01_supervised_learning.ipynb

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              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 600x400 with 1 Axes>",
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            "layout": "IPY_MODEL_5cc82fb531ad4d46909a50dcc7ab999c",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 600x400 with 1 Axes>",
                  "image/png": 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      "cell_type": "markdown",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/badlogic/genai-workshop/blob/main/01_supervised_learning.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Supervised learning\n",
        "In supervised learning, our goal is to create a model that learns how to map inputs to outputs, based on examples of input-output pairs.\n",
        "\n",
        "The output values can be limited to a fixed set of categories, or **classes**. For example, in spam detection, we learn to map from an email text to the two possible output values `spam` or `not spam`. This type of task is called **classification**.\n",
        "\n",
        "We can also learn a mapping from an input value to a continuous output value. For example, we can learn to map from the number of cylinders, maker, and age of a car to its fuel efficiency given in liters per 100 kilometers. This type of task is called **regression**.\n",
        "\n",
        "We can use supervised **machine learning models** for both of these tasks."
      ],
      "metadata": {
        "id": "Cq-oa4l__Zlx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## Data\n",
        "\n",
        "Before any learning can happen, we need to identify and collect data we want to learn from. Data is abundant and can be sourced from various platforms such as the internet, personal devices, or enterprise databases. However, not all data is immediately suitable for learning. For example, text data may be stored in binary formats like PDF, or markup formats like HTML; image or video data may be too big to handle or simply have the wrong aspect ratio; time series data may have missing values or outliers; or the data is \"polluted\" in some way, which all makes learning hard or impossible."
      ],
      "metadata": {
        "id": "_7L_rT3KzSfJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### Data Preprocessing\n",
        "Generally, we need to apply **data preprocessing** in some way, to bring it into a format and onto a quality level so it can serve as input to a machine learning model. For example, for learning how to detect spam, we'd collect thousands or hundreds of thousands of emails and extract the raw text by stripping any markup or formatting. Each resulting raw email text could possibly then be used as a direct input to the machine learning model. One such input is then generally referred to as a **sample**, as in: a sample from the set of all possible emails. However, usually, raw text (or audio, or images) can seldomly be passed to a model.\n",
        "\n",
        "Instead, raw data often has to be transformed to a numerical representation, such as **feature** vectors, or more generally, tensors. Each entry in such a vector represents a feature or attribute of the original raw data. For example, a simple raw data entry like {\"color\": \"red\", \"weight\": 150, \"type\": \"apple\"} can be converted into a numerical vector. If we encode \"color\" as red=1, green=2, yellow=3; and \"type\" as apple=1, banana=2, the raw data entry could be represented as a vector [1, 150, 1], where the first entry represents the color, the second the weight in grams, and the third the type of fruit. Deciding which information to choose from the raw data and how to convert it to a vectorial or other numeric representation is called **feature engineering**. Some machine learning models can be very sensitive to how the data is represented numerically, while other models like deep neural networks require much less care or no feature engineering at all."
      ],
      "metadata": {
        "id": "n3Ilz0g2zWA5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### Data Labeling\n",
        "For supervised learning, we not only need clean samples, but also expected outputs. For example, we can collect millions of emails, but without the information which email is spam and which email is not, the model will not be able to learn to differentiate between the two classes. We need to also assign a class (or expected output value) to each collected sample. This process is called **data labeling**, and is most often done manually by humans. The class (or expected output value) assigned to a sample is called the sample's **label** or **target**.\n",
        "\n",
        "Depending on the task, it may not be necessary to create one's own data set. Practitioners have collected, preprocessed, and labeled a lot of datasets over the decades and made them available through public repositories. For example, you can find tens of thousands of data sets for different machine learning tasks on [Hugging Face](https://huggingface.co/datasets) or [Kaggle](https://www.kaggle.com/datasets).\n",
        "\n",
        "If you indeed need to create your data set based on your own data, you can use tools like [Label Studio](https://labelstud.io/). If you don't have the human resources for labeling, you can use services like [Google AI Platform Data Labeling Service](https://cloud.google.com/ai-platform/data-labeling/pricing), or [Amazon SageMaker Ground Truth](https://docs.aws.amazon.com/sagemaker/latest/dg/sms.html)."
      ],
      "metadata": {
        "id": "P2FLqswszZQQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## Models\n",
        "A machine learning model consists of two parts:\n",
        "\n",
        "1. An **architecture** for learning and applying the mapping from input values to expected output values.\n",
        "2. A set of **parameters** that encode the learned mapping, and which can be stored for later use.\n",
        "\n",
        "There is a plethora of different supervised machine learning models for classification and regression tasks. They differ in what types of input and output values they can handle, what types of mappings they can create, their computational complexity, and the amount and quality of data they need to successfully learn the mapping.\n",
        "\n",
        "Examples of supervised machine learning models are [k-NN](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm), [Naive Bayes classifier](https://en.wikipedia.org/wiki/Naive_Bayes_classifier), [Support Vector Machines (SVM)](https://en.wikipedia.org/wiki/Support_vector_machine), [Decision Trees](https://en.wikipedia.org/wiki/Decision_tree), [Random Forests](https://en.wikipedia.org/wiki/Random_forest), [Logistic Regression](https://en.wikipedia.org/wiki/Logistic_regression), and [(Deep) Neural Networks](https://en.wikipedia.org/wiki/Deep_learning).\n",
        "\n",
        "Within the machine learning community, sharing models is standard to advance the state of the art. Scientific descriptions of models can be found in papers, e.g., on [arXiv](https://arxiv.org/list/cs.LG/recent), [Google Scholar](https://scholar.google.com/), or [Papers with Code](https://paperswithcode.com/sota). Implementations of models, including data preprocessing, model parameter layout and plumbing, and training and inference algorithms, are often derived from these scientific papers and contributed to open-source machine learning frameworks like [PyTorch](https://pytorch.org/),  [TensorFlow](https://www.tensorflow.org/), [scikit-learn](https://scikit-learn.org/stable/), or higher-level frameworks like [Hugging Face Transformers](https://huggingface.co/docs/transformers/en/index). A more recent development is the sharing of trained models. Pre-trained models for a wide range of machine learning tasks can be found on platforms like [Hugging Face](https://huggingface.co/models)."
      ],
      "metadata": {
        "id": "ni4s_Sc1zcYb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## Training\n",
        "For a supervised machine learning model to learn a mapping from input values to expected output values, we need to present it with labeled samples. The model will then (usually iteratively) learn the underlying patterns in the data, from which it can construct the input/output mapping. It encodes its learned \"knowledge\" in its parameters. This process is called **training**.\n",
        "\n",
        "For example, to train a sentiment detection model for product reviews, we need to present it with a set of product review texts (samples) and their corresponding sentiment like `positive`, `neutral`, and `negative` (labels).\n",
        "\n",
        "The data set consisting of samples and labels we present to the model for training is called the **training set**.\n",
        "\n",
        "To help decide which machine learning model to use for a task, and how to configure its **hyper-parameters**, that is, parameters that are not learned but specified as part of the model configuration, another labeled data set called a **validation set** is sometimes used.\n",
        "\n",
        "Most training algorithms are iterative. First, the parameters of the model are initialized in some way, for example, randomly. Of course, this \"random\" model is unlikely to give any meaningful or correct outputs.\n",
        "\n",
        "Next, the training data (or a subset thereof called a **batch**) are presented to the model. For each sample, the model uses its current parameters to map it to a label. These labels are then compared to the expected labels found in the training set. The result of the comparison is then used to adjust the parameters of the model in such a way, that it will (hopefully) generate more correct labels in the next iteration. This process repeats until some stopping criterion has been reached, for example, after a fixed number of iterations over the entire training set, often referred to as **epochs**, or if the model parameters do not change significantly anymore, in which case the model is said to have **converged**.\n",
        "\n",
        "How the adjustment of model parameters is done exactly depends on the type of model. For example, for many model types such as neural networks, a **loss function** is used, which models how well the labels generated by the model correspond to the true labels for the samples in the training set.\n",
        "\n",
        "The training objective then becomes minimizing the loss function by adjusting the model parameters such that the difference between the model outputs and the expected outputs is as small as possible.\n",
        "\n",
        "This class of problem is called an **optimization problem**, which, depending on the model type, can be solved in various ways. For example, for neural networks, the optimization problem is solved via [backpropagation](https://en.wikipedia.org/wiki/Backpropagation) through [stochastic gradient descent](https://en.wikipedia.org/wiki/Stochastic_gradient_descent).\n",
        "\n",
        "We can observe if and how well the model is improving during training, by logging or visualizing the losses of each training iteration."
      ],
      "metadata": {
        "id": "RKZNQwV1zgOf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## Evaluation\n",
        "Once model training is complete, we want to evaluate its quality. For this, we need another labeled data set called **test set**.\n",
        "\n",
        "The evaluation is done by asking the model to assign labels to previously unseen samples. This is called **prediction** or **inference**.\n",
        "\n",
        "We can then compare the model output to the expected labels of each sample in the test set.\n",
        "\n",
        "The comparison between expected labels and labels predicted by the model can be done via different evaluation metrics and scoring functions. Commonly used metrics in supervised learning are [accuracy, precision, recall, F1 score](https://en.wikipedia.org/wiki/Precision_and_recall) for classification tasks, and [mean squared error (MSE)](https://en.wikipedia.org/wiki/Mean_squared_error), [mean absolute error (MAE)](https://en.wikipedia.org/wiki/Mean_absolute_error), or [R-squared](https://en.wikipedia.org/wiki/Coefficient_of_determination) for regression tasks.\n",
        "\n",
        "The result of the evaluation metric tells us how well the model can predict labels for samples it has not seen during training. This gives us an indication of whether the model **generalizes** well to unseen data, or wether it has **overfitted** on the training data, meaning it may have learned to predict labels for the training data very well, but fails to predict correct labels for novel data.\n",
        "\n",
        "We can also compare different models for the same task by comparing their evaluation results on the same training and test set.\n",
        "\n",
        "[scikit-learn](https://scikit-learn.org/stable/modules/model_evaluation.html) and [Hugging Face](https://huggingface.co/docs/evaluate/en/index) both provide frameworks for evaluation."
      ],
      "metadata": {
        "id": "6ITH3fVAzi_g"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A simple linear binary classifier\n",
        "Let us illustrate the above concepts by building a simple linear binary classifier. \"Binary\" in this context means, that we have two classes or categories we want the model to be able to discern. \"Linear\" means, that the samples of the two different classes can be separated from each other by a line (or hyper-plane in higher dimensional spaces)."
      ],
      "metadata": {
        "id": "HjJ8ARubzud-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Data\n",
        "For illustrative purposes, we'll genereate a synthetic dataset instead of using real-world data. The synthetic data samples will have 2 features. Each sample can thus be represented as a two dimensional vector. You can think of them as the properties of a real world object, like a car's maximum speed and weight. The reason we only use 2 features is that such data is very easy to visualize.\n",
        "\n",
        "Let's use [scikit-learn](https://scikit-learn.org/stable/) to generate the data and a [Pandas DataFrame](https://pandas.pydata.org/) to inspect it:"
      ],
      "metadata": {
        "id": "hB-o8T96zw_l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate 100 samples, split into 2 clusters, with 2 features each. Each cluster has a center point (centroid)\n",
        "# around which samples are randomly generated with a standard deviation of 1. We also fix the random seed to\n",
        "# make things reproducible.\n",
        "from sklearn.datasets import make_blobs\n",
        "samples, labels = make_blobs(n_samples=100, centers=2, n_features=2, cluster_std=2.5, random_state=42)\n",
        "\n",
        "# Use Pandas DataFrame to display the data in a table inside the notebook\n",
        "import pandas as pd\n",
        "df = pd.DataFrame(samples, columns=[\"Feature 1\", \" Feature 2\"])\n",
        "df[\"labels\"] = labels\n",
        "df"
      ],
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      "execution_count": null,
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              "0   -3.707133    8.550139       0\n",
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              "4    5.208529    5.241027       1\n",
              "..        ...         ...     ...\n",
              "95   0.068301   11.342486       0\n",
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              "97   2.522895   -1.813948       1\n",
              "98  -3.058377    9.907068       0\n",
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              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-42b7ed95-7f02-4ebd-8799-93e66d291aee button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 100,\n  \"fields\": [\n    {\n      \"column\": \"Feature 1\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 4.358699452966607,\n        \"min\": -9.058560383277111,\n        \"max\": 9.355343589254428,\n        \"num_unique_values\": 100,\n        \"samples\": [\n          -4.779257811855778,\n          5.534347237098809,\n          -3.660794550452219\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \" Feature 2\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3.9803165555521995,\n        \"min\": -1.8139483777739294,\n        \"max\": 13.644981589470666,\n        \"num_unique_values\": 100,\n        \"samples\": [\n          5.483526874860093,\n          3.3751309998613177,\n          11.65709169374561\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"labels\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0,\n        \"min\": 0,\n        \"max\": 1,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          1,\n          0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can use [Matplotlib](https://matplotlib.org/) to visualize the generated data (and [NumPy](https://numpy.org/) to help wrangle the data for visualization a little):"
      ],
      "metadata": {
        "id": "pdzOZ2gzazuz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "def visualize_data(samples, labels):\n",
        "  plt.figure(figsize=(6, 4))\n",
        "  class0 = samples[labels == 0]\n",
        "  class1 = samples[labels == 1]\n",
        "  plt.scatter(class0[:, 0], class0[:, 1], c='blue', label='Class 0')\n",
        "  plt.scatter(class1[:, 0], class1[:, 1], c='red', label='Class 1')\n",
        "  plt.title('Data')\n",
        "  plt.xlabel('Feature 1')\n",
        "  plt.ylabel('Feature 2')\n",
        "  plt.legend()\n",
        "  plt.grid(True)\n",
        "  plt.xlim(np.min(samples[:,0])-1, np.max(samples[:,0])+1)\n",
        "  plt.ylim(min(-1, np.min(samples[:,1])-1), np.max(samples[:,1])+1)\n",
        "  plt.axhline(y=0, color='green', linewidth=1, alpha=0.5)\n",
        "  plt.axvline(x=0, color='green', linewidth=1, alpha=0.5)\n",
        "\n",
        "  plt.show()\n",
        "\n",
        "visualize_data(samples, labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "id": "7qvxX8T-bE2j",
        "outputId": "7cba7157-3a0d-4497-b337-46ba0230434d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Model\n",
        "If we look at the visualization above, it's very easy to draw a line that separates the samples of the two classes from each other. This is what we mean by \"linearly separable\".\n",
        "\n",
        "While not a great model, we can use a parametric line equation to create a binary linear classifier:\n",
        "\n",
        "$y = mx + b$\n",
        "\n",
        "The parameters of the model are `m`, the line's slope, and `b`, the bias.\n",
        "\n",
        "To make predictions using this model, we take a sample and plug in its `x` coordinate. The model then generates a `y` coordinate for us, based on the line slope and bias. If the sample's actual `y` coordinate is above the predicted `y` coordinate, then we assign the label `0` to the line, otherwise `0`. The line is called a **decision boundary**, as we use it to decide which class a sample belongs to.\n",
        "\n",
        "This model has some (severe) deficiencies, which we'll explore later. For now, let us put the above model architecture into a simple function to predict the label of a sample given the model's parameters `m` and `b`."
      ],
      "metadata": {
        "id": "VPAPu26ZbZMq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def predict(m, b, sample):\n",
        "  x, y = sample\n",
        "  line_y = m * x + b\n",
        "  return 0 if y > line_y else 1"
      ],
      "metadata": {
        "id": "yVEZHV-dioUf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can then use the `ipywidgets` package to create an interactive visualization to explore such a model's parameters `m` and `b` and their effect on prediciting the label of one or more samples.\n",
        "\n",
        "The visualization lets us manually set `m` and `b`, uses the `predict` function to generate labels for all our samples, and then visualizes the result, including the line modelled by the parameters."
      ],
      "metadata": {
        "id": "zcushJ62lkbU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import ipywidgets as widgets\n",
        "\n",
        "def visualize_model(m, b, samples, labels):\n",
        "  m_slider = widgets.FloatSlider(description='m (slope)', min = -4, max=4)\n",
        "  m_slider.value = m\n",
        "  b_slider = widgets.FloatSlider(description='b (bias)', min=0, max=10)\n",
        "  b_slider.value = b\n",
        "\n",
        "  def plot_model_and_data(m, b):\n",
        "    plt.figure(figsize=(6, 4))\n",
        "    plt.xlabel('Feature 1')\n",
        "    plt.ylabel('Feature 2')\n",
        "    plt.grid(True)\n",
        "    plt.xlim(np.min(samples[:,0])-1, np.max(samples[:,0])+1)\n",
        "    plt.ylim(min(-1, np.min(samples[:,1])-1), np.max(samples[:,1])+1)\n",
        "    plt.axhline(y=0, color='green', linewidth=1, alpha=0.5)\n",
        "    plt.axvline(x=0, color='green', linewidth=1, alpha=0.5)\n",
        "\n",
        "    # Draw the model line\n",
        "    x_values = np.array([np.min(samples[:,0])-1, np.max(samples[:,0])+1])\n",
        "    y_values = m*x_values + b\n",
        "    plt.plot(x_values, y_values, '-r', label=f'y = {m:.2f}x + {b:.2f}')\n",
        "\n",
        "    # Predict labels for the samples based on the current model and\n",
        "    predicted_labels = np.array([predict(m, b, sample) for sample in samples])\n",
        "\n",
        "    # Draw the samples, colored by class\n",
        "    class0 = samples[predicted_labels == 0]\n",
        "    class1 = samples[predicted_labels == 1]\n",
        "    plt.scatter(class0[:, 0], class0[:, 1], c='blue', label='Class 0')\n",
        "    plt.scatter(class1[:, 0], class1[:, 1], c='red', label='Class 1')\n",
        "\n",
        "    plt.legend(loc='best')\n",
        "    plt.show()\n",
        "\n",
        "  out = widgets.interactive_output(plot_model_and_data, {'m': m_slider, 'b': b_slider})\n",
        "  return widgets.VBox([m_slider, b_slider, out])\n",
        "\n",
        "visualize_model(0, 0, samples, labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452,
          "referenced_widgets": [
            "c4e485f379374e0a8f0b24488f8c6f7d",
            "dfd9373cc6bf4213a4b10b489be1621d",
            "dc8f9787cc0542ff9dd9f8186fc219d3",
            "1e824fd96e044b5fb6b9b1c5a4d4b34a",
            "e7c5f3e1a32346d2875d28db1e6209d8",
            "55af09c29bb94884814f293d70c8ceec",
            "9d19e516a8894808b701645b8afb879a",
            "5eee57b417874be388d731b9039b6ef9",
            "c096f7e2dc74433a9d884489768ccace",
            "6f7b2aef449d4edab0faf3297f9c7b7c"
          ]
        },
        "id": "MO3Knxfvfaaw",
        "outputId": "993c404a-c8f3-4718-92e9-b8bb670cc2ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "VBox(children=(FloatSlider(value=0.0, description='m (slope)', max=4.0, min=-4.0), FloatSlider(value=0.0, desc…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "c4e485f379374e0a8f0b24488f8c6f7d"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can manually play with the slope and bias slider, until we find values for our model parameters `m` and `b` that we think produce a line that separates the samples of the 2 classes well, just based on visual inspection.\n",
        "\n",
        "But that's not very precise, nor efficient, nor will we be able to do it for more complex or higher dimensional datasets.\n",
        "\n",
        "Instead, we need an objective measure that tells us how well the model can separate the samples of the two classes via its decision boundary. That is what we use **loss functions** for.\n",
        "\n",
        "The most naive loss function in this case would be to count the number of samples the current model predicts the labels for correctly, divided by the total number of samples. This is the accuracy metric mentioned in the evaluation section above."
