codes/course2/Optimization methods.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": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Aduan\\Resource\\Jupyter Notebook\\DeepLearning_AI\\COURSE 2 Improving Deep Neural Networks Hyperparameter tuning, Regularization and Optimization\\week6\\opt_utils.py:76: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l-1])\n",
      "C:\\Users\\Aduan\\Resource\\Jupyter Notebook\\DeepLearning_AI\\COURSE 2 Improving Deep Neural Networks Hyperparameter tuning, Regularization and Optimization\\week6\\opt_utils.py:77: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], 1)\n"
     ]
    }
   ],
   "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 import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils 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": 4,
   "metadata": {},
   "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": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-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 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\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": 8,
   "metadata": {},
   "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[:, k * mini_batch_size : (k+1) * mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k * mini_batch_size : (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[:, mini_batch_size * num_complete_minibatches : m]\n",
    "        mini_batch_Y = shuffled_Y[:, mini_batch_size * num_complete_minibatches : m]\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": 9,
   "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",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \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",
    "</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": 22,
   "metadata": {},
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\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": 24,
   "metadata": {},
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[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 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "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",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\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": 26,
   "metadata": {},
   "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": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n",
      "s[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "s[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "</table>\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": 28,
   "metadata": {},
   "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 - np.power(beta1,t))\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l + 1)] / (1 - np.power(beta1,t))\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) * np.square(grads[\"dW\" + str(l + 1)])\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\" + str(l + 1)] + (1 - beta2) * np.square(grads[\"db\" + str(l + 1)])\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 - np.power(beta2,t))\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l + 1)] / (1 - np.power(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": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09245036 -0.16498684]]\n",
      "b2 = [[-0.88529978]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n",
      "s[\"dW1\"] = [[0.00121136 0.00131039 0.00081287]\n",
      " [0.0002525  0.00081154 0.00046748]]\n",
      "s[\"db1\"] = [[1.51020075e-05]\n",
      " [8.75664434e-04]]\n",
      "s[\"dW2\"] = [[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\"] = [[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 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  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]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\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": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Xg0MDsOcWkL77BMbQQCI6N/PpQ3GO8SbVHmyGYDO9/vcs0aP7XvUeiqKQuT+WoqQMwto1Kq55kx1Ofqt7l2rTUuHC6khRyQQEVyLL2LQFGEMC3cbZev8HnF2wuVjVXh/gR2jL+gzZ/AmiyYiiKKT8eYCz8zehM+hpOHYA1bu39Gq7ZHcgWe2uJJwLv1fL+SwWt3sYe3ZBsTqLaDZR68ZODFz0huaUNKo8WmH1dUhA7UgCo6PIvSxlHcC/ZhiBDUqenl5eOPKL+Ov52Zz6cS1Oi43qPVrR7dMpRHRsWnyNMSSQ2oPKR9w2uHFt1d+P7HBSrU3J4kmCILjsvcRmgMRVu3GqZPoBmEIDQS9iTVaP1QmiDn2ge6Fz2o5jbs4MwFloJefoWWK+XUXzR4aycdxbJC7f5bpGJxD77Uqa3D+Ybp8+puqIRKPBY3V3+MPfsOcUuEmNSUU2UtbvI33X8Ss6SA2Nqo4WQ/sH02fuCxiC/IsTMHQmA/pAf/r++GKlz7QVWWblgGeInbPK9QCWFdK2HWFl36fJOX6uQmzo9O5DHun7op+RqH7tvfdnKyFFSZkoTvWaO9khcaXffvWerT30D88t2FycQHIpziIbp35cS/wf2/92ZgCygrPQSux3q0jbdqTEdics3aFaQ+a02LwWvWto/FPQHNo/mIjOzbjt+BzaPHcXdW7tRuupd3Dbse+qxCw7ZcN+ck8meBRDSxY7B978wevrCpPS2fvKd6y/bToH3/kJS1p2mca3pueQtPovV5xKJ4DgcviN77uJAfNfK9M9LyWiSzO8ea3wTk2o2b+9a9zL0evo9NYDHocFUfR6P51eJPa7laoNNp1FNk79tK7Edhu8lEuIRgOGYHOJ76OhURXRthz/AWQeiCN53T4Mgf5Ej+6DX0RI8TlzrQg6vuGb7DVfkrEnRrX4VpFl0rYfVX3N+e1HWTN4GrLDiWxzkLRqN4c//I0hmz4mrG0j1deo4SiwsKTLZCwpWcVbazqDHnOtcLrOmIz+kvT/vLgk9rwwm6Q1e9H7G2l8/2A6vDr+qn3HIjo1JbJbC9J2HEO+JI4pmk10eutBTGFBJCzdgaPAArIrTq3zM1JrYAciu7XwuF+DMf04PmuxRyG3PsCPJvcP5vSvf6oboihe687UaDFlBDsf/1zVOTa4q3+J76OhURXxyQpNEIRvBUFIEwRBde9DcPGZIAhxgiAcEgShZHIN/3IUWWbjuLdY3usJ9r30Dbuf/S/z6o/lzPxNlW3aVfGvGeZRN3YRcy3PImlFUdh099s4CyzFq7qLxcpbJrxfqrFj56zCmpHrFieSHU6saTnE/bC2+FhB/HmWdJnMucXbLnSGzuX4Z4tYNfCZ4sLpKzFo2Ts0f2SYKx4mCIR3bMJNK98jsmtzghvXZtjuWUTf1htjtSAC6lWnw/TxDFz4huq9Ijo2pfmkYa4t0gvbxfpAP6r3aEWjewbRcOwA1TIHfaAfDUqQ3HKRxuNvot6IGxDNJgS9iOhvRPQ30uvb5zBHhZX4PhoaVRGfZDkKgtAHKADmKorSWuX8EOBxYAjQDfhUUZSrdgX8t2c5xnyzgl1PfeExmxb9jdxx5mf8q1erJMuujqPAwm917/IUsDX70efH/1B/pLuyfu7JBJZ0ekQ1jqQzGrgr4Vf8IkNLNPbaof8hccVu1XP1RvVi4ILXAdgx5RNOfr3CIxNSH+jPgAWvlSpZxVdq/Oe3HyVu7hoki43o0X2oM6QbOlFEsjtYNeAZsg6ecsuCjOrfnhsXv1liBZSLZB6II3nNHvQXVv1V+bOkoXEp5Z7lqCjKZkEQoq9wyQhczk4BdgqCECoIQk1FUVJ8Mf71yvEvFqtuDQGc/X0TLaaMrGCLSo4h0J+b13zAumEvIVnsILhkrdpMG+PhzIALhc5eHIJAqQrF/WuGI+h0HqssQdS5rUKS1+9XTet3Flg4v+1IqRyar5JwatzQiho3eLZgEY0GBm+Ywemf1hP341p0Bj1NJtxM9B19S+3MAMLbNya8fWNfmKyhUWWoqBhabSDhkv8nXjjm4dAEQZgITASoV69ehRhXVXHkFakel+1Or+eqEpFdmnNX0jzSth3FkVdI9RtaYQoLVr02pFldjGFBOIs8HXhwkzqlWkE0nzSc0794CgvrjAaaTRxa/H//6qHkxSR6vF70N+FfwtXgpSiyzImvlnL880XYsguo2b89HV6fQEiTOqW+lxqi0UCT+wfT5P7BPrmfhsb1RkVlOapNX1Wn3IqizFYUpbOiKJ0jIyPVLvnXUOfW7qq6fKLJSE0vqvHW9ByyDp7CkV81HJ5OFInq05a6Q3t4dWbgWuH0/eE/Lh3IC+9ZZzJgCDLTe87zpRozolNTurw/EfFCGYM+0B/Rz0jXjx91EzJu9fQdqnEpBGgwpvQJEpsnvM+e52aTeyIB6/lszs7bxNLOk8mNSbj6izU0NK6ZilqhJQKXFv7UASq3cVQVpiAhjV1PzCR+2Q6QZNd04IL7F81+1BrUkciu7rJNjgILm+97j8QVuxBNBmSHkxZTRtL5vYfLtCVVGUT1bcfIw99w/IvF5Bw5Q3inZrR4dLhqEsnVaDFlJA3u7Efiqr8AqDOkK37hIW7X1BvZkxaPjeLoJ/PRGfQIgoCiKAyY/5rHtVcj50Q85xZsdm2vXkCRZRyFFva9/C39500v9XvQ0NAoHRXl0JYAjwmC8CuupJBcLX6mjj2vkGXdprh6fF1slqkAOoGQpnVo8dgot22zi2wYPZ2UDQdQnFJxluCJWUswhATQ/qV7KvAdXBtB0VF0/XCS1/OKopDx10nyYhMJaV6PiE5NvV7rFxlK43sHeT0vCAKd332IFo+NIGXDAQyB/tS+ufNVU/bVSN10UF3SUXbJVWloaJQ/PnFogiD8AvQDIgRBSASmAwYARVG+BFbgynCMA4qAqlc4VUWIm7sGe16RR+dn0Wig0d030uLRER6vifluJclrPFUenEVWjv7fPNr9Z5zqKk1RFLKPnEGRZKq1aeChXlHVsGbksvrm58mLSXQ5D1kmtHU0N6/+AFO1II/rC5PSifl6OdlHzxHRuSlNHxziVsN3kYDakVd0fFdDURQSV+5yq0e7FEOQVrCsoVER+CrLcexVzivAFF+Mdb1zfvMhJJXECMnqahzZ7iX345a0bHY8+qnX+zkKrTgLrR4P1fNbD7Nx3FvYcwoAAb3ZRJ/vXyhWZL+Ioihk7osl/3QK1VpHE9qifpnfW2mIPZHG+hUx5OVYaNupNn0HNWbz3e+QffiMW2Zi5p4YVvR+klFHvnV7/eVF2okrdnLovV+4detnVGsV7VNbj89cTPK6farnRLOJ5lM8JyGyw4mjwIIxNLDSZco0NK4XNKWQKkZgw5roDHq3omBwpZyrCQ6f+W3jFR+IxpAAj8SHwiRXWxQ3IdwCC+tvn86IfV8R0tQV7rSkZbNm8AvkxSYi6HTITonqPVsxcNEbGALcxXV9yYrFR1n0y0EcdglFgdgT6axafJSW249jUEmzzzl2jpP/W06zh24FLhRpj30LZ4Gl+BrJYkeyOtgy4X2G//Vfn9p76L1fPDIqLxLZtTmtLml6Kdns7H7mS2K/W4UiSZjCguj03sM0GX+zT226XilMSmfX07NIWLIdgDq3dKPbp1OKuyBo/Lv5Z2QL/ItoPnEogsFz609nMhQ3lrwUe3Y+ks2L9JEg0O7lezy2G2P+twJZxTHIdifHPl/kilPtOcnKfk+TdeQ0zkIrjvwiJIuNtK1H2PnYZ2V7cyUgJ9vCwp8OYLdJxTEpu10iN9fG2abtvL7u0Ls/F/+ceyIeW1ae50WKQvbh01gzc31qs9WL3qQ+wI+Wj9/m1mds07i3if1uJZLFhmx3Ykl1rbBP/7rBpzZdj9jzClna5VHiF21FtjuR7U7il+5gaZdH1f/eGv86NIdWxQhqWIv+v76CIdhc/E8f6E+vb55TbXwZ1bcd+gB1ianIbi0whQezbdJHHHz7RwqT0gHIOR7vIRoMoDglsg6eYknHR1jR72lyTyTAZYryktXOmV//xOklXnStHN6XjE4l3ifLCmk1vNclWlKyin9W5KsUYfu4BWBQQ/VWPYrkivFdJP9sKokrd7tlQoKrfcvel77xrVHXIXFzVmPPK3SPL8syjgILJ/+3ovIM06gyaFuOVYDCpHQKzqQS1Lg25qgw6g7twdi0hZzfegRkmeq92qD3M6q+tkaftkR0bk76ruN/iwGLOoxBZopSMtnx6Kc4CyzoTAYOvvsz/edNJ6JzUxKW7fAsPDYZKDiXhiU1E8XhuYK7iAI48gq92nQtCDq8Cobo/b2PF9y4dvHPoS3qYQgJUFVZCWleTzUx5Fro9M5DbL7vPbffp+hnpOaADm5F1TlHzqAzGlSbshacSfWZfNb1SsrGg6pbu5LFRurGA7R9fkwlWKVRldBWaJWIo9DC+lGvsKDJeNYOe4n5De9m47i3cFrtiEYDtQZ0oNaNna7oOARB4KaV79Lu5bsJqF8dU0QIje++kZqDOmJJziyOI8k2B1KRjU1j36TRuIGIJmOxCO5FdHoRa1r2FZ0ZuOJ5a255gVWDnuXc4q2lkqW6Gu071UFWWWHp9Tr63tqKoEsc10VEs4kOb/6dOCvodPSZ+x/0Zj+Ey4q0e337nM9svUj07X244b9P4R8Vhs5oQPQz0ujeQfT/3b32LDA6Ctmp3sXaFBGiObOrEBhdA0HvuR0viDoCo6MqwSKNqoZPxInLi+tdnHjj2DeJ/2O724xd9DfS6O4b6Tn7mWu69w9Bt6quUAzBZvr+/DLBjWqx5YEPyNwTA0C1Ng1o9cyd7Jj88ZVltQRX766LmYb6AD8aTxhMj88fvyZ7L2Xj2lh++vovnE4ZWVYw+ekJCzfz6ge3oHfa2frwDBKW7EAQdRgC/en84UTVpIr808kcm7mYnKNniejcjOaPDiegdvmpzyiKgj0736VMclmn6Iss7fYomQfi3CYNotlEh+njafPcP2OFkX82ld1TZ5G4cjeCTqD+qN50nTEJ/xrlq9afG5PAHx0e8WhLJJpNDNv5heqWvMb1x5XEiTWHVklYM3OZV3eM6vaT6GdkbPrCMmcSKorC98abPGrZwOXQes+ZViwQbM8tQFHAFBqIo9DCLzVu95qxpw81I+VbPWvk/I2M2Df7mrtAX0pifA6b18aSm2OlTYdadO0VjdH49+zckV+EPbcQ/5phbvVz+WdTiZu7Bmt6DrUGdKTusB5uSRmVjTU9hw23Tydjbww6owHZ5qDZpGF0/b9J/whFF2tGLgtbTsCeVVAs/izoRcw1wxh17DufZL9eaev17ILNbLn/A4QLzVMVSabn18/QcMyAax5X459Buavta5QeS0oWOoNe1aEJog5bRl6ZHw6HP/zNa+KDbHe6uilfwBgSWPyzIcCfZo8M5cSsJW5JI6KfkYZ3DyT+j+04Jc/VmyIrJK7c7VOHVqdeKOMe7OL1vCHI7FFbd/q3P9n6wAcokoxsdxL3/RqCG9diyOZPMQSWX5lBafCLDGXI5k/JP5NCUXImoS3rqxaF+xJrRi4oSonb71yJE18uwVlgdetkoDglbFn5nP55A80evrVM95XsDvZPn8OJ/y7BkVdESMv6dJsx2aMuMvp2V0ud1E0HQVFcSVFlUHbRuD6p+lPC6xRXPMVLrEoQ8K9Ztu0b2eHk0Ds/eW1Q2eGNCW5O7CLOIivrhr/Eyf8udc1+BUAAfbAZRZI58+uf2DLVU6MFUYdYDgkipcGWU8DWBz5EstiR7a44lbPAQu7xeA6+/WOl2qZGUIOa1OjZulydWfbRsyzpPInf6tzJb3XHsKjtQ2Tsjbmme6Zs2K86CXMWWkndWHaJr03j3uLYZ4uKt7tzj51j/W3TSV7nqYCj9zdRZ3BX6tzSTXNmGm5oDq2SMAT602LKCI8vpD7Aj7bTxniNwVwNS1q217o00WyilheV/u2TPiZ53T4kq92VVq64YmVSoRXZ4XTF47xtT8sK9W/z7HFWkSQu34kgen6cJZuDuLlrKsGiysWamcuK3k+SuT/uQs2Wg5wjZ1g1YCqFiellvm9g/RqqW6M6g56A+mUrbs6LSyJxxW6P2JhksfHXtK/LdE+Nf+AjJLgAACAASURBVCeaQ6tEOr/3MG2mjcEQbEZn1GMMDaT9q+Np++LdZb5n6pbDqjVm4Io3mGt7Ktc78os4O3+zx8xbcUqqcbiL6Ax6RH8jPWY9WekdjyWbw6vDvbhi+6dSljh3zDcrVX8nks3J8ZmLy2xLi8dGofPznGwJepFmDw0p0z0z9saotkkCyDl6pkz31Ph3osXQyhlLWjY6vajaC0zQ6Wj/yr20fXEcjnwLxmDzNSUGyA4nO73pOgoCdYd0U3U81oxc1dWNNwS9juo3tKLWoM40GjeQIBVJroqm9s2dVZ2voBepN/yGSrDo2pCdEgff/pFjny3CnpNPSLO6dPngEeoO7cH5rYfZ88LXZB08hV9kCK2m3kGLR0e4fXYy98Z4rHgAZLuDjD0ny2xXRKemdP/8cXY+9jm6C4o2iqzQZ+4LBDWsVaZ7BtSO8Oq0TeHee+hpaFyO5tDKibSdx9j64Ifkn04BRSG8QxN6fz+tWCfxUnSiiCnUM65VWjL2nPQaOwOFHl8+pXrGXDuiVA5NNBrp8v4jRHZrUQYry4eA2pG0ef4ujsz4vbhcQfQzYgg20+GNCZVrXBnY9tD/cWb+puKM09wTCfx515u0e/keDr79Y/HxgkIre1/4H7knE+jx+RPFrw9tFY1u6Q6PDgCCQbzm9Pam999Cg9F9Sdl4AEEUqdm/PXp/dbWaklC9Z2v8q4eSX2SFS2oQRbOJ1s/ceU22avy70LYcy4H808msHvQcuRckpmS7k/TdJ1je8wnseYXlNq6gF73OdAVRxBgcoHpONBpo9/I9HvE80d+Izqh3K8AW/U1U79mKiMsajAI4LTZ2PP4ZP4YM5Xu/m1nY6n6SN+6/hndUOjq8NoEBC16nzq3diOjcjNbP3cmow9+Ua+1ZeVCYmM6ZeRs9yicki40Db8z1OO4sshLzvxUUpWQWH2v28K2q5QqiwUCLx0e5HStISGPHlE+Y3+RelvZ4jNO/brjqNqchyEy9YTdQd0i3a3Jm4BIHuHnthwQ3ro0+0N+1BW8y0Pjem2j11N/CzoqikLBiF+tGvsLKAVM5PmsxTpXOFBr/XrQ6tHJgx+OfcXL2Mg/FDb3Zj87vP0yLKZ4iw75AkWV+rX0n1vPuYrmCqKPmgA7cvPoD769VFE58uYQDb/yANS0HU3gwbV8cR+2bu7D3P/8jdeMB9AH+NJ80jDYqSStOq50Fze+jKD7NY+y+v71Cg9v6+O6N+oiMtAIO70/GYBTp0KUOAYHqD+bCAhvJiblUCzMTUf3aV9JXI37pdjbf++6VC9wvwxBsps/c/7htr6btPMbGsW9hy3CJMesMeoxhQUhWOzV6taHDa/chGvUs6TwZR4HFrVi+yQO30P3Tx3z7xq6Coihk7o3Bcj6b8I5NMNcMdzu/47HPiPt+9d8rcLOJwPo1GLbzC63n3L8IrQ6tgsncG6sqH+UsspK5L7bcxs09meAZNxHAWC3oqsojgiDQYvIIWkwegWR3oDPoi4tbb1z85lXHjvlmhYczA1ciyo5HPiZ6ZK8qUzisKAq//7CfNUuPI+gEBEFgzn938dDjN9C9d3TxdbKs8Mt3e/hzVSx6gw6nQ6Zx80gee74PgUHXtiq5EubaEVdMxlFDkRX8It01Kqt3b8kdp38i92QCh97+ibOLtlBw2tUo/uz8TSSu2EWNnq1x5Ls3lHUWWon5ejmtnh5NUAVKSgmCQETnZqrnsg6dIva7VW6fb6nIRsGZVI7NXES7/5Q9kUrj+qFqPGGuM0Jb1leNSYn+JkJaeFeMv1b+vON1HPkWj+OhLesTWIqUatFoKLWuYNx3q7yes+cUUJiUUar7lScH9yaxbvlJHA4Zu03CZnWiz8pm3qsLSIlJLb5u2YIjbFwTi8MhYSly4HBIxBxP45N3/ixX+8I7NHGlx1/2GRLNJiJvaIWoItIs+huRbA6PGKogCBgC/Tl7STwOAFnBWWAhef0+9WQaUUfKevWmpZVBwtKdHj0CwdX94fRP6yvBIg1v2GxOFv16kKkPL+TJ++cz96td5OZ4PpfKA82hXSPntx9l64MfsuH26Zz6cS2S3UHrqaPRmTxTm3UGkSYTBpeLHXlxSeSfSfVMXVcgfecx7LkF5TLuRS5vInq5DVVpS2jNshPYbK6Ho8FqocOW5XTe+Acttq1lVZv72DV1FrIkseqPY9ht7ittySlz7lQWKUm+7al2KYIgMGjlewQ3q4s+wA9DcACiyUD06D7cvPp9ag7oiOhvQgwwFYv1SkU21o94md+jx5F7MsHtfue3HEYwqm/GKN6K+3VClfqbCXqd10mWmmCxRuUgSzLvvbyG5QuOkpleSE62hY1r4nh16nIK8tUl9XyJtuV4Dex99VuOfjT/QiGyQtKaPRz5eD63bvmUAfNfY8v9H+AstKDICuaa4fT79RWfty65iLPQiqD3Mj8RBFeNWRmGzj+byt4X/0fiyt2IRgON77uJ9q+O95CSajFlJOe3HXHLUrtIRNdmPsni9BUFeX8nErTduZaA/Gx0igKy6+F+cvYy/GuGU1ig3vNN1OvISCukZu3S/0IzD8Sx7+VvSN91AlNECK2fuZOmD97i8bAOrFudUYe/IXNfLEXJGYS1b0xg3eoADFr6NjnHzrLvte9JWLoDxSkVx5UcBVZWDXqOO8/+XLzFawgJ8OoMRLMJFMWjRxuyQp1bu5X6/ZUX0bf34cDrc+GyEkvRbKLpA7dUjlEaHhzYm0RSQi6OS0IukiRTmG9j/YqTjLirbbmOr63QykhuTAJH/+931zbOhVWRs9BKztGzHJu5mDqDuzImaR5Dt89kxL6vuD1mLhGdmpabPaGtotHp1ecnAbUj8CtD4XNRSiZLO0/mzLxNOHILsabncPzzRazs9zSy5D6zjx7dh9o3dfHoZWasFsiAhW+UeuzypG3H2ugNOgJzMzEX5rmc2SVIRTaOfvQ71cLU9R+dDoladUrvzNL/OsGKXk+SuPIvbJl55J1MYPfTX7DryZnIkkTc3DWs6PMUS7tP4einC5AsNiI6NaXesBuKndlFQltGk7b1iGcRvaLgyC10aR1eoNaNHRFElYxHPyMtpowkoktz9IF+IAiIZhOi2UT/36f7RGjYVwQ3rk27V+9F9DfBBUetD/QjvGNTmj0ytJKt07jIkQMp2KyeW8MOh8z+vxLLfXxthVZG4hdvQ7J7KnLIdifHPllA2+fHIOh0FdbSQqcX6THrSbY88AHyxdm2TkD0M3LDV1PL1GvryEe/4ygogkviMpLNQW5MIkkrd1N3aI/i44JOx6Dl75Dy536OfjwfR6GVBrf3odmkYW5q+FWBm4a1YOvyowRknUfx8nuxpucw+p4OfP/VLrdtR6NRpF2XOoRHqpdAXIm/nvnSI83cWWjl5Oxl5JyIJ33HseKVVvaRM8R+u5KhO2Z61Su0ZeerHlcUGcslma6i0cCgZW+z5pYXUGQF+ULST0TX5nR4fQKiyUDqpoOc33IYU3gwDe7qh194+ewkXAvtXhhHncFdifve1bm6/ohe1Lm1W5X7fP2bCQoyIYo6JJW4bFBw+SVSXURzaGVElmTV7TW4oKdod5RZj/HS+1hSsghqXOuqs2V7XiGnf1oHkuyqR5MkghvXpt8vLxPeoUmZxk9es1dVNspZYCFl00E3hwau2E+tAR2pNUBdL/JSzp7K5PC+ZIwmPV161icsvGLiNbLDyeFps+iweA2SIoBTXSYsqGFNeg1ohFOSmf/jfiyFDnSiQJ+BjRlzf6cyjZ2++7jqcUEUOX+ZZJlUZCPvVDKxc1bR4lH1Mo/w9o1J3+V5T2eBldTNh2hwV//iiUz1Hq24K2ke8Yu2YknLoXqPlkR2b1l8vma/9tTs197jXlWN8PaNCW/fuLLN0PBCz/4NWb7oKJdt4GAy6blxiGftqq/RHFoZqd69pddzOr2evJjEMq/O7LkFbL73XZLX7UNn1CM7JVpNHU3H1+/3utL68843SN100M0BFSVmkLBiV5kdmn+NamQf9jyuMxnwr1E27UZZVvjqk63s25WA0yEjigK//7Cf8Y90pc+N5f+g2v3sl5z6YR2yzXH57mgxotlEp3ceAqDfoCb0GdiYokI7fv4G9N7ilCVAH+iPPctzVSU7naplHlKRjdO//OnVoXX58BFW3zxNVeIq9ruVRPVp69YnzBDgT6N7BpXZfg2Nq1E9KogJk7ox58td6AQBRVFQFBg4pCntOnt2m/c1WgytjIR3bOxdLkoAU1jZ24Ksv206SWv2IlntOPKKkIpsHPtoAcc+Xah6ff7ZVM5vPuQRT3EWWTk6Y94V5LCuTMsnb1PNXhR0OhrdfWOZ7rlj0xn27UrAbpOQZQWHQ8bhkJg7ezeZ6eWnogJ/K2qoOQC40KiydgQ9v36GBqP7Fh/X6QQCg0zX5MwAmk0cqppyr9Pri+NCl6N2/UVq9GpD80eHq56TbU72v/Z92Qy9RvLikjj+xWJivl2JNbP8skE1qia9BjTi4//dxt0PdWbMhE68O3MYd91Xtl2N0qI5tDJiDAmk9uAuHinDgl4kskszzLU8Ve1LQm5sIuk7jyPbPZ3ToXd/Un1NwZkU1TIBcGW9qfWvKgl1b+1Oq6l3oDMZXJJEQWb0Zj/6/fqyh4pDSVm/8qRHKjy4CoN3bTtbpnuWFEtaTnGn48vRB/ozZMun3Bn/K43GDiw+LtkdpO08Rsa+mDJPDC7SYfp4avRui95sQvQ3YggyYwoLotc3zyKq/P30AX40e+jKDTPPb1VZQl8g/0IRdUWhKAq7nvqCxW0f4q/nZ7PryZnMqzuGU79odWL/NoKC/eg7qAkDhzQjskb5NrC9FG3L8RroPWcaqwY+S/7pZBRZQdDpMNcKp99vr5b5nvlxSeiMetVVhDU9F9kpeWj0hTSr6yFCexFTtSBXZlgZ6fj6BJo/MpTkdfsQ/U3UuaXrNXV/tlrUY1ZOp4ylSP2cr/CP8t40VXFKhLao57ale+b3TWybOAMUBUVWMAab6f/7dKr3aFWm8UWTkZtXvU/m/ljSdx7HPyqMOkO6IpqM5J5M4PAHvyHbXcXRerMfdYd2J3r0lSXDLKnZ3k9WsKxd/OJtxHyzwmMCte2h/6NGrzYemZoaGr5Gc2jXgF94CCP2zyZt2xFyjp0juEltovq2uyaJp5Dm9bz2M/OvGa4qOGuuFUG9kT2JX7LdrZ5Ib/aj/fTxJc5wVGSZ5PX7yNh9Ev+aYUSP7oMxOABzrQgaj7+pbG/oMjp2q8v51HycDvfVjsmkp02HsrUfKSl6PyMtn7iNY58udMs2vFjLdKl4c+b+WLbc/76buoazwMLqm6dxx6kf8YsMLbMd4R2aeMQ1O0y/j+jb+3D61w1INgf1R/ai+g2trvi3yz5yplinUY1rab2SsS+GtG1H8YsMod7wG0rUGfr4F4uKszQvRZEUTv+0jrYvjCuzPRr/TGRJJi21AD+zgdBq5V8Gojm0a0QQBGr0akONXm18cr+gBjWpdWPH4u7RF7nonLzRe840dj01i7i5qwEQTQbavTqe5pPVYyyX48gvYuWAZ8g9mYCzyIre38Tup2cxaOV71LihbCsSNQYPb8nWDafIz7PhdLqcmtEk0qJNDZo0L39V/I5v3g/Asc8WulZeQPNHhtH5/Ylu1x356HfVrVpFkoj9fjVtnr3L57ZVa92ATm89WKJr7bkFrOjzlKoDuUjHNx8otQ2S3cH6ka+SuvkgiqygM4hsn/wJN61496orU2tGnupx2e7Amql+TsOFzeZk5+YzxJ1IJzIqiD4DGxEaVnWUWsrCrq1nmfvVbhx2CUmWiW4YxqPP9ilTyUtJ0dT2Kwin1U7Cku0UJqYT0akpNfq09Tr7dhZZ2fHop5yZt9FVS2bQ0/61+2j5xG1XXW05rXbs2fn4RYaqrua8sWPKJ8R8u8pjdWgKD2ZM8u9eOwqXhfw8KysXH2PPjnhMJj39Bzeh76AmiJck2WQdPEXKnwcwhgZQf1QvjCG+VRqRbHYs57Pxq14NvZ9n4sXSbo+S8Zd6I8ymD99Kz6+m+tSe0nJ81h/smTbbq0NrfP/N9P7m+VLfd/8b33P4/d88tryNoYGMSZ1/xVKUvS99w5GPfvf4DOkD/ek/71XqDO5aanv+DWRnFfH6sysoKnJgszoxGHQIOoGpLw+gRZuKE4f2JSeOnGfGm+vd4uU6nUBomD8ffjnqmhKsNLX9Sibr0ClWDXwWye5AtjnQGfWEtoxm8NoPPfTynEVWYr5dScHZVKL6tSN6dB8a3TOoxDVtej8j+jIkbMRdSGW/HNnhJHXzIWoNvHptWUkJCvbjzvEduXO85z1lSWLTuLdJWL4TRZLR6UV2PvY5/edP9+kDUTQZCaznXbA5sntLMg+cQrlMEFcf4EekSi84cG3ZpmzYT/aRswQ2iKLukG4+nQhcSu6JeK/OLLR1dJmcGcDJr5apxm8VSSZp9V/UG+a9+3erp24n9tuVWDPzijUiRX8jYe0aUfsm1eePBvD9l7vIzbEiX6hrdVzYjp/5wSY+m3OH20Tvn8If8w55JH/JskJRoZ2DexLp1L18RNo1h1YOSHYH5xZsIXndXvyjqhHz3Wpsl2y5yHYnWQdPsfu5r+j55dPFxx0FFpZ1n0L+2dTi2M35LYdJ33n8qu1frtnmK2RCOvJL3pfrWjn51TISl+8sfv8Xneyfo1/nrqTffL5S80arp0cTO2cVzkscmiDqMASZaTCmv8f11sxcVvabSsG588h2JzqTHmOQmSGbPyGooe9jg2FtG6IP9MNZ4O7UBFFHRBf1FiwlQa1bA4Asyxz9eAGbx7+HIsnUvbU7nT+Y6Jbo4RcZyvB9X3HgzR+IX7wN0c9I04eG0GrqHVWmdVBVQ5ZkDu5JKnZml+J0ypw6mUHTllUzmcZul0BRMJo83UhKonps12GXSE1WV7jxBdqnzMfYcwv4o8NEtj0yg9jvVnH4w3lYU7M8rpNtDk79sMatM/DxLxaTfzrFPRGh0Mqpn9eTsS/G4x5FqVlsefADfqw2nB+rDWfrw/+HJe0KWW9XoEZv9RigbHd6PVceHJ+5CGeRSp2YAOcWbb3q62VZwWZ1XLXj8tUIio7ilj8/IrxzUwS9iKAXqTmgI0N3zlRVbdn28AzyYhJxFliQ7Q6c+RaKUrNYf9v0a7LDGw3GDEDv7weXlSGIJkOp43uyJCHZXBOaGr1au3Uov4hUZOX81sM4cgtxFlg4O38TSzpNwnpZUoq5Zjg3zHqKMcm/c8fpn2j34t2qW7oaLpQL/9QQBAGnt24IlUhaaj7vvbKWR8b+wiNjf+XNaatIjM9xu6ZWXXXpNINRpGadsicrXQ3NofmY/a/PJf90SvHM2Wt7DkCyOtxSq0//skF1pSRZHSQs2eF2zJ5XyNIukzn1wzocuYU4cguJm7uGpV0fxVFQ+t5D3T56FH2gv1uxuD7AjzYvjK1QXT+7ly7NslPCnuO98FpRFJYvOspj4+cx6e7fmHLvPFYuPnpNji2iY1OG7/4vd2f9wT25S7l59fuq25TOIiuJK3Z59uuSFfJik8iN9b0oqyHQn1u3fUZk1xboTAZEPyNBjWpx47J3CG1Rv0T3sGXns+met/khYAg/BNzKHx0muhxlgLuj1BkNCKLo9llWJBlngYUT/13i8/f2b0IUdTRtUd1D1Btck7PGzSt2dWaxOIg/m01Bnrr4QGGBnTeeX8mJI6nIkoIsK8TFpPPWC6vIyfr7uzvizrYYTe4xfJ1OICDQRLtO5acYom05lhBreg4IwlXbv5z6ST0WpUZ4pyZuWzHekjgEnYDusn5Wsd+twpad7/6QcUjYMvOI+2EtLUqY3XiRsHaNGL7nvxx8+yfObz2MuVYErZ+9k/ojepbqPtdK7UGdOfXjWo+mk4Koo2Z/71qDi349yMrFf/cvKyyws/CXg9jtEiPuvLaWFVeru3OtKNWTdXQGEXuOb3rRKYpC6qaD5J9OoVqraCK6Nmfo9s+xZuYi2xz41wwvVYnGir5PkReTWCyXlnXwFDsf/YTeP/yH0z+vLxYrNoYEkr7zmMc9JKudpLV7aP/KvT55f/9W7pvUlTenrcJhl3A6ZQTBtZK5b1I3jMaKEV6WJZlfv9/HhlUxLnFhp0SHrnV56PEemPz+jt9v/fMUNpvTvcRRAbvNyYrFxxj3gCtW2qxVDSY+2ZO5s3djtTiQZYVGTSKYNLVXucYENYd2FTL3x7JlwvvknkwEFEJbRdN7zjTC2jRUvV5xlkBNQhAQ/Y10++Qxt8NNHriFnBPx7p2FcT0ULy+wTV67x+M6cG1RJq/dU2qHBhDStC59vn/B63lFUUhYtoOYr5fjKLBQ//Y+NL1/cIlqlEpK++njif9jG478omKnJppN1B3SjbB2jVRfY7c5WbX4uEcQ2m6TWL7wKLeMbFUuD4acrCK2bTxDbo6FvObNCTh0BOGyDSRFVqjm5bNSGoqSM1g54BmKkjOLV/WhLetz0+oPyrSCTlqzpzjedynOIhuH3vmJIZs+Kf677n3pGzL2nPTcbRAEAuqUf6mFm31WO5bkDPyqV7umAv+qRO26obzz+XDWLDtOzLE0qtcI4ubhLWjQuGxqPGVh8W+H+HN1DA67hAPX33n/7gS++kTmiRf6FV936mS6qtKPJCmsWXqcgEBj8QSyyw316dS9HhlpBfj5GwgO8d1zwhv/SocmOyVyT8SjD/QnKNp7WmxhUjor+011S4rI2h/Hij5PMTpmrmpxbb0RN3Dqx3UeX36dQU9I87pY03OJ6NKMDq/d51Fc2/ShIZxdsJmMv07gLLAiiDp0RgPtXhxHSNO6bteaa0UgiDrVlYy5dtlkt67G9skfc/qn9cXZdem7T3Bi1h8M2zXLZw+XoOgoV2LB63NJWvMXxpAAWkwZSbNJw7y+JiO9EOEKk77szEJq1PTtvv2BvxL54sPNKIpLj9LYuDPG8Ia037wcveRyEnqzH53fe9gnMaQNo18j/1Sy29876+Bptk+cQf95pY/TZe2PU50QAWTui2V+o3u4dcdMTGFBnN92RHXrXPQ30vLxUaUeuywossy+6XM49skCEFwTx8b33US3Tx+75q4WVYGwcDNjKkjv8HIkSWb10hMejsrhkDm0N5mcrKLimrioWsHoDToPYQRwzbOWLThCnXqhxVmMOp1A9ah/mPSVIAiDgU8BEfifoijvXXa+H/AHcObCoYWKolRK18cz8zay49FPkOxOFKdEcNM69J/3qofDADjx36XqPc9sDk5+vZx2L97tca7TWw+QtHI39txCVzxMEND7m2j36r20fX6MV7sURUG2ORi04l1S1u0j/o9tGIL8aXTvTartMppPHs6pn9Z7pFjrjAaaP+L94Q8uhx7/xzYSlu7AEBpI0/sHe139XOTslqNs3nAGKbI+4XIifpZCpCIbBWdSOf7FYtpOG3vF15eGoOgoen9X8rTzkFC/4iLty5El2eczQ5vVwawZW1xZXhewOxWk0DDSB91Eg33bCWxQk/Yv30PdW7tf83gF586TdeCUx+RFtjuIX7oDR6Gl1M04A+pGIvqbcKrFWxWXzNrWBz9ENBpUW9Qg6uj83sNllgErLQfe/IGjH893c8Jxc9ciWez0njOtQmy4XrEUObwmn+gNOtLTCoodWr+bmrDqj+M4Uf++2W0SKxYdK7e0/KtxzQ5NEAQR+AIYBCQCfwmCsERRlMs33bcoilKprWXPbz/Klvs/cHMC2YfPsKL3U9xx9mf0l2keZuw5qRoPk6x2Mvb+nXUo2exYM3LxiwjBXCuCUUe/5cSXS0lcuRtzzTBaPDaKqD7e4zjxS7az66kvKExMR6cXaTh2AN0+feyKq57wDk3o9smj7HryCwSDHgFXG5LuMx+/Ytsap8XGqgFTyT56zvUw0+mI+Xo5HV6/z2t23J+rY/jhy70oTTsAAqdadaFu3BEanDyAZLVz6qd1PnVopSUg0ESnbvXYtyu+uIYHwGAQ6dKzHv7m0q+QChPTSVjqSsSpO7wHAbX/3lo7vD9FLREQSVJICq/Li6kLSv8mroA1MxedQa+aMCQIrlT70jq0+rf1ZudTX3g9r8gy57ccRqfXqX4H9H5Gmk8q/bZ2WZAdTpdyy2UrSsli48y8jXT5v0lXjW1reMdsNmA0iqqrLodDosYlK6ywiACefrk/H7/1JzabZ69EcBWKVxa+iM51BeIURTmtKIod+BUY4YP7+pxD7/7sWTSqKDgtNs4t2OxxfbXW0aqFsTqTgWqto5Elib0vfcPPkaNY0Ow+fo4YxZ4XZmMICaDdi3dz65ZP6T9v+hWdWfL6fWwc9xYFZ1NRnJLLQfy8nrVDX7zq+2n28FDuSv6dXl8/Q8+vn2FM8u80vf+WK77m2OeLyDp05u+ZuSwjWWzsf3UO+WdTPe1LyOWnb/YgKQKy3oCs1yOLehIatSI7wrVdW17Fw6Xhwce606p9LQwGEX+zAYNBR5uOtZgwufQrpEMf/MqCpuPZ/eyX7H7uSxY0Gc+RGfOKz9vtTq+51k6VvmbXSmiL+l6V/o2hQfhXL72upN7sxy0bZuAX5b2vnSLLKF6a2MoOZ5myacuCNTNPtV8cuL6L+WcqtqvA9YZO1DH09tYeWYlGo0jXG+oTHOo+WWrRJorHX+iLQSUuLegEGjer2LjqpfjiSVQbSLjk/4lAN5XregiCcBBIBp5VFOWo2s0EQZgITASoV8+3y9bck/Gqx50FFvLikj2Ot5gykpNfLfNIx9YZ9DSbOJR9L33D8ZmL3eqmjs1cjOyQ6Dpjcols2vvS/zxmnrLNQeaeGDL2xRDRsekVX28KDaTBnf1KNBZA3JzV6koQikL8oq20enq02/HN6+OQVLbzZFFPUnRzIoqyafrgkBKPX16Y/Aw8/VJ/MtMLSUvNp0bNIMIiSq8Zl77rOAfemOuxGto3fQ5RfdsR0bkZLdvWnenfJQAAIABJREFUVG0xL+gE2pZDSrLe30SH1yew/9U5HqLKXT9+tMxFy2FtG9Fj1lP86a1WTlZUO5YDGILMGIO9aw2mbj7Eofd+Ji8uifCOTWj34t2EtXVta18Uwc6PSya0Zf0rysCBq7egt96DstV+xTj4vx2nU2b/7gRij6dRLdzMDf0aEhLquZofMqoVklNm+aKjyLKrKWfP/g25+6Euqvdt1a4mteqEkJSQ47ayMxpERtxVcXWrl+MLh6b2Sbx8WrcPqK8oSoEgCEOAxYBqG2VFUWYDs8Gl5VhWo2SnRNLqvyg4m0pYu0ZU79masLaNyD+V4tFWQx/kT2hLz9qdoAY1uXHp22we/y72bFfqtSk8mL4/v4wpLJhjMxd7boMU2Tjx5VI6vDGhRNtAOcfOqZ8QIPvgaUJb1Ed2ON2U4K8F2VtdnKyonivIs6mqGCAIOP3NRHZpTtOHKt+hXSQ8MuCaxE9PzF6qurUnWx2cnL2MiM7NCK3mz9DbW7N80dHiQLper8Pkp+fO8R3KPPaVaD31Dsy1Izj45g8UxKcR0rQOHd964JrkwJwWG1vGv3f1Cy9