{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolutional variational autoencoder with PyMC3 and Keras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this document, I will show how autoencoding variational Bayes (AEVB) works in PyMC3's automatic differentiation variational inference (ADVI). The example here is borrowed from [Keras example](https://github.com/fchollet/keras/blob/master/examples/variational_autoencoder_deconv.py), where convolutional variational autoencoder is applied to the MNIST dataset. The network architecture of the encoder and decoder are the same. However, PyMC3 allows us to define a probabilistic model, which combines the encoder and decoder, in the same way as other probabilistic models (e.g., generalized linear models), rather than directly implementing of Monte Carlo sampling and the loss function, as is done in the Keras example. Thus the framework of AEVB in PyMC3 can be extended to more complex models such as [latent dirichlet allocation](https://taku-y.github.io/notebook/20160928/lda-advi-ae.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Notebook Written by Taku Yoshioka (c) 2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To use Keras with PyMC3, we need to choose [Theano](http://deeplearning.net/software/theano/) as the backend for Keras. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%autosave 0\n",
    "%matplotlib inline\n",
    "import sys, os\n",
    "%env KERAS_BACKEND=theano\n",
    "%env THEANO_FLAGS=device=cuda3,floatX=float32,optimizer=fast_run\n",
    "\n",
    "from collections import OrderedDict\n",
    "from keras.layers import InputLayer, BatchNormalization, Dense, Conv2D, Deconv2D, Activation, Flatten, Reshape\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "from theano import shared, config, function, clone, pp\n",
    "import theano.tensor as tt\n",
    "import keras\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "import seaborn as sns\n",
    "\n",
    "from keras import backend as K\n",
    "K.set_image_dim_ordering('th')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1\n",
      "0.9.0\n",
      "2.0.4\n"
     ]
    }
   ],
   "source": [
    "import pymc3, theano\n",
    "print(pymc3.__version__)\n",
    "print(theano.__version__)\n",
    "print(keras.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load images\n",
    "MNIST dataset can be obtained by [scikit-learn API](http://scikit-learn.org/stable/datasets/) or from [Keras datasets](https://keras.io/datasets/). The dataset contains images of digits. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://s3.amazonaws.com/img-datasets/mnist.npz\n"
     ]
    }
   ],
   "source": [
    "from keras.datasets import mnist\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "data = pm.floatX(x_train.reshape(-1, 1, 28, 28))\n",
    "data /= np.max(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use Keras\n",
    "We define a utility function to get parameters from Keras models. Since we have set the backend to Theano, parameter objects are obtained as shared variables of Theano. \n",
    "\n",
    "In the code, 'updates' are expected to include update objects (dictionary of pairs of shared variables and update equation) of scaling parameters of batch normalization. While not using batch normalization in this example, if we want to use it, we need to pass these update objects as an argument of `theano.function()` inside the PyMC3 ADVI function. The current version of PyMC3 does not support it, it is easy to modify (I want to send PR in future). \n",
    "\n",
    "The learning phase below is used for Keras to known the learning phase, training or test. This information is important also for batch normalization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, BatchNormalization\n",
    "\n",
    "def get_params(model):\n",
    "    \"\"\"Get parameters and updates from Keras model\n",
    "    \"\"\"\n",
    "    shared_in_updates = list()\n",
    "    params = list()\n",
    "    updates = dict()\n",
    "    \n",
    "    for l in model.layers:\n",
    "        attrs = dir(l)\n",
    "        # Updates\n",
    "        if 'updates' in attrs:\n",
    "            updates.update(l.updates)\n",
    "            shared_in_updates += [e[0] for e in l.updates]\n",
    "        \n",
    "        # Shared variables\n",
    "        for attr_str in attrs:\n",
    "            attr = getattr(l, attr_str)\n",
