M05N04_Hyperparameters_and_Model_Validation.ipynb

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      "source": [
        "<!--BOOK_INFORMATION-->\n",
        "<img align=\"left\" style=\"padding-right:10px;\" src=\"https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/PDSH-cover-small.png?raw=1\">\n",
        "\n",
        "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
        "\n",
        "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
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      "source": [
        "<!--NAVIGATION-->\n",
        "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
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      "source": [
        "# Hyperparameters and Model Validation"
      ]
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        "In the previous section, we saw the basic recipe for applying a supervised machine learning model:\n",
        "\n",
        "1. Choose a class of model\n",
        "2. Choose model hyperparameters\n",
        "3. Fit the model to the training data\n",
        "4. Use the model to predict labels for new data\n",
        "\n",
        "The first two pieces of this—the choice of model and choice of hyperparameters—are perhaps the most important part of using these tools and techniques effectively.\n",
        "In order to make an informed choice, we need a way to *validate* that our model and our hyperparameters are a good fit to the data.\n",
        "While this may sound simple, there are some pitfalls that you must avoid to do this effectively."
      ]
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        "## Thinking about Model Validation\n",
        "\n",
        "In principle, model validation is very simple: after choosing a model and its hyperparameters, we can estimate how effective it is by applying it to some of the training data and comparing the prediction to the known value.\n",
        "\n",
        "The following sections first show a naive approach to model validation and why it\n",
        "fails, before exploring the use of holdout sets and cross-validation for more robust\n",
        "model evaluation."
      ]
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        "### Model validation the wrong way\n",
        "\n",
        "Let's demonstrate the naive approach to validation using the Iris data, which we saw in the previous section.\n",
        "We will start by loading the data:"
      ]
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      "source": [
        "from sklearn.datasets import load_iris\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target"
      ]
    },
    {
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        "Next we choose a model and hyperparameters. Here we'll use a *k*-neighbors classifier with ``n_neighbors=1``.\n",
        "This is a very simple and intuitive model that says \"the label of an unknown point is the same as the label of its closest training point:\""
      ]
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      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "model = KNeighborsClassifier(n_neighbors=1)"
      ]
    },
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      "source": [
        "Then we train the model, and use it to predict labels for data we already know:"
      ]
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      "source": [
        "model.fit(X, y)\n",
        "y_model = model.predict(X)"
      ]
    },
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      "source": [
        "Finally, we compute the fraction of correctly labeled points:"
      ]
    },
    {
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      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(y, y_model)"
      ]
    },
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        "We see an accuracy score of 1.0, which indicates that 100% of points were correctly labeled by our model!\n",
        "But is this truly measuring the expected accuracy? Have we really come upon a model that we expect to be correct 100% of the time?\n",
        "\n",
        "As you may have gathered, the answer is no.\n",
        "In fact, this approach contains a fundamental flaw: *it trains and evaluates the model on the same data*.\n",
        "Furthermore, the nearest neighbor model is an *instance-based* estimator that simply stores the training data, and predicts labels by comparing new data to these stored points: except in contrived cases, it will get 100% accuracy *every time!*"
      ]
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        "### Model validation the right way: Holdout sets\n",
        "\n",
        "So what can be done?\n",
        "A better sense of a model's performance can be found using what's known as a *holdout set*: that is, we hold back some subset of the data from the training of the model, and then use this holdout set to check the model performance.\n",
        "This splitting can be done using the ``train_test_split`` utility in Scikit-Learn:"
      ]
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        "from sklearn.model_selection import train_test_split\n",
        "# split the data with 50% in each set\n",
        "X1, X2, y1, y2 = train_test_split(X, y, random_state=0,\n",
        "                                  train_size=0.5)\n",
        "\n",
        "# fit the model on one set of data\n",
        "model.fit(X1, y1)\n",
        "\n",
        "# evaluate the model on the second set of data\n",
        "y2_model = model.predict(X2)\n",
        "accuracy_score(y2, y2_model)"
      ]
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        "We see here a more reasonable result: the nearest-neighbor classifier is about 90% accurate on this hold-out set.\n",
        "The hold-out set is similar to unknown data, because the model has not \"seen\" it before."
      ]
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        "### Model validation via cross-validation\n",
        "\n",
        "One disadvantage of using a holdout set for model validation is that we have lost a portion of our data to the model training.\n",
        "In the above case, half the dataset does not contribute to the training of the model!\n",
        "This is not optimal, and can cause problems – especially if the initial set of training data is small.\n",
        "\n",
        "One way to address this is to use *cross-validation*; that is, to do a sequence of fits where each subset of the data is used both as a training set and as a validation set.\n",
        "Visually, it might look something like this:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-2-fold-CV.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#2-Fold-Cross-Validation)\n",
        "\n",
        "Here we do two validation trials, alternately using each half of the data as a holdout set.\n",
        "Using the split data from before, we could implement it like this:"
      ]
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      "source": [
        "y2_model = model.fit(X1, y1).predict(X2)\n",
        "y1_model = model.fit(X2, y2).predict(X1)\n",
        "accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)"
      ]
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        "What comes out are two accuracy scores, which we could combine (by, say, taking the mean) to get a better measure of the global model performance.\n",
        "This particular form of cross-validation is a *two-fold cross-validation*—that is, one in which we have split the data into two sets and used each in turn as a validation set.\n",
        "\n",
        "We could expand on this idea to use even more trials, and more folds in the data—for example, here is a visual depiction of five-fold cross-validation:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-5-fold-CV.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#5-Fold-Cross-Validation)\n",
        "\n",
        "Here we split the data into five groups, and use each of them in turn to evaluate the model fit on the other 4/5 of the data.\n",
        "This would be rather tedious to do by hand, and so we can use Scikit-Learn's ``cross_val_score`` convenience routine to do it succinctly:"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "from sklearn.model_selection import cross_val_score\n",
        "cross_val_score(model, X, y, cv=5)"
      ]
    },
    {
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        "Repeating the validation across different subsets of the data gives us an even better idea of the performance of the algorithm.\n",
        "\n",
        "Scikit-Learn implements a number of useful cross-validation schemes that are useful in particular situations; these are implemented via iterators in the ``cross_validation`` module.\n",
        "For example, we might wish to go to the extreme case in which our number of folds is equal to the number of data points: that is, we train on all points but one in each trial.\n",
        "This type of cross-validation is known as *leave-one-out* cross validation, and can be used as follows:"
      ]
    },
    {
      "cell_type": "code",
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            "text/plain": [
              "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
              "       0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1.,\n",
              "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
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          "execution_count": 27,
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      ],
      "source": [
        "from sklearn.model_selection import LeaveOneOut\n",
        "scores = cross_val_score(model, X, y, cv=LeaveOneOut())\n",
        "scores"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "Because we have 150 samples, the leave one out cross-validation yields scores for 150 trials, and the score indicates either successful (1.0) or unsuccessful (0.0) prediction.\n",
        "Taking the mean of these gives an estimate of the error rate:"
      ]
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      "source": [
        "scores.mean()"
      ]
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        "Other cross-validation schemes can be used similarly.\n",
        "For a description of what is available in Scikit-Learn, use IPython to explore the ``sklearn.cross_validation`` submodule, or take a look at Scikit-Learn's online [cross-validation documentation](http://scikit-learn.org/stable/modules/cross_validation.html)."
      ]
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      "source": [
        "## Selecting the Best Model\n",
        "\n",
        "Now that we've seen the basics of validation and cross-validation, we will go into a litte more depth regarding model selection and selection of hyperparameters.\n",
        "These issues are some of the most important aspects of the practice of machine learning, and I find that this information is often glossed over in introductory machine learning tutorials.\n",
        "\n",
        "Of core importance is the following question: *if our estimator is underperforming, how should we move forward?*\n",
        "There are several possible answers:\n",
        "\n",
        "- Use a more complicated/more flexible model\n",
        "- Use a less complicated/less flexible model\n",
        "- Gather more training samples\n",
        "- Gather more data to add features to each sample\n",
        "\n",
        "The answer to this question is often counter-intuitive.\n",
        "In particular, sometimes using a more complicated model will give worse results, and adding more training samples may not improve your results!\n",
        "The ability to determine what steps will improve your model is what separates the successful machine learning practitioners from the unsuccessful."
      ]
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        "### The Bias-variance trade-off\n",
        "\n",
        "Fundamentally, the question of \"the best model\" is about finding a sweet spot in the tradeoff between *bias* and *variance*.\n",
        "Consider the following figure, which presents two regression fits to the same dataset:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-bias-variance.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff)\n",
        "\n",
        "It is clear that neither of these models is a particularly good fit to the data, but they fail in different ways.\n",
        "\n",
        "The model on the left attempts to find a straight-line fit through the data.\n",
        "Because the data are intrinsically more complicated than a straight line, the straight-line model will never be able to describe this dataset well.\n",
        "Such a model is said to *underfit* the data: that is, it does not have enough model flexibility to suitably account for all the features in the data; another way of saying this is that the model has high *bias*.\n",
        "\n",
        "The model on the right attempts to fit a high-order polynomial through the data.\n",
        "Here the model fit has enough flexibility to nearly perfectly account for the fine features in the data, but even though it very accurately describes the training data, its precise form seems to be more reflective of the particular noise properties of the data rather than the intrinsic properties of whatever process generated that data.\n",
        "Such a model is said to *overfit* the data: that is, it has so much model flexibility that the model ends up accounting for random errors as well as the underlying data distribution; another way of saying this is that the model has high *variance*."
      ]
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      "source": [
        "To look at this in another light, consider what happens if we use these two models to predict the y-value for some new data.\n",
        "In the following diagrams, the red/lighter points indicate data that is omitted from the training set:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-bias-variance-2.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff-Metrics)\n",
        "\n",
