3. Latent variable models and pseudotime.ipynb

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   "source": [
    "## Latent variable models and pseudotime\n",
    "\n",
    "In this notebook we will go through what we mean by \"pseudotime\". And the relation between latent variables and clustering."
   ]
  },
  {
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   "metadata": {
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   "outputs": [
    {
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     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "%run ../scrnatb/scrnatb/toolbox.py"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "What's a cluster?\n",
    "\n",
    "Many definitions, but:\n",
    "\n",
    "\"A group so that distances between the members of the group are closer to each other than to members of other groups.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "%run ../scrnatb/scrnatb/gp_utils.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false,
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       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "fig, ax = plt.subplots(1,1);\n",
    "\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "cc = point_sprayer(ax, std=0.08)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(117, 2)"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "XY = cc.return_points().T\n",
    "XY.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MmdYQcHtnl4uDBVHMmLUKu/4OyZ/4uwEoPB/GF3/zX0b2BRlcRUUFP3zlZcKWzqHmskZo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\nCGFQEuBCCGFQEuBCCGFQ/z9Pogc0RcsI9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a56da20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=3)\n",
    "cluster = kmeans.fit_predict(XY)\n",
    "plt.scatter(*XY.T, c=cluster, cmap=cm.Set3, s=50)\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We are willing to partition data and assign meaning in this way about distance.\n",
    "\n",
    "What about contiguous data, like this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('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",
       "            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",
       "        this.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 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);\n",
       "        canvas.attr('height', height);\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'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "fig, ax = plt.subplots(1,1);\n",
    "\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "cc = point_sprayer(ax, std=0.08)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(174, 2)"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "XY = cc.return_points().T\n",
    "XY.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qoqN91uVPD79BVEXZ3LWrtVqilxdz7Mo1VpWXcONqLcvK9UxNuzBHaANS1yVJ\nIjc7nONne1FI0Fj1GjvWBZ/ojYvR0z9oJz7WJ1IZKRoOnD5L6dL1fvvJssytqmsMDnYxOlTDM1sC\nhXnrWjXHrhzhsR1fBMBDNDAesF9dwxg7tyaTlW7E7fbyzomDmGO28uqeg3z+udS56/Z4ZF57u43k\nhBDiY4KXSFhdHsVbR1+mrjaF7AwC7oVCIWGJ0jHjcLFn/yDrN3+V/PwsZFnmB9/7M5YWDrwrRryT\n06f/htFJE5kpdiJNHs43aFHpCnn6ua9/qLh5i8WAx+PhJz/8K7JSOinO1TA76+FK5SB6fazfvmq1\nAmNIG5I0S1TUfPhjd3cHB/f+I4U5M/SHjeH16gKuV5ZlPF4vSoWCEL2KcON7IpZkGJ0y4fHIAZEt\nXf0WfmtnOb+OPIgFvgZIAf7AarXGAKH3E2/ALwTqk4rFYvhA4/zG57/Gv/38P6muqUcZosMzbSdR\na8Tl7YbYwGw57bgdWdbOnWt5bik/v3kGy5I8v/1G6hrZmVkUMKb7jXNgcIy8zesJjfT304ZEhOOe\nnQXu1EAxhnDgyAnKglQavMsrB94k+6ltIElMDfvS8dNKi2i/XkWfrZH8TT6vdVRKEp3VdXhcTlSy\nxBe3P4dSI/NGu43wpMAUfp1bYnBwEofDQZ/HRWyQB5ciNYHjpy4wbQe328v4hAuzOfgal0nxYbjd\nULLYzPdetlFnCyEnM/ABV984TukSf5+9SjHhdy+7u1tpqP4Ry4vs5C3W8Mb+LnzTPP6oVApmHQNz\nx5qi11J563W/FXwcsx7qbOM883jK3DE7N8O3f/QKX3gm0Zeoc0eUPF6Z53em8uqb7eRkBl+N3uXy\n0t/bTK5xgKiY4JZyVKSOlrYJYmPjycxezuDgJDcqz5GT2ovmPSGZFSvCeeudZkZGtBTkxBMXA9Mz\nVfzNX7xASloJS4p3EJ/gf+12+wyTk5NERkYFhKHC/Hfz+LHXWJLbjV7nO+fI2Kxvrc8gJMbK3LxZ\nxeLF8xU0D7z9bVaVuQA1i/IiOXGmm41r/YuEXbk+QEGumfrGMQCUKv/v0dUqJU8/9+ccPfhvZCQN\nkpSgZWTUyS1bKDue+vqC0aSH5UEE/LvAD61W6xl8U7u/89BnWeAMDw9zueoaofoQVpSWs6ZkOVfb\nbMyoJRRGGSNq0qPjuVFrw5yXjST5YnWHbtSyNbfIr6+YmBg2Judy+lIVHks4KBQo+kdZmZZLatLD\nZZP1jQz0fujLAAAgAElEQVQRWhAoOAAK1fwPLiozldf2HMBojMCaEdxPOuydJeKOJfbuycrk4kJq\nj56c+1upVpNa4vOgybLM9ZoavvTCs7x2+DCu6EjU71pceKytk7JkXyTK7KwDSRt8IlFrCGO8d4Ki\noi2cuniZtct11NwepSAnMOyy1jbGkgIzkiTx/JNpvLGvjcEhB5aoeT/66Pgs0zNuv/okAG7vvH/U\n6/XSUP1Dntsh4ftagyEsuCXq9cq43CHY7TPMzs6SZS2h0QY/2r0bo64Xu8ONKVzLzscCSwuE6mYw\nGiLZtjGwaqEuNI36lklWBkmCra4bJSJCTXamkapbQ8THBVrqtsYx1q2Kx9YygcfjQalUMjRwm6Kc\n4A+FaIue7MwIbt4aYsmiKEJDVMTHzFKS10RV5f/Bbn+JjMx8pqenOH7k+2gVbRhC3VyZCMNgWkrF\nPSJlZqcb0evmpcQUoaWze4r01MBY/Z4+mfzS1Lm/Bwb6iYro426phHCjBlOEhgNHOoiK0iFJYLe7\nSUsxYjbpcLvlO/046embZnpGon/YQsmyzxMeHsEzL/xvGhpquNlYS2RkArueX0l0tHFBCPgH4UGi\nUBzABy89t4CRZZnXDr5Nj8ZLVH4WPXYH5974MS6lRMaa5dyVF9nr5caZa+xauYFzN67jlEAnK/hc\n6TqiLfNW+ezsLCcvnmXa5aA0IYOk2Hi8Xi9Jy5I/0KosSTFxdPUPYggS/udxzU+eDXd0IYXpOFV7\n/Z4C7r1HRSVJkt6V5izTZ2tiZmycmKwMdIZQmttb+MuXf4A7JoK6g8eYGZ/EGBuNNOsi3RBJ+QuP\nAb55BO30bNBzjN1upmTNdkJDw0D/GPuP7qGza4JFeaY5FwjAxKSLiUkXRoNPmE3hGpLiQ6mpH2Nq\n2oWk0OGRzTS3DvAHv+0vmA0ts8QmVcz9XV11nnXlLt4dV5ySFEadbYw8q/+D4/i5GcZH2mmu+nP0\nOpmaoXAiYjaSU/ibKKe/zdjELBvXxAVdvHhy2hvwWl9nG6OlfRI8MqDl/3y3h69/yYparfBFYlwa\nICkhhNYuBTqtEqfLy9SUi7Cw+QfS5JQTWYbwcC0erzRnIcuyGvkeLjrZC1FmHfUNo3Nt4UYNU9Nu\nihdpuHRzLxmZ+Rzc9y+sWTp+J2lGA3gZHDrL+bNqVq7eGeQT9J+o1WmVzMy4cTo9aDTzhoTH44uU\niYqa/01MTIxjeM88e8mSaI6d8kX0hOjVaO9MGFdWDZGeYuDE2WFe+Nw/43S6iUwKZfl7avJkZxeQ\n/SlJ6hGZmPfh+IXTTKRHYzH5LDdtaAjJ61bQfOkas9PTcyVeJYUC3aJMegf6eXHrU0H7qmus50DN\nFcwlBai1WqpHRrl07ihf2vbMB15Sa1FOAS9/+28p+swuvz4mBobQhvnGJssygy1thEREMIoLp9Pp\nFwVwF5MU3DoeaG7F7XQx0tVDf0MziYvyiMlKp7O6jtZLVynZ9TiGGAuutg7CkxLI35bnq6IIzAyP\n8ssj+3hm8+NIkkRxQgY3WjsIT5t/a5gZHiVNFeYTbyAto4STtlf4+ks5nLnYz41bI2jUEv2DDiLN\nOrZvmp9knZ5xo9UqWbvS52t981gyq9Z/mdSeNnYf+DnpCUMYDVDfokdjWMtj2yrmLLHJ8d6A+ON8\nawQXrg6we28Hq8stzM7KXK/V0dVt5/e+FArctYI93Kjdy+XrUXzlM2ZGx5xcvDbIyqWBLjRzVAF7\nj43w1Bbf/b1VN4rbI7Nj87zoTEya+Ofv1FFcaMIrQ152OBcq9ehCE4FhVpXHcvFqPx6PTFiomvFJ\nJ8MjDnbtSGPG7kEbMh9TsKTkMWquXWdRnr8Lyu5wzz1g3v2gGZ9wkpvtkwGXo5kf//B/kp85gkLh\nr6qWKDWN168AQQRcGYcsN/h9B1eVx3L0VDdRURGkJanoG1QwNpXMlu3+9WRSUtI4ciuEhPfMMa5f\nk8DuvQMkJaUyPdnL8Mgkao2WsekEVq77PAmJqYHj+BQiBPw+NI8OEBIkQzCtrIiWK5VkLp/3KYdG\nmumqbiVYSSiv18uhW1eIWVky1xZiNqGvKOONUwf5rSeeD3LU+/Otn3wPszWT+lPnCDVFoA830mdr\nxGl3YF2zgp7bDYz39pG+tATnzAxdV24iSb6ytgcvnGZMdiLJEKcLY0PJCn5x8QSW8iVzP8SZsXFG\nOnvIXbeKmsMnKH5qPoI0pWgRsdkZdFbV4JVl2iurMCXG01lVi9NuJyo1mcjkRDp7+hkZGcFsNrOy\nZBkhNVVcu1qLXZJRe2WsUfGs37R9rt+b197ii5+JR5IkKlb4hNnjkZmYclJbP+4nEsfO9LJ1g0/Q\nXS4vsuQTnfj4VOLj/4yhoUEmpqdYtjYlYKIuIamA2w0Xyc32F6oVZdF8/+c91Pe+gEqtRR3Sxhdf\nOB9w74vytVyp7AYMmE1a7A7/FHmPR+bto26Kl30Or9fD7kO70UjtDA0N8aXP+r8FGQ0aKlbFU9ea\niSVSR1N/Cms2b6Sjo4G6hh+Sl61kxdJYvF4Zh8PNkRNdbFqXyK3bLqZd2Wx/fD72Ozo6lubwLVy5\n8Tali40oFBLdvdPU3h5hQ0UisizjdvsmfqdnXMiyjFLpuzey144prJ20lOARG0rGglr3y1c+y6kj\nf+dX18TjkdGGLmL52t+lu6uNRWXJREYG5hGo1WqM5hX0DpwmLnreiOgfcrFoyU7WrPW5bYaGBrhZ\neRyQ0eo+uuiZhY4Q8PvgUgR3KyiUSt5rNLscs4Sqg9c7uXDlIqF5mQHtkkLBsOSZ81++HwODA5y5\ncRk3MpLDRb/CxaI7/mjH1DRj3T0YY6KJzc5ktLsHY3QU8XfCG8d6+4jShDAzM8MPjr6FZVUpoXcu\nYsgxy9tnj/KFDTv4p1e+jy4pDtnrRROix1qxgu6aOnLWB4YyakND8Lhc9DU2U7Lrcb9tbdduoNHr\niczP5p9/+l22rVjHqrLlFBUspqjg3lGoGmVfgCtCqZQwhWu53TBGblY4I2MO6homKMwzobkTnrfv\n6BhFK/3HEBVlmQvffC9p6bm8+qNBstJD/CoHtrRPEmHwEh5hJjExnfN9VwJ86XeJtoRQectOSWEI\nG9fEcatulIPHu1FIUNNk4Mln/3ou9DA29g85ffzHJMadCdrX8hIT/ROJrKh4FovFwN63XmW4/xJD\ngyM0NbsJD9ei0RhBlUb52i8wNDVO0fLFQZNTlq/cQX9/MT9/+U9IT5aJjQ5h83qfxX/iTC+x0Tqu\nXB/AMethVfl8pIgsy0SaQxgYtBNtCQzl8xIW9G3RZDKzdvOfcun8bmRPD6BEo89k17PPPVA5h9UV\nu7h6xcDlmxeR5ElkyYAlrpw1azcDcPzoKyjcF1l8x7d/6+pFvKrlbNj04n37/TQgBPw+hHiDT2rN\njE/4lWoFGKms4bPb/C1pr9fL7sP7uNJYQ+Ez/uIyt49Kicvlel8BP3n5HJUTfVgKc5AkiZnRMWYO\n185t14aGMNrTh8sxS0pR4Vwa+136a2383uOf4eD5U1hW+ScSqXVanAUZNLU18+zax7g01Ud4+rvc\nHKPjJC4KfBMBn/8/e1VgiFZKyRIaz10irawIfVYKNVon46ePsr1i032v0+u991fSbnfT0jFJfeM4\nCbEhxETp6B+0c/JcPzrTCw+ctAQwPDxEVKSW/Ue6CNGrCAlRMTbuxGzS8MyOBN4+XUNiYjoyYbhc\n3oA4bgAUEbQPxGPuqCYtWceiPBPWrHDePAQ7n/lGQElXhcIX7haMqWk3Gq3Pej9y6DWM2iNkFWsA\n3wNoctJFXauV7U987b7XNTs7y8Xz+3E6+kjLKMfjnmFwdJDBUQ8KVSKFS7+Arf4GWtUlVhfrkSQJ\np9PD2Yt9LFkUidmk5fhpXxTI8IgDW9MYSoVEelo4esP85zww0MfVy+/glfWUllVgMpnZuuOD1xwp\nW7oJCPxu1NZcIzLkEokJ8y6hRblaurovUVOTTUFB6Qc+568DQsDvw/KcQo7abJisGXNtsizTeuwM\nUZnpeD0eZienmKptYtuipWi1/n7HPcfeYdIaR3ZGNN01t0laHDixEury+mUinrh4hsahXpxKCPFI\nPLZ0KQa9icqRbqKL548PMUUQa81ienSMUFMEPXU2EhflIUkK6o6dIrWsmJBwI/aJSRqOnOLLm58i\nOSGJd25eJCyIFRUaaaLlZhMvbtmJVHOTq1duMY2MCplYB4x39gQNE3RMTQfURwHf5KdCpaKtsoq0\n0mJUGjW2jmo23Cmbey8UWitj4+eJCPf3T9fUjzE6FYs1w0DZkiimZ9xcqxomVK/E4/YwOW5Dlre9\n73zCzMw0F878J7GmThbn6unps+OVZZYUmAgNUSFJEk0tdmLjfZmjRaXbOXzmGjs2+I+5s9tJqKmU\nouIN1NZcpqrhGkqFC5ccw/J1O4MmySSkLKO+8hhutzegXvjew8Os274ej8dDX/dZygr9r99gUKNR\n3GZ8fIywMEPQB/7gYB+nj36T5SW+uQFZlrlZ68IS/zRLiucncHNyFtHbu47rlYfo7aljcryFp3ak\nzUWSFBVG8dPXGliUZ2Z5WQxut8yFK6MkZvgyPg/s/Q/CtLfJs2qYnHKzb88h8go/Q7a1KGBMH5aO\ntvOUFQTO2SQmaLhac14I+K96AJ9kcjOtzDqdXLp8iwmFB4VHJkqh5X9+7qu4XG6uVl8nwhjB0ic/\nF+BjdbvddMxOYgn1CUH7yCgzo+OEmOatsrGWDsqS5/2hvzyyn+HECELSC7j783+zqRZFWz9R6wK/\nqMmLC7jy+puUPrOTmfHxuQzR3PVr6Kq5Te/MDGqdjtyUDKxZvlRwBfcWOOlOTkxJwRJKCvwLQn1n\n98t442P8xHq4o4vx3v579jc5MEhMduZcgk9odirVddUsLV56z2OWlu9g/4FmVhb1kJbsE82rN8eo\nackmJXmCH/78OoX5ZrLTjWjUCjq6Z9i5LZmp6T7e/OV/IHmaCAtxoVDHk5CygZw837mcTifHDr9K\nc/1ekuJcRBhCKMg1U5BrYmjYweXrQ2xYE4csy1ytMbJxu+9hGRoaRmTi53jj4OuUL3FiCFNy6YYH\nh7eU5at9Vf/yC5ZB0NkPf9LTc6mvWcorb1xiw5o4EuJCcMx6ePtgL5akL6BWqxkcHCA8dBwIfABk\npUr8/Ef/jdSUMDyyhaS09SwpmndtXT7/M9aukOFOcWNJkigq0HDh2tvkL1rhVw8mLi6JuO1f5tzZ\nA+jkt2jvnCInyxd909k9xdZNyUSZffdfrZaoWBnJrdvv8PabHSzOtmEI8xkrRoOaVWVezl/9KXHx\nmQwM9GEyRfrVq/kwSLjusy14nfRPE0LA34cleYtYkrcIr9frF1IH8Ni6zXP/7+/v52TlReySF52s\noCgtB9ng+xH2NTSh0mjosTUge7x43G7sfYN8pmIrZYt9y4tNTIzTgQPLe5JywjNTqb1xi/xgVq5C\nQZjZRPPFq0yNjvm1JxXOuzyclfVz/4/ThTHkmEWt839bGG3rZEvWfIkAh8PB4XMnGXLOoAAyLfH0\nXqunYWoYTYQR54wdnSGM6Kx0buw9SFiUmTCzmbgc3wNpoKkVc0rSnA8ewDU1gyE0+Hqdd1EoFGzZ\n8QfU19/g5vEbeL0K0rLWEGG6zmPLezlzIYLyEgsdXdNkZxgpL/W5GMJCwag5z2d23S2xOkN13StU\nXhslJ28lZ4/9A09v9bCxLAaA9s4p9h/pZMfmJKIidczMuLl1e5qapkiKl/svEpGZuZiMjELqb99g\nun2C/OKlD5WGPjIyAsiYzZFsffz/4frVPN46cgyvZwin28T2J/9xroJgWJiBGfs9IoKG7Kwo05OY\noAemaGl/g5pbGgoWlePxeJC8HQQrt7ok38vVKydZsXJzwLalyzZyeO8xvJ4BurqnSEwIY3LKNSfe\n76YgR8Put8+zqjhwXkH29HN47zfITFPQ2ahkdDKeig1fwev1cOncz8HTCXhBmciSkl0kJmUE9BEM\nhSoaj6dnbqL1Lh6PF4Uq5oH6+HVGCPgDcr9046q6W5zotBFZlINKknDJMgeqbjHY2s5ARyeSQkH+\nprV+x7idTtrqOucE/FLlNcz5wWO01RFGRls6MKUHJu2khUUSazBRMzgZsIya7zwuLJp5sdlWsYnv\n7fkZzoLMuQzO0bZO4sfdWJf5rHS73c5/vP0KppUlaO5Yzx0TkzDcz58//UUOnDpKl+SlrqqWJU9u\nIyTc57sd6+2j7vhpNCo1qrBQdGGhNJy9iFKtwuv2MNvTj/V3/8f9bvMcOTlFkDP/St7Z9PrcAgmh\nIaqA9SPBVw/j3RTmGajbe4BLI528uFNGoZh/CKYkhTE67uTl15oxm7Qo1XpmVF9h4zbre7sF7qTx\n5xXP3Z/6+ltERkZjsdxbRFqaa+hufZsEyxCSJFNbGUls8g5Kl26kdGnwwkp6vR6vMgOvtz1gMre1\nfZINFfNhlOkpai7dPE7BovI7BkbwhRy0GgVOpz3oNo1GQ0rWLrpaXmdqeppzl3qZmAhu2UqShFoT\neI5rNwbJyTbNiX5iPMjyCEcP/Ase9wSb1+rwvRUogX6On/x/UemXsm7D85jNwStc3mX5yqc48k41\na5bJfvkI564q2LJj4az9+agQAv4hkWWZ07YqolbMi83dSoTdbW0Ywo2kFAdGXag0Gnqd88tuGcLC\nfOVqwwOz18IjIgjtHWU2OnIuvhtgqLKGJ0tWkJacyraKDXznjZ8RsboE5Z3FIbweD6MXKnnxyc8i\nyzK79+3hZncLTtmLa18zZlMkWYkpbMnOmxNvgHfOHCNyTZmfu0RnNDCVncQtWx1PbdnBvhOHCH0h\n3y/zMiIuFjwyWWMeztRXEVKc77cknH18ktcP7fVbS/RBke74dySFhGPWE1ANsLd/BrMpMP2+pABu\n1jWjUAR+1ZcUmOkfsLN2VSzf/XEHpRXBC5LdRZZlzp58GYO2hvwsL719MocumolP3UpWVq6fVT48\nPMB438vs2qIFfJOrS3Fy+tIr9PVFERsbmLV5lyee+j1+9uO/JjN5kMR4LQNDDqprhliyaF7sPB4v\nY+NOPK5BwBeO55XigLGA/qpveyivWB/QfpfCxatIS1/M5Yv7CY2YYWyqCYK4LmbsbpyuwHTvGbs7\nwGKXJIn8rHGGRuzczXS9y/rVkZy5cI5r5+qJTnrGzw30XgwGAxUb/4jLF14DT4evUZlMxcaHm7T+\ndUUI+Iekq6sTT2xwf1/C4gL6GhrnfMDvxfMuf/TSolIu7XuVkOX+E0GyLGPyKPniU89x8PQxOqZa\n8UhgQMUzS1aQdCcLTa3W8NUnX+SdM8cYdPmsrSiVjueeeAGNRsM//eg76ItzyV3mq1g30tlNf2ML\nEzNTWDP9rc5ht4OQIC6bsOhIGm42sSRvEdfbG8nIDxShiMQ4hgYaiImPw5ye6rdNH26gQ2r7QLWZ\nnZ54vN4m1q6MZc/+dp7YkkRIiO/rOzTsYN/hTr78+UABnpx0o1Dev1iTVqOkYqWZjo5GUlLuLeIX\nz77OutLbmE0+QUqIg5LFDn76+jfxTiYwMp1FxYYvoVQquXLhF3x+Z6A7Y80yLW8cPUhs7L3X8jQY\nDDzzwv+msvIiJy7dxOGYYe1SJT19M9TZRpmc8mWkpqUYcDsl9r31bbZs+wrZuTu4dfsnLMqd/+z6\nBpwotOUY7lFs7d3n3Lj5MwD0dHdwvfJfKVk0f99kWeZSpY7VFc/T1PoamWnz0nGvdUtjY/S0tAcW\n/ZIkCY1aSXGhhovX3iQvvzxoctldoqJi2P7E7913/J9WhIB/SLxeL1KQFGoAhVJBSEQEwx1dRCYH\n1sIIe9dKmkqlkg3WJRy5fJOokgKUKhWOySkc1fV8dp0vk3Hb2vuH4Ol0Op7eHFiu/eSFM4SvKvGz\n7s1JCag0anpsTdQ32sjJCu46eC8S8ON9u/GEB6+iBz4Xw6RGIphERxfmcvnGNR5bH+iPvR8ly57m\ntX1/z3M7JJ7ekcLZS/3M2N20d2twyYmkxOiCRqBcu+XGZElBljsCttuaxklP9Qnbkvxw9hyvuq+A\ny65bmE3+D2NfwlEMk1N2VpS2cuDkj1i78SVmp2sYnzBxpdJX9y0hPoR8awSSJKFV3b8uR19vD9/9\n9/+OyTiOJUrHwIyD7/5ohCe2pbBmhW8OQZZlrt8cIi5ZR0JcK//5/3+D1NRonE4F//XzTkwRCiLC\n1ciEER45+8C5BgDxCck4XV/h0s23wNODjBJJlcqWHZ8nPNxEdZWHi5XHUCuHcbmUjE0EF9/e/pkA\nt9ZdPF7fG1XRIrh86Sir12wPup/g/ggB/5AkJ6cg3TgPqYH+6eH2TrJWlVN37DTGGIufu6H7xi2e\neM/SX4W5BWQkp3L80lkcXg+JoUaefulrjIzMfKgxto4NEpKRE9BujImmv6mV+vZmPwGPVusZf8/i\nDc4ZO5O9/eRrQxkIVSIN2PF6PAEhhFPDI4z09jIbFdzimx4do7u356GvISzMwPJ1f8qbJ/agUXQj\ny+HI6gye/uyTOJ1ODrz5R+w73MnmdfFoNUpmnR72vNNNZv5XSUnN5Rd7/5Fntklz8dx9A3bqmybm\nClCNjDoJDbv3UmRerxedeor5OuHz+FbX6aEg14RR10BXVwejo0NUVnvZsCYOpVKiuW2S3XvbeGpb\nMhNT944E8ng8/Me3v87WDeGEG30PfcesB2OYisy0eb+/JEmUFlk4c6GXru5pNq4JJ9I8TnXtCJvX\nmkhMmHcv2B1V7H/72+zc9fvve5+9Xi/T09MkJmaQmvonQfcpXLyKwsWriIjQcejgPvqHjjA04iDq\nXRUkZVnm1PlRlhQETvb29E4TecflolErcDo/3Pf704wQ8A+JJEmsTM/jfF0j5rz5ScjeqlrUep9V\nmLt+Nc2Xr4Hs80tPj4yyMWMReVmBohoaGsYTG7bO/f2gVtP9kO8TGu31egnT+WfdbV+7mf/Y8zPC\nyguZGR2nv6kFbWgICuB4Qxt5L+zEkBTH7RNnyF2/Zk7EnTN2Wq/ewJIYzXBnV9D1PHtqbZTFBL6N\nPAihoWFUrA9cMkyv17N2y//i2qWf8d2fVKPTwpTdwMp1f0xGhi8aZ8X6P+PEtYN0t58m2jxJlFnH\nE1vmx3H8gpI1m+/ti1UoFDiC+H/Bl72ZGO8TqoRoJ7fqa1mcH8H61fMp6RmpBuJj9L5J08S19zzP\nxQuHSYh1+9W7rr09QtHi4A8XWZbR61VEmvXIsszYuJPCfP+JQb1OhcnQTH9/DzEx944