Week-7-CADL-Lecture2.ipynb

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    "# Session 2: Training a network w/ Tensorflow\n",
    "<p class='lead'>\n",
    "Creative Applications of Deep Learning with Google's Tensorflow<br />\n",
    "Parag K. Mital<br />\n",
    "Kadenze, Inc.<br />\n",
    "</p>\n",
    "\n",
    "<a name=\"learning-goals\"></a>\n",
    "# Learning Goals\n",
    "\n",
    "* The basic components of a neural network\n",
    "* How to use gradient descent to optimize parameters of a neural network\n",
    "* How to create a neural network for performing regression\n",
    "\n",
    "<!-- MarkdownTOC autolink=true autoanchor=true bracket=round -->\n",
    "\n",
    "- [Introduction](#introduction)\n",
    "- [Gradient Descent](#gradient-descent)\n",
    "    - [Defining Cost](#defining-cost)\n",
    "    - [Minimizing Error](#minimizing-error)\n",
    "    - [Backpropagation](#backpropagation)\n",
    "    - [Extra details for notebook only](#extra-details-for-notebook-only)\n",
    "    - [Local Minima/Optima](#local-minimaoptima)\n",
    "    - [Learning Rate](#learning-rate)\n",
    "- [Creating a Neural Network](#creating-a-neural-network)\n",
    "    - [Defining Cost](#defining-cost-1)\n",
    "    - [Training Parameters](#training-parameters)\n",
    "    - [Training vs. Testing](#training-vs-testing)\n",
    "    - [Stochastic and Mini Batch Gradient Descent](#stochastic-and-mini-batch-gradient-descent)\n",
    "    - [Input's Representation](#inputs-representation)\n",
    "    - [Over vs. Underfitting](#over-vs-underfitting)\n",
    "    - [Introducing Nonlinearities / Activation Function](#introducing-nonlinearities--activation-function)\n",
    "    - [Going Deeper](#going-deeper)\n",
    "- [Image Inpainting](#image-inpainting)\n",
    "    - [Description](#description)\n",
    "    - [Building the Network](#building-the-network)\n",
    "    - [Training](#training)\n",
    "- [Homework:](#homework)\n",
    "- [Reading:](#reading)\n",
    "\n",
    "<!-- /MarkdownTOC -->\n",
    "\n",
    "<a name=\"introduction\"></a>\n",
    "# Introduction\n",
    "\n",
    "In this session we're going to take everything we've learned about Graphs, Sessions, Operations, and Tensors and use them all to form a neural network.  We're going to learn how we can use data and something called gradient descent to teach the network what the values of the parameters of this network should be.\n",
    "\n",
    "In the last session, we saw how to normalize a dataset, using the dataset's mean and standard deviation.  While this seemed to reveal some interesting representations of our dataset, it left us with a lot more to explain.  In the case of faces, it really seemed to explain more about the background than the actual faces.  For instance, it wasn't able to describe the differences between different races, gender, expressions, hair style, hair color, or the other many various differences that one might be interested in.\n",
    "\n",
    "What we're really interested in is letting the computer figure out what representations it needs in order to better describe the data and some objective that we've defined.  That is the fundamental idea behind machine learning: letting the machine learn from the data.  In this session, we're going to start to see how to do that.\n",
    "\n",
    "Before we get into the details, I'm going to go over some background on gradient descent and the different components of a neural network.  If you're comfortable with all of this, please feel free to skip ahead.\n",
    "\n",
    "<a name=\"gradient-descent\"></a>\n",
    "# Gradient Descent\n",
    "\n",
    "Whenever we create a neural network, we have to define a set of operations.  These operations try to take us from some input to some output.  For instance, the input might be an image, or frame of a video, or text file, or sound file.  The operations of the network are meant to transform this input data into something meaningful that we want the network to learn about.\n",
    "\n",
    "Initially, all of the parameters of the network are random.  So whatever is being output will also be random.  But let's say we need it to output something specific about the image.  To teach it to do that, we're going to use something called \"Gradient Descent\".  Simply, Gradient descent is a way of optimizing a set of parameters.\n",
    "\n",
    "Let's say we have a few images, and know that given a certain image, when I feed it through a network, its parameters should help the final output of the network be able to spit out the word \"orange\", or \"apple\", or some appropriate *label* given the image of that object.  The parameters should somehow accentuate the \"orangeness\" of my image.  It probably will be able to transform an image in away that it ends up having high intensities for images that have the color orange in them, and probably prefer images that have that color in a fairly round arrangement.\n",
    "\n",
    "Rather than hand crafting all of the possible ways an orange might be manifested, we're going to learn the best way to optimize its objective: separating oranges and apples.  How can we teach a network to learn something like this?\n",
    "\n",
    "<a name=\"defining-cost\"></a>\n",
    "## Defining Cost\n",
    "\n",
    "Well we need to define what \"best\" means.  In order to do so, we need a measure of the \"error\".  Let's continue with the two options we've been using: orange, or apple.  I can represent these as 0 and 1 instead.\n",
    "\n",
    "I'm going to get a few images of oranges, and apples, and one by one, feed them into a network that I've randomly initialized.  I'll then filter the image, by just multiplying every value by some random set of values.  And then I'll just add up all the numbers, and then squash the result in a way that means I'll only ever get 0 or 1.  So I put in an image, and I get out a 0 or 1.  Except, the parameters of my network are totally random, and so my network will only ever spit out random 0s or 1s.  How can I get this random network to know when to spit out a 0 for images of oranges, and a 1 for images of apples?\n",
    "\n",
    "We do that by saying, if the network predicts a 0 for an orange, then the error is 0.  If the network predicts a 1 for an orange, then the error is 1.  And vice-versa for apples.  If it spits out a 1 for an apple, then the error is 0.  If it spits out a 0 for an apple, then the error is 1.  What we've just done is create a function which describes error in terms of our parameters:\n",
    "\n",
    "Let's write this another way:\n",
    "\n",
    "\\begin{align}\n",
    "\\text{error} = \\text{network}(\\text{image}) - \\text{true_label}\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align}\n",
    "\\text{network}(\\text{image}) = \\text{predicted_label}\n",
    "\\end{align}\n",
    "\n",
    "More commonly, we'll see these components represented by the following letters:\n",
    "\n",
    "\\begin{align}\n",
    "E = f(X) - y\n",
    "\\end{align}\n",
    "\n",
    "Don't worry about trying to remember this equation.  Just see how it is similar to what we've done with the oranges and apples.  `X` is generally the input to the network, which is fed to some network, or a function $f$, which we know should output some label `y`.  Whatever difference there is between what it should output, y, and what it actually outputs, $f(x)$ is what is different, or error, $E$.\n",
    "\n",
    "\n",
    "<a name=\"minimizing-error\"></a>\n",
    "## Minimizing Error\n",
    "\n",
    "Instead of feeding one image at a time, we're going to feed in many.  Let's say 100.  This way, we can see what our network is doing on average.  If our error at the current network parameters is e.g. 50/100, we're correctly guessing about 50 of the 100 images.\n",
    "\n",
    "Now for the crucial part.  If we move our network's parameters a tiny bit and see what happens to our error, we can actually use that knowledge to find smaller errors.  Let's say the error went up after we moved our network parameters.  Well then we know we should go back the way we came, and try going the other direction entirely.  If our error went down, then we should just keep changing our parameters in the same direction.  The error provides a \"training signal\" or a measure of the \"loss\" of our network.  You'll often hear anyone number of these terms to describe the same thing, \"Error\", \"Cost\", \"Loss\", or \"Training Signal'.  That's pretty much gradient descent in a nutshell.  Of course we've made a lot of assumptions in assuming our function is continuous and differentiable.  But we're not going to worry about that, and if you don't know what that means, don't worry about it.\n",
    "\n",
    "<a name=\"backpropagation\"></a>\n",
    "## Backpropagation\n",
    "\n",
    "To summarize, Gradient descent is a simple but very powerful method for finding smaller measures of error by following the negative direction of its gradient.  The gradient is just saying, how does the error change at the current set of parameters?\n",
    "\n",
    "One thing I didn't mention was how we figure out what the gradient is.  In order to do that, we use something called backpropagation.  When we pass as input something to a network, it's doing what's called forward propagation.  We're sending an input and multiplying it by every weight to an expected output.  Whatever differences that output has with the output we wanted it to have, gets *backpropagated* to every single parameter in our network.  Basically, backprop is a very effective way to find the gradient by simply multiplying many partial derivatives together.  It uses something called the chain rule to find the gradient of the error with respect to every single parameter in a network, and follows this error from the output of the network, all the way back to the input.\n",
    "\n",
    "While the details won't be necessary for this course, we will come back to it in later sessions as we learn more about how we can use both backprop and forward prop to help us understand the inner workings of deep neural networks.\n",
    "\n",
    "If you are interested in knowing more details about backprop, I highly recommend both Michael Nielsen's online Deep Learning book:\n",
    "\n",
    "http://neuralnetworksanddeeplearning.com/\n",
    "\n",
    "and Yoshua Bengio's online book:\n",
    "\n",
    "http://www.deeplearningbook.org/\n",
    "\n",
    "<a name=\"extra-details-for-notebook-only\"></a>\n",
    "## Extra details for notebook only\n",
    "\n",
    "To think about this another way, the definition of a linear function is written like so:\n",
    "\n",
    "\\begin{align}\n",
    "y = mx + b\n",
    "\\end{align}\n",
    "\n",
    "The slope, or gradient of this function is $m$ everywhere.  It's describing how the function changes with different network parameters.  If I follow the negative value of $m$, then I'm going down the slope, towards smaller values.\n",
    "\n",
    "But not all functions are linear.  Let's say the error was something like a parabola:\n",
    "\n",
    "\\begin{align}\n",
    "y(x) = x^2\n",
    "\\end{align}\n",
    "\n",
    "That just says, there is a function y, which takes one parameter, $x$, and this function just takes the value of $x$ and multiplies it by itself, or put another way, it outputs $x^2$.  Let's start at the minimum.  At $x = 0$, our function $y(0) = 0$.  Let's try and move a random amount, and say we end up at $1$.  So at $x = 1$, we know that our function went up from $y(0) = 0$ to $y(1) = 1$.  The change in $y = 1$.  The change in $x = 1$.  So our slope is:\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\text{change in } y}{\\text{change in } x} = \\frac{(y(1) - y(0)}{(1 - 0)} = \\frac{1}{1} = 1\n",
    "\\end{align}\n",
    "\n",
    "If we go in the negative direction of this, $x = x - 1$, we get back to 0, our minimum value.\n",
    "\n",
    "If you try this process for any value and you'll see that if you keep going towards the negative slope, you go towards smaller values.\n",
    "\n",
    "You might also see this process described like so:\n",
    "\n",
    "\\begin{align}\n",
    "\\theta = \\theta - \\eta \\cdot \\nabla_\\theta J( \\theta)\n",
    "\\end{align}\n",
    "\n",
    "That's just saying the same thing really.  We're going to update our parameters, commonly referred to by $\\theta$, by finding the gradient, $\\nabla$ with respect to parameters $\\theta$, $\\nabla_\\theta$, of our error, $J$, and moving down the negative direction of it: $- \\eta \\cdot \\nabla_\\theta J( \\theta)$.  The $\\eta$ is just a parameter also known as the learning rate, and it describes how far along this gradient we should travel, and we'll typically set this value from anywhere between 0.01 to 0.00001.\n",
    "\n",
    "<a name=\"local-minimaoptima\"></a>\n",
    "## Local Minima/Optima\n",
    "\n",
    "Before we start, we're going to need some library imports:"
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /anaconda2/lib/python2.7/site-packages/tensorflow/python/compat/compat.py:175: disable_resource_variables (from tensorflow.python.ops.variable_scope) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "non-resource variables are not supported in the long term\n"
     ]
    }
   ],
   "source": [
    "# imports\n",
    "%matplotlib inline\n",
    "# %pylab osx\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as colors\n",
    "import matplotlib.cm as cmx\n",
    "plt.style.use('ggplot')\n",
    "import tensorflow.compat.v1 as tf\n",
    "tf.disable_v2_behavior()"
   ]
  },
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   "metadata": {},
   "source": [
    "One pitfall of gradient descent is that some functions contain \"minima\", which is another way of saying a trough, or a concave point, or put another way, a dip in a function.\n",
    "\n",
    "Let's say, purely for illustration, that our cost function looked like:"
   ]
  },
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   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Some Parameter')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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25iPFG4C074B3+ni879+BfOGbsK6W8GffIXznNQfJjTGpYAVcqjQ187WNDDGxfDF06AhlLTskOPb69IvWOy2e5zqJSYPwmUfQR+6BYaPxfvyrqKFzC4gI3tgJeD/5XzhhEHrvfxM++0h0JrAxJqNZAZcq3RPRjkfrBRcLunIxHD8wa9YBiZcHFUNto0yWU1XCpx5Cn34IOeMcvK/9EOnUpdXPI5274H3rJ8gZ56JPPYQ+fI8VccZkuOz4bhZDkpcXFXHWC8453bsXqlci/Qe5jpJUcuIwWL8G3bLRdRSTIvryk+izj0SbEK7/RptOEJGCAuQL30Qu+CQ65Tn06YeTmNQYk25WwKVSogy1NXDurV4GYYj0r3CdJKlkUNM6uEW2Di4b6fxZ6OP3w+ixyHW3JOX4NxFBPvUFZNx56LOPEE5+JglJjTEuWAGXQlJcCrYGzjldHm1gyJYdqPsd1x86FIFtZMg6umEt4T2/gF598L7wzaRO/YsIcu3NMOp09NF70bnvJe25jTHpYwVcKhWXwpZNaH296yS5beUS6FGCdO3uOklSiZcHAyttJ2qW0YZ6wrtvBw3xbv5RShpPS14e3pe+A737Ed77S5spMCYDWQGXSk07Udm0wW2OHKfLF2VN+5CDyaBhsLYG3brZdRSTJPrcY7BqeXTnrTR1u6alsBDvqz+AsJHwd7fbD5rGZBgr4FJIEk294Gwa1RndtiXqxZetBZz1g8squmo5+vxjyOnjkZGnp/x6UlaO94VvQdVS9PE/pfx6xpjksQIulYqbesHZTlR3Vi4ByLoNDPv1HQCFHWwdXBbQhgbCP98FHTsjV9+QtuvKqNORcy9BX33W2tIYk0GsgEul7j0gL896wTmkK5eCSFToZCHJy4OKIbYTNQvoS3+D1Svwrvka0rFzWq8tV1wHpb0I/3QXumd3Wq9tjDk2VsClkHh50KPEjtNySFctg559UrIQPC7kxGGwZnU0XWwykm7ZhE56DEaehoxK/dTpwaSwPd7134RNG9An/pz26xtjWs8KuFQrLrXjtFyqWor0y867b82a18GxxI7VylT65F+goQHvqi84yyAVlch5l6F/fx61I9qMiT0r4FJMEmV2B84R3boZtmyCLC/g6DcQCtvbNGqG0lXL0KmTkQmXpHTXaUvIxM9BjxLCh+5GGxudZjHGHJkVcKlWXApbN6P79rpOknuqlgIgfQc6DpJakp8PAwbbTtQMpKqEj/4x2rjwCd91nGgq9dNfgpoqdMpzruMYY47ACrhUa24lstF6waWbVi1r2sBwgusoKScnDou+6W7f5jqKaY1578Piuchln0GKOrlOExl1BgwdhT79kPUXNCbGrIBLMWlqJWKH2qefVi2Fst5ZvYGhWfO5qLYOLnOoKuEzD0enhJx1ges4+4kI3me+AvX7bEODMTFmBVyqNZ3GoNZKJP1yYAPDfsdXQLt2No2aSea9D8sXIZ+4CskvcJ3mQ6SsHJlwGfr239FVy13HMcYcghVwqda1O+Tl22kMafaPDQzZvf6tmeQXwADrB5cpVJXw6YeguBQZO8F1nEOSiz8FRZ0I7S6cMbFkBVyKiedBsfWCS7vmDQy5cgcOkIGVULMS3bXTdRRzNPNmworFyMXxu/vWTIo6IZf4MH8WOnem6zjGmINYAZcOiTLUCri0yqUNDM2kohJUYdlC11HMUYSTHovWvo0913WUI5LxF0NJT8In/oyG1lbEmDixAi4NpLjUplDTLNrAUI60L3IdJX1OGAx5eahtZIg1Xb4IlsxHzp8Y27tvzSS/ALn8Wqheib77uus4xpgD5LsO0Mz3/YuAu4A84N4gCG4/6PPXA78Aapo+9JsgCO5Na8hjVVwK27eie/cghe1dp8kNq5YjFUNdp0grKSyEvgPQJfNdRzFHoC89CR06Imee5zpKi8iYcWifx9FnHkFPOTs6f9cY41ws7sD5vp8H/Bb4OFAJfMb3/cpDPPTRIAhGNv3KjOIN9u9EtXVw6aE7tsHmOujb33WUtJOKobByMVq/z3UUcwi6YS06cxpy9oUZc3dYPA9v4mdh/Rp02quu4xhjmsSigANOBZYGQbA8CIJ9wCPARMeZkkaaCzibRk2P1SsAkONysYAbAg0NsGKJ6yjmEHTyM+AJMuFS11FaZ8Sp0G8g+uyjaEO96zTGGOJTwPUGVh/wfnXTxw52pe/7s33ff9z3/ePSEy0JiqPTGGwjQ3po9crojT65V8AxMLpxbevg4kd37kDffBk55Wyke7HrOK0iIngTPwcb16NvvuI6jjGG+KyBk0N8TA96/xng4SAI9vq+/1XgfuCQW7h8378RuBEgCAISiUQys35Efn7+Ea+hxcWsb9eODju30znFWdLtaGN3Yev6WvZ1L6bkhNT3gIvd+BMJ6o7rT96qZXR3/LrPdq0d/85pk9mxdw/dr7qOggz8e9PxF7D5xSdofPGv5F15Tc5+7e11n7vjj9vY41LAVQMH3lHrA9Qe+IAgCDYe8O4fgDsO92RBENwD3NP0rtbV1SUp5qElEgmOeo0eJexavZK9Kc6Sbi0ae5o1Ll0IvfulJVccxx/2H0Tj9NfZsH4d4qVuwXkcx55OrRm/hiHhs4/BgMFs7VIMGfr3phdeQfirn7BjyiR2nnSa6zhO2Os+d8efrrGXl5e36HFxKeCmAxW+7/cn2mV6NfDZAx/g+36vIAjWNL17GbAgvRHbqLjUNjGkgTbUw5rVyLDRrqO4U1EJr78A1VU51Qcv1hbOhvW1yKWfdp2kbYaNgT792fnXv6DDTokalZuco+tq0WULoXYVuq4W9u2FxgbIz0d6lEQnjPSvgAGV0e54kxKxKOCCIGjwff8W4EWiNiL3BUEwz/f9nwAzgiB4GviG7/uXAQ3AJuB6Z4GPgSTKot5kJrXWVEf/keTgBoZmUjEUBXTJfMQKuFgIp0yCTl2QMeNcR2kTEUE+fiWNf/gvvFlvw+ixriOZNNG6degbL1E3ezph8zrj/Hwo6QUdiqK3d2yPzs7dvjVaA5WXDxWVyNgJyOixVswlWSwKOIAgCCYBkw762K0HvP1D4IfpzpU0xWXRi3vProxpH5CJNId3oDaT4hLoUQJL5sGES1zHyXm6aQN88C5y4eVIQTvXcdpMxozDe+ZhGic9jjfqDEQOtYTZZAtdvQJ9/nF0xlsgkDd0FOGZFyCVI6C0/JB9AXXPLli6AF04G505Db3vTvThe6L2ORddgXTq4mAk2Sc2BVzWS0Q7UalbD32Odxolq61eAe3aQVnL1hBkKxlYiS6ajaraN1jH9PUXAUU+dpHrKEkheXkUXX4N2393Byz4ACpHuo5kUkB3bkef/Av62gtQ2D46OWTCpXQ/cfBR14FJ+yIYNgYZNga94vOwZB762gvoS39DX3s+eq6LrkTa2R25trAFDGkiTa1EbB1camn1Cijvl9LF+xmhohK2boYNa47+WJMy2tiIvvVK9M2suR9kFuhwzsehWw/C5x93HcWkgM6cSvgvN6GvvYicewneHX/Eu+oLSI/W78AUz0MGDce78Xt4P/41VI5En3mE8Lavo/NnpSB97rACLl2a/vPWOivgUkVVYfWKnJ4+bdZ8jJguyay9Plln3kzYsgkvQ47NaikpaIecPxEWzo7OdjVZQev3ET50N+HvbofiUrx/vRPv6huQok5JeX7p3Ze8m36I9+2fggjhnbcSPvAbdO/epDx/rrECLl06d42m9uw0htTZvBF2bs/pDQz79eoDHTtH6+CMM+GbL0f/9k86xXWUpJOzL4SiTnYXLkvolo2Ed/wAnTIJueCTeD+4I2U/DMuQEXi3/Rq56Er0zZcJ/+M7aM2qlFwrm1kBlyYiAsVl6EYr4FLGNjDsJ54HA4fYwfYO6bYtMHs6csY5SH6B6zhJJ+2LkHMvgVnv2DffDKc1qwj/83uwthrv5n/Gu+qLKX/NSkE7vCs/j/et22D7VsL/+DY6482UXjPbWAGXTokyWwOXQlodFXC2SSQiFUNhfS26dbPrKDlJ354CjY3IuOyaPj2QTLgE2hWiLzzhOoo5Rrp4HuEd34fGEO+f/hMZmd4GzVI5Cu/Wu+C4Ewh//3PCZx+NlsOYo7ICLo2kuNSmUFNIVy+Hkp7WpqWJDBwSvbHU7sKlm6pGZ4aeMAgp7+s6TspIpy7I2Rei019HN+Vmd/5MpovnEf7q36Brd7wf/gLpO8BJDunWA+87/46c9jH0qQfRP/0P2tDgJEsmsQIunRKlsGsnumuH6yTZafVKW/92oH4DoF07m0Z1YcXi6ESQM893