      ],
      "metadata": {
        "id": "JMXEKCtbh26u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def accuracy(predicted_labels, labels):\n",
        "    correct_predictions = sum(p == l for p, l in zip(predicted_labels, labels))\n",
        "    accuracy = correct_predictions / len(labels)\n",
        "    return accuracy"
      ],
      "metadata": {
        "id": "GKcKvjn3v28W"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "To turn it into a loss function, that goes down as more samples are labeled correctly, we need to invert it, that is, subtract the accuracy from 1."
      ],
      "metadata": {
        "id": "cJvHC0Xcv3LM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def loss(predicted_labels, labels):\n",
        "    return 1 - accuracy(predicted_labels, labels)"
      ],
      "metadata": {
        "id": "Zg18ywAdppg7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can modify our visualization above, to also output the loss each time we change a parameter. This way, we are no longer as dependent on visually judging how well the current model works."
      ],
      "metadata": {
        "id": "8W3ZzSSAoKms"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def visualize_model(m, b, samples, labels):\n",
        "  m_slider = widgets.FloatSlider(description='m (slope)', min = -4, max=4)\n",
        "  m_slider.value = m\n",
        "  b_slider = widgets.FloatSlider(description='b (bias)', min=0, max=10)\n",
        "  b_slider.value = b\n",
        "  loss_label = widgets.Label(value='Loss: ')\n",
        "  def plot_model_and_data(m, b):\n",
        "    plt.figure(figsize=(6, 4))\n",
        "    plt.xlabel('Feature 1')\n",
        "    plt.ylabel('Feature 2')\n",
        "    plt.grid(True)\n",
        "    plt.xlim(np.min(samples[:,0])-1, np.max(samples[:,0])+1)\n",
        "    plt.ylim(min(-1, np.min(samples[:,1])-1), np.max(samples[:,1])+1)\n",
        "    plt.axhline(y=0, color='green', linewidth=1, alpha=0.5)\n",
        "    plt.axvline(x=0, color='green', linewidth=1, alpha=0.5)\n",
        "\n",
        "    # Draw the model line\n",
        "    x_values = np.array([np.min(samples[:,0])-1, np.max(samples[:,0])+1])\n",
        "    y_values = m*x_values + b\n",
        "    plt.plot(x_values, y_values, '-r', label=f'y = {m:.2f}x + {b:.2f}')\n",
        "\n",
        "    # Predict labels for the samples based on the current model and\n",
        "    predicted_labels = np.array([predict(m, b, sample) for sample in samples])\n",
        "    loss_label.value = f\"Loss: {loss(predicted_labels, labels): .3f}\"\n",
        "\n",
        "    # Draw the samples, colored by class\n",
        "    class0 = samples[predicted_labels == 0]\n",
        "    class1 = samples[predicted_labels == 1]\n",
        "    plt.scatter(class0[:, 0], class0[:, 1], c='blue', label='Class 0')\n",
        "    plt.scatter(class1[:, 0], class1[:, 1], c='red', label='Class 1')\n",
        "\n",
        "    plt.legend(loc='best')\n",
        "    plt.show()\n",
        "\n",
        "  out = widgets.interactive_output(plot_model_and_data, {'m': m_slider, 'b': b_slider})\n",
        "  return widgets.VBox([m_slider, b_slider, loss_label, out])\n",
        "\n",
        "visualize_model(0, 0, samples, labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484,
          "referenced_widgets": [
            "3c0f875bd54e4eaabc971f3b10a95a8c",
            "32888cdb4586445d8fabf6a4d4b611d0",
            "2296d0b5a7a34a2485dc282285188479",
            "0c8bc293e4ad4c86912e1fb3b1afd3ea",
            "34a19f264430484c981332a748cd5bae",
            "afe2b5be58884cd5ae1c00e4e2a647a9",
            "de4060744d0f487e88afdbc5ce415ce8",
            "b2fba0fee9d54bf89a3fb04dea939d8f",
            "e6f8a03173af41a38e7785952f029b51",
            "e4bdd798d83b40f18dea4447cbb53131",
            "0324ff6230e6471b9735a725812229a4",
            "8d9d5af59b7547d992101506a9559469",
            "5cc82fb531ad4d46909a50dcc7ab999c"
          ]
        },
        "id": "sJD6FoZNoViO",
        "outputId": "57cd2452-461b-45f2-a079-930fcfdcbc8f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "VBox(children=(FloatSlider(value=0.0, description='m (slope)', max=4.0, min=-4.0), FloatSlider(value=0.0, desc…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "3c0f875bd54e4eaabc971f3b10a95a8c"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now adjust the slides until the loss becomes (close to) 0, and manually optimize the model parameters.\n",
        "\n",
        "We can also write some naive model training code to do this work for us.\n",
        "\n",
        "### Training\n",
        "Our training algorithm will simulate us randomly adjusting the sliders, thus modifying `m` and `b`, for a couple of iterations. Of course, we won't have the machine interact with a UI.\n",
        "\n",
        "The training algorithm works like this:\n",
        "* **Input**:\n",
        "  * The initial `m` and `b`, we can set them to 0, or initialize them randomly\n",
        "  * The training `samples` and their `labels`\n",
        "  * The `loss_function`to calculate how well the current model parameters work\n",
        "  * The number of `epochs`, which is the number of times we adjust the parameters, and evaluate them on the full training set\n",
        "  * The `learning_rate`, which defines how much we want to adjust the parametess in each epoch\n",
        "* For `epochs` iterations\n",
        "  1. Predict labels for all training samples using these modified model parameters\n",
        "  2. Calculate the loss and store it\n",
        "  2. If the loss is smaller than the previous best loss, record the current model parameters and loss as the best parameters and loss\n",
        "  3. **\"Optimize\"** the best model parameters `m` and `b` so far, by adding a random number between `0-1`, scaled by the `learning_rate`\n",
        "* **Output**: the best model parameters and loss, along with the history of losses"
      ],
      "metadata": {
        "id": "Y1GuqJJxt8ei"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "def train(m, b, samples, labels, loss_function, epochs, learning_rate):\n",
        "  min_loss = float('inf')\n",
        "  best_m, best_b = m, b\n",
        "  losses = []\n",
        "\n",
        "  for _ in range(epochs):\n",
        "    # Predict labels with new parameters\n",
        "    predicted_labels = [predict(m, b, sample) for sample in samples]\n",
        "\n",
        "    # Calculate loss and record it\n",
        "    current_loss = loss_function(predicted_labels, labels)\n",
        "    losses.append(current_loss)\n",
        "\n",
        "    # Update best parameters if loss improved\n",
        "    if current_loss < min_loss:\n",
        "      min_loss = current_loss\n",
        "      best_m, best_b = m, b\n",
        "\n",
        "    # Randomly adjust m and b\n",
        "    m_adjust = random.random() * learning_rate\n",
        "    b_adjust = random.random() * learning_rate\n",
        "\n",
        "    m = m + m_adjust\n",
        "    b = b + b_adjust\n",
        "\n",
        "  return best_m, best_b, min_loss, losses"
      ],
      "metadata": {
        "id": "rKHbgHaEuiHa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now train a model based on our data. As is common practice, we split the data into 80% for training (training set), and 20% for evaluation (test set). This is also referred to a **train/test split** of the data.\n",
        "\n"
      ],
      "metadata": {
        "id": "-lBV2ANiuolC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "training_samples, test_samples, training_labels, test_labels = train_test_split(samples, labels, test_size=0.2, random_state=7)"
      ],
      "metadata": {
        "id": "vb6hd95ZvFB0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let us train our model, giving it 200 epochs to find good model parameters. The inital `m` and `b`are set to zero. They could also be randomly initialized. The learning rate is set to 1, which means the parameters will be updated by a value between 0 and 1 for each epoch."
      ],
      "metadata": {
        "id": "JLT6I1UFvl-7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m, b, best_loss, losses = train(0, 0, training_samples, training_labels, loss, 100, 1)\n",
        "visualize_model(m, b, training_samples, training_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484,
          "referenced_widgets": [
            "21090c992e1b4415a00a97de2a5ac913",
            "784e744f60eb489a8bd8bebfb3bf38e9",
            "8823b6ab6f57487a9c78e4a07e5434ab",
            "e5b06ada77554850a23cc17aa0a4f2f1",
            "18492953fc074aafb9d3f281ec96cf49",
            "d2f009e9e4aa4318817b59e140f61625",
            "79b5f6ed6e7548c980f3769902b103ad",
            "4522eedf4b12455195f2087536843cc0",
            "6c01f59cc0664e219e975983a7aff3d1",
            "77b2f58370c84859ab5a3dca4a4f950a",
            "57f48d547a6a49e1987a181afc0a0a0a",
            "4971ce780d834be9a2ecadec64462234",
            "9e4462400ecd469c8f23f7f5ed5e4620"
          ]
        },
        "id": "lU96II4qvgrU",
        "outputId": "7ca19af4-e0fe-4715-fc82-8220c79fa266"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "VBox(children=(FloatSlider(value=3.5591833314538746, description='m (slope)', max=4.0, min=-4.0), FloatSlider(…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "21090c992e1b4415a00a97de2a5ac913"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can also visualize the loss during training"
      ],
      "metadata": {
        "id": "QfPVs5zAFfBn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def visualize_loss(losses):\n",
        "  plt.figure(figsize=(10, 6))\n",
        "  plt.plot(losses, marker='o', linestyle='-', color='blue')\n",
        "  plt.title('Training Loss Over Epochs')\n",
        "  plt.xlabel('Epoch')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.grid(True)\n",
        "  plt.show()\n",
        "\n",
        "visualize_loss(losses)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "DLkVWuYfFi7G",
        "outputId": "92c08228-d8e4-4ce9-aa09-34de0477f0ab"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The best loss was found after only 8 epochs. The model parameters for that epoch were choosen to be the final model parameters, as subsequent epochs yielded worse loss.\n"
      ],
      "metadata": {
        "id": "A9zgjgwsFr4i"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Evaluation\n",
        "How does the trained model fare previously unseen data, such as the data in the test set? We can calculate the accuracy of the model for the test set:"
      ],
      "metadata": {
        "id": "J4ns03Zs4xZk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy([predict(m, b, sample) for sample in test_samples], test_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MR0SqFcA46MF",
        "outputId": "f0290781-f2d9-4888-b6cb-5c3dc6f7df53"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "A value of `1` means that the model was able to assign a correct label to each sample in the test set. We can also visualize this.\n",
        "\n"
      ],
      "metadata": {
        "id": "4WoCjVlS5Bkk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_model(m, b, test_samples, test_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484,
          "referenced_widgets": [
            "e6ad6ab12db74c07b4c9448e1b60758c",
            "2d899d03a625453fbdbdcc9ba7f6010b",
            "a330516acb93422a8e87e8e0c457bde8",
            "721e72d1a07e486c967bf43cd36c42f6",
            "277e069f978d42478eff560901f7f328",
            "714781daa590430fa49a554b3153e193",
            "27f2ffd8e9cf41d2927f3dd73f35e7f7",
            "d533b24906444c5d873380e881ccfad7",
            "602cea3ecd6c44e2bbddb99a190d3a21",
            "d6ed71f619694ff5a459c9dcd75a19ce",
            "99e213f9336549a2a9e8afa3f6cb8360",
            "453bbc58f2e34620b637148f5e68a621",
            "e302a933215143a78b1d1815376cf917"
          ]
        },
        "id": "_ImcGEHc5A2H",
        "outputId": "37dd2b01-d479-4ab2-f4e8-b733e596e2cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "VBox(children=(FloatSlider(value=3.5591833314538746, description='m (slope)', max=4.0, min=-4.0), FloatSlider(…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "e6ad6ab12db74c07b4c9448e1b60758c"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Based on this evaluation, it appears that the model generalizes well.\n",
        "\n",
        "However, as stated earlier, this model has severe deficiencies. Let us analyze them.\n",
        "\n",
        "To begin with, let us swap the labels for each sample. That is, `0` becomes `1` and `1` becomes `0`."
      ],
      "metadata": {
        "id": "R1PJY6DX59tu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "swapped_labels = np.array([1 if label == 0 else 0 for label in labels])"
      ],
      "metadata": {
        "id": "m0lbK1YRELIV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The samples stayed the same, only the labels changed, indicated by the swapped colors of the samples in this plot:"
      ],
      "metadata": {
        "id": "4n4NuuRKEmNJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_data(samples, swapped_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "id": "DQsEiQGnEkpK",
        "outputId": "501d170a-bdd6-4f08-9fa2-0a1b22335ebe"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can train a new model on this dataset. We'd expect it to arrive at the same or a similar set of model parameters."
      ],
      "metadata": {
        "id": "T1qNdT4kE5Fu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m, b, best_loss, losses = train(0, 0, samples, swapped_labels, loss, 100, 1)\n",
        "visualize_model(m, b, training_samples, training_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484,
          "referenced_widgets": [
            "439d35e4d38d4e9bbb89082fa63c74df",
            "22ebd7cee94d4a3a8d473ca7976238a9",
            "97603c31ab5443dc8d7dea5cfb64b1b3",
            "6f505b47176a42578a60556ccd37c875",
            "37a7d3e7e5a348b89a2ae32eb34f25b1",
            "5229d10021b342f591853c8b13c388c7",
            "5b6b401ab3ea4b4c9417647a2c672b48",
            "2f589a28726140ce9f85f4b523e1ae75",
            "159474f6751449c7a56b82a8d51a5d15",
            "75cdc39da6a040f5afc29828fee02f6b",
            "4352762c87254ce38717070dd3332d0a",
            "50c8c997a21d43ada3a9d1f3b629920d",
            "f22f6e1f30d940d8b06851fb5a9c0ba3"
          ]
        },
        "id": "2T8TaVIJEMuL",
        "outputId": "f76be1a3-1549-42d4-a420-bcfe3622a31a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "VBox(children=(FloatSlider(value=0.0, description='m (slope)', max=4.0, min=-4.0), FloatSlider(value=0.0, desc…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "439d35e4d38d4e9bbb89082fa63c74df"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_loss(losses)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "4WXe7V8AT3gO",
        "outputId": "d361c773-be95-412c-c2fc-04ade01f1dd1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "However, it clearly fails to do so. In fact, the training loss increases.\n",
        "\n",
        "The problem lies with our simplicist `predict` function. It will always assign class `0` to points above the decision boundary, and class `1` to points below the boundary.\n",
        "\n",
        "However, in the training dataset, the classes are swapped, and the samples of class `1` are always above the decision boundary. The model will thus always assign the wrong label to those samples, and is unable to make any meaningful progress.\n",
        "\n",
        "This model this has **inherent limitations**: it can only be used for:\n",
        "1. Data that can be classified into one of two classes\n",
        "2. Data that is two dimensional\n",
        "3. Data, where the samples with label `0` are assumed to be above the model's decision boundary, and samples with label `1` are assumed to be below the decision boundary.\n",
        "\n",
        "While these limitations are extreme, similar limitations may crop up in real-world applications when using much more complex models. However, as in the case above, these limitations might not be apparent during development, as the training and test set might not allow us to identify such issues."
      ],
      "metadata": {
        "id": "VZyn0rKtIFrq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A binary linear neural network classifier\n",
        "Let's create a better, more realistic classifier. All the same principles will apply.\n",
        "\n",
        "As a model, we will use a [fully connected linear feedforward neural network](https://en.wikipedia.org/wiki/Feedforward_neural_network), with 2 input neurons (one for each input feature) and 2 output neurons (one for each class). We will train the model using a stochastic gradient descent optimizer with [cross-entropy loss function](https://ml-cheatsheet.readthedocs.io/en/latest/loss_functions.html#toc-entry-1). We do not care about the mathematical intricacies here. Instead we want to focus on the general \"workflow\" of training and evaluating a supervised machine learning model.\n",
        "\n",
        "> **Note:** In practical applications, we may often also not care much for the internals of a model and simply treat it as a parameterized black box that takes some input and generates some output. We also need to understand the limitations of a model to successfully apply it to a task. This too does not necessarily require us to understand the internals of the model either. All that said, a deeper understanding of iternal mechanics is always beneficial.\n",
        "\n",
        "We will be using [PyTorch](https://pytorch.org/), a machine learning framework, to train and evalute the model. We will reuse the training set and test set data we generated above for comparison."
      ],
      "metadata": {
        "id": "GEVec5MYVZyX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch.optim import SGD\n",
        "from torch.utils.data import DataLoader, TensorDataset"
      ],
      "metadata": {
        "id": "f78jiRR6Ivcw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Data\n",
        "\n",
        "As a first step, we need to convert our sample and label data to [PyTorch tensors](https://pytorch.org/tutorials/beginner/introyt/tensors_deeper_tutorial.html). These are optimized data structures to store vectors (lists of numbers), matrices (two dimensional arrays of number), or more generally tensors. They also allow us to push the data to GPUs or TPUs for faster processing.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "nWJxJub_AR_-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "training_samples_torch = torch.tensor(training_samples, dtype=torch.float)\n",
        "training_labels_torch = torch.tensor(training_labels, dtype=torch.long)\n",
        "test_samples_torch = torch.tensor(test_samples, dtype=torch.float)"
      ],
      "metadata": {
        "id": "jy0P-yIfA7cA"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we create [PyTorch data sets](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html). Data sets wrap our samples and labels and make them easier to handle."
      ],
      "metadata": {
        "id": "LndVijYZONoi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "training_set_torch = TensorDataset(training_samples_torch, training_labels_torch)"
      ],
      "metadata": {
        "id": "2ZzDi0gCOOA9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Model\n",
        "\n",
        "Next, we define our linear feedfoward neural network using Torch's [`Linear`](https://pytorch.org/docs/stable/generated/torch.nn.Linear.html) class. The first parameter specifies the number of input features. The second parameter defines the number of classes."
      ],
      "metadata": {
        "id": "cs1WHEgRBigz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nn_model = nn.Linear(2, 2)\n",
        "nn_model"
      ],
      "metadata": {
        "id": "9EXMXVCvPPOu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1c1315ab-3baa-48d0-a7b6-661bb0fa178d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Linear(in_features=2, out_features=2, bias=True)"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We also need a function to make predictions for a new sample. The function `predict_nn` takes a model and one or more samples, where each sample is a tensor with the same number of features that the model was configured with.\n",
        "\n",
        "It then uses the model to make a prediction. The prediction isn't the class to be assigned to the sample directly, but a list of probabilities, one for each class. We return the class with the highest probability.\n",
        "\n",
        "> **Note:** passing only a simple sample to the model for prediction is not very efficient, especially if we perform inference on a GPU or TPU. The function thus expects an array of sample tensors, and returns an array of labels"
      ],
      "metadata": {
        "id": "b0dvApDkd5E6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def predict_nn(model, samples):\n",
        "    with torch.no_grad():  # Disable gradient computation for inference\n",
        "        logits = model(samples)\n",
        "        _, predictions = torch.max(logits, dim=1)\n",
        "    return predictions"
      ],
      "metadata": {
        "id": "xzakOm5Yd_o8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Training\n",
        "For training, we use Torch's [stochastic gradient descent optimizer](https://pytorch.org/docs/stable/generated/torch.optim.SGD.html), which will adjust the models parameters during training based on the gradients generated by an instance of Torch's [Cross-Entropy loss](https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) class. To iterate over the training set, we'll use Torch's [DataLoader](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html) class. It cuts up the training data into batches of a specific size, which we then present to the model for prediction. This batching mechanism is needed by many models, be it because the full training set does not fit into working memory, because the model can only deal with a maximum number of samples at a time, or because the model will generalize better when optimized per batch, instead of the full training set.\n",
        "\n",
        "The training loop conceptually works very similar to our naive training procedure above:\n",
        "\n",
        "* For each epoch, we iterate through the training set one batch at a time (`batch_size=10`).\n",
        "  * For each batch we:\n",
        "    1. Reset the gradients in the optimizer\n",
        "    2. Get a prediction for each training sample in the batch\n",
        "    3. Calculate the loss by comparing the predicted labels with the expected labels\n",
        "    4. Perform back propagation to calculate new gradients\n",
        "    5. Use the gradients to update the parameters of the neural network via the optimizer\n",
        "\n",
        "We also keep track of the average training loss for each epoch. Let's put all this into a new training function called `train_nn`:"
      ],
      "metadata": {
        "id": "S0f-Cv56YtE5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def train_nn(model, training_set, epochs, learning_rate=0.01):\n",
        "  optimizer = SGD(model.parameters(), lr=learning_rate)\n",
        "  loss_function = nn.CrossEntropyLoss()\n",
        "  training_loader = DataLoader(training_set, batch_size=10, shuffle=True)\n",
        "  losses = []\n",
        "\n",
        "  for epoch in range(epochs):\n",
        "    total_loss = 0.0\n",
        "\n",
        "    for samples, labels in training_loader:\n",
        "      optimizer.zero_grad()\n",
        "      outputs = model(samples)\n",
        "      loss = loss_function(outputs, labels)\n",
        "      loss.backward()\n",
        "      optimizer.step()\n",
        "      total_loss += loss.item()\n",
        "\n",
        "    average_loss = total_loss / len(training_loader)\n",
        "    losses.append(average_loss)\n",
        "\n",
        "  return losses"
      ],
      "metadata": {
        "id": "91x7125JYzeD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's train the model:"
      ],
      "metadata": {
        "id": "AMdMxPLMcnxP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "losses = train_nn(nn_model, training_set_torch, 500, 0.01)\n",
        "visualize_loss(losses)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "y2dQJmCicqAu",
        "outputId": "9e6b5281-80d8-4a84-f2fe-8da650791f70"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The model converged more or less quickly at around epoch 50. Subsequent improvements were not big in terms of training loss. As such, we could have stopped training earlier.\n",
        "\n",
        "We can also calculate the accuracy of the model on the training set."
