{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Sheet 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: Cross-validation methods provided by Scikit-Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to experiment with the methods `sklearn` provides to us.\n",
    "\n",
    "**Task**: For this we generate a *toy* dataset containing only the numbers from 0 to 9, i.e.,\n",
    "\n",
    "    X = range(10)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = list(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Leave One Out Cross-Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `LeaveOneOut` is a simple cross-validation.\n",
    "Each training set is created by taking all the samples except one, the test set consisting of the single remaining sample.\n",
    "Thus, for `n` samples, we have `n` different training sets and `n` different test sets.\n",
    "Leave-one-out cross-validation (LOOCV) can be computationally expensive for large datasets.\n",
    "\n",
    "You can import the function `LeaveOneOut` by\n",
    "\n",
    "    from sklearn.model_selection import LeaveOneOut\n",
    "    \n",
    "The documentation can be found [here](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.LeaveOneOut.html#sklearn.model_selection.LeaveOneOut).\n",
    "\n",
    "With\n",
    "\n",
    "    loo = LeaveOneOut()\n",
    "    \n",
    "you generate a so-called *iterator* in python.\n",
    "An iterator is an object that can be iterated upon, meaning that you can traverse through all its values.\n",
    "\n",
    "The command\n",
    "\n",
    "    S = loo.split(X)\n",
    "\n",
    "generates a leave-one-out cross-validation iterator `S` across the set/list/array `X`.\n",
    "\n",
    "**Task**: Execute the above commands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import LeaveOneOut\n",
    "loo = LeaveOneOut()\n",
    "S = loo.split(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, you can always access the next item in the iterator `S` by typing\n",
    "\n",
    "    next(S)\n",
    "    \n",
    "**Task**: Try this out multiple times and see what changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 3, 4, 5, 6, 7, 8, 9]), array([2]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, iterators are used in loops:\n",
    "\n",
    "    for train, test in loo.split(X):\n",
    "        print(\"Training set: %s\\t Test set: %s\" % (train, test))\n",
    "\n",
    "**Task**: Try it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set: [1 2 3 4 5 6 7 8 9]\t Test set: [0]\n",
      "Training set: [0 2 3 4 5 6 7 8 9]\t Test set: [1]\n",
      "Training set: [0 1 3 4 5 6 7 8 9]\t Test set: [2]\n",
      "Training set: [0 1 2 4 5 6 7 8 9]\t Test set: [3]\n",
      "Training set: [0 1 2 3 5 6 7 8 9]\t Test set: [4]\n",
      "Training set: [0 1 2 3 4 6 7 8 9]\t Test set: [5]\n",
      "Training set: [0 1 2 3 4 5 7 8 9]\t Test set: [6]\n",
      "Training set: [0 1 2 3 4 5 6 8 9]\t Test set: [7]\n",
      "Training set: [0 1 2 3 4 5 6 7 9]\t Test set: [8]\n",
      "Training set: [0 1 2 3 4 5 6 7 8]\t Test set: [9]\n"
     ]
    }
   ],
   "source": [
    "for train, test in loo.split(X):\n",
    "    print(\"Training set: %s\\t Test set: %s\" % (train, test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = list(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[train[0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Fold cross validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `KFold` divides all the samples into `k` groups of samples called folds (if $k=n$, this is equivalent to the Leave-One-Out strategy) of equal sizes (if possible).\n",
    "The prediction function is learned using `k−1` folds, and the omitted fold is used for testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can import the function `KFold` by\n",
    "\n",
    "    from sklearn.model_selection import KFold\n",
    "\n",
    "Check out the documentation of the function [here](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html#sklearn.model_selection.KFold).\n",
    "As for LOOCV, create a test example that shows the behaviour of the function.\n",
    "For `n_splits=2`, you should obtain\n",
    "\n",
    "    Training set: [5 6 7 8 9]\t Test set: [0 1 2 3 4]\n",
    "    Training set: [0 1 2 3 4]\t Test set: [5 6 7 8 9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set: [5 6 7 8 9]\t Test set: [0 1 2 3 4]\n",
      "Training set: [0 1 2 3 4]\t Test set: [5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "kf = KFold(n_splits=2)\n",
    "for train, test in kf.split(X):\n",
    "    print(\"Training set: %s\\t Test set: %s\" % (train, test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2 - Cross-validation for a diabetes data set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diabetes data set contains ten measurements (age, sex, body mass index, average blood pressure, and six blood serum measurements) for each of the `n = 442` patients.\n",
    "\n",
    "The response variable is a quantitative measure of disease progression one year after baseline.\n",
    "\n",
    "**Task**: The data set is part of scikit learn, you can import it using\n",
    "\n",
    "    from sklearn import datasets\n",
    "    diabetes = datasets.load_diabetes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "diabetes = datasets.load_diabetes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create a pandas data frame to hold this information.\n",
    "\n",
    "**Task**:\n",
    "Create a pandas data frame `X` holding the ten predictor variables. You should name the columns in the data frame using the optional argument `columns=cols`, where `cols` is given by\n",
    "    \n",
    "    cols = [\"age\", \"sex\", \"bmi\", \"map\", \"tc\",\n",
    "            \"ldl\", \"hdl\", \"tch\", \"ltg\", \"glu\"]\n",
    "            \n",
    "Store the response variables as an numpy array `y`\n",
    "\n",
    "**Hint**:\n",
    "As in the iris data set, the diabetes dataset is as a python dictionary. The predictor variables can be accessed by `diabetes.data`, the responses via `diabetes.target`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "cols = [\"age\", \"sex\", \"bmi\", \"map\", \"tc\",\n",
    "        \"ldl\", \"hdl\", \"tch\", \"ltg\", \"glu\"]\n",
    "X = pd.DataFrame(diabetes.data, columns=cols)\n",
    "y = diabetes.target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to try two different estimation approaches here.\n",
    "1. At first, we use a plain training set/validation set approach, where we exclude $1/5$ of the data from training.\n",
    "2. Our second approach is to estimate $5$ different models using 5-fold cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1st approach: Simple splitting into training and validation set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part, we want to train a linear model using a subset of our samples.\n",
    "We have done this by hand so far, but there are also methods provided by `sklearn` which will do this work for us.\n",
    "Use the function `train_test_split` from the module `sklearn.model_selection` to divide your data inta a training and a validation set. SInce this selection is made randomly, you should set the optional input `random_state` to fix the seed of the random number generator to ensure comparability, e.g., by setting `random_state = 1`.\n",
