{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1bba0128",
   "metadata": {},
   "source": [
    "# Supervised regression\n",
    "\n",
    "This is an example of how to build and optimize neural networks with PyTorch with the objective of predicting a known feature in the training dataset.\n",
    "\n",
    "The logic here is very similar to the classification problem and the code is also very close, but the final objective is to minimize the error in the prediction of the missing feature. This is achieved by minimizing the mean-squared-error between the prediction and the target features. As noticed during the presentation, by minimizing the mean-squared-error, we assume that the underlying error distribution is Gaussian. One could use the mean absolute error instead when assuming the distribution is Laplacian.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d0681795",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Collecting torchbnn\n",
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      "Installing collected packages: torchbnn\n",
      "Successfully installed torchbnn-1.2\n"
     ]
    }
   ],
   "source": [
    "!pip install torchvision torch pandas numpy matplotlib ipympl torchbnn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "23feddde",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "from typing import Tuple\n",
    "\n",
    "# import standard PyTorch modules\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "import torchbnn as bnn\n",
    "\n",
    "# import torchvision module to handle image manipulation\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import axes3d\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb1286f0",
   "metadata": {},
   "source": [
    "We start by generating some fake dataset, which is simple enough that we can visualize the results easily. For this reason, the dataset will contain only two independent variables and a third feature variable which we want to determine in test data.\n",
    "\n",
    "The simulated example data will be $f(x) = (3 + \\kappa) x^2 + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=10)$ and $\\kappa \\sim \\mathcal{N}(\\mu=0, \\sigma=0.03)$.\n",
    "\n",
    "In this case we do know the true model, so it is interesting to take some time to pinpoint the role of $\\kappa$ and $\\epsilon$. These variables add fluctuation to the results. $\\epsilon$ adds Gaussian noise in a way that is completely independent from $x$ and cannot be traced down to a particular functional dependence. $\\kappa$ changes a specific parameter of the model, in this case the coefficient 3, by around 1%.\n",
    "\n",
    "When fitting a model, the nomenclature *epistemic uncertainty* is often used to refer to uncertainties coming to effects related to different functional models. That is, one can imagine that there are different functions that may fit the data due to the effect of $\\kappa$, such as: $g(x) = 3x^2$ or $h(x) = 2.95x^2$.\n",
    "\n",
    "The nomenclature *aleatoric uncertainty* is used to refer to whichever uncertainty cannot be tracked down to a given model dependence. In this example, different constant factors could be added to the model $g$ to account for the fluctuations in $\\epsilon$.\n",
    "\n",
    "We will see these two effects later on, when we discuss Bayesian Neural Networks, so that we can predict the effect of those uncertainties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5d457cd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(N: int) -> np.ndarray:\n",
    "    x = 2*np.random.randn(N, 1)\n",
    "    epsilon = 10*np.random.randn(N, 1)\n",
    "    kappa = 0.03*np.random.randn(N, 1)\n",
    "    z = (3 + kappa)*x**2 + epsilon\n",
    "    return np.concatenate((x, z), axis=1).astype(np.float32)\n",
    "\n",
    "train_data = generate_data(N=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48433f6f",
   "metadata": {},
   "source": [
    "PyTorch allows you to create a class that outputs a single data entry and use that to feed input to your neural network. We will use the following class to feed the data to the neural network. This looks useless if all your data fits in a Numpy array, but notice that if you have a lot of data and cannot load it all in memory, this allows you to read data on demand, as you need it and only the needed samples are stored at a single time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "30205402",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyDataset(torch.utils.data.Dataset):\n",
    "    def __init__(self, data: np.ndarray):\n",
    "        self.data = data\n",
    "    def __len__(self) -> int:\n",
    "        \"\"\"How many samples do I have?\"\"\"\n",
    "        return len(self.data)\n",
    "    def __getitem__(self, idx):\n",
    "        # give me item with index idx\n",
    "        return {\"data\": self.data[idx, 0:1], \"target\": self.data[idx, 1:]}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cc0b0774",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\n"
     ]
    }
   ],
   "source": [
    "my_dataset = MyDataset(train_data)\n",
    "print(len(my_dataset))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6dccfac6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'data': array([-0.5583114], dtype=float32), 'target': array([-11.577045], dtype=float32)}\n"
     ]
    }
   ],
   "source": [
    "print(my_dataset[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "527089bd",
   "metadata": {},
   "source": [
    "Plot some of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "067b8105",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\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(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\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",
       "                img.type = 'image/png';\n",
       "            }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, 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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "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.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\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",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(train_data[:, 0], train_data[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e517975c",
   "metadata": {},
   "source": [
    "And now let us define the neural network. In PyTorch, neural networks always extend `nn.Module`. They define their sub-parts in their constructor, which are convolutional layers and fully connected linear layers in this case, and the method `forward` is expected to receive an input image and output the network target.\n",
    "\n",
    "The network parameters are the weights of the `Conv2d` and `Linear` layers, which are conveniently hidden here, but can be accessed if you try to access their `weights` elements.\n",
    "\n",
    "We will not directly output the label probabilities, since we do not actually need it to optimize the neural network: we need only the logits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d908ef86",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Network(nn.Module):\n",
    "    \"\"\"\n",
    "        This is our parametrized function.\n",
    "        It stores all the parametrized weights theta inside the model object.\n",
    "        For such a simple example data, it was not necessary to have such a complex model:\n",
    "        this was only done here to show the interface provided by PyTorch.\n",
    "        The forward function receives the x values and outputs an estimate of the target.\n",
    "        \n",
    "        The nn.Sequential object allows one to apply each step in the given list of parameter\n",
    "        in a sequential way. An alternative would be to create each of these layers manually\n",
    "        and apply them one after the other in the forward method.\n",
    "    \"\"\"\n",
    "    def __init__(self, input_dimension: int=1, output_dimension: int=1):\n",
    "        \"\"\"\n",
    "        Constructor. Here we initialize the weights.\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "\n",
    "        hidden_layer = 100\n",
    "        self.model = nn.Sequential(\n",
    "                                   nn.Linear(input_dimension, hidden_layer),\n",
    "                                   nn.ReLU(),\n",
    "                                   nn.Linear(hidden_layer, output_dimension)\n",
    "                                    )\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"\n",
    "        This function is called when one does my_network(x) and it represents the action\n",
    "        of our parametrized function in the input.\n",
    "        \"\"\"\n",
    "        return self.model(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c5620dc",
   "metadata": {},
   "source": [
    "Let us create one instance of this network. We also create an instance of PyTorch's `DataLoader`, which has the task of taking a given number of data elements and outputing it in a single object. This \"mini-batch\" of data is used during training, so that we do not need to load the entire data in memory during the optimization procedure.\n",
    "\n",
    "We also create an instance of the Adam optimizer, which is used to tune the parameters of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "988e1979",
   "metadata": {},
   "outputs": [],
   "source": [
    "network = Network()\n",
    "B = 10\n",
    "loader = torch.utils.data.DataLoader(my_dataset, batch_size=B)\n",
    "optimizer = torch.optim.Adam(network.parameters(), lr=1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ee54520",
   "metadata": {},
   "source": [
    "Now we actually repeatedly try to optimize the network parameters. Each time we go through all the data we have, we go through one \"epoch\". For each epoch, we take several \"mini-batches\" of data (given by the `DataLoader` in `loader`) and use it to make one training step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d15d655d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/100: average loss 378.81588\n",
      "Epoch 1/100: average loss 275.14966\n",
      "Epoch 2/100: average loss 209.67680\n",
      "Epoch 3/100: average loss 177.45487\n",
      "Epoch 4/100: average loss 161.36641\n",
      "Epoch 5/100: average loss 151.22071\n",
      "Epoch 6/100: average loss 143.62892\n",
      "Epoch 7/100: average loss 137.58497\n",
      "Epoch 8/100: average loss 132.61164\n",
      "Epoch 9/100: average loss 128.38996\n",
      "Epoch 10/100: average loss 124.72414\n",
      "Epoch 11/100: average loss 121.49631\n",
      "Epoch 12/100: average loss 118.62273\n",
      "Epoch 13/100: average loss 116.04727\n",
      "Epoch 14/100: average loss 113.73365\n",
      "Epoch 15/100: average loss 111.67534\n",
      "Epoch 16/100: average loss 109.85956\n",
      "Epoch 17/100: average loss 108.26555\n",
      "Epoch 18/100: average loss 106.88248\n",
      "Epoch 19/100: average loss 105.69173\n",
      "Epoch 20/100: average loss 104.67635\n",
      "Epoch 21/100: average loss 103.80502\n",
      "Epoch 22/100: average loss 103.06343\n",
      "Epoch 23/100: average loss 102.43223\n",
      "Epoch 24/100: average loss 101.89756\n",
      "Epoch 25/100: average loss 101.43507\n",
      "Epoch 26/100: average loss 101.03641\n",
      "Epoch 27/100: average loss 100.68191\n",
      "Epoch 28/100: average loss 100.35821\n",
      "Epoch 29/100: average loss 100.06578\n",
      "Epoch 30/100: average loss 99.79758\n",
      "Epoch 31/100: average loss 99.54630\n",
      "Epoch 32/100: average loss 99.31432\n",
      "Epoch 33/100: average loss 99.08812\n",
      "Epoch 34/100: average loss 98.87219\n",
      "Epoch 35/100: average loss 98.67368\n",
      "Epoch 36/100: average loss 98.48651\n",
      "Epoch 37/100: average loss 98.31420\n",
      "Epoch 38/100: average loss 98.15310\n",
      "Epoch 39/100: average loss 97.99930\n",
      "Epoch 40/100: average loss 97.85031\n",
      "Epoch 41/100: average loss 97.71002\n",
      "Epoch 42/100: average loss 97.57293\n",
      "Epoch 43/100: average loss 97.44047\n",
      "Epoch 44/100: average loss 97.31417\n",
      "Epoch 45/100: average loss 97.18990\n",
      "Epoch 46/100: average loss 97.07419\n",
      "Epoch 47/100: average loss 96.96548\n",
      "Epoch 48/100: average loss 96.86184\n",
      "Epoch 49/100: average loss 96.76805\n",
      "Epoch 50/100: average loss 96.67791\n",
      "Epoch 51/100: average loss 96.59360\n",
      "Epoch 52/100: average loss 96.51472\n",
      "Epoch 53/100: average loss 96.43937\n",
      "Epoch 54/100: average loss 96.36539\n",
      "Epoch 55/100: average loss 96.29459\n",
      "Epoch 56/100: average loss 96.22356\n",
      "Epoch 57/100: average loss 96.15634\n",
      "Epoch 58/100: average loss 96.08934\n",
      "Epoch 59/100: average loss 96.02401\n",
      "Epoch 60/100: average loss 95.96307\n",
      "Epoch 61/100: average loss 95.90349\n",
      "Epoch 62/100: average loss 95.84973\n",
      "Epoch 63/100: average loss 95.79636\n",
      "Epoch 64/100: average loss 95.74215\n",
      "Epoch 65/100: average loss 95.69529\n",
      "Epoch 66/100: average loss 95.64951\n",
      "Epoch 67/100: average loss 95.60449\n",
      "Epoch 68/100: average loss 95.56373\n",
      "Epoch 69/100: average loss 95.52165\n",
      "Epoch 70/100: average loss 95.48233\n",
      "Epoch 71/100: average loss 95.44179\n",
      "Epoch 72/100: average loss 95.39826\n",
      "Epoch 73/100: average loss 95.35763\n",
      "Epoch 74/100: average loss 95.31944\n",
      "Epoch 75/100: average loss 95.27754\n",
      "Epoch 76/100: average loss 95.23919\n",
      "Epoch 77/100: average loss 95.20086\n",
      "Epoch 78/100: average loss 95.16258\n",
      "Epoch 79/100: average loss 95.12233\n",
      "Epoch 80/100: average loss 95.08201\n",
      "Epoch 81/100: average loss 95.04595\n",
      "Epoch 82/100: average loss 95.01281\n",
      "Epoch 83/100: average loss 94.97996\n",
      "Epoch 84/100: average loss 94.94827\n",
      "Epoch 85/100: average loss 94.91624\n",
      "Epoch 86/100: average loss 94.88639\n",
      "Epoch 87/100: average loss 94.85546\n",
      "Epoch 88/100: average loss 94.82733\n",
      "Epoch 89/100: average loss 94.79647\n",
      "Epoch 90/100: average loss 94.77049\n",
      "Epoch 91/100: average loss 94.74167\n",
      "Epoch 92/100: average loss 94.71930\n",
      "Epoch 93/100: average loss 94.69341\n",
      "Epoch 94/100: average loss 94.66904\n",
      "Epoch 95/100: average loss 94.64581\n",
      "Epoch 96/100: average loss 94.61936\n",
      "Epoch 97/100: average loss 94.59652\n",
      "Epoch 98/100: average loss 94.57301\n",
      "Epoch 99/100: average loss 94.55085\n"
     ]
    }
   ],
   "source": [
    "epochs = 100\n",
    "# for each epoch\n",
    "for epoch in range(epochs):\n",
    "    losses = list()\n",
    "    # for each mini-batch given by the loader:\n",
    "    for batch in loader:\n",
    "        # get the input in the mini-batch\n",
    "        # this has size (B, C)\n",
    "        # where B is the mini-batch size\n",
    "        # C is the number of features (1 in this case)\n",
    "        features = batch[\"data\"]\n",
    "        # get the targets in the mini-batch (there shall be B of them)\n",
    "        target = batch[\"target\"]\n",
    "        # get the output of the neural network:\n",
    "        prediction = network(features)\n",
    "        \n",
    "        # calculate the loss function being minimized\n",
    "        # in this case, it is the mean-squared error between the prediction and the target values\n",
    "        loss = F.mse_loss(prediction, target)\n",
    "        # exactly equivalent to:\n",
    "        #loss = ((prediction - target)**2).mean()\n",
    "\n",
    "        # clean the optimizer temporary gradient storage\n",
    "        optimizer.zero_grad()\n",
    "        # calculate the gradient of the loss function as a function of the gradients\n",
    "        loss.backward()\n",
    "        # ask the Adam optimizer to change the parameters in the direction of - gradient\n",
    "        # Adam scales the gradient by a constant which is adaptively tuned\n",
    "        # take a look at the Adam paper for more details: https://arxiv.org/abs/1412.6980\n",
    "        optimizer.step()\n",
    "        losses.append(loss.detach().cpu().item())\n",
    "    avg_loss = np.mean(np.array(losses))\n",
    "    print(f\"Epoch {epoch}/{epochs}: average loss {avg_loss:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4980bf4",
   "metadata": {},
   "source": [
    "Let us check what the network says about some new data it has never seen before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "09646d29",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_data = generate_data(N=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e315b5dc",
   "metadata": {},
   "source": [
    "And now we can plot again the new images, now showing what the network tells us about it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7a06a4c0",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "predicted = network(torch.from_numpy(test_data[:,0:1])).detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bab0ce43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\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(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\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",
       "                img.type = 'image/png';\n",
       "            }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, 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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "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.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\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",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], label=\"Test data\")\n",
    "ax.scatter(test_data[:, 0], predicted, label=\"Predicted\")\n",
    "ax.set(xlabel=\"$x$\", ylabel=\"$f(x)$\")\n",
    "#ax.set_yscale('log')\n",
    "plt.legend(frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {
    "elbo.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6bd7c62d",
   "metadata": {},
   "source": [
    "## What about an uncertainty?!\n",
    "\n",
    "The method shown before finds the neural network parameters which maximize the log-likelihood of the data. But not all parameters are equally likely and we can estimate an uncertainty for them.\n",
    "\n",
    "With an uncertainty for the parameters, we can propagate the uncertainty through the neural network and obtain an uncertainty on the prediction of the regression output.\n",
    "\n",
    "This can be done assuming each weight in the network function has a given probability distribution and instead of fitting a single value for the weight, we fit the parameters of this probability distribution. For the example shown here, we assume that the probability distribution of the weights is Gaussian and we aim to obtain the mean and variance of the Gaussian.\n",
    "\n",
    "We are going to include the epistemic uncertainty through the variation of the weights. That is, the fact that the weights vary and lead to different effective functions allow us to model different $f(x)$ dependence relationships and this is attributed to the epistemic uncertainty.\n",
    "\n",
    "We additionally assume that the data collected has some aleatoric uncertainty, which means that every point is uncertain by some fixed unknown amount. To model this effect, we assume that the likelihood function $p(\\text{data}|\\theta)$ can be modelled by a Gaussian distribution with a certain standard deviation $\\sigma_a$. This standard deviation will be used to model the aleatoric uncertainty.\n",
    "\n",
    "The final loss function to be optimised here is:\n",
    "\n",
    "$\\mathcal{L} = -\\mathbb{E}_{\\text{data}}\\left[\\log p(\\text{data}|\\text{weights})\\right] + \\frac{1}{M} KL(\\text{weights}|\\text{prior})$\n",
    "\n",
    "The first term is assumed to be a Gaussian with the standard deviation given by the aleatoric uncertainty (assumed to be the same for every data point, but this could be changed to be data-point specific as well!). The second term corresponds to a penalty for varying the weights away from the prior assumption that the weights are Gaussian with a mean zero and standard deviation 0.1. In this equation, $M$ is the number of batches used.\n",
    "\n",
    "It can be shown that by minimizing this loss function, we obtain weights mean and standard deviations that approximately optimize the posterior probability given by the Bayes rule: $p(\\text{weights}|\\text{data}) = \\frac{p(\\text{data}|\\text{weights}) p(\\text{weights})}{p(\\text{data})}$. The proof follows by algebraically trying to minimize the Kullback-Leibler divergence between the true posterior given by the Bayes rule and the approximate posterior, on which the weights are assumed to be Gaussian and the likelihood is assumed to be Gaussian.\n",
    "\n",
    "![elbo.png](attachment:elbo.png)\n",
    "\n",
    "The details of the derivation can be consulted in the following paper:\n",
    "\n",
    "https://arxiv.org/pdf/1505.05424.pdf\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f8d501ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "class BayesianNetwork(nn.Module):\n",
    "    \"\"\"\n",
    "        A model Bayesian Neural network.\n",
    "        Each weight is represented by a Gaussian with a mean and a standard deviation.\n",
    "        Each evaluation of forward leads to a different choice of the weights, so running\n",
    "        forward several times we can check the effect of the weights variation on the same input.\n",
    "        The nll function implements the negative log likelihood to be used as the first part of the loss\n",
    "        function (the second shall be the Kullback-Leibler divergence).\n",
    "        The negative log-likelihood is simply the negative log likelihood of a Gaussian\n",
    "        between the prediction and the true value. The standard deviation of the Gaussian is left as a\n",
    "        parameter to be fit: sigma.\n",
    "    \"\"\"\n",
    "    def __init__(self, input_dimension: int=1, output_dimension: int=1):\n",
    "        super(BayesianNetwork, self).__init__()\n",
    "        hidden_dimension = 100\n",
    "        self.model = nn.Sequential(\n",
    "                                   bnn.BayesLinear(prior_mu=0,\n",
    "                                                   prior_sigma=0.1,\n",
    "                                                   in_features=input_dimension,\n",
    "                                                   out_features=hidden_dimension),\n",
    "                                   nn.ReLU(),\n",
    "                                   bnn.BayesLinear(prior_mu=0,\n",
    "                                                   prior_sigma=0.1,\n",
    "                                                   in_features=hidden_dimension,\n",
    "                                                   out_features=hidden_dimension),\n",
    "                                   nn.ReLU(),\n",
    "                                   bnn.BayesLinear(prior_mu=0,\n",
    "                                                   prior_sigma=0.1,\n",
    "                                                   in_features=hidden_dimension,\n",
    "                                                   out_features=output_dimension)\n",
    "                                    )\n",
    "        self.log_sigma2 = nn.Parameter(torch.ones(1), requires_grad=True)\n",
    "\n",
    "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Calculate the result f(x) applied on the input x.\n",
    "        \"\"\"\n",
    "        return self.model(x)\n",
    "\n",
    "    def nll(self, prediction: torch.Tensor, target: torch.Tensor) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Calculate the negative log-likelihood (divided by the batch size, since we take the mean).\n",
