notebook/06-03-Hyperparameters-and-Model-Validation.ipynb

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    "---\n",
    "---\n",
    "# Hyperparameters and Model Validation\n",
    "---\n",
    "---\n",
    "![image.png](img/chengjun.png)"
   ]
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    "<!--BOOK_INFORMATION-->\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)!*\n",
    "\n",
    "<!--NAVIGATION-->\n",
    "< [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](05.04-Feature-Engineering.ipynb) >"
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   "source": [
    "![image.png](img/socrates4.png)"
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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"
   ]
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    "\n",
    "The choice of model and choice of hyperparameters are perhaps `the most important part`.\n",
    "- we need a way to *validate* that our model and our hyperparameters are a good fit to the data.\n",
    "\n",
    "There are some pitfalls that you must avoid to do this effectively."
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    "## Thinking about Model Validation\n",
    "\n",
    "Model validation is very simple: \n",
    "- Applying the trained model to test data, \n",
    "- Comparing the prediction to the known values.\n",
    "    - The use of `holdout sets`\n",
    "    - The use of `cross-validation` "
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   "source": [
    "### Model validation the wrong way\n",
    "\n",
    "Let's demonstrate the naive approach to validation using the Iris 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. \n",
    "\n",
    "Here we'll use a *k*-neighbors classifier with ``n_neighbors=1``.\n",
    "- This is a very simple and intuitive model \n",
    "    - \"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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    "Then \n",
    "- we train the model, and \n",
    "- 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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    "Finally, we compute the fraction of correctly labeled points:"
   ]
  },
  {
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     "execution_count": 4,
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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",
    "\n",
    "- In fact, this approach contains a fundamental flaw: \n",
    "    - *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, \n",
    "    - it predicts labels by comparing new data to these stored points: \n",
    "    - except in contrived cases, it will get 100% accuracy *every time!*"
   ]
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    "### Model validation the right way: Holdout sets 留出法\n",
    "\n",
    "- We hold back some subset of the data from the training of the model, and then \n",
    "- use this holdout set to check the model performance.\n",
    "\n",
    "This splitting can be done using the ``train_test_split`` utility in Scikit-Learn:"
   ]
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   "source": [
    "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, test_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: \n",
    "- 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\n",
    "- 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\n",
    "        - especially if the initial set of training data is small.\n",
    "\n",
    "*cross-validation* does a sequence of fits where each subset of the data is used both as a training set and as a validation set."
   ]
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    "### Model validation via cross-validation\n",
    "\n",
    "Visually, it might look something like this:\n",
    "\n",
    "![](./img/figures/05.03-2-fold-CV.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#2-Fold-Cross-Validation)\n"
   ]
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    "# Here we do two validation trials, \n",
    "# alternately using each half of the data as a holdout set.\n",
    "# Using the split data from before, we could implement it like this:\n",
    "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\n",
    "- we could calculate the mean value to get a better measure of the global model performance.\n",
    "- This particular form of cross-validation is a *two-fold cross-validation*\n",
    "    - that is, one in which we have split the data into two sets and used each in turn as a validation set."
   ]
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    "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",
    "![](./img/figures/05.03-5-fold-CV.png)\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."
   ]
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    "#  We can use Scikit-Learn's ``cross_val_score`` convenience routine to do it succinctly:\n",
    "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; \n",
    "- 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:\n",
    "        - we train on all points but one in each trial.\n",
    "    - This type of cross-validation is known as *leave-one-out* cross validation"
   ]
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       "       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",
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       "       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",
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   "source": [
    "from sklearn.model_selection import LeaveOneOut\n",
    "import numpy as np\n",
    "scores = cross_val_score(model, X, y, cv=LeaveOneOut())\n",
    "scores\n",
    "#np.sum(scores)/len(scores)"
   ]
  },
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   "source": [
    "Because we have 150 samples, the leave one out cross-validation yields scores for 150 trials, and \n",
    "- 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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   "source": [
    "Other cross-validation schemes can be used similarly.\n",
    "\n",
    "- use IPython to explore the ``sklearn.cross_validation`` submodule, or \n",
    "- take a look at Scikit-Learn's online [cross-validation documentation](http://scikit-learn.org/stable/modules/cross_validation.html)."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "<div><img src = img/ml2.png width = 600px></div>"
   ]
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   "source": [
    "## Selecting the Best Model\n",
    "\n",
    "> ### Question: *if our estimator is underperforming, how should we move forward?*\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"
   ]
  },
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   "source": [
    "## Selecting the Best Model\n",
    "\n",
    "The answer to this question is often counter-intuitive.\n",
    "\n",
    "In particular, sometimes \n",
    "- using a more complicated model will give worse results\n",
    "- adding more training samples may not improve your results!\n",
    "\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",
    "\n",
    "Consider two regression fits to the same dataset:\n",
    "\n",
    "![](./img/figures/05.03-bias-variance.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff)"
   ]
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    "### The Bias-variance trade-off\n",
    "\n",
    "The model on the left has high **bias**\n",
    "- The data are intrinsically more complicated than a straight line.\n",
    "- Such a model is said to **underfit** the data: \n",
    "    - it does not have enough model flexibility to suitably account for all the features in the data; \n"
   ]
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    "### The Bias-variance trade-off\n",
    "\n",
    "The model on the right has high **variance**.\n",
    "- Here the model fit has enough flexibility to nearly perfectly account for the fine features in the data, \n",
    "- but 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: \n",
    "    - it has so much model flexibility that the model ends up accounting for **random errors** as well as the underlying data distribution;"
   ]
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   },
   "source": [
    "![image.png](img/ml3.png)"
   ]
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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",
    "![](./img/figures/05.03-bias-variance-2.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Bias-Variance-Tradeoff-Metrics)\n"
   ]
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   "source": [
    "$R^2$ score, or [coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination)\n",
    " measures how well a model performs relative to a simple mean of the target values. \n",
    "- $R^2=1$ indicates a perfect match\n",
    "- $R^2=0$ indicates the model does no better ``than simply taking the mean of the data``\n",
    "- $R^2<0$ negative values mean even worse models."
   ]
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    "**Validation Curve**\n",
    "\n",
    "If we imagine that we have some ability to tune the model complexity\n",
    "\n",
    "\n",
    "<div><img src=\"img/ml4.png\" align = 'left'></div>\n",
    "\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",
    "\n",
    "For **high-variance models**, the performance of the model on the validation set is far worse than the performance on the training set.\n",
    "\n"
   ]
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    "- The training score is everywhere higher than the validation score. \n",
    "    - 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**\n",
    "    - 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**\n",
    "    - 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. \n",
    "    - The trade-off between bias and variance.\n"
   ]
  },
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   },
   "source": [
    "**Bias-Variance Decomposition**\n",
    "\n",
    "![image.png](img/ml5.png)\n",
    "\n",
    "https://en.wikipedia.org/wiki/Bias-variance_tradeoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Validation curves in Scikit-Learn\n",
    "Using cross-validation to compute the validation curve.\n",
    "\n",
    "A **polynomial regression** model:  A generalized linear model in which the degree of the polynomial is a tunable parameter.\n",
    "\n",
    "A degree-1 polynomial fits a straight line to the data:\n",
    "$$y = ax + b$$\n",
    "\n",
    "A degree-3 polynomial fits a cubic curve to the data:\n",
    "$$ y = ax^3 + bx^2 + cx + d\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In Scikit-Learn, we can implement this with a simple linear regression combined with the polynomial preprocessor.\n",
    "\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": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-06T03:47:21.340972Z",
     "start_time": "2021-08-06T03:47:21.329542Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now let's create some data to which we will fit our model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-06T03:47:26.883803Z",
     "start_time": "2021-08-06T03:47:26.871837Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can now visualize our data, along with polynomial fits of several degrees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:16.570441Z",
     "start_time": "2020-05-18T14:04:15.673880Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Question\n",
    "\n",
    "The knob controlling model complexity in this case is the degree of the polynomial \n",
    "\n",
    "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; \n",
    "- 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": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T15:04:33.215177Z",
