notebooks/Example 3 - Fitting.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from cpyment import CModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now try fitting the parameters of a SIR model. We'll create two models: one to perform the fit with, and a target model to generate the data we will fit on. The data will be generated by extracting random points from a trajectory for the target model and adding some noise. It will then be used to fit the original model on.\n",
    "\n",
    "Note that in this case we're passing data for all three states (S, I, and R) to the fit. This is not always necessarily the case. In general, for a model with N states, data can be passed to `.fit` in two ways:\n",
    "\n",
    "* as a $(:, N+1)$ Numpy array. In that case the first column is time, and the following N are the states. Wherever data is not available, put np.nan, or None.\n",
    "* as a list of dictionaries. In this case each dictionary should contain a member `t` and then can have other members with the labels of the various states (e.g. `{'t': 0.54, 'S': 0.3}` would be valid for a SIR model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "fmodel = CModel.make_SIR()\n",
    "\n",
    "btarg = 4.5\n",
    "gtarg = 2.1\n",
    "tmodel = CModel.make_SIR(btarg, gtarg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate some random data\n",
    "N = 1000\n",
    "t = np.linspace(0, 3, N)\n",
    "y0targ = [0.9, 0.1, 0]\n",
    "\n",
    "traj = tmodel.integrate(t, y0targ)['y']\n",
    "\n",
    "# Extract some data from the early part of the curves\n",
    "data_i = np.random.choice(range(int(N/2)), size=30, replace=False)\n",
    "data_x = t[data_i]\n",
    "data_y = traj[data_i] + (np.random.random((len(data_x), 3))-0.5)*0.1 # Data made artificially noisy\n",
    "\n",
    "data = np.concatenate([data_x[:,None], data_y], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now fit\n",
    "\n",
    "sol = fmodel.fit(data)\n",
    "\n",
    "fittraj = fmodel.integrate(t, sol.y0)['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Target parameters:\n",
      "  beta = 4.5\n",
      "  gamma = 2.1\n",
      "  y0 = [0.9, 0.1, 0]\n",
      "Fitted parameters:\n",
      "  beta = 4.295777537404503\n",
      "  gamma = 1.886508545886076\n",
      "  y0 = [0.89721105 0.09473709 0.02272892]\n",
      "Fitting quality:\n",
      "  R2 = [1.04088253 0.68137292 0.93272533]\n",
      "  MRPD = 0.16863007152887752\n"
     ]
    }
   ],
   "source": [
    "# Fit results?\n",
    "\n",
    "print('Target parameters:')\n",
    "print('  beta = {0}'.format(btarg))\n",
    "print('  gamma = {0}'.format(gtarg))\n",
    "print('  y0 = {0}'.format(y0targ))\n",
    "\n",
    "print('Fitted parameters:')\n",
    "print('  beta = {0}'.format(sol.C['beta']))\n",
    "print('  gamma = {0}'.format(sol.C['gamma']))\n",
    "print('  y0 = {0}'.format(sol.y0))\n",
    "\n",
    "print('Fitting quality:')\n",
    "print('  R2 = {0}'.format(sol.R2))\n",
    "print('  MRPD = {0}'.format(sol.MRPD))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // 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",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc4e93f1828>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "for i in range(3):\n",
    "    ax.scatter(data[:,0], data[:,i+1], label='SIR'[i])\n",
    "    ax.plot(t, fittraj[:,i], lw=0.8)\n",
    "    \n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fitting can also be partial, where some values are constrained to take fixed amounts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "constr = {\n",
    "    'S0': y0targ[0],\n",
    "    'I0': y0targ[1],\n",
    "    'R0': y0targ[2]\n",
    "}\n",
    "sol = fmodel.fit(data, constraints=constr)\n",
    "\n",
    "fittraj = fmodel.integrate(t, sol.y0)['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitted parameters (with constrained y0):\n",
      "  beta = 4.322251856176114\n",
      "  gamma = 1.966654467152744\n"
     ]
    }
   ],
   "source": [
    "print('Fitted parameters (with constrained y0):')\n",
    "print('  beta = {0}'.format(sol.C['beta']))\n",
    "print('  gamma = {0}'.format(sol.C['gamma']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // 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",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAgAElEQVR4XuydB3hUxfrG3/QCSSAJKYQAAUE6MZDQBZUroGIvKAhIsVPE+zeoVxErqJciCIiAKCiCoHJRBKVJryEU6YROCgRSID2b/zMHNqRssmd3dpPds+95njxRMt+cmd98m3kzM983TkVFRUXgQwIkQAIkQAIkQAIk4DAEnCgAHWas2VESIAESIAESIAESUAhQANIRSIAESIAESIAESMDBCFAAOtiAs7skQAIkQAIkQAIkQAFIHyABEiABEiABEiABByNAAehgA87ukgAJkAAJkAAJkAAFIH2ABEiABEiABEiABByMAAWggw04u0sCJEACJEACJEACFID0ARIgARIgARIgARJwMAIUgA424OwuCZAACZAACZAACVAA0gdIgARIgARIgARIwMEIUAA62ICzuyRAAiRAAiRAAiRAAUgfIAESIAESIAESIAEHI0AB6GADzu6SAAmQAAmQAAmQAAUgfYAESIAESIAESIAEHIwABaCDDTi7SwIkQAIkQAIkQAIUgPQBEiABEiABEiABEnAwAhSADjbg7C4JkAAJkAAJkAAJUADSB0iABEiABEiABEjAwQhQADrYgLO7JEACJEACJEACJEABSB8gARIgARIgARIgAQcjQAHoYAPO7pIACZAACZAACZAABSB9gARIgARIgARIgAQcjAAFoIMNOLtLAiRAAiRAAiRAAhSA9AESIAESIAESIAEScDACFIAONuDsLgmQAAmQAAmQAAlQANIHSIAESIAESIAESMDBCFAAOtiAs7skQAIkQAIkQAIkQAFIHyABEiABEiABEiABByNAAehgA87ukgAJkAAJkAAJkAAFIH2ABEiABEiABEiABByMAAWggw04u0sCJEACJEACJEACFID0ARIgARIgARIgARJwMAIUgA424OwuCZAACZAACZAACVAA0gdIgARIgARIgARIwMEIUAA62ICzuyRAAiRAAiRAAiRAAUgfIAESIAESIAESIAEHI0AB6GADzu6SAAmQAAmQAAmQAAUgfYAESIAESIAESIAEHIwABaCDDTi7SwIkQAIkQAIkQAIUgPQBEiABEiABEiABEnAwAhSADjbg7C4JkAAJkAAJkAAJUADSB0iABEiABEiABEjAwQhQADrYgLO7JEACJEACJEACJEABSB8gARIgARIgARIgAQcjQAHoYAPO7pIACZAACZAACZAABSB9gARIgARIgARIgAQcjAAFoIMNOLtLAiRAAiRAAiRAAhSA9AESIAESIAESIAEScDACFIAONuDsLgmQAAmQAAmQAAlQANIHSIAESIAESIAESMDBCFAAOtiAs7skQAIkQAIkQAIkQAFIHyABEiABEiABEiABByNAAehgA87ukgAJkAAJkAAJkAAFIH2ABEiABEiABEiABByMAAWggw04u0sCJEACJEACJEACFID0ARIgARIgARIgARJwMAIUgBIDrtPpcPHiRfj4+MDJyUmiJpqSAAmQAAmQAAlUFYGioiJkZmaibt26cHZ2rqrX2tR7KAAlhuP8+fMIDw+XqIGmJEACJEACJEAC1UXg3LlzqFevXnW9vlrfSwEogT89PR21atWCcCBfX1+JmmhKAiRAAiRAAiRQVQQyMjKUBZy0tDT4+flV1Wtt6j0UgBLDIRxIOI4QghSAEiBpSgIkQAIkQAJVSIDzN0ABKOFwdCAJeDQlARIgARIggWoiwPmbAlDK9ehAUvhoTAIkQAIkQALVQoDzNwWglOPRgaTw0ZgESIAESIAEqoUA528KQCnHowNJ4aMxCZAACZAACVQLAc7fFIBSjkcHksJHYxIgARIgARKoFgKcvykApRyPDiSFj8YkQAIkQAIkUC0EOH9TAEo5Hh1ICh+NSYAESIAESKBaCHD+pgCUcjw6kBQ+GpMACZAACZBAtRDg/E0BKOV4dCApfDQmARIgARIggWohwPmbAlDK8ehAUvhoTAIkQAIkQALVQoDzNwWglOPRgaTw0ZgESIAESIAEqoUA528KQCnHs1UHKtQVYeepK0jJzEGQjydiIvzh4uwk1VcakwAJkAAJkIBWCNjq/F2VfHkXsARtW3SgVQcTMX7FISSm5xT3LNTPE+P6tkDvVqESvaUpCZAACZAACWiDgC3O31VNlgJQgnhVONC13AK89fMBvHVfc4T4eVbaWiH+XloYh6IypfRrfzMHRFEESow3TUmABEiABLRBoCrmb1snRQEoMUJV4UBiOzd22X7sOn0FPwzviLBaXgZbLMp1nbiu1MpfyYJCBAoBuTn2bm4HS4w5TUmABEiABOyfQFXM