      ],
      "metadata": {
        "id": "V0MunxUXFP2v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nn_model.eval()\n",
        "with torch.no_grad():\n",
        "    predicted_labels = predict_nn(nn_model, training_samples_torch)\n",
        "    print(f\"Accuracy: {accuracy(predicted_labels, training_labels)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GnzZAzElltQ5",
        "outputId": "47b512a5-0105-46e3-d810-553ae367ee83"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 0.987500011920929\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The model could not achieve 100% accuracy on the training set, despite it being easily linearly separable. Let's investigate."
      ],
      "metadata": {
        "id": "35ogCB_nl6Sj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Evaluation\n",
        "We can now evaluate how the model behaves on unseen data and whether it generalizes.\n",
        "\n",
        "To do so, we switch the model to evaluation mode and disable the calculation of gradients, which are only necessary for training. This makes computation more efficient and reduces memory usage.\n",
        "\n",
        "We then predict the label of each test sample and calculate the accuracy accordingly.\n",
        "\n",
        "We can also calculate the model's accuracy on the training set:"
      ],
      "metadata": {
        "id": "MlwnVyx2ltm_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nn_model.eval()\n",
        "with torch.no_grad():\n",
        "    predicted_labels = predict_nn(nn_model, test_samples_torch)\n",
        "    print(f\"Accuracy: {accuracy(predicted_labels, test_labels)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u_KAPFfcFZuO",
        "outputId": "4f3c9b2b-4be5-431c-818b-dac57af082a6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As before, we can also visualize the labels the model assigned to the test data graphically. We can also visualize the models decision boundary by generating a grid of points, predicting labels for them, and using a contour plot to color the background of the visualization."
      ],
      "metadata": {
        "id": "OZ2tdmvrjOkO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def visualize_model_nn(model, test_samples, test_labels):\n",
        "    # Create a mesh to plot the decision boundaries\n",
        "    x_min, x_max = test_samples[:, 0].min() - 1, test_samples[:, 0].max() + 1\n",
        "    y_min, y_max = test_samples[:, 1].min() - 1, test_samples[:, 1].max() + 1\n",
        "    xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.01),\n",
        "                         np.arange(y_min, y_max, 0.01))\n",
        "\n",
        "    # Predict on the mesh grid\n",
        "    mesh_samples = torch.Tensor(np.c_[xx.ravel(), yy.ravel()])\n",
        "    mesh_predictions = predict_nn(model, mesh_samples).reshape(xx.shape)\n",
        "\n",
        "    # Plot the decision boundary\n",
        "    plt.contourf(xx, yy, mesh_predictions, alpha=0.5, cmap='coolwarm')\n",
        "\n",
        "    # Scatter plot the test data\n",
        "    scatter = plt.scatter(test_samples[:, 0], test_samples[:, 1], c=test_labels, cmap='coolwarm', edgecolor='k', s=20)\n",
        "    plt.title('Test Data and Decision Boundary')\n",
        "    plt.xlabel('Feature 1')\n",
        "    plt.ylabel('Feature 2')\n",
        "    legend = plt.legend(*scatter.legend_elements(), title=\"Classes\")\n",
        "    plt.gca().add_artist(legend)\n",
        "    plt.show()\n",
        "visualize_model_nn(nn_model, test_samples, test_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "P45hkKZ3jnZb",
        "outputId": "75594f2d-4a0f-4437-c6b8-220b3c24c483"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now also visualize the models output for the training set a little better, and see, that it was unable to classify one sample from class `1` correctly."
      ],
      "metadata": {
        "id": "p4iO2Hkgla79"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_model_nn(nn_model, training_samples, training_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "tac_Dysokbqg",
        "outputId": "216ef1a0-0106-488e-8578-4edc0ea28005"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ideally, the decision boundary would be located such that the samples of each class are as far away from it as possible. This would yield better generalization, and also fix the one misclassified sample of class `1` in the training set.\n",
        "\n",
        "We can try to more complex neural network model."
      ],
      "metadata": {
        "id": "MtdGsO6ynx72"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A (not so) deep neural network classifier\n",
        "Creating a more complex neural network is very simple with Torch. Let's create a neural network architecture that has:\n",
        "\n",
        "1. A linear layer with 2 inputs and 64 outputs\n",
        "2. Another linear layer with 64 inputs and 64 outputs\n",
        "3. A final layer with 64 inputs and 2 outputs\n",
        "\n",
        "The first layer's input size is equal to the number of features of our samples. The last layer's output size is equal to the number of classes. The additional hidden layer gives the model more \"degrees of freedom\" when it learns how the data is shaped.\n",
        "\n",
        "We also need to decide on an activation function, that is, a function that is used to calculate a value based on the weighted inputs to a neuron. A common choice is the [ReLU](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)) function.\n",
        "\n",
        "Here's how we can define and instantiate this model:"
      ],
      "metadata": {
        "id": "wbhUKv_HoQEY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class SimpleDeepNet(nn.Module):\n",
        "  def __init__(self, input_size=2, hidden_size=64, output_size=2):\n",
        "    super(SimpleDeepNet, self).__init__()\n",
        "    self.fc1 = nn.Linear(input_size, hidden_size)  # Input to hidden layer\n",
        "    self.fc2 = nn.Linear(hidden_size, output_size)  # Hidden to output layer\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = F.relu(self.fc1(x))  # Activation function for hidden layer\n",
        "    x = self.fc2(x)  # No activation here if using CrossEntropyLoss\n",
        "    return x\n",
        "\n",
        "deepish_nn_model = SimpleDeepNet(2, 64, 2)"
      ],
      "metadata": {
        "id": "eiGJnDlQoxqF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next we can train the model as before."
      ],
      "metadata": {
        "id": "-0IeTC2kpa0s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "losses = train_nn(deepish_nn_model, training_set_torch, 500, 0.01)\n",
        "visualize_loss(losses)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "dDhxn6UWnxnc",
        "outputId": "bde0131d-ba5e-4bdd-e0c4-acee17cd59dd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "What is the model's accuracy on the training set?"
      ],
      "metadata": {
        "id": "RQQovh1Fp9Q5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "deepish_nn_model.eval()\n",
        "with torch.no_grad():\n",
        "    predicted_labels = predict_nn(deepish_nn_model, training_samples_torch)\n",
        "    print(f\"Accuracy: {accuracy(predicted_labels, training_labels)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "II2KSlZnqBuO",
        "outputId": "98b35b7d-f103-41b0-ad26-569bfb6012b1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Looks like it got it perfectly. Let's see how it does on previously unseen samples from the test set."
      ],
      "metadata": {
        "id": "HOl0gVGuqFkI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "with torch.no_grad():\n",
        "    predicted_labels = predict_nn(deepish_nn_model, test_samples_torch)\n",
        "    print(f\"Accuracy: {accuracy(predicted_labels, test_labels)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cnHVSY_fqLS5",
        "outputId": "c0f808c4-6309-49f4-970e-d88298f28625"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "And finally, let's have a look at the decision boundary it learned."
      ],
      "metadata": {
        "id": "tsigZ8DGqPqf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_model_nn(deepish_nn_model, training_samples, training_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "iBetsv8DqTyA",
