Logistic_Regression_with_a_Neural_Network_mindset_v6a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression with a Neural Network mindset\n",
    "\n",
    "Welcome to your first (required) programming assignment! You will build a logistic regression classifier to recognize  cats. This assignment will step you through how to do this with a Neural Network mindset, and so will also hone your intuitions about deep learning.\n",
    "\n",
    "**Instructions:**\n",
    "- Do not use loops (for/while) in your code, unless the instructions explicitly ask you to do so.\n",
    "\n",
    "**You will learn to:**\n",
    "- Build the general architecture of a learning algorithm, including:\n",
    "    - Initializing parameters\n",
    "    - Calculating the cost function and its gradient\n",
    "    - Using an optimization algorithm (gradient descent) \n",
    "- Gather all three functions above into a main model function, in the right order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color='darkblue'>Updates</font>\n",
    "This notebook has been updated over the past few months.  The prior version was named \"v5\", and the current versionis now named '6a'\n",
    "\n",
    "#### If you were working on a previous version:\n",
    "* You can find your prior work by looking in the file directory for the older files (named by version name).\n",
    "* To view the file directory, click on the \"Coursera\" icon in the top left corner of this notebook.\n",
    "* Please copy your work from the older versions to the new version, in order to submit your work for grading.\n",
    "\n",
    "#### List of Updates\n",
    "* Forward propagation formula, indexing now starts at 1 instead of 0.\n",
    "* Optimization function comment now says \"print cost every 100 training iterations\" instead of \"examples\".\n",
    "* Fixed grammar in the comments.\n",
    "* Y_prediction_test variable name is used consistently.\n",
    "* Plot's axis label now says \"iterations (hundred)\" instead of \"iterations\".\n",
    "* When testing the model, the test image is normalized by dividing by 255."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Packages ##\n",
    "\n",
    "First, let's run the cell below to import all the packages that you will need during this assignment. \n",
    "- [numpy](www.numpy.org) is the fundamental package for scientific computing with Python.\n",
    "- [h5py](http://www.h5py.org) is a common package to interact with a dataset that is stored on an H5 file.\n",
    "- [matplotlib](http://matplotlib.org) is a famous library to plot graphs in Python.\n",
    "- [PIL](http://www.pythonware.com/products/pil/) and [scipy](https://www.scipy.org/) are used here to test your model with your own picture at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import h5py\n",
    "import scipy\n",
    "from PIL import Image\n",
    "from scipy import ndimage\n",
    "from lr_utils import load_dataset\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Overview of the Problem set ##\n",
    "\n",
    "**Problem Statement**: You are given a dataset (\"data.h5\") containing:\n",
    "    - a training set of m_train images labeled as cat (y=1) or non-cat (y=0)\n",
    "    - a test set of m_test images labeled as cat or non-cat\n",
    "    - each image is of shape (num_px, num_px, 3) where 3 is for the 3 channels (RGB). Thus, each image is square (height = num_px) and (width = num_px).\n",
    "\n",
    "You will build a simple image-recognition algorithm that can correctly classify pictures as cat or non-cat.\n",
    "\n",
    "Let's get more familiar with the dataset. Load the data by running the following code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Loading the data (cat/non-cat)\n",
    "train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We added \"_orig\" at the end of image datasets (train and test) because we are going to preprocess them. After preprocessing, we will end up with train_set_x and test_set_x (the labels train_set_y and test_set_y don't need any preprocessing).\n",
    "\n",
    "Each line of your train_set_x_orig and test_set_x_orig is an array representing an image. You can visualize an example by running the following code. Feel free also to change the `index` value and re-run to see other images. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = [1], it's a 'cat' picture.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFP8PtCDlIBzpyuwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f979eb47780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example of a picture\n",
    "index = 29\n",
    "plt.imshow(train_set_x_orig[index])\n",
    "print (\"y = \" + str(train_set_y[:, index]) + \", it's a '\" + classes[np.squeeze(train_set_y[:, index])].decode(\"utf-8\") +  \"' picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many software bugs in deep learning come from having matrix/vector dimensions that don't fit. If you can keep your matrix/vector dimensions straight you will go a long way toward eliminating many bugs. \n",
    "\n",
    "**Exercise:** Find the values for:\n",
    "    - m_train (number of training examples)\n",
    "    - m_test (number of test examples)\n",
    "    - num_px (= height = width of a training image)\n",
    "Remember that `train_set_x_orig` is a numpy-array of shape (m_train, num_px, num_px, 3). For instance, you can access `m_train` by writing `train_set_x_orig.shape[0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training examples: m_train = 209\n",
      "Number of testing examples: m_test = 50\n",
      "Height/Width of each image: num_px = 64\n",
      "Each image is of size: (64, 64, 3)\n",
      "train_set_x shape: (209, 64, 64, 3)\n",
      "train_set_y shape: (1, 209)\n",
      "test_set_x shape: (50, 64, 64, 3)\n",
      "test_set_y shape: (1, 50)\n"
     ]
    }
   ],
   "source": [
    "### START CODE HERE ### (≈ 3 lines of code)\n",
    "m_train = train_set_x_orig.shape[0]\n",
    "m_test = test_set_x_orig.shape[0]\n",
    "num_px = train_set_x_orig.shape[1]\n",
    "### END CODE HERE ###\n",
    "\n",
    "print (\"Number of training examples: m_train = \" + str(m_train))\n",
    "print (\"Number of testing examples: m_test = \" + str(m_test))\n",
    "print (\"Height/Width of each image: num_px = \" + str(num_px))\n",
    "print (\"Each image is of size: (\" + str(num_px) + \", \" + str(num_px) + \", 3)\")\n",
    "print (\"train_set_x shape: \" + str(train_set_x_orig.shape))\n",
    "print (\"train_set_y shape: \" + str(train_set_y.shape))\n",
    "print (\"test_set_x shape: \" + str(test_set_x_orig.shape))\n",
    "print (\"test_set_y shape: \" + str(test_set_y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output for m_train, m_test and num_px**: \n",
    "<table style=\"width:15%\">\n",
    "  <tr>\n",
    "    <td>**m_train**</td>\n",
    "    <td> 209 </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**m_test**</td>\n",
    "    <td> 50 </td> \n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "    <td>**num_px**</td>\n",
    "    <td> 64 </td> \n",
    "  </tr>\n",
    "  \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, you should now reshape images of shape (num_px, num_px, 3) in a numpy-array of shape (num_px $*$ num_px $*$ 3, 1). After this, our training (and test) dataset is a numpy-array where each column represents a flattened image. There should be m_train (respectively m_test) columns.\n",
    "\n",
    "**Exercise:** Reshape the training and test data sets so that images of size (num_px, num_px, 3) are flattened into single vectors of shape (num\\_px $*$ num\\_px $*$ 3, 1).\n",
    "\n",
    "A trick when you want to flatten a matrix X of shape (a,b,c,d) to a matrix X_flatten of shape (b$*$c$*$d, a) is to use: \n",
    "```python\n",
    "X_flatten = X.reshape(X.shape[0], -1).T      # X.T is the transpose of X\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_set_x_flatten shape: (12288, 209)\n",
      "train_set_y shape: (1, 209)\n",
      "test_set_x_flatten shape: (12288, 50)\n",
      "test_set_y shape: (1, 50)\n",
      "sanity check after reshaping: [17 31 56 22 33]\n"
     ]
    }
   ],
   "source": [
    "# Reshape the training and test examples\n",
    "\n",
    "### START CODE HERE ### (≈ 2 lines of code)\n",
    "train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T\n",
    "test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T\n",
    "### END CODE HERE ###\n",
    "\n",
    "print (\"train_set_x_flatten shape: \" + str(train_set_x_flatten.shape))\n",
    "print (\"train_set_y shape: \" + str(train_set_y.shape))\n",
    "print (\"test_set_x_flatten shape: \" + str(test_set_x_flatten.shape))\n",
    "print (\"test_set_y shape: \" + str(test_set_y.shape))\n",
    "print (\"sanity check after reshaping: \" + str(train_set_x_flatten[0:5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:35%\">\n",
    "  <tr>\n",
    "    <td>**train_set_x_flatten shape**</td>\n",
    "    <td> (12288, 209)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**train_set_y shape**</td>\n",
    "    <td>(1, 209)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**test_set_x_flatten shape**</td>\n",
    "    <td>(12288, 50)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>**test_set_y shape**</td>\n",
    "    <td>(1, 50)</td> \n",
    "  </tr>\n",
    "  <tr>\n",
    "  <td>**sanity check after reshaping**</td>\n",
    "  <td>[17 31 56 22 33]</td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To represent color images, the red, green and blue channels (RGB) must be specified for each pixel, and so the pixel value is actually a vector of three numbers ranging from 0 to 255.\n",
    "\n",
    "One common preprocessing step in machine learning is to center and standardize your dataset, meaning that you substract the mean of the whole numpy array from each example, and then divide each example by the standard deviation of the whole numpy array. But for picture datasets, it is simpler and more convenient and works almost as well to just divide every row of the dataset by 255 (the maximum value of a pixel channel).\n",
    "\n",
    "<!-- During the training of your model, you're going to multiply weights and add biases to some initial inputs in order to observe neuron activations. Then you backpropogate with the gradients to train the model. But, it is extremely important for each feature to have a similar range such that our gradients don't explode. You will see that more in detail later in the lectures. !--> \n",
    "\n",
    "Let's standardize our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_set_x = train_set_x_flatten/255.\n",
    "test_set_x = test_set_x_flatten/255."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you need to remember:**\n",
    "\n",
    "Common steps for pre-processing a new dataset are:\n",
    "- Figure out the dimensions and shapes of the problem (m_train, m_test, num_px, ...)\n",
    "- Reshape the datasets such that each example is now a vector of size (num_px \\* num_px \\* 3, 1)\n",
    "- \"Standardize\" the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - General Architecture of the learning algorithm ##\n",
    "\n",
    "It's time to design a simple algorithm to distinguish cat images from non-cat images.\n",
    "\n",
    "You will build a Logistic Regression, using a Neural Network mindset. The following Figure explains why **Logistic Regression is actually a very simple Neural Network!**\n",
    "\n",
    "<img src=\"images/LogReg_kiank.png\" style=\"width:650px;height:400px;\">\n",
    "\n",
    "**Mathematical expression of the algorithm**:\n",
    "\n",
    "For one example $x^{(i)}$:\n",
    "$$z^{(i)} = w^T x^{(i)} + b \\tag{1}$$\n",
    "$$\\hat{y}^{(i)} = a^{(i)} = sigmoid(z^{(i)})\\tag{2}$$ \n",
    "$$ \\mathcal{L}(a^{(i)}, y^{(i)}) =  - y^{(i)}  \\log(a^{(i)}) - (1-y^{(i)} )  \\log(1-a^{(i)})\\tag{3}$$\n",
    "\n",
    "The cost is then computed by summing over all training examples:\n",
    "$$ J = \\frac{1}{m} \\sum_{i=1}^m \\mathcal{L}(a^{(i)}, y^{(i)})\\tag{6}$$\n",
    "\n",
    "**Key steps**:\n",
    "In this exercise, you will carry out the following steps: \n",
    "    - Initialize the parameters of the model\n",
    "    - Learn the parameters for the model by minimizing the cost  \n",
    "    - Use the learned parameters to make predictions (on the test set)\n",
    "    - Analyse the results and conclude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Building the parts of our algorithm ## \n",
    "\n",
    "The main steps for building a Neural Network are:\n",
    "1. Define the model structure (such as number of input features) \n",
    "2. Initialize the model's parameters\n",
    "3. Loop:\n",
    "    - Calculate current loss (forward propagation)\n",
    "    - Calculate current gradient (backward propagation)\n",
    "    - Update parameters (gradient descent)\n",
    "\n",
    "You often build 1-3 separately and integrate them into one function we call `model()`.\n",
    "\n",
    "### 4.1 - Helper functions\n",
    "\n",
    "**Exercise**: Using your code from \"Python Basics\", implement `sigmoid()`. As you've seen in the figure above, you need to compute $sigmoid( w^T x + b) = \\frac{1}{1 + e^{-(w^T x + b)}}$ to make predictions. Use np.exp()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: sigmoid\n",
    "\n",
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    Compute the sigmoid of z\n",
    "\n",
    "    Arguments:\n",
    "    z -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(z)\n",
    "    \"\"\"\n",
    "\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    s = 1/(1+np.exp(-z))\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigmoid([0, 2]) = [ 0.5         0.88079708]\n"
     ]
    }
   ],
   "source": [
    "print (\"sigmoid([0, 2]) = \" + str(sigmoid(np.array([0,2]))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <td>**sigmoid([0, 2])**</td>\n",
    "    <td> [ 0.5         0.88079708]</td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 - Initializing parameters\n",
    "\n",
    "**Exercise:** Implement parameter initialization in the cell below. You have to initialize w as a vector of zeros. If you don't know what numpy function to use, look up np.zeros() in the Numpy library's documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_with_zeros\n",
    "\n",
    "def initialize_with_zeros(dim):\n",
    "    \"\"\"\n",
    "    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.\n",
    "    \n",
    "    Argument:\n",
    "    dim -- size of the w vector we want (or number of parameters in this case)\n",
    "    \n",
    "    Returns:\n",
    "    w -- initialized vector of shape (dim, 1)\n",
    "    b -- initialized scalar (corresponds to the bias)\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    w = np.zeros((dim,1))\n",
    "    b = 0\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(w.shape == (dim, 1))\n",
    "    assert(isinstance(b, float) or isinstance(b, int))\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.]\n",
      " [ 0.]]\n",
      "b = 0\n"
     ]
    }
   ],
   "source": [
    "dim = 2\n",
    "w, b = initialize_with_zeros(dim)\n",
    "print (\"w = \" + str(w))\n",
    "print (\"b = \" + str(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "\n",
    "<table style=\"width:15%\">\n",
    "    <tr>\n",
    "        <td>  ** w **  </td>\n",
    "        <td> [[ 0.]\n",
    " [ 0.]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** b **  </td>\n",
    "        <td> 0 </td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "For image inputs, w will be of shape (num_px $\\times$ num_px $\\times$ 3, 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 - Forward and Backward propagation\n",
    "\n",
    "Now that your parameters are initialized, you can do the \"forward\" and \"backward\" propagation steps for learning the parameters.\n",
    "\n",
    "**Exercise:** Implement a function `propagate()` that computes the cost function and its gradient.\n",
    "\n",
    "**Hints**:\n",
    "\n",
    "Forward Propagation:\n",
    "- You get X\n",
    "- You compute $A = \\sigma(w^T X + b) = (a^{(1)}, a^{(2)}, ..., a^{(m-1)}, a^{(m)})$\n",
    "- You calculate the cost function: $J = -\\frac{1}{m}\\sum_{i=1}^{m}y^{(i)}\\log(a^{(i)})+(1-y^{(i)})\\log(1-a^{(i)})$\n",
    "\n",
    "Here are the two formulas you will be using: \n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial w} = \\frac{1}{m}X(A-Y)^T\\tag{7}$$\n",
    "$$ \\frac{\\partial J}{\\partial b} = \\frac{1}{m} \\sum_{i=1}^m (a^{(i)}-y^{(i)})\\tag{8}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: propagate\n",
    "\n",
    "def propagate(w, b, X, Y):\n",
    "    \"\"\"\n",
    "    Implement the cost function and its gradient for the propagation explained above\n",
    "\n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)\n",
    "\n",
    "    Return:\n",
    "    cost -- negative log-likelihood cost for logistic regression\n",
    "    dw -- gradient of the loss with respect to w, thus same shape as w\n",
    "    db -- gradient of the loss with respect to b, thus same shape as b\n",
    "    \n",
    "    Tips:\n",
    "    - Write your code step by step for the propagation. np.log(), np.dot()\n",
    "    \"\"\"\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    \n",
    "    # FORWARD PROPAGATION (FROM X TO COST)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A = sigmoid(np.dot(w.T,X)+b)                                 # compute activation\n",
    "    cost = (-1/m) * np.sum(  (Y *np.log(A)) + ((1-Y) * np.log(1-A)) )                                # compute cost\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # BACKWARD PROPAGATION (TO FIND GRAD)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    db = (1/m) * (np.sum(A-Y))\n",
    "    dw = (1/m)*(np.dot(X,np.subtract(A,Y).T))    \n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(dw.shape == w.shape)\n",
    "    assert(db.dtype == float)\n",
    "    cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return grads, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dw = [[ 0.99845601]\n",
      " [ 2.39507239]]\n",
      "db = 0.00145557813678\n",
      "cost = 5.80154531939\n"
     ]
    }
   ],
   "source": [
    "w, b, X, Y = np.array([[1.],[2.]]), 2., np.array([[1.,2.,-1.],[3.,4.,-3.2]]), np.array([[1,0,1]])\n",
    "grads, cost = propagate(w, b, X, Y)\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))\n",
    "print (\"cost = \" + str(cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\">\n",
    "    <tr>\n",
    "        <td>  ** dw **  </td>\n",
    "      <td> [[ 0.99845601]\n",
    "     [ 2.39507239]]</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** db **  </td>\n",
    "        <td> 0.00145557813678 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** cost **  </td>\n",
    "        <td> 5.801545319394553 </td>\n",
    "    </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 - Optimization\n",
    "- You have initialized your parameters.\n",
    "- You are also able to compute a cost function and its gradient.\n",
    "- Now, you want to update the parameters using gradient descent.\n",
    "\n",