        "The score here is the $R^2$ score, or [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination), which measures how well a model performs relative to a simple mean of the target values. $R^2=1$ indicates a perfect match, $R^2=0$ indicates the model does no better than simply taking the mean of the data, and negative values mean even worse models.\n",
        "From the scores associated with these two models, we can make an observation that holds more generally:\n",
        "\n",
        "- For high-bias models, the performance of the model on the validation set is similar to the performance on the training set.\n",
        "- For high-variance models, the performance of the model on the validation set is far worse than the performance on the training set."
      ]
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      "source": [
        "If we imagine that we have some ability to tune the model complexity, we would expect the training score and validation score to behave as illustrated in the following figure:\n",
        "\n",
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-validation-curve.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Validation-Curve)\n",
        "\n",
        "The diagram shown here is often called a *validation curve*, and we see the following essential features:\n",
        "\n",
        "- The training score is everywhere higher than the validation score. This is generally the case: the model will be a better fit to data it has seen than to data it has not seen.\n",
        "- For very low model complexity (a high-bias model), the training data is under-fit, which means that the model is a poor predictor both for the training data and for any previously unseen data.\n",
        "- For very high model complexity (a high-variance model), the training data is over-fit, which means that the model predicts the training data very well, but fails for any previously unseen data.\n",
        "- For some intermediate value, the validation curve has a maximum. This level of complexity indicates a suitable trade-off between bias and variance.\n",
        "\n",
        "The means of tuning the model complexity varies from model to model; when we discuss individual models in depth in later sections, we will see how each model allows for such tuning."
      ]
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        "### Validation curves in Scikit-Learn\n",
        "\n",
        "Let's look at an example of using cross-validation to compute the validation curve for a class of models.\n",
        "Here we will use a *polynomial regression* model: this is a generalized linear model in which the degree of the polynomial is a tunable parameter.\n",
        "For example, a degree-1 polynomial fits a straight line to the data; for model parameters $a$ and $b$:\n",
        "\n",
        "$$\n",
        "y = ax + b\n",
        "$$\n",
        "\n",
        "A degree-3 polynomial fits a cubic curve to the data; for model parameters $a, b, c, d$:\n",
        "\n",
        "$$\n",
        "y = ax^3 + bx^2 + cx + d\n",
        "$$\n",
        "\n",
        "We can generalize this to any number of polynomial features.\n",
        "In Scikit-Learn, we can implement this with a simple linear regression combined with the polynomial preprocessor.\n",
        "We will use a *pipeline* to string these operations together (we will discuss polynomial features and pipelines more fully in [Feature Engineering](05.04-Feature-Engineering.ipynb)):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "SdK_BxnVqmTT"
      },
      "outputs": [],
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.pipeline import make_pipeline\n",
        "\n",
        "def PolynomialRegression(degree=2, **kwargs):\n",
        "    return make_pipeline(PolynomialFeatures(degree),\n",
        "                         LinearRegression(**kwargs))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "rH0TDjY0qmTU"
      },
      "source": [
        "Now let's create some data to which we will fit our model:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "04-aQ7vjqmTU"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "def make_data(N, err=1.0, rseed=1):\n",
        "    # randomly sample the data\n",
        "    rng = np.random.RandomState(rseed)\n",
        "    X = rng.rand(N, 1) ** 2\n",
        "    y = 10 - 1. / (X.ravel() + 0.1)\n",
        "    if err > 0:\n",
        "        y += err * rng.randn(N)\n",
        "    return X, y\n",
        "\n",
        "X, y = make_data(40)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "kW7YzttLqmTU"
      },
      "source": [
        "We can now visualize our data, along with polynomial fits of several degrees:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "dHC0tIuqqmTV",
        "outputId": "b7996969-deb3-406b-f68b-9a6e1e1824d7"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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nkzvu+JOvmyeEEM04XSrfbM/lsy3Z2J0qAOMH9+aK2UlERwb6uHVdQAeUNpSgRXSK4uIiLrzwIpYsuRWAuLh45s49l++/3+rjlomuRFVVUlI2U1xcRHR0X6ZMmYbRKDVbhHdpus73B4r5YF06pVUOAAb0DeHquckM6R/h49Z1DbqjFq3OiTE0yqvX7ZZBi67r4Hb6rgGmtk13lJQU89RTj7Jjx3ZCQkL49a9vb3J806YNLF/+AllZmfTu3Ztzzz2fG25Y0ji9Ul5ezr/+9Rhbt27BaDSyYMHFHDp0gDFjxrFkya0sX/4C27dvpU+fvmzZsonzz7+QP/7xbvbu3c1///sMBw8eIDw8nOnTZ3Hbbb8hKCgY8FSLfuml5/n66y+ora0hISGJm2++jbPOmgLA8uUv8OqrL7X4PY0dO55nnnmRGTNmMWPGLMDz8zlwYD/r1q3h7LPntKmvRM+zatVKli69i4KCgsbHYmNjWbbsMRYuXOTDlonuJDW3ghWrj5BZWA1ARIiVy89OYvKIaAyyyLZVtLoK6r94ioir/uL1a3e7oEXXdepWPohWnOazNhijB2G6dOkZPcftdvPHP/6O4OBgnnnmRVwuJ08++Ujj8ZSUzdxzz1+4/fY7mTRpCvn5efzzn4+Rk5PNAw88gqZp3HXXHaiqyhNPPI3ZbOE//3mK3bt3MmbMuMbr7N27hyuuGMGrr/4PTdNISzvC73//a66//ib+8pd7KCsr49ln/8Wdd/6WF154FUVRePDB+8jMzOD//b8H6N27D5s2reeuu+7goYeeYNq0GfzsZ9dxySWXtfh9mc1N53tVVeW882bhcDgYPHgIN930yzPqJ9EzrVq1kiVLrvN8IDlBYWEhS5Zcx/Llb0jgItqluLyO99eksyP1KABWi5EFUwZw3qR+WMwymtdaWmUxdZ8/gV59FDogyOt2QQuAQteLhnfs2EZmZgYrVnxMXFw8AH/7273cdNPPAXj99VdYuHARl1xyOeCZXvnzn//G7bffRmFhAYWFBRw8uJ+33nqf/v0HAvDAA49w2WXNF/AuWXIrwcHBx8+5h4kTJ3HjjTcD0K9ff+6770GuvPJidu7cQZ8+0Xz77Ve8/PLrDB06HICrr76WtLQjvPXW60ybNoPAwEACA1s3v6vrOs8++xIVFRU8/fST/OlPt/P888sxGGTlvWiZqqosXXpXs4AFPK8nRVFYuvRu5s9fIFNF4ozV1Lv4dFMWq3/IQ9V0FAVmjYnlkpmJhAXJJoEzoR7Nov6LJ9Ht1SghvTEEeX8qrdsFLYqiELDobz6fHvLs1W/9IqT09DRCQkIbAxaAQYOGYLPZAEhNPcTBg/v54otVjccbfolnZWWSlZVJSEhoY8ACEBERSf/+A5rcJyIisjFgATh8+DB5eTnMmzezWZuys7OoqKgA4He/u7XJMbfbTXCwp0rp66+/whtvvNri9zV69DiefPLpxr+bTKbG4CckJJRbb72RPXt2MXbs+JY7RvR4KSmbm0wJ/ZSu6xQU5JOSspnp05u/joVoiVvV+Pr7HD7dnEWt3Q3AyMRIrpyTTHzv4NM8W/yUO28/9d/8B1x2DFEDCJj/BzB4/0NEtwtawBO4YLb6uhlnrKVPkiaT50ekaTrXXHM98+cvbHZOVFQvcnNz0HXttPewWpv2i65rnHfefK6//hfNzg0Pj2Dr1s0APPvsSwQGBjU53jA6cskllzF37rxT3u/QoYPU19cxbtyExmOJiUkAHD1actp2i56ruLjIq+eJnk3XdTbvKeCVlfsoLq8HIK53EFfNTWZkgncXjfYUrvSt2Ne8CJqKMXYYAefdjmLpmBIG3TJo6YoGDx5CTU01GRnpjW/mOTnZ1NR4Mi4mJiaRnZ1FfHy/xufs3LmDd999mz/96S8kJw+ipqaG7OwsBgwYCEBVVSV5eTmnvG9CQhKZmelNrpuTk8Uzz/yb2277DQkJnrYcO3aMadOGNp7zwgvPYjAYuOWWXxEaGkZo6KnTVn/11eds3LiOd975qHEI/8CBfQAMHJjYmi4SPVR0dF+vnid6rszCKt5dncbh3AoAQoMsLJ6ZwMzRsRgMXW9Zga/puo5rzxc4tr4H6JgSJ2Gb80sUY8flrpGFBH5i/PiJDB8+kmXL/h/79u3l0KEDPPjgfY2jGT//+fWsW7ea5ctfICcnmx07tvHQQ/+gurqKqKhejB8/kREjRvHAA57nHzmSyv3334Pdbj9lWumrr76W1NTDPP74Q2RmZrB//z7uu28pOTnZxMf3JzExiWnTZvLEEw+zceM68vPzeOutN3jzzdeIjY1r9fd36aVXUFFRwRNPPEJOTjYpKZt55JEHmD17LoMGDW53/4nua8qUacTGxp70dawoCrGxcUyZMq2TWya6itJKOy+u3M8D/7edw7kVWMxGFs1I4OFfTuHssXESsLSBrrpxrH8Vx9Z3AR3z8HOwzf1VhwYsICMtfsNgMPD44//in/98nD/84bdYrVauu+4mCgs9c/lz5pzL/ffDG2+8wptvvkZISCjTp8/kV7/6cVv0gw8+xpNPPsodd/wKq9XK4sVXkJWV0WwHz4lGjhzFU089w8svP8+SJdcREGBj/PhJ/OY3dzRupf7HPx7mxRef5fHHH6a6uorY2DjuuuvvLFjQ+t0a/fr15+mnn+fZZ//NkiXXEhgYyLx58/nlL3/dxh4TPYXRaGTZssdYsuQ6FEVpMo3aEMgsW/aoLMIVzdQ73Hy2JZuvt+XiVj3T59NHxXDzJaMw6hpu9+mn1EVzur2G+m+fRS04CIqCdeo1mEec2yl1lxS9pYUUfkZVNcrKaps97nI5KS0tJCoqBrPZv1Z5m0yGTv0HUVFRwf79e5k8eWrjOhiXy8WFF57DH/94NxdcsKDT2uItp/v5mkwGIiKCKC+vlV8+Hchf+rnlPC1xLFv2aLfY7uwv/dwdqJrG+t2FfLwhg+o6FwBD+4dz1dxBJMWHST+3g1ZZRN2X/0KvLAKzjYBzbsPUf2yL50ZGBmE0endCp10jLc899xxbtmzhjTfeaHzs4MGDPPjgg+zbt4/w8HCuu+46lixZ0u6GilMzGo3ce+9fufjiy1i8+HJcLhdvv/0GFouZKVOm+7p5QrTbwoWLmD9/gWTE9QP+mplY13X2ZpTy7pp0Co55PuhGRwZy5Zwkxib3kgrM7eQuOEj9N8+AoxYlOIqA8+/AGNXv9E/0ojYHLa+99hpPP/00kyZNanysvLycm266iXPPPZf777+fXbt2cf/99xMeHs5ll7WcfEx4R0hICI899i9eeuk5Vq78CEVRGD16DE8//QLh4eG+bp4QXmE0GmVbs4/5a2bi3JIaVqw+woGscgCCA8wsmj6Q2ePiMHn5035Po+s6rr1f49i6AnQNQ59EAs67HUNgeKe35YyDluLiYv7+97+zY8cOEhISmhx79913sVgs3HfffZhMJpKSksjOzuall16SoKUTjB8/keeff8XXzRBCdFP+mJm4osbBR+sz2LinEB0wGRXOndCPhdMGEGiTCsztpbsc2Nctx53xPQCm5KnYZt2E0sZyNe11xuHn/v37CQsLY+XKlYwZM6bJse3btzNp0qTGNRUAU6ZMITMzk9LS0va3VgghhE+cLjMxwNKld6Oqaqe0x+FUWbkxk7++kMKG4wHLpKF9WHbLFK6cmywBixdolUXUffyAJ2BRjFinXevZ0uyjgAXaMNIyd+5c5s6d2+KxoqIiBg9uun21T58+ABQUFBAV1fbEPSZT8/hK0/xzfrJh2lRROqQyd49jNCot/vwbFnh5e6GXaEr6uXP4ez+npGxsVWbibdu2NBZH7QiarrNpTyHvr02nvNpTgTkpLoxrzh3EoH7hp32+v/fzmVJVlS1bNjWuL5o6dbpX1hc5s3ZS9+0L6M46lMAwgs//LaaYIWd0jY5YQuTVLc92u71xm2yDhoyoDoejzdc1GBQiIoKaPW63Gzl2zHDSNzVf6y7/KHxF0xQMBgNhYYGN5QxaEhraMZkXRVPSz53DX/u5pqai1ee19PvaG3YfOcorK/eTUVAJQJ/IQG68cDgzxp48j8/J+Gs/n4kPP/yQ3//+9+Tl5TU+Fh8fz7///W8uvfTSNl1TV12UrXmL2q0rAbDGDyX60j9hCvF+HaG28GrQYrPZcDqb1vxpCFZaW1CvJZqmU1VV1+xxp9OBpmmoqu5XW9cUxROwqKomIy3toKo6mqZRWVlHfX3zIWej0UBoaABVVfWoqv/8/Lsb6efO4e/9HBwc3urzysubp6hoj4Jjtaz47gg7jxwDIMDqSQ43b1I/LCYjFRXN3x9Oxt/7ubU+/fQTbrzx2mbTdfn5+Vx++eW89tqbXHTRxWd0TbWymNqvn0M9mgmAddR5BEy7mmq3CdrwMw0LC/B6MVyvBi19+/alpKRpHZmGv0dHR7fr2i0FJarqnxFBw2tIAhbvOF1QqqqSJKozSD93Dn/t50mTphIbG0thYWGL61oURSEmJpZJk6Z6rf1VdU5Wbsxk7c4CNF3HoCjMHhfLohkJhAZ6RvXbei9/7efWUFWVv/71z6esfP7Xv97Feedd2OqpIldaCvYNr4HLDtYgbGcvwTxwPKoOtLGfOuI90KtBy6RJk3jnnXdQVbWxo7Zs2UJCQkK71rMIIYTwrc7MTOxyq3y7PY9VW7Kod3hGWccm9+KKOUnERHXM1FNX4s3K57rLjn3T/3CnbgDA2Hcwtrm3Ygj2z/dsr47bXHbZZdTU1PD3v/+dtLQ0PvzwQ/7v//6PW2+91Zu3EUII4QMLFy5i+fI3iImJafJ4TEysV7Y767rO1gPF/P2lrby3Np16h0r/6GD+/LNx3H75aAlYjvNW5XN34WFq37/HE7AoCpbxFxOw8G6/DVjAyyMtUVFRvPzyyzz44IMsXryY3r17c9ddd7F48WJv3qZHmTFjIn/7271ceOFFvm5Ku73yyou88sqLzR5fuzalyTZ5IYT/6qjMxGl5laxYfYT0gioAIkKsXDorkakj+2KQTLZNtLfyue524tj2Aa69XwM6SlAktjm3YIod5sVWdox2vVM88sgjzR4bPXo0K1asaM9lRTeVnn6E88+/kF//+vYmj0vAIkTX4s3MxCUV9by/Np3thzzrH61mI/On9Of8s/pjNfu+NIA/aqh8frr1RS1VPldL0rGveQmt0jMKYx4yE+vUn6FY2r5ZpjPJu4XoNOnp6Vx66eVERfXydVOEED5WZ3fx6eYsvtuRh1vVUYAZo2NYPCuR8GCrr5vn19qyvkh3O3H+8AnO3Z+DrqMEhGE7+6aTFjv0V90yaNF1Hafm8tn9LYa2ZWIsKSnmqaceZceO7YSEhDQbkdi0aQPLl79AVlYmvXv35txzz+eGG5Y05sYpLy/nX/96jK1bt2A0Glmw4GIOHTrAmDHjWLLkVpYvf4Ht27fSp09ftmzZxPnnX8gf/3g3e/fu5r//fYaDBw8QHh7O9OmzuO223xAUFAx4qkW/9NLzfP31F9TW1pCQkMTNN9/GWWdNAWD58hd49dWXWvyexo4dzzPPvIjdbqegII+BAxPb1DdCiO7BrWqs3ZnPyk1Z1NR7fk+PGBjBlXMH0a9PcIffX1VV1q5dS1paJr16RftNsccz1bC+6Kd1oGJiYptVPnfn7cO+4f/Qq48CYEqegm3atSi2ju9vb+t2QYuu6zz1w3NkVGb7rA2JYQO566zfnNFz3G43f/zj7wgODuaZZ17E5XLy5JM/Tr+lpGzmnnv+wu2338mkSVPIz8/jn/98jJycbB544BE0TeOuu+5AVVWeeOJpzGYL//nPU+zevZMxY8Y1Xmfv3j1cccUIXn31f2iaRlraEX7/+19z/fU38Ze/3ENZWRnPPvsv7rzzt7zwwqsoisKDD95HZmYG/+//PUDv3n3YtGk9d911Bw899ATTps3gZz+7jksuabm2lNnsCeAyM9PRNI01a77lqacexel0Mm7cBH71q9vp1UtGXoTo7nRdZ9eRY7y7Np3iMk9eldheQVw5J5lRiZGdUoHZU+zxbgoK8hsf84dij211uvVFWl0ljpS3caelAKAERWCddi3mhAm+bHa7dLugxaPrLdrasWMbmZkZrFjxMXFx8QD87W/3ctNNPwfg9ddfYeHCRVxyyeUAxMXF8+c//43bb7+NwsICCgsLOHhwP2+99T79+w8E4IEHHuGyy5ov4F2y5FaCg4OPn3MPEydO4sYbbwagX7/+3Hffg1x55cXs3LmDPn2i+fbbr3j55dcZOnQ4AFdffS1paUd4663XmTZtBoGBgadNHpiRkQ5AcHAIy5Y9RllZKf/97zPcfvutvPLK/06Z8VYI0bVlFVWx4rs0DudWABAaaOaSmYnMHBOD0cvJx07GH4s9ekNL64t0XcN1aD2Ore+Csw4UBfOIc7FOvBTF0rUzAXe7oEVRFP4w/lc+nx7yfGpofWad9PQ0QkJCGwMWgEGDhjS+maemHuLgwf188cWqxuMN//iysjLJysokJCS0MWABiIiIpH//AU3uExER2RiwABw+fJi8vBzmzWu+qC47O4uKigoAfve7ptvW3W43wcEhgCegeuONV1v8vkaPHseTTz7NggWLmDlzNqGhoQ3fHYmJSSxefCGbNq3nnHPOO0XvCCG6orIqOx+sy2DL/uOLPk0GzpvUjwunDCDA2nlvP6cr9qgoCkuX3s38+Qu65FTRidxFR3BseQvteFZbQ68B2GbehLH3QN82zEu6XdACnsDFavRdFcq2aukfVMPOGk3Tueaa65k/f2Gzc6KiepGbm4Ounz5rYUMtqB/vqXHeefO5/vpfNDs3PDyCrVs3A/Dssy8RGNg0R0JDeuZLLrmMuXPnnfZ+PwYsHr169SYsLKxZFmUhRNdW73DzxdYcvvo+B9fxbKpTRkRz2awkosI6f1TVm8nY/JVWU4pj67u407d6HjAHYJ14CeYR56IYunYgdqJuGbR0RYMHD6GmppqMjHQSE5MAyMnJpqamBoDExCSys7OIj+/X+JydO3fw7rtv86c//YXk5EHU1NSQnZ3FgAEDAaiqqiQvL+eU901ISCIzM73JdXNysnjmmX9z222/ISHB05Zjx44xbdrQxnNeeOFZDAYDt9zyK0JDwwgNDTvlff7732fYuHEdb7zxbuPcdWFhARUVFSQkyOJcIboDTdPZsKeAjzZkUlXrqUM3OD6Mq84ZREJM6Gme3XG8lYzNH+kuB87dn+Hc/QWoLkDBPHQWlkmXYQjwXZ93FClD7CfGj5/I8OEjWbbs/7Fv314OHTrAgw/e1zia8fOfX8+6datZvvwFcnKy2bFjGw899A+qq6uIiurF+PETGTFiFA884Hn+kSOp3H//Pdjt9lMucLv66mtJTT3M448/RGZmBvv37+O++5aSk5NNfHx/EhOTmDZtJk888TAbN64jPz+Pt956gzfffI3Y2LhWf39z5pxLQUF+4+LhXbt+4O9//zOjRo1h8uSp7e4/IYRv7cso5d5Xv+f/vjxMVa2TPhEB/GbxSO7++XifBizQ/mRs/khX3Tj3f0vtO3fh/GElqC6MMUMIvPQ+bLNu6pYBC8hIi98wGAw8/vi/+Oc/H+cPf/gtVquV6667icJCz5DmnDnncv/98MYbr/Dmm68REhLK9Okz+dWvftwW/eCDj/Hkk49yxx2/wmq1snjxFWRlZTTu4GnJyJGjeOqpZ3j55edZsuQ6AgJsjB8/id/85o7GrdT/+MfDvPjiszz++MNUV1cRGxvHXXf9nQULWr9obciQoTzxxNO89JLnPhaLmRkzzuY3v7mjU3YNCCE6Rt7RGt5dnca+zDIAgmwmLpqewNzxcZiM/vG5uD3J2PyNrmm407bg2PERerWn6rUS0hvr5CsxJUzs9r9PFb2ln6CfUVWNsrLmZbFdLielpYVERcVgNvvXGhaTydCpFUQrKirYv38vkydPbVwH43K5uPDCc/jjH+/mggsWdFpbvOV0P1+TyUBERBDl5bVdtlprVyD93Dm6Wj9X1jj4aEMmG/YUoOtgNCicMyGehdMGEhzQtlxVHalh9xDQYjI2f989pOsa7qydOLd/gFbu+TCrBIRhmXAx5iGzUIz+NwYRGRmE0cuBq/99l6JNjEYj9977Vy6++DIWL74cl8vF22+/gcViZsqU6b5unhCim3C6VL7alsvnKdk4nJ4KzBOG9Oby2UlER/hvKvgfk7E1zdPSUjI2f6JrKu6MbTh3rkIrz/M8aA3CMuZCLCPPRTH5b/Zg/Qx20LaWjLR0kM4eaQH44YftvPTSc6SlpaEoCqNHj+FXv7qdpKTkTm2Ht8hIi3+Qfu4c/t7Pmq6Tsr+ID9ZlUF7tACAhJoSr5g5icL9w3zbuDCiKzr59P/h9RlxddeFK3YRz9+foVcd3WJptWEbOwzL6AhSrf1a81nWd9MosNuZv5YaJi+kT7N3koTLS0o2MHz+R559/xdfNEEJ0M4dzynlndRrZRdUARIVauezsJM4aHu2zCsyqqrap0rTRaGT27NmMGTPJL4ND3VGL69A6nPu+Qa8tB0CxBmMedR6WEef4ZbCi6zr5NYXsPLqXH0p2U1LnWWtzPYu9fi8JWoQQQrSoqKyO99aksfOI503IZjGyYOoA5k3sh+UMKjBruobd7cChOqh323Hrbtyailtzo2oqbt2Nq+HPmhutIeeU0vClITDyfN2zexcfvL+C0qOlaC4V1a0SGRbOzb/4FWfPnI1JMWE2mLEYLdhM1hMSfvovtbwA175vcB3ZBG7PdnElKALL6AswD52NYvavaSBVU8msyuFA6WF2luyhpP5Y4zGLwczE6LGEW72/g6lbBC1dYIZLtIH8XIXwjZp6Fys3ZrJmZz6qpmNQFM4eG8ui6QMxWt0ccxylpqaGGlcdNc4aaly1jX+uddVR567Drjqwux3Y3XbvZyi3wuCfj2/2cAp7SNm2p9njCgpWoxWbyUqAyUqQNRATZqwGCzaTjUBzAEGmQALNgQSZAjxfzYEEmgIJMgdgM9kwKN7fCaVrGmruHpz7v0XN29f4uCGyH5aR8zANmopi9I9Fzaqmkl9bSHpFFofKUjlSkYFDdTYeNxlMjIgcwtg+oxjVazgBJhsmg/dDjC4dtDQMBTqdDiwW/4pCRfs5nZ55c6MfrooXorvRdZ2K+mq+3HWIjYcycSq1KHEO+kTqhEfqpGnfc+/2Slyau833MCpGbCYrZoMZk2LEaDBhMhgxGUyYlB//bFAMKCjHF3Lqx9vnaeOGDWtxOBwoRgMGsxGjyYDBbMJo9vzdbLUQ2bsXbs2FU3WhH//Prtqxq3YqHEDzJZKnpKAQaAog0Hw8oDF5gpof/w9q+vfjx61Ga4sjPFrVUVypG3Ad3tA4BQQKpoHjMI+chzFmqE9Hhhyqk+K6EopqS8ipziO7Kpfc6vxmP/tgcxBDIpIZ3Ws4I3sNw2bq+GzHXfrdwGAwEhAQTE2N54dusbT8AvEFTVNQVRkpaAtd13E6HdTUlBMQENyYYE90H21djyDaR9VUyh0VHK0v5Vh9Kcfqyxq/Ftcew6Uf/+Q8EBqWvlcD1T95kw8yBxJiDibIHESwJYhgc8P/gQRbggk0eUYnrEbPyIbNaMNqsmJu5yfvTZs2cN8Dd5z2vI8++ozpM2ei6RpO1YVDdWBXHTjcDlw4MdkUSisrqXXasbvt1LnrPSNErjpq3fWer8dHjByqEx2dWncdte46qC9tdXtNirFx1CbIFECg04mtuoyA6lICVZ1Ag0ZgeCihsaMIGzSDkIh4TKaOLWjYMFVX7aqh3F5BuaOSCnsl5Y4KyuzlFNcdpcxe3uJzA0wBDAztx5CIZIZGDiYuuG+HjECdSpcOWgBCQyMBGgMXf2EwGNA0/1vk1ZUEBAQ3/nxF97Fq1UqWLr2rSS2Y2NhYli17zG+3nXY1TtVFcd1RimuLKTr+ibmoroSjdcdw6+qpn+yyERUQQb+IXkTYwgi3nvh/KGGWUMw+mrL48svPWnVeQzp+g2LAZvJMCzUUGmncpRXYul1abs1NXWMgU0+tq5ZalyeAqXXV/fj3E/931+HW3Lh1lSpnNVXO6h8vaAIifrKY1nkE9h9p/KtBMWAxWLAYPetyrEYLFoPnq9noGaVSFKVxRKrhKwpN1gk1rBvyBGae4MzutrdqK3KwOYi+QX2IC45hYGh/BoT2o3dAVKcHKT/V5YMWRVEIC4siJCQCVW37sKU3GY0KYWGBVFbWyWhLGxmNJhlh6YYaEnz9dL1SYWEhS5Zc5/cJvvyNpmscrTtGXk0BeTWFFNQUUlRbQqm9/KRvTGaDiaiAKEKNYZQeM1JYqKPbAzGpwcwbPZgFMxKxWfzvrUFVVd5//91WnevNdPwmg4lQSwihlpBWna9rGu6iVOrSt1KVu4NaZx11RoU6o4H6gGDsfQZgD4umzqCfEOh4Ap/64wGFpmuN01kdxWq0EG4NJ8IaRoTN8zXcFkZ0YB/6BvYh2OJ/u5SgGwQtDQwGAwaDf+RqMZkM2Gw26utVv9xSJ4QvqKrK0qV3tbjAWtd1FEVh6dK7mT9/gUwVtcDudlBQW0hedSF5NQXkHw9STrbINcgUSHRQH2KCPG9C0UHR9A3sg5UgvkjJ4ZvtebhVDQWYNqovl85KIiLEf9cGpqRsprT02GnPi4rq1enp+HW3AzXvAK6sH1BzdqHbqzEA4UCELQRTwiRMSZMx9h2EcoqRioapG6fmxKE6capOnKoLp+rEoXn+7lCdaLqGpmue1Tq63hjooIPJcMJaoePrhGwmGwGmgMZ1OQGmgHZP1flK12y1EKLLSUnZ3GRK6Kd0XaegIJ+UlM1Mnz6zE1vmf5yqi7yafLKqcsmuyiWnKo+j9aUtjp5YDGZig2OID44hLjiGmKBo+gZFE2wOarLGz61qrNtVwCcb91FT7wl0hg2I4Kq5yfSPbt0ogi+1tgLzZZdd2SlBr1ZVgjtvH2ruXtx5++GEnTRYAjENGIs5aQrG+OEorQwQDIrBs9iXjl3X0pVJ0CKE6BStfdNp7XndhaZrFNYWk1uTR2FaIYePZpJfU/hjrpIThFlCiQ+JJS44hvjgWOKDY+gd2OuU6wx0XWd3einvrUmjsLQOgJioQK6Yk8yYpCi/2bxwOq2d8pk/v2PqrOmOWtwFh1Dz9+PO2/djltrjlOAoTAPHYxowDmPM4FYHKuLMSK8KITpFa990vLkewR9VO2tIr8wiozLLM4pSnY/zxE/px4VYgj0LIEP6MSA0nn4hcYRYgk97/RN3ZpmCojlUGsyhnAoAggPMXDwjgbPHxvpNBebW6sxKzbquo9eUohalohYdQS068mPdn8YbGjH2TcYYNwJT/zEYovp3mQCwK5OgRQjRKbz9pqPrOqgucDvRNRU0N2gq+vGvqMcf+/EGNKZYPfHvigIGk6dKrtEERrPnz4bjf27HG5Gma5TUHSW9Mov0Ck+gcrSFLbM2o5UBofEMjU6irzWGfkFxhFvDzvjeDTuzyqrsDJn2c+JHzEFRKjAoOuefNYAFUwcSaOuav/aNRiPLlj3GkiXXoShKi5Waly17tE1TQ7q9BrU0B+1YFurRLNTiNPTasmbnGcL6YowfgSl+pCeXikWmcTpb13z1CiG6nJO96ViMBnoF24gMsvDA0j+gZWxFra9Gtzf8X4Puqkd32cFlR3faj//ZAafbvusNBuPxQMYMZhuK2QZmK0oLf3YZzeQqTrLUGjLdlWQ6yqjTHE0up6AQExRNYtgABoYNICG0H30Ce2Mxm9pVMHHVqpX88tabSZx4CaMnXoLJ7En0lX9oA4c3vcElI54i0NY1i6c2+LFSc9Mt862t1KxrKmpFMbUlZdTnpOEuyUI9loVe00LuFcWIodcAjH0HYew7GGPfQRgCvJ+WXpyZLl3l2V/5e7XW7kL6uXO0t591Zz1aVTFaVQl6TSnpe7eTvncbERaFmLAAeod4KYum4fhIicGIYjB6/m448VP38V91+k+/aqC6PSM0qsszStNKDkUh22YmI8BMRoCFfJsJ9SejI2ZNJ97hYmC9i4F2F/3dBgLNgSjWQBRLIFgCUaxBGG1BBISF4dDN6KYAOH5csZx4bkCLu09cLjcXXHkL0SMWYAv25DYqyz/IgXWvUFF0pHEUa8eOfd1iZ9apkhPqmoZeV4FWcwy96ihaZRFaeQFaZSFaZfFJf75KaB+MUf09gUp0MsbeiX5X76eriYwMwujlaUgJWjqAvJl2DunnztGafm5YA6CV5aJVFHreKCqL0SqL0esqTn8TxYgSEIJiC0GxBXu+BoSg2EJRbEGeN2yzDd1oYd/hVErKKonsE8P4ydMxWgM8z/fSegL9eBCD5kZXjwcyqhtddeKw15BencORmgLS64vIcVag/WRHT4huYKBuYaALBtjdxNbZMTjrwOWNnBsKWGxNAplqt5nUonoqXBbqdTOVtQ7SD20lN/sgVXYXVfUuz1e7i9ff+ojpM2Z5oR2+obsc6PWVaHWV6PWV6A1fa8vRqo+hVR9Dryk79QicyYKlVzyE9EVpCFKi+vtl9eSuToKWLkLeTDuH9HPn+Gk/66oLrSzPswagNBetLBe1NBecdSe9hmILQQmLxhAchSE4CiUoEiU4EkNwpOfPtpDTBh2+yKRrdzvIqMziSEUGR8rTya7Oa7arJ8IazuCIJAZFJJEclkCvgMgWvxddU8FZj+6oRXfWoTvqjn+tBWcdiqsei+KivqoCze45hqMW3VmP7qhruqW2jXRAsQSgmAM8owgm649fTRbPVJfpx8c9f7Z4jhmMx/83HR/J+vH/xpEt5fhNGvro+FfP24wOmuYJBt3OH9cjqS5wuzxfXXZPnzjr0J310NBHDf3kbmUfKEbP6yukF4awaAzhsRjCYzBExGIOiyIyMkR+b3QCCVq6CHkz7RzSz53DYK/AWpNLZfp+XEVpaMeyPCMRP6UYMUTEev4P6+t5szj+tb2fYk+WSbchOPBWJt3WBClRtggGhSeRHJHI4PBEogK8U2ridK9nXXWhO+upqahk3bY0Dh3Jx6o4CTK46B/qZPe69wky6YTazJ7/A8yENPzZZibAD7PctonJghIQhhIQRnm9myqXhjmkF/2Hj8cY2htDSC+UwAiUk2TUlt8bnUeCli5C/lF0Duln79N1Hb36KO78A6j5B066i0KxBmPoNQBDZLxnHUBUPwzhsZ5dN16mqioTJow4aWK69qzXcKkuMiqzOVyeRmp52kmClEgGhScyKCKRQV4MUn7qdK9nl1vl6225fLYlG7vTM/0xblAvrpiTTO8wKxMmjDjlzqz+cXFsWb8Jg9vhGblwO8HtQHc7wOX5qruaP4bL4RkFOb5Dy7NT68f/m/zdM5bj2ZF14u6s418VRQGj+ceFzSbL8a8n/N0a1LiWp3FdT8PXgFAUs61do27ye6PzdETQ0k1CbyFEW2n1Vah5+3DnH0QtONB8J4WiYOkzEKVXAkrvJIzRySihfTotJ4U3M+lqukZudT6Hyo5wuDyNjMosXFrTUaMoWySDIhIZHJ5EcngiUQERXvk+2krTdb4/UMwH69IprfLsRBoQHcLV5yQzpP+PbTvdduB7//EIpmDffi/eIPWrzlx3qqouQYsQPYyu62hlubizd+HO2Y1WkgEnLiY1GDH2ScIYNxxjzBCsMUlE9ony2SfT9mTS1XWd4roSDpWnkVqWRmpFBvXu+ibnhFlCGRKZzJCIZAaFJ/k8SDlRam4FK1YfIbPQUyU4IsTKZWcnMmVEXww/CRrbux24K5D6VWeuu1VVl6BFCC/y1080uqahFh3GnbENd/auZlM+hqj+noRZscMw9h3cZKunYvJt5tQzzaRbbq/gcHma5/+yNCqdVU3OCzDZGByexODIZIZGJBMd2HmjRq1VUl7He2vT2XH4KABWi5ELpwzgvEn9sJpP/npauHAR8+cv8MvXoDdI/aoz0x1HpSRoEcJL/O0TTZNAJXM7ev0Jb94mC6a4ERj7j8HUbzSG4I5Zp+ENp8ukawm2Mnj6SHKijvJdyuMU1x1tctxkMJEUNpAhEckMjRxEv5C4U9bq8aWaOif/+yaVb7flomo6igIzR8eyeGYCYcGtyxliNBq77Ru21K9qve46KiVBixBe4E+faNSyPFypG3Ef2YJeX/njAWsQ5oHjMSVMxBg7zLONtQv4aSZdg9lI1JC+RI+Mo8+oeCIG9kIxKGwsSAE8GWf7h8YzJMIz5ZMYNhCL0ezj7+LU3KrGtzvyWLkxs7EC88iESK6cm0x879PXG+oppH5V63XXUSkJWoRoJ3/4RKPba3ClpeBK3ejZktygIVBJnIQxbniXqjzbMNVWWFyIubeNv7y2jB25OwkeEIHxJ1MkfQP7HF+XMohB4YkEmrtGTRhd1/kh9RjvrU2jpNyz1ia+dxBXzklmZGKUj1vnfzqzaGJX111HpbrObzAh/JSvPtHouo5alIpr/3e4s3b8mJ7cYMTUfyzmwTMw9hvVIduQO5Ku67zz+Tu8/uXr2PqF0Ht4DGaXFawQltwLAKtmJtYUzYzB0xgaNYhwa5jP2tvWdUyZhVWs+O4IqXme0bCwIAvXXTiMCYOi0GUnbos6smhid9NdR6W61m8zIfxQZ3+i0Z31uNK24Nq/Gq08r/FxQ68BmAfPwJQ8BYMtxCv36iyl9eXHF88eYW/RfhwBLhIXj2o87qyxU7K/gJJ9+dxxzR1ceeGVfrF4ti3rmEor7XywPp2U/cUAmE0Gzj+rPxdNH0hs3zDPLi1NopaT6Qm7pLyhu45KSdAiRDt11icaraoE596vcKVu+rGOjcmCOXka5uFzMPYa0K7rd6YaZy2pFekcPp4v5Wj9CblhFHA7XBw7XETJ3nyK9+VRkVUKx6faHt5/H5dfcLnPP02f6Tqmeoebz1Oy+XpbLq7jW8enjujLZWcnEhlqw+TjXVpdSXffJeUN3XVUSjLidgDJuNg5/KWfGzK2nu4TTVsr7KpHs3Du/hx35rbGysRKWF8sw+diHjy9wwu9eaOfHaqTtIpMDpcfIbUsjbyaQvQTcsMYFAMDQuIJrLXy7L1PUppahHaKe3300Wc+XTx4Jll6URQ27C7k4w0ZVNV5FtkO6RfOVeckM7BvaONz/OX13N31tH5ueTQwrlNGpSQjrhB+qCM+0ei6jpq/H+fuz1HzD/x4r36jsIw637Oo1k+37QKomkpWVS6Hy49wqCyNrKoc1J9U3o0JimZoxCCGRCaTHJ5IgMnGhx++x9EDJ18f1MDXiwdbu47pvc83sq/YRsExz4eu6IgArpyTzNhBvfxiekt0f91tVKpDghaXy8UzzzzDJ598QmVlJcOGDeNPf/oT48eP74jbCeFz3ppn13UdNXcvjh0foR3N9DyoGDAlTcYyZj7GqP4d0fx203SNwtrixvT4aRUZOH5SlTjCGs7QyEEMiUhmcEQyYdbm6266yuLB0wVNIb0GMHzWTXy9XwVqCbKZWDQjgTnj4jB5+ZOnEKfTnXL3dEjQ8vzzz/PBBx/wyCOP0K9fP1566SVuueUWPv/8c6KjozvilkL4XHs+0TSMrDi2f3g8rT6e9SpDZ2MZdR6GkF4d3Pozd6y+rHFNyuHyNGpcTadwg8yBDD6eK2VIRDK9A6JOO7rQVRYPnixosgZFMGTaNfQbMRfFYMSgwLxJ/Vg4bSBBNv/OFSNEV9AhQct3333HwoULmTFjBgB/+ctfeO+999i1axfnn39+R9xSCL/Qlk807oKDOLd9iFp85PhFLJhHzMUy5kIMAaGnfnInqnJUc+DYEQ6XeYKUUnvTUgAWg5nk8MTGOj5xwTFnnHm2qywe/GlwZTBZSJpwCUmTFmOyeHLElOf8wPMP3EbfKEkOJ4S3dEjQEh4ezpo1a7j22muJiYlhxYoVWCwWhg0b1hG3E6JLUsvzcWx9FzVnt+cBoxnz8LlYxszHEBju07YB2N120ioySa1MJ60inezK/CbHDYqBgaH9G0dSEsL6Y/JC8rqusKX1x+DqeuJHzGHItGsIOD4aVl54mIPrX+OJB/4uAYsQXtYhu4dSU1O58847SUtLw2g0YjAY+Pe//80555zTpuupqkZVVf3pT/QTRqOB0NAAqqrqUdXuvzrdV7pqP2t1ldR//yHOg2s9u4EMRqzD52CbcBGGIN9VGHZrbjIqsjlUlsahsiNkVuag/STLWXxwDEOiBjEsMplBEYnYTLYOa4+qqmzZsqlxqm3q1Ok+H2E50YGsMv77wTYq6j1tqqss4dDG11FqsnjooUe56KKLz+h6XfX13NVIP3eesLAADAbvruHqkKDliy++4PXXX2fJkiVER0fz3nvv8fnnn/Pmm28ydOjQM75eQyp0IboyzeWgcuunVGz5CN3pybMSOGQykXOuxRIV2+nt0XWdnMp89hQdYm/xQQ4eTWu2eLZPUBQjo4cyKnoII/sMIczmP9NVvpJXUs2rnx7g+wOexbiBNhMTEkzEBpQRHxfDzJkz/Sq4EqI78XrQkp+fz/nnn89rr73GxIkTGx+/5ppriIiI4Nlnnz3ja8pIi2hJV+pnZ9ZO6je+iVblqUBs7JNIwLSfYY4d0qntqLBXcrDsCAdLUzlYeoQqZ3WT4yHmoOMjKYMYGplMr8CoLtXPHam6zslH6zNY80M+qqZjUBTmTojjkpmJhAa1v/ik9HPnkH7uPB0x0uL1NS179uzB5XIxatSoJo+PGTOG9evXt/m6XTEJkKpqXbLdXY0/97NWdRT75v+h5uwCQAmKxDr5SkxJZ6Eohg5vtyepWwYHy1I5VHaEwtriJsfNBjODwhMZGjmIoZGDiAmKbrJ49sT2+XM/dySXW+PbHbms2pxNvcMNwNjkXlwxJ4mYKE9iP2/2S0/t584m/dzxOiJ1rdeDlpiYGAAOHz7M6NGjGx9PTU1lwICuk2ZciPbQVRfO3V/g3PkpqC5QjFhGn49l/CIUc8etA9F0jdzqfA6WHeFQWSqZldm4T0jqpqDQLySWoZGDGRoxiMTwgZi7UOVnb2lNkUNd19l2qIT316ZzrNIznde/TzBXzU1m2MBIXzRbiB7P67+tRo8ezcSJE7n77ru599576du3Lx9//DFbtmzhrbfe8vbthPA7atER7OuWo1V61jwYY4dhnX4dxoiOWbdS4ajkQGkqB8oOk1qWRq27rsnxSFsEQyMGNSZ2C7Z0bNp/f9eaIodp+ZWsWH2E9PwqAMKDLVw6K4lpI/tiMMj6OiF8pUMW4lZWVvKvf/2LtWvXUllZyeDBg/nDH/7AWWed1abrSe0h0RJ/62fd5cCx7X1c+74FdJSAMKxTf4YpabJXF5KrmkpmVQ77Sw9xoPQweTVN08nbjDYGRyQxNNKzNqV3QPtSxvtbP7fHyYocNvTP08+/SZkhgW2HSgCwmA1cOHkA55/VH6ulYxfXdqd+9mfSz52nI2oPScHEDiD/KDqHP/Wzu+Ag9nWvoFd7FtqaBs/ENvVqrxUzrHRUc6DsMAdKD3Gw7Aj17h8Xpiso9A+NZ0TkEIZFDWZASD+MBu+9wfpTP7fHqYocmqxBDJp8BQnjFmAwmlGAGaNjWDwrkfBga6e0r7v0s7+Tfu48UjBRCD+ju+w4UlbgOrgG8Cy0tc26CVO/Uad55qk1rE3Zc+wAB0oPkVPdNLFbkCmQYVGDGRE1lGGRgwmxSBKz02mpyKFiMDJg9AUMnnoVluPZh2PDFX65eCL9o5vXRhJC+JYELUK0kVqSQf3qF9CrPDtyzMPnYj3rCpTjadzPlFtzc6Q8g93H9rPn6H4qnVVNjvcPiWNE1FCGRw1lYGi/M06R3xW1ZsFsa/20yGF04iSGzbqR4Mg4AKpLczm4/jXuv+vXErAI4ackaBHiDOmahnPXKpw7PgZd84yuzL4ZU9zwM75Wvbue/aWH2XN0P/tLD2NX7Y3HrEYLwyOHMLLXMIZHDSHU0rPeSFuzYPZMNBQ5DO2TyPCzb6LX8dEwR10Fhze/Te7eb9B1jb59fVtBWghxchK0CHEGtOpj2Ne8iFqUCoAp8SxsM284o7Urda46dh3dzw8lu0ktT0c9YUtyiCWY0b1GMKb3CAaHJ2E29szKwCdbMFtYWMiSJdexfPkbZxy4DB4xgamL/0LkQE+OHNXtJPOHlaR9/wFuZz2KohAbG+fzCtJCiJOToEWIVnKlb8W+/jVw1YPZhm36dZgGTWvVzpx6dz17jh7gh5LdHCw70iRQiQ7szeheIxjde0SPmfY5FVVVWbr0rmYBC/xY0mPp0ruZP39Bq6aK7E43n6fk8PX3OUQlTAEg/+A6Dm18k/rjC6f9qYK0EOLkJGgR4jR01YUj5R1c+78DwBCdTMCcX2II7XPK59ndDvYdO8COkj0cKD3UJMlbbFBfxvcZw7g+o+gbdOrr9DQtLZg9ka7rFBTkk5KymenTZ570PE3T2bi3kA/XZ1BV66mpNCg+jDhLIU+9s6IxYAH/qiAthDg5CVqEOAWt+hj13z6HdjQDAMvYBVgmXopyki3Fmq6RVpFBSuEOdh7di/OEAoTRgX2Y0Gc046PHEBMU3Snt74p+umC2Leftyyzl3dVp5B31pEroEx7AFXOSGD+4N4qi8PPL5nttga8QovNI0CLESbhz91C/+gVw1II1iIDZt2AaMLbFc0vqjrK16Ae+L/qBMnt54+O9AqKY2GcM46PHEBvUV6qVt0LDgtm2nJd/tIYVa9LYl1EGQJDNxEXTBjJ3QjymE/JFGI3GU47SCCH8kwQtwi94c2tre+m6hnPHxzh/+BTQMfROIODcX2MI6d3kPKfqYmfJHjYWbCWjMqvxcZvRxoTo0UzuO5HEsAESqJyhKVOmERsbS2FhYYvrWhRFISYmtsmC2cpaJ59syGDd7gJ0HYwGhbnj47lo+kCCA3rmYmYhuiMJWoTPeXtra3voznrqV7/QWJXZPHwu1qk/QzlhF09x3VE25qewtXBHY50fBYVhkYOZHDOB0b1GYOmhu368wWg0smzZYyxZch2KojQJXH66YNbpUvl6Wy6fpWTjcHrWDE0Y3JvL5yQRHRHok/YLITqOBC3Cpzpia2tbaVUl1H/1b7TyfDCasM36BeZBnk/zqqay+9h+NuSnkFqe1vicSFsE02MnMyVmAuHWsE5pZ0+wcOEili9/o1kw27Bg9sIFF7FlXxEfrE+nrMoBQEJMCFfNHcTgfuE+arUQoqNJ7aEOILUtWudUtWDgx2mAHTv2tThV5M1+dhccxP7Ns+iOGpTAcALOux1jn0TqXHVsKvietXmbqHBUetqFwoioocyMm8LwqCHdfouyL1/PLU0bpuVXsWJ1GllF1QBEhlq57OwkJg+PxtCFp+Lk90bnkH7uPFJ7SHQr3tra2l7OA6txbPof6Kpn/cp5t1Nm0FmT+gmbC7c17gAKsQQzPeYspsVOJiogosPaI3504oLZ4rI6nv/kAD+kerYq2yxGFkwdwLyJ/bCYZeePED2BBC3CZ7yxtbU9dE3DkfI2rn3fAGBKmsKxCfP5KmMVu47uQ8czCBkb1Je5/WcxMXosZoP8k+lsNfUuVm7KZM0P+aiajqLA2WPjuHhGAmFBFl83TwjRieQ3sPCZ9mxtbS/d7cS++gXcWTsAKB53Pt9aHez94dnGc4ZFDuacfrMYGjlIdgD5gMutsfqHPD7dlEWdww3AqMQorpyTRFxvqWotRE8kQYvwmdNtbQWabW31Bt1eQ91X/0IrTiMnwMrapMEcqN4J1Z71KhOix3DegDnEBcd49b6idXRdZ8fho7y3No2jFZ4CkvG9g7hq7iBGJET6uHVCCF+SoEX4zKm2tjaw2+188cVnXttBpFUdpf6LJymoP8qXcZEcCjCBvRgFhbP6juf8AXOIlrT6PpNeUMmK1Wmk5XkWPYcFWVg8K5EZo2IwGGS0S4ieToIW4VMNW1v/+MffUV5e3ux4RUW517Y+q0ezKPzmKb4O1PmhVyS6omBQDEzuO4HzBsyhT2Cvdl1ftN2xyno+WJfB1gPFAFhMBi6Y3J8LJvfHZpFfU0IID9ny3AFkS92ZUVWV8eNHUFh4Zlufz6Sfq3J38cX2V9kcYsF9/BP7uN6jWJR0AX0Ce5/yuT1dR76e6+xuPkvJ4pttebhVDQWYNrIvi2clEhlq8+q9/J383ugc0s+dR7Y8i24pJWXzSQMWaN/WZ03XWL/vAz4r2kpdmBWA5NCBXDJoIQlh/dvVbtF2qqaxflcBH2/MpLrOBcDQ/uFcNXcQA/qG+Lh1Qgh/JUGL8LmO2vqcUZnFir1vkeesAKOBaN3E4pE/Y2SfkbIbyEd0XWdPeinvrkmjsNRTAqFvZCBXzklmTHKU/FyEEKckQYvwOW9vfa521vBR2mdsLfJsZ7apGhcYezPn7Dswmaxtbqdon5zialasTuNgtmftUnCAmYtnJHD22NgmFZiFEOJkJGgRPteWqr4t0XWd74t+4IMjnzYWMpxYWc/CyDH0mvkLFIP/vTH6U3XrjlJe7eCj9Rls2luIDpiMCudO7MfCqQMItElhSSFE60nQInzuTKr6nkxpfRlvH/6Qg2WpAPR1uLi0pJqkIedinXyVX047+FN1647gcKp8+X0OX2zNxunyLHg8a1gfLjs7id7hAT5unRCiK5LdQx1AVqe3Tctv4nEsW/Zoi2/iJpOB8PBAPtrzDR8e+Qyn6sSEwjml1cwqryNgwmIs4xf5bcDSUnXrhrZ2ZnXr0znT17Om6WzaV8hH6zOoqPHUbUqKC+XquYNIipNK2Ccjvzc6h/Rz5+mI3UMStHQA+UfRdmcyXVLjruat1A/YXXQAgERTGIvTM+jtUrFMvBTreN++6Z/se2lvdevOdiav5wNZZaxYnUZuSQ0AvcJsXDEnmYlDevtl8OhP5PdG55B+7jyy5Vl0eydW9T2VnSV7efvwB9S66jAbTCwMSGDS7k0YAMuExT4PWE419RMREeEX1a29qeBYLe+uSWNPeikAAVYTF00byDkT4jGb/G8tkRCia5KgRXQpDtXJu4c/JqVoOwAJ4f242hhP2NZPALCMvxjrhIt92cSTTv0UFhayZMl13HLLr1p1nY6qbu1NVbVOPtmYybpdBWi6jtGgMHtcHIumDyQkUCowCyG8S4IW0WUU1Rbz0r43Kar11Aq6IGEui7BR+c2rAFjGL8Iy4RKftlFVVZYuvavFXVC6rqMoCh988G6rrtUR1a29xeVW+WZ7Hp9tyaLeoQIwblAvrpiTTN/IQB+3TgjRXUnQIrqEbUU7eevwBzhVJ2GWEG4a8XMSSwupXP0SAJZxF2GZsNjn6yZSUjafduqntPQYUVG9KCsrbdcWb1/QdZ2tB4v5YG0GpVWeCswDokO4am4yQwdE+Lh1QojuToIW4ddcmpv3j6xkY34KAEMikrlpxDXYCg5Tt+ZlAKxjzsc88VKfByzQ+imdyy+/khdffL7NW7x9ITW3gv99nUpmYRUAESFWLp2VyNSRfTH4Qd8LIbo/CVqE36pyVvPintfJrMr2TAcNPIcLE85FKzhE/bfPg64TPHoupmnXoKr+sQmutVM6F1ywgMmTpzVbrBsTE3vSLd6+UlxWxwsrD7Bpj6edVrORC6f057yz+mM1+1dgJYTo3iRoEX4ptzqfF/b8H+WOCgJMAfxixDUMjxqCWpJO/Vf/Bs2NOXEivRfcRkWlHfCPoOVMsvsajUbmz1/gtxlxa+0uPt2UxXc78lA1HUWBmaNjWTwzgbBgKYcghOh8ErQIv7OzZC+vH3gHp+YiOrA3t46+kejA3qhledR98RS4HRjjRhA071coBv94g29wptl9W7vFuzO5VY01P+SzclMmtXY3AOMG9+by2UnEyCJbIYQPSdAi/Iau63yVvYZPM74EYFjkYH4x4ucEmgPQqo9R//kT4KjF0CeJgPN+h2L0z7o1CxcuYvnyN7rE1M+JdF1n55FjvLcmjeLyegDiegXxs3mDOHviAEnGJYTwOQlahF/QdI33UleyPn8zAHPiZ7A4eQFGgxHdUUv9F0+h11VgiIgn8II7Ucw2H7f41BYuXOTXUz8/lVlYxYrVaaTmVgAQGmjmklmJzBwdg9UivyaEEP5BfhsJn3OpLl7b/za7ju0DHSaYR7I46XjAorqo//pptIoClKAIAub/AcUW7Osmt4o/Tv38VFmVnQ/WpbNlfzEAZpOB88/qx/zJAwiwyq8HIYR/kd9Kwqfq3fU8tOZJyoxVqC6V759dzXsp/+Xp2IdY9sCjnBNYgFp4GMwBBMz/A4bgSF83uVuod7j5PCWbr7fl4jo+5TN1RDSXnZ1EZKh/j2IJIXouCVqEz1Q7a3hw/ZNUG2tx1TnZ9MSXHD3gWQNSWFjIoRWPcvaswaAYCZj3W4yR/Xzc4q5P1TQ27C7k4w0ZVNW5ABjcL5yr5iaTEBPq49YJIcSpSdAifKLSUc3TO1+g2lCLvaKO9Q9/RmV2aePxn00ayK2zBgNgmXkDpvgRvmpqt7E3o5R3V6eRf8xTMT06IoAr5iQzblAvv0jMJ4QQp9NhQcvHH3/Miy++SG5uLv379+e3v/0t8+fP76jbiS6kwlHJ0ztfpLjuKHWlNax74FNqiiobj88e3Jf7Fo4F4J/fHuCcEQrTfdTW7iCvpIYVa9LYn1kGQJDNxKLpCcwZH4fJy2XjhRCiI3VI0PLJJ5/wt7/9jbvvvpvZs2ezatUq/vCHP9C3b1/GjRvXEbcUXUS5vYKnd75ISf0xrJqFz/+xktriqsbjg/uE8u+rJmE0KLy7I4tn1h5i5NX+X+3YH1XWOPhoQwYb9hSi62A0KJwzIZ6Lpg8kyOaf28WFEOJUvB606LrOv//9b2644QZuuOEGAH7zm9/www8/8P3330vQ0oOV2yv41w//5Zi9jChbBNO18bxZ/HTj8chACy9eN5Vgq5ktGSXc88lOwL+rHfsjh0vl6+9z+DwlB4fLU4F54hBPcrg+EZIcTgjRdXk9aMnIyCA/P5+LLrqoyePLly/39q1EF1LtrOE/u17imL2MXrZIfj/+VsLMoY0p700GeOZnk+kXEUR2WQ2/fft7VB1iY+P8stqxP9J0nS37ivhwfQbl1Q4AEmNDuWpuMoPiw33bOCGE8AKvBy1ZWVkA1NXVsWTJEg4cOEB8fDy/+tWvmDt3rrdvJ7xAVdUOTYJW767n2V0vU1x3lAhrOHeMv40IWzhAY8r7+xaOZXJCb6rtLn75xhYq7a7jx/2v2rE/OpRdzorVaWQXVwMQFWrj8tlJnDWsjyyyFUJ0G14PWmpqagC4++67+e1vf8uf/vQnvvrqK37961/z6quvMnXq1DZd12TqOgsGjccXNxq7wCLHTz/9hL/+9S4KCvIbH4uNjePhhx/joosubvf1naqT/+55jdyaAkIswdw58VZ6B/2Ya+WSSy4hvu4+kip2o2k6d7y7jbSj1cTFxfPQQ4+esg1dqZ87SmFpLSu+S+OH1KMABFiNXDQ9gfPO6ofF5J1gT/q5c0g/dw7p587TEZ+XFL2lUrTt8Pnnn3PnnXdy7733cs011zQ+/stf/hKAF1988Yyvqeu6fFrsAB9++CGXX355s2rEDX39/vvvc+mll7b5+m7VzWMbn2dX0QECzQHcN+dOBkY0zbVSl7GboneWga5RPmA6qcYYYmJimDlzpoywnEJljYN3vjnMF5uzUDUdg0HhgikDuOb8oVKBWQjRbXl9pKVvX8+iycGDBzd5PDk5mbVr17bpmpqmU1VV196mdRqj0UBoaABVVfWoqn8WmFNVld/97vZmAQv8GCTefvvvmTXr3DYFD5qu8cret9lVdACzwcxvxv6CMCIpL6/9sQ2VxVR/+AToGpYh00mY+0sSjwdMVVX2096jK/Szt7ncGt9sy2XlxkzqHJ4KzGMH9eKqcwYR1ysIzeWmvNzt1Xv2xH72BennziH93HnCwgIwGLw7ouX1oGX48OEEBQWxe/duJk6c2Ph4amoq/fv3b/N1u2J1WVXV/LbdmzZtbDIl9FO6rpOfn8fGjRvbVD/n0/Qv2Va0E4Ni4JZR1zMwZECTvtDdDuq+fBrdUYehTyKW6TfgdLrbtLbGn/vZW3RdZ9uhEt5fm86xSk9A169PMFfNTWb4QM90W0f3QU/oZ38g/dw5pJ87nnfncTy8HrTYbDZuvvlmnn32WaKjoxk9ejSfffYZmzZt4rXXXvP27UQbFRe3LvdJa8870ZaCbXyZvRqAa4ZcxoioIU2O67qOfcP/oZXmothCCDj3t3z25ZcsXXoXBQUFjefFxsaybNljLFy46Izb0J2k51fyzuojpOd78tmEBVu4dFYi00fGYDDItKkQoufokORyv/71rwkICOCf//wnxcXFJCUl8Z///IfJkyd3xO1EG7Q298mZ5kg5XJbGW4c/AOCCAXOZGjup2Tmug2twH9kMioLt3F/z+dqNLFlyXbOpqsLCQpYsuY7ly9/okYHL0Yp6PliXzvcHSwCwmA3MnzyAC87qj9Ui632EED2P1xfidgRV1Sgrqz39iX7CZDIQERFEeXmt3w4/qqrKhAkjKCwsbHFdi6IoxMTEsmPHvlavaSmqLeaJHc9R765nQp8x3DjiZxiUpvOZanEadZ8+DJqKdfKVGEeez4QJI5qMsLS2HV2hn9uizu5i1ZZsvt2ei1vVUYDpo2JYPCuRiJDOX2TbXfvZ30g/dw7p584TGRnk9V1aUjCxhzIajY05UhRFaRK4NOweOpMcKTWuWp7b/Sr17noSwwZw3bArmwUsWn0V9d8+C5qKaeAEzKPns3nzxpMGLOCZSiooyCclZXOb1tZ0JW5VY92uAj7ZmElNvSdPzbABEVw1N5n+0SE+bp0QQvieBC092MKFi1i+/I1ma0liYmJZtuzRVk/JaLrGq/veovR4tttfjroBs7FpbRtdU7F/9zx6bTmGsL7YZt+Moigduramq9B1nV1px3hvTTpFZZ5dcjFRgVw5J5nRSVGy3V8IIY6ToKWHW7hwEfPnL2hXRtxPM77iUPkRLAYzvxx9AyGW4GbnOLd/hFpwEExWbOf9DsUSAHTc2pquIruomhWrj3AopwKAkEAzl8xIYNbYWIxe3ioohBBdnQQtAqPR2Oapl10le/k6ew0APx92BXHBMc3Oceftw7nrMwBsZ/8CY0Rc47EpU6Y11h861dqa7lZ/qLzawYfr0tm8rwgdMBkNnDepHxdOGUCgTf5ZCiFES+S3o2izotoSXj+4AoC5/WYyMXpss3O0ugrsa14EdExDz+b7IifFu99rMqLjzbU1/s7udPNFSg5ffZ+D8/giwMnDo7lsViK9wgN83DohhPBvErSINql323lx7+s4VCeDwhO5JOnCZufouoZ9zUvo9VXUmEK5+M7HyMo9scbRj3lYvLG2xp9pms7GvYV8tD6DylonAMnxYVw1N5mk2DAft04IIboGCVrEGdN1nXcOf0hxXQnh1jCWjLwWo6H5SIhz12eo+ftRFSOXPfUhWSVVTY7/NA9Le9fW+Kv9mWWsWJ1G3lFPMdE+4QFcPjuJCUN6yyJbIYQ4AxK0iDO2tWgH24t3YVAMLBl5bYsLb91FR3Bu/wiAx75LJe0nAQv8WONo6dK7mT9/QbvW1vij/KM1vLsmnb0ZpQAEWk0smj6QOePjMXehquVCCOEvJGgRZ6S47igrUj8GYEHCeSSGDWh2jm6vwf7d857KzWFJvLz6w5NerzvmYamqdfLxxkzW7cpH18FoUJgzPo5F0xMIDjCf/gJCCCFaJEGLaDWX5ubVff/DqToZHJ7EeQNmNztH13Xs65aj15ahhEWz05jcqmt3hzwsTpfKN9tz+WxLNnanCsD4wb25YnYS0ZGBPm6dEEJ0fRK0iFZbmf4FuTUFBJkDuWHE1c0y3gK4Dq3Dnb0TDCYCzvk1vQ7ntOraXTkPi6brbD1QzIfr0imtcgAwoG8IV89NZkj/CB+3Tgghug8JWno4VVVbtfh1f+khVuduAOC6YVcSbm2+40WrLMKx5S0ArGddhrHXAKZExHfrPCypuRWsWH2EzMJqACJDrVw2K4nJI6IxyCJbIYTwKglaerBVq1Y222Z84jbkBjWuWt44+C4AZ8dPZ1Sv4c2upWsq9WteBLcTY+wwzKPOB7xf48hfFJfV8d7adH5IPQqA1WJkwZQBnDepHxZz1/pehBCiq5AtDD3UqlUrWbLkumbFChu2Ia9atbLxsfdSP6HaWUPfwD4sbiEfC4Bz56doJRlgCTheV+jHl1ZDHpaYmKbZcmNiYhu3O3cVNfUu3v72CEtf3soPqUdRFJg9NpZHbp3KwmkDJWARQogOpOgtjdn7GVXVKCur9XUzWs3fS5+rqsqECSNOWl25Ycpmx4597Cs7yIt7X0dBYZ55OupRR7NpJLUknbpPHgRdwzb3VszJU096X2/mYenMfnarGqt35PHp5ixq7W4ARiVGceWcJOJ6N9/y3Z34++u5u5B+7hzSz50nMjIIo9G7YyMyPdQDpaRsPmnAAj9uQ167ZQ3f6JsByP0ulVteer7xnIZppAXnn++ZFtI1TEmTTxqwQPtqHPmKruvsOHyU99emU1JRD0B87yCunJvMyIQoH7dOCCF6FglaeqDWbi/eVLOdaksNlXllbH11TZNjDdNI65/8A7F1xShBkdhmXN8RzfWZzMIq3vnuCEfyKgEIC7KweFYiM0bFYDDIIlshhOhsErT0QK3ZXhw3KYFiSxm6qrHtuTVoPxlG1XWd2YP7EluXCeBZx2IN6pD2drZjlfV8uC6DlAPFAFhMBs4/qz/zp/THZpF/MkII4SvyG7gHmjJl2im3IVuCbUz85WwADn26i/KMo83OCbGZefCScQAcjRxBYlzzHUVdTb3DzWdbsvl6Wy5uVUMBpo3sy+JZiUSG2nzdPCGE6PEkaOmBTrcNedTPJmMJsRKk2jjw/vYWr/H3+aPoGxpA5rFqMqL6kdhZje8AqqaxfnchH2/IoLrOBcDQ/uFcNXcQA/qG+Lh1QgghGsiW5x7qZNuQB08dQeI5wwCYahvfbFoI4OxB0VwxYSCapnP3Rz/Qu29cp7TZ23RdZ0/6Me59ZRtvfHWY6joX0ZGB/O6yUfz5Z+MkYBFCCD8jIy092MKFi5g/f0HjNuTeffqw3ryDgtoipsZMYtHgi7j/J9NIwVYTD14yHoD/S0mn0GXrktlsc4qreXdNGgeyygEIDjBz8YwEzh4bi8nLW/SEEEJ4hwQtPdyJ25C/zVlHQVoRQeZALkm6sMVppL/NH01MWADZpTU8+e0Bnv3va10qm215tYOPNmSwaU8hOmAyKpw7oR8Lpw0g0CYVmIUQwp9J0CIAKLOX81nmNwAsTlpAsMWzE6hhGmnp0rtICnRz1UTPtNBj63N49r+vdZlstg6nypff5/DF1mycLs+U16Shfbh8dhK9wwN83DohhBCtIUGLAOD91JU4VSdJYQlMjpnQ5NjChYu44Jw5VL79F3DXUtZrBK+ueqVLjLBoms6mfYV8tD6DihonAEmxoVx1ziCS45oXfRRCCOG/JGgR7Dt2kN3H9mNQDFw9ZDEGpfmaDve2D7C4a1FCejPw4t+jdIGA5WBWGStWp5FTUgNArzAbl89OYtLQPo3FGoUQQnQdErT0cG7NzQdHPgXgnH6ziA1unnjOXXgY16G1ANjO/gWK2dqZTTxjhaW1vLs6jd3ppQAEWE0snDaAcyfEYzb5f7AlhBCiZRK09HBr8zZRUn+MUEsIFwyc2+y4rrpwbHgNAPPQszHFDuvkFrZeVZ2TTzZmsm5nAZquY1AU5oyLY9GMgYQEWnzdPCGEEO0kQYsf8nY15JOpdtbwReZ3ACxKvACbqXnWV+euz9AqClECQrFOvtLrbfAGp1vlq5QcVm3Jot6hAjA2uRdXzEkiJqp7lBYQQgghQYvfWbVqJUuX3tWkCnNDRWVv79T5NOMr7KqdfiFxzRbfAqgVBTh3rgLAOu3nfldbSNd11u/M49VP93Os0g5A/+hgrpo7iGEDInzcOiGEEN4mQYsfWbVqJUuWXNesHlBDReXly9/wWuCSV13A5oLvAbh80KJmi291XcOx/jXQ3Bj7jcaUeJZX7ustaXmVrFhzhPT8KgAiQqxcOiuRqSP7YpBFtkII0S1J0OInVFVl6dK7WixgqOs6iqKwdOndzJ+/oN1TRbqu80HaKnR0xvcZTXJ4QrNzXIc3oBalgsmCbcZ1frPbpqSinvfXprP9UAkANouRC6cOYN7EfljNsshWCCG6Mwla/ERKyuYmU0I/pes6BQX5pKRsbsxg21YHy1JJLU/DpBi5JOnCZse1ukocKSsAsE68FENI73bdzxtq7S5Wbc7iux15uFUdRYFZY2L5xcWjUFQVdws1koQQQnQvErT4ieLiIq+edzKarvFx+ucAzIqfRlRAZLNzHFveAmcdhl4DMI+c1677tZdb1VizM5+VGzOptbsBGDEwgivnDiIhNpSIUBvl5bU+baMQQojOIUGLn4iObp4fpT3nncz24l3k1xRiM9o4v4Utzu68fbjTt4KiYJt5E4rBN1Muuq6z88gx3luTRnF5PQCxvYK4ck4yoxIj/Wa6SgghROeRoMVPTJkyjdifVFQ+kaIoxMTEtquisktz82nGVwCcN2A2weamu4F01YV905sAmEeci7H3wDbfqz2yiqpY8V0ah3MrAAgNNHPJzERmjonBaJAKzEII0VNJ0OInWqqo3KBhVGHZskfbtQh3Q95myuzlhFlCmdNvRrPjzj1foVcWeXKyTFzc5vu0VVmVnQ/WZbBlv2cKzGwycN6kflw4ZQABVnmpCiFETyfvBH7kxIrKJy7KjYmJZdmyR9u13dnutvNl9moAFiTOw2JsmiFWqynF+cNKAKxTrkaxBLb5Xmeq3uHmi63ZfPV9Lq7jC2qnjIjmsllJRIU1T3gnhBCiZ5Kgxc8sXLiI+fMXeD0j7tq8TdS66ugT2IspfSc2O+7Y8jaoTox9B2NKntque7WWqmls2FPIxxsyqar1VGAeHB/GVecMIiEmtFPaIIQQouuQoMUPGY3Gdm9rPlGdq55vc9YDcOHAeRh/srjWnbsXd+Z2UAxYOykny76MUlasSSP/qGfnT5+IAK6Yncz4wb1kka0QQogWSdDSA6zJ3UC9u56+QdFMiB7T5JiuurBvPmHxbWS/Dm1L3tEa3l2dxr7MMgCCbCYWTU9gzvg4TEZZZCuEEOLkOjRoyczM5NJLL+Wee+7h0ksv7chbiZOoddWxOncjAAsS5jVL1+9ZfFuMEhCGdeIlHdaOyhoHH23IZMOeAnQdjAaFcybEs3DaQIIDzB12XyGEEN1HhwUtLpeLP/3pT9TV1XXULUQrrM5Zj121Exccw9jeI5sca7r49qoOWXzrcKl8vS2Xz1OycTg9FZgnDOnN5bOTiI7ovMW+Qgghur4OC1r+85//EBTkX1WBe5oaZy1r8k4+ytK4+DZmiNcX32q6Tsr+Ij5Yl0F5tQOAhJhQrpqbzOB+4V69lxBCiJ6hQ4KWbdu2sWLFCj7++GNmz57dEbcQrbAmbyMO1Um/4FhG9xrR5Ji78PDxxbcK1mnXenXx6+Gcct5ZnUZ2UTUAUaFWLpudxFnDoqUCsxBCiDbzetBSVVXFXXfdxdKlS4mJifHadU2mrrNI03h8QanRhwtL6131rMvbBMCFSfMwn1ABWdc06ra8BYBl+Bys0QO8cs/C0lpWfJfGD6lHAU8F5oumJ3D+Wf2wdEAFZn/o555A+rlzSD93DunnztMRn1G9HrTcd999jB07losuushr1zQYFCIiut5UU2hogM/uvfbABurdduJDY5gz5KwmU0OVP3yDeiwbt8FMXlAi00Nt7coDU1Xr5J1vDvP5pkxUTcdgUDh/ygCuOW8o4SFWb3w7p+TLfu5JpJ87h/Rz55B+7pq8GrR8/PHHbN++nU8//dSbl0XTdKqqus6CXqPRQGhoAFVV9aiq1un3d6pOVh36FoB5/WdTWVHfeOzzT95n8JH3iQq08OiqHbzytxXExsbx8MOPcdFFF5/RfVxujW+35/LJxkzqjldgHpPci6vPSSaudzC62015udt739hP+Lqfewrp584h/dw5pJ87T1hYAAYv14vzatDywQcfUFpa2mwdy7333svy5cv57LPP2nxtt7vrvbhUVfNJu9flplDtqiXKFsm4XqMb27Bq1UoOvvM4U2cNIetYDW9sTQegsLCAG2+8luXL32hVqQBd19l++Cjvr03jaIUdgPjewVx1TjIjBkYCnfvz8lU/9zTSz51D+rlzSD93vBZq/7abV4OWJ554Arvd3uSx8847j9tvv50LL7zQm7cSJ+HS3Hybsw6AeQNmN2a/VVWVZx+7hzeuHg3AQ1/uxaV6XlG6rqMoCkuX3s38+QtOOVWUnl/JitVppOVXAhAWbOHSmYlMHxWDwSCLbIUQQnQcrwYt0dHRLT4eFRVFXFycN28lTuL7oh1UOCoJs4QyJebHGkMpKZu5aWwfrCYjG9OK+e5QYZPn6bpOQUE+KSmbWywhcKyinvfXpfP9wRIALGYDF5zVnwsm98dmkcTKQgghOp6823Qjmq7xXc4GAOb2n4nZ8OOP15m3n/kj41A1nQe/2HvSaxQXFzX5e53dzWdbsvhmex5uVUMBpo+KYfGsRCI6YZGtEEII0aDDg5bDhw939C3EcftLD1FcV4LNaGN67OTGx3VNY4QjFYC3t2WSWlx10mtER/cFwK1qrNtVwCcbM6mpdwEwbEAEV81Npn90SAd+F0IIIUTLZKSlG/nueCXnGXGTCTDZGh93p20hwF5GtcPN06sPtvhcRVGIiYll8uSp7Eo7xntr0igs9ezYiokK5Io5yYxJipIKzEIIIXxGgpZuIrsqlyMVGRgUA7Pjpzc+rrudOLZ9AMDRXmMpq/sURVHQT1jW3RCI/Onvj/PP9/ZyMLscgOAAM5fMTGDWmFipwCyEEMLnJGjpJhpGWSZGjyXCFt74uGv/t+i1ZShBkYy+4naWhwxm6dK7KCgoaDynf+IwFtxwP2vSzeiUYzIamDcpngVTBhJok5eIEEII/yDvSN1AaX0ZP5TsAeCcfrMaH9ftNTh2ehL9WSddimKysHDhIubPX0BKymbyC4sodvZmfyHkVHjyFZw1rA+Xn51Er3DJFimEEMK/SNDSDazJ3YiOztCIQcSHxDY+7tj5KTjrMUT2w5Q8rfFxRTGgBSexpUihssYJQHJcGFedk0xSbFint18IIYRoDQlauji7286Wwm0AnNP/x1EWrfoorv3fAWCdfCXK8VTK+7PKWPFdGnlHawDoHW7jitnJTBjSWxbZCiGE8GsStHRxKUU7sKsOogP7MCxycOPjjm0fgubGGDccY/xI8o/V8t6aNPaklwIQaDWxcNpAzpkQj7kLVdAWQgjRc0nQ0oVpusb6vM0AnB0/rXGkRD2WhTttCwDu0Yt54+tU1u8qQNN1jAaFOePiWDQjgeAAs8/aLoQQQpwpCVq6sENlRyiuO4rNaGVy3/GAJx2/Y+u7ABSHj+Kp9wqwO1UAxg3qxRVzkukbGeizNgshhBBtJUFLF7YubxMAU2MmYTueTM6Vuxc1/wBu3cB/swZh11QG9A3h6rnJDOkf4cvmCiGEEO0iQUsXVVJ3jP2lnhIJs+KnApCaU47hqzeIBjY4hqAHRXHL2UlMHhGNQRbZCiGE6OIkaOmi1udvRkdneNQQdEcQz365F3fmdn4RchSHbsIydiEPTR2K1Wz0dVOFEEIIr5CgpQtyqE5SCrcDoBxLYOlXW9E0lb+E7QLAMup8Lpg2woctFEIIIbxPgpYu6PvCndS77eAIZPtuTw2hxfEl9K2rBGsQIRMX+LiFQgghhPdJ0NKF6LrOD6lHeTd9NdjAVRxPXO9grpo9kIHff4EOWMZciGKR3UFCCCG6HwlauojMwipWfHeEI2U52EaWg6Zw2eizmTc2GfehNTiqj6IEhGEZca6vmyqEEEJ0CAla/FxppZ0P1qeTsr8YAGtCHgBj+4zk/NGD0N1OnD+sBMAy7iIUs9VnbRVCCCE6kgQtfqre4ebzlGy+3paLy+2pwDx5ZBSHgotxanB2P08BRNf+79DrKlCCozAPO9uXTRZCCCE6lAQtfkbVNNbvLuSTDRlU1bkAGNIvnKvOSSZXPcCew06iA3szKDwR3VmPc9dnAFgnXIJilLT8Qgghui8JWvyEruvszSjl3TXpFByrBSA6MpArZycxdlAvAN7elgLA9NjJKIqCY+9X6I4aDGF9MQ2a5rO2CyGEEJ1BghY/kFtSw7urj7A/qxyAIJuJi2ckMHtcHCajpwJzdlUueTUFmAwmJsdMQHfU4tzzFQCWiYtRDJJETgghRPcmQYsPVdQ4+Gh9Bhv3FqLrYDIqnDMhnoXTBhJkazrVs7lwGwBje48k2ByEY/tH4KrHEBGPKXGSL5ovhBBCdCoJWnzA4VT56vscvtiag8PlqcA8cWgfLp+dRJ/wgGbnO1UXO4p3AZ7iiLqjFuferwGwTLgYRTF0WtuFEEIIX5GgpRNpus6WfUV8sC6dihonAEmxoVw1dxDJ8WEnfd7uo/uod9uJtEUwOCIJ545PfhxlSZjQWc0XQgghfEqClk5yMLucFauPkFNcA0CvMBuXz05i0tA+KKepwLzl+NTQlL4TUJz1OPc1jLIsklEWIYQQPYYELR2ssLSW99aksyvtGAABViMLpw3k3AnxmE2nXzxbWl9Gank6AFNiJuLc9w046zFExGFKmNihbRdCCCH8iQQtHaSyxsHrXx5i9Y58NF3HoCjMHhfLohkJhAZaWn2dlKId6OgMjkgm0mClZu/xHUPjZS2LEEKInkWCFi9zuVW+2pbDqk1Z1NrdAIxN7sUVc5KIiQo6o2tpusbWwu0ATI2ZiHPft8dHWWIxJcooixBCiJ5FghYv0XWdbYdKeH9tOscq7QD0jw7mqjnJDBsY2aZrHinPoNRejs1oY0xYIs4vXwZklEUIIUTPJEGLF6TlV7LiuyOkF1QBEBFi5foLhzMuKRJN09t83a1FOwCYED0GDq4DZx2G8FhMCZKXRQghRM8jQUs7lFTU8/7adLYfKgHAajYyf3J/FkwbSN/oUMrLa9sctDhVJ7uO7gXgrF4jcX72NACW8YtQDDLKIoQQoueRoKUN6uwuVm3O5tsdubhVHQWYMTqGxbMSCQ+2YjK1P6jYc3Q/DtVJlC2S+JxUXI5aDOExmBLPav83IIQQQnRBErScAbeqsXZnPis3ZVFT76nAPHxgBFfOSaZ/dIhX7/V98U4AJvUZjXvzFwBYxl0koyxCCCF6LAlaWkHXdXYdOca7a9MpLqsDICYqkKvmJjMqMeq0yeHOVJWzmoNlqQCMq3Gi26tRQnphSprs1fsIIYQQXYkELaeRXVTNitVHOJRTAUBIoJlLZiYya0wMxg4a9dhRvBtN1xgQEk/4/vXogGXMhVLJWQghRI8mQctJlFXZ+XB9Blv2FaEDJqOB88/qx4VTBhBg7dhu21bkmRqaYAhHry1DCQjDPHhGh95TCCGE8HcStPxEvcPNF1tz+Pr7HJxuDYApI6K5bFYSUWG2Dr9/cW0J2dW5GDAwIn0/AJbRF6CYWp9FVwghhOiOJGg5TtN0Nuwp4KMNmVTVeiowD4oP4+pzBpEQE9pp7WhYgDs0oA9BFXvAGoR52OxOu78QQgjhryRoAfZllvLu6jTyjtYC0Cc8gCvmJDF+cG+vL7I9FV3X2X58amjM0VIALCPORbEEdFobhBBCCH/Vo4OW/KM1rFiTxr6MMgCCbCYump7A3PFxmIydv7U4tzqfY/YyzIqRocUFYLJiGTmv09shhBBC+KMeGbRU1jr5eEMG63cXoOtgNCicMyGehdMGEhxg9lm7dpTsBmCY04BV1zEPn4NiC/ZZe4QQQgh/4vWgpaKigqeeeoq1a9dSU1PDkCFD+OMf/8jEib6vSux0qXy1LZfPU7JxOFUAJgzuzeVzkoiOCPRp23Rd54eSPQCMOnYMDCYso873aZuEEEIIf+L1oOUPf/gDpaWlPPXUU0RGRvLWW2+xZMkSPvzwQ5KSkrx9u1bRdJ2t+4t5f1065dUOABJiQrhq7iAG9wv3SZt+KqsqlzJ7ORZdYUidA/PQ2RiCInzdLCGEEMJveDVoyc7OZtOmTbz99tuMHz8egL///e+sX7+eVatW8fvf/96bt2uVwznlrFidRlZRNQCRoVYuOzuJycOjMXTiItvT+aFhaqimHgsKljEX+rhFQgghhH/xatASERHBiy++yMiRIxsfUxQFXdeprKz05q1Oq7isjnfXpLHzyDEAbBYjC6YOYN7EfljM/pVZVtO1xqmh0TV2is3RFO89zJQpURiN/tVWIYQQwle8GrSEhoZy9tlnN3nsiy++ICcnhxkz2pfRtbWVk6vrnHyyIZPvduShajqKAnPGxXHp2UmEBnVOgjbj8Z1HxlbuQEqvyKHCUYlV1Rhc5+TK595mT/5zxMbG8fDDj3HRRRd3ZHO7rDPtZ9E20s+dQ/q5c0g/d56OmMxQdF3XvX9Zjx07dnDzzTczdepUnnvuuTZfR9f10+ZLcblVPtuUyTvfpFJ7vALzxGHR3LRwOP37dl5yuLZY+t5DpGq5jKuyM3BrOtcs39Dk+B133MHFF1/MzJkzZeRFCCFEj9VhQcu3337Ln/70J8aMGcMLL7yAzdb2FPiqqlFVVd/iMV3X2XaohHe/S6OkwnNOvz7B/OzcQYxMjGrzPdvDaDQQGhpAVVU9qqqd8lyX28WtH9+JOdTG9QUVPPXCWtYcLmrxXBl5aepM+lm0nfRz55B+7hzSz50nLCwAg5cLC3dInpY333yTBx98kHnz5vHEE09gsbR/Wsbtbv7iSi+oZMXqNNLyPOtlwoIsXDorkemjYjAYlBaf09FUVWXbti3U1FQQHBzOpElTTzk68vGGTzGH2rCpGobsY6xNbTlgASgsLODGG69l+fI3WLhwUUc0v0tSVc0nP+ueRvq5c0g/dw7p547XEUMiXg9a3nrrLR544AGuu+46/va3v3k9ygI4VlnPB+sy2HqgGACLycAFk/tzweT+2Cy+y5e3atVKli69i4KCgsbHYmNjWbbssZMGGYeqj4ANhtc6eG3jkVP+kBumyZYuvZv58xfIVJEQQogexavv8JmZmTz00EPMmzePW2+9ldLS0sZjNpuNkJCQdl2/zu7ms5QsvtmWh1vVUIBpo/py6awkIkKs7Wx9+6xatZIlS67jp7NthYWFLFlyXYujI5quUWr1lBAYcLSae3flnvY+uq5TUJBPSspmpk+f6b1vQAghhPBzXg1avvrqK1wuF9988w3ffPNNk2OLFy/mkUceadN1dR1W/5DHxxsyqTm+yHbYgAiunJPMgL7tC4S8QVVVli69q1nAAqceHUmvyKJeUbGpGuu/PYDzDOZXi4tPPo0khBBCdEdeDVpuu+02brvtNm9eEoDyajtvfp0KQN/IQK6ck8yY5KhOrcB8Kikpm5tMCf3UyUZHdmWuA2BonYvHUjIac9q0RnR03/Y1WgghhOhiusRGdVXTCQ4w8/N5g/nHkrMYO6iX3wQs0PpRjxPP03WdPWWHARgbOYR/PvsKMTExp72GoijExsYxZcq0tjVWCCGE6KK6RJXnAKuJR26dQqDNdxWYT6W1ox4N56mqyndr3qHMoGHSdIYNX8SkqHjmz19ASspmvvzyM1544blmIy8NgdqyZY/KIlwhhBA9TpcYaQkOMPttwAIwZco0YmNjTzr6c+LoyKpVK5kwYQTbDnwOQGhRJTPOOZdVq1ZiNBqZPn0mDzzwCK+88mazkZeYmFjZ7iyEEKLH6tCMuN6iqhplZbW+bsYpNeweAlocHVm+/A0Aliy5jshAC9c8ey1FNjNF72xl4ye7Gs85MSBRVZWUlM0UFxcRHd2XKVOmyQjLCUwmAxERQZSX10q+hQ4k/dw5pJ87h/Rz54mMDPJ6uYQuMdLSFSxcuIjly9846ejI/PkLGncYXXXucIpsZhRdZ+t3BxuDnKVL70ZV1cbnNoy8XHrpFUyfLin8hRBC9GxdYk1LV7Fw4SLmz1/QYkbcTZs2UFBQgMVkYOSswawB3NmlOKvtgORfEUIIIU5HghYvMxqNzJgxq3H40eFwsWnTBlat+gSAi0bFkxUZBMC+9YebPV/yrwghhBAtk6ClA3366Sf89a9/bpLD5eqzh/De8UXFed9nNnuO5F8RQgghWiZBSwf58MMPufHGa5ssyp2c0As1oTe6olCVfYy6YzWNxxRFISYmVvKvCCGEECchC3E7gKqq/P73v2+W3famqckcCPbUSMrZmtH4uORfEUIIIU5PgpYOsGXLJvLy8po81j8yiBnDYjkSYAEgf1tW4zHJvyKEEEKcnkwPdYCWFtNePyWJtGArboNCTVElVbllLFnySxYuvFjyrwghhBCtIEFLB/jpYtpgq4nLxw/gyyDPKEvBjiwAFi68mOnTZ6KqKps2bZAkckIIIcQpSNDSAaZOnU58fDz5+fnous7l4wcQZDOz//iuocKdOU3S+i9deleTHUaxsbEsW/aYTBcJIYQQJ5A1LR3AaDTy73//GwCDQeH6KUnkW03YLSZcdU6OHSpi2bJH+eKLz1iy5LomAQtAYWEhS5Zcx6pVK33RfCGEEMIvSdDSQS699FJeeeV1LhyXzICoYHZbPINalWmlvPzi/zVJ6/9TJ0vrL4QQQvRkErR0kA8//JC///0vXDysFwDbjJ5tzWcPnsHChYtISdncbITlRCem9RdCCCGErGnpEJ9++gk33ngt8eEBzB58FtVGBUevEAAeueNe4t3RHDiwt1XXkrT+QgghhIcELV6mqip//atn2ufnZyViMCh8WuUpiliWXoK9oo5f/vJGNK11JdElrb8QQgjhIdNDXuaZ9snHZjZyxYSBAGwzebq5aFcOQKsCFkVRGncYCSGEEEKCFq9rmM5ZOCqe8EALWRW1GBI861oKd+a06hqS1l8IIYRoToIWL2uYzrluShIAb+SWYw60Yq+spyy9pFXXkLT+QgghRHMStHjZlCnTmDduCCNjw7G7VPYHeBLKFe3Kgea7m5u5884/s2PHPglYhBBCiJ+QoMXLjEYj/7juAgA+3ZNH5Kh4oPVTQ7NmzZYpISGEEKIFErR4mVZXSR+7J//KqsIaQuMi0FSN4j25p3yeLLwVQgghTk2CFi9zHVoHmkptQC+KwjxTQ6WHi3DVOU/6HFl4K4QQQpyeBC1epGsqroNrAfjnqq30HdsfOP3UkCy8FUIIIU5Pkst5kTtnN3ptGXZMvL3lAPNvnAhA0e6Wg5Y77/wzs2bNZsqUaTLCIoQQQpyGjLR4Uf66FQC8vuEAocl9MFnN1JfXUplT1uL5Q4YMZfr0mRKwCCGEEK0gQYuXfPPx20TUexLLvbMtk+jju4aK9+Sd9DmSol8IIYRoPQlavEBVVVK/eAWDQWFjWjHZZbVEjz550CI7hYQQQogzJ0GLF6Rs2cgFg6MAeHtbJtZQGxEJvQEo3tc0aJGdQkIIIUTbSNDiBXrubvqE2CiptvPtwUL6HJ8aqsg6hqOyvsm5slNICCGEaBvZPeQFiZpnLcv7O7Jwa3rjepain0wNPfDAw9x8820ywiKEEEK0gQQt7aRVFhNSW4Cm66zYkQ1A39H9ABqz4CqKQkxMrAQsQgghRDvI9FA7uQ6tA6Dc1pf8ijrC+kUSEBmE6nRz7HCRrGERQgghvESClnbQVReuwxsAiDv7KpYvf4Pk6cMBOHqgAM2lyhoWIYQQwktkeqgd3Jk70O3VKEERmPqPYeHA8WTHl3CgLJVzR8/mzyt/y6RJU2WERQghhPACCVraoaHOkHnILBSDEZfm5khFJgA3zr+GED0ct1vzYQuFEEKI7kOmh9pIrShALTwEioJ56CwAMiqycGkuQi0h9AuL9XELhRBCiO5FgpY2ch1aD4Cx3xgMwZ7EcofKjwAwPGpw4wJcIYQQQnhHhwQtmqbx9NNPM3PmTMaMGcMvfvELsrOzO+JWPqGrbtypmwCwDDu78fGDZakADO81xCftEkIIIbqzDglannvuOd555x2WLVvGihUrUBSFW265BafT2RG363Tu7J2eBbiB4Rj7jQagxllLbnU+AMMiB/myeUIIIUS35PWgxel08sorr/C73/2Os88+m6FDh/LPf/6T4uJivvnmG2/fzicatjmbB09HMXh2BqVWpAMQG9SXUGuIz9omhBBCdFdeD1oOHTpEbW0tU6ZMaXwsNDSU4cOHs23bNm/frtNpNWWoeXsBMA+Z2fj4kXJP0DIoPJGNG9fz9ttvs3HjelRV9Uk7hRBCiO7G61uei4o8dXhiYmKaPN6nTx8KCwvbfF2TyT/WDNenbQJdxxQ7FEvUjzuEjhwfafnvA/9m39c7Gh+PjY3j4Ycf46KLLu70tnZ3