    "        \"\"\"\n",
    "        error = prediction - target\n",
    "        squared_error = error**2\n",
    "        sigma2 = torch.exp(self.log_sigma2)[0]\n",
    "        norm_error = 0.5*squared_error/sigma2\n",
    "        norm_term = 0.5*(np.log(2*np.pi) + self.log_sigma2[0])\n",
    "        return norm_error.mean() + norm_term\n",
    "\n",
    "    def aleatoric_uncertainty(self) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "            Get the aleatoric component of the uncertainty.\n",
    "        \"\"\"\n",
    "        return torch.exp(0.5*self.log_sigma2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7b9beb21",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the neural network:\n",
    "b_network = BayesianNetwork()\n",
    "\n",
    "# create the object to load the data:\n",
    "B = 10\n",
    "loader = torch.utils.data.DataLoader(my_dataset, batch_size=B)\n",
    "\n",
    "# create the optimizer to be used \n",
    "optimizer = torch.optim.Adam(b_network.parameters(), lr=0.001)\n",
    "\n",
    "# the Kullback-Leibler divergence should be scaled by 1/number_of_batches\n",
    "# see https://arxiv.org/abs/1505.05424 for more information on this\n",
    "number_of_batches = len(my_dataset)/float(B)\n",
    "weight_kl = 1.0/float(number_of_batches)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68ba2e2",
   "metadata": {},
   "source": [
    "The criteria for finding the optimal weights are based on the Bayes' theorem, on which the posterior probability of the weights is proportional to the likelihood of the data given the weights and to the prior probability of the weights. We assume the prior probability of the weights is Gaussian corresponding to a unit Gaussian centred at zero and with standard deviation 0.1. This prior has a regularizing effect, preventing overtraining.\n",
    "\n",
    "We can translate the Bayes theorem and the assumption that the final posterior distribution is also Gaussian into an optimization procedure to find the posterior mean and variance of the posterior distribution. The function optimized to obtain the mean and variances of the Gaussians for the weights is the sum between the mean-squared-error (corresponding to a Gaussian log-likelihood of the data) and the Kullback-Leibler divergence between the weights distribution and the prior Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fbea6b0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "kl_loss = bnn.BKLLoss(reduction='mean', last_layer_only=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b92ed4b0",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/500  total: 58.60563, -LL: 29.30297, prior: 0.49401, aleatoric unc.: 1.70738\n",
      "Epoch 1/500  total: 29.89883, -LL: 22.77377, prior: 0.51578, aleatoric unc.: 1.74675\n",
      "Epoch 2/500  total: 24.01581, -LL: 19.56905, prior: 0.54058, aleatoric unc.: 1.78531\n",
      "Epoch 3/500  total: 20.88541, -LL: 15.23512, prior: 0.56686, aleatoric unc.: 1.82458\n",
      "Epoch 4/500  total: 18.42086, -LL: 12.56114, prior: 0.59138, aleatoric unc.: 1.86375\n",
      "Epoch 5/500  total: 16.78540, -LL: 11.47957, prior: 0.61184, aleatoric unc.: 1.90320\n",
      "Epoch 6/500  total: 15.74639, -LL: 10.39981, prior: 0.63168, aleatoric unc.: 1.94387\n",
      "Epoch 7/500  total: 15.23265, -LL: 10.92122, prior: 0.64618, aleatoric unc.: 1.98676\n",
      "Epoch 8/500  total: 14.43628, -LL: 14.04801, prior: 0.65764, aleatoric unc.: 2.03084\n",
      "Epoch 9/500  total: 13.75567, -LL: 9.28419, prior: 0.66495, aleatoric unc.: 2.07617\n",
      "Epoch 10/500  total: 13.46332, -LL: 9.24567, prior: 0.67066, aleatoric unc.: 2.12401\n",
      "Epoch 11/500  total: 12.68328, -LL: 8.02405, prior: 0.68236, aleatoric unc.: 2.17244\n",
      "Epoch 12/500  total: 12.16965, -LL: 10.14399, prior: 0.69100, aleatoric unc.: 2.22149\n",
      "Epoch 13/500  total: 11.89046, -LL: 10.02692, prior: 0.69707, aleatoric unc.: 2.27265\n",
      "Epoch 14/500  total: 11.31826, -LL: 8.22698, prior: 0.70348, aleatoric unc.: 2.32503\n",
      "Epoch 15/500  total: 11.15097, -LL: 8.46218, prior: 0.70463, aleatoric unc.: 2.37917\n",
      "Epoch 16/500  total: 10.78811, -LL: 6.91465, prior: 0.70900, aleatoric unc.: 2.43505\n",
      "Epoch 17/500  total: 10.27545, -LL: 7.55249, prior: 0.70822, aleatoric unc.: 2.49083\n",
      "Epoch 18/500  total: 9.88403, -LL: 7.78374, prior: 0.70896, aleatoric unc.: 2.54750\n",
      "Epoch 19/500  total: 9.49734, -LL: 6.96424, prior: 0.71104, aleatoric unc.: 2.60481\n",
      "Epoch 20/500  total: 9.18567, -LL: 6.83609, prior: 0.71782, aleatoric unc.: 2.66279\n",
      "Epoch 21/500  total: 8.77549, -LL: 6.85847, prior: 0.72051, aleatoric unc.: 2.72092\n",
      "Epoch 22/500  total: 8.64839, -LL: 6.52611, prior: 0.71736, aleatoric unc.: 2.78174\n",
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      "Epoch 26/500  total: 7.61942, -LL: 6.63054, prior: 0.72667, aleatoric unc.: 3.03244\n",
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      "Epoch 28/500  total: 7.29471, -LL: 6.51807, prior: 0.72927, aleatoric unc.: 3.16509\n",
      "Epoch 29/500  total: 7.12159, -LL: 5.48303, prior: 0.73176, aleatoric unc.: 3.23374\n",
      "Epoch 30/500  total: 6.79870, -LL: 6.10557, prior: 0.73237, aleatoric unc.: 3.30124\n",
      "Epoch 31/500  total: 6.60342, -LL: 5.65072, prior: 0.73511, aleatoric unc.: 3.36955\n",
      "Epoch 32/500  total: 6.63333, -LL: 6.37231, prior: 0.73616, aleatoric unc.: 3.44177\n",
      "Epoch 33/500  total: 6.25342, -LL: 5.67089, prior: 0.73999, aleatoric unc.: 3.51138\n",
      "Epoch 34/500  total: 6.25324, -LL: 5.80523, prior: 0.74006, aleatoric unc.: 3.58479\n",
      "Epoch 35/500  total: 6.06724, -LL: 4.63822, prior: 0.73928, aleatoric unc.: 3.65814\n",
      "Epoch 36/500  total: 5.97354, -LL: 4.87066, prior: 0.73962, aleatoric unc.: 3.73306\n",
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      "Epoch 42/500  total: 5.24329, -LL: 5.24680, prior: 0.74535, aleatoric unc.: 4.19924\n",
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      "Epoch 58/500  total: 4.23197, -LL: 4.01298, prior: 0.77028, aleatoric unc.: 5.62054\n",
      "Epoch 59/500  total: 4.24475, -LL: 3.99289, prior: 0.77126, aleatoric unc.: 5.71866\n",
      "Epoch 60/500  total: 4.16691, -LL: 3.89405, prior: 0.77055, aleatoric unc.: 5.81574\n",
      "Epoch 61/500  total: 4.16522, -LL: 3.96328, prior: 0.76699, aleatoric unc.: 5.91432\n",
      "Epoch 62/500  total: 4.11586, -LL: 3.69259, prior: 0.76921, aleatoric unc.: 6.01400\n",
      "Epoch 63/500  total: 4.07180, -LL: 3.89622, prior: 0.77077, aleatoric unc.: 6.11181\n",
      "Epoch 64/500  total: 4.07462, -LL: 3.86786, prior: 0.77294, aleatoric unc.: 6.21290\n",
      "Epoch 65/500  total: 4.01141, -LL: 3.77488, prior: 0.77207, aleatoric unc.: 6.31128\n",
      "Epoch 66/500  total: 3.99999, -LL: 3.65617, prior: 0.77586, aleatoric unc.: 6.41138\n",
      "Epoch 67/500  total: 4.02086, -LL: 3.71232, prior: 0.77457, aleatoric unc.: 6.51647\n",
      "Epoch 68/500  total: 3.96727, -LL: 3.82445, prior: 0.77131, aleatoric unc.: 6.61852\n",
      "Epoch 69/500  total: 3.91331, -LL: 3.59059, prior: 0.77492, aleatoric unc.: 6.71576\n",
      "Epoch 70/500  total: 3.92368, -LL: 3.87038, prior: 0.77663, aleatoric unc.: 6.81692\n",
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      "Epoch 72/500  total: 3.90254, -LL: 3.84058, prior: 0.77568, aleatoric unc.: 7.02362\n",
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      "Epoch 93/500  total: 3.71866, -LL: 3.61358, prior: 0.78299, aleatoric unc.: 8.93002\n",
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      "Epoch 95/500  total: 3.72439, -LL: 3.60700, prior: 0.77858, aleatoric unc.: 9.05974\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 98/500  total: 3.72790, -LL: 3.58224, prior: 0.78028, aleatoric unc.: 9.25964\n",
      "Epoch 99/500  total: 3.71771, -LL: 3.66020, prior: 0.77745, aleatoric unc.: 9.31000\n",
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      "Epoch 195/500  total: 3.72410, -LL: 3.62442, prior: 0.81648, aleatoric unc.: 9.83962\n",
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     ]
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      "Epoch 292/500  total: 3.69757, -LL: 3.58311, prior: 0.82735, aleatoric unc.: 9.77046\n",
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      "Epoch 351/500  total: 3.70254, -LL: 3.67832, prior: 0.82772, aleatoric unc.: 9.73065\n",
      "Epoch 352/500  total: 3.70162, -LL: 3.63990, prior: 0.83119, aleatoric unc.: 9.72532\n",
      "Epoch 353/500  total: 3.70578, -LL: 3.60402, prior: 0.83188, aleatoric unc.: 9.73709\n",
      "Epoch 354/500  total: 3.70272, -LL: 3.62950, prior: 0.82930, aleatoric unc.: 9.73685\n",
      "Epoch 355/500  total: 3.70043, -LL: 3.62746, prior: 0.82995, aleatoric unc.: 9.73355\n",
      "Epoch 356/500  total: 3.69946, -LL: 3.61545, prior: 0.83072, aleatoric unc.: 9.72545\n",
      "Epoch 357/500  total: 3.70071, -LL: 3.67021, prior: 0.83015, aleatoric unc.: 9.72398\n",
      "Epoch 358/500  total: 3.70548, -LL: 3.63582, prior: 0.82771, aleatoric unc.: 9.73216\n",
      "Epoch 359/500  total: 3.69811, -LL: 3.60202, prior: 0.82758, aleatoric unc.: 9.72475\n",
      "Epoch 360/500  total: 3.69686, -LL: 3.64973, prior: 0.82581, aleatoric unc.: 9.71591\n",
      "Epoch 361/500  total: 3.70717, -LL: 3.65881, prior: 0.82941, aleatoric unc.: 9.72619\n",
      "Epoch 362/500  total: 3.70385, -LL: 3.65302, prior: 0.82832, aleatoric unc.: 9.73025\n",
      "Epoch 363/500  total: 3.70743, -LL: 3.64934, prior: 0.82749, aleatoric unc.: 9.74160\n",
      "Epoch 364/500  total: 3.70326, -LL: 3.58934, prior: 0.82753, aleatoric unc.: 9.74316\n",
      "Epoch 365/500  total: 3.70402, -LL: 3.62665, prior: 0.82742, aleatoric unc.: 9.74414\n",
      "Epoch 366/500  total: 3.70585, -LL: 3.68176, prior: 0.82632, aleatoric unc.: 9.74891\n",
      "Epoch 367/500  total: 3.70568, -LL: 3.62934, prior: 0.82647, aleatoric unc.: 9.75294\n",
      "Epoch 368/500  total: 3.69735, -LL: 3.63394, prior: 0.82584, aleatoric unc.: 9.73833\n",
      "Epoch 369/500  total: 3.70665, -LL: 3.60627, prior: 0.82508, aleatoric unc.: 9.74506\n",
      "Epoch 370/500  total: 3.70283, -LL: 3.64191, prior: 0.82496, aleatoric unc.: 9.74463\n",
      "Epoch 371/500  total: 3.69990, -LL: 3.63656, prior: 0.82942, aleatoric unc.: 9.73714\n",
      "Epoch 372/500  total: 3.70170, -LL: 3.65815, prior: 0.82560, aleatoric unc.: 9.73377\n",
      "Epoch 373/500  total: 3.70135, -LL: 3.66173, prior: 0.82487, aleatoric unc.: 9.73149\n",
      "Epoch 374/500  total: 3.70539, -LL: 3.60903, prior: 0.82451, aleatoric unc.: 9.74010\n",
      "Epoch 375/500  total: 3.69980, -LL: 3.63325, prior: 0.82713, aleatoric unc.: 9.73296\n",
      "Epoch 376/500  total: 3.69921, -LL: 3.60023, prior: 0.82868, aleatoric unc.: 9.72724\n",
      "Epoch 377/500  total: 3.69869, -LL: 3.66106, prior: 0.82731, aleatoric unc.: 9.72021\n",
      "Epoch 378/500  total: 3.69702, -LL: 3.62505, prior: 0.82719, aleatoric unc.: 9.71488\n",
      "Epoch 379/500  total: 3.69819, -LL: 3.60678, prior: 0.82717, aleatoric unc.: 9.71085\n",
      "Epoch 380/500  total: 3.69677, -LL: 3.62688, prior: 0.82746, aleatoric unc.: 9.70245\n",
      "Epoch 381/500  total: 3.70501, -LL: 3.60229, prior: 0.82751, aleatoric unc.: 9.71364\n",
      "Epoch 382/500  total: 3.69922, -LL: 3.57855, prior: 0.83100, aleatoric unc.: 9.71044\n",
      "Epoch 383/500  total: 3.69865, -LL: 3.63590, prior: 0.82836, aleatoric unc.: 9.70802\n",
      "Epoch 384/500  total: 3.70344, -LL: 3.59795, prior: 0.82755, aleatoric unc.: 9.71421\n",
      "Epoch 385/500  total: 3.70533, -LL: 3.64661, prior: 0.82573, aleatoric unc.: 9.72334\n",
      "Epoch 386/500  total: 3.70198, -LL: 3.61014, prior: 0.82611, aleatoric unc.: 9.72450\n",
      "Epoch 387/500  total: 3.70406, -LL: 3.64215, prior: 0.82555, aleatoric unc.: 9.73054\n",
      "Epoch 388/500  total: 3.70490, -LL: 3.63847, prior: 0.82456, aleatoric unc.: 9.73703\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 389/500  total: 3.69739, -LL: 3.60615, prior: 0.82374, aleatoric unc.: 9.72495\n",
      "Epoch 390/500  total: 3.70646, -LL: 3.59768, prior: 0.82653, aleatoric unc.: 9.73402\n",
      "Epoch 391/500  total: 3.69914, -LL: 3.65293, prior: 0.82449, aleatoric unc.: 9.72576\n",
      "Epoch 392/500  total: 3.70214, -LL: 3.62112, prior: 0.82444, aleatoric unc.: 9.72820\n",
      "Epoch 393/500  total: 3.70022, -LL: 3.57499, prior: 0.82906, aleatoric unc.: 9.72694\n",
      "Epoch 394/500  total: 3.69050, -LL: 3.60771, prior: 0.82554, aleatoric unc.: 9.70561\n",
      "Epoch 395/500  total: 3.69285, -LL: 3.68116, prior: 0.82755, aleatoric unc.: 9.69149\n",
      "Epoch 396/500  total: 3.70537, -LL: 3.61828, prior: 0.82465, aleatoric unc.: 9.70394\n",
      "Epoch 397/500  total: 3.69655, -LL: 3.61455, prior: 0.82317, aleatoric unc.: 9.70052\n",
      "Epoch 398/500  total: 3.70530, -LL: 3.62109, prior: 0.82612, aleatoric unc.: 9.71183\n",
      "Epoch 399/500  total: 3.70086, -LL: 3.61040, prior: 0.82481, aleatoric unc.: 9.71438\n",
      "Epoch 400/500  total: 3.70211, -LL: 3.64791, prior: 0.82474, aleatoric unc.: 9.71751\n",
      "Epoch 401/500  total: 3.70449, -LL: 3.66220, prior: 0.82469, aleatoric unc.: 9.72471\n",
      "Epoch 402/500  total: 3.69559, -LL: 3.68538, prior: 0.82521, aleatoric unc.: 9.71284\n",
      "Epoch 403/500  total: 3.70262, -LL: 3.61727, prior: 0.82641, aleatoric unc.: 9.71845\n",
      "Epoch 404/500  total: 3.70541, -LL: 3.65800, prior: 0.82866, aleatoric unc.: 9.72628\n",
      "Epoch 405/500  total: 3.70215, -LL: 3.66135, prior: 0.82954, aleatoric unc.: 9.72948\n",
      "Epoch 406/500  total: 3.69729, -LL: 3.64724, prior: 0.82800, aleatoric unc.: 9.72026\n",
      "Epoch 407/500  total: 3.69719, -LL: 3.63176, prior: 0.82775, aleatoric unc.: 9.71121\n",
      "Epoch 408/500  total: 3.70596, -LL: 3.66872, prior: 0.82940, aleatoric unc.: 9.72126\n",
      "Epoch 409/500  total: 3.70204, -LL: 3.63414, prior: 0.83020, aleatoric unc.: 9.72397\n",
      "Epoch 410/500  total: 3.70021, -LL: 3.64946, prior: 0.83012, aleatoric unc.: 9.72245\n",
      "Epoch 411/500  total: 3.69402, -LL: 3.61718, prior: 0.82774, aleatoric unc.: 9.70823\n",
      "Epoch 412/500  total: 3.70567, -LL: 3.61743, prior: 0.82851, aleatoric unc.: 9.71849\n",
      "Epoch 413/500  total: 3.70361, -LL: 3.64554, prior: 0.82617, aleatoric unc.: 9.72331\n",
      "Epoch 414/500  total: 3.69468, -LL: 3.60278, prior: 0.82620, aleatoric unc.: 9.71184\n",
      "Epoch 415/500  total: 3.70510, -LL: 3.64241, prior: 0.82747, aleatoric unc.: 9.72071\n",
      "Epoch 416/500  total: 3.70178, -LL: 3.59014, prior: 0.83144, aleatoric unc.: 9.72354\n",
      "Epoch 417/500  total: 3.69967, -LL: 3.63795, prior: 0.83206, aleatoric unc.: 9.71923\n",
      "Epoch 418/500  total: 3.69828, -LL: 3.60308, prior: 0.82796, aleatoric unc.: 9.71243\n",
      "Epoch 419/500  total: 3.70307, -LL: 3.66544, prior: 0.82524, aleatoric unc.: 9.71768\n",
      "Epoch 420/500  total: 3.70183, -LL: 3.61180, prior: 0.82254, aleatoric unc.: 9.72192\n",
      "Epoch 421/500  total: 3.69221, -LL: 3.63945, prior: 0.82239, aleatoric unc.: 9.70423\n",
      "Epoch 422/500  total: 3.69980, -LL: 3.61604, prior: 0.82302, aleatoric unc.: 9.70583\n",
      "Epoch 423/500  total: 3.69928, -LL: 3.63499, prior: 0.81947, aleatoric unc.: 9.70428\n",
      "Epoch 424/500  total: 3.70064, -LL: 3.64438, prior: 0.82250, aleatoric unc.: 9.70499\n",
      "Epoch 425/500  total: 3.69506, -LL: 3.61971, prior: 0.82166, aleatoric unc.: 9.69757\n",
      "Epoch 426/500  total: 3.70398, -LL: 3.62597, prior: 0.82278, aleatoric unc.: 9.70802\n",
      "Epoch 427/500  total: 3.70216, -LL: 3.65498, prior: 0.81911, aleatoric unc.: 9.71137\n",
      "Epoch 428/500  total: 3.70190, -LL: 3.64064, prior: 0.81833, aleatoric unc.: 9.71579\n",
      "Epoch 429/500  total: 3.70573, -LL: 3.66083, prior: 0.81893, aleatoric unc.: 9.72434\n",
      "Epoch 430/500  total: 3.69885, -LL: 3.65177, prior: 0.82123, aleatoric unc.: 9.72031\n",
      "Epoch 431/500  total: 3.70198, -LL: 3.67658, prior: 0.81868, aleatoric unc.: 9.72134\n",
      "Epoch 432/500  total: 3.70692, -LL: 3.63311, prior: 0.81943, aleatoric unc.: 9.73138\n",
      "Epoch 433/500  total: 3.70009, -LL: 3.59875, prior: 0.81951, aleatoric unc.: 9.72938\n",
      "Epoch 434/500  total: 3.69864, -LL: 3.63859, prior: 0.82302, aleatoric unc.: 9.72290\n",
      "Epoch 435/500  total: 3.69655, -LL: 3.66607, prior: 0.82137, aleatoric unc.: 9.71333\n",
      "Epoch 436/500  total: 3.69973, -LL: 3.65163, prior: 0.81886, aleatoric unc.: 9.71366\n",
      "Epoch 437/500  total: 3.69769, -LL: 3.68498, prior: 0.81805, aleatoric unc.: 9.70730\n",
      "Epoch 438/500  total: 3.69672, -LL: 3.64131, prior: 0.81733, aleatoric unc.: 9.70155\n",
      "Epoch 439/500  total: 3.69554, -LL: 3.62049, prior: 0.82319, aleatoric unc.: 9.69490\n",
      "Epoch 440/500  total: 3.69749, -LL: 3.62081, prior: 0.82234, aleatoric unc.: 9.69433\n",
      "Epoch 441/500  total: 3.70329, -LL: 3.59532, prior: 0.82169, aleatoric unc.: 9.70249\n",
      "Epoch 442/500  total: 3.69808, -LL: 3.62759, prior: 0.82254, aleatoric unc.: 9.70274\n",
      "Epoch 443/500  total: 3.70494, -LL: 3.65422, prior: 0.82270, aleatoric unc.: 9.71221\n",
      "Epoch 444/500  total: 3.69976, -LL: 3.65673, prior: 0.82426, aleatoric unc.: 9.71188\n",
      "Epoch 445/500  total: 3.70325, -LL: 3.64046, prior: 0.82422, aleatoric unc.: 9.71596\n",
      "Epoch 446/500  total: 3.70594, -LL: 3.65127, prior: 0.82255, aleatoric unc.: 9.72795\n",
      "Epoch 447/500  total: 3.70256, -LL: 3.65205, prior: 0.82299, aleatoric unc.: 9.72941\n",
      "Epoch 448/500  total: 3.70255, -LL: 3.66160, prior: 0.82127, aleatoric unc.: 9.73019\n",
      "Epoch 449/500  total: 3.70477, -LL: 3.65332, prior: 0.82186, aleatoric unc.: 9.73749\n",
      "Epoch 450/500  total: 3.69821, -LL: 3.62343, prior: 0.82277, aleatoric unc.: 9.72872\n",
      "Epoch 451/500  total: 3.69862, -LL: 3.61988, prior: 0.81971, aleatoric unc.: 9.72094\n",
      "Epoch 452/500  total: 3.69956, -LL: 3.64692, prior: 0.82058, aleatoric unc.: 9.71754\n",
      "Epoch 453/500  total: 3.68746, -LL: 3.61281, prior: 0.81960, aleatoric unc.: 9.69424\n",
      "Epoch 454/500  total: 3.69136, -LL: 3.61534, prior: 0.82130, aleatoric unc.: 9.67839\n",
      "Epoch 455/500  total: 3.70947, -LL: 3.63629, prior: 0.82276, aleatoric unc.: 9.70095\n",
      "Epoch 456/500  total: 3.70455, -LL: 3.62145, prior: 0.82456, aleatoric unc.: 9.71287\n",
      "Epoch 457/500  total: 3.69434, -LL: 3.64094, prior: 0.82408, aleatoric unc.: 9.70524\n",
      "Epoch 458/500  total: 3.69588, -LL: 3.62607, prior: 0.82356, aleatoric unc.: 9.69614\n",
      "Epoch 459/500  total: 3.69965, -LL: 3.67129, prior: 0.82353, aleatoric unc.: 9.69692\n",
      "Epoch 460/500  total: 3.69278, -LL: 3.64340, prior: 0.82238, aleatoric unc.: 9.68522\n",
      "Epoch 461/500  total: 3.69769, -LL: 3.66663, prior: 0.82365, aleatoric unc.: 9.68477\n",
      "Epoch 462/500  total: 3.70174, -LL: 3.64461, prior: 0.82374, aleatoric unc.: 9.69469\n",
      "Epoch 463/500  total: 3.69422, -LL: 3.62371, prior: 0.82634, aleatoric unc.: 9.68775\n",
      "Epoch 464/500  total: 3.70086, -LL: 3.65318, prior: 0.82430, aleatoric unc.: 9.69298\n",
      "Epoch 465/500  total: 3.69787, -LL: 3.66150, prior: 0.81959, aleatoric unc.: 9.69327\n",
      "Epoch 466/500  total: 3.69348, -LL: 3.64051, prior: 0.81754, aleatoric unc.: 9.68517\n",
      "Epoch 467/500  total: 3.70298, -LL: 3.65390, prior: 0.81789, aleatoric unc.: 9.69441\n",
      "Epoch 468/500  total: 3.69817, -LL: 3.65901, prior: 0.81541, aleatoric unc.: 9.69768\n",
      "Epoch 469/500  total: 3.69301, -LL: 3.63411, prior: 0.81612, aleatoric unc.: 9.68669\n",
      "Epoch 470/500  total: 3.70037, -LL: 3.61972, prior: 0.81542, aleatoric unc.: 9.69086\n",
      "Epoch 471/500  total: 3.70139, -LL: 3.60899, prior: 0.81560, aleatoric unc.: 9.69815\n",
      "Epoch 472/500  total: 3.70118, -LL: 3.68662, prior: 0.81407, aleatoric unc.: 9.70126\n",
      "Epoch 473/500  total: 3.70042, -LL: 3.64964, prior: 0.81481, aleatoric unc.: 9.70599\n",
      "Epoch 474/500  total: 3.70516, -LL: 3.62561, prior: 0.81684, aleatoric unc.: 9.71484\n",
      "Epoch 475/500  total: 3.69569, -LL: 3.62760, prior: 0.81538, aleatoric unc.: 9.70852\n",
      "Epoch 476/500  total: 3.69344, -LL: 3.63575, prior: 0.81317, aleatoric unc.: 9.69601\n",
      "Epoch 477/500  total: 3.69725, -LL: 3.66014, prior: 0.81203, aleatoric unc.: 9.69300\n",
      "Epoch 478/500  total: 3.70594, -LL: 3.65619, prior: 0.81437, aleatoric unc.: 9.70621\n",
      "Epoch 479/500  total: 3.69992, -LL: 3.61516, prior: 0.81284, aleatoric unc.: 9.70868\n",
      "Epoch 480/500  total: 3.69582, -LL: 3.64135, prior: 0.81684, aleatoric unc.: 9.70021\n",
      "Epoch 481/500  total: 3.69739, -LL: 3.60619, prior: 0.81517, aleatoric unc.: 9.70025\n",
      "Epoch 482/500  total: 3.70488, -LL: 3.63401, prior: 0.81520, aleatoric unc.: 9.70766\n",
      "Epoch 483/500  total: 3.69736, -LL: 3.61727, prior: 0.81478, aleatoric unc.: 9.70594\n",
      "Epoch 484/500  total: 3.70235, -LL: 3.63803, prior: 0.81578, aleatoric unc.: 9.71074\n",
      "Epoch 485/500  total: 3.70031, -LL: 3.64106, prior: 0.81726, aleatoric unc.: 9.71344\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 486/500  total: 3.70281, -LL: 3.65334, prior: 0.81765, aleatoric unc.: 9.71675\n",
      "Epoch 487/500  total: 3.69665, -LL: 3.62427, prior: 0.81798, aleatoric unc.: 9.71068\n",
      "Epoch 488/500  total: 3.69354, -LL: 3.60938, prior: 0.81778, aleatoric unc.: 9.69865\n",
      "Epoch 489/500  total: 3.69664, -LL: 3.66371, prior: 0.81562, aleatoric unc.: 9.69401\n",
      "Epoch 490/500  total: 3.70017, -LL: 3.61261, prior: 0.81859, aleatoric unc.: 9.69709\n",
      "Epoch 491/500  total: 3.70181, -LL: 3.64116, prior: 0.81858, aleatoric unc.: 9.70037\n",
      "Epoch 492/500  total: 3.69507, -LL: 3.62122, prior: 0.81482, aleatoric unc.: 9.69759\n",
      "Epoch 493/500  total: 3.69890, -LL: 3.65301, prior: 0.81908, aleatoric unc.: 9.69581\n",
      "Epoch 494/500  total: 3.70058, -LL: 3.65166, prior: 0.81909, aleatoric unc.: 9.69850\n",
      "Epoch 495/500  total: 3.69788, -LL: 3.62267, prior: 0.81817, aleatoric unc.: 9.70015\n",
      "Epoch 496/500  total: 3.69267, -LL: 3.64171, prior: 0.81855, aleatoric unc.: 9.68762\n",
      "Epoch 497/500  total: 3.70465, -LL: 3.66362, prior: 0.81682, aleatoric unc.: 9.70045\n",
      "Epoch 498/500  total: 3.70106, -LL: 3.66015, prior: 0.81733, aleatoric unc.: 9.70227\n",
      "Epoch 499/500  total: 3.69741, -LL: 3.64281, prior: 0.81737, aleatoric unc.: 9.70153\n"
     ]
    }
   ],
   "source": [
    "epochs = 500\n",
    "# for each epoch\n",
    "for epoch in range(epochs):\n",
    "    losses = list()\n",
    "    # for each mini-batch given by the loader:\n",
    "    for batch in loader:\n",
    "        # get the input in the mini-batch\n",
    "        # this has size (B, C)\n",
    "        # where B is the mini-batch size\n",
    "        # C is the number of features (1 in this case)\n",
    "        features = batch[\"data\"]\n",
    "        # get the targets in the mini-batch (there shall be B of them)\n",
    "        target = batch[\"target\"]\n",
    "        # get the output of the neural network:\n",
    "        prediction = b_network(features)\n",
    "        \n",
    "        # calculate the loss function being minimized\n",
    "        # in this case, it is the mean-squared error between the prediction and the target values added\n",
    "        # to the Kullback-Leibler divergence between the current weight Gaussian and\n",
    "        # the prior Gaussian, set to the unit Normal distribution\n",
    "        nll = b_network.nll(prediction, target)\n",
    "        prior = kl_loss(b_network)\n",
    "        loss = nll + weight_kl * prior\n",
    "\n",
    "        # clean the optimizer temporary gradient storage\n",
    "        optimizer.zero_grad()\n",
    "        # calculate the gradient of the loss function as a function of the gradients\n",
    "        loss.backward()\n",
