparsity loss: 0.0635647 \tTotal loss: 0.692785\n",
      "21 Train loss: 0.679045 \tSparsity loss: 0.112192 \tTotal loss: 0.701483\n",
      "22 Train loss: 0.678573 \tSparsity loss: 0.264933 \tTotal loss: 0.73156\n",
      "23 Train loss: 0.677744 \tSparsity loss: 0.0534583 \tTotal loss: 0.688436\n",
      "24 Train loss: 0.676244 \tSparsity loss: 0.140858 \tTotal loss: 0.704416\n",
      "25 Train loss: 0.676486 \tSparsity loss: 0.085809 \tTotal loss: 0.693648\n",
      "26 Train loss: 0.67521 \tSparsity loss: 0.142642 \tTotal loss: 0.703738\n",
      "27 Train loss: 0.675095 \tSparsity loss: 0.348553 \tTotal loss: 0.744806\n",
      "28 Train loss: 0.674198 \tSparsity loss: 0.134755 \tTotal loss: 0.701149\n",
      "29 Train loss: 0.674033 \tSparsity loss: 0.170091 \tTotal loss: 0.708052\n",
      "30 Train loss: 0.673151 \tSparsity loss: 0.0400267 \tTotal loss: 0.681156\n",
      "31 Train loss: 0.672193 \tSparsity loss: 0.171876 \tTotal loss: 0.706568\n",
      "32 Train loss: 0.672589 \tSparsity loss: 0.156392 \tTotal loss: 0.703867\n",
      "33 Train loss: 0.6717 \tSparsity loss: 0.0956853 \tTotal loss: 0.690837\n",
      "34 Train loss: 0.672122 \tSparsity loss: 0.214324 \tTotal loss: 0.714986\n",
      "35 Train loss: 0.671421 \tSparsity loss: 0.715228 \tTotal loss: 0.814466\n",
      "36 Train loss: 0.670731 \tSparsity loss: 0.18471 \tTotal loss: 0.707673\n",
      "37 Train loss: 0.67112 \tSparsity loss: 0.185369 \tTotal loss: 0.708193\n",
      "38 Train loss: 0.670398 \tSparsity loss: 0.151452 \tTotal loss: 0.700689\n",
      "39 Train loss: 0.669494 \tSparsity loss: 0.063735 \tTotal loss: 0.682241\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 40\n",
    "batch_size = 1000\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch})\n",
    "        reconstruction_loss_val, sparsity_loss_val, loss_val = sess.run([reconstruction_loss, sparsity_loss, loss], feed_dict={X: X_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train loss:\", reconstruction_loss_val, \"\\tSparsity loss:\", sparsity_loss_val, \"\\tTotal loss:\", loss_val)\n",
    "        saver.save(sess, \"./my_model_sparse.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_reconstructed_digits(X, outputs, \"./my_model_sparse.ckpt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To speed up training, you can normalize the inputs between 0 and 1, and use the cross entropy instead of the MSE for the cost function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "logits = tf.layers.dense(hidden1, n_outputs)\n",
    "outputs = tf.nn.sigmoid(logits)\n",
    "\n",
    "xentropy = tf.nn.sigmoid_cross_entropy_with_logits(labels=X, logits=logits)\n",
    "reconstruction_loss = tf.reduce_mean(xentropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Autoencoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "from functools import partial\n",
    "\n",
    "n_inputs = 28 * 28\n",
    "n_hidden1 = 500\n",
    "n_hidden2 = 500\n",
    "n_hidden3 = 20  # codings\n",
    "n_hidden4 = n_hidden2\n",
    "n_hidden5 = n_hidden1\n",
    "n_outputs = n_inputs\n",
    "learning_rate = 0.001\n",
    "\n",
    "initializer = tf.contrib.layers.variance_scaling_initializer()\n",
    "\n",
    "my_dense_layer = partial(\n",
    "    tf.layers.dense,\n",
    "    activation=tf.nn.elu,\n",
    "    kernel_initializer=initializer)\n",
    "\n",
    "X = tf.placeholder(tf.float32, [None, n_inputs])\n",
    "hidden1 = my_dense_layer(X, n_hidden1)\n",
    "hidden2 = my_dense_layer(hidden1, n_hidden2)\n",
    "hidden3_mean = my_dense_layer(hidden2, n_hidden3, activation=None)\n",
    "hidden3_gamma = my_dense_layer(hidden2, n_hidden3, activation=None)\n",
    "noise = tf.random_normal(tf.shape(hidden3_gamma), dtype=tf.float32)\n",
    "hidden3 = hidden3_mean + tf.exp(0.5 * hidden3_gamma) * noise\n",
    "hidden4 = my_dense_layer(hidden3, n_hidden4)\n",
    "hidden5 = my_dense_layer(hidden4, n_hidden5)\n",
    "logits = my_dense_layer(hidden5, n_outputs, activation=None)\n",
    "outputs = tf.sigmoid(logits)\n",
    "\n",
    "\n",
    "xentropy = tf.nn.sigmoid_cross_entropy_with_logits(labels=X, logits=logits)\n",
    "reconstruction_loss = tf.reduce_sum(xentropy)\n",
    "latent_loss = 0.5 * tf.reduce_sum(\n",
    "    tf.exp(hidden3_gamma) + tf.square(hidden3_mean) - 1 - hidden3_gamma)\n",
    "loss = reconstruction_loss + latent_loss\n",
    "\n",
    "optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(loss)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Train total loss: 18001.2 \tReconstruction loss: 14354.6 \tLatent loss: 3646.63\n",
      "1 Train total loss: 17302.7 \tReconstruction loss: 13486.1 \tLatent loss: 3816.68\n",
      "2 Train total loss: 16325.4 \tReconstruction loss: 12567.7 \tLatent loss: 3757.69\n",
      "3 Train total loss: 16941.6 \tReconstruction loss: 13052.6 \tLatent loss: 3889.02\n",
      "4 Train total loss: 16673.8 \tReconstruction loss: 12839.9 \tLatent loss: 3833.88\n",
      "5 Train total loss: 16383.3 \tReconstruction loss: 12508.7 \tLatent loss: 3874.66\n",
      "6 Train total loss: 15648.4 \tReconstruction loss: 11832.8 \tLatent loss: 3815.56\n",
      "7 %Train total loss: 15907.0 \tReconstruction loss: 12143.8 \tLatent loss: 3763.18\n",
      "8 Train total loss: 15872.5 \tReconstruction loss: 12038.6 \tLatent loss: 3833.9\n",
      "9 %Train total loss: 15420.3 \tReconstruction loss: 11644.6 \tLatent loss: 3775.71\n",
      "10 Train total loss: 15999.1 \tReconstruction loss: 12129.5 \tLatent loss: 3869.58\n",
      "11 Train total loss: 16154.9 \tReconstruction loss: 12284.2 \tLatent loss: 3870.7\n",
      "12 Train total loss: 15481.6 \tReconstruction loss: 11666.2 \tLatent loss: 3815.42\n",
      "13 Train total loss: 15576.5 \tReconstruction loss: 11801.2 \tLatent loss: 3775.25\n",
      "14 Train total loss: 15782.9 \tReconstruction loss: 11895.7 \tLatent loss: 3887.27\n",
      "15 Train total loss: 15508.3 \tReconstruction loss: 11727.9 \tLatent loss: 3780.4\n",
      "16 Train total loss: 15466.9 \tReconstruction loss: 11666.9 \tLatent loss: 3800.0\n",
      "17 Train total loss: 15219.6 \tReconstruction loss: 11360.4 \tLatent loss: 3859.22\n",
      "18 Train total loss: 15374.5 \tReconstruction loss: 11628.4 \tLatent loss: 3746.09\n",
      "19 Train total loss: 15262.0 \tReconstruction loss: 11468.8 \tLatent loss: 3793.2\n",
      "20 Train total loss: 15163.3 \tReconstruction loss: 11352.9 \tLatent loss: 3810.43\n",
      "21 Train total loss: 15339.5 \tReconstruction loss: 11580.2 \tLatent loss: 3759.32\n",
      "22 Train total loss: 15197.4 \tReconstruction loss: 11348.5 \tLatent loss: 3848.95\n",
      "23 Train total loss: 15343.7 \tReconstruction loss: 11550.6 \tLatent loss: 3793.11\n",
      "24 Train total loss: 14853.6 \tReconstruction loss: 11181.9 \tLatent loss: 3671.65\n",
      "25 Train total loss: 14637.4 \tReconstruction loss: 10916.0 \tLatent loss: 3721.44\n",
      "26 Train total loss: 15004.4 \tReconstruction loss: 11292.2 \tLatent loss: 3712.22\n",
      "27 Train total loss: 14917.5 \tReconstruction loss: 11225.5 \tLatent loss: 3692.04\n",
      "28 Train total loss: 15104.2 \tReconstruction loss: 11358.8 \tLatent loss: 3745.44\n",
      "29 Train total loss: 14395.7 \tReconstruction loss: 10824.8 \tLatent loss: 3570.91\n",
      "30 Train total loss: 15255.5 \tReconstruction loss: 11510.6 \tLatent loss: 3744.89\n",
      "31 Train total loss: 14855.2 \tReconstruction loss: 11204.1 \tLatent loss: 3651.12\n",
      "32 Train total loss: 14774.8 \tReconstruction loss: 11062.5 \tLatent loss: 3712.32\n",
      "33 Train total loss: 14579.1 \tReconstruction loss: 11007.1 \tLatent loss: 3572.03\n",
      "34 Train total loss: 15027.7 \tReconstruction loss: 11324.6 \tLatent loss: 3703.06\n",
      "35 Train total loss: 15009.0 \tReconstruction loss: 11298.7 \tLatent loss: 3710.32\n",
      "36 Train total loss: 14772.0 \tReconstruction loss: 11156.7 \tLatent loss: 3615.29\n",
      "37 Train total loss: 15132.8 \tReconstruction loss: 11451.8 \tLatent loss: 3680.98\n",
      "38 Train total loss: 14868.3 \tReconstruction loss: 11245.9 \tLatent loss: 3622.44\n",
      "39 Train total loss: 14954.9 \tReconstruction loss: 11349.6 \tLatent loss: 3605.36\n",
      "40 Train total loss: 14580.1 \tReconstruction loss: 10964.2 \tLatent loss: 3615.88\n",
      "41 Train total loss: 14897.7 \tReconstruction loss: 11050.5 \tLatent loss: 3847.2\n",
      "42 Train total loss: 14886.3 \tReconstruction loss: 11220.7 \tLatent loss: 3665.6\n",
      "43 Train total loss: 14451.2 \tReconstruction loss: 10788.3 \tLatent loss: 3662.9\n",
      "44 Train total loss: 15022.1 \tReconstruction loss: 11283.7 \tLatent loss: 3738.38\n",
      "45 Train total loss: 14703.5 \tReconstruction loss: 10989.4 \tLatent loss: 3714.11\n",
      "46 Train total loss: 14678.0 \tReconstruction loss: 11072.1 \tLatent loss: 3605.95\n",
      "47 Train total loss: 14784.8 \tReconstruction loss: 11096.9 \tLatent loss: 3687.88\n",
      "48 Train total loss: 14694.4 \tReconstruction loss: 11074.7 \tLatent loss: 3619.67\n",
      "49 Train total loss: 14270.6 \tReconstruction loss: 10604.3 \tLatent loss: 3666.28\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    for epoch in range(n_epochs):\n",
    "        n_batches = mnist.train.num_examples // batch_size\n",
    "        for iteration in range(n_batches):\n",
    "            print(\"\\r{}%\".format(100 * iteration // n_batches), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "            X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch})\n",
    "        loss_val, reconstruction_loss_val, latent_loss_val = sess.run([loss, reconstruction_loss, latent_loss], feed_dict={X: X_batch})\n",
    "        print(\"\\r{}\".format(epoch), \"Train total loss:\", loss_val, \"\\tReconstruction loss:\", reconstruction_loss_val, \"\\tLatent loss:\", latent_loss_val)\n",
    "        saver.save(sess, \"./my_model_variational.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_variational.ckpt\n"
     ]
    },
    {
     "data": {