nSTlZMKlECo65TnXUUwr7C/euifwvvuzqH+kQ1LQDvnSt5HLPotOm0J49+1o/T6nmeLOCrg02t9GYOMGt0GykO7ZDRvWIH2sgGsm+QXQfxBqGxnSTqdNgYJ2GX/yQktIogxGn46+/iK6d4/rOKYFtGoZ4a9+At2LoztfXbu7jgREa8W9S69GPvtVmD2d8H9ui5oCm0OyAi6dmnvB2TRq8tVUgaptYDiIVAyF1SvR3fafYLpoQz06/Q1k5GlIUUfXcdLCO28i7NqBTn3VdRRzFLphbXTnrWMnvG//O9Kth+tIH+GdczHypW/D0vmEd/2bFXGHYQVcOhU39YKznahJ13yElk2hfphUVIKGsGyh6yi5Y+57sHM7cvp410nSZ8Bg6H8i+srTaBi6TmMOQ3dsi4q3hga8b92GdC92HemwvNM+hnfDd2H5IsJf/SSaZTEfYgVcOnXqDIUdouO0THKtXgFFHaMzQM0/nDAIPM/WwaVROO3vUe+3ylGuo6SNiESNfdfXwpwZruOYQ9CGhqhBb916vFv+Bel1nOtIRyUnn4l8+TuwdCHhb/7d1sQdxAq4NBIRSJSiNoWadFq9Avr0t3M/DyLtO0DfAehSWweXDrprB8x+Fzn1bCQ/t46altFjoUeC8OWnXEcxh6DBvbB4LvL5r0d35jOEd8pZyBe/BYvmEN7732jY6DpSbFgBl27FpdYLLsk0bITqlbb+7TBkYCUsX4zW17uOkvV0xlvQ0JBb06dNJC8POfdSWDQHXbXcdRxzgPCNl/5xwkIGvja908cjn/4SzJyGPni39YlrYgVcmklTM197ASbR+rWwb6+tfzsMqaiEhnqoWuI6StbTd/4OPftAv4GuozghZ50Phe3RV+wuXFzoyiXoQ3dD5Ujkis+7jnPMvPMmIh+/Mtrt/PTDruPEghVw6VZcCrt3gfWCSxq1I7SOrGm6xNbBpZZuqoMl85HTzs7ZqXwp6oSMOw999w10yybXcXKe7tpJeM8voEs3vBu+i+TluY7UJnL5ddHr69lHCKdMch3HOSvg0kwSza1EbBo1aapXQF4e9MrejvdtIZ27Qs8+VsClmL73VtTK5uSzXEdxKmrs24jaN1inVJXwgV/DxvV4N3wP6dTFdaQ2ExHk2pthxKnow7/P+bNTrYBLt+LmZr62kSFZdPUK6NkHKci+A8OTRSoqYdkCa/GQQjr9Deh7AtKzt+soTklpLxhxGvra8+jeva7j5Cx97Xl4bypy+bX/OFYvC0heHt4N34MBgwn/+Et06QLXkZyxAi7dmk5jULsDlzyrV9j06dFUDIVdO6G2ynWSrKR162DF4py/+9bMO38i7NyOvj3FdZScpGtWo8F9MGw0csHlruMknRQW4t38z9CjhPB//yNnOztYAZduRR2hQ5GdxpAkunM7bNkIvfu5jhJrzT+B2zRqajRP5cjJ2X90VotUVEK/gdbY1wFtqCe895dQ2B7v+m8iXnZ+m5dOXfC+/q/Q2ED465+iu3a6jpR22fmVjTERgeJS1FqJJEfNKgCk9/Fuc8Rdogy6FYMVcCmh09+A/iciJT1dR4mF/Y1911bDvJmu4+QUffphWLUM77pbYnPGaapIzz54X/0BrKsh/MMv0Mbc6hFnBZwLTa1ETNtp85Rgb9vAcCQiglRUokvmWQubJNN1tbBqOXLyma6jxIqMGQfdiq2xbxrpsoXoC39Fxp2HjDrddZy0kCEjkM9+FebORIM/uo6TVlbAOSDFpVC3zr6RJkPNKujQEbonXCeJv4qhsGWTTd8nmU5/A7Dp04NJfj5y7idgwQfRSSkmpbS+nvD+X0P3HsgyqRO1AAAgAElEQVSnv+w6Tlp5Z1+IXPBJ9NVnCac85zpO2lgB50KiFPbugR3bXSfJeFpbBb375mzfrdYQ6weXEjrjTRhYidg5vB8hZ18I7QrRl592HSXr6XOPwprVeNfcjHQoch0n7eTKzze1F/kDOu9913HSwgo4ByRhrUSSQVWhugoptw0MLVLeF4o6wVIr4JJFa1ZBTRVyik2fHop07IyMm4C++xq6dbPrOFlLV69AX3gCOf0cZPgY13GcEC8P78vfhvLjCO/5Obq2xnWklLMCzoXmXnA2ldU2WzdFJ1rY+rcWEc+DgUPQJXawfbLojDdAvGi9lzkkmXAZNDaif7fGvqmgjY3R1GlRp+i80Bwm7YvwbvkX8PIIf/Pv6M7sPvHICjgXiqPTGGwnahvt34Fqd+BaSgZWwtoadNsW11Eynqqi09+EE4dm/W6/tpCy8mhq6++T0H3W2DfZ9OUnoWop3me/khWnLbSVJMrwbvoh1K0jvCe7d6ZaAeeAFHWMprKsmW+baE3TDlSbQm2x5nVwNo3adg0rl8C6GuQUa957NN75E2HHdnSaNfZNJl1bE7UNGXU62F3g/eTEocjnvgrz30cfu891nJSxAs6VRGnOdo9Omtoq6Nod6Ww/dbbY8QOhoJ1tZEiCPW9OBs9DRo91HSX+KoY2NfZ9yhr7JomGYXTWaUEB3me/ahu5DuKddQFy3kR08jOEr7/oOk5KWAHnSnGp9YJrI61ZFS3MNy0m+QXQ/0Qr4NpIVdn71mQYPMJ+gGiBfzT2rYG577mOkxX0zZdhyXzkqi8i3Xq4jhNL8qnrYdho9KG70UVzXcdJunzXAZr5vn8RcBeQB9wbBMHtB32+EHgAGANsBD4dBMHKdOdMFkmUofNmoqr2k9Mx0DCE2lVRmwLTKlJRiU56HN2zC2mfe+0GkmL1chrX1SIXXuE6ScaQMePQJ+4nfPkp8k46xXWcjKbbt6F/fQBOHIaMO891nNhqPvg+/M/vEd79n3g/+u+sOi0lFnfgfN/PA34LfByoBD7j+37lQQ/7ErA5CIKBwJ3AHelNmWTFZbBvH2y3xeTHpG4d7Ntrd+COgVQMBQ1h+SLXUTKWvjctmj4deZrrKBlD8vORCZfAwtnoquWu42Q0/ev9sGeXTZ22gBR1jHamhhrtTN29y3WkpIlFAQecCiwNgmB5EAT7gEeAiQc9ZiJwf9PbjwMTfN/P2FeuJKKdqLaR4Rg1HaFlO1CPwQmDQDybRm0DnTmVgsqRSOeurqNkFDnrAihsj75ix2sdK122EH3zZWTCZYi1UGoRKSvH++r3YW014b3/jYbZsTM1LgVcb2D1Ae9XN33skI8JgqAB2AoUpyVdKjQ187VWIsdGm1qIUH6c2yAZSDoUwXH9rYA7Rlq7CtZW0/6Mc1xHyThS1Ak583z03TfQLRtdx8k42thI+ODvoFsxcunVruNkFBkyArn6Bpg9Hf3bX1zHSYq4rIE71J20gw8KbcljAPB9/0bgRoAgCEgkUntOZn5+fquvEXbswAag467tdExxvlQ6lrEnw5a6tTSUlZPo4/YnUFfjb6vtJ41h10tPUty1K1JQcEzPkaljb6sdrz7DTqDjuHMpytH+b2352jd86jo2TnmODm9PodM1X01ystRz+brf9dxjbF+9gq7f+3fa93Hzw2sm/7vXT13H9o3r2f3CE3QcVEmH8R9v1Z+P29jjUsBVAwe+GvsAtYd5TLXv+/lAV2DToZ4sCIJ7gHua3tW6urrkpj1IIpHgmK7RqTM7V61kd4rzpdIxj72NGlcsgZ59nFz7QK7G31ba5wTYt4+6me8gAwYf03Nk6tjbqvGNV2DAYLRr95wcP7Txa59fCCNPZ+fzf2X3OZcghe2TGy7FXL3udetmwgd/D5Wj2F4xnB2OXnuZ/u9eP3ktrFzKtt/ezo72HaPm5i2UrrGXl5e36HFxmUKdDlT4vt/f9/12wNXAwacfPw18vuntTwGvBkFwyDtwGaO4DLXzUFtNG+phbTViGxiOXcUQADtWq5V0/RqoXmG939rIO38i7NqBTn3VdZSMoY//Cer3RScu2MaFYyb5+dF6uOJSwt/8DF1b7TrSMYtFAde0pu0W4EVgQfShYJ7v+z/xff+ypof9ESj2fX8p8G3gB27SJlHCesEdk3W10NgItoHhmEmX7lDWG126wHWUjKLvTwNARp/hOEmGGzA46kdojX1bRBfNQd/+O3LhFdHRZKZNpFMXvG/+GDyP8H9uQ7dudh3pmMRlCpUgCCYBkw762K0HvL0HuCrduVJJisvQD6ajYRgdNG5apPkILduB1TZSUYnOnGavv1bQ96ZCv4FI0yYkc2yixr6fRO/5OcyeDtaO5bC0oYHwwbuhuBT5eFZ9C3RKSnriff1Wwv/6EeGvf4r33Z8h7Tu4jtUq9r+2S4lSaKgHO1i8dWpWgedBWR/XSTLbwErYtQPWrD76Yw26qQ5WLEZGne46SlaQ0WdAjxLCl62lyJHo5KdhzWq8z9yIFBa6jpNVpH8F3o3/BKuWZ+TB91bAObT/p3ibRm0Vra2Cst7HvHvSRJoPtrd1cC2zf/p0jK1/SwbJy0MmXAqL56IrlriOE0u6qQ595hEYcSoy4lTXcbKSjDglOvh+zgz0wd+hmjlL662Ac6k4auZrh9q3Uk2VNfBNhpKe0LUHWD+4FtGZU6G8L9LT7vwmi5x9ARR1Ipz0mOsosRQG90IY4n36y66jZDXvYxchF1+FvvES+rcHMqaIswLOpeLm0xisgGsp3bsn+vuy9W9tJiLROrgl8zPmPyxXdNvm6OBw232aVNK+KDpea9bb+9e2mojOex/em4pcfFVWnd8ZV/LJa5CzL0SffyK665kBrIBzSArbQ+euNoXaGrWrQRUptztwSVFRCZvr7DV4FDrrneh1N8Z2nyabTLgUCjugkx53HSU2tH4f4UN3Q2k5cuEVruPkBBFBPncTMnYC+szDhM/H//VoBZxriTKbQm0FbToD1VqIJIdUDAVAl9o06pHoe9OgtBf0Pt51lKwjHTsj4y9Cp7+Brj+4f3tu0hf/CuvXRD3fbK1v2ojnIZ+/BTn1Y+hfH4j9BpsWF3C+73/3MB//dvLi5B4ptl5wrVJTBe3aQYm1cUiK3n2hQ5GtgzsC3bkDFs1GRo+1BqopIud/EvLy0Bf+6jqKc7phLTrpcWTMOGToKNdxco54ecgXvwVjxqLBHwmnPOc60mG15g7crYf5+L8kI0jOSpTBxg3WzLKFtGYV9OqLeHmuo2QF8fJgwBA72P4I9IN3obHR1r+lkHTtHh1yP/VVdNMG13GcUVXCh+8Bz0P8L7mOk7MkLw/vy9+FEaeiD/2e8NVnXUc6pKM28vV9/9ymN/N83z+HDx8qfwKwPRXBckZxKTQ2wJZN0CM+h+TGVk0VUjnSdYqsIhWV6Nz30O3bkM5dXMeJHZ05Nfq3efxA11Gymlx0BfrGi+hLTyJX3+A6jhvvvw1zZiBXfQGx7wdOSX4+3le+T/j7O9CH7yHcuQO9/mbXsT6kJScx/LHp9/bAfQd8XIF1wNeTHSqXSKIUhWga1f7BHpHu2AZbN9n6tySTiqHRa3DpfLAmtR+ie3bBvPeRj11k06cpJsWlyGnjoyLu4quQLt1cR0or3bOb8JE/QO9+yLmXuo5jACkowLvph+j9v0affojtjfvQy66Jzck1Ry3ggiDoD+D7/gNBEFyX+kg5pqmZr25ct7+xqjmM2lWAHaGVdMdXQH4BumSenTJwEJ0zExrq7ezTNJGPX4lOexV95Snkis+7jpNW+swjsLkO78bvIvmxOeUy50leHlz/DejYmX0z34bzL4eOnV3HAlqxBu7g4s33/XN83z8r+ZFyTI+S6HfbiXpUWhMVcFgLkaSSggLoX2Hr4A5l5tSo1c/AIa6T5ATp2QcZMw6dMinaPJIjtHplVLSeeT4y0H6QjxvxPMT/Ij1+8UckJsUbtG4X6mu+749revv7wCPAI77v/yhV4XKBtCuErt2hznaiHlVtFXToCN2LXSfJOlIxFFYtQ/fsdh0lNrR+HzpnBjLqDNs0k0byiatgz2705SddR0kLDUPCB38HRR2RK3PrrmMmERG8GBVv0LpdqMOAt5vevgEYD5wOfDXJmXJPcSlqrUSOSmuqovUhthYp6aRiKIQhLFvoOkp8zHsf9u6x6dM0kz79o7twrzyDbt/qOk7K6dTJsHQBcuX1SCfbRGRarjUFnAeo7/sDAAmCYEEQBKuB7qmJljskUWZTqEehqk1noNr6t5SoqIz6cC2c7TpJbOjMqVDUEQYNdx0l58jEz8G+vWgGdMNvC92xDX3izzBwCDJ2gus4JsO0poB7E/gN8F/A3wCairm6FOTKLcWlsLkObWx0nSS+tmyCXTttB2qKSGF76H8iumiO6yixoA0N6AfvIiNOtQXlDkivPsjp46O1cJs3uo6TMvr4n2DXTrzP3RSbnY0mc7TmFXM9sAWYDdzW9LHBwF3JjZSDEqXQ2BgVKebQmg66tjNQU0cGnwQrl6K7drqO4t6iObBrpzXvdUguvRo0RJ971HWUlNB576NvTUYuvBzpc7zrOCYDtfhHyyAINgI/Ouhj8T1jIoNIoqypF9w6KC5xHSeW/nEGqk2hpooMGo4++2h0rNaIU1zHcUpnToPC9mBNo52Rkp7IWReir7+AnncZ0rOP60hJo3t2ET7wG+jZB7n0M67jmAzV4gLO9/0ComOzrgXKgVrg/4CfBUGwLzXxckRxUy+4unXIicMch4mpmlXQtYct8k2lAYOjfnALZyM5XMBp2Ii+Pw0ZfnK0S9w4I5dejb49hfCJ+8m7+Z9dx0kafeKBqOfb9+9ACtq5jmMyVGumUH8OnEe063RE0+/nAnekIFdu6VECIraR4QiiHah29y2VpKAdDBhsGxmWLoDtW8F2nzonXbohF10Js95BF811HScpdNFc9O+TkAmXIgMGu45jMlhrCrirgMuCIHgpCIJFQRC8BFwO+KmJljukoAC6FcMGK+AORcNGWLPK1r+lgQw+CapXRMeW5SidOQ3yC5DhY1xHMYCcPxG6Jwgfuw8NQ9dx2kT37iW8/1dQ0hP55DWu45gM15oC7nDNt6wpVzKU9EQ3rHGdIp7q1sG+fXYHLg1kcFPLjCy529Faqoq+Pw2GjkLaF7mOY4iancvl10LVUvTtv7uO0yb69IOwYS3edbdEO7+NaYPW7I9/DHjG9/1/A1YB/YjWxD2WimC5Rkp6onNmuI4RTzXNZ6DaHbiUO74CCttH6+DG5OAOzJVLYVNd1IfMxIac9jF0ynPo439CR56KFHVyHanVdNlC9OWnkbMviu50G9NGrbkD90/AK8BvgfeAXwOvAt9LQa7cU9ITtm2xo4wOQZtaiNDrOLdBcoDkF0BFJbrwA9dRnNCZUyEvDxlxquso5gDieXifuwl2bEefesh1nFbTvXsI/3wXdOuBfOp613FMljjqHbim808vC4Lg+8CtTb+aP3cHMJp/HLFljlVpr+j3urXQp7/bLHFTuypaM9K+g+skOUGGjEQfuw/dtAHpkTttbVQ1KuAGDY/VgdUmIv0GIOMvipr7jpuA9B3gOlKLaXAfrKvF+38/QTrY1LxJjpbcgfsR8PphPjcFyJ693Q5JSc/ojfVr3QaJIa2pgnJb/5Yu0tT7TOfPcpwkzWqqYP0aa94bYzLxGujUmfDBu6PNTRlAZ72Nvv4CcsEnkSEjXMcxWaQlBdxI4IXDfO4VwLZqJUNJdAdON1gBdyBtqId1Nbb+LZ1694Ou3SHHCjidORVEkJGnuY5iDkM6dkL8L8LyRegrz7iOc1S6ZSPh/b+GvgNs16lJupYUcF2Aw3UaLABsriEJpGMnKOoEthP1w9bWRMeM2R24tBERZMgIdOHsjG/b0Bo6c1p0qHjX7q6jmCOQ08bDiFPRJ/+Crq1xHeewtKGB8Pc/h/p6vC9/J1pfakwStaSAWwhccJjPXdD0eZMMJT3tDtxBmjcw2B24NBsyMmpmW73SdZK00HW1UFNl06cZQETwrrkJCgoI/3xXbKdS9W8PwNIFyHW3IL2y5xgwEx8tKeDuBH7v+/4Vvu97AL7ve77vXwHcDfwylQFziZT2AivgPqx2FeTlQc/erpPklOa1OrogN6ZRdeZUAGSUnb6QCaRbMXL1jbBsIfrik67jfITOnIq+9CRyzsV4p57tOo7JUkfdhRoEwUO+7/cE7gcKfd+vAxLAHuDHQRA83JYAvu/3AB4FjgdWAn4QBJsP8bhGYE7Tu6uCILisLdeNpZKe8N5baEMDkt+aFn3ZS2uqoKy3TT+kmXQvhl7HRRsZLrzCdZyU0xlvwfEVSHHu7LrNdHL6ePSDd9An/w+tGIIMrHQdCQCtXkF4313Q/0Tkqi+5jmOyWIv6wAVB8EugN3Ap8N2m3/sEQXBnEjL8AJgcBEEFMLnp/UPZHQTByKZf2Ve8QVTAhSFs2uA6SXzUrrLpU0ekciQsmY/W73MdJaV0XS2sWoaccpbrKKYVRATvuq9DcSnhPf+Fbnd//Jtu3Uz4659ChyK8r/0wOibRmBRp8W2eIAi2AS+mIMNEYHzT2/cDfwe+n4LrxJ6U9EIhmkZt7guXw3TP7ujvYuwE11FykgwdhU5+BpbMg8pRruOkjE5/AwA5eZzjJKa1pKgj3le+T3j79wjvuxPv6/+CeHlOsui+vYS//Rns2I73/duRbsVOcpjc0ZqTGFKlLAiCNQBNv5ce5nHtfd+f4fv+277vfzJ98dKoqRecnYnaZM1qwDYwOHPicMgvQOfMdJ0kpXTGmzCwMqeaFmcT6TcA+fQNMPc99LE/OcmgDfWEd98BK5dEO04zqMmwyVxpWWjl+/4rQM9DfKo1TYD7BkFQ6/v+CcCrvu/PCYJg2WGudyNwI0AQBCQSiVZnbo38/PykXEN79GB9QTs67NhK5xRnTpZkjf1Qds96m21A92EjyY/p30cqxx8Hm4eNonHBrEOOMRvG3rBqORtrquh8w3coauVYsmH8xyp2Y//UtWzftoldzzxKUb8TKLrET9mlDh67Njaw9Ze3sXfODDrf9E8UnX9Jyq4dB7H72qdR3MaelgIuCILzDvc53/fX+b7fKwiCNb7v9wLWH+Y5apt+X+77/t+BUcAhC7ggCO4B7ml6V+vq6toS/6gSiQRJu0aijF1VK9ib4szJktSxHyRcNA/atWNzXgES07+PVI4/DsJBJ6Gz7mXDgrn/OC2kSTaMPXz5GRCPnYNPYlcrx5IN4z9WcRy7XnI1rK5i+313sbOgEBmTminxA8eujY3o/b9Cp01Brvoiu0af2erXUaaJ49c+XdI19vLy8hY9Lg5TqE8Dn296+/PAUwc/wPf97r7vFza9nQDGAfPTljCdSnpaM98mWlsFvfo6W9NiQIZFB63o3OybRlVV9N03YPBwpIs178104uXhffk7cMIgwnt+Qfju4U6ATA7dt5fwd/8ZFW8TP4t3QXau7DHxFYcC7nbgfN/3lwDnN72P7/sn+75/b9NjhgAzfN//gOj81duDIMjKAk5KekLdOlTVdRT3amwHqnNl5VGD6bnvuU6SfKuXw/pa5OQzXScxSSKFhXjfug0GDkHv/SXhW5NTch3duZ3wzh/D7OnIZ7+Cd8nVKbmOMUfivNlYEAQbgY9sMwyCYAbw5aa3pwLD0xzNjZJesHcPbNsSnUeZo3THNti6CXrbEVouiQgybAz61sto/T6k4HCn6mUeffcNyMtDRlvz3mwi7YvwvnEb4f/+DP3zXYTrqpGJ1yB5ybmTX794HuHP/xm2bsK78Xv2A4BxJg534MwBpLRpndH6HJ9GrVkFgJTbHTjXZPgY2LcPFs9zHSVpVDXafVo5CunUxXUck2RSWIh3y78iZ1+IPv8E4Z23ols/0h++VbSxkfDFv7LpR18FwPunO6x4M05ZARc31koEaFr/BmBTqO6dOBwK2mXXNOryRbBxvX0DzmJSUIB37c3IF74JyxcR/uvXCF96Em2ob/Vz6fz3CX/yTfTxP1N4yll4t/4P0r8iBamNaTnnU6jmIMVlIGJnotZUQVFH6NbDdZKcJ4WFMGg4Ons66n8JEXEdqc10xpuQX4CMPM11FJNi3tgJaP9BhMG96GP3oa89j4y/GDntY0iXbof9c7pvb3Sm6WsvwtL5UNIT72s/out5n2Djxo1pHIExh2YFXMxIQQF0T8D63C7gtGYV9O6XFcVCNpARp6AP3h01Vy7P7HWJGjai09+E4WOQoo6u45g0kF59yPvmbeicGYRPP4wGf0Sf+DMMGIz06Q+9+kBePjQ2wKY6dMViWLEE9u6G0l7IVV9EzrkYKWhn/yeZ2LACLo5Keub0FKqqQk0VctrZrqOYJjLiNPTBu9FZ7yAZXsCxZAFs3WRnn+YgGX4yecNPRmtWodMmo0vmo29Njgq1Znl50Kc/csZ4ZPRYGDQc8Wy1kYkfK+BiSEp7oe+/7TqGO5s3wu6dYBsYYkO6F8PxFeisd+Diq1zHaROd8Qa0K0ROOsV1FOOI9O6LfOoLAGgYwtbNoAr5edChY1bttjbZy36siKOSXrBjG7p7l+skbjRtYBBrIRIrMvI0WLEY3bLJdZRjpg316PQ3kRGnIoXtXccxMSCeh3QvRnokkC7drXgzGcMKuBja30okR6dRtamFSKavtco2zQv+dfa7jpO0wZz3YOd2ZOy5rpMYY0ybWAEXR81nTubqTtSaKujaw/pzxU1532h95qzMLeDCaa9GDbKHjHQdxRhj2sQKuDgq6QWA5uhOVK1dZf3fYkhEkBGnwYIP0D27j/4HYkZ3bIPZM6L2EUnqym+MMa5YARdD0qEIOnXJySlUDRuhdpWtf4spGXkaNNRDBjb11elvQGMDcsY5rqMYY0ybWQEXVyU90VycQt2wDur32R24uKoYAl26Ec5403WSVtNpU6L2EH36u45ijDFtZgVcTElJr9xcA1fTtAPVWojEknh5yJixMGcGYQbtktY11bBisd19M8ZkDSvg4qq0Z9QR/BjO7ctkWlsVHSVWfpzrKOYw5OQzYd8+9s14y3WUFtO3Xoa8POS0j7mOYowxSWEFXFyV9AQNoW696yTpVV0FiTLr0RVnAyuhaw/2vDXZdZIW0YZ6dOqrcNIpSNfuruMYY0xSWAEXU9K0EzXXplG1pgp6H+86hjkC8Tzk5HHsnfl2ZjSb/mA6bN+Kd9YFrpMYY0zSWAEXV0294HLpTFTdtxfW1SJ9jncdxRyFnHwm1O9DP3jHdZSjCt94EbonYOgo11GMMSZprICLq67doV1hbt2BW7MaNET62AaG2DthEF6iDJ0e792ounE9zJ+FjDsP8az3mzEme1gBF1MiErUSWZ9Dd+Cqox2oNoUaf+J5tB83AebNRLdtcR3nsPTNVwCQM89znMQYY5LLCrg4K+sN62pdp0if6pXQrl20A9fEXodzL4bGRvTd11xHOSRtaEDffBkqRyLFpa7jGGNMUlkBF2NSVg51a9GGBtdR0kJrVkJ5P5vqyhD5fU+A4yvQtyajqq7jfNSst2HLRrxzPuE6iTHGJJ0VcHFW1hsaG2Fj9rcSUVVYvcI2MGQYGTshunO6arnrKB8RTn422gw0fIzrKMYYk3RWwMWYlJVHb6yrcRskHbZtgR3bwAq4jCKnng35BejUePWE01XLYOl8ZPzFdkfXGJOVrICLs7LeAGgurIOrXgmA2BmoGUU6dkJGnY6+8xpaH59TQ/TVZ6FdoW1eMMZkLSvg4qxTZyjqlBN34LSpgLMdqJlHxk6AndshJj3hdPs29J3XkTPOQYo6uY5jjDEpYQVcjIkIlJXnRiuR6pXQrQfSuYvrJKa1KkdAcSnhlEmukwCgr02ChnrknEtcRzHGmJSxAi7mpKw8N+7A1ay09W8ZSrw85JxPwOK56OoVTrPo3j3o5Geic09793WaxRhjUskKuLgrK4dNdejeva6TpIw2NMCa1YhNn2YsOfN8aFcYrT1zSN94EXZsx7v4Kqc5jDEm1ayAi7umjQxsyOKNDOtqoaHB7sBlMOnYCTnjnGgzw/ZtTjJofT364pMwaDgyYLCTDMYYky75rgP4vn8VcBswBDg1CIIZh3ncRcBdQB5wbxAEt6ctpENSVo5CVOT06e86TkpodTTtZj3gMpucewn62gvoGy8iDu6A6dtTosa9X/hG2q9tjDHpFoc7cHOBK4DXD/cA3/fzgN8CHwcqgc/4vl+ZnniOlUa94HRtFq+Dq1kJeXnQs7frJKYNpLwvDBmBTpmU9pYi2tCAPv849BsIQ0am9drGGOOC8wIuCIIFQRAsOsrDTgWWBkGwPAiCfcAjwMTUp3NP2neAbj2y+kxUra6Cnn2Q/ALXUUwbeRdeAVs2om+9nNbr6psvwYa1eJd+Jtq9bYwxWc55AddCvYHVB7xf3fSx3FDWG12fvQUc1Stt+jRbVI6EgUPQSY+j9fvSckndsxt95hE4cSicdHJarmmMMa6lZQ2c7/uvAD0P8al/DoLgqRY8xaF+pD7s6dm+798I3AgQBAGJRKJFOY9Vfn5+Sq+xrd8J7Hn7tZSP41i0dezhjm1s2FxHx0FD6RjD8R1Nqr/2cXa4se+99ia2/PgbdHx/KkUXfyrlOXY8+kd2bttC9x/9nHYlJSm/XjP72tvYc1Eujz9uY09LARcEQVvPs6kGjjvg/T7AYW9JBUFwD3BP07taV1fXxssfWSKRIJXXCLv2QLdtYUPVCqRj55Rd51i0dey6eC4Au7qXsDvFX6dUSPXXPs4ON3bt1Q8qKtke/JmdI89A2hWmLINu20z4twdh9Fi2FfeENH4t7GtvY89FuTz+dI29vLy8RY/LlCnU6UCF7/v9fd9vB1wNPO04U9pIcyuRLNzIsP8ILZtCzRoigjfxc7B1E5ri0xn0rw9A/T68y69N6XWMMSZunBdwvu9f7vt+NXAG8AfqGIUAABuUSURBVJzv+y82fbzc9/1JAEEQNAC3AC8CC6IPBfNcZU67nn0A0LXVjoOkQPVK6NgZuvZwncQkkQwaDsPGoM88gm5KzU+sOn8W+tZk5MLLEdvBbIzJMc77wAVB8Dfgb4f4eC1w8QHvTwLicdhiuiXKID8f1qw++mMzjFavhD7H287BLOR95kbC275OGNxL3ld/kNTn1r17Cf/vt1BajlxydVKf2xhjMoHzO3Dm6CQvD0rLs64XnIYh1FTZDtQsJaW9kE/48N5UdM4h+3MfM336Qahbh3fdLSldY2eMMXFlBVym6NUn++7A1a2FfXuhdz/XSUyKyAWXQ88+hA/eje7elZTn1Pnvoy8/jZx1ATJoWFKe0xhjMo0VcBlCeh0HG9alvcN9SjVtYJAsPSLMgBQU4F13C2yuI7zvzuiuaxvohrWEv/8FlB+H+F9KUkpjjMk8VsBlip59QEPIooa+Wl0FIlDe13UUk0JSUYlc9UWY9Q46KTjm59G9ewj/9z8A8L72o+iUEmOMyVFWwGUI6RXtRCWLdqJqzcpoEXqhrWHKdjLhUuT08ejTD6Mzp7X6z+vePYR33w41q/Bu+C5S2isFKY0xJnNYAZcpmnrBaTatg1u9wta/5QgRQa65GfoNJPz9HYRvtvysVN25g/DOW2HeLOTaryHDRqcwqTHGZAYr4DKEFLaH4lJYkx134HTXTtiwFul7gusoJk2ksBDvOz+FwSPQ+39N+NRDaGPjEf+MVi0l/PkPoGop3lf+Ce+sC/5/e3ceZVdZ5nv8+1YqIYQkJFCQSmUOJCEhQJgik40MMtggSutD6NYGFaN9W7FFuhHwXm1sbNBlK6uxWwa90KjAI32jIAFCQBqkiR2QQCYyVVIZKiFkJgMpktr3j72LdSiqUqeGc/bZ5/w+a2XlnD0+T71neM67h7dI0YqIlLbU7wMnnTB0ePnczHftSgAVcBUm9O1H1Vf/N9EDPyH63UNEc18gXDqNcOpZhKpeAERRBG9tIHriEaIXZ0P/gVRd+23CxBNSjl5EpHSogMuQUDucaOkCouZmQlW2O0+j1fXxgxEq4CpNqK6Gq68lnHAqzY8+SHTvD4ke+AkcMRQGDoJ1q2D7VujVi/DRywh/fgWh3yFphy0iUlJUwGXJ0OHQ1ARbN8WHU7NsdT0MHEQYpCG0KlEIAU46g6opp8Grc4iWLSTauB62byFMnAJHTSAcexLhiNq0QxURKUkq4DIk1A4ngviGvhkv4KI1K2GE7v9W6UJVFZx8BuHkM9IORUQkU7J9HK7SDB0BQJTxCxmid9+F9at1/puIiEgXqYDLkDDgUOg/IPv3gmtcDfv3w4ij0o5EREQkk1TAZU3tCKLGbN8LLlq9AtAVqCIiIl2lAi5jwrCR0NgQ32ohq9ashIMOBp2gLiIi0iUq4LJm2CjYvQu2bUk7ki6L1tTDiNGZvxWKiIhIWvQNmjGhLhl6al1DuoF0UdTcDGtWEXT/NxERkS5TAZc1dSMBiBqzWcCxcT3s3QM6/01ERKTLVMBlTBgwEA4dDOtWpx1Kl0Rr4hEYdAGDiIhI16mAy6K6kUQZPYRKw3Korn6vJ1FEREQ6TwVcBoVho2D96vh8soyJVi2H4WMI1b3TDkVERCSzVMBlUd3IeEzUTW+mHUmnRM3NsHoFYZRu4CsiItIdKuAyKAwfHT/I2mHUtzbAnt0w6ui0IxEREck0FXBZ1DImasYKuGjVMgDC6HHpBiIiIpJxKuAyKPQ9GGqGxGOKZknDcujd570CVERERLpGBVxWDRuVvR64huUwfDShujrtUERERDJNBVxGhbqR8OY6on3vph1KXqLmZmioJ4zW+W8iIiLdpQIuq4aNgv374c3GtCPJz5uN8QgMo3T+m4iISHepgMuoMCweEzVaszLlSPITNbRcwKAeOBERke5SAZdVtcOhujckQ1OVvIYV0KdPHLeIiIh0S+pnk5vZp4HvABOBqe7+cjvLrQLeBvYD+9z9lGLFWIpCdXV8IUNWeuBWLYcRYwm9eqUdioiISOalXsABC4DLgbvyWPYcd99U4HgyI4wcS/Snl4iiiBBC2uG0K9q/Px6B4cMXpB2KiIhIWUj9EKq7L3b3JWnHkUkjxsKut2FLide06xqgaS+MGZ92JCIiImUh9QKuEyJglpm9YmbT0w6mFISRY+MHa1akG0gHovq4Pg9jJ6QciYiISHkoyiFUM5sN1LYx62Z3/22emznT3RvN7EjgaTN7w92fb2d/04HpAO5OTU1Nl+LOV3V1dcH30Zao/8lsDIGDN22gfwr7h/xy397YQNOhg6k55tiSPtTbFWm1fSmo5NyhsvNX7pWZO1R2/qWWe1EKOHc/vwe20Zj8v9HMZgBTgTYLOHe/G7g7eRpt2lTYQ4w1NTUUeh/tGjKMXUsW8k5K+88n9/2LX4PR49i8eXORoiqeVNs+ZZWcO1R2/sq9MnOHys6/WLnX1dXltVwmDqGa2SFmNqDlMXAB8cUPFS+MHAurS/dWItGunbBhnQ6fioiI9KDUCzgz+6SZrQVOBx43s6eS6XVmNjNZbAjwBzN7Dfgf4HF3fzKdiEvMiDGw5S2inTvSjqRtK5cCEHQBg4iISI9J/TYi7j4DmNHG9EbgY8njeuCEIoeWCWHkWCKANSthYun9iaL6JRACjNEQWiIiIj0l9R446aYRRwEQleiIDNHKJVA3ktC3X9qhiIiIlA0VcBkXBgyEwTUleR5c1NwM9Ut1/puIiEgPUwFXDkaOJWoowXvBbWyE3TtBBZyIiEiPUgFXBsLoo+HNdUS7d6UdyvvoBr4iIiKFoQKuDIQxEyCKYNWytEN5v+WLod8hUDs87UhERETKigq4cpBc4Rklt+woFdGyhXD0JEKVXmYiIiI9Sd+sZSD06w+1w0qqgIt2bItv4DtuUtqhiIiIlB0VcGUijBkP9UuIoijtUGLLFgEQxh2bciAiIiLlRwVcuRgzAd7eDps3ph0JkBw+7dMHRh2VdigiIiJlRwVcmQhj46GqSuUwarRsEYyZQKjunXYoIiIiZUcFXLkYNhp694H69Au4aM9uWLNSh09FREQKRAVcmQjV1fENfVcuSTsUWLEYomZdwCAiIlIgKuDKSBgzAVbXE+3bl2oc0bJFUFWlERhEREQKRAVcORk7Ht5tgnWrUg0jWrYQRh1N6HtwqnGIiIiUKxVwZaRlyKpoxRupxRA17YWVy3T4VEREpIBUwJWRcPiRcPiRREsXpBfE8kWw713CMSekF4OIiEiZUwFXZsL4Y2HJgtRu6BstmgfV1TBeV6CKiIgUigq4cjPhONi5AxrXpLL7aNE8OGoi4aC+qexfRESkEqiAKzNh/GSAVA6jRju2xfd/m6jDpyIiIoWkAq7c1AyBw2pgyfyi7zpa/BoAYdKJRd+3iIhIJVEBV2ZCCITxxxEtTeE8uMXzoF9/GDW2uPsVERGpMCrgytGEyfHA9hvWFm2XURQRLXoNJh5PqOpVtP2KiIhUIhVwZei98+CKeRh1wzrYuokwaUrx9ikiIlKhVMCVoyNqYXANLCnehQzRonkAhIkq4ERERApNBVwZCiEQJkwmWjKfqLm5KPuMXp8LR9YRjqgtyv5EREQqmQq4cnXsifF5cA0rCr6raPdOWPI64cTTCr4vERERUQFXtsLkkyFUxT1jBRbNfwX271cBJyIiUiQq4MpU6D8QjjqmKAUcr86BgYNgzPjC70tERERUwJWzcPypsHoF0dbNBdtH1LSXaMGfCFM+RKjSy0lERKQY9I1bxsLxpwIQzX+5YPtomv8K7N1DmKLDpyIiIsVSnXYAZvYD4FKgCVgBfM7dt7Wx3EXAHUAv4F53v62ogWZR3Qg4/Mj4MOqfXViQXez94/Nw0MFwzPEF2b6IiIh8UCn0wD0NTHb344GlwI2tFzCzXsBPgIuBScCVZjapqFFmUAgh7oVbPI+oaW+Pbz9qbmbv3D8QjjuZ0Lt3j29fRERE2pZ6Aefus9x9X/J0DjC8jcWmAsvdvd7dm4CHgMuKFWOWheNPhaYmeOP1nt/4G6/TvG0LnHR6z29bRERE2pV6AdfK54En2pg+DFiT83xtMk06MmEy9D2Y6OUXe3zT0X8/QzhkAGHKh3p82yIiItK+opwDZ2azgbZu0X+zu/82WeZmYB/wyzaWC21Miw6wv+nAdAB3p6amptMxd0Z1dXXB99Ed2886n71/mM1hh9xE1cH9emSbzbt28tarL3HIeZfSf2hdj2wzi0q97QupknOHys5fuVdm7lDZ+Zda7kUp4Nz9/APNN7OrgEuA89y9rcJsLTAi5/lwoPEA+7sbuDt5Gm3atKlzAXdSTU0Nhd5Hd0QnnUk0+zE2Pf07qs44t0e22fz8k9DUxEHnXFzSuRdaqbd9IVVy7lDZ+Sv3yswdKjv/YuVeV5dfp0gpXIV6EXADcLa7725nsbnAODMbA6wDpgF/WaQQs+/oiXBELdF/PwM9VMBFLz4DQ0dQffRE2Fy4+8yJiIjIB5XCOXB3AgOAp81snpn9FMDM6sxsJkBykcNXgKeAxfEkX5hWwFkTQiCcfi4smU+0eWO3txetXwv1Swhnnk8IbR3dFhERkUJKvQfO3Y9uZ3oj8LGc5zOBmcWKq9yE088hevRXRC/9nnDJFd3aVvTi01BVRTjtIz0TnIiIiHRKKfTASRGEmiEw4Tiil54lam7u8naiXTuJ/utJwomnEw4d3IMRioiISL5UwFWQ8OELYOP6ePD5Loqe/R28s4dwifVgZCIiItIZKuAqSDj1LBgyjObHHuxSL1y0ZzfR7EfhhKmE4WMKEKGIiIjkQwVcBQlVveLz39Y1wKsvdXr96LmZsHsnVd08h05ERES6RwVchQlTPwy1w2h+7KFO9cJF7+whmvUbmHwSYfS4wgUoIiIiHVIBV2HiXrhpsK6B6JX8h9eK/Gew622qLr2ygNGJiIhIPlTAVaBw6lkwfAzRr35KtPmtDpeP5s0hemEW4cLLCWMnFCFCERERORAVcBUoVPWi6kv/APv20XzX7UTvvtvustH2rTTffyeMGEO4TINfiIiIlAIVcBUq1A6j6nNfg5VLiR6+hyj64BC00bbNNP/b92DvO1Rd8w1Cde8UIhUREZHWUh+JQdITTjqDcMEniWbNINqwjqorpxOGjQIgeuN1mu/+ATTtpeqa6wh1I1OOVkRERFqogKtw4S+uige6n/EAzbd8DY6sgx3bYPdOqB1O1fW3qngTEREpMSrgKlyoqiJ85GKik88kmulEWzYRJh4Phw8hnH0hoW+/tEMUERGRVlTACQBhwEDCFdekHYaIiIjkQRcxiIiIiGSMCjgRERGRjFEBJyIiIpIxKuBEREREMkYFnIiIiEjGqIATERERyRgVcCIiIiIZowJOREREJGNUwImIiIhkjAo4ERERkYxRASciIiKSMSrgRERERDJGBZyIiIhIxoQoitKOodDKPkEREREpK6GjBSqhBy4U+p+ZvVKM/ZTiv0rOvdLzr+TcKz1/5Z5+HMq/7HPvUCUUcCIiIiJlRQWciIiISMaogOsZd6cdQIoqOXeo7PwrOXeo7PyVe+Wq5PxLKvdKuIhBREREpKyoB05EREQkY6rTDiArzOzTwHeAicBUd3+5neUuAu4AegH3uvttyfQxwEPAYcCfgM+6e1MRQu82MzsMeBgYDawCzN23tlrmHOBHOZOOAaa5+2/M7D7gbGB7Mu9qd59X4LB7TD75J8vtB+YnT1e7+8eT6eXe9lOAfwcGAvuBW9394WTefWSs7dt7D+fMPwj4D+BkYDNwhbuvSubdCHyB+O9wrbs/VcTQuy2P3K8DrgH2AW8Bn3f3hmRem6//LMkj/6uBHwDrkkl3uvu9ybyrgG8l0//J3e8vStA9JI/cfwSckzztBxzp7oOSeZluezP7OXAJsNHdJ7cxPxD/bT4G7Cb+HPtTMi+1dlcPXP4WAJcDz7e3gJn1An4CXAxMAq40s0nJ7NuBH7n7OGAr8Yd8VnwTeCaJ/Znk+fu4++/dfYq7TwHOJX6Rz8pZ5O9b5pf6F3gbOsw/sScnx9wPsLJue+K2/mt3Pxa4CPixmQ3KmZ+Ztu/gPdziC8BWdz+a+EfL7cm6k4BpQMvf4d+S7WVCnrm/Cpzi7scDjwDfz5nX3us/E/LMH+DhnDxbirfDgG8DHwKmAt82s8FFCr3b8snd3b+e8xn/r8D/y5md6bYH7iN+z7bnYmBc8m868Q/W1NtdBVye3H2xuy/pYLGpwHJ3r096WB4CLkuq93OJP/AA7gc+Ubhoe9xlxDFDfrF/CnjC3XcXNKri6Wz+76mEtnf3pe6+LHncCGwEjihahD2rzfdwq2Vy/yaPAOcl7XwZ8JC773X3lcDyZHtZ0WHuyQ+1lvf1HGB4kWMspHzavj0XAk+7+5akh/ppDlwQlJrO5n4l8GBRIisCd38e2HKARS4D/sPdI3efAwwys6Gk3O4q4HrWMGBNzvO1ybTDgW3uvq/V9KwY4u7rAZL/j+xg+Wl88M19q5m9bmY/Sg5BZUm++fc1s5fNbI6ZtRQ6FdX2ZjYV6AOsyJmcpbZv7z3c5jJJu24nbud81i1lnY3/C8ATOc/bev1nSb75/0Xyen7EzEZ0ct1SlXf8ZjYKGAM8mzM5623fkfb+Pqm2u86By2Fms4HaNmbd7O6/zWMTbd09OTrA9JJxoNw7uZ2hwHFA7rk/NwIbiL/Y7wZuAG7pWqSF0UP5j3T3RjMbCzxrZvOBHW0sV85t/wBwlbs3J5NLvu1byee9mtn3eQfyjt/MPgOcQnx+Y4sPvP7dfUVb65eofPJ/DHjQ3fea2ZeJe2LPzXPdUtaZ+KcBj7j7/pxpWW/7jpTke14FXA53P7+bm1gLjMh5PhxoBDYRd7lWJ7/YW6aXjAPlbmZvmtlQd1+ffElvPMCmDJjh7u/mbHt98nCvmf1f4PoeCboH9UT+yeFD3L3ezJ4DTgT+kwpoezMbCDwOfCs5xNCy7ZJv+1baew+3tcxaM6sGDiU+/JLPuqUsr/jN7Hzi4v5sd9/bMr2d13+WvsQ7zN/dN+c8vYfk/Mdk3Y+0Wve5Ho+wcDrz2p0G/G3uhDJo+4609/dJtd11CLVnzQXGmdkYM+tD/EJ/1N0j4PfE54YBXAXk06NXKh4ljhk6jv0D50YkX/wt54N9gviCkCzpMH8zG9xyeNDMaoAzgUWV0PbJa30G8Tkiv241L2tt3+Z7uNUyuX+TTwHPJu38KDDNzA5KrjweB/xPkeLuCR3mbmYnAncBH3f3jTnT23z9Fy3ynpFP/kNznn4cWJw8fgq4IPk7DAYu4P1HIUpdPq97zGwCMBh4KWdaObR9Rx4F/trMgpmdBmxPfpym2u4q4PJkZp80s7XA6cDjZvZUMr3OzGbCe+fDfIW4ARfHk3xhsokbgOvMbDnx+TI/K3YO3XAb8FEzWwZ8NHmOmZ1iZve2LGRmo4l/pfxXq/V/mRxOnA/UAP9UjKB7UD75TwReNrPXiAu229y95UOs3NvegD8Drjazecm/Kcm8TLV9e+9hM7vFzFqurvsZcHjSnteRXJmbvNed+MvrSeBvWx1mKml55v4DoD/w66SdW77kD/T6z4Q887/WzBYmeV4LXJ2suwX4LnEhNBe4JZmWCXnmDvEP9IeSHywtMt/2ZvYgcVE6wczWmtkXzOzLyWFygJlAPfGFSfcA/wvSb3eNxCAiIiKSMeqBExEREckYFXAiIiIiGaMCTkRERCRjVMCJiIiIZIwKOBEREZGMUQEnIiIikjEaiUFEisrMzgK+DxwL7Ce+79TfufvcFGMaDawEdiWTNgE/dffb0oopX2a2CrjG3WenHYuIFI964ESkaJIht34H/CtwGPHAz/8I7D3QekU0yN37E9+w9P+Y2UWd3UAyvFYmJHeW1/eASAZl5oNGRMrCeAB3bxlubQ8wq2VmUkzcBHwROJh4RIOvuvv2nF6yzwO3EI8IcCPwCvHoCCOBX7j7V3K293ng74Fa4mGtprt7Q0dBuvtLZrYQmAw8aWZ3AJcTj3u6jLjH8IVkH99JlnuHeHil68zsdeAO4rvU7yEeE/c6d29K1omIx5P8ehLbj4H7gF8Q90w+CXwmZ/lLiEexGE080sOX3f11M3sgyfsxM9tPfCf47yfD/fwLMAloAL7m7s8l23oOeJF4DMeTgOOI7zAvIhmiX14iUkxLgf1mdr+ZXZyMH5jr6uTfOcBY4iLtzlbLfIh4nNEriAufm4HziQsfM7OziR98grgYvBw4AniBVuP0tiXplToz2d6ryeS5wBTiXsNfEQ8l1TdntcuAR4BBwC+JDw1/nXj4sNOB80iG38lxEXAycBrwD8DdwF8RD0c3mbgXEDM7Cfg58CXiodjuAh41s4Pc/bPAauBSd++fFG/DgMeJC77DgOuB/zSzI3L2/VlgOjCAuMATkYxRD5yIFI2770jOgbuBeEzB2mQs4S+6+5vEBcy/uHs9gJndCCwws8/lbOa77v4OMMvMdgEPtgysbmYvACcSj8f7JeCf3X1xMu97wE1mNuoAvXCbgAjYAHzT3Z9J4v5FzjI/NLNvAROA15JpL7n7b5LHe4h7BVusMrO7gLOJC84Wt7v7DmChmS0AZuXk/USSx/3EvZF3ufsfk/XuN7ObiAu/1uMOA3wGmOnuM5PnT5vZy8DHku0B3JczTrOIZJAKOBEpqqSguhrAzI4hPmz4Y+Iepzre3yPUQPw5NSRn2ps5j/e08bx/8ngUcIeZ/TBnfiA+7669Aq4mGdj7fczsG8A1SXwRMJC4d63FmlbLjyc+hHkK0C/JIbeoyyeP2pw8rjKzr+bM75PE0pZRwKfN7NKcab2JBxpvM14RyR4VcCKSGnd/w8zuI+4tA2gkLkBajAT2ERc3wzu5+TXAre7+y+7EaGYfJu4xPA9Y6O7NZraVuBhsEbVa7d+JD79e6e5vm9nfAZ/qYggtedzazvzW+14DPODuXzzANluvIyIZowJORIom6XH7c+Bhd19rZiOIe97mJIs8CNyQHEJ8C/hesuw+M+vs7n4KfNfM5rn7QjM7FLjA3X/dye0MIC4i3wKqzeybxD1wHa2zA9iZ5Pw3yfpdcQ8ww8xmE1+I0Y/4AoTn3f1t4uJ2bM7yvwDmmtmFwGzi3rfTgOXuvraLMYhIidFFDCJSTG8TX4Twx+T8tTnAAuAbyfyfAw8AzxNfcfoO8NU2ttMhd58B3A48ZGY7kv1c3IVNPQU8QXwBRkMSU0eHIK8H/pI433uAh7uwXwDc/WXi8+DuBLYSXzF6dc4i/wx8y8y2mdn17r6G+KKKm4iLxjXEV+Lq816kjIQoUk+6iIiISJboF5mIiIhIxqiAExEREckYFXAiIiIiGaMCTkRERCRjVMCJiIiIZIwKOBEREZGMUQEnIiIikjEq4EREREQyRgWciIiISMb8f5n6AGaAwTdOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca()\n",
    "x = np.linspace(-1, 1, 200)\n",
    "hz = 10\n",
    "cost = np.sin(hz*x)*np.exp(-x)\n",
    "ax.plot(x, cost)\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_xlabel('Some Parameter')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll never really ever be able to see our entire cost function like this.  If we were able to, we'd know exactly what parameter we should use.  So we're just imagining that as any parameters in our network change, this is how cost would change.  Since we know the value of the cost everywhere, we can easily describe the gradient using `np.diff`, which will just measure the difference between every value.  That's a good approximation of the gradient for this illustration at least."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "gradient = np.diff(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we follow the negative gradient of this function given some randomly intialized parameter and a learning rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4mI8VbwDSsRPeaePxvnsX8sV/gnW1hD/6FuE7rztIboxJBSvgUqWpma9tZIiJZYugU2cob90hwbHXt3+03mnRPNdJTBqEzz6GPnYfDB+N94OfRw2dW0FE8MZOwPvh/8Jxg9H7/5vwuceiM4GNMRnNCrhU6ZmIdjxaL7hY0BWL4NhBWbMOSLw8qBxmG2WynKoSPv0I+swjyOln4/3j95Au3dr8PNK1G943foicfg769CPoo/dZEWdMhsuO72YxJHl5URFnveCc0717oXoFMmCw6yhJJccPh/Vr0C0bXUcxKaIvP4U+91i0CeH6r7frBBEpKEC++E/I+Zehk59Hn3k0iUmNMelmBVwqJcpRWwPn3uqlEIbIgErXSZJKBjetg1to6+CykX44C33yQRg9FrnulqQc/yYiyKe/iIw7F33uMcJXn01CUmOMC1bApZCUlIGtgXNOl0UbGLJlB+p+xwyATkVgGxmyjm5YS3jfT6B3X7wv/lNSp/5FBLn2Zhh1Gvr4/ejc95L23MaY9LECLpVKymDLJrS+3nWS3LZiMRSXIt17uk6SVOLlwaAq24maZbShnvDeO0FDvJu/n5LG05KXh/flb0Gf/oT3/8xmCozJQFbApVLTTlQ2bXCbI8fpsoVZ0z7kYDJ4OKytQbdudh3FJIk+/wSsWhbdeStL3a5pKSzE++ptEDYS/vpO+0HTmAxjBVwKSaKpF5xNozqj27ZEvfiytYCzfnBZRVctQ194AjltPDLytJRfT8or8L74DVi5BH3y9ym/njEmeayAS6WSpl5wthPVnRWLAbJuA8N+/QZCYSdbB5cFtKGB8A/3QOeuyNU3pO26Muo05JyL0dees7Y0xmQQK+BSqWcx5OVZLziHdMUSEIkKnSwkeXlQOdR2omYB/etfYPVyvGv+EencNa3Xliuug7LehL+/B92zO63XNsYcHSvgUki8PCguteO0HNJVS6FX35QsBI8LOX44rFkdTRebjKRbNqGTnoCRpyKjUj91ejAp7Ih3/T/Bpg3on/6Q9usbY9rOCrhUKymz47RcWrkE6Z+dd9+aNa+DY7Edq5Wp9Kk/QkMD3lVfdJZBKquQcy9F//YCake0GRN7VsClmCTK7Q6cI7p1M2zZBFlewNF/EBR2tGnUDKWrlqJTXkUmXJzSXaetIRM/D8WlhI/cizY2Os1ijDk8K+BSraQMtm5G9+11nST3rFwCgPQb5DhIakl+PgwcYjtRM5CqEj7+u2jjwqd813GiqdTPfBlqVqKTn3cdxxhzGFbApVpzK5GN1gsu3XTl0qYNDMe5jpJycvzw6Jvu9m2uo5i2mPc+LJqLXPpZpKiL6zSRUafDsFHoM49Yf0FjYswKuBSTplYidqh9+unKJVDeJ6s3MDRrPhfV1sFlDlUlfPbR6JSQM893HWc/EcH77D9A/T7b0GBMjFkBl2pNpzGotRJJvxzYwLDfsZXQoYNNo2aSee/DsoXIp65C8gtcp/kIKa9AJlyKTvsbumqZ6zjGmBZYAZdq3XtCXr6dxpBmf9/AkN3r35pJfgEMtH5wmUJVCZ95BErKkLETXMdpkVz0aSjqQmh34YyJJSvgUkw8D0qsF1zaNW9gyJU7cIAMqoKaFeiuna6jmCOZNxOWL0Iuit/dt2ZS1AW52IcPZ6FzZ7qOY4w5iBVw6ZAoR62AS6tc2sDQTCqrQBWWLnAdxRxBOOmJaO3b2HNcRzksGX8RlPYi/NMf0NDaihgTJ1bApYGUlNkUappFGxgqkI5FrqOkz3FDIC8PtY0MsabLFsLiD5HzJsb27lszyS9ALr8Wqleg777hOo4x5gD5rgM0833/QuAeIA+4PwiCOw/6/PXAT4Capg/9MgiC+9Ma8miVlMH2rejePUhhR9dpcsOqZUjlMNcp0koKC6HfQHTxh66jmMPQvz4FnTojZ5zrOkqryJhxaN8n0WcfQ08+Kzp/1xjjXCzuwPm+nwf8CvgkUAV81vf9qhYe+ngQBCObfmVG8Qb7d6LaOrj00B3bYHMd9BvgOkraSeUwWLEIrd/nOoppgW5Yi86cipx1QcbcHRbPw5v4OVi/Bp36mus4xpgmsSjggFOAJUEQLAuCYB/wGDDRcaakkeYCzqZR02P1cgDkmFws4IZCQwMsX+w6immBvvoseIJMuMR1lLYZcQr0H4Q+9zjaUO86jTGG+BRwfYDVB7xf3fSxg13p+/5s3/ef9H3/mPRES4KS6DQG28iQHlq9Inqjb+4VcAyKblzbOrj40Z070LdeRk4+C+lZ4jpOm4gI3sTPw8b16FuvuI5jjCE+a+CkhY/pQe8/CzwaBMFe3/e/CjwItLiFy/f9G4EbAYIgIJFIJDPrx+Tn5x/2GlpSwvoOHei0cztdU5wl3Y40dhe2rq9lX88SSo9LfQ+42I0/kaDumAHkrVpKT8ev+2zX1vHvnPoqO/buoedV11GQgX9vOv58Nr/0Jxpf+jN5V16Ts197e93n7vjjNva4FHDVwIF31PoCtQc+IAiCjQe8+1vgrkM9WRAE9wH3Nb2rdXV1SYrZskQiwRGvUVzKrtUr2JviLOnWqrGnWeOSBdCnf1pyxXH84YDBNE5/gw3r1yFe6hacx3Hs6dSW8WsYEj73BAwcwtZuJZChf296wRWEP/8hOyZPYueJp7qO44S97nN3/Okae0VFRaseF5cCbjpQ6fv+AKJdplcDnzvwAb7v9w6CYE3Tu5cC89MbsZ1KymwTQxpoQz2sWY0MH+06ijuVVfDGi1C9Mqf64MXagtmwvha55DOuk7TP8DHQdwA7//xHdPjJUaNyk3N0XS26dAHUrkLX1cK+vdDYAPn5SHFpdMLIgEoYWBXtjjcpEYsCLgiCBt/3bwFeImoj8kAQBPN83/8hMCMIgmeAr/u+fynQAGwCrncW+ChIojzqTWZSa0119B9JDm5gaCaVw1BAF3+IWAEXC+HkSdClGzJmnOso7SIiyCevpPG3P8WbNQ1Gj3UdyaSJ1q1D3/wrdbOnEzavM87Ph9Le0KkoenvH9ujs3O1bozVQeflQWYWMnYCMHmvFXJLFooADCIJgEjDpoI/dfsDb3wO+l+5cSVNSHr249+zKmPYBmUhzeAdqMykpheJSWDwPJlzsOk7O000b4IN3kQsuRwo6uI7TbjJmHN6zj9I46Um8Uacj0tISZpMtdPVy9IUn0Rlvg0DesFGEZ5yPVI2AsooW+wLqnl2wZD66YDY6cyr6wN3oo/dF7XMuvALp0s3BSLJPbAq4rJeIdqJStx76Hus0SlZbvRw6dIDy1q0hyFYyqApdOBtVtW+wjukbLwGKfOJC11GSQvLyKLr8Grb/+i6Y/wFUjXQdyaSA7tyOPvVH9PUXobBjdHLIhEvoefyQI64Dk45FMHwMMnwMesUXYPE89PUX0b/+BX39hei5LrwS6WB35NrDFjCkiTS1ErF1cKml1cuhon9KF+9nhMoq2LoZNqw58mNNymhjI/r2K9E3s+Z+kFmg09mfhB7FhC886TqKSQGdOYXwX25CX38JOedivLt+h3fVF5Hitu/AFM9DBp+Ad+O38X7wC6gaiT77GOEdX0M/nJWC9LnDCrh0afrPW+usgEsVVYXVy3N6+rRZ8zFiujiz9vpknXkzYcsmvAw5Nqu1pKADct5EWDA7OtvVZAWt30f4yL2Ev74TSsrw/vVuvKtvQIq6JOX5pU8/8m76Ht43/x1ECO++nfChX6J79ybl+XONFXDp0rV7NLVnpzGkzuaNsHN7Tm9g2K93X+jcNVoHZ5wJ33o5+rd/4smuoySdnHUBFHWxu3BZQrdsJLzrNnTyJOT8y/BuuytlPwzL0BF4d/wCufBK9K2XCf/zW2jNqpRcK5tZAZcmIgIl5ehGK+BSxjYw7CeeB4OG2sH2Dum2LTB7OnL62Uh+ges4SScdi5BzLoZZ79g33wynNasI/+vbsLYa7+Z/xrvqSyl/zUpBB7wrv4D3jTtg+1bC//wmOuOtlF4z21gBl06JclsDl0JaHRVwtkkkIpXDYH0tunWz6yg5SadNhsZGZFx2TZ8eSCZcDB0K0Rf/5DqKOUq6aB7hXd+FxhDvO/+FjExvg2apGoV3+z1wzHGEv/kx4XOPR8thzBFZAZdGUlJmU6gppKuXQWkva9PSRAYNjd5YYnfh0k1VozNDjxuMVPRzHSdlpEs35KwL0OlvoJtyszt/JtNF8wh//m/QvSfe936C9BvoJIf0KMb71n8gp34Cffph9Pf/gzY0OMmSSayAS6dEGezaie7a4TpJdlq9wta/Haj/QOjQwaZRXVi+KDoR5IzzXCdJOZlwCYSKTn7edRTTBvuLt54JvFt/FPWPdEgKOiBf/iZy6efQqZMJ770Trd/nNFPcWQGXRvvbCGzc4DZIFtI9u2HDGqSvFXDNJL8ABgxGbSND2unUyVDQIeNPXmgNSZTD6NPQN15C9+5xHce0gq5cSvjzH0LPkujOV/eeriMB0Vpx75Krkc99FWZPJ/yfO6KmwKZFVsClU3MvOJtGTb6alaBqGxgOIpXDYPUKdLf9J5gu2lCPTn8TGXkqUtTZdZy08M6dCLt2oFNecx3FHIFuWBvdeevcBe+b/4H0KHYd6WO8sy9CvvxNWPIh4T3/ZkXcIVgBl04lTb3gbCdq0jUfoWVTqB8llVWgISxd4DpK7pj7Huzcjpw23nWS9Bk4BAYcj77yDBqGrtOYQ9Ad26LiraEB7xt3ID1LXEc6JO/UT+DdcCssW0j48x9GsyzmI6yAS6cuXaGwU3Sclkmu1cuhqHN0Bqj5u+MGg+fZOrg0Cqf+Ler9VjXKdZS0EZGose/6Wpgzw3Uc0wJtaIga9Natx7vlX5Dex7iOdERy0hnIV74FSxYQ/vI/bE3cQayASyMRgUQZalOoSafVy6HvADv38yDSsRP0G4gusXVw6aC7dsDsd5FTzkLyc+uoaRk9FooThC8/7TqKaYEG98OiucgXvhbdmc8Q3slnIl/6BiycQ3j/f6Nho+tIsWEFXLqVlFkvuCTTsBGqV9j6t0OQQVWwbBFaX+86StbTGW9DQ0NuTZ82kbw85JxLYOEcdNUy13HMAcI3//r3ExYy8LXpnTYe+cyXYeZU9OF7rU9cEyvg0kyamvnaCzCJ1q+FfXtt/dshSGUVNNTDysWuo2Q9fedv0Ksv9B/kOooTcuZ5UNgRfcXuwsWFrliMPnIvVI1ErviC6zhHzTt3IvLJK6Pdzs886jpOLFgBl24lZbB7F1gvuKRRO0Lr8JqmS2wdXGrppjpY/CFy6lk5O5UvRV2Qceei776JbtnkOk7O0107Ce/7CXTrgXfDrUhenutI7SKXXxe9vp57jHDyJNdxnLMCLs0k0dxKxKZRk6Z6OeTlQe/s7XjfHtK1O/TqawVciul7b0etbE4603UUp6LGvo2ofYN1SlUJH/oFbFyPd8O3kS7dXEdqNxFBrr0ZRpyCPvqbnD871Qq4dCtpbuZrGxmSRVcvh159kYLsOzA8WaSyCpbOtxYPKaTT34R+xyG9+riO4pSU9YYRp6Kvv4Du3es6Ts7S11+A96Ygl1/792P1soDk5eHd8G0YOITwdz9Dl8x3HckZK+DSrek0BrU7cMmzerlNnx5J5TDYtRNqV7pOkpW0bh0sX5Tzd9+aeedNhJ3b0WmTXUfJSbpmNRo8AMNHI+df7jpO0klhId7N/wzFpYT/+58529nBCrh0K+oMnYrsNIYk0Z3bYctG6NPfdZRYa/4J3KZRU6N5KkdOyv6js1qlsgr6D7LGvg5oQz3h/T+Dwo541/8T4mXnt3np0g3va/8KjQ2Ev/h3dNdO15HSLju/sjEmIlBShlorkeSoWQWA9DnWbY64S5RDjxKwAi4ldPqbMOB4pLSX6yixsL+x79pqmDfTdZycos88CquW4l13S2zOOE0V6dUX76u3wboawt/+BG3MrR5xVsC50NRKxLSfNk8J9rENDIcjIkhlFbp4nrWwSTJdVwurliEnneE6SqzImHHQo8Qa+6aRLl2AvvhnZNy5yKjTXMdJCxk6AvncV2HuTDT4nes4aWUFnANSUgZ16+wbaTLUrIJOnaFnwnWS+KscBls22fR9kun0NwGbPj2Y5Ocj53wK5n8QnZRiUkrr6wkf/AX0LEa3rk/jAAAgAElEQVQ+8xXXcdLKO+sC5PzL0NeeI5z8vOs4aWMFnAuJMti7B3Zsd50k42ntSujTL2f7brWFWD+4lNAZb8GgKsTO4f0YOesC6FCIvvyM6yhZT59/HNasxrvmZqRTkes4aSdXfqGpvchv0Xnvu46TFlbAOSAJayWSDKoK1SuRCtvA0CoV/aCoCyyxAi5ZtGYV1KxETrbp05ZI567IuAnou6+jWze7jpO1dPVy9MU/IaedjZwwxnUcJ8TLw/vKN6HiGML7foyurXEdKeWsgHOhuRecTWW1z9ZN0YkWtv6tVcTzYNBQdLEdbJ8sOuNNEC9a72VaJBMuhcZG9G/W2DcVtLExmjot6hKdF5rDpGMR3i3/Al4e4S//A92Z3SceWQHnQkl0GoPtRG2n/TtQ7Q5ca8mgKlhbg27b4jpKxlNVdPpbcPywrN/t1x5SXhFNbf1tErrPGvsmm778FKxcgve5f8iK0xbaSxLleDd9D+rWEd6X3TtTrYBzQIo6R1NZ1sy3XbSmaQeqTaG2WvM6OJtGbb+GFYthXQ1ysjXvPRLvvImwYzs61Rr7JpOurYnahow6Dewu8H5y/DDk81+FD99Hn3jAdZyUsQLOlURZznaPTpraldC9J9LVfupstWMHQUEH28iQBHveehU8Dxk91nWU+Ksc1tTY92lr7JskGobRWacFBXif+6pt5DqId+b5yLkT0VefJXzjJddxUsIKOFdKyqwXXDtpzapoYb5pNckvgAHHWwHXTqrK3rdfhSEj7AeIVvh7Y98amPue6zhZQd96GRZ/iFz1JaRHses4sSSfvh6Gj0YfuRddONd1nKTLdx2gme/7FwL3AHnA/UEQ3HnQ5wuBh4AxwEbgM0EQrEh3zmSRRDk6byaqaj85HQUNQ6hdFbUpMG0ilVXopCfRPbuQjrnXbiApVi+jcV0tcsEVrpNkDBkzDv3Tg4QvP03eiSe7jpPRdPs29M8PwfHDkXHnuo4TW80H34f/9W3Ce/8L7/v/nVWnpcTiDpzv+3nAr4BPAlXAZ33frzroYV8GNgdBMAi4G7grvSmTrKQc9u2D7baY/KjUrYN9e+0O3FGQymGgISxb6DpKxtL3pkbTpyNPdR0lY0h+PjLhYlgwG121zHWcjKZ/fhD27LKp01aQos7RztRQo52pu3e5jpQ0sSjggFOAJUEQLAuCYB/wGDDxoMdMBB5sevtJYILv+xn7ypVEtBPVNjIcpaYjtGwH6lE4bjCIZ9Oo7aAzp1BQNRLp2t11lIwiZ54PhR3RV+x4raOlSxegb72MTLgUsRZKrSLlFXhf/S6srSa8/7/RMDt2psalgOsDrD7g/eqmj7X4mCAIGoCtQEla0qVCUzNfayVydLSphQgVx7gNkoGkUxEcM8AKuKOktatgbTUdTz/bdZSMI0VdkDPOQ999E92y0XWcjKONjYQP/xp6lCCXXO06TkaRoSOQq2+A2dPRv/zRdZykiMsauJbupB18UGhrHgOA7/s3AjcCBEFAIpHaczLz8/PbfI2wcyc2AJ13badzivOl0tGMPRm21K2lobyCRF+3P4G6Gn97bT9xDLv++hQl3bsjBQVH9RyZOvb22vHas+wEOo87h6Ic7f/Wnq99w6evY+Pk5+k0bTJdrvlqkpOlnsvX/a7nn2D76uV0//Z/0LGvmx9eM/nfvX76OrZvXM/uF/9E58FVdBr/yTb9+biNPS4FXDVw4KuxL1B7iMdU+76fD3QHNrX0ZEEQ3Afc1/Su1tXVJTftQRKJBEd1jS5d2blqBbtTnC+Vjnrs7dS4fDH06uvk2gdyNf720r7Hwb591M18Bxk45KieI1PH3l6Nb74CA4eg3Xvm5PihnV/7/EIYeRo7X/gzu8++GCnsmNxwKebqda9bNxM+/BuoGsX2yhPY4ei1l+n/7vWya2HFErb96k52dOwcNTdvpXSNvaKiolWPi8sU6nSg0vf9Ab7vdwCuBg4+/fgZ4AtNb38aeC0IghbvwGWMknLUzkNtM22oh7XViG1gOHqVQwHsWK020vVroHq59X5rJ++8ibBrBzrlNddRMoY++Xuo3xeduGAbF46a5OdH6+FKygh/+SN0bbXrSEctFgVc05q2W4CXgPnRh4J5vu//0Pf9S5se9jugxPf9JcA3gdvcpE2ihPWCOyrraqGxEWwDw1GTbj2hvA+6ZL7rKBlF358KgIw+3XGSDDdwSNSP0Br7toounINO+xtywRXR0WSmXaRLN7x/+gF4HuH/3IFu3ew60lGJyxQqQRBMAiYd9LHbD3h7D3BVunOlkpSUox9MR8MwOmjctErzEVq2A6t9pLIKnTnVXn9toO9Ngf6DkKZNSOboRI19L0Pv+zHMng7WjuWQtKGB8OF7oaQM+WRWfQt0Skp74X3tdsKffp/wF/+Od+uPkI6dXMdqE/tf26VEGTTUgx0s3jY1q8DzoLyv6ySZbVAV7NoBa1Yf+bEG3VQHyxcho05zHSUryOjTobiU8GVrKXI4+uozsGY13mdvRAoLXcfJKjKgEu/G78CqZRl58L0VcA7t/yneplHbRGtXQnmfo949aSLNB9vbOrjW2T99OsbWvyWD5OUhEy6BRXPR5Ytdx4kl3VSHPvsYjDgFGXGK6zhZSUacHB18P2cG+vCvUc2cpfVWwLlUEjXztUPt26hmpTXwTYbSXtC9GKwfXKvozClQ0Q/pZXd+k0XOOh+KuhBOesJ1lFgKg/shDPE+8xXXUbKa94kLkYuuQt/8K/qXhzKmiLMCzqWS5tMYrIBrLd27J/r7svVv7SYi0Tq4xR9mzH9Yrui2zdHB4bb7NKmkY1F0vNasafvXtpqIznsf3puCXHRVVp3fGVdy2TXIWRegL/wpuuuZAayAc0gKO0LX7jaF2ha1q0EVqbA7cElRWQWb6+w1eAQ6653odTfGdp8mm0y4BAo7oZOedB0lNrR+H+Ej90JZBXLBFa7j5AQRQT5/EzJ2Avrso4QvxP/1aAWca4lym0JtA206A9VaiCSHVA4DQJfYNOrh6HtToaw39DnWdZSsI527IuMvRKe/ia4/uH97btKX/gzr10Q932ytb9qI5yFfuAU55RPonx+K/QabVhdwvu/feoiPfzN5cXKPlFgvuDapWQkdOkCptXFIij79oFORrYM7DN25AxbORkaPtQaqKSLnXQZ5eeiLf3YdxTndsBad9CQyZhwybJTrODlHvDzkS9+AMWPR4HeEk593HemQ2nIH7vZDfPxfkhEkZyXKYeMGa2bZSlqzCnr3Q7w811Gygnh5MHCoHWx/GPrBu9DYaOvfUki694wOuZ/yGrppg+s4zqgq4aP3gech/pddx8lZkpeH95VbYcQp6CO/IXztOdeRWnTERr6+75/T9Gae7/tn89FD5Y8DtqciWM4oKYPGBtiyCYrjc0hubNWsRKpGuk6RVaSyCp37Hrp9G9K1m+s4saMzp0T/No8d5DpKVpMLr0DffAn961PI1Te4juPG+9Ngzgzkqi8i9v3AKcnPx/uH7xL+5i700fsId+5Ar7/ZdayPaM1JDL9r+r0j8MABH1dgHfC1ZIfKJZIoQyGaRrV/sIelO7bB1k22/i3JpHJY9Bpc8iFYk9qP0D27YN77yCcutOnTFJOSMuTU8VERd9FVSLceriOlle7ZTfjYb6FPf+ScS1zHMYAUFODd9D30wV+gzzzC9sZ96KXXxObkmiMWcEEQDADwff+hIAiuS32kHNPUzFc3rtvfWNUcQu0qwI7QSrpjKyG/AF08z04ZOIjOmQkN9Xb2aZrIJ69Ep76GvvI0csUXXMdJK332Mdhch3fjrUh+bE65zHmSlwfXfx06d2XfzGlw3uXQuavrWEAb1sAdXLz5vn+27/tnJj9SjikujX63nahHpDVRAYe1EEkqKSiAAZW2Dq4lM6dErX4GDXWdJCdIr77ImHHo5EnR5pEcodUroqL1jPOQQfaDfNyI5yH+lyj+ye+QmBRv0LZdqK/7vj+u6e3vAo8Bj/m+//1UhcsF0qEQuveEOtuJekS1K6FTZ+hZ4jpJ1pHKYbBqKbpnt+sosaH1+9A5M5BRp9ummTSST10Fe3ajLz/lOkpaaBgSPvxrKOqMXJlbdx0ziYjgxah4g7btQh0OTGt6+wZgPHAa8NUkZ8o9JWWotRI5Iq1ZGa0PsbVISSeVwyAMYekC11HiY977sHePTZ+mmfQdEN2Fe+VZdPtW13FSTqe8CkvmI1dej3SxTUSm9dpSwHmA+r4/EJAgCOYHQbAa6JmaaLlDEuU2hXoEqtp0Bqqtf0uJyqqoD9eC2a6TxIbOnAJFnWHwCa6j5ByZ+HnYtxfNgG747aE7tqF/+gMMGoqMneA6jskwbSng3gJ+CfwU+AtAUzFXl4JcuaWkDDbXoY2NrpPE15ZNsGun7UBNESnsCAOORxfOcR0lFrShAf3gXWTEKbag3AHp3Rc5bXy0Fm7zRtdxUkaf/D3s2on3+Ztis7PRZI62vGKuB7YAs4E7mj42BLgnuZFyUKIMGhujIsW0rOmgazsDNXVkyImwYgm6a6frKO4tnAO7dlrzXofkkqtBQ/T5x11HSQmd9z769qvIBZcjfY91HcdkoFb/aBkEwUbg+wd9LL5nTGQQSZQ39YJbByWlruPE0t/PQLUp1FSRwSegzz0eHas14mTXcZzSmVOhsCNY02hnpLQXcuYF6BsvoudeivTq6zpS0uieXYQP/RJ69UUu+azrOCZDtbqA832/gOjYrGuBCqAW+D/gR0EQ7EtNvBxR0tQLrm4dcvxwx2FiqmYVdC+2Rb6pNHBI1A9uwWwkhws4DRvR96ciJ5wU7RI3zsglV6PTJhP+6UHybv5n13GSRv/0UNTz7bt3IQUdXMcxGaotU6g/Bs4l2nU6oun3c4C7UpArtxSXgohtZDiMaAeq3X1LJSnoAAOH2EaGJfNh+1aw3afOSbceyIVXwqx30IVzXcdJCl04F/3bJGTCJcjAIa7jmAzWlgLuKuDSIAj+GgTBwiAI/gpcDvipiZY7pKAAepTABivgWqJhI6xZZevf0kCGnAjVy6Njy3KUzpwK+QXICWNcRzGAnDcReiYIn3gADUPXcdpF9+4lfPDnUNoLuewa13FMhmtLAXeo5lvWlCsZSnuhG9a4ThFPdetg3z67A5cGMqSpZUaW3O1oK1VF358Kw0YhHYtcxzFEzc7l8mth5RJ02t9cx2kXfeZh2LAW77pbop3fxrRDW/bHPwE86/v+vwGrgP5Ea+KeSEWwXCOlvdA5M1zHiKea5jNQ7Q5cyh1bCYUdo3VwY3JwB+aKJbCpLupDZmJDTv0EOvl59MnfoyNPQYq6uI7UZrp0AfryM8hZF0Z3uo1pp7bcgfsO8ArwK+A94BfAa8C3U5Ar95T2gm1b7CijFmhTCxF6H+M2SA6Q/AKorEIXfOA6ihM6cwrk5SEjTnEdxRxAPA/v8zfBju3o04+4jtNmuncP4R/ugR7FyKevdx3HZIkj3oFrOv/00iAIvgvc3vSr+XN3AaP5+xFb5miV9Y5+r1sLfQe4zRI3tauiNSMdO7lOkhNk6Ej0iQfQTRuQ4txpa6OqUQE3+IRYHVhtItJ/IDL+wqi577gJSL+BriO1mgYPwLpavP/3Q6STTc2b5GjNHbjvA28c4nOTgezZ2+2QlPaK3li/1m2QGNKalVBh69/SRZp6n+mHsxwnSbOalbB+jTXvjTGZeA106Ur48L3R5qYMoLOmoW+8iJx/GTJ0hOs4Jou0poAbCbx4iM+9AthWrWQoje7A6QYr4A6kDfWwrsbWv6VTn/7QvSfkWAGnM6eACDLyVNdRzCFI5y6I/yVYthB95VnXcY5It2wkfPAX0G+g7To1SdeaAq4bcKhOgwWAzTUkgXTuAkVdwHaiftTamuiYMbsDlzYiggwdgS6YnfFtG9pCZ06NDhXv3tN1FHMYcup4GHEK+tQf0bU1ruMckjY0EP7mx1Bfj/eVb0XrS41JotYUcAuA8w/xufObPm+SobSX3YE7SPMGBrsDl2ZDR0bNbKtXuE6SFrquFmpW2vRpBhARvGtugoICwj/cE9upVP3LQ7BkPnLdLUjv7DkGzMRHawq4u4Hf+L5/he/7HoDv+57v+1cA9wI/S2XAXCJlvcEKuI+qXQV5edCrj+skOaV5rY7Oz41pVJ05BQAZZacvZALpUYJcfSMsXYC+9JTrOB+jM6egf30KOfsivFPOch3HZKkj7kINguAR3/d7AQ8Chb7v1wEJYA/wgyAIHm1PAN/3i4HHgWOBFYAfBMHmFh7XCMxpendVEASXtue6sVTaC957G21oQPLb0qIve2nNSijvY9MPaSY9S6D3MdFGhguucB0n5XTG23BsJVKSO7tuM52cNh794B30qf9DK4cig6pcRwJAq5cTPnAPDDgeuerLruOYLNaqPnBBEPwM6ANcAtza9HvfIAjuTkKG24BXgyCoBF5ter8lu4MgGNn0K/uKN4gKuDCETRtcJ4mP2lU2feqIVI2ExR+i9ftcR0kpXVcLq5YiJ5/pOoppAxHBu+5rUFJGeN9P0e3uj3/TrZsJf/Hv0KkI7x+/Fx2TaEyKtPo2TxAE24CXUpBhIjC+6e0Hgb8B303BdWJPSnujEE2jNveFy2G6Z3f0dzF2gusoOUmGjUJffRYWz4OqUa7jpIxOfxMAOWmc4ySmraSoM94/fJfwzm8TPnA33tf+BfHynGTRfXsJf/Uj2LEd77t3Ij1KnOQwuaMtJzGkSnkQBGsAmn4vO8TjOvq+P8P3/Wm+71+Wvnhp1NQLzs5EbbJmNWAbGJw5/gTIL0DnzHSdJKV0xlswqCqnmhZnE+k/EPnMDTD3PfSJ3zvJoA31hPfeBSsWRztOM6jJsMlcaVlo5fv+K0CvFj7VlibA/YIgqPV9/zjgNd/35wRBsPQQ17sRuBEgCAISiUSbM7dFfn5+Uq6hxcWsL+hApx1b6ZrizMmSrLG3ZPesaWwDeg4fSX5M/z5SOf442Dx8FI3zZ7U4xmwYe8OqZWysWUnXG75FURvHkg3jP1qxG/unr2X7tk3sevZxivofR9HFfsoudfDYtbGBrT+7g71zZtD1pu9QdN7FKbt2HMTua59GcRt7Wgq4IAjOPdTnfN9f5/t+7yAI1vi+3xtYf4jnqG36fZnv+38DRgEtFnBBENwH3Nf0rtbV1bUn/hElEgmSdo1EObtWLmdvijMnS1LHfpBw4Tzo0IHNeQVITP8+Ujn+OAgHn4jOup8N8+f+/bSQJtkw9vDlZ0E8dg45kV1tHEs2jP9oxXHsevHVsHol2x+4h50FhciY1EyJHzh2bWxEH/w5OnUyctWX2DX6jDa/jjJNHL/26ZKusVdUVLTqcXGYQn0G+ELT218Anj74Ab7v9/R9v7Dp7QQwDvgwbQnTqbSXNfNtorUroXc/Z2taDMjw6KAVnZt906iqir77Jgw5AelmzXsznXh5eF/5Fhw3mPC+nxC+e6gTIJND9+0l/PV/RcXbxM/hnZ+dK3tMfMWhgLsTOM/3/cXAeU3v4/v+Sb7v39/0mKHADN/3PyA6f/XOIAiysoCT0l5Qtw5VdR3FvRrbgepceUXUYHrue66TJN/qZbC+FjnpDNdJTJJIYSHeN+6AQUPR+39G+ParKbmO7txOePcPYPZ05HP/gHfx1Sm5jjGH47zZWBAEG4GPbTMMgmAG8JWmt6cAJ6Q5mhulvWHvHti2JTqPMkfpjm2wdRP0sSO0XBIRZPgY9O2X0fp9SMGhTtXLPPrum5CXh4y25r3ZRDoW4X39DsL//RH6h3sI11UjE69B8pJzJ79