    "        # ask the Adam optimizer to change the parameters in the direction of - gradient\n",
    "        # Adam scales the gradient by a constant which is adaptively tuned\n",
    "        # take a look at the Adam paper for more details: https://arxiv.org/abs/1412.6980\n",
    "        optimizer.step()\n",
    "        \n",
    "        ale = b_network.aleatoric_uncertainty().detach().numpy()\n",
    "\n",
    "        losses.append(loss.detach().cpu().item())\n",
    "    avg_loss = np.mean(np.array(losses))\n",
    "    print(f\"Epoch {epoch}/{epochs}  total: {avg_loss:.5f}, -LL: {nll.item():.5f}, prior: {prior.item():.5f}, aleatoric unc.: {ale:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15f3f633",
   "metadata": {},
   "source": [
    "To evaluate the effect of the uncertainty, we perform the prediction many times for the same data and take the average and root-mean-squared-error of the predictions, since each prediction performed with the Bayesian Neural Network leads to a different results, using a different weight, selected from the final Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a3d244e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "b_predicted = list()\n",
    "for k in range(10):\n",
    "    p = b_network(torch.from_numpy(test_data[:,0:1])).detach().numpy()\n",
    "    b_predicted.append(p[:,0])\n",
    "b_predicted = np.stack(b_predicted, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85fed034",
   "metadata": {},
   "source": [
    "We can now take the average result for each sample, and their root-mean-squared-error as an estimate of the mean and epistemic uncertainty for the results.\n",
    "\n",
    "The aleatoric uncertainty is fitted as an independent parameter. Since we assume the aleatoric uncertainty is independent, we can calculate the total uncertainty as the sum of squares of the epistemic and aleatoric uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4a56960d",
   "metadata": {},
   "outputs": [],
   "source": [
    "b_mean = np.mean(b_predicted, axis=1)\n",
    "b_sigma = np.std(b_predicted, axis=1)\n",
    "aleatoric_uncertainty = b_network.aleatoric_uncertainty().detach().numpy()\n",
    "\n",
    "total_uncertainty = (b_sigma**2 + aleatoric_uncertainty**2)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ef3d430",
   "metadata": {},
   "source": [
    "Let's check how big are those uncertainties found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4d01c41f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average epistemic uncertainty:  0.83653456\n"
     ]
    }
   ],
   "source": [
    "print(\"Average epistemic uncertainty: \", np.mean(b_sigma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "67d456a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aleatoric uncertainty:  9.7015295\n"
     ]
    }
   ],
   "source": [
    "print(\"Aleatoric uncertainty: \", aleatoric_uncertainty)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "364bdcd7",
   "metadata": {},
   "source": [
    "Note that the aleatoric uncertainty is very close to the standard deviation of the $\\epsilon$ component of the model we created in the beginning! Clearly the model could fit the uncertainty coming from that component of the noise.\n",
    "\n",
    "It is not easy to estimate the effect of the epistemic uncertainty, as it is different for every data point (as it is scaled by $x^2$), but we can plot it to take a look at its effect.\n",
    "\n",
    "Note that the uncertainties are the standard deviations of Gaussian models and therefore they correspond to a $1\\sigma$ quantile band, which is a 67% confidence band. The quantile corresponding to $2\\sigma$ corresponds to a 95% confidence band in a Gaussian model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8b9142e8",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\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(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\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",
       "                img.type = 'image/png';\n",
       "            }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, 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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "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.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\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",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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Hh6ukJAQ9ejRQ6+88kqNXYunC1heQZE27j+hlVsPadnGg1q59ZA27j9Bn1/4FG/oG19WAD59+rTjSWZoaKhuvPFGjRo1ynFPNMZo2rRpjvXj4+NljFG7du2UkJCgxMREXX/99fLz81NAQIBTixhJiouLkzFGnTt31tixYzV+/PhK3SPPnz+voUOHOs4rISFB8fHxuuKKK3TrrbeqVatWLgH4gw8+cATdHj16KDEx0TEgoX1E/wsD8JEjRxQcHKyAgAANHDhQd999t8aPH689e/ZIkpYsWeL4u3HjjTcqMTFRnTp1kr+/v6ZPn04ABgAf5On6OQjAXo0CBljD5d43vqwALElFRUV6+eWXFR0drQYNGigoKEgtWrRQnz599Ic//EGHDv3UlPuDDz7Q5MmT9Ytf/EINGzZUcHCw2rVrp9GjR+uTTz5x2ffXX3+tsWPHKjIy0hFOKxsYCwsL9cgjj+hnP/uZgoKC1Lp1az344IMqKChQ69at3b4GacOGDerXr58aNGig0NBQ3XDDDVq5cmW5/ZHffvtt9e7dW/Xq1XOE3ZycHMfytWvX6pe//KVCQ0MVHh6umJgYvf/++8rJySEAA4APon7ueQRgL0YBA6yBvvEAAECifm4FBGAvRgEDrIO+8QAAgPq55xGAvRgFDLAe+sYDAOC7qJ97HgHYi1HAAAAAAOugfu55BGAvRgEDAAAArIP6uecRgL0YBQwAAACwDurnnkcA9mIUMAAAAMA6qJ97HgHYi1HAAAAAAOugfu55BGAvRgEDAAAArIP6uecRgL0YBQwAAACwDurnnkcA9mIUMAAAAMA6qJ97HgHYi1HAAAAAAOugfu55BGAvRgEDAAAArIP6uecRgL0YBQywqKIiKSfnp6moyMMnBAAAagP1c88jAHsxChhgUfn5Unr6T1N+vodPCAAA1Abq555HAPZiFDDAoi6TALxhwwYNGTJEDRs2lM1mU/v27TV79mydPn3a7frp6ekyxpQ5paamumyTn5+ve+65Rw0bNlRISIji4uL0xRdfuN3/yZMnFRERodtvv73K15KTkyNjjJKSkqq8raclJSXJGKOcnBxPn0qNsv++ZGZmevpUAKDWUD/3PAKwF6OAARaUmytlZ0sJCVJcXMm/2dkl8y1kyZIlCggIkDFGPXr00NChQ9WyZUsZY9S1a1edOnXKZRt7oOndu7eSkpJcpuXLl7tsM2HCBBlj1L17dw0YMEB+fn7q1KmTiouLXda99957Va9ePR0+fLjK1+NLATgzM1PGGKWnp9fYOVyKsEoABuCLqJ97HgHYi1HAAAspLJSysqSMDCk5WerYUYqKKvk3OblkflaWJfoDHzp0SMHBwTLG6JVXXnHMLygo0IgRI2SMUUpKist2VQ00R48eVZ06dXTLLbfo/PnzkqTf//73MsbojTfecFp3586dqlOnjh5//PGLuiYCcPUQgAGgZlA/9zwCsBejgAEWUVgoZWZKkydLMTHSoEFS9+5Sz54l/956a8n8KVNK1iss9OjpPvzwwzLGKDY21mXZN998o5CQEAUGBur48eNOy6oaaN555x0ZY7Rs2TLHvKNHj8oYo9mzZzutGx0draioKBVe5GdDAK4eAjAA1Azq555HAPZiFDDAIrKySsJv//7S1KnS7NlSdPRP0+zZJfP79y8JwVlZHj3dhIQEGWP0yCOPuF1+7bXXyhijRYsWOc2vaqD529/+JmOM/vnPfzrm5efnyxijSZMmOeYtXbpUxhi98847Vb+YH5UOwEePHlVSUpKaNGmi4OBgdevWTQsXLnS73YcffqjJkyerS5cuCg8PV3BwsKKiopSamqrvv/++3OOcOHFCKSkpioyMVFBQkDp37qy//vWvZZ7jihUr1LNnTwUHB6tJkyYaO3asjhw5UqUAHB0dXWYf7At/LmvXrlVMTIzCw8Nls9nUoUMHt9fVunXrMvdpP6f8/Hy9/PLLGjJkiNq2bavg4GCFhYXpxhtvdPqCo7Sq/r5U9CVGWZ+TMUatW7dWcXGxHn/8cbVv315BQUFq0aKFHnjgARUUFLjdX15enh599FF169ZN9erV0xVXXKGOHTtq2rRpZfZTB4CKUD/3PAKwF6OAARaQm1vSvDkmpiTkpqe7D8Dp6SXLY2JK1vdgn+DY2FgZY/TnP//Z7fKbb75ZxhjNmDHDab490IwdO1bTpk3TxIkT9fDDD2vLli1u97NhwwYZYzR//nzHvO3bt8sYo3nz5kmScnNz1axZMw0bNqxa12QPT3FxcWrVqpUiIiI0cuRIxcbGqk6dOjLGKCMjw2W7Xr16yWazqUePHrrttts0aNAgNW3aVMYYde7cWbkX/Jzsx4mPj1eHDh0UERGhuLg43XTTTY4+1QsWLHA5zvz582WMUUBAgPr166eRI0eqadOmatmypQYPHlzpAPzYY4+pd+/ejr7apftgr1u3zrHeo48+KmOM6tSpo/79+2vUqFFq0aKFjDHq0KGDjh075lh3xowZ6tq1q9v+3bt375Yk7d69W8YYRUREKDo6WqNGjVJ0dLQCAwPLfBpd2wF41KhRuuKKK3TTTTdp8ODBCgsLkzFGY8aMcdnX0aNH1alTJxljdOWVV2rIkCEaNmyYunbtKj8/P55aA7ho1M89jwDsxShggAV88IGUklIy4JV91OeyAnB6esl6KSnShx967JRHjx5d5qjNkhQVFSVjjEsoLW8U6GHDhrmExfz8fDVt2lRt27bVzp07dezYMcdAWNu3b5ckzZo1SyEhITp48GC1rskenuxNu/Py8hzLNm3apHr16snf31/btm1z2m7t2rX67rvvnOYVFBQ4Bu/67W9/W+Zxhg0b5nSc1atXyxijVq1aOW1z4MAB2Ww22Ww2p/B2+vRpx5cRNdkEetOmTfL391doaKg2btzodF32Pt4jRoxw2qaisHr8+HG9/fbbOnfunNP8/fv3q02bNvL399eBAweqtM8LVScAG2PUsWNHp3PYv3+/GjRoIGOMPv/8c6dt+vfvL2OMEhMTnX6GkvTZZ585gj8AVBX1c88jAHsxChhgAYsWScOHlwx0VZkAnJxcsv4FzYtr01/+8hdHUDt79qzTMvtTW2OMbr75Zqdlixcv1hNPPKFdu3YpLy9Phw4d0tKlS9W8eXMZY5SQkOByrCVLlsjPz88pLNubP+/Zs0eBgYH6/e9/77TNmTNnHINmVZY9PPn5+WnPnj0uy1NTU2WM0YQJEyq1vzNnzqhOnTrq3r272+PUr19fJ06ccNmuS5cuMsY4BbE5c+bIGKPk5GSX9ffs2eP4fGoqAN95550yxmjOnDkuy77++mvVrVtX/v7+TqNtV6e/7oIFC2SM0XPPPec0v7YD8L/+9S+XbaZOnepyDhs3bpQxRpGRkS7hFwCqi/q55xGAvRgFDLCABQtKXnU0eXLlAvDkySXru2kmW1vy8vLUqlUrGWM0cOBA/ec//9GpU6f0j3/8Qy1atHA0GR44cGCl9nf06FE1bNhQxhitX7/eZflHH32k6dOna9KkSXrjjTcc4TY2Nlbt2rVz9NFctmyZoz9qWFiYZs+e7fLEsSz28HRhYLX79NNPZYxxe888fPiwXnjhBU2bNk133XWXo/lvSEiIQkND3R6nX79+bo8zbNgwGWP00UcfOebddNNNMsYoOzvb7Tbdu3ev0QDctm1bGWPcfhEgSfHx8TLGOL22qrJhdd26dXr44YeVkpKicePGKSkpydFkfurUqU7r1mYADgwMdPtqLXvT80cffdQx75FHHnHbxB8AagL1c88jAHsxChhgAZfhE2BJ2rFjhyMEl55atWqlBx54wNE8tLJmzpwpY4zmzp1bqfVXrFghY4zWrFkjSdqyZYv8/Pw0cOBArV69WtOnT5cxRs8++2yl9mcPT0OHDnW7/OTJkzLGKDw83Gn+k08+qaCgoDKbdhvj/GfUfpw777zT7XHchTR7k/K9e/e63cY+KFlNBWCbzSY/Pz/l5+e7XT5t2jQZY/TMM8845lUUVk+ePKl+/fqV+zmNGzfOaZvaDMAXNju3c/dZpaSkyJiy+8ADQHVQP/c8ArAXo4ABFnAZ9gG2O3PmjBYuXKipU6dq0qRJevHFF3Xq1ClHAL6waXJ57M2q3TXzdXfc1q1bKy4uzjEvMTFRoaGhOnXqlGNedHS0WrRoUanjX0wAtjf3DgsL06uvvqovvvjCacRg+2BY7o5TlZDWoUMHGWP02Wefud3GUwG49JcLFYXViRMnyhijPn366P3339fx48cdT1zffvttt59JTQfgsWPHlhmAW7du7Xab8gLwCy+8UKnzAoCqoH7ueQRgL0YBAyzgMhwFuiL2Jrn//ve/K73NvHnzZIzR9OnTK1w3LS1NwcHB2rdvn2Net27d1LNnT6f1Zs2aJWOMfvjhhwr3WVETaPvo06XvmfagX3qUarszZ844+ua6O05VAnDfvn0t1QTaHrir0gS6SZMmCggI0MmTJ12WvfDCCzUSgNevXy9jXAdfs7N/jtUNwDSBBnApUT/3PAKwF6OAARaRlVXyft/L5D3A5Xn//fdlTMkrgCrr/Pnz6tWrl4wxWrJkSbnrfv7557LZbC5Npbt16+ZyzHvuuUfGGKenwmWxB1N/f3+3TY0ffPBBlyfUycnJMsZo9erVLusvXLiw3CbQVQnAaWlpZQ7AtXfvXvn7+1cpANvfmzx79my3y8sbBOubb75RSEiIyyBY9lDo7hVOkhQYGOjSfNzO3se5ugF4//79MsaoS5cuLsuOHz+u+vXr10gALj0I1unTpyt1bgBQWdTPPY8A7MUoYIBFFBZKmZkl4TYmRrr1Vql7d6lnz5J/b721ZP6UKSXrFRV5+oy1bds2FV1wHlu3blWzZs3k5+en9957z2nZt99+q4ULFzo1EZZK3uNrbx5bmUAxaNAgtWnTRmfOnHGaf8cdd8jPz0+ffPKJJOnUqVNq2bJlmX07L1T69UQDBgxwOo8tW7YoNDRU/v7+Tu8s/uMf/yhjSt4dXFhY6Ji/a9cuRUZG1lgA3rdvn4KCghQcHKwPSzV9P3PmjAYOHOg4TmUDsP0chg8f7nb5xo0b5e/vr/r162vz5s2O+WfPntWoUaPcbmsPijNnznS7z86dO8sYo9dff91p/lNPPeU4/+oGYEmOfumlv5TIy8vT0KFDy/ycqhqApZ9C+x133OHyO/u///3P6TVIhw8fVlRUlKKioip9HQB8F/VzzyMAezEKGGAhhYUlT3YzMkoGuurYUYqKKvk3OblkflaWJcKvVNK/tnHjxoqNjVViYqKuv/56+fv7q06dOnrppZdc1j9w4ICMKXn9T69evTRixAjFxsY6Rn8ODw+vsMn0mjVrZIzRm2++6bJs+/bt8vf3V1hYmIYOHao2bdrIGKMXX3yxUtdjD4WDBw9Wq1atFBkZqZEjR2rAgAEKDAyUMUZpaWlO2xw/ftwRdNu2bauRI0cqJiZGgYGBGjFihGNEanfHqepATU8//bSMMQoICFD//v01atQoNWvWTC1atNDgwYOrFIDz8/PVpEkTGWMUHR2tu+66S+PHj3cagdv+RLdOnTqKiYnR7bffrpYtW8oYo/bt2+vYsWNO+zxy5IiCg4MVEBCggQMH6u6779b48eMdzaiXLFniCKA33nijEhMT1alTJ/n7+zsGLKuJAPzKK684PqebbrpJcXFxioiIUPv27TVkyJAaC8CHDx929M1u2LCh4uPjNXz4cP3iF7+Qn5+f0znbf/cv/F0AAHeon3sed2svRgEDLCg3V8rOLnnVUVxcyb/Z2Zbr87tgwQJHCA4MDFSzZs00evRobdu2ze36p06dUmpqqqKjo9W8eXPZbDaFhISoc+fOmjFjhlNzWncKCgrUrl07DRgwoMx1srKydM011ygwMFAtW7bUvHnzKn09pYPpkSNHdMcdd6hx48ay2Wzq2rVrmSHs0KFDGj16tJo3b67g4GB17NhRjz32mIqLi2s0AEvS8uXL1aNHD9lsNjVq1EijR4/W4YJqxU4AACAASURBVMOHy92mLJs3b1ZsbKzCwsIcfZUvvMY1a9aof//+CgsLU1BQkK666io98MAD+u6779zu8+2331bv3r1Vr149t09b165dq1/+8pcKDQ1VeHi4YmJi9P7775f5mVzsu4UzMzN19dVXKygoSBEREfr1r3+t48ePlzsKdFUDsCT98MMPysjI0NVXX626desqNDRUnTp10vTp03Xw4EHHegRgAFVB/dzzuFt7MQoYYFH5+T+N+pyeXvJ/AADg9aifex4B2ItRwACLIgADAOCTqJ97HgHYi1HAAIsiAAMA4JOon3seAdiLWaKAFRVJOTk/TRYZ4AfwKMoFAAA+yRL1cx9HAPZilihgPOkCAAAAJFmkfu7jCMBezBIFjAAMAAAASLJI/dzHEYC9mCUKGAEYAAAAkGSR+rmPIwB7MUsUMAIwAAAAIMki9XMfRwD2YpYoYARgAAAAQJJF6uc+jgDsxSxRwAjAAAAAgCSL1M99HAHYi1migBGAAQAAAEkWqZ/7OAKwF7NEASMAAwAAAJIsUj/3cQRgL2aJAkYABlwUnStSzoEcx1R0rsjTpwQAAGqBJernPo4A7MUsUcAIwICL/KJ8peekO6b8IsoFAAC+wBL1cx9HAPZilihgBGDAxeUSgDds2KAhQ4aoYcOGstlsat++vWbPnq3Tp0+7XT89PV3GmDKn1NRUl23y8/N1zz33qGHDhgoJCVFcXJy++OILt/s/efKkIiIidPvtt1f5WnJycmSMUVJSUpW39bSkpCQZY5STk+PpU3FyOX+mVZGZmSljjNLT0z19KgC8gCXq5z6OAOzFLFHACMCAi8shAC9ZskQBAQEyxqhHjx4aOnSoWrZsKWOMunbtqlOnTrlsYw/AvXv3VlJSksu0fPlyl20mTJggY4y6d++uAQMGyM/PT506dVJxcbHLuvfee6/q1aunw4cPV/l6Luew5s0B2KrXVhoBGEBNskT93McRgL2YJQoYARhwkns2V9n7spXweoLiXotTwusJyt6XrdyzuZ4+NYdDhw4pODhYxhi98sorjvkFBQUaMWKEjDFKSUlx2c4egDMzMyt1nKNHj6pOnTq65ZZbdP78eUnS73//exlj9MYbbzitu3PnTtWpU0ePP/74RV0TAbjmnT59Wrt379bRo0cveh9WvbbSTp48qd27d+vbb7/19KkA8AKWqJ/7OAKwF7NEASMAA5KkwuJCZe3JUkZOhpKzktXx+Y6Kmh+ljs93VHJWsjJyMpS1J8sSA2I9/PDDMsYoNjbWZdk333yjkJAQBQYG6vjx407LqhqA33nnHRljtGzZMse8o0ePyhij2bNnO60bHR2tqKgoFRYWVv2CRAC2Km++NgBwxxL1cx9HAPZilihgBGBAhcWFytyWqclrJytmYYwGLR2k7i92V8+Xeqr7i91169JbFbMwRlPWTlHmtkwVFl9cyKspCQkJMsbokUcecbv82muvlTFGixYtcppf1QD8t7/9TcYY/fOf/3TMy8/PlzFGkyZNcsxbunSpjDF65513qn4xPyodgI8ePaqkpCQ1adJEwcHB6tatmxYuXOh2uw8//FCTJ09Wly5dFB4eruDgYEVFRSk1NVXff/99ucc5ceKEUlJSFBkZqaCgIHXu3Fl//etfyzzHFStWqGfPngoODlaTJk00duxYHTly5KJD4rp165SQkKDGjRsrKChIrVu31tSpU/XNN9+4rFv6GH//+9/Vu3dvXXHFFQoPD9fQoUO1e/fucq+1tPPnz2vZsmW68cYbFRERIZvNphYtWqh///56/vnnHeuV11/8wIEDTvvMysrSzTffrCuvvNLRHz0tLU25ua4tJ6Kjox37eP3113Xttdeqbt26atasmWbNmqWzZ89Kkj7//HPdfvvtaty4serWraubbrpJ27dvd9lfeU2gz58/ryVLlqhfv36Oc2vbtq0SExP173//292PpdzzvdCBAwdkjFF0dLTT/NJlbceOHYqLi1N4eLhCQkLUp08frV+/vszjffTRRxoxYoSaNm2qoKAgNWvWTDfffLMWL15cqfMFUD2WqJ/7OAKwF7NEASMAA8rak6XJayer/8L+mvr3qZr97mxFZ0Y7ptnvztbUv09V/4X9NWXtFGXtyfLo+cbGxsoYoz//+c9ul998880yxmjGjBlO8+2V8rFjx2ratGmaOHGiHn74YW3ZssXtfjZs2CBjjObPn++Yt337dhljNG/ePElSbm6umjVrpmHDhlXrmuxhLS4uTq1atVJERIRGjhyp2NhY1alTR8YYZWRkuGzXq1cv2Ww29ejRQ7fddpsGDRqkpk2byhijzp07uwQw+3Hi4+PVoUMHRUREKC4uTjfddJOjT/WCBQtcjjN//nwZYxQQEKB+/fpp5MiRatq0qVq2bKnBgwdXOQA/++yz8vPzU0BAgK6//noNHz5cP//5z2WMUdu2bV2aLdsD8D333CM/Pz/17NlTt99+uzp16iRjjMLCwvTpp5+6vdYLA3BqaqqMMQoNDdUtt9yixMRE9e3bV40aNVLr1q2djtmuXTsZYzRgwACn/uKlmxvff//9MsYoODhYffr00W233abWrVs7+qfn5eU5Hd8eKO+77z7VqVNH119/vRISEtSoUSMZY3TnnXfqs88+U6NGjfSzn/1Mt912m7p06SJjjK688kodO3bMaX9lBeDi4mINHz5cxhjZbDb1799fo0aN0vXXX6/g4OBKtzaoTgCePHmyQkJC1KFDBw0bNkxdu3Z1fFY7d+502d/TTz8tPz8/GWMcP+N+/fq5/GwAXDqWqJ/7OAKwF7NEASMAw8flns1VRk6GYhbGaOrfpyo9J91tAE7PSdfUv09VzMIYZeRkeLRP8OjRo8sctVmSoqKiZIxxCaXljQI9bNgwl7CYn5+vpk2bqm3bttq5c6eOHTvmGAjL/iRu1qxZCgkJ0cGDB6t1TfawZm/aXTo0bdq0SfXq1ZO/v7+2bdvmtN3atWv13XffOc0rKChwDN7129/+tszjDBs2zOk4q1evljFGrVq1ctrmwIEDstlsstlsTiH39OnTji8jqhKAN2zYIH9/f7Vu3drpieb58+f1u9/9TsYYDR8+3GkbewA2xuill15y2sYeaLt37+72WksHvfz8fNlsNrVp00YnTpxwWr+oqEgffPCB2+OWdW32VgLdunVzCoiFhYWOn8HMmTOdtrEHytDQUH344YeO+V999ZUiIiLk5+enjh076v7779e5c+cc13nnnXfKGKO5c+c67a+sAGzvKtClSxeXkctPnDhRK0+AjTEu/eLvu+8+xxdRpX3wwQfy8/NT/fr1XT7vs2fPOrXEAHDpWKJ+7uMIwF7MEgWMAAwf98EXHyjlrRTFvRbnGPW5rACcnpOuuNfilPJWij784sOKd36J/OUvf3EENXtzUTv7U1tjjG6++WanZYsXL9YTTzyhXbt2KS8vT4cOHdLSpUvVvHlzGWOUkJDgcqwlS5Y4nkjZJ3vz5z179igwMFC///3vnbY5c+aMY9CsyrKHNT8/P+3Zs8dluT3kTZgwoVL7O3PmjOrUqVNmKKxfv75LAJTkeNJYOuzMmTNHxhglJye7rL9nzx7H51PZABwfHy9jjN5++22XZefPn1e3bt3k7+/v9JTVHkRvuOEGl20KCwsdI4B/9NFHLtdaOgB//fXXjifglVFRALY/0XT3M8vPz1dkZKTCw8MdQVb6KVBeGGSln54mt2vXTkVFzv3t7a0PLgyb7gLw2bNnFR4eLj8/P23evLlS11qW6gTgX/3qVy7bHD9+XMYYlye6t9xyi4wxeuKJJ6p1vgCqxxL1cx9HAPZilihgBGD4uEWfLtLwvw1XclZypQJwclayhv9tuBZ9uqjinV8ieXl5atWqlYwxGjhwoP7zn//o1KlT+sc//qEWLVo4mgwPHDiwUvs7evSoGjZsKGOM276JH330kaZPn65JkybpjTfecITb2NhYtWvXTgUFBZKkZcuWOZq+hoWFafbs2U7Bpzz2sHZhYLX79NNPZYxxe888fPiwXnjhBU2bNk133XWXo5luSEiIQkND3R6nX79+bo8zbNgwlyB50003yRij7Oxst9t079690gH43LlzqlevnkJDQ92+SkqSpkyZ4tL32h5En3vuObfb2J8q/uEPf3DMK6sJtP135A9/+IOOHDlS7vmWF4DtYbpjx45lbm9vHl46INsD5bp161zWf/7552WM0fjx412W5eXlyRijDh06OM13F4DXr1/vaIJdXdUJwL/73e/c7rNhw4YKCgpy/L+4uFh169aVMcbtK8wA1B5L1M99HAHYi1migBGA4eMWbF2ghGUJmrx2cqUC8OS1k5WwLEELtrr2E61NO3bscITg0lOrVq30wAMPyBijxMTESu9v5syZZT6Vc2fFihUyxmjNmjWSpC1btsjPz08DBw7U6tWrNX36dBlj9Oyzz1Zqf/awNnToULfLT548KWOMwsPDneY/+eSTCgoKKrNptzHOf0btx7nzzjvdHsdd4LM3Kd+7d6/bbeyDklUmAH/zzTflnmvpacmSJS7n9X//939u9/vMM8/ImJJ+tRde64UB+N1331Xjxo0dx2nbtq2SkpLcPpEuLwBv2rSp0tdSurmxPVDu37/fZZ/2MFvW76G7J6fuAvDrr78uY4xGjhzpdj9VUZ0AXPo1ZaXZvyiyO3bsmIwxatKkSbXPF0D1WKJ+7uMIwBfYsmWLHnvsMQ0dOlTNmjWTMSWDW7hz7tw5ffjhh5o1a5auu+46x0ibP/vZzzRx4kS3f3wl5z5i7qZevXrVyLVYooARgOHjLscnwHZnzpzRwoULNXXqVE2aNEkvvviiTp065QjAFzZNLo+9WbW7Zr7ujtu6dWvFxcU55iUmJio0NNTp6VV0dLRatGhRqeNfTAC2N/cOCwvTq6++qi+++MLxNFqSYzAsd8cpawAkd4GvQ4cOMsbos88+c7tNVQLwV199JWNK+r+WHlTK3VT6CWlFAfjpp5+udACWpB9++EFLly7V2LFjnb5IuTAwlheA7Z9/06ZNK7yW0qNUlxcoyxvRWap6AB41apTb/VRFeee7b9++cgNwWSOulxWAIyIiqn2+AKrHEvVzH0cAvoC971TpqawA/L///c+xTvPmzRUfH6+hQ4c6+ruFhoa6bYJlrzS0a9fO7R/yspo0VZUlChgBGD7ucuwDXBF7k9zKDvIjSfPmzZMxRtOnT69w3bS0NAUHB2vfvn2Oed26dVPPnj2d1ps1a5aMMfrhhx8q3GdFTaDt/T9L3zPtQb/0KNV2Z86ccfTNdXecqgTgvn371lgT6KKiItlsNl155ZUVruvuvMpqAm1/4l6ZJtDubNiwQS1atJAxRn//+99djuvu2g4dOiRjSgbAqoraCMA12QTaPtCZu1Gb33///RoJwDSBBqzDEvVzH0cAvsC8efM0d+5cvfXWW45vTMsKwJ9//rkGDBjgMqplQUGBxo0b52guWFjo/E7PqlQaqsMSBYwADB93OY4CXR57hbxz586V3ub8+fPq1auXS7Nbdz7//HPZbDaXJqrdunVzOeY999xT6Qq9/b7r7+/vtqnxgw8+6PKEOjk5WcYYrV692mX9hQsXltsEuioBOC0tTca4H4Br79698vf3r3QAlqQBAwbIGOPyt6k89vPq3bu3y7KioiLHU9zSfbir+rfsN7/5jYxxHrXY/hmXFf6joqIUEBBQZosqd2ojAJceBKus13xVln306ZUrV7ose+ihh2okAEs/DYL15JNPVut8AVSPJernPo4AXIHyAnB58vPzFRYWJmOM3n//fadlBGDAt2TtydKUtVMum/cAS9K2bdtcRsndunWrmjVrJj8/P7333ntOy7799lstXLjQqYmwVPIe34kTJ8oYo8jISJ0+fbrc4w4aNEht2rTRmTNnnObfcccd8vPz0yeffCJJOnXqlFq2bOnySqGylO56MmDAAKfz2LJli0JDQ+Xv7+8UZv74xz/KmJJ3B5f+InPXrl2KjIyssQC8b98+BQUFKTg42Om1PWfOnNHAgQMdx6lsAP7ggw/k7++vNm3auG2FdOTIET3//PNuz8sYo7/+9a+O+efPn3eEsK5du1Z4rQcPHlRmZqbLz7mgoEC//OUvZYzRsmXLHPPtQe7C87FbvHix4ymwuyekn3/+udP5SrUTgCXpt7/9reNz+fLLL52WVeU1SH/9619lTMkI3KU/t+zsbIWEhNRYAH7//ffl5+en8PBwp98zqWSk7wtfg/Tggw8qKirKbQsI4LJTVCTl5Pw0XfD3rTZZon7u4wjAFbjYACxJPXv2lDFGr732mtN8AjDgWwqLC5W5LVNT1k5RzMIY3br0VnV/sbt6vtRT3V/srluX3qqYhTGasnaKMrdlquic5/4w20VHR6tx48aKjY1VYmKirr/+evn7+6tOnTpO74m1sw/WU79+ffXq1UsjRoxQbGysY/Tn8PDwCgPBmjVrZIzRm2++6bJs+/bt8vf3V1hYmIYOHao2bdrIGKMXX3yxUtdjv+8OHjxYrVq1UmRkpEaOHKkBAwYoMDBQxhilpaU5bXP8+HFH0G3btq1GjhypmJgYBQYGasSIEW5DxsUEYOmnPrYBAQHq37+/Ro0apWbNmqlFixaOkY4rG4Alaf78+QoICJAxRtdcc42GDRumQYMG6eqrr1ZAQIDCwsLcntekSZPk5+en6667TomJiercubOjS4/9y4fyrnXbtm0yxigkJER9+vTR6NGjFR8f7xgU67rrrnN6tZZ9cDObzab4+HiNHz9e48eP1/Hjxx3r2JuiBwQE6Nprr9WIESM0YMAA/fznP3cbzGsrABcVFTn6Z9tsNsXExOj222/XDTfcoODg4Er/jT9z5oxjILRWrVpp2LBhuu666+Tv7+8YPK4mArD005c69p9FYmKi+vfvr0aNGrlct/13oqzPCrisWKg+aon6uY8jAFfgYgNwcXGxmjRpImOMy5MSe6Xhhhtu0IMPPqjk5GT95je/0dq1ayv9So/KsEQBs9ANB/CkwuJCZe3JUkZOhpKzktXx+Y6Kmh+ljs93VHJWsjJyMpS1J8sS4VeSFixY4AjBgYGBatasmUaPHq1t27a5Xf/UqVNKTU1VdHS0mjdvLpvNppCQEHXu3FkzZszQ4cOHyz1eQUGB2rVrpwEDBpS5TlZWlq655hoFBgaqZcuWmjdvXqWvp3RYO3LkiO644w41btxYNptNXbt2LTNIHDp0SKNHj1bz5s0VHBysjh076rHHHlNxcXGNBmBJWr58uXr06CGbzaZGjRpp9OjROnz4cIXvyi3Lli1bNGbMGLVs2VKBgYG68sordc0112jy5MkuLZNKH+Ott97S9ddfr5CQEIWFhSk+Pl67du1y2b+7az116pSeeOIJ3XrrrWrTpo2Cg4PVqFEj9ezZU88995zLk31JWrp0qbp37+7oo+ouvL777rsaOnSoIiMjFRgYqCZNmqh79+6aNWuWtm7d6rRubQVgqWQwzFdeeUW/+tWvVL9+fQUHB6tt27YaM2aM06uuKnL48GElJiaqQYMGqlu3rq699lq98cYbFY4CXdUALJU8CbZ/KREYGKjmzZtrwIABWrp0qdN6BGB4FQvVRy1RP/dxBOAKXGwAXrJkiYwxaty4sUuTwPJGge7SpUuZI4FWlSUKmIVuOIAV5J7NVfa+bCW8nqC41+KU8HqCsvdlW7bPL3zDxYZsALgsWKg+aon6uY8jAFfgYgLwl19+qUaNGskYoxdeeMFl+SeffKJZs2bp448/1okTJ3TixAm9++67jv5RrVu31smTJyt9PHtBunCy2WyeL2AWuuEAVpFflO8Y9Tk9J135RZQLeBYBGIBXs1B9lADseQTgClQ1AOfl5alHjx4yxighIaFKxyouLtaNN94oY4weeeSRSm9HAAYuLwRgWA0BGIBXs1B9lADseQTgClQlABcWFjpeP/GrX/3KbV+nitgHgenTp0+Vt72QJQqYhW44gFUUnStSzoEcx2SVfr/wXQRgAF7NQvVRS9TPfRwBuAKVDcDnzp3TyJEjHSNSfv/99xd1vL1798oYo/bt21/U9qVZooBZ6IYDAAAAH2Sh+qgl6uc+jgBcgcoGYPt7Ljt06KCvv/76oo/38ccfO955WF2WKGAWuuEAAADg8pNXUKSP9x3Xyq2HtGzjQa3cekgb959QXkElW1BZqD5qifq5jyMAV6AyAfg3v/mN4/19Bw8erNbxZs2aJWOMfv3rX1drP5JFCpiFbjgAAAC4fBQWn1P2rmN6OnuvHlq1QymLtyh54WalLN6ih1bt0NPZe5W965iKiit4jaiF6qOWqJ/7OAJwBSoKwE8++aSMMYqMjKz064tefPFFHT9+3Gne+fPn9eKLL6pOnTry8/PTli1bqnXekkUKmIVuOAAAALg8FBaf0/LNX2rO6p0as2CD7n51k1JXbFfamzuVumK77s7cpDELNmjO6p1avvlLFZYXgi1UH7VE/dzHEYAvsGbNGvXq1csxGWPk5+fnNG/NmjWSpG3btsnPz0/GGF1//fVKSkpyO61bt87pGK1bt1ZgYKC6du2qIUOGaMiQIWrbtq2MMfL399dzzz1XI9diiQJmoRsOAAAALg/Zu45pzuqdGv3Sx5q7eqeeemevyzT3x+VzVu9U9q5jZe/MQvVRS9TPfRwB+AKZmZkyxpQ7ZWZmSpJycnIqXLf0+nbPPfecBg8erLZt2+qKK65QUFCQWrdurTvuuEObNm2qsWuxRAGz0A0HAAAA1pdXUKSns/dqzIINZYbf0iF4zIINejp7b9l9gi1UH7VE/dzHEYC9mBUKWNHpXOWkJzmmotO5Hj0fAAAAWNvH+47roVU7dHfmpnLDr326O3OTHlq1Qxv3n3C/QwIwSiEAezErFLD83O+Vnh7tmPJzL+71UAAAAPANK7ceUsriLUpdsb1SATh1xXalLN6ilVsPud8hARilEIC9mBUKGAEYAAAAVbFs40ElL9ystDfLb/5sn9Le3KnkhZu1bGMZb2MhAKMUArAXs0IBIwADAACgKngCjEuJAOzFrFDACMAAAACoCvoA41IiAHsxKxSwWg/ARUVSTs5PU1EZowECAADAkhgFGpcSAdiLWaGA1XoAttANDgAAABeH9wDjUiEAezErFDACMAAAAKqqsPiclm/+UnN+fML765c/0l8yXtbLD7+iv2S8rF+//JHGLNigOat3avnmL1VUfK7snVmofmiF+rmvIwB7MSsUMAIwAAAALkZh8Tll7zqmp7P3au7rm/XW0GRlJSTrraHJmvv6Zj2dvVfZu46VH34lS9UPrVA/93UEYC9mhQJGAAYAAEB15BUUadPuI/rvhOna+ev79N8J07Vp95Gy+/xesO3G/x6+qG0vBSvUz30dAdiLWaGA1WYAttoNDgAAADWkig85auzpcQ2zQv3c1xGAvZgVClhtBGCr3uAAAABQQ6oQgC/sPzzhpXXKHpGid0dNUvaIFE14aZ1T/+HCWqwjWqF+7usIwF7MCgXsUgdgK9/gAAAAUEOqEIAvHEH62TU79NEdUxzTs2t2VH4E6Rpmhfq5ryMAezErFLBLHYCtfIMDAABADalkAHb3DmF39cNKv0O4hlmhfu7rCMBezAoF7FIGYKvf4AAAAFBDKhmAP953XA+t2qG7Mzc53hdcVv3wqXf26u7MTXpo1Q5t3H+iVi7DCvVzX0cA9mJWKGCXMgBb/QYHAACAGlLJALxy6yGlLN6i1BXbK1U/TF2xXSmLt2jl1kO1chlWqJ/7OgKwF7NCAbuUAdjqNzgAAADUkEoG4GUbDyp54WalvbmzUvXDtDd3KnnhZi3beLBWLsMK9XNfRwD2Yp4uYLknvlL23+Zp6l1NNXlchKbe1VT/Wv64ck98VSP7t/oNDgAAADWEJ8CoIQRgL+apAlaYf1pZi9KUkdFXE2ZGKXZ8kPqPD1Ts+CBNmBmljIy+ylqUpqKz5b+/rSJWv8EBAACghtAHGDWEAOzFPFHACvNPK3P+eE1OvVox0xpo8LTGShgXrOFJIUoYF6zB9zZWzLQGmpLaRZnzx6sw//RFH8vqNzgAAADUEEaBRg0hAHsxTxSwrEVpmpx6tfpPa6CpqddoTlpvJSWFOaY5ab01NfUa9f8xBGctSrvoY1n9BgcAAIAawnuAUUMIwF6stgtY7omvlJHRVzE/ht/09Gi3ATg9PVpTU69RzLQGysjoW60+wVa+wQEAAKCGVCEAFxaf0/LNX2rOjw9AJry0TtkjUvTuqEnKHpGiCS+t05gFGzRn9U4t3/yliorP1dZVEIAtgADsxWq7gH3wf88p5YFOirsvwjHqc1kBOD09WnH3RSjlgU76MGv+RR/Tyjc4AAAA1JAqBGCppI6YveuYns7eq7RlG/ToHYP0yB2D9Ogdg5S2rKRVYPauY7VeNyQAex4B2IvVdgFb9KeJGj69uZJnRlUqACfPjNLw6c216E8Tq3Xc0je4ua9v1ltDk5WVkKy3hiZr7uubPXaDAwAAQA2pYgC2yyso0rr/7NM9M36pSff30j0zfql1/9nnsS5xBGDPIwB7sdouYAueuVMJ90Vq8gNXVyoAT37gaiXcF6kFz9xZI8fPKyjSpt1H9N8J07Xz1/fpvxOma9PuI/T5BQAAsJqiIikn56epqIL62kUGYEnKz/3eUf9MT49Wfu73F33a1UUA9jwCsBfzlSfATqpxcwQAAEAtqWqdjQCMGkIA9mK+0AfYBQEYAADA+gjA8BACsBfzhVGgXRCAAQAArI8ADA8hAHsxT70HeEpql1p5D7BbBGAAAADrIwDDQwjAXswTBaww/7Qy54/XlNQuipnWQIPvbayEccEanhSihHHBGnxvY8X8GH4z549X0dkaDqgEYAAAAOsjAMNDCMBezFMFrDD/tLIWpSkjo68mzIxS7Pgg9R8fqNjxQZowM0oZGX2V/nqjywAAIABJREFUtSit5sOvRAAGAAC4HBCA4SEEYC/m6QKWe+Ir/Wv545p6V1NNHhehqXc11b+WP16zfX4vRAAGAACwPgIwPIQA7MWsUMBq/YZDAAYAALA+AjA8hADsxaxQwAjAAAAAcEEAhocQgL2YFQoYARgAAAAuCMDwEAKwF7NCASMAAwAAwAUBGB5CAPZiVihgBGAAAAC4IADDQwjAXswKBYwADAAAABcEYHgIAdiLWaGAEYABAADgggAMDyEAezErFDACMAAAAFwQgOEhBGAvZoUCRgAGAACACwIwPIQA7MWsUMAIwAAAAHBBAIaHEIC9mBUKGAEYAAAALmopAOee+ErZf5unqXc11eRxEZp6V1P9a/njyj3xVbVO/2JZoX7u6wjAXswKBYwADAAAABdVrLMVnc5VTnqSYyo6nVvu+oX5p5W1KE0ZGX01YWaUYscHqf/4QMWOD9KEmVHKyOirrEVpKjpbu3VFK9TPfR0B2ItZoYDVdgCu6s0RAAAAHlDFAFyVOmVh/mllzh+vyalXK2ZaAw2e1lgJ44I1PClECeOCNfjexoqZ1kBTUrsoc/54FeafrtFLK48V6ue+jgDsxaxQwGo7AFupjwcAAADKcAkDcNaiNE1OvVr9pzXQ1NRrNCett5KSwhzTnLTempp6jfr/GIKzFqXV6KWVxwr1c19HAPZiVihgBGAAAAC4uEQBOPfEV8rI6KuYH8Nvenq02wCcnh6tqanXKGZaA2Vk9K21PsFWqJ/7OgKwF7NCASMAAwAAwMUlCsAf/N9zSnmgk+Lui3CsW1YATk+PVtx9EUp5oJM+zJpf45fojhXq576OAOzFrFDAvD4AFxVJOTk/TUVFl/Z4AAAAl7m8giJt/O9h/XfCdO389X3674Tp2rT7iPIKyq5HVbaOt+hPEzV8enMlz4yqVABOnhml4dOba9GfJl6qy3Vihfq5ryMAezErFLDaHpSq1gNwbq6UlPTTlMugWwAAAO4UFp9T9q5jejp7r+a+vllvDU1WVkKy3hqarLmvb9bT2XuVveuYiorPuWxb2TregmfuVMJ9kZr8wNWVCsCTH7haCfdFasEzd17qy5dkjfq5ryMAezFLFLBafi1RrQfg77+XoqN/mr6nyTUAAMCFCovPafnmLzVn9U6NWbBBE15ap+wRKXp31CRlj0jRhJfWacyCDZqzeqeWb/5ShReEYJ4Ao6YQgL2YJQoYARgAAMDnZe86pjmrd2r0Sx9r7uqdenbNDn10xxTH9OyaHZr74/I5q3cqe9cxp+3pA4yaQgD2YpYoYARgAAAAn5ZXUKSns/dqzIINmrt6p556Z6/bAPzUO3s198cnxE9n73XqE8wo0KgpBGAvZokCRgAGAADwaR/vO66HVu3Q3Zmb9NQ7e8sNwE+9s1d3Z27SQ6t2aOP+E459VPU9wFNSu/AeYLhFAPZilihgBGAAAACftnLrIaUs3qLUFdsrFYBTV2xXyuItWrn1kGMfVanjFeafVub88ZqS2kUx0xpo8L2NlTAuWMOTQpQwLliD722smB/Db+b88So6e2nrp6VZon7u4wjAXswSBYwADAAA4NOWbTyo5IWblfbmzkoF4LQ3dyp54WYt23jQsY+q1vEK808ra1GaMjL6asLMKMWOD1L/8YGKHR+kCTOjlJHRV1mL0mo1/EoWqZ/7OALwBbZs2aLHHntMQ4cOVbNmzWSMkc1mq3C7hQsXqmfPnrriiivUoEED3XLLLVq/fn2526xfv1633HKLGjRooCuuuEI9e/bUq6++WlOXYo0CRgAGAADwabX9BLi03BNf6V/LH9fUu5pq8rgITb2rqf61/PFa6/N7IUvUz30cAfgC8fHxMsY4TRUF4OnTp8sYo7p16yo+Pl4DBgxQnTp1FBAQoFWrVrndZtWqVQoICJCfn5+io6M1bNgwhYeHyxij6dOn18i1WKKA+WoALiqScnJ+morKfrE7AACAN6vtPsAXqvX6YTksUT/3cQTgC8ybN09z587VW2+9pWPHjlUYgN99910ZY9SwYUN99tlnjvkfffSRgoKCFBYWpu+++85pm++++05hYWEyxmjlypWO+ceOHdNVV10lY4zee++9al+LJQpYLQbg3BNfKftv82r3G76yAnAtB38AAACrqs1RoN35f/buPCzKev//+D3s4oKgbC6QK8q+igqKuZQbiooi67DNMBu7MLIMWH1/bSezMs85ZUlipZGoodUxRCxNBLRSxKVCU9yXzAOEMnhevz8GRkAWldkc3o/ruq886MCt5/rMfT/nvu/PhwKYtEUB3IOeAnj+/PlgGAbr1q175PcSEhLAMAzeeuutdl9/8803wTAMFi9e/MhrduzYAYZhsHDhwl7vu0YMMBWEoFqf8aAAJoQQQgjpkarWAe4MBTBpiwK4B90FcGNjIwwNDcEwDGprax/5/R9++AEMw8DPz6/d16dPnw6GYbBly5ZHXnP//n0YGRnByMgIjb2MJo0YYEoOwdZZ/oRiR9ksf4ndz/LX1Nig0J9PAUwIIYQQ0rOm5gcoqLwIScsV3tgPSvEW2x9roxbhLbY/Yj8oRejGMkh2VaGg8iKkzQ/avZ4CmCgKBXAPugvgn3/+GQzDwNzcvNPfr6+vB8MwMDU1bff11md9q6urO32dp6cnGIbBL7/80qt914gBpuQQLMrPhlDsqL513noKYIkEYLOBvXvpWWBCCCGE9GlNzQ9QXH0N64rPIvPzQwjmuWMlzx3BPHdkfn4I64rPorj62iPxC1AAE8WhAO5BdwH81VdfgWEYuLm5dfn61tj973//CwC4e/eufHKtu3fvdvqagIAAMAyDoqKiXu27RgwwJQZw3e2rWLNmBma3xG9url+nAZyb64d4sTNmJ5pizZoZin0muKcAzsqSfT0ri64EE0IIIYRA9kzwwZM1EKROBj/FG4LUyTh4sqbdM79t9XaeFwpg0hYFcA+6C+DPPvsMDMPAx8eny9cPHz4cDMPgypUrAIDLly/LA1jaxdXA0NBQMAyDzz///LH2sXUgddwMDQ3VP8CUGMDff/UeeOn28E+ylL+hdRXAubl+8E+yBC/dHj8UrVfYPlAAE0IIIYQ8uceJUkXN80IBTNqiAO5BdwH86aefgmEY+Pr6dvn61rWEWwP40qVLPQZwSEgIBfBjyN8Qh8Dk4eCssnusAOasskNg8nDkb4hT2D48UQBLJA9vhabboQkhhBCibmpctrGnKFXkPC8UwKQtCuAe0C3QvaTEAN74TgQCkqwgTHd8rAAWpjsiIMkKG9+JUNg+PFEAt240MRYhhBBCNIEaJ+3sKUoVOc8LBTBpiwK4B4qYBGvw4MHtvt66BjBNgtU7z9wVYApgQgghhGgSDQ1gRc/zQgFM2qIA7kF3Afz3338/1jJI06dPb/f17pZBampqgpGREQwNDWkZpB48c88AUwATQgghRJNoaAAr+hyPApi0RQHcg+4CGADmzZsHhmGwbt26R34vISEBDMPgzTffbPf1N954AwzDYPHixY+8ZseOHWAYBvPnz+/1vmvEAKNZoCmACSGEEKKZNDSAFX2XHwUwaYsCuAc9BXBxcTEYhsGQIUPw66+/yr9++PBhGBoaYtCgQbh9+3a719y+fRuDBg0CwzAoLCyUf/369esYO3YsGIbBvn37er3vGjHAVLAOsEjspLnrAFMAE0IIIURTdJz0qq5OIwNY0fO8UACTtiiAO9izZw+8vb3lG8MwYLFY7b62Z8+edq9JTEwEwzAwNjbG4sWLMW/ePOjp6UFHRwfbt2/v9Ods374dOjo6YLFYmDFjBgIDA+UTZiUkJCjk76IRA0zJAdw6Q6BI7CSbITCh+xkCe5om/4k9bQDTjNCEEEIIUbWO52V37mhkANMVYKJMFMAd5OXlyWdp7mrLy8vr9HUeHh4wNjaGiYkJXnzxRRw8eLDbn3Xo0CHMnTsXgwcPhrGxMTw8PLBp0yaF/V00YoCp4NYaRa0R91SeNoDpajAhhBBCVO0ZCWB6BpgoEwWwFtOIAabCZ0vqbl/FvoI3EB9lDWGkJeKjrLGv4A3FPvPbUW8DWCIB2OyHV4PpSjAhhBBClOUZCWCaBZooEwWwFtOIAabiyRVU/gbX2wDOyABcXICwMFkI19Upd38JIYQQ0nc9IwEMKHaeFwpg0hYFsBbTiAFGAdx9AIvFgK0tMG1a+9cTQgghhCjaMxTAipznhQKYtEUBrMU0YoD14QC+nyXBJUEybrhPxslIEU5Hx+OSMAX3syQUwIQQQghRvWcogAHFzfNCAUzaogDWYhoxwPpgADc1P0DJT3+gLFyE/cs4ODvBHXv8o/D1oijsX8ZBWbgI57iJeJCRSQFMCCGEENV5xgK4VW/neaEAJm1RAGsxjRhgfSyAm27dRkHlRbxUcBSF/jEoWhiFGnsPlAZyULI0FkULo1DoH4MDgRxUR4nQnJZOAUwIIYQQ1XhGA/hp/nxb0oY6lOay5Zu0QX1zrmjE+XkfRwGsxTRigPWxAC4tOwPJriqwN3yP/UF8HAnm4aKTF8qCeSgL5uFIMA/7g/jYMY+NA4EcnI8WUgATQgghRDU0JIDrbl9F8RevP9EV3V6d46n4fLQ7GnF+3sdRAGsxjRhgfSiAm6dNx4adlQjdWIaXC47icJio0wA+HCbCgUAOds5nozwoFg9sbCiACSGEEKJ8ag7g3jzTSwFMFIUCWItpxADrQwF8d9JUvJx/CNF5FXh3z4luA7gsmIeihVE4EBCJe8NGUAATQgghRPnUGMCtszoLxY6yWZ0Tu5/Vuamxof2uUwATBaEA1mIaMcD6UADfcJ+MpH/vh3j78ccK4JKlsfh2QTjqrYZTABNCCCFE+dQYwEX52RCKHZ96XV8KYKIoFMBaTCMGWB8K4Otu3oj/Zwmyd1Y9VgCXBnLwzXwKYEIIIYSoiJoCuO72VaxZMwOzW+I3N9ev0wDOzfVDvNgZsxNNsWbNjHbPBFMAE0WhANZiGjHA+lAA0xVgQgghhGg0NQXw91+9B166PfyTLOXnaF0FcG6uH/yTLMFLt8cPResf7joFMFEQCmAtphEDrA8FMD0DTAghhBCNpqYAzt8Qh8Dk4eCssnusAOasskNg8nDkb4h7uOsUwERBKIC1mEYMMKkUKC19uEmlSv1xNAs0IYQQQkgX1BTAG9+JQECSFYTpjo8VwMJ0RwQkWWHjOxEPd50CmCgIBbAW64sDjNYBJoQQQgjpAl0BpgAmFMDarC8OMGlDHUpz2fJN2lCn3B/YIYCbbt1GQeVFvFRwFIX+MShaGIUaew+UBnJQsjQWRQujUOgfgwOBHFRHifAgLZ0CmBBCCCGq0SYE72dJUPHz7zjFTUZVbBJOcZNRcfoy6u8p/m49egb4ob54fq5pKIC1WJ8cYCp+g5PevonSxS7yTXr7JpqaH6Dkpz9QFi7C/mUcnJ3gjj3+Ufh6URT2L+OgLFyEc9xEPMjIBMRiCmBCCCGEqEZjI5olOagRpKIsXISX8w9h9xIOigI42L2Eg5xtlVhXfBbF1dcgbX6gsB9Ls0A/1CfPzzUMBbAW65MDTMVvcHXXa8GOs5Rvdddr5ftxP0uCS8IU3HCfjJORIpyOjsclYQruZ0mArCzZRgFMCCGEEBVpqm/ASU4S9gfxUegfA8GGfShezkNJEB/Fy3ngfngQoRvLINlVhYLKi2hSYAQX5WdDJHaidYD74vm5hqEA1mJ9coCp+A3uztXz8Es0kW93rp5vvx9ZWbKwbQ3erKyHX6cAJoQQQogKlfz0B/YH8bF9YQz2B/Hx/o5KHA4Tybd395xAzq4qhHx4BJJdVSiuvqawn93U2IC89TEQiZ0wO9EUCxPMERBphEC2MQIijbAwwRyzW+I3b30MpPfbn8NRABNFoQDWYn1ygFEAE0IIIYQ8ov6eFO99fQKF/rL4PRwm6jSA3/7uLHJ2VSF0YxnWFZ9V6DPBTY0NKMrPxpo1M8BdZYc5MQaYFaOPOTEG4K6yw5o1M1CUn/1I/AIUwERxKIC1WJ8cYBoawPfFGagVJON0dDyqYpMe3g6dmkYBTAghhBClO1JzCznbKrFrcaw8eLsK4Le/O4vovApk7jiB8nO3Fb4vdbevYl/BG4iPsoYw0hLxUdbYV/BGu2d+O6IAJopCAazF+uQA07AAbs7IxJ+eU3AkhIf9y2Lx9aJoFAVw5BNilQfF4m/rEfifry8FMCGEEEKU5vPyCwhdX4qCBdHYtTgWRQEcZG36AYdChZ0GsHj7cfC2HEXhsVql7M+TBi0FMFEUCmAt1icHmAYFcLMkB9VRIpxz8MTO+WwULYxEydJYlATx5UsiffViGP40t8YNVy88mD6dApgQQgghCtXU/ADF1dcQ80kFnn/5G2yaFYFP5rCxeQ4bK17/GgULovH1Ui5+DBO2C+DsnVXgbK7E1vILStkvCmCiLhTAWqxPDjANCuAaQapsvd9xbjgQyEFZMA9Hgnk4HCaS//r7JVG4YWaF8xPd8afnFApgQgghhChMU/MDFFRehGRXFeasPYCpuXvwyRw2Pp8bhU/nRmL+miJ8PCsCn8+LwleLY7Fu93GNvQIsbahDaS5bvkkb6p7gh1EAk4cogLVYnxxgGhLA9X/VoSxchJ3z2Tjn4ImyYF6nAXxkRSz+NLfG6bEuqHX2Qv21m0rdX0IIIYT0HcXV1yBpmdWZm1+JJWuLkTcnAgULolGwIBqRb+/F5/Oi5BGclHdYJc8AA09xRbc353gUwKQNCmAt1icHmIYEcPmpS9i3goeihVG46OTVbQD/ZTEMZ8a5osbeA5W/1Ch1fwkhhBDSN9Tfk2Jd8VmEbixDzq4qvP7NaYSuL5XHbmsAFyyIlkdw6PpSvPHtaaXNAt0WBTBRFwpgLdYnB5iGBPD2Q6fxatgCrA2fjy+et8PBYG63AXxughvOTnDHV6Unlbq/hBBCCOkbjtTcQuaOE4jOq5Bf1U3KO9zuim9rABcsiEbe7AgsWVuMuC1HlbIOcEcUwERdKIC1WJ8cYBoSwFtKT2Alzx1sgTuSVgzDgZDYbgP4/ER3nLFzx5fFJ5S6v4QQQgjpGwqP1YK35SjE2x8+1/t20XF8tZgjj+D5LxXh07mR+HxuFD6Zw8bUnD2YvfYAJLuqUFB5EdLmB0rbPwpgoi4UwFqsTw4wFb7BXbtSiw/fS8PSYH0sCdbD0mB9bFwvxrUrtfji4EkE89wRwXd7rACmK8CEEEIIUaSt5RfA2VyJ7J1V8gB+d88J/BgqxNdLuShYEI0Vr3+NzXPY+GQOG5tmR+D5l79BzCcVKK6+ptT4BSiAifpQAGuxPjnAVPAG11Bfh3fWJoMtcsPz3MFw4DOYIGDgwGfwPHcw2CI3SHJjEM53QxDXBYGRQ/BO9HxsiPbHoWAuPQNMCCGEEKXr7Arwu3tOyNf8PRgiRNbHP6AogINdi2NRsCAaoetL8fmRP1SyfxTARF0ogLVYnxxgSn6Da6ivQ5ZkGfz4prBJ1sGIZBZGJDEYmchgRBKDESks2CTrYDpvMMJWmiIwxgGTBAPAFrkhRuSB70NiaRZoQgghRAvU35PiSM0tFB6rxdbyCyg8Vovyc7eVNmnUk+rsGeC2AXw4TIR3C8vwPicA73MC8ErofGRvLVParM8dUQATdaEA1mJ9coAp+Q1u7T+EmMIfiGEpOhiWysKYJF3Yt1z9tRcwGJOki2GpLAxL0YF3rA4igobCk98fYQLXTgOY1gEmhBBCni1NzQ9QXH0N64rPInPHCfC2HAVncyV4W44ic8cJrCs+q5JbiHvScRbozgJ43fZDiE7wQoTQEyu4bli7u1JlAU8BTNSFAliL9ckBpsQ3uGtXarGAPwzDUlgYlsqCq8gI3gJjuHMZ+eYtMIaryKglghnMitCDL9cYgRwnrOS64NtlkSgJ4qNkaSyKFkbhqxfD8Ke5NW64euF/06crJoClUqC09OEm1YxPogkhhJBnXVPzAxRUXoSkZZmg6E8qIN5+HNk7qyDefhzReRUI3Vgmn0SqSc0R3HYd4JxdVZ0GcITQE8u5bogQeuLbyjMq2zcKYKIuFMBarE8OMCW+wX2wIQPOIkOYpTOy+BUO6DSAvYUD4CoyglkaA0c+g8XB+mDHuyGM74pXQl/A/wtbgNdC5qJ4WQzKg2Lxt/UI/M/XF/DzU0wAa9CbPCGEEKJNOgalfHblNltOy+8rexmhx9Ex2LkfHkTxch5KgvgoXs4D9/1vsKIlfvkp3qj7SzW3PwMUwER9KIC1WJ8cYEp8g4tL9oBtsg6Gp7Bk8dtNAHsL+mN4MgObJAYLQ1lYnTUV8WmTEJcsO8AIkyfhd2EC7qemAba2wLRpFMCEEEKIBuvsluKutpyW4FxXfFbtzwS3vWU7Z1sldi/hoCiAg91LOJB8UoKYBC8kpE1BTs70niNUgSiAibpQAGuxPjnAlPgGFygcBatUFsYl6vUYwJP4/TFOxMAylcHscBbi0yZhddZUZEl8ZG/0kmlozBIDYrHyAlgiAdhsYO9euhWaEEII6aXOJpXqbovOq0DmjhPdTyqlwseW6u9JUXH6Mk5xk1EVm4RT3GQcOnYK2ZLpjx+hCkQBTNSFAliL9ckBpsQ3uOWiUbBaxcK4hK4D2ItvDE9+f3jwjDFWxMAqlcGscAahfBew490gTPVCTs501QRwVpbse2Zlqf3NnhBCCHnWdbasUHebePtx8LYcReGx2q6/qYrDTNpQh9Jctnyru177ZBGqQBTARF0ogLVYnxxgSnyDi1/l1eMt0J68fnDl9cMEkT5M0xkMSWMwJYoBO9gaQVETECZwBT/FG5JsXwpgQggh5BmytfwCOJsrkb2z+9ufW7fsnVXgbK7E1vILXX9TFYdZx+i8c/U8BbCK9cnzcw1DAazF+uQAU+Ib3FdbXoazyAhD0hm4dDIJlhuXwbh4PYxI1sGQVQwMshkMEjNw5TLwDzPEiuD+iAgyRwTfHQmp3hTAhBBCyDNEG64Aa1IAd7waLW2o6/4FFMBEQSiAtVifHGBKfIOru30VAaLh8nV+Xdosg+TGZTAqQXbL84DVDAyzGBhnyr42M5zB9GhdTI7VwaIwQ4QFmSFa4Io9GUEozQhGqbclpNOVMAs0BTAhhBCiMEp5BrgPB/AT/90pgImCUABrsT45wJT8Bvflx2nwFQ1qiWAWRifqYiKfwXOJstud+2Uy6J8hi+ARyQwmcVjwjXoYwI58FuaHGSIq2ALxaZOQm+WD3MUmaPTzoQAmhBBCNJhSZoGmAFZNAKtwsrGe9Mnzcw1DAazF+uQAU/KBpKmxAf9+OxxzhEPwXLIuRiSzMDyZgYlYdtV3wGrZry1XMRgdz8CBz2BMPIMxCQzGxTMYL5ItjTQ7Qg88gSMkWVPBDu2PvYsdUbrYBdLbN3u/kxTAhBBCiMLV35Niw/7fELKxDDPfOoDQjWVI/eIXvP7N6cdbB7izCKMAVk0Aa5A+eX6uYSiAtVifHGAqeHNsamxAUX42xFlTMFcwBKPjGZimyZ73HZ2oK9uSdGGTxGB0AgN7AQMnPgsOAhZGJzAwS5OF8PJQY6xe7QmXeH2ExZmDHWeJuuvdPCf0uCiACSGEEIVpu47u6sLjWPjeD/B9vQTuL+/F1Ff3Yf67P4C9qRxpX/6C6LwKhG4sg2RXFQoqL0La/ODhN+rsHIUCmAKYqBwFsBbrkwNMhW+Odbev4j9b1mBOOAv2AgbuHAZT+QPgFG8I22QdOPNZ8OLqyJZH4urIt/EiBkPTGEyJ1UVi1DDYpupiWuIg+CWa4M7V873fMQpgQgghRCGamh+goPIiJC23NEd/UoG0L38B++NyzH/3B0x9bR/cX/4Ovq+XYOF7P2D19uNYV3wWxdXX2scvQAH8yM5QABP1oADWYn1ygKn4zfHO1fNYGqIHnygGs8MYTBYYwzZZF64iI3nwunMZuMcxmCiQ3Qo9Mkn2vPCIJAbB4f1hF8+iACaEEEI0UHH1NUhabmnu+NzvG9+eRmrBLwjdWIaZb5UiZGMZNuz/retnfimAO+wMBTBRDwpgLdYnB5gaAnhZqD6mRzKYEs3ASWSAMUl68Bb0hxdXBx5cBuNEsgmxLFNl4TtoNYMBGQzM0hk4CVh4MZTB9PgBFMCEEEKIBlH4pFcaFsA5GVPwbX4u4qOsIYy0RHyUNfYVvIG621eVug8Pd4YCmKgHBbAW65MDTB1XgCOM8EI4CxMFDMYm6MIx3hDegv7w4Mqe+bVMlU2MZZrOwGKV7FlhszQG5mmyW6E9OAyWhephhmggBTAhhBCiIRS+7JGGBHBOtg9SY23AjjABJ3ks5sQYYFaMPubEGIC7yg5r1sxAUX42pPeVfN5AAUzUhAJYi/XJAaaGAJ4tGIjFIToYG8/ANkkHTkJDePGNMV4kWxfYRCz774jkh/97ZDIDRyED2yTZbNFzw1lYFmZAAUwIIYRoiMJjteBtOQrx9uOPFcDi7cfB23IUhce6mNBSAwL4vzcvIz7KCoGRxvDh6mJBwlAERBohkG2MgEgjLEwwx+xEU4jETshbH4Omxgbl7QwFMFETCmAt1icHmBoC2C/RBMvCDODFYWCexoJdgj48BP0wIrnz+LVKZWAXz8BRyMK4eNkV4EkcBotDdFF7uqL3O0UBTAghhPTa1vIL4GyuRPbO7m9/bt2yd1aBs7kSW8svdP4NNSCACz9KRWCkMaZy9bA80hhZGd5gs03kmyTbB/FiZ8xqieCi/Gzl7QwFMFETCmAt1icHmJoCeIZoIBaG6sAhSR9D0xmMSNWBWbrsdmeLVbLbn1vjd1QCg4lC2ddHJDNwiZNts8MZ/GfLmt7vVGMj7mdJcEmQjBvuk3EyUoRT3GRUnL7c6XNJ9fekOFJzC4XHarG1/AIKj9Wi/Nztrp9hIoQQQvoAbbsCXHf7KnKyfeHD1cXySGOw2SadBnBurh/ixc6YnWiKNWtmKO+ZYApgoiZ1AP1IAAAgAElEQVQUwFqsTw4wFb451t+TYl/5T5giGogpooHw4/TDEqE1RqfoYngqCwMyZBNemaUzsGyJ3eHJsv8OTWNgnCn7vVEJDMbEMxgrYhAlskPj309/u1FT8wOU/PQHysJF2L+Mg7MT3LHHPwq7l3CQs62y3dIMbdc1zNxxArwtR8HZXAnelqPI3HGi62UcCCGEkD5A254B/nbrK/BPtICDkIXnY/UwK0Yf4Um2CGUPfCSAc3P94J9kCV66PX4oWq+cHaIAJmpCAazF+uQAU8GbY9twzNj0LbwE/eHF7w8vQX8kpa7EMsFojEzRwdA02ZJHo1uu+I5KkF0BHriaQb9M2URYVikMhifJrhAPyGDgKDLA6qzFaKive6r9Kqi8iJcKjqLQPwZFC6NQY++B0kAOipfzwP3wIEI3lkGyqwpbyy9ga8UF+bqGsR8fxgdrPsJHr2zCB2s+QuxHh+V/tqDyIpooggkhhPQxTzoLdPi/D+LLt/Lx9959QGkpIO1wJ5WaAripsQFF+dlYkmSNUSm6sEliMDaBwbgEBu6JRvCO08XcaAOEswe1C2DOKjsEJg9H/oY4he8TAApgojYUwFqsTw4wJb85tkZmazhGr9+FSYIB8i1m3TZEiPwxlT8QQ9NkV3ztBQyeS5QtgdQvk0H/1QwGp8ui1zSdQf8MBkaZDAyyGAxYzcBRaAhh6qQnnn2xda1C9obvsT+IjyPBPFx08kJZMA+Hw0R4d88J5LSsZRi5qRyRm8rl6xq+u+cEDoeJ5FvbPyvZVYXi6msK/XckhBBCngXdrQPcNn5DPjyClwqOokaQ2vU5iBoCuKmxAXnrYyAUO2JisgEs02Tzj7gIWLK5SJL1YJsk+98zY/WRmTVZHsDCdEcEJFlh4zsRCt0nOQpgoiYUwFqsTw4wqVT2qWvr1vHT117qeCB8s6AE3sIB8u3NghJIvizHylh3OPFZGJEsm+XZrPWW51UPo9cwSxa9hlkM9LIZ6GfLAtkoi8GoRF28/VrgY8++2PZT6pcLjuJwmKjTAH77u7PIKDyOaa+XwPf1EmTukH2tswB+7HUNCSGEEC31yAffeRUQbz+O7J1VEG8/jui8CvkdU9sP/YoHkhyNCuCi/GwIxY6YlWiKOYlmmJisD0chC95xuvCO08X0hIFw5bPkERyUNIKuACtZnzw/1zAUwFqMBphidXYr1FtfHsCyyCHy7a0vD8hmgtxUhKUr+8GJz4IDT/bcr/kqBiMTZRNjGbTEr1GWLHr1s2VRPFjMwDBT9msnkSG+3JT+WPvW9jml1pjtKoBTv/gFU1/dh6mv7UNqwS/dBvBjPdNECCGEaLHu5szI/vInbH8jD2fEL6H5tdeB8HBAItGIAK67fRVr1szA7ERTxIudEZk6Bh6JRhiTwLQLYO84XXkE+yUMQkb2FHoGWIno/Fz9KIC1GA0wxepsMox3C8vwxfN28u3dwjJZGBdVgr3SEovCDDFWxMA2kcEEgWzyK4PsltudM2SbYcuvh6QxGJHCwpA02S3Rg8UMAkQjHmv2xbYzVfYUwJzNlfB5vQQ+r+0DZ3NljwHc46yWhBBCSB9Qf0+K8nO3262aUHH6Mu6LM2TLDk6bJtu6Wn5QxQH8/VfvgZduD/8kS+Tm+iEjewqmJwyCbRIDVz6rXQB7x+liTCIDj8R+iEwdS7NAKxGdn6sfBbAClJaWgmGYHreXXnpJ/prc3Nxu/6xYLO71ftEAU6zOlkN4f0clLjp5ybf3d1TKAzgizg3hK03hwZHF7dBU2dVeXcnDW50Ns2RXe03TW2aITmHBMpUFE7Hs6y7xRij69OUe963tWoU9BXB0XkVLAJfIY767AO5xXUNCCCGkr2pslAWvBgZw/oY4BCYPB2eVnfy25qCkEXARsOQR3DaAHYUsTEzWx5xEM1oHWIno/Fz9KIAV4PTp02Cz2Z1uYWFh8qjdv3+//DWtAezj49Pp6woKCnq9XzTAFKttZD5WAAs9ERTriHmhLIyNZ2CaJnvWV7flWd/+LcskDWmZLEu2RBILFqtkyyOZpjOwTdZBfNqkHvdN0VeA3/vqJxT8Ix8F/8jHB2s+guCTI3QFmBBCCGnVOufI3r1AWBgwfbrGBfDGdyIQkGQFYbqjPIAzs7wxM0ZfHsHjkvXgKGTBRcDC+HgGlmksTEw2gEjshLz1MU88IecToQAmakIBrGTffPMNGIbByJEj8eDBw6VkWgM4Ly9PaT+bBphiPekV4HCBB4LinOEfZoD54QYYukp2xdc4Qxa45qsYDEt+GL+yjQVT+brBLFilsrBcNKrHfVP0M8Dv76iU/3rX4ljkbKukZ4AJIYSQVnV1AJsti18nJ8DXV+MCuLMrwJJsH4RHDMTcKAN4c3XhnmiEcQmyZZFskhmMStHFkiRrFOVnKzd+AQpgojYUwEoWEhIChmGwevXqdl+nAH72dPYMcHcBHBTnhlCBK2bw+mNFSH9Ypchmgh6ySjYpVuvWNoCtUhmYiGXxOyZBF1arWAgU9hzAip4FujWA9wfxUegfg/e+PkGzQBNCCNF49fekOFJzq91zuuXnbiv+GHbnzsPbnm1sAB8fjQvgjs8AtwYwm20CNtsEoeyBCE+yxaxYfTwfqwcHIQv+iRb4z7b/p7B96NaT/t2VvNKHqtD5ufpRACtRfX09+vfvD4ZhcPLkyXa/RwH87OlsFuiuAliy7Ues4LohMt4N0xMHgRdhDQe+7LnfARmdB3Br/FqmsjAuXg/DU1iwSdJBXJLnY+2fItcBfn9HJfYH8bF9YQz2B/FR8tMfSv7XJYQQQp5edzM1Z+44gXXFZ1FcfQ3S5gc9f7PutEbY7t2Ai4vsyq+GBnDHWaA7BjCbbYKsDG+w2SZYHmkMH64ucrJ9lTfpVUdackX3SdH5ufpRACtRfn4+GIaBm5vbI7/XGsDh4eFITExEXFwcXnnlFRw9elRhP58GmOJ1XAe4swDO2VWFsPe/Q4TQE8JUL/glmmB1xiQEBBthyCoGehLZUkgWqxhYpsr+a5oui1+rVAajE3XhKDCAWRoDB6Eh/vV+xmPtW+tahS8VHEWhfwyKFkahxt4DpYEcFC/ngfvhQflahVvLL2BbxQX5uobcDw+ieDkPJUF8FC/nQbBhHwr9ZfFbHZOA5m++feY/cSWEEKKdHlmr95Ou1+otqLyIpqeNYKlU9swvmw0EBz8MXw0NYEC2DrBI7IRZLRHcWQAvjzTGVK4eAiONUfhRqkJ/frcogImaUAAr0QsvvACGYfD2228/8nvdzQK9bNky1NXV9frn0wBTvI4HWcGGfaix98A5B0/U2HtAsGGf7ArxF0ewSbgM32auBDvOEhKJL/hCR7hzWBi4umXN33TZs8Bm6bIQHpHMYHy8HhyFhhiWogPrFBZmxVpib0XVE+1fyU9/oCxchP3LODg7wR17/KOwewkHOdsq230C3vbT8pxtldi9hIOiAA52L+Hg5fxDKAsXoUaQisb01agVJOMUNxlVsUnYefg35dxORgghhDyFjh9Otz6m1HZrvQNKsqsKxdXXnu4HtZ3xuW34anAANzU2IG99DERiJ8xONMXCBHMERBohkG2MgEgjLIgfCh+uLgIjjREfZaW6q78ABTBRGwpgJbl69Sp0dXWhq6uLq1cffTPZsmUL3nrrLVRXV6O+vh61tbX47LPPMHz4cDAMg4CAgMf+Wa0DqeNmaGhIA0wJ2objy/mHcHaCO87YuePsBHe8nH8I64rPouSnP/BAkoPGLDFy2bbIlUxDXLInwpYPgSeHhSEtV33NVzEYnsRgdDwDO6Hs6u+wFBasU1jwihuAsPiQJ599ubER97MkuCRMwQ33yTgZKcIpbjIqTl/uNFrr70lRcfqyPHBPcZNR+UsNGjOzUSNIxZEQHkqXRuOw7wL86LMA76SvR/aXPynudjJCCCHkKXX2eFJXW07Lh9fris8++Ye4rVd/w8Jktz5PnfpMBDAgi+Ci/GysWTMD3FV2mBNjgFkx+pgTYwBO8liwI0yQGmuDHMk0NNbdUfjP7xIFMFETCmAlWbt2LRiGwdy5c5/odVeuXMGQIUPAMAx+/PHHx3oNBbB61N+TovKXGtxwn4zrbt644T4Zlb/UyA6qLW/qbQOYk+SBoFhHhK4YDJ8oHdgktix9lMRgZMs2PFn23K8PdzDCBPMQ+9EPT77+busBpfVT6q4OxJ29pmVrunUbJzlJ2B/Ex875bOyZF46aie648tx4HJs2H2+lvofwfx/s/e1khBBCSC90NkFld1t0XgUyd5x48pUNWq/+TpsG2NoCU6Y8MwHcqu72VewreAPxUdYQRloiPsoa/9myBjkZU+STZFEAKx8FsPpRACuJm5sbGIbBZ5999sSvXbVqFRiGQU5OTq/2gQaYCrTOAtm63Wk5cLS8qUuzMlC62AWl2WHYyF+ElXEuCI9zQ+RKCywJMsK0SF3Y8xlMEDBw4DOYFmuCJbEOEKTHIG3rEfC2HH2qK8C9DeDSsjPySbAOBHJQviIWFx088Je5NW48Nx7VMxdhc84HCPvXod7dTkYIIYT0QmdLFHa3ibcff/pja0sAP7CxwV1XTzRYDsMNZw80WA7DXfdJaPbx1egABoDGujvy2M3N9cOdq+fb/W8KYOWj83P1owBWglOnToFhGAwYMAANDQ1P/PoPPvgADMOAw+H0aj9ogKlADwHcNkJ/E8Qjgu+OoDg3sEVuiIxzQGSwFeaEMVi8UhcBK3WRtJqH1778ofefUvcigO9nSbBhZ6V8Eqwjwbx2AXzX3Bq1jh4oC+bh5YKjT387GSGEENJLW8svgLO5Etk7u7/9uXXL3lkFzubKp7q7qjkjE3+6e+OuxTD8MdYJt8ws8etYZ9wys8T58S6odfTAn+7eeJCRSQH8WDtDAUzUgwJYCTIyMsAwDCIiIp7q9a+//joYhkFycnKv9oMGmAo8QQDfFachJt4DK7huCBO4IjLeDWFCJ4xM0cEkYX94CwfgzYKS3j+n1MsArk1Iw8v5h7Brcax8PeF2ATzUquUqsD+2v/oxYj86/HShTgghhPSSqq4AN9U3oDpKhPMT3XHDzAq/jnLAn0Os8McEV/w5xApnxzjh9FgXnJ/ojuooEZolORTAPe4MBTBRDwpgBfvf//4HW1tbMAyD4uLip3q9t7c3GIbBp59+2qt9oQGmAk8QwI1ZYiSkeiNC6IllsU4IE7h2GsC9nqmylwF8ipuMpH/vR/FyXpcB3HoV+EgwD1mfVzzd7WSEEEJIL6nqGeCSn/7AgUAOTo11wZ/m1rho54K75ta4ZO+Ou+bWuDjRDecnuuP0WBccCOSgRpBKAdzjzlAAE/WgAFaw77//HgzDYNiwYXjwoPOJgW7evInNmzfj3r177b5eV1eHuLg4MAwDKyurp7p9ui0aYCrwBAEszcrAvsxQbBIuw5uRc7Gc44xlsRMxIkUHXoL+mCQYgOj1u9qtVfhUMyz3MoCrYpMQ/88SlATxHyuA13xx9OluJyOEEEJ6SRWzQNffk+K9r09g53w2zk90x18WwzoN4IsOHjg/0R0757NRFi5C/V8dlrSkAO6wMxTARD0ogBWMw+GAYRikpaV1+WfOnz8PhmEwaNAgeHt7Y/ny5ZgzZ4589ufBgwfj0KFDvd4XGmAq8AQB3Lo1S3JwmitETLwHgnkOGJGiAw+BMbwE/ZGx6dveLy9EV4AJIYT0IcpeB/hIzS3kbKtE0cIo1Dp6dBvAtY4eKFoYhX0reKg4fbn9N6IA7rAzFMBEPSiAFejevXswNTUFwzA4fvx4l3/uv//9L8RiMfz8/DB8+HAYGhrC2NgYDg4OSE1NxaVLlxSyPzTAVOApAhi5suWRsrN8wU91x8hUHXiLBmCKaCBKKn7u/WRSKngGuG0Acz88SM8AE0IIUZum5gcoqLwIScsV3ui8Coi3H0f2ziqItx9HdF5Fr+6uKjxWC9HHP6JkaexjBXDJ0ljsXsLBzsO/tf9GFMAddoYCmKgHBbAWowGmAr0I4FzJNIizvGGbqotpiYPgl2iCO1fP936flD0LdJsAPhDIQeQ/D9As0IQQQtSqqfkBiquvYV3xWWTuOAHeFtnjObwtR5G540Sv7q7aWn4B/I2HUBrI6TKAL0xwQ42dG86Od0XhPDY+mxuJN3Z2+FCbArjDzlAAE/WgANZiNMBUQAsDGLndrwPcGsCy55wi8VLBUVoHmBBCiEaovydF+bnbKDxWi63lF1B4rBbl5273/CGtVAqUlj7cpA//fHdXgGvt3XB7iCVOjXJE1SgnHB/lhLwZIfhwZjjC3y9tH94UwB12hgKYqAcFsBajAaYCTxnA0qwMlGaHYXfGMrjE62O6hgVw063bOMlJwv4gPnbOZ2PPvHCcm+CGO0Ot8KeZJW6aWcpnutx+6Nenf16ZEEII0QTdxFhXzwD/ZW6NX8c64/pgC/xiY49fnnNC1Whn5M0IwSdz2Ah6d3+7W6+b6hs0LoDrrteiNJct36QNdT1/E0Xp5kMHbUbn5+pHAazFaICpwFMGcOuv74gT4RdnCD8FBrC0oU52IMsOQ+liF0izMp44gHHnDpolOagRpOJICA8HAqLw63hX3DKzxC1TC/w51Aq1jh44x02EtL53s5UTQgghatdNiHY1C/TtIZaoHuWIqyYWOPmcI6rHOOPkaGd88nwoChZE462vfmk3+VbJT39oXAA33rzaJ6/CqhOdn6sfBbAWowGmAr0M4DpxMtih/cHmWoAdZ4m6672fSVl+cJNMQy7bFo1Z4qcKYPkzweIMXIpLwA3XSai3HIYGC2vcGzYczT6+sr8HHSwJIYQ863oI0Y7rAF8Y74IbppY4buOA64MtZLdAj3bGz885YdsL4fh6KRfv7jnRbvml974+gftZknY/Q/6htYquwFIAqx+dn6sfBbAWowGmAr0MYKk4DaXelij1d5Jdrb19s9e7pOgARlYWIBYD06YBNjbAyJGy/06b9mgA99HbmQghhDzjegjgpvoGVEeJcH6iO26YWeGUjT2uDbbALzYOuDbYAsdt7PGzrSyCdy+Mwo9hQnkAv/3dWUTnVSBnWyUuJaS3+xmPBKmSn8GlAFY/Oj9XPwpgLUYDTAV6GcAQiwFbW1lMtn19L7Qe3CQSX7DjLLE3O7jnT5UVFcB9dEILQgghz7iejl+NjWjOyMSf7t64azEMZ2wdcMXEXBbAJhY4aeuA6jHO+M3OFWXBPBwOE7ULYPH24xB9/CNOcZMpgPs4Oj9XPwpgLUYDTAU0OICzJD7wSzRBlsSn54MqBTAhhJC+rIdngMtPXcLp6Hhcd/FCndVw1Ix2xLXBFjg92gm3zCxxbpwLLrSsA3ykkwDO3lkF/sZDqIpNUmsAP3LL9e2bdNxWMTo/Vz8KYC1GA0wFKIApgAkhhDz7Ojl+tV1bOGdbJb5eFI2z411xa4gVztjKbn0+M8YJf5lb4+JEN1zsJoA15Qpwt8d7Om6rBJ2fqx8FsBajAaYCFMAUwIQQQp4N3c1T0XE5wPoGFFRehKRlAivuhwdRsjQW5ye648+h1jhlYy+/BfqWmWWPAawpzwBTAKsfnZ+rHwWwFqMBpgIUwN0HcF0dTYpFCCFE/aRSYO9egM2WbRJJt8evkp/+gKRlCaOcXVV4d88JHAnmydcBvjDeBdcHW+DYSNlkWL+Pde4ygFtngV635yd8lx3ebsZnCuC+h87P1Y8CWIvRAFMBDQvga1dq8fG/JOCEWyAq1AxLg/UhirZFlniyegKYDqyEEEI0QWPjw2Ny63G5i+PX/SwJ3vv6BEI3liFnVxXe/u7sIwHcug5w1XOOuDzIHCefc+z0GeC26wB/W3nmkdilAO576Pxc/TQygJuamlBVVYX9+/dj586d2L9/P6qqqtDU1KTuXXum0ABTAQ0J4Ib6OryzNhkxCZOwhPscno/Ug1+ULqZFMlgYZoCgkAF4+w0eGv9u6PwbPEYAN/v44p71cDRYWKPechhuuk7CJWEK6v+qe7zvQwdWQgghqtbYCKxbB7z5JjB79sPjbTcBXJuQhpxtlYjOq5DfwtxZAP9lbo1fxzrjqok5fh5pj5OjnXFughtKAzkoXs4D98ODCN1YBsmuKhRUXkTdX7fbxe6tWzfxQ9XvEKROBj/FG4LUyTh4sgb195R4txQdp9WOzs/VT2MC+MaNG3jzzTfh5+eHfv36QUdH55HN2NgYM2bMwD/+8Q/cuHFD3bus8WiAqYAGBHBDfR0kOUFYxh+LybyBmM4djPlhhvAPNcTsMAbTonUxOVYHgXGjIckJQkN9J8shdXNAbM7IxPloIWodPfDnECvcGGyO64MtUDXaCTvmsbH603Ls/uUypM0P6MBKCCFEs7Qep1vvYvLx6TGAT3GTIfr4R4i3H+82gO+aW6PW3g03TS1xwsYBp8Y449fxrtjjH4XdSzjI2VaJdcVnUVx9DdLmBw+XKcyZjoS0KVi7uxKZnx9CMM8dK3nuCOa5I/PzQ+1eo3B0nFY7Oj9XP7UH8K+//oqVK1fC0NAQLBYLLBYL5ubm8PX1xaJFixAWFgZ/f3/4+vpi6NCh8j9jaGiI4OBg/Pbbb+r+K2gsGmAqoAEB/M7aZCzjj4U3byACeeMQLXLH8lBjzI0wgG8Ug+ktAewoNMQS3ii8szb50W/SxQGxWZKD6igRvg+IwolRTrhqYo6rg8xx1cQCP9s64qPpwZi25mv4rz+INV+dxN936+jASgghRHM8RQBXxSaBv/EQsndW9RjAl+zdcWeoFc6OccIf9u646ToJJyNFOMVNRsXpy+2u5jbW3YEkZzr4Kd6IEHoibMNeRH+wD+ECD0QIPREu8ED0B/vaXTVuUnQEUwCrHZ2fq59aA1gkEsHAwAC6urqYPXs2Nm3ahHPnznX7mpqaGnz00UeYOXMmdHV1YWBgAJFIpKI9frbQAFMBNQfwtSu1iEmYhMkt8RsV7475PEt4cXXgyGdhTDyDMQkMxsUzsIvXh02yDhbwh+HShd/bf6MuDog1glSULuPgsxnBOP7cwwCWXQF2xtY54Xj+lW/hnPsfvPD2Abzy5TE0S3K6PrDevAkIhQ+3uk6uRhNCCCG9JZXKJl/cvRtwcQF8fZVyBfiSvTv+HGKF38Y644brpIfzY3QSk411d5CQNgURQk8s57ohe1MRcv4vFdEhQxEZMgTRIUOR+//SIPmsVP7ccHH1NcX+u1AAqx2dn6ufWgO4X79+SExMxOXLl5/q9ZcuXUJCQgKMjY0VvGfagQaYCqg5gDd//CqW8EZjepwpouLdMYs/FC4iI9gkMRidwMBewMCJz4KDgIUxSbowS2dgl6AP0SpPNDW2eR64kwPi/SwJysJF+HxOGLY+H4yfbR1xfbAFbgw2xw1TS1SPcUbhPDZC15fixXUH4LzmP1j29j6c5aV0fWA9f172923drl59yn94QgghpAt1dUBcHODlBbi5ySZv9PF57AB+3GeAWwP4ppklzo93wV3Pyd0G8K1bNxGT4IWgWBfEhFgjWuSBQN4ozIzSx4xoPcyM0kcgbxRiEiYhJYuL0H+VYl3xWcU+E0wBrHZ0fq5+ag3gqwo6+VXU99E2NMBUQM0BvOalUMyKM8eiOFvM51vDVWQE22QdOPNZ8OLqwJ3LwIurAy+uDrwF/WGXoIehaQymC01QlJ/98Bt1ckCsTUjDd8vjkD8zFPnTV6JqtDNumHYewCv+fRg+r+3DtDVfY29gHO5nSboOYBsbwNJSthUW0tJIhBBCFEcqlR1bLCyA/v2BgQOBESOeKIB7nAXafBjOj3HCLTNLnB7jhGuDLXBunAvuT/HpNoB/qPodETw3hK80w+JwI/gIBmEmzwwLwg2xKMwIC8INMZNnBl+BCYIE4xEVvwgZXxxB+bnbivv3oQBWOzo/Vz+1PwPcVk+3P5MnQwNMBdQcwJnZSzEjbggC4p7DZOFA2CbrwlVkJI/ejgHs0hLI4xP1sWbNDNTdvtp+f1sO/BU//459K3jImxOBj/2CsXlaEKp7COD57/6AqTl78OXCaFxKSO8+gAcOBIyMgBkzZDNz0gGXEEJIb0mlsrV+V6wAjI0BA4OnCmDkdr4O8OGVPPxm54rrZpaotpmIqyYW+GmkPa6aWODMaCfZZJHu3niQkdlpTH5x8CSiVlpiUZgRJnN0EdQyb0dQ6AD5Fi1yx0qBHXwEg7CMNxa8tBgUHqtV3L8RBbDa0fm5+mlUAFtaWuLYsWPq3g2tQQNMBTTkCrAfzxTO8UYYk6QHb0H/LgPYUWSIcYl6cEowBC/dHj8UrZfvb7MkBzWCVJSFi/By/iF8NjcSG6aH4p8+QfjYZwV+snXENZOuA9j/vYOY8dI3+GxuJE5xk3sOYF1d2UnJtGmd/r3r70lxpOYWCo/VYmv5BRQeq0X5udvKXR6CEELIs6t1rd8pU2Tx24sAbqpvQEHlRUh2VSF0YxliP/gB2+excXyUEy6bWODnEXa4YmKOquccccPUAmfHOOH0WBecn+iO6iiRbD6MDjGZt3s/lgcPwORYXSwOM0K0yL3TAI5O8MJKgR2m8gdhZZwH8vdVKvbfiAJYrej8XP00KoANDQ0xcOBAfPvttz3+2SNHjqhgj55tNMBUQEOeAbYXGWB8oj6c4g27DeDRibpwFhniBdFQBCYPR/6GOABAU30DTnKSsD+Ij0L/GAg27EPBgmj8a0YY/uUThI1Tl6PSxgFXBskmwbphatHpFeBZr3yLz+ZGoio26fECePhwwMlJNklJaSkglaKp+QGKq69hXfFZZO44Ad6Wo+BsrgRvy1Fk7jih3OUhCCGEPHs6rvXr7d3rAEZjY7vjUcy/v8fm50NxzMYRVwZboNpmIm6YWuL3cbL1gC9OdMNv9m7Y7DMG69gL8FniCkgb2k/0uO7tDCwMM8T0aL2HsdtFAEcneGEGzwyLuKPw3oaXFftvRQGsVnR+rn4aFcAHDx6EmaOH2/sAACAASURBVJkZ9PX1sWnTpk7/TFVVFRYtWgRdXV0V792zhwaYCmjILNBjE/Rgm6wDl3ijLgPYRWgIm2QdTBYOQEyqHQKSrLDxnQgAQMlPf2B/EB/bF8ZgfxAf7++oxN7AOHw8KwL/8glCnu8KHLNxwOVB5rgycCiuDX40gGe8uR8vvrYXBQuiH/8K8LBhgLk58PzzwIsvQrp7D74sOyf/xD36kwqItx9H9s4qiLcfR3RehXKXhyCEEPLs6bjUkZeXQgK41fW7jVj9aTk+nRWGU2OdcXOIFc6PccJfLZNg3W0J4F+d3JAYaIUgjgtiErxw69ZN+feou30VohQ3OPFZ8OCyMCNaD4t5IxAhcOwygBdwbDGHZ4F/vM5W3L8VBbDa0fm5+mlUAAPAmTNnMGrUKOjo6ODllx9+4vX7778jJCQEurq6YLFYGDFihBr38tlAA0wF6uoANvvh1rqsj4rXAZ7KHwTzNBbGJ+h3GsDOPAY2yTpwERkhIH44OKvs5FeA6+9J8d7XJ1DoL4vfw2EivL+jEodChdjyYiT+5bsSG32W4ydbR1wZZI7LA4fiqol5uwBetP4gfF8vwZxX/4Pvlsc93jPArQE8aJBshk5bW5yPEeKlgqPyZ65aZ99su+W0PJOllOUhCCGEPHuUHMBHam4hZ1slihZGdToLdNsATl5hjZVcV4QLPXDwZA2aGhtQlJ+NNWtmYHrCQFilMhiZxGBsPANnkSEmC/pjDlsfK0L6twvgCKEn/DmjMZs/FP9cG6a4fysKYLWj83P107gABoBr167B09MTOjo6iI6OBpfLhYGBAVgsFqytrfHuu+/i3r176t5NjUcDTAWkUtmtu61b64zGKgzghvo6cJLcYJegjyHpDEYn6sKez8CJz2AiX7Yckk0SAxehEV4QmiNb4gv/JEv5M8BHam4he2sZXgmdj/c5AXifE4B3C8twOEyE3Us4+NgvBP+eHIijNg64YiIL4Csm5jgxygmF89hY9vY++L5eghfWHYD/m9+hLFzU8yzQnQTwAxsbVARxEPnPA13Gb9sIDt1YpvjlIQghhGi01vkhdpSfR8k/t+H7DwpwZuNnaPadprQALjxWC9HHP6JkaexjBXAE3w3BPHd8XlKBvPUxEIodMTvRFK6JhrBJYjBOxMCez2B0kq585Qa/aD2sCOmPaJG7fJ3gAN5zWCiykj+upBAUwGpH5+fqp5EBDABXrlyBubk5dHR0oKOjA0tLS7z99ttopIH52GiAqZEKAxgArtf+hgDRcDyXrIsJ8XoYG89gTMvmyGfgxdHBYqE1siW+iBc7Y3aiqXwW6MJjteB9tB/hAg/5bVfrth/C4TARfgwT4osXwrHJdwXKR9rjcssV4MuDzPGzrSPyZ4Zi5ivf4oV1BzBr7QGs+aISNYLUrg+s3QTwPevh+NlnLt5KfQ8F/8jHum+ru43g6LwKZO44odjlIQghhGikjvNDJHz4PX70WYDDvgvwi+881Dq44093b/xv5EiFB/DW8gvgbzyE0kDOIwH8h4MbvnI1Rc6iYchcMhzLIs0QLnDDSp47/u8VDoRiR8xKNEW82BkRyaPgLGBhdAIDT64OPPnGcBbIotiJz8Jstj6CuM5YwXVDhNATs4VDEZc28eGElYpAAax2dH6ufhoXwHV1dfi///s/mJmZgcViQUdHBywWC4sXL6arvk+IBpgaqTiAAaAoPxuxqybANd4IU2J1MT1aD75RDBZEGiAkYgAk2T6IFztjVqIpRGIn+TrAW8svgPNhCSKEno8E8OEwEX5cGYcvZ4XgmI0jLg0yx6WBQ3FpkDmO2Thiy6wwzHn1P5i77ntk7zyB7Yd+xQNJzlMFcL3lMPw2xhFnnSbjnIcPDsSuwjt7jncZwOLtx8HbclSxy0MQQgjROE3ND9rPyPzxYeStfg9XnhuPy7bj8esYJ5wZ7YTzE91RbzkMDzw9VXYF+HdHV6xa0F/2+JGgPyYJ+yOU74LQWEcIkrwwuyV+c3P9IM7wgnecLmyTGLjwWfAW9sckQX848WR3anlydBDCs0dMghciE+3bfVitMBTAakfn5+qnUQH86quvYsiQIdDR0UG/fv2QkpKCS5cuYfny5WCxWJg6dSpu3bql7t18ZtAAUyM1BHBTYwPy1sdAsMoePlxdzIjVwwvhLCxj90NApBEWJphjdkv85q2PgfS+7CDX3RXgw2EiHAnm4ciKWPw63hXXBlvgSpsrwIXz2Mj8rPzhzMz1Dd0fWHsI4Jrn7PHfQWaoHzwEN54bjw1flnUZwNk7q8DZXImt5Rd68/8UIYQQDVdcfe2RNXnLV8TiL4th+MtiGC5NdMEfdq44PdYFfw61wh17F5U9A9xZAC/nOiMmbAQiEsbCP8kSubl+yM31gyTbB3OjDeAiYME2iYFnQj/4xA+AV5wORicwcBKwECSyhSDd6ZEPqxWGAljt6Pxc/TQqgFksFvT19cHlcnHp0qV2v5eUlAQWiwU7OzucP39ePTv4jKEBpkZqCGBAFsGFH6WCHWGCJWwjTI9iMDNGH3NiDMBdZYc1a2agKD9bHr+A7MCe+fkhBMW5dRnA5SticdHBA3+ZW+N6yzrAFxzccTo6HhWnLz98DrenA2sPAXzuuYn4u19/3Dc0wt/9B+JgeDy+fD2v09uh6QowIYRov/p7UqwrPovQjWXy+SE6C+Baezecn+iOG6aWuDTOAf/T11dYALdOFrlzPhvnJ7rjL4thODfBGXtczPDp82OwYqURJgmM4dUSwYEcJ0SHDMWSRGtwVtm1C+Bw9iDMjNWHi4CFUSm6GJeiB0chC+PjGdgkM3BNMur0w2qFoQBWOzo/Vz+NCuCQkBD8/vvvXf7+2rVroaOjAysrKxw9elSFe/ZsogGmRmoKYABorLuDnIwpSOOOwrJQffAjzREfZY19BW90ehtV/T0p1u6ulD9z1F0A3xlqhZuDLXDX3BrNPr49n0A84TPAF8Y4oMHIGFI9fUj19HFpgivKgnl4d88JegaYEEL6oCM1t5C54wSi8yrk7/9dBXCtowdumlnij9H2eKCnuAAGZMsFHgjk4NRYF/xpbo1T9o4IDjLCkkhT2At14SnoBy+BMTz4xggTuIITPhSLEy0hTHdsF8BstgnC2YMwN9oAfgmD4JHYD+NaJqu0SmUwPWFgpx9WKwwFsNrR+bn6aVQAP44vvvgChoaGGDhwoLp3RePRAFMjNQdwbq4fsiQ+8Es0QZbEB7m5fmis6/p7f1t5Rj7rZITQE299eUA+I/SGaH/8uCJa/sn6nSGW+NtquGyfFRjAD0aOxJXxjmgw7DmAaRZoQgjpGwqP1YK35SjE248/VgD/OcQK52wnolnBAdxU34DqKJHsWGhmhaPj7DA1Vh9eAmMMT2HBjWcED77sKjA3yQPxUVZYlvToFWA220S+iTO8wE4ehVkx+vDi6cBFwMLqDG/FPvPbEQWw2tH5ufo9cwEMAAcOHICpqam6d0Pj0QBTo2cogOtuX8Xeba+BE2YOdrAZwoOGgJvKAZvrhAihJyL4btgxPwSnx7rgzlAr1FtYy2bZVHAAw8YGdxxc0NivP+7r6qNJTx+X7FxQ/bw/tr/6sXxmaFoHmBBC+o5tP9bgrfQN2BOdjlJeBr58Iw/vffVT1wE81Ao1thMUHsBobERzRiZueEzCHtch2OhnAwehLjz4sgCewjGEf5gBloTogc82Rxh7IPwTLTAvYWiXASzJ9pF/7flYPSyN7Id9BW8o9x+UAljt6Pxc/Z7JAAaAU6dOqXsXNB4NMDWSSmXrAu/dC7DZgESicQHc1NiAovxsrFkzA9xVdpgTY4Dno/UwM0ofSzgjsTx4ACJXWiKE44y9S8JR6+iBv62G438jRshOIpQQwA88PXHfeACkevq4r6uH30bZ49x4F/zmPBlnXKZg24p4sDeUQrKrClvK/sCPv91E4bFabC2/gMJjtSg/d5uuCBNCiBbZ9cMZlE2di8u243F9tB2OrOTi/R2VKr8CjMZGICsLjX4+yFk8CEkhlhiZooNJ/H6YFcHAP4SFF8NZ8rk3ZsbowyOxH0an6GJhojkkOdO6DODlkcbw4eqCHWGCmxfPKPcflAJY7ej8XP3UGsCnT5/WqO+jbWiAaYC2BxoNCuDWGaOFYkfMTjTFwkRzBEQaIZBtjMWRRnhBaIYpHF0EhBuBEzoUp2NjZc/82tjIY1UZAQwvL/xv4EA06xtAqqePP8Y64vfRjrhlZolbQ6xwbqI71hdW4B//OYO1e88gc8cJ8LYcBWdzJXhbjiJzx4mHM1I3P+j1vyUhhBD1qvj5d5yb4IabQ6zwl8UwlK/gdBvAynoGGI2NkGZlYO8iB7BD+yOYY4ZRSQyWhuphZgQDLw4Dn2gGL4Qz8tUXPBP7YcQqHYxYpYPZiabIzPJ+JICFaQ6YytVDYKQxUmNtun1cSSEogNWOzs/VT60BrKuri5CQEFRVVT3V63/++WcEBQVBT09PwXumHWiAaQA1BLC0oQ6l/5+9Mw+rskwf/3POYT0HOCxnAwFXVGSTxRXTcsk01yw3QBbZkU1URLamZuY70zTj1EyzNTNN21ROZmnLzzG1psVMq3Eta1JzQ0BBBEEB+fz+eOEAiWYuYfJ8ruu9QsBzjqfrOc/9ee/7ue/SWDYWLSA2xUxx8ZhLBHj9M0Vk5AcyoXU+4bfvShcWjOCBOK2yKcdq+dei4dREjKTO7EWdyZNzZi9qIkZyIb/ghgswLi5gZ0eLnR1nQ8KoCAyjzuRJg7uBuoH+bPnVk5Su/YyoJ7eR8I+PyX95F0Xr9pD/8i4SnvqYqCe3UfzqHtbsOEKjlGCJRCL5cdLQAKtXc/4nD1Nt7kWFm4kqo+cVBfhmdYFu+3lDYT6FsT6MS7EnMkvHhFjBpBjBkHTB8ETB6MWCMQmC6fH2RMU6s6pwJBOz3awSPCzb0XqzuW084YQsV+6P05IZb6Gk+A4pwD0AGZ93P90qwA8++CDOzs6o1WpCQ0N59NFH2bFjB42NjV3+/vnz59m2bRs///nPCQwMRK1W4+zszEMPPfQDv/IfB3KB3QK0lUK3lUMXF990AW7b3BoK8ymN7U1p8R2dBLj2dBkPPngnE1vlt6tzSYUFyl3q+2O1jErSkDjPjWfG9uHVIDdOuhs55W7moH8oHy1MZfOnh9uzrTdQgLGzgxEjYNQo5ed6PfWWXrw7O57YJ961jsP49iXPCEskEsmPnKYm2LABQkIgMJBGnRPVHmYq3C38Z3ZClwJ8M+cAg3JzeWPRAqJTjIRk2nJnsh2RcQJznsBzqcC0TGDKE3jnCgIzVIxI0TAvx5tVxaO5N9tIv6UawrMdGb/YhgkdxhOWFI0hL9GXkm/t1TcNKcDdjozPu59uPwNcXl5OVlYWrq6uqFQq1Go19vb2DBo0iJEjRzJp0iRGjBiBn58fdnZ2qNVqVCoVrq6u5ObmUlFR0d3/hFsWucBuMbrKBneDAL/72uOkrhjC9Bxzl405omKdicnpzYTFtoxbbMOQdMEdcRqi7rNn/jwH1g51pcJg5gu/ENZNjeUna3a2Z1uvsLFeKCxm57ufUmf24oJWx0W1mvMmCy3OzlclwC0uLtQYPXltcjQPrdnZpfzKLtESiUTyI6e2FlJSYOhQcHKCXr1ocXamzuRJldGT1+6JJv2Jt9k6M44qoydVBk++7BfIF/2COOQfRp3Zi5aIiBsuwA211RQWR3JHtgt+mYI74gQeywX2hQJdgcBlpUCfL3BfoVymZYKIbEdm5lgoKhnDlGwDM7JNRC9yISPObB1PWHnkC+teLAW4ZyDj8+6nWwV4wIABrF69GoD6+nqefvppHnjgATw9PVGpVJdcnp6ezJ07l6effpoGuUC/E7nAbjF+YAFuKixg68wQthZFs7U0lqZztQA880QK9+f2umQ0Q8wiZ+6Jt2NEsoawbAf8MgX9swQ+OQLfbMGYOMHUhSrmzrXllTA3DgWF8c79ScQ+8W57trWLjbW5uISv0/PYFrOEX/zxLU65mzlnr6VZpeaMm5HzjjrqzV5KZ+krCHCTkzNVBguvT4nuci6wnBMskUgktwFHj4LJBFotqNXg6QkuLrR4e1Pv6c3H85J46Jn3eeveRVR6WDjlYeHwwGCODgmlKmxE+15ykwR47BIn7opW5FddLLArVOTXfYXAuEzgtkIRYeMygWGFICLHkflLfUnIG8T0JWaSYkykLR1Bet5I3tv7NadOVUoB7mHI+Lz76VYBVqlUxMfHW//84IMPsm3bNgAqKirYu3cvH3zwAXv37pWZ3mtALrBbjK7KoW+iAHcawdRhU3vyt4uYlWMhY0WgdcNdVTiC8YttCUlX0TtH4JdrQ0C6IDBN4LdEuZPdP1MwPkYwbYFg3jw7nhs/gPcXJPPQmp3t2dYztZ020sZTp9mblMOWeWmsnb6Ypb96lSoPCw0OigCf1huos9dS7WGmzuzFxYiIywrwBZ0zp9zNbJ0Zx+9e+ZitqQXW67ev77pEgPNf3kXqsztZ+8nR639PJRKJRHLzaWqCF15Q5NfGBoSwCjA+PtC7NxfylrPjv1/zxaI06iy9qLP0oiY0guZRo5W9tK2a6CYI8KpVI7h3oQrTUkV+1SUCTZHAtkjgsErgvFIRY0ueIsGmFQLzchWRS5yZk96X8SnuxMx3Z35qGAtSw1j1z/f59YYdZC0fRUnJWCnAPQQZn3c/3SrAWq2W+fPnW/+sUqlISEjoxld0eyEX2C1M2wbUDQLcVQZ4Xo63VX6HpqkYvURHRLKaiGQ1AekqBmQKhiUKwpMUCZ49X03mPAvvLkzksdd3W7OtH39+vNNGunXbF2yZl8bL0xazZV4af3lmM2eMnjQ46rioUnPW3US9o44KV5Nybisg5DsF+N3Z8fzxxfc5EhhBed9BlPcdxCsP/YnVb+3rJMBF6/aQ9PQOXtj+zfW/pxKJRCK5ebTdIN64EebMUT7/1eouBZj8fGWvbNs/e/dW9onIyGsW4LrzTWzff4z9ybnsScxhf3IuH39+vNMRmrOVx1kc44rHMoGqRCBKBKJU+VpTrAixpljgUKhkgS15AteVAvd8QWCmPXckuzI+2YO4BQYWZUQQkx5Owp/fJvqJjSzKiCBt6QiKS8ZKAe4ByPi8++lWAQ4ODsbb25szZ84Al2aEJdeHXGC3MN0owN8+A1xQNIqxWS5W+R2RomFURrsA98tSMsETFinyG54kmD5fkHm/wSrAbdnWdR9+1enM7xPrdrB2uiK/H0YvuUSAa9yN1DvoqHQ1UaY38XUff5p0TrR8Rwb4jy++z5GAcM4YPalz9WD/nffy8s//2kmCZQZYIpFIfiR03LdGjPjBBLix7hyb9p1k9aYDlLy4gw2zk1g/K4kNs5MoeXGHdaxefV0tKwoiMOcpoitKWwW49VKVKNngtsu+UMkEu+cLPFYIvJeqCci05/7UviTH+JKQNYyErGE8un4HxS9+wAPJoSzKiCBr+SgpwD0AGZ93P90qwL/85S9RqVQYjUYSEhJQqVTMmDHDKsSS60MusFuYbhTgb3eBjsvrT3i2A/2zBCNSNJ0EODBN6XDZP1MwMkEwKkEQnKKIcPRcR367eCq/2fCpNdv60n8OWDfRo1nLeeiZ93l1ZiIfRi+5RICbVWpOuRiotddy0sXIcRcje3sN5JyDliYbW5ptbWkZPrzLM8AdBbjBUUdFbz/2jZ/Oyz//m1WC5RlgiUQi+RHQ0ACPPAKTJ8PEie3yepMFuLlgFS+//yXFrU0Tk//yHpseSGXzvDQ2PZBK8l/eI+rJbRT9azsrC2fSb6lGkd8O0qsqaZdhdUlrWXRrabTjKoFxuVIK7bFcMDDbloQl4SSmhXQS4N9s+JTfxM/gJwum8kTSLM5U/cACXFvbfjxr61YlGy+5qcj4vPvpVgFuaWmhoKAAJycnawfotqt3797MnDmT0tJS1q1bx8GDB7vzpf4okQvsFqYbBRiUOcBL8oOYkO3GpGx3/HNtrWMbRqRoGJmhpW9W+8ZtWK6MdzAtU4S4V65gcpQgLiOER9fv6DIDvD85l5w/bWHTA6mXCHBbE6xyZw9q7bSc1Bsp05vY22sgdfZaGjW2NNrYUhkwlIsjR17SBfoXf9/SSYBrDBaOBobz0YJUHnt9t+wCLZFIJD8G2sYdBQWB2axIbnj4DyLAB5Oz+cmanSz8y0eUvLqHx17fbd2rPoxeYt1L4rKjCc5wwK7w0tJnVUnnTLC6tRxaVaKcC3ZbIXAqUK7IdBcKihOs8tsmwG3P++rMRN6em6ocJbqZfNe8Y8lNR8bn3U+3j0ECaGho4O2330alUtG3b1/CwsJwcHCwdn9uk2JXV1fGjh1LVlYWTz31VHe/7FseucBuYbpZgBsbzvHU7xazJD8I/1w7zMtV+GUKQtJVBGSoMC1X4bRSuYOtK1C6W+rzlU6XjquU8i6fHMGsaAd++dKmLs8A70nMIfMPm9ncWv7cJsCn3M3U2TnSpFJR6eJBnb2WClcjJ11N7PMeZM0AX9DYcHhAIFXB4ZfMAU791esc8g/rUoAfag1o5BxgiUQiucVpaFD2QV9f0Ot/MAFuvmMsHy1MJe4P71hnynclwL966W3Gp3igWylQdcj+itJvlUF3+LOqWLnaOkTbFQk881QsWjKUR15577ICvOmBVDbMTlJuJN/s91wKcLci4/Pu55YQ4DY6ngFubm5m9+7dPPPMM+Tl5TFhwgQMBkMnKZZcGbnAbmHaGn5s2AAhITB27A8qwKBI8Ppnipid40nfpRp8cwQDsgReS5XRDY6rBC75ivi6rhDoVygybFeo3OG2KRL4ZAtmJ/ch+g9bL+kC3VUG+Pd/30S5m4laO0drCXRHAd7fQYAbbWz5ss8Qjg4O4aK3N+j1tPj4sD8mlf/7+xY+HxBCpbuZegcd1R5mDg4OZf20eOL+8A7Fr+5hzY4jNDVfvP73UyKRSCQ3loYGWL1aKX2+6y7rTc4fSoBrho9my5wkkv/ynrVvRFcCnJg5Eu+lamtW1yrB3xbgLjLDqhKBTbHAaaUgMs2FR9a8zaPrd1xWgDfPS2P9rCTlKNHNfu+lAHcrMj7vfm4pAd66dSvvvffeFX/n6NGjbNiwgZ/+9Kc/0Kv68SIX2I+A6mpFUtuuH1CA23jrhYeZkW0iIEPF2CQbBmQJ3FpLn11a5ddxlVLOZQ0CWkc/qIuVEq95qUPY+NnhThtrV2eAS3+7gTK9kbO2jjSrVFQ4e1Brr6VCb6RMb+QLn0HUO+hosrGlycaWr/oO4fCAIM57einBka8vzctX8O47uzgaGE6Vh4VzDlpOuZn4cuBQtsxJ4vfrPuaL/J/Q/OivlQBLbu4SiURy69BW9hwSopQ+e3sr1w8owBVhI3ljRgKF//y4fXrAhk/5fdIs6/XIs+sJynTAYZWy36lK2s/3WgW4tF16O54Lbvt9myJBYIY9K4oW8Zt/H7iiAMsMcM9Bxufdzy0lwJIbi1xgPwJqayE2tv2qrb3+x/yeAlx7uoySojFEJmuYmKCcBXZvzfzq85VyZ3XJt+5qFwlsC9sDAssyFY//8gEaq0932QV689xU3rgvmbkrX+CYiyLATSoVJ53cOWvnyAlnA8ddjHzpO5gGx3YBPtw/kP/1C+Sc2dMqwOTnQ1kZzZFjOO/ZiwtaJ+pMnlQOHc6xjKXUHT56428qSCQSieT6aWt4NX48uLkpUtsNAlweOoLXp8fz4Es7rQL8bTlNyhyBZZkK2yKBY0H7qCOby0hwmwh33C89lgtmJfnx6Ju7upTs32z49Ic/A9xWgSabXnUbMj7vfqQA38bIBfYj4GZsRN9TgAHW/jWP++O0DMxU4ZmnjG1wKlDmGbZ1tbRpzQBrihX5dShsleBiJTs8KlvH+r+vvGQO8Oa5qTw9KZZn7o5lcs7THHPuLMA1to4cc/bguIuRA76DOgvwgEC+6htInelSAbYGOm2B0R13KP/WsjKlpDw4GPr3h5//HN5+W27yEolE0t1UVyuf1T4+YG/fLr+3QAa4owAnpoUwMdUD55XKXqhfoexzbc2tNFeQ4LbSaG2BYEKKO1G/23jFc8aPvb6bLfPSWDt9MdtilihHiSS3NTI+736kAN/GyAXWQ7kGAT5beZzMeAsjkzU4FbQ2ulqliK+quL30WV3cLsFtV1uzD5eVgvyC4dQW5FkFuPHUabbOT+OZu2P5w7goRYC/lQGusXPkeGsGWCmB1l5VBviKAtz2M71eCXoKC2WZl0QikXQnHTs+G42KnN4kAW4Oj+Bi6zi9C1od54wWasKGc9HH57JngDsKcHKMLyPSdbitUKYguK5QssBto45si1ozwcUdRiF1kF/7QkF4ipp1G9+m+NU9V+w0/dCanbw8bTFb5qXxdXqe3Kt6ADI+736kAN/GyAXWQ7kGAW6oraakKJJ5sTrMeQKHVcrm3lbGZZ1t2CEbbFvUfs5J1brhh2Y7sCV5klWA605W8mF0Bs9OjuP5e+KYsexZjjkbqLF1oEm0l0CfdFGaYLWNQbrSGeCOAnzRx4cmnRPnzJ6Uhwzj84RMdm7fT3PkmHY5DghQZks+8ojMBEskEkl30NQEGzfCggVgMilZ2ZsgwBfHjKHe0otjfgE0amxo1NhS76DltKuRQwNDqDF6Uh06jKYxd1zSBbpTCfRCAyFLHPDOVWNeprI2g7QvbC+F1nSojOqYDbYrFESkqFm62IezZ06zZseRK84ajvvDO2yZl8bepBwuFpdIAe4ByPi8+5ECfBsjF1gP5RoFuLR0HPkp/RmeokJX0HqHu/Vqa3hlW6SMdGi7NK3nodqE2LRCkBtrtgrwx5/9j01zU/nnPfG8NDWB+/Of55izsUsBLnczsc+7dQ7wZbpAtwlw47HjVIWNoMboSb2DjtPuJg4MHMobMxL42V83czQwnHpLL1pcXKBXLyXb0LevIsJvviklWCKR5ITf2gAAIABJREFUSH4I2o75bNwI0dEwerQiszdBgC+OHk3F0GFUGSx85TtYEWAbWxoctFS7mTjQP4gKNzOHBw+lPGwE/0vK6jQHuKMAxy30YFiGlkFZtljyVFjyVLjkK40hHVZ1roLqmAVWFwv6ZQrSY42UFN9BQ201jc0X2bTvJKs3HaDkxR1smJ3E+llJbJidRMmLO3j8jd18nZ6nyK9sStUjkPF59yMF+DZGLrAeynUIcEnBKGbEOeC6UhFa2w7dn78tv7YdzgQ7rlLKw5wKBJMXO/D/Ch5ga2ks/3r7M56/J46n747lbxMWcf/Kf3KitQt0mwDXtDbBKtMb+dxnELV2Who1Xc8BbusC/epbOznkH0alm5lzDlqqPcwc8g9j832JZP32TT4fEEKVwcIFnRMtXl5KsKXVKpmHBQtuTLMxiUQikVyepiblhuPkycrNx8BAGDnypglw1dBhHPIPUyS33xCaNDY02dhy3lFHjYeZI/6hVBksfNE/iIMBEfwvKYuX3//Smp1N+PPbxKSHsygjgrgFBu5MdmPIEnt8ctX45qqx5CkCrCtQzvfaF3Yug1aVCIx5gjkLbCgsHEVp6TgaatubMNadb+Ljz4+zPzmXPYk57E/O5ePPj3caHygFuGcg4/PuRwrwbYxcYD2UaxDgpnO1bC2NZWtpLL9O8KfvUo1S4tV6zklT3LX82hQLbIsFulUC/UrlGpWsIT+lP6Wl4yh9Zgt/m7CIJ8fH8M8p8aT+dK11DnDHM8DHWs8A7+k1kLN2jlxovXNfGTCUlpEjOwnwoYQM/u/vW9jfP4Rqg4UGRx01BgtHA8P5aEEqf3zxfWsQ1OCoo8FkaQ+2XFyUc2KyM7REIpHcXBoa2iXV11f5HB8x4oYIcN3JSo4lZ1Jn6UWdpRcVgaEcHBjC/tabn8f8AqwC3NBaAn2gfxCV7ma+8gtmn99QPlqYSvXpGjbtO8mv173PsuIcFs33IGa+O3MWaLkrxZ2gDHuCMxzwyVXTL0eDd67AnCdwWy6sDbKcWm8YG/IE984T3JHtQmFx5CUCbH1Pvi27cixRj0PG592PFODbGLnAeijXIMAdN+DGogLuy7LgtFJp5iFKFRG2/VbW16b1cmrN/OpXCnzz1IxI0ZAZ70lR8VjS//AWf7ozmqfvjmXNvQlWAa6zd6RZpabcWSmBPu5s4JizgV2eftTaOdKoUZqXtAwfrpztahXgiz4+bJ+XSOqjGzjkH8YZo2eXAnw0MJwqg4VzDjpqPEy0dBTgIUPgZz9TZgTLM8ESiURy42kbd3TXXe3jjm6AALf4+nJocQZPrNvBO7PiOeVhodLDwhd9A9ndO4D/9gnilLuZowOUM8AXNDbU2TtS7mJgl28AZXoTe/sG8lm/YF67N473Pz3A+meKKC4Zx6KsAUyIt+XOBBvuTLAhNNOB3rlq/DPtCF5iT+9cNX2yBX2yBD45Aq9cgXGZwGOZwLJUMDpeMCbJnjHZzlKAJVdExufdjxTg2xi5wHoo1ynAlJbyzadbCE5XoSlq72qp7iC+bc0/dK3i61wgcF0pCMt24M5EGzLizOTmjybl92/y1/ExPDVpUZcCfMrFg1p7LWUuRo67GNnt5UedvZaLtq3jK0aM6CTA5z178c6sOLJ++yZHAsKvKMBnjJ6cc9BR7WakSefULsC9eimNsUJClDNpshxaIpFIbixdjTu6TgFu8famztKLd2cnkPjYRl6fEkOVwZMqoydf9A3kU58hfNo7kJOuJj73GcgFtSLAtXaOVLgY2Ns7kGNuRv46og9/GtmP/Bl3kp49jfQVgUzMdmNatpFZcQ7cH6tlVpwDYZmOeOWp8MxTE5Bpx/B0HYFpKvpnCvpmCfpnCvyWCHxzBMMXC6bPVzMsXcvcRA82Fi1ga2ksTee+tb9IAZYg4/NbASnAtzFygfVQboAAN1SWkZvgjU9u+yiktkZXdkXK+SeXlQK3FYr8OhcI/JbaMCnLjUmL7ciM9yQ9bySpv3+T5+6J428TFnUqgW4XYAN19loqXI2U6U3s9vLjnIOWFruuBfic2Yu37o3h4b+8fVUCXO+oo8rVQKNW11mA20rp7rhDlkNLJBLJjeYmCHC92YsqoyevTY7mZ899wPa5iZwxeXHG5MWX/QLZ5RvA7r5B1pup59UaLmhsOGevpVJvZHe/AF4M1jMr2pXp0W4svN/A9MV9GLtET2Z+MMVFkcTG6q1XcnYoI1Od8cpT0StPRfASe+5I0DAsURCSIhicLhiSLpgYI7g7WjAsxZ5haTpyF3jSUJjf9b4rBViCjM9vBaQA38bIBdZDuUECXFIUycJFTpjz2s/9OhQqWV+Xlcr5J8dVivz2zdMwJdvAyCwdo5I1LIh1IinaSFpeCj+ZN56iufew/L67iSt9oUsBLtcbOeFiZG+vgTQ4tspqqwA3jxjJeU8vLuicOe1h4aXxC8h9/C2+uQoBbnDUcVpv4IIUYIlEIrm5tHV83rpVmfc7ZswNE+AWZ2dqDBYq3C38Z3YCv39lRycB/qp/ILs7CPBnngMuEeDP+g8hZ4ojw1K1jEp0ZM48LSNSnJifMYii4rGXCHBqdjjzUoZyZ6obfXI1BC+xZ1y8hsh4QWS8YFK04O4owYyFNvjmCMLTHBmWpiNnvhRgyZWR8Xn3IwX4BjFu3DiEEJe93nrrrS7/3tNPP82wYcPQ6XS4ubkxZcoUPvjggxvymuQC66HcAAFuOl3J1tJY3lgxmxnxjphazznpWztg6gqUry15goAcO8ZkOzMsS0uvZSoGZgrGJdowId6WGYk+zF3gRNx8M/clBDNjxVOU6Y3U2ikCXOniQa2dI2UuBsr0Jr7wGcQFrVKu3GJnR3VQKEcHh1DtYeaco45yVxP/uGMes4vXsq9/MKfdzdefAa6sbA/atm6VZ4IlEonkWui4j+TnKw0Hr1GAW+zsaFGraRGCOncjDY46TrmZqHS3sH1u0iUCfMgviL19Avi0d+AlAnza0YGH79SRd6+JO+JtCE11ZOoCW6ZG2TEmSU90eji5+aMvEeC0nAgWpIYRkx7O2DQ3JqR68ECUllkLNNwdLZi60IYBmYKIDC3eS9VMj9Mza5EbayYNpKmwQAqw5LLI+Lz7kQJ8g2gT4Dlz5hAbG3vJtXv37kv+Tm5uLkIIHB0dmTlzJpMnT8bGxgaNRsMrr7xy3a9JLrAeyg0QYKqrrV+vjR/FrFgH/NMFQ9IEgzOUKzRFcE+8LVOzPAjKscMtX0WfpWrGJGm4P1bLjFh77kxxZWSimpnRDiya70Hig09x0tVkFeAKZ+UMcIWrkZOuJmV0hc6JFjs7mm1sOTwgkAN9AjjlZqLe0YlT7maeG7eASctf5LPegZS7mjjnoP3+Z4A7CnBZGRQXQ2yscm3cKCVYIpFIrpaOs35jY5XP02sU4BZvb6r9g2iysaVZpeaiEJx2dqeutVfESTczG6fF8vjajzsJ8NHBIezvG8gnvoEcczGyy6tdgI87OzBqsQ2hKQ545QpCUh2YMU/DuFgNd8f3YlZCCLFLIigqHN1JgLOXDScmI5x5KaHcl9aXyalG4hd6MDxDh89SNaFpDnjnqRmWoSMwQ8Mfx/ryz7EDOD18xOX3XSnAEmR8fisgBfgG0SbAhw4duqrf37x5M0IIPDw8+PLLL63f//DDD7Gzs0Ov11NVVXVdr0kusB7KDRbgsytzyYg1ck+MiogkwYjFgrsWCe6JURGZpKF3nga3fEFQjj0zsk3ExDoTG6tnUawLCenBTF9oz4gkDTNjHFi1dB6nPSycs9fSrFJTpTdQ76Cjyt1MhZuZEwMDaXF2ptnWjkYbW77sPYTDfsHUGCw0aJ04Y/TklUlRTFv1L3b3DVKyyfZaTrubr74LdFcC3PZetb1fMgCRSCSS76apqV18o6Nh7FjlM/QKAtzi4kKTzolmG1vqjBbqjBbOWzxpcXGhzuTJN339adTY0KxScVEIqvUe1NlrOeFs4ITexL8mLmTJE2/zUQcBPuYfwv/8gvmsd6AyUaCDAB91smfUYhuGtgpwcKoDM+dpGBuv4Z5YX+6NC+KB5KGk5kSwKNbFKsCrVo1mcdYw5iaHMid1ABNTPYhb6HaJAA/P0BGZZMvHA/05GhhOc+QYKcCSKyLj8+5HCvAN4vsK8NSpUxFCsHr16kt+lpWVhRCCRx999Lpek1xgPZQbLMANhfmsWjmMOdF23B2lyG9kvGB0gsAvU9BrmYrh2VrmL/WlsHBUpzvoS3JCmbvQiekL7RmZqCExJZC1Ia5sHOjA5j4qqjyM1DvqqHA1UWWwUB0QQouzM002tlzQ2PDNgECODAqxCnCN0ZON0xYR/dNX+ay12+dZO0cqXU0cCbjKOcBXEuAxYyAsDFJSICNDdoiWSCSSy9Emv9HRSlf9MWOUz9TLCHCLtzfVQaGc1zrR4KClUWPDaVcjp1yNVLubOOeoo9LNxFc+g2iyseWiSimBrnE1cM5By0kXI2WuZp4dO595v3yTjdMWdRLgI0NC2dMvmGOtJdB1ajUb+6pZ42+Lf7qakBT71gywIzPna7gzzoZ7EnoxIyGYWYtDWJQ2lIUxztb9q7gokqzlo1iUEcHURF8mpRg6ZYDD0xy4M8GWlTM9efguJ77wD6YqbET7eyAFWHIZZHze/UgBvkF8HwFuaGjA3t4eIQRHjx695Of/+c9/EEIwbty463pNcoH1UG6wADcVFrCxYC7RyUbC09SMixPcHSO4N1rNqGQNo7J0FBSNorR0XKczVFGxzkRn9+auBFvGJtjgny4Yl+jCnAcEExepmBQt+NrgRp29lmoPM3VmL1oiImjSOdFoY0ujxoZjg4IvEeBtDywm57dvsadfMGV6I2ftHDmpN3Jg4FA235fIkt+8wZ5+QVS4mal31FFnMCtl1ba23y3Ao0Ypv2MygdkMa9fKcmiJRCLpioYG5bPzjjuUz9PIyMsKcEuvXkp21y+IOgcd5+wVAa52N1HlZuKUq5Gz9lpOuBj4XxcCXO+go1xvpMxVyQBPLnmNdXdHdxLgo0NC+d+gUE7ojWzr1Y+fjRZMjBaMjRX0yxBMmadmYpRgfIxgZIIgIE0QlGbHrMVDWJAaxtykIOZHOVmzwMVFkRSXjCVt6QjuSnVn2mJfYhd4EZGuw3upmmFpjuRO1bLLL4Bqg4Xy4HBaOt4EkAIsuQwyPu9+pADfINoEuKioiLS0NDIyMnjsscf45ptvLvndzz77DCEERqOxy8eqq6tDCIGbm9t1vSa5wHooN1iAKSykIT+Pwlgf7ki1wzdPhe8yNXOibJmUYMvivAGUlo6zCnDMImfuibdjRLKGsGwH/LIE/bOUWYm+OSpGxQsmxAj6ZAk+t7jR4Kij3uxFi48PDBvGBa0TjRpbGjW2HB0YxKH+QZxyU7IDp9zNbJ4Ry2+eeZevBg6lws1ErZ1yNmx3vyD+NXkRUQ+vY0+/oNbzwUoTrAYHLU0aGxp1TrR4eX23ADs7g4OD8r1HHpEBiUQikXyb7yHADSZPqjzMfO7r31mA3UyccTdT7W6i1l7HcWcDX3gPpFFj00mAGxx1VLgaOdEqwFMfXM+aCQs5bfDsJMBHAsI56Wpia9/eBKQKPHMFY2MEY+KUHhY+OQJznsCUpzRydFop6Jut4Z5UC3OTApm70Imo1ixwcVEkpaXjyFgRxLglrixeEk5M8hAi0rQEZGiYEePCy6FuHA4Mpd7Si5bRo5V/vxRgyXcg4/PuRwrwDeJyXaBtbW156KGHOv3ua6+9hhCC0NDQyz6eq6srQgjOnj17za9JLrAeyg0U4AuFxRxLz2XvohRenOjHvAUOBCzR4Jun5r6FNoxfbEvacn+rAK8qHMH4xbaEpKvonSPwy7UhMF1FcJrAb4nAtEzQP1NwV4wyO/HvYVpqtVrqzV5c9PbhbNBQ6h10XNDYcEFjw37fwez19eek3kitvY6TehMvjV9A4i838NXAoVQbLJxz0FLuamRv/2DWTY0l6uF1fO4XQpWHhQZHpQnWOXstF9Q2NLRmhFu8vb9bgNVqMBggKEgZ6SEzwRKJpKfTcdTRxo1QUPCdAtxiZ8dpNyNlLkb2+fhTa6+l1s6RC2obKlwMlOsNVFg/443s9fK7RIDPO+o47W7ipJtSAj3j4Q08f+cCKj0snQT4qyGhrAnSs+ReN9yXKfI7OF3g2jrBwG2FoFeOoG+mMtnAvlBgVyjwylNxZ4ob9y/QsiC6XYAz84OZkO3GkvwgXvzzUjKXD2f0EifGJNuRM8/MGR8vmkeNBl/f9n+/FGDJdyDj8+5HCvANori4mGeffZavv/6a+vp6Dhw4wM9+9jMcHR0RQvDb3/7W+rvPP/88QggiIyMv+3i9evVCCMGJEye+87nbFtK3L3t7e7nAeiI3QIAbT53m6/Q8tsUsYcucJN66dxH7BoawNtiVByfoGB9vx6K59pdkgOfleFvld2iaijuynBiWrCYiWU1Augq/LA3hiYKwJKUs7b65Kh6+w4aj7gYq3c0c7jeEOnst59U2nFfb8JnXQD71HsRJFyO1DjpOupp4btx8pq36F3v6BXPK3Uy9g3KGeP+AENZNjeMXf9/SPgdY60SNu4nzjjoaW+dBVrsZqTd7XZ0AOzsrgU1+vgxKJBJJz6Zjw6vYWEV+8/OvKMAt3t402dhy0sXAcWcDe1sFuM5eEeCTLgZOOHtw0sXA2daZ8Pt6+XFBY0PztwT4jMFCpYeFf01cyITCdTw1Zi7lbmaqjJ4c9gviQP8g/jswiKX3aglPsuXORQLfbIH9qtY59gXtEuyVq9yU9c1VoytQRNiwTDBqsZpZMQ7MinNgWpaRia3y+9TvFlN7uozi4jHEJpuIjdKx8d7BNPX2Uf7dUoAl3wMpwN2PFOCbzMaNGxFCoNfrqa+vB+C5555DCMGYMWMu+/e8vLykAEuujesU4ObiEl7ZvIct89JYO30x66fFs3VmHIf8w6jysHDUYGT5PToyZzgzI8aBe7OMlJaOo6BoFGOzXKzyOyJFw+gMHRGtAtwvSxC8xI5xsYJxiwShyYJJUcrXn3u4c8LFyBe+gy4R4E+8B1HmonR7rnAz8cqkKGJam2CVu5qotVcywHv6BfHO/UmdxiB1FOAmjZIBPuVioMZg4aKv79UJsI8PLFigBH5yTrBEIumJfLvh1dixiuR+hwDXm724oLFVJFdv5ECfIdQ5aK1VOZV6IyddDJQ5G6hpHXX0hffAVgFWdRLgGoOS7d04LZb7/+8Nnhk7n5NuZio9LPyvfxCHBoXwVXAoy6dpmTlf4JMl0BQL1MVKlte+9bIrUv7rtkLQL0dDvxwNzisFziuVCqU7EjRMWmxH8rJBPPjgnax/poimCw00natla1E0W6cHsXWEmabRI9vFVwqw5HsgBbj7kQL8AxAREYEQgi1btgCyBFpyk7lOAf46PY+fPvcBL09bzJZ5aXy0IJXtcxM5EqBIZbnZTP5UHRmzDMxd4MS4DD2Z+cHE5fUnPNuB/lmCESkahqeoGZGuJSJZTXCaCu9cQd8cNYMyBAMzlDvwwSmCKfMFTwU5sWaInj2+AzsJ8C7vQXzmPZgTrdmBk66KACf+cgN7+gVzwkVpglWuN/K5X8glc4C7FGC9gSoPM+e9vK9egCMjr+59lEgkktuRb5/3veOO7xTg5lGjqTFYuKCxpczZQPllBLhcb6DcxUCNndZ6BvhKArx9bhIpv/s3b0yJ4YzJizpLL46FDOXnc3z4xYI+PDBXxeAMgW2hQFXSLsAOqwTaAoFDqwTbFQn0KwWDsm3pm6vBuEwQkC6YG60jM96Tt9f8ktrTZZd/D0aNkgIsuSZkfN79SAH+AViwYAFCCJ5//nng6ptgubq6XtfzygXWQ7kOAb5QWMy2mCUkPraRLfPS+DB6ySUCfNpo5vUQd14Y68fyWf2YlzaA8dluTMp2xz/XlsAMlVWAh6dpCUwVuOQLdCsF2lXtd+BtiwSOqwR9MgXT5wnGRQl+N8xClb1DpwzwZ60Z4Bp7LWV6I2sntgvw8Q4CfHBw6FUJcLWrkVNuJuosvaQASyQSyZVoaIBHH1VGw4WFQWCgIntXIcA1YcOp8jBzQaOUQF8uA1yuN1CpV7pAH3c2sNdrwBUF+D+zE0h8bCPb5yUqlTy9e1N9xzDGZbkwIUVLQIrApkggSluvEoG6RPmeXaGy7+gK2iXYsFwwJNMOnxw1QWkqlsRZKC0dR0Nt9aXvhRRgyQ1AxufdjxTgH4B77rkHIQSvvfYaAPX19Vc1Bmns2LHX9bxygfVQrkOAj2Yt5+25qaQ/8TYfRi/pUoBrDBZqjJ4cDQxn3b0xLMmdQULuEPxz7TAvV+GXKQhJVxGYrqJPtgpdgSK7qhKlHM2muL0sTVUi0BQJPHMEYxcJ4qfrKHdsF+BPvQayw2sgx52V7MAJFyPPjZ3PzMKXlTnAemUOcLmrkUP+YVcnwG7XKcC1te1NYGRJtEQiuZ2prFQaAZpMoNUqY+SuUoArgiM45WaiUWNLud5AmcsVBNi1XYB3Wfp3eQa4xmChyujJa5Oj+elzH3AoIUN53lYBHp/kQECqsrdY5be0swirSlrPAxcqEmxTrPy3X7YG31w1QzJUZMSZpQBLbioyPu9+pADfZCoqKtDpdJfI7pQpUxBCsHr16kv+TlZWFkIIHnnkket6brnAeijXIcD7k3PZMDuJ0n+8d1UCvPm+RDL+tJlfPpLF7BxP+i7V4JsjGJAl8MtUuj7bdZDfjuIrStqDElEs0K8Q3HefuKIAH3Mx8o8x84h6eB37+gdT6Wa2ngH+wTLAHUdEyWBFIpHczpSVKXLn4gJ2dt9LgMuDwhUBtrGlUq90gf68t/9lBbjWQccJZwO7PftzQa1kgC8KQbXeg3oHHZVuJircLbw7O4FXNu/hwvJlbB1hZusIM2um9sUvo3Vv6Up+O1xtEuy4qv08sGmZoHeumpB0FZnxnlKAJTcVGZ93P1KAbwDbtm1jy5YttLS0dPr+oUOHiIyMRAjBjBkzOv1s06ZNCCHw8PDgyy+/tH7/ww8/xN7eHhcXF06fPn1dr0susB7KdQjwnsQc1s9K4uFnP7gqAd56fxJpT77PC9u/4a0XHmZGtomADBV3JdowZrEGfb4ivOpW+e0kvl3cnXdaKfjQXVxSAt0mwMddjLx41wJK/7yJbwLCqfKwUGevpdLNxBc/1BngNgEuLlY6ocrmWBKJ5HajbdzR2rVK9vcaBNiaAbax5bSbkXK9kT3eg6m1v4wA2ysC/Lm3H40aW5pVai4KwWlnd845aKnyMFNj8uLQ4gyaTp2mNj+X2Cgd8fPsGZImUF0u83sZCW47F2xbJHAuEPTO0zB+sQ35Kf2lAEtuKjI+736kAN8AnnrqKYQQeHp6Mm7cOObNm0dkZCQODg4IIQgICKC8vPySv5ednY0QAq1Wy8yZM5kyZQo2Njao1Wpefvnl635dcoH1UH7gDPCSv33A2k+OUnu6jJKiMUQma3ggTsuoRDWOq9qzv1cS345f98kU/GK44M1+anb08ms9A9wuwK9PieaPL77PkYBwKlvHIFW5m/l8QMjN6wLdlQC3BUITJ8LkyfDIIzJwkUgktwdt+0henvKZeA0C3HYGuNHGlhoPM6fcTHze25+z35oDfLL1Omuv5aTeyLH+Q2ixs6NFrZRA17kbadQ6cd7ipXxu5+fTdLqSDQVzCEvXMC5aOUpztfLbdrWdCbYpUppj9V2qIWqRMyUFo6QAS24qMj7vfqQA3wD2799PWloaYWFhGI1GbGxs0Ov1jBw5kl//+tfW8Udd8dRTTxEeHo5Wq0Wv1zN58mTee++9G/K65ALrofyAZ4DXT4un5MUdbD+oVCus/Wse98dpGZ1sg2+Ocr5KXdKhLO1qytOKBSPjBeOjBFt79+PTtiZYrWeA19+jCPAh/zAq3cycd9RRb/bkkH/YzZkDfCUBjoxUfm42K+fkNmyQmWCJRPLjpC3ru3WrUtlSXHxNAnwhv4BjKZmcbC2BvqBRMsBnDGYO9g+kzqHzHOAyZ6UL9Fl7LafdzTQNDVWeS60GIcDTU3l+Hx/lefLzaagsY8XKcCZGCXT5319+27LAbcdynFcKJma4kZfoa51rf7UC3DxqNOc9e1ERHEF5yDAqhw7nWMZSLhQWSwGWdImMz7sfKcC3MXKB9VBuchfoNgFWhDOWx9/YTd15RfrOVh4nM97C/XFaXPI7lDxfhfh2vGwLBWNiBP830sDHPgOtAtyWAf7F37ewv38I1QYLjTonWry9qRg6jC1zEol6eB27+wZR7mqizkHHab3BWm7X4KijzmCmxdv7xgqwiwsYjTB+vJIJfvttKcISieTHQ0OD8tk1ebJy5ecrn3FXEOALecs5lpxJxdDh1Fl6UREczvGgCD6Yn8I7s+L5akAw5Xoj5zU21jFIB/sH0uCoo8FBS6PGhlOuRir0ylXv6KTcnAwP/04BPnvsaxJj3LAs/f77y7crkGyLBEMy7MhZNo2iwjFXLcAXR46k3tKLYwFhVBksfDUgmAN+Q/ly4FC2zEliW8wSNn96mKbmi50fQwpwj0fG592PFODbGLnAeig3eQ5wjcFCtcHC/taS482fHm5/mNpqSooiyUv0xSf36hqSXO5yWaHMCH58mCffuHhQY69kgF+4awGpj27gkH8YdWYvWpydafH25nTYcP7fzASiHl7HZ72DWkckaSl39qDO3pFGjY0iy15e7YHUjRRgJycwGMDdHQYOhKQkpWO0RCKR3OpUV7dnNnv3VsT3MgLc4uNDVdgIts9L5J1Z8Xw5cCiVHhb29glkV98gnr4rin9NXMjBgSHWMUhlzgalw3OvQZ3OAFfoDVToDVS7m7igUz7Lr0aAX3oincB0FXaF1yG/pUr21ydXTXz2AxQ9u5U1S+eztTSWraWxNJ371ud3BwFu8fWlPDCUaoOFL/oHUelu5tB0L86iAAAgAElEQVTAEA75h3FwcCjrp8WzdvpifrJmJ2t2HKGxTYKlAEuQ8fmtgBTg2xi5wHoo1ynAzcUlvLJ5D1vmpbF2+mLWT4tn68w4DvmHUeVhodLNRKWbmUP+YeyLX0JT3bn2h6mttt49nxxvi22R6Nzt+fuUpxULfLMECdPsOOjmwdlWAV53dzR/eul9qsJG0OLjQ4uzM3Wm9ox0xurX+cIvhAo3M3UOWipc2gX4gvYmC7CTkxKwqVRgb6+UEMpgRiKRdDN155v46OtTrP3kKC9s/4a1nxxl+8HT1J2phdWr4ec/h7592z8bLyPALV5e1Jm9OOQfxmuTo3l9SgwHB4dS6W5hd+8AdvoG8vdxC/nXxIV82T+YMwYLTTa2VOiNnHA28JnXQGrsHDlr58h5tYZyF0WAazzMtLRJ7ncIcG1uBjMzjTgWfEdjxavI/vbNVrN8VRT5L+9iyd8+YH9y7uVFtIMA13t6c9hPmURwePBQaoyeHPEP5UhAOEcDw/loQSpb5qUR+8S7FL+6h037TrY/hhTgHo+Mz7sfKcC3MXKB9VCuU4ApLaXx1Gm+Ts9jW8wStsxJ4q17F3HAbyin3M1KJ06jJ1VhI7hYsKrT4zadq7XePV+dEIA+v3Ow8X2DE02RYGiSYLfJtbVBion/3BdP+YFDirz6+tKoc6Law8z+ASFsmZNI6Z82cWDgUCrdzZxzUMYeNTi0l0DXGy03T4B1OiVga7sGDZLngiUSSbfR2HyRTftOsnrTAVa9spvUZ3eS9PQOUp/dyapXdvPEuh1URYyiZfTozlnWywhwg9FClcHC/v4hvDs7nu1zE/kmIJxydzP/9Q1gb79gXro7hmfHzmdvn0BrF2hlDrCSAa6x69AES2+8qgxwk96ZrcOMbBzmwaw4R5xWXl+FkShVpg4sSh3LI2/8l6J1e0h78n32JOZ8pwA3R46hxuTFgT4BVBssHBsS1qUAfxi9hIfW7CTqyW2s3nRAOSokBViCjM9vBaQA38bIBdZDaWtksnGjMqanuPh7C3Cb5F0oLOZYxlK+WJRGecgw6sxeSidOH5/2Tpetj1t3vont+4+xPzmXPYk57ExIIjDL7rqDFE2RYFii4BU/FcdcjWyZGWvNAF/09uG8o846BmntlFiiHl7Hrj5BlOlN1NorGeBz9loa1UoTrBp3ExdvxhngrgTYy0s5SycDGolE8gPT2HyRNTuOUPzqHqKe3EbCPz4m/+VdFK3bQ/7Lu0h46mMSH9vIwYAIKoIj2jOwlxHgFjs7ajxMVLRWAG2fm8j2uYl8PSiUk25mdvkGsH+A8jn8r4kL+a/vEE7qjdYS6HK9kQN9hlBrr7VW5dR4mKlyN3HK1Ui9tuszwA29zDxylx1TYjVMjha4L7/2/hIdS5/vXKRh5i9fZcnzn3yvDHBNxEiqDJ582TeAGqPnFQX4sdd3k/DUx6x6ZbfSLFIKsAQZn98KSAG+jZELrIfzfTbVywiwVfTaOn36+ioBUlsX0MJCGuvOWTMMJS/uYMPsJNbPSmLD7CQyMu9FW3B9AixKlSYl4YmC4rvseWXKfOsZ4DMGC/UOOmW+ZL9g/nFXFDOL1rK7XxAnXRUBLnfxsGYb6uy1VLsaOe95g7tAX06APT1hwQI5K1gikfzgbNp3kuJX97DwLx9R8uoefvPvA/zm3wdY/dY+1vzqGdb86hmeXfV79vsN5fDgoTTqnK8owBdt7ah2M1LpbuZIQLhVgA/4DaXM1czePoFWAV53dzT/9R3CCWcD5zWtZ31dOwiwXbsAn/EwU+2uNC08Y7BQPSSIZhtbLqqUMUgnexkYs1jFpGhBr9z2sXrXXP5cohyvuT/Gj3EPvcbcP31I7N+2U/LiDo5lrfhOAa4cOpxTHhYODwi6KgHOf3kXqc/uZO0nR6UASwAZn98KSAG+jZELrIfzAwhwc8EqXn7/S2uGIfkv77HpgVQ2z0tj0wOpJP32Fe6OssHmGmY0XpIJLhaMihX8v7nzrV2gK9zM1NopsyM/6x3ES3fHkPjLDezrH0y5m4k6By2nXAzU2SvnzWrtWjPCJs8fToBHj4aFC9tnBcsO0RKJ5CZTd76J1ZsOEPXktk7y+5t/H+Cx13e3j7mbm8gh/zC+6B/Eea1Te3VMFwLcbGtLlauRKg9LJwH+wi+kSwHe5TuE460CXKk3dhLg2m8JcI2HmdrWm5kHfQfRqLGhTiP49UhB8QQHQhIE/TKVub2aYkV+1a0jjL6v/LotF0x/QMWcpCDG/3Q9k37zDtMe/w+Pv7FbGV30HQJcHjKMSg8Lh/2Cr0qAi9btIenpHbyw/RspwBJAxue3AlKAb2PkAuvhdJzp+F3Zx2sU4IPJ2fxkzU5rhqFjYPVh9BJWv/w+cUkhBKWqvn+g0sVlv0qQcr8Hv3vm/3HIP4wyvZGzdo6UuSgZ4LVTYrsU4LaOo7V2jpx09qDW+AMK8KhRyu+1PV+HsnGJRCK5GXz09SlWvaKU37aJ7+OvbOerURP434g7Oe3dl4/mJvLR3ESOBoZzYEAw9Y46zlu8rijAp10NVBksV50BbhPgchcDZS5G9voM5mwXAnza1UitvY4TzgY+9x5Ig60Nr/kJglMFgzNUjF0k0K9QqoF0Ba3ze0vaZ81frfy6LxNMmy8YnuLInKQg7v6/DYQ+9G8WPrlNmWhwJRGVGWDJDULG592PFODbGLnAJFfNNQhwc+QYPlqYStwf3rFmGL4twI+t3cbvk2bxq6jx+KerUN0ACe67RFC4IoojAeGU6Y3U2DpywsXAvv5XL8BnDJYuBbh5xEianJy4oNVxUa3mgqOO855eNI8afWMEODISJk5UMsGrV8tARyKR3BTWfnKU1Gd3kv/yLn7z7wP89vVdfLgglSaNDU1qDc1qDZ/MjLYK8KFBQznnoKOurTrmOzLA3wSEs3lGLG9OjWFvv2BOuJr4zHeI9XN43d3RfObjz7FWAS5z9uC4s4H/9hpEjZ2j9VhKlZvROgv4rL2WMhcj+/r48YtIFXfFCFzzBYNTBX2yFOl1WCVwXqmIr6p1hq/mKiRYVSzonSUYHyW4J8qJ6dFuLLvvLsY8uJ4xv9hM3pr/KhMNrkKA5RlgyfUi4/PuRwrwbYxcYJKr5hoEuCZiJFvmJJH8l/e6LK17b2EGhX/7D+tnJfHqzET+MnEG/TKvX4JVxYKxiXr2BgZw0tV0QwS4uWAVVRGjOOYfQoOjjnP2WppVaurtHanyMHMsIJSDydlcLC65ogC36HS0CGG96j2MnA2NUAS6d29Fhn18ICgIQkJkh2iJRHJTeGH7NyQ9vYOidXt47LVP+O/kOdTq3ayfTRdVKj6dHmUV4MODv1uA284An3Q1sa9/MGsmLOT5Oxfw396BHNeb2Ontz6e9A3luQjSvTIpip7c/x5wMnFfbcMLZgxPOnbtAn1drqHAxUOZs4KSLgVp7HSf1Rj7y60ufLIHbMuXYS0CqIrqiVJFem+LO54Bti1ozwV2JcInAtlAwIEMQGaPCP13N45E+PDmqP8/fHcXMRzcx+4n3WbPjyHeL6M3qAv19qrUktwUyPu9+pADfxsgFJrlqrkGAK4cO540ZCRT+8+NOAvxBVAZv3JfMmnsTmPuLN3h6Uiz/mBTL3yYsYv6iifTPUDo7X28p9MgEFV+66qmxdeS4s4E9/YKuqQS68dhx9sUv4WBABAf6BnDOQUu9g5aLKjUN9lqlw3T/IN65P4m9STk0njp9iQC3uLjQ6KjjgoNjJwGu1ntw2C+Yo0NCqff0pmXkSOX98/EBs7m9QZYMeCQSyQ1k7SdHSf/HR/z5wb/yatHj1Lm40aSxuawAX00GuMXOjtOuBk64GPnUN5Dnxs3npfEL2dNXyQDv9PHnY+8Anhy7gKfGzGWH92CrAJc5GzjRmgE+a6c0wbrQ+v3jTh6UuRiotddy3NXA4+MseOQKhi0WmJcK7DrOky+9dPyRqkQRYpui9sxwx71iaLLgzmjB0BQHRifasmPwEL4YFMam2Yks/tO7V87OduRmzQGW9DhkfN79SAG+jZELTHLVXIMAl4cM4/Xp8Tz40s72Bivrd/HazCT+eU88f5uwiKk/2cBz98Txz3vieXpSLOOzH2XiAoFPtrjm8RVtl7ZAEBkn+OlIwdd6d3b6BvDM+CgSf7H+ezXBevedXbxzfxL7/EI5PDCY8446Ghx1igA7aKkxWDg8eCjrpsaxZV4aW7d90UmAW7y9uaBzosHekXo7h04CfMbVwJf9AvmiXxBVRk8qA0OVOZc+PqDXt58tlkGQRNJjqDvfxEdfn2LtJ0d5Yfs3rP3kKNsPnlYyhDfoMX/1+h5+nfc4/xk9lf1jJ9PgoL2iAF/dGWA7TuvbBfhfExay7u5o5fPWXRmD9IlvIL8fPZc/jJjDx70GK2eA1TaccFJKoHd7D6bWXmu9KXnSxcAxnTtlzgbO2ms54mFk8WwngpMFjgWKzF5Nt+c2CdZ0aIylLhb0XyK4M0YQGasiZ4qJh+9y4n+BQzkSNIx37k8i7g/vXDk725EOAtzi60t5YCjVBgtf9A+i0t3MoYEhHPIP4+DgUNZPi2ft9MX8ZM1O1uw4QlPzxfbHkALc45HxefcjBfg2Ri4wyVVzgzLAOU99aJXff06JJ+43G1lzbwJr7k3guXvimFHwZwJSBOOiBM751yHArUGRS75g6nzBfg93dvgE8Mcx85m0/EV2973CGCS39jFIzZFj+NNL77NuaiwHAyI4Olgpga53UEqgz9k7csrNxMGBIWyZk8ja6Yt5Yt0OpVNoqwDXm71ocNRRZ+fIefvOGeCzbkaODR7K4UFDqXC3cHhgMA1mLynAEkkPpLH5onVk3KpXdpP67E6Snt5B6rM7WfXKblZvOsCmfSfbZek6HjPjT++wOWISX1r6cdSzDw32jpcV4KvpAt3i7EyTjS2n9AYq3Mzs6RfMM2Pn89y4+crnrZuZPX0C+LR3IH+InGcV4LYxSMedlBLofT7+1DlcKsBHXNx508+B50N0BCa3ljh3+Lzv6vO/49eaYqUU2rZIEV9VicB1uSAyVmmelXqvPdv7DqbczcTRIaEcDIhg3dQ4frJm59VnZzsIML17c3HkSOotvTgWEEaVwcJXA4I54DeULwcOZcucJLbFLGHzp4c7//+UAixBxue3AlKAb2PkApNcNTfgDPAv3vycqN9ttcrvmnsTOgnwUxMXMTP/KYrGaxm7SHBn1HWUQrdmBNQlAq9cwfK7bPjTyN78YexcJix7gU97Byodou21SslzBwE+426yBnk1ESP52V83s35aHEeChvF1/0DOtXYobVapqLV15KTeyN4+gaydEss/74nnwaffU2ZFFhbSPGo0NQYL5xx0NNg7cuEyAnx0SChVRk8O9A2kxmhRnr9NgAsK4M03laZYq1fLMUkSyW1IY/NF1uw4Yh0Zl/CPj8l/eRdF6/aQ//IuEp76mKgnt1H86h7W7DhC41VI8JUes/Qf77GnXzAn9CZOuhios3XoUoDfnR3P5wNCvnMOcJPOiUYbW07rDZwxevLVwKGsuzuaNRMWsqtPEGWuZnb3DlDEeHwUfxn9AJ/6+FOuN3JBY8tJFwNlLgb2+igZ4Dr7thJoD75ydqXoLkfuni8ISBGIq+wT0SbBqhKBfaHSHMtppSLDTisFo+IE2lUCwzLBX0Od2NHbnzK9if39gtg/MJR37k/i5fe/vPrs7LcEmFGjlIaQo0Zz3rMXFcERyoikocM5lrFUuVHa1WP8f/bOOzyqOm2gd1qmZWYymZqQQk8PXTrSm6IgHRJ6BMXOIlJd1y2uuquru65lFbChKAprWxYVUReFANKrCtISEkgI6fV8f9yZyUwy6cEA3z3Pcx9KQjLR/G7ec98mCfD/e6T4vOWRBPgGRjpgEvWmGaZAL3p3L+P+soXVw2Z4pNctwG+Pms2rQ5K5ffGbnA6ysj5aSY85AiEPNaIU2vW0X71cDHy0SwUGJwmMTjLx8PjBDHn4LfZExnPeZCPXS4CLZAquBGjJMFi4YnNSHi5msX/z/H/4fNxcjkZ15VBELLkBlQKcF6DlgsnGvsg41gyaztrhM5n0xCccTHlAnAba9SayLQ5RgDW6WgX4sj2U423jybY4xDJDtwAvWVL537ddu8op0VJgJCFxw7DlUDorNx7wrIzz3svrvla53u7TM9qAj/nsx/vYumApWxcs5etZD3ImtgsZwQ7SjVauKNWUyBWee1OZTMZ/B09g04gkTsZ0JSOxOxVGY40CXKILpEShItts47IthNNx3dg+YS5f3DaLYx06k2lxcrx9Ij9Fd2HTLbN4fcBk9kbEctFsp1Sp4pJZ3AN8JCLGswe4WK7krMnCa/F6uswS+30b2xojXynuCA5YLrbHxNwl0P4ugS4pAnPGyPnJbOaHiFjOGW0caZfAmcQe/Hzn/eLkZzeNFGD69q38tX//ynV3/j6GNPBKAik+vxaQBPgGRjpgEvWmGfYAT3/lO0b+aTNvjpzlI8Ci/M5gzbCZjF/yFmkmGxe1ap7uJXDnMPFJfWME2D0FVHBlgQcmK7l1dhx9H1zNrvA4zhltXAnQcT4wmCsqUYBzArScDwwm3Wgj0+LkZExXHnj2UzbdMov97TqzLzyGPFd2wi3AGUFixuDd4cm8MjiZEas28eXku8R9kInduWS2U6CtnwCf6pDApWC7OGimqgD36QM6HQQFQZs2sHGjFBxJSNwA5BWV8syWY0x/5bsa5ddbgn2mBtfzY/5t0272DbuDAoOJAoOJjPA2nIvuxGV7KBeDbOR6CXC5IFAmyPjfyCnsmDyPrK49qejTR+z1rUGAi/0IsHsP8Om4bly2h3Imtgtn4rvx8ZjZvHHzFH4IjyXTJcA5FgeXrU5OtY8Xh225MsCnzBbuHCoj8t6mz4XQLhMwLRHld+I4GUljBT5uLydHoyXTZOVwm3jSg+ycjulCWf8B1dtPfg0BlpBAis+vBSQBvoGRDphEvWmkAJctXcb73x5n5cYDDHl6K71XfczaYWKp8JsjZzH6t//2lES/OXIWk5auIz3I7hJMOQcsRoZNFQhc0rTgR7FC3PF4+2QNA+7/OzvCYjljsHqE1y3AV1x/Pmuwcs5kZ3+bBKY89gFvD0tiT5tEDkXGkl+DAG8YNZO1w2cyYOkH/HtsCsVLlpKR0I2LLgEuUGsprDIE64rZ6ivAHRO5aK5BgHv3hoAAkMtBpZLWJElI3CB8/9NFln0g7oOtTX7dl8/e2Hp8zGc/3sfXSfdQoNVTLgiUy+TkBNs4F5XIZXsoOVYH+SoNJXLfEujzyXMpXrRYvLf37VurAPvLANckwFvGzeOtgVPZEx7jyQDnWBzkWJ2ci0r0CHCRXMEps4V+yY28/6+qvOQrBeyLBAYlCdwyVeBvPR38t42cfKVCvI8brRyIjONCkJ2MxO5w882SAEu0GFJ83vJIAnwDIx0wiXrTSAFm+XJK8vLZciidO19PZfDjn/HqkGTWDJvJ2mFiufD6W+bwyR13svG2eUx8RBTg3AAtpTIZPwYFMeV2gaHTBayLmibBspXisJPu87R8Fd7BR4DdOyfdAnzOYOWs0UZqeByjlrzLK/2n8kPbRI60jqtVgFcPncGwlRvZdPs8zt79EBmJ3cgIEkut81Qa8lW+AnzJaOGndgmcrk8G2C3AgiBeWi1MmlTnmqSrMVFWQkKi+diw