Dbza5ujh4caSxc1ez49FPi78b+adTSFy2k0HL3yWocS1W9n0aa3oOslNGEHUENYhi8IYZXrM1RaOBlk/extFPFrh930R/I/VG9sIvMpScE/Ec/2IxebGJ1OjZhuaThl1TR4TrgcICG29OW0VWZpFLI9IosvCXgzz1Yn9atavpdq0gCAy/sy1DRrUiN8dKYLAJk4oCyEV0OoH/vH0Tv83Zy7aNp3HYJRo3j+TuB7tQu27l/d594dASgUszKurgWoUVoyhK3iU/rxAEYZYgCBGKomT4YHwP8k4ls7Lf0zjyCpEdEoKoI6R5XbrMmEziqt1uXwpB1GEMCaDeSPV6q5r92nPnuV/JPX4OdDpCmtVFEATy4pK8fqF1eh2FCemENr/6CtM/Kox8ldWh7JQ48fUytk/6GEVRCGlWl05vP4gtOx+dqKPOkG6YwkqfuddwbH+OfDjP46Et6HXUG+6p09emYy12bz+Hzeo+UxeR6XZTc25+4Sl0YsXUylQEtvRcUHHgiiy7qWKMHNOORs0iWfXHMXJzLLRuX4vBw1uUq0J6w7v60/AuT9mtspK8bq/XhqdXtOOeQbSYMlL1nGSzs+uJme4TPVnBWWRj+6SPMYYFUXDuvFuCS+6JBLY+8CE3/vGW1zE7vD4ByebgxKwl6PQ6JLuT6Dv6csOXUzn3xzY23f028oVEr/ObD3P0k/kM3fkFIU3qlPr9XS/8Omcf6ecLihOmHBeSmD5/fxMzv78DvcHze6s3iCWeEPr7G5gwuTsTJndHURSPVbYkyRw5kEJejpVqYf6Ieh0164SUaxsZXzi0v4AmgiA0AJKAMYBb4yNBEKKA84qiKIIgdMUVu8v0wdgeKIrC+hEvU5SS6fZgyj58lpNfLWPggtfZNukjrOdzUGSZyB6t6DP3hSum/gqCQGjLaLdj/lFhXlVAZIeEuVbJakiqtWmg7tBsDjJ2nyh+DzlHz7J+5CuIZhOCTofilOj+xRNXjZldTuupd3Dmt40UJaYXb5XqA/xo9shQQpp5Znp26l6PZQuOkJKYh8Px92okONTMyKcGXVfODKDu0B6kbDjgtrXH/7N31uFRXekf/9x7R5MQJUgCJBBcQ3B3ilOs7tt22223stv2t+3WhXbrxla27go1oLi7BIInBIi7y+i99/fHQMgwd2JMAqX5PE+ftpO5c88kM+c95z3v+/3i+h21nzHM7bE+/SMa3cOtMVFqOAus8Tqbw2uKsDDhhNfrSk9kIpzybDVRHE4yVu7GXlrhNRMhShKDX7qD/k/cSEVaLua2YRiDA5DtDjbd6O5bJ1vtyDYH2+58nSmrX67/G7xE2LH5lNfq3yMHc3z62T3385CeWsx/Hl+FzerAbpNRVRAlAUkUGDQiir/cPfy8FPe9cd4BTVVVpyAIdwMrcJXtf6Sq6iFBEO44/fN3gfnAnYIgOAELcJXaSL41JUdSKD+V7bHKVk4LBo/6+CEWnPiKysx8dH4mjCEN65HQB5iJuWESyZ+vdjuTksxGOl09vk4pwvLUHHK3a5REVw3a81dU/Yu7/e63aDWsV512gmcwBAUwa8+7HP9kBacWb8IY0oJuf51B5CRtNXSdTuTR5y9j6eJDbF53AllWGDwiilkL+uDnf+lp9MVcN5GDr37vajo+Xd0nGvX4t29Fp6vHX+DR+Za242I95bpqQxCQTN4Xf3p/k3dxAdV1/qxVNSmIIo7Sylq/N/oAs5u0V972I2hG5dOqKloO738WvAUzVT27W2sMFFnhpSdXU1psPedxFUVW2bU1lRaBpipVEV/ik/I0VVWXAcvOeezdav/9NvC2L+5VG7aicgSdDtAofFAUZKsdyaB3K8NuKEPf/DuqU+bEV2sRDTpkm4OOC8YwbNE9NY+xuJz1Vz5DzqYE5DrKZGmhOJwkfriMwS/dUa/r9P5metx1ude00bkYTXrmXhPL3Gu8S081hOzMUoqLLLTrEExAC2PtFzQBOj8TM3csIuGFrznx1VoAOl07gb7/utqtrSPlRCGrlx2jIK+cnn3bMHZy1zq/B0ulnYS9mciyQu/YiCZRUNDCGBpI3MK/EP/ox1U7UtGod+k4yopmQYjObCTmeu/u5UE9ovCLDKM0KcPtcZe4c3/ytnlKaAEYgvzqnNUAlzPF/oVfkvjBsiZ1g/gj0bNPGw7sy/SI97Ks0K2Xd+uk8+XY4VysFu/zmsMus25FIlfcEOfzXdqFr7f2MaH9YlCc2qvOgKjWHv5j54Nk0DPygwcZ9NIdlKfkENChFcbQQGSbneKjqZhaBmn2x6y/8hnX6lGjabs+qE4ZS5Zn5taaX4I1v4QWHdsgGS++XVRxkYU3Fq4jPaUYSSfidMiMn9qNq28eUGctwsbEEBTAwOdvY+Dzt2n+fOPq43z+v504HK6y9sQjefz+yxGeenl6recP2zae5KO3tyFKrvcpO1XmXduPqZc3TYPyufS+bz4t47py6I0fqUzPo+2EOHreM5eCvUls/stLWHOLXUt6wZV96HrrtBodzAVBYPzip1k+5j5kuwNnuRVdCzOm0EBGffwQqT9tYeeD77oXd/gZGfL6XXWu1lQcTpaOvIfSY2leF4SCKNJ2QtyfdncGcO2tA3nqweXY7XJVpbLBKDH/2lj8AxpvXigt8e6ifgZFdrli6AJ8u5C95AKaPsBM/yduZN9Tn3mUOA996++NMmEaQ1pUpS4PvvY9+578zKX84XASMaE/oz9/pOrn5ak55GxKqDGYSX5GVFmpVeRY528icvLZslpbURkbb3iezNV7q3rD+j95I73/scDjWlVVyd12mIwVu9AHmOl45dgaDS99haqqvPzUGjJSi13Vk6dTH+tWJBIa5seU2T0bfQzng8Xi4PP3d7qphDjsMk6HzNcf7+buh8Z4vTYnq5SP3t7mdi3A4q/3E9M1/IL5XrUZ3dejV9Jv2hCuyvyenE0HOPXDBkS9RMcrx3s1N61OSK9orkj9hpPfb6D8ZDYhfTrSYdZwRL2O7nfOwhwRxr6nP6P8VDZBXdvT/+mbvKa8tUhZstlls+Tl+yH5GdH5mRj+zn11fs1LkbaRQTz3xkyW/3yYowezCW3pz5RZPejZt23tFzcQu83JgfhMrJaaU9lmP32DBA9q45ILaAB9HrySFh3bsH/hl1Sk5RHSpxNxT99E65GN2x+R9OkK4h/72K0vLXP1XlZNe5gZ21wZ14rUXESjXttQUxCInDKIXvfMxdw2lDVzn8CaUwSi4NJ2FIWqA3XRoMMvsiXR1XrQVk1/hIK9iSh2Z1UwjH/8E4xhgXS58bKq5ylOmbXznyRrzV6clVZEvZ74Jz5pUJFJfUk5UUhuVplHK4BLMufQRR/QjiRkI0oi4B6UVBX27crQvug0G1cna/av2e0yq5YeveiMHAVB0Ax2dUHnZ3L7zFUnavaI83JxyFixS1uyC1dbTd9HrqXLzVMwBjeNGezFTFi4P9d56SVrDF55Zi3Jx/JqfI7BKDH3mljEBlTY1sYlGdAAouePIXq+99VyY7Dv6c88zCkVu5PCAyco2HecsNjOBHVr79Ud2hgWyKRfn6tKvcxP+pyigydxVljxiwhj/3NfkrJ4E4Io0unaCcQ+fkOV8G1hQjKFCcka6ulW9j31mdvkkvjhMrJW763awZ7ZLW6/600iJw1sVAX1/NwKrx/kUi8eTBcToih4MYqhRoFkcKnzy7JWAQNuXlJNRWVWAYkfLqPkWBrhg7rT+cbJ9XYEtxWWcvK7DVjzS2g9sjdtxvRr9LSxMTwYQSdpVhm3GdOP3ueIAzTTNJw8XsCJpHw3+bnqiKJAi0Ajc6+JZexkzTbk8+aSDWgXgoo07ZWJqJMoTcogLLYzpvBgYq6b6DLzrBb8dH4m4p66ye0cQRAEN5uaEe/9gxHv/UPzHqWJ6Yg6Ca3apYp093Ede+83j7J0cKUDT32/wUMtxJe0jw7BqbFLAWjdtulUuRtKj75tNBvNRUlgwJCaq0179mvLrm2pHj19eoNE7/Mooa6ssLPsp8Ns33gSURQYOT6Gy2b1qLExNmfzAVZO/ReKrKBY7aQu2cy+Zz9nxta3CexcN7WTjFW7WTvncVRcpfI6s5GwuC5MXvFio7pUd715CkfeWoJ8TkDT+ZvocddFqbr3p+BEUv65mhVV+AUYeP3DeRgMUqMueJodq31IQJT2GZTilAnqdrbBc/g799Pz7jnoAsyIBh3GlkEMeumvNVqk1EZgt/ZeVUACOrinsrSCGbiKTM7dYfqa1m1b0Du2LXq9p27cgutrVtlopE6PemE06rj1nmEYDBLS6cIOo0lHULCZq26u2f5j8IgoQsP83Cq7RFHA7KdnwtRuDRqPzergyQeWsfynQ+TllJOTVcYv3x/guYdXeNWVVBWFdVc+g7PCinI6W+CstGErLGPzba/U6b7OSitr5z2Js9LmWpgpKs4KK/m7jpGw8MsGvZe6EtStPUPf+juSyYDO34TOz4RkMtD7wStpO65xlFqaqZ2QML+q78S5BAebMRp1jb57b96h+ZD+T97Ilr++6rbzEg16wmI7V+nYgWvHNvCF24h79hYc5RYMgX4N1uM7Q2ifTrSM60rerqNuxSSSn5HYJ29ye27UnJEcev1Hj6ITyagn8jLf94acy98eGM23n+xh4+rjyLJCULCZK28awEANywlFUfn958MsW3KIslIbLVv5M/+6/gwb7d1RoLEZPCKaDh1DWb8yiYK8Cnr0ac3wMZ0wmWv25dLrJR77z1QWf72P7RtPIcsKcUPaM/+6/g1uW9i87gRFhZVuenoOu0x2Zim7t6cydJTn76kw4YR2qbuikrNhPwff+JGed19eY9N8+vKdmpOTbLWT+MEy4p6+uUHvp650vWUqHWYNJ+3XbSgOJ+2mDWlys9Fm3OkbF4neIHkUhBiNOqbNaZqzceFiWPV6Y+DAgeru3bsv9DDqxZFFP7H30Y9QnDKKU6bd1MGM+vihep9NNAR7STmbbnmJ9GU7EHUSok6i/zM30/NudxNGa34JP/e/HWt+SVVQ0/mbaD9zGGO/erTRx3kGWVaw22VMJu8rt68/3s3a3xPdzAcNRokbbh/MqAmePnF/Nl58cjWH9mmrzQ8bHc0d/xjl8Xj+7mMsn/BPnGXahRWSn5EOM4cz9mvvn4WkT1ew/e43q8xeq6MP9Oe64l/q+A58g5b0UjNNT3pqMa88vYbKCjuCIOB0yEya0Z0rbojz2d9HEIQ9qqpqrrybd2g+psddl9Pt9hmUp+ZiDAusqrTK35vI7v97n7ztRzAEB9Djrsvp/cAVVX0ymWvjSVj4JaXHMwmNjSH20etoObB+aShDUAATfnwKW3E5toJSAjq00rR2MbUMYva+9zn0+mJSl2xC18JMjztnE3PdxPP/BdQDSRIxm73vTCvK7axZnuihamC3yXz3eTwjxsU0SqXUxYricJKz+QCK3UmrEb3RB5jx96LWIggunzgtQmM7I+l1eCuslittpP6ylcIDJ9zOcKvTdlysh4TVmRtHTG4a52VFljnwwtccfO0H7IVltOgcwcAXbid6rmcQ/6NTmF/Bwf1Z6HUS/QZGNppKz5ED2Xz76R6yM12OFfOujaVv3Nkz1fzcctJTigkN96dDtKf1ULsOwbzy/lxOJOZTXmajU9eWTSoc0BzQGgFRryMw5uwhf0F8EstH3191duWssLLv2c8piE9i3LePk/TJ72y7+82qVGVFWi6Zq/cwYcnT9erPOYMxOKDWkmVTWBADnrmZAc80bmrofMhML0anEzVleirL7VRW2C8ahZHGJnPNXtZd8VRVEFGcMkPeuJvxU+LYtzvdbQcLrvTm6InaO1hRJzHqk/9j3VXPeLhFnEFVFLLWxnsNaAEdWhM+rCfZ6/adc6FK6waU+TeEbXe9QfIXq8+q+h/PZOMNz6PKCh0XNG2Fc2Oy+Kt9LFtyCFESXUa+ispt941g8HBPh5DzYeOa43z09raqwo5TyYW89uw6brh9EKMmdOa917cQvzMNnV5ClhXaRgbxz8fHe9jRiKJA5+4XJv3bXBTSBOx++AOPQgy50kbab9soPHCCHfctcp9YVBW50sa2v71xURRCNAUWi4Oliw/y5APLeP7RlWzfdJLAILNXPTpRFDCZfLceK8irIDuzVNsq5wJTmVXAmtmPYS8qx1FaiaO0ErnSxo573yasopDLZvZAb5DQ6UX0egm9XmLONf2I6hTq9TXbzxjGrJ3/RR/kRQxYr8NQw6LIabWTt/Oo5s8OPP+1V0NSX2HJKST505Wa9k27H3qvUe/dlCTszeD3n4/gcCjYrE6sVid2u8z7r2+hIK/CZ/dRFJVP/rvdo0pRUVS++GA333y6l/hd6TgcCpZKl+BwWkoRry9c77Mx+ILmHVoTkLddW79OEEVO/bDRq+J5RVoetvySS97XyVJp54l/LqOwoLJqN3YyqYC4Ie3o2DmM5GN5bv1beoPEyPExmvYX9SUjrZj/vryJnKwyBAH8/A385e5hbmmWxiDtVBErfjlCZkYJnbq05LKZPQhvrR1Ajn+2UjNAyBY7h177gfnfPs6oCZ3ZtysdQYQBQzrUyQIkuGc0cU/fxO6HPU1mUVSi5oz0em3J0VREUdRsE7EXlWHJKcKvbd21GetLYcIJRJNBUy2kPC0X2Wa/KGXf6suq345is3kmh1VVZcv6ZGYt8M1uOOlIrnaPJC6R43W/J3osLhVZJf1UEdkZpbSJrL+VVWPQHNCaAENICxylnlVlgijiFxGGIntTvlaRzI2fUis6eJJDr/9IaVI64UN70vPvc5q0YmzV0mMU5ldW2dMA2GxO9uxI496Hx/Ljl/tITy1GkkScDoU+/SO42gdK3ZZKO889vIKKCnvVosJus/D6wnWMndSFvgMi6ds/4rQyiO/YuzONd17ZhNOhoCgqp44XsHH1cR5+djIdO3sGgbKTWdrN+KrqcpbA1Q5x2awe9R5L97/NJntDAum/70R1KogGCcUhY2oTwncdriaoazv6P3Uj7aa6m9AbQ1p4VepXFRV9QON5XgH4R7b0en+dnwmxBjuoPxIlxdotNk6HQmmJ71psLJU1y+x5y5RIOpGiwsqLJqA1pxybgJ73zEXy8wxMokFHl5unuCzkz6kAEnQSERPjGn1iSPl5C78OuYvjn64gZ9MBDr/xI0t630JhQnKj3rc6OzafcgtmZ3DYZY4dyuWJl6bxxItTueP+kTz/9kzufXgsBsP57862bTzpuu+5auROlTXLE3nn5U38+77fqCj33cQhywofvLkVu02uSm/KsorN6uSjRds0r2k9og86jc+BaNCd93mVKEmM/+FJpm96g4HP3+ralYkC5SeycJRWkL/7GGsXPEXyV6vdrguIak1Iv04I5wR7Ua+j3dTB5O8+xpo5j/PbsLvY+8THWPOKz2uc5xLcM5rg7h0QzhEflsxGuv9t1iVT8dg3LgKd3nOaNpp09OzTxmf3ienWEm8SOJIkEByqPQ85HTLtoi6eDFJzQGsCet4zh6g5I12NoAFm9C38MIYFMnnFf5AMesb/+BSm8CB0AWYESUTXwkxAh1aM+ODBRh2X4nCy+ZYXkS22s8UGdieO0kq23vFao967OnovwUkURQxG18/aRYUQO6gd4a19pyaSmVbiUUxRHavVSW5WGV/8b5fP7pl6skhTzxEgI7WYygrPnVj0gjGYwgLdJ29BQDIb6XXfPJ+MK6x/F7rfNZvUX7ahWNzHIFfa2Hn/Ox6ZhPHfP4l/h9boWpiRzEZ0AWaCenYgtF8nVs38N6k/byFvx1EOvPgti3vdQnlqjk/GeoaJvz5HSO+O6PxN6AP9kUwGOlw+ggHP3OLT+1xIJs/ojtmsd6vm1esl2kQE0m+g79LiLQJNjByrXQB0xfX9ueqmAVXfxTMYjBKjJ3WmReCFsT/Sojnl2ASIksSYzx+h9IkMcrcewtgyiMhJA6pK6oO6teeKlK9JWbKZ8pPZBPeKpt20IY1ufZG/J1G79BrI352Is9KKzq/xP6zjJnchI7UE+zlnBaIkMHhEdKPdt11UCEaTzkOKqjpOp8LOLSncft+IOq36K8ptnEouJKCFkQ4dQzyukXSiV3kgQLMNQWcyMGPHInbct4iUxZtQZYU242IZ+ubffeLrd4bSpAyvxRyOCguV6fluajj+7cKZn/QZmWv2UpacRXCvKAK7tuOHjte6pUgVmwO7s4w9j3zImC8e8dl4/dqGMXvvexTuT6YiLZeQvp2axDGiKQkMNvP0q9P58at9xO9MR6cTGTk+hlkL+iD5OBX+l7uHEd4mgGVLDmGzygQEGrnqpgGMGu8ShZAkge8+iycvp5yAFkamzO7B9Lm9fTqG86U5oDUhgZ0jverkSUYDna5qWkdkUSfVXEV5nuoldWXk+Bj2bE/j6KEcbFany6pdEpl3bWyd9R2dDpmE+EzKS2106RFO20hPH7pzGTIqmu8/j8duc9YYZGTZddblTdYHXIf0i7/ax/KfDqPTSyiKSnComX88Op42EWfPF9pHBeMfYPAIooIo0KVHK69qI+ZWIYz96tGqv1ej2CCFttA09QRQZUWzIlIQRVdrySTX/yd/tcYjDXjm+rTftFOq50tovxhC+8XU/sQ/KKEt/bntnoa7E9QVURK5/Mp+zL6iL7KsephvDh4RzeAR0Rd1E3tzQPsTExbXBZ2fyUMxQhBF2ozp26gCs9WRJJH7Hx3H0YM5xO9Mw2jWM3xMxzoFJXCpfL/05GpkWUFVQFFV4ga35477R9RY0GE263nshSm8+9pmUk8VIju1o1rHzmFIkkhmegnLFh8i5UQhbdsFMX1ur6rS+C3rT/D7L67y6jNq47lZZbzw6Epe/d/cqnEIgsBdD47mpSdWIysqDruM0ajDYJT4y93Dan2vdZ1IFEWtd9O5X9swwgd3J3fbYTcle1GvI2JiXJ3sWCSDd9UXUdc83fwREAQBnc77Z+diDWbQLH11SWErLuf4pyso3J9McK9outx0GaawmoNC9sYEVk1/uEp1XfIzofM3MnP7Ilp0bDwjQF/hdMjcc/MPVJS7n/sYjBJzr667E3RxkYU1y47x+y+Hq87VBFHAoJf4v2cm4XDIvPr0WhwOVzGHILjOMu58YBRxg9vzr7t/Jiu91ON1TWY9dz04yqMNoLTYwqa1yWRllNKxcxjDx3bCXIsWZG0oisrynw6xbMlhystshLX0Z961sYwYp302okVlVgHLx/+Tyox8VEVBEEVadGrLlNUva7qvn4ujrJKv2873aAMQDTq6/XUmQ9+4u97vq5lmqlOT9FVzQLtEKD58iqWj7kW2OZArbUhmA6Jez9T1rxIWW7PmYWVmPokfLackMZ3wwd3pfMNkDIG19zFdDMTvTOPd17ZgtXiWHYe19OPVD+pXNJGwN4Oliw9RkFdBTLeWzFrQh4h2Qfzf334mJ6vM4/ktAo28+fF8/nb9d5qlzwajxDW3DGTcZV3rNY6G8NWHu1m30lP38vpbBzF6Ut39p1RFIXvDfkqTMgjs1o42o+vncXbqx41svOEFl+u63YEuwIx/+3BmbH2rSTRNm7m0adZy/BOw4frnsRdXcOYwSLbYkS12NlzzLHMPf1LjtX4RLYl99PomGKXvKSu1oXpR96ioqLm3Rou+cZEeu6mSYgsF+dqqDHa7TEZaCR06hnDsUK7mc6JjGq/B+AwV5TbW/p7o0f5gt8l8/8U+Rk7oXOcUpCCKIAgceednihJOovMz0vXW6Qx4/tY6paGj542m5cBuJH26gsrMAiLG9ydqzkhNXdE/O8mJeXz7aTwnj+fjH2Bk8ozuTJnVw+e9j41NyolCtm44gc3qJG5Ie3rHRlwQndXmT9gFRlVVTn63nqOLfsJWVE77mcPoff98TOHByHYHqT9tofhwCoFdIomaN1pzQqnMLqT4cApalQ3lKTmUncp29bpdgnTpEY7iJcvQxUd6cpIkeA2aqqJiMErMv7Y/Lz25Gns13UmdXiQ6JkyzWdrXZKaXoNOLmv18lRU1616qqkpaSjGV5XaiYkIpjU9k1fRHkC2utKGzwsqx936l+PApLlvxYp3GExDVmv6P39DwN/QnIDkxjxceW1W1o7bbKlnyzX7SThXx1/u9q7Q0Ngf3ZfLbj4fIzy2nU1dXlqJdB++9Zj99m8DSHw/icMioKmzdcJIu3cP5x2PjfV6JWRvNAe0Cs/WO1zjx1ZoqG47S4xkc//h3Ji5d6NLvK63AWWZBF2Bm5z/fYdqmNwjq0s7tNVSn7DUlJAiiV0WFS4G2kUHEDWlP/I40t2BiNOpqNQytC+mpxbz6zFqvGo+hLf1p1aYFrdsGcu8jY/nyg11kZZSi00mMGNeJa25pGuX5kFA/N0+06tSke5msuXSOAAAgAElEQVSdUcqrz62luNCCKArIToUxh9dXBbMzyFY7OVsOUrDveK0p7KZEVRROfrueY/9bimyz0+mqcXT9y7QmaTc5X775ZK9HH6TdJrNrayqXX1XmMwf30mILFouT8Fb+te78Vi09ynefnR1Xfl4F8TvT+L+nJ9G5m+cCMSOtmN9+POgmIG6zOkk8ksvmtcmMqUeq2xc0B7QLSPGRFJdaeLXJQ7E5sBWWsXrWo1hziqr6xJzlFpwVVtZf8TSz4993ex2/yJb4RbakLDnT4x6GkACvrQKXCnfcN4IVvx1l1a9HqKhw0KV7OAuu71+jOG9dcDhknn90JeWlnkohOr2IwaDjrodGVy0mesdG8Pzbs3E4ZCRJ9EnKxW5zTQ6CINC1ZysPp+8ztGwVQEy3liQdyXNr3NYbJEZN0Na9dDoVFj66gtJiq9vm3pKY6nViKNiTeNEENFVVWXfF02Ss2FW1ICzcn0ziB8uYse3tiz6onTxeoPm4JAkkJ+add0ArKqzk3Vc3c/xYHqIoYjRKXHvrIK/muFaLg+8+3eu2MFQVFbtN5rP3dvL0q9M9rtmx+RSyhiyW3SazYdXx5oD2ZyJjxW7NRlbF4cSSqfFhV1VKEtMoT8lxa3AVBIFRHz/Eyqn/QrY5XDs2nYRk0DHqk/+7qMtsfYEoiUyd3ZOps33rirtvVzpOjRQeuJQVFr45E0VRKS6yEBRsqvo9ews69WXH5lN8+PY2V2BUXQpdf71/BHGD22s+/+8PjeG159aSeqqoSvey34BIr7qXCXsysFllj0y13WhC5/Q8fxQlCb+Ixk+f1pXsDfvdghm4VE1KkzNJ/HAZPf8+9wKOrnb8/PSUaFgjIXDeHmKKrLDwkRXk51aczi4o2G0uebWgYBM9+3pWMJ88XoCkE0FjTKkni3A4ZI/PtuxUvPayetN/bEyaA1odURWF8lPZ6PxNmFuf38r/DJLZ4KGFV4WApgq/IEk4yj2dhluP7MPs+Pc59MaPFOxNIqRPJ3rfP5+gbtqTXzO1U5Bf4TWN57A7efXZtZxMKgABQsP8+Mvdw+ne2zdKFempxXzw1laPlNQ7r2zi2ddnaq7eAwKNPPafqWSmlZCXW05k+yBatvJeVViQV4Hs9Jy80mJ60/nQLiS5WqpaENAFmIioxZ8vf/cxkr9ag+JwEj1vNG3G1K9Csj6k/rwFp4afm1xp48TX6y76gDZpRnd++e6A244IXOny89VpPLAvi9ISq0eq3G6TWfJNgmZAM5p0XlProiQgaWQc4oa0Z+VvRz39+AwSw0ZHN/wNNJDmgFYHUn/ZytY7XsNeWoEqK4T178KYr/593oUW0XNHsfP+/3o8LpkNiAY9jhLPyjrJpCeou3aQCuwcybC37jmvMTUDeTnlbFpznFPJhV4FW60WJ8eP5VcVi+Rml/PKM2t48uVpRLY/f7HW1UuPau4OZafCupWJXHWj97O5iPZBRLSvvWesQ8cQ15nKOUE7K6or7f1kWuzbh2jQoyoKppZBTF7+Qo1ybDsffJej7/zikr1S4fgnK2g3fQhjv3rUVTlZRxwVFvJ3HkXnZ6LloG5er5WMegRRQNWwPZEaSRSgIiOPfc98QfrS7egCzHS/YyY9/ja7QRWc0+b0Iu1UEXt3piOKAoIgYDBKPPjkxPOucszOKPW6GMvO8OyXBFc1rtGoLQUXO1DbdaJTl5YMGhbF7u2pVdcZjBLhrQIYP6XxW1XOpTmg1ULu9sOsv+ZZt0bR/J1HWTbyHuYnf3FenkvGlkG06BxJ8cGTbo+rToWh7/2drXe8hmyxu6oXBQHJbGDYovsQpcbVePwzs3NrCv97fQuyoiI7lXNNEACQdIJrIj0npeJ0KCxdfIjb7z1/maK8nHK0ZBVlWSUvu/y8Xx+ga89WtI0MJD212G3yM5h0XPbxP4gM0ZG/OxFTWCAtB3evcaeVt+MIx975xe174qywkr50BylLNhM9b3SdxnT03V/Y9cC7CDodqqqgD/Bjwk9PEz6ou8dzO10zgcNv/eRRwKLzN9H11ml1ul99qMzM5+fY27GXVFQpqez594dkrt7DxF+eq/dOVJJE/vbAaLIzS0k+lk9gsImefdv4pDKwTUQgOr2omfbzZvUiCCB4ubXqJXsoCAK33TucuKHtWb8yCZvVydBR0YwcH4PR2PTh5Y/V7HAB2L/wS1dQqYaqKNjLKkn5act5vXbOxgTKT2Z5PK4CRQdOMm3D63S4fAQtYiJoN20Il6186ZKylgeX0kf8zjQ2rjlOdkYpKScK+eGLeL7/Ip5TydqH5o2FxeLgf29swW6Xqw66T68lqv5pHx1C3OD2blVdZ1AUlZQThT4ZS7derTVdCAxGiW69fJPWFASBfz0ziSEjotDpXEUsbSIDue+RcXTuFo65VQjtpw0hfEiPWifr5C9X49TwbHNWWEn8aHmdxpO1Lp6dD7yLs9KG43R1ryWrgBWTHsRe6pmtCO0bQ5+HrkQyG12pe0FA528iYtIAOl45tk73rA8JL3ztytJUS9PKlTay1+/3auJbF9pEBDJiXCf69I/wWZl7n/5taRFo8ihMMhglLr9S23LoVHIhNot2RfTenem888omLJWef2NBEBg4tAMPPD6Bfy+8jAlTu12QYAbNO7RaKT50SrO/y1luoTQxHQBrQQnZGxLQmQ20Hd+/zru2zNV73A60z6A6nKQv3c6g/9zOhB+fOq/xX8ycPF7Ay0+txulUURQFp8N1wHwmiKz85QijJ3bmutsGNUlhy8H4TERRhHN8mFXV5WT91qcL0OlE1q1IZP+eDI9zA0Gg1lSfLCvE70rncEI2QcEmRo6L0XSXHn9ZV1b8cgSn42zRhii6pLRGja+7lFVtmP0M3H7fSP7y9+E4nUqDJyLZ5gAv5y+a5qQaHHjxW0/nbFzCxie/XU+32zyr7Po/cSNRc0e5Wl8qbUTPHUXr0X0b5fOSvmwHqlYa2Gona+0+Wg2rm8xaUyBKIo8svIx3X9lEclI+kiiiN0hce+tAevXTlrSzWhwINVTm7t6WSkFeBY++MKWxhn3eNAe0WgjuGU35qRyPoKbzNxPYtR0J//mafU99hmg4/asUBMb/8CQRE+JqfW1DcACiUY+iYSOvpWx+KeF0yLz81GrKy7QnO1V1qXBsWpNMr35tOLQ/i+2bUlBVlQFD2jPvuv4Eh/jW/NSVntGelBVZqVIfH1ql0u95ED59jvdJzWpx8NwjK8jJKsNmdaLTifz6w0Fuv3e4h01OQKCRJ16ayuf/28XB+EwEAfoOiOT62wZj9vP9+ZAkiee1O4g+E1TOWaBJfkZirplQp9co08hWgGuXV57i3UsttE8nQp/3XZD3ht6LOLNo0GMIrv37qqoq61cmsXTxIUqKLbTrEMyC6/trFmj4gtAwPx5ZeBklxRYslQ5atQ6o8WyuY+cwr1594Pp+pJws5FRyQZOo3zSE5pRjLfT797UeB8yCKKJvYUbnb2L/s18gW+04Sitd/5RUsObyx+rk0NvxynGaK0mdv4ked13us/dwMXIgPhOnF3X76thsTt57bQvrVh6nvMxGRbmdLetP8MQ/l2qaYZ4PvWPbap45iCLEDj7bzG72M/DIc5NpGxmIwShhNOloEWjkzn+MqvGL/vN3B8hKL6k6PHc6FRx2mf+9sVUzldOqTQv++dh4PvrxWj784Vrue2Sc5m7uYiBi0gDaju+Pzv9subnOz0RIr2hirptYp9doNayXZtWvroWZlgMaXmDgtNp9Ii7Q8+7Lvfa2RdfhKOC7z+P56qPd5OWUY7fJnEgq4LVn17F/T8Z5j60mgoLNtIkIrLXQRKcT3ayOtBAEgfRU37qP+5LmgFYLrYb2ZPQXj2BqHYLO34Rk1BM2qCvTN7/JkbeWaKcMFYUTX6+t9bX924Uz4oN/IpkMSH5GRIMOyWwkesEYOl3dtN5oTU1Zmc2rmeS5VD/TAldhRGW5nQ0rk3w6phaBJuZf19/lzHt6naHXS/gHGLnievcdd7uoEF5YNJtnX5/J4/+ZwpsfzyduSM0tEpvXJVdZy1RHlAT27fY+qQmCcNH3EgqiyPjFTzHi/X/SdkIcrUf1YfCrdzJt4+t1TsH3/dfVnotHvYS5dSjtZ9ZurXMu+buP8cvgO/mixXQ+C5jGmjmPY8lp+Bln5xsmEzVvlOu7atS75gOzkdGfP4y5VUiN15aX2Vj1q2d5u90u89WHvnNEPx+++WSv1wrIMwhAeA2tIBea5pRjHYieM5Ko2cMpO5GFzt+EX1vXKrwyI1/z+bLFzomv1+CotBJz9QS3JuhziblmIhETB5CyeDPOCguRUwYT0iu6Md7GRUXX7q28Hbm4IYqCZm+M3e4y9JxaQ4qvIUyd3ZNOncNYtfQoRQWV9O4fwYSp3bw2utZHzUFLUQFc6VUtDcY/GqIk0enq8Q1ejAV1a8+Uta+w/e43yd+TiChJdLh8BMMW3Vtv9/aSpHSWj/vH2QWnDGlLt/Pb0LuZe+xTJEP9rXoEUWT0p/+iz0NXkblqD/oAE1FzR2EMrXlXAy7xXm9amzlZZZpNy01FYX4Fq5cdY/XyY141S8H1XQwO86Nrz1ZNOLr60RzQ6oggih4SUm3GxlKSlK55UJy34ygF8cfZ//TnDHvnPrrceJnX1za3CqH7HTN9PuaLmTaRgS4Nxp1pHqvWMxiMEmaznrJSm0dQEwR8foZ2hm69WvuskrA6sYPasW3DSY/3osgqffpH+Px+f0TCB3Vn5o7/ItsdCJLY4BaVAy9+41GMojplrAWlpCzZTKcrxzV4jCG9ouu96GwRZELR6JcDVxagqUV8z5CcmM9/Hl+F0ynXGMx0OpGoTqH8/V9jPLIFTofMzq0p7N6WismsZ/TEznRvhO9PXWgOaOdBn4euJPnL1ThKKzUrIc/Y2W+783XaTRnkM4WRS4U77hvBil+PsPK3o1RW2Inp2pKOncM4lJANwIixnejasxXP/t/vHmoKeoPExOndLsSwG8z8a2NJ2JOBxeKo6vsyGiWmXN6LkFC/Czy6i4uG7KCqk7ftcJUOanWc5RYK9iSeV0BrCO2jggkL9ycro8RtqtDrJUaOj6mT7qfTIbNrWyrxO9Px83cFjk5dWjZ4TKqq8t7rmzUbqasjSSKPvzhVUxvVbnOy8N8ryTxzNizArq0pTJzWjStraP5vLHwS0ARBmAK8AUjAB6qqvnDOz4XTP58GVAI3qaq61xf3vpAEdGjNjG1vs+uBd8lcs9cVwLR0zQSBlMWb6X7nrKYf5EWMKIlMvbyXh6v0gnOed+NfB/PJeztdNi6qq/R9/rWxxHT1jT1MY3JG504QBEJb+rPwrVms/PUIB+IzCQw2M3lG9+bdWSPQIibCZal0DpKf8YI4sQuCwD8eG8cLj62itNiK87QGYmCQkSmze9R6fVpKEQsfWUFlNY+/zWuTmX1FX2Yu6NOgMRXmV1KYX1njcwxGidETu3gV+l67IomM1OKzC07VJa+1aukxRoyLqdF2pjE474AmCIIELAImAenALkEQflFVtXqn4VSgy+l/hgDvnP73H57g7h2Y9NtCAL7vdI2rxP8cVFnGWelZPNJM3Rg5oTP9h7QnYW8miuJKz52veGtjU1Fu5+uPdrN90ymcTpnO3cO5/rbBRHUKZf51/Zl/3flb2zTjnT4PXknWmr0eWo+iJNHRyxmfoqg4nQp6vYggCFSU2/j+i3h2bDqFLKvEDmzHlTfGNbjSNLx1C6bN6cVXH+2uSjuXFFt58oFlPP7iVNpGavcwFuRV8NQDyz3O3xwOhZ++TWDo6GjCW/vGaqY6fv56ps3pxfS5vb0+Z8vaZI/sCbjOi/dsT/3jBTRgMHBcVdUTAIIgfAPMBqoHtNnAZ6prubpdEIRgQRDaqqqq3XjyByVqziiOLPqpKtV4BkGSaDd18AUa1aWBf4DRq+1Fdex2mT3bU8nPKaddVDD9BkQ2ufuvIis89/DvZGeVVRWCJB3J47lHVvD0K9O9Sg9Vx+GQWbciic1rk1FVleFjOjL+Aiow/NFoPbIPQ976OzvuXeSSKVNUDIF+jF/8NMZz+skcDpnvP49n/cok7DaZsHB/FlwXy5JvEsjLLa/6G+7aeorDCVk8//YsWgTWf0FlqbTz9cd73GTGnE4FWVb48oPdPPCEdr/eb6fNM7VQFJU929OY0gCnidCWfoS19CM7s8zjZ63btuA//51da3VtHeq6mhRffDsigbRq/5+O5+5L6zmRgEdAEwThduB2gA4dOvhgeE1Hn/+7ihPfrsNWUFrVLK3zN9Hp6vEE94y+sIP7E5CZVsLCf6/AYZex2ZwYTTqCgs08+vxlBAY3TgGJFgnxmaeV7N3PcBx2mV9+OFCr1qMsK7zw6EpSTxVVFcxkZ5SybeMpHvvPlAtWDfdHo+vNU+l01Xjydx1DMhtoOaCrptDxO69sImFvZpWcWX5uOe+/saXK8PQMiuJqjl+97BhzrupX7/EcO5yrqQ2qqnBov/e1fU0/A7w6tteGIAj89f6Rp4tCXEo9Or2ITidyxz9G1qlVZOS4Tvz45T6PXZpOJzJgaNPP375Yumq963N/w3V5jutBVX1fVdWBqqoODA9v2BmJqqokfbKCJX3+wlet5rJqxsMUxPu2Z0kLc6sQLt//P/o8eCUhfTrRelQfRnzwAMPf+0ej3/vPjqqqvPH8esrKbFitTlTVpYifn1vOR4u2N+lYTiYVYNU4aFcUlaSjebVev2d7GmkpxW7Vn3a7THZGCds3nvLlUC95dGYjbUb3JXxQd81glpNVRsKeTA9tTllWNXsGHQ6Fg/salliSJNFrRa832xag5t2gAHGDGm4R1alLS15YNJtpc3rRf3A7ps3pxQuLZte52GT8lK5Edgg6mzkQXOduE6Z1a/J0I/hmh5YOVP+NtgPOtU6uy3N8xq6H3uPYu79W9aCkL99F9vr9TFnzCuFDaj+APR9MYUHEPX0zcU/f3Kj3acadrPRSCgsqPJZJsqySEJ+J3ebE0ETpupCWfi4bDptnUAtrWXs14+5tqZqVZzabqzx61IQYn4yzGUg7VYROp90fpolAgytSKys8dSqrXlaAwoJKQsM8X/uyWT1IfbNQMxhOnNq1xhS2pdJOZYWDkDA/r5WUIaF+zLsmtg7vwBODUcejz09h59YUdm1NxXymbN9HvoD1xRff8F1AF0EQOgIZwFXANec85xfg7tPna0OAksY6P7PkFHLk7Z/c9RFVFWeljR33L2LG1rcb47bNXGAsFgeShrAwAKcbl5sqoA0ZEcXXH+3xeNxglDwqOrUwmXUIgnbBrMncfIZWH4qLLHz90W727EhDVVX6DYjkmlsGVhmfhoX71ytlZzBITJ7haWVTG6qq8uWHu73+XJQEvFXuDxregePH8liz/BioZ3dz86+L9VqwUV5m44O3tnJgbyaiKGA06bj6loGMGOt7zUudXmL4mE4MH9P4epq1juV8X0BVVacgCHcDK3CV7X+kquohQRDuOP3zd4FluEr2j+Mq22+07UvutsNIXgR/83cda6zbNnOBaR8d4tUKPry1P37+jWP4qIXZz8BDT03g9efWY7c7EQQBp1NhztX96DcgstbrR0/ozLaNJz1W5EajjrGTujTWsC85rBYHTz6wjJJiS1VT894daSQezuWFt2cTEGgkOiaUlq38ycoodWt8NhglBg7twO7tqVU7G9npahdpiFJG2qkiLJWec9IZ2rQNJNjLzk8QBK65ZSCXzezBoYQsTCY9/QZEYDTpKSqsJCW5kKAQM9ExoQiCgKqqvPjEatJTi6vOAO12mU/e2U5AgJF+A2v/DP5R8clyT1XVZbiCVvXH3q323ypwly/uVRvGkBZeS2+qC6c2c2lhMEhcfctAvvxwV1UgEARXA/aNdwxpFC1EVVVJO1VESbGVqE6hbq0EMV3DeeOjeSQdzcNqddKle3idg2rn7uFMntGdFb8ePT0hqeh0EqMndqZn3/NzSf8zsXXDCSrL7W6BSlXBanWydkUiM+b1JvFILhOndWPV0mPk55YjSa704+gJnbn21kHceMcQDu7LQpYVevVtS0CgEXCV0u/b7XKa7j+onddgdAaHQ6mxefqmO2vvYgoL92f0hM6Aq5L2w7e3sW3DCXR6CUVRCQ3z44EnJlBcaCE7s9SjKMluk/nxq33NAe2PRKuRvdEFmHCUuTcMSiZDo7jYNnPxMHZyF8JbB/DrDwfJzS4jqlMos6/o0yhWF/m55bz67FrycyoQJQGnQ2bMpC5ce+ugqolLlMQGS2gtuD6O4WM7sWtrCqoKA4Z2oEN0zQK4Fwt5O45w8rv1qKpKxwVjCB/a84KIKx89mKN5jumwy+zfnc6GlUmUl9lAANmp0q13Ky6b2ZPomLOLE5NZz8Bh7tV6P3+bwK8/HHRVLArw5Qe7uPKmAUya7j0VGdUxxOvvILJDEF171u9zsmzJIbZvOonDoVQVr2RnlfHiE6uZNreX10V9TmbN4sN/dC65gCZKEpOXvcDvEx9AsTtRHE4ESaTl4O7EPXNLo95bVVXyth+mPCWH0H4xBPeIqtf1jgoLJcfSMLcOwT/y4lfBuBjp1a+tVwNDX3EmpZObU+6mf7dxzXHC2wQwZVbdeoJKS6wUFVTSqk2ApsdZZPtgIq9s+kqxhqKqKtvufpPjn65wubwLkPj+UjpdO4Hh797f5EEtLNwfSRKQz9FQFARITynGZnO6nVMmHsqlbWQQ2zacIGFvBnqDjtETYpgxr3fV+euxQzn8ttizL+y7T/fSrVdrt0WHctrMde/ONMxmPTPm9ebn7xJw2M+atkqSwIx53huXvbFCQ7lfVVSKiyzITkWzPQCoOju8VLnkAhpAaL8Yrkz/lrSlO6jMLCB8SHfCB9X/ILc+VKTnsWLyg1Sk5yMIAopTps2Yvoz/8Sl0ZmON16qqyr5nPufAi98g6iQUu5NWw3sx9pvHMLWs2QH5j8iJpHz27khDpxMZMiraq0LChcRul9m9LYX0lGLaRAYyZEQURpNLXzDpaB7FRRYPMVe7TWb5T4drDWg2q4P339zKvl3p6HQSsqwwbnIXrr55QKM2gTudCtmZpfj5GzSr6c6XrHX7SP5s5VnXaRWclVZOfLWG6PmjiZw00Of3rImxk7uweukxZNl94pckEeW0M3p17HaZVb8dRRRdPWdgZ9mSwxxKyObfCy9DFAXW/p6oqYzhdMpsXH2c624dBLiKkF58YjUpJwqxWZ2u9LdeYujoaHZtTcVqcaCeLvD4eNF2ysvs9So2KS/TrpgUBIEWgUZCwvzIySpzawcwGCUuv6pvnV5fUdQ66UtebFySAQ1AMhqInjuqye63evajlCZluAmiZq/fz84H3mX4ontrvPbY+79x8CWX/fyZr0rOpgOsmvYvZu58pxFH3bSoqsoHb21l55YUHHYZQRT4bfEhZs3vzawr6vZFawryc8t55v9+x2JxYLO6GrS//WQP/144hYj2QRQVVHpdAZeVei/NPsO7r27hQHwGTodSpRqxflUSJrOOedc2jiTWpjXH+eqjPciygiKrdOgYwl0Pjq5VxklVVSoz89H5mVzn0zVw/NMVmv6AzgorSR//3uQBrXXbQP56/wjef2Mr4uk/mCwrjJ7YmS3rT6BZEcuZYObC4ZBJO1XEof1Z9OkfQVmpVTOdpyhQVnL2va9bkcSp5IKqXdQZB/bNa08gikJVMD3z+Hef7mHw8A5ez+KyM0o5cjAbk0lP7OB2RLQPIj3F02hTdip07BzGv56dzKKXNnIyKR9JJwIC86+NZdBw71kjRVb49ceDrPjlCBXldsJbB3DFDf093NQvZi7ZgNaUFB9NpeRYmoe6t2y1c/yTFQx98+4abTD2P/elx0SgOJwUH06lYN9xwmI7N8q4m5o929PYtSX17JdcVlFkmV9/OEjs4PYXzRnR+69voaTEWrUDs1md2Gzw9ksbWPjmLKI6hnqksc4Q2b7m3WZRYSUH4jM8mnbtNpmVvx7l8qv6+dxK5EB8Jp+9v9MtRXXyeAELH1nBS+9e7nVXmLZsB1vveA1bfgmqotBqRG9Gf/Yvr+lw2eI9mJ9r5dJUDBwWRd+4SA4fyEZVVHr0aUNlhZ0Nq47X+TVsVidHD2bTp38EsYPak3Q0T7MCtXqxxaY1xzX7xhRF1WyiFgSB+F3pjLusq8fzP/7vdrZtPImAy5NMfQdmzOtNbtYBt92iwSDRf3A7wlu3oLjIQlSnUPJyyjDodUyc0Y3xU2t2/f70vZ1s3XCiatx5OeX8742tKAoMHRVd26/poqDZsdoHWHOKEPXaawPF4az1y2zJKtB8XNCJlCU3Wv95k7N+ZZLmIb3TKbN1XfIFGJEn5WU2khPzPb2hVMjNLicvp4w2kYH0jm2L3uC+SBFFgT6xEThraNLNzy1H50W6yikrWCq0S7vzc8tZvzLJVblXUb/g8PO3CR6Tq6KolJfbSIjX/nzl7TzKuiueojI9D9lqR7E7ydmYwNKR96I4tO1GOl4xVrOSWOdvomMT27VUx2DUETuwHf0Ht8dk1hPa0p9hY6JdzuTV8Lbr1utFWpwuEhk9IYagYDM6nej28/DWAW67H2/eZ95QvVyzZd0Jdmw6icMuY7fLWK1ObFYnv35/gMBgk9uYA4NN3HjHEEqKLTx232+sXZ5IUYGFnOwyvv88nrf/s8Fra0tpsYUt65I1HbW//XSP1+suNpoDmg8I6dtJs+8NwD+yJTq/mtsFAjpql2IrDpngnvUrLLmY0QpmcFojrxZPpqbC4ZC9Fi+IolCl4HHXg6OZMLWr28SmKCqrlx/jyQeXYbVofx5atw30GvAMBgk/f3cfMFVV+fqTPfzrrp/58sNdfPrODu69+Qd2b/O0RvFGTpan+CyA06GQc44wraPcwpFFP7F69r/PnoWdGYusYCssJe03dykxh0Nmy/oTrM2UUDtEIiMP8AUAACAASURBVFU7M9b5mQjt36VJ0/914eY7h3L5lf0ICjah04lEx4Rx+VX9NMWfBUFg6CiXMLbJrOfJl6cxcXo3QsJc4r5TZvfk0XM0NoeNifZY8ICrgVrSaQk6ollOv/K3I9g0dnoOh0JBXoXbOWBJkYUvP9jNssWHqKywI1fLGNltMvv3ZrLy1yMoGj5xaSnFXhdaRQUWTRmwi5HmlKMPMIa0oMff53B00c9uNjGSn5FBr9xZa3VX3NM3s/nWl90mENGop9WIXvWulLyYGTQ8ilPHCzwO1Y0mHXFDGq5H50uCQ8wEhZjJzy33+JleLxHRLqjqv6fM7snqpe7N+jark+yMMpYtOcRcDTmhwCATg0dEs2trinu6yCgxY34fj/Tf3h1prFue6DGhvPfaFjp3C6+1/8npkDH76Skt8Tzb0ulFIqqlSC25Rfw6+G/Y8ks8bFeqXq/CRvHhFKLmjASgvNTGUw8to6TYis3qRN99FK39kukn5xAQYKTzDZOIuWGy1wzGhUKURKbP7cX0uWeVW1RVxVJhZ83yYwiieFqtReWO+0e6uaMHtDBy9c0Dufpm72eCE6d1Z+v6k+TlllfteoxGHUNGRnHkYA4lxRbX44JrITN9Ti/NCsSKcu3duNaOyeFQ2LnlFCFhfjidngFIdip891k8a39P4t8LJ7sJdoeE+Xn0rZ3BYJTcFm4XMxfXp+wPzMAXbsO/QysO/OcbrLlFBHVrz4Dnb6P9tNobJjtdNR5HhZU9D3+As8JVPddxwRiG/fe+Jhh50zFmUmfWrUgkL6e8SgzWYJTo0j2c3rG+Nbm025ws//kwm9YkI8sKg4Z1YOaCPrXafgiCwC13DeX1hetwOBRURa2qULvpziFuASd+ZzqiJMA5m0uHQ2bLuhOaAQ3glruGYvLTsWm1K80qSSLT5/Vm2uWe1ZErfzuqubNVVZWtG08yrQYpLUVWePnpNRTmV3i+TxGCgs1uLQ57HvmAyqwC1BpSpjo/I4Fdzu4kvv10DwX5lVWToUOG9MgY8s3deOuTBU0mN+YLBEHg6lsGMnF6dw4lZGE06IgdFKnZUlEbJrOeJ16expZ1yezckoLZz8DYyV3oGxeBzepk45pk9u1KI6CFifFTu9LdS79ir35t2bw2uUbx4nOpyWLI6VTIyynjw7e3cf+jZ33hItoFERkVTEpyodu99AaJCVO7/mEqHoWLOTc6cOBAdfdu7/pnlxqKLGPNLcYQ5F9rmvKPitXiYO3viWzbeBKdTmTM5C6MGh/j00IIRVZ45uEVpJ0qqgqcOp1IYLCJZ1+fiX9A7RNU6slCfvvxEKknC4loH8T0ub2J6equQL562TG++WSPh1I7uLymXvtgXo33sNuclJfZCKx2JuN0Kqz45TBrlidiqXSgKApWi3Y6dtqcXlx5Y5zX19+3K53/vrJJU+i4bWQgDz83maBqq/QvQmbhKPEMflWIAubwYBac+grJ6Pod3n7V15qvbzbrueOfI4kd2M776zWjyfFjeSz5ej+pp4oICjaRm1WO3X62Z05vkHA6ZI+2A3BlAOZf158vP9ipmao8g04nsujzKzCZz6a4S4otvPrMWjLTS5AkEadDYeCwDtx6z/CLaocmCMIeVVU1t8d/nOXTnwBRkvBr63tVi4sJk9nlgjttTu0ivQ1l3+4MMlKL3QKN06lQVmpj3WnJo9ro0DGUvz1Q87lP7MBIvvnYU4RYpxMZMjK61nsYjDpCz1lNL3pxAwf3ZWn2OlXHaNLRo0/N6hJ7d6ZpBhuAoBCzWzDbsv4ElkqH1wlB1OsI7h3NuO+eqApm4L34QQXNtFddsducZGeVuXqqGqhu/0fk4L5M3li4vurvX1psRW8QieoUSn5uBSazjvFTumK1Ovn958NuRRwGo8QVN/RnxLgYDidksWd7qvezL8H1O64e0IKCzTz1ynTSU4ooyKukXVRwg925LxTNAa2ZS46EvRmaE7nDLrN3R1qDlBm0aNkqgOnzerFsySHXBKS6JpXgEDMz59f/HiknCusUzPQGiXZRwbWmaY3Guqn2p5wo5JP/bie6bRRt0o4jnnOBaNAxc9c7hPbxVFPvExdB/K50j6pQWVbo2af+upOqqrJsyWF+/i4BQRCQnTKdu7fibw+MctPKbGxysspY/NU+Du3PwmTWM2FqVybP7IEkiRTmV7Dsp8Mc3p9FUIiZy2b18MlOVFVVPntvp8ff32FXyEwv4e3PrqhKJ6qqSmioH7/8cICSIgstWwew4Lr+VZWWd/5zFMmJeSx8ZKXmwiI4xFxVuXku7aJCaBd1cbTQ1JfmgNbMJYd/gFFT8gioEpf1FXOu6kePPm1YuzyR8jIrsYPaM3pCjNvK91xUVWXNsmP8+sNBSoottGwVwLxr+1FeavdaHq3Ti5hMevQGidETY5gxt3et5xojxnVi/cokzSKcMdVU+1ctPYrDqXCyRxyhuRnoHXYk2YkiCIh6HUMX3aMZzACuvnkAxw65NBOdDqWqyOGKG+Ia5HCwZd0Jfvp2v9vOI/FwDi89uZqnX53eJPJZudllPPHPpdisThRFpazUxuKv93PscC5X3zyQJx9Yis0qI8sKGWklJB/LY8rlvZh7df1drKtjqXRoFiOB65w19WQhXbq7lP4FQWDclK6Mm+K9t6x9VAgdO4eSdDTf7XGDUeKG2xtHsPtC0xzQmrnkGDU+hhW/HvGQPDIadUyY2s3n9+veq7XXQ30tlnyzn99/OlJV7JGX43LVHjoq+rTau+eKOrxVAC8sml2vcUXHhDFjXm9+/fEgsuwqcNEbJIaOjKb/oLM7irzTmpQOo5ld4+fQOvU4oXkZ2Ex+qCMG4xzYH1VVNSfAVm1a8Pzbs1j121EOJ2QT2tKfyTO707VH/S1WAH7S6JmTZZWczDJOHi+os5MyuBYOm9cm88v3BykuqqRNRCALru9P37ia1eZ/+jYBm9Xhphhit8kc2p/Fx//djqXS4bbrtdlkli0+yPgpXd2qIeuL3iCdbobzXNTIslLvBcKilzdx6kSR22OCAFNm9bxkFfebA1ozlxxtIgO57tZBfPG/XVWl1yAwfmpX+sb5tpqyvlgtDpYvOeyxa7LbXOlQVWMyMxglJs9smBbp7Cv7MmhEFLu2piA7FfoPbk/Hzu7ntD16tyb5WB4Oh4Ks05PZqQeZnVzO7kIFvPH8elq3bcHDz07WnFSDgs3Mv843kl1FBZWajwuiKw1Yn4D2y/cHWPrjoaqFQ+rJIt56YQO33TeCwTVIQB3an+UWzM6gyCqJR3I1U7iSTuRIQjbDxnSs8/jORa+XiBvSnvgdaW5pQkFwCS2faRmpC7nZZRzan+VRsKSqsHldMvOubZhD9cVOc0Br5pJk7OQuxA5qx94daTidMv0GtKN125q1CJuC7MxSl7aexjmZzSZzx/0j+d+bWwBXo7aquvr3xk6uWbaoJiLaBTG7Bq3M8VO7sXLpUZxOu8dkraqu3rrMtBK++GAXt987osHjqAvhbQLISve0OFEUtVZZsepYLQ5+++Gg58LBLvP1h7sZNKyD15Sbn7+B4kKLx+OSJKIKKrJmnY3goTwCLgUOp6wSEmquU4rvpjuGkJVeQn5OOU6ngk4vYjTquO+RcfVKEWamlaDTiZoVuIX5lX9Y8eHaaA5ozVyyBIeYGV/DGcOFIDDY7F0aS4W+cRH/3955x0dVZv///UxNI0BCSAglIfQqYOgtFFFZXXTV1Z/u6iqWXVcsa9f9Kpa1997L2lZdyyKK0iF0kA4JJIQ0EpJACqlT7n1+f0wSGObOJAEkhef9evHKMLfMee5N7pnnPOd8Dq9+dBnbfj1AZYWT/oOiieka/tva1D6Iuc/O5JN3N7JzS55hzZPbrbN+VSbXzxlX/yCUus7u175n90vf4Cgpp/OYgZz95PUnpT16yZXDeOfl1V5hR4vVk+XXo2dEo8+Tm13q94tDaUk1yUv3MW5ST0N1jKjoMPJyynzed7k0pp7bh+WL0+tFpeuQUjJ4+NHZf/6BMt56YRW5WaUIIegYGczsOeMaDE2HtbPz2IsXkLLjIDlZJXTqHMaAQdH+dbn80Dmmnd9C6fD2QW3SmYGSvlIoTisRkSH0GdDZp+7OajUxekIcNrsFm91SOyvrQ3RsO9JSC/n03Q38+50NpO4qOOW6ehXlDlJ2HGTIsC5c89dRXhmQx6K5dS9nt+r65/j1gfeoyDyIq6ySA79s5KcJt3Fo894TtmXkuDj+dP1IwtrZsdnMWKwmRozqzp3/N7Xhg4+hXXiQ3we6rks+fXcjd970HUUF3tJfmqaTurPA8DghBOfOGkjX7h0ICvJcI6vNjM1u5pZ7JtVnIFZXOXn8vp/JyijG7dZxuTQKD1bw/KNLOHig4QabJpNg0FldSBzTg8U/7mHOX/7LnGu+5sFbfyB9T1Gjxh/bvT1xCRG1SvtHsdnNpyzLtyWiCqsVitNMxREHzz+2xDOLMJtwu3X6D45mzj2T6nuuQV0a93pWLcvwNIUE7DYLiWN7cMNt4046S83t1vnozXUkL90H0vMgNZtNuDUNaeALevTsyGMvXgBAeUYe3w2ebSi8HTmiL2Hx0VQdOESX6WczcM5FBHduWhq4rumUllQTHGoj2CBjVEpJ8aEqpJRERoUaXou5d/1EVkaxX5UNYRLE9ezII8//rv698iM13DH7G8PEnOAQK3c9PI2E3pFs35LH3t2FtO8QzNhJ8V4yUksW7OHLjzb7KLyYTIJJ03tz7c1jGhy/w+Hm7pu+o/yIw8t+e5CFx178HdFdGp61V5Q7ePP5ZPbsKsBiNaO5dWZcOIBL/zSsVWc4qsJqheIEcbk01q7cz/rkTGw2C5PP6c1ZiV1P6oEQFm7n4Wdnkp1ZQtHBcrp272AYVkzdWcDqZfu9wm8Oh5tN67IZNSHupGqfpJQ8/8hidu84OhvxtDbRMJsFWEBzex6kQnhmIn++cVT9vgWrdyEsxmK2hzfv5fCWNJCSw1vT2fPWPC7c+Cbt4gPXpRUVVDDvq+3s3JZPaKiNGRcOYMLUXj77ZaQd4u0XV3H4kCeBJLJTCDfePsFHyeXW+5N4+v8WUnK4ylA1Q+qSAzllHC6qrC8gDgm1YbaYDR2ay6XROToMk9nEsMRufq9/9v5iQ7kyXZdk7y8OeA3qWL8qk5rasgEvG5waP323u1FOMaydnbvnTqekuIrS4mpiuoYbfjloS6iQo0LhB6dT4/H7fubTdzawc2s+mzfk8Mbzybz/6tpTEvbrEd+Rs8f08LtGtnpZBg6n74PRUeMmecnJtdtJSylib4px+ErTJJGdwujVtxMdIoIZPrI7/3zyPK9U/KBO4YGdeu310R0uHCUVbLr3nYD2FB4s56F/zGfVsgyKD1WRk1XKp+9u5IPX1nrtV1JcxdMPLeJgXjkup4bLqXEwr5ynH1pE8XEZkhGRITz1+ixuuHW8T+itDpNJUH1MZwSz2cTMiwb6JHhYbWYSx/Twmon5o2v3DoYJIiaToFuPDg0eD5C5r9hQHEDXJZnpxu2m/NExIoSevSPbvDMD5dAUCr+sXJRGXm6Z17d7R42b9asz2bf3UIAjTw1ut27YHRk8s4VA6Lpkx5Y8/vfVdlYuSfd6aAPs2p7fgDSV5KFnzuflDy7ltgeSiEvwTsiInX42JnsjH5C6Tu5P6wPu8s3nW2u1K48O2OFws25VJvkHjiZoLFmw11hJXtNZumCPz/tCCBLH9SDcT0G9xWKiy3FfKC68bAjnXjgAm92MPcjiqd2bGM/sOeMCjqGO8VMSDLUPLVYT5xkIUBsRE9sOm0H7GSH4zZOEWjMq5KhQ+GHNiv2GXYddTo1Na7Pp3c+4czNAdbWL1B0HMZlNDBgcfUKq86PGxxnqMdrtFsZO8l/vVFXp5IkHF1J0sByHw43NbuHz9zdxzyPT6+u4goOtftVUAM5qIJxpslqY8fNTLJxxD7pLQ9c0pFtD6hLp9r1m/sKTdezamm9Y3wWwe/tBunT1pOznZJb4ZBiCp7dbTmaJz/vgcWrX/HU0bzyX7NOy5083jPRJ0DGZBJf+aTi/v2wIxYeraN8hqEmK+6Fhdu5/fAZvPJ/M4cJKhBAEh1q5fs44unZv3AxtfFIC336+zSdL02ozc34jneKZiHJoCoUfAqU2m83+t61cnM4n72zw1C1xtKdWU3u+DUvsSp/+UezdXVj/ILbZzcT1ivDqjnw8X3z4K/kHyuof/HUO8cV/LePl9y/BZDYxakI8X3+6BQwcmj3I4tUnzB+dRvTl8ryvyV2wgZrCUiJH9GZB0j9wH+fQTDYLCVcEzlIMCrZSfsS3B5vZLAgOOToT7NGzIzu35hk6tb0pRSxZsIep5/X1CYcOH9Wdex89h++/2s6BrFJiuobz+8uGMCCA3qTNbiEm9sRmQz16RvDUa7MoKijH7daJ7hLepFT50DA79z56Dq89s4LyIw6E8IRDr715DPG92raA+cmgHJpC4YdJ03uTtb/YZ5ZmtZoZNT7e8Jj96Yf55N06gdmjx735QjJPvHIhUdGNL+4uL3cQHGKtD7GFhNo4/+KBzJw10G87Dykla1fuN3zgOx1u0lKL6DcomojIEK6fM473Xl2Drsn6UF90l3bc88j0Rivcm21W4mYdLbae9Mn9rLjqCaSmoztdWMKCCekSydlPzA54nqnn9eW7L7b5FEJL6XFGx+638IcUw/FVVTr5z0e/ciCnlKtv9O1D2Lt/FHc9NC2gHRVHHBQVVtCpc2iDvfMaQ1Pu9/H07B3Jc29f7Okc4dLpHt+xRbVxaYkoh6ZQ+GFcUgLrkveTvucQjhp3fbbf9Jn9fNaU6lj0Y6qhOoOmSZYvSueyRkpEOR1uHrlrASUlVfXOpqrKyU/f7mLi1F4BHY6/wm0hhFdvtbGTejJoaAwb12bjcLgZMiyW7vEnp7Ied9EE/pDyIWkf/eJJ208aRtwlEzHbAq+3zbhwAKk7C0jZeRDNrWOxmJFI5tw72SuZoWNECPc+eg5vv7iKgvxynzCl06GxYlE6vfpGkZ9bRniHIMZM7NmgUr/bpfHhm+tYn5yJxerpN5Y4Lo7r/j7WcC3rdCGEaLXK982BqkNTKAKgazrbN+excU0WVruZCVN6BVw7e/LBhaTuMi7MHTspnr/+I3CPtTqSl+zjk3c3+KyfWSwmps3sx9Tz+hLe3k7qrkK2rM8hKNjKhKm9iEuI4PH7fiYt1TeD0Woz8/IHlzaqwWlzsW/vIfbsKiA0zEbi2Di/tkopue6SzwxrzITwXCeXS8dqMyMEzLl3ckBR4o/eWMeq5RleX0asNjOjJ8Rzw62NSwZRnB5UHZpCcYKYzCaGjezGsJGNq/kaODSGfXsP+WQh2oMs9B/ceEX+vSmFhmnbbrfOwh9SWPbLXlxODZPJk9ghBCxfmMaFlw7mqutH8uSDC3G5tPoHvs1uYdYfh/h1ELu35/Pt59vIyy0jKjqMWZcPZcSohtf8dF2Sk1mCrkt69Ox4Up3Hq6tdrFq6j9W1jmXVsgyump1ouGYkhGdtrbLCt7BbSurryOoc1GvPrOTVjy+rV/M4lppql48zqzt2fXImV81ObLLSfUF+OYUHy+nSNZxOncOadGxz4XbrpO8pQtd0eveLOqFEpuam9VmsULRgpp7fl4XzU3HXtmsBMJkFoWE2xk427ilmRFR0KFarcSsZKalf16vLUpTSUzc37787GTUhnrnPzeR/X28nPbWIiE6hzLxooNda1LFsXJPFOy+trl+/qqwo5s3nk7niL2cHbLeTnlrEa8+spKrKWZ+0cP2t4xrlCI9H1yVP/99CcrJK69fH9u4u5IkHFjL3uZnEGggTJ53bh4U/GId4j0cI2LE5j8SxPXy2lZXW+E3YMFsEpcXVjXZo1VVOXn16BXtTirBYTLhdOoOHd+HmOye2aAexa1s+rz+7sv7Lka5L/vK30Yxrwu9sS0CtMCoUp5B24UHMfW4mwxO7YbGYsNrMjBofx9znZhrODvwxYWpvxAkIyOqazsY1WcR2b8/f/jGRW+9LIjqmHQv+t5tvP99KWam3inydrqFRO5uv/r3Fb73bkdJqnp27mJLiKhw1bmqq3VRWOHnz+WRys4zT5wORsuMgeblHfJI9nC6N77/abnjMxVec5SmJqNVT9KdBCbVdAwzUOwA6RgT7LZTX3DqRUY1LkAF4+6XV7NldiMupUV3lwuXS2Lkln4/fClyH15wUH67ipSeWUVnhpKbaRXWVC0eNmw9fX0dWRuOUTVoKLfcrQytESklZajbuagcRQxIwWdXlPROJig7jtgeSTuocEZEh3HZ/Eq8/m1zbRkYahiCPR0qJpnmcwpoVGXz4xjpcLs9sMWPvIRb9uIeHnz2/Ph39SGm1YdgOQHNrHMguNQz5rVyyz7CGze3S+XleCtcHKEKWUrJrWz5rlmegaZIxE+PJzS41nGlJXZLuR9HEajVz50PTyM4sISPtEB06BrNiUTqbN+T4FKS7nG4GDjVO0bfZLcy4oD8L56f6ZLSaLWZSdxY2qiHmkbIadmzxLSlwuTTWr8rk6ptGeWl1thRWLk43XIt0uXV+mZfCjbf/ti2DTiXqiXuKKN6RwdJL5lKddwhhNiPMJsa+eTsJl09pbtMUp5mdW/P48uPNHMguJSw8iPN+P4DzZg1scsuOwcNiefXjy0hLKaS62sUrTy73W3xch8ViZvjI7jgcbj56c73XA9rl0nG7nXzyzgbunjsdAHuw1e/sxOXSWfzjHq43SIrIP3DEcPam65L8AIryUkree3UNG9dk1zvoLRtz6RwThtVmNnTaHSIDy031iO9Ij9rszJjYcLZuzEU/fkxCcCC7FIvFxPbNeQgBQ0d0JaydR0HkkquGYzIJfvjvTq9rXFPt4rVnV3DPI9Pp0z9wF+7SkmosFrNhSYEwCSrKnS3SoRXmlxvaLHVJ4XHdCFo6KuR4CnCVV7Eg6Q7K0w/grnLgKq/CWVrBqtnPUrhud3ObpziNbN98gJefWE72/hI0TVJWUs13/9nGv98+sZCTxWJiwJAYYmIb0E7EoyAyfkoCcQkRpKUUGjpQKT3KG3XfyIODrQwZ7r+L97rk/RwuqvR5P6FPpKFeocVi8hEJPpbUnQVsXJ3t5bgcNW5PCr7BLMFutzDz4oaLvOuorHAa1mrpmuSD19dyx+xv+fdb6/nozfXcPvsbli9Mw+Fws3pZBjmZpYbXzOnQ+O4L47DnsUTHhKEbtbrGs77YvmPDOpDNQZ8BUdiDfOc2FquJfgMDO/GWhnJop4D9Xy5DNxCR1aqd7HjmP81gkaK5+OKDTYbrUSsWpfPhG2vZt7dx/ayOZ/f2g34Fds1mwfCR3bj5rolc89fRte+Z/OpACuHdL/L6OeP89o80m03s2e1bhjAuKQF7kMVnnc9sMXHuhQP8jmPtyv2Ga1lOh0ZcQgTt2tsJCrYSHGLFajWTOK4HqTsL+PqTzQ2uzRXklzP/mx1+NSoPF1XhcmnU1Lhx1LhxOTVPX7QbvuWTdzewZWOuXymw/bWCwLqms+3XA/w8bzdbN+Wia0c/yx5k5bzfD/Bx9Da7mVmXD22xRdHjJvckOMTq7cyFJ6R7zu/6N59hJ4AKOZ4CjqTn4a6s8d0gJWV7ck6/QYpmQdclebnG4TZdlyxfmM6aFfuZMCWBq28a3aQWNEHBFr8hy4hOodz+oHdou0//KDDY3WQSDEvs5vXZYeF2wsLtlJf5Sk8hhKFKe3CwlYeePp/3X1tLWkohAN3iOnLd38fUt2IxwmgWVkdQiJVXPriUPbsLqax0snTBHjat9czmTCbBwh9SmXX5UMMGlYt+TOXLjzejabrf/mdGuFxag0LPdfuVFFfxxAO/cKSsBrdLx2I1EdbOzoNPnEtEJ8+Y/3DlMEJCbcz/ZheVFQ7atQ/iosuHtrjO6cdiD7Ly8LMz+eTtDWzdlIsE+g+K5uqbRtGhkYoxLYWTcmhCiAjgSyAeyAT+KKX0+RolhMgEyvFoAbn9FcW1VjoOTcASFoy7wjuDTJhNdEr0n/asaFuYTIKgYCs1xynbH4vTobF62X5Gjotj4NAuHCmtZtFPe9i1NZ+OESGcc2F/+g/yrVcbMaq7YaaczWY2fFharGZuvmsirz69Al2TuN069iALwSFW/nRMX7M6ks7pw8/zUnwSM0wmGOwnJNk5ph33Pz4DR41HJd+fgO+hwgqcTo2YLu0YPTGe9auzfAWXgyyMT0rwiDkPiWHlknTSUovq1wB1XeJ0anz/5XZGjO5ObLejafyFB8v58uPNAdP3haDB9cdAaG6dt15YxaHCynqH6XbrOB0abzyfzD+fPK/2cwTnXzSI82YNRHPrmC2mVtFMMyIyhNseSPKMTUpMJ1FP2Jyc7AztPmCJlPIpIcR9tf+/18++U6SUv33PjWYg/pKJbLr3HbRqB/KYEITZbmXovVc0o2WK08208/uyaH6qT9jxWBwON6uW7qNzTDsevvMnampc9Yvy27cc4JIrh3HeLG9F9ZBQG3+/axKvP7cS8Eg1WW0W+g7ozAw/Ib6hI7ry1GuzWL4ojaKD5fQd2JlxkxMIMphx/f6PQ0nfU0RG2mHcLg2L1aOwcceDU7FaA0s/+Ut0yMsp4/XnVlKQX47JJLDbLVx782jOSuzKtk0H6p2aPchC736dGDX+qODy8oVphp0ONE1nw6pMLrrirPr31q/KRPcTKqyTKxswJIaUHQcNz9kY2ncMJj21yGf2p+uS/emHKS2ppsMxa2RCCCwNXDddl+zYnMemtVlY7RbGJ/WkV1//KjSnA08UoOU7YH+crEObBSTVvv4YWI5/h9ZmMdttXLD2NZKvfYaCldtBQLuEWMa9dQcdBsY3t3mK08gf/t9ZFOSXs+3XA2hu/+Evp1Pjy483U1nh8Jo5OB0a//10KxOm9CLsuB5ew0Z248V3L2HDmiwqKxwMGBxDr36d3qniCgAAErBJREFUAs4AIqNCueTKYQ3abbOZuffRc9i35xB7UwsJbx9E4pgehs6vMThqXPzrgZ+pqHDWr+U5aty8+fwqHnhiBuMnJ5C8dB+6Jhk7uSeJY7p7zQrcfr4Q6JrEeVyI0Fnjri9VOJ6o6DAef+kCdAkPzJlHmbumfl+LxdMNQQvYF86T1j/l3