+0TzCH/8zbN2Ed+O37QcA40wc7sCZA0hZ0zqj9Tk+jVqzCgCpsDtwrskJY2DfPlg0z3WUpFHVaPdp1SikSzfXcUySSWEh3i3/ipx1AfrCnwjvvp2NjzzN3LFX8/6x5zB37NVseuqVNj2nNjYSvvRnNn3/qwB437nLijfjlPM7cOYgB7QSkcp4dBZ3QWujM1CxKVT3jj8BCjqgc99DhmVJP7hlC2HjeuTSz7lOYlJECgqQa28mHDiETXfdTfWcKWjTsan1NetYddtPASi+7JB77PbTD98nfPx3ULuKwtPGU//ZG5GiLqmMb8wR2R24uCkpBxE7E7VmJRR1hh7FrpPkPCkshMEnoLOnZ83aTJ3xFuQXICNPdR3FpJg3dgJr13bcX7w10917qf3x/S3/IZo2KUybTONdt0Xr3er34f3j9+n+nR9Z8WZiwe7AxYwUFEDPBKzP7QJOa1ZBn/6IiOsoBpARJ6MP3xs1V67I7HWJGjai09+CE8YgRZ1dxzFpUL9uU8sfr1lH+Oh90Lsv5OVDYwNsqkOXL4Lli2HvbijrjVz1JeTsi5CCDvZ/kokNK+DiqLRXTp/GoKpQsxI59SzXUUwTGXEq+vC96Kx3kAwv4Fg8H7ZusrNPc0hBRRn1Nes+/vEuHdC3X40KtWZ5edB3AHL6eGT0WBh8AuLZZJWJHyvgYkjKeqPvT3Mdw53NG2H3TrANDLEhPUvg2Ep01jtw0VWu47SLzngTOhQiJ57sOopJk4rvfIVVt/0U3b13/8ekUyEVP7oV79JzYOtmUIX8POjUOat2W5vsZT9WxFFpb9ixDd29y3USN5o2MIi1EIkVGXkqLF+Ebml5OioTaEM9Ov0tZMQpSGFH13FMmhRfdi797ryVgj7RGuOCPuX0u/NWii87F/E8pGcJUpxAuvW04s1kDLsDF0NS1guF6ESGHDwUWZtaiGT6WqtsIyNPRZ/6Izr7XeSsC13HOTpz3oOd25Gx57hOYtKs+LJzW7Xj1JhMYXfg4qj5zMlc3YlasxK6F1t/rrip6Betz5z1ruskRy2c+lrUIHvoSNdRjDGmXayAi6PS3gBoju5E1dpV1v8thkQEGXEqzP8A3bP7yH8gZnTHNpg9Azn1E0nrym+MMa5YARdD0qkIunTLyUPtNWyE2lW2/i2mZOSp0FAPGXg2qk5/ExobkNPPdh3FGGPazQq4uCrthebiFOqGdVC/z+7AxVXlUOjWg3DGW66TtJlOnRy1h+g7wHUUY4xpNyvgYkpKe+fmGriaph2o1kIklsTLQ8aMhTkzCDNol7SuqYbli+zumzEma1gBF1dlvaKO4A31rpOkldaujI4SqzjGdRRzCHLSGbBvH/tmvO06Sqvp2y9DXh5y6idcRzHGmKSwAi6uSnuBhlC33nWS9KpeCYly69EVZ4OqoHsxe95+1XWSVtGGenTKa3DiyUj3nq7jGGNMUlgBF1PStBM116ZRtWYl9DnWdQxzGOJ5yEnj2DtzWmY0m/5gOmzfinfm+a6TGGNM0lgBF1dNveBy6UxU3bcX1tUifY91HcUcgZx0BtTvQz94x3WUIwrffAl6JmDYKNdRjDEmaayAi6vuPaFDYW7dgVuzGjRE+toGhtg7bjBeohydHu/dqLpxPXw4Cxl3LuJZ7zdjTPawAi6mRCRqJbI+h+7AVUc7UG0KNf7E8+g4bgLMm4lu2+I6ziHpW68AIGfYEUrGmOxiBVyclfeBdbWuU6RP9Qro0CHagWtir9M5F0FjI/ru666jtEgbGtC3XoaqkUhJmes4xhiTVFbAxZiUV0DdWrShwXWUtNCaFVDR36a6MkR+v+Pg2Er07VdRVddxPm7WNNiyEe/sT7lOYowxSWcFXJyV94HGRtiY/a1EVBVWL7cNDBlGxk6I7pyuWuY6yseErz4XbQY6YYzrKMYYk3RWwMWYlFdEb6yrcRskHbZtgR3bwAq4jCKnnAX5BeiUePWE01VLYcmHyPiL7I6uMSYrWQEXZ+V9ANBcWAdXvQIAsTNQM4p07oKMOg1953W0Pj6nhuhrz0GHQtu8YIzJWlbAxVmXrlDUJSfuwGlTAWc7UDOPjJ0AO7dDTHrC6fZt6DtvIKefjRR1cR3HGGNSwgq4GBMRKK/IjVYi1SugRzHStZvrJKatqkZASRnh5EmukwCgr0+Chnrk7ItdRzHGmJSxAi7mpLwiN+7A1ayw9W8ZSrw85OxPwaK56OrlTrPo3j3oq89G55726ec0izHGpJIVcHFXXgGb6tC9e10nSRltaIA1qxGbPs1YcsZ50KEwWnvmkL75EuzYjnfRVU5zGGNMqlkBF3dNGxnYkMUbGdbVQkOD3YHLYNK5C3L62dFmhu3bnGTQ+nr0padg8AnIwCFOMhhjTLrkuw7g+/5VwB3AUOCUIAhmHOJxFwL3AHnA/UEQ3Jm2kA5JeQUKUZHTd4DrOCmh1dG0m/WAy2xyzsXo6y+ib76EOLgDptMmR417v/j1tF/bGGPSLQ534OYCVwBvHOoBvu/nAb8CPglUAZ/1fb8qPfEcK4t6wenaLF4HV7MC8vKgVx/XSUw7SEU/GDoCnTwp7S1FtKEBfeFJ6D8Iho5M67WNMcYF5wVcEATzgyBYeISHnQIsCYJgWRAE+4DHgImpT+eedOwEPYqz+kxUrV4Jvfoi+QWuo5h28i64ArZsRN9+Oa3X1bf+ChvW4l3y2Wj3tjHGZDnnBVwr9QFWH/B+ddPHckN5H3R99hZwVK+w6dNsUTUSBg1FJz2J1u9LyyV1z2702cfg+GFw4klpuaYxxriWljVwvu+/AvRq4VP/HATB0614ipZ+pD7k6dm+798I3AgQBAGJRKJVOY9Wfn5+Sq+xrf9x7Jn2esrHcTTaO/ZwxzY2bK6j8+BhdI7h+I4k1V/7ODvU2PdeexNbfvB1Or8/haKLPp3yHDse/x07t22h5/d/TIfS0pRfr5l97W3suSiXxx+3saelgAuCoL3n2VQDxxzwfl/gkLekgiC4D7iv6V2tq6tr5+UPL5FIkMprhN2L0W1b2LByOdK5a8quczTaO3ZdNBeAXT1L2Z3ir1MqpPprH2eHGrv27g+VVWwP/sDOkacjHQpTlkG3bSb8y8MweizbSnpBGr8W9rW3seeiXB5/usZeUVHRqsdlyhTqdKDS9wT5cdIAABvaSURBVP0Bvu93AK4GnnGcKW2kuZVIFm5k2H+Elk2hZg0RwZv4edi6CU3x6Qz654egfh/e5dem9DrGGBM3zgs43/cv932/GjgdeN73/ZeaPl7h+/4kgCAIGoBbgJeA+dGHgnmuMqddr74A6Npqx0FSoHoFdO4K3YtdJzFJJINPgOFj0GcfQzel5idW/XAW+varyAWXI7aD2RiTY5z3gQuC4C/AX1r4eC1w0QHvTwLicdhiuiXKIT8f1qw+8mMzjFavgL7H2s7BLOR99kbCO75GGNxP3ldvS+pz6969hP/3KyirQC6+OqnPbYwxmcD5HThzZJKXB2UVWdcLTsMQalbaDtQsJWW9kU/58N4UdE6L/bmPmj7zMNStw7vulpSusTPGmLiyAi5T9O6bfXfg6tbCvr3Qp7/rJCZF5PzLoVdfwofvRXfvSspz6ofvoy8/g5x5PjJ4eFKe0xhjMo0VcBlCeh8DG9alvcN9SjVtYJAsPSLMgBQU4F13C2yuI3zg7uiuazvohrWEv/kJVByD+F9OUkpjjMk8VsBlil59QUPIooa+Wr0SRKCin+soJoWksgq56ksw6x10UnDUz6N79xD+738C4P3j96NTSowxJkdZAZchpHe0E5Us2omqNSuiReiFtoYp28mES5DTxqPPPIrOnNrmP6979xDeeyfUrMK74VakrHcKUhpjTOawAi5TNPWC02xaB7d6ua1/yxEiglxzM/QfRPibuwjfav1ZqbpzB+Hdt8O8Wci1/4gMH53CpMYYkxmsgMsQUtgRSspgTXbcgdNdO2HDWqTfca6jmDSRwsL/396dR9lVlvke/76VCoSQhAQKSCpzIAkJAcIoYyODDDaI0voQurVBRbRvK7ZIi4D3amNjgy5bWWK3DHqhUYFH+kZBwhSQBmliBySQicypTEBICAkZSEjVe//Yu1iHoip1qlLn7LPP+X3Wyso5e3yees/wnHcPL3Vf/y4ccgTxrp/Q8rtfE5ubd7lObFpMy/e/CU2LqfviN6g75awyRSsiUtkyvw+cdMGQYdVzM99VywBUwNWY0KcvdV/538S7f0r8/b3Emc8Qzp9COPZkQl0vAGKM8MZrxIfvJz47HfoNoO6KbxMmHJFx9CIilUMFXI6EwcOIC+cQW1oIdfnuPI0rliYPhquAqzWhvh4uvYJwxLG0PHAP8Y4fEu/+Kew/BAYMhNXLYeMG6NWL8JELCH95EaHv3lmHLSJSUVTA5cmQYbBjB2xYlxxOzbMVS2HAQMJADaFVi0IIcNSJ1E0+Hl6cQVw0l7j2Vdj4JmHCZDhoPOHQowj7D846VBGRiqQCLkfC4GFESG7om/MCLq5cBsN1/7daF+rq4OgTCUefmHUoIiK5ku/jcLVmyHAAYs4vZIjvvguvrtD5byIiIt2kAi5HQv99oF///N8Lbs0KaG6G4QdlHYmIiEguqYDLm8HDiWvyfS+4uGIJoCtQRUREuksFXM6EoSNgTVNyq4W8WrkM9twLdIK6iIhIt6iAy5uhI2HrFnjrzawj6ba4cikMH5X7W6GIiIhkRd+gORMa06GnVjdlG0g3xZYWWLmcoPu/iYiIdJsKuLxpHAFAXJPPAo61r8L2baDz30RERLpNBVzOhP4DYJ9BsHpF1qF0S1yZjMCgCxhERES6TwVcHjWOIOb0ECpNi6G+/r2eRBEREek6FXA5FIaOhFdXJOeT5UxcvhiGjSbU9846FBERkdxSAZdHjSOSMVHXvZ51JF0SW1pgxRLCSN3AV0REZHeogMuhMGxU8iBvh1HfeA22bYWRB2cdiYiISK6pgMuj1jFRc1bAxeWLAAijxmYbiIiISM6pgMuh0GcvaDgwGVM0T5oWQ+893itARUREpHtUwOXV0JH564FrWgzDRhHq67MORUREJNdUwOVUaBwBr68m7nw361CKEltaoGkpYZTOfxMREdldKuDyauhIaG6G19dkHUlxXl+TjMAwUue/iYiI7C4VcDkVhiZjosaVyzKOpDixqfUCBvXAiYiI7C4VcHk1eBjU94Z0aKqK17QE9tgjiVtERER2S+Znk5vZp4DvABOA49z9+Q6WWw68DTQDO939mHLFWIlCfX1yIUNeeuCWL4bhYwi9emUdioiISO5lXsABc4ALgVuLWPY0d19X4nhyI4wYQ/zzc8QYCSFkHU6HYnNzMgLDKWdlHYqIiEhVyPwQqrvPd/cFWceRS8PHwJa34c0Kr2lXN8GO7TB6XNaRiIiIVIXMC7guiMBjZvaCmV2edTCVIIwYkzxYuSTbQDoRlyb1eRgzPuNIREREqkNZDqGa2XRgcDuzrnP33xW5mZPcfY2ZHQA8bmavuPvTHezvcuByAHenoaGhW3EXq76+vuT7aE/sdzRrQ2Cvda/RL4P9Q3G5b1zTxI59BtFwyKEVfai3O7Jq+0pQy7lDbeev3Gszd6jt/Cst97IUcO5+Zg9sY036/1ozmwocB7RbwLn7bcBt6dO4bl1pDzE2NDRQ6n106MChbFkwl3cy2n8xuTfPfwlGjWX9+vVliqp8Mm37jNVy7lDb+Sv32swdajv/cuXe2NhY1HK5OIRqZnubWf/Wx8BZJBc/1LwwYgysqNxbicQtm+G11Tp8KiIi0oMyL+DM7BNmtgo4AXjIzB5Npzea2bR0sQOBP5rZS8D/AA+5+yPZRFxhho+GN98gbt6UdSTtW7YQgKALGERERHpM5rcRcfepwNR2pq8BPpo+XgocUebQciGMGEMEWLkMJlTenyguXQAhwGgNoSUiItJTMu+Bk900/CAAYoWOyBCXLYDGEYQ+fbMORUREpGqogMu50H8ADGqoyPPgYksLLF2o899ERER6mAq4ajBiDLGpAu8Ft3YNbN0MKuBERER6lAq4KhBGHQyvryZu3ZJ1KO+jG/iKiIiUhgq4KhBGj4cYYfmirEN5v8Xzoe/eMHhY1pGIiIhUFRVw1SC9wjOmt+yoFHHRXDh4IqFOLzMREZGepG/WKhD69oPBQyuqgIub3kpu4Dt2YtahiIiIVB0VcFUijB4HSxcQY8w6lMSieQCEsYdmHIiIiEj1UQFXLUaPh7c3wvq1WUcCpIdP99gDRh6UdSgiIiJVRwVclQhjkqGqKuUwalw0D0aPJ9T3zjoUERGRqqMCrloMHQW994Cl2RdwcdtWWLlMh09FRERKRAVclQj19ckNfZctyDoUWDIfYosuYBARESkRFXBVJIweDyuWEnfuzDSOuGge1NVpBAYREZESUQFXTcaMg3d3wOrlmYYRF82FkQcT+uyVaRwiIiLVSgVcFWkdsioueSWzGOKO7bBskQ6fioiIlJAKuCoS9jsA9juAuHBOdkEsngc73yUcckR2MYiIiFQ5FXBVJow7FBbMyeyGvnHeLKivh3G6AlVERKRUVMBVm/GHweZNsGZlJruP82bBQRMIe/bJZP8iIiK1QAVclQnjJgFkchg1bnoruf/bBB0+FRERKSUVcNWm4UDYtwEWzC77ruP8lwAIE48s+75FRERqiQq4KhNCIIw7jLgwg/Pg5s+Cvv1g5Jjy7ldERKTGqICrRuMnJQPbv7aqbLuMMRLnvQQTDifU9SrbfkVERGqRCrgq9N55cOU8jPraatiwjjBxcvn2KSIiUqNUwFWj/QfDoAZYUL4LGeK8WQCECSrgRERESk0FXBUKIRDGTyIumE1saSnLPuPLM+GARsL+g8uyPxERkVqmAq5aHXpkch5c05KS7ypu3QwLXiYceXzJ9yUiIiIq4KpWmHQ0hLqkZ6zE4uwXoLlZBZyIiEiZqICrUqHfADjokLIUcLw4AwYMhNHjSr8vERERUQFXzcLhx8KKJcQN60u2j7hjO3HOnwmTP0So08tJRESkHPSNW8XC4ccCEGc/X7J97Jj9AmzfRpisw6ciIiLlUp91AGb2A+B8YAewBPisu7/VznLnADcDvYA73P3GsgaaR43DYb8DksOof3F2SXax/U9Pw557wSGHl2T7IiIi8kGV0AP3ODDJ3Q8HFgLXtF3AzHoBPwXOBSYCF5vZxLJGmUMhhKQXbv4s4o7tPb792NLC9pl/JBx2NKF37x7fvoiIiLQv8wLO3R9z953p0xnAsHYWOw5Y7O5L3X0HcC9wQblizLNw+LGwYwe88nLPb/yVl2l560046oSe37aIiIh0KPMCro3PAQ+3M30osLLg+ap0mnRm/CTosxfx+Wd7fNPxv58g7N2fMPlDPb5tERER6VhZzoEzs+lAe7fov87df5cucx2wE/hVO8uFdqbFXezvcuByAHenoaGhyzF3RX19fcn3sTs2nnwm2/84nX33vpa6vfr2yDZbtmzmjRefY+8zzqffkMYe2WYeVXrbl1It5w61nb9yr83cobbzr7Tcy1LAufuZu5pvZpcA5wFnuHt7hdkqYHjB82HAml3s7zbgtvRpXLduXdcC7qKGhgZKvY/dEY86iTj9QdY9/nvqTjy9R7bZ8vQjsGMHe552bkXnXmqV3valVMu5Q23nr9xrM3eo7fzLlXtjY3GdIpVwFeo5wNXAqe6+tYPFZgJjzWw0sBqYAvx1mULMv4MnwP6Dif/9BPRQAReffQKGDKf+4AmwvnT3mRMREZEPqoRz4G4B+gOPm9ksM/sZgJk1mtk0gPQihy8DjwLzk0k+N6uA8yaEQDjhdFgwm7h+7W5vL766CpYuIJx0JiG0d3RbRERESinzHjh3P7iD6WuAjxY8nwZMK1dc1SaccBrxgV8Tn/sD4byLdmtb8dnHoa6OcPyHeyY4ERER6ZJK6IGTMggNB8L4w4jPPUlsaen2duKWzcT/eoRw5AmEfQb1YIQiIiJSLBVwNSScchasfTUZfL6b4pO/h3e2Ec6zHoxMREREukIFXA0Jx54MBw6l5cF7utULF7dtJU5/AI44jjBsdAkiFBERkWKogKshoa5Xcv7b6iZ48bkurx+fmgZbN1O3m+fQiYiIyO5RAVdjwnGnwOChtDx4b5d64eI724iP/RYmHUUYNbZ0AYqIiEinVMDVmKQXbgqsbiK+UPzwWtF/Dlvepu78i0sYnYiIiBRDBVwNCseeDMNGE3/9M+L6NzpdPs6aQXzmMcLZFxLGjC9DhCIiIrIrKuBqUKjrRd0XvwE7d9Jy603Ed9/tcNm4cQMtd90Cw0cTLtDgFyIiIpVABVyNCoOHUvfZr8KyhcT7bifGDw5BG99aT8u/fQ+2v0PdZV8n1PfOIFIRERFpK/ORGCQ74agTCWd9gvjYVOJrq6m7+HLC0JEAxFdepuW2H8CO7dRddiWhcUTG0YqIiEgrFXA1LvzVJclA91PvpuX6r8IBjbDpLdi6GQYPo+6qG1S8iYiIVBgVcDUu1NURPnwu8eiTiNOc+OY6woTDYb8DCaeeTejTN+sQRUREpA0VcAJA6D+AcNFlWYchIiIiRdBFDCIiIiI5owJOREREJGdUwImIiIjkjAo4ERERkZxRASciIiKSMyrgRERERHJGBZyIiIhIzqiAExEREckZFXAiIiIiOaMCTkRERCRnVMCJiIiI5IwKOBEREZGcUQEnIiIikjMhxph1DKVW9QmKiIhIVQmdLVALPXCh1P/M7IVy7KcS/9Vy7rWefy3nXuv5K/fs41D+VZ97p2qhgBMRERGpKirgRERERHJGBVzPuC3rADJUy7lDbedfy7lDbeev3GtXLedfUbnXwkUMIiIiIlVFPXAiIiIiOVOfdQB5YWafAr4DTACOc/fnO1juHOBmoBdwh7vfmE4fDdwL7Av8GfiMu+8oQ+i7zcz2Be4DRgHLAXP3DW2WOQ34UcGkQ4Ap7v5bM7sTOBXYmM671N1nlTjsHlNM/ulyzcDs9OkKd/9YOr3a234y8O/AAKAZuMHd70vn3UnO2r6j93DB/D2B/wCOBtYDF7n78nTeNcDnSf4OV7j7o2UMfbcVkfuVwGXATuAN4HPu3pTOa/f1nydF5H8p8ANgdTrpFne/I513CfCtdPo/u/tdZQm6hxSR+4+A09KnfYED3H1gOi/XbW9mvwDOA9a6+6R25geSv81Hga0kn2N/Tudl1u7qgSveHOBC4OmOFjCzXsBPgXOBicDFZjYxnX0T8CN3HwtsIPmQz4tvAk+ksT+RPn8fd/+Du09298nA6SQv8scKFvnH1vmV/gXejk7zT20ryLHwA6yq256krf/W3Q8FzgF+bGYDC+bnpu07eQ+3+jywwd0PJvnRclO67kRgCtD6d/i3dHu5UGTuLwLHuPvhwP3A9wvmdfT6z4Ui8we4ryDP1uJtX+DbwIeA44Bvm9mgMoW+24rJ3d2/VvAZ/xPg/xXMznXbA3eSvGc7ci4wNv13OckP1szbXQVckdx9vrsv6GSx44DF7r407WG5F7ggrd5PJ/nAA7gL+Hjpou1xF5DEDMXF/kngYXffWtKoyqer+b+nFtre3Re6+6L08RpgLbB/2SLsWe2+h9ssU/g3uR84I23nC4B73X27uy8DFqfby4tOc09/qLW+r2cAw8ocYykV0/YdORt43N3fTHuoH2fXBUGl6WruFwP3lCWyMnD3p4E3d7HIBcB/uHt09xnAQDMbQsbtrgKuZw0FVhY8X5VO2w94y913tpmeFwe6+6sA6f8HdLL8FD745r7BzF42sx+lh6DypNj8+5jZ82Y2w8xaC52aanszOw7YA1hSMDlPbd/Re7jdZdJ23UjSzsWsW8m6Gv/ngYcLnrf3+s+TYvP/q/T1fL+ZDe/iupWq6PjNbCQwGniyYHLe274zHf19Mm13nQNXwMymA4PbmXWdu/+uiE20d/fkuIvpFWNXuXdxO0OAw4DCc3+uAV4j+WK/DbgauL57kZZGD+U/wt3XmNkY4Ekzmw1same5am77u4FL3L0lnVzxbd9GMe/V3L7PO1F0/Gb2aeAYkvMbW33g9e/uS9pbv0IVk/+DwD3uvt3MvkTSE3t6ketWsq7EPwW4392bC6blve07U5HveRVwBdz9zN3cxCpgeMHzYcAaYB1Jl2t9+ou9dXrF2FXuZva6mQ1x91fTL+m1u9iUAVPd/d2Cbb+aPtxuZv8XuKpHgu5BPZF/evgQd19qZk8BRwL/SQ20vZkNAB4CvpUeYmjddsW3fRsdvYfbW2aVmdUD+5Acfilm3UpWVPxmdiZJcX+qu29vnd7B6z9PX+Kd5u/u6wue3k56/mO67ofbrPtUj0dYOl157U4B/r5wQhW0fWc6+vtk2u46hNqzZgJjzWy0me1B8kJ/wN0j8AeSc8MALgGK6dGrFA+QxAydx/6BcyPSL/7W88E+TnJBSJ50mr+ZDWo9PGhmDcBJwLxaaPv0tT6V5ByR37SZl7e2b/c93GaZwr/JJ4En03Z+AJhiZnumVx6PBf6nTHH3hE5zN7MjgVuBj7n72oLp7b7+yxZ5zygm/yEFTz8GzE8fPwqclf4dBgFn8f6jEJWumNc9ZjYeGAQ8VzCtGtq+Mw8Af2tmwcyOBzamP04zbXcVcEUys0+Y2SrgBOAhM3s0nd5oZtPgvfNhvkzSgPOTST433cTVwJVmtpjkfJmflzuH3XAj8BEzWwR8JH2OmR1jZne0LmRmo0h+pfxXm/V/lR5OnA00AP9cjqB7UDH5TwCeN7OXSAq2G9299UOs2tvegL8ALjWzWem/yem8XLV9R+9hM7vezFqvrvs5sF/anleSXpmbvted5MvrEeDv2xxmqmhF5v4DoB/wm7SdW7/kd/X6z4Ui87/CzOameV4BXJqu+ybwXZJCaCZwfTotF4rMHZIf6PemP1ha5b7tzewekqJ0vJmtMrPPm9mX0sPkANOApSQXJt0O/C/Ivt01EoOIiIhIzqgHTkRERCRnVMCJiIiI5IwKOBEREZGcUQEnIiIikjMq4ERERERyRgWciIiISM5oJAYRKSszOxn4PnAo0Exy36l/cPeZGcY0ClgGbEknrQN+5u43ZhVTscxsOXCZu0/POhYRKR/1wIlI2aRDbv0e+AmwL8nAz/8EbN/VemU00N37kdyw9P+Y2Tld3UA6vFYupHeW1/eASA7l5oNGRKrCOAB3bx1ubRvwWOvMtJi4FvgCsBfJiAZfcfeNBb1knwOuJxkR4BrgBZLREUYAv3T3Lxds73PAPwKDSYa1utzdmzoL0t2fM7O5wCTgETO7GbiQZNzTRSQ9hs+k+/hOutw7JMMrXWlmLwM3k9ylfhvJmLhXuvuOdJ1IMp7k19LYfgzcCfySpGfyEeDTBcufRzKKxSiSkR6+5O4vm9ndad4PmlkzyZ3gv58O9/OvwESgCfiquz+Vbusp4FmSMRyPAg4jucO8iOSIfnmJSDktBJrN7C4zOzcdP7DQpem/04AxJEXaLW2W+RDJOKMXkRQ+1wFnkhQ+Zmankjz4OEkxeCGwP/AMbcbpbU/aK3VSur0X08kzgckkvYa/JhlKqk/BahcA9wMDgV+RHBr+GsnwYScAZ5AOv1PgHOBo4HjgG8BtwN+QDEc3iaQXEDM7CvgF8EWSodhuBR4wsz3d/TPACuB8d++XFm9DgYdICr59gauA/zSz/Qv2/RngcqA/SYEnIjmjHjgRKRt335SeA3c1yZiCg9OxhL/g7q+TFDD/6u5LAczsGmCOmX22YDPfdfd3gMfMbAtwT+vA6mb2DHAkyXi8XwT+xd3np/O+B1xrZiN30Qu3DojAa8A33f2JNO5fFizzQzP7FjAeeCmd9py7/zZ9vI2kV7DVcjO7FTiVpOBsdZO7bwLmmtkc4LGCvB9O87iLpDfyVnf/U7reXWZ2LUnh13bcYYBPA9PcfVr6/HEzex74aLo9gDsLxmkWkRxSASciZZUWVJcCmNkhJIcNf0zS49TI+3uEmkg+pw4smPZ6weNt7Tzvlz4eCdxsZj8smB9IzrvrqIBrSAf2fh8z+zpwWRpfBAaQ9K61Wtlm+XEkhzCPAfqmORQWdcXkMbggj0vM7CsF8/dIY2nPSOBTZnZ+wbTeJAONtxuviOSPCjgRyYy7v2Jmd5L0lgGsISlAWo0AdpIUN8O6uPmVwA3u/qvdidHMTiHpMTwDmOvuLWa2gaQYbBXbrPbvJIdfL3b3t83sH4BPdjOE1jxu6GB+232vBO529y/sYptt1xGRnFEBJyJlk/a4/SVwn7uvMrPhJD1vM9JF7gGuTg8hvgF8L112p5l1dXc/A75rZrPcfa6Z7QOc5e6/6eJ2+pMUkW8A9Wb2TZIeuM7W2QRsTnP+u3T97rgdmGpm00kuxOhLcgHC0+7+NklxO6Zg+V8CM83sbGA6Se/b8cBid1/VzRhEpMLoIgYRKae3SS5C+FN6/toMYA7w9XT+L4C7gadJrjh9B/hKO9vplLtPBW4C7jWzTel+zu3Gph4FHia5AKMpjamzQ5BXAX9Nku/twH3d2C8A7v48yXlwtwAbSK4YvbRgkX8BvmVmb5nZVe6+kuSiimtJisaVJFfi6vNepIqEGNWTLiIiIpIn+kUmIiIikjMq4ERERERyRgWciIiISM6ogBMRERHJGRVwIiIiIjmjAk5EREQkZ1TAiYiIiOSMCjgRERGRnFEBJyIiIpIz/x+s7w6JOpe7UAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca()\n",
    "x = np.linspace(-1, 1, 200)\n",
    "hz = 10\n",
    "cost = np.sin(hz*x)*np.exp(-x)\n",
    "ax.plot(x, cost)\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_xlabel('Some Parameter')\n",
    "n_iterations = 500\n",
    "cmap = plt.get_cmap('coolwarm')\n",
    "c_norm = colors.Normalize(vmin=0, vmax=n_iterations)\n",
    "scalar_map = cmx.ScalarMappable(norm=c_norm, cmap=cmap)\n",
    "init_p = 120#np.random.randint(len(x)*0.2, len(x)*0.8)\n",
    "learning_rate = 1.0\n",
    "for iter_i in range(n_iterations):\n",
    "    init_p -= learning_rate * gradient[int(init_p)]\n",
    "    ax.plot(x[int(init_p)], cost[int(init_p)], 'ro', alpha=(iter_i + 1) / n_iterations, color=scalar_map.to_rgba(iter_i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What this would mean is depending on where our random initialization of weights began, our final cost might end up being somewhere around -0.5.  This is a local minima.  It is, based on its surroundings, a minima.  But it is not the global minima.  In fact there are a few other possible places the network could have ended up, if our initialization led us to another point first, meaning our final cost would have been different.\n",
    "\n",
    "This illustration is just for a single parameter... but our networks will often have millions of parameters... I'll illustrate the same idea with just two parameters to give you a sense of how quickly the problem becomes very difficult."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Cost')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import axes3d\n",
    "from matplotlib import cm\n",
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "x, y = np.mgrid[-1:1:0.02, -1:1:0.02]\n",
    "X, Y, Z = x, y, np.sin(hz*x)*np.exp(-x)*np.cos(hz*y)*np.exp(-y)\n",
    "ax.plot_surface(X, Y, Z, rstride=2, cstride=2, alpha=0.75, cmap='jet', shade=False)\n",
    "ax.set_xlabel('Some Parameter 1')\n",
    "ax.set_ylabel('Some Parameter 2')\n",
    "ax.set_zlabel('Cost')\n",
    "# ax.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that in practice, as the number of your parameters grows, say to a million, then finding a local minima will more often than not turn out to be very good minima.  That's good news for deep networks as we'll often work with that many parameters.\n",
    "\n",
    "<a name=\"learning-rate\"></a>\n",
    "## Learning Rate\n",
    "\n",
    "Another aspect of learning what our parameters should be, is how far along the gradient we should move our parameters?  That is also known as `learning_rate`.  Let's see what happens for different values of our learning rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3, figsize=(20, 6))\n",
    "for rate_i, learning_rate in enumerate([0.01, 1.0, 500.0]):\n",
    "    ax = axs[rate_i]\n",
    "    x = np.linspace(-1, 1, 200)\n",
    "    hz = 10\n",
    "    cost = np.sin(hz*x)*np.exp(-x)\n",
    "    ax.plot(x, cost)\n",
    "    ax.set_ylabel('Cost')\n",
    "    ax.set_xlabel('Some Parameter')\n",
    "    ax.set_title(str(learning_rate))\n",
    "    n_iterations = 500\n",
    "    cmap = plt.get_cmap('coolwarm')\n",
    "    c_norm = colors.Normalize(vmin=0, vmax=n_iterations)\n",
    "    scalar_map = cmx.ScalarMappable(norm=c_norm, cmap=cmap)\n",
    "    init_p = 120#np.random.randint(len(x)*0.2, len(x)*0.8)\n",
    "    for iter_i in range(n_iterations):\n",
    "        init_p -= learning_rate * gradient[int(init_p)]\n",
    "        ax.plot(x[int(init_p)], cost[int(init_p)], 'ro', alpha=(iter_i + 1) / n_iterations, color=scalar_map.to_rgba(iter_i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the first case, our learning rate was way too small.  It looks like we didn't manage to get any better cost than where we started!  In the second case, just right.  In the third case, our learning rate was too large.  Meaning, we overshot our minima, and moved past it.  So our cost has the effect of going up and down, instead of just going down like in the second case.\n",
    "\n",
    "We'll learn more tricks for changing this landscape to be a bit more concave, reducing the number of local minima by regularizing the landscape through many different extensions to this same basic idea of following the negative slope of our gradient.  Before we can get into them we'll need to learn how to create a neural network.\n",
    "\n",
    "<a name=\"creating-a-neural-network\"></a>\n",
    "# Creating a Neural Network\n",
    "\n",
    "Let's try a simple example network.  We're going try to find a mapping of an input `X` to an output `y`, just like in our example of mapping an input image to either a 0 or 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0xb40f4f850>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's create some toy data\n",
    "\n",
    "# We are going to say that we have seen 1000 values of some underlying representation that we aim to discover\n",
    "n_observations = 1000\n",
    "\n",
    "# Instead of having an image as our input, we're going to have values from -3 to 3.  This is going to be the input to our network.\n",
    "xs = np.linspace(-3, 3, n_observations)\n",
    "\n",
    "# From this input, we're going to teach our network to represent a function that looks like a sine wave.  To make it difficult, we are going to create a noisy representation of a sine wave by adding uniform noise.  So our true representation is a sine wave, but we are going to make it difficult by adding some noise to the function, and try to have our algorithm discover the underlying cause of the data, which is the sine wave without any noise.\n",
    "ys = np.sin(xs) + np.random.uniform(-0.5, 0.5, n_observations)\n",