COnt6D2ND\nlwnTTzHjUIMqm02PvRTUvTExMcabr/8LhTnj7Nyi4sLlEW65IDc7nJFxGB5PwJq/jKHhvVy5PkDx\n4igkSaK6dpjZWQ/ld6KBauudLFl27/shuD9CwD8CSguLiOo0c66yklm8aFHwbF4Zp29cZri1g8i0\nZLJWLGOguZU+WxNLk7LYvnHr+3f8EWFW6Rh3u+cmN+/inLHj6B6gYqe/KGo0Gn7n6c+z//gh2ka6\nsG6YF7ZunY7p0THCzCayVy+n5fJ1AGRkhju6KHtmJ4PV9SRHxVJ77BQpRYsxWCJx2u20XqlEH6on\nLzWwrMCHJTIyhi3bv3HP7SEhoWzZ/lv09Ozk5JFvk6TvRpIkhkecnLykIi33C++7sIFCu5iBoWtE\nR82/mciyzPWqYZ59IhWAnkE1krefjWsChVKvVyGjZOl9BKu3u4HE99T/VigkPB4vEPgw7+6d5vmn\nfCF5LpeXEH3wn3Rupoaa2ivExASfQD535k2iQk+Tm6Lm7oo4LlcTB/Z+iyef+aOA/U+f+DGryqaR\n7hRBW1keh9PpYd+RKZ54+q9YE+e7/oPvTKD0XOfIyU5mZtxsXp+E0XCnbvioi1mWLJhFmD+JCAH/\niEhNSgmo552WkkZdfR2HDp1hfGYKi9HEb5RvZFHux1vq8rFV6/nO269geVdkicftpmbfYX5jw+Oo\n1YEWllqtxqOQyFy70q89Pjeb+tPnyV23GrVOR+YKX6KMx+XC6/agVKnQOj2sLijmzGgHk0PDDDS3\n+OqIlxbhrqwnO8gK9B8XarWazdv/kK6uFvacuEGYwcLqTaseaFWa8pVPc/6ME51URVbKLAPDdvoH\nHGxe6xMru8PD2EwmOq10z4k9g8F03wWWw01xjI5W+rUV5Jq5UjnAymWxQY+ZmnYRbtT6Fp5wBg8l\nHB5xERkZ3PqWZZnRwcvklPiPS61WYDG109PT+X/bu9fgqM77juPfXd0BIQkQQiAkhIUfIYuLuBjM\nHWMMmFIcMNh1pxc3dDpt2rrNtC96SRM3bifjCambzmSScdNp0zbp2JmxawfHwdSEYGOwA7K5GB7A\nEndQhNEKSQh0277YVSIh7UWLVjoP/D6vpHOOdv/6C37n7HPOcw4TJ07utT0dtb8M727p6SmsWTmC\nQz/fzfoNoTtQr1u/jbq69fgP76GxIcCRk02kpzXRFcxkzLgq1j4W/UDmo+qfcfHsXgg2EAyOIHfs\nHBYv25jwHTzvNgrwJKsor6CivCL2hkmUlZXFH254kh17/48LzQGaW5oZ0dbFV3/v2aiXYrV0tfcZ\n4/b5/RSaaRx7YydTljzIyLxc6mvOUF9zBrN8MdcvXGZWYUnohlVH4YPaE6T400jr9JNtL7Fp41PJ\n/nXjUlQ0laKiqbE37MHn87Fk+dO0tT1BTc1pTta+RnnpVZpvdFB9rJMrDVNZvurznLTVnLtwlOKi\nvpNh/BnRd17LVzzOS996jbmzu345eSUtzc/oUWkc/LieueGhlM7OLt7df4XSkrG8dyDAY6sL8Pt9\ndHR09TtV/5PTI/nc1v6fyHTzZitZGU309yzKsikZHLfVvQK8q6sLv78D6LsjGpGVyqkTu2HDrx4h\nUFBQSMHqgf/dPzywE3/7DhbM7n6fGzQEdvP2Ww08uu6ZAb/e3UgBfo8YOXIUW9f2dzP+yDLw09bP\n7W3SFmIAAAx7SURBVENzJ04g++I1yhp97HnnLRiVyZi8XJoPfsKsSaUsfTB07XesOw+6Kj09nfLy\nCsrLK2houEZN3UWKp0/hgfCletMr5vHWG7vYmt/U63r13ftucZ95LOprZ2RksOU3vsoPvvc3zJk1\nirKpozl7rolPbAMtNzo4dvwao7PT+SyQwZz5W5heUUXz9avsP/ifzJuVwkPzC/jJOxcwZbmUTR1N\nQ6CdwzaLBYu2RTxqzcjI5GZb/1eLXKlvY0LhlF7LUlJSuNmWC/R9QMeRT64xfVoKdXV1FBQkPlMy\nGAxy+fxuFs3rvZPIy02j9vxHNDc36zpwFOASxdJZ83j52AHGVfa+xLCx9jzLy6Yzo7ySJQsWJfx8\n0btBXt6YPte0+3w+Hln3F+z42Q9I89WQ4m+ntT2f+8x6iibHHv+vnFHFs3/5P7z77i5e/M6/Ulx4\ni2n35TCrciypqX4CjW2cujCb1Y92PzxkCpNLytm/70cEu1q4v3It4/KL+OjUUfLyCvncluhDRH6/\nn5T0ctrajvd6gg7A6TO5bH5qZp+fyRk7l8PH3uh1wrQhcIvG622UloympaUJSDzAA4EAudn93xOm\nvMzH0aMHWLhwVcKvf7dQgEtEkwon8VBdMfver2ZEeSn+lBSaT9Qwc+wkZpTfG4+sSlRaWhrL+rli\nJl4+n4+FC5dz/epbLKi67RNQTjqcOUxraytZWaFhj5EjR7HqtmGKsmn93wK4P4+seYYdr/8LY7Jr\nKStN5cov2qk9P5Zlq/q/fe2Klb/O9/9jJ4HGy6Sl+uns6iIrM5WlD01g/6EUZi4sHeBv3FtmZiat\nN/u/AisQ6CA3Tyc+QQEuMSycPY/5M6qoPlxNW0cH89c+0e9JTxl8ly5dpDC/he6p+D2VTGznTO0p\nplf0PTpORFpaGo9v/iJ1dZc5eaKawoklbF4ceQeQmppK1bzNdLb8iKKJvxrmOH+pnfzCh+O6/PXE\n8WpqTv8UX7AJfNncd/8q7jeh3ycrK4vWjmKCwSt9hn4+PZ/D4wtnJPib3l0U4BJTSkoK86ru7fsu\nD4ecnFxqjvX/X/RaAKYVD/5RaEFBIQUF/T9S7XYPP7KJt3dmcuDj9/DTRGdwFJOnLGPh7MUxf/bD\nAzvpat3BgzO6w/86p2v/jUNNG5kzbyUAK1Z9np07tjNrehNjx6TTcqOdg0fSmLPgd3QVSpgCXMSj\ncnPzaLxRRDBY3yuwgsEg9YFClsQZtMk0u2ops6uWDuhnOjs7uXJhFw/ddtliWWkq+w7+hKq5K/D5\nfOTmjmHL089z6OBeztszZI0cx4ZNq6NehnmvUYCLeNjK1X/Azh+/SPnUaxSOz6Cu/hbHP81h5erI\nN8PyutraU5RMbKa/E5SF4xo5d+4sJSVTgNC5gLnzlgGRZ8neyxTgIh6Wk5PHlqee49jRg3x8+lPG\nj5/C5ifnOz2EkJaWwa0ID9Npb/f1eTShRKYAF3HAA5VzeaBy7nCXMSiKi6fw0YdjKC252WddfUM+\niyYM/9CQK2LPHxYRGUQ+n4+KmVv5oLqDzs4gEJpZ+v7BTiqrnhzm6tyiI3ARGXLT7p/J+IKv8MH+\n1wl2XseXksuKRzfGfPCE9KYAF5FhkZOTy+o1iU92Eg2hiIg4SwEuIuIoBbiIiKMU4CIijlKAi4g4\nSgEuIuIoBbiIiKMU4CIijoprIo8x5gVgCZACfM1a+2pSqxIRkZhiHoEbY1YAFdbaRcA64MVkFyUi\nIrHFM4SyB9gS/joAjDDGuHsvSxGRu0TMIRRrbRBoDX+7DXgzvExERIZR3DezMsZsBJ4BHk1eOSIi\nEi9fMBj7YNoYswZ4DlhjrW2MsbmOzkVEBm7AQ9MxA9wYMxrYC6yy1l6N4zWD9fVNA61jyOXnZ6M6\nB4cLNYLqHGyqc3Dl52cPOMDjGUJ5EhgLvBw+eRkEfttae2GgbyYiIoMnnpOYLwEvDUEtIiIyAJqJ\nKSLiKAW4iIijFOAiIo5SgIuIOEoBLiLiKAW4iIijFOAiIo5SgIuIOEoBLiLiKAW4iIijFOAiIo5S\ngIuIOEoBLiLiKAW4iIijFOAiIo5SgIuIOEoBLiLiKAW4iIijFOAiIo5SgIuIOEoBLiLiKAW4iIij\nFOAiIo5SgIuIOEoBLiLiKAW4iIijFOAiIo5SgIuIOEoBLiLiKAW4iIijFOAiIo5SgIuIOEoBLiLi\nKAW4iIijFOAiIo5SgIuIOCquADfGVBpjThtj/ijZBYmISHxiBrgxZgTwTWBX8ssREZF4xXMEfhNY\nB1xOci0iIjIAMQPcWttlrb01FMWIiEj8UpPxovn52cl42UGnOgePCzWC6hxsqnN4JSXA6+ubkvGy\ngyo/P1t1DhIXagTVOdhU5+BKZCcz0MsIfQN+BxERSYqYR+DGmDnAdqAEaDfGbAY2WWsDyS5OREQi\nixng1tpDwMohqEVERAZAMzFFRBylABcRcZQCXETEUQpwERFHKcBFRBylABcRcZQCXETEUQpwERFH\nKcBFRBylABcRcZQCXETEUQpwERFHKcBFRBylABcRcZQCXETEUQpwERFHKcBFRBylABcRcZQCXETE\nUQpwERFHKcBFRBylABcRcZQCXETEUQpwERFHKcBFRBylABcRcZQCXETEUQpwERFHKcBFRBylABcR\ncZQCXETEUQpwERFHKcBFRBylABcRcZQCXETEUanxbGSM+QawEOgC/sxa+/OkViUiIjHFPAI3xiwD\nyqy1i4BtwDeTXpWIiMQUzxDKKuA1AGvtCSDXGDMqqVWJiEhM8QT4BKC+x/dXw8tERGQYJXIS0zfo\nVYiIyIDFcxLzEr2PuCcCl6Ns78vPz76jooaK6hw8LtQIqnOwqc7hFc8R+E7gCQBjzBzgorW2JalV\niYhITL5gMBhzI2PMPwLLgU7gC9baI8kuTEREoosrwEVExHs0E1NExFEKcBERRynARUQcFde9UCIx\nxlQSmqX5DWvtt25b9wjwD0AH8GNr7fN38l6JilFjLXCO0D1egsBvWmujXSKZNMaYF4AlQArwNWvt\nqz3WeaKX4Vqi1emJfhpjsoB/BwqADOB5a+2OHuuHvZ9x1OiJXvaoJxM4Cvy9tfZ7PZYPey97ilKn\nJ/ppjFkOvBKu0QccttY+22P9gPqZcIAbY0YQui/Krgib/DOwmtA143uMMT8MT8UfMnHUGATWWmtb\nh66qvowxK4AKa+0iY8wYoBp4tccmw97LOOv0RD+BDcCH1tqvG2OKgbeBHT3We6GfsWr0Si+7fQn4\nrJ/lXuhlT5Hq9FI/f2qt3Rph3YD6eSdDKDeBdfQzqccYUwp8Zq29ZK0NAm8SuqfKUItYY5gPb8ws\n3QNsCX8dAEYYY3zgqV5ClDrDPNFPa+3L1tqvh78tBs53r/NKP6PVGOaJXgIYYwxQTu8djGd62aOe\nfusM80w/iVBHIv1M+AjcWtsF3Ar1rI/b75/yC2Bqou+VqBg1dvt2uHF7rbV/PTSV9Rb+Y3UfGWwD\n3gwvA4/0EmLW2W3Y+9nNGPMeMAn4tR6LPdNPiFhjN6/0cjvwBeB3b1vuqV4Suc5uXulnhTHmNWAM\noaGe7hGCAfdzqE5iemXPd7svAV8kNElphjFm03AWY4zZCDwD/HGUzYa9l1Hq9FQ/rbWLgY3Af0fZ\nbFj7GaVGT/TSGPNbwD5r7dnwomj9GrZexlGnJ/oJnAK+Yq19nNCO5rvGmEgH0jH7mawAvwQU9vh+\nUniZp1hr/8taezV8pP4mMGO4ajHGrAH+itA4XVOPVZ7qZZQ6PdNPY8wcY0xRuKaPgVRjzLjwak/0\nM0aNnuklsB7YaIx5n9Cnrr81xjwcXueJXoZFq9Mz/QwPj7wS/roGuEKob5BAP+/oKpQeeu0prLVn\njTHZ4ZMzlwh9PHx6kN4rUb1qNMaMBl4GNlhr2wntmV8ZjsLCtbwArLLWNvZc56VeRqvTS/0ElgEl\nwJ8bYwqAkdbaq+Cpfkas0Uu9tNY+1f21MebLQK219p3wOq/0MmqdXuqnMeZpoNBau90YMwEYD1yE\nxPqZ8FT68I2tthP6R9geLuJ1Qo37X2PMEkL/2YPAD621/5TQG92BOGr8E0IfY24A1dbaPx3qGsN1\n/j7wZeAkoR1NEHgHOOKVXsZZp1f6mQl8F5gMZALPAeOAgFf6GUeNnuhlT8aYvwPOEPrbe6aXt4tQ\npyf6GX4YzveBXCCN0N+9gAT7qXuhiIg4SjMxRUQcpQAXEXGUAlxExFEKcBERRynARUQcpQAXEXGU\nAlxExFEKcBERR/0/sXsCRmDPl/cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a7e9518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=3)\n",
    "cluster = kmeans.fit_predict(XY)\n",
    "plt.scatter(*XY.T, c=cluster, cmap=cm.Set3, s=50)\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zuTDrdAvifRtJksiNjuZMZyeSpODaB79goza0ayTOEMHI7CzxBv93l2aI4FRt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a26d1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=5)\n",
    "cluster = kmeans.fit_predict(XY)\n",
    "plt.scatter(*XY.T, c=cluster, cmap=cm.Set3, s=50)\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p8TjmbOiMxgXxXniWkkRkahJt12uQFAo+aG1HWxw4nd4QFcHM6JhXwIGQODNV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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a058908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=10)\n",