        "outputId": "76a62450-19ec-43a6-fdf7-ebf2956b39ac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Avx04cIBhw4bh7u6eb/aJVqu9Lce0adNu+4v61i+j/2a59QP839fIzs7myy+/LFCugt6/oCIjI7GxsWHatGn5rjtlypQHut6/xcfH88wzz2AwGHjrrbfy2p9++mmuXLnCrFmzbjsnIyMj75FN586d0Wg0vPvuu7f1FtyrRyIuLi7fa1tbW6pWrYqqqncdDxYZGYmtrS1Tp07Nd+1vv/2WpKQkHn/88ft/wg9p5cqVAHlTt/39/alVqxZz587N9310+PBh1qxZk2/do3LlypGUlMTBgwfz2qKjo1m6dOkDZdFqtbRt25Zly5Zx8eLFvPZjx46xevXq246F/P8mSUlJzJ49u9D37dWrFwkJCQwYMIDU1FSLWs9LmJf09IgSoXnz5gwYMICJEyeyf/9+2rRpg42NDadOnWLx4sV8/vnndOvWLW913y5dulCuXDlSUlKYNWsWLi4ueT/87e3tqVq1Kj/99BMVK1bEw8OD8PDwfI+n7mTTpk1kZmZiMBiIi4tjy5YtrFixAldXV5YuXZq3fgrAE088wffff4+rqytVq1Zl27ZtrFu3Lm+a7y21atVCq9UyadIkkpKS0Ov1PProozRq1Ah3d3f69OnD0KFDURSF77//vsCPFQp6/4Ly9vbmf//7HxMnTuSJJ56gffv27Nu3jz/++AMvL68CX+fkyZPMnz8fVVVJTk7mwIEDLF68mNTUVCZPnsxjjz2Wd2yvXr1YtGgRL7/8MlFRUTRu3BiDwcDx48dZtGhR3hou5cuX56233uK9996jadOmPPnkk+j1enbt2kVAQAATJ068Y5Y2bdrg5+dH48aN8fX15dixY0yfPp3HH3883/is/34dRo8ezfjx43nsscfo2LEjJ06c4Msvv6RevXpF/sv3ypUrzJ8/H7hZ9B44cICZM2fi5eWV79HWxx9/TLt27WjYsCEvvvhi3pR1V1fXfGtQ9ejRg1GjRtGlSxeGDh1Keno6M2bMoGLFigUeYP9f48ePZ9WqVTRt2pRBgwaRm5ubt/7Rv4urNm3aYGtrS4cOHfKKlVmzZuHj40N0dHSh7hkREUF4eHjeYPfatWs/UHZRAplhxpgQD+2/U9Zv+frrr9U6deqo9vb2qrOzs1q9enV15MiR6tWrV1VVVdW9e/eqzzzzjBoUFKTq9XrVx8dHfeKJJ9Tdu3fnu87WrVvVOnXqqLa2tvedvn5ryvqtDxsbG9Xb21tt1qyZOmHCBPX69eu3nZOQkKD27dtX9fLyUp2cnNS2bduqx48fV4ODg2+b3j1r1iw1LCwsb4rvrenrW7ZsUR955BHV3t5eDQgIUEeOHKmuXr36rlPcH+T+t6Zk/3eK/63P+d/3MRgM6vjx41V/f3/V3t5ebdGihXr48OE7fk538u+voUajUd3c3NSIiAj11VdfVY8cOXLHc7Kzs9VJkyap1apVU/V6veru7q7WqVNHHT9+vJqUlJTv2O+++06NiIjIO6558+bq2rVr897/75T1mTNnqs2aNVM9PT1VvV6vlitXTn399dfzXfe/U9ZvmT59ulq5cmXVxsZG9fX1VQcOHKgmJCTkO6Z58+Z3nBJ/t2nj//XfKesajUb18fFRn3nmmXzTyG9Zt26d2rhxY9Xe3l51cXFRO3TooB49evS249asWaOGh4ertra2aqVKldT58+ffdcr6nZYYuNO/94YNG/L+ewoLC1O/+uqrO15zxYoVao0aNVQ7Ozs1JCREnTRpkvrdd9/d9jUODg5WH3/88Xt+fT766CMVUD/44IN7HidKF0VVi3EkohBCCFEMPv/8c4YPH8758+fvOMtMlE5S9AghhChRVFWlZs2aeHp6FnogtCjZZEyPEEKIEiEtLY0VK1YQFRXFoUOHWL58ubkjCQsjPT1CCCFKhPPnzxMaGoqbmxuDBg26bYNaIaToEUIIIUSpIOv0CCGEEKJUkKJHCCGEEKVCqRrIbDQauXr1Ks7OzkW+1YAQQgghTENVVVJSUggICECjefD+mlJV9Fy9evWhNyEUQgghhHlcunSJsmXLPvD5paroubV0/PQ5B7F3uPMy8kIIIUwvwvUMxpULcapWy9xRhBVIzcig7oiRd90CpqBKVdFz65GWvYMzDlL0CCGE2Tis+Rnnug3NHUNYmYcdmiIDmYUQQhQrP1+DuSOIUkqKHiGEEMXK/8dx2Om15o4hSiEpeoQQQhQ7m4q1zB1BlEKlakyPEEII84qIGoOtjSwZcj+5Oh25entzxyg2uqwMdLm5pr+Pye8ghBBC/Iu+cm1zR7BYRiAhpBwGF9dStZ6cqqpok5NwP3/GpI+gpOgRQghRLCKixpg7gsVLCCmH6u5BgI8PDg4OlIayRwXS09OJ0WpJADzPnzHZvSym6Nm4cSMff/wxe/bsITo6mqVLl9K5c+c7Hvvyyy8zc+ZMPvvsM4YNG1asOYUQQjw45+p1zB3BYuXqdBhcXAnw8cHL09PccYqVg/3NR3lXDQZydTqTPeqymIHMaWlp1KxZky+++OKexy1dupTt27cTEBBQTMmEEEI8LOnlub9cvT2KouDg4GDuKGbh4OCAoigmHctkMT097dq1o127dvc85sqVKwwZMoTVq1fz+OOPF1MyIYQQRUF6eQqmNDzSupPi+LwtpqfnfoxGI7169eL111+nWrVq5o4jhBCigKSXR1gKqyl6Jk2ahE6nY+jQoQU+Jysri+Tk5HwfQgghip/08hQfra0tPyxcaO4YFskqip49e/bw+eefM2fOnEJN4Zs4cSKurq55H7LDuhBCCGt36fJlXnjpJYJCQ7FzdCQgMJDItm359bffzB3N4llF0bNp0yauX79OUFAQOp0OnU7HhQsXeO211wgJCbnreaNHjyYpKSnv49KlS8UXWgghBBFRY6SXpwidOnWKeg0asHnLFt5/7z1279jBrytW0KxpU14dPtzc8SyeVRQ9vXr14uDBg+zfvz/vIyAggNdff53Vq1ff9Ty9Xo+Li0u+DyGEEMJa9R84EEVR2LNzJ72fe47w8HBqR0Twzttvs3PbtjueM3joUMIqVMDB2Zmg0FCG/+9/ZGdn572/c9dOGjZpgrObGy7u7lSvVYvNW7YAcOrMaSLbtsXN0xNHFxcqVqnCkp9/zjt3z969tGjVCidXV7z9/Oj61FPEXIvJe3/e999TuWpVHJyd8fD2pkmzZqSkpJjoq3N/FjN7KzU1ldOnT+e9PnfuHPv378fDw4OgoCA8/7NmgY2NDX5+flSqVKm4o4pSLCcni60bl3Jg9zp0OlvqN+lA7Xpt0Wis4u8HIYpVRNQY5D+NonPjxg02bdrEqFGjcHZ2vu39//6evMXZyYlvvp5JYNlA9u7bx5BXX8XZyYl3x40DoFef5wmvVo2vvvwSnVbLrj17sLW1AeDlgYPIzs5m7Zo1ODs5cfDgwbx7x8XF0bZdO3r27Mnnn31GRno6r7/xBk92e4qtmzZx8dIlXurfnzFvv02Pp58mMTmZqPVRqKpqmi9QAVhM0bN7925atmyZ93rEiBEA9OnThzlz5pgplRD/yMxMY8Jb3Th9YhcuHtUwGrLYFLWIRs27Mvi1GVL4CHEHjtXk0VZROXb8OKqqUqVy5UKd9+EHH+T9/woVKnDsxAl++fnnvKInOjqaoUOHULNGDYB8M6SvXLlChw4dqFfn5r9j5X91NHz86adUq1qVqZ99ltc2b84cylesyOHDh0lOScFgMNCjR3cqlCsPkHcdc7GYoqdFixaFqv7Onz9vujBC3MHvy77i3OmDVG/8BS7uN38o3LjyJ1s3vEf9Rk/QoHEHMycUwnLINPWiZ3zAHpLv5szhyxkzuHjxIunp6RgMBhwdHfPe79+/H8OHj2DhgoW0aNGCZ3v2zCusXn75ZUaOHElUVBTNmzWjR/fu1KtbF4BDhw+zfccOnFxdb7vniVOn6NyxIw0feYQ6devRtGlTIiNb0avns3h5eT3Q51EU5E9TIQpo68ZlePi3yCt4ALzLtMLZrTLbNy8zXzAhLJQMYC5a1apUQVEUjh0/XuBz/lq/npcHDqR1ZCS/LFnCjq1bGTpkCDk5OXnHfDLpI/bu2kXbtm3ZsHEjEXXqMH/BAgCGDRnCsaNHeaZ7d44cPUqTZs2YOGkScHMnhUcffZSd27fl+zh0YD9tIiPRarVs2rCBpUuWULlSJWbO/JrK1apx8uTJov3CFIIUPUIUUE52Jjrd7cvDa3WO5GRnmSGREJZJenlMw9vbmyZNmvDdd9/dcTBwXFzcbW2bNm3C39+fiRMm0KRxY6pVq8bFO8xkDg8PZ8xbb7Fp/XratmnD3Llz894rFxrKayNGsOq33xjQvz9z580DoGbNmpw8eZIKFSpQtUrVfB+3xv0oikKrVq349OOPOXLwIDY2Nvy4aFFRfUkKTYoeIQqoVp1HiYtZT3ZWQl5bWvJZkuL2U6P2o2ZMJoTlkV4e0/jqyy8xGo3UqV+fefPnc+TIEfYfOMAHH35Ig0aNbju+UsWKREdH8+3s2Rw7fpwPPvww36zntPQ0+r74In+sXsWpM6f5888/OXDwIBX/HrvTb8AAli5fzsmTJ9m6bRubNm+mQoUKAIwYNoykpCQ6P9mVTZs3c+z4cZYuX87TzzyDwWBg/caNvDlmDJu3bOH02bN8/8MPJCQkmHVXBYsZ0yOEpevYbSjbN6/k4KYX8QyIxGjIJPbqOsoGVaZZq+7mjieERajjdgqjuUOUYJUrVWLXjh2MHTeOt95+mxs3buDu7k718HCmTf38tuN7dO/Oxs2bGTlqFNnZ2bRs2ZIRw4fz8SefAKDT6oiPj+elfv2Ji4vDzc2N9u3a8cnfj7AMBgPDR4zg2rVrODo60rx5c76cPh2A4KAgNvz1F6+NHEmHTp3Izs4mICCAR1u2RKPR4ObqypYtW/j6669JS0vD39+fcWPH0rVLl+L7gv2Hoppz7lgxS05OxtXVlW8XncPB4fbpfkLcz43rl1i+aAp7d65FZ2NLw6ad6NhtKI5Otw/kE6I0ksUIH1ymozMp5StSPiwMe3vT7TRuqTIyMjh99izOp09il5b/8V1KRgaVBw4hKSnpodbck54eIQrB2yeQl1751NwxhLBIfr4Gc0cQ4p5kTI8QQogi4f/jOOz0WnPHEOKupOgRQgjx0HL0N9d9salYy7xBhLgHKXqEEEI8tPqrRmBro5g7hhD3JEWPEEKIIqGvXNvcEYS4Jyl6hBBCPJSIqDHoZCiPsAJS9AghhHho9lVlmrqwfDJlXQgrlZ2dyZ4dq0iIiyYopBpVazSRnd5FsYuIGoN82wlrIUWPEFbo7On9fDTuWZISr6HV2WHIzSSsfASjxi/ExbXodjBWVZWc7ExsbO1QFBmkKu7MsZr08gjrIPW5EFYmNyebj8c/h1HxIKLFPBq0/YNqj0zm8uXzzJo2okjuoaoqa3+fzdAX69KnayADnq3CkgUfkZubc/+TRakhG4sKayNFjxBWZv/eP0lMiKF8jZE4OAWhKApuXrUpW+F59uxYRVLijYe+x8qfp/Hdl6+j2FSgQq3ROHk045cfJ/NNERVVouSQLScsm8Ggsn1vAivXXWP73gQMhuLZeWrSxx8TGBKCvZMTterUYeOmTcVy3/uRx1tCWJnE+GsA2DsF5Wt3dA5FVY0kJ8Xh6ub9wNfPykxn6U9T8A/pSlj4EAB8yrbF3imQDX9Npcszr+HrF/LA1xclg2w5YflWb7jBl3PPk5D4Tw+tu5sNg/qE0Lb5g/+MuJ/v5sxh7LhxfPLRRzRu0phPPp1Mx86dOXroEAEBASa7b0FIT48QVia0XA0A4mO25muPi9mMnb0LPr5BdzqtwC5fPE5mRjLeZVvna/cu0wZUlZPHdj7U9UXJ4P/jOOnlsWCrN9xgwuen8hU8AAmJOUz4/BSrNzx8j/DdTJ02jWd69OCVwYOJqFmL7+fMwc7Oji+/+spk9ywoKXqEsDJhFSIIr9WC0wc/5PLpBSTc2MXZw1O5enYxTzw5EL2dw0Nd38nZHYCs9Jh87VkZN187Obk/1PWFEKZlMKh8Off8PY+ZMfe8SR51ZWVlcfToUSIjI/PaNBoNTZo0YedO8//BJEWPEFZGURRGvDmbJi06cfn0HI7ueJ3k2Ci6936TLt1fe+jr+/qHUqFyfS6d/IaM1EsAZGfGce7IVFzdfKleq/lD30NYt4ioMdLLY8F2HUi8rYfnv+ITc9h1ILHI7x1z7RoGgwF/f/987T4+Ply/YbrepYKSMT1CWCF7B2cGvDqV3v0mkJIcj7unHzY2+iK7/qAR03nvzSfZu74XDk5lyEi/hp3egZHjFqCzsS2y+wghit6N+OwiPa4kkaJHCCtm7+CMvYNzkV/XLyCMz2ZuY9vm5Vy+cBwv77I0btkNJye3Ir+XsC6y5YTl8/Yo2B8mBT2uMPx8fdFqtURHR+drv379Oj7ephs8XVBS9Agh7shWb0/zVj3MHUNYINlywrLVq+mGu5vNPR9xebjZUK+mW5HfW6/XU7VqVf7880+efeYZAIxGI1u2bOHFF14o8vsVlozpEUJYhOSkWDb8+SNRa+YTF3vV3HHEHchihNZBq1UY1CfknscM7BOCVmuaVdaHDhnCwh9/5IuvZrD/wAF69+1LRkYGAwcMMMn9CkN6eoQQZrfmt++YN+ttDLk3xxhoNFo6dx9Ot56jZPsLCyMDmK3DrXV4/rtOj4ebDQNNvE7PC88/z/Xr15k48UNiY2OpXLkyy5YupUyZMia7Z0FJ0SOEMKsTR3cwe8ZI/II7E1SpL4qi4+rZRfyy8BOCQqrRoHEHc0cUQB23UxjNHUIUStvm3kQ28WLXgURuxGfj7WFLvZpuJuvh+bc3Ro7kjZEjTX6fwpKiRwhhVn+umouDcyBh4UNRlJtP3IMq9SU5fj9rf58tRY+FMC6dJ708VkirVXiktqytdYuM6RFCmFV8bDT2jqF5Bc8tDs7libsRfZezRHGSLSdESSFFjxDCrILDwklJOIAhNz2vzWjMJSluJ6Hlws2YTNwiW06IkkKKHiGEWbV54kUUcjmy4zXiojcRf207x3a9QWZaNI8/Ocjc8Uq9HL2juSMIUWSk6BFCmJWvXwhvvr8Ed1ctx/eM4diuN9DrEnj9nfmUqxBh7nilXv1VI7C1kRl0omSQgcxCCLOrWKUeH06L4sa1ixgMufgFhMlUdQuir1zb3BGEKBIW09OzceNGOnToQEBAAIqisGzZsrz3cnJyGDVqFNWrV8fR0ZGAgAB69+7N1auygJkQJYWiKPj4BeNfppwUPBZCtpwQJY3FFD1paWnUrFmTL7744rb30tPT2bt3L2PGjGHv3r388ssvnDhxgo4dO5ohqRBClB6y5YQoSSzm8Va7du1o167dHd9zdXVl7dq1+dqmT59O/fr1uXjxIkFBQcURUQghSg3ZckKURBZT9BRWUlISiqLg5uZ212OysrLIysrKe52cnFwMyYQQomSQaeqipLGYx1uFkZmZyahRo3jmmWdwcXG563ETJ07E1dU17yMwMLAYUwohhHWSXp6SQzUYuLFmE5dmL+HGmk2oBtMvNLl6zRoi27bFr0wZtLa2/LBwocnvWVBWV/Tk5OTw9NNPo6oqM2bMuOexo0ePJikpKe/j0qVLxZRSCCGsm/TyWL8rC1byV7lH2d15IIcHj2N354H8Ve5RrixYadL7pqalER4ezicff2zS+zwIq3q8davguXDhAn/99dc9e3kA9Ho9er2+mNIJIYT1k8UIS4YrC1Zy8KXRt7VnX4/Lay/T0zT72nXt0oWuXboA0Of5501yjwdlNUXPrYLn1KlTREVF4enpae5IQtxRWmoSm6MWE331DH7+oTRp+RROzrLhn7AO9VeNkF4eK6caDBx/85N7HnPirU8J6N4eRVu61iSwmKInNTWV06dP570+d+4c+/fvx8PDA39/f7p168bevXv59ddfMRgMxMTEAODh4YGtra25YguRz7nTB/hgzFOkpSXj6FSW9NTLLP5hEqPfXUz5SrLAmxDC9GL/3Er29bh7HpN1LZbYP7fi3aZpMaWyDBZT9OzevZuWLVvmvR4xYgQAffr0Ydy4caxYsQKAWrVq5TsvKiqKFi1aFFdMIe5KVVWmfjQARetNnUe/Rm/nRXZmHCf2jGHqR/2ZMmsnGo3VDaMTpUhE1Bjp5SkBMq9cK9LjShKLKXpatGiBqqp3ff9e7wlhCc6e2kfM1dNUe+Qz9HZeANjaeRJc5WUObR3KqeO7qFS1wUPdQ1VVdm/7nc3rF5ORnkrVGk2IbNdHHp8JIfLYlfEt0uNKEvmzU4gikpZ2cx0ovZ13vnbbv1+npz3cOlGqqjJr2nAmf9CHY8fOcDk6m8U/fMToV1sRHxf9UNcWQqaplxxerRph63Pvca96Xy+8WjUqpkSWQ4oeIYpIWIVa6Gz0XL+8Kl/79cur0epsKVfx4XYMP3ZoC1Fr5lOu+v+o0XgGVet9QETzuSQnp7Dkh0m3Hb9r62+MH9WRQb1r8N6bXdi7a81D3V+UfPJoq2RQtFoqf/C/ex5TacJrJhvEnJyczI4dO9ixYwcAZ8+eZceOHZw+e9Yk9ysMKXqEKCJOTm507PoKl0/P5+S+94m58Csn93/ApZNzeLzzy7i4ej3U9Xdu+w17R398gx7Pa7Nz8Men7OPs2Jx/3Y3fln7J5A/6EB2TjqPHo1y+nMDH43uy9vfZD5VBlEzSy1PylOnZgRrfTLytx0fv60WNbyaabLo6wJZtW2nUtCmNmt4cJD1u/HgaNW3Km2++abJ7FpTFjOkRoiTo9uwbuLr58NvSrzhzaB1e3kH06f8BbTv0e+hrGwy5KJrb/5PVaG0xGP9ZZTU9LZmfvp+If8iThIUPBW4+Gjt98GMWznmPZo92R2/n8NB5zM1oNPLX6nms+30e8XHRhJavQaenhlK1emNzR7NK0stT8pTp2YGA7u2J/XMrmVeuYVfGF69WjUw+Tb1d28cwZGeb9B4PSooeIYqQoii0eeJF2jzxIkajsUhna0XUa82632eTcH0bHr43n8XnZCdz4/If1K7fJu+440e3k5OdgX9o13y5AkK7sv/S75w5uZeqNZoUWS5zmfPVKNb+PhtP/2a4+UZw7uw23n+zC8PfnEO9hu3NHc9q+PmaflsCYT6KVlvqpqXfixQ9QphIUU9Pr1Unklp123Bg9xg8/BpjY+tO/LWN2OjgqWdH5h1nY3NzFXKjISPf+YbcdAB0Nta/Snn0ldOs/X02oVVfISCsGwCBFXtzbNebzP92HHUaPCbLAxSQ/4/jpJdHlBryU0EIK6HRaHjtrTn07v8+rk6pKLnHaN6qCxM//xP/MuXzjqtSrSHOrt5cPPEtRkMWAAZDJpdOzsHDqwzlK1r/IomH9m9E0WjxC/5nXIKiaPEL7sz1mLPcuH7RjOmsh/TyiNJGenqEsCI6G1se69CPx+4xRkhnY8vLr05h8gd92RPVA0eXiqQmHQNjNq+P/QFNCVh23sZGj2o0YjBkoNH+03OVm5MKgK2tnbmiWRXp5RGljRQ9RSgp8QaqquLm7mPuKKKUq12/LR9/sZF1f8zlWvQ5/Mv0JrL98/j6hZg7WpGo0+AxdDobzh/7mnLVR6DR6MjOSuDq2QVUrPoI7h5+5o5o8WRjUctVWpfiLY7PW4qeInDm5F7mzHyT0yd2AxBWIYI+/T+gYpV6Zk4mSjP/MuXp9dJ75o5hEi6unrw4+BO+nvoqSbE7sXcMIiXxCPb2Trw0aJ6541mF+qtGYGujmDuG+BddVgaqqpKeno6Dvb254xS79PR0VFVFl5Vx/4MfkBQ9D+la9Dnee/NJbOwCqFDrLRRFQ/T5xbz/1pNM/PwvygRWMHdEIUqkFq17Elq+JuvX/EBCfAwh5drRss1zuLp53/9kAYC+svWP7ypJdLm5aJOTiPn7EbSDgwOloSxVuVnwxFy/jjY5CV1ursnuJUXPQ/pjxdeo2BD+yBS0uptrn3j4NWbf+uf4Y/kMXnplspkTClFyBYdWo8+AD8wdg4z0FC5dOIaTszsBZS3/D52IqDHorH9oV4nkfv4MCcBVgwFFKQ0lz02qqqJNTsL9/BmT3keKnod05uR+XD3r5hU8AFqtHW5eDTh1Yp8ZkwkhTE1VVZb++CkrlkwjKysNgLAKtXnlf1/mm1FnieyrygBmS6QBPM+fIVenI1dfeh5x6bIyTNrDk3cfk9+hhHNz9+HatdO3tWekXcAvVAZTClGSrf71Gxb/8CEBYd3xLhNJVkYMF0/M4r03n2TK1zuwtcBfWrLlhHXQ5eaiy00xd4wSR9bpeUiPtn2OlMQTXDwxG4MhE4Mhi0unvic5/jCt2vYydzwhhImoqsrKn7/Au2xbQqsOxMm1Ap5+Talc5wMS4q6yffMKc0e8K5mmLkor6el5SBH1WtO150h+WfgxV84sAEXBaMyh01PDqCtL4QtRYmVnZRAfe5kKtXrna7d3KouDUwBXLp0wU7K7k14eUdpJ0VMEuvUcSfNWPdizYxWqqlK7fht8/UPNHUsIYUI2tnY4u3iRmngMn7L/7H2WlXGDjLRrePkEmjHd3UkvjyjNpOgpIt6+QTzWsb+5YwghiolGo6HNEy/wy4+TsXMse3NMT3oM545Ow97BmcbNu97/IsWoWfLPyAgRUdpJ0SOEEA+oS/cRxMdGE7V2OueOTAPA3TOA/43/EQdHFzOnyy9lz37p5RGlnhQ9QgjxgLRaHf2HfkaX7sM5fWIPjs7uVKvRBK1WfrQKYYnkv0whhHhI3r5BePsGmTvGXUVEjcHe1bJ6noQwB5myLoQQpYAuyPJXihbC1KToEUKIEkymqQvxDyl6hBCihJMBzELcJEWPEEKUUNLLI0R+MpBZiIegqip7d64mas0CkpNiKV8pgsc69MfHL9jc0YQApJdHiH+Tnh4hHsJP8ybwyXvPcfLkORJTXPhz1Y+MGtKS82cPmTuaKOWkl0eI20nRI8QDir5ymuWLpxBU6SVqNJ5BxYi3iWjxA1obL+Z+/Za54wkhvTxC/IcUPUI8oD07VqHV2VEm7Km8Np2NE/4h3Th+eCtpqUlmTCdKszpup8wdQQiLJEWPEA/IaDSioABK/jeUm69V1OIPJQRgXDpPenmEuAMpeoR4QHUaPEZubgbR53/JazPkphNz/hcqVW2Ik5Ob+cKJUitH72juCEJYLIspejZu3EiHDh0ICAhAURSWLVuW731VVXnnnXfw9/fH3t6eyMhITp2SLlxhPmUCK9K+80DOH/uKw9uGcurAR+zb0IuczKv0emm8ueOJUqr+qhHSyyPEXVhM0ZOWlkbNmjX54osv7vj+Rx99xNSpU/nqq6/YsWMHjo6OtG3blszMzGJOKswlOyuDzVGL+WXhJ2zfvJzcnGxzR+K5F9/l1Te+JTjYCzvdJZq27MjEqX9SrmJtc0cTQgjxHxazTk+7du1o167dHd9TVZUpU6bw9ttv06lTJwDmzZuHr68vy5Yto0ePHsUZVZjBxfNH+WDM0yQlxGBr5052ZgJePsG8PWEJvv6hZsulKAqPNOnEI006Fcn14mKvsmPzctLTU6hWowmVqzVEUZT7nygEN6ep29rI94sQd2MxRc+9nDt3jpiYGCIjI/PaXF1dadCgAdu2bbtr0ZOVlUVWVlbe6+TkZJNnFUXPaDTy2Qd9MRidqN1iPvZOZUlLPsvJve8w9aMBTPhsjbkjFomoNfP5Zvr/UBQtWp0dPy/4iJp1Ihnx1hxsbe3MHc/sVFWVArAA9JWll1GIu7GYx1v3EhMTA4Cvr2++dl9f37z37mTixIm4urrmfQQGBpo0pzCNk8d2EnP1DCFVh2LvVBYAR5cwgiq/zNlTe7l88UTesdnZmZw6vpvzZw+hqtYzeyr6ymlmTRuBd5m21I38hbqRy6hc9z0O7d/Isp8+M3c8s8nOzuTHue/Tv2dlenbwZvSrrdi9/Xdzx7JIEVFj0FjFT3QhzKdE/ycyevRokpKS8j4uXbpk7kjiAaQkxQHkFTy32DveLGKTE28A8Nfq7xnUpwbv/O8xRg9tyYgBj3Dy2M7iDfuANv61CJ2tE2Hhr6KzcURRFDz9muJTtj1Ra34wdzyzUFWVKRNf5NdfZuDk0Zyw6sNJTNLx6fu92bZpmbnjWSTHajKAWYh7sYqix8/PD4Br167la7927Vree3ei1+txcXHJ9yGsT2j5miiKhtir6/O1x0avR6ezJSi0Gnt3rmbWtOE4uNajRpOvqNbgE9Iz7flgzNPExV41T/BCSEmKw87eB43WNl+7vWMZUlPizZTKvE4d382+XaspX3M0YeFD8A/uRNUGn+Dh25gf535gVT15piZbTghRMFZR9ISGhuLn58eff/6Z15acnMyOHTto2LChGZOJ4uDlU5ZmrXpw4diXnDs6g7iYTZw9/DmXT82lbYd+ODm78+svX+LqWYMKNd/A2a0ybt51qVLvQwwGlb9WzzP3p3Bf5SrWJiXxDOkp5/PaVNVAXMx6ylUsnr/eVVXl+OFtrPntO3bv+IPc3Jxiue/dHD+yDZ2NI57+zfLaFEXBp+xjXI85S2LCtXucXfrINHUh7s9iBjKnpqZy+vTpvNfnzp1j//79eHh4EBQUxLBhw3j//fepUKECoaGhjBkzhoCAADp37my+0KLYvPTKp7i5+7Dmt++4evYnHJ096PbsKDo/NQyAyxdP4ub3RL6BrjobJ5xcK3Pl4kkzpS64Rs26sGLJVI7ueA3/0Kew0Xty/fIfpCQc45URi01+/+SkOD5+91lOn9iNomhRVQOeXmUZOW4BQSFVTX7/O3FwdMGQm0luTjI2tm557VmZN9BotNjZySJ8AM2SfybF3CGEsBIWU/Ts3r2bli1b5r0eMWIEAH369GHOnDmMHDmStLQ0+vfvT2JiIk2aNGHVqlXY2cmsltJAp7OhR5+36dZzJGlpSTg5u6PV/vPt6+MXRHzi0XznGAxZpKecxtvX8nsD9XYOvPPhcubNepudW77BaMwlMLga/QfPp3qt5ia//6xpw7l44QxV63+Em3c90lPOcvrARD5+9zmmzNqZ72tdXOo36sDcr9/i7OGplK/xP7Q6B9KSz3L17ALqNGiHvYNzsWeyRCl79ksvjxAFpKil6MF4cnIyrq6ufLvoHA7yA7NE2Ry1mC8+HUjZ8s/iH/IkuTmpXDzxNYmxu/j4i034lyln7ogFlp2dSU52Fg6OLsUyRTsx4RqDeocTFj4Cv+AOee2piSc4sHkAo8b/RK06rUye4062bVrGF58MRNHYoLf3IS35PH4B5RgzcRkenv5myWRJmiX/LEWPKBVSMjKoPHAISUlJDzU+12J6eoR4GI1bdCMm+hzLFk3h8umbs50cndwZ9sY3VlXwANja2hXrujxJCTdQVRVHl7B87Q4uN79uCXHRxZblvxo27UyFSnXZFLWIpMQblKsQQYMmHWXdor9JwSNE4UjRI0oERVHo1nMkbR5/gWOHtmKjtyO8RlNs9fbmjmbxfPyCsdU7EH9tG87u1fLaE65tBSA4LNxc0YCbA9m7dB9h1gxCiJJBih5Rori4etGgSUdzx7Aq9g7OtOvYnxVLpqKqBtx9GpCadIorp+dSrWZzwsrXMndEcQcRUWOw02vNHUMIqyJFjxCCp58bjaLRsGrFLK6cWYhGo6Nhsy68MHCSuaOJe7CpWMvcEYSwKlL0CPEQsrMy2LXtN+Jir1I2uDK1ardCo7W+v741Wi3de71J56eGEXvjCq7u3jg5uZk7lrgLWYxQiAcjRY8QD+js6f1MGtuT5KTr2Ng6k5OdQtmgKox+b5HVzizS2zlQJrCCuWOIApABzEIUnlWsyCyEpcnNzeHT9/ugajyo3XI+9duspEbjL4i9EcvMKa+aO54owaSXR4gHJ0WPEA/g8P4NxMdeISz8Newdb26E6uxejcCKL3Jw319Wsd+XsF7SyyPEg5GiR4gHkPT3zu4OTkH52u2dgoF/dn4XoihJL48QD0eKHiEewK1p3LHRG/K1x0VvQG/nZHULIgrrIb08Qjw4GcgsxAMIDKlC3Ufas2/3ZDLTruDkVomE6zuJubCcJ595DTt7J3NHFCWM9PII8fCk6BHiAb3yv69YMHs8UWsXkHMqAydnT7r3fouO3YaaO5oooaSXR4iHI0WPEA9Ib+dA34GTePaFcaSmJOLi5oVOZ2PuWKIEis3QmzuCECWCFD1CPCRbvT0esseXMKHW20dKL48QRUAGMgshhBCiVJCeHiGEsGCWurForsHAuv0HOXrpEgEeHjxRry5O9nbmjiXEPUnRI4QQFs7SNhaNTkjgmUmfciomBnetDUmGHN5b+BNzRrxKvQrlzR1PiLuSx1tCCGGhLHWa+uvfziHxejyfaYP4XgnlO20oZbIUXvp8Olk5OeaOJ8RdSdEjhBAWzNIGMF9LTCTq8BF64k4F5ebjLC/FhlcUb2JTU4k6eNjMCYW4Oyl6hBDCAllqL09CahoAAYptvnZ/br6OS0kp9kxCFJSM6RGiCB09uJl1f8wlLvYqIWHhtO3wEgFlK5g7lrBSltbLAxDs442rnT2bslKopv1nqYZN6s1iJ6JcqLmiCXFf0tMjRBH5Y/lM3nuzMwcP7Cch2ZkNfy3jjaGPcvzwNnNHE1amjtspc0e4K3tbW17p2J5f1USmGGLYYkxhniGW6ep12taqSdXAQHNHFOKupKdHiCKQlHiDH2aPxz+kK6HVXkFRFAyGTI7ueJ1vvxzJR19sRFGU+14nLvYqyUmx+Jcph52dY4HvbzQYiL56FltbPd6+Qfc/QRRKdnYm2zYu5cjBzdjZO9K4eVcqVW1gsvsZl86zyF6eWwa2ewy9jQ1frvyddcnRONra0qvFo7zR7UlzRxPinqToEaII7N/zJ4bcbAIr9skrbrRaOwLCenB891tcjzmPr//du/3jY6OZMWUIh/evB8DO3pkOTw6mS4/X7lssbdu0jPnfjiM+9jIAYRUi6D/kM4LDwovmkyvl0lKTeHd0Zy6eO4SLexVyshNZ+9t3dHpqGD36vF3k96vjdgpjkV+1aCmKwoutI3m+1aMkpaXhZG+PrU5+nQjLJ9+lQhQB1Xjz19R/CxRFufkE2Wi8+68xgyGXCWO6ER+XSIVab2LvWJbY6PUs/uFDbPV2PPHkK3c999D+DUz9qB8evo2p1mAYuTmpXDkzn/fe7MInM7bg5u5TBJ9d6fbzwo+4evksNZt+jZNrRVTVyJUzC1m+eAp1GjxGhcp1i/R+xqXzsHd1KdJrmopWo8HD2dncMYQoMBnTI0QRqFG7JRqNjsunF+a1GY05RJ9bjF9AefwCwu567r5da7h66QQVa4/Hp2wbnN2rElp1EL5BHVjx8xcYDLl3PXfF4qk4u1Wmcp13cfOui1dAC6o2+ITMzHSi1swv0s+xtNqyfik+gY/j5FoRuFnIlinXAzsHH7ZuXFqk9/LzNQCgC5LB70KYgvT0iFIrPi6auBtX8PELxtXN+6Gu5eHpz1PPjeKneRNIid+PvXM5kuP2kJ0Vy8B3frjnI6pLF45jq3fF2a1yvnZ3n/pcu7iSlOR4DIZcolZ/T/TVM/j4hfBom+fw9g3i/LkjuPs9kdejBGBj64ajSyW2bvyFg3vXo7ezp1GzJ2ncoitarfwnX1hZWem42eTveVEULTobZ7Iy04r0Xv4/jrPILSeEKCnkJ6AoddJSk/h62nB2bl0JqopGo6Ppo0/zwsBJ2D7Ebumdnx5OUEhV1v4+l7jYc9Rr0JR2nV8mJKz6Pc/z9CpDdlYymenR2Dn457WnJp1Er3fk8oXjfPJeLwxGcHStwK5ta/jtly/53zvz8fQMIDX5TL7rZWZcJyXxGKmJCu4+Phhy4znw2WB2b/+DYaO/Q6ORDt7CCK/ZjGNH1xAQ2hWt7ub3R3L8YVKTzlC91htFdp/YDD1geVtOCFGSKKqqquYOUVySk5NxdXXl20XncHCQ59Cl1cR3unPs8E6CKvXD2b0aibF7uHTyWxo378LA4dOLPU9mZhpD+tZGY+NHWPhw7B0DiY1ez9nDk2ndrg+7d6wmx+BK5bofoLNxwpCbzok9YzHmXqLrM6/x3ZevE1zlZfyDO2HITefQtlfJyUqgVtNZ2DkGABAXvZHje97htbfnUfeR9sX+OVqzC2cP887r7dHZeOAZEElOViKxV1YTUq4aYz9cgc7G9v4XKYCIqDHY2ijoK9cukusJUZKkZGRQeeAQkpKScHF58DFv8iefKFUuXTjOwb1/ElptGH7BHXF0KUeZsKcJqtiPzVGLSUy4VuyZ7OwceWP8QrTEs3/jS2z7oy2n9k+kdr3W1G/8BLHXLxBY8UV0Nk4AaHUOBFXuR1JCDH4BYbTrOIALx2eyfVU7dq3rSlZGDL6B7fMKHgBP/2Y4uZZj17bfi/3zs3bBYeG8+8kfhNeIIO7KMrJTd9G+c3/efG9xkRU8t5TWgkdVVRZt3sIT496n9tARPPfJZ2w5dtzcsUQJJI+3RKly5dIJANy86+Vrd/Oux7mj04m+cgY3d99iz1WuYm2mfreXQ/vWk5wUS1iFCAKDK3Pk4CYAdDb5eyZvvc7JzqR3/wk81rE/hw9sxNbWju+/GYui3D4uRFE0ebPM7if2+mWSk2MJKFMeO3unh/zsrF9waDWGvznbZNePiBqDrhQP5Zm4+Ge++H0VdTWOtFD17D12lu6HP+HLQQPoWL/e/S8gRAFZTU+PwWBgzJgxhIaGYm9vT7ly5XjvvfcoRU/nRBHw9rm5Wmxq4rF87SmJRwHw8jHfarI6nQ0R9VrTPPIZAoNvDmouVyECO3tnYi4sz3dszPnl6Gz0VKxSHwAfv2AebduLJi2fol7Dx7hxdTVZmbF5xydc30lK4inqNHjsnhniYq/y/ltPMuSFWrw1LJKXe4WzZMFH95xyL4qGfVXLXYzQlK7ExTPjj9X00ngyTlOGXlovPqUsDRQn3lvwEwb53hNFyGp6eiZNmsSMGTOYO3cu1apVY/fu3fTt2xdXV1eGDh1q7niiAFRV5czJvcTHRRMcWu2ei/WZSliFCELL1+Lckc9QlP/h7F6VxNi9XDw+k1p12+QVRZbCzt6Jp597g3mz3iIz/TIuHhGkJh4m/tp2nu71Jk7O7red06XH/9i7cy37N/TBw7cJubmpJFzbRo3aj1K34d3H8xgMuUx4qysJCclUqPUW9k6BxF1dz88LPkKvt6dD1yGm/FRLLUvdWLS4bD56DKOq0kHjltemURSeUNx4O/Eyp6OjqVSmjPkCihLFaoqerVu30qlTJx5//HEAQkJCWLhwITt37jRzMlEQMVfPMnlCXy5dOJLX9kjTLgwcNvWhZkwVlqIovPbWXD5+rxdHdvwvr71yeCMGjSj+QcwF0a7TADw8/Vm59EuiLy/B1z+UZ56bQeMW3e54vKdXAB98vo7fl33Fgb3rsXN2oGOnD2j1WO97Tlnft2sN0VdOUaPJV3nT553dKpObm8bKX76kfeeBMuXdRCx5ywlTs7OxASADFYd/tWf8vS61rPQsipLVfDc1atSIr7/+mpMnT1KxYkUOHDjA5s2bmTx5srmjifswGgx8OPYZUlKzqfbIpzg4hxF/bQu7tk3D0cmVlwZ/Uqx5PL3LMPHzPzl1fDfXY85TJrAioeVrFmuGwmrQpCMNmnQs8PFu7r707DuWnn3HFvicSxeOY2vnds/1gmSF56JV2nt5AFrWCMfBxoY5ubG8qvFFpyikqgYWkUB4YFlCfOR7ThQdqyl63njjDZKTk6lcuTJarRaDwcCECRN49tln73pOVlYWWVlZea+Tk5OLI6r4jwN7/+Ja9Jl8PQh+QU+Qk5XIhnXf07Pv2GJfQkBRFCpWqUfFKjJI8hYv77JkZybevl5Q4gn0ekccnVzNmK7kKs29PAAuDg582Lc3w2Z9x0EyCDLYcFzJwsbWhh9feL5AG/UKUVBWM5B50aJF/PDDDyxYsIC9e/cyd+5cPvnkE+bOnXvXcyZOnIirq2veR2CgZY3XKC2ux1xAo9Hh5FopX7uLezVyc7JIjI8xU7KbVFUlNyfbrBksQf1GT+Ds4sXJfe+SmnQKgyGTa5f+IPrcYh597DlsbPTmjlii3FqMUEDXRg1Z8+5YOrVsim9EJV7u0J6/Jr5HzdAQc0cTJYzVLE4YGBjIG2+8weDBg/Pa3n//febPn8/x43dez+FOPT2BgYGyOGExO7hvPRPHdKN6o6m4eNTIa79w4juuX1zCzB+OYWfnWOy5srMyWPzDJP5a/T3paUmUCaxM157/o2HTzsWexVKcObWPT9/vQ0Lc1by2+o07Mvi1L7G1tTNjspInImpMqe/lEaKgimpxQqt5vJWenn7b8vlarfaeU2n1ej16vfw1ZW7hNZtRNrgqp/ZPILjyQBxdyhF3bQtXzyzgsY79zFLwqKrK5A/6cvjAJnyDOhPgFExczEamTnqJ3NxsmrZ8utgzWYJyFSKY+u0eDu/fQHJSHGEValE2qNL9TxRCCCtgNUVPhw4dmDBhAkFBQVSrVo19+/YxefJkXnjhBXNHE/eh0Wh4Y/yPTP/4ZY7vHfd3m46WbZ/jmT7mGch56vhuDuxZR6U64/Hybw6AT2A7Tuwdy6J5H9K4ebdSu0eVTmdDrbqR5o5RokVEjcHe9cH/WhVCPBirKXqmTZvGmDFjGDRoENevXycgIIABAwbwzjvvmDtaiXb88DZ+Xz6Tq5fP4F8mlHYd+1O1RpNCX8fTK4Cxk1Zw9fIpEuJjKBNYyawzgU4e24FWZ4+nX9O8NkVR8C7ThuO73yYx/hoeXv73uIIQD0cXVMHcEYQodaym6HF2dmbKlClMmTLF3FFKjU1/LeLLzwbj5BKGk1t1jh87zO7tnek/9HNatrn7rLl7CShbgYCy5v9h7+jkhtGQRU52IrZ6j7z2rIzraDRa7Bxk6wVhGjJNXQjzKZ399+K+srMymDPzTbz8W1GjySzKVR9GjSaz8CnblnmzxpCZmWbuiA+lXqMnsLHRc/bwFHJzUgFITTrF1bMLqNOgnQx0FyYlA5iFMA8pesQdnT6xh/S0RMqW74Gi3Pw2URSFMuV6kpmRzIkjO8yc8OE4ObnxyuszSbqxnd1/dmXf+mc5sKkfnp4e9B34obnjiRJKenksV05uLqv27OOrP1azbv9B2fOrhLKax1uieCl/D+JVjYZ87ap687VGa/1bQtdr2J6p3+1ly/olJCZcJ6x8Leo3egKdja25o1kEo9HI0UObuXT+GF7eZYmo11q+NkVAenksz+noGHp98hkX4+Kw02jJNBoo7+vLD6+PoKyXp7njiSIkRY+4owqV6uLs6s3l0/OoWHs8Go0O1ZjLpVNzcXRyp1LVBuaOWCTcPfx44slXzB3D4iQl3mDSuGc4d3o/Gq0tRkM27p4BjBq3kODQauaOZ5X8fA33P0gUO1VV6T/1C0hMY6o2mDBFzwklg49jrzF4xkyWj3nT3BFFEZLHW+KOdDa29Bv8CQnXd7Bv/bOc2Ps++zb0IuHaZl4c/LEsVFfCzfx8GFevXKLaI5/xyGOriWg+m5xcRz55rxcGQ66541kl/x/HSS+PBdp75iwnoqMZoHoRptxc162SYs8Lqie7z5zl1NWr97mCsCZS9Ii7qtfocSZMWUvDJq3xdEujfsMWvD95Talesbg0iI+LZt/uNQRWeBE3rwgURcHBOZRy1f9H7PWLHDmwydwRrY708liu60lJAAQp+R/dBv1dAF1Pkj0bSxJ5vCXuKSSsOv2HTnmgc3NzstmzczXRV07j6xdC3YbtZf8mK5CUcB1UFQfn0Hztt14nmHmvNGvk/+M4WYzQQoUHBaEA29RU2ituee3b1FR0Gg2Vy5QxWzZR9ApV9GRkZLBnzx48PDyoWrVqvvcyMzNZtGgRvXv3LtKAwjrFXD3LhLefIvb6BWz1rmRnJeHuGcBb7y+hTGBFc8cT9+AXEIat3oH4a1twdq+S1x53bTNwsxAWBZejv7nNiixGaJkCvb3o8kgDvtmxiwRDLlUUew6q6SwlkV6PtsDTRZavKEkK/Hjr5MmTVKlShWbNmlG9enWaN29OdHR03vtJSUn07dvXJCGFdVFVlc8n9SM9w0itZt9Rr/VyIprPJTtHz+QP+mIle9yWWvYOzrTr2J8rZxZw7uiXJMbu4fLpBZw99Cm16rYmOCzc3BGtSv1VI7C1UcwdQ9zDJy8+T6/IR1muS+Ed4xVW2aYzsP1jjHumu7mjiSJW4J6eUaNGER4ezu7du0lMTGTYsGE0btyY9evXExQUZMqMwspcPH+U82cOUKXeBzi6hAHg4BxMSNVXOLL9Nc6c3Ev5SjKg05I9/dxotDodvy/7mqtnF6HV2dK0ZTf69P/A3NGsSmzGzce5+sq1zZxE3IvexoZ3n+3B6G5duJGcjLerK/a2sjxDSVTgomfr1q2sW7cOLy8vvLy8WLlyJYMGDaJp06ZERUXh6Fj8O2ULy5ScFAuAvVP+Ytje8ebrpMQbxZ7JkhgNBhISruHo6IKdvWVud6HRannq2Tfo9NQw4mOv4uLmLatUP4DW20eis/4lrUoNe72eIG9vc8cQJlTgx1sZGRnodP/USIqiMGPGDDp06EDz5s05efKkSQIK6xMUUhWt1oa46A352uOi16MoGkLK1TBTMvNSVZW1v89m8PM1eeX5GrzUowLTPxlIakqCuaPdla2tHX4BYVLwPAT7qtKrKYSlKHBPT+XKldm9ezdVqlTJ1z59+nQAOnbsWLTJhNVydfMmsv3zrPn1O3KyEnHxrEVK/CGizy+hRetn8fQKMHdEs/hr9Ty++/J1vMu0oUr5oWSkXmLXtgVEXznDe5+uQqORFSRKkoioMcg/qRCWpcBFT5cuXVi4cCG9evW67b3p06djNBr56quvijScsF69XnoPRydXVq34hqvnFmNn78ITTw7mqefeMHc0szAajfyycDLeZVpTMeLvFV59wdG1Ike2D+fw/g3UqN3SvCFFkXOsJr08QlgSRS1FU2mSk5NxdXXl20XnpLu+mOTmZJOSEo+zs0ep3rcpMeE6A3tVpXKd9/D0b5rXrqoqu9d1ovPTr9Cl+wgzJhRF6dbGorICsxBFIyUjg8oDh5CUlISLy4OveSWLEwqT0tnY4u7hZ+4YZufg4IzORk9G2sV87dlZceRkp+Lm7mOmZMJUpOARwvLIE2chioGt3p4mLbpx9exCEq7vQFVVsjKuc+bAJPR2jjRoLGPiSopmyT+bO4IQ4i6kp0eIYtLrpfeIvnKWoztHobNxJDcnHXt7Z157ay4OjrJFQUmRsme/9PKUIieuXGHqyt/YfvQEzvZ2dG3amH5tWmNna2PuaOIOpOgRopg4OLowdtIKjh3awplT+3Bx9aJ+oyewl/FlJYZsLFq6HL5wkS4TPsQlF5qojsSnZPDpz8vYduw43782DK1M37M4UvQIUYwURaFqjSZUrdHE3FGECfj/OE56eUqRj5YsxStXYbISiN3fBU4zYxrjjhxl/aHDtKpZOtcks2QPVIZ+//33NG7cmICAAC5cuADAlClTWL58eZGGE0IIISyRqqpsPHKESJyxU/75VVpHcSBAq2fD4SNmTCfuptBFz4wZMxgxYgTt27cnMTERg+Fmd66bmxtTpkwp6nxCCGEVIqLGYO8qY7NKC0VRsNXZkKEa87UbgUyM6G1kTI8lKnTRM23aNGbNmsVbb72FVvvPpjJ169bl0KFDRRpOCCGsiS6ogrkjiGLUoUE9/lBSuKJmAzd7f5aqCcQbcuhQv66Z04k7KfSYnnPnzhEREXFbu16vJy0trUhCCSGENYmIGoOimDuFKG6junZhx/ETDIq9QFXFngTFwGVjFoPbP0aNkBBzxxN3UOiiJzQ0lP379xMcHJyvfdWqVbftyyWEMK2cnCx2bF7ByeO7cHZ2p0nLp/AvU97csUolp3AZwFza+Li5surdsSzavIVtJ05Szd6ero0eoVGVyuaOJu6i0EXPiBEjGDx4MJmZmaiqys6dO1m4cCETJ07km2++MUVGIcQdJCfF8t7oLly+eAwnlxCyMuNZ+tNnvDj4Y1o91sfc8UqNW1tOiNLJyd6OF1q34oXWrcwdRRRAoYuel156CXt7e95++23S09Pp2bMnAQEBfP755/To0cMUGYUQd7Bg9niuX4umZtNZOLlWwGjI4tzRL/j2i9epEdESb98gc0csNWSauhDWoVADmXNzc5k3bx6RkZGcOnWK1NRUYmJiuHz5Mi+++KKpMgoh/sNgyGXLhl/wC+mKk+vNwbMarZ6QKgPRavVs3bjUzAlLB+nlEcK6FKro0el0vPzyy2RmZgLg4OCAj49slChEcTPk5pCbk4Wt3jNfu0Zrh87GkYz0FDMlK32kl0cI61HoKev169dn3759psgihCggW709oeVrcePKalT1n60PEmN3k5kRS5XwRmZMVzpIL48Q1qfQY3oGDRrEa6+9xuXLl6lTpw6Ojo753q9RQ5bdFqI49Oj9Fh+O7c7hrUPxDHiUrPQYrl1aSZXwxlSPaGHueKWC9PIIYV0UVVXVwpygucMGaoqioKoqiqLkrdBsiZKTk3F1deXbRedwkE0erZqqqpw/e4iM9BRCy9UotZt2Ht6/kSULPubU8Z04OrnTPLIHXXu+jp2d4/1PFg/sVi+PFD1CFI+UjAwqDxxCUlISLi4PvvL5Ay1OaC5Xrlxh1KhR/PHHH6Snp1O+fHlmz55N3bqy8mVpcvb0fqZ/MojoyycB0Ns58WSPEXToOgSllK0QF16rGeG1mpk7RqkkBY8Q1qfQRc9/FyUsLgkJCTRu3JiWLVvyxx9/4O3tzalTp3B3dzdLHmEeKcnxTHirG1obP6o1+AQbvQfXLv7Gwjnv4uruQ/NWsmyCtTq4N4qliz7j3OmDuLr5ENmuF+07D0SrLfSPKZPy87Xc3mwhxL0V+qfJvHnz7vl+7969HzjMvUyaNInAwEBmz56d1xYaGmqSewnLtfHPH8nMTKdOow+w1XsAEBY+hOzMa6z8+QspeqzUzq2/8tnEvri4V8Uv5FkyUs+zcM77XDh3lFf+N8Pc8fLx/3Gc9PIIYaUKXfS8+uqr+V7n5OSQnp6Ora0tDg4OJit6VqxYQdu2bXnqqafYsGEDZcqUYdCgQfTr1++u52RlZZGVlZX3Ojk52STZRPG5evkUji4heQXPLS6etbl44iszpRIPw2g08sN37+Lh04DKdT9AUW6OG3TxqMGW9R/ToesrBIdWM3PKm5ol/4wsBiCE9Sr0lPWEhIR8H6mpqZw4cYImTZqwcOFCU2QE4OzZs8yYMYMKFSqwevVqBg4cyNChQ5k7d+5dz5k4cSKurq55H4GBgSbLJ4qHj18I6SkXyc3O/6snJeEQ3j6yArE1SoiL5nrMWXwCO+QVPADeZdui1eo5cnCTGdPll7Jnv/TyCGHFCl303EmFChX48MMPb+sFKkpGo5HatWvzwQcfEBERQf/+/enXrx9ffXX3v+5Hjx5NUlJS3selS5dMlk8Uj+aRPdBptRzfO4aUxONkZdzg4sk5xF6Nol2n/uaOJx6Ard4egNzsxHzthtxUjMYc9HoHM6S6XWyG3twRhBAPqUiKHri5WvPVq1eL6nK38ff3p2rVqvnaqlSpwsWLF+96jl6vx8XFJd+HsG5u7r6MHLcAxRDDwc0vs/vPp7h65gc6dhtK6/Z9zR1PPABnFw+qR7TkytkFZKbHAPy9j9gMtFod9Ro+buaEN7XePlJ6eYSwcoUe07NixYp8r1VVJTo6munTp9O4ceMiC/ZfjRs35sSJE/naTp48abbZZMJ8qlZvzLTZ+zh+eBsZGalUqFwXN3fZDsWavTjoI8aP6sje9c/h7FaRzLQr5Oak8vKwabi4et7/AiYmM7aEKBkKXfR07tw532tFUfD29ubRRx/l008/Lapctxk+fDiNGjXigw8+4Omnn2bnzp18/fXXfP311ya7p7BcOp2NrE9Tgvj6h/LJjC1s/Osnzp0+gJt7JM0jnyGgbAVzRwNuztiyd5We4qJmNBrZdPQYZ6JjCPbxpkX1cLR3WABXiKJS6KLHaDSaIsd91atXj6VLlzJ69GjeffddQkNDmTJlCs8++6xZ8gghipaDowuPdbj7bExz0wVZRgFWUlyJi6PXJ1M4ER2NTlHIVVXCfHz4/n/DCJGNrIWJFLqkfvfdd0lPT7+tPSMjg3fffbdIQt3NE088waFDh8jMzOTYsWP3nK4uhBBFISJqjPTymMCgL2eSeC2Oj7WBLNWUZ7I2iMy4JAZM+5JC7o4kRIEVuugZP348qampt7Wnp6czfvz4IgklRFFSVZXNUYt5780ujHqlBd/NGMm1aPNtp1IccnKyiL5ympTkeHNHsWq3ZmxJL0/ROnnlKrvPnOVFPKmi2KMoChUVOwaoXhy+dJmD5y+YO6IooQr9eOvWxqL/deDAATw8PO5whhDm9e0X/+PPVXNx86qN3j6YjX8uY9NfSxg7aTkhYdXNHa9IqarKr79MZ/niqaSlJqAoGuo+0p6XXvkEF1cvc8ezOq23j8ROrzV3jBInJjERgFAl/zIAt15f+/t9IYpagYsed3d3FEW5WZFXrJiv8DEYDKSmpvLyyy+bJKQQD+rs6f38uWouYeHD8Q/pBEBuThqHt73Cgu/G8+b7S4olh9FgICnpBg4OLujtTLfuzB/Lv2LB7PH4BXcmJLwZGakXObBvLhPf6c6Ez9aikUGihWZTsZa5I5Q4lcoEoFUUtqtpdFFs89q3q6koQJWyZc0XTpRoBS56pkyZgqqqvPDCC4wfPx5XV9e892xtbQkJCaFhw4YmCSnEg9q7cw22ehf8gp/Ia9PZOOIb1JlD+z8jOysjb3E8U/lz1Vx+XvgpCXFX0elsadT8SXr3m4Cjk+v9Ty4EgyGX5Yun4Rv4OOWqDwPAzas2Ds4hHN42jEP71lOzzqNFes+SLCJqDLY2t/dqi4fn6+ZGj2ZNmLdxC+kGA9UVB46QwWI1gS6PNCDQW3olhWkUuOjp06cPcHOTz0aNGmFjY2OyUEIUFUVRUFX178ey/3pDNdzsrbzDo9qi9OequXwz/TW8y0RSue5AMlIvsW3Tj0RfOcv4j3+746PiB5WYcJ3kpOuUqZh/vSwXj5rY2Dpx4dxhKXoKSV+5trkjlFjv93oWBzs75v+1noU58eh1Op5p1px3ejxt7miiBCv0mJ7mzZvn/f/MzEyys7PzvS+rHgtLUq/h4yz5YRLR536mTLnuAORkJxFz4Rdq1G6Fra2dye5tNBj4eeGneJdpTcWIt/LanVwrcmTH/zhyYFORrjXk6OSKzkZPeso5PHwb5bVnZcSQk52Ku4dfkd2rpJNeHtOz1ekY90x3Xu/SiZjERHxd3XCyv/9/j9EJCfywfiMnrlyljKcHzzZvSoWAgGJILEqCQhc96enpjBw5kkWLFhEXF3fb+waDrFwqLEdQSFXadx7I78tmEB+zAVt7P5Jid2Frq6PXS6ZdYiEp6QYJcVepXHdQvnZXrzrY2Dpx5tS+Ii167OwcadryKTZFLcDeKQgP38Zkpl3lzKGPcHRyp14jy9jOwdLdmrElvTzFw9HOjnJ+BSvI9509S49Jn2LMyaUSdmwlm9lr/2T6y/3pUL+uiZOKkqDQRc/rr79OVFQUM2bMoFevXnzxxRdcuXKFmTNn8uGHH5oioxAP5bkX36VKeEPWr/2RlOQ4GjZ8nrYd+uHpZdq/Du0dnNHqbMlIzb/RbXZmLLk56SaZTdXrpfe4fu0iR3aPQaPRYTTm4uzixcixP2Bn51jk9yuJWm8fiU4mbFkcVVV5bdZsAnI0vKuE4KRoyVGNTFav8b9vZ/NojXAc7UzXcytKhkIXPStXrmTevHm0aNGCvn370rRpU8qXL09wcDA//PCDrJAsLI6iKNR9pD11H2lfrPe1s3OkcbMubNu8ECfXCrh61SE7K44zhz5Gb+dIgyYdi/ye9g7OvPX+z5w+sYezp/bj6u5N7fptTfoYrySyryobi1qa09HRnIiOZqwmACflZlVqo2jogxebss6x4fAR2teVfzdxb4UueuLj4wkLCwNujt+Jj7+5+FmTJk0YOHBg0aYTwsr16j+Bq1fOcmTH/7CxdSY3Jw29nSMj3pqDg4OzSe6pKAoVKtelQmXp7i+siKgxyKx+y5SVkwuAg5K/G87x7zV2M7Nzij2TsD6FLnrCwsI4d+4cQUFBVK5cmUWLFlG/fn1WrlyJm5ubCSIKYb2cnNwY//FvHDm4iTMn9+Hq5k2DJh1NVvCIh+dYTXoLLFGlMgF4Ozvza2oiVTV2eTMfV6qJ6DQaGlWpbOaEwhoUuujp27cvBw4coHnz5rzxxht06NCB6dOnk5OTw+TJk02RUQirptFoqF6rOdVrNb//wcJspJfHstnodIx55mmGfv0t19VcahvtOaVksduYxpAn2uPn7mbuiMIKFLroGT58eN7/j4yM5Pjx4+zZs4fy5ctTo0aNIg0nhBDFSXp5LFvXRg3xdHZmxu+rWHfpMmW9vJnSujvdGsnCuKJgCl30/FtmZibBwcEEBwcXVR4hhCh2EVFjZMaWlWhRPZwW1cPNHUNYqUJ35hoMBt577z3KlCmDk5MTZ8+eBWDMmDF8++23RR5QCCGKg8zYEqLkK3TRM2HCBObMmcNHH32Ere0/G8WFh4fzzTffFGk4IYQwtYioMdi7ykryQpQGhS565s2bx9dff82zzz6LVvtPf3DNmjU5fvx4kYYTQojioAuqYO4IQohiUOii58qVK5QvX/62dqPRSE6OrJMghLAe0ssjROlS6KKnatWqbNq06bb2JUuWEBERUSShhBDmFx8bzfHD24iPjTZ3FJOSXh5hbvEpKWw+eozjl6+YO0qJV+jZW++88w59+vThypUrGI1GfvnlF06cOMG8efP49ddfTZFRCFGM0tNT+PrzYezYugJUFUXR0KBJJ/oPmYx9CVpUUXZSF+ZmMBp578dFzPkzipy/N+uuFRzMF4MHEOLjY+Z0JVOhe3o6derEypUrWbduHY6OjrzzzjscO3aMlStX0rp1a1NkFEIUoy8/HcTeXX9SLnw4Ec3nEhr+Kru3r+GrKUPNHa3IyU7qwpymLF/Jd2v+pLvqxkxtCGM0Ady4HEPPSZ+Sk5tr7nglUoF7es6ePUtoaCiKotC0aVPWrl1rylxCCDO4Fn2OPTv+oELNN/AJfAwAB+dgNIqOnVs/5sa1i3j7Bpk55cOLiBqDnV4W5hHmk5Oby3dr1vGE4koPjScAZRRbvFUbhsZdYM2+AzxeT5ZRKGoF7umpUKECN27cyHvdvXt3rl27ZpJQQgjzuHL5FACuXvl/2N56ffXy6WLPZCo2FWuZO4IoxeJTU0nMyKCG4pCvPUzR46LRcSYmxkzJSrYCFz2qquZ7/fvvv5OWllbkgYQQ5uPje3N19ZTEo/nab7329g0s9kxFTcbyCEvg7uSEs96OY2pGvvZLahbJxlyCvb3NlKxkk+31hBB5ygZVokp4Y84fnUpczBZyc1KIi9nMhaPTqVazOQFlrXumU2yGHpCxPML8bHU6erdqwTISWWFMIF7N5aAxnUnqNfxdXXmsjsyGNoUCj+lRFAVFUW5rE0KULENHzeKzD17g+O638toqV2vE0JEzzZiqaLTePlJ6eYTF+N+TnYlLSeWbzVv42nhz+Eh5X1++GzoIvY2NmdOVTAUuelRV5fnnn0evv/mXUmZmJi+//DKOjo75jvvll1+KNqEQwmRUVeX8mYMkJ8URHFYNN3df3Nx9GP/xr5w7fYCY6HP4BYQRWq6GuaM+NOnlEZbGVqfj0xefZ0TnDhw6fxFPF2fqli8nHQomVOCip0+fPvleP/fcc0UeRghRfK5ePsWUD/tx6fxhADQaHZHt+9C73wS0Wh2h5WsSWr6mmVMWndbbR8rqy8IilfH0pIynp7ljlAoFLnpmz55tyhxCiGKUk5PFB28/RWaWjqr1P8LeKZDYq1Gs/e1bnJzceOq50eaOaBKy+rIQpZsMZBailFFVle+/GUNc7FUMRgOx0esxGrMpW74n/iFPsmrlt+Tmlqx99CKixqCRn3b3tef0GQZ9OZPWb43lpalfsPWYbCItShb5MSBECZWdncnenavZtnEpCfH/rPnx3ZcjWfvbd7h61sLNqzaJN3ZxYNMAUhKP4+JZg/S0RFJTEsyY3DQcq8lCb/eyYucuOk/4kD17DhJ0NZVjB47x1KRP+GH9RnNHu6fohAQ2Hz3G2RhZN07cX6H33rIUH374IaNHj+bVV19lypQp5o4jhEXZv3sdX3w6iNSUeODmeJ0nnhxEw2ZdWPfHbMLCX8U/pAsAIVVe5tDWoZw/OgMnt0o4OLri5OxuzvhFStblub/s3FzGzPuBR3BkFP5otQqqqjJVucb4BT/RqUF9nOztzB0zn4zsbN6YPY9ftu/A+Pc6cs2qVmHay/3wcpGxW+LOrLKnZ9euXcycOZMaNax/RokQRe3G9Ut8+n5vbOwrEtF8LvVbL6Ns+d6sWDKVnxd8hM7GEd+gDnnHa3X2+Id0ITn+AFfP/UzbJ15CpytZ02WtacZWcno6569fJyun+B4xHjh3ntjUVLppPND+PXNIURSe0niQlp3FthMnii1LQb39/QJWbt9JP8WLr7UhvK7x4/Dx07wwZfpti+kKcYvV9fSkpqby7LPPMmvWLN5//31zxxHC4qxfMx9FY0ul2u+g1d1c4j6wYm/SUk5z8vgeQAXVmO8cVb25uWHL1s/QtefrxR3ZZCKixljNjK3k9HTGzF/Isu07yDUacXdwYED7x3jl8XYmn8J86/pG8hcLt75LFCyrpyw+JYUlm7fSW/Ggg+Zmr2SAYouDUcP4s2fZf+4cEWFhZk4pLJHV9fQMHjyYxx9/nMjIyPsem5WVRXJycr4PIUq6G9cu4eAcklfw3OLkVpXM9DRyc9K5cvbHvL+Gc7KTiT63hMrVGtF/6BS0Wqv7W+ierGHGlqqqvPj5dFZt30VvPHhPU4bGGbZ8uOQXpv36u8nvXzMkGF8XF35S48n9+/vCoKr8aIzDWW9HoyqVTJ6hMOb9tYFc1UjN/+xbdWsfq9PR1rtvlaqqHLl4iQ2Hj3A9McnccUocq/rp9uOPP7J371527dpVoOMnTpzI+PHjTZxKCMtSJqgSWzctJyc7ERtbN+DmD9Kk2F0EhlSmekRzlv00mYRrm7C1L0Ny3G5sbW14YdBH5g1exKypl2fPmbNsPXGSMZoAGmicAIjAEcUAM39fRf+2bbCzNd0jRxudjg/79qbftC8ZwAWqGvSc1GRzVc1iSu8Xcfh7UVpLkJ2by7er16AAR9UMyin/jDW6tY9ViI917lt14foNBn4xgwMXLgKg02jo2bwZ7z7bAxudVf26tlhW81W8dOkSr776KmvXrsXOrmAD6kaPHs2IESPyXicnJxMYaP0bJgpxLy1a92TFkqkc2zmKwIovoLN1JebCChJv7OH5l2bToHEHKlVtwPo1P5CcFE/jxi/S5okX8fQKMHf0IpOjv7lSvDX08gAcPn8BLQr1lPwr3DdUnFiZkcjluDjK+/uZNEObiFr8NvZtvlv3J6evRPOIrw99WrWkTvly9z3XYDSy/+w5snJyqBUWatIi6cjFi8SnpxOhOPC9MQ4HtNRRHDilZjLNeI0gT0/qli9vsvubSq7BQM+PJ5Mdn8w7mgCCFFu2qKnMW78BFwd7Rj/V1dwRSwSrKXr27NnD9evXqV37nwGJBoOBjRs3Mn36dLKystBqtfnO0ev1edtmCFFauLp589aEn5kxeQhHd44CwNHJnRcGfUyDxjcHMNeq04padVqZM6ZJ1V81wmp6eQB83FwxoHKFHAKxzWu/QBZaRcHD2alYcoQHBzH5xb6FOmfrseMM//pbLifcXObAWW/