      "image/png": 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5y1tCNlG/0TUU3rwAKEd5AVCO8gKgHOUFQDkGNkbJ1VdfneZ9fX0trf/Upz4Vsrlz547o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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115e0eed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_reconstructed_digits(X, outputs, \"./my_model_variational.ckpt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate digits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train the model and generate a few random digits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_variational.ckpt\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "n_digits = 60    # try 60 digits\n",
    "n_epochs = 50\n",
    "batch_size = 150\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"./my_model_variational.ckpt\")\n",
    "    codings_rnd = np.random.normal(size=[n_digits, n_hidden3])\n",
    "    outputs_val = outputs.eval(feed_dict={hidden3: codings_rnd})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GDRvk4pSrrrqKwsJCeYZohj1Ce1QPHTpUegjU1dXRrl07uQf7mxr8hMaej+ea\njGT4QLmEH374YZYsWRKWt3LTTTdJiCSajYpqamp44YUXAPMwrA6UahyqUconn3xCv3794uZ6xVgQ\nrXcSDAaZP38+s2fPBsywR1ZWloRForl//Pe+bY1Go9Fo4hRLpAr/j8NJfagqobniiitYu3atZLVO\nnjyZm2++Oew2pRPkeMeiVpkswzDweDzs2bMHMJNrkpKSTuZU9m2/GJUXrNovqtP/d0gGOem5VhmV\nmzZtkuYYX331FcnJyVx++eUAXH755a1dlha1uW5FSzLm8vE9iMhaDAaDNDc3i/vY7/eTkZEh7tho\nzrXf7xe3dlNTE6+99po01vn1r38trTCj4CnR8vF/uN1unn76aR5++GHADD2MHz+e5557DjAvBDpJ\nD8Z3FrA2qZxVvGjKlCm88cYb0npv6tSpjBo1SrJYFSoz8zvUU0ZFOcs/pjffb+M7jzu0W5bf78du\nt0cyU/9Um+u2OGY4iXEHAgHJhFbVH614W933nusYdsXS8vF/qFao6krIM888k9/85jdSf90KB6VT\nWzmrjXjlypXccccd/M///A8A119/PQkJCSeTgBRV5dyK6MUVPU61uW6LY4ZW9GJBqx7iTrW5botj\nhrY7bkHHnDUajUajiTPapOUcQU7F01hbHDO0zXHrMbceWj6ix6k2Zmi74z7ygzFSzhqNRqPRaL4B\n7dbWaDQajSbO0MpZo9FoNJo4QytnjUaj0WjiDK2cNRqNRqOJM7Ry1mg0Go0mztDKWaPRaDSaOCNW\nt1LFa/3WqVg71xbHDG1z3HrMrYeWj+hxqo0Z2u64BW05azQajUYTZ2jlrNFoNBpNnBErt7ZGo9Fo\nNG0Kv9/Pli1b5ObDTp06kZiYGJHbxLRy1mg0rY6631td1wrmzU/qxrgYXY2o0ZwwhmHg8/kA87pi\nm80m1xZ36NAhYrKslXOMCO1pbhjGyV7grTkBWvaTjxdF4Xa7AXj33Xf56KOPSElJAaCoqIjbb79d\nTuvxMt5joa5zbWxsZOvWrcydOxeA7OxsfvzjH5OTkwOA3W6P6+eIZ1rKrzoIqb+3Wq1h+0lbmmf1\nDKHPaLFYYvYMwWCQgwcPsnDhQgC2bNlCamoq+fn5ABQWFpKcnByR/VtrBI1Go9Fo4oy4vTIydFzB\nYBAAr9dLTU0Nb731FgCLFy+mrq6OzMxMwDy1BwIBevXqBcDNN99MQUEBCQkJwHc6QUYlPT8QCNDQ\n0MDWrVspwx0wAAAgAElEQVQBqKys5IwzzhCr4nucwqJeCmEYhpzYwRzzCZ5wIzrXSn4CgQCNjY2U\nlZUBsGjRIlatWkVFRYU5CIuFQYMGcfPNNwOQl5cn8mKz2Y71PK0+14ZhUFFRwTXXXAPA0qVL8fv9\n8tkWi4UOHTrw/vvvAzBw4MATlZGIy4dhGAQCAaqrqwGYN28eU6dOFfef1WrlBz/4Affddx8AXbt2\nxW7/VsfdScvHN+1tJ2OFfQevS0TmOnStud1uGhoaxNW6ZcsW3nzzTTweDwCJiYkUFhZy9dVXA5Cf\nny/hhG8gLkqpgsGgPMPevXtlHebm5uJwOFrKfET3D+UBWrp0KXPmzGHIkCEAOBwOMjIy5L337t2b\n7Ozs1tz3hLh1a6uHDV0MTU1N3H///cycOVO+Dt3E1M//5z//AeCVV15h7Nix/P73vweguLgYm80W\nrUc4CrW4ysvLmTBhAuvWrQPMZ/3hD3/Iiy++CEBOTk5U3Dhqbr/LZxmGgd/vp6mpCYBdu3bxwQcf\nsH37dgDat2/PxIkT6dmzJxBbt6VhGDQ3NwPw/vvv8/jjj7Nz504ZV3Nzsyw+gC+++ILPPvsMgEcf\nfZThw4cDRFxW1PxXV1dz4YUXijwcy7VXVVXFs88+C8CLL75IYmJiRMf2XVFj9Hg8lJeX8+9//xuA\n5cuXs3PnThoaGgBzs3O5XPTp0weASZMmHU85f28CgQA1NTUcPnwYgJUrV5KWlgZAt27daN++Penp\n6YD5jkNj43a7XZSCej6/3y/y5PP5qKmpAUyXZkJCQtTkXCmuRYsW8a9//YuNGzcCUFtby6FDh+QZ\ngsEgTqeTPXv2APDEE08cTzlHjZbu6tBDdEVFBWvWrAHMsMhZZ50FfOMhOWIEAgHee+89AH7+85+T\nn58vB50uXbrQ3NzM5s2bAVMeDMP470wIs1gscmJyOp0UFhZSVFQEwNatWwkEAjIxVqs17OXX1tby\n8ccfi2V9//33k5ubKz8bTfx+P19++SUA1157LTt27BBlbbPZ2L59e9QODupzIXyBtBQwZR2DeRBa\nt24d8+fPB0yvxbp162hsbATME2VxcbEo51hhGAYNDQ1MnjwZgLfeeovGxkZ5jvT0dNLT00UxNDQ0\n4PF42L17NwAvv/wypaWlABFXgCrGPGTIEHbv3n3UxhWqvGw2m4xxzZo1DB48OGLK7bugLOXa2loA\n/vnPf/Luu+9SWVkJmF6uQCAgis7lclFdXS2br9rUoPViokquZ8+ezcsvvyzrLS0tTazMbt26MXDg\nQMaNGyefHQgExMJ3Op3YbDYZ96xZs1i7dq18RnFxMaNHjwZMi85ms8m6jaQCCQQCrFq1CoD//d//\nZe/evfK8KSkpOJ3OsINSMBikvr4eMGWntef6RFGWvzoUK4WrDhT79+9n3rx5uFwuAC666CKysrLC\nfjYaBINB3n77bX79618DprxMmzaN0047DTDnLzk5mb179wKQmppKx44dIzIWHXPWaDQajSbOiHvL\nGY6c9lJTU/nFL35B9+7dAfjb3/7Grl27wn6urq5O3D+BQAC73U5dXR0AmzZtOpm47vfG6/Uyd+5c\n7rnnHsA8JQLianI4HLhcLnEZqxNjJAgtC1CW17FOpSr7U41p0aJFvP7663z66afy/YaGBjkJd+zY\nkR/+8Iff+m9GA7/fz+OPP86//vUvwLQiUlNTZU6HDBlCTk6OzMGePXtYuXKljFe5RAHatWsXsecI\nBAI88MADMoZQq9lms9G+fXs5kTc1NdHc3CyW80cffUTfvn0lmzsWc+33+1m3bh2PPfYYYLqO/X6/\nuIs7d+6Mz+cTWW9oaMDr9fL1118DkVl/ShYPHToUVrY1cuRIRo4cCUBpaSmBQEC+d/jwYfbv34/T\n6QSgpqaG1157TcI1VVVVBINBOnToABxxi4O5btUeE2mqq6v55S9/CZjxWLvdTkZGBmDGlFNTUzl4\n8CAAO3bsOMqjGEuLGaC+vp7FixeLZ61Lly4AMuYZM2ZQWVnJhAkTADMnIRYhyCVLlvDLX/6S008/\nHYA333yT1NTUo0KnK1euBMxwni6lwtyEkpKSJBbx7rvvsmvXLlEgNptNlC/AoEGDyM3NpVOnTvJ3\nXq8XICoxGKUA3nrrLe677z7Z9MF0tSm3qcfjweVyUVVVBUBBQUFExtNS4aakpBzlPlUbnMfjCdtM\nX3rpJbZs2SI/Z7Va8fv9sqldfvnlFBUVxbTkAeD111/nhRdeCEuOueCCCzjjjDMA0y1ptVrZsWMH\nYB6EmpubxZ02cOBA2Ygjid/vlxCB2sCUTBYVFXHJJZfQv39/wAwhLFy4UOK3GzduxO12i3KOJmpe\np0+fzhNPPBGWWDdixAj69u0LQElJCRUVFfzzn/8EkJ9T5WCRiNWqeezfvz/79u3jggsuAOCSSy6R\n0JYKfSl58fv9dOnSRQ4Rq1evpkOHDpKjkJiYSEJCAldeeSUAP/7xj8U4SEpKioq8B4NBXnnlFdav\nXy/POXz4cC666CIA+vbtS3Z2NrNmzQLgnXfewTAMbrzxRoCwGHo08Xg8/Pa3vwXg2WefJT8/X5J5\nVVhEGU6JiYlMmjSJbt26AZHP92iJ2puvv/56unXrxjvvvCPjOtbPqnFHUga0W1uj0Wg0mjijTVnO\nYFqjqhxjzpw5BAIBOWV16tSJq666iquuugowy2J8Pp9kWlZXV8uJOVIZdgrDMMTSfPjhh6murhZX\nXufOnenevbtkWzY0NEQl+1Y9r0pESk9PP+qEqn7GbrdjGIb8bG5urmR/qp9rbGyU5LwpU6bE7IRu\nGAYHDhwA4A9/+AN1dXUyljPOOINbbrlFvk5KSsLlcsmzBINB3G63uL07d+4clVO71+sVKzI5ORmL\nxSIlgNdffz0DBgyQuff7/fh8Pkm+a9euXUzmurm5mb/85S8APPnkkzQ2Nso4xo4dy8MPPxzmpVqx\nYoVYGMqqVclUkZhj9W927NiRMWPGiBUWKuehrl71/8zMTPFyFRUVUVFRIV6MpKQkBg0axBVXXAGY\nCWMnUJrZKgSDQT744APZx4qKinjsscfCKiOCwSDFxcWA2fAlIyNDEhuj6c1S77muro5LL71Umnfk\n5uby1FNPUVJSApjvqqGhQTxY5557LkVFRTFxZfv9fqZMmQKYbuoZM2Z8434cDAaZPXu2eIL69Omj\n3dpgulxvv/12iSeCubjatWsHwEMPPcRll1121OJJTU0FzE1QuXAjrZy9Xi9Tp04FzJhiMBgUBXDu\nuefSo0cPUShKcUfaTanqkFVZybFiZWpxqIzVESNGAKZrLDTrddasWXTs2JFf/OIXwBEXeSxwuVzc\ncMMNgBnPdzgcUrLzq1/9iuLiYvbt2wcgWa3Kzblt2zbat28vbu1QIikjDodD6pqHDh1K//79ZbPt\n3LkzZWVlvPvuu4B5CK2urhaFMWjQoKi5VAHJqH3++eelLLG5uRmbzSZjfuCBB+jatauMSdWsKiWo\nQlKh7uXWRsluamoq3bp1E1n1er0i6+pzQ93aPp9PDhFNTU1hVQe9e/emZ8+eEr6JVXy/pqZGFMYV\nV1xBr169wg5owWBQSseSk5MZNmxY1HMSDMOQOvdJkyaxfPlyOXC+9tpr9OvXT96R2+2mvLxclHnn\nzp3DQo0tKxciyY4dOyQT/sEHH5ScglDUeBobG3n77bclfKPkORK0CeWsNocXX3yRV155RSYqISGB\nTp06MX36dMDctBwOx1EvUwlEcnJy1EoKQuMpYCqvMWPGAGYphMfjkWQan89HSkoK2dnZER2TQinn\n42GxWGRT6t+/PxaLhTlz5gCmsCYnJ4fVIkYbJRdvvvkmX3zxBWDKRFFRkcS6Bg4ciMPhkE3C4/Gw\nc+dOibs3NDTQrl07WWxnnnlmmEKJFA6Hg2uvvRYwFV1oDLa+vp6XXnpJ6vmVxaTKAMeNGxe1MirD\nMFi+fDlgeiXUvFmtVnJzc7nuuusAM08iGAyGPcPHH38s1r+SJZUIFMnmR4mJidTU1DBv3jz5etiw\nYYDZC9lms4kXoqGhgaVLl4pSsdlslJSUMHToUMBcK7FuNWqz2ejbt68kT+3bt4/a2towJbJ582Y2\nbNgAQM+ePbnllluiIiMqdgzmQfePf/wjAMuWLePss8/mkUceAeC0007DMAzJq5k5cybbtm3jRz/6\nEWCuh5aNpyLdglQd0J5++mnJ8xk7duwxP0vlWjz11FNUVFTw9NNPA8c2cFoLHXPWaDQajSbOiHvL\n2efzSeesX//61wSDQTmtFBQU8Mgjj0hs5Xgn3Gg2UHc4HBJfW7RoEbm5uVI6k5eXx0svvRQWj8vM\nzIxp97JvQs2X0+lk69atLF68GDDdUkOHDpVyjmhbFsFgUMICTz31lFiX6enp3HTTTVI6k5CQEHYC\nT0xMJD8/n48//hgwXeI+n49zzz0XMN9NNJpKWK1W8UqoshdVSfDBBx8wc+ZMcbUbhoHD4eC2224D\nzNKZaHWQa2hoELlVTS3AXGslJSXicaiqqsJisYirddGiRezYsUOeyWazhVlHkbScHQ4HNpuNjz76\nCICvvvoqrOFLQUGBeACWL19OTU0NeXl5AIwZM4axY8cer4VrVLFarQwbNkye55133qGuro7HH38c\nMK26mTNniov11ltvjUoOiyrL/OCDDwBzHao8m/bt2zNw4ECRmdWrV/P555+Ll3Pr1q107NhRvHiZ\nmZkkJCTIe8rJyRFrtbi4OCIWqpLNpUuXSjVHyyoe9YwqRPnKK68wePDgsKYkkSJulbNyOXz22Wfi\nomxqasJisYg756yzzpJWi4qWccJQt0uoYo/0grPb7VLK4fV66dWrF127dgXMZIkXX3xRhEPFgaMV\nD/8+2Gw2vF4v5eXl8vWdd94p8fxoU1VVJWGByspKqa/93e9+x1VXXSWbU8t59Pv9VFdXSww6GAzS\nqVMnCgsLgSMbe7QJBoNSzvP888/jcrnCFFhaWhq33347EL0QQiAQ4Mknn5SaTsMw5LMLCws544wz\nwrqW7du3Tzptbd++HYfDIQcQl8tFYmKi5F1E+uCTmZnJ4MGDAbMGWymJBQsWYLFYZOP3+/3Y7XbZ\nI2bMmMHmzZt58MEHgSNhkViuR6vVyrXXXiutUVeuXMmKFSv405/+BJhJa/X19ZIom5ubG5U+Dh6P\nh3fffVdc1zt37pR5TE1NZfbs2bz22msA0m9Cfb+pqYnGxkY+/PBDAKZNmyY95AF+9KMfSSiiS5cu\nra6cDcOQHhlut1sO8+p7apzNzc18/PHHEtpxOp1MmDAhKgmZcamcQ2MTjz32mFgQNpsNu90uC7xr\n167U19eHLfjQjUtNcuidstHCYrFIDPmyyy7D6/XKc3z00UfU1NSEXRrhcrnk+5G6guxkUPXQykLN\ny8ujpKQkJpuW1+vlhRde4I033gBM6/iWW24BzNaoTqfzqAOaUnRut5tXX32Vr776CjCt0D59+tC5\nc2cg8j3B1Ti8Xq/82W6309DQIAlg9fX1R7VVPfvssyW7O9KENo6YPn26WDOha++cc84hKSlJFHd9\nfT1er1eyb+12Ozk5OZKUVFtbS3Nzs6zFSM6xxWIhJSWFO+64AzBldcGCBcCRela1T3g8Hvr27St9\nzVetWsUnn3wiF6V88MEHdO/ePabK2WKxkJWVxV//+lcAnnnmGTlkgmn9JyYmipKM9OFN7Vt79+6l\nurpa9rn09PSwDPk+ffrI+965cydlZWUsXboUMC3lkpISken6+nratWsn3sarrrpK4sCqcqS134E6\nDGdmZkouRCAQwOv1Sk35hx9+SF1dnSQIGoYRtX4O8aUBNBqNRqPRxKflDEdO75mZmVJLW1xcTGFh\nIYMGDQKgV69eHD58WCzOtLS0sEvHVTmHclHY7fao3s6iXDFZWVm4XC6pa546dapcGADmybipqUli\n0JmZmTG91CCU0Ftjvv76a3HF5+fnR73WVo2ltraW6dOny3stLi5m4sSJAEdZzWDOryqr+fTTT3nn\nnXdkfs8880x++tOfRr12NRSHw0F6ejrnnXceAK+++upRpSRXXnll1LwpyjJauHBh2IUcycnJksU8\nYsQIysrKJHbrdrvJyMiQZ+jTpw9r1qxhyZIlgGmhWiwWqYOO9DzbbDYJdVx77bVceuml8rnHuuBF\nuecnT57M/PnzxQPw2GOPMXXq1Jh7sqxWKz169ADgkUceobKyUsoYDx48GNW9TclDx44dGTdunFwi\nkpmZKZ4SZb0rWdq0aROPPvool19+OQA//elPw64+VV3b1Dp0Op0Rn3Nl1Xfr1k3ed9euXdm4caPc\nUrdhwwauvPJK+dnKykrq6+ujUvUTHxqgBYZhyMJ68sknSU5OBo64e0NdlMqdBqZrxOFwyIZRX1+P\n1WqVTbxTp04x2XytVit2u11ca1u2bBFlAaYgDho0SP4u9NaoSBCalBMaR2z5M6Gxl9raWjZv3iwL\npmfPnjFz9S1atIiqqirZjK655hrpQ32sMan7ksEsY6usrJQ2r7fffjvt2rWL+uarXHVwRGGohJ6G\nhoajlLNyLUcDJX+LFy/G6/WG1QSrWtrq6moyMjI4//zzATM2m5GRIbH+Q4cOMXPmzLBywqSkpKjE\nnFtis9m+sXxQKQXljn322We54YYb5EYrr9crcelYYhiGKK6srCxSU1PDroh0OBxRC3uotZKcnExR\nUVFYQ5eWY1ZjVPP585//HDCV4Lcd7qMhH8pVnZeXJ4lsgUCAjRs3Su+Me++9lyFDhkgd9H333cfh\nw4clCflYxkBrEbfKWSmM3Nzco5K4QmN1NptN4odLly6luLhYNu3s7Gzy8vLIz88HonMa+yZCDwmh\ntZ9gZjZeeOGFYXHPSBIa9wxVEi1/JhgMyoGhrq6Oqqoq2QAieSnEN6GUxNy5c7FarfJeL7nkkm+0\nGgzDwOVyyX2se/fuJTU1VeoxVa/taBE61+rP6p5slcmqemiH/lxZWVlUGjOExufVOlTz3tzcLLW0\nycnJXHrppdKkRnUtUwflFStWsGTJkrBrUYcNGyabXrRpmYMQ+vc2m01koKCggEsuuUSUSq9evWJy\nCA3t/90SdZhTc221Wunbt68k30Wa73qhhmEYvP/++4DZi2DSpEniBY117Xho8ll+fr7kTixatIiC\nggJJ3lWZ4sqSrq6upqGhIazTpPr3Whsdc9ZoNBqNJs6IO8tZ1ZWpk+uxbq9RX6tY7YwZMwAoKytj\n+fLlEpO++OKLKSgoEKsqVic1dTpXtww5nU4pCwPTvTJ8+PBvbasZCVqWiIRmRKoxKzdlx44dwyzp\nSF0w/m2oTHG3201iYiJnnnkmgIRAjoXP52PKlCksW7ZM/m7UqFHSfz2aZVOhVqm6iQzMeNy0adPE\nymhZXWC320lLSwvLnYgUFotFrEjVIjI03KI6ax08eJBDhw5JCCktLQ2Xy8WmTZsAM6O4trZW5Ckl\nJYVrrrkmKvW3J4PX66W2tlayd4cPHx7VPBU119XV1SLvWVlZYTFlwzDYuHGjuGJV2Wa0Xe/Hs5p3\n7tzJM888A5iu4/Hjx8f8StlQlKfh3HPPZc2aNYA57926dZMM9IyMDDweD1u3bgXMcYdeZxnJ3hlx\np5z9fj8HDx6URazizaGoDa6pqYlXXnlFkk7q6urIzs6WO0F79+4d8xrFUFScMzU1lbq6urBNsF27\ndlET3NDwQOhnfZt712azkZ+fL40/orlhhY4BjlxXqdoZHj58OKxpBBy5+nL16tW88sor4oZq164d\n//jHP2IyfjjS+KCsrIzXX38dMGO769atk80YwmXA6XSGXSMajRp9gOuuu44DBw5IA4bGxkaZ15qa\nGjZs2CD1wiNGjMBqtcpBedu2bfj9fpnn4cOHM3LkyJhvzi3dxapkTR06ZsyYwcqVKyU2Hs3cCq/X\nK6VGM2bMEFm++OKLw3ppl5eX8/Of/1zi+R07duSqq66Ki30u9OKLRx55RHpSPP3003LBS7wQahyp\nMrTt27djs9kksa2qqoqNGzfKoTMrK4tJkyZFJYE07pSzy+Vi6tSpkmgyePDgoxq8q7tW77zzThYt\nWhS28U6aNEnuOY3VBnwsLBaLHDj8fn9Y3Cs9PT2iHZO+iROJl9TX17N7926x6qqqqnC5XDLH0bBA\n1Wf16dOHJUuWSG3qM888w0033QSYByCbzcbq1asBuOmmm8LG+U2N7aOFmqeysjK523b//v1HWcuh\nNfs5OTkUFBREPV8iKSmJBx54gFtvvRUwGwKpphLqLm91u9fChQspLy+XigTVWEdZIFOmTCExMTFq\nnc1axvZbVnAoLBYLlZWVcn+v6lx1zjnnAGbeSrTG3NTUJE05/vOf/8i+tmfPHnr27EllZSUA8+fP\np7KyUvI/brrpJomRxpLQW+x+/etfs3jxYqk1z8nJiSvFHIrFYhFPYIcOHQgEAuLB2Lt3L59++qn8\n7I033kiPHj10nbNGo9FoNP+NxJ3lXFtby8cffywuv7Fjx0rf48bGRj744AMpSWpoaAirnfz73//O\nD3/4w5iXPRwLq9UqLvqWWZih90xHA+WaDC1Lg2Nb0Gpc8+fPZ8+ePWJ1TJ8+nYSEBLmqMSMjI+KW\nnbIkb731VjZu3MiiRYsAeP3116UdZ+fOnfH5fLz55puAWdJjs9nEm3LLLbfELGM/ND6Vnp4uLSVD\ny+rUz9lsNimtuuSSS2JmGdlsNrEqfvKTn/DjH/8YMGPm9fX1ElrYs2cP+fn5Up6ydetWLBYLP/nJ\nTwAYMGBAxOddyarb7ebQoUPSQauhoUHk1uPxkJmZKTd8uVwutm3bJm1ob775Zrp06SJZ5dH0vtls\nNrGG6+rqJMwxb948li9fHnYFZlFRkVw5es8998SFlzAYDEq9eEVFBRdddJH0H4jHewOOheqEqHRI\ncXExv/3tb7nwwgsBM3YeLf1iiYU7FfjGDz148CCDBw+W1mpKkYQSehnD8OHDxdXWsWPHk3U3HO+X\nT2qyVI3oWWedxYYNG0RZP/7441x33XUnkyzzbeM+asxqE/P5fMdMuAtFxUh/9atf8de//jUshFBa\nWsq0adMAs4b8BDeI7z3XKkaoDmnTpk0TF7fL5aKpqUnG7XQ6GTVqlLT6bIX7V09orlui5Pnzzz+X\njWvfvn1hCjoxMZEOHTpw/fXXAzBx4kRycnJOJrHxpMb8jb94DHexUoJutxu32y1KMDEx8USV8wnL\nh5LN/fv38/LLL/PKK6/IWNT85uXlcfbZZ3PZZZcBZulUcnKyKGeVoxKaGHmCfK+5VjXBKrZ5ww03\nsHbtWuBI/28luxdccAHXXXed9J5uhbyak5KP0NJMlTi1b98+SktLJawRATdwRPfqsH/o/5KUwTxk\nnORB4ztPhHZrazQajUYTZ8Sd/zctLY377rtPrqk7fPhwWCODrKwsxowZA8Bdd93FoEGDYp4B+l1R\nLqurr76aP//5z/JcjY2NUR17qOfheChrZ8uWLWGJbB6Ph+HDh0sGejRDCSrZSLUNHDhwIP/85z8B\n86KC3bt3i5UxceJEbrnllpjdntUSdeoeMWKElG/U1taydOlSyRDNy8ujc+fOkjEcTxUHoYRamKoL\nnnoGiP7taqEhg549e0ri3/79+0Vuc3Nz6datmzTDyM7OPmZDjGjPt3KnlpSUAKYcq8z3FStWMHjw\nYAnN5OXlHXUVajwQDAbFU1JYWBh32dnfl9CrUKP6ufHm1lYoxRUMBkUII1lT9n9ExVXi8/koLy+X\n+tzs7Ozjdts5Dt/LLaXuEf62Ra7cw++88w6PP/643OrTv39//vWvf51Mx6dWm+uW9cNWq1WeKQKd\niCLiIo4wp9qY4Vvc2l6vl9dff10OaI899pjEDCdOnEh2drYcTCOg4E61uT6hdRh6096psFdHgO88\nKXGrnGPEqfjCW2XMwWCQYDAoMdNAIHDMGvQTQM919DjVxgwnEN/3eDzitYqCJXeqzXVbHDO03XEL\n8eUX0Wg0Go1Goy3nFpyKp7G2OGZom+PWY249tHxEj1NtzNB2x33kB2OknDUajUaj0XwD2q2t0Wg0\nGk2coZWzRqPRaDRxhlbOGo1Go9HEGVo5azQajUYTZ2jlrNFoNBpNnKGVs0aj0Wg0cYZWzhqNRqPR\nxBmxuvgiXourT8XC9rY4Zmib49Zjbj20fESPU23M0HbHLWjLWaPRaDSaOEMrZ41Go9Fo4gytnDUa\njUajiTNiFXOOGqG9w0Ovi2uti+DVv6/+vVPhcnGN5r8Jv9+Px+MBIDk5Wa9hTVxwyilnwzCorq4G\n4OWXX+b9998nPT0dgJtvvpkf/vCHADgcDpxO50kvRPX7J/rvBINB3G43AAcPHsTlctGpUyfA3CAc\nDofeJFoBwzAIBAJYraaTKNYHqNDDnCIQCOB2uzl48CBgymZmZiaJiYkA2Gw2LQutjJr/9957jwkT\nJpCQkADA3//+dy699NK4nG815mAwSENDA42NjQDU1dWRnp5OTk4OQKvsa9EidD34/X6CwSAACQkJ\nsmb/W/nvfnqNRqPRaOKQU8JyVqcvj8fDZ599xqOPPgrAhg0b8Hg8pKWlAfC3v/0Np9MJwA9+8AP5\nc7TH6ff7qays5LHHHgPgww8/xOPx8IMf/ACAX/3qV/Tr109O89Een6KtnL5bYhgGzc3NAMyZM4cd\nO3Zw9tlnA9ChQwfS0tJEJux2e9Se0+/3U1tbC8Cnn37Kxx9/DMCqVauoqKigoaEBMK2G5ORkLr74\nYgDuu+8+8vLysNlsURnnfwM+nw+Ad999F5fLJW7tsrIygsFg3M21YRgyxp07d/L888+zZ88eAHbt\n2oXT6WTKlCkAXHDBBTgcjqiODb7ffqF+t7a2lk8//ZTu3bsD0KtXr6jvf9+VYDCI3+8HoL6+nnnz\n5jF79mz5etCgQQBMnjyZlJSU7+0BiDvlfKKxYMMwaGpqAky39fvvvy+/36FDBwoKCsTd07NnT3r0\n6Nlr7PMAACAASURBVAFAYmJiVJVPMBgUt+XLL7/Ma6+9xu7duwFzowgGg8yZMwcwX/Bzzz1HUVER\nQMQ2CiVgav4OHTqE1+sFwOv14vf7Ze5ycnKwWq1HuYe/r1s/kgQCAf7zn/8AMHXqVLp06UJ+fj5g\nzm11dTVDhgwBoEuXLtjtkVsGavNpbm5m48aNPPPMM4B5aKivrwdMZezz+cLmsr6+nunTpwOm8n7r\nrbdEHuJprhWhLlcAl8vFli1baNeuHQBFRUURnecTRR2EPv30UwzDELlOS0uL2/lVY37uueeYO3eu\nKOvm5mYSEhJYunQpYBoe2dnZcfkcLVHy8u9//5vXX3+dRx55BCAqsqI+2+/3yx7bUpEahhGmjKuq\nqliwYIHM9VdffUVZWRmHDx8GzLW5fv16AK699lqKi4u/9+ElflbL/3GiD1BfX895550HwOrVq7FY\nLPTp0weA2267jZKSEnJzcwFISkoiMzMTIKqnMp/Px6effsqdd94JwI4dO/D7/SKASjDUaX7p0qX8\n7ne/4/nnnwcgNTW1VRfarl27ADPetnLlShG0uro6GYMS3FBlnJaWJvOXm5tLfn4+t99+OwCnnXYa\nmZmZMbc4DMNg48aNssgDgQC33347I0aMAGD37t0899xzzJs3D4Dnn38+ohtBIBAAYMuWLTz++OMs\nWbIEMOe3a9euAIwaNYohQ4bQsWNHwMxB+PLLL2WMa9as4fzzz2ft2rWAKcexIBgMyvM0NDRQX18f\n9nVNTY1Yc0888QRlZWX0798fgNmzZ9O+ffuYjLslwWCQjRs3Aub+YbFYZI9QVk88ofJT1H4wY8YM\n3G635CT4/X6sViuVlZWAeTBqrYTX78KxPudYuRXHsiBdLhcAb731Frt375Y1EOl4s9vtZvPmzQBU\nVFTImurYsSOBQEDkuqKigsrKSvGybtu2ja1bt4qhdeDAAVJSUmQOCgsLmThxIgCdOnXCarV+7/eg\nY84ajUaj0cQZcWc5nwgNDQ1ceeWVrF69GjBPmO3btxeraciQIVgsFpKTkwHTVRJqCUYaZYX+9a9/\n5fe//724Ma1WKwUFBfz4xz8GoLi4mBUrVvDRRx8BpgX74YcfUlZWBkC/fv1azSJ1u928/fbbADz7\n7LPU1tbKKVFlNiuUS0f92eVySSZ8WVkZfr9fXK/t27fn8ccf52c/+xkQHbfUsfD7/fz5z39m7969\nAEyZMoULLrhA5q++vp4lS5ZIBn/o80YCJW9du3Zl4sSJYkkMGDCAK664AoDOnTuHZdgGg0F+8pOf\nkJWVBcCf//xndu7cycqVKwEYPXp0RMfcktBcia+++gowvS4bNmwQd59yraqwSHl5Oc3NzWLtV1RU\nxI3l3NzczCeffAJAdnY2GRkZXHjhhYD5LlrmXsQawzDYunUrM2fOlK9TUlLEi1VTU4PX65Xs7fT0\n9Lhwaft8PnG92+32ozKwDcMQmV6zZg2ZmZkSfookwWCQ/fv389xzzwGmNaz2q7POOouMjAyZP5fL\nRWVlJR06dADMcGhycjKnnXYaAPn5+RiGQe/evQFzbfbq1Qs4eQ9Xm1TOSggHDx5MeXm5/H2XLl14\n+eWXGTp0KGC6i0OTO07GxXCiBAIBUVz3338/LpdLXtZll13GU089JUlJVquVG2+8UdxWf/zjH2lu\nbhZ3c9++fU8q6ULh9/tpampi1apVwBGXUkZGBmCWYGRnZwMwdOhQDh8+TEVFBWC6wn0+nySaVFZW\n4vP55ABSWVnJAw88wJgxYwDIy8uLyQaxbds23n33XfLy8gD42c9+FpYcs3//fg4fPkxqaipAxBNn\n1GaUnp7OmDFjGD58OGAuXCWXLcu7LBYLSUlJ8gwpKSl4vV72798PtF6N/oly6NAh3nnnHcCMEdbX\n10v5X4cOHSguLhZZqq2tZePGjbLpKVmPNYZhsGnTJpm/0tJSKioqqKqqAsxDRceOHaN6iD8egUCA\nd955R1yphmGQmJgoB2cwFaEK1cVDGabP52PVqlW8+uqrgLk333bbbbLu7HY7Pp9P9ki3282gQYOi\nksgWDAYJBoMik01NTQwbNgyAESNG0LNnTzHovF4vtbW1ksi5Zs0axo8fL+NsbGykS5cudOvWDTDX\nqlrXJ2tQabe2RqPRaDRxRpuynA3DYP369WJ9NDU1YbPZxI3w1FNPcfrpp8uJMhAI0NjYKBmj0bCc\n1WevX7+ee+65J2ycN9xwA2Amy7RMSHM4HNx2222AmRyxceNGcdd7vd5WSwLauXOnuKY7duxIUVER\n48aNA0z3uUqIsdlsYW7upqYmysvLmTt3LgDTpk3D4/GI5QxQXV3Ntm3bAMTqixbKs/DQQw/hcrnk\nOdq3b4/FYpHnmD59OhaLRUIK0XK/2+127Ha7JPG0HLv6D0wZqqurk58944wzcLlckq0bbcs5NONc\neVLq6upwOp2MHTsWgAkTJpCdnS3y0NTUxObNm8VSUhZ1rAkEAqSmpkoVwrBhw9i2bRsHDhwATMt5\n8ODBIhextkDVGKxWq1RVJCcnU1RUJJ4Uv99PUlKSVCBEu0Q0FCUr1dXV3HXXXezcuROAiRMncujQ\nIVJSUgBkTapyQsMwOP/886PSeMRqtdK5c2cGDBggX19++eUAlJSU4HQ6xeoNBoOkpqbKc6nvq7XY\nvXt3unbtKlZ4azY5ahPKWcW13nvvPa655hqJa9lsNn76059yxx13AGbstqmpSRREWVkZX3zxBeec\ncw4AY8eOjfjLVy73SZMmcejQIfn7gQMHSv31N2WKq834/PPPZ9OmTSK4DQ0N8r2TefFut5t27dpJ\nPXV1dTV33323xFNaulpDlbPf78fr9UoM0TAMUlNT5XmDwSBZWVmUlJSc9Di/D8pFv2DBAux2O7/9\n7W+BI25l1Y1t4cKFOBwOJk2aFJNxfhOh5RoqVldaWgqYLvEVK1aIYvR6vcdU8pEcG5h9A1SM0Gq1\ncvXVV/P//t//A5B6TiUvBQUF2O12iTPHUmGEosJcqg6+traWNWvWSHgsGAzSr18/KblMSkqKuYyo\nNakUREpKCunp6VKKaRgG/fr14+qrrwZil+8ROsY5c+ZQXl4u73/EiBHk5eWFua2VyxjMMauDXqSx\nWq0kJiYycuRIwDw4qhwUteepdx4IBKirqxN5aWxsxGazScy5Q4cOJCUlRUSvxL1y9ng8Ere4++67\n8fl8Iqw33HADTz/9tCg7v9/P5s2b+fLLLwF444032LNnj1idqhFFpAgEAlLHumHDBhHUTp068d57\n7x3X+lUC4fF48Hg8kkBWXl4uJ/2TQcVDbr31VsBM0lGbKByxlsHcpLxeL+vWrQNg1qxZrFixgh07\ndgCmgCclJcnG7fF4KCkpESGPNurQ4HK5yM/PD0ssMQxDnqOiooIOHTrQpUuXmIzzWIQmgoG5aWVk\nZIjHxzAM3n77bVEga9eu5Ywzzohq8xSAuXPnStyzoKCAyZMni2XcMkablpZGUlKSWCexVnChNDY2\nsmzZMgD27dvH2rVrJXFpyZIlvPbaa9x0002AmfATaknF6jlCDwkWi4X9+/dLnNzpdHLPPfdIvkgs\n51opsVmzZmG1WjnrrLMAGDlyZNgzGIZBeXm5yHxBQYGUUUUDVRoKZnKmMqTWr1+Pw+EQT09NTQ1f\nfPGF5DGVlJSQlZUlHoBIlo7qmLNGo9FoNHFG3FrO6kT13nvv8Ytf/AIwrSK73c7/Z++8w6uq0sX9\nnpKck14ggUAioQsEkC4CioMKKig6KrY7inq9OKNebFiujgWd0dEZy1z1zogFvVcZnLEhDlIEBkFA\nRDpSQ0hCEkggvZ2yf3/s3/rYJ4QinIau93nmGRNOkrXXXutbX1//+Z//CcDTTz8d4C6z2WyceeaZ\nUkazf/9+KioqKC4uBkKr5agOPh999BFgWpLKIn3kkUfIyso6rkarrNZt27bh8/nEfb9z505xcZ6q\n+6Rz587ye1NSUnA4HAG/0xqvb2hoYPbs2YCpCTc2NopG6fV6qa+vl9/l9/sxDCMiLjXDMMTF5/V6\n8Xg8osHHxsZSU1PDI488Apia/S233BJ1rQGt3deUa1iNMSMjg9TUVCn/efXVV+nevbuUWoUaFUf+\n5JNPJIyRnZ19RDctdXkBmB6KmJgYcWNaM4sjieoeZy3xamxslOdwuVxs3LiRt956C4BLL72U/v37\nB8QUw43NZqNz584iv0pKSigsLJS5TktLY9CgQRG/KMLn8/GPf/wDgFWrVtGxY0duuukm4HC2vrUs\nb8aMGbLWL7300rDKDqvlXFxcLJ6U5cuXc/DgQflcTU0NXbp04ZJLLgHMXJpwtfyN2sNZCdfnnntO\n4okxMTHcfvvtTJ8+HTjy9hW73U5MTIy4IFTHq6O1Zgs2e/bskdpkQNxMl19+ucRw4egbXAnB77//\nPiBBqE+fPkFTLGw2mwjMlkkvNpstwH0XExMj/Z3bt29PXFycKDobNmyQjmxgCt/y8nLZbOHs7QuI\nGzsxMZHq6mqJOXfp0oWXX35ZFDa73U67du0C6rejweVqfS/Jycmi7IApfIcPHy7dxRYsWMDrr7/O\ntGnTgNDPtRqHVRFWHalUKZXNZqO5uVnyPebMmUNtba10DCsuLg44YCJFTEwMXbp0ka9V21Tlphw+\nfLi0TwX43//9Xzp37hyxcA2Yc9u7d29R1iorK/H7/SLPMjMzA7pUhRu1Pnbv3s0rr7wCmArlpEmT\nZK59Pl9A/fiOHTv4+OOPZT30798/7ONX8+dyuaRb2Pbt28nPz5czx+VykZGRIWs/nDfEReXhbBiG\naLaFhYUyiWPGjOH5558/anKUCuarDEHVM1Vl5oZyUv1+PwsXLpTEI5vNJnHi+Pj4gGsL1f9bF6th\nGHLwqfiXWrgqrneqtIxtqrFYlRb1GbvdTnJysjS8OO+88/D7/aJVfvjhhxQUFAQkhO3evVsWdTgT\nlmw2G4MHDwbMJgLLli0TDV5dIaqUhtTUVNLS0uQ9xcbGRsXhDIfnPjY2NkA5s9vt5OXliaBbv349\nmzZtkozRtLS0kD6DOvwvuugi8aQsX76c8847Tw6thISEgCY1FRUV+Hw+aZP5z3/+k1tvvVXqRyOF\nw+Fg6NChAYqGy+XioosuAuDOO+9k3759kgm9adMmeR8QuXiu9YpZtX/Ve+nfv39ErWYlAx5//HEx\nqkaNGsWIESOk53RNTQ0JCQmScX733Xezb98+yatQDaPChbXBUmNjo1SXXHrppezdu1daoW7ZsoVd\nu3aJ0WWtgQ81Ouas0Wg0Gk2UEZWWs9fr5bPPPpP/VqU+r732WqsXiVstUK/Xy5///GfAjFEnJiZK\nzWsoNTPDMCRuAabLWLV0s9vtARddtFYL5/V65SalyspKbDabZC+eSLz6x9Ca5d4aLf+mw+GQloET\nJkzgu+++Y+fOncDhUqBIuS2VJfT666/z1ltvybiWLVtGRUWFWGxjx44lNzdXLGmrezCSWN9Fy5u+\nVH20mnuXy0WPHj1C3npUoeb2oYceknn9/vvvKSkpCeha5vf7jyiZUl6g4uLiqLiVymaz0dTURFVV\nFWC6tePj46WsJicnh6SkJAmTpKSkRNRlrGhoaJAYswrFqOoPt9tNQ0NDQA1xuPD7/Xz88ccALFq0\nSHJSMjIy2Llzp/RqyMvLo1OnTuJJWblyJYCEzbp27RqR2n0wPZPqsqRevXqRlpYmMuGLL77g2Wef\nZerUqYB57XC4rPzI75ZWsAbo3W43jz76KGBunGNNimEYrFmzhjlz5sj3Ro4cKYd7KLFe6Qama1LV\n+MXGxhITExNwcFkPaBWvfe+99wAzPuNwODj33HOB4NeIqoV3Mkk66hnS09PxeDxyQNhsNnJzc8Pq\nzrai5rJNmzZMnTpV3Kt33303ZWVlUkb33HPPBbTYU7kA4Ra+Vjelije3Fl5Q/11dXS3COTc3lwED\nBogwDvX41bg6d+4sTWgOHDjAhx9+KDHl9evXs2PHDlEoXS4Xu3fvFrfl2LFjIx5vVmzZsiWgB0Fi\nYqK4551OJy6XS5Lt1JqO9OG8Y8cOcQnD4XULZm5NZWWlyJtwjVXJPBVCcjgcYghdfvnlJCQkyHpI\nSkrC4/Hw/vvvA6ZSdNZZZ/H6668D4c9RgcPrOj09XWRtfHx8QKjvyiuvZP369fzxj38E4Prrr2fz\n5s1hqduPusPZMAzWrVsnm37gwIHSveVoFp/1Wr4pU6ZIYlVOTg5vvPFG2F58y9iUSgizxpsV1phH\ndXU1b7/9tlzlaLfbSU9Pl8vTQyXUTkaoWzsAffnllwHP27Vr14hsMis2mw2n0ymx8YULF+L1euWS\nCfVO1NwHs6PPiaD+7vbt23niiScAUzj813/9lyiRysJUc1tTU8MXX3whsb0uXbrQp08fmetwXg2o\nhFJ2djZTp06VvbZz504WL14sz7B161aWLVsm3qNhw4ZFhYfC4/Hw+9//XqoM1Nxt2rQJMC24+Ph4\ncnJyAHNPR1qp8Pv9zJo1K0CZdrlc8i7q6upYtGiRWPvhVCYaGxtlHY4cOZKnn34aMC96aXnJRUND\nA++++66M8aOPPopoDoK1qYu114N17txuN/fcc4/ce7B79242b94clqtFI79bNBqNRqPRBBB1lrPX\n62Xu3Lniwuvfv79oZi0v8Pb5fDQ1NTFjxgzAdFnW1NRI96fZs2eLpRRqbDZbgEvX6/Wyfft2Ga+1\nJZyqB1WW8iuvvMK8efPEMnK5XNx111106tQp5GNuaGgQrfF4mctK+wX47W9/S3l5eUCZzVNPPRU1\n1pEqpaqqqiIzM1OyzlvGPSPhzgYz2125A7Ozs3nwwQePsDSUG3P69OksXbpUxn7uuefSrl27iHet\nspZ/de7cmbq6OhmzCuNcddVVQHituWPR0NDAjh07Ajwn6gYtMDPS+/XrJ3s5XDWtx6OkpCQgFyE1\nNVVizlVVVZSUlEhmdLt27cIyZsMwiImJkZDRoEGDRPa23Geqvlz1MB82bFhEu/RZZRkgYY2W82az\n2cjMzJR2rqqEdMCAAa1+PphE3eFcX19PYWGhbJ49e/ZIDPkXv/gFPp9PWkiuXr2aBQsWSHJBc3Mz\nPXv2lHtPw/ny7XY7ffr04YsvvgDMA2LJkiWAeb3e6NGjA9xSdXV1cv3evHnzqKurk5Kp4cOHc9dd\nd0ldY8tGD8FcEDU1NdKzuXv37kdNKjEMA4/HwwsvvAAgbjZ1oAwZMkRcmJHEMAw2b94sc+9wOPjD\nH/4g8biWykOkBO+ePXskHFNTU0NRUZGUcyjB8cwzzwDmXMfFxUkjmgEDBoSsn+/J4vP5cLvdkgCW\nmZlJSkqKuFqj4YAD85BT5X5gHiIdO3bktttuA8y9l5iYGFVXRoIZC1XKWExMDElJSSLf1PfVYROu\n+6jtdjupqanccsstQGCfBIUaS319PS+99JLEoGfMmBHRcIHX65V2uHFxcUe0oW2Jcr+7XK6wNdSJ\nusNZdXtSVuSCBQukV7a6CUnVoClNUWm5V1xxBS+++KIkoYRzY9ntdn79619L5uLOnTsl7vnYY48x\ncOBAyWRMTExk3759Uvju8/kYMGCACN877riD+Pj4VscfzGey2WwkJyeLhf/555/LjV9JSUkBSQ+V\nlZXce++9Yu15PB7sdrvEGGfOnBnx2ByYCtpTTz0lyXnZ2dlMnDgxQNiGS3i1hpqjK664QpRIm83G\nzJkzJRvb4/HwxBNPSPa+3+/nrLPOYsqUKYBpdURD5jMc9gTs37+foqIiUSgTExPJysoKe1z8aKh3\nvmzZMuBwAlJ2dja//vWv5dKFpKSkqFJ6wJy7cePGiXXf1NRESUmJxPu7detGU1NTRLqwqUskWsPa\nMe6DDz6gsrJSsrND7RU8Hs3NzWL0VVRUSNJxenr6ER6s/Px8yUlwu91yZ32oia5VqNFoNBqNJvos\n54SEBC6//HLeeecdwLTYlBW0Z88eHA5HQJvDK664Qq6M7Ny5c0SzhTMzM6W39u23387GjRsB8xmW\nL18e0AIuJSVF7qEeMGAA559/Pv379wdMqyMclpGKk6sav1WrVnHnnXcCpiU0YMAA0YqXLFnCxo0b\nxRVrt9vJycmR0ogzzjgj4tYRmFnk69atk7GMHDkyaHdhBwM1rvPOO49LL70UMFtdzp49m/nz5wOm\ne3L//v3y2by8PH73u9/JVZ/R0tXMGrfbvHkzhYWFEouLi4sjMzMzaix8xY4dO8RDAXD++eczefJk\n6bMcbVYzmGvmtttuk+5s27Ztw+v1yg1hPp+P8847T8q/ouEZlNWsvINvvfUW6enpcsd9pMdos9nE\nOztnzhzxcj700EN06dJFPC1r1qzhyiuvlLr4G264gU6dOv0865ydTicPPfQQHTp0AMx4m1qEYF7v\npdwKkyZNIjk5OWoEgConAvjss89YvHgxYDbGyM/Pl7jGgAED6NevnxzOPXv2JDU1VeIax1q4wY45\nq7gRmI1F1H29JSUlbN++XQ7jhoYGDMOQg65Hjx7Mnj1bnjfSm0259FasWEFdXZ2Mc8KECVETZ7aS\nlJTEq6++Cpjv/91335V13tDQQHp6utw5PW3aNFJTUyM+xy3xeDx8+umngJn/0b59e4ntZ2dnH1G7\nHUnUO7/vvvvIy8uTvXbRRReRmJgYFWviWLRr105K7+655x4OHTok8mTUqFFcc801Eb2cozUaGxul\nPriuro7x48fTvn17IPJjjIuLk7bO//d//8eHH34ImG1mBw8ezNatWwHTSPF4PIwdOxYwZXm4Ls2J\njp2j0Wg0Go1GsEUoOSZyGTnH5njq3I8at7I6GxsbKS8vF7d2fHx8QBKF6khzClbGscZ9wmP2+/1y\nG88DDzzAZ599Jm5Lj8dDWlqaZGbefvvtZGdnh2rMcJJz/c033/DAAw+I5fz++++TmZkZTAsuKHNt\nxev1UllZKaV1VVVVpKamSvZ7EMqQgj5mv9/P6tWrufXWWwHT1X7llVdKs5dOnTqdqvs9qOsjjAR9\nruWH/7+s9ng81NTUiCu2Xbt2Adb/Scx5SMbc2Ngo15xu3bqVm2++WUpbg2A5n/L6UI1oli1bJqWX\nmzZtoqmpScKjubm5/PKXvxR3fBC8LCf8w/pwDuRnKRDUGvD7/ZIB+uSTT7J+/XoOHToEmN3W7rjj\nDrn9yVraEYIxwynMdWt9qoNIyIRvCAn6mOvq6nj11Vel/eJVV13FtddeS9++fQEzPHWKCtHPci9G\niJArFGHeh3CccVvLQP1+vyj3dXV1FBcXS15CCPIm9OF8kvzsBYK1HMPn80kphLoru2XP51PgZz/X\nYSQklnN1dbX0B09KSsLtdgeznE6vj/DxUxsznL7jFnTMWaPRaDSaKENbzoH8FLWx03HMcHqOW485\neOj1ET5+amOG03fchz8YyW5JGo1Go9FojkS7tTUajUajiTL04azRaDQaTZShD2eNRqPRaKIMfThr\nNBqNRhNl6MNZo9FoNJooQx/OGo1Go9FEGZG6zila67d+irVzp+OY4fQctx5z8NDrI3z81MYMp++4\nBW05azQajUYTZejDWaPRaDSaKCNSbm0NIb89SaMJGz6fj8bGRlnTCQkJek3/SAzD+FFz1rK7o57v\nnxY/icNZXffl8Xiw2WxyF2cQ7/ANOn6/X26AMgwDp9OpN1cIsQoyqxDUc35qWK8b3bNnD4WFhYB5\nD27Hjh3lXu0gX7sXNAzDCLiJzW63R2RNqHmsr68HIC4u7qjjsM45mPeBW28DU3IvmuWf5vhE5475\nEVRWVvLII48AMG/ePNq0acOrr74KwKBBg4J5hd0pozaVuoR81apVAKSkpHDdddfRoUMHQG+qYGAV\nXJs2beK9994DYP78+aSlpXHTTTcBcO211wbjAvVTxuPxUFBQAEBhYSFZWVl07twZgJiYmKhcE4Zh\n0NDQAMCBAweorKykXbt2gHmFpNPpjKr9B4cP44MHDwLw+uuvM2PGDHJzcwF44oknOPfcc8OuTCjZ\n4Ha7gWMrjYZhYBiG3L3u9/tpbGyUMbtcrqibd82PJ/p2vEaj0Wg0P3NOa8vZMAzKy8v59ttvATh4\n8CA2mw2v1wtEl8tSjRVM7fwf//iHuPzi4+OprKzkvvvuAyA1NTUqLaXTBZ/PR1NTEwDFxcW89NJL\nrFmzBoDS0lJKSkpYvnw5AGPGjIlYfFRZ93v27GHatGkyJoC+ffuKdT9y5EiysrKIjY0N+xiPhc1m\nE2uturqaVatW0aZNGwC6d+9OSkpKJId3VAzDID4+HoDLLruMOXPm8PXXXwNwxx13sHjxYvFihRq1\nBux2+xEx5Jaof/f5fJSUlJCfnw/AihUr2Lx5M506dQLMNT1o0CASEhIAcDgcUSELDcOgsbERgFde\neYUPPviACRMmAPD4449HdejDOvcVFRXs378fgJKSEuLj4xk4cCBgyvJgzXV0zsYJ4vP52LVrl7io\n3G43WVlZtG3bNsIjC8Tv97N9+3Zuu+02AL777jv8fj/Nzc0AtG/fntraWtavXw/AiBEjokIQG4Yh\nik5paSkxMTGkpqYCpuvMugjV4m0tyS2cgsHn83HgwAE5jD/99FPWrFlDSUkJYMb0HA4He/fuBWD3\n7t106NABl8sV9rHW1tYC8P7777N27VpqamoAM8zRrVs3id9++OGHXHXVVeTk5ABElctSKZE7duxg\n1apVMsbs7OyoVDBtNhsOh0P2V/fu3Zk1axZTp04F4Msvv2T16tVcfvnl8vlwoPbNseLMSl5s2LCB\nd999V5S5vXv3UldXJ7k2b775Jpdccgk33ngjAAMHDhRFKZzr23qoeb1eioqKxAD5/PPP8Xq97Nq1\nC4CJEycyaNCgsI3teKg8pqamJrZu3crvf/97AL766iuqqqpkbbvdbmJiYrjuuusA+OMf/yihiVPl\ntDucDcOQiSsoKODtt98WKykhIYGRI0eKoI00amHu3LmTyZMns27dOsBcqElJSaI1tmnThqKiLmhX\nJwAAIABJREFUIt555x0AevbsSVZWVkS1XZ/Px/r163nqqacA+Pbbb8nJyeGBBx4ATO1cWf4AdXV1\nFBQUkJWVBZjWvxKA4XgOZYEUFxfz0UcfMXfuXMA8NGpra0XJUONRFl5SUlLEEoCUgvDee+9RUlIi\n8zl69GjOPfdcNm7cCMCyZcvYtWsXzz77LEBUWaRqje/YsYNly5YFHGrReDhDoALpdDpJTU0lLy8P\nMA+NPXv2hH1Mx4sxNzQ08M033wDwH//xHxQUFARY3bGxsTLfdXV1fPzxx5JcNnHiRHkvbrc76Ovd\nOp9qTE1NTdTV1YmlvH79ej744APWrl0b8LNK4Vi8eDEDBw6MuIVvGAZNTU2i3L/yyivMmTNHnkOh\nxtnU1ERjYyMff/wxYHpe+vTpE/CZkyU6d49Go9FoND9jTivLWVnN1dXVgGmB9uzZk4qKCsB09zU2\nNkoGaaS1MDWOadOmidUMMHjwYJ599llxAW7bto2HH35YsnX79u3LvffeG9E46MKFC7n99tvZt28f\nYFqYgwcPlrhWfX09hYWFYqEuWLAAwzD405/+BJjegHCOX2ngX375JR988AEHDhwAIDY2lsTERLGc\nHQ4HLpdLrM/u3bsTGxsb9rn2eDy8/vrrAJSXl+N0OhkzZgwAd999N+3bt5d1XVhYSFlZmYQ9Ro0a\nFfG1rVDrpbm5OcCiz87Oxuv1Shyxtbin1ZX7Y2t8T4WW5VMOh4P+/fsDpsenpZUUSk7Eu+DxePj0\n00+55557ADMz3jAM8bScffbZDBw4UMIkFRUVFBQUiJxct26drC31HpQL/FTx+/2yt6qqqli4cCFg\nvtPm5mYJMbpcLq6++mp69OgBwJIlS1i1apWsj44dOwZlPKeK3+8nPz+fJ598EoCvv/4ar9cr8xUT\nE4PNZiMpKQmAmpoaGhsbRf6odwOnfv6cFoezetimpiYKCwvl0EtMTKRv375s3rxZ/r2oqChi47TS\n1NQkL3jhwoX4fD5GjBgBwIwZM8jJyQlwAR08eFDcULt37z5uckgoMAyDxYsXAzBp0iRqa2slxnzX\nXXcxZcoUEQhVVVW88cYbfPjhh4BZHnbFFVfQrVs3gLDWbStXFMDy5csDXMTx8fF4PJ6AGFFqaipn\nnXUWQNjLqNR73bNnD//6178A8/1nZGRw6623ApCXl0dMTIwoQo2NjVRXV4urbdSoUWEb7/FQ8e+m\npiZiYmJE2ColWX3dWv2w9etw5yUoYer1evF6vZxxxhkAjB07Fq/XGzQBeyoo+bB3714effRRUdbA\nVH4ffvhhAG6++Wbi4+MD4rubNm3irbfeAszDefbs2QBceOGFdOjQQd7bqYQefD4fpaWlvPnmm4AZ\n+lJJaEOHDmX8+PFigKi/c/bZZwOmwrFu3ToZx4ABA056HMGkrq6Od955hy1btgCQnJxMt27dyMzM\nBEz5ERcXJ6GPgoICKioqxJXdtWvXoK0Z7dbWaDQajSbKiHrL2ZoxvHnzZrZs2cLw4cMB09Wan58v\n1nLbtm3p1auXaMGR0HpVstrHH3/MP//5TxlH586dJeOvU6dOOBwO+WxFRYVYzYC4fsJNeXm5ZHjW\n1NSQnp7Ou+++C5hJSoZhiMY4b948/v73v1NZWQlATk4OkydPFos13HOvks/69u3L3r17Zc20adOG\nDRs2iKWUlJTEyJEjJRkvWO69E0VZQ6+//rqU1gFcfPHFnHfeecDhRhTKC+H3+6mvr5dniCaUtRYb\nG0t5eTnLli0DTMtJWU0Q+RCTQoXGlMzo0KEDbrdb3K9DhgyR5LBIYhgGdXV1ADz99NMUFBSIvEhL\nS+OTTz4RK7SlV8IwDPLy8ujevTtgepOef/55wHQnT506VWToyaDWcFVVFe+//z7z588HICsrizvu\nuAOA4cOHiwvYOi4lHzweDx6Ph/bt2wOErXTtaKiGLn/605/461//Kh6f0aNHc8UVV8iedDgcGIYh\nXiybzcbBgwfJzs4GzHfzsyqlUot01apV5ObmkpGRAZhxrm3btknNWY8ePfjVr34VtFT2H4thGFRV\nVQHw2WefybjPPPNMXnzxRQYPHgwcdgWqRb5hwwYaGxsly3z48OFhd/MBPPTQQwGx2unTp3P++efL\nWJcvXy4KxoYNG6iqqpJDccKECQwaNCgiGbo2m03m7pZbbmHkyJEcOnQIMGNGqoYVzLnv16+fZJWH\n+9BQZX/r1q2T8ExCQgJTpkwJ6A5ljcH6fD78fr8oQuGMzx4Pq+JcWVkpYZBOnTqRkJAgyk+0jBfM\nEjZ1OKekpJCeni7jbt++vQjgSGLN5ldhMSU3pk+fzvDhw4+515qamsQ4KCgoIDExETAPcqX0ncrY\nwFTQi4uL5R1fe+21ErprrWbZmsG/fPlybDabKAmRyPtQGIYhNePvvfceNpuNSy65BIB7772Xzp07\nS+6NzWYjJSVF5Mfq1asl/gwEtVLotDiclQDIzMwkNzc3oA3moUOHSE5OBsx4UXZ29nHLEiA0SShe\nr5etW7cCZlvRX/ziFwDceeed9OnT54j6VPVcK1aswO/3S4xRWRzW2mF1kKvfEcxxqwSYBQsWyN+J\ni4sjPj5eam1ffvll/v73v4vyoXqDK6F22223haRM40RRmz41NZVBgwaJYrRu3bqAhA2Aiy66KCIN\nDwzDkKSuH374QcZ02WWXceaZZx4xd+rwVr3XVdJMpA8OhWEYomzs378fwzDo3bs3YLbObWk5RQux\nsbEiM1QDGpU89cMPP0RFO1fDMEQZU3tOjXny5MmtHsxqXdTV1bFgwQL5jMPhEMv0wgsvJC4u7pSU\naDU3I0aM4ODBgwHy91g1+IZhSGLsrl27SExMlEMwkrX7fr+fL774AjDnLi8vjyeeeAIwZbHNZqNr\n167A4XwFtV7q6urIycmRfJFgeuJ0zFmj0Wg0mijjtLCclbsvLy+PVatWkZaWBphZzWvWrBEXQ6dO\nnVptg9da5qXqXhMsDVnFiJRbY+jQoUyaNAmAM8444whN1e/3s23bNgAWLVqEYRgSQ1LWqLJiPR6P\ndI9KTk4OepMVq5tdzUdNTQ0PPviguK0rKirw+XwytpqaGgzDEI1SzX2kUR2glAa7YcMGGhoa5Lky\nMjLo0qVLxMrUVqxYARy2hsCMaylPDhz26qj34na7adOmjXRQ8vv9Ebs9SaEy5JcsWQJAfn4+fr9f\nslYjPb6jYbPZsNls4uZtamrC5/NJ/H/r1q0kJydLqCeSa1plZ/t8Pux2O+eccw7QunXm8XikC95n\nn33G3LlzRS726dOHIUOGAHD11VeLpXuyqPfarl07evbsKW7y5uZmaYva2rv3er384Q9/kGfLysqS\nuHgkLeeDBw/y5ZdfAmZY47XXXhMvZssbvpxOJ36/n5UrVwKmFyYnJ0f2ZjDXfNQfztZ4YlJSElu2\nbGH16tWAKXirq6slzV3dzqImUm1Eq0tYTZ7f7w/qgjAMg927d4vbsl+/fnJDj8PhCOhQ1dTUxIoV\nK5g+fTpgJmK5XC5JCAJzIasksW+++UZKIS6//HLGjx8fVLes2uxTpkyRG70aGhpoamqScXfq1Inz\nzz9f4iuvvPIKNpuNq6++GghurOVUMQyD0tJSwIxtWd/1j+m8Fuywh9/vl0PAMAxZp/n5+Rw4cEAU\nH7vdzp49eySJp6mpiYSEBJYuXQqYa6NHjx5ywLjd7pCEO1rD2mO4qqpKwge9e/emtraWTz/9FIB/\n+7d/O+XYZqiIj4+XBJ6DBw9SWFjI3/72N8DsVBUNa9nv98utdepKSPW+GxsbcTgcItd27NjBzJkz\nKS4uBsxa27i4OFlPI0eOlEQtVep0Kqg15nQ68Xq9UnaUmppKr169AHOOreWUfr+fmTNnSv6HYRiM\nHj1a1kgklCC1lsvKyiQx7emnn6Z3795HjEc9h5Lz6jBvamri+uuvD4g7B4uoP5yBgEYGBQUFctFF\nXV0ddrtdYrt5eXnEx8cHHLpWa9Da61VZ2MESZrW1tXz++efs2LEDgHHjxon2XV9fT1VVlWSyzpgx\ng02bNok1bBgGycnJEscoKiqioKBAGnx88803ctjY7XbJNA4War7uv/9+sfZLS0upra2VWFVOTg4u\nl4uXXnoJMAVEbGwsl112mYwrGjAMgwMHDjBt2jTAjIVaE1EyMzOprq4+alZ5y3ufW/vMyeL3+6VR\nhMPhkDG9/fbbzJw5Uz7ndDqpqqoKiO9XV1fz3HPPAWZtdr9+/bj99tsBM4ZubaUabKxzota01+sl\nLi5O2kLm5eUxefJk8Qa9++67PPnkk1FpPdvt9oBEtaKiIkmEPHToEPX19RFNTgJTOVbKmDrk1Bi/\n++47kpOTZa6//PJL8vPzGTZsGGB6YiorK8Xj2KdPn5BcR+v3+0lISJC8g6VLl8rhn5iYSLt27eTv\nff/997z44ovyfIMGDeKll14SSzsSWCsN7r33XsCcq2PNkdfr5YEHHuCHH34AYPz48YwYMSIk8i86\nJKpGo9FoNBrhtLCcFUrLVTVpYLppJk+eDJhlEVar2eo6VF9brWhrfPpkNWXl9n3hhReYMWNGgLWs\nNMrdu3fz9ddfi1VdXV0dMBa32023bt1Ei5w1axYVFRVy60xxcbFk7lpLKoKN2+2WGLLKirf+rfLy\ncmbMmAGYWnOHDh0iVpLUEvUea2tr+c1vfsOcOXMAWq0NLi8vl4svWnYyC2UmtM1mY+jQoQCsXLlS\nvCEHDx6kqamp1Zu91M8BEubweDwUFBRIlr21FWWw8fv9AdaywuFwkJCQIJaSujZv+/btAGzcuDGq\nSr6s+Hw+8Vrl5+eza9cu8TycddZZ5OXlhXROj4XqdPfpp59KuZeqglBfv//++/Tq1UvGfOutt5KY\nmCjeAIfDQVlZmfx7t27dQlLS5nQ66dGjh4RqEhISZE3W1tZSVlZGWVkZYLqL9+zZI/vuzTffJCUl\nJSrWR1ZWlsjeo1nAak8uXbqUZcuWybr/93//96CEClrjtDiclXBYvXo1RUVF4uaOjY1l2LBhEnM+\nVpxA/R71GVWeZI1Pnwzq0HzjjTcoLy+XTbBmzRp2794NmIdxRUWFCLf4+PiAOKjT6SQrK0ueo6Gh\nAcMwJCkhNzdXGquo2FGosM6HVbg2NTVx1113SRMSh8PB888/H/YmHq2hbu0BeP7555k7d+4Rh7KK\nI44cOZK2bdse052tUDkLwcLpdDJx4kTAbI6ibp2qqKhg3rx54rasq6vDMAxxS06cOJEePXowb948\nwHS9XnTRRXKHrNPpbPWqzmBgjZMfPHhQ4p7t27cPmB/lKlbrYcuWLXg8nqiI31pRiZtqLr/88ktK\nS0vF7XvxxRdz/vnnR6yBkYrJvvzyyxLWUIqQKqVLSEhg2LBhohinpKQE3ClQVFTEd999Jwlkbrdb\nZCgEL1nPZrPRtm1bxo8fL7/X2kJ0w4YNssaLiorwer0SBgtmm8uTRf39EymdUzXnV111FfX19SKb\nhwwZErKQXtQfztYLuhctWkRcXJwsypiYGAYPHnzMDEFrnNkae7QmKpzK2JRA9Xq92O12OYCrq6tl\nXO3bt6dr165SoN+2bVu+/fZbvvrqK8C0iFQNN5jae21trcSWExMT5ZlDpaVZn0lhTabbuHEjCxYs\nkH9r164d48aNi3jGMJiKw6xZswB46623xPpQuN1ubrjhBgCuvPJKEhMTj0igau05gv1sSpiBWdus\nBJXP5+NXv/qVZLIuWrSI1NRUWR+dOnXCMAx5hr1799KrVy/5XaGsJ7bb7WJlLlmyRBRIVdNq/bs9\nevSQ9dLY2IjX6426w7m5uZlFixbJBQ1btmwhJSVFnjE9PZ0uXbpEJIeivr6e3/zmN4DpLVMHamJi\nIm3atAnovW+9YGHjxo2sXr1asrUNwyApKUnWi9PplN+lqhmCgc1mC0hMtcqOxsZGKisrJW5eV1dH\nUlIS11xzDYAktFn3X7hlyYl4TQ3DoL6+XpTq6upqEhIS5E6BUBonOuas0Wg0Gk2UEfWWMxyu9ysr\nKyMvL0/KN+x2O126dDmq9tJSM7Jq+tbvnQrKfZqenk5DQ4NYDikpKVxwwQWAmU07ZMgQSbf3eDxU\nVFSIJep2u0lPTxdLKDU1lbZt2wbU1h3LwgsmLTPblcY9f/586uvrZb7uvPPOkGYInwhqrgsKCuSy\nc9VVST2Hy+ViypQpcoNPcnJyRGtwW4YNFC