    "            if isinstance(attr, tt.compile.SharedVariable):\n",
    "                if attr is not model.get_input_at(0):\n",
    "                    params.append(attr)\n",
    "    \n",
    "    return list(set(params) - set(shared_in_updates)), updates\n",
    "\n",
    "# This code is required when using BatchNormalization layer\n",
    "keras.backend.theano_backend._LEARNING_PHASE = \\\n",
    "    shared(np.uint8(1), name='keras_learning_phase')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Encoder and decoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we define the convolutional neural network for encoder using the Keras API. This function returns a CNN model given the shared variable representing observations (images of digits), the dimension of latent space, and the parameters of the model architecture. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cnn_enc(xs, latent_dim, nb_filters=64, nb_conv=3, intermediate_dim=128):\n",
    "    \"\"\"Returns a CNN model of Keras.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    xs : theano.TensorVariable\n",
    "        Input tensor.\n",
    "    latent_dim : int\n",
    "        Dimension of latent vector.\n",
    "    \"\"\"\n",
    "    input_layer = InputLayer(input_tensor=xs, \n",
    "                             batch_input_shape=xs.tag.test_value.shape)\n",
    "    model = Sequential()\n",
    "    model.add(input_layer)\n",
    "    \n",
    "    cp1 = {'padding': 'same', 'activation': 'relu'}\n",
    "    cp2 = {'padding': 'same', 'activation': 'relu', 'strides': (2, 2)}\n",
    "    cp3 = {'padding': 'same', 'activation': 'relu', 'strides': (1, 1)}\n",
    "    cp4 = cp3\n",
    "    \n",
    "    model.add(Conv2D(1, (2, 2), **cp1))\n",
    "    model.add(Conv2D(nb_filters, (2, 2), **cp2))\n",
    "    model.add(Conv2D(nb_filters, (nb_conv, nb_conv), **cp3))\n",
    "    model.add(Conv2D(nb_filters, (nb_conv, nb_conv), **cp4))\n",
    "    model.add(Flatten())\n",
    "    model.add(Dense(intermediate_dim, activation='relu'))\n",
    "    model.add(Dense(2 * latent_dim))\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we define a utility class for encoders. This class does not depend on the architecture of the encoder except for input shape (`tensor4` for images), so we can use this class for various encoding networks. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Encoder:\n",
    "    \"\"\"Encode observed images to variational parameters (mean/std of Gaussian).\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    xs : theano.tensor.sharedvar.TensorSharedVariable\n",
    "        Placeholder of input images. \n",
    "    dim_hidden : int\n",
    "        The number of hidden variables. \n",
    "    net : Function\n",
    "        Returns \n",
    "    \"\"\"\n",
    "    def __init__(self, xs, dim_hidden, net):\n",
    "        model = net(xs, dim_hidden)\n",
    "        \n",
    "        self.model = model\n",
    "        self.xs = xs\n",
    "        self.out = model.get_output_at(-1)\n",
    "        self.means = self.out[:, :dim_hidden]\n",
    "        self.rhos = self.out[:, dim_hidden:]\n",
    "        self.params, self.updates = get_params(model)\n",
    "        self.enc_func = None\n",
    "        self.dim_hidden = dim_hidden\n",
    "        \n",
    "    def _get_enc_func(self):\n",
    "        if self.enc_func is None:\n",
    "            xs = tt.tensor4()\n",
    "            means = clone(self.means, {self.xs: xs})\n",
    "            rhos = clone(self.rhos, {self.xs: xs})\n",
    "            self.enc_func = function([xs], [means, rhos])\n",
    "            \n",
    "        return self.enc_func\n",
    "    \n",
    "    def encode(self, xs):\n",
    "        # Used in test phase\n",
    "        keras.backend.theano_backend._LEARNING_PHASE.set_value(np.uint8(0))\n",
    "        \n",
    "        enc_func = self._get_enc_func()\n",
    "        means, _ = enc_func(xs)\n",
    "        \n",
    "        return means\n",
    "\n",
    "    def draw_samples(self, xs, n_samples=1):\n",
    "        \"\"\"Draw samples of hidden variables based on variational parameters encoded.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        xs : numpy.ndarray, shape=(n_images, 1, height, width)\n",
    "            Images.\n",
    "        \"\"\"\n",
    "        # Used in test phase\n",
    "        keras.backend.theano_backend._LEARNING_PHASE.set_value(np.uint8(0))\n",