    "plt.scatter(xs, ys, alpha=0.15, marker='+')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So now we can see that there is a sine wave looking thing but it's really noisy.  We want to train a network to say, given any value on the $x$ axis, tell me what the value should be on the $y$ axis.  That is the fundamental idea of regression.  Predicting some continuous output value given some continuous input value.\n",
    "\n",
    "<a name=\"defining-cost-1\"></a>\n",
    "## Defining Cost\n",
    "\n",
    "We're going to use tensorflow to train our first network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# variables which we need to fill in when we are ready to compute the graph.\n",
    "# We'll pass in the values of the x-axis to a placeholder called X.\n",
    "X = tf.placeholder(tf.float32, name='X')\n",
    "\n",
    "# And we'll also specify what the y values should be using another placeholder, y.\n",
    "Y = tf.placeholder(tf.float32, name='Y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for parameters of our network.  We're going to transform our x values, just like we did with an image and filtering it.  In order to do that, we're going to multiply the value of x by some unknown value.  Pretty simple.  So what that lets us do is scale the value coming in.  We'll also allow for a simple shift by adding another number.  That lets us move the range of values to any new position.\n",
    "\n",
    "But we need an initial value for our parameters.  For that, we're going to use values close to 0 using a gaussian function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  7.,  20.,  73., 144., 249., 242., 148.,  72.,  35.,  10.]),\n",
       " array([-3.143046  , -2.5248964 , -1.9067469 , -1.2885973 , -0.6704478 ,\n",
       "        -0.05229831,  0.5658512 ,  1.1840007 ,  1.8021502 ,  2.4202998 ,\n",
       "         3.0384493 ], dtype=float32),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "n = tf.random_normal([1000]).eval()\n",
    "plt.hist(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to do that, we can use the tensorflow `random_normal` function.  If we ask for 1000 values and then plot a histogram of the values, we can see that the values are centered around 0 and are mostly between -3 and 3.  For neural networks, we will usually want the values to start off much closer to 0.  To do that, we can control the standard deviation like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  3.,  11.,  53., 108., 214., 252., 197., 112.,  43.,   7.]),\n",
       " array([-0.35473275, -0.28878838, -0.222844  , -0.15689963, -0.09095526,\n",
       "        -0.02501088,  0.04093349,  0.10687786,  0.17282224,  0.23876661,\n",
       "         0.30471098], dtype=float32),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FxLqI+DbtUz68ryrOYaqV+5SIuAh4LvD9BrKdzpJyD1mdU3w8M6Y63PgJ4MWNpFvcuJ6aZKm5twD/ONBE9dTKHRHbIuL7tPforx9EkDN6jj4ivgK8pMtNf1n3MTLzMeD8asrmHyLizswc6Mku+5G7epzVwN8BmzNz4Htw/co9ArrtmS/cE6szpmmjmKmO2rkj4k+BjcBrB5qonlq5M/NjwMci4s3Au4HN/Q5yRhd9Zr5usdsi4mhErM7MI1UhHuvxWLMR8RDwe7R/VR+YfuSOiBcCXwDenZn3DijqL+jn8z1kPU/x0TFmJiImgV8GHm8m3qLq5B5FtXJHxOto7zS8tmNKdZiW+nzvo32QRN+d0UXfw37aP1l3Vpd3LxwQEWuBH2fm/0bErwAXM6A/pixBndzPBf4e2JuZdzQbb1E9c4+QOqf4OPX9fA34Y+CfM3PYe8/jemqSnrkj4kLg48DlmTkqOwl1cm849fcy4I+ARxgA5+gXtxO4LCIeof0fqOwEiIiNEfGJaszLgfsi4lvAvwEfzMzvDCXt/6uTO4DXANdGxIPV1wXDifuMOrmJiH8H7qD9x82ZiPjDpoMudoqPiPiriDj1P+HcBrw4Ig4B72Txo4gaUyd3RPxORMwAbwI+Xv2WOlQ1n+8PAM8H7qhez4P/j1h7qJl7e0Q8FBEP0n6d9H3aBvxkrCQVzz16SSqcRS9JhbPoJalwFr0kFc6il6TCWfSSVDiLXpIKZ9FLUuH+D64o+aJpbSp7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = tf.random_normal([1000], stddev=0.1).eval()\n",
    "plt.hist(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /anaconda2/lib/python2.7/site-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n"
     ]
    }
   ],
   "source": [
    "# To create the variables, we'll use tf.Variable, which unlike a placeholder, does not require us to define the value at the start of a run/eval.  It does need an initial value, which we'll give right now using the function tf.random_normal.  We could also pass an initializer, which is simply a function which will call the same function.  We'll see how that works a bit later.  In any case, the random_normal function just says, give me a random value from the \"normal\" curve.  We pass that value to a tf.Variable which creates a tensor object.\n",
    "W = tf.Variable(tf.random_normal([1], dtype=tf.float32, stddev=0.1), name='weight')\n",
    "\n",
    "# For bias variables, we usually start with a constant value of 0.\n",
    "B = tf.Variable(tf.constant([0], dtype=tf.float32), name='bias')\n",
    "\n",
    "# Now we can scale our input placeholder by W, and add our bias, b.\n",
    "Y_pred = X * W + B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to use gradient descent to learn what the best value of `W` and `b` is.  In order to do that, we need to know how to measure what the `best` is.  Let's think about that for a moment.  What is it we're trying to do?  We're trying to transform a value coming into the network, `x`, which ranges from values of -3 to 3, to match a known value, `Y`, which should be a sine wave which ranges from -1 to 1.  So any value into the network should make it seem like the network *represents* a sine wave.  Well we know what a sine wave should be.  We can just use python to calculate it for us.  We just need a function that measures distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this function will measure the absolute distance, also known as the l1-norm\n",
    "def distance(p1, p2):\n",
    "    return tf.abs(p1 - p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# and now we can take the output of our network and our known target value\n",
    "# and ask for the distance between them\n",
    "cost = distance(Y_pred, tf.sin(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function is just saying, give me the distance from the predicted value to the assumed underlying sine wave value.  But let's say this was some natural occuring data in the world.  Or a more complex function, like an image of oranges or apples.  We don't know what the function is that determines whether we perceive an image as an apple or orange."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# cost = distance(Y_pred, ?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we do have a limited set of data that says what a given input *should* output.  That means we can still learn what the function might be based on the data.\n",
    "\n",
    "So instead of our previous cost function, we'd have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = distance(Y_pred, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where `Y` is the *true* Y value.\n",
    "\n",
    "Now it doesn't matter what the function is.  Our cost will measure the difference to the value we have for the input, and try to find the underlying function.  Lastly, we need to sum over every possible observation our network is fed as input.  That's because we don't give our network 1 `x` value at a time, but generally will give it 50-100 or more examples at a time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = tf.reduce_mean(distance(Y_pred, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"training-parameters\"></a>\n",
    "## Training Parameters\n",
    "\n",
    "Let's see how we can learn the parameters of this simple network using a tensorflow optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /anaconda2/lib/python2.7/site-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.cast instead.\n"
     ]
    }
   ],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.01).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<TODO: Describe Train/Test sets, use test set to visualize rest of number line>\n",
    "\n",
    "We tell the optimizer to minimize our `cost` variable which measures the distance between the prediction and actual `Y` value.  The optimizer knows how to calculate the gradient and follow it in the negative direction to find the smallest value, and handles updating all variables!\n",
    "\n",
    "We now just need to iteratively run the optimizer, just like we would run/eval any other part of our tensorflow graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda2/lib/python2.7/site-packages/matplotlib/figure.py:457: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6423955\n",
      "0.52144283\n",
      "0.4644201\n",
      "0.4376248\n",
      "0.42588288\n",
      "0.42139143\n",
      "0.41991425\n",
      "0.419237\n",
      "0.41884857\n",
      "0.4186797\n",
      "0.41857404\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We create a session to use the graph\n",
    "n_iterations = 500\n",
    "\n",
    "# Plot the true data distribution\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.scatter(xs, ys, alpha=0.15, marker='+')\n",
    "with tf.Session() as sess:\n",
    "    # Here we tell tensorflow that we want to initialize all\n",
    "    # the variables in the graph so we can use them\n",
    "    # This will set `W` and `b` to their initial random normal value.\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "\n",
    "    # We now run a loop over epochs\n",
    "    prev_training_cost = 0.0\n",
    "    for it_i in range(n_iterations):\n",
    "        sess.run(optimizer, feed_dict={X: xs, Y: ys})\n",
    "        training_cost = sess.run(cost, feed_dict={X: xs, Y: ys})\n",
    "\n",
    "        # every 10 iterations\n",
    "        if it_i % 10 == 0:\n",
    "            # let's plot the x versus the predicted y\n",
    "            ys_pred = Y_pred.eval(feed_dict={X: xs}, session=sess)\n",
    "\n",
    "            # We'll draw points as a scatter plot just like before\n",
    "            # Except we'll also scale the alpha value so that it gets\n",
    "            # darker as the iterations get closer to the end\n",
    "            ax.plot(xs, ys_pred, 'k', alpha=it_i / n_iterations)\n",
    "            fig.show()\n",
    "            plt.draw()\n",
    "\n",
    "            # And let's print our training cost: mean of absolute differences\n",
    "            print(training_cost)\n",
    "\n",
    "        # Allow the training to quit if we've reached a minimum\n",
    "        if np.abs(prev_training_cost - training_cost) < 0.000001:\n",
    "            break\n",
    "\n",
    "        # Keep track of the training cost\n",
    "        prev_training_cost = training_cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After running the code, we should see our original noisy data.  We call that the training data since it is training the network.  And we see the output of the network as a solid black line.\n",
    "\n",
    "Now you might be thinking, wait, that looks like nothing like a sine wave... I mean it has got the general trend of the line I guess.  But it doesn't curve at all!  We're going to get into why that is in a moment.\n",
    "\n",
    "But first, we're going to have to learn a bit more about the different between training and testing networks.\n",
    "\n",
    "<a name=\"training-vs-testing\"></a>\n",
    "## Training vs. Testing\n",
    "\n",
    "<TODO:>\n",
    "\n",
    "<a name=\"stochastic-and-mini-batch-gradient-descent\"></a>\n",
    "## Stochastic and Mini Batch Gradient Descent\n",
    "\n",
    "Now remember when I said our cost manifold would have many local minima, and that we'd learn some tricks to help us find the best one?  Well now we're ready to talk about two ways of helping with that.  One is using what are called mini-batches.  This is useful for a number of reasons.  First, it is generally impractical to look at an entire dataset.  You might have millions of images which you couldn't ever try loading all at once into a network.  Instead you would look at some random subset of them.  Second, we avoid trying to generalize our entire dataset, allowing us to navigate through more fine grained terrain.  In order to use mini batches, we simply iterate through our entire dataset, `batch_size` at a time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[10 11 12 13 14 15 16 17 18 19]\n",
      "[20 21 22 23 24 25 26 27 28 29]\n",
      "[30 31 32 33 34 35 36 37 38 39]\n",
      "[40 41 42 43 44 45 46 47 48 49]\n",
      "[50 51 52 53 54 55 56 57 58 59]\n",
      "[60 61 62 63 64 65 66 67 68 69]\n",
      "[70 71 72 73 74 75 76 77 78 79]\n",
      "[80 81 82 83 84 85 86 87 88 89]\n",
      "[90 91 92 93 94 95 96 97 98 99]\n"
     ]
    }
   ],
   "source": [
    "idxs = np.arange(100)\n",
    "batch_size = 10\n",
    "n_batches = len(idxs) // batch_size\n",
    "for batch_i in range(n_batches):\n",
    "    print(idxs[batch_i * batch_size : (batch_i + 1) * batch_size])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that this is not the best idea, because we're always looking at the same order of our dataset.  Neural networks love order.  They will pick up on any order you give it and use that to its advantage.  But the order of the data is entirely irrelevant to our problem.  In some cases, it may turn out to be exactly what we want to do.  For instance, if we want to learn about how something changes over time, like audio, or letters or words in a sequence which form sentences.  Then we will have to make sure we're sending data in a certain order.  But for now, we really want to avoid using any order.\n",
    "\n",
    "So we'll have to randomly permute the indexes of our dataset like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('# of batches:', 10)\n",
      "[37 81 44 47 91 24 79 57 74 40]\n",
      "[ 1 99  7 46  9 28 85 61 25  3]\n",
      "[20 75 88 29 73 94 54 15 76 60]\n",
      "[ 0 69 34  5 23 62 35 68 52 11]\n",
      "[93 16 65 41 13 67 72 83 27 80]\n",
      "[26 17 70  4 59 32 19 90 92 36]\n",
      "[71 64 87 33 31 58 42 97 98 89]\n",
      "[ 8 86 12 96 30 66 63 55 18 78]\n",
      "[22 95 50 51 82 48 43 45 53 56]\n",
      "[ 6 39  2 84 21 49 14 38 10 77]\n"
     ]
    }
   ],
   "source": [
    "rand_idxs = np.random.permutation(idxs)\n",
    "batch_size = 10\n",
    "n_batches = len(rand_idxs) // batch_size\n",
    "print('# of batches:', n_batches)\n",
    "for batch_i in range(n_batches):\n",
    "    print(rand_idxs[batch_i * batch_size : (batch_i + 1) * batch_size])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we've done above is look at a range of 100 possible indexes by chunking them into `batch_size` at a time.  But we've also randomized the order we've looked at them so that we aren't prioritizing learning one part of a dataset over another.\n",
    "\n",
    "We can implement this into our previous code like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6082645\n",
      "0.50464433\n",
      "0.45707688\n",
      "0.4340627\n",
      "0.42441216\n",
      "0.42094356\n",
      "0.4197232\n",
      "0.4191328\n",
      "0.41880116\n",
      "0.41864672\n",
      "0.41856572\n",
      "0.41855043\n",
      "0.4185403\n",
      "0.41853598\n",
      "0.41853335\n",
      "0.4185318\n",
      "0.41853145\n",
      "0.41853124\n",
      "0.41853088\n",
      "0.41853058\n",
      "0.41853046\n",
      "0.41853046\n",
      "0.4185305\n",
      "0.41853064\n",
      "0.41853055\n",
      "0.41853052\n",
      "0.41853043\n",
      "0.41853046\n",
      "0.41853046\n",
      "0.41853052\n",
      "0.4185305\n",
      "0.41853055\n",
      "0.4185304\n",
      "0.41853058\n",
      "0.41853046\n",
      "0.41853058\n",
      "0.41853046\n",
      "0.41853046\n",
      "0.4185304\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853067\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853052\n",
      "0.41853046\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "batch_size = 1000\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.scatter(xs, ys, alpha=0.15, marker='+')\n",
    "ax.set_xlim([-4, 4])\n",
    "ax.set_ylim([-2, 2])\n",
    "with tf.Session() as sess:\n",
    "    # Here we tell tensorflow that we want to initialize all\n",
    "    # the variables in the graph so we can use them\n",
    "    # If we had used tf.random_normal_initializer or tf.constant_intitializer,\n",
    "    # then this would have set `W` and `b` to their initial values.\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "\n",
    "    # We now run a loop over epochs\n",
    "    prev_training_cost = 0.0\n",
    "    for it_i in range(n_iterations):\n",
    "        idxs = np.random.permutation(range(len(xs)))\n",
    "        n_batches = len(idxs) // batch_size\n",
    "        for batch_i in range(n_batches):\n",
    "            idxs_i = idxs[batch_i * batch_size: (batch_i + 1) * batch_size]\n",
    "            sess.run(optimizer, feed_dict={X: xs[idxs_i], Y: ys[idxs_i]})\n",
    "\n",
    "        training_cost = sess.run(cost, feed_dict={X: xs, Y: ys})\n",
    "\n",
    "        if it_i % 10 == 0:\n",
    "            ys_pred = Y_pred.eval(feed_dict={X: xs}, session=sess)\n",
    "            ax.plot(xs, ys_pred, 'k', alpha=it_i / n_iterations)\n",
    "            print(training_cost)\n",
    "fig.show()\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting process is also know as Mini-Batch Gradient Descent, since we are taking smaller batches of our data and performing gradient descent.  Further, it is Stochastic, meaning the order of the data presented is randomized, and is also commonly referred to as Stochastic Gradient Descent.  When the two ideas are combined, we have the best of both worlds: the mini batch part which allows us to get more stable updates; and the stochastic part which allows us to move to different parts of our cost's manifold entirely.  I'll just use Gradient Descent as we'll always want it to be in batches, and to be the stochastic kind.\n",
    "\n",
    "Let's stick all of the code necessary for training into a function so we don't have to type it out again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(X, Y, Y_pred, n_iterations=100, batch_size=200, learning_rate=0.02):\n",
    "    cost = tf.reduce_mean(distance(Y_pred, Y))\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)\n",
    "    fig, ax = plt.subplots(1, 1)\n",
    "    ax.scatter(xs, ys, alpha=0.15, marker='+')\n",
    "    ax.set_xlim([-4, 4])\n",
    "    ax.set_ylim([-2, 2])\n",
    "    with tf.Session() as sess:\n",
    "        # Here we tell tensorflow that we want to initialize all\n",
    "        # the variables in the graph so we can use them\n",
    "        # This will set W and b to their initial random normal value.\n",
    "        sess.run(tf.global_variables_initializer())\n",
    "\n",
    "        # We now run a loop over epochs\n",
