Optimization_methods_v1b.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color='darkblue'> Updates to Assignment <font>\n",
    "\n",
    "#### If you were working on a previous version\n",
    "* The current notebook filename is version \"Optimization_methods_v1b\". \n",
    "* You can find your work in the file directory as version \"Optimization methods'.\n",
    "* To see the file directory, click on the Coursera logo at the top left of the notebook.\n",
    "\n",
    "#### List of Updates\n",
    "* op_utils is now opt_utils_v1a.  Assertion statement in `initialize_parameters` is fixed.\n",
    "* opt_utils_v1a: `compute_cost` function now accumulates total cost of the batch without taking the average (average is taken for entire epoch instead).\n",
    "* In `model` function, the total cost per mini-batch is accumulated, and the average of the entire epoch is taken as the average cost. So the plot of the cost function over time is now a smooth downward curve instead of an oscillating curve.\n",
    "* Print statements used to check each function are reformatted, and 'expected output` is reformatted to match the format of the print statements (for easier visual comparisons)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils_v1a import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils_v1a import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)]- learning_rate*grads['dW' + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] -learning_rate*grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 =\n",
      "[[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 =\n",
      "[[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 =\n",
      "[[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 =\n",
      "[[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 =\\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 =\\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 =\\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 =\\n\" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 =\n",
    "[[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]]\n",
    "b1 =\n",
    "[[ 1.74604067]\n",
    " [-0.75184921]]\n",
    "W2 =\n",
    "[[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
    "b2 =\n",
    "[[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost += compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost += compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, mini_batch_size*k: (k+1)*mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, mini_batch_size*k: (k+1)*mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k*(m-mini_batch_size*np.int(m/mini_batch_size)): (k+1)*(m-mini_batch_size*np.int(m/mini_batch_size))]\n",
    "        mini_batch_Y = shuffled_Y[:, k*(m-mini_batch_size*np.int(m/mini_batch_size)): (k+1)*(m-mini_batch_size*np.int(m/mini_batch_size))]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] =\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] =\n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] =\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] =\n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] =\\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] =\\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] =\\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] =\\n\" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "v[\"dW1\"] =\n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db1\"] =\n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "v[\"dW2\"] =\n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db2\"] =\n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta*v[\"dW\" + str(l+1)] + (1-beta)*grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta*v[\"db\" + str(l+1)] + (1-beta)*grads[\"db\" + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)]- learning_rate*v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)]- learning_rate*v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = \n",
      "[[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = \n",
      "[[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = \n",
      "[[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = \n",
      "[[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = \n",
      "[[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = \n",
      "[[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = \n",
      "[[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = v[[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \\n\" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = v\" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 = \n",
    "[[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]]\n",
    "b1 = \n",
    "[[ 1.74493465]\n",
    " [-0.76027113]]\n",
    "W2 = \n",
    "[[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
    "b2 = \n",
    "[[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]]\n",
    "v[\"dW1\"] = \n",
    "[[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]]\n",
    "v[\"db1\"] = \n",
    "[[-0.01228902]\n",
    " [-0.09357694]]\n",
    "v[\"dW2\"] = \n",
    "[[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]]\n",
    "v[\"db2\"] = v[[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = \n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = \n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW1\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db1\"] = \n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW2\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db2\"] = \n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \\n\" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \\n\" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \\n\" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \\n\" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \\n\" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "v[\"dW1\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db1\"] = \n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "v[\"dW2\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db2\"] = \n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "s[\"dW1\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "s[\"db1\"] = \n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "s[\"dW2\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "s[\"db2\"] = \n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1*v['dW'+ str(l+1)]+(1-beta1)*grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1*v['db'+ str(l+1)]+(1-beta1)*grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v['dW'+ str(l+1)]/(1-(beta1 **2))\n",
    "        v_corrected[\"db\" + str(l+1)] = v['db'+ str(l+1)]/(1-(beta1 **2))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2*s['dW'+ str(l+1)]+(1-beta2)*(grads['dW' + str(l+1)] **2)\n",
    "        s[\"db\" + str(l+1)] = beta2*s['db'+ str(l+1)]+(1-beta2)*(grads['db' + str(l+1)] **2)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)]/(1-(beta2 **t))\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)]/(1-(beta2 **t))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] -learning_rate*(v_corrected[\"dW\" + str(l+1)]/(np.sqrt(s_corrected[\"dW\" + str(l+1)])+epsilon))\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] -learning_rate*(v_corrected[\"db\" + str(l+1)]/(np.sqrt(s_corrected[\"db\" + str(l+1)])+epsilon))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = \n",
      "[[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = \n",
      "[[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = \n",
      "[[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09244991 -0.16498684]]\n",
      "b2 = \n",
      "[[-0.88529979]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = \n",
      "[[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = \n",
      "[[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = \n",
      "[[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = \n",
      "[[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n",
      "s[\"dW1\"] = \n",
      "[[ 0.00121136  0.00131039  0.00081287]\n",
      " [ 0.0002525   0.00081154  0.00046748]]\n",
      "s[\"db1\"] = \n",
      "[[  1.51020075e-05]\n",
      " [  8.75664434e-04]]\n",
      "s[\"dW2\"] = \n",
      "[[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
      " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
      " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
      "s[\"db2\"] = \n",
      "[[  5.49507194e-05]\n",
      " [  2.75494327e-03]\n",
      " [  5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \\n\" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \\n\" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \\n\" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \\n\" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \\n\" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \\n\" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 = \n",
    "[[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]]\n",
    "b1 = \n",
    "[[ 1.75225313]\n",
    " [-0.75376553]]\n",
    "W2 = \n",
    "[[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]]\n",
    "b2 = \n",
    "[[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]]\n",
    "v[\"dW1\"] = \n",
    "[[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]]\n",
    "v[\"db1\"] = \n",
    "[[-0.01228902]\n",
    " [-0.09357694]]\n",
    "v[\"dW2\"] = \n",
    "[[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]]\n",
    "v[\"db2\"] = \n",
    "[[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]\n",
    "s[\"dW1\"] = \n",
    "[[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]]\n",
    "s[\"db1\"] = \n",
    "[[  1.51020075e-05]\n",
    " [  8.75664434e-04]]\n",
    "s[\"dW2\"] = \n",
    "[[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
    "s[\"db2\"] = \n",
    "[[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
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pOWkUwU3qEtmtJb0/fpResx/xuC68Y1OfiT+B9aMuqz234tQsEn9ZR8qqHcgq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I8dQMdp/sebcSSfp+77GZdTx1HWW/bVJ1t48JmpxMSdCuKH9ufw9AO/4HR69TYL8ux8+OZ60lJy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\nv5qYYyZ0Z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f814101e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    m = X.shape[1]                   # number of training examples\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "        cost_total = 0\n",
    "        \n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost and add to the cost total\n",
    "            cost_total += compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        cost_avg = cost_total / m\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost_avg))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost_avg)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.705272\n",
      "Cost after epoch 1000: 0.668312\n",
      "Cost after epoch 2000: 0.631616\n",
      "Cost after epoch 3000: 0.592466\n",
      "Cost after epoch 4000: 0.576420\n",
      "Cost after epoch 5000: 0.546602\n",
      "Cost after epoch 6000: 0.524537\n",
      "Cost after epoch 7000: 0.530889\n",
      "Cost after epoch 8000: 0.495379\n",
      "Cost after epoch 9000: 0.469526\n"
     ]
    },
    {
     "data": {