    "**Exercise:** Write down the optimization function. The goal is to learn $w$ and $b$ by minimizing the cost function $J$. For a parameter $\\theta$, the update rule is $ \\theta = \\theta - \\alpha \\text{ } d\\theta$, where $\\alpha$ is the learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: optimize\n",
    "\n",
    "def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):\n",
    "    \"\"\"\n",
    "    This function optimizes w and b by running a gradient descent algorithm\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of shape (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    learning_rate -- learning rate of the gradient descent update rule\n",
    "    print_cost -- True to print the loss every 100 steps\n",
    "    \n",
    "    Returns:\n",
    "    params -- dictionary containing the weights w and bias b\n",
    "    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function\n",
    "    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.\n",
    "    \n",
    "    Tips:\n",
    "    You basically need to write down two steps and iterate through them:\n",
    "        1) Calculate the cost and the gradient for the current parameters. Use propagate().\n",
    "        2) Update the parameters using gradient descent rule for w and b.\n",
    "    \"\"\"\n",
    "    \n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        \n",
    "        \n",
    "        # Cost and gradient calculation (≈ 1-4 lines of code)\n",
    "        ### START CODE HERE ### \n",
    "        grads, cost = propagate(w, b, X, Y)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Retrieve derivatives from grads\n",
    "        dw = grads[\"dw\"]\n",
    "        db = grads[\"db\"]\n",
    "        \n",
    "        # update rule (≈ 2 lines of code)\n",
    "        ### START CODE HERE ###\n",
    "        w = w - learning_rate * dw\n",
    "        b = b - learning_rate * db\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Record the costs\n",
    "        if i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "        \n",
    "        # Print the cost every 100 training iterations\n",
    "        if print_cost and i % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "    \n",
    "    params = {\"w\": w,\n",
    "              \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return params, grads, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.19033591]\n",
      " [ 0.12259159]]\n",
      "b = 1.92535983008\n",
      "dw = [[ 0.67752042]\n",
      " [ 1.41625495]]\n",
      "db = 0.219194504541\n"
     ]
    }
   ],
   "source": [
    "params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)\n",
    "\n",
    "print (\"w = \" + str(params[\"w\"]))\n",
    "print (\"b = \" + str(params[\"b\"]))\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\">\n",
    "    <tr>\n",
    "       <td> **w** </td>\n",
    "       <td>[[ 0.19033591]\n",
    " [ 0.12259159]] </td>\n",
    "    </tr>\n",
    "    \n",
    "    <tr>\n",
    "       <td> **b** </td>\n",
    "       <td> 1.92535983008 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **dw** </td>\n",
    "       <td> [[ 0.67752042]\n",
    " [ 1.41625495]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **db** </td>\n",
    "       <td> 0.219194504541 </td>\n",
    "    </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** The previous function will output the learned w and b. We are able to use w and b to predict the labels for a dataset X. Implement the `predict()` function. There are two steps to computing predictions:\n",
    "\n",
    "1. Calculate $\\hat{Y} = A = \\sigma(w^T X + b)$\n",
    "\n",
    "2. Convert the entries of a into 0 (if activation <= 0.5) or 1 (if activation > 0.5), stores the predictions in a vector `Y_prediction`. If you wish, you can use an `if`/`else` statement in a `for` loop (though there is also a way to vectorize this). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: predict\n",
    "\n",
    "def predict(w, b, X):\n",
    "    '''\n",
    "    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X\n",
    "    '''\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    Y_prediction = np.zeros((1,m))\n",
    "    w = w.reshape(X.shape[0], 1)\n",
    "    \n",
    "    # Compute vector \"A\" predicting the probabilities of a cat being present in the picture\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    A = sigmoid(np.dot(w.T,X) + b)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    for i in range(A.shape[1]):\n",
    "        \n",
    "        # Convert probabilities A[0,i] to actual predictions p[0,i]\n",
    "        ### START CODE HERE ### (≈ 4 lines of code)\n",
    "        if (A[0,i] <=0.5):\n",
    "            Y_prediction[0,i] = 0\n",
    "        elif (A[0,i] > 0.5):\n",
    "            Y_prediction[0,i] = 1\n",
    "            pass\n",
    "        ### END CODE HERE ###\n",
    "    \n",
    "    assert(Y_prediction.shape == (1, m))\n",
    "    \n",
    "    return Y_prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions = [[ 1.  1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "w = np.array([[0.1124579],[0.23106775]])\n",
    "b = -0.3\n",
    "X = np.array([[1.,-1.1,-3.2],[1.2,2.,0.1]])\n",
    "print (\"predictions = \" + str(predict(w, b, X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:30%\">\n",
    "    <tr>\n",
    "         <td>\n",
    "             **predictions**\n",
    "         </td>\n",
    "          <td>\n",
    "            [[ 1.  1.  0.]]\n",
    "         </td>  \n",
    "   </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What to remember:**\n",
    "You've implemented several functions that:\n",
    "- Initialize (w,b)\n",
    "- Optimize the loss iteratively to learn parameters (w,b):\n",
    "    - computing the cost and its gradient \n",
    "    - updating the parameters using gradient descent\n",
    "- Use the learned (w,b) to predict the labels for a given set of examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Merge all functions into a model ##\n",
    "\n",
    "You will now see how the overall model is structured by putting together all the building blocks (functions implemented in the previous parts) together, in the right order.\n",
    "\n",
    "**Exercise:** Implement the model function. Use the following notation:\n",
    "    - Y_prediction_test for your predictions on the test set\n",
    "    - Y_prediction_train for your predictions on the train set\n",
    "    - w, costs, grads for the outputs of optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: model\n",
    "\n",
    "def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):\n",
    "    \"\"\"\n",
    "    Builds the logistic regression model by calling the function you've implemented previously\n",
    "    \n",
    "    Arguments:\n",
    "    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)\n",
    "    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)\n",
    "    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)\n",
    "    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)\n",
    "    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters\n",
    "    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()\n",
    "    print_cost -- Set to true to print the cost every 100 iterations\n",
    "    \n",
    "    Returns:\n",
    "    d -- dictionary containing information about the model.\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ###\n",
    "    \n",
    "    # initialize parameters with zeros (≈ 1 line of code)\n",
    "    w, b = initialize_with_zeros(X_train.shape[0])\n",
    "\n",
    "    # Gradient descent (≈ 1 line of code)\n",
    "    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)\n",
    "    \n",
    "    # Retrieve parameters w and b from dictionary \"parameters\"\n",
    "    w = parameters[\"w\"]\n",
    "    b = parameters[\"b\"]\n",
    "    \n",
    "    # Predict test/train set examples (≈ 2 lines of code)\n",
    "    Y_prediction_test = predict(w, b, X_test)\n",
    "    Y_prediction_train = predict(w, b, X_train)\n",
    "\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    # Print train/test Errors\n",
    "    print(\"train accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))\n",
    "    print(\"test accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))\n",
    "\n",
    "    \n",
    "    d = {\"costs\": costs,\n",
    "         \"Y_prediction_test\": Y_prediction_test, \n",
    "         \"Y_prediction_train\" : Y_prediction_train, \n",
    "         \"w\" : w, \n",
    "         \"b\" : b,\n",
    "         \"learning_rate\" : learning_rate,\n",
    "         \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following cell to train your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693147\n",
      "Cost after iteration 100: 0.584508\n",
      "Cost after iteration 200: 0.466949\n",
      "Cost after iteration 300: 0.376007\n",
      "Cost after iteration 400: 0.331463\n",
      "Cost after iteration 500: 0.303273\n",
      "Cost after iteration 600: 0.279880\n",
      "Cost after iteration 700: 0.260042\n",
      "Cost after iteration 800: 0.242941\n",
      "Cost after iteration 900: 0.228004\n",
      "Cost after iteration 1000: 0.214820\n",
      "Cost after iteration 1100: 0.203078\n",
      "Cost after iteration 1200: 0.192544\n",
      "Cost after iteration 1300: 0.183033\n",
      "Cost after iteration 1400: 0.174399\n",
      "Cost after iteration 1500: 0.166521\n",
      "Cost after iteration 1600: 0.159305\n",
      "Cost after iteration 1700: 0.152667\n",
      "Cost after iteration 1800: 0.146542\n",
      "Cost after iteration 1900: 0.140872\n",
      "train accuracy: 99.04306220095694 %\n",
      "test accuracy: 70.0 %\n"
     ]
    }
   ],
   "source": [
    "d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "\n",
    "    <tr>\n",
    "        <td> **Cost after iteration 0 **  </td> \n",
    "        <td> 0.693147 </td>\n",
    "    </tr>\n",
    "      <tr>\n",
    "        <td> <center> $\\vdots$ </center> </td> \n",
    "        <td> <center> $\\vdots$ </center> </td> \n",
    "    </tr>  \n",
    "    <tr>\n",
    "        <td> **Train Accuracy**  </td> \n",
    "        <td> 99.04306220095694 % </td>\n",
    "    </tr>\n",
    "\n",
    "    <tr>\n",
    "        <td>**Test Accuracy** </td> \n",
    "        <td> 70.0 % </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comment**: Training accuracy is close to 100%. This is a good sanity check: your model is working and has high enough capacity to fit the training data. Test accuracy is 68%. It is actually not bad for this simple model, given the small dataset we used and that logistic regression is a linear classifier. But no worries, you'll build an even better classifier next week!\n",
    "\n",
    "Also, you see that the model is clearly overfitting the training data. Later in this specialization you will learn how to reduce overfitting, for example by using regularization. Using the code below (and changing the `index` variable) you can look at predictions on pictures of the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 1, you predicted that it is a \"cat\" picture.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9798e8deb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example of a picture that was wrongly classified.\n",
    "index = 3\n",
    "plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))\n",
    "print (\"y = \" + str(test_set_y[0,index]) + \", you predicted that it is a \\\"\" + classes[d[\"Y_prediction_test\"][0,index]].decode(\"utf-8\") +  \"\\\" picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also plot the cost function and the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9798eb6be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot learning curve (with costs)\n",
    "costs = np.squeeze(d['costs'])\n",
    "plt.plot(costs)\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (per hundreds)')\n",
    "plt.title(\"Learning rate =\" + str(d[\"learning_rate\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**:\n",
    "You can see the cost decreasing. It shows that the parameters are being learned. However, you see that you could train the model even more on the training set. Try to increase the number of iterations in the cell above and rerun the cells. You might see that the training set accuracy goes up, but the test set accuracy goes down. This is called overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 - Further analysis (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on building your first image classification model. Let's analyze it further, and examine possible choices for the learning rate $\\alpha$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Choice of learning rate ####\n",
    "\n",
    "**Reminder**:\n",
    "In order for Gradient Descent to work you must choose the learning rate wisely. The learning rate $\\alpha$  determines how rapidly we update the parameters. If the learning rate is too large we may \"overshoot\" the optimal value. Similarly, if it is too small we will need too many iterations to converge to the best values. That's why it is crucial to use a well-tuned learning rate.\n",
    "\n",
    "Let's compare the learning curve of our model with several choices of learning rates. Run the cell below. This should take about 1 minute. Feel free also to try different values than the three we have initialized the `learning_rates` variable to contain, and see what happens. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "learning rate is: 0.01\n",
      "train accuracy: 99.52153110047847 %\n",
      "test accuracy: 68.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.001\n",
      "train accuracy: 88.99521531100478 %\n",
      "test accuracy: 64.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.0001\n",
      "train accuracy: 68.42105263157895 %\n",
      "test accuracy: 36.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEKCAYAAAD9xUlFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPhoKSimlfDQUlFJK+WgoKKWU8vn/1bp60qC60qYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f979835e6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rates = [0.01, 0.001, 0.0001]\n",
    "models = {}\n",
    "for i in learning_rates:\n",
    "    print (\"learning rate is: \" + str(i))\n",
    "    models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)\n",
    "    print ('\\n' + \"-------------------------------------------------------\" + '\\n')\n",
    "\n",
    "for i in learning_rates:\n",
    "    plt.plot(np.squeeze(models[str(i)][\"costs\"]), label= str(models[str(i)][\"learning_rate\"]))\n",
    "\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (hundreds)')\n",
    "\n",
    "legend = plt.legend(loc='upper center', shadow=True)\n",
    "frame = legend.get_frame()\n",
    "frame.set_facecolor('0.90')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**: \n",
    "- Different learning rates give different costs and thus different predictions results.\n",
    "- If the learning rate is too large (0.01), the cost may oscillate up and down. It may even diverge (though in this example, using 0.01 still eventually ends up at a good value for the cost). \n",
    "- A lower cost doesn't mean a better model. You have to check if there is possibly overfitting. It happens when the training accuracy is a lot higher than the test accuracy.\n",
    "- In deep learning, we usually recommend that you: \n",
    "    - Choose the learning rate that better minimizes the cost function.\n",
    "    - If your model overfits, use other techniques to reduce overfitting. (We'll talk about this in later videos.) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7 - Test with your own image (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on finishing this assignment. You can use your own image and see the output of your model. To do that:\n",
    "    1. Click on \"File\" in the upper bar of this notebook, then click \"Open\" to go on your Coursera Hub.\n",
    "    2. Add your image to this Jupyter Notebook's directory, in the \"images\" folder\n",
    "    3. Change your image's name in the following code\n",
    "    4. Run the code and check if the algorithm is right (1 = cat, 0 = non-cat)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 1.0, your algorithm predicts a \"cat\" picture.