    "        prev_training_cost = 0.0\n",
    "        for it_i in range(n_iterations):\n",
    "            idxs = np.random.permutation(range(len(xs)))\n",
    "            n_batches = len(idxs) // batch_size\n",
    "            for batch_i in range(n_batches):\n",
    "                idxs_i = idxs[batch_i * batch_size: (batch_i + 1) * batch_size]\n",
    "                sess.run(optimizer, feed_dict={X: xs[idxs_i], Y: ys[idxs_i]})\n",
    "\n",
    "            training_cost = sess.run(cost, feed_dict={X: xs, Y: ys})\n",
    "\n",
    "            if it_i % 10 == 0:\n",
    "                ys_pred = Y_pred.eval(feed_dict={X: xs}, session=sess)\n",
    "                ax.plot(xs, ys_pred, 'k', alpha=it_i / n_iterations)\n",
    "                print(training_cost)\n",
    "    fig.show()\n",
    "    plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get closer to a sine wave, we're going to have to be able to do more than simply scale our input with a multiplication!  What if we had a lot more parameters?  What if we have 10 different multiplications of the input?  What does your intuition tell you?  How are 10 more multiplications combined?  1000?  A million?\n",
    "\n",
    "<QUIZ>\n",
    "\n",
    "Would we be able to find a good representation then?  Let's try and see how we might do that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6932561\n",
      "1.9479373\n",
      "2.0277994\n",
      "2.9309804\n",
      "2.7257824\n",
      "2.9928095\n",
      "1.8321297\n",
      "3.3479152\n",
      "2.4750013\n",
      "3.2157686\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We're going to multiply our input by 100 values, creating an \"inner layer\"\n",
    "# of 100 neurons.\n",
    "n_neurons = 100\n",
    "W = tf.Variable(tf.random_normal([1, n_neurons], stddev=0.1))\n",
    "\n",
    "# and allow for n_neurons additions on each of those neurons\n",
    "b = tf.Variable(tf.constant(0, dtype=tf.float32, shape=[n_neurons]))\n",
    "\n",
    "# Instead of multiplying directly, we use tf.matmul to perform a\n",
    "# matrix multiplication\n",
    "h = tf.matmul(tf.expand_dims(X, 1), W) + b\n",
    "\n",
    "# Create the operation to add every neuron's output\n",
    "Y_pred = tf.reduce_sum(h, 1)\n",
    "\n",
    "# Retrain with our new Y_pred\n",
    "train(X, Y, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, the training takes a lot longer!  That's because our network is much larger.  By adding 100 neurons, we've added 100 more multiplications, and 100 more additions for every observation.  Since we have 10000 observations, that's $(100 + 100) * 10000$ more computations just for computing the output, or 100 million more computations.  But that's not all.  We also need to compute the gradients of every parameter!  Having all of these extra parameters makes it much harder to find the best solution.  So as our network expands, the amount of memory and computation will grow very fast, and training becomes more difficult.\n",
    "\n",
    "Despite increasing everything about our network, looking at the cost, we're not doing much better!  Why is that?  Well, we've added a lot more multiplications.  But it hasn't changed the fact that our function is still just a linear function.  Multiplying a millions times wouldn't help but instead just make it harder to find the same solution we found with far less parameters.  But also, the cost is going up and down, instead of just down.  That's a good sign that we should probably reduce the learning rate.\n",
    "\n",
    "<a name=\"inputs-representation\"></a>\n",
    "## Input's Representation\n",
    "\n",
    "In order to get more complexity, we could consider changing our input's representation.  For instance, if you are working with sound, it may not be the best idea to think about representing the sound as a signal, and instead you might want to explore using something like the discrete fourier transform.  Or if you're working with text, there may be other representations that will allow you to learn more useful features of your data such as word histograms.  There may be other possibilities depending on your application.\n",
    "\n",
    "<a name=\"over-vs-underfitting\"></a>\n",
    "## Over vs. Underfitting\n",
    "\n",
    "One technique for representing curved data like a sine wave is to consider the different polynomials of your input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2271007\n",
      "0.566452\n",
      "0.41874215\n",
      "0.4097697\n",
      "0.40918717\n",
      "0.4091469\n",
      "0.40914437\n",
      "0.4091519\n",
      "0.40914452\n",
      "0.40914342\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instead of a single factor and a bias, we'll create a polynomial function\n",
    "# of different degrees.  We will then learn the influence that each\n",
    "# degree of the input (X^0, X^1, X^2, ...) has on the final output (Y).\n",
    "Y_pred = tf.Variable(tf.random_normal([1]), name='bias')\n",
    "for pow_i in range(1, 2):\n",
    "    W = tf.Variable(\n",
    "        tf.random_normal([1], stddev=0.1), name='weight_%d' % pow_i)\n",
    "    Y_pred = tf.add(tf.multiply(tf.pow(X, pow_i), W), Y_pred)\n",
    "\n",
    "# And then we'll retrain with our new Y_pred\n",
    "train(X, Y, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use the 0th and 1st expansion, that is $x^0$, which just equals 1, and $x^1$.  So $x * W_1$.  That's exactly the same as what we've just done.  It starts to get interesting once we add more powers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6467924\n",
      "0.35524622\n",
      "0.41133228\n",
      "0.46704978\n",
      "0.31311932\n",
      "0.32921782\n",
      "0.4493184\n",
      "0.704025\n",
      "0.58583754\n",
      "0.42533088\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instead of a single factor and a bias, we'll create a polynomial function\n",
    "# of different degrees.  We will then learn the influence that each\n",
    "# degree of the input (X^0, X^1, X^2, ...) has on the final output (Y).\n",
    "Y_pred = tf.Variable(tf.random_normal([1]), name='bias')\n",
    "for pow_i in range(1, 4):\n",
    "    W = tf.Variable(\n",
    "        tf.random_normal([1], stddev=0.1), name='weight_%d' % pow_i)\n",
    "    Y_pred = tf.add(tf.multiply(tf.pow(X, pow_i), W), Y_pred)\n",
    "\n",
    "# And then we'll retrain with our new Y_pred\n",
    "train(X, Y, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we really don't want to add *too many* powers.  If we add just 1 more power:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.831084\n",
      "4.587636\n",
      "4.2336164\n",
      "4.4655504\n",
      "1.5912591\n",
      "3.2759976\n",
      "2.6710777\n",
      "2.718561\n",
      "2.3449523\n",
      "3.8749964\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Instead of a single factor and a bias, we'll create a polynomial function\n",
    "# of different degrees.  We will then learn the influence that each\n",
    "# degree of the input (X^0, X^1, X^2, ...) has on the final output (Y).\n",
    "Y_pred = tf.Variable(tf.random_normal([1]), name='bias')\n",
    "for pow_i in range(1, 5):\n",
    "    W = tf.Variable(\n",
    "        tf.random_normal([1], stddev=0.1), name='weight_%d' % pow_i)\n",
    "    Y_pred = tf.add(tf.multiply(tf.pow(X, pow_i), W), Y_pred)\n",
    "\n",
    "# And then we'll retrain with our new Y_pred\n",
    "train(X, Y, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The whole thing is completely off.  In general, a polynomial expansion is hardly ever useful as it requires us to know what the underlying function is, meaning, what order polynomial is it?\n",
    "\n",
    "<a name=\"introducing-nonlinearities--activation-function\"></a>\n",
    "## Introducing Nonlinearities / Activation Function\n",
    "\n",
    "How else can we get our line to express the curves in our data?  What we'll explore instead is what happens when you add a non-linearity, which you might also hear be called an activation function.  That is a really essential ingredient to any deep network.  Practically every complex deep learning algorithm performs a series of linear, followed by nonlinear operations.  By stacking sets of these, the complexity and power of expression grows far greater than any linear equation could.\n",
    "\n",
    "We'll typically make use of one of three non-linearities for the rest of this course:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "x = np.linspace(-6,6,1000)\n",
    "plt.plot(x, tf.nn.tanh(x).eval(), label='tanh')\n",
    "plt.plot(x, tf.nn.sigmoid(x).eval(), label='sigmoid')\n",
    "plt.plot(x, tf.nn.relu(x).eval(), label='relu')\n",
    "plt.legend(loc='lower right')\n",
    "plt.xlim([-6, 6])\n",
    "plt.ylim([-2, 2])\n",
    "plt.xlabel('Input')\n",
    "plt.ylabel('Output')\n",
    "plt.grid('on')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What each of these curves demonstrates is how instead of just multiplying an input by a number, creating another line, we *non*-linearly multiply the input value.  That just means we will multiply our input by a different value depending on what the input value is.  This allows us to express very complex ideas.  If we do this enough times, we can express anything.  Let's see how we can do this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.8196836\n",
      "0.27469856\n",
      "0.270456\n",
      "0.2686735\n",
      "0.26759753\n",
      "0.26686227\n",
      "0.2663019\n",
      "0.26579016\n",
      "0.2653632\n",
      "0.26493865\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We're going to multiply our input by 10 values, creating an \"inner layer\"\n",
    "# of n_neurons neurons.\n",
    "n_neurons = 10\n",
    "W = tf.Variable(tf.random_normal([1, n_neurons]), name='W')\n",
    "\n",
    "# and allow for n_neurons additions on each of those neurons\n",
    "b = tf.Variable(tf.constant(0, dtype=tf.float32, shape=[n_neurons]), name='b')\n",
    "\n",
    "# Instead of just multiplying, we'll put our n_neuron multiplications through a non-linearity, the tanh function.\n",
    "h = tf.nn.tanh(tf.matmul(tf.expand_dims(X, 1), W) + b, name='h')\n",
    "\n",
    "Y_pred = tf.reduce_sum(h, 1)\n",
    "\n",
    "# And retrain w/ our new Y_pred\n",
    "train(X, Y, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<TODO: Graphic of fully connected network, matrix>\n",
    "\n",
    "It turns out that multiplying our input by a matrix, adding a bias, and then applying a non-linearity is something we'll need to do a lot.  It's often called a fully-connected network, since everything is connected to everything else, meaning every neuron is multiplied by every single input value.  This is also sometimes called a linear layer, since we are linearly combining the values of the input to create the resulting neuron.\n",
    "\n",
    "You might have seen this depicted like so:\n",
    "\n",
    "\n",
    "<a name=\"going-deeper\"></a>\n",
    "## Going Deeper\n",
    "\n",
    "Let's write a simply function for creating the same type of network as above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear(X, n_input, n_output, activation=None):\n",
    "    W = tf.Variable(tf.random_normal([n_input, n_output], stddev=0.1), name='W')\n",
    "    b = tf.Variable(\n",
    "        tf.constant(0, dtype=tf.float32, shape=[n_output]), name='b')\n",
    "    h = tf.nn.tanh(tf.matmul(X, W) + b, name='h')\n",
    "    return h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now take a look at what the tensorflow graph looks like when we create this type of connection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'X',\n",
       " u'random_normal/shape',\n",
       " u'random_normal/mean',\n",
       " u'random_normal/stddev',\n",
       " u'random_normal/RandomStandardNormal',\n",
       " u'random_normal/mul',\n",
       " u'random_normal',\n",
       " u'W',\n",
       " u'W/Assign',\n",
       " u'W/read',\n",
       " u'Const',\n",
       " u'b',\n",
       " u'b/Assign',\n",
       " u'b/read',\n",
       " u'MatMul',\n",
       " u'add',\n",
       " u'h']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first clear the graph\n",
    "from tensorflow.python.framework import ops\n",
    "ops.reset_default_graph()\n",
    "\n",
    "# let's get the current graph\n",
    "g = tf.get_default_graph()\n",
    "\n",
    "# See the names of any operations in the graph\n",
    "[op.name for op in tf.get_default_graph().get_operations()]\n",
    "\n",
    "# let's create a new network\n",
    "X = tf.placeholder(tf.float32, name='X')\n",
    "h = linear(X, 2, 10)\n",
    "\n",
    "# See the names of any operations in the graph\n",
    "[op.name for op in tf.get_default_graph().get_operations()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The names of the variables in this network aren't very helpful.  We can actually do a much better job here by creating our variables within *scopes*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear(X, n_input, n_output, activation=None, scope=None):\n",
    "    with tf.variable_scope(scope or \"linear\"):\n",
    "        W = tf.get_variable(\n",
    "            name='W',\n",
    "            shape=[n_input, n_output],\n",
    "            initializer=tf.random_normal_initializer(mean=0.0, stddev=0.1))\n",
    "        b = tf.get_variable(\n",
    "            name='b',\n",
    "            shape=[n_output],\n",
    "            initializer=tf.constant_initializer())\n",
    "        h = tf.matmul(X, W) + b\n",
    "        if activation is not None:\n",
    "            h = activation(h)\n",
    "        return h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've also moved from using a single random value, to using an initializer.  This initializer will create a new random value every time we call `sess.run(tf.global_variables_initializer())`.  We also pass some more sensible values for the initial mean and standard deviation.\n",
    "\n",
    "Now let's look at the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'X',\n",
       " u'layer1/W/Initializer/random_normal/shape',\n",
       " u'layer1/W/Initializer/random_normal/mean',\n",
       " u'layer1/W/Initializer/random_normal/stddev',\n",
       " u'layer1/W/Initializer/random_normal/RandomStandardNormal',\n",
       " u'layer1/W/Initializer/random_normal/mul',\n",
       " u'layer1/W/Initializer/random_normal',\n",
       " u'layer1/W',\n",
       " u'layer1/W/Assign',\n",
       " u'layer1/W/read',\n",
       " u'layer1/b/Initializer/Const',\n",
       " u'layer1/b',\n",
       " u'layer1/b/Assign',\n",
       " u'layer1/b/read',\n",
       " u'layer1/MatMul',\n",
       " u'layer1/add']"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first clear the graph\n",
    "from tensorflow.python.framework import ops\n",
    "ops.reset_default_graph()\n",
    "\n",
    "# let's get the current graph\n",
    "g = tf.get_default_graph()\n",
    "\n",
    "# See the names of any operations in the graph\n",
    "[op.name for op in tf.get_default_graph().get_operations()]\n",
    "\n",
    "# let's create a new network\n",
    "X = tf.placeholder(tf.float32, name='X')\n",
    "h = linear(X, 2, 10, scope='layer1')\n",
    "\n",
    "# See the names of any operations in the graph\n",
    "[op.name for op in tf.get_default_graph().get_operations()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that everything that is part of creating a linear connection is under the scoped tag we have given it.\n",
    "\n",
    "If we create multiple linear connections, this becomes really useful for understanding what's in our graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'X',\n",
       " u'layer1/W/Initializer/random_normal/shape',\n",
       " u'layer1/W/Initializer/random_normal/mean',\n",
       " u'layer1/W/Initializer/random_normal/stddev',\n",
       " u'layer1/W/Initializer/random_normal/RandomStandardNormal',\n",
       " u'layer1/W/Initializer/random_normal/mul',\n",
       " u'layer1/W/Initializer/random_normal',\n",
       " u'layer1/W',\n",
       " u'layer1/W/Assign',\n",
       " u'layer1/W/read',\n",
       " u'layer1/b/Initializer/Const',\n",
       " u'layer1/b',\n",
       " u'layer1/b/Assign',\n",
       " u'layer1/b/read',\n",
       " u'layer1/MatMul',\n",
       " u'layer1/add',\n",
       " u'layer2/W/Initializer/random_normal/shape',\n",
       " u'layer2/W/Initializer/random_normal/mean',\n",
       " u'layer2/W/Initializer/random_normal/stddev',\n",
       " u'layer2/W/Initializer/random_normal/RandomStandardNormal',\n",
       " u'layer2/W/Initializer/random_normal/mul',\n",
       " u'layer2/W/Initializer/random_normal',\n",
       " u'layer2/W',\n",
       " u'layer2/W/Assign',\n",
       " u'layer2/W/read',\n",
       " u'layer2/b/Initializer/Const',\n",
       " u'layer2/b',\n",
       " u'layer2/b/Assign',\n",
       " u'layer2/b/read',\n",
       " u'layer2/MatMul',\n",
       " u'layer2/add',\n",
       " u'layer3/W/Initializer/random_normal/shape',\n",
       " u'layer3/W/Initializer/random_normal/mean',\n",
       " u'layer3/W/Initializer/random_normal/stddev',\n",
       " u'layer3/W/Initializer/random_normal/RandomStandardNormal',\n",
       " u'layer3/W/Initializer/random_normal/mul',\n",
       " u'layer3/W/Initializer/random_normal',\n",
       " u'layer3/W',\n",
       " u'layer3/W/Assign',\n",
       " u'layer3/W/read',\n",
       " u'layer3/b/Initializer/Const',\n",
       " u'layer3/b',\n",
       " u'layer3/b/Assign',\n",
       " u'layer3/b/read',\n",
       " u'layer3/MatMul',\n",
       " u'layer3/add']"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's connect the output of our last network to another one!\n",
    "\n",
    "# Wow we just made a Deep Network!  Let's make it deeper!\n",
    "h2 = linear(h, 10, 10, scope='layer2')\n",
    "\n",
    "# Again!\n",
    "h3 = linear(h2, 10, 3, scope='layer3')\n",
    "\n",
    "# Now when we look at the names of the operations in the graph, we can directly see which operations belong to each layer!\n",
    "[op.name for op in tf.get_default_graph().get_operations()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<TODO: Also, we can visualize our network using Tensorboard...>\n",
    "\n",
    "<a name=\"image-inpainting\"></a>\n",
    "# Image Inpainting\n",
    "\n",
    "<a name=\"description\"></a>\n",
    "## Description\n",
    "\n",