    "\n",
    "**Task**: Split your data into a training and a validation set using the function `train_test_split`.\n",
    "Your validation set should contain 20\\% of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Check the size of your sets. The training set should contain 353 samples, while the test set contains 89."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(353, 10) (353,)\n",
      "(89, 10) (89,)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape, y_train.shape)\n",
    "print(X_test.shape, y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**:\n",
    "Fit a linear regression model to your **training** data. Use the appropriate method in `sklearn`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "lm = linear_model.LinearRegression()\n",
    "test_model = lm.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Use your model to predict the response on the validation set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_pred = test_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Until now, our plots were always of the type predictor against response or against regression line.\n",
    "Another way to display the quality of a regression fit is to plot the true values against the predicted values.\n",
    "The closer the values are to the identity $f(x) = x$, the better the fit.\n",
    "\n",
    "**Task**:\n",
    "Produce a scatterplot of the true values in the validation response against the predicted values. Label the axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
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       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
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       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
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       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
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       "\n",
       "    this.context = undefined;\n",
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       "    this.rubberband_context = undefined;\n",
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       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
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       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
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       "\n",
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       "mpl.figure.prototype._init_header = function() {\n",
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       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
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       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
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       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
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       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
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       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
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       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"577.2999793541438\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Predictions')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib notebook\n",
    "plt.scatter(y_test, test_pred)\n",
    "plt.xlabel(\"True Values\")\n",
    "plt.ylabel(\"Predictions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Compute the mean squared error $\\text{MSE}_\\text{val}$ on the validation set.\n",
    "You can either use the method `mean_squared_error` from the module `sklearn.metrics`, or you can implement it by yourself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for whole validation set:  2992.5576814529445\n"
     ]
    }
   ],
   "source": [
    "### Method 1:\n",
    "#import numpy as np\n",
    "#def mse (x,y): return np.power(y_test - test_pred,2).mean()\n",
    "#mse_test = mse(y_test, test_pred)\n",
    "\n",
    "### Method 2:\n",
    "from sklearn.metrics import mean_squared_error\n",
    "mse_test = mean_squared_error(y_test, test_pred)\n",
    "\n",
    "print('MSE for whole validation set: ', mse_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: What is the proportion of variability that is explained by this linear fit. *Remember*: A `LinearRegression` has a method that computes exactly this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 score: 0.43843604017332694\n"
     ]
    }
   ],
   "source": [
    "print(\"R^2 score:\", lm.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2nd approach: Use K-Fold Cross-Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we want to use cross-validation to select our model.\n",
    "Scikit-learn is a powerful library and possesses numerous modules and functions.\n",
    "Here, we explore the function `cross_val_score`, which can be imported by\n",
    "\n",
    "    from sklearn.model_selection import cross_val_score\n",
    "    \n",
    "This function performs K-fold cross-validation and returns a score for each fold (this is the $R^2$-score by default).\n",
    "    \n",
    "**Task**: Please read the [documentation](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.cross_val_score.html#sklearn.model_selection.cross_val_score) and import the function `cross_val_score`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The functions expects as a first argument an `estimator`.\n",
    "We are informed by the documentation that this should be an \"estimator object implementing ‘fit’\". This is fulfilled by all estimation methods used so far (e.g. linear models, logistic regression, LDA).\n",
    "In the case of a linear regression fit, this could be\n",
    "    \n",
    "    model = linear_model.LinearRegression()\n",
    "\n",
    "**Task**: Perform a 5-fold cross-validation for a linear model on the diabetes data set and print the scores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48231812211149394\n"
     ]
    }
   ],
   "source": [
    "n_fold = 5\n",
    "model = linear_model.LinearRegression()\n",
    "cv_scores = cross_val_score(model, X, y, cv=n_fold)\n",
    "print(cv_scores.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the function `cross_val_predict` in the module `sklearn.model_selection` to make prediction on the diabetes data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict\n",
    "cv_pred = cross_val_predict(model, X, y, cv=n_fold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Make a scatterplot of the true values in the test response against the predicted values. Label the axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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uXbErBWKjWgVeJaeUxGRG+qiEDKMYAeA8vKxIDvt9LG87GrnazG7a0fMYqFYi1aBZ7HLVTTkhroohAwj2AEAmtJObctDR8inGW3bVAshK+tptAo8q+ueioTcUBeFkGEEOwBAU9pCxjVhnry0K7fbRg+04annY99PJ2+Fomtc1OoE5aEIKsKW5uSGukpTCO3du1cWL14sH/7wh+W0006TkSNHyoUXXijLli2Tw4cP9/vdRx55RKIoqnlce+21NR//+9//vlx22WUyYsQIOfnkk+Wqq66SH/3oR6nOmWAHAGhKO7UtzRSqvCTLtWitnxl4WFlP4xoXE259PPP756RVlC3NyQ11laYQmj9/vgwfPlyuvfZa+drXvibr1q2TT3ziExJFkVxwwQXy+uuv9/5utRBatGiRfOMb3+h3bNu2bdBjP/bYY9LS0iKTJk2Se++9V+666y4555xz5MQTT0xVDBHsQDhFGDkEBtKY2pa2KMhLwlmlvUFC3+TbyudJ0ac8ZrGbYFbIDXWVphDauXOnvPLKK4N+/uUvf1miKJL29vben1ULoa1btzZ93KNHj8rZZ58to0ePlldffbX35y+88IKMGDFCrrjiisTnTLADYRRl5BB2hSq0tba/TrPNsqUCIA7tDRIsJt2uz7F1eXduBoiyvL9UFsgNdZWmEKpn9+7dEkWR3HTTTb0/61sIHTp0SI4cqf+m6O7uliiKZMmSJYP+bdasWVKpVOSll15KdG4EO5C9Io0cwqaQhbZmUth3Z7bJS7tUCiyLkq6fGbeg9o1VLQ6mpO16WXxOVdbvfeWK3FBX6Quhxx9/XKIoksWLF/f+rFoInXTSSb1rg8477zzp6OgY9P9fvny5RFEkXV1dg/7t/vvvlyiK5LHHHkt0bgQ7kK2ijRzCHguFto9zKPLUKtf1M2P//7XztYW3LxrroCwWQ0WLTXJDXaUuhN566y259NJLZejQobJnz57en//d3/2dXHfddfLggw/KP/3TP0l7e7ucf/75EkWR/K//9b/6Pca8efMkiiL56U9/OujxOzs7JYoiue+++5qey/79+2XHjh39jo6ODoIdyFDRRg5hi6VCW7srlZf7CyXhmkjPbN8e+pQTSzPl0eoAUdFik0JIV6kLoc997nMSRZEsW7as6e8ePXpUWltbJYoi+Zd/+Zfen994440SRZE8++yzg/4/1Wlzd911V9PHv/322+vuVEewA9ko2sghbLFWaGt2LIr83rH2uvk2MC5aV3Tn+vkXLTYphHSVthCqbpLw2c9+Vt5+++1Y/59NmzZJFEXyla98pfdnjTpC1d+nIwTkQ9FGDmFL0RKyvopcLFjq5IWQ97gtWmxSCOkqZSFU7b7ccMMNcuzYsdj/v//7f/+vRFEkN998c+/PWCMEFEfev/BhW5EL7aIXCxbWdoWS97gtWmySG+oqXSG0ZMkSiaJI/vIv/9KpCBIR+cd//EeJoki++tWv9v7sySefbLpr3IsvvpjoXAl2IFtFGzmELUUvtIteLJR1W/0ixG2RYpPcUFepCqE77rhDoiiST33qU/LWW2/V/b1f/epXg372u9/9Tv7oj/5IKpWK7N69u/fnR48elbPOOqvufYSmT5+e+HwJdiBbRRs5hC1lKLSLXizkbSc4DUWJ26LEJrmhrtIUQu3t7RJFkZxzzjny9a9/Xb7xjW/0O/pObTvttNPk4x//uCxbtkwefPBBWbx4sZxzzjkSRZEsXLhw0GN/+9vflkqlIpMmTZK2tjZZtWqVjBkzRkaOHNmvaHJFsAPZK9LIIWwpS6FdxmKhyIoUt0WITXJDXaUphGbNmlV3V7YoiuTyyy/v/d3//b//t0yePFlGjRolQ4cOlVNPPVWuvPJK+cd//Me6j/+9731Ppk6dKsOHD5eTTjpJPvrRj8ozzzyT6pwJdiCMoowcwh4K7doOHj4i6wYkqOsUElRfj1s2xK0d5Ia6SlMI5RHBDoRThJFD2ESh3Z+v68F11sX1tIHcUBeFkGEEOwAUE4X2O3x1Guhg+EHchkduqItCyDCCHQBQVGnWnjSa8lakNS3AQOSGuiiEDCPYAQBFlXQ3smZTtOZs2JnocYE8IDfURSFkGMEOACiqJPeniTvlzfVxgbwgN9RFIWQYwQ4AKKor1/Q4FSzTV22VcQs61QuhK9f0iAg7zCEfyA11UQgZRrADAIrKtSN0wZLvqxdBfTtN7IiGPCA31EUhZBjBDgAoKtc1Qr6OuTHXFFEMwQJyQ10UQoYR7ACQHlOebHLZ3c3HlLgx8zfJ+EWdMn5hvMcet6BTZrZvJ4YQFLmhLgohwwh2AEiHKU+2xd38YNrKLV4KoTnr3XaYixNDFN7widxQF4WQYQQ7ACTHTTXzIU6x6rqxwpj5m2Tu+p1NH9d1nVKzGKLwhm/khroohAwj2AEgGW6qmS8HDx+RjgFdlI4+XRTXgmXs/E29N1dt9LhJCqx6MdQRc80TxRDSIDfURSFkGMEOAMkkvVknbHJ9Pedu2BnrcbU6QmPmb5JxMdcaUXgjDXJDXRRChhHsAJBMkpt1QpfmWhmnjRUWdsb+G6F2rqPwRlLkhroohAwj2AEgGdcpT9WbakKHj7UyPtZ8uRRYmgeFN5IiN9RFIWQYwQ4AydARCsfnJhUhCyzNg8IbSZEb6qIQMoxgB4BkWCMURhabVDTbACGJRgUWHSF/2GrcHbmhLgohwwh2AEiGXePCCFWAaiTUfQus6au2yqV3PumtEKLwZqvxpMgNdVEIGUawA0ByWd1HiFHtd4WYkqidUPvuDlF4c4+vNMgNdVEIGUawwwoSPeSV71FnRrX7y3qTCu2EOov1QmWLiYHo1qZDbqiLQsgwgh0WkOgh73ysKRFhVLuWLDtC2gm11g5y4xbUvp8Qn5fvYP1eOuSGuiiEDCPYERqJHlAbo9q1ZZnkav8tjXsKnbvocdl34JCXwrso2NExHXJDXRRChhHsCIlED6iPUe3asvzc0E6oXR+v2aBQllOK8zR9mXt8pUNuqItCyDCCHSGR6AH1MapdX1adZO2E2vXxBhZ1fZ9PllOK8zZ9mfdOOuSGuiiEDCPYERJfVkB9jGo3lkVyHrojNOHWx2tOe8tySnEepy8zyJYOuaEuCiHDCHaERKIH1MdAQXO+NqmoCr1GqNbjZTk1MK/Tl/N63laQG+qiEDKMYEdIJHpAfXke1c7TepJGQu4aV+/x8rxZRJby2MmygtxQF4WQYQQ7QsrzlyzgW15HtfO2nqSZUPcRqvd4WQ4g5X2wqmixmBVyQ10UQoYR7Agpr4kekBXNJDyLLk3IUXifz087oU7zeFlOKS7C9GXf0yeLiNxQF4WQYQQ7QmP6gn1FmeaUVxpJeBYj4yEHNrSeX6NY106okz4eHSH4Rm6oi0LIMIIdFjB9wYZaSeCc9Ttl/CLuYh9amiQ8q8GGUFNdtZ5fXj6HWCME38gNdVEIGUawwwqmL4TVKAmkW5dfeb75aJbPL0+daXaNg2/khroohAwj2AHETQJJgPInyxH9EOtJ8rYddRxxpqJyHyH4RG6oi0LIMIIdKDeXJNBXAg1/ir6eRONvWpr+5TI9L8upfHmZNggd5Ia6KIQMI9iBcnNNAn0mtdCn0aWJu1mGayy1ruhOvfmGxvOzsiFAks5LllOKmb5cHuSGuiiEDCPYgXJzTQJdEkyElzbJd+kEpO0uJuksaBQxFraItjY9D+VGbqiLQsgwgh3wJw/bTrsmgVmPkiOdNNO+knQo0q43G/h4Pp9flWsxNbN9e7oXxdPzALSQG+qiEDKMYAf8yMuceq2OEImZTUk7DWk6FGl2IKz1eD6eX1+uRci4BZ3q718r0/MAEXJDbRRChhHsgL487bKksUaobFN18tDp6ytJPKbtUAxcTzJ1ebe3wjrt+y3plD7N96+F6XlAFbmhLgohwwh2QFfe5vpr7BqXRUFnpfjIS6dvINfz1u5Q+O54pH1dkkzp03z/0hGCJeSGuiiEDCPYAV15nOufdF1HVom/leIjT52+Wlx2/dLuUGTR8Ui7q9mGp56XcQs7g7x/8/i5UVZWBmV8IjfURSFkGMEO6MrryG6jYmP8wk6Zu2FnkG1zrRQfeev0pRW6IzRt5Rbnc9ZIUGe0bQvy/i1bfOWVlUEZ38gNdVEIGUawA7ryPNff2n1CLCWHZRux136+SdaiuSSVWglqyPevlaJ/oDJ0QOKw+vr4QG6oi0LIMIId0JXXjpBFGgv2tRK4sr2u2kVokrVocYtbzQQ19OtsreNg7Xzq8V2sWRqUyQK5oS4KIcMIdkBX2ToHPqVJSrUTuDx3+pLSHgFPshat2ftDO0G18P610pnNSwcki2LNQlxkidxQF4WQYQQ7oKtsI4c+JS0+fCRwoTsFoWgnmdNWblG9jtoJqo9OWB6nleXlcyyrYq1s739yQ10UQoYR7IC+vIykWpck+fCVwJVtRLgvzQ6FdmfNR4Kq9f7Ny7SyWvIQ71kWa2XrCJMb6qIQMoxgB/zIcxJkRZJkzFcCl5cRcuu0CxdfCWpW9yWy+jmQhw5IlsVaHq6HJnJDXRRChhHsgD9W5vrnVZLiw2fCop3c5nXaVBrayavP1zvp+zdt0WwhLvLQAcmyOMlDh0wTuaEuCiHDCHYAlrkWH74TOK1OX1k7hkXc3EDznKzERR46IFkWa2XrCJMb6qIQMoxgB2CdS3KYRQKXttOX92lTaWk+f4sJatIYtBQXFgvMgbIu1iy9Pr6RG+qiEDKMYAeQB3GLD+sJnMXEPQTNzoe1BDVJp8JaXFg7n1pCvNetdOx8IzfURSFkGMEOoEisJ3DWC7Usaa6hs5SgJulUWIwLawXmQKHe62VY+0luqItCyDCCHYBPIRZ+W07g8rD2Iq+sJKhJihqrcWGpwKx3flbf63lGbqiLQsgwgh2ALyGTKKsJXB5240I6SToVluPCSoFZj9X3ep6RG+qiEDKMYAfis7CtbV5YGKm1mMBZG/knpv1wjX9rcZE3Ft/reUZuqItCyDCCHYiHUcf4rK/TCcnSWhBi2i+X62spLgByQ10UQoYR7EBzFrobeUJSV5+VIpGYzkbcTkWWcWG9C2j9/MqA3FAXhZBhBDvQmJXE1RcfSQfTfBoLXYQUPabzKou4sN4FtH5+ZUFuqItCyDCCHWisyN0NX0mH5YXfVoRM+Ioc03nnMy5CF+B5P78yITfURSFkGMEONFbU7obPpKOo10xbqAXevD62+YgL611A6+dXNuSGuiiEDCPYgcaK2N1wSTrGL+p0TjroONhWxJhGY9bfk9bPr2zIDXVRCBlGsAONFXH03DXpmLthp9PjuxRaY+dvkhlt21gMnaEixjQas/6aWz+/siE31EUhZBjBDjRWxJFK16RjzHz3KXJxp971PVgMnY0ixnRf7Do2mPUuoPXzKxtyQ10UQoYR7O74ki2XIs5dn75qa6IixfW5NVr4rVl0WWbx86KIMV1V9F3HksaT9Y6L9fMrG3JDXRRChhHsbor+JYvairab0dTl3c7FSdLOQHXh98z27TLWY9FlkeXPi6LFtEgxn1NfaeLJehfQ+vmVDbmhLgohwwj2+Ir+JYvGLCe1rlpXJCuE0ozCli3RycPnxbyNuxqe27yNu4Kdm6sid7lE0seTy/UZt6BTZrZvz7SDWfTXL2/IDXVRCBlGsMfDhzREwm13rC3J1Lgx89PNyy/T1Jc8fF7koVBzEbrQ9jkFUiuekqzb6/u4vmOhaDGZZ+SGuiiEDCPY4wn9JQs3FtdlWJJks4S0xUmZFkNb/7zIQ6HmKmSh7btbrBlPSdft9S1CfH6+FqnznmfkhroohAwj2OMp02h23vFF2pxrYqWRsJfpPWT9uVov1JIIVWhn0cXQjqeBne0Zbdtk3MLOWI89bmGnjK/zu1qfr0XpvOcZuaEuCiHDCPZ4yjSanWdMrYjHpSPQN8lJk4ikTb5DdPmS/k3rnxfWC7UkQjwn1/tlTV+1NVHc+o6npAMjfL4WF7mhLgohwwj2eLjBALIAACAASURBVIqYOBRNEaf7+OS6XiBtcpPm9QnR5UvzN61/Xlgv1JII0eVKU0C4xK3veEo6VZbP1+IiN9RVmkJo7969snjxYvnwhz8sp512mowcOVIuvPBCWbZsmRw+fHjQ77/22mvyhS98QUaPHi3HHXecnHvuubJ8+XI5evRozcf//ve/L5dddpmMGDFCTj75ZLnqqqvkRz/6UapzJtjjKeJUkqLhNXIXZ72AZqGRpGMXossX929OW7ml5ui+9VjMslDLqpMXYiBEo4CIE7e+48m1MLYY09BFbqirNIXQ/PnzZfjw4XLttdfK1772NVm3bp184hOfkCiK5IILLpDXX3+993fffPNNufTSS2XIkCFy8803y4MPPijXX3+9RFEks2fPHvTYjz32mLS0tMikSZPk3nvvlbvuukvOOeccOfHEE1MVQwR7PHQb7LM+Cm9V3/v8TF7aJRNve0ImL+2SGW3bvMzLd+m0hHjfJZ02GPq8Xbgm1rMffjrROWbdycu6aNYoIOK8/r7jSbsjxOdr/pEb6ipNIbRz50555ZVXBv38y1/+skRRJO3t7b0/6+jokCiKZPXq1f1+d968eRJFkWzbtq33Z0ePHpWzzz5bRo8eLa+++mrvz1944QUZMWKEXHHFFYnPmWCPj/UnthVxuk9RxV0MnbfpTqE7WXFpFHvNhHr+WRZfM9u3qxQNceLW5/XUXiPE52v+kRvqKk0hVM/u3bsliiK56aaben82bdo0OeGEE/p1iUREfv7znw/63e7ubomiSJYsWTLosWfNmiWVSkVeeumlROdGsLthRzK76AgVT4jXNM3ouIW1TXElvadMnHMO3RHLatexWQ8/rVI0xI1bX/GUpDDm87XYyA11lb4QevzxxyWKIlm8eLGIiBw7dkyGDx8uU6dOrfn7733ve+Wiiy7q/e/ly5dLFEXS1dU16Hfvv/9+iaJIHnvssUTnRrC7Y2tPm7LuHnCvIv9CdPnSTneqtdud1c+LDU89L+MWxNs22aVwsb5GSsuMtm0qRYNL3PqKpzQ3Wy3Sa4p3kBvqKnUh9NZbb8mll14qQ4cOlT179oiIyMsvvyxRFMknPvGJmv+fKVOmyOmnn97739Xpcj/96U8H/W5nZ6dEUST33Xdf03PZv3+/7Nixo99RnaJHsCPvshyFtjzSXyR56whpnUNWDh4+IuMXuRVCcZLcsnRntTYZsPL8095sVevzFeFRCOkqdSH0uc99TqIokmXLlvX+bP/+/RJFkVx//fU1/z/Tpk2TESNG9P73jTfeKFEUybPPPjvod6vT5u66666m53L77bdLFEU1D4K9PIrcychiXULWax+K/Ho1k7c1QmPm52ttRNLn2ixxz/N6PZf3m9YmA2niVvvzoUNhvRADQflHIaSrtIVQdZOEz372s/L222/3/rxZR+iSSy6J3RHatGkTHSHEVoZOhs/nmPXahzK8Xo3kZdc4lyLBkqSJfLPCJa8dIdf3m8YmA2niVvvzIW3sl+EzqSwohHSVshCqdl9uuOEGOXbsWL9/O3bsmJxwwgmsEYKTtCN/lnex0uZrHn2WHYoyvV6NZHUd+r6/pizbnDgZzNPaiKRTu5oVLnlcI5QkzjQ2GUgatz7eF66vW+vybnPr3qCD3FBX6QqhJUuWSBRF8pd/+ZeDiqCqyy67rOGucXPnzu392ZNPPtl017gXX3wx0bkS7PmQduQv9C5ORZHVSHeZX69aBf+c9TvrrmXRGIX2sTYiD1Mak3aEmhUueYvfNOebdJOBrHZ5c7m+ee3kQR+5oa5SFUJ33HGHRFEkn/rUp+Stt96q+3tr166teR+hm2++WaIokh/84Ae9Pzt69KicddZZde8jNH369MTnS7DbF3fOdqMv1TyO0FqU1dqHsr5ejQqS8Qs7Ze6GnaZ3y6q+B+MOXIQulpJM7YqbWM/buCvW483buCuDZ9pY2vdb1nHr6/Mhz2u7oIvcUFdpCqH29naJokjOOecc+frXvy7f+MY3+h19p7a9+eab8qEPfUiGDBkiN998szz00ENyww031N1E4dvf/rZUKhWZNGmStLW1yapVq2TMmDEycuRI2b17d+JzJthtc/nCa5SgMNKnI+l1dE14y/h6hZgK6DKyPm5BZ6yuVNznMW/jruDrv5JM7crDfYRcabzfstwm3dfnQxk/d1AbuaGu0hRCs2bNqrsrWxRFcvnll/f7/d/+9rfy+c9/Xs4880w57rjjZPz48fLVr35Vjh49WvPxv/e978nUqVNl+PDhctJJJ8lHP/pReeaZZ1KdM8FuV5KR6nojf4z06UgyEptkWmPZXq9QibPr67mma0/DZFf7xpRZFENxP2fGLeiMfT5562jm7f3m63znbNiZq9cN/pAb6ipNIZRHBLtNSROqeiN0jPTpcE3Y4yaE01Zu6dchKtvrFSpx1r7OGruIDYyhLLoljYr1sfM3ydz1O53OI2/xy/m6D7xZ6OTBH3JDXRRChhHsteVx7v6Y+fVH/vI2QmtZ3ISho2efczFb7RCV7fUKlYhqj6xr3VcmxGurObUrbx2WvL3ftM/X1xRJ5Be5oS4KIcMI9sEs3LslaUJVL0HM25x96+LESJruwDqHIqoIr1eoxFm7AEu6HXWav2lR3josoT4fkw64aZ+v62fV3PU7VZ4/7CI31EUhZBjB3p+Ve7ckTagajfxZeW5F0WwEPU134NxFj6vsFpgXoRJn7ZF1Hx2h0N2SJEJ1WNJ08rP+fEw74KZ5vnkrXOEfuaEuCiHDCPZ3WeqaJEmo4pyThW5XWaTtDrhstBB6Kmcjcc5NK3F2vQ6hR9aLmnSG+CzV+GzL6vNRq4jROt+8TWWEf+SGuiiEDCPY32VpnniShCrul16W27yWWdruQN+ttxu9XpaLW5dCLm3inPQ6aI6sa+8aF/dzJnQhXO8muJqfW41ov4Y+Px+1i0SN86UjhIHIDXXlqhB688035ZVXXgl9Gpkh2N9l6cvANaEKvXgXg6XtDsQZdbU83dH13NI8l7TXQbOY1LxBax66vI3+/rgFnTJuYfN7L6VhqZMfh6UBN8vnhLDIDXWZLIQee+wxWbBgQb+frVixQo477jhpaWmRGTNmyBtvvBHo7LJDsL/L2vSAuAnVOr6UMhV39D1td6BZoW05AUx6bkmSeq3roNkJaPY85m3cFet8s1wnkkTcvz93w85E1zXLaZVZsTTgVmX5swRhkBvqMlkITZs2Tf7iL/6i97//9V//VSqVipx//vnyp3/6p1KpVOSv//qvA55hNgj2d1n8ggo92ov+XF+PNN2BZgmb1QTw4OEjMuvhpxOfm2tBYvk6+JzSGDp59f33414fi5/bjVgbcKsKXVTDFnJDXSYLodNPP11WrVrV+98LFiyQk046SQ4dOiQiItdff71ccMEFoU4vMwT7u/KaUBVV6HUPAyVNFBoldGkSR4sJYJLnmvbcLF6HuNK8t0N/Xrn+/dYV3V52cLNaWNRjOV4ZeEMVuaEuk4XQcccdJ4888kjvf0+dOlU+/vGP9/73Aw88ICeffHKAM8sWwf6u0COseJe1L+S0sVFNeKet3BI7wWvGWgKYpvuV5tysXYeshE6ok24G0uz96/pem9m+3WxhUUvoAraZsg68oT9yQ10mC6HRo0fLkiVLRETk1VdfleOOO05Wr17d++9tbW0ycuTIUKeXGYK9P6YHhGfxNdBMXrSKPNdEtHVFt7dkxvd6qEZCFwShhC4A024PXy/OXd9rs1NMwwyBATfkAbmhLpOF0J//+Z/LGWecIX//938vN954o7S0tMi//du/9f77X/3VX8kHPvCBgGeYDYJ9MGvdiDKxmiRoJ9sao65JdqXzFb9pd8hrXdGdePrj6q69Tn9rTdde9ecfQugCMO328PXev66PO6Ntm8nPjEYsDvYAfZEb6jJZCP3kJz+R97znPVKpVKRSqchnPvOZ3n97++23ZcyYMfLpT3864Blmg2CvjekBYVidNhJ69L2WNF0Y7QQrbVJcK2GNs1nAup59cumdTzoWQntUn3sood8rGjePrXVOSd5reSwsGHCDZeSGukwWQiIiBw8elO9+97vygx/8oN/PX3nlFbnnnnvkmWeeCXRm2SHYoUVjc4PQo9x5O6+k63K0R8bTTpNyTVyTbsqQ5WvjW+juqcbNY2u9Fknfa3ksLBhwg1XkhrrMFkIg2KFDKwmx2HkRCT/63kjSokDzHLU7Qo0S+LQ3LC3KZgki4adY+Xgt0rzXKCwAHeSGuswXQr/73e9k//798sILLww6io5gR1qayZjVzkvo0fc459e6vDvYtdOYJhU30fXRhfDJ9zbwoTsh2t056+81oAzIDXWZLISOHTsmy5cvlzPPPFNaWlrqHkVHsCMN7aTFeudFq+DzIWQ3TaNAiZMs+1qX4ktWRUroTkj17091LMbrvRbW32tA0ZEb6jJZCH3pS1+SSqUikyZNkptvvlmWLFlS8yg6gh1paBcu1keDQ4++NxK6m5Z2mlScgs3XTmU+lDGZ13z/Wn6vAUVHbqjLZCH03ve+V/7kT/4k9GkER7AjDR/Jt/UEMvToez0WumlppknFiRlf967RZr2g90nz/Wv1vWaV72mYKA9yQ10mC6Fhw4ZJR0dH6NMIjmBHGq6J6ZRlm2M9rutoMAmAneS7mrzObN8uYxUKob4FW9KOUNYdBAtFaUhF7+ZY/Lwp+jVHtsgNdZkshCZPniy333576NMIjmBHHPW++Ge2b/c2Kh93NJgE4F3WumnzNu5KVQQNLNhcC4zW5d1BOgihpylaUNRujsXPG2vve+QfuaEuk4XQd77zHfmDP/gD2b9/f+hTCYpgRzONvvjHLehMndymPbfQCYCl0WEL16NKYwOFWp0/C12vZqxuA490LL2/qvLynkC+kBvqMlkI3XHHHfKhD31IRo4cKddff73cdtttcscdd/Q7vvKVr4Q+Te8I9nzKKvn2tQBeYyqQhQTA0uiwhevRV5od3hpdO4vJ6EB0hIon1Pur2Wd92adhwg9yQ10mC6FKpdL0YPtsWJQ0+XYtnrLaEjmp0AlA3IR82sotmXSIQl+PgVyLgQm3Pt5v+lSjeLVUgNbi+lqs6dob9HzRXIj3V5w4d52ePLN9u8LVQNGRG+oyWQg9//zzsY6iI9jzJeloeJLE0edNMjWmAoUcdU9SJPpO0K11IdJMD4sTr5bXoLjGx/iFncGLNzSW9fsr7mf9ebc94XRek5d2KV0RFBm5oS6ThRDeQbDnR9KpGUmLp7T3bPGdhIdch5GmSEya8Dbr6Flbl5I0cXTptIVek9VIkmmlFEN2+dohsxaf3fiJtz2heFVQVOSGuswXQocOHZIf//jH8uMf/1gOHToU+nQyRbDnR5KpGWnmtae9Z0uzc0srZAckTZGYZP1Aww0rFnbKtJVbZMKtbomT746Q73itdV2tFRIbnnpexi+Kv6EIi9ntSvKeTxqPPrvxdIQQB7mhLrOF0J49e+S//bf/JkOHDpWWlhZpaWmRoUOHyp/8yZ/Inj17Qp9eJgj2/EiS+KeZ1+769+LeM0Yr2Qu5JiZtkehyLpY3rGgkSRGukQBaK4ZWd+0x87pY2uEwb5LEZtLPOp/d+Blt2zxcHRQNuaEuk4XQz372MznllFOkUqnIFVdcIX/1V38ln//85+WKK66QlpYWOfXUU+VnP/tZ6NP0jmDPjyRTn9J0TVy/+Oeu35lpohpyl7S0iUrcboyvKTJZdR5cp2VqJIDWuipW1m5Z32DCuqTvxSSFrfVuPIqP3FCXyULo2muvlREjRtR8kf/5n/9ZRo4cKZ/85CcDnFm2CPb8SJJQpVk3kqTQyDrZCrWVctrORdz1Ob6myGSZ9LrEhFYCaCnZs7B2Kw9bjudBku5sksLWejcexUduqMtkIXT66afL/Pnz6/77LbfcIqeffnqGZxQGwe4u1PSSJFPB0o5GJ0mgst7NK8RId9pOTdzkSHuKTKiR/7gxofV8Ld2XJ3RHyNr9pdIKPb1vyrLNTq9nksLWuRu/IdtuPIqP3FCXyULo+OOPl7Vr19b997Vr18rxxx+f4RmFQbC7CTm9JIs1F7VG0vMwpSbEVspp1u7E7VhodEiq9+dZ07VHVnftNb0+RKsD5ntHPBeh7+8U+u8PlKaQsfBZlEVhm4dufBZCF71lRm6oy2QhdO6558o111xT99+vueYaOffcczM8ozAI9vgsTC9xPQet0WDL92wJqVHykeQ6D6TRIblyTU9ukiStNVGWOkKhOzKhO1J9pYlDC5+/ItkVlnnoxvuUl8+soiI31GWyEPryl78sLS0t8sUvflFeeeWV3p+/8sor8qUvfUlaWlrk1ltvDXiG2SDY4wmRzNQbDVvXs8/pC8JKAlFU1eRj2sot6tdZo0Pi47x80tglz9IaIZGw70ELa5RE0l2D0MVkqHMpazHAd1Z45Ia6TBZCr7/+uvyX//JfpFKpyJAhQ+TMM8+UM888U4YMGSKVSkUuv/xy+f3vfx/6NL0j2OPJenpJsy/Ajp59TiN/Zf1CzZr2ddbokIxbGO8+NpbWhyTptPU+3wWdZp5HX6HegxY6QmmLB2vT+7JM1IvU5YnDUtFbZuSGukwWQiIib731ljz44INy1VVXyQc/+EH5wz/8Q7nqqqvkoYcekrfeeiv06WWCYI8ny2TC15ds2b5QQ9G+zr7uI1TrmP3w02bm4/e9jtNXbY1fCC20WQiJhHkPWigi0p6DhWJuIAaX/LAQryA31Ga2EALBHldW00sYDdNXhAW3G556XsYtiNfZ0T4sJHUkR8lZ+ExJW8hYmd43EINL+iwWvWVEbqiLQsgwgj2erD6ci5DwWSo8ijRqu+/AodjT3HwcIa9V2vefpZgMIfSai7SFDMlxeVgtesuG3FCXiUJo/fr1sn79enn77bf7/Xezo+gI9niyKlDy/oVvqfDwOcUwVFI9b+OuYIVQyA5kmuTIUkyGlOY6pI35NJ9rBw8fkVkPP53J5y/Cy/t3YFGQG+oyUQhVKhVpaWmRI0eO9PvvSqVS92hpaQl81v4R7PFkNb3E2miYSwIUetR54Hn7eL1CJtVZrhWylmAmTY4sxaQFSaZyacR80oEk39vTN7tWZe4ihlKEWRFFQG6oy0Qh1NPTIz09PYP+u9lRdAR7fFkkVZZGw1wSIAvrEPry8WWa9L4eGsmU1v110h6hRl+TvJ6hYrJICbTWZ17SG4QmiVGNopYuYjjWvkvKitxQl4lCCLUR7G58f0FaGQ1zTYCsnHeVdkF58PAR522oNWNF435CGkeo+fhJkqMQMVmkBFo7IXX5TElS+GtdX7qI4fEahEduqMtkIfTpT39afvjDH9b996efflo+/elPZ3hGYRDs7nzuFGRhNCzJOVjqZInoTzGcs2Gn0+PNjfn7cb/IXa+vryPkfHzX5CjrmCxa8uarqxqnUHT927Mffrown794R5EGFfKI3FCXyUKoUqnIt771rbr//rd/+7esEUIQoROqJAmQtbVNmknwwcNHZKxjwRD39+MmU67Xt9HRuqK7t4CfnbNF6C7JkWZMNpvu5iOBDj3FzlchGWcgKdTAirXOdtmxPXk45Ia6clkIPfDAAzJs2LAMzygMgt2mkKNhSZIQax0hzYTG97S0OMmUVkdoYBLuksCPnb9JZrZvD77eJW5ypBWTcd6L2gm0hdFwX4MbcQq8UAMr1j7HgFDIDXWZKYR2797duy12pVKR//E//kfNLbPvuece+cAHPiB/9Ed/FPqUvSPY7Qo1GpYkCbE2kqo5Qu97WlqcZEqrGKuVQCdZlJ6HqSkaMRn32kxbuUXtNQ/dEa7yURTELfBCFSTWOttAKOSGuswUQkuWLOm3NXajrbNPPPFE2bRpU+hT9o5gx0BJkhCLc+s7YibCzRJKzWlpSZOptLvGNStckmxTnEUynoZLIVQrJl27ZRqvuaX3kY8uV9yYCjWwkvZ+R0XZLRAgN9RlphB6/vnnpaenR7Zu3SqVSkVuvfXWQdtl/5//839k165d8vvf/z706WaCYMdAae75YSV5jpPYx+1qWOgIVZ+T62NPW7kldhex2oGc0bZNfY1T1lyvVa048Dklst5rbqmzqlmUuT7WvgOHghSEPu53lIfuKTAQuaEuM4VQX0uWLJEf//jHoU8jOILdrzyOEqZJgCwkBHGT4HUxk0jX5OjK1W4dJJdkdsNTz8v4RfG28U6aJFpKxpNw7Z5NXf5kzfemzwK43jWztkZFa3AjSUyFGFjxeb8jiiHkCbmhLpOFEN5BsPtjoShIKs2Xe9q1TWmKR1+7d8V9zHELOp1Gs8fO3yTTV211eo6ru/aoJN31WEvGXaXt5Iydv0nmrN8p01dtdf7/pY07i2tUND7HksZUiM9QX/c7sto9BWohN9RlshC67bbbZNKkSXX//YILLpClS5dmeEZhEOx+FGGUUDMJiVvcpP2bvroZrq9nkmlscZ+j70LFYjLuItQ9l+JumNDo9bVahKYd3EgTUyE2jfF1vyNr3VOgHnJDXSYLofPPP1++8IUv1P33L37xi3LhhRdmeEZhEOz6ijRKqJGExE0qNIpHzd27kj6POL+f5jn6LlSsJuNx+d7colGSm7aQd+32renak9FVTcdHTPmedmz5fkeAb+SGukwWQiNHjpT777+/7r/ff//9ctJJJ2V4RmEQ7PoYJXxX3OKmo2df6uIxyY1PXe99MrN9u0xe2iUTb3tCJi/tkhlt2xoWhn2TqemrtqpMn/J5o8t1Pftk6vLuXMdviI5Q39drYAI9s327zH74aZnRtq1pwr66a6/T313TtTfWNQm9VrFo91mqXs8Jt7oNdFjrngL1kBvqMlsIrVixou6/r1ixQkaMGJHhGYVBsOsr8iihS0LltLZmYfwNAMbM3ySzH3560Dm4JpFxr71W0qWVDPootJN2ryx2NH3fALfWUS8GXGMn5L17fNLskoeedpym05unz3qUG7mhLpOF0Ic//GFpbW2t+W9vv/22TJ06VSZPnpzxWWWPYNeX9zUW9