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD8CAYAAABq6S8VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvUnMZcuW3/VbEbs5zddkc2++/tWt+96rKsMAsE0jecQA\nyQJLxhOEBzCwRDEBCYkBlkcgTxCiERISohBIRkICIRggZAkBI4zBLhuMwA1Vz1X1qt6r++7NvNl8\nzTlnNxGLQcSOHXufc748mTfvq7yvvpX68pyzm4jYsSNWrPivTlSVe7qne7qne/rqkvmDbsA93dM9\n3dM9fTG6Z+T3dE/3dE9fcbpn5Pd0T/d0T19xumfk93RP93RPX3G6Z+T3dE/3dE9fcbpn5Pd0T/d0\nT19x+tIYuYj8SRH5/0TkhyLy57+seu7pnu7pnv6wk3wZduQiYoHfAP4p4MfArwN/VlX/zjuv7J7u\n6Z7u6Q85fVkS+T8G/FBVf0tVW+C/Av70l1TXPd3TPd3TH2oqvqRyvwX8Xvb7x8A/fuziy4tz/dqT\nD6YHs42CxB/D/6oKCppdJPF/MQUiAhKPiCBiQCZFol5RFPUeVR8+vQ/nNJyTdMN4Z2rJ3kYmb7Ds\nHROEk0hec6VI1q4DdU+OKqiisa+G3ZeqJ3xVvCcd917x6lGvOOfoe48b+sTHclQha6FCOi5MTsXf\nwuxw7N8D7T7Q30MRIgLq8V4RARPLLUpLUZSUZYEtSooiDOmyqiisRYxBjMUYk8ruu562ben7nr7v\nAej7nq7rYn8pXsf+IntmYzSVVViDMYKJ7TEytrewoR1iDMYW2PjbFgXGhHY578NzAd57uq6jbTt2\nTcNuuwNg17QI4HUc42O/hLHtvd/vy2MkJ4xDPXzN/NaTNvPiT7joRNJT5c6Do+vgNaeV9LMjXyym\nB/rtM1X98HX3fVmM/LUkIr8K/CrAkw8e8x/9O/9WdtZPmJUhDAbvPd47XN/jnMN7j8QLRQSDUK6f\nYK3FljUAZV1hbAnWAuOLaZoG73radke729BsNzS7LQCua+j7loqB6WQMPv05clhKJP8+zOhxEFuZ\ndrWIHP0uk0Vo/zo7nxt7kyX8Dn3kIlOOjAroXZv6b7eDtm0B2O1aNruW7XbHq5fXPH9+xfVN6JPd\ntqXtPF2nqBcCegZOoescXddh7dhWY0x4J1bScwx9NLRj6MO8H1UVJDI4F56jKAxlYXH9jm63xRpY\nrSsAnjx5wpMnH/D1b36Dh48/5MOvPQHga1//Jg8fPsRWJdXygsUiTJC+7/n86VM++eQTPv30Uz75\n5BMAnn76GT/84Q9DXzUtXdfhnEttktj/Z+clZ+slAJfnKy6XJatSWFaWsyq847oULi4usNZSLles\nzx9y/jgIKucPPuDs/AFlvYCiTIvCbtfy2bNn/OQnn/Dbv/07/J2//RsA/NZv/4jNZstm2yFiMbHf\n+95T1kuKomK73WL3V/eDJCcwcvWHx+r83pNgWWlOatcp5Hx10nWjwKJ7x1JZxp1UlvevX4gOrXuT\nuiPXMfL6hah5/EuT392n//ePXnsTXx4j/wnwnez3t+OxRKr6a8CvAfzS93/xS1j4RuZ7jCbnRPfu\nSUyb2e/sD8IAn3wnDJJctlbVyUTIf08XBDl47pQJeIhEBGMMxpgkrSIeY0xcGMdyvYfee7quoCiG\nv/ng84A9WNe83fNnOfaM8/s1XuPN4f4xhWDjwlxVFdWiZrlcslqtWC4Dk10sFhR1hbUWYwr6Przb\ntu3pnOJU2LU911e3ADx/8YrPnn6Oeo9zYfETv784Oy3puvB+fdfjVxVNZehqg66C8NBVFjCUZUnl\nBUyFiYKFsTViC2rvWF08TM9R1zXr9ZoHDx7wwQcf8PWvXwGw3bV88slP6foNzumEqQ5jMLzj08bH\nzz620lfbMO6keZddcqh/T96NA7RXb1Z3pC+rl38d+IGI/KKIVMA/D/z3X1Jd93RP93RPf6jpS5HI\nVbUXkX8F+B8J4tt/rqp/+8uoa79uxyGJUdUzou1M4BLws5U0QjnqsmvCp/f+TlglSEj5d0llTjYA\nIqge3q4O5yCHVsbrdW8vN5cCcik+lGGtTWUZS3yOiDfH7b2q4lTpe6WqGqqqoizbWFYzQj05/EMO\nAU3bESAJmUjn+fNzVFIREJvekRfwKBgBa5CioIgSbr1csFidsVyfc3Zxzvr8DIDFehVgNSkQU9BF\nLHy7a2nanrbt2Wx2PH8VJKBnL17SdQPUA4JNYk4OcW1uG9TFrbJTtO3pa4uuyoTbi1aobqlrj9oK\nW3cU2wBRFYst1WKFtRbnXNolWWtZLBZcXFzw+PFjnjy5AWDXdNzebtjuerbbZnyHxkx2haMO4G4a\n4KKfGZ2Ma/980KHd5pvsgtzN529V75eGkavqXwb+8pdV/jGSQfE2dJ5XUIfRAi+aWEfgvT7g7z4o\nNiVj2Ph9CCXHxqf4WyxTBMRPfqd7Ye/lziGZ+bnUFqbl7Y+Lw4x8uCfh1QPDZizbWoO1bbreqdD3\nPkAWVUFZltPOhYjJ54vlYRgrH9T5ApcvTodJUDMuWCoDSzdgJCgMy4hHL5cs1yvOLgZGfgnAcr2i\nWqxCvbakibh803U0TcvtZsuLl694/uIlAFevrvEIYgxF1lepvRFmaTtH34VzjXisd+A8BcKiDBhu\nZUC9wxQ+Lf4DA3Wuw/seg9L3fcbIS6qqYrVacXl5yaNHjwDYbBuePn3Gi5c37HZtBq2Aj2W/Lex2\nnE5lPKdc9+4Y+REd7P51s8/59zeht4FWDgstpzF0293GIsM97V0XZ/QHpuz8csnvfQ9KNJkx5SmT\nnpB4vJtj5m5yn0aJ3ZjQjYoDnb64QVo3aidq/mCFka3ciaHn5zJFU7xmPkjizQd/D8xoT1klIxMu\nitGiw3vonNJ1jqoOTHxg5GI0k0wl7W1yRea8WYNEnv/O23HnjkQEjUzAo0EiFxBrMIWlqEK76uWC\n5XrF6mzN+jyTyFcriqoKyiot0agL6DvPrul4dXXDs89f8PJlxKKbFo9gMaiEPzMYrXjFx4XdyAKJ\n7eqcsm16xAsbY1gugtQf+sxQO8EPz5Csf3oMntJO36O1lrIsWS6XnJ2dcXkZFqSb2y3n5+dUVTXZ\nGRgjyeJIRE5Syv3B0LtcZH7W+P6b01x4eVNam+ky1J74Wn/uGPkoTQ9byDJ0rPGIN5NV3eT34Md7\n4qQNyi4/MmDV8Q83PR7kOQAkX0iG93JkPN+l9Dt07E0lchiZbWLsUUKHYL43UN/3VK6gbAIDD8rO\nOUx1XNk5tDOvNz92SCI/9KwB7xmZVpDIY++KDQrMqCQsqwV1XUfJ/Iw6KjurxZKiKGj7Du8L1ERr\nDw0Kz+vrW16+vOLmNloq9RrgFDFI/POxH4NJJjjnqe0yda/re1pV6B2ltdzuwnsvyx6RktqFd+Wd\njhYwvQN1CB5bjDuesiwxRYExBV3Xc35+DsD5+S3r9Xq6M2JgGCMkeCojf/fS+883ndRf853oMK5n\nQoyesBBNeMcb0M8dI58bWYsOsEmYf8OCZ/A4PKKeUfYbbho60x+AVhTFzVbb6Q5gArVEUtzsd8bo\n8mvzTxkx/dw2/k22qzkTz6W54bhisUWQJK218W+wdDkRe5Wxf05ZlObt24OPABGLSmhXZtSIiA/S\nshmxZVNUlGUddxABOy+KIkjvzkL27BAWrN1ux2azSaaXwz3GGGy8Pm+Xi5ZIaIEfdnlecC4IDtum\nZ9WGa5rWU5bgvMH5qI9wg0loD84h3ifLIIiMXBUwLBaLZC65XC6pqmpvdzXXt7gTGflgJXM37dm3\nzj4HOkHi1PL115xI/kSTwXcJrZxCp0AnYZf9+rK6t9xY/eHSRNzTPd3TPf0c0nshkQuyL/llNrzD\nShakCUWjDfQhSwnf9WihmD4q9goHeEQsuT3+4BAD2Yoapaau63Bti9HZ8ig+4LTJmiScH7wDRXIc\nOd4S69RuKpnm182Pv+5TKPfum/7el4CP2XiXVZn6oSwdZe+C/XMVlG91HaSgDz98zLPPX7HbNmGz\nEO2WXe/p+x4xUNqxLNUAJ5jYliDthu9zGGAfw4dd21JG5WFdFqAdu80t3rVcXJxxcXEBBHvxqqqC\nBJ5J0c45RMO7ubp+ye3VNQC3V9dcXV1xc3MTnJjiC0pqAx1hkHH3BibqCyxVOt42DilKihK6vuM6\nwjTnZyuMLVEJEnvXuaRQbnY7bm+uKAtDVV1mvWCQKC1ba6mq+Ox1nXBzVeV2E5RhVblANTxnVVWc\naotyitWK+mPjal8p/zqSO2C4Q3XMy5wYFZzo9PQu9QUnPeMd83hy3QnaWjN37jvRyui9YOR7CK+O\n1iX591PJKHsQS/AWtROMfHqJT5CKUeiT5csBvHu4fijHK2ICdhNUgZlSz49wwV1OQfNjr4MkhmtD\nPadcc6yezPRS/PS5RMJzZSSGvRc2Yvf7g/5tHVCMMen9BIXlcLygmkASNZUNkAhq0iR2ffD6DZ6a\nPZvNBoDr62uuX12xubmla9pxMWfAMUcGnmCt7BF636cF3jkH2tNbi/eetg+Tbtc7eg/eQe+mViu+\nd6jz+N4lx6OhrNAGiY5aozfzqFCeM9Hj/f5FSNnHd/f1HSfOylNd9FN5GeNWnckkp9V5Wn+8uz6z\nJ/bFKTW6PZb8FWLkx+htBqjMlHGiQaISBcQj0a7VoHjRYJosmswWQ71Bwel9f6SW6eBUHOqHwR0m\n2ND+JCWmZxml5lGCnK7kr2fw3HFuPtl1n9Hq/NjUckdiPBFjZzuBQ2EIUn/st3f++01eZ2FKksWR\n94j3iAqlLSiLmqoIEqs6H6TeXcd2s0GihN33DsXQti031x0vnj8D4LNPP+HTn/4+zz9/yub2Gu+C\nWWJlC3oX3ve8mfMFXzNRXQA1wZfXxV1k7xyd8zR9F+O5GIoYvmCI7+JjyIQUNqHvEVVUZZ/B57u3\nuQJN+RKY+aiWO6jHib9P4avvol1JoXtiUadc9k5tad5h3+seSz4txMF7w8jv3FK9qRSAx8wm38jc\no9RtDGDwOdzgRwsAVXdgi3YAaiFnpH466USSJYzVqHAbnmX4y47BGAwqmRsOVYlMdinz/piaPOUM\nN1+gRkY+V+BOHisy7dzSZVpmvlPx4zHdf2+DBj+n8fexCaAU1qZdpfYBHjMKVoIycoBsmt2Ozc0t\n16+u8N5zexMk76IqcSo0TUOz8ymmyie/97v89Pd/zMvnz2i2tymeiykswd/gSJMimWI0KbVFWIRN\nYdGuZ0AkPErb9/SuoO9D8LHehkXCd4GJu67HZYy867qk7MxhP+99UlQfWtxV3y2UMKdDkNwblvDG\n9R37/Y43Hj9X9J4w8v2XN2x14c1Xz+luTCdfB2glbMXn21U/fAlb2rhVPrw9nDP14TOzLsm4wqkA\n0SHzvfnxoag5tHJYIt8vO+/b44x8jNGSH5tr35P1y6yc+eLxphK50RCNEYJEHqILCqIG3zu6XZBU\nmtsdm9tbXr18yW7XBIYMiC3pvaNpGrY3LT/96U8B+MmPf8znT5+yublBu25cdNVj5/1woL19vyNa\nMtJrgFmcC4HI6EJZu92Ofr0IsE6EVYaYNt4HWCVYsoySt/c+GPKz/07mVkd5H3sGb+N3KRVmdWcL\n8SELo9eWpaei94f1Onl7VE/D23/W0MrpgSdf319vvE5Gek8Y+d0r8dvRIek5g1xEp5KO+IzpRInI\ndyeVP7hLh3JHXFl8JpnjmA5Wyf4OveTRTX88fxin3McwD/fd+Hz5MZcdHzHygYnvWx+GfjykaJ3X\n+kUkcjwprLB4xVgBMYhX2m3LzXVQXtZVRf2qosAixXVaqBVD03c0TcP1y2uePQvQytOnT9lsNqjr\nCGjHAMQ7bPasZop4Jdq0G6wf4Js+RB2Ujq7rGdb9TbNDJYQWSH3rZ+/OK8575gtqkAPGndDwHuY4\necDzNelevizK8fK3ksjfGCPPnkemz6Z/CNz9hWNw7t30898z93RP93RPP+f03kjkOc2tVk7xiBrp\nsOehibDKsF22xuBUI/oxlRqGraoexR7nxzMJWXzCb3Lc2hp7UPs/3JdLZq9TeOa/w/2HpaXjdUyP\n7UMrgxnlMTf/qXI2L+eY9D1X6r6OvPcJv0bGel3fs9tsuZLxuq7r2Nxu8QK9j0pCH+Ksb5qWZhOg\nF4Db21tEhMIKWll8FKPV98G5KIeNDgy7sjLJqSYog5XKFgRvzfg+MtFexCLZDsYgGD28zc7hrFwi\nP2S1Aswk8ncLrUyUqjOpfGjraXQqfn/Xzm1sx7ujd9lfp9Ep4Wzt3OT5RHovGflA72rLeJf5qYgk\ni5U5xnu8/vmAyxjlAeY5/xzO5XWdYmqY7j9y6V3lHGP0d/XxnHkcb+PrrVaOHTtKGexgJDBAwdL5\nlqZpUiKFZnsbGPlmg/PBUgSg90rTtux2LUaUm5sQTbDruuDSX1ao8XQywjdFEcxQ0ng58Lir1ZIi\nguTOOYwxlFYo7GAxFbwx58x3/DSBuR+ApuZ/wFFFZ+pTdCL4vCsamGZi4HeYJN5Zzjuaw++Wib+/\ntOe7ciK9J4zco3aXpCHBoC5MLu+DTTcEm2FMhZSKEY/PXq+Pv2u5CAMsSk2uCNmBxJSTUK6qSt/2\nMROMUpqSugiONp0YOq+0frfHyA5OKhmTIczH7cB8vbfTewelaDoW2+UzZWmmOJ2UbWcx0SaOBuP3\n3B17snD4sb2t3zEA4aYWSizbxtNrQ+8bNGJ2tvLUC0OxUXbbLeKj84opcDZkCHKyTo5CUjjwLUoX\nHDkMFGV4gEVVcn62ZLlaUBqb2lkYm5hyIxeUMQ5MZQucc7TdDt+fUViTEl5sb27x2nC7aSjEJIlG\nvMdoR116yvUZl2fBgci7YAFTGos1BRBisyTbbbF4CenhNHoJqbGIWLxAXY4v2Gj4KwDRi1S3QfjW\n40cYUUwMuFWUq/As5w8x6we4as3ivKZcFanvrQms0hgZn70s8b1jUVas6yXtbRefQ6koMBRYY9no\nljnNlYVhdEwl7cn1iXmfxkyMH3ceeVmT+mZTRaNlzvy60tTZrm5cPEZNgODYf8ZDVBi759Sks+c2\nMoYOGPUN+89gOTyH8t9+L0bh8HzT3x2eIayvm/T9KOBZmaMJXzE78vACBxtvQmAnwNpMkYgN232R\nuN0OoTzDyRCHQ3Sf2R6THObSUn78LpOrtzPDGqTWZN5y4C8cHyT8/Ph4jOzau9tzbBucS/fhmpjR\nSAkhfY88Qb7gTOdJhD2cGxW9QnCoivBMXRrqRRikX/vwA87PlqzPllR2dO6pipK+79lutzS6nLwD\n51yy+S7MmCHo1YvPA1xhhUIMMtt+icJPX73i4iKGt10uEDztdof3PYu6jMeXbLdbEBsCbIlFB02v\nhN8BOuuT6aOgkZELRkeT1wKljmnfjAlerTbCLVZG5eU+dMBokpr6XFP8G2sttoh1u9ACEY8Yg50J\nEPnObWLwJPk1s+vfkOwkgmMOveTtn7Vr0sbhm8FIaK96g48L4pSRmxMVenH+W0Bz3pHNB0wap4OC\nmbibHhezUL+fwErDM81+76v5Z8/qSE4HMjLzw73yFZbIB17ik01yEVOTzbahGpMoS8AeVUaX1oGx\nGD/dis4x3oH2t7zHt69jO98UHzx8/7wNx8p+nSniXcz7UH0H73PjwBGVzC19viCaeDRKrIMpmNi0\n3vR9n0zzLOBxiPEYE8Kzrs9CQKsnT55webHm7HzFoqyoIzNd1HXMI7rjeudS6IO2bZPLfWjP2OYH\nl0u8jzlc+9GcL0hZwSLna8tvJgm+sBaGhA6uT4zRWsuTJx8gYsFIkMbjw6hYQgJvwatDkuQde8QH\nbHPwATDqgwVMtLapqjEcsC0Ea4gWMoZkbxD9DIZwFUM/GgNVXVLXJfXCUi/ClPVufHfGeGZh346O\ng6mO5jDz3U9ccphS6sA76tMs0JWqTM9n5oRhmgpqNI3BEDp42Ikqe8LqIdauY9q7cF/+XOM9PuX6\nzXUM+x7lfiY7A8nVfmDwfo/5+knbNB4zFGHzLB4zmKPK9Kq3pXurlXu6p3u6p684vRcSORoysSdp\nQRylAcqCIsNQ+z5IPV4AE5PzmkwqMILpbdL+AxkGHa/JpNJjCqb020fIIr8HktflQIMEMAc+csDk\n4GMfkZTuslrJazjkqHFMoj9k8SIiqHcMiRLUh+3lgP0abDpnsIAEaZyCJB5JPE4MaTDA+4RUeVY9\nxgTo4sFFiLG9PluxXq+5PDtjsViwXo0hW1WVpmm4aLc0TXT6aZrkqt57H7w14zlVDfb6TpDChAQe\nWZ+KCNIVKR6GiCIoa5YUVqki5FEYC4O1TsxEJAkjl/F5GbFV0RDewfgIrww7Sg3b7SGeva1KymFH\nYARjQju8l9k2e6h3HL+2EOrasliWnK1q+jaEJnC9j9ZV4fpiApkc35UdOz75faIvfFHYO8tR1ZRA\nezwne9flfaAZHBKkcU3HtDjArvZgCrM3T/K6U4KRLPQykpCV8d54q8/6IkfZpzWOV4yyuT9wRSap\np7hOZgJTvq1y+L1g5KpK23SpowoxaFEgajCVzLaDBOaMjdv/2DFxwJj4shPTGjziTrASOASz3GUy\n+KbPOK//0PlDFi7ze+ZM+1gbjy0K+XGjPuHKYdenASePfTDABWiAVQSL4gIzBzwFKj4yyAaTKaqc\nj0kUZJHyUUKIWDhmva85W68BWK/XGA2MW22dYoW3bYuPcb2bruXmesPNNtRTVQt8xPq9V9yAr6om\njPSjr33MOiacWFQl7e6WF8+fcf3iGX0XFgQjwmJRI8QwC9g0pkQETFRW23HK2GhKaFQpkDETHh7t\nHd73oY+NIULmwWQRD+oioxqhq4GBG6MJUzdGWFSW1aJgtS7oXWDkREOAxPROZOSnnDuVmeS5Xo+V\n2WfeqtNrzOR3DrsMhhvJDDgy4e7gnNsHFXzGGfeUnhG38elZSZ/DX065P9O89n2NlUZIcdouCerV\n8F1DPP28AgM40QOL0un0/jDyXZdyZrZAaQt8GdyZE75oI26pguLTdyBIZeaAK3P8vRcq/5AEPvv9\nRU0GX/fM8/bk5Z6iZD3E/OfXH2LykzKcT4ucAngXlM0Ejb2RfGEMZ4J+ItpSi4noYoE1eV7QHvU9\nvYbFoSxLVqtguXFxds75xZrz83PWqwXryMjPV+GzaRp656ijmNmVht6FHJdDsot6FRjz5cMHrJZn\nXD58yOMPv8bjx4/D8QePODs7oyxLGr/ADFKUOrY31zz96U/40W/9Jr/7Wz8E4Pmzz6hikDArs8Vc\nRr2LKRejslNDjxQqYQGIVViEm+tXOJcHvYrv2Xu8d3gfFWBpwo+6nPCMsSwrVHVBVVvWqxJ0MX2H\nzsf3f2z3dtr3/Hd/ogncyGQP1wvQucxTUc2s/vFU0G1ME0p7N61jd9SvY/rsfZctHma6YAzXdv3g\nozDi6XNGrhoY83yaz3/bnDEjs6hOMLxbp0HRKZrb28UFO0y+tzazfG8YeR8VWgB4pbeCqyrUdbjI\nyBersxAFzwYp0DghBfwWi6hgZ6nJ9A5mO2fge8cVyBhhDqtMIRfS+fnn8N1HSe+Y0UrSlosJNrvD\ntYNAHI8NGvx5/x1acO6CVhL5YPUQKwn3D9DK5HrJmPnA6kEZg4FZa8eY406SFYb3nsIKVRRL1+sl\nZ8sVq1WQzJfLoARdLKrYfqXZGeywiCiotnhjWK1WPFgssTET0C//yj/IYrnm7PIB5xcPWKxDzk5b\nlgx75qo6o4lhbJvtLfVqybe/+11Wy5K6DM/+k0XB9uYKQ9hdmAzemDB1U6UesVHdZX3oKzP0v0K7\ntTiBds/Ez0XlbAcKOc8Min2LiEvKzsKAtUpdBasfI6H+wZRWNcZ893OGtf89/32nFH1iDOwh4Ndd\nzHzn8q3CXIIff/d9nxajMb/plJG79oj7+lyS9Zox7XwujN/z0BMTZaeMx0SCFfM+I5fJ9zKy0X0d\ncXyeoVmtR5PfwiAkDGeHPvkZW62IyHeA/wL4WmzFr6nqfygi/ybwLwFP46V/QVX/8l1lqYZV1EVn\nDnUeZ4MkZ1Sj9BK25N4IEicOxqSIhaDBqOXI8jn3qvqDsFp50zKOQTmv2w3kk/X1eHv+PV+cwvXz\nWMt7i56OxwtjQ0wUoM+CJQ1p7ooscYK1lsJajAkMMS/bIDw4f5AW9t2uxe4a+kJZrNY8+OBDzi8f\nAHB+8Yh6ueby8jHLywcQGXwo0kDfhymS7Nst9D1iDefn53z00XcBePxgxd/86/9HgEtEA5POTSnj\nY+fSqokaBDEjUx/qNibgq1YUF4Cm1NeDzbqBLDbMlDmM41KxBoxR6tKkMMxVUURmbwM7dNPxkX/m\nlEdKPCqR+9OCU+1kHzbZ+93vtwtm2LpaOkYbck1WJ3mic8F2hxi5mQnkJnSFSNi5Jzg2q19McihL\nGPnwb3Z9eaArkuA2jNfZVNShXWML8dEGJgTuMwmzkXTP2/MU+GISeQ/866r6f4rIOfA3ReR/iuf+\nA1X9d79Qy+7pnu7pnu7pJHprRq6qnwCfxO/XIvJ3gW+9ZWEhI3kMTdq7Fgto1aB+gY8KnlsriCkw\nZUlR1skZA6CQgJePadfiCjdI6TPc03VdtFUv6K2lybK4QLCRraNdcx4bepBuc8uCXOI9qjT1U7x6\niDN9oF/v6KZwv59JzfOt3kB5dpk55c8wnpcQ69v0ezE/ysKGGNptQ2EsRUzD1rYdXdMiYmm6hkLj\nNlNdUvyIBgx02Iq7rkNEqeuas+WSug5SdFWUIfmxGG5fXSfIx5qK9WqB2IJ6veb87BHLRbCAubz4\ngHq5pl5egJYQA1Y6DxhFpKJtNqm9Kyt0W4/zPUVZppRq1louLy/xXUvX7nBdk3a5pbUUZUlRFGz7\nEXKyUcGp3qcY4xCete+DgtZFSGzQ81SLBWdnZyxWS3R1xnIZ9AJVVWGNDf1tTNqlmLi1Xy0qHjy4\nAA3X12UJEiV79YiWE0k8l/zzMZWP2fmubPhti2rEqWMZQ4z0PJVfXdpUT54II693GS2SBiXmcC78\nxbrxwZ7VkRFSAAAgAElEQVRfbTw+1J2HPvbpXeXtTVJ8enZPWZbjOX/oek9VlHtl5X2Vdid9f1SH\ndmj+5VYzyVkxOjOVVZHaMyrlo9FBwjVnWwD/M/TsFJGPgH8E+GvAnwD+VRH5F4G/QZDaX7y2DPVp\n+4lzOHV04iiMRzTMzl2hGCko3BKvSslUsWltGaCXvGNPVEoeVHY6j3qfgmelz5liJGzPZPoXCoJU\n7rClvQtJn7Ro7zOUEzDyU55pMNucD7ypk1RwR4cw3MQ7TBEYirWSsETvPatlzWq54HbToP0OCA42\nlYXN7c3kOQfFtYn1mQx/9L4HVYZwwT7CMF5dYIrqUAqIW3xHmNAignqLUGJsnNRahGvVgpRJZxIs\ncSxGTMxWP0xcg8XhDTR+jEeeL9D5Ij3vP2vG5xAdvAL3ffu8gBvGs5FRV2Mk/t5nAEM7AiMYTRlD\nDtWC5aJK/VpWFvGh/8Qoha8nTGhgSnPmlIdcnjP+xIDM1ATQuQAVOQe5dYnIwACH/g6fQ2h1VcVl\nC4fP6jd7Skj2se7svKoejIg7F3wClJj1rexfJyJI5gg3TOY8Br4M/aWjXiw3M85nrTWDk9GIratq\nUoIONRdicIMLrhsdk3Jesu9cdBp9YUYuImfAfwv8a6p6JSL/MfAXCe3/i8C/B/y5A/f9KvCrAI8f\nXob0YvFpOtfhfIM6QEu6Ppq6aYfYgrLqKP2aXFOvHnwBhZ16doqYhIPN6k/xRubS54Dh5tID3J2J\nZc4IgDRoRQSxhzH5ucR8CLvPr4eA98/vOSQd3MXIEwZONYJ8alAxFF2PrYIEWpYxEFRt2W6hsIpR\nRx/d5a0pqS34EtrOJEaTByQoioiJSzapY3RD53t8H/0EbJB+XNejUiSJxjvBqcegqAbXeWsDY951\nPbQdtuwopUzKI4ciJtR1u7tlEaU5Ix7tGuj7ODmjfXdM3hwWMIvRKgkWxtqQGNkYJKh3w/G0kDvU\naMK7B72Eione/TYlvDC2RG0R/B9MMVHGO/XgJdmHD321rGvWyxWubZLkVhQG4kIY9AxTCTOXio8p\nOHPpOmf4nR8lXO99mgvOuUlZw3MO1wApTd1QnhtsOAbG732Yk94nnBgvaVEgw49DsvMYTVQ1vLMZ\nBVv//LmyslTSuamOaczcNX/+Y32VGxPk71hERi/ccAanQYjI71cM1oYwDg5JC58ZdgM6tOPURBxT\n+kKMXERKAhP/L1X1v4uN/jQ7/58C/8Ohe1X114BfA/jed7+lhQjN4G7ve3zX0opDfUMfB4m6FhPj\ncXjvw/uN76dSwXiPlOOEDG2I1iIHJPO5BDZn5MeYbH5vfJbXMuacqeb3HwoTe+x7Osb+PfPrYWRO\nMGXek3In0IpBxVFUnrJsqaqC3oUBd3a24vrqltLCshY2mxi8qeuwpmRVmWjtMEBJwYzRmhD4qSiK\nUQrLU+q5caF0Llhg9H0P2cRxojgXDDOSzXjG0IrCUpYlphptvy0m4RKX5fm4S3IdbbPFdSF3pnPD\nYgFGCtQoRaE4GSeUMSYx8sJ0pCmrIH5gThY1o7VFMI1VMAGWsXWAGGxVYosSKcu448ktOYIt/BwO\nqaqK5XKNdw47BHMygroOiExUx6k8l8YPSd5zASW/1vnxnkG8Vucwxo7CjOpo1eV9lu09+nYE8T1J\nnkSrENSEDlIyCTzAHWRW2IkGJq6DwnBSWlRQjgHlwjMMt2hSIur8noxfhq6XCH9mx2L9Yc5JUmcL\nEhcfAR0dAiGM2UKCufPQh4Ovi7egPgg7g256cHYKApCkMMxvSl/EakWA/wz4u6r672fHvxHxc4A/\nA/y/J5RFURqK2CGF8TgJMS3y2BZdrxh6sAbbV5i2iRHswiS0qhi3mDAzY+4O85kzcZtZVRQxU3uO\nZQ+DeC7B52Udw9KkuOPcHcz7kKStMXLboYUlPzbgsocWjeE6b2e26dZTOkdV15R1SxWZbmENDy7X\nLOpyknHH9Urfd3z+4hVm8RCvUWqKwbeKwlBVFXVpk+QiEoJMDZajI9Nw+KGf7TgBkCgJSk+nDZ1r\naNsQCa/tKkwhFF1BZT1m8MYUEFNAYdnebqjLwZQxSEUKqPP0bViQmqZBxGBsGfrHZDFohv4SizWe\nweMTr3jxiDfksZI9Eec2FmMtRV1TL4Lde7lcUi5qymoRJPVsDIXoizCFQ4K0UpiSZVWnLEZGoReD\nEDBhlzsH3QGt5FJ1euczRu9dttWPMIl34/dwbXj3oQ5NC6Jzw2IUYIrOjderZhi5y8wME/Md8PWh\n7uliNLne5zHw/YyRj7i56v49w3ONzz/8SebJOUjcJpadgymDI+KcqwxLRbBoGlny6NEpRsFLCnLm\nJLQxyJrjDuJN6YtI5H8C+BeA/0dE/lY89heAPysi/3Bs0e8A//IXqOOe7ume7umeXkNfxGrlr3BY\nS3enzfghEhGqoqStgqTTtRb1Fq+ewpohtDiY4Ohq1AfPQVxSlPWuDcqJGOw/0WAJkLY5h+GVuUTu\nvWdZ10mKic+c7sljm+dlHYMwtDwMg7wNtOIp9o7Nr4cRWrlL6vdl1idqENPTVT22slRVkVkjNDx+\neMFiseLF588ph5HjlaurG376+SsW1qIzZ5LSFpSlnUArtpDoPGSSIjSngDmbtPO2KmAMDsVpy665\nwUSvz2pVYEuhcwW2V7wd+jPEiTHOgndIhB4keob2qrRty+3tLQCvXl1jTAF4CrHJlRumIXtNMVpO\niFHoQcWi4iDtBnpsWSHGYMqSerGgWgav1nqxolquqKoKl40VLwFmUgJUk+tj+raLO8MiqTMEBd+B\nWIyU7HxzkkTeR4l8wLLDu3UjXKlK000x8mNWK03TpjqOWa1s3Uza9yOsMzr+SHZ+lNTHcsL51k1x\n7aG8HD5CTdZG2euT5D2aKTsnyt58d0KQyAO0ksvjBHgwKqwnZUnGJ+IdATP3wVFJiMFxx53BpP1v\nSe+FZ6dICKRfR4VQXwUrBIGJ5QSAKewYChQdlRbe4UXSS8zx62PQisi+whNGRr5YLCaMPIdWjjHy\nYxDGoK3+WUIr8zRhh+puy0wJGvVDRQy7GuClqNQshL5vWS4uOPv2N1lGTt40DbtHD6kM/MZPOyQi\nK6HPJcFU1tqkxR9+F8Yml/uhvUmxJP0Q6zUE7LI+WrR07NoNPia8WF8sKXqL6yydVewQNMtYLMFT\ncrlYM9h9tbcbXr18zu2rF1xfPefZp58B8PmzZyzrCsEGGIxxQpqorFJVjJkyADECdmhzPI7BFgVS\nFJRVRblYUi8CRl4vV5SLJUVZohP9xDCZR2gAQJyw27X0vUN7TUpz7T1977Fi0AKaXbcPkWTMfKC2\nbdOYHkx1g65gVFI2PjOhu5ORNwcZea7s3Om48OWQyhw+GiEUmTJyN7a/k+nzzWGUcM4xwiqZfiAt\nFqGdRW4okWCfMR756Cp/OFnMALWoMsKJjHFecsY8YPveu+z7iFF5nSpS34beC0aOBN3QFKO2CBoC\n6g+h3dQg1mBsDM5vRguCYTUdBtahgD4Hq76D0VVVdbCsQSI/ZEd+TCJH3J1MNj++d+/st59lsT/U\n/vnnMUZu7dSU0XiNyj2DFGMCh/ViySc/+X0WZcVHH32Uou29fPGCJx/W/OJH3+Y3/5v/9WD/ztOV\n5TqGeX9B8CZtRZPOxBhB1OA7h6qj67dpQv7Oj/4+y/UZ5+fnVIvlmE/ThMXCWMsnP7mhb4OPws3V\nS65evUC7hkUhqA+TMJjQ2ZDgYGh7tDzwMkhqoV8m0QFjP/hZ2AQbLV2sDYtiGT1OhwXSFgW95u94\nyqRy6rou2DP7QSFIZJ4K4pKN/ikS+TFGPjBz7z2tjp6XufQ8t1oJwcym0vWckXdZNMq5Dfm0vTlG\nv183gLNTJjlK61Pl8MgjNQXN8t5N+tbOrUoO8IlT457Mrdn8PO46gZknA43ZTkF1/Hxbej8YOSBl\nhRmcI0yBdZeJYeamTTkDGDKnABjjEPGU+CAJxoluXYvBYX03kaJLa3FRrhOxiK2xi3iuWGG9Z2f7\nSVijY1QeCq8ZaXg3S7tfypwZwzQ92zGqbP3aa4DkaHNnfdolJwURAbugXFroFLft8NsokQssS0tz\n/Tk//uEV3/7a1wH4he9/neuXL1Bt+XN/5p/gf/urfxWAv/WbVyhwZjvOSktV1JRVfL+LRzhzhi8v\nKM/O8ZGZXm23lGXBxcOHFNvnqfO8CwO/FBugh15xUYvWNQ3N8xue+Z+kbfbwLGkBqUYpL5SjmEXI\n2mNtUEKuz89Cujo/SuOaSVeDRbChTLsB9Y7etzhvgiQ5dK4Nk3tZlZydr1mszyii1YrYEqHA2gqR\nJX5wuBLFFIZ2e8vt9RWbq+B60Ta3dO0WUYfznts+LEjOOXoF7zyvrm/i4jZu14PkK/ROkk+JigVd\n4b2n8y5Fl+w6Q9sH6z7nPatC2W5DPV3fI0VQpm6aPkne1pTc3joQHxaYON/Eu+hvEY5tmmnyiflu\nYaChLfmxuVTdtVPmGz79cUacHZNwIO3Md37flDFn3An6GN7qqMdMiSUgGmrsWSXHe2V6LGfw47k8\nRhIpBsu8rNfR+8HIRbBRSgEogni0x8gHU7mckZ+SbXyg+SCZU14WBIjhFDqF+d4VsyT/fkpZhzxC\n35b2+0sOStEQpMm6KqnKKjHG3W6Hc46iMHz729/gT/2pPwXAR3/37/Hrf+NvcLvtKKuCs7NVuidI\nykESbJom5adcrRY453j56jnL2syklmgap9Otro1mgdYJIn6fkRMyGA1xU5xzICMzGUw5vdmbjYzx\nMIKORUToul1yDHOuw3eDJNtP2lsUFUVVYsoCY8tk926MxdgSTIGRcTeicUL3ztN1Hbt2zI602+3G\n589gPu99MhXsul2CY7wDp0PMcpMYuUfYbnY0TUPnR12S832ESUKk0c9fXFHWg8drSbNruN01tF2f\n8uUY6Wi6NjHwZH6oDonhi4FJWOFDf+ncgC1nGLPGf8dMzt4Ejnhb6CLfbX8ZbZjypDdrW07vjiPc\n0z3d0z3d0x8IvRcSeVB2lhNpKo9Bnttx5xJ5rqCcY8vzVXS+/ZorXOZlBYx8cVL7T5Gii5mjwyEl\nZv4cd5HZT1741mRtMen3Qesf8kaWIVogAXP23gcrD9ezjXk218uaB48e8ujBJc82hsuHISrh2eUF\nDx4+5Df+/m/RK/SuC7FCCBZGxqwRCVJ5yqdZFvgoHVbVKkkogzIqxxKH3a0tyxDaWATXa5IYRSRY\njRiDKSSzPALfB7zUa/BShZAAwfsQnc5nkiKE7W7yMu23I0zTO5wPMVYGDHagxWJBXS2o6iVlvcDG\nWC9SVlCUGFsjjA5bzvf0vafpeja70Zpmt9lwfXObdhA5Fu29x8U+aXa3qU+8H6Rx8M5MMOPbm036\n7pJ+YLBYcbTbDbvrlzx4/AgIu7C23XFzc03X+5SQOkj9Q8Eu6ysfpfKgWOzkWHyUfS/KQ5/TY3Zy\nfv79rmOnnHvdPbkBxcT44EiZx2pSnaLvX0QSH+i9YeRVVU1w4rnzDYyMPN/6z8339AAjPzR48uPD\n/bm7tqpSmtVJ7T8J6ojxYg5Zutz1+xDJiYzcz0ZIXvTw3c76yksII2pMsaeIbJ2jub2hKm2Cneq6\n5vz8nLOzC86//ojtLmCdjz58zMff/0X+oU+e8vd+84fcbDe0UeFY9hU+bu2LwiStf9sGeGK5rKPJ\nViCd/0UvPIjpxgaLEevHmOASnkFEUgKIoU9Uh8BMCn4Mstb3fVJkqvoUbmDCTLrdaFURswB5H1Sd\nozK3YLFaxmBeK8p6AcWQfHmBsTVqC4RxEXUe2s5xs9lxdX3D86vAyLfXr3h+dYvo1Gqkc5kZH0Kz\nu04MYVAmehccdJJnigo3Nzcsl0uc77m6epmeY7mqUXXc3t7y4YMzqkFpLEoVLcqcU5pBQeqm82i0\nwhiYeAjS4LLwvXcx8mPZhqbXTc0Ph9FxCka+//vNwYicV+TM/FRGPj4HP6eMHKEoqsSgimIcsDlT\nzjvvmKWGIyoNsizZMGrw03VJQouJBExoCYxmcJbTJPJTmO/AeN6Gce+VdWKW81Olj3GvYNJn0rlE\nY26xw0QTLi8vefLkawCs6pK2bfn000/5+tmDgV/h1FEUNb/0yx/znV/8Dr/9o9/jd37398I9qwXe\n97TtjtW6ShK59kF5tlgs2ESPy1BnlKQze+MEnGrmfejHSTG8dxGZ2Cb30WyPmLlmiHViRGl2OyC4\nS6u6GVNxIYCVbydB1NT3KQlFCsxlChb1krKuKaoFRVmjQ5CvokStxZsCVYv68Jxd17FpGq5vNrx4\ndcWzz58DcHN9xcur62BeGyVwCM/TuZGJNe0mtdd7wAXPyxAGYWSYpbHcbm7ompY25j21BvAF6/WC\nB5dnfOvDR7RNXFydR9ZLwOBeXdFv4iJmQr+G5VAzKcHgpIcY48j1h2y/9xWU+Rw/JqHP6VQGPi0r\nHTlU4oEjcd7OyhqYeX7N60qb7DAPHL+rrNfRe8HIYWq2d+wFDXSM+YmEkEaH6NigyFfZASIZjtm3\n7NRDNFg65G3NP9N1/oDSbUanr+DzvpC9706nCsJQ/n4IVGMMzjmapsEYk9K2FdZivKPrGz5//lly\nRRdbcn3zitb1rM7P+f4PPubJ1wPz37YNm9sdXd/QdR2LxTo1t+s8XdfitZi8s/FvhFgA3MDgZgrH\nBMGJBKY2sXPuQggBM2aKURHU9VHqi84bmTQ5TL0aReO7FHxIQmENZVElBaEpqmRyWBQlUpQgQ45T\ni1PLELJ1kGzb3nG72XF9fc3nL16lEAjXV6/YbqPVispE2ekG5xokBDHzY385p+hggz3wUq/YRc2L\nFy/wfceDyxAK+OxsRV1aPvjgMd/69jdYmOAgBXB1fYvtHW3nJnPUiOC8x8eMVrn9tZcihkHYZ+LH\nmOwxBj45lpmGHoNX7pLCv4jkm986WDWN8+X198yvO/b9bfNLvB+MXIixMYb4YYHmL/Z1uFSQ0/Z7\nYr6CHirzEDwyxHh5Hb0J7vY6CfyUsvLM3l+kLiDFyIi/gMCwvQvb9xTERw2IpYspudoo0RpguVqw\nNmvWTx6F+CaAKUsUw2bXcn1zxfr8giEbz/NXV9zc3LDZbHCuY7cLIXFLGxhV1zRQXUwlmPhH+h4h\nhq5LjNw5N8lYJBIi0/nGTZxMxA9RDQl2lQSB0kr8ogTPThnrDwYsHiuaeeyF6wtrqKuCRVzETFUn\npyexBkTSDsfFUYqGhXKw5W7blma34fb2lqurKIUDr168xMi4uLr47p1zOI0MXQUyix3cIIkH2GQA\nyUXhetNT1zWXHzzmm98IC+sHjy6o64qz9ZLz83N8c5tGhApsn71kc3NLt2vGhUQC9u7UBz/FGfPt\n467JjC9kgo+pz6R4zfB2mCwK4/d9seRUBj68w7eh4bZDMynVcSLzPcSw0xifV/iG9H4wciVu4edS\nqk4+hwmkqhPPu1SMKmKPSd7sXyt57OIDXpQnprw6pfeTJXLGaOK32XUnMHLdt4E9ROYERq46RhIM\nDjDB3tXp6GkHoEZYLBacn1+wPjvDmgAjbLcbDJ7SFixcRxdxcL8zlFXNar3mvFrS9o6nT0P2v/MH\nD1ksFtzc3PDq1Yuk2KujGWLfO6QiOXvlbR3+BrPBvvcBp+7dxGElSNsGowbddUk69NHGWURi+QN0\nJNR2HGlhwRjGm09cpPSCz6RSFSitoS4tVWx/URUxoUlwWNuXzCLj833C6H3f0XUhMmO727DbRIx8\nc0sdQ0XkjLyP0njvp+M+lC8hsYYnmjXGca2ORw8+4Aff+4iPP/oFPnj8EAiM/OGDS5pmy7Nnn/H7\nP7pmtQyLUtP1dN1Trq6u2Gx2uAh/OhE672P4VUk6jbl0vZjnQWNfsJrAFAcl8+HOXLAKK8JhCX/v\n0P5587qL7j6VT61TJfK9Npxw3al0b354T/d0T/f0Faf3QyLPLEamh6cS8hw/PqQ4nFtqHK9y36pl\nTsU7dLwZHEJeRyZLPJt/5lSW9eT4MfwxJdVg2JofKFNc8mCEwRxNk85gMAPNXbS/9a1vJX1Cbwyr\n1RlVVdC2bcKJPYam3dErrIylqpaYKDU+f/6ci4sLzs/Pcc7x4sXnAOy2LWUV6nxxdZvqNsagrqNt\n2wBF6Bg2YbO5QV1MftC3Ey/grut48uQJm+4qve8ixnaxJsTwGYKNisY40hokfPU9g69muNYES562\nTQ5M1XpJVVXB6UcKBsC9dx1FUaG+x/cdpijTbkOKGpUSFei2O/omwErb61e8ePopP/39H/P82dOU\niPx8veTm5iaUmweUUsDYENvah2zvfR/OVVXFarXi5tUN292Ob379GwD8A7/8K/wz//SfpDRCWQiL\naEK6qAx1XVEWho8//pgff/iYv/bXfz3274beOZqu5Wbb4OP4XJ8/pDSKIjgV7AF8G0D6UWk9SN6H\nLFT6LGnEUZgkyyB0DFc/Xsb0+2BWO79+fl8OY06tvjInPqZzNn2fS+35tMvLyuv7SkMrzN1Z3/6a\nd6ifPD3p0kmWJ2+2KIgMW9DwezrATnvIuxaDNNEw5DGbB4y87z29V9o4wZqmw6vQq6frHOdnQdnp\nuoYmxvm43jynqsOWvF6ug/20DXE7+r5nCBJ3eXlJ1wYc/vzsMjHf50+f8erlFajiyvNx4faepgnx\nx0tbgDDmd207RBVDiB44dLMRpUApBYxvR6FAJaTvUsDLmBTAeUxlsepw2qNEbIKQpMLgQpRGKyks\nRLCMipi7gPfRTBZQ0wIGb3aItSMcA6gEpLzfbeijfqDb3dDvbsF1lEZZlkPAsILKrHEqNE3Dtmlj\nHSGFnfOKtG1k8hFv32kwKVwu+e53vsMf/6N/DIB/9I/+MR49fhBisqNJB6T07LqOpgm/v/PdX+DT\nZ8Fq5pOnz7m6uqZte4rCUtThvQfYKniLDhj+MIZyRSBzYeiIls+W+4LOfPyaExn53VYr4dPLdDGZ\nmxQO50brt+MGFu+S59h5KA93Ghd6bxj5KRqDlGjgDtK3zHl3mN4h8nSqmWFum3rkHpWZQ0H2N7ku\nVxrlAz1TIoWcLHFwa2AGXedouy4Gawr92XQtxgR371c31zz58DEQpL+2bcF7TGmSMqzrOoqqxjnH\nZrNDpcXEGDHV4gzvO1SF1WrFeh2sVkpTAobb6xturq4oshg2XdeAV/rSBqedPjC0vt2BV4wPC8Zk\n52OUwkKh3ZjdRRRRwfqoEE1KC0/hqrCoqSNPemuNYsViBKQoU4IMa6MyTx3e+aSw84Ocn4VdHepx\nvUONBbH45pYuYuHd5grf3FLRcV5b1uU61i3JHPbmdsPVzW2sw1DWC9q25dW14l2XYv4sFgu+8eQb\nfO973+NXfumP8P2PvwfAhx9+SLdrGNzoh7mivg27EHEIcHb+kO9+9DEAf+V//3U2bUdR1qwqy+ri\nEoDNtsMbxeg0G45q0AYNNt9DpM7XKSYP5vCcfZcDxw/tRk9h5F1S8udGEPMohEIOAhw2RFAGT6y5\nmXQuhAWT6KzkI+xgD5n46jHy95AOZXt9+8JOuyotVrMt6kRSGP7LDgx/5IdHm+twOh+w4Zu3o7WD\nc8GKouvcJLQpBCetIYv58+fP6b/z7VCHWPo+mCRenD9gF5WdqhoyevlgplYuaparMwCKouLiYoH3\nSt87hmH44PIR6oWn+hmfvfp92jYmeI4x5b133F4HU7wySi5+UK5KgaBILMtKSJZbGaEu+j1rFiTm\nWxyWPwV8g/GaFJCDsth6E8pDoRphQCsGUVL8cBeZv3fQeo+xfbQmcYmxGVuDCU5Mpm+QLnha0m6o\nxHGxLFnZ81RHVQTJW8Wy2TVcRc9M5xVrLde3GwzKSkL/AXzzm9/k44+/xy//4Ff49re/m8IH397e\nsqxqVG1YfIbAUdZgo+mlqvLs5StWF8FD15uCql6yNjUOWJ0F79xd/4o6QXdmZNyqQSIQm8ZAPh4P\nfT/0Oz+W5sAbMvK76sh96u5q1zSL0WH46BDl0Eq6Phcy39LM8Bi9F4z8kDR5kE6Rak/EyE+hU0s6\nzRvz9Dc33+Ltnz+tnHwQHvsUM6bp6vs+uLln1h8DQ1mtVhSqlGXJyxevkqVJaQ0ejY43Y0orYwrK\nsmaxWiFFRb085+w8WEl8+uwZhQ2Bt9q2TZL3xdkZjx495uLsgp0brVw2t7eUZYFFcF0D3lEvY2RH\n72JkaIsVpRgSJotBBCojLPfD0+3NI6Pgmj7oWIYOTuawIcCVwaFSzaxpNCaF9sjgZOY9vumg6GOS\nL0mT2NseMRYvUCKUUS9RG8/FwrKQMwzr1CdDQg5jDE5hF6GVtve0vePl1Q3LqmDx+EM++ugjAH7h\nF36Ri4sHrJfrAJ9ERl6WJeViGaTv3o3xrvqWPqZrUxy3N7dcREYupqJeX9Btt2jv046nKmtsOdr6\nJxt2RvNOAdoDzmuHGOGAkd/JfA8kg5h/h8O+GPM6C1PsnTtW//CXz6dJ9EbDwfvdjINItkM7BhNn\n/lNvRPdWK/d0T/d0T19xei8k8veW5ETR9xRF7alrpozYNky/Q5QGZLrWH8PIh6sOYuTD7ywDi/ee\nXkOsZGMsRVlR1kFSWi3PEIWzi3PavmOzDcrH9aKO9yp975MkWS1WLJdLqnqJxPALg+OPkYLttknB\nuZomWDY82z7n7OyMRw8e8oPvfy9ZYP9oc0vXbKEsKQYLkniuLCxGg+QtEqxSIDj3eKMB3yZ3959J\nkElSM/Qx6YLRqPwarCsG339j0IXidYgDFGzRNSYIH9pUoDRdH2ysxaCFpLEUJGQbHJAok0S+LMCu\nKnRZUlpDVYwxhIwxqFjEFmkcbZuWm9sNy7riyaNLPvj4Bzx58gSAhw8fY6RIIS/Gd29SSNw8bov3\nBk9Ib+dVKBZrmij9tl6xVQW7Fonp9iDEb094rte04xDvkBgSQ/CUjEGzpv09Ha1DwotD1ybq+73z\nh5Ucr70AACAASURBVGCVXCI/VqbYw+061M65RJ4nzlDV5Dk7b4eVaXkmC653TCLXdiaSd6f5jHyl\nGPlJMU3eaY2nYeSnKWFPh1buirL2JlryU3BEr+OE7n3IRj6YHlZVhcZtstu1uKriwYMHNLc3WXaZ\nAGk0TUPpKoqYCUdEgqULDUVlwba4XWCojz94QtN00ZnHs9kE3HdzfcPz5y/Z3m54+LVLvvPNbwEB\n7/7ss8/Y3t5g8BTGpngndVEieOrSouooUno4ARcwcNc3E8ad/5ks2H/fdSETUWx/OWg1I/qOtTGe\n+cBkA+sWBYxiB9sxC7RdNF8pENdibMwZ6gSMg6hotdG5qzKKrSuqwlAWdjIGyrIMGYKMSTlDVZXd\nzvD4wTmXDx5y/q1vJh1GIVCWlqpcYW3BbUwOstlsghVR1g9DWcE704B4lvWSzz4LKfCuNxuqesly\nBdgiOWLVywVdFxdIHeEUYkwaxWFUsTJNbnIMxigzq5WjzHeWO/fQuIYxHMNd9WkMmXAKbj8w8WN5\nSbU/fN8cWnHZAnOMkcvcUSlaZ72O3iNGforEegozfEuQ6UumN8XIh3smGOEbBtg6poyZTATmSpwx\noUdRFPgs2bAxhrOzM+g7hvc1lNG1XfD8i2PV9j3KjsWq58GjBYvlInklPn36ebQ9Dzj5wIA+fPSY\ntm3Z3m64fvmKR4+C8u7sfIUo/N7tLb1zWIE+TqrleolosCDBj3lBg/dmsKDou232jBKj8+nEIgE/\npBhzwcxNBDdYp5guSNYxXdfwGkRCvckzOEmoPeIVsR5RF5R0A25sDKCIN3jXoSnUgcdaqMqCqhhT\nrfV9z6Iq2fQdmmsOo4364uyMrz35kM5a6hgqt64qjC1wvqNtR8sja22MfBjMQZsuMIm2a6OFUkjd\ntnh0yWefB9v+25stZxeXFGVNUS/YbMOuarVacXNzE5m2R/ygTwiK1CHTjTfTMLaHvsPIyO+Uyg/Y\nmh9i5jkjP3Q9QHeATRxr38C08zDXuVTuD4TyCELXrKxs/h6byjK3WjmRvhAjF5HfAa4J3LNX1T8u\nIo+A/xr4CPgd4J9T1Rd3lgOTXInHaO4sM/8+XPPaLRr70u4h5yI9sGweukf2cvDtt0/ktC1SuDi7\nd7Y9g3H7laTqbJuX113FWOOjcoZ4fbwuHhgSFtdxgDqneIXa1pSr6HauCq5H+w758ENMts0UE5Ry\njXbYaG62XFTUyzNsUdG7Hc1GsFWUzsTRuQ3ienrv2ESnmF3TICYwnLN6yWfRUeh8veKX/8j3WVTw\nu7/993HdNiXqXljHYlGl8Kx9jCZoraVxHdfNlvZFZgZogzOIKQymCEwVggmm73u6pqXreipbsC6D\nlY2NCkdVDZnuI4Pv256276iKEGulic9xc3XNxcUFvXf4ZoNXn8ZuWYS46X3vuLg4p9vGuCZ6w7Je\nsFp6nOto4u7Fe6VpoXXKzW7HzoU6bL3m8Xd+wMWjD9Gzcyq7xsWxsmkMKsREvybFKaeCbe9ZLCpK\nK7RN2AlJ31DjOV+UFIWhKxb8lb/+fwFw9vjDZGJ6fnGRkkg75zg7W+8xyPkYPGMf5rhrh3jX3HUx\nGunryhnSxh1rl6pyni0c879Dx3OJvO8F52SUypf1a+s7dm4eCdIUfwCMPNI/qarPst9/HvhfVPXf\nFpE/H3//G++gnpPomBR66vlT6SSY58jgPpWODep5lMZgmnc8d+HQ3lzST8eza4yAmmBKphrjkkcn\nDFuUWFtAaRFXIC4wGvU9PpquVdUiWTV4pwETF4fQUZQdpgwTse16quWCerFK4XEh2KQP3qQPLy9T\nmFXnHA8uzvnOd75DIYrvdyzjROzaHZ9//jmqSlEUnEXzuJcvQ6ztze0OqRfjJIxhXUUF+p4uTc6e\n8/Pz8Hza0npBY7q1znfUZejn3e0WFxcLUajLApEK6zRFflyvz3j16lVIXGEKeh9iowCIV4qqpCgX\ndM6xXI8ONk275fpmE6xLYo7PwsPV7ZYeixQl6yEw12LNcn1GWZbp3Q5vXuI7DpY7NjFyEcH3IYIl\n3qVxVBQFXbNDNZg6fvL0aTK9rOM7kaqiriq8Gy1SBrv1OSPNx2E5iyF+iMEBJ+Ha7YlWK/n8ONS2\n4ZnnbTqVkc8TTLuZZ+ehBWb+PMcY+cn+JjP6MqxW/jTwl+L3vwT8s19CHfd0T/d0T/cU6YtK5Ar8\nzyLigP9E/3/23ixWkiy97/udE3tud7+39u7qnuluDjnkkBJJ0ZIXmZIs+0GGDViyHmTDMETCgO0X\nLw+C4Qc9GYYNw9CDAPrdhm0YAgVD1GKRoETBkjkaSeSQs/Va3bXd/eYay1n8cE5ERubNvJVV3SP1\nSHUKF5UZGRlxIvLEd77z//7f/7P2V4Aja+1T//kz4GjVF4UQvwT8EsCtw/0XipGB82aABeXDev5q\nvFO7wutuv297pSteL7xfOky9/fr+rXO0IAtafVyF293Ublpirir11iz9b5jtVxa1sIr6Loo6SaZd\ndcljn0liCaQgIEVag618anmRUxYzqtKgpjmVBx+LvEQECUIEhFFKkgoiX6orjpNGPdFa2yRRzhOS\nKmxZNl7adDplNrkiDQMePnwIpuTKY7hHb7/J08dPnNcoRKOTHkQhqnKl6aY6aDL5jHHl7bJOhygJ\nCf2PrLXm1t27rj+VQpXaScACoXCrhDiMuFIzitIxdoSxJFGItZpJURFb9zj14w5h0gXplAe1hdHU\nF3GoLGGiicKEfjfBWAcDaGsRMiIKQ8Iwcl4zMJnm5IVGxgFRlpJ03Ioj7g2Is4Hz3GXoCjh4+EYK\niaDWhwma7UK4vhRFicTOdWn82Km9zk8++ajJrM88bCBlTJrGLsMWCEO5MkC57NXKDXHtjZgm6sXB\nTmvtQtnIdf1ql2dc9rzb32tw8BVl9urPKmNXHmu5/22NmXZf2ufUZjOCxXL7vIb8j1hrHwshDoG/\nJYT4bvtDa60VYjX47Y3+rwD82FfftnaTVNQVeuTLP7qxeuX2a8a9fSyWjFzNGFjuUr19af/6yDf9\niFpvhpG/qN/WWqy8eRlYt+XEiFVLPWFt60K9boZoaZDU2iUyJQoEURgQWktVeggFgSkrlK3I5JzV\nAE6v2o1dSRBEhB520dpihQFpCMKwgWOCIHLbgdHoqln+VkVOlY8RvS7p/i5x2EFVzgAGMuLWrVsk\nScJoNGoKNdy/9wZhEvPs2XMiK+YsG2tIOxn9wYCslzXQjjGG7e1tB2sEIVZZKo+16koRCgc7ZOMT\n6rFqrcaoiulkRD4ZN8ykEkHU7SEIMFh0pSg9xdIqQxIIiCSF0tRsMyMj0rgDGCazgrHP4MxLRZr1\nCJIOUdYlytxEFScdwjAGGQJ1MlaNoZhGs0OIeRBWSpeJakyEsAbj72FVVU1C19XVFc+fPm5EvtoB\n6SSJUf53F8KVZ1xlMNv/6zlc3Wxf9YysM+QLDkx43fguvwYWpB3WTjBLRnUdtNJ2hto03fb2slqN\n9S/fizacs5wxWu+Tt0TGXqZ9LkNurX3s/z8WQvwV4OeA50KI29bap0KI28DxC4+DXVA/W9eWa+St\nMkx1QdkXGcRVFXqWPVZr1nixa9qqAVq/V3rzH2jdQK5bqauNDHm7osvaa9BzBoqrZ1mn74vGk6uP\nJYOQMHKaI2F9HpmDDJxOtZUNr0opg9FOzEkGhrKEKHVP9a3bd73eiECIoMmU1DixJ+XreZ6fu9BL\nVeZs+8DaJ598Qq+TcrDvGC2fPXqENhWj0Ygir5rr//o3vsH+/gFZ1uHOnYcU/gEpyxKkIIwjJ9TU\nCqCXZUmUdYizDqGUVHUWpS+oYC30Y9mwQ7SumI6HyDhlsLNPVNe5lIKLiwsXU5CSwELsmSPIkDTt\nkGQpo9MnJJkLqEqlOD874+rqCoBe13neg90OadbFBr5gs1/JKAPCuFWBlAJjNM3KStZlDd1fPSnX\nzIs0TRHWMMrdyqIoCtLYGfezszPK2YRu6hkwidPLiSIXCK23N/z2tZ6vO2dlF732VQbO3csXUwaj\neL2Bbu/3MmXjXmTIdYvyuOyl1++FvB4HWHXOVdj98rnNK8qCvLIhF0J0AWmtHfnXfwL4i8BfBf5D\n4L/z///qi45lrePwbtpuMnS157uJIX8ha2XFWmLVBHDToHpZj/ymPtfvy0ptZMhrD6C+1nbfm8G+\nMIFKtHWc6Ybp4IOdRggMFmUcr7v+tYyQaCEx0iX8RJ5HHoaBS9MPAmSQEIYxoU/CyLIulReZstpi\n/KKt9NWCyrIkCXVDJTQIqqpiohXlbEJVpHQ7LhgYRRGnT0/59re/TakV/b4zgPcfPqTbG5B1etg0\nIPAPZFhpZmVBrhS2Mo2caRhGTE2Frgwm0IQSTD0pWUlZOWM+6HWR3pBbXSEqTRrEpHFE7O+31hVK\nRG6lISXIoAl2Wpwcrggknf5283udnzzl/Q8fYa3lzTff4uDObX/tkjBKXZk3I9A1/9lIrNZOzCuo\nWUj482v3+1kHJTUp80IQh5Hrkg+Q1/uHYYbVitlsRr+bNbBJGIYYE3inALpLDI31htxDGFw35Muv\nwcE77eO0v1O3II4Xtr1oUljlVK3r7zpDLsV8Ypp/tuhQhuHqfi2ffxX8ee38KwpxbNI+j0d+BPwV\nbxBC4H+11v51IcRvA/+HEOI/Bj4B/vQLj2QMqihfuNtyW/Wjb2rI2ypj6+pn1l95kVe+bnAuvl+J\nMK1tN/V/WZfC2tUFbesHtfbM22XtmmtQJe06pwbZcKaFaErmIISgUmBthcCg/cRbGeuMkwhJQpfR\nCdDt9IjTjDBICWOX4RnF7rOzk7Om3mMYRySZexAiGWLjFIEklDN6e05hsZhNmE3HCAm9Xo84lE2W\n6PbeHnlV0tva4vHjx2zv7ANQlopZUVEqw9jIxhsy1mGak6LECkk3dIYpSDpkQQzaMCkUmGKuWFiV\nVKVTgyxKp5kOkEQxaTYgEGCNYuSphMV0RhR1MFI4DfMgIvEJQZU25GVBNa1Iw5TPPvsMgI8ePcbI\niPv3H3D/rbdI/X0cT3NXF9NKrBCNKJiVEuM4htS8ifZY01r7gt9mcWWVCpQqicNgLv4VBC7GIAVh\nGHKwt9sk+xjjJjulFNYY0niRtrfqdft/EwXXtq96TlYZ3+X34gbIZNW4v6lfyyuAxiNegnjWacAs\n9JHFSWhVn5b7tQ5aEfrVTPIrG3Jr7YfAT63Yfgb84qse93V73V631+11e7n2pcjstLw6q2N51luF\nta/atx21htVY+fIkvA6K2cQ7kS+5ZHrRiuImeKluSqkmiNX2wq21jYdutWZe7dwlj1gBiLrgRF24\nN3D7WQlWY1RdTcidQwbufJFqpTErS2UqKg1FaQhC5+Vpa6mUQaOccmIdjAsgL0uKomCnHzAauQLE\n0/GQOAoIgpDR1RUYRRzPYaOdnV3eeustTk7P6Q5cZfgwTgnjhPF4TNrvzSvcy5BwVmCtxiAbLfSt\nrS2m06lnyIxRZT6X2rEapUp0VfHJ8wsSX1nn6PCQN+7dpdtJubq6ZDhxTJrxcOzudyAJooROp0vq\nVx02CNFoCq2ZXg756NPH7jt5ybvvvst7734NGUbMpr4gddpjOJ4iArfqEX7cChlSa7EaA+3RbK3F\nmroWa52x6sdEGDGZTDBJ3HjkNRc9kAFpmhKGkuFwCDj8PAxCTKUwxpKE84pRC+dbsxLVrZXvTdCK\nUtehyuX3gtXe/fJ37Ap2yLV+rXh+jTEL3wWQN3jiTVtiwKzrW60q6v5WB1tleJ2Rtkn7UhhyV+h2\nNbbcbuFSAsImxgxWQyf10nEZO178f5Fmv+4cy0HYVVCM2jAavWkafjvBpx10arcFGuG6c0jZzFga\nsMY4Y45FiLksbRQF6KqiUsppaPhbk4QBYRqiA+jF2VzmNI6dSJCQKGMoyhlKOyZG1uvR6XRJOhmz\n2Yypl8Td3d/h4OCA8XhMIGY8feaMnLRQ5FPyKdw+OOAH73+PoyPHar0aDpvqQ7/4x/8NSn+flbF8\n+tlj9vb2UPnY6a3gjEGaZVyWBXv7h5ycOqlc6QOsusiZDq/odbNGuGp0NUGrwpVlCyOStOevo0+u\nNGoypdPrsX/ocO3L4Zinj58QxwkP334LGScN22SaF1hCHj35mPz5IwePAH/0X/9jvPHGQ54fn6BU\nifVG6/ziijBOEVaiEQg9NzBCGoQIEMIyGo8IPeyRxBlhFLkgtLYNw0drDRns7u5S5jOGFy6wGvoA\nqCoLut0uMsjodF0MYjKZOC0c4SdCb2fCKFxprJb/l/a6wXRG085ZYNYuwD+LaWrtofpifRSgldm5\nenKw1mKC1f1a3r8uqH1jE4uQTxvqXHnuBcEys5BctK7Axoval8OQi6UAnF2ssl23Nl61FpMzm3n2\n64J/9XtYUa1jTdsI39vQQK/SUn7RPutWJ+vO3X4vhWgCLNK6CvGCee3AuhwYRjsBLVMhjGmYJgKD\nNApjKibjqvESgyAkjFPiqEOSdul1s3mFoCQlzlIskquyZDp1NSnjYUi322V7e5vnT8/Y9oHLb3/7\nd+j3Ogx6XU7Pz9jf328yN7e2trBW0N92lWvqzE4hA+Ksg0aQCIX1/PbRZMJnj8acX46JAkHmsesk\nFFhrKEZXTIbn3D38CvnUeaVWTakmE+Ik5ODgFl2fjbm9tUsnS9CqpNKmmURA8ODBG8gwYLC9izE0\n/PqyUFRGE0UxJs3obznd753dA4yVlAqskJ5WCFHSQRsQ/l9tnKytI5kWi6sKVFcoms1m6OkEK6QL\nMnsDn6YpxhiqqkLrVmZnIBpD4ibguRFSSjXPXXvctZ+dm52o1mfWgrVYYxCyhQuLzTITgzrI2Nq2\nfGZrLaFYYQzbk4YQjWhV/d7W/1r7O8P6YkOul+yW8Uyi+lB26RbQ+h3xMgouNcU2Jehetn05DDlA\nK1W7DtwsBnBoeL3rlmduttvMkNdCTY1RW2XMN7yp9TmvDarWaxlstmQy1YsN+YtWAC/TRBgQtIOd\nXjdGWv9w11okusTqwgVHWwR7aQ1WlaAqoiih9Gntw8mEsjhHWQjClCjpNMqI+wdHBHFMWVWUWjVp\n6kkSgzFEUYhRZeN1X5zfIYsjEBajFYf7R8i6nmbgijRs9bYYTaZ0ew5aKZSm0+1SFBVyNmyU6GZX\nE55++hmzQnE52GJ7x9EYy9GILMuoZlOk0gyymPOnTiLo6uQYhGK3d0jZ65Flzlutx9BsNmM6GnJ5\n5epcTiYT3nvvPYIopNvpM57llFWLORLH7O7uUlEw6LsJqNvtklcuACvDmMpDVCKMMIVyRtziV0lz\no1FPqLPZrFmWR2FCmqRY4bj8tYc6m83Y6g/cpGJ0w0yJAtEY6SzLIABRSy0gMUhEkFNV1aIT0bZU\ny1ar9siZOzltmG9VMPBFrUkIbBnh9uv6s2DB2148xtxOL8Kn9SUsG91NDPk8IchLJbQSrNrbm/NI\n2Qi2OYVk0TCkxIpCHJu0L4chF+KaoVu1zJHBzRiZAESw2Y2oB/0qr7z5f0MFg/om3ohrb6htHm7Q\n/cBscL5WuxFaEYvvA2Sz3LPWgpdZtarCVgWmqhBWzRV+rYGqhKog6Q0aLy8IAnRHIIKIrDMg6w6a\nwsxPnj0nSjLy0lH66iSusiwYT4YcVof0er3G0Hz961+nmE4o8hlaO29y99AxWq6urgik0yYJS9V4\nNEEYEIYxw3FOgsF4Y1bMJkzHI5SGi7NTMt+nQEjiMKKTpCT7exTTCc+eOGjn5PlT7t45RPrycbXH\nZ3ECY5PJiJOTZ4yHDtNXXqkw9vU9w1A2ao1pFiNF6HDpTBJ4z7soKqZ56bISZUjuMXKtLKKdyVu7\nksJiW0KpYRhSecZWPhuhjMYKSRynxGnS7KO1pqoKQincxIkz5KoswBjSNIVgHkOq+eJB4OilbTbL\nupXxwjNZa62I2sg5j9Wh9/O2Ge3u+vO46hmQQtz4ed3/Vf1etjvt5KK1vVLXGSjuWpfRgtZ+cs15\nX25ua9qXwpAL4WhPLzJMqxKCrg2kjTXEFw34SmhlRSr8qrb8Y6+6jjpR6UUtWlFNfLktZ5xuEitY\nZ8wrMzcUzf2ts2x9UWGAqiwwVYFVuYNZmsFrsKpAKsVweNkqvqypFGgL8nLY1KoElxC0d3CIAc4u\nzrkaOwM4no6I4n16vQ6mMhSFS1gxWiOBfr/P5eU5ZVkyneS+jy5Aq5QiiqKGlpikHUplqLRiZ3eL\ni0uHB6uyQlqJUZrpaNrABlEQE4cJg8GAAHj6+FOGFw5amU2mJEnCeDQk3TLN4jGoc6aMYjIaUXn1\nw8GgR5lP6WYZRilCCVFYB3QjtLakcUgyGJDPvJRsWbpJjYCyKMhnbuKJsw7WmEZ6ovbIsSxk5Xa7\ng8aQV5FuDHkUJY0hj6KIYpY73rgMm3ErhU8gsj51PQrmYLgMFv/8/VVKrcSBl59Jaa4buUbkq23w\nN1hVtvS3WuP8esFkIa7HjJbf66VjrYNqw02Cj0sJSMvGeY6br7impfMZ+2rQyutSb6/b6/a6vW4/\n4u3L4ZFzXUeh/X/d2sVe1y2FNl2baK03CHZu5pEvB0VXegMbJnZuEmBdxtHWeeQ3BVvr90apBcF8\nACN8hXVlmxWOVgWoHFsVWKNaS0OFqAqsUlSyaLRLkiQi67iMThkmyCDBes9/OhvTzXsknYwkjQjz\nWu8EptMxn3zyEVu9pKEYnp6est3vEUjB8fExd2/fWVj6z4qSSiuMCChLH3AMNGHqWB3a6Cb7ToYR\nu7t7jCYFaZohmszDkDTtUVWaYjbi5OSM0FPtkszpmlxeXbCzN2200KsyJBCWfDrl6uKsWckc7G0j\nsYRSYHWFFAGRh/xkKCnyKdoYYubshSiSBAHkhSLP52XPkiShKhXCWqw1DQtEWA1mHjIrioIgcver\n2+26Z8Vj5MrU0FXZjPswDOcUXOO8a+mDfcaKJtgaRJLY4+ROjtd/hRKj1EI8yw8IF9D026Qo25uv\n/fnRuJlH3vZoRXsVvmQngmD1M9hq7QLaN3nkwQY2wIaLwdUaH18+Vptive569brSQS9oXwpD7iIU\nLw52+tCue+1HQn3Z8/03hVbq/z9/sNMuRe5XBT3FhvxQswYaabdwDT1reYm6UTBJyoabHNZqeBYC\nKTFCNHUHja4QSoFyHOxmnWg1VhcIVRJ250GcsiypqhmVglJZlLYor6T4sz//8/T7XXpb2+zs7XJw\n68CdwxhG4zHHx8eMryz9nguCCiGYTqcInLKdlJIk8RmZQcBockwgQ6pKNdDUbDZja2eXKCq5ujoj\nil2AUhDQ6Q0o1IStnQOyTs1yiVCe7345nBLFGYPtXd8vTV5UBEGE0RXUcgtGYaxFlTnj4agpjhIG\ngjSJiELJdFYgQzMvkRYFTK3BCsf1pqn/KcHXukzTFBnMMyjDMPRVhswcXzC24Thbq6mMofR1VMdq\n6hgsMlhgrdQGLgyDhjsO8xJk1rpMRtvKOaiNfhRFxHG8wGBZxpnr123DKNuVpG6AHjZxYGwwf7bt\nwrO/uF8QOlbIYr+WDrbwnCyalfb/azT/FlrUokXO8fFFHZp2f5ftzAIt+kfakLOeC92+yHUDZ9Xr\nF7Ubg5xrUvbXtfbsu6ofbqBudqxNEqPMistctYpZRRdbfi9lOI/8C0EgXNFhKV39xmZ/YzFWgTFI\nq2h0h61GeGpiEyB1J3BKgnFAN4gdRu6pfh988D47u3sc3r5FlMQob8wGgwHbO1tMZxNOnj7is08/\nAeDdd9/l+ckpD+7f48033+TZk6eNN3nr1q1GnW88y+n1XYLP1eiMKIoIwhBTCmJvyAulKCvLaDLj\n9r0OW57+l3V6TKY5s1nOZJoz2N4ln7lzXF6dM5sVbG8P6He6dHu+gETWQWJJ44QgEAT+N+52u41h\nLsucyCaEvjpSEsXESYggQJTzeozWS/hGMqAz2GbqsfPL0Zg0yRq5gNrCuDqhbjAIhBO28ga7182c\n8fY88qLFI7ceB28nxDXj1/rU/hY1sR3sDIJgYfV20/OxTEt80bO00bO2Yp9V+PqL9JBgUVK2jdmv\nisO9uFu26V57tWHM9e3LlyFE/ec2huI6MrFJ+1IYcgMUy52uf4z2Zhl4+1HP9kvLqpeYzJYHmhvI\n9Wv8gN/MI5dCvvDcdoWqWfsrtV2UjQu8OogkACf/3jq2tX6pKRYOalwZYb+6oGEGCGrlQUEUJM1i\nKESDLrFlDuNLzPAc5bnUYjIktgqsK6prPORiwN23MCZM5/UZVWXR2jKe5lxdHtPvb/HOuz8GwNHR\nEY+fPWZy9YwoCtnZc17x8WeP6HY73DvIiCYhZ56KqS4+YzeNSciZDivSwRZjX/brlD7h3R/nXIaY\n7QGFv8+dXomaXaJHZ+SBBM+2CDodvvs7v8uD+w+59/aDRqf8eHhK1u2g04Dtu0ccP3/KU89V7x3c\nojfoESQJ8e2HzLwWu84Nt7Z7JHGHfneH0xNPP5yG9PbuMJU9xPYtwl6HqytHZcwrgQ47RJHgTBvE\nlvP6KyERnS6BteRaIWL3o2zt9JiMxm7CxVJ645/PHPwSe095Mh6TUcsEl+jxjDCM6XZSup72WVGQ\ndTsIoRE2R3vvWoaKtKcx1omxaW0Qvp6dFK7MXRRbMgKEr8GZpILRqGr049s5HnWVpyAIqKZdlttN\nTseNkEgwn/jaLOxlpzmQc2ilngAXOOLgOfnz7deg2vp5XLEqX/aobbAaWl2+lk2yzuMgvrbPJu1L\nYcj/WbW2MX9ZD+KH3VYlWog2tPQKLagHr/T8WyuQwjZJP8YarHYa20ZV11Yaq/rQhsCKouCtt94C\nQFWGjz56RK/X4b13f4wkyRhP3NL/gw8+IIgDRhdXHB0d8uGHHwOwt7/F06fO2xZ5xf6+E8A62Ntl\nOBy6h10GvnCwyxLdshZhPXMosOh80vRL+pWF1iVTz7YYjUa88cYbvPnGQ66urhh7ml9RVLy3Txrn\n6QAAIABJREFU/x4SwZMnn7kixL4+pVKKwWBAp9MhDATWOCNXTnMePX6CtoatrS1qpch+fwtXLs8C\nAqsNywsyIbyHy5KHayyGxXEZRRGj0QT0vE9pKhmPx5S4FUAYhi4DE3cv3LaIsiwb7zpNE7/yrTMJ\n6/wHBViEfPG4b3vkNVTTjjc1Y6QeGyu84npsrzrX8v7rjrXwnVXb1jw/K8fzmrZJjGllf5aur33d\ny8e9drxXfLxfs1Zet9ftdXvdfsTbv9AeOayepf9ZtnX9ucmLWdekEE01o8WkH4HLElxc1hlVYcrC\nByrnXjl4qVMPPwn3peZ41jpoSSL4/ne/Bzge91e+8hV2tvc4Pjvn+PiY/paDUPb2dyiqijgJmc1m\nDAZuu9aa3d09qqrkYnSCnDk/o6o03W6fvd0DzodjjNLs7e8t9D2KAiIRMBxf+WNVSOuW3UVVUk3d\nsrYsS95+512ODm/z7d/7DpOJW64PtreRUpJlCdPZGClhd9vh55PJmK2tLTqdDiqMGkz/ajLh4vgp\nt3Z2ODy63Wiw9Le3qIx1iU5SNsJi7ibbJrAfBWHDjGp75FrreUatMQwGA4wBXVZNKTthZRNXCn1p\ns+s4sPtt2kWWg0BitKZSpil2IoxGBpYAQRBeZ5C0Pcq29G3Y6K/rBe2QdrsGQ6x51jYZ1+KGgOiC\nEkDrvW2S+272sNced028bDGp7vr9Wl7tr/1u6zufp/1zZ8hf5ge6aan3RRv3lcvIda89fLFpf9Zl\n9Qrh1TlcEH8pyOIe2MCqJsBqVElVzCjyGVUxcyXA/MOeRCES6XVVDNbMl4n1w9vr9ZpjzWYFTz77\nlMl4hpQhSRIReqM1HA7J8ymHt28Rx1vs+yzNjz/+kMlkwng85mD/YB6jEAGlKpv7kec5sYdKoq4l\nCAVREBKHoJQP7KkSVZUYVZLnBTNfMzPt9hj0txFCcH5+zuWliwG88cYblLmrYB8HIVpXZF0X1Myy\nlDiOHSMmEOTe+I9GI6dZEiUcbu02Jb+SJKGY5FhVEcQJ1syLZFirkCLASumZI3OoQiKw0hcgEHND\nLhFsb29T+mQe9wVBr9ejLEsmkwnKGjp9N5Ek4bxmZb/fJ/ZMHqVKwjBE2QoQTa1UYzWRcMZZECxM\n/O1xV8MpdYvjmDrtfp1G0Fo4ZMmot4OPq/YRQizo5i/X+F2UdLHN89M4KXg8vb6u1vVZWPij/r/l\nCLVP136/7CTdCAGtgZkW2iuanX/uDPnLtGX87cuAkbcnlVV4noDruavNbnO1woXviMXs1XmkHAQW\nYXyRiCKnmE0p8ylVkaOrAnyAppt2CFCgPfVMzw0NeIw8n7KzvefPLHny+Cnn55fs7h0Qx2mD4RZV\nSZZlnJ6e8PDhQ54+dbW6syzj7OwMZRVKW46OHC0xAL773e9iCOht7zAYbDe6O1JKEk//koimYLJV\nmsloSD6bcDWaNBowd+7caQxPr9vls0cuDT8QUBUlxiiyLOPx41O0vy93795xAb8oolLzws+qKNk/\nOCLp9uhtb2OfPXPbvYeqtXZVO7VpihlrYwkCV9s0COw1jNxa5xnroPXb+8C3pl2AwYlfTadT8umM\n7mDb6aTg4wXaMXmcLK3nhAeCIJBYYgJdzil/NvTB+OtqmW0vXwixwGZpG/Llkmj1XzsX4ybM+6ZY\n1XyFsUjhXVWwXVgfVJRudbNwDubBz7anXfd11WS0Cvtffr3ska9rP0yb8i+0Ia/bl9UjX/7evE/L\nS0zL3Ly3KYfuT/rjL0T6/V9gNaquqlTllEVONRtTFTm2KhFeWkDWySv+odWNIXcsB2stqig5ef4c\ncJrj+3u7VErz+LNHIAJu3b0HwPbWFnGSkFclH330EdILzBwcHHDn3l2m0ylVoZn4QGQSh1TGcHFx\nQV5Zsq3dBlqRUhJnGWVZoqxoxLQqXXF1MaacjhlNpg39sNffwlpI0w63b9/m9779HQCeP3/O1tYW\nVeGYOZcXZ0w8THO4v08gJXEUcXJyyaOPPwScHOytWz45KYyIU8fQmJUlxiqMLpA4Aayay11VTgIW\nIZCohj1RT7TSurJ69ewshCDrZJTlsAliAqhCcXp6itaabr/H9s5Wo4MipaTT67kybUo3RjbNumjv\nlesoac6hTeHGjcRLXNUjxo0WN+wEQsw1WKS0jiWFRClDENQ69G2DKK8Zv3XPVZt+vC5IKFZZblZ4\n59qfxxvzdqtzPoIVK4DlGqRtm7DWiLsNK/u13F4b8pdoL4t9fZlZK7AC11s7wUhALywxnQc/fwjq\nSxKiLkRgXc6e9zy1qtDFlKosvDdeIj2zoSgKsBqrHBRTU6lqfNQYQ9Y9IMlqHesZ5yenGAH9fpfB\nYJvd3R0ALoZXlKpgsL3L1WjIvQNn4Cut6PV6XF4OuXf7HpeXjs6nlFMRVErx6aePGcxKuluHAKQy\nIEtipuMRQtqmwIJQiovLU2yRM6ng4OgOAJ1Ol5oJkkZxozl+dvIc9eA+1lqmoyHSwszrpJ+cnHB0\n64Cqqrg8O+bjD94H4M0Hv0jW6WJFQKk1e4dH/tpHzhAYjUAjTIVsaVYLEbhSesY2bBZhriv5tVsc\nx8Rx3HjdeVSS5TPCJHaZnOFco0fKsPG2lTW1dUYphQwkARFxrBuVQK0k2lSOaWP0SudheVXX/ryq\nqpaBX6xLuSm08jIY+ao928bcsXC9p13vbBcdts+DkV+7Byv2X+UYbvLZq7bXrJXX7XV73V63H/H2\nz51H/rLtR4W10v78pQIiwhAgEFa0FsvGLe2FcJVxvFSt0CXosuGRC+9RAlRl7oKcKzzyynvks5NT\nQi+NWhQFReXwZoF1leW1w7UHgx7IgPPzU3Z3d5l4z/fw1hHGGO7evU8+LZjMHLRSVQHT3Acr05Q0\n6TDz6eiDfYijCKM1WhuChq5gKCYTUAUVKXsHzoOP0w74LMrxeExUF0UuSqaTEVEUMR1P6HU7XA7d\nSuXy/BRrLZPJhNnlJSfPHKbf6/XQWKIoZlJM2d53mP5oMkF4vZrAukISNYdfWAvCFbgWej3HuP3/\n+fk5SZIRx7FbGQFFUZIkSYNTV1XVrIaEEM1+Ne8cnE56f9BFBJJQxA1uLySgBFqVTgXxBudwGVuu\nufqbBvg2YXO8iHfdBBpb2+rM9ibh2KNTzTHkUtJf8zCIJsppjb0W7KxvRh30XDh/fS/afdtghX9T\nHOBV2ysbciHEu8D/3tr0FvDfAtvAnwdO/Pa/YK39ay841rUams2FtTAut4RvDXSzvlJ1+9iLgb4V\nWPUNn63q0yYZW8stfIH4Tn3Ihka2jPu1Bk3NdFiFui9E73WFRPr08VbxCOPkaY12ErTVzFXoKWdj\nitmUajZ20rRYvDwK4/GYXpZBEDCdTpl41oiUkjCcL+Urb3CNUkSBq4m5t7eHFQEXF6eul2GIRRLG\nqaP57ToDmKUdpJSugk6YkufO8I+GFyRx1sA4baz44uwcZQQ7gwH55IpzL4krtKKYjNkdZNzavUsS\nO0giSTJ0WTEej9nZ2ub0xGH6+9tbxEHA0cEBf+/v/B0XWPQT3OHhPpPhiMHONifPnrDvqxFZbZxe\neCTpDrapfIWg4XhEMR7y9ht3sKZEVwVGu/Pv7u4yyhWTWUlPzlWv2ho7UkqyxBngeTq9RFvTGKAk\nTYmTpBmL5+fnzRiJoogwjjDGoJRp9Gc6/R5hEGGsQltLvSC3pmZvSIQMyadFc6zaUAeBdNBGI7Pq\nHIEwgCS2DYtJEFAUhaOvaoMWL5acgNVwUntbzURpN9M8K4v7tY33NamUQFwLbLahoOW2iR75y0JE\ny9fVtiubnG9Ve2VDbq39HvANAOEErR8DfwX4j4D/yVr7P3yOYzf/L892N92mLwJruqk/y69/GO1F\nx7fWtrwEP/sv7yTmQkxSWI8X6sZbEcaC0S6Ts5iiS6/trQqELl3AUDgmR5O+H4ZUVdV4YW0OMSIg\nyzKsjOd84iggCGOyJCYIBCIUDKQzvsYKtBAEntJXq/ZFUYQII6QxTMZFI3QVJx20KknThEGSEiYJ\nF+cOP3/jK++iDfS6XR5//ANSL072ybPP6KQRnSzlzjtfa5QMy0qTZSmdLOHq9Ly5Zd1Oxu7ODh+8\n/32GVxcMtreYeb2Tg739psrO+PyE0N//OHQKg1pKhJBNya8gctorZTFD6pAQiII5I8SKwAUWtUZ7\nemedHRlFkRMGa9EPF37axkudv7fW0tsaYD1jpy41lqYpgYyw/hhV5eqSCuuC03W9UCGCVj1MSRiu\nVwat+7PsHC0b/horf1kselVrPPmmJOGSwW7dECEERtimmpBp6W6se45XvV7ntH2edhMjrb3Pqn69\nqH1R0MovAh9Yaz95NUO62U1ub1tl5F/qjK/wA32eH/fFBvrm7zRLtoU9WpEc5t5HE/gRvhyYNWDn\nJemUUk2lHTO+apbhZT5zXrzVCGEJA0FUR/elJM9zFzBrGXKLo+Vl3T5lYVH+AQqCkDRLiEOJUZWr\nj5k5zQ8RhOSlotCa8XjciOlXpSHr9gnDkMHWTgMLGGM4OX5CpEN2dg8Y7B6gvDc5GY6QUczx0yfE\nUnJyeuzugYDAGu4cHqDTrKkaE8UpWFzS0cUFfZ9gs7s14JMPP+DJ08+4ODthb2+vMd5FUVAUBR+9\n/xGnz5/T33UwTRRFGCTYAIsrjgwQd1LULCSfTrChoNPtk/givs7YS2QgMbmi8CuYPM8dQ6XX9RPw\nPMHGPVNL0IuvCVlP7FmcteAuB6eFoaM5qgV1Q4O1xhvzGo8QSBHO5V/NasO27LWGYejGV2s81FWI\nGoO/4aOyqujwMpusXgy4z0VjrP3O9YdNkLP9uRU1/ZDFICgeWbGuZmf9SNXfNBvgmPJG93KxraMV\nLwdhX9Yp/aIM+b8P/G+t9/+ZEOI/AL4J/BfW2osbv22vG7rm/brtcG1gvUz7vMb4n5Znvsl53LD2\nTZhmFDrjZdwDb3STLKPKqtGm1qPLhramihlWlQirCSSEQjQeudbGYeuAsnPZ0TSNSTKn9VFMc0wj\nxBQihcVqRV5oCCwdX6lmNBmRdgbsHe3SH+wSRs5g55ViPJoxnU5Jun0GHj7Z3d0nCiVaa4e5C+Ek\nYH2LoojR5ZgwDBleuKE2uzjH5iNGR3vMLq/YGTg4RCnN5dUFIW6iun3rFuCM9bd/95/wzjvvkGUZ\nSRIx6LkEm8ePH7Ozt8sHH3yPfHzF7XsPALdiURYqa7FGYr2lidMORSCYzUaIKKDf7xN6hoibtAyI\nEGtMM4lOJpOGq27SdHFV2jLkjX/exn+F229eh9bdqyqv0K1EqiAIvLE3CDFPr5EidHLGtYqfXRx/\ni5XeabbXRYODAGpEIIqspyACKIINZaXbbZ0tMI3KoDeGgUCa605g2/AvUxOdsRYbm95Nnr+bMk7X\nfucFnvfLOsSfm7UihIiBPwX8n37TX8bh5d8AngL/45rv/ZIQ4ptCiG9e+lqHr9vr9rq9bq/by7cv\nwiP/N4FvWWufA9T/Awgh/hfg/171JWvtrwC/AvDOV9+y62ZhwaJ30H6/av9N25fVI1913cufGSlW\nZrWtOpYwBmMNSpVUhfPI82KKKkqUUqjJuEkYUWWBUSVOY1wgvFYHOAw3iiIsmkKppvBBp9MhSlK0\n1khEk4oua1gncEExtwTHH6sCTJPy3eh3yIgo0qRZl35/m66HYtIkZG9vB2uUw3LDCO11m5WRqKqk\n20l59MEndDzP+tF3j7l/OHB8eBFQ+Cr2x2enqOmMnX6HnZ0dJrsusejs9Jhep8vtW4e8cf8es8mE\nni9sMR1PMEqztbVFP0sZ9DzWbwzaBxRtPK8mEyWxU11UJUaEhK1lvrYax3avWSws/A8rEly8R25o\nrbwQc2aG6w00LHrnpWq7IlvRztdvNdMjQHgpZuepi1b93OXvL79fLgix6L1b5Es65GtX5rBwYxqb\nIOyCV94mTrS/W++z7vjrAp5fZMxtnRd+Y7LRhu2LMOR/lhasIoS4ba196t/+O8C3NznIemjlhmDE\n5zCm/7QN+cti5DdCK1ZihGmNa/9EN82XZ9OVKwihFVVRkBc+RX46I8+nLpEjn83T7HXljKW1IF1B\nmhpOwWqCMCZCooHIL+PjtIMQrtxaHLcobUIQ1sG7OG5oieACkxa4uLjg8mpCnDiD2elts71zQK/X\nRxEwmzg2zXA4Jg4kUSixlC6o50u3WRxj5uz4hHKWMxm6bMxumtDv9hj0e1yG83MXeUU3TSlnObPJ\npOlvGif8xHvvUuUFg36ff/DN3+b23fuuX4MtTk5OuH//PurJPbYGfcAxdHRsyUtFGLoyboAPrLr7\nlkQBgRRUlYNQKpFgTEClLXGr0lENCbh7uFihx+G5i3CAXYIH4iSm8pOVKkqsdZCTDQWm8kWZK00Y\nykZ/p7YZ7v96vIlrRV5WGZ1lw1lvrw15bczFBhjzclt3btOuImZahZy9MW8+i6LmgWr6aRbZIe1C\nPG0D/ipxMKFf/ho3Meov0z6XIRdCdIE/Dvxya/N/L4T4Bm5kfLz02Y1tpTG3i++XL/OH7SXf6CH8\nENrqoObm5257c1prMBpdKado6ANrs9mMfOYMeUfN60Nao0BrXyzCgtVYWRunEOMfnE6nMy+dJgSl\ncrzyRIQLD3RRFERpQhQHiAAKz44RMiBJI9LuNnHSJQh92bbIYe3WWoQU8yrvJCSBBKuZTKeMZyWF\nX0Vsbe/T7/c5PT3FGsXJiWO9plHEaHTF1UWfs+4Fe17JsCxLuknMkydPqKYjMh+EPDw8ZGtri88+\n+9RdU15w5jVVtvb2EcIFAt95+22q0HnkeZ4jOooSjTCWzE8Yhf+twjDwYmE0gdNSlNggQWtLFISI\nzOPqng8extG1SjzKaKxd8tyYB8gMNZ/b/Y7OIxUEMgIkpqarCsdGcZNz/eewZ2ktWIFFI5bIB3Vf\n6sAmzLHzZXpvGIZNPdAgCOAlMfIFjHsp4LfwWooFA1xX4LLWevGv6zG0tjGvDflNHvmmMTirX0w/\nrvvfTD43BDxfpX0uQ26tnQB7S9v+3Csea+37TYzpP0to5YdBeVw+x/UPfdBsRat7M9dGmVdyAaiq\nuVRtZq0z4PX5rMWZBoFpDfw0TZnlJRZJN00bQ56XqqElllWJ9QlERVUhKkGYhHR6GRrLZOqSeHZ2\n9xzX2VMFa0ErW02plCGOCy5GU8rc16AcXjI8P2U4vEQpRZh0CD2j5fDoLp1OhzzPOXvymF7feffD\n56fc3jlgPB5zfn5O7CmOlydn2Krk+PiYrU5C6vVRojBgOBzS6/UYTsbcu3ePoe9vlmXcu3ePZ8fP\n+catWzwfeYiqLAmtSy6KrW0KT9f3MhCyqY2pfFFoHWqsdEbQScH61PoFIzX3yKWUUKfN2+sp5+6X\nEu6++PuZJF2MMlSl84qlv/Z+2vG1T2sjVfPINdZTVB1kszr4tmyA6pVc24NvJwiJttv/graJIVvw\nYv11N31pqoaJlYbcWieHMO//dZvyqoZcbVpZfU1buPZX9BO/HJmd1jSluOomWz9a+/WCHKucR/Pr\nFgThtcFmrHFZW63tNdVq+Q/mP2Dc0q9oTr+GO9tcyroJyJrryzvrKqOzcG49Zw204JOF44bOiC0V\nfPNlr0zDFEiDiKoqKUZDistz8pHjTZvZjEgXxNYi41aikhDYIAACjBCo9n0MO2jpdaiTLoH3ltU0\nZzoeUVUVR1+5P6edae20taXhKr8ijRMGHe95G8Xk7BiT5ygtCLwnGyQZo7ykv7VFcPoBTz94BMDx\n8yuePr3g+PkFRkvvpbrx8vzsCf/aH/0j/MGf+xlmTJG+X6MyROy+zel0Rm/ylNEHT9xvZS2Pn8/I\nS0Wvs4/2+08Q7B7c5smz57z/7IIq7rG/dxeA/u4tgrhLEHYYo5GJGxcXZ+fc3r7P7Z0dZrOgWVk8\nf5pzMY7ohF224x102EH48nDbdkygKg4FDFXaGOYgcBBK0u3Q6feY+YSryWxKEKYIERAgkd6VNEqj\nSoVWBqs0omvRnkcufAKADUO0hdyvXiYqJ+kmGKuxRiE8HVWaWmxMIBHMZiuS6uT14uRSOklj3R7n\nUYi0AUKB0YJAb+aRO0O2qL54LZHPXH8eV0Eh1roMCyHb2cz+eP69XOMELbfa+bnJmZRis/Js1ZKN\nW9WK2erzvah9OQw515dRy0uszY8zl9P0W3DBH7Nk4K8vqRbPYxvvctETaOGErT1Z8ZqWByANXJ8s\nFo2461grTdha2h/Nv7u6/qfFGapm+WidhOq1JeYar2ehbyze9zzPiaKIxGcT1mn1s9kMIQRJknD8\n7IQ0dkMqTVPS2JcWKw3DyRClXL/zUjEYbIGNuJrkRL4w8fZuxOXFkB988DHi6hNOTj2VcKoZjWeM\nZiWXFyO6/R79bVeM4u13fpzf+/4H/Nrf/nX+xJ/8YxwdOeGq+w/epKgU/a0dRtOLBot+/PhxoyEu\nhGhS/W/fuctkMsFaV8V+Op02dL7BYNBQA0/OjpGJw8ijOKUsS0SeY6OUykNHSRjQ62T045her8dk\nMkb7+qPjsiCQGafn5+zuP2DqVx0ykmTdDkoNOTs7I/aB3t29fb+PdYku9Q8SuDiGFQYtDVE7DCpc\n+bt6og9quMu2qIwrE31Mswp70SpzFTSwavsPG4rctL3qqnkjJy24OWu7bus029stDJft12bttWjW\n6/a6vW6v2494+3J45CvggzYe9zKe+bL3WdOgVm1vf2fdsZZxwZv6dZM3sqARg/OqrWl7yzU7xH+O\nS6m3C8daU04Lv1Kwxi+QHWanvLiV1pp5MeD5dTRw65KnYYxpvLn6szzP2dnZIcsyJrOCqyvHDinL\nskkr3+53Gy+2m3XIsow4CsBKz2Jwxzw7v8DYAFVBQESRu3M8e3rC2fmQ0WhENbrg6bELXE7GirwI\n6Ozs8uRiyvOnp1SPXRGHJBV0ugnv/cRP8Bt/7+/z1a9+FYCvf+0n2N4/JAhjLi8vXXFkHFMmyzK6\nXZdBORy6CkF3792fxw2yjCTrsu0DpL1ej6Io6Ha7jKYWf4lEWYe8UkhVEEcJ+dQdK5aWW/t7dBNN\nEkWoIOR3vvUtAH7/Ox9RVoI06xGbbzX9un3/Nm+89ZCtvV2yLKX0sMf52SlRlriKNq1VpTIGJRSV\nqNBYMiKEbFEaRf0br6ALGgtCYuvxRM02qXxW5/ox/rKe7SZe6BfdNsHZN3V42xpQa5/vL3DRETdm\n4EcYWvki9mlXrKn/N+Y6vLDcln98l9rOtV98Aa5vXvtBvtTH9ntjl/rQnlzMHO221mmEC2ohpUUD\nD2C4jrU1on/MMXKlPFfcp+M35xbGLbeXrrm+V8a4CaHdXyHDJiV7NpstVGyv4w1qUqKnrm/lcMKV\nlAjP97YGrMdAkTFXwyGlvqI0UCjbbFfaMMkrfvcf/UOOjhz97/DePSazgLwKGalPKWSC9JRFFRtG\nxvCt73xAHMKHn7mKP4dH9wjj59y/nxJKwdSLaVk7r7IznU6bB7WuNm+MIcsyBgPTGPIwDBlNpgwG\nA7p7e2hqlk0HLd31h8GcmdLNYrLQIvWMb37zt5lNJnz8mWPk7t2+z9OnF3z46QnpeETfC3AdP3vC\nk88ec3j3Ngd3jrh9z+PznS6TcgrSaY3U4lrG/7NCY6VGiHDORZcW6YuNGOsmeMBnbpp5EHIJyqyL\nUMRt4SbrGDJuUpgH49wxLEL41PbmAwiEbf6qDQ35D4MwsOqZftm2ipO+/H7TPNFlzv2qFtvF32TT\n9qUx5OumyDpaDzTiPzcepjlcC+9dYcjbHsZyxHyTFUDbM1+LnbX7YRaxL9cf3Sg41ni8tMz9pJXH\nNaySDrP+uxYX3AWoSqe8pyvVTGbt/jfp+0uTXh3Aan8nSTtYa8nznNls1myvec95ntNJ40bPpaic\nDECeF8yKnCKv8OQUSgMySlE2RBGwtefUDx++9SazUvPJN79JFMe8+dZDALb37vH8ZManT68QaZco\nC7E+Cnx4e59eN+ajD3+fSZkTF+78/+T3vs2DBw+4vLzk6OiIJ09csLOTJowmzoDnec5bX3kHcFRN\nKZ1aowgi8lLNE5WiGJgym80Isz7Wuoc76+0QRAMnR4Ch4wPHg6zD8PySD3/wu/zjb32TfFbxfR9s\n/e1/9F2upoJOf4efPerz2aefADAtC95+7x2+IX6atJOSeQ2Y4vQ5u4cHCOnKwnnVXawVhIHAxBJj\nQGrjknrq0SAs0joZAVOPa+OMtTvWdS5zzQG3LS9007jV2mdmQ+P5RSLpqwz29Wf71Y+1HEPYxEBv\nul/MnN75Mu1LY8jXwRfr9lnXVnnk9SBtb1/mwLYj5OvOt65fy8vHVYa9pvhhFo2m9Rzk5ljeG59/\n11O82gbXrI5+G79fbcidEa8WEjSgFcEXciFw2r5X2hv0JlgrZQPT1EYPaLzYoii4mi1qh8xmMypl\nQAYEUdJoqsQiRNmQrNPj7ptf4Y23nTHdP7zLDz76mMtJxS/8Sz/PV77yYwCcXilMkHM+usJEEZaQ\nq6lLFlInJ/x7/+q/zV/+lb/Ef/6f/Hm++zu/464lz3n08Ue8/ebbSALw97/b7TIcDpnNZpTlnEM/\nmUxI05RefwDSCVjl5bx0WrfvkoJCmZCkXhK326Xb22E6KbC6pJd6bfP8kve/97v8xt/6NT799FP2\nju7yzte+DsBv/IPvcjYueDI64Q8c9njgJ6ur0ZAnT58y/q0Jo3zKH953q4EgidFVgbCCMAqI6ko8\ngUSE0nvDkmpi556326OpUSm9mTTCoHRJoAXIudjTuvHfHhf1fssO0Crosf23qZH7YUEwnzdrchPY\n9FX6sq7dBOXc1L4UhtyyGvZYHiSbXdjijV+PkeuFwdY2ajUN6vq03ZrV258tGcOVr/XSBIN2RQbq\nftk5Q8aCL+owb6aFda5bmTja4vwe1DKpWlegzbXrcfe3dRktQ97+c/fLNOp67cHWTsnBEwBlAAAg\nAElEQVSezKaUhdunKBUEIVv9Hjt7Bxwc3qa75YzTpNAMZ4qo0+Odr/0UW/tOuGo0KxiWmtNxzqC/\nQ6/rDP/F8IogEHz86COePh8y2D8k9Z/1t3tYYdjb3+FP/sk/wQ9+9x8DMOhn/D9//df46i//MsfH\nxw12X5alY5oIgY0cfg4QJylxHFNVFXmek2Sd5sGb5qUTvgpDCgISPyEpK5FBSBAoAikwlWOg/P3f\n+jv83d/4a7x574hbRwecDXNOvGRuf3sP2U85vZiy/+A2f+pP/7sA3L53l9//7nf4tb/5N/itv///\nkm05fvu7775LWeaEkSCNQxJPfYyjgCh04zfAYmwKXvs7QLgYjJBoMTfkAa7ghA0CokBig5o+uyg/\nu1C02Huf14i+9XbrJoQaXrDWMWbqv+U6A+vaF23IvwhYBW6OpTVOzobQyiZ9EO157yXmitesldft\ndXvdXrcf8fal8MgFS0JBNQa1hEW1pUvXHmuOSwA1JOFYI+3gY13sVggQLq+tSfNdJ0jVZrEsY4er\nXrffSzxMsRDs1ND2ysFph88veH5d7WMtn6O55horr7VTFFYbRAuDB+8tiZrrsgYKWsLIlVJNdZ4o\nihpPpc7qFEIwyueVZdJ+l25vwNbuHvsHR+ztH5D1d913kGRb+wRxB5F0mdWoU5ySbA0oAsk7b71J\nXa/4+PkTyqmhnI0wuuLk+eMml+7tN3+eq/Pn/OW/9D/z+OMfcLjngocffPeUP/D1Iy6eP6Gz3eHg\nwOHwn15ccHVxRpx22N7da/jw/X6/YbFcXo0YbO8gvDDYaDSi1x/QH2xBGhH46j2ToqSrHZaeBAHD\nY6eF/pt/+2/y9ht36HYSPv7kEW+8+5N88v/9PgCX4wljZfjpn/1D/Nd/8T9t7tfVeMR7P/2TXOQT\nfv3Xf53LkWPABHHE6fEzkjCkk4Z0vWaNTkJsGBBKgZEW0TtqMHI3nl2gU8K8AIm1roSfNVgZI+rC\nEsAiFDKXq21457jV26JX6eIsLAgp13Cg/ws2hFbU/Nlt/7+8bZP2Is/3ZbzzTaCVTR3njRCFV4SC\nvhSGHMQ1w/gilsm6tu7GLxvg5SVfG0ZoMjaXAiTLr+tWsxVu2jfwA34uIlTDGMpNKvV+cdgKgNZp\n0zhs3d8TGfjrq5X2/f5m6ZqNUmijGmy7DkQK67RMAiGQoWiuu2a2WGubxKK2IQen291meyiluLq6\ncvothWkgjGIyoW8Mg6NDZrpiWBQcvLVbXyRH9x9yNS2dEfcByjKviAcD9u7eZnR1QbfnE1mqGW/c\ne5OvvnWfk3/4wQKh7ie/9pAHdw6Zjc/Rk0v6ievXOw9Tjp8856MffJ+f+1f+ELnPlLRG+4IVBoxG\n+SSex599ysGtOyRZl2BacH455OHDh/6HdMHc8XRGIQWVcgyYP/jTP0FVVFxNzumnPT54//vuPqqS\n3Z0tqmLK3Xt3uLq64NkzR5ecTqck/QG/9Zu/yXce/1sMBi6x6f3332drsIMKBTNdNTBUHMfcv/uA\nH3zn9/jeo0dse0jp3q1Ddgdddvo9BtsDTmcjksRh91EQOCqicZN4PQ7DwBWAyPOcoszpZi6gmkRB\nM86iKELls4UYSP1b1zBa/bot7tUeQ/WE3+l0ODt1FNL2RFFrybQDkHWFpDau3oZ7hBALWZbLMGD7\nuV+XxNP+7nJJtVU2px1bq/vZft28bwt23WAr2gyY5fM0UPAr2Dz40hjyF8x4L3FxMph7vK0DzP/a\n23xbts31+6Y02mLHrv1AsjUnL++7vL0d1pTWIBAYYRrqmFEaZ2Ts0g/sCySbRU/ZnWaRQVN/pHWF\nUfqaqM/8gREuuFpPXK0HpxFE9QdLkqQpTLAcGKsf8MvxmChy1LwwjrCh5OTinCenp2zvjUi9ZGw6\n2CIaDymtIOz0GQy8ASoVZ5MJ3a0+Jyef8u6PuQDh9z/8lE8+fp80MIT+Hr51zxmhd+4fMuglXCrJ\nKAnY6nhvOa+wYU7ojXBdgziKIrI0YZYXDVYOziOv4wBpmhLGoGvpWV2Sdrpue6frslJxAdJARAz6\n23z0/vf41V/9VQAGvZ6ru5kllJMpnTTi6Mhd+2jyLXrpgCgN+S//m/+KP/Nn/iwAP/MzP8PTx89I\nt/oEWcLQB3O7vQG39nYRVYWsKk48y+X3nj4lDQWDTkaWJvTfe4/+9g4AnW4XESRk3R5pr+fiFcDF\n1RVxnBJ4aQvR0lSZ01e1i8HU7A5jHIfdDYaFFeU13ByabfVf26huUqR5HUvkprYpHr6KmbZ8/Db7\nZl0AePkYq063yqC3n+dlMsZ85x9lQ27twqzWbFv1+gVN+gDOAlLT+mtvq1sdqHnRgFg32y5H5lcG\nbn3wch6EtS6A6YND9XZdlc0xRCuJZ8F4qxIj2ueZK8E5b9ptrcoCXZVePGteh1F6I16jK+2BWZft\nst7jqs+RZdm8FFjr+mvjp5Sit7PTXG8Yhsg4wgqQcUSlSz5+9BEAd958SG98CVEGcdqkOAehZGun\nx7s//lX+7l/9v3jw8D0AHtx/A0uHKMz44IOPuLiEf/kPOiPfDRXVZEoxPKOajlA+5X00GjEbwXA0\nYzK6akqtJVFIkiQUnpHSTsPPK01ZlqRpigzj5hpLpbEiIE47lGVB4jmAxWRMlg7AOKndY+993v3a\nmzx44w20njD8wfdBKB7cd9IBkYAksHR3u8zUiKM7rmzc8dkxX3nnbX7/299hPB6Teu86ryq0gbv3\n3qQbJXzo+/vs0ceo2YThcMzJ8TFJINk/dPDR4a3b9AcexlIKpIOIsiQBKZrfMVga3278GL9yqw2N\nLw3XGKPaQ133RNmFP9GqVdoYRiGcTpJoPau1eqGgSWyyYk62bT877baKMrzOiC6zblYda9VK/sWv\nrx1q5b5t5twqgw4gwlcLW345DDnrPfCXh1deLTrdPte6QdF+v24WX7VsAv8jitZSzcz57caoZiJW\nSiHsfPnaQCtt79zDAfPCsrLxxN0+bntVVeCxbXCsBf+Fhf61+1tPSqGUC5+1dbPbS86qqqg8xTHM\nJJkv7CCEYDadopRi//CIMAp4+sSJYEWdlP7WFr2dQ7SaovyKQQH9TsRP/fi7dB/9HD/4+DMA3njw\nNkd37lBpyc/85NfY39/lD/3CzwJwfvqEyXTE+PKC8XBEntfFMyBMAzr9fUajUQNhhFIgsaRJzGB7\nm36/31x3GApmkxlZt0fS6SK9aFpo5sZvO43peGOapX0sEY8ffcr55RUP33wbgEeffYrmp+n1evR6\nHWYV7G65FcSb93f54NNHEHX5C7/059jp9+o7z/GTZ5w8P0bKgF/4hT/szh3EnF1ccnt/n7sPH9Lz\nRS0ePHjAdHTJ+PKcy6tzLo3i6sIxY6IgpNPpkSQJk/G4oUtu7+4zK0qUnGcau9/UUUqVUiDMAlVV\nSnkNRnmZVsMJbYO7zoje5I2veqbWefGrvO3l5/b6Knx1BnfbSVt3HrGkfbSuX+u88Pb7V2XXvGat\nvG6v2+v2uv2Ity+FR25ZPUu9SjNtbe3WsW46/vXlmd9ed66937XIPY1mhcU2qfiuL3MOuzDVIubt\nve1GndCzSnRZB3Qco2XlcqzMl9QJJaaFk9cXYFQF/jyLPTYY43AV3ZIHqJuUklV3vx1YqoOfeZ43\nWLO0LqUcHBZ9fn5OMRmTTxy+3PVe/bNHH9Pr/f/svWmsZdl13/fb+8x3emPNQ1dVd1dzaJoUBytm\nZIcSqTiWHRgBAkXWFwkxoNhxoHyLbSSGgcAGHATIJwWJDcRwHMiWLdhRIjpWpFiwRNFk2BIlDs1m\nT9Xd1d01vvlOZ9w7H/Zwzr3vvqpXLRpoBbULhffeueeece+11/6v//qvAUEQMIoiepnxfLUMUEnE\nc9cuID/5x/ndb/wuAEF6wJnNM9y8eZNrVy+TJiGzqdF6CaWmmE0YHx1x9+593n3fSAccjWF7PUaF\nI6bjh5SlgR1cNZvRaMSlC+e81klZlgRxap63TbtP3eoiMMUeyqohAwIb8KOuEUJSlw3vvvs+W9sG\nPnlw7xYPHu4yuHaWra0t3nznNnfvGNjl2pWzPNzZ58KV83zi2efo2/JwBwdHvHXrNr/25V/jv/gr\n/yWziWHTbF3ZpqlqpmVNQ0BgVxBrcUCWjxjMt9kscvLZEe/dNdmjk8kR44N9ev0+g16GtucoisIy\nQRa906ZRXq9e06BsHARauG25LN9pPcfloOKq1g1wdtsxb3yFTVj1vZPw7+7fUrZ/r4JclrcvH3fh\nb3Xcm16176me2R91jPyk7MgnNehNsxwIPI5HQZvZ6dqqBy+XcPvHBWS0NnBJN7LvtpeqtL+3LBT3\nudJ1i2tXlTfii9eufAaobiq7XdpD1bQBz8WIvUBZClr3GTVm8nE4fef+/P+lpbTLgnTG3DEIptMp\nVVWRJAmbozVCe7hqnhPLgKTXR5cl+dEBfRskzKc5O+/epsoLtsZjzl00Ven7a5uEccTG1jq9z/5J\nCowhvfXqm3zv+9/g8oXzXNreQqiIudVOOdrfY+f+A3b29tnZnVHax9sfxly8/nHOXrnJ7rvveK2V\nJOuZa93eZnt72zJYbDWlpiEMDYYuhPD4eRAlKC2QUlPPpqjETFa7B3O0TNjY2ODg4IjDPQNtbG6f\n441bb7G2lrC9vcWsmHMwMdj9l37081x/9jk+89nPczbtMT00Qc27r7/JN//N7/LZFz/J9midKLDK\nXFoSJxnTqmRWl8SWlSPTiFr2EFlIL9hgsBt4+Gvv4Igin7O3u8vm2XOkli7Z1CUiiPx7dJMxysQG\niqJA0xA21SL6LSUEAZIQYTmhUsjFRCCHqaOQ9r9GeUN+Eibs2nJ5ObfPwrYlo7r8f7k9Chp1gd5l\nI/4oHH7V30KIY3zlk/bvxphOglnU6ebHY+3DYcj5wWHkrnOuelCPOu4qo36SIV/1e9fIdQ25N9aq\nMOdUi9660oZ+6Io4NE21YMR9tmmHxRJSI7Skwd2rQOMw7RZvl1Ia+pmWKCW8199VuuuyVrreF0sD\nZD6fe7zUpeSDodNVVcVgMLC1C8058smEpqnoj4bURc7e+IjcepkyTth/8ICjw0P2dnaZjo0xW98+\nw3C0ztnzF9DJiM98/scAuHz5Od743itMD3Z57+49iske+3tGHOvB/TvcvTelamBnFwYbTsf7Kmtn\nLpHriDzPvcrhRhSzvr7O9vY2cRz7fhBHEePplCTrG7XDsup4e5KmakiShIGEzFUb2j/k4cEO165/\nhGeffZavvGeCubrK+e7dNynLAz7xiec5e/Ysw3UTfAziIWfP7XL+4ja3v/cykS2q8crv/gGf+fiL\nvPCxT3Jx+yzp0NAPh8MRk2KOlhFKako7YhslqAKAkDgO6QnB1qb5TpIk3Hmwy+7uQ5QWbJ2zGvFZ\nD6W1zfZV3pjpxkzMZZUbPFwcd3ocXvyk43GZCnjSeDyNF73Kxi0b8kcZ5sXPjh/ncUb8RIN+SpLE\nKvrh8k/F8RXyadqHxpB3o9I+JKdXyUM9uh2n5q3uPMeWUku/Az4B6XFsFtfBu4Vn3bV41UEb0OtC\nJU5rhU4VlaZp2S1dL1x170NiZW5thXsA3aD14pJZSonUwhtld19KKVRjYR3ReindZfMyS6AoCp8I\npLX2HnlZlp43rMqKs1dMuv3G2oi9vT2iIKLUUInKB4UOdh6S9AuS/oC6aVcRew93SAdD8smUwZXn\nGdoq9h/7xBmef/Ymr/z+7/L2a9+FakggzURy+dJ57t67hxYxOwcF69vXzb1E2yjRZ/dgSl3XXq1x\nfb1mbWiMddMYGAFglKbc39ljuLZBv9+nqo9o3PO0rKAkSWhmR4xtgeeqqrh/9x5nzl7h3//Tf4aH\n901w9lu//xWyfo9vfetbvPbat/nEJz7OtetGT0bLMVXR8Nabr3Ln29/BgV4/9vnP01vb5srlKyRR\nTM+WoNvf32e4uU4toWoqxrmZkMbzA+o6J0oisiBhM02obJHluq6R0gS3Z7MZ8dhcbxBGJslJmQB7\n01jD0rTMI6UUKpDHDKCbxJ+0dWt8dttJjtQjvXK9uO+qAOqj4ItFj3xx26Mcu+V2zIk7Yfty6z6L\nE+3RKSsXLbcPhyEXIIJ2mXZS80tB21a99LoRIJYelBeqarFiMzsqhDP8QnnDrbWhBAZiCX+zlVfa\nP7sPvUE2pkam8MkRFUIZESzdWIEmNxi0hroBbRkCbkZurFCTBiEWMzuFuQRKZSV23ewtzDkC+7m7\nyLXhGqouKYqaQitqKxfbBAIlInSoCXRnid00BICUEUFjEoVqWyE8kRFVXiOCEF2XTKe2nmV/wNr6\nOmGSkGXr7HTqXJ699ixFUZDv7SF1gLI0uM3tAUopytkMlef0beftnT1LeJRz6xu36d+7w/kLFwA4\nc/4CSdrj+U/+MS595Cbjg0OesRopR3u7XNzfR5Y5e3ffY26ZG/XsFnv37tHTDQ8yzbQxXr9IJf3N\nPipoQEQEiRkCk/mcqtGIKCMvFEHYZzoxz6XXH9LLhszzik0tuf3Om4BZjYSTfQ7fETwz+hQ/9RNf\nAOA/+tKP8OZb7/Dd773CO+++x+5RyM63ZvY8ewyHQ65cucK1L/2MT9IKBj3OXDhLf3ONKNAUlTHY\nadgQFjvouqCcTwlKM4ENLZMkkIpgUvLaPgTC0gyzs4QqYzp5n2CWs2GdCF2MQQgSrUhD4Wl+ha7I\nQhBJYvpis0PrbAoEEq0FdR1644+WhGFEEETEUUroyvUJiSIwzCulKMo2yU4I6VcBaOH7vNaNvZaV\nkRmEXSGEtpKUa974ixbaoWOYlw1m9383yWlZHA7w8YCqqhZXqhyvS5pjk81WXH23uXHmoMvufXiv\nvTmdNs1ye8paedqetqftafsj3h7rkQsh/j7w54AHWusX7bZN4J8A14C3gZ/UWu/bz/468Bcx7uLP\na63/78dfxukiuqdaNgl1fF/R+fwUGN+xwPHKSPKS/CvaY9sLkrnaFln2WHmrJqiVSb5w+/nv4P5c\nWu5prGjp6QCn8XhMaJXtsiwjtR5NWRqmSV3XzMdTDwVpC5EQgbJFrJumhZcaZTSvhRAtG0GaoGAQ\nRf44gF+qg63fmaaeY+7w9SAImM1mC+nr29vbDIdDDnZ3iCLL4w5DhusbjNY2WFs7xyDrEdrEr0vn\ntnnw3nvs3XmfB3XN2GqnRE1Nf9hjmPUo9JE/d6/XIxASXTcoBGHslrSa4XBIOZ9zsLdLr79mEmgA\nrWrmcyNzMC/G/t0rpTg82kfekexcvIh2fpGQXL/xDJvbW0zmOVXdMJmZ6zo6nFBrRZb1ifo9trZM\nEtXW5jpJHBAIDXXFZGxWHIdHe0SBBKkRZpnmn3GpFWqu0UoggyGJDc5GUUgdRWRZRlXkTCZmNYJu\nfHA3CAKvteLGRjfQ7ZoZM21Cix9X2sKAIjgmb+EYLtAyfDyU2ElyW8bF9Qqf1nnXQoiF/rVwfUt/\nP05x8VS4d+fvVXzwkyCZJ20flDe+3E4DrfwD4BeAf9jZ9teAf6W1/jtCiL9m//6rQoiPAT8FfBy4\nCPw/Qoib2lM1/nBtOXCyijYk9RK+p10/NEXQ2taBRcRqXMpjgi7CrbumtU2rN53QwCqmU7d4uDPg\nTb2EkTdu30VD7s6wypD71eOxDr98fXaZqGkx+440qRO+ApCq8Xh3U9d+wBV1YSlp5tVlWUajFGEQ\nIqX0jA4ZBkRRhAxDBMECVukSS4Ig8GwQMEY+jmNGo5GRv7XGt6oqk/YeBMhRj9Ju37l3l4P9fdbW\nN9k8s40UIWloKXX5jL3dh9y69Qa3375FPTffWc8SkiCAQLDZW/NUwkGagdKU9RwhY6QyOHwgYHPU\nZzKdMlamSlAS2+IOZUE5z+1zSBn2zfZ8NmU2GTObzVi7tUGSGSMZRgmj9S3OnN3iQhyT5yWzuZm8\nXMV5pRRlrdjYMHTCXhqSz6ccHe4yG4+ZTowhn87GaN0Qx5GZEHvmPsI4MVK0BKbIRhjT7xtcPQgE\njarMhFiV7O+bItb5fMr6+rovzSekC7BJRCC9tnyXMqgVVmZaoLXwUJDp1wCSQDZIaZPOLCQRRYay\nGVqo0PXDqqp8glELVVgHxgVfV+DVxqlojm3v/lzeftKxllt3suhuWzbiy0HUZebbadpJ5++e84O0\nxxpyrfVvCyGuLW3+88AX7O//K/Cvgb9qt/+S1roA3hJCvAH8ceBrjzqH4HQz0+PEcACEsg/D4d3W\niAshjXX051ELNTGhdbx9UNBphKvF7c6It/vVXgNlQcO7I0LlcbgOa8XjcwsYHZ3rWpqQug9sqZ1E\nP3UDQNVtin4QCC+G1O/3vSGv7SALCNCNy+azlYsstzwIAoSU3igjjQfWNA29LPbekDMGbvA6ehuY\nGphHR0fMZrNjnddVG5pM7zA+NAYo7Q0Io5id7B4P7m8wGo1IUzORHDzc5cG993lw/y5KNZw5YzRN\nzqwNqPOCfDYjkTGx5VLLRlPNc8qqIUo1gX3uoWhIIkkuFYISqUuksmJoqgQ1RxAQR5IwaN9VloRM\n5jn37twmyYwhHYzWDIuHhigQ1KH0XHkZRmbCms3Y6sN033C/9yZjY8iPDhgfHRrPHMgyg1s3qqRU\nVZv1WzfEaYIMjcFUYUhsvW0JJEnJYDhkOj7icH8XgNnMas1kGQhB4OQshBPH0pRVRSDDdmUoNSaE\nY1eUPtFYIUTL0gqCNhNUysATAKJOWKssy4XCJK6PeIfshE7s+sgqlssqu7EqKLvcz5aDqyfZn1Xn\n6eLuT2J4H2WwTxOsfVT7oMHOc1rru/b3e8A5+/sl4Oud/d6z2x7bnsSQL7NSFvap285pjqvR2hhx\n539AxwkXClsZq5u4bn6oZXNqvr+4L2aZbg1201S+8MNCIKWjXuiu23ni3aCMvRx/HcuTy6q/hF70\n0Z3MbV7myMAEoIIF6dmS+Wxm6jMGcgFaCYKAOIoJpa3DWXdS8eva6LDQpuw3WlnvsiaQhYcwnHfn\nnoMrbAwGapnNZkwmE+I4ZjAwaepxHHsOdzmZ0BQ2iFSVZP0hVT5l5/59kMIXWMiSlPnsCBlotrY3\nOLtpuOqDOGYWjJnMx6i8ILSzXz6dIIVAaUiimNAGjEVVU+kJvTggSiKEmlPO3cpGYOjbNQf7R0xn\nhpMeR4KLl87y8OGuhULM/mfObiGoqfIpQSDIkhTRd6uRhvl8zGw6hvERe3s7AIwPj6xDoEhE7aGj\nWDQM1tcQYUAYxQQWHguTHjKMkGGAFCFFGNKGvBRShCRJSpTEnptcFRXzPCeKYxIktQ3WByIgCCKC\nQFtfp2u0BLb2FND1QAXQsrWWK3C5YKBd+PkAo2O/dGHGTkde6RW738NwdQm6Zdvh+ln3+134aOGU\nnUliFftllV1aYNJw3AY9qj0Kuvm36pE/rmmttRAn+YMnNyHEzwE/B3B2e/MDe+THDLn1BDxHVou2\nyrzQ6K54d8eIc0wEaNXMvmTERQfv1obStZwQ5KCTcIUHYBgmy0qCHd3wVk1l8R6dfoX2O7afdb4Q\nRZHRpbbJH42jpzWlp5oFhC333g5IqSWNkPZ7yh/LqyMGgYdWGm2usWkajo6OOl5/4DumM86uvf76\n69QWxunSNd0qIQxDrl65Rp4bD74uCuaqARkwy3PmRW548EASx+i6JpSCJA789smsBKFI0pTJZEJt\n33s+mSK1JEwSIkFbqDqfUmnoD0ckATTFhHltJpI4Soksd3w82UfZ6x30e6TZeeq64p333qMs3HBq\nqJuCw6OCw+khUZh4xkVelhwdTRiPxxwevetXMGmkQAvSNCPLMr96OTqaMJuOieKUIAgJbaJQEqeE\nSYqQxoCXQno5ZaEb70wkSUa/Z+CbmTqiaTRSGnhMOcNvhbSEnbw7JCrbXw3bRIq2VqqJa8kFQwlO\n3rbBTSrdFVocx4uwo/2O4bQLb8iXszVbA3fcuK4yjKsgj1VQSfe6T4I8ToJpTrI/j2r/Nj3yD8pa\nuS+EuGBPfAF4YLe/D1zp7HfZbjvWtNZ/T2v9Wa31Z9dGg1W7PG1P29P2tD1tp2gf1CP/P4GfAf6O\n/fl/dLb/IyHE/4AJdj4PfOM0B3xSaGVVgMIcx3nWdoaDDqQivAJgLWwGpG6Dh50a5GYf5Sqd2GMv\neePSCRkqBdYLcl44YBJ9rHsjwsWUd90okBKlLRZtYZy6k5mpOwudhSxgt9poj+b36X6SpSl1bXDJ\nuqxaCAVtvHUhiIP2uiqLYRZNgW4cHGK+s76+Tt00hNpk+DloRaFNELSqmBX1ApyivFeY+P9gCiDX\ndc10OjVys/O5397v98myjNnRYee6CvLDmjBLWNtYZ3OjxfUnkwlZv08/C+jFkefwF7M5SZSg0BSz\neZtkVip0XBOlKWkYIey7mk9nNFpjVEQNX15aDDcQCinM85JaUVucuqrnxEnGxvqIo6ORr1Y/OTpg\na2sLKSVlVbI3PmTuVBnzksl8xmw240w081BUGLUFRdxqBczqazyZEcQ1sxpS46iTFJok1cjYxCVk\nv+eTnoQw96HrmiRJWF9ft92m8awOGYU+DUHKENmBPdwqzBxLgDY8KSFBiC6jJfABbsdn0DqwHnFt\nV3DmGTqP3O1XVZVfCSplMPO2VG5n1dr53zSLK+STPHPnkZ+kXLiKJNE936pzLHvjy/DKadujArN/\nmHYa+uE/xgQ2t4UQ7wF/E2PA/6kQ4i8C7wA/CaC1flkI8U+B72FUSf/KD4qxYq/lsQEGweKLMsFN\nY8SF0isYKq0R7wYzgWPylO1J1IJhVar2mZBKNSuzMQPhIB+rj+JnDQmNasu1LbWTys49aj93KCOS\npImCkLDXYtZ1U6IqQ6fT8uTUZDMQzWdVVVE3DVHTEIuWfqgFSKWIoogkCTwbxi1xgQUWg3leBovP\nsowoijwkEFkK48HBAaKqOHfOhF6Ggx7V/j5NMSMSI5I4QVUG9rh0/gxJEjGfThGtWFUAACAASURB\nVImCgMrCMfPZjOl8zv7+PoMwwVkJiUAiiGRAFIQ+q7bM58gwYjYZU6mKJEtJhGGnNHWOwAhJ1U3J\neDy2z6RhfXOD0WjA5SsXmczMNZVlzt7+Dhub26xvrJEUGRObQJUkOTIyEFUWh9SFufeizNFa+1hC\nZgOno/VNLl27QNUI8qqhstm8tYgQOiCWiddOz+2xpAARh9RNTRCG9Kz07Xw+B1UbCEtGaNUmqEhp\nDHJDG9A0n5mgroNR2rFn/2bJQVlKvPH90wY3lYoWZCxcf2gh0ZPHdjehpr2+kw3vakfvZNbKqv1W\nfdY9/knHfJL2h4VV4HSslb9wwkdfPGH/vw387Se5CIFY0HHosjy6OPVphK4MDqeoa9Op67puU+Cl\n9nY8DiO0VqCE1x5Z4Hh36E7+PEIRWKEg04ltsMhee2gHhOpgea4sm6ttuaBm2DRol9npPHLraQZC\nGIW2Ttq88zBq+xxcYQCBydITwhgp59nkeQ6q5e26uUOgPQWxKOYLz93rUtvrcQY7iiJii3VXVeVr\nMQrLGV5bW6OXtUJTYRj6smKTycRj34BnygghvPqge1fz+dwcf57z9ttvm3cVh2xsbbJ1Zpu0n1I1\nFZENBk7HBwg9IEliinnuvXsN7B0csru3T6lD75VOp1NEEJCmGZPJhA1bA7Pf67F3eEScpui5ud/I\nivznU8P93tjYYDAacf+hUTLc2dmjamrOX7jEaH2dMLaGvKqJ4piiKmE2Qwvp+dtxljJcX0NrwcH9\ntwgt+ccJkcm0oSfDdv8koxYRFdAEkeeqizAlyAbE/QFxkpGkbf+YTSdUVYkkQEpNHJtjbW9vG737\nIKIoChrn6yhtJjoZsrmxDfneAuZtDGKwwA+XUjKdzBFCLTBQggC/n1GQNDrwTdN4x8I7N/ZYTROa\n/iBPFsBy/dP97LK+uqs/wAfPu83ts8rD7h7fjXn38yQxr+7v3QBvl1a5vDp1Y+Ok5lZjrj2JYf9w\npOgvteVAwjGmh22rlkuCxaQDqa1/LaxX7mc/451pKdHaLu06TrxGU4Pl2poP2sIMsLzQkF3miEtK\nQvkYqg8RufNrjRLCB5W69xL4zty5V03LBVc2wOjvxcAdEmGW9+6gHa0YseK5PcnS0IgpiZZ5496J\nUih7L2WpFrzwuq7J89wbbTdw3d/ud2d8Z7MZeZ5T1zVB03h6nAz71lvNEaFhvaxZOVctzAAJREie\n5n4QFUWJkAEyCGlyxXg689cVJQmzfE69s+cnXRlHnhYnoxilBaWFlRqEhQgkWZaS2FqXcToljBLi\nOCWMU6I48/tXtSIIInN8AZGFleI4pVGKPM85e+k6B1Zq4PDwEBGE9Ic9hBCMx4YP//7De8TphLTX\npz/aYDgyE1I6GCHjDCEDai0YxomB6zC02aYKCNFIFE1tA47SaK9IaXjjwid7SQgkEmOEGi1QXq7C\nBBmdIxFYmQVjrEs/JhcNUGukl8fwSUFHB610PzPMl5ZN0j3mMuyyitH2g4AxuhPEiZTnUx73g2jV\nnLZ9aAz5SZSe7rbucuyklxRihKYc1NCAgUK8J222R4GL0NdAgNAduMNWEQ+EXq3/4vBA++eyET/O\nO2+hG7fNsx+1nVDcZLHcyRf48O2s3d1HSoO5K9exl7gugRCw8LzaFcBpm1KmjqNcMuSqMYa81obm\nWXcSn4qi8HrlWrfVVvb29gjD0EAVnQzQIAgYjUb0ej1oWpw46yVsbKzRG/btgNeUFloZDAbGk7Ir\nj7o272YymXF4OGY2yxmkQ8vuMHCX0gLlzZwDZs02EcQIGVIrjS11SZSkBEFAoyTzvCQvzKopLxry\nsqaoGmSEpwZGQQRlRZSkIAKUkMRW+nYwGJgFopiglKY3Ml6aDvqW/mmM0ig2+2ejLdKshwxj4jQj\nTMwkEsYRhAFI414URUFp7101hnlSY7V83DvRtgRfGCBEW3BZSIkURoNdISjrtu4rdrUsRUAgw47n\nbVZY7v11PXhhobcgEAteqT/ikjF3+yOOUwBFh5K4rB7YFat7lIPXbU9qzFdlky7bqcdlkrr2/3tD\nrlk05CfhbCfhWN3ftVu64YxtY4y4EBbva4VvTEe2nrjUtOZVLhie9vyLdTeX6YrOiC9uVcDxEnHG\nSwaWMLiFYrUL5z4+oblUfS20N+JSiAWbHYgVQRylUTxZsEYptZC67QeuVtRNQ6UUgcw6XHWTBOQw\n324nzrLMT0heHZKWfhgEAZeuXfHY+WRyxMODPYLxAaOhCYi6weOOL4xkGNqSpstaUSsIZAJBiLB1\nNqumptYGsljb2mKwZlLkZ3lO3AvRMqJuMFRAq72d9oYgAuZFgYgE2opTxWmfXn9EOhiRpn2QrvZo\nRM2cNBuADKka5ScSHUQEoSBO+8zzmqTnDHnCbDImz3OkVAwGZsWx3e+zsbFBUTXkZcXcUkhnswki\nLAgjUxSbLGn10wWoJgJVo5sabe9dq4aZ1gSBuf7aevDSerQikIQI74W3zQQtgyA6Zsjde+xO4EEQ\n+KxevaTNvww/uGboj8f73UJfXuHlr3L4ftBe+aOglSdpqyaF5XbaSWG5PRXNetqetqftafsj3j4U\nHrknza3wyJe3wyLGu+zpKuqFcmtd3FtKSeg9AeU/152/ofVF2kBHi5W016aWKIGrvfHl+d97BMpR\nKG0g08Ha7vpUF4hhEZd2WGgHI3feuOp45FIDYYshumehxPHl7uNaF4uUUraVTDSehaCaytMC8zz3\n+PiqgJTDPHu9ng/sGVaD0V55+dXXuHDBsFa2zp1HCg2iIRRwdHTE3q4JOI5G66bwcxATRTGTcW7P\nX1IWRs+kVJqZxciVUmyfT+iN1kjSPtIJTYmANIqZVyVVpYjSkMDCG73BBkrBeL4L8wKLYBBGGXE6\nIIwylAioHOasFQQJOogJwohAKGoLZeVFYwKpSUrSyzg8NFrh5dGYeV7T1Ka6zs4Dc3/31V3Onj2L\nBvPMndsahARNDKpASUkpN5Gun9pVmHLB9c64cYla3fHVOOaWDM2qc2ml67I0zU9XTDkgDONjuinQ\nBiObpoEl6enu8RbhQekH60kQq6MyrvKqu995VMDwST3yx+3/Qb3zH3T7kBjyR0Mry4ES11a9JNUs\napp0Wxd/VsoISTmRK6d5Yj5zkXptAp8e0G4HgFBG1RDwRrI9owt2Hg9yrkr772q+OMjFyTX7jmJx\n+CfpOGZfGygS0s9QywUoTtN8sMtCH+52Gt2Ws5vNpoYpAy37pHPv7nz7+/torYnjmLW1NS/2NBqN\n/HI9HPX9/g/2d6GpWV8bsrmxzkDAPDfBwL29PRPADFMCWTKdGvphkVeUZcV8XiLWRijLjU76Pc5d\nvMTWuXM0CiKLXY82BszrkvzgEB0oomRAkBj2QxD1EWjiuKScFCg3bEKBkBGNEpRFQ1nbequiJk56\nTGcFyIogin2QsKw1Wph7j6KMJDHwUb8/JApCdFNS5DMOD4w+yvjoACkc4Vv7zM44TYizlFD0CaOI\nw8NDwsgY00gKtGpQZUFdFl6fRcq2YEjToQAKJI1Wre5M2LIrHBziDHh3jDp4xVFO3XZHPa3rGiFb\n5teyM3CSQV60A121xOMp+t3AqGuPUkl8UkN+Gn2n07Y/LE3xUe1DZciXf1825MuFXFcZ8qY+7s2b\nWJ/zAsz2um5sAoZJEdcdj7GL52njMi9d4xJ+v+CKt174qte8GMhp2SntdtmZhFoGSjeOsNwphcBi\n49Zo+yuxQSGOT4BP2gm7+HUYht4jb3RL6eoKYxVF4SlXLr3fnXMwGHh8vGkaL7Pqgp1pmlIKyZFV\nACxmU/q9lEYr9vb3OTzY42jffHbxwgXiyKSvV/MGqY2BL4Y1eV5RlYeMJzPOnjfe/flzF9jY2kbI\nEBlIUsvXjns9yplAhilZEtIbriOs8c1rRRJnDNc2EZnE1a0qy5r+cESUZKYQiDQGUIQhRd2ws7dL\nXSs2t7bZ2DZBShlEICSakKIoSCz/MN7YRjcFVTlnPotIrW1cH2QgauZzo01zaPVnCCS9fp/RaES/\n30ell2nT4iM0AiVtUQThtkuvcNmVRhBImsZ60doki3WDl64Z9cNuoQhhCkvEbTzJBTvdOWSHxbTM\nNOk2t8rtjquu7K3uYPuurTLOp/n9SVoXsz7JkJ8G+waOxQV+kO3DYci903lyYBMe/+J8W1Frs/3f\nOb5e5KsvGvLGaG+bAyxerv1ue42n6yTLYlvd61sO0KzqNMvQUteQL9xj9zpX6FO013N6Y96tpG46\n9/FV0qoqKkmSkGXZQuHZOI69YXcGHYzxn8/nBEFALrUPEK5tbtHPIqbTCYf7e2RxxLVr1wCTNZol\nPUAwaWYIYQxdgPDMmYP9+9x47lkAzl44T1lX3N95yNrGpsmewWiaEEYIGZJmfbJe35d6K/KKJB3Q\nH45Q09Lzsst6SlNryrKmUT5RkgiJahr29w+ZzubEvR7b4QV77ym1atACYhFSq1bmFaUIhCSLE2TP\nTDBJAOPJAU1VMJ8esm/LzDWNUT+cjA3LZ3B+nbSxgdO4AdVQFnOaIveQSxBIIrviUaqbo9EaS+dp\nr6Ldmc/Ntm72pGMgue0LTJWO4e/2l2VjbggKx/X83fjsbl/Zl09ptH8Q0Moy1PuDNOQflNnyoTDk\nSmnKouUWS2EYGY0ytSWxGWhamIj8AibXqYWplCLQ0no8zlvGJMU0DYWuF6h5DoLRjTI0uqUOmEvl\nix6b/Zu2M4uWMjiZtYMFWlx+AXd3FC2P3WtTBk7pBaMdhYkZTCwKCy0Ycl0bRoJLwVMGVw0ERFIa\nPBnIIit2JCtUU1PZ+yvLkqK0TAMLBwCkaY9eNmA6nXM4PkKKkMGa1d4WkkFvgApDDouWhRLGGUk/\nhaLg4eEO6ZotMtwz73PQH5FXJeP5nH7fJIc8HI9J05Q4TqgjRYXF1bWkbkLKMuTMYI1JYTz18e6Y\nIz2jnyVsb14jCiRF6VgzIYGFtoI4Ii9MibTBKOI8Q3qJ4o03cr73ne8DsNFbpy4rIiEZTGrees3U\n2bx58yZprw+HE/S0Im4kU4u1zqKQuNb0zpwl27rId77zOgB1UzHsga5K8z5sEtposEWkc86twSRS\nhPUuswMLTQyGxElCFCaU4QWPt6tIonUKqmE+TxjbVPxJ0/DwUNBUParkPOGakekNdEMUBKggYl4L\noodvU9kxMbfp8EmW0k+zVjs+CCiKEoQgShPi1K4SrLesapOUU6C8PIRJJLXYehB42QKCgLKq0FLS\n6ABlJ0Rl//n+7LxoKQxVUoSgJSICYW8+1MKugE0GdAvFNR5r10r5WErXuLoENoeLm2IXrWOx/Lv7\n28F+7ngnwbarYN3ucd1ktqr54hpLbJtuW4aaZJP7z57EqD9lrTxtT9vT9rT9EW8fCo8cbFDFT4gt\ntCA787vWJsC4AD0s4GmrmS5iAWtfzQTpfseltUu9nFqzuhk4ozObr/jttG35+ldt11o/8sjLASBT\nmACazpLVeQLDtTVfoWc+nxPUtddBqRrtudxr6xtorW1xAOUZBK4QxHQ6ZTQa8eCBEcJ08Yydh2+z\nsb3F5uYm9+8bJkbW6zGZTEjThq2zZ/y+8/mc4XDI5UtXSSLJxqb17qXJ5oyDkLyYsbfzkANb9WZn\n5yHPXLlEXVbcvfs+o74JUPb7PeI4Jk1TtM545513APjN3/rXUDXk0xl/7OMv8ulPfhqA19+8xdrG\nJmWj6G2E3Ll/j3t7ppDzOM+5euNZLsxz9o92qexK6NLFi6xvrBEGRjRqNjPvqCxLX7QjiCLCNPHL\n79lsZvpwGBH3YkKrnaJqW4AjN8wfX7WpaRgMBsRhQJxEhNJ5dw2VTbiqqoIoaN+3C0A6/e9lKK4L\nuS30GdlmUK7CyNvvLsplrPJI2/7qvr8YqFwoLGFhHhmwEM/RuoUZdedaul6wg/u6nrO7tq4Xvfz7\nwn0vP4fO76sgpmXv/bTQyqprWPb8vaS01sdswKPah8SQn2y8loMf3cCg5HiA8tgDUG3RB3PQpeWK\nWqyivXz+lduWziE74+LJldlXn3P5Xo5BLF2oBde53TLNHKubmFFVjYdWzDMzA/bg4MAHkRKLZee5\nycRM09QnpjRK2ZSbgLouqSqz9g+rkiRJ2NjYYH+Sc+PGDcDg4FmWMRyYoghN03Dz5kfM+S02niQp\n5y5e8OJYUkqOjo44OpwQh8IHTvP5nOl0yhRIooDz5y9y+fJlAF579fucP3eRg8M96ndrBmsGvhFK\nI0TNaDRCBkOevfk8AL/39W9w7+5dqiLnW9992ae8nz9/ETmbUjYKnSbc293jwKoJHhU5W/MZe4d7\nNE3Npp1ghsMhSinKpqEscyYTI6ZV1zVRGvkYgZYhhc0G1XWDDkLCqkLWtS+35pbX7p06Jkhf9rl0\n/gJCK8M8VA6XrVA+YFwx299Z0P4O44goSkwmpze0HdE5LW3l+g60IF0xiGhhXK3CqRe+t8JgrnKs\n3LnNZCH8PQYIU1RDWK0g4cZ7W6dTOQ0gFpP6utRId72rCks8zmA/DlrpkgyW7cJpIRA34awO9Jpj\nVrbPrzrPo9qHxJADWrHsZwq9aIRVXXkRKTNLqxM7nFMu7BpEsZTNKPRiKbYF2Td3WUudsUsp/LfR\njkftj2PkyysJaDtj15C7DuNxxG6HE67wQ0cVsTbSo71Bn1Rl1ArKTlWfyWTCvKhI05TzF03wbmNj\nA7Txyq/cWPMD79133+XWrVtMJ3Me7O6QZRmf+pTxfq/fuMHa2hphGHF/5yHf/va3AcMPl1ISRymX\nLpwjszUwsywjSVNUU0GjTAai9ebOn79A2u+xLhTP3XyBkVX6m06nDMSA7e1t3r2/zydf/AQAw8Ea\n792+ze79h7z52pvsHhlM/Zlnn2dvPCZOewzWN9gQAUP7HA9mU85dvECSpWyut/c4K3ICNHEc+opH\nYGM5VYkSoIMQQYPVxyUMIoQIqGvFbH+fxNJTjIibGeRxHBPbajgygFF/QF0WzPMZpZ1ADXc+IEkS\nwlCi86k3ZkEUEoax98h9T3FjQYoFTFUIgQhM9qYQAhm2htzca9MZN6237CaO7grZYdqucMkqD17Y\nSkNegMuEqrwh78aW3NgUQlBXrZRDt78v49erVBLds+1OKAv3f4Ih797bST9PG0DtTmTL1+aelVsB\nP2n70BjyYw+3Y8R9dHjBUDc0HFcY0027NOn+RC/pMXj95EU4ZeV33XdYpAHK7osULuV+8RtPCq50\nJ55VHo2ZwKwh73jk7jqcZ/64Y7l0+7KuvVpclmU0jWae56AlSS8jtQJRr7/+JtduXOeHnn+BLOvz\nYMfAJHfu3CEvTTHlcmfXa2LnuVEiHAwG/Jk/92e5ceMG775raoz8wbe+xXg8pihKKtV4Wdi6rrlx\n4wYvvPCC50SbV6OoqsJS5xqqSpLblfra+jpJHFkZ3YS33noLgJn1jmdFztqZK9y+ayoTnr9yibPn\nL/Dqd7+HDGK2trfNfmXF7Tt3uXztOmcvXmDr4kXmNsh+7+FDNrbWzeQhBZHlWddNRRSHjAZ9Gwzs\nlFqLQgIRoKUwMIoNLCZZDxGEKDdonTCPag1NEAQE1pBHccBkMjEeuWjVJZWSYI1mVRXEadLxyGNv\n7JTWKJdAphqUAKEEBB1jFbgUfJss1IoOHes7brLoGtEutNKlH0KbtOY+0zRG16hj5IXU5prss+v2\nUwML1gse+bJBPMmQroInlu/D3ctJhnxZlXXVM3mcqqFrTiyuey53HEcHrZcVV0/ZPlSG3D9klmAS\n6yk7Qy5RnhrW9da71KdFL/o45CI66oVCr4ZW/HF8Ek/nGpd270Iqq0qwnbYtyNxqfexvdx3oxfVL\nN/rtDLkrdtvt+O5YXcqfYwPUtaKsjdxu1u+xsbFJzybrXH/2Od579w4vvfQSRVW3xZW1kbVtmgaC\nVlv8Ix/5CJ/73OfI5yVf+8b/y2/8xm8QRbbeZGRkVIfDER977lkPk0gpmUwm5PMCSBhPDNXu6OiI\nsiwJ7T00dUljPdPJ0ZjNzXUG/R5BEPDQSsyura0RhxFKwd740OvSDIZr9HsJz7/4cda3z3L/rsH0\n502DTFKmRcmD3T366yNCVwhjNITA1Lisy5ozW0afJUkSmrqiqBvCJGbzjJkUptMpcZIQxBEII2wV\nJFaWNs1oNOSFqW9qIe92MFsGhltRFqWmygtCKQhCaRK7aA2M6yNRlCxAK1JK4wjVLV/csD9amWN3\ncidR6/6XVcvBUmic9IoQoi0zKATawTF2ArAdGKGFmZ+0oEst1jToWi8k4oEVlNMaULa0rcWLbaZw\nXdeoulnAyB07petpu/OsHDNLxtf1eXe8k7Brl6DWPe7yeZ7EI++e07XuKqbNnH0y4/GUtfK0PW1P\n29P2R7x9aDxyoRufoKI7rBWh2wLEyvKllcN39SIG18XJfdNqAWd3nrjSGoceur0XuOBCoBQrMXGX\nUu+9c2FdFliEV55wVoWTl2/LHvnykRcx8kWurMMj3TLXPaemaej3+5RWr3Ve7JNlGWfPX2Rzc5PZ\nPOf99w0kMX7tdcbTOU2jSXuZTzlvGsNySZKUIE744he/6K/3N3/zN7l/7yFhEnP16lWeeeY6AMPR\niLIsefhwh7feeotvfetbgPGS1tfXDZd93pZB6/f7DAYDqqriaH+fvd1dxmPjrV++eJ4oSsiLkqos\nyPo2OFtrDudHxnNqJOfOnDXPRGtC4NmbL3Dh4lW+852X7TOBOC85mE154+23ufb8s6xbjH64NgQ0\nZV2RRj3PWlF2KTw+OqCqCl+8QinFbJYzjBOSrEftvFNM3m8QRiRIwt6AqjYrizIvjC5NXRvWis3g\nrJuSJIyMFEKh/MrClHMzHnQcx4i6XOQtC2FzFNqEq9LKFCi0z/Z0/UMLAVKiRbCgSNntW20ymFkR\nOP12h8V3+5aTWvbSQZ0+Z7zrtiygtPdjdjSxLzBQm1fPrBsv5ew8cncd7viu363yyJfJEK5vueN1\n77O7PfQJVGphv1XnO21bBa24ZxN1VjxP4pV/OAz5CbCGw627RlhrU1cwsKu25ZfmkmS6HbGLq+vO\nNtVJLw+W6Cbm+8cfpAnMLGLTHklZcRteDOvEmz/elo34sc/sP3/mpcvsBjkXDHznc6XMkvtwMvNM\nk4sXL9LUmt2Dfd5++x3KqvIa10mc0WhBo03SknuSkYxYX9/gzNmzrG1s8vWvf93cr1LcvHmTf/fz\nf5Kirrh16xZf+9rXzHXZQd3vDxiur3n2wnQ6pSgKRsN1fvTHvuRhmt2dHW7ffpv7d+8RJyHP37zJ\n1atXAbh3931QNePDI4SsuXnTZHDevXuH+kixtrbGPEy4v7NjrkvDlUtXmTUN11/4KOcvXwPgK1/5\nCvdefoUgjmiEoT72R2ZSyKuCoioRQjPL5xxZyEcKwebmBlVT83B3D+dyCCHYOzzgQhCyGfeotfbG\nP5ERWT8lThNEEGDjd53KTIvVqcqypC5KJBoh8dBKEAjw9EJNLEXrOPikGqvRrtpzGEO8uBBXQCCM\nRrmBKdqCJ+anQAiHo7e0U6UcLNNlxiikVEjZGOPc6Zutwao8mwqMA+UNl27hUZfoU9clTVUTWr33\nrvFbBUF2g5qPZbXZdhKrZVWFoO553HM9TTsJvu3ek4g6NM0nSOn/cBhyFik8QrsgjsHIdGM8y8SW\nGpOY7Eo38wPUVek9hOWZWNgMsS7e7oyHw+Mbjj/oySw3noh/qR0sulNSrRXNcpi+61QNtTumWozU\nu2vrRvjdsaDt9Mu4nBCCsiiJQ0mWmo6dRCFxKMHqxtQdZkOSJKYuZtV4alNVVQSBKSf2p/7UFzz3\n+/uvvMZkPmN9fZ0kzRC1wl1uUVc0jQYpmMxn/lldufoMzzzzjFEy7Pe5efOmv7fXXnuNr3/tG/RH\nQw4ODnwgNIwitre32d3dI0oTL7R148YNPvWpTyEIePW1N0gS845u3brF5uYml69e4dOf/jTjowNu\n3boF2ALTjSZKYtY21sntPWa9PlnWQynFxsUr7FveeRSnEIQUtea9e/fIUhMD+PQPf57X3rrNaH2N\nrN/jzv0HnLcVikYba2ihePhwn7PnLhv2lH2+WmsGo3VUtw9rGK1tUDeanf19lBZIZ4RETNGMqWrF\nYC0gTswQ7PV6BiNX5p2FjhooNZEMPEbuNeh1442+1g1BEPrz53lu+7Q2QWuL9SdZSlU13gN3RTWE\nWixthuhKMLQruiAMCTp65Mq6yKaSUteBksRJRpxkPs5hjJ4JWhfz3OD6scP0Izs+jXCdLxKuTZUo\nIWJEFJtCHUtjYxV1uKoMsypJEv9ZURSUZenvZVm36aTmKioFnTiAmcQWJ1wwE4+LF0kpvY0xzKJw\nJUYeeOZR6B1UaG3DaduHwpBrrWmqEt2JiLubDiU0usMbpS1gLIWXyjhGRfIp5NLwUduZtX2YcslP\nXllZZ0Vz8EkbaG1w0Xahu3BI6wU4873c6VZFxN3P5X27wZ1VEfblYw4GAw4PDxmPxwgZMrRL/62t\nLcIoQSnFSy+95FmXveGAbNDnaDxBI8j6A8ZHJlloMp2gEBzsH3H5mat84Qs/6k7Oq6++SlU1/N7v\nf9MrGUZRxGAwYGtri6KuTGDPJhFVdc0bb7zBiy9+givXnuHHf/zHAfjmN7/Jl7/8ZdZGG8i05xOV\nhsMhQgR86cf/NC994+vcvn2b4cCwQF599VX6/T5ntje5e+ct6sZ48dubW5RlThRFjB/cp6ktwyDp\nU9QN1cEhh+MZUWiW2KqqCZKUJOujZMC9B/e589DASuvra2yd2WRgz+kkaZVWRjUwMjVBHXshyVIe\nPNhBBiEyNqnwYWSNUBiCCIhiwXg8Zi0wXn8SxSRJwtwG7d2E3+/3KWZztDbGdm6LS5dlThJFrK2t\nsbY25Ghvd+H9V8oENqVsBa2EDIki0+ud9+1arRoUGtFIjq9Ehf8vPCRjKgHvsAAAIABJREFU6tN2\n+9ty/wNTbxXcJNcyYxAKrbtsl5at0TqircHUatForhoH7vvLMAi0iUPu99O2VV53dzXQtVXOBp00\nRp143CK33xzPTQ5dCvSjPPjl9iEx5LbwbIfoD9Zb7mSmGS+lXYJpFmc2aCES7fFgB9IZMEB3jt1t\nrXJK27o8WfNzUUnQeUeNMoZcaL2Ax5vizo4yeHxS6C71uiuI7mfLbRELbye+7jFd29nZIY5jzp8/\nT9YbEFhDU9c1k8mE2WxG2hssLGXTNGN7e5u9vQN299/ztDmQbG1t8mf/wz/P+voGX/03/waAt956\nizTtUTU1URR57HEymZjkjLKhPxqyvb3Nd7/7PQC++KUvMZvN+BN/4vO89uYb/I2/8TcAM8FMp1Pu\nvH+P51/8FGfPGa765sYGn/rUH+N/+oX/kc3NdaJQcvnKM/6an7t+nelkQr/fZz4xxl/pmqvXrhtP\nPOvj4IQwTqlqRdMUxFFAYw3/bJZzNJ7RKM2g6NPrx/SGPf/eH9y/y3w+5YWPf9avIIRuTEUfYeM3\n9n1kWUYUJ1SNRiKJktQb8rJWICRhnBBU+YLBce/UrDJb2ExrzXyeU9Wlz+zMsox+lhGGoZEMVi1U\nYfLmJEJY4ogzvlojwxC5BK1oM5ws9a0hZBHDXdW6q8tHGXLXHxzMV1UVZSjQddeQqbZeqlxUHDTP\nozSGvm7HY5dls2w0u++iexy/Cn8CQ+4McxcK6t6fN8AcF43rThyOOro8dt3xXLKQS7RDCR8TONV1\nPm4HIcTfF0I8EEJ8t7PtvxdCfF8I8W0hxP8uhFi3268JIeZCiD+w///n01/K0/a0PW1P29P2Qdpp\nPPJ/APwC8A87234D+Ota61oI8d8Bfx34q/azN7XWn3qSi9Da4bau2rerqm1nXL2IH9NhsrgWCI0M\njMe+jEUFYjExwR6k3eeEXE23VG6rDHW/08aWDJvm+FGEbmdV1Rz3EtzybDmDs30uq69rlYaGEG3M\n2H3PFTJO05SyajxOPJvNzPI+ijxzBaBpFFVdEwpB2svo9YdsnzNsj6w/II5SXnnlFW6/+54PREoZ\nUtYV/X6fJEl8dmPfamXv7x3CVPL888/z/PMvALC5tcV4POYXfuEXmMxn/jnfvn2b+XzOT/0nP839\ngylHNuvyc5/7HL/6q/+CZ25c5+azz7G9vcmbb7wGwM3nP8Lh0T4b6+vM7s4RNpFmfbjO3Tv3WVsf\nkq2vG3wfE6iVMkIEAVGcMp8bD+jewx3uPdzhrNhmtLFO1h+S2sBTFEh66YDNtZF/ZmDqfhq53Iay\nKHwMoG4ahsMRTaOpyxp1NEHGFjoIQoJIIBvzjNyxJsXEP9MwDH2fd9pCziOUofEqsywjSRLKsmQ+\nn9JU9YLWShAEIA3zyqe5K0UYpwih/OcAEtnWutUarTsBPtvRtQjQImhxdQx/XOvFtWb3b601ic0d\nMPGEhqKQXjrCjUF/XhogWOjXjibQxaOXJZWXi1R0OeauLe93WtjCsXO68TgHhXTZOq45LLy7YlnW\nYl91/hYCciZZoZ/AJX+sIdda/7YQ4trStl/v/Pl14D8+9Rkf1bxcbbuECgTIoFPiSSvPenCBTGjN\n8jJUISz90H12GkjFDaIoaoMr9gLtd9w2i+N3ZXNpDb/uLvf0cQrTo6CVVdhfF0YKgmVo5Ti2vrGx\nQZ7n7OzskBeVD7yGYUgUm8rwWkTs7hp8dX1j0xrjGc8+/xyb22f59rfNQuytd26T9YfMZnOKoiCz\nBRmCKPQ64rPZjD0rNHXp0iWEEFy4cIGbH/2IoTPODCTx1a9+lXfffZezZ8/SPLjvDdjNmzf52Mc+\nxr/48v/F1Y+8yE/+5E8C8Iv/8H/j2rVn+OxnPsPBwZ55FrbDv/Lq9+llCS+//DKjft/PZnfu3OHS\npUvs7B1wdvMc0hZSDtOYQMYUhdELv3v3PgCvv/YmDx/skuc5ZZnTVBc4d95IxiZpjzgKiKKAWjVU\nNns4lTEyCIiFwbddILDX65OXNTKMqBrFeDpDFua9DoYj4jQy2jVhSGVpK45+6DI4I5slmqYpVV6Y\nyVZon5yW5zllnvt+MZ1OfVAzDEOiJEaIwBfABsjLkgTpjXgkrLytNTSuEElTNI81OMs/T2ph6Pqo\n9obPnG/xuzJYHBPm3IvJbF0s2gUsu1ro7nq7WvfLUMeygX9c6xrgVXGp7vZl52rZkD9KgOtJn+ty\n+0Fg5P8p8E86f18XQvwBcAj8N1rrr6z6khDi54CfA9jeGBnWRfuZ/yll+0CcLrGvbqLqhQcCndTf\nDg2xa/Tdo5TyuA/tDLhrxwOQ9ti+s9ntTWODN9pnrZn9j6f9d4/d9ca7NCl3PycFc6RYrETuPfKl\nZzyZTAzrRxsBLGkxQiEERVkzn8+RITz/vGGa3LFp7J/+7Gd48OABv/7rv845i1OfO3eO733/NbSG\nNMu498AYwCzL2Nra4ujQeOKf+9zn/Lsqy5IvfOELFHXFr/zKr3jj3yhDCwS4fPkyn/iE0UF5//33\n+dVf/VVuXH+OH/3iF/m7f/fvAvDRj36UmzdfoG4apAz52jdeQtp3lSQZR+MxFy9e5OG9+zi1vQsX\nL1MUOdvb2+b5ahcHaCjqnJ3dA44OZ+zv25qZdc3WmTNMx2Pu3r1PEklGVot9OMiMQZzX1PGar7NZ\n1yVYfLOfZpSlYbP0hubdRHGMUAJVNsjIDLUozYji1HjHYQjWmDpa4fjQsHvS2Lyr4ahvPGwRIgPR\nxmWairosvfpht+KPK7/nV4y+RxjvEikIdZta771z5VLsu4bGjS1X7s2nhQKr+nX3r+M6JQufdsa5\nz6BsDD0R2rHsAoWOqtn1xr0UwRL90D0Pdw6HT3ftxGmbu75lzvpJxtfh4MvGvjvel3F293+ZLnna\n9ocy5EKI/xqogV+0m+4CV7XWu0KIzwC/IoT4uNb6aPm7Wuu/B/w9gOeuXtRdxTV7bCQaKdullrbc\nZ5NUUB7b371AsMaVxQhzNyK8vCQSK+Aap77Xesu1N+Jam8IQ/nPRCWwueRRaGwrZimfwSI98lR6E\nu/bjwc7VbJc4jo130miqjpiQUyeM0yFvvf02AB//+Mc5c+YMv/07X+Xe3QdcunrFL79f/u4rbGxv\nMZnOKIqCS5cuATAej9l5uMezzz7LxuYar776KgA//MM/zI0bN/iNX/9XfP/11xgMBp7mGCcJaZpy\n8+YLPPfCTX7t134NMMb/R37kR/j0D32WX/utr3Ln/XsA/PzP/zxZlvHPf/mXOTg44Mb1Z9i1E8mF\nCxcoi3XuvP8uo411zw6aTCZsbW5SFBVxVXM0MV1wf/8IrQLGkzl1BcOhUUtM04yNjQ2K+ZyqniNp\nfAHkyXiPq5cvcuXKJQ5YNBp1h242nZlAa5ylyCCiajRBGDIc9pB2dedgBY1kPp9bOMEEzqMoIgxD\nmqZhOjVetJCazbV1r34Y2dVpFAVUwihEVlW14JnWdU2elwRBs8CAiWPpjdICc0K60mzGSVqlELTK\nWDWdMdZt3b+78gCOrqm1WuzPAUgZWfpe6RPZ3ApWSklgJQfcM3Qeuatm1B0/DobpEigc3bDrNJ2m\ndWGU7qTUpT8uG+xlQ959hm7SWbXS6U5Iy9Tjx7UPbMiFED8L/Dngi9pelda6AAr7++8JId4EbgK/\n+5hj+Q4Mi0pp7nO33WeHdaLIwMKMJvSi5oqf2U9ggpzUyrJcMrLGkPvjdWfmFYbcaUkIpQk72g7u\nOyfh4t1l7arOgODY81k1+GazGaGtFpOmKVmHO+s4wNvb2zz3vJF4ffDgAV/96tcIw5BnnnmGyXyG\nsnS3jY0NDg4OKCuTKVhZo3z16lXOnjnPvCx4++23+emf/mkAXnrpJX7pl36J0XCdMI6M/ogrkVaW\n/MRP/AR3797jd37nd7h+/TpgJp0XX3yR3/rXX+HNt97lb/2tv+Wv61/+y39JlRdsbm7Q6/XYs/Db\nuXPn+IPf/z2ODicMhj1T5QdjzO7eu8fGxgZ79+7x8KGBjxotGQ03iZMeWdYntvxu1cD6+jp5HKOb\nlCCEqjSrjMnRLq+99hq3336LK5/8nKdFGrij9bYcm2U6mZNkAl3NyXohvVFLP5yXFUVZI4OI/b0H\nNLbUW5akjEYjRqMRQgif2RmExigkUYwMBPlsbq5pckRTVbaA9UX2dnb9pGvyElrP1emj+MLWHWVE\nMC5A02iva5IEyamw5GWnYXn/Lq7tcOaTjFNXcrlrBxxdLwwltY1zdPHpZdilu9LtZqgu0wWfBLpw\nMEn3mdR1faIxXsWkcdftvn/MaZWLMsZPOuF8IEMuhPgPgP8K+Pe01rPO9jPAnta6EULcAJ4Hbj3u\neBoWkmKapjFJQcLQlQLZcjm7uLg9p/8ptCXUi0VqD2CTgjpYFNo/cIlGKeE9AUfqV7PZQsdaxujc\ni8nn+bFrMedwhlegmlZneHmfOBI44f06WISKnKctRPtSs7BPFAVeIbBpaublnDyf0TStxvVwY0RT\naxoZEMQJaWozFfOCQITcuPEcYVzx3rum3NmDBw9I0hAhA+Zz4+nZscOsqNCYpJDB+pAXPvJRAG7d\nepu33/8un//8j/Dpz36SX/7nvwzA+7ff5eL5c0zGY+rJnEGvz/ktw2P/2Mde5KXf+m36ozV0XjK1\nXPWP/YlP8s0/+B537u/wn/3Mf86dW3cA+OY3f49MJ7x/+21+7N/5PK+8/F0+98c/A8A3vvY1NjY2\nOPORjzCezpnOTXdUQYZMIu7uT0jliM3+eQCvkhilCXGSGmErQIYBjS5IRgky7BmutTLe+mBtm7ys\nKKqKb3/vtleLLMWMXs8UsIhFzPCMyZANk4SirhkNR2S9nnm3tu8Ms5SyLJnNJmz3At566zYA9y08\ndOnyVc6sDalrQ9sTgfE6795/SFEUHpKK+tvMDg85HOckZcCZMxsdGqmiLGqKoqKel2jV9ssLFwxU\nplVDVbo+aVQJo0ARBSDqouMtyw7xoPHJbjWSujHGTCOPGVJzVEE1NecIggBBRBimhEFFlRd+sqqU\nJk7MiiKJUj/hay2oG0WlGspCk9kEIlc0wyXgLJdtcwa8m/jjvuMmk8yOnaqq/KrGed9u/zAMQYfI\nMCQMIAycVw9SaaBBq4rZvJ1g2qIesmVDuGsLA4QSSMf3tNcrtUSoALSgcRlBQUAQHV/Fn9Qea8iF\nEP8Y+AKwLYR4D/ibGJZKAvyGfeFf11r/JeBPAf+tEKLCQHN/SWu9d+qredqetqftaXvanridhrXy\nF1Zs/l9O2PefAf/sg1zIcuRWcHL1ETpLGNckT7Zccksts5xZTPV1P5eXg6vS6GExgcFd5/HzHU+3\nXRWhNprgzUICgjunwwTLskbRUNlDNspgi1pAlMSeKTCeTOj1BiRZShQm7O6bOfX8uQtcv/4sL7/8\nCnV9RD4v/Tmy/gCNoCiMpzIvzGdahIxGIz76sRd55bXXeemllwCTSPOzP/uz5GXNL/7iLzIaGq9/\nfX2do4NDhoMBTVnx4osv+mDnK6+8QlmWjO/fJ8kyfuSHfgiAL3/5y8zmBX/5L/9l3rm9y63X3/DP\n5Dvf/v/Ye9NYy5brvu9XVXs8051v95sHTiIpiYoGy5ZEUhJk2UYsUyYSm4ngKRocxIkTJJ8sGEgA\nw98SJUEC2JaTgLYF2zDiQbLCJLKpiKRF05JJUxP1qEe+uV8Pt+9wxj1X5UMNe59z+z0+yQnwCHQB\nF7fv6XP23mfvqlVr/dd//dcX+fEf+7P89m/9Jh/4wAf41Kc+BUCaxuFeKSX6cnRhqXdRmpCqSXhG\ncRwTpzlpbku4VeyYG5GyVFEZoeIIpEQ7uKpuG6t50rZUje4rOB3W739GI5scTZKE1rXM816hf5aL\nxcIW8DQNqbQdjABG4ylpNgpwmC9eieMYIQSjLKGqqkDvnE6n7M2mSAHz+RxT14PPpEgZkaYpSUJg\n7Pg1Y6EFSd+GTYSfIUtkd+zCfm+WyByez8+trShYyp4SLNiCPXY9WX8sHxkPcfEHwRtDhspuUZ8f\nQ/jmQeX+/lqGXnzXXSdQ7CYth5DPENbZhXrf6F7tFmu91fG2qOyEnWQeZstY+2ewmxzcwuPe5NiS\nPpHpmSqBazpoRDF8UL+rjPEb6DYMj9E21bXJ9KA8gF+4uw+8xwojVqulK2N2UJRu0bpFKk2SxKSp\nx+NtNZsxhvv3L3jmGSsolaU5v/ALv8B4POXq8k4wTPl4hF6v2RQl8+WaKIo4dsnAw+MbXF4t+Oxn\nP0vVdoxHFl74iZ/4j/nsZz/La6+9RhzH3Lplm0ecHB7xyCOPcO/uXb7nD3wXVxc91e/++SVF3aAN\n/LmPfpT/5eN/C/ttJH/yP/wRzs7O+PV/82vh/p3fv8fHPvYn+OpXv8L3fd+H+Tt/++PkuTXYbVtT\nlhuQNsSPY68AGINL6habFu1bpCGJjFXfa00MocGIYDKdoeKEKMmcMXeQXmuou9bNGbn1XHw1q+fR\n+/kQx7HtqFQUjlliw/+yLJFSkmUZbbliMt0LnxkaB//d67oOuiFZUvRUws2KJEmIlWAyytBtFZLz\ndd0SRylZNrKqlLJnKw1xcT897bmsUNaDjLgxJrw5GKQBw8JwHcr0w68NpRQYjR5wv3tHrN8Qhqce\nYs4YaJ1S5PCzQ+zbf8Yb72Gi1x+/3zCuV2kO/x46b0KILUzcY+QB6vV8fGVzGiqyLLLWCc61ndNU\nN+3WNfj7IqSr/BbXncK3Ot42hhyu0/8AiyU5zNuqw7UBT7eFOO7Gi+ulr8BW8+bhCA9qpyWc/4wQ\nBjNYXMPP7LJGdjPaD8QLd3bhBxlxsAt3ODl3Eyxaa9fcd7govfKjoOt0mEB5PqIoCtarOe9+9zcE\nb+5f/+q/IU1Tnn/+eU5PZlSNMw6XFifstEGo2BYFueThK6+8QpaPKcuSmzcf5d/9oT8GwM/8zN8m\nTXMuLy+5cWPKnvMwz+7cRQnJH/pDf4gvfP6L6Kbl9dctCyVNUzSCP/1n/iw/83f/fuCe/7kf/XEk\ngk984hMs5lXQNnnyqcdsM4h3PMMv/4tPM52Ofec02rahaWtkZeVhPc1PCAPS8pijTCGFZ25ExJkk\nSiPiNCJyHrlwHrkGS89TCdIVF3UxKLdoR2m21RjZG/IszfqkfNNSNS11UVIVxVbSTQpBnqSMspxS\nDJL6QpAkaaDJFYVNaq4vL0Ph0HQ8QjlFxmKzYn55HyEE0+mUODkMz3e12tDUHUI4eeGBV9on1LwX\nbm300DkSZnsNWUPebc1T4wplhNgm8W5FmUIEbr31yCW63U5S+vkbyup3nHEpJUIbpBRbPWd3CRHX\nPiO2+eLeUQtr04s0Kem6ORHIC4BVHhSCDuMidoLip10jHa3RVhI4sMfA9s3199Xn/FratqGu+zzZ\nkE1j32fQWiHT35tJfnsYcmMwXXvdYApsNZlPgjZVqLCyPPJua+JI2Su9+cKfrUnG9oPdLRbyOi1e\nPlKm0ZanPjTku1lsH5Zq3XsvRtsH9GYe/u6EWy6XWzxZP7w2s9batYyK+i7kIqYTAq1bmrrrE6tG\nUlct73rXe7h16zavvmKTmlk24vLykoODA1pd07b9fc/yEfsHM4SKmS9XvPKKTcZpFK/fvkun4Yd/\n+If5zGd/2V5X3TC/vOL49AZVtaZ0LJf3ve99HO4f8OnP/DKH+we89PodZgf77rtofv/v+05efOkV\nzs7O+ME/+IcBy4D52X/6czz33Jd45zvey/37lhnzQ3/0j/Abv/5FvvF97+b27VcZjXMitw7TNHIL\nTKOUDIYDAUYIZCRQRtrkExAlEhkr4kS5hLEzcpGr2JRu3gjw0o8SiZARWkOWJcRxT2XzrCApRfCW\n67rm/PycJPHskF5gykZcsFjMySfjQY9GQ5qnZFlqIa31KsyHuiqCCNnIsWwSOcE0Fmq5un+Po5uH\nYT7keW6T3F1HVVVEqoeChmMr9Dca7dsd6usG0rBtOLcqpR/AovK/t/ST3rROo18nciDMJdxnDb2n\n/aCKyuExh9S/IYFi6A1HrqBMCkGkZICf/BgW8RgtbOci3V+vdno2FjzwcIxVouz3Ax1el5LAagr3\nA+g6haUpd04JcfrA7/W1xtvCkFv6U7dlMAUG44zcEJMORlF314yjMX3l5q4XvlvBOazFFKZDDjyE\nvgJsO2zbZa3413epSLuk/gfRnd7II1+v18Rx3MsDDM7hcVpjtrtx2wy5P39f2pskGe95z3v5tV/7\nDe7duxdK8ReLVYACruYLps6LnkymKKVoOkOxXDOfL7m6tPzr5WZNpw0/+ZN/mU99+lP80i99GoDH\nn3qSpmkoN2taveJDH/qQvd6q4Td+6zc5OTnh+ee/ymy6HwppnnzyKZ56+ll+6qd+iu/7gT/In/3x\nHwfgL//kX+K1129xenLCYnnJv//v/XEAfuGffYLv/dAH+dmf/cfMphNG6R6L5RUAh4eHdoNDIxVE\nzovWWMU8IQVKGZRjA6GslreMJDISiMiHxQqUIopTojhFJQmRKy8XQtEZEXD4IX/fU17ruh5AG/UW\nt/tBgnB1XaOa1BdqBhbGfNlSFetwLClt4whpDFf373Hu1sjh/ozjw31SBa+99hp37zbh+Y7HEwQu\nlzLAceM4DpRabXrM18rnWnjORnb9PA3Gfre1ohABBkRs3xP/2+zMbf/5a5hzZ5/dA/FuIVwjlz7/\n4Rkl/li7NMNhtOxf99rmAUPfgXD8s9rC9IUYbLS7G09vB3wtgKGj0wz+tu+LYolUEWU1OI5noQmB\nNi2dpUn9riDd4XjY6u3heDgejofj63y8LTxyBskDIHT58Tukx0OjKMJ0LcJIOqJtOGSHxTIcYsv7\ndvCIy0ajWwx9Kyuw3lEkBVVzvcDBn2vXy/ae9y6m/iC8O1zXG4SjQzjHj2HFZ9vpLc0P7TjoKrLd\n5H3o/9jjT/IvP/erpGnK3v4B5+dWNGv/8AAhBKvlmsl0xtGRbRqcpiln55fcuXPH6qJIFZgQAB/5\nyEd4+eWX+cVPfpKTUyumdX7vjMcee4zz83O+54PfwXphu9eXZYUQiq989UWefOoZbt++Q+0qS/+d\nb/12/s7f/Xu8/5s/wI/+2I/xP/2P/4P7TGkLUtKUJ554ghdedMJY73wHn//Vf8VqtcToBtNVQee6\nqgrW6zXdQKDM3hOJNnbOpJMUJXs+cZLFpEniGiQ71opK6Iwtqw9c4MhFRdhEnRCKti62nnnbtqFp\nwfCZZUmKbjvqsgqVn/bCjK2qTTPqTpMNYJrLy0uqqiJWgsi9P0tjTNtihKGtS1YLG9XouiCWkCYx\nN44PuLNa9U1W2pYkto1DpOwhumFuSZs+Am7blk63dF3j5vH1ea/Ntg6KHkSlYqeQZXsuD/RFtN7y\nooceudjxoP3nwUpSGASp45d79lbfsHhbx8Tj50PY0ke03vv2zUGGJILdVnZeMOuN2DF9tDKo9HXP\nwMOjfs5JKcP938rHyW3xr99NM4nheFsYchvOdcGAD6mBEk1nekaHEb3RHhYG7ZbE9nj4dSMOLiwS\nBj0wyj5xGjl9F99XcLcgyEIXve6EMVbJzUIxnfvbUg79d4nkG1MUh//2hnM4Kfx7/ORqXPOBYSmz\nn5B5Pg4dwj/1qX/B3t4eG9fp6OTkBLAGU2vNdDrl5JGjYGTmV0vOzs6Yz5fuPmtqxxT49m//dp55\n+mn+2l//ad7xjmdYLCyGu78/45VXXuFjH/sYt+++QNvYe3z//jlV1fDII49w+/ZtsnTMs+/8BgDO\nr+YUm4r//L/4L/nMZz7Db//2b4fvcePkmNViznve87384i/+IgDf/V1/gOe/8hx70wl1WfL66xec\nHFtBKylguVqH++zXs0aCcKwdUVsWCxBHCU2n6VpDqztUa++VVB3ZaAoeCx4oAHbYZJfWmqJcb8Fd\nm80maNoMF24URQFSyZ1uuJ8TnW6IE2sEh23uzs/PaaqCo6MjRg5G0I3m1q1XOTrYY286YeS6Jm1W\nC+7evsXB3oyjg32atO+0tFwuydKOvb0DRqNxUKbw1MahMfX3fVhCP0x2Budkx5B3DDrRv0kO6NqG\nsEP3A59LenBLteHw92ooL7ALofjvsytU5Y1+gEyGVEYESIUw9Pi8VBghECqy30/rIc0H6POywmnD\nGDO0FdK248NCeXEckWXJm9AWZUjs/l7G28KQ72aq7WTqMF1HZ2QwsCj7EGIlnOZEdP3hO054N3iA\nvmx/aOyrwlYTegNujA687OGuOvQwhsnOYQTgDaNPxPrPD/ng+7O96197mOF3YzabsdlsKMuSJElC\nFaFSisViwdXVFWk+IktHAUdtm4aDgwOeeOIJLi4u+K3ftIYxy0aslhvSNGU8Gofr0h3s7R3w6GM3\nuX9xwUtOa6XrOoywZM3jo2OapuPMefEf/vCH+fjH/xaPP/oYV4s5+/sWV7+8nPPDH/kh7t55nVuv\n3wrHmk72mM0OWJcVo8mUomz55g9YvvjP/MzP8Gd+9Md47fbr/Nz/8YlgAG/evMnv/M5zfPSjH+Xj\nH/84f/4nLHb+8Y9/nMkosyJfaPKsLyG/e/cubdsSxQlqvabpfLJSEccJWZ6jVIRKnPEVglzk5KOU\nTvd6OtNZTtPULqlpKx19BxujO+qmo201i7OzMOc2mw2LxYKyLLeaavgWY5PJJFDX/P8ZY0KuQ6N5\n7dz2El2vlsxmMyphWC8XVBt7vTdPTmz0tFoxzpKQO9lgHY66rnn+y7/N09/ybSEHURQVWZoNKI2E\nObRcLp1hbgfessWovecoWnnd0djpKKSF1XnxCV1/T6qqwhhjOexZFBKEbdvS1BVlUQScvo+g+42x\naw2pY32kaY6KYqq2oa76PJT3uKMoYjQaIaUMm1jT2G5Ufi364Smc3lMfrukH5beCXEGaXosg/D3x\ndsBj975C1NMePb5eVZakkec5Sqlwn/1xhhub5zfsXv/XGm8LQ+4MmXQ0AAAgAElEQVQfSrihuqXT\nPVThPekoigInPMAcA0qQ/z30Nrqus3CM87x3myyju2uJUZ80rbtu66Hvski8RxwSSLuexgCK6XaO\nNfw9fL1pmuB5VFXF1ZVN6llmhLRtz+KEO2f3ODg4AODk+Jjj41Oee/4r1HVNPrabxmKxYLY3odOa\n2/fOGI2sB/XYE48jhOCFl15ivlyEDjJGWEjHhnkRi9WcH/mRHwHg85//vOVkl2ve8653B3Gs7//e\nDxNFkhdeeIHLq9scH1pP+fXbd2lbw8HRDe5fXPH7vuP38/KrlmP+nX/gu/nQhz7MX/gL/wnzxSVH\nR/YzL774It/zPd/Da7de4SN/7If4whe+AFjO9ChRLMoV09GYg6PDoFXedR2RikOhFNhnkqQWOivW\nJU3VhLLvOI4xGpRKrZfpoqo4SmnagtFEWAMCNE7NcD5fcv/inMV8hWxXWxzmtmmIpCKJYnLH38/z\nnKIoUEKipLLKhp7H3rbUZYVuO9ZNQ1s7JoNuiYWGOAIjaJxhuro853B/hula5vP5FsxYlQWr1Yok\nkrz44otBs+b0NOfunTPm8zk3bz6Ccl782WATGnrX3j7716LBPO/pkfLa/PXFTsmgN6aUMpTNt9qQ\nxj112EvqDgt7AKQS1K5bklKSXXaKP69fbx5O8dfcN5XuIQ8PefnPeIbRUJjsrYxhMZcfu+u7qrwd\naKnrNkSGXgMffP/c/p72WuMCHsDDfzOm2wOv8y2/8//HIbDNJHxEV+O+iNNyCLtnWweja4y5Rif0\nv7XWdI4bHTxyB6V4jXApJaH9W9gwegilM4a2bQJkAf3E222YPOSHeiqVPUff4/CNOK/Da7fHqq8p\n2fnr9TheUVUcHx+H84/HU1584WW61jC/WrHvenNmWU6xqem6liTOGLkiHq8vUdc167K/9qKwNLeD\noxNUHPPe9743qBx+8pOfZDqdYoxhtV7wwQ9+0J17zMsvv0yxXiGECIJSN2/e5PxyQXX3Ls++872g\nIsau6vND3/Zt/PW/8Tcpqoqj41OUh4+15tmnn+aTn/xnPP30Uzz3nG0N98gjjxArSbE2tLUrrnBc\neQxEaYQUEW3dULkFoqIUjWWTrNtV8GTjOKFrQZoIjew3MSNRccpm5Vgm0YVrKgzr9Yb5ck1RFOhq\nuaXf4Q2DUmInlFYoJSyPPVIBbrOYvvWKy7ovEhNojJ6QKoFSKVcbC10trtacHh8R5xn37t7h0qk4\nHh0d2blQFMRxzmq1CrryR0cnTKdTaidVHCl77tFoxHK5vGYgPC7uPePdArcHeeSerePvwdDAe+XB\ntmkxXc/S2axX1OWGrqmR9BuGEpK62fZy/XzQpsf167Y3ykM22C7bxEfFQx0W7yx6umjtNXGF48NL\nFX78NSEkSZpZoy8kxjkJNlrzkK3YgqiG92yX7TbMc+3m18K/B3CT0bsu5huPh6yVh+PheDgejq/z\n8bbwyDG95+yHxGw1Xga2MaM3KC5Ab7dlCjoczhv3x8vTBCN7fEqYLnB6hzv+kEEyDKneKJM99CiG\nv+OoT2L6Yw0z2MPXN5tNwN6GjAOPv2X5iDTNA37+xS9+kSwdsV5vOD29GbziyWTCcrkkSVKOjg4D\nd/X27dt0XcdsNiGO0vB+JWMm4xl5bj28H/iBH+Szrsny/v4+XdeFSs8nnrSe+r/67L/k3r17HB3s\nMV93xA7CUFHCfLnh5PQGV1dXfN/3/yDrjfX+X33tdf7Nr32R0XiKlIKXX3kJgD/5Jz7KZz7zKb7l\nW76FX/mVXyF3sejNmze5PL/P8fEpq8Wc5XwZdE3qukYYiTE2+vHToq5apNS02tCVDa1xjYLbmiIq\nSaINnQYfYOtOMJ7MWK1sA+ZWE7x1gUJIwWSUsumKgb534pghNpfivT/vpUspg+qen0NN01CWJVVV\nkSUqyA+3bUtTrCGOGaU5qStU2jRwdXXF8fExWZYFqK0oCk5PTxlNpmw2Gw4mk1AhWxQVN288Sp7n\nzOcL2qZvvxegvEFlJ9iScv9/agda8R75cE57Hrn/7kMY0cMRRhjWrrBps9mwXi1p6xKJhVw8k8hg\nQl4B+rxF03QYbHWl7kDRwyG7SdTh3/78w1oPpZSVNPDPxikZeix8yF7xQ2sdomMftfvzDdeuL7jC\nSAQqHGsLgmtbdGdLnIwQMMgP+PpWKeRWgeLXHbSijQ5Vi0DAtIPokPvOvifi0IiHCTSgAA03BU8x\n7NgOaYbav5YZc70s2eP2D6rsHEIuQ/x7aMiH+F6s4q1jeancoWYD2KRM6Vp4jcfjsKj8/UnTlNFs\nCki+8sJX7WfyMa+++ho3bzzK+cVVwM6bVnN8coMkiajqIiyqzmiMgPlysVVMcXh4yGg0YrFYMB5P\niaKIl19+GbCt2zabDbpp+L7v+35+/ud/HrB4sE/saVkF7ZDXbt3l0Ucf59brd/nBP/IRlqs1SW6N\n7z/43/8RKk4ZjTJWq0WAgo6Ojtjf3+f27de5vLzkxOHt6/Waum6ZjOwGprueIZKlI1uZqgVJmoK0\ni6rtLE4ZxQlZMg4SpEiB7EQoo28cRCNQNE2HkBIRxbbcX/mu647JIgR7e3vhfqVpGopwqqraMhre\niASm0aCs3z//472spwxWFXW5gVah0yi0ehvnGffv30cKuzH7fELTNMRpzt7enm3lJ3sWSdM03L59\nmzwfE8dJuN6zszP29/ftnDRmC6eVvlBqR+Yi0PjYzuUwMNhttS3R7IuYlIHzszvhGa5XS3Rbk8YR\nkYzxfplGMBrbrklN3fVJ/LawzpWrvPQytsPKag/j9Ma/CZruaZpuwaJDw75bcDfE/P3fQ1j3QSP8\nn/HwqXIQ23ZC0z5zr01jOy0J0ecBoLdjnlK8C798rfG2MOTBwA3as/mHFSux9WV3k5tDA/6GvwcP\nxL8/aBjrdmuHBZ9A3VY+Gx4TtoV7fHJyF6/bTQ49GJvc5p4Ple+22nd1HUmSWGZD13FxcR4SeLdf\nv8vJyQlXVwuOj09DQ+HJZIJSMW3bsdlswmQXUtJ1tmlvlI0RzmhoDFVjS/Y/8IEP8LnPfY7Dw0PA\niT0Z+Nbv+A5++Zf/BaeOR/7888/zjd/4jZydnTGZTCjcZiulpKoqWqP5zu/8Tv75Jz9NkllDfvfs\nPkop24+yafiu7/ouwKoinpyc8H/9n5/g0cce6zs0ac3xwSGr5ZKqKjg+PApaJFk2wpgWhCRLcoQz\n5GXdIqSy7A05yG9giFWCRCFNi/Esl66zehtSIq3NJnK67tIZOCNhkk/C3EnTlMlo5JLj/TyYTSa9\nvjWghAg63pGUZElCE8ckSmCcPII0HdJ0dK2mLDa07hxRFCEFXF7NSbOco2NLIV0ul9SNrYEYjSfc\nvXNrgMkKKt2gNcxmUWDM5HkesG2rJNGzVmwDi+uds/x4kFHxc9r3HYXr5fNDjf+2bRHmesedtuvr\nRpRSiNaeq+s62k4jjLJl9E78yxtcv76GldV+HXlj6p/JsCWcMSaoEHQW8cZoex5vH5RtImrF0nRH\no7ugtdJhQs2CEIKuHtKTbWTof/z9NQakVI7XH6FUtHVd9O/curdvdbwtDLk3fmYHLtFab2k62JBw\n8LlBe7ZdulTwjhxXfPfz3rvfbcYMAw76Dltltwx5mLx4s9cBuuY6PBMm7uCheeqW9zS8hzCduvL5\npuHu+TlpmrNc2uKb8XjMxfkVJyc3LBXPeZJKRlxeXlLXJUKYwKgvi4LOebVKxeS5ZxZotG4YTca8\n853v5Atf+ALHx7ZYaD6f8x3f+m28+OKLNE0TWCPf/M3fxL07d5mMx2zaZR+NCMHde/f4kx/7U/zK\nr/xrnn7Hs/yjf/xPw3c5ODjgS7/5G0zHaYCILs7v8ulf+kXe/a53Ml8sg7E+2N8Pm6owVjlQ+GYJ\nrnRbCoUUUeiGMx6nCGnZN21TI/HQgDWmkYyIZEfiSveTKGY6HtN0HXXb0VUlWnvtkjG5k71N01G4\nLr/pet7yEHLx0dZws/ZzyUsVl5tlMHSRhMnIbmxVsWblGlWnacpoNKLTFrrxlLYss978/YvLMC/9\nnFYqZn/vkCTJLEXQdSc6PT1lPp8PeOHb9EPvkZvmugHx7dnC34P/2117XuOlrLelCaIoIlaxu5cR\nxnXQarqazWbjoI/UKk8CUVRT1Q0dBinUtXXo19CwaC1xBV0+4h7WgAyvc8g4K8vymkM1NLAeGnlQ\ngxkhRFCXDNcTxaRJT5EVNKEuQUmFknG/Rnc2vlb3HvnXpSGPlaRj0GTZPQRhdqh69DfsQe3Nhsd0\n/7g20cB5mGz325Ni+z3Ced1DOpS/viEcsmvAH/QAvCHfzfzvekBd1wV6lOeegoUd1ut1kIm1nOE+\ndBuNrBDW/v5hMIzL5ZK2s6prbVuDcNcgPYdXU5Zl6DrjQ+U0Tanrmul0GhT1nn32WZbLJRcXF9v3\n09jFU9c1KlbU9Tpc0zvf+U7bQSeP+J3f+Z0tuOvWrVscHR2xN83D63fvWpnb8/NztOnvd9M0vPji\nyxwfHbA3nZEkGXli78vV1YI0zazB7oytwgSyfISQUViA/XOWYHrNam8CvEG2c69DIEOf1ThWZGlM\nnqfko8nW8x3S3Yah9BBXHeKd3pts25bFndfCcbIsY5xnbIRgPp+zWlgsvM5GHB4eMpnOtpgph8cn\nKKW4urpCSsn+/n6AVozpdVC01iGymc/nPdxn+uIpIXpoRQhB9wAV0m2lIoKOytAZgZ41UhQFy/Vm\ni+Gju4QkshtxmigcCYW2bliv10gpGeUToqTXVVdFSd21GL0dmQ/pg8Mo1v+/f5ZD1tcQu64r+3pV\nWo661lYcy3dTiiITHEx7rP5+2XyM87wRJGl/bg8reRVLf31RFAUJ4+G63zXkKrDc+hzNWxkPWSsP\nx8PxcDwcX+fjbeGRG6BF0OEz4hIhBbFLUATmht44pbYO09oEwtBbVkqhzIYGHbBPlApJj2GIu5+k\nwbP2u/vuLpmK7USEH0qYrTtXFIU99s7xhp6YUTIkOAFXTp8H77tPhhkSKZBJjgRq5yHcu5izWq1Y\nFjVyMiY/mAa2yWK1IhKS/ZN96rbkS1/5dcBV6tEXVSi2v48xkE8Fo8x6t5vNBmMMNx5/kpdfeZXz\ni0ueesb2oVRJxp1752ycZzQ+sj0wL6oOndkKxk1jmDu8VEcx3/29389yueDk+Ihf+9VPBs9/ojrq\nuGU1X/HDP/iHQ+HP+a3bvO+Z97JarVCxDhDGxd0zpJSsVyVSJeh1EUruxXjMum2trG0iKbvCPcOE\n2SxH6xiZPRJgh9ZouiRmozs6GRG5706aUhiBlhGtkGhtaLVPhgumaUY8mWKiGdE4cc+qo1UKFOSz\nCN8Fal4UoDs2mxUqU5YD7xo5C2lsQrudM8knPdYfZzRlQ7MpaesmSDpcnt3j9q1X+aZv+iYuz8+Z\nOzjtt7/0G3z4wx9mNT9nNpshzZix+y6+oEtKCSrGa4EW5YLxdIJAoug12m0eSdAZMNrQZdk1D8/O\nGc2wnk5FIjSvrirXFHppOyB1XcdklFIubWWw6DbQlQgRE8mcLMsRAbsfW5jQaFarVd/pKFGMYoHS\nmqqt2Kz7qMZHNrusGf87cuQCH41UZe28Zbv2Dg9sTcOcDroaISKkhLay86Ta2CKjyWRCGkWIOA5r\ntCgKaie/oJSidayV6XRKmqY0TcO6qYI9adqGlauzyJIIhKFu7HVFpgvMp6ZpuH91P3zHYZTxtcbb\nwpALtlkkw8TFMIwflsvSXdcssDTDt3jOgMtvC9j4/xsmLYeQQB9+95/zmhr+Z5cyaOGSdJspswOp\nDLPpPjTPsiyce7m0eOre3h7LrqWrG1wujulo3Gfwqzocy05iicRDCdtaFZFQCCG5uLgM1xHFMccn\nJ7z00kucnt4Myc579+5RVc0ghMZdb0xdW82RjojSGaYPfvC7ef755/nQBz/Iz/7sP+HElZoDVLpk\nNBpZw9W13L59G7DyBOti41qw9S3VxpOJK2m37IeiqkKLttFohIwi0tw2dqibXgxJay+foIgz1wLO\nPx8pUEKFMN6+JsNm3LZdkHnw8IwxxjFoavfMDJFIMXRUVUnlBLWka5TQtTXFOkEJa5QAEhWRJjH7\n0xlt02/6dV1z//59ayxUPzeqquLs/hnPPfccs9ksvN8bjMcee8zO10FRjjfiNkErAtzU547EA+Ch\n/t8PCtP954bLq+s6dNM6SqU1gOWmoKqqnunlZSEeUB3pl7an+em22YJNRGtQA0E7HaBPu6kY0+vD\nDNeohTa8GFkgmLoNQAA6OEFeI2fIQBuON2KtDQkOfp74SlIvkuaPOZTt8PZhqAHjbY1vD+jf93WH\nkcN1Q/4gcZmxo68ZYxDabGFgodLyLXZK2mWXDJMh3oP1VZ9D3ZbhTzDkbTvont0/JG0MpmnotCaR\n280ohv8eXos/t48ghs0KvLbEZrGwDAB/Xxyn2rcU85PBeti9pnsU9Q0G0jTFRBKDZLmxBmg8HlM1\nLaPJlLPzC97znvdsUdfiOEZJiUCHTSSWikZX1MWGkjiUia/Xax577DHOzs4so2WU9Rtjayf6k08+\nyZ07dwIOf3h4TFO3FusVJmC+tgdmx7rYUBTWUIi2Z/Pk4zGzyKr9qQEVrqgryrpCip4mmGUZGidI\nJqNgyKVSaCHBGaeqrkPitKnqML/K9aqPqmJJqwRd07BZL3tWkNEIaYgiRVMVlFKHhS+l1caJlELE\ncYgU6roOi3mzKkMy+fLykiRJWCwWPPLII6EyOc9z1ut1yJ0MvTchHO6qJEoOmiZI0Rtt2Rtlo0Ne\n/xp/uZ+jBmFEaGuG0JgWqrpmvV5SFTY5O1RYNMYE9s3QCPZ/m/AMkyShMTrUSgBWPkH2vTelbwYx\noPh6Q7slyWHMVtWtH17mommaMOeGypRDewJsrcHhPfGGP+ijuO/RVH03qDRNA21amA6J/W6dBN32\n1aCdUki3ybRtuyWat7v5vdl4mxjy602WYZt4D3bH8zuadA936L0bY6x8qfvxw/9tMIGjYg21ASnt\nJB1cjS+y97oJ/TlswsMmOxR9Kb5xf0vHze15pdZ4SqSM8NxRf37bANceSw28sDy3nvh6vQ7hnOUE\nx2jtlBSl6AtWnDdujLmWeOo6O9HrtkG6hGunbWekTmtaTLheGSUURcFitWE83UPJmFu3bELOX0eY\nxE7xrSw0dbXB6JooyYMh/9znPssf/IHv5x/+w3/I0dERxXoZJm8cx1RVxfu/9f18/vNfYLpnBbis\nSJEridbtgDoWkeY5SZaSZBll3UNUi9WKsu0YT2dMZ7OQkltuCmgcLU3oIGw0Ho+p2wYjBErFwZDb\n5J1EOkPUNA2e6FzXNV1jvSolLZ0VQBhDV9vinrosQk/JNIqJlVW765qakhYpXAFT1VKsrDdYXlxy\neWmjoTRNOT09pSxLzl57NRT3KKW4cXKTNE0thDJIHg6TrFJuC8i1RqOMsEUqsk/eWx4zbNO/7C8t\n3FcbOII9pNI7NvYzGu3ZKWVJU/cNvJMkwWDX48XcJme10QES6WmAg85UWYbp2kBTdBeMVL0XG4Ve\ntP21eVLA0An0DJihc+idJe+0eY/c30tgixXko9ZhrYd3kHzy0kOimZtbZVnSeVkPZX/sRUmS2LKn\nMJaK2Hm5Ad3RxREYTde2RAPqse7+PzTkQoj/DfijwD1jzDe61/4b4MeBM/e2nzTGfML9318CfhRb\nNPcXjTH/99e+jO0uOt6oD3VQwHp5HjtKVK9HAgOowjRf+3Rc1z14EM5WFMUDaY1Bh/kBtMMtPrqj\nRsVxjIm2RYf8+33238tn+gq3um6szKqjYnnooKoqUhWRKBkmvO/KLoUgS9NQHZbnOXXbYSpo6prW\nFRt0laHRHaqpUHXfa9KomEk+Yr5YcXJ6k/Ory6B+OMpzu8jqCiWgdpho55oSx5Hi4PiYV16yBUTf\n8O738Morr7BarUjdxPfe5yjLSZKEw5NjW5XoCpjmV0viNKGtGwureO8Nq+E9mkyYzPZZbdas3LFW\nm5LlcsnVfM7R8bH1qgfPLhvloAm836Fm+e4YFnBBr3sRILKmZZSPwmI3ndUTqYoldbkJCzeJJUJ0\nSN1RVgV1qZHeGSk3wUjfe/mVcO6DgwM2mxXr9Zr5/DJgzsfHxxjTsbc3paoKvBrybM8pK3Y1s70p\nm7afv62vrdACoi7UCSg314xwtjuQoR2v2q/BLUPegTa0bn347jfS4JpLrynWm7CekiQBYYjdxhIg\nBUXQOemN+baXO6QVglsfsrcNu5ixh16HNsKY7UK+IXTllRmbpgnUXa9f5KGQYWFRURQB3nwQzOHn\nSpb5nEmD1tbRSdM4aO9obZlPXn/HHm+YR+uwzuxbh1J2x1vxyD8O/M/A3955/b83xvy3O1/sfcDH\ngPcDjwL/XAjxbmNMx5uMXTrRg/Br6KshtdYY1V2DJ5RS6Leo/DjEpoYRAPTefaP79wAuCpCBlhiM\nctd77tYDHH4PFRbPcLKGsl03Gf1un+c5V1dXtoQ7y7aKg7xIEU1ncVC3EGohabTtQC7jKDQlyPMc\n1XYYIeiELXkGqLuOptZQVxjRUbvJu96UvP/976d2C+COSzICRCoJYa/uWhqX2OtcUifPc5Io5rkX\nrITuX/yL/yk/90//CQq7+ZRVGaASpZTF+pdLJrMZyp1jOrUVq9EoYjTu6VtJkqDi2Ip+SYGIIyKH\nn7faUN+9S1mWASICqNsmRGxSyR72EMIJorW02oQCDKkUURT3tESpQgGIAHTXWWVJFSO14yA3tRXB\nWi3ZrJdkDrfPEknTVLSloihtAhm3iVZVxXK+oGkriqIIOQhjDC+//DKXl5dczq9CfsBHWVmW2SRw\n0hszT5k0xoCSvchSZ424kSbo94PFzgOkYgSdNxzCwywe3htg2ro3iJ1uHMnAXtd8fhlEzHysK2pj\nvcuB5w0QxVGg5Q2rJ3d/D9ebd/B2I/M3G0LY6lt/bn/+sixtAxK37ocKjFJaSuRw49lsNsGz36VY\nDiVApIMaAaQwREqQJhECTV31sKjWmkgJm/4wJnwGY8DRXaXY5r2/UXHWg8bXfKcx5tPAxVs83keA\nv2+MqYwxLwJfAX7fW76ah+PheDgejofjdz3+bTDy/0wI8aeBfw38V8aYS+Ax4HOD97zmXrs2hBA/\nAfwEwNHeZCtj+0YeufdSoE+q7GoX273J//jh/x5giK0eJDsBRCD8W/K/HjTf7TFnhADXespfWtN6\nrzraauLcexPWq1IyHpSKu5JfgxXacQmppu6QIiJN8q1QUju9BiVjOiq6ptdknoxGCCFYbdZ0TUPu\nkp9KKSJX+WgEGOFwucayRbTWFHXZe1+rkqbVGCRffu450C2TsT3WuixCebUXIQMn5aoksZKc3bnL\nU48/AUBVFCwur1wUEVEUBTPX5DmNE46Pj0NDaA9VqMQmZG34bcK9svBUapkmccz+/j57B9aTzcYT\nEIqyqW2C0OPBKISKKaqG6WTM2rFpiqoKrBXR9kVdcZIQpX0FomcP+eeutdUeX9YXW4m1qizZrK5Y\nLhaUruxadxVJGlM2bWBz+OqXui5ZL+dsNhsUved7dXXF3bt3Wa1WaNHrpqRpytHRUS/oJPrydSEE\n0+nUStnORnStjyA6tNAI5YWg7LqJEuvBYwRaMqAS+gYqdoVI04PorYuW66akq3v8uusadGujYhXJ\nQPftXORicfswfQN27qnAQ4ycHeZYiIBVn//RWlM6uGkIh2qtaTvbqg6g0x1ZnrLZbLYSlwb7eWMM\n4/GY2d5xuF5va5SjKsN24/Tdwj0fofjXfc6jdno7Qhvqogw4/FA7SWgDne4jG0A3LUbYiMoX1dpj\nv0XmBr93Q/7XgL/iruOvAP8d8B/9bg5gjPlp4KcBnn701Ayr74YUnCEF0Zc2d53lkQ//Lxh+QfgJ\n5/Kv0b/euaQDpsenfZjdGY02mnwQ3g7HbjbZl9LvajN7bLVtW2QcWVqZ6sNGLaxugxBgnAGar5aM\nx2PyaLylj+ITRY3uwGXSvaEfTyz9cLFYoOmQYxG+jxECGSkUMYnpX++MRmNoWh0qQaUQLDcFnYYv\nP/87PPvMU2ycAdRdw2SUESmF7tqA/+VpRhxbps7rr7/ORz/6UQC+9KUvhQ25KArSNA0La3+2R57n\nXF7eCRl+gMVixd7eAUmSsF4vUU4BMEpSZKTQQKIU4+ksbFZpllE2LfcvztmURUhyj8fjgMvvzWTA\n57XWJJmvK+hCPkEqhXRVxNFAywOwFDi3AOernqophKCpa6piw2bVyxMY3XB6ekrXVHQuSbxxhqYu\nKzarNVdXVySRpCjtYvddoZRSRHHEeGI51jdunrC3N6Wua5IkCvNESsiyhEceucHLL79MHKVIV7mL\nFOAMzTChG8cxVVkPaHwDHrnoKYnDPI6hs5rgjdf3tvNRtx1pmhInEZFUIRleliV1XYLWW8n9kLAc\nqAJeW7uml60Ay7nH9HkyvxaGsOZuBaf/2/d/9c7fkBq8t7cXxMeWSysF4bs8+XNbnSLFZrMJm7tf\n98MuQFJKNk473tuBKJLUdc3CVef65zoaZe76Gltpjd+oGrrOQkGDXhThWt7K+D0ZcmPMXf9vIcTf\nBH7e/XkLeGLw1sfda286pLK8TD8ZvJJc4hIR3mDVZRUMmhZt0Elw14GVqnTHHBT3+ATLsPBm6N17\nup+XRg1dRJptwN1PGN+UwU+ebDwKXpwQom/x1DZoo60RZ1sECywm7MvbPd1MSjsJQgLTY9QuS14U\nBYm2xtcbQCOs53Z8fMy6KIInkKYpozil6Vrqq8s+SefpUUaTj/fZbOz7zy8u+FN/6kf49P/zS9y6\ndZvZZMrhvi2ciCNrDMd5RlNXJE7OdrFacri/R13XjPKcG05M6wuf/1WaylIm92YzxIBO6DfWqq5p\ndReU/g6Pj2ialjhJ2DvYD9+jrmviNCWKEiazPSbTaejKkgb9b9YAACAASURBVE+mvO8b389Xv/Ii\nL77ycqBiRklMUZZko3wLc+6M5vLykjiOOTw6Cc9cu3t6tVzYe6PigXaJpYbdu3ePrlyE+ai1lRyu\n65rxKA+G5vz8nOloTN2UofTcdw9aLBacnZ1ZpkdVhPk7mdjS/yRJOD46DIqQBwcHdJ0tGrEtw1xC\n0/UL/cpXvmLzDcVmKzpN0zzkZsJ8LGuMFG5+J0GsqnZJwDi2tNRis0K7tFZTVlxeXHBxcUHTVEzH\ndtOfzWZ0umW1WFrap9vY27rEdB25m5+Z20TKyvY2rYuS8Xi8JVtbliWbzYb9mW1c4teCigR0fWHY\n2Mky3Lt3j67ruHHjBvv7+yyXS+7duwfYyKaua+sMuQS9Xz+PP/54sAVDnN6vY/8Z6JOds9ksGHs/\nV8bjcVjLHpP38/T+/fvcu3cvtJUDQiTi+edZloXzr9frUIg3Ho9Rss8j/W7G78mQCyEeMcbcdn/+\nceA33b9/Dvi7QoifwiY73wX8yls55pBK6JMOlaP8XIdP7BgmHcAaSiUj28rLc06dtobRIIUijuzN\njaOdRqhG0LU+1Gvp2uvJFa8aJ1VEnAgil9yqqoraSaIOJ0bXdcRxbEWPHHQ0/I7GMdns4uyjEesN\nSrquT9a0reeva+s9SrmlwIaUlp2gJMJ1ZRllOa02LDcF68WSsuwFlzKnhFd1MVVl7+/pyQlVVbFe\n2/6Ri8WC6dhVPhIhYgVSoaI4RBZdKyiqmq7TPPHEE7z66qvhXk2n02DoptO+Z2g5n9uCIMd59xtS\nnttGwaPRiKqtyB33O45jZBSDtMUXQgjGM7vBNJ3t8xilCWmeISPnxauYJLWedu02Xv/+um1Aii2q\nm9+ATdvZ91RN2EiiKgJtvcKmrvESGEIIpBLEyXbVcNM0nF2ck6dxoLB543R+fsnFhTU2xXq+1cFm\nOp0ynU6ZTCZhnm82G/YPDoIj4hkpQ4ZHHyHKrd8hKvWRWKDZysCWsnMuDtCCkTb6aAeJOuvoSHQr\nw7k63dI11plSSiDpm0gvl0vKsuTgYC+0uPOJ+izpq6z9hpilKRcXF5RlyXw+7ymZWcwozUKisSg8\nVLFxG9mK8TgnjhV7e3Y+RJEkyxJ80ZBnlNjNYoWUE2azw9A83Cc5fQ2Gn4v2vqhQtf0gYkWgP7pn\nUVUNRVFhjGA8nm7JCtvPWZE6K3HrTa900VhNVTWM90/D67udmt5svBX64d8Dvhc4FkK8BvzXwPcK\nIb4Fi1a8BPx5AGPMbwkh/gHwJaAF/sLXYqyApXkN8W6PibWu0KafcNuTd9fDNcZQt2bL+EsZunw6\n7zzuX9d9s2Qb1jhea2cQWqDEg8t/fYjmr8vjgsBWeOYnxmQyCdTJQBFrW8vj7mx477cMISUqihBS\nUjeNw8Zt0ZFx74vTBCuJ6SGhvtosapotWdCua0OfxMRNjCzLgoeISiicN/XUU09xfs/2dcwyy1JZ\nl9YbynWCFAkChYoFwim+aVOx3FQoKXn/s+/gpa++YM+tDbPJxHJr3YbmDaM3MFbtLglVl1GS0Lba\nsUUk2ajnDXed1QqvqoayaTl0XlAuItZlwWx/j8PNmtIZICEleWy90rKsA2zmN++6rq0UbN2HuFXV\nG/a67otGlFLgKgarpkJGfZTk54IxJmwivugEYL1YBhYSwGI+Zz6fY4xhOT8Pz/DgYI+9vSmPPnqT\n/aPDrQIiqRxeLM2gy7rGVzca023BGLbGwEJllp3iHRRrTPwRvDGJItu8YVhR2vfHtIZ6lOXWKDtg\n3WPiaRqTu4prf3+ltI2hfeGXHz469pGMdDDRZDxmPB6zuLoMBt0+QwtnRVHEeDxGy57ZtV6vbb/S\nJCHP82CAm6axuvlaMxqNgoe9XC65vLxkNpsFJwJsJKS1DoJWuzZoWLXdO1W9XWrblspDalKQ5Bm5\nUuwdHoQo0EsWVLWNiLToPe50lINjVQ37AO86rV9rfE1Dboz5Dx7w8v/6Ju//q8BffctX8HA8HA/H\nw/Fw/FuNt0Vlp3Yhit/BhmGLz05DX8bsOaJbiRHhJSfbrZZNw6rHYVHBMLmyW6gTXnPcXOPDw0Ey\nSPjuA0CSWQ1lj3/5KKEoCrubRypc07VK1AeULvvr2pW79OeO0gRtLDfcDxkppLbnUM6rXK1WdMbq\nb88m08BeyHMrHbspC4RQ5C5KOT065N69O0zGY87v32M8GgXviM7e77rTxLHCCwQYIsqqsBrje/v8\nuoMQbMNhwyjLKJtqK7KJXNSSZRlJnvfslCjGmJZWdzZB614vioKqrplMZjS6C94LQD7OSYWxyUVt\nghRuUVeoyDUXcJASgHDRmseYfWGIje5u9/IFhvDdh/NpqBHvIcCu6zCdoXAa4utNQZokrNcbXn/9\ndc7OzqDrYZf1em2hp1EecNeTkxMeffRRbty4QT4Zh3ma53mQZ2jblm5n/vg5YQuKr2f4tRgqpEhX\n3en+7ZONcWQ7BmlB15oAS4B1wNM4QY6E5Yq7tWAjUkOWZCHPAzCbTTg9PmLi9HH8WK760v22bZnP\n56Fp+Wo04uTkhPPzc+7evRu8ayENy6oO3PPRzEZhe3t7aK1ZLpdIKRmNRgHGWK1WLBaLa2uxbduQ\ne7LtD73kr32GQgjyvGeKeUgwFPSZXoDL26oe2vUNZlIODo9RSpGPJj0nHIlUEhWBNoKmtXrw9tkp\n4iRDSJsDa7vtYsK3Ot4WhlwgrmkKe2xxS50QEaALSU9pgl4trKxW18KSrSz8YFMYCmD5Y/hz+w1j\nGFINy4GHk9QbRv+5Ie7qN51hCO7/zx9r+D284JA/t5/Uw9BRRLazjNeACedSw4WKwy9j8tQ2RYgj\ne4w4jm3fSF1Qm5qTY0vlW68WSGFIIkWWpOSjvp9n27YYKRgXJZnJwkTUUtFoyWTPdu1JXd4gThRl\nVdgETrktCBQ26UiFJBBAmuXEqQlsA//99GZjJ3yW2qYSSlK54qak8+yJFIRkU1ljWp6dBSrnkEnk\n54bV29iwWVr4RGvNfL5gOp269247EMvl0i5c6tCoREoXElcWuvLJ0dVqhTBW4uH++SXzq75zve/X\nGccx7/+Gd4RE2c2bNzk+Pg7PZpjs8nOiruugtTJ0TnbnuHBG2khfc98zpey8tvPQM2CEEOiuF3dK\nDMSOStk5IxbFKqhk+jlUl13QQ59ObT5jf7bHaDQKol5+LazWiwBh+rVeOthutVqRZVlI/Pn7WJQJ\nk3w0qHa2zzbLMtI05vy8pK4T8jwNtmO1WpAkEfv7e+zv7/dURgmjUeYqOXvHzVd7jkYjlFJh87aJ\nZc14PA5EDJ909YWJw8IiO6/bkFOQMho8Q1dktkNn7tdCQ9cZ2lYj5LZj+lbH28KQ+8qqIbgfxzGl\nEJRl2Wf2R+OApXumyTAzHMcxWmiXCBySWN3kNyIYgLJqtqoxew66xQ6FspQq6327tkwyQnhcfSBJ\nO5rEKGUX/Hy56HnRynaDaQf6LP4Z9lotXuzee3n95iFlFDyN4EVvNkjVYTq91d9viNl7o+E7rvgJ\n59tLxVGEyDKM1rRFGQz5Sy+9xLve9S5WyzmT6WirK4rH7uZJTt3qcF1ZliGjlOObj3Lv3r1AZURo\n6rp0XlFLa3rtlCiJrRCWZstgWyNrDehsby88966z7bgmkwmjyZg46hkBVVMzjhPSNGZ2sM+N4gYA\ny8Was/P7rIsNSbRtyLMscx5Vf6+ytqMs68Afb5q+DVxd12xWa6qixCT999Bas3FqiLrrmwaXzhBV\nVcXl5ZzFctXLqVYNs8mYRx99nJs3bwZDPp1OrXGsa1bFhuGI0yRsQEOtIP+sfbL+QbqFflPCzTZL\no7O0Vy8bgJF0XUtR2U1mqnqnJnbCXk1bEw0YZEoJ6tI2AzGm49mnnwGssF1ZlrRdHTYl6BunWxre\nyD0Ha9hat85OT0+RUgYJgySNePLJJ7lx44Y1pI1dV75r0mg02qqA9d93PB6Hc3gnbDwec3R0FNbQ\nMNryctKehmjnXK9w6o32UM3Q2wZL3bT3fblac35+bl+nZ7OoyLLgPKY/tHVdZxtMawNCKpraUaBb\nQ1N/zfRiGG8LQw59B3KwDyPLsiCBORSy8T+KHl7xn/Hhkfe0/fCecBBD4rouypCh4h/QZrOxui5u\nsgylK4flv76c3lMHe6GrPGTF38iD8klK/3ccx7RtG7wybzBHDubQWmMiK3zVDDx/hLBJ0wFcYydN\nTiSVS3i6ZC2CJIqJ8jEyzUj9Btp10HXMxmNW8wVLpzQI0DYaQ4WKFpYp4m5XOhqT5CNuPvIYX/7V\nL5Lmjj4VqeDdelqdH2mahoS0lHLLkCsV2+1tkHgaz6ZbHsqwTF1rTas7dG0plY89atmv988vefHl\nl1itVhwfH4f5kAwW8WZThmcVOymFqqpYrVZsVptwPv/sxuMxpH0Cz3v1TWP1w/19r+uaNEq5vJhz\ndv8+RVHjU/5dB9nJmMcefzJcPxCSwkmSkJlsiwo7m80Cm6keGET/+a7rEAP9Zu+N92X3Q02TGLCa\n/joskS7MufV6jYplmHdCCDaF3cQmk0kvsyDs/Z5Op+i2p8n69nZtqwNlE0CbntMthGA0GhHHvoDK\nRrqjLOXw8DAkmduu5vT4hOl0ynK5DFCih0KOjo6CFop/jv7vurbt4/xz39/fZ39/n7ZtLQ1yQMX1\n87Qoii2oc7FYhER9nudBQTOKItbrdYgyIwfTRK1GOa9bRgkyGlCcVUTVdKhYoJF0LqJtNRihSHNb\n93D3dQsN+kjhrY63hSHvOiso7zPMnnepnKfpF14SJwFaEXq76tMbsCRPAkvDv+5hkmFWeKiENtwQ\n/PCFLEOa1IOy2mAxXJ85H+qjTKeWguQnyNCQ++ENlD+uf79v3ut37qE3ECdWB8RT0QSCyBtxtlk2\nVoXPUrjaalDpZgxIyfHBjMpVH+7NZsznc05OTvjqV7/qdKYdRm4s3bEoKoSMiOKe7RHHKfv7h2Hj\nA1spube3x3w+p21b8km+pWNhGSAdWT4KRiDPc/LRhJHDkVtHB01yu0muNmsoBXGa90bdPYuqqpgk\nMw6ODsO9L8uS+/fv26bQLiw2xpAtLcvCUsXsvRqlWdDiODs7YzlfBjhrqNpXVWWInprSGv3OwTu+\nGUTbarrOUukWi5okgdHUzu2uaQPbZb1e9RFBlnFycsJkMmGiZkFITAhhm0H4vI3bWP182HVadufW\nri2QUgadnOH6aXXfjb5oeyjPU/M26/UW99tg4YhnnnkK0/U04LZtme3ZYpqr84vgXY/GWehFW1XV\nVmGQcjBqWVfMZjNu3rRNSxbLK9aLJavVyhbsOCfB8649VXN4rOPjY+7fv896bYuu/PCUTi+SNSza\n89feNE0w1oDD8esQwfloUykV8jRDT31/fz/cN99j15/D/7+lHvbaP/67+OjC2yfv/L3V8bDV28Px\ncDwcD8fX+XhbeOQIgZERrc/kassZN1FCPJKozIaZXdcR5zbTL3bw81prGiGgMagoA+GqQesag00m\nqihDyB4D6zpbfixktCVC7z312clNu3P717OcKEmQWtNFGxqHhcZCoGMrByvzSYCEuihFZGMmoym4\n0Lv1oVuWMXJl5FKpwIDJJhPmRcHKeQLC7fA1sKwqllXF6WjKbDTmaM9W//lS9Pl8zijPODzYD7f2\n6uqKqjXk45yVsV60jzSapuF0dsqtW64AIzakqiVVLfuTmINpwt17Tmc6SjBCko1zVBxx6cLfvKiZ\npWPurTbEIxCJ++5ScLkqaOkYHx5gpMQ47vlkNCEa5QgjSKZTMlcl2ikFozFKa9uWzuPzXYduNXE2\nRsUxbadRDjiINCyu5laCVG2InW8yyzIOxmOKPGf/9CaJ08O4e/cu6+UarW3izfPpV22BGkesLpbI\n1LB/Y0o0YApNJhP29/dYXlbBmwLDNJmyKVYsz+cYl7PIkoTz8zOKdctYQiygW9uIII3gaCyYRDXp\nyWMBQjk6OiY5PIKplS/oXIhupGDe2i4/cjRiNPWa2EmIFGohUG1L53JBptOINkIoX0jlS94FRdXS\nth3CaJwCAkoYqnLN5vwOF3fv0UwihOkbXjx6Y58zaiJRo3B8+AtbLTsajYjTlKLoO1ndXlyG4p93\nvvddYb1lWcbl5SX3l3MOZnsB3lgsFhweHHB+fs7NKCZKbfSy2jSULQgRU5uGrrLnWCxLpztTMZke\nMp0dBO+7blrSbMp0dsSNm08ED7eua156+XXyPOf09FGi1M7fqqowMubg4AAj41C49eUvf9kmfvMJ\nVWtojUTGdq5II2m0oDWSNMkHxT3w6KOPu+rUK9cgHZq24vj4GBVJothw584tyqqvGs6yhGyUU1QX\nnJzYwibPsnmr4+1hyF02PYTlTp4T+rAWeo0DD4UMC3FC0ctsbytp4UtoPR1qWI5bVVXoONN1XTDk\nnu4Ux9EWNjvE4nwiEwiQiqcjDZOdPmEyc7CFP3+apiEb7osR/PV6jRWP20FfwOTx5SE10cM8/vr9\n/drb2wuSAkNNk7quQ3a9LMutMN3T46qqYjKZ8Mgjj9jrUjFV01J3UJQli5W7rtuv89hjjzGfz7cq\nDxVO2wJQcWylf10kX9e1pWw6Y7RVJOWM92xveo0t5P8Wgq3PeMhqKNkwmUx4+umng3SqnFgjt16v\neemllxDC8Pjjj4eS86at2Nvbozg6pusaG+q6+VgUhcNbW8ZjFbDdslSUYk2nU9u2xNMrJTTNjFFe\nW4Ek02uB5FnC4eEhBwcHHD/5JI89ZjXlTk9PXfWmrYBUUZ/81lpjpECKHkKQSiDlgCorejqsn7Ne\nbjkIiQmvt24rnnt5ZhNghyiKAn0PLC0SrFTA5eVloGvaCmDbmWiU97CZJyD438fHx+EeRlGEblpi\nqUKZPtjkuy/O2ixXofeoL3Nv6waJ6J02xzibzWahO71nV/muSaPR6Bq84gkRSqmg657lCVLC1fwC\nhGG2Z+fD4088GtZunudEsWS1XoTv0ukGqaDTDefntnlGHMdMp9OAp3s7sClWXF5ecHBwwHpt17WX\nYGjblsXiKqzfWb4XrtXbl7cy3iaGXGzpH3iBmqH6HBBuau64x56iCH0m2VePDfHYy8vLgEN5nGvY\nq2+3QtRParGTEfdG2m86Q+0Fz/P1HVugN6j+uheLRcDmPEXLJ02GLASf5PSZd+h7EWZZhtTNFie9\nLEs6bUjSvp0awNV8QacNUZwwnkz7JF3b0bQdk/GEdVFtSSCE5J9LwE7d/VqsrJZHLCUaQezw9svL\nS05PT7l16xZN15IOVH+ElMRK2ShGqZAgFa1jHrl76is9vWdj6aUmVPImrmJSY/Adj0JSSgmEhihW\ntG3Dcm0NTZZnPPXM02SjnPOipnUr16suCmG4efMm0nn2TZtwcnJCPZkihE1sxm4+zudz7t69y9XV\nJXGc0PmsW6iqdLkMV0EZCUGSxKSJcptX3+rt5o0bfMM3vJtnn32W02efDYZylE8s5U3YueE1VRaL\nhcvnODVB70VLZ4yd/faKjmClKKSyPUitIfdOggwMJ0vf7b+Hfz1NU8qip1Lmec79+/dJ44Szs7O+\nIjGyztb9+/fRgxoQYwxXV1d2zqcZmdPqqasKkoSqLkOnnPHINV/OUnTTEAlbibyYX7n5IIOj1bQN\nsZsH/nOjPMPojmJTh9fSJKYqC9KTY1bLLhwrTVOUFKyWC6QglNUbYzg7O+OFF17g6OiIGzcs62lv\nz9IovaZSaCUJgVThacNG94JsVnXRSWHk9p5M2glx7OoAumaLtujL873zWJQ9sWNIEPha421hyL1H\nMWwF5nfroZc2VFDzhmaYqOi6jqK2iZQodapnTU3dtRR1RZz1fNPF1Spwr5P/t703i5E0y/K8fvfb\nbTdzM3dzj81jyaWqsrOoZQSaUlNCCA1MC6mBB5h5GiSk0UgIwQMPjQaJEW8gDU9ISI1mxIBQDw/D\nMm9Ao+mZ6UYNXV1dlVWVWVGREZGx+O5uu9m3f5eHu5h5dmVlUlPdkZFpRwpFhLm52Xfvd79zzz3n\nf/7/WrQBQVQNK45ukzfXAOtI1mwim5X9TWrLzeq8sTjNEa5PWNObVRDheD5eUFIT600sz3P8sIbr\nh9RqNfsZWZKAcBUTYCGvkYyZ+THRurne0WhkC8ebpxxTbR8MBlxcjXFcU8xVm1AY1Wi327Ypwv6O\nH+C7Lo7nU8vVZ03PL2m32/zwhz9kL1rfQ8tPYVRhvMBSINSaHo7wWCUxTu5ttLarwpdq9hjbOTHF\nJs/RsnzCsQgc33fJskS9vtEaHwQB7XYLxxGEScH4Shfd6nX9sCoumHipHsJ2u61gYcKhKBTyKN3A\nFJv7HTqhLQ5LmRMEHp4riOMVjtQF61pAkaeUpRJiCLSMG8CbD97gwYMH7O3tKfmvTF3vopiSpqlq\nLHMFSHMKLDUqRDlnD5P+c3A9qRy6IxTLpZH+04V8E5HbQEj/3LOb/bq5qCxLhFTPWKfTuYZCmUwm\nOAiurq7s2rp1cIN2u83l5SXz2YwbN27YuTo+PiZJEoa7e1Taw5gI8+zkWLXhr/ZtVOo4DlWZ47mC\n0WjEQjtfJTQC9SgkaLcsmoVAI7tWS8ZXl2RZZk+OjUYDIT0Cz6UqlKIVQOh7FJkqUNbCgKCmESi+\nj6gkl2fn1IKQoquKzFGzie+4OH7ASMNHTRBYq9XAD+yacPXuulwuydOYPFXMlE3D0On5BIFvN/vl\ncsnp6TEA5yenOI5DLfAp0ozhwbrILV8/HLmOijYeQrtDaQQHrFkRNyP0NeB/TTJkaDHN681m00K4\nNjlRPt7duRmZGoghcO2Ib6BomwgYw4poGn8+DvgXQthj6GYl24xtM71guvgs3GwjdWTSC63Q00du\nO4O4rmK0U6cU9Vn9vor2kiRhMpmtSauSTHe+1QnD1bWoX+hqvOcHlNXSXle326VCsEoy1SlYrZXF\n80w9vL3be5bnpZISTzg2Nea6LoZ+OgxDC33zPM/mqR3PVYo7yyV5ttpAjSjSJsfxcB1FMmZksYoi\nY7Va4GoFGtcyiVWEkU9U26EXtDjXKZQ4jjk/PyfLEnWi0pFvVFPH7noYUZaKr2NpEDsoR9/ptJFp\nznKhcp9Z6lOvqyBgNhFUmqq21Wrhuw7zxZRkuSKKIgYaq787HFCvq++IVyurjlSr1XAdiJcLlvMZ\noc4TB1Goxuf4OL6HNLSsQoCrnLcQRo3WsHnpzkyh+Fg2G4KkNMRZleXwztNYSdJlGWWZ21MYrOUV\n4+XKMgGCcpi7u7sKUaJTT8YM5NZ1XQrdxNNu1gl9l9VixunxS1xZkevmLSkle7u7lGXJfDaxKbhO\nq2H5y8syJwq0u6oKoiDCdRTbYpnnLOfqniSrBZ1Oh8VswnI+tQLI9Uh1YjpUNOsRY10zabVaFmNu\nlIVABUEXFxd2M/F93wYppqFrs0MY0Lws64DTBHRFodKnq3hhodWbGrKKj6mlSfkMjrywNbjPYlvU\nyta2trWtveb2uYjIpcRGs+r/15tzzOumI8pEvZ637nw0xU5PR9YmWo7j2BZaTCEC1E5sKDfXhPDr\n6aiqCnSkbHbpzU5Sww1uzBQUN5nYNiP+CqlyfGJddJvNVJRsiqWAxZOa5iJhkBA6ByiEoJQK82sa\ngnAchbBwHIqqsnwcQmPwV0lyDZPe6/fV6aQoCGv1jU7QgrkUNse5iZ2dzpeUUnXE1htNi7e9se8y\nn89Jk5iirGxuV8q1WIbEuVaszPMcgRap9deFpyxRdLNX4xGDXh20NiZVjiy9tcakxIoAp1lKkqW4\nqwVCNNbNGXoOG40Gq9Lj9u3bdj2Mx2NWqwW9Xs+q5EymI9X40WrTaKj8Z7nRcKXmSJLECySa49qp\nCDwVfaWhS6rrBlWZg6goigwpS+r1yHb5NZp1vNBDeIJWo24Fmx1Z6dQS5FnBMjeFNRfFWFhowkMd\ne+nmrdIRuKj32LoBqk2fskJSUbHO7Qr1D4X91qe9eLliOVfCz2kc06ivn4XFYkG32yXwfIbDoaWY\nbbfaNJtNbt68yXw2s9/t+z6Hh4fqdCdhEav3F3lK5bt4rqBRj2g16zQ1RXJVVdTDQNUI8szqsUah\nTxiqNMrF+al9RqbTKf1+H9/zGfR7NBoNW+y8urri9OTIFhttZ3QUMJlMWCwWjK4iCNa1Msdx2Nvb\nu1ZcXCwWFEVBvV6n1+vh+749jRhWUxOlz/VpQM1BTT/zbBTFVafre++9R1mWvPnmmwyHujZSr9sI\n3nEczifrfPtmk+Sn2efCkZtFYBygSSmYgWweQ4Brx/VNpEsQBPiOY7s7zWfP50q9JQgCe1QKgsB2\nfpmmn00HnGUZnm1Hdu3vbKJlNjtOsyy7hgwx320agRr1pkaQqN8pVUuX4j33FX82QFPzGBdFQbxK\nbDqi3epYZMz48ow0yzdqCoHNgW92XRqVFC8Irx31TJHWkA6ZDakwogXVeq7NJqqUXzIWSU5Uq1ML\n1fUO9obMJioXX8jKolZKJG4lqOSaUybXcmfSUQK1pjHCPITzlRJhyNKE+Ww9/3mekucpYVjD8T2c\nDaoDdU8bSClYxCu6ujZijvdBFBKv1ipIQRDw4MEDFosZUkoW3tyOb7lcUg8jguC6oIlRXV8s5rh5\njGOQOa6gLBIEHrUooNRFrvlc8YyXeUYQ+rQ7LeqN6wiEWq1Gu9Wwa3y+mKruRV3/MCo+RVwxHA51\nvnvN3yEcSSULdbMqB1wXoYutpfSQmLRLhRBmQ9JC4LK0YtKw5hBfLWZKUalbt9c5m82upR/s2pko\nKt5ut0vg+xYdkue5JZ+qipKriVpbR0dz6lENISsOhnvcuLFPW98TUzT1HBfXgcA3TXc5LgHtTpss\nXjGZG073C4LAYzS6JIoi9vYGLBbqZ1mWMB5fsVzOrZq9eT2OlywWM87OJPfeeldfb4asKoZ7u/pZ\n0kilmgoaG/UaSbxitVzzGvmei6xKilzVy8xmXAmo2yt/GQAAIABJREFUSpVqKYucUKeCBKoxr1lv\nMJvNFL2G4XtPVE0vlyoQdVy1TlxPEEbr+/Bp9rlw5Ea7z+yexjEauN3Hi4qb+WizGJMkUTCxqqSU\nlXWozXaLRqtpkTCjiY4o2m1WSUxeqtbhRqtpd+QkSYjThEgjQ4wzM1hzE/3bjlPt4D/eubmJvGns\nNFWRRxdfXM+l0Wri+orrobujihxGgi3JUiaz6fr3W03CWnSNJ3mzK9DzPNttZrsV63V7/Wma2us1\ncyqEoKhgrjHOssxxPJ8o8Nnptq+dOgaDAaPRiNFEORxTONsdHjCdTmnWI6XcbjyQVDzwju6clWKj\nKItQ6i95yWy2sE5gtUro9XpEUcTFxfG1jSfLOjSbBfV6ExEKi3BpNhtEtRrTxVLBO3UR1vFcWyjv\ndLpW7SnLMh1huZydnV2Dapp7aOZwk0QtyzImkwk7NYdmQ63HwHc0wZdPrRZhiofJaknoe1S656Hd\nbts1tNQdko1GgziO7XdkScrRi5dKcWlnh71d1d1Yq0U0GjU2ecSVCaVwL1XdxnM2fiqlUvipFEun\nU2ooo6O7nKVqmTfoiixPbU+GKexasquFitQDz7fIL4CTl0f0ej1bTDXjm8/nzGYzarXamsMcuDy/\nsJDdXq9HbbNLVEpcoWpZ/X7f6llOR2OS5crC+UzBuEgzOs0WT58+ZSYn3LtzaHnaG1GNzr37FoJs\nBDIW0xmyKGlENZq1uqUOMDKEg8HgGqumkX4TQvDw4UNmsxmHh4eAgorOZioQUHOgpn1d1zJF+ev0\nIYPBwNbvXr58qdf8ihs3bhBFkQpe3TVy6+Nd4L/IPheOXIjrxO3mhsdxzNXVlS0m7O3t2bTDNdIa\n1lH0cjG35DSgHHa327WOznzH0dGRbZc1hU1TFTffd3V1dQ05EgSBIrjXXA6baRYjHmFurvmcy8tL\n1cDkudSaDUveb5R0vvrVr1Kr1WzzQBRFLJOY8XRCWqwpU5M8w9VkSq4fUsoYoZ1pKVUR0nU9Wp3e\nmldEE0BNp1Om8+WaKdIPLcdDrR7S2yjmUhXEywWT2eJay7ArVPRVSkjzkkqnfJr1iOcvj5nP50SO\nQ6AxwO1uj7qW1Sqq6yeYPM+JityeYow8m4JcKl3WvcGOdfCj0cjOt5SSUDYIdIFU4f99+v0+/Z1d\nC2XMsoyw3sDxg2tpnU6no6GjEZPJhJPFujFkMlFOoaoKe7QGhaFWNAwRk6MPbXQvy5zVYkVVZIDD\nQjeTGCbEXq/H/v4+h4eHFlVhNgjXdTk5MSJb6+JaxXW6Zd/3ieOYnZ0BWZ7bhhXP06cwVMrMFVhC\nLaqCsnLIswIpMsvrYZ6H+XxOsx4ReOo70jjBcxT2fnx1ycXFhXWarqt0K+e56kcwa7vT6dhxXuk1\nDnBwcECapjx//pze3a51foPBgCAIODk5sZwn5iRmIvLnz59z//59PL2usyzj2bNn7O4qSb7Ly0tA\nYds7nQ5hGHJycsJ8Prd49cvLS/r9Po1Gg/F4bJ+Fhw8fcuPGDVzXZXd3l49OR3begyDg1q1bhGHI\n06dPAXj06JEtTB4cHBAEgYWKuq7Ls2fPEEJwdnZGt6vWQ6PRoNfrcnz8UtNTqKCx2+2SJDFSluzs\ndKnVNk/tcHp6zrvvvstweMDxWPPMbMAdP4t9Thz5dak3o4lpMKTGNh3xx3kINhnN1jzB2Kin0WgQ\nRdE1HLlhmzOOeXM3VhGGsGRGsM5fG4WQTRIdw8hmSHnM9Rrnn+clVYXlBHe1JuR0OldUsxoOpa69\nwvMC2u3utQ1JSsl0OmW+WFJvNK0qvSF7MiRdZh5UpXzJKk7w/ICW5nMOI8VxjXAYj9danp12i3Z7\nQLJaMB2PyJI1oiXLMmaLlR67T+Svuc3LsqQWBtdqDEVZInFwvUDnciWOs57foihYJvE1UrIw8Gze\ntCwWdn6XC3WETmJFi7tarWi2zNhd/cfTUmbmmOusObnlmktnExEUBIFdczOd51Uc8ljeEVg3iFVV\nSZkXJCt1SsmSVEWclaQsMy2gpuak1WoxHA7Z3d291vwiXE/P5fIaH/poMka4Dru9ATu9gdV5zfOS\nNM3J8hwh1lSoru8hgSLX8Fyx0Q/gB3iuB8KhlNhNV+l2SxwXy+Bp5iSKInxX5YobjZqFBpqGG1c4\n15rmzGnN8zz29vbsmmu327rJZcbJyQnNjk7BDQY0anUWi4V9Tsxpz3VdJrMpVaF4bsx6GA6HHByo\nE18cxxydrje+47NTFcHv7XI5HvHyRMH5Op0OeVUSRCE7u4M1H1KWstKBIa6D1NqYw90B3W6XKPB5\n9uwZo8sLdb07PR48eMD+vurujgKfZn2t5ylkRZYq4W1Z6UalNCZeLZjPJlRlTqd9H1AII891qUWR\nTY9GHY2Fj2oEQcB8OuMnP/oxfldtSL1ezwpEfxbbola2trWtbe01t89FRG5I/E1kaHLAhkLS5MgN\ndjtNFd/FZpu86baShNcRMALiNFFdb45Y63IiSfOMWJPbh7WIQPMj42jkS1b8KbJ5gyHdZDk0DTa1\nWo3xeGxTAkII2u22ZvrLcT2Plo6i4yRRvB+rFe5GF5eJ9vcPDtgU7c00ssY0eQwGA3ucXCwWFjWz\nmdd++PChYvuLIobDoe1aC8OQJEmo1WqcX66bPNqoo2SZq0jUD2v2BHNxcaHm3HGUwK1moquFAWm8\nxBUSx/WtwkmWFbaIbAVDxJpetygKKCv8UNCI1oIXgas64Gr1hkWULOorijTDawSsVgmuH2g6VhQH\nieMhHA8hsIVeR/hIobpQq6qyQgkm72lQTGZtKbHgHkmSEEWqeWWlj/4nJydcXV2RpgkR1wtVVJIy\nL1glsWVrbDQauL7H/v4+w719xYWTpHptxyRJpiNjlyTVUbEbsDPocvPmTQaDvXXkW1VkWUFZSoRb\nKYFtLIyfCgdHOORFCphoXRVihWUJ1RQXlORFiieUkpbUyZhaLaQqMpJVjh+49oQJKiJ/9uwZaZzY\n1CHA1fkFw+GQqqrodbv29LLU/OymZ6MsDf0DpHmBH0aEtTpOmlFrKOBBp9Ph8mJEvV63rJVmDeF6\nfPTiJbu7u1bVx0T8s9k6ujfz5fsh9bpCVW3m7m/evM2TJ09YLmPA4atf/aq93iRJ7CnapJTa7TZv\nv/02o9HINh6aVnxzMjFF3VWsnndV5E4ZDHZ0H4Ca38ePH3F1NebrX/86zWaTk5MTktgUxufcvHmT\nOI45PT1FzLWQS57ie589zv5cOPJNZASsZY4ajYZq8tBHRqPSssmxYo5OxonVGzXr5GH94BouDnPD\nzPvNe4UQ12hLHccBqbq51uojC+UUdDORyaWb1xzHIUkSC9EyHaiO41A5rpURA+j3+7YTdDMfZgjz\nTV7WfFae55rD2WcZJ0znC3ydJ07TlLyscMsKp5LWmXV3FF9zraaOb3FqlOTVRhfVG5ZywIx7rUTj\nEIU+LZ3qSNPUtumvkvRaPcNwp2dlAUasOYkZSEEQRLZJIgjXhRy1+ahUiYHmOa5ysGVVUI9q1lkd\nDF0+ev6Cw06P2WTKjVu3rOiDiBQ5lOv5Kp1i8orCRVaCSiqEy2bhyYiT9Pt9m7s+OT3CdV3G4zGD\nwQ79ft+SZj179swWjT3hralGN5rDVovYOtl6vc7hnbvcuXNIq9WxXClmHuNVTpKkLLPEbuCtbo9m\nswXCpawqIp1CCX2PsCxxHJ9CVuSl6cYsdEt9RBCGFEm6Lo5VJbIsQTt5K+ghPbI0UxwmssI3Rfx2\nm+V0wng8pioydgY71+gyms0mWZLanLh5Zo3qfaCfVVCO0dR7BoMBXqS+YzpbqMaXVkel26RDp6vG\nHgQBjq/+1JotewuvRhOVuqvA80P2DxQvzcnJCa4XMJ1OefThE2q1Gnfv3gVgMp2zilPq9eW14PCt\nt97C80PKSn3uZj0sz3OCQMET14X3FcPh0NY0jMCGeRbNa57nsaehhI8fP2YymRBFkWqg0w1XioYj\ns02HZVlaSUKTatrZ2eHevXuEOv3pui55soY3f5p9qiMXQvxd4F8HzqWUv6Zf+5+At/VbusBESvkN\nIcRd4APgof7ZH0op/8anXoSOZjcXSUMra2+27pv/m1zwJo94HKvOtHanZTl+YZ3fNMiOTdEHE3mY\nSNtEslVVUavVSNPs2vcbR5xlmeWuNp9lnL9BJOh5QkpJHMcErRarNOFKo2aWyyVJnqlCqLtGJOzs\napKhLGW+Wq5JqDyXSkAhq2uFVVhDpgyaxixe047e7XavEUqZB3I+n5PmJa2WbiWu1akkZMVamm5z\nvnb7PbKiYrZYrougjiDwXI3sKGxXaZIk6tpdB+EKQhESOYGdX0PuryBX6/y1Oem4LjQbmmsliPCc\nY5Iko6okvheuRTKEh+MoQQpHuBRijd6QuFSlxPWuK6Ab5E+n07HFuMl0xHQ6xROORTiZ056Zv+l0\nQjZN7dhNwb3KVU2mVVOnrf7OgPv33yCq1ygLiZQQBMoxl4VAyjlFUeG4Lv3BOgKsqopSqlZ6X0ef\nbuDjVhVFUUKFkrRDR6vCwfNDgiDCFw7lRst9leeagybAD8wG6mvOHg8qaWFzMtB6spR2HW/qU3Y6\nHVaL5TVUVr/ftxQOqhirOldHoxGNRkPxkrfbzFMVYZZS0Gh1VPR9eUno+1aE5Pj4mHanp6CL9SaN\nuorUj46O6O70WSUZjhfYHoFao0Wr49Hr75KXkqurK8bTuZ1HL4jwjJaoCaqCiJ3BHrfu3CXLMi6v\nFGpltVKdt632Abt7feJkadfDs+dPcRyHfr9PrR7aQERKSa0e2jV185a6h8Z/HB8fW/QPwI0b+yyX\nMVWlxDvCMLT1rVu3bumi+A0GgyXSX+P3LSXBZ7DPEpH/d8B/Dfz35gUp5b9j/i2E+NvAdOP9j6WU\n3/jMV4DihtgE45uI/ONsggYfbtgKN1MrjUaDdruNHwXkWpoJwPE80jzHy3Mcz7Oah1lR0Gi1CDWZ\nlYFZgaaWrNeZz+dMJhMbnezt7RFFkeKDWKyLccY5CKFkpjbHYjeRRovZbEYcqwfk7OyC+XxOv9+/\nRvI1GKTU63XtkNfCrmUpyfOSMKzROFDwqUwf5aN6SOQFCj6WZKTZutDbSjKirFCFVvMg+D6OtyJO\nczsmUBtVnikoWqVPC4a4CpRDmy2UKIS/oUhjyL1Wmdw4Ia2J+8tSIISkrmlAha9ayLMsI0ljVov1\nvDuodnwhXMJAnwaSGfv7N7i4vKI32FXFYFe3qjsuruPjuj5SuDZdoPy8g5TqWFwVaw4YJSZS0Gw2\nbbrp8PCQn/70p/iOanB6+fIlXXNS0Pw5SZIgdXMVgCyhkmqNesK166HfU0U21/ERVMyWK6Z6jCrl\nJOjtDBCRe400K0kShOdSb7YJ9BpSgrwVaaYk5gKNeCiJKQtJUSkUUUuLNoD6v1JdKnHcyqaoHEcJ\nFSuEy5rIqxIqBdasqRNfs7kWDk4SpQxkgpWPBztJknB1dWWfnSRJuHfvnp2jyUw52H6/T1irk2Q5\nx8enHBwc0OmpYp5wfWbzkYpyg8jO++VoTJxmOJ5PXlbMNS/O/TfeJI5jJpMJ3/z2X2A8HtuTa6/X\n48MPP0QKRyFRanV7HaVUfQ9pmhJouGYWJ8SLJZOrEdPRmNGFQsacnJxwdnxCv99nf3+fZrNpT9O1\nWo1WvWFBFFmqxnj7xgG9Xo/5ZEoar6jr56rf6+FIBxfBYjpjMZ3h69PevcNDRebXaJKuYh49fgxw\nTe/0s9inOnIp5T/RkfafMqG85b8N/Muf+Rt/jpVlYTsc9Xdek2oyzsGoYm86zs1mHc/zKKlsNG/s\n7OyM1Wp1DRmjcqGRTauYBhJjrutaaslNUWjTWLRJQpWmKWEYWvyxcfwGZdPr9VgVBWEUEekHdDaf\nk+m8eaKhbwCO63J4eKiO3EJQ07CuNE3J8pyoViOdL+1xEJQjNSiMTVpao54ynepmE/1wGu6ZGzdu\n2BMGQOA5CFlpjoxKj38tc1ev18lLSb/XtTjy1WplU0uev6ZZVSktd4NoTODrFk6FYVaOqaHFdUEt\n3ixLqCqPVq3L0joNBTm7uLzS6wGL3jB5UNfxkY5DZWoglUotlFIosqQsv/Z+g1Iy97bdbqsjcJox\nGl0yn89pvfOOXXe1mkJyxNMRwlsjedRJUD900tn4Do9Wo01W5FyMptfYBHs7fUU4tZxS6Y06r0oc\n38PzfMqyYmFFr9XcxllKKQWBfn+aaaZNzTe+yXrpoyiDKxwQa6UZmaf6lFVoGlwN89Myb+ZkaqC6\nxtI01amCNUS3ygtLk3x6csKjR4/sXO3u7ip+77Ii0xuoF4RcjSeISpIXJctVzFKjf3Z2+vzxH3+f\nnZ0dzs8vMBqjjutxNRqRxomK8nU6TSJYxQmL5YrDw0P2D25wenpq70ma5YwnU4b7B/YEc35xqQjk\nohqO69EM1T08ODiwLKpHR0f2PpnThwnKNrmVzJo3PmI6U9G98RVSKsiv8UGbsNuqqhiPx+RaO/jF\nixf0d3ZZLRWO38RNTuD9uebI/0XgTEr5aOO1e0KIH6Ci9P9USvlPP+1DlPbh4k/B6eI4voapNa30\npki1CTMcj8dq8trNax2cnucxmUxsXmuTVXFTsX4TIrZarYjj2C5Ks+DTVB2rzTHYOF8DaTNK2+bB\nMbhXgLPpnL29Pe7cUVqNrusq2FMUcXl5aQsp4/HYSkJJKW1BM0kSzs/PFfmW3njMQjEnFXNaMdHR\narWy3Ne9Xs8WTk2uv9PpUG+2YKEiinoUELRblEXO+Wmm6gdi3VzUarVYxik7OzskhrVvsSBeqWN3\n2OyvYX66NmD4zV1XUNMP1dXownbe9ft9eyxfLucW1x+GISc6j1ivN/G9gFarw3y2ZP9gLY0Hju1Y\nZIPOwXbzS1UbMQVKs3mb+ogI1srmu7u7nB2fWMkvE60bTHmz2cRvt9c1k1jxxudpdq3harmMLWzv\n7OKcFy9e2Hu1PzwgqtVYLpfXCub1uoLHrkMJnVbSVKhlIVmVMZnujp3rolgU1W2AYubedVVuXFFm\nrVODRaVOsXmaUatHuO6arG4+n3NxcaEaYeqhjbyNIzu8fUczSqpndDaeUK/XaTQadLtdPvroI3W9\nQWBTLb4WnjDPyMXFBb1ej72DfZazOU+ePAHUJv2Nb3xDBQra2QHcvHnTruc0z+jpufre975HURTs\n7+9bPv/NOtpwOLx2PwDOz8+p1VTxPssynn14ZL+71WrRbre5e/euZXF8+fIl4/GYfr9vtUo3SbOm\n06nV0G221myn7Xab73znO3z00XP7/pcvX3JxccEbD96i293Rc6SeuUePHrHYVz0H7Xabe/fu2Xvy\n/0fq7Z/Vkf9V4Hc2/n8C3JFSXgkhvg38r0KId6SUs4//ohDirwN/HWCn0/z4j7e2ta1tbWuf0X5p\nRy6E8IB/C/i2eU1KmYLSgpJS/rEQ4jHwFvC9j/++lPK3gd8GuHNzKFeVQ8BaoceRLlUpVONOpBz9\nOM5JkjmtVgspBVI6a45gL6IK6sgsRkqHJDE8LQ6O4+O6AtcNSHQxA1QTyfHxMVVVMRgM7LHKcHWH\nYZ1lsu5m88KIZ8+e2TbvWnMNn8qyjHqrzc07h7Y7bP/mLR4/fszJ+QW1WkDoSPKVJt5Zzdlp1dnf\n36ddi/DkmlDKKSrSZMl4PCbUknVGxPaNt98klgX50RF7Q9XGTSU5OzrSyALJvm7vbjQarDRVaK/f\no6m5lo9OjplnKfliDlVpTy9uGNLf26MKI56cnjPo7XB+qU4K1XzG9INnCh4WxxuQQkmz0dPInIxY\n54LDSFCUfepOE48St3KQOpp0pcCVLrVanSQtmOu6weVYRVNho868gN1bKjopy5LFKuH+V97hB+/9\nEOl6VKbWUWaIwkW4Do50FL0rUA/9dectNaJmQ89JUxUVlxVX45HtbixlZVFSOzs7tJpNm3ddzuY0\nohr37tzhg7jk3n1VIP2jP/ojjidHVCKktTug0Hn7i9mCvfmKi+mU999/nzAMuXP3pr7eFcVSNZxN\nLkvCGypirUoYj1SpqdVq4YWabDZVBdVeq8l8PudMt3abLstQSCIHFo6PoQgwpxFXn1BMOUMIoaLx\nQBB5gnSp0iQnx89p1EK+853vcHl5yeOf/dTC8O7sDXEch9nV1bVUpqgq0tWSZLlgtZizq0WvDw8P\nuX3rJr1ej8vLS7799gNAnYwiWZBmBTf39nmyjHmmFeNDP0JKmIxn3L1zC6HHMRlf0moEpPWAyeSS\nD46fAZDEGc1mk6kj2WnUGZ+f2prJm/fvc+T5/MEf/AEP7tyip+UQV6FPr9tgfHWFLEsaPbXmpS94\nfvqSu9F98kqys6dOYaXwWKwyFquM7k6kO7RVzrvRjMgLl/FkwmF7lwq1tga7u6SZy2g0o5Ih7Y76\njlu320S1j4jqbcbTOeeXI54/f67GkiRM53NLC9zpqrrBzZs3SeI/H9KsfwX4qZTypXlBCLELjKSU\npRDiPvAm8OTTPsh1Xc33rIocholQCMFisbAPVFmWnJ6eMhwOlbrLRlu/zWHOxlYCClTle7FYKGhP\nGNrjnOlAM+3Si8XCpkJarRYHBweEYcjFxYVNSXQ6HdvmGwSBTWGYz6uqynIwmNfWLcpKV/DiQnWO\nSakUaoxCuMl33717lyxVmNVNgn+DEFitVriNiMFgsEZPpJk6ulfS5sMBbty4QTGpbBrhQqdvzs/P\n8UOFlXaDda7fdDbGcUyv1+PWrVvcv6+60/7xP/o9lonipYhqNQa666zVapFkKckqZsWaUqAoCsbj\nMUWq0xqVtHnXTem+TT4JQymQZRku7poULAppuapV/eDgppVeA6i3msRxzDJeEQQR9Q0iJpOiaXgN\n+1nGGRnSNJPSurw65+HDhwSuSomURUFHb9StVsvWcFqtlt3Y33rrLa02JK4hqB49esT5+Tme7zAa\njXjnnXeupedms5kKVuot0kylMJrUabUbtuvUpD1c1Po8OzvjZz/7mb3e/f19+oMeUS1gPLmiObyx\nfqDkxyTgNhI2Ckq4YjQa2SLz2fGJTWNGUUS/37fXe3Z2ZlW0NnVtx+Mxo9HIcquYOXnjjTfWufPT\nU85PlXs4PLynU0eqk3p3dxdX1zmMVsBPf/pTjo6O2NPIrRs3bnB5ccbj6ZSHDx+y31dO9uDggN6g\nTxynxKmqCe3roEagOE3efvttHMfh/fd/DMCzJ0956+03kFJy/PII0arZ6/3Wt77F0dEJZyfnNr16\ncXHB1dUVQRDw4sULhG6vN1ZVFZEuMAud5fvBD34AwIMHD+h2uxaGKaW0hfXJZKKUqHTe/Pz8HN/3\n6XQ6qo9BpwAnk8k1CodPs88CP/wd4F8CBkKIl8B/JqX8O8Bf4XpaBeC7wH8uhMhRaPi/IaUcfdp3\nOEJYciHAwp/q9bpq8tloo2632+zs7NiClWklrtfrCqXRallkAmAr8MZB2OhaCxYXRcFgMLCLCdTE\np2lq29fNdZl8n8lHG0dqIrnpVDHCbbbu7+/vk2UZ5+dnzGZze4Ko1+uMRiNevHhBnpcWvRDHMQJV\nRDFNDaCc3Gg04vHjx3SGA1UYOlURzWqxpN/r0el01Fi0iMLPfvYzTs7PaDab7O0P7Xx3Oh2E62gc\nu8tSc7gI1yFOE+IkoZKSJ88+soiWr/3aOxy/PFLKLMsVM71ZZHnObD4niWPcZmhzqmZ+A9fDc1zy\nPLM1hWazqeY4WQsLgMpf53lOiaQe1i30su77BPXINk8cHR2tN9edHmUhSZMYIVxcYahz1WZSq9XI\nk9zmyKkU1bBpJJnoe5is1Cnj9s1bfPMbXydNU06PVNt3WZZ2fbiuy9HRkZ3L4XBIu93myZMn1Bt6\nfQhVH0mzmMViwa1bt64FI8vlksFgcK14GIah7ZkwUoOgHPJsNuPJkyecnZ3ZvP39+/dpNps4jqO4\nPIrCytZdFzepMMVDKklRKshnGifMtUDGxcUFz5494+TkhF6vxxv3Du3GZwRRTLHb1DMMjvrk5ITH\njx/zzW9+0z4bP/nJTywp21JvFi9fvmQRr0C4tNtdBrt7tv5jqJ9brda1utd8Pme5XHJwcMCtWzfw\n3TWzped5LBYr9vb2KIrCniCeP3/Ow599QJyskOWO9Q+pDvyiKKLdbvP0QjlJszkt54p50wRzDx48\n4O033+Lx48eMRpfUwjVWvijXtbXlcsk7735dPYerFRcXF1xcXFighrmHAE+ePCEMQ+7du2cDvPff\nfx/XdTk4OGA4HDIaq3U9GAw26kCfbp8FtfJXP+H1f/fnvPYPgH/wmb9dW6VRKiYyNHhvIQTD4dA6\nvz/8wz+0C8o4ZnPENw47mSuiKpMuaLVahHrnTNPULp7pdGrZzoxoqplwU5EuioJut2sfHliLyG4W\nqgaDgVX7GQwG9oafnZ1ZzOh8PqGq1myG5pouLy8Zj6d27Hfu3KEWNbi4uFCdXnq773a77O/v2+q5\n0S4F5cin0ymNmmok0qzTFjtunM9MO41mu0Wn10UIwSpN7OJtNBr0uz2ieo2vvvM10jixfA/tVotm\np835ySmz2YxmXY2xXq+TlYWiQc1jQs3BkiQJi/mcPEnpdboIyTXEkO/7lsdmE/MfxzGyKqnVGvhC\nd9pKzdfsKbhps9WyxbgyywkM3aezsfCrgkITc1GtC4GGtTJezjk7O+NURz2zqYqAxpdXfOcv/gs0\nGg0ePlTtEHt7e/za196hKHNu3r7Fy5fqWDwajWzR3HTbgooYj46OGF9dXFPLASwL3mAwIGh07OWG\nno8sSnKZ4oQhlb6HSZLwu//7/0Ecx+zu7vLWgzcA2Ol0WUxnFuc8T7M114q7QVdbCTYdeZplFKl6\n1ozzo1QbynQ8YTlf0G7UroECTOFWSiVYDQpOaDakyWRiG6vq9briwmk22d3dZeKqe7tYLDk9P+Pg\nxi1msxl5UdqIvNPpcO/ePZrNJi+ePWWh6WoSS38+AAAMWElEQVTH4yt8z2E42OVrX3uXPFef9d57\n73FycoLjOEznMy4vL4nfje18TSYTRVrWadvipSPh4c8+YDgccvvwDrXdNflXlqY8ePCAOE75/d//\nffW8tXssl0sajQayzJGytCfKqOYThSGx1kYwp3zP8xSsstPh5OTErmtT9Df85avV6hrfu0EKJUnC\n+YWKe/M8f/34yKWU11Iou7u71pl7nmcj4U6nY1EhBiViWASn06mlgiyripV+0JcrJVFlSPFNaiPX\ncMCu41CUJS9e2gwRN24oPcJCT6Y5IhnUyN27d2k0GjYqPD09ZbFYcH5+bjcAUNAiIZRi9s2bN4mi\n9QNiOsXa7TaNRss+II1Gg2ajbZsqTOOLEcU4OzuzyAvjODzHZXx1ZSOnl8+Uo7m8vLRdb/PlgpGO\niDe7Mu8fvkmtrjbKZr1hYYxFUTCezlhrKTvkRYUbRgz2rkdm0+WK8Xyh4I4aljidTrm6vFQ43eWK\nwFuTY5nI0zjVWqE2BV/DwKRUivGb1AxpnlGvK8SBEntW0fKzZ8/o9XeVKLW3xjm7rossS0UfoDU/\nQQt7FwWTNGU5Xzdc7O3tsbvT5/nz54xGI3zHtScxw7pZJqrJxZyeLi4uSDQs9O69e7zx4L79vCAI\nkGXO5eUlP/7xjy3V6c7ODl99+yv0ezsQ1u0GY8Zq1rxJ27148YJHjx7xzjvv8NZbb9n3GY5913WZ\nTCYkYi0G4fs+DhWV5ynKWnNRsuTZk6dMJorU6atvqZ6+O3fusFqteP7sI2azmWXsBOzJZZNUDNSG\nGIYh7777LnEc203PnGLv3LlDHMc81rjoZrNNu93m3Xff5epqrATAre6qb53vo0ePuHGg0iRxvOLe\n3TuKfno0YpWokVyOJri+CpAurq74x7/3e/b7u90uYejjivVJFmCwu8MHP1UbVqvVItSvdzsdZrOZ\nhaP2e2pdNxoqmKryglarxXQ6ttSz9+7evtZoeKrRVdPplJnWLz0+Prbpv9u3b/OVr3yFXq/H1dUV\nR0dH19ZWHKuT29HREffuv2mve1O45tNsS5q1ta1tbWuvuX0uInKBsMUxUMWPer1u21RNRLyzs2OJ\n6S8uLijL0h4/TMt3t9mgXi9spDMej6kqaDRaxHFqyZZarciSa/m+z9XVlU17RFEdx/FI0wWr1cru\nrOqzKttUYt6fZZlN7ZjCEKA5iZVazNOnTymK0qaJVMv3VLV2tzo2Uj89PUVwwXK5ZG9vz6ZWiqKw\nxauLiwsWi4VFJ4yvRixmM+4d3mWxWNiC2Gw2o9XtKIx8LcLREVt3p0eF6sI08wgq5WLEPE6fPePi\n6oqFHnsQReztD7n34D6O49g5mU2m7Az61JsNLi9OaETrHHmn3cYTDvPpjMvzC5sKUlSpa26OVlel\nGCpd23Acl1JWqtkFKLKMNFVcM3GS0O3t2Hn8kz/5E2rNl+wOhgwGA4qmRivVjNiGErQ1EaaQ0mLb\np9OpFT7oDnd5+P4HREGouFUKJckF6qTy+PFjhvt7SAE1nQvv9LrcuHWTIsvZ2dlBB4HkacZgMGA8\nviLLMo6OjuzJscwLOi3VfLQq1xHj3t4ezWbT5uHNmn/69Clvv/02w6FCj2xyeHsbwidxldtUn5Al\nDoqi10EgNedHVVU8e/aMxXyK53kMdPQ5m01J4hW7u7tKjUhWNo1gAAgmpWleNyLne3t7vP322/bZ\nHQwGzOdz5vO5RXiBinDHM1WIj+OYm7duI8VauOPk5ESLVA9smmY+n6rTT1nRarXIShWh3rv/gOFw\nSKfb5ujFS05PTxnrNZ8kK85Pp9y6fYPFcsZ7P1IFyL3+gH6/T57nPHr0iG//+l+0c9JqtZhMJpwe\nn9mU7EcffaTSmGnK3nDAarXg5FhF5J12gyRdsVgscByo11WaxtB+DIdDarWaRZqZepuh8DDvBXX6\nN4LgYbiuMRndhc9qnwtHDlghCVDHxk0tTpPCyPOc27dv0+l0bP7Z5PnCUMmZha7DfD5fKwTpwtrV\n1dU1AnpTbPR9pUVoFFtAHXOtwkhRWKcTBIHlGHdd1zqT8/Nzdnd3LW/L5ueY/PNwOOTlyyPrZKMo\n4vDwUPOmxBZpEoYhJ8cn9sEwauqTyYRbt25xcHBAFahCk+HFPj89s80anuddI/M/vTjn/PycVRIT\nbLTi4wg6nQ6j5XyNvnEdxldXtFotTk9PkQJLBPX02Ufcv3+ffn2XoihsmmY0GtFqtbh5eIfFfGwf\nfEM6lcUJP/rhe5wsFnZz3eyAXS7XvC2Vrnn4vk+erzljfN8nLwo836cmrhe50zTl+dFLrq6ueNf/\n59bOTAjcmmL5q1yXSqe7lnoDPTk65tGjR7YIGi/nBEHA3TuHHL14RhSthRdOTk74yU9+wjtf+ypv\n/9rX8SP1+u3ikHv37pGuFM/1B+//xN6rw9t32N3dZafb5eDgAKk5wRuNhmITTFNEWLMP671797h7\n9y6tVovc98hSw3GdcHBwQLxacnJ8tN6QNCOfKd4lwkGWWppQKDEUIaEUlSUYo6yUHqmQNKIanu5Q\nHekW+5s3b9JptUnTmOPjY7tOTR7XdV37LJqN/PHjx5ycnNg1FIahvZ/D4ZBbN9TzeXBwk3/6f/8B\nT5484fJyRKPZwvHWjJ9lWdLr9XjzzTcJAzWO2WzCkydPGPR2ODgYsndDQTidQNUQxpMpru/x3e9+\nl5MjtVHu7faZTCYMB7vkec73v/99ALqtNjfv3Lac/iZNIoRQ6/fgFrPJ3KbNPvzwCc1aHanTU+1m\niyu96S4WC5LVgiLNuDw756137qrv6Ha5vLzk6dOnhGFo06V5rjb6LMu4ffs2H374oe1ENSyRoKCb\nV6O5npPKBnGfxcRmW/qrMiHEBbAELj/tvV8QG/DlGSt8ucb7ZRorfLnG+yrGeiil3P20N30uHDmA\nEOJ7Usq/8Kqv48/DvkxjhS/XeL9MY4Uv13g/z2PdFju3trWtbe01t60j39rWtra119w+T478t1/1\nBfw52pdprPDlGu+Xaazw5Rrv53asn5sc+da2trWtbe2Xs89TRL61rW1ta1v7JeyVO3IhxL8mhHgo\nhPhQCPFbr/p6/ixMCPGREOJHQogfCCG+p1/bEUL8n0KIR/rv3qu+zl/GhBB/VwhxLoT48cZrnzg2\nIcR/ou/1QyHEv/pqrvqXt08Y798SQhzp+/sDIcRvbPzstR2vEOK2EOIfCSHeF0L8RAjxH+rXv3D3\n9xeM9fW4t4Yp8FX8AVzgMXAfCIAfAl97ldf0ZzTOj4DBx177L4Hf0v/+LeC/eNXX+UuO7bvAt4Af\nf9rYgK/pexwC9/S9d1/1GH4F4/1bwH/8c977Wo8XOAC+pf/dAn6mx/SFu7+/YKyvxb191RH5Pw98\nKKV8IqXMgL8P/OYrvqY/L/tN4O/pf/894N94hdfyS5uU8p8AH6cq/qSx/Sbw96WUqZTyKfAhag28\nNvYJ4/0ke63HK6U8kVJ+X/97DnwA3OQLeH9/wVg/yT5XY33Vjvwm8GLj/y/5xZP3upoEflcI8cda\n4g5gKKU0zPGnwPDn/+praZ80ti/y/f4PhBDv6dSLSTV8YcYrlAD7N4H/hy/4/f3YWOE1uLev2pF/\nWezXpZTfAP4y8O8LIb67+UOpzmpfSPjQF3lsG/bfoNKD30Dp1v7tV3s5v1oTQjRROgP/kfyY/u4X\n7f7+nLG+Fvf2VTvyI+D2xv9v6de+UCalPNJ/nwP/C+oIdiaEOADQf5+/uiv8ldsnje0Leb+llGdS\nylJKWQH/Lesj9ms/XiGEj3Js/6OU8n/WL38h7+/PG+vrcm9ftSP/I+BNIcQ9IUSAko/7h6/4mn6l\nJoRoCCFa5t/AXwJ+jBrnX9Nv+2vA//ZqrvDPxD5pbP8Q+CtCiFAIcQ+l6fr/voLr+5WacWra/k3U\n/YXXfLxC0VX+HeADKeV/tfGjL9z9/aSxvjb39nNQLf4NVIX4MfA3X/X1/BmM7z6quv1D4CdmjEAf\n+L+AR8DvAjuv+lp/yfH9DurImaPyhP/eLxob8Df1vX4I/OVXff2/ovH+D8CPgPdQD/jBF2G8wK+j\n0ibvAT/Qf37ji3h/f8FYX4t7u+3s3NrWtra119xedWpla1vb2ta29s9oW0e+ta1tbWuvuW0d+da2\ntrWtvea2deRb29rWtvaa29aRb21rW9vaa25bR761rW1ta6+5bR351ra2ta295rZ15Fvb2ta29prb\n/wf+48g8sKTSdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f97983244a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## START CODE HERE ## (PUT YOUR IMAGE NAME) \n",
    "my_image = \"cat2.jpeg\"   # change this to the name of your image file \n",
    "## END CODE HERE ##\n",
    "\n",
    "# We preprocess the image to fit your algorithm.\n",
    "fname = \"images/\" + my_image\n",
    "image = np.array(ndimage.imread(fname, flatten=False))\n",
    "image = image/255.\n",
    "my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T\n",
    "my_predicted_image = predict(d[\"w\"], d[\"b\"], my_image)\n",
    "\n",
    "plt.imshow(image)\n",
    "print(\"y = \" + str(np.squeeze(my_predicted_image)) + \", your algorithm predicts a \\\"\" + classes[int(np.squeeze(my_predicted_image)),].decode(\"utf-8\") +  \"\\\" picture.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What to remember from this assignment:**\n",
    "1. Preprocessing the dataset is important.\n",
    "2. You implemented each function separately: initialize(), propagate(), optimize(). Then you built a model().\n",
    "3. Tuning the learning rate (which is an example of a \"hyperparameter\") can make a big difference to the algorithm. You will see more examples of this later in this course!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you'd like, we invite you to try different things on this Notebook. Make sure you submit before trying anything. Once you submit, things you can play with include:\n",
    "    - Play with the learning rate and the number of iterations\n",
    "    - Try different initialization methods and compare the results\n",
    "    - Test other preprocessings (center the data, or divide each row by its standard deviation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bibliography:\n",
    "- http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/\n",
    "- https://stats.stackexchange.com/questions/211436/why-do-we-normalize-images-by-subtracting-the-datasets-image-mean-and-not-the-c"
   ]
  }
 ],
 "metadata": {
  "coursera": {
   "course_slug": "neural-networks-deep-learning",
   "graded_item_id": "XaIWT",
   "launcher_item_id": "zAgPl"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}