labs/IntroToAutogradAndBackpropForNNets.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro to neural net training with autograd\n",
    "\n",
    "In this notebook, we'll practice\n",
    "\n",
    "* using the **autograd** Python package to compute gradients\n",
    "* using gradient descent to train a basic linear regression (a NN with 0 hidden layers)\n",
    "* using gradient descent to train a basic neural network for regression (NN with 1+ hidden layers)\n",
    "\n",
    "\n",
    "### Requirements:\n",
    "\n",
    "Standard `comp135_env`, PLUS the `autograd` package: https://github.com/HIPS/autograd\n",
    "\n",
    "To install autograd, first activate your `comp135_env`, and then do:\n",
    "```\n",
    "pip install autograd\n",
    "```\n",
    "\n",
    "### Outline\n",
    "\n",
    "* Part 1: Autograd for scalar input -> scalar output functions\n",
    "* Part 2: Autograd for vector input -> scalar output functions\n",
    "* Part 3: Using autograd inside a simple gradient descent procedure\n",
    "* Part 4: Using autograd to solve linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import copy\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Import plotting tools\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Import numpy\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Import autograd\n",
    "import autograd.numpy as ag_np\n",
    "import autograd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PART 1: Using autograd's 'grad' function on univariate functions\n",
    "\n",
    "Suppose we have a mathematical function of interest $f(x)$. For now, we'll work with functions that have a scalar input and scalar output. \n",
    "\n",
    "Then we can of course ask: what is the derivative (aka *gradient*) of this function:\n",
    "\n",
    "$$\n",
    "g(x) \\triangleq \\frac{\\partial}{\\partial x} f(x)\n",
    "$$\n",
    "\n",
    "Instead of computing this gradient by hand via calculus/algebra, we can use autograd to do it for us.\n",
    "\n",
    "First, we need to implement the math function $f(x)$ as a **Python function** `f`.\n",
    "\n",
    "\n",
    "The Python function `f` needs to satisfy the following requirements:\n",
    "* INPUT 'x': scalar float\n",
    "* OUTPUT 'f(x)': scalar float\n",
    "* All internal operations are composed of calls to functions from `ag_np`, the `autograd` version of numpy\n",
    "\n",
    "**Important:**\n",
    "* You might be used to importing numpy as `import numpy as np`, and then using this shorthand for `np.cos(0.0)` or `np.square(5.0)` etc.\n",
    "* For autograd to work, you need to instead use **autograd's** provided numpy wrapper interface: `from autograd.numpy as ag_np`\n",
    "* The `ag_np` module has the same API as `numpy`, so you can call `ag_np.cos(0.0)`, `ag_np.square(5.0)`, etc.\n",
    "\n",
    "Now, if `f` meeds the above requirements, we can create a Python function `g` to compute derivatives of $f(x)$ by calling `autograd.grad`:\n",
    "\n",
    "```\n",
    "g = autograd.grad(f)\n",
    "```\n",
    "\n",
    "The symbol `g` is now a **Python function** that takes the same input as `f`, but produces the derivative at a given input.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return ag_np.square(x)\n",
    "\n",
    "g = autograd.grad(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 'g' is just a function. You can call it as usual, by providing a possible scalar float input\n",
    "\n",
    "g(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2.0, 2.0]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[g(-1.0), g(1.0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot to demonstrate the gradient function  side-by-side with original function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'gradient of f(x)')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_grid_G = np.linspace(-10, 10, 100)\n",
    "\n",
    "fig_h, subplot_grid = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=True, squeeze=False)\n",
    "subplot_grid[0,0].plot(x_grid_G, [f(x_g) for x_g in x_grid_G], 'k.-')\n",
    "subplot_grid[0,0].set_title('f(x) = x^2')\n",
    "\n",
    "subplot_grid[0,1].plot(x_grid_G, [g(x_g) for x_g in x_grid_G], 'b.-')\n",
    "subplot_grid[0,1].set_title('gradient of f(x)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1a:\n",
    "\n",
    "Consider the decaying periodic function below. Can you compute its derivative using autograd and plot the result?\n",
    "\n",
    "$$\n",
    "f(x) = e^{-x/10} * cos(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return 0.0 # TODO compute the function above, using 'ag_np'\n",
    "    \n",
    "g = f # TODO define g as gradient of f, using autograd's `grad` \n",
    "\n",
    "# TODO plot the result\n",
    "x_grid_G = np.linspace(-10, 10, 500)\n",
    "fig_h, subplot_grid = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=True, squeeze=False)\n",
    "subplot_grid[0,0].plot(x_grid_G, [f(x_g) for x_g in x_grid_G], 'k.-');\n",
    "subplot_grid[0,0].set_title('f(x) = x^2');\n",
    "\n",
    "subplot_grid[0,1].plot(x_grid_G, [g(x_g) for x_g in x_grid_G], 'b.-');\n",
    "subplot_grid[0,1].set_title('gradient of f(x)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PART 2: Using autograd's 'grad' function on functions with multivariate input\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, imagine the input $x$ could be a vector of size D. \n",
    "\n",
    "Our mathematical function $f(x)$ will map each input vector to a scalar.\n",
    "\n",
    "We want the gradient function\n",
    "\n",
    "\\begin{align}\n",
    "g(x) &\\triangleq \\nabla_x f(x)\n",
    "\\\\\n",
    "&= [\n",
    "    \\frac{\\partial}{\\partial x_1} f(x)\n",
    "    \\quad \\frac{\\partial}{\\partial x_2} f(x)\n",
    "    \\quad \\ldots \\quad \\frac{\\partial}{\\partial x_D} f(x)  ]\n",
    "\\end{align}\n",
    "\n",
    "Instead of computing this gradient by hand via calculus/algebra, we can use autograd to do it for us.\n",
    "\n",
    "First, we implement math function $f(x)$ as a **Python function** `f`.\n",
    "\n",
    "The Python function `f` needs to satisfy the following requirements:\n",
    "* INPUT 'x': numpy array of float\n",
    "* OUTPUT 'f(x)': scalar float\n",
    "* All internal operations are composed of calls to functions from `ag_np`, the `autograd` version of numpy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x_D):\n",
    "    return ag_np.sum(ag_np.square(x_D))\n",
    "\n",
    "g = autograd.grad(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0.]\n",
      "0.0\n",
      "[0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "x_D = np.zeros(4)\n",
    "print(x_D)\n",
    "print(f(x_D))\n",
    "print(g(x_D))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3. 4.]\n",
      "30.0\n",
      "[2. 4. 6. 8.]\n"
     ]
    }
   ],
   "source": [
    "x_D = np.asarray([1., 2., 3., 4.])\n",
    "print(x_D)\n",
    "print(f(x_D))\n",
    "print(g(x_D))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: Using autograd gradients within gradient descent to solve multivariate optimization problems "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper function: basic gradient descent\n",
    "\n",
    "Here's a very simple function that will perform many gradient descent steps to optimize a given function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_many_iters_of_gradient_descent(f, g, init_x_D=None, n_iters=100, step_size=0.001):\n",
    "\n",
    "    # Copy the initial parameter vector\n",
    "    x_D = copy.deepcopy(init_x_D)\n",
    "\n",
    "    # Create data structs to track the per-iteration history of different quantities\n",
    "    history = dict(\n",
    "        iter=[],\n",
    "        f=[],\n",
    "        x_D=[],\n",
    "        g_D=[])\n",
    "\n",
    "    for iter_id in range(n_iters):\n",
    "        if iter_id > 0:\n",
    "            x_D = x_D - step_size * g(x_D)\n",
    "\n",
    "        history['iter'].append(iter_id)\n",
    "        history['f'].append(f(x_D))\n",
    "        history['x_D'].append(x_D)\n",
    "        history['g_D'].append(g(x_D))\n",
    "    return x_D, history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Worked Example 3a: Minimize f(x) = sum(square(x))\n",
    "\n",
    "It's easy to figure out that the vector with smallest L2 norm (smallest sum of squares) is the all-zero vector.\n",
    "\n",
    "Here's a quick example of showing that using gradient functions provided by autograd can help us solve the optimization problem:\n",
    "\n",
    "$$\n",
    "\\min_x  \\sum_{d=1}^D x_d^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x_D):\n",
    "    return ag_np.sum(ag_np.square(x_D))\n",
    "\n",
    "g = autograd.grad(f)\n",
    "\n",
    "# Initialize at x_D = [-3, 4, -5, 6]\n",
    "init_x_D = np.asarray([-3.0, 4.0, -5.0, 6.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_x_D, history = run_many_iters_of_gradient_descent(f, g, init_x_D, n_iters=1000, step_size=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make plots of how x parameter values evolve over iterations, and function values evolve over iterations\n",
    "# Expected result: f goes to zero. all x values goto zero.\n",
    "\n",
    "fig_h, subplot_grid = plt.subplots(\n",
    "    nrows=1, ncols=2, sharex=True, sharey=False, figsize=(15,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(history['iter'], history['x_D'])\n",
    "subplot_grid[0,0].set_xlabel('iters')\n",
    "subplot_grid[0,0].set_ylabel('x_d')\n",
    "\n",
    "subplot_grid[0,1].plot(history['iter'], history['f'])\n",
    "subplot_grid[0,1].set_xlabel('iters')\n",
    "subplot_grid[0,1].set_ylabel('f(x)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try it Example 3b: Minimize the 'trid' function\n",