+wwL3tjFkvf31UuAl7y/jwVv7GLD7jN1fszlb+/g61kPkm0Locwjt9UFuCBAS6lLgBEE8UHbwoWee3tZ7z6UBhrIs4eQ52zFsekpYh/r/Q/67QGuTYD/N3k+b7oywFUF+Od28eSqdWRq1DzZU+DOkeL6okbf911DsExLBAYlC4yZoqTPbDnb27alWK6kWKEkT60l3Whld7jYA3wmtgvlA6QMsETLIcXnLY8kwDcw0gGTqDdNEGD3D/ivjl5gwcvf8OaIWWy8fR7/HpvC8te+5tvpC9medA+bbp/HmEVviKXJKi2lgoyzBjOb2qtY1V/DguEC5sU1DzqpbyYgYLlA/AKBlf0D+FNfFadMZo8Ai3uAgzlvFAV4V0Qcfe5/kxf6TuaHtokcjIj19KdVCrDNUwL96pAZTPjTJ/x7bAqHZt/D6ZgupJvEUutclYb8KhngjMBgDkfGcrxdQq09wMWLFpPTuTtlSlVlhkappCw6GpKS/Erw1ZgoKyEh0fys2/ELKWtTWfFh7eXP7mvFhwdIWZvKuh2/1Pgx3/nfT/z1N8+xc+g4cs1WSrzvHX4EuFCt9WSAvQW4bPHDZHXtydm4rhRo9Vw028m0ONk8chpfjk9h54RZlOgDfaZAZ1mdtQrwVxNSeGfwVA62jicjyEaJVwn0sdaxZGm0rItRcOsUAeeDTSh7dslvwAqB+PkCC4ebeXCkg98O1LMnor1HgPPVOjKMVn4Ij+W8ycbJqM5kde8tCbBEiyHF5y2PJMA3MNIBk6g3zSDAeUWlPPfJfjaMmcuXk+9ie9I9/P2DVLYn3cP/khby7ujZjHxgLWcNVo8AXzAEcyVAyzmDlRNBFpJulaF7pDKj615r4SPBNQixZ1/ko2JG4aY5AgOSBY5aqgtwmlEsgd4ZHkev+97gH30msyMinh/CorkSoPW8visqDWlGK/si4lgzcBpvj5rNgue38O+xKXw1IYWfO3bivNFaKcBVMsAXjcHsD48RA8FgJ4cixYxIrs1Jsd7A5a43cWLW3eyYPI9THRIpUSjFEkZBoFSuICfYRn5oOOVdu8L8+R4RvhoTZSUkJK4OzZ4BLixk390Pk2YPo1gVQJkgo1yQ1SrA/jLAZXffzeHkBZ41SPkaPVnBDrJsIWy7NYl/3zqbj4ZOpUCrp1gXSJlKLIHOMDs4GdPVrwCfjOnKh6NnsW3sbE5FdSbb4qBYoeJikI1Ms53dkVH8rr+SO8YJdFjY9L5f2SpxeNaYSTK+aNuBVNf8h/2tOlAkV/hkgA+2jifT7OCoawhW8ZKlkgBLtAhSfN7ySAJ8AyMdMIl60wwCDPDFnlN8Ofku3r9VlGC3AH9yx528NXIWw+5fUynAMhkZRgt5ah1pRhs/ma0k3xZI/HwxiytzZXMDVtQdJMlWiX3ASq/31T8iTodeMiiAjzqoyFPI/Qvw/W/wfJ9JfB8ez+5WUdUE+KzByq6wWNYMms7G2+excvXXbLp9Hu+OSGZfRBxpLgHOUarJU6mrlECLGeDd4bGcNdk5EBFLRpCdTLOdfK2eI20TeG/oNN4ZPJXjbeMo8VpTUiJXkGmwUKjRU6rRUmEywaBB8OmnfL7vbLNPlJWQkLg6NGsPcGEhPP44xRYr5V73mroEOD+gcg2SW4B/mTrbZw1SkS6Qy1Ynl+2h7Bg/i++nLuDr25LJU+so1OopU6nItzrIsjo50r4TH49KZuvtszgZ05UsawjH2iVypH0nvpqQwuEZd1HWuw8FjlBKlSqyg+1cMNn4tm17Bk0WCL+/CWvwvC7tUoFecwS6pgTwRZtKAd4b0p4imYIiuZJcVw/w8XYJXLaFcKx9Ij/FduPswockAZZoEaT4vOWRBPgGRjpgEvWmmQS4JC+fgykP8OXku9gwZi53/+NzNk+Yz9sjZ/PyoGRGPfg6Zw1WclQaUYANFnIDdKSbbJwJsvFsbyed5ojBkWqFuOe3zgyBawBKwArxck+Hlq8UaHOvwO2TBBYPVXBZ5V+Ab7r3Df7eZzI7IhLYFx5DbhUBPm+wsjs8ltcHT+eTO+5kwd+38OaIWawZOI094bGkG8Ue4CtKDblVBPhCoJkfwqJJDYvhrNHG/vBYsiwOsiwO8jR69kbE8a++E1k3aCon2sb77OksVSjJDrKSr9ZRqlBSLpeDWk1Zu3bsHTWR2c993mwTZSUkJK4ezTIFurRU3BH+xz9CRAQVCoXPvaY2Ac4OtpOv8hXgCrmcPbdN96xBOhvb1a8A7xw/iwKtXrwPKVWUh4RS4GwlljqPnc1nt8zgWIfOXLQ4ORnVmTPx3fj5zvspX/ywKITh4VQEBFDkDCHDYufvvUOIW+A1xb8J8qtYIa45GjhN4IFRNrZHRrMnMt6vAF8wWvklujOXbSGcjOrMseiuHJlzryTAEi2CFJ+3PJIA38BIB0yi3lTdTZib2ygBprCQspWr+OnuRXyXfA+/e/1b1t8yh1eHJPPSwCTuWPKWTw9wWmAwOa4S6HNGGzvD2vG7/gomjBWIulvM4ipW1iG/qwSULgH2SLPrbe7esFsnCfyhj8BHHVScNZpJM1o56xLgHve+zgt9J5MamcChiFjyvHqAc1Va0k02DraOZ82g6bw9ajZjf/8Rrw6Zwcv9p7I/Mt4zBMufAKfpg9gVGkVqqxjOmeycaBtPjtXJZavTI8DvDJ7K6wOmcCgy1icDXKpQctlso1Cjc5VGiwFuuUpFlsXBfc9+2mwTZSUkJK4uTdoDXFgo7gYfOhRat4bAQJB5CW8tApxlCyEzyOaTAXZPgf5mxGQ+HpXEmfhutQpwoVZPvkZHiVJFkcPp2QN/dv59HJ1xFxc69SDP2YqcbjdR1rdf5c8MlwCjVlMa3or3uhroPVNA3gyZX2GVQMKdAg8NDeChkTp2to7iQGQcP7ROqCbAVwK0pBktHG4dz8VgByejOnM0qisHZ90jCbBEiyDF5y2PJMA3MNIBk2g03oFAAwXY/e+Kl68kde9PfD5pgZgxHTaTSY+s47zJ5imBTg8MJkel5azBylmDlf2hHchWa9jUXmDm7QIjpwsYl3j1AHv9KnPJr8LVKyxf6Wdg1iqxRC7qboHh0wQGTRN4M17PaZOFs0ZXBvi+N1xToDvVugd4zaDpvDwomVt/9xGvDE5mzcDpHGwTT7pr3/AVpaZaCXSaPojU0Ch2h4kCfNwlwJeCHeRq9OyLjOPD4Um8N2Qa+8JjKJZXF+AirZ4ShZIytwArFORp9GyedBfvPbGaZ/QjfPsAACAASURBVD471OSJshISEleXan37q2vv2/cMrysshMceg+Bg0GjESfF6vY8AVwgCZS4RdgtwdpCVE23iSDc7yDDZyPNag+TeA7yhz1g2jUjiTFzdAlyo0VOiUJFvc1Te/90T7N1C6BZALwEujQhjawcVG3sY6JzSfPLb9h4Zy27px4Z4M+/FBbErIpq9EbHsiYznrNHGvtD2FMkrBfi8wcKe8BjSg+wcaZvAsairlAEeMKBycOHWrdIaOwm/SPF5yyMJ8A2MdMAkGk0zCLC7lPrAvAdYN2o2rw+fybiH3/LZA5xpFEug04xWzptsHGjVkdwAHflKBZvbyXhmdDB95ogS6y3AMleJs3KlnyFZfqaEqlYItHpAoN8MgTvuEDhmDuasyc6OsDh63/8mbw1N4kjHLhyKjCU3wHcK9AWTjX0Rcbx68zSPAL8xYhZvDE7y6QEWBdh3CFa63ixmgMNiOGuyczgyjhyrk0yznVy1noOt4/lweBIfDk9if4QowOV+BLjUW4BlckrkCi5ZHFwMjeREz4F8Ne83PPux/wE79ZkoKyEhcfVp8OT20lJxF3h0NMhkYu+uTOYRYKqUQLvvHWUyGVkmK8dax5JudnDBaPXJALsF+O0eY3h74FSOdRB3ldcqwFpRgPOs9Rfgoj692djdzMjJAm3uE+/ZTZbfRwU0SwWGP/Bn3h08jXSzg/MmO3vDYtgVFsOuCLEH+IDXEKxclwDvjRCnQO+NiONwxy5XpwfY335hCYkqSPF5yyMJ8A2MdMAkGk0zCvD+ufezdthMXh6UzJxH13PBXCnAF41W8tQ6MoJsXDDbORohDqEqVigpU6oo7N2D30wyE3mfOBXaLbSKFZU9v/UJquQrxcu4RKDfTIED1iCXAMcy5Dfr+OS22ZxO6MFP7eLJ9yqBdvcA742I440h011rkD5m423zeHtoEnvCYz1ToK+o6hBgo52DEbFc9hbgNpUCfCgitkECXBigoVyQUSZXUBBoZNPSZ/xmg6UMsITEtUVeUSk7fr5U++7u0lIxizh1KlitlfvBqwiw+6qQ+ZZAXzbb+LFtHBnBTrKD7RSqtT4l0GWCjPd6386afpM50DaRHzt0arYMcNnSZZycu5AT8Z24Z7SKhDtd9+9mkF/1coHx4/X0X/YO64eIApwWZOeHsBhSw2LYHRHvephaXYD3RcSSHmRnd3gshzp0Ju83SyQBlmgRpPi85ZEE+AZGOmASjaYZBXjP7PtYO3wmLw1MYsHvN9QqwMcjon0EuLTXTXx0a0dGTBMwPVwpwMoVlT2/te4J9rM+SbNMIGWkwLpYA99FxDJh1Qa2T53P6YQenInuRIHGvwC/Png6Lw9KYuSjm/jvxPm8PTSJXWGxnDNYxR5gPwKc5iXA50yiAGcFO/xmgA9F1k+AK+SiAOcrA3x6AE9EJfLuYy9Wk2CpB1hC4jqjas+vXl+nAHv/uUIu50qwjeOtY8myhXj2APsIsEzGpn7jeL3/ZH5oncCRtgkUNqAHuCYBLu/Xj0Oz7+GLcbN4sU84/ZKbZ9qzsEog8BGBm5MFRs/oQP9l7/Du4GmkBdlJC7KzN/wayABPnQozZ/rd2y4h4Y0Un7c8kgDfwEgHTKLRNGcGeN4DrB3euAwwPXtS2Lcnvx+mpftccS2SOxhSrPQaeNXAS7lCzAQ/OMLCgqc/5LupCzid0IMTbePIU+u4UqUE+kDreP41YCov3DydQcs/YP0tc3h3eDK7w0UBrikD7O4B3hUew/kgcQ3SRbO9Wg9wXRngEj8Z4DwvAa4QBLK1BrZ1G8LzS/7OXz49KE2BlpC4XsnOrrzfGo2NEmB3D7B7DVJVAS6Xyfjk5vG83n8KP7RO4GCbeAq0+rqnQIeG+hXg8ogIcrrexKnYrnwwaiYvDxrLHePFB47NkfkNWiwwbLo4+Oq+sX0ZumoDr/efzPkgO2lBDvZHxNajBzjW0wN8tDl7gPv1g06dxHJ1qe9Xoh5I8XnLIwnwDYx0wCQajfdU6M2bYenSq9ID7C3A6UF2Drp6gL0FmN69uRTqZMkggfgFrl2/VbO7jbhUywW6zhOY89vn+WpCCseiu7I/IlbcAxzgPQTLxsE24hToNcNmMnDZB/xryAzWDUviB+8S6BqGYO0KjeKHCLEXb79LgL2nQL83dFqtPcDVpkDLZBTLqgtwrlLNj/ZIvug+jL8seo5H3/9B2gMsIXG9kJsLCxeK19y50KdPowW4XCYny2TlVPv4WgV467BJrB8yjT2R8eyLjCNfU12AffcAB0CrVj4CXLb4YbK69iTHHsrPHTuxr00CL/abyIxxQRiWNI/86pYKDJ8i8MigAB69Wc9LA+5g9G//zb/6TiQtyOG5tx5sHce+NgmcN9nY78oA/ypToPv3F0ufs7N/tW8XiesbKT5veSQBvoGRDphEs+D9Q78RAnz4zgf5aGwK62+Zw+xH13PeZHOVGLuGYKkrh2AdjYgiT62jRKHyEeDLDiefddSwoZOBfnOUBC519f42UYKVKwT6pASyZvAUdrVOYHcrsQTbZw+w0coP4bG8MzyZj8amMOXPn/LCzdNZO3A6+yLjfPYAVxXgdL2Z3a3E9RzpZocnA3zZ6iRfK/YAvzFgCusGTfU7BdpnD7BLgMtkMkrlCgqqfK48pZp0o5UzZic72nXl5THzeWx9qu9EWQkJiWsL937fxx4DsxnsdggLE+99TRDgSyYrv3RIqFWAd4+ZxiejktjXJoE94bHkqnVkBTvIsoWw7dYk/n3rbD4aOpUCrZ5iXSAVAb4CXLb4YQ4nL+BkTFcygp3sbxvHCzeFM3aylqCHm35/FlaJ8jt4qsCk8XKOm4M5Y7TxSp+JjFi1iXWDppIW5CAjWLy3Hmgdx+H2nbgQZOdweEePAOcGaMk02fglukvz7gHu0wcSEsSpzzNnig8xJCTqgRSftzySAN/ASAdMolloogCfuW8xn09awMbb57Hi2Y/EEmiXAGcYxCnQF0xiCfTJNrGeXrNyVaUA5ztCyNfqybI4+fqOJCbcGUG7e8U+4KYGWYoVAuPG6/gmPJZdoVHVBPiswcqe8FjWDUvm22kL+c3LW3l1SDIv95/K3ghRgPM0OnJVGvKrlEBnBAazPyKGvRFxnA+ycyhS7AG+bHVSqAvkePtE1g2eyr/6TqwmwCVyBZkGC4UaHWVKlWfKa7lLgAsDNNUF2GAhN0DLZY2eNEsIh+5dQmlefgt940hISNRKYSH86U/QrRs4HKBUgsHQLAJcnwzwnjHT+W7SXI6078T+1vHkafRcNNvJtDjZPHIaX45PYeeEWZToA6kwGMQVTF4CfHLOQraNm83hdp3IsoWwp2Ms4ybJMS9uBvl9VCyf7pIiMGq8wIcdVZwyiuvrVvebxD0vfM7Xd8whyxZCutnBvvAY9kbEcqBtolhNFNbR0wNcoNaRY3FwOkYU4GPtE/kptlvTe4D79ZNWHkk0Cik+b3kkAb6BkQ6YRLPQRAEuXr6S75LvYcOYuTz10n+4bAuhQKOjzJWlyNeIWYfLthBOt4vz9JpVBAR4BLgoJJQCbSCZwQ6+nzSPp1d/yO1TFMTNFwdhNTXQUq4QGJgs47luDrLUmhozwJ/ccSd/e38n62+Zw5qB0z1ToHPV/gX4ojGY423j2B8Zx1mTnf2uIVhZFgcF2kCOtU/gncFTeW/INI62jnOVOotDrUrlCnLMNkp1gZQrVZR5BFjuV4ALVBoumqzkq7UUy5WUyeSUGINg9GipNE9C4lojNxdmzYLAQJDLK69mEOD69gDvGTOd7yfN42iHzvwc1YliXSB59hDynK04Nj2Fswsfovj+B8XXYDT6CHBZ337smDyPTSOSOBHbhY86W1g6RNc8mV/Xg8ku8wSCfiPwQmc1WWoNaUYraUEOPhg2nTf/s5eyxQ9TEBLGZXsohyLj2BMeyw+tE0gz2TkSHkWxXCkO7tLqPQKcZXVytF0CZxJ7ULxkaeMEeMAAsefXLb+S+Eo0ECk+b3kkAb6BkQ6YRLPgXseRlCSWezVQgHn0UX66exFfTr6Le/74AVlWJ4VaPeUyOVeC7RS6Bq9kWZ2ciIiu7DXzEuDysDCKdIFkmh1sGzebv739OcvGteKWKQKhD4iToGudBl2PK/ARgZ5zBNZ3lJOt1vjtAV5/yxz+un4Hn09awLvDkznYJp50k63GHuCLhmAOR8aKmWKzg2Nt47kUbCfTbCdfq+dkVGd2Tk7hxKy7yencnTKlqjJAVSopDwkBg4GyeghwoVpLjsVOkUbnFejKQKuFdeukIE1C4lohN1csmQ0I8JXYZhbgQ+ExZAQ7uGS2URDgX4C3jZvNkfadOBvXlQqjUby/R0bCokXi/X3RIr8CnNO9F1+Nnc3Ho5I5ntCFxSMCxHV1zSC/8hUCN80SiL5L4JYpAseDDOSpdVwKtnPJGsJnt8xg09aD4gCuyEjKIyI4H9uZI20T2NcmgQyzg1NtYihVKCn1EuBTUZ3Ft0V3Jqt777p/ftUkwDffLK07kmgSUnze8kgCfAMjHTCJZqNqFriBAly2chUHUx7gyZf+Q4bZQb5azABfNtso0OjJNNvJMDv4pV1cZa+ZlwATHk5JoIFsq5ONw5N44rUvOZ7QhUW36hmSLMprk7IOq8Q9ldbfCEweJ3BR6y3Adg63TeD1wdN5a+Qslr/6NVsmLuCT22aTntCNi2Y7V9Q6cpTqagJ8IdDMnrBo9kfGccnqJLtTN/LtIeTZQyjWG8jpdhPFixaLgVzv3r4BsUoFoaE+AlzRYAF2BdUDBohrVT7/XBLh64S8olK+/+li7btiJa4vvPt9jUZfgW0GAfbeA3zJaOFAeDTnTHbSjVbyVBpK5AofAd4+agobhydxMqYr2V16iJ+rngKc0fkmPrtlBp/fPoM3BrdnyHRxsKD7ftrY+7FslUDnFIGN7QU+by1QLBfINloo1OrJsTrJtDj5auxsUvf+5BFgIiMp79WLjMRuYj+y2cGPEdGUuAS4UKPjYpCNo20TyLI6yUjsTsWAAY0T4JUrxYcX0rojiSYgxectjyTANzDSAZNoNqpmgRsowG4J/nrzTnK8SqCzvEqgc2whZMd1quw1qyLAFUYjeY5Qto2bzYKnP+Jgx0Te72wm6XaBqLtdQ7GaknVYKa5Wan2fQMoIgQWjBdK1AR4BXjcsmbXDZnLvC1+w8fZ5fDl+HufiupJtcZCr1pGn0pBfRUrdGeADkXFk2ULITuwmBpjh4WAyifsj3atE6iHAPhngKrJdGKDhcrBdnBrt6iV2l1MXWe2UORzQtSvMny8Na7mGKSkrZ8uhdJ7ZcoxlH+xnwRu7SFmbyoI3drHsg/08s+UYWw6lS4PNrkeys8XdvhERouw2owBXeAlwmUzGJZOFY5GxpAU5SDNYuaJUU+wS4HJBoEyQ8dnA8WwbN5uMzj2o6NOnQQJ8oVMPPho9nScm92HcJDn6R3wfKDb2QWTIgwLzb9WTq1ZSLpNTIQjkBFkp0urJtjjICHayc3IKeemZPgJM796U9+kjTqS2hXCqbSwlCiUlChUFGh3ZwXbOxHahwNlK/Fr9ZXDrI8C1vV1Cop5I8XnLIwnwDYx0wCSaFW8J7tRJzCo2QIB59FE4eZLy8HBK9YGUy+XkW+0U6wIpcoZSHh4OPXpUBlpVBBiTiYrwcE7OWciL737Lz9FdSLfY+TgqgAeHyQh5sGlZYJkra6FaLhA3X2BQssDrsTLOm20cbpvAO8OTWTNsJnOe2cyGMXP535T5nI7tQmaQWMZdqNFRqNb67uY1WTkT3UksvQt2cjamE+VhYQ0WYO8e4DKZjBKZgvwqa5DylGouuIZg+Qa6AhcDg8VgUBlAicFI0YpVUvB2DVJSVs761NOsdO1vnrNmJ0ve38eKDw+w5P19zFm9k+mvfMfKjQdYn3qaEkmCrw/ca+U2bBCnPAcGVpffJgpwuUzmWaFWLpOTE2zjXFQiFy1OMk028lSaagK857bpnJyzkIp+/cR7UQME+Fznrvz5lhhunqXAvqgZSp9d8ttjtsDqm8MpVPkKcKFWT0aQnSxbCCfnLhR/tlQRYPr2FXcSh4eTk9BZfHCoUlGi01PkDKGst2u1VN++jRNg7/WA0tAriSYgxectjyTANzDSAZNodtwS7C4BW7mywQJMRIQY5CkUouC5g66IiDoFmIgIWLKEvFNnyOneizxHKMW6QC47Hfx1mJnQh5oWgLl/r1ohEH6/wIAZAssGqtjTPo51w5J5begMbnv8I76cfBep0+/iZFRnLprtFOkCKdToKK4iwFfMNs5Gd+ZMbBcyLU5OdUygKCS0wQJcoaqcAl0m+N8DfEWp5nxgMFdUGoqqCHC6LkgcjCWIE6Qzwtuy5x9rKS0q/tW/hSRqZsuhdFZuPMC0l79n1cYD/PW/x6pdq1xvl/Y7XweUlsKnn8KYMRAVBYmJ4r2vmQVYPOv+BfiyPZQci4OCAK1PZUiZTEZeygLx3tO/f4MEuCQijOeGWegyX07gI/VYSVeHHMtXCkTcJzBxvMCqwXoOte4grsJzSX1GoJlctY6LZju5zlaUL364VgH2/Cxx/xxx/zft27dpAiwh0UxI8XnLIwnwDYx0wCSuCrUFCY0U4PKwMIpCWnExNpFiXSBlKnENUlmPm/wKMGlplYGOK2gr6debpcmhBC5tugALrqFa2qXiIJblQwL5583jeWVwMvf98wsOpjzAodn3cKJDItnBjnoJcJY1hB/bxZNvD2mwABMQ4AlwSwUZRTI5udUEOIBzelGAq2aAMwPNFMuVlAqyyvVOraM4MW46pZ9+JmUyrgHyikp5Zssxpr/yXY3y6y3B01/5jme2HJN6gq9VSkvho4/EahmlUrzfBQZWXs0swGW1CXCVKdBuAT6fPLfBAlwQ5uSu2xS0uVcgYLnYNtLUypv2CwWWDlbwSccA0oNtHAvrSLFC6fma0vVB5AboyDTbuWwP5eTchZRevCQJsMR1ixSftzySAN/ASAdM4qpQWxlYAwW4IiSEEn0gOVYnWRYnP7eOEfcAK1SUKFSci0okK7EbFWFhdQow/ftT8shifr+sH5rGSrC/AG2lQMT9AotGRPDOLTP47OvDlK9cxcFZ93C8fSLZlnoKsC2EE+3iyWuEAFfNABfJ5OQqVD6fK0dRKcBVM8DuEugymUzMIAsyihUqijRaLsfEi4G6JMEtyvc/XWTZB/uZs3pnrfLrvuas3smyD/az4+dLLf3SJaqSmQk33STe57wFV6+/igIsNEyABRknJs1skAAXq5X8pZ+KiPvF1XHuuQmKxs5fcJU9j50ocNgWRL5WT7rJxoGQ9hS5HtiVux7gFWhEAc4IdrJt3Bw++OIAZYsflgRY4rpEis9bHkmAb2CkAybxq9MAAa5w9QAXaPVkBtnJDHZwqm0shVo9JUoVJQolx1vHcqpDInn2EHFFRx0CzPLlZB3fx7gpMgxL6pGZqG/mYpWA/SGBlVPaUnopEx59lCNz7vXNAKv99wCfjupUrwxwWc9elHutQSpTKCmyOaio2gPsKoGulgFWBNRYAu1PgMWPJ6M4QEPJ+AnSYKwWZsPuMyx4YxdL3t9XLwFe8v4+Fryxiw27z7T0S5fwJjcXpk6tPqRKECjV6ijR6ijW6nzObnMLsDgEy8qp9vE17gEuE2QcnTCjXgJcYTBQEKjnyd4CHe8WM7/ylaIEq5eLV509wKuq/xq0WGDceIHlA7X8EhTMFbWOcwYr+xztfAQ4I9DsWYOUZQth04gkfv/m/zg5Z6EkwBLXJVJ83vJIAnwDIx0wiV+dBghwuVxcg5Sn1pFtcXDZFsK5DvEUavWUKlWUKlX80j6eo5FxZFsclAQa6iXApefO8OmYGKaPl9HqviqBVxNXJQU9LPDzjs3w6KOcuftBTw9wgVZPXoD/KdBHW8fxY4dEMoP99wCXLX6Yk3MWcjamEyUKpWdyc4lcQbZJnH5a6lUOWCYTBbjqEKwrSjVpgZYGCrAg7srU6iA6GuLjYeNGKRvcAqzb8Qspa1NZ8WHt5c/ua8WHB0hZm8q6Hb+09EuXcFNYKK448srwVp3UXhCgpSBA65FVHxFuhABXCq2vAF8wBHMkIoYLwQ6yzPZGZ4DLHnyIPL2OtYlyus8VUC8TkK8Ss77yVaIEB6xowBAs131Yt1RgxCSB1Z30nDEGk2awkBOg42yghf1OXwF2l0BfMNnItDjZNnY28/62mR2T51EeESEJsMR1hxSftzySAN/ASAdM4lenngJcYTCIuypNVgq0ei5bnX4F+GxUIqc6JJLpGjRVHh5epwCTlkbpgH582tPC7NsFIu8TgzR/fb6NkWDHIoFzD86jeMlSzsR2Id1kI1etI1elIV/lK8AZhmD2h8ewPzKOtCAHZ6pMgS7v04fDM+5i27jZHGsT5xHgCkGgVK7gotFCvlrn6t+t7N3zNwU6t5ECXOL1vhWCQEGrcIoee7xBwZ+0s7bpSBng6xj3cMC5c8Hh8Cu/5YJAQYCGQrW2WqWI52qgAHt/7FLBV4AzDBYOhkdzPshOhslGvkpTTYAP3pEs7iGvRYBPJM3hpW4Khk0XMC4RM7/yVQKKFeKv7jJoeX3vrasEApcIDEgW+H0fgTNmC2kGq48AHwhp75lZ4BbgPLWONKONdLODzbfO5O5/fM5XY2dTFBomCbDEdYcUn7c8kgDfwEgHTOJXp54CXKoPpMwlwIV1CPDpqE6uLGsgRSGt6iXA9O9PaWQ4m+O1JI8XiLlLIPCRylVHTcoGrxJof7+MD2b14mRsJ9JNNq4EiAJcUCUDfMlo4WBELLvDxX2cZ6I7+ewBzu7cg23j5rBpRBKnOib6lCiWKpRcNtvE3uJ6C3BDS6AFiuUKn2xUuSBQpNFxfMEiSvPya/3fLe2sbT6kHuDrlMJCePJJGDxYrOrw6uOvKrhFai1FGh2FGp1/AZY1XoCrZoAvGi0cax1LutlBmsHidw/wNyMms2PyPLK69vS7B7h4yVL+Miaa3rMETEvE6fiee+hK8feyVZV9wO4/1zTsSr5SbCUZPk3g/Y4y8hUKMk02zhssnPcIsJX9znaeqfWeDLBazACfD7Lz4fAklr26jc9umUGes5UkwBLXHVJ83vJIAnwDIx0wiV+degpwsU5PmUwsga6PAGdbHORr9eQ7QustwEREUGoy8GnPYIYmi3t9I+8T9/w2dTCWcoXAgBQVK0caOGkOrncG2HsPcIXRyNm4LmwamcS2cbM5G93JrwAXafX1EuCGlUALNQqw+0oLjWDbX16lxLUqqWqWd33qaf782REe2bCvzp21b3x3km9PZEoZ4lqQpkBfZ7jFd/RoCA4W5VelEi9/cluHAJcL4i7fisDAeglwhZcA+yuBvmi0cCg8hnMmO+cDLeQofAW4VJDx737j2Dh8OidjupKR2F2cs+AS4LIHH2LLhEl0ulOGdqmY8RWqPkBcVSm3bgmWuy5vEZatFPuEwx4QSL5dwcb2crLVGorlSi4YrZwL9BXgfVUEOM1VAp0RZCMtyM76IdO494Uv+HR0siTAEtclUnze8kgCfAMjHTCJX52rLMB5DRRgjEZKw0L5NF7NiGSB2yYLxM8X+89kjZ1c6groghcL3DZVzpudtPXrAa6yB7g00MDJqM58NCqZL26byYm28T49wN4CXKLwEmChaQJcWkWAS2oQ4BJBIDcwiPR+g9n6v6PVsrzj/vEtw/7yFf2e+ILZr+3g6c1Hq/epfrCfkc9sY8zz3zDj1e+lDHEdXAt7gKVy9nqQnQ0jRoBGUzmMyi2/TRTgUp2+UQLsvQe4TJCRHhjMD6FRnDHaOFeDAG/qN453B09lX5sEjrRLoFCrp8gZSnl4BDsmTSNugWvHbz0GW8lWiWXQqhUC2mVefcGrRPlNuFOc9ry9XXtyAnRcCdBSJFeQXlWADaIAF3kJ8HldEFcCtKQZbZw32Xl9wGRmPP2f5s8A17bhQEKiGZHi85ZHEuAbGOmASfzqXGMZYIxGaNWKUmMgW9sr2RyvZeYdMuLu8uoLbuSlXSoQ/oDAqGkCC0YJ/Km/kmyt2icozTZZORPtfwp0sd7A4TYJvDtkGuuHTONARCzFct8hWJeMFr8C7G8IVq5SXesUaPdezVJBRlEVAfZbjunORMvkHE3oxdxnNnuyvEve38fov31N58c20+sPWxjz/DfMW7PTR4Kf+s9R5q1JZfhfvyLxt/9h4FNbWfTuD34zxOtTT1MiSTAlZeWsTz3NSleGd87qmrPq61NPU1pW3mzCKpWz15PsbBg6VBxYJXhNcG4GAS6TySjWVhfgCr3eR3RLNFrKheoC7MkGy2SkBQazJ6QjZ4w2MQPspwT6zR638lrfSeyOiGdPeCy5ah2Xgh0cdQTRxnuAYF1DraqUOQcsqyyXVi8XiF8gcMdEgZUD1eyM6MgVPwKcZrD6ZIC9h2C5BficwcpZk51X+k7k5mUf8NHIJAqbswdYQuJXQorPWx5JgG9gpAMm8atzDfUAewswBgMEBFBoNvDwGC1DkgVsi5pYBr1SwPiIQLt7BW6eIXDHJIGzBt/dvFlGCyfbJ3A6xncPcEVYGAXaQPZGxLG2/2TevHkKh6oIcLFMQbo+mLwArV8BzmuAAF/Qm8WSQj8Z4NI6BLjC9Vq+mHQnWxcs5dmP97Ho3b3c+tzXDHzqS257/hv6PfEFY57/hnve2u0R4Hve2s2Y58S39f3T59z63NcsWr/3V81mXo/UV0QLikubTViriXct5ez/7x9WnDzpf49vEwXYLa7eAlwRHk6pPpAitdZzXygTxGnSZdUEuqoAm/khNIqzRhtpBmu1HuBSQcYb3W/lpd4T2B0Rz96IOHLVOo4Hm+iwsAFTnd0S7HXJXRlh5QqB1vcJ3DJJYHWCjl+MFva2ivLJAKcZLNUF2OFfgM8brJwz2Xmp9wS6/2Y964dMI9fZioqICEmAJa4rzcwRcAAAIABJREFUpPi85ZEE+AZGOmASvzpVS8hycxs0BfpU21jyNTpKFOIe4FPt4jjVPqHBU6BrEmB3T/ComQqGTxP3WTZWgBUrxJUgqhUCmmVif9uIqQLvdRAokYuBaKYhmEORsRxuE09GsNOTAS5whJKn0bMnPJa3B03lw+FJHG0d5yPARTIFZ12BX5Fc4RHg0hoywHlKNekGsQTaN9CtFOBSPxlg777jmq5yQSDbFkJWSDgfPvoP5r/2HUOe3srov33NpBe3eyR40ovb+fNnR3ji0yNMenE7/Z74gtue/4bRf/uaIU9vJWVtqtTPWk/yikrZ8fMlv5nd5hbWa6H0+prHfW9bt04sfW5mAa6aAS6/6SbyHKEUavXkqzReAiyjIEBDaZV/W1WA0wOD2dsqinMmO+lG/wK87qYxvNJnIqkRcewJj+WCVk23uXWUPdejFFrhuie2u0fggaEynuwt42eTmfMGK3tDo/yWQKcZLFxRiwK819HWrwCnGa2cNdp5uc9ERqzaxDuDppJlC6EgJEwSYInrCik+b3kkAb6BkQ6YRItTNSNcwx7gzCA7F8x2joZHkRugo1ihpFiu5FB4NPvCo7lottd7D3BtAuzuCd7aw8bnN9kYNkPe8GCvSsDnnQFRrhAzy3NHC1xRiAK8PyKGvRFxnA+yc7RNHIXOUHKsTnI1evZHxvPmwCm1C7DKnwDLq2WA85RqMk1WCjW6KutOBC7og2oW4HpkgMsFgSKVmjK5nEvOcHZ36seoRz9izHPfMOnF7Ux6cTsDn/zSk+X1zhBPenE7Y577hkFPba1xwrE00bhhNKewSsO36qCwEH7/e4iNBZtNLLdVKK6KAHv3AGcndCHb6iRfo6PQNVvAfZ7zVepqAlx1CFZ9BPhNVwZ4R1gc2yI6MHeU2NrRqPuhO/u7UsD0sED3eTL+3N/I+SALRQqla9Kzlf1h0eQEaEUBlokCfN7gJcAGK3urZIDT9JUl0GeMNtb0n8yCv29h27jZZAQ7ybGHUtazlyTAEtcNUnze8kgCfAMjHTCJFqcWAa6Qy8m32slT68TSNqONg606egS4SK5kb6so9oZFk2m2U6w3UNHEDLDnz65Jp/l9e9DrHl39VyLV9H5V1ipplgp0nyNwwKLjaOs4DkTGcdZk51BkHDlWJ1nBDvI0eo60TeCNAVN4b8g0jrSOo8g1kMotwOf8CHCZIKPIjwAXBmjIsdgp1empUFWWYpcJAhnuEmjBXQItq3MIlj8B9s5UHQ7twITf/dsjwN5Z3pS1qT4Z4toywO6dtvPW7OTJ/xyRhi/VQXMLq7R+qRYKC+Gxx8QJz27RVSrrFOAaz1A9p0CXt2rFuehEMs0OCrV6CquUQOep1D4l0P72AF/wEuCaSqDXdr2FF3uJAvx0LxMR99ez77eW+6NpicDAmUpmTLSS2i6ajCAbxQoVaQYr5wxW9od5ZYBl3iXQ4hCsc3UI8DmTnQ+GT+e593eyY9I8Mi1Osqwh5HTpLgmwxHWDFJ+3PJIA38BIB0yixalFgFEoKLQ5yFfrSDNaSTPZORzmlQFWKDkWGcvx1nFkmu0U6AIpcDatB7iqANO/P+l7vqH1/fXoeavt7d4CvKqyRDpmgcD2Nu3ZGyGuQToYEctFs138erSB/NghkfeGTuP1AVPYHx5DkayqAJurlUDX1ANcqtVRHhoqfq1VBPiyyUKpUkWZTF7nHuC6BNi7L3jqb9Z4BNg7yztn9U4GPbXVkyH2zg5XFaqn/nOUma/tYPBTW5n04nZp+FIdNLewbth9hgVv7GLJ+/vq9fGWvL+PBW/sYsPuM7/yV/4rU1gIf/iDeB/xFt1aBLhCpaJcWbMA56s0FKi1de4BLnKE8Ev7BDKDHRRp9RQEaHwEuEClqV2ABRkXDMHsC4virNHudw+wuwf4n73G8nhfA23vbdpkfGGVuGt9+DSBpeP78fiEoexvG+cRYDHTa63sAXY92LtgtHK+hinQVQU4zWgjM9jJ9xPn8fcPUtkxaR5Z1hAuWpxcTOgqCbDEdYMUn7c8kgDfwEgHTKLFqSMDfCVYzABnBTu4ZHHyU+sYrx5gFWc6JnimQOdp9OTYQihetLhZBfjyzyd55c5hdFjo2nVZQ1a3sUFhu4UC37XuSKbFyfG28WK5t8lGgS6QM7Fd+GT0DN4dPI3draKrCbC/EugyWXUBRhDEVSmur9WdAXYHzFeCRAEu9yPA9ckAV9QgwJMeWs1tz39Tawa4an9wVfmdt0Z8366/+y+jnv36uh++dLXXCDW3sK7b8Qspa1NZ8WHt2WTPaqsPD5CyNpV1O35plq/nmsN7v6/Z7ClprkuAK5RKyhRKSl2rzPwJcK5STZ5KQ36A1v85k4sCnGdz8lPbOLIsTlcPsLpBAlwqVJZAnzHaOF+DAL/UbSCDkwMIXizu8G3KvS5guUDXFIHn+oby6qCpvDd0mjj7wCXAGSYb6Sabbwm0XMGlIBuZQTYuBdnI1+hJN9k4ENLeZw9wRqCZPLWOS8F2LttD2TEppVKAbSFkWpxkxHeRBFjiukGKz1seSYBvYKQDJtHiVB2KdeaMjwBfNtvI1+jqnAKdY3WSr9WTZXVy9s77mkWAKyIiyOrakxff/ZYt4+fwUt9Ibp4pI/ARsY9N5iXATcqMuEqi9zsDOdUhgQtBYiBYoA3kbGwXvp84j43Dk9gTVl2Az/kZglUfAXZnodwfq6kCXC4IFFYR4BK5ggUPv8azt9zFK3fcy/Nj7mbs01t8eoD7PvGF3wnRVSdFd35sM8P++pXfDHFNvazX2r7aX2uNUHMLq5QB9iI3F+bOBadTFF+5vHLPbx0CXK5QUipXUCKvWYDzVBpyXZe/98FLgH9sG0e21UmBRk+esuECnBZoZm8te4BzlAI9Z8vEnl/vKc6NvMeFPCiwYqieQx078c7wZN4YMIV9EbGkm0QBvmC0kma0cSAsmitqHbmu6fb5NidFjhDKW7UCk4k8ewgnwqM8e8vLBYFso4VCrZ4cq7O6ADcmAzx1KsycCZs3S7t+JVoEKT5veSQBvoGRDpjENUdams8QrKwgKwWautcg5VidFGgDuRjs4OiMu5oswBVhYeQ5W3EypisLnv6If986i59iu/F9x47cMU6g40Kxl025UlzpoVjRwLUgfi7FCoGvOrYmI8jOhSAb+Vo9Z2O7sGNSCp+OTmZvTQLspwe4WCYntxYBLlMqaxTgcpmMkkaUQOcpqpRcyxX8btm/+NnZmiyNgSsBWr6PvolXlz3Pb95OZeCTX5L42/8w/Jmvqu0I/ut/j3kmRff6wxZ6/WGL3wyxv17W7PziBovm1ZblX3ONUHMLq9QD7EVamngvCQgQz5RMVi8BrhAEShUKSuSKWqeqFwaI2d+8KgLs+Vh+MsD5Gl29BNhnCJZLgN17gKsKcK5SoNfspu9C9zzgWyYwbZyMfe3jOB3Xjc9un8OHw5M4GBlHurGyBPqCycax1uK+4UKNjnKlShRT92UyUeQM5Zc2MZQolJTL5FQIAjlBVopqEOAG9QD36wedOsFHH4kPZCX5lWghpPi85ZEE+AZGOmAS1xxVBbjKGqRaBVgnCvChpAVNFuACRyhZthCOtO/EE699yXdTF3A6oQdH2sWxMSqAKWMFhiYJJN4pYF8kBng+06IbKcPapQJHLSbSjFauqHXsj4zng2HTeW/INFGA5fUogXYNwcpV1C3A7uC4qgCXNiIDfEWuqibArz/1JhdNNk+vXrFCyeGorjy36Flmvfwttz3/DSOf2cZKP9nKRe/uZdhfvqLzY5trzBBXFa9HNuzjiU+P1Fs085txV25t/JprhJpbWKUp0EBmpihPPXqIgusue26IAMtrF+ByQaAgQEOhWutTAu3zseXVe4DzNTpyGyrArj3Au/0IcJ5SYMo4cYWb+14mX9n4DLBspcCgWXIu2O0cbZvAyZiufD91AdsnzOPnDuIO9xKliotBNrKCHfzSPp48jZ4irTisr6oAl4eFca59bL0EuMFToPv3F0ufs7Nb+jtO4v85Unze8kgCfAMjHTCJa45rIANcHiquIcoIdnIypiv/fOdbjwAfbxtHtkbLhiglQ5IEElMEBiYLOB8SUC9vnlLBqAUC+ywmcgJ0pLaK4ZU+E3mlz0R2t4qqkgGW1yrAVxSqOgW4PhngxgpwiVzB7x55iUyTjTKZuIO0XCaj0GTml+G3cfC19bz5zY+VsrraV1ZHPbuNrr/bzJC/bPWbIfaXybzjH98y7ZXv6iWayz/Yz283HbzqWdnmEMiGZKivhrD+v90DXFgIf/4zDB7sK7uNEOCSeghwnkrjudxnzp8Ae0+BbkgG2PNwSpBxXl9ZAn3eYCHH1QP88BCB4MWVFS2KleIlW+Xb9lEv+V0l0OY+gfTu3SkICeNUVGeOtO/EVxNS2DEphdMxXcixOilVqsixOMi2ODjeOpYCrZ5SXaB4T/YS4AqjkSJnKKfbxviUQF/2I8B/ePN/bBqRVL89wEajKL5PPgnPPCP1/Uq0OFJ83vJIAtxE8vPz+fDDD5kzZw4JCQkYDAZ0Oh2JiYk89thj5ObmVvs3jz76KIIg1HgtWbKkWV6bdMAkrjm8BLgleoArDAZyLXYyguykmx0c69iZR1/awv+mzOd0Qg9OtI0nV60jW61hcxuBJ/oqeXC4kgEzBYxLhMbtDK56rRKIvktgTYLAjvBoXuw1gRd6jic1tGECnKvwFdL69ACXyWSNngJdtQS6RK7g74+vJsfi8GRqkMkqM2hGI2U9evDVtoN+M7CTXtzOoKe2MvPVHXXK71//e4xH3t/HoKe2MuTprfUSv5HPbmPM898w+aXtV1XqmpKRbWzfcHMLa7US7tW1PyxoSMb8WuvV9lBaKpbCxsWBRlN9pVEjBLjUJcC1DcGqrQe4QianIjDQZw9wnrp6BjjfzxqkqgKcpjeLU6Bda5BSgwUGTfPK/Hpd8lWVQlzfVg/5SoG29wq8ePNwfo7uQnlEBBmJ3TgZ05UPR8/k49HJnOwoDjB0Z4Azg+z80iGBYn0gFe6HkmFhVLRqRaE9hCJdIFkWBycjoihWVA7BuqA3k6/WkWVxkGUN4ePRycz722a2jZtNnrMVFRERdQvwokWS+EpcM0jxecsjCXATeeWVVzziGhcXx8SJExkxYgQGgwFBEIiOjubChQs+/8YtwH379mXmzJnVrvXr1zfLa5MOmMQ1R2YmJCSAzUaFUskVizgFOtviqFWAvadA5z2wiNTvD5HR+SbyHKEU6wIpCgmlrG+/GgW4wmCgTKmiSKsn02jlvNHKeZOdva0TGLvifV4fnMT+9p05Ein2p10J0FImk5EXoOVHSzCzbwsg5u5mEmCXBAcvFrh1ioKX+o/glT4T/QqwvyFYpW4BrrIGqa4p0O6MSmMEuEKoPgSrVK5g37sfi8Nr5PJKYaia0Vq6lLzLuez4+ZKPBD31n6OkrE2tdy/r7Nd20O+JLxj17LY63/eJT48w8Mkv6fmHLcx/Y9dVLettbE/u+tTTPtI547Xvmb16B9Ne/o4J//wfo57dxq3Pfc0jG/ZVy1BfDWFt7iFev9ZQsEaRnQ1jxkC7dqBWVx9q1cQMcF0CfMWPALv3ABdpdBTYQyjt3sMjwFe8BLhUEMhTqimt+m9d59ktwO4p0IeDgxgzScCwpP7Z3VozwavEVo6u8wSe6yveuw63S6QgJIzyPn3I6tqT76ct4KuxsznRPtFTAp0dbCfH6iQ7oQsVRmPlQ8lWrcizOckOtpOn0ZNptvNL62jPA7tyQSBdH0RugI50k41Mi5Ovxs7mHx+mcnLOQlF+IyNrFmCdDux22LBB6vmVuGaQ4vOWRxLgJrJ27Vruuusujh8/7vP358+fp0uXLgiCwNSpU33e5hbg1atXX9XXJh0wiWsO94qRQYPAbKbQEUKBVk9GkJ0sq9OvAJ/qkOjZm3vZFsKOyfP4w7++4HjHzlx09chlWxycie/Gz3feT+nZcz4CXBEaSrFOL04cVeu4YLCQ5hLg3RHxDHjoLV7oO5mdkQnsDYsmN0BLjkpLqSAjV6XhjMnCC93DmTbehH1R04dheV+aZQKJ82WsGtqR70M7+F+DVIMA59ciwFX3AF8yBHsyKtUEWNa4NUhlCiV5n28VJ7i6MsB+B/tERfkdOtPQzOmoZ7fR74kvmF2P91/07l4GP72V7o//l5S1qQ3KyjaUxk5lXrnxACs3HmDKS98x+7UdTHpxO7c+J66Scme6h/3lK/o98QWzXtvBfw6k+XzeqyWYeUWl1R5WNDRj+2sOBWswubmQlCRKrltum0GAS+UKil1XbQJ8RaUhxyW0Vd/ufuiWbbZzqn08WRb/ApxbRYDd57yqAG8Nj6TDwsZNsfeRYK9p+JH3Cdw7VGBbeBQv9BzPi70msCcinsv2UMp694H+/SlespRz8+8jI7E7efYQylQBFDlDKA8Lg549xQeTLgEutIeQFWznYpC4Gi7H6uRc+1hPy0aFIJBlCCZXrSMjyEa2LYRz8+8jLz1T3AkfGelfgG+6Sbwn2u3iQ9fMzF/ve0xCog6k+LzlkQT4KrJ9+3YEQUCtVlNcXOz5e0mAJf5f4y497NSJ8rg4inWBZFscZJgd/Ng6hkKNKMAlChUn2sRyrHUc2RYHBdpAsq1ONo1I4r5nP+Xn6C6eNSEXzXZP79nGz3ZR3q+fR4AL7U4KNTqK5UoKtXoumcQM8DmTnV0RcQxa9Dav9J/KjogE9rSK5kqAlhyVhlJBxhWVhrMGK6mtYni+93juHRlG8OLmE2D3AJrW9wr8rn8guXJZnVOg3QJcNSNbmwBf0JvFvZpeGeDSJgpwiVzBW399i2yz3dMD7B2Ee16XwwFduogZmfnzRQGh4b2sQ57eyuCnttYr05qyNpX+f/6CPn/8vF6C3ZTVPo3JAKesTeXO11OZ+vJ2pr38HWOeE3clD3xK3J085rlvGP23rxn41JeeKdnz1qaSnV9c7fM3h7A2lprKmz/ad65Fe4r9vq7D5yj64xMwYkT13b5NEGDPeZApKJI1XoDdPfQFGh3pRiuHwmNIM4kVMnl1CLC/NUg/GQy0ubdx96Vq/cCrxD7hyPsEVg5Q8KMxmJ3hsbzQczz/7DWe1Ig4MoIdXO56U2UrypIlopCGh4tZ9rAw8fdeAlyhUpFjdZBhspEdbKewBgHOCbJSqNWTGWQnxx4q7oLPzq5dgHv3FjP8Q4eKD12l8meJawgpPm95JAG+iuTn53vKo8+fP+/5e0mAJf7fU1goDiP54x8pb92aAmcoObYQfmkXR4FGR4lCRYlCyan28ZyJrhyClWF2sG3cbP75zrecjuvGZVuIZz+k2Hs2iz+99iVZXXtCRAQVRiM5Fjv5ah0lClGAM40WzhusnDXa2BMZz+il61l98zR2RiawKzTKR4BzVBrOBFrY2SqG53tP4tm+E7klaSjWh5pRgl0Bp3WRwMODBYrl3gJsrr4HWBD3ABdULUnW6si3OSjW6qtNgc4MrCrAQpMFuFimYMXiF7gY5DUES/DtRawQBCrsdlHK1WpR0r32bzakl3XaK98x7h/f1ks056zeSZ8/fU7/J76oVwa4rl25tdGYHuB5a8RrzHPfeOT3tue/YdKL26tdtz3v2pP8l6/4x5cnmv8sNoLass+L39vL5Je21zj9uznLz+v7uh745+cc6tKPgkAj5XK5b4VCEwS46nkokik8k9xrFGClhiuqmgW4UKPjgtHKD6EdOW+0kRvg2wNckwB7P3wqkAvcPq7+Jc9V70Vyl/B6Wj5cLRuzRgmcMJk4a7CxMzyWf/aawIu9JpAaHsf5IDunojs3SIDLXaXRmUE2cqyOWgW4SCuWR2dZxQxwjQI8YAAkJsIf/yj+jPn8c6n0WeKaQ4rPWx5JgK8iBw4cQBAEVCoVRUVFnr93C3BycjL3338/8+fP5/HHH2fXrl3N+vmlAyZxzZOdLQZMkZGUh4dzJaELxbpAylQqypQqrnTqSnGPnuTYnORp9GRbnXw/aZ5fAT4T342vJqSw4OmPOBPfjfLwcEoDDWSbbeSrdZR6CfA5g5WzRrtHgN0Z4FSXAF9xlUC7BTi1VQwv9J3MM32nkvjgW9wzqgch9ze/BNsXCTzXXaBILgbU6fpgcgO0ory6hLVM5l+ACwM0XAqykq/WUqLwFeBLhuBqPcANEeByoXoPcLFMwT//sIbLXkOwyoXqGeACs1UUYO8+YYMBZs2i5HJOvXtZn/j0MI9s2Fcv0UxZm0r3x//L4Ke3smj93quaAW7MVOY716Yy67XvGf23r2uVX/c19C9f0fV3/+XOtaktPjyqrvLmcf/4lp5/2EKfJ76o13Tv5tor7O91LX97Bx/PeZgt4+d5WgD8fX+XuaTYczVCgEvldQvwFaVavGoYglUuk1Gg1pFmsLAntCPnjDZy1TryVfUX4GK5wNxRAkIT5hXIXALsFmjtUoHRUwTy5HLSAoM5a7CyIyyWl3pP4OU+E9kdEcc5k53j7RIrZzHUQ4DLlCoumf+PvfMOb7Jc//iTvdOmGd1lCLSlmyECrSwVRUCRDUWGVKvi8ShqZbVupofhTw/oUcQtiuMge5QhILtsEAUOLd2DtunIaL+/P94kTdIkTUcobZ/vdT2XGJo3b5P3ebk/ue/7e6tRrNC4BcDFPr4oVPrh8vRnnQPwoEF01BHVXS8an7e+KAB7ULNnzwYhBKNGjbJ53JUL9NixYx06RzdFdINR3fUy9+PFxDB9WvfeywRHZvfOfv1QGtsHJUpfVIgYEyxXAPzH5GSmPDo8DtX+gdBJpCj2VqFKyABwpVCCfJnSpgT6wde+w9r4SfgjOBInA+sDcJZUiZPBPfHpoMlYEz8FUS9+hzXxU7Aq/hEI5rVsOTRnEUGP5wm+6ckAZr7Mh8leOwJgux7gCp4QJQq15Xe1DowLpArGnIfFblIG2JkL9Ffvf+0SgGsIQanch3G2NQOweQkEwPDhMC5egj0nbzTYy3q7Quc2aD71+THEvbkDfd7eiemf/oGkDccxd2MGlm675BEIa6wr86JfzmHsR4fwwPv7MHj5XpfwO2HtYYxacxC9396JCWsPNxsUm6uGftekDcdx/9I9uPedXW7Nd27Olw/OzuuNTafxU9pHyAqNQpVIAq1ICiMhFgC2v971do9bRhm5AGD7PaJ3F4BduEDXsFioEIhwS6rE6UYCsIEQFPMJHp5CwFnYcvcl7kKC/jMI/idgo5rNRbbUB5kyFY4FR+CTAePx6cDxOBUSiVteGlzqGoXSvvc1DoC91Sj2cQ+AS5S+KFD64cK0ZArAVG1aND5vfVEA9pC2bNkCFosFHo+HjIwMm7/78ssvsWLFCly4cAFarRaZmZn4+uuvERgYCEIIHn/88Ua9lnkj2S+BQEA3GNXdLYOBKVFbuZLp0xo3rh4A50f2QpEPY4LlDgC//fFu/NkjlnGIlkhR5FUHwBVCxgQr10uNHG9fnOoUiYEvfY0PB0y0AWCbHmCpChkhEfhyWCL+7/4piPrnd1iTMAXrBk3E4r5eLRpskjQGgns+S/BxNMEtqTcqBGLbDLCpBFprB8BVAhFKlRpUWwFwLanrAWYywAwAVzcBgO3nABvcBOASmQIGiaQ+AJsXiwVMmgRtYUmDvawNwdeKHZcx87OjGLB4N+Le3IHI1G2IX7IHw1akY+SaA5iw9jDmfH3SJivZEmW4jXVl3nj8JkatOYiBS/ZgxOoDDQLwiNUHMHDxboz64GCzQbE5cifbPWv9MQxZno6H/sUYeE1Ye9jpFw/NLT93dF5vf3UQV/vej3KJzHItGi2rPgDXEAKDnYmbns2xAGm9cmkuF7UOAFjnRg+wqwyw+cst5p7jY5MBdqcH+JaYoPdsx2OOmpoFFswn6D2bjTweD6V8EarZXFMGWI0TIRH4z8DxWB8/ASdMGeAzIRG4Fh6HrOdfZvp03cwAFyk0KPHRoMJU5nwtJBR6TiMzwAMHAu++y/xbQmf9Ut3logDc+qIA7AFdvHgRCoUChBCsWrXK7edlZ2dDqVSCEIJDhw65/TwKwFTtQlVVzKxGOwDOi4hDoULDOIS6AcDvfboXV6wA2DoDXCEUI1emRJ6XGnk+vjjTJQpD5n5rAeC6