     "start_time": "2020-05-18T15:04:32.612764Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bIQkvk6ThBZ9/biQ3t4wR4JpG8COTUVu0JPfp57wTnBBnUdtcQNaXmyi4ZRyBixehP/SHt0MSXiRJwwuWLzdy0UV2evSwu+zX//ZfDIf+IP+BByG4/FkmhahzJhP5U58EwO+L/3g5GOFNXk8aa9euZejQoQwaNIgVK1acc/zgwYPccMMNDBs2jHvvvZfs7GwvROk5Bw7o2L277AZwvw3rALAMvsYLkQlRMfW887H2SMDvizXeDkV4kVeThtlsZt68eaxcuZI1a9awevVqDh8+7HLO7NmzSUpK4osvvqB169a88847XorWM5YvN+Lnp3Hjjec2gJvW/x/Wbt1RY+O8EJkQlSsadj2G3w6iP3zI26EIL/Fq0tixYwcJCQmEh4cTGBjI4MGDWb9+vcs5qqqSl5cHQEFBAf71eA2J/HzHkq7XXWejSRPXY7pTyRj3/IJlyLXeCU6IKii67l+AVFE1Zl6dLjUlJYXo6GjndkxMDPv373c55/HHH+fOO+/k+eefJyAggI8//tita1S0AlVloqMrWNyiGj74wLF2RlKSkejos5YM/c9HAATdfCNBlVzX03F5kq/GJnG5p9y4ottDz54ErfuCoDmz6jYo6uHn5WW1EZdXk4aqqihnVOxrmuayXVhYyLRp03j//ffp0qUL7733Ho899hiLFy+u8jV8abnXhQsDadsW2rfPJzXV9Vjop59haNGKjJgWUMF1fXVpSfDd2CQu91QWV8A1iQTPeIKMH37BfsGFPhOXtzS0uCpb7tWr1VNxcXGknvHtmZqaSkxMjHP7jz/+wM/Pjy5dugAwevRodu3aVedxesJvv+n46adypkDPzcX0zTaKhlwjo7+FzytKvB5AGsQbKa8mjZ49e7Jz504yMjIoKChg48aN9O7d23m8ZcuWnDp1ir/++guAzZs3Ex8f761wa2T5ciMmk8bo0efO42PavhWlqEjaM0S9oJ7fFOulPSRpNFJerZ6KjY3lwQcfZNy4cVitVkaOHEmXLl0YP348SUlJxMfHM2fOHKZMmYKmaURGRvL88897M+RqKSiATz4xcu21NiIjz60q89uwDjUsHOvlV3ghOiHcVzTseoKfehL9X4ext2nr7XBEHfL6uqGJiYkkJia67FuyZInzcZ8+fejTp09dh+VRX35pICurnDXA7XZMm9ZjGXA1GI3nHhfCBxUlOpKG3xdryJ/yiLfDEXXI64P7GoMPPzTSurVKr172c44ZftqFLj0dy5ChXohMiOpRmzbD2v0yTFJF1ehI0qhlf/yh44cfDOWuAe63YR2a0Yil/8C6D06IGigaNhzjgf3o/vrT26GIOiRJo5YtX27EaNS46aay1wA3bViHteeVaKFhdRyZEDVTlFg80G+tlDYaE0kataiwED7+2MA119iIjj63AVx/+BCGw4cokqopUQ+pzZpj7X6p9KJqZCRp1KJ16wxkZOi49dZyShnrSyYolKQh6qeixOEYf92H7u+/vB2KqCOSNGrRhx8aadFCpXfvcxvAwdGeYe3cBbVZ8zqOTAjPkCqqxkeSRi3580+F7783MHasFV0Zn7KSlobhpx9lGnRRr6nNW2Dt1l2qqBoRSRq1ZPlyEwZDBQ3gX29AUVXpaivqvaLE4Rj370V35G9vhyLqgCSNWlBUBKtWGRg82EZsbNmTJfqtX4f9vPOxdelax9EJ4VnOKiopbTQKkjRqwfr1BtLTdWWPAAcoLMS0bbOjakomKBT1nNqiJdZLukm7RiMhSaMWLFtmpHlzlT59ym4AN323HSU/X7raigajKHE4xn17pIqqEZCk4WGpqQrffmvg5put6PVln2P6ah1qUDDWXr3LPkGIeqa0F9XnXo5E1DZJGh52/Lijuik+vuxSBqqKaeNXWPsPBD+/OoxMiNqjtmyFtesl+K2VZWAbOkkaHmY2O5JGeQ3ghn170JtPUSRdbUUDU5Q4HOPePeiOHvF2KKIWSdLwMLPZ8ZHGxJSdNEwb1qHpdFgGDqrLsISodUXDilf0kyqqBk2ShoelpCgoilbmXFMAfl+tw3r5FWhNIus4MiFql9qyFdaLpYqqoZOk4WFms0JkpFbmekq6o0cw/HZQlnUVDVZR4vUY9/yC7thRb4ciaokkDQ9LSVHKrZry2/gVAJbBQ+oyJCHqjFRRNXySNDzMbNaV2whuWv8VtovayZrKosFSW7WWKqoGTpKGh5nNSplJQzmdhXHnd1I1JRq8osTrMf6yG90/x7wdiqgFkjQ8SFUd1VOxseo5x0ybN6HYbNLVVjR4UkXVsEnS8KCMDAWbreyShmnDOtSoaGzdLvVCZELUHbVVa6xdukoVVQMlScODUlIcA/vOaQi3WDB9vYmiQUMod24RIRqQomHXY9z9M7rj/3g7FOFhkjQ8qGQ0+NlJw7jze3Q52dKeIRqNokSpomqoJGl4UOkUIq5tGqYN69D8/bH07uuFqISoe2rrNljjL8bvC6miamgkaXhQSorj43Rp09A0/DZ8haVPPwgM9FJkQtQ9RxXVT+hOHPd2KMKDJGl4kNmsEBKiueQG/cED6P85hmWwrJ0hGpfSKipZnKkhkaThQY4xGq5VU34b1qEpCkWDpKutaFzUNhdg7dxFloFtYCRpeFBZA/tMG9Zh63YpWkyMl6ISwnssw67H+PMuqaJqQCRpeFBKis6l55Qu+STGvXtkWVfRaDkH+n0pvagaCkkaHmQ2u05WaNpQPEGhdLUVjZS9TVtsneKliqoBkaThIbm5kJ/v2qZh2rAOe6vW2C9q58XIhPCuomHXY/zpR3QnT3g7FOEBkjQ85JxlXnNzMX27naLBQ0FRvBiZEN4lVVQNiyQNDylZ5rUkaZi2bUGxWLBIe4Zo5OwXXIitY2epomogvJ401q5dy9ChQxk0aBArVqw45/hff/3F2LFjGTZsGHfddRenT5/2QpSVO7uk4bf+/1DDw7FefoU3wxLCJxQNux7jrh/QJZ/0diiihryaNMxmM/PmzWPlypWsWbOG1atXc/jwYedxTdOYMGEC48eP54svvqBDhw4sXrzYixGXz2UKEZsN09cbsAwcDAaDlyMTwvuKrrkOANOWr70ciaipaieNvLw89uzZw7Zt2wCqVQLYsWMHCQkJhIeHExgYyODBg1m/fr3z+MGDBwkMDKR3794A3Hfffdxyyy3VDblWmc06/Pw0wsJw9EvPyJCutkIUs7fvgD02DuP2Ld4ORdSQ20kjLS2NBx98kMsvv5wxY8Zw//33A7By5Uquvvpqfv755yq/VkpKCtHR0c7tmJgYzGazc/vYsWNERUXx5JNPMnz4cGbOnEmgj87fVLI2uKKAaf06NKMRa78B3g5LCN+gKFj79MP0zTbHamWi3nKr7iQjI4PRo0dz4sQJunXrRlFREf/9738BCAgI4OTJk4wfP55Vq1bRrl3l3UxVVUU5o2eRpmku2zabjV27drF8+XLi4+N57bXXmDt3LnPnzq1yzJGRwW68Q1fR0SFVPjczE5o2heioYNj0FfTvT1SbptW+tqfiqmu+GpvE5Z5aiWvYtfDxR0QfPwzdu1frJRrV5+UBtRGXW0ljwYIFJCcns2jRIvr168cbb7zhTBq33347HTp04O6772bRokW89tprlb5eXFycS8kkNTWVmDOm24iOjqZly5bEx8cDcN1115GUlOROyKSn56Kq566kV5no6BBSU3OqfP7x44G0aaOSvv9PIg8dIvf2uylw4/m1FVdd8tXYJC731FZcStcEooDc/6yloMVFPhNXTTW0uHQ6pcKbbbeqp7Zs2cLVV19Nv379yjx++eWXM2jQIPbu3Vul1+vZsyc7d+4kIyODgoICNm7c6Gy/ALjkkkvIyMjg999/d16/U6dO7oRcZ8xmHbGxGrrjjjl27G0u8HJEQvgWLSYGW6d4TNu3ejsUUQNulTQyMzNp3rx5hefExsaSkZFRpdeLjY3lwQcfZNy4cVitVkaOHEmXLl0YP348SUlJxMfHs3DhQqZPn05BQQFxcXG8+OKL7oRcJ4qKIDPTMVmhzpwMgD3ufC9HJYTvsfTpR8CSRZCXB0FB3g5HVINbSSMuLs5ZHVWe/fv3ExcXV+XXTExMJDEx0WXfkiVLnI8vvvhiPv30U3fCrHMla4PHxmroi/uhq3HneTMkIXySpW9/At9cgOmH77EMGOTtcEQ1uFU9NXjwYHbu3MmqVavKPP7ee++xe/duBg4c6JHg6oszx2joTp1CM5nQmjTxclRC+B7r5Veg+flh3CZdb+srt0oa9913H9u3b+eZZ55hxYoVqMVd5x5//HEOHjzI4cOHadGiBffdd1+tBOurSpZ5jYnR0CWfdJQyZL4pIc4VEIA1oSem7VvJ83YsolrcKmkEBwfz0UcfcdNNN3HixAn+/PNPNE1jzZo1HD16lH/961989NFHhIaG1la8PunMKUR05lNSNSVEBSx9+mP4/TeZUqSecqukcfz4cZo1a8bMmTOZPn06f//9N9nZ2QQGBtKmTRtMJlNtxenTzGYFnU4jKspR0rB1ivd2SEL4LEvf/vDsDIzbt1J0k2/O8CDK51ZJY9y4cUyePBkAvV5P27Zt6datG+3bt2+0CQMcDeFRURp6PehOnUI9T0oaQpTH3rETalQ0JmnXqJfcShppaWmVdrltjErGaCi5OejyclFjJWkIUS6dDotMKVJvuZU0LrvsMnbs2IHFYqmteOols7l4jEayY4yG6kaXYyEaI0uffujSUtEfPODtUISb3GrTuPHGG3nuuecYPHgwvXv3pmnTpvj7+5d57rhx4zwSYH1gNivEx9vRnSpOGufJwD4hKmLt2x8A0/atFMR38XI0wh1uJY0pU6Y4H69evbrc8xRFaTRJw26HtDTF2d0WpKQhRGXUuPOwte+AafsWCiZN9nY4wg1uJY05c+bUVhz1Vnq6gt1enDROnQLALm0aQlTK0qc/Ae8vhYICCAjwdjiiitxKGsOHD6+tOOotlzEaO06ihoRCcPWnYxeisbD27Ufg2wsx/rjTWV0lfF+11iLNy8tj06ZN/P777xQUFBAeHs6FF15Iv379CGpkk5CVzjulopfutkJUmSWhF5rJhGnbFkka9YjbSWPLli088cQTZGdno2ml61QoikJoaChz584td+r0hsilpJF8UrrbClFVQUFYeyTIlCL1jFtdbg8cOEBSUhJFRUXccccdLFy4kE8++YR33nmHe+65B7vdzpQpU5zrXzQGZvMZ806ZpaQhhDssfftjOPgrSkqKt0MRVeRW0njzzTfR6/WsXLmSqVOnMmDAAOLj4+nVqxcPPvggH3zwAQCLFy+ulWB9kdmsEB6u4W9S0Z1KlnmnhHCDtY+jVsL0jSzMVF+4lTRKpj3v2LFjmcc7derEwIED2bVrl0eCqw9SUhRiYlSU9HQUmw27lDSEqDJb/MWoTZogU4rUH24ljfz8fKKioio8JzIykuzs7BoFVZ+UTCGiP1U8RkPaNISoOp0OS+++GLdvhTPaSIXvcitptGjRgh9++MG5jsbZ7HY7P/zwA82aNfNIcPWB2VwyRqNkNLgkDSHcYe3TH735FPrff/N2KKIK3EoaiYmJ/O9//2PGjBnk5+e7HMvMzOSJJ57g0KFD5yzf2lBpmqN6ynXeKUkaQrjDUtKusV2qqOoDt7rc3nnnnXzzzTf8+9//Zt26dXTs2JGQkBBSUlL4+++/KSgo4JJLLuGuu+6qrXh9SnY2FBYqxcu8JqMpCmpMrLfDEqJeUZs1x9b2QkzbtlBw3yRvhyMq4VbSMJlMvP/++yxZsoT//Oc/7N6923msWbNmDB8+nPHjxzeatTVKutvGxmroDiWjRUWD0ejlqISofyx9+xOwYhkUFYGfn7fDERVwe3CfyWRi4sSJTJw4kby8PHJzcwkKCiK4EU6d4TKw71QydpndVohqsfbpT+DStzHu+gHrVX28HY6ogFttGgApKSnMnj2b9evXExQURGxsLMHBwQwZMoRZs2aRk5NTG3H6pNKkoTpW7JPZbYWoFmuvK9EMBkzbZbyGr3MraRw/fpyRI0eyfPlyl1HfBQUFqKrKihUrGDFiBCmNZHRnybxTMTGOLrfS3VaI6tGCQ7Be2sPR9Vb4NLeSxoIFC8jIyODll6wxjn8AACAASURBVF92WVsjICCAjRs3Mm/ePE6ePMm8efM8HqgvMpt1BARohPhZ0KWlSXdbIWrA2rc/hv17UdLTvR2KqIBbSWPXrl1cc801XHvttWUev+aaa7j66qvZvn27R4LzdSVjNPQpjnU0pLutENVn6dMPRdMwfbvN26GICriVNE6fPk1ERESF58TFxZGbm1ujoOoLxxgNVQb2CeEBtq7dUMPCMcqUIj7N7RHhO3fuxGazlXlcVVV+/PHHRjMi3GxWnD2nQFbsE6JG9HqsV/VxNIbLlCI+y62kcf3113Po0CGmTp1Kamqqy7H09HSmTZvG77//zr/+9S+PBumrSuedKilpSJdbIWrC0rc/+hPH0R8+5O1QRDncGqdx22238f3337Nu3Tq++uorzjvvPIKDg8nLyyM5ORlVVenVq1ejGBFeUADZ2aVTiGgmE1qTJt4OS4h6rWRKEeP2LdgvvMjL0YiyuFXS0Ol0LF26lOeee46EhAQKCwv566+/yMnJoVu3bjz77LMsWbIEg6Faq8jWK6Xdbc9YR0NRvByVEPWb2rIVttZtkKnSfVe1vt1HjhzJyJEjASgsLMRsNhMVFdWo1gc/ezS4GisD+4TwBGuffvh9shosFmgkUxLVJ1UqaZSsC372Mq6vvPIKV1xxBUOGDKFHjx5MmTKFzMzMWgnU17gs8ypTiAjhMZa+A9Dl5WLc/VPNX0zTCHjzdYxbvq75awmgCknjqaeeYuLEiaxZs4ajR48697/66qssWbKEwsJCevbsSUJCAhs3bmTs2LFYLJZaDdoXlFRPlbRpyBQiQniG9cqr0PR6jDWdKl3TCH7iEYKfnkbA+0s9E5yoOGls2bKFjz/+mA4dOrB06VL69u0LgNls5t1330VRFGbNmsU777zDO++8w+uvv87hw4dZtmxZXcTuVWazgsGgEeWXjS4vFzVOShpCeIIWGoat26XUqF1DVQme+hAB7y5BM5lQsrI8Fl9jV2HS+PTTTwkPD2fZsmX06tULv+Ipi9evX4/NZqNFixbOtg2AAQMG0K1bN9avX1/lANauXcvQoUMZNGgQK1asKPe8bdu20b9//yq/bm0zm3VER2sYzCWLL0lJQwhPsfTph2HvHpTMDPefrKoEPzKZgA/eIT/pISwDB6PLahzV5nWhwqSxf/9++vbte8605zt27EBRlDK/xC+++GKXaqyKmM1m5s2bx8qVK1mzZg2rV6/m8OHD55yXlpbGCy+8UKXXrCtnD+yTMRpCeI6l7wAUVcX43TfuPdFuJ2TKRAKWf0DeQ4+SN20mapMmKI2krbUuVJg0Tp8+TWys60p0qqo6F1+64oorznmOwWDAarVW6eI7duwgISGB8PBwAgMDGTx4cJmllOnTpzNpkm+t6JWSUrw2ePJJQEoaQniSrVt31JBQTNvcmPXWbickaQL+q1aQ9+gT5D8+AxQFLTzCUdKQUeYeUWGX25CQkHN6Q+3fv5/c3FyMRiOXXXbZOc85cuRIpfNTlUhJSSE6Otq5HRMTw/79+13OWbZsGR07duTiiy+u0mueLTKy+otDRUeHlHssNRWuuAJCcx2fT5POF0EdLURVUVze5quxSVzu8Ym4BvQn4NutBEQFO8dAlRuXzQbjxsEnq2DWLIKmT8c5AKBZHBQVER1sgMDAWgnVJz6vMtRGXBUmjfj4eHbs2IGqquh0jkLJl19+CThKGQEBAS7np6am8t1333HVVVdV6eKqqqKcMSBO0zSX7T/++IONGzfy/vvvc+rUqaq9o7Okp+eiqu7fYURHh5CaWvaCUjYbpKQEExpqIf/PI/iHhJJeoEFB7S9AVVFc3uarsUlc7vGVuPwTriJkzRrSd+1DbXNB+XFZrYRMuBv/L/5D7vSnKbh3Mpxxnr8hgBAg/dAx1PObejxOX/m8zlbduHQ6pcKb7Qqrp0aNGsXx48d56KGH+Omnn1ixYgWrV69GURRuueUWl3MzMjKYMmUKhYWFDBs2rErBxcXFucxhlZqaSkxMjHN7/fr1pKamcsMNN3DPPfeQkpLCmDFjqvTatSktTUHTHG0aeuluK0StsPR1tJlWuJqfxULoPXc4EsbM5yhIeuicU9Timg/pQeUZFZY0BgwYwC233MKKFSvYsGED4CgNjBkzhj59Stfxve+++9i5cydFRUUMGTKEgQMHVuniPXv25PXXXycjI8O5kNOsWbOcx5OSkkhKSgIcqwaOGzeOlStXuv0mPe2c0eDS3VYIj1Nbt8HeoiWmbVsovOPuc0+wWAi9+zb81v8fubPmUHDvxDJfRwt3JA1dVib2Woy3sah0GpEZM2YwePBgtm7dis1mo1evXs7xGiX++usvgoKCuOeee5gwYUKVLx4bG8uDDz7IuHHjsFqtjBw5ki5dujB+/HiSkpKIj493+w3VBde1wZOxXtHLyxEJ0QApCpY+/fFb829HnfCZiooIvWssfhvXkzPnJQrvurfcl1GLk4b0oPKMKs091aNHD3r06FHu8c8+++ycbrlVlZiYSGJiosu+JUuWnHNes2bN2LLFNyYxK5lCJDbajs58SrrbClFLLH37EfDhexh+2Q3XFtdgFBYSesct+G3eRM4Lr5ZdCjmDFlFa0hA159Yst+WpbsKor5wlDX0aitWKXdo0hKgV1it7o+l0mEqmFCkoIGzcTY6E8cqCShMGSEnD0xr+HOa1ICVFoUkTFb/0ktHgUtIQojZoEU2wdb0E07YtkJ9P2K2jMX63nZzXFlI4ZmzVXiQoCM1olJKGh3ikpNHYlIwG15+SgX1C1DZL3/4YfvkZhgxxJIwFi6qeMMA5wE9KGp4hSaMaUlJ0xVOiO8aOSJuGELXH2qc/it0O339PzsLFFI12v9u9GhEhJQ0PkeqpajCbFS64QEWXfBJNUVBjYit/khCiWqyX9qDwhlH43zyKot6DqvUaWngEiiQNj5Ck4SZNc7RpxMaq6Myn0KKiwWj0dlhCNFxGIzmLluIfHeIy0tsdakQEuhMnPBxY4yTVU27KzASLpXiG2+ST2OPO83ZIQohKOCctFDUmScNNzjEasY42DfU8SRpC+DpVGsI9RpKGm0qWeY2JcfSeUmMlaQjh67SICHR5udAIlqKubZI03FQysC+uSSG6tDQpaQhRDzgH+MmkhTUmScNNJdVT51EysE+ShhC+TqYS8RxJGm5KSVEICtIIzi5Z5lWShhC+TqYS8RxJGm4qXRvcMbDPLm0aQvg8KWl4jiQNNzmShnrGFCKSNITwdaUljQwvR1L/SdJwk9msc5Y0NKMRLTLS2yEJISohJQ3PkaThppQUxTHvVPJJRynjjDXNhRC+SQsJRdPpZCoRD5Ck4Ya8PMjNLU4a5lNSNSVEfaHToYWFoZOG8BqTpOEGl2VeS0oaQoh6QQ2PQDkt4zRqSpKGG1JSXKcQsUt3WyHqDS0iQkoaHiBJww0lJY3zQ7LR5ebIFCJC1CMyPbpnSNJwQ0nSOE8r7m4rJQ0h6g01XEoaniBJww1ms4LJpBGRL2M0hKhvtAgpaXiCLMLkhpJlXvXmxjmFSEFBHrm5p7HbrWUeT0nRoapqHUdVOYnLPfUtLr3eSHBwGAEBQRU+39EQfhrsdtDrayvMBk+ShhvM5pIxGo6k0ZimELFaLeTkZBIeHoXR6IdSxvgUg0GHzeZ7XzYSl3vqU1yapmG1FpGVlYbBYMRoNJX7fC0iAkXTULJPo0U0qe1wGyypnnKDI2mo6MzJqCGhEBzs7ZDqTE5OFsHBYZhM/mUmDCG8QVEUTCZ/goLCyM2tuDutTFroGZI03OBYG1xDn5yMGhfn7XDqlM1mwc8vwNthCFEmf/8ArNaKF1iSqUQ8Q5JGFVkskJ5eMu9UMmrc+d4OqU6pqh2dTuqBhW/S6fSoqr3Cc0oXYpKkUROSNKooNbVkNHhJ0mhcJQ1AqqWEz6rK32ZJO4Z0u60ZSRpV5JxCJNrmmHfqvMZV0miINE3zdgiiDklJwzMkaVRRyTKvzQLSUKxW7I2wpNGQfPvtNl566fkav05y8kmuvPJStm79usrPmTTpHqZOnVLjawv3aOHhgJQ0akq63FZRSkrxaHC1eGBfI+pu2xCtXr2SwMDAGr9OZGQUb731Hi1atKjycx5++HH0erlfq3MGA2pIqJQ0akiSRhWZzQqKohFlkSlERCmTyUTnzvFuPad16za1FI2ojExaWHOSNKrIbFaIjNQwphSPBpcpROqtSZPuYe/eXwC48spL+eSTL1i3bi07dnzHxRd3Zd26tbRu3YZFi94lLS2NxYsX8uOPO8nKyiQ8PIL+/a9mwoQHMJlMJCef5MYbhzFr1lz69RvI7NlPU1CQT5cul7B69QoyMzPp1KkzDz/8OK1atXZePzAwkFdfXcAvv/xMUtJ9LFy4hLfeep3//e93IiOjGTfuDhITr3fGfOjQH7z++qv8978HiIiI5O677+XddxczaNA13HXXvWW+z2PHjjB//qscPLgfVdXo3LkL99+fRNu2FzrP+fzzz/jkk1WcPHmCuLg4brrpVkaMuAFwtPmsXbuGTz9dxfHjx4mJiWHEiBsZNWqM8/lXXnkp99xzPxs3ricjI51HH32Cfv0G8vvvv7Fo0QIOHNhPQEAAAwYMYsKEJPz9/T3+7+kOVSYtrDFJGlWUklLa3RZAjZU2jfrq4YcfZ9asGfj5+TNx4hQiI6MAOHz4D0wmE8899yIWiwVVVXn44QdQFIWHHnqM4OBgfvxxJytXLqNp06aMHHlTma//88+7OHnyBJMnP4Kq2pk//xVmz36aJUs+KDemp5+exujRY7j77gl89tnHvPDCc3Tu3IXWrduQkZFOUtJ9tGjRkqeffp60tFRee+1lCgsLKnyfTzzxCNHRMTzzzBxU1c7SpW8zdeoUPvnkC/R6PatWLWfhwvmMGjWGhISe7N37Cy++OJvg4CD69x/E228v5KOPPuSWW26ja9du7Nmzm4UL55OVlcU999zvvM677y5m8uRHCAsL5+KLL+Hvv/9i0qTxdOrUhWefnUtmZgZvvfUGycknefHF16rxL+Y5mkxaWGNeTxpr165l0aJF2Gw2brvtNm655RaX419//TWvv/46mqbRrFkz5syZQ1hYWJ3HaTYrpd1to6LBaKzzGHzR6tUGPvrI8VkoiuKVHkk332xl9Ghblc9v3boNgYFBBAYGulQt2e12Jk9+mPbtOwJgNp8iJCSEKVMedd6dd+9+GT/+uJO9e38pN2nk5+fz4ovziYpyJKPU1FTmz3+Z06ezCAsLL/M5I0eO5qabbgXgoova88032/jhhx20bt2GTz5ZhaapvPzyAkJCQgAIDw9n+vTHyn2PmZmZHD16hNtvv5vLL78CgNjYODZt2kBBQQGBgYF8+OF7DB2ayAMPPAjAZZddzsmTJ9i3bw/du/dg9eoV3HzzWGeC6NEjAU3T+OijDxk1agzhxQ3LPXokMHz4SOe1589/hYiISF566TVMJse0Hs2bt2DixPHs3fsLXbt2Kzfu2qZGRGA4edxr128IvNoaZzabmTdvHitXrmTNmjWsXr2aw4cPO4/n5uby9NNPs3jxYr744gvatWvH66+/7qVYS5OGXbrbNlgtW7Z2Po6NjeONNxbTps0F/PPPMXbs+I5ly94lMzMDi6XsSRsdzzvPmTAAYmJiACgoKCz3OZ06lSavkJAQAgICnSWJvXt3c8kl3Z0JA+Cqq/qir2DSvbCwMJo3b8GLL85mzpxn2bZtM3Fx53PvvRMJDg7m2LGjnD59ml69ers8b+bM53j00Sc4ePAAVquVfv0GuhwfMGAQVquVgwd/de4rqXYrsWfPbnr0uBydTofNZsNms9GpUzxBQUHs3v1TuTHXBS08QkaE15BXSxo7duwgISHBeccyePBg1q9fz6RJkwCwWq3MnDmT2NhYANq1a8fatWvrPE5VdQzui41V0f2aLI3gZxg92ua8y/fVie6qKiAggIAA16lSvvxyDYsXLyIjI53IyCg6duyMn58fUH6Jyt/fz2VbURz3ZppW/mdzdl2/Tqc4Z3TNysqiVSvXxnO9Xu/8f1MWnU7Ha6+9ybvvLubbb7fzf//3BX5+fowZM44777yH7OzTAEQUT61xtpycbACaNHGd2K9kOy8vz7kvPNz1nNOns/j888/4/PPPznndtLS0cmOuC2pEhGPuKU0DGaxaLV5NGikpKURHRzu3Y2Ji2L9/v3M7IiKCq6++GoDCwkIWL17M2LFj6zzOjAwFm80xw63+VDK2S7rXeQyi7u3Zs5sXXpjN7bffzYgRo5xfsOPHj6vTOKKiosk66+5YVVVOnz5d4fNiY+N44omneOwxlYMHf2Xt2jW8994SWrVq7ezBdfbrHjt2lNzcbEJDQwHIyMggOjrGeTwjIx2gwiri4OBgrryyj0uVVYnyqufqihYegWK3o+TmoIWEejWW+sqrSUNVVZfh/5qmlTkdQE5ODhMnTqR9+/YMHz7crWtERlZ/JtroaEd1QPFM6FzUSocuLZWAC1oSEB1SwTNrV7QXrp2SosNgqLw2syrneMPZcRkMehSldL9Op5xz3m+/HURRFO66624MBke7TWpqKn/99SfduzfBYNA5x1vo9Y7PR1EUFEVxeR29XinjHJz7zjx2Jp3O8TrdunVj9eqPKCrKJyjI8ff8/fffY7PZnOec7dChP5gyZRKvvDKf9u07cMkll9ClSxc2bPiK1FQzAwYMJDQ0jJ07v6dfv/7O573zzlukpJh56aV5GAwGtm/fTKdOHZ3Ht279Gr3eQHx8vPO6er1rDBdffAnHjh2lU6dOzv/P6enpzJw5jZtuGkPz5s0q+JeqWEV/XzqdrvL/G80dHViidFbw4P8jb/yfrIraiMurSSMuLo6ff/7ZuZ2amuqs/y2RkpLCXXfdRUJCAk8++aTb10hPz0VV3W+cjY4OITU1B4DfftMDgYQV/A1ATmgkhcXH6tqZcdUlVVUrrXry1eqpsuIKCgrm0KE/2LVrF506dXb+jZx5Xrt2HVBVlVdeeZl+/QZgNp9i2bJ3sVgsFBQUYLOp2O2O8+12x+ejaRqaprm8jt2ulXEOzn1nHjuTqjpeZ8SI0Xz88WoefDCJW265jaysTBYvXlh8llLmZ968eSsCAwN55pkZ3HnnPYSGhvHVV1+i0ylcfnkvQMfYsXewaNECQkPD6N79Mvbt28OWLV/zwguvEBwcxsiRN7FixTIURUfXrpewd+8eVqxYxujRtxAYGOy8rt3u+n7HjbuLCRPu5IknpnLttcOwWCx88MFSUlLMXHDBRdX+G6ns70tV1Ur/b5j0AYQBmX8dxxYUWa04zuat/5OVqW5cOp1S4c22V28Le/bsyc6dO8nIyKCgoICNGzfSu3dpw5zdbue+++7jmmuuYdq0aV6bMK9kNPj5mqPXRWOcrLChGT36FqxWK488ksQff/yvzHO6d7+MBx54kB07vuWRRybzwQfv0LfvAG6//W4OHfofFkvFU3F7SlhYOPPmLUTTVGbMeIz333+HBx54COCcNpgSBoOBl19eQLNmLXjllbk8+ugUjh49wosvznNWTd18861MmfIo27Zt5rHHHuSbb7by9NPP07t3XwDuvz+J8eMnsHHjeqZOfZAtWzYxceJkJkx4oMJ427fvwPz5i8jKymT69KnMnTuLqKgYFix426WqyxtKpkeXNTWqT9G8PGvb2rVrefvtt7FarYwcOZLx48czfvx4kpKSOHXqFA888ADt2rVznt+5c2dmz55d5df3RElj/nwTs2f7kbJoOdETxpKx5Xvsbo4C9hRv3dWcOnWUuLiWFZ5Tn0oavqCqcR04sJ/CwkIuvbSHc9+xY0cZM+YG5s59hSuv7OOVuOpaZXFV5W9U/9t/adIngdNLP8AyzL2q7vI0tpKG18dpJCYmkpiY6LJvyZIlAMTHx/P77797IywXZrNCaKhGQEbxFCIyGlzUoRMnjjNnzrPce+8kOnToSEZGBsuWvUvz5i247LIEb4dXrzgXYpKSRrV5PWnUB44xGiq6U6fQjEa0SM/UhQpRFYMHD3V2Y12yZBGBgYH06JHA/fcnFXf/FVWlFvfekqlEqk+SRhWULPOqSz7pKGVI/25Rx0aNGuMy55OopoAAtIAAKWnUgG/2j/QxZrOOmBjNsfiSVE0JUa/JpIU1I0mjEprmKGnExJQs8ypJQ4j6TCYtrBlJGpXIzYX8/OI2jeRkWbFPiHpOjZCSRk1I0qhEydrgzcKy0eXmoMbJZIVC1GcyaWHNSNKoRMna4C0MJd1tpaQhRH3mnLRQVIskjUqUlDTOp2SZVylpCFGfSUmjZiRpVKJkCpEoywlABvaJuuflSRsaHDUiAqWwEAoqXvlQlE2SRiXMZh1+fhrBp08BUj0lSl155aWsXPkhAOvWreXKKy8lKyur3PNnz36asWNHuXWNb7/dxksvPe/cfuedt7n66quqF7AAHCUNQEob1SSD+ypRumLfSdTgELRg35wCWXjXFVdcyVtvvUdwcPWn4i/L6tUrCQwMdG4nJl5Pz55XevQajY165qSFUt3sNkkalTCbSxZfOiUr9olyRURElLsKnifFxMQSExNb69dpyM4sadi9HEt9JEmjEikpCm3bqqVTiIh6b/bspzlwYD8ffeS6HOldd42lVavWzJjxLHl5uSxZ8hbffruN9PQ0goODSUjoxeTJj7is1V1i3bq1PP/8M3z55deEh4djs9lYsmQRX331JYWFhSQm/gtVdf2KysvLZdGiN8u9xqRJ97B37y+Aoyrsk0++YN26taxatZxNm74