    "\n",
    "Given a 2-dimensional vector $x = [x_1, x_2]$, the trid function is:\n",
    "\n",
    "$$\n",
    "f(x) = (x_1-1)^2 + (x_2-1)^2 - x_1 x_2\n",
    "$$\n",
    "\n",
    "Background and Picture: <https://www.sfu.ca/~ssurjano/trid.html>\n",
    "\n",
    "Can you use autograd + gradient descent to find the optimal value $x^*$ that minimizes $f(x)$?\n",
    "\n",
    "You can initialize your gradient descent at [+1.0, -1.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x_D):\n",
    "    return 0.0 # TODO\n",
    "\n",
    "g = f # TODO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO call run_many_iters_of_gradient_descent() with appropriate args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# TRID example\n",
    "# Make plots of how x parameter values evolve over iterations, and function values evolve over iterations\n",
    "# Expected result: ????\n",
    "\n",
    "fig_h, subplot_grid = plt.subplots(\n",
    "    nrows=1, ncols=2, sharex=True, sharey=False, figsize=(15,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(history['iter'], history['x_D'])\n",
    "subplot_grid[0,0].set_xlabel('iters')\n",
    "subplot_grid[0,0].set_ylabel('x_d')\n",
    "\n",
    "subplot_grid[0,1].plot(history['iter'], history['f'])\n",
    "subplot_grid[0,1].set_xlabel('iters')\n",
    "subplot_grid[0,1].set_ylabel('f(x)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 4: Solving linear regression with gradient descent + autograd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe $N$ examples $(x_i, y_i)$ consisting of D-dimensional 'input' vectors $x_i$ and scalar outputs $y_i$.\n",
    "\n",
    "Consider the multivariate linear regression model:\n",
    "\n",
    "\\begin{align}\n",
    "y_i &\\sim \\mathcal{N}(w^T x_i, \\sigma^2), \\forall i \\in 1, 2, \\ldots N\n",
    "\\end{align}\n",
    "where we assume $\\sigma = 0.1$.\n",
    "\n",
    "One way to train weights would be to just compute the maximum likelihood solution:\n",
    "\n",
    "\\begin{align}\n",
    "\\min_w  - \\log p(y | w, x)\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toy Data for linear regression task\n",
    "\n",
    "We'll generate data that comes from an idealized linear regression model.\n",
    "\n",
    "Each example has D=2 dimensions for x.\n",
    "\n",
    "The first dimension is weighted by +4.2.\n",
    "The second dimension is weighted by -4.2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "D = 2\n",
    "sigma = 0.1\n",
    "\n",
    "true_w_D = np.asarray([4.2, -4.2])\n",
    "true_bias = 0.1\n",
    "\n",
    "train_prng = np.random.RandomState(0)\n",
    "x_ND = train_prng.uniform(low=-5, high=5, size=(N,D))\n",
    "y_N = np.dot(x_ND, true_w_D) + true_bias + sigma * train_prng.randn(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Toy Data Visualization: Pairplots for all possible (x_d, y) combinations\n",
    "\n",
    "You can clearly see the slopes of the lines:\n",
    "* x1 vs y plot: slope is around +4\n",
    "* x2 vs y plot: slope is around -4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qko4EgBUANgD4FyHEP5/9219IKf8hwDYR4inFIjmnQZqqrmh1RKVpEsmpdMHIaHJKw9an3iwQQyvkt2PurFo8sfkKTKU1T0SOu3MSN3BqR1mb/1h9jeHOtXrOyt/d+Ef4f/54MT44PYF7n+vDgzcuBRpK92XVI11KOhJSyv8NQI07REhAlBt92RlRZb/z0emJXKh008pF+ObP3nAkqH5GCLgygriBEzsytvlEgc3rOSt//tg/Yevq6WXC2WkQM31I5UiXqnUkCCFlsFOJMvudB156G9vXdmJeS8IwC9yvippWcVIvg5AsTuzIafXJ5kRNbt+Z7JJVVcpd24GOBCEhxc6IKvudI8eHcd/zfdi6ugPtTbWOXsx+Rwj0CkEFnWxGwocTOzJr80bOSnvT9BLQOWenJ8IeZVNyaoMQUh47KyTyv5Nd6nlNRzt2b+jKVWS0+mL2a6VGFtXni0k4cGJHZm1eLxlz+9pO/Nd9b2BgdBJPbl5h6XiqwogEISHFzohK7zvfuHoJlrRPC+qhLVfiyc0rbGWuexEhKN7FMVsmPDtf7NZujqT6sLv0U9PkdOn39V1lbT7rrDyx+QocvH0ltl1/Me57vg8Do5MFnw97lI0RCUJCip0RVanvOEnkqo2ZKxNsBdWXeZLwYte28r/X1liLbddfjIvmNKC+Noo5DfoObSQi0N5UB61BoqE2hgdvXBq6VRnlEFKGohZJSZYtWyYPHz7s6jGtlmu2gtXSzl62JcyYvI+B90Qv7FMlBkYmsWbnIVNlgvMpNyK0e9yQQfsMACPbemLzFRAQ1W6T+ZiyT0YkCCGOsJMoZrS5V2NdLFd/QtO0UCegEXXJt9ml85uxaeUiNCdqkJrS8FfP/DpXMKo4ShH2pEivoCNBiAJ4WfLZa+wkihUvd2trrMXJMxO46aFzZX93b+jCNR3teKG33/RxCTFD1mbbGmtx+2eXFJSb3r62EwMjKRw5PjyjnoqfSZFh0gQmWxISMNnR+Zqdh7Bi+8tYs/MQ+k6O5BIL3TyPXuKiU+wkihWP7DatXJTbWhlAbmOj71zbUXDcR26+FBLS9Wuwglf3kczErXtdfJyWRA1+cNMy3HbV4pwTAZzbknvTykW53/OjDVZs3Unb/dIEt2BEgpCA8aPks1Fy2dxZtUimnI148jPTJ6Y0RAWQiJceoRWP7PKLYuWHmqMRgadvXYFkKoNEPIqTZyZx085XAku+TKc19PWPzFgqywRQ93Er2dboOH8wpwFNdTF8/wuXYDg5hV0Hj+HI8eFcwSjg7Dbl8SgGRiZzkYHFbY0lkyI1TWI4mcKHwxPoftSenYStDDwjEoQEjB/zrkbC9Mbx066NeAZHU7jxB69hxfaXcd2DpY9XPLIbT2UwryWBpfObcftnl2DbM7344p7X8MU9r+HkmUmcPzuBjIZAq/9pmsQHp5M5JyKINlQTp8YmdZ/3qbFJS8cxsv0Pz0zgS2dtbNszvbj9s0uwdH4z5rUkclt1P3LzpTh5ZrIgMvD2wChaG+K6S4+zTssbx0/nnIj8c5q1k7DlYtCRICRg/Cj5bCRM9WcjB05fiFZL/OYvdzu05UpcMn+2Yag5e5ygxXVwLIX+kclQCXyYmZjSf94TU5ql4xjZTf6zzE5p3HbVYuze0IX/c95sPLl5BRrrYpbsOtsP6uNRR3YStjLwdCQICRg/itEYCdNwcir3u5MXop2XfH5RqY811GLJ3CYsam8wPE45cfU6dyGVzmBwLBUqgQ8zUSF073W0zMxAsR3UxCK6xyl2Bk4MJbGovRGfOm8W5s5OoK2pFlNpayuHsv0gG9EoPqdZOwlbgSrmSBASMH4Uo9Er1btjXSfufa4v9xknL0Q3stkjEYFETQzXdLRjbdd8NCdqMJycwoGe47l7UnwNWXH1o3hVPBbFgZ7j2L62syDLP7vxEnGXRDyKHes6c0m4WZstlX9jtKw4azdtjbW47arFWDinHifPTGLp/GYcOT4M4Gw+RE20wF6s2nX287sOHpthJ1YcgbAVqGJBKgNYkEp9WJDKGvnLyWpiEYxOpHHTQ7905cXr1os8ndbwm5Mj2JSXpLZrfRc+ObcJsVjEcEmcH4WCstd4/4t9WNs1H60NcbQ31eKC2QnE7FfypH0aoGkS7w6O4b3B8VzF1I+31mNha4OhTRnZwdO3Tu9pUZwAmXWmsyWri+3Vql0XV7687arFZStfKg4LUuXDlzEJE3ovTACO1pUXl8Ge0yAdj3jy2zl3Vi2e2HxFrqCUneMNJadyTgQwHUbe9GhPziEwKuXtR/5EdpR495rOUIwSw04kIrCwtQFNdTWm77eRHWRXJhUnQN6x/yge33i54eqLwbEUPlZfg33dyyGlLNsGs5GE7LE1TUNGwtSxVaZqHAlCwoLRKKg2FnEtggDMdCzcaqeTNtl1CPwqFOT0nhFrWL3fpezAyLYAzDiHsW0nytp2uTbnR7a+fMVFM6Y/wriU2PVkSyHE1S4dZ5UQok8I8TshxF1uHJOQMGC0AuK9wXGllh1aXalhBrvZ6mFLTiPeUMoOrNiWF7ZdfOy1XfMNVyiFDS8iEj8CsMDJAYQQUQB/B+BqACcA/EoI8bSUsteF9hGiNOWWaub/Lchlh15MJ5RKqCxF2JLTiDeUsgMrtuXlVFn22PlF2Nw+h9/YciSEEE8b/ROAVvvNyXEpgN9JKf/17Pl+CuB6AHQkSMVjFJ4dTxUKTNDLDr2YTnDiEHDagQDGdmDFtrycKsseO7tE1I99O7zG7tTGvwewG8D3dX5GXWjXhQCO5/1+4uzfCKl4jMKzH2+tVyp079V0Qn59ieLKgYQ4waxteTlVlj12dimxSn3aLnanNl4DMC6l/J/F/yCE6NP5vFX0nm7BOlUhxEYAGwFgwQJHMymEuI4T+zQaOQFQKnTP6YTwQv0sjZe2nb/6R9M00ytCVMaWIyGl/I8AIITo0Mlb+G+OWzUdgZif9/s8AB8UtWEPgD3A9DpoF85JiGs4tU+j8KzT0L3bWxNzOiGcUD/LY2b1hd2+VGn9xmmy5T4hxF4A9wKoO/vfZQCWOzzurwAsFkJcBOB9AF8CcKPDYxJS1fhR/VFl3HaiiH+o9uyqvS8V43T552WYjhy8gumX/wcAVjhtlJQyDeBWAM8DeAvAPinlr50el5BqxsslbU7xep+MrPDn7+LodLdT4g9Onp1XdqVyXwoCpxGJKQBJAAlMRyTekVJa25rNACnlPwD4BzeORQhRd2tiP0Z3RsKfX0JbtVFvtVL8HKIR/e3jy5U/99KuVO1LQeE0IvErTDsSnwbw7wD830KI/Y5bRQhxHVW3JvZjdFdO+I1GvVNTGXwwnMR7g2P4YDiJdNqVcRLJI53Wcvf4w+Ek3h0cK3gOHw5PoK2x0GEw89L20q5U7UtB4dSR+DMp5X+TUk5JKT+SUl4P4Ck3GkYIcRdVqz/6MborJ/x6L537X+xDX/8obtj9Kv6vHQdxw+5X8ZuTI3QmXCS7SVv2Hn9h96s4eeac43BiKInuR3tw21WLC75n5qXtpV2p2peCwtHUhpRyxpZxUsq9To5JCPEGVZdrGhX/ScSjGBiZzLW1JVGDoeSUrbaXq2qo99JZ2zVfdwOxfd3LcUFzYsY5iHX6Rydn3OM79h/F1tUd6N7bk/vbRXMacjZS/Ozyp0IS8SjSmsRUWoMQAtd0tOOF3v7c+dyKGqjal4KCm3YRUkWouOxM7yX/yM2X4uSZyYK/7VrfhQde+i1e6O23PN9dTvj1nJnWhrjuiDadYUTCLaYymu49bk7U5H6f15JAfW1U99kVb9t956oluGP/0QKbAVBgM25FDVTsS0FBR4IQhamGBEC9l7yExE07X5kRDdi6ugMv9PabTrgrPo/RZ/WcmbamWt1ISSzq+l6HVUtNNFKyHHz25T+nQb8KZf6U1NbVHTknAiiMIH33c/4XfKqGvpuFjgQhiuJG1nlYxKz4Jf/+0HjZkaqbeRR6zkxzXQy71nflQu/ZEW57I0ehbtHeWKt7j89vrsWhLVeWtdn8KSmjTbCklLiwpd61NpvpU9VWZ4KOBCGKYmbJYinCLGZGeRPDyamC393MkteLWHxybhP2dS9HOqMhFo2gvbEWsRgjEm4Ri0WM73FD+e/n24kfm2CZ7VNO+27YYI8gRFGcZp2HuWiOXlb8rvVdONBzPPe7H1nysVgEFzQnsKC1ARc0J+hEeICTe5xvJ7sOHsOOdd5ugmW2T1VbnQlGJAhRFKdbGYdZzPSmGloSNbh7TSe++zm1p2mIfxTbSSIexRObr8BUWvPERsz2KS+3IVcROhIBsPCuZ4NuAgkB5ZYsliPsYqY31VCJYWHiDD9XT5jtU077btigI0GIojhdq+63mIUlsZNUJ27Yp9k+VW11JuhIEKIwTkZbfopZmBM7SeXjln1a6VPVVGeCmUOEVDBZMbuwpR5tTfpr8d0gzImdVvB6l9JKQ5X75aZ9+tWnwgQjEoQQx4Q5sdMsjLpYQ6X7VQ32GSSMSBBCHFMNuyFWS9TFLVS6X9Vgn0FCR4IQ4phq2A2Ro1prqHS/qsE+g4RTG4SQshhlvOf/vbUxjqdvXYFkyvss9SBWiIR9Oa3fuHG/3HzOrY1xPHbLZYgJgVg0gqmMhsGxVEWvpvALOhKEkJIYzXUvbmvE2wOjvs+BBzX3Xm21AZzi9H659Zz1jrNjXSfufa4PA6OTzHNxASGlWlnHQogdAD4HIAXgGICvSimHS31n2bJl8vDhwyWPyyJQlce791xr5mOBq4MZ+1SZgZFJrNl5aMbIcl/3ctyw+9UZf/d6PwGj9vixj4EHkZCKtk8n98ut52x0nK2rO9C9t8c32wkpph6WihGJFwF8S0qZFkJsB/AtAFsCbhMhyuB3WN9ornsqowUyBx7k3Hs11QZwAyf3y63nbHSc7E6yVo7Jomv6KOdISClfyPv1NQDrgmoLIaphJtzrttgZzXXXRCOB5AwwV6E6cOs5l9tJ1uiYxf2oJVETyFReGFB91cbNAH6u9w9CiI1CiMNCiMMDAwM+N4uQ0nhln0ZL6k6NTQI452is2XkIK7a/jDU7D6Hv5IijQkBGGe/tjbWBZMIzA985YdBPt56z3nF2rOvEroPHDI+p24/6R3D/i31KLGdVjUByJIQQvwBwns4/fVtK+dTZz3wbwDIAn5dlGskcieqkGnMk3h8ax4rtL8/4+8HbV2LBx+oxOJbyJH/AzKoNP0O9FRRiDrzRKufwuPWc849TE4sgFhElVxeVy6vI59CWK3FhS729C1QfdXMkpJSfKfXvQogvA1gN4KpyTgQh1YRRmPadU2NoqI15lj9gNNcdVM6A1fNWkOMReqw8C7fsS/c4DcafN+pHxZELTqlNo9zUhhBiFaaTK6+TUo4H3R5CVKK1IY7d67sKwrTb13bigZfezgkzK/gV4sV0D7FHWJ6FUT/6WEO8oO/tXt/FKTUo6EgAeBBAE4AXhRD/LITYFXSDCFGFSETg/OY6bLv+Yjy+8XJsXd2B+56fXg+fHd2FNX/Aqw2eVCrVXO3YfRZ+b/5VKq9i6+oOPL7xcmy7/mKc31zHyBbUXLXxB0G3gRCVaU7Ecd7sOt1CP35uHe4mXhaZUqlUc7Vj51kEUYCsuB/VxCIYnUjjlX8dxL6eE7k2NCfUd9D9QDlHghBSmnLOQhhrHRiNVN0oFMTloupg51l4aRulKO5Hcxpk6Bx0v1BxaoMQUoasyF3YUo+2plrLJYP9DBObwcuogVfTPSreR7+we+12noUXtmGn/U76XKXDiAQhVURQ+1SUw8uogRfTPareRz9wcu12noXbtlHNz84rGJEgJKTkj6p+PzaJ/pGJsiMsVRMPvU4SdXs0qep99AOn1271WbhtG6WKumX7U//IBH4/Vp3RJjswIkGIAlitc5A/qmprrMWdq5bgjv1Hy46wVE08DFuSqKr30Q/8vna3bcOo/eOTGaz/0esldwgFwHokOjAiQUjA2Flbnz+q2rRyUc6JAEqPEJ3UmfA6JyBMc9DVXK8jiGs3axtmbNSo/e+cGivoQ3fsP4pNKxfl+tNwMhWKGhhBQEeCkICxEyrOH1U1J2pMjxDthonDUkjIL1oSNXjsa5dh/6bl2L3x/StsAAAgAElEQVShC9d0tIemXocTNE1CQuLRP7sMP/7Kp7F0frMytUrM2qheH9i9vgsPvPR2weeKdwhNpjJVO51VDk5tEBIwdkLF+Qlow8kp08lodsPEQS3BUxFNkzN2gdy9oQuL2xqVjqI4RS9Jcff6LpzfXIfmRPAhfrM2qtcHohFgYHSy4HjFO4RmpKza6axyMCJBSMDYCRXnj6p2HTyGHes6TUcZ7EwhVHNOQDF6L6zuvT0YOvvSqVR0r/vRHmQ0BO5EANZstLgPNCfK7xBaV1O901nlYESCkIDJOgV6lSqNKB5VJeJRPLH5CkylNU+SwIIq6pROa+gfncRURkNNNIL2xlrEYsGOf6rVqfLqut16xk5sVK+SZSwi8OCNS3P9CYDlflot0JEgJGCsTjcUr/A4f3bC8xGhHWfHKem0ht+cHMGmR3ty59y1vgufnNsUqDNRrZUyvbhuN5+xmzYqINCciONjDYX9