6XS7prxcTE8Mwzz9C5c2f5LBzuHJeQkEBycrJYLaF8\nFrvdLl6b9u3bs2nTJsCsF+/Vq5fUzFZWVvKvf/1L1ktycnLUdDKzUlNTwzfffMO5554LmO7VlStX\nyi1lQ4cOJTU1NeyWs2EYLFmyROLK1tr8xsZG9uzZE3AV7qpVq8QrUV9fj9frlXhunz59uPrqq6Uf\nhNXCDfVzKXm4c+dO/va3v4lnMScnhyFDhsi9Aa11aAxnjoLf75fcJbvdfsReUmu3vLycW265RW4+\ndLvdzJ07V/ZqKIn6w9nv98sL7t69O/v27RPXbkNDwxF32x4tmablfwcDm80mruhZs2Yxa9YsKYe6\n5JJLpLRBbXZr7DspKSngWsNevXpJXaLqMxtJl7HaPCqk8O233+L3++WA+PWvfx1xl7baXCtXrpSy\nEpVXoGKjkyZN4sknn5Q101I4hVNAWA9kq3CorKykqKhIxvjggw+Sm5t7xDjUwbd161bOPvvssM2/\nmsuxY8dKGeNf/vIX+vXrJ0Jqw4YNrF27Vua3T58+EWmRejSUIqcaBSmFfujQoQF1z0lJSdJ4J5z4\nfD7Wr18va8IajmtoaKC+vj4gBNfU1BRQYpqWlsaFF14IwDXXXMPQoUPlGa2/KxQNbKy/Wx3O8+fP\np7a2VhSEG2+8kfHjx4sCYc39Uc/f0lAK1fo2DIP9+/dLGKB79+4BzUb8fr8k7952222sXr1a9uZH\nH30Utitbo2f3HAWfzyfF9du2bWPXrl1igXbv3l1iW9C6/z/UAkwl7Zx11ln0799fNpA1vq2w1ljX\n1NRIEkqbNm3o0aPHKSenBRufzye9cJcvX47dbufuu+8GCEnR/Y9FKQ7z58+XxvQ+nw+32y0dkR54\n4AHi4+OPsFitiSvWdxVqq9rqAVFK59///ne+++47qde3rgWFz+eT5BrVMEM1rQn1IWhNnPmv//ov\nAL766iu5kAHMuvh27dpJh7CHH344KpIFFep979ixg5UrV8rYCgsLKSkpkfWclZUVkW5VdrudcePG\n8T//8z+AOZ9Wz591THa7HYfDIVboOeecwy9/+Uu5WMe63tXnrXIplOtb7Un1d9U+HDx4cEDildqD\nKj+ksrKSlJQUMVislSLBHq/X62XGjBni9cnNzRUvhMfjYe7cudxzzz0AlJSU4HQ6efzxxwE499xz\nwyafdcxZo9FoNJooI+otZ0Bq5bZs2UJtba3UD7dt2zagjES5JCNheaq/e6yYjtVybt++PaNHjwbM\n+FxGRkaAdhxp61nFmz/66CPgcJaiyjCO9Pj8fn9A72E1tw6HgzZt2kipQ2Zm5hFZxXB4/C3da60R\n7E5hCmU579+/n86dO4u7zOVytVrqpayMtWvX0qVLF0aOHAmE3nK2oizMCRMmMG7cOMn/qK+vZ9q0\nabKGMzIyoqZrHBx+h4sXL2bLli0UFBQAptfq7LPPFguvZdvJcGG32+nfv7/cE7x27Vrp37x161Zy\nc3MlpNSuXTuGDBkSULXS2hq3EsqcFevvVBZ6c3Mzdrtd3PSqlt/6ufLycuk1f/DgQc466ywpF2vT\npo2stWCNWa2BqqoqFi9eHOA9U/lBb731FrNmzZK9CXD77bdLCWs4vSpRfzg7nU5pKbljxw7Wr18v\n9zlfc801AQlh0SQMWkONz+VyMX78eCnfyMjIOML1GmlsNhter1eERWxsLOecc45snkiP0eFwyFju\nueeegNanY8aMkTXT2t3e1rErl9/RNp1hGHz++ecAQW2barPZRIE455xzaNOmjfRib20d2+12UlJS\nAHO91NXVRTSma7fbcblc4g5MT08/omwx0mvEijWRMTk5WZql9OnThzFjxtCzZ0/AXOeRkiMxMTHS\n4/mSSy7h4osvBlpXDqNpbhU2m00O49TUVDp27CgHbFFRETt27JC5bWpqYuvWrXLv+hlnnEFBQYH0\n5r7gggtO+YKOo7Flyxbq6+slZPf1118foZyrvXXPPfcwffr0iIRoovs002g0Go3mZ4gtQuUO0Vdj\nYXI8dTRo4w6ylXGsHz7pMVdVVXHTTTcBsGnTJv74xz9KN6AguHeCOtfHytIPMqc019ZxqkswVIKP\nNfv2WG7toqIi0tPTA26xCuWYI0TY9mKQ+anN9Y8as0rOraqqYuvWreKhSE5OZvfu3ezfvx8wm6x0\n6NBB1nnXrl254YYbxEJ1uVzHW9cnvT4aGxuZMmWKNBJpamoKaKU8atQo/vSnPwHQs2fPYMuSE/5l\n+nAORAsE9UOGEXA4A9x3330S5wyC60/Pdfj4qY0ZTs9x/2zGrNojyx9oUdffsp74JKokTml9NDQ0\nsGHDBgBmz54t8fyBAwcybNiwUHa204fzSaIFggWfzyelEU1NTcTFxQWz8Yie6/DxUxsznJ7j1mMO\nHj/F9RGAjjlrNBqNRhNlaMs5kJ+iNnY6jhlOz3HrMQcPvT7Cx09tzHD6jvvwB6Ox/61Go9FoND9n\ntFtbo9FoNJooQx/OGo1Go9FEGfpw1mg0Go0mytCHs0aj0Wg0UYY+nDUajUajiTL04azRaDQaTZSh\nD2eNRqPRaKKMSN05F63F1T/FwvbTccxweo5bjzl46PURPqJyzMe5R/2nuD4C0JazRqPRaDRRRuRu\na9doNBpN0Gjt1qfTmZ/CM5wK+nDWnDCGYfzsN0w0oa7kMwxDrvBU78h6Fd/PnZ/LurVe0XgSVzCG\nhOO4pjXH4LQ7nP1+Pz6fDzAvzW7tknq1EPSCCB7WeQdwOp16fsOM1TLyer0cOnQIAI/HQ3JyMmDu\nCZvNRlpaWkTGGEnU/BiGgc/no6amBoDm5mYyMjKAEz+0rHNtPdyjdc0bhiFjdjgcER6NifVOZ5vN\nFnWK4tHul7aO+8CBA5SVlVFRUQHAsmXL2Lt3Lz179gTgjjvuICkpKSTrIrpmS6PRaDQazelhOSsN\nx+fzUV9fz/LlywHYsGEDdrudXr16AZCTk4PdbqdNmzYAtGnThtjY2KjRdq3PUV1dTUlJCWBqurGx\nsaLdu91u8QK0/Nnm5mZ8Ph9ut1t+NpQoDbK2tpYNGzaQkJAAQL9+/U74b0eza6vlrWzROEaFehdV\nVVV8/PHHrFq1CoCYmBg6d+4MwMSJE+nQoUPYrBQ1fx6PR/4HsHXrVjZt2kTXrl0B6N+/P0lJSeLl\nCsX4Nm/eDEBqaio7duxg2bJlAFx99dWkpqYCEBsbC9Dq3lLfb2k1ny5YnynS69gwDBoaGmhsbAQg\nKSnplN651+uVtRMsrNay2lt+v5/m5mZKS0sB01KeO3eueKmKi4spKyuTM2f06NEMGTIkJPN9WhzO\nyp1aW1vLP/7xD+bMmQPA7t27cTqdJCYmAtC1a1c2bdpEbW0tAGPHjuWhhx4iMzMTiGz8TS1WgHff\nfZclS5ZQVFQEQIcOHUhLS6Nv374AXHbZZWRkZMhi9Hq9chDa7fawupTV5po5cyaFhYVcd911wIlt\nfvWzPp+PmJgYEYzhxDAMPB4P69evB+C5555j7ty5Mp8dOnTgiiuu4MYbbwSgZ8+eERnnsVDPsH37\ndgBeeeUVNm7cKAramWeeyfjx4wFo3769fD8c46qrqwPg73//Oz/88AOrV68GzIOyubmZAQMGADB1\n6lTOPfdc2avB3ot+v18UgZdeeonS0lK8Xi8Ae/fuFeXFGvZSWA9kJaiVktHc3IzL5SImJkY+G22o\n9aEOmJiYmIjHnD0eDzt37hQDZNCgQbRp0+ZHjcmqGNnt9pAq+VYls7y8nB07dgCm7P3lL39Jx44d\nAdi2bRtbtmyhbdu2gLn3QjXPp8XhrNi1axdz5swRi8Hr9eJyueTQq6+vp7CwkObmZgBmz55NVVUV\nf/jDHwBIT0+PSDzGMAwOHTrE+++/D8CMGTPw+/3ygpOTk0lKShJBV1ZWhtPplLE6HA4RDupwDocA\nbmxs5JFHHgFg/vz59O/fXxbp8RZkY2MjV111FQDDhg0jISGBe+6554R+9lRR8w3w8ssvM2/ePLZu\n3Qocjs+OGTMGMOdz7969fPjhhwBMmzYtpIL4aFZZa39LCdumpiaWL1/Ogw8+CMDOnTtJSkri17/+\nNQB33XWXeDTUoReOOW5oaJA1/d///d/U19dLnNfhcJCUlCSf37JlC0OHDpXDOdjYbDZ55263mz59\n+lBdXQ2YAvRErS6Px8OGDRt48803ASgqKuLOO+9k9OjRACH1xP3YxDVltPzwww+sW7dO8gzOO+88\n4uPjQzLG46HW7KxZs/jNb37DyJEjAXj77bfx+XwB6/NYz2qNoft8PtauXUv//v0BQiL7rHlMPp8P\nl8sFQMeOHcnJyRG51759e3w+H3FxcYCpCIVqPeiYs0aj0Wg0UcZpYTkrrebQoUPs3r1bNKrY2FgG\nDx4sGnpTUxM1NTUcOHAAgPLycmbPni0W6AsvvEBKSgoQHveUGmd1dTWffPIJCxcuBGDIkCFcc801\nZGdnA5CWlkZMTIxo+oZh8MMPP8hzZGdnS8ysbdu2tG3bNuTj93q9zJgxg48//hgwNcYJEyZIVvDR\n/r5yJV555ZXMnz8fgEWLFtG9e3exnEOJYRgsXLiQK6+8EjC9JQ8++CATJ04EzDwEq8tv//79PPbY\nY2J1hTrGqH6/3++nqakJMNet1+uVuVOWe1VVFQDLly9n5syZ7Ny5U37POeecw9133w1AYmJi2F2Y\nyqWt9mbfvn3p2rWrhGrq6uooLi6W9dKnTx+Sk5NDFlqy2WySa3LjjTdSXFwsX2dkZByktB27AAAg\nAElEQVTXSlPPUVFRwa9+9Svy8/OBw1b4eeedF5Jxt3SnH8uytK5Nn8/HDz/8AMBTTz3FP/7xDwnN\nKCs/EpSXlwPw/PPPk5mZyV//+lcAMjMzA8IHfr//iMoaq7Vs/e/Kykq++uorCfuFAnVGOJ1OKioq\nqKysBEz5kZqaKmGOsrIyvv/+ewmhBDsObiXqD2drsH7lypXU1dWJy6ZDhw706tVL3Bwej4e4uDj+\n9a9/AdDQ0IDH45FEEWsdYDhQwnfTpk00NjZy++23A+bhnJKSErARDcMQ1+T+/ftZvny5PGfPnj3J\nysoCTBd4KF3zSkjNnDmTxx57jPr6egBGjBjB+PHjxd3TEsMwaG5u5vHHHwdg3rx5AUrU7373u5CN\nWf19gBdffJH777+f9u3bA2bSYHJy8lEFXUxMDJ06dSIvLw8whXEo3ZYqDp+fn8+3334LwL/+9S+2\nbNkisW6fz0daWprM/cGDBykrKxMldNy4cUyfPl1cxJGILdpsNlJTUyXWnZycTE5ODmvXrgXMmPPG\njRs544wzAHP9uN3ukOZ9qPlLTU0lPj7+iNIzMIWwdf8YhkFTUxP//Oc/AbjvvvvYu3evzGlKSgq9\ne/cOeTjM4/GQn58v8+VwOAJq162ljE1NTaxatYrf/OY3gLmWMjMzufzyy4HQruFj4fP5JPTSvn17\nXnvtNXEHq5jx0UrSfD4ffr9f3pP13e3evZsrr7wypKE89fdqamr4/PPPJVaenJzM8OHDxZCqra1l\n0qRJksOgFOlQoN3aGo1Go9FEGVFvOQOS4FVWVhbQYKF79+5kZGSIhpmenk5aWhr79+8HzASxyspK\n0bhcLlfYNErDMKRwvbCwkLKyMi677DIZZ0sLwjAM0Ro//fRTtm/fzr//+78D0K1bN7GiQzl+v9/P\nrFmzALjzzjtpamqSMIDVUlPjBQK0+eeff57XXntNPqO0ygEDBnDBBReEbOx+v1+S/h5++GEppQHE\nG9ESlUT46quvsmvXLu68804gdG4q5Vn4/vvvATNh5osvvgCgpKQEr9cbMD9xcXHilk1JSaFLly70\n69cPMN2YPzbzNdjYbDacTqdY8+3bt2f//v0sWrQIgLVr15KcnCyu97S0tJCPV/3+mJgYHA5HwBq1\nWmw+n09kSm1tLc8++6wktinZofbbDTfcwPnnnx8Sy9m655ubm0lISBB3qt1uD0gCbW5ulq+9Xi+r\nV6/mzDPPBExP3HXXXceFF14on48EBw4cEA/EO++8Q9euXQPGYnVrt3RjNzc3c+jQIZExViu5b9++\nOJ1OmatQVFMoObZkyRIWLlwo4zrnnHMCvC39+/fH6XQeN7wXDKL+cDYMQ+JYhYWFJCcni4uhc+fO\nNDc3S+lU//79GTBggExkUVERHo9H4rXhzNQ2DEME/dKlS9mwYQMXXHABAO3atTui1MHn8/Hee+/J\n50ePHs2gQYMAU1CE+lAGM070xBNPAGbWYkJCAh988AEAubm5rSoU6md37NjBzJkzxW2bmprKqFGj\n5PcezR1+KqgNlJ+fz8svvwyYoY5du3Yd0wXW2NjINddcA0BpaSlvv/12WHIRDMOQPIKlS5eyd+9e\n4LDLVc2v0+kkJSVFXILx8fGkp6eL2zI1NTUqui3ZbDY5nLOzs3nzzTdZsWIFYCrGN9xwg6zhcCsS\n1tIb61yp76m92dzcTH5+PgcPHpR/j4+P57777gNMJTU1NTVkHcKUTHK5XGRmZrYaerPZbJIdDGZc\nPCMjQ8rULrroIvr27RvwmXCiFJ3f/e535OTkAGbcu7U12rK2WMmLoqIi2rVrJ3LC6XQeEWO3hsmC\njTpDvv76a5KSkiQz/LLLLsPhcNChQwfAVJpVrwn1HD/bUiqv10tBQQFwuG5WsXfvXrZv3y4WRWxs\nLD6fT7Qvp9NJbGys/Hs4D2drM5RevXqxYMECiRE999xzjB07Vj7r8/n49NNPpXzj8ssv59Zbb5UD\nJpSCzev18sknnwDw6KOPinBISEhg7dq1dO/e/ahjMAxDSpQuvvhiysvLZUOOGDGCmTNnAqblF4pn\nUEkaL7/8Munp6QB8+eWXrR7MamM3NDQwYcIEiY0+/vjj9OrVK+RrQ7UvtLbVVHOiSuPUuLOzs+nf\nv79YbzU1NTQ0NISsRvhUUGPxer0sX75cSqlyc3N56KGHQhqTOx6trTn1PTXulJQU8vPzRUGy2Wx0\n7dpV8kPS0tJCmsRmtfaPVmankqeU/CstLSU1NZXBgwcDptfieMpvqC7FMAxD6u/fffdd/vKXvwAc\ndTxKvjQ0NLB3714pi/X5fFx22WWy5q394n0+X0Add7DLxAzDkKYjsbGxXHjhhaJUdujQgebmZlkf\n8+fPZ86cOZJ0d80114SsPDB6drlGo9FoNBogii1npSXt3LmTP//5z4CZeWttEVhWVkZiYqLEWnJz\nc2lsbJRMu0OHDmG328WdHO4GJMp1NmXKFEpKSqSs4K677uLNN9+U0oDZs2fzt7/9jUmTJgFmN6Vw\nWByGYbBjxw7uuusuwNRQ1ZiffPJJunTpclQt2+/385e//IX7778fMGPONpuN3r17A/DGG2+EPC6j\nXEurVq3inHPOAZDGLgpVJqMy5x955BG+//57idfdfvvtIS2HsOJ0OsXaufTSS2V+OnbsSMeOHaU8\nIysri+3bt8s6Xr9+PYZhiOstGvnkk08oKiqSPabcwdGKWpN1dXXs3r1bvu9yuZgwYYJ4OMLV1EVZ\n0dZSIyUDPR4PRUVF4qWqrKwkMTFRvBQul4ukpCSxVlsbq9UzEOz1rhr4WMsDrWVh6uuGhgb+93//\nFzCbkhQXF0vo5oILLqChoUHCJNYxOhwO4uLiQiYTm5ubpexz+/btOBwOevToAZhz3dTUJCGo+fPn\n8+233/LVV18BZpno22+/HRJXe1QezoZhSBnJCy+8IC7ImJgYBgwYIF1nBg4cSO/evSUeAGbsQtUo\nVlVVkZycTLdu3YDItd6LjY1l+vTpsuBef/11xo8fL4IsJSWFqVOnSvJMuJSIuro6fvvb30oSis1m\nk5KttLQ0Dh06JEJKjUlt8nHjxrF48WIRJm63m7POOotnn30WICBRL1So+bzuuuukPefmzZvJzMwU\nV1NsbCw1NTWyuWbNmoVhGCIkwtlJyW63i+v67rvv5vrrrwfMOmW32y0bvL6+nt27d7NhwwbALCVx\nuVxS9xxNKAXp1VdfDWihOXny5Khyv7dEreM77rgjQOlJSUlhxIgRAQdBJOSG1+tl3759gBm+e/TR\nR9myZQtgHmT9+vWTcp6amhoOHTokZVipqak4HA5JerS6ZQHOOOMM+fpUy5N8Pp/U39fU1IibeuTI\nkcTExEhS7IYNG3jttdfYtWsXYMrmESNGSMmj6vSo5IzV5R8qeahkV1NTk8xtQUEBnTp1krk3DIM+\nffqQm5sLQKdOnRgzZgwvvfQSYMqTXr168eijjwZ9fFF5OPt8Pt5++23ArAFVGbfTpk3jxhtvlMSH\nloX6fr+f/fv3S52zx+NhyJAhYk1FMrvV6XRy7733AvDmm29SUVEh40lOTub6668Pu2Vvt9vp2bOn\nzFebNm0YOHAgYGbblpeXM3z4cMC07srLy5kyZQqAZB0r6+i6667jpptuEos0HHOtBOh//Md/UFhY\nCJjJYQcOHJCEDpVMpZqp+Hw+rrvuOhFs4cSanZqamipJaCqzWHmE6uvrSU5Opri4WL5ubGyUev2J\nEydGvHcymM+jEvHKy8uJi4tj6tSpABFLTjoRfD6fZMqr7HJ1SA0fPpwBAwZEbG6t9baqKdHq1asp\nKSmR9R4fH8+5554rnpcffviBRYsWyZg7dOjAtm3bRLF2u9384he/AMzKD9UPQv29U3lWv98v8rlL\nly5ivS9cuJCUlBQ5nFeuXMnYsWMZN24cYCqkdrtdqipKS0vle3Ck/AiFoqf+hsvl4vzzz5fv9+zZ\nk06dOskzdejQQRTnzMxMunbtKvJjxIgR/PnPf5Y2x8EcZ/SqthqNRqPR/EyJOsvZMAx27dolMQCP\nxyM3Id1yyy3HbDTu8Xh4/PHHxSURHx/Pk08+GbaY4rHw+/1yhV27du1obGwUt1NcXFxELA2XyxXg\nicjLy5NYy5YtW1i0aJHULRYXF1NaWipxLpvNxplnnsn06dMB89YZt9t9xAUM4SAuLk7G3Vp2ucfj\nYfbs2YD5zE8++WREXK5+v19KdsrKyiSbPzExEa/XG5CNW1ZWFtDO1e/388033wBmLW5WVlbE13Vp\naSkvvvgiYM5rXl6edFqLVvx+P0uXLuWOO+4AzAoQl8slllLPnj0D2nmqOHCoSqmsWEsTKyoqJMac\nnZ1N165d5ZrCyZMn07FjR/G0HDhwgGHDhol7vrKykpycHLG0Bw8eTM+ePQGOuDTnVJ/H4XDw1FNP\nAXD99deLhVleXo7NZpP9OHHiRNq2bRvgHWxsbJQQpMPhkIt/jkaobqVyOp1S0RMfH09WVpZ83Vq3\nNZvNxllnnSX/Xl1dHZIa7MifWi3weDxMnz5dYgC9e/eWmsOjPbh6ac8++yxLly6VBf7b3/6WXr16\nRdz95/F4uP/++yVxYsKECfz1r3+VuOfy5cv5+OOP+dWvfgWEz/1ut9s544wzuOWWWwDTva4EfseO\nHdmzZ48capWVlfj9fvn3UaNG8dJLL0nI4MCBA1Fxd3Zrf/+TTz4Rxejmm2+Wsqtw09TUxAsvvACY\nLV2VcpaSkoLL5RI3d0pKClVVVZJcA+a7UvHx+Pj4iMdzDcPgxRdflHyFlJQUzjjjDCmrUQl60YKS\nEYsXL+baa68VJQnMskGVt5KTk0NhYaHMdVxcHIZhBDQEUQR7rVuvlW1sbJS/tX37diZNmiQJoy6X\nC6/XKzkIXbp0we/3i5Ld0NBAcnKy5F2oKySt8xAs7Ha7hLbOPvvsgMYvZWVlstda66vu8/kkpJaZ\nmUlcXNxR59RaWhVsDMOQEMHo0aNJSko6bohRjSU2NpaGhoaQtIaOusO5tLSUvXv3SkLYhAkTxMI4\nGkrDfOaZZ/D5fHTp0gWAe++9N6JCTBXnP/PMM7z11lvSNOCpp54iIyNDtPWbbrqJ119/nWuvvRY4\neo1gKHA6nRKbsnolGhsbWbx4sQgAn89HSkoKQ4YMAeDaa6/F5/OJtt7Q0BDy3sknw/79+7n55pvl\nTu/f/e53Ebk2FMwkH5UQs3TpUhHEdrsdl8slik7Pnj1JT08PsN7i4+Olj/WpXlwfDDweD8XFxTKv\n2dnZZGVlBdybHC0YhiFJpZMmTQo4mNU4lXAtKCigvr5eFKOcnBxcLpfIoFDd9d2yf3a7du1EIaio\nqKB3797ytWEYVFdXy97LyMjA5/OJQqH2cTisfWv2t/Vver1e0tLSjsgPsl5sAeaBDmYDqXbt2h11\nrKG8vtV6RaTb7T4h+aA6yVVWVtKnT5+QZJJHlyTVaDQajUYTPZaz0lw3b95MRUWFaFyDBg06pqtj\n9+7dDBs2DDC1tfj4eFauXAmETss9Ebxer/TrnT17NllZWdKJS/UZVu6gjh07sn37dslstJaGhQMV\nu4LDGuGjjz7KokWLRJN3u91ceOGFknHerl070tLSJH6lLIxoQcWAJkyYgGEY0jM8IyMjIuNRt46p\nbNUFCxYcYbWpr+Pi4o6o82zbtq3EwSIZa7Zeg2qz2aRMMSEhgaqqKpnfaLKca2treeCBBwAzC9o6\nNqfTid1ulzyVgoICzj777ABLesCAASF1Z6vfabfbZd2WlZXJFbMpKSm0bdtWrPm9e/fy5ZdfcvHF\nFwOmp80aUopEq1QgoJVyQ0MDXq9X5IPqcqZQ3iDVo8LtduN0OsNqOSu5t3fvXvFiteyTcLSfU14s\nwzB4+umnQ+KNi5rDWVFcXCzJBGA2mFBCSQl/5S5+6aWXmD59urjA4+PjWbNmzQlNcKhQwuvAgQO8\n8cYbgOk2mTp16hFNOZSQ7d69OytWrJD4XTgPZ7/fLy6/d955R0pM1DtQdYiPPPIIt912myg8rd03\nGy0YhsE777wDwLZt25g0aZLUxkdqzEr4Tp48GYAxY8bw1ltvAfDdd98RGxsrylqfPn3YvHmzrHeP\nxxMQF43kvKukNaVEqwTBXbt2MXbsWOl7H2m3Oxzei99++600GnE6nQG5E3FxcXTv3l0Spm6++Wb6\n9u0rB2FiYiLx8fFhU4iUe3TDhg1SM6yu21QHnyovVXMdzgt9WkPNc0lJCa+++ipg5gqNGzdOnsda\nv6x+xm63SwLpiciTYCaEGYYhd08vWrRIwnXHo7m5meuvv55t27YBZoxaKUnBJmoOZzXho0ePJjMz\nU+pWX3nlFYnTdevWjfLycj766CPATJTweDxyGK9YsUI0+Ujj9Xplw3fu3JkOHTqIYIuLi8Nut4t2\nnpOTQ3p6Ot999x1A2JLYVAz0t7/9LWAeEmqMDoeDtLQ0nnzyScCMi0fSE/Fj2LlzJ9OmTQNM4frn\nP/85Kg4La3yuS5cukuXa3NzMvn37JL6/a9cu1qxZI5cIlJaWkpubG/H59/l80ud+48aN1NTUyD5t\naGigvr4+quqblTBPSEiQXskrVqygurpaxpmRkcGoUaPkIpTu3bvjdrulU1XL+59DHb9V7zgmJka6\nyWVkZLBu3TqRc+eccw7Z2dkyxkgryVaPj+ovkJeXd0QSWEvLubXfES58Ph8LFiwATM+mSkDu2bMn\nCQkJAUqEx+ORevj777+fwsJCrrrqKgBee+21kO3LyEssjUaj0Wg0AUSd5Zybm8vDDz/MY489Bpiu\nknfffRcIvDsYTBfVuHHj5N+Tk5MjrkUq2rZtKyVK7733Hps3bxbNt3PnzqSkpEh8adu2bQGlNOHC\n5/NRVFQk2avJycn06dMHMLNab7jhBslSjXRN7YnS2NjI+PHjOXToEAAPPfTQUe90jjTKqnC5XAEt\nFVNSUgLutt2zZw8dOnSIeEy/sbGRuXPnAvD5559TWloqtalJSUk8+uijp9wOMpgoWdCnTx+xdPbt\n28fevXulxGf06NHcdNNN0vrS5XIFxD7DGb6x2WzyjseOHStyzu124/f7A+6ldzgcUSPrFKmpqfzy\nl78EzLV9vDi4NXv7RAj286oqlfz8fOl4uH79em688UYJGcybN4958+aJjExJSeHVV1+VyppQerOi\nTuI6nU6uueYaSbGfPn26NMJQ8S21sR577DFuvfXWiAstK2oBxcbGSmOMm2++mTVr1rBkyRLATKZR\nLkswN1/Hjh0l5uj3+8NS7hMbG0tFRYUoDePGjZOa8szMzKhwBZ8oKg/huuuuY/fu3dIM4z//8z+j\nToi1RLm71TvPzs5m3LhxcomISp6J1MFn7UGshNiWLVvwer2iMJ9//vl06tQpquZajSU+Pl7uwu7R\nowdFRUXiEs7KyiInJ0fc3JFui6r2XHp6+hEHVzTNrRVrG8yW3zvRnz0ewb432eFwMGbMGMCUzypH\nZc2aNXz//fcB4YV+/frJpUVDhw49Zj12MDl9pK9Go9FoND8TbMHuGHOCHPePqnE1NzdTVlYGmM1G\n3G63XM6QkJAQbOvueOrQj5osZVU0NDRIohWY2mJpaalcCbhq1Sp69OjBqFGjADMB5Edazsca91HH\nXFVVxb59+6R5QVZWlmRXhkEzDNpc+3w+nnnmGQD+8Ic/kJiYKBnoIch8P6m5/rFYWzmqr9U7OQnr\nLihjbmhokFK6uXPnEhcXx4033giY15wmJiYGc90EdS/KD/3/y0esck9l0geJsKyPIBOxMVvX+I98\nB0FdH2H0UpzwL47awzlChEQgtPqLWgiHU+SkNpfP5wu2YPoxBG2ua2pqmDhxImDeljVnzhxpHxmC\nTRYxQXYKpSRBG7P1vmHDMI4okQkiYduLQUYfzj8CtZ68Xu+P7bL1U1wfgR/Uh3MAP8UXfjqOGX7E\nuK0XFVhb8YWIn9pcn45jhtNz3EEZc7Djr5zkmIM5Dp/PF0xvIZye6yMAHXPWaDQajSbK0JZzID9F\nbex0HDOcnuPWYw4een2oHwq+pdwSvT7CR9S7tTUajUaj0RwF7dbWaDQajSbK0IezRqPRaDRRhj6c\nNRqNRqOJMvThrNFoNBpNlKEPZ41Go9Foogx9OGs0Go1GE2Xow1mj0Wg0migjUldGRmtx9U+xsP10\nHDOcnuPWYw4een2Ej5/amOH0HbegLWeNRqPRaKIMfThrNBqNRhNl6MNZo9FoNJooI1IxZ41Gcxpj\nGAZ+v59t27YB4Ha7SU1NJSUlBQC73R7qyxpOGut9Aq1dKhGt4/45EOR77k9r9OEcIlpeKGIYBl6v\nV7622+3Y7abjwmaznRYLUQlkAI/HQ319PbW1tfD/2jvz6Kiq+4F/XmYymYREEkggBJNA2AWRRRYl\neihCoQoYqlItVsQi1aPWUvC4tKfHc6TVUyxa0VqqaF2pHFlboqKoZTECZVPAkLAmJEDIAlkmmczy\nfn+83/0yLywCZoaxvZ9/WDKZ93333Xfvd79AYmIiiYmJtgPTvw/3pLk4PB4P999/PytXrgSgoaGB\n1NRUbr/9dgCmTJlCv379cLvdEZfNNM3TNl01b/1+P42NjRw9ehSA3bt3k5aWRlJSEmDN6/T0dNLS\n0gCIjY2NakXjUtLc3IxpmpSVlQFw2WWXcdlllwGnr2ktz2pWz8jr9QJQXFzMiRMnOH78OAA33ngj\n8fHx8l2XGrWeqz/V2h1OtFtbo9FoNJoo43tlOXu9XqqqqkhISAAsa83hcESFZtWSM8mktMdgMEgg\nEDjt/6OZYDCIx+Nh//79AGzevJkPPvhANMkuXbpwyy230LdvXwASEhJwOq3pZZpmRDRNda1QC980\nTZqamvD5fAC4XC6CwSBxcXHAKQ+Gel4tPR7hspq+zbUa+hm/309JSQkFBQUA7Ny5k7vuuovMzEzA\ncim7XK5Wl/FMqHF9//33yc/PF8+JaZpUVVXx5ptvArBu3TpuueUWfv3rXwPIeEeK0PEMfdeOHj1K\nQUEBn332GQAHDhzA6/XSsWNHwBpLn89HVlYWAKNHj2bYsGG0adMGiA53fej8VgSDQXnfwi2fepfU\nWK5fvx6AjIwMRo0aJX+PjY2VcXM6nQQCAVnrTNOkvLycl156CYB///vflJeXc8MNNwDWejJw4EDg\n0qyPanzr6+tZv349S5YsAeCrr74iOTmZ+fPnA9CzZ8+wrW3fi81ZLQBz5swhPz+f1NRUAO68807a\nt28vD2/w4MF06NAhKje7UDePz+ejtraWxMREAJnA0YZpmvIi7t+/n7/97W988cUXAFRXV1NdXS0b\nSHp6OoZhiFurS5cu8hwisZgpOffu3cvcuXPZvn07ABUVFdTX18vP3W43MTEx4jJLTU1l8ODB9O/f\nX+Tetm0bAGPHjmXIkCGtKr8ar0AgQHNzM2C5B+vr6/nmm28AqKys5MMPP+TLL78E4MiRI3g8HtuC\n/MILL8hCNnfuXHr06AEgC3S4UPK7XC5xBQP06tVL5AHLTVlaWiru48zMzLAraKEKWUxMjMhqGIa4\nTysqKtiwYQMfffQRACdPnsQ0TZvi7PF45DvffvttZsyYwezZswFk3igiuVErJaOqqor8/Hy2bt0K\nQFNTE9dee62Mf1paGi6XKyzjrZRfgKSkJDp16iTXCQQCsqapdUB91ufz4ff7ZbxqamrIz88XJamo\nqIhAICDvQHJycsQU+lCUq33Hjh2AtecUFBTQ2NgIWIpyTEwMDz30EABLly61vQetSdRvzsFgkAUL\nFgDWguT3+8Vi2LFjB1VVVTJJDcPg7bffZsCAAfLvaELJYxgGRUVFdO/eHbA2jGjzAASDQWpqavj9\n738PwKJFi6iqqpKfx8XFkZCQIC+jz+dj9+7dVFdXA9CxY0eJN4Zrw1AvfnNzM6+++ioAjz/+uChz\nYB9zdV8qjghQVlZGZWUlNTU1AHz55ZfU1tYCllI4YMCAVrH6WsbY9uzZw3vvvQdYlvDu3bsl3ubx\neGzWnkLJrJSmnTt3ArBr1y4uv/xywPImhXMeqTGvqqoiKSmJq666CrAWse7du8u1y8vLKS0tFS9X\nMBgM+2Krrq025jPFnL/++ms++eQTGWsVNw0lVNa6ujpWr17NrbfeCkCPHj1kIz/TdcKFz+dj165d\nAMyaNYtNmzZJDothGHz00Ud89dVXgGXNjR8/nk6dOomcrSWjYRjyPsfHx9O5c2fGjx8v123Xrh1g\nrQ+hBonf78fpdIpCWl5ezq5du6ioqACsjd3pdDJ8+HAALr/88oiuh0quDz74gBdffFGU+8bGRmJj\nY+nTp4/IXVtbS0lJCWDlLAwdOjQssuqYs0aj0Wg0UUbUW84NDQ08/fTTgOW+cbvd3HPPPYDl1j5w\n4AC/+MUvAMv9N3/+fF5++WUg8nGu8yUQCNCpUydxZ/v9fgKBgGQ6n8nCCHXRhRPl/t26dStTpkzh\n0KFDgGVNuFwuKZXJzs62ueOrq6upqamR3w/9WbisC6Xtvvnmmzz66KOANV8MwxA5hw0bRp8+fcT1\nNGjQIBobGyVG29TURHx8vHxXVVWVWCjp6emnxfYuFsMwCAaDYpW/9NJLLF26FLC0czUHwBprwzBk\nHiQnJ5OVlSUeoy1btuDxeBgxYgRgPYtIzXU1Hh6PB6/Xy9ixYwHLogyNe2dnZ5ORkSGegmAwGHYr\nM/S71XiDNU+Um/Ktt97i8OHDIpeSKTQUFhcXJ/9u164dCQkJ8tyCwaB8r8PhCGsYITTnYNu2bZIJ\nX1paCiDrhdvtpq6ujuXLlwPQqVMnSktLue+++wAr/tvSg/RdnoOal3FxcWRlZYmF7nQ6bd6LUJxO\nJ6Zpyhx3OBwcOHBA3MWxsbFceeWVzJkzR747UjQ1NTFz5kwAli1bRl1dnXh8Ro4cyYwZM8Ryfvvt\nt/nzn/8sFv8XX3zB1VdfHZZQatRuzmpiLl68mBMnTgDWhBo0aJAkmcTGxpKampTEonIAABlKSURB\nVCqfbWpq4rPPPpM4V3Z29iWQ/OwoOTdv3szatWvp2rUrYMWIvF6vLLbt27c/bXJHynWmEjSefvpp\njh8/LtdNSEhg5MiR9OvXD4AOHTrQ3NxMUVERYG3GTqczYokzKgEJ4IknnpA4odPp5KabbuJPf/oT\nAJ07d8bhcNhenjPJpVyEdXV1Eldvamo6zeX5XQiNqeXn59PU1CTyuFwu21gPHjyYn//85wCMGTOG\n+Ph4kaW4uJilS5fKYp2VlRXxhDCXy0VycjJXXHEFYF+Y1T05nU5R1lpLybkYWcvLy3nqqacA2L59\nO42NjTZ5nE6nuGOvv/56unfvbtuAUlNT6datG4CtVDCcc1wlMoK1AUybNk3WNdM0SUlJIT09HbDi\nu42NjbLRNTQ0UFhYyKpVqwDIy8sTZVUlRIbex8WinnFokleoghkIBGzlooFAQJT91157jV27dsnv\nDhs2jL/85S+kpKTI58ONUsh/97vf8Y9//EPuoVevXsybNw+AgQMH4na75bO1tbW2nIR9+/YRDAbD\nsjlrt7ZGo9FoNFFG1FrOSgN79dVXxWJwu90sWrRIEo2UdhVasnPy5ElxQUUqWeN8UYlKr732Gp9+\n+qlkfg4fPpzU1FR69+4NINnokSJ0rJ988knA0hANw5BmDHfeeSeTJ08WDfHQoUMUFBRIYoTH48Hj\n8bB582YAunfvLlpwOJ6DaZqS6VlfXy9yjR07lldeeUUsofO1btQcSkxMlHvesmVLq2nEyqpYtGgR\nYGWrquefkpJC165due222wAYP348HTt2tFkd6jsAcnJyuP322+ncubNN9kig3MHV1dUcO3ZMPCe5\nubm2z6mmOwcPHgSs5KH09HR5d8NdUWGaJg0NDQDcfffdbNmyBbC8IaFWs2EYJCQkiHt+ypQpdO7c\n2Za4BKcs5tBwQzhQsh07doy5c+cC8MYbb3Dy5En5TNu2bRk4cKAklHbv3h2Px8OHH34IWCVORUVF\n4prt0aOHJMk2NDSQnJzcamGy0KQvFboAKwv+nXfekec9ePBg9u7dy9q1awFYv349mZmZUnr5+OOP\nk52dHbH12jRNmZvvvfeeeHgmTZrEs88+S/v27YFT7nmV6PrJJ5/Yss5TU1PDJnPUbs7KpaMGEKxF\nqWPHjrbBaG5uloELBoN4vV75dzRtzoFAQOIay5cvx+l0ymbcvXt3Bg4cKDHFSGKapsSwnnnmGVkE\nVFnUtGnTAJg6dSpOp5MDBw4AVr3frl27OHz4MIDUEi9cuBCwXsarr74aCM/mYZqmKAaXXXaZbMb3\n3HMPcXFxtmzn0MX0bPMh1H2tfreysrJVN5GmpibpqBUIBOjQoQMA06dPZ/LkyaKUud3uc9Y9ezwe\n26IYyZKTuro6AD7++GMqKiqkkiIvL4+UlBQJDwQCAXbv3i11z4FAgHHjxjFmzBjg7PfYWgQCAYlf\nbty4UTZbhbp2bGwsXbt2laoDr9fLvn37RHGqqKjg4MGDEiJT7uFwYJomR44cAWDChAmS+6BkVwpC\nTk4OAwcOlLjs9ddfT0lJibRSTU1NJRAISAZ/fHy83K+qCgnX2KtY7JQpU9iyZYtcp02bNjgcDrmH\njIwMbr31ViZOnAhYIchIlsCapimGhMfjkXDcrFmzSE1Ntb1TgUBA1pqDBw9imqYoHZMmTQqb3FG7\nOat4oloMAIYOHWobCNM02b9/v610BrDFZqIB0zR5/vnneeuttwAr0ahv376MHj0agBtuuAGv13tJ\n6vr8fr8soEePHrW9TBMnTiQvLw+wFoaysjLZyMvLyzFNk4yMDMBq5tDQ0CD3sGHDBmki0BrxrZb4\nfD7Z3HJzcyXe9s9//pPFixfLfXTr1o0777xTNu+kpCScTudpsTBlsYQmtQ0YMEASWdRnLxbTNCks\nLJS52jJ2ea7vV2VYapEuLS2lTZs2EmeOpLWhFK3q6mopnwPL2u/du7eMndfrpaGhQfJFevToQYcO\nHSLSKMM0TTZs2MDrr78OnEpyVDgcDrGMZsyYQY8ePTh27BhwavFV3reCggIOHz4scufk5JxW69xa\nBINBkaOmpsbW7hdOKY0HDx6koKCAH/7wh4D1Dp84cULyQVJSUhg0aJA0VklLS7Mlm4Y2MWnNNccw\nDNnk3G43fr9fxt7j8djGPSMjg+HDh4vSE0nvj5JVKWSA/F2tKQrlgXniiSeAU4qxkju0fLC10TFn\njUaj0WiijKi1nJWFptzbYFlzoR1qgsEgRUVFosk2NjZiGIa4tQOBgM2FE2kXt5Jz/fr1zJ49W8p5\nHn30UUaMGCExo/3797N+/Xqx7rp16xYRWU3TpL6+ng8++ADAll2ZmprKddddJzJVVVXh9XrF9ZqX\nl0d2dra4sZ566imOHTsmlmFtba1o+uGIN/v9fokNu91uNm7cCMDx48dtLkzDMHjmmWfEyszMzGTI\nkCHSZnD48OHExsaKi7CkpEQamvzkJz9ptdBIMBhk3bp18l2NjY2SufrCCy9QWFgozRz69u1ryyAG\nK66uulp9/vnnzJ49O+KeFsMwxALr2LEjxcXFYt1t2rSJTZs2iQWkyu5UXHzMmDH069cvIhaSz+dj\nwYIFklUb6kFzOBz079+f1157DbAs+tBMc5/PR3FxsTTfWbt2re2gjFGjRkmjjNYe/5iYGInBzp49\nWyoOysrK8Pl8ch/V1dVs375dZN6/fz+JiYlizeXm5tK1a1eZ0y2z6MO1thiGQXJyMmCFyCZOnCjj\nFggE8Pv94hHdunUrX331FYMHDw6LLOeDysAPBAISzvvwww+ZNGmSuK1PnDjBI488Iq1zwaqmeOaZ\nZ4DTO8a1JlG7OSt3GZx6CeLj423B+KamJg4ePGhz7xmGIS5OVRcdDrfq+aDiR8o1/Jvf/AawYoxO\np9PmSt2zZ0/EymFCqaiokG5JDodDkkgmTZpEbm6uyJSWlkZmZqZMRtUCU5WDNTY20tTUJM8mIyMj\nrCcSGYYhtYcq8QxOL9lRiVhqThQXF3PgwAFJJuvSpQv9+vXjxhtvlM8r96D6ndaSd+zYsfz1r38F\nrLmhNrbDhw+zcOFCccOqDmYqvpmZmWmLsbtcLmbMmNFqsl0Iym05cOBAdu/eLUlXzc3Nthpgv9+P\n1+uVDaJXr14kJCREROmsrq7m8OHDtrwDdd3OnTuzYsUKURpabrAqBq3uU3Vrq6ysBKw62CFDhsjv\ntmZei2EYMl733XeflMotX76c119/XcrwGhsbiYmJkWS8ffv2kZ2dLetMVlYWcXFxlyRMpq7Zp08f\nZs6cybPPPgtYSnPomQKlpaX89re/ZdCgQQCt3ib32zAMQ3J8cnJy2LdvHwALFy6koqJC3NsrVqzg\n008/ld9LSEhg+PDhjBw5EghvvkfUbs6q13FCQoI80LKyMgoLC2XR2rNnD1VVVbbNV7WdBCvu5XK5\nItbAIxS/3y/NUNxuN7/61a9s9dlwSqMvKSmhU6dOcl+RkjMYDPLNN9+IdyIhIUGSuKZPn25rXqCS\nOVrGR5WVeuTIEVvz/WuvvTZsiRKqrlBZ8Q8++KAsZCUlJSQlJYl8JSUlfPbZZ9LqsqSkBL/fb2vw\ncPToUfEAJCcni/UyYMCAVl14e/bsyYsvvghYdc5qQSguLqasrEzmeXNzM4ZhiNLU0NBAU1OTbOaJ\niYkUFBSIBRdJ1POdNm0asbGxsjmrRMzQWuyKigqZA6r3ejhR1z506BBVVVW29169c/PmzSMjI+Os\ni6rK3lZejEWLFhEIBOTZbNmyRf7esra7NQmNz06bNo2pU6fKuvaHP/yBL774QqxSVVmhWqlGSgk6\nF06nk9zcXElSq6mpweVysW7dOsDKWTl58iSPPPIIAKtWrQp769mWKE/mY489xjvvvANYvfnfeust\nyZWoq6vD4XCIAeDz+ejUqVNEDD4dc9ZoNBqNJsqIWstZuSz79+8vTcg///xzqqqq+MEPfgBYVlBM\nTIxoQOpggcLCQsCy5sJZ+nAuPB6PWJX33nsvDzzwwGnxNpXJuGnTJtxud8QzFk3TZM2aNTbLWbl0\n1ZFvysIIzXCGU+0R1clJqh5UHbXXu3fvsHZPglMu1h49etCrVy8A6bIWahnfdtttvP/++4DlloyJ\niRGrW9VWKlmTkpKkJrQ1teOYmBjcbjfjxo0DrBisssACgQA7d+4U615ZGSossGHDBtasWSOZvCp8\ncCk8QupaWVlZTJ8+XcIgXq/XVta4Zs0a3nvvPbnHo0ePytwIN5s3bxZPjpJZxe9HjBjxra5IdYwo\nYPsOsMr2Ip3DouRR9zB16lS+/PJLeW9dLhddunSRZxHOuPK3EXrqWlpamoRfMjIyaNOmjZTG3nLL\nLZSWlsphHa+//jozZswIayisJeoZ5+Xlybr38ssvs2TJEhnbmJgYEhMTZR85evQomzdvFss6tEyt\ntYnazVmltr/wwgtMnjwZsArbt23bJgtAu3btyMjIkCQD1ZNYudrCXdN3JtTkjImJ4cc//jFgndbS\ntm1bmxyhMcR9+/YxderUiJfG+P1+1q1bJ+PldDoloUPJEdp8oaX8FRUV/OxnPwMsRSMmJobp06cD\nhDV+ruJ8Spk512IbehQgWEpD586dbT3C4+PjJT8gPj5ePtvaLSdb1iaHbv5Dhw5l6NChts+r6998\n8808/PDDLFu2TL4nEAhcklLB0JOQQo/1U2erK1dsIBBg3bp1oiiHswexQo1HaK90Jauaj3V1daSl\npZ1VjmAwSGFhIbNmzQLs9wvWuxzarjL0Z5Giurra1mzJ7XbTt29fkfVS9XcIPXWtrq6O5ORkmQ/x\n8fE4nU4xuhYsWMCMGTNkLf/0008ZPXq0tIONJA6Hw2ZUhK6DnTp1Ijc3V/o7VFZWUllZSX5+PmD1\nVfif25zVC9C/f3/eeOMNAJ577jl27dolg6GSlNSEAOtFUQkbWVlZET/bWS2ogUCAnJwcwLLwWm5s\nXq9XMkZramoYM2ZMxBPXGhsbqa2tlYXM6/VKhqs64q2l3GpBOnHiBPfcc4/EalXtn9qcw7k41NbW\n4nQ6z+lpUHLW1dWxatUq8b4kJSVx+eWXS4MG1cBEac7Nzc2SlKMskUhwpvFS/+d2u20dolR3o0tR\nfaAUyiVLlpCenk6XLl0Ay9OVmJgoY9e1a1fp4wxW05pw9SBWKEWhW7dutoTL0AqOl156iZkzZ0oN\nsJpDyivx5JNPsnLlSkkAU6jNPTc397Ts50igKhQA2zsK1ntbVlZ2yTZk5QEsLCyUXg4ul4u8vDzZ\n9Fp2dezZsye5ubmSmHnkyBEqKysvmcKj5s6RI0fIysqSvJOJEycyaNAgyQ/Zvn07lZWVkrDc3Nwc\nNmtfx5w1Go1Go4kyotZyVjidTokjDh06lMrKStEYU1JSaG5u5t133wUsd4/D4ZAWgSoeEEktLDSO\n2LIzkdLkvV4vy5Ytk1aODz30ECkpKRHXFv1+v8116/P5RGZlKaifK83966+/Bqy4V3Fxsfxueno6\nn3zySVjr/pRWvWfPHqqrq7nuuusAyxpWmq/qpLVp0ybAOl1r165dUhpx00030blzZ+lslpaWZiu3\nO1vbz0gTDAbFo7Fjxw4pmwHrpKQJEyZEfL54vV6p71yzZg2macq7NmvWLNq0aSNjVlZWxsGDByVk\nov6MBD179qRDhw7SXdA0TSmLe/PNN1m6dKmt6qCmpkZ+rjL5W9ZGX3PNNYAVs45UDwKFmgsqW7u8\nvNx2YlpMTAz19fWnrTeRwDRN8To89dRT0jvbMAxWr17NzTffDMBdd91Fu3btpN3vqlWrOHz4sDwj\np9PZqqWLF0Lo88zMzCQ7O1sy3wcNGkTbtm2l7Co9PZ3a2lrpw+HxeIiLiwvLnIj6zTmU2NhYOTtU\nEQwGJRlo7969uFwuGchwH1t4JtRL7/F4JE4RHx9PmzZtbOUYCxYskL6y99577yVxSbndblJTUykr\nKwOsF0018yguLiY7O1sW1cOHD/PRRx/x97//HbAWCMMwxB28ZMkSunbtGpH7WLlyJatWrZJGIvff\nf7/EiIqKinjllVf4+OOPAeRsVpXkpVxtymXtcDhs8yRcoYWWC/65zuwGbMfrzZkzhyNHjogLNjMz\nk2uuuSbic8YwDFHIqqqqaG5ulgY2Xq+XH/3oR9IYZtasWRw6dEhk7tChQ8TkbdeuHQMHDpQF1Ov1\nyrt34sQJW4gA7OOu4rXq+bjdbu644w7++Mc/Avaa+nCgZAlVKKqrqzl69Kj8u6KiwhZycjqdJCQk\nSMgg0gmCKjGzublZ1oumpiYqKytlvvzrX/8iJydHarVLS0tpaGiQ59K2bVuJT18K1Hs/YsQIioqK\npO/2VVddRd++faWssaamhpiYmNMOTwkH36vN+UwYhiGdXlQGsYoXXYqDJNQL0qFDB3mA9fX1nDhx\nQuTauHEjeXl53H///UD4NoRvw+12c+ONN7J//36RU1nGd999N126dJFJWV5eTnV1tcT3HQ4HEyZM\nkHNPMzMzI7YoDB48mEWLFrF48WLAahSgFtNjx47Z+pSnpqYyefJkZs+eDViWcmg2rvKstIytq5+1\nFqoZirJunE7nafX56meqZ/Uvf/lLAHbu3IlhGLIxPP/887a+wJHC5XKJ5Txt2jRKSkok52Dx4sUs\nWbJEPC7qzGSlBI0aNSpinoi4uDgef/xxtm3bBlh938+WLKWUptAM7Li4ODmUZv78+Vx99dVn7LYV\nzoQ8n88nytnKlSspLy+XeygsLJQaZ7DWjwkTJtiytSOFYRiSXPnEE0/IWlJUVITf7xfLeMuWLWzZ\nssXW3RFOxfz79OlDz549IyZ3S9S6nZOTQ3Z2thw6snDhQpKTk9mxYwdgKRUxMTGiVIQzL0XHnDUa\njUajiTL+KyxnFdeYP38+fr+frVu3AogrM9LygGVlqBaBtbW11NXVictn1KhRdO/e/ZK06wzF6XTy\n4IMPsnfvXsA60Ulp59988w179uyxucri4uKkH/hDDz3E7bffHlFtXV1j+PDhjBgxgjVr1gCW61pZ\nZQ6Hg+TkZImFzpw5k6uuuuqcYx0J2YPBIB6PR7LGN27cKKd2KWtehRfy8/NZvXq1xOfA6mV99913\nA1bG8KWIhxuGIbHX1atXM336dIkx+v1+/H6/WBQqvKRCN+PHj4+YzCrcsnz5csBqm6t6I588eVJK\nLOFU+aXKlejfvz+PPfYYw4YNA04ddXi267R22VJoRz71961bt1JcXCylU8ePH7edANelSxcGDx4c\n8coUhbrukCFDpAPYs88+y7vvvitZ8qoNamgGfWxsrGRFP/fcc7bOfpeKuLg4fvrTn0p29ooVK6iu\nrpYM+WAwSHJyspT3hnMNNy7RsYqtelEVQ+ratSter5fnn38eOHUG8QUsCt82My5KbnVEW2iZVWid\naytMyHN9wTllDj2UftmyZbKg7dixA5/PJ+7Ta6+9lnHjxkkDmNAa1zDIfE65g8EgO3fuFLd2VVWV\nuPl69+7NrbfeypVXXglYLr8LGd/zWGwvaKxDmzKUl5fzyiuvAFZCjHIJezweXC6X7bpNTU3i8uvf\nvz9jx47lgQceAE41X7kALnp+nPWX/j9BUJVW7dixg+LiYgklXXHFFXTr1s0W279AvvO7GNqIRm0S\n5eXleL1eSWJKSUkhPj5eSutSU1NtJXrnmgvqYJ0W70GrjHXosZXvv/8+8+bNEze31+vFNE1Jcpw/\nfz4333zzd2li1OrzIxAI4PV6pTnRihUrWLlypYTJsrOzGT16NHfccQdgJVpd4HoSlrUarPVFyfnw\nww+Tn58vTUnatGnDHXfcwXPPPQcg4Y4L4LwXI+3W1mg0Go0myvivsJxVFuOVV16Jx+ORZurTp0+X\nzjTnSdi0MbBnYrZyiVeraeuhpwqZpikWTxi6rV30WCs5Qy0j9XfVnOR85byI5K+LGmuv14vP55Ns\n+Dlz5kjrwvr6eoLBoGjh7du3JycnRzLh8/LyGDZsmFjMF/EMWt0yigBhfRfDSKuNtXoXq6qqmD17\nNqtWrQKs+d62bVvuvfdewMqMv5ASxmAwGBZrP8KEdX6o8F5ZWRlz587lP//5D2Blb8+bN++7hPPO\nf6H5b9ic1T0cPHiQiooKiTU7HA5b7OY8+J9fECLIBY/1mUpeTvvS8MesLsqtrf5UbULXrl0rma3l\n5eXEx8eTnp4OwLhx42zlXqHZ5ZGQOUrQ7+L/EwwGqaurk1PukpKSGDlypGQ3t0K1h54fkeN/a3Nu\nRf4bH/j3UWb4fsqtZW499Pxo+cst1upo87xFmP/G+WFDx5w1Go1Go4kyvvelVBqNRvO/wKUuM9JE\nlkvl1tZoNBqNRnMWtFtbo9FoNJooQ2/OGo1Go9FEGXpz1mg0Go0mytCbs0aj0Wg0UYbenDUajUaj\niTL05qzRaDQaTZShN2eNRqPRaKIMvTlrNBqNRhNl6M1Zo9FoNJooQ2/OGo1Go9FEGXpz1mg0Go0m\nytCbs0aj0Wg0UYbenDUajUajiTL05qzRaDQaTZShN2eNRqPRaKIMvTlrNBqNRhNl6M1Zo9FoNJoo\nQ2/OGo1Go9FEGXpz1mg0Go0mytCbs0aj0Wg0UYbenDUajUajiTL05qzRaDQaTZShN2eNRqPRaKIM\nvTlrNBqNRhNl6M1Zo9FoNJooQ2/OGo1Go9FEGf8HhK3yDi1l5ckAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d450c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,50)) # not shown in the book\n",
    "for iteration in range(n_digits):\n",
    "    plt.subplot(n_digits, 10, iteration + 1)\n",
    "    plot_image(outputs_val[iteration])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_digits_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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N0KFDG2jCwjXQmFx/q9XKhRdeKAXUmjVrWLZsGT/99BNz584FwovUYrGQkpJCy5Yt5d+W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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f821390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_rows = 6\n",
    "n_cols = 10\n",
    "plot_multiple_images(outputs_val.reshape(-1, 28, 28), n_rows, n_cols)\n",
    "save_fig(\"generated_digits_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Encode & Decode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_variational.ckpt\n"
     ]
    }
   ],
   "source": [
    "n_digits = 3\n",
    "X_test, y_test = mnist.test.next_batch(batch_size)\n",
    "codings = hidden3\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"./my_model_variational.ckpt\")\n",
    "    # encode from X\n",
    "    codings_val = codings.eval(feed_dict={X: X_test})\n",
    "    # decode\n",
    "    outputs_val = outputs.eval(feed_dict={codings: codings_val})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the reconstructions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5N2DAAJG/+eYbkfWDXVJFx44dRR4/frzI11xzjXeM/u4WSGV6jcbevXtFfuKJJ7xjXnrp\nJZE3btwocnFxscj6MyKI7kcErR2J9uf6tdq1a4vcvHlzkY8cORJxDs45l5OTE3EeicIdCADAhAIC\nADChgAAATHKifacXkrifVP8u/Le//a3IQb/5jlVhYaH3Wr9+/URevXq1yOvXr6/yeWOleyTOOff+\n+++LfMwxx4Rx6tT4YhaJFvfrWe9BdcMNN4j88ssve8foNRm6d6D3mNJ7UjnnXL169UTevXu3yPv2\n7RNZ92Z0/8I5fx1I//79RR4zZozIel1X0AOnjjvuuIjniJOo1zN3IAAAEwoIAMCEAgIAMMmYHsgf\n/vAHkfX3ipVx0UUXiXzXXXeJHPSdacOGDUUuKiqK+OdazZo1vdf+8Y9/iDxt2jSRp0+fHnHMIC1b\nthRZ94j0fjxt2rSJ+RyOHki2ivv1/Pnnn4v8s5/9TOSvvvrKO6ZHjx4i6+u3Q4cOIufn53tj6Ov3\nwQcfFPm5554TWfdEgtSqVUvkrl27iqx7M19//bXIjRo18sYcPXq0yMOGDRNZr2HTa08qiR4IACAc\nFBAAgAkFBABgQgEBAJhkTBNdL+hbtGhR1GNuueUWkSdNmiRyZR7sohcwXnbZZSLrpps2duxY77Wp\nU6eKrBcn6Y3kdEP8wIEDEc8ZpH79+iLrZmIl0UTPTnG/nufOnSvyTTfdJLJuiDvn3L333ity69at\nRdbNar1Y0Tnn3nzzTZF//etfi7xnzx6R9WfEWWed5Y05YsQIkfXiRH3OtWvXihx0Pesf3+iNYfWP\nZu6++25vjEosPqSJDgAIBwUEAGBCAQEAmGTMA6U2bdoU8zHr1q0TWX8nqjdn0wt8nHPu/vvvF1n3\nPHSPafjw4SI/9NBDUeepv2fVi4j0wqTKjKm/l+3bt2/UY4BE0Yv8dI9O9zOcc+7LL78UWS+e09fv\nFVdc4Y2xcuVKkfVDp/SD2W6++WaRb7zxRm/MgoICkXVPc+jQoSJPnDhR5CVLlnhj6l7Mxx9/LLLe\nLDXo4Vnx2ICROxAAgAkFBABgQgEBAJhkzDqQHTt2iHzaaaeJvHHjxqhjtG3bVuTS0lKRg3og0Vx9\n9dUi33PPPSKH9GCnZGEdSHYKfTPFQYMGiawf5OSc328sKysTWa/Z0hsOOuf3G5s2bSqy7i/qnmZQ\nbybaPHVPRM976dKl3hh//etfRW7QoIHIAwcOFPnkk0/2xmAdCAAgaSggAAATCggAwCRjeiCa3m9G\n/7baOeeefvppkaM9HEb/Btw5f8+ZV199VWT93WNOTka3CTL6L4fvFPfref/+/SLrPaleeukl7xjd\n09C9BU2vLXHOufHjx4us14roz4BEXM9Bfw/dJ9Hv0f8WQb3WSsydHggAIBwUEACACQUEAGCSsT2Q\nytDrOrZt2xbx/YWFhd5r7dq1i+uc0hw9kOwU9+tZfy7p/uRtt93mHaP3sfrmm29EPumkk0TW/Q7n\n/LVglXkmUCrS/37GXg09EABAOCggAAATCggAwIQCAgAwyeomOuKOJnp2Cv161p9TQRsh6td0A1zn\nymx8mOVoogMAwkEBAQCYUEAAACb0QBBP9ECyE9dzZqIHAgAIBwUEAGBCAQEAmFBAAAAmFBAAgAkF\nBABgQgEBAJhQQAAAJhQQAIAJBQQAYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkF\nBABgQgEBAJhQQAAAJrlJOm/Uh7UDSBtcz1mKOxAAgAkFBABgQgEBAJhQQAAAJhQQAIAJBQQAYEIB\nAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgQgEBAJhQQAAAJhQQAIAJBQQAYEIB\nAQCYUEAAACYUEACACQUEAGCSm6TzHk3SeRGunGRPAEnB9ZyZol7P3IEAAEwoIAAAEwoIAMCEAgIA\nMKGAAABMKCAAABMKCADAhAICADChgAAATCggAAATCggAwIQCAgAwSdZmigCQcY4erfq+kjk56bMn\nKXcgAAATCggAwIQCAgAwoQcSZ2VlZSIXFRWJ/Pbbb4t80kkneWNMnDhR5A0bNoh8zDHHiPzaa6+J\n3KBBg0rNFchmQf2KgwcPirxy5UqRV61aJfLSpUtF3rhxozdmcXGxyA0bNhS5efPmIv/6178WuUmT\nJt6YBQUF3mvfpvsoYfVVuAMBAJhQQAAAJhQQAIBJTjx+t2yQlJPG6siRIyK///773nv+/Oc/i7x6\n9WqRP/zwQ5HD+C7ylFNOEXnmzJlR3xOS9PkBO+IpLa5n/Vmn+5POOTd69GiR58+fL7LukVSrJv8b\nvEaNGt6Y5eXlEY+pV6+eyN26dRP5xhtv9Mbs3LmzyPn5+SLn5eVFPKdzlfosivoG7kAAACYUEACA\nCQUEAGDCOpAINm/eLPIZZ5yRpJlIv/rVr0Ru1KiRyB988IF3TMuWLUWuU6dO3OcFpBLd89BrNPr0\n6eMd8/XXX0ccs3r16iLXrVtXZN3PcM65AwcORByjdu3aIhcWFooc1KfOzZUf3brHkaj9tLgDAQCY\nUEAAACYUEACACT2Qb/nnP/8p8jnnnBP1GL3vlP4d+Pjx40WuzHeT+jvR4cOHi6y/Q9Xffy5cuNAb\nc/v27SLTA0GmidbzOO2000TesWOHN4a+PvW1OHjwYJF/85vfiNysWTNvTH296nPotSV676yg/fL0\n50zQOo9I54wX7kAAACYUEACACQUEAGBCAQEAmLCZ4rf8+Mc/FllvpDZgwADvmNmzZ4usm25Zhs0U\ns1NKXM/6hyJ6w0HdNA9qPPfu3Vvkp59+WmS9IDceC/j0pq2acSPEeGAzRQBAOCggAAATCggAwCRr\nFhLqDc2cc+7qq68W+YQTTog4xrHHHuu9luU9DyAp9OI755wbNGiQyLrnofsGffv29cZ46623RC4o\nKLBOsdL0QsN0wh0IAMCEAgIAMKGAAABMsqYH8tRTT3mv6d94R6M3ZwOQHKtXr/ZeW7ZsWcRj9MOf\ngq5/vUkhIuMOBABgQgEBAJhQQAAAJlnTA7n11lurPMb69eu913bu3Clyw4YNY/pzANHpPfuef/75\nqMfodR+tW7cWuby83DtGv5abKz8ik/XgplTFHQgAwIQCAgAwoYAAAEwoIAAAk6xpol9xxRXeaw8/\n/HBMY+zatct77fbbbxe5S5cuIk+aNEnkf/3rXyK3adMmpjkA2Ug/dKlTp07ee+rVqyey3nCxXbt2\nIj/yyCPeGLt37xZZb7B67rnnitysWTORgzZczc/PF1lvnpjOjXfuQAAAJhQQAIAJBQQAYJKjF+gk\nSMJPWlxc7L2mvwN94oknRP75z38u8kMPPRTzefW/b61atURu0aKFd8zw4cNFHj16tMjNmzePeR4J\nkr5f5qIqQr+e9XW0f/9+7z3Tpk2LOEbNmjVFXrBggfee5cuXi6wfRKfn0ahRI5F79uzpjXnhhReK\n3LlzZ5H1Z0IK9USiToQ7EACACQUEAGBCAQEAmGRNDyQsH3zwgcibN28Wee7cuSL/+9//Fjlog8ZD\nhw7FNAe9PqVBgwYxHR9HKfPlLRIq4dezXhfinHMVFRUi616CPkb3N5xz7osvvhB5yZIlIi9cuFDk\nxYsXixx07bZv317kkSNHinzOOeeI3KRJE5GDNnBMUJ+EHggAIBwUEACACQUEAGBCDyTJ1qxZ4702\nYcIEkVeuXCnymWeeKXJRUZHIzz77bJxmFzN6INkpY65n3SfRfRXdN9F72+m1ZM7517jeL69Vq1Yi\nn3322SKffvrp3pjR1o7EqUdCDwQAEA4KCADAhAICADChB5IG9PeuH3/8sciXX365yNddd503hl4r\ncuedd8ZpdgI9kOyU8Os56HMrEWsj9Hl1j2TPnj3eMbpPoteOlZeXi1ynTh2Rg3ogvXv3jnhMnHoi\n9EAAAOGggAAATCggAAATCggAwIQmehrSi50ef/xxkV9++WXvmLZt24o8ffr0+E+MJnq2ivv1rD+X\noi3wc865vLw8kZPxYKagTR4PHjwocklJich6A9ZXXnlF5K+//tob89prrxVZb9hYo0YNkXNzc79j\nxhHRRAcAhIMCAgAwoYAAAExMX4ylohkzZoj8ve99T2T9IHvngh/Ukor0d6j6oVS33nqryGVlZd4Y\nugcCpDLdS9ixY4fIy5Yt8475wQ9+IHJhYaHIieiJBJ1D9yOqV68ucs2aNUX+7LPPRA56SNWCBQtE\nbty4sciNGjWKPtk4SI9PUABAyqGAAABMKCAAAJOM6YHoh7J069ZN5Hfeecc7pk+fPqHOqTKWLl3q\nvbZ9+3aR9caHejNFINOUlpaKfM0114gcdA2MGTMm4jG6FxFE9zCirZOrzPoU3cPYtGmTyH/84x9F\n1j2Q448/3htz586dIuu+is5h4Q4EAGBCAQEAmFBAAAAmGdMD0b+D1t9l9u/f3ztG7ydz/vnni3zc\ncceJ3LBhQ28MvW+N/m52zpw5Eeelv8t0Lvh71Fi0bNnSe+2SSy6p0phAIukHoOnrauvWrd4xkydP\nFnnjxo0iDxkyRORmzZp5YxQUFEQcY9++fSLrfsUnn3zijbl27VqRDx8+LLL+DNC9mqA1HRdffLHI\n+rMqUfuAcQcCADChgAAATCggAACTjH0eiP5t9dVXX+1PIgF/d/078TD239I9jw8//NB7T1D/JgQ8\nDyQ7xf1C0vu5DRw4UOSg/4/r3qFeC6H7AkHXon6mSHl5ecSs+xlB9Hny8/NF1n2X7t27i/z73//e\nG7NNmzYih7Tug+eBAADCQQEBAJhQQAAAJhQQAIBJxjbRtenTp3uvTZw4UWT9cPt40P++lVng07Vr\nV5GDHob1bffee6/ITZo0qeTs4o4menaK+/Wsrxu9sPCBBx7wjpk/f77Iu3fvjpgPHDgQdR76RzDR\nrmfdhHfOX+TcqVMnkW+55RaR9UawusnunHO5uQlZA04THQAQDgoIAMCEAgIAMMmaHkgQvSHbU089\nJfLpp58u8uLFi6OOuWTJEpH1gp+ioiKR7777bm8MvXla0HegKYoeSHZK+PWsexPOOXfw4EGR9+7d\nK7LugaxatcobQ298qB8G1aBBA5F79Oghsn6wnXPO1a5dW+SaNWuKHG3BYxLRAwEAhIMCAgAwoYAA\nAEyyugeCuEuZL2+RUFzPmYkeCAAgHBQQAIAJBQQAYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBA\nAAAmFBAAgAkFBABgQgEBAJhQQAAAJhQQAIAJBQQAYEIBAQCY5CbpvDx4CMgcXM9ZijsQAIAJBQQA\nYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgQgEBAJhQQAAAJhQQAIAJBQQA\nYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgkpuk8x5N0nkRrpxkTwBJwfWc\nmaJez9yBAABMKCAAABMKCADAhAICADChgAAATCggAAATCggAwIQCAgAwoYAAAEwoIAAAEwoIAMCE\nAgIAMKGAAABMKCAAABMKCADAJFnPAwGAlHP0qHy0SUVFhciHDx8W+dChQxHf75xzNWrUEDk/P1/k\natXkf8fn5KTPY3W4AwEAmFBAAAAmFBAAgAk9kJAtXLhQ5N27d0c9Rn8Pe+6554pcUFBQ9YkBWebI\nkSMiHzhwwHvPf/7zH5Hfe+89kZctWybyxo0bRS4qKvLG1H2SAQMGiHzbbbeJ3LBhQ5F1jySVpO7M\nAAApjQICADChgAAATHL09+0JkpSTxurzzz8XecuWLd57rr32WpH1v+e6detELi8vj3pePUbbtm1F\nvvvuu0UePHiwyHXr1o16jpCkzw/YEU8peT2XlZWJ/Mc//lHkBx980Dtm7969Iufl5Ylcr149kXV/\nQ2fnnNu/f3/EMXv37i3y1KlTRW7durU3ZvXq1b3XQhD1euYOBABgQgEBAJhQQAAAJlndA9HfTS5a\ntEjkCy64QOSSkpKoY+p/zw4dOois98UJovfT0efdvHmzyN26dRP5zTff9MbU392G9B0qPZDslBLX\nc2lpqchDhgwR+Z133hFZrwtxzrmaNWuKfPzxx4vcpUuXiO8P6nHq61f3VjXd8xw1apT3Hr02TO+v\nFSf0QADym+QcAAASBElEQVQA4aCAAABMKCAAABMKCADAJGOb6PrvFbRx2o9//GOR9cZpFkOHDhX5\nueeeE9myEeK+ffsijjl27FiRg/43nT59usi//OUvRY7TQ2xoomenhH+IbNu2zXvt7LPPFnn58uUR\nx6hfv7732vjx40UeMWKEyHXq1BFZXzdBGx/qH+usWrVK5Llz54o8e/ZskYN+eDNu3DiRhw0bJnJu\nblz2yaWJDgAIBwUEAGBCAQEAmGRsD+Szzz4TWS+2q4zrr79eZL0o0DnnrrjiipjHjbcPPvhA5Pvv\nv997z5w5c0T+9NNPRf7e974Xj6nQA8lOoV/P+kFsQdezXmCrP9tOP/10kYMW3EbrcWj6HJXpJUbr\nzz7zzDMiP/roo94YhYWFIj///PMi68WIxh4nPRAAQDgoIAAAEwoIAMAkLj8WTgX6QTBjxoyJeQy9\nVuKiiy4SOUEPcYlZr169RL7wwgu99+geCJDK9EaHt956q8hffvmld4zuLeg1WTNnzhTZsiZLs/QW\n9DG1atUSWa/ROnz4sDfG5MmTRb7hhhtE1j0R3duJF+5AAAAmFBAAgAkFBABgkjE9kB/96Eci63UO\nQW6//XaR9XeP6ULvtRO0T1D37t1Frlu3bqhzAqqiuLhY5DfeeEPkoIdBdezYUeQweh5h0D2R2rVr\nizxy5EjvmFmzZom8evVqkTds2CBy586dqzLF78QdCADAhAICADChgAAATCggAACTjGmiL1myROTK\nLPAJq7GUaFu2bBF5xYoV3ns+/vhjkfUiq8r86ABIFP3QtKKiIpHz8vK8Y1555RWRgx7ElA70Z5fe\nONE5f3FhSUmJyC+//LLINNEBACmFAgIAMKGAAABMMqYHohcW6Yfbn3LKKd4xw4cPD3VOidKuXTuR\n9YOwnPO/E122bJnIr776qsiZ8m+D9DRv3jyRKyoqRG7durV3jH7N+BCllJOb639M641dd+3aJfLS\npUtDndN/cQcCADChgAAATCggAACTjOmB6J6H/v4zVR8GFYb27dt7rzVt2lRk/QAu3ROhB4JkWr9+\nvcj6YVENGzb0jon1GtdjVkYy+iq6/+Ocv4GqXhdz6NChUOf0X9yBAABMKCAAABMKCADAJGN6INFc\neumlyZ5Cwuh9r5xzbvPmzUmYCWATrZ9RWlrqvab3h8rPz484RlAPRPcOdM9D9xoS0RM5ePCg99q6\ndetE1uvg6tevH+qc/os7EACACQUEAGBCAQEAmGRND+Spp57yXhs7dmwSZhK+yZMne6/p5wU0adJE\n5FGjRoU6JyAWzZs3F1mvU9L9jsqoTL9C9170MYnoeeh+xjvvvOO9R68D0c8+ufzyy+M/sQDcgQAA\nTCggAAATCggAwIQCAgAwyZgmerQHSu3YscM7ZuvWrSLrDQdTVVlZmcgXXXSRyPrhUM75/x6/+MUv\nRE6XvzuyQ4sWLUTWzWv9ACXnYm+sBzXEgx7eFDa9oFF/Ll111VXeMbVq1RL5Jz/5ich9+vSJ0+wi\n4w4EAGBCAQEAmFBAAAAmGdMDmTdvnsjnn3++yNu3b/eOef/990VO1Ycoff755yIPGTJEZL2xmu53\nOOfcHXfcIfK4cePiNDsg/s466yyRZ8yYIbLueTrn3LZt20Q+5phj4j+xONBzX7t2rciDBw8Wuaio\nyBujU6dOIt92220iFxQUVGWKlcYdCADAhAICADChgAAATHIsD5aPg9BP+sUXX4gc9Fvqb775JuJ7\nLr74YpGjPeQmXvQ6jyuvvFLkmTNnRjw+6GEy+nvWunXrGmcXUfg7zSEVxf16Li8vF7lnz54i6+vb\nOecuuOACkR999FGR9dqJRGyM6Jy/PmXRokUijxgxQuTi4mKRGzRo4I35+OOPizxs2DCR47SeJeo/\nEHcgAAATCggAwIQCAgAwydgeiDZ//nzvtUGDBkU8Ztq0aSJfcsklVZ6HfhDMlClTvPd8+umnIs+Z\nMyemc6xevdp7rV27djGNYUQPJDuFfj3PmjVLZL2XWxC9Xmrq1KkiN27c2Dsm1r5IRUWFyHv37vXe\nc+edd4o8e/ZskXfu3Cmy3gdMfw4551zfvn1FDmkPL3ogAIBwUEAAACYUEACASdb0QILovbB69+4d\n8xijRo0SecCAASIvW7ZM5EmTJkUdM9qzTfTvwt977z2RE9TvCEIPJDuFfj3ra+Kyyy7z3qPXR+n+\nRL169UQeOXKkN4beQ08f89FHH4n88ssvi6z7l845d+DAAZH1epR+/fqJPHnyZJFbt27tjRm0310I\n6IEAAMJBAQEAmFBAAAAmFBAAgElWN9H1333Pnj0i33vvvSK/8MIL3hj6ITZ6zGgLk7p37+691r59\ne5EnTJggst4sMaSNES1oomenhF/PQQ+UevLJJ0X+v//7P5H15qlBi++iPYhJb/Kor/caNWp4x5x4\n4oki33PPPSLrJroeI1GbPgagiQ4ACAcFBABgQgEBAJhkdQ8kVps3b/Ze27dvn8gLFiwQecWKFSJf\ne+21Irds2dIbM4V6GrGiB5KdUuJ61p9l+sFMr7zyisjvvvuuN8bnn38ucmlpacRz6kV+Y8eO9d6j\n+5yFhYUiJ7HHEQ09EABAOCggAAATCggAwIQeCOIpZb/MRajS8noOWkuiX4u2rkvnoE0OU7jHEQ09\nEABAOCggAAATCggAwIQeCOIpbb/sRZVwPWcmeiAAgHBQQAAAJhQQAIAJBQQAYEIBAQCYUEAAACYU\nEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgkpuk87LpHpA5uJ6zFHcgAAATCggAwIQCAgAwoYAA\nAEwoIAAAEwoIAMCEAgIAMKGAAABMKCAAABMKCADAhAICADChgAAATCggAAATCggAwIQCAgAwoYAA\nAEwoIAAAEwoIAMCEAgIAMKGAAABMKCAAABMKCADAhAICADDJTdJ5jybpvAhXTrIngKTges5MUa9n\n7kAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgQgEBAJhQQAAAJhQQAIAJBQQAYJKsvbAA\nIOUdPSq3+crJYbu3b+MOBABgQgEBAJhQQAAAJvRAYrB582bvtZtvvlnkF198UeTcXPlPfP/994t8\n3HHHeWNeeOGFIlevXj2meQLw6X7Gvn37vPe89tprIi9YsEDkwsJCkU866SSRu3bt6o3ZuXNnkevU\nqSNytWrp+9/x6TtzAEBSUUAAACYUEACASY7+XjBB0uIZyocOHRL56quv9t7z5z//OeIYlt+R6x7I\npEmTRG7VqlXUMZKEH8lnp5S8nvW1V1JSIrLuRzrn3KxZsyIe07FjR5Fr1Kgh8pYtW7wx9efIlVde\nKfJVV10lsu6bJhHPRAcAhIMCAgAwoYAAAEzogURwww03iDx16tSYx4jHXjpNmzYV+d133xW5devW\nMY8ZEnog2Sklr+fDhw+L/OGHH4o8YcIE75g1a9aI3L17d5GHDBki8u7du0XW68Ccc+6TTz4RWa8l\nWbVqlchNmjTxxkgSeiAAgHBQQAAAJhQQAIBJyvzgOBXp70yDvPnmmyLXq1dPZN0D0b8znzJlStRz\nbN26VeS+ffuKvGzZsohzALLRkSNHRNZrNCoqKrxjBgwYIPKoUaNE1muwdJ/lq6++8sZcsWKFyGVl\nZSIvWrRI5PPPP98bI1VxBwIAMKGAAABMKCAAABMKCADAhCZ6DPSCPuec69evn8g1a9aMOEaPHj1E\nDnpY1AMPPBBxDN2oKy0tFZkmOhC9iR60aWGfPn1E7tChg8i1a9eOeI7rrrvOG3PdunUiz5s3T2S9\n+HDEiBEip/IDp1J3ZgCAlEYBAQCYUEAAACb0QL5lw4YNIusFer/5zW+8Y6L1PDT9ves999zjvUd/\nZ/rqq6/GdA4AzhUXF4v8wQcfiKwX9DnnXKdOnUTWD4zS/Qjdwzz++OO9MW+55RaR9cJBvWBZP8Tq\nmGOO8cZMFdyBAABMKCAAABMKCADAhB7It0yePFlk/V1kGPLy8rzX7rzzTpHpgQDR6Y1L169fL/L2\n7dtFDupf6h6lvj6jrckIWtd1yimniKwfKLVr1y6R586dK3Iqb67IHQgAwIQCAgAwoYAAAEyyugey\nadMmkZ977rmI7x8zZkyY0/mfBg0aJOQ8QCbR+1Lp9RW619CtWzdvjBNPPFHkeOxDpdeS1K9fX2T9\nwLjXX39dZL03VrzmFQ+pMQsAQNqhgAAATCggAAATCggAwCSrm+jl5eUiHzhwQGS9AKhhw4ahz8k5\nf/O0tm3birx27dqEzANIJxUVFSLrTUn1Ir/OnTt7Y+gHRuXk5FR5XnoMfX3reR86dKjK50wU7kAA\nACYUEACACQUEAGCS1T2Qe++9N+Kfn3HGGSLXqlUrzOn8j14kVFBQkJDzAumstLRU5MWLF4usHzDV\ns2dPb4x49Dw03eP45ptvRD7uuONEHjlyZOhzihfuQAAAJhQQAIAJBQQAYJI1PRD9/adzzr3//vsi\n6wfSjBs3LtQ5fRe96dvy5cuTMg8gVelr1Tnnli5dKrLeLFWv++jSpYs3RlX7DUHz+vrrryOe44QT\nTog6r1TFHQgAwIQCAgAwoYAAAEyypgeyb98+77U1a9aInCq/t/7d734nsp6XXhei9/gBMp1+eJRz\nzs2bN09kvZ6qb9++IusHPcXD4cOHvddmzJghcklJicjf//73Ra5Tp07c5xUW7kAAACYUEACACQUE\nAGCSNT2QVKX3yXHO3ytHu/LKK0Vu0qRJXOcEpLqg62bVqlUi615hp06dRI5Hz1P3YvQaLuece+aZ\nZ0TWz/to3LixyLqnGbS2JFX6tdyBAABMKCAAABMKCADAhAICADChiR7B7t27RW7WrFmVxywrKxP5\n8ssv994zc+ZMkQsLC0W+6aabqjwPIJ3pRrRzzhUVFYl88OBBkXXD29KI1g1tvShQ/8DFOX8zxYYN\nG4r8ox/9SOT8/PwqzzNRuAMBAJhQQAAAJhQQAIAJPZAIzjnnHJFXrlzpvSfWjc+2b98usu53BDnz\nzDNFbt68eUznBDJN0OK6bdu2iax7IB999JHI5557rjdGXl5exPOUlpaKfOmll4o8f/58b8zcXPkx\n+8Mf/lDk3r17i0wPBACQ8SggAAATCggAwCRreiCNGjXyXjv77LNF1g+k+eqrr0R+9tlnvTHGjBkj\nsl47Mm3aNJEfe+yxqHOtV6+eyLfffnvUY4BsEvQwKL1eSvdEPvnkE5HXr1/vjdGyZUuR9eaIet3W\n22+/LXLQg670ZonXXHONyLVr1xZZPwgrlaXPTAEAKYUCAgAwoYAAAEyypgeif1vtnHP9+vUTWfdA\ntIULF3qv7d+/X+RHH31U5C+//FLkyvyme/r06SL36NEj6jFANtEPXXLOX1+hexxr164VOagfqR9C\n9dZbb4n8xRdfiHz48GGRdb/DOf96Pvnkk0XWa09Sed2Hxh0IAMCEAgIAMKGAAABMcoL2lEmApJxU\n099ndujQIe7n0P+++jffd9xxh3fM9ddfL3JQ/yZFpc+Xt4inlLiei4uLRe7Vq5fIuh8ZtGZD91b0\nc0fKy8tF1mu2Xn31VW/M0047TeQ02usq6sS4AwEAmFBAAAAmFBAAgAkFBABgktVN9IqKCpEnTpwo\n8oQJE6p8joEDB4p83333iXzqqadW+RwpJGW7gQhVSlzP+rNMb544ZMgQkYuKirwxdGNdN7ybNm0q\n8uOPPy5y//79vTHTqGmu0UQHAISDAgIAMKGAAABMsroHounvP++66y6RJ02aFHWMwYMHizxnzhyR\ngzaByyBp8+Uu4iotrufNmzeLrPsXzvmLi8844wyRzzvvPJFbtGghcm6uvz9tGvU8NHogAIBwUEAA\nACYUEACACT0QxFPaftmLKuF6zkz0QAAA4aCAAABMKCAAABMKCADAhAICADChgAAATCggAAATCggA\nwIQCAgAwoYAAAEwoIAAAEwoIAMCEAgIAMKGAAABMKCAAABMKCADAxH8CfGLw4CEgc3A9ZynuQAAA\nJhQQAIAJBQQAYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgQgEBAJhQQAAA\nJhQQAIAJBQQAYEIBAQCYUEAAACYUEACACQUEAGBCAQEAmFBAAAAmFBAAgAkFBABgQgEBAJhQQAAA\nJhQQAIDJ/wPI5dUjcxVaLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123a17490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 2.5 * n_digits))\n",
    "for iteration in range(n_digits):\n",
    "    plt.subplot(n_digits, 2, 1 + 2 * iteration)\n",
    "    plot_image(X_test[iteration])\n",
    "    plt.subplot(n_digits, 2, 2 + 2 * iteration)\n",
    "    plot_image(outputs_val[iteration])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolate digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./my_model_variational.ckpt\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1202d6b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180303d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118ba9910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116aec610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_iterations = 3\n",
    "n_digits = 6\n",
    "codings_rnd = np.random.normal(size=[n_digits, n_hidden3])\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"./my_model_variational.ckpt\")\n",
    "    target_codings = np.roll(codings_rnd, -1, axis=0)\n",
    "    for iteration in range(n_iterations + 1):\n",
    "        codings_interpolate = codings_rnd + (target_codings - codings_rnd) * iteration / n_iterations\n",
    "        outputs_val = outputs.eval(feed_dict={codings: codings_interpolate})\n",
    "        plt.figure(figsize=(11, 1.5*n_iterations))\n",
    "        for digit_index in range(n_digits):\n",
    "            plt.subplot(1, n_digits, digit_index + 1)\n",
    "            plot_image(outputs_val[digit_index])\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coming soon..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  },
  "nav_menu": {
   "height": "381px",
   "width": "453px"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": false,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {
    "height": "444px",
    "left": "1px",
    "right": "20px",
    "top": "89px",
    "width": "212px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}