HmBRXTAqYwB4/eAp+CBhCuJe/h6r4ydjXcIkZIREYL+GB1FLZoJNwaf3awSTRxPkC3hujUFyDcDeNj3A1aTONMddAC5lNR6AawlBscQbepELACamcUl9+wJPP20xyXIkV6D56g8ZeHjlfvQzmUYNNIFvv3d3MZnWZXsRv2QPRn1w0FKa25ARU2Nm2Lrjyrw54xYOXS3Asm2XMHj5XkSkbsPQ5ekY+9EhlwA8eNlePPB+Osb9+1CzQLG5cqffOWnDcQxbwZh5DV62FyPXHHBZht4SGWDzeSV/tBfnBj1a7xp0F4At17ZplJF5tJC14VUNm1Pv52sJM7bMHQAuNUGwQwAmLJRyhciU+OCUfw9kydUo54tc9gDr2ATrowmCXzSVLLeASz3b1PP76CQR/n3vIyjliSwAnCtTIluuxsmQCFMJ9DgcC+6JLC8NTgX3xLmu0dg7NgnHJiahOLYvaoOCXPYAF3qrkSNTIt9LjXKBBDlyNS4GdmdK1k1jkNzqAU5IoFlfqjYjCsCtLwrALazMzEyEhISAEIKXX3650c9/5ZVXQAhBampqs8+FbjCqNiUnANycDLB9D7A5A2wG4IvdYjB6wQ9YGz8JxzpF1ZVAm+YAl/OEuCVTWUqgPxo0Ffe99gPWxE/BRwMn4lRwT2TLVbgu5qD3rBacE2wG4UUEIS8Q5PCJjQlWYwC4hti6QBuaCsBNyACbAVjXEABbg3BwMPD225YMjj2Ebjx+Ex/uvYql2y7ZgOYTH/5uGRs087OjWLr1EmZ/fhyjPjA7LDMQ2e/dXRj2fjpGrTnodFZuc0YMOXJlPnS1AJvP3LIbs2mZAAAgAElEQVQcL2nDcfR5Zye6zd+CqLTtGLB4Nx781z6M/3d9EB5tOv8Rqw8gacPxVs0Au+N4Pff7DIxcwzhYj1jNjHVyZUTWEj3Am05m4h8f78OxwaNRzePXu34bAmA9qQ/Ataaft7+eDSy2pWS6qQDsbAySwQqAT/r3QJZMxdyPnABwCZ9gaCIBd0HLfvkW8iLBk495Y9WAx/DxvWNQyhOZzPgYAL4lZ0yw1vYfh3+bTLDMGeCL3WLw35Ez8evDibgRGgutxh+1fH49ADbPZs/3UiFLqkSuXIVyoQR5XmpcDuph6dk2exg06AJNAZiqDYnG560vCsAtqIKCAoSFhYEQgpkzZ6K2trbRx1i3bh0IIUhKSmr2+dANRtWmZDAAmzYxcxvF4hbpAbZ3gTb3AOfI6wD48YWb8HHCZBzvFIVTQWEo54uhtQLgbDkDwOsSJmHdkEQMmv8TPrx/Kj5OmIzTIQwAl/HFyOVzMW0UgeKVlp0VTNIIhPMIzsvryiT1bPdLoGsIQZHUBzo2FwbSdABuSgm02xlg+6VSwfjwIzjx0Vf4YcUXWPjDqXoQumzbJXy49yo2Hr+Jzw9dx9NfHMfINQcwb1MdnC3ffhlzvj5pM2M3fske9HprB0auOYBl2y7VA9mWnmHr7HiP/d/viErdhnvmbUFE6jb0fWcXhixnsrz28DvqA8YtuiXMopojd2YeL9l6CRPWHkb8kj146F/7MGR5utOMcbPLz033jHK/QJRIvS0Zw8YDsO3jehPEmp9nfSw9i+0wA6wzAXBDPcCuANhYD4DVDABz+PUAOEdIEGDO+rbUvSaVIOhFgrV9BPgmYTw+HDAR6/o+bgPAOaYe4KNBjAv0Z/ETkNE5CjneGpzvHIm/w+Lwx+RkHBgzC5e6RKFE6Qsjrz4AG8RS6Dlc5MlVyJGpLACc763B1eBQi2lfDSHIlypQLmDmvVf6BzHgW1LC9BoPH84sOuqIqg2JxuetLwrALaSysjL06dMHhBA88cQTMBqNTTrOkiVLQAjBSy+91OxzohuMqs2ppISZ29ilC6BQAP37w9jvvia7QNebAyxkXKBz5GrkKhgAnvjGTyYX6EhkBIUzczcFdQCc66VGRkgEPho4EWsHJ2Jgyo/4eEgivhqWiHOdI5Fr6tMr5QqRLeTg+eHMvEzuwpYNTrkLCdZFMyWPjQXg215KS0lhSwGwns3B58u+bHYPsMPX43BgZLFRzePDQFioYnOR7ReC7VP+gQXfHK0Hob9fzXdZmrtk6yXM/T4DM9cfxZgPf0f/93bj4ZX78d6Wi43uM7Y3tDKXTjd2Ju57Wy5iyPK96LloG8IXbkXogq2IfXMHBi3daykfNsPvFNO84JYaF9RUuTvzeM7XJzHqg4O4951duH+p41FUzZoDbDAAW7cy4CMWu7x23QFgnd3j5iyuwQEAGzwMwGW8+hngUjsAPi8jkL3WwvCbRsBbQLAkgYdCjR92PDwFnw6aXC8DbHGBDu6JzxMm4JvBk3GuSxSyvRkTrJsRzBeRRyck4UZoLAq8NYyhVWCgBYBr5XJUiyTQsbmWMUj5XmqUCcTIkVtlgE0AnCPxhlYgRrnGH7UhIXUAnJZWtyj8UrUh0fi89UUBuAVUXV2NIUOGgBCC4cOHQ6fTNek4tbW16NevHwgh+Oqrr5p9XnSDUbU5GQzMjFizM3R8PNC/P6r8AlApbvwcYMjlqA0IgE4sgZ7DRYVAjHyTCVa2lwZnukRh9IIfsS5hEo6GROFMcDgqBGKUmzLAWr4IhQoNznWOxLqESfggYQp6z92IdUMS8c2DiThvBcDlPCG0PAF0bIJvwwnikkwQ3JIl0QsJHp5EcEtI6gMwX+gcgOXMGKQaGxOsunnDTSmBrmax8Y85a1DkrW6SC7Sr19Oz2A4BoZonwK2u4SjRBCAn+B7sih+Nt749grc2n3cJZvaZ4IFL9qCvyaW4qU7T5uzl+zsuY3PGrSbNxH3uqxMYtGwvotK2I/qN7QhbuBUxb+zAkOV7LaZdMz87iskfH24aKLaw3J15vHz7Zcz+/DgGLt6Nfu/uwhMfHXKZRXdUSu5Q5eVMn7jZLd50TdlfJ40F4GoXAGywO5bBZQ8wu0UywFlSBoAzZSqUWgFwNZv5EozfQkZX9tnfkeMJ8pVqFKv8sfWhyfj6gUR8FT8eZXwRtAIxdBwu8uRMD/CpkEhsenAqfhg2Bac7RSJX4Yu/ukdbKnGOTkjCzfA4FCg00HN5qPbztwCwQSpDlZCpyilV+uK20hfFCg20phJoSw+wqQQ6T6JAhVCMKr8Aptw5JYW5FtLT6xad9UvVhkTj89YXBeBmymg0YsyYMSCEICEhARUVFS5/vqCgABs2bLCZCwwA5eXleOaZZ0AIgZ+fX4PHcUd0g1G1Sdk7Q0+ciNrgYOgkMpSo/PDr8ESmzDksDiUqP1QKJShUaHCpWwz2jUvCL9tOwDBgoGUMklblC51YYpkDXKJQI89LjWxvDU6GRGLE6xuxYchUnOwSjQxTCbS5B7hCIEKpyg9/94ixmGAlvL4Jnwydhi+GJuJsp0jkedkCsDmgLRISjB5PwG/B/jxzoOrzCsEnUQR6dl0AXclzDsBFMh/mMTYbNSzzGKRGArCdCVY1YWNc4jJky5Q2YGF/LPs5wA1l68zZNGfnZA0fZkip4PBxumc/vPXlQacwNmqNuRc4HcNWpGPg4j0Y99Gh+rOGf3Rv1vC/dl7BzPVHMXHdYTz9xfEmzcRdseMyZn9+DI+uPoC+7+xEROo29Hl7Jx5dfQAz1x/D9E+PNg0UPaTGzDxe+NNZPLxqPyauO4zXfshoVB+1RQUFjLvvvfcyFSGxsQCP5/LLFE8DsLMS6JYC4DKeELekSpyyA+ByLsHUxxhfAE/Ab+8ZBEVCAQoUGhQq/bB/VCKOTE7GwceeRKVIYmoj4aHQS4VsLzUyOkfhq0GT8MX9k3CuazQKlH7I7BlXD4CLfXyh5/JQofazALBOIkWlHQCbxyAV+/iaXKDrMsAlciUqhGJUaPzrAJhmfKnasGh83vqiANxMrVq1yjLDd8yYMZg+fbrDVVBQAAC4fv06CCGQy+Xo168fxo8fjwcffNDi/uzt7Y3ff/+9Rc6NbjCqNq+qKibYCQlBrVyOSr9AHJ04G+/+Zw/+7BGLQh9fVAiZ3rDMyN74K+kf2Ls3A5mRvVGs9EOFUIIiL5Ul2KoSSVCm1ECr8Uex2h9XesTin6u24r8jZ+DMPTE4GxyOcr45A8xGlUCMYh9fXL4nChuGTMXHQ6dh/OIt+PWx2fjvyBn4s1s08r3VTHmeHQDXEoLrMhnGPsGC12umvuAWLFkUzid4ZgRBBZd5LS1XgCJvFSoF9ecA50sUFgCuZbOhI6zmAzCLjSemLkWW1AcGK4CwLxmt1WgAmYx57RYGYJvHCQs3O/VAidof+cFdkRUeh32zXsY/1x+ywO/oDw5axgpZmzOZy3GnfHIEYz78vcESX/NK/OQIEpbuwQPv72vyTNwVO+qy00NXpOPed3fh0dUHGgeKd1DOSsSXbruEud+fRtKG45i07jAeeH8fnv7iOH48cdP1eCtzOfPDDwNqdV3/v0gESCTM52u6dox25lOOINjTAKxjsS3XuycAuJzHzAG2zgDf5BNEP+0Z8CWpBF3nEGT3joVeIoVW4w+tXyCyZj0HXco8GF96GXqJFNUiCfRcHvLlKtySq3G6UyQ2DpuCnx9KxNUesbitCXAIwCVKBoC19gAscAzAjuYAl3gxAKylAEzVTkTj89YXBeBmKi0tzQLArtb169cBML3CKSkpGDRoEAIDAyEQCCAWixEREYG5c+ciKyurxc6NbjCqNi8rAIaXFxASAt3cV3Hi6EXkx97LjDoSS1HtHwDDgIG4MHMOFn+2F5e6xaDAxxeVpoyvudyuQiBGiULNOJOGhMA4MB4njl7EpVkvIDeuH26ERqNSKEGlUAwji40KAVMCfT00Btsfm4WfR8/GU6t2YO/EZ3FkcjL+6h5tyQBreUJU8IQ2QW2uRIEDQV0xaQwbwS8yPXYtGcDy5xM89zDTF1zOFSBXpkQ5TwSdeY6pKYA3zwGuYTEZYL3JDKs5LtA6FgdPJa3ELZnSAgSOTINqNBrUSqWWmaqeAmBzds4aZMxAXs7m4bomBO8+8y4mfeh4PE/qL+cwbEU6hi5PdwuAl267hFFrDiLuzR2YtO6wU4fjIcvT8cCKdPR9ZyeGrkjH9E+PImnDcczdmGEzH3fptktI+uI4Hl19AC99d9rlyKXWlL2p18z1R5H4yRGMWnMQQ1eko8/bOxH35g4kLN2DiesO4/0dlxmA11YAK1YASUlAWBhTwszjOTVCc/j5OoHcOwrAxJULdMMAXNaIHuBMmQrHFQSalz0Av2kEnIUE8U/zUJ7Qj8m0y+UMpHbqxDjyL1hgceavlclQw+OjRKFGrrcGF+6Jxp7RM3B4/FNMO4oTAG5sBtghANMMMFU7E43PW18UgNux6AajavMyGIDNm4GoKMDXlwHhlBQgJ4cZe2Hq80VwMIp79WNMsJb/huvhvZj+YLEUpT4aGwDOkylRqNCgwj+QOUZODhPoDRoE9O+PWpkMBokUNWw2dCIJKjT+KO11L6peex3nk/6Jd746hE2jnsKvj87A+c6RyJGrUC4Qo4xbPwOcJ1XgZGAYjgSGYm0sHwNnEEheb+EgdgHB//UyOcNKlSjjCVFtBcBGQlAo9bGUFBoJCzrCsvTXNRWAq1lsPPvsauTKVS4BuESqQAVfVC975xKASdMB2GEW2vQ7lPOEyFH4IiM4HDOWbrEB0H/tvIJHVu1nxii5UQI99/vTFuBzNubnqc+P4b53d6HP2zsRmboNUWnb0f+93Ri2It3S4zvn65OW0uiWmIl7J2QeE/X+jsuYuO4wEpbuQdybOzD09R9wPjDUUg1RJJQi31sFrVDCfCYsllsu4I4+u1orGHX0+boqr280ALOcA3A1YVtMs5oCwO66QP8e2BXPDicQtHS/rynrK0sheGasAvvHJqK4Vz/UDhjgEoDN4+mqNX4oVvrhcvcYHJ0wG0cnzHYJwM56gCsFjDFhobcaBd5qlPhonAJwkcwHlSIJtN1CGW+IzZtpzy9VmxaNz1tfFIDbsegGo2oXqqpieoHN4y4WLKgHwDVBQciM7I2fR0zHks/2IjOSMciqFEpQKFdBKxBBx+ainC9CjtQHt2Qq5HgzZdO3//4fsGABjAn3ozS2D/QSKXRiCWrYbBjEEtQEBTHZkQULYFyUivQjl3Fk2hxsHjkDGSERuGUag+QMgDOCwnAyOByZcjUOBXfDS8PYEM1r2aCWvYhgcV+CTKm3QwAukftYAkp7ANY7CdjrBe8OAHj6U+8j20UGuIYQ5IrlKOMJWx2A7VclT4CzD4zG6l/rypJnfnYU8Uv24JFV+11mfud+fxqPrj5gGl+0E09+erQeTC/ffhljPzqEuDd3IHTBVkSkbkNk6jbLTF9rl2dzf7D1TFxnrtKtmhEuLweeegoIDARYLMvnrXcCi45WUwDY8tlbXVeujttWAdg8B/i8XIr+MxjTuxbP+i4iCH2O4LKcYOfQcfh1eCKuh/dCfnQf1LoBwDUBAShV++NStxjsHzPTJQBf7xGDPC819FweytV+0Gr8kRMWgyqRBFqBCNVsDnJNY5DyvdTQCiUo8tHYAHANISiQKVHiF4TqN99mvCFo9peqjYvG560vCsDtWHSDUbUbVVXZjrywA+Bq/wBcC4/Df0eaHKIje6PAxxdagZgpC+YzwVYZX4RsqQ+ypCpkytU43SkKL67ait8nPoObUX1xo3sUKoViVAjElh7gUpUfSmL7ombefOa1S0qgW7AIv098GhkhEZY5wGVcISr4tiXQORJvnAgIxYmgcGTJ1TgZEIa/vBQYM9YDZjapBP2eJLjFZ9crgS6QKmwywNVWMGDgcJsMwOMSl+GWVQ+wIwDOETEA7KhvskkA7OI4ZgB2B8SY352DrO4R+CntI6zcdgGv/3gGQ0wmWfY9vda9uiPXHEDcmzvQbd4WRKVtxyOr9tfL5s75+iRGrDqAqLTtiEjdhri3diLmjR0YvGyvwzm/Mz9jDK9W7LiMzWccu0rf8Z7gqirgrbcYKBKJbMyn3P0sGwvBLj8vq+vK1XHvVgAub6AE2kBYyOFzEZlEQDxgdsVdwLRMVHAIalgsnBo1FfvHzMSlbjG4ERYLvUTWIAAjMBCVfoG4Ht4Lvw5PxP4xM+sB8JHJyfjtkWnICOmJXC81dBweCr0Z88ELweEoMznt66wAOFeuQplAjDwvNa6FhNoAcIlCzTj7l5R4/pqnoroDovF564sCcDsW3WBU7UYGg+3Ii4ICGwCu8PXHnz1isecJZkbw1dBY5HprUG4qebYGYHMGOEuuwfHgCAye+w3WD56CjK4x+LNrBKpEtj3ABd4a3AiLxYWZc2BclGqZP7lvXBIyQiKQI1cxs4P5QlTy6/cAHw8IxbHAMGTK1TgZGIYcuQpXvbwR8kLLB7gklUA0j+CqyDqoJsiTeEPHtgVgcw+wwQTLTQHgCdOW25hgeRqAawhxCB+W5zUiA2x9zFJvFbLCY7Fl6j8wYeVuTPnkiI3Jk9mtedQHBzFw8W70fnsnQhduRY/5DADf9+4uDFi825LNfW/LRUxYexjxS/Zg0LK96PvOLvRcxJRAD1mejrEfHcLDK/djyPJ0DFy8G9Fp29H3nV14+fvTeOPX85b+WntXafvxQXpPQXBmJgNCEkmTQLW1ANjVZ3ynAFjXDAAu5RIMfJK0+Hxfc5XI0w9bvx8snBw1BX9MmI3r4b1w+Z4oVIulTMVLAwBcGxyMvNi+2D9mJn4dnojL3WNQrPLHjdBY/B0Wh28eSMSGhIk4HcwAsJ7LAHCulxpnAkNRxhdbqnLy5Spky5TIlatQLpAgW66qG4PEYsHIYiMnpi+MS5bSzC9VuxGNz1tfFIDbsegGo2q3KimxAWCthnF0Th+XhDVfH8CFe6KRbTKnypUpUWYC4HK+CLkyH2TLVbjlxYxBGvjSV/hwwERkdI3B3/dEolokQZVIghoWG1Umh+lLXaOwb1wS/n5uriUD/NuomThlCvC0QucAfCooDMeDwpEl1yAjKBz53hoUeGtwTcJu8X5gS6ZnIcHfsvoAbDCZX1kDcHNKoMdPW9YgAGcL7yAAk8ZlgK2PW0MIKgUiXIgZgBUbj9RB6PpjSPzkCB54Px3RadsRmbodPRdtQ/iirQhdsAVhC7eg7zs7ce87u9D7rZ0YueYAJq9jssSDl+/FuH8fwpDl6YhM3Yaei7Yh9s0dFqOoyNRtCFu4zZJJfsBkkjX548NOxwyZHas9MhfYPIf7sceaXKbcFgDY/u/uZAl0GVeIMgcAXMwn6DXbM/BLUgkGTSMo49gCcPqDE/DHhNnIjOyNK92iUSmSoNo8a9cFACMkBDXx8bg+63kcnTgb18LiUKj0w5/donHhnmh8NSwRX94/CVe6RuG2yg8GLg8FXmrkyNW41CmcGRvHZwC4wEuNPC+mBLpcIEGOXI1z/t0YAOZwYRCKYPzqa9rzS9WuROPz1hcF4HYsusGo2q3sANg6A5y2difOdY1CtpcaZQIxcmQ+lgywBYBlDACfCIlE/xe/wrqESTjROQqXOjMZYGsALlX54UZYLH4eMR1Hps2BNrcAmf941dIDnCt3DsB5UgXOBIfjZDADwGdDeqLYxxcFCg3KBGL8FhIMqYcgWDiPoITPBPA5Ym9UOwFgZxkrdwB4XKIbANzCGeBqF8epbiIAWx9fz+GhMmUeTvxnI1Ztv4DXfsjA0BXp6LmI6ePtuWgbYt7YgYGL96DP2zvQc9E2RKZuR1TadvR6awfi3tyBwcv3YsjydIxYzRhdjVpzAL3e2oGYN3Yg9s0dCFu4FWELtyIybTvi3mQej0zdhrg3d6Dfu7sw5ePD9WYG20Pw1E+OYOWuKy3XE1xVBbz3HtCtG8DheBSAXYFwcwHYHRfoVgVgnhBantDmZ86oCAJf8hD8LiJ4cApBDpcNvU1rBAtbBo3F4fFPITOyN66HxqJCKKkbNdQAACMhAUhJgW7uqyjtcx+0foHIieyNKz1i8d1D07Dv8Zm4GR6HUpUf9Fwe8rxUyJGrcaVzT+Z+aeoBLvBiDLBKfDSoEElQoNDgYlAotCIp9HIvoEsXpuWFiqodicbnrS8KwO1YdINRtVuZjbEeeADo0gXV/oGWHuCXVm/Dmc5RyPFSo4zvGIBvWQA4Agkvf42PEybjROcoXAjpiUphfQDO7Mkce/eEZBzP+BsXn34Jv42aaXKBVjstgc43AfCp4J7IkqtxNqQnbqv8kO/NAPDxwHCs6vsAwp4lHun5U79E8KeMIEfk1WwALncAwPZzgO9EBtiTAFxLmN5IhIYCvXtD99RsHH1+Ph5dugMxbzCwOnQFU8I8Ye1hPPj+PvR9Z5cJfnciKm27BWT7v7cbo9YctPT5Dlq2FwlL96Dv2zsRv2SPBZIfXrUfI1YdwH3v7Ubfd3Yi9s0dTmcG249YMhtmNVsmt3VjeDhqOI5L4psKwM4+R2fHdgeAXZW4O3s9T5dA61hsVLM4DfYAa3lCVPJFqCUEmRKChOkE/BYej2ZenAUEy3qxkCX3gZYntAFgI2Hh1/gx2DN6OjIje+NGWNMAGCkpzJ87dUJpr3txLbwX/jtypsUF2gzAuXIVcr3qALhCIIaOzUG+XIUihcZmDNL17lG4EHEvcu67n7nP09JnqnYmGp+3vigAt2PRDUbVrlVVxQRoCQmoCQmxuEA/vWwzMjqbMsB8MXLtANjcA2wG4KGvfIuPEybjZOdonAvpiQqh2CEA73liNjaPScKv6edxbvY/8duombhyT5TNHGBHAJwRHM6YYHlpcKFTBEpVfpYM8PHAcPz7vnH4qN/jSBsoanF3aHNPcNJDBLc5xDEAuzkGqV4GmLDx2OQlNgBsDwwMAMvuWAl0UwHY5rVYLMDPDxAIAEJg5HCQLVfj4Ve+wegPDloMrCasPWwpbzZDcGTqNoQu2IrQhVsR88YO9H9vF+KX7MGjqw9gyHLG9dn+GBPWHsaI1QfQ952d6PvOLjzwfjril+zBhLWH6zlLW69mj0wylzsnJ8P46EiUhEagXOIFoxOItIfVlgRgd4/bXAA2OAFgXYtlgF0DsJYnQAVfhBI+H6t7E4hf91DWN40Zc7Q9KABZcg1y5SqHALxpwOPYOmKa0wywLmUesmY9C51YCp1YCiOPh2pfP9QEBzsE4ILoPpZKHEcAnFcPgLnIk6tQ4K22AeCM+Ifxr1fWYM9H39HSZ6p2KRqft74oALdj0Q1G1a5lDuATE4GYGBT3vg/7xiVhbOomBoDlZgCu7wJt7gE+ERJpAeBTXaJx1gUAp49Lwn8fT8IPu87i4tMvYcvombgWGoNChQZagRjlPCEqeHY9wFKmB/hkcE/c8tLgatdIGwA+ERSOj/qNxb/vG4fTQWH4W0rQ6R8eCIpTCbo9T5DHJ1YATO4IAN9qAwBsA2JsNgPAXK4NkOVIFDgWeR+eXLG9HgQ/+P4+DFjMZHBDF2xF9/m/ITJ1GwYs3o0Jaw9j8sdH8Khp9JE9/E5YexiDl+/FgMW7LVnjwcv2YuSaA5i7McMpAC/8+RySNhzHt0f/1/i9Y66gGDoUtV5ezFgavghavtByXbh8jxrxfrYkAOuJLQjffQDcsAt0lpCNhGmeA1+SSuDzCsEliQgZgaHIkquRI1OhnFsfgH/s/zh+eySxXg9wbUgIbjz5DP6Ykoz9o6ahQihGhVAMPYeHEoUapWp/FPfqh5pXX7MB4Lyo3hYvBvcywFzkWgGw1luJ/M49sD5lDZ77/I+7fh42FVVTRePz1hcF4HYsusGo2r0MBmD3bmDlShhXvI99H36Df36wE6c6RSJLVr8E2uwCnSNXI8ebAeCEl7/Gp/dPxuku7meAM//xKvaOnY0r3aJxW+WHSpEEWn79MUjmHuDTwT2Rq/DF9e5RFgAuF0hwKrinKQM8FicDQ1HN5qCYTxCa7JkAWTSP4H8i0iQALufwOwQAWzLAdgBsfv0igQS7+j+CxJW7bCDW7Ozc5+2diEzdhoGLd2PkmgOY/9NZJG04jmEr6nqCrZe5RHrI8nRL3/CI1QcwbEU6kjYcb9kMcFUV8PbbTAkrn49aLhcGU2VEGU8ILV/YYAa4sctdAHYHgnWkaQBsLs13BsB3qgf4ipjAe66HwDeNgCwiCH2WoIBHkCNV4ExgKLLkGmTLlCjjCpxmgG1coAODoPULxIHR0/DziOnY+tAUS1uInstDkZcK+QpfXA/vhYvTkmF89TW3MsD2PcD1M8B+zCilyN547sPdLVfeT0V1F4rG560vCsDtWHSDUXU06Y012HbwIi52i8YtUwY4W2pbAp0nUyLfW41chS9Omkyw1g+eglNdot3uAdYtWIQ/piTj8j1RKFH6olIkQQVfVK8EukDmgwudeiIjJAJ5Pr7IDItBqcoPRT6+KBdKkBESgXX9x2GtKQNsDp7LuQTBnhiTlEbAn09wQd44AK4lBFU8Qb2Af+K05TZzgNsqANsCEQtVSjVqTUZQjn5eTwhu+obg3WfexaQPbaF2wOLdGLh4N57+4jgWmRybJ607jCHL0zFqzUGH8Dvqg4M2ztGj1hzEkOXpmLX+WMv1AJeUAA89BPB4NqCpY7FRxhehnC9CBV90VwKw+eerSfMA2PNjkDhOe+qvSwn48zyX+eUtIEh+kKDS1OqQLVHgbGAobnk5B+Bf48dg26PTbOYAV/oGoFjtj/8Om4x945JwbOwMVIkkqBZJYODyUKrUoFjlh4v3xGD/mJm4Puv5BnuA7V2gHfUA34jph2u9BmL79Jcw/cP0ljV4o6K6y0Tj89YXBeB2LLrBqDqkSkpQGHcvCnx8bTLAOjYXWoEYBXIl8r01yFX44kRIBOJf+i+lt/QAACAASURBVNoCwO66QCMtDX8l/QNXukUhR870ADsqgTabYJ3vHIlCpR+ywhkAvq30g9YEwJ8MGI9PBozH2eBwCwDXEIIsIUHgPz0TMHMWEqzuRaBju58BruTWB+Dk5FXIlinvKAB72gTLSFi47eUDoxvzkXWEhSKpN7b2HY7hb23FwMW7EWUqff7Pgb+x8fhNLPrlHB54fx/6vL3TAsEjVjOga4bf2Z8fx3u/1c0OfuD9fS4zwG67QBsMwKZNzExfU0+zPWTqWGyU80XQ3gUA7AyC2w4AO54DnC8kEHnI7Z2kEfi+RHBVVnf+ZgA+ExSKHG9f5MhUKOUKoLNzgf6x/2P4+aGpuB7eC/nRfVArk6NU5Yd8Hz8cGD0Nf0xOdgjAt9X+uB7eC78OT8TRibNhHBgPdOoEY/8BFi+GA2Nm2QBwkUKNPC81zgWFMZ4JVi7QuZ2646c31+Kztz9D4r9/98yILyqqu0g0Pm99UQBux6IbjKpDqqQENfHx0PoGoEIosfQAmwE4T6ZEjlyNbG8NMjpH4eGU77EuflKj5gAbF6Xi/Iw5uHRPFHLkKpTxxSjjOugBljAAfOWeKNzWBNQBsMoPFSYA/nTgBHwWPwGnAsNsALiaxUaGXIjYJOIRh2jWIoLopwly+A0DTw0h0NqVQOtYHLzy4v8h9w4DsKdLoGsIC8UyBQwsttvPqSZs7Osch7iXv0eP+Vtw33u78MrGDGw7l43t57LxysYMDHs/3QLBw1akY+QaJnM85+uTWLGdGXk05+uTGPXBQcS+uQMP/mufwx5gt+YAGwzAL7/A2CMURh7P5bnrWGxT/++dA2BXJlaujnHHAJjdciXQ12QEkpY2tzOvVILwZIJSbl1FhxmAb0kUyAgMRZ7CF7lyFcocAPDmhDE4PP4pFPfqh9oBA2CQypgxbUo/HB07wyUA34zojd8eYcYdlfa5jzHOGjgQxb36Yd+4JPw6PBE3QmMtAFyq9EWhQoNLncJRxq+bA1yo0OBaWBye+3A3pn7CzN/eePwmDMaaO/rPBhXVnRSNz1tfFIDbsegGo+qQMs0Irg0Ohl4iRZGXClqrHuBcmRK5XkwJ9Lmu0Xhi0Y/4algiMrrG4M8uTAa4UiiGkcVGhUCEAm8NboTF4sLMOahZlAqUlODv5+Zi37gkXOoaxZhgCRkXaEcAfDooDOc7R6JY5Y8bPaJRomTmAGuFElzqGoWvB0/Cx/3H4XhAKKpZtgCcJfZGEV+AFX09A8EkjUD5KkG2sGEAqeDaArCezcFbr69DjhUAG0l9AG4LY5CsX8tIWCiR+0BP3Adg5pwJSrhClHIEqGRxUCSUopIngJ4ngEGhgI6wUEnYMBICPWHBYPV+mR/Tszko5wtRwhOhksVFJeGgksuDjs1BJU+IajYXRUIZtCYgMYrFgJcX4OMDyGSASASw2TDyeG4DfEcCYLd7gJsMwHUl0Do2wcq+nhtxxF5I8NAUgjIusZyrfQb4dEAPZHtrnALwrqHjbABYL5GiUKFBscrfLQBOf2wGtj36JPJj77UAcE18PC7MnIP9Y2bhctcoFCg00HN5KPHRoNjHF5dCwlEmEKOcL0aZUIIL4X3ww6QXkPrdMazcdQW7LuRS+KVq96LxeeuLAnA7Ft1gVB1SdjOCawICUS2SQM9hMsD5ph7gAqUfroX3wkffHsThSc/gZlRf3OgehUpTf5qRxUaVgCmBLonti5p584G0NGhzC3Bk2hz8PGI6boQxGY4qsRSVAhGq7HqAi+RKnA0Ox/nOEShQ+uHqPZEoMgWC1WIpbobH4tshk/HxgPE44QSAy3gMvJ9UMqXLngimZa8RZElcQ0WlXQ+wns3BO/M+timBdgzAd38JtPVrGQhBoUzhMtPsLnh5etnP5m2MO7Plve4gAMzArOfnAOvYHOQJCaKe8dyXVrIUgnUxBHp23e/gCIAzAkKRZeoBti+BNrJY2Dl0HH4dnmgpgdZJpChQaFCsdg+A94+Zia0jpiEvpq8FgJGQAOO8+bj+1PPI7BmHYqUv9FweCr3VKFRo8L/uUagSS6H18kHxPaHYt+JT/HT0Oo5eK6I9v1QdRjQ+b31RAG7HohuMqsPKNCJJP3kKtN3DoBdLYeRyUSWS4LaPBuVqf2j9AlHa9z5ob2QCCxbAmHA/SmP7QC+RQieWoIbNhkEsQU1QEBPYLVgApKXh2Om/sHtCMn55dDqu9WDGIFUIGROsKoHIJiguU6jxZ9cI/Gkqgc6PjEOFxh/VfgGokcvxV/cYbEiYiM8TJuBcSM96JdDWAGwgBH/KCYQeKqcUvU6wPrIuqLaHCkcZ4AWvfIRbUtcl0G0RgPMk3i5fx13w8tRyBL7NAWBzD7C7Y5Ca+760RwA2Z4C/70rA8tAXVcL5BHFJBFdF9feZPQDnSX2YMUgmAC7nCmDgcOuew2Lh1Kip2D9mpsUEq0okaXYGGAkJzL0yJQXG/gNQ7RcAI48PrdoPFRp/lMX1QU2XrswXlMuWMV9Y2klbbcAffxdi08lMfHv0f9h0MpMCMlW7Eo3PW18UgNux6Aaj6qjSG2uw+0wWNi3+FKcHPoxSqTf0HC4qhWJmjqXKD5X+QaiNjwdycpiAbdAgoH9/QC5nyknZbOa/wcE2APzTnnP4bsRMfPNgIs53iUSutQmWXQa4TKHGje7RuNotGlq/QOb4wcFAcDAMUhnOd4nEpwMn4IdhU3C5cwR0bK4VAHPqAXANISjkE3R/lnjEHIu3gCBpBEEFtz5UOOoBfu651Q26QDcJgFmt5wJtIAS5Eq9WB2BXkNtS8Gt+r8v5IpTzhCjnUQBm3hPnAKxzAsDXxQQhL3hmX5I0AnkKwSvDCMo5zDzhhgA41wzAcjXy5CpU8oUOAfiPCbMtY5AqRRIUNbMH2BqAMXBgnQFbUBDz58mTgenTmRnuBkO9+/auC7lYuesK5v90FslfnkDShuNI/vIE5v90lpZIU7Ub0fi89UUBuB2LbjCqjii9scbivjvjo3347ZFpKPFhyvCqhBIUeqlQ4M2U+eXH9oU+65bbAGxclIoFnx3Ap8OexGeDpuBMp0jkeamhdeICXSxX4kqXCFzsEoly3wAbAK4SS5EREoEvEibi54cS3QZgA2GhmEswbKqHSqJTCR4fx/QwWgfYZWyeBczMkDB5+ooGXaCb0gOsd9K/eqcAOEfsGQB2B1SbAr7NAeBqFhtlPBFKuULT50QB2BUA61ls6O2ujYvezJdHngBfkkqgmctUf5jPyR0AzpYocNK/B7LkGuR5qVDJFzkF4MzI3rjSLdoCwE11gW4QgKOigM2bgfR0h/Brvm9P/eQIZn1+DCk/nsHCn88h5cczmLX+mI1Jlp5CMFUbFo3PW18UgNux6Aaj6ojadSHXMn/1jU2n8eN7/0HG8HEoU6hR4huI2z4alCiZIO96eC/s33fGbQD++7m5mL1qB9YOTsSXwxJxqWsU8r3VjAkWvz4A55nGIGWEMD3AJdG9UWvKhFSKpDgdEoFvBk+2AmDXJdBmAK5msZHLYyFppIcC71QCyWsE57zrAmwzANdaQcKc51fbmGC5ygAbmwDAjsbhuAJg3V0OwObfyVOrKYCqY7FRSgHY5nFXAGywA+A/vQjYHur1JWkEnV4guMUjlvuCgRBo3QDgWxYAViNXroKWJ7TMAa4l9QH4emgsKoQSlCh9mzwH2CUABwczf1dS0uB9O/WXc07HfzXogE5F1QZE4/PWFwXgdiy6wag6mrTVBqzcdQVTPzliE0St+fUUzj/4OC4MHYX8Tt1QqvZDsdofl7rFYO33v0OXMq9BANalzMORaXMwYckWfPHQdHwxZKoNAJfzhNA6BOAwZIT0RK7CFzd6REOr8UdtUJBDALbtAebglgsALuPwoGMTfBzjOXMskkrw5EiCCg5BKcsWgPUsDpYu/AT5XioL3LYUAOuamAHuyADcVECtbgUAbuzxmwvABtJyAGwugdaxCT7oTUA8tffSCMKSCYqFfBtzPSNpPADnyVUotzPBsgfgG2EMAJdrGH+EA6On4ecR07H1oSmoFDKj4fRcHoq8VMhX+OJ6eC9cnJaMmldfaxiAFQpg6FCXPb+O7tvNmoFNRXUXi8bnrS8KwO1YdINRdTT98Xch5v90FrPWH7MJmlZuu4CNy7/Aj+99iguDR+C22h+3NQG43D0W7/5nD7Kee7lBAM567iXsnpCM5A92YeOjs/D54Km40CUS+d5MD3AZVwitnVNynlSBjKAwXOzCjEG63CUSJUpfVPoG1CuBvuQAgF1lgMs4dUB6QUHAn0881n8Y+hzBdYEtCOjZHHz1/te47eMLI8u5C3SuqAljkJrYA9wWANh6tSb4mldrlEC3ZQCuJmyc8yboPsdz+42kEoQ9R5Drq4JeLIVBJLa8vrsAbC6BznSQAa4hzLgvRxlgrcYftSEhuPHkM/hjSjL2j5qGCqEYFUIx9Bwe46Gg9kdxr34M/KakOAfg+HggJoZZmzfXK3tu6L7tbM1afwzzfzqLo9eK7ui/L1RULSUan7e+KAC3Y9ENRtXRtOlkJpK/PIGUH884DJxWbruAn978N/K6hiKvayj+Du+FVz7YjkuzXmgQgC/NegGbxyQh7fOD2PLE0/juoWnICIlAnpc1ANefA3w2OBx/dY/GbU0AbvSIRoFCg1KVH/R2Jljn3XCBdgbAtYTgsphA/bLngnL/lwhu8+peT88yAbDSFzWmjK153qp1YJ4nljcpA9wRANi8Wgt+a03XWRlfhFIeBeCGAFjLJZg6ioDlwZJnkkowaCpBeb84ICSEuR9JJJbP20gItLyGAThHosApEwDnyBwD8PGRU+r1AFf7BTAwO3cudCnzkPXUc9CJpdCJpTDyeKj29UONuZw5JcU5AM+bByQmMoZX06cD5eVNvm/br5QfzyD5yxPYdDLzzvzDQkXVwqLxeeuLAnA7Ft1gVB1N3x79H5I2HMfCn52X0a367QzSk+chPXkefpv1Gl74cDfOz5jTIACfnzEH/308CW9/eQiHEp/H5pEzcL5LJHLkKpTxnQCwVIHzIT1xs2ccbmsCkBXOjE0q9vGFQSrDX92jsSFhIjYkTMSZ4PBmAXAZh4+/5HKMf9xzPYmS1wjyBHWQ8PmyL20AuIbUh4tCiTe0fBEF4BZYFIDrPqPGvF5LAPANKYH8FQ9mfdOYVobVcQT6QH+gXz/nAOxmBtgMwNkyJcodAPCBhybauEBXi6XM2DcTAGPBAua/cjmz+HwgMJA5r4YAeNEixuk5Pd2h6VVj79vWa+HP55C04Ti+Pfq/O/MPCxVVC4vG560vCsDtWHSDUXU0NSWTMOfTQ43OAB9OnIPDk5/BX92jkStXWwFw/RLoq10jkWkFwCVKXxQqNNBJZCiO7YNfhydiQ8JEnAoKQzWreQCcLfVBEZ+Pj2II+B5ypWUtIvhdw5zfyrRP6wGwfQa4SOKNCkEjAbiV5wDfrQBsXi0FvwzsMWOQPAXAjtadNsFqLgBf9PZgn70p6+v/IjNKqZwvglbth5p773UKwI1xgc6Uq3FLyswBtgfg3cPGY/+YmbjYLQZ/do9GlYgpgdb6BSJr1nOMN0JTATgtzWG/b0vdt2kGmKoti8bnrS8KwO1YdINRdTQ1pZcs9bvjjeoBfu7D3TicOAdHJicjq2ccChWaujnAdhngQpkPrneLqgfABSYArhkwABemJWPzI4k43UwALjUBcBlPiGo2B1e8CGSveShjtYggeTjBvBeX4rbStge4fgm0V+MzwE0E4JbKAOfe5QDcksvTAHw3uEA3B4BzhJ77Msmc9X18AkEplzm/Mp4QBV5qlEQ5LoFu7BgkMwCX2ZlgGQgLPw98HN8OmYxzXaNx6Z4oVAglKFBoUKj0w/5RifhjSjJuPPkMamUy9wA4Pp4pezZnfl1kfZt736Y9wFRtWTQ+b31RAG7HohuMqqOpKW6ia7acbZQL9OzVO7B34rMOAbiSbwvARXIlbobGOM0AY+BAGF99DddnPY9r3aKaVQJdyuHjloQBYHOgW8wnCPyHhyA4lSDyaQ6uesktcOsIgHNF8jYHwHd7BrglVzWLDS1fhDIKwHUAbNqH12QE8lc9B7/chQTHVXXnYSAslPKEyJEpkRUaxfTamgDY+ndpKgDr7QB404DHsXHYFJztEmXpAS5W+qJY5Y+tD03GzyOm48DoadCJpQwENwTA5uyvm5nf5ty3qQs0VVsWjc9bXxSA27HoBqPqiGrsPMndZ7KYjMX06cCECQ3OAX7nq0P4ceRT2DcuCVk941Ds4wutEwAu8VIiKyzWBoCte4AxcKAliNT17Qc9h2vjAp0tUaCM33QAriEEhXyCgBc9B8HS1wiy+XVgYx+Y5zTFBZpmgO/YqjZlgMv5IpTTHmDUEoISLsFTIwjYHix75i0gyBbYnofRBMC3pEr81SUC1QGBNgBsbjFwB4BvWQFwtsxcAs21ea0t9z+Bnx+aiuvhvZDVsxeqxVLcVvnhtiYAR8fOwL5xSdj8wGRUiiTQS6TOAfj++xmnZ3P2183Mb3Pu23QOMFVbFo3PW18UgNux6Aaj6ojSG2uw8fhNLDJlCmatP4aUH89g4c/nkPLjGcxafwxTPzmCRb+cw8bjN2Ew1jABW3o6sGkToNE4BWDjolT8tOcc9k58Fj+PmI4r3aItAOzIBKtMobIBYGsX6Fq53AaA0b8/jFxePQAubwQAZ0t9UM4X2QS6BkJwwUuEYE9BsKmM86Lc8RzgtgjAeRLvDgXAZTwGgLV8mgHOFxJ0e9Zze4WkEcheJbglqH/eRsJCKZcB4Ish4ajwDXAAwKxGmWBlmVygy7nCegC8ddBY7B8zE5mRvR0C8B+Tk3Fg9DRoBWJUiySodQTA8+bVOT03EX6bfN+momqjovF564sCcDsW3WBUHVV6Yw12XcjFyl1XMP+ns0j+8gSSNhxH8pcnMP+ns1i56wp2XcitH0SVlwPPPAPExjJ9d3YAjLQ06AuL8Pdzc/HHlGRcD41FkUJjyQDXB2C1BYCL1bZzgOHlVQ+Aa3m8uqCcxcEtsbfbAFzG4SNXpoTWDoCNhCBX7I08PsGwqZ4L7LkLCW6K6wNwtrBtAbCRsJAvVXQYADb3AJfxhB0egM/6EIjneQ58SSpB/BSCbF7969sagLOkSpwLDoPWAQDXEBYq3BiDZC6BzvLSIFeuqtcDbCQs7Bgy1jIGyRkAHxs7AxVCMapEEtTw7AB43jy3nZ49et+mompjovF564sCcDsW3WBUHV3aagOOXivCppOZ+Pbo/7DpZCaOXity3TtWVcUAaUgIA6l2AIySEiAtDbqUeSjtfS8qNP7QSaSoFIhQZVcCfdtbhRvdo3Hlnijk+/jhRo9oaDX+qA0KcgjA4PPrgnITALtbAl3GFSBfroKWL7ILdBkArmZzUckmWNmHgHhoTJLPywSZEtvAPFsoa1MAbCAEBVKFy3FL7oJXW1h6NgeVQjG0pgywsYV/l7YAwMVcgpkjPTvflzWfIF1NUMYTopwndA3AEh+cCQx1CMBGwkKl6YsK6+c6zwBrkCNTotSBCdav8WOwY+STyIxwDcCVQgkqhWIYeTxbAG5Cv6/H7ttUVG1IND5vfVEAbseiG4yKqgkyGIDNm4GoKMDX1ykAY8EC5nGTUU2tVAqDSGwT1BbLlfjrnkhcD41BqSYAJdG9GfgNDnYKwGa3Vz27rgdYx+bCSFiWANgRAJdzBciVKVHOY37eGjZyxd6WYxgJC0fUnoNgaQrjapsvbJsAzGSAO04JtIHNQbVIgiqhGBV8UaPhtCnvy90EwFligk4vejbrG/osQRGP2aPlLgDYYALgTIkPMgJDUaz0g0EiRa1dD3CV6YsK2+c6L4G+JXUMwN/1G42Nw6bgSnemSsUpAIskqLiDAExF1d5F4/PWFwXgdiy6waiomqiqKmDZMmD4cOCBB2xnWzoBYEilNm6ttYSgQqlGQVQvlPa6FzUhIQzkBge7BcBGDhcFMmW9EmgzAJc7yAA7K4HOkyig53BhZLFhJCzoCQvXpASSFM8F/ZJ5BGujCW4KJXcMgFtiDrCRsFAkU0BH2M0GvbawDGwOKgRiVAhEHQ6AS/gEmpc9B7+chQTPPkhQyWFeszEAfCYwFPkKX1SJJNAJRTbvnSMAts7cG1ks5EgVyAgMtWSAy3lCGDi2PcA/DXgcXyRMwrmu0fire4z7GeCoqGYZXlFRdXTR+Lz1RQG4HYtuMCqqZshsjGV2iF60yC0ABiF1y9+fAduBA5kxIW4CMAhBLY+HSpUGlUIxdGyuDQDrWBxUcPk2AXQlT4giLxUqBCLoObYAXChVwMDhoobFRg2LBQNhoYbFQjGfoPMLxGN9wexFBImjCPL43DYFwKVeSug7CACbe4DLeR2rBPqUmoDrwfm+4tcJLnrZnlcZV+CyBNoMwLekSvzZuSdKVH5M/61Va0UNYaGS1wAAExZypUwWOdtLg3wvNVM2bQfAP/Z/DBuHTcHpzlG41DUKVe70AAcF0ewvFVUzRePz1hcF4HYsusGoqFpAZhA2r/LyOwLA4PGAgADUymSo4fJQYyqBrmGxYGBzYDBlhSzALJGgSuOHaqHYEuiag90SuQ8zYskKgM0l1SVcgkcneA6CySKC/jMIyriNgLJWBWBzD3DHAWCm/7djuEBruQRPPUI81gJA0gj8XiQo5tU/LzMAl/EELgE4R6ZEZo8olKr9USWSoIJnC8DVAtcl0EZSlwHOVfiiyFuNKoHI5r5gJCxsvI8B4IzOUTjfJRKVIolzF2ixBLViMTB4MFMds3s3zf5SUTVRND5vfVEAbseiG4yKygOqqrqjAAyZjHmczWYeZ7OZvxOL6+CXEOiFYpQqNagSih1kgH2gcwLAejYH5VyCpOEehALTvOBbQjehrBUB2EAIciUdZw6wnsWBVtC2TLBcPd8VABfyCfrM9OCXPakEA6YRlDr4sscWgJ1ngMt4QhR5q3ErNBqlan9UmwDY8vMsFgxCEWqsrk9nGeCLIeEoVPqhVOXrEID/mzAGXyRMwpkuUTjbKRIVQomLOcAy5p41dy7N/FJRNVM0Pm99UQBux6IbjIrKA2pBADb2H4CsZ17A5SefRX5EHIzcur5edwHY/PNVfCEKTSXQBjsAzpcoGBMsFlP6rLcDYHPgfE5JoJjrOUDgLCA4o2gYeFwBsCt35pbKAOeKOyYAl/Pu7gywzo3nOwPgi95MX7qnrm3ePII1cQRaNsvptVvGFaCM6xyAjYSFCoEIt5W+NgBcxa/7ebBYjNcAi2X3/Lr/N7LYKJArcaNbJG5rAhwCcA2LhV1Dx2HjsCk41SkSp4N7QisUo1jpi2KVP7Y+NBk/j5iO/WNmojwgGDW9egF9+zIGgTTzS0XVLNH4vPVFAbgdi24wKioPyLo3ePLkJgFwbVAQ9FIZsiLisO/xmdj26JO42jWSKVM2B7EcLmr9/d0G4AqeECUKtcMS6NteSgsAGwkLOmLqAyYEOhbHJhjXsQnmDfJcNpi9iGBVLwI92znENBWAW8oFOk/ScVygrecA360AXPf5Nvx8+9fTsQmWeHD0F0kjUL5MkCsgqGaxUc3mNADAzHIIwCwWqoRitwAYLJbNvcYaiI0sNgpkSlztEoHbaucAfHLUFOwY+STOdY3GmZAIaAViFCg0KFT6Yf+oRPwxJRl/J7+EmmlP1s37pfBLRdVs0fi89UUBuB2LbjAqKg/Kel5wIwC4NigIWo0/KsVSXL4nCr+NmIb0x2bgRo9oCwDXEMadV6vUoNYFAFsH0FV8IUqVGocAXOathIFjDcDEAsDVrPoBu45N8GkEAcuDpaKB/yS44OUMdFoXgAtlHWcOcDWLjTKeCKWmzOTdCMD2GWB3e4BL+Ez/ucdKntMIJK8T5PNN8OsmAJc6AOBawkBpYwG47vh1mWcji4U8qQ/OBoUhz8cXxQqNQwA+NWoq/pgwG5e7x+DPbtGoEkuh1fhD6xeIrFnPQZcyj6l2SUujZc9UVC0oGp+3vigAt2PRDUZF5UE1EYCrfANQrPSFVijBjbBYHJ2QhKMTZiMrLMYmQNWzOSjxVsEgltoAcC2bjRouFzqB0CZ4rhKIXAMwl2cB4GriGoDN67Avk7H1FDywUgmefJQZE2P9uncagG3hzAzAHccEq4wnQuldnAFuignWUQ2BYL7nrl2SSuAzlyBbYDo3dwGYJ3SaAXYGwNY9wNYAbP+emn+mhsVGvkxp4wJdYeUCXUvqAHj/mJm41C0GWRG9UCuXMxUtnToBr75al/WlmV8qqhYVjc9bXxSA27HoBqOi8qAMBiZAfOYZoFcvBoSlUpcAbOx3H0rVfsj31qBSLEVWzzinAGxgc1AgU6JaJEEtj2cpcaxhsWFgc1DFE9gEwBU8AYq9HZdAl3krTXOAmdLnhjLA1uuWmKDzHA+WkKYSiF5nYNsCZXfYBMsWJDogAJtKoO92F2h3SqBzxAQPTPRs1pcsIkgcYfvFjTsAbJ4D7LQH2AEA27tAOwJgpmrE6v9ZbBR7qXApJBzZXhrkylXQ8uoD8OFHJuGXhxJxPbwXSuL6Ml/kmQE4JYVmfamoPCQan7e+KAC3Y9ENRkV1B2QG4cmTAaXSJQCXxvZBidIXBQoNqhoCYA4XhXIlqoRiZgySKeA1sljQOwDgcq4A+XJbEyxzcFxqAmCDqffX3Qyw9TH+G0Igec2zGbW4WQTZotYH4Hypd4cB4GrCZIDvZgA2L1cArGMTpCR48Isa0zWqfongrIPS/eaWQDsywbKfAwzinglWDYuNUh81/uoSgVyFL3LlKpRxBdCzOTavtW3wWOwfMxP5sX1RO2AAA8ARETBGRePSx1/hp6PX8e3R/2HTyUwcvVYEbTXNAlNRtYRofN76ogDcjkU3GBXVHZLBAGzdyoAucQ7AhVG9UOSjQbGPr1sAXOKlQqUpo2t2bTbPATYHxeal5QqQS0RfvgAAIABJREFUK1NCyxdZxiCZg90SuQ907OYBcCmLh+/DCaSvexAw0gjIQoJ37mWAxtF5eH4OMAt5Uu+O0wNM2Cg19QDf7SXQzgD4goJA+qpns77sRcyosFKO4zJ8dwG41AUAm8cg5XupcLVLBAoUvqgSSaCznvndCAC+FRqNQqUfCrzUKOMKoLMGYBYLp0ZPxfVZz6M2Ph5ISEBt167488XXsS95HlK/O4bkL08gacNxJH95AvN/OouVu65g14VcGIw1rX3HpaJq06LxeeuLAnA7Ft1gVFR3UAYDsHEj4O0NcDhMz25AgA0A50fGoVChQbHSTQD2VqFCwMz1NRK7Emg7AK7gMRngcp4IerYtABfJbAG4MSXQ5mOUsnjQsQn+1ZdAsMDDEGyaG/xFBEEZ3/Y86Bzgll3WANzWTLB0bIIP4zyc9U1jxnf9KTefA9ujAFzKFSJHpsTVLj1RqvaHQSJFrbW3gAmAa4h7AHxbE4BSpS8q+EJLBriWENSy2NAlP8uUOickoOb++5HXqx/e+eoQpn5yBLM+P4aUH89g4c/nkPLjGcxafwxTPzmCRb+cw8bjN6GnEExF1WTR+Lz1RQG4HYtuMCqqO6yqKmDpUmDUKCA0FBg6lIHfZmSAKwRi6NkNA7CWK0CBXIVyvgg6OwAukCpQbQPArCYBsBk6NkQQ+Lzs2YybGYTFrxOMmERwSXHnADinA80BbqsA/D8ZwYBED19/aQTCeYzLs/X75SkANhIWynlC5MpUuNEtEsYg04i15gKwaQyS+Ysxi5v8888z88yXLcPllDexZdZrePL/9iH1l3P4184r9VbqL+cw5eM/sOiXc9h1Ibe177ZUVG1WND5vfVEAbseiG4yKqpVkPSs4MRGIj29yD7C7AGzuAdbyRZZSR3NgnS+pA2D7OcCNBWDzyhEQRDzN8TiAWMMwWUQQ8xTB4QDnMEcBuHGrLQFwNSHIFRE8MMnzWV+SRiBPIbghrP9+eRSA+SLkyRkArg4IbDEAruSLYGDbmmBdHvckLj79Eg6cvYml2y5h6idHnMKvNQRP/eQIVu66QnuCqaiaKBqft74oALdj0Q1GRdXKqqpiMiwJCU12ga50VgLtwAQrV6ZEOU9k2+tHCHLF3nYA3LQSaHsQGDN+IUaPvQOZYEcwnEoge5Xg4ckEGeq6c6IA3LhVzbr7AbiUT7AhkqDHs3cGfEkqwZTRBOWc+ufqSQA29wDnyFQ4HxyOEpUfMwfcAQC72wNsBmDrEmgzbO8eNh6bxyQh+eODGLnmAEatOYgV2y+7BOB/7byCWeuPYf5PZ3H0WlFr32GpqNqkaHze+qIA3I71/+3de1zUVf4/8PfcuQqKSmp2s9TasjIveaksNMukslay3DRdMHe3tsxc8wKmZpKKKGaLua3SZV3v7m/NGyoKigGaoF/zWq2alzQzAbkN8Pr9McwIzDAMMPCZy+v5eJxHyTgzh/nMGc9rzo0NjEhh5h2i//AH4P77gd6963wOcKFv1QBcqlKhRKXBda2+Sgc4T2vAhYAQ5Op8UFSpo2uUqgG4IZtgVQ8CL42Yi5PNmmHswMY9L9jRQNzhz4LPugiu6u3/PvZCGtcAKx+Az/sL3u4vCB0n0Ey9cX2b4r2kmSr4NvhG26n+ZUpTBODzASHIadcJl5qHotjP9hrgugTgqy1aI09bNQAb1Wr8+6+zsOT9f+CZuB3oOmMbwuJSELk8C3NrCcET1+Rg7Bf7sfbAWaU/YYncEvvnymMA9mBsYEQuwGgEtm8H4uOBDz9E2b33Ir91GxT4BeBYh/uwcdCrSHnuNfyvYxeUaLQVZ3qaRoDzQ1rD6B9QZRfoUpUKxSoN8m0E4PMBLZCr86kyAtxoAVilxpjXF+BCYAiMosL3zQTdRzXRCJ0jgTha4DNZcOubgshnBCeDGYBdKQDn6gVf/U7Q5zVBwESBqnLQbeoZBRXvGZ/JgjM+guKKNqFUAL4QGILD7TvjYnDrKscglYuYgq+fX63nAJsD8K+t2uDnZi2rBOByMS2x+Owfmy0jun1jd6DnrGSEL0rDG18dsBuAp64/jKikLKzIOK30pyuRW2L/XHkMwB6MDYzIxVy9ajpupH17lAQE4qffPYhdz4/C5mdG4OQd91oCcLkISjValLdpg/LAQBi1lQKwmAKwrRHgmgLwz/7NGyUA/23cYlwKanljdFoEOS0EvpNcIATbCjjvCeZ3q7qztM0A7E1ToBs5ACffIrh7rClcqqMVDrl23hudxgqu6Ex1VioAl4oK13Q+OBcQgsM3mwJwnt4P+RV/37ykoUDvY3X/0krXrUylxtVg01FKl1qE4lJQK+RpfSwzTIoMvvipUxcsWr0X87cdR1RSFsLmpaB/3C70jd2BiMR0xG46yhFgokbC/rnyGIA9GBsYkYspLATmzAH69wc6dEBpn7449/pfcWzEn3Dpdw+iVHsjZEKnMx2jFBiIUq2uSgC2NQU6194IsL/zR4CLVRq8N/4TqwBcKoJzfi4agqfdCF/NxgvmdTeFYa9eA+yEAJzdStB3hEA7uVrAdbWga6Oopwo+6C4oUVfabVqtYADW+uAn/xbIbtcJF4JaIVfvi7xKAdgoph3fq9errKI9l4tplsivQS1x+s77cKVlG/wS3Aq/+TdDXvNWyGvRCqkj3sKCjTmWQDt+5UEMTkhFvzk70W/uTgxOSMX4ldlcA0zUSNg/Vx4DsAdjAyNyQZWnRMfHA5s2AZMmmc4L1utvrPWrFIDLqgVgWyPAuVo9LgSEVByDZD0FutgqAJtuL25gAP652Y0AbO6kl4spBLca5+IBKEYgUwVRAwW/GhiAawrA2a0ET75imqos1Udx3SDk1nTtO/5JcNpPUFLp/esyAbhtJ/xcMQKcW20E+LrOdgC2/L9KjestWyP3/q7Iu6kdfmkRihO/645dkROQMnZSlfA7f9txfLT5KCIS09E3dgf6x6UgbF4KopKyuAs0USNh/1x5DMAejA2MyA2Yd4q2E4CrjADbWQP8c2BIlWOQbkyBNgXgUhsjwA0JwO+89TEuBIbYDMDlIvhVL3himBsEpBiB/wTBP+4XFKoZgMvEtGY6/PcClTnwKn2NnFhUUwVb2964bsUuEoCNlQLwoYop0Ll6X6sAXKDzqbKRWOU1wJYzftu2BR5+GL/eeTfOtL8Ln0/+GPGbj9Q4qvvGVwcQvigNPWclo2/sDoxelslzgIkaCfvnymMA9mBsYERuoA4B2Dy6U6LWoKDaMUj5WgMuVzsH2JkBOFdtvQY4cswC0wiwynYALhPB1YDm2HKzaaqp0sHHkSDcYaxgd6jOawPw4vsEmimeF3rNxX+i4Jyh6nVrqgCcpzUgV+tjCbTVb7eMAAe0wP+172yZAu1IAK78Z0sAnj4d2e9Mw8rh4zDlXxl2N7aat/UYIpdnIiwuBV1nbMXTC3Zj4pocTF1/GBPX5GD0skwMX7oP0RsOY1XWGRhLy5T+5CRyW+yfK48B2IOxgRG5AfNRSRERgK9vrSPAlnOAK+8M62AAtrUG2NEAnKfRW3X43xv/Ca4Et0KZSm03ABf6+OEnP8Htf3GTYBUj6DdckKv1ngC8I1Sg9eDgKzGCbq+Zrmn192hREwXgfJ0B+Tof5OmsN7GqHIDPBZh2gT5vYw2wvQBsfkyo1cDNNwMXLuCb73/B5HWHbI7o2grB4QmmM4Ejl2di7Bf7EZWUhbFf7MfkdYcQn3wcyUcuMvwSNRD758pjAPZgbGBEbsJoBNauBVq2NJ3zKTWvAa4pAJunQOfZOAe4oQG4XAQF2qojzsUqDeZNXYpfgltZRoDNm2BV7phf9gvCdb0vyir+zu52glvecI+g5TNJ8H92jk/yhACcpxZM7O0e16O+RTNFsPBB0/T26tfKZgBupF2gC/Q+KDT44rqNXZwrB+DzASH4v/adca5ZXQKwymYAzi8yIj75OIYv3YeYDYftBmDz+t45m49i9/FLWHvgLFZknMbaA2eR8cMVrvklchL2z5XHAOzB2MCI3EheHjByJODvbwq/lQJwuU5n2eW1TKWyGYBztQZcCAhBro0AbO8cYEdHgKsH4CKVGn+MirecA1xuIzCUieBnvyDk6X0tU7jN5XiQoPVbbhC8YgQvDRGcCfC8AHzWX/BgpBtcgwZcu3siBWd9ze/NqkG3KQIwKv3/dZ0pABfofe2uAT4XEIKcdp3wU0UAtjoGqYYAXCoCo1pr+tyIjDR9pgBIPnIR0RXrd2sKwVzfS9R02D9XHgOwwgoLCxETE4O77roLBoMBbdq0wahRo3D2bMPP12MDI3IzeXnA668DXbsCN91kCcDQ6y0jqKV2AvB5/xY2A/AF3yCrAFxaxwCcb2MK9B+j4nG+lgB82S8I+TYCsLnsaC9o+5aYdhdWOjDZK9GCvsMFl3zcPwBfMQjG9RcYJrvA69pIwVcVLfio4ngj8/uyKQJwcaUAbF7OYP47ptFfX+TXMAXaHIDP+rfAt2064qdAUwC+rrMfgMtFYFSrke/jjwvdept2ljfeGK0tKS3DqqwziK4Y4R29LJPre4kUxP658hiAFVRYWIjevXtDRNCmTRtERESgR48eEBG0atUKp06datDjs4ERuSHzMUlz5gCPPw60agXo9Sg3bzSlUtncBKvyOcDVA/B5GwG4zmuAq22CVaI2TYG+GNjSEixsTYH+2a+ZzRHg6uV0gOCVZwU6V1+HGiP4U5gpWLlbAC5WCz55UNDyXRd4HRvx+vR9peoXFU0XgDUoUWutArA5BBt9/VBQlwBchynQ+T7+OHlvDxz97N9Vwq9ZSWkZko9cRHzycUxed4jre4kUxP658hiAFRQdHQ0RQa9evZBXMVUJAOLi4iAiePTRRxv0+GxgRG6ssBCYOBFo3960O7TatNFUuUoNo0aDQhu7QP8caPscYFsjwM4IwPHTPqtyDnBNAdh0vI5juyrn6gWLHhTc+kalI3hcMBCrpgq2t3GfAHysueDWN13ztXRG0UwV9Bop+D7Q+nd3hQCMigBcaKg5AJeKCrk60y7QB9t2rHENcOVzgMtEUKQ3YGevQVjz4T+Qn19o92Mlv8iIjB+ucH0vkYLYP1ceA7BCSkpKEBwcDBHBt99+a3V7ly5dICLYv39/vZ+DDYzIjZl3h46MBEJDbxyRpFajXKtFcbUp0IV6H/zWojUKffxQotZWDcD21gDXsGmPVQCuNgW6WKXB9PcScTHQfgC+WBGAaxsBrvLYorbUKVcv2HyH4LXBAr2rjQ7HCO6MEpz3dd0AfKqZ4ME/utjr5qTXXjNVcH+U4IM+gvP+NX8RUVsAtjoGqR4BuLgiAJu/fKoegMtFUFQxBbrQYHsNcKmokK/3xYXAEGS3vbEGOFdTNQDnaw0VbU2FQoMPUnoNwowV+7h2l8hNsH+uPAZghezcuRMigg4dOti8fcaMGRARTJs2rd7PwQZG5AEKC4FZs4BbbgE0GtMOrzodig3VArDBF9dCWqPIxw9GTR0CsIMjwNe11gH43bcX1x6AfR2bAl1TAK5ej8xWgkdfrXRkjysEuxjBgyMFR5srH3jN5aKvoO+rLvL6OOH1lRiBTBXc/IbgxRcF2a1qfq8qE4A1FQFYaxV+zQG4UO9j9xgkY8UI8MXAlshp1wnnm7VCno1zgK/rfFCg88GvzUKwvU84ZqzYx7W7RG6E/XPlMQArJD4+HiKCoUOH2rx948aNEBE8//zz9X4ONjAiD1FYCEyfDgQHAwYDyrU6qynQ5hHg6gG41AkBuNxGAC5SqfH66wtwMTCkSQNwUbXHORks+PPTgg5/FtNGWkoGvhjTztZzet4YkWzKkqsX/L87Bd1GuHHwjblRVNGC5uMFrzxnus5FlQJtTa+BUwJwPc4BLlZpUFwxBbqmAGwOv+ZAaysAm3eBPnRzZ1wIao18g1+VXaBLVGr87+Y7sevxIdg4cjwWfp3DtbtEbob9c+UxACtk3LhxEBGMGzfO5u3Z2dkQEXTt2rXez8EGRuRB8vJQGhmF3+7pgrzmIbhuYw3w5WYtcV3vW2UKdKlYH4NUXPHfOk2BVuutgsCIUXFVdoG2FYAv+NZtDXBdA3D1OiXfIuj4J9NooaIjxDEKFqVDbD1eH80Uwd2vC7bfUnOorW8ALnViAC52MADbbENaA3J1PsjV2Q/AP/m3QHbbTjgf1ArXffxQWHFucJmoYDT4IG1mAtZl/Mi1u0Ruiv1z5TEAKyQqKgoigilTpti8/eTJkxARdOzYsdbHMjek6sVgMLCBEXmIktIyrN73A5ZNX4oVz7+OC8GtqnSi87QGXKjYBdpqE6xKAbhUVCiWuk+Bzq22CVaRqPHqqDicqyUAn/cJbNIAbP6dzT/LaC3QT3SjYOgppVrAVUULfCcJukQJZvat2wh5UwfgkooAXGrjuYpV9gNwTV8olYlpp/ZcrcGhAPxtG9MmWNd9/JAb0AzXDb7Ib30TMGgQcPWq0h9HRNQADMDKYwBWSGRkJEQEU6dOtXn7iRMnGICJyCL5yEVEbziMVz79BrO+3Iuzd/7OKgCfrykAO2EX6GvVA7BKjTf+koCLtQTgcwoHYHPZcIfA/28Mwo0Zcs0juQ9ECtLb2g+kjr4XmiIAV98F2ljRfuoagIscCMDXHAnAAS1woCIA/xbYHP/XuRs2vToO332xzuYRR0TkXhiAlccArBBOgSYiR+UXGRGffBzDl+5DzIbDWLAxB7tf/SsutQhFkVqLIpUG17QGXAgIQV4tI8D1DcC2RoBff30BLlU6Bqn6lFFXCsDmcqCV4GYPPg6oKULvrW8IYh51bBTXFQJwXY9BMq+hLxWVVV1LVGqUNCAAm0ttAXh/m474rvXt+LHdnZjzxhws2HKE052JPAT758pjAFYIN8EiIkd98/0vmLzuEEYvy8T8bcctJXb9t/hk0Bik3fYATgeF4nwNAfiiXzCK1VqUOjkADxsxFxcqbYJlKwArPQW6prK3DUeE61LUkwVx3QQl6vqFV3cKwOYp0GUVbaR6AK7vCLBlDXBtAdi/BeL6voLZT47Bx+F/wfRVWTziiMiDsH+uPAZghTh6DFJMTEy9n4MNjMgzrD1wFmO/2I+Ja3KqBODxKw8ifP5O/GXEbGx+4AmcbH0rcnW+VgH4Z//mKNHUEIAd3ATL1hToiFfn4nwtAbipN8FyNACXi6BYbdqx2e89BmGbJUagmyJ4bqjgkk/dQqsrBmBbO5HbWgNs2UVdZfu83/quAb6xCVbNxyBd0/rgp8CW6P7m57gnejNeWcojjog8DfvnymMAVkhxcTGCgoIgIvj222+tbu/SpQtEBJmZmfV+DjYwIs+wIuM0opKyMHX94SoBOCopC2HzUjB4/k7MeGM+dj74BK74BVUJwKXinABcfQS4WKXB6Mh40wiwquYAfNGFA7C5XPAVPPISQ3D14PvSEMGZgPoFX1cKwOa1vDUdxVVSLQCXaSuOMlKpgGohuCFrgGsLwIVqLf7XrDXSbnsA3SesxuNzU7B450mGXyIPw/658hiAFTRlyhSICHr37o38/HzLz+Pi4iAi6Nu3b4Menw2MyDPUNAI8elkmHp+bgvCENAxbnIpZf5mH7Lu6Is/gB/O5oeYAXNzAAJyn0Vt1+N96cxEuBra0BODqmwaVieCin3MDsK3w0dAAbHodBHMeEtNZwkoHUCVLtGDIC/Uf8XXHAGxUqS3/DxFApzP9tyIAVz7LtyFrgM0BOM9GAC4Vwfmg1vhkwGuIfHU2Hp6+BR9s5LpfIk/E/rnyGIAVVFhYiJ49e0JE0KZNG0RERFj+HBISgpMnTzbo8dnAiDxDTWuAzSPAgxamIiIxHcMWp+KDv8zDwdvug1GltuzKfDmgOYpr2gTLwQCcX0MArm0N8AXfZsjT+dQYPuoagO2NABc3IACb//+cr+C+EeKdo8Exgm9a2A6RDMA3ArCtL3OKVeoGjQAX6Az4auBreHTa1+g5Kxmv/TOD636JPBT758pjAFZYQUEBoqOj0aFDB+j1eoSGhmLkyJE4c+ZMgx+bDYzIM1TfBbryGuDBCanoN2cnIhLTEZGYjucXpODdV2fi6G334reQ1rju3wxXmoWgWHMjABdXhIG6bIJlKwCPGDUP5wJuHINkLwA3xRRoZwRg067ZQfimlcDvXS8JwjEC7STBYV/T7+9tAbjyiG5tAdjohBFgcwA2lzyNAf95oD96Td6AnrOS8fKn+/DvzNOc+kzkodg/Vx4DsAdjAyPyHJXPATaH4I82H0VEYjr6xu7As4vS8OyiNPSN3YHwRWn46+cZWPPhP3C4XzjOtbutSgAukkoBuJ4jwEUqNZ57ORY/BbSwG4Cbcg2wMwOw+XlW3ymQqR4chGMED78iuKDTVHxR4XkB2N4u0HUOwGqNzQBc4sAmWPk6A/IqAnCxWoML/i1w8Oa7sSBsNJ6YsRmDE1Lx5lffYsvh8wy/RB6M/XPlMQB7MDYwIs9RUlqGVVlnEL3hMIYv3YfRyzIxcU0ORn6WgbC4FDwwfSsenpWM8EVpiFyehY82HcVfP8/AzDfjkdLlUVzXGqqsATYHYKOja4DV1QKwqPFstQBsaw1wUx6D1BgBuFwE+VrBC896WAiOEdz5uiC7hSBf72tZm+ptAbhMbkyBNgfdmgIwRFCm1lSZMm157zkwApxf8Rpf8Q/Gb82aI/GvH2Hiv/djwupszN1yDLuPX+KaXyIvwP658hiAPRgbGJFnKSktQ/KRi4hPPo7J6w5h7Bf78cflmRickIoBcbvwSOwOhCekYfzKg3h5yT6EzUvBQzGb8Maw93Gs7Z0o0PmgWK1FcUUQLhPTmaeOBBCrEWBR44U/fFTlGCTzmuPK9zvXlAFY1TgB2FxOBwoGDhOo3HmjrBjBrX8RnGh24zXL0/vimtZzA7D5ixlnBOByrRalNgOwY2uAv2t9O7Y+8hxO/n4EjL9dU/ojhYgUwP658hiAPRgbGJFnyi8yIuOHK1h74CxWZJzGqqwzWLzzJD7afBST1x3CkMV70Dd2Bx6csQ0D5u/CsMWpSJi4CAcHReD87Z2Rb/Cr0xTochEUaA1WAXh05HxcalZ1F2hFA3AjjQBXL7l6wacPCG59o2JU2JVHhivqZ5gk+P2LgpPBVX+XIpUauTpTAM5lAK41AEOrRbnG+kujoloCcKkIfvFthr+9HIOZG7I5xZnIi7F/rjwGYA/GBkbkXfKLjNh9/BLGVOwOPXzpPoxflY2PNh/F/G3HEb/5CNZN/zsutb/DMvXZ0TXA17XWm2C9985iXApyoQDcyCPANYXh+d0EN78l0E29ETgVL9GCluMFH/Y01dHea3bNCwKwqTgnAEOjsawJrtweTGuAtTbP+M3XGrCmS388N3szdh+/pPRHBREpiP1z5TEAezA2MCLvU9ORSeayYGMOUke8hbzgljBqtCjU6GyGBqsOvt7HOgCP/6TJA7C9c4BLFAjA9oKXO5RiLxkBtheAix3cBKvWAKzWoMRGAC7Q6rGtx0D0mrwBgxNSGYCJvBz758pjAPZgbGBE3mftgbMY+8V+TFyTYzMAm0Pw7tHjcaHjvTjXvoOlww57xc/PqsPvagHYyABc51LkJSPA9qZAV39PNWQE2ByAzW0hz+CHrT0Gov+0jQiLS8ELi/dg7YGzSn9MEJGC2D9XHgOwB2MDI/I+KzJOIyopC1PXH64xAJunQ6+a+zn+/ddZ1lNAbRV7AdjOLtAcAXbtUiQMwM4MwMVqLUpUalzzDcS+zj3x7muz8disbQhflIaXl6QjcnkmVmScVvpjgogUxP658hiAPRgbGJH3cWQEuHKZ/tkOfH/7PSgVVb0C8MXAllWOQfK2NcD2gpc7FHcKwMWVrlFdn88otU+BNv+8TKtFudQtAJeoTVOgc3388VPzNlgyMBIDP9yKwQmpiEhMxxtfHcCE1dkY+8V+jgATeTn2z5XHAOzB2MCIvE9ta4Crl9HLMvH+V+m48NzQGyNftkq1AFykUuPtNxfhQmCI3QBcr3OAVa69C7SjwcsdijsGYHv3d0YANlYcDVZWMbXfoRFgnR65wS2R/sTzWPnSWxizJBVRSVlVNqEbvSwTk9cdQsYPV5T+mCAiBbF/rjwGYA/GBkbkffKLjIhPPo7hS/chZoP9adAxGw5j+NJ9iE8+jvxfrgJRUUCHDoBabTMAV+70F6nU+MNr83AuoGoArj4F+oJvM+TpfCzhw5HCANx0xdMCsK1S1wBcUrEzelnFUWHlcmNTuDKNxuoc4DIR5AUE4bvHBiHhP9/W3taKjE5r6998/4vlOLS1B84i44crTnt8Imoc7J8rjwHYg7GBEXmn5CMXEb3hMF759JsaQ3BMxe3RGw4j+chF0x2NRmDDBuCWW2oNwCUqTUUAbmEJwEapIQDrnReA7a0BLmIArnNxpwBcUs/XurY1wCU2ArDpfiqr5zKq1FazGfK1emzuPhDLov+O+M1HHGtrDVBSWobkIxcRn3wck9cdwtgv9iMqKQtjv9iPyesOIT75OJKPXORZw0Quiv1z5TEAezA2MCLvVFJahlVZZxBdMeo0elkmJq7JwdT1hzFxTQ5GL8vE8KX7EL3hMFZlnanaUS4sBGbNAu66y7T+0TwaXBGAzSG4VKPF+xMTcb6WKdAXfJsht44jwCX1DMAcAa57cacAbHTg/vXZBKt6ALZMgRaV1XOVqNSW3cbLRPCbXyA+6z8Cg2K3on9cCl77Z4bjbc0ZbXu5/bZdwhBM5HLYP1ceA7AHYwMj8l4NHiW6ehV4/nlg4EDAx6dKADaflbopcbXVMUjVw8VF32bI0/vWKQCbA4itcFPCAOzU4g4BuPK1qe3+9TkH2DoAayv+bB2AjWoN8pq1wJW2t+KXdrdhffTHmLbmIJ6K341nF6VhxGffONzW6jOFud6zO4jIZbB/rjwGYA/GBkZE+UVGZPxwpf7rBK9eBfr3B9q3twrA2f/+L642b22RthYGAAAgAElEQVQJwGU2wsVlv6CmC8DcBbrOxZ0CsHkKdH12gS6VG5ta1RqANXYCsEaLY30GYM2H/8CquZ9bpjzHbDiMYUvS8e6qbPzrm//ZbWv1/XKq3uv7uSaYyKWwf648BmAPxgZGRA1mNALbtwNTpgB6fZUAnL89BddCQmsMwOUi+NU/GPl1DcAqTY1ToDkC7NziTgG4vscglVU8Z2kNAdhqF+iKAFxqIwAX6w34f5Pm21zr68guzw2ZwlyfHd656zSR62H/XHkMwB6MDYyInObqVeCJJ26cjarTAWlpKGjdpsrIWvUAcq1ZC1w31DUAq2sMNwzAzi1eFYAdPQapWgA2379Yp8f3XfsgYV2GzcA5cU1Oref8NmQKc13P+HakPkTU9Ng/Vx4DsAdjAyMip7p8GejT50Y5fBjl7dqhrCKwVt8Eq1wEV/yDcd3gawnJjpRSrgFusuIOAdj8GEUO3N/ZAbhQpcFvPgH4vwf6YFfkBCzYWHP4nLr+MKKSsrAi47TN5tPQKcwrMk4jKikLU9fbv6+j9SEiZbB/rjwGYA/GBkZEzlDjZj3/OwvcfDPK1WpLgKgeLq4GNkeRr58lJNsrlunVWm2VHadthRVbhQG47sUdAvCN61v7/e1uglXHKdDFGh1OB7XGskFRmPufgw0ecW3oFGaOABN5BvbPlccA7MHYwIioIWrbrCdx5R4UtG6D8oqjksptjPIWhbREeUCAJSQ7UhiAm664QwA2vw8aGoAd3QSrwMcPxTo9Mjt1R+Kg1zFk3nanrLltaIDlGmAiz8D+ufIYgD0YGxgR1Zcjm/WMStiOrMefQ4mPrykEq1RVd4oWAUJDUR4QUKcp0OWVAnD1EGxvCrT5/OD6TrEtFwZgVw7AJQ7cv6bnKxOx+R6sPgJcKoJtDzyBzY+9gJgv9yIyKROvfOqcXZcbOoWZu0ATeQb2z5XHAOzB2MCIqL4c3azntYXbkfHkUPx6f1fgppuqjN6aA7DRz79OAbhMo7EO0ubb7Iwkm49PYgB2vLhTAK7vOcDmqfm1BeBSEeRrdAgftxwvLUnH3C3H8HXOOaedu+uMKcw8B5jI/bF/rjwGYA/GBkZE9WFrpOmjzUcxfuVBRCVlYfSyTEQlZWH8qmxMXncIw5fuw4ItR1CwYhUQElIltJa1bo0iX796nQNsKwSjWjiucj+OANe5uEMANr8XyioF1bo+X+Up0NX/frGoUKJS46pPAHZ16I4no/+DYUvSEb3hMFZknMaKzNM3ZkIss39sUfWzeytzxhRmq5kZDagPESmD/XPlMQB7MDYwIqqPyh31eVuP4Y2vDiAiMR2DE1IRNi8Fj89NQdi8FAxOSEVEYjrCE9IwaW0OsvYfBzp1qhJQi1q0RKFP3QJwSaUNs+oSgOs7BbpyMYrgor93BeBcnS+u6XyQ1wgB2Fap9/VRNSwA29oFulRUOBfSBpn39sHS8LEY+OFWRCVlVRlF3Xz4vN218PHJx5F85GKtYdNZU5hrW5vvaH2ISBnsnyuPAdiDsYERUX2Yp2pOWJ2NyOWZCF+Uhr6xO9Bv7k4MWpiK8IQ0DFqYin5zdqJv7A6ExZnC8Jq0E8DMmcAttwAGA+Dvj/wWrVBQx2OQiiuCrPnPjgbgYieNAF8KCPaeAKwyBeDcigBsXi9bn8eqadp6Q18r89+3FWAdDcDGGu5fqDMgbvT7GLY4Ff3m7sTghFSMX5ltM4TmFxmx+/glzNl8FBNWZ2PC6mzM3XIUu49fcnidrTOnMOcXGZHxwxXr3dm55pfIpbF/rjwGYA/GBkZE9WHerGfkZxmW8PvsojREJKZblWcXpaHnrGT0jd2B6A2HTQ9QWAjExwNz5uDCgz1x3eDn1ABc2/0aEoBLReVdAdiJI8CNFYDNxVjpeepyHWyNAJeKoEijw4G7e2LEvC14tuJ9HpGYjthNR62mIe89edkpo66cwkxE7J8rjwHYg7GBEVF9rD1wFlFJWRi0MNVu+DWX/nEp6DpjK8Z8nlV19MloxJ45S3AtMBildTgGqXoArhx67G2CVd9jkKqGJVMAtnfckjNDndLFPALsrDXAjRmAS+p5f/MIsFFUKBNBvtaAI+07Y0vf5/CH+GRL+A1flIY3vjpgtRHVmM+zMHFNjt0d0SuH1hIHQjCnMBN5L/bPlccA7MHYwIioPr75/hdELs9E79nb0W/OTrvhNyIxHf3m7kTvD7cjcnmm1Zmj3+T8DxlhQ/BbQLDDwaXERgA2F6OdYFrkpAB8JbA5isXxwN6QUKd0cacA7Mg5wLavqakUqrUo1Ojw90dewdOzt5qm8c/daQm/kcuzMG/LMaujiJ77eA+GLUl3+s7LnMJM5J3YP1ceA7AHYwMjovrILzJiTFIWus7Yhv5xu+yGX/Po2aCFqYhcnlnlyBbzYy38OgerB41EkVrnUPipKQBXPrLGdkBqeAAuExWuBYXAqGIArk9pzDXA9Q3AZSLI8/VHxt0PY0enXnh44hr0nr29ykZub3x1wCr8zt92HO+sPIiweSnoH7eLZ+8SkVOwf648BmAPxgZGRPUVveEw+sbuQM9ZyXbX/5pHz0b+MwNRSVlYkXHa6rGSj1zEjBX78J8eT+P7lu1RqNbaDSy2pkCbg0xTBODc4LoHYHctljXAjXAMkhIB2NZjl2h12PPynzDxi314asFuhM3bhYHxu01Hea3MrrLmt3oZsngPwuJS8MIne+t9dBERUWXsnyuPAdiDsYERUX2tyjpjOvYoLsX2DtDVpo5OWJ2NsV/stxoBBm5s/PPK0n14OHojkvq8aDfE2AvAJfYCsIoBuK6lsc8BdjSkOvL36xOAiww+ONXtUSSsy8DoZZn42+psvLsq2+GjiAbE7UJYXArGrzzoUACeuCanxnZARASwf+4KGIA9GBsYEdXXN9//gvfW5CA8Ic3uGcDmqaO1jXyVlJZh8c6TGJyQiv5TNmBPp4dxLqg1rmv1VoHV3hToxg7ApaLCb0EtvCcAq9wvADtyDFKZCAp8/bHnlT9jwcacKtOT/5t9zuGjiIYtScdzH6dh6nr7YbnymuGaZkIQEQHsn7sCBmAPxgZGRPWVX2REfPJxDF+6D5PW5mD8ymxEJWVh9LJMq6mjjq59zC8y4qPNRzE4IRXDl+5D5D/SEf9OPL67t0eV82frHYDrOQW6rMr/q/BrYHOUeMsaYAVGgOt7TJUjAbhQNLju44dT3R7BmplLEL/5iNUGVXU5imjimhy8XrELNEeAicgZ2D9XHgOwB2MDI6KGSD5y0eGRMkd3v7X1mAnrMnDg/kfwQ6tbkK/zwbngVjZDbGONAFcJwKr6TYF25wDcWGuAa3pdGisAl4ng67sfwbIX/4L3V2bZPVfX0aOI9p68jMnrDmH0skyuASYip2D/XHkMwB6MDYyIGqIuI2WVw0V9HvOlJel45IOt+EvUPEx4dSaO3XyXVQht7AAMEUCtRlloKMo0GpcKwPZ2VW5oADaPAOc1cgCGjZ85IwCXiaBA74MfW9+CQZNWIzwhzeFzdWs7iqjyTAjuAk1EzsD+ufIYgD0YGxgRNZSjI2WOhF97j/nMwlT0mJWMJ+alICIxHe/8YzcODnwRV1uGolijQ75Wj18N/nZ3kG7oGmBzAMZNNwFa+ztVN3YArn6cUGMG4FydL3J1PsjXN+4UaPPvUN8AXFLpz6UiKNYZcKn9HTj41FAs/M8BjPwsA5HLMzF3y1GnnqvbGDMhiMh7sX+uPAZgD8YGRkTOUttIWUMfc9bX32HYknS88MlefLTZ+liav36egZjXP0Jax+74xbcZim1MUW7oMUiuFIBrCsNOD8AqNXL1vsjT++J6Iwfg+r5W5r9/XWeAUa3B5ba34ae7H8Su0e9gwUbT2tzJ6w5hcEIqxiRlYfneH5wWfoHGmQlBRN6L/XPlMQB7MDYwInIXtU01nbf1GCKXZyJ8URr6zNiCcRHROB/UEgUaHQpEg0s+gfgxsDWKVep6BWBLyHRiAHZ2cG2MAFysUiNP74t8vS8KDb5VNiNrrLDr6OOXiaBA54NzzVrikn8w9j32LA6Gv4KF/zlQ5X0x6p8Z6Bu7AwPidmHI4j0NnqFgS2PMhCAi78T+ufIYgD0YGxgRuZPappqaw06f2dvRZ/Z2PDZnJ56K34WHZmzDvVP+iz+9PB27OvXA9y3aokTqttlSYwVgZwdWZz9m5QBc5OPn9NFfRwKwedS+SKNDkd4HxTo9rrZsg++6PorX4rbi5U/34bV/ZliNvk5YnY2n4nej56xkPDwrGU8t2I0Jq7NrHJktcUI4bYyZEETkXdg/Vx4DsAdjAyMid1LbVNNRyzLwVPxuPLMwFYMW7Mbghal4esFu9J69Aw/N2IrH5uzEcx+nYdSyDPzl42Tsv6cnrvkEIE/ngwJ1zZtaVVln64JToJsiAOc1QQA2igrFGh0uhbZDvo8/CjQ6XPYPxqbuAzH2k501TitekXEaWw6ftxp9fWHxHgyI24W+sTsw6p8ZmLflGNfmEpHLY/9ceQzAHowNjIjcTU1TTV//PAsvLUlH+KI0PLVgN15blmEJTBGJ6eg2cxt6fJCM8EVpiFyeiXlbTWEodtNRTPziG6x7LhJX/ZrZD79uEICdHYKrT4Fu6O9RKqbR3AKVBpd0frgY1BJXm4Xgp85dsG7aJ4jffMQSTqeuO4SnFuzGS0vS8bfV2bVOK648+rp8748Y83kWBiekYtJa+2f0cndmInIl7J8rjwHYg7GBEZG7qj7VdMb/O4Ixn2fhpUTrNcLjV2ZjcEIq+sTuQN/YHQhflIY3vjpgFYQWrd6Lnzp1wVX/YJSKoFSlshuA6xI0mzoAO2ttcbFKjXyDLwp8/FCgrz0Al4rpKCpjRdA1iml35jytASdvvwdj529C79nb8cD0rRVfRmTZHJmtfG7uhNXZWL73xzpNK/7m+194Pi8RuSX2z5XHAOzB2MCIyBPUtkFW7KajiEhMR9/YHRgYb5oSG5GYbnM36ZgNhzEqYTsODn4ZJQMGAgaDWwfghobhYpUahT5+KPb1r3ETrFIRFKh1+MW/OXb1GYxxS3dj6N/34tGPduC+aVvQcfLXuCd6M3p9mIweHyTjoRnb8PTC3XjjqwN2w+/8bccxcU0Oxn6xH2sPnK3Te2LtgbMY+8V+TFxjf/S3oc9DRORs7J8rjwHYg7GBEZEncGS0742vDiB8URr6xu5An9nbMTghFeNXZdtfD5qXB0RGAh07AubR4GoB2NFg6a4BuESlgdE/AOUBATD6+qOs4nexnLWrUmP7/f3wh/hk/PnL/Ri9LNPyOvebuxNPxe/GQzO3ofsH2/DIRzvQ/YNt6D5zGyL+vtcyDd1embr+MKKSsrAi43Sd3hMrMk4jKikLU9fbPpfXWc9DRORs7J8rjwHYg7GBEZEncGS0b+6WY4hcnoXwRWno8UEyus3chojEdMfOar16FQgPB+66C2jRAmjbtkoArmu4bIzdnxsrABvVGpQHBgKBgUBAAMo1Ghg1WvwS0BxfDo7En5amYfyqbHy0+WiVLxmeXZSGiMR0RCSmY9DCVITNS0FUUhaGL92HrjO2ISwuxeY09NpGZvOLjPjm+19qnQ7NEWAiclfsnyuPAdiDsYERkSdwdLRv7pZjlpDWZ/Z2PLMw1fGzWo1GYPt2YM4coF8/66nRDoRMZ5/72xSlTKM1hd9WrYD77wd69cKZR/pjVcSbeH9lluW1/WjzjWnmlcNvRGI6whPS8PjcFIxelonxK7MxIG4XHpi+tcZp6LbW5u49dblO5+xyDTARuSv2z5XHAOzB2MCIyBPUdbTvnZUHEZGYjklrc+p+VqvRCPz3v0DnzjWOtDpSlA62Dhet1hR+77vP9HsbjTZf7/ErD2JwQir6zdlZJfxWHwE2r8d+YPpWDJi/y2oaevUp6cOX7kPc1mP4Yt+PN46/Wp5Z45FI5vN8a1sXbut5uAs0EbkC9s+VxwDswdjAiMgTNPlon9EIrFplCoa2dor2oACMVq2AP/4RmDcPKCys8fWOSspC2LwUDFqYahWA+83daVpzvTLbsh47LC4FD87YhuFL99UYSs3rseduOYboij/XFGZtneebfORive5HRKQk9s+VxwDswdjAiMgTKDbaZw7CLVt6XAiGiCncT5pkCb72Xu/RyzLx+NwUhCdUnf78bMWa4IjEdMRuOmqZiv7ykn3oG7sDYfNMU6PNI7rvrDyIIYv3YEDcLgxbko53Vh7EOysPYtiS9Dpf25LSMqzKOnNj5HiZ/ZFjm1PfiYiaGPvnymMA9mBsYETkKRQd7bt6FXjmGdPmWG4Wfmuso04HdO8OXL7s0OttawTYHH5tnbs8YVU2hizegzFJWZi87hDGfJ6F5z7eg7B5KQiLM5XnPk7D0L/vRVhcCvrN2enQsUnVR/dLSsvqtHaYiEhp7J8rjwHYg7GBEZGncInRvsuXgZ49AX9/9w3APj5At26W9b6Ovt4vLN6DJ+aloPfs7Ri0MBX95u60hN/I5VlWwdUcVHcfv4S9Jy9j4pocDFuSjv5xu/DCJ3sxfuVBTF1/GBGJ6eg2cxt6fJBseay5dkJwTbs55xcZkfHDlVp3jyYiUhr758pjAPZgbGBE5ElcYrTPaAQ2bDBtkuXnd2MqsZPCr7PDtOVx1Grg5puBtWvtBt+aXu+/rc42reudvhWPfrQDgxNMI8G2Rm2rT1W2N3pvnlr95PxdNY4mVy48z5eI3B3758pjAPZgbGBE5IlcZrTv6lXg+edN06NvusnlAnBBYBBw663APfeYQruDwbc68+s94/8dsYzivv55lmXNr71p6LWt3648tdrWemJHR4CJiNwF++fKYwD2YGxgRERN5MIFU9C85RaU6PS46hOIAp0exTo98gKDUKJSoVitQakIjKJCqUjF/5tKsQiMag0QEAA0a2Y6h1inA3x8YNRoUaDzQZFaizz/IBT4+qPA4Isigy8K/AKQFxCEAh8/FOkNMKrV+C0gCGfb3ob/bs5y6q9Yn2note3gXf14peo7SvM8XyLyNOyfK48B2IOxgRERNb0VGacRlZSFqevt72rs6LTeJj8Gyo66TkOv7Qznjzabzg3uG7sDzy5Kw6CFqXh8bgp+/8leRCVlYcRn3+DFT/bi95/sxdC/78WAuF14d1U2fr5WWEtNiYhcE/vnymMA9mBsYERETa+20FfXab2KHQNlh6PT0B35MuCNrw4gfFEa+szegV6zt+P+97ei14fJeHhWMu5/fyvum7YFv4vejE5TNqHbzG149R/fcHdnInJb7J8rjwG4gY4ePYrY2Fg88cQTaN++PfR6PUJDQzFkyBCkpqbWeD8RsVsKCxv+7TYbGBFR02uMEVtFj4FqAEe+DJi39RhGL8tEn9gd6DRlEzpM2oi7p27CfdO2oPPUTeg45WvcNflrdJ66Cd0/SMZT8bvx8qc3plqXMAQTkRth/1x5DMAN1K5dO4gImjVrhgEDBiAiIgL33nsvRAQqlQrx8fE27yci8Pf3x8iRI22WkpKSBteNDYyIqOk1xohtSWkZvtj3I8Z8noUBcbswMH43IhLTEZWUhXdWHmyaY6DqwdEvA/785X48NmcnOk3ZhLujN+Hu6M3oVBGCu3+wDb1nb8djc3aiT+x2hC9Kw6h/Zrhc2CcicgT758pjAG6gAQMG4F//+heKi4ur/DwxMREiAo1GgyNHjljdT0Rw6623Nmrd2MCIiJThzBFb87rbuK3HMOKzbxAWl4I+s7ejx6xk9Jm9HWHzUjDis28Qt/WYy00LduTLAPM64IdnJaP7B8l4aOY2PPD+FvSZvR2Pz03BUwt248VP9iIiMb3KTtGT1x1qkuneRETOxP658hiAG9GTTz4JEcH7779vdRsDMBGR56rPjskOPc7yTIxfeRBRn2chIjEdA+N3o3/cLoz5PAtf7PufS04Hru3LgPErD2LA/F14YPpWPDE3BY9+tAP95pp2hbZV+s2p2Cl6VTZ3hSYit8P+ufIYgBvRhAkTICIYM2aM1W0MwEREnq2uOybb4q5rfyur7cuApxfsRtcZ2xAWZzoP+Im5OzFoYWqNAXjQwlSEzUtBVFIWzwUmIrfD/rnyGIAb0YsvvggRQUxMjNVtIoKWLVvigw8+wJgxY/D2228jKSkJeXl5Tnt+NjAiIuU5umOyrfu52u7P9WXvy4CIxHQ8MTcFI/+Zgdf+mYHH56YgPCGtxgAcnpCGx+emYPSyzFqPkCIicjXsnyuPAbiRnDp1CgaDASKC/fv3W91e0+7PISEh2Lhxo1PqwAZGROS+XOn8X2ex9WXA3C1HEbncNCoclZSFsHkpHAEmIo/F/rnyGIAbgdFoRN++fSEieOmll2z+nREjRmDLli04d+4c8vPzcfDgQbz66qsQEej1emRkZDj8fOaGVL0YDAY2MCIiN+Xs84RdVeWgP35lNgYnpHINMBF5LAZg5Xl9AH7xxRfRqVOnOpXawunYsWMhIrjjjjtw5Urd/lGeNGkSRAQDBgxw+D4MwEREnmdFxmlEJWVh6nr705/NxV2nA1ee6j1pbQ4iEtPRN3YHnl1kPQ2au0ATkbtjAFae1wfghx56qMbpyDWVlJSUGh9v+vTpEBGEhobi5MmTda7Pb7/9Bo1GA51OZ3W0Ul2xgRERuS9vGQEGqm72NeqfGQivCLqVQ7A5/PIcYCJyZ+yfK8/rA7AzffzxxxARBAUF4eDBg/V+nDZt2kBEcO7cuQbVhw2MiMh9eeIa4JpU3in65U/T8VT8boTFpaDnrGT0+nA7en2YjJ6zkhEWl4Kn4nfjlU9rP0KKiMgVsX+uPAZgJ/nyyy+hUqng5+eHPXv21PtxysrK4O/vDxHBtWvXGlQnNjAiIvflSbtAO6LyTtHvrcnBkMV78MTcFPSN3YG+sTvw+NwUvLB4DyatzXHoCCkiIlfE/rnyGICd4Ouvv4ZWq4Ver8fWrVsb/FgigjvvvLPB9WIDIyJyb55wDnBdVd4pevneHzB3y1HM3XIMy/f+6PARUkREror9c+UxADfQnj174OvrC61Wi/Xr1zt0n9WrV+P48eNWP9+1axfatm0LEcH8+fMbXDc2MCIi91Z5avDwpfswepnpuKCp6w9j4pocjF6WieFLOR2YiMhdsH+uPAbgBgoODoaI4Pbbb8fIkSNtlqVLl1a5z8iRIyEiuOuuu/Dkk09i6NCheOCBByybbA0bNgxlZQ3vxLCBERG5v8pTgyevO4SxX+xHVFIWxn6xH5PXHeJ0YCIiN8L+ufIYgBvIkV2jR44cWeU+mzZtwvDhw9G5c2cEBwdDq9WidevWePrpp7F69Wqn1Y0NjIjIc1SeGrwi4zSnAxMRuSH2z5XHAOzB2MCIiIiIiFwH++fKYwD2YGxgRERERESug/1z5TEAezA2MCIiIiIi18H+ufIYgD0YGxgRERERketg/1x5DMAejA2MiIiIiMh1sH+uPAZgD8YGRkRERETkOtg/Vx4DsAdjAyMiIiIich3snyuPAdiDsYEREREREbkO9s+VxwDswdjAiIiIiIhcB/vnymMA9mBsYEREREREroP9c+UxAHswNjAiIiIiItfB/rnyGIA9GBsYEREREZHrYP9ceQzAHowNjIiIiIjIdbB/rjwGYA/GBkZERERE5DrYP1ceA7AHYwMjIiIiInId7J8rjwHYg7GBERERERG5DvbPlccA7MECAgJgMBgsDY2FhYWFhYWFhYWFRbliMBgQEBCgdEzwagzAHiw0NBQBAQGKN3RXKQaDgV8IuGDhdXHNwuvimoXXxTULr4trFl4X1yzefl0CAgIQGhqqdEzwagzA5DXMHzzkWnhdXBOvi2vidXFNvC6uidfFNfG6kNIYgMlr8APXNfG6uCZeF9fE6+KaeF1cE6+La+J1IaUxAJPX4Aeua+J1cU28Lq6J18U18bq4Jl4X18TrQkpjACavwQ9c18Tr4pp4XVwTr4tr4nVxTbwuronXhZTGAExegx+4ronXxTXxurgmXhfXxOvimnhdXBOvCymNAZi8Bj9wXROvi2vidXFNvC6uidfFNfG6uCZeF1IaAzARERERERF5BQZgIiIiIiIi8goMwEREREREROQVGICJiIiIiIjIKzAAExERERERkVdgACYiIiIiIiKvwABMREREREREXoEBmAjA6tWrMWDAAISEhMBgMKB9+/YYMmQI0tLSlK4aAZg+fTpEBCKCFStWKF0dr3T06FHExsbiiSeeQPv27aHX6xEaGoohQ4YgNTVV6ep5vMLCQsTExOCuu+6CwWBAmzZtMGrUKJw9e1bpqnml69evY/369Rg9ejTuu+8+BAYGws/PD126dMH06dORl5endBUJwJUrV9CqVSuICDp16qR0dQjAhQsX8Pbbb+Ouu+6Cj48Pmjdvjq5du2LChAlKV428CAMwebXS0lK88sorEBH4+/tj4MCBeOmll9CrVy/o9XrMnDlT6Sp6vWPHjsFgMEClUjEAK6hdu3YQETRr1gwDBgxAREQE7r33XogIVCoV4uPjla6ixyosLETv3r0hImjTpg0iIiLQo0cPiAhatWqFU6dOKV1Fr7N06VLLl3K/+93vMHToUAwcOBCBgYEQEXTu3Bk///yz0tX0eiNHjrT828EArLz09HQEBwdDRHDPPfcgIiICTz/9NG699VZoNBqlq0dehAGYvNrf/vY3iAgGDRqEK1euVLnt119/xYkTJxSqGQFAeXk5Hn30UYSGhuK5555jAFbQgAED8K9//QvFxcVVfp6YmAgRgUajwZEjRxSqnWeLjo6GiKBXr15VRhbj4uIgInj00UcVrJ13SkpKwp/+9CerfyPOnz+PBx98ECKCl19+WaHaEQBs374dIoIxY8YwALuAc+fOITg4GL6+vli3bp3V7RkZGQrUirwVAzB5rRMnTkCj0eCWW27B9evXla4O2fDpp59CRPDll19i5MiRDMAu6sknnyifSDcAAAnfSURBVISI4P3331e6Kh6npKTEMmLy7bffWt3epUsXiAj279+vQO3IlvT0dIgIDAaD1RdG1DQKCgpw55134p577sGJEycYgF3Aq6++ChHBokWLlK4KEQMweS/z6O+HH36odFXIhgsXLiA4OBhhYWEAwADswiZMmGAZaSHn2rlzJ0QEHTp0sHn7jBkzICKYNm1a01aManT9+nXL9Ojz588rXR2vNHHiRKhUKuzevRs//vgjA7DCfv31VxgMBgQFBaGwsFDp6hAxAJP3euihhyAiyMrKwg8//IBZs2ZhzJgxeO+995CcnKx09bze0KFDYTAYLFMMGYBd14svvggRQUxMjNJV8Tjx8fEQEQwdOtTm7Rs3boSI4Pnnn2/imlFNDh8+DBGBTqdDUVGR0tXxOjk5OdBqtRg9ejQAMAC7gP/+978QETzzzDMoLS3F6tWr8dZbb+HPf/4zEhIScPHiRaWrSF6GAZi8lo+PD0QEH3/8MQwGg+Ube3Pp378/rl27pnQ1vZL5H8vp06dbfsYA7JpOnTplaT+chut848aNg4hg3LhxNm/Pzs6GiKBr165NXDOqSWRkJEQE4eHhSlfF65SVlaFHjx5o2bIlfvnlFwAMwK4gNjYWIoLRo0ejV69eVv0tf39/rFq1SulqkhdhACavVFhYaPng1Wq1ePLJJ3Ho0CHk5uYiOTkZt99+O0QEL730ktJV9Tp5eXlo3749OnbsWGX0hAHY9RiNRvTt25dtpRFFRUVBRDBlyhSbt588eRIigo4dOzZxzciWr7/+GiqVCjqdDtnZ2UpXx+ssWLAAIoJly5ZZfsYArLyJEyda+lv+/v747LPPcPnyZfz444945513ICLQ6/XIyclRuqrkJRiAyW29+OKL6NSpU52KeZfB/Px8SwC+9dZbrTYqOXToENRqNVQqFXeCrqOGXBcAePPNNyEi2LFjR5XHZQBumIZeF1vGjh0LEcEdd9xhtYs6OYd5NHHq1Kk2bzdv8MMArLzvvvsOzZs3h4hgwYIFSlfH65w5cwYBAQF47LHHqvycAVh57777rqXPtWTJEqvbf//730NEMHz4cAVqR96IAZjclnkNb11KSkqK5f5qtdruyIr5nM2lS5c20W/kGRpyXTIyMqBWq/Hqq69aPS4DcMM0tL1UN336dIgIQkNDcfLkyab7RbwMp0C7h7Nnz+KWW26BiOCdd95RujpeafDgwdDr9fjuu++q/JwBWHnmfy/UarXNdfGbNm2CiKBdu3YK1I68EQMweS3zNOdPP/3U5u0REREQEcyaNauJa+a9pk2bBhHBAw88gMcee6xKCQ0NhYjg7rvvxmOPPcajFBT08ccfQ0QQFBSEgwcPKl0dj8ZNsFzf5cuX0blzZ4gIRo0ahfLycqWr5JVEBMHBwVb/dvTs2RMiAl9fX8vPKp+nTY0vKSkJIoK2bdvavP27776zbBxH1BQYgMlrvfDCCxARxMbG2rw9LCwMIoKFCxc2cc28lzkAO1Leeustpavrlb788kuoVCr4+flhz549SlfH4zl6DBJ34FZGbm4uunXrBhHBCy+8gNLSUqWr5LXqMrvl6tWrSlfXqxw6dMjyJYStL4jS0tIgImjevLkCtSNvxABMXmv58uUQEQwcONDqttzcXMtarrS0NAVqR9VxCrTyvv76a2i1Wuj1emzdulXp6niF4uJiBAUFQUTw7bffWt3epUsXiAgyMzMVqJ13KyoqwuOPP275d6T6XhLkGjgF2jWYZ93t27fP6raZM2dCRBAWFqZAzcgbMQCT1yoqKsJtt90GEcHy5cstPzcajRg1ahREBPfeey+ns7kIBmBl7dmzB76+vtBqtVi/fr3S1fEqU6ZMgYigd+/eyM/Pt/w8Li4OIoK+ffsqWDvvVFpaiiFDhkBE8Mgjj+D69etKV4lqwADsGhITEyEi6N69Oy5fvmz5+f79+xEcHAwRwerVqxWsIXkTBmDyavv27YO/v79lE5kXXnjBEopDQkJw6NAhpatIFRiAlWXuoNx+++0YOXKkzcIN4xpHYWGhZR1jmzZtEBERYflzSEgINyFTgPm4HRHBkCFDamwTlTv6pAwGYNdQVlaGoUOHQkTQokULDB48GP369YNer4eIICoqSukqkhdhACavd+LECQwfPhyhoaHQ6XS4+eabERUVhdOnTytdNaqEAVhZjqyrGzlypNLV9FgFBQWIjo5Ghw4doNfrERoaipEjR+LMmTNKV80rObpfwY8//qh0Vb0eA7DrKCsrw+LFi/Hggw/Cz88P/v7+6N27Nz7//HOlq0ZehgGYiIiIiIiIvAIDMBEREREREXkFBmAiIiIiIiLyCgzARERERERE5BUYgImIiIiIiMgrMAATERERERGRV2AAJiIiIiIiIq/AAExERERERERegQGYiIiIiIiIvAIDMBEREREREXkFBmAiIiIiIiLyCgzARERERERE5BUYgImIiIiIiMgrMAATERERERGRV2AAJiIiIiIiIq/AAExERERERERegQGYiIiIiIiIvAIDMBERkYt5+eWXISL44IMPrG5LS0uDwWBAq1atcOrUKQVqR0RE5L4YgImIiFzMyZMnodVq0bx5c1y7ds3y82PHjqFFixbw8/NDZmamgjUkIiJyTwzARERELigqKgoighkzZgAALl68iNtvvx0ajQYbN25UuHZERETuiQGYiIjIBZ09exY+Pj4IDg7GuXPn0K1bN4gIli5dqnTViIiI3BYDMBERkYsaN24cRAQtW7aEiGDatGlKV4mIiMitMQATERG5qLNnz0KlUkFE8NprryldHSIiIrfHAExEROSCysvLMXToUIgIRASRkZFKV4mIiMjtMQATERG5oLfffhsigvDwcLRu3RparRYnTpxQulpERERujQGYiIjIxcTFxUFE0LNnTxQUFFj+PGzYMKWrRkRE5NYYgImIiFzIypUroVKpcOedd+LSpUsAgIKCAtx0001QqVTIyclRuIZERETuiwGYiIjIRezatQsGgwGtWrXCqVOnqty2YMECiAgGDx6sUO2IiIjcHwMwERGRCzhy5AiCg4Ph5+eHjIwMq9sLCwvRrl07iAjS09MVqCEREZH7YwAmIiIiIiIir8AATERERERERF6BAZiIiIiIiIi8AgMwEREREREReQUGYCIiIiIiIvIKDMBERERERETkFRiAiYiIiIiIyCswABMREREREZFXYAAmIiIiIiIir8AATERERERERF6BAZiIiIiIiIi8AgMwEREREREReQUGYCIiIiIiIvIKDMBERERERETkFRiAiYiIiIiIyCswABMREREREZFXYAAmIiIiIiIir8AATERERERERF6BAZiIiIiIiIi8AgMwEREREREReYX/D5TXX3IviExRAAAAAElFTkSuQmCC\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], alpha=0.5, label=\"Test data\")\n",
    "ax.errorbar(test_data[:, 0], b_mean, yerr=2*total_uncertainty, alpha=0.5, fmt='or', label=\"95% band total unc.\")\n",
    "ax.errorbar(test_data[:, 0], b_mean, yerr=2*b_sigma, alpha=0.5, fmt='og', label=\"95% band epistemic unc.\")\n",
    "ax.set(xlabel=\"$x$\", ylabel=\"$f(x)$\")\n",
    "#ax.set_yscale('log')\n",
    "plt.legend(frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8cfb5d35",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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