Kkwri/xEVMIu3cuWLZOHDx8u+ZmFdz3rU2uIX7x7z7VmPhZ4Lzdjn2YJspiO31txfzCcxA27X53x4trXvRwXNCdKfNMZ5a7T5WcQGvvUzZHY0IU5DXFEIhFb9uD2M7ZroyxSZYipi2dEgpAQEWTSo997eExlNN1QejqjeXZOMy+USERgcVsj9nUvRzqjIXY2HF+pL5z8l/PcWbW5KbSMJvG9Z3vxQm+/7Rev28/Yro0ymdgZTLYkJER4OT+v2t4RNdGIbnJbLGosW06vwcxS3OyqjRt2v4r/sOMgbtj9Kt4eGA38fnlB8ZLK6x48hMHRFGpiEdz4w9fxQm8/AOOlkOWeh51nbKbNVm2gWvNe3IKOBCEhwqtiQCrWiWhvrMWu9V0FmfS71nehvVF/hOj0GjRNIpXO4PtfuAS7N3Rh6fxmADNfKNVUHtvoWjOahq2rO/D4xstz96r4Ppl5HlafcTns2kA1FxhzA05tEBIivEp6VDG0G4tF8Mm5TQVTCPXxCE6OTOjOfzu5Br0pje1rO3Hf89MlkvNfKNU0etW71rbGWvx+dArbnuktuFcPv/JOwX0yeh77updDSpl7hsXP2MnKHLs2EEQycSVBR4KQEOHVnhSqvhxjsQguaE7kXvQ37DbOXXByDXovoC0HjmLb9RfjvNl1BS+Ualq1oXett121GN1nV1kA5+7VY1+7rOA+GT2PD4aTWLfr1YJn6FbyrF0bCNteL6qh7NSGEOJ2IYQUQswJui2EqIQXe1KoHto1M53g5BqMXkCL2htzzkp27j2VzuCxr12Gazrac+eo1NGrXinwi+Y06N6raEQU2KLR88g+My+mhJzYQJj2elENJR0JIcR8AFcD+Leg20JINeD1Nt5OMTPSdHINRi+gRE0050Tkz73f+MPX8fXPfAKvf+uP8eTmFRW5TDCbVHrjD1/Hul2vYtszvfj6Zz6B+ri5l7Xe89i+drpaZBa3o16q23GlourUxv0A7gTwVNANIaQaUD20a2Y6wck1lJsjNyqLXcnLA42u+elbV5jKJyh+HkII/OXTb+LI8eHcZ9yOeqlux5WKco6EEOI6AO9LKd8Qgg+fEL/wu06EFcwmw9m9hnIvIFVzSLzE6JqTqYzpl3X+89A0iW9cvQS9H454mtCosh1XKoE4EkKIXwA4T+efvg3gLwBcY+IYGwFsBIAFCxa42j5CnOK2ffpdVVI1/BhplnoBVVqCpRn7LHXNdl7WqkULqr1PuYlSJbKFEH8I4CUA42f/NA/ABwAulVJ+ZPQ9lsiuTqqlRDbL95bGjxeCh88g8AdoZJ92rzkML2j2KdOEr0S2lPJfALRnfxdCvAtgmZTyVGCNIiRgVKzxoEcQLxC/Xgiqjab9wM41u/U8vLalsPSpsKDkqg1CyDnCMD8fVGVMP6tMVuPyQKvX7Mbz8MOWwtCnwoTSjoSUciGjEaTaUb3GAxBc2Wi+ENTCjefhhy2FoU+FCaUdCUJIONbGB/VC5wtBLdx4Hn7YUhj6VJhQKkeCEDKTMMzPB7WqgXskqIUbz8MPWwpDnwoTdCQICQF+rI13kuDm1Qu9XJvceCGEYZVBUFi9N3pFqKJierrCreJgbj0v1ptwDzoShJCy2fZ+vNCttin/3HZfCFwGaIzdexOJCLQ2xG3f11LOSEuiBm8PjPJ5KQZzJAghJRPczGbRu72qwY+ku6CSRMOAk3vj9L5mnZEzE2ncsPtVXPb//uO03fWP4P4X+/i8FIOOBCGkZIJbJa/I4KoPY5zcG69Wb3Tv7cHarvmOjkvch44EIaRktn0lr8jgqg9jnNwbL1dvFOfd8HkFDx0JQkjJ5XBBvWz9WKLHZYDGOLk3btxXI7trb6rl81IMpfbasAv32qhOqmWvDb8wSqgMMiHRr300Aly1obR9Ork3Tu+rkd0tbmvEUHKKq2z8IXx7bRBCgsNo9UOQa+79WKLHZYDGOLk3Tu9rKbvj81ILOhKEkLJQvEkQ0O7CAXMkCCGEEGIbOhKEEEIIsQ0dCUIIIYTYho4EIYQQQmxDR4IQQgghtqmIOhJCiAEA75X4yBwAp3xqjgpU0/WWu9ZTUspVfjVGDxP2CVTPM6uW6wTMXWtY7NMJYXjmbKM+puyzIhyJcgghDksplwXdDr+opuutlGutlOsoR7VcJ1Bd11qKMNwHttEZnNoghBBCiG3oSBBCCCHENtXiSOwJugE+U03XWynXWinXUY5quU6guq61FGG4D2yjA6oiR4IQQggh3lAtEQlCCCGEeAAdCUIIIYTYho4EIYQQQmxDR4IQQgghtqEjQQghhBDb0JEghBBCiG3oSBBCCCHENnQkCCGEEGIbOhKEEEIIsQ0dCUIIIYTYho4EIYQQQmxDR4IQQgghtqEjQQghhBDb0JEghBBCiG0qwpFYtWqVBMAf/uj9BA7tkz8lfgKH9smfEj+mqAhH4tSpU0E3gRBDaJ9EZWifxCkV4UgQQgghJBjoSBBCCCHENnQkCCGEEGIbOhKEEEIIsQ0dCUIIIYTYJhZ0A0i40DSJwbEUUukM4rEoWhviiERE0M0iFcrCu5619Pl377nWo5YQFaD+qAkdCWIaTZPoOzmCWx45jBNDScxrSeAHNy3DkrlN7MyEEE+h/qgLpzaIaQbHUrlODAAnhpK45ZHDGBxLBdwyQkilQ/1RFzoSxDSpdCbXibOcGEoilc4E1CJCSLVA/VEXOhLENPFYFPNaEgV/m9eSQDwWDahFhJBqgfqjLnQkiGlaG+L4wU3Lcp15XksCuzd0QdM0DIxMQtNMl2YnhBBL6OnPD25ahmgEeH9onBoUIEy2dIlqyCaORASWzG3Ck5tXIJXOIKNJfO/ZXrzQ28/EJ0KqiCD0rlh/amIRjE6kcd2Dh5h8GTCMSJRB0yQGRiYLPN7iv6XTGvpOjmDNzkNYsf1lrNl5CH0nRyrSO45EBNqaahGPRXHjD1/HC739AJj4REilkq93vx+bRP+ZCfzb78fx5vuncetjR3zVu6z+XNhSDwGBmx76JZMvFYARiRLoLTd65OZLMZnWCv62e0MX/vYXv51h0E9uXoG2ptqAr8IbmPhESOWTr4FtjbW4c9US3LH/aE77tq/txH3P9wWid9QgdWBEogR6y43eGxyf8bfuvT1Y2zW/4LtmDVov4uEVmibx+7Hpc/3b78fQPzJh+3xMfCKk8snXwE0rF+WcCGBa47YcOIpNKxcZ6p1TfUunNXwwnMR7g2P4YDiJdFrL/Rs1SB0YkcijeN5P07QZHm99PKrrBbc2xAv+Zsag/SywomkS7w6O4eSZiYIRhd3zZROfittefB8IIeFF0zRsXd2B5kQNWhvjutrXnKjR1Tun+pZOa/jNyRFserQn9/1d67vwyblNiMUi1CCFYETiLFmjz89zODWWwjUd7QWfG09ldL3g9qbaGdnE5QzazwIrg2MpvDc4PmNEYfd8+YlPh7ZciSc3r2CSEyEVhKZJnBpLYdszvfjintdw/PdJXe0bT2V09c6pvvWPTuaciOz3Nz3ag/7RSQDUIJVQNiIhhIgCOAzgfSnlaq/Pp2f03Xt78NjXLkPvhyM5j/fjrfW6XvAFsxO5bGKzWcx+zvGl0hnDaIrd82UTnwghlcfgWArde8+9yB946W3sWNdZENHcvb4L5zfXoTkxU++c6ttUZmZE+MRQEunMuekNapAaKOtIAPg6gLcAzPLjZEZGH42IGQ4CAF2nwapBZ+f48s/r1RxfPBbNRVP8OB8hJNwUa+KR48O497k+PL7xcgAoO2Byqm810Yju92NRBtJVQ8knIoSYB+BaAD/065ylEneyy43ammoRiYiCJUjZv9nBqMCK0ZRIqcQjM+f6eGs9dqzrtDwFQwipPvQ0cWB0EvFY1JT2mdU3I11rb6zFrvVdBd/ftb4L7Y2MQKiGqhGJvwFwJ4Amv04YROJOcYGVUh5+ucQjM+da2NqA5voaPL7xcmQkUFcTwZwG+44QIaRycaqJZvStnK59cm4T9nUvRzqjIRaNoL2x1pTeEX8RUqpVNEkIsRrAn0gpNwshVgK4XS9HQgixEcBGAFiwYEHXe++95/jcKlen/GA4iRt2vzojzLevezkuaE6U+GbVE8gD9MI+q5GFdz1r6fPv3nOtRy3xDKXt02tNpK4pj6mHrWJEYgWA64QQfwKgDsAsIcSjUsr1+R+SUu4BsAcAli1b5oo3ZJTnoIKDYSbxyC9K3Q8V7pUKeGGfhLiFWfsslfvlRl/3SteK29aSqMFQcqrqdckrlHMkpJTfAvAtAMiLSKwv+SUP8bPWQylUSTwqdT8AeHqv6KQQogZu6aIXuqbXtl3ru/DAS7+1vC8QNcccnGwyIFuR7cTwOD46PYG2swk+QdVzVyXxqNTacC/rYujV+ajU/UwIUZ3hZAofnZ7A979wCXZv6EJbY62tvu6Frunp0KZHz1UfNqtL1BzzKBeRyEdKeRDAQb/Pq+fRZmvKHzk+HEg992zi0c+6l2MqoyESEUjEI757x+XWhntVF8PISank/UwIURFNk/hweAJbn3pzhj5a7et6CZVtDXFH0xBGGtWcqCn4vVxbqTnmqYqIhNV673oGlK0pDwRXeyESERhOTuHGH76Of7f9ZVz/4Cu+e8illsl6WfueG/QQ4j962jk4lkJ3UcXJLQeO4rarFtvq67FYBBc0J7CgtQHnzarD706NOYoCGOnQcHKq4PdybaXmmKfiHQk74alSHm2QtRf8LKltRKm14VbrYliBG/QQ4i9G2mmkjxfNaXDc193QOD0d2rW+Cwd6jud+N6NL1BzzKD214QZ2wlNGFdnmtUyXwQ4q4UYFD7nc2nCzdTGswg16CPEXI+3c171cVx/ra6OO+7obGqenUS2JGty9phPf/Zx5XaLmmKfiHQk7hmlkQOfPTgSasetnSe1SlFoS5lXteyvFuwghzjHcNkBAVx/nNDjv925pnJ4OWdUlao55Kt6RsGOYqhpQtXvI3KCHEP8w0s5IJFI1kUdqjjkq3pGwa5gqGpCqDo6fcF03If5QSjurNfJI/dGn4h0J1Q3TKio6OH6hSnEwL6iCUtAkZASlnapqXCXrj1MqftUGcM4wne7WqRJWl7RWAiqsWiGkmlBFO1XQO+qPMRUfkQgSr8Jg1eoZq7BqhRDiDKu6qIreUX+MqYqIRBB4WV61Wj1jrusmJNzY0UVV9I76YwwdCY/w0vir1TP2suAVIcR77OiiKnpH/TGGUxse4aXxq1JPwm8qLXGWkGrDji6qonfUH2MYkfAIL8Ng1ewZq5L8RQixjh1dVEnvqD/6MCLhEV4WVqFnTAgJI3Z0kXqnPnQkPMJr41d1rTUhhBhhVxepd2pDR6IETpdv0viJCrDYFQkKIw2lLlYWdCQMUGXtslNY0pUQEgRBaSg1z3+UTLYUQswXQrwshHhLCPFrIcTX/W6DKmuXneBlLQuz5w+6Gh0hJBiC0FA3NY/6ZR4lHQkAaQDflFJ+CsDlAP5cCNHhZwNUWbvshCCdoaCdGEJIsAShoW5pHvXLGko6ElLKD6WU/3T2/0cAvAXgQrfPU8rjrIQqZkE6Q2Y7NL1+QiqLbJ8G4LuGuqV5pfSLmjUT5XMkhBALASwF8Lqbxy03f+fl8k2/CLKQi5kObWYOlfOdhISH/D7d1liLHes6ccf+o75pqFuaV0q/9DRrcVsjhpJTVatTSkYksgghGgEcAPBfpJRniv5toxDisBDi8MDAgOVjlxsx5y9TOrTlSjy5eUXoEi2dFnJx4nmbieiUewZhDi86tU9CvMQr+8zv00eOD+Pe5/qw7fqL8b/u9EdDrWqekcYZ6ZcQQlezPjidDKVOuYWyjoQQogbTTsRPpJRPFP+7lHKPlHKZlHJZW1ub5eObGTF7VcXMr9CYE2fI6UvcTIcu9wzCnPDq1D4J8RKv7LO4Tx85Poyv/v2vEBWwpaFWtdKK5pXSOCP9igroalb/yGQodcotlJzaEEIIAD8C8JaU8q+9OEdQYX+/l0TZXbNt9BJ/cvMKU8czU3im3DOohITXasBKnQrWqKhs3NRVu1ppVvPKaZyefg2OpXSvr9hpqDadUjUisQLABgB/LIT457M/f+LmCYKq3x70KNush+/GS7xcRKfcM6iEhFdCqgk3ddVNrdTTvXIap6dfete3e0MXDvQcLzhOtemUkhEJKeX/BuBpMkKpEbOXCX52X9ButMmKh+9HxKZc1CLbae9/sQ9ru+ajtSGO9qZatCRqXGsDIcQ9yvVpKzpmVivLHdNI9+bOqrWscXrX15KowTeuXoLeD0dwYiiJazra8Z1rO5BKZzAwMlkViZdKOhJ+oRcC83rqwc4L2q02WZmu8GvVSqkwZCQisLitEV//zCfQvbcn1BVGCakWjPq0VR0zo5Vmjmmke09svsKWxuldX9a50DQNp8ZSuPGHr1eVXqk6tREYXk892An9udUmK9EQVVatDCWnck5Etr3VlshESCVgVcfMaKWZYxrp3lRac03jss5FJBKpSr2qioiEG+E0TdPw+7FJJFMZZKREXU0UcxqsZyHb2f3OraRDIw9fCIH3h8ZntEWFzXWYcElIOCnWXU3TdPuygMQHw0lMZTTURCNob6xFLBYxpZVm9MFI92piEdensKtVryrekXAjnHZNRztGJtMYODU5o7iKHQ/W6gvarXwFvemKXeu78JdPv4kXevuVC8NpmoQQAvs3LcfgWAq7Dh7DkePDVZfIREjY0NPd3Ru6cE1HO17o7c99rvvfL8SHZybxnx/tKdCkT85tyjkTpbTSjDYaTdOOTqRx00O/dHUKItuetsZabFq5CM2JGoynMkjEK1uvKt6RsLqMUc/ovnNtB44NjGHrU2/aXg7phNaGOB65+VK8NziO+ngU46kMPt5abzlfodjDF0LknAjA32sqh54QbV/biYdfeQdf/8wnoGla1SQyERI29HS3e28PHvvaZbmkxHktCWy44iJ8ac9rBZ/b9GgP9nUvxwXNiVKnADBTr40SHYsjG9EIcN2Dh1zX86xWnzwzUTDo3L2hC1NpDZFIpCI1q+IdCauhJj2jS6UzqI9HAw1ZTaa1nCOT9Z7tkO/hvz80XjA6ANQJw+kJ0ZYDR/HTjZfjr/7Hr5WMoBBCpjHS3WhEFGjreCqt+7l0RjN1nny9LpfomO8gvD807omeRyICjXUx3PTQ0RlO1NbVHdj2TG9FalbFJ1vaqUVQvH542uAzgdU0sJtsWbx2Op3WCn5PxNWt02AkRB+dnpgRQan0RCZCwkYp3c3X1ppoRPdzsaj5V5OVRMesJmakxE83Xo7/fstleHzj5blpFze0byqtnwvSnKipWM2qeEfCjQIprQ1xfLy1HjvWdfpewAqwl8CjV/71NydH8O0nj+Z+P3lmEo/cfGkg15TfTiu17qu9ghwhYcCs7rY31mLX+q6Cz+1a34X2RuvTC+V0Ml8T/8O9B3H7z94AANzz899g2zO9uO2qTziuUZPN69LTruHk1Iw2VQoVP7VhZ5WE3jEWtjagub4Gj2+8HBkJ1NVEDFdtuF3Qyk6ypV4UY9Oj0+G1F3r7c57x4xsvx77u5YgKuD5/Z7dQzJK5Tbq5Krs3dOFvf/HbgnOoEkEhhJzDrO7GYhF8cm4T9nUvRzqjIZa3aiMfM5paTif1NPGO/UexdXUHuvf25HIzzptVZ1oD89tVE4tgdCKNe37+Frav7cSWA+dyJLav7cR9z/fNaFOlUPGOBODOMsZIROBjDbVAQ+nPeVHQyuilWirh0Mg7b87zuE8MJXFiKIlv/uwN1+ftnBSKMap1X1xBLoxbuxNSLZjV3VgsUjKx0qymGq3OiEamcyIyUpbUxBNDSXwwnMTp5JQpLdRr1451nRgYSeG+5/uwdXUHWhviOG92Hf7qf/w6t+KsEjWrKhwJP3G62ZUexd59RpP43rO9JRMOjbzzbHgt/3cvVmuYuQ9ma93n4zS6RAgJF2Y1tVgnsxGC7OqMH3/l0yU1MTt1+l8e/2dTWlguwtG9twcAcGjLlbh7TSe++7nK1ayKz5HwG68KkmRfqvFYFDf+8PWyCYd6c5S71p/bXCYbbtt18JhrbczHSqGYfKwmwlZahySEFGK1Im9WHwRErk4EADzw0tsz8tx2rJvWwHw9NKuFZqK+egmmlahZjEi4jNebXZntVEaby9y9phPfWZ3Bsf5R3Pd8H44cH861sSbmnl/ppFBMpYX9CCH2saupxVp55Pgw7n2uD49vvBwApvVOAt++9lMYHEvl9DDraJSrU2PUrvFUJvf/1aJnjEi4jNfbk1sZxReP3mOxCNqaajGvOYHzZtdhYHQy9/0d6zoxOpE23FbcKmbugyr7eRBC1MWupupp5cDoJOKxKC5sqUd7Ux3mNNaioTaGbc/05pyIHes6cetjR7Bm5yH0nRwx1ESjdl0yf3bV6RkjEi7jxiqRUrgxio9EBObOqsW26y9GfTyK4eQU7n2uDwOjk67kSWQzmT9WX4N93cshpTS8Dyrs50EIURe7mmpGK/OPnZyajtTe+9y5SG2p3DG9SsFRAWQ04PzZiapwILLQkfAAL1+ObjkqyVQGX/37X834u9M8CeMM6+rqWESfhXc9G3QTcnjdlnfvudbT41cTdjTVrFZmj/3+0PgMTSyXLxGJCLQ2xF1fqRc2OLURQtxIOLST6GgGr7dhJ4QQs1jRSruaSM1z4EgIIWYJIRbp/L3TWZNyx1klhOgTQvxOCHGXG8ck53Cay2FUkbJat9ElhIQbq5qY1cDxVBpbV3dg6fzm3L9Vm+bZmtoQQtwA4G8A9AshagB8RUqZjQn9PYA/ctIoIUQUwN8BuBrACQC/EkI8LaXsdXJccg4nUySlCsR4vWqFEEK8wIomGu1OnL/yo5o0z26OxF8A6JJSfiiEuBTAXiHEX0gpnwDgxqTQpQB+J6X8VwAQQvwUwPUA6Ei4iN1cjmwor62xFltXd6A5UYOPTk9g7qxaLukkhIQWs5qYP52xdH4zNq1chNpYBPeu68SO53+Db1y9pKo0z64jEZVSfggAUspfCiGuBPCMEGIeADfWD14I4Hje7ycAXJb/ASHERgAbAWDBggUunJKYJZXOoK2xFrd/dklBPfnd67vQnIiz+iRon0RtaJ/OyE7hLp3fPFMHN3RhcVtjVWme3RyJkfz8iLNOxUpMRw3+DxfapfcEChwUKeUeKeUyKeWytrY2F05JzBKPRXHbVYtznQeYnhPsfrQHg2MpT6tPGuVmqAbtk6gM7dMZ2SncTSsXzdTBvT0YytuKwCxh0TY97EYk/jOAiBCiI5u3IKUcEUKsAvAlF9p1AsD8vN/nAfjAheMSF2htiOOiOQ2+J1V6sSEaIYRYJTuFOzaZdkUHw65ttiISUso3pJRvA9gnhNgipkkA+GsAm11o168ALBZCXCSEiGPaOXnaheMSm+R7y4NjKdTHvVk+WgousyKEqEA2MfOC5oQrOhh2bXNakOoyANsBvAKgCcBPAKxw2igpZVoIcSuA5wFEATwkpfy10+MSe+h5y4/cfKnvSZVcWnoOlQo7EVKNRCIC7Y212LW+C5se7cnp4K71XWjJ27jLDGHXNqeOxBSAJIAEgDoA70gpNcetAiCl/AcA/+DGscJAtqy0lwmKds+h5y3f9NAv8fStK3xNquTSUkKIXezqX6nvDSWn8MBLv82tXhs++/vdazotrYgLu7Y5dSR+BeApAJ8G0ApgtxBinZRyneOWeYwfL24rbfF6fszKOYrvjZG3nExlcGFLvSvtMwOXlhJSHbitz3Y1ttT3