FwGaz8dFHy1m37gvM5lM0a9acW2+9g0GDhgCQnHySG28cxty5r/LZZ5+wb98vhISEMnz4SG677a5yP6P09DRee+1lfvnlJwoLC2nXrgPjx0/gkjNWrdy+fQvLlr3HkSN/0aRJJImJ1zN27B3OJQy2b9/Khx86joeGhnHNNddxxx3jMRgcXzsjRyYyYMAg9uzZzbFjR7jzznsYNWoMx4//w8KFr/Hzzz+h1+vo1esqHnjgYaKimpQZq7vUcJkevSakTaMSZrPOUT0lU4g0GFdfPYR//jnG4cOHnPtOnjzB//73GwMHDgbgmWem891327nvvkm8+uob3HTTrWzatJ73319apWssWPAKn366iltvvY2nn57N4cOH2Lx5k8s5Tz31ZIXXePjhx7noonbEx1/MW2+9R2Rk1DnXmTXrKT74YCmJicOZO/dV4uMv5tlnp7N27RqX8+bMeYZOnTrz4ouv0avXVSxZsoidO78vN/7nn3+WEyf+4YknZjJ37iv4+/szdeoU59ri27ZtZtq0qVxwQVuef/5lRo4czbvvLmb58g8A+Pzzz5g27VHat+/I88+/zA03jOKjj5bz/PPPuFxn1arlJCT0ZMaMWSQk9CQjI53777+bU6eSmT79GR555AkOHPiVhx6aiNVqrdJnXxnnTLfSplEtUtKoQGEhZGUpxMXYZQqRcvitXon/R8sBxzyO3ujoU3jzrRSNrvpkft27X0aTJpFs3fo1bdteCMDmzZsIDw/nsssup6ioqHiBpidISOgJQLdul3LgwH7nnX9FsrNP8/nnnzF+/ATnJIPdu1/GyJGlSwA4rmGr8BqtW7chMDCIwMBAOpexfsuffx5m8+aNPPLIE1x//Q0A9OiRQG5uLm+/vZChQ0uv16/f1dx1170AXHJJd7Zt28wPP3zPFVf0KvM97Nv3C7fddhdXXtm7OJa2rF69goKCAkJDw/jgg3fo3v0ynnxyJgCXX34F6enpHDiwD1VVWbJkEQMGDOKRRx53xhUUFMzLL89hzJhxzs+9RYuW3HnnPc7rvvXWG1gsRcyb9ybh4Y4ZaTt27MzNN49g06YNDBo0tNLPvzJS0qgZKWlUoKS7bcvgVBSrFbu0aTQIer2e/v0HsnXr1859W7duom/fgRgMBvz8/Jg3byEJCT1JTj7Jrl0/sGrVco4c+RurtfLV+g4ePIDdbichofQL2c/Pz+UL2s/PjwUL3qz2NQBncunff6DL/oEDB5GVlcnRo38793Xq1Nn5WKfTERUVTUEFXU47d+7C0qVvMXPmk2zYsA6TycjEiZOJjY2jqKiQQ4f+oFcv115c99+fxAsvzOPIkb/Jyso8J66rr3aU4vbtK028rVq1cTnnl19+plOnLgQHB2Oz2bDZbMTExNKqVWt+/nlXVT6WygUFoRmNUtKoJilpVKAkaTTXFY/RiJWkcbai0WOcd/m+uuJbWQYOHMKnn67mzz8P4+/vzx9//I/Jkx9xHv/uu+0sWPAqJ0+eIDw8nHbtOuLn539Ou0RZcnIcq6WV3CmXaNLEdR2Wb77ZzmuvvVytaziuk41eryc0NMxlf0SE4zp5eXkEBDh6Xvn7+7ucoyi6Csd/PPvsHN57bylbtmxi8+aNGAwGrr12GFOmPEp2dnbx+yu7jaHk/UdEuB4PCgrGZPIjLy/vjFhdOw9kZ5/mv/89QN++5y4uVVb1XLUoClpYuJQ0qkmSRgVKphA5n2QA6T3VgHTuHM/55zdl27bNmEwmYmJi6dKlKwD//HOMGTMeZ8iQ63jjjbudvZVmzHicI0f+qvS1w8IcX+KZmRlERUU7958+fdr5+J9/jjFt2tRqXwMgNDQMu91OdvZpl8SRkZHuEkd1hIaGMXnyw0ye/DCHDv2PjRvXs2rVcs4773xGjLgRgKyz7tRTUswcP/4P4cXVP5mZGS7Hc3JysFiKzklyZwoKCiYhoSd3333fOcdCQjzXnVmNiEA5Xf6YGlE+qZ6qQMkUIlFFMhq8IRowYBA7d37P9u1bGThwkLPXzx9//I7VauXWW29zfpkXFBSwf//eKrXZdO4cj8lkYvv2rc59NpuNn3/+0bld1Wvo9fpyr1OS5LZs+dpl/+bNG4mIaEKzZi0qD7YMWVmZjBhxrTP+Cy9sx8SJk4mLOw+z2UxgYBAXXNCWTQr1rwAAHX9JREFUHTu+dXnep5+u5tlnZ9CyZSvCw8PLjMsR98UVvqejR4/Spk1b2rfvSPv2HWnd+gLefXcx+/btrdb7KYtMj159UtKoQEqKgk6nEZpXXNKIldHgDcmgQdewfPn7AEyd+qRz/4UXtkOv17No0esMHz6SrKwsVq36kIyMdEwmU6WvGxQUzM03j2X58vcxmUxcdFF71qz5lPT0dJo2berWNYKDgzl06I/iuv7OLtdp2/ZC+vbtzxtvzCM/P5+2bS/k22+3s3nzRh566DF0uurdE4aHR9C8eQvmz3+ZgoJ8YmJi2bnze5KTT9K7d18Abr/9bmbMeJwXXphN//4D+PPPw3z66Sruvz8JvV7PHXeMZ968lwgNDeOqq/pw+PAh3n33bfr1G0ibNm3Lvfbo0bewfv3/8cgjSdx4400YDAZWrVrBgQP7ue++idV6P2VRIyLQJSd77PUaE0kaFTCbFaKjNQzmU6hR0WA0ejsk4UGtW7ehTZu2WK0WLrqovXN/ixYtmTbtGd57bzGPPjqZJk0iSUjoxbXXDuPVV18kLS3VpdqpLHfffR9+fn785z+fkpOTTZ8+/Rk2bDi7d+9yXuOpp55l6dK3K7zG6NG3MHPmkzzySBLz5y865zpPPfUcS5e+xccfryQ7+zQtWrTiqadmMWjQNTX6bJ5+ejYLF85n0aIFZGdn06JFS2bOfI7LLrscgH79BvLss3P54IOlrF//JbGxcUycOJkbbhgNwA03jMbPz59Vq5bz5ZdriIyM4qabbuX22++u8LpxcXG8+eZSFi1awLPPPoWiKLRr157XXnuTiy5q57E2My08At1v//XIazU2itbAZ0NLT89FVd1/i9HRIVx9tY2UFIVdsdeiS04ma8t3tRCh+3GlpubU+XVPnTpKXFzLCs/x1YZwics99TWuqvyNlgia8Tj+Kz4k/a8TNY7LW/8nK1PduHQ6hcjI8tuPpE2jAqXzTskUIkI0JFp4BLrcHPDQgMHGRJJGBVJSHMu86mUKESEaFOcAvwpmJRZlk6RRDrsdUlMV4iIt6NJSJWkI0YDIVCLVJ0mjHKmpoKoKrQNKlnmVpCFEQyFTiVSfJI1ylPTGa2mQgX1CNDSlJY2MSs4UZ5OkUY6SpHGeehwAu0whIsuOCp/l7t+mlDSqT5JGOUqSRrS1pKTRuFf40usNVZ5IT4i6ZrVa0OurPuxM2jSqT5JGOUqSRljeSTSjEa2JZxaAqa+Cg8PJykrFYimSEofwGZqmYbEUkZWVSnBweOVPKHleaBiaokhJoxpkRHg5Tp2CiAgNU2rxOhrVnJKhoQgICALg9Ok07HZbmefodDpU1fcGhUlc7qlvcen1BkJCIpx/o1V8MbTwcClpVIMkjXIkJ0NMjOpYfEnmnAIciaOi/5gNbWRsbZO43OPpuNTwCBRJGm5r3LfPFXAkDc2RNBp5e4YQDZEWITPdVockjXIkJ+OYQiQ5GXuclDSEaGg0KWlUiySNMmiaI2m0iMhGl5uDGiclDSEaGlXW1KgWryeNtWvXMnToUAYNGsSKFSvOOf7bb78xYsQIBg8ezLRp07DZym6E9aTTp6GoCC4IKFl8SUoaQjQ0WoSUNKrDq0nDbDYzb948Vq5cyZo1a1i9ejWHDx92OefRRx/lqaeeYsOGDWiaxscff1wHcTk+luaG4ilEpE1DiAZHDY9AOX3aMdGcqDKv9p7asWMHCQkJhIc7+lcPHjyY9evXM2nSJABOnDhBYWEhXbs6lrUcMWIECxYsYMyYMVW+hk6nuB1Xbq6Oli2hVXg2tGwJLVtW63Vqiy/FcjZfjU3ick+jiKtVS5QWLdDn56KFVX2MR1ka0udV2XO8mjRSUlKIji5dAS0mJob9+/eXezw6Ohqz2ezWNSIi3Oi7XWzIEDhyBGAUzBhFzf6cPK+iBVK8zVdjk7jc0yjimjQBJk3AE8N2G8XnVcyr1VOqqqIopVlN0zSX7cqOCyGEqFteTRpxcXGkpqY6t1NTU4mJiSn3eFpamstxIYQQdcurSaNnz57s3LmTjIwMCgoK2LhxI71793Yeb9q0KX5+fuzevRuAzz//3OW4EEKIuqVoXp59bu3atbz99ttYrVZGjhzJ+PHjGT9+PElJScTHx/P7778zffp0cnNz6dSpE3PmzMFkMnkzZCGEaLS8njSEEELUH14f3CeEEKL+kKQhhBCiyiRpCCGEqDJJGkIIIaqs0ScNX5wwEeCNN97g2v9v7/zjqT77P/6SX4VkttaalHR33I0lRZEfJRFx0Ggo3NIvqnska9RdWULRaqulybrZYzRli0e2WGxRaLQK1ZZKND9K8vP4/ev6/tF9PrdP59DR7Rz7ruv5ePjD9eNcr/P+XOd6fz7XdX3el60tbG1tERkZKTTf3NwcDg4OcHBwEKpdHHh4eMDW1pZpt7i4mJWfn58PLpcLKysrHD58WCKakpOTGT0ODg6YN28e9u7dyyojaXu1trbCzs4OVVVVAESzS01NDVavXg1ra2v4+vqira1N7LpOnz4NOzs7cLlcBAcHo7tb8Bz4lJQUmJiYMLYTx3V9XldwcDCsrKyYNjMzMwXqSOK3OVBXTk4Oq58ZGhpi48aNAnXEbS9hY4NE+xd5hXn8+DExNzcnjY2NpK2tjXC5XHLv3j1WGVtbW3Ljxg1CCCHBwcEkMTFR7Lry8vKIi4sL6erqIt3d3cTT05NcuHCBVWbjxo3k+vXrYtcykP7+fmJiYkJ6enqE5nd0dJBFixaRP/74g/T09BBvb2+SnZ0tUY13794llpaWpL6+npUuSXsVFRUROzs7oq2tTSorK0W2y4YNG8j3339PCCHk888/J5GRkWLV9eDBA2JpaUl4PB7p7+8n27dvJ3FxcQL19u7dS9LS0kZUy1C6CCHEzs6O1NbWDllP3L9NYbr4PHnyhFhYWJDy8nKBeuK0l7CxIS0tTaL965V+0hgYMFFBQYEJmMhHWMDEgfniYuLEiQgKCoKcnBxkZWUxY8YM1NTUsMrcunULMTEx4HK52Lt3L7q6usSu68GDBwAAb29v2NvbIyEhgZVfUlKCadOmQV1dHTIyMuByuRKx10BCQkKwdetWqKqyIwpJ0l5nzpzBnj17mOgFotilp6cHV69exbJlywCIp689r0tOTg579uyBkpISpKSkwOFwBPoZANy8eRMpKSngcrkIDAxEc3OzWHV1dHSgpqYGO3bsAJfLxZEjRwTOBpfEb/N5XQOJjIyEq6srNDQ0BPLEaS9hY0NFRYVE+9cr7TSEBUwcGBBxJAImvgwzZ85kfgwVFRVIT0/HokWLmPy2tjbMmjULH374IVJSUtDS0oLo6Gix62ppaYGRkRGOHTuG+Ph4JCUlIS8vj8l/kT3FTX5+Pjo7O2FjY8NKl7S9wsLCoK+vz/wvil0aGxuhpKQEGZlnMUTF0dee16WmpgZjY2MAQENDAxITE2FhYSFQb+LEidi0aRPOnTuHyZMnC0z9jbSup0+fwtDQEOHh4Thz5gx+/fVXfPvtt6w6kvhtPq+LT0VFBQoLC+Hp6Sm0njjtJWxskJKSkmj/eqWdxp89YOK9e/fg7e2N7du3s+5oFBUVERsbixkzZkBGRgbe3t7IyckRux49PT1ERkZi/PjxUFVVhbOzM6vd0bZXUlIS1qxZI5A+WvbiI4pdhKVJyna1tbX4xz/+AScnJyxYsEAg/9ixY5g3bx6kpKSwbt06XL58Wax61NXVcezYMbz55psYN24cPDw8BK7XaPa106dPY9WqVYNGppCEvQaODerq6hLtX6+00/gzB0y8du0avLy8sG3bNqxYsYKVV1NTw7rzIoQwdxDi5Ndff8WVK1cGbfdF9hQn3d3duHr1KpYsWSKQN1r24iOKXVRVVcHj8dD3nwOBJGW7srIyuLq6YsWKFdi8ebNAPo/HQ3x8PPM/IQTS0tJi1VRaWooff/yR1ebz12s0f5s//fQTli9fLjRPEvZ6fmyQdP96pZ3GnzVg4qNHj7B582YcPHgQtra2Avljx45FVFQUKisrQQhBYmIiLC0txa6Lx+MhMjISXV1daG1tRUpKCqtdXV1dlJeX4+HDh+jr68P3338vsQCTpaWl0NDQgIKCgkDeaNmLjyh2kZWVhb6+Ps6fPw8ASE1NFbvtWltbsXbtWvj5+cHb21toGQUFBXz55ZfMLrmEhASx244QgvDwcDQ3N6OnpwenT58WaHO0fpsNDQ3o7OyEurq60Hxx20vY2CDx/vVSy+d/Ic6dO0dsbW2JlZUVOXHiBCGEkHXr1pGSkhJCCCG///47cXJyIsuWLSMBAQGkq6tL7JpCQ0PJnDlziL29PfN36tQplq6MjAxGd1BQkER0EULI4cOHibW1NbGysiLx8fGEEELs7e3J48ePCSGE5OfnEy6XS6ysrEhYWBjp7++XiK4ffviB+Pv7s9JG217m5ubMrpvB7LJjxw6SlZVFCCGkqqqKuLu7ExsbG+Lt7U2amprEqisuLo5oa2uz+tmnn34qoOvq1avE0dGRWFtbEx8fH9LS0iJWXYQQkpCQQGxsbIilpSWJiopiyozGb3OgruLiYrJy5UqBMpKy12BjgyT7Fw1YSKFQKBSReaWnpygUCoUyPKjToFAoFIrIUKdBoVAoFJGhToNCoVAoIkOdBoVCoVBEhjoNyqDcvn0bu3fvhrW1NXR1dTF37ly4uroiMTFRYtF+R4KCggJoaWkhLCxMrO0cPXoUWlpayMrKYtL6+vqQkJCA9vb2EW+vqakJxsbGuHDhAgCgqqoKWlpaAn86OjowNjbG2rVrmX36f2UOHz4MFxcXgXhVlJFBcq/FUv7f0N/fj6NHj+L48eOQlZWFmZkZzM3NwePxkJubi7179yIjIwOxsbEYO3bsaMv90zB//nxs2bIF06dPZ9K2bduG9PR02Nvbj3h7ERERUFdXh5WVFStdTU2NFUWgvb0djx8/Rm5uLnJzc5GTk4P9+/dLNMSLJFm/fj2Sk5ORkJAwaHwoystDnQZFgC+++ALR0dGYM2cOjhw5gkmTJjF53d3d2LFjB9LS0hAUFIRPP/10FJX+uViwYIFA7Kb6+nqxtFVYWIjU1FR89dVXAnlqamr45z//KZBeV1cHHx8fpKamQlNTU+hZEH8FlJSUsGHDBhw+fBg2NjasYH6U/x06PUVhUV5ejujoaKiqqiI2NpblMIBn4bQjIiKgpqaGjIwMlJWVjZLSV5uYmBhwOBwYGhqKXGfixIn47LPPMHbsWMTGxqKlpUWMCkcXZ2dnEELw9ddfj7aUvxzUaVBYpKamoqenB6tXr4aysrLQMrKysti1axfCw8Px2muvsfLOnz8PV1dXzJkzB3p6enB1dcUPP/wg8BlaWlrYuXMnCgsLsWrVKujq6sLExASHDh1CX18f7t+/j7Vr10JPTw+mpqYIDQ1FR0cHU5+/TpGcnIzExEQsXboUurq6sLe3x9mzZ0X6rq2trTh48CCWLl0KHR0dmJqaYs+ePayng4qKCmY95/lQ0mvXroWWlhbS0tIACK5paGlpobCwEABgYGAADw8PpKamQktLS+jpah0dHdDT04Obm9uQuu/du4fc3FxwuVyRvudApkyZgmXLloHH4+HSpUusvLq6OoSEhMDMzAw6OjpYsmQJoqKi0NraKvA5f/zxBwICArBw4ULo6elh/fr1KCsrg6WlJTw8PJhyQUFB0NLSQklJCZYvX453330Xrq6u4AeiePjwIQIDA7Fw4ULo6OjAxsYGMTEx6OnpEWhzOPqUlJSwePFiJCUliWU96VWGOg0KC34YZ1NT0yHLmZub47333mMddnTgwAFs3boVVVVVsLOzg62tLaqqqhAQEICoqCiBzyguLoa3tzdUVVXh5uYGOTk5xMTEYPfu3XBzc0N/fz/c3NwwYcIEJCQkCB1ov/nmG4SFhUFXVxdOTk5oampCcHAwjh49OqR+Ho8HNzc3xMbGYsqUKfD09ISenh7OnDmDlStX4smTJwAADQ0N+Pv7o62tDfv27WPqJyUlITc3F9bW1oMO3lu2bIGamhqAZ/PsK1asgJWVFRQUFIQ60qysLLS3t8PBwWFI7fy6L7pGg8E/I+L69etMWk1NDZydnZGUlARtbW14eXlh+vTp+PLLL+Hh4cEaeB8+fAgXFxekp6dj3rx5cHV1RWVlJVatWoWmpiahbfr6+mLq1KlwdXXFggULICUlhdu3b8PJyQkZGRkwNDSEl5cXJkyYgEOHDsHX15eJyDpcfXxMTEzQ3NyM3Nzcl7ITZRBGJIoW5S+DkZER4XA4ww5mdvXqVcLhcIijoyPrqNX6+npiZ2dHOBwOKSwsZNI5HA7hcDis40XLysqY9P379zPpPB6PzJ07lxgZGTFpv/zyC1M2PT2dSX/69CmxsLAg77zzDnMUJ7/svn37mHIhISGEw+GQhIQE1vfIysoiHA6HfPDBB0xaX18fcXFxIRwOh2RnZ5PKykoyZ84cYmxsTBobG5lyR44cIRwOh2RmZjJp7u7uhMPhkObmZiZt+/bthMPhkKKiIlbb69evJ9ra2i+0vZubG9HR0SG9vb2s9MrKSsLhcIi7u/uQ9bOzswmHwyFbtmxhta2lpUV+/vlnVtmvvvqKcDgccuDAASZt48aNAnbv6uoibm5uAu1/9NFHAm0R8uzoYDs7O/Luu++SmzdvsvLCw8MFrs1w9PH5/fffCYfDIaGhoUPagzI86JMGhQV/nltRUXFY9fhTQtu3b2c9faiqqmLbtm0AgO+++45VR05ODqtWrWL+19TUZKa7BobqVlJSwowZM1BfX4/Ozk7WZ+jp6cHa2pr5//XXX8fGjRvR29uL9PR0oVp7e3uRmpqKmTNnYvXq1aw8CwsLzJ07F5mZmcy0x5gxYxAeHg55eXmEh4dj586daG9vR3h4OFRUVEQz0AAcHR0BgJnWAp6F3M7Ly4O5uTkmTJgwZP3ffvsNGhoaL31OA//wIP73e/LkCS5duoRFixbB3NycVdbd3R2TJ09mrm9DQwNycnKgr6/PsrucnBwCAwMHbZN/zCif4uJi3L17F87OztDR0WHl+fn5QVZWlmlzOPoGoqmpiTFjxuDWrVtD2oMyPOjuKQoLFRUV1NXVoaWlReCc7aG4c+cOxowZg3nz5gnk8dPu3LnDSp88ebLA6WcKCgpob28X2PEiLy8P4NnurYHbfIWdNDd79myh7fEpLy9He3s7+vr6hE5jdXV1oa+vD6WlpYx2TU1NfPDBB4iKikJFRQXc3Nxe+jwCQ0NDvP3228jIyEBwcDCkpaVx/vx59Pb2vnBqqr29HR0dHQJrScOhra0NAJizR3777TcQQtDU1CTUHrKysnj06BFqa2tx9+5d9Pf3MzYeiK6u7qCHW/Gn6fjcvn0bwLO1EWFtKioqorS0FISQYekbuHFDTk4OSkpKaGxsHMwUlJeAOg0KC3V1ddTV1eHhw4dDOg0ej4eOjg7m9K/W1lbIy8sLPQJz/PjxGDduHGshGwDGjRsn9LMHO0ZTGMJOH+M7HGELpMB/n6YePHiAzz//fNDPbm5uZv1vaWmJgwcPghACPT09kTU+j5SUFLhcLmJiYlBQUICFCxfi3LlzUFFReaEj4vF4AAa3nShUVVUBAHOQEN8eRUVFKCoqGrReU1MTMwC/8cYbAvnS0tKD9pnn3+fht3n58uUhj0Nta2sblr7nd/uNGzdO4DpS/jeo06CwMDU1xfXr15GXlzfkwHj69GlERUXB19cX/v7+UFRUREdHB3g8HsaPH88q29XVhc7Ozv/p7ngwurq6BNL4g8xgU0f8qTcHBwdERkaK1A4hBLt27QIAKCsrIyIiAqampsN6GhuIo6MjYmJikJ6ejmnTpqG4uHjIc6f58L8T33m8DPzT7vjXl//EsWnTJvj5+Q1Zt7q6GsDgDpn/FPMi+G2GhYXB2dlZpLKi6HseHo/3wuk+yvCgaxoUFlwuF7KyskhISBh0YOro6EBycjIAwNjYGADw97//HcCzc8Sf59q1ayCE4G9/+9uI671586ZAGv9uVFdXV2id6dOnQ05ODrdv32a2fg4kPj4e0dHRrGmNU6dOoaCgAO+//z7+9a9/obGxER9//PFL69bU1MTs2bNx8eJFZGdnA8ALp6aAZ9N0ysrKLz3lUlNTg4sXL0JZWRmLFi0C8GxrMIBB5/6PHDmCEydOoLu7G9ra2pCSkkJJSYlAufv374vsNIZqs6enB/v372fesRiOvoF0dXWhvb0db731lkiaKKJBnQaFhbq6Ory8vNDY2Ih169YxW0/58Hg8BAYGoqKiAubm5jAwMAAAvPfeewCAQ4cOoaGhgSnf0NDA3M2LMigOl8zMTJajqqurw/Hjx6GgoAAbGxuhdeTl5bF8+XLcv38fcXFxrLyCggJERkbiu+++Y+5Qq6urcfDgQbzxxhsIDAyEg4MDjIyMkJGRgR9//HFIfbKysgAg9L0DR0dH1NXV4eTJk5g2bRrmzJkj0neeOXMmKisrhT5lDUVjYyMCAgLQ09MDX19fZspIXV0dBgYGuHTpEjIyMlh1UlNTcezYMVy+fBlycnKYNGkSjI2NkZ+fj5ycHKZcd3e30G3Vg2FgYIApU6bg22+/xY0bN1h5J06cQFxcHLPuMRx9A7l79y6A/97QUEYGOj1FEWDr1q2or6/H2bNnYWFhgcWLF2Pq1Kmora1FXl4eGhoaMHfuXNbUjoGBAdasWYO4uDjY29szu1wuXryIuro6rF+/nnEwI4mioiK8vLxgbW0NJSUlZGVl4enTpwgNDR0yfMRHH32EGzdu4MCBA/jpp58we/Zs1NbW4sKFC5CRkUF4eDjGjBkDQgizW2rfvn3MC48hISGwt7fHxx9/jPnz5w869cafY9+xYweMjY1ZsZBsbW0RERGB6upqoWE/BmPx4sW4du0aSkpKhNq0urqatWDc2dmJ6upqXL58Ga2trVixYgXWrFnDqrN3716sXr0afn5+MDMzw8yZM1FeXo7s7GyoqKhgz549TNmdO3fCxcUFvr6+WLp0KSZNmsT0C+DZbrMXIS0tjQMHDmD9+vVwd3eHhYUF1NXVcevWLfzyyy+YMmUKAgICXkofH/57KPynYcrIQJ0GRQBpaWlERETA1tYWSUlJuHPnDnJyciAjIwMtLS34+flh5cqVAls+g4KC8M477yAxMRFpaWmQkZHBrFmzsHv3boGgeiOFvb09pk6dipMnT6KpqQmzZs1CWFgYM/UyGKqqqjhz5gxiYmKQmZmJr7/+GqqqqliyZAk2bdrE3J2ePn0aV65cgYmJCWxtbZn6Ghoa8PHxwWeffYbQ0FAcOnRIaDs+Pj4oKytDXl4eKioqWE5DRUUFRkZGuHTp0rCewiwsLPDJJ58gNzd3UKcxcIFfVlYWr732GubPnw8nJycsXbpUoI6mpibOnj2L6Oho5OTk4MqVK3jzzTfh4OCAzZs3M4vm/LLffPMNPvnkE+Tn56O3txeGhoY4fPgw7O3tRV6k19fXR3JyMo4fP44rV67g4sWLeOutt+Dh4QEfHx/WYvtw9PHJy8uDsrLyS+9yowhHigib1KVQ/uQUFBTA09MTnp6e2Llz52jLeSn6+/thbm4ONTU1nDp1alh1165di7KyMvz8888i3dmPFP39/aisrMTbb7/NTL3xqaysxNKlS+Hm5oaQkBCJaRJGbW0tzM3NsWHDBvj7+4+qlr8adE2DQhklkpOT8fjxY7z//vvDruvr64tHjx4NuV1VHEhJScHR0RFcLldg4fnkyZMAhL87I2nOnj0LeXl5GhpdDNDpKQpFwvj7+6O0tBTl5eXQ1NRkTXuJir6+PpYvX44jR47AzMxMYmdjSElJwdXVFf/+979hb28PMzMzSEtL4/r16ygqKoKJiQnrTfHRoKWlBfHx8di8efNLb4mmDA590qBQJMzrr7+OmpoazJ49G9HR0QLTPKKya9cuPHr0aNBwKeLiww8/ZDYFpKSkMJFkt23bhi+++GLUD3eKjY3F1KlTBRb7KSMDXdOgUCgUisjQJw0KhUKhiAx1GhQKhUIRGeo0KBQKhSIy1GlQKBQKRWSo06BQKBSKyFCnQaFQKBSR+T9asdlB6lzlWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 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",
    "                                          'polynomialfeatures__degree', \n",
    "                                          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', fontsize = 16)\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('Complexity (Degree)', fontsize = 20)\n",
    "plt.ylabel('Score', fontsize = 20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This shows precisely the qualitative behavior we expect: \n",
    "\n",
    "- the training score is everywhere higher than the validation score; \n",
    "- the training score is monotonically improving with increased model complexity; \n",
    "- the validation score reaches a maximum before dropping off as the model becomes over-fit.\n",
    "\n",
    "The optimal trade-off between bias and variance is found for a third-order polynomial; \n",
    "- we can compute and display this fit over the original data as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:17.364864Z",