HqKeepG/ko6aIiM3fj1874sZqJYnPjP88ytIAb3Z6wiq3cfjzwEHO37jB59ogymlu/mHfVfEgxWBgzrq/GN6po0l7+0oLqyl6WrVqxaFDh/K19e3bl8qVKzNq1KjbCh4hSrOw8rX46IuNXL5wnKysdIJCq2Fra1lTjk3Fz9cAWE8vD0CrmjXwcXZmSto1huNLGWzYp6azkATa162Dh1PxFD2FdTk2jt6TP6e8wYah2kAc0PBrdiJvz1+Av7u7SXYKrxpYlmBPT35JSGSsEkAcuZxTs1htTOKUrYFODeoX+T2Lw9mYazhotPke1wFUVxxYkpVAXEqybFVRBKym6HF2diY8PDxfm6OjI56enre1CyFuzsgJDKli7hjFzv/HcdjpreuPIL2NDbOHD+X5z6bycsp5bBUN2aqROmFhTOxjufsc/rBhIxqDkTFKAA7KzXkxgzU+XFVz+HrVapMUPRqNho9efJ4+kz/nJeMFKqu2nNHkEK/kMO2FfhY1/qgwQnx9SDcaOKdkEar88zkcUTNwtLXFw9nZjOlKDqspeoQQ4n5u9fLYVKxl3iAPoFZYKNs//Yg1+/dzLSGRakGBNKxcyaIf1ZyJjqECdnkFD9wstsNVe9ZcNd0MqiZVq7Buwnjm/rWeU1eu8pi3F71atqBakPWO2YysWYMgT08mJcTQX/XKG9OzlERefLQ19ra297+IuC+rLnrWr19v7ghCCAvi/+M4nKtb73YTdrY2dKxfz9wxCizEx5tNHCBTNWL3r8LnKJmE+Pma9N6hvr6Me6a7Se9RnGx0Oua/PpwB02bwzpUrAGgUhaebNGZUty5mTldyWHXRI4QQt9yasSWKT88WzZi1ei0fqtH0whNHNKw0JrJfTWNG29bmjmd1yvn5sfb9cRw8f4HrSUlUCwokwMPD3LFKFCl6hBAlQv1VI6y6l8cahfj48N2rQxg+61teTbm5toydTsdbT3a1qh4rS6IoCjVDQ8wdo8SSokcIYfXquJ3CeP/DhAm0rBHOrs8+ZsfJU2Rm51CvQnlcHR3uf6IJpWVmEp2QiJ+bm8VtlCrMS4oeIYTVMy6dJ708ZmSj09GkqvlnCmbn5vL+T0tYsH4DGTk56HU6ujdtwjvPPC0DgQUgRY8QwspFRI0xdwRhId6a9wOLN22hG27U0Dpw1JjBT+s3kpKezvSB/c0dT1gAq9twVAgh/kt6ecS1xER+2rSZPoonz2q9qK440F3jyYuKF8t27OTSjVhzRxQWQIoeIYTVsvZeHqNRRiIVlRNXrmJQVRr8Z/+yRxQnVODY5cvmCSYsijzeEkJYNWvr5VFVlTl/RvHFyt+ITkrCxc6e7s2b8E73p9Bo5O/QB+Xn5gbAOTULf+Wf8Tvn1CwAfP9+XxStG0lJ/LJtB9cSby6o+Xjduha9R5gUPUIIq2StvTwf/byMqb/+BoATGtTMLGatXsvmI0dZ8+5YKXweUMUyAdQrV45vz13CTdVRBTtOkslMJZbwwLLUCAk2d8QS56+Dh+g39QuMBiNeGhtmGrKYvHQFi954nTKelrm+kPzXJYSwWtbWy5OQmsqXv/8BwEsab37QlmO+thxDNL4cu3yFuX9FmTmhdfti0ADcfT0ZabhEZ8NpXjNcwt7Tla+HDLbo7TysUWpGJoO+mEl1o555mlC+VoL5QhtMelwSb8yZZ+54dyU9PUIIqxMRNQZbG+v7JXbw/AVyjUYqoqezxj2vva3iygZjMj9EbaRvZCszJrRuZTw9WDthPJuPHuNMzDVCfHxoFl4VrZl7z1RV5eD5C1yNj6dSmTKEmXiLjuKwdv8BUrIyGaQNxUm5ucFvsKKnu+rO9EOHiUtOwdPF8jZJlaJHCGFVbi1EqK9c29xRCs3FwR4N4KvcPubBX7HlRFZW8YcqYjEJicz4YxXr9x/ERqejwyP16de2dbHtfq7RaGgWXo1m4dWK5X73czk2jv7TvuDAhYt5be1qR/B5/xdxtLPehROT0tLQouDxnzLCBx0qkJyRLkWPEEI8LGteiLBmSAguDg7sSk8jSc3FVbn5IzhdNbBNTaVz9aZmTvhwohMS6DDufVJT0miiOpJJBlOWruDPfQdYNHrkAw1wNRiNLNiwiZ82bCI+JYXaFcoz+PF2VAksa4LPoGgZjUb6TP6cxGuxjNeUoZyiZ7eaxsz9B3nr+x+Y0u9Fc0d8YHUrlMeAykY1hZaKC3CzR+svNRlfFxcCvbzMnPDOZEyPEMJqWOvg5Vs0Gg1fvNyfXGC44SLLjQmsNCYwzHARg62WAe3amDviQ/ni1z9IT0ljuhLEYK0vr2n9magpw95z51i2fccDXfO1b2czeu736C/GEhFvZNuufTwx/n32nD5TxOmL3vYTJzl+9Sqv4kMdjSNuio5IjSs98WDpth3Ep6SYO+IDCw8Oon2d2kxTrzPLcJ21xiQmqNFEqSm89mRndFqtuSPekfT0CCGsirX28tzSokY4K955i9e+nc03V64A0LhKZcb27E6Ij4+Z0z2cP/ftp5nqhKfmn18tlRR7qmoc+PPgIXo0a1Ko6+0/e47FW7YxVONLG40rAL1UT143XGLQjJl4O7ugKArt6tWmz6MtLe5x0YXrNwCoin2+9qqKHbkGI1fjE/BwtrxHQAU1/eV+fLZ8JfP/Ws/y9ETK+/oyrVMPnmz0iLmj3ZUUPUIIqxARNQY7vWX+9VhYNcNCWDdhPDm5uaiAra5k/CjWabVkY7itPRsVmwf4yz/q0GFcNDpa/f34BMCASopqICEuntD4bIzAR+eXsnL7Ln5+a1SxjR0qiPIBfgAcVNOJ+NeiiQfVDGy1Wsp6eZorWpHQ29jwRrcnGdW1CzkGg1V8H8vjLSGExbv1WMumYi3zBiliNjqdVfyiKKjmNauznpS8BQEBthpTOGXMoH3dwg8812m15KJiQM1r+1VNIhEDU7TBjNIGMFobwCeashy9dIkf1m8s1PUT09I4cvESCamphc5WEHXLl6dWcDBTuM4GYzJX1GyWGxNYqMbTvWkT3Bwd738RK6AoitV8H1tHSiFEqWftj7VKui9++4O56/4CYKjhAjVxIENROaFm0L5ObdrVKXzR075ubT5c8guLlXh6ajxRFIWtxhQaKI6EKP/06JRT7KiDI6v37KVf29b3vW5mdg5jFyzkp01byDEY0Gk0dG3UkPd79SzSniJFUZg9fCivfPU1Hx8/AYBWUejWqCHjevYosvuIgpOiRwhh0ax98HJpsOHwET5Y/DNdFXc6KW6sV1NYpSZxVc3h5XZtefOprg+0Vk45Pz/+16UTnyxdzhbS8TVoOU8WPtw+C8yoqGgLuADhG3PmsXzbDp5VPKiuteeImsGCrdtJz8riq8EvFzrnvfi4ubLojdc5G3ONq/HxVAjwly0xzEiKHiGExZNeHss2P2oD5bT2PI8XiqLwJB48iQevGS9x+mr0Qy0OOLxTB+pXrMCizVuIT0mhkcHItqPHOKNmUk65OXD5hJrBXmM6YwvwCC06IYGft22nn+JFh78XiKyk2ONo1DJt125GX79BsI/3A+e9mzA/3xKxKKG1k6JHCGGxIqLGoCsZY5eL1fpDh1mwYSOxScnUKhfGC5GtTDpoNiY+gSCjDkWbv6clWLUhOj7hoa/fuEplGlepDEBaZibdPviIEZcuURdHjIrKXmM6tcJC6dm82X2vderKVYyqSj1N/vE0df8eaHziyhWTFD3CMkjRI4SwSLcea9lXlV6ewpi8bAWfLltBOa09ZYw6Fp45z8L1G1k8eiThwUEmuWf10BBWXrhMpmrETrnZq5OtGtmnyaRVSI0ivZejnR0/vzWKH9ZvZPWevWgVhbF1a9OzeTPsbW3ve36Ax82NME+rWfj9azf2M2pmvvdFySRFjxDCYpnqsVZGVhaHL17C0U5PlbJlS8xmlOevX2fyshU8o3jQE08UrUKaamBU9hXGzl/Iz2+NMsl9X2jdikWbNvO24QpdVDcUYDlJJGuM9H/s/gOLC8tBr6df29YFGrT8X+UD/HmkQgW+PXsBJ6OW6oo9R8lgphJLRGgI1YICizyvsBxS9AghLI4pBy9/s2Ydn/6yjOTMm3/ZV/L35/MBL1E9JNhk9ywua/btx0bR0E3jkVfIOSpaOquuTDl1ioTUVNydnIr8vuX9/Vg4cgRvzp3PxMs3F1ysHBDAD72fpVKZMkV+v4f1xaAB9P1sKm9f/Gc/rCplyjDzlYElpgAWdyZFjxDCosRm3JwybIpenmXbdzB2wY+0U1xpq/UhSTUw/1o8PSZ9wqaPPrDI1XENRiN/HjjI+kNHsLXR8US9utQtX+6OxxqNKhpuX4BNy81f5OptZxSdehUqsOa9cVyNj0dVb+54bqkFhJ+7G7+PH8POk6c4ExNDiI8PDStXsti8ouhI0SOEsCitt4802WOtGb/9QV2NI4M1f8+iUaCcqueFzPMs2ryVl9u1Ncl9H1Rmdg7PfzaVTceOUVZrRxZGZq1eS782kYx9pvttv6Qja9bgvZ8Ws1JN5Enl5tiUTNXICpKoHRqKhwl6ef5NURTKeFrHKsOKotCgUkUaVKpo7iiiGEnRI4SwGM2Sf8aUWzCejo7hOdzztbkpOkI1dpy6Gm3COz+YWWvWsv34CcZrylBHccSoqizXJDJrzToerVmDZtWq5ju+fIA//dpEMmvNOnaRThnVht1KOmla+PFZWQxPCNmGQghhMVL27DfpmjyBnp6cIDNfW5pq4IKaZZH7IP2yeStNcKTO39OrNYpCZ8WNIK0dv2zdfsdzxj7TnS8H9setUjAX/B2JbNyAP8aPuesjMSFKE+npEUJYhIioMZh6SEXftpG8Oe8HgrGlreJKEga+U2NBq6FNRE2MRiOah1hIr6ilZmTi/p8f04qi4GbUkJaZecdzFEWhU4P6dGpQvzgiCmFVLOe/biFEqVXH7RQATuGmXZOnd8sWDGr/GD+SQC/DWV4xXOCYJptcg4E277xL49dHs2jzFpNmKIxG1aqwRUkjXTXmtV1WszmiZtCwciUzJhPCOklPjxDC7IxL5xXLVhOKovDW0914qU0kO0+e4uMlS7l2I47uigf+Ghs2xacy/JvZKIrCU40bmTzP/Qx5oj2r9uxleM4lIlVnMlQjq5Vkgr29ebpJY3PHE8LqWE1Pz8SJE6lXrx7Ozs74+PjQuXNnTpw4Ye5YQoiHZI4NRX3d3HC0s+PM9eu8pfGnm8aDxhpnRmn8aKQ4MWXpClTVlBO8C6Z8gD/L3h5NjVpV+UmTyGp9Bh2aNWbp22/gZG9n7nhCWB2r6enZsGEDgwcPpl69euTm5vLmm2/Spk0bjh49iqOj4/0vIISwOLcKHnNsKLr/7DnctDaEY5/XpigKTRRnPoqNJjEtzSQL+RVWlcCyfDN0sLljCFEiWE3Rs2rVqnyv58yZg4+PD3v27KFZs/tvMieEsEyFKXjSs7LQajTobWwe+r4ezs6kGnNJ1hhw/dePwitkY6fT4aDXP/Q9hBCWxWoeb/1XUlISAB6yOZwQVqkwj7W2HT9Bh/ETqDBgMBUHDGbA9BlciYt/qPt3bFAPW50Nn6vXSVBzUVWVfcY0lpHIk40bFklhJYSwLFbT0/NvRqORYcOG0bhxY8LDw+96XFZWFllZWXmvk5OTiyOeEOI+CvNYa++Zs/T46FPKo2eoxpdUDKzce4iuZ8+xdsJ4nO3t73uNO/FwcmLG4JcZ+MVXPJ9zDkeNlmRjLvXKlWNM96ce6JpCCMtmlUXP4MGDOXz4MJs3b77ncRMnTmT8+PHFlEoIURgFfaz1+YpfKYMtE5Wy2Py9kE8j1YkBCRdYvHkrL7Ru9cAZImvVYOdnH/Hrrj3Ep6QQUS6MJlUqW9RaPeLOktPTWb5jF1fj46lcpgyP1Ym4b+9cfGoqS7Zs5fTVGAK9vXi6SSN83dyKJ7CwCIpqCVMUCuGVV15h+fLlbNy4kdDQ0Hsee6eensDAQL5ddA4HB8vbWFCI0iAiakyhxvFUH/Qqj2Xa0VOTf8XkUcbLlK8XzpcD+xd1RGHhdp06TZ/Jn5OakYmH1oYbhmyCPT356Y3XCfT2uuM5hy9cpMekT0jNyCBEY8clYxYanZbZw4fSpGqVYv4MRGGlZGRQeeAQkpKScHFxeeDrWM2fM6qq8sorr7B06VL++uuv+xY8AHq9HhcXl3wfQgjzeZDp6e5OjsSoOfnaDKrKdSXX5BtoCsuTnZtL/6lfUDZL4VttCLOVEKZrg8lKSGHEN9/d8RxVVXn1q1l4ZBr5ThPKZ0ogczShVDDYMmTG12Tn5hbzZyHMxWqKnsGDBzN//nwWLFiAs7MzMTExxMTEkJGRYe5oQohCKOz09O7Nm7KBFDYZUzCqKpmqkTnGWG4YsnmqifkXEBTFa+Pho1xPSWGg4o2XcvNxVoiipxcebD1xkks3Ym875/jlKxyPjqY3nrgrN0d1OClaXlS8uJ6SwtZjx4v1cxDmYzVjembMmAFAixYt8rXPnj2b559/vvgDCSEKpbCPtW7p17Y1e06fYdK+/bhpbMjCSKZqYEz3p6gZGlL0QYVFS0hLBcCP/ON3/P4ugBLSUm97xJX69z5lboo2X7s72nzvi5LPaooeKxt6JIT4l4dZddlWp+PboYPZefIUm44ew87Ghifq1yXEx6cIEwprEREWBsAGNYW2imte+3pjCs56Oyr4+992TrWgQJz1dqzJTmKg9p+VrNeoSeg0GupVKG/64MIiWE3RI4Swbg+z6rKiKDSoVJEGlSoWYSJhjcr7+9G5QX2+2rmbS4ZsKih69qjp/KUm80aHJ7G/w6KSDno9I57syPiFi7hhNFALe06omWxQU3j5sbYyg6sUkaJHCGFSEVFjsNNr73+gEAX0Wb8XKOvtxffroliWmUCAmxvvP9GT51u1vOs5/du2wdPZma9+W8WcmBjKenkyoU0H+tzjHFHyWN2U9YeRnJyMq6urTFkXopiYc28tUfIZjEbSMjNxtrdH+XsNJ1EyFdWUdenpEUKYlBQ8wlS0Gg0uDg7mjiGsiNVMWRdCWJeHGbwshBCmIEWPEKLIyWMtIYQlkqJHCGESUvAIISyNFD1CiCIVETUGnUzWEkJYICl6hBBF5tZjLfuq0ssjhLA8UvQIIYqUPNYSQlgqKXqEEEUiImoMGvmJIoSwYPIjSgjx0Jol/wyAYzXp5RFCWC4peoQQDy1lz355rCWEsHhS9AghHoosQiiEsBZS9AghHpgsQiiEsCZS9AghHooUPEIIayFFjxDigUREjcFOL6sQCiGsh+yyLoR4YDYVa5k7gihhrsbH882adWw/ehwnB3u6Nm5Et8YN0cp6CKIISNEjhCg0P1+DuSOIEujctWt0enci2RmZ1FcdiFfiGHF8NhsPH2H6y/1QFMXcEYWVk6JHCFFo/j+Ok7E8oshNWrIUXUY2U5UgXDU3fz1FkcynO3bybItmNKpS2cwJhbWT/kIhhBAWYc2+/bTFBVfln7/HWyjO+GptWb1vv/mCiRJDih4hRKHIujzCVBRARb2t3QjyaEsUCSl6hBCFJo+2hCm0rVObVaSQoObmta1Tk7lhyOax2hFmTCZKChnTI4QosBy9o7kjiBJsVNcudD56jJfTLlDX6ECcYuCwMZ2nGzeiQcUK5o4nSgApeoQQBVZ/1Qjp5REmE+zjzar3xvLdur/YfvQ43g72TG/ciE4N6snjLVEkpOgRQhRIbIbe3BFEKeDr5sbobk+aO4YooWRMjxCiQFpvHykrMAshrJoUPUKI+7o1Y0tWYBZCWDN5vCWEuCfZSV1YsrjkFH7ctJkTV65S1tOTHs0aE+Ttbe5YwkJJ0SOEuCspeIQlO3zhIj0mfUJaRiblNXasVrOZ8fsfzHxlIG0iapk7nrBAUvQIIe6ojtspjEjBI+7OYDTy54GD7DhxChcHezo/0oBgn+LpZVFVleGzvsUj08h0TQiuio5MjHysxjD862/Z/fmn2NvaFksWYT2k6BFC3CY2Q48xap4UPOKuUjMyefaTyew+cxZfrZ4UNZdPli5nYp/neK5Fc5Pf/0x0DEcvX2GMJiBv2wo7RcMLeDEg4zwbDx+hrSxoKP7D6gYyf/HFF4SEhGBnZ0eDBg3YuXOnuSMJUeK03j4Se1cXc8cQFuyjX5Zx9NwFPtCU5VslmHlKKG1xYfTc+Zy7ds3k90/PzgLARck/o9CVm6/Ts7JNnkFYH6sqen766SdGjBjB2LFj2bt3LzVr1qRt27Zcv37d3NGEKDFujePRBckKuJbianw8m44e47yF/KxTVZUlm7bQXnWhhsYBuNnL8pLGGwdFy9JtO0yeoVKZMng4OvKHMQlV/We/rt/VJLSKQoNK1v/9azQazR2hxLGqx1uTJ0+mX79+9O3bF4CvvvqK3377je+++4433njDzOmEsH4ycNmypGdl8b9v57By126Mf/9ibxlejakDXsLD2dlsuVRVJTkzA29N/gx6RYMbOhLT0kyeQW9jwxtPdWXknHnEqQYiVHtOkcUWYwoDHmtDgIeHyTOYQkZWFpOXr2Th+o0kpKdTKziY4V06EVmrhrmjlQhW09OTnZ3Nnj17iIyMzGvTaDRERkaybdu2O56TlZVFcnJyvg8hxJ1FRI1BUaTgsSSjZs9j9e69vKx487U2hNc0fuw7epIB02aYNZdGo6FOuTDWk4LhX70sJ9QMLhsyqVeheHpZnm3RjG+GDEIX4ssSmxTifJ2Y2Ps5xnR/6qGvnZSWTkZ28T4iU1WVFz6fzrd/rKFZhi2DND4YLt2gz5Sp/LFnb7FmKamspqcnNjYWg8GAr69vvnZfX1+OHz9+x3MmTpzI+PHjiyOeEFYrR+8oe2pZoGuJiSzbsZN+ihftNW4ABCi26I0KH5w8yeELFwkPDjJbvtee7Myzn3zGm1yhpepEnJrLr0oy4YGBPFa7VrHlaFenNu3q1C6y660/dJgPflrCkcuX0Wk0PFY7gnHP9sDf3b3I7nE320+cZOPRY4zRBNBA4wTAY6or45WrfLT4Fx6rHSF7kD0kq+npeRCjR48mKSkp7+PSpUvmjiSERYmIGiMFj4W6cP0GRlWlhuKQr73m36/PxMSYI1aeZtWq8sNrw7AN9mG68TrLdSl0ataYn974HzY6q/l7Op+tx47Te/LnaK7G85rGj+fxZPveg3SbMIn0rCyT33/7iZO4aHTUVxzz2jSKwqOKMydjYorlsWFJZzXfmV5eXmi1Wq79Z1bAtWvX8PPzu+M5er0evV42SRTiTvx8DYA8zrJUZb08UYBjagbByj8/x46qGQAEW8Cqw83Cq9EsvBrZubnoNBo0Guv+O3rK8pWEKXa8r5RB+3ePSj3VkYGx5/ll23aTT8V3cbAnQzWQphhx4p9ZaXHc/PraybpDD81qvkNtbW2pU6cOf/75Z16b0Wjkzz//pGHDhmZMJoT1iYgag/+P46TgsWABHh60r1ObOcQTZUwmUc1luzGVL7hB7dBQaoaGmDtiHludzuoLHoB9Z8/RGMe8ggegjGJLOa09e8+cNfn9O9SrBxoNM43XyVRvztw6q2aylCQer1dXFlssAlbT0wMwYsQI+vTpQ926dalfvz5TpkwhLS0tbzaXEOL+ZIaW9fjkxecZ8tUsPj14KK+tbrkwZr4ySMZ2mICHoyMxiTn52nJUlRtqLh5OTia/v4+bK5Nf7Mvwb75jh3oOT2y4ZMikgp8f43t2N/n9SwOrKnq6d+/OjRs3eOedd4iJiaFWrVqsWrXqtsHNQog7k4LHurg4ODB3xKucvhrN6egYynp5mnXwcknXo0UzPl+2klpGBxopTmSiMsd4gyQ1h6eaNCqWDE82eoR6FcqzZOs2ElJTqRUayuP16qC3sSmW+5d0ivrvVZ1KuOTkZFxdXfl20TkcHMy3xoUQ5iAFjxD3lpWTw4DpM1h74CAuGh1ZqpFcVCb0fo5eLU2/tYa4u5SMDCoPHEJSUhIuLg++WrxV9fQIIR6MFDxC3J/exobZw4aw69Rpthw7joNeT4f6da12oUNxOyl6hCjBYjP0tN4+Eju9FpuKtcwdRwiLpygK9StWoH5F69/GQtxOih4hSijp3RFCiPysf46hEOI2UvAIIcTtpOgRooSRgkcIIe5MHm8JUUJIsSOEEPcmPT1ClABS8AghxP1JT48QVqyO2ymMS+cBUvAIIcT9SNEjhJWKiBqDESl2hBCioOTxlhBWSB5nCSFE4UlPjxBWRIodIYR4cNLTI4SVkIJHCCEejvT0CGHh/HwN+P84DpCCRwhLo6oqB89fICE1lfDgILweYjNMYXpS9AhhwaR3RwjLdeLKFQZN/4rj0dEA6DQa+kY+ypgeT6PVyIMUSyRFjxAWSKaiC2HZMrKyeGbSp9inZvO+pgx+ig0b1BS+XbMOD2dnhnZ43NwRxR1I0SOEhZGp6EJYvl937+F6cjIztSEEKLYAdFc8iVdz+Xb1Wl55vB0a6e2xOPIvIoQFkcdZQliHczHX8dLa5hU8t1RTHIhNTSU1M9NMycS9SE+PEBZAih0hrEuIrzexhmyitdn4/6vwOaKm4+nohKOdnRnTibuRnh4hzEwKHiGsT4d6dfFxceEDNYb9xnSuqTksMsbzh5rEi20jZSCzhZJ/FSHMxM/XIAWPEFbKXq9nwcjXsPFx423jZV40nGMB8fRt3YpXnmhv7njiLuTxlhBmIMWOENavctky/DXxPfafO0d8Sio1QoLxdnU1dyxxD1L0CFHMpOARouRQFIWIsDBzx8ijqionrlwlLTOTqkGB2Nva3v+kUkSKHiH+396dRzV9pnsA/yYICaAJssiigCwWHBfEaeXA3LpyFatWbetUxztFy2hV2trqbdW5p0Ss1qVUHa11aS3MjHZandvqzNTl6IxLXeooRTtSoIKgBQHbWpFF2fLcPzrkNkJAtoQk3885Oce8v/f98bx55Ofjm/eXmElDseOs1aBbQD8LR0NEtubLggK8vH2n4cMStWpnvPrUVMyKHW3hyLoOFj1EZsDVHSLqTN/fKceMtW/BqxpIVvaGRuGAQ9Vl+J9dH8Bd0wOPD3vE0iF2CSx6iDoRix0iMoePTp1C1b1qLFf2hVbx4z/toUoVvpU6bP/0EIuef+PdW0SdhAUPEZnLlRvFCFaqDQUP8ON+oyFwxtf/fruLWPQQdTjeik5E5tbHwwPXpRpVojdqz5F78PfwsFBUXQ/f3iLqQCx2qDOJCDKvf4Oq6moMCgyAs0pl6ZCoi5g+/D+w5dODWKsvxrPwhBYOOChlOC0VWDN2qqXD6zJY9BB1EBY81Jkyrl7Fwm3vIe/mTQCARq3Gfz85BQn/GWvhyKgr6O3hgfcXPo8Xtr2LxMprAIBuSiUWPBaH/xo53MLRdR0seojaibeiU2f7tqwMM9auh1+tAiuVfaBRKHGwugxJuz+El1bLTaoEABg5aCAubEzBqa+yUFldjaiH+sHbzc3SYXUpLHqI2oGrO2QOH352GjU1NdApg6BROAAAEh3UKNXzzhwypnJ0xJiIwZYOo8uyio3MBQUFSEhIQFBQEJydnRESEgKdToeamhpLh0Z2KvLYa4g89hqcHBUseKjTXblRjBCl2lDwNIiAM3JLSiwUFZH1sYqVnuzsbOj1emzfvh2hoaG4fPky5syZg8rKSqSkpFg6PLIzXN0hcwv08sRBqUYV9HBR/P//VbNxD/6enhaMjMi6WEXRExcXh7i4OMPz4OBg5OTkYOvWrSx6yGx8vOvh++FyACx4yLymD38U73x6EGv0xZjVcGeO/jbOSgVSxj5p6fCIrIZVFD1NKSsrg7u7e7N9qqurUV1dbXh+586dzg6LbBRXd8iSenu4I/WlF/DCtnfxYsWPd+Y4Ojhg4WMTMX34f1g4OiLrYZVFT25uLjZv3tziKs/q1auRnJxspqjIVrHgoa5g+MABOL8xBWezc1BVXY1H+oXCU6OxdFhEVkUhImKpH7506VKsXbu22T5ZWVkIDw83PC8qKsKIESMwcuRIvPfee82ObWqlx9/fHzv35MPFpUf7giebx1vRiYi6hvK7dxE+/wWUlZVB045i36IrPYsXL8asWbOa7RMcHGz4840bNzBq1CjExMRgx44dLZ5fpVJBxU8spTbg6g4Rke2xaNHj5eUFLy+vB+pbVFSEUaNG4ec//zlSU1OhVFrF3fZkZWpVrhh2aBEAFjxERLbGKvb0FBUVYeTIkQgMDERKSgq+/fZbwzEfHx8LRka2hKs7RES2zSqKniNHjiA3Nxe5ubno06eP0TELbkkiG8KCh4jI9lnFe0SzZs2CiDT5IGqPhk9WVqscWPAQEdk4q1jpIeoMXN0hIrIvVrHSQ9SRvrurYsFDRGSHuNJDdoXFDhGR/eJKD9kNFjxERPaNKz1k84bf+V+Up1+Ek6MCqvChlg6HiIgshEUP2bTIY6+hHFzdISIivr1FNoqblYmI6H5c6SGb01Ds8O0sIiL6KRY9ZFO4ukNERKaw6CGb0FDsACx4iIioaXZV9DR8bcXdqnILR0IdKeLkSlQA6D5gCACg/O5di8ZDREQdq+Lf1/X2fv2UQuzoC6wKCwvh7+9v6TCIiIioDb755ptGXzzeGnZV9Oj1euTk5OBnP/sZvvnmG2g0GkuHZBZ37tyBv78/52zjOGfO2VbZ25ztbb5Ay3MWEZSXl8PPzw9KZdtvPLert7eUSiV69+4NANBoNHbzl6kB52wfOGf7wDnbPnubL9D8nLVabbvPz8/pISIiIrvAooeIiIjsgt0VPSqVCjqdDiqVytKhmA3nbB84Z/vAOds+e5svYL4529VGZiIiIrJfdrfSQ0RERPaJRQ8RERHZBRY9REREZBdY9BAREZFdsLmiZ9WqVYiJiYGLiwvc3Nya7HP9+nVMmDABLi4u6NWrF1555RXU1dU1e95bt25h5syZ0Gg0cHNzQ0JCAioqKjphBu13/PhxKBSKJh/nz583OW7kyJGN+s+bN8+MkbdP3759G8W/Zs2aZsfcu3cPiYmJ8PDwQPfu3fHkk0+itLTUTBG3T0FBARISEhAUFARnZ2eEhIRAp9Ohpqam2XHWluctW7agb9++UKvViIqKwj//+c9m++/duxfh4eFQq9UYNGgQDhw4YKZI22/16tV45JFH0KNHD/Tq1QtTpkxBTk5Os2PS0tIa5VOtVpsp4vZbvnx5o/jDw8ObHWPNOQaavlYpFAokJiY22d/acnzy5ElMmjQJfn5+UCgU2Ldvn9FxEUFSUhJ8fX3h7OyM2NhYXLlypcXztvZa0BSbK3pqamowbdo0zJ8/v8nj9fX1mDBhAmpqanDmzBn8/ve/R1paGpKSkpo978yZM5GZmYkjR47gb3/7G06ePIm5c+d2xhTaLSYmBsXFxUaP3/zmNwgKCsLDDz/c7Ng5c+YYjVu3bp2Zou4YK1asMIr/hRdeaLb/yy+/jL/+9a/Yu3cvTpw4gRs3buCJJ54wU7Ttk52dDb1ej+3btyMzMxMbNmzAtm3b8Nvf/rbFsdaS548++giLFi2CTqfDF198gYiICIwbNw43b95ssv+ZM2cwY8YMJCQkICMjA1OmTMGUKVNw+fJlM0feNidOnEBiYiI+//xzHDlyBLW1tRg7diwqKyubHafRaIzyee3aNTNF3DEGDBhgFP+pU6dM9rX2HAPA+fPnjeZ75MgRAMC0adNMjrGmHFdWViIiIgJbtmxp8vi6deuwadMmbNu2DefOnYOrqyvGjRuHe/fumTxna68FJomNSk1NFa1W26j9wIEDolQqpaSkxNC2detW0Wg0Ul1d3eS5vvrqKwEg58+fN7QdPHhQFAqFFBUVdXjsHa2mpka8vLxkxYoVzfYbMWKELFy40DxBdYLAwEDZsGHDA/e/ffu2ODo6yt69ew1tWVlZAkDOnj3bCRF2vnXr1klQUFCzfawpz8OGDZPExETD8/r6evHz85PVq1c32f+Xv/ylTJgwwagtKipKnnvuuU6Ns7PcvHlTAMiJEydM9jF1rbMWOp1OIiIiHri/reVYRGThwoUSEhIier2+yePWnGMA8sknnxie6/V68fHxkTfffNPQdvv2bVGpVPKnP/3J5Hlaey0wxeZWelpy9uxZDBo0CN7e3oa2cePG4c6dO8jMzDQ5xs3NzWiVJDY2FkqlEufOnev0mNvrL3/5C77//nvMnj27xb67d++Gp6cnBg4ciGXLlqGqqsoMEXacNWvWwMPDA5GRkXjzzTebfdsyPT0dtbW1iI2NNbSFh4cjICAAZ8+eNUe4Ha6srAzu7u4t9rOGPNfU1CA9Pd0oP0qlErGxsSbzc/bsWaP+wI+/39acTwAt5rSiogKBgYHw9/fH5MmTTV7LuqorV67Az88PwcHBmDlzJq5fv26yr63luKamBrt27cKzzz4LhUJhsp+157hBfn4+SkpKjHKo1WoRFRVlModtuRaYYldfOAoAJSUlRgUPAMPzkpISk2N69epl1NatWze4u7ubHNOV7Ny5E+PGjUOfPn2a7ferX/0KgYGB8PPzw5dffoklS5YgJycHH3/8sZkibZ8XX3wRQ4cOhbu7O86cOYNly5ahuLgY69evb7J/SUkJnJycGu398vb2toq83i83NxebN29GSkpKs/2sJc/fffcd6uvrm/x9zc7ObnKMqd9va8ynXq/HSy+9hF/84hcYOHCgyX5hYWF4//33MXjwYJSVlSElJQUxMTHIzMxs8Xe+K4iKikJaWhrCwsJQXFyM5ORkPProo7h8+TJ69OjRqL8t5RgA9u3bh9u3b2PWrFkm+1h7jn+qIU+tyWFbrgWmWEXRs3TpUqxdu7bZPllZWS1ufrN2bXkdCgsLcfjwYezZs6fF8/90j9KgQYPg6+uLMWPGIC8vDyEhIW0PvB1aM+dFixYZ2gYPHgwnJyc899xzWL16tVV9nHtb8lxUVIS4uDhMmzYNc+bMaXZsV8wzNZaYmIjLly83u78FAKKjoxEdHW14HhMTg/79+2P79u14/fXXOzvMdhs/frzhz4MHD0ZUVBQCAwOxZ88eJCQkWDAy89i5cyfGjx8PPz8/k32sPcddiVUUPYsXL262CgaA4ODgBzqXj49Pox3fDXfr+Pj4mBxz/2apuro63Lp1y+SYztCW1yE1NRUeHh54/PHHW/3zoqKiAPy4gmCpfwzbk/uoqCjU1dWhoKAAYWFhjY77+PigpqYGt2/fNlrtKS0tNWte79faOd+4cQOjRo1CTEwMduzY0eqf1xXy3BRPT084ODg0upuuufz4+Pi0qn9X9fzzzxtumGjt/+QdHR0RGRmJ3NzcToquc7m5ueGhhx4yGb+t5BgArl27hqNHj7Z6ldWac9yQp9LSUvj6+hraS0tLMWTIkCbHtOVaYFKrdgBZkZY2MpeWlhratm/fLhqNRu7du9fkuRo2Ml+4cMHQdvjw4S6/kVmv10tQUJAsXry4TeNPnTolAOTSpUsdHJl57Nq1S5RKpdy6davJ4w0bmf/85z8b2rKzs61qI3NhYaH069dPpk+fLnV1dW06R1fO87Bhw+T55583PK+vr5fevXs3u5F54sSJRm3R0dFWs8lVr9dLYmKi+Pn5yddff92mc9TV1UlYWJi8/PLLHRydeZSXl0vPnj3ld7/7XZPHrT3HP6XT6cTHx0dqa2tbNc6acgwTG5lTUlIMbWVlZQ+0kbk11wKT8bSqtxW4du2aZGRkSHJysnTv3l0yMjIkIyNDysvLReTHvywDBw6UsWPHysWLF+XQoUPi5eUly5YtM5zj3LlzEhYWJoWFhYa2uLg4iYyMlHPnzsmpU6ekX79+MmPGDLPPrzWOHj0qACQrK6vRscLCQgkLC5Nz586JiEhubq6sWLFCLly4IPn5+bJ//34JDg6W4cOHmzvsNjlz5oxs2LBBLl68KHl5ebJr1y7x8vKSZ555xtDn/jmLiMybN08CAgLkH//4h1y4cEGio6MlOjraElNotcLCQgkNDZUxY8ZIYWGhFBcXGx4/7WPNef7www9FpVJJWlqafPXVVzJ37lxxc3Mz3H3561//WpYuXWrof/r0aenWrZukpKRIVlaW6HQ6cXR0lH/961+WmkKrzJ8/X7RarRw/ftwon1VVVYY+9885OTlZDh8+LHl5eZKeni7Tp08XtVotmZmZlphCqy1evFiOHz8u+fn5cvr0aYmNjRVPT0+5efOmiNhejhvU19dLQECALFmypNExa89xeXm54d9eALJ+/XrJyMiQa9euiYjImjVrxM3NTfbv3y9ffvmlTJ48WYKCguTu3buGc4wePVo2b95seN7SteBB2VzREx8fLwAaPY4dO2boU1BQIOPHjxdnZ2fx9PSUxYsXG1Xax44dEwCSn59vaPv+++9lxowZ0r17d9FoNDJ79mxDIdVVzZgxQ2JiYpo8lp+fb/S6XL9+XYYPHy7u7u6iUqkkNDRUXnnlFSkrKzNjxG2Xnp4uUVFRotVqRa1WS//+/eWNN94wWr27f84iInfv3pUFCxZIz549xcXFRaZOnWpUNHRlqampTf5d/+kCri3kefPmzRIQECBOTk4ybNgw+fzzzw3HRowYIfHx8Ub99+zZIw899JA4OTnJgAED5NNPPzVzxG1nKp+pqamGPvfP+aWXXjK8Pt7e3vLYY4/JF198Yf7g2+jpp58WX19fcXJykt69e8vTTz8tubm5huO2luMGhw8fFgCSk5PT6Ji157jh39D7Hw1z0uv18tprr4m3t7eoVCoZM2ZMo9chMDBQdDqdUVtz14IHpRARad0bYkRERETWx+4+p4eIiIjsE4seIiIisgsseoiIiMgusOghIiIiu8Cih4iIiOwCix4iIiKyCyx6iIiIyC6w6CEiIiK7wKKHiDrMrFmzoFAoGj066osR09LSjL4c1hJOnjyJSZMmwc/PDwqFAvv27bNoPET04Fj0EFGHiouLQ3FxsdEjKCjI0mE1Ultb26ZxlZWViIiIwJYtWzo4IiLqbCx6iKhDqVQq+Pj4GD0cHBwAAPv378fQoUOhVqsRHByM5ORk1NXVGcauX78egwYNgqurK/z9/bFgwQJUVFQAAI4fP47Zs2ejrKzMsIK0fPlyAGhyxcXNzQ1paWkAgIKCAigUCnz00UcYMWIE1Go1du/eDQB477330L9/f6jVaoSHh+Odd95pdn7jx4/HypUrMXXq1A54tYjInLpZOgAisg+fffYZnnnmGWzatAmPPvoo8vLyMHfuXACATqcDACiVSmzatAlBQUG4evUqFixYgFdffRXvvPMOYmJisHHjRiQlJSEnJwcA0L1791bFsHTpUrz11luIjIw0FD5JSUl4++23ERkZiYyMDMyZMweurq6Ij4/v2BeAiCyvbd+hSkTUWHx8vDg4OIirq6vh8dRTT4mIyJgxY+SNN94w6v/HP/5RfH19TZ5v79694uHhYXiempoqWq22UT8A8sknnxi1abVaw7eTN3zb/MaNG436hISEyAcffGDU9vrrr0t0dHRLUzX5c4mo6+JKDxF1qFGjRmHr1q2G566urgCAS5cu4fTp01i1apXhWH19Pe7du4eqqiq4uLjg6NGjWL16NbKzs3Hnzh3U1dUZHW+vhx9+2PDnyspK5OXlISEhAXPmzDG019XVQavVtvtnEVHXw6KHiDqUq6srQkNDG7VXVFQgOTkZTzzxRKNjarUaBQUFmDhxIubPn49Vq1bB3d0dp06dQkJCAmpqapotehQKBUTEqK2pjcoNBVhDPADw7rvvIioqyqhfwx4kIrItLHqIyCyGDh2KnJycJgsiAEhPT4der8dbb70FpfLHeyz27Nlj1MfJyQn19fWNxnp5eaG4uNjw/MqVK6iqqmo2Hm9vb/j5+eHq1auYOXNma6dDRFaIRQ8RmUVSUhImTpyIgIAAPPXUU1Aqlbh06RIuX76MlStXIjQ0FLW1tdi8eTMmTZqE06dPY9u2bUbn6Nu3LyoqKvD3v/8dERERcHFxgYuLC0aPHo23334b0dHRqK+vx5IlS+Do6NhiTMnJyXjxxReh1WoRFxeH6upqXLhwAT/88AMWLVrU5JiKigqjzx3Kz8/HxYsX4e7ujoCAgPa9SETUuSy9qYiIbEd8fLxMnjzZ5PFDhw5JTEyMODs7i0ajkWHDhsmOHTsMx9evXy++vr7i7Ows48aNkz/84Q8CQH744QdDn3nz5omHh4cAEJ1OJyIiRUVFMnbsWHF1dZV+/frJgQMHmtzInJGR0Sim3bt3y5AhQ8TJyUl69uwpw4cPl48//tjkHI4dOyYAGj3i4+Nb8UoRkSUoRO57I5yIiIjIBvHDCYmIiMgusOghIiIiu8Cih4iIiOwCix4iIiKyCyx6iIiIyC6w6CEiIiK7wKKHiIiI7AKLHiIiIrILLHqIiIjILrDoISIiIrvAooeIiIjsAoseIiIisgv/ByuGyRCEDEecAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see, the decision boundary is no longer just a straight line. Due to the model's hidden layer, it is able to learn non-linear decision boundaries, thereby better modelling the training data, and hopefully, the true data distribution.\n",
        "\n",
        "Also note, how we could re-use all our previous code for training, evaluation, and visualization. Modern machine learning is quite modular, and many concepts and mechanisms like loss function, optimizer, or evaluation metrics transfer nicely between machine learning models.\n",
        "\n",
        "It also enables us to combine multiple models to form a single model, to build even more powerful machine learning applications."
      ],
      "metadata": {
        "id": "C5esY6L5qgvs"
      }
    }
  ]
}