ACA5lcYLvf14obe/4Hvf/Zy1SELYtc2pI/FnUsrDZ///IwDXCyE2ODym56iW2GI0P+bGBlpmztHaEM912kQ8ipNnJgvuzWNfu0wJb9nrDdEIIcHjhT7b1Vi9793/Yh++96d/iIGRSfSPTLqijWHXNkd7beQ5Efl/2+vkmH4QdGLLzGU+mqvzY3rLiIyiCpqmoe/kCNbsPIQV21/GG8dPz7g333u2F7s3dHm2NboVvFxaSggJHi/0WdM0bF3dgcc3Xo7dG7qwdH5zWY3VNInkVOGqjKXzm/HlKy7Crz84g+5He/DAS29j+9pOV7QxzNpWlbt/BpnYoudt797QhWs62gvCY3ZH/EbefGtjXNdzzkgUdNr6eHTGvXmhtx/brr84tN4yISQ8uK3PmiZxaiyFbc/0FpSzfviVdww1NqujH52eKNDNbN2I73/hEpwYSuLEUBL3Pd+Xy5GY15Koui3EgSrd/dOrnS/NoOdtd+/twXeu7XDFqzXy5mMRobshjZSyoNMOJ6d0700kEgmtt0wICQ9u6/PgWArde3sKNHHLgaP4zrUdhhqb1dHiiENrQxwnhpIFOnnk+DC69/bgmz97A/FYtCq1sSojEkEmthh529GIcGXEXyoxUm8ObnAsVeBx7zp4DDvWdeKO/UdduTcqJbUSQtTHbX0upblGWpT9TnHE4dwoon4AACAASURBVPzZddNLPA8ew/a1nQWlsc20sVL1sCodiSATW0ot83EjsbLU8fU2pCnutAOjk5g7qw5PbL4CU2nN0b1xM2mqUjugirBGBQkSt/XZztLK/O9kIw7zWhJ4+tYVOb287/k+bLv+Ylw0pwH1tVHMaSgdqbWjh2HRvap0JAD7O186xetoiNXje+lUubUaRbVVNoQQb3FTn+1ortF3mhNxNCfitvTSqh6GSfeq1pFwil1P0etoiJ3je+VUWUmaKnU//VgeSwgJP0Y6YkcTS33Hju6Y0cP89gshcP+LfaHQvYp3JLwIDanuKQYVbSnGbEix3P0Me/lYQog9rOh3OR3JaqLZY7qto+X0UK/929d2YmAkhSPHhwGoq3sVvWoj+2CyNRLW7DyEvpMjjrdndbLO2as2qUg2PFhuNUq5+xnkKhtCSDBY1Uozuhyk/pbTQ732bzlwFJtWLsodQ1Xdq2hHwqvCU05GyEEXw/KT/PDgoS1X4snNK3SjNuXup1mHhBBSOVjVSjO6HKT+ltNDo/ZndU5l3avoqQ2vQuJONliptjC9mfBgufsZ9vKxhBDrWNVKM7octP6W0kOj9l/QnMChLVcqrXsVHZHwKiTuZITMMP1MzNzPMJePJYRYx6pWmtERlfXXqP3nzapTXvcqOiLh1VJLJyPksO/y5gWMOBBCivFiKbvK+htmHRRShj/Jb9myZfLw4Rn7hwFQs6CHim2qYAK/saXsMwuLQFUe795zrZmPhcI+g8KrVXfUX9OYujHKRSSEEDsAfA5ACsAxAF+VUg7bPZ4qSyHzUbFNVmFnJIR4jRdaGbT+VqJ2KudIAHgRwLeklGkhxHYA3wKwxckB7T64Snzgdsm/F4l4FCfPTCpbR4MQUrmU02WVdTud1tDXP5LbRKxStFM5R0JK+ULer68BWOfkeHaLR6ledMpr8jtjTSyC0Yk0bnrolzgxlMSPv/JpbH3qzVBUXCOEVA7ldFlF3c7XUgnM2Im0ErRT9VUbNwP4uZMD2F03XE31HoopLtry+Z2v4OSZCbQ1Tht6fTxaVUtYCSFqUE6XVdPtYi396PRERWpnII6EEOIXQog3dX6uz/vMtwGkAfzE4BgbhRCHhRCHBwYGDM9ld91w0OuNg0SvM96x/1yFteHklLJLqFTBrH0SEgRhtc9yuqyabhdr6eBYqiK1MxBHQkr5GSnlxTo/TwGAEOLLAFYD+E/SYFmJlHKPlHKZlHJZW1ub4bnsrhtWeb2x1xh1xuZEDQBg18Fj2LGuk5UmS2DWPgkJgrDaZzldVk23i7V018Fj2L62UDt3b+gKvXYqN7UhhFiF6eTK66SU406PZ7d4VCWWZdY0iYGRSbw/NI6BkUnD+vJGnXE8Ne3VD4xOYu6sOjyx+YqSpa8JIcRNyumyCrqdr7NCiAItPXJ8GA+/8g5+/JVPY/+m5fjJ1y7DJ9oaQ6+dytWREEL8DkAtgMGzf3pNSrmp1HfKrYP2Y9WGypnCgLXkUb3M4u9/4RJoUqImGsEFzQmcN6tOqesrQeCNZB2J6oR1JLzBjVUbXul1sc5e09GO2676BDY9ek5L/+7GP0JEAB+cnsCBnuO4e02nyomW4awjIaX8A7ePaXfdsNnvBZUpbKUzGCUhFWcLa5rE2wOj+Ntf/BZ7b74U/SOTGE5O4Z6f/ya3le2hLVeGxYkghFQY5XS53L+7pdd6+lussy/09gMA9nUvx1RGw28+GsFfPv3rnJYCwHc/F/68O+UciTBi9iXtJlY7Q3aubun8ZmxauQjNiRoMJ6egaZrhtaztmo9tz/Ta2pyMEEJUxA29NtLfWXWx3HHztVaTEv1nJitWT5XLkQgjQWQKW13mFI9FcU1HO27/7BJse6YXX9zzGrY904tTY6mCXIn8a9FLDAp7ngghpLpxQ6+N9DebE7F0fnOB1n5pz2vQpMSDNy4tTLRcH/5ES4ARCVdwsq24Xax2htaGOL5zbQdu/OHrBcbfvbenwBPPv5Yjx4dx3/N92Hb9xVjU3ohEDauCEkLCjRt6baS/UQH84KZl+Oj0BLYcOFqgtd/82Ru45/N/iK2rO9CcqMF4KoPzm41zzcKkoYxIuEAQmcJWlzlFIgLRiCjrfBRfy8DoJM6bXYd5zQnT29gWF2FZs/MQ+k6OGK4SIYQQv3BDr430NxKJYMncJixqb9DV2rqaKLr39uCbP3sD582uQ3NC/5xh01BGJFzAi+1fy3mjdrbDNeOJu3EtQeSMEEKIGZxqnKZJSEg8+meX4Z1TY3jgpbcxMDqZ099IRCBRE9PV2guaEzi05UrXkuNVgY6ES7i5o5yZREo7ncGs8+H0WlSrLkcIIfnY1Tg9bd69vgvnN09HF7L6a6S1ZpfNh01D6UgoiFlv1Gpn8CJyokcQOSOEEOI1etrc/eh0nlm+jjrV2rBpKHMkfMBsRcksXnqjWefjwpZ60zkPVlGhuhwhhDhBT7etaLMTrQ2bhjIi4TF2ip+EzRstxq/IByGEeIGRbrc2xn3R5rBpKCMSHmNnW9sweKPloix+RD4IIcQLjHQ7FhG+aHOYln4CjEg4ptwDtzNNobo3GlRJcEII8Yp8Lc9IqavbyVTGc20Oo74yIuEAM2t97W5rq/KI3k6UhRBCVKVYy4/1jxnqttfaHEZ9pSPhADMPPAzTFFYJ29IkQggpRbGWP/DS29ixLpjtAcKor5zacICZB676NIUe5aZrwp4MSggh+RRr+ZHjw7j3uT48vvFyAPBFt7O6CyB0+sqIhAPMTluoPE1RjJnpmkqMshBCqhc9LR8Yncz9mx9ORFZ3b33sSGDRELswIuGAlkQNdq3vwqZHe3JJMbvWd6ElUVPwOU2TGE6mkExNJ/HU1UQxp0FNh8JMMawwRlkIIcQIvUqUO9Z14tbHjuTKXy9ua8SZySlPdDxfd08MJXHvc/Y2SwwKOhIOGEpO4YGXfpvbzW347O93r+nMvXQ1TeLdwTGcPDOBO/YfVT4L1+z8nJslwQkhJEjyB0fJqQyO9Y/i3uf6cOT4MADg/hf7cOeqT2JgZNITHdebWvnq3/8Kh7ZcGQqdVXZqQwhxuxBCCiHmBN0WwLjK2Qu9/eje24Mv7nkN3Xt78EJvf8FLd3AshfcGx3PGB6idhWt3lQkhhFQCUkqkMlrB39Z2zcfx3yc90/Gw666SEQkhxHwAVwP4t6DbAhiv6507q7ZsUkwqnUF9PBqaLFw7u4qWI5tEpGkaMnK6ozqZDglbsRZCiNroafz2tZ247/npqERrQxwZTb+2hBs67lR3rUyfe6GfSjoSAO4HcCeAp4JuCGCcN/DE5ivKPvx4LIrxVMbXLFwnhuJ2/kO2g97/Yh++fMVF2HLAWVgwjMVaCCFqo6fxWw4cxdbVHdj2TC/am2pxbGDMNR3X02i7umtl+twr/VRuakMIcR2A96WUb3h9LrObaRnlDUyltdzDP7TlSjy5ecWMB9LaEMfHW+t9y8I1s+qiHG6uMsl20LVd83NOBGA/LBjGYi2EEPXI1//kVFpX4z913rS+XzA74ZqOG2k0AFu6a2X63Cv9DCQiIYT4BYDzdP7p2wD+AsA1Jo6xEcBGAFiwYIHlNljxzErVTSiXdBiJCCxsbUBzfQ0e33g5MhKoq4l4tmrD7BbkfpF1wpoTNa6EBcNSrMWpfRLiJdVun8X6/+OvfFpX4xPxWE433dJxtzXayvS5V/oZSERCSvkZKeXFxT8A/hXARQDeEEK8C2AegH8SQsxwOqSUe6SUy6SUy9ra2iy3wYpn5rRuQiQi8LGGaU9zwcfq0d5UZ9r4VNqC3A5ZJ2w4OeVKMlFYkpKc2ichXlLt9mmnkqVVHTfSbrc1On/6PB89XfRKP5XKkZBS/guA9uzvZ52JZVLKU26fy+q+8kHUTVBpC3K7eRdZJ+z+F/uwfW3njBwJq2FBL5JBCSHVhdeVLEtpt12NNtLg/Onz4hyJYl30Sj+VciT8xOrDDKJugp0QWGtDHI/cfCneGxxHfXzaU/14a73jVRd2E3SyTtjdazqhaRr2dS93tGqDxbAIIU7R0/+B0UnEY1FXdL6Udue/zNsaa3HbVYtx0ZwGSEhomjRcaVFKg81Ou3iln0o7ElLKhV4dOwwjW7shsMm0hq1PvVlwXU5wOqfnthPGYliEECd4rf+ltDv7Mn/61hX4cHgC3XmVkY0GaOU0ODvtgobybfNCP5V2JLwkDCNbOyEwL5ItjTqFpmkYGJlU9v4RQogeXut/Oe2ORAQyGnJOBFBaq1XX4Kp1JAD1R7Z2vGYvki2znaKtsRabVi5Cc6IGEsDIZBpf+fGvWM+BEBI6vNR/M9ptRauLHZOl85ux5T9+EuNTGbx7agQPvPR2bk+QIDS4qh0Jp3hdYdGO12wmimG13dm8i+KCJzvWdaKtsTa30UyQy0wJIcRrzGqnGe0up9X556qJRfDIzZfipod+ibbGWty5aglu/9kbM6pwBqXByhWkCgtuFH4yg9XiUOWWqtppdyQi0FgXm1Hw5I79R7Fp5aLc51Ss50AIIW5gVTvLaXcprS4+1+d3voLJtIanb12BB29cOkOLtxyY1uKgNJgRCZuoVvgpSzlP2G67p9KabhiuOW/L9FL5G9wfgxASZtzW/FJaPTAyaXiu7O/5ZLXYafTZLnQkbKJa4ad8Ss392W23URhuPJXJ/b9R/gb3xyCEhB0vNN9Iq0udq5QW60Wf/dBdTm3YJCwVFoux226jMNwl82cb7jOShftjEELCjp+aX+pcelq8e30XLpk/u0CD/dRdRiRsEoY6FHrYbXfJKZMya5dVjt4QQogZ/NT8Uucym4Tvp+7SkbBJGOpQ6OGk3XaXS3lVtpsQQvzCT80vdy4zWuyn7nJqwwFubrftJ3632+mmZ4QQogJ+aqfTc/mpu4xIEM8Ja/SGEELCip+6S0eC+ILqVUQJIaTS8Et3ObVBCCGEENvQkSCEEEKIbehIEEIIIcQ2dCQIIYQQYhs6EoQQQgixjZDS3d0qg0AIMQDgvRIfmQPglE/NUYFqut5y13pKSrnKr8boYcI+gep5ZtVynYC5aw2LfTohDM+cbdTHlH1WhCNRDiHEYSnlsqDb4RfVdL2Vcq2Vch3lqJbrBKrrWksRhvvANjqDUxuEEEIIsQ0dCUIIIYTYplociT1BN8Bnqul6K+VaK+U6ylEt1wlU17WWIgz3gW10QFXkSBBCCCHEG6olIkEIIYQQD6AjQQghhBDb0JEghBBCiG3oSBBCCCHENnQkCCGEEGIbOhKEEEIIsQ0dCUIIIYTYho4EIYQQQmxDR4IQQgghtqEjQQghhBDb0JEghBBCiG3oSBBCCCHENnQkCCGEEGIbOhKEEEIIsQ0dCUIIIYTYJnBHQggRFUIcEUI8c/b3i4QQrwsh3hZCPC6EiJc7xqpVqyQA/vBH7ydwaJ/8KfETOLRP/pT4MUXgjgSArwN4K+/37QDul1IuBjAE4M/KHeDUqVMeNY0Q59A+icrQPolTAnUkhBDzAFwL4IdnfxcA/hjA/rMfeRjAnwbTOkIIIYSUI+iIxN8AuBOAdvb3VgDDUsr02d9PALgwiIYRQgghpDyBORJCiNUA+qWUPfl/1vmo7jyNEGKjEOKwEOLwwMCAJ20kxC60T6IytE/iJkFGJFYAuE4I8S6An2J6SuNvADQLIWJnPzMPwAd6X5ZS7pFSLpNSLmtra/OjvYSYhvZJVIb2SdwkMEdCSvktKeU8KeVCAF8C8I9Syv8E4GUA685+7MsAngqoiURRNE1iYGQS7w+NY2BkEppmOrk49FTztRNC1CRW/iO+swXAT4UQ3wNwBMCPAm4PUQhNk+g7OYJbHjmME0NJzGtJ4Ac3LcOSuU2IRPRmxiqHar52Qvxg4V3Penr8d++51tPjB0XQyZYAACnlQSnl6rP//69SykullH8gpfyClHIy6PYRdRgcS+VepABwYiiJWx45jMGxVMAt855qvnZCiLoo4UgQYpZUOpN7kWY5MZREKp0JqEX+Uc3XTghRFzoSJFTEY1HMa0kU/G1eSwLxWDSgFvlHNV87IURd6EgQX3ArSbC1IY4f3LQs90LN5gm0NpStpK4kVu5LpV07IaQyUDHZklQYbiYJRiICS+Y24cnNK5BKZxCPRdHaEA9lsqHV+1JJ104IqRwYkSCe43aSYCQi0NZUiwtb6tHWVBvaF6md+1Ip104IqRzoSBDPYZKgPrwvhJBKgI4E8RwmCerD+0IIqQToSBDPYZKgPrwvhJBKgMmWxHOySYJPbL4CE1MaogJIxDnqtpo8qWkSg2MpJloSQpSCjgTxHE2TGE6mMHBmEt2P9rC8cx7Z5MlysDw2IURVOLVBPCX7Anzj+OmcEwGwvLNVTo1N6q7wODXGCvKEkGChI0FsY6aYUnaJY308yhUKJjC6pxNT+is8Jqa0IJpJCCE5OLVBbGE21J5d4jicnMK8lkTBy5ArFAopdU+jQujevyhnNQghAcOIBDFN/mj5ozMTuP/FvrJTFdkljrsOHsP2tZ1coVCC4WQKH52ewPe/cAl2b+hCW2Nt7p4m4lHsWFd4/3as62TSKiEkcBiRIKbQGy1vX9uJgZEUjhwfBqA/VZFd4njLI4dx3/N92Hb9xbhoTgPqa6OY08DKjFk0TeLD4QlsferNgvt73/N9SKUzOH92AnNn1WHb9RejPh7FeCqDubPq0JygI0YICRY6EsQUeuWctxw4iq2rO9C9tweA/lQF94cwx+BYakYy6pYDR7Ht+osRj0URiQgsbG1AU10N7yMhRCnoSBBTGJVzzk5NlJqqMLvEsZoxur8L5zRA0zQMjEyitSHO+0gIUQ46EqQsmiaR0aRust8FzQkc2nIlR8gOyeaSFN/fk2cm8KU9r7FuBCFEWZhsScoyOJbC957tnZEsuXtDF86bVcedKF1Ar1z2jnWd2P7z3wBg3Q1CiLowIkHKkkpn8EJvPwZGUti6ugPNiRoMJ6cwhxEI1yjOJQGAWx87kktkBVh3gxCiJnQkSFmyYfcjx4cLEiuf3LzCtzZUwz4T+bkkAyOTGBgtrFqpSt2NangWhBDzcGqjCjFTkTIfO7tUWj1Hufb2nRzBmp2HsGL7y1iz8xD6To44OqZqFN+vlkSNqzuDuvU8quFZEEKswYhElWFn8ye9JZwtiRrDUanbG0zpLT295ZHDeHLziopYxWB0vxa3NVpeNqsXLQDg2vOo9GdBCLEOIxJVhtGLoFwSXzbsfmFLPVob4nh7YNRwVGr3HEYYLY2slHwBo/s1lJzK3XMzyaxG0QKjDb/sPI9KfxaEEOswIlFluPEiKDcqtXOOUvPuRksjVcgXcAO3Xs5Gz+WxWy5z5fiaJiGEwP5NyzE4lsKug8dw5PhwRT0LUnksvOvZoJtQ8dCRqDLMvJTLJdOVe/FZffGXmwrJL7Pd1liL265ajIvmNEBCQtNk6BP9nDhK+c8qI6XuczHa8MvKy9+oRPrDr7yDb1y9RDd3g0mZhFQHnNqoMsolTppJpsu++PLJfzFZTc4sNxWSzdF4+tYV+N6fXoytT72JlfcdxOd3vlIRiX52klmBmc/qWP+Y7nNJxKOOEzeNSqT/5XUX6+ZaMCmTkOohsIiEEGI+gEcAnAdAA7BHSvm3QoiPAXgcwEIA7wK4QUo5FFQ7K41ye1+YSabLjxDkRxCyLyar+2uYCe1HIgIZDTP2o6iERD+7+5EUP6sHXnobO9Z14o79RwueS3MijuZE3NF+J0bPSEr9iBCTMgmpHoKc2kgD+KaU8p+EEE0AeoQQLwL4CoCXpJT3CCHuAnAXgC0BtrPiKLX3hdmXerkXn5X9NcyG9is50c/OfiTF9+PI8WHc+1wfHt94OQDMeC5OXuBWp18q+VkRQgoJbGpDSvmhlPKfzv7/CIC3AFwI4HoAD5/92MMA/jSYFoYXJzUDyk1bZMlfxeG0PLbZ0L7ZtlUCZp6h3v0YGJ1EPBZ1vWy51emXanpWhFQ7SiRbCiEWAlgK4HUAc6WUHwLTzoYQoj3ApoUOpzUcyk1beIHZ0H4QbQsCs8/Qz/thdfqlWp4VIQQQUgab/CSEaATwPwHcLaV8QggxLKVszvv3ISlli873NgLYCAALFizoeu+993xrs8oMjExizc5DM0LQVuamVc62t9G2QBruxD6NnuETm6+AgJhRbKqCnlU1Ejr7DBsqLf98955rg26CVUzZZ6ARCSFEDYADAH4ipXzi7J9PCiHOPxuNOB9Av953///2zj9KivLM99+nf800M+AgzoAGjF4ukp1wx5Ah/uLcHF2jYRMi16BJ9DCrJgaIyzFrEiS7yq67xLtBdPfG4zWMa0wMhhsV5MSrGyHxxnv3giQyGSUGQ5CAd4g/GCaMzAxD9/TUe/+Y7qZ/VHVXVVdXVVd/P+dwmO6pqXqr3ud963mf9/mhlHoEwCMAsGDBArqCp3Fib9rMfr3Zl4TTLxM7vgReUIl8GvXhycQ4ln3vl0VWCiefh5P9Wit9VY9w/iRO4mXUhgD4HoA3lFL/nPOrZwHcBODb6f9/4kHzahYxyBkw8bjNkfuSiMfCSGkKSlMYV4BSCvFYGO+dSJQ1vTudKrteMHJsPHRsxJEoiEz/apqW16cKCu8OJrKRMexX4gZWLQY1uKoPPF7mkVgIoAvAn4vIq+l/n8KEAnGViBwAcFX6MzFJWID1SzvynOLWL+1A2OT8nhv/v2pzL/a/O4S7t/0Gb/aP4HPdL2Ph+l/gtb73TaVcdjpVdr2g59jYvawTD754IO84u9kp9783hLu27c32aaaf9/ad0A2vZb8SQkrhmUVCKfV/Ybz/cqWbbQkSoVAIj+86hLWL29ESj2JwdAyP7zqEe6/tMPX3uS+JtYvbsXrLXqxd3I41W/dmXxyTYmFT2ycMAbSHnmNjOARHyopn+je3TzP9/MD1F7JfCSGW8UXUBnGOaU0x3HHVXNve8pmXxPxZLbigrRkPXH8h2iY3oLW5IfvyGBwdM5VToBo1MurFga/Qv0DTlCNREJn+bYlHs/3SEo+itbkBZzbFPOtXPeqlrwmpdahIBAy7WRIzxCJhXN3ehpsuOx9dj/0q+9LacF0H7nthP3r7BrHxpYO6GRQLX2pOhwDW8958pf2aIaME5CqDmlK4c9FcbNj+O6xf2pG1VLjVr3rUc18TUmtQkfA5dlZlpbzly51vWlMMd3+6HTc++su8PfDVW/Zi3ZJ5uOUHr6B/OIHpUxrxzG2XYSyllfTad+Lll6Ee0y47uSrXNAUFhSe+dDHePXEKD904H6s292JcU/jmM7/BkeOj6B9KYu3idkxriuGcljhmTGmser/qUY99TUitQkXCxzi9KjNzvlBIEA6J7h747NYm7FxzhaUXh5MhgPW2N+9k/+udq7urE8985TKMjp1+rr19g1ixqQcAsHPNFYbXqXZoZ731NSG1DKt/+hinvePNns8ovXE8FnE89XIpctNEvz04ilAI+P7NH8P8Wdl8ZYFOu+xk/+uda8WmHogIJsUivktnnZHB+bNa0N3ViSeXX4IfL78E0XDIVup3Qkj1oCLhY5xelZk9n92y1nYwqilRWIb6c90v4w/9J/E/fvUW7lw0F/NntQQ+7bKT/W90rtGxcWiahu6uTlf6uxwZeUimxvH0ikvwt5/6ENY9tw+ff2Q3vvH0azjYP4xVm3tZlpwQH8GtDR/jpHe8pimMa8rU+dzYA8+0ych0r7eCXrN1bzZU8cnllwTek9/J/jc618Gjw7jlB6/g6vY2bL71YoRD4tlzLZSH79/8Maz9yetFvjprF7djxaYe+kwQ4hNokfAxTloGBkaS+Nbz+4qSVXV3deqez8nqnqXaZGS6N1pB54YturXF4hVO9r/euTZc15FNcrVj31Hc+OgvEYuEPXuuhfJglK+kJR7N/kyfCUK8hxYJH+OkZSCZGseOfUezXvmZZFVnVcnSYCbSoJTp3mgFnQlbDKpfRC5O9n/huQBg1eZe9PYNZo9x88WsJyOF8mCUr2RwdCz7czQSym6FBN1CRYhfoSLhc5zyjs+8mHO98jNVQc2gN/EDxZUnAZiONChlutfLVbB+aQce33Uo0H4RhTgZHZF7rv6hhCOZMvUolJWp8SiOj47lfT7QP1ych6I5PyGWXr6STD6TzN8Mn0rhL3PynTDXBCHuQ0WiTqgkiZCeL8MPv3gREimt6HzTpzRkv5s/qwUrL5+NkUQK7544VZSToFSbQiHB9CkNWLdkHlomRdHcEMGpsXHccNEHMX1KsLc03KBaSaUKZeXq9jbcfuUFWJlTCKy7qxPf+fnv87a0/uVn+/EP18zDE1+6GIeOjeDBFw8U5SuJRkKIhAQP3Tg/mzb8mod2Fm2N0W+CEHehIlHDWElWZMVMXnheBVXky/DWwMkiR7gv/3APnlx+SVaJ+MYn5xZlSSzMWVGqTaPJcdzyg1eK2rdzzRVAkyOPsO7I7dvpUxrKJhWzc95cWVnaOSurRACnw06//dn/hB37jgIA5s9qwU2XnY/ru18+rWws68TZLY1oieu0Kd33fzx+krkmCPEBdLasUQrDI82Ew5lxoNQ778lEsS+DkSPcuJowka+8fHZeoS+jHAil2mSUz6Ie/COqQWHfXvPQTgwMJ3H2GfGKHCxzz3vk+GieXOQ6x2Y4cnwU57TEs/lA9GRlxRM9GNdQsk2UD0L8ARWJGsXJZEW5uRzePXGq6LyHjo0UTdgnk+O6k3hjNJQ1kZtZLRrlkQDczWdRD1Sr/HfueTMOkhkKPwMT/fjWwEncfuUcADAtK4Vk5OPq9jZ0d3Viy8pLsfnWizE1HdVBCHEHbm1UgJWtBas1E8od71SyosI97S0rLy0674MvHkD3sk6syNnnntoUxQPXX4ivP/1anjn6rKYGnNXUgHdPnCqbA6FcCmi9rY+p8WggK0JWS5ZyjwWQV8UVcGYrIFcWN750MK/w19aePnx3SG1mkwAAHbtJREFUWSe+kiM765d24P7t+/GdG+Zj55orICK28mWEQoI5rc346icuwIpNPboyVO6ZBEmGiP8575vPmz728Lc/XcWWOAsVCZtYqYOQSmnYf3TI9GRn5txOJSsqXKUOjCSLzts/nMDZLY3ZF7qI4J5nX88LJT2ZHMfZLaedKWdMaSzrzGemMFNupEFQK0JauS+jmhlz2yYjEgmVPTa3iivgzFZAriLQ2zeI+7fvx7ol8zC7tQnxWATRMLBuyTxMioUxODqG+7fvR/9wAvHoRM6KSkqkHx8dy44roLzDZVBliBAv4daGTcyaiTVN4e33R3UnOyOTsplzO2X2L7RsZFaUhedticeyvgwzpjTijqvmon84gRWbevD1p1/DjDMmHOMy5FoTdq65AttuW1g0WVu1qlTLNO81Vu7LqGbG2++PFvnH6B27esve7JaCU1tFYUGezPQPJxCLhNAQCaF1cgOmNMYw44xGfP3p17BiUw/6hxN51zUjK0ZQhgjxHlokbGJ2AhsYSeLoUMLSZGfm3E4lKyq0bPT2DeLxXYfw1IpLoZTSPa/Za5fLgWDVqhLUipBW7svo2KNDCcRjkbznbXTs7LZmy1VcSxEKhfD4rkN5ic4e33UI917bkf59eXmxmy+DMkSI99AiYROzHuPJ1Hh2u6DcsVbPbTWNtZ5jo55l446r5mLGlMaS53UihbZVq0pQvfSt3JfRsbl+EOWOjUfDjqY+n9YUwx1Xzc0W11r33D589RMX5Dk9VivlOmWIEO8RpWq/et6CBQvUnj17XL2m2b3W/qEE7tq2Fzdddn5eToXurk782Ywptn0kyrXNSsZJoDhDpVv7xVYc31IpDW+/P7H6HhhJYmtPH+64am655+L5xnc5+bTqI/HGuyfy/G0yGT/vvbYjb1Xvhj9Apv8ECiPJcfRb6xtH22DW+bTUM/HAEdP38lltrDggAtadEK2e3y/4xNnSlHxSkagAM5OOpikcHhjB0aEEzmqOIRwSNEZCaG1uLHKOs3puo7/TmyinNcfw2Yd3FZmAq5kF0MlJ2YqTYQE1MVE7qVDlniseCyOlKUeSTum1OdMnaxe3Y91z+1yVr8K2VBr14pEjZk3IZzWhIqFPLSkS9JGogFBIMK0plp2UBkaSuhNYIqXhGzlhkhOppEv3j909YyNnss1fvtjVvWGnJ2UjJ8OgpEO20t+RSAgzp05CYyyMtimN+PvPfBjx2IRp3s2XYW6fGCWecsP3wOo9Gz1rM1FEhJBi6CNRAWayS7rtJW7kTBZOh+jlUs29Yafvm05yxQwMJ3Hjv+7OZqnc/94Qjo0kXJO33D4xSjzlhu+BU7JGGSPEHrRIVICZFYzbk5ORF3s8FtaN1Q+HJmoWOG32dvq+ncqbERT8YHnK7ZPCRFRmQkud2vpyStYoY7VBrW5VBBkqEibRm/SSqXG0Njfkhb1tfOlg3gTm9uRkVNWxJR5DSzyWDcGLRkIYPpXKVk902gTu9H1Xq1plLaJpCsnUOB64/sKszAETNStCNrNE2iG3TzJhw5tvvRjhkFTs9GgFp2SNMkaIPehsaQKjSe/sMxrwxjtDWL3l9Cpsw3UdmDtjMs5s8i4bo5mVXv9QIltkKYOTznHVuG+bK9hAObPpPdcHrr8QDdEQVm3uRWtzA+5cNDdPJqspb3atCk7Kn5OyxqgN96GFQZ9AOVuKyCoAP1JKHa+4STWKkRn5qRWXZifszPert+zFM7ddlv1bpxJHWcGM456maUWWlN6+QcdM4NW4b7sOqEFCTxa//vRrWLdkHo4cn6i8ed8L6RTVbc2IR6srb3b7RG87orW5AcnUuOWtNidljTJGiHXMbG3MAPCKiPwawGMAtisXzBgisgjAdwCEATyqlPp2ta9phNEebGpc0/1+LKXlfee3yUnTFI6NJLPherm5CJw0gfvtvoOAkSxOip3ut96+Qdzyg1ewc80Vvn3+hdsR82e14M5Fc/H5R3bbsipQ1gjxjrJRG0qpuwHMAfA9ADcDOCAi/1VEZlerUSISBvDfAfwFgHYAN4hIe7WuVw6jbHiRcKgms+QNjCSLan+s2boXf/eZD+dlIyxV4pt4g5EsnkyOF33nZzkszEh5+5Vziqx7X/7hHhwbSejKIGWTEP9gKvwzbYF4N/0vBWAqgC0icl+V2nURgDeVUn9QSiUB/BjAEqcvYnYyMkrD29bc4EjhLLfI3O/JZAprF7dj/qyW7O+OHB/Fu++fwoH+YWiaMhXaStwj03eapqG7q7NI5j44bVLNyCFQXKhrdltTnnWiu6sTD1x/IZJjGu7atjdPBlMpjbJJiI8w4yNxO4CbABwD8CiA1UqpMREJATgA4M4qtOsDAPpyPh8BcLGTF7DioFVqDzbzvaZpGFeAUsowMZWX6N3v+qUduH/7REnpTL2Gv37yVWy7bSEAMDmPTyjsu6vb24qiIwCY9hHwwKFQl9ztiP6hBGZOjaO1uQHf+OTcvDDS9Us70D+URG/fYNY3ibJJiH8wY5E4C8BnlVKfVEo9rZQaAwCllAZgcZXapTer5S03RGS5iOwRkT39/f2WL2A1iY1R0aFMdss/nRzD57pfNrVC8sIsq3e/a7buxcrLZ2cn640vHczG3zM5T2VUKp+5FPbdjn1HceOjv0QsEs7KotmiWHYtTdWW2YzV7/Yr52SVCCBfTjOfxwx8kyib5nFSPgkx4yPxd0qptwx+94bzTQIwYYGYlfN5JoC3C679iFJqgVJqQWtrq+ULOPmitKKUuLllkDv5Z3Je5HLk+CjmtDVj7eL2PMtELBJmlcQKqVQ+c/FKVjO4IbMZ697stia0Njegu6sTTy6/BN1dnWhtbkBL2ndn5tQ4ojXqm+QnnJRPQvyaIvsVAHNE5HwRiQH4AoBnnbyAky9KKxO9WymzCyf/zz+yG3cumpvnFzFzahyRkGDdc/uySkRmb91qeWZSPbyS1QxuyWwoJGhuiODORfklye9cNBeaUjXrm0RI0PFlZkulVCqdv2I7JsI/H1NK/dbJaziZxc5KZr1SE3n/UMKxfWu9yX/1lr24//oL8f7oGKY1xdA2uQFnT2k03Fu3E5vvl/33IOGVrGYwq3w40fcpTenmZnlq+SXYdttCTI1HcXx0DFMaI3hqxaUICxAKhRyXM8oxIebxpSIBAEqpfwPwb9U6v5NJbKxM9LFIGFe3t2Fp56xsMqitPX0Y11Q2058T2QiNJv/pUxqLKpFarZJohEdlmAOPV7KaoZTykfvCHdcUvvX8PuzYd9R234+l9P0fVLrtbsgX5ZgQa/hWkXADp5LYWJnop8ajuP3KC7DyiZ7sJPXdZZ340e7Dpr3QzayWjCb/w8dGqubtzjLM1cMLWc1gpHxMjUd1I4FyIyzM9n1GpgEYKi1uyRflmBBr+NVHouYw6zV/fHQsq0QAE5PUV57owUfPm5Z3nNG+tVnHNz0fh+5lnXjwxQOmrmMHRnrUBmZlNff43JwP225biLnTJ+P46JhhJFDms5m+z5XpVZt7seG6Dl3/B7fki3JMiDXq2iLhBUaTVKFp2Wjf2uxqSW/lGQ4B/cMJU9exA8swBxc9i4iRLOdGWJjp+1yZLlUrxC35ohwTYg1aJFzGyAO/bXKDKS90K6ulwpVnS9yZSAyjnAKM9KgvjGR5cHTMUt8XynSmVkhYkGcxcUu+psaj2Hzrxdiy8lJ0d3Xi6vY2yjEhJaBFogTV8Nw22m8+54y4qX1rq6ulwnuY09pckdNeOUc0tyudEuewKu96stzd1YmzmmLYdttC031vVqbLyZcT41XTFA70Dxfd05zW5rqWY6ulvn1SArumqaVnTkXCgHIvTLuTVqnJsJQjV+71Nt96cZF3vN5qqRre5+W2VliFsTYxIyt6Mu+E4ljKmVMvJNrIAdkJWdeT7xWbeuhoSUgJqEgYUOqFWWkYmhNhld1dnVi3ZF7JGPpqeJ/TES2YlJOVUi/qSl+wesr11Hi0yDJQaow5JeuUb0KsQx8JA0pNKG5l+stgtEoKhUIlve6rMSkydXYwKScr1Zb5Qn8evYiQUtdzStYp34RYh4qEAaUmFLdXLXavV41JkQ6VwaScrPhd5p2Sdco3IdahImFAqQnF7VWL3etVY1IszCnw1IpLceakKAZGkq5UMSXVoZys+EXmRUS3AqlTsm6UM6NUNVW3K/kS4jdEqdoX/AULFqg9e/Y4fl4jh0q3U+imUhp+995QXjbMjcs68aHpkxGJlNYFq1UzoIbSCHvemGrJp9OUkhW3+1vvehuXdeLBF39vmILb7foYDj2TmpDPakYQWD030adKURum5JOKhE3cnLT6hxK4a9veovoc917b4Zknef9QIlsbJMPMqXE/erfXxERdC3jxos5cT0Rwz7OvY8e+o9nfey1vDo2BmpBPKhL+x0tFglEbNnEzzDGZGseOfUfzJlEA+PvPeOdJTu/2+sPt0N7c6/3x+Mki+fda3jgGCJmgLhSJWi8J7KeUvZlnOa4Uvn/zx/DgiwfQ2zfoaZuIM/h5nPhpDJRrUzwW1s1/UU/QylBfBN7Z0myRKz/jF0/y3Gf58ftewtqfvI47F83F/Fkt9G6vcfw+TvwyBsq16YdfvAjvnUj49jkSUg0C7yNRQ3v5JfHDatHoWT65/BI/r7w8b1At+EjUwjjxwxgo1yYFhc8+vMvKc6wJ+aSFwf/QR6KKeLGPWY0Jr3B/OhN25uakavQsAfjmZUPs4Yf9/nLjplIfDTfG5R+Pn/T8ORLiNoFXJNzeW3UjTM6r0Es/7lMTZ/C6b6st026NGa+fIyFeEHgfCbdLAptJJVxpEhu76Yo1TeFPIxPX/X9/GsHRoVOWru3HfWriDOX6ttqJl6zKtNX2OJXiu9wY4hgh9UigLRJelAQuZyJ2YmVkxwytaQqHB0bw3olTWL1lr+1iYywTHkxK9a0bq3krMm2nPU5s3ZgZQxwjpB4JtEXCqNjV8dGxqq2wyqUSdmJlZCdd8cBIEm8NnMxOgHavXVhciRNkcDDqW7MyW8mYsiLTdsaQEym+zY4hjhFSbwRakTBahWiaVrVQt3KmTSdWRnbMp8nUOCbFwnQEI5YxI7OVho9akWk7Y8iJLQeOIUL0CfTWhpHj07iC7orGiVC3cqbNSp2xMp7nUxojeGrFpQgLEAqFyppPY5EwTibH6QhGLGNGZo2sBGbHlJUtATtjyMz5y0V1cAwRok+gLRJGqxClVFVXFaVMm5WsjApXfZ/rfhl/Ojlmag92WlMMH5w2CRuu66AjGLGEGZl1wtJmdkvA7hgqdX4zFhWOIUL0CbRFwmgVMjCS9GxVUYkzViWrvlBIcN60JrRMiuLJ5ZdgXAGN0RDOauIeLimNGZl1M+yxGg6NZsYWxxAh+gRakQD0k9hkVjSFXt9urSrsJtapdNUXCgnObGoAmixfmtQ55WTW7THldAExs2OLY4iQYgKvSOhhZ0WjaQqDo0mMJscxrhQao2HXVyKNsRC+f/PHMCkWxuDoGDa+dBD9wwnuzxLPqVbYYyql4ehwAmPjGqLhENqaGxCJOL8ja2RRaYyF8PbgaNWvT0gt44kiISIbAHwGQBLAQQC3KKUG07/7GwBfAjAO4Hal1PZqtMHKisaJHAyVkkppeGcwgbU/eT17/Q3XdWD6lEbuzxJf4LSVIJXS8Lv3hrDyiZ6szG9c1okPTZ/s+Mtcz6Lywy9ehHcGE65cn5BaxqvR8DMA85RSHQB+D+BvAEBE2gF8AcCHASwC8LCIeL7cdioHQyUcHT49oWWuv3rLXsSjYe7PkkCiJ/Mrn+jB0eGE49fKtajsXHMFtt22EPFo2LXrE1LLeKJIKKV2KKVS6Y+7AcxM/7wEwI+VUgml1CEAbwK4yIs25uKH+PGxcU33+mPjmivXJ8RtjGQ+VSWZL4zqSLp8fUJqFT/Y574I4Kfpnz8AoC/nd0fS33lKbvx4LuW80p3MnhkNh3SvHwn7oQsJcR4nZd7OWOSYI8QcVfOREJGfA5ih86u7lFI/SR9zF4AUgB9l/kzneN0RLyLLASwHgHPPPbfi9uZSmJhmajyajR8v9JEw8k9wuj5BW3MDNi7rLNqvbWtm+W4/Uk35rBf0ZP67yzoRCwv6hxKmnTntjsUgjznKZ/A475vPWzr+8Lc/7di1RSlnq/iZvrDITQBWArhSKXUy/d3fAIBS6p/Sn7cDuEcp9XKpcy1YsEDt2bPHkXYZTTpzWptxIjGWjtooHz/eP5TAtQ/vLPICryR7ZsaDPTWuIUIPcrN47kDipHzWG7kyHwoJNu06hO5/P2xJMa9kLLow5mpCPq2+pIj/MalImJJPT95CIrIIwBoA12SUiDTPAviCiDSIyPkA5gD4lZttM0pMc3x0DGc2TeyfnnvmJLRNbiw5gTmR6a+QSCSEc1riOHdaE85piVOJIIEnI/PxWARfeGQ3uv/9MABrzs6VjEWOOULK49WoeAjAZAA/E5FXRWQjACilfgvgKQD7ALwA4K+UUq5Ww3FKAXCi2iAhZIJKxiXHIiHVxZM8Ekqp/1jid/cCuNfF5uSRm5hm/qwWrLx8NqY1xSAi0DRl2r/BbKa/coWCCCHmU3DrjScns25yvBJSTF1mtixFZtL5l5/tx02XnY81W+0loDJbbdBJh0xCgooZZaDUeHIi6ybHKyH61MWGn5XQr4wCcM8187JKBGAvAVW5aoZG/hhuJbkixO9kxu47749iWnMMz646nTCq8AVeajyZrSxaCo5XQvQJvEXCzioiFJKqlxoHquOQSUhQsDp2qz2eOF4J0SfwFolSq4hSlgo3HLToBEaIMWYtAJlxDKCq44njlRB9Aq9IGK0iNE3D/veGcO3DO7Fw/S9w7cM7sf+9oawykdmTzUwc1SiL7MY1CKlVzFgAMlaLax/eiVWbe7Hhuo6qjSeOV0L0CfzWhpG397iC7monk6SmWmWRc3HjGoTUKmYiNXKtFkeOj+K+F/Zj3ZJ5mN3WjHjU2fHE8UqIPoG3SBitIsz4QDjhoFUON65BSC1ixgJQaLXo7RvELT94BWFBVcYTxyshxQTeImG0ihgYSZqKSyeEeIMZC4DZ/BKEkOoReIsEoL+K4H4nIf6nnAWA45gQ7wm8RcII7ncSUvtwHBPiPXWrSACnVzt65KbCjUZCiIQEo0njiYqpcwnxhlLj2Aq5Y1hEEBYgFAoZjmWOeUImqGtFwgi9RDgbruvAfS/sR/9woigpDlPnElLb6I3h9Us78PiuQ7jjqrlFY5ljnpDT1IWPhFX0EuGs3rIXKy+frZsUh6lzCalt9Mbwmq17sbRzlu5Y5pgn5DS0SOhglAinJR4FALQ2NyCZGscfj59ELBKGpmlMnUtIDVNqzOuNZU3TsHZxO1riUQyOjmHjSwfR2zfIMU/qEioSOhiFlA2OjmH+rBbcuWguPv/I7qxJs7urE1e3t2HHvqN5xzMEjZDaoNSYLxzLmqZwbCSJdc/tK9oG4Zgn9Qi3NnTQCynbcF0HNr50ELdfOQert+RXBV2xqQd3f7qdIWiE1Ch6Y3790g5s7ekrGssDI0ms2NRTtA1y96fbOeZJXUKLhA6FIWUhEYQE+M4N8wHoZ8QMh4QhaITUKIVjPhO1ce+1HUVj2WgbJBwSjnlSl9SFImE2TKvwuKnxKA70J/I8szfferFhJj0nQtAIIe5SOO7PPiNecn4AoDsHRCM08JL6JPCKhNkwLb3jurs68Z2f/z7PhPmt5/ehu6sza9rkNgYhtYud+aG1uQEbruvIbnFmtj4jtEaQOiXwKrTZMC2941Zs6sHSzll5x+3YdxRnNcWw7baF2LnmCmy7bSFjxwmpUezMD719g9kqoz//2sexdnE77nthP0aTjNgg9UngFQmj/czCMC2j4wotDTOnxhEKhVgBkJAAYHd+yFQZHRiecLzsH04wYoPULYFXJDJhXbnohWYaHdc2uYHRGIQElErnh0x4KOcFUs8EXpEwWx3Q6LhzzohzG4OQgFLJ/NDd1YmPzDyD8wKpewLvbGm2OmCp4xiNQUgwcWJ+IKTeCbwiAZivDkilgZD6g/MDIZUR+K0NQgghhFQPKhKEEEIIsQ0VCUIIIYTYhooEIYQQQmxDRYIQQgghthGllNdtqBgR6QfwVolDzgJwzKXm+IF6ut9y93pMKbXIrcboYUI+gfrps3q5T8DcvdaKfFZCLfQ526iPKfkMhCJRDhHZo5Ra4HU73KKe7jco9xqU+yhHvdwnUF/3WopaeA5sY2Vwa4MQQgghtqEiQQghhBDb1Isi8YjXDXCZerrfoNxrUO6jHPVyn0B93WspauE5sI0VUBc+EoQQQgipDvVikSCEEEJIFagbRUJE7hGRP4rIq+l/n/K6TU4jIotEZL+IvCki3/S6PdVGRA6LyG/S/bnH6/ZUAuUzWARJNu0iIhtE5HcisldEtolIS/r780RkNEfWN3rYRt/JpIjMEpFfiMgbIvJbEflq+nvfzhF1s7UhIvcAGFZK3e91W6qBiIQB/B7AVQCOAHgFwA1KqX2eNqyKiMhhAAuUUn6P/y4L5TNYBEk27SIiVwP4X0qplIisBwCl1BoROQ/Ac0qpeR63z5cyKSJnAzhbKfVrEZkMoAfAfwHwOfh0jqgbi0QdcBGAN5VSf1BKJQH8GMASj9tESAbKZ52hlNqhlEqlP+4GMNPL9ujgS5lUSr2jlPp1+uchAG8A+IC3rSpNvSkSq9JmtsdEZKrXjXGYDwDoy/l8BD4XPgdQAHaISI+ILPe6MQ5A+QwOQZPNSvkigJ/mfD5fRHpF5H+LyH/2qE2+l8m09WY+gF+mv/LlHBEoRUJEfi4ir+v8WwLguwBmA/gIgHcAPOBpY51HdL4L+r7VQqXURwH8BYC/EpGPe92gUlA+iwiyfNaUbNqljExnjrkLQArAj9JfvQPgXKXUfABfA7BZRKa433p/y6SINAPYCuCvlVIn4OM5IuJ1A5xEKfUJM8eJyL8CeK7KzXGbIwBm5XyeCeBtj9riCkqpt9P/HxWRbZgwVf4fb1tlDOWzfuSz1mTTLuVkWkRuArAYwJUq7ZCnlEoASKR/7hGRgwAuAOC2U6pvZVJEophQIn6klHoGAJRS7+X83ldzRKAsEqVIO7BkuBbA6161pUq8AmCOiJwvIjEAXwDwrMdtqhoi0pR2RIKINAG4GjXcp5TP4BA02bSLiCwCsAbANUqpkznft6YdHSEi/wHAHAB/8KCJvpRJEREA3wPwhlLqn3O+9+0cESiLRBnuE5GPYMJ0dRjACm+b4yxpz+hVALYDCAN4TCn1W4+bVU2mA9g2MeYQAbBZKfWCt02qCMpncAiabNrlIQANAH6Wfha7lVIrAXwcwD+KSArAOICVSqk/ud04H8vkQgBdAH4jIq+mv/tbADf4dY6om/BPQgghhDhP3WxtEEIIIcR5qEgQQgghxDZUJAghhBBiGyoShBBCCLENFQlCCCGE2IaKRAARkRdEZFBEfJOwhBAAEJGPiMjL6aqGe0Xk8163iRBSGQz/DCAiciWASQBWKKUWe90eQjKIyAUAlFLqgIicg4nKhn+mlBr0uGmEEJvQIlHDiMjH0qu6xnQ2vd+KyDyl1IsAhrxuH6lv9OQTQEwpdQDIppE+CqDV04aSukdE1onIV3M+3ysit3vZplqCFokaR0S+BaARQBzAEaXUP6W/vxzAN2iRIF5iJJ/p310E4HEAH1ZKaR41kZBMlc1nlFIfFZEQgAMALlJKDXjasBqhnlJkB5V/xETO+FMAqEETv6Ern+m6AZsA3EQlgniNUuqwiAyIyHxMpDjvpRJhHioStc+ZAJoBRDGx8hvxtjmE5FEkn+mS0c8DuFsptdvLxhGSw6MAbgYwA8Bj3jaltuDWRo0jIs8C+DGA8wGcrZRalf7+cnBrg3hMoXwC+BqAnwL4n0qp/+Zl2wjJJV0B9DeYUHrnKKXGPW5SzUCLRA0jIn8JIKWU2pwuy7tLRP4cwD8A+BCAZhE5AuBLSqntXraV1B968omJUs0fBzBNRG5OH3qzUupVg9MQ4gpKqaSI/ALAIJUIa9AiQQghpO5JO1n+GsD1mcgiYg6GfxJCCKlrRKQdwJsAXqQSYR1aJAghhBBiG1okCCGEEGIbKhKEEEIIsQ0VCUIIIYTYhooEIYQQQmxDRYIQQgghtqEiQQghhBDb/H/sUhNqFcnw/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 540x540 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(\n",
    "    data=pd.DataFrame(np.hstack([x_ND, y_N[:,np.newaxis]]), columns=['x1', 'x2', 'y']));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the optimization problem as an AUTOGRAD-able function wrt the weights w_D\n",
    "def calc_neg_likelihood_linreg(w_D):\n",
    "    return 0.5 / ag_np.square(sigma) * ag_np.sum(ag_np.square(ag_np.dot(x_ND, w_D) - y_N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1521585.0576643152"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Test the function at an easy initial point\n",
    "init_w_D = np.zeros(2)\n",
    "calc_neg_likelihood_linreg(init_w_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-357441.84423006,  367223.20042115])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Test the gradient at that easy point \n",
    "calc_grad_wrt_w = autograd.grad(calc_neg_likelihood_linreg)\n",
    "calc_grad_wrt_w(init_w_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Because the gradient's magnitude is very large, use very small step size\n",
    "opt_w_D, history = run_many_iters_of_gradient_descent(\n",
    "    calc_neg_likelihood_linreg, autograd.grad(calc_neg_likelihood_linreg), init_w_D,\n",
    "    n_iters=300, step_size=0.000001,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# LinReg worked example\n",
    "# Make plots of how w_D parameter values evolve over iterations, and function values evolve over iterations\n",
    "# Expected result: x\n",
    "\n",
    "fig_h, subplot_grid = plt.subplots(\n",
    "    nrows=1, ncols=2, sharex=True, sharey=False, figsize=(15,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(history['iter'], history['x_D'])\n",
    "subplot_grid[0,0].set_xlabel('iters')\n",
    "subplot_grid[0,0].set_ylabel('w_d')\n",
    "\n",
    "subplot_grid[0,1].plot(history['iter'], history['f'])\n",
    "subplot_grid[0,1].set_xlabel('iters')\n",
    "subplot_grid[0,1].set_ylabel('-1 * log p(y | w, x)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try it Example 4b: Solve the linear regression problem using a weights-and-bias representation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above example only uses weights on the dimensions of $x_i$, and thus can only learn linear models that pass through the origin.\n",
    "\n",
    "Can you instead optimize a model that includes a **bias** term $b>0$?\n",
    "\n",
    "\\begin{align}\n",
    "y_i &\\sim \\mathcal{N}(w^T x_i + b, \\sigma^2), \\forall i \\in 1, 2, \\ldots N\n",
    "\\end{align}\n",
    "where we assume $\\sigma = 0.1$.\n",
    "\n",
    "One non-Bayesian way to train weights would be to just compute the maximum likelihood solution:\n",
    "\n",
    "\\begin{align}\n",
    "\\min_{w,b}  - \\log p(y | w, b, x)\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An easy way to do this is to imagine that each observation vector $x_i$ is expanded into a $\\tilde{x}_i$ that contains a column of all ones.  Then, we can write the corresponding expanded weights as $\\tilde{w} = [w_1 w_2 b]$.\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\min_{\\tilde{w}}  - \\log p(y | \\tilde{w},\\tilde{x})\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now, each expanded xtilde vector has size E = D+1 = 3\n",
    "\n",
    "xtilde_NE = np.hstack([x_ND, np.ones((N,1))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Define f to minimize that takes a COMBINED weights-and-bias vector wtilde_E of size E=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Compute gradient of f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO run gradient descent and plot the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 5 setup: Autograd for functions of data structures of arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Useful Fact: autograd can take derivatives with respect to DATA STRUCTURES of parameters\n",
    "\n",
    "This can help us when it is natural to define models in terms of several parts (e.g. NN layers).\n",
    "\n",
    "We don't need to turn our many model parameters into one giant weights-and-biases vector. We can express our thoughts more naturally."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demo 1: gradient of a LIST of parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w_list_of_arr):\n",
    "    return ag_np.sum(ag_np.square(w_list_of_arr[0])) + ag_np.sum(ag_np.square(w_list_of_arr[1]))\n",
    "\n",
    "g = autograd.grad(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type of the gradient is: \n",
      "<class 'list'>\n",
      "Result of the gradient is: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[array([0., 0., 0.]), array([0., 2., 4., 6., 8.])]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_list_of_arr = [np.zeros(3), np.arange(5, dtype=np.float64)]\n",
    "\n",
    "print(\"Type of the gradient is: \")\n",
    "print(type(g(w_list_of_arr)))\n",
    "\n",
    "print(\"Result of the gradient is: \")\n",
    "g(w_list_of_arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demo 2: gradient of DICT of parameters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(dict_of_arr):\n",
    "    return ag_np.sum(ag_np.square(dict_of_arr['weights'])) + ag_np.sum(ag_np.square(dict_of_arr['bias']))\n",
    "g = autograd.grad(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type of the gradient is: \n",
      "<class 'dict'>\n",
      "Result of the gradient is: \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'weights': array([0., 2., 4., 6., 8.]), 'bias': array(8.4)}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict_of_arr = dict(weights=np.arange(5, dtype=np.float64), bias=4.2)\n",
    "\n",
    "print(\"Type of the gradient is: \")\n",
    "print(type(g(dict_of_arr)))\n",
    "\n",
    "print(\"Result of the gradient is: \")\n",
    "g(dict_of_arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 5: Neural Networks and Autograd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's use a convenient data structure for NN model parameters\n",
    "\n",
    "Use a list of dicts of arrays.\n",
    "\n",
    "Each entry in the list is a dict that represents the parameters of one \"layer\".\n",
    "\n",
    "Each layer-specific dict has two named attributes: a vector of weights 'w' and a vector of biases 'b'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Here's a function to create NN params as a 'list-of-dicts' that match a provided set of dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_nn_params_as_list_of_dicts(\n",
    "        n_hiddens_per_layer_list=[5],\n",
    "        n_dims_input=1,\n",
    "        n_dims_output=1,\n",
    "        weight_fill_func=np.zeros,\n",
    "        bias_fill_func=np.zeros):\n",
    "    nn_param_list = []\n",
    "    n_hiddens_per_layer_list = [n_dims_input] + n_hiddens_per_layer_list + [n_dims_output]\n",
    "\n",
    "    # Given full network size list is [a, b, c, d, e]\n",
    "    # For loop should loop over (a,b) , (b,c) , (c,d) , (d,e)\n",
    "    for n_in, n_out in zip(n_hiddens_per_layer_list[:-1], n_hiddens_per_layer_list[1:]):\n",
    "        nn_param_list.append(\n",
    "            dict(\n",
    "                w=weight_fill_func((n_in, n_out)),\n",
    "                b=bias_fill_func((n_out,)),\n",
    "            ))\n",