      "image/png": 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72WiGRAcxOTmqRz4z2N+HX12SzvVThzBxyPGf+ePzR3C4pJrLH1vKbucScaZt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\nMzMrPBdDMzMrPBdDMzMrvHcbmjBfYpVGqAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8146609cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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v4nt5/sQ4z7zgNsrJ45vYF7F7RL+8G4TePivUWFqW1MocqtRneIbRlTJbQo+Z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1/g3fxEvHTPnm4oKb9w/M7iI4d/pDt3bzG6tlfOMbq8xejadtMWm52FTmNLlWjikl06opS+paPK\n7njpFIvnxhhZrTA5u9n0Ltrhn1ptuaHec4xsbJOtNqgNpSkXetRr0TlOzW36K2KD/p1rp/KsTvkL\nhO5/7TqZevN1xRSO0fUVlqcylIsFvBZbPhrZNAsXiruJt13HlJNSWigztlJpeSRv+A2tJVpKlCLS\npDw+RK7SYGylsnvdspFJsdDi+mOq7nHm7VVSDQ9z/rW+iXSK2fuKBx4pHmRiYfNOndtg1er40haN\njLExkcdCtnM0cqmWSXKvqBMk+I2fx1YqoY2lt4d02jVqOvUqfe1rf5qsTjKxYMbK6VFuXZrghzMF\nFs6Pc+tSiUaLo8lTcxuk637j4p3tGOm617p0XTecv7+xVbWf8eBU5FsPPkA9vX/hznqpyFahizZj\nERraCj9adOYXzZdoKVFKX/v6j/151CEkViPrd9SojmTbLrYZ2ajt78UY3H8U5rm2vSTTdY/hzRrf\neeQR1k5NUMv6lXdqmQy1oSFe/KVfPNJznyS/oPv++x1QT8H8hfHD14+VntGpV+l7V7ynuJz6ZNRh\n9Kc2W0pCOml1xKWMRiZFpt5cocDhb+2YurmOOcdLjz9BvrzA9OwsG8Uibz34ALXh5JSAq+YzeKkU\n5jWvNnYGC/cWtTUkJjQL0veuXc1Acg4yEqVcyDGyvt38Rz64f8fIWpXS7TKZml/oe2UqT7l4QDIz\nY2lmNEiIzfnYgHSwEGe43GBt4hz/955393BUJ8iM+QvjTN9Y8+vlGoCxODOqJBkjmgkR2Wd4Y5uJ\nhU2y236/R78x8tC+U7BLp0fJVeqk63cW8zQyKZZO+1syRtaqTM5u7F5rzNY8Juc2AQ5MlluFHPMX\nxikubpHdbpCuefuuFaUcjK1UWNm7BSRh6rk0sxdLfglBD7aHj68dmByOrlHKQPiT5z4bdQiJMby5\nzfTNdXJB8YFM3WNiYZPC8v79fF4mxa1LJRbPjrEyPcLi2TFuXSrtrngt3S63XJAzcXuro1i281lu\nnx/n1o9MtC+E4JH8guZm1IeCZtxKkrGjRCkD4zO/Oxd1CIlQWmid3EqLW60TkhlbYznWJvN+78Q9\nf+jbtd9K172uk1s13/oE2PawkoscLyVKGRiVn30m6hASIdsmuaU8t1tcvFM7Lbbu5q/27C65LZ0e\nxbM71yr9Gq6wNJPc066SDEqUItKk1ia5eSnruoTdylQe765v8cy/v+u4hjPMXiyxXhqiMpxhvTTE\n7MVSTzqPiIRRopSBcsV7KuoQYm9leqRlcludzHd9FFguDrM0M0o9k/L3BgYLfTZLh9vCUc+lWZ4p\nMH9fkeWZgvYYyonQWzEZKMe1VcQ8R3GxTGHV74qxNZZleXr0yGXcolAp5Fg8U2Ai2NLhpY2VyTwb\nE4dLbpvFYTaLw/41SV1LlARSohQ5Kue45501cpX67iKY0dVthjfr3LpUikVN0W5tjQ+xNT7U2+Sm\nJCkJlby3uyJH1OutIrlKvSlJQlD3tOExslbt6XOdOCU3ESVKGUy93CqSqzRa3p9yapEk0g+UKGUg\n9XKrSD3XZpWoQU2LTUQST4lS5IgqI1ka2VRTbXAHODM2i0NRhSUiPaJEKQOrZ1tFzJi7UGRrNOsn\nSPx6nfP3jh/YPFhE4k+rXmVg9XKriJdJcfv8OHjO73SRwJWuItKa3u7KQOt5sfSUKUmK9BklShER\nkRBKlDLw1FVERMIoUcrAe+DTX4g6BBGJMSVKGXjXrmb46q/+R9RhiEhMKVGKAFtffDnqEEQkppQo\nRQi2ioiItKBEKRJQr0oRaUWJUkREJEQkidLMfs3MXjczz8weCXncL5jZd83s+2b25EnGKIPn2tWM\ntoqIyD5RHVFeB34FeLHdA8wsDfwl8EHgIeA3zOyhkwlPBpW2iojI3SJJlM65N5xz3z3gYY8C33fO\nveWc2wb+EXji+KOTQaatIiJytzgv9TsHvLPn8xvAT7Z7sJl9DPhY8Gn1p68/d/0YYztuU8Bi1EEc\nUXLH8OhzO7eSO4Y7NIZ4SPoYkh4/wHsO+43HlijN7AVgpsWXfs8596+9fj7n3NPA08Fzf8s51/ba\nZ9wlPX7QGOJCY4iHpI8h6fGDP4bDfu+xJUrn3ONH/BE3gfN7Pn9XcJ+IiMiJifP2kG8C95vZRTPL\nAb8OPBtxTCIiMmCi2h7yITO7AfwU8JyZPR/cf9bMrgA45+rAJ4DngTeALzjnXu/wKZ4+hrBPUtLj\nB40hLjSGeEj6GJIePxxhDOac62UgIiIifSXOp15FREQip0QpIiISIvGJsotyeG+b2Wtmdu0oy4SP\nQz+U9DOzU2b2ZTP7XvDvRJvHxW4eDnpdzfdU8PVXzezhKOJsp4P4P2Bmq8Frfs3M/iCKOMOY2d+Y\n2YKZtdz/HPc5gI7GEOt5MLPzZvZVM/tO8Pfot1s8Jtbz0OEYup8H51yiP4AH8TeSfg14JORxbwNT\nUcd72DEAaeBN4BKQA14BHoo69j3xfRp4Mrj9JPCpJMxDJ68rcBm4ChjwPuAbUcfdZfwfAL4UdawH\njONngIeB622+Hts56GIMsZ4H4AzwcHB7DPjfJP0udDGGruch8UeUrrNyeLHW4RjiXtLvCeBzwe3P\nAb8cYSzd6OR1fQL4W+d7CSiZ2ZmTDrSNuP+/6Ihz7kVgKeQhcZ4DoKMxxJpzbtY593Jwex1/t8G5\nux4W63nocAxdS3yi7IIDXjCzbwfl7pKmVUm/I/8H6KHTzrnZ4PYccLrN4+I2D528rnF+7TuN7f3B\nqbKrZvbekwmtp+I8B91IxDyY2X3AjwPfuOtLiZmHkDFAl/MQ51qvu3pUDu8x59xNM7sH+LKZ/U/w\nDvBEnHRJv+MQNoa9nzjnnJm123cU6TwMqJeBC865DTO7DPwLcH/EMQ2iRMyDmRWAfwJ+xzm3FnU8\nh3HAGLqeh0QkSnf0cng4524G/y6Y2T/jn7I6sT/QPRhD5CX9wsZgZvNmdsY5Nxucillo8zMinYcW\nOnldI3/tQxwY294/FM65K2b2WTObcs4lqch1nOegI0mYBzPL4ieYzzvnnmnxkNjPw0FjOMw8DMSp\nVzMbNbOxndvAz+P3xEySuJf0exb4SHD7I8C+o+SYzkMnr+uzwIeDFX/vA1b3nGaO2oHxm9mMmVlw\n+1H83/sfnnikRxPnOehI3OchiO2vgTecc59p87BYz0MnYzjUPES9SumoH8CH8M+TV4F54Png/rPA\nleD2JfzVgK8Ar+Of7ow89m7GEHx+GX8V15sxHMMk8BXge8ALwKmkzEOr1xX4OPDx4LbhNxF/E3iN\nkNXVMY3/E8Hr/QrwEvD+qGNuMYZ/AGaBWvC78NEkzUGHY4j1PACP4a8heBW4FnxcTtI8dDiGrudB\nJexERERCDMSpVxERkcNSohQREQmhRCkiIhJCiVJERCSEEqWIiEgIJUqRPmZm/2ZmK2b2pahjEUkq\nJUqR/vZnwG9GHYRIkilRivQBM/uJoMjzcFAB6XUz+1Hn3FeA9ajjE0myRNR6FZFwzrlvmtmzwB8D\neeDvnHNRlwcU6QtKlCL944/wa79WgE9GHItI39CpV5H+MQkU8Du7D0cci0jfUKIU6R9/Bfw+8Hng\nUxHHItI3dOpVpA+Y2YeBmnPu780sDXzdzH4O+EPgAaBgZjeAjzrnno8yVpGkUfcQERGREDr1KiIi\nEkKJUkREJIQSpYiISAglShERkRBKlCIiIiGUKEVEREIoUYqIiIT4f69YE6duXwavAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8146518f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.705286\n",
      "Cost after epoch 1000: 0.668378\n",
      "Cost after epoch 2000: 0.631717\n",
      "Cost after epoch 3000: 0.592568\n",
      "Cost after epoch 4000: 0.576488\n",
      "Cost after epoch 5000: 0.546674\n",
      "Cost after epoch 6000: 0.524619\n",
      "Cost after epoch 7000: 0.530958\n",
      "Cost after epoch 8000: 0.495551\n",
      "Cost after epoch 9000: 0.469689\n"
     ]
    },
    {
     "data": {
      "image/png": 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xxIT5MyUhvEs+M9jPm59dOopvTIllWmJEg2Miwo8uTCYzv4wrHvuSlKziLomp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\nEdF5KYYREdF5KYYREdF5KYYREdF5vwEeJCcfTf9qigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8146624748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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6UMj5lEtlOtO7m2s7kZ/iYudJVBpfs8fN0BVzKDStLTBMa2FOywqk5ZbqNF+r\nPZK7XcwzdMxGoaahCjAwaNHV3Xgc0wKnzUDnvcr1HjXqeyM902w3eAbX3tmYtIgIiAzlkWR+1m24\nsDtlZfJ6meOnNq/uIiL09Nn01E2puHa5FOpdlcvBxIyxkzGmJ8o12bZkyiCeMFha2Dh3trIc7LS0\n4NHdYzYUAO2EVyw8wXhyBMew8AwLw/cw8Hnd7NcZPBVnesIJhifXGabmXsXBYZtkKjgP31fSXSY9\nfVvvkdwIwxCOjcUYGlE8V7FsCT1Gb7/VIGpfJZkKJnscdopFn8U5h2JRSSSEvkF714qioFVAwLcs\nrp8/x4nnL9ZCrwCuZfHMnS/eteNG3LxEhvKI4fvaYCSrqAYG9OSZ7bcYuOsJhPvBFI+ztyQCHVFD\nMC0hs+qxvETosN8wqgVAXT0eyU3MR9yITq/A269/hu92nWUmMUBPeZXbV58n7ebBCMLRnqe4rmI3\nGSbPU7KZYPZiR9rkxOn9EYw3N9BgTXeZlEtB1KAqRxhPCqPHD7/iVD7vMX6l3HATl82UOH46tql5\nmOuxXn/kV9/4t/jRP/0zeuYXUBEM32P87FmefMXLdnTMiAiIDOWRY71J9eXS9gtmigW/cQZhE4lK\nXqxZR7QzbWCZ4DQd2raFjrSwstRaBKQahB93w1ACJPwyL1n+XtvtYYYpm/GYvF5ee2DaYWDIom/g\n4EN1IoFSUG+/RanoVyqX97bubqfqRlVmp8In18xOOZw+t73P++UfehG/8VGPb/7uc7zV+xBXbruV\nx3/gVZTrmoOdRIIHf+ad9M3M0Lm8wtLQIJne3p2cSkREjchQHjEss6KkHTbtYgfhrfnZNkkxCHRO\nQ0KETtln4noZty7yWq26dRxlZanNKCxoX2q6D3heEKpuXtv8bDAyK76LYcKdYJqbH7+1Har9tAsL\nQetPfa57u4QNjl7v8Y141RO/xH84+wcMTUxiVb5ot377ccYuXeKTP/cu/CZVjMXhYRaHh7d1rIiI\ndhyOK0LEphFD6Bto7ZkUgcGh7d/3FNZp3wi7WFcb9Ztl81TX+gXbGclAiODg7tGymfAS3SAsfPP0\nKi7MuczPrfXHVnPd+dw2Z4fRvg2mWcBiMyQeuo+3vusyg5NTNSMJYHoeqWyOU88+t81VRkRsjchQ\nHkH6BywGh62axFw8LoydjG07lFku+23bO0TCx3MV8j7uOmHgdq9VbYfYzeKOrbJeK+LN0qbo+9oy\npgzWct0SZ7/DAAAgAElEQVTbpbcv/Cau3dDqdiQeuo9f+sAI/dPTSMiHYjsOg+OT215nRMRWiEKv\nhxTPU3w/0Fttzh2JCL39Nr39u5NPm51qH3bt7m1V6YGg8KdNBDgUOxa0YXR2Gtixg70/6+w0maX1\nnEU4UtM7VJWFOZelimpSPCEMHbNJpYLh10Hrj5KIC4MjdsON1HoDp3eS6+4ftPA8ZWXJqxUidfeY\nLb2i61E/YDnX1YUf4o46lkWmLxrCHLE/RIbykOG6ytREmUJFBs60hJFRe0/HXlUl58IYHA7/iiSS\n4Y36YYhAT69J7xZnN+4Vli0MDlnMzTb2TnZ1m0dKT3V22mFlaa23tVRUxq+U6ekzWV5ce7xQCMLk\nJ07Ha+dnmbTPde+gcEhEGD4WY2BIccqKHVu/wreeV3/nfdz9q4WGAcsTZ89QjsexHAejckIKqGFw\n6fYXbnudERFb4XBcuSKAwEMYv1pqKHxwnaDh//S5+J5VPooBGuJhBKHS8ItcLGaQ7jbJ1CnNiAS5\nqHpvRSQwTD29rV8131dmpspkVoLKWMumclOw91/L3gGbVKfJamU+ZGdXYCQPwySUzVD12sJCp0sL\nrR9mEFJ1ai0w1Vz34lyrOtNAU667XPaZn3XJ5zxMM9ivq9tc970yTcFMbv69fP+974VfLbSu2zD4\nzDvfwWs//SCDk1MgwmpvL1++954GwfPO5RVe9DdfY3BykpW+Pp58xctZHImKeiJ2h8hQHiJKRQ0d\nfaUKS4suw8f2po+uqzvwQOoRgfQGF8ORUZtUyghCfz6kuwz6BmxKRZ+lRRfPDdpHenqtFkUZVeXy\n80Xcugio68D4VYfjp2RfBkfHE0bLyK0wSobNxY4T5Kwkw6UFTuSnQ4t2c2aCmUQ/KbfIcGlhTwt7\nayPBtpBTLRUbIwf9AxV1pvngs7LswMkcv1rGjgUtKomk0TDc23OVmclgxufg8M5D/5uZHZnv6uJz\n97+DWLGI+D6lVKphe/fCAm/6g4/XvM6euXlOXLzEQz/x40yePbPjNUZERIbyEOGuc/Err9PjuKNj\nusF0imZiMWF4ZP0LoYjQ3WvR3eQtpjrMDdsashm/wUjWMzPlcPbC4cgVLsR6+OTo6/FFcMXCVpfe\n8go/NvklrIobrsCjfS/mqe4LGOqBCEmvyJsnvxQIH+wBti1bLjyq73+Fxlx3ta+0+prlkjI1XiaZ\nktDh3ksLLn0D1qbDqmFsdXZkuXmoaoWXfukRrHK5VploAIbr8srP/yV//vd/fp0ZdBH7huqR/hyO\nTkLmJiCeDL/4iUBqj3Jn87NOqFarr3urK5rPtq+sXE/4YD9R4AvDr6Js2LiGDSLEslnsqTme9IZr\nkzwudZzg6e7zeIaJY8ZwDJuM1cHnRvZugLBpCt29ZmiFaVe3EXpNsmMGuawXOoEkbFamKuRz7dWa\ndlL0s5sDlofHx0MvZKlsllhp70a8RWxMIltm9OISJ59Z5Pizi3TN549kaXnkUR4Q5ZLP/JxLIe9j\n20L/oEVHpxk6YcIwoWePCmHa9RS6TiD7tl1tUd9XPC+8ahdaR0vVYx4OZ5KslSJrpQKroD4v/OYj\n9M9cr2wVLorLydNxnhy90DLFRMVg2U6zanXQ5YaMXdkEvqcotPXahkZsTFMqGrVBm9DQsUC31rKD\nath6acHMikd21SORNDh+KtZQzbzViIUq2/pu3HmPS+o3fiUo2tklSokksVK55XEVwbWiS9xBEc87\nDE5kMCpfLdNXuhcKGL6yPNRxsIvbItG36AAol3yuXlrL+1QLdoaOWQyP2sSTwtKCh/pKR9pkYNDe\nUYhrPQwRvJDSR2V7kRLfD3JY1XCuYQQX9GaBge5em/nZcCPdvwPhhN2kvn/v2NXn6J+5jllXqeQB\nE9fLlM+Fh6gNlLKx9TyeU/aZmnAo5IMvSCIpjIzFiDcVc1Wl7gaG7BYJusFhm/5Bk8vPlxpC3KqB\nXOHyotsg12fZEjp/0zCCfZoLfpIdW2/zSTx0H2/6wEho0c5OePLld3HXQw9j14kSuKbJpRe+oEW5\nJ2L/6J7P14xkFUMhvVRkZSCF7vLQgb0kCr0eAPNzbmjeZ3Yq+EPv7bM5eyHBuVuTjIzG1vW+dkpY\n+A4glTS2ZZynJgIjWb24eh5MTzotai+WJRw/Zbccu2/ApLfv4PVWIRBc73JyoD6jV55pMJJVnLJy\ndv4ipt8aSjbUp6+8sqVjqq9cu1yqGUmAYiF4zHV8ZqfLPPfdAs88VeDa5VKtQCfMa3ed8BFoVWH6\negYGw4UCBoYsjo3ZmNaaYERH2mBsiwLtD3z4fn7pAyNb2mezPHvni3nmJS/GNU3K8RiuaTJ+7ixf\n+5Ef2pPjRWwOu9y+Wdd092aQ+14R3W4dAPlsewm1Usknkdi/2GNvv0km41EqVHs8gkKRY9uYVOG6\nSi4T3rKwMOe2FPh0dFpceIFJqRi0h8QTgrEdrbM95Ieuf5lvyCnixfZFObesXuK5wVvIWUlcw0LU\nx9Rg1JexaUmGgGzWxwu5hqgP16+WccprkoGFvM+1yyVOn09gh91MrXOf0/wZdfdaqCrzsy6eF4T7\nBwYsevosRIJZpa5bmRqzxRuo99/73obeyF1HhG++/m6+86pX0rW4RK4rTaGzcw8PGLEZnJiF6Tqh\nX0PXOlx/5xsRGcoDoLnXsJ5CbmeG0in7gUcHpNPmur2Xvqdcu1Ku5aeqHsPYSXtbXqzrtq/adULC\nesExhURy/fNdiHXzWM8LWYj30Fde4fuXnmagvLzl9W2V5UWHxel5zjIfeMi02h7ThE7b4++Mf45n\n06e5njpGh5vnRSvP0+usbvmYTtkPHVmmSmjrkO/D8oIT2uZi24JlS2hxlFNWMisu6bqh0T19dmAw\n/aC3tt5LFZFwY7wBzbMj95JyIsH86LF9O17E+iwPJhm+5iB1Xz9fYLUvCUco7AqRoTwQkikTZyXc\nUq4nLbYRy4sOs9Nu4MMoLMwGJfwDQ+GhzPm5oB+uatiq4dLpCYdTZ7durGOx9i0L21W8mYn38+nR\nu/HEQMVgxe7keuoY90w9wmhxbluvuRmcsh+8l/W5ubrtVRty7HgsMCLqcfvqRW5fvbij4yaSRiAA\n0Wwsq0NjQt7fYpvJHCLBDMt2A7knxx1uSZsNk2FEBNmFgMZ+GsiIw0k5aTN7vIve2RyxkodnCqv9\nSTK94W0+h5nIUB4AXT1mLY9Xj0hwodwOrqMtF3ZVWJx36ewyQ0XIm6trqxQLiufplkNshhFU7y40\nqb0YBlvS+qznrwZe0lhRKgauGPzVwPfz1vHPbes1N0M20z6HEk8K6bRJd4+16/njZMogHhNKdTcw\nSFA9HJZvhCBk3Y5Ecv3gb7Ho79pcUNhAQECV0997hhd84zFi5RJXL5zn6Ze/rG1/ZMTRp9RhM33m\n6GvyRobyAEh1GMQT0jCiSgRicaGjc3uGcr3RUZkVl0Rib1R9mukftLFjwsKci+cqyQ6DwSGb2DaF\n0Ofj4cN3F2PdoaHQ3UJV2xqYdNqkf9BueG4+57O6HIS8u7pNOjq3J4cnIpw4E2d+1mF1xQMNFJIG\nhmymxsvkc37LTciGkznWsZROWUmm2m/fChv1Rt710MPc8vgT2E5Qhtu5/E3Ofvd7fPLd78KN78/3\nMyJiO0SG8gAQEU6cjrM47zZcXPsHrX3VGu3qMlkO0QtNJLdesNHwut0WXd2789WK+2WKZqvHEfPD\niwR2i84uk/lZt8XGiATb6mkWJ8+ueqS7TEbG7G19noYhDI3EGGoqEh09EWNuZu1YyaQwNBrDttvf\nhKi/fjGRuUtXgJqgeRuS2Sy3fevbDZXDlueRzOU5/53v8L27Xro7C4mI2AMiQ3lAGMZaD9xu0Jk2\nmZ0OHx3Vzmj1D9nkcj6Oo7UCDkPg2Njm7u5VlaVFl6X5oFIymTIYHLF3ddbkHcvP8Fjv7Q3hV8t3\nedHK3g7tjcWMljCyCPQNWA39jKWS3yJOrgqZVY+ePotkavfMuWEEkzmGj9HSNxmGX2k1WY/t5I4L\neZ+5WYdS0SdmC8d+73UbCggMTE3jmWZLi43luoxdvhIZynb4lXF2R6z4pRmr7NG5XMR0fIodNrmu\n+JEq6IkM5Q2CZQtDI1ZDMU/twt7GcJmmcPpcnFzGp1j0sWNCuit8/mQYczNOwzinfK7SrnB29yad\n3Ln8PfJmku92ncNQD19MLmSu8NKlp3bl9dejf9Am3RUoJUEwq7L5vcxl/NDIpipkMy7J1N6EFDfj\nqS4vuqGVslUGhqwtt+MU8h7Xr6xpwhY95bmf+Qqn7+ngygtua79fZ0foAGZfhGx315bWcDNguD79\nU1mSueDmt5SwWDjWiRs/JLJVWyCRKzM4nkE0SJWksmW6FgtMn+pGzaPRJhIZykNOZtVjbsbBdRTb\nFgaH7ZbQX5V0VyBSXSwqhrlxewhQ65Fr95rt8DxtMJJV1A96JrfThxm6PuAHFr7FXUtPkrE6SLs5\n4v6a5+z7yvysw8qyh/pB/nfo2PZzos3E4gYDQ+1fyzDajHWU9tJz+0W7Yi2AoRFzW4O/Z0M0YS3X\n5WX/80tcue3WtnJO8yMj5NJp0svLmHVqG75p8sz3v2TL67ihUWXk6gqW49fSC/Giy8jVFSbO9RwZ\n4wKAKgOT2QaFHkPBcny6Kgo9R4Ej9I7fPDiO4pR9lpccpsbXmszLZWVyvNwy7UNVmZ0uc/HZItOT\nDksLLoWcv6eKPk5Z20rcFYu7r7oR9x0GyssNRhJg8nqZ5UUP3wu8uFw2kAd03f0RXk63ucEQgiKc\nZlSVuRmH575XUde5VKRY2BuVknaRARFIdWzvHrnUxkNN5POMXbzEHV/9ay48/gR2sxi5CF94+0+y\nODyEa1k4tk0xkeCRH3sTywMD21rLjUoi52B6fmM7EoGkYsfK0RJ5t8seEpInNxRSq636vIeVyKM8\nRJRKPpPXy7UG8TBvQDUIedZfoJeX3Jp3Vx8GnZ50GA3x7DxPyax4OI5PKmWS2kaFprXOmKdYfH88\nqVLJb6kChcCrXVlyGypT9wrTEkZPxJi8Xg7EFgAURsbs0CKb6TqJP4BCRZ5uLwZz9/SZFAut749l\ny7Y/o+XuXrqXlkK3ve5Tf4HlOLi2zV0PPczn3/5WFo6tVSTl02ke/Jl30rG6il0qs9Lfhx4yJabD\ngOX4oZXKhq4vC3cgqJLMlulYLeMbQrYnTjm59nfnr3Nd0SP00UeG8pDg+8r1y6VNCQ40K60sLYTL\nxmVXPXxfGzyLYsHn+pVSzaguGR7xeFCFu9ncJARarZ1dJtmmflAR6B/YH63WclFD456qUNjAS1ux\nOnmq+zyrdiejhRluW71MTNuP/lqPzrTJ+dsS5LNBvrKjwwgdUeY6Gto/qwqLCy4jo7ubz0x3mRRy\nfqDrWlmOYcDYydimb4yKxUBAvbPf54Fb3oCeVF75hS82CJB7FUmnattH9f+7P/FJ/uzv/72WcGyu\nK8pJrofTJg/pC5STh+iSrcrgeIZE3sGoKFd1rJZYHkiS6Q9Cql7MxI2Z2CWvwUP2BTI9R6d/9hC9\n6zc32YzXIpTejuaQque1DzP6fnBxhCDsN3m93HAc9aFUVJYWtu6BHRu1mTWpVX3aMWH4mL1t0YSt\nYscl9M4boWXSRj3jySE+N/JaPBFUTCaSwzzRfRt/Z/zzJP3thbYMQzbM85bLfluJv90Mv6oGoXrD\nEIZHY/QO+BTyPpYpW4oerCy7zC14+I6ysqS84uoXWenr5Vuv+QFe/NePYnpeMMrKtkjmW6te44UC\n3YuLrPT379q53QyUkhbluEms5NVyewr4pkE+Hd+XNRiuT9dCgVQ28BQzfUlyXbGGm55k1qkZSaiG\nh6F3vkCuO4Ff0XOdG0szfG0Vo07EONcVJ9e9P+eyG0SGcg9xXWVx3iGX9bEsoa/foiMdfjF1HW0b\nyqynOtGhno4Og8xq64XWtKRhtqNTmTHZjCqsLntbNpRSaVcYGlm7MLe+tlLI+zhlJZ4wdtWIJhIG\n8aRQKjS+d4ZAb5v5nQp8aegVDe0mrmHhIzzW+0J+YOFbu7a++mMu210Uuww8ppEQ674bLTW+rw19\nlrGYMDxqk+owt1zc5PvK/KKHV5dvth2HnvkFRJUH/tF7iecLlBNx3vSHfxRqKGFdrYOIdogwe7Kb\n7rk8naslUCh02iwNdexLm4h4PseuLGO4Witisaez2MUEy8NrcyRT2XLLGC0AFAYmMswdT6OmgRsz\nmTjXQyLvYro+paSFGzta1buRodwjXFe5crFYkx0rl5RCvszAkNUwB7BKImmEehtVoXLfD5rDB4Zs\nuptmOw4M2+SypQZPUQSGj22h4X0Hf38iElrY47rK9SulQBC9cl7JpMFY09DgnXDiZJyZqbW8XyIZ\neFHtCpmyVoqi0Rri9A2TKx1ju24ol+1OPjvyWnJWKjCQYz63PfZl+mfGa8+ptvHslKmJctCuUnmv\ny2Vl/GqZU2fjbVuE2nHud36Sp974J8RoLLiwPI+7Hn6EVC7LN15/N4bnUUglQ1WSSskUq3192z+h\nTWK4Li/8xmOcf/JJULh4+wt4+mV34dmHY1zbdlBDWB7uaDBM+0XnchHD04ZKT0Oha7nIan+y5in6\nhoR+7gLECy4j11aZOt1du4gVO47u53GghlJE3gj8NmAC/5+q/qem7XcDnwAuVx76c1X9N/u6yDqq\nrQhVNZ10l8ngkI0ZMul9acFpyTeqwvysS0+v1ZLDSqYMEimDYn7tQleVtTt5JoZUVLHDDF8sZnD6\nfJyleZd83icWM+gbsFq8t3bTJESgu2fjO7xy2adY8LFtqRj29Y3d9dlAai7hZrEq8xoLBZ+F2fBp\nF9vBMIORYCNanYCy/posPwgXhmH7rYINO8FH+NToD5E344GaA4ABT991Ny97+BMkshniicAr32kh\nj+tog5GsUtX73Uq7TuKh+/iHvwxvbBPiEOCWbz/Bam8fJ55/npHx8drFsrqHY9s89BM/vr3p31tB\nlR/90z9jYGoaq5I3vePRr3Hi4mUe/Omf2vvj34Akc06op6gStKkUOoPvUrY7TudysWE6SBWDQGQg\nkXcodhx9ecIDM5QiYgK/A/woMA58XUQ+qapPNz31y6r65n1fYBOqgXdUr8+6suSRz/mcPtdaCJPL\nhleuiQTVms1C1CLC8ZMxlhbcoPhCA/H0vgGrrfdVKvkszLqB8YoFguRDx9p/KUWEsRMxrlWLefzK\ntPqU0TZUWT336UmHzMpaUYhtBQVAYZ6bh8EjAy/l+dMnEd9HxeDExac4/cy3QIOhwYO7PMN3s55z\n0i8xUpxnKjGIyppx2onaT7nk4/sQj0vDJI6J5DCOYa0ZyQpqCMWXvJA7Fh7fNcnCstM+/1kqbT7/\n+cCH7+fxD/TAsFJMJjEdJ7SHzHZdvu/RvyFRKGC5a3eEAniGwROveiWLI8NbP5EtMnx9nP7pmZqR\nhKCvs2d+ntHLV5g8e2bP13Cj4domitsaZNLGOZJOwmJpKEXfTD48IKVglzyK++8U7zoH6VG+HHhe\nVS8BiMgfA28Bmg3loaCQ9xuMZBXXVbIZr0UmzrKEUoilVA1yh56nLMw6rFZ6Iru6TQYGbfor/zai\nWPS5dmltfJLjBKHdY8dt0l3tP9Z4wuDcLQkyqx6uqySTBsnU+t7h8pJLptq8XhfWmxwvc/JMa0L+\n0f47uJg+iW9YQawAuH7uhcQLWUavPbepXOxe8sMzf82nj91Nxu5AFHwxOJe5ygsyl7b0Ok7ZZ+Ja\nMM+z+vYNj9q170LBjIfm6HwxyVrJXdX1jcWMtu/rZvLCtakf1QHLIvzlW+/jDX/8JyRz4RfCRD4f\nGrI3fZ++2dlNr30nDE5OYrqt1cqW4zA4ORUZym2Q6UvQsVpq8BQVcGNmS0VutjeJKPTM5ltvqAxw\njlgush0HaSjHgOt1v48Drwh53qtF5AlgAvhlVQ3VLhOR9wDvARi2k7u81KAyNDRv7UMx79PV3fh4\n34BFPlduuXjFE8EA3CsXSw3T6pcXA+/01Nn4pi6gcyEKKaowO+XQmTbXfQ3DkJY853qEKfBAUKnp\nuopVF3r2Eb7XdQ7PaHx937K5duEORq8917agab9IeSXeOv455uJ9ZK0kg6Ul0m5+S68RRBjKtYHU\n1fdnesIhHjeIJwxGivNoiD9m+Q4n89M7Po+G17SErh4zSAvUt+sYG+c/282OXO3v57PveDs/8ZGP\ntsjPKSCeF+ptuqbJykD7SlfTcTj71NMcu3adTHc3z955B7nutT+gVCZD5/IKK/19lFLrK7fk02k8\ny8JwGsPmrm2TT3euu+9NiSqJvIPpatuiGiduMT+Wpn8qWxMLKCcs5sbSoaHsbE+C7oUC6mlDCN6z\njCOdl6znsBfzPAacVNWsiLwJ+B/AhbAnqurvAr8LcFuyZ8c+i+8H1ZqGISSSgh0TDIFmkQmRoC2i\nmVSHGWivzri1gbuJpMHoiRi5bEWIvP6OraK8k8/6mzIk7doJXLdS+LOLtmi9tpVgOsXa+bti4km4\nB+PEE5gWDA0f/B+PAEOlRYa2KXRSLPi4IW05qrC0GPREdrk5bs1c4tn0aVwjOGfTd+l2spzNXm/Z\nd6cMHwtGnC0tuPgVkfqhkfXl/DYasPy6T/1FSzy3+lvYVyxoYzB59o47Ql8vVixy78f+K8lsFtt1\n8QyDFzz2GF/8O/cxf2yE1376QcYuXca3TAzX4/nvu52/+dEfaZtrvHrLBV72xYcaQsQK+IbBldtu\nRTyPk89fpG96hmxPN5dvu+2mHelllb2gTcNfUybJp+MsHOtoeX8LnTHGz/dilX3UFDyr/XdIDWHq\nVDf9MzkSFW3afGeMxZHW1z2qHKShnABO1P1+vPJYDVVdrfv5QRH5v0VkQFXn93JhK0suM1NO7TOu\nNmkbZqvREAO62nhnPX02XT0W5ZJimmBXLljFgt86wZ6Kd1rcnKE0Q9YSLAgmr5co5BXDgJ4+i3S3\ngVMOcmj2NjRQ02mDpcVWJQTTbO3ptNWlwy2QtZsSE6oM5OY5ez4R2ox/1HDdNhqvBIU1VV4z/xij\nhTme6j6PIxbnste4ffV5THZftk5E6B+wNyX4sO6A5QodK6t0Ly62eI3rfXoqwmff8TaKneGJqRc9\n+jVSmQxWpdLN9H1M3+e1f/Eg42fPMHbpcrCtsv3ck0+T6enh6Ze/LPT1PNvms/e/g9d94lOkV5YB\nIdeV5uEffzOo8pbf+31SmSy24+DYNt//8Jf5zDt/itX+va/GPWwMTmQw3UZpvFSmRDFlkQtr/hfZ\ntAi7FzOZPdG1dlPVZCDFV2IFFzWCalnfNGrVs0eBgzSUXwcuiMgZAgP5DuD++ieIyAgwo6oqIi8n\nKKZa2MtFFQs+M1NOgxyc78P4tSAfNzPpkM8FF7lEUhgZi60rfl31SOuxY4IYtBhLMcK90zBiCamF\n/RpQyOeCxz0vEChfmAuMvSp0pA1Gx2INRScb0T9ok8l4eG7j38HIWKvCiwCvmf8mfzn8alwxQQRR\nH1M9XrP6xA1hJCFocwkLR4vQMHxbgHO565zL7b4HuV02GrBcxXKdthXC7fAsa10v4vQzz9aMZD3x\nfIHzTz7dMobLrrR+tDOUACsD/Xzy776b1Ooqwpryz8u/8EU6V1Zrr2k7Dqbj8JoHP8uDP3N/29e7\nETEdD6vstdzkGArppWK4odwOIZ99x3KRvplcsLnub6aUtJgf7cSzD38e88AMpaq6IvKLwOcIojgf\nUdWnROQXKts/BPwk8A9ExAUKwDtU97YUZHnJDb0Aqh9Ix504Hcf3g7DpdqdDpLtM5qYdmi8XhgRy\naBvhukqxsLW3oep95jI+83MOg8ObDz+ZlnDmXIKVZZd8Lqiw7emz2ob0TuWnuHfyS3yr94Us22kG\nS4u8dOkpep3MltZ8mLFsobfPZKkufysSPN7dezgzGrXhyn+2ueev9PXhxuyaJF2VsN65hu3rTLdw\n2/U2qoaO4QKINQustyHfJI13+plnWgyvAfTNzGCXSjjxo6MMs1PChMlr2/bwkhoruPTN5ELbTeIF\nl+Hrq0ye6Tn0IdoD/YtW1QeBB5se+1Ddzx8EPrifa/LaTJ1QwK/8ze20Wd4whJNn4kxNlGsGL5EM\n+gHXe23fV6YnHLKZ9uOTNkIVlpc8BrdYuW+YQm+/Te8m1chGSgvcM/3lrS+wDT7CQqwHQekvL+9E\nH2HXGBi2SaTMSk5QSXeb9PQ1tvPMxXp5uuscRTPOmdwE57LXNhV2VWAmMUDG6mCgtLjjm4zEQ/dt\nOFy5BRG+fO89vP7PP4FRCZE6to1rWcRKJQy/MYynQDGVYnkdybrvveRO7nroSw1asb4IiyPDxIol\nehYXG57vAzPHx7a07NFLl3nxVx8l0UYtSGDLnvJRx42Z+IZgNOXVfWFPZfHSS+F9lhB8DqbjEy+4\nlFIHX7ewHofz1vcA6ewyyWVbG7dRSHbsXkw9Fjc4dTZR02k1TUFVKVd63uyYtIQ1Z6Z2ZiSrhOU2\nPU9xHcWy5cDnKDYzmRjkCyOvxsMEgZjn8IaZrzBYCp9isV+IBIOu243aejp9lr8eeAmeGKgYjKdG\neKr7HD8+8dC6xrJgxvnU6OvJWinQwJCcyE/zIzNfxdyGKFziofv4pQ9sr3F16vRpPvF3380t336C\nztVVpk6f4tILbmNgaprX/MWDdGSyQYWjaaKWxUN/+y3regfP3nkHQxOTnHr2GXwJ1KgKqRQPv+XH\nSC8t88P/7c8xPQ9DFc8w8CyLb7z+7k2v9+yTT/Gqz/9lra+y2fv1RZgZG8ON3WQFPSIsjHY2DFD2\nBVzbYLVv78TJjaZxYWGY7t6MmdtNZI8jmQfCbcke/cj5jXMwYagfjD0qlbQhpNY3YDEwtHd3PcVi\nMGKrWghiVcY3VXvgfF95/nvFtkZSBJDWvGcYqQ6DE6eDu8hglmWgD1ptWO/uNRkaaZW/U1/JZDwK\n+T2cq/IAACAASURBVCD82t1thaoS7SYFM87HT95bqxqtEvPK/PTVT2LrIRs7VKEsFh87/ZaWNhnL\nd/mB+ce4LXO5zZ7w4MgPMp4aQsVs2O/7l57iJcvf29I6Hvjw/Tz+yZ6tLX4L9M7OMnx9nEJHB9fP\nn8O3NnfvnV5cYmBqmny6k5kTx2vGtWd+ntv/5uv0zC8wPzrCky9/WUPryHqI7/O23/kQiUKjJ1lt\n/3VjMZxYjM/89E/dtBNMzLJH53IRy/UppmxyXfEg57MH2EWXwfEMltveWPoCU2d69kX79eFfv/eb\nqnrXdvaNPMomxBBOnImzsuySXfVrlaMdnXv3QVZHbNV7eo4TKAGdvSWBaUot7Bu6ZoHBYZuubpNy\nWZmZLLcdsGsYMDSyZnQW5tyaiHa94pBlSYPwgecFNxDV3k8RWJh1OXE6vqfTQp7rPIWG/JmpCJc7\njnNL9uqeHXsnTCcHMNVvyUO7hsXFzhNtDWVZLCaajGR1v6e7zm3JUL7/3veuCQjsEUtDQywNDW15\nv0xfL5m+3pbHlwcG+Kt779nWWhL5PJbTKkMogGtZ/NU9b2D8/Dn83eydOmJ4MZOVob2XyjEdj5Fr\nK4hPS3i++rsvwRSRoyCQHhnKEAxD6O2z6d2nCvKwGYUQGK7MikdPn4VpgWFSE1mvp6PToLc/+CiT\nlnD6fALfD9RiXCcYoVUsKolkkGe061o6lhZai5dUaRm7tTDnNAgkVA3r1ESZM+f3LnRTMON40vqH\n5GFQNA9vMUbMd0MNPOoT99pPdm/Xgxps29yf6255kR0rq7zgm9+kb2aWxeEhvnvXS7fkiYnncfK5\n5xm9fIV8Os3zd7xoTz25UqL99zDT28O1W2/Zs2NHNJJeKrYYySquAb5tkumJkz0iMykjQ3kIaDdi\nS5XaWCwRYWjEZnqiUZHHMIKikmaqBSV2TNrqv6pqWzGB5gr+zEpI3pagEria29wLRguzPNV9AUca\nz9FAOVaY25Nj7gbDxXlsdXC0sV3CUp8Xrl5su1/SL9PlZFmONYYbDfU4nRtvs1dAiwxd/etmy/TM\n5rEdD9cyWB5Mke9qf6PROzvLGz/+x5iuh+n7DE1McuGJJ/ns/e9gaWhw3XVAoL7zxo8/QPfiIrbj\n4JomL/ra13nob7+FyTOnN9x/O/iWxfPfdzvnv/NUg/arY1s88epX7ckxI8JpHtRcRQ1YPJamkD5a\nOeKj0/F5AxNorbY+XhUsr9LVbXH8dIyOTiPIEfaYnDoXX3dI8XqICPF4uIGLJ5r6I9ezg3uYpjxe\nmGGouFCbPgJBvu5kfpLBcngxjysGS3Y6dJzWfiHAvVOPkPSK2J6D7ZUxfY+XLj7JaHF9A3/37New\nfQejEm+3fJekV+KupSfb7vOqj9zRVkAgmS0zMJEhVvYQBdvx6Z/K0rFSbPt6r/jC/8QuO5iVOynT\n97HLZV7+hb/c4MwDbv3Wt+lZWKi1llieh+W6vPbTDyKbnVC+Db72Q6/n4u0vxLVMHNumHIvx2A++\nlquRN7mvlBMWfqilpEUv9igQeZSHgGQqECYvNI3YSiSFVFOlbSplkjq1e1+0oWM241cbNWlFgsfr\n6e41WZhrDdPGE9Kg9brbCHDP1CN8r+ssz6ZPY6hyW+YSt2SuhD7/O10X+Hr/9wHgY3AqN8Hdc187\nkKKfvvIKP331U0wlBimbNiOFOZJ++7BrleHSIm+/9hme7jrLip1mpDjPLZkrxDQk7k5df2Qbembz\nLX1shkLPXJ5cd3joa2hyMnTO4PDEJC//wl/yjdffvW7hzpnvfq/Bq6tiui69c3MsDu/NZBE1TR59\nw4/yjde/jkS+QD7deVPnJA+KTG+C9FIRVW3ISRY77CORk2wmMpSHgNqIrcXKiC2C+ZA9fRYiQduI\nU1YMQ0JDnKqK+mxL9SbVYXLyTJyFOYdSUYkngiKe5gKd3n6LfM6nkK94AwKmAaNbmHO4XUyU21cv\ncvs6IUuAy6kxvtZ/B25dpenVjlEe4WX88Oyje73MUAyUseLWJ2l0eAVethSq/9/ARkYSwHbCbxJM\nt5JoDgkXOLZFrBxeGHPhiSfpyGR56L6faHvM9kZUA/WePcaN/f/svWmQbOd53/d737P0vs0+d99A\ngLxYSIIASRCkCJGSuMiURJVIipLDWE7JseJyXFYqUZgPqXyxFZfkUlIVR1Q5rMiyFNMqSjQtbgYp\nSiSFnSAAAsQO3G3u7DO9d5/1zYfT3dM9fU5Pz9yZO8vtX9UF7u319Hae93ne5/n/TSylGF9YpJ5O\nU8vdml2uN4xSSE+hpEBtozvW1yULZ3KMLdaI1x18IajmYxQnBovcH1RGgfKAIKRgbMJgbJNOZ63q\nMT9nd7peY3HB8ZOBD6TvB6MdbccIwxRMzxrb7tCNJyTHTw1ujJFScOK0SbOhaDZ8dEOQzmxt3nwz\neabw1p4gCeBJnTdTJ7CkQWyXjZn3kwd+/Ns8vfJmb5BUisnr1zn56mt4usGbb7uD8tgYri4xnP5y\npz9gYfXq3Xdz+zPPhmaFuudx7NIlUqVS5OjGy2+/h7HFxR6vyrYgQWlsj7vklOLuRx7jrsefwJcS\n6fssHT/G3/ziJ46MGk+s7nRMk2tZMzBT3uXfYqJiMT5fC0TUgVrGZG02jZIC4SuSFQuz6eHENGqZ\nGGrT98lt678eAUaB8gBjW4HfYXe5s9kIxkbOXIixMGdT7XK1d2zFXEuTdi9GNoQQJJKiZ990P1GA\nJzQ0FTQO1PRwezWBwpLmkQmUX/rCZ/n87zSALhEBpXjvtx7m7IsvojsuvhTc+cSTPPGhh5g78xbG\nF3plxHwBxfFE5Mn16Q88SLpY5ORrr4c2MviaRna9GBkor58+FSqbJj0PodSeKuOcfvkV7nz8iZ4g\nP31tjvf/1df561/+pT173ptFbrlOdq3REQ5IVG2aKSPSBmsnxGo2k3PVnvJ7qmKjeWVWjmWYvVRC\nej5SBd+l/HKdhdO5Q1lWHYaDccYbEUpxLVx31nEVtYrfEyTbKAVrK+F7WUcFH8HjY3fxxbOf5Itn\nP8n/d+rjXE7OMttYQoQoLmjKI71Nv8kwPCRvpE7wo/wdXE7OsrXmyO7gCtnR4/n8x38rdPRj+uo1\nzr74EoYT2LppvkJ3Xe7/9l/jGT5r0ylcTbRUdATrk0mqhejWfF/X+ZtP/iKv33kRP+TkK12P0gAH\njgvPv9AXDAVg2Dazl68M8ap3zsUnnuqRyAPQPI9jly4Ta2xTxu+Aodke2bUGUm300EkF8ZpDvL57\nC8HxhVrfZQKI113GFqport9ZeEkF0lOMLVR37fkPGqOM8gBjh7mDtLAsv6Ok03c/6+ZIQik/MLO+\nUe3b7fLIxNt5OXOuU2atGGm+Pf0AP7X0BJeTx3ElqNY8ou67vGf1GeQOpN+6qWlxvnL8w1iaiSs0\ndOWRcuv84tx39ixTvZaY4gcT91I2MmjKY3U8FbmneOall9FChu2VlBx/8xJvXHwbtVxsY+J7yMzj\n2Qcf4PQrr2LYdufE7Oo610+fIlMs4RoGdsj8Yma9GOoSInxFqlzuu3w3SdTDF0W+lJiNJlZi943d\nbxaJiGAoFCQqNs3U7vQM6E70MjBRdUIbveJ1N/L7edgZBcoDTDIlqUfozqbSQRdqGPE9Lo26bqD+\nU6102Y0dM4nF975AYQudlzLn+qThXKHxUvYcv3ztWzxduMh8YpKMU+MdxRc50Vi84ef93uS7qOmJ\nTgB2hKRoZPiT059g3Cpyb/EFTtUXbvh52iybBb418/7OYsAVOpmiheYpVo9l+m7va4GlWZjJsi9b\nn4sQ2x7lqWWzfOPXf5X7vvNdpq/NBaLohsGxS5eZuXoN6Xu8cN99PPPgAz0nyKWTJzj70st9ziMC\nWJmdQXoe8XqdZiIxtOzdsFw/c5rzzz+Ptqn062ka1fxwcngHFV+KSCPUQXvO20UJIsXMj57o6dYM\n/IYKIbLApFLq9U2X362Uem5Pj2wE+bzO+qoXiA50jY1kcxrxhCRX0Dryc22EDHRp9wqlgj1Su0si\nr9kI5O3O3Rbfc+3Xuh5Hovqk4RCCkpEh59Z4aPmJXX1OH8HV5GwnSG48p8QTkqXEBA/H3seDy09x\n+y5J6v2o8FY82ft8UgX7ROuu32d6+8bb3spbnn0OuankKJRi7tzZGzqW4sQED3/6VwD48H/8MjNX\nrgTzla2M8W1P/ZD1yQku33F75z5v3nE7dz/6GLJc6VhdObrOwqmTnHj9DT76p/+hs1f5wn3v4tn3\nvXfXMpFnH3gPp155FWwbzffxCUrJj//Mh1DycO82NdIR4iGCyFGfnVDJxsiWrD75OU8T1DMm6ZLV\ns+etgEbaOJLZJAzYoxRCfAp4CfiyEOIFIUS3c+r/u9cHNiIY9zhzLkZhTMMwAnGAqRmd6WNBZ+zU\njMHEtI5uBEbQybTk9NlYpE/kbtCo+6GG0UpBqbj3e6NptxEpDTexj24irtR5bOLtu7ZvaZ2ZRIX8\nPJUAPcRtYXV2hufecz+upuHqescO63uf+Pld6/SM1+rMXL3aESFoYzgOF594qucyX9f52t//NV56\n+z3UMmnK+RzPvu8Brp85zV2PPY7hOOiu27rvk1x8svf+N0I9m+Wrv/E5XnrnO1idmuLqbRf4L5/+\nFS699Y5de479QknB0oksvhT4kuCPINiD3sVGmtJ0CtvUOoLyiuB5Fk5lKU6mcEwNX9D54xqS1Zn0\nrj3/QWNQ6vF54F6l1LwQ4n7gT4QQ/7NS6i/ZUy2WEd1oumBqxmQqxCVJCMHYuMHY+M3zcrNtFVp7\nUYpIIfbdRFce9xRf5Nl87yiIrnzuHWLucCdIFMfri8wlp/uzyi4codPUYiS9aMUbgHUjyzP52yma\nWaabq9xdfJm0t9Fk8sCPf5vf/6+WSGH3/9AUOEb4Mfz4gffyxsW3ceKNN/F0nSu3XQjdP9wpptXE\nl7LPDBnoc+wAsONxnvrQQzz1oYc6l/3Kv/lDDKd3QWW4Lnc+9gQv3H/f5ofYMY10mqd++oO79ngH\nCStpcPVCgXjdQShoJvWBZtk7QUnBwtkcsbqLabm4huwZQVk4s3GdY2o0U0c3m4TBgVJTSs0DKKWe\nEEI8BPyVEOIkt2aZegQQj9iHbCsJ3QzuXf8JCdfimcJbaWgxJq113rv6DBN2ccv7+giez14I9GOl\nzun6dd619jypLYLbB1ae4ivHP4wjdRyhR54UzJbyTk2LB6Vgp0qqKwjOxaf45uz7Ox6VK7ECL2fO\n8ktzD5N3qh2DZX08SbJiQ1d3oy+gko8PPCnWcjlefsfbt3wfdkIln8fTtL59R09K5s6eGeox4rXw\nRptYs3lkG0H2BCloRpRhdw0hsFIGVipkIT7ouiPIoEBZEUKcb+9PtjLLDwJfAS7ejIMbcXNQSuG6\nCk2KLdV94glJPCFpNnqbjDQNcrmb0xsmgIuV17lYGazUE8bfTt3HG6mTnWz05cwZLieP8emr3xjY\nvZpx6/zqla/xRuoEl5LHuJw6ji83Sl2a73JH5Q2EUvz11P28kTqFpjw8oXG6NsdPLz2OxOf7k+/q\nyYR9oWFLwWPj91D6307z7O8Fox9uTGPhdI7CUo1Yw8XXAoPdyoCRjmExGw6Jqo0Sgvo2bI6UlDz2\nsx/mwa9/E+m6SMDVNJyYyXMPvGeoxyhOjDO2vNJ3eblQGAXJEQeWQWe2fwxIIcTblFI/AVBKVYQQ\nHwE+c1OObsSeUy65LM07HReRdEZj5rgxcOTjxGmTlaUNRaBURmNq2tiRhN7NpKIneT11Cq8rwCmh\nYUuDFzPneHvp5YH315XHW6qXeUv1Ms9nL/Dk2F34QqIQvKVyifeuPMPThYu8kTqJJzU8gue5nDrG\nE2N3ce/6C5SNEC9AIXkzc5Krm+YjnbjO0qld7NJUirHFGqmS1elozK02WJtOURvS7ujyHbdTzeW4\n+ORTpEslrp8+xUv33kszNZw02ZM//UE+9OWv9IgBuLrOkz/9we29lhEjbiKRgVIp9SyAEOJ5IcSf\nAP8KiLf+/y7gT27KEY7YMxp1r8+2q1rxuH5VceJ0dAOIlNH7pgeZ5VgBqbxOAGvjSZ35xOSWgbKb\nO8uv8dby69T1BHHP6oiuv5C70De64kmdn+TOc//aj5FK4YWsJ/ybMIsaa7ikNnUrCgVjizUaabOv\nkzaK1dkZHvm5n+XcT15kYmGBcz/5Ca/deRF7iPnEhdOnefhTv8zbv/8I+ZUVymNj/Oj972Px1Mmd\nvqwjh3R9UmUL6fk0UyZWIrrUfyBRCsP28KXAM46GUs8wtbJ3A/878AiQAf4UeN9eHtSI4fA8Ra3a\nyurSWo+Lh+cFXpO6TqQea5gbiFJQr/l76jG5X2Sceqh0mlQeOWf7qiIaiswmxR9Hhu/ZuEJH4nO+\nepnX06d6gqkvoDy29wa2ybIVORuXqDmBIMEwj1Op8PF/96cYth14Teo6dz/yGF//9V+lPD6+5f2X\nTpzgv/zqp7Zz6LcM8ZrN5LUKECxismvNXZen2xZKEWu0mnaMrZt2EhWb8YVqR77QjumsnMjgDbkI\nO6gMEygdoAEkCDLKN5UK0QkbcVMJMj97o9NDOUzO6GSyOvPX7I7Lh6YLZo6FC6WHjXlA8Dtw3aMX\nKCfsdfJ2hbVYDl9svB9S+dxZevWGHlsBP8mebzWkhDy3tY4AHlx5GnPW5Ln6CWgNdddysV3Ze9yS\nASc4FXWVUqSLTbJrTaSvaCYNLj75N8TrdWRrlaW7LtJ1eeCbD/PNXzs4uzLC95m5coVkpcrK7Cyl\nia2D+L6iFBNz1b6MP15zSJXtoRcyu4XwFdNXShhWq8tZgKdJFk7nQqsPhuUycb3Sc/yxpsvUlTLz\nZ3OHKyvexDCB8kngPwH3ARPAHwohflkp9St7emQjIvE8xfWrLbH0ri/l8oLL+opLd1Oi6wRC6WfO\nxzA3GTwnkhLb6m/1VwpM8/B+qaMQwMfm/5bvTr2bueQ0QkHSa/DBpSfIuv3altvhsbF7+EnuwkaD\nT6uDUygfTXm8f+WHAHzg/7nI//rle9BsD93xcWLa0CXPG6WWjXUcJzbTiOheLCzWeobLkxWbE6+/\n0QmSbSQwef060nV3XWlnJ6TKZX7uz75ErNlEKIVQiqvnz/H9v/fxAys6EGu4oXN3UkGq1LzhQCk8\nn9xqg2TFRklBuRAPHjMigOWX6hiWtxH4VLD4GF+osnyi3xUks97/3RKA7niYTQ87sf/fi50yzJH/\nQ6VUexp4HvgFIcTf38NjGrEF1Uq4v6BSECL3iVKBwPrUbG87+fiETqXk0T0/LkSg7HPQG3N2SsK3\n+djC97GkgSc0El7zhoeCLWnwQu62niahtpxczq7wkcUf8JEvnOOfOR/h818OGnY8U8PbhQFxzfYY\nW6yRqDkoAfVsjLWpZOgIiZ3QKY8lyK71zjyuzKZDby9dn0ypt1wrCLpf+6WRACEOTBD6wFf/ilSl\n0hPQT7z+Bm/50bO8fO879vHItiKiNn6D2ZjwFbOXSj1i5mOLQUf12my4UECqbPUZfgduJU7oKI8W\noQ+rBGghIhmHiS0DZVeQ7L5s1Mizj+yk8G3b/T9Aw5ScPh9jZcmlXvPQNcHYhE4mdzQ24AcRjILs\njph50ciENgkhBAKfxv/wGX7tX9UARTZfpzwWbW+1HYTnM3u5hPQCrSKhIFmyMJouC2fCS12lySS1\nXCwYD5GC+oAmHsPyQjU/F05e4Nill9H8jWjpScnVC+cHB0qlGFtcIl0uszo9vWdmyvFqjfHFpb6s\n13Bd7njmmQMbKK2E3tpD7z1uX0D1BrPJVKnZEyShlamWLcrjidARITFoXL4trt9FM2kQrzt9wVUq\nDnU2CSNR9D2nXvdYWXSxmj6GIZiYMkhnbywQpdLRQ/9hbiJCBALrYZim5NiJPR5cPsIsmwWWYwU8\nEfKZKp96Ps9f/nkFoz2OsdIgXnMCQ9sbDJapkoXwewX9JGDYHrGGi5WMaCwyNSpjW3eoeoYMTXDe\nuOOdJCtrZIurncyimsvy2M/9TORjxep1PvznXya3to4SAul5vPnWO3j0Iz+7vSxUKXTHwTWim0o0\nz430u9RCjKh3g4nr85x//gU0z+XS7bdz/eyZ7X++QrB8PMPUtXJQ5lRBNlbPmNQzN/YbjdfdvgDW\nxmy6oYGynjJIVZw+vVcrrkFIl3Y1HyO73gTX74gvtkUyboVmnhE7pF7zuHZ5w3jZshTXr9lMHzPI\n5Xf+1humJBYXNBu933zdCAQBquVeMQCpQa4w+qh3E0fofH32A6zEChtGxMoPVOnbaJJGk75VfKzh\nYjZd7MSNqZqY3ftHmzAsLzJQDotralgJg1ijN0vwDJ1vfeZT5NZXKCwvUy4UWDx5YmBgePBr36Sw\nvNKjE3vmpZdZnZ4eOsM7/+Pneef3vk+80cQxDJ5/9308/+77+563ls3STCZJb7Lz8jSNS7ffzm5z\n1yOPcvdjTyA9D6kUZ156hasXzvP9n//YtoOllTS4dr5AsmKjeYpmysCO3/hv1zVkWBIIEBnEHFMn\nrOoSJVChNMn82RzZ1j5oWyTjRoP8QeBwh/kDzvKiEzp+EVy+cxVAq+ljNfvv79gwNq4zOa1jmAJd\nh1xB48z5ONoR2XP0kCzFxigaaRSwEJ/glfQZVs1+M+O95JHxt7MUG8OVOo5moIQMTkLKRyofx5DU\nkkZ4IGsFyxvFjgXC1GE4sd0pny8fz9BImygRZDeOLlk+kcFJGKwcm+XVe+4OZiAHBATDspi9crlf\nTN11eevTTw91HKdeeZX3PPwdkrU60veJWRZ3P/oYdz4e4hQjBN/7+Y8FwvBa8D44hkE1m+HH77l/\n+Bc/BKlymbsffTzo/G39pg3H4eRrrzNz5eqOHlNpklo+Tnk8sStBEqCaj/d1NiuCIGlFlEUzm9xD\nIAi0qbJNZrUeWr7yNUlxKsX18wUWzuSoZ6ObhQ4TozRjD4kSCffcVvKhBV2prqswY2JoA+Rq1Qst\nsQLUqj7jkwaFmyiUfrN4PXWCv528DxD4nR9f4LGhEMw0V/jI/PfR2NvGAQW8mjnTI2EHgVl0PC54\n5WQeJQWZYpNErX/PBhm9im8jPJ9k1UEoRSNlhA5u13Ix8qsNlLdRfvUBx9QiT37bRWmCleOZoMTr\nq8DzcJsnPt1xwh1fAMMebp/4Hd//QY+aD4DhuNz1+BOhWeXyieN85b/5B1x47nkyxSILp05y6Y7b\n8Yzd/V0ce/MSSoq+5ibNcTj56mssnD61q8+3U1xTY/lEhvHrVWRrxtGJaQPnM6UX/jsSQH6lgWn5\nrB47uo4h3YwC5R5i6CK0iUbKQF/12mWbes3v7C2OT+qMT279Q5ZChO5HChEtLnDYWTVzfHfq3b2q\nN639sfY5aj4+wQ/HLjLZXOO5/FtoanFO1q/zjuJLJDxrV4/Hj3ARaTRVp4O0lo2RX270fFAKAo3V\nAYLWiarNxFyl8+8CUJxIUhnv3VdUmmT+dK636zVjsjad2vVVvJIiCAg7oJFK0UilyGwuhUrBtfPn\nhnqMVLkSernmuBi2HWolVs9keO59793+AW8DVzcIK2gqKXDNIUqOSpFeb5IpWaCgljWpjCV2/F4P\nopkymbtQQHd8lGBL1RwrETTnRI2sJCsWRSdxZNR3BjEqve4h41N63/lKCCiM6yxcd6jXgr1E3w/O\npavLLpVy+OhHN5kBzUBHtWP1heyF/uC06c31pM6Ps7fx19PvYSExRdHM8kL2Nv78xM/RkLu3TyKA\n2cZSX/uxgkC5pIWvSRZPZXEM2fHts1ti52HNEBBkkhNzwdB295/8Sh2j2V+u9UyN5ZNZrtwxztXb\nx1k9ltl1y6UbRgj+7mMfwdH1jhm1q+tYiSTPPPjAUA9RjFD8seMxnGEC0h5x7UJ4oFdS4/WLb93y\n/pNzFQrLdUzLw7Q9cqsNpq+UwrvydgMhcE1tqODWSAaL0sgjEWJDjOCIM8oo95BsTsf3FMtLbnBO\nFcEeYn5M441XwuXjVpedgYEQQDcEM8cNFuacLmUemDlmYBwxNZ02VT050AuyjSt7dTF9qWETzDm+\naxf9Kh9c+SFfOf5hVEzHcYNAqIQIsrku7LjO9XP5YI5MiC1LrolqeClSqKDLtbhLe1Y3m8VTJ/nP\n/+Bz3P70j8itrbFw6iSv3nP30H6ZT//U+/nQl/+yT0z96Q+8f9vZc7pY4v5vf4djly7ja0FA++EH\nf2q4DHATTizGd3/pF3joL/9TZ7RD+j5PfOihLeX8zIZLfFNpXqqgEStRdWjsYxOM2XDJrzYGzxgr\nhRvhjXrUOJy/ukNEfswgV9DxvaD7VAiBbUfvoTm2YmXJIZXRSCSiv4TZnE4qrVGrBiu6VFo7Mg07\nYZyqzzOfmOqxqOpD+UgUfojo+dXkzK4GyoJT4ff//Wl+/beLmJaLHdep5uLhM4lieHHoQbNrYq+y\njJtEpZDvMXHeDgunT/GdX/4l7v2b75FbW6WeyfCjB9/H5Tu218VqNJt8/E/+FLPZRCqF5vtc+PEL\njC2t8I1f+8yOStbzZ07zpX/yjzn+5iWk5zF/5jTWEALxsYYTmq5JBbH6PgVKpUhWbPJLtUhdYAj2\nwu24jhu7NULIrfEq9xkhBFrXO20YAiFBhVQtfD8owa6tuGRzGtPHjMh9R00TZG+SB+R+c3vlTZ7P\n3UZVT27sU7Y1/IRE9100321llJvurHzSbrhh8E6If/eT/PPfm4F/acPEcPZSw9JImUC/nF6w/3hz\ntT4PGgunT/G1z/36DT3GhR8/j+Y4PWIEuudRWF5mYmGBldnZHT2uZxhcectt27uPLltSR72X+2Lr\nZq89QSmmL5cxreiZy/bFjYzJ6ky/ZZz0fNLrTWINFyemUSnEj8Qe5q1xlj1gCCGYmjFYvN4/PtJG\nKSiXPDI5LVTQ/FbDUB6fvPYwz+du4430SWKezW3VS9S0BEUzy1Rzldsrl/jasZ9iJVboET3XMeWN\n4wAAIABJREFUlc9dxVd25Ti+9IXPdsyV9wJfl6xPJSks1TsreiWCxiArOfq53ijji0sYEaIDuZXV\nHQfKnVBPm4xJ0dO13GYoXddW9pcsW4HoQz5GMznY3WMQqZI1MEhCECjnzufxQ4Kf5njMXiohfIVU\noGoOmfUmi6eyNzwzvN/s6y+vZQL9fwAa8G+VUr+76XrRuv5jQB34r5VSww1eHXByeR3DEKytBKo9\nYb9dpaBc9EaBsoWpXN5ZfJF3Fl+MvM1H5n/AwzMPsBQbR+IjlOJ9K08zY63e8PN/6Quf5dmv7kGQ\nVArpqcCTUgqqhQRW0iBZtpB+0Ml66DwJDyhrU1OcfuXVvlETgNL42PAP1F7h3shnIgULp7JMXiuj\nOxvBspKPBWM4g+7aCkpaK8gqAourSiFOcTrEHHwIkhV7YJAM7OASoUESAhF12RX027KK4ws15s/e\n3Dnn3WbfAqUQQgP+L+BngGvAk0KIryqlftJ1s48Ct7X+vBv4v1v/PxIkUxrJlEal7LEwZ+Mfbt3g\nA0HCt/jE9e9S0xI0NZO8XdmVucrPf/y34Ku7cICbSFRsxhZraJ6PIsgc16ZTODGd0uQog9xtXrvr\nInc/9jjSdTst/66mURwfD88mlWoJeotA0g9IrzfIrzSQnsLTBMXJJLX8zmzSXFPD1zVw3U4FIVO0\nMGyf5RMRM45K9QRJaAUlAgePaiEeqZ4zCCVFqHqPIpjNLU0kBqrsJGvhoySG5SE8/+B1Y2+D/fwl\n3g+8ppR6A0AI8R+AXwC6A+UvAP9OBTI2jwkh8kKIWaXU/M0/3L0jlZaRGq3Z/Cib3Akpr0HKawy8\nTclI82LmHHU9zqn6Amer10KD6uc//lt7coxmw+nx7wtUTyykUqwcy2x5f+H55FcapMrBjGg1G6M0\nkUQd4aauG8VOJPjar3+W9zz8bWauXEVJyZtvvZ0nP/TTfUHJbLpMzFU6zheuqVHLmORWG53PTPcU\nY4u1YA85t/1gGa85mE23r/M1Xnci9Xrb8nZRn3K85lDdQaCs5OMkqnZPE48CPE0M5SfpS5ARa9Io\n7d3Dwn4GyuNAt8bTNfqzxbDbHCew++pBCPGbwG8CTBtbd5wNg++rmzLEL6Xg2EkzMGJmw8EmV9Ai\nxcxH3BiXksf4zvR78YRACY03Uyd4Lnc7n7j+1+jK4+0fdfmY/Kd7egy5lUZfZ2EwyG0jXX+wT6VS\nzFwpo9sbeq+ZYpN43Yl0DhkRUBkr8PCnf2Vg+VR6PtNXyh0VGwgyo7zVPzIRzLk2dhQoYw0ntLtU\ntDpfwwKlYQ+eXdypWIGVMiiNJwK1p1Y9V0kxtIB/JR/vWURA0B3byJiRc8OHhSNT21FK/RHwRwB3\nJPI31Edfr3ksXnew7SBQZnMaU7PG0BJzOyGd0Tj3ljjVsofvK1JpjVh8FCT3Ag/Jd6fe3TNq4kqD\ndTPLi5lz/OYfJHjoyw/u+XEYtjfQv29QoExUnZ4gCa0ZPNsjXnNoDlD+GdFiwMk/Vbb6hv5DGlQ7\n6M7u75tEPaZjaqH2ZwC01Jl2SnkiSTUfJ1538DWxreag8ngCs+mSqDmdN8uJaaHdsYeN/QyUc8DJ\nrn+faF223dvsKpbl9zh+tLtPXVdx4vTetufruiA/dmTWLgeW5VghVHvUlTqL73sPD31567LnbmAl\ndHTH7j8SFe3Q0Ma03MhMxGy6o0A5DEp1sjPH1HoCgub4AxtbNrPTwftYLUJgAhARTQv1tElBEwhX\ndeuNALB0IhOZUQrPJ153AEEzZUTeztdlIGa+XYRg5UQW3fYwLBfX0HAOqUDGZvbzVTwJ3CaEOEsQ\n/D4DfHbTbb4K/JPW/uW7gdJe70+ur4Qr5tRrPo7tY5ijLO+wYyivz0mhzfPXfLhJOtaliSTJqg3+\nRgNFu7Nwq/KZa4RnFUpsHWRHBMozk3OVjvC3r0mWj2c6BsNWQscX9AXLQKu393JfwPrU9rMm3faI\nNSOqCgSfcShSsNDW+G0pOVlxjZXjmciZxWSpyfhCaz63pSC0fDxDM7X7CyrX1I7cd3DfAqVSyhVC\n/BPgWwTjIV9USr0ghPhvW9f/IfB1gtGQ1wjGQ/7BXh+XZUUo5guwbYUxWqgfesbsIgnPoiK0Hv9I\nXwR2RDcL1wx0X/PLdWJ1F18TlMYTQ83Q1TMmhaXeGTwF+HKw4PqIILOavlrqaTyRrs/01TLXzudR\nmqSRNnFMDaOrvO2LIIBWczHyKw10x8cxJcXJ1I5UdILsLppqIfq76BkayyeyvfusviJVahKru7iG\npJoPlKJ022N8obYR3Fv3mbxW4dqFwqHuRr1Z7GterJT6OkEw7L7sD7v+roD/7mYeUyIhaTb6N8uV\nglhs9IU6Cgjgo/Pf4z8f+2kayTh+63xVzcf2xGTWsFxSRQvpK+oZMxBOb5X5nJgenPC2iWplFePz\n1Y63pZXQWZ1NH/rGib0mVbHDNxuVIlWxcQ2NVKmJawgc0yDW9EBAJRejMpYAIUIbdxIVm8x6E+n7\n1DIm1cLgyoCnyeCz8nsPRgG1jDmcok3reyQ8PxgZcYOSsS8gt9pg8VSWeC28YQiCxrGdjrbcShyN\nAvIuUpjQKRW9nplGIQJXDv2ICo7fihScCi9dPEa85qB5Ciuh70m5KFVsMrYY6Ga2xz+aKWOgD+Cw\nuKbG4ukcwgvm/A78WIhSXHjux9z5xJPE6w2WThznhz/1AUoTg8XDdxvN9SP3d5PFJjHL63xevghk\nBVeOp9FcP5BmM7W+Rqvccp3s2kbHp2E1SJdsFs7kIoNlI2UEhtj0zi4qoDi1PWnE3Goj2Fdt/bt9\nHBPXqwMXfzJKGmxED6NAuQnDkJw6F2N5waFe99Ek5Md0xib27q3yPUVx3aVa8dF0KIzpJFPDnbQ9\nT1EuuliWIhYX5HI68qCfMA8A7dnIvWx6EZ7P2GKtf0au5pCo2jS20m5VikTVJl5z8PTA9T5MA/Sw\nlM7e/oNHeNtTT2E4QQZ8/PU3mL56lb/63N+nUijctONoJgyyon80RwHxTXuGUgX+oDOXSxiWhxIC\noRTVfCzYlxQC6frk1nofTyrQHY9UqUm1sDGuZjYcCot1Ys2g1F7NmqTKNtJXnft7usSwvG1ppKbK\ndqhnoub6WHE9sku2sQd7lEeRUaAMIRaTe97h2sb3FJfesHAd1dluqFVsJqd1CuOD9REd2+fyG1bH\nz1IIWF1yOX0udmSajhZi4zw+fg8rsTwpt8G96y9wW/XKjh9vt+cjjaZLYSk48XmaoDwWD/Y5hSBe\ndzrzaN1IFZzYBgVK4SumrwQn5+5S2tKJLFZqb3QzzaZLqhSIF9QzZugM307RLZuLTz7VIx0nAd1x\nueuxx3nkox/ZtefaCiupYyV0Yg23Z//R1SV6SLYpALMdQFs/0nTRwjE1qoUEsYaDL0AL+ZwTNacT\nKA3LDWYzW7fTPEWmaGHFtJ6mHsP1mZyrsHwi2+NvOoio5jRBUJKvp02S1UCirt2QVNlKwUcpzKaL\n2fRwDdmzZXCrMQqU+0xx3e0JkhD8FpcXXXL5wdnhwryD5/Xez/Ngcd65aYF+L1mMjfG1Yx/szDuW\nTIPvTd5HU8a4q/zqth5rLwQEdMtj5nKpU6aTvqKwVEdzFaXJZJB9hNyv3XQziPR6oxMkobuUVmHu\nQmHXT1i5lTrZ1Y2sKF1sUs3FWJ9JR95Hui6nX3mVifl5yvkCb1x8K06Ev2R2fR1f9i/epFJMzt1k\noS0RDNGn15uku1SNlCYYW+h3boF+WTepILsWZIu+JkOzNUWvC0iUwMTmLLZ9eX65zkIq138sviKz\n1iDdWtRUczEquRj5TcP+CrDiOr6hsXosTbNkkSpb+FJQKSQGLriEr5i6WsbsMgv3dMniqVxHyu9W\nYhQo95lqxY+Ur2s2/cgSrFKKejW8Q7cWcflh48mxu/r8J12p89TYnVwsv4Yc4N3Y5r1fvBtx38/w\nwd8ZLGe3E3Kr9U6QbBOcQBuUxxM0kwYqZExdia3dIdLlcIFq6Qezf84u+gDqtkd200lWKEiXLGr5\nOHbILJzZaPDxf/9nJKo1DMfB0XXe8YO/45uf/QzFyYm+29eyGTSvv0nOB8pjN6/s2kEIqmMJqmMb\nZVHhKcZCLM6ikF7whlkJHU+TCNfv3WsUgVpNG7PpDjZC3kSoAo9STF0pYXYtonKrDeyYjt3KTNt4\numDlWBqUYny+SrJid0rHAlhJ6JH7p7mVep+0nnB8xuerLJ3afvPZYefWWxocMLSIyodSbLnXGJVU\nHJXqyGos3HHAE5KGNjjQPPDj3yb+3U/y0Jcf3JMgCRBrRJz4hEC3PZCC5RMZfBmU9hStxo1WtqAP\nkCKLKqUF1/VfqdseE9fKnHhljWOvr5Neb/Qpy0SRqNqhlwsFiYrVd7l0Xe7/9l+TKpUxnKBl2HBd\nDMvifV//Ruhj2fEEVy6cx9V7v/C+rvPj9xwMnwOlBZmmL0XwmUmBT3j2ryBQrYEgQz2VxTElvqB1\nX1idSfUM3NsxbYil3QZOSOYWrzs9QRKCxZlpBSVS2Fi4SVchfUV2tdFxBtFaFljxmkNhKXpRkCpZ\nfQs10Xp+4W/nVRwNRhnlPlMY16lV7b5zmmEIYrHos6UQgkxWo1zadLJtSe4dBTJOjabWX8oTQNwL\nP7lDECSD4DizdwdHoOaiO35fsBRKdcpTVtJg7lyBY6+vdxweIAiy05dLzJ0vhI5zVPNxjE2NQO1S\n3mYVmG4fQEFwMiws1dFtfyjLJdX5T8h1m4Lyxcef4J5HHkN3+p0iJFBYXsFsNrFbJVjp+kxcrxKv\nO1y5cD+GLZi98hoAzWSSx37mQ6wcu3kekFthJQ2uXigEAUEFwTDWdJi8VulUDxTBeE53Z6prasyf\nzQeyhL7Cjul9n2t5IkmiVuopv/oiCKCbg58voDjZ3/kaa0QrMnU/W/vvhaX+zBCC4JouWkjXZ30m\n3dckNnCtrTb36R59RoFyn0mmNCandZYXXYQIvoOGIThx2txSjH1q1sBq+tiO6vSYm6ZgcuZwm6S2\nedf68zw8/b6e8qvuu1wsvRppnRX/7id3lEHqthfoW0pBI20OJSxdmkh0Tqht/JbWpt/ViZqs2j1B\nEjb2NJNVO1QurJqLEas5gXJP6w5KiFDrpexqoxMk20gF2WKT8kSi51g2I12fTMmK1JztPrazP3mR\ne/7u0Ujj4zZ+W8RBKWYulzqLCaXpvHrXe3n1znezdCJJM508mOUPKXq6oZspk4XTObJrDQzbw0oY\nlMfi/V2pQgwsidtxnaUTWcYWaxi2h5JBabY4kSBTtAJBcU/hGpL1yWRoR7ary2id100IgsAaVVkQ\nQLLqELtU5Pq5Qs93vp42SW/6XihaWfEh6bLeTUaB8gBQGDfI5XUaDR9NDzLJYRxLNE1w+nyMRt3H\nthRmTJBIyj13O7lZnKov8FNLT/DoxDtoaDE05XF38RXuXX8h8j5//Mo2h6eVIr9UI1PsKjEKweLJ\nzJau7HbCYOV4hrGFGprro0QQ4NY3ZXGa44XuNwo1QExbCFaPZyg3XWINF08PAnj3gHmq5TKSiPAB\nVEJgWB5WMvrENjFfDfwCu+/X+rM2nerpirz70ccHBklfCJaOH8eNBSf4eN0NZha7XxbgS4lhC5qH\n6HvqxHVWh7A+2worZTB/Lt/nXFIZSwRiBu329U3otkeiFlSelBAo1a/zGoanCVxDDxZ0IdcLgr3W\nZMWi1iWiUJxMEq87PQIGCMHqsejmrqPMKFAeEKQmSKW3XzIVQrQMoPfgoA4AF2pXOV+7iiN0dOUN\nbODZiblyvOaQKW7aj1GKqZa811YZTyNtMnfeQPgqWJGH3N6OR+iGCrDjgz9zJ673CUvH6g5T18qg\nNjKL0GKYUgPFumVLJLuvdEwg8t2t2CJdn2SlGvo4gS6pgZWI84Of/2jnct0J34MNXE6ORsPZjtlG\ng0F2pU5utatKooJGnXYzkWtqOKYkUXX6yrflsTjNpMHs5TL44R6WUoHR9KCrwdbXJdfP5klVbMyG\nE3hx5mIDqxNHmVGgHHHgEYCpBpf7vvSFz247SEIwBhGe7alI49z+Gw9WxWmkTVxDQ3d6dUOdmLbR\nEDIsSgVi3pvizOaX4AtopoyBQ+vCV+EBluD1d99u9lKJcn6C8aW5vts7hsH3/97HmTt3FtU1AhLW\nLds+trb4+HaJ12xyLZ3VZkKnNJHEjd28PXnp+qTKFprr00wZPTZUmuORqDkoAg/G3QgqRtPt83gE\nwFMsnMnhSxF8xr5ifKFKqmJ3ZnfLY4nOTO/1szkKizWS1f6FkS8Ifw+loJaLDaU9fNQZBcoRh563\nf9Tl818N75DdikF7PWLIrtGtn0SwcDpLbqUR+BwSjIeUJgbv0YmWyHWi6uAZkko+HjRthHQdtuXW\n2o9Wz5isDZiBhKAxyNck0u2NuooguLdJlS2k5/Pm295FfnUR6bmddnlX13nkIz/LtQvn+x7fjutY\nCYNYYyPTUQROHbUd2DilSk3GusS9UxWbZNVm/kwOdxfHZaKI1R2mrpaB4HuTWW9iJXSWTmbJrDXJ\nr9Q3brxYY2U2TWMndlVdpEpW5HfUbHobQUwKVo9lWHd9NNcP3GW6Fm+eobFyLM2J14vITUL6Sood\nfR63EqNAOeJQ894v3n1DJsv1bIx43elfsSuwttij3A5KkxSnU0N1oUIw0zd7udjxRVQEJ83SeCLy\nPnYscJRQUgznci8Eq7Opno7OYLxBUJzY6Lg0Wwo2tWyBpz/w85x5+Rmy68vUUxl+8q77uHzHbZFP\nsXQiQ261QbrURKigSaQ4mRzu+LpRisJivXeuD6A1arOyTWF5zfFIrzcxbY9mwqCajw1uUmln8ptm\nTWMNN9B5Xe+vTEzMV5lLGTeUWW7dfdqLr8tww2+lmJyrIkLcZuZPZ7f/edxijALliEPLxhjIzqll\nTVKljaynLe+1Opve15NHZr3RYx4sCE7MubVmqCxe2yIs9CQ5gGbKZP5snsxaUM60knrwOF0n9/Z8\noFRQz+T5ybs+CGw0/Zx4bZ3V6VR49iQFpckkpZBRh+0QCJmHZ9Jt95RhMRsu01dKoIKRlnjNIbfW\nYP5MLrJUbVpeaCYvW8IMUVlfourcUOmynjFJF5vhOq3b0CmONdxgQdh1WfCdUuiuwhtJvg5kFChH\nHFqeXnmTG56VFIKlk5mOULmvSWq52L4bz7YHxPtRFCdTnWFxoYLA3kwaOz4hu6Y2UKqulouTX232\ndVp2Rl48xcR8lQVz7xztfU1GZldhQvGDGJ+v9g3sK0+RX65HdrbutAh/o+X7tv9ldzBWAtanktta\nFG0eY9o4vuC63dT1PYqMAuWIQ8mXvvBZnv29ne1L9iGCubm9dBLZLn5Uc1BrCH7uQoFk2UbzfJpJ\nAyuh79lMoq9LFk5lGV+o9qm/tGnv2a3NbgRc3bJ5y7PPceL1N6hnUrx07ztZmd2ZuICSgmo2FuyX\nbu7sHFCO3ozw/FBpOEHgJ6m5fmjgdcxoPddqLkZ2vT/rE/S6c0jXJ79cJ1mxoTVKVJrYogwtBOsz\naWq5OImqBSLYT9zuQs6LmL9UYvsLjVuRUaAcceiIf/eTuxckDyiVQoJYo9KnzOMaWqdDsVrYGN/o\ndFwKQT1t7O5QuFIIpShOJpGOz3jLX7MbQe84iGFZ/Pwf/wnJag3ddfGB06+8xmM/8yFev+vOHR3G\n2nQK0TJXbj99cTIZKtgQyYDFhFRw/PV1qrkYa9OpntvGG15kh7BjBlWI1OasbzK5ISDu94ovQLCw\niNcdFk7ntlzk2AkdO66RKllMXSsjXYUd11mfSg6VxdcyZlCF2BzsRXDdiMGMAuWIQ8c//729laY7\nCDTSBpVCnOx6M+hmVcHKf+lEf2kws9qgsFLvnAPHgJXjmW3tYUWRLDUZX6h1SrwQ3incHkdpc8cP\nnyZZqaK3hNAlgUbsux/+DprjML64RGl8nNfvuoiVGDIjbHV2rnk+mtuaEQ3LxjYN8/dcJQWNtEEi\nZEyi3RyUKgUWWpUuwXTDCtf1FYBp+6xNp6hlYyQqNkoGTWLdKj2pVra6WT3JsLyhx5Ayq40eh5B4\n3WHmcomFM7ktRfKVJlk8mWVyror0gi5nX5MsH0/fkko722UUKEccGvbCKms3idWdoKwG1LKxHc8K\nAiAExakU5bEEsUZg8htWXjWaLvmVfheTiblAMOFGToKZ1TqF5aBZqt1MBK1uSTYcFXyCk263U8ap\nV1/rBMludNflvu/+Lbrn4eo69zz6GN/4tc9QnOh3HOm5n+2RWWtgNl3suB4Esc1BUgUC4Lm1JsJv\nScFNpWhsyphWZ9NMXSl3FIn6NGtbZeTuQOkaWmjp0hfBHi9CYCWNyIAXprfafd2WgdJXfTZa7cCe\nG7Lr104YzJ3PY1jB5+LEtIMpIXgAGS0lRhwKDnqQzC9WmbpaJrPeJLPeZPpKidxyfes7boGvSxpt\nE+WQk1qqHN1xmaw6O35e4fnklxuhgQRa5sdxHceQVMbizJ/J9QRlKxHd5doOoLrrolsWD3zjWwOP\nxWi6zL5ZJFO0iDc9MkWL2TeLmJu6XfPLgYKNbCnQGI7PxPUKsVrv++BrkoUzudDsvI3c1OHaSAdj\nHj0CTgRycrUBBtxtHCPoHA5jmP1G3fFDPwgBnX3joRBiQ+1pFCSHZhQoRxwKXvofP7XfhxCJ0XQ7\nMnjtwNL2pRxkpbUbDBTH3qLjUro+6WKT9HoTbZPcXKzhRg7xCYIAsXAmx/XzBYpTqb4OzBff9U4c\nozejDtvjk8D4wiK6HR3Ux1p7ou37tt/fscUuST1fkQmZZZSKXiGAzosQWCkjVOJPAY3NGV5LNKKZ\n1DtjMVZcZ+FMbqAqU5taLhZotG56Hk+XNAYYKLfxdBH5Wbvm6DS+14xKryMOPLsxL7mXJCt2+ElM\nBV6P3SW8zei2h2F5uKbckRlz1JydgIFdvO29xzaFpaAxpn2sviairbdazzuIuXNnee497+aeRx/D\nlxpCKTTXDR2XUEKEej62ifL9NJteR0Rc86K1Y0MNkAGEYG0mzeS18obgAi0LrZC5T8/QWDqV68xT\nbmfOVmmShdM5xuerxJpBJtxMGqzOpofK7JQmI7t+S+M3NqM6YmtGgXLEgeagB0kYcMIU4SbLwZ0U\nE3OVVqdqkBnaicCGaTsnYCuhU8u2Oi7bD93uuIxo+5euz/hCrS/7yi/XaaRM3JgWCLnrErGpASXo\nvB1Ogu75976HV97xdibmF2gmE5x58WXe+sOne/YuPSm5fvYMvh59KvKlQAsZ9lctRwuIHnFQBO4Y\n+aVa6ChGM2UwfyZHdq3ZstDSKY8lBs4o7lSIwo1pLJ7ZWaAFWJtJoQQd+ytPCtanU1hDZKQjboxR\noBxxoPnvH5kHDvYoSD1jkms11IRdF0ZupUGi1pLOa93PbLiMLVS3ZeektbQ926dcVxeszqaxUgOy\nyWq46bVQwZ5naTLQoF08lWX6SrmjBSuAWtpg7VgmvNs0BDse5/rZMwCUxsaYnJ9nfGERlApGWTIZ\nHvnIzw18jGo+1ldW9QU9zUMIQWk80Scg3j2KEas7LIaMYrgxvWf+sw+lOso8uzGvumPFp9ZM5fp0\nCumrIAsf7TPeFEaBcsSBZSe2WfuBa2qsTacYW6z1XL46m47MTDIhriVSBWMEqxGehH34ipnL5Z5A\nqbuBSs7cuUJ0MBu4dblxpWtqzJ3PBx2bXhAkbqSL1jMMvvWZTzGxsEBhaZlKPs/CqZNbvtbiZBLN\n9XucMRopo688Wh5P4GuC/PJGQ08bqQIZuuxqINXnaYJaPr5lI43RdJm6VglGKgSACMTO93P2UIho\nQYoRe8IoUI44kHz+47+134ewLWr5OI20SaJmA6LTJRlFmG4osCGgOsR5MFm1kV6/MbL0gsYWO67j\naYJ0yeoaq4jTSBsUlkKeWkBjcwenEL0G1sMG8SiEYGV2dnsKPSKYnyw6HmbDxTE13LAheyGoFhIY\ntk92vdl/tQoyeUnwFmfXm6zOpKjnIsy+fcX01fKG24YK/jNxvcL82fy+yxyOuHmMAuWIA8d7v3g3\nfHm/j2L7+LrscYkfRDMVPvRux7Shy5qG7UXqd+aX69A19yeAeMMlU2yycDpHcSLZmb+EIEhW8vFI\nD8lUqUl+uYHu+ri6pDiR6DF2jjzGpotpeTimDB57h0HWbLqMX69iOF5Lxk9ndTazoXzThWNqoUbZ\nsNHm354LHV+o0cjEQsuhiZrTN59K636pkrU9oXeliNccdMfHjms39F7cFJQiUXXQXB8r0W8efqtx\na7/6EQeSR3/jOf71dy8caQWe9akUsXoJoVSPa8lWHpLd2DEdJUGENHxK6CuxtrOisYUai2dyNNMG\nybKNUIp6NhYZJJObfCB11++UmaOCpfAVU9fKPbOOTkxj8WR22+Vb6frBXmlXFh6vBw4g18/l+wJO\nLWuSX66Hirj3H2ggFBHWIax5fuiIjSDYGx4WzfGYvlLuuY/VatwadlF0M9Etj5krpZ6qRyNlsnJ8\nuA7do8hoAGfEgaT50F/wL772b/ib3x1e8Pow4Zoa18/lKY8laCR1ymNxrp/Lb0vNp5E2ArHrrsu2\nqtoKCMYTlMKJ6dSyJobtMXW1zOwbRVIlqy845JcbEfOJ0d3I+eV6x8ey/cdoen37uMOQLjX7jqkd\nrOL1/vnL9iiGHd+YefQ0EbE1KyI7k5sRajk+0EgN/zmNz1fRW5Zp7T+xhktu9WB2c0/OVZCe6jne\nRM0mXewvZ98qjDLKA4BSinrNx7YUZkyQTEnELbpy28wjd/0+/4KgHPvPnDt59qsHuwN2O/i6pJqP\nUc+YOObwJdcOQrBwOkdhqU6yYoHaQoCgRXusQrc9Zi+XEK0+Fc3zGFuoojkJyl3GzXpE9qS5Pvg+\nyP71drpk9QdXtm5WEn4gQ5cqW0DgsGHYXqT8m+6EH5sb01g4k0N4PghBrOEwebXSv4ja9eaNAAAX\nIElEQVTwFVYifK/RNbWO2Hn7+dsLkfxKAzthRPpXdl6P5xOv98+Btn0sb9Snc7fRbQ/d8cJl/YoW\n1cLRXLhuxShQ7jOep7jypoXjKJQKzpW6Ljh1Noamj4Jlm0d/4zk+zXP8wRfv5kdnD39ZVro+k3MV\nzKbbChqKtanUUPt+3fiaZHU2HQyuez6nXl0ffHsRjFsAwUjLJmU0qSC32qAylujs27mGxIgISPnl\nBsXpVP8VUapAWygJTV8pYVgbgTG32sDTROSeo7XF3lm7zNtMmYG6jdvbDYuAZNkGKUhWLHwpqebj\nncx+bTqFJ0WgH8vGe2XYPpPXKiycHbxwG5jd36BX5Z4w8PO5aUdx4BiVXveZpXkH21IoH1DBAt22\nFYvzO9fpPMo8+hvP0XzoL/i6/38e6rLs5FyFWLs06SukH0i1xUJKicOSbIkXbEYRBMi2w8f6ZBDY\nohRv2tlmm+JEIvQcKQjGXMI6eJspo+8+CgbOIcZrTk+QhCA4am4wM9j9eL6AZsIYuslEuj66p0Iz\npbHFGuPzVVIVh3TJYvpKifRanWTJYuZSiWwrSG5+7YblbSlR6GsSJ6aFvhcH0d7KNWVot7Yvgr3f\nW5VRoNxnKuXwH1ql4qEO4orzgPDMN3Qeuev3uecTxf0+lG2j2x5msz9ICQVTV8pMXy7tKGBGdcFC\nIHwwfzbPclcDiWv2n8CD41A9Sjf1XHygxJwMkY9bn0rhtzJBaAVqKVidCck+W8SabngXL0EJtpKP\n4WoCV5fUMibS9znx6hpTVwa/X4mKzfTVcmRG1N6Haz+XVDC21Ajk5iwv8iQZjOL4SM8nt1xn5s0i\nk1fLxGu9gg4rs2mU7H0vXEMeuLIrEIzvHEt3FlYQ/H+z7ditxqj0elAZxcih+PQ/+jOePWQzl5ob\n7JuFNai0xzimrpZZPpHt8Xhs77dFKbtEdcEqGQTKzXN/pfEEsbrTE5x8AY202SeUYCd04rX+cRZE\nuHxcu1kpVbSINV3smEY1Hx8oDefqMtTKSolAPaeWi7E+E+jnTsxtmFon6i6xkPcLWh6OK/XIPc5B\nzU/DZBGa43U8HqUCLI943enRzXXiOnPng/dCdzzshBFkkwew4xXAShrMnS+QLjXRHB8raQQKU7dw\n38S+BEohxBjwJeAMcAn4lFKqb3NFCHEJqAAe4Cql3nXzjvLmkEpLqpX+FXkqPWroGZZ7PlE8VE0+\ndkzf2tlDQX6pxsLZPEbTZXy+itnyEWwmjWDVvynoNNIGniYR/oYIQdDxKUNNnK2WKPfYYg3RUrKp\nZWOshew5FieSTNdLfUG1OJ6MPIH6mqQynqAS9Rpdn1Spie4qmq2TcWGpf6wjkLrbOP7CYr9Obff7\n1Ub4KjRItoOj31L5gaH0HfpQApIVZyNIdh/Lcp1qLt5xFmm/F4cFX5eUR2LrHfYro/wd4DtKqd8V\nQvxO69//U8RtH1JKrdy8Q7u5TM2aNBtNPB9UK9GQEqZnR0LHw/K5tzT55/t9ENtAaaIz8B+V6UAg\nuSZdn5kr5U4ggw1n+74Zwpb1VWGxTrIadMHWMybr06nIYFbPBl23mtfaB4zKVhM6i6eyFJbqmE0X\nT5eUxhPUcluLo4cRqztMXS0DrQ7QYhM7prF4MsPEQg3dDjovHVNj+Vh647iUiux0bS8k2uiO1/IE\n671dO0iWxhPYCZ3Ja5WhuoXDMOxwQ2YlBKY1hCHzJlLFJvmVOprbMp6eTNIYQoB+xN6yX4HyF4AP\ntv7+x8DfEB0ojzSGITh7W5xKycNq+sTikkxOQx7QssxBpPnQX3DPFz57qLLKyngCN6aRXWsQCxkf\ngKCkmWrNEG6WqWvPEDY3iZ/7mmT1WJpVhhcuQAi8ITqs7YQRiIrfKC3nlM1ZmGl5xOsu82fzneH8\nvrJuy5IrzE1k8209TUYGQCuhd0ZgipPJjpIRKhAtdzWJafeOSbQz0bY4xPpUknjNwbT8kP1mhbdN\nPdb0eoPC0sbiyXB8JuarrAixv9qyI/YtUE4rpeZbf18ApiNup4BvCyE84AtKqT+KekAhxG8Cvwkw\nbRyeEgeAlIJcYbRdfCP8gfE8D/Hgfh/GtmikTRppk8xqnfxK71B/kPHEMZvbnyE86Bi216Oy00Yq\nSJctKuOJSNssgNJYnPxq+PvVja9L6iljw6Wl67bdZcXKWJAZx2sOviZoJg2kr5iYqxJvOJ3AWM3G\n0D0/GCEpBHJ/TkzvSN21UQSZsLsdf1Gl+r4D7fckv1wfBcp9Zs/OzkKIbwNhw27/S/c/lFJKiMjC\nx4NKqTkhxBTwsBDiJaXU98Ju2AqifwRwRyI/aoW5xXj0N57jni8cTkGCylgC6UN2raXUIqA0lqCa\nj5MqWX1mvW3sHRg97zmt0qiniUipuv4hja7rhkjCKuMJpOp6vwjKqNWQGdTVYxnG56skq3Znv3N9\nKtnX9ONrknpXidPXBEunskjXR/pBGTSsfG0lDdankhSWNjJSJ6YF3cXbQKhAzD4M3Rk8gjJi79mz\nX5pS6sNR1wkhFoUQs0qpeSHELBDiZQBKqbnW/5eEEH8J3A+EBsoRIw4tQlCaTFIaT6B5fpBNtU7K\n9WyM/Eqjx0DZF0HpcDtydzeDVLFJYamOaJWKaxmTtZl0376na0o8XSKc3pJlIIYwhODCgPdrM0oK\nVo5nEJ6P5kUHvCh8XbJV3l4tJKjl4hiWi6/JHbmKKBEEZy0kWLpbqP+M2Hv2a47yq8DnWn//HPCf\nNt9ACJESQmTafwd+Fnj+ph3hiEPHp//Rn+33IdwYUgSSaF0nciUF82dyVHMxPE3g6oLyWCIQ1D5A\nxKs2Y4s1ND/QCBUKkhWbsYVq/42FYPl4Gl9uCCH4IhDerm6nOSjk/YpCtQPYHnWSKxnYke3YeksI\nihOJzuxiG1/Q57s54uazX0vS3wX+oxDiHwKXgU8BCCGOAf9WKfUxgn3Lv2yNSOjAnymlvrlPxzvi\nkHDYRkWGwdcla7Np1vb7QAaQWw3fX0tVbNY8v1OG1Ryf8YUq8VogEOCYknrGpJ6J3fJWTtVCAiUE\n+ZUGmutvdL2O9if3nX35ZiqlVoEPhVx+HfhY6+9vAPfc5EMbccj59D/6MzhkHbAHBeH5FJbqHUHy\nRspkfTq5pfA3RDcWKQhKnhodLVe9q+Rq2D6ZorVrM3u67ZFbqRNrGTyXxxN9IxrC88kv10mVAwWd\nWtakOJnctv3XXlDLx7et9zti79n/b8aIESP2H6WYuVLuOGVIBcmqzczlUqiW62aaST1cTEqIYF8Q\nAiNgz+8bdRG+6gTnG8GwXGbfLJIq2xiOT6IWzGomuh9bKWYul0kXLTRfofmKdNFi5nJ5SxGIEbcu\no0A54sjxB8ZoK3u7xOsuut2raxrMayomr5YxLDfqrgCUJpIoSZ9w+fpkorMvqDteuMm0Yktx8WHI\nL9URakNlZ0O3td4Jgomqg+70vk7ZOrZEdWREMCKcUaAcceR49DeeO5Ri6fuJYbmh+sJt7dmZS6Xe\nzGwTrqkxfyYfaMrqAiuus3Is0+Nf6MT00PEPX4C9C/uTUW4omud35jZNK0J4XQXXjRgRxq29ez7i\nyPIvv/Lv+Jj8p/t9GIcGJ6aFyr1BqzyqYHyhxrUB4tiuqbFyPBP5HM2kjmNqPUbMikBRp77ThhWl\nmJqbY2J+EbMuKE6eQMnePdXAZiw4ZsfUIoXXnf0ew1CK7EqDbMu6zEoYrE8ncQ7ivOwtxugTGHEk\neeYbOnx8v4/i8NBMGoFBs90vx9ZGoDAtb+fZnxAsnsoFjTSVDS3a4mS0sPogpOvy4T//CyYWFpB+\noJjjS50fPfhRmqlgfMYXBHq0rVnOetqkIAXC6xVe96XYebDeJcbnqyQrdmcREWj6lrl+NjdUQ9WI\nvWNUeh1xZBmVX7eBECyezlHPmNEOb4qBvpTDoDTB+kyKa7eNce0tY6zN9rugbEZ6PkbT7WsquvjE\nU0zOz2M4DprnYTgOhtXkbT/820DgXQSBeG2qyw1FBsLx7eYjRZDpLpzO7Z/tlVL8/+3dX2wcVxXH\n8e/Zf17ba+86dhonIWkTVJoWeKAKpZQKFVQhiIRCQUjwQPtQqepDBTzwUAmBBEKIFtGHSlSiEkhF\nFFAlCkRNQtRUrSpUtSpUaZu0lP5RRZM4cVzH/722d/fyMBPHjnfHu/baM7P7+0hWxutxfO5ce8/u\nnXvP7b44S/fE/LIlNpcmOvWMFsOJSxbpHaW0rDjuVRmmSjLByM4eusaL9A9NL3sV7fCGVqsuqK84\nuqbmSc+VWehIMpNr0l6LzrHl3LQ3I9bfv3NiSyfjA94EoWtfP0mqtPy+YgJH9+QYFwdSzORzVKos\n+Sinkwzvzi8m3lo7pmyWwvAMPWPFqu/kDW9DawmXEqWILDPT20GmWKZnrLh437KcSjBc5f5jolRh\n+/vjJMoVzHn3+vqSCYauya/6TnE1fcPTl+vc+rNWe0dnKaeMqb5OLGA5RzmTqJoklwo7QYK38XPP\nWDFwY+n5Dg27hk1Dr9LSnvtFvHaSiQQzxrZ1c3ZvHx8O5hje1cvZvQXKVd5Nbjk3RbLkbVx8aTlG\nslSpXrquEc5b31it2k+vPxT53vX7KCVXTtyZLOSZzTWwzViIOmaD3y0684rmS7iUKKWlvfDJX4Ud\nQmyV096OGnNd6ZqTbbqmFlbuxeg/vh5WcTX3kkyWKmSnF3hj/34mtvSxkPYq7yykUix0dPD8V+Mz\ni8sr6L7ycQeUEnB+d+/a68dK02joVVrekcrDWiqyUWosKQnYSasuLmGUUwlSpeUVChze0o6BM5OY\nc7x4+0E6Z4bZOjTEVD7Pe9fvYyEbnxJwc50pKokEVlk+29gZDF+d19KQiFAvSMvTUpGNM5PL0DU5\nv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8141049b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.704815\n",
      "Cost after epoch 1000: 0.134190\n",
      "Cost after epoch 2000: 0.127524\n",
      "Cost after epoch 3000: 0.125077\n",
      "Cost after epoch 4000: 0.144570\n",
      "Cost after epoch 5000: 0.140557\n",
      "Cost after epoch 6000: 0.124222\n",
      "Cost after epoch 7000: 0.144125\n",
      "Cost after epoch 8000: 0.132892\n",
      "Cost after epoch 9000: 0.121368\n"
     ]
    },
    {
     "data": {
      "image/png": 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T5DugfUNu7BfPR7M2MnT4DKas3FLp8NuTlcvdny5gYSkBlZdfwDXvzeaOj+cX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\nMsVpMiThqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81416b7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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G4GMQ8C2rf8TUpSTLi64entxmmLp7FadmbNIZ/TqCQJHNmYyOH7xHci8MQ5ib\nTzA9q/A9hWVL6D7GJiyWF3sLf9IZPdlj0KnVAjbXXGo1RSoljE/Zx1YUFYZhaKGI0nanJ94cZfYg\nE0vUHQ8P9rfoDBIEqsNINlFKG9CLVw7fYuDtJhAe6CkeVx9OaR1RQzAtobjtU8gTOuw3jGYBUG7U\nJ72P+Yh7MexX+ct3P8nXcldZSU0y6mzzuu1XyHoVnvjKDwPw26/9IJ6nsLsMk+8rSkU9e3Eoa3Lh\n8ukIxpt7aLBmcyZOXUcNmnKEybRw7vzgK05VKj4Lt5yOk7hSsc75y4l9zcM8LLPnEiy4dT1mrOFd\nDmUNxqce7ENcLFF3PDzY36IzyG6T6p364QtmatWgcwZhF6lGXqxbR3Q4a2CZ4Hbt2raFoaywle8t\nAlJKhx+Pw1ACpAKH1xde7LjtiS99oHWQ+Kef/g5qb/+lju2los+9u87ODcsuk9MW45O7z5c8DUS0\nUtDYhEW9FjQql082hnhUdaMmq0vhk2tWl1wuXzvc5x0E+qRhq+CjlCKXM5mYtjtONkxTuHQ1pb/H\nriKZPPn3bNB54ksfgNhQHgsP9jfpDGKZElmmmThCeGt9NSIpBlrnNCRE6DoBt2/U8doiryI6L+S6\nKtRI7tzx0EvdF3/7d3cEnH7og7N6MG0D39eh6uaw5uZlfdUbqAkrpqnHb53UAV8pxeaay8svVnnp\nqzVuvFzTYeojEDY4erfb96KpILW57uG5er5qPu9z+0Y9VMkoldbj2h50I/n484/G3uQx8mB/m84g\nYgjjk709kyIwNX34AEF1l/aNsLxns1G/WzZPqZ1+wSgjqYUITi6Y8ZEPv6dnEO0XPj6q9S0h0hjo\nsPCD006wseaxvrbTH9vMdVfKhzeWUW0why2qqVVVo02p7Ual0wSl7biiNYy4FeT4iQ3lGWRi0mJq\nxmpJzCWTwvzFxKFDmY4TRLZ3iISP56pWArxdwsBRz9Vshzip4o4wI9nOc8+8b1exhQelTbEZzozK\ndR+WsfHwk7ioodV7EdV/qwL9HYzpRbeCxBwncY5yQPF9RRBovdXu3JGIMDZhMzZxPPm01aXosOvI\nWK9KD+gz+oiK/FDshG7DGB42sBMnd362m5Fs8n+963t594c/jOo6ORDhTE3vUEqxseaRb6gmJVPC\n9JxNJqOHX+vWH0UqKUzN2h0nUrsNnD5KrntiysL3FVt5v1WINDJq9vSK7hc7IaHzVZstPDGdxK0g\nJ0NsKAeqsX7GAAAgAElEQVQMz1MsLTpUGzJwpiXMnrNPdOxVU3IujKmZ8K9IKh3eqB+GLtM3GTvg\n7MaD8NhTHk8b79/XfavDw/zet7ydJ37nU/iNRvXmPMuzpKe6uuyyld/pba3XFAu3HEbHTQqbO7dX\nqzpMfuFysvX6LJPI3sOj5PdEhJm5BJPTCtdR2IndK3z3YmjYwDB65f9EOPY+17PO488/ynMfi43k\nSRB/0wYIpRQLt+sdhQ+eq4sZLl9LnliBghj0eFfQDJWGH+QSCYPsiEmxTWmmWcjT7q2IaCWcsH62\nIFCsLDkUt3QOyrJpnBQc/Gv5Y+9674Hm6734xjewfPkiPz79Mgs//QcM57SRHIRJKPuh6bWFhU7z\nG70fpg6puq0WmGaue3OtV51psivX7TgB66selbKPaerH5UbMXd8r0xTM9NHfSxHh4tUkSwtuK4+e\nSOh+1PaUgOMEbK571CoBiaQwPmmfiBLUIBPnJU+O2FAOEPVauBSXUpDf9JiZO5k+utyI9kDaEYHs\nHgfD2XM2mYyhQ38BZHMG45M29VpAftPD93T7yOiY1aMoo5Ti5is1vLaor+fCwm2X85fkQB70YZuq\nC5OT/HAwyafWv5Xf/aZ/Enm/umHz6tAFylaamfoGFyrLoUW7ZTPFSmqCjFdjpr5xooW9rZFgB8ip\ndlf0Tkw21JnW9Wdl2drJXLjtYCd0i0oqbXQM9/Y9xco9PeNzauZ0Wmls2+DilSS+rwvHukUX6vWA\nOzd21liv697N+QsJhrJnJ5R+FB5//lH4WL9Xcf8SG8oBwtvl4Ofs0uN4pH16ejpFN4mEMDO7+4FQ\nRBgZsxjp8hYzQ+aeCkGlYtBhJNtZWXK5+tD+DnCpF549chn8kz9a5Z++8GxPryXARmKUj597O4EI\nnljYymPM2eK/vvcprIYbroDfH/9TfGXkIQzlgwhpv8a33/sUWa9ypLVFYdty4MKj7pxee6672Vfa\nfE6nrlhacEhnJHS4d37DY3zSOlJY9aBE7Wtt2Q0fQL7kcnX47EQJDstjT3mD700qtcsswMHnwYpN\nDDjJdPjBTwQyJ5Q7W191Q7VaA3WyuqKVUnRl5W7CB9383Eupve+0D7p7LUEbwF+feRzHsPEMG0RI\nlErYS2t82Z9pTfK4MXSBr45cxzdMXDOBa9gUrSF+bfbkDl6mKYyMmaEVprkRI/SYZCcMyiU/dAJJ\n2KxMpaBSjlZrOkrRz3ESVf3quSpytNn9wuPPP7rv3Hw/SJUczr2a5+LXNzn/0ia59cqZLC2PPco+\n4dQD1tc8qpUA2xYmpiyGhs3QCROGCaMnVAgT1VPouQrPU4fWFg0Che+HV+1C72ipdsx9Rsuee+Z9\nB8pL7sUXPj7KF555H//w//sXAJSsDCUro62CCnjtZz/NxMrdxr2FV8Xj4uUkXz73UM8UEyUGBTvL\ntjVEzgsZu7IPAl+hiPakpme1Oo3WqNVtQtNzWrfWsnU1bLu0YHHLp7Ttk0obnL+U6KhmPmjEIiwE\n2i9MU0LFB5rtSPcz8qZ3wMcGU1ggWXGZWixiND4aM1CMbFQxAkVheqi/izsgsUfZB5y6VrQpbumh\nx9VKwOIdh0LeZeaczdSshZ0QLEu3Z1y+mjqxEJcRcSRRHO4gEwQ6ZPfKizVuvlzj1a/XQgcOj4xF\nh3Un9iGckHrh2YMvbp80hQmk7Wxl7vbLTKzcxfT9xkXn9RbvOjhG+GsxUJHbdsN1Au7crPPyizVe\nebHG7Rs16iHeW1Pq7qFvSPPwa1Ncvp4iM6TzylMzNtcfSWJ17V4p3ZvYPZQ66sTFMHq/ByKQHjrZ\nNp+DMDYR7llnR8Jbm+4XjiPtcJKMrFdaRrKJoSCbryEhJzaDzGB80x8w1te80JzK6pI+eI2N21x9\nKMW1R9LMnkvs6n0dlbDwHUAmbRzKOC8tuhS3/ZYsnO/D8j23R+3FsoTzl+yefY9PmoyN725cHnvK\nO/FJ7c898z7e+s4iObcMKuDcra9jhjQfuo7i6vqrmEHvyYChAsadrQPtVwWKOzfrHeHEWlXf5rkB\nq8sOL3+tyte/UuXOzXqrQCfMa/fc8BFoTWH6dianwoUCJqct5uZtTGvHQxvKGswPkED76LjF6LjZ\nqrpuzlWdmeu/bu9J8fjzj574b+Co2E50s67pna2YeBx67QOVUrSEWr0ekEqdXqXe2IRJsehTrzZ7\nPHShyNwhDoSepygXw1sWNta8ngKfoWGLh77BpF7T7SHJlGDsoXV2kH7Jo/Lij/wlvvXJX+OP5RLJ\nWnRRzsPbN3h56mHKVhrPsBAVYCo96svYtySDplQK8EOOISqAu7cdXGdHMrBa0Z7n5esp7LCTqV3O\nc7o/o5ExC6UU66sevq/D/ZOTFqPjFiJ6VqnnNabGDNhMTBFhejbBxJSuGrdtOdGTy0Fg4It3ADdh\nYXpu6NfQs86WjxYbyj7Q3WvYTrV8NEPpOoH26IBsdndx6MBX3LnltPJTTY9h/qJ9qAON50VX7bpu\nVFGIkErv/no3EiN8bvS1bCRH+Y3hYexNDzd18l/df/nfrfC2GwWu1te1h0yv7TFNGLZ9vmPh13gp\ne5m7mTmGvArfuPUKY+72gffpOkHoyDKlCG0dCgIobLhMzfae2DQNRlhxlOsoilse2bah0aPjtjaY\nge6tbfdSRSTcGA8QpimkM4O9xuOgmRoYdApTaWbuuEjb1y8Q2B5PwxkLiceGsg+kMybuVril3E1a\nbC8Kmy6ry572YRRsrOoS/snp8BDU+pruh2satma4dHnR5dLVgxvrRCK6ZeGwijcryQn+47kn8cXQ\nBTKfg1nZYvVCjnrm5EJrQ9vbvPk3X8D3dj6Q9p9204bMnU9oI6J8Xrf9Kq/bfvVI+02lDS0A0W0s\nG0Njwt7fWsRkDhE9wzJqIPe9BZeHs2bHZBgRQR6M1sMzyWNPnR3Rfidts3o+x9hqmUTdxzeF7Yk0\nxbHjqVQ/TWJD2Qdyo2Yrj9eOCIdWE/FcpY1k1ySPzXWP4ZwZKkLeXV3bpFZV+L46cIjNMHT17kaX\n2othcGitz9+ZfH1HRakAomB8pczSlZOT67r40iuRQrbJtJDNmoyMWsce4ktnDJIJod52AoPo6uGw\nfCPokHUUqfTuwd9aLTi2uaB7oZTu2c1vaG3a4YZAxaCFcgeV00w7HBf1IZvlE/ydnhZnK1B8n5AZ\nMkimpKN4QgQSSWFo+HAfyW6jo4pbp3cWOjFlMztvk0iKDkvmDC5dTZI4ZIXkenIs9Ha77p9oP5ao\nIDLFl82aTEzthKeVUpRLPksLDvcWHErF8F7Ffe1XhAtXkoyOm5iWDu2OjplcvpYiM9TbH2kY+5jM\nsctSDtKzelTWVlyWF11qVYXjKPIbPrderRMccArNg0rm//gf+72EB5bYo+wDIsKFy0k21z22Czqf\nmBvRExZOU0UklzMphOiFptJHK9jIjVjkRo7nq5UMHGpmb6hGGSfbJHf3+nVe/+nP9NzuWRbDXRNG\nusXJS9s+2ZzJ7Lx9qM/TMHRxynRXUeO5CwnWVnb2lU4L0+cS2Hb0SYjaowzfPKUjgOeqDqF2aFRF\ne4pC3mN88v6tUD0OBr0V5H4nNpR9wjB0D1xU/vCgDGdNVpd7NeG0Ukv4xzwxbVMuB7iuahVwGAJz\n8/ureFVKkd/0yK/rSsl0xmBq1j7WWZPf/t3TfPQXtzv6sQKB7RPOcxTHRvn8W5/gsd/5PSQIEKUI\nTJMv/uk384tPPN4SJajXgx5xcqWguO0zOm4da3GJYejJHDNz+r3fywgHjVaT3ThM7rhaCVhbdanX\nAhK2MDFtM7yHpmqtGoQWeikF5XLA+OSBl/FA4GPwTX/e510D3gqyF5bjM1yoYboBtSGbci55pgp6\nYkN5n2DZwvSs1VHMIwLjkxbJCMNlmsLla0nKxYBaLcBOCNnc/pu011bcDi+hUm60K1w9nkknjz3l\n8fQfWYyNJhku1EEEUYrySJKtyfSRn38vvvKWN3P3+nUuff0lBMXthx9ma3IC0JWHnwh+kt/8hfDI\nplJQKnqkMyfTb7gfT7Ww6YVWyjaZnLb2bMfpplrxuXtrRxO25ivu3XWYPWeT22XslWlFF3oNejVt\nP6iYKX5r6o0sZOYIXjWYSW6xMTeMlzx7lVapssPUQhFRusYgU3LIbVZZvjSCMs9G9i82lANOcdtn\nbcXFc3V/2NSM3RP6a5LNaZHqWk1hmHu3hwCtHrmo54zC93tDaaCrNTfWvEP1Ybbz+POPtnrF8jPD\nFCYzWG6AbxsEbT8uw/N4/Wd+l4e++CVMz2Pp0kX+6FvfTnHseAoItifG+dITfzp029PG+/nw9/4S\n6//oZq+xlGjpudMiqlgLYHrWPNTg79UITdjVFXfXaTOptG4v6ZbKE+FE55SeRQKEXzn3rRTtIZQY\noCBZ85i9vcXitdEzY1wAUIrJe6WOiJChwHIDcvkaW5OZ/q3tAJyhd/zBwXUVrhNQyLssLew0mTuO\n4t6C0zPtQynF6rLDqy/VWL7nkt/wqJaDE226dh0VmSKs1Y6uuiFvekfH/8o0cFNWh5EEePKXP85r\nPvcnJGs1LM9j/sZNnvmFXyRZOZmpHd38rdJTGCEnI4KWUOtGKcXaisvLLzbUdW7UqFVPRqUkKjIg\nApmhwxmneoSH6nu6oGx91aWw6eH73QZROH85SSqti9jE0KIGc+cTkRGPB5XF9AxVK6WNZANd7a0Y\n2to9lD5o2I4fKldnKMhsO31Y0eGIT+UGiHo94N5dp1WJGOYNKKVDntk2D7CQ91reXXsYdPmey7kQ\nz873FcUtH9cNyGRMMocYRWTtMuYpkTyagd5v4cLIxgZzd+5ieTtVvYZSmJ7Lw5//YqQneJw46TS/\n9u3v4ts++asEVbcV9p6dt0OLbJbbJP4Aqg15upMYzD06blKrBj2fk2XLoT8jywoXMABYWnBb05TW\nVvSQ6PZ2J9sWLl1N4ToBQaC/J/f7CKzDsGUPE1ZzbajdZeH6glKkSw5D2w6BIZRGkzjpnUhFsMvn\nq87Q+VFsKAeEIFDcvVnfl+BA94EqvxEuG1fa9gkC1eFZ1KoBd2/VW0Y1b/gkk7oK9yAC0palQ7al\nrn5QEZg4QgXjE1/6wL6r+0bX1glCcmyW5zO5tLzrYy3HJ5uvYbk+tYxNaSR56JDW4tUr/Oz3/QA/\n/vov4Pzd32NoyAgdUea5KrR/VinY3PCYPXe8+cxszqRaDrSua2M5hgHzFxP7NlC1mhZQ9z3FcM5k\nfMLs6ddt0i1csXjX4epDyZ59DYqY+qAy4RSwkoLfVZsXCDjpATpkK8XUQpFUxcVoKFcNbdcpTKYp\nTuiQqp8w8RImdt3vMP2BQHH07AgPxN/YAaFU9Pc9O687pNod5mqn/TmV0oUXQdB2UAugXlPkNw7e\nazl3zu4QVbcTwvzFxKFFE4ADlcBvj48hIW+aZ5rkp6PLKFNll7mbBbL5GpmSy+hahXM3tzCOINTs\n2zb/y5ffyCf+7V+JnOPpOEF0uPoYw69KKYJAV8XOnEtw+XqSmTmb+fMJrj2cIrlPz3Wr4HHnRp2t\nvE+pGLByz6WQ9xtFQDuSh1Fj0XxPndjA8fuZZ//wvWyZCYK274oCAtOgkk2eyhoML2B0pcy5V/PM\n3izokG/X2VG65LaMJOhzMUPB2Hq147e0Np/FtwwCoXUp55KUR07ntRwHA3R6cv/heYrNdZdyKcCy\nhPEJi6GIMnrPVZGhzHaaEx3aGRoyKG73HmhNSzoOYm5jxmQ3SsF2wWdi6mCeoDTaFaZn9drDPFKl\n9Bgx11EkU8auRvSgGpb56Wk2Z6aZXF5pTfbQBxSTrz/2WPiDlGJiqbe4QLyAkfUq+dmjzcnrnmnZ\nXFPBzlHLGfgsIyF1ssfRUhMEqqPPMpEQZs7ZZIbMAws+BIFi5V5n4Y5S+qRK5RTXX5PC93Se8c7N\n+q4nazEH4+0/VkMujjCyVmF4uw4KqsM2+ekh3T98wogfMHergOGplidlL5ewaykKMzu/j0zJ6Rmj\nBYCCycUia+ezKNPAS5gsXhslVfEwvYB62sJLnK3q3dhQnhCep7j1aq0lO+bUFdWKw+S0FdpcnUob\noX1mzbP2INDN4ZPTNiNdZfiTMzblUr3DexSBmbkDNLwf4fcnIqGekucp7t6qa0H0xutKpw3mu4YG\ng65y5WMH3/dvfOd38Ob/8l+4+rWvYwQBa3Oz/P4730E1Oxx6f9MNMELGczTL1vMcz0DZ5xrGsmAP\n859m30bZymgDOR/wms/9NhMrCzv7brTxHJWlRYdycScn6TiKhdsOl64mD1wwE9X3CLC+6uN5enC0\nUtEepWkJicTJH9iDQEdEmqPDRkZNxiasMzmL8iMffg98XAtqFGaGOgzTaTFcqGH4qiPcaCjIFWps\nT6QJGpM/AkNCBwUIkKx6zN7ZZunySOsgVhs6u6ISfTWUIvJtwD8HTOD/UUr9o67tTwK/Atxs3PRL\nSqn/9VQX2UYQKNZX3ZaaTjZnMjVtY4ZMes9vuD35RqVgfdVjdMzqCc+lMwapjEGtsnOga8raXbyS\nQBqq2GGGL5EwuHw9SX7do1IJSCQMxietHu8tapqEiD647IXjBNSqAbYtDcO++4Ho7ipsJkZIeSWs\nxrzGajVgY7Vz2sVjT3mHHhvkJRP87tNP8btPfRsSBKioo3YDZUjkOUFwzAfW557+AR59ZYEtL6XL\nPAEM+Oobn+RNv/UrpEpFkintlR+1kMdzVYeRbNLU+z1ou45hRBdrAWzlfRJJoVwMqFZ67ygC8xf2\nnws9LErpk4H2oqWNNY9S0efild786CDz3DPvg4/3exWQLruhnqIS3aZSHdbfpdJIkuFCrWM6SBMD\nXQeQqrjUhgZndulh6ZuhFBET+L+BdwALwB+JyMeVUl/tuutvK6W+/dQX2IVS2juq13ZCpFt5n0o5\n4PK13kKYcikI7UQX0dWt3ULUIsL5i4mdM2OlxdPHJ6PPjOv1gI1VTxuvhBYkn56L/lKKCPMXEtxp\nFvMEjWn1GWPXXjalFMv3XIpbO0UhtqULgMJaUHwMPj35zbxy+aI2XmJw4dWvcPnrfwJKDw2eagiN\ntPdLHgmRPY0kQGAZ1FIWqarXW1wwdricSXYzj+04FKYmCdrWkCq75INMjwCJMoTa61/LoxtfOLYD\nueNGe4D1+sHzn8mUYFqCFzEeTSnYXNOKTD37FJiYMo+Uq94v1YoWy+gJEdcVlVIQmeqIicazTRRe\n7wml6pwj6aYs8tMZxlcq4SefSmsy107fKT52+ulRvhl4RSl1A0BE/h3wF4BuQzkQVCtBh5Fs4nmK\nUtHvkYmzLKEeYimV0iEp31dsrLpsN3oicyMmk1M2E43LXtRqAXdu7IxPcl0d2p07b5PNRX+syZTB\ntYdTFLd9PE+RThukM7t7h4W8R7HZvN4W1ru34HDxSq9x+f2JR3k1e5HAsHSsALh77bUkqyXO3Xm5\ns0r2Te+Aj52uhuX6fJaZO9tYbsPwK11cUDpgFd7Q9jbf+rFfJpfPExgGSoTf+/Pv4PZrHgHAjMjb\nBWJSstLH6u0kEkakB3gYgyUinL+U2LUSO7JCW0G9duBdHopqJWJ+Z6CjF2fFUA7SjMnieIqh7XqH\np6gAL2HidikDlcbSiILR1UpvZagB7hnLRUbRz6rXeeBu2/8Ljdu6eUJEviginxSR10U9mYh8n4j8\nsYj8ccE//kbWek2FS5UFUKv0/lLHJ63QvF0ypRVK7tysU8j7+J5u1i5s+g1Pb39FEWtRCilL7p7P\nYRjCyKjFxKQu9NjrgB2mwAM6j9VdHBQgvJi7hm90GuvAsrnz0KMArYNXv4SeA8tg6coIKxdzrM8N\nc+/qKJtzwwcTWVeKd/67f8/o+jqW55FwHJL1Om/9xH9idG0NgHpEKb8VuFys7N6+clAsS8iNmj0v\nQYzD5z+TSYMLl6NP2tr7djv2Kbv30gaBIr/pcu+uw9qKg+t0/n5cV1Ep+6GFZ91YtiAhRzGR3urw\nQeXx5x89vZ0pRarsMLRVx4royXSTFuvzWXxTWlWq9bTFyoVc6G+kNJpCmZ0lagrwLeNM5yXbGfRi\nns8BF5VSJRF5Gvhl4KGwOyqlfhr4aYDXpEePXIIXBLpa0zBEy28lBEOgW2RCRLdFdJMZMrX26orX\nGribShucu5CgXGoIkXeFixxn/+GiqHYCz2sU/hzjidxubSt6OsXO6/fExA87cgFuMoVpwfSMrUOu\n/RR6FulojD4oU/eWSJfLGF2WwvB9XvO5z/P7f/4deAmT8kiSoa16K+dj2YqRUomrpbshz3o0ZuZs\n7IS05j2mMwbTs/ahR5wBLC0evG1IBEbHwg8tvq+4faPeUeWd3/A5f0m3FS0tOJRLO2Hk3Ki5a1Fa\nNqeHAfREf0VvU0pR2g6o1XzshEEuZ0a27/SDg/QNHxXL8Zm5s40R7JzhVLJJNuaGegxgdTjBwvUx\nLCdAmYJvRX+HlCEsXRphYqVMqqybPyvDCTZne5/3rNJPQ7kIXGj7/3zjthZKqe22658QkX8hIpNK\nqfWTXNhW3mNlyW19xs0mbcPsNRpiECkGPTquhaKdusI0dxqta9XocFGttj9DaYasRS8I7t2tU60o\nDANGxy2yIwauA8mkHKrZO5s1yG/2nn2aZu9Zu608hrwqJbsrMaEUk+V1rl5PYZhyPHnJPpKqVFAh\nBwFDKYaKxdb/mzND1DI22XwNCRSbuQRDP2hi/uDxy9aJCBOT9pEEH9pxnWBXUfUozl9ORHpzG2tu\nTyuUUrC04DCUNSmXgg5Pdbvgk0hI5BguwxAuXk5yb2FH0cqyhXMXdK7+5it1PK8xHUe0bvKlK8ev\ngnRYTjOiMrVYxPQ6NX8yxTq1jEU5LO0gsm8Rdj9hsnoht/PBdf02JFAkqh7K0EVzgWm0qmfPAv00\nlH8EPCQiV9AG8t3Ae9rvICKzwIpSSonIm9Gh4o2TXFStGrCy5Hb8WIMAFu7ofNzKPZdKWR/kUmlh\ndj6xq/h10yNtx07ocFG3sRQj3DsNI5ES3XbRjYJKWd/u+7oCcGNNG3ulYChrcG4+gRygwnNiyqZY\n1GHi9t/B7HxvVaMAb13/LL8x8wSemI2JHwGm8nnr9hcxTBmofMxhWZuba/VutuNZFgtXr+zcIEIl\nl6SS28nlfvGTGb7Y1Ws5iOwxyjIUMSC6rhhK272VuaAjIduFcNWi/Mbu8yqTKYMr11O4ri6ga54M\nrtxzOlqTlALl6zaaS1f7rwqTeuFZ+ODp7Mt0fSzH7/lkDAXZfC3cUB6GkJPHoUKN8ZWy3tz2+dbT\nFuvnhvHtwc9j9s2kK6U84AeBXwO+BnxUKfUVEfl+Efn+xt2+E/iyiHwB+Eng3eqwo+P3SSEfIc8V\naOm4C5eTPPQNKa6/JsWlq/tXOWknmzNDR7EZwp5z/UAXENWqB3sbmmo85WLA+lrv3MrdMC3hyrUU\nUzMWw1mDsQmTy9eTDA2Hr/VSZYln7n2Ki5Ulck6Rq6W7PLvw60w6BR576uChvEGkNjzEV775Dbj2\nzgHcM03K2WFe/cZv3NdzDPoJQyIhHHAKV2u8WxQRUXn90Iiv9H5kHQFs2+iImBS3/dDK81pV9V0g\n4SMffg8/dIqphzBh8ta2EzykJqoe4ytlDNUQ9mDnkqx6zNzdjv7gB4i+5iiVUp8APtF120+1Xf8Q\n8KHTXJMfUUCggKDxgz1qI7NhCBevJFladFoGL5UW5s73NuK3EwSK5UWXUjF6fNJeKAWFvM/UzAHX\nbApjEzZjE/u7/2x9g6eWf7vjtiO1gihFoq77V92kORC5jz/5lrexcW6O13z2cyRrdW498hAvfvMb\n8BI7xjNR8xjO1zD9gEo2STmX6Fh7c67l5z/Z+VNUwEpqkqI1xGR9kzG3yGkjor+Ti3ecjkhCUwAj\nDMvaXXB9dNxkLUQrNpUWAp9Qybv00MGsdbnos77W28fcTr+/PV/4+PGMgdsvXsIkMASj6wQhEE5U\nFi+bD++zBP0ZmG5AsupRzwx20c+gF/OcOsO5nTxJB+rgP9jdSCQNLl1Ntc5sTVNQSuE0et7sRO9k\nhZWloxnJJmEHOd9XeK7CsuVE5igeRVQgWXGZWizqM1+lNS/X5rP9F4gW4c7DD3Hn4dD6MobzVcZW\nK62BtamySzZvsnxxpGO6+9PG+/nEUzvGsmom+dVzb6dkZfTrFeFCZZk/t/K7mKG11yfH0LDJletJ\nCnkP14GhYYPsiJ5KsrTg0BrcIjq8f24PwfXRMYtaRYvDN62VZQrnLiRxnYCF207H99swdPHXftkq\neD3Se92kM+Gi9adFXyIJImycG+4YoBwIeLbB9vjJhaENP2wOSifmETSWT4vYUHaRy5kUNjzqddVx\nFj0+aWGFKPAclaZRqtX0iK1mg7dl6YKEZg9cEKidXsYQpBHPCCsS6iaT2TH4epal1gdtVhqOjJlM\nz/ZWGqpAUSz6VCta4GBkxApVJQrjxR/5S4fKxxhewPTd7U5tVi9g5u42C9fHTkX78jCIHzC2WunR\nlLXrPkPb9Z6c0NPG+3nh+c/we9/7RV6YegsFexglO6HthcwsXxx9hNcXXjytl9DCThhMzXQKWWSG\nTK49kqZWC6iWA0xLpw32irY0vdSJulZ5smxp9fHatsmlq0k21z3q9YBU2mBi0tp3AZpSKrRtqolh\n6MvcfP+8l36mHmpDCe5dGWW4UMPyAmoZm3IuSWge6Biwax52Iwq02x6c1OCbocFf4SkjhnDhSpKt\ngkdpO2hVjkbl446D5oitdk/PdbUS0NWHU5imtMK+oWsWmJqxyY2YOI5i5Z4TOWDXMLRGZ5ONNa8l\not2uOGRZ0iF84Pt6bmJziLQIbKx6PTMHw0i98Oyh8zFD2xGDapUiU3QGdgJBsurpqtju9hEFQ9tO\naPHE2z/2Vj75h3+Wn3n33Q4jCeAZFl/NXeuLodyNVMo4lKB7ImmEVp4mU8aB5faa+F50SLhZfDY8\nbDSMGsoAACAASURBVByokO04OTYVqiPgJ0y2pk9eKsd0fWbvbCFBp5FsN5rNKSJnQSA9NpQhGIYw\nNm4zNn46+wubUQj6GFvc8hkdtzAtPanBDzkhHRo2GJvQH2XaEi5fTzXGLGkN0PyGR62mSKV1ntFu\nK93Pb/Tmi5qVhu2GcmPNbRnJ5n2U0hWEV65Hh24ee8rj6SMULZheEJrjEEWouPmgoDVlQ5SZgGCX\nsN8z/1OVS7YBIZ+zL6f7c3WdYOe7kxLGJvbv3YH28IrbPpXG9JyRMfNEZ1Eauxxv7YR0DDvvB3/H\n3V+R1/2AbocK9yQ9AwLbpDh6cDWsfhEbygEgasSWUrTUSUSE6Vmb5UW3J4czGZLDaYbA7IRE6r/q\nuYXha+ouhChuhZf1u85ObjOMp433h+9gn9SG7NCCACUMdAFAPW0RGIIEqvOMWqA4Fn1wCCyDmmGS\noPODMZTP5fJCxKP25nZmjj8Yf5RtO8uwV+ZNm1/i2i7PV6sF3LlZb4XyqxWt0XvhSnJfHmQQ6AiE\n46jWc2xueMxfTJxYdEYrTplsFXqHiU8ecITccZN64Vm+8MHTLeDpJ92DmpsoAzbnslSzZ0so/ex0\nfN7H6BxN7+1NwfImuRGL85cTDA0bOkc4anLpWvJQLSr6+YVkRIViMtXVH7lbtCpi23EULdQytjY6\nbfsIRCuHROY2AoVV9/rrcYqweiGnZcAMITC0kSxMpvc08Btzw1o6rPG/FXik/TpvzH/5UEu5nZnj\n12eeIJ8cxTdMthI5PjX9Fl4avhT5mNV7Tk++Owh0b+J+KGx6OHXV8RxNYYGT7PCanrNbUn7SKDCa\nmrHIjvTPmzztVpBBwEl1/mZbKHr0Ys8CsUc5AKQzWpi82jViK5UWMl2VtpmMSebS8X3RpufsnkpD\nEX17OyNjJhtrvWHaZEpOpMipfTGrF3IMF2oMbTkgUBpN6iKEEIY3q4ytVfRD0VJaG3PDfSn6cZMW\ni9fHSFY8jCCgnrb3pUbipG3uXR1luFDHdnzeeeOzPFy8RUIdrhDkDyb+VI/2rmdY/MHEozxcuh36\nmGpEn26tqnPgU7P2roU72xGFZ4HSusndIhzHhYgwey7B9IzC8xW2JX3LSTY57VaQQaA4liKbr6GU\n6shJ1obsM5GT7Cb2KAeA5oityWmLRFL3oU1OW5y/pOfpNdtGokceKYJDNlBnhkwuXkkynDWwbWE4\na3DxSpJM1xiwsQmr5fmK6MZxy4Jzhyy8OBAilMbSrFweYeXSCOWRVKiLmy46jK1VdpqbFaRLDuPL\npZNfYxQi1IdsqtnkgSS7fNtkayrD+nyWf/O2dx7aSAJs2eFDrCtmGj/iELCbMMBWwefe3d09y8gI\nhNr9uY8Lw9RtTrVa0CO6fpp85MPv2ftOg4xSGF6wq2BBGIFlsHx5hNqQjRLwDaE4lmLtXPaEFnqy\nxB7lgCCG1rPsluoql3yWFp1W1WsyJcxf0HMgg0C3djSlv+yEMDNnHzgHlEobzF/cvXrUMPTYpVpV\ntcr6h7N7D28+TUY2qj0DZw0FQ0WHTT9AmWf3vDBKmKAdpfRnU9z2MQwhN2KSSBoMuxW2E70HqFRQ\nxyDciIyOmhTy0UVmlbI2QFHFOaPjVmg/o2kJiX3KNB4WpRQbax6b616r5Smd0QMJTqJHOIrHnvJ4\n7oS8yWTFbQ1NLucSepjyMf8W08U6E0tlLaIOlLMJNhvRGQkUmWKdRM3HTZqUs0lU13vrNfVf7wPO\n7pHjAcCpByzecVoaq0rp0Nfdxjiu5UWnQx/TdRSLd5zIySJHRUT3vI1NWGRze4/nOnGU0me6jTfA\n9MJ7aBTRsyHPEk8b748cyaSUYuWey91bDvkNn401j1uv1ilsurxp80tYQadHagUeb9j8SmR/2+SM\nzdBw9OFBJFxFp0lmKHw+5gkrUAJaT3ZzXacJmtKNlYoWSDgtHn/+0SMXskUxslZh+u42Q9sOQ0WH\nyXslphaLxyoFlyw7TC2WMBvFaII+4Zxa2MbwAs7dKDC+XCaXrzG2Umb+Rj5ybNf9QGwoB5jCZrju\nrOspysWAUrG3ElUp2FwfDD3VF77jMyfzxEoxulrmwkubXHhpk3M3CqRLDrWMHT4zVATPPoavulJk\ntuvkNqqkS87paVS2nQy8/WNv5YkvfaDnLtVK0JMXVApWlz0ub93hv1r7LBmvqucR+nXevPEFvnH7\nlchdGoYwfzFJbjT8fVOKXSdwbBf8UAdHBbSGCpwUGxshogMNLzhKovK4+ZMr10/keU3HJ7dZbemm\ngo6apMouqcrBNJx3Y2K53HObAKmKx/hyCdMLWtEbQ4Hhq/6mOE6YOPQ6wDgROUmAen1nZl/P4+qn\nk5NRgR5mHVXUUf33nwPj+Busx1bKDLfNeLTdgMnFIhtzw2RKLgSdBQT56cyRw1KmGzB7e0tLcild\nwerZJiuXcgQnFNJNlV3Gl0tYbqDbSkaTFKaHePJHq/zTF56l9vZfat03qngGdPj+NdYtHindIsDA\nYG9ZsSaTUzal7U4xDBHtMbpOgGEYoeHM9p7bdpQifOrNMRLWa9za5qt9q0kdlqMIbOxFOsIYitI5\n+trQ8dQMWG70dyRdcnu2NY1oS43kPiP2KAeYzFB42whKa3BGHRhTmZP9WD1PsXinzktfq/Hy12rc\nvlGjXjsd4yy+6jCSrdv/f/beNEbW7Lzv+513q33rve++zHCTuIiidsYYWktEUjZjGlZoBbEAGlBs\n2ZADKbDHNJBvSSSBEhIDjkMmICIrESwZsmNG0liQnKFlikNREk0OKa6z3bX37trr3U8+nKrqWt63\nunqpru573x/QM31rPbX0ec55zvP8/xLyVYeNWyVaRQvP1LCzBjvXCmdiITS4ihZ05ejcgKuvHLD6\nRo1082zTepbts/ywjtmdsDQJharD4oZatf/8x9eGCkVi5yZxeJ0A9GMESVDydTdup/rfRU1XPqSt\npjoWePWbNrvb3lhKNRP33UWdictQ4nmS8CReXkeQi9FkPo6N3UmZZZAE5eUY9wFOErI4LnLCQ13+\nQ4zjM3FGFUIUhRB3Iy6PPihJOFPK5a6W6sCXVggolnTSGY1SRR+bjISmdGlnhZTqjLTZOAyMdkc1\nl59HWkuP6Y0UqMDlWzp7Vwo8vlth60bpbFbYUpJpRa+iNQlp22f5UYNc1T79c3Up7rbHRBZ6hUla\nV0T6y58u94NlqWxMXFSdhlRa4/qtFG96W4Z0WusLoffO//Z3fSVyPkChqCsRipHvbjan0WoEfPub\nNq9/2+aVb0QH2tOwuGKMqfQIAasR+sVnza99a7ZKM518jHiIQFWDnxGNYmosIEog0AWtcmqsR1IC\nnbz5RO4mYUKgFEL8JPAN4LeFEH8hhPiegav/z1kPLEGVuN+6k6KyoGOaShxgZc1g9YqqjF1ZM1la\nNTBMZQSdzWvKvX2GMmGddhiZOpNSOTfMmiCmxUICbnp+/VmaRPVvntGEb0aY7IKaEI0Bt4Uvf7rM\nxz74s6QzGgtLxmH7TvfnLCs9fV/SaY8vVKRUqjuDaJrg5p0UlYqOYYBpChZXDLI5ofpxw8MCtf1d\nn4MzPFc3TY3bd9NUFnVSaVWdff2WRbE825Omj33wZ2feMyk1wfa1Yl/EItTU8cL+au5M+xNrqzlc\nS3nV9H5CAZs3ilSXc3iWrkQxxKELyd5adBvSk8Ckb87HgO+WUm4IIb4X+HUhxD+WUv4b5m/n9tSg\nG4KVNYuViGyOEIKFRZOFxfOT53JdGZl7kZIxIfYvvWDwqy9unmkqSmqC+mKG4kgriFK9yZ7Z8wwh\nBHbWJN0e31UO3SyUaIEkPOIMzHR8ins2puvjZEzqC+kxl3c3bWC67vjzSfAiCpM+9sGf5X/83f+V\nUlmn2QyVCXhRP9N2iEm9umFEnNN1JZ+4sn542Svf7EQWoO3t+SycocycYaq/m/Mi/eKHT+SOcxKc\nrMmDZyrq+yjBzhpn3vokNcHm7RKpto/l+PimNtSCsnnr8DrP0rFzT+5uEiYHSl1KuQEgpfyCEOJ9\nwO8IIa7zdKapEyBW57OnJDTKW375t+CMy+RrixkCXVDas9GCEDdtcLCSxZvGrkdKCgd2V7RZ0slb\n1JazsTvVHnvrOdbeqKGFsu/nF0XYLWzS/RDDCfAtbSgIploeKw/r/cew7IB8TZ2tDu4IaotZsg1X\nNej3HltAo5yOnRSn6bU8DaalMhcyogsgO6GVZJC4QpswUGn9ubccnYDTCv+fCE1gx6Rhz4yuWIaT\ni1jATLruCWTSt7sxeD7ZDZrPAR8CvmPG40o4R6SUeF44lbpPOqORzowXaug6lErnVETdVep59EyF\nB29eZOtmCTcz3R/s4kaT8k4b0wsxuoVBa69XEUfowgamzuO7FfbX8rTz5tgZTSigWUqBgMXHDa68\nesDKozpXXquy1Otxk5LFzeZQab9A7UQr28Pl+H5KZ/NmCTurNDN9Q6O6nKW6MnnXPKnXssd2aoEv\nVN7OF8tvpWZMb7kkhBK0GPrshfrspxUdj9MWjjIqvyx84x/+5LyHkDBjJs1sfxfQhBBvk1J+DUBK\n2RBC/DjwkXMZXcLMqdd8tje8fvl/vqCzdnWyjue1mxa724eKQLmCzsqqOVfX+GnQ3YBswx1K2QpA\nCyX5qk1jcXIQkpqgVUrRKqXIH3So7HT6Z5KtUoqD1Ryl3c7hc3SfJ9N0KW+3qS1lMLzxgNwvrR/B\nSxts3ygd+3WK7/lR4OXx8QOfXXo33yrcxhc6GiFfrLyN9+5+kbc0Xp/qsYslZbV1sOvjeSHZnEZl\n0Zxa73d5zeTR/Qht4bXLuTP5wa/8As8935n3MBJmTOyOUkr5ZSnlt4HfEkL8I6HIAL8KnN4WImHu\ndNoBm488guCwsKLZOFrHU9PU+c8zb8nw7FszXLlmxdpsXSQsx4/MmWoyOlBNolnJ8ODZCo9vl3n4\n7AL7a3kQgsKBHSmjV6jaSpg9rrT/DIW7n3u+o87MRthIL6sgqRkgBKHQCTSDzy59Nx1t+jReJqOx\ndkW5dAQ+1Kv+1BXPubzOtZsWmayGritpuWs3LfKFyyeUPasgqfkhhf0OpZ0WqbZ3fsIWZ4WUmI6P\n7j05Sj3T5Mq+D/gl4HNAAfi/gR+a5aASpiMIJK1md1eX14dW9UGgvCYNg9iUVpQbSE/Hc5LH5HH4\n0gsGfPDUD3MmBKYeXYgEeCepGBSCYOR+WkxfYK/Vo1VIkW0M94GGAuoLZ9tW8PMfX+Odn/gp/sv/\n5jf6l72av44foUguCHmQXY91EhnF8yT3XrO754pqR7i343PjznSWb0qI//IFxlH+wec2gLOtck23\nXJYfNgD1nSnu29g5k52rhfkUy0hJqtMt2jGPLtrJNFwWN5t9EXU3ZbB7rXBkDcBFZ5pA6QEdIAOk\ngdelHHWqSzhv+ju/3ndWeiyvGRSKBhsP3X4Zv24I1q5EC6XHKaQIoVoBzmqX+HvhP52Z7uVxcFM6\nnqVjjZjKSgHNCWbKUyEl+QMbKRjrf4Ru64oQ7K/l0IJQyY11b9sqpSaaOZ+UL3+6DAPBUutaHo0O\nTwBaTH2eBL5WvMvLpTfj6hZX2lu86T99dqgop5eN2HrkcuPOxXGsl1L2F33pjEZqCsPpafnYB38W\nPn1mD6eQkqVHzeGjga48Xa7u0ipNNi44a0QoWb1fw3S6O0MBga6xebMU6YRjOj5LjxtD40/ZPiv3\n62zcLl3qqthpvjl/igqU3wP8Z8DfFEL8q5mOKmEiQSB5/ECd88iQfk/azqbP/dds2q2wP3n5nhJK\nj5K1y8Qo+EjJzB0e5kLX27LTtf6RQrVabF8vnroHrbzd7lt8wWEw6vWf7a+qohmpCXauF3l8u8z2\n1SIPuwVCs5pEen2WAM8276FHrHElguvtjcj7//Hid/H5xXdRtwrYeorX89doNaLXyZ3ObJR2ToLn\nhrz2bYfHD1y2Njzuvebw+IFzJsIGUVq7Z0Gq40dm5jUJudrpxSxEEFLebnHl1QPWX68qgYwJ70d5\nu43pBH3bOi1U0naLMZquhQN7bJEoAMMLsOzLnYadZkf5t6WUf9b9fQP4kBDiv57hmBKOoNmIccmQ\n4EVIQUqpBNZX1ofPoRaXDBq1YEzHc2HJuPCFOSclNDR2rhcRXc3WUBenDlJaEFKsDk8SvZ2bZ2ns\nXBsPxIGlj6VtT4LuBixstci0PKSAdjHF/kp2rIWk12f5zuo3+FL5rajwKJEI/vLWS6TC8S9OR0/x\njeJdggGZGyk0Qk1Dj5n3Lsqm4fFDd8y/tdkIqe77VE7Rd/yu9/szLt6JCVynfGNFKFl/ozYkZr6w\n1SLV8dlfjxYKyNUjpCJRWq9Rmq56jD6sFKpd6jJzZKAcCJKDl/36bIaTMA0nSXxHWSKZlsbNuyl2\nt33arQBDFywsGRRKl//86CikHpdsPD6GGyCFQIysznuTRq7mkKs7ADTLKeoLmTOJKCIIWb9XQwu6\nVkgSsjUH0/bZvDWe6ur1Wf7RH7zB/ewVdBlwq/WQTBhdvLVvltBlQMDw92Hz+jNcfeMbaOHwF/Eo\nf1IpJY6tNF7TaRHrZXlafE89z/jzQ/UgOFWgzP7yP4IZBUonYyDFeHK833p0CnI1eyhIQnenWneo\nL2YiMypi0l+IZKwwrSfKEVXM5mYut//G5R79JaDdDtjd8nHsENMULK2Y5IunC0RxPoFxbiI9jc0o\nLEvjyrXZNi5/6QWD33v/xTinPGss21dppYiUo0StpHu2SACl3Q7plqcMbU8ZLHM1BzHglALqLMV0\nA1IdHyc7HhA+oP0cL37ys7z00fH2kVEKfosgovjnjTe/i5W9h6TrdXWBUBJ1a1fiv0e+L3l4z8F1\nZP97WijprF05nv6qlBIZKk3juPtNSq+eprpiUpXr0uMN7n71L9ADnzfe/GYe3751/M9XCHauFlh5\nWFdCE1LtxtoFi3bhdH+j6bY/FsB6WLYfGSjbOZNcY1iNSgJOWoeIKu1mOUXxwAY/7J/p9UQynoZi\nnoQT0m4FPLx32DPmOJLHD11Wr5iUTqE7aVoaqbTA7gx/8w1TCQI068M+lZoOpUryUZ8lIpSsPKhj\n2arlpLcPGJ1URPd8p4cm1VmUZftTiyTEYXXPj6IwnSAyUILytPzMV36Uz739VyY+ftFvsWbvspFe\nJhxIvwpd48rtDLmag2OHWCll6D0p4G08cvu7vN53s1ELSKfF1Du82oHPzrZH4IPWFf9X+rbDz2uY\nAt0QY6lXISBfPNmE/QOfekdskHz7517iHZ//AloQoEnJrW98iwfP3OU//sQHjh0snazJw7sVsg0X\nPZDYORN3GsWpI/BNLWoTCMTrJ3uWgarlHHmsmCMDqWts3C5R3FO9xKGuUV9InzrIXwQud5i/4Oxs\njRvIStm7/OSJP8cOI1NLngsLiwbLqwamJTAMKFV0bt1Nn6nm51yREqvjKzd1KUm1PXLddON5Utlq\nYdl+v8ihX3zc/fFMjU7ejA5k3WB5WtyUPqYQ1MNLTc5axPVajvJjm3/M7dZDtDBAkwF5r8mPbX6W\nJa9OJqtRXjDI5vSJQTIIZKRZs5RwsD9dkUejHrC14fWrbcNQtaREmZQLIVi/1lUQEr3LVABdPKGe\nbJwRc65e5x0v/QmG76N1/6ZNz+P6K6+ydv/BiZ5L6hqtcpr6YuZMgiRAs5wes86SqCDpxKRFCzUn\n0jEnV3cp7EUbAIS6RnUlx+O7FTZvlWgXUxfn4PoUJNuMGTIqEt4j8FUKSOjqPMX3JVZKTFTDGaTZ\nnGTSG7K4bJ7qHOaikq07Xed1OVxW2n3bnIzJ9rVCZFroTJEyttAhFPDwmQpSExSqNpnW+JkNWvwq\nvv9YQUi26SGkpJMzx0TTQbWVlPc6yGDAqBrVExo3+Q0S1Ws5iiV9fmT783hCxxcG6XB88jwKGRLZ\nlgJMXSW7G7Po3N/1I3eV2azO7WfT1A58PFeSzWkUSvrUf2OD/OYnfoovfzy6X/LK628oIYmReK97\nHte//QqbN28c+/lmgW/p7FwrsPi42e/19VL6xP5MbYKlXXm3g+WE7F15ch1DBkkC5QwxDRFZRKNp\n6hzl4T2Xdivsn9ksLhtTrXg1ISLPI5W10uVfvUVh2j6LG8M9Zv0Y2b0s1fEo77ZxMqY6FwxCOjmL\n+mImsu/rNET1SvYu71WctoopygMyd72hSiFoTxC0zjRdpQ/bpYJyRmksZoZuJ3WNjZul4arXgqVa\nUab8Hoz2WsZhygAzSg19CnSDyFQoQH5Kr0wvRvknDNWPHvEwvZqA0/ADn3oHH/vteFEB3zCJSmhK\nTeBbU6Qcu/23hZoDElpFi8ZCRgXfM8bOWTx6poLhhUhB5OJrECcT75ijScg2HKpe5sjHeRJIUq8z\nZHFl3ExXCKgsGmw+9vr9jj0D3L2dcQPcKAoTioEuasXql14w+MwvZo6+YQxxPVqDaFLdbulxg3TH\nx3JDigc2669X+2bHZ4IQytpo5GIJSrmkS6hrbN0o4pla37fP7Yqdx+16RRCy9Khx2LvW/SnvtiPT\ny4Gls3O9yP23LPLgzYvsXSkc23JpsNdyFgghWL86LKYuhAqg0wayVExfr66rheeseN9vv3fi9Q+f\nuRN5udR0Xv2Otx75+MuPGlR22lhOgOUGlPY6rN6vzU62Tgh8S58quHWyah8VOxIhDsUInnCSQDlD\niiWDlTXlti6EqtRbWDIoL+i0mmFkKmlvJ6IRcgTDFKx1Jx6h9SoAYe2KiXmBNVfb//CXTnxf3Y/u\n0RpltHimJ3peODh9w/Yg+6t5ZZ7bHVQolF5rT1igh5s2eHynrH7uVti8XZ4obpBpRn/+Qqoq11ky\ny2CZzencekaZkOfyGovLBrefSU+t/rS8ZkYuOpdWx9OuR+G6IQ/vOXzzLzp862sdNh+7kc45R7mw\nAHipFC/+tQ/hmSauZeFaJr6h84Uffh/1xcWJ97U6PumR1LwmVSFW3PfgvLA6PuW9DgPHvONIiR/h\njfokkqReZ0x5waRUMQgDugFT4LrxuxvPlexue+QKOplM/JewWDLI5XVaTbWiy+XP1qT3otHJRfdo\nDRJ3lSYh03KpLZ+dsbOf0nl8p0y+amM5Pm7aoFlKR6d4hZg6PTWpd220T3MWzNLT0rK0MdGLacnm\nlJj69qaH68h+WvW4GZQgkNx/zSHoboSkhHo1wLFDbtxO9YPuD3zqHUfuJnts3LrJb/79v8vV199A\nCwI2bt3EyRydPUl1vMgvrSYh1fbozKNaVEqyDZfydiv2eAHUWbibNvBTT0cIeTpe5ZwRQqAPvNOm\nGW+AO1jNVyzprE7oM9N1QfG8PCDnTKucpli1wTtsmu79HfeKaEKhJpnRP3AJM1n5hoZGfensgi9A\nJ2cBrbHL1fnj+Wh9fkD7OV781HS9ludJNqdz6+7pjhZqBz4jOglICY4tsTuSTFYcK0j2CEyT+296\n9nj3MbTIKqdQHF3sNROkZPVeHcuJ77nsXdwpWOytjXuZakFI/sAm1fHxUjqNSvqJOMN8OvbNFwwh\nBCsRqaRBpIR6LYgsq38akZpg42aJ2mIGJ6XTyRrsreWoLqZpFiyqy1ke363gpSLODgVKDecSEBoa\nBytZQnHYahIKVRjkZM9vUfS+337vzDRN54ljy9jjv54eclwryFnTzltILTqHMJUAupRk6w5LD+ss\nPWqQbrmnOtvM1ZyJQRLU9/Hh3TK7V8fPwnUv4MprVUp7HbItj+K+zZXXqlid+aaRz4K5BkohxI8L\nIb4phHhFCPF8xPVCCPFPu9e/LIR49zzGOQtKZYNrNy1yeQ0jZv7rpYWeFL70gsE7/2r1xPeXutrB\nbd4us32jpHrNlnPsXS2oSkFdY/taASdjdM8Mu+eGa7lTN/fPFClVsVG3bL9ZybB5q0RtMU2jkmb7\nepH9tekrWc+KaXstLxOptIh9G62Uxm9+4qf4+Y+vHf1APdeB06AJNm8U8UxByOHCqFFOKQ3iSXf1\nAq6+csDS4ya5pke24bL8oEF5u33i4Yyamo8SClQFecwOsbzdRgtk/zEEKsOjWrouN3MLlEIIHfhn\nwPuBt6FcSd42crP3A892f34G+OfnOsgZo85dUqysWzOt3LtI/E//z7+Y6eOHhsbWzRKP75TZvFHi\nwbMVWqWLY/00SqbhcvXVKtdePeD6t/dZ2GhCKPFSBrXlHAerOaWwM6e2n5//+NoTFSxLZYMxVT4B\nqZTg+z8cqHaZQaRE9wJ07zCzkz/ocO2VA258c5+r395XLhwnxLd0QkPvqzsJoFB1lCdlXCCWXYHz\ngf5ZgZrMCwe2EuM4AXG7Wwm4ls7eep7aUnxmJtuKbiUxnQAR05N5WZjnAdf3Aq9IKV8DEEL8S+BD\nwNcGbvMh4F9IJWPzeSFEWQixLqWM9gS6pOTyWqxGa7F8+fP78yAwdYIjNpGGG5CvKrHoTr6rp3mO\nAcnqeEP+fUr1xEGTkt0rhSPvL4KQ8m7nUHC9mKK2lEWecVHXNMIElwXdENy8nWJrw+v3MBeKOivr\nJh/U/97QbS3bZ+lRo+984Vs6rYJFae9Qu9cIJAtbLXWGfIIFWbrl9RWeemgS0m0vVq+3J28X9ymn\nWx7NEzjTNMppMk136IxfAoEupvKTDDWlUhWFvOT93fPcx1wFBjWeHnYvO+5tABBC/IwQ4s+EEH9W\nDaLdEI5LGMoz8a87Ck0TXLludQUD1GVCKPm5ODHzhNORabisv16luG+Tr7ssbjRZu1frO7OfB6Xd\nzljhkWrkdo/u+5SStft1FegDiR5IClV7Zj14s+61PE+slMb1Wyne9LY0z741zfo1i+/+ieFdmBaE\nrN6vY3aLx3ptG+Xdzlh6UvW5nsxRJNXxIqtLRbfyNQrziB3jScUKnJxJbTGD7B1bCGVDN62Af6Oc\nHpNUDFEiGDNXy5oxT0zJpJTyk8AnAd6SKZ9qpmi3ArYee7iucjooltSK8yTyV9OSL+jceVOa4b7T\nFgAAIABJREFUZj0gDCW5vH6mjuwJA0jJ0ojKT28izFdtGudU+GO6wUT/vklqQpmmh+EG46/BDUi3\nPOwJyj+noedr+SQwqRUkV3fGFhxxMnygDI3PmrjH9CwdKWLUobrqTCelvpSlWU6TbnuEusA+Rtq/\nvpjBsn0yLa//ZnkpPbI69rIxz5n4EXB94N/Xupcd9zZniuOEPLzn9qXnetWnjx+czS51EoYhKC8Y\nLCyZT2yQnEV/3nGxbJ+oKU/5883+c+7hZMYrdAGQ8Q4NPSzHj92JWDMWiP/YB3+Wd73/fEXoZ4EE\nVv5yjh/7je8fC4q6F04sbBnlpO1HqVaMwAQgRvtYurTzFqE+fJ7YKwTavlaI3VGKICTTcMg03ImZ\nk9DQaBdT2LljHkUIwe61Ihu3y+yu59m8WWLzVvnYSlEXkXm+gj8FnhVC3BZCWMBHgE+P3ObTwN/q\nVr9+P1Cb9fnkwa4fqZjTboV4E4QCEqbnxb/+2bk+vxQidmsQnuNfRG0pi9SGhxJ2W1mOSp/5pj7m\nBgFqN3pUkD0LPqD93FTKNReV7dQCv3HjJ/jlrb/C2hs1rr5axRpwdOlVTo/Sa9cZJBRwsHL8XZPh\nBqTsmKwC6jOORBNs3izRyZv9AOmkdR7dLePkoneT2ZrNtW6V7NJGk2uv7Kt2khngWzqdQgrvjJxP\nLgJzC5RSSh/4+8DvA18HfktK+RdCiL8jhPg73Zv9HvAa8ArwvwMzPyRxnBjFfEGkwHnC5cNL6QSG\nNhYrQ6HsiM4L39L7E16gCTxTY381N7GysEe7MN6DJ1HtMJME18+Sy9pr6Wgmv3PlOZpmDsdW7QyG\nH7L6oN6vzuzkLTxr2MYsFOB0+3e9rr+ja2nsXimcSEUnHXMG2aNZif8uBqbOzrUi99+8wP03L7B1\nq0yga+RqNgsbTYq77f45t+EGLG62DrWDQ4kWwvLDxqWvRj0v5hrypZS/hwqGg5f9bwO/S+Dvjd5v\nlmQyGnZn/LBcSkilLn8KIQEQgu1rBdbu15UsXDfaNMupmZjMmo5PruqghZJ2wVLC6d2Ulpcy2LlW\nPPZjyu6uYnGj2fe2dDIGe+v5cy2ceO75Dp/5yi8caQJ9kXgtdx2hM55VkJJcw8U3dXI1G98UeJZJ\nyg5AQKOUUufXQkRWuGYaLoUDGy0MaRUsmpXJmYFA19RnNZIGlUCrYE2naNP9HokgVC0jvkoZhwJK\nex22bhRJt6ILhkAVjrXOcXF4WXly9sZnRGXJoFYNhmSuhFCuHNMKOCdMpvOvvgja8STCzho/ZfDw\nmQrploceSJyMMZOUZa5qs7CldDN77R92zpzoAzgtvqWzdbPU3RWIM28LmZbnnu/wqy9+GPt9/3ri\n7aSU1A589vcCAl+SyWosr57/eXxHT+NIc9yUWEK2apNygv7nFQolK7h7NY/uh0qazdLHCq1KO21l\n7dYNSKbTIV9z2bxVig2WnZyJFEOWqoD6d3XleNKIpb2OOlft/rs3jqXHzYmLP+0cqvqfBJIt0gim\nqXHjTopcXkNoYBjKJ3LtyuyUXcJAsr/rcf91h0cPHNqt6RuGg0BysOex+djlYN+LdEG4aHzpBWPu\n55SAssvKW7RKqZkESRGELGyplFdvItSk6nPLNKc4H5KSTMOhsqlSaXpMy4jUtbkFyR4///E1fvMT\nPzXxNrvbPtubykg5DJXJ+L3Xnb503Hnx/77rh6LPd4G0HYx9Xpmmy9q9Gldeq7L8sMHVVw+obDX7\nBUCaH1La74xVIBteQK42LEZgdTxW36hx4xt7XHv1gGbRItDFkGRhYGjHtq/K1d3IyVz3Q5y0Efl6\noactnHAUyY4yglRK49rN8xGgDgPJG685+N6hBmWr4bK8alBZnBycPTfk3mtO389SCNjb9rl5J4Vp\nPRlroFTbo7zTxrJ9AkOjupQ5UWP3rDBtn8p2m5TtE+iC+kJanXMKQbqtzJRHU3y96trOBJFzEUpW\n79cwnWAolbZ9rYiTm82izbL9vpVXu2BFNrtP4sufLvPlmPaRMJAc7EUUyoWwt+uzfvV8Jux3vd/H\nEQZOxiDVOWz0DwX4hobhh5G+p1av6Kb7AvJVB8/SaVYypDoeoQA94nPOtDyaFXXmbDo+q/fr/edU\nva8OTkofKuox/ZDlRw12rhWH/E0nERcIBSol385bZJtKok52b9+opCcvEKXEsn0sO8A3taEjg6eN\nJFDOmeqBPxQkQf0t7mz5lMoG2oSdwuaG17cL6t0vCGBrwzu3QD9LrI7HyoPDiUXzQlWUEEiaF0Dk\n3HACJVIgD30vK9ttdF9SW84ihYitaAyPOEfMH3T6QRIGU2kNHj1TOfMJq7Tbprh3KICQr9o0SykO\n1vKx99F8n5vf+jZLGxvUyxVe+4634qXTkb2WvZ7kqEyf3T6fHeVgv+T29SL5A5v8gKqR1AULMbqk\no++2JqG4b9OsZAh1LfIMsLc77BEnMJGOqHzVJJR32mzmSuNjCSWF/Q757qKmWUrRKKUo7w3valU1\nrEFo6uxdyWPXHHJ1h1ATNCqZiQsuEUpWHtSHWo0CQ2PrRongKfGgHCQJlHOm2Rg3cAY1D9p2SDYX\nveKTUtJuRk8wrZjLLxvlnXasCkqzkp776ra01+4HyR5qAu1QX8xgZ01kRJu6FEe7Q+Tr0QLVWigx\n3QDvDH0ADTegODLJCgn5mkOrnMaNKPO3Oh0++H/9BplmC9Pz8AyD7/rsH/PvfuojVJeXxnwtDVPE\nCgaZ1uw+xx/41DsQ3/OjgDpL7SMEzYXM0IJLBJKFCIuzOLTuMYeTMQh0DTFiLi6FUqvpYdn+VObj\nPSIVeKRk5X4Na2ARVdrr4KYM3O7OtEdgCHav5EFKFjeaZBuuWrxJ9a3czRix56el3faYtJ7wQhY3\nmmzfOH7x2WXn6VsaXDD0mMyHlEzcTUJ8nHhSsiNWzDmNkEqybd6kOjETnxBKmFoT7Fwr9OXAemdQ\nortbmCReHZdKU9eNX2m4AUsP61z71j5XXj0gf9CZWsou7rxUSMg0nLHLNd/ne//w/yNXq2N6qsXB\n9H1Mx+GHfu+F/u0Gey2laZIpGmPfTSFgcflsU8k/+JVfIP3ih0m/+GHe99vv5bnnO8NBMgbZlWsL\nNdF3ngmJ3v1LUKo13RexfaOIZ2kDrjWoNpKBRYab0ifYco/jRezc0m1vKEiCWpxZjkqRwsD5qi/R\nQklxr9N3BtFD2T8nr2zHLwpyNWdsoSa6z3+eMo8XhWRHOWcqiwatpjs2p5mmIJWKny2FEBSKOvXa\nyGTbldy76Lz00Zf5zFd+dOIE5psaehAdTIILoB3pWTqGF0ZUT8p+esrJmjy6U+HKqwd9dwhQQXb1\nXo1HdyuR7RzNchqzWwjUo5fKG1WB0b2A9TeUTq1ATYaV7TaGG1JdPboRXvb/E3HdSGT7jj/5Au/8\n3OcxvHGnCA2o7Oxi2TZuWu2kfvg3f5D3/8h1vvZaBnEj5G1f/iyLj+8BYOiwesUikz39ej394of5\ntW+p5/zY8x1gCqusCJysyYNnKiogSBUMU7aneg7loYyd1MRQZapv6WzcLitZwlDipoyxz7W+lCXT\nqg2lX0OhAuho8AsFVJfHK19TnXhFpsFn6/1e2R7fGYIKrvmqg+aHHKzlx4yiJ/51ydE63SefJFDO\nmWxOZ3nVYGfL75/hmKbg2k2rr0UZx8q6iWOHuJ7s15hblmB57QJ7Lw4g//QPgPg2kepSluVHjbEJ\npFFJn3mvoOEGSt9SE3S6hrpHUVvK9CfUwfG1CxbhgGxXtukOBUk4PNPMNl3axfE0bLOUItXyyPZ2\ne0IFrZ1r420lxb1OP0j20CQUqzb1pczQWEbR/JBCzYnVnB0c2+2vfZ13/vFLmP5k+bqw52MlJWv3\nanzFy6shGzpfefdzWG+3+Rv3XiAn3CO/43GkX/zwsG/kx0/0MNFoYkgr185ZbN4sUdzvYLoBTsak\nvpAe73MUYmJK3E0bbF8rsrDVwnQDpKZSs9WlDIWqo1xJAolvahwsZyP1en1Di9d5HUGgAmtcZkEA\n2aZH6o0qj+9Uhr7z7bxFfuR7Ienuip8ASbrjkgTKC0Bl0aRUNuh0QnRD7SSnmUB0XXDzbopOO8R1\nJFZKkMlqJ558Lhp23mJvLacKZAKJ7Mq7TaNcMzVSUt5uUagOpBiFYOt64UizZzdjsnu1wMJmC90P\nkUIFuIORXZzuBZHnjUJOENMWgr2rBeq2T6rjExgqgA82mOe6LiOZGB9AKQSmE+BM2LEtbTSVX+Dg\n/bo/+6u5oarId7z0JxODZCgE21ev4qfUBJ9u++gj53YIQWCYvFK5w7tq34x9rCiGguNZBsYp8NIG\ne1NYnx2FkzPZuFM+DF7dz7OxkFFiBr3y9REMNyDTUpknKQRSHi6MJsXMQBf4pqEWdBHXC9RZa7bh\nDPm2VpezpNvekIABQrB3Jb6460kmCZQXBE0X5PLHT5kKIcjmdLKXX6A/knYpTbuYQoRSrXjPeBGQ\nbnkUqiPnMVKy8rDBwymqSzt5i0d3zYnjc9NKN3Q0WEoBbnryZ+6ljTHNzFTbY+VhHeThziIyGSbl\nRLFuLQgjJ1CBSnsPKrZofki20Yx8HAn4pomTSfPZn3h//3LDi0ubG1StyUGnJ7r+j/+Lv3VopnzO\nwXGmHKPAoLjbprQ3cEQhVaFOr5jIt3Q8SyPT9MayL/WFNHbWZP1eHcJoD0tNgmkHMFBgGxoaj2+X\nyTVcrI6nvDhLqYnZiSeZJFAmXHzE7FRn8lU7ZrcnY41zx288eXydvIVv6hgDO8tQKM1Z+5i9ikip\n0tEjG9HRlxAKsHPmRBk0EcroAIt6/YO3W3+jRr28xOL2o7Hbe6bJf/wrH+TRndtI7XAijaqW7Y1t\nzd4bu7xX+PPfet/Jx3rBccQmId1yKe12MLwQO2NQW8rip87vTF7zQ3J1B90PsXPmkA2V7gVkWh4S\n6Iyk30+KaftDRtF9AsnmrRKhJtRnHEoWN5vkGm6/d7e+kOn39D6+XaKy1SLbHF8YhYLo91ATtEqp\nIyu0nwaSQJkwN1766Mu88xPfebhjmAOTznrElFWjRz+JYPNmkdJuR/kcotpDakvZiTtWEUpyNZtM\n0yMwNRrltCraiKg6FKgJr/do7YLF/oQeSFCFQaGujZlES1Rw75GrO2hByOtvew/lvS20wO+Xy/uG\nwed+/Md4+Mzdscd30wZOxiTVOdzpSCDUNX79vT/O//DCP++Lqj/3fAd+e+JwleD35mGBU67hkm26\nbNwq4Z9hu0wcqbbq6wX1vSkc2DgZg+3rRQr7NuXd9uGNt1rsrufpRJw/H4dczYn9jlp2cBjENMHe\nlQIHfojuh8pdZmDxFpg6u1fyXHu1ihYMp22lJmidcpxPOkmgTJgr/7P5Vd43oaBn1rSLKdJtb3zF\nLsE54ozyOEhdo7qam6oKFVRP3/q9at8XUaImzdpi/Pmsm1KOElIT07ncC8Heem6oolO1NwiqS4cV\nl1ZXwaZVrPDFv/QT3Prmlyge7NDOFfjae76He295NvYptq8VKO11yNdshFRFItXlLFITfOyDPwtT\ntG0AICWVreG+WqWUo1ptdo8pLK97AfkDG8sNsDMmzXJqcpFKbyc/0mua6vhK5/VgPDOxtNHkUc48\n1c7y6OrTYUJDizb8lpLlR03ESJAMNcHGzeJ035enmCRQJjzVtIoWudrhrqcn77W3np/r5FE46AyZ\nBwvUxFzatyNl8XoWYZGT5ATsnMXG7TKFfZXOdLKGepyByb3XH6hJaBfKfO09zwGHRT/XXjlgbzUX\nvXvSBLXlLLWIVofjoPth5A6/X9l5DKyOz+r9GkjV0pJueZT2O2zcKsWmqi0niNzJa11hhrhdX6bp\nnSp12S5Y5Kt25ON3jmGnlur4akE4cJn6TkkMXxIkkq8TSQJlwtONEGxfL/SFykNdm5lI+nHoNYiP\nI6ku5/rN4kKqwG5nzRNPyL6lT5Sqa5XSlPfssUrLfstLIFnaaLJp6TMz6w11LXZ3NdoDeBSLG82x\nhn0ZSMo77djK1pMm4U+bvncyBs1SaigYSwEHK9ljLYpG25gOx6euO66u79NGEigTErouIlF9a/Mi\njCsO6jbBP3qmQrbuogchdtbEyRgzk2QKDY3NG0UWN5tj6i89emd2++uHAddwXN705Ze59uprtAs5\nvvHd72Z3ff1EY5CaoFlMqfPS0crOCenoUUQQRkrDCZSfpO6HkYHXs+L1XJulFMWD8V2fYNidQ/ND\nyjttsg0Xuq1EtaXs5MyFEBys5WmV0mSaDgh1nnjchVwQ038pxfEXGk8jSaBMmCsvffRl+OB8vSkv\nIo1KhlSnMabM45t6v0KxWTls3+hXXApBO2+ebVO4lAgpqS5nlTB9119zEMFwO4jpOPzEr/062WYL\nw/cJgZvfeoXP/+gP8+rbv/NEw9hfzSG65sq9p68uZyMFG2KZsJjQJFx99YBmKcX+am7otulOEFsh\n7FkqC5Eb3fUtZw8FxEMlvjCo5FQ4sEm3PTZvlo5c5LgZAzetk6s5rDyso/kSN21wsJKdahffKlgq\nCzEa7IW6LmEySaBMmDsv/vXP9l0dEhSdvEmjkqZ4YKtqVqlW/tvXxlODhb0Old12fw5cAHavFo51\nhhVHtmazuNnqp3ghulK4147S4y1//kWyjSZGV4JQQ2nEft8f/Ht0z2Nxa5va4iKvvv07cDJT7gi7\nlZ37QYjud3tEo3ZjI838Q1dpgk7eJBPRJtErDsrVlIVWY0Aw3XSidX0FYLkh+6s5WsUUmYaL1FSR\n2KBKT667Wx1VTzKdYOo2pMJeZ8ghJN32WLtXY/NW6UiRfKlrbF0vsvyoiRaoKudQ19i5mn8qlXaO\nSxIoExLOiFTbU2k1oFVM4WZO8eclBNWVHPWFDKmOT6iLyPSqafuUd8ddTJYeKcGE00yChb02lR1V\nldorJoJutSSHjgohatIddMq48e1X+kFyEMP3+Z4X/wNGEOAbBu986fO88F99hOrS0sSxGG5AYb+D\nZfu4aUMFsdEgKZUAeGnfRoRdKbiVHJ2RHdPeep6V+/W+ItFoANS6aeTBQOmbemTqMhTqjBchcLJm\nbMCL0lsdvO7IQBnKMRutXmAvTVn162ZMHt0t902hvZT+5DgozJhkKZGQcAaUt5qsPKhTOLApHNis\n3q9R2mkffccjCA2NTs9EOWJSy9XjKy6zTe/EzyuCkPJOJzKQADhZAydt4JkajYU0G7dKQ0HZycRX\nufYCqOH7GI7DD77w+xPHYto+669XKVQd0nZAoeqw/noVa6TatbyjFGy0rgKN6YUsPW6Qag2/D6Gu\nsXmrFLk776GNVLh28qrNY0jACSUn15pgwN3DM1XlcBTTnDcaXhj5QQjonxtPhRCHak9JkJyaJFAm\nJJwS0/b7Mni9wNLzpZxkpXUWTBTHPqLiUvND8lWb/IGNPiI3l+r4sU18AhUgNm+VeHy3QnUlN1aB\n+fX3vBvPHN5RR53xacDi5haGGx/UF7pnor379t7fha0BSb1QUojoZVT+pRELFiFwcmakxJ8EOqM7\nvK5ohJ01+m0xTtpg81ZpKtWoVimlNFpHnicwNDoTDJR7BIaI/ax9K5nGZ02Sek1IOCXZhhs9iUnl\n9TiYwhvFcANMJ8C3tBOZMcf12QmYWMXbO3vsUdlWhTG9sYa6iLfe6j7vJB7duc3L3/99vPOlzxNq\nuvIQ9f3IdgkpRKTnY48430/LDvoi4noQb1YeaYAMIAT7a3mWH9YPBRfoWmhF9H0Gps72jVK/n/I4\nfbZS19i8WWJxo0nKVjthO2uyt56famcndS226re2eLoe1YSjSQJlwtx56aMv8+KnuLQFPbETpog2\nWVZ3kiw9anQrVdXO0M0oG6bjTMBOxqBV7FZc9h66V3EZU/av+SGLm62x3Vd5p00nZ+GndCXkbmiI\nkQIUVXmrTSV59tUf+H6+9V3vYmljEzub4dbXv8lb//yLQ2eXgabx+PYtQiN+Kgo1gR7R7C+7jhYQ\n3+IgUe4Y5e1WZCuGnTPZuFWiuG93LbQM6guZiT2KJxWi8FM6W7dOFmgB9tdySEHf/irQBAerOZwp\ndqQJpyMJlAkJp6RdsCh1C2qirouitNsh0+pK53XvZ3V8Fjabx7Jz0rvanr0p1zcEe+t5nNyE3WTP\n43IEIdWZZ21ZadBu3Siyer/e14IVQCtvsn+lMLUfqJtO8/j2LQBqCwssb2ywuLkFUqpWlkKBz/34\nfz7xMZrl1FhaNRQMFQ8hBLXFzJiA+GArRqrtsRXRiuGnjKH+zzGk7CvznEW/6okVn7o9lQerObRQ\nql14cs54LiSBMiHhlPiWzv5qjoWt1tDle+v52J1JIcK1RJOqjWAvxpNwjFCydq8+FCgNX6nkPLpT\niQ9mE48uD6/0LZ1Hd8uqYjNQQeI0VbSBafL7H/lJljY3qWzv0CiX2bxx/cjXWl3OovvhkDNGJ2eO\npUfrixlCXVDeOSzo6aFJJUNX3FNSfYEuaJXTRxbSmLbPysOGaqkQAEKJnc+z91CIeEGKhJmQBMqE\nhDOgVU7TyVtkWi4g+lWScUTphgKHAqpTzIPZposWDKdGBSrVWDiwcdMGgS7I15yBtoo0nbxJZTvi\nqQV0Ris4hRg2sJ42iMchBLvr68dT6BGqf7LqBVgdH8/S8aOa7IWgWclguiHFA3v8aql28hrqLS4e\n2Oyt5WgPGBYPEUpWH9QP3Tak+s/S4wYbt8tzlzlMOD+SQJlwIXjpoy/zqy8+c+hgfwkJDW3IJX4S\ndi666d1N6VOnNU03iNXvLO+0YaDvTwDpjk+harN5s0R1KdvvvwQVJBvldKyHZK5mU97pYPghvqFR\nXcoMGTvHjtH2sZwAz9LUY58wyFq2z+LjJqYXdGX8DPbWC4fKNwN4lh5plA2HZf69vtDFzRadQioy\nHZppeWP9qXTvl6s5xxN6l5J0y8PwQty0fqr34lyQkkzTQ/dDnMy4efjTxtP96hMuFN/1+ivA5Q2U\nx+FgJUeqXUNIOeRacpSH5CBuykBqICIKPjUYS7H2dkULmy22bpWw8ybZuouQknYxFRsksyM+kIYf\n9tPMccFShJKVh/WhXkcvpbN1vXjs9K3mh+qsdGAXnm4rB5DHd8pjAadVtCjvtCNF3McHqoQioiqE\n9SCMbLERqLPhadG9gNX79aH7ON3CrWkXReeJ4QSs3a8NZT06OYvdq9NV6D6JJA04CQlzwLd0Ht8p\nU1/I0Mka1BfSPL5TPpaaTydvKrHrgcuOytoKUO0JUuKlDFpFC9MNWHlQZ/21KrmaMxYcyjudmP7E\neC/J8k6772PZ+zHtYOwcdxryNXtsTL1glW6P91/2WjHc9GHPY6CLmKNZEVuZbMeo5YRAJzf957S4\n0cToWqb1flIdn9LelF6c58zyowZaIIfGm2m55Kvj6eynhWRHeQGQUtJuhbiOxEoJsjkN8ZSu3J4m\nQkOjWU7RLlh41vQp1z5CsHmzRGW7TbbhgDxCgKBLr63CcAPW79UQ3ToVPQhY2GyiexnqA8bNRszu\nSfdDCEPQxtfb+ZozHlw5ulhJhEqGLld3AOWwYbpBrPyb4UWPzU/pbN4qIYIQhCDV8Vh+0BhfRIQS\nJxN91uhbel/svPf8vYVIebeDmzFj/Sv7rycISbfH+0B7Ppan9ek8aww3wPCCaFm/qkOzMr1Ty5NE\nEijnTBBI7r/u4HkSKdVcaRiCG7dT6EYSLJ9UND9k+VEDy/a7QUOyv5Kb6txvkFDX2FvPq8b1IOTG\ntw8m316odgtAtbSMKKNpEkp7HRoLmf65nW9qmDEBqbzTobqaG78iThXoCCWh1fs1TOcwMJb2OgS6\niD1zdI44O+ulee2cpdRt/OFqWARk6y5ogmzDIdQ0muV0f2e/v5oj0ITSj+XwvTLdkOWHDTZvlyc+\n/8Td/Sm9KmfCxM/n3EZx4UhSr3Nme8PDdSQyBKRaoLuuZGvj5Dqdl5WXPvryvIdwbiw/apDqpSZD\niRYqqbZURCpxWrJd8YJRJCpA9hw+DpZVYItTvOntNntUlzKRc6RAtblEVfDaOXPsPhIm9iGmW95Q\nkAQVHHVf9QwOPl4owM6YUxeZaH6IEcjIndLCVovFjSa5hke+5rB6v0Z+v0225rD2Ro1iN0iOvnbT\nCY6UKAx1DS+lR74XF9Heyre0yGrtUKiz36eVJFDOmUY9+g+t0QiQF3HFOWM+84tPfmrHcAMsezxI\nCQkr9+us3qudKGDGVcGCEj7YuF1mZ6CAxLfGJ3A1DjmkdNMupSdKzGkR8nEHKznC7k4QuoFaE+yt\nRew+u6RsP7qKF5WCbZRT+LrANzRaBQstDLn27X1W7k9+vzINl9UH9dgdUe8crvdcmoSF7Y6Sm3OC\n2ElSteKEaEFIaafN2utVlh/USbeGBR121/NIbfi98E3twqVdAdW+cyXfX1iB+v+o7djTRpJ6vag8\nfTHyqUH31blZVIFKr41j5UGdnWvFIY/H3nlbnLJLXBWs1FSgHO37qy1mSLW9oeAUCujkrTGhBDdj\nkG6Nt7MgouXjesVKuapDyvZxUzrNcnqiNJxvaJFWVlIo9ZxWKcXBmtLPXXp0aGqdafukIt4v6Ho4\n7rZjzzgnFT9Ns4vQvaDv8ahJwAlIt70h3VwvbfDornovDC/AzZhqN3kBK14BnKzJo7sV8jUb3Qtx\nsqZSmHqK6ybmEiiFEAvAbwK3gDeAn5RSjh2uCCHeABpAAPhSyvec3yjPh1xeo9kYX5Hn8klBz5OK\nmzKOdvaQUN5usXm7jGn7LG40sbo+gnbWVKv+kaDTyZsEuoYID0UIVMWnFmni7HRFuRe2Woiukk2r\nmGI/4syxupRltV0bC6rVxWzsBBrqGo3FDI241+iH5Go2hi+xu5NxZXu8rUNJ3R2Ov7I1rlM7+H71\nEKGMDJK94Bh2VX5gKn2HMaSAbMM7DJKDY9lp0yyl+84ivffishAaGvVEbL3PvHaUzwNPHNV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8146464ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  },
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