     "start_time": "2020-05-18T14:04:17.163235Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Notice that finding this optimal model did not actually require us to compute the training score, \n",
    "- 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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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",
    "\n",
    "For example, let's generate a new dataset with a factor of five more points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-07-31T03:14:58.131419Z",
     "start_time": "2024-07-31T03:14:57.890100Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'make_data' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-e192003f084c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m200\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mravel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'make_data' is not defined"
     ]
    }
   ],
   "source": [
    "X2, y2 = make_data(200)\n",
    "plt.scatter(X2.ravel(), y2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We will duplicate the preceding code to plot the validation curve for this larger dataset; \n",
    "- for reference let's over-plot the previous results as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:18.229455Z",
     "start_time": "2020-05-18T14:04:17.578243Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree = np.arange(21)\n",
    "train_score2, val_score2 = validation_curve(PolynomialRegression(), X2, y2,\n",
    "                                            'polynomialfeatures__degree', 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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It is clear from the validation curve that the larger dataset can support a much more complicated model: \n",
    "- the peak here is around a degree of 6, but a degree-20 model is not seriously over-fitting the data \n",
    "- 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: 1. `the model complexity`, 2. `the number of training points`.\n",
    "\n",
    "A plot of the training/validation score with respect to the size of the training set is known as a **learning curve**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "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: \n",
    "    - 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: \n",
    "    - 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.\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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![](./img/figures/05.03-learning-curve.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Learning-Curve)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The notable feature of the learning curve\n",
    "- The convergence to a particular score as the number of training samples grows.\n",
    "    - 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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Learning curves in Scikit-Learn\n",
    "\n",
    "Scikit-Learn offers a convenient utility for computing such learning curves from your models; \n",
    "\n",
    "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": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:19.382826Z",
     "start_time": "2020-05-18T14:04:18.231235Z"
    },
    "code_folding": [
     6
    ],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4nc4K5bm5ucFR6vv06dPY1SMiIqImhm0LImpITSYUsdvtmDRpEk6ePFmhbP/+/Zg2bRrGjRuHBx98sNJRlomocURHRyM+Ph67du3Cs88+C7fbHSw7c+YMFi5cCK/Xi4svvjh4iz0iIi2wbUHUNLBtQUQNqUlcPrN371489NBDOHbsGNatW4f27dtHlE+aNAmPPfYY+vfvjwceeAAXXHABbrzxRo1qS0Tbtm3DnDlz4PF4EBsbi44dO8LpdCIzMxM+nw+dOnXCG2+8UeFvmYiosbBtQdS0sG1BRA2lSfQU+fDDD/HII48gNTW1QtmpU6fgcrnQv39/AMC0adMqvSc6ETWeoUOHYs2aNbjhhhuQlpaGY8eOITc3Fz169MCCBQuwfPlyNlqISFNsWxA1LWxbEFFDMWpdgZp4/PHHqyzLyclBSkpKcDklJQXZ2dmNUS0iqkbHjh3Bm1sRkV6xbUHU9LBtQUQNoUn0FKmOoiiQJCm4LISIWCYiIiI6H2xbEBERtRxNoqdIdVq3bo3c3Nzg8tmzZyvtCludgoJSKIruh1ZpUZKTY5CXZ9e6GhSGx0R/eEz0icelbmRZQmJitKZ1qI+2BQC8/74bX3whY/duI0pLJRiNAv36+XHZZeqjVy8FcpP/earp4N+mPvG46A+Pif7wmNRdde2LJh+KtGvXDhaLBd999x0GDRqElStXYsSIEef1GooiGIroEI+J/vCY6A+PiT7xuDRt9dG2AIDx47248koBrxfIyDBg82YDNm0y4tNPLQCAVq0UjBjhx+WX+zBqlB9pafzeNDT+beoTj4v+8JjoD49Jw2myv0/Mnj0bP/30EwDgmWeewZNPPonx48fD4XDgpptu0rh2RERE1NQ0VNvCZAIuu8yPBx7wYONGB/bts+Nf/3Ji1Cg/vv7agHnzotCvXwxGj7Zh0SIzvv3WAI+nvj4VERERVadJ3JK3oeXl2Zm86UxKSixyc0u0rgaF4THRHx4TfeJxqRtZlpCcHKN1NepFTdoXigLs2ydj82YjNm0yYNcuA3w+CdHRAsOGqb1ILr/chy5dBIQAPB714XZL8HoBtxvweKSyKeD1hubdbim4vccjla1Tt/F41PcWQp2qDym4HLk+9AitlyLWSRLQt68fQ4f60a+fAqMO+yLzb1OfeFz0h8dEf3hM6q669oUO/8siIiIiahlkGejXT0G/fh7Mnw/Y7cDWreplNps3G7F+vRUAYDIJeL31O9irJAnIshpoyHLoUXG58u3C13k8wMcfmwAA0dECl1yiBiRDhvgxYIAfFku9Vp2IiKjeMBQhIiIi0omYGGD8eD/Gj/cDcOPoUQmbNxuRlSXBbAYsFjUgsVgAsxkwm0XZFLBYQvOB9ep2FbcxmdRAoz5lZ0vYscOAbdsM2LHDgCeeUJMQi0Vg0KDQALODBvkRre1YukREREEMRYiIiIh0qmtXga5dvVpXo0bS0gSuvtqHq6/2AQDy84GdO43BkGTJEjP+8Q/1LjwXXaRg6FAfLrvMj0sv9SMuTuPKExFRi8VQhIiIiIjqXVIScNVVPlx1lRqSlJQAu3erPUm2bzfi3/824/nnJciyQN++SvBymyFD/EhO5lhvRETUOBiKEBEREVGDi40FRo/2Y/RoPwAPHA7gu+8M2L5d7Uny9tsmvPyyGQDQs6cf3bsrSEwUSEgQSEhA2Lz6CCxHR9f/pUBERNRyMBQhIiIiokZnswHDh/sxfLgfgHpnnL17ZWzfbsSOHQYcOSKjoEBCQYEEj6fq1MNkEoiPD4QkofAkMTF8vUDbtkBRkeGc9RKi5glLYBDa8IFnqxqQtvy2lW0fWA5sH5hX36vmj4CqBssNf9/y08A8EVFLwVCEiIiIiDRnsQCXXqrg0ks9WLAgtF4IwOkECgvVgKSoSJ2qyxXXZ2VJ2L9fDVTs9vJn97ZG/UxNWSCUCQ9MoqMF+vdXcPHFflxyiR8DB/oRG6t1TYmI6oahCBERERHpliSpvUpsNoG2bc9vrBGvFygqklBYCJjNMSgsLK3xe9aEEICilH+oT664HpWsl6AoodcR4tyPwPuqD6nabcLfM/w9Au8d/pzIMlQoUxQ1gPruOwOeftoMISRIkkDv3mpIcvHF6qC5XboI9jQhoiaFoQgRERERNUsmE9CqlUCrVkBKCpCbq2hdpWahuFgdDyYjw4Dduw345BMT3nlHHQ8mOVnBxReHepNcdFHTuAWzoqg9klwuCU4n4HSqU68XMBrVh8kEGI2ibBpYJyLKDee+QotqQFEAlwtwOCKPR2BqMgFWq4DVCkRFqbcpt1rVdVFRPA50fhiKEBERERFRjcXFAZdf7sfll6vjwSgKcPCgjIyMQFAiY/16CwDAYFDvLnTJJf5gUNKhQ+16k3i9gN0O2O1S2UOdLy1V50tL1fnAybPLFXky7XCElsuHHy5X/XRvkaTKQ5NAYGI2qyftUVHq1GarfFpZuc0WWh8VpS5brQI+n/rZHQ41RFAfgf2B4LLDIZXbLrAu8nlCAEZjNIxGtb7qFMFlkwllj/D5qsskCRHHIvA+5YOOyACkbsfDZAoEJer+CgQogeCk/FSS1O+x3y/B5wP8fnU5NB9aH1kmldtOnZckBI9TILgJP66hegWOcWC7UJnNFnouAJSWquWyXB/fVAonCSHOrx9iM5SXZ4eitPjdoCspKbHIzS3RuhoUhsdEf3hM9InHpW5kWUJycozW1agXbF/oC/82G1d+fmRvku+/N8DhUE90U1PVniQDByqIjbUgO9sdEXKUny8tVefd7pqfKKsnn6LciWkgTIg8QQ0vD5ygBtYbjepJrtcrlU3Vk1+vV4LXi7B1kcs+nxQ2H/n88kFNeBjgcKiv1VACnz86OhS0RC4LREebUVLihder1tfjUT+POgU8HqlsirJtpOC24cseT+hyMqOx8lCnqhAofLn8OotFrUcgaHG71VBLXVbnA+sCyy5X+DRyndMZCILU4MpgUIMHo1GEzYfKDAZRbruK69WeLhWDufBA7ny+z5Udw+pCtfAQLbCfy2+jBl0iWP9AkBdYF1ovgqFeYH1VwYwQ6qDZgUAufBoI4CLLwssj17lcUo0vKwxcKljZpYWB1+jZUyAjo/KKs6dIE+L3o0LyHf6HVvm6iml4375+zJnjhZFHn4iIiIgaQFIScMUVflxxhdqbxOcD9u+XsXu3GpJkZBiwdq0JACBJZkRHAzExouyhznfsqIStr1geEyMinhcdrQ4Ga7U23V/ThQgEJ6GwpPxUDU9C68zm8BNfdR9UHnjUbL+kpJiRm+uql88T6D1hMtXLyzUrfn/l52/h00DQYzBEISfHHexhU9m0oEDCqVOR341AEFnfwntEBcISv1/tzXI+oV5UlCj7vqrf28DfcGqq+ndc/o5Zld2dq7pH+HPbtxcALJXWg6fFGnG7gbw8CWfPqo+cnMC8HFwXeNjt6h9Edbejq47RGOp6ZTYDH39swvr1Rvz7367zHrCMiIiIiOh8GY1Av34K+vVTcPPNXgDq2CRpabEoLbU32RCjvkmS+gu+2QzExwfa6U23vR7oOUEVGQwIhgCqqo+zOiaS57zfI3D3rvIBisMhBXs9+Xyhnk2Bh7o+cp3PJ4VtX3GdLCMinAwEcuFhR/h8Y4/9IssSGIpU46WXTCgpCQ2eFD5YUvjgSYHrAsOvEyy/TpKA/Hw1zMjNjQw31GU19CgurjzgsFoFUlIEWrUSSEsT6NNHQVyciBhIKPy6tPABhcLLwqflk9mPPjLinnusGD3ahqVLXbjySn8j7GUiIiIiopC4OCAmRj1pI6L6F373ruRkoCkHbA2JoQiA118347ffGq5rUXKyKBv5XOCii/zB+dBDCQYh0dE1vw1cbV1/vQ8DB5Zi9uwo/PGPNsyZ48HDD7thNjfs+xIRERERERHpCUMRABkZpfB6RXAgpPKDIQW6BlU3eFJgWVGAxMRQb4+kJKHLLmPdugmsXevA//6vBS+/bMaOHQa88ooTXbowPSQiIiIiIqKWgaFImYrXu5UPB5pfWGC1Ak8+6cawYX7ceacVY8ZE4x//cOGaa3xaV42IiIiIiIiowXFII8LEiT5s2lSK3r0VzJkThbvussDh0LpWRERERERERA2LoQgBADp0EPj0UwcWLHDj/fdNGD/ehgMH+PUgIiIiIiKi5otnvRRkMgEPPujBsmVOnD0rYdw4G957zwTR/K4cIiIiIiIiIuKYIlTRqFF+bN7swF//asVdd1nxzTcGPPOMC7GxWteMiIio6diwYQ3sdntwuXv3dFxwQX94vV6sWfNJhe179eqLXr36wul0Yv36zyqU9+17EXr06ImSkhJ8+eXnFcr79x+Ezp27oaAgH199tbFC+aBBg9GhQyecPZuDrVu3VCgfPHgY2rRpi6ys09i5c2uF8mHDRqFVq1ScOHEc3323s0L5yJFjkZiYhN9+O4I9e76rUD5mzFWIjY3F4cMHsW/f3grl48ZNRlRUFA4c2IcDB/ZVKJ848RqYTCb8/PMe/PrroQrlU6f+HgDwww8ZOH78aESZ0WjEX/7yJwBARsYOnDyZGVFutVoxfvwUAMD27d8gOzsrojw6OgZXXDEBALB162acPZsbUZ6QkIhRo64AAGzZ8gUKCwsiylu1SsGwYZcDAL74Yi1KS+0R5WlpbXDZZcMBAOvWrYLL5Yoob9++Iy6+eAgAYPXqFfD5Isd/69SpKwYMuBgA8OmnH6I8PX/3TCYDBg68rFl/9yZNmgag6Xz3TCYDvF4/gOb93QOazr97u3fvxp49P1Yob27fvXD1/d2LiYnBDTdMr7AdwJ4iVIW0NIEPP3TigQfcWLXKiDFjorFnD78uRERERERE1HxIQvDiiLw8OxSlxe+GKu3cacDcuVbk5Ej429/cuPVWLySpYd8zJSUWubklDfsmdF54TPSHx0SfeFzqRpYlJCfHaF2NesH2hb7wb1OfeFz0h8dEf3hM6q669gUvn6FzGjzYj02bSrFggRUPP2zFN98YsXSpE0lJWtesZjwewGgEZHZ0oSZECMDhAAoLJRQUqI/AfGGhhPx8CX4/YDRakJgokJAggtPw+ehoNHiISURERETUVDEUoRpJTATeftuF11/349FHLbj88mi8/LILQ4b4G+w9hQBcLqC4WEJJiTpV56WyeaCkJHK5snK3W4LZLNC2rUCHDgratxdo316JmG/bVsBsbrCPUq+cTiA3V0JOjoTcXLlsKoVNZeTlSUhMFOjaVUHXrgq6dVMfXbooiNHwB1iXCzh1SsKJEzJycyUYDGpgpU5F2HxgvQjOV7YutK2AwQDYbPoLvzwewG5H8HtZWBgKNUIhB4LL4SGIx1N1mmG1CsTGAsXFJrjdVW9nMkWGJElJAgkJiFgXPrXZALNZwGoFLBb178Jq1d9+JSIiIiKqDwxFqMYkCbjlFi8uvdSP2bOjMHVqFO65x4M77/TAYIjcVgigtDQ8tKg8sAgEHeWX7XaguDgGXu+5f+KOiRGIi1MfsbFAcrIoO/kXiIsD4uIE7Hbg5EkZJ07I2LxZRna2EUKEXluSBFq3FmjfXg1OAoFJeHBis9X3Hg3tK5cLOHtWDTUCwUZk0BEKQOz2yvdJYqJASoqC1FSBfv0U5OdL+PZbAz76yBSxXevWoaAkFJgIdOqk1DkYstuBEydknDypBh+B+ZMnZWRmqp+hodlsAjab2kMiOjp8WtV85etsNgG/H7Db1e9t4PusLtd8fXXBBgBERYUCicREgW7dlOB8QgLKhRmhACMqKtCV0g6nExG9SELTyPWFheqx+PlndV1pac27kJhMAhaLGpSo0/D5ytaFQhWDQX1+IMgymUJBWGg+FIxFPkSw3GRS/x3yetWHxwN4vRLc7sCyBK8XZctSWbm63uMJbR++3ucD2rat/78FIiIiImoaOKYIeM1vbdjtwP/8jxUrVpjQt68fcXEiIvQoKQH8/upPuGRZDTHUMCMQbKghR1qaCSaTG3FxCCsLbR94TkwMKgQyNeF2qz0WTp4MncCHz58+LcHni6x/cnIoIElOFvD51BOswAla+LzHA/h8Utk0dPJV+XLV+yk+XiA1VUFKikBqqkBKiiibj1zXqlXVPV0cDuDYMRlHj8o4cuAsO+EAACAASURBVER9HD0q4+hRCXl5oZBClgU6dBDBXiXhvUzatRNIS4vF4cMlwXDpxAmpbD60/woKIj+L2SzQrp26zzp2DO2/jh3VzyCE+vl9PsDvV/eNzyeFzVe+Tp2PfJ7XCzid6ol+aSnKTSU4HJHrXK66X1NiswnExKjfS3WqLsfEhC8jYn0g3EhKEoiPV8ON2qrr9aUeD8r1TlH3odsNuN3lp4DLpX6nA/Nut/pddrkQ3NbjCS9T14UfO0Vp3Gt5TCY1eLFY1HmzWQ1XzGZ1XpKA06clnD0b+bfQsWPk30Jgvm1bcc5eM7zut244pgg1FP5t6hOPi/7wmOgPj0ndcUwRqncxMcBLL7kwapQPb71lhiQBHTooiI0NhRjhAUYo+Aitq26sg5QUE3JzPQ1Wf4sF6NpVoGvXyi//8fuB7Gypwsn/yZMyDh1ST/5NJgQfZrP6C7fZrP6ybbGoPQ4Cy4ETscAJWugROmFLTg719AiEHxZL3T+rzQb07augb1+lQllBAYJhiRqUqPM7dpjgcIQOTuAX/5KSyPsy22yBS5EEBg70okOHQO8adV1q6rlPIAFtThh8PlQISsLn7XYJRqP6PQ2EGuHhR3R07QI5PTGbgdRU9Tg1FkUpH3iFQi+vNxB6qQFjZDgWCsGqCjjU5fD5mo+nUliICsHhkSMytm+P/FuwWtWeaIGQJBQgCiQnC47fQkRERNTEsKcI+EuOHjEN1ZYQQE6OFDxBPHJEhsFgRqtWrrBLjNTeDjwJ1A7/ThqeEGpAGv63oAYmEn77TY7o6RUfr/Yu6dHDgMRED9q0UXuWtG4t0KaNgtatm87YReG9iAoLgaIiKWxZQlGR2ruoqEhCUZG6nwJhVHhIVdW8GgaLclN1fWIiMHlyHbpQ6QjbF/rCfzP1icdFf3hM9IfHpO7YU4SIzoskAWlpAmlpfgwdqvamSUkxIzfXq3HNiBqXJAGtWwu0bu3H734X2bPM5wMyM6WI3la//irj+++BkydNcDorJoatWilo00aUPZRyU3U+NrZ2dwwKjE/kcEhwOtWpw1FxWloqlQs5IkOPoiIpondMZWJj1fFt4uPVhySpQYrDIQUvowqM5aKO8xIa7yV8PKfKdOoETJ58/p+fiIiIqDYYihAREdWC0Ri6DG/s2FBgkpISi5wcO4qKgKwsGVlZUthUnT95UkJGhhH5+RWvL4uODgUlrVuroUMo5Kg86AgEIeczZovNFrqFc0KCQOfOSlnQod6dKD4+FHyEbxcXp3722hBCvQQqMDhuICwJD1FkWQLQQCNbExEREZXDUISIiKieSRLKbn2soHdvAKh8/CKnEzhzRsKZM2pocvp0+LyMbdtkFBdLZXdVQnAaE6OOBRO+rvJp5WXx8dpcyiNJoTsLqcIvLVHn1VCEiIiIqJY8HhiOHYXh8CEYDx+E4fAhyAYZ+O8HlW7OUISIiEgjUVFAly4CXbpUHpoQERERUeWk4iIYDh8qCz8OwVAWgBh+OwbJH2pb+du2g2/0mCpfh6EIEREREREREemPEJBPn4ro9WH49TAMhw7CkJMd2sxkgr9rN/h79YF7ylT4u6fD3yMd/u49IGJiIcsSqrqxJ0MRABs2rIHdbg8ud++ejgsu6A+v14s1az6psH2vXn3Rq1dfOJ1OrF//WYXyvn0vQo8ePVFSUoIvv/y8Qnn//oPQuXM3FBTk46uvNlYoHzRoMDp06ISzZ3OwdeuWCuWDBw9DmzZtkZV1Gjt3bq1QPmzYKLRqlYoTJ47ju+92VigfOXIsEhOT8NtvR7Bnz3cVyseMuQqxsbE4fPgg9u3bW6F83LjJiIqKwoED+3DgwL4K5RMnXgOTyYSff96DX389VKF86tTfAwB++CEDx48fjSgzGo2YNGkaACAjYwdOnsyMKLdarRg/fgoAYPv2b5CdnRVRHh0dgyuumAAA2Lp1M86ezY0oT0hIxKhRVwAAtmz5AoWFBRHlrVqlYNiwywEAX3yxFqWl9ojytLQ2uOyy4QCAdetWweVyRZS3b98RF188BACwevUK+Hy+iPJOnbpiwICLAQCffvohytPzd89kMmDgwMv43YN+vnsmkwFer5qCN+fvHtC0/t07fvxI8LgENLfvXrj6/u7FxMTghhumV9iOiIiIdMjng+35JTBt/xaQZQhJAmRZvWZWlgEpfF6CkGVAQtVlZfOSwwHDkV9hPHwIkqM0+HZKXDz8PdLhHT0Wzh491eCjRw/4O3Wp9aBnDEWIiIiIiIiI6LxI2dmIu20WzFu/hveCCwGzCZIQgCLU0dUVBZKiqPNCCa5D2bpQmQiuC07NZvi7doNzxky110d6T/i6p0OkptbuNn3VfQ4hhDj3Zs1bXp4ditLid4Ou8F7c+sNjoj88JvrE41I3siwhOTlG62rUC7Yv9IV/m/rE46I/PCb6o8djYtq2FbG3/gVySTFKnvon3H+YoXWVqlVd+6LivQCJiIiIiIiIiMpTFEQtXYL4aZMgYmNR8Pkm3Qci58LLZ4ioyZMzj8O84XNIHi+E1QpYrRAWC4TFCljVaWi9Wgaruk5YrIDFUvdueEIAPh/g9wM+HyS/D/CFz/vU7oBGI2AwQBiMgNEQmjcYgmWQm0BerSiA2w3J7YLkcgEuFyS3G5LLCbjUqeR2qdeHRsdAREeHTaMhbNG1vu6TiIiIiBqfVJCP2HlzYdmwDq6rp8H+z6UQsXFaV6vO2CIloiZJysuDZeUKWJd/CNPuigNrnq9AiBIeqkCS1FDD5weUsoDD5wPKAo9g2OHzqddE1hMhSaGQRDZAGMsClMC8wQAYjIDZiESUDU5lMACSDGEwAIayQapkNWARgaBFDpVFrJNDz5M8XqAs6JBcLjX4cDkhud1q8OFyqUGI2133z2m1hoUlYYFJpfNlU4tFvT7V6wW8Xkg+L+D1qVOfD/B5IXl9gNcbmvf7gtvDVzbv86rH0ucHjAb1dU1mCLP6gNkCYTGr6wJTswWwmCFMZsBigTCZ1OeZLRBmkzo1mYF4K0xZeWX70KnuN6ez+mWXE5Kz3HLZdlD8Ze9tUfdZYL7sAYtVraMlEPoF5gPlFvU5gbDQbFb3gccDyeMBvB5I7rJpYF3YesnrKbetW933nrD1QOQAabJU6QBr4QOoQSrbrvzgaq1bA2+/WefvFxEREdUf457vETfrJshnslDy5NNw3XxrvY/toRWGIkTUdJSWwrJuDSzLP4R5yyZIPh98vXrD/uAjcF89DSI5We2l4FZP3OEMO4EP9GRwuyJO7tWT/kAA4ILkCm0DoKw3R1nvDqNRnTeGzxsharSN+s+tpCihHiX+QMiiqPNlvUzg96vzweVAmRrOSGXbGIwSfE43JL+ibqsoanijKOr2gYGsFLVc8niC20iKUNeFPQd+P2AyqcGQxQphi4ZITi7rcVN2wm21ANYo9eTaGlWxJ05ZWaAnDhQFksMBqbQUUqk9cmq3h60LrZdzctRlR1mZ01njr4iQZTVMMpogTCbAZIQwmgCTST0+JlNEGWSDun89Xkged9iJvhsoWwe3Wx007DwkVFdHg0Hdd1Fl+6tsv8FqhYiKgoiPV/dxYL1BVuvkdqvfZbdLDSvcLnWfucrWeTyhIMvjrnVwJYzGUNBjMqvH2mQCzGXBkNkEYTJDRNnUuprMaqNIUQCEBlCTwgdMU0TVZaJsXWBgNiIiItIPIWB98zXE/O1+KKlpKFy1Dr5Bl2hdq3rFUISI9M3rhfmrTbAs/wiWz9dAcpTC3649nHPvgOva38Pfp29kSh0LtJTTKmtKLEp0NuhWg/D7ITnU4AROpxp6mEzqZUfhoYfJ1HCXHvl8atjg9QBlvSfUwKSsJ4Xbrfa+cLuRkBSDApeoGHqULcNkapg6lqcooYAnEBaWhT0wmSoGHWZLw+7DGpJlCcma1oCIiIgAAHY7Yu+eB+sny+EeeyVKXngZIqn5/S/NUISI9EcIGHfvgnXFh7CsXAE5Lw9KQgJc1/4e7ut+D+/gyzQ/caNGZDBAxMZpe82qsazHD6IBnCN4S4mFTw9hlSyHeuzEtZywkIiIiOrOcGA/4mbNhOHIryh94G9wzL+r2ba/GYoQkW4YDh6AZcWHsC7/GIbM3yCsVrjHTYD72t/Dc/kYdUBUIiIiIiJqMJYP/4PY/7cQIjoGRR+vgnfYCK2r1KAYihBRJCEg2Usg5eVBzlcfUl4eEGWEGSaImFiIuLiyX+5j1Ud0TK2TY/n0KVg+WQ7L8g9h+vlHCFmGd8QolP7PvfBMnNwsRrQmIiIiItI9lwsxD96LqHffhOey36HklTehpLXWulYNjqEIUXPndEaEG3J+HqT8PMjB+XzIeWch55Wtz89Tx0aoRHw1b6MEw5JYNTiJjYWIjYMSG5oPD1KkwkJYPl0O07atkISAd+Ag2B9bDNfV10KkpTXMviAiIiIiogrkY0cRd8ufYPppLxzz70LpfQ+plw+3AC3jU1KLZtj/C+T8PChpraGkpUHExDaN20f5fGqPjZIS9S4dJSXqsr0Est0OqaRYXV+uLLAsFxaoQYejtNKXF5IEkZgIJSkZIikZ/k6doQwcBJHcCkpSMpSkJIjk5LL5ZCSnJSD/+Jmy9yqGXFICqbhYXS4pDtZVLi5Wl0uKIZ8+BWPZdnKpveJH7NoNjv+5D+5rr4e/a/eG3qNERERERFSOee1qxM6/DZAlFL23DJ4rr9K6So2KoQg1T14vLGs/Q9RrL8O0c3tEkbDZoKSmQUlrDX9ZUKKktQ6uCzxEYmLdBhMSQr1dZkEB5MICSAUFkAoLIFc2LSoMBhtySYn6vBrehlRYrWrPjJgYKLFx6rR1a/h791EDjWQ19FDKwo5A0CESEgCDoeafJyUWfltSLXcG1DuIlJYFOCUlgCzD3yO9aQRURERERETNjdeL6Mcehe2l5+HtPwDFr70DpWMnrWvV6BiKULMinT2LqHffhPWt12HIOg1/p86w//0J+PpcADn7DOTsbHWao84b9/0EedNGyPaKd4oQJhOUlNSw0CQUoIjoaEiFhWrYUVXQUVgAyeersq7CYoGSmKT21ohPgNK6NURsD4josstNYmKCl6IogeWYuLD1MWqvl8a6vWddGQwQcfEQcdVdhENERERERA1NzjqNuNl/hmnXDjj/cgvsf3+yxd7UgKEINQvGvT8g6rWXYfnkY0geDzyjRsP+zLPwjLmyZr09SkshZ5+BIScbUk42DOEBSvYZGI4fh2n3Tsh5eRWeqsTEqsFGQiJEQiL8vdtCJCRCJCSo6wJl5aaIimqAPUFERERERFQ101ebEXfbLEgOJ4pffgPua67TukqaYihCTZfXC8vqleolMrt3Qtii4frjn+CcNUe9LON8REdD6doNStdu1W/n8UDOzYHkcJSFIAlNp6cGERERERG1XEIg6oXnEP34o/Cn90Tx6++e/3lTM8RQhJocKScndIlM9hn4unRV71ryhxkNf2mG2QylXfuGfQ8iIiIiIqL65HAg9q47YF3xMVxXT0PJsy8C0dFa10oXGIpQk2H84Tv1EpmVK9RLZEaPhX3J8/CMvqJuA6ISERERERE1U/KJTMT9eQaMP/8I+4OPwDn/Lt7sIAxDEdI3jweWzz5F1Gv/hum7DCjRMXDe9Be4br4V/u49tK4dERERERGRbpm2bUXcrJmAx4vi95bBc8V4raukOwxFSJ/OnIHtn0thffsNGHKy4evaDSVP/B/c02+EiI3TunZERERERET6JQSsb7yKmIfvg79LVxS//R/+qFwFhiKkLx4PYv7fQuCj/yLa64V77JUouWUOvKPG8BIZIiIiIiKic3G7EXPvXYj64F24x12FkhdfafixF5uwJnGW+dlnn2HChAm48sor8f7771co37dvH6699lpMmTIFc+bMQXFxsQa1pPpgWf4hoj54F7j5ZuTv+B7FH3wML8cMISKiesa2BRERNUfymSwkTJ2AqA/eReld96D47f8wEDkH3Z9pZmdnY8mSJfjggw/w6aefYtmyZfj1118jtnn88ccxf/58rFq1Cl26dMHrr7+uUW2pThQFtheeha9vP+Cll+Dv2l3rGhERUTPEtgURETVHxoxdSLhiJIz7f0HR6+/Ccd/D/HG5BnS/h7Zt24YhQ4YgISEBNpsN48aNw7p16yK2URQFpaWlAACn0wmr1apFVamOzOvWwnj4EBzz7uRoyERE1GDYtiAioubG8p/3kDB1AmCxomDtRngmX611lZoM3YciOTk5SElJCS6npqYiOzs7Ypv77rsPDz30EIYNG4Zt27bhD3/4Q2NXk+pKCNieXwJ/x85wT7lG69oQEVEzxrYFERE1G14voh+4B3ELbod38FAUbNgMf5++WteqSdH9QKuKokAK6zUghIhYdrlcePDBB/HWW2/hwgsvxJtvvol7770Xr7zySo3fIzk5pl7rTLXw9dfAd7uBF19ESptEAEBKSqzGlaLyeEz0h8dEn3hc9K0x2hYA2xd6xL9NfeJx0R8eE/2p9Jjk5gIzfg9s2QLcdRfMTz2FVkbdn+Lrju73WOvWrZGRkRFczs3NRWpqanD50KFDsFgsuPDCCwEA06dPx3PPPXde75GXZ4eiiPqpMNVK3N8fg6lVK+RNug7ILUFKSixyc0u0rhaF4THRHx4TfeJxqRtZlho8TGiMtgXA9oXe8G9Tn3hc9IfHRH8qOyaGn35E/J9vhJyTjZIXXob79zcABU6Naqh/1bUvdH/5zNChQ7F9+3bk5+fD6XRiw4YNGDFiRLC8U6dOOHPmDI4ePQoA+PLLL9GvXz+tqku1YNj3MyxffgHn7NuAqCitq0NERM0c2xZERNSUWT75GImTrgD8fhR+tl4NRKjWdN9TJC0tDQsXLsRNN90Er9eL6667DhdeeCFmz56N+fPno1+/fnjyySdx5513QgiB5ORkPPHEE1pXm86D7YVnoUTHwPmXW7SuChERtQBsWxARUZPk9yP68f+F7YVn4b10CIreeA8irKcj1Y4khGjx/TrZvVU7cuZxJA3uD+fs21D691CDk9329IfHRH94TPSJx6VuGuPymcbC9oW+8G9Tn3hc9IfHRH9SUmJx9nAm4ubOgnnTRjhvuhn2J/4PMJu1rlqTUV37Qvc9Rah5s730PCDLcM79q9ZVISIiIiIi0p9ffkHCpMkwnDyBkqefhetPN2tdo2aFoQhpRjp7FtYP3oXruulQ2rbTujpERERERES6Yjh8CBh/OWRrFAqXr4ZvyGVaV6nZYShCmol67d+QnE44/7pA66oQERERERHpjvW/7wNOJwo2b4PSsZPW1WmWdH/3GWqm7HZEvfEK3FdNgj+9p9a1ISIiIiIi0hchYF69Erj8cgYiDYihCGki6r23IBcWwjHvTq2rQkREREREpDuGX/bBeOwocO21WlelWWMoQo3P40HUv1+EZ+gw+C6+VOvaEBERERER6Y5l9UoISQKmTtW6Ks0aQxFqdJYVH8Fw+hSc7CVCRERERERUKcuaVfAOGQqkpWldlWaNoQg1LkWB7YVn4etzATyjr9C6NkRERERERLpj+PUwjAf2wzNpitZVafYYilCjMm9YB+Ohg+pYIpKkdXWIiIiIiIh0x7J6JQDAPZGhSENjKEKNRwjYlv4T/o6d4L56mta1ISIiIiIi0iXz6lXwDroYStt2Wlel2WMoQo3GtHM7TBm74LjtDsBo1Lo6REREREREuiMf/w2mH/fAPfFqravSIjAUoUYT9fwSKMnJcN0wU+uqEBERERER6ZJlzWcAADfHE2kUDEWoURh+2QfLF+vhvGUuYLNpXR0iIiIiIiJdsqxeCe8FF0Lp3EXrqrQIDEWoUdheeBbCFg3nzbO1rgoREREREZEuyVmnYcrYxbvONCKGItTg5BOZsHzyMZwz/wyRmKR1dYiIiIiIiHTJvDZw6QzHE2ksDEWowUW99DwgSXDO/avWVSEiIiIiItIty+pV8KX3hD+9p9ZVaTEYilCDkvLyEPX+O3BfNx1Ku/ZaV4eIiIiIiEiXpLNnYdr+LQdYbWQMRahBRb3+MiSnE4477tS6KkRERERERLpl+Xw1JEXhrXgbGUMRajilpYh6/WW4x09g9y8iIiIiIqJqWFavhL9TZ/gv6Kd1VVoUhiLUYKLefxtyQQEc8xZqXRUiIiIiIiLdkgoLYPrmK3WAVUnSujotCkMRahheL6JeegGeIUPhu2Sw1rUhIiIiIiLSLfP6zyH5fBxPRAMMRahBWFZ8BMOpk3DOZy8RIiIiIiKi6ljWrIK/bTv4BgzSuiotDkMRqn+KAtuLz8HXuy88Y67UujZERERERES6JdlLYN78JdwTJwMyT9Ebm1HrClDzY/5iPYwH9qP4xVd4PRwREREREVE1zBs3QHK74ZnEu85ogTEU1Tvb80vg79AR7qnXal0VIiIiIiIiXTOvXgWlVQq8lw7RuiotEkMRqlfGHdth2rUDjtvuAEwmratDRERERESkX04nLBs3wD1hMmAwaF2bFomhCNUr2wtLoCQlwXXDTK2rQkREREREpGvmzV9CcpTyrjMaYihC9caw/xdYNqyD85a5QHS01tUhIiIiIiLSNcvqlVASEuD93XCtq9JiMRShemN78TkImw3Om2drXRUiIiIiIiJ983hg3rAOnvETOfSAhhiKUL2QT56AZcVHcP7xTxBJyVpXh4iIiIiISNfM32yBXFzES2c0xlCE6kXUv18AADjn3qFxTYiIiIiIiPTPvHoVlJhYeEaO1roqLRpDEaozKT8PUe+9Dfe066G076B1dYiIiIiIiPTN54Pl89XwXDkOsFi0rk2LxlCE6izq9VcgORxw3HGn1lUhIiIiIiLSPdP2byHn58M98Wqtq9LiMRShuiktRdTrL8M97ir4e/XWujZERERERES6Z1m9EiIqCp7RY7WuSovHUITqxLL2M8j5+XD+dYHWVSEiIiIiItI/RYF57Wp4Rl8BREdrXZsWj6EI1Yl89iwAwNf3Ao1rQkREREREpH/G3btgyD7Du87oBEMRqhPJUQoAEFE2jWtCRERERESkf5bVKyFMJniuGKd1VQgMRaiOJIcDwmwGjEatq0JERERERKRvQsCy9jN4Rl4OERevdW0IDEWorpwO9hIhIiIiIiKqAePeH2A4kQnPJN51Ri8YilCdSA4HhI2hCBERERER0blYVq+CMBjgHj9B66pQGYYiVCeSk6EIERERERHROQkB8+qV8A4dDpGUrHVtqAxDEaoTycHLZ4iIiIiIiM7FsP8XGI8e4V1ndIahCNWJ5HAA7ClCRERERERULcvqlRCSBPeEyVpXhcIwFKE6UXuKRGldDSIiIiIiIl2zrFkF36VDINLStK4KhWEoQnWiDrQarXU1iIiIiIiIdMtw5DCM+3/hpTM6xFCE6kRylHKgVSIiIiIiomqY13wGAHBPZCiiNwxFqG6cToYiRERERERE1bCsXgnvgIFQ2nfQuipUDkMRqhP18hmGIkRERERERJWRT2TCtOcHuCderXVVqBIMRaj2hIDk5C15iYiIiIiIqmJZswoAOJ6ITjEUodrzeCD5/bwlLxERERERURUsq1fB1+cCKF27aV0VqgRDEao1yVEKALx8hoiIiIiIqBJy9hkYd+9kLxEdYyhCtSY5nQDAy2eIiIiIiIgqYV7zGSQh4J7E8UT0iqEI1ZrkcABgTxEiIiIiIqLKWNasgq97D/h79tK6KlQFhiJUa5IzEIpEa1wTIiIiIiIifZHy8mDatlXtJSJJWleHqsBQhGqvtCwUiYrSuCJERERERET6Ylm3BpLfDw/HE9E1hiJUa6GBVtlThIiIiIiIKJx59Ur4O3aCr99FWleFqsFQhGotNNAqe4oQEREREREFSEWFMH+9Be6JU3jpjM41iVDks88+w4QJE3DllVfi/fffr1B+9OhRzJw5E1OmTMGsWbNQVFSkQS1bnkBPEURzoFUiImpa2LYgIqKGZN6wDpLXy1vxNgG6D0Wys7OxZMkSfPDBB/j000+xbNky/Prrr8FyIQRuu+02zJ49G6tWrULv3r3xyiuvaFjjliPYU4SXzxARURPCtgURETU0y+pV8LduA9+gS7SuCp1DvYUiubm5+P7777FlyxbY7XYAgMvlgtvtrtPrbtu2DUOGDEFCQgJsNhvGjRuHdevWBcv37dsHm82GESNGAADmzp2LGTNm1Ok9qWaCY4rw8hkiImogDdG+YNuCiIgalN0O8+aN8EycDMi674fQ4tXpCAkhsGzZMkycOBEjRozAjBkzcNttt+HkyZMAgG+//RaXXXYZFi9eHGzInK+cnBykpKQEl1NTU5GdnR1czszMRKtWrfDAAw/gmmuuwSOPPAKbjZdzNAbJwVvyEhFR/Wvo9gXbFkRE1JDMm76A5HKpt+Il3TPW9omlpaWYN28etm/fDiFEcL0UNojMqVOn4HA48Pbbb2PTpk1466230LZt2/N6H0VRIl5TCBGx7PP5sGvXLrz33nvo168fnn32WSxevBiLFy+u8XskJ8ecV52ojOQHjEaktE1qkJdPSYltkNel2uMx0R8eE33icam90tJSzJo1q0HbF43RtgDYvtAj/m3qE4+L/vCY1NEXa4GUFCRMHgcYDPXykjwmDafWocg999yDbdu2AQC6dOmCYcOG4d13343YJi0tDfHx8SgqKkJmZibmzp2LFStWwGis+du2bt0aGRkZweXc3FykpqYGl1NSUtCpUyf069cPADBp0iTMnz//vD5LXp4diiLOvSFFiD5bAKstGnm5JfX+2ikpschtgNel2uMx0R8eE33icamb+++/u8HbF43RtgDYvtAb/m3qE4+L/rS0Y2La/i0Mhw9BxMZCxMVBiYmDiIsLLouY2PO7BMblQvLqNXBPuw72fEe91LGlHZOGIMtSlT9W1CoU+frrr7Fp0yZIkoRbb70VCxYsgCzLFRot48aNw4gRI/DQQw9hzZo17O39IQAAIABJREFUOHz4MD755BNcf/31NX6voUOH4vnnn0d+fj6ioqKwYcMGLFq0KFg+YMAA5Ofn48CBA+jVqxc2bdqEvn371uZj0XmSnE4IdicmIqJ6smPHNmzd+nWDty/YtiAiIgCQCgsQf8O1wWEBqqLExIaCklh1qsTFh5bjQusMJzIhl9rVW/FSk1CrUGTFihUA1EbFwoULq902KioK//jHP3Dq1Cns2bMHa9euPa9QJC0tDQsXLsRNN90Er9eL6667DhdeeCFmz56N+fPno1+/fnjxxRfx0EMPwel0onXr1vi///u/2nwsOk+So5SDrBIRUb1Zu/YzAA3fvmDbgoiIAMD6zluQHA4UfrIGSmoapOIiSMXFkOwlkIuL1fmSwCNsXVEhjCcyIRUXQ7aXVAhVlFat4B02QqNPReerVqHI3r17IUkSpk2bVuPnzJgxA3v27MGBAwfO+/0mT56MyZMnR6x79dVXg/MXXXQRPv744/N+XaobyeEAOMgqERHVk337fmq09gXbFkRELZzHg6jX/g3P8FHw/m543V7L64VkL1EDk+JiiFatALO5fupJDa5WoUheXh4AoEOHDjV+TseOHQEAJSW8Fqq5kBxO9hQhIqJ6U1BQAIDtCyIianiWVZ/AcCYL9n8urfuLmUwQiUkQiQ1zAwpqWLW6JW9U2Ymw0+ms8XPy8/MBANHR7FnQXEiOUt6Ol4iI6o3VagXA9gURETUwIRD17xfh65EOz+grtK4NaaxWoUjgV5ndu3fX+Dlr1qwBAHTq1Kk2b0k6JDkcHGiViIjqTbt27QGwfUFERA3LtGMbTD/ugXPOX8/vzjLULNXqGzBy5EgIIfD+++/j7Nmz59z+888/x5o1ayBJEoYPr+P1WqQfTgeEjZfPEBFR/bjsst+xfUFERA0u6qUXoCQlwXX9H7SuCulArUKRmTNnIi4uDoWFhZg5cyZ27dpV6XbHjx/H3//+d9x9990QQsBqtWLGjBl1qjDph9pThN2ViYioflx33R8QExPL9gURETUY+egRmNevhfPPswCOj0io5UCr8fHxePrpp3H77bfjt99+w5/+9CcYjaGXuu+++1BQUICcnBwAgBACkiRh0aJFSEri4DPNheR08vIZIiKqN3FxcXjkkUW477672b4gIqIGYXv1JcBkgvMvt2pdFdKJWl9ANXLkSLz22mtITk6GEAJerxeSJAEADh48iOzsbAghIITA/2fvvsObKt8+gH9PuksppaUDKFNkUxCQWagyStmrgCAoQwEFUfypr4AyBEQcoAxFhiC7ssssSxAoIKvMAh1sWuheSVdy3j9CD41NR9K0SdPv57q4SHKec86dnLb3k+c8w8HBAT/99BP69OljsMDJ+AR5GmDHRhEiIjKcDh28Wb8gIqISISQmwHbLRmQMGgLR3d3Y4ZCJ0KunSI727dvj2LFjCAwMxIkTJxAaGoqEhARkZ2ejUqVKqF+/Pry9vTFkyBBUrFjRUDGTKcjMhJCdzZ4iRERkcKxfEBFRSbBdvw6CXA75hEnGDoVMiF6NIjExMXB1dQUA2NjYYMiQIRgyZIhBAyPTJijkAACR4/CIiMhA4uJiWb8gIqKSkZkJu9UrkNnpDSibNDV2NGRC9Bo+8/nnn8PX1xe7d+82dDxURgjyF40inGiViIgM5JtvZmLo0AGsXxARkcHZBO6CRXQUFB+wlwhp0qunyJ07d5CYmIjMzExDx0NlhNRThMNniIjIQCIiwpCcnMT6BRERGZYowm7FcmS/Wh+ZXbobOxoyMXr1FElLSwMA1K9f36DBUBmSljN8ho0iRERkGPIXvRBZvyAiIkOyOhcMq2shUEyYBMj0XmuEzJRePxF169YFAISGhho0GCo7Xg6fYaMIEREZRq1atQCwfkFERIZl99syqJydkT7kLWOHQiZIr0aRqVOnQhAE/Pzzzzh79qyhY6Iy4OVEq2wUISIiwxg//kPWL4iIyKBkkRGwDjoAxehxABeJIC30mlPE3d0dH3/8MX755ReMHTsWNWvWRPPmzVG1alVUqFABgiAUuP/777+vV7BkOnJ6iqACG0WIiMgwXF3d8f77E7Fq1QrWL4iIyCDsV/0GWFlBMWa8sUMhE6VXo8jAgQOlx6Io4uHDh3j48GGR92elpezjRKtERGRoY8e+LT1m/YKIiIpLSEyA7ZaNyBg0BKK7u7HDIROlV6OIKIoFPi9IYXd5qGyQ5hTh8BkiIjIQ1i+IiMiQbNevgyCXQz6By/BS/vRqFFm/fr2h46AyRpCrVyBiTxEiIjKUJUtWQCYT4OjIMd9ERFRMmZmwW70CmZ3egLJJU2NHQyZMr0aRNm3aGDoOKmMEhQIAe4oQEZHhvPZaK8hkAlxcHIwdChERlXE2gbtgER2F1EVLjB0KmTgu0kz6kcshWlgA1tbGjoSIiIiIiOglUYTdiuXIfrU+Mrt0N3Y0ZOL06inyX8nJyfj3339x9+5dJCYmQiaToVKlSqhbty7atGmDypUrG+I0ZEIEeRpE+woAx3ATEVEJYf2CiIj0YXUuGFbXQpDy4y+AjP0AqGDFahRRKBRYtGgRtm3bhoyMDK1lLCwsMGjQIEybNg12XBfabAgKBUReTyIiKgGsXxARUXHY/bYMKmdnpA95y9ihUBmgd7NZfHw8hg4dio0bNyI9PR2iKGr9l52djW3btmHw4MGIj483ZOxkREJaGsBJVomIyMASExNYvyAiIr3JIiNgHXQAitHjADaaUxHo3VPk448/RlhYGACgdu3aGDJkCJo3b44qVapAqVQiLi4OISEh2LFjBx48eIB79+7hiy++wOrVqw0WPBmPoFCoh88QEREZ0IwZ/8f6BRER6c1+1W+AlRUUY8YbOxQqI/RqFDl8+DAuXLgAQRDg7++PmTNnwsrKSqPMK6+8gjZt2mDMmDGYM2cOtm/fjjNnzuD06dPw9vY2SPBkPII8jcNniIjIoE6ePI6QkMusXxARkV6ExATYbtmIjEFDILq7GzscKiP0Gj6zd+9eAICXlxfmzp2bp8KSm5WVFebOnQsvLy8AwI4dO/Q5JZkYQS5nTxEiIjKow4cPAmD9goiI9GO7fh0EuRzy8R8aOxQqQ/RqFLl27RoEQcDw4cOLVF4QBLz99tsQRRG3bt3S55RkahQKiPbsKUJERIYTGnqL9QsiItJPZibsVq9AZqc3oGzazNjRUBmiV6NIzoRmdevWLfI+derUAQA8e/ZMn1OSiVEvycuJVomIyHASExMAsH5BRES6swncBYvoKCg+mGTsUKiM0atRJGfpu5SUlCLvk1PWxsZGn1OSieFEq0REZGg2NrYAWL8gIiIdiSLsVixH9qv1kdmlu7GjoTJGr0aR2rVrAwD+/vvvIu+TU7ZGjRr6nJJMjCCXc6JVIiIyqBo1agJg/YKIiHRjdS4YVtdCoJgwCZDp9RWXyjG9fmI6d+4MURQREBCAK1euFFo+JCQEAQEBEAQBnTt31ueUZGIEeRrAniJERGRA7dp1YP2CiIh0ZvfbMqicnZE+5C1jh0JlkF6NIiNGjEDFihWRnZ2NsWPHYt26dUhNTc1TLjU1FevWrcPYsWORlZUFOzs7jBw5sthBk5FlZUHIymJPESIiMqiBA4fAwcGB9QsiIioyWWQErIMOQDF6HMDvJ6QHS312cnZ2xpw5c/DZZ58hPT0dCxcuxI8//og6derA2dkZgiAgLi4O9+7dg1KphCiKAIB58+bB2dnZoG+ASp+gkAMA5xQhIiKDqly5Mr74Yjpmz/6K9QsiIioS+1W/AVZWUIwZb+xQqIzSq1EEAHr16gVLS0vMnDkTiYmJyM7ORnh4uEaZnMqKo6Mj5s2bB19f3+JFSyZBUCgAgKvPEBGRwXXt6gsnJwfWL4iIqFBCYgJst2xExqAhEN3djR0OlVF6N4oAgK+vLzp06IDt27fjzJkzCAsLQ2JiIkRRRKVKldCgQQN07NgR/v7+cHBwMFTMZGxpaQDA4TNERFQiWL8gIqKisF2/DoJcDvn4D40dCpVhxWoUAQAHBweMHj0ao0ePNkA4VBYIcg6fISKiksX6BRERFSgzE3arVyCz0xtQNm1m7GioDCv2ekUKhQLBwcFat23duhU7duxA2oueBWQeXs4pwp4iRERUMli/ICKigtgE7oJFdBQUH0wydihUxhWrUeSPP/5A586dMX78eGRlZeXZvn37dnz11Vd44403sHPnzuKcikxITk8RLslLREQlgfULIiIqkCjCbsVyZL9aH5lduhs7Girj9G4UmTdvHn744QekpKRAqVTi4cOHeco8efIEoigiJSUFM2bMwNq1a4sVLJkGTrRKREQlZfHiH1i/ICKiAlmdC4bVtRAoJkwCZMUe/EDlnF4/QefPn8fGjRsBAG5ubpg+fTqqVauWp1xQUBB++uknVK1aFaIo4qeffsLdu3eLFzEZnSDPmWiVjSJERGQ4ly9fxPbtAQBYvyAiovzZ/bYMKmdnpA95y9ihkBnQq1Fky5YtAAB3d3ds374do0aNgp2WlUgcHR3Ru3dv7Nq1C66urlAqlVi/fn3xIiajeznRKhtFiIjIcHbv3gGA9QsiIsqfLDIC1kEHoBg9DuBqmGQAejWKhISEQBAEvP/++3Bzcyu0vJOTE9577z2Ioohz587pc0oyIS8nWmWjCBERGc6NG9dYvyAiogLZr/oNsLKCYsx4Y4dCZkKvRpG4uDgAQOPGjYu8T5MmTQAAz58/1+eUZEpyeopw+AwRERlQYmICANYviIhIOyE1BbZbNiJj0BCI7u7GDofMhF6NIo6OjgAAec4qJEWgVCoBADY2NvqckkyIIE+DKJMBvJZERGRADg4VAbB+QURE2smioyHI5cjs/IaxQyEzolejSI0aNQAAJ06cKPI+Z86cAQB4enrqc0oyIYJcoe4lIgjGDoWIiMxItWrVAbB+QUREheCKM2RAev00de/eHaIoIiAgACEhIYWWv337NjZs2ABBENC5c2d9TkkmRJDLAc4nQkREBta585usXxAREVGp0qtRZODAgahUqRKysrIwevRoLFu2DI8ePcpT7unTp1i5ciXefvttKBQK2NnZ4Z133il20GRcgkLOSVaJiMjgevXqi4oVHVm/ICIiolJjqc9Ozs7O+P777zFx4kRkZGRg+fLlWL58ORwcHODk5AQASExMRGpqKgBAFEUIgoAFCxbAxcXFcNGTUQhyNooQEZHhOTk5YebMb/DFF1NZvyAiIqJSofdgLB8fH/zxxx/w9PSEKIoQRREpKSl49OgRHj16hJSUFOl1Nzc3rFy5Ej169DBk7GQkgjyNjSJERFQiOnTwZv2CiIiISo1ePUVytG/fHvv378fZs2fx999/4/79+4iLi0N2djYqVaqEevXqoUOHDujevTusrKwMFTMZmaBQcDleIiIqMaxfEBERUWkpVqMIAFhbW8PHxwc+Pj6GiIfKArkcYtWqxo6CiIjMGOsXREREVBqK3SiSkJAAURTh7OwsvZaZmYk1a9bgxIkTyMjIQLNmzTBu3DjUrl27uKcjE8CJVomIqKSxfkFERESlQe85ReLj4zFlyhR07NgR+/bt09g2YcIELFmyBNeuXcOdO3ewfft2DBw4EMHBwcUOmIxPkMs5fIaIiEpEQkIC6xdERERUavRqFFEqlRg3bhyOHDkCURTx+PFjadvevXtx9uxZAIAgCHBzc4MoilAoFPj000+RlJRkmMjJaAR5GsCeIkREZGBKpRJTp05i/YKIiIhKjV6NInv37kVoaCgAoEWLFnjzzTelbTt27AAA2NraYseOHTh58iTWr18Pe3t7JCUlISAgwABhkzFxolUiIioJR44cQljYXQCsXxAREVHp0KtR5MiRIwDUFZYNGzagffv2AICUlBRcuHABgiCga9euaNSoEQCgTZs2GD58OERRxN9//22g0MkolEoIGRmcU4SIiAzu5El1HYH1CyIiIiotejWK3Lx5E4Ig4O2334al5cu5WoODg6FUKgFA4+4OoK64AMCDBw90Pt/evXvRq1cv+Pr6YtOmTfmWO3HiBLp06aLz8anoBIUcACDaVzByJEREZG7u3AkttfoF6xZEREQE6Ln6TEJCAgCgZs2aGq/nnuisXbt2GtsqV64MAEhOTtbpXM+ePcPixYuxc+dOWFtb46233kLbtm1Rr149jXKxsbFYuHChTscmPaS9aBSxszNyIEREZG6SkhIBlHz9gnULIiIiyqFXTxGZTL1bzl2bHDmVlnr16sHFxUVj27NnzwAAdjp+mQ4ODka7du3g5OQEe3t79OjRA4cOHcpT7quvvsLkyZN1OjbpTpCnAQCHzxARkcGVVv2CdQsiIiLKoVejiKenJwAgLCxMei0iIgKPHj2CIAjw8fHJs8+JEycAADVq1NDpXM+fP4erq6v03M3NTaoA5Vi/fj0aN26M5s2b63Rs0p2gUABgowgRERle1arVAJR8/YJ1CyIiIsqh1/CZdu3aISwsDKtWrULnzp3h6uqKRYsWSdt9fX01yh85cgR79uyBIAh5ur0WRqVSQRAE6bkoihrP7969i8OHD2PdunWIjo7W5+3AxcVBr/3KJRv1f5WqVgFcK5boqVxL+PikO14T08NrYpp4XfTj7d0R9+5Flnj9ojTqFgDrF6aIv5umidfF9JjsNYlXz2vo6GhX4t9FTI3JXhMzoFejyIgRI7B161Y8fvwY3bp1g729PVJSUiAIApo3bw4vLy8AQHh4OObMmYNLly5BpVLB1tYWI0aM0OlcHh4euHjxovQ8JiYGbm5u0vNDhw4hJiYGgwcPRlZWFp4/f44RI0Zg8+bNRT5HXFwqVCpRp7jKK6unsXACkJglICsmpcTO4+paETEleHzSHa+J6eE1MU28Lvrz8+tfKvWL0qhbAKxfmBr+bpomXhfTY8rXxCI+Dc4AkpMVyDDRGEuCKV+TskImE/K9WaHX8Jk6derg22+/hZWVFbKzs5GcnAxRFOHq6ooFCxZI5bKzs3HhwgWoVCpYWlpi/vz50tCbourQoQPOnj2L+Ph4KBQKHD58GJ07d5a2T5kyBUFBQdizZw9WrlwJNzc3nSstVHSCnBOtEhFRyahZsxamT59Z4vUL1i2IiIgoh149RQCgb9++aN68OQIDAxEbG4u6detiwIABcHR0lMrUqVMHNjY28Pb2xuTJk9GoUSOdz+Pu7o6pU6finXfeQVZWFvz9/eHl5YX3338fU6ZMQbNmzfR9C6SHlxOtckleIiIyPF/fnujYsW2J1i9YtyAiIqIcgiiKJdqvMysrC1ZWViV5imJj99ais928ARU/mYS4yzeh8tRt0lxdsIuY6eE1MT28JqaJ16V4CuremhvrF6Qr/m6aJl4X02PK18QiPAzOHVohecUaZAwaYuxwSo0pX5OywuDDZ3Rh6hUW0lFOTxE7rj5DRETGw/oFERERGUKJN4qQeZHmFOGSvERERERERFTGsVGEdCLI5RAFAbC1NXYoRERERERERMXCRhHSiSCXA3b2gCAYOxQiIiIiIiKiYmGjCOlEUCg4dIaIiIiIiIjMAhtFSCeCPI2NIkRERERERGQW2ChCOhHkcjaKEBERERERkVlgowjpRFDIIdrZGTsMIiIiIiIiomJjowjpRi6HaF/B2FEQERERERERFRsbRUgnnGiViIiIiIiIzAUbRUgngjwNoh0bRYiIiIiIiKjsY6MI6USQywH2FCEiIiIiIiIzwEYR0gknWiUiIiIiIiJzwUYR0onAiVaJiIiIiIjITLBRhIpOpYKQns6JVomIiIiIiMgsWBo7ACpD5HIA4ESrxaRSKZGeLkd6uhxZWZkQRZWxQyqS589lUKnKRqzlBa+JaSqP10UQZLCysoatrT1sbe0hk1kYOySzUFbzhakqj7+bZQGvi+kpyWvCfEGmiI0iVGRCTqMIe4roLTs7C/Hxz2FtbQN7+4qwtraBIMggCIKxQyuUpaUM2dmstJgSXhPTVN6uiyiKEEUVMjMzkJ4uR2pqMpyd3WBpaWXs0Mq0spwvTFV5+90sK3hdTE9JXRPmCzJVbBShIhMUbBQpDpVKifj453BwcIS9fUVjh0NEZBCCIEAQLKS7fnJ5CuLjn6NKFQ/eAdQT8wURmSPmCzJVnFOEiow9RYonPV0u3fEjIjJX6l4N1khPlxs7lDKL+YKIygPmCzIVbBShIhPkaeoHbBTRS3q6HLa2/OyIyPzZ2lZgJbcYmC+IqLxgviBTwEYRKjJBoQDAiVb1lZWVCWtrG2OHQURU4qytbZCVlWnsMMos5gsiKi+YL8gUsFGEiiynpwiHz+hHFFUQBP7KEZH5EwQZV0opBuYLIiovmC/IFDDjUpFJPUXsKxg5krKLqwYQUXnAv3XFx8+QiMoD/q0jU8BGESq6nIlW7eyMHAgRERERERFR8bFRhIrs5fAZ9hQhIiIiIiKiso+NIlRkgjxnolX2FCEiIiIiIqKyj40iVGTSkrxsFCEiIiIiIiIzwEYRKjJBoVCvPCPjjw2VfeHhYcYOAZMnj4e3d2t06dLB4Me+fPkivL1bw9u7NTZsWGfw4xMRlRfMF0RE5o3fbqnIBHkah85QmZeamoqff/4R48aNNHYoRERkwpgviIjKB0tjB0BlhyCXc5JVKvOWLl2E/fsDjR0GERGZOOYLIqLygY0iVGSCQsGeIlTmqVQqY4cgWbZsZYkdu2XL1jh9+mKJHZ+IyNwxXxARlQ8cPkNFJ09TzylCREREREREZAbYKEJFpp5olcNniIiIiIiIyDxw+AwVmSBPg8qlirHDINLLmjW/Y+3aVRqveXu3BgC0aNFS6po8f/5sHDy4D/Xq1cfq1euxatVvOHRoH1JSUuDi4oo33+yKDz+cIh0jIyMDQUEHcPbsGYSF3UFSUiKys7NRsaIj6tR5BR07eqNv34Gw0zL0bPLk8QgJuQxra2scPx6sNbYpUz7F0KEjcPLkcezduxt3795BSkoyKld2RuvWr8Pf/y3Ur98wz7EvX76IKVMmAgAmTJiMUaNG5/ksHBwccOjQCcTFxSIgYBPOnDmFZ8+iYWlpiVq16qBr1+4YMMAf1tbW+X6uCQkJCAjYhNOn/8HTp09gZWWJ2rXromfPPujXbyA2bVqP339fBgB6dc/OyEhHYOBu/PPP34iICIdcngYHBwdUrVodbdq0w8CBQ1ClSv5/l5RKJc6ePY39+/ciIiIMsbExsLa2QZ06ddGlS3f06zcQNjY2+e574sRxHDlyEKGht5CcnAQ7O3vUqFET7dt3xKBBQ+Ho6Kh1X3//voiOjsKQIcMxatRoLF78A86fPwtRFFG1alWMHDkGvr5+UnlRFHH8+BEcOXIIt2+HIikpEfb29qhVqw68vX0wYMBg2LOnHlGpMMd80bJlawwdOtwk80WfPn3Ru/cA5gvmCyKjYaMIFZkglwM12FOEyo+5c2fi2LHD0vOoqCewtbWVnt+5cxvTpv0Pz58/y7NvfHwc4uPjcOnSv9i5czuWLl0BV1c3nWNQKlWYM+crHDlySOP158+f4cCBfTh06AA++2wa+vUbqPOxAeDq1RBMn/4/JCUlabx+8+Z13Lx5Hfv378XSpSvg6Fgpz763b4fis8+mIDExQXotMzND2vfYscPw8mqhV1wA8OxZND79dDIePLiv8XpiYiISExMRGnoTW7duxKxZ89G58xt59o+Li8WsWdMREnJZ4/XMzExcv34V169fxZ49O/Djj0vh4eGhUSY6OgozZ07DrVs3NF7PykqS3l9AwGbMmjUP7drlv0RmWloqJk8ej4cPH0ivRUZGwNXVVXqekBCP6dM/x/XrVzX2TUpKwrVrIbh2LQR//bUZ8+YtRNOmXvmei4iMx9TzxaFD+3H48EGTzReHDwcxXzBfEBkNG0WoyNTDZ9jyTGXTgAGD0bnzG1i9egXOnDkFAFi7dhMAwM4u7891ZGQ4wsPvolmz5hg1agxsbW1x5swp9OrVDwCQlJSIqVMnITk5CRYWFujVqy86dPBG5couSElJQljYXfz112YkJibi8eOHWLbsZ8yZ863OcW/dugFxcXGoXbsOhg4dgVdeeRUpKck4eHAvjh07ApVKhZ9//gFt2rSDh0dVnY6dkZGBL7/8FHJ5GgYM8EenTj6oUKEC7ty5jQ0b1iI2NgYREWFYufJXfPbZNI19o6KeYsqUiZDL0yCTydCrV1906dId9vb2uHnzOjZtWo8rVy7hxo1rOr/nHN9+OwcPHtyHhYUFhgwZjjZt2sHR0REJCfE4e/YM9uzZiYyMDMyd+zW2bNmlcQcwIyMDU6ZMlCrILVq0RL9+A1G9eg3ExsZgz56d+Pffs7h//x6+/PJTrF69HpaW6pSYkJCATz6ZhMePHwIAvLxaoH//QfD0rInk5CT8888JHDgQiJSUZPzf/03Fjz8uweuvt9X6Hg4d2g+VSoU+ffrDz683UlNTcfHiebz2WisAgEKhwEcfTcT9+5EAgK5du6NLl+5wc3NHSkoKzp1Tv8/Y2BhMnToZv/++FnXrvqL3Z0pEhWO+yIv5gvmCyJyxUYSKTJCncfUZKrNcXKrAxaWKxh2sV19tkG95lUqF6tU98fPPy2Fjo77b17Jla2l7QMBmJCer75ZNmvQxhg4dobF/+/be6NmzD0aNGorU1FScOnUS2dnZUkWqqOLi4tCqVRt8//1ijW677dp1gKNjJezatR2ZmZk4ejQII0eO1unYWVlZUKlUWLhwscbdq6ZNvdC+fUe8884wpKen48iRQ/jkk881Yl+yZBHk8jQAwMyZc9GtWw+N/bt164FJk8ZLFUVdRUdH4dKlCwCAsWPH4913x2lsb9/eG7Vr18WiRQuhUChw5MghDB8+Utr+559rpAquv/8wfPLJ5xr7+/i8iW+/nYMDB/YiPPwujh4Ngp9fbwDAypXLpbj9/d/Cxx//D4Ig5Dp3R3Tp0hVffDEVWVlZmDuU/i5IAAAgAElEQVR3Jv76a4/GXeEcKpUK3bv74csvv5Ze8/buLD1eufJX3L8fCZlMhtmzv0WXLt009m/Tph38/Hpj0qT3oVDI8d13c7Fy5bqifoxEpAdzzBcVKzpi9+4dJpkv/Px6YsKE95gvmC+IjIYTrVKRcaJVKm969uwjVXD/KzY25kXF2QWDBg3VWsbV1U26w5OZmSFVinX1ySefaR3HPHDgYOlxeHiYXsfu3PlNrd15q1WrLt3NSktLw9OnT6Rt0dHROHXqBACgW7ceGhXcHC4uVTBt2ky9YgLUlfscnp41tZbp3bsf+vYdgPfem4jGjZtKr4uiiH379gAAqlf3xOTJU7XuP2nSx7CysgIA/PvvOQDqu34HDuwFALzyyqv46KOpGhXcHK+/3g6jRo0BoO76fvDgvnzfy4AB/lpfT0lJwd69uwAA3bv75ang5qhfv6H0BebWrRu4efOG1nJEZDymni/69x8kPWa+YL4gIk3sKUJFo1JBkMvZU6SUBARYYssWK2OHoUEQBIiiWGLHHz48C8OGZZfY8fXRpEmzfLdNnz4LgPrOjkyWf/uys7OL9DgzM0vnGFxd3VCnTl2t26pX95Qey+VynY8NqO8s5adaNe3HP3PmH+lx7959892/efMWqF27rtTVVxeenp6wsLCAUqnEsmWLYWVlhQ4dvDXuPtrY2OD//u+rPPveunUT8fHqSnK3bj3yvdtaqZIT1qzZABeXKqhUyQkAcPnyBSiVSgBA3779YWFhkW+MAwf6448/1BMunjt3BgMH5q3MWlhYoGHDRlr3v3LlEtLT0wEg3+7UOdq374hVq34DAFy69C+aNGlaYHkqP0wxX5Q05gvtmC+YLwDmCyJ9sFGEikahAAD2FKFyxd3dvdAyORXc7OxsREdH4enTJ3j06AEiIsJx8+Z1RESES2VFUaVzDFWrVst3W+7Z5XMqZqVx/PDwu9LjBg0aF3j8xo2b6FXJrVTJCX37DsTu3dsRE/Mc06d/Bnv7CmjZshVat26DNm3aoWbN2lr3ffTo5SR12lZayK1u3XoazyMjI6THBX3JAYDKlZ1RrVp1PH36BJGR2t+jk5NTvqsVhIXdkR7PmzcL8+bNKvB8OXLfhSUi02Dq+SL3XCjMFy8xXxARwEYRKiJBahThRKulYdiwbJO7C2ZpKUN2tu6VtLLM3t6hwO3p6enYuXMbjh49hIiIcK0VTZlMBpVK/8/N1jb/3lm5u+nq24unoOPnlvv4OXfVLCws8l1iMEflys56xQWou4FbW1thx46/oFQqIZen4fTpf3D6tPrOY/XqnujSpTuGDh2BypUr54ovXnpcqVLeVRAKkntVhaLE7uzsgqdPnyA5OVHrdvsCGpITE7XvU5iUlGS99iPzZIr5ojxivniJ+UI75gsi08VGESoS4cUEWWwUofJEy9BgydOnT/Dpp5Px+PEj6TUrKyvUqFETtWrVQYMGDdGiRSsEBR3Arl3bSiHa0pOVpf4CplKpIIqi1jHUhmBpaYkpU/6Ht99+FydOHMOZM6dw9eoVZGRkAACePHmMDRvWYteu7Vi0aKk0Tlzfu6DAf+/OFv6+cs4lCNq7xBf02SiVL7/ILljwY5FXg6hQoeAvX0RU+pgvtGO+eIn5gsh0sVGEikTIGR/KRhEiAMDs2TOkCm63bj3g7z8MDRs2zjMeec+eHcYIr0Q5OanHU4uiiKSkJOm5NvpOFpibi0sVDB48DIMHD0NmZiZu3LiGf/89h2PHDiMq6ilSU1PwzTczsXnzdshkMo27kbnv5BVF7tUmEhLi4OHhUWD5hIT4F/sVfAe0sHPZ2toWuLoFEZVdzBfMF+oyzBdEpoqrz1CRCAp1owgnWiUCbt++hVu31DO6t2zZGrNnz0fTpl5aJ2h79iy6tMMrcfXq1Zce3717u8Cyd+6E6nUOlUqFp0+fSMss5rC2tkbLlq0xceJkbNq0XRrH/fjxQzx8qB4bXrv2y4kGc49n12b27BkYMWIwpk37H0RRRL16r0rbcq5xfmJjYxEdHQUAqFWrdpHfW466dV+RHl++fKnAsk+ePMa6datx+PBBPHqk37KVRFT6mC+YLwDmCyJTx0YRKpKcniKcaJXKOkN03c3dBbpBA+0zxQNAVNRTXL9+VXpenG66pqRjx07S48OHD+ZbLiIiHHfv3sl3e0G+/34+hg7tj48//gBPnjzWWsba2hqtWr0uPc/MVHeTbtSoMSpUUP+tOn78SL5j9DMyMnDu3Bk8fPgASUlJEAQBLVu2lr6s7N27p8Dx/bnv6ha2GoA2rVq9Lq1WsH9/IOQvhilqs2nTn1i9egW++eZr3LhxTedzEZHumC+Kj/lCjfmCyLSxUYSKROopwuEzVMZZW1tLj/VdljBnOT4AuHjxPLKz805yGBcXi6+//hJZWS+XVczMzNTrfKamVq3aaNu2AwAgKOgATp8+madMamoq5s+frfc5OnR4WZFetmyx1okB09PTcerUCQDqCepyVhewtrZGv36DAAAPHtzHmjW/az3HsmU/IzU1FQDQt+8AAOrJ8nx9ewJQ3zVcvvwXrftevPgvNm5cBwBwcqoMP78+ur1BqLt5d+/uB0A9GeHcubM0fl5yBAefxv79gS/2cUGXLt10PhcR6Y75oviKli9SmC8KwXxBVLI4pwgVTU5PETs2ilDZ5uJSRXq8cuVy+Pn1hkwmK3Qpvty8vFrAxaUK4uJiERZ2Fx9//AEGDRoKD4+qSE5OQkjIZezfvyfPbPFpaakGex/GNnXq5xg7diTk8jTMmPEF+vYdAB+fN2Fv74C7d29j8+YNiIrSfylAb+/OaNSoMUJDb+HUqZN47713MHDgYHh61oQoinjw4D527AjAvXvqpQ1HjBgFW1tbaf8xY97H6dMn8ejRQ/z55xqEhd1Br1594erqjujop9i3bw8uXDgPAGjRoiV69Ogl7Tt58ie4cuUSoqKeIiBgE27fvoX+/QfB07MGkpOTcerUCezbtwdKpRKCIOCrr+boNUYcAD76aCquXLmEZ8+icerUCYwd+zaGDBmOunXrISUlCWfPnkFg4C7pXJ99Ng02NraFH5iIio35wjAKyxdbtmwo1tKxzBfMF0TFxUYRKpKXw2fYKEJlm7e3D9atWw2lUont2wOwfXsA3N09sGPHviIfw8bGBl9//Q3+7/+mIiMjA1evXsHVq1fylKtRoyb69OmP335bCgC4dy8SzZo1N9h7MSZPzxpYuHARpk//HCkpydi9ewd279acJLBTJx+kpKQgJOSyxh3XopDJZJg//wd8+ulHuH8/EnfuhOK77+blKScIAgYM8Me7747TeN3e3h6//PIbvvzyU9y9ewfBwacRHHw6z/4tWrTEggU/QSZ72XHS0bESli5dienT/4e7d+/ke32dnCrj66+/Qdu27XV6b7lVquSEZctWYtq0zxAefhf37kXi++/n5ylnY2ODzz6bhk6d3tD7XESkG+YLw2C+YL4gMnVsFKEiEdhThMzEq6/Wx3ff/YQ///wDERHhUKmUsLS0RHp6usado8K0bt0Ga9duwpYtG3Hx4gXExj4HoK601KlTF2++2Q09evSEUqnE2rWrkJ6ejuPHj6Bfv4El9dZK3WuvtcKmTduwdetGBAeffjFJoIB69eqhX79B8PPrjY8+mgAAsNNjkmY3N3f88cdGHDgQiJMn/0ZkZDiSk5NhaWmFKlWq4LXXWqF37/5o0qRpvvuvWrUehw8fxNGjh3H37m2kpCTD3r4C6tdvgJ49+6B7dz+NCm4ODw8PrFq1HkePBuHYsSO4cycUyclJcHR0RPXqNV5c31563/HLrWrValizZgOOHg3C338fxe3boUhKSoSFhQWqV/dE69ZtMXjwUFSrVr3Y5yKiomO+MJyC8sWAAYPh69uL+aIImC+ISoYgaht4V87ExaVCpSr3H0OB7Jb9AodvvkZM5FPAoeTXPHd1rYiYmJQSP09pio5+AA+PWsYOQ2+WljJkZ+c/iRiVvrJwTd599y1ERITjlVfq4c8/txo7nFJRFq5LadD3b55MJsDFpeTzTGnQt35R1vOFqeLvpmnKuS7lMV+YqtL+XdHlb55FeBicO7RC8oo1yBg0pIQjMx3m+N2otBVUv2BPESqSnIlWweEzROVeZGQEfvttCapXr4E+ffprLEuYW2xsDB48uA8A+ZYhIiLzxXxBRGUBG0WoSAS5HKKtLaCl2yARlS+VKzvj/PmzUKnOICrqCb77blGepSuVSiV++eUnaaUFH5+uxgiViIiMiPmCDI6DHKgEsFGEikSQp3GSVSICAFSuXBmdOvng5Mm/cebMKUyZMhF9+vRH1arVoFQq8fjxIwQG7kRo6C0A6uUSO3d+w7hBExFRqStKvti7dxdu3boJgPmCdPCfxjWi4mCjCBWJoFBAtK9g7DCIyER8/vkMxMbG4ubN67hy5RKuXLmktZyPz5uYNm1WKUdHRESmgvmCiEwdG0WoaORyiHrMBk5E5snJyQm//bYGR48exrFjQbh79w4SExOkmf4bNWoCP7/eaNOmnbFDJSIiIyosXzRu3AQ9ejBfEJHxsFGEikRQyNlThIg0yGQy+Pr6wdfXz9ihEBGRCSsoX3BVICIytjIxa+bevXvRq1cv+Pr6YtOmTXm2Hz16FP3790e/fv3w4YcfIikpyQhRmjeBPUWIiMiMsG5BREREQBloFHn27BkWL16MzZs3Y/fu3QgICEB4eLi0PTU1FbNnz8bKlSsRGBiIBg0aYOnSpUaM2DwJ8jQux0tERGaBdQsiIiLKYfKNIsHBwWjXrh2cnJxgb2+PHj164NChQ9L2rKwszJo1C+7u7gCABg0aICoqyljhmi1OtEpEROaCdQsiIiLKYfKNIs+fP4erq6v03M3NDc+ePZOeV65cGd27dwcApKenY+XKlejWrVupx2nuOHyGiIjMBesWRERElMPkJ1pVqVQQcq1DLYqixvMcKSkpmDRpEho2bIiBAwfqdA4XF4dix2n20hWwcHGCrWvFUjulaymeqzQ8fy6DpaXJt0MWqKzHb454TUwTr4t6YkVT/TteGnULQP/6hTnkC1PFz9U08bqYntK8Jjrlizh1z3VHRzvARHNMSTHVnGoOTL5RxMPDAxcvXpSex8TEwM3NTaPM8+fPMW7cOLRr1w7Tp0/X+RxxcalQqcRix2rOqqSmQQFLpMWklMr5XF0rIqaUzlVaVCpVmZ5dnbPDmx5eE9PE66KmUqn0+jsukwklfrOiNOoWgP71i7KeL0wVfzdNE6+L6Snta6JLvrCIT4MzgORkBTLM7LtCQczxu1FpK6h+YfLNsh06dMDZs2cRHx8PhUKBw4cPo3PnztJ2pVKJiRMnomfPnpgxY4bWOz1UTKIIKOQQOdEqERGZAdYtiIiIKIfJ9xRxd3fH1KlT8c477yArKwv+/v7w8vLC+++/jylTpiA6Ohq3bt2CUqlEUFAQAKBp06aYP3++kSM3I+npEESRE60SEZFZYN2CiIiIcph8owgA9O3bF3379tV4bdWqVQCAZs2a4fbt28YIq9wQ5HIAgGjPiVaJiMg8sG5BREREQBkYPkPGJ8jT1A/YU4SIiIiIiIjMCBtFqFCCQgEAXJKXiIiIiIiIzAobRahQOT1FOKcIERERERERmRM2ilChpJ4iXH2GiIiIiIiIzAgbRahQUk8RDp8hIiIiIiIiM8JGESqctPoMh88QFceBA3vh7d0a3t6tcfRokMa2NWt+l7bduHFdr+P7+/eFt3drTJ483hDhaiWKIiIjw7Vuy4n/008/KrHzExGVB8wXRESlh40iVKiXS/Jy+AxReXb7digmTBiDLVs2GjsUIiIyYcwXRFSWWBo7ADJ9UqOIHRtFiMqz8ePfhUqlQq1atY0dChERmTDmCyIqS9goQoXKmWgVFdgoQlRSxo2bgHHjJhg7jAKpVKoCt58+fbGUIiEiKr+YL4iIDIvDZ6hQLydaZaMIERERERERmQ82ilChBLkcoo0NYGFh7FCIiIiIiIiIDIbDZ6hQgkLOSVapzAsI2ISlSxcDAObM+RZdu/rmWzYk5LI0I/+ECZMxatRoje3h4WE4cCAQISFX8Px5NFJTU2FrawtnZxd4ebVA//6D0KhRE53iW7Pmd6xduwoAsGLFWjRt2ixPmbi4WGzfHoDg4NN4+vQJrK2t0bBhYwwbNgJt2rQr0nmuXg3BkSMHce1aCGJjY5GWlgp7+wpwc3NDixYtMWjQ0DxjwP39+yI6Okp6fvDgPhw8uA8AMH36LPTq1ReAejUBAGjTpj0WLVqq9fyRkRHYuXMbrly5iOfPn0EURVSp4ooWLVpiwAB/NGzYqMDPx8HBAYcOnUBcXCwCAjbhzJlTePYsGpaWlqhVqw66du2OAQP8YW1tXaTPQ5uTJ48jKOggQkNvIiEhHra2ti9ibIV+/Qagfv2GBe5/69ZN7Nq1E9evX8WzZ+rPrVo1T7Rt2x5Dh45AlSpV8t33xo1rCAzchatXryAmJgYWFhZwd/dA69avY9CgoahZs5bW/ebPn42DB/ehXr36WL16PVat+g2HDu1DSkoKXFxc8eabXfHhh1P+c67rCAzciZCQy4iNjYWlpSWqVq2K119vB3//t+Dh4aHjJ0dkHswzX1ihYcMmJpkvlixZrvX85SFfhIbeRGDgbpPLF1OmfPKfczFfkHljowgVTi7n0Bkq83x9e+LXX5dAqVTi6NGgAiu5R44cAgDIZDL06NFTel2pVGLJkp+wc+c2iKKosU9qaipSU1Px8OED7Nu3BxMnTsbIkaMNFv+FC+cwY8b/Qf5iOBsAKBRynD8fjPPngzFq1JgC98/ISMfcubNw4sSxPNtSUpKRkpKMiIhw7N69AzNmzIavb08tR9GfKIpYsWIZtmzZkGes+ePHj/D48SPs3x+IQYOG4KOPPoWlZf7p6erVEEyf/j8kJSVpvH7z5nXcvHkd+/fvxdKlK+DoWEmnGLOzs/H111/i1KkTGq/nXNv79+9h9+7tGDlyNCZOnKx1/6VLF2HHjr/ybIuICENERBgCA3di7tyFeP31thrbMzMz8eOPC3DgwN48+96/H4n79yOxa9d2jBs3Ae+8M7bA9zF37kwcO3ZYeh4V9QS2trYacf7884/YvXv7f2LIQEREOCIiwrFz51/4+OPP0L//oALPRWSOzDNfgPkiF+YLNeYLIjU2ilCh2FOEzEHlys5o27YDgoNP4dy5YKSkpKBixYp5ymVnZ+Pvv9UVwddeaw03N3dp27p1q6UKTM2atTB48DDUrl0H1tbWiIqKwpEjB3H27BkAwMqVv6Jjx86oU6dusWO/e/c2Pv/8E2RnZ8PS0hKDBg2Bt7cPbGyscfHiBWzZsgEbNqyFTJb/iMgfflggVXAbNmyMAQMGo3p1T8hkMjx9+gSBgTtx/fo1KJVK/PDDt2jbtj0qVXJ6se8vyM7OwpgxbwMAOnbshPfemwgAcHcv2t2hJUsWYdu2LQAAJycnDB06Al5eLSCTyXDr1g1s3boJsbEx2LHjL8jlcsyYMVvrcTIyMvDll59CLk/DgAH+6NTJBxUqVMCdO7exYcNaxMbGICIiDCtX/orPPptWpNhybNy4Tqrgdur0Bvz8esPd3R1paWkvYtyIpKQkbNy4Dk2besHbu7PG/gsXzpPuiFatWh3Dhg1HgwaNIJfLcebMP9izZydSU1MxffrnWLduM6pX9wSgnpBwzpwZOHnybwCAh0dVDBv2Nho0aAilUomQkMsICNiM1NQUrFz5K7KysvKdZDEyMhzh4XfRrFlzjBo1Bra2tjhz5hR69eqnNc7GjZuiX7+BqFPnFWRlZeLmzevYtm0rYmNj8MMP38La2ho9e/bR6XMkKuvMMV9YWlriypVLzBfMFxLmC6KX2ChChRLYU4TMhJ9fbwQHn0JWVhZOnjyOPn365ylz7lwwkpPVd5R69uwtvS6Xp2HTpvUA1BWYFSv+0Liz1KxZc/j6+mHZsp+xdetGqFQqnDx53CCV3MWLv0d2djZkMhkWLlyMtm3bAwAsLWVo0sTrxdCI95CYmKh1/0ePHiIo6AAAdaVm2bKVGt2Fmzd/DT179sFXX/0fTpw4BoVCgXPngtGjRy8AyPMeHB0r4dVXGxQ5/mvXQqQKbs2atbBkye8aXYK9vFqgV6++mDp1Mu7cCcXBg/vg7d0ZPj5d8hwrKysLKpUKCxcuRrt2HaTXmzb1Qvv2HfHOO8OQnp6OI0cO4ZNPPi/wDuJ/7d8fCABo3boNFiz4UWNbq1avo317b4wbNxJKpRKBgbs0KrkXLpyXKo7Nmnnhp5+Wwt6+grS9bdv2aNSoCebPnw2FQo716//AtGkzAQBHjwZJFdxmzZrjp5+WaOz72mut0LNnH3z00QRERT3FunWr0bFjJzRs2DjPe1CpVKhe3RM//7wcNjbqu30tW7aWtv/zzwkpTn//tzBlyqcaX45atGiJPn36Y8qUiYiICMeiRQvRoYO39IWHqLwwt3wBqP/WMl+YVr5o2tQLixYxXxAZGydapUIJcjnAniJkBry9O6NiRUcA6oqFNkeOHAQA2NnZaVSyIiMjUK1aNdja2mLo0OH5drXN3X06Njam2DFHRobj+vVrAIDevftpVHBz1KxZGx98MCXP67mPUb16DVhbW+Odd8bkO346dxfomJjnxYz8pS1bNkiPv/76G61jpB0dK+GbbxbA4sWEzhs3/pnv8Tp3flOjgpujWrXqUjfjtLQ0PH36RKc44+LiAACenjW1bq9X71W8++44jBo1Br6+fhrbAgN3AVB3oZ858xuNSmqOnj37oH599ZeDCxfOS13qN29Wfz7W1taYM+dbrft6eFTF9OmzAKi7lufso03Pnn2kCu5/bdny8ova5MmfaL1bXKmSE/73vy8BAAqFAnv37s73XETmivmC+aIghsoXX301h/mCyASwpwgVSlDIIeo41pKKxyZgM2y3bDR2GBoEAfjPsGiDSh8+EhnDRpTcCaCuRHTt2h27d+/AlSuXEB8fB2dnF2m7utvqKQCAj08X2NnZSduaNvXCxo3bACDPGOfcch8vMzOz2DHndK8GgO7d/fIt162bLxYtWoiMjIw823x8usDHp0uece3/lTv2rKwsPaLNKzs7G5cuXQQA1K/fsMAJBatX90SbNu1w9uwZ3L59C0lJiVrvOBU0SWC1ap7SY7lcrlOstWrVQljYXezfvwc1atRA79794eDgoFFm7NjxefbLzs7G+fNnAah/TmrUqInsbO0/I/PmfQ9LS0u4urpBEATEx8chPPwuAKB9+44a3e//67XXWqF27bq4fz8S//57DiqVSmsltUmTvJMuAkBycjJu3LgOAGjZslWBd0WbNWsOB4eKSE1NwaVLFww63wEZlinmi5LGfKEd80XZyxeenjXyPQfzBVHpYaMIFUqQy6Fyr2rsMIgMws+vD3bv3gGlUonjx4/A3/8tads///yN9PT0F+V653cIqWKRlJSIp0+f4MmTx7h//x7u3r2Na9dCpHKFVSqL4sGD+9LjevXq51vOxsYWdevWQ2jozXzLCIIgPY6Pj8PTp0/w+PEj3L9/D7dv38KNG9ek7QVV5HXx7Fm0NNlffpWv3Jo0aYazZ89AFEXcuxeJFi1a5ilTtWq1fPe3z9WrTalU6hTryJFjMGvWNGRlZWHp0sX49dclaNrUC61bt8Hrr7dFo0ZNpDuTucXFxUrvsbCVBqpVq67xPDIyQnpctM+nKe7fj0RqagqeP3+udcZ/d3ftFeXw8LvSz+T+/YFS9+/C6HoHlchcMF+oMV/kZe75IizsDvMFlStsFKFCCWmcaLW0ZQwbUeJ3wXRlaSnL9+53WdK0aTPUqFETjx49xNGjhzUquUeOqLtIu7m5a4yrze3mzRvYtm0LLl78F4mJCXm2FzR5nT4SEuKl4zo6OhZY1tnZucDt58+fxa5d2xAScgWpqSl5ths6dkD9RSBH5cqVCy1fufLL9/Df1QJy2NraaX39v3T9ktG1a3coFHIsX/4LUlKSoVQqcfXqFVy9egVr1vwOR8dK6NTJB0OHjsArr9ST9su5RgBQqZJuvepyv8fc7z0/ue/OJicnaq3k2ts75HkNQL5zCBQmJSXvzwqZDlPMF+aC+YL5Ij/MF9oxX1BZxUYRKpSg4ESrZF78/Hpj1arfcOPGNURFPUXVqtWQkJCAixfPAwB69OiltcK3bt1qrF69QuM1Z2cX1KpVG6+8Ug+NGzdD/foNMHLkEIPFmvtunSiKGs//K7/uraIo4vvv5+cZ6+vm5v4i9lfRrJkXHBwq4uOPPzBM4C+oVC8rmgXF/rL8y4Y3mazw8obWp09/dOvWA6dPn8SpUydx8eJ5qSKanJyE/fsDcejQfnzyyecYONAfAJCdrdsdxtxEUbeGxtx3MwVB+5eS/D5mpTJbevzuu+Pwxht5JybURibLe7eTqLxgvlBjvsjLvPPFy32ZL6g8YKMIFU7OniJkXnr06I3Vq1dAFEUcO3YYI0eOxvHjh6VKgLau0GfPnpEquC4uLnjvvQ/Qvr13nkngoqKeGjRWFxf18VUqFZKSkuDklP+s7snJyVpf3717h1TB9fSsiffem4A2bdrlmfzv8uWLBor6pdx3wuLj4wsomVMmTnqc3+SEJc3W1hbduvVAt249IIoiwsPv4sKF8zhx4jhu3boBpVKJn3/+AW3btke1atU17sjmd7cyP7k/n9x3EPOTu0xhd4L/K/fnqVKpdFoRgqi8Yr5gviiI+eaLl+WZL6g84OozVDBRVPcUqcBGETIfHh4eUnfnf/45AQA4evQwAKBRo8aoVat2nn127domPZ4zZwH69h2gdVb8Z8+iDRpr7uUNCxr/rVKpEBkZrnXbzp1/AQAsLCywaNFSdOvWQ2sF0tCxA+ox0XYveprdunWj0PI3b74sU7NmLYPHU5D4+DhcuXIJqamp0muCIBoguyIAACAASURBVODVVxtgxIh3sHLlOgx7MUxBqVRKk+VVq1YdNjY2ACBNgpefHTv+gr9/X0yZMhGPHj3EK6+8Km0r2uejnvjOzs4erq5uOr2/3F24r1y5VGBZpVKJtWtXYd++3RpzBxCVN8wXzBfamH++eHku5gsqD9goQgXLyICgUnH4DJmdnLt7oaE3cft2qJTI/fz6aC3/+PEj6XGDBo3yPW5Q0EHpsa4Tt2nTuXMXqRvx/v178i0XHHw637tOT548BgBUrFgxz8RtuR05ckh6rC32onRn/i8LCwu0aqX+QnHnTihu3w7Nt+zjx49w6dK/ANSTBBZlzLShBAUdQL9+PfDRRxNw4sSxfMu1a9dRepyZqV65wdLSEs2bqyf4u379aoFfFs6cOYXo6CjcuHEdVaq4wtnZRap8BgefLnBZzsuXL+LhwwcAgNatX9d5TH+VKq7Sl6YbN64VWKk+fvwI1qz5Hd99N09aPpKovGK+yIv5wrzzhasr8wWVL2wUoQIJL2bIBofPkJl5442usLOzgyiK+OGHbyGKIiwtLdGtm6/W8rmX+jt37ozWMvv27ca+fS/HYRtiiUUPDw/4+LwJADhx4jgOHNibp0xsbAx++eXHfI+RE3tiYqLWu4eiKGLNmt/x77/npNe0LbFoZWUNAFAodFu6cNiwt6XH8+bN1OjynCM5ORmzZk2XKtfDh4/U6RzF1aZNO1hZWQEA/vzzD40J/3LL/UWgYcOXy0X6+w8DoP5yMG/eHK3X/vjxo/j3X/Xdwm7dfKUlPN96S/35ZGZmYvbsGVqXhoyOjsaCBd8AUH/ZyP2Z6uKtt15+rt98MxMxMc/zlImKeoplyxZL58p5b0TlFfPFS8wXhs0XCxZ8w3xBZAI4pwgVSFAoAACifQUjR0JkWHZ2dvDx6YJDh/bjzh313aj27b01KrO5denSHdevXwUALFgwF/fuRcLLqwWsra3x+PEjBAUdlO5a5UhLS9V2KJ198skXuHz5EpKTk7BgwTe4fPkiunf3Q6VKFXHt2jVs2vQn4uLiYGdnB8WL31nN2LshIGAzAOCLL6ZixIh30LBhIwiCgHv3InHgQCBCQ29p7JO7S3AOF5cqiIp6gvPnz+Hvv4/Cw6MqqlRxLbRb7muvtYK//zBs3x6A+/fv4d13h2Po0OHw8moBQRAQGnoTAQGb8fz5MwBAt2490KNHL30/Lr1UruyMwYOHYevWjYiKeiLFWK9efdjb2+PZs2gcPLgP584FAwBatXodzZu3kPbv0MEb3br1wNGjQbhw4TzGjRuJoUNHoG7dekhMTMDZs6elcfpOTpUxfvwkaV8/v944efI4Tp/+ByEhl/Huu8MxbNhwNGjQCEqlEiEhl/HXX1uQnKy+szty5GitS08WRa9efXHy5HEEB5/G48cPMXr0cAwdOgItWrSEUqnEzZvXERCwSVp5YOjQ4YUuG0lk7swhX1So4IBbt64zXxiAIfPFxYv/Ml8QmQA2ilCBhBct0KJd0ZY0IypLevbsg0OH9kvPtU2Yl2PgQH9cuHAOwcGnIZen4Y8/VuYpI5PJ8NZbI3HlyiWEht7EvXuRBomzSpUqWL58FT7//GNER0fh0KH9GnEDQL9+AxEbG4Pg4NN59h87djyuXg3B7du3kJAQj+XLf85TxsrKChMmTEJAwGbExDzH/fsRecr4+LyJrVs3QqGQ4+uvvwQAjBnzPsaNm1Doe5gy5X+wsrLG1q0bkZAQj99/X56njCAIGDp0OD74YEqhxysJEyZMQnR0FE6cOIbY2Bj8+usSreW8vFpg7tyFeV6fPn0WLCxkCAo6iHv3IrFw4bw8ZdzdPfDddz9pzC8gCALmzFmAhQvn4fDhg4iKeoKff857J9fCwgLjx3+IESPe0fs9CoKAuXO/w4IFc3H0aBCSkpKwatVvWssOGjQEkyZ9ove5iMwJ88VLzBfMF//FfEFlHRtFqEDCi26P7ClC5qhly9Zwd/fAs2fRcHSshA4dvPMta2lpie++W4S9e3fj8OGDiIgIg0KhgK2tLTw8qqJZsxYYMGAw6tV7FatW/YbQ0JuIjY3BtWsh8PJqke9xi6pOnbpYvz4AgYE7cezYYTx69AiiKKJu3boYMMAfPXr0whdfaK+QVKjggOXLV2HHjgAcP34UDx7cR2ZmBuzs7FG9uidatmyNAQMGo3p1T4SF3UFQ0EHcunUT0dFR8PCoKh1nwoRJsLKywtGjhxEb+xx2dvZa7xBqI5PJMGnSx/D17Yndu7fj8uWLiIl5DpnMAu7u7mjZsjX69h2IevVeLfxgJcTKygrz5i3EmTOncOjQfty+HYq4uFgAIpycKqNx4ybo0sUXb77ZVet4eWtra3z99Vz06zcQu3fvxLVrIUhIiIeFhSVq1aoNH583MWjQEFSo4JBnXxsbG8ycORf9+w9CYOAuXLt2FXFxsbC2tkbVqlXRtm0H9O07ANWrexb7fdrY2GL27PkYMGAw9u8PxLVrIYiLi4VKpYKLSxV4ebVA//6DDPJzS2Quyn6+UKFu3VeYLwzEUPmid+/+2Lt3N/MFkZEJoiiKhRczb3FxqRpro9NLVueC4dTPD4nb9iDrxTjV0uDqWhExMSmldr7SEB39AB4epTs7uiFZWsqQna0ydhiUC6+JaeJ1UdP3b55MJsDFJe8XgbJI3/pFWc8Xpoq/m6aJ18X0lPY10eVvnkXYXTh3bI3k3/9AxkD/Eo7MdJjjd6PSVlD9ghOtUsFeTLQqcqJVIiIiIiIiMjNsFKECCXJOtEpERERERETmiY0iVKCcJXk50er/t3fn8VHU9x/H35uLWxRIoCCHHA2KKCrlVAKKAUlSIByCnMID5PbRBw8sKNaHFgltQQrl0gpY7kuBEm65HlUoGOQSQsIVIIBhMSFAsskm2fn9wS/bhBxADNnJ7uv51+7O7OxndzKZ9+MzM98BAAAAALgbmiIoVPYteVWBM0UAAAAAAO6FpggKxS15AQAAAADuiqYICuW8fIYxRQAAAAAAboamCAplsdlk+PlJPj6uLgUAAAAAgGJFUwSFS02RUY7b8QIAAAAA3A9NERTKYrPJKE9TBAAAAADgfmiKoFCW1BQGWQUAAAAAuCWaIiiUJTWVQVYBAAAAAG6JpggKZUm1SVw+U2wMw3B1CQDwyPG/7tfjNwTgCfhfBzOgKYJCcflM8bFYvGQYDleXAQCPnGE4ZLEQMYqK/QUAT8H+AmbAXyAKxeUzxcfX1092e7qrywCAR85uT5evr5+ryyi12F8A8BTsL2AGNEVQKIstlbvPFJOyZcsrLS3V1WUAwCOXlpaismXZdxQV+wsAnoL9BcyApggKl0pTpLiULVtednu6UlNvu7oUAHhkUlNvy263E3J/BfYXADwB+wuYhY+rC4C5WWw2miLFxMvLW1WqBCgx8brs9jSVLVtBfn5lZLF4yWKxuLo8ACgSwzBkGA7Z7elKS0uR3W5XlSoB8vLydnVppRb7CwDuiP0FzIqmCApmGP8/0CpNkeLi4+OratVqKC0tVampt5Wc/EupGUzPy8tLDkfpqNVTsE7MyRPXi8XiJV9fP5UtW16PPVaFgFsMSvP+wqw8cdssDVgv5vMo1wn7C5gRTREUzG6XJSuLW/IWMy8vb5UvX0nly1dydSkPxd+/kqxWTuU2E9aJObFeUFxK6/7CrNg2zYn1Yj6sE3gaxhRBgSy2u4O8cfkMAAAAAMAd0RRBgSyp/98U4fIZAAAAAIAboimCAnGmCAAAAADAndEUQYE4UwQAAAAA4M5oiqBgKZwpAgAAAABwXzRFUKD/XT5TwcWVAAAAAABQ/GiKoED/u3ymnIsrAQAAAACg+NEUQYGyzxRRBS6fAQAAAAC4H5oiKBADrQIAAAAA3FmpaIps2rRJXbp0UXBwsJYvX55nenR0tMLDw9WpUyd98MEHyszMdEGV7seSmiKJgVYBAO6HbAEAAKRS0BRJSEjQzJkztWLFCm3YsEGrV6/W2bNnc80zYcIE/elPf9L27dtlGIbWrFnjomrdi8Vmk8RAqwAA90K2AAAA2UzfFNm/f79atWqlxx9/XOXLl1enTp20bds25/QrV64oLS1NzZo1kySFh4fnmo6is6SmyvDxkXx9XV0KAADFhmwBAACy+bi6gPu5fv26/P39nc8DAgJ0/PjxAqf7+/srISHhoT7Dy8vy6wt1Q5byZWU0ftplvw/rxXxYJ+bDOjEn1kvRlcRvVxLZQuLvwIxYJ+bEejEfs64TrzJ+Ut26slSsaNoaHxVP+77FrbDfz/RNEYfDIYvlf1/AMIxcz+83/UE88QSXh+Rr6hRp6hRVddHHV61a0UWfjIKwTsyHdWJOrBdzK4lsIZEvzIht05xYL+Zj2nVStakUF6dKrq7DBUy7TtyA6S+fqVGjhqxWq/O51WpVQEBAgdNv3LiRazoAAEBOZAsAAJDN9E2RNm3a6MCBA0pMTJTNZtOOHTvUrl075/RatWqpTJkyOnz4sCRp48aNuaYDAADkRLYAAADZLIZhGK4u4n42bdqkzz//XBkZGerZs6eGDRumYcOGady4cWratKlOnz6tyZMn686dO2rSpIkiIiLk5+fn6rIBAIBJkS0AAIBUSpoiAAAAAAAAxc30l88AAAAAAAA8CjRFAAAAAACAR6IpAgAAAAAAPBJNEQAAAAAA4JFoigAAAAAAAI/kcU2RO3fuKDQ0VPHx8ZKk/fv3KywsTMHBwZo5c6aLq/Nc966XSZMmKTg4WF27dlXXrl21c+dOF1foWebMmaOQkBCFhITor3/9qyS2FTPIb72wrbjWrFmz1KVLF4WEhGjx4sWS2FY8FfnCfMgW5kO+MB+yhTmRL0qY4UGOHj1qhIaGGk2aNDEuX75s2Gw2IygoyLh06ZKRkZFhDBkyxNi7d6+ry/Q4964XwzCM0NBQIyEhwcWVeabvv//eePPNN4309HTDbrcbAwcONDZt2sS24mL5rZcdO3awrbjQwYMHjT59+hgZGRmGzWYzOnToYERHR7OteCDyhfmQLcyHfGE+ZAtzIl+UPI86U2TNmjX66KOPFBAQIEk6fvy46tatq9q1a8vHx0dhYWHatm2bi6v0PPeuF5vNpqtXr+r9999XWFiYZs+eLYfD4eIqPYe/v78mTpwoPz8/+fr6qkGDBoqLi2NbcbH81svVq1fZVlyoRYsWWrJkiXx8fPTLL78oKytLt27dYlvxQOQL8yFbmA/5wnzIFuZEvih5HtUU+fTTT9W8eXPn8+vXr8vf39/5PCAgQAkJCa4ozaPdu15u3LihVq1aaerUqVqzZo2ioqK0bt06F1boWRo1aqRmzZpJkuLi4rR161ZZLBa2FRfLb7288sorbCsu5uvrq9mzZyskJEStW7dmv+KhyBfmQ7YwH/KF+ZAtzIt8UbI8qilyL4fDIYvF4nxuGEau53CN2rVra+7cuQoICFC5cuU0YMAA7du3z9VleZwzZ85oyJAheu+991S7dm22FZPIuV7q16/PtmIC48aN04EDB3Tt2jXFxcWxrYB8YUJkC/MgX5gP2cKcyBclx6ObIjVq1JDVanU+t1qtztMs4ToxMTHavn2787lhGPLx8XFhRZ7n8OHDGjx4sMaPH6/u3buzrZjEveuFbcW1zp07p+joaElSuXLlFBwcrIMHD7KtgP+ZJsT/S3MgX5gP2cJ8yBclz6ObIs8//7wuXLigixcvKisrS5GRkWrXrp2ry/J4hmFo6tSpSk5OVkZGhlavXq3XX3/d1WV5jGvXrmn06NGaPn26QkJCJLGtmEF+64VtxbXi4+M1efJk2e122e127dq1S3369GFbAf8zTYj/l65HvjAfsoU5kS9Knke3/cqUKaNp06Zp7NixSk9PV1BQkDp37uzqsjxe48aNNXz4cPXt21eZmZkKDg5WaGioq8vyGAsXLlR6erqmTZvmfK1Pnz5sKy5W0HphW3GdoKAgHT9+XN26dZO3t7eCg4MVEhKiKlWqsK14OPKF+ZAtXI98YT5kC3MiX5Q8i2EYhquLAAAAAAAAKGkeffkMAAAAAADwXDRFAAAAAACAR6IpAgAAAAAAPBJNEQAAAAAA4JFoigAAAAAAAI9EUwQwqdOnT7u6BA0YMECBgYFq2rRpsS/74MGDCgwMVGBgoL744otiX77ZTZw40fn9rVarq8sBAHgI8oV7I18AD4+mCGAyt2/f1pQpUxQeHu7qUgAAgJsgXwBA/nxcXQCA3CIiIvT111+7ugwAAOBGyBcAkD+LYRiGq4sA8D8TJ07U+vXrJUkxMTEurgYAALgD8gUA5I/LZwAAAAAAgEeiKQIAAAAAADwSl88AJvGPf/xDc+bMyXdaixYttHTpUkn/O/21cePGWrdunWbNmqUNGzYoOTlZAQEB6ty5syZMmOB8b3p6ujZu3Kh9+/YpOjpaSUlJysjIUOXKldWoUSO1b99evXv3Vvny5fN87oABA3To0CH5+fnpxIkTuaYFBgZKkiZNmqTBgwdrx44dWrt2rU6dOqXk5GRVq1ZNLVu21KBBg/TMM8/kWfbBgwc1cOBASdL48eM1fPjwPL9FpUqVFBUVJavVqsWLF2vPnj26du2afHx81KBBA73xxht666235OfnV+DvmpiYqMWLF2v37t26fPmyfH191bBhQ3Xv3l29e/fWl19+qRkzZkgq2unEaWlpWrNmjXbu3KnY2FilpKSoYsWKql27ttq2bau33npLAQEBed6X8zTm7777Tv7+/nlef1C7du3Sk08+meu1jIwMrV+/Xtu2bVNMTIySk5NVqVIlNW7cWJ06dVJ4eHihvxsAwD2QL8gX977+oMgX8BQMtAqUYn/84x+1efNm5/P4+HiVK1fO+fzkyZMaNWqUfv755zzvvXHjhm7cuKEDBw5o5cqVWrJkiapXr/7QNTgcDo0fP16RkZG5Xr927Zo2bNigf//73/r444/Vu3fvh162JEVFRWn06NG6efNmrtePHj2qo0eP6ptvvtGSJUv0+OOP53nvTz/9pGHDhikxMdH5Wnp6uvO9mzdv1ksvvVSkuqS733HIkCE6f/58rteTkpKUlJSk48ePa/HixZoxY4Y6duxY5M+5Hx+f3P/KL168qJEjR+rcuXO5Xk9MTNT+/fu1f/9+/etf/9LcuXNVv379R1YXAKB0Il+QLyTyBTwHTRHAJPr06aOOHTtq1qxZ2rNnjyRpw4YNkpTvUZbY2FidPn1aL774ot555x2VLVtWe/fudd5qLykpSUOGDNHNmzfl7e2t8PBwtW/fXtWqVVNycrKio6P11VdfKSkpSXFxcfrLX/6izz777KHrXrRokaxWqxo0aKDBgwcrMDBQycnJWr9+vbZs2SKHw6E///nPatu2rWrVqvVQy05LS9OoUaOUkpKivn376rXXXlPFihV16tQpLViwQNevX1dMTIxmzpypjz/+ONd74+PjNXDgQKWkpMjLy0vh4eF64403VKFCBR07dkz//Oc/dejQIR05cuShv3O2iRMn6vz58/L29tagQYPUtm1bVa5cWYmJidq3b59Wr16ttLQ0TZgwQdu3b8/3iM69xo0bp0GDBhU6T86/kQEDBqhGjRrOaVarVf369ZPVapWPj4/Cw8P16quvqmrVqvrll1+0c+dObdiwQefPn9fAgQP1zTffPFBdAIDSiXyRF/kif+QLeCqaIoBJ+Pv7y9/fP9cRiaeffrrA+R0Oh+rUqaPFixerbNmykqRWrVo5p3/11VfOox/vvfeeBg8enOv9QUFB6t69u0JCQnT79m19++23yszMzHNU4H6sVqtat26tzz//XGXKlHG+3q5dOz322GNatWqV7Ha7Nm/enOsU1geRkZGhO3fuaMGCBWrXrp3z9RdeeEHt2rVTWFiYbDabIiMjNXnyZPn6+jrniYiIUEpKiiRp+vTpCgkJyfX+kJAQ9e/fX3FxcQ9VU7YrV67ov//9ryRp7NixGjlyZK7pQUFBatCggT755BOlpqYqMjJSQ4YMue9ya9asqZo1axY4fc2aNc7A0qZNG02aNCnX9I8++khWq1XlypXTl19+qebNm+ea3qFDB3Xu3FnvvPOOrFarIiIiNHPmzAf6zgCA0od8kRf5Ii/yBTwZA60CpVj37t2dgeVe169fdwahfv365TtP9erV1aJFC0l3T/u89xTSBzV58uRcgSVbnz59nI+Levu/119/PVdgyVa7dm21adNGknTnzh3Fx8c7p129elXffvutJCk0NDRXYMnm7++vTz/9tEg1SXdPD85Wt27dfOfp2bOnevXqpXfffVfPPfdckT8r24EDB5xHrOrVq6e///3v8vb2dk6/cOGCdu/eLUl6++238wSWbO3atVOPHj0kSdu2bVNCQsKvrg0A4D7IF+QL8gU8CWeKAKVYs2bNCpwWEREh6e4RHy+vgvuf1apVcz622+0PXUP16tXVsGHDfKfVrl3b+Tj7qMrDevnllwucVqdOnXyXn32kQ5LzdN/8NG/eXA0bNtTZs2cfuq46derIx8dHmZmZmjZtmvz8/BQUFJTraFKZMmU0ZcqUh152fs6dO6dx48YpMzNTlSpV0rx581S5cuVc8+zbt0/ZY2e3bdu20OUFBQVp7dq1cjgcOnTokMLCwoqlTgBA6Ue+IF/kRL6Au6MpApRiOa/1LEh2YMnIyNDVq1d1+fJlxcXFKTY2VkeOHFFsbKxzXofD8dA13DsqeU4VKlRwPs7MzHzoZd9v+Tmvhc7KynI+jo6Odj5+9tlnC13+c889V6TQ8sQTT6hXr15auXKlEhISNHr0aFWoUEEtW7ZUmzZt1LZt22IbZCwxMVEjRozQrVu35O3trc8++0wNGjTIM1/O713Q0bv8XL58uVjqBAC4B/IF+SIn8gXcHU0RoBSrWLFiodNtNptWrFihyMhIxcbG5hscvLy8ihRWsuUcjf5eFovF+biod/8uyvKzTz319vbOc7TjXlWrVi1SXZL0wQcfyM/PT8uXL1dmZqZSUlK0e/du5ymmderUUZcuXTRo0CBVqVKlSJ9ht9s1ZswYXbp0SZI0YcKEfE/3le4OflcUt27dKtL7AADuiXxBvsiJfAF3R1MEKMVy7rTvdfnyZQ0dOlQXL150vubr66unnnpK9evXV5MmTdSiRQtt3LhRK1asKIlyS0xGRoaku0emDMMo9Hf6NXx9ffX+++9r2LBh2r59u/bs2aOoqCilpaVJki5duqQFCxZoxYoVWrhwYZGu+508ebIOHz4s6e6pum+//XaB8+Y8mrV27dpcp9oWpqiBCgDgnsgX+SNfkC/gnmiKAG5q/PjxzsASGhqq/v3769lnn82zI1u1apUrynuknnjiCUl3j+4kJSUVulMu6uBvOfn7+6t///7q37+/7Ha7fvzxR33//ffavHmzrly5olu3bmnChAnaunVroddf32vevHnauHGjpLsj2t97W8B75Txq9dhjj6levXpF+j4AABSEfEG+IF/A3XD3GcANnThxQseOHZMktWzZUjNmzNALL7yQb2f/6tWrJV3eI5fzVoOnTp0qdN6TJ08W6TMcDocuX76sAwcO5Hrdz89PrVq10vjx47Vt2zbnYHVxcXG6cOHCAy9/y5Ytmj17tiTpN7/5jebMmSM/P79C39OoUSPn44MHDxY6708//aQvvvhCW7Zs0c8///zAdQEAPBf5gnxBvoA7oikCmExxnIqZfX2oJDVp0qTA+eLj4/Xjjz86n+c8PbI0a9++vfPxpk2bCpwvJibmvqGmIB9++KE6duyowYMHFziQWHaAyZaenv5Ayz527JgmTpwowzBUrlw5zZs3L9co/gXJOZL+smXLCh18bubMmZoxY4b+8Ic/MBAaAHgA8sWvR74gX8A90RQBTCZnt76ot5nLPr1Tunvv+exrYHOyWq169913c00ryi3zzKhBgwZ65ZVXJEkbN27Url278sxz+/ZtTZo0qcif0aFDB+fjiIiIfAd6s9lszs+uUKGCnnrqqfsu98qVKxo1apTS09Pl5eWl6dOn65lnnnmgmpo2barf/e53kqTY2FhNnTo137pWrlyp7777TtLdo17Nmzd/oOUDAEov8sWvR74gX8A9MaYIYDL+/v7OxzNnzlTXrl3l7e39wDsuSXrppZfk7+8vq9Wq6OhoDR48WP369VOtWrV08+ZN/fDDD1q3bl2e0cRv375dbN/D1T788EN1795dKSkpGjt2rHr16qXg4GBVrFhRJ0+e1MKFCxUfH1/k5b/66qtq2rSpTpw4oV27dqlHjx7q27ev6tWrJ8MwdP78eS1btkxnzpyRJA0dOrTQke4l6c6dOxoxYoRzdPuRI0eqSZMmOn/+vOx2e4Ej7FerVs35dzNlyhT16NFDd+7c0fLly3Xq1ClnXVarVdu2bVNkZKSkuwO5ffLJJ49soDgAgHmQL4oH+YJ8AfdDUwQwmY4dO2revHnKysrS0qVLtXTpUtWsWVN79ux54GWUKVNGf/vb3zRixAilpaUpKipKUVFReearV6+eevbsqenTp0uSzp49qxdffLHYvosr1a1bVwsWLNCYMWOUnJysVatW5Rn07bXXXtOtW7f0ww8/3Pd62nt5eXlpzpw5Gjp0qM6ePauTJ09q8uTJeeazWCzq27evRo0add9lnjx5UrGxsc7nc+fO1dy5c+/7vjFjxmjs2LGS7q7TZcuWafTo0bpy5YqOHDmiI0eO5HlP5cqVNX369CKNWA8AKH3IF8WDfEG+gPuhKQKYTOPGjTV//nzNnz9fMTExcjgc8vHxkc1mu++RgJxat26t9evXa9GiRTpw4IASEhIk3T31tVGjRurcubN+//vfKzMzU3PnzpXNZtPWrVvVu3fvR/XVSlyLFi20ZcsWLVq0SHv37tW1a9ckSYGBgXrzzTfVrVs3DRw4UJJUvnz5h15+jRo1tH79en399dfauXOnYmNjdfPmTfn6+iogIEAtW7ZUOWGZEgAAAZtJREFUjx499Pzzzxfr97qfp59+Wlu3btW6deu0a9cuxcTEKDk5WX5+fqpXr57at2+vfv36qWrVqiVaFwDAdcgXxYd8Qb6Ae7EYBZ0vBQAeICwsTLGxsfrtb39b6KBpAAAAD4p8AZQeDLQKwO2cOXNGw4cP15QpU3T69OkC50tISHDexq5x48YlVR4AACiFyBeAe+LyGQBup2rVqvrPf/4jh8Oh+Ph4zZ8/P89gX1lZWZo6dapzdPxOnTq5olQAAFBKkC8A98TlMwDc0tixY7Vjxw5Jd6/97dmzp5588kllZWXp4sWLWr16tU6cOCHp7u3vFixY4MpyAQBAKUC+ANwPTREAbikxMVEjR47U0aNHC50vODhYU6dOVaVKlUqoMgAAUFqRLwD3Q1MEgNtyOBzavHmzNm/erFOnTikxMdE5cnvTpk3VrVs3vfzyy64uEwAAlCLkC8C90BQBAAAAAAAeibvPAAAAAAAAj0RTBAAAAAAAeCSaIgAAAAAAwCPRFAEAAAAAAB6JpggAAAAAAPBINEUAAAAAAIBH+j9AD5xk/qKs7gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import learning_curve\n",