37ZOiQJQYoSqwoGEsNuekIov15/A8eRr+OnFTmgYWKNcq7edTMXTX2832ptFwzuiU+MAo+VYgARIgARIgAS0SqAq5m9bZ0cBKDFC1nYgQ+f5RCzHew+2wMBOEaVavjz+Akb9GG+0N1P7ReKhyDCj5ViABEiABEiABLRKwNrztz1wowCUGCVrOlBF5/n0zX2vbwsM7nJLBHIFUGIgaUoCJEACJOBQBKw5f9sLSApAiZGylgMZO88nmixWAn8b0Q0t6voqPdDbJKXnlAsCET/nGUCJgaYpCZAACZCApghYa/62J0gUgBKjZS0HUrua5+PpiqUvdsbtIT5KL/SrhuK/S0YCMwpYYpBpSgIkQAIkoDkC1pq/7QkUBaDEaFnLgdSe5+vTKkSJDv7x+U64LahmsQhkHkCJQaUpCZAACZCA5glYa/62J3AUgBKjZS0HUrsCOPqeJsjX6fDT7vNY8sKt6GDeBCIxqDQlARIgARLQPAFrzd/2BI4CUGK0rOVAxs7z6ZsstnZn9L8De8+l47d9F7H4hU4I9/eW6BFNSYAESIAESED7BKw1f9sTOQpAidGypgOJ83wvLoyrtHX6wI5Nb9yFD38/jDWHk5WVwLoVJIuW6CpNSYAESIAESEAzBKw5f9sLJApAiZGytgNNXXMMk9ccN9pCkdw5umFtvLBgD/adT8P4B1uhd6sQ3vhhlBwLkAAJkAAJOCIBa8/f9sCUAlBilKztQGqDQYZ2aYiVB5NKXQMX7OOB8Q+15N2/EuNLUxIgARIgAW0SsPb8bQ/UKAAlRsnaDqR2BbCyLswaEFVKBDJARGLAaUoCJEACJKAJAtaev+0BEgWgxChZ04HUngF0cgJ0JZP+lelPiK8Htoy9R9kONnS1XKifJ8b1bcGVQgk/oCkJkAAJkIB9EbDm/G0vJCgAJUbKWg6k5iYQU5q9cGgHXMvNx0sL48rdEsIk0aaQZFkSIAESIAEtELDW/G1PbCgAJUbLWg6kNg9gn1bB+ONgstEedIjwx5nU60jKyDVYltfEGUXIAiRAAiRAAhoiYK35254QUQBKjJa1HEht8Merd92G6etPGO2Bn5cb0rPzjZYT0cSdGgcYLccCJEACJEACJGDPBKw1f9sTEwpAidGylgOpXQH8flgH/PunfUhKzym3tSu6pV/Ze65LBD5eedhoT6f2i8RDkWFGy7EACZAACZAACdgzAWvN3/bEhAJQYrSs5UDGbgIpuWX716Ek5WyfeErGgpQ82+fn5Y6nv95utKdcATSKiAVIgARIgAQ0QMBa87c9oaEAlBgtazqQiNg1Jux6twpVWm8sutdYUAnPAEo4AU1JgARIgATsjoA15297gUEBKDFS1nYgY8KuZNON5ffTC8qyGWMYBSzhADQlARIgARKwSwLWnr/tAQoFoMQoVYUDGRN2pjTfFEFpSr0sSwIkQAIkQAL2RKAq5m9b50EBKDFC9uhAQlDuSEjFF+uO40JaDla82gW1vN0lKNCUBEiABEiABOyLgD3O35YmTAEoQdSeHSi/UIfh3+1GXoEO85+LgburswQJmpIACZAACZCA/RCw5/nbUpQpACVI2rsDXc8twFOzt6FJkA8mPdkWTuJeOT4kQAIkQAIkoHEC9j5/W2J4KAAlKGrBgVIyc/DIl1vRLzocI+5pIkGDpiRAAiRAAiRgHwS0MH/LkqYAlCCoFQc6nJiBJ2Ztw4THWuOBNnUliNCUBEiABEiABGyfgFbmbxnSFIAS9LTkQOuOJOPVH/bih+EdERleS4IKTUmABEiABEjANAJZ+Vk4k3FG+Tqdcbr4vy9eu4g1T6yBq7OraRUaKa2l+dtcMBSA5pIDoDUHmrv5FGZuOInlr3ZBWC0vCTI0JQESIAESIIHSBPJ1+RCC7nT66VIiTwi+lKwU+Lj5oKFfQzTwbVDq6/bat8PF2cWiOLU2f5sDhwLQHGo3bbTmQEVFRXj714PYezYNS1/shBoelv2LSwI1TUmABEiABOyEQG5hriLyTqadxIm0E8r3hPQEnM88rwQblhR4DX1vCT5/T/8qC0bU2vxtjmtQAJpDTaMCUHRLpIcZ/M1OeLm54qtn28HFmZHBEi5CUxIgARLQLAG90NOLPCH0TqafxLnMc/By9ULjWo3R2K+x8r2RXyNE+EUgtEaoxVfzzAFMAQhQAJrjORoWgKJr6Vn5eGTGFvRsEYy37msuQYimJEACJEAC9k5A7A4lZyXjyJUjOHrlKI5ePYpjV48pQs/b1RuNajXCbbVuU0Se+C4EX7B3cJWt5pnDlwJQYwLwyy+/xGeffYakpCS0bdsW06ZNQ0xMTIW+MWXKFMycORNnz55FYGAgHn/8cXzyySfw9PRU5U9adqBTl68rIvDNPs3wVHR9VTxYiARIgARIwL4J5BXmKVu2QuTpxZ74fj3/OsR2bVP/pmjm3wxNazdVxJ6tC72KRkPL87daD9TMCuDixYsxcOBAzJo1Cx06dIAQdz/99BOOHj2KoKCgcjx++OEHDBkyBPPmzUPnzp1x7NgxDB48GP369cOkSZNU8dO6A207mYoh83dh4bAYtGvgr4oJC5EACZAACdgHgeyCbEXk/ZP6D/65/A+OXD2CU2mn4Onqidv9b4cIvlC++9+uiD0PFw/76JiKVmp9/laBQDtbwEL0RUdHY/r06Uq/dTodwsPDMWLECIwdO7Yci1dffRWHDx/G2rVri3/2+uuvY8eOHdi8ebMadpqLAjbU6W+3nsb09Sew4tWuCPFTtzKqCh4LkQAJkAAJVBmB/MJ8ZdtWEXup/+Dg5YPKSp+fhx9aBrREy8CWaO7fXBF7dWvUtentW0tAowDUyBZwXl4evL29sXTpUjz88MPFvjFo0CCkpaVh+fLlBlcAX375Zfz555/KNnFCQgLuv/9+PPvss3jrrbcM+ldubi7El/4RDiREZnp6Onx9fS3hk9VWR6GuCDtPXYG4GSTIxxMxEf5KAIg4+xG7bD+OJmVi8Qud4OlmPBS/orqqrXN8MQmQAAk4EAFdkU6Jwt13aZ8i9ITgE+JPBGboxZ743iqwld1u4coOJwWgRgTgxYsXERYWhq1bt6JTp07FfvHGG2/g77//Vlb1DD1ffPEF/v3vfysip6CgAC+++KJyJrCi57333sP48ePL/djeBeCqg4kYv+IQEtNzivsW6ueJcX1boHerUOQWFKLf7O1oFFgTnz/RptK/DI3VJfuhpT0JkAAJkEBpAuJ83oHLB7AvZR/iL8Urwk+c5RMir3Vga0Xoif+u51NP8yt7an2DAtCBBeCGDRuU834ffvihcmbwxIkTGDVqFIYPH4533nnHYVYAhWB7aWEcisr0WJ/8ZeaAKEUEJmfkoO+0zXixe2MM6RphkI/autR+QFmOBEiABEigNAGxYCHy6emFXnxKPI6nHVdW8iLrRKJtUFvluwjWcHN2I74KCFAAakQAmrMF3K1bN3Ts2FGJGtY/CxcuxPPPP49r167B2dnZ6AfH3h1IbNV2nbiu1MpfyU4LESjO/W2OvVvZDt579iqe+XoH5gxqjy63BZbiY2pdRuGyAAmQAAmQAMR2rjirtzt5N3Yn7cae5D1Iz0tHi4AWaFvnhtgT34NrBJOWCQTsff42oasVFtVMFLBYxRNn+UTqF/GIIJD69etDBHsYCgJp164devbsiYkTJxbDWbRoEYYOHYrMzEy4uBg/62bvDiSifJ/+ertRP1o0vCM6NQ5Qyi3ZfQ6frDyM/73aFeH+3sW25tRl9MUsQAIkQAIORkAIPnFeT4g9IfqE4BMJl4XIax/cHu1D2itbulqKyK2OIbb3+dsSzDQjAEUaGBH08dVXXylCUKSBWbJkCY4cOYLg4GAlRYw4Jyjy/IlHnOcT6V5mz55dvAX80ksvQQhDUZeax94daHn8BYz6Md5oV6f2i8RDkWHF5cYtP4gdp67g55c7w9v9xnVx5tZl9OUsQAIkQAIaJiAE3/Grx7E9cfuNFb6UPcqq3x1Bd6BdcDtF9Inze24u3M61pBvY+/xtCRaaEYAChkgBo08EHRkZCRHkIVYGxdOjRw80bNgQ8+fPV/5fBH189NFHWLBgAS5cuIA6deqgb9++yr/VqlVLFVt7dyBzV+3EdXHPzt2BgBoemP7MHcqhYnPrUgWahUiABEhAQwSSridh28Vt2Ja4DTsSdyCnIEdZ2YsJiVEEn0jF4urMu9itOeT2Pn9bgo2mBKAlgJhSh707kP7cXlJ6TrkgEMGh7BnAkmxSr+UqQSEiIGRYt0aQqcsU5ixLAiRAAvZG4FreNexM2qms8gnhJ65QE9u4nep2QqfQTmhdpzUDNqp4UO19/rYELgpACYpacCB95K7AUDISuGwUsCFM+qCQ+c9Fo0OjAMjUJTEMNCUBEiABmyIgInXFVWobz2/E5gubsf/SfoT7hKNjaEdF9EWHRMPH3cem2uxojdHC/C07ZhSAEgS14kAyufsWbD+DqWuO4/eRXRHs66mIwMpyCkrgpikJkAAJ2CyBrPwsZUt30/lNyldmfqayutetXjd0qdsFoTVDbbbtjtgwrczfMmNHAShBT0sOZO7tHeIv3deX7MPZK1lY9HxHuLk4K9vBhm4VkUBNUxIgARKwOQLito1NFzYpK30iWjesZpgi+LqFdVMCONxd3G2uzWzQDQJamr/NHVMKQHPJ0YGKyWXnFeKRGVvQuXEg3u3bQoIoTUmABEjAdgmI6Fxx48bas2ux/ux6XLh2QdnOvbPenYroq+9b33Ybz5aVIkABqJFE0NXl13SgW+RPX76OvtM345NHW+OBNnWra0j4XhIgARKwKIH8wnzsStqFdefWYd3ZdcgpzEGPej1wT/17lPN83m638qFa9MWszKoEOH9TAEo5GB2oNL41h5IxenE8fnm5M5oE84CzlHPRmARIoNoIiPN8Wy5uUVb6Np7bCC83L9wdfjfurn+3kq6FV6xV29BY7MWcvykApZyJDlQe32erj+CPg0lY/koX+HgycamUg9GYBEigyghkF2QrZ/lWn16tfA+tEaqs8omvloEt4exk/HrQKmssXyRNgPM3BaCUE9GByuMTASCD5u2Ej6crZvSPUpJE8yEBEiABWySQV5inpGlZdWoVNpzfgGDvYPSO6I3eDXujca3GtthktslCBDh/UwBKuRIdyDC+skmipSDTmARIgAQsSCBfl4/tF7dj1elVypk+Pw8/RfD1ieiDprWb8o9WC7K25ao4f1MASvknHahifHFnr6L/1zvw/fAOiKpfW4ozjUmABEhAhoBIVyWid/938n+K8PNw8VBEn/gSN3Jwp0KGrn3acv6mAJTyXDpQ5fjmbErAN1tOK0mia3kzH5aUs9GYBEjAZAIXr13Ebwm/YcXJFbicfRm9GvbCA40eQFRwFM/0mUxTWwacvykApTyaDlQ5PvFX9/ML9kCnK8LXA9vD2ZnnAaUcjsYkQAJGCYh7d/868xdWJKzA3pS96Fy3M/o27qukbvF09TRqzwKOQYDzNwWglKfTgYzjS8/Kx/3TNuHZjg3wQnceqjZOjCVIgARMJSASNItcfT8f/1k51xfhF6GIPnGuL9Ar0NTqWN4BCHD+pgCUcnM6kDp88efS8PTs7VgwNAbtG/qrM2IpEiABEjBCQGzr/nriV0X4iZW/Bxs/iAdve1AJ5uBDApUR4PxNASj1CaEDqcc3b/MpzN6YgJWjusG/Bs8DqifHkiRAAiUJFOoKsfXiViw7vkzJ19c+uD0ea/qYkqjZzYW5R+kt6ghw/qYAVOcpFZSiA6nHJ84DvrQwDjkFhZg3KJrnAdWjY0kSIAEASdeT8MvxX/DziZ8hRODDtz2MR5s8ino+9ciHBEwmwPmbAtBkpylpQAcyDV96dj4emLYJT8fUx8s9bjPNmKVJgAQcjoD4w1Gc7Vt0ZBH+Pv+3EtDxWJPH0K1eN7g6uzocD3bYcgQ4f1MASnkTHch0fAfOp+PJr7bh2yExiIngeUDTCdKCBLRPQNzFK1K3COGXmpOqrPQ9efuTCKsZpv3Os4dVQoDzNwWglKPRgczD99220/hy/Qn8PrIbAmt6mFcJrUiABDRH4FT6KSw+uhjLTyxHuE84nmn+jJKsmelbNDfU1d4hzt8UgFJOSAcyD5/Y1nn1h73IyMnHt8/F8DygeRhpRQKaICB+H2y5uAULDi1QtnvvbXgvnm72NNoEtuENHZoYYdvsBOdvCkApz6QDmY8vMycffadtxuPt6uHVu5uYXxEtSYAE7JJAXmEefk/4Hd8d+g5Xcq6gX7N+eKLpE8zbZ5ejaX+N5vxNASjltXQgKXw4eCEdT8zahoXDYtCuAc8DytGkNQnYB4H03HQsOboEPxz5AT7uPhjUYhAeaPyAcj8vHxKoKgKcvykApXyNDiSFTzGeu/kURI7AlSO7wc+bObzkibIGErBNAucyzmHB4QVK4uZWga0U4SeieZ2dnG2zwWyVpglw/qYAlHJwOpAUPsVYnP8Z9u1uuLk4Y+aAKJ75kUfKGkjApggcuXIEX+//GuvPrUfPBj0xqOUgtAxoaVNtZGMcjwDnbwpAKa+nA0nhKza+cj0PfaZuVM4CijuD+ZAACdg/gfiUeHx94GvsTNyppHERwq9uzbr23zH2QBMEOH9TAEo5Mh1ICl8p4+0JqXjum134+