bgmVFknpK7doDHzde99MlDfonH6qq3OyVO9pGnfgUNOj7PvwCGV55hlsplG2nsuucRWo0IiSexof3aELhq0zyX0tOM075Ux8+11T4F6yA11mSyEHnjgAalUKjJ79mz51a9+1fvzX/3qVzJr1ixpaWmRtWvXBjzDbBDs+orYEYpb1PRNYkItWndJbjXvfRJ3G/G0Sa5mRyhp0VCUXQ/jHhd95fux18odPHxEVnftTTQNUvOzI3TRUIvVzVDi0LipsbXuKVAPuaEuk4WQiMinPvUpqVQq0tLSImeccYacccYZ0tLSIpVKRa677rrQp5cJgl1f0dYIdTg8n75f9qEWrcc9pq3c0vB5+76xbNIkVzNZdn2OrSu6ve/YpUWjGK0eE297wuvfrMaO5meH82u7vDuT9UNpNmAJOciUtsNteeAAGIjcUJfZQkhE5O/+7u9kxowZct5558kHP/hB+dM//VN59NFHQ59WZgh2fRZHYpNKktRXkzPrHaG563c2fO5Jki7NaVn1klzN6VNF7F72VWvjgnEL3NajjZm/SSYv7Wr6t9IUwNXrqvnZkfb9Z7Hrl/W0477TW103RrB8HYFmyA11mS6Eyo5g9yPU3HzN3aGSJvXVpM51BDVJgprmGL+os+F1SZJ0aa2LymrXuKKuZ2v0PkhSsMxs397076UpgPteV63PDq2OrM8k3vXzKsvCPW1HccKtj+emewoMRG6oi0LIMILdn6x3a9L+e0mT+mpS5zq6HWK3r0ZTi5IkXVpdsEavleb0KdfznXjbE0G2X3YR530wZ8NOtWsokn7a1MCEXeO9rBWLvrrWSZ5jVtOONaa35q17CvRFbqjLRCG0fv16Wb9+vbz99tv9/rvZUXQEu19Z3RXdRwcqaSLVNwFwPS/NdR1pk5UkSVcWo/Ca06fSJvDWpv3Ejbd1Pftk/KJ4Hcg4hUDaoqNWwp72s0NzYEF7HWPSz6u0sR+nA6U1vdX62k+gEXJDXSYKoeqmCEeOHOn335VKpe7R0tIS+Kz9I9jzz9eapKRJ/cAEwHXkt1YCOPvhp9WSur5Ho6leSa5rVqPwWoWvVtJnoRhyfb3ibgIS57mlKYB9dVw016tpdjfSfl4ljf24n0MaBaT1tZ9AM+SGukwUQj09PdLT0zPov5sdRUew55+v6SIz27erJQBpR7d93BsmToLnmnRlOQqvNRVSYxqQhcQvyftA6xqmKYBdi0iXdTVaOxhqrg3T+Lxyfd1c3scagxkWBgaANMgNdZkohFAbwZ5/vhYQz0rQhfGZAGjfG6ZeklXr78ZNurIehdeaeqkxJTH0VKBpK7ckur4a1zBJAZxkWmGSwk3jtdXsCGl9XsV93Vw7UNNXbU18naxNFQWSIjfURSFkGMGef752/prRts3pcacu7276mGl3tWuU1MW9gWXf36/3dwee54y2bTL74adlZvv2psmyxVH4OAYmlhNveyJYsuwqyTXXvL4uyfbY+ZtkTdeeRMVqnMevlYgPfG1bV3Q7XSvNIjfrnQqT3CvL5fcn3Pq4t7WfQCjkhrpMFEJxN0dgswTkja+OkHbCojUNqd5I8OquvU7nW+8+QhrnGXoUXmMb9bxsrZ12m3ctcQuVOet3Or8u2usAQ97rLOt7V7n+vanLwxWJgBXkhrpMFEK1NkdoaWnpPWr9jM0SkAe+1ghpJixZ3FfJJbkbt6D2PYQ0z7NvwTZ91Va5YMn3MkmwQq17mbZyS6LzTSvpuiwfCWyjaz9uYWfde2U1e118vMdD3essqy2wq1wL+umrtpq5IbbmfeEAF+SGukwUQgM3QXjyySdl8uTJMnr0aLnzzjvlO9/5jnznO9+Rr371qzJ69Gi55JJLpLu7+VSfvCPY9YT60vI1uquVsGQ5+px2+pDP83R9/H0HDjnHU5LnXy9uV3ftpEmaMQAAIABJREFUcXr9fSTNcSRZ3O4zga3VsZwb875F9a6fry5K1vc6E8m+G+U6xXdG27ZgRWJfIV4boIrcUJeJQmigJUuWyIQJE+TVV18d9G+/+c1v5AMf+IDccccdAc4sWwS7jtBfWj6+uLUSlqxHgJO+FlmcZ9zXad7GXc7PIcnr1ehajV9Uv4PhM3F1lWTr6iySyGqBObN9e+z1a/Wun89pilnd66yvLAsN101fZj/8dO85hvpMt1CIodzIDXWZLITGjBkjK1eurPvvK1askLFjx2Z4RmEQ7OlZ+dLy8cWt8dyyXhMg0ji5q9cBcR05TnqezV6neRt3JbrmroVc3C6F65H1mgmLU/jSrBGrdf1CvId8y6rQcL0NwMz27b3/3xBFYsj1W0AVuaEuk4XQ8ccfL3fddVfdf7/rrrtk2LBhGZ5RGAR7Ota+tHx8cadNWCwtutfcdS7NedZ7nfYdOJQ4nlyTZdfnazUJz7rj2EzaXQNrXT9rz1FLFoWGpc+fOIr6WiNfyA11mSyEJk6cKJMmTZLf/e53g/7td7/7nUycOFEmTpzo/Lh33nmnXHPNNfK+971PoiiSMWPG1P3d22+/XaIoqnnMnz+/5v9n48aNcvHFF8uwYcNk1KhRct1118nzzycfOSPY0ynLl5ZLwjKw42JlG2bt+xD5OM808ZRkipiPI8S231YGIzTuI1Xr+mWxvqyo8tZNy9v5opjIDXWZLIQefvhhqVQqMmHCBLn33nulq6tLNm/eLF/72tfkAx/4gLS0tMjXv/5158eNokhOPfVU+chHPiInn3xyrELo7rvvlm984xv9jn/9138d9PttbW0SRZG0trbKunXrZOnSpTJq1Cg588wz5aWXXnI+VxGCPS2+tPqzemNOzRud+jzPNPGUZNMAH0eIGLcyPTXpDnZ9j9YV3al2NJy7fieL7PvI22BV3jpYKCZyQ10mCyERkXvuuUdGjBjRb9vsSqUiI0aMkHvvvTfRYz777LO9/3vChAmxCqGf//znTR/35ZdflpEjR8rFF18sR48e7f35zp07pVKpyGc+85lE50uwp8OX1rs0Oi6+Ruw1EtQszjNNPGk/x6RHqEQy6RROzd0etYrReuerMdAwZn65Ftlb6hjGweAaLCA31GW2EBIR+e1vfyuPPvqorFixQlasWCGPPvqo/Pa3v1V5bJdC6LXXXpM333yz7u/+zd/8jURRVLNLdfnll8uJJ54oR464f4AT7OnwpfUOrY6LrwRNu1ti5Tz7xpPLa+C6PijtrmfNaBUjrmtOtBfsa09PrPX3NQpeCwl/lqx0DOPIWwcLxURuqMt0IeRT3ELopJNOkiiKpKWlRS655BJ59NFHB/3uTTfdJFEUyc9+9rNB/7Zw4UKJokh2797tfI4EezpJv7SKdqO8tMnZ2PmbZMqyzd6ug2uCWi/x9z21KG0SFDfhm7Pebce4uTF/P+nOhCGmcvlIjrUL7oEFi+YUz7Il0KFvcRBX3jpYKCZyQ12mC6HnnntOHnzwQVm2bFnvFLUjR47ICy+8kKjD0lezQujuu++Wz372s/LII4/Id7/7XVm9erWMGTNGoigatKPdxz72MYmiSF5//fVBj3PfffdJFEXS2dnZ8Hz2798vO3bs6Hd0dHQQ7DHUK1yS7PKVly9kF64J4AcXPyFTlm3OrOBwPb+Z7dsz3zZXRCcJihNf2vccCrk9exJWbkLsWrBoPn5Ru9ONhNgOO4k8dbBQTBRCuswWQrfccosMHTq0d41Qd3e3iIi8+uqrMmLECLn77rtTPX6zQqiW1157Td7//vfLcccdJ//+7//e+/Pp06dLFEVy7NixQf+f6rS5Wp2kvhrtUkew16d535eifsH52rFM6zrkabqJRozESfiS/B3NRDLkyLevePCxKYevDTGKsl6xaN31qiIOmCE/KIR0mSyEOjo6pFKpyOc//3nZvHmzVCqV3kJIROSTn/ykTJ8+PdXfSFIIiYi0t7dLFEWyYcOG3p816ghVfz8PHaG8fWnFTRbnbdzlZRQ+L3ztWKZ1HfJ27bNKgkImW67FSOvybrXPDJ9r+7S3ae9bsGgOOBShI1T0YiEvHSwUD4WQLpOF0AUXXCBXX321iLyzI9vAQmjFihVy1llnpfobSQuhTZs2SRRFsnr16t6fFWGNUN6+tJLcu6PRl1aeuhKufO5YpnUd8taNyyoJCpVspS2e03xm+N7tUWt3t4EFi+aAQ54+X2rJ2/u5bPI26In+KIR0mSyEhg0bJh0dHSJSuxB66KGH5Pjjj0/1N5IWQnfffbdEUSTf+ta3+p1Po13jRo4caXrXuDx+aWkXLkXeYc7HlCAf18FyMV62xEGruxH3Net7fSfc6harSWKwWmC63lC40eeK1oCDha5nGnnr8JaN5c9ZxEMhpMtkIXTKKafIqlWrRKR2IbR48WL5gz/4g1R/o1EhdPToUXn55ZcH/fzAgQNy1llnyQknnCD/8R//0fvzX//61zJ8+PC69xG68cYbE51jFsGe1y8t7cKlaPccGpi4T1u5Ra348XkdLE43KWPioHnPnWavXdoOTZruSZrixdeucXmPpyJ31/Muj4OeGIxCSJfJQui//tf/Kn/8x38sIoMLoddff13GjBkjf/Znf+b8uBs2bJClS5fK0qVL5bTTTpNTTjml97/b2tp6f+83v/mNDBs2TD71qU/JihUr5IEHHpBbbrlFRo0aJZVKRdatWzfose+55x6JokhaW1ulo6NDli1bJqNGjZIzzjhDXnzxxUTXIYtgz+uXlnbhUqSOkObUnzxfBw1lTRw0p1M2+sxIu2Yn7eBMmuKl3k1V0zyXIsRRkT5LiySvg54YjEJIl8lCaPPmzdLS0iLXXXeddHV1SaVSkQ0bNsimTZvkkksukaFDh8o///M/Oz/u5ZdfXndntr7doTfeeEM+85nPyPnnny+nnHKKDB06VN7znvfIzJkzpaenfkL9zW9+Uy666CIZNmyYnHrqqXLttdfKc889l+QSiEg2wZ7XLy3t885rQTiQ9mLwvF4HDWVOHDSnU9Z772n8DY3CIe7Okn1f60Z/t1kHcV3PPnNdT01F664XRVG+40AhpM1kISQicv/998uwYcOkpaWldwvtlpYWGTZsmDzyyCOhTy8TWQR7Xr+0tD/U85T0atw3SeMIfR18K3vioFVU1/vMSDstTaMIcnnfj52/SdZ07YkV8xaneGYlr4NrRcfrUhwUQrrMFkIiIr/85S/l3nvvlc997nPyP//n/5S777478TSzPKIjVJ+PwiUP06AajTaPW9DppeCxeB2ykMV7w/ImDFqFUL3r4np9J9z6uHpBUfZi1weuqU15HfTEYBRCuswVQm+88YY89thj8swzz4Q+leBYI9SYj8LF8sL4rKe91TtCX4eshNzGOfQ11pwaV+8zw0JilteBIMvy1F0vE2K9OCiEdJkrhI4dOyZDhw6V9vb20KcSHLvGNecjmbQ4rcXnFtguR+uKbnMx4ItW4lCr6zNn/c5YjxmqGMpiK2gLiZmFYqyI8tBdL5s8D3qiPwohXeYKIRGRc845p98NS8uK+wjFY7Fw0ebzpqgaiaDlKV5JaSQOaXfwCzX4oLV9dqPPjNVde50ea03X3uDPk1Hy+Cx3PMso74OeeBeFkC6ThdAXv/hFmTp1qrz99tuhTyWoLIOdLy3bNO9an+aolQgWNXbSJg5aUxlDjMymvaFqnNd9ddcex0Joj/rzDDFKXsRBg3rKMEiVJ3kf9MQ7KIR0mSyEfvKTn8hFF10kH/nIR+Sf/umf5N/+7d/khRdeGHQUXdbBzpeWXWkTU61jYCKYxRdryMQx6fPLYvtpn1wL74m3PeH8mWGhG5P1KHlRBw2QH8Rg/lEI6TJZCFUqld6jum12raPoCHZUWegIDUwEs0giLXxpJzkHzamMIdaluJ5/6/Ju5yLVyvqcuMXutJVbUhXgLkV1mbpGyB6DnvlGbqjLZCF0++23y5IlS5oeRUewo8o1MR23UH8r7YEJv+9pRZamcbgmDjPbt6td9xAdobQdrThFqoWOUJXLWq4kBbjL9Ry3oFPGL6r9/mXEHgC5oS5zhdCBAwfkhz/8oezbx44lRQ52RjzduHZf9h04JLMfflqleKqXfPlMZPO+sHfy0i61QijU7k0aa5waJe1ahbTWZ0m12J22ckvq55b2uWr+bQDFUuTcMAQzhdCxY8fkpptukiFDhvROfbv00kvll7/8ZehTC6aowW5hulMeuXZIXAuVGW3bnLoe01dtdXr86au2xn6ued/qdeJtT6gkvKGLPJ+73mkUu9qfJb4KcO2praHjAkA4Rc0NQzFTCH3ta1+TSqUiZ511llxzzTVy4YUXSqVSkY997GOhTy2YIga7pelOeeSS+PlegzF1ebfT47cu74792JamTSWh1RGy8D7oOy1w+qqtcv6S7zk9h0ZFaprPAx+fJb4KcB+bnVgr/gFko4i5YUhmCqHJkyfLeeedJ6+99lrvzz772c/KkCFD5JVXXgl4ZuEULditTnfK2zS9uOtVfBcTrSscC6EV8QshKwvpk5rRti1VkmuxM5q0O9QsrpJ0dax0buK+Z3xsdmKt+AeQjaLlhqGZKYRGjhwpf/3Xf93vZ7t375ZKpSI//OEPA51VWEULdovTnfIwTS9poeb7evucGpf3jpDzrmsruk3v3pRmvVCcItV1MwornZu4BbiPGyJbK/4BZKNouWFoZgqhSqUi3/zmN/v97Ne//rVUKhXZsmVLoLMKq2jBbi25zcM0vTSFmu8OnM/X02LR7MJq9zOJtDvI+XgfW+ncxH1czftKZfX5CMCmouWGoZkqhL71rW/1+9nLL78slUpFurvjT6kpkqIFu6XpTnlIVDUKNZ/Fns9iJQ+vTzNJrr3FaZppuxk+ilQrnRuX56axC5/v6wrAvqLlhqGZKoQ++clPysqVK3uP22+/XVpaWmTOnDn9fr5y5cpB0+iKqGjBbqkjZL3joFkI+Jr+57tYmbdxl3MhYY3Ltbc6TTPN+hZfRaqFzk2S59boNX7/Ardru+/AoSSXDkDOFS03DM1UIeRytLS0hD5l74oW7NrFR5rRc9dEatrKbKdn+rhWPu4k7qvjFPdx523c1fBxLHRY4lx7y9M00+x45ut8LXRu0gwg1IqH1V17vT0nAMVRtNwwNDOFUE9Pj/NRdEULdpfR1rHzN8nqrj11E9a0o+dJkrssk1BL3bNmrN7LxWqHZSDr0wCTdIR8Xd9qYTuzfbuMdTgXzc6Nr+eWp/c8gHCKlhuGZqYQwmBFDHbXefK1kg6NEdukyV1WSail9VRxaHacNEb7LXdYBrI+TdP1/GY//LSX90nS7bu1Oze+PgPy9p4HEEYRc8OQKIQMK2qwJ0loqsmM1uh50gXgA5NQX1Ovyjw6nPa5W++wDGT9tbZwPZNsNGCp6xeH9TgAYENRc8NQKIQMK3KwHzx8RNZ07XWe3qI1ep50O9u+yYfP6TPWuwQ+pR0Zz9u1y0MnIGSHzXVK7Yy2bSbvxdRM3uIWQBhFzg1DoBAyrOjBnuSLX3PUNMkoczUJzWJBdehR+FDSvsZ5G1nPy/mGWnPlfHPa5d1mth53Ueb3PID4ip4bZo1CyLCiB3uSBFB79Hzayi3O55A2YYk7nS5P61w0pR0Zz0OHpa88dQKyXjcjkm77bt9FmrayvucBxFf03DBrFEKGFT3YkySs2qPnSZLQNImr66h6XnY+05S20MxLh6WKTkBjabbvzmPx4OM9b2EbeQA6ip4bZo1CyLCiB3uShNXH/XVck9CkiXbS0d4Qo/DVv+s7ear3Nzpivs61ksLQHZYk141OQH1pO0J5LCI13/NlHEwBiqzouWHWKIQMK3qwJ0lYfYyex01CpyzbLFev3SGTl3Y5nfeVa3rMjfo3S9azSJ6a/Y15G3clOoeQ1zrNdSNhrS3pDo/1PkPKhAIbKJ6i54ZZoxAyrOjBnjRh9fHlnvQeJXGOJJ0snwu+4xQgvpOnuK9htTvkOjLuKwFsVEBq/M1Q3b8sJO0wJt3hsd57sSysDb4A0FH03DBrFEKGlSHYkyaPvubRV5PQKcs2qxVCSXa703pOSa+3z+QpqwRNO0YaPd74hZ0ybmEnSWcdaV8LrbgNvTFGlkJPEQXgRxlywyxRCBlWlmBPmiT1LVymr9oqrSu6pXV5t0xftVVmtm+XWQ8/LTPatjl3VjRHoKtJr4UF35rPK03ylGWCptVh0SwgXZ5TERa5a3XnNLq2ZeoI5W3TEADxlCU3zAqFkGFlCvY0CatLglSrsBqYbLau6FZLeKt/y8KCb821FmmSp7wlaD4KyDjPqQhrhrS7fwM/J1zfq2XqeuRtG3kA8ZQpN8wChZBhBHtzSUfqq0mkr7VBAxNVCwu+tYqxtMmT9QTNZ2Ec9zm5buBhtUvku/vHOpj68jbgACAeckNdFEKGEeyNpRmpP3fR47G3aI5zjO2TlNbqZFlY8K01PS/tuVhO0HxumhH3OSWNFYtdoixea3ZGq401QkAxkRvqohAyrMzBHmdtRNouS9zF7S5Hs+2RNf7GlGWbE11THx0h62uEXGivA0r6nNLGtaWEP6vuXxGmEWqjWwYUU5lzQx8ohAwra7DHTWp8JPZpj2YJhVbHYc6Gnc4L6LXXCGWxa9zY+ZtkddfeTO6rlEUnaMz8TTJ+Uaes7tpT9/XT2GHQSlKbZfevyFuPJ0W3DCiesuaGvlAIGVbGYHf54vYx1UvjaNbBSLvgu1EC3OweNZrJfhb3EYr73NLysZFEvWPcgtqdyOpz1IhrK9OcrHb/yoRuGVAsZcwNfaIQMqxswe46lWNG27bMkleXozqqHXfr4ywLlLgFyLyNu7wnT0m6Y76SNq3u4rgFnTJ+Ue1CJ+5UzGkrt6jFYGgHDx+J/bzHLewsdffGJ7plQHGULTf0jULIsLIFu+vo8eyHn1YrHjSPKcs2O4/Caq5PGb+ocUIZ99yySJ4OHj4ia7r2yNiYz83XtC/N+zzVum5ruvbKeIeCIO15WNkK+eDhI3U7YIOe9wIKIQBopmy5oW8UQoaVLdhdR+Vntm9P3EmJm5z5PAYWQ1OWbVZ77Lkbdja81pZGiENMnxrYrZt42xOprnezLpnrc0wbn5odoTQ3dXV93q0runN741gAyELZckPfKIQMK1uwJ9lhKmknZV3PvswWxzdKnvsmetqbP+Rl7n/W22lrbpHdurw7VgHp+hzTTo8bWCwmLWbSri/R2PghL3EMAFkoW27oG4WQYWUL9qQJsUti2zexynK75DgJq5Vd3bKW5Q1WtV/zuEVZ0iI/6f2E+r7uSYsZjR3HNKccAgDKlxv6RiFkWNmCPc0UqYFTvWa2b5fZDz8tM9q2NZz6ldUNNOMk0j62cM7DLlxZdYR8XN+4RVnS59g3ruNOnexbNMQtZqat3NKvQ6R1DxqtLmdeinoA8K1suaFvFEKGlS3YQ90A8ODhIzJ3/c7YC/Z9JtKhOhYhZbVGyMcW2QOvb70paKu79jg9br01Xi7dnSSFX/UxtF4TzWueh6IeAHwrW27oG4WQYWUM9hA3AAw5Ra5WoaLZpbKye1hfA4uFGW3bYu+UlqYA9nED3r7JeaPXbfyiTucNEOrFeNyNLtIUIa5rlOoV3JpduDwU9QDgWxlzQ58ohAwra7BneQNAH9OlkibSA89rYLI7d/3O3CePaYu8NK+99g14+xZlPorptF3PNIWfa3e0UcGt1RWyWNQnkWYXPgAoa27oC4WQYWUO9qy2d/YxXcpnojvHsRiyNJ0oTbGgUQD72pXPpZgeu8Dtb6R5/bQLv0ZHvYJbs7tprahPIstBHgDFVObc0AcKIcMIdv98TJdyTaRdHDx8JPaNOS0tMHcpFsYt6JSZ7dvVC2Dne/nUuc4DE1afxXSa5D/L2K5VsGl3yeaub3xvLOtCTPsFUDzkhroohAwj2P3LctS8eoxf1Jkq2cljQhXipqkDuW7Gse/AoVhdSZ8FR5rpYGkLtLjT42oV3L6mnFqKaRehNoIBUDzkhroohAwj2P0L0REavzBdISQSf4qNlfUIWd80tR4fRaTPYjrNddh34FCqvx13w4Ra18pXl8xnkeDzvWJhIABAMZAb6qIQMoxg9y/kGqG0xVCjdVQHDx+RORvqbwme9XqELG+a2oz2Og2fxXSahDhtbHf07Et8raxek3p8r92xMhAAIP/IDXVRCBlGsCcXd3Q3zdqV1uXdqRI6X6PbG556PvZ21FkVQ9YSQc3NOJzXHsXcRntgfLh2LNIUI33/dpJrZbVLVksWU00tDQQAyDdyQ10UQoYR7Mm4ju4mTYQ0uknao9uuC9SzWo9Q5KlBrus/4l6LvvGWpGORphixtkOfryIhq7U71gYCAOQXuaEuCiHDCHZ3SYuaJImmxoJwzYQn6flkUXQUfbG4a9y5xFvSmE5SjGhNmbS6k17a80z6XinyQACAbJEb6qIQMoxgd5M22a5OAZrZvl0mL+2Sibc9IZOXdsmMtm11pyCl3SJYc3Q7afKZ1ehzHne7c+FaTMeZcpYmpl3jYfbDT6sVoD5vVKxZJGTVqSn6QACA7JAb6qIQMoxgd6Mx6pqkM5TmppGaRUjS6Ui+1yP0XdsyZdlmMxs4+KB9I+A0MR06+da+j5CP88xy7U7RBwIAZIPcUBeFkGEEu5u0o7tpEpVqAjzVcQMFzZtEJl0TMvA6aG4j3KhIHDt/k0xZtln1pqlFEzKmNaQZJMjiPLNeu+N7dzoAxUduqItCyDCC3U2a0V2t0fMkU4K0kp+kHaG+XQTNRC10El4EGh2L0Mn3wcNHZPbDT6cqgHydZ4i1O9pdQwDlQm6oi0LIMILdTZrRXY2EqNpJiXsjyjiFlYuka4TW/f/nolm4hJ6WVRRaHYvQybfr85h42xOZnCdxCiBvyA11UQgZRrC7SVPMuCZqM9q29fvbaacAaY00Jz2HdT37Yv9/xy/s7HePmVrT6FZ37cn8+RdRUXYbs3wfHTqXAPKE3FAXhZBhBLubNKO7rona2Pn9t0JOWgBVD61NE5KeS9ybfFaPuet3Nl3/E+L5J6G5JsrHuRWhY2H9PjrrevbVfQ+wdgeAJeSGuiiEDCPY3WV5z5Ux8906KY0OzRFw7QXqWRxZ7lzXt9jpaPD6WUmAi9CxsNzZavR+Gbew02yXDUA5kRvqohAyjGBPJsni8KTra1w7KfUO7RHwg4ePSKvjDnYhj2krt6g+/77SFoZ94yVU9yj0hgdpWe1sFaHIBFAu5Ia6KIQMI9iTc10c7vMGkHEOH6POSbfTDnX4SDY1pi1WE/PQxUjoDQ/SslZ0WC3OyszyNFXACnJDXRRChhHs2fJxA8iQSVbS6X6hDu3roFnczl2/01QSn1ehi8m+LE/XKyNLsQFYRm6oi0LIMII9exueet55oX/aw8cX/MHDR2RWynu3hDg0k82k0x1rHXFjgs5Bc1Y6W9Y3cCgTa91CwDJyQ10UQoYR7GHMbN+eWeI/d/1O9fPP42YJPpLNUB2xgcUc031ssryld5kwRRFwQ26oi0LIMIK9MV8JpmsnYdzCZBsm9L0fj5ZQ0/u0Ds1kM9Qaqb7FHNN97KIjZANTFAE35Ia6KIQMI9j761v4TFm2ue50pbQJpssI5dj5mxJPQdNOgg8ePiLjF+nsYhfqKEJHqFrMMd3HNhJwGyhIATfkhroohAwj2N+VZLpXmgTTtbMybkFn7M6Qr07AnA3xFvRbPiyuEUpyc1im+9jHa2QDUxQBN+SGuiiEDCPY35F0ulfa5EVzrc2UZZsTLwqPMwUwyylxvjaTGDt/k8xo26a2fkZr1zjXArOjZx/dhpygaxceHSHADbmhLgohwwj29Mls2gTz4OEjsqZrr0ryP23lFue1THHWmCS9RnGf09j5m2T6qq29hdz0VVtTX4tmh1bXLE2BmOT6Votvkrv8YB1XWAwaAG7IDXVRCBlGsKef3qSRYGpuw+ySZMVN4ufEvMfNwGPayi2xfm/gOWa59karGGqU6K7r2dd0O2fXzgHTffLFypbeZcQURcANuaEuCiHDCPb0SbdGguk78a+V7Ltu2JDk73b07JMNTz0v4+usbXr/wneKrIFT8lZ37U31fP/4ziczvy+PRqLr0jkI3RFiy27kCVMUgfjIDXWVqhC688475ZprrpH3ve99EkWRjBkzpuHv/+pXv5JPf/rT8p73vEeOP/54Of/88+WBBx6o+/sbN26Uiy++WIYNGyajRo2S6667Tp5/PvkHN8GefgtkjQTT9zbMtZJ9X12ogX9zw1PPO+80N35h/I0hah2tK7qdft/XfXmSPE7cgirkdB+meiGPiFsgHnJDXaUqhKIoklNPPVU+8pGPyMknn9ywEPrNb34j48ePlxNOOEEWLlwoDzzwgFx11VUSRZEsWbJk0O+3tbVJFEXS2toq69atk6VLl8qoUaPkzDPPlJdeeinR+RLs6bsxGglmFlPBBp5nFl2oUPccmnCr23omH/fl8Z10hZruw8g68owpikBz5Ia6SlUIPfvss73/e8KECQ0LoQULFkgURfIP//AP/X7+3//7f5f/9J/+kzz33HO9P3v55Zdl5MiRcvHFF8vRo0d7f75z506pVCrymc98JtH5EuzpOiNaCabv7szAZF/Ebxdq7vqdKjuqjVvQmei+Ra6FkPZ9ebIqFrIuSlhrAQDFR26oq1SFUF/NCqGzzz5b3ve+9w36+datWyWKIlm+fHnvz/7mb/5GoiiSr3/964N+//LLL5cTTzxRjhxxTzoI9nS7xoVIMJMeA9cy+eoIjV/Y2TslTOPx1nTtkdmON5RtXe42NU7zvjxZFwtZTvdh9y0AKD5yQ10UQjX88pe/lCiK5C/+4i8G/dsbb7whlUpFPv7xj/f+7KabbpIoiuRnP/vZoN9fuHChRFEku3fvdj5Hgv0drlO4fMwn9z3xtO7ZAAAgAElEQVSNbGBHyFcXqnpdtAqtibc9IdNXbXXa/GB11x7nhF0ryQ9RLGQ13Sf0Bg0AAP/IDXVRCNXwL//yLxJFkdxyyy01//3000+XKVOm9P73xz72MYmiSF5//fVBv3vfffdJFEXS2dnZ8Hz2798vO3bs6Hd0dHQQ7P9fo5H1sfPT3bBU4xzSHrU2BND8WwOLQ98bQNQ7Qt+Xp8jFAlt2A0DxUQjpohCq4Qc/+IFEUSSLFy+u+e9nn322TJw4sfe/p0+fLlEUybFjxwb9bnXa3KOPPtrwfG6//XaJoqjmQbC/I+RC2up0shlt22Ty0i6ZeNsTMnlpl8xs3y5zE97HZ2CyP5BGF2rCrY/XvEZZ3guo+hz7FmKh7stT5GKhyEUeAOAdFEK6KIRqaNYROu2002J3hNrb2+kI5VycdR5JtqEemOy7/u00yW4WG0BMX7W1YbEa4r48RS4WWCOkg3swAbCMQkgXhVANjdYI/f73v2eNUA4kvUfMwP/PnA3xuj3VKV8DO1ZzN+yse8PSuGuZ+j7u5KVdKsluFhtArOna4/TcGnX5XG/iuqZrb82/p10sWEqa2TUuPe5lA8A6ckNdFEJ1jB49uuGucXfeeWfvzx566KGGu8aNHDmSXeMylCSZSdt5abZTmdaUvrTJbt/EfcqyzV4Lodbl3YmeX63CYtmmn6gUYZrFgsWkmfsIJce1A5AH5Ia6KITquOWWW+reR2jo0KH97kn061//WoYPH173PkI33nhjonO0HOyWRsL7SpLMaO0Il9VUo3kbd8U6n3kbdw26Nr67QH2PCbc+7vS8NM+v0ZQ2jYTXctJssUCzjm4agLywnBvmUakKoQ0bNsjSpUtl6dKlctppp8kpp5zS+99tbW39fveVV16RcePGyfDhw2XRokXy4IMP9q4FqrWJwj333CNRFElra6t0dHTIsmXLZNSoUXLGGWfIiy++mOh8rQa71UQrSTKjOUUsi/UkSRO2uIl739339h041K+T9b4F/goh7e3Jm21ykCaG85A0h9xYJI9YXwUgL6zmhnlVqkLo8ssvr7szW63u0L//+7/L7Nmz5fTTT5fjjz9eJk6cKOvWrav7+N/85jfloosukmHDhsmpp54q1157rTz33HOJz9disFseCU+SzGhuGpDFDmOu59u6vFtWd+2tu07JJXFvXeF2I9TWFfGmxvlYrxSnKE1aLJA0F0+RN9EAUCwWc8M8K1UhlDfWgt3aSPjA6XkTb3vCOZnR3EY6i+Qoi22v6yXuWhsWDORjBzufxQdJc/EUeVt1AMViLTfMOwohw6wFu6WRcI31JFOWbVa9sWitm6Jqr6PK4kao9RL3g4ePyLiYnaVxCztjP0/t4s53EU7SXDwUtwDywlpumHcUQoZZC3YryYLmepJpK7d4Sb59raPKoiPUKHH3MTVSu7jzPS3TyvsAeiwN8gBAI9Zyw7yjEDLMWrBbGAnXXk8St8Phknz7XEeVxY1QZ7Rta3gOjW4eO35Rp/Pz0irustqog6S5eKxN+wWAeqzlhnlHIWSYtWC3MBLuoxAYtyB5MTQw+fadUGVxI9RxC5sXM5q7kqV9TSfe9kSmO6KRNBeT5Y1gAKDKWm6YdxRChlkLdgsj4T6mhsWdHjd3/c6miX8W10h7q+nQCV/a4i5Ex6WsSbPV+4dpsXprAACospYb5h2FkGHWgt3CSLiPzQKuXNOjlgBl1TXL4uaoWXYzkhZ3ITsuZUuay/J8uQcTAMus5YZ5RyFkmMVgDz0S7qMjVC1GNBKgLNdRVc/X9f4+LkeW3ZYkxV3o5LssSXPo9z0A4B0Wc8M8oxAyzGqwhxwZtn7PmRDrqHyuG8p6x7O+hcWUZZtlbJ3zKlIHwjoLnWAAwDus5oZ5RSFkmOVgDzUSrp30ayduodZR+Vo3FOoeONW1KDPbt8vkpV0y8bYnZPLSLpnRtq2QHRfLLKwNBAC8w3JumEcUQoYR7LVpJv3aXQWXQm3s/E0yfdVWtQXnWvdECtkREinPWpS8sLBbJADgHeSGuiiEDCtTsLvuRrXhqefrTpuK2wnylVCnWfif5px8bCQxeWlXpjuDsRbFHgv3DwMAvKNMuWEWKIQMK0uwJ+0ArO7amyipz2JqVZpd3ZIm+T42ksiqeBRhLYpVdIQAwI6y5IZZoRAyrAzBnqYDYD1x7ruOavqqrbE7WEnP1cdGEpqFmvb5sxYlG7wuAGBHGXLDLFEIGVb0YNcoZPIylSqLZNLleo5b0Cn/r707D5Kivv8//lmuvQBll/XgZoEosCiiqwYkJiSWlEgIFQuNByCHplTiFbkUkXBpIZeAu4BGA1HLWIaIgnFRsTTWtyw0URMTTRQjKHIJERBYcHn9/shvJjs7Z8/0zHy6+/mo6qrY9Mz2fPgseb/mc3TP6RvSCkKN/y7cfMAmIw92sv0LBwAIEr/XhrlGELKY3zu7W+HAC4vrc/mg1VSDYeMRq3Nn1zn+u3C73VmLYi+vfOEAAH7n99ow1whCFvN7Z3czHNj+YMtcFvnpBBSnfxep7lDnpDBmRMhuXvjCAQD8zu+1Ya4RhCzm984+5MHNjgrfIQ9uTvm93Zyy5YZcF/lOg6HToJaN9U6sRbFfNr5wsO13FQBs5vfaMNcIQhbze2cfOP8VR4XvoPmvpPS+Nn5zbXuRn80d51L9LKxFCR4bf1cBwGZ+rw1zjSBkMb939kH3OwxC9ycPQjatZWj8TXcudo3LRDZ3nHMyumXT3x+yi79rAHDO77VhrhGELOb3zu721DibRhTy8RyhTHx1qF6VU9PbRS7Z4XS9E6ME/mfT72rje2KKHgDb+b02zDWCkMX83tndXjdjy/SzVL/ptqnI/+pQvSqnZScIpbPeyfbNL5AZW35XQwjfALzC77VhrhGELOb3zu52MWTDrmNOvukOHYMfeDXnRX7Tb7+drteyqYiF99jwuxrCFD0AXuL32jDXCEIW83tnd3t6jA3PoUlnrU2u1wRlMm0vdNi83ikfmFbljA2/q5KdU/QAIBG/14a5RhCyWBA6u5vfxtrwLXO6u6/latQk3Wl7TY/qOZtc+3vzOqZVOWfD76pk3xQ9AEgmCLVhLhGELBaUzu5WIWlDUeP0m+5sF3qNpTNtL9H9EgCYVpUuG35XJXsCGQCkKii1Ya4QhCwWpM7uxuJ4G6a5pDsi9J27N+oHCzarz4wX1Wv6RvW990WN+fVb+nj3Qdfuzc0tssf++i19dag+0Jsa2NDfvMqWtrNlih4ApCpItWEuEIQsRmd3Lt/f0GfjeTy3PPmOK/fm9kNTgzLqE48toxpele/fVYkRIQDeQ23oLoKQxejsqWu8WL16zqa4i/mzXby7Of3M7TCU7rS9fBaqNqOIzly+p1cSZgF4DbWhuwhCFqOzx9Z0h67BD7wa9xk43ab8d2G/W1O2UtkdzK0NCZoemU6Tc3tEqHHBGsRpX0yrckc+p1faMkUPAFJFbegugpDF6OzR0t362Y1vlp18e73m//6tyqnuPqB07K/fyuj+szFtr+k35UHaRpoRIX+wYYoeAKSK2tBdBCGL0dkjZTLSkujbXDdHeRoXS18dqtcNv9mS8jN3kh19730xo/Zz8u2303sO4i5yTKvyj6D1XQDeRW3oLoKQxfzS2d0YJXBj7U2sQjSVAijT6TOhqT9n3JPZ/feavjHjv4tUA12qzwlyer2fCkqmVflLkHdABOAdfqkNbUEQspgfOnu+nhEU6xh0/ysRRc7E32xJ6XWpXpfsm/9M1+hkOiLk5O/E6b2mOoLk1UAQL8yn2i/9FAABAPnjh9rQJgQhi3m9s7s59z5bC/3dLPJDR7y1IJmGuUzXCDWW7NvvXKwn8opkwfGWJ99hWhUAICe8XhvahiBkMS93drenDWVr6+dsHPF2B8t0ep+bD1dNJtvriWzg5tqw2tc+ZloVACDrvFwb2oggZDEvd3a3F5Lnc0TI6ZGo0E93wwe3HqrqRLbWE9mwjXQu1oYBAOA2L9eGNiIIWczLnd3trYWzOVXL7SNZqEtnC/B8Ta/KxnqifI8IpRrwJq5xZ20YAABu8XJtaCOCkMW83NndftikG7vGZXK4vRnAV4fqtajuQ09sMuD2eqJ8BoYgTPkDAPiXl2tDGxGELOblzp6NUYJMniOU6XFDiqMDTkZuvBQgEvHSFLJsjizaMOUPAOBvXq4NbUQQspiXO3u2ivxEU7Uqp27Q4AdeDY9a9Jq+wZUCN1S8u/3QRa9NKUvEzR0Csymba82S/f248TytVOXyZwEAcsfLtaGNCEIW83Jnz+YoQaoPPjx3dp0rBW7j4j2dhy7GK0qHPLg56yMOuSyI3Q6K2ZDN3QcThflcto0X/h4AAOnxcm1oI4KQxbze2fM9SjBi+Z8yKmzdKBoTFaVO16Cccc9GR0EmHwVxOkExl/LxoNhc/h7k+3cOAJBdXq8NbUMQspgfOns+v512Oj1v0PxXXC3es7mmKVnbURDH5rRP3PCbzNaG5XL9lJfWagEA0uOH2tAmBCGL+aWz52uUIJ+FYa52uYtVgFMQx5dO22QS5nO5IYZfNt8AAMTnl9rQFgQhi/mxs2d7zUrT9x/8wKspFYUTf7PF1XvK1XOPuk15QT9e9kbE/VIQJ5bOaFm6YT6XG2L4afMNAEBsfqwN84kgZDG/dfZsT5NL50GlldM2qHJq7N3lMrmnbK1FSXR49QGn+ZCrKZtuP0/Llp8FAMgPv9WG+UYQspifOnuq38LXvPZxWiNGqb5/4+21s/FsoBCnRemQBzeHRxzOuCezKXXVczZREKcgF1M2GRECALjJT7WhDQhCFvNLZ3djvUyib+nTWfeR7XU0mRSlmW7x7HR0iYI4e1gjBABwk19qQ1sQhCzml87u5nqZWGEonQIw20VjJu+fzYd+UhDnFrvGAQDc5Jfa0BYEIYv5pbO7WdjHKuDSGX3J9jQiJ0Vp0w0P3AiObjz/Bu7gOUIAALf4pTa0BUHIYn7p7JlO9Wp6NB3BSGeReDYXlofCTKo71jUNJjWvfZzxVMJU1wlREOdGLp+nlc9ndwEAsssvtaEtCEIW80tnd3uqV9PRGZtGhNLZuS7WccuT72TcRhTEdsnl87Ty9ewuAEB2+aU2tAVByGJ+6exuP1On6eiMLWuEUp2WlMrRa/pG1WYwMhS6XwpiAAD8wy+1oS0IQhbzS2d3Y9e4RKMz2d41rnLqBo1Y/qeE23m7/RlDYSYUZEYs/1PO1v1k+6G3AAAgPX6pDW1BELKYnzq7m6MlsUZn0lkknsk9NZ1a5vaoV6zAl4uF8EynAwDAXn6qDW1AELKY3zq7G+tnEo12JFtXc8uT77h+T6FgkI0tr2Nt0JDNoMKOYwAA2M1vtWG+EYQs5sfOHm/NSm2KIyrxivBMivim9/TjZW+octoGR8HM7Z3xuk6Jv0FDNtb98AwaAADs58faMJ8IQhYLWmdPd7TD7SI+nY0UsjEilMsHnWb7AbMAACBzQasNs40gZLEgdvZ0RjvcLuLT2Vrb7TVCuR51yfYDZgEAQOaCWBtmE0HIYnT21LhdxKfzsFW3d43L9TqcbD5gFgAAuIPa0F0EIYvR2VPjdhGfbrByY2e8fO3MxogQAAD2ozZ0F0HIYn7s7Nl4Ro3bRfzCug8dvd+iug/Dr3WyC13ltA0a/MCrVjzolDVCAADYz4+1YT4RhCzmt86era2f3S7iF9Z95DAIfRTx+li70I399VsRD2XNdehJFkCdTO3rNuUFjVj+Jx6yCgBAjvmtNsw3gpDF/NTZ3XxGTdOifsTyP6lyqrPtrhPx2zSxVANoOlP7eMgqAAC546fa0AYEIYv5pbO7ub21Gw9ATTY64qeNA5wG0HTblzAEAED2+aU2tAVByGJ+6exuTV3LZDOC0MhFKqMjfhkRSjeAhqb2/XjZG+rmoH2ZJgcAQHb5pTa0BUHIYn7p7G4ECydFfeW0Dfrxsjei1uOkGqQm/maLK8EtV+KNcDld69T0c7CBAgAAdvFLbWgLgpDF/NLZ3ZhqlmlR7iRI9Zy+QT2nubfmKJsSjXClOpoTL4D6ZWQMAAC/8EttaAuCkMX80tndKKgzfQ+nQeqGNamNCqWzuYMbW4ZL7jy3KFEA9dNaKQAA/MAvtaEtCEIW80tnd2OKVaZFeTpByo3tvp2+R6qhyckIV7rhkREhAADs4pfa0BYEIYv5pbO7sWtcpkX5kAc3pxWkmj4TyMkzgNzcsa1paHIaLtMJoKwRAgDALn6pDW1BEErAGBP3OHLkSMS1O3fu1PXXX69TTjlFhYWF6tevn1atWpXRz/dTZ8/0OUKZFOVr/u/fGa+Xccpp+Ev184Xax2kwTOUeMhl1yvdaKQAAgsBPtaENCEIJGGM0ePBgrV27NupoaGgIX7d//3717NlTxcXFmjZtmlatWqVhw4bJGKP77rsv7Z/vt86eyVSzdIvydNfRZDq64TS4OX0grNOpgqkGrFh/Z5m8HgAAuMdvtWG+EYQSMMZozJgxSa+bOnWqjDF69tlnI84PHz5cLVu21NatW9P6+X7s7LmcapbuOppEoxupruFxe8SmaUhz+v7xRsRSWevkxlopAACQOT/WhvlEEEogFITq6+t14MCBuNd17txZ3bt3jzq/efNmGWM0f/78tH4+nT1aLtbRJBodSfVnuz1i0/gIhS8nr1lU92HaAVTKLMACAAB3UBu6iyCUgDFGpaWlat68uYwxKisr08SJE7V79+7wNV9++aWMMbr66qujXn/06FEVFBRo5MiRaf18OntsqRbl6YyauDVFLJsjQpcseo31OwAABBC1obsIQglUV1frgQce0Lp167R27VqNHj1aBQUF6t69ezgMvf322zLGaPLkyTHfo6KiQtXV1Ul/1rZt2/Tmm29GHLW1tXT2Rpw+j8fpqMyQBzfH/blOQ0c2dnVrPCIksX4HAICgIQi5iyDk0MMPPyxjjCZNmiRJev3112WM0YwZM2Je37lzZ/Xt2zfp+86cOTPuDnV09vTWqbj1HJx0dqxzEp4qp6W2UULj98+kXQAAgDcRhNxFEEpDRUWFKisrJSUfEWrfvj0jQhlKd+TDrefgpBuoUr3v2tc+zmiaG+t3AAAIBoKQuwhCaTjvvPPUpk0bSYnXCB05coQ1QhnKZC2MW+tonE6xCz2MVUp9xIZpbgAAIBlqQ3cRhBxqaGhQWVmZevXqFT7XqVOnhLvGzZs3L62fRWfPfFTHjYCR6RS7VEdsmOYGAAASoTZ0F0Eojp07d8Y8P3fuXBljdOedd4bPTZ48Oe5zhFq0aKFPPvkkrXugs7uzzifTgOHWFLtUMM0NAADEQ23oLoJQHLfeequqqqo0depU1dTUaOHChRo6dKiMMerTp4/27dsXvnbfvn2qrKxUSUmJpk+frtWrV+vyyy9PuIlCKujsmU1LayyTgMFW1QAAwAbUhu4iCMXx3HPP6dJLL1XHjh1VWFio4uJiVVVV6d5779XBgwejrt+xY4fGjh2riooKFRYWqm/fvqqpqcnoHujs7u38linW8AAAgHyjNnQXQchidPbcTktLhjU8AAAgn6gN3UUQshid3b5paazhAQAA+UJt6C6CkMXo7P/FtLRg++pQvWqahM8awicAIICoDd1FELJY0Dt74wK4es4mdUswEkQI8iemIwIA8D9Brw3dRhCyWJA7e6ICuNuUF1Q9ZxPT0nyOkUAAACIFuTbMBoKQxYLa2SmAYdvaMAAAbBDU2jBbCEIWC2JnpwCGZNdugQAA2CKItWE2EYQsFsTOTgEMyZ7nRwEAYJMg1obZRBCyWBA7OwUwJOmSRa856geXLHot37cMAEDWBbE2zCaCkMWC2NkpgCERiAEAiCWItWE2EYQsFsTOTgHsbW4984cpkgAARAtibZhNBCGLBbGzUwB7l5vP/GHTDAAAogWxNswmgpDFgtjZKYC9KRtbnrONOgAAkYJYG2YTQchiQe3sFMDeks3w6uYoEwAAXhfU2jBbCEIWC3JnpwD2jmxPZ/zqUL1qm6w7qk1j3REAAF4X5NowGwhCFgt6Z6cA9gY2uAAAIDeCXhu6jSBkMTo7vIAtzwEAyA1qQ3cRhCxGZ4cXMCIEAEBuUBu6iyBkMTo7vIAtzwEAyA1qQ3cRhCxGZ4cXsOU5AAC5QW3oLoKQxejs8Aq2PAcAIPuoDd1FELIYnR1ewpbnAABkF7WhuwhCFqOzw2vY8hwAgOyhNnQXQchidHYAAACEUBu6iyBkMTo7AAAAQqgN3UUQshidHQAAACHUhu4iCFmMzg4AAIAQakN3EYQsRmcHAABACLWhuwhCFqOzAwAAIITa0F0EIYvR2QEAABBCbegugpDF6OwAAAAIoTZ0F0HIYnR2AAAAhFAbuosgZDE6OwAAAEKoDd1FELIYnR0AAAAh1IbuIghZjM4OAACAEGpDdxGELEZnBwAAQAi1obsIQhajswMAACCE2tBdBCGL1dXVyRij2tpavfnmmxwcHBwcHBwcHAE+amtrZYxRXV1dvstUXyAIWSzU2Tk4ODg4ODg4ODhCR21tbb7LVF8gCFls+/btqq2tVV1dXd6/gfDCEQqOjKDR1n47aG/a2q8H7U17+/XIVlvX1dWptrZW27dvz3eZ6gsEIfjGm28ybzZXaOvcor1zh7bOLdo7t2jv3KGtvYEgBN/gH53coa1zi/bOHdo6t2jv3KK9c4e29gaCEHyDf3Ryh7bOLdo7d2jr3KK9c4v2zh3a2hsIQvAN/tHJHdo6t2jv3KGtc4v2zi3aO3doa28gCME3tm3bppkzZ2rbtm35vhXfo61zi/bOHdo6t2jv3KK9c4e29gaCEAAAAIDAIQgBAAAACByCEAAAAIDAIQgBAAAACByCEAAAAIDAIQgBAAAACByCEAAAAIDAIQjBM4wxcY8jR45EXLtz505df/31OuWUU1RYWKh+/fpp1apVebpze82bN09XXHGFunfvLmOMunbtmvB6p+365JNPasCAASoqKlJ5ebmuuuoq/fvf/3b5U3iHk/aeOXNm3P4+ZcqUmK+hvf/ro48