    "\n",
    "        enc_func = self._get_enc_func()\n",
    "        means, rhos = enc_func(xs)\n",
    "        means = np.repeat(means, n_samples, axis=0)\n",
    "        rhos = np.repeat(rhos, n_samples, axis=0)\n",
    "        ns = np.random.randn(len(xs) * n_samples, self.dim_hidden)\n",
    "        zs = means + pm.distributions.dist_math.rho2sd(rhos) * ns\n",
    "        \n",
    "        return zs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a similar way, we define the decoding network and a utility class for decoders. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cnn_dec(zs, nb_filters=64, nb_conv=3, output_shape=(1, 28, 28)):\n",
    "    \"\"\"Returns a CNN model of Keras.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    zs : theano.tensor.var.TensorVariable\n",
    "        Input tensor.\n",
    "    \"\"\"\n",
    "    minibatch_size, dim_hidden = zs.tag.test_value.shape\n",
    "    input_layer = InputLayer(input_tensor=zs, \n",
    "                             batch_input_shape=zs.tag.test_value.shape)\n",
    "    model = Sequential()\n",
    "    model.add(input_layer)\n",
    "        \n",
    "    model.add(Dense(dim_hidden, activation='relu'))\n",
    "    model.add(Dense(nb_filters * 14 * 14, activation='relu'))\n",
    "    \n",
    "    cp1 = {'padding': 'same', 'activation': 'relu', 'strides': (1, 1)}\n",
    "    cp2 = cp1\n",
    "    cp3 = {'padding': 'valid', 'activation': 'relu', 'strides': (2, 2)}\n",
    "    cp4 = {'padding': 'same',  'activation': 'sigmoid'}\n",
    "\n",
    "    output_shape_ = (minibatch_size, nb_filters, 14, 14)\n",
    "    model.add(Reshape(output_shape_[1:]))\n",
    "    model.add(Deconv2D(nb_filters, (nb_conv, nb_conv), data_format='channels_first', **cp1))\n",
    "    model.add(Deconv2D(nb_filters, (nb_conv, nb_conv), data_format='channels_first', **cp2))\n",
    "    output_shape_ = (minibatch_size, nb_filters, 29, 29)\n",
    "    model.add(Deconv2D(nb_filters, (2, 2), data_format='channels_first', **cp3))\n",
    "    model.add(Conv2D(1, (2, 2), **cp4))\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Decoder:\n",
    "    \"\"\"Decode hidden variables to images.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    zs : Theano tensor\n",
    "        Hidden variables.\n",
    "    \"\"\"\n",
    "    def __init__(self, zs, net):\n",
    "        model = net(zs)\n",
    "        self.model = model\n",
    "        self.zs = zs\n",
    "        self.out = model.get_output_at(-1)\n",
    "        self.params, self.updates = get_params(model)\n",
    "        self.dec_func = None\n",
    "        \n",
    "    def _get_dec_func(self):\n",
    "        if self.dec_func is None:\n",
    "            zs = tt.matrix()\n",
    "            xs = clone(self.out, {self.zs: zs})\n",
    "            self.dec_func = function([zs], xs)\n",
    "            \n",
    "        return self.dec_func\n",
    "        \n",
    "    def decode(self, zs):\n",
    "        \"\"\"Decode hidden variables to images. \n",
    "        \n",
    "        An image consists of the mean parameters of the observation noise.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        zs : numpy.ndarray, shape=(n_samples, dim_hidden)\n",
    "            Hidden variables. \n",
    "        \"\"\"    \n",
    "        # Used in test phase\n",
    "        keras.backend.theano_backend._LEARNING_PHASE.set_value(np.uint8(0))\n",
    "\n",
    "        return self._get_dec_func()(zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generative model\n",
    "We can construct the generative model with the PyMC3 API and the functions and classes defined above. We set the size of mini-batches to 100 and the dimension of the latent space to 2 for visualization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Constants\n",
    "minibatch_size = 100\n",
    "dim_hidden = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We require a placeholder for images, into which mini-batches of images will be placed during ADVI inference. It is also the input for the encoder. Below, `enc.model` is a Keras model of the encoder network and we can check the model architecture using the method `summary()`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (100, 1, 28, 28)          0         \n",
      "_________________________________________________________________\n",