eXOaB7qa7mKWRMJkECVERAr+juSdigrfgcvH8RTzZ7CwBYDGdhRZSPAF6klwPmbAlCtrxgsRweSwlfOePJfx/Db/otYMaIrvN2Z5d+ydFkbCViPgBB+4l7e2Qdm43T6aQxoPkDJ4efn4We9l7JmEpAgwPmbAlDCfQA6kBS+csYFhTo8M2cHGgZ449PH21q2ctZGAiRgcQJC+Ikr2mbEz0ByVjIGtxys3NhRw62Gxd/FCknAkgQ4f1MASvkTHUgKn0HjxPRs9Jm6CeMfbImHInntk+UJs0YSkCcghN/Wi1vxZfyXuHDtAoa2GqoIP97YIc+WNVQNAc7fFIBSnkYHksJXofFfh5IxZnE8fhvZFQ0C1K0kFOqKsPPUFaRk5iDIx1O5Z9jF2ck6DWStJODABERQx/T46UhIT8BzLZ9Tbu3wdvN2YCLsuj0S4PxNASjlt3QgKXyVGr/3v38Qd/Yqlr7YGe6ulecJW3UwEeNXHEJiek5xnaF+nhjXtwV6twq1XiNZMwk4EIG9KXsxfe90HE49jIEtByrn/Gq613QgAuyqlghw/qYAlPJnOpAUvkqNcwsK8eiMrejcOABv39+iwrJC/L20MA5FZUro1/5EbkGKQOuNE2vWPoGjV45iStwUxCXHoX/z/ko6FwZ3aH/ctd5Dzt8UgFI+TgeSwmfUOOHSNeW+4OnPROGuZkHlyott364T15Va+StZSIjAED9PbI69m9vBRmmzAAmUJpB4LVHZ6l19erVyvm946+Go7VmbmEhAEwQ4f1MASjkyHUgKnyrjZXvO46OVh/HHqG4I9vVUbPTn/bacuIzp608YrWfR8I7o1DjAaDkWIAESAMRdvXMPzMWiI4twT4N7MOKOEQiryYAs+oa2CHD+pgCU8mg6kBQ+1cYiIESc71s4rAP+OpRU7ryfsYqm9otkRLExSPy5wxPILczFosOLlNs7WgS0wGvtXlO+8yEBLRLg/E0BKOXXdCApfKqNr+UWKFvBrcN8sWJfYrnzfsYq4gqgMUL8uSMT0BXp8HvC75i2dxp83X0xpt0YdA7r7MhI2HcHIMD5mwJQys3pQFL4TDLefz4ND03fYrL486/hhnceaIkQX6aGMQk4CzsEgX2X9mHizom4lH0JI+8Yifsb3Q9np8qj7h0CDDupeQKcvykApZycDiSFzyTjbSdT8fTX202yKVuYqWGk8NFYQwSSrycrkb1rz65VcvkNbjUYXq5eGuohu0IClRPg/E0BKPUZoQNJ4TPJeHn8BYz6Md4km7KFmRpGCh+NNUAgpyAH3/7zLeYenIse4T2U7d6QGiEa6Bm7QAKmEeD8TQFomseUKU0HksJnkrHaFcBXejTGol3ncOV6nsH6mRrGJOwsrBEC4uq2P8/8iUm7J6GWZy2MjRmLO4Lu0Ejv2A0SMJ0A528KQNO9poQFHUgKn0nG+px/Sek5Bs8B6oXd54+3Rf+5O4zWzcAQo4hYQCMEEtIS8NGOj3Ay7SRGRY3CQ7c9xHN+GhlbdsN8Apy/KQDN9x4AdCApfCYb62/9EIYlb/4oubWbW6BTtVXM1DAm46eBnRHIys/CV/u/wg+Hf8DjTR/HK5Gv8Oo2OxtDNtd6BDh/UwBKeRcdSAqfWcbG7v1Vu1XMFUCz8NPIDgiI7d5159Yp0b3B3sH4T8f/4Hb/2+2g5WwiCVQdAc7fFIBS3kYHksJntrH+JpAjSRn4fPVRTHisDfq2ravUp3armNfDmY2fhjZM4FzmOXyy4xMcuHxACfDgdq8NDxabVq0EOH9TAEo5IB1ICp9FjP84kIjYZfvx+8huCPf3VupUs1Xcu1WoRd7PSkjAFgjkFeZh3sF5ypfI5TfqjlFKsAcfEiABwwQ4f1MASn026EBS+Cxm/NYvB3AkMQOLX+gEN5cbSWyNbRVb7OWsiASqmUB8SjzGbR0HN2c3vNPpHbSt07aaW8TXk4DtE+D8TQEo5aV0ICl8FjO+nluAXlM2ohhwtggAACAASURBVHmoL4Z0iUBMhD9cnJ2U7eCdp64gJTMHQT68CcRiwFmRTRC4nn8dU+Om4tcTv+KFNi9gYMuBigjkQwIkYJwA528KQONeUkkJOpAUPosYc6XPIhhZiZ0R2Hh+Iz7Y/gHCfcIxrtM4NPBtYGc9YHNJoHoJcP6mAJTyQDqQFD5pY/1Zv5IpYfSVitQwMwdEgWf9pDGzAhsikJqdiom7JmLz+c14vf3reKTJI8zpZ0Pjw6bYDwHO3xSAUt5KB5LCJ2Wsj/ZNTM+psB5x9y+jfaUw09hGCIjULr8l/KaIv+jgaLzZ4U0EeQfZSOvYDBKwPwKcvykApbyWDiSFT8qY+f6k8NHYjghczr6M97e9j32X9uGdju+gZ4OedtR6NpUEbJMA528KQCnPpANJ4ZMyXh5/gTd+SBGksT0QWHV6FT7a/hE6hnbEWx3eQm3P2vbQbLaRBGyeAOdvCkApJ6UDSeGTMla7AjhvUDTubs6tMinYNK5yAldzrir39+5I3IG3O76N3g17V3kb+EIS0DIBzt8UgFL+TQeSwidlbOzGD1G5u4sz7msTiilPRUq9i8YkUJUE1p1dp2z5tqnTBu92eheBXoFV+Xq+iwQcggDnbwpAKUenA0nhkzY2duPHJ4+2wqerj+E/9zfHo1H1pN/HCkjAmgQy8jKU+3vXn1uPN2PexAONHoCTk4hn50MCJGBpApy/KQClfIoOJIXPIsbG8gCuO5KMkYvisWJEV0QE1rDIO1kJCViawJ7kPXhz05to5NcI4zuPR3CNYEu/gvWRAAmUIMD5mwJQ6gNBB5LCZzFjYzd+vL/iEHaeTsWylzrDw9XFYu9lRSQgSyBfl4+Z8TOx8PBCjIoahWeaPcNVP1motCcBFQQ4f1MAqnCTiovQgaTwVZlxbkEhHp2xFR0bBeCdB1pU2Xv5IhKojMDZjLOI3RiLnMIcfHrnp2hSuwmBkQAJVBEBzt8UgFKuRgeSwlelxgmXrqHvtM2Y/kwU7mpmOCrY2EpilTaYL9MsAZHUWdzfO2HnBDza5FGMbjcaHi4emu0vO0YCtkiA8zcFoJRf0oGk8FW58bI95/HRysP4Y1Q3BPt6oqTgO305C4t2nkVSxq2bRcRNIuP6tuB1clU+Utp9YXpuOsZvG4+45Dh82PVDdA3rqt3OsmckYMMEOH9TAEq5Jx1ICl+1GL+2OB7JGTkY0KE+Pvj9MCq7Sk4ff8k7hatlqDT3UiH63tj4Bpr5N1MCPQK8AjTXR3aIBOyFAOdvjQnAL7/8Ep999hmSkpLQtm1bTJs2DTExMRX6Y1paGt5++238/PPPuHLlCho0aIApU6bgvvvuU+XDdCBVmGyq0LXcAtz1+QZcysxV1S4hAkN4p7AqVixkmICuSId5B+dh9v7ZDPSgk5CAjRDg/K0hAbh48WIMHDgQs2bNQocOHRQh99NPP+Ho0aMICip/5isvLw9dunRRfvbWW28hLCwMZ86cQa1atRTxqOahA6mhZFtlxLZvh4/X4PK1PJMatmh4R3RqzBUbk6CxMK7kXMFbm97CmYwz+LzH52gZ0JJUSIAEbIAA528NCUAh+qKjozF9+nTFtXQ6HcLDwzFixAiMHTu2nLsJoShWC48cOQI3Nzez3JEOZBa2ajVSe4Vc2UZO7ReJhyLDqrXtfLk8gUJdIeJS4nAp6xLqeNdBVFAUXJytkxpod9JuJco3MigS73V+Dz7uPvIdYA0kQAIWIcD5WyMCUKzmeXt7Y+nSpXj44YeLnWPQoEEQ27zLly8v5zBim9ff31+xEz+vU6cOnnnmGcTGxsLFRd2EQAeyyOewSitZHn8Bo36MN/mdXAE0GZnNGaw5s0aJvE3OSi5uW7B3MMbGjEXPBj0t1l4hMuccmIO5B+diTLsxeOr2p5jbz2J0WREJWIYA52+NCMCLFy8qW7hbt25Fp06dir3jjTfewN9//40dO3aU85hmzZrh9OnT6N+/P15++WWcOHFC+T5y5EiMGzfOoIfl5uZCfOkf4UBilTE9PR2+vr6W8UrWYlUCpq4A8gygVYejyioX4m/MhjEoQlGpdzrhRqjPpB6TLCICL2dfVrZ8L1y7gM+7f47mAc2rrI98EQmQgHoCFIAOLACbNm2KnJwcnDp1qnjFb9KkScq2cGJiokEveu+99zB+/PhyP6MAVP+hq+6S4gxg14nrkJSeU0YKlG8Zo4Cre7Qs836xItdrWa9SK38laxYiUKwErnpsldR2cHxKPF7f8DqigqMwrtM41HSvaZkOsBYSIAGLE6AA1IgANGcLuHv37srZvzVr1hQ71h9//KFEAItVPnd393IOxxVAi38Gq6VCcX/wSwvjlHeXXg8q3RzmAayW4bH4S3cl7cKQ1UOM1juv1zxEh0QbLVe2gEjs/OPRHzF5z2RG+ZpMjwYkUD0EKAA1IgCF+4ggEJHyRaR+EY8IAqlfvz5effVVg0EgIvL3hx9+QEJCApydnRWbqVOnYuLEiRBbymoeOpAaSrZZRojA8SsOlcoD6OXmjBe7N0bDwBoI8vFETIQ/XJz164C22Q+2yjiBlQkrEbsp1mjBid0m4r5G6lJA6SvLLsjG+9vex/bE7fhv9/8qq398SIAEbJ8A528NCUCRBkYEfXz11VeKEBRpYJYsWaJE+QYHByspYsQ5wU8++UTxzHPnzqFly5aKjYgUPn78OIYMGaKcARS5AdU8dCA1lGy3TMmbQITMe/vXg/js8Ta8+cN2h8yslllrBfBcxjmM3jAaNd1qKuf9RFQxHxIgAfsgwPlbQwJQuJxIAaNPBB0ZGYkvvvhCWRkUT48ePdCwYUPMnz+/2Du3bduG1157DfHx8Yo4HDp0KKOA7eOza5VW/r4/EW/9cgArR3VDWC0vq7yDlVY9Af0ZwJSslHJBIKI15pwB3Hh+I8ZuGouHGj+EMe3HwM3ZvFRSVU+DbyQBEhAEKAA1JgCr2q3pQFVN3Prve/Pn/TiefA0/Pt8Rri43jgbwsX8C+ihg0ZOSkcAVRQFXlC9Q3Ooxa98sfPvPt0qgh6lbxvZPkj0gAW0Q4PxNASjlyXQgKXw2aZydV4gHp29Gn1YhGHPv7TbZRjbKPAKG8gCGeIcgNia2VAqYivIFjo4ajdWnVyMhPQGT75qMprWbmtcQWpEACVQ7Ac7fFIBSTkgHksJns8ZHkjLwyJdbMXdwe3RuHGiz7WTDTCdg7CaQivIF6t8kRJ+IFvbz8DP95bQgARKwGQKcvykApZyRDiSFz6aNf9hxFpP+OoaVo7oqEcF8tE/AWL5AQSDYKxirH18tlS9Q+yTZQxKwfQKcvykApbyUDiSFz6aNRW631xbHIykjB98P68h0MDY9WpZpnLWihS3TOtZCAiRgSQKcvykApfyJDiSFz+aNr+cWKOcB72sditd5HtDmx6tsA41t95Ytb818gXYHjw0mAY0T4PxNASjl4nQgKXx2YXwsORMPf7kFM/pHocftQXbRZjYSqCiQY2zM2Arv/OUKID2HBByHAOdvCkApb6cDSeGzG+Ole87jo98P4feR3VD3Zn7AkkmkeWuIbQ1lRYEcFaV80bderBje89M9SM1JNdghc/IF2hYZtoYESEBPgPM3BaDUp4EOJIXProzfWLoPJy9dV/IDrj2cXO4aOd4bbBvDaSyQozIRt+XCFoxePxo5hTnlOmNMPNpG79kKEiABtQQ4f1MAqvUVg+XoQFL47MpY5Ad8ZMYWhNf2wprD4kaJ0o/+xuCZA6J4lVw1jqy527hLji7B57s/x7ud3oWniycm7JyA5Kzk4p4YyhdYjd3kq0mABCQJcP6mAJRyITqQFD67Mz6enIl7J28sJ/70HREiMMTPE5tj72bUcDWNrqmBHGLFcPKeyVh+cjmm3DUF7YLbKS03NYCkmrrL15IACZhJgPM3BaCZrnPDjA4khc/ujLedTMXTX2832u5FwzuiU+MAo+VYwPIETFkBbBnQEm9uehMn009ixj0zUN+3vuUbxBpJgARskgDnbwpAKcekA0nhszvj5fEXMOrHeKPtntovEg9FhhktxwKWJ6A/A5iSJbbpy27UA/ozgAv6LMCoDaPg5eqFKT2moJZnLcs3hjWSAAnYLAHO3xSAUs5JB5LCZ3fGXAG0jyHTRwGL1pYUgfpAjn+3/zcWHF6A6OBovNf5Pbi7uNtHx9hKEiABixHg/E0BKOVMdCApfHZnLFK/dJ24DknpOQbPAfIMoO0MqaE8gCKQ45Emj2DBoQUY1HIQXmjzApyc9OE7ttN2toQESMD6BDh/UwBKeRkdSAqfXRqvOpiIlxbGKW0vv8EIvNazCV69u0mpIBDmDKy6oS4ZvOHv6a8IvNTsVNTxroOk60n4YPsHeKfjO+jbuG/VNYpvIgESsDkCnL8pAKWckg4khc9ujYUIHL/iEBLTy+eLE50qmRPQUFnmDLTO0Fd2+8eFaxcwc99M/Lf7f9ElrIt1GsBaSYAE7IYA528KQClnpQNJ4bNrY7GqN33dCUxec6xcP/Sbis/fGYHZG08xZ6CFR9pQipb159ZjzIYxBgM/xOtrutXEnF5zICJ/+ZAACZAA528KQKlPAR1ICp9dG+vPA1a0Cig65+wE6AztE0NEozJnoDkOYGiVL8grCLm6XKTnpldYZaBnINY8sQYuzi7mvJY2JEACGiPA+ZsCUMql6UBS+OzaWG1EsLFOMmegMUK3fl7RHb9qa5jXax6iQ6LVFmc5EtA0gcLCQuTn52u2j25ubnBxqfgPPs7fFIBSzk8HksJn18ZqcwIa6yRzBhojdOPnxu74VVPL822ex8ttX+YqoBpYLKNZAkVFRUhKSkJaWppm+6jvWK1atRASEmIw2p/zNwWg1AeADiSFz66NLbUC+P2wDuhyW6Bds6iKxqu94cNYW4K9gzE2Zix6NuhprCh/TgKaJJCYmKiIv6CgIHh7e2syFZIQuVlZWUhJSYEQgaGhoeXGkvM3BaDUB5wOJIXPro2N5QRU27nvh3ZAlyYUgMZ4qb3j11g9+mTQk3pMogg0Bos/1xwBse177NgxRfwFBGj/usrU1FRFBDZt2rTcdjDnbwpAqQ84HUgKn90bixQvL97MCWhuZ7gFrI6cpVYAxdv018GtemwVt4PV4WcpjRDIycnBqVOn0LBhQ3h5eWmkVxV3Izs7G6dPn0ZERAQ8PT1LFeT8TQEo9QGgA0nhs3tjsQrY7sO/kJZl/kFqBoGocwNjd/yKWrxcvODr4YvkrGRVlTIoRBUmFtIQAb0ANCSINNTN4q5U1l/O3xSAUj5PB5LCZ/fGMucAmQbG9OGv6I5ffU2Te0zGXeF3YUb8DMw+MNvoCyZ2m4j7Gt1ntBwLkIBWCFAA3hpJzt8UgFKfazqQFD67NzY3ElifKHrmgCj0blX+cLLdg7FiBwzlAaztURvvdnq3+Eyf2u1irgBacaBYtU0SsHcBeOnSJbz77rv4/fffkZycjNq1a6Nt27bKv3XpUv6GH64AVu6GTkUiXIaPWQQoAM3CphkjtSuALs5OENvF+odXwcm5gNgOFnf6rjy1EqOjRuOp258qdZbP2HYxzwDK8ae1/RKwdwF45513Ii8vD5988gkaNWqkiMC1a9eiZcuWePDBB8sNDAUgBaDVPq0UgFZDaxcVG4sE1m/zinN+D07fjF6tQvDoHfUQE+EPIQr5mE5A/L06OW4ylp9Yjtn/mo3b/W83WElF28WMAjadOS20Q8CSAlD8/tt56gpSMnMQ5ONp9d9rInWNWPHbsGEDunfvrmpQKAApAFU5ijmFKADNoaYtGxEJ/NLNSOCSS+llt3nFL8pB83Zi/nPR6NBI++kXrDHKuiIdPtz+IbZc2ILZ985GA98Glb7G0HZxiHcIYmNimQLGGgPEOm2egKUEoPi9N37FIZS8CtPaOxsFBQWKABw2bBgmTJgADw8Po7wpACkAjTqJuQUoAM0lpy07tb8Mv99xBv/98xj+92oX1KvtrS0IVu6N2NZ9d+u72HdpH+bcOwchNUJUvVHYxaXE4VLWJdTxroOooCimflFFjoW0SMASAlD/R2/Zs2NVcbZ52bJlGD58OER6l6ioKGUlsF+/fmjTpo3B4aIApAC02ueYAtBqaO2uYrXbIf/59QD2nEnDspc6wdvd1e76WR0Nztfl4+1Nb+Po1aOK+BNCjg8JkIDpBGQFoP7YS8mVv5KtqIrsBqIPmzZtwvbt2/HHH39g586dmDNnDgYPHlwOCAUgBaDpnxKVFhSAKkGxWDGB/EId+s/ZgTo1PTD9mTs0eQ2TJYc7vzAf/7fx/3Au85xy5i/Ai9vnluTLuhyLgKwAVBv4VpX5TcWW8F9//YUzZ85QAJrozowCNhFYyeIUgBLwHNg09VouHpy+Bf2iwzHiniYOTKLyrucW5mLMhjG4nH1ZEX9+Hn5kRQIkIEFAVgCqTX1VlTccTZo0CR9//DEuX75MAWiib1AAmgiMAlACGE2LCRy6mIEnZm3FpKci0auluvNsjoQvuyAbI9eNhPg+s+dM+Lj7OFL32VcSsAoBWQFYnSuA4l7fJ554AkOGDFHO/Pn4+GD37t0YMWIE7r//fsydO5cC0ESvoQA0ERgFoAQwmpYiIA5Tv75kHxa/0Amtwri6pYdzPf86Xln7ivK/X97zJWq41aDnkAAJWICArABUm/pqc+zdFk91lZubi/feew9//vknTp48ifz8fISHhyui8K233jJ4tzHPAFbuNBSAEh8qbgFLwKOpQmDmhpOYv/UUlr/SFSF+pS8rd0REGXkZeGnNS/B29cYXd38BL1ftX1jviOPMPlcPAVkBKFqtNvVV9fSw9FspACkAreaHFIBWQ+swFYvExrHL9uOfixlY8kIn1PBw3Mjg9Nx0PP/X8wjwDMDkuybDw8V4ni+HcRR2lAQsQMASAlAvAqs6D6A53acApAA0x29U2VAAqsLEQkYI5BXolCTRQvx99Ww7i2+d2MMACPE3/M/hCK4RjEndJ8HNxc0ems02koBdEbCUABSdVpv6qjoBUQBSAFrN/ygArYbW4SpOz8rHIzO24J7mQXj7/hYO1X/9yl+QdxDFn0ONPDtb1QQsKQCruu3mvI8CkALQHL9RZUMBqAoTC6kkcPrydUUE/l+vZnimQ32VVvZdTJz5e/7P51HHqw4m9eDKn32PJltv6wQoAG+NEOdvgEEgEp9YOpAEPAc0VbNlor8z+OuB7dG1SaCmKenFX6BXoCL+3F3cNd1fdo4EqpsABSAFYEkfpACU+ERSAErAczBTtfcFCyw/x53HuP/9g59f6owmwdrMfyfE3wt/vgB/L39M7jGZ4s/BPg/sbvUQoACkAKQAtNBnjwLQQiA1Xo05l6dP+vMolsVdwC8vd0aQr7bSw2TmZeKFv15Abc/aFH8a9312z7YIUABSAFIAWugzSQFoIZAarsbcy9NFepjXf9qHI4mZWPxCR/h4aiMqVi/+annUwpS7pnDlT8O+z67ZHgEKQApACkALfS4pAC0EUsPVyFydlF+ow9Bvd0OnK8K8wdFwd3W2a1JC/L3414vw9fBVxB/z/Nn1cLLxdkiAApACkALQQh9cCkALgdRwNbKXp1/LLUC/2dvQJMgHk55sCycnJ7ukJa53E0mexZ2+U++aSvFnl6PIRts7AQpACkAKQAt9iikALQRSw9XIrADqsaRk5uDRGVvRt21dxPZuZne0sguylZU/seI37Z5pFH92N4JssFYI2LMAHDx4MNLS0vDrr7+qHg7mAawcFaOAVbtS+YIUgBLwHMTUUpenn7x0DY/P3IrRPZtiUOeGdkMvtzAXr659FQW6AszoOYN3+9rNyLGhWiRAAcgVQK4AWuiTTQFoIZAar8bcy9PL5g10c3HCwHk7la3g3q1CbZ5afmE+Rm8YjbTcNMz+12zUcKth821mA0lAywQsKgB1hcCZrcC1ZKBmMNCgM+DsYjV8XAG0PFquAEowpQCUgOdgpqbkARRoKir/cGRdfLvtDOY/F4OYCH+bpShW/N7Y+AbOZ57HnF5z4Ovua7NtZcNIwFEIWEwAHvofsCoWyLh4C51vXaD3RKDFg1bBSQFoeawUgBJMKQAl4DmgqZqbQPTi76WFcSgqw0gf/iGuifvfvotYNLwjWoX52RzJQl0h3t7yNo5eOYpven2DWp61bK6NbBAJOCIBiwhAIf6WDAQq+g315HdWEYEUgJb3WApACaYUgBLwaGqQgNq8gc92aoC5m07hpxc7oVGdmhXSVCs6LTUcuiId3t/2PvYk78E3vb+BuOaNDwmQgG0QkBaAYtt3SqvSK3+luuYEiJXA0Qcsvh1MAWh5H6IAlGBKASgBj6YGCZgSNfz3sUtYse+iIgLr1vIqV5+p287mDolY8YtLiUPK9RT8dfYvHLlyBK+1ew3i3+t410FUUBRcrHg2yNx2044EHI2AtAA8tQn49gHj2Ab9BkR0M17OhBIUgCbAUlmUAlAlKEPFKAAl4NHUIAFT8gY+2LYu3vrlIHaeSsWSFzohoKZHcZ3mXD9nzpCsObMGE3ZOQHJWcrG5E5xQVGJ7KNg7GGNjxqJng57mvII2JEACFiIgLQAPLAWWDTXemsfmAq0fN17OhBIUgCbAUlmUAlAlKApACVA0VU3AlBXATo0DILZ4R/24F2dSs/DD8A7KlXFqt5E3x94NF2fzE0sL8Tdmw5hSYs9QR4UgFM+kHpMoAlV7AguSgOUJSAtArgBaflCqsUYKQAn4XAGUgEdTgwTMyRuYV6DD8O92Iye/EN8OicHes2l4+uvtRgmLIBIhIs15xPZur2W9Sq38VVaPEIFiJXDVY6u4HWwOcNqQgAUISAvA4jOAiQaCQEQDeQbQAsNUZVVQAEqgpgCUgEfTCgmYkzcwO68Qz87dAV8vN9zfOgSv/7TfKOGp/SLxUGSY0XKGCuxK2oUhq4eYbDuv1zxEh0SbbEcDEiABeQLSAlA0oTgKWPxPyVwFN3cTrBQFbE7veRNI5dQoAM3xqps2FIAS8GhaKQFzAjgycvLx7JwdcHNxxu4zV40SllkBXJmwErGbYo2+o2yBid0m4r5G95lsRwMSIAF5AhYRgHoRWC4PYBjQe4JVUsCY23MKQApAc33HqB0FoFFELCBBwJwULulZ+cr2b8Lla8jJ1xl8u/g7PcTPEzJnAOccmIOpcVNN7h1XAE1GRgMSsBgBiwlA0aIqvgnEHAgUgBSA5viNKhsKQFWYWKiKCVy5noe+0zbhQlpOuTfrQz5mDogy+zo5kePvpTUvwd3ZHRl5GUaDQEQjeAawip2AryMBAwQsKgDtgDAFIAWg1dyUAtBqaFmxJIHL13LxwLTNSM/KQ3aJlcBQP0+M69vCbPF3KPUQhq0ehtfbvw4/Dz8lClg8JdO+lG06o4AlB5PmJGAhAhSAt0By/gZ4BlDig0UHkoBHU6sTSMnIwZNfbUNEYE08GBmKEF8v5f5gc1O/nEo/hcGrBuO5ls9hcKvBSvsN5QF0dnKGuBFE/4R4hyA2JpYpYKw+4nwBCVROgAKQArCkh2hKAH755Zf47LPPkJSUhLZt22LatGmIiYkx+jvhxx9/xNNPP42HHnoIv/76q9Hy+gIUgKpRsWA1EUhMz8ZTX23HnU0D8f6DreBsZt6/xGuJGLhqIPo26ouRUSNL9UZ/E8ilrEvKzR9tA9ti3+V90P8/bwKppsHna0mgDAEKQApATQrAxYsXY+DAgZg1axY6dOiAKVOm4KeffsLRo0cRFBRU4S+C06dPo2vXrmjUqBH8/f0pAPkrU3MEzl/NUgJDut4WiI8ebm2yCEzNTlVW/jqEdsDbHd6Gk5P5yaM1B5cdIgE7IkABSAGoSQEoRF90dDSmT5+u9E+n0yE8PBwjRozA2LFjDX5ECwsLceedd2LIkCHYtGkT0tLSKADt6JcZm6qewMW0bPSfswPtGtTGxMfaqN4GFkEeQ1cPRSO/Rvik2ycQ27t8SIAE7JMABSAFoOYEYF5eHry9vbF06VI8/PDDxf0bNGiQIuqWL19u8NM6btw47N+/H7/88gvU3DOYm5sL8aV/xBawEJnp6enw9fW1z98IbLXDEBBnAsVKYKswP/z3ibZwdalczGUXZOPFv16Ej7sPJt81GW7Obg7Dih0lAS0SoACkANScALx48SLCwsKwdetWdOrUqbh/b7zxBv7++2/s2LGj3Gd58+bN6NevH+Lj4xEYGKhKAL733nsYP358ubooALX4q1KbfbqUmYsBc3bgtqCamNIvUkkabejJL8zHiPUjkFuQi5k9Z8LT1VObQNgrEnAgAhSAFIAOLwAzMzPRpk0bzJgxA3369FF4cAXQgX4LOnhXRZ5AIQLDanth+jN3wMPVpRQREdQxdtNYnM08i7n3zkVN95oOTozdJwFtELBnASjm6G+//VYZCFdXV9SrVw9PPPEE3n//fXh6Gv4DlXkAK/dbTUQBm7oFLFb97rjjDri43Jr4xJlB8Tg7OyuBI40bNzb6iWcUsFFELGCjBMSNIQPn7YB/DXfMHNAOnm43PgtFRUX4eMfH2J64Hd/2+Rb+nv422gM2iwRIwFQC9i4Ak5OT8c033yA/Px979uyBOOb14osvYuLEiQZRUAA6gAAUXRRBICLli0j9Ih4h6OrXr49XX321XBCIcIoTJ06UIvOf//wHYmVw6tSpaNq0Kdzd3Y1+tigAjSJiARsmIO4Ofu6bXXB1dsLXg9rD19MN4oq3Hw7/gIX3LUTdmnVtuPVsGgmQgKkELCkAy6Z/sna6J0O7dI899hhOnTqFuLg4CkBTnUHc0FQk/uTXwCPSwIi/Br766itFCIo0MEuWLMGRI0cQHByspIgR5wQ/+eQTg71VswVc1pACUAOO4+BdyMorwMvfx0GcDXz67mTM2D8J3/T+Brf73+7gZNh9EtAeAUsJQEMJ4IO9gzE2ZqzVEr6XnaMPHjyIf/3rX2jQoAG2b99OAWiGu2pGFvuJIwAAIABJREFUAIq+ixQw+kTQkZGR+OKLL5SVQfH06NEDDRs2xPz58ykAzXAUmmiXQH6hDoN//A7786dhQucpuL9pN+12lj0jAQcmYAkBKMSfuAKy7PWP1r7yUQjAhQsXKuf9CgoKlIwc4siWWOgRK4GGHm4BV+7smhKAVf255gpgVRPn+6xBYP+l/Rj+53C0ch+Of45HYMHQGDQJ9rHGq1gnCZBANRKQFYBi27fXsl5Izko22AshAsVK4KrHVsHFuXRwmWy3hQC8cOECZs6cievXr2Py5MlKMMicOXMqrJoCkAJQ1u8qtKcAtBpaVlxFBE6nn8azfzyLF9u+iGeaPYOpa49j/tbT+GZwNO6oX7uKWsHXkAAJVAUBWQG4K2kXhqweYrSp83rNQ3RItNFyphQouwUszvmLK19Hjx6NoUOHcgXQFJg3y3IF0AxoehMKQAl4NK12AuKuXiH++kT0waioUcXtmb/lFD5bfRQzBrRD96Z1qr2dbAAJkIBlCMgKwJUJKxG7KdZoYyZ2m4j7Gt1ntJwpBQyd01+0aBHGjBmDhIQEeHl5lauOK4BcATTFx0wqSwFoEi4WtiECmXmZeG7Vc0qwx4ddPix3v+/y+AsYu+wAxj/YEk9Gh9tQy9kUEiABcwnICkBbWgEUDMRZQHG2X6wC/vvf/6YANNExuAJoIrCSxSkAJeDRtNoI5BXm4eU1L8PNxQ1f3P1FhVe8bTuZihcW7Mbgzg3x2r+alhOJ1dYBvpgESMAsArICUH8GMCUrpVwQiGiQtc8Aiqtdf/3111J9nzBhAiZNmqSkg6lRo0apn3EFkCuAZn1Q1BhRAKqhxDK2REBXpEPsxliczzyPub3mwtvNu9LmHU/OxOBvdqFDhD8mPNYG7q6V3x9sS31lW0iABEoTkBWAojZ9FLD475KRwNaOAjZnLCkAKQDN8RtVNhSAqjCxkI0QECk/P931KTZd2ITv+nyn+paPlMwcDJ2/GzU9XDHr2Xbw83KzkR6xGSRAAqYQsIQA1IvACTsnlIoGDvEOQWxMrNXyAJrST31ZCkAKQHP8RpUNBaAqTCxkIwS+OfgNvjv0HRb0WYB6PvVMatX13AKMXLQX565m4ZvnYhBWq/yBa5MqZGESIIEqJ2ApASgaXtU3gZgDiwKQAtAcv1FlQwGoChML2QCBFSdXKHf8ivQMzQOam9WigkId3lvxD1YdTMbsge0QxTQxZnGkEQlUFwFLCsDq6oMp76UApAA0xV9MKksBaBIuFq4GAuKvdLHqN33vdIyMGokBzQdIJWgV28giT+Cnq47iw4db4bF2pq0kVgMCvpIESOAmAQrAW67A+VtDdwFXxyecDlQd1PlOtQTEYe0Ptn2AK7lXik0sdV/npuOX8Mr3cegXUx+xvZvBxdlJbbNYjgRIoJoIUABSAJZ0PaaBkfggUgBKwKOpVQkI8ffahtfKvcOSkXoJl65h2He70cDfG188fQd8PBkcYtVBZeUkIElALwBF7jxDiZMlq7c58+zsbJw+fRoRERHKHcIlH87fXAGUclg6kBQ+GluJgNj27bm0Jy5nXzb4Bkvm6krPzleCQy6kZWPOwPZoGFg6D5eVushqSYAEzCBQWFiIY8eOISgoCAEBAWbUYF8mqampSElJQdOmTeHiUvpuYs7fFIBS3kwHksJHYysR2Hh+I15Z+4rR2i11X2ehrgifrDyMn/acx5R+kbjr9iCj72YBEiCB6iGQmJgIkVBZiEBvb29NJngXZ5WzsrIU8VerVi2EhoaWg835mwJQ6hNIB5LCR2MrEMgvzMeTvz2JE2knjNZu6fs6f9l7Hm//chDP39kII+9uAmeeCzQ6BixAAlVNQIijpKQkRQRq/RHiLyQkxKDI5fxNASjl/3QgKXw0tjABccvHm5vexD+p/+BMxhmjtVtqBbDkiw4nZuClhXvQIKAGpjwVido13I22gwVIgASqnoDYDs7Pz6/6F1fRG93c3Mpt+5Z8NedvCkApV6QDSeGjsYUJfL7rc6w7tw7ze83HMyufQXXc1ym6lJGTj9eX7MOhixmYNaAdWtfzs3BPWR0JkAAJyBHg/E0BKOVBdCApfDS2IIFv//kW8w7Ow8I+CxHuG17t93XqdEWYtfEkpq09gXF9WyjpYviQAAmQgK0Q4PxNASjli3QgKXw0thCB3xN+xwfbP8DcXnPRMqBlca0iFUx139e59cRljFi0F92b1sH7D7dS7hOWfUTQyc5TVyDuKA7y8URMhD/zEMpCpT0JOBgBzt8UgFIuTweSwucwxta8M3Prxa0YvX40pvSYgs5hncsxtea71Q5gckYORv8Yj6SMHHzR7w6pLeFVBxMxfsUhJKbnFL8+1M9TWWXs3ap8pJ/aNrIcCZCAYxHg/E0BKOXxdCApfA5hbGgVzlK3cRxKPYQhq4fg7Q5vo2/jvjbNU6zazfr7JKavO4HX722KoV0jTE4/IcTfSwvjUFSmp/o7SGYOiKIItGkvYONIwHYIcP6mAJTyRjqQFD7NGwvxN2bDGBSVkSyWuI3jXMY5DPhjAJ5r+RwGtxpsNyz3nLmCkYvi0TS4Jj5/oi0CanqoarsQkF0nriu18lfSUIjAED9PbI69m9vBqoiyEAk4NgHO3xSAUp8AOpAUPk0bi63XXst6ITkr2WA/ZW7jSM1OxcA/BqJ7eHf8X/v/M3klrbrBp2flY+zP+7HnzFVMfioSXW4LNNqkbSdT8fTX242WWzS8Izo11v4NB0ZBsAAJkEClBDh/UwBKfUToQFL4NG28K2mXsj1r7DE1F19WfpZSb32f+phw5wQ4Ozkbe0WV/1xNkIZIRrto5zl89PshPNE+HLG9m8HLvfRVTSUbvjz+Akb9GG+0L1P7ReKhyLDicmraYrRSFiABEtAcAc7fFIBSTk0HksKnaeOVCSsRuynWaB9NuY0jX5ePEWtHoKCoADPumQF3F9tLsmxqkMbpy9cxZkk80rLzMenJSESG1zLITO0K4PdDOyg3kIgIYVH3op1nkZSRW1wnA0aMuiQLkIBDEOD8TQEo5eh0ICl8mja29AqgWDF7e/PbOJ52HN/0+gY13WvaDD/9KtuaQ0mYu+V0uXYZC9IQ9l/dzBk4vFsERtzTBG4upVc29WcAk9JzygWBiBeKd/h5u8HT1UWJNq7oMdYWm4HKhpAACViVAOdvCkApB6MDSeHTtLH+DKClbuOYvGcyVp9ejYX3LUSgl/Ezc1UF19CKn6F3qwnSEDeHiNVAVxcnZTWwabBPqar0UcDiH0tGAou6y0YGV9Z/NW2pKn58DwmQQPUQ4PxNASjleXQgKXyaN9ZHAd8QLOUlyn+7/xf3NrzXKIeFhxZi9v7Z+K7Pd2jo19Bo+aoqUFFalsrebyxII7egEFPWHMf8Lafxco/GeKF7Y7i73loNNCQ4Q3w9kFOgQ1qWafeavnN/cwzuEsGo4apyGL6HBGyIAOdvCkApd6QDSeFzCGNDeQD1HVeTD3DVqVUYt3Uc5tw7B63rtLYZZsbSslTU0LJBGhWV23cuDbHL9is/nvhYG7QtcTawbGCHrqgI/efsMIsNzwSahY1GJGD3BDh/UwBKOTEdSAqfwxj/efpPvP736+X6aywf4I7EHRixbgTESmG3et1sipfaoIyyjTa2AliyfF6BDl/9fRJfbjiB/h0aKAmkvd3LXyWnNkLYEECeCbQpt2JjSKDKCHD+pgCUcjY6kBQ+hzA2Nx/gkStH8Nyq5zA2Ziweuu0hm2NlquiSOXd3IiUTY5cdQHJmDj55pA26Nil9BtJcMaqHKtM2mxsYNogESEAVAc7fFICqHKWiQnQgKXwOYWxONPCFaxcwYOUA9G/eH8NaD7NJTqaILkussul0RVi44ww+XXUU9zQPwtv3NUeQr6fCxliEsFqApqxOqq2T5UiABGyTAOdvCkApz6QDSeFzCONPd36KBYcXGO2rPh/g1Zyryi0fnet2Vlb/nJz08sloFVVawBTRZclzdiINzIe/H8LfRy9h9L+aYlCnBnB1cYY5ASllgak9n1iloPkyEiABqxDg/E0BKOVYdCApfJo3FgEgr214TVU/xY0gLQNaYvifwxFSIwSf3vmpYheXEodLWZdQx7sOooKi4OJc8W0Zql5kwULG0rIM6dIQ/2oRgpgIf4tH2m4+fhnv/u8g3F2c8cHDrRDd0F8RgWKrWCSVNufhCqA51GhDAvZJgPM3BaCU59KBpPBp2tjY2b+SnQ/xDsGKR1ZgzIYxyCnMwcyeM7Hp/CZM2Dmh1F3CaqKGqxqqqTd/WLJ9IkhkzuYETF93An1ahWJsn2Y4lpSJ/nNNiwg2dAaQV8hZcqRYFwnYHgHO3xSAUl5JB5LCp2ljtWf/BIRJ3Sdh44WNOJR6CPN7z4eI/hVisGzuQGNRw9UFtLrF0oW0bHz42yFsOn4ZL3ZvhIXbzyA5I1dVcmhD5xOrU9RW1xjyvSTgaAQ4f1MASvk8HUgKn6aN1d4F/GzzZ+Hp6onfEn5TbvkI8AxAr2W9Sq38lQQlRKBYCVz12Cqb2g62hcHcnpCqnA+8mJaDK9fzVDWp7PnEis4SWiKQRVWDWIgESKBKCHD+pgCUcjQ6kBQ+TRurXQEUkb5C/IlbPhr5NYJaO3FmMDokWtMMzemciBb+ee8FfPDbIWTlFSC/8NYNLELsvXN/C9Su4Y6UzBwE+XiWOp9oLLk108WYMyK0IQHbJMD5mwJQyjPpQFL4NG2s5i5gP3c/5Ony8NW/vkJkUKTCQ+3KoT5qWNMQJTonxN+sDSfx1cYEtKzri4GdGqJv27qVBqOoTW3DYBGJgaEpCdgIAc7fFIBSrkgHksKneeOK7gIWK0liXcrd2R2TekxC9/DuxSy4AmhZtxBpYz7/8yhW7LuIJ9rXw4i7myD4Zv7Asm9Sm9ya6WIsO0asjQSqgwDnbwpAKb+jA0nhcwhjQ3cBBxQU4LqzM97KKsIjd00AWjxYzELNyiHPAJruOuI2kf/+eQwbjl7CwM4N8FL3xqjl7V6qIq4Ams6VFiRgrwQ4f1MASvkuHUgKn8MYF/7zK+JWvIBLLs7K2t9n/v7on5GJYemZNxg8+V0pEVjxyuGNUASxatizQU+H4WfJju4/n4bPVh9F/Nk0PH9nIwzpGoEaHjfuFzaW3JpnAC05EqyLBKqXAOdvCkApD6QDSeFzDGNdITClFZBxEVecnTGwbjC6ZOVg7JWruCHnnADfusDoA0CJJM+GVg5FvsDYmFiKPwt4jljt+2z1EZxOzcKwbhHKGcGaHq7FN4qIV9wKH1FGSXlmDohC71ahFmgBqyABEqhOApy/KQCl/I8OJIXPMYxPbQK+fQBZTk4YGhqEsPwCfHopFWItsNQz6DcgolupfxLbwbZ8E4i9D2BRURE2HLuEaWuPI+HydQzpEoFBnRti28nLGL/iEBLTc4q7aMnr7OydG9tPAlogwPmbAlDKj+lAUvg0Y1ypUDuwFPnLhmJEcB0UODlhRlIKSp88u4nhsblA68c1w8SeOiKE4NaTqfhi7XEcSszA4M4NFSF4PPmawXQx9tQ3tpUESMAwAc7fFIBSnw06kBQ+TRgb2qoteWWbbv0EvH1oNk66uWFeYjJqFpXcWCyBwMAKoN0CEtveZ7YC15KBmsFAg86ltrdtuV87ElIxbd0J7D17FQM6NsDgLg0R6udly01m20iABMwgwPmbAtAMt7llQgeSwmf3xvpgjQqvbGv8NPbtmYW/anhjYWISAgt1Bvps+AygUtAehdSh/wGrYpUzj8WPOOPYe2KpQBdbH/y4s1eVPIJii/iBNqEY3q0Rmof62nqz2T4SIAGVBDh/UwCqdBUuIUuB0qCxPl1Lclaywd6JoIGauiK4Fumw8GIy6hcUVEzhyQXlxZE9CinR5iUDy4RPiG7fDKEoE+1sD26RcOka5m4+hWVx5xHd0F+JHO56WyCcnPRhIfbQC7aRBEigLAEKQApAqU8FHUgKn/nGlloZk6hn18XtGPLXcKN9ePdSKp64dr3icj3eAnrElv65PQqpEtHOhjtbyUqnUYrVX+DytVws2HYG3207jRA/LwzrGoEH2obCw9Wl+hvHFpAACZhMgPM3BaDJTlPSgA4khc88Y0utjMnUc+h/WLluLGJ9jE/+z6Zn4I0raRX3tWzwh70KqZvRzkYH1c7POmbnFWJp3Hl8s+UU0rPy8VR0OPp3bICwWjwnaHTsWYAEbIgA528KQCl3pANJ4TPd2FIrYzL13LTd5emOIaHBRvtQu7AQ689eQIVSsawgslchdWApsGyoUR7QSLSziBzeciIV3247jQ1HU3B3syAM6tQQnRoHcHvYuBewBAlUOwHO3xSAUk5IB5LCZ5qxpVbGZOopYVsI4K76YbjqYnwVUET/Rufklu+vlz/wfydKR8haWkhJbHObNED2KlxN6qThwuevZuH7HWfx486zCKjpgWc7NsDDkWHw83azQO2sggRIwBoEOH9TAEr5FR1ICp9pxpYSGDL1lLH91L8WFvgZjwydmHIZ913PUicAZdpX9g0y29ymjc6NiGXlxpNEA0EgojL7PgOoBkdOfiF+25+IhdvP4HBiBvq0CsFT0fXRsZE/VwXVAGQZEqhCApy/KQCl3I0OJIXPNGNLrYzJ1FPGdpenh6pt4ApXAAWBslvARlcoAfiIq+P2Ay6VrDDJbHObNjK3She/U/yTgYvU7DAK2FwUx5IzsXjXOfwcdx6+Xm54sn04Hm9XD8G+nuZWSTsSIAELEuD8TQEo5U50ICl8phlbamVMpp4ytmIb+N7wukgR28AG0oI4FRUhuLAQq85drPgMYN0owL0GkJsB5GYCORlATjqgyzfOx9kVcPG4Ye9VC/AUX343vo79AeRVFH1s4dW4ktvMqSeBPd8AmWIl8ObjGwb0nmBXeQCNw1dXIregEGsOpWDx7nPKFXN3NqmDJ9rXw13NghhBrA4hS5GAVQhw/qYAlHIsOpAUPtOMLbXFWEk9QtDFeXriUs1A1Hl0LqJCouHiXOKMXxnbPADP1A3BUfdbK3F1Cwpxe14eGufnIzy/AHdlZaO2zlAC6Jvdbz8MqNce8PC58eXpC3j4AkJsbvj4xm0a+kes/PV8D7jtHqAgFyjMu/GVew3ISbvxlZ0GJMYDcd8Z59vmKaBRD8C/MRDYBPD2N25TtkRF28xRg4GAxnZ3E4jpANRbXEjLxtLd5/Hz3vO4ej0P97UOxUORYegQ4Q9nZ+YVVE+SJUlAngDnbwpAKS+iA0nhM93YUluMBupZ4+2FCQG1kezqWtyukle6Ff/jTdtCFOGNOgE47+aK8ZdSkevsjIj8fHjpinDKzQ0XvHzQID8fjbIzK+inilU4cwM41G5zN+wKiKvpxKrdtSTAJxQIagEEtwCCWgLBLYE6twOuHob7UB3bzKIlpnAxpazpHmmWhYgg3nsuDcv3XsCK/YnwdHVG38i6eOSOMDQLMX6m1KyX0ogESKAUAc7fFIBSHwk6kBQ+84wNrjiZscVYoh4h/sYEBd44tVZiK9fp5g0Wk3pMQs+wO4GLccDZ7Sg69CvezzuDPR4emJ+YDH+dDjrPWjgc1Q/nIjojwKcuooKi4HLk95s3Y4iKq/BMnDnb3GLlMOUQkPzPre/Jh4CCHCCkFRDW7uZXeyDgthv9UYI+Slz5VmpEVQhcczzAlMAWU8qa0xYL2OQX6rD5+GX8svcC/jyUhIYBNZSr5/q0DkXjOjUt8AZWQQIkYIgA528KQKlPBh1ICp/5xpZa1dEVovD0ZvTa/haS8zNKt6eoCBH5BeiSnYPueTp0yC2Ak5sXUL8jpno747esM1jQehRCdEWVb3NaSrCaQstS2+VidfDqKeBCHHBhz42vxH2AizvgH3Hjv409lkz8rGbFsdn9wJmtwNGVwPYZBlpnu9fSXcstwF+HkrDyQBL+PnYJEQE10Kd1iLJV3CSoJiOJjfkaf04CJhDg/E0BaIK7lC9KB5LCZxPGu5J2YcjqIUpb3HVF6JCTg7uvZ6Fbdg78dDrs9vTANi9P9LnnU7Rq8SS+PfQd5h2ch3n3zsOV3Cu4lHUJdbzr3FjxK3lesGTvLCVYTSFmqe3ysu8szL+xSrjzayB+ofEWWSrxs9HoaCfAqzbg5lnJqqS+uVZanTROQ3UJIQbXHUnBHwcSsf5oinLTiBCCfVqFonmoD8WgapIsSAKGCXD+pgCU+mzQgaTw2YTxn0d+wrq1sYro65qdgysuzljv7Y2N3l6I8/BA3s3D+RO7TURuYS4+2/UZhrcZju8Pf4/krFsBGgbPC1Z3D625+qh2m1lE/0YPqzxljRpOat+npi59mcpWJ6tDtFfQ9qy8Amw4egkrDyQqotC/hjvuaRaEe5oHo0Mjf0YTmzLmLEsCNwlw/qYAlPow0IGk8FnMuFBXiLiUOHWrceKtImpWnM878BN0Cetx1NUJ67y9sc7bC8dERK+BlC6vRL6irPwNaTUEM+JnoKjUmT6R5lhsLRZhUsST6BneA2jQufQNHxbrrYkVWUvIGN1mBiC2zN1rAvk5QEQ3oPHdN778GxlkXGnP1Aa2mIKnotVJGz47KJJNbzuZirVHkrH2cAoysvPRrUkd3NM8SEktE1izgoAdU7iwLAk4AAHO3xSAUm5OB5LCZxHjNWfWYMLOCcZX48TW5Ym1wIElwJGVN86wtX4ChS0eRq91zyMlK6WcqBMNFMKulkctZBdkQ6wCfrzz41LvKtmJUnn/fOsCvSdqO/edmm3mZg8AyQeBk2uBk+uUIBol2rjJvcDtvYGG3SqOMi4Jt6pWANWcM2zxoEV8V7YSEU18KDFDEYJrDyfj4MUMtK3np9xLfGfTOmhZ1w8uTC8ji5n2GiXA+VtjAvDLL7/EZ599hqSkJLRt2xbTpk1DTEyMQff9+uuv8d133+HgwYPKz9u1a4ePP/64wvKGKqEDVe9vBiH+xmx4DWIiLBW9e/P/J/WYjJ6eoTdy4u1fciNhcqvHgDZPKilO9CuH68+ux4LDCxSxV3JlT///Hi4eGNdpHEJqhBSfF6ys5zdu/hBZAgFo/fYLU7eZRXLq01uAY6tufImk12JV8PY+N0RhjUDDaNWsOJrijsIXnvrhxsqk/uymmnOGQtiPPmAbq7tl+puSkaNsEYszg1tPpsLV2QldbgtUkk93bRKIurW8TCHEsiSgaQKcvzUkABcvXoyBAwdi1qxZ6NChA6ZMmYKffvoJR48eRVBQUDlH7t+/P7p06YLOnTvD09MTEydOxC+//IJ//vkHYWFhqhyfDqQKk1UKCfHW68c7kZyXXm470Uunw33XruOp6zlomq9DYoMYZLZ6BE3bDoTLzevTDK0cOjs5Q1d0K2lzgGeAsvI3Mmok+jfvj5UJKxG7KdZof27d/Wv7wQZGO6OmgLnbzEKoJx24IQRF1G7i/htJsZv2BkQ0r8hBWPKpcMVRTSMrKFNypVbtKqMlI5slml6ZaUGhDvvOp2PT8UtKmhmRd7BhgLeyXXxn00B0iAhADY9bOS+t1AxWSwI2S4Dzt4YEoBB90dHRmD59uuJwOp0O4eHhGDFiBMaOHWvUCQsLC1G7dm3FXghJNQ8dSA0l65TZdXE7hvw1vFTlLXLz8ERmJvpcy8JZN1cs86mJlTVqINPFWSmnD9QQ/z1mwxiDW77iZ882fxbN/Jvhv3v+i2dbPIthrYcp9iUjhivrVbm7f+1AMFhnlEysNSMROL4aOLoKSFgP1KoPNH8QaPEQENL6htA3tOIobkgR+Qqzr5bJt6jm/SXSwohbVZYNNW5kqchm42+yWImMnHzl7KAQhJuOX8aFq9loXc9PEYIikCS6oT9qUhBajDcrsn0CnL81IgDz8vLg7e2NpUuX4uGHHy72vEGDBiHt/9s7E+goqvTtP1lIyJ4QsrCFRQKyCIisKosaB0XGcRlHnTku4zoijMiIQUcFFSWAf8YPBAUVlzluuDIiioKyKzLGgSCCKDshIUAWsq/feau6s3bS1V1d3dXdT53Tp5Lue6vu/d236z59733fW1CAVatW2bXGs2fPKiOFMmo4adIkm+krKiogL+shBiQis7CwENHRjOBvF7ILE6zZvhDpe19DcF0dLispxV+KzqJvZRVWR0Yowm+PDWcOa2Dn6JBoFMrIoY1D0sjIX2BgIP5wzh+U0T/roYw6fjih9fWCre3964WCwYVN5dylZKp4/1fAnlXA/i/VqWGrGOw0BDjyrbpNXmSS6nDTatBtLbe3jNRe8yLwpob1fT4g6I/ll2L7gTP47sBpbD94BrJN3cDO0RjZKx6jenXAsB4dEN2+YYtDLRSZhgS8iQAFoI8IwOzsbGXadtu2bRg9enS9DT788MPYuHEjtm/fbtcuJ0+ejLVr1ypTwDIlbOuYPXs2nnzyyRYfUQDaxevyBD9ueBKbdr6Km4qKURkQgHeiI/FJZGT9aJ/eG6Z1HIKFV7yGgKCm02TqusPpykhTk709ZDoTwMKTp5BWWtb09j4gGPTy1JW/qkx1IJHRv32fq3sm9/u96mDTbWTDejxbo4OO3PiWVcCq+wAZiWzm5a1exnen9LMLyrD94GlFFIogPHy6BP07R+OClDgM7R6HoSlx6BoXxviDjtgT05qaAAUgBaBioBkZGZg/fz42bNiAQYMGtWq0HAE0wfdZtif7dgnqslYiMxh4PSZaidlXayN0i57SZpw8hauCYm168irrB7fOarJ7SHJ1NdJP57cUfxKceMZvpnQa0MPHY3mrK4GDm4A9n6ijfrIryYBrVeceWT8oazhlJxAZHYxIUPc63vcZ8P1y+0WWkVq53krrEhA3bt9nv3RuTZFbVK4IwczD+cg8ko892UWIiwjB0JRYRQyKKDyvSwzatwtya7l4MxJwFQEKQB8RgHqmgJ977jnMmTMH69atw7BhwxyyLRqQQ7icTyyduEz5bXkeOLgRGHwTMPxurPvgT5geqa7vq3PwoT3rAAAgAElEQVSxALTnyVtzYCMyV96AvKAgJNTUYGh5BWx2heMfBcbbdxxxHo4f56ypBg5tAnZ/COz5FAiLUYWgvJIGNjgHOerc4ahnsx80QVllDbKOFypi0CoKC8uq0L9zDM7vFotBXWOUV8+OkQw94wf24AtVZP/tIwJQjFGcQCTki4R+kUOcQFJSUjBlypRWnUBk1O+ZZ55Rpn5HjRrlsE3TgBxG5liG2lrgl89V4Ze3Dxh+JzDqPiDS4tW95z9Yt/peZMTHIjfYRR6NdXVIrqnBF0ezLYKulWk/LWFJwjoAM37l6J9jre5c6uoKNc6jiEHxKI7pCgz8oyoGJebj8wMdm9p11rPZudJ7XS4JvXT0TJkiCH88kq+IQ4lJGBgQgAGdo3Fel1ic11XOFIVe17h+UmD23z4kACUMjDh9LFu2TBGCEgZm5cqV2Lt3L5KSkhTPXlknOHfuXMW8JezLE088gbffflsJB2M9IiMjIS8tBw1ICyUn0sg0nwRs3roIqCgCRk0GLrgdaG/D0WbPf1Dz6QPIrCtRRuPia2rwz4R4nAwKsjkqKE4eMaExKKgoaBH3T6YLxSdU8zq+NsOSBPh+DEAnmtYtWcSBRELL7P5IdSBJOBdI7A/selddx9d09aZaJF+P1+gG8BJ65te8YmQdK8Tu44XYJaIwu0gZERzYOQYDu8Qo6wrPTY5C78RITh+7oU14i9YJsP/2IQEozSwhXKyBoIcMGYJFixYpI4NyjB8/Hj169MDrr7+u/C9/Hz58uIV1zJo1C+LsoeWgAbVCydnRE9kyTII2b30eaBcOXPSAGrQ5uI3trRQRdgtqAGS2D1VEoISAWRoboxSu8dSw1Qt44fiFymdzt8/FybKT9ZVodR2fpHBo27AugOyBa5IdI7TYss+mkUDTP69WRwYPbFBHYyXci/WIZlsZ2fZWUbjLIgp/PlGEvTlnUVpZg14dI3BuJ1UQKq9O0egc056OJkY2CK9dT4D9t48JQHfbNg3IBnFn9lEVL88f3lCFX3g8MHaGGvIjUF3f1+phmYZdV52PjPi4JtPAMTUiCYHCoIaVeck1dUjv8xekXfwIKmsqMe2baTievx+3H/4JXaurW1/HJxdqy5PXWcHrboP19/uVnAJ++hj47wp1SUGXocDIe4G+VwEh4f5Ox231l+nj7MJy7LWIQasoPJBXrASn7pccjb7JUUhNikTvhEickxiJxKhQCkO3tZB/3Ij9NwWgLkunATXD5+g+qiL8/vsasPX/AZEJwLh0tTO2I/ysW7jlHd6MI9v+hSVx6mhf8+3gxIfz/vxCpFRXWxw1KpV1fZV/XIHpuV/jdNlpLEtbiuilFzq2PkyX1TCzKQicOQhkfQDseg84m6OO1p53A9BzLNdseqiByqtq8OvJYmWEUMShTCfL/xKjUIJUn5MQqUwdy8v6d7e4MARbAr17qNi8rZcSYP9NAajLdGlAjfA5so+qLNj/wSr8koDxM4G+E1ts6WarcWxt4aaE+rDhBRxgIzBzFQIwvUtX5HUagOW/exkSFFqJL8fQH7q+C16bWWznxP/UvaJFEAYEAuf9UV16kDxIk016bd29pODigfxbXrH6OllcLwwPnipR1vH27BiBXgkR6NExQtnurnu8nCOUUcPAQMtOL15SVxbTfQTYf1MA6rI2GlAjfFpDbQy7E/j5UyC6EzBOhN+VmjtZaxDmpiGY7TehdWu2KgD/SOyInOBgvDx+EWL6TGjIzNAf9kH6egoJKyNhhkQMio3GdlOFoIwMyrZ0PExFQNYXHs0vU0YJZfr40OlSJYD14dOlyC4sQ2hwILp3iED3+HBFHCrnePXcKSaM4WpM1ZruLwz7bwpAXVZHA2qET0ZPtOyjGtsduHI+IOLLgdh91m3YcktzHW6zeSdP4fKSUsxI7IjjwcF4JeckYq59WR3paXxwLZ/DbH02g3gS712jeqP/9g3QdbgqBgdcA0hwbx6mJiDTybLd3aFTpThkEYXWs7wvnsmdY8OU3U26xoaji5yVl/p3cnR7CkRTt7D+wrH/pgDUZUU0ICdGAG/9FOg11mHuO3J24I61dzicTzIsP5GL96OjcMQi/mIlviC3Z3OKpV9mKs4DfvpIHRnM2QWk/k4Vg6kTgHa2t430S05eUunK6lrI1neytlDE4PF8Oasvee9EYZkSz7BTbPsm4rBLbJgycpgcE4rkmDBlXSIP7yXA/psCUJf10oAa4dMSGFlCbkzLcmqR/ZoDa5C+2bEdNWQNYGJNDQaVV+Bwu3bKyF9cbR0Q3dnpcugyGGb2fgKnf1OFoDiPlJ4BBvwBOO9PQPeL7DoveX/l/aMGVTW1yCkst4jC0nphKGIxt6hCEYjlVbWKAEyOaY9OMe2RFG373CEihN7LJjUb9t8UgLpMkwbUDJ8lJl9LqJaF2DqC7To6AijiT7yAz6+oQHFgIF49YRF/Ujgd5dBlMMzsOwTEeeTYf9UpYokxGNxe3XVERgYbb0PnOzVmTSwEJIxNUVk1ThSVKUJReRWp5xOF5ZB9lOUsW+WFBAUiMToUCVGhSIhUzx0tZ+W9Ru9zX2X3mhj7bwpAXRZHA2qETzrD9U8Bx3aoI3wVZxs+dEGwXesawJOlJ6HFCSSpXTQ6lxbgbF21Iv46yLSvC8qhy2CY2TcJ1FQBv30NZL0P7P0MkHWusr5UnEfiuvtmnVkruwTEe9kqDE8VVyDvbAWs57xG/58qrkRNbR