RqOhyVfRMaSfO4f0c+eQfu48HbEfxetBS329p6qxxWJp8rjVaqWysrJN1zQYFCIigtrdtvbSdY3q41NDERPnEXK8TRX1lRTWlqBrOoc37W3ynIKCfG688Vref/99Lr300k5vc08QGhrg6yb0CNLPnUP6uXNIP3dNXg9abDYb4Fnb0vBnAIfDQUBA214kmqZTVVXnlfa1hytvP+7KErAE4IoeTXl5LQBb83cDUJF9DFdt88XGuq5z++2/Z9ascyU7rhcZjQZCQwOoqqpHVSWJX0eRfu4c0s+dQ/q584SFBWAweHdEy+tBS8O0UElJCf379298vKSkhKFDh7b5uv6QWda+31Mc0Zw8FVUxw/E2rTvo2f5csr/gpM/Nz89j48aNTJ8+86TniLZRVc0vXh/dnfRz55B+7hzSzx1P171/Ta9P6g0dOpTg4GC2bt3a+FhVVRUHDhxg4sSJ3r5dp9HtNbiztgOetP0nKnAVA3D0QP4pr1FYePKgRgghhBCn5vWRFovFwrXXXssTTzxBZGQkcXFxPP744/Tt25d58+Z5+3adxpW2BVQ3hqh+GHoNaHy83F5BvdGBrmkcPVh0ymuUlh7r6GYKIYQQ3VaHFEy8/fbbcbvdLF26FLvdzqRJk1i+fHmzxbldha7ruA570vabh5zdJEV/6vGtzuUZx3DXnzp5XlRUr45rpBBCCNHNdUjQYjQa+fOf/8yf//znjrh8p9OOZaOV5oLRhHnQ1CbHGpLKlZxmagggJkaKKAohhBBtJRvVW8F1yLMA1zRwIoq16dbrhqRyapH9lNeIjY1jypRpHdNAIYQQogeQoOU0dLcTV3oKAOahTRfgltaXUWovx6AYuOPaP6AoSrPqzg2PLVv2qGx3FkIIIdpBgpbTcGfvBGc9SnAUxtimW7Yb1rMMCOnHJQsXs3z5G80yAcfExLJ8+RssXLio09oshBBCdEcdsqalO3GlbgTAPGgaitI0xmtYzzI4IgmAhQsXMX/+ArZt20JNTQXBweFMmjRVRliEEEIIL5Cg5RS02nLUvH0AmAfPaHJM1/XGkZaGoAU8i5BnzJhFREQQ5eW1krxICCGE8BKZHjoF15EtoOsYowdhCItucuxo/TEqHJUYFSOJYQNOcgUhhBBCeIsELSeh6zruI56pIdOQGc2OHynPAGBgaH8sxq6Zf0YIIYToSiRoOQntaCZaeQEYzZgTJzU7fqQiE4BBEYmd3TQhhBCiR5Kg5SRcqZ4iiKaECSiWwGbHMyo9QUtyWEKntksIIYToqSRoaYGuun7MzTK4+dRQub2CUns5CgoJYf2bHRdCCCGE90nQ0gJ39i5w1KIERWCMHd7sePrxqaF+IbHYTLZObp0QQgjRM0nQ0oImuVkMzbsorTILgKRwmRoSQgghOosELT+h1VWi5u4FwDR4eovnNIy0JMl6FiGEEKLTSNDyE/+/vXsNiqp+4wD+PbvAIvc0FAJzkVgd//3lIrBQ2Uw2zTRNMzm9qgYsImSmvCQZNtMYpvgGcHCYiRAtqzEqR4rKmoYpe5F5Se3f6KQVqNxvJrCAwF5//xewCLJAh3YPHvf7mfHN2QfOsw87ex7P73Js9ScB4YBm4VJowyY/lXnQOoj2G50AgNgwvcLZEREReS82LeMIIW4ODbmYgAsAl00NEBBYGHA3QvyClUyPiIjIq7FpGcdxvQmO7hZA4wPfWKPLmMu9DQC41JmIiEhpbFrGsdadAAD4LEmApAt0GXN5dH+WpZyES0REpCg2LaOEwwFb/ejeLHGuJ+Ba7FY09rUA4J0WIiIipbFpGWVvuwgxZAJ0gdAu/q/LmMa+JtiFHaF+wbh73nyFMyQiIvJubFpGWetPAgB8Y42QtD4uYy6P259FkiSlUiMiIiKwaQEACJsZtqvnAAC+96VPGVfP/VmIiIjmDJsWALaG/wHWYUjB4dAsus9ljEM4cNXUCIA74RIREc0FNi0YNzQUlz7lsE/LQBuG7Wb4a/0RFRShZHpEREQENi1wDPWNbds/3dCQc3+WpWFLoJG8vmxERESK8/qrr+3yLyPb9ofHQBMWOWUcnzdEREQ0t7y+abHWj2woN91dFiEErjhXDoXqFciKiIiIbuXVTYvD1AFH1xVA0sBnim37AaDH3AuTpR8aSYMlIdEKZkhEREROXt20WOtGJuBqo/8DTUDolHHOVUPRQZHw0/opkhsRERFN5LVNixDi5qqhaYaGAOCqqQkAEBO6xON5ERERkWte27Q4ui5D9HUBPjr46FdNG3ulb+ROiz7kXiVSIyIiIhe8tmlxDg356JMg+eqmjrNb0dLfBgBYyjstREREc8YrmxbhsMN25RcAIxvKTad5oBV2YUewbxAW+PMhiURERHPFK5sWe9sliOF+SP7B0EatmDb2yugk3JjQJXxIIhER0RzyyqbFWn8aAOATkwxJ4/qJzk43J+FyPgsREdFc8rqmRditsDWcBQD43Jc2fawQY8udY0I4n4WIiGgueV3TYms+D1iGIAXeBW1E3LSxvWYTTJY+aCQN7uWmckRERHPK+5oW59DQ0lRIMzz40DmfJSooEjpuKkdERDSnvKppEdZh2Bp/AwD4zjA0BABX+zg0REREdLvwqqbF1vgbYLdAClkEzd36GeM5CZeIiOj24VVNi7X+FADANzZ1xuXLVocNLf2tALipHBER0e3Aa5oWMTwAe8sFADOvGgKA5v5W2IQdQb6B3FSOiIjoNuD2pqW9vR15eXl48MEHkZKSguzsbNTV1bn7NLJZG84BDjs086OhvStqxvir3FSOiIjotuLWpsVisWD9+vW4fv069u3bh6qqKgQHB+P5559Hd3e3O08lm+3y6Kqh2JnvsgA3m5alnIRLRER0W3Br03L27Fn89ddfKCoqwv3334+4uDgUFRVhcHAQx44dc+epZHEM9sLedgkA4Btr/Ec/c7WPk3CJiIhuJ25tWuLi4lBZWYlFixZNOC6EgMlkcuepZLFdOQMIAc3CpdCEhM8Y3zPci16zaXRTucUKZEhEREQzkYQQwpMnOHDgAEpKSlBTU4Ply5fP6ncIIeBwzD5Nx40ewG6D5B8EyW/ejPEWuwV9lgH4aLQI04XKPp8kARqNBg6HA56trndjnZXBOiuDdVYG66wcjUZy+5zQ6Z8WeIuWlhY8+uijU75+/PhxhIffvJNRW1uL0tJSZGZmzrphAQBJkqDVzv6Na0MWyIqfp/XHPD//WZ/PSaPxmsVZc4p1VgbrrAzWWRmsszrJutNitVrR1NQ05et6vR5arRYA8Mknn2DXrl144oknUFRUxA8IERER/SseGR4qKSnB/v37kZmZiTfffJNLhomIiOhfkzU89E8UFxfjwIEDyM/PR3Z2trt/PREREXkpt95pOX36NNatW4fMzEzk5uZOeC0gIACBgYHuOhURERF5Gbc2Ldu3b8fhw4ddvrZhwwZs3LjRXaciIiIiL+PxJc9ERERE7sAlPURERKQKbFqIiIhIFdi0EBERkSqwaSEiIiJVYNNCREREqsCmhYiIiFSBTcssOBwOlJWVYfXq1YiPj8eLL76IxsbGKeN7enrw2muvISUlBSkpKdi+fTsGBwcVzFid5Na5rq4O69evh9FoRHp6OjZt2oS2tjYFM1YnuXUe7+uvv8ayZcvQ0tLi4SzVT26drVYr9uzZg9WrVyMhIQEZGRm4dOmSghmrk9w6X7t2DXl5eTAajTAajdi8eTM6OjoUzPjOUF5ejszMzGlj3HEtZNMyC+Xl5fj0009RWFiIzz77DJIkIScnBxaLxWX8pk2b0NzcjA8++ABlZWX4+eef8fbbbyuctfrIqXNPTw+ysrIQGBiIQ4cOYf/+/ejp6cFLL70Es9k8B9mrh9zPs1Nrays/xzLIrfOOHTtw5MgR7Nq1C9XV1QgLC0NOTg76+/sVzlxd5NZ5y5YtaG9vx8GDB3Hw4EF0dHTg5ZdfVjhrdXNe22bilmuhIFnMZrNITEwUVVVVY8dMJpNYuXKlOHr06KT4X3/9VRgMBlFfXz927KeffhLLli0THR0diuSsRnLrfPjwYZGUlCSGh4fHjrW3twuDwSBOnDihSM5qJLfOTna7XTz77LNi3bp1wmAwiObmZiXSVS25dW5qahIGg0H8+OOPE+IfeeQRfp6nIbfOJpNJGAwG8cMPP4wd+/7774XBYBDd3d2K5KxmHR0dIjs7WyQkJIjHH39cZGRkTBnrrmsh77TI9Mcff+DGjRtIS0sbOxYSEoIVK1bgzJkzk+LPnj2L8PBwxMbGjh1LTU2FJEk4d+6cIjmrkdw6p6en45133oFOp5v0mslk8miuaia3zk4VFRWwWq2TnjFGrsmt8/HjxxESEoKHH354QvyxY8eQnp6uSM5qJLfOOp0OAQEBqKmpwcDAAAYGBvDll19Cr9cjNDRUydRV6ffff0doaCi++uorxMfHTxvrrmuh25/yfKdzjnVGRkZOOL5w4UK0t7dPiu/s7JwU6+fnh7CwMJfxNEJunaOjoxEdHT3h2L59+6DT6ZCSkuK5RFVObp0B4Pz583j//fdx5MgRdHZ2ejzHO4HcOjc0NGDx4sWora1FZWUlOjs7sWLFCrzxxhsTvvRpIrl11ul02L17N3bu3Ink5GRIkoTw8HAcOnQIGg3/Tz+TNWvWYM2aNf8o1l3XQv5VZBoaGgIwUuzxdDqdy7kTQ0NDk2Kni6cRcut8q48++ghVVVXIy8vDggULPJLjnUBunQcHB7F161Zs3boVer1eiRTvCHLrPDAwgKamJpSXlyMvLw/vvvsufHx88Nxzz+H69euK5KxGcusshMCff/6JxMREfPzxx/jwww8RFRWFV155BQMDA4rk7C3cdS1k0yKTv78/AEya1GU2mzFv3jyX8a4mgJnNZgQEBHgmyTuA3Do7CSGwd+9e7N69G7m5uXjhhRc8mabqya1zYWEh9Ho9nnnmGUXyu1PIrbOvry/6+/tRWlqKhx56CCtXrkRpaSkA4IsvvvB8wiolt87ffPMNqqqqUFxcjFWrViE1NRUVFRVobW1FdXW1Ijl7C3ddC9m0yOS8vdXV1TXheFdXFyIiIibFR0RETIq1WCzo7e3FokWLPJeoysmtMzCyRPT1119HRUUF8vPzkZeX5/E81U5unaurq3Hy5EkkJiYiMTEROTk5AIAnn3wSb731lucTVqnZfG/4+PhMGAry9/fH4sWLubx8GnLrfO7cOcTExCAoKGjsWGhoKGJiYtDQ0ODRXL2Nu66FbFpkWr58OYKCgnD69OmxY319fbh48SKSk5MnxaekpKCjo2PCPgHOn01KSvJ8wiolt84AkJ+fj++++w579uxBdna2Uqmqmtw619bW4ujRo6ipqUFNTQ0KCwsBAJWVldi8ebNieauN3DonJyfDZrPhwoULY8eGh4fR3NyMJUuWKJKzGsmtc2RkJBobGycMTwwNDaGlpYV1djN3XQs5EVcmPz8/ZGRkoKSkBPPnz0dUVBSKi4sRERGBxx57DHa7Hd3d3QgODoa/vz/i4+ORlJSELVu2YMeOHRgcHERBQQHWrl3LOy3TkFvnzz//HN9++y3y8/ORmpqKa9eujf0uZwxNJrfOt36ROyc+3nPPPZw7NA25dU5OTsYDDzyAbdu2YefOnQgLC0NZWRm0Wi2eeuqpuX47ty25dV67di3ee+89vPrqq2NN9969e+Hn54enn356jt+NunnsWvgvlmh7LZvNJoqKikRaWppISEgQOTk5Y/tUNDc3C4PBIKqrq8fi//77b7Fx40aRkJAgjEajKCgomLCfCLkmp85ZWVnCYDC4/Df+b0GTyf08j3fq1Cnu0/IPya1zf3+/KCgoEEajUcTHx4usrCxRV1c3V+mrhtw619fXi9zcXJGamirS0tLEhg0b+HmehW3btk3Yp8VT10JJCCE812sRERERuQfntBAREZEqsGkhIiIiVWDTQkRERKrApoWIiIhUgU0LERERqQKbFiIiIlIFNi1ERESkCmxaiIiISBXYtBAREZEqsGkhIiIiVWDTQkRERKrApoWIiIhU4f/iVDPko5ZH6AAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn; seaborn.set()  # plot formatting\n",
        "\n",
        "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n",
        "\n",
        "plt.scatter(X.ravel(), y, color='black')\n",
        "axis = plt.axis()\n",
        "for degree in [1, 3, 5]:\n",
        "    y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)\n",
        "    plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))\n",
        "plt.xlim(-0.1, 1.0)\n",
        "plt.ylim(-2, 12)\n",
        "plt.legend(loc='best');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "9oUVR1ydqmTV"
      },
      "source": [
        "The knob controlling model complexity in this case is the degree of the polynomial, which can be any non-negative integer.\n",
        "A useful question to answer is this: what degree of polynomial provides a suitable trade-off between bias (under-fitting) and variance (over-fitting)?\n",
        "\n",
        "We can make progress in this by visualizing the validation curve for this particular data and model; this can be done straightforwardly using the ``validation_curve`` convenience routine provided by Scikit-Learn.\n",
        "Given a model, data, parameter name, and a range to explore, this function will automatically compute both the training score and validation score across the range:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "iEt2HhjXqmTV",
        "outputId": "e4c70f10-c80b-4b20-bc0a-e8e6ef1039d9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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1ErkhQZKqubqaglksIjIz8+v8vBqNCqGh/sjKyq94erKbyMoC2rULgMkkYNu2fLRqVXW8DvXLL0Rov+7QnDmNgvFPIH/OWy6I2rk86frVlkajQqhgQtGLs6BfsgiCyQRJpULRw2OQ/9xMSPXq1e7EkgTVubPWxCZhp7XV5uyZMsUsjZvAFN8dps5dIAUGATodJK0O0GqsP3U6e9Ji/amDpLUmMKVvW5+jLdMl5XANTRagqAhCQQGEwgLHnwX5QEEhhIJ8CIWF9mPW2/lAYdnHVCkpUF++VFJltRqmHr2sSc/gOyE2uKF2710NeM3vqILryPrVXliYP9Tqqrvc2aJDAICfftLCZBLQpo2lWknOtTgA2YOFhKDwtTeQ//AYBLz6MvQbf4DvF0uhX/cNCqZMQ+G4/wF6feXnsFigOXoY2l07oE3YBU3CTqhTUxyKSIIAS+s2MHXrbk1u4rtXPS2/LgmCtXvK1xcS6qDlRZKgPnYU+o0/QL/xR2iOHoZu21botm0FZjwLU2xnGAbfBeOQO2FpUYuFL4moTrBFB2zRAYDhw32xbZsGM2ca8NRTxmo9x1a/7MMnENytM4SCAuR+9AkM9490crSu4UnXr7bKq6P2723wf/kFaA8fBABYmjZD3suvwXjnXSXdkYWF0O7bU9JasycRqryrDueWdDqYO8Zak5pu3WGKi4cUEip7/ZxFdf4c9Bt/hP6n76HZs9thKxJz65thGHwnjEPugrldhzrr1vXW31ElYf1qr7otOkx0wEQnJUVAhw7+kCQBiYl5aNq0er8StvoZ7xoG3Q8bYIrvjuzvf1HM2BxPuX7Xo8I6WizQf/0V/F9/xd4yY+zeE+bYLtbE5tAB6wDhUsTAIJi6xsMc3x2mbj1g6hhr3VVeRnJdQyElBfpffoL+p++h3f4XhFJLh1saN7F2bw0ZClNc/HXNAPPq31GFYP1qj4lODXh7ovPpp1rMnOmDzp0t+Pnngmo/T6NRITTxb+C22yCp1cjavE1RiwN6yvW7HlXWMS8Pfh/Nh9/CDyEUFTk8ZIlqUKobqgcsN7dxu2nb7nANhews6Db9Cv3GH6H7fZN1dlkxsV4EDHcMgXHwnTD26lt1F+E13KF+zqb0OrJ+tccxOlRt69ZZVz6+915TFSWvYTAAkyYB4ArIihUQgILnX0LRw2Pgu+hDCIWFMHXtBlO3HhCbNFVM650zSSGhMNz3oHW5hYIC6P78HfqNP0D3689QpafBd+Xn8F35OcTAIBgH3Wpt7RkwiNPWieoIEx0vd+GCgL171VCpJNx1Vzk7c1bCZ+GHwD//QIzkAGSlExs2UsRMOtn5+VlbbwbfCZhM0O7YDv1P30P3809QpyTDZ91a+KxbCzE8HLmffgFTrz5yR0zk8TxwKVSqSxs2WFtzeva0oH796vdiqi5fgs+71hWQC199gysgE9WUVgtT3/7Ie3s+Mg+eQNbGzSh48ilYmjSFKiMDwfcPg8+K5XJHSeTxmOh4uXXrrI1699xTs9acgJdfgFBQAPTuDeN9DzgjNCLvoVLB3KUr8me9hsxtu1F0z3AIZjMCn30K/i8+B5hr9vkkohJMdLzYyZMqHDumhlYrYciQ6o/P0f6xBfofN0BSq4GPPuI4DaK65OuLq4uXIf/5FwEAfksWIfg/90HIzZE5MCLPxETHi333nbU1p39/C0Kru7yJwYCAF6ZZb477H9Chg5OiI/JigoCCqdORs3QlJF9f6P7YgpDBt0B17qzckRF5HCY6XkqSgO++s47Pueee6rfm+C7+yL4CcuHzHIBM5EzGoXcj+4dfYWlwAzT/nETo7f2h/Xub3GEReRQmOl7q4EEVzp1TwddXwm23Va//X3X5Evzfsw5Azps9B+AAZCKnM3foiOzf/oSpUyxUWVkIvu9u+Kz8XO6wiDwGEx0vZWvNufVWc7WX6wh4+QUIhYUwdusBwwgOQCZyFbF+FLLX/1wySPmZyfB/6XkOUiaqBiY6XkgUgQ0bajbbSvv7ZvsA5Lw33+UAZCJXsw1Sfm4mAMDvk4UIGHkfkMNBykSVYaLjhRIS1LhyRYWgIAkDB1Yj0Sk1ALnwscdhadPWyRESUbkEAQXPPIecpSsg+fpCu2UT0L07BykTVYKJjheyzbYaPNhcra11fBd/BM3ZM7BE1kfBtBlOjo6IqmIcOgzZ3/8CscENwPHjCLylHwcpE1WAiY6XMZmAH36wdVtVPduq9ADk/FmvcQVkIjdhjumE3M1bgbg4qLIyOUiZqAJMdLzMtm1qZGSoUK+eiN69LVWWD3hpBgcgE7kpqUEDYOtWGDlImahCTHS8jG2n8qFDzdBUsaWr9vfN0P/0PQcgE7kzX1/kf/Y58os31vX7ZCGCR93PlZSJijHR8SJFRcDGjdWcbcUByESeQxBQ8OzzyPnsC+tKyr9v5krKRMWY6HiRzZs1yMsT0LChiK5dK++28lv0IQcgE3kY4133IPv7X2CJalCykvKO7XKHRSQrJjpexDbb6u67zVBVcuVVly/Bb/47AID82XM4AJnIg5hjOllXUu7YybqS8oi74PPlF3KHRSQbJjpeIi8P2LTJmujce2/ls63sA5C794Rh+P2uCI+I6pAY1cC6kvLd91oHKU+dZB2kbKl6AgKR0jDR8RI//6xBUZGAFi1EtG8vVljOYQDy3HkcgEzkqfz8cHXJcuQXdz37fbIQQRykTF6IiY6XsO1tNWyYqeLcxWEA8v84AJnI0wkCCqbNsA9S1m/ZBP9ZM+WOisilmOh4gcxM4M8/1QCAe++teLaVz7dflwxAns4ByERKYbzrHuQuXQEA0G/8gV1Y5FWY6HiBH3/UwmwW0K6dBS1bVt5tBQBFo8dCCgxyVXhE5ALGfgMhBodAlZUFzd49codD5DJMdLyAbbZVpWvniCJ02/4EABj7DnB+UETkWhoNjP2tn23dll9lDobIdZjoKFxSkoAdO6zdVsOGVTzbSnPkEFRZWRADAmHuFOuq8IjIhYwDbwUA6DZvkjkSIteRPdERRRELFixA7969ERMTg7Fjx+LChQsVlk9LS8PUqVMRHx+P+Ph4PPXUU0hOTnZhxJ7l++81kCQBcXEWNG4sVVhO++cfAABTz16AVuuq8IjIhYwDBgEAtIcPQpWcJHM0RK4he6KzcOFCrF69GnPmzMGaNWsgCALGjRsHo9FYbvkpU6YgKSkJy5cvx/Lly5GcnIwJEya4OGrPYZttVdXaObq//gQAmPr0c3JERCQXKSICpuIWW13xmDwipZM10TEajVi2bBkmTZqEvn37onXr1pg/fz5SUlKwaVPZptXc3FwkJiZi3LhxaNOmDdq0aYPx48fj6NGjyMrKkqEG7u3cOQH79qmhUkkYOrSS8TmFhdAm7ADA8TlESlfSffWbzJEQuYasic6JEyeQn5+Pbt262Y8FBQWhTZs2SExMLFNer9fDz88P69evR15eHvLy8rBhwwY0a9YMwcHcpuBaGzZYW3N69bIgMrKSbqvEBAgGAyxRDWBpGe2q8IhIBsZbrImO9s/fAVPlLb1ESqCR88VtY2saNGjgcDwyMhJJSWX7j/V6PV5//XW8+uqr6NKlCwRBQEREBL788kuoKtu8qRo0mrrP+dRqlcNPV7N1W40YYam0fvrtWwEA5n79odGqq31+uevnbEqvH6D8OrJ+5ejSBWK9elClp8NnbwLMvfo4Kbq6wWvo2dyhfrImOoWFhQAAnU7ncFyv1yMnp+wy5ZIk4eTJk+jUqRMee+wxWCwWzJ8/H08++SS++uorBAQE1CoOlUpAaKh/rZ5bHUFBvk47d0WOHAGOH7eOKx41So/QUH3Fhbf9CQDQD74d+lq8D3LUz5WUXj9A+XVk/a4xeDCwYgUCt/0BDL3DOUHVMV5DzyZn/WRNdHx8fABYx+rYbgOAwWCAr2/ZN+Wnn37CqlWr8Mcff9iTmsWLF6N///749ttvMXr06FrFIYoScnMLavXcyqjVKgQF+SI3txAWS8UL9TnD559rAehwyy1mAAZUNIRJyMxA8L59EABkd+4OKSu/2q8hZ/1cQen1A5RfR9avfNo+AxCwYgUsP/yI3BmznBjh9eM19GzOrF9QkG+1WopkTXRsXVapqalo0qSJ/Xhqaipat25dpvzevXvRvHlzh5ab4OBgNG/eHOfPn7+uWMxm5/2CWSyiU89/LUkC1q61Xtphw0yVvrZu61YIkgRz65thiqgP1CJOV9fP1ZReP0D5dWT9rinfpz/8VSqoTxyHeO48xMZNqn6SzHgNPZuc9ZO1U7B169YICAhAQkKC/Vhubi6OHTuGLl26lCnfoEEDXLhwAQaDwX6ssLAQly9fRtOmTV0SsyfYv1+FCxdU8POTcOutlcy2AqDb+icAwMhp5UReQwoJhTkuHgBnX5HyyZro6HQ6jBo1CvPmzcOWLVtw4sQJTJkyBVFRURg0aBAsFgvS0tJQVFQEABg2bBgA4Omnn8aJEyfs5XU6He69914Za+JebIOQb7vNDP8qhtzo/ipeKJCJDpFXMRTPvtJtYaJDyib7MO/JkydjxIgRePHFFzFy5Eio1WosXboUOp0OSUlJ6NWrFzZu3AjAOhtr1apVkCQJo0ePxpgxY6DVavHVV18hKIibUALWTYk3bLDtbVX51FHVhfNQnz8HSaOBqUcvV4RHRG7Cvp7Otq1A8X8miZRI1jE6AKBWqzFt2jRMmzatzGONGjXCyZMnHY61aNECixcvdlV4HmfXLjWSk1UIDpbQv7+l0rK21ZDNneMgBQS6IDoicheWtu1giWoAdXIStDu2wzTgFrlDInIK2Vt0qG6tW2fNXYcMMUFfyYxyANAWJzocn0PkhQTBvnggu69IyZjoKIjJBPz4o3V8zj33VD4IGaII3bY/AQDGPv2dGxgRuSVuB0HegImOgmzdqkZWloCICBG9elXebaU5ehiqzEyI/gEwx3Z2UYRE5E5MfftB0mqhOXcW6rOn5Q6HyCmY6CjIunXW1py77jJDXcVODto/i2db9exlXT6ZiLyOFBAIU7eeANiqQ8rFREchCguBn3+u3mwroNS08r7stiLyZvZxOkx0SKGY6CjE5s0a5OcLaNxYRFxcFatPFhVBm7ATAMfnEHk7+27mO7YD+dXfAobIUzDRUQjbbKthw0wQhMrLahMTIBQVwVI/CpboVi6IjojcleWmlrA0aQbBaLSuqUOkMEx0FODqVWuLDgAMG1bFbCuUrJ9j6tMPVWZFRKRsggDjLYMAsPuKlImJjgJs3KiBwSCgZUsL2rWretM07dbfAXD9HCKyclhPR5JkjoaobjHRUQDb3lb33GOusoFGyMqE5uABAByITERWxh69Ifn4QP3vZahPHJc7HKI6xUTHw6WnC9i61TqXvDqzrbTbt0GQJJhbtYYY1cDZ4RGRJ/Dzg7FnbwDsviLlYaLj4X78UQOLRUCHDha0aFF1k7OO2z4QUTm4HQQpFRMdD/fdd9VfOwcAtLb1czitnIhKsW0HoU3YCSE3R+ZoiOoOEx0PduWKgF27rN1Wd99d9Wwr1cUL0Jw7C0mthqlHT2eHR0QeRGzWHOaW0RAsFmi3/iF3OER1homOB9uwQQNJEhAfb0ajRtXvtjJ3joMUGOTk6IjI03CTT1IiJjoerPRsq+qwdVtxfA4RladknM4mQKx6qQoiT8BEx0OdPSvgwAE11GoJQ4dWI9ERRfuqp9z2gYjKY4rvDtE/AOrUFGiOHJI7HKI6wUTHQ61fb23N6d3bgoiIqrut1EePQJWRAdE/AObOXZwdHhF5Ir3eumI6AN2mX+WNhaiOMNHxQJJUMtvq3nurN9tKVzy40NSjJ6DVOi02IvJs3M2clIaJjgc6dkyFkyfV0OkkDB5cvfE5Otu0cq6GTESVMA607nul2bcHQkaGzNEQXT8mOh7I1pozcKAZQdWZPFVUBG3CTgAcn0NElRNvaAhzm3YQJAm6PzbLHQ7RdWOi44F++MHa9XTvvdWcbbVnN4TCQlgi68PSqrUzQyMiBWD3FSkJEx0PYzYD589bd+7s3t1Sredoi9fPMfXphyp3/SQir2dPdP7YDFiq93eGyF0x0fEwmZkCJEmAIEgID696thUA6Lb+DoDr5xBR9Zi6dIUYHAJVVhY0+/bIHQ7RdWGi42HS060tMuHhEtTqqssL2VnQHNgPgAORiaiaNBoY+w8AwE0+yfMx0fEwGRkliU51aLdvgyBJMEe3gtjgBmeGRkQKUrIdxCaZIyG6Pkx0PIytRadevWp2W3HbByKqBeMA6zRz7aEDUKUkyxwNUe0x0fEwNU10bLsQmzitnIhqQIqIgKlTLIDiva+IPBQTHQ9Tk64r1cUL0Jw7C0mthqlnL2eHRkQKw93MSQmY6HiYtLTqt+jYNvE0x3aBFFidlQWJiErYpplr//wdMFVvuxkid8NEx8PUpOtKy/E5RHQdzB1jIdarB1XeVWh375I7HKJaYaLjYarddSWK9hYdTisnolpRqWDsfwsAdl+R52Ki42HS062XLCKi8kRHffQIVOnpkPz8YYrt4orQiEiB7Kskcz0d8lBMdDxMSdeVWGk5XfG2D8aevQCdztlhEZFCGfsNgKRSQXPiOFSXLsodDlGNMdHxIEYjkJtbva4r2/o5Jo7PIaLrIIWGwRwXD4DTzMkzMdHxILbxORqNhODgSgoaDNDu2gEAMHL9HCK6TgZ2X5EHY6LjQUrvc6Wq5Mpp9+yGUFgIMSISltY3uyg6IlIq+3o627YCRUUyR0NUM0x0PEjpRKcyttWQjX36AYLg7LCISOEsbdvBEtUAQkEBtDv/ljscohphouNBqruGjn1/K04rJ6K6IAgls682/ypzMEQ1w0THg1Qn0RGys6A5sB8AByITUd3hdhDkqZjoeBDbYOTKEh3t39shiCLMLaMh3tDQVaERkcKZ+vSFpNVCc+4s1GdPyx0OUbUx0fEg1WnR4bRyInIGKTAIpm49ALBVhzwLEx0PYlsVudIWHftAZI7PIaK6xe4r8kRMdDxIVftcqS5dhObsGUhqNUw9e7kyNCLyAvbdzHdsB/LzZY6GqHqY6HiQtLTKt3+wbeJp7tQZUlBlKwoSEdWcpWU0LE2aQTAaodv+l9zhEFULEx0PUtUYHe1fpdbPISKqa4IA4y2DALD7ijwHEx0PUVAAFBRUkuiIon0jTxPXzyEiJ3HYzVyqfE0vInfARMdD2Mbn6PUSAgLKPq4+dhSq9HRIfv4wdY5zcXRE5C2MPXpD8vGB+vIlqE+ekDscoiox0fEQpbutytvVwdaaY+zRE9DpXBgZEXkVPz8Ye/YGwO4r8gxMdDxEVTOuuH4OEbkKt4MgT8JEx0NUOhDZYIB21w4AXD+HiJzPtp6ONmEnhNwcmaMhqhwTHQ+RllbxYoHavYkQCgog1ouA5eY2rg6NiLyM2Kw5zDe1hGCx2BcpJXJXTHQ8RGVdV9qtvwMonlZe3gAeIqI6xlWSyVMw0fEQlXVd2Qci9xvgypCIyIuVTDPfBIjlL2JK5A6Y6HgIW6ITEeH4B0XIyYZm/z4AgKl3X5fHRUTeydStB0T/AKhTU6A5ckjucIgqxETHQ1TUdaX9ezsEUYT5ppYQGzaSIzQi8kZ6vX2WJ7uvyJ0x0fEQFXVdcVo5EcmlZJo5Ex1yX0x0PIAkVZzo2GY8GPtyfA4RuZZxoHXfK83eRAgZGTJHQ1Q+JjoeID8fMBjKdl2pLl+C5sxpSCoVTD17yRUeEXkp8YaGMLdpB0GSoPtzi9zhEJWLiY4HSEuzJjl+fhL8/EqOa7dtBQCYO3WGFBQsR2hE5OXYfUXujomOB6hwfI6926qfq0MiIgJQKtH5YzNgscgcDVFZTHQ8QHp6OasiS5J9/RwTt30gIpmYunSFGBwCVWYmNAf2yR0OURmyJzqiKGLBggXo3bs3YmJiMHbsWFy4cKHC8iaTCe+++y569+6Njh07YtSoUTh+/LgLI3Y929Ty0omO+thRqNLTIPn5wdSlq1yhEZG302hg6t4DAKDdtVPmYIjKkj3RWbhwIVavXo05c+ZgzZo1EAQB48aNg9FoLLf87NmzsXbtWrz22mv49ttvERISgnHjxuHq1asujtx1SrquShYLtK+G3L0noNPJERYREQDAFF+c6CQw0SH3I2uiYzQasWzZMkyaNAl9+/ZF69atMX/+fKSkpGDTpk1lyl+6dAlr167F3Llz0a9fP7Ro0QJvvPEGdDodjhw5IkMNXMOW6JSecaW1r5/DbisikpcpvhsAQLt7J7eDILejkfPFT5w4gfz8fHTr1s1+LCgoCG3atEFiYiKGDBniUH779u0ICgpCnz59HMr//vvv1x2LRlP3OZ9arXL4WVuZmdbnR0YWx2k0QrfzbwCAOGCAU2Kvjrqqn7tSev0A5deR9XOR2FhIvr5QZWZCd/YUxNY319mp3aaOTsL6OZ+siU5ycjIAoEGDBg7HIyMjkZSUVKb8+fPn0bhxY/z2229YsmQJUlJS0KZNGzz//PNo0aJFreNQqQSEhvrX+vlVCQryva7nZ2dbfzZrpkdoqB74ay9QUABERiKoRxygkvcDcr31c3dKrx+g/Dqyfs7mD8THA3/+ieDD+4DuXer8FeSvo3Oxfs4ja6JTWFgIANBdM8ZEr9cjJyenTPm8vDxcvHgRCxcuxPTp0xEUFIRFixbhoYcewsaNGxEeHl6rOERRQm5uQa2eWxm1WoWgIF/k5hbCYql9c25Skg8ANXx8ipCVZYHP9z/BF4ChTz8U5BTWWbw1VVf1c1dKrx+g/Dqyfq7j0yUevn/+CcOWP1Bw33/q7LzuVEdnYP1qLyjIt1otRbImOj4+PgCsY3VstwHAYDDA17ds9qfVanH16lXMnz/f3oIzf/589O3bF9999x0ee+yxWsdiNjvvF8xiEa/r/LYxOmFhFpjNIjR/WsfnGHr3c2rc1XW99XN3Sq8foPw6sn7OZ4jrBl8Aml07nRKLO9TRmVg/55G1z8PWZZWamupwPDU1FVFRUWXKR0VFQaPROHRT+fj4oHHjxrh8+bJzg5WJKF4zvVySoDl8EABgiu8uZ2hERHbmuK6QVCqoL16A6sq/codDZCdrotO6dWsEBAQgISHBfiw3NxfHjh1Dly5l+3i7dOkCs9mMw4cP248VFRXh0qVLaNq0qUtidrWcHMBstrXoSBBysiEUT70Xb2goZ2hERHZSQCDM7WMAcJo5uRdZEx2dTodRo0Zh3rx52LJlC06cOIEpU6YgKioKgwYNgsViQVpaGoqKigBYE50ePXrgueeew549e3D69GlMnz4darUad999t5xVcRpba05QkAS9HlClpQEAxKBgoFR3HxGR3OzTzHftkDkSohKyz2ebPHkyRowYgRdffBEjR46EWq3G0qVLodPpkJSUhF69emHjxo328h9++CG6du2KiRMnYsSIEcjLy8OKFSsQFhYmYy2c59rtH1Rp1m4+MSJCtpiIiMpTsnDgLpkjISoh62BkAFCr1Zg2bRqmTZtW5rFGjRrh5MmTDscCAgIwe/ZszJ4920URysu2c7ltscCSRCdStpiIiMpjGzeoPn4UQk42pOAQeQMighu06FDlSgYiW0erC8WJjsREh4jcjBQZCfONLSBIErSJCVU/gcgFmOi4uZJ9rth1RUTuz9aqww0+yV0w0XFzZROd4sHIbNEhIjdk6sYNPsm9MNFxcw5r6IBjdIjIvZmLZ15p9u8FimfMEsmJiY6bK9Oik5oCgIkOEbknS/MWECMiIRiN0BzYL3c4REx03J0t0SmZdWXruuIYHSJyQ4JQMk4ngevpkPyY6Li5a7d/YNcVEbk7UzfbgGQmOiQ/JjpuzGJxTHSEq7kQDAYATHSIyH3ZByQn7rb+ISOSERMdN5aZKUCSSva5srfmBAQCfn5yhkZEVCFzm3YQ/QOgys2B+vgxucMhL8dEx43ZWnPCwkRoNByfQ0QeQqOBOa4rAE4zJ/kx0XFj18644qrIROQpOCCZ3AUTHTdWZsZVKgciE5FnsI/T2bUTkCSZoyFvxkTHjVW8WCC7rojIvZk6dYak1UKdnATVxQtyh0NerFaJTmZmJt555x3cc8896NWrF06cOIGPPvoImzdvruv4vJpt53Ju/0BEHsfPD+YOHQFwnA7Jq8aJzqVLl3DXXXfh66+/Rv369ZGRkQGLxYJz585h8uTJ+PPPP50Qpncqu1ggu66IyHOUjNNhokPyqXGi89ZbbyE8PBxbtmzBRx99BKm47/Xdd9/FgAEDsHjx4joP0ltxnysi8mTc4JPcQY0TnZ07d2LChAkICgqCIAgOjz3wwAM4depUnQXn7WwtOhER7LoiIs9j6hoPAND8cxJCRobM0ZC3qtUYHbVaXe5xo9FYJvmh2ktPt16e8PDi7R/SORiZiDyHFBYOc6vWAADt7l0yR0PeqsaJTpcuXbBkyRIUFBTYjwmCAFEU8dVXXyE2NrZOA/RmDts/5OdBKH7P2aJDRJ7CFG+bZs71dEgempo+4ZlnnsHIkSNx6623Ij4+HoIgYOnSpThz5gwuXLiAVatWOSNOr2M0AtnZtkRHhFC8ho7k5wcEBMgZGhFRtZniu8F3xTJod3OcDsmjxi060dHR+PbbbxEfH4+EhASo1Wrs2LEDTZo0werVq3HzzTc7I06vk5lpTXLUagkhIaXG59Rjaw4ReQ7bgGTNwQNAfr68wZBXqnGLzvr169GtWze8++67zoiHitkGIoeFSVCpuFggEXkmsVFjWG5oCPWVf6Hdtwem3n3lDom8TI1bdObOnYsjR444IxYq5dp9ruyJTmR92WIiIqoxQYCpG9fTIfnUONEJDw9Hbm6uM2KhUipMdDgQmYg8jKlrcaKzi4kOuV6Nu67uv/9+vPrqq0hISEDLli1Rr169MmWGDRtWF7F5tbKLBdrW0GHXFRF5FvvCgXt2A2YzoKnxVw9RrdX4t+3NN98EAGzYsKHcxwVBYKJTB9iiQ0RKYWl9M8TgEKhysqE5cgjmjlyGhFynxonOli1bnBEHXYP7XBGRYqhUMHWNh37Tr9Am7GSiQy5V40SnYcOG9tuFhYXIy8tDSEgItFptnQbm7bjPFREpiSm+uzXR2bUThY8/KXc45EVq1VG6Z88evPPOOzh8+LB9U88OHTpgypQp6NatW50G6K3S0qzjxG2JjlA8RkeK5BgdIvI89hWSE3YCkgRwuyBykRrPutq3bx8eeeQR5ObmYsKECZg1axaeeOIJZGdn47HHHsP+/fudEafXcei6KiiAKj8PAFt0iMgzmTt2gqTXQ5WeBvXZ03KHQ16kxi0677//Prp06YKlS5c6bO45ceJEPProo/jwww+xbNmyOg3SG9m6riIiRHu3leTjAykgUM6wiIhqR6+HqVNn6HbtgDZhFywtWsodEXmJGrfoHD58GP/973/L7GCuUqkwatQoHDp0qM6C81aFhUBeXskYHYfxOWzuJSIPZZ9mzg0+yYVqnOj4+/vDbDaX+5jJZLKP2aHas7XmaLUSAgMBVSq3fyAiz2eOt47h1HCFZHKhGic6sbGxWLx4MfKv2ZwtLy8PS5YsQZcuXeosOG9Veg0dQeCMKyJSBlNcPCRBgObcWQgpKXKHQ16ixmN0nnnmGdx777245ZZb0K9fP0RERCAtLQ1//vknDAYD3njjDWfE6VU4tZyIlEgKCoalTTtojh6GdvdOGIcOkzsk8gI1btFp2rQp1qxZg/j4ePz1119YtmwZ/vrrL8THx+Prr79G69atnRGnV0lLq2ixQHZdEZFns2/wyXE65CK1WkfnpptuwsyZMxFR/MWbnZ2N5ORk3HTTTXUanLcqu/1D8T5X3LmciDycKb47fJcu4Qaf5DI1btHJzc3FmDFj8PDDD9uPHTp0CMOGDcOECRNQWFhYpwF6o4wMx8UC2XVFREphire26GiOHoZwNVfmaMgb1DjRmTdvHk6dOoWpU6faj3Xr1g0LFy7EkSNHsGDBgjoN0Btd26Ij2NbRYaJDRB5ObHADLE2aQRBFaBJ3yx0OeYEaJzq///47nnvuOdx66632YzqdDgMGDMDUqVPx888/12mA3qgk0REBlOq6YqJDRApgH6ezm91X5Hw1TnTy8/MRFBRU7mPh4eHIysq67qC8ncOsq6IiqIqbdzkYmYiUwNZ9xXE65Ao1TnTatm2Lb7/9ttzH1q1bh1atWl13UN6u9D5X9u0fdDpIQcFyhkVEVCfsKyTv2wMYjTJHQ0pX41lXTzzxBMaNG4d7770XgwYNQnh4ODIzM7FlyxYcPXoUixcvdkacXkOSHMfocPsHIlIay00tIYaHQ5WRAc3B/TDHxcsdEilYjVt0evbsiUWLFkEQBCxYsAAvv/wyPvjgA1gsFixcuBB9+vRxRpxeIz8fKCoqnejYxuew24qIFEIQYOpa3H2VsEvmYEjparWOTufOnfHxxx8jNDQU2dnZ+Oabb5CdnQ0/P7+6js/r2FpzfH0l+PtzajkRKZOpWw/of/4R2oQdKJz4lNzhkILVuEXn0KFDGDBgAL788kvo9XosXLgQH3/8Mb7//ns88sgj2LJlizPi9BplFwtkokNEymMq3uBTu3sXIIoyR0NKVuNEZ/78+bjxxhvxwAMPoKioCN9//z1GjhyJ3bt3Y8SIERyjc53K7HOVat34jmvoEJGSmNvHQPLzgyorC+p/TsodDilYjROdgwcP4oknnkDjxo2xc+dOFBUV4e677wYADB48GKdOnarzIL1Jerr1ktj2uRI4RoeIlEirhalznPVmAqeZk/PUONFRqVTQ6XQAgK1btyIoKAgdOnQAAOTl5cHHx6duI/Qy7LoiIm9Rsp4ON/gk56nxYOR27dph7dq18PHxwc8//4x+/fpBEARkZGTg008/Rbt27ZwRp9couypycaLDDT2JSGHsic5uzrwi56lxi8706dOxc+dOjBw5Emq1Gk888QQA4M4778T58+fx9NNP13WMXqX0YoEAt38gIuUydY6DpFZDfekiVP9eljscUqgat+i0adMGv/32G86cOYOWLVvap5TPnj0bsbGxiOBYkuvi0HVlMECVkw2AY3SISIECAmBu3wHaA/uh3bUDhuH3yx0RKVCNW3QAICAgADExMQ7r5tx2221McuqAbdZVRIQEVbq1NUfSaiGFhMoZFhGRU5jii7eD4IBkcpJaJTrkPOVu/1Avgts/EJEi2fe9YqJDTsJEx41IUkmLTukNPTk+h4iUytTVunCg5vgxCNlZMkdDSsREx43k5gImU+lEh2voEJGySRERMN/UEgBnX5FzMNFxI7Zuq8BACT4+gFDcosNVkYlIyezTzF24waf6+DH4LP8MsFhc9pokDyY6biQtzXFVZHZdEZE3cPXCgepjRxFy560IfG4qtH/96ZLXJPkw0XEjZfa5sic67LoiIuWyJTqaA/uAwkKnvpbqyr8IHjkcqqu51vspyU59PZIfEx03UnZVZC4WSETKJzZrDkv9KAgmE7QH9jntdYScbASPHA510hX7MdtaZaRcTHTcSJl9rop3LmeiQ0SKJgilxuk4aZq5wYCgR/4DzfFjsNSPguGWW60vnZvrnNcjt8FEx41U3HXFRIeIlM3UzYnjdEQRgU89Ad3f2yAGBCJn1VpY2lj3ZRRyc+r+9cityJ7oiKKIBQsWoHfv3oiJicHYsWNx4cKFaj33hx9+QKtWrXD5sjL2SHFo0TGZoMqyrinBRIeIlM5sG6eTuLvOZ0L5vzYLPuvWQtJokLtsJSztO0AMCgIAqHKY6Cid7InOwoULsXr1asyZMwdr1qyBIAgYN24cjEZjpc/7999/8corr7goStcovaGnffsHtRpSWJicYREROZ25TTuIAYFQXc2F+tjROjuvz2eL4ffxBwCAq+9/DFO/AQAAKSgYALuuvIGsiY7RaMSyZcswadIk9O3bF61bt8b8+fORkpKCTZs2Vfg8URQxbdo0tG3b1oXROl/priuH7R9UsuejRETOpVbDHNcVAKDdXTfjdHQ/fo+Amc8BAPJfeBmG+0faH5OKW3TYdaV8Nd69vC6dOHEC+fn56Natm/1YUFAQ2rRpg8TERAwZMqTc5y1evBgmkwkTJ07Erl11s8CURlP3yYRarXL4WZX0dGu5qChAcyUdACBFRjoltrpQ0/p5GqXXD1B+HVk/z2Lp0RP4Ywv0CTthfvwJALWvo3rXTgROeAyCJMEw5lEYn5kGTak9A4VQ60bJqtwcWf/GKu0aXssd6idropOcbF2/oEGDBg7HIyMjkZSUVO5zDh06hGXLlmHt2rVISUmpkzhUKgGhof51cq7yBAX5VllGFIGMDOvtFi38EHja+r8MzQ0NnBpbXahO/TyZ0usHKL+OrJ+HuHUg8Pqr0CXshC7Ez2Ez4xrV8eRJYNQDQFERMHQo9EsWQ6+55uuucRQAQJN31S3+xirmGlZAzvrJmugUFi8MpdPpHI7r9XrklDNArKCgAM8++yyeffZZNGvWrM4SHVGUkJtbUCfnKk2tViEoyBe5uYWwWMRKy2ZkAKLoX/y8fBScvwQ/AIbQcBRk5dd5bHWhJvXzREqvH6D8OrJ+HuamNgjRaiEkJSHnwFGIzZrXuI5CSgoCb7sN6sxMmDvH4eqipcBVAwCDQzkVtAgGIGZlI0fGv7GKu4bXcGb9goJ8q9VSJGui4+PjA8A6Vsd2GwAMBgN8fctmf3PmzEGzZs3w4IMP1nksZrPzfsEsFrHK8ycnWy9WaKgEQRCBZGsSZwmPcGpsdaE69fNkSq8foPw6sn4eQquHuWMstIkJELZvh7lRU/tD1amjkHcVwQ8Mh/riBZib34jslWsg6XyAcp6nCigZo2M2WRxaj+SgmGtYATnrJ2unoK3LKjU11eF4amoqoqKiypT/9ttvsXPnTnTq1AmdOnXCuHHjAAB33nknXn75ZecH7EQlM65sqyJzDR0i8j72hQNrupO5yYSgx0ZDe+gAxHr1kLN6HaR69SosLtpmXVksQL57tppT3ZC1Rad169YICAhAQkICmjRpAgDIzc3FsWPHMGrUqDLlf/vtN4f7Bw8exLRp07BkyRK0aNHCJTE7S9nFAm3bP3CfKyLyHqZu3YGP3q/ZwoGShIBnn4Lu982Q/PyQ8+XXEJvfWPlzfH0haTQQzGaocnMgBgRcX+DktmRNdHQ6HUaNGoV58+YhLCwMDRs2xDvvvIOoqCgMGjQIFosFmZmZCAwMhI+PD5o2berwfNtg5htuuAHh4eFyVKHOpKVdk+iks0WHiLyPKS4eAKA5fQpCejoQVfXfQL935sL3qy8hqVTIXbIc5tguVb+QIEAKDoaQkQEhJwe4oeH1hk5uSvb5bJMnT8aIESPw4osvYuTIkVCr1Vi6dCl0Oh2SkpLQq1cvbNy4Ue4wna70YoEAu66IyDtJoWEw39wGQPX2vfL58gv4z3sTAJD39nwYb72j2q8lctFAryBriw4AqNVqTJs2DdOmTSvzWKNGjXDy5MkKnxsfH1/p457EoevKbIZQPNeciQ4ReRtT1+7QHD8GbcJOGO6+u8Jyus2/ImDa0wCA/KnTUPTfMTV6HdvqyKrc7NqGSh5A9hYdsiq9z5UqIx2CJEFSqSB5eJccEVFN2Tf4TKh4nI7mwD4EPTYagsWCogceQsFzL9b4dezbQHC/K0VjouMmSic6QvEsNCksHFCr5QyLiMjlbDOvNIcOljsjSnX+HIIfug9CQQGM/Qbg6nsf1mp6uBTMritvwETHTZS7zxW7rYjIC4mNGsPSqDEEiwWaPbsdHhMyMhD84L1QpafB1K4DcpetBLTa2r2ObQdz7nelaEx03IRtnyuHRCeSiQ4ReSd7q86uUgOSCwoQPOp+aM6egaVxE+R+tRZSQGCtX4NdV96BiY4bMJmArKySWVcla+gw0SEi71SS6BSP07FYEPS/R6HdmwgxJAQ5X30LsX7ZhWVrgl1X3oGJjhvIzLQmOSqVhNBQdl0REZm69QAAaPYkAiYTfJ9/FvpffoKk1yNnxRpYoltd92tIQSXbQJByyT69nEoGIoeFSVCruYYOEZEluhXEkBCosrOB0aPh89VXkAQBuQs/g7l4Vtb1Eu3Ty5noKBlbdNxA6RlXQOlEh9s/EJGXUqns3Vf46isAQP5rc2EcWvG6OjUlBYcAYIuO0jHRcQNlEx2O0SEiMnUtabkpenIyCsdPqNPz27uuOBhZ0ZjouIGyG3qy64qIyDD0boj16gGPPYbCV+bU+fm5BYR34BgdN+Cwz5XFAiEjHQAgcXo5EXkxsVlz5Jw8h9CwACArHxDFOj2/xHV0vAJbdNyAw6rImZkQRBGSIEAMrydzZEREMqvFisfVZZ9eXlQEGAxOex2SFxMdN+Cwz1WabfuHMEDDBjciImeRAoMgFSdS7L5SLiY6bsC2KrJ1sUCOzyEicgmVyr6yMncwVy4mOm7AoUUnNQUAEx0iIlewd19x5pViMdFxA7ZZVxERYqmp5VxDh4jI2STOvFI8JjoyKyoCrl4tvc+VreuqvpxhERF5BZHbQCgeEx2Z2VpzNBoJwcFcQ4eIyJVsXVcqdl0pFhMdmZVeLFAQSiU6XEOHiMjp2HWlfEx0ZOawWCAAoXiMjsQxOkRETleyg3m2vIGQ0zDRkVlaGrd/ICKSi8iuK8VjoiMzh32uRBGqdG7oSUTkKlJQCAB2XSkZEx2ZOWz/kJUFwWIBAIj12HVFRORsEmddKR4THZnZVkUuvf2DGBoKaLVyhkVE5BXYdaV8THRkVrrriuNziIhci7OulI+JjsxKZl2JTHSIiFyMXVfKx0RHZuXtXM7tH4iIXMO+1xVbdBSLiY7MHLuuOOOKiMiVxOJZV6qruUDxZBBSFiY6MsrPBwoKyu5cLjHRISJyCVvXFQAIV9mqo0RMdGRk67by8ZHg7w8IHKNDRORaOh0kX18A7L5SKiY6Miq7z1Vx1xX3uSIichnRNvOKU8wViYmOjK7d54qzroiIXM/WfaXizCtFYqIjo9IzriBJ3P6BiEgGXEtH2ZjoyKj0qshCdhYEkwkAt38gInIl+1o6OdnyBkJOwURHRqW7ruzjc4JDAL1exqiIiLyLfRsIdl0pEhMdGZV0XYlcLJCISCbcwVzZmOjIiPtcERHJr6Trii06SsRER0blb//ARIeIyJVE+zYQTHSUiImOjEonOkLxGB2JXVdERC5lm3WlYteVIjHRkYkkseuKiMgdcAdzZWOiI5OrVwGjsfSsKyY6RERysO9gzjE6isRERya2bit/fwm+vlwVmYhILvYdzNmio0hMdGTisCoyAFUqp5cTEcmBXVfKxkRHJqVXRYbErisiIrk4dF1JkszRUF1joiMThxlXuTkQjEYATHSIiFzNvnu5xQIUFMgcDdU1JjoyKZlxJZZs/xAYBPj6yhkWEZH38fODpFYD4DgdJWKiIxPHfa44PoeISDaCUNJ9xbV0FIeJjkwcFwu0JjoSu62IiGRhWzSQU8yVh4mOTLj9AxGR+xDtqyNnyxsI1TkmOjJh1xURkftg15VyMdGRiWOLTvFgZLboEBHJgl1XysVERwaiCGRmWhOdiAh2XRERyU3kooGKxURHBtnZgMViTXTCwpjoEBHJjTuYKxcTHRnYVkUODpag06FU1xXH6BARycG+DQS7rhSHiY4MHPa54vYPRESyKxmMnC1vIFTnmOjIwLYqcni4CCE/D0JhIQAmOkREchHZdaVYTHRkkJZWasZVagoAQPLzB/z95QyLiMhrcdaVcjHRkYHDqsipxeNzItmaQ0Qkl5KuKyY6SsNERwYlG3pyfA4RkTuw72DOrivFYaIjA27/QETkXmyzrrh7ufIw0ZEBEx0iIvdi77oqLASMRpmjobrEREcGJbOuJK6hQ0TkBqTAIPttdl8pi+yJjiiKWLBgAXr37o2YmBiMHTsWFy5cqLD8qVOnMH78eMTHx6N79+6YPHkyrly54sKIrx9bdIiI3IxaDTEgEAB3MFca2ROdhQsXYvXq1ZgzZw7WrFkDQRAwbtw4GMtpOszKysKYMWPg7++PL7/8Ep9++imysrLw2GOPwWAwyBB9zZnNQGam9W1nokNE5D64g7kyyZroGI1GLFu2DJMmTULfvn3RunVrzJ8/HykpKdi0aVOZ8ps3b0ZhYSHefPNNtGzZEu3atcM777yDM2fOYN++fTLUoOZsm3kKgsR9roiI3AjX0lEmjZwvfuLECeTn56Nbt272Y0FBQWjTpg0SExMxZMgQh/Ldu3fHxx9/DL1eX+ZcOdf5i6nR1H3Op1arHH4CQHa2bTNPQK9XQZVuHaOjalDfKTE4U3n1UxKl1w9Qfh1ZP8/nyjpKwdZxOpq8XEgu+nus9GvoDvWTNdFJTk4GADRo0MDheGRkJJKSksqUb9SoERo1auRw7JNPPoFer0dcXFyt41CpBISGOm9V4qAgX/vtoiLrz/r1BYTqAOTnAwCCo5sDgZ65MnLp+imR0usHKL+OrJ/nc0kd64UDAAIsBsCJ3wnlUfo1lLN+siY6hcV7POl0Oofjer2+Wi00K1aswKpVqzBjxgyEh4fXOg5RlJCbW1Dr51dErVYhKMgXubmFsFhEAMC5c2oAPggNtSDnn3MIBiD5+iLbJABZ+XUegzOVVz8lUXr9AOXXkfXzfK6so59fAPQACq6kwuCiv8dKv4bOrF9QkG+1WopkTXR8fHwAWMfq2G4DgMFggK9vxdmfJEn44IMPsGjRIjz++ON45JFHrjsWs9l5v2AWi2g/f2qqGoB1Q08xydqiJUZEwmyRAEhOi8GZStdPiZReP0D5dWT9PJ8r6mibdSVlZ7n8/VT6NZSzfrJ2Ctq6rFJTUx2Op6amIioqqtznmEwmTJs2DYsXL8b06dMxdepUp8dZlxynlnMNHSIidyFy1pUiyZrotG7dGgEBAUhISLAfy83NxbFjx9ClS5dynzN9+nT88ssvePfdd/Hoo4+6KtQ6Y0t0wsNLdi7njCsiIvlJQSEAABVnXSmKrF1XOp0Oo0aNwrx58xAWFoaGDRvinXfeQVRUFAYNGgSLxYLMzEwEBgbCx8cH69atw8aNGzF9+nR07doVacUtIgDsZdxd+YsF1pczJCIiQsl+V9zBXFlkn882efJkjBgxAi+++CJGjhwJtVqNpUuXQqfTISkpCb169cLGjRsBAD/++CMA4O2330avXr0c/tnKuLv09PIWC2TXFRGR3Nh1pUyytugAgFqtxrRp0zBt2rQyjzVq1AgnT56031+2bJkrQ3MK2z5XjmN02HVFRCQ324KB7LpSFtlbdLxNuV1XkUx0iIjkxq4rZWKi40IGA5Cba0t0RAjFiY7EFh0iItlxrytlYqLjQrZ9rtRqCcHB4PRyIiI3IgYWJzpXcwFRuWvaeBsmOi7kMLXcUAhV3lUAHKNDROQO7F1XkmRNdkgRmOi4UFpa2fE5kl4PKTBIzrCIiAgAfHwgFS9Twu4r5WCi40K2GVfh4aWnlkcCgiBnWEREVMz2H0+BM68Ug4mOC9m6riIiuP0DEZE7sq2lo+LMK8VgouNC5a+KzPE5RETugjOvlIeJjgtV2HVFRERuoaTrKlveQKjOMNFxofK3f2CiQ0TkLsTgEADgrCsFkX0LCG/i0HWValsskGN0qGqiKMJiMTvhvAKKitQwGg2wWKQ6P7/cWL/ro1ZroFJ51/+HuQ2E8jDRcaGSdXRKVkUWI7lzOVVMkiTk5maisDDPaa+Rnq6CqODF0Vi/6+PrG4CgoDAIXjI71L6WDhMdxWCi40IcjEw1ZUtyAgJCodPpnfJlo1YLimztsGH9akeSJBiNBuTlZQEAgoPD6/w13JF9MDK7rhSDiY6LFBQABQXlTS9nokPlE0WLPckJCHDeopIajQpms3JbPFi/2tPp9ACAvLwsBAaGekU3lsiuK8VR/m+tm7DNuNLpJARoiuxrNHAdHaqIxWIBUPJlQyQH2++fM8aIuSN2XSkPEx0XKd1tpc6wtuZIOh2k4hH+RBXxlrER5J687fevpOuKiY5SMNFxkXLH59SL4PYPRERuRAwKAcAWHSVhouMiXCyQiMj92bquuAWEcjDRcZG0tNKLBXKfK/IuycnJ2Lz51+s6x759e9CrVxckJV2pVvmNG39Ar15drus1yfs4bAEhKXe2njdhouMinFpO3uz112chIWHndZ2jffsYbNjwCyKrufbUwIGDsGHDL9f1muR9bLOuBJMJKCyUORqqC5xe7iKlu66EFNuqyEx0yDtIdfA/Y61Wi/DwetUur9f7QK/3ue7XJS/j7w9JrYZgsUCVmwPRz0/uiOg6MdFxEVuLTkSECNURW4sOu66o5iTJui5TXdFoAHMNZg77+dVsDP3EieNx4MA+HDiwD/v378XatT9gxIih6NOnH3bv3oXMzEzMmfMWWrZshU8++Qg7dmxHRkY6goND0KdPP0yaNAV6vQ/27duDyZP/h2+++R4NGtyAESOGYtiw4Th+/Ch2794FnU6H224bjAkTnoJGo8HGjT/gjTdewa5d+wAAvXp1wfTpM/H775tw6NBBBAUFYfjw+/Hww2Pssf722y/44ovPkJR0BS1a3IRBg+7AggXvYvv2PeXW7dKli5g//x0cPXoIoiihffsOePLJp9GixU0AgMLCQnzyycf444/NKCjIR3R0azz55FNo06YdAODIkUNYsmQhTp48Do1Gg169+uLJJ59GUPE4kfLep06dOmPVqhVYv34dMjPT0aRJU4wc+TBuvfWO6l8UqpggQAoKgpCVZe2+imogd0R0nZjouIhj1xUXC6TakSTgzjv9kJioli2Grl3N+OGHwmonO2+88Q6mT5+CyMj6mDJluv34+vXf4q235iMwMBA33ngTXn75eaSmpuC1195CWFgYjhw5hLlzX0WTJs1w//0jyz33smVL8MQTk/G//03C7t078f778xAd3Rq33z6k3PILF36AKVOmY+rU5/DrrxvxyScfo0OHjoiJ6YS//96G11+fhccfn4hevfpg375ELFgwv9K6zZr1Am66qSU++2wlzGYzPv74fbzwwrNYs2Z98eMzcO7cOcyY8TIaNWqM//u/LzB16iSsXv0drly5jEmTHsfQocMwZcp0ZGVlYv78tzF16kQsWfK5fXG+a9+nJUsW4rfffsbUqc+hWbPmOHx4P+bNexN5eXm49977qndRqFJSYDCQlcUdzBWCiY6LlOxzxTE6dH0EwbMGSAYFBUOj0UCv1yM0NNR+vFu3noiLi7ffj4uLR4cOndCyZTQAoEGDG7Bu3dc4c+ZUheeOj++O++57EADQuHET/PjjBhw6dKDCROeOO4bittsGAwDGjXsC69Z9g0OHDiAmphO++mol+vUbiIceehgA0KRJU1y6dAlr1vxfha9/5cpldO3aDQ0a3ACNRoMZM17GhQvnIYoiLl++hB07tuPddz9EfHx3AMCUKdPh5+eH3NxsrF79f2jRoiWmTn0OANC8+Y2YPfsNjB79IBISdqJ7955l3qfCwkKsWbMKL730Cnr27A0AaNq0Cf799wpWrVrBRKeOiMHBUIMzr5SCiY4LSFLJGB3rzuUpALihJ9WcIAA//FBYx11XNdtCoKZdVxVp1Kixw/177rkP27f/hd9++xmXL1/C2bOnceXKv2jUqEmF52jatLnDfX//AJgr6Ydr2rTZNeX9YTKZAAAnT57A+PETHB6PielUaaIzbtwELFjwLtavX4vY2DjEx3fHgAGDoFKp7Ala27bt7eV1Oh0mTZoKADh79jTi4ro5nK9Fi5sQEBCIM2dO2ROd0u/T+fNnYTQaMGfOLLzxxiv24xaLBUajEQZDEccl1QGHmVfk8ZjouMDVq4DBUNyiE2iAKjsbAMfoUO0IAuDvX3fnq+kYnbqi15dsbSFJEp57bgrOnDmNQYNuR//+A/H440/i7bdfr/QcWq22zLHKBj7rdLoKy6vVakhSzfaMGj78fgwYcAt27vwbe/fuxieffIxlyz7B8uWroNFY/7xWlBRKklTuY5Ik2p8LOL5PomiN9dVX37QnbaU39dRqy9aPak4K5DYQSsLp5S5g67by85MQWFi8/YNGAykktLKnESlGVdsI/PPPSezc+Tdee+0tPPHEJNx66x1o1Kgx/v33Up3M2KqOm25qiaNHDzscO3bsSIXlMzMz8N57b8FkMmHw4KF46aXX8MUXXyEjIwP79++ztzYdP37M/hyz2Yx77x2CzZt/xY033oSDBw84nPPUqX+Qn5+PZs1uLPc1mzZtBrVajeTkJDRq1BiNGjVG48ZNsHPn3/jqq5VesemmK5S06DDRUQJ+Klygwu0f+EeJvISvrx+Skq4gtbjb9lrh4eFQq9X4/fdNuHLlX5w4cQwvvfQ8MjIyYDIZXRLjqFGP4M8/f8fq1V/i8uVL+PnnH7F27eoKywcFBWPHju14663XcerUSfz772V8991aaLVatG59M5o0aYq+ffvjvffewt69ibh48QLeeecNmEwmdO7cFQ888BBOn/4H7733Fs6fP4f9+/fi1VdfRHR0K3Tp0rXc1wwICMCwYcPx6aeL8MsvP+Hffy/jp59+wKJFCxAWFu6st8briMWJjopdV4rArisX4GKB5O2GDRuO11+fhdGjR+LHHzeVebxevQjMnPkKli37BN999w3CwsLRo0cvPPDAQ9i2batLWnW6deuBadNmYMWK5fjkk4/RqtXNuPvu4Vi37utyy2s0GsybtwAff/w+nnpqAoqKitCyZTTefvt9NGzYCADwwguz8PHHH2DWrBkwGAxo06Y95s//GKGhoQgNDcW8eR/g008XY+zY/8DPzx+9e/fDE09MdOi6utakSVMRGhqGpUs/QXp6GiIj62PMmHEYNeoRZ7wtXoldV8oiSK5qF3ZjFouIzMz8Oj+vRqNCaKg/3n/fgClT9Bg0yIy1d36KoKcmwDjgFuSsXlfnr+lKtvplZeXXaDCrp5C7fiaTERkZSQgPb+DUsRc1HYzsaapbv/379yI8PBxNmjSzH1uxYhl+/HEDvv56gxMjvD7Ovn6u+j2siByfQ99PPkbASzNQdO8IXF28zKmvJfffGWdzZv3CwvyhVlfdM8K+ExdwmHHFFh0it7R79y5MmTIR+/btQXJyMrZv34qvv/7KPh2dvIcYHAKALTpKwa4rF0hLsyU6IhMdIjc1Zsw4FBYW4rXXXkZ2dhYiI+vjgQcewkMP/Vfu0MjFbF1XKiY6isBExwUcFgs8xESHyB3pdDo8/fSzePrpZ+UOhWRmn3V1lYORlYBdVy5Q/vYPXEOHiMgd2RMdtugoAhMdF0hPt/7kGB0iIvcn2rquuI6OIjDRcQFOLyci8hz2Fp2CAqB4ixDyXEx0nEwUS826CjFByMy0HmeiQ0TklmyDkQHud6UETHScLDsbMJutiU4E0iBIEiSVClJYmLyBERFR+TQaiP4BAAAhJ1veWOi6MdFxslRrTxUCAyX45hTvWl4vAlCrZYyKiIgqY+u+UnHmlcdjouNkxZOsUK+eBKF4fI7EbiuiGhkxYiiWLv0EALBx4w/o1atLpeV79eqCjRt/qPb5k5OTsXnzr+W+HnknzrxSDq6j42S2Fp169SSoUm0DkTm1nKi2Bg4chPj47nV6ztdfn4WoqAa45ZbbAACffroCer2+Tl+DPAv3u1IOJjpOZkt0wsPFUmvosEWHqLb0eh/o9T51es5rt/wLDQ2t0/OT5xHZdaUYTHSczNZ1FRHBqeVURyQJKCiou/NpVEBNNtvz8wMEodrFX399Ns6fP4dPP/3Cfiw1NQUjRgzFe+99hC5duuKnn77H2rWrceHCBahUAlq3boNJk6aiVavWZc63ceMPeOONV7B9+x77ud577y3s3bsHgYGBmDBhskN5SZKwatUK/PTT97hy5V/odDrExHTC009Pww03NMTEieNx4MA+HDiwD/v378XatT9gxIihuOOOO/Hoo48DAHbs2I7PP/8M586dgZ+fP2655TaMHz/B3urTq1cXTJ8+E7//vgmHDh1EUFAQhg+/Hw8/PKbC92XVqpVYv34t0tJSUa9eBIYMuQujRz8Kofi9TUzchaVLl+DUqZMICgrGbbcNxrhxT0CtVsNgKMKKFcvx22+/ICMjDU2bNsOYMePRp08/+3u0bNkS9O7dDz///AM6dOiEt9+ej/Pnz+Gjj+bj4MH98PPzQ2xsHCZOfBrh4fWqfT29hRTEriulYKLjZA5dVxeZ6NB1kiSE3HkrtIkJsoVg6toN2T/8Wu1k54477sTkyf/D5cuX0KhRYwDAb7/9jHr1IhAb2wVbt/6BefPmYvr0mejUqTMyMjLw/vvv4M03X8Xy5asqPbfZbMYzz0xCQEAAPvpoCUwmI959902HMqtX/x9WrFiOF198BTfd1BJXrvyLt99+HR9+OB9z587DG2+8g+nTpyAysj6mTJle5jX++utPvPjidIwdOx4vvjgbly5dwrvvvonk5Ct4/fV37OUWLvwAU6ZMx9Spz+HXXzfik08+RocOHRET06nMObdv/wsrVizDa6/NRePGzXD06CHMmTMLDRrcgNtuG4yjR4/gmWcm4777RmLGjJeRkpKMV199ESqVCuPHT8Ds2TNx8uQJTJ36HG68sTl+/fUXzJw5DXPnzkOvXn0BAMnJSUhLS8XSpV/CYDAgPT0NTz75GAYOvBUTJ05BUVERli37BP/736NYsWI1fH19q3U9vYUUZOu6ypY3ELpuTHScrKTrSoJqL7d/oDpQg9YUd9CpU2fccEND/Pbbzxg7djwAa6Jz++1DoFKpEBwcjOeeexG33z4EABAV1QBDhw7DvHlzqzz33r2JOHfuLNasWY+GDRsBAF54YRbGjPmPvUyjRo3x4ouz0atXH/v5+/e/BVu2/AYACAoKhkajgV6vL7fLauXK5ejTpx8eeeQxAECTJs0gSRKef34qzp8/h2bNmgMA7rhjqH2n83HjnsC6dd/g0KED5SY6V65chl6vQ4MGDREVFYWoqCjUqxeJ+vWjAADffPMVbr65LSZNmgIAaNq0GaZNm4n09DScP38O27ZtxVtvzUfPnr2h0agwZsw4nD79D774Ypk90QGARx55zP6+fPrpIoSH18PUqc/ZH3/11TcxZMhA/PHHZgwePLTK99ub2HcwZ9eVx2Oi42SlZ12x64qumyBYW1PqsOtKo1HB7MSuK0EQcPvtQ/Dbb79g7NjxOHXqJM6ePYM5c94GAHTsGIvz58/h888/w+XLl3Dx4gWcPv0PRLHqmM6cOY3AwCD7lzkAtGzZCj4+JWN4evfui4MHD2Hp0k9w6dJFXLhwDmfPnkFENT+HZ8+exqBBtzkc69gxtvj1T9kTnaZNmzmU8ff3h6mCVXVvvXUwfvrpezz44D1o0aIl4uLi0bdvf0RFRdnPGxcX7/Ccvn37AwC2bNkEAOjQoaPD4zExsVi8+COHY40bN7bf/uefE7hw4TwGDertUMZoNOL8+XPlxunNuIO5cjDRcTKHrismOlQXBAHw96+789V0jE4tDB48FMuXf4rjx49iy5ZNaN++A5o0aQoA2Lz5V7z22ssYNOh23HxzW9x55904e/YM3nvvrWqd+9qBxACg0ZT8aVu58nN8+uknGDx4KDp16owRIx7E9u1bHaaTV35+AHBM7ETRUuZ1dDpdtWIDgJCQECxfvgpHjhxCYmICEhJ2YvXqL/Hoo49jzJhx0Gg09rE65URU7lFRtDjEA8Bh0LYoSoiN7YJnnnm+zHMDAgIreC3vZZ9ezv2uPB7X0XEye9dViBlCZgYAJjrkfaKiGqBTp87444/N+P33Tbj99jvtj61cuRxDhw7Diy++guHD70fHjrH499/LACpOFGyio1shL+8qzp49Yz928eIF5OXl2e8vX74UY8eOw7PPPo+7774X7dq1x6VLFxzOXXFSAbRo0QKHDu13OHbwoPV+06bNq1H7sn79dSO++24tOnToiEcffRxLlnyOoUOH2bvTmjW7EcePH3N4ztdfr8LYsf/BjTfeBAA4dOjANTEdsLculefGG1vgwoXziIysj0aNGqNRo8YICgrCggXv4uzZ07Wqh5KVJDrsuvJ0THScyGIBMqy5Deqr0yGIIiRBgBQeLm9gRDIYPHgo1q9fh+zsbAwceKv9eGRkfRw+fBAnT57Av/9expo1/4d1674GYO1WqUxsbBe0adMOc+a8jCNHDuPEiWN4/fXZUKlK/rTVr18fiYkJOHfuLC5ePI8lSxZi69Y/HLqVfH39kJR0BampKWVeY+TI/2Lr1j/w+eef4eLFC/j7722YP/8d9OjRu9LEojIGgwEff/wBfvnlJyQlXcHBg/uxf/9etGvXAQDw0EMP4+jRw/j000W4ePECdu78GytWLEfv3v3QvPmN6N69J9599038/fc2XLx4AcuXf4rt27di5MhRFb7mPfeMQF5eHmbPnolTp07i9OlTmD17Jo4dO4rmzW+sVT2UTGTXlWIw0XGizExbszdQz2L9AyqFhwMa9hiS9+nXbyAA65iZgIAA+/EpU6YjNDQMEyeOx/jxo7Fjx3a8+OIrAIBjx45Uek6VSoV33nkfTZo0w9SpEzFt2tMYOPBWhISUDCqeNes1FBUV4bHHHsaTT47H2bOn8eyzM5CVlYmkpCsAgGHDhuPcuTMYPXokLBaLw2sMGHALXn75Nfzxx2aMHv0g5s2bi1tuuRWvvVb1YOmK3HXXPXj00fH4/PPP8J//jMDLLz+P+PjuePrpaQCs44zmzn0XO3f+bX/NESMewOjRjwIAXnllLnr37ou33pqDUaMewPbtf2HOnLfRv/8tFb7mDTc0xEcffYKiokJMmPAYJk4cB0FQYcGCRQgN5d5717K36HAwsscTpKrahr2AxSIiMzO/zs/7zz9q9Orlh9BQCWc/+R4h9w+D+eY2yNq6q85fSw4ajQqhof7Iysqv2WBWDyF3/UwmIzIykhAe3gBabdnxH3WlxoORPQzrd31c9XtYEbk+h+rTpxDWozPE4BBknLrotNeR+++MszmzfmFh/lCrq26vYYuOE2VkWPv9HQYi1+P4HCIid2fruhJyc4BqzAAk98VEx4nS0qyJTkREqX2uIpnoEBG5O3vXlSRByM+rojS5MyY6TpSebk10wsM5tZyIyKP4+EAq3uKD20B4NiY6TmRLdLjPFRGR5+EO5srARMeJbImO42KB3P6BiMgTcAdzZWCi40SOiU7xPlcco0M1xImRJCdv/v2zj9Nhi45HY6LjRKUTHaG4RUdi1xVVk1qtBgAYjQaZIyFvZvv9U6u9b/2vkq6rbHkDoevifb+5LmQfoxNugSojHQDH6FD1qVRq+PoGIC8vCwCg0+kr3aqgtkRRgMWi3P+1s361I0kSjEYD8vKy4Osb4LDatLfgDubKwETHiWzTy+tr0iEUr7YqhteTMyTyMEFB1hVrbcmOM6hUqmrtFO6pWL/r4+sbYP899Da2rituA+HZmOg4idEI5OQUJzqwbv8ghoUBWq2cYZGHEQQBwcHhCAwMhcVirvPzq9UCgoP9kJNToMhWD9bves+v8cqWHBvOulIGJjpOkplpTXJUKiDYwKnldH1UKhVUqrpffl+jUcHHxweFhRbFLj/P+lFtcb8rZZA9VRdFEQsWLEDv3r0RExODsWPH4sKFCxWWz8rKwjPPPIO4uDjExcXhpZdeQkFBgQsjrh5bt1W9eoA6vXjGFRMdIiKPIQax60oJZE90Fi5ciNWrV2POnDlYs2YNBEHAuHHjYDQayy0/efJkXLp0CZ9//jkWLFiAv//+G6+88oqLo66abZ+ryEiUbP/ANXSIiDyGFMSuKyWQNdExGo1YtmwZJk2ahL59+6J169aYP38+UlJSsGnTpjLl9+/fj927d2Pu3Llo27YtunfvjldffRUbNmxASkqKDDWomG3GVWQkuCoyEZEHKum6YqLjyWQdo3PixAnk5+ejW7du9mNBQUFo06YNEhMTMWTIEIfye/bsQUREBFq0aGE/1rVrVwiCgL1792Lw4MG1ikOlEhAW5l+7SlTgwQcF3HYb4O8P6IXngMlPwickFPrgun0dOdlmOgcH+0KJa4opvX6A8uvI+nk+Oeso3HMncOYMNBptnX9H2F9D4dfQmfVTqaq33IasiU5ycjIAoEGDBg7HIyMjkZSUVKZ8SkpKmbI6nQ4hISHllq8uQRCgVtft+iShodZ/VpFAZKT8/YROovRZGUqvH6D8OrJ+nk+WOvr5ATfeCAGA2skvpfRrKGf9ZH1nCwsLAViTldL0ej0MhrKrwRYWFpYpW1l5IiIi8m6yJjo+Pj4AUGbgscFggK+vb7nlyxukbDAY4Ofn55wgiYiIyGPJmujYuqFSi2cl2aSmpiIqKqpM+aioqDJljUYjsrOzUb9+fecFSkRERB5J1kSndevWCAgIQEJCgv1Ybm4ujh07hi5dupQpHxcXh+TkZId1dmzPjY2NdX7ARERE5FFkHYys0+kwatQozJs3D2FhYWjYsCHeeecdREVFYdCgQbBYLMjMzERgYCB8fHwQExOD2NhYTJkyBbNnz0ZBQQFmzZqFYcOGsUWHiIiIyhAkSd4JbRaLBe+99x7WrVuHoqIixMXF4eWXX0ajRo1w+fJlDBw4EHPnzsW9994LAMjIyMArr7yCbdu2Qa/X4/bbb8eMGTOg1+vlrAYRERG5IdkTHSIiIiJnUfbEfSIiIvJqTHSIiIhIsZjoEBERkWIx0SEiIiLFYqJDREREisVEh4iIiBSLic51EEURCxYsQO/evRETE4OxY8c6rNp8raysLDzzzDOIi4tDXFwcXnrpJRQUFLgw4prJzs7Gyy+/jD59+iA2NhYjR47Enj17Kiz/3XffoVWrVmX+VfaeyOnff/8tN95vvvmm3PKedv0SEhLKrV+rVq0wcODAcp/jSddw4cKFePjhhx2OHT9+HKNGjULHjh3Rr18/LF26tMrz/Pzzzxg8eDDat2+PoUOH4q+//nJWyDVSXv1+//13DB8+HJ06dcKAAQPw1ltvoaioqNLzDBgwoMz1fPbZZ50ZerWVV8cZM2aUibdPnz6VnsdTruHDDz9c4Wdy/fr1FZ7Hna5hVd8LbvkZlKjWPvzwQ6l79+7Sn3/+KR0/flwaO3asNGjQIMlgMJRbftSoUdJ9990nHTlyRNqxY4fUv39/afr06S6OuvrGjBkj3XXXXVJiYqJ05swZ6bXXXpM6dOggnT59utzyc+fOlUaNGiWlpqY6/DObzS6OvHq2bNkitW/fXkpJSXGIt7CwsNzynnb9DAZDmWuxfft2qU2bNtLXX39d7nM85RouX75catWqlTRq1Cj7sczMTCk+Pl6aOXOmdPr0aWnt2rVS+/btpbVr11Z4np07d0pt27aVVq5cKZ0+fVp68803pXbt2lX4O+4q5dUvMTFRuvnmm6VPPvlEOn/+vLR161apb9++0vPPP1/hea5evSq1atVK+uOPPxyuZ25uriuqUany6ihJknTPPfdI7733nkO8GRkZFZ7Hk65hVlZWmc/W+PHjpdtvv126evVquedxt2tY2feCu34GmejUksFgkDp16iStWrXKfiwnJ0fq0KGD9OOPP5Ypv2/fPik6Otrh4m3btk1q1aqVlJyc7JKYa+L8+fNSdHS0tHfvXvsxURSlQYMGSe+//365zxkzZow0Z84cV4V43RYtWiTddddd1SrradevPEajURoyZIj09NNPV1jG3a9hcnKy9Oijj0odO3aUbr/9docvkcWLF0u9e/eWTCaT/di7774r3XbbbRWeb+zYsWXejwceeEB66aWX6j74aqisfs8884w0ZswYh/Lr16+X2rRpU+F/rvbu3StFR0dLOTk5To27Jiqro9lsltq3by9t2rSp2ufzpGt4rR9++EFq06aNdOLEiQrLuNM1rOp7wV0/g+y6qqUTJ04gPz8f3bp1sx8LCgpCmzZtkJiYWKb8nj17EBERgRYtWtiPde3aFYIgYO/evS6JuSZCQ0OxZMkStGvXzn5MEARIkoScnJxyn3Py5EncdNNNrgrxutUkXk+7fuX5v//7PyQlJWHGjBkVlnH3a3j06FEEBwfj+++/R0xMjMNje/bsQVxcHDSaki38unXrhnPnziEjI6PMuURRxL59+xw+wwAQHx9faRetM1VWv7Fjx2L69OllnmM2m5GXl1fu+U6ePImIiAgEBQU5Jd7aqKyO58+fh8FgcPicVcbTrmFpBQUFePvttzF69Gi0atWqwnLudA2r+l5w18+grJt6erLk5GQAQIMGDRyOR0ZGIikpqUz5lJSUMmV1Oh1CQkLKLS+3oKAg9O3b1+HYzz//jIsXL6JXr15lymdmZiI9PR2JiYlYuXIlsrOzERMTg2effRbNmzd3Vdg18s8//yAiIgIPPfQQzp8/j6ZNm2LChAno3bt3mbKedv2uZTAYsHjxYowePRqRkZHllvGEazhgwAAMGDCg3MeSk5MRHR3tcMxW1ytXriA8PNzhsdzcXBQUFCAqKqrMc+S6ppXVr02bNg73jUYjli9fjrZt2yIsLKzc5/zzzz/w8/PDpEmTsH//foSFheHee+/Ff//7X6hU8vw/t7I6/vPPPxAEAV988QX++usvqFQq9O3bF08//TQCAwPLlPe0a1ja6tWrkZ+fjyeeeKLScu50Dav6Xpg/f75bfgbZolNLhYWFAKxfdqXp9XoYDIZyy19btrLy7mbv3r144YUXMHDgwHI/xP/88w8AQK1W46233sL8+fNRUFCAhx56COnp6a4Ot0pGoxHnz59HXl4enn76aSxZsgTt27fHuHHjsHPnzjLlPf36bdiwAQaDoczAz9I87Rpeq6ioqNzPI4Byr5FtEG91P8PuxGw2Y/r06Th9+jRmzZpVYblTp07h6tWrGDx4MJYuXYoHHngAH3zwAT788EMXRlt9p06dgkqlQsOGDbF48WI899xz2Lp1KyZMmABRFMuU99RraLFYsHLlSjz00EPlJnClufM1vPZ7wV0/g2zRqSUfHx8A1i9M223AejF9fX3LLW80GsscNxgM8PPzc16gdWDz5s149tlnERMTg/fee6/cMt26dcPu3bsRHBxsP/bxxx+jf//+WLduHcaPH++qcKtFp9MhMTERGo3G/iFr164dzpw5g6VLl6J79+4O5T35+gHA+vXrceuttyI0NLTCMp52Da9V3jWy/bEs7xrZ/gCX95zyPsPuwpacJyQkYMGCBZV2jyxfvhwGgwEBAQEAgFatWiE/Px+LFi3CpEmTZGvVqcikSZPwyCOP2LtpoqOjERERgQceeACHDx8uU1dPvYa7d+/GlStXcP/991dZ1l2vYXnfC+76GXSv33IPYuvGSE1NdTiemppaphkOAKKiosqUNRqNyM7ORv369Z0X6HX68ssvMWnSJPTp0weffvqpQ1J3rdJfkID1F7tRo0ZISUlxdpi14ufnV+Z/EtHR0eXG66nXD7B2Se3fvx+DBw+usqynXcPSyrtGtvvlXaOQkBD4+flV+zPsDlJTU/Gf//wH+/fvx6efflplF4lWq7V/QdpER0ejoKCgwrF2chIEocxYFFtXiG24QGmeeA0Ba5LQoUMHNG7cuMqy7ngNK/pecNfPIBOdWmrdujUCAgKQkJBgP5abm4tjx46hS5cuZcrHxcUhOTnZYT0S23NjY2OdH3AtrFq1Cq+99hr+85//4P333y+366Z02fj4eIc1PfLy8nD+/Hm3HNx64sQJdOrUqcyAtyNHjpQbrydeP5t9+/ZBEAR07dq10nKedg2vFRcXh71798JisdiP7dy5E82bNy8zNgCwfqnGxsZi9+7dDscTEhLQuXNnp8dbUzk5ORg9ejQyMzOxatWqMgM4ryWKIgYMGIBFixY5HD98+DDq1atXaeueXJ555hk8+uijDscOHz4MAOX+DnraNbTZu3dvldcPcM9rWNn3grt+Bpno1JJOp8OoUaMwb948bNmyBSdOnMCUKVMQFRWFQYMGwWKxIC0tzf6lERMTg9jYWEyZMgWHDh3Crl27MGvWLAwbNswtWwTOnTuHN954A4MGDcLjjz+OjIwMpKWlIS0tDVevXi1Tv/79+0OSJEyfPh2nTp3C4cOHMWnSJISFheGee+6RuTZlRUdHo2XLlnjllVewZ88enDlzBnPnzsWBAwfwv//9z+OvX2knTpxA48aNyzQFe/o1vNbw4cORl5eHmTNn4vTp01i3bh2++OILPP744/YyV69eRWZmpv3+mDFj8NNPP2H58uU4c+YM3n77bRw/fhyjR4+WowqVmjt3Li5duoR33nkHYWFh9s9jWlqa/YuldP1UKhVuu+02fPbZZ/YBo2vWrMFnn32Gp556Ss6qVOjOO+/E33//jUWLFuHixYvYunUrXnjhBdx55532mViefA0B6+fu9OnTZQbt2rjzNazqe8FtP4N1NlHdC5nNZuntt9+WunXrJnXs2FEaN26cdOnSJUmSJOnSpUtSdHS09O2339rLp6enS5MmTZI6duwoxcfHS7NmzZKKiorkCr9SixYtkqKjo8v999xzz5Vbv2PHjkljx46VOnfuLMXGxkqTJk2Srly5ImMtKpeRkSHNmDFD6tmzp9S+fXvpgQcekBITEyVJ8vzrV9qsWbOk+++/v8xxT7+Gzz33XJk1Sg4ePCjdf//9Urt27aT+/ftLK1euLPOc/v37Oxz77rvvpEGDBknt27eX7rnnHmnHjh1Oj706StfPYrFI7du3r/Azafu7c239TCaTtHDhQmngwIFS27Ztpdtuu01as2aNLPUpT3nX8JdffpGGDRsmdejQQerZs6f05ptvOnzOPPUa2qSnp0vR0dHSX3/9VeFz3PUaVvW9IEnu+RkUJEmS6i5tIiIiInIf7LoiIiIixWKiQ0RERIrFRIeIiIgUi4kOERERKRYTHSIiIlIsJjpERESkWEx0iIiISLGY6BAREZFiMdEhIrezbt06tGrVCpcvX5Y7FCLycEx0iIiISLGY6BAREZFiMdEhIlmJooiFCxeiX79+iImJwYQJE5CTk+NQ5p9//sHjjz+O2NhYxMbG4sknn8SlS5ccypw5cwbjxo1DbGwsevTogfnz52PGjBl4+OGH7WVatWqFjz76CMOHD0fnzp2xcOFCAMCVK1cwdepUdO3aFTExMRg9ejSOHTvmcH6DwYC3334bffv2Rbt27TB06FBs3LjRSe8KEdUVbupJRLJ66623sGLFCvzvf/9Dx44d8csvv2DDhg0wmUzYsmULTCYThg8fjhtvvBHjx4+HxWLBokWLkJmZiQ0bNiA8PByZmZkYMmQIwsPDMWnSJFgsFnzwwQe4cuUKOnbsiJUrVwKwJjoajQZPPfUUWrVqhaioKERERGDYsGHw9fXFxIkT4evriy+++AJHjhzB2rVr0aJFC0iShHHjxmHfvn2YPHkyWrRogU2bNmHNmjV46623MGzYMHnfRCKqWJ3uhU5EVAM5OTlS27ZtpTfffNPh+KOPPipFR0dLly5dkqZOnSp1795dunr1qv3xrKwsqXPnzvbnvf/++1L79u2l5ORke5nLly9Lbdu2lUaNGmU/Fh0dLT344IMOr/Xee+9J7du3ly5fvmw/ZjAYpIEDB0qTJk2SJEmStm/fLkVHR0s//fSTw3OfffZZqWfPnpLJZLrOd4KInIVdV0QkmwMHDsBkMmHgwIEOx++44w777V27diE+Ph4+Pj4wm80wm80ICAhAly5dsGPHDnuZTp06oX79+vbnNWzYEJ06dSrzmtHR0Q73d+7ciZtvvhn169e3n1+lUqFPnz728+/cuROCIKBv3772MmazGQMGDEBaWhpOnTpVZ+8JEdUtjdwBEJH3so3FCQsLczgeERFhv52dnY2NGzeWOx7G9rzMzEy0bdu2zOMRERFIS0tzOFavXj2H+9nZ2bhw4UK5zweAwsJCZGdnQ5IkxMbGllsmNTUVN998c7mPEZG8mOgQkWxCQ0MBABkZGbjxxhvtx7Ozs+23AwMD0aNHD4wZM6bM8zUa65+wqKgoZGRklHm8vGPXCgwMRNeuXTF9+vRyH9fpdAgMDISfnx9WrFhRbpmmTZtW+TpEJA92XRGRbDp16gQfHx/88ssvDsf/+OMP++2uXbvi9OnTuPnmm9G+fXu0b98e7dq1w+eff45NmzYBAOLi4rB//36H1pu0tDQcOHCgyhi6du2Kc+fOoXnz5vbzt2/fHt9//z2++eYbqNVqdO3aFQUFBZAkyaHMqVOn8PHHH8NsNtfNG0JEdY6JDhHJxt/fHxMmTMCqVaswb948bN++Ha+//rpDojNhwgRcvHgRjz/+ODZv3oxt27Zh0qRJ+Omnn9C6dWsAwH//+1/4+/vj0Ucfxa+//opff/0Vjz76KIxGIwRBqDSGRx55BKIo4pFHHsHGjRuxc+dOvPTSS1ixYoW9lalv376Ii4uzx5qQkIBPP/0Us2fPhkqlKtP1RkTug9PLiUh2K1euxBdffIGUlBR06tQJd9xxB2bPno0tW7agUaNGOHr0KObPn499+/ZBkiRER0dj/PjxDoOYT506hddffx379++Hv78/HnroIWzfvh0hISFYvHgxAOv08okTJ2LSpEkOr3/x4kW8++672LlzJwwGA5o1a4aHH34YI0aMsJcpKCjABx98gF9++QUZGRmoX78+hgwZgieffBJ6vd41bxQR1RgTHSLyeAcPHkR2djb69u1rP2Y2m9GvXz8MGTIEM2bMkDE6IpITByMTkce7cuUKpkyZgieffBJdu3ZFYWEhVq9ejatXr+L++++XOzwikhFbdIhIEb766iusWrUKly5dglarRUxMDJ566im0b99e7tCISEZMdIiIiEixOOuKiIiIFIuJDhERESkWEx0iIiJSLCY6REREpFhMdIiIiEixmOgQERGRYjHRISIiIsViokNERESK9f8LASCGVawO9gAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from sklearn.model_selection import validation_curve\n",
        "degree = np.arange(0, 21)\n",
        "train_score, val_score = validation_curve(PolynomialRegression(), X, y,\n",
        "                                          param_name='polynomialfeatures__degree', param_range=degree, cv=7)\n",
        "\n",
        "plt.plot(degree, np.median(train_score, 1), color='blue', label='training score')\n",
        "plt.plot(degree, np.median(val_score, 1), color='red', label='validation score')\n",
        "plt.legend(loc='best')\n",
        "plt.ylim(0, 1)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('score');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "y7YxJixnqmTV"