      "conv2d_1 (Conv2D)            (100, 1, 28, 28)          5         \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (100, 64, 14, 14)         320       \n",
      "_________________________________________________________________\n",
      "conv2d_3 (Conv2D)            (100, 64, 14, 14)         36928     \n",
      "_________________________________________________________________\n",
      "conv2d_4 (Conv2D)            (100, 64, 14, 14)         36928     \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (100, 12544)              0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (100, 128)                1605760   \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (100, 4)                  516       \n",
      "=================================================================\n",
      "Total params: 1,680,457\n",
      "Trainable params: 1,680,457\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Placeholder of images\n",
    "xs_t = tt.tensor4(name='xs_t')\n",
    "xs_t.tag.test_value = np.zeros((minibatch_size, 1, 28, 28)).astype('float32')\n",
    "# Encoder\n",
    "enc = Encoder(xs_t, dim_hidden, net=cnn_enc)\n",
    "enc.model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probabilistic model involves only two random variables; latent variable $\\mathbf{z}$ and observation $\\mathbf{x}$. We put a Normal prior on $\\mathbf{z}$, decode the variational parameters of $q(\\mathbf{z}|\\mathbf{x})$ and define the likelihood of the observation $\\mathbf{x}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    # Hidden variables\n",
    "    zs = pm.Normal('zs', mu=0, sd=1, shape=(minibatch_size, dim_hidden), dtype='float32', total_size=len(data))\n",
    "\n",
    "    # Decoder and its parameters\n",
    "    dec = Decoder(zs, net=cnn_dec)\n",
    "    \n",
    "    # Observation model\n",
    "    xs_ = pm.Normal('xs_', mu=dec.out, sd=0.1, observed=xs_t, dtype='float32', total_size=len(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the generative model above, we do not know how the decoded variational parameters are passed to $q(\\mathbf{z}|\\mathbf{x})$. To do this, we will set the argument `local_RVs` in the ADVI function of PyMC3. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "local_RVs = OrderedDict({zs: dict(mu=enc.means, rho=enc.rhos)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This argument is an `OrderedDict` whose keys are random variables to which the decoded variational parameters are set (`zs` in this model). Each value of the dictionary contains two Theano expressions representing variational mean (`enc.means`) and rhos (`enc.rhos`). A scaling constant (`len(data) / float(minibatch_size)`) is set automatically (as we specified it in the model saying what's the `total_size`) to compensate for the size of mini-batches of the corresponding log probability terms in the evidence lower bound (ELBO), the objective of the variational inference. \n",
    "\n",
    "The scaling constant for the observed random variables is set in the same way. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also check the architecture of the decoding network, as we did for the encoding network. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         (100, 2)                  0         \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (100, 2)                  6         \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (100, 12544)              37632     \n",
      "_________________________________________________________________\n",
      "reshape_1 (Reshape)          (100, 64, 14, 14)         0         \n",
      "_________________________________________________________________\n",
      "conv2d_transpose_1 (Conv2DTr (100, 64, 14, 14)         36928     \n",
      "_________________________________________________________________\n",
      "conv2d_transpose_2 (Conv2DTr (100, 64, 14, 14)         36928     \n",
      "_________________________________________________________________\n",
      "conv2d_transpose_3 (Conv2DTr (100, 64, 28, 28)         16448     \n",
      "_________________________________________________________________\n",
      "conv2d_5 (Conv2D)            (100, 1, 28, 28)          257       \n",
      "=================================================================\n",
      "Total params: 128,199\n",
      "Trainable params: 128,199\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "dec.model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use ADVI to fit the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 1.9145e+07: 100%|██████████| 15000/15000 [3:02:18<00:00,  1.28it/s]  \n",
      "Finished [100%]: Average Loss = 1.9133e+07\n"
     ]
    }
   ],
   "source": [
    "# In memory Minibatches for better speed\n",
    "xs_t_minibatch = pm.Minibatch(data, minibatch_size)\n",
    "\n",
    "with model:\n",
    "    approx = pm.fit(\n",
    "        15000,\n",
    "        local_rv=local_RVs,\n",
    "        more_obj_params=enc.params + dec.params, \n",
    "        obj_optimizer=pm.rmsprop(learning_rate=0.001),\n",
    "        more_replacements={xs_t:xs_t_minibatch},\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the trace of the negative ELBO obtained during optimization, to verify convergence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IdSaa2Vwzez143M/MZgXb+ndwETDMrFXweEWwPKvKa9wYzF9qZic1cn3tzexF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\nFkbBLSLSwii4RURamP8PLKGOaIsuiGQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x142b34da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(approx.hist);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can plot the distribution of the images in the latent space. To do this, we make a 2-dimensional grid of points and feed them into the decoding network. The mean of $p(\\mathbf{x}|\\mathbf{z})$ is the image corresponding to the samples on the grid. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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27tzJhRdeCMDq1auBvCx9WfB9v7Cttt3+W7p0adaeHTt2AP0H+xV5AUPh1o5X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\ns88mZs3jCPsFfQ8TzZiHhYdp4crcuGHDhiQ3beAeHqvFvMgzkDHKXIS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K5XPsBcDwMlfu\n3bs3zfc+72GDsFLojvkBpgy5mC+oW0W19ZJs7WwUm/I6bLDemzdvllTP8ejMY5PQKbphvub+fmLC\nunXrkt5g2pGbCu/Uruq3XhsIZikQCAQCgUCgDWYMs1RVVUcGxiuL5nEjsDHECvgJ01w9w8ZPjeeK\nV8b+Nff3rDnPMGjV3k41OfKsvrwNvPYq41zxpFrFj/gerzMHpVgtr8VSQunv3DevNo4XwG/w2mOU\nSueJgVLMksfB4DGxl71y5cqms8v6zRjzbDhiGWBB8JD4HG3A+3nuueeaGLVSlg7ywFbk8ki15wyD\nNohsfMfPkeJ99Imni91gL65D140zSsShfOxjH0vVjOkXTqzHC+82Xqj0OeIgYP+wQ7IKYVWletzz\n2yV2k3GELaMbqsdzLhWsCPFD1KmCgWknY7dyESfi8SHUUKN/f/zjH0uqvXrPOs1jeagTxnfJnoUx\nRV76hfPaYGAYb/0yuNjfli1bkq2gL9gsTjZAftgM5kU/5w8QN8PcDrOJTNg4bdy6dWuSqxPb2Uku\n2gIDw8kJsO7o7pOf/KSkmqGDgXnjjTfSbzPXIC9yoTvYQOYLbJCxjB1whianVDgjB0q7Cbm8tPOn\nP/3ppLbA5sJIUgMPBpG4Iu4De8Zzm7bzfM/rMiE3emM+pE4dTHXELAUCgUAgEAhMIWYVs+TR/zAI\n8+bNSytPVuh+NhqesGetuRePB8y92TvlPnyP+/UTw+HeNr+NDDAJXsMELxa4Z9gqZonv8Fv8BvvX\n7M97DZpOLEWnmJ68X5GDK32Jt0EMDt4or/20cGctvM4MngUsDhkZS5cuTTECMEGDAo+ZNsKK4N0i\nK544MQmHDx9OrAIeoWdw4vmhK48TwRPG+4INwdPsNlYuh9eBwcvEDuhbYr84R8qrj7vH7dlhsAJ3\n3nmnJOnGG29MclMdn6uzdL0CmdyLx+NmDNx5551JP/w28qNfdEXfoiNs7ZZbbpFUx02gO2wdHX3v\ne9+TVLNnHn/Si1zEYBE/iTzoiDgRZCN+hKwnPxkBXa1atSrZLcwA3/XMXeJdYF4GkStHnqH161//\nWlLN/GB7xOIQc+SxnegM+LjC7pCR76N76po98sgjib3ybC1Hp7HHvAGjSP/xnGF8wLzwPti1a1fx\nrDueG4DvelbtvffeK6m2SWyeub803trtNviZj8Q/OeOKXWGjnOfJvOnVyP2MV8/0GxsbS59hfBOH\ny/musF39ZtWCGbNYagdfXPgCaP369U1BbSyofMDwvh8t4YsklAiNzmTPQEKpJcqyF3ihN7YqmAR4\nn9/iwYXhIDttOnr0aFMROeTyyZ0JlgmTAeSHmzpK7zMB5wUyfRuJK3IxMXjAJhMTxg6QybfdeFCx\nAOS6Y8eOtE1AcGivgacOnxx4IBO4y4TGVgEy/uEf/mHSI4G59JkfBMlDjkUSumIRweRAf6H/QYqv\ncW8m0I9//OOS6uBhAlCRgUWoJx0wnthWQDfYHQ/yJUuWpANfv/Wtb0mqH+ZelLRfYIs8JBhX2OWG\nDRt0xx13SKpLhWB7LK6Ry4u8sgXAvdAl2wc8DL///e9LqrfCBi2LINULCnTw9a9/XVL90GMrkIUO\ngd/MaR4gnKdxs7DgN7ALgmW3bNkiqX4gYS/timz2Atq0fft2fec735FUb6/cdtttkmobYj7B1ng+\nMNd76RLGGTqlvziOibIp2OEjjzyS9NlvsoH/HZvEPpiXGF833nijpNoxyufK0pErPA+wXdrM/MAc\nyGsWNMjf6VnWzTjkHvQdcrIYQi5sEFlwnFng+aIT2bgf/fXqq6+mRS3b7Fx5bngJmn4R23CBQCAQ\nCAQCbTArmCVQChqdN29eolI99R3KFg+RK56/FxH0gmTuaeJ14GH1exCrVD5CgfdZddMmvD1kgP3C\n68uLUtJHsBR4X3gqsBZ4VwTkkW7Zabuq0yo9T62HvUMeKFhYF7x0qGmCStGNp5XmaaO5jGyvQM/j\nfXzve9/Tz372M0k1AzKolwG8QCBeG/DAxI0bN+qzn/3spPaxhYccHnDKd/kttgT+6Z/+SVLtcXtx\nvl5Af+CF4YX+8Ic/lCR9/vOfn9Q2vHjYCpg1ZHFdw27gOfJ79913n77xjW+k/0v9H97cSTaCSb/7\n3e9Kqr3gj3/84ymI2LfAYQSxOS/z4R4v7ATBpTAuzth2w7x0y1LQX8xNsN/YCfbGFgi6ga1Ahpxp\nYr7DntkKY34g8Bgb9oD4QWUDx44dS8wHfQpzwBzNlbkeW2NOZ/5xppK2w5LBtMDI5AeVD5p2XgLP\nD3TGvAtjx7Ycc9tpp52WmDNPugAw1twDXWH/yIUtdsu89DIeYb3QHfMvLCjMEs82dOZJCuwaoENk\ngJHbunVrmnucUfPwjUERzFIgEAgEAoFAG1TD8t4GakRVNUZGRjquAFlR4/XlJdRZocIEwTrAPuE9\neUor3gb3gpXA66J/WKUTF0Ago6eB5+C3O5UOwDPwImkwR6TMwgbxOWTiioc5f/78JJcHVQNW/Hi+\n3/72tyXVjBksTgnt0kilyWnIBOPBlFAUjZgDXuPV01Z+w48nQCewNvwd+Sm4SfzQXXfd1ZReX0I/\nwdE5crZTqu