    "Now we've got most of the tools we'll need to perform much more complicated tasks.  We'll first explore a fun application: painting an image.  This network is just meant to demonstrate how the previous networks we've learned can be scaled to more complicated tasks without much modification.\n",
    "\n",
    "We'll follow an example that Andrej Karpathy has done in his online demonstration of \"image inpainting\".  Let's first get an image that we'll try to teach a neural network to paint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:3: DeprecationWarning: `imresize` is deprecated!\n",
      "`imresize` is deprecated in SciPy 1.0.0, and will be removed in 1.2.0.\n",
      "Use ``skimage.transform.resize`` instead.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10aa45d90>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6o8N0nSpKFKLvU10QSBGbeywO9JOZVTWH+Uxs9z0PQRBEKay5iY3PMRft1c+GKcfIOeu5qW94RIr6ZZCJ9ODxGcxWPOw5Hl6XlWmaj3RKTX/FyD3YdfeVG6tSobmyLFVM5+cJ1s6tWfPCuY0JtUhJS+7O90I9H57v5l6n4ziDAFD737FIew0NjZcQXvTNvVwudzuA2wHAcRw4d34GGzb24Jvf/5xoxx1dVOotkYAxoCEbioONzTaYOpUYdptljvF9H9nGJrz8xlvPuy+nOmGoGVAICz9tVYnish1XR+VKpYjOng347c/8x7wfr1ToTd7WQtRPAJBMEpNsoJAGiKwsbLhqUsW1LP780koZTSt68IbbPw0AuLFI8z9bJP6AeY4n5sL+87xtKkVSSFt7JxZCEARIpjO46Mpwjvh88425+fRa7NfmJeVkLL7M8ad7rczCtHkL0YOVS3ms27AZX/lWyClgMynCnOfTRV+0rVgdldX4+K6elVE5pnjf8PtYOCMFPhoaGnD9ja+aVxcoN5b6eTE834U/nMvluhzHGczlcl0Azi7U0HGcOwDcMTe+t9/2SXz9O3+CN938W6KdxzzORqb2izqXiZRZiyYwHZc72jtfThfzl3/lVaKusYluPs8PcN2Nr8PDP7prvqjPLmRCSY1liwt27hRR6kdP2YF+8N5/jcpHnnsUn/mHe/AHv/ba2oGcaprO7V25d4o+Vq2i81QtG8kEjXHFyp6orO52TzEq6NGxEVx0/VvQ98TdAIDBYdrJf+jhB6Ly7j0HRB+nh8lC0d0pb+ZkmuZuxzW0RfTWX/nvop1XZVaaALh4+y4899TjtTHzOeYvBlXlYCKw8oDj1zPbRIFERlwGcY2ODkflz/3ZH+F//cM/4X/+5kcAADMnH4vqVsj3CbyAzvs9H/1CVN56+bWi3b59T0blrpUyUInfS1V2v1SqLq575XV45KGQ+4+/DEqKqjxX9773vwdLwfMV9e8E8N5a+b0AvvM8+9HQ0Pg5YCnmvK8h3Mhrz+Vy/QA+CeCzAJxcLvdBAKcAvPXFHKSGhsYLi6Xs6r99gapXv8Bj0dDQWCYsu+deb28L4vHYPJc5nlrKtqTuXvEoUs206Lirr1kn2r3xtpdFZXUDhXuZWVaslibbmp/GmhNlKnoxH7LY5FFTMzO9kvOkA4CdICVxaGgGbtXD0FBoNrLZ5tO2bWujcjIpo/P2PUvmzdNnBkXdZZtI/4/HmZlI2Zo7sJ9SYfcNDKP36tfh8d2hHuqxa7Gyi/YJuoakCezEAJm51Pnm3PG9bE+iVMiLdtwjzzRtBH4At6avyhTXdIylzLfFSTmV/Rbe/+wsbVqW5DCQzZA5r7W9E7FYDK21jcgzh+j32pT+eYToLCM0VTdd+e0SV/K7BYJnn5mTEYNpGEjUNqb5pqbrKfOtMsMuAu2rr6FRh9ALX0OjDrHsov7qNe2Ix2PzbLE8BVDMkKK+xUTPS7eR6PnGN0qTSVsbidFVxUOMm+BDUg4DlmnOE+c51EALLi4bLEXXfHs/E1GVVF6XXvmKqLx/79OIxZPo7NkEAOg/QRyCLY3Ey76SmeUAYPVqykR78bQS7MQ42xDQHEyMy8Annnprw4aNSCQS2LAhzLw7ztpOz1AfPd3STyv93PGoHFey1Bom9b9mNdnIVdOnNIv7CD0Awnnn4rLHGsYsNRDHYHULqwEmy9BcLslxHDl+Iip3d3fDtuPo7u4GADzLTH+VquTc4x5zUzzwSU3zxc47pqh/3MVSrItAnpPNztuNyfNUOSwXg37ja2jUIfTC19CoQ+iFr6FRh1h2Hb+jsxkx25qniwXsGRRTou6a2Siv2Up6ZluLdLvkhJr+vGeaIYu1v3l+38ECxwAweFQVjx9QdXxmezIU5+6unrVR+a3v+ghaWjvw1neFrqE/uevforoeRr6RTsg9j9YV3VG5rbld1M1OU96BSoXMV0FV5pRLsPnfuHodkokELlofmkfLa4gQc2CQUpGPjEjP7FSczbcn5/Gm174hKq/sJh921YwrfdNDfX3ONZoTn4o4CSVmQvThqXtHpBdnGijPQEunTGOdZLfc2cFexONxrFoVzkO6iea4NCt1fH7lCwUy56nRpzwqcd4YTb4MeR7AQPznERCmMgfWvCCC80O/8TU06hB64Wto1CGWXdTf8/QZFGerUCRsIXInFXK3bsbnXthDXmvlqy4X7eI9JALHFPGbEyMYtUBINawXOL9IaYn018Y5y3P9R3WKZyD3cNt40WVIJlPYeNFlAIDutl+L6oI8eeS5FSk2ukyMnDorPfc8TvjAiCxsRX0aZEQcK1pbEfgeSvlQjM00kkgMFj1XmiVyEADIMB65l7/qNlF3w02/FJUTCRZGPP/Cs2IA0zSjsGOP8+rzQ+aZWc9dVmHb5AGZTEhvyGxDo9o8QplZhj3FDMiCEAXZSbEo54qrLYFyf3P10mBp3SzTqHmYhveTq2irHCq5x2LQb3wNjTqEXvgaGnWIZRf1+09NoVLx5hFI2BUK+NgI6WXWwLzrxo+TaHvq/odEu4ve/MaobGbkTrgndlKN6H8spniBiU/qbj33yKOpsxTvP+4NqHruWTZL42THYRgGYrXvGldujOrK4ySaT0zTzjoA5McpWCZQRpxmnHuzeQpuOntW7shPTtF8nz7Vh65KGadP9QEAVnaTbDs5QdeirV1mxP3Ah4hU46rrXifqbHaegbjYivrE5sc0DBiGERGgSPH4XNevVncepiGXqQV27HzXjK6tV+P+mwvwqTBK7ZLUupBg3VS4WlSSoj6X59UdeGMBJqO5Iv3nmX8Vn0dfi/oaGhqLQC98DY06hF74Ghp1iGXX8efseGlfKkvr3NNRudeUdROMhNJl0VADj+0T7VpWUxTbypdfs+AQ5kx2hnEOHV8wu6qUrecm6TDUlEj8s2LOs5hJKR5PwDDNeZFtAOA3kLeYW5b6ebaZIt/GBkdEXYzZfJpbyPtPCRbD+DglPsrnC/A8H/nansBsmfYGZmbJG23bTkm6tP7iq9knRefkaaE5Z6ZqzeMRj9F1CT/bfI7NhaMhuVZfUU7U8LhezEguVBMs++x5HgKQjs/3h2alAySaUvTrnAS0UimLdiJduiH3IbheL7xPrQCAERGS8DFayn0VxC7sHa7f+BoadQi98DU06hDLLup3dTTAjpm45RVrxfeVR49GZVPm04DFecfZ98WClLtO3vtIVM70yAyzqdUUeBL4ARCE/01LenCJlEsKmcdCATwyyAKwYmTK8gP5bJ2aILK3gekz6OzpxrEjIQnE5ASJ35USEWysb5fnubKTcgt0KB55XpkGmWykRBzZkhSBs8zs17mmG/FEAqvWhUE6FuPmBzPLreiWSShMi2UgVoKAZCILNgdKqi1upjOCADDoWG4K5eKwmteE9xFTReCFAn0UHz+TJ7Xw/dr9USMEYRd+tqJw7jEJnmfxLStBOlzUn5dCi5sj2fBVzz1+nJrl2Qy0qK+hobEI9MLX0KhD6IWvoVGHWHYd/7+9dReaWzJ4zTtvFd/v8clkNfLQblEXYyYZ7pHpKaFYhUFyQ+275wFRtz5H0WN2OkOUjpbMj8ddcQ1TIUzk6a8ZOSg30QHA5AS5a+59RpocH32M9iEOHzuIf3e+ht/9g98DAIwz91jOx/jx2ynSDQA62iiSLJuWUWVcnS5OUj640vSYaJdpJhITMx4DDCP8D+DMGYrca2gnEo1kViaOc10ePacSjlJZ5vGU+q0nrq0HwIA/14ZHVAa8nbzwvrdwXr2Fc0mqbrM0yHm0F+xklK0SlKvMnMd0/Kqy58Hdj001DwPfv+DKu+GL/9zyHCg6vaec92JYSgqtXgBfAbAS4Vq5w3GcL+RyuVYA3wCwFsBJADnHcSYW6kdDQ+Olg6WI+i6A33YcZyuAawB8OJfLXQzgdwHc5zjOJgD31T5raGj8AmApufMGAQzWyjO5XO4AgB4AtyFMpgkAXwbwAIBPLNbfrpdvQyabQrpR8uWtuv66qFw82SfqJo+TGuAy2c1V01MzKWls3xFRl179RFReffPNCPwA1WIJZoviubeAtxggI+E4ycXUeEG0++H37orK3/quI+r6hyjSLgh8FEtFPHsoJBfh0VcZZlLzIW03EyyyzjalmtGUbY3KXoKJnq6MViwYNOa+vpNYVymjr+8kAGBsinjlLn0ZS0umeiiy8SrWJeAcHnnA/NRSXGz3giCMipv7jvPq854VWxYX7z2Fz056Yi5M02EYirnQIAmfRxDG09LLsuyR7O8KlUM1BfPoPEXUZx6FXGS3jFAhmbPiGUz/U8+leoG7dRfUPJfLrQVwJYDHAXTWHgpzD4eO8xyqoaHxEoJxvqcgRy6XywJ4EMBnHMf5di6Xm3Qcp5nVTziO03KO424HcDsAOI6zfTZfRCKVQDEvsxZWGFVRaUxuRFUZ9xF/YaiOHNzRR9k/QbyJHFbijU3INjUhPzWFWFxu7p2LjmsOfKZU326OqUlyvpmYlNwCFWXTZ+vWrThw4EDttwl8w6dnpWTSTafoLW9b0oHHYm9lfm095Q0kNqLcKhpaOzEzHm4G8jdXKks0XLGYnKulQvrNKFKaqAqQSKYiCivBgsYdbFSCLfZx3v3MMyjFaN4M5a3rsfmYmBxHW1s7xsZC3oMxdj9Wq3J3L8b87hubKPtRJis3XbkjUSaTwUIQ4w+AZDqD0myh9pHTlMnj/JoU1NTcAsxn5pqHJS38XC5nA/gegLsdx/mr2neHAFzvOM5gLpfrAvCA4zhbztcPgGDf489hw7Z1+OnDj4iK0/t/GpWP/MtXRV0/E/VLbOXbyupuZje9nZTn1fv6V0bl1TffjOteeysevucHaOPUz5ALZ97glyjq/+C7P4zKi4n6jz/+BHbt2glgYVH/zz7xPtHHVZdsjsodLZ2iToj67GaemZAP05EpCu4ZPDuM69/2UTzw9S8AUEV9soa0dpD3IyC989SddoPdpLbFRX3lAcREc8/3sGbLNvQd2g+ARFxAisfzRX3qU30I8wd0cyd5HtrJrGg3MUHkJt/61lfx3g98CF/+538CAHz5X/81qhsaHBDHtdn0ILjpDUQEs+sVrxXtKhV6se3afpWo4x6KlQr157ketl2xC/ufeRyAnONKRc5jsRQGBd38hjcBS1j4S9nVNwB8EcCBuUVfw50A3gvgs7X/31msLwBIpZIwTROGwqufbCf30pU3XCfqRs9+PypXZyjqyTsPtaJRkTfA8CNkImy8aDO8ShmTfSfQpuSlM5iLKhRX3BhLY10t0Tj2PrNftPv29/4jKvcPnhZ1HR10nsmEjUTcxpre0L147CzdfDF215sKY0sLY8IZUph1SkW6IeJMGpjOy4fTkWPHovLg2FlcWynjyMkwF14yQ4JbPEELJBFXUzOzRavo1ryOm57mSVScE792THQs17vZHHgqyw43Kyrhf3yfJhBjWlzfn/tvM916ZVe3aOuxPAbVKs29W5UL01cppzhEXgBuEqwiCPzINMhNpmpWbHXfYDEsxY7/cgDvBrAvl8s9U/vu9xEueCeXy30QwCkAb72gX9bQ0Pi5YSm7+g9jYdHh1Qt8r6Gh8RLGsnvuzUlv8zy4mBjWeslWUdd9/FRUPvbgU1G57C7Mrx5THlXuKPkWDT+1B9W3zmL4qT1Ye5VMtW2naEpMxSOP64/HDlFa5f37pXfe1Azp05s3yT2Ei7aSfv7E40/BD4KItKFQJv3OZmmPd+85JPrYtXNXVE6zDSUAOHqSifBniJh0nBF0AhAhYbFYDIABo7ZvcayP9NgTX/12VP7lN0vu/N5eFgFpLqzjC51cfYUwEdWCDcMwYCkblgBQZWSSrqf+FleLVPMsM5Wxw+b/ArXLpDOwTBOZdLgJdxvT3Vd0yqjPx37yYFQucVHfU0V9ttGq7FFwfb3EVMhqpQo/CFCufcfPWo0I9ZW9k8WgffU1NOoQeuFraNQhll3U93wXQDBv95XbmedSKM2h57qdUfns0ZNRudIn+eYkpExpM0Fp+nAfvFIF04f7UCnI3e5kE+1oq0Qcw/302wP9JOpDSYl06cXEj3/rG14v6u6970dReXxiBp7rYXwi5LXj5jxuArvznsf5FsvtAAAgAElEQVREHwePkqWgq1Pa+BuyZCPOZCnFVSqhXGomGvb19+PNxQp2P3sSAPDkXlIXzk5S7oITfdKj8oPve3dUvmSbtOQKXjyeFkrNM8B33WHAME0kayQh3NRXYanBfJW4j++YKxYQM0ZzYCeoPH9Pn76JJ5IwDBPxWuqvdevJDLhhg1RDeSbgBx8gj81ZJd0YD7BRfQG4BaDMiPsr1SoC30epRuohvRAlp5+rkiouAv3G19CoQ+iFr6FRh9ALX0OjDrHsOn5o2gnmc6MHC3tVpZhX3+pXEJd74ex/yT6YmuMrnPhxZtbJj4whcF2UR8YwqeitTT3klsrz3AHA2OhQVB4epOPaWmSIwuZtN0flFR0rRd3MNO0pZFNxmKaBbCr8nQp3bWX67cys1OeeO0zmzcPHpGcg39rgHm6eYgLj81OquvjEdAH/eW9oKuW6NZ/Fu390FzgqjFDyw//jdlF36WWkC3PdVM1jAIM++zBhGCZiNTOqz6hVRd44UzUFM482U16z9vZVUTkRJ/OsStghxxir5VwIl4fvcf1ZzuPll+1g46B5O/Ds06JdNsNzCaqxjMz0yeIcPdcNoxVrrtfCvVkZv7pvsBj0G19Dow6hF76GRh3i55BCK+S0Vz2szhdaySPhOplX39k9B0S7/AGKfPMUUV+EdRbKgB8gKJQx9Mwzot26l1EUHwqTou74TynQ58wA8dl1rtgo2jVkKGIuUNIXb9t2cVQeHRmCZVloaAxNcEOD5PFnM5HYV8yF5arP6tRnNyMqYaJ+VfFyFKOaRzJHMCVhnsDDTzwclTs7JB1DcxOFpW7YuIZ+al5YLgtQCXwgCKIgHS46B4KnX4rzgUl+eM2tUrVKMBOef94gHUnYEbA2PJS6qJjpeHDM5ZfuWLDdiaN7o7Iqlkt+QlOWDSP6zi3TOFzVJOhqzz0NDY1FoBe+hkYdQi98DY06xLLr+NViAUHgz3PdVKmQODjJY7qJqKBWXrVNtDvRR3q3X1zYvBGrcenEEGD6kCTlDCaoj3Sf5PcPDlFk4Fiepe4uy7G3dxCR6NqLpKnvjW8k2oJiqYJMJoud14TEI08+Qa65YyNE2TWPR54TN6jMNyof2dz356UU80Od9hxKPu8/nUzMq5/Do49LRqUN6zZE5bY2iiBsaJAkq3wLxIOJAEy3Z3q9wWizuAkQAGyD7g+u0wPA4Gkyd2ay9NtWUo28ZGm9g9ps1M6d689TU5JBnucgaGohs/Nll10t2lXLpPOXS9I8azOCE05GOnc95v6fL3+geh8sBv3G19CoQ+iFr6FRh1h2UX/o8YexekOvytsgxHk1co/DYrx3mV7Jl9dxOZnVJp6Qpj7uqWYbPgwEsA0fyRlJQpndR0SZzZBMwLvayYw0FacIwlFTmttOHKLotrgSFdfcSSrINTtvQCbTgGt23gAAKMyQV99DIz9mYxddKIQM5sKVmC82Rp/Zx7n+1d9RoTIXd3eS2XJmWs7Vvmf3ROWLGfnIjh2Xi3Zc1A8MyPTUTKQPOIe/IuaeHSb1bGhoWNRxL7kuxqh8pu+YaNfFuPTi8ZAQJF4TwcfHyUNxcLBfHFdhhCkrimRus21J9RGPU9RkqSSZlrkpkZNyuK6HIAgiTkGuBriKedatXlgKLf3G19CoQ+iFr6FRh1h2UX/vV76CS25+LSaf2yu+jzdSiqeqK3c9ucdVjHnxGUrAR9e126OyNyRpp4MzFGCzZk0L4okY1mxowfbrJbFCm01iHapS9t2wgnanL8kT9/zp3k2i3dP7yVKQPCJFvpn8TFTOtHXADzyUSuF3nSvJ68xUg1kYRMCKIn973MtPDF/Kx1z0N5T/QpVgv5VMyh3zRmZhaWVlAJieIa/HI0eOR+WLL5ZzlUiRyuTBQoAgCkAR6glPbRZT1CcWJBV4Kp8didUjY0TccuaMDM5qbydCE9MwYcCIstoODNDO/Qy77gDQ2UFchhsYZ6K6y17IU5KVBoXTX1CHq+nAAqIuLzHPPVVduNBsufqNr6FRh9ALX0OjDqEXvoZGHWLZdfzpU0PwK1Uc+JrMj9d5G3GXGy0y4SAnZORprFT3JbuJPLM23nq9qMscJq+7Sy/rRkNzCje+8QpkG6W+ZXIdS4l4ymap7bYG0tmGh6SJJ5ug52n/mVOiLiGSdAbwXReFsdAE1ZCh/jtZosxSsSj6sEUEl6gSJjCXRZW5CvkD57JQU0ZxW19HB41j+3bpjWax30rF5bXIMj12+iyZ2Gb2S2/I+MVX0odkNvxtf76Ob7DrrnonJhLkhRe4Uvc12bvtueco1dnoqDT7reggvvxSuQw/8FEqh3tNhw5TXoOGrLxfrrqMohKTNo33wKHnRLtSkcydPSuuFHU+25fg5kff8xAggF+7J6s8r56i06s8/othKbnzkgB+DCBRa/9Nx3E+mcvl1gH4OoBWAE8DeLfjOKqBUkND4yWIpYj6ZQA3Oo5zOYArANySy+WuAfA5AH/tOM4mABMAPvjiDVNDQ+OFxFJy5wVA5MJm1/4CADcCeEft+y8D+BSAf1isvyC0UGD84FHxfTl1d1Re+TqZYjjeRtlheTCP+tTyyyQSb+uVIllHC3GjxxDANEykUwl4BSlGGwkSxX0l4yk3bXW2kFpxxRmZnmrIJBPVk8clJ57PRNE15XXwqlVMnAnFTiNJv73zKhKrs2lpRisVyeTY0CzNaEWmFhw5Qtz/piIa8oAbz/NhmSaymXDcs0Uyp/K04Ym4VMGaGqkP25RztbKdvCpH+0msHnn8XtEuO0RitLX9JmBNL/zh0NRmrKRrJtwG1Yy4Aeeik8FZw0M0/wcPkjdhYVa2e+iRR6NyW2srXv3a1+KRR0KikcNHWJ6BszKXw7bN5JVox2iM5ZI0+3HiDFVM5585SUe54iLwA5Rr3nzcs3KeqO9emDlvSTp+LpezADwFYCOAvwNwDMCk4zhzV7sfQM8Ch2toaLzEYJwvT7iKXC7XDOA/AfwxgC85jrOx9n0vgB84jnPpOY65HcDtAOA4zvaBn+7Bii2bMHpYhsOaaXpL2o3K5h5z2OCUXTy7Su1konJK8X+JefSmNQBYbd3wxs5Ip3VIZ4pAcV5XN17mUKrIp+00iwsoKI4WMba5l4gn0NnTg+E5BxEmUXjsLVYqSamEJ2BUw5t9cRy9udXLzJlqgwDYsmULDh06NK8Pm8dGZGRIrWXxMFH5Azajx3LZplSTJecqzubDyDQinsmiUqgJmDxpqXBUUuMOeOCB4sDDNjhnZqZZM9lHmY0xFrPQ3d0ThdzmZ2hjrqpkrFnJKMe4f/7cxuC5xpjJpEUdj7fg7QI/QFNzC6Ymw1BgX9SdO2Fs58ouYOHs1hEuaOEDQC6X+ySAWQCfALDScRw3l8tdC+BTjuPcfP6jEXyyuRu33/9D/PNNsmnmSuKiU0X9BibqJ9N08505cVi0s9jivrRRnldHnkS+GAI0v+dTmPzKpxBUpIgaY6K+q1w8t0Ax1cVJuokOnJEx2ncVmah/VIr6HYy+e03vOvzOZ/4Un/+DPwQgRf3pCi325w4+K/p4PqK+Sietivr3P/AQbrj+FQCkqN/JAnGu3fUq0cfzEfVvaZI8huvWUAoqa/tNWL3zOpya4/Ljon6cqTuKqO9z60VFPiTPDJCH3n0PEB27KuqfOk2WmbbWVvzxn3wan/7kHwMAHnyIAqZUUf9jv/HrUbmrmywDR47LFxvfkb/m6p2iLpWic5OifhWv+6W34Id3fiv8zDz3eKotAKjWLFAf/fgfAEtY+EvZ1V8BoOo4zmQul0sBeA3Cjb37Afwywp399wL4zmJ9AaSnKPyRmNpDi9hgNxsApK4nAkyXcbmrOn5zkXTtjphctDEWDmhaFgzDgGlb8CryjVyZogVtZzKirsQWTzxJT/d0Wd701yaoz7FWmdtusJ8eBE8OnUGhkMeTu0MSi84uRkrJJJtLNl0i+38VLcC2TpmG+957KLqwrZUWX0rdJ2DEEIVCHql0CtsuDQW2fkZe0ZBhbrktraKPRiYAjChRcYUZmoP8JEVABkk538EgufPaT98F45LLYD8d8vcHV7yG2vXSi8FXWSj4C18xwR49SvfVKHPZ7e6SrsM/fYYerkePHEWhUMDjjz8BQO7tqPkg+GLk7sGWksa65NH9ODsrH04xJh1Vq9ycHBKkeHOReOwlbaqhkhf2/l7Srn4XgPtzudxeALsB3Os4zvcQvvF/K5fLHQXQBuCLF/bTGhoaPy8sZVd/L4Arz/H9cQA75x+hoaHxUseye+65gYEapZmAUSG97fQjPxV1rRvWReXYmrVROaWweXTPUkSep5jiynkiubAzaTS4Lkpnx5BolhtW1Qkmhs3b+OMbaST+9fRIPbuVbSJZHVIffSBGm0FPnhpE4AeoFkIR8eBzZG4C445rOHVS9FEcJZF1zVbJO9jG5O81N5CovGGLjEIcGqSIMytmo7W1He9854cAACeOkYnt4HOUd8AIJNnGmTMUaTh5VtYVzpKOm5kmcT7VKtUFeGR2jRXGYHguYoVQNXB33xnVVdgGp7FGnnPA0mRPTY6LumMnaBwXbbwoKl+14xWiHdezn3jiESQTCWzeFPIGrmAp3L7z/R+K40pMvC8wLn01TfbkNN0TQ8MycjTbQFGfgcLvj4A2/DyRQkshq9GcexoaGotBL3wNjTrE8qfQqkHNeMopxKZGpkVd/0OPR+XGNhIVV/pyd3QFC9aIQRJgWElGh10MU2j5RRdeSknXlSBTXGVCmukststvMJttY5sU9S3mwbXFlbvdvetIpOww29AUj+HWtaEoee8p6vM4o3GedKX4akzT58nDklswyJDYGO8gHrmDe/aIdqksnUtjcwsq5TL6joQ74BbTw9qaycIyOixNceVpEmeDGemp1neGTImX2cxE1S2aIciyAJtKBUHgI6iJz7PjZA2YGvtmVG69jcy7AABm4p1VxtGYIpv5ZVtI1B8bPCHanTy6Lyrbpgej9h8AehhBiqGkZhsbo2vR3UWZeY+fOCnaTUzS9bx8m+QdnJigMVeZadL3fHieh6mpUKXiVgPeDgB8XxNxaGhoLAK98DU06hB64Wto1CGWXcePGT4MA7AVHb/o0WdXMVWM7KHoqOnuJ6LytpUyDVIMZMJTn2iGSd5RpmmEvOlmEt6Ekva4gRE+KKSOPjPRGIwkEp7cJ0gysobitNyv6LDpPN+2pQmtSQtv2xLq5U0WeXf9n5Okt45VpG/3EDNtDY3JfYgk+xwfIYLRySHpQdjG9P8zVRel/Ptx8NHQVda2aa44waM7LfcaCmwfYnhGnme3TXPXlaWyHSiee+xc3GIc8AO4NbfjapHm22IkpeaoJDdxV5GpMpOSHoppRlq6e/dPovL4lLKPdJp0/ng8hSDwUa25bPf1naTxKrp0Xx+5BHe0035Iz8pVol2KEZX2nZbjn5igvZOf7iUS2nK5ghtf93r8zf/+3wAUP1zFeXEuRdof/ulnsRToN76GRh1CL3wNjTrEsov6cxK+qQRaeMxMovogBcyrLzlAUVSJxg7RrlIi0dBUVIlEE5m5TNsGDAOmbcOvymAek2UuVQ0kBgvlNFi4rWpKsZMkmmeU7LAVFvk2MjCO3qqLkYFQhL4kQ8/hGAXx4b/6pNmyP8FSS9lNos5lIZ48JHV2Wpq58rPkydhUceGVy5iuebk1M3PkYRaROFFUsryyUNydTUlRt50Na3MrXb+EEkZs8zwJrgsgqP0HSgXyBuSisjEq01/5HRSo5CohzM/tIdXwECPUyDb3inYFdtzI2FEUi0U8tz808aWZubCgeOSdFpz7P4rKJSX4i4f9Fh9/StTN5Ok8CyyAJwgClCsVHD8pVYMXAvqNr6FRh9ALX0OjDqEXvoZGHWLZdfykHcA05qdcPl9sUSJOemFXI+ONVyKxDE6Npewh8NTbsXQKge+jWpxFrFmaygym3/oqvRHT0+KMO9+vSjaXIE46v2VKnTbBmG96N3QjnrDRuyE0rflsX6KjQDr4mkYZzbV/nH7vJ/0yKm66SL/N9f2yKV2YOaNN3gY8y0K+Rq1VrJAun2BT0B2X53JDN+n117TI+U6y1OFNjEqtpblFtOPUXnNMXnP/OTGpFdC8GWckUWt15YaonE7I/l2L9PP9feQC3DAur63NzI/5/Cw8z8dEzSW5n7kqlxTT7YnTZ+gDL7/Eod/4Ghp1CL3wNTTqEMsu6res6oEVt1VnN5gg0UtlCkwm6Jt0lsRNSzEhBZxQUiEmEDzkQRUBArhBFYYS5YQKPQttxQusNEt8f2o6ZjEOJvqbKgsuI0mcS4U9d+6WTefTxNJprV0pz6Wrjfq/qltGBp7N03n6TM0YrMhZTV9zY1Q+3HcCmXQKV++8DADQNkgm0+opEvtXt0r24x4W2ZhOy1spxSIl02weY7aichicRy70P5sz9SbiNB9lxhicVExq1QkSsads+S575jkiFZkp09xMlyVppgrXDzA6Uz5vm19k6De+hkYdQi98DY06xLKL+pvf/h4kW9sQU7LUWmXyLLOULf+uLiJe6F5DZAqlkhTXSnkKGmlpkR5zPuPIjzVkYVoWEi1ZxFJSXeCJFhKK153HxPRqgcqGJcfL1Yp4VhkH4wJ0S0UEvg+v5jVWLlDgSJwRaiQU8bhSpB3/1qQU4TOMh7CR8dttjMnznG4la0ahuhLxuI2e7pBwIs1oyjclqY/mtOwjnWKZf5XUVdN5FtzDbjM1jwPP6BszTQQga0qSeetNjtC1bleUwcoIec8NK6rV8ChZfoIL5aD+/zH0G19Dow6hF76GRh1CL3wNjTrEsuv4K1/2CtiZLHpf/Wrx/fS3KANXwpc63PpVLNSrQp5q4yf7RLtEkk6nEl84meRMXx8aKxVM9PUhraSFSrSQeYyn5AYAgxFUTM+Q7tjYKvV4ntDQVPRzi5m2TDsG0zQRT4f7HQZLD1ZmpJGxRmmyy7DP+WlJgFkqEWFFaoaluFaiFWcecOi3GtbCr5RR7g+j15qnycNtzRqWt1DZDykzooyh09K7sFgmc14iTfq/obxrXB4dmZD9c+fLGUZoUpqQ55xspijNWUPmlKsoKbU0Qix54ddSZT8JYMBxnDfkcrl1CPPmtQJ4GsC7HcepnK8PDQ2NlwYuRNT/KADO5fw5AH/tOM4mABMAPvhCDkxDQ+PFw5Le+LlcbhWA1wP4DMJEmQaAGwG8o9bkywA+BeAfFuvLSqZgmCa6b7xJfH/mwMGoXDp8XNR1dtEwy2UyNcUMaUKKM8+3siIOVlnAhxEEgO/DL5WQZ6mkgDAn+RxsxZxnMbF9aIpEyHSTFKNtkSte1nFR3y0EoTxby6yaYKY/y6JzLilc8dxEmMpIs+h0ns7bZya2SlEKYxmLzmWFGd4IK2qvgcoqSlk2k6DzzNpSfZotkFpRKUhvus5VpI5UGaWJmtfdZaJ4UJPt5/77zDuyygKHCkq+A7uN5b3PSs5909TbWOfCUmfl/wXwcSDyq20DMOk4ztxV6wfQc64DNTQ0XnowVIcKFblc7g0AbnUc59dzudz1AD4G4P0AHnUcZ2OtTS+AHziOc+k5jr8dwO0A4DjO9lKhiHgygdkp+RYrnKXNoWpZ+ki3NtNb0mJvU68i3/jCLz5QQmqV80z0rEd5QEoWgNyMM5SQWh48XJxloatxKTgZrJ2pMPWKUfg+Yp2r4Q7Pp1bikofK7Ap2nmrosOuyOAHmCKWev8ckkbIZR2vPaowP1MbBdtUyFpOAlCAK7qhULclrFmMUZtxxhksygJQArFgMdudqVGvz4bP+y8x5irMAA4CRJEkvb0rm5QGWoHJeosnzYOvWrThw4MDiDV9kXOg4duzYAcwPd5mHpYj6LwfwS7lc7lYASQCNCCWA5lwuF6u99VcBOGcwsuM4dwC4o/Yx6DtwEmu2rsWeex8Q7Z78u/8VlQcVUf9t/+3iqNxk08WbOjMo2qWYCGy48kZURf11/8/XcOL33g6VCSDTSbTTqqjvs0W176dEx7x+tbQM2AaNMd0uRU++AN3CLDo//jcY/vPfBACYFl2vOYppACjNyph7k51nsSx3sYeHKcCmMUVqQEXhgJsMaGGezPYi95m/g/MHHw5/mz38dqVJFO9KyAfh9CTt/g8o16x9Fc1j1aAF3Noo56papvNsamnFyt/5Wwx9/iMAgBlGqX3iEKmCPV2SutraSPTaj2Y3iLrf/4u/jcoT03Iez4fdu3fj6quvXnL7FwsXOo7FXuRzWHThO47zewB+DwDm3viO47wzl8v9B4BfRriz/14A31mwEzk0AECitU18u/b1r4/KvtLVjEE3sDdFXPHpJmnmMhmHerpNEjLwBR64LizbRuPKbpQmJJlHcWT4XIeEYG+xosskD182jDNTYqBIHgbTrc1kEjDM8D+UqL4YvdWSWUmoWWFmtGRKEolkm2he4+ztGm+Qc3XmLOnF3tQ04HnhfwCpSy6L6p48Sw+Sl1fJVRgA/DI9FBpXyAdcieU4iFl0LhUlfblgZJmTNIz5Lyz+WzOTcv+mcYKu2cysNJ96Po/65ISu9e2++7PsfHwC4UbfUYQ6/xdfmCFpaGi82LggBx7HcR4A8ECtfBzAzhd+SBoaGi82lt1zLwhqErQS0da0nkxIm296rajzmN4aayRRzk5IvdV2SRS1lUgyrvv4lSpgmLASCaRapMpRZp5wxTHFG82n33YZh7/nSbXCjLMNJiXS0GfjCEwLMGr/AQQxLoqy4zwpHtspaucrOl0LE/W5Z11R2SD0y6TitK5eA8uOoXVleOwqlk66681vi8p77vhz0UcTG6K57WWiziuQ/t+eZJuRnrxmVoWl2rYtwDAR1MyyXkAbwOUynedsXm7qtjA+wbNDihmXbQA3Z2mTWM130MA++56LZCKOLRvWAgBKbB9lakrhOGTciL7/i6M+aCOnhkYdQi98DY06xLKL+kbtz1REYIvZuzvbpfjdwjausz6JWuXhI6KdnSIRWzVriM8G/QmePgAW33WHTMdUztNOOLO8IWbLabQYZXSlJMcxPk073GPFRjRWbBw8HQaZFF3GLWiRCLkiLX0eGhKsT19RA5iNv8h2x8fHJGlJYzYTlVt37kIyk8GmnbvCL5qJW2/dxZdE5ZNbrxJ99D/2UFR+6oAUv32bUlRd+3JSHSaGxkS76XHyxLyk0caNRgpPJkJ3kK4qqVpnJ+m84hlpqy8ya4jC8o2P3P6rUXnntddE5fWbNot27Sso0Mf3XHT19OKuu+8J+2cq00B/vzju4YdpDu75r/ui8t59+0U7nhrrpQD9xtfQqEPoha+hUYfQC19Dow6x/Oa8ms+USsjA/bLjiv4fYyT8FvPOMxT93GW6WIzpsOGBdFy1XEXgB6iWqyICDJC+72r6K+6Sz2nk44r/OQtaw8Hx1aLuRJzcj2fjGWwzsnjCvg4AkGe6amuGfjs7Q96KAHBRYW9U7m2VOrOIUWBbAQXm/goAK1aS22vv5q2IJ5Po3Ry6vsZ71vIOo9Laq3aIPgp7HqUx+lLv3nAVnWf7KtKfrbS8LiWTNnCeHujHNdUATw+E1/UqFgHZz7YQDinput1B+jyj8Or32GQ+LFXp/iiVpBdilRGCzBYL6PA9zNTITzuZG/emi7aJ4254DZmef+3XPxKV777rh6Ld3/09Ba4+/cxeUed6akL2Fx/6ja+hUYfQC19Dow6x7KK+7/lAEMwLXuGRb3FFXLMbKUjF5GJ/SoqXgUsmk8qYDL4x0yRSVgoFBL6HSj4viCDCgTBR35CifpJxwhWZGa1QkBFyh0bJlLW/eYuoK8dp/E1NHmAFMJtCUc9mca9WJwXVNF22Vvb/DJuPsbtF3ap2mgM+x56rZPRl6pQZiwOGEQUG5YdOR3WpJvJKbOuh8woPpD5TphRXH390X1QuVjZRH+0yWMhKMq+74bNwqy7O1kJp7z5OAZ+PsLRZ4ycU09hxIuZoU6Ih3/7eD0flV9z4GqpQAoEmJkhl+scv/Ck+/vFP4x/v+GsAgMcITXbteoU47sYbbo3KPatIrXvnu98j2l2zkyLsPvv5vxB1X3O+GZVLpeVJ26Xf+BoadQi98DU06hB64Wto1CGWXcd3q2UEQTDPpdZgDDmxojQ9mT7p0B7j1feVqDUrQ3q8pUSjcddcy7ZhGAYs20ZFYbfhZA2uMkaL5XKLJxj5Y0lGAp5qInfQ5BqZWjrNmG9Wr7WQSFpYe1Fo4mpqJVNXZ/f6qHz2lIw4G21ZGZX3n5JsNG2NxFTDSSiqCgFGhev8lgXAiEye04eei6qaO6n/uEIIUnJpTtc0SALMxlaKtpwaIDfXwT7p8jrQT2SnI8/ej0rxo+h7NnR9/ekwmTGnWeRb3FyYWapbyUGw+6kno/J/PXBPVB4bly7Mo6PkOnzwwAH899s/hh989y4AgB/QeT762KPiuLvuvjMqv/lN74jKN7/2l0S7Nevoev7JH/2RqGtooHvkji9+KSrPpQafuydfSPIQ/cbX0KhD6IWvoVGHWHZRv1oJRX1VWLPLLPItf1rUcYID0yCR1VD57JhXnyoUxRgTa0jEYcC045LwAkCVEUOYSielAqkFKVZZqEpSB+5nt2JKitgpm4mN9+fxsluqePT+kDOuzNI/XXE5M/s1SFXCZbM3qpCAjE1QH5ZJ6pNflSfDPSUNKwYYRvgfgD9N0YAe4+mPNUmizIpP44oful/UJUsUqRZn3nklS5rbhkZIRdg/OoBZt4q9o6H4P+6emxXXU1Qwzn+x9znJSHvw8KGobPJ8B4o5z2NmYs8PUKm66D8Tjo2rpYND0+K4/tOkIhw5ejQqH2a/CwDve/ftUbmNRQICwMd/67ei8sQkzf2/f/0b4bhrpDXeC+jhp9/4Ghp1CL3wNTTqEMvvuZefAXwPgRIcE58kAdmakWmtwNIgeTxwRuE4qzA+NDsrxW+e2MItlhAEYRqmqPcAABm0SURBVHCEr3jnVQP6rYpiXQgYpXY6QTvw04FM8ADQzv3guNyRv2hzV1S+ZgWQSZm45tKQPnzEJ1Gae9qp6shptktuVKUXW4mlyvJ9Gj8fOwCkGOe+aVohOUptbg1u6ShybkF5zapgor4ila9vp/k5MUVi9WBezsfQKJFtjFd9eEGA8WqtMyaOc3H7fNTx6hiLHqfXJpxvf9yo/YZbUzVEW08eOT5O81+cpevyzep/iHaFPAUFve89vyrq1q5eE5V/92O/E5X37N2LVCqFbReHwVN79z17nlFfGPQbX0OjDqEXvoZGHUIvfA2NOsSy6/gn7/k+NlxxMSpT0tMLLA2SaqaDSCBJ5VhS0a15NJqii/GMj1Y8FnruxWOwlISXlQLpyFMKeYVbJnNKIkPHZZql9996FiE2oBB29mwhL62Nmy5CujGNK197Rdg/U0IH+kn33b//sOhjukR13a4k4nRdGvPEOM1xNi3Taa/opEi7arWCIAhQrYbnbrGU1B7jlPeUZKauT3OQL0hTU7qZPOj25KmP0ark1Z+ZoT0E3/cRgMhQXmiW+qX2Fyj/z9uWNSqWyHR7+FCfaFepUFq4vHJfffj234zK65mH34c+8H60t7fhQx94PwDgY5/4PdafnMcLxZIWfi6XOwlgBoAHwHUcZ0cul2sF8A0AawGcBJBzHGdioT40NDReOrgQUf8Gx3GucBxnjn/pdwHc5zjOJgD31T5raGj8AuBnEfVvA3B9rfxlhDn1PrHYQcd/eBeu+x+3Y/gpGezQbbM0S4qoby+QkspQAnEMxm9fys+KutIIeVh5VRcdrovps+OwYsqzzyBTXLko+5+dJRPbEDNzXblCmqg68yejcqH5MlF34BkSihLpOLq3rMXpgXBs936PyCtOHCbzT2eXzDNwSReJg6lhOY/FWerfYxx+vWvXiHaIk5pUnJ6C73so1jz24j6JkRVGgOEVpdoSM5lXoiGz1E4yDr6ZFF3PgaMnRTvOcXghIvZLEkzuL5flvXOSkYrc6/2XqIsxPsj/68Mfi8q33nwLmhqbcOvNtwAA/uEf74jqDhyUnoEXiqW+8QMA9+Ryuadyudyc72Gn4ziDAFD737Hg0RoaGi8pGGp47LmQy+W6Hcc5k8vlOgDcC+A3ANzpOE4zazPhOI6alB61B8XtAOA4zvbBffvQtmEDCuOSGitu0BMyFkiaKNNc4Pl0nmw5/E0CQDgMBUGARM9alAdOzkvFzv2hecLFsE/WP3P8SSclBVjFoA28siXz14NRVKUzNjKNGRSmw7f79BS9UcslGq+tZOpJsI1Kc1bOY8ygPvi5JJPS399iNGJGQxPimSZUCuEbP2AZg8wM2xSMU1gyAEwP0lsMZSkNGDZJFFPM576kMuTy0GEAW7duxYED0t/+54EXehwmu9HiCSkdNTXS/dLR0RmVgwCIJxKo1DZVjx47FtWVSpLubQ47duwAMC8UZh6WtPA5crncpwDkAfwqgOsdxxnM5XJdAB5wHGfLeQ8Ggs+t34T3fOfbePyr/y4qum3ane50JZ10InFuUd9URH23TCJqURX1Z2jn3au62PinX8LRP3z/PFF/igWonFXSJXFRv2DRxbpy6ybR7pRNlMvHFVE/SNC4rnhZJ3bduAOP/yiMGV+qqL9xBS3A1DNfFXXtMfLuKszQAt6yaaNol91Iaa3ir3wDel9+C04/Esafe48Sj196x6uisree0mkBwD1/+kn6cHSfqLNXEv/cPcy77cA+aaEYZRxzg56PJ3bvxs6rQ366n6fIv3v3blx99dWLN2Tgq81Q3iiJOL0oVq9ZKeped8vNUZmL+q7no2ftOgycPAEAeOOb3xzVLSTq19bzogt/UR0/l8tlAJiO48zUyq8F8GkAdwJ4L4DP1v5/Z+FeCP5kHnB9HPneD8T39tWMuGHilKjLNJL7Z5JFxSWUaKUKy09WLSnkkow0wvdc+FUXhbOj8BSyzSLjV1fFAZelyR4rsv49+bbrrD5M/RnyLTmQ6onKj959Gtt2XIZH7w6jEWeG6C28agWZw9a1SbNl8jARSqxuGRZ1Y6P0YOntobdHNivNedNFemM0zUwj8DxUaw+K4giZC10WLRZT3jLpGM1pkJCuz4Ns2Z4+PRiVPcUMVeCmWuX/SxHqgo6xdO/GAi7GAOAy8/LAgEy/fv+DD0Tl3h56YL73XR9EzLLQ3BQSoFx7DeX+Ww4dvxPAw7lcbg+AJwB833GcuxAu+JtyudwRADfVPmtoaPwCYNE3vuM4xwFcfo7vxwC8+sUYlIaGxouLZffcixkGDAMYPy03pYaYJLp1tdwQO7zvZFTetr49KttZKUZn2ii6zbLlBorH+PmqswXE4jG0d7fP49Uv5mkvIK1w6R1jXmZTTGQNqnLDqilLfaydvlPUxUZIpZlOrYXtltE1chwA0BZnUYhTZH7smCSCBwDobmCiOORvt7VQVGIz48QfHZe+VWWL1KfqwBB6K1WMDoR7KxNHaW9j9VWk0hSnpJcgWGRgVdkrOTRJczA6wSLYDKm2zOLC00er4vaKVtoDcZX8AVMz5CXn+ecm9lj896icScl7opltzJkscrRYkudVYKZQ15UqKvfS/P7d343K11z9MlyWbcChQ+Em4zU7d0Z1X/k3ubczLz/EItC++hoadQi98DU06hB64Wto1CGWXcefMzF6gdTTBgZJJ9yxRXKjX7yGPhs+6XBWWtq3YynaG1DNKTGL9gNi2SzMmI1URyeqihvqRJ702KLCbrMiRjp+mUemKbpvUyvtNTRnpc6ZsvdT/+VnkQp+BRe73wMAVBlLjp0lfTSRkM/nMtMRZ/JSX5zKk555/BT5Q5TKUgdcs4NSP7tjo/A9F/mxcF9hZoZ8CKaY66k5K1NLc3feMwox5jGmt86aNFfTgdyTqD4P211nm7zuf/e3fx+VM4rZ8s8//7mo/KMHH7zwHwMQZ/tFq3tl2vM1q2nPJh6ndsND0szad/pkVOa+IgBQnKX9ohPHT0Tlu+79HtZs2oy77g3vj5ddc2NUl07LfbDpaUkCuhj0G19Dow6hF76GRh1i2UX9ShD6IBcUosziDImAZ8fGRN2aDhLtAmaS8SpSfK2a1Ec8kxF1dkq6/RqWiXg2Oy8NV2MDqRUqr/5KJpdWZ+k4V5VXWTqwTLNMOxVnEXPJSgVWzERLWyi2lctUN83mo++0JG4YHiG1yK0qBBhMLehsI9NTW7MUDeNMlRibnUHg+3Bnw99pZvOdbie1xbWkd16+Qn2cLslbaWyS1ILAoDpVsucmMN9fmDfeYmmzrtm5S9S95mZykU4q5rZvfvsbUfn+H/+YxnEBruqNDWQi3bBeuj5v3XpxVOb++DFLmpMnJsmcmi9IlYmbIMfH6Vo/+tgjeNd7b8ejjz0CANh1NaXozir3txb1NTQ0FoVe+BoadYhlF/VnPcAHkFcCbJrZI2hoSgYxtDbRjnwD445LNUjufIuFOyr06lHoKxAG6TS6HmbGJ1CakWJ0foYCUSpl2UkiTePoXUXjb2mR0cgBE1kryk74LDvt44N5dFV8HBwIRfeBAfJmtFwS9dMJKZZuXkXibEuznAObRYG5TOWYmZRkIRbjzu/asRl2IoGujWGW3/QmCrKcSNA5c7EcAPpdGsepovQMnGFWhKpB89i1sle0myrS/AyPyqhMDpvlRXjVK68XddlGmoOxUZkFV6SyWqJ4b9bUirn/DSxHQ3u7TAHW0UE0FDwtmRoUFWPjVz0PfTauEiN/OdU3gEqlilN9YZ6JKXYN02nptXqh0G98DY06hF74Ghp1CL3wNTTqEMuu4xd8A14w36yTYuYaVzGxDU+S3sYtPieHpQcUJ9/oaGsUdY1NZM6qzs4i8DwUJ6dQyksdvGkFi/5TKJKCgBFPMM9DU+E7yY+TOfL4wTOibn8/6d0xy8e15QoOHQmJOLauozGvbCeWFtOQew0prnfHZLTbyDClGI8xejBVN003kQ6a3bQVdiKFrk1hjrbY5iuiuqf+81+jcu96Yu0BgKEY6fgzZUmwUWH6biWg63nqjOSbry6RdiMWo2uhEofyyLSTfSdF3YkT9HmpBjzLssK8CzXzJffIM01VP/fFcTReuR/Cf13V8QVlHLu/x8en4boexsdDU92x40S91ZBR9rcWoqdbAPqNr6FRh9ALX0OjDrHson41CNMkpRWRKcXE2Zgph8VJLu88ROJOuShF4FsZb19zs/RsqjJihHgiDsMwEE/E0dQqA4IMxjdfUryhAia+xpmHmKeYiTwW1DHhymdrgll51m5ahUTKxobLVgEAWlpoLMkYzU86LsV53yfRVuUMjJnUtr2dTE2BIl5WGR9j3LLD+ah5m5UYu/DBfXuj8opuml8AqDBx1p2RfHx8Tri5quLL8S6VGqPI0nd9/vN/Luoe/PH9UXl0fFTUDZ+VXqBLQeCH7qVz6drK7Le5Bx4AzLB7xGbqyOysDPDi5BsVJY2YJ3IL0FxNF0rwfB/ThXBunW9+m37Llh6K8biaqv380G98DY06hF74Ghp1CL3wNTTqEMuu48/pflnlkeN5pHP6vtRHDw+QjnVgkMpvulhGvrU2kN6jZtJpaCcznRW3YdoxZDtWiGg/QBJKBhVJGpFixIou05mrCt98khGCbNnYKeomt14XlS//5Q8gu2odrv1saDIzPfq9yaeJm7+85yHZf5mlllbyDKZZ5hufZbPZd1qaFWdbSf/fEdjIwsBwEOqoTUz/Lwd0oQLFZJRIklmxrPDls8spPGWfH92lzAr0xNNPibqnnvkp+y1lv+V5EGx6tXTdc8dy4owzZwZE2xaWDjzBshPN5GXq9FmWa9FT/Mn5kHkaeCNmATBg1MyyK1cSeQrn2AeA6nc12aaGhsYi0AtfQ6MOseyifjIeg2EYiBlSJJtlZq/xvBQbB0ZIbuxNkclE5VAvlOi4eEJGLxWnKQov8F20Vl3MnD0LXxFRuZUxo3C7waLp4hOXUCKlqsz8owpgpSqZf/LlPNp9H/lyKBamsqRKdL3mtqh8XDFv4om76LdjMmGnzZJjPnWCot32xeS5GFM0xlN/+1f41b/YgG//7V8BADovJc+9DCMmMRRRv6u7Kyr/NCnNSSYXZ2fpt9Skbs8nXdb89FQLE3g8H8z1P/e/yHgZ87PSW5SbDxsbSPUsFKSoXxUmvIWTvfIa1YOwqYm89UZHJKdfS5NUexfDkhZ+LpdrBvBPAC6pje0DAA4B+AaAtQBOAsg5jjOxQBcaGhovISxV1P8CgLscx7kIYTqtAwB+F8B9juNsAnBf7bOGhsYvAJaSLbcRwCsBvA8AHMepAKjkcrnbAFxfa/ZlAA8A+MRi/a19+Q4ksml4MfnT+QqJa0NjCo8cy1Lb3UzC0My0FKRHGYFHU6MkQqiyNNluoQDfrWL27IgI/gCApjWrorKp5JQ3mB5gMPF7Mi+9tHYfoXE8evS0qJsJKOf61mkf7//YH+M//+UOAMDOG2+J6rp7ibCiadt20cfxx34UldcrxIA8L/2hMTrnLe/IiXZN7Nz+888+i1KhgMOP7QYAnDhyJKq7/E1vicrZrPSG7OpiFgsloKnEOPeKF5iK/aUGl6ktM3lJ3HKy73hUtlnQ0siI9CCcYNaiqpJCayH+P9uOwTDC/wBwlmUx3ss8KgHgkovnpbc8L5Yi6q8HMALgS7lc7nIATwH4KIBOx3EGAcBxnMFcLtdxnj40NDReQjAWYxvN5XI7ADwG4OWO4zyey+W+AGAawG84jtPM2k04jtNyjuNvB3A7ADiOs334yFG09q7C0IHDoh3357Ysxc7pc79yHt4ofyvOcrQnFN9lbh+F7yGxagPK/cegbjdZCTpO3cziMNhxrmIrnmXhwXklXNVj2zepxia0dXZjbDi0sWfY5pDNxq9uiJUZRVVi3kYRjWW8wFiH29pFO4tN3uTQEHo2bcHAkZCmymDhpWlGK5ZW6KRmWUKN0RFJeVVm7L/+Bbzxt27digMHDize8EUGHwe/z2wlGSsPxTUMul/UJJZVxq68VIZfyzKxZcsWHDoUXpdUijaReX8AkEqGviMbN20E5t8y87CUN34/gH7HcR6vff4mQn1+OJfLddXe9l0Azp7rYMdx7gBwR+1j8LX/+Tt4+19/Hn/z6jeIdjNM1G9qmhV1fp6J+q10M9vKwlyzgW7MDb3rRZ3Hs5UWCtjyl9/Aod/+lfOK+rGU3K1fuqhPzjLzRX06z6033Yr3f+yP8aW/+DSAhUV9W7mOx7/4+ai83pBORuUSidhff4rE0HXv+IBop4r6//fd9+OPbr4h/L022snnov6OVxC9MwA89eSTUfmL/3iHqDs5TPxwRRb0o7rTqEtg9+7duPrqq/HzBh+HzYKRunukYMszEp9P1B8apod1RVm0Cz0ImhobcP8DD+CG668HAFx2yTbqb0jyE86J+t/+7v859wkpWHThO44zlMvlTudyuS2O4xwC8GoAz9X+3gvgs7X/31nKD6655WbEmxrRdvkl4vuxJ8j7Kp9XFnSGFlZzhhZOuSBNWQEzzU2NyTdQJk4XpbF9BcyYjcb2FUi2SDOIxU1zyoOFR1g9e5Ju7CdGFL75zOao/NSUXPhVRoBpHxtAuVzF0WOhN1hbD+nWw8P08Ni+41rRx5hHv7dWMRjmi+RFeGaMHgKtw3I+PMaXv2ltB5LxGDatDW/q5hj12cqkKFeJKjOZpFMsKpJNlUUQ4hcbXCc/dUouuFMYjMov9FZGSPphROQfPJWXKkWtWSMjJxfDUu34vwHgq7lcLg7gOID3I7QIOLlc7oMATgF46wX9soaGxs8NS1r4juM8A2DHOape/cIOR0NDYzmw7J572RUdsGI2Vr5SpkEaHCCR2BiSYmk6zXjq4iReVopSzPWqJAqVClL3NZOk/xuWCR/ArGXCrUh9y2ZeYGcnpffVgydJdB5rIn3r5IwU/57YfS+1m5D7FStsyrZ66ngV5XKAU8fDMWRbyERz062vi8rDfZRBFQC8KeLfR6NUR/Iz9HubW2g+Bp78sWi3j5nbGmYKmHU97DsbmpzetJH4+VZ1co8/uddQZCQUCcU8m2E7YqUFPNN+EXEhqbeeD3garrhtwjTC//9fe+cWYlUVxvGfzowax5EcL4054y0klC7jEGIYUUPEVJI9xFdRPfXoQ0ER1IsQCPVS9hCBqERQDX8sw+hllC72JOUFMrrgROSllJgRpzEnHO1h7ePe++Q0Wees7bC/HxzOPnv2Oes/Z61v773W+s5/AZwZTqcE26/LD9YezazG+6/K+e8SHceZrHjgO04J8cB3nBISf+28s8NcuDDGaEt+Rnd5T2pQceKj/tzfjmdSc1sqme3p+T7+nxk/jG+G833rnwfS/tGC1hnMHznHnn0/sLIzn3P0+x9pv17f5c02229/5NL27Pb0fbv7d+SOOzea9tMWzMhPWy6ae/Ol7bbKbJqnVmirrAZgZnN6Hp6fMco8vOfj3Gfc0JT+31PJ5yHMqqSJP93L0im7z3/Lfx/TM8tpD41cYAwYmhrqZPB8WjfLMvP9zTVLULeOpEaWbbPyOQ8jGfOK0dG0X3x2rMYoAyfLvMy6Dos725g2rYXFi0Jq9OBgmipzfXtH7n1HBr7nSvArvuOUEA98xykhE+bq15nJPpvjOJOBCXP1Y1/xpwBTzGx/dbuox9WgwXW4jgbpmBC/1XecEuKB7zglpKjA3zLxIQ3natAArqMW15GnITpiD+45jnMV4Lf6jlNCombumVkvwbG3Cdgq6eVI5W4H1gGnJN2U7Gsjsj24mXUCbwPtBDOaLZJej63FzGYAe4HphDawQ9JGM1sK9AFtwAHgycRctaGYWRPwFXBc0roidJjZT8AwIZnwvKTbCmojUazso13xk8p9A7gPWAk8ZmYrIxX/FtBbs68Ie/DzwLOSVgBrgA3JdxBbyyjQI+lWoAvoNbM1wCvAa4mOIeCpBuuo8jTBsr1KUTrultQlqeo9UUQbiWJlH/NWfzVwRNKPydm7D1g/wXvqgqS9wGDN7vUEW3CS54ci6PhF0oFke5hQqQtja5F0UVL1RwktyeMi0EPwVIyiA8DMOoAHCFc5zGxKETrGIWq9ZKzst0Gwspd0uhE6Ygb+QiBrQHcs2VcUOXtwIKo9uJktAVYB+4rQYmZNZnaIYJK6GxgATkuq/gIoVv1sBp4n9eGcU5COi0C/me1PnKEhfr1krewPmtlWM6s0QkfMwL9cRlEppxTMbCbwPvCMpDMTHd8IJI1J6gI6CHdjKy5zWEPrx8yq4y7Zda+LaidrJXUTuqIbzOzOCGXW0gx0A29KWgWM0KDuRczAPwZ0Zl53ACfGOTYGJxNbcP7JHrzemFkLIejfkfRBkVoAklvJzwhjDteaWXXAN0b9rAUeTAbW+gi3+JsL0IGkE8nzKWAn4WQYu14uZ2Xf3QgdMQP/S2C5mS1N3HofBXZFLL+WXQRbcLgCe/D/Q9J/3QZ8K+nVorSY2bxk9Bgzuwa4hzDe8CnwcCwdkl6Q1CFpCaE9fCLp8dg6zKxiZq3VbeBe4DCR60XSr8BRM7sx2VW1sq+7jqgJPGZ2P+GM3gRsl7QpUrnvEdb5mwucBDYCHwICFpHYg0uqHQCst447gC+Ar0n7tC8S+vnRtJjZLYRBoiYSm3RJL5nZMtJptIPAE5JGx/+kumq6C3gumc6LqiMpb2fyshl4V9ImM5tD/DbSRRjo/JuVfT11eOae45QQz9xznBLige84JcQD33FKiAe+45QQD3zHKSEe+I5TQjzwHaeEeOA7Tgn5CyizmcHA44G9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage.data import astronaut\n",
    "from scipy.misc import imresize\n",
    "img = imresize(astronaut(), (64, 64))\n",
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of using a network to go from some x position to the value of a sine wave, what we're going to do instead teach a network to go from the location on an image frame to a particular color.  So given any position in an image, the network will need to learn what color to paint.  Despite the seeming complexity of this task, it is remarkably similar to what we've just done.  Let's take a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4096, 2), (4096, 3))"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We'll first collect all the positions in the image in our list, xs\n",
    "xs = []\n",
    "\n",
    "# And the corresponding colors for each of these positions\n",
    "ys = []\n",
    "\n",
    "# Now loop over the image\n",
    "for row_i in range(img.shape[0]):\n",
    "    for col_i in range(img.shape[1]):\n",
    "        # And store the inputs\n",
    "        xs.append([row_i, col_i])\n",
    "        # And outputs that the network needs to learn to predict\n",
    "        ys.append(img[row_i, col_i])\n",
    "\n",
    "# we'll convert our lists to arrays\n",
    "xs = np.array(xs)\n",
    "ys = np.array(ys)\n",
    "\n",
    "# Normalizing the input by the mean and standard deviation\n",
    "xs = (xs - np.mean(xs)) / np.std(xs)\n",
    "\n",
    "# and print the shapes\n",
    "xs.shape, ys.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we're going to do is use regression to predict the value of a pixel given its (row, col) position.  So the input to our network is `X = (row, col)` value.  And the output of the network is `Y = (r, g, b)`.\n",
    "\n",
    "We can get our original image back by reshaping the colors back into the original image shape:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10ab1c4d0>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(ys.reshape(img.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember before, we were using regression to input to our network `X = x`, and output `Y = y`.  The only thing that is changing here is the number of values in our input and output, and what they represent to us.  But Tensorflow can handle any number of values we give it, so this is actually a pretty simple modification to the network definition.  We'll stick with the convention of using the variable `X` to denote the input to the network, and `Y` to denote the output of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=[None, 2], name='X')\n",
    "Y = tf.placeholder(tf.float32, shape=[None, 3], name='Y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"building-the-network\"></a>\n",
    "## Building the Network\n",
    "\n",
    "For our model, we'll make our first deep neural network!  Instead of having a single fully connected layer, we'll have many layers.  We'll make use of a for loop to simplify the creation of the network. The network will look like:\n",
    "\n",
    "<TODO: wacom/motion-graphic>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_neurons = [2, 64, 64, 64, 64, 64, 64, 3]\n",
    "\n",
    "current_input = X\n",
    "for layer_i in range(1, len(n_neurons)):\n",
    "    current_input = linear(\n",
    "        X=current_input,\n",
    "        n_input=n_neurons[layer_i - 1],\n",
    "        n_output=n_neurons[layer_i],\n",
    "        activation=tf.nn.relu if (layer_i+1) < len(n_neurons) else None,\n",
    "        scope='layer_' + str(layer_i))\n",
    "Y_pred = current_input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of this code is pretty much the same as what we've done in previous networks.  We setup our cost.  Except before, we only ever had 1 feature.  In this network, our output is 3 vaules, `r`, `g`, `b`.\n",
    "\n",
    "<a name=\"training\"></a>\n",
    "## Training\n",
    "\n",
    "In order to better measure the error, we'll sum the error across all 3 values.  There are many ways we could have approached this which we'll get into in later sessions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = tf.reduce_mean(\n",
    "    tf.reduce_sum(distance(Y_pred, Y), 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to use a different type of optimizer called `AdamOptimizer` which in general will work better than the original `GradientDescentOptimizer`.  It's pretty similar, except it has some tricks to help with gradient descent.  Getting into the details of it is beyond the scope of what we have time for.  So long as you're not working with sequential data or building a recurrent network, it will probably always work better than just using GradientDescent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.AdamOptimizer(0.001).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the code is pretty much the same.  We create the optimizer exactly the same way, by giving it our cost.  And then create a session to iterate over chunks of our training data.  Every 20 iterations, we're going to draw the predicted image by evaluating the predicted image tensor, `Y_pred`, and giving it every location in the image to predict, the `xs` array.  This will return us the predicted color values for those locations.  This process will take awhile!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 172.17854)\n",
      "(1, 162.1358)\n",
      "(2, 158.38873)\n",
      "(3, 152.67969)\n",
      "(4, 149.76804)\n",
      "(5, 146.23723)\n",
      "(6, 143.35861)\n",
      "(7, 140.4002)\n",
      "(8, 137.55347)\n",
      "(9, 139.33987)\n",
      "(10, 131.58356)\n",
      "(11, 128.87686)\n",
      "(12, 126.50136)\n",
      "(13, 113.796906)\n",
      "(14, 119.55303)\n",
      "(15, 108.97501)\n",
      "(16, 111.56414)\n",
      "(17, 106.996185)\n",
      "(18, 104.297424)\n",
      "(19, 105.574936)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 103.14761)\n",
      "(21, 98.95816)\n",
      "(22, 106.02545)\n",
      "(23, 97.30605)\n",
      "(24, 101.48321)\n",
      "(25, 103.80437)\n",
      "(26, 96.34882)\n",
      "(27, 97.87338)\n",
      "(28, 93.826904)\n",
      "(29, 97.40483)\n",
      "(30, 93.31227)\n",
      "(31, 94.69197)\n",
      "(32, 91.03031)\n",
      "(33, 91.86284)\n",
      "(34, 91.35516)\n",
      "(35, 91.92512)\n",
      "(36, 88.39188)\n",
      "(37, 91.73926)\n",
      "(38, 90.32792)\n",
      "(39, 87.044876)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(40, 86.786514)\n",
      "(41, 93.14215)\n",
      "(42, 86.90954)\n",
      "(43, 89.64491)\n",
      "(44, 90.974625)\n",
      "(45, 83.94623)\n",
      "(46, 85.426605)\n",
      "(47, 88.150696)\n",
      "(48, 87.28512)\n",
      "(49, 83.61746)\n",
      "(50, 83.941605)\n",
      "(51, 81.95358)\n",
      "(52, 80.97114)\n",
      "(53, 80.375)\n",
      "(54, 84.43106)\n",
      "(55, 80.47572)\n",
      "(56, 81.070435)\n",
      "(57, 78.38652)\n",
      "(58, 83.07626)\n",
      "(59, 77.81444)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60, 82.479416)\n",
      "(61, 82.116066)\n",
      "(62, 79.87164)\n",
      "(63, 75.32407)\n",
      "(64, 77.02017)\n",
      "(65, 79.4736)\n",
      "(66, 76.34559)\n",
      "(67, 80.20185)\n",
      "(68, 80.303505)\n",
      "(69, 74.76511)\n",
      "(70, 75.103195)\n",
      "(71, 76.6705)\n",
      "(72, 79.33567)\n",
      "(73, 79.13271)\n",
      "(74, 73.49722)\n",
      "(75, 73.89087)\n",
      "(76, 72.38709)\n",
      "(77, 75.07342)\n",
      "(78, 73.17832)\n",
      "(79, 71.93903)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(80, 72.92389)\n",
      "(81, 70.56337)\n",
      "(82, 74.76998)\n",
      "(83, 77.33362)\n",
      "(84, 73.1083)\n",
      "(85, 68.37868)\n",
      "(86, 70.41844)\n"
     ]
    }
   ],
   "source": [
    "n_iterations = 500\n",
    "batch_size = 50\n",
    "with tf.Session() as sess:\n",
    "    # Here we tell tensorflow that we want to initialize all\n",
    "    # the variables in the graph so we can use them\n",
    "    # This will set W and b to their initial random normal value.\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "\n",
    "    # We now run a loop over epochs\n",
    "    prev_training_cost = 0.0\n",
    "    for it_i in range(n_iterations):\n",
    "        idxs = np.random.permutation(range(len(xs)))\n",
    "        n_batches = len(idxs) // batch_size\n",
    "        for batch_i in range(n_batches):\n",
    "            idxs_i = idxs[batch_i * batch_size: (batch_i + 1) * batch_size]\n",
    "            sess.run(optimizer, feed_dict={X: xs[idxs_i], Y: ys[idxs_i]})\n",
    "\n",
    "        training_cost = sess.run(cost, feed_dict={X: xs, Y: ys})\n",
    "        print(it_i, training_cost)\n",
    "\n",
    "        if (it_i + 1) % 20 == 0:\n",
    "            ys_pred = Y_pred.eval(feed_dict={X: xs}, session=sess)\n",
    "            fig, ax = plt.subplots(1, 1)\n",
    "            img = np.clip(ys_pred.reshape(img.shape), 0, 255).astype(np.uint8)\n",
    "            plt.imshow(img)\n",
    "            plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After letting this run for a few minutes, we'll see the image becoming more like the original image.\n",
    "\n",
    "<a name=\"homework\"></a>\n",
    "# Homework:\n",
    "\n",
    "Head over to the [notebook](session-2.ipynb) for more details.\n",
    "\n",
    "<a name=\"reading\"></a>\n",
    "# Reading:\n",
    "\n",
    "Cauchy, Augustin (1847). Méthode générale pour la résolution des systèmes d'équations simultanées. pp. 536–538.\n",
    "\n",
    "H. Robinds and S. Monro, “A stochastic approximation method,” Annals of Mathematical Statistics, vol. 22, pp. 400–407, 1951. \n",
    "\n",
    "Sutton, R. S. (1986). Two problems with backpropagation and other steepest-descent learning procedures for networks. Proc. 8th Annual Conf. Cognitive Science Society. \n",
    "\n",
    "Yann Lecun. Efficient BackProp. 1998.\n",
    "http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf\n",
    "\n",
    "Kingma, D. P., & Ba, J. L. (2015). Adam: a Method for Stochastic Optimization. International Conference on Learning Representations, 1–13.\n",
    "\n",
    "J. Schmidhuber. Deep Learning in Neural Networks: An Overview. Neural Networks, 61, p 85-117, 2015."
   ]
  }
 ],
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   "display_name": "Python 2",
   "language": "python",
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