    "import warnings  \n",
    "warnings.filterwarnings(\"ignore\")  \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",
    "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",
    "    ax[i].set_ylim(0, 1)\n",
    "    ax[i].set_xlim(N[0], N[-1])\n",
    "    ax[i].set_xlabel('training size', fontsize = 30)\n",
    "    ax[i].set_ylabel('score', fontsize = 30)\n",
    "    ax[i].set_title('degree = {0}'.format(degree), size=24)\n",
    "    ax[i].legend(loc='best', fontsize = 30) \n",
    "#fig.savefig('figures/05.03-learning-curve2.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "When your learning curve has already converged \n",
    "- *adding more training data will not significantly improve the fit!*\n",
    "- 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",
    "- in the right panel: by moving to a much more complicated model, we increase the score of convergence (indicated by the dashed line)\n",
    "- at the expense of higher model variance (indicated by the difference between the training and validation scores)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "If we were to add even more data points, the learning curve for the more complicated model would eventually converge.\n",
    "\n",
    "![image.png](img/ml6.png)\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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Validation in Practice: Grid Search\n",
    "\n",
    "The trade-off between bias and variance, and its dependence on model complexity and training set size.\n",
    "\n",
    "In practice, models generally have more than one knob to turn\n",
    "\n",
    "- plots of `validation and learning curves` change from lines to multi-dimensional surfaces.\n",
    "    - such visualizations are difficult\n",
    "    - we would rather simply find the particular model that maximizes the validation score.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Validation in Practice: Grid Search\n",
    "\n",
    "Scikit-Learn provides automated tools to do this in the `grid search module`.\n",
    "\n",
    "Here is an example of using grid search to find the optimal polynomial model.\n",
    "\n",
    "We will explore a three-dimensional grid of model features; \n",
    "- the polynomial degree, \n",
    "- the flag telling us whether to fit the intercept\n",
    "- the flag telling us whether to normalize the problem.\n",
    "\n",
    "This can be set up using Scikit-Learn's ``GridSearchCV`` meta-estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:19.388024Z",
     "start_time": "2020-05-18T14:04:19.384428Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Notice that like a normal estimator, this has not yet been applied to any data.\n",
    "\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": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:20.431169Z",
     "start_time": "2020-05-18T14:04:19.390055Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "grid.fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now that this is fit, we can ask for the best parameters as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:20.437265Z",
     "start_time": "2020-05-18T14:04:20.432897Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'linearregression__fit_intercept': False,\n",
       " 'linearregression__normalize': True,\n",
       " 'polynomialfeatures__degree': 4}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:04:20.651021Z",
     "start_time": "2020-05-18T14:04:20.438725Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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13y/b2J46dQq5ubnQfnEbtbCwEHv37h1xkNP40d3Ti/KbrSirMqKsyjhw5mOaLhx5c1IwLT0WU9OjETnKrTqJyDmvg3z69OnYsWMHurq6EBYWhhMnTmD27Nm+rI0krLunFxdvGHGmogmlVUbYeh0IDQ5A1j1xmL1Qi9mTtCNakTZecGEPicnrIF+4cCEuX76MwsJCBAUFYfbs2di4caMvayOJ6bU7UFZlRHGZfiC8o8ODsSg7BfdO02FKWvSYHNYrNVzYQ2Ib1TzyjRs3MrwVoL65E5+VNqK4XA9TZw+iNEFYlJ2C+6frMCUtxifT/+SMC3tIbFzZSU7ZHQ6cu9aMY2dqcaOuHQFqFbIztXgoOwWzJsUpsuftChf2kNgY5DRIZ7cNn1xswEdn69BiskIXE4onlkxG7qwkv++bLTZvx7m5sIfExiAnAEBbhxVHPq/ByQv16LE5MD0jBk8tnYqcyfGKGDoZzTg3F/aQ2BjkCtdqtuLwv6pRdLEBdruAB2cmYvkD6chIjBS7tDE1mnHu8bgFK8kLg1yhOrtt+GdxNY6frYMgCMidlYSVuROQGKsRuzRRjHace7xtwUrywiCXGH/PR7b1OvDxuTocLL6Fru5ezJ+VhNULJ0IXE+az95AjjnOTnDHIJcTf85FLK5vx9rFrMLR1I2tiHL6+OFNxQyiucJyb5IxBLiH+mo/cYurG3uPXce6aAclaDX78RA5mTXKxQ71CcZyb5IxBLiG+no/scAg4+u9aHDh1E4IgYE3eJCx/IINzwF3gODfJFYNcQnw5Tnu7tQu7D13Bjfp25GRq8dQjUxGv8HFwovGKXTMJKczLRHDg3T8Sq82OknL9iF7DIQj46Gwdtv/5NBqaO/Hdgpl4YW02Q5xoHGOPXEL6L+v3HruKzu4vjznrsPSO6KanqasHfzp4GZdutmDWpDh8K3+GonYgJFIq9sglJjcrCaHBd/9+7b/p6crVmlb8/M+nUVHThqeXT8NLX89hiBMpBHvkEuTJTU+HIODwv6qx75MqJMSE4cWv53BKIZHCMMglaKQ3Pbu6bfjDu2W4cKMZD8xIwIZHp991SDERjX8cWpEgZzc9hy5OaW6zYPMfTuFiZTPWLZ2C51ZnMcSJFIr/8yXI3eKUa7Vt+J/7y+BwCHjpiRzMmije4h4ecUYkPga5RLlanPKvy3rsPnQF8dGh+PnGXISM0Q6zzgIbAI84I5IABrmMHD9Ti73Hr2Nqegx+UDgbaQmRMBjMfn9fV3vABAepecQZkQQwyGVAEAS89+lNHCy+hblT4rHpa1kICgwYs/d3tQfM0K/14xFnRGOLQS5xDkHA/z16DSfP12NhdjI2PDoNAeqxvUftaTBz61eiscVZKxLmEAS88UEFTp6vR/68DHwrf/qYhzjgOpjDQwPczq4hIv9jkEuUQxDwxuEKnCprxOoF9+DriydDpRLn7ExX0yHXPzING/KnDwS9NioEG/Knc3ycaIxxaEWCHIKAPUcqcKq0L8Qfe2iSqPW4mw7J4CYSF4NcYgRBwFsfXsUnFxuxav49+NrCiWKXBIB7dRNJGYdWJObdoioUXWjAytwJePyhiaINpxCRfDDIJeTYv2vxwb+qERKkxj9LqvHT/1U84n3IiUi5GOQS8fnl23jno+tQqQCrbfDCG4Y5EQ1nVEF+4sQJFBYWIj8/H7/85S99VZPilN9qwZ8OXUZggAqCMPgxd/uQExF5HeS1tbXYvn07Xn/9dbz//vu4fPkyioqKfFmbItQ3d+L1/WVI1mrQaxecPocrJYloOF4H+bFjx7BixQokJSUhKCgIO3fuRE5Oji9rG/c6LDa89o9SBAUG4MWv57hceMOVkkQ0HK+nH1ZXVyMoKAibNm1CY2MjFi9ejBdffNGXtUmWL7Zu7bU78Pr+MrSYrdi8fi7iokJRmJc5aHMqgCslicg9r4PcbrfjzJkzeOutt6DRaPC9730P+/fvR2Fh4Yi+X6uN8PatB9HpxvZYs5Nna7HnyFVYbX2HIxtNVuw5chVRkaFYfF/6iF/n9XcvoqKmDS+tuxfz5qQBAFYvjkRUZCj2HL6C5lYL4mPD8Ez+jGFfd6zbLyVKbjvA9iu9/XfyOsjj4+ORm5uLuLg4AMDSpUtRWlo64iA3GjvgcDgfEx4pnW5stnG90xuHygdCvJ/VZscbh8qRlREzotf4+Hw9DhffQv6DGZg9IWZQG7IyYvDr53IHPd9VG8Vov1Qoue0A26/E9qvVKpcdYK+DfMmSJdi8eTNMJhPCw8Px6aef4qtf/arXRcqFJwcjO3Oz0YS9x64hO1OLNS6GTHjqDhF5wusgz8nJwbPPPov169fDZrNhwYIFWLNmjS9rk6SRHozsTGe3Da/vv4SYiGA8u2om1Oq7V226OsQB4J4mROTcqPZaWbt2LdauXeurWmTB2xuSgiBg96EraOuwYst/uxcRYUFOn+fqEAeeukNErnDTLA+52wnQlQ9P1+LCjb4T7zNTol0+b7RDN0SkPAxyL3i6E+D1ujb842Ql7pumw9L70oZ97miGbohImRjkfmax9uKPBy9DGx2Cb+XPGLSbobObmpxLTkSe4qZZfvbO8eswmrrx3VVZ0IR++Xuz/6Zmf+/7zpuaPHWHiDzBHrkfnb1qwKmyRqyaPwGT0waPiw93U3PH8wsY3EQ0YuyR+0l7hxVvHqnAhMRIrF5w9yk/vKlJRL7CIPcDQRDwl8MVsNrseLZgJgID7v5r5gZZROQrHFrx0EhWXZ4qbURppRHrlk5Bany409fhTU0i8hUGuQdGsuqyvcOKv564ganpMfjqMFMNvZ2PTkQ0FIPcA+5WXd4Z9E0tnfj88u1hg5kn0xORLzDIPTDcDcqScj3+8s8r6P1iR8e2Thv3SCGiMcGbnR4Y7gblP07eGAjxfjxvk4jGAoPcA4V5mQgOHPxX1n+DstXc4/R7OJ2QiPyNQysecHWDMiE2zOX3cDohEfkbg9xDQ29QOgQBv3zzDDQhgbD12mGzfzm8wumERDQWGOSjdKq0Ebf0Zny3YCYATickorHHIB+Fzm4b/nGyElPSojFvZiJUKhWDm4jGHG92jsJ7n95EZ7cNTz0yddD2tEREY4lB7qW6pg58fK4ei+ekIiMxUuxyiEjBFDO04suT6QVBwN7j1xAWEoDHF03ycaVERJ5RRJD7+mT6CzeaUVHThqeXTXV5iDIR0VhRxNDKcHukeMrucOAfJyuRFKfBojkpviqRiMhrighyXx7icKq0EY3GLqzJy0SAWhF/fUQkcYpIIl8d4mDtseO9T29icmo07p0a74vSiIhGTRFBPtweKZ44+u8atHf24IklkzndkIgkQxE3O31xiIOpswcffF6DuVPi7zpImYhITIoIcmD0hzi8/9lN2GwOrF3MvVOISFoUMbQyWs3tFhRdaMDC7GQka52fwUlEJJZRB/mvf/1rbNmyxRe1SNY/S6oBAAXz7xG3ECIiJ0YV5CUlJdi/f7+vapGk5jYLTpU2YlFOCrTRoWKXQ0R0F6+DvK2tDTt37sSmTZt8WY/kHCq5BZUKWJk7QexSiIic8jrIf/azn+Gll15CVFSUL+uRFEObBZ+V6ZGXk4q4KPbGiUiavJq18ve//x3JycnIzc3Fvn37vHpjrTbCq+8bSqfz386D75y4AbVahadXzUTZjWbsOXwFza0WxMeG4Zn8GVh8X7rf3nuk/Nl+qVNy2wG2X+ntv5NKEATB/dMG+9a3vgWDwYCAgAC0t7ejq6sLjz32GLZu3Tri1zAaO+BwePzWg+h0kTAYzKN6DVeaWruwddfnePjeVExMiRq06RbQt6BoQ/50UQ+S8Gf7pU7JbQfYfiW2X61WuewAe9Uj/8tf/jLw53379uH06dMehbgcHCqpRkCACityJ+CVPWdcbrrFE4GISGycR+5Ei6kbJZf0WJSdgpiIEJ9uukVE5GujXtlZWFiIwsJCX9QiGUf/XQtBAJY/0DcGro1yHuaebrpFROQP7JEP0WGxoehCAx6cmYD4mDAAvtt0i4jIHxSz18pInThXB6vNjvwHv5w37otNt4iI/IVBfgerzY7jZ+qQnalFWsLgu8Oj3XSLiMhfOLRyh1Oljeiw2LBiHldxEpF8MMi/0Gt34MjnNZicFo2p6TFil0NENGIM8i/8u6IJRlM3e+NEJDsMcgCCIODov2uRrNUgO1MrdjlERB5hkAO4Ud+Oar0ZS+9Ph5pncRKRzDDIARw7UwdNSCDmc1YKEcmQ4oO8xdSNc1cNWDQnBSHBAWKXQ0TkMcUH+Ufn6iBAwMP3popdChGRVxQd5NYeOz650IB7p+oQHx0mdjlERF5RdJCXlOvR2d2LR+4X/4AIIiJvKTbIBUHA8bN1yEiMwJS0aLHLISLymmKD/HJ1KxqaO/HI/elQccohEcmYYoP85Pl6RIQF4YEZCWKXQkQ0KooM8rYOKy5cb8bC2ckICuSUQyKSN0UG+aeljbA7BOTNSRG7FCKiUVNckDscAj650IAZE2KRGKcRuxwiolFTXJBfummE0dSNxXO5AIiIxgfFBfnJ8w2I0gRh7pR4sUshIvIJRQV5i6kbFyub8VBOCgIDFNV0IhrHFJVmn1xsAARgUQ5vchLR+KGYILc7HPi0tBFZE+Ogi+G+KkQ0figmyC9VtaDVbEXeHN7kJKLxRTFB/llZIyI1QciZzKPciGh8UUSQd1hsuHCjGfNmJvEmJxGNO4pItc8v30avXcCC2TzKjYjGn8DRfPMf/vAHHD58GACQl5eHn/70pz4pytdOlTUiIyECGYmRYpdCRORzXvfIi4uLcerUKezfvx/vvfceysvLcezYMV/W5hN1TR2o1puxIDtZ7FKIiPzC6x65TqfDli1bEBwcDADIzMxEQ0ODzwrzlVNljQhQqzBvZqLYpRAR+YXXQT5lypSBP9+6dQuHDx/GO++845OifKXX7sCnFxsQoFbhR//jFLRRISjMy0RuFsfKiWj8UAmCIIzmBa5fv47nnnsOP/zhD/H444/7qi6f2H2gDO99UnXX1yM1Qdj42Gwsvo9ndRKR/I3qZufZs2fxwgsvYOvWrVi5cqVH32s0dsDhGNXvEOh0kTAYzC4f/6D4ltOvm7tseO1vF2Ayd8u6d+6u/eOZktsOsP1KbL9arYJWG+H0Ma+DvLGxEd///vexc+dO5Obmel2cN0rK9dhXVIkWkxVxLoZLOiw29PQ6XL5GT68D+4oqZR3kRETAKIJ89+7dsFqtePXVVwe+9uSTT2LdunU+KcyVknI93jxcMRDSRpMVbx6uAIBBoXzmapPb1zKarP4pkohoDHkd5Nu2bcO2bdt8WcuI7CuqvKun7ax3/Xn5bcREBKPTYoPN7nwIRxsV4tdaiYjGguxWdrrqRd/59RZTN67VtmHx3FR8c8UMhIfefcBycKAahXmZfquTiGisyC7IXfWi+79eUq7Hz3Z/DgHAyfP1AIDXXszDdwtmDjxHGxWCDfnTOT5OROPCqGatiKEwL3PQGDnwZe966Ph5W0fPoPFzBjcRjUey65HnZiVhQ/50aKNCoMLg3vVw4+dEROOV7HrkwJe966FzSUcyfk5ENN7IMsjv1D+n3GiyQgXA2fwUzk4hovFM1kF+8mztoDFxZyHO2SlENN7JOsj3HL7idPVmf8+cm2QRkRLIOsibWy1Ovy4A+POWh8e2GCIikcg6yONjw2BwEubaqJBBY+fsmRPReCa76Yd3eiZ/BoIDBzchKECF7Ewt3jxcMTBbpX8/lpJyvRhlEhH5layDHACCg75sQoAa+OaKGSitNHI+OREphmyHVkrK9dhz5CqsNvsdX1UB4HxyIlIW2fbI9xVVDglxwO4QsPvQZZffw/nkRDQeyTbIXfWuXR06xPnkRDReyTbIPeldc7dDIhrPZBvkhXmZCAm6e59xZ3Y8v4AhTkTjlmyDPDcrCd9fmw2VavjncVyciMY72QY5ADS3WSC4GBMHOC5ORMogy+mHd67adIWrOYlIKWQX5ENPAXJlx/MLxqgiIiJxyW5oxdkpQENxXJyIlER2Qe5udSbHxYlIaWQX5MP1tjlfnIiUSHZj5IV5mXjjgyuw2b+crhIcqGaAE5Fiya5HnpuVhAXZyQOfsxdOREonu0SGgWUAAAd7SURBVB45AHR02RAdEYw92x+F0dghdjlERKKSXY/c1utA2c0WzJkcD7XazbJOIiIFkF2QV9S0wtpjx9wp8WKXQkQkCaMK8oMHD2LFihVYtmwZ3n77bV/VNKzz15sREhSAGRNix+T9iIikzusx8tu3b2Pnzp3Yt28fgoOD8eSTT+LBBx/E5MmTfVnfIIIg4MJ1A2ZNjENQ4Mh2PiQiGu+87pEXFxdj3rx5iImJgUajwfLly3HkyBFf1naXW3oz2jp6MIfDKkREA7zukTc1NUGn0w18npCQgNLS0hF/v1Yb4fF7Hj1bD7UKCAkNwub/U4LmVgviY8PwTP4MLL4v3ePXGw90ukixSxCNktsOsP1Kb/+dvA5yh8MB1R2bgQuCMOhzd4zGDjhcncvmwr/KGqCLCcOfDlwa2G/F0GrBb/eew7krejy9fLpHryd3Ol0kDAaz2GWIQsltB9h+JbZfrVa57AB7PbSSlJQEg8Ew8LnBYEBCQoK3L+dWe2cPbunNMHX1ON006+PzDSgp1/vt/YmIpMrrIJ8/fz5KSkrQ0tICi8WCo0ePYtGiRb6sbZBLVUYAgMVqd/mcfUWVfnt/IiKp8npoJTExES+99BKeeeYZ2Gw2rF27FtnZ2b6sbZCyKiOiw4MRoAZazD1On+NuZ0QiovFoVEv0CwoKUFBQ4KtaXLI7HLhU1YJ7p+ow455Y/PHgZafP4z7kRKREsljZWVlvQpe1F9mZWuRmJWHJ3JS7nsN9yIlIqWQR5GVVRqhVKsy8p28159PLp+O7BTOhiw0DwB0QiUjZZLH7YVmlEZPToqEJDRr4Wm5WElYvnqK4KUhERENJvkfearaipqkD2ZlasUshIpIkyQd5/7TD2ZMY5EREzkg+yEurjIiNDEGaLlzsUoiIJEnSQd5rd+DyrRbMnqT1aPk/EZGSiHazcySn+9TpOxCpCcYDMxJdPl/ppwQpuf1KbjvA9iut/cO1VyUIgmc7VxERkaRIemiFiIjcY5ATEckcg5yISOYY5EREMscgJyKSOQY5EZHMMciJiGSOQU5EJHMMciIimZNFkB88eBArVqzAsmXL8Pbbb9/1+JUrV1BYWIjly5fj5ZdfRm9vrwhV+o+79h8/fhxf+9rXsHr1ajz//PNob28XoUr/cNf2fidPnsTDDz88hpWNDXftr6qqwtNPP43Vq1fjO9/5zrj62QPu219eXo41a9Zg9erVeO6552AymUSoUgIEidPr9cKSJUuE1tZWobOzUygoKBCuX78+6DkrV64Uzp8/LwiCIPzHf/yH8Pbbb4tRql+4a7/ZbBYWLFgg6PV6QRAE4fe//73wi1/8QqxyfWokP3tBEASDwSA8+uijwpIlS0So0n/ctd/hcAjLli0TioqKBEEQhB07dgi/+c1vxCrX50by81+3bp1w8uRJQRAE4Ve/+pXwu9/9ToxSRSf5HnlxcTHmzZuHmJgYaDQaLF++HEeOHBl4vL6+Ht3d3ZgzZw4AoLCwcNDjcueu/TabDdu3b0diYiIAYNq0aWhsbBSrXJ9y1/Z+27Ztww9+8AMRKvQvd+0vLy+HRqPBokWLAACbNm3CU089JVa5PjeSn7/D4UBnZycAwGKxIDQ0VIxSRSf5IG9qaoJOpxv4PCEhAbdv33b5uE6nG/S43Llrf2xsLB555BEAQHd3N3bt2oWlS5eOeZ3+4K7tALBnzx7MnDkTOTk5Y12e37lrf01NDeLj47F161Y8/vjj2L59OzQajRil+sVIfv5btmzBtm3bsHDhQhQXF+PJJ58c6zIlQfJB7nA4Bu1FLgjCoM/dPS53I22f2WzGxo0bMX36dDz++ONjWaLfuGv7tWvXcPToUTz//PNilOd37trf29uL06dPY926ddi/fz/S09Px6quvilGqX7hrf3d3N15++WW88cYbOHXqFNavX4/NmzeLUaroJB/kSUlJMBgMA58bDAYkJCS4fLy5uXnQ43Lnrv1AX89l/fr1mDZtGl555ZWxLtFv3LX9yJEjMBgMWLNmDTZu3Djw9zBeuGu/TqfDhAkTMHv2bADAqlWrUFpaOuZ1+ou79l+7dg0hISHIzs4GAHzjG9/A6dOnx7xOKZB8kM+fPx8lJSVoaWmBxWLB0aNHB8YEASA1NRUhISE4e/YsAODAgQODHpc7d+232+3YtGkT8vPz8fLLL4+rqxF3bX/hhRfw4Ycf4sCBA9i1axcSEhKwd+9eESv2LXftnzt3LlpaWlBRUQEAOHHiBLKyssQq1+fctX/ChAnQ6/WoqqoCAHz00UcDv9QUR8w7rSP1/vvvCytXrhSWLVsm7Nq1SxAEQXj22WeF0tJSQRAE4cqVK8KaNWuE5cuXCz/+8Y8Fq9UqZrk+N1z7jx49KkybNk1YvXr1wMfWrVtFrth33P3s+9XW1o67WSuC4L79Fy5cENasWSOsWLFC+Pa3vy00NzeLWa7PuWv/yZMnhYKCAmHVqlXChg0bhJqaGjHLFQ1PCCIikjnJD60QEdHwGORERDLHICcikjkGORGRzDHIiYhkjkFORCRzDHIiIpljkBMRydz/BxXuLhpKdKLrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 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)#.hold=True);\n",
    "plt.axis(lim); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The grid search provides many more options, including the ability \n",
    "- to specify a custom scoring function, \n",
    "- to parallelize the computations, \n",
    "- to do randomized searches, and more.\n",
    "\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",
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    "slideshow": {
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   "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",
    "\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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](img/chengjun2.png)\n",
    "\n",
    "<!--NAVIGATION-->\n",
    "< [Introducing Scikit-Learn](06.02-machine-learning-with-sklearn.ipynb) | [Contents](Index.ipynb) | [Feature Engineering](06.04-Feature-Engineering.ipynb) >"
   ]
  }
 ],
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