2iQoNbCMSOkSHoEBGKDhHtEBcegvjIEOUcGx7CNYp2W6DtBOy/KQB1mRANCEDuT8DXz6i7LMg+vRdOBUKjgMPbgOJcIDIJ6H6hU9O+zRvH6gUs7zcWgdYdPiYPmYyUqBTEto/Fu3vfxfHi41je907EV5a6tBy6jIaZfZtARTGw7/MG55EuF6hicMB1QES8b9edtXOKQG1tHfJLKyFCUERiXnG5RSyq/58pqVQ+P12snmUXFfGfiwlrB5li7hAegjjLuYMIRuv/EfJ5KGLD2ilpo8PaUTQ2aiH23xSATn1hrZn82oBkLdSGDODn/6j79I75BxCZqIunlsy24gAmhycjfUQ60rqnoaKmAg9+8yBOl5/G8suXK/v+8iABjxCw7jwiI4PHM4FzLlVHBc+dCIREeKRIvKn3ExAPZxGFVmFY/7e8V6q+r3xWUoXTJZUoKK1Etax9BhDVPlgRg7ZeIhDb+kw8p33p8Ov+29KQAXWyoIGHUwT80oCKsoGN84H/vQ0MukHdvcPNMdLqdwIpzUNCeAKGJg5FUGAQSqtK8cA3D6Csugwvpr2IqJAop9qVmUjA5QTyD6mBpkUMFhwFzr1KXS/YazwQ1M7lt+MFScBKQLp4GTWUNYnNX0U23rOmkc8KSqsaxGNoMCLbByvOL9azCEr5P6p9O8u55efWzyRPREiwaUYh/bL/bva1oADU8ZzwKwMqOQ1sWQjseBXoewVwyT+Bjqk66Lk2a0lVCe5ff79y0SWXLUFEO46wuJYwr+YSAvJ7OydLnSLO+hCoqQQGXKuKQYk16EBsTJeUhxchgTYINBaPZ8urUVxRBfVcjWLLWf63fibv2/pc3rceESFBioCUfZ9FEIaHBKl/K/8HITxE/lbPkZbzNed3cblw9Kv+u5U2pgDU8fX3CwMSZ45vlwDbXgBSRgGXPQ50GqyDmuuzFlUW4b519yE8OByLLl2EsOAw19+EVyQBVxMQx6TDW1UxuGcV0D5WnSKWV+K5rr4br0cCHiMg6xxLKhuEY1F5NUorq1FSUaOeK2tQUlGN0gr1b+tn8p7ke/uuUS7f1s8v+m87LU4BqOMr4dMGVFUO/PdVYPP/AfGpQNos1ZnDZEdBeQHuXXcv4tvH41+X/AuhQaEmKyGLQwIaCMj+2Pu/UqeIf/lCHV2X+IIDrwNiumq4AJOQAAk4QsCn+2+NICgANYKylcwnDUj2Q/3fW8DGeUBYB+CyJ4DUy005NXWq7BTu/epedIvqhgVjF6Ad11LpsGZmNQ2B8iJ1L2IZGTy0BRBPYvEi7v8HdQ9tHiRAAroJ+GT/7SAVCkAHgTVO7lMGJNNRez4BvnkGqKtV1/hJpxMYqIOQcVklxMs9X96DAR0H4JmLn0G7QC6kN442r+wxArINnXja//SxGlqp20h1VFDEoBu87j1Wb96YBAwm4FP9t5OsKACdBCfZfMKAZFH6r+vUIM5Fx1XvRBF+Pce6JHafDrytZv2t4Dfc89U9uLTbpXhk5CMIDDCnSDWi7rymHxM4m6uuFZR9iSXgespoVQz2uxqI6OjHYFh1EnCcgE/0345Xu0kOCkAdAL3egI58B6x7Ut3gXkRURVEDDdkv94p5QP+rdRByfdasvCxMXj8ZN/a9EfcPuZ/7bLoeMa/oDQQkHNNPn6gjg9mZQI8xqjdxv98D4R28oQYsIwl4lIDX998uoEcBqAOi1xqQhKFY/7Tqgdj7cmDPxzYo6N+/Vwdam1m/O/Edpn0zTRF+t/S/xdWX5/VIwDsJFBxRRwZ3f6SGmJHYgiIG+15JMeidLcpSu4GA1/bfLmRDAagDptcZUN4vwMYMdb/SYXcCFz0AvDwekNEEm0cAICOB07I8Ph0sO4A8uuVRPDbqMVx9jrlGJXWYELOSgGsJnDmoruWVkUHZprHHxeqo4LmTgKhk196LVyMBLybgdf23AawpAHVA9RoDkm3bxKtXpoyG3AyMeQiI7QYc3Ay8Mck+gdtWAz3H2E9nUIqP93+Mud/Pxbwx83BJyiUG3YWXJQEfI5B/GNi7WvUoPvq9GmhaxGC/SUBcDx+rLKtDAo4R8Jr+27FqOZSaAtAhXE0Tu8WAamtU77/iXCAySY3FFxikrdQyGrBpgboFlew0MPYhIKZbw/Xy9qqf2zuuf1Xd0N7Nh0ShX7F7BV7JekUJ8Dw8ebibS8DbkYCPEBAHkn2fqWLw4CYgsb/qPCKCMKGvKcM8+Qh5VsOkBNzSf5u07tZiUQDqaCDDDWjPf4Av0ptO0WpxzpBf/iLsdq0EBl4PjJsBdOgF2Lqelvp7YARQ9vuVUb/1R9Zj6WVL0S++n5aSMg0JkIA9AmX5wC9rVTEoEQDkR6EyMvh7oPP5FIP2+PFznyBgeP/tBZQoAHU0kqEGJGJt5a0A6pqVsBXnDBkplIXgP7yujvDJIvBx6UDH3mr+Vq/XFgDPrAEsqy5D+qZ0HC46jBfTXkTnyM46WolZSYAEWiVQWaKKQBGDIgpDIoA+E4C+E9VQUO24rSKtxzcJGNp/ewkyCkAdDWWYAYmYe36gdueMHSuAL/8JVJU21KbxSKHd69mC4Bkv4PzyfEz5egqCA4KVad+Y0BgdLcSsJEACmglUV6qRAWQrun1rgJJTqkexeBOnTgCikjRfiglJwOwEDOu/zV7xRuWjANTRWIYZkFbnjGuXq9u2HdxooxaNBFxYnDZnj8ZXie4CXJHh1jiAR4uO4r7196FPXB/MHTOX+/rqsE1mJQFdBCRA/MmfgV8+B/Z9DhzPBDoPUcVgnyuBpAGcKtYFmJk9TcCw/tvTFXPg/hSADsBqntQwAxKnjQ/vtF+ywGBA9r+tKmslrWUKN2028NHd9q83ZgaQeK7jzibNrizr9zJPZiKvNA8J4QkYmjgUQXYcV3af2o3719+PiT0nYsbwGdzdw35rMQUJuI+AbEm3f60qBn/7GgiPB/pcob56XMSpYve1BO/kIgKG9d8uKp87LkMBqIOyYQakdQRQwrlsfs5+DSY8C6x91H46Fzh7SLy+jO8zkFuaW3+/pPAkzBwxE2nd02yWQRw9Ht38qBLg+dYBsu6RBwmQgGkJVJUDhzar08T7v1KniiXeYO809RV/DkcHTdt4LJiVgGH9txchpgDU0ViGGVD9mr0TNpxALAWWKVqtI3vXvQysmwUUtXY91zh7iPibvmE66po5rgRAnY5eOH5hExFoDfOyfNdyPHPxM60KRB1NxKwkQAJGEpCp4lO/qI4kIgZlDaGsP7aKQdmiLjTSyBLw2iTgFAHD+m+nSuOZTBSAOrgbakBavIC1ru2TkT0J/aB4FcvR2LPYNc4eMu074cMJTUb+GqMVESgjgV9c/4UyHVxZU4mnvn0K3574FosvXYz+8f11tASzkgAJmIKAeBUf2gr8+pUqCguPASmjVUGYejmQcC5HB03RUCyEof23l+ClANTRUIYbkM04gI2cM+yOFDYb2bN3PR0sduTswB1r77B7hRUTVqB3bG9lT9/ymnJF/CWGJ9rNxwQkQAJeSEB2Ifp1vSoGJQC1/GgVz+Je44Ce44DoTl5YKRbZFwgY3n97ASQKQB2N5BYDsu4EcvYEUJIHRCQAUZ0adgSpHynUOLKnZ2eRNlitObAG6ZvT7dKcPnQ6Vv6yUgnsLNO+YcGMM2YXGhOQgC8QkLWDR78DDmxUIxdk/wjEp6piUERh94uAsFhfqCnr4AUE3NJ/m5wDBaCOBnKbAdnbEcQFI3vOeO42Rqd1BFAE3y39b1EcPgIDAnXQZ1YSIAGvJlBWABzaAhzYoApCGS2UUDMiBmV0sNtIoF17r64iC29eAm7rv82LABSAOhrHLQakZS1g/6sBHSN7znjuNsdmXQN4svRkCycQa1pZBzjnojm4uvfVOqgzKwmQgE8SKMpWRwetglDWLYsIFA9j2QO9yzAKQp9seM9Uyi39t2eqpvmuFICaUbVMaLgB2d3BQ7/3rqOeu23hsl5L0jT3BJb3Hhz6IO44z/46QR1NwqwkQAK+QEDxLt6vjgyKZ7Fsbykjhl2HqWJQpou7jVC3ruNBAk4QMLz/dqJM7s5CAaiDuOEGpDUeYPP4fRpHAx313NWCytZoYkhgCB4f9TiuSb1GyyWYhgRIgASaEhBBKFPEihjcqnoaF+cAnc+3CMKLgZSRQHtuHUnT0UbA8P5bWzE8mooCUAd+ww1I644g178KnPdHtSb21gs2qq/WdXviuTs8ebhmUiIs3/jpDby06yWM6TIGz178LEKDQzXnZ0ISIAESsEsg/7A6Mnh4i3rOPwQkDQRSRgFdR6gjhLEpDDtjF6R/JjC8//YCrBSAOhrJcANydARQ63pBS521eu7OGzMPE3tN1ESqtq4WK3avgAR3fmL0E5jUa5KmfExEAiRAAroIyBpCEYLHdgBHvwdydqlb1okQlLWEIgo7DeY6Ql2QfSez4f23F6CiANTRSIYbkCNx/qQezw8E5CFo82i5XtDVI4AF5QX459Z/4reC3/Cv8f9SQr3wIAESIAGPEKgsVUPNHPteFYTyqigCOg2xiMIRqihkLEKPNI+nb2p4/+3pCmq4PwWgBkitJXGLAWmN8+foaCEAe567zXfvaAvVzrydeGjjQ+jXoR+evuhpxIRyLY4O02JWEiABVxOQdYRnDqhC0CoKT+4BIpOBLkPVEDSd5Xw+EN7B1Xfn9UxGwC39t8nq3Lw4FIA6GsgtBiSjgJueA7a/qG7nZj1kL+ArMgAJASOHM+sFAbTmudva/r3Nccl+vm/ueRNL/rcEU4ZMUWL8BQRYtpfTwZZZSYAESMBwAhVngRM7geOZQHamei44DMT1tIjCoeo5eRD3NDa8Mdx7A7f03+6tksN3owB0GFlDBsMNyJZDh0TKHzkZGPsQEBjUUBgnRgCtmW157iaHJyN9RDrSuqe1SqiwohCPb30ce8/sxYJxCzA4YbAOmsxKAiRAAiYgUHJanTq2CkI5yy5MHftaROH5QPJ5qsNJaKQJCswiOEPA8P7bmUK5OQ8FoA7ghhqQgw4dSiBoZQ3gCSUKX8uj7ZiBju4EsitvFx7e9LCyr69s6cYpXx2GxKwkQALmJSBTx7IVp3WUMPt/qoNJySmgQy9VDMpLHEzkHJlEz2PztmZ9yQztv72g/lJECkAdDWWYATkbAFrrekEdda6urcbLWS/jtd2vYfLgybh1wK3c0k0HT2YlARLwUgJnc4GcLCBnp+WcpcYqjOioThlbhaH8HX9O0xkbL62yLxXbsP7biyBRAOpoLMMMSMd0ru04gM3WCzpZ52Nnj+GRzY+gqLIIGWMy6OXrJEdmIwES8FECFcWAOJbIukJFHGap/8soYkIfILE/kNhPPSecC8R0AwK5J7onrMGw/tsTlXHynhSAToKTbIYZkJMOHfVV0bgTiNaqi6PH6gOr8ez2Z3FVr6vwj2H/QFhwmNbsTEcCJEAC/kugploNUi1C8OTPDefTvwLtwlQhaBWFifJ3f04ju8FaDOu/3VB2V92CAlAHScMMSM8IoI762Moqo31zvpuD7Se246kLn8K4buNcfAdejgRIgAT8kEB1BSAisLEoFJEoO5yIs1/HPkDHVPUcbznHdQeC2vkhLNdX2bD+2/VFNeyKFIA60BpmQDodOnRUqUnWLce3YPa22UiNS1Vi+3UM6+iqS/M6JEACJEACtghUlgB5+4BT+4FTvwCn5bxfXV9YV6M6niiisHcjkZgKhMWRpwMEDOu/HSiDp5NSAOpoAUMNyOLQUQMgs30I8oKCkFBTg6HllVCCv/zpzYYYgDrq0Nqo33M7nsNXh7/CQ8MewnWp1zG2n4sZ83IkQAIk4BABGRgoOGIRgxZxeOpXVSSWnATCO6ojhhLDUERiBzn3VP9nYOsWqA3tvx1qWM8lpgDUwd5oA1q3ZS4yfnkLuUENgZWTauows89fkHbxIzpK3nrWzcc2Y/a3s5Eam4pZo2ehU2QnQ+7Di5IACZAACbiIQFmBOp0srzMH1R1P8i3n0tNA+1iLIOzVTCD28tv1hkb33y5qWUMvQwGoA6+RBiTBmR/c8GCrpZO9dtsK0uxotWSt34IdC5SdQWYMn4Fre1/LUT9HITI9CZAACZiNQHmhKgqtglD5+5AqEouOA+3CgdjuQGw3IDZFfYl3svW9iASfjGtoZP9tNhNorTwUgDpayigDkqDM41aOg+y00doRGxqLDX/agKDGu4E4URfx8F1/ZD3mbp+rrPWbfeFsJEckO3ElZiEBEiABEvAqAlVlqtOJbH8n08vWV+FR9W/ZAUUiPsR0bRCHilDsbhGJKeoIoheGsjGq//am9qcA1NFaRhnQd9nf4e6v7rZbspcvfxmjOo+ym661BNnF2UpoF9nV46HhD+H3vX7PUT+naTIjCZAACfgYgcpSoPCYKgYLGwnEAotALM4BAoOBqE5AdGfLq0vD31GW96KSTee9bFT/7U0WQAGoo7WMMqDFPy7G8l3L7ZbsnkH3YOr5U+2ma56gqrYKb+15C0t3LsUVPa7A9AumI1bWiPAgARIgARIgAa0EqsrVbfKKsi2v45b/jze8dzZHvZqMFDYRiSIau6jvi0CUc/sYt003G9V/a0VnhnQUgDpawSgDWpy5GMuzNAjA8+7B1KGOCcCdeTvx1LdPQbZ0e2L0E7gg6QIdBJiVBEiABEiABNogUFMFFOeq+9TLmkNFLDYSiDKKKNvqVZcBwe2bCkKrMLzoAZePIBrVf3uTLVAA6mgtowxIgi7f9eVddkv2yu9ewchOI+2mkwSnyk5BRhY/P/g57j7vbtw+4Ha0Y0BRTeyYiARIgARIwEACslVeRZEqBK2CUDnnACWngGtfcvnIoFH9t4GUXH5pCkAdSI0yIMUJ5L1xKKxswwkkJBYbbrTvBFJVU4W3fn4Ly3Ytw+jOo5Xp3q5RXXXUmllJgARIgARIwLsJGNV/exMVCkAdrWWkAbkiDMymY5swf8d8hASFIH14uubRQh1ImJUESIAESIAETE/AyP7b9JW3FJACUEdLGW1AIgIlPMvJspP1pUwKS8LMkTPbjAF4oOAAFvx3AbJOZWHqkKm4vs/1CBZPLR4kQAIkQAIkQAIwuv/2BsQUgDpayR0GJNPBmSczkVeah4TwBAxNHNpq7L+ckhy8uPNFfHbgM1yfej0mD5mMmNAYHTVkVhIgARIgARLwPQLu6L/NTo0CUEcLmcWAJGD0q1mvKmv9+sX3w019b8KVPa/UHSRaBxpmJQESIAESIAHTEjBL/+1JQD4lAJcsWYIFCxYgJycHgwcPxuLFizFixIhW+b7//vt4/PHHcejQIaSmpmLevHmYOHGi5vbwtAFV1FTgnZ/fUUb9JKxLZW1lfdmTwpMwc0TbU8WaK8qEJEACJEACJOBDBDzdf5sBpc8IwPfeew+33norXnrpJYwcORLPP/88RODt27cPiYmJLVhv27YNY8eOxdy5czFp0iS8/fbbigDMzMzEwIEDNbWNOw2o8VSwbAN3sPAgVvy0AiGBIThWfKxFeQMQoLy3cPxCl+4ZrAkME5EACZAACZCAiQm4s/82KwafEYAi+oYPH44XXnhBYV1bW4tu3bph6tSpmDlzZgv+N954I0pKSrB69er6z0aNGoUhQ4YoIlLL4S4DEmeQjO8zkFuaW1+s4IBg/KXfX5S4fo2dRJqXOy40Duv+uA4hwSFaqsQ0JEACJEACJODzBNzVf5sZpE8IwMrKSoSHh+ODDz7ANddcU8/7tttuQ0FBAVatWtWiDVJSUjB9+nRMmzat/rNZs2bhk08+wc6dOzW1mTsMyF44GC0FFREou36kdU/TkpxpSIAESIAESMCnCbij/zY7QJ8QgNnZ2ejSpQtkWnf06NH1zB9++GFs3LgR27dvb9EOISEheOONN3DzzTfXf7Z06VI8+eSTyM1tGGlrnLGiogLysh5iQDLKWFhYiOjoaJe3tUz7Xv7B5cgry9N9bZkS5nSwboy8AAmQAAmQgA8QoAAEKAAdEICzZ89WBGLzwygBuCNnB+5Ye4dLvmoiAMUx5Ivrv6B3sEuI8iIkQAIkQALeSoAC0EcEoLumgN09ArjmwBqkb0536fdL9g8ODAjUFFfQpTfmxUiABEiABEjAJAQoAH1EAIo9iROIhHyR0C9yiBOIrPObMmVKq04gpaWl+PTTT+vN8cILL8SgQYNM4wTiyhFAayVjQmKa7DHMcDEmeRqxGCRAAiRAAm4jQAHoQ3jWxVQAAA3bSURBVAJQwsCI08eyZcsUIShhYFauXIm9e/ciKSlJCREj6wQl7Iscsl5w3LhxyMjIwFVXXYV3330Xzz77rKnCwMgawAkfTsDJ0pOoQ12LL4Z1WnfG8BmY890c5FfkO/zlYbgYh5ExAwmQAAmQgJcToAD0IQEotighYKyBoCWcy6JFi5SRQTnGjx+PHj164PXXX683W4kT+Nhjj9UHgp4/f77pAkGLF/D0DdOVMjcWgc2FW2V1JdI+SHNaBHJ9oJc/zVh8EiABEiABzQQoAH1MAGpueRcldJcB2YoDmByejPQR6U1Cu7QmFrVWd8WEFRiePFxrcqYjARIgARIgAa8k4K7+28xwfMIL2FOA3WlAjXcCSQhPwNDEoTa9eW2Jxebr/lrjNW/MPEzspX0rPE9x531JgARIgARIQA8Bd/bfesppZF4KQB10zWpAzcWi/H/3V3fbrSlHAO0iYgISIAESIAEfIGDW/tudaCkAddD2FgPS6kzCGIE6jIFZSYAESIAEvIaAt/TfRgKlANRB15sMSKsziQ4czEoCJEACJEACXkHAm/pvo4BSAOog620GpNWZRAcSZiUBEiABEiAB0xPwtv7bCKAUgDqoeqMBaXUm0YGFWUmABEiABEjA1AS8sf92NVAKQB1EaUA64DErCZAACZAACXiIAPtvxgHUZXo0IF34mJkESIAESIAEPEKA/TcFoC7DowHpwsfMJEACJEACJOARAuy/KQB1GR4NSBc+ZiYBEiABEiABjxBg/00BqMvwaEC68DEzCZAACZAACXiEAPtvCkBdhkcD0oWPmUmABEiABEjAIwTYf1MA6jI8GpAufMxMAiRAAiRAAh4hwP6bAlCX4dGAdOFjZhIgARIgARLwCAH23xSAugyPBqQLHzOTAAmQAAmQgEcIsP+mANRleDQgXfiYmQRIgARIgAQ8QoD9NwWgLsOjAenCx8wkQAIkQAIk4BEC7L8pAHUZHg1IFz5mJgESIAESIAGPEGD/TQGoy/AKCwsRGxuLo0ePIjo6Wte1mJkESIAESIAESMA9BEQAduvWDQUFBYiJiXHPTU12l4C6uro6k5XJa4pz7NgxxYB4kAAJkAAJkAAJeB8BGcDp2rWr9xXcBSWmANQBsba2FtnZ2YiKikJAQICOK7Wd1fpLhSON5OQqI6NNaSNJTto4SSqyIivtBLSlNNKmZOzr7Nmz6Ny5MwIDA7UVyMdSUQB6QYNyrYK2RiInbZysnbVMe8gyBi5faJ0bbYo2pZ2A9pS0K22syEkbJ2dTUQA6S86N+fgl0AabnLRxogAkJ+0EtKfk94+stBPQlpI2pY2Ts6koAJ0l58Z8/BJog01O2jhRAJKTdgLaU/L7R1baCWhLSZvSxsnZVBSAzpJzY76KigrMnTsXjzzyCEJDQ914Z++6FTlpby+y0saKnLRxklRkRVbaCWhLSZvSxsnZVBSAzpJjPhIgARIgARIgARLwUgIUgF7acCw2CZAACZAACZAACThLgALQWXLMRwIkQAIkQAIkQAJeSoAC0EsbjsUmARIgARIgARIgAWcJUAA6S475SIAESIAESIAESMBLCVAAmqDhlixZggULFiAnJweDBw/G4sWLMWLEiFZL9v777+Pxxx/HoUOHkJqainnz5mHixIkmqInxRXCE1euvv46//vWvTQolXtTl5eXGF9SDd9i0aZNiTz/88ANOnDiBjz/+GNdcc02bJdqwYQOmT5+On376Sdne8LHHHsPtt9/uwVq459aOshJOl1xySYvCCefk5GT3FNoDd5EoBB999BH27t2LsLAwXHjhhcpzp2/fvm2Wxh+fVc6w8tdn1Ysvvgh5SV8mx4ABA/DEE0/gyiuvZP/nhu85BaAbILd1i/feew+33norXnrpJYwcORLPP/885KG5b98+JCYmtsi6bds2jB07VgkLM2nSJLz99tvKgzgzMxMDBw70cG2Mvb2jrOSh+sADDygsrYds2ZeUlGRsQT189c8//xxbt27FBRdcgOuuu86uADx48KBiO3/7299w1113Yf369Zg2bRo+++wzTJgwwcO1Mfb2jrKyCkCxqcY7qMh31Ze3k7riiitw0003Yfjw4aiursajjz6K3bt3Y8+ePYiIiLDZSP76rHKGlb8+qz799FMEBQUpAxmyNdsbb7yh/Hj98ccfFTHY/PBXmzLqKUgBaBRZjdcV0ScP1RdeeEHJIfsLywjM1KlTMXPmzBZXufHGG1FSUoLVq1fXfzZq1CgMGTJEEZG+fDjKSh6qImQKCgp8GUubdRPBa28EMD09XRF70qFbD+nshdsXX3zhN+y0sLIKwPz8fMTGxvoNm+YVzcvLU36gbty4UflBauvw52dVYx5aWPFZ1UCsQ4cOigi888472f8Z/IShADQYcFuXr6ysRHh4OD744IMmU3S33Xab0vmuWrWqRfaUlBRlqk6EjfWYNWsWPvnkE+zcudODtTH21s6wkoeqjGh16dJFEdZDhw7Fs88+a/OXpbGl99zVtYga6cCFjYw+W4/XXntNsTHZK9hfDi2srAKwe/fuSuBjGTmdPXs2LrroIn/BpNTz119/VUZtsrKyWp158NdnVXND0MKKzyqgpqZGmf2S/k9GAPv378/+z+CnCgWgwYDbunx2drYiTmRYe/To0fVJH374YeWX9fbt21tkDwkJUYbJb7755vrPli5diieffBK5ubkerI2xt3aG1bfffov9+/dj0KBBipB57rnnIGu+ZJ1b165djS2wSa6uRdT06dNHWSspO81YjzVr1uCqq65CaWmpsubLHw4trGTqV0TgsGHDFAH4yiuv4N///rfyXRUR7Q+H/Ji6+uqrlR+pW7ZsabXK/vqsagxEKyt/flbJjwjp/2RtdmRkpLKsqbU17bQp1z5hKABdy9Ohqzkjavz1C+AMq+aNUVVVhX79+ini+emnn3aorbw1sRZRQwGotq4WVrbsYNy4cZDRLhGC/nDcd999kLWTIv7a+iHlr8+qxjaglZU/P6tkdufIkSPKj3SZDZMfVTIAYmsEkDbl2icMBaBreTp0NWemNf11WsUZVrYa44YbbkBwcDDeeecdh9rKWxNrETWcAtYnAGfMmKGIIRnF8fVjypQpytIUGUnv2bNnm9X112eVFYojrPisaiCQlpaGc845B8uWLWuBxd9tytXPFwpAVxN18Hri2CAhXyT0ixwyZSBGLg+P1pxAZFpOvKesh4RkkGlOf3ACcYRV86aQNSbiWSbTCwsXLnSwpbwzuRYBKE4gMuUrUzHW489//jPOnDlDJxANzX755ZcjKipKCZPiq4d4aIpjmjgUyRS4rP+zd4gTiD8+q5xhxWdVA4FLL71U6QNlXWTzw19tyt53zdnPKQCdJeeifBLaRBa9yq8dETeyEH/lypVKvC0JVyIhYmSdoIR9kUPWC8qUU0ZGhrJG691331UcG/wlDIwjrJ566imIh3Tv3r2V9UriWSbOMhIfz9b0goua1OOXKS4uVhbpy3H++ecrYldi14l3nTxYZa3f8ePH8eabbypprGFg7r//ftxxxx34+uuv8fe//90vwsA4ykq+nzLyJT8kZM2STFfJj7cvv/wSl112mcfb3qgCTJ48WVmbJaN/jWP/xcTE1K8R5bNKpe8MK399VsmzSGL+yXPp7Nmz9WHN1q5dC/lhRZsy6hutXpcC0Fi+mq4uIWCsgaAlnMuiRYuUmIByjB8/Hj169Gjya0g8pSRQrzUQ9Pz58/0mELQjrB588EFlVEYCbMfFxSlx8ebMmaOIIl8+WgtWLOJZflVLgGexHUlnPeRv4SVx3WRdlwQa94dA0I6yku/a8uXLFQEtHvwy8i6Ba20Fh/YlG5ORZFuHeItb7YTPKkun6gQrf31WSagXiTsqgdTlx4R8n2RGQsQf+z/jnyAUgMYz5h1IgARIgARIgARIwFQEKABN1RwsDAmQAAmQAAmQAAkYT4AC0HjGvAMJkAAJkAAJkAAJmIoABaCpmoOFIQESIAESIAESIAHjCVAAGs+YdyABEiABEiABEiABUxGgADRVc7AwJEACJEACJEACJGA8AQpA4xnzDiRAAiRAAiRAAiRgKgIUgKZqDhaGBEiABEiABEiABIwnQAFoPGPegQRIgARIgARIgARMRYAC0FTNwcKQAAmQAAmQAAmQgPEEKACNZ8w7kAAJkAAJkAAJkICpCFAAmqo5WBgSIAESIAESIAESMJ4ABaDxjHkHEiABEiABEiABEjAVAQpAUzUHC0MCJEACJEACJEACxhOgADSeMe9AAiRAAiRAAiRAAqYiQAFoquZgYUiABEiABEiABEjAeAIUgMYz5h1IgARIgARIgARIwFQEKABN1RwsDAmQAAmQAAmQAAkYT4AC0HjGvAMJkAAJkAAJkAAJmIoABaCpmoOFIQESIAESIAESIAHjCVAAGs+YdyABEiABEiABEiABUxGgADRVc7AwJEACJEACJEACJGA8AQpA4xnzDiRAAiRAAiRAAiRgKgIUgKZqDhaGBEiABEiABEiABIwnQAFoPGPegQRIgARIgARIgARMRYAC0FTNwcKQAAmQAAmQAAmQgPEEKACNZ8w7kAAJkAAJkAAJkICpCFAAmqo5WBgSIAESIAESIAESMJ4ABaDxjHkHEiABEiABEiABEjAVAQpAUzUHC0MCJEACJEACJEACxhOgADSeMe9AAiRAAiRAAiRAAqYiQAFoquZgYUiABEiABEiABEjAeAL/H/lLCfOwhnjEAAAAAElFTkSuQmCC\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc4e92a1f28>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "for i in range(3):\n",
    "    ax.scatter(data[:,0], data[:,i+1], label='SIR'[i])\n",
    "    ax.plot(t, fittraj[:,i], lw=0.8)\n",
    "    \n",
    "ax.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}