    "    return nn_param_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Here's a function to pretty-print any given set of NN parameters to stdout, so we can inspect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pretty_print_nn_param_list(nn_param_list_of_dict):\n",
    "    \"\"\" Create pretty display of the parameters at each layer\n",
    "    \"\"\"\n",
    "    for ll, layer_dict in enumerate(nn_param_list_of_dict):\n",
    "        print(\"Layer %d\" % ll)\n",
    "        print(\"  w | size %9s | %s\" % (layer_dict['w'].shape, layer_dict['w'].flatten()))\n",
    "        print(\"  b | size %9s | %s\" % (layer_dict['b'].shape, layer_dict['b'].flatten()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 0 hidden layers (equivalent to linear regression)\n",
    "\n",
    "For univariate regression: 1D -> 1D\n",
    "\n",
    "Will fill all parameters with zeros by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (1, 1) | [0.]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(n_hiddens_per_layer_list=[], n_dims_input=1, n_dims_output=1)\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 0 hidden layers (equivalent to linear regression)\n",
    "\n",
    "For multivariate regression when |x_i| = 2: 2D -> 1D\n",
    "\n",
    "Will fill all parameters with zeros by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 1) | [0. 0.]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(n_hiddens_per_layer_list=[], n_dims_input=2, n_dims_output=1)\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 1 hidden layer of 3 hidden units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 3) | [0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (3,) | [0. 0. 0.]\n",
      "Layer 1\n",
      "  w | size    (3, 1) | [0. 0. 0.]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(n_hiddens_per_layer_list=[3], n_dims_input=2, n_dims_output=1)\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 1 hidden layer of 3 hidden units\n",
    "\n",
    "Use 'ones' as the fill function for weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 3) | [1. 1. 1. 1. 1. 1.]\n",
      "  b | size      (3,) | [0. 0. 0.]\n",
      "Layer 1\n",
      "  w | size    (3, 1) | [1. 1. 1.]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[3], n_dims_input=2, n_dims_output=1,\n",
    "    weight_fill_func=np.ones)\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 1 hidden layer of 3 hidden units\n",
    "\n",
    "Use random draws from standard normal as the fill function for weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 3) | [ 1.24823477 -0.70553662 -0.13712655  0.23659527 -1.72792202 -1.66701658]\n",
      "  b | size      (3,) | [0. 0. 0.]\n",
      "Layer 1\n",
      "  w | size    (3, 1) | [ 0.23254128 -1.57423719 -0.26868047]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[3], n_dims_input=2, n_dims_output=1,\n",
    "    weight_fill_func=lambda size_tuple: np.random.randn(*size_tuple))\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: NN with 7 hidden layers of diff sizes\n",
    "\n",
    "Just shows how generic this framework is!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 3) | [0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (3,) | [0. 0. 0.]\n",
      "Layer 1\n",
      "  w | size    (3, 4) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (4,) | [0. 0. 0. 0.]\n",
      "Layer 2\n",
      "  w | size    (4, 5) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (5,) | [0. 0. 0. 0. 0.]\n",
      "Layer 3\n",
      "  w | size    (5, 6) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (6,) | [0. 0. 0. 0. 0. 0.]\n",
      "Layer 4\n",
      "  w | size    (6, 5) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (5,) | [0. 0. 0. 0. 0.]\n",
      "Layer 5\n",
      "  w | size    (5, 4) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (4,) | [0. 0. 0. 0.]\n",
      "Layer 6\n",
      "  w | size    (4, 3) | [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "  b | size      (3,) | [0. 0. 0.]\n",
      "Layer 7\n",
      "  w | size    (3, 1) | [0. 0. 0.]\n",
      "  b | size      (1,) | [0.]\n"
     ]
    }
   ],
   "source": [
    "nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[3, 4, 5, 6, 5, 4, 3], n_dims_input=2, n_dims_output=1)\n",
    "pretty_print_nn_param_list(nn_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup: Function that performs **prediction**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_y_given_x_with_NN(x=None, nn_param_list=None, activation_func=ag_np.tanh):\n",
    "    \"\"\" Predict y value given x value via feed-forward neural net\n",
    "    \n",
    "    Args\n",
    "    ----\n",
    "    x : array_like, n_examples x n_input_dims\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    y : array_like, n_examples\n",
    "    \"\"\"\n",
    "    for layer_id, layer_dict in enumerate(nn_param_list):\n",
    "        if layer_id == 0:\n",
    "            if x.ndim > 1:\n",
    "                in_arr = x\n",
    "            else:\n",
    "                if x.size == nn_param_list[0]['w'].shape[0]:\n",
    "                    in_arr = x[ag_np.newaxis,:]\n",
    "                else:\n",
    "                    in_arr = x[:,ag_np.newaxis]                    \n",
    "        else:\n",
    "            in_arr = activation_func(out_arr)\n",
    "        out_arr = ag_np.dot(in_arr, layer_dict['w']) + layer_dict['b']\n",
    "    return ag_np.squeeze(out_arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Make predictions with 0-layer NN whose parameters  are filled with the 'true' params for our toy dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "true_nn_params = make_nn_params_as_list_of_dicts(n_hiddens_per_layer_list=[], n_dims_input=2, n_dims_output=1)\n",
    "true_nn_params[0]['w'][:] = true_w_D[:,np.newaxis]\n",
    "true_nn_params[0]['b'][:] = true_bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'predicted y|x')"
      ]
     },
     "execution_count": 46,
     "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": [
    "yhat_N = predict_y_given_x_with_NN(x_ND, true_nn_params)\n",
    "assert yhat_N.size == N\n",
    "\n",
    "plt.plot(yhat_N, y_N, 'k.')\n",
    "plt.xlabel('true y')\n",
    "plt.ylabel('predicted y|x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Make predictions with 0-layer NN whose parameters  are filled with all zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'predicted y|x')"
      ]
     },
     "execution_count": 47,
     "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": [
    "zero_nn_params = make_nn_params_as_list_of_dicts(n_hiddens_per_layer_list=[], n_dims_input=2, n_dims_output=1)\n",
    "yhat_N = predict_y_given_x_with_NN(x_ND, zero_nn_params)\n",
    "assert yhat_N.size == N\n",
    "\n",
    "plt.plot(yhat_N, y_N, 'k.')\n",
    "plt.xlabel('true y')\n",
    "plt.ylabel('predicted y|x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup: Gradient descent implementation that can use list-of-dict parameters (not just arrays)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_many_iters_of_gradient_descent_with_list_of_dict(f, g, init_x_list_of_dict=None, n_iters=100, step_size=0.001):\n",
    "\n",
    "    # Copy the initial parameter vector\n",
    "    x_list_of_dict = copy.deepcopy(init_x_list_of_dict)\n",
    "\n",
    "    # Create data structs to track the per-iteration history of different quantities\n",
    "    history = dict(\n",
    "        iter=[],\n",
    "        f=[],\n",
    "        x=[],\n",
    "        g=[])\n",
    "    start_time = time.time()\n",
    "    for iter_id in range(n_iters):\n",
    "        if iter_id > 0:\n",
    "            # Gradient is a list of layer-specific dicts\n",
    "            grad_list_of_dict = g(x_list_of_dict)\n",
    "            for layer_id, x_layer_dict in enumerate(x_list_of_dict):\n",
    "                for key in x_layer_dict.keys():\n",
    "                    x_layer_dict[key] = x_layer_dict[key] - step_size * grad_list_of_dict[layer_id][key]\n",
    "                    \n",
    "        fval = f(x_list_of_dict)\n",
    "        history['iter'].append(iter_id)\n",
    "        history['f'].append(fval)\n",
    "        history['x'].append(copy.deepcopy(x_list_of_dict))\n",
    "        history['g'].append(g(x_list_of_dict))\n",
    "\n",
    "        if iter_id < 3 or (iter_id+1) % 50 == 0:\n",
    "            print(\"completed iter %5d/%d after %7.1f sec | loss %.6e\" % (\n",
    "                iter_id+1, n_iters, time.time()-start_time, fval))\n",
    "    return x_list_of_dict, history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Worked Exercise 5a: Train 0-layer NN via gradient descent on LINEAR toy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_regression_loss_function(nn_params):\n",
    "    yhat_N = predict_y_given_x_with_NN(x_ND, nn_params)\n",
    "    return 0.5 / ag_np.square(sigma) * ag_np.sum(np.square(y_N - yhat_N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed iter     1/100 after     0.0 sec | loss 4.343353e+01\n",
      "completed iter     2/100 after     0.1 sec | loss 4.330311e+01\n",
      "completed iter     3/100 after     0.1 sec | loss 4.319213e+01\n",
      "completed iter    50/100 after     2.7 sec | loss 4.242465e+01\n",
      "completed iter   100/100 after     5.2 sec | loss 4.234312e+01\n"
     ]
    }
   ],
   "source": [
    "fromtrue_opt_nn_params, fromtrue_history = run_many_iters_of_gradient_descent_with_list_of_dict(\n",
    "    nn_regression_loss_function,\n",
    "    autograd.grad(nn_regression_loss_function),\n",
    "    true_nn_params,\n",
    "    n_iters=100,\n",
    "    step_size=0.000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 1) | [ 4.19568065 -4.19965201]\n",
      "  b | size      (1,) | [0.09469614]\n"
     ]
    }
   ],
   "source": [
    "pretty_print_nn_param_list(fromtrue_opt_nn_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a137fc390>]"
      ]
     },
     "execution_count": 52,
     "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.plot(fromtrue_history['iter'], fromtrue_history['f'], 'k.-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed iter     1/100 after     0.0 sec | loss 1.521585e+06\n",
      "completed iter     2/100 after     0.1 sec | loss 1.270163e+06\n",
      "completed iter     3/100 after     0.2 sec | loss 1.060293e+06\n",
      "completed iter    50/100 after     2.8 sec | loss 2.686671e+02\n",
      "completed iter   100/100 after     5.4 sec | loss 4.457975e+01\n"
     ]
    }
   ],
   "source": [
    "fromzero_opt_nn_params, fromzero_history = run_many_iters_of_gradient_descent_with_list_of_dict(\n",
    "    nn_regression_loss_function,\n",
    "    autograd.grad(nn_regression_loss_function),\n",
    "    zero_nn_params,\n",
    "    n_iters=100,\n",
    "    step_size=0.000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 0\n",
      "  w | size    (2, 1) | [ 4.19465049 -4.19892163]\n",
      "  b | size      (1,) | [0.11288017]\n"
     ]
    }
   ],
   "source": [
    "pretty_print_nn_param_list(fromzero_opt_nn_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a14080860>]"
      ]
     },
     "execution_count": 55,
     "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.plot(fromzero_history['iter'], fromzero_history['f'], 'k.-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create more complex non-linear toy dataset\n",
    "\n",
    "True method *regression from QUADRATIC features*:\n",
    "\n",
    "$$\n",
    "y \\sim \\text{Normal}( w_1 x_1 + w_2 x_2 + w_3 x_1^2 + w_4 x_2^2 + b, \\sigma^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 300\n",
    "D = 2\n",
    "sigma = 0.1\n",
    "\n",
    "wsq_D = np.asarray([-2.0, 2.0])\n",
    "w_D = np.asarray([4.2, -4.2])\n",
    "\n",
    "train_prng = np.random.RandomState(0)\n",
    "x_ND = train_prng.uniform(low=-5, high=5, size=(N,D))\n",
    "y_N = (\n",
    "    np.dot(np.square(x_ND), wsq_D)\n",
    "    + np.dot(x_ND, w_D)\n",
    "    + sigma * train_prng.randn(N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x540 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(\n",
    "    data=pd.DataFrame(np.hstack([x_ND, y_N[:,np.newaxis]]), columns=['x1', 'x2', 'y']));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nonlinear_toy_nn_regression_loss_function(nn_params):\n",
    "    yhat_N = predict_y_given_x_with_NN(x_ND, nn_params)\n",
    "    return 0.5 / ag_np.square(sigma) * ag_np.sum(np.square(y_N - yhat_N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize 1-layer, 10 hidden unit network with small random noise on weights\n",
    "\n",
    "H10_init_nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[10], n_dims_input=2, n_dims_output=1,\n",
    "    weight_fill_func=lambda sz_tuple: 0.1 * np.random.randn(*sz_tuple))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed iter     1/300 after     0.1 sec | loss 1.195763e+07\n",
      "completed iter     2/300 after     0.3 sec | loss 1.165899e+07\n",
      "completed iter     3/300 after     0.5 sec | loss 1.113150e+07\n",
      "completed iter    50/300 after     9.5 sec | loss 3.516704e+06\n",
      "completed iter   100/300 after    18.8 sec | loss 1.907578e+06\n",
      "completed iter   150/300 after    29.2 sec | loss 1.964786e+06\n",
      "completed iter   200/300 after    39.2 sec | loss 1.749155e+06\n",
      "completed iter   250/300 after    51.1 sec | loss 1.575341e+06\n",
      "completed iter   300/300 after    61.6 sec | loss 1.659934e+06\n"
     ]
    }
   ],
   "source": [
    "H10_opt_nn_params, H10_history = run_many_iters_of_gradient_descent_with_list_of_dict(\n",
    "    nonlinear_toy_nn_regression_loss_function,\n",
    "    autograd.grad(nonlinear_toy_nn_regression_loss_function),\n",
    "    H10_init_nn_params,\n",
    "    n_iters=300,\n",
    "    step_size=0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot objective function vs iters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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": [
    "plt.plot(H10_history['iter'], H10_history['f'], 'k.-')\n",
    "plt.title('10 hidden units');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot predicted y vs. true y for each example as a scatterplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "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": [
    "yhat_N = predict_y_given_x_with_NN(x_ND, H10_opt_nn_params)\n",
    "\n",
    "plt.plot(yhat_N, y_N, 'k.');\n",
    "plt.xlabel('predicted y|x');\n",
    "plt.ylabel('true y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, subplot_grid = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=False, figsize=(10,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(x_ND[:,0], y_N, 'k.');\n",
    "subplot_grid[0,0].plot(x_ND[:,0], yhat_N, 'b.')\n",
    "subplot_grid[0,0].set_xlabel('x_0');\n",
    "\n",
    "subplot_grid[0,1].plot(x_ND[:,1], y_N, 'k.');\n",
    "subplot_grid[0,1].plot(x_ND[:,1], yhat_N, 'b.')\n",
    "subplot_grid[0,1].set_xlabel('x_1');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More units! Try 1 layer with H=30 hidden units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize 1-layer, 30 hidden unit network with small random noise on weights\n",
    "H30_init_nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[30], n_dims_input=2, n_dims_output=1,\n",
    "    weight_fill_func=lambda sz_tuple: 0.1 * np.random.randn(*sz_tuple))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed iter     1/50 after     0.1 sec | loss 1.184375e+07\n",
      "completed iter     2/50 after     0.2 sec | loss 1.087085e+07\n",
      "completed iter     3/50 after     0.4 sec | loss 9.449709e+06\n",
      "completed iter    50/50 after     6.7 sec | loss 2.035457e+06\n"
     ]
    }
   ],
   "source": [
    "H30_opt_nn_params, H30_history = run_many_iters_of_gradient_descent_with_list_of_dict(\n",
    "    nonlinear_toy_nn_regression_loss_function,\n",
    "    autograd.grad(nonlinear_toy_nn_regression_loss_function),\n",
    "    H30_init_nn_params,\n",
    "    n_iters=50,\n",
    "    step_size=0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot objective function vs iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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": [
    "plt.plot(H30_history['iter'], H30_history['f'], 'k.-');\n",
    "plt.title('30 hidden units');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot predicted y value vs true y value for each example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "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": [
    "yhat_N = predict_y_given_x_with_NN(x_ND, H30_opt_nn_params)\n",
    "\n",
    "plt.plot(yhat_N, y_N, 'k.');\n",
    "plt.xlabel('predicted y|x');\n",
    "plt.ylabel('true y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, subplot_grid = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=False, figsize=(10,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(x_ND[:,0], y_N, 'k.');\n",
    "subplot_grid[0,0].plot(x_ND[:,0], yhat_N, 'b.')\n",
    "subplot_grid[0,0].set_xlabel('x_0');\n",
    "\n",
    "subplot_grid[0,1].plot(x_ND[:,1], y_N, 'k.');\n",
    "subplot_grid[0,1].plot(x_ND[:,1], yhat_N, 'b.')\n",
    "subplot_grid[0,1].set_xlabel('x_1');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Even more units! Try 1 layer with H=100 hidden units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize 1-layer, 100 hidden unit network with small random noise on weights\n",
    "H100_init_nn_params = make_nn_params_as_list_of_dicts(\n",
    "    n_hiddens_per_layer_list=[100], n_dims_input=2, n_dims_output=1,\n",
    "    weight_fill_func=lambda sz_tuple: 0.05 * np.random.randn(*sz_tuple))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed iter     1/30 after     0.1 sec | loss 1.194856e+07\n",
      "completed iter     2/30 after     0.2 sec | loss 1.140156e+07\n",
      "completed iter     3/30 after     0.3 sec | loss 1.064044e+07\n"
     ]
    }
   ],
   "source": [
    "H100_opt_nn_params, H100_history = run_many_iters_of_gradient_descent_with_list_of_dict(\n",
    "    nonlinear_toy_nn_regression_loss_function,\n",
    "    autograd.grad(nonlinear_toy_nn_regression_loss_function),\n",
    "    H100_init_nn_params,\n",
    "    n_iters=30,\n",
    "    step_size=0.0000005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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": [
    "yhat_N = predict_y_given_x_with_NN(x_ND, H100_opt_nn_params)\n",
    "\n",
    "plt.plot(yhat_N, y_N, 'k.');\n",
    "plt.xlabel('predicted y|x');\n",
    "plt.ylabel('true y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, subplot_grid = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=False, figsize=(10,3), squeeze=False)\n",
    "subplot_grid[0,0].plot(x_ND[:,0], y_N, 'k.');\n",
    "subplot_grid[0,0].plot(x_ND[:,0], yhat_N, 'b.')\n",
    "subplot_grid[0,0].set_xlabel('x_0');\n",
    "\n",
    "subplot_grid[0,1].plot(x_ND[:,1], y_N, 'k.');\n",
    "subplot_grid[0,1].plot(x_ND[:,1], yhat_N, 'b.')\n",
    "subplot_grid[0,1].set_xlabel('x_1');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try it yourself!\n",
    "\n",
    "* Can you train a prediction network on the non-linear toy data so it has ZERO training error? Is this even possible?\n",
    "\n",
    "* Can you make the network train faster? What happens if you play with the step_size?\n",
    "\n",
    "* What if you made the network **deeper** (more layers)?\n",
    "\n",
    "* What other dataset would you want to try out this regression on?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}