3q9ttvlzQRRwLbQr/4kRLYHp4RgZnY3I9+9CNJNZNQSpHuRzbiOWgLNvelL31JUvMx\nBrTd4x2Qgft5MDF2981vfjMxILAzvfZ9t4VEPd2fWL9NmzalWCqYMk/sQE68dlKdkRsmDnbMjyzq\n9ViYbuRyePwlzAOMC3FjxIfAMPk427dvX5ofkAt5SgdrT8dzxHcUYI6QA3nZZWDu82Kc2BnPAtic\nUszOVOqs9H3murwEizTxrOD/jC1nGJkPuJaKc/Z7VNEguvbY4FwuSU0FjL1ILjLBCh45cqRoi6Ud\nmxZ4uNFoXN6p7cEsBQKBQCAQCLTBjGGWuikd4B44nsNJJ52UvCViKmCayP5iz9dT/1m58pq4D7x2\n9ljJ2MG77yb2oNNK3D1BvFgYEzxCYnuQjfeJ7WFVjse8YMGC5GXgNeHRIw8ZBOyVw8aUPMdS27vZ\nD3aPnvbC4hFLAaOGfHj3fD5PF5Vqjwkvg/gKZMuPzWBfvhOG4T3l9/Hin5s2bUrsBZlUyOt77mSQ\nkNVBQUPeHzS1vl27uWKT6IqDpCmahw3yOTxi+pvjPGg7cScwta+99trAhUJ7hbN/c+bMaYrxYwzy\nGWyNq8fR8RrbPBHzaqkQLcAWvTBtq4OpidHxTLmZAJcLeVwuH8udjlGaicBWXTapudxHv7oa1pzX\nC1xnyOnwTMbSYdBS+UDydt85jmCWAoFAIBAIBAbFjGGWOvxdUnPMSn5cCHugXtgRxokYC/7Ofjce\nMR4jBa3whNm7JzbJi2YNAt+DL9WToq20He/Xiz3SB3Pnzm1ilmAn2K/ntRc4mwp7KGUxuoeP14Tc\n6JB9e/RPW/EU0Q2yINuw6vQMglbxMp5xxdWPr/FCj71mHA2j3T72/FgGZwGxVewOFoy254dfS8MZ\nR72i1RFAbptek4fXzqg6WzFD5tOWr93T9uOjwPj4eDfe+IxBSV7HbJLJ0en4KWl2ygW6kU/qTsY+\nmLJglgKBQCAQCAQGxaxglrr4fvq/szS+J+qZAH7kCJ4iMRcncs++tDdf+lz+ed8TRg5nkGaC/h0l\nuUsxGehyJsZXtEKn2BLXzUyXpxUGiB8IBAKB6UQwS4FAIBAIBAKDYlZV8C4h91KdXSh57bMB3tYT\nEd9xIvB+l/v3gV05EXV4AoFAYKoQzFIgEAgEAoFAG8wYZqmbOksljIyMNDFJM8GzHVY11/DKA7+P\neD/b//tVtpBr9uH9LNswEcxSIBAIBAKBQBvMGGZpkFVtXndmJjBKw/rtWOm//1BVVVOtnveDnku1\nfFy2bjI8T0S/lDITQbdxZl6vyc+pms54tVLW5SDZlq6vE5G52apOVv7b/dqP6yy/TpctdsoEHh8f\n77nOmtcK6+HMtKHB5fLK5GRp9yPbdFVkD2YpEAgEAoFAoA1mDLMUCPw+oNFovO+y+6TumQWPLWzH\nCk8nSr/dbWVhv89MqPnlv403jxcPeolZmQnnqbkNuVz9xuDMhHHpssEKDdI21/eJgMvlbGCv4wxM\np2zBLAUCgUAgEAi0QTBLgcAUwj3EJUuWpPc4u45q8VN5Pt9Uwz1GGAg/W44z5E477TRJE+cZ7t69\nW5L05ptvSqrPlZsudqaqqkn6kZor/nPmHef1cQ4hOqStnWKepgO0gXP81q5dK6k+Y9HP5UNnnEl4\n4MCBGXGuogO5OAPTz/t03QDkQm7G20yUDZ1x/ieyMTccOnQo/R8dITdyzST4+OccUGzR50JO0MA2\neX8msGPBLAUCgUAgEAi0QTBLgRMGjzlwlLJaZpJH6HCZli5dKqn2FNetW5c8YzzdnTt3Sqo9xL17\n9066FyidgTcdcSQlxqT0PmwFjA0swB/90R9Jkm677TZJE97w888/L0l66KGHJEkPP/ywpJppwrsc\nNnLWDz2deeaZkqTVq1dLqj3i3/3ud5Jq1osrOsQjxgPmNZiOjJ2FCxdOum7atEmSdOGFF0qq7QZ7\ncwbmrbfekiTt2LEjsX0nIovPAQuBjpDrrLPOklTrEZ0gH7rgfdqObkpZYdNZdwjZYJBOPfVUSbX9\nOeu3e/duHThwQJLSFXmcDXQ5pvM0C+SCqUV3wBlo5HN4NmCrNk+XvoJZCgQCgUAgEGiDWcUseY0P\nXs+ZMyd5gO5dAVafeFOsxj1exDMqgHtWw/QQffUMK8GVfV72s1mtA7z3fL8XL4MVu3tTvhrH63SP\nGAxSXR05iPtAN3gbK1eulFTHs/B3dIoHhe727dsnqWZgPPbHGZhDhw4V4xQG9UbQHW1Xk6RFAAAg\nAElEQVSFNYJJOvvssyXVjMXpp59ezN554403JEmvv/76JDm57tq1S1LdDx6DMQyZSvWGSt5pyXvF\nJomXufXWWyVJX/rSlyTVun/hhRf0zDPPTJLHx9awPUefR+bOnZuYL/TFaz775JNPSqrHHjrxrB7g\nr0v1iUqve5GD/mHc0Ofr1q2b9NrZLxiX1157bdLf83ufqOy3XDaXi+v69eslNcvFeNixY4ekeh5l\njPK6JNtUMhSuM+Z0mCV0dsopp0iq52/mulZtQw6P+5nO0yxajSmpHi/M8TBOAMaWtjMHIDfzCJ9r\nJ9tUM0zBLAUCgUAgEAi0waxglnwVzmtWrevWrUsr8tNPP12StGHDBkn1ipbVpmcQ4FVt375dUr3f\njefICpfXeVZCft9+VrOeaYPHAzuxYsUKSbWXe95550mqM4n4O55XXpPjnXfemSQX8R9vv/32JHn2\n7NkzqT9czn49SzyN+fPnp/YtW7ZMUu0RoqtzzjlHknTuuedKqlkZl4s2oiNkgZF59dVXJSnFW/C5\nnTt3JjlK8Qr9ykfbXHfYHTo6+eSTJU3YKn2LXvG20Cty4fnDNCEnNkt/TIVH1W2cQ6nmDTJdf/31\nkqS/+qu/klSzAniQ27Zt0xNPPCFJiWHCdkss57CA7pYvX96kJ+YP+h7Plj5nHnG5S23mt3y+6CcD\nslTBGpuDlTjjjDMk1XEwMJLMXc5g5m0qVX3uVI9q0Lgfl23OnDnJZmBnkQs50Q3jHtuCjQHIwHPE\ndwm8llFu+8OSK98NkWomCZmYA3gfmWCVDxw4kPQF0BVsLf3hMVq8djZ0ENlcLtpC+5njGF8waNig\nP4/RAbspnk3H5+i/I0eONOmN16VdlH4RzFIgEAgEAoFAG8wKZolVJatSPAM8jc2bN6cMCd6DncDT\n5zt4V6xQX375ZUkTsRNSMwODd/Liiy9Kqr2WYdR/YBXubcS7gGk5//zzJUkXXXSRpOb6IjBsuYeE\nnMjx1FNPSZKee+65Se+TiQTol0HrWuRxArAMeBvEhSDXBRdcMOnv9Af3oF+wAzwlsneQweMsiHXi\ne8NApzPE3FPCXvAQq6pKnh8MCkwbHhHt5jvEXpRYv07s5iAeY+m1e6noCg/yox/9qCTpL//yLyXV\n7CEe5aOPPipJ+uY3v6mnn35aUs2kdVsHZ1CPkfG3ePFibdy4UVIdW4Vny/wAA1tqo8eilM5jc521\nsqNOcpUYAc88JFuM8ecMJfbFXJGzXH52VycmdlhxMf69uXPnJoYZ22K80DbmMtgXbMzjUdsxR920\npfReN3BduUzojLkPGbA7vj9nzpym89Sc3eZ1KYu0NF/0I5vbP7sHzOUwtOyeID+68XpLOWMk1f3B\nnOj1l/I2T3X2dDBLgUAgEAgEAm0wq5glVpl4qZdccokk6YorrkiMEh4hK09W5h4bwOrbK6byOb4H\nWAHDCrQ6Lb1XeNYbtTWQ5QMf+ICkuk4Ke/cAT4rYnLxWBfLhNRLPgEdTOvV52PVURkZGkv48GwXg\n4dJ+2kLbaTNMGjqGtfEMR3QEE3Pw4MEpq0nksSf8Nv2PF597wb6X/tJLL02Si34gBgvPOa+wLHXP\nwAwST1eCZ2qSyUiM0le+8hVJNUtK/zzyyCOSpK997WuSJmorOZvZbXv7jRvx+LK1a9fqsssuk1TH\njsB2eb0hr3Hl90Tv9Asy4Vl75mKrqsu9yuWZR8TyXHzxxZLqcQBLBsMEY4nNItvo6GhTRXKvaN7u\njL9+ZChh4cKFia1gfiR2k3EB6+/jxeXyuc7jbbztvJ8zUsOSi7mMccMV1h3W3GtH7dy5s6m2F/p3\ntsUzdUv9MIw5359hMGUwSzBoyMHzFfvHRr12FOMG+/JYupGRkab2M590irPrFcEsBQKBQCAQCLTB\njGaW3GPyKqdc586dm+I/WJlu27ZNUs2+sBrnnqx0PYsFb8T3Tj1WYZBzvDyegTaRzYAnhdz8BvFU\n7kGxSsezWLBgQeorGDGvo+QZI63iFgZBzrjwm+iGvkQer6/jsQd+rhi64zf4vldXRpdHjhyZ8rOF\nSjE+eHF5HBZ97TZGG9EJcjg7Sr8MkyXrVFfJbZXX2Oott9wiSfqLv/gLSfXYpO0///nPJUl/+7d/\nK0naunVrkuVEnfaO13rWWWfpYx/7mKRaPs+KLZ2zButJfCHzELrDlhmb2CS6K8XTdAOPf8GbJwaQ\nNhKvSBYljBK/iWzY48qVK1P7mIM8DgbGDXlcrkHPX2PcLFmyJPU5ctEmbIiMX/reK5P7c8R/w1ln\n2k7/HD58uKmW0aBxcowb5jRkYweAGFrsEJ3t37+/aS7jnlyxC49tdFbU55FBZINJ9bgydkXoa+Th\nWcD48OdrqfYg7/N7+Xve/lJl837RcbFUVdV/kvRvJO1oNBoXHX/v/5L0P0t65/jH/l2j0fjh8b/9\nH5K+IOmYpL9qNBp3DdRCNR/C5wUnt2/fnhYOUMwEMvPg8SA4DzpmoYKyvDiWH5w5SMeXUlZ98GLs\nr7zyiqR6cfTss89Kqrd4MIo8YJwJBuP1opwuH3IN6wGcPwygRXk40QYmWOTkwYSctKlVAHsuEw9k\nrsjG746NjQ1NLl8E+SIDG8VmsS8CiI8ePTppuyP/jgcvMqHweioPlexUdJK2okN0snnzZkn1Iomg\nffr+O9/5jiTp61//uqT6gZaX3pjOYxikyQ9iaWIbn4eUO1fME8jPtiLfZVHINh5yYcM4bWyrcH9s\n1YvG9hOEz9bHBz/4QUl1mAL24luKvk3BYikveouzdfXVV0/6DcDC6/7775c0+WGeyz+oLk866aRk\nU8hF+5GLB7AXOCwF22PD6BIgPzrBVvfu3ZueC+hv0EBvnjcE4bPYZuFH0gp2k29b5cHeUj0f8JoF\nGP2E7QI+X5pf+gFzF3J5WRi2Snk+Yx9+1BM26YsjDyDPg9uRzx19f2YPim624f6zpNtbvP//NhqN\nzcf/sVD6gKQ7JV14/Dt/U1VV64O/AoFAIBAIBGYBOjJLjUbjl1VVndHl/T4l6duNRuOIpJeqqtom\n6UpJv+6ncaxWWdWz+uTKanv+/PlphYrHgxcFs+TBboB78T5eBb+dsxN5W4bBVPgK2CltvDWYB7at\n8mA/qV5Rs9UzOjraVIAOeGo78gxTrly2o0ePpnvTFrxPvHP3bLxgGx6gl8pH/+jYKd5h0a+t5HI2\n0JkmPCzoaIJuV6xYkfoeoG/6hd/AyywFQE/HAZI+bvBab7jhBknSnXfeKakua4EsP/zhDyVJf//3\nfy+p1g39lic3OGM4bJbTgSzY1ebNmxOrgE3BIPBZPH/0SRKGHymCDDBV2IEzSxTihE2l33oBuiGI\nFpaCNrJNRWC3Hw+E3fjxQxdeeKFuvvlmSXUwNWBs8Vts/cEcsOVXsulukc8BXqjxl7/8paSacacP\nffvMdyQYg7BlyObHodBm7v/WW28l+TzJwtFpTHp5B5hJ7GXLli2SagaG7al8DvBg+3z7VKqTFLBp\nD1vg89gkcnpZnV5kg63D9pyBJXSE3RB+248x8fm09NzmvmvWrElsE/brhaaRy7dne8UgAd5frqrq\n8aqq/lNVVSuOv3eKpNeyz7x+/L0mVFX151VVPVRV1UMDtCEQCAQCgUBgStFvgPfXJP3fkhrHr/+P\npP9JUqt845ZL7Eaj8XVJX5ekqqpafgbP0gPR8P7YU16zZk1a2XJlz91jAfygU0/x9QNo/RDXUiBm\nP16+l2X3sv1eKoDPsYL2OIJ8te2FLvEWPMjambRhsRStioV5rA06Qg4/toE0Whglvg9LgbfH69KR\nJnlczLAC10vBoc6KEeBI0dSNGzc2sZXYMyUEsEE/1gBmEQ96KpklP74AXV177bWS6gNxiUlA/nvv\nvVeS9Hd/93eSag/S42K4jo6Opv7wkg9eSmJQ0F+MDdiilStXpt8mVoRYI+SmP2An8Jy5J3J6mjbM\nAbbswfrOEveiS9pEG2F7mAPx5ulPH+Me+Aw7ePXVVye98h3mC7x1YlKuueYaSXWZE7x8GLTf/va3\nkno/ugbZli5dmpgS2gvr4kdkeFkY5g1KKBDED7ME/GBhdEsM2J49e3TfffdNkosAbLfNToVhmR+Y\nw4llBDAvHp+Yzy/OGNE/+WHdUn10jx8Pho6wecYsNkj/dlMOAj35gcDYPTpi7uI56kktHhvJ/Wgr\nz2ueDfzO+vXrk7yw3uiRMiXs0AycdNDPlxqNxtuNRuNYo9EYl/QfNbHVJk0wSXnU3KmS3uyrZYFA\nIBAIBAIzAH0xS1VVbWg0GtuPv/y0pCeP//+/Sfr7qqr+g6STJZ0r6cFBG+keOHvvObPCSpYVqaf8\n432wUvXCgJ6lgwflh0yWMIh3716EM05+zItncfB3Vt8jIyPpXuy/47Egl2dklQ5X7Bd5sTr3UGDz\nkIdsFzwEL2yGLNgBOuFzeGleGJLXBw8eHHqBMpfJS1B4phF/3759e7JJjyHAa8JGueJBAmJQ3KMe\nhmx+D1gYGLLPfe5zkmoWgz7+9a8nwhJ/8IMfSKrHEUwMumKcItPY2FjSJ7EGni4NazNoVgu2jid+\n6aWXprbB5voxC64bbI1xBRsIy4nOsGXGJF4//UG8jKf150UqOzGHMC38BlfuQT8yX/p9YKBo21VX\nXSVpIo2d7xL3RP/ATMNa8V3ipq677jpJNZPAvOOH2oJOsT2LFi1KfQ4rwVztJUcAYw6b/ZM/+RNJ\n0uWXXy6p1iF2B0uELvg788+6detSsVXkwiad/e1WLlgedAYDg83TX84sjY6OpvkexuxDH/qQpIms\nTqkea7BgZIZ75jM7Fx/5yEck1f36L//yL5Ka483a2aPHNMLqecFQL6Xhz2HGG3F0xEDBdKLTvOwK\nY46+5bPYJPMtsW7YUa/zZTelA74l6SZJq6uqel3S/ynppqqqNmtii+1lSX9x/Mefqqrqv0p6WtJR\nSf+20WicmCIqgUAgEAgEAkNAN9lwn2vx9jfafP7fS/r3gzTKweraPaY844iVKN4i3gUrXJgT9/xZ\nyT/55AQ5BnvlR0oMO6YnbwP3xktBPn4bOYl7wCPEg/DDCOfNm9eU9YbnivfAynyqMo7aHXDoe+h4\n7XhZeCke34EO0TXeOV48Xgj9k2fFDavWBigd98AVr4wYGGTZvXt30349TBteOnLh2cKE8Ft4nW6b\nwwReGn366U9/WlLNAtKfMErUU8K+8OpoO/FBvA9z895776X201ePP/64pHqswmq4l90r+E1k4Do+\nPp48YDKDvM4SYw2vFHaPrDY8Z3TJa+ovcTQTts38xOf9CCCp+7mGNjKesHtszj1pfhP7oh94/6WX\nXtJvfvMbSdJPfvITSbWNedwLOqJviZNhTHLP0rEoJfC5+fPnp9/0OFIf0/QtNguTxGu+98wzz0iS\n7rnnHknNTBXzB0zbggULklzMwcxBJXbL4Vm0XjOwlB3msTzLly9P8wTPOuYL2vDggxObObBgftD4\nlVdORM2gM+yAuDMYGPqrHXNd+pvPg36MiR/A7UUtvf4UNkqbeVa+8cYbaX5w1gnmDDt47LHHJPUf\nuxTHnQQCgUAgEAi0wYw+7gQ48+IR80uXLm0qI8+V1aVX/ebzZCmx/4sX4rV/8NKGyTD5qpxVt1fZ\nRm7iHWBi8CjxhPBCFixYkFbgHv8D0+T1XZDTq2MPQ073KpEPBg1Wj6qufM6zvwDeBx4VRwWQ5YKH\nyfcPHDjQlLUybEbNPSW8YLKqYPbeeuutpjom2DHxL3i6eER4s8Sb0V8lxmUQnXmGFceYfPjDH5ZU\njxuqJ//iF7+QVNsq8QLohvg67JBxmGf08TcYBOSC3fC29ao7vFZnHIiv2Lt3b+pbbJDYCq/qTAwO\n3rrHGiEfbcyPZUBeqTkusRVKY9CPnvHswVINID+QHG+dORC7fOihhxI7gS3STq91R7wPDEDplIWS\nDP6+19XZs2dPYlL9SBXGGvMfv40NMl8yr8ICwpY50+CsH/PrKaeckrLWfK7tVS76xWNKS/FB/B7j\nbsOGDU1xgNybauqwvegO+ZDLs0IZF/Sfx6+2k82z+3iNDeaVtnO4LfqRPciIXXEfWGeY4F27djUx\njzwHYKe8Cv+0ZsMFAoFAIBAI/L5gVjBLAEbCMyvmzZvXdE4Oq248QTxl3zOmHg6xFB//+Mcl1Stb\nMgPY32Zv2dmOQeCxS6zK8QyIo2D1joflLFfuIdEf9AOeEZV5YWf80NphHaQLRkZGmjLFyE7AK/c2\n4LX62XfIizeCB/nZz35WUs2CUB8FtvDFF18sVqXtF6UDHuk/YuH8YOZjx44lO/a4BJgwWEyYD5gl\nbBTvy+vNDEOe/HBZqe5T2EzkwnuFiSGmA0YJjxCb9dg5sGLFiqaDpL1CsceDdQvuw9injhBtA6+8\n8kry7NGX11