    "cluster = kmeans.fit_predict(XY)\n",
    "plt.scatter(*XY.T, c=cluster, cmap=cm.Set3, s=50)\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A rather large problem in machine learning / statistics in general, is how to pick the number of clusters for clustering algorithms. Above we can see by eye that 3 clusters would be good. Here though, by design, there is nothing one would consider a cluster separation.\n",
    "\n",
    "Yet, the data could be partitioned into groups by clustering. The key is that it wouldn't matter how many clusters we would want to find.\n",
    "\n",
    "And clearly, some clusters will be closer to each other than other clusters.\n",
    "\n",
    "We conclude that putting the data in to discrete categories is not what we are interested in. We want a _continous variable_, that we did not observe, which describe the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For data like above, this problem was solved by PCA 100 years ago. (Karl Pearson 1901, Harald Hotelling ~1930 indep)\n",
    "\n",
    "(One can even show that PCA is equivalent to K-means clustering with an infinite number of clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dG/Z+3LQ3dPhBedvQNDXTR5/6jd+ztc18F8b9JGHsbomh8KTsqZPMyGLgihKx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\nAppCZGfcli1bws8//2xrU/F6Vb0B+n8CKlzHyoaxrAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='img/pearson-pca.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But what about when the data has a shape which is not a nice flat thing?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('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",
       "            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",
       "        this.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 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);\n",
       "        canvas.attr('height', height);\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'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "fig, ax = plt.subplots(1,1);\n",
    "\n",
    "plt.xlim(1, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "cc = point_sprayer(ax, std=0.08)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(94, 2)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "XY = cc.return_points().T\n",
    "XY.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Since PCA is a linear projection, it will not be able to \"unfold\" this structure.\n",
    "\n",
    "There are many graph based ways of dealing with this. For example the bioinformatics tools Wanderlust uses a kNN graph between the points, and find the closest path along the graph between points. This gives a parametrization for the points (using a given point as 0). Monocle does the same thing, but uses as Minimum Spanning Tree in stead of kNN graph.\n",
    "\n",
    "Another strategy is to use spectral embeddings, such as Diffusion Maps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We will use a **Baysian Gaussian Process Latent Variable Model**\n",
    "\n",
    "The derivation of a GPLVM is somewhat involved and out od scope for this section.\n",
    "\n",
    "To get a gist of it. Say we have multiple Gaussian Processes, here two, mapping from X (here 1-dimensional) to Y_0 and Y_1.\n",
    "\n",
    "In section 1, we said that the hyper parameter for a Gaussian process can be optimized in terms of the likelihood. It turns out, when we have multiple GPs at the same time, that in the same way the X-values of the model can be optimized!\n",
    "\n",
    "We can find the X-values, such that the combined Y-values are well explained by Gaussian Processes to the Y-values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The value of doing this rather than another method, are\n",
    " - GPLVMs can model more dimensions than observations without overfitting\n",
    " - Choice of covariance function allows flexibility. RBF is a good non-linear one usually.\n",
    " - Likelihood gives quantitative value of how good the model is\n",
    " - Can predict and generate high-dimensional data\n",
    " - Can measure uncertainty of the model\n",
    "\n",
    "In addition, the Bayesian version of GPLVM offers\n",
    " - Improved performance by inducing inputs\n",
    " - Can measure uncertainty of _X-values_\n",
    " \n",
    "It also matches well with the physical world: Given an observed trajectory, we assume it has been generated by a noisy low-dimensional process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import GPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we assume that the latent low-dimensional space is 1-dimensional. So we are saying that there should be a 1-dimensional parametrization of the point pattern we drew based on two Gaussian Processes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m = GPy.models.BayesianGPLVM(XY, input_dim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m.optimize(messages=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: bayesian gplvm<br>\n",
       "<b>Objective</b>: 139.44076507289077<br>\n",
       "<b>Number of Parameters</b>: 199<br>\n",
       "<b>Number of Optimization Parameters</b>: 199<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  bayesian_gplvm.        </b></th><th><b>           value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  latent space.mean      </td><td class=tg-right>         (94, 1)</td><td class=tg-center>           </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  latent space.variance  </td><td class=tg-right>         (94, 1)</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  inducing inputs        </td><td class=tg-right>         (10, 1)</td><td class=tg-center>           </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>0.00616009873741</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.bayesian_gplvm.BayesianGPLVM at 0x2b1e8a6716d8>"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let us plot the input points colored by inferred 1-dimensional variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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fOHLkMBUVZdXXTGDs2EwmTJjI22+/TmlpCQUFBQwZMozMzMnExcmOGCJ4JFEK\nEWKsVivjxk1gzZrlXp9TJiZ2Yvr02fzwh/+B99WwDJYs+YBbb83EbrczbNgNHDlyEMMwSExM9DrK\nNTIykrKyMpxOZ50BRA5HJUuWfMBDDz3qM16z2cxDDz1GVZWDEydOYLVa6d9/AB988C4vvPBT7HYb\nJpMJt9vN0qUf8NFHixgx4mYef/wbNUncl9OnT7Jq1XIuXryAy+UkPT2doUNvYsqU6X5fJ0RtLd0U\nvb0IjVoI0UruvfdLTJo0DavVjtvtBjwtyYyMrnzvez9gw4a1fp9jVlZWsGLFJwDMmDEbk8mMYRgk\nJCT4fE1iYiL5+fl1jplMJr744nSjYrbZ7AwZMhSlBrJp03r27dtFRIS95tO82WwmLS2NmJgYjh49\nyO9//xu/1zt06AALF/6Fq1cvY7NZiYyMpLCwkA0bVvP22683KiYhQom0KIW4zoMPPsz8+feydu0q\nysvLGTbsBgYNGgx4lozzNy3DYrGQl5cLeBJUfHwc+fn5frugfI+yrWpy7Lt2bfc5IjYuLo7s7Gyu\nXLnIoUMHGD78Rq/nffLJEiIi6l/Dbrdz5MhBvvjiNL169WlybCL8hErXq7QohfAiKiqKuXPnce+9\nX6pJkuBJNtdamt643W5iYz3rrBqGgWF4EqHT6fT5GofDUafb9ZqkpKQmxex2u8nJueL3HLPZTERE\nBHv27PJafvjwQUpLfW9YHB0dxYYN65oUV0uVl5e1u5WRROMEYWWeoJAWpRBNMGfOXDZuXIfb7fJa\nbrVamTNnLuBJSunpGZjNJq5evUpaWprX1+Tn59cb4VpV5WTChElNiq0pby4ul/fEffbsFw2uGOSv\n67k1rV27kgMH9lNcXIhhQKdOSdxyy62MGzc+KPcXLdeekl1LSItSiCaIiopm2rRZuN31B/O43W6m\nTJlRZ+eOW2+dgNttEBUVRV5eXp3pJ4ZhcPnyZaKiouq8oVRVVTF+/ERGjbqlSbGZTCY6d+7q9xzD\nMHA6naSnd/Za3rNnTyoqKv1eIzIysklxNceiRf9g795dWK1mOnXqRFJSJ0wmg40b17Bq1fKA31+I\n2qRFKUQT3XnnfDp1SmLHjk2cOfMFJpNnHuXEiVPIzKy7gfqUKTNYt24NxcVFREdHc/XqVcCTDF0u\nFykpKQwcOASTyYzDUUlcXBzTps2if/8BzYpt0qSpLFr0NjZb/T/tvLw84uLiMJnMzJ59u9fXDx16\nAzExH+G3P9TTAAAgAElEQVR2e29xlpWVMWnStGbF1lg5OVc4fvyI16kx0dFR7Nmzg8mTpzU4cle0\nvVBpUUqiFKIZMjMncffdc7l0qQDDMLw+Y7zGYrEQGxtLYWFhzcCdtLS0mjf64uJifvzjn7VKXCNH\njqawsIBVq5YBBjabDYfDwdWrV4mKiiIyMooHHnjIZ5IxmUzcfvs83n//nXoDeiorHQwaNIxevXq3\nSqy+rF+/xu98z8jICDZsWMvMmXMCGodoOUmUQgi/I2DB09VZUJBPRESEz2eUBQWenT42bFjH5csX\nq7tQuzBt2myGDBna5JimTJnOhAmTWL9+Dbt378TpdDN8+E1kZHSut6nz2bNfsHr1Cq5cuQQYpKam\nM336LB5++DFWr17BxYvZuN1OTCYT5eWVHDt2hOee+x7p6RlMmDCZESNaf9F1h6PS7xus1WqluLio\n1e8rWp8kSiFEg0wmEzabHcPwPvgHPINj3nzzbzXrwhoGXLhwnoULX2HevHuaPKgHPIumz5w5x2+r\na8+eXSxZ8j4REf9qXV66dIHXXvsTc+fexVNPPQ14dkA5evQgMTH/WhKvtLSYJUvep7CwkMmTpzY5\nPn9iYz0rFvn6EFJZWUl6uu/l/YRobTKYR4gA8zfn0DAMiooK6y2eDmCxmPnkkyXNmk/ZEKfTyT//\n+WGdJHlNRIS9+r4Orl7N4cCBfV67aiMjI9i0aW2dqS9ut9vv9JnGmDlzDqWl3pcRBHC5DG69NbNF\n9xDBIdNDhBCNctdd9/C73/3K65SSsrIyEhN970lZVeVg/fo1rf48buPGdXhfhs/DbDaxZs1qCgvz\niI72t12XwaZN64mNjWPnzq3V8zgNkpNTGTVqDBMmTGxybNHRMWRmTmXbto11WrEAJSVl3HbbHSGz\nNFqoa0/JriUkUQoRYN26deeb33ya999/h/Pnv8DlcmGxWOnRoxc2m52LF8/7fK3VaiU3N6fVY7py\n5bLXkbHX39fprPL7Zme326ufg1YSGRlJQoJnpKrT6WDjxtXk5eVy553zGxVTdvYFsrLO0aVLNyZN\nmkpaWjpbt24mL+8qJpOJ1NR05s27L+CDiUTrkUQphGi0Pn368swzPyQvL48rVy6RkdGZxMROvPfe\n21y4cNZnC8nlchEf77vF2VyRkVG43W6f9zUMg4iISCIiIvyeV15ejsPhJCWl/ipCkZGR7N+/mylT\npvsdxXr69Ck++eQjCgvzsdvtVFY6SEhIZPbsuXz9699sXgVFuxAqiVL6L4QIoqSkJAYOHExiYicA\nZs++HZfLXxeohRkzZrd6HDNmzMbh8P3ss6KikpkzZzNr1m2Ul/tePi4vL5/ERN9bgUVHR7F6te8F\nArKzL/Duu69jGC7i4+NrtUrdvP/+Pxq9MLwQgSSJUog2FB+fQGbmZK9rwTqdTqZNmxWQifWxsbGM\nGnULDoejXlllpYObbhpFQkIi8fEJjB8/ycd5lfTrN8DvHFKz2UxZWZnP8lWrltV7DvmvGGNYs2Zl\nI2oj2iuz2dyir/ZCul6FaGN33XUPyckpbNu2icuXL9Ws9JOZOYVbbhkbsPvOn38v8fEJ7N69g4KC\nPAASE5O45ZbxdQYPzZ59OwMG9Gb58lVcvZqD2WwiPb0zU6fO4OzZM+ze7XvHEpfLRVyc7xbnpUvZ\nfgcLXbx4ocF6VFZWsmbNCnJyPLH17dufceMmtKs32nAVKl2vjUqUSqlfAeMBC/CC1vqjWmVngHOA\nG88wuge11hcDEKsQISszcxKZmZNq1oIN1hvMtGkzmTZtJkVFhdX7Znp/HjpmzBj69h1S73ivXn3Y\nvn2Lz0RZXl7hd8Suy+V7fum1csMwfP7/OH78GB999B5xcbE1Lds9e7azY8c2nnjiKeLjfe8DKgIv\nVBJlgx+5lFKTgMFa63HAbOB3151iALO01pO11lMkSQrRfG01fyw+PsFnkvTHZrMxdeosr88xy8sr\nyMycQlSU7xajv9bmtbh8/f9wOBx89NF7dOqUWKf7NyoqitjYKN58c2EjayGEf41pUW4Crm1eVwBE\nK6VMWutrIxBM1V9CiDB0660TSEpKZvPmdeTkXMEwDFJSUpk5c67PzaGvGTJkOPv27fS6I4nD4WDQ\noOE+X7t27SpiY70/3zSZTFy5comXX/49FRXluN0uYmPjuPHGkYwZc2vTKiiaLVRalA0myuqEeG0D\nuseB5bWS5DWvKKV6A1u01j9o5RiFEO3coEGD62xw3VjTps3kwoUssrLO1kl6ZWVlpKSkc9ttd/h8\nbU7OZZ9dvkVFRTgclVgsEBsbXXN8x44tZGdfYP78e5scq2i6UEmUjX7arZS6E3gE+NZ1RT8CvgNM\nBIYppRo3u1gIIYCHH36MO+64m9jYBKzWCKKj45k5cy6PP/6kzzdaz76avqe35OTk0Lt373qvj4mJ\n5uRJzZkzMu0kGMJqCTul1EzgWWCm1rq4dpnW+q1a5y0HhgEf+rteaqrvycehKJzqG051hfCqbyDr\nOmXKeKZMGd/geYZh8M477/DZZ59x/vx50tPT6y1mUFRUREKC70E8iYkJ7Nu3nZtvvsHvvcLpZyv8\nazBRKqXigV8BU7XWhV7KFgFztdZVeFqV7zd0zZyc4oZOCRmpqXFhU99wqiuEV33bS13/+tdXKCsr\nJjIykn79+nH8+HEGDBhQZypIUVERnTt39nud/Pwiv/VpL/UNhkB+IGhPrcKWaEyL8j4gGViklDLh\nGeW6HjistV6qlFoG7FRKlQGfaq0XBy5cIUS4+uyzI+TlXSU+3vPGbjKZ6NevH6dOnSI2NpaMjAzc\nbjdFRUXExsaSlFR/Wb1rbLbWX8RB1Bc2iVJr/Srwqp/yl4CXWjMoIYS43t69u2qS5DU2m40BAwZQ\nUlLC3r176dy5MwMHDuTs2bM+E2VxcQkzZsg2XcEQKolSlq4QQnQI/vbljI2NJTU1lZ49e2Kz2UhI\nSODixfpTuisqKkhI6MSwYf6nrQhRmyxhJ4ToEKKioikqqvDTSjFRXFxMXFwcqamp5ObmcurUKSwW\nCxaLhbKyMsaOzeTuu2VqSLCESotSEqUQokOYMmU6Cxe+QmlpCS6XC7PZXLMFWPfu3cnI8AzguXYs\nOTmZ5ORk3G435eXlDBo0jHvuua+NaxFeQmW9XUmUQogOITU1jdLSUrp27VpnRxWHw8HRo0d5+uln\n6Nq1K6+/vpC8vDw6dUrE7XZTWFhE9+69uP/+L7dh9OEpGC1KpdSLwBg8640/rbXeW6tsGvA/gBNY\nobV+vjn3kEQphOgQPvlkCd26da23Go/dbmfo0KEcPLiffv36841vfIvLly+xZ88ubDYbEyZMJDra\n+1J3IrACnSiVUplAP631OKXUQGAhMK7WKb8HpgMXgU1KqQ+01sebep/QaBcLIULeF1+c9rlkndVq\n5dy5L2q+T0/P4Pbb72TmzDmSJEPbVGAJQHUCTFRKxQJUL6uaq7XOrl52dXn1+U0miVII0SGUl/ve\nALox5SL4grCEXQaQU+v7q9XHvJVdAfyvROGDdL0KITqEhhYJsNsjghSJaKw2GPXq74bNDkYSpRCi\nQ0hP70x5ebHXN1/DMGpGvbYWwzDYt28vFy9eICkpiTFjbsVisbTqPUJdEBJlNv9qQQJ0wfM88lpZ\n7V+KrtXHmky6XoUQHcLcufPIzy/EMOru8mcYBvn5hcyZc2er3Wv//v384Q+/Yd++7RQWXuXYsUP8\n4Q+/Yfv2ra12D9EqVgP3ACilRgAXtNalAFrrs0CcUqqHUsoK3F59fpNJohRCdAgJCYk89tiTWCwR\n5ObmkZubS25uLhaLnUcffcLv2q5NcfbsFyxdupTk5E7ExHgGAkVGRpKamsz+/Ts5dOhAq9wnHAT6\nGaXWegewTym1Dfgd8JRS6uHqbSEBngTeBTYB72itTzanHtL1KoToMJKTk3n00a9TVeWguLiE2NjY\nOnMqW8OmTetJTEz0WpaYmMiuXdsZPlyWwGuMYDyj1Fr/4LpDh2uVbaXudJFmkUQphOhwbDZ7q7Ug\nr5efn0tycief5QUFeTWr/wj/QmUJO/lJCyFELYbhbqAcXC5XkKIR7YG0KIUQopbY2Hi/5TExMT4X\nPhB1SYtSCCFC0IgRoykuLvZaVlpaxsCBQ4IcUcdlNptb9NVeSItSCBFWCgryWb78n1y5chmXq4qI\niEi6du3B7bfPw2azMWLEKMrKCti9ew+pqSmYTCYMwyAvL48uXXowdeqMtq5ChyEtSiGE6GDy8vL4\n29/+gmE4SUtLoXPnziQldaK4OJ8///klnE4nAHfddRcPP/x1oqLiACt2exT33PMgCxZ8qW0rINqE\ntCiFEGHjk08+Ii0tpV5Lx2q1EhsbzerVy5kz5w7AMxXlnnvub4swQ4a0KIUQogNxOp1cvXrF55u3\n3W7n/PmzQY4qtAVhUfSgkBalECIslJaWNPjmW1XlCFI04aE9DchpCUmUQoiwEBMTW2+d2Os1tEOJ\naJr21CpsidBI90II0QCr1UpKSrrPZOlwOOjevRdlZaUcPXqU7OwLQY5QtFfSohRChI25c+fx97+/\nWm9AT1VVFUVFpcAlXn31ZaKiIqiqqsJisTF69FhGjhzddkF3YKHSopREKYQIG506JfHoo09Uz6O8\nhNPpJDIyks6du1FQUERkpI3o6PQ6r9mzZxuGYTBq1M1tFHXHJYlSCCE6oISERL70pYfqHFuzZiVJ\nSYleB58kJSWxd+9OSZTNECqJUp5RCiHCXlbWOSIiInyWu1xOsrLOBzEi0Z5Ii1IIEfbcbv+7gdjt\nNgoLC+nWrXuQIgoNYTU9RCn1K2A8YAFe0Fp/VKtsGvA/gBNYobV+PhCBCiFEoERERPktLy+voGfP\nXsEJJoSETderUmoSMFhrPQ6YDfzuulN+D9yFJ5HOUEoNbO0ghRAikMaMGcfVq7leywzDID4+kdjY\n2DrHc3Nz+fDD93jvvbf56KP3KSjID0aoHUqorMzTmHbxJmBB9b8LgGillAlAKdUbyNVaZ2utDWA5\nMDUgkQohRID06zeAvn0H1EuWDoeDS5eucM89dRdDX7ZsKe+++zqG4cRmM+FyVfL22wtZtWpZMMMW\nQdJg12t1Aiyv/vZxYHn1MYAMIKfW6VeAPq0aoRBCBMHMmbdx4kQ/du/egctVicsFXbt25777Hqqz\nYs/27VvJyblI584ZNcfMZjOdO3fmwoWz7N27W0bIVmtPrcKWaPRgHqXUncAjgL/N2ELj/4oQIiwN\nGKAYMECRmhpHTo73zZs/++wQSUmJXssSExM5dOhTSZTVwm0wz0zgWWCm1rr2b0820LnW912rj/mV\nmhrXlBg7vHCqbzjVFcKrvuFUV/Bd34qKMsB7ovSUl4bd/ytfwqZFqZSKB34FTNVaF9Yu01qfVUrF\nKaV64EmQtwMPNHRNX5/UQpG/T6ahJpzqCuFV33CqK/ivr9vt9vtat9voUP+vJKk3rDEtyvuAZGBR\n9SAeA1gPHNZaLwWeBN6tPv6O1vpkoIIVQoi2Fh/vuzUJkJDQKUiRtH9h06LUWr8KvOqnfCswrjWD\nEkKI9mrkyDHs2LGJlJTkemU5OVeZNMnfMI7wEjaJMlSUl5ezf/8eDMNNUlIKgwYNCZkfohAieIYN\nG05paTF79+6kU6dEoqKiKCsrp6CgkDFjbkWmkv9LqLzHhkWi3LFjC5GRNmbPnkZERARZWVls2rSG\nvn0V3bv3bOvwhBAdzJgxtzJ69Bi2b99CQUEBvXt3Y+zY8SEzyrO1hMr/j5BPlHv37mTEiOF069at\n5li3bt1YsKAbH3/8CQkJicTHJ9SUVVRUsHfvLiwWz6ehigoHw4ffRFKSp5vl0qWLfP75cUwmE8nJ\nqQwcODhkPjUJIRrPYrEwdux4tm/fQl5eLtu3b2Xs2FuxWCxtHZpoZSGdKA3DoLKyvE6SBCgpKWHH\njh3Y7TaWLHmfu+++n5iYWC5fvsyxYweYO/d2IiMjAc8Itw0bNpKdfYGLF7NQqh933TUXk8nE2bNn\nWbduBTfcMIrU1LS2qKIQoo3s3LmNTz/dQ0pKMpGRkVy4cIY//3k/o0ePYfToMW0dXrsQKo2IkE6U\nWVnnUap/nWNbtmyhqqqKSZMmYbPZmDJlChs3bsLpNMjLy+XBB++vc77ZbGbq1Cl88MEHzJw5jeTk\nfz3A79mzJz179uSdd95j8uSZ8klSiDBx5MhhPvvsEN26da05Fh0dTXR0NIcO7Sc+PlGeVRI6iTI0\nOpB9cLmc2Gy2mu8PHjxIeno6U6ZMqTlus9mYPn0aPXp0JT4+xue15s6dy/79+72WzZo1g/3797Ru\n8EKIdmv//t2kpqZ4LUtLS2XPnh1Bjqh9CqdF0Tusbt16cPy4rvk+KyuLAQMGeD13yJDBfh88R0RE\nYBiG17JOnTrhcFS0LFghRIdRVFTYonIROEopq1LqLaXUFqXUBqVULz/nvqOUWtjQNUM6UVqtVhwO\nN4WFnl/a2q1LbxrqOvWVKIUQ4cb/e0FZWQk7d27D6XQGKZ72yWw2t+irmR4A8rXWE4CfAy94O0kp\nNR3o3ah6NDeSjmL8+IksX76KTz/9tMFzy8vLfZZprenRo4fXssLCQqxWu9cyIUToiY72/ZgGwOl0\ncv78aV577Y9s2LAmSFG1P23U9ToV+Kj632uBW68/QSllB54Dnm/MBUM+UZpMJqZNm43JFMnp02f8\nnpufn8+FCxfqHS8vL2fRokX06eN9B7GVK1czcqTsFiBEuBg8eBgFBQVey3JyckhMTCQ6Opru3buR\nnX2OzZs3BDnC9qGNEmXN9o/VW0K6lVLXD1x9FngZaNSivCE96rW2rl27MXToCA4dOszw4cPqle/d\nu5ebb76ZU6dOcfDgQYYMGUJERARHjx4lPz+fIUNu5IMPPmLYsCE1r8/OzmbTpq0MHXojVmvY/K8U\nIuyNGXMr+fl5fPHFKbp06YzZbMbtdnP69GmAOmMhEhMTOXbsCBMmTGpXA1RCgVLqMTz7JF/rCzcB\n17dazNe9ph8wSmv930qpSTRie8iwendXaiAHDuxj2bLlTJ48iejoaMrKytiwYSNFRaWkpaUwdepk\n3G43WmsKCwsZOXIk//znJ8yYMQ2LxcL58+dYvHgpZrOZ+PgEpk6dJb/8QoSh2bPnkpeXx+bN6zl4\n8CAREXZ69uxJTEz9btnISDunT5+ib99+bRBp2wn0e6PW+q/AX2sfqx6ckwEcvtaS1FrXflh8G9Bd\nKbUdSABSlFLf01r/xtd9wipRAtx440iqqhy89trfcburMJlMdO3aDYvFgtUayeLFS4iNjSIqKpr8\n/AJOnDjNtGlzagb6dO/eg+7dvT+rFEKEHpfLxdatmzh37ovqKWd2Bg4cwsiRo0lKSmLevHsoLCwg\nJcX3riFWq5WKivAbGd9GjYg1wILq/94B1On31lr/Hvg9gFJqIvCwvyQJYZgoATZvXs/8+XeQnp5e\nc8wwDD7++BMGDhxOUlIylZUVDBwYI61FIcJYVVUVCxf+meTkRJKT/7W9ltaHOXXqc+6917P9blRU\nNIZh+Hy/KC4uoU+fvkGJuT1po7Ve3wOmK6W2ABXAVwGUUs8AG7XWu5p6wbBLlEePHmbUqJvqJEnw\nfPK54465LF68hKlTZ2G1xrZRhEKI9uLjj5eQkZFab2pZYmIiJSUlbN26ifHjJzJhwiQ++WQxXbp0\nqXcNp9NJYmISUVFRwQo7rGmt3cCjXo7/0suxTcCmhq4Z8qNer3f16mV69vS9Y0iXLukUFOQHMSIh\nRHtkGAY5ORd9zr+OjY3l1KkTAHTu3IVhw27i3LnzuN3umnOKioq4fPkqd999X1Bibm9CZWWesGtR\n2mz+q9y9e3cuXLhMYmLr7FJeWVlJUVEhMTGxshasEB1IWVkpDS0s4HBU1vx7zJjxDBw4hI0b11JS\nUorJZEapodx006h29aYfTKFS77BLlFVV/lfKuHTpMsnJLd8J5Pz5c5w8eZz4+BiioqLJy8ujqsrN\n+PETsdlkcQIh2ruIiEhcLrffc8zmuh9+ExM7MW/egkCG1aFIouygYmPjycnJITU11Wt5VlY2/foN\nadE9zp79gqtXs5k7d06d4w6Hg8WLlzB79h0y71KIds5qtdbZq/Z6bre71XqeQlWobNwcGrVoghEj\nRrN27XrKysrqlW3YsInevVs+z+nMmc+ZODGz3nG73c7cuXNkZwEh2pnCwgLWr1/Dxo3rqrtcPcaP\nn0RWVna98w3D4Ny580yfPqdemQg9YdesMZlMzJhxO2vXbsRkMoiJiaay0oHD4aBv34F069a9Rddv\naD5VbGwsVVWVPsuFEMFTVeXggw/epbS0mC5dOmMYBm+//Te6du3CrFnz6NWrD1OmzGTr1o1UVVUQ\nGRlJeXk5kZEx3HffV4iPj2/rKrRr0vXagVksFjIzpwCePxSLxdpqXQSFhYUkJSX5PUe6XYVoH95+\n+3XS0pLrzJHs2bMHFRUVLFr0Nvff/xX69etPv379ycvLIy8vl/T0DOLi4towahFsYdf1ej2bzd6q\n/eipqalkZ1/ye47DUdVq9xNCNM+pU59jtZq8fnCNjIyktLSY3NyrNceSkpLo16+/JMkmkOkhwquo\nqGgKCwt9rtJx4cIFkpK874wuhAicixez2bdvNwCDBw/l8OEDpKX5HuHetWsXdu7cxm233RmsEEU7\nFfYtykAYPXocixd/VG/T1kuXLrF7936GD7+pjSITIvw4HA7efHMha9cuJzLSSlSUjZ07N3Po0EG/\nr/PsCCKbtbeEtCjDgGfbnJNUVVXRu3dfIiMjG/W6+PgEMjOnsmzZasxmFzabHafTTVxcAtOnzw5w\n1EKI2hYtepu0tOQ6Xazp6ekUFRVRUlJCbKz35Srz8vIZOlQ+1LZEe0p2LSEtSh92797Oli3rSEiI\nomvXVA4c2MW6dSvrtRK9uXTpIjt2bCEqykZqaiput4HT6WLIkOFBiFwIcc3Fi9m43VVen0P27duX\n48eP+3xtUVEJQ4fK32xLSIsyhG3fvoXBg/vTtWvXmmOdO3emoqKCf/5zmd9nFpcuXeTUqWP1Fhtw\nOp18+OESZsy4HbtdVuYRIhj279/jdaFy8HSt9unTh/37P2Xo0CE1f5fl5eXk5ORw5513BzNU0Y41\nKlEqpYYCS4AXtdYvX1d2BjgHuPEsjPig1vpiawcaLA6HA3DVSZLXREZGMnLkDZw4oRkwQHl9/dGj\nB+slSfBMCZk37w7Wr99cMzVFCBF4/lomqampWCx27PYY8vNzAUhLy+CrX/0q+fnlwQoxZLWnVmFL\nNJgolVLRwB+AtT5OMYBZWuuQ+K3at28348eP81net29fli9f7TVROhwOYmOjfb7W84nV/9qRQojW\nM2TIMLZt20BGRobX8uLiYnr27M3NN4+tc1zmOreOUEmUjXlGWQHMBny1Ek3VXyHB4XA0uG+c2ey9\nuqWlpcTH+59jZbHIY2EhgqVXrz44HK46W1/VduXKVUaPHhPkqMJHqDyjbPBdW2vt1lo3tObaK0qp\nLUqpn7dSXG2mR49enDhxwme5w+HA8DFiPC4ujrw8/3tZVlW5WhKeEKKJFix4gHPnssjNza05VlRU\nxKlTZ7jzzgXt6g1ZtE+t0bz5EfAdYCIwTCk1vxWu2WZ69+7D0aPHfJZv3LjJ5ydQq9VKWVklLte/\nkmFZWRmff/45ly9fJjc3l6iomFaPWQjhW2xsLI899iSDB99EUVEZRUVldOvWm6997SnS09PbOjzR\nAZgMX82j6yil/gvIuX4wz3XnPAmkaa3/28+l2v0M3uzsbLZv387UqVOJiIgAPLsFbN++nZSUFG66\nyffcqpKSEpYuXcqkSZPYtm0bsbGx9OjRg/z8fI4cOcKtt97K8OEy5FwI0W4ErEm9Y8eOFr3fjx07\ntl0095v6xLpO0EqpeGARMFdrXYWnVfl+QxfJySlu4m2Dy2aL4+abM9mwYQvgxmQy4XBUccMNI0lO\nTqmJ/9y5s5w8eRy73YbbbWAyWbjllnGMGTOJRYve59FHH6lZR7Znz57ceOON7N//KVu37kGpgW1Y\nw8BITY1r9z/b1hRO9Q2nuoL/+hqGwbp1q8nOPo/D4XkqFR+fyLhxmS3efagtpKYGbu3aUOnWbsyo\n1xHA/wI9gSql1N3AP4EzWuulSqllwE6lVBnwqdZ6cUAjDpKoqCgmTJjss3zPnp3Ex0dx222zao6V\nl5ezfPly7PZIHnzwAa+LrY8YcRMrVqwKyUQpRKgzDIN3332LhIRYevasmxTXrVvBhAlT6dOnbxtF\n1/6ETaLUWu8HfGYMrfVLwEutGVR7d/FiNlFRNm688cY6x6Oiopg/fx5vvfWW35Gz6elp5ORcITXV\n94LMQoj25+DBT4mMtBITU38aWK9ePdm2bZMkyhAkcxWa4dixw4waNdJrmclkIibG+9qR1yQmJlBS\nUhKI0IQQAXTixDG/+81aLJ7VuYRH2EwPEfXZbDa/P0SbzX9D/dy5LDIyOrd2WEKIAHO5/K/1HBcX\nx6VL2UGKpv2TRBnGfE1eviY2Nhattdcyl8tFcXFpg4saCCHaH4vF/4fgwsIiOneuv/xluAqVRCnr\nNDVDTEwceXl5PrtgysoqOHcuGzCh1ICa46WlpaxYsYqpU2d5fV1jHD16mIsXs7DbPT86h8NJt249\nGThwcLOvKYRonIEDh3Dy5GckJyd7LTcME+np3pfLEx2XJMpmGDFiNMuWfcRdd92JzWarU3b8+HGS\nk9O44YYRfP65ZsOGDTidBm63G5stgpkzb8dma97uIbt37yAtLYnZs2fUOX7s2DH279/DiBGjm10n\nIUTDhg+/kWPHjnjdx/L06TNMnjzDxyvDU3tqFbaEJMpmMJvNzJhxOytWrCE+Poa+fftQUlLCmTNn\nSUlJ54YbRgDQv79i3LhRrTL/rKysFJerkv79+9UrGzRoEGvWrMPhcMgWXkIE2L33PsjGjes4d+4s\nDhYAVWYAACAASURBVIcDkwni4hKYNWuudLuGKEmUzRQREcH06bMpLy8jK+s80dGxTJ48M2D327t3\nFxMmjPVZfuutY9mzZxfjxk0IWAxCCE8rafLkaW0dRocgLUoBQFRUNP37e9+bsjUZhttvazE6Opqq\nKkfA4xBCiHAjibKNGIbBgQP7KCjIw2Ix43S6SEvrzNCh3teBNZnMfrtWy8rKmv3sUwghAkFalKLZ\n3G43y5YtZcKEcaSljag5fv58FqtWfcKMGbfV+wUbNeoWdu7cRWam967V7dt3MnbsxIDGLYQQTSGJ\nUjTb1q0bmTFjKnFxdUfNde/ejaioKHbv3sEtt4yrUxYdHYPZbOfzz0/WG9Bz7NgxYmMTZCCPEKJd\naYtEqZSyAn/Hsz65E3hEa/3Fdec8D0zCs9HHEq31r/1dUxJlG3C5quolyWtSUpIpLd3nteyWW8Zx\n9OhhVq5cg81mATwbQXft2oORI28OWLxCdHRVVQ42b95Afn4eJhNERcUwefI0oqLqr9kqOrwHgHyt\n9ZeVUtOBF4D7rxUqpYYAk7XWtyqlTMBRpdTrWusrvi4oiTLI3G43ERH+W352u81n2ZAhwxgyZFiz\n7+90OikrKyU6OgarVX78IvRdvnyJZcs+om/fPnTv3gWAqqoq3nvvTcaPn0S/foEfjBeu2qjrdSrw\nevW/1wILrysvBCKUUnY8OdAFlPm7oLxTBpnJZMLp9L9epMvlavX7FhUVsHPndiIirMTHx1FUVIzD\n4WTUqDF06uR7kWchOrqVKz9myJC6K1fZbDYGDRrI5s0b6NWrr3xoDJA2SpQZQA6A1tpQSrmVUlat\ntbP6WJZS6gPgLJ5lXH+qtfa7S4X8dgSZyWSiqsr3WrGGYfgtb47i4iK2bt3IbbfNrvOLaxgGK1as\nZMyYCSQmSrIUoefYsaMkJSX6LO/Tpxfbtm1m4sQpQYwqfAQ6USqlHgMeB4xrtwSufw5lvu41vYF5\nQC8gAtiulHpPa33V131kUfQ2MHDgEDZv3uK1bPXqtYwYMapV77dr1/Z6SRI8v8SzZ89i795drXo/\nIdqLM2dOkZbme9/XqKgoCgrygxhReAn0ouha679qrcdqrcdVf43F0+2aATUDe7jWmqw2Gtilta7U\nWhcBh4Ch/u4jLco20LVrN5zOKlasWEVGRvr/b+/eg6LK8gSPf5MkeaOAIAooguhBFAV8I2pZallV\nlmVZz57q3u3qnd4/Jmand7ojJnp3Y3p7e6Knd6djuzd6/piYmN2e3ejo7tm17K6Xj6qyLBUVUAHf\nj6MoiooiKk8lIR93/0hAkMwEIZOEm79PREXBPTdvnuMh83cf5/wOM2akc+fOHZqamlm8uISUlNSA\nvl9EhO8zO4vFgtVqjiHcQjzLarXidruJiAjMNYHL5cJisQTseCIo9gPv9P7/deDgM+V1wL8HUErZ\ngELgur8DSqAMkezsHLKzc2hubqK5+SFZWXksXhyckatWq/8PdUSENSjvK0SorVq1hj17/sjcuXO9\nlt+9e5dFi7wvwj5QeflBbt++icPhANxER8exeHExBQV+L0REaPw/YLNS6ghgBz4AUEr9EDiktT6u\nlPpSKXUMzy3bf9JaN/g7oATKEEtLSyctLT2o7+F0+h8c9DyDhwzDoKOjHbAwZcqUMdZMiOCaOjWJ\n2NhEHj9+THx8/KAyh8NBZ2cXeXnz/B7js88+IjraSl5e7qDtly+f5cmTxyxbtjLg9TaLUAzm0Vq7\ngX/jZfvfDfj5J8BPRnpMCZRhwGq10dXV5XWx6J6eHkb6qPr48Qra2h6RkpKEYRi0traTkpImczjF\nhPbGG2+ze/fH3L59h6ysTKxWK7du3SY6Oo733vuW39fevn0Lu/0x6emzh5RlZWVx8eI5SkqWExER\ngWEYPHjQjNUa6XOt2nAjmXnEpFFW9gK7d3/Myy9vIi7u6QTrrq4u9u37gq1bdwx7jIMH95Ofn8eM\nGcWDtt+6dYujRw9RVvZCoKstREBYLBa2bdtBT08Pp05V43Q62bHjPeLjvSf9GKim5gSzZ8/yWZ6Z\nOZOTJ4/T1tZKU1MjcXExuFwunE43ubnzWLVqTSCbIkJEAmUYiIyMZNu2HVRUlONwdGO1RuByuYmM\njGLr1h1DFp9+VkvLI+LjY5gxY+jK7bNmzeLmzQa6up4AiUFqgRBjFxUVNSQ15HDcbrffq6LExEQO\nHTrA8uVLyc+fP6isufk+Bw9+FdZLcskVpZhUrFYra9duGNVrT52qYf16318wK1euoKrqOLNnvz7a\n6gkxIVmtVgzD8PmF39LSQmxsDAkJQ69O09JSuXz5SlgvqG6WQCljnMWwLBb8Doe32Wy43YHPJiRE\nqJWWruX69Xqf5ZcuXWbFiuU+y3NysqmoKA9G1SaFYM+jHC8SKMWwIiM9g4F8aW9vJy4u3me5EJNV\namoaaWkzaW5uHlJWX3+D+PgEvyeR0dHR2O32YFZRjAMJlGJYK1aspqrKd/ae48dPyMhXYVqbNm0h\nM3MO16/fROurXLlSR0PDHVavXs/s2XP85m5uaWkhPX3os/1wYZYrSnlGKYYVHR1NauoMTp8+Q1HR\nkkFl1dXVzJqVi9UqSQuEeRUVLaWoaGhigrS0NHbt+h35+fleX3f3bhObN28LdvVEkEmgFCOyeHEx\nN2/eYP/+g/1rYTqdbgoKCsnMzApx7YQIjdjYOPLzC2louMbs2U/nWhqGwdWr1ygtXTehrozGm1na\nLoFSjFh29hyys+eEuhpCTCjLl68iLW06NTUncDi6AQsxMbFs2fIaqalpoa6eCIARBUql1CLgY+CX\nWut/eKZsE/C3gBPYp7X+acBrKUKmq6uLiopyDMNFREQELpeLhISprFq1xjRni0KM1Zw5ucyZkzv8\njmHGLN8RwwZKpVQc8Pd4Vor25lfAZuAucFgptUtrfTlwVRSh0tHRwcGDX7Bly+ZBC9u2tLSwe/dH\nvPbaDtN8EIQQwpeRjHq1A6/gCYSD9C6A+VBr3ai1NoC9wMbAVlGESkXFYV55ZcuQ1d+Tk5NZtWo5\nJ05UjvhYd+82cvjw11RVHcPh6Al0VYUIiO7ubmpqTlJRUUF3d3eoqzPphc2o195M7N1KKW/FM4CB\nE4zuA3L/wQQcjh6ioiJ9zhFLSUnh9Olzwx6nra2VI0cOkpU1k1WrlmK32zly5AA2W8yoMwUJEWhu\nt5u9ez+hs7ONzMxMurosVFfXkJAwla1bt8v6k6M0kYLdWAR6MM+I/lXS0sIrJ+hkbG9TUxPTpvlf\nASEmxjakbQN/dzqd7N69i5deeqn/AxMXF8fatWU0NTVx+nQVmzdvDnzlx9Fk7NvRMnNbf/Ob3zBt\nWhKzZmX0bysoWNC7cMBHfPDBB6GrnAi5sQbKRmDmgN8ze7f51dzcMca3nTzS0hInZXu7uy20tbUN\ns49jUNuebWtl5VFKS0sHnVW63W7Onj1Le3s7TU33WbRo2ZBbu5PFZO3b0TBzW5ub79PV1UVGRsaQ\nstjYWBwOB+fPXyE9faaXV09+wTwBMssV5fPeTxjUaq31TSBRKTVbKRUJvAZ8GajKidCJjY2lq8v3\nMxq73Y7NFu33GE+edJKY+PRDeObMGQ4ePEhWVhZlZWUsXVrCrl2/5+bNG4GqthDPrbr6OLm5vp8Y\nzZkzh5qak+NYIzHRjGTUawnwCyAbcCil3gI+Beq11p8Afwb8X8AA/kVrXRfE+opxtHBhEeXlR1i3\nbu2g7Q6Hgy++2M+2bW/6ff3As8mLFy8SHR3Niy++2L8tJyeHnJwcjhw5RkJCAtOmpQa2AUI8o6mp\niZMnKzEMN1ZrJKWla/2uDgJ9f8fG+FXSRMxyRTmSwTy1gM9RF1rro8DzLfImJoXMzCwsFgsHDhzC\nZoskPj6O9vYO3G5617H0v3SQYYDL5cJqtdLY2MjGjd4HRJeVlVJefozNm18NRjOEAGDv3k9xOOzk\n5uZgsVhwu9189dVeurq6iY+PISlpqtfXtbe3k5IiiQPC2eR8OCTGTUZGJhkZmTgcDux2O/Hx8SMe\nAbhs2UoqK6soKSkedAv2WZ6h4IO3tbW1cvHieSIjbSxZUhy26/mJwDh2rJyEhBhSUp4+h4yIiCA/\nX9HY2MihQ4d4443tXl974sRJvve9vxqvqpqKWa4oZcyzGBGbzUZiYuJzDZOfOjWJGTOyOHy4HJvN\n5nffvg9Ud3c3e/Z8zLlz1SxYkMecORmUl+/n4MH9GIbc/hKjc/v2TVJSvI/izsjIICYmmhMnTuBw\nOPq3OxwOTp48yfz5855rzrAwH7miFEG1YMEiZs3KZt++TyguLva5n9PpWfh5375P2LTpxf6RsDEx\nMZSVraGlpYUDB75g06aXx6XewjwePnzA48edfvdJT0+nsLCQCxcu4HK5+ie8FxUVERMTw7VrN8an\nsiZjlitKCZQi6BISEklLm0F7eztTpkwZUl5Xd43s7LlcunSeRYsKvE4XSU5OxmqFJ08eyyLRYsRc\nLhefffZHIiP9LwNnGAbR0dGUlJT42MMcX/hidOTWqxgX69dvpKrqJNeuXevfZhgG1dU1tLU9Jj9/\nAY2Nd8jK8r1k17JlS6muPjEe1RUmUVFxhIKCfL+LK4Mnf7Ev3d3dJCYOPcETwwubFHZCBILFYuG1\n13ZQV3eVw4ePYbVG4HYbFBUt7V+KaLjPhc1mw+VyjUNthVk8etRMXl4u06dPp76+npycnCH7XLx4\nicTEJJxOp9e7GZcuad5991vjUV3TmUjBbiwkUIpxlZc3j7y8eV7LbLYo7HY7MTExXsuvXq0jJ2du\nMKsnTConJwetNSdPnqSgoID4+HhaW1u5ePEiycmpfPvb32XXrt+TljaNmTM9GXgeP37MlSt1rF27\nQUZdhzm59SomjJUr11BZWeW1zDAM6utvMmfO0CuCyaqnpwe73R7qapiazRaN2+0GQCnFsmXLuHnz\nJjU1Ndy/f59p01LZvPkVoqKieP/9D5g9ex43btyiqakJhwPef/8DWWdSyBWlmDiioqKYN28Bhw+X\nU1q6un9KSWdnJ0eOHGPduk0hrmFgnDlzitu3b2CzeVZnsdu7SU1NZ9WqNaGumumsWbOOL774lIUL\nFwKeuZN9P7tcLq5cuUZSUnL//krlo1S+qXPbjie59SpEEOTlKTIysjh+vAK324VhuImLS2Tbtrcm\nbfL0gaqqjhEdHUFp6apB2+/fv89XX30u018CLCoqmtbWDiorK1m+fHn/31BLSwvXr9/knXfeD3EN\nzU0CpRBBEhcXz4YNk3v5LW8cjh4ePrw/JEgCTJ8+nXv3mnj48IHkvB2hlpYWOjraSUubTmxs7JDy\n7u5uPvzw95SVrcZut3P27FnAs4JNa2sbb7/9vtfXicCRQCmEeC7Hj1dSXLzEZ/miRQuprT3J5s2v\njGOtJp+rVzVnz9YSFWUjPj6O6uoKLBYrmze/SkJCQv9+hw59RXHxYiIiIoiLi2P58uWDjnPiRAU7\ndrw73tUXk5AESiHGSXe33e8VzPOkBwyEzs5OamtPYhgGxcVLmTLFe1LwiaSuTnP58jkKCxf2b8vK\nysLtdvPRRzt5991vEh3tWf6to6MNmy3T57Gczh56enpkRKsJKaXWAzuB72it93opfw/4AeACvtZa\n/7W/48moVyHGydSpybS2tvosdzqdWK3+M8gEgsvlYs+ejykv3092dgY5OVlUVBzi00//MCjX6UR0\n9uwplJo/ZHtERATFxYs5fPjrER8rJiaaJ08eB7J64hmhSDiglMoFvg8c9VEeC/xXYIPWuhTYpJTK\n93dMCZRCjJOSkmWcO3fBZ3lt7SlWrgz+inW7d3/MggXzSUxMoKamhpqaGvLy5rJ48UI+++yPQX//\n0Wpvb8dq9f2VFRUVRWdne//vFov/r7euLjsJCb5XtRFjF6LMPI3ADqDdW6HWugso1Fo/6d30EJjm\n74ASKIUYJxEREeTl5XP27LkhZXV1dSQnpxIfn+DllYHT1NSEy9VNZWUlcXFxrFq1iqVLl3L58mWq\nq6tJTU2hoeFGQN7LMAza29uGTUg+Uo8fdxIb6z0ZRR+L5ekKM+npnvzC3rjdbqKiYk0xkloMprW2\na639LjWktX4MoJQqBLIB7xO4e8lfiTCtU6dqaGpqJCLCgmEYREREsmbNupAmVS8oWMStW4lUVVVj\nGE4slggMA+bOVaSlTef48QpiY+NYuLAwKLdhq6ur6O7uZsOGp2uxR0ZGUlJSQktLC1evXsVudzB7\n9pxRv4dhGJSXf82DB/eJi4vF5XLhcDjJzs6lpGT58AfwITU1lY6O4eY2Pj33X7NmPR9++HtycmYP\nWg/V6XRSW3tapoaYgFLqT4HvAgaezPUG8GOt9f4RvHYe8DvgT7TWfnNjSqAUprR//z6yszMpK1vd\nv83pdPLFF7vZsOGlQZPMx9usWdnMmpXd//vjx5189dXnNDbGk5eXx5MnT9i372NSUtIoLV0X0Pdu\naLjBq696n6uZnJyM0+kccz7dPXs+IStrBtnZg5dVu337NhUVRygtXTuq49psUURGRuNyubyeRNy/\nf39QikOLxcI777zPkSOHaGi4jGG4AAsJCVN4991v+UyVKAIn2NNDtNa/Bn79vK9TSmUBfwS+pbUe\neovnGRIohelcvHiezMx0MjIyBm2PjIxk06YXKS8/zNatb4SodoO53W727PmYDRvW9496jYuLIzU1\nlcbGuxw7Vs6aNYELlklJSX4X0Z4/fz5Xr9aP+viNjXeIjo4kKSlpSFlWVha1tadwOBzDLuTty0sv\nbWXXrt+zZEnhoEB37949Ojq6KCsbnL3JYrGwbt2GZw8jxskEmEfpqwL/C/gzrfWZkRxEAqUwnYaG\n+kFXkgNZLBbi42Pp6OgYdDsuVE6cqGLZshKvU0MyMmZy40aVzyuo0Zg61f8UEKvVyty5Q0eVjtSZ\nM7Xk5+f5LF+wIJ/jxyspKxtd8I+NjeUb3/jXHDt2mJYWT0C3WCzk5s5n3bqiUR1TBE8oAqVS6lXg\nrwAFlCil/kJr/bJS6ofAIeARUAb8jVKq73btL7XWu30dUwKlMJ2ICP8fzpkzZ3DvXiOJiSrodTEM\ng+vXr+Fw9JCTM7d/jl+ftrZHzJuX7ePVoNQ8zp8/y5IlxT73eR4REZF+A++VK3W88sr2MbyD4ffL\nMTY2lidP7o3h+J7l1l54wRx5f0Xg9c6bHDJ3Umv9dwN+fa5RcxIoxYR161YDFy6c6Q98brdBYWEx\nmZm+F3cGT3Dyp6Wllby8goDV05fKyqM8fNjE7NmziIqK4tChL3C7YfPmV0c82jIuLo6HD5sCVqfV\nq8s4fHg/y5YtHVJmt9uJiooZ07M7q9Xmc11HgAcPHjB9evqojy9EKEigFBPS+fNnaG9/xNq1g+cV\n1taepq2tlYKCRT5fm5iY5PfWaktLa/9i0cFy9OghUlKmkp//tP7p6el0d3fz6ad/4M033+vdasHt\ndvvMynP1ah2LF49+pOizpk5NYv78RVRUVFFcvKQ/U1B9/Q2amprZvv3tMR1/9eoyDhzYS1GR91R9\n16/f4J13vjmm9xCTxwR4RhkQMo9STDgORw+3btWzZMniIWUlJUXU11/xOzJz5cpSjh6t9Jpl5tSp\nM8yb5zcJx5g5HD20t7cyc+aMIWXR0dHMmzeXy5cvArB8+Wpqa095PY7b7aatrZNp0/zOhX5u+fkL\n2L79be7cuc/585c4e/YimZlzePPN98b8LDQxMZEZM2Zx/frgAUGGYXD+/HmKipab5stTDC9ECQcC\nzjLcbaogMMJpnbdwWtcuUG09evQwSuUSFxfntbyjo4MbN+74Xb/R4ejhwIEvMQwXKSnJPHnyBLu9\nB6UKyM31Pdjkefhq77Fj5eTkZPnN63riRA1btrwGwOnTtTQ13aakpLj/yrKtrY3q6lpeffWNQYm+\nQ+V5+7auTnPx4rn+RZOt1khWrCglPX3oycNEFGaf26BFpJaWljEFmOTk5AkRLeXWq5hwurvtPoMk\neK5ahsv2YrNF8fLLr+F0OmlrayU2NnbcEg3Y7f6Tn8Pg9GpFRSU8ejSHkycrAQPDMJg6NYW33vqT\nccn9Ggx5eYq8vOAPlhJiPEigFBOOxWLxOzLT6XQSETGyABIZGTnu6zvm5s6lvr6enJwcr+We+g9+\n6pGSksKWLVvHo3oBd+1aHdev12GzRbJixeqQZj4SE8tEun06FvKMUkw4JSXLOX3a9zzgmppTrFgx\ndPHjiSInZy4NDbd9lldX17B6ddk41ig4mpvvs3Pn77h79yZK