      },
      "source": [
        "This shows precisely the qualitative behavior we expect: the training score is everywhere higher than the validation score; the training score is monotonically improving with increased model complexity; and the validation score reaches a maximum before dropping off as the model becomes over-fit.\n",
        "\n",
        "From the validation curve, we can read-off that the optimal trade-off between bias and variance is found for a third-order polynomial; we can compute and display this fit over the original data as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "DVy5CvsqqmTW",
        "outputId": "22a6701a-2479-4a81-cb72-d0a40dc7c223"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(X.ravel(), y)\n",
        "lim = plt.axis()\n",
        "y_test = PolynomialRegression(3).fit(X, y).predict(X_test)\n",
        "plt.plot(X_test.ravel(), y_test);\n",
        "plt.axis(lim);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "BdUd4sbeqmTW"
      },
      "source": [
        "Notice that finding this optimal model did not actually require us to compute the training score, but examining the relationship between the training score and validation score can give us useful insight into the performance of the model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "KVG34wBKqmTW"
      },
      "source": [
        "## Learning Curves\n",
        "\n",
        "One important aspect of model complexity is that the optimal model will generally depend on the size of your training data.\n",
        "For example, let's generate a new dataset with a factor of five more points:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "sSeJH5h6qmTW",
        "outputId": "4ddbb69f-94a3-4c50-b97b-edf81495c343"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "X2, y2 = make_data(200)\n",
        "plt.scatter(X2.ravel(), y2);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Gq7NXbAVqmTW"
      },
      "source": [
        "We will duplicate the preceding code to plot the validation curve for this larger dataset; for reference let's over-plot the previous results as well:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "3VtA00omqmTX",
        "outputId": "428a1b1e-59d5-4154-f96c-d47ad872caf8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "degree = np.arange(21)\n",
        "train_score2, val_score2 = validation_curve(PolynomialRegression(), X2, y2,\n",
        "                                            param_name='polynomialfeatures__degree', param_range=degree, cv=7)\n",
        "\n",
        "plt.plot(degree, np.median(train_score2, 1), color='blue', label='training score')\n",
        "plt.plot(degree, np.median(val_score2, 1), color='red', label='validation score')\n",
        "plt.plot(degree, np.median(train_score, 1), color='blue', alpha=0.3, linestyle='dashed')\n",
        "plt.plot(degree, np.median(val_score, 1), color='red', alpha=0.3, linestyle='dashed')\n",
        "plt.legend(loc='lower center')\n",
        "plt.ylim(0, 1)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('score');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bOZionIJqmTX"
      },
      "source": [
        "The solid lines show the new results, while the fainter dashed lines show the results of the previous smaller dataset.\n",
        "It is clear from the validation curve that the larger dataset can support a much more complicated model: the peak here is probably around a degree of 6, but even a degree-20 model is not seriously over-fitting the data—the validation and training scores remain very close.\n",
        "\n",
        "Thus we see that the behavior of the validation curve has not one but two important inputs: the model complexity and the number of training points.\n",
        "It is often useful to to explore the behavior of the model as a function of the number of training points, which we can do by using increasingly larger subsets of the data to fit our model.\n",
        "A plot of the training/validation score with respect to the size of the training set is known as a *learning curve.*\n",
        "\n",
        "The general behavior we would expect from a learning curve is this:\n",
        "\n",
        "- A model of a given complexity will *overfit* a small dataset: this means the training score will be relatively high, while the validation score will be relatively low.\n",
        "- A model of a given complexity will *underfit* a large dataset: this means that the training score will decrease, but the validation score will increase.\n",
        "- A model will never, except by chance, give a better score to the validation set than the training set: this means the curves should keep getting closer together but never cross.\n",
        "\n",
        "With these features in mind, we would expect a learning curve to look qualitatively like that shown in the following figure:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "Ty48rZMhqmTX"
      },
      "source": [
        "![](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/figures/05.03-learning-curve.png?raw=1)\n",
        "[figure source in Appendix](06.00-Figure-Code.ipynb#Learning-Curve)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "7Cgzwn84qmTX"
      },
      "source": [
        "The notable feature of the learning curve is the convergence to a particular score as the number of training samples grows.\n",
        "In particular, once you have enough points that a particular model has converged, *adding more training data will not help you!*\n",
        "The only way to increase model performance in this case is to use another (often more complex) model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "nfsgFl0JqmTX"
      },
      "source": [
        "### Learning curves in Scikit-Learn\n",
        "\n",
        "Scikit-Learn offers a convenient utility for computing such learning curves from your models; here we will compute a learning curve for our original dataset with a second-order polynomial model and a ninth-order polynomial:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "VszHPGNHqmTX",
        "outputId": "650a82ba-bd5f-474f-bdd9-e609926bd4e0"
      },
      "outputs": [
        {
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            "text/plain": [
              "<Figure size 1600x600 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from sklearn.model_selection import learning_curve\n",
        "\n",
        "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
        "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
        "\n",
        "for i, degree in enumerate([2, 9]):\n",
        "    N, train_lc, val_lc = learning_curve(PolynomialRegression(degree),\n",
        "                                         X, y, cv=7,\n",
        "                                         train_sizes=np.linspace(0.3, 1, 25))\n",
        "\n",
        "    ax[i].plot(N, np.mean(train_lc, 1), color='blue', label='training score')\n",
        "    ax[i].plot(N, np.mean(val_lc, 1), color='red', label='validation score')\n",
        "    ax[i].hlines(np.mean([train_lc[-1], val_lc[-1]]), N[0], N[-1],\n",
        "                 color='gray', linestyle='dashed')\n",
        "\n",
        "    ax[i].set_ylim(0, 1)\n",
        "    ax[i].set_xlim(N[0], N[-1])\n",
        "    ax[i].set_xlabel('training size')\n",
        "    ax[i].set_ylabel('score')\n",
        "    ax[i].set_title('degree = {0}'.format(degree), size=14)\n",
        "    ax[i].legend(loc='best')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "1SmMxRvHqmTY"
      },
      "source": [
        "This is a valuable diagnostic, because it gives us a visual depiction of how our model responds to increasing training data.\n",
        "In particular, when your learning curve has already converged (i.e., when the training and validation curves are already close to each other) *adding more training data will not significantly improve the fit!*\n",
        "This situation is seen in the left panel, with the learning curve for the degree-2 model.\n",
        "\n",
        "The only way to increase the converged score is to use a different (usually more complicated) model.\n",
        "We see this in the right panel: by moving to a much more complicated model, we increase the score of convergence (indicated by the dashed line), but at the expense of higher model variance (indicated by the difference between the training and validation scores).\n",
        "If we were to add even more data points, the learning curve for the more complicated model would eventually converge.\n",
        "\n",
        "Plotting a learning curve for your particular choice of model and dataset can help you to make this type of decision about how to move forward in improving your analysis."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "BjKGJWRlqmTY"
      },
      "source": [
        "## Validation in Practice: Grid Search\n",
        "\n",
        "The preceding discussion is meant to give you some intuition into the trade-off between bias and variance, and its dependence on model complexity and training set size.\n",
        "In practice, models generally have more than one knob to turn, and thus plots of validation and learning curves change from lines to multi-dimensional surfaces.\n",
        "In these cases, such visualizations are difficult and we would rather simply find the particular model that maximizes the validation score.\n",
        "\n",
        "Scikit-Learn provides automated tools to do this in the grid search module.\n",
        "Here is an example of using grid search to find the optimal polynomial model.\n",
        "We will explore a three-dimensional grid of model features; namely the polynomial degree, the flag telling us whether to fit the intercept, and the flag telling us whether to normalize the problem.\n",
        "This can be set up using Scikit-Learn's ``GridSearchCV`` meta-estimator:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "p4-ye7UYqmTY"
      },
      "outputs": [],
      "source": [
        "from sklearn.model_selection import GridSearchCV\n",
        "\n",
        "param_grid = {'polynomialfeatures__degree': np.arange(21),\n",
        "              'linearregression__fit_intercept': [True, False]}\n",
        "              #'linearregression__normalize': [True, False]}\n",
        "\n",
        "grid = GridSearchCV(PolynomialRegression(), param_grid, cv=7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "pJucdRfrqmTY"
      },
      "source": [
        "Notice that like a normal estimator, this has not yet been applied to any data.\n",
        "Calling the ``fit()`` method will fit the model at each grid point, keeping track of the scores along the way:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "collapsed": true,
        "deletable": true,
        "editable": true,
        "id": "juUYTjDoqmTY"
      },
      "outputs": [],
      "source": [
        "grid.fit(X, y);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "AiV4Hd2kqmTY"
      },
      "source": [
        "Now that this is fit, we can ask for the best parameters as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "aZcshBAeqmTY",
        "outputId": "3b07723a-f6bc-4caa-9cc6-515bc35aa11b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'linearregression__fit_intercept': False,\n",
              " 'linearregression__normalize': True,\n",
              " 'polynomialfeatures__degree': 4}"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "grid.best_params_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "kFixvas3qmTY"
      },
      "source": [
        "Finally, if we wish, we can use the best model and show the fit to our data using code from before:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "wls3674yqmTY",
        "outputId": "1424781b-600f-421a-f632-b6c4886e988b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "model = grid.best_estimator_\n",
        "\n",
        "plt.scatter(X.ravel(), y)\n",
        "lim = plt.axis()\n",
        "y_test = model.fit(X, y).predict(X_test)\n",
        "plt.plot(X_test.ravel(), y_test);\n",
        "plt.axis(lim);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "ZmtDUHL0qmTY"
      },
      "source": [
        "The grid search provides many more options, including the ability to specify a custom scoring function, to parallelize the computations, to do randomized searches, and more.\n",
        "For information, see the examples in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) and [Feature Engineering: Working with Images](05.14-Image-Features.ipynb), or refer to Scikit-Learn's [grid search documentation](http://Scikit-Learn.org/stable/modules/grid_search.html)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "bEfJeidfqmTZ"
      },
      "source": [
        "## Summary\n",
        "\n",
        "In this section, we have begun to explore the concept of model validation and hyperparameter optimization, focusing on intuitive aspects of the bias–variance trade-off and how it comes into play when fitting models to data.\n",
        "In particular, we found that the use of a validation set or cross-validation approach is *vital* when tuning parameters in order to avoid over-fitting for more complex/flexible models.\n",
        "\n",
        "In later sections, we will discuss the details of particularly useful models, and throughout will talk about what tuning is available for these models and how these free parameters affect model complexity.\n",
        "Keep the lessons of this section in mind as you read on and learn about these machine learning approaches!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": true,
        "editable": true,
        "id": "9UYOYZKPqmTZ"
      },
      "source": [
        "<!--NAVIGATION-->\n",
        "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.03-Hyperparameters-and-Model-Validation.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
      ]
    }
  ],
  "metadata": {
    "anaconda-cloud": {},
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3.9.7 ('py3')",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.1"
    },
    "vscode": {
      "interpreter": {
        "hash": "7a6b41cc1ffbe7f6292ade58ee9ab0c89bd7fa770a77f101cc95d5710b4e5fa9"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}