fzuBZnhug3GG28dWJ38Jz97DiPC+kFniUKI+dVxvG8veacn9WI/W3fvj3dy2OpvC6O\nx+KUMqd6lY/f2bNnT7JzbIsrzJDXV4JBgS1HLmo+wYYBn1+cDRwbG2uqE9Uv8+6Z3bSN2D7mLM7/\nBPm5fbSP5yCsKMySnz/o/eN240wd115kw66xG+Z45mJi99ClZ705I8k44j7ojvszfo4ePdpUKxE9\n+uHx/ciVI5ilQCAQCAQCgTaYVcySn6XGSvnVV19NK31WkXjA7vGzv4+HiLfOCpiaFVSmJebCzx1z\nL20YTIxXD0cG9lzxwJHJz0TL6/ew2iZmC0bpE5/4xCT5br994oxksncG8XRzoI+RkZGmKtfoj31n\nwG97PRBnFPCYuKILsiGIYSLO5qc//Wnqy0Hhla3d8/asS2RChjz7i/f8O8iFXp31wZbdyx8E3ANb\nYzzAatFGPGHGEZ4gTBRsBp8nDgtGCRuF0V23bl1TlXkYRc8M6pVZcl1hh4x97G/79u3J48U2/RxC\ndMG9vBaPn7qeyyfVuqI/YIu9JliOTuwF44O4OBgFWD5+m5gkdEd/MkcwNpDx8OHDSSfAz5/k3vwW\nmazIg75LlbtLsnn85ttvv51sje9gY7AwsP2uA5h25knPBEaXzKueZQxDt3Tp0iZGsJRd20ln2Bf6\nZzzALDHeyJ6ESUG2VatWJdvkb37uotfOQ8/IxTOB+zDusJ/SGWqtZOP/zFmwdp79ydyMXfhzhnmE\ntvE92oRs6AjZFi1alHaBmIPQP/2DfZdi+bpFMEuBQCAQCAQCbTCrmCWAh4nncPjw4bRC9wwRvEhW\nl3wOD4gVLfu91KD44he/KKmOi+F0dfaHvcLqMMFq288IwxOm7XhKrKBzT9w9YFboxFDcdNNNkmp5\nv/e970lq9tJ6hdcFmTdvXlO2Cl5jfpJ2Lm+rs91yODMDEwE7hhdDrArecKt7dQvuQfxHJ2apxIIc\nOXKkWP3bPV5+q3Ty9jAYJcBv8JueRer7/16/jBgDdEq2GJ4m34eJIW5o/fr16Z75Ke9SzTD2q7PS\nOKJGEjI2Go2mE9uZNwDth20gnoxYQD8TEHaT/iQGxU+Vb1dNuCS3sy/MA9yTLDdYijvuuENSncHI\neEEm2JK8CrPH1aFnZ6v4LeYZfoM+Ls2P3cr27rvvpnvxm7D9n/rUpyTV2aHM8cjBHA1Lho7RoddI\nIo6TOZ+6Q0uXLk3sHX3cq1zOqnMfaj7B0HH94z/+Y0l1P+aMFnORn0PIvXnGef0t+o+xx9jmN5g/\nS2xgK9n4bfqS2CLswLPSP/OZz0iqmSjk8hpXjFlkdBaMZ0mj0UixiIxd5g3mE+Tr9XxCRzBLgUAg\nEAgEAm0wq5gl96TzE+Dzs3OkehXJKpPVNgyL/x1WBrYKj/HP/uzPJNXn7uCtcY5QO2ap24wJz6gC\npRoteMh4TsiWVyb1uhbsa+M90CbkweP3NpTQbZ2UJUuWJA/GqxbT/lKGUanyN/3F/ciOwWMEXjtq\nEHjcEDEaeG1eqRjZ/Ny/hQsXpveQCzm4J7EYsH78Bt4oXpmfqzQMuP4ZJ8gNo0LcCN4sbWAcAewL\nr55xhRd/5MiRxD796le/klSzUYzNTrFKJVt0bx5Pk3o7xGWdeeaZiQnymj7YprMT9BNjMc9Wkmqb\nQ5ZHH31UUn1OF2wQnnKrOaLT/MH7zGnUD6Jv6XviMGk7dgSD52cUzpkzp4mVhTnifeJDsFnYqocf\nflhSzSyWsoZ7kY2K0vQtzDFMCfMLuoNhQv+0EXgNKMYussGWwYq8+eabab5Hf6UM1E5y+ckR7GgA\nWBJko99hg15//fU0fzAWmdth/XgeMHa5x+bNmye9Rv/IBMtVOu+unWwek0f9Ne7FHA1bR9thg2B/\nsBd0TT8xvrCzPB7L9cU4Jz6K14NmDQezFAgEAoFAINAGM4ZZqqqq69gEPKA8O4xVpXsNXrcB76MU\nD+MZSXi33AdPy5mbflA6aZlVtZ9LRVs9O85jXkZGRpoqxrJnjFfhzJqzHf2CfqGNK1asSO3Hw0Nu\nfps4MK4wAc7awW5wb2ILbrvtNkl1LAOsAF79nj17Bq687iwOTBxsFl4p9yfzgitezdq1a5Mc6ADb\nxOu69tprJdUME146Xrt7jsPIxEQ+7onXidfqzBB25PESzix6/SGYGsbX008/nSp1UzcH1mVQ+bz+\nGPYFs4Q9nnnmmSkrFjYGO2a+QE7kcwaR17QdzxoWBw+ZK/bQbtx1YgydOSN2h/Fx/fXXS6rtCJsl\nbhFGCu8/z7JFX7AuXruIz6I72AkYNPqhxLx3iu3LZSP+he9wb2r3oDvkcubdTzPgtbOm/CbzL7XE\ntm3blipHk1E4DLmkeoeCtsLMkMkL08Rct3r16jR2sF/0ihzEsOYZyVI9Vz3wwAOSmplWdh36kY33\nmNO5J/3Fa86zQy7aBBuK7WJ3jF3eZz7NmU76gb5knPPbjLlBdxiCWQoEAoFAIBBogxnDLHWDUo2b\n5cuXp1U1Hj6rTT7jZ6KxQs3vIdXeCVdWsGRDsLfazSn2nfavvQ4Gv4UHRP0IPAevvIpM3Cc/bwvP\nEE/5ox/9qKT63Bw++9BDD02Sb9CMAT+36qSTTkrtJ9ODtrHSx8PBu4A5QV6PKWD/noy+G264QVLt\nfeBh3H333ZImPNFBvQpnFj3eCBnZi8dGvdbL6Ohokh8Plu+yf48t4kH/9Kc/lSRt3bpVUt0/eKfD\nOK/QmRJYLOJDYCYZZ7TZ4+oANgnLh9cK80Bm55NPPpnGlGd1DlpN3jOr6CdsnfsfOnQojWfYPXSD\n3rFnzxLjCgPHeKL/iLFg3mHMdqollre/E5CD3+K0AZgj7Oi6666TVNsmXj0yo8tjx441xWRxDxhH\n2B70SbZfN7FYJXlLn6NvOa+O12RSUWXeMy5hY5CLvkZ+2oqM2CgMJ/FE27ZtS781TLmkerxhD54l\nhg6RZe3atTr11FMl1c8Lrsx/XnMQuWCoYZYYdzAvtKFTm9vBa5nRX16xHAaN2De+x2tsk+8z7zCf\n8vrFF19sqtBO3yHXsE7bCGYpEAgEAoFAoA1mFbPkTE3ONOGNw17gXbDahpXAQ4ZZYoVKLAb7+7AW\nrM7JyOi0r9sLSidM01YYCBgmXhObwxWmAaxcuTJ5H+wNez0UPODvfve7kmpvrVt0qsBL/4yPjyf2\nzjOpaAvVXvGy8N7xCGCcYF7QFdkfeP14gn/zN38jqY6nKFWk7QVeZwjPCW8VJoL4CWJ8/PytxYsX\nN3mCyEmf3XvvvZKkf/3Xf5VUe7owcJ49OMyYJTw52Jdvfetbk9pIZhU6wVYZi352E94sMR9k3BBX\n8O677zadS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JLGK16/fn2Sz+MzgGeHTRWqqkp9i6cHO0G9ILwGdEcsgrM0eC8ea+BeL95u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\n/kP2p/8m6b+X9NXj1+9l73+5qqpvayKwe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uxZcOebe2IQYLfO7tuzj8Og3HrrrZKq82xk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x13f264a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn = 10\n",
    "zs = np.array([(z1, z2) \n",
    "               for z1 in np.linspace(-2, 2, nn) \n",
    "               for z2 in np.linspace(-2, 2, nn)]).astype('float32')\n",
    "xs = dec.decode(zs)[:, 0, :, :]\n",
    "xs = np.bmat([[xs[i + j * nn] for i in range(nn)] for j in range(nn)])\n",
    "matplotlib.rc('axes', **{'grid': False})\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.imshow(xs, interpolation='none', cmap='gray')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0b4"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 6,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