D7M/2YnGFROmM0mqqucXg6tITRN58XHl9UrwggByUvSmT6zH5dfc3ajz6Pw5mQdWrSUMh9ASpkvhPCXEiOBhUIICbwtpQzcvrYVEtotivMWPYurvArN6SIo0lfZQNH2sVjNzLl3MgX5R1j0YyrLF6b7hMLsQRZGT4jn3VfWGIbBzBbBru35jJ4Q77MtLNz+m63HCCHo3T+K3v1PfpawflWWR+Xk+Howl8aP3+7mlnsmBZQTGz0xnrwDR3yunc1u9lEiOSuxG7/8kOqTbGK1mpgwpVf9DPKR52byzefb2LgmCyEEoyfEMWxkN157eqWXTJgQHskzm82M5tY5f9YALvjDIM/M22CGZ7Wa6RzTNFX9tSv2s3d3Yb3Ndeovi3/aw5iJPf2KXysC06BDE0IsBowqEh9swueMl1Lm1Tq8RUKIVCnlSj+fdyNwI0CPHr4yNS0da7sQWl6lieJ0E90lnCv+kkhWRglZ+4rrH1w2u5mevSMZMbp7wJ5q/jIaWwv5uWWGNWVSQl5OaYPHTzu/H8lL9nG4qLI+fGu3Wxg+qptPWUCvfp0YOiKW7Zvz6q+z1epJk59+TJZeeIdgrr15DNfePMbr+Edf/B0Lvt9FRtphYrqGM/OiQYS1s3GkrIbY7h3qk2L+fOMo3nt1jZdTs9nNXDk7sckalisXpxtme7qcGuuSM5VDO0EadGhSyun+tgkhCoQQXWpnZ12AQj/nyKv9WSiE+A4YBRg6tNrZ2zvgUdtveAgKRcvEYjFx7yPTWb08g1XLMgCYOLUX45ISMJtNjJnYkxWL031CXrouGTKsS3OYHBApJSk7DrJ6eQa6Jhk9IZ6hZ3c1zL7sGtcBe5DFx6kJk2hUi5qgYCtzn5vJ8kXpbFiVic1uZsq5fRk5Ls4nxCqE4Oa7J7F2xX6W/rIXR7WLkePjmD6zf6M6C8TEhnPtzWN93j++l9noCfGEtw/i+y+3k5dbRkxsOBddPpRBZzX9XvkrD/BsCxwCVfjnpNrHCCGeBQ4fkxQSIaW857h9QgGTlLK89vUi4FEp5c8NnV+1j1G0ZSorHDx2788UH/boIVosJkwmwU3/mEDimJYVnZBS8uHr61iXnFk/s7AHWeg/KJrbH0jyyYpzOtzceeN3lJc7vFL1bXYzDz19/kn3XWvtLFmwh/989KtPCNNut3D3I9MaVCU5k/kt28c8BXwlhJgNZAOX1X5gLPCelHImEA18V/utygJ83hhnplC0dULD7Dz+0gVsWpdNyo6DdIgIYdK03gHruJqLPbsLvZwZeJI8UncWsHFtttd6n5SS7P0ljJ+SwKa12RQfqsRkMtG+YxDX/X3sGe/MACZO683Kxenk5ZbVOzV7kIWzR3cP2G9PERjV4FOhOIMoLa4iZUcB9mALg4fFNrob80dvrmPZwjRD9ZEhw2O56+FpgKc26+UnlrFnVyEul1afSXj1jaOYOK3XKa3JOlxUSWWlk9iu4X5T5B0Oj9MVwlMs3JJauLhcGmuWZ7AuORObzczkc/owfFS3VlG31pyoBp8KxRmOlJJvPtvKgv/trpVg8jw0b71vcqPWgDwFt/7PXcei+Smk7iyoT+So+/nJOxtIHNujyY0yjThcVMlrz64kZ38JZotAILj8LyOYcq539uf6VZm8/9pahBD1Pb5m3zLWMHu0ObBaPU5s8jl9mtuUNkPrTqVSKBSNYvP6HBb+kILbpVNT7aam2kVNtYuXn1hORbmB5NVxjJ4Qbyhga7dbGJd0tAnk0l/SDIvKhUmwef3Jy8Dpms4TD/5CZvphjy5jtZvqaheff7CJrRtz6/c7kFPKe6+sqe3VdrTH13uvrCEvt+yk7VC0TJRDUyjOAH6el4LDoIbK4XBz543fsuD73QE1EAcOjWHYyG5eTs0eZKFnn0ivGY+jxlj2S9d1qgNIgjWWndvyqSh3+NjqdHhksepYumCPoUix262z9Oe9J22HomWiQo4KxRlAWUm132011W6+/WIrh4oq+fMNIw33EULwt39MYOvGXFYtzcDt1hmX1JPEsT28arCGDu/qSev3cY7ihNLbj6fwYIXftPaiY3p3Hau5eCy6LikqqDhpO04VVZVO8nLLaN8hmKjosOY2p9WjHJpCcQYwYEgMRYUVfjUPnQ6NFQvTuOjyIbQLDzLcRwjB8FHdGX6cUsexXPz/zmLzhhxqql31tVZ2u5lR4+O9BIWbgpSSnPlr2fveT5QdLCNW60BOTAK6xfvx1aXr0fP3HxzN7u0HfcKfNruZAYN9xZ9PN1JKvv5kCwvnp2KxmHC7dXr2imTOvZMI79Ay+6a1BlTIUaE4A7jgksHY7Ra/fc/A09Axe3/gnmMNERkVyuMvXcDkc/oQFR1GXEIEV980mutu8S1cbixr/voiK678Fzk/rOXIxt3Ebd/A2cnzMbmPhjBtNjN/uPKoYPGk6X0ICrZiOuYJZzJ5CrYnTut9wracKhbNT2XRj6m4nBrVVS5cTo19e4t47tGlzW1aq0bN0BSKM4Co6DDmPjuTLz761St54lg0TadDxMnPDiI6hdY3Gm0sOZklZO8vITIqlL4DO9erjxz6dS/7PluMVnU0ccXkdhNSXUH3rD3kDTiLkFAbf7phJAOHHg1phobZmPvcTD57fyNbNx1A4BF3vvK6xEaph/yWrF25n88//NWnN5ymSfIPlJGVUaykr04Q5dAUijOEmK7h3PHgFD57fyPLfknzEv41mQQxseF07d7B57i6djdbNuQS1s7OlHP70M+gZ9uJ4HC4efmJZaSlFnnS64HwDkHc99gMIqNCyZ63Bs0g0US43Qw3FXP7mxfRoWOwofxWZFQot96XdErsPFUsWbCX/3y0yW+jU7PZxKHCCuXQThDl0BSKM4w/Xj2CQ4WV7NiSh9lsQkpJZFQod/xzqs++VZVO5t79EyWHqzyKFgJ+XZ/N7y4e5NWT7ET5/P1N7N1d5NU12lFYyQuPL+VfL1+IyWJGmATSIA/EbLMQEdl6Oiprms5/P90SsCeb263TtYfvlwpF41AOTaE4w7Bazdx2fxIF+eVk7y8mMiqUnr0jDRUqfvx2F4eLKusbkFLb5mT+N7sYP6XXSWXm6ZrO6uUZXs4MQOqSwoPlHMgpJf6yyWx/6nM0t/c+5hA7fa47/4Q/uzkoPlSF2+3fmVksgoFDY4iJDT+NVrUtVFKIQnGGEt2lHSPHxZHQx3+T0HXJ+486s+PwtxbXWFwuzW9zTZNJsHFNNjnVFgbfcwXmEDt1GR6WsGCiRg2g3/UzT+rzTzehYbaAtX6jxsdzy92TTqNFbQ81Q1MoFH7xqysoqFPPqkdKiZQYrmcZYbNbiIwKNawLq6l289N3uzAJgckcxPUfPYxz1SbcFVX0mDWebjNHYzI3ToeypRASamNYYje2bsr1+pJgNpsYMCSam+6Y0IzWtQ2UQ1MoFH4Zl9STn77d7RMWRErOHu2pR6s44uCz9zeyYXUWmqbTZ0Bn/nzjKHo0oKovhOCq2Ym88VyyoVzWsb3U3v4mgxffu+GUaEE2J7NvGcsLjy8lK6MYk0kgdUlsjw787c6JzW1am0Cp7SsUZxhSSlYsSud/X22ntLiayKhQLrnqLMZOSvDZt6baxWP3/UxRQQWOGjfCJLBaTFx85VnMvGgQbrfOA3Pmcaiw0kvBIyjIwmMvXUDnmHY+5zyenVvz+PqTLeTllqHr0jDEabObuer6kSS1ESHf7MwS8mubhKqMxqah1PYVCkU987/Zybyvd9Rn2xUVVPDB6+uoqnQz7Xxvxfq6ztEbVmWxdWMOYeFBTD6nN/G9IgHYsiGH0pJqHzkqp0vjx293ce3NYxq0Z/CwWAYPiwXgrpu+MwxBupxaQPmu1kaP+I4NzmAVTUc5NIXiDMLpcPPD1zt9UsedDo1vPttC0ozeXtqM4MmKHD8lgfFTfGdwGWmHvEKDdeiaJC2lsMn29R3YmcNFFejHTdJsdgu9+nZq8vkUZxYqy1GhOIMoyC9H+Pmrd7k0SoubNguKjArz2yT0RDpvz/rjEJ8mnBariS5dw72UQBQKI5RDUyjOIMI7BPlNldd1SUgTZaHGTIxHGGQ12uxmZl48qMn2RXcJ559Pnsegs7pgtpgIDrGSNKMP9z8+o9HZk4ozFxVyVCjOINp3CKbfoGhSdhZ4OTaL1cTZo7sTHGxt0vnC2tm56+FpvPLkclwuHSFAc+v88eoRDBgSc0I2do/vyD2PTD+hYxVnNirLUaEIgNuts2ZFBslL9iGlZMKUXkyYkoDF2rpqoI6lotzBC48tJSerBLPZhObW6dW3E7c9OKXJDq0OTdNJSy3C5dTo3T/qhM+jUDREoCxH5dAUCj9oms6zcxeTsfcwDocn8cFmNxOXEMF9j83AYmndEfvs/cUU5JcT2729oSixQtESCeTQWvdfpELxG7J5fQ4ZaUedGXiyAbMzSti4JqsZLTs19OgZwchxccqZKdoMyqEpFH7YsCbLMCXd4XCzPjnz9BukUCgCohyaQuEHm83so1dYh9XeetfQFIq2inJoCoUfJkzphd3mmwhst1uYNK13M1ikUCgCoRyaQuGH/oOjmTA1AZvdjBAghCcpZPTEeAYPU0W+CkVLQ9WhKRR+EEJw9U2jGT+lFxtWZyF1nZHj4+jdL8p/WxWFQtFsKIemUDRAr76dlI6gQtEKUCFHhUKhULQJlENTKBQKRZtAOTSFQqFQtAmUQ1MoFApFm0A5NIVCoVC0CVq0OLEQoghozaJ5nYBDzW3EKaKtjKWtjAPUWFoibWUc0HLHEieljDLa0KIdWmtHCLHJnyp0a6OtjKWtjAPUWFoibWUc0DrHokKOCoVCoWgTKIemUCgUijaBcmi/Le80twGnkLYylrYyDlBjaYm0lXFAKxyLWkNTKBQKRZtAzdAUCoVC0SZQDu0UIoS4TAixSwihCyH8ZgcJIc4TQuwRQqQLIe47nTY2FiFEhBBikRAirfZnRz/7ZQohdgghtgohNp1uO/3R0DUWHl6p3b5dCDGiOexsDI0YS5IQoqz2HmwVQjzUHHY2hBDiAyFEoRBip5/tremeNDSW1nJPugshlgkhUmqfXbcZ7NNq7gtSSvXvFP0DBgD9gOVAop99zMA+IAGwAduAgc1tu4GdzwD31b6+D3jaz36ZQKfmtrep1xiYCSzA05N6DLC+ue0+ibEkAfOb29ZGjGUSMALY6Wd7q7gnjRxLa7knXYARta/bAXtb69+KlFLN0E4lUsoUKeWeBnYbBaRLKTOklE7gP8Cs3966JjML+Lj29cfARc1oS1NpzDWeBfxbelgHdBBCtMSuna3l96VBpJQrgeIAu7SWe9KYsbQKpJT5UsrNta/LgRSg63G7tZr7ohza6acrkHPM/3Px/QVqCURLKfPB80sPdPaznwQWCiF+FULceNqsC0xjrnFruQ+NtXOsEGKbEGKBEGLQ6THtlNNa7kljaVX3RAgRDwwH1h+3qdXcF9Xgs4kIIRYDMQabHpRS/q8xpzB4r1lSTQONpQmnGS+lzBNCdAYWCSFSa7+9NieNucYt5j40QGPs3IxHDqhCCDET+B7o85tbduppLfekMbSqeyKECAO+AW6XUh45frPBIS3yviiH1kSklNNP8hS5QPdj/t8NyDvJc54QgcYihCgQQnSRUubXhhcK/Zwjr/ZnoRDiOzwhsuZ2aI25xi3mPjRAg3Ye+wCSUv4khHhDCNFJStkSdfgC0VruSYO0pnsihLDicWafSSm/Ndil1dwXFXI8/WwE+gghegohbMAVwLxmtsmIecA1ta+vAXxmn0KIUCFEu7rXwAzAMOvrNNOYazwPuLo2g2sMUFYXYm1hNDgWIUSMEELUvh6F5+/68Gm39ORpLfekQVrLPam18X0gRUr5gp/dWs19UTO0U4gQ4mLgVSAK+FEIsVVKea4QIhZ4T0o5U0rpFkLcAvyCJ4PtAynlrmY02x9PAV8JIWYD2cBlAMeOBYgGvqv9u7UAn0spf24me+vxd42FEH+t3f4W8BOe7K10oAq4trnsDUQjx3Ip8DchhBuoBq6QtelpLQkhxBd4sv86CSFygYcBK7SuewKNGkuruCfAeODPwA4hxNba9x4AekArvC8t8xorFAqFQtE0VMhRoVAoFG0C5dAUCoVC0SZQDk2hUCgUbQLl0BQKhULRJlAOTaFQKBRtAuXQFAqFQtEmUA5NoVAoFG0C5dAUCoVC0Sb4/0jQUoAnJz2NAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 33,
   "metadata": {},
   "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",
    "    \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",
    "\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\n",
    "            cost = 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",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\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": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690736\n",
      "Cost after epoch 1000: 0.685273\n",
      "Cost after epoch 2000: 0.647072\n",
      "Cost after epoch 3000: 0.619525\n",
      "Cost after epoch 4000: 0.576584\n",
      "Cost after epoch 5000: 0.607243\n",
      "Cost after epoch 6000: 0.529403\n",
      "Cost after epoch 7000: 0.460768\n",
      "Cost after epoch 8000: 0.465586\n",
      "Cost after epoch 9000: 0.464518\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
    "collapsed": true
   },
   "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": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690741\n",
      "Cost after epoch 1000: 0.685341\n",
      "Cost after epoch 2000: 0.647145\n",
      "Cost after epoch 3000: 0.619594\n",
      "Cost after epoch 4000: 0.576665\n",
      "Cost after epoch 5000: 0.607324\n",
      "Cost after epoch 6000: 0.529476\n",
      "Cost after epoch 7000: 0.460936\n",
      "Cost after epoch 8000: 0.465780\n",
      "Cost after epoch 9000: 0.464740\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
    "collapsed": true
   },
   "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": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690552\n",
      "Cost after epoch 1000: 0.185501\n",
      "Cost after epoch 2000: 0.150830\n",
      "Cost after epoch 3000: 0.074454\n",
      "Cost after epoch 4000: 0.125959\n",
      "Cost after epoch 5000: 0.104344\n",
      "Cost after epoch 6000: 0.100676\n",
      "Cost after epoch 7000: 0.031652\n",
      "Cost after epoch 8000: 0.111973\n",
      "Cost after epoch 9000: 0.197940\n"
     ]
    },
    {
     "data": {
      "image/png": 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4rWZMRmKIxcViL4VhGIaZIyxyaXBYjQB4EgHDMMxShkUuDS6eDs4wDLPk0VXkiOgqIjpORK1EdPsM++0kohgRXafnerKBp4MzDMMsfXQTOSIyArgLwB4AGwDcQEQb0uz3PQBP6bWWucAz5RiGYZY+elpyuwC0CiHahBBhAA8AuCbFfn8J4GEAAzquJWuUmXJetuQYhmGWLHqKXA2ALs3tbnmbChHVALgWwN0zHYiIbiGiZiJqHhwczPlCU8ExOYZhmKWPniJHKbYl5+P/EMBXhBCxmQ4khLhHCLFDCLGjrKwsZwucCcWS87PIMQzDLFlMOh67G0Cd5nYtgDNJ++wA8AARAUApgKuJKCqEeFTHdWWEEpNjdyXDMMzSRU+R2wdgNRGtANAD4HoAN2p3EEKsUP4nonsBPJ4PAgcADgu7KxmGYZY6GbkriehPM9mmRQgRBXAbpKzJFgAPCiGOENGtRHTrXBa7kBgNBLvFyCUEDMMwS5hMLbmvAngog20JCCH2AtibtC1lkokQ4tMZrmXB4JlyDMMwS5sZRY6I9gC4GkANEf1Yc5cbwLI/+zt5EgHDMMySZjZL7gyAZgAfAPCWZrsXwBf1WlS+4OJJBAzDMEuaGUVOCHEQwEEi+pUQIgIARFQMoE4IMboQC1xMnDYTlxAwDMMsYTKtk/sDEbmJqATAQQA/J6J/0XFdeQHH5BiGYZY2mYpcoRBiAsCHAPxcCHEugMv1W1Z+4LCauE6OYRhmCZOpyJmIqArARwA8ruN68goXW3IMwzBLmkxF7tuQ6t1OCSH2EVETgJP6LSs/cNokkROCp4MzDMMsRTKqkxNCPARNTZwQog3Ah/VaVL7gtJoRiwsEI3EUWIyLvRyGYRgmSzLteFJLRL8hogEi6ieih4moVu/FLTZq/0qeKccwDLMkydRd+XMAjwGohjQu53fytmWNS51EMOOQBIZhGCZPyVTkyoQQPxdCROW/ewEszMybRUQZt8MF4QzDMEuTTEVuiIg+TkRG+e/jAIb1XFg+4LCyu5JhGGYpk6nI/Rmk8oE+AL0ArgNwk16LyhfU6eBsyTEMwyxJMp1CcAeATymtvOTOJz+AJH7LFtVdybVyDMMwS5JMLbkt2l6VQogRANv0WVL+oGRXssgxDMMsTTIVOYPcmBmAasnpOVU8L3DbzCAChn3hxV4KwzAMMwcyFar/B+BVIvo/AAJSfO5O3VaVJ1hMBlQXFqB92L/YS2EYhmHmQKYdT35BRM0ALgNAAD4khDiq68ryhKYyB9oGWeQYhmGWIhm7HGVROyuETcvKMiceau6CEAJEtNjLYRiGYbIg05jcWUtTmQP+cAwD3tBiL4VhGIbJEha5WVhR6gAAnBr0LfJKGIZhmGzRVeSI6CoiOk5ErUR0e4r7ryGiQ0T0NhE1E9G79FzPXGgqcwIATg9xXI5hGGapoZvIEZERwF0A9gDYAOAGItqQtNuzALYKIc6BVFj+U73WM1eq3DbYzIaUySe/fKMDr7QOLcKqGIZhmEzQ05LbBaBVCNEmhAgDeADANdodhBA+MTWR1AGpPCGvMBgIK0qdaEtyV0Zicdzx+FHc92r74iyMYRiGmRU9Ra4GQJfmdre8LQEiupaIjgF4AmnahBHRLbI7s3lwcFCXxc5EU5kDbUnuypbeCQQjcfRPBBd8PQzDMExm6ClyqfLtp1lqQojfCCHWAfggpB6Z0x8kxD1CiB1CiB1lZQs/4aep1IGukQBC0am5cm91SF3O+ljkGIZh8hY9Ra4bQJ3mdi2AM+l2FkK8CGAlEZXquKY50VTmQFwAncMBdZsicoPeEKKx+GItjWEYhpkBPUVuH4DVRLSCiCwAroc0XVyFiFaRXGFNRNsBWJCHc+qaSqUMS63L8kDnGIwGQlwAQ9zbkmEYJi/RTeSEEFEAtwF4CkALgAeFEEeI6FYiulXe7cMADhPR25AyMT+qSUTJG5rKpFo5JcOybzyInrFJnN9UIt1mlyXDMExeouskASHEXgB7k7bdrfn/ewC+p+cacoHLZkaZy6pmWO7vlFyVezZV4ZXWYU4+YRiGyVO440mGNJVOZVi+1TEKq8mAy9aVAwCLHMMwTJ7CIpch0jQCyZJ7q2MUW2uLUOm2wWQg9I2zyDEMw+QjLHIZ0lTqxGgggr7xII6cGce2hiIYDIRyl5VjcgzDMHkKi1yGKMknjx3sQSQmcG69NCi9otDG7kqGYZg8hUUuQ5RGzQ81dwMAtjdIIlfptrG7kmEYJk9hkcuQuuICmAyEkwM+NHjsKHVaAQAVbhv6J3jWHMMwTD7CIpchJqMB9R47AKiuSkASOV8oCl8oulhLYxiGWVTah/wIR/Oz8xOLXBYonU+2NUyJXGWhZNFxXI5hmLMRXyiKK3/4In69r3Oxl5ISFrksWCknnyRbcgDQz3E5hlm27GsfwTvd44u9jLykbzyIcDQ+bVJLvqBrx5Plxvu3VsMXimJtpUvdVimLHJcRMMzy5du/O4oiuxn/85nzFnspeceAVzr3DeRpbgKLXBZsqinEndduTthWWcgixzDLnYlgBLF43rXVzQsGvZK45es5kEVuntgtJrhsJnZXMswyxheMIpKniRWLjSpyeXoO5JhcDuAyAmY5I4RA92hg9h2XMd5QFKOByGIvIy8ZkEVuwBtEPA+tXRa5HFDpti2YqT4W4Nl1zMLy3PEBvPv7z6NnbHKxl5KSJw/3oqV3Qrfjh6IxhKNxTEZiCEZiuj3PUkWx5CIxgZE8PD+xyOUAyZLTX+S6RgLY8Z1n8NyxAd2fi2EUukYmEYsLtOdh9pwQAl9+6BD+68U23Z7DH5oStjG25qahJJ4A+VlKxSKXAyoLrRjwhhIC06+dGsbTR/py+jzH+ryIxgX+yCLHLCDjk9KJvTcPYy4j/jB8oSgGffqFC3zBqUYPo3loqSw2AxMhVLjzt16YRS4HVLptiMUFhjU/tK89+g6+8diRnD5Px7B0Jf3m6ZGcHpdhZkIRuXw8gXWMSLHCYZ9+4uMNTVlvLHLTGfSFsLmmCADQN55/uQkscjmgIqlWrnXAi1ODfvSOBzGeQ/dGuyxyx/u9GPHzjy3fiMcFnjzcu+ziNorI5WP2XOewLHL+hbHk2F2ZSCgaw1gggg3VbhDlZxkBi1wOULueyBmWTx6eclMe68tdQLxjOACbWfrI2JrLPx5/pxe3/u9+PPb2mcVeSk7JZ3dlp8aS0yuzT9uXli8uE1GSTqoLbSh1WvOylIpFLgckF4Q/eaQP9SVSM+djfd6cPU/7sB+Xri2H1WRgkcszorE4fviHEwBy+5nnA3ntrpQtuWhcYCKoj5WlFTnObk5EEblytxWVbhv6vfn3HWGRywGlTiuMBkL/eBBdIwEc7pnAx86rR5HdnLMTXjgaR8/oJFZXuLC9vhhvnB7OyXGZ3PDI/h60DflhMxtwcmB5idxEXltyUxmfQzrF5bwJiSfsrtSi1MiVu2yoyNPZmrqKHBFdRUTHiaiViG5Pcf/HiOiQ/PcqEW3Vcz16YTQQypxW9E0E8ZScUblnUxXWVbpy5q7sHg0gLoBGjx27VpTgaO+EeoXNZM+Th3tx/5u56Zoeisbwo2dPYmttIfZsqsKJ/uUlcsr3bNgfyrtxKh3DAdQUFQAAhnTKsFQsuWK7mRNPklBErsxlRYXbmrW1f+cTR/G3Dx3UY2kquokcERkB3AVgD4ANAG4gog1Ju50G8G4hxBYAdwC4R6/16E1FoVQr9+ThPmyocqPeY8e6SjeO93lzEitQ3DINHgfOayqBEMBbHeyynAtDvhC+/NAh/NuzJ3NyvF/v60LP2CT+5sq1WFPhQv9EaFldgIwFInBZTRAisSZqsZkMxzDgDWFbvZTZp1eGpS8YhYGAqsICTjxJYnAiCCLA47Cg0m3DaCCSVeLVm6dHdE9W0dOS2wWgVQjRJoQIA3gAwDXaHYQQrwohRuWbrwOo1XE9ulLptqKl14u3Okdx1aZKAMD6KhcC4Ri6ctASScmsbPTYsb2+GBajAW+0scjNhR8+cwK+UBT9SbWNc2EyHMO//bEVu1aUYPfqUqypkGYOnlwm1pzS6WONPHkjn+Jyyu9qmzz6Sq8MS18oCqfVhBKHJeeWnBCL2warczgwr2zgQV8IHocVJqMBFXJuQqbTCIQQOD3kR6PHMefnzwQ9Ra4GQJfmdre8LR2fAfD7VHcQ0S1E1ExEzYODgzlcYu6odNsw5AtBCGCPLHJrK90AgJbe+Z/wOoYDcMk/NJvZiK11hXidk0+ypnXAi/vf7EKp04JYXMzbMvnf1zsw6A3hy1euBRFhTYUkBif6fblY7qKjWKTKeKl8issp3o1z6opABAx59RE5bzAKl82MIrs5p5bc8T4vNn7jqUW7IIrFBa7+8Uv4tz/O3aMxMBFCmUsqBFfGjmWafDIaiGAiGEWDxz7n588EPUWOUmxLedlCRJdCErmvpLpfCHGPEGKHEGJHWVlZDpeYO8rlD7ipzIFV5dLV/JoKJ4ikL/N8aR/2o6HUDiLpbd21ogSHe8bh12R+5ROxuMB397bkXSD6u3uPwW424vY96wEAZ8bmt77HDp7BjoZi7FpRAgCoKSpAgdmYMi732qlhNRttqaCKnCze+fR5Ks0RmkodKLFbMKRTer8vFIHTakKxPbeW3IHOUQTCMbxwYnEu3Ae9IfhC0Xk9/4A3hHJF5JQs8wy/I6flNnErSpeuJdcNoE5zuxbAtAIiItoC4KcArhFCLNmUQeUqZs+mSlWI7BYTGj2OnCSfdAwH0KAx689b4UEsLvBWx+gMj1o82gZ9+M8X2/D7w72LvRSVV1uH8OyxAfz5pauwqUaysnvH5950OBYXODngxTl1Reo2g4GwusI5LcNyLBDGx376On72yuk5P99ioIhcvccOq8mQX+7KkQBcNhOK7GZ4nJaEjkO5xBeKwmkzodhuxvhk7ubKtcuW6L72xfHIKN/9I2cm5lwaMeidsuQqXEq9cGbfEaUXauMSFrl9AFYT0QoisgC4HsBj2h2IqB7AIwA+IYQ4oeNadGdTTSGcVhOuOSfRIytlWM5syT2yv3vGLurRWBxdIwE0asz6cxuKYTRQ2lKCF08M4quPHFq0bDgl1Tpf3FvxuMCde1tQU1SAmy5qRFWhlJHXOw9LrnMkgGAkrsarFFaXu3AyyV352qlhxEV+xbQyQSkfKCwwo6rQpuvnmW18qmMkgPoSybvhcVh1KyHwhWJwWk0oslsgxNR7Ml8US7S5fXRRYnPKZykE8Poc4vvxuMCQb8qScxeYYDMbMrbk2of9MBBQV7xE3ZVCiCiA2wA8BaAFwINCiCNEdCsR3Srv9o8APAD+nYjeJqJmvdajN2srXXjnm1eqMRnt9vZhPwLh1G7FY30T+NKDB2fsc3lmLIhoXCRYcg6rCZtrCvHSySFEYolC9uThPnzmvn24/80uvNMzPo9XNXcUt86ZPBnP8lrbMI6cmcDfXLkGNrMRbpsJDosRZ+ZhySlu6LVJn/maCicGvKGElm4vtQ4B0LfHoh6Ma0ROz2kbbYM+bPzGU7j0B8/jL361H3c91zqrB6RzOKDGc0pdVv0suWBEsuQcZgC561/ZPhwAETDsD6uuu4VEETmzkfDaqaGsHz8SCCMaF6rIEVFWY8dOD/lRW2yHxaRvubauRxdC7BVCrBFCrBRC3Clvu1sIcbf8/81CiGIhxDny3w4916M3iptSy7pKN4TAtCt7hZ/8sRWAlErbmqaIeCqzMtGsf9+WKhzqHsf7fvwymmWXx2MHz+AvfrUfq8qlE+/bXWNzezHzRHF/5Islp4j9ZevKAUifVVVRQUaWXDASQzQ23SI+0e8FEbBazqhUUJNPNJ/nK7LI6VXLpRfjC2TJNXdI8an6EjsOdY/h+08dx+f/d3/a/WNxga7RAOpLpN+Ex2HRr4QgFIVLtuSA3BSECyHQMezHu1aVApCsuYWmb3wSNrMB5zd58Oqp7CNFg2qNnE3dVuG2ZZxd2T7s191VCXDHE91ZXyWd8FJdlbYO+PDEO734yI5amI2EX73RNW0fYMqt0ZiUhXTz7ibc84lz4Q1GcN3dr+HP7t2Hv3rgAM5tKMZDt16AqkLboomc6q5MY8m9eGJwQa28lvd4CbgAACAASURBVN4JVBfa1BMVAPmkPfsaPvCTl/H//jDdm36834v6EjvsFlPCdiXxSEk+6RoJoGM4ALORlrTIVRRKJzA9ekS2DvhgMRnws0/vxEt/dxn+4tKV6BwJTPNSKPRNBBGJiSlLzmmBNxTVpTm2LxhVE0+A3LT2GvSFEAjH8J515Si2m+cVlzvQOYqL/umPWX+3eseDqCoswEWrSnFywJd1pvGApqWXQmVhZpacEAIdQwGs0DmzEmCR0526YjvsFmPKMoK7nmuFzWTEV65ahys3VuLh/d0pf6TtwwEUmI1qgFfLlRsr8YcvvRufu7gJL5wYxLtWleK+m3bBaTXhnLoivN21OIkpiksnVS1aNBbHzfc14/tPHV+w9bT0TmB9lTthW3VhAc7MYplEY3GcHPClHFR7os87zT0NSBmWdotRtd5flq24S9eWY9gXzjr+ctdzrbj5vn1ZPSZXjE9G4LAYYTYaUOW2IRyL6zL9+WS/FyvLnDAaJG9Ig8eBWFykvRBSLvyUHrGlTum3MZzjDMtYXMAfjqmJJ0BuLDml/KGx1IFzG0rQnCKBrHM4kNEFxVNH+tEzNpl1FrckcjZcuNIDQIobZ8OALGblmvNSheyunO07PuwPwxuKJoRg9IJFTmcMBql2KtmSax/y47dv9+Dj59fD47Tixl31GJ+MpMxG7Bj2o8FjT+kOBaT43FevXo83/v49uPemXSiwGAEAW+uK0DUyqVusYibG/NKJIFUtWu94EOFYHC+dHNKtc7yWYCSGU4P+aSJXWSjVNs6UnDPsD0MIyWrTdjEJRWNoG/JPi8cBcoZluVO15F4+OYRKtw27VpQgGhdZd0N54fggnjs+iFA0cyslGInh3ldO4xP//QZ65mExj09GUFggndyzTRHPhtZBn2oBA0CDLF6KGCSjjNhRRM6jiFyOv+t+OZbu1Lgrc2HJqZmFHgd2Nhbj9JA/obzkWN8ELvnBc/hhBl15lFBFtp9z33gQlYU2bKwuhMtmylrklEG1ZUkiF47GZ60nbF+g8gGARW5BWF8lZVhqr27ueq4VZqMBn724CQBwQZMHjR47fvXG9H6K7cOBjLoCKI2iFZTU9oPdC++y1Abnk2vRlBPXkC+ElhyOIkrHyX4fYnEx3ZIrskHMkvGonHiEkNxCCm2DfsTiYlpmpcLqChdO9PsQjwu8cmoIF60qVU8G2WYBtg1J6z81MHtywmQ4hp++1Ibd//wcvvm7o3i5dQh3/O5oVs+nZSwQgVsVOSkjNdciFwhH0T06idUakauX3VjKUNRkOkYCMBkI1XLfSo9TEqBcu4OVWXIumwlumwlGA+Uk8aRjOACjgVBTXIAdjVKNpbZN313PnUJcAP/5wqkZxSsYieFQtxRvzsb9H4sL9E9IlpzRQHOKyw1MhOC0mhLc9ZVJszXTcXqBygcAFrkFYV2lG2OBCAa8IQgh0NI7gd8c6MENu+pRLgdtDQbCDbvqsa99NKGQOBYXUhZZafa+6801hTAQ8HbnwovcWGDKAkiOe3VqTlwvnsg+qytblPKMDdWJIqeUEcx0ctBaodrkAOUzWpdG5NZUODHkC+GVU0MYC0Swe3Wp6lLL5kQ8HoioophJ4+dP/exNfOeJFqwqc+KBW87Hl69ciyeP9M254HdCa8lleALLlrZBP4RAgshVuGywmAzoSiNynSMB1BYXqBd1Zc65XUDMhtKc2Wk1g4hQVGDOibuyfdiP2uICmI0GbKpxw2oyYJ/8/To95McTh87gmnOqAQD//OSxtMc51D2OsBy3zEbkhnwhRONCvXC5cKUHnSOBtO93KgY1heAKlYXS7dmycNuH/TAaCLXFBRk/31xhkVsAlJZIN9/XjB3feQZ7fvQSjAbCre9embDfdefWwmI0JHTH75uQXHtz6e/msJqwpsKFA4uQfDIaCGODbDklZzB2jPhhMRqwpsKJl07q3+3haO8E7Baj6gJTqC6STtozZQwqmWJlLmtCcsDxPi/MRkr7uayW3Zg/f6UdAHDhKo9qbWSTBXhqaCor9/gsIjcRjODN9hF8/pKVuP+W83F+kwc3716BFaUOfPOxI1m5OxW07spSpwUGyr0lpxTOa7NUDQZCfYldjb0l0zkcQL3mvZ/Le5sJypgdp02yVqTWXrmx5JR4lNVkxNa6ItXt+B/PS16er713A27evQK/fftMghdBi/KdbPDYs8p8Vfatll3QF66Usjxfa8vcmhv0hlCaJHJTA6RnEbmhAOpkkdcbFrkFYFNNIRo9dkRicVy6rhzf+sBG7P2r3WqMQ8HjtOJPNlXi4be61QnEHbJZP9f+btvqi3Cwa2xBYl9aRgMRNHikpJvkWrTO4QBqSwpwydpyNLePpq0hzIQhXyhler+Wlt4JrK10wWBIjGmqltwMGZZKBtlVGytxsHtMjd8d7/OiqdSZtsZHSUj547EBrKt0odxlm5Ml1zYoff5Oq2nWxIIjPZLFep7cYgyQTqDfeP8GnB7y46cvZd9tRStyJqMB5a7M66Ay5WS/DyYDTUtCaCixp43JdQz7Ey5a7BYTCszG3LsrQ1MxOQBSay9/oiX3SusQ7s2ik40QQkqf1/ymdzYW4/CZCbQOePHI/h5cv7MOZS4rPn/JKpS5rLjj8aMpkzma20ewutyJjdXurGJyffJ3XjkHralwwuOw4PUsXJYD3uA0S07xTPWNz/w5nB5amPIBgEVuQXBaTXj+by/Fk399MX7wp1vxqQsbsbLMmXLfm9+1AsFoHNfc9TKO93nV1j9z7dS9tbYIE8EoTqe5Ik7FiD/7DEAtQgiMBcIoslukNP0UMbmGEjsuXl2GcCyO17O4etQSisZw6Q+ex72vts+4lqO9E6pVqcVhleIsM1kmA94giu1mXLDSg2AkjiNnpPjH8X5v2ngcIF0hKyfGi+RaqGK7ZAllkxzRNigJwMVrSmcVuXd6JIt9c01hwvZL1pbjyg0V+MkfW7NOTtCKHDA1UiqXtA740FjqmHZVX1diR+dIYNp3cSwQTtnYt9SV+9Ze2pgcABSl6F/505fa8C8pSkzSMeIPwxtMzCzc2ViCWFzgC/e/DQC4RfbyOK0mfPnKNdjfOYbfHUpMSovHBZo7RrGjsUTKFB6bzPh3q1hyyoUeEeGClVJcLtNjSH0rEy/ULSYDPA7LjBdCSo2g3tMHFFjk8oytdUX49S3nIxSJ40P//goe2d8Ni8mgxkOy5Rx51tbBDF2Wx/omcP53n8Vt9x+Yc48+XyiKaFyg2G5GdVFBQkxOCIHOEclVs6OxGDazYc5xuf7xELzBqFponYqesUl4g9FpSScK1UUFMzZpVrqs72iQxrk0t4/CF5ISJdZWpL5QAaSThpIt+K7VksgZDYQShwWDWbjU2gb9qPfYsbG6UH4t6eNBh7rHUVNUoGYaavn6+zYgLsSM8Z1klDE7WpGrcue+ILx1wJcQj1No8NgRCMemlQUoMd26JPezx2HNeQmBLyS931OW3PRJBMf7vJgIRjEZzswdPHXhOrX+7Q3FIJJc6x/aXqMOggWA686tw4YqN773+2MJLucTA154g1HsbCxGdVEBgpH4tHjhgDeIrd96Gm8mTSzpHQ/CajKoZRGA5AHomwhm9Pn6Q1EEwrGUZU2zdcYZ9IXgD8em1f3qBYtcHrKtvhiP3fYurCx3orljFA0l9mmutkxZXe6Cw2LMqChcCIGvP3oYBOCJQ724/eFDc3JzKieBYrtlWi3aaCACXyiKuhI7bGYjzlvhwYtzjMspbsYDXWNprz6V+sR0IjdbQbhytVrutqHBY0dzx4g6GkUZpZSOtRUumI2EXY1T7kOPI7v2U6cGfVhZ5lTdnycH0o/wOdwzPs2KU6grseND22vwx5aBjC9e1EJwzYmwstCG/hyKXCgaQ/uwP63IAdPLCKYGCCdZck5Lzqc8JMfkipNmyo1PRtTvd6bF1GpzB427zm0zY12lGwYCPn/JqoT9jQbC7XvWoWdsEg81d6vblUSVnY0lapZpcvLJO93jGJ+MTIt9KzVy2rIkZT3do7Nb+2oheAqRq0yy9kf84QRxbh+aqhFcCFjk8pTKQhse/NwF+NQFDfjozrrZH5AGo4GwubYwI5F7eH8P9rWP4o5rNuGv3rMaD73VjW+niQXMhHISKLKbUVWUWIum/MCVeMrFa8rQNuhH9xwGyypuxrFARL06TubomQkQpc+CrCoqmPHKVZtBdm5DMZrbR9WG26lq5LR84fLVuPemXXBYp1KsS12WjONGsbhAx3AATWUOdf3pXJbj8nuwuTa1yAHSydAbimaUpQkkdjtRqCy0wRuKqrGq+XJ6yI+4AFaleC+Vll2dI/5pj5HuTxa5+VlyN9+3D787mDgoRXmdDstU4kkoGletNu172Z9xO6sADIRpmYV/fslK/P3V61PWju1eXYpzG4rx78+1qoKx7/QIKtxW1BYXqJZfsju6Vb4oSu5h2zc+OS0noFZulJzJb1EpBE9nyfWMTeI/nj+FD971Crbf8Qf8leyGBRa2Rg4ATLPvwiwWNrMR37pm07yPc05dMf775TYEIzHYzMaU+4wHIvju3hZsry/CdefWgkhySfz05dPwBqMod0sWyIg/jA9tr8XVm6vSPp/iMil2SJacUoumxFiAqavwi2VX3osnhnDjefVZvS6tOB3oHE35o2npnUCjx5EgNFqqC20Y8YdTvjdCCGmUiNy2aGdjCR7Z34OnjvShwGycNf25pqggwe0ESJbcwdHMXMfdowGEY3GsLHWqXVTSidxhOVa4ZQaR29Gg1GONprVstSgi59aKnHuqIHxVCusrW5ST8KoUMera4gIQTbfk3uoYxZoK57R2ah6nBSP+MOJxkbXnwxuM4JmWAZQ4LHj/1mp1uy8YhcNiVEsVitX+lWEUWAoSJoxkGqvsGPajuqgAVlPi9037vMkQEf768tX4xH+/iQebu/GJ8xvQ3D6CHY0lICI1UzjZkjs1KL2/h3vGIYRQLbczY0F1BqJClSx6mVhySiG4tqWXQk2RDWOBCL735DFsqS3E5evL8eSRPrzaOoQLV5Xi9LAfJgNN+23oBVtyZwHn1BUiEhM4ciZ94fX3nz6G0UAYd3xwEwwGAhHhH967Hp+8oAEP7+/Gf73YhhdODOJA5xi++sg7M6ZRK/cVy5YcMPXjU05YSjxlVbkTVYW2OZUS9I5PwmU1wWk14UCaWsCWvgm1f2gq1JE7Kay58ckIwrG4Glzf2SjF5V44MYg1Fc45uZBLndaMJ1grmZVNZQ55Tp0rrRWmFASnc1cCQF1JAUqd1oxnEE6kseSA3JURnOz3wUDSa0zGZjai0m1LqKuMxQX2y8kWyXgcVsTiAmNzGIXTNSJ9P/uSrDFllpzCVGsv6Tt+vG9CzbAdyPBzzbS5QzLvWjVlzZ0e8uPMeBA75VhxicMCq8kwTeSUi4ghX1hdX1wuBE+25GxmI8pd1gwtOcVdOT1X4MbzGvAvH9mKV2+/DI/d9i785MbtqCkqwLcfP4pYXKB9yI/6EjtMC1A+ALDInRWcUyf9ENIlnxzqHsMv3+jEpy5sxMbqqZMkEeHb12zCkW/9CU7euQdv/P3l+OVnz4M3GMGPZmg3pMTkpOzKRBHpHAmgwm1VrSYiwsWry/By69CspQDJ9I4HUV1UgK11hTiQokenLxRFx3AA62eInSkinKqR9IA3sW3RyjIniu1mCDFV+5gtpS4L/OFYRkkKylW4kom7rsKV3pLrGUddSUFCA+pkiAjnNhRlLHJjk7LbOZUll6MMy9YBH+rl+Gwq6kvsagsvQEqM8oaiCXFOBaVmay4ZlsqJPTne6A1F1aQTAJrWXtJ3/HifF1tqCmE1GVQX3mwobfqyhYjwxcvXoHc8iK88fAgAVLEnkiwjbRKVEAKnBv2qq/uw7LIc8kuF4NWF0wWqtrgg45icyUAJ3w2FEocFH9peq8YJbWYjvnr1Ohzr8+Kh5q4FLR8AWOTOCioLbagqtKXsehGPS8kmpU4rvnjFmpSPd1hNqptjXaUbH91Zj/95rUM9CSejxuQKzFNuFDm5o3M4gIaSxC/4RatL4Q1GZx0um0zv+CSqimzYVleMll7vNOE4lqbTiZZqtVZu+glq6mp1al7WufKVc6rGzJlQ6si8Vu7UoB/FdjOKHdKJdU2lC8P+cMrHHuoZw5aaomnbk9nRUILOkUBGSRLKPLzUllxuJkicHPCqY6FS0eCxJ7T2UrrO7JCtai2lDqW1V/Zxua5RxZJLfF98wSictqnXr3VXCiFwrM+LtZUulLutGbkrxwJhjAUic06fv2iVBzsaivHm6RE4raYEt3N1UUFCTG7IF8b4ZATv21IFoqm4nGKFK91OtNQW2zMqMzkzNokylzVjb8Z7N1dhR0MxfvD0cXTM0ZKdKyxyZwkfP78BL5wYxB+P9Sdsf+itLhzsHsc/XL0ebtv0q7JUfOkKafDod/e2pLx/LBCBy2aCyWiA3WJCYYFZrZXrGPGrfQkVtsguNqUGLVP65AyxbfVFiMXFtOC60s5rpviTctJObclN77KuXDnPx5IDMuuW3zboQ5MmVqUkupxIuhgY9YfRNTI5Y9KJwnZZpPdnYM2NT0pJF9qYnM1sRJHdnBNLLhqL4/SQf9o8Pi31JXYMekNqw4A320dQXWhTkyS0eOZQbK+gtLMan4wkTAJRZskpaCcR9I4H4Q1Gsa7ShQqXLaPEk3SZoZkixeaki9HtDcUJvWqri2wJ7krlInRLbRGaSh04LDcLUKy9qjSW3JmxyRkzcCOxOF48OTgtpjfbur/+vg0Y8oUxGYmhcQ5tCucKi9xZwmd3N2F1uRNff/SIesIYD0TwvSePY2djsdonLxPKXFb8xaWr8EzLQMoatdFAWL3iBabS9IORGPonQtPaa9WX2OGymtQfYSaEojEM+cKoKixQG1HvT2p9dLTXqw77TIfNbITHYUlpyQ2q87KmHn/NOdW47txaNYkjWzyKJZdB/KZtyI+VmliVIqzJ7b0Ucd8yQzxOYVONGxaTISOXpXbMjpZK9/QC/7nQMRJAJCZSJp0oKK27ukakQmcl2SIVpWprr7m4K6fEQRtvVGbJKajuSn94ajJ8pVuqDcvAOm5PUT6QLRet8uCzu1fg0xc2JGyvLirAgDekZl8q8biV5U5srilULyIVKzzV76KmuACR2PTJIVreaBvBWCCCPZvSJ5+lYmtdEa7dVgNg7s0t5gKL3FmCxWTAndduRs/YpBpP+5c/HMdYIIxvfmBj2jE+6bjpokbUFhfgDjmYrGU0EEkoMlUKrpUEgmRLzmAgbKh2qxmCmdAvtw2qLLTB47SiwWNP6O8nhMCh7jFsqHLP+tqqilLXyg14Q7BbjAknuarCAvzgT7eq44yyRY0b+Wc+EU8EIxj0hhIsuVKnBSUOy7S4nCJyGzMQOavJiC01hSnnlyWT3O1EoanMkTD1fK4o8/ZmsuSmRu740TUyif6JEHamsSCKlI4ycygj6B4NqJ+z1kpNTjyxmAxwWIwYDUQSSknK3daMJmJ3JI0ImgtSUtgGXLauImG7EgNTfhunBn2wW4yoctuwqaYQveNBDPlC6J0IwmI0oMQxPX47VUaQ3mW593Av7BYjLllblvXa//7q9fjs7hVZWYHzhUXuLGLXihJ8ZEct/vul03j0QA/+5/UOfPz8hoRkk0yxmY340hVrcKzPO60GT2nppaBYcskzwLRsqilES+9ExsknvUlXo9vri7G/c6oo/Kkj/ThyZgJ/srEi7TGm1leQ0jIZSNFlfb54MowbqZmVmit+IsKaCud0S657HI0ee0pBSsW5jcU43DM+6xTt8clIgqtSYUutNKdwZJ7dRVploUzX4g6Ycut1jgTUZsQ7U8TjgKmOMtm6K4UQ6B6dxDa5O5A2tuYNRhIucoCp1l7H+yZQVWhDod2MCrcNvgzqB9uH/agqtKVNtJkPybVyrQM+NTNX+Y0f7hlH75iUWZnq4k8pi+lJI3KxuMBTh/tw6bryOb2GMpcV//DeDbq8/nSwyJ1l3L5nPVw2E/7612+jyG7Bl9Ikm2TCVtlNqBR3KkjuykRLbjQQUU/OqaYBb6pxIxiJo20osx6byb33ttUXYdAbwpnxICbDMdzx+FGsq3Th4+c3zHQYaX2FtpRNmgcmgimLXeeDzWyEy2qa9UTcJsdTmpIEYF2lGyeSZhO+0zOOzbWzJ50onFtfjEhMqNl26ZhIY8kptXiH5jmn8OSADzVFBWlrGAFJUNw2EzqGJZFz20xYM0OiSqnTmnXiyZjchUdxQSvuSiGEFJOzJa6v2GHGaCCsJp0AQIVcLzZbhqU0fUCfeFRy15O2Qb/qCt5YI8Wlj5yZUIelpkIRynRlBG+eHsGwP4yrs3RVLiYscmcZJQ4LvvbeDQCAr1y1dsaU89lQi3WTZlCN+SPTLDkAeOP0CFxWU4IAKmivNDOhV80Qk469TS6TONA5iruekxoRf+sDGzOqxakqKoA3OP0qfDBFA9pc4HFaMrLkpM78iSfENRUu+MMx1Z007AuhZ2wyo3icgpIhOpvLMp27cnNNIYimavPmQjwucKh7fEZXpUK9x65acjsaS2bM6PM4s2/S3CWf0NdVSS3wFHflZCSGuMA0S67YLlmLpwZ9UyInf09mqpWLxwVO9HlntFzng/I7OzM2CX8oip6xSfW53DYzGj12yZKbmExZPgBIF2GlTmtad+WTh3thMxvm5KpcLHQVOSK6ioiOE1ErEd2e4v51RPQaEYWI6Mt6roWZ4sPn1uLlr1yKj+7MrsNIMlaTEdWFBejUTDiIxOLwhqJJiSfS1WFz+wjqPfaUbpKmUgdsZkPGySd945Nw2UzqCWhdlQtWkwGPHujBPS+24dptNTivyZPRsarSZFgOeEM5t+QAuf3ULCfiU4NS/Vhy0sfaSumk9du3e/DHY/14YF8XAGSUWangcVqxotQxa/JJOpFz2cxoKnXMy5J7+mg/Tg/58f4tsyc8NZQ4cLhnHKcG/diZJulEwePI3pJTTuh1xfaEKQu+pL6VCkV2C471ehGJCbUGrTyDOWonB3zwhqLYVp/a3TpfJIGy4Mz4pNr6TNuVZmNNIQ51j6N/PJSyfEAhXa1cPC7w+8N9uGRN+YzWd76h20qJyAjgLgBXAOgGsI+IHhNCHNXsNgLgCwA+qNc6mNSkSsGeC/UliXVManNmh9ZdKZ0AAuFY2oC7yWjA+ip3xmUEZ8aDao0bAJiNBmypLcQzLQNwWk346p51Gb8G1c0zHlSHnQbCkmWXqm3RfPE4LepJKB1tg/6UXUDWVLhgMRnwg6enRrtYTQZsnKEWMBXb64vx/PGBhFZPyaQTOUAa4fRS69C0xwcjMQTCsZRJDQrxuMCPnj2JFaWOjLJ66z12PPGONGYmXTxOIZMLiGSU8oHakgJUum2qu9KbNEtOodhuRlROtlpbIb3vU+7K9M+tZP9ur8/ctZwtSpKXNrNSYVN1IZ6Qx/XMlHFcW1yQsjvS/s5RDHhD2LO5Mser1hc9LbldAFqFEG1CiDCABwBco91BCDEghNgHYP7z5JlFocGT2JFiTG3OPHWS0/r/kzMrtWyqLsTRMxMZTT5IFVdQrpD/+vLVCWn/szHVs2/qdajlAzq4K6UTcXprIxYXOD3snxaPAyQr6pkvvhu/+fML8ehfXITHbrsIz335ErgyrHFU2NFYjGF/OG1j61A0Nm3MjpbNtYUY9Iam1cvd8fhRXPmvL87Y0eXpo31o6Z3AX162KiN3spJhaTEZZrVYPc7MO8oodI0GUFhghttmlsfESJ998iw5BeW7bTQQVpZLFyJOqzS0dSZLbn/HKIrtZl0bEytz5VoHfDAmubu1Ld/SxeQAuSB8dHLa73DvO32wmAy4bF157heuI3qKXA2ALs3tbnlb1hDRLUTUTETNg4NzG8vC6EO9x45hf1iNZynNmbXtfqwmo1rDlNztRMumGje8oWhCr8J09I5Pqhaiwkd31uHWd6/Epy5szOo1VBcWoNhuTnDfJbf0yiUepxUjgXBCJunrbcP44TMn8N29LfjqI4cQjsYTauS01Hvs2FZfjHPqirCltki1RLNBsYjuebEt5UWF0py5KEX8FJAyLIHEuFw4Gsfjh3ox5Avh0bd7Uj4uHhf44TMn0VTqwAdmaEisRbH+z6ktmtbUOBnle5ZNhmX36KSaVajMQovHxbQJBApKTLmp1KGuh4hQ4baif4aY3P7OUWyrL866XCcbJEtuUm2Xpn2/tNZ+9SzuynAsrjZhBqQknCcP9+Li1aVZX1AtNnqKXKpPck5TOIUQ9wghdgghdpSVLZ2A59mAIlrKCJ1RtTlzortKicvNlFmmJp/M4rJUCsEr3Yk/1JVlTty+Z920ONZsGAzSVOTXNFORk1t65ZIypwVCTF0QxOMCf3n/AfzwmZO499V2PH20H40eO3atyCymOBdWlbvw2d0rcP+bnfjyQwcRSSrdmEgxgUDLxmo3TAZKiMu9cmpILSD/2cunU45oevpoH471efGX78nMigOABtnySdXKK5kKd+pu/DPRNRJAney+r3RbEY0LDMvTu4HpMTnFFZvc9aZ8hmGh44EITg36dXVVAlJowB+O4UDX6LQEl2KHRc2enMmSqymenmF5sHscZ8aDuGoJZVUq6Cly3QC0g9BqAZxJsy+zRFHrmGS315hmlpwWxSU4UxHsGnnI6GzJJ4oAzRRXyJYLV5aidzyoxspStfTKFcntpw71jGPQG8K/fnQrjn9nD97+xyvx/N9eqvu8rb+/ej2+fOUaPHKgB5//3/0JdXOpZslpsZmNWFPhSrDk9h7qhctqwtfftwEnB3x46WRiNxytFZdJwolCTVEBvvuhzfj0RY2z7qu0cDvam1kCk1IjV1eSePLvnwiqlpzLmvgeKO7K5BmFFW5b2hICpYG4XkknCoqI9U+EVFeqlk01bpiNpNZrA2OvyAAAEzRJREFUpqJOFbmpC4U/HO2D0UC4fP3SclUC+orcPgCriWgFEVkAXA/gMR2fj1kElBibknyinSWnpa7EDovJMKMwWUwGrK10zZp8olylVxXlUuQkq+nVU8MAprqsJ1ukuaDUqXTLly4InjnaD6OBcOnahT2BEBFuu2w1vn3NRjzT0o/P/qJZtb5mEzkA2FonZesJIRCJxfH00X5csaEC126vQZnLip+9cjph/webu3Csz4svvGd11mNWbthVn1F8tNxlRanTMuNYKS2DvhBC0biaiFWhyZL0BaX3INmSU0Rge5JgVbis6J8IpbRg93eOwUBTtaV6oXVdp2qXdtNFK/A3V66dsQyjpmh615M/HO3HrsaSeZUcLRa6iZwQIgrgNgBPAWgB8KAQ4ggR3UpEtwIAEVUSUTeALwH4GhF1E1F2aWLMouK2mVHisKjtikYDYZiNBEdS26vPvbsJ//uZ82Y9uW2qLlQHPKZDSXbIpSW3otSBqkIbXpNFblAuH5jLzLjZ8CTFjZ5p6ceOhuJFO4F88oJGfO296/HSySE1AzATkdtSW4TxyQg6hgN4pVVyVV69uQpWkxGfOL8Bzx8fVLP8nm3pxz88ehgXrvTMOBx0vhARNsgJTJmgzJFLtuT6NJacw5r4XW4qc+L1r74HF64qTdhe4bZhMhJL2fXkQOco1lS4pmVq5hqtyK1MMdT2/CYPbn33yhmPUWCRYuiKyHUM+3Gi34fLN8zePSgf0bVOTgixVwixRgixUghxp7ztbiHE3fL/fUKIWiGEWwhRJP+feZdeJi+oL7Gjc0Ry8ymF4MnB9XKXLaN+dRtrCjEaiKRsmKygdFGfqdYnW4ikuNyrp4YQjwvdauSAKUtuyBdC10gAx/q8uGKRTyA37KqHw2LEr+W6u1RjdpJROp8c7B7DE7Krcvca6cR/43n1sJgMuPfV03ijbRh//sv92Fjtxj2f3JHQOV8PNlS5cXLAi3B09hZxStxJicmVOa0wkDRXzhuKwmIypEx2SRXTUspNkqcRxOMCb3eOqRMg9MTjsKhDXOdTdF5TVKC+N384Kk0uuZJFjjlbafDYEyy5VB1NMmWTnAGmdD4ZC4Txx2P9CZmIyYXgueKilaVq492BiaAu8TgAcNtMsBgNGPKF8WyLdAJ5z/rFPYE4rCa8b0s1Hj/UC18omnLMTjJrKqQC/P0do6qrUhGEUqcVHzynGv/3Vjduvq8ZtcUFuPemXbpbMoCUFBOJibRT1LUo1oqSbGEyGlDqtEqWXDBxzM5sKK7O5LicUgSe7N7UA4OBUF1oQ5nLmnEv01QoZQSAVLi/rtKFunk0lV5MWOSYedNQYseZsUmEo3GMBSLzcrutr3LDaCA8uK8LN9/XjJ13PoM/u7cZv3yjU92nV54jl2suXKXE5YZkd2XunwOQrEal/dQzLQNYWebQPckkEz6ysw6BcAyPHzyTdsyOFrPRgA3Vbjz0VrfqqtRy00UrEIzE4bKZ8D+fOW/GAvFcoqTKZ5J80jUSQKnTArumTKCy0Ia+idC0CQSzoVwUJY/cUaZjbNM5s1JhY00hdszTaqwtlgawDvtCaG4fWXRPw3xYOr1ZmLyl3uNAXEjdz0cD4ZSdOjJFydp79tgAKtxWfPrCRrx0cgj3vdaOT17QACKSRS53rkqFqsICNJU68MKJQQz7w7pZcoBk6Zwe8uPtrjF8ZvcK3Z4nG7bXF2F1uRO/bu5CU6kzI0tga20RDnSOJbgqFdZXufFfn9yB9VWuOdXyzZVGjwN2izGjuFz36CRqkrr/VLht6BwOwGygrCzPqdZeie7K/Z2jKLKbEyZK6MmPPnrOvI9RW1yAUDSOB5u7ERdgkWPObpQygo5hvzxLbn5X7P92wzYM+0LY0VgCo4Hw8Fvd+JuHDuKV1mG8a7WU6p9tG6tMuWClR+0HqUdLLwWP04Lnj0uNDa5YZFelAhHhozvr8J0nWjAWSD1mJxklLqd1VWpZjJOjwUAZt4jrGg0kdAIBpKGwb54eQaHdnJXIOa2SCz25Vm5/5xi21RXpWgSuJdvM1VQo2ab/81o7KtzWae/RUoLdlcy8UdoudY4Eps2Smwuryp04r8mjJii8d0sVShwW3PdaO8LROIZ8oRmLWefDRatK1SGwZU59LTlAKizWu3YqG67dVgOzkXB6yJ+RJXd+kwcuqwl/uqNu1n0Xko3VbrT0emdsEReLC5wZm5wWa6ostGF8MoIhX2haS6/ZSB6eOh6IoHXAtyDxuFyixCjPjAdx+fqKBRNoPWCRY+ZNmcuKArPkHorGxbwST1JhMxtx/c46PNvSr6a4z9SWaD5coJlckE3/y2xRygguXVuue7ZhNnicVtX6ykTkqosKcOibV+KClfp1Z5kLG6vd8M3SIq5/IohITKgtvRQUN3XHcCDrRJkKV2LXE6UIfCEyK3NJjca9vJRdlQCLHJMDiAj1JXZ1QrgeBdQfk4ef/uCp4wBmbks0H4odFmyQu2boGZNTrMQrNuRfB4mPyFZZur6VyeTjVf6GKsm9NlNRuDJ9oK54uiUHSJZeNoknAOT+lVMi99Bb3bCZDboXgecah9WEEocFTqsp7y5gsoVjckxOqPfY1XT4TE+O2VBTVIArN1TiySN9AHJbCJ7M7jWlaB30qS5FPbhwZSkuX1+Oi9fkXy/W3avLcG5DMc6pW1rWh5Y1lU6YDISjveN47xYp63NgIog/u28fGj0O/MnGSrXParIlV6mx4J3W7L7LUmsvqevJG6dH8MShXnzx8jULUjqRa85tKEaZyzprU+x8Z+m980xe0lBihxL+SG7plSs+eWHDlMjpmK33hctW4wNbq9WiWj3YUO3GTz+1U7fjzwejgfDw5y9c7GXMC6vJiFXlzgRL7vtPHcfxPi/6xoN4XJ6rRjQVf1Ko0FxAZR+TsyEUjWM0EMG3fncUNUUFuOXipnm8ksXjvz65Y8bOQ0sFFjkmJ2inC+Q6JqdwQZMHq8ud6BsP6npl7LCa1IkIzNJlY3UhXjwpZbAe7hnH/+3vxmd3N+ErV63DWx2jeOpIH6wpOpq4rCbYLUYEwrGsv2eKi/vHz55ES+8EfnLjNhRYlq4llI+u6GxhkWNyQr1nqgZIrx6MRIQ7r92M00M+XY7PLC82VLvx8P5uDHiD+PbjR1Fit+C2y1bBaCDsWlGSts0cEaHSbUPbkD/7xBPZ1Xnvq+3YtaIE79289EbTLDc48YTJCY0aS65oHu2EZmPXihJ8dGe9bsdnlg9KLeW//uEE3jw9gi9esQbuDAd+KmI1l8QTQHKDfuP9G5aFJbTUYUuOyQnVRQUwGgh2izEnxagMM182yCJ3/5tdWFPhxPU7M6/lUzIss+ldCUjiaDMb8KHttezyzhNY5JicYDYaEmprGGaxcdvMqCspQNfIJL7+vg1ZXXzN1ZKzmY148q8unpbMwiweLHJMzlhX6YI3OH2WFsMsFh88pwYDEyHsXp1dqUal7HZ0zCHBqTEPmm0zU7DIMTnjn6/borbEYph84G+uXDunx+3ZXIUBbwgrPCxYSx0WOSZnLNZka4bJNRVuG/7uqnWLvQwmB3CGAMMwDLNsYZFjGIZhli0scgzDMMyyRVeRI6KriOg4EbUS0e0p7ici+rF8/yEi2q7nehiGYZizC91EjoiMAO4CsAfABgA3ENGGpN32/P/t3X+wVHUZx/H3B0kJMFBLpqBEEtKhSTRFCzNGHGzMCWp0ZIxi+mU2UuLUWGSTZdn0QzP/SJBBA9NEhzTRsRSpkP7gl2glEOloxjWS64AQKijy6Y/vd7nLcne593IvB/Y8rxnm7n737DkPz9x7njnnu/t8geH536XAjJ6KJ4QQQvn05JXcaOAZ28/afh2YB0yo2WYCcLuTpcBASdHsLYQQQrfoySI3GFhf9bwlj3V2mxBCCKFLerLItdeZtPabwh3ZBkmXSlopaWVra2u3BBdCCKH59eSXwVuA6o6oQ4D/dGEbbM8CZgFIapX0fDfE93bgpW7YT7OK/NQXuWks8tNY5KexrubnuPYGe7LIrQCGSzoeeAGYBFxSs80CYKqkecAZwBbbGxrt1HbnmtDVIWml7dO6Y1/NKPJTX+SmschPY5Gfxro7Pz1W5GzvlDQVeBg4DLjN9mpJl+XXZwIPAecDzwCvAp/rqXhCCCGUT4/2rrT9EKmQVY/NrHps4PKejCGEEEJ5lbnjyayiAzjIRX7qi9w0FvlpLPLTWLfmR+liKoQQQmg+Zb6SCyGE0OSiyIUQQmhapSty+2oaXTaS3i3pT5LWSlot6Yo8frSkhZKezj+PKjrWokg6TNITkh7MzyM3VSQNlDRf0j/y79GHIkeJpCvz39VTku6S1KfMuZF0m6SNkp6qGqubD0nT87l6naTzunLMUhW5DjaNLpudwNdtnwScCVyec/ItYJHt4cCi/LysrgDWVj2P3OzpJuAPtk8ETiblqvQ5kjQY+Bpwmu33k75KNYly52YO8LGasXbzkc9Dk4CR+T0353N4p5SqyNGxptGlYnuD7VX58f9IJ6jBpLzMzZvNBSYWE2GxJA0BPg7MrhqO3GSS3gacDdwKYPt12y8TOaroDbxVUm+gL6mjU2lzY/sxYFPNcL18TADm2d5h+znS96lHd/aYZSty0RC6AUlDgVOAZcCgSveZ/PPY4iIr1C+Aq4BdVWORmzbDgFbgV/mW7mxJ/YgcYfsF4Hrg38AGUkenR4jc1KqXj245X5etyHWoIXQZSeoP/BaYZntr0fEcDCRdAGy0/XjRsRzEegOnAjNsnwK8Qrluv9WV55YmAMcD7wL6SZpcbFSHlG45X5etyHWoIXTZSHoLqcDdafvePPxiZW2//HNjUfEVaAzwCUn/It3aPkfSHURuqrUALbaX5efzSUUvcgTnAs/ZbrX9BnAv8GEiN7Xq5aNbztdlK3K7m0ZLOpw0qbmg4JgKJUmk+ZS1tn9e9dICYEp+PAW4/0DHVjTb020PsT2U9LvyR9uTidzsZvu/wHpJ78tD44A1RI4g3aY8U1Lf/Hc2jjTnHbnZU718LAAmSToiN/ofDizv7M5L1/FE0vmkeZZK0+jrCg6pUJLOApYAf6dt3unbpHm5e4D3kP5YL7JdO2FcGpLGAt+wfYGkY4jc7CZpFOmDOYcDz5IarfcicoSk7wMXkz7F/ATwRaA/Jc2NpLuAsaTldF4ErgF+R518SLoa+Dwpf9Ns/77TxyxbkQshhFAeZbtdGUIIoUSiyIUQQmhaUeRCCCE0rShyIYQQmlYUuRBCCE0rilwIB5iksZUVDbr4/omSvtudMVXt+zpJ6yVtqxk/QtLduSP8stwCrvLalNxB/mlJU6rG50ka3hNxhtBRUeRCOPRcBdy8vzup09H9AdpvgvsFYLPtE4AbgZ/kfRxN+q7TGfl911QtlTIjxxpCYaLIhdAOSZMlLZf0pKRbKgVB0jZJN0haJWmRpHfk8VGSlkr6m6T7Kid6SSdIelTSX/N73psP0b9qDbY7c0cMJP1Y0pq8n+vbiWsEsMP2S/n5HEkzJS2R9M/cb7OyBt7PJK3I+/pyHh+rtH7gb0gNAPZge2mlWW6N6k7x84FxOebzgIW2N9neDCykbSmVJcC5uQN/CIWIIhdCDUknkbpUjLE9CngT+HR+uR+wyvapwGLSVQzA7cA3bX+AVDwq43cCv7R9MqlvYaWAnAJMI61rOAwYk6+KPgmMzPv5YTvhjQFW1YwNBT5KWhJopqQ+pCuvLbZPB04HvpRbI0G64rradmfWUtzdEd72TmALcAwNOsXb3kVaHuXkThwnhG4VRS6EvY0DPgiskPRkfj4sv7YLuDs/vgM4S9IAYKDtxXl8LnC2pCOBwbbvA7C93fareZvltltyIXiSVKi2AtuB2ZI+BVS2rfZO0tI21e6xvcv206S2WicC44HP5viXkQpSZX5seV6fqzPqdYTfV6f4jaQO/CEUIm4jhLA3AXNtT+/Ato364rVXACp2VD1+E+hte6ek0aSiOgmYCpxT877XgAH7iKFSfL5q++E9Ako9OF9pEFc9lY7wLfn24wDS4pctpF6EFUOAP1c975NjDqEQcSUXwt4WARdKOhbShyskHZdf6wVcmB9fAvzF9hZgs6SP5PHPAIvzunwtkibm/RwhqW+9g+Y1/QbYfoh0K3NUO5utBU6oGbtIUq883zcMWAc8DHwlL6OEpBF5MdOuqu4UfyFpRQbn44yXdFSehxyfxypGAKv347gh7Je4kguhhu01kr4DPCKpF/AGcDnwPOkqaKSkx0nzUhfnt00hzYf1pa0TP6SCd4uka/N+Lmpw6COB+/OcmoAr29nmMeAGSXJbd/V1pPnBQcBltrdLmk26Bboqf0CkFZi4r/+7pJ+SindfSS3AbNvfIy3H9GtJz5Cu4CblXG2S9APSMlYA11Z1kB8EvFbngywhHBCxCkEInSBpm+3+BcdwE/CA7UclzQEetD2/yJjaI+lKYKvtW4uOJZRX3K4M4dDzI6Dubc+DyMu0fe0ghELElVwIIYSmFVdyIYQQmlYUuRBCCE0rilwIIYSmFUUuhBBC04oiF0IIoWn9H9Or+SEM4hTYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {
    "collapsed": true
   },
   "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",
    "    </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 $\\alpha$)"
   ]
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    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
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