+0owZM3TBBReoffv2at26tc4++2zNmTNHhw4dirr+wIEDuv3229WpUye1atVKvXr10vz583X8+PGY7//SSy/poosuUmlpqU466SQNGzZM77//frY/lrWctPdjjz0Wt19feeWVMd+f9o60fft2jR49Wn369NHJJ5+soqIi9ezZUxMnTtTWrVujrqd/p89JW9O3vYkgBM8wxmjw4MFau3Zt1NHQ0BC+bv/+/erZs6eKi4s1bdo0rVq1SsOGDZMxRvfdd18eP4F9jDEqKyvTj370I5100kkJC3On7bps2TIZYzRo0CDV1NRo9uzZKi8vV4cOHfTFF19k8VPZy0l7h4LQ4sWLo/r7X/7yl6jrae//mTJlikpKSnTllVdq6dKlqqmp0ahRo2SM0VlnnaXDhw+Hrz127JguvPBCNW/eXJMmTdLq1at13XXXyRijsWPHRr33c889p2bNmqmqqkoPPfSQFixYoC5duqhNmzaBLWCctHeoWJw+fXpUv37jjTei3pv2jvbOO+9o8ODBuuuuu7Rs2TKtXr1ad911l8rLy9W2bVt98MEH4Wvp35lx0tb0bW8iCMEzjDEaM2ZM0uumTp0qY4yeffbZiPPDhw9Xy5YtY35jFlSffPJJ+H+fccYZCQtzJ+26d+9etW7dWgMGDIj41nHLli0qKCjQ+PHj3fsQHuKkvUNB6NNPP036vrR3pC1btmjfvn1R5++++24ZY7R8+fLwudraWhljtHDhwohrb7nlFhljIgqY48ePq3PnzurUqZO+/vrr8PnPPvtMpaWl+uEPf5iFT2M/J+0dKhY3b96c9H1pb2feeustGWM0ceLE8Dn6d3bEamv6tjcRhOAZoSBUX1+vAwcOxL2uc+fO6t69e9T5zZs3yxij+fPnZ/M2PStZYe6kXR999FEZY/T4449HXX/xxRerTZs2qq+vd+W+vcpJEDpw4ICOHTsW91raOzXvvfeejDG68cYbw+cGDx6s4uLiiFELSfr000+jrn3llVfijoCOGTNGBQUFgRt9SyRWezcuFg8ePJiwX9LezuzevVvGGF1xxRXhc/Tv7IjV1vRtbyIIwTOMMSotLVXz5s3DU4wmTpyo3bt3h6/58ssvZYzR1VdfHfX6o0ePqqCgQCNHjszlbXtGosLcabveeOONMsbon//8Z9T106ZNkzFG7733nmv37kWpBqG2bdvKGKNmzZrpvPPO0zPPPBN1Le2dmo0bN8oYoxkzZkiSGhoaVFJSooEDB8a8/vTTT9c555wT/u/58+fLGKO6urqoa1euXCljjJ577rns3LwHNW1v6X/FYqhfG2PUp08f1dbWRr2e9k6svr5ee/bs0RdffKE33nhDl1xyiYwxeuyxxyTRv92UrK0l+rZXEYTgGdXV1XrggQe0bt06rV27VqNHj1ZBQYG6d+8eDkNvv/22jDGaPHlyzPeoqKhQdXV1Lm/bMxIV5k7b9fLLL5cxJupbSElasWKFjDHasGGDK/ftVcmC0OLFizVhwgQ99thjWr9+vRYuXKiuXbvKGKMFCxZEXEt7J/ftt9/qwgsvVIsWLfThhx9K+u+UQmOMRo0aFfM11dXVqqioCP93aDrR3//+96hrN2zYIGOMVqxYkZ0P4DGx2luSnn76aV111VVavXq1nn/+eS1fvlz9+vWTMUY333xzxHvQ3ok988wzEQvyKyoqIv5toH+7J1lbS/RtryIIwdMefvhhGWM0adIkSdLrr78e9Q1kY507d1bfvn1zeYuekagwd9quQ4YMkTEmYhOLkNA0rlgjG0GSLAjFcuDAAfXo0UOtWrXSjh07wudp7+RuuukmGWM0Z86c8Llt27bJGKPrrrsu5msGDx6s0tLS8H+PGzdOxpiItV4hoakuTYujoIrV3vEcP35cgwYNkjFGb7/9dvg87a0qC5kAAAxwSURBVJ3Yrl27tGnTJq1fv17z58/XgAEDNGPGjPA6Qfq3e5K1dTz0bfsRhOB5FRUVqqyslJR85KJ9+/aMCMWRyYhQ03ZNNEKxfPlyRiiUXhCS/td+a9asCZ+jvRMLLdqfMGGCTpw4ET6f7Bvz8847L+VvzF944QW+xf3/4rV3IqH2+9WvfhU+R3s7s337drVr10433HCDJPp3NjVt60To23YjCMHzzjvvPLVp00ZS4rUsR44cYY1QAumuEYrVrqxZSS7dIBT6P8nGu0DR3vGF1lqNHj06asSsoaFBxcXFrKFwUaL2TuRvf/tbxOi+RHun46c//amaN2+uo0eP0r+zrHFbJ0LfthtBCJ7W0NCgsrIy9erVK3yuU6dOCXc3mzdvXi5v0TOSFeZO2vWRRx6RMfF3MWvdunXgdzFLNwgtXrxYxhg98cQT4XO0d2z33XefjDG69tpr4xblF110UcJdtRp/4/vyyy8n3enp888/d/dDeEgq7R3PunXrZIzR3Llzw+dob+cuu+wyGWPC62bp39nTtK3joW/bjSAET9i5c2fM83PnzpUxRnfeeWf43OTJk2VM7OfdtGjRIuacXCQvzJ206549e1RSUhL3uTbjxo1z/f69JlF7Hz9+XHv37o06v3v3bnXs2FHFxcXatWtX+DztHW3WrFkyxuiaa67Rt99+G/e60DrDps9ZmTRpkowxev3118Pnjh8/ro4dO8Z99seQIUPc/yAekWp7x/q3/JtvvlH//v1VUFAQMXJJe8f25Zdfxjz//vvvq6SkRD169Aifo39nxklb07e9iSAET7j11ltVVVWlqVOnqqamRgsXLtTQoUPD21M2fpjfvn37VFlZqZKSEk2fPl2rV68Or6GIt9g/qNasWaPZs2dr9uzZat++vU4++eTwfy9btiziWqftumTJEhljNGjQINXW1mrOnDkqLy/XaaedFthvulJt7/3796uoqEjXXHON7r//fq1atUqTJ09WeXm5CgoKVFNTE/XetPf/hNZFdenSRY8//njUU94bT0c5duyYzj//fDVv3lyTJk3SI488otGjR8ddZP773/9eBQUFqqqq0rJly/Tggw+qa9euat26dWCnHzpp7/bt22vkyJGaM2eOVq9erRkzZqhLly4yxmjatGlR7017RxszZozOPvtsTZkyRTU1NVq2bJluuOEGlZSUqLCwkP7tIidtTd/2JoIQPOG5557TpZdeqo4dO6qwsFDFxcWqqqrSvffeq4MHD0Zdv2PHDo0dO1YVFRUqLCxU3759YxaPQXfxxRdHbAna+Ig1WuG0XX/729/qnHPOUVFRkcrKynTllVdq69atWfxEdku1vY8eParx48erX79+Ovnkk9WiRQudcsopGjFihF577bW47097/9eYMWPitrMxRhdffHHE9f/5z3906623qkOHDmrVqpV69uypuXPnxt0R6o9//KMGDhyokpIStW3bVpdddpnefffdHHwyOzlp7zvuuEPnnnuuysvL1aJFC5WVlemSSy7RunXr4r4/7R1p/fr1GjFihLp06aKioiIVFhaqsrJS48aNi7n4nv6dPidtTd/2JoIQAAAAgMAhCAEAAAAIHIIQAAAAgMAhCAEAAAAIHIIQAAAAgMAhCAEAAAAIHIIQAAAAgMAhCAEAAAAIHIIQAAAAgMAhCAEAAAAIHIIQAAAAgMAhCAEAAqW8vFzDhg3L920AAPKMIAQAPmOMSfn49NNP8327Efr166dWrVpp7969ca85fPiwTjrpJHXt2lUnTpxw/DMIQgAAiSAEAL6zdu3aiGP69OkyxmjkyJFRf3bo0KF8326EJUuWyBijpUuXxr1m7dq1MsZo1qxZaf0MghAAQCIIAYDvbd68WcYYzZw509Hr8hGS9u7dq8LCQvXv3z/uNT/4wQ/UrFkzffbZZ2n9DIIQAEAiCAGA7yULQi+++KKMMXryySe1dOlS9e7dW61atdKUKVMkSaeeeqouvfTSuK976qmnIs4fPnxYs2bNUu/evVVYWKh27dppxIgRev/991O63yuvvFLGGP35z3+O+rOtW7eqoKAg6n4WLVqkIUOG6PTTT1fLli3VoUMHjR07Vp9//nnUezQNQgcPHpQxRjfffHPUtcuWLZMxRlu2bIk4v3fvXt1+++3q3r27WrZsqVNOOUXXXXedtm3bFnHdwYMHNX36dPXq1UtFRUVq27atevfurcmTJ6fUFgCA7CEIAYDPpRqE+vfvr65du2rWrFlauXKl1q9fL8lZEDp69KgGDhyoVq1aacKECaqpqdG8efPUrVs3lZaW6t133016v3V1dTLG6JZbbon6sxkzZsgYo9/97ncR50877TSNHTtWCxYs0MqVK3XTTTepqKhI3bp109dffx1xbaZBaM+ePerRo4fatGmj2267TStXrtSMGTNUXl6u008/XTt27AhfO2rUKBUUFGj8+PFauXKlli9frltvvVXnn39+0nYAAGQXQQgAfC7VIHTqqadq3759UX/uJAjNnTtXBQUF2rRpU8S1X331lU477bSY79PUiRMn1K1bN5WVleno0aPh8w0NDerSpYvKy8tVX18f8ZpY0/j+8Ic/yBijFStWRJzPNAhdf/31Ki0t1QcffBBx7UcffaSioqLw+zQ0NKioqEijRo1K+pkBALlHEAIAn0s1CE2dOjXmnzsJQn369FFVVZX27NkTdVxzzTVq1aqVjh8/nvSeZ82aJWOMnn766fC5l156ScYY3XbbbXFf19DQoP3792vPnj3atWuXCgsLNXr06IhrMglCx44dU2lpqYYPHx7zMw4cOFC9evUKv76iokK9evXSP/7xj6SfGQCQWwQhAPC5VIPQo48+GvPPUw1CJ06cUPPmzZNu2b179+6k97xt2zY1a9Ys4ueG1g799a9/jbp+48aNGjRokAoLC6N+3vDhwyOuzSQIffLJJ0k/X9u2bcOvf/rpp1VaWipjjHr27Klx48bp2Wef1bfffpu0DQAA2UUQAgCfSzUINd30ICTelLbnn38+4nUNDQ1q1qyZ+vfvr02bNsU9mk5ri2fo0KFq1qyZtm/frn379qmwsDDm2ppXX31VBQUFqqqq0kMPPaT169eHf1ZJSUnUDnFNg9ChQ4fiBqHFixdHBKGPP/5YxhhddtllcT/f5s2bI95jz549WrNmjcaPH6+uXbvKGKPvfve7KbcDACA7CEIA4HOZBqE+ffqouro66vzSpUujXved73xHHTt2TOtBp00988wzMsZozpw54ZGZlStXRl03YcIEFRQUaOfOnRHn9+zZI2NM0iB04sQJFRUV6Wc/+1nUe0+aNCkiCB09elTFxcX63ve+l9ZnOnHihO68886oaX8AgNwjCAGAz2UahH7yk5+oqKhIu3btCp87fPiwzjzzzKjXzZ49W8YYLVmyJOZ7NQ0ridTX16uiokI9e/bUOeeco5KSkqgd4CTpxhtvjBmEfvGLX6QUhCSpqqpKnTp1ihil2blzp8rKyqI2SxgzZoyMMXr++edj3neonerr62Peb+iBsLW1tUlaAACQTQQhAPC5TIPQyy+/LGOM+vbtq6VLl+r+++9X7969dcEFF8TcPvv73/9+OIAsWLBAtbW1mj59uqqrqzV06FBH937HHXeE196MGTMm5jWh7bb79u2rJUuWaOnSpRo6dKjOOOMMtWnTJqUgVFtbK2OMBg8erBUrVmjWrFnq0KFD+DM2DkJ79+7VmWeeqWbNmunqq6/W0qVLtXz5cv3yl7/UmWeeGZ5it337dpWUlOjqq6/W/Pnz9eijj+ruu+9WWVmZ2rVrF7HNNgAg9whCAOBzmQYhSVq1apV69Oihli1bqrKyUosWLdLGjRtjvu7YsWNauHChBgwYoJKSEpWUlKhnz5667rrr9Morrzi69w8++CAchF5//fW41z311FM666yzVFxcrIqKCl177bXasWNHzNAT69yJEyc0a9YsdezYUa1atVJVVZWeeOKJuA9U/frrr3XPPfeEHxrbpk0b9e7dWz//+c/1zjvvSJK++eYb3XXXXTr33HPVrl07FRYWqlu3bho3bpz+9a9/OWoHAID7CEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAocgBAAAACBwCEIAAAAAAuf/AfKVtkbAaiqtAAAAAElFTkSuQmCC\" width=\"639.3999771332749\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Predictions')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make cross-validated predictions\n",
    "predictions = cross_val_predict(model, X, y, cv=n_fold)\n",
    "plt.scatter(y, cv_pred)\n",
    "plt.xlabel(\"True Values\")\n",
    "plt.ylabel(\"Predictions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Compute the $R^2$-score this model. You can use the function `r2_score` from the module `sklearn.metrics`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross-validated Accuracy: 0.49532382463572844\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "accuracy = r2_score(y, cv_pred)\n",
    "print(\"Cross-validated Accuracy:\", accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Caution**: Altough this $R^2$-score is higher than the score for the training/validation set split, they are not really comparable since we computed them on different subsets of the data.\n",
    "To get a more reliable comparison, we must keep part of the data as a so-called *hold-out* data set to be used for estimating the true learning error."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}