5TJr1kwOHNjH55/vHnbksQgPZnlG\nOaIrSqXUL4FVgBv4S6119YCyeqCht8wAvqm1vhuEuoowkZSUjNNp0NTURHr64KkEd+/eJSLCFvTk\n4WO1evV6Dh06SGnp6v71Dg3D4PTpM2RkZE/4+g/H8wz4c0pLn56w2Gw2lixZTGtrK19//SUbN24J\nYQ2FCJxhA6VSah2Qp7Uu7V2z65+BgWP2DeDl3qVLhAiIF198icrKY1y+fIXk5CQMw6CtrZ3U1Om8\n8MLGUFdvWOnp6bz88naqqo7S3W3HYgHDgJKSFaaYR1hRcZTiYu9TQJKSkrh2rX5MqeqEmEhGckW5\nEfgYQGt9WSmVpJRK0Fr3jaaw4DufnhCjtnr1mt4A2YrFYmHq1KH5Qyey2NhYNmzYHOpqYBgGNTUn\nePiwGYDExKmsXFk6poFCnZ3txMb6TvyQl5fLuXNnKClZNur3EJPfRLp9OhYjeUY5A2ge8PuD3m0D\n/aNS6ohS6mcBq5kQeD5oSUnJky5IThSPHj1i587fEh8fxZIli1iyZBFpaUn84Q//wr17jUF738jI\nSJzOofNYhZiMRjOY59lThB8BPwDWA4VKqTfHXCshREAcOLCPdevKSE5+uqxYYmIi69aVUV7+9agH\n3dhsUTidTp/l165dp6CgcFTHFuYRToN5Ghl8BZkB9A/W0Vr/tu9npdReoBDPOl8+paWFftWG8RRO\n7Q2ntsLEbu+FCxfIzZ3j8wtn0aIC6urOU1pa6rX8WQPb+vrrr7Jz506Kioau2OFwOIiKspGTM3N0\nFZ8gJnLfivE1kkD5JfBfgP+plCoB7mitHwMopaYAO4FtWmsHnqvKD4c7YLhkvICwy/ARNm2Fid/e\nM2cuUFi4wGd5SkoKZ89eZN684dvgra1KFXL8+AmWLFncn0j9zp073LrVyI4d70zof5vhTPS+DSQ5\nIRjesIFSa12plKpRSh0DXMCfK6W+DbRqrT9RSu0BqpRST4BTWus/BLnOQogRMgz/y14ZhnvUx1Zq\nATk5c6moKKer6wkAubnzWL1aFkoWHhPp9ulYSK7XIAu3M9NwaStM/PY2Nd3j0qUz5Od7TyXX0NBA\nSsoM8vKGX6h5orc10MKpvcHM9drZ2TmmAJOQkDAhIq1k5hHCpNLTZ9Da2k5PT8+QMpfLxc2bt0cU\nJIUId5LrVQgT27r1Dfbu/ZS4uGgWLizAYrFw6dJl2to62LZNBqiL4DLLrVcJlEKYmM1mY/v2t2hp\neURtbTWGYbB4cYkpsgMJMV4kUAoRBpKTU9i48aVQV0OEGbNcUcozSiGEEMIPCZRCCCGEH3LrVQgh\nRFDIrVchhBAiDMgVpRBCiKCQK0ohhBAiDEigFEIIIfyQQCmEEEL4Ic8ohRBCBIU8oxRCCCHCgARK\nIYQQwg+59SqEECIozHLrVQKlEEIIU1FKrQd2At/RWu/1Ur4Y+DVgAJ9qrX/q73hy61UIIYRpKKVy\nge8DR/3s9k/Ad7XWK4AFSqkYf8eUK0ohhBBBEaJbr43ADuCfvRUqpaYD8VrrMwBa628Od0AJlEII\nIUxDa20HUEr52mUO0KKU+t9AHrBLa/0rf8eUQCmEECIogn1FqZT6U+C7eJ41Wnr//2Ot9X5/1cIT\nLF8HuoFKpdSXWutLvl4ggVIIIcSkpLX+NZ5BOc+jCbigtW4FUEodBRYCPgOlDOYRQghhVkMuabXW\nN4BEpVSSUioCKAK0v4NIoBRCCBEUFotlTP+NhlLqVaXUQWAL8DOl1Oe923+olFrZu9sPgM/xjIz9\nUmt9zm87DMMYVWXGwGhu7hjv9wyZtLREwqW94dRWCK/2hlNbIbzam5aWGLQHiS6Xa0wBxmq1ToiM\nBfKMUgghRFCYJTOP3HoVQggh/JBAKYQQQvgxoluvSqlfAqsAN/CXWuvqAWWbgL8FnMC+4XLmCSGE\nCA9hc+tVKbUOyNNal+KZ2Pn3z+zyKzzpgsqAl5RS+QGvpRBCCBEiI7n1uhH4GEBrfRlIUkolACil\ncoCHWutGrbUB7O3dXwghhDCFkQTKGUDzgN8f9G7zVnYfmBmYqgkhhJjMQjGPMhhGM5jHX+0nTsuE\nEEKIABjJYJ5Gnl5BAmQAdweUDbyCzOzd5o8lLS1xxBU0g3Bqbzi1FcKrveHUVgi/9gaJKS6eRnJF\n+SXwNoBSqgS4o7V+DKC1voknZ95spVQk8Frv/kIIIYQpjCiFnVLqZ8B6wAX8OVACtGqtP1FKlQE/\nx7O8yS6t9f8IYn2FEEKIcRWKXK9CCCHEpCGZeYQQQgg/JFAKIYQQfkigFEIIIfwI6jJbSqlFeLL6\n/FJr/Q/PlNUDDXjyxxrAN7XWd4ceZXJQSv0cTxo/K/DftNYfDSgzXT7cYdprmr5VSsUC/wdIB6KB\nn2qt9wwoN1XfjqC9punbPkqpGOA88Dda698M2G6qvu3jp72m69tACVqgVErF4ckL+5WPXQzgZa11\nV7DqMF6UUi8ABVrrUqVUCnAK+GjALr8CNuOZf3pYKbWrNx3gpDSC9pqmb4FtwEmt9X9XSs0G9gN7\nBpSbqm8Zvr1m6ts+PwIeetlutr7t46u9ZuzbgAjmFaUdeAX4Dz7KLZhkMipwGDje+3MrEKeUsmit\njYH5cAGUUn35cCfzB85ne3u3maZvtdY7B/w6G7jV94sZ+9Zfe3uZpm8BlFIKyGfwyYAp+xZ88aWP\nWgAAAiRJREFUt7eXqfo2kIIWKLXWbqDb0y8+/WPvH+QRrfV/ClZdgq03QPSdhX0X2DsgaHjLh5s7\njtULuGHa28cUfdtHKXUMT+ap1wZsNl3f9vHR3j5m6ttf4Jkb/sEz283at77a28dMfRswoRzM8yPg\nB3gSGRQqpd4MYV0CQim1HfgO8O/87GaaMzY/7TVd32qt1wDbgd/52c00feunvabpW6XUvwIqejOM\ngcnzWI+gvabp20ALWaDUWv9Wa/2g98pzL1AYqroEglJqC/Af8dzj7xhQNJp8uBOen/aaqm+VUiVK\nqSwArfUZIFIpldpbbLq+Haa9pupbYCuwXSlViefOyF8rpV7sLTNd3+K/vWbr24AK6qjXAQaduSil\npgA7gW1aaweeM5gPx6kuAdfbnp8DG7XWbQPLtNY3lVKJvQMjGvHcyno/BNUMGH/tNVvfAuuAbOD7\nSql0IF5r/QDM2bf4aa/Z+lZr/Y2+n5VSPwbqtdZf95aZrm/9tddsfRtoQUth15tA/Rd4PnQO4A7w\nKZ7O+UQp9Rd47pM/AU5prb8XlIqMA6XUvwV+DFzBc1JgAF8D58yYD3cE7TVT38YAvwZmATHAT4BU\nTJrreATtNU3fDqSU+s/ADTx/z6bs24F8tNeUfRsIkutVCCGE8EMy8wghhBB+SKAUQggh/JBAKYQQ\nQvghgVIIIYTwQwKlEEII4YcESiGEEMIPCZRCCCGEHxIohRBCCD/+P8XaFzDKFkd+AAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a803908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(8, 6)\n",
    "plt.scatter(*XY.T, c=m.X.mean, s=75);\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have identified the X-values in a way which looks sensible. Note that there is no way for the model to know what is start and what is end of the curve. This is not a limitation of the model, it is just a simple fact of curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "What does the underlying trend explaining the data actually look like according to the model?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Xnew = np.linspace(m.X.mean.min(), m.X.mean.max())[:, None]\n",
    "Ynew = m.predict(Xnew)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hi8jJOY1hGKSlDWDevBsIDz/3s0KIrtcF740+QN2h1jz/tkMASqm7gFXAeQ0F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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a803860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*XY.T, c=m.X.mean, s=75);\n",
    "plt.colorbar();\n",
    "plt.plot(*Ynew.T, lw=3, c='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very nice smooth curve which likely mimics my hand movement as I drew the shape."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How certain is the curve? Making confidence intervals in 2D is tricky. We can visualize the confidence intervals by sampling from the posterior.\n",
    "\n",
    "(Recall that the curve we are showing above is the mean of the posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu, va = m.predict(Xnew, full_cov=True)\n",
    "size = 100\n",
    "samples = []\n",
    "for i in range(mu.shape[1]):\n",
    "    smp = np.random.multivariate_normal(mean=mu[:, i], cov=va, size=size)\n",
    "    samples.append(smp)\n",
    "\n",
    "samples = np.stack(samples, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j72U32E3ncrm8GEOveZ5/AHgDXZ7MTxZF8cULtv0E8COABb5YFMVPPZdjXEoy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\nnd68wScmr/HA5nnkPJhWUcJXT3+G62KJt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dwes+iGHJmLODIIWNuumeQK1TSIRlNsb3Js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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e89c4d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*XY.T, c=m.X.mean, s=75);\n",
    "plt.colorbar();\n",
    "for s in samples:\n",
    "    plt.plot(*s.T, c='b', alpha=0.1)\n",
    "    \n",
    "plt.plot(*Ynew.T, lw=3, c='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## how does this relate to Single Cell Time courses?\n",
    "\n",
    "When we sample single cells from a time point in e.g. a stimulation experiment, we invariably see that the cells inside that time point are **heterogenous**. In fact, almost every single cell paper is about how heterogeneous populations of cells are. This makes sense, why else would you bother studying single cells?\n",
    "\n",
    "But _what do we mean_ when we say cells are heterogenous within a condition? (e.g. at hour 2 of a stimulation)\n",
    "\n",
    "From the point of view of trying to describe the data with a model, this means **some aspect of the data is not being properly modelled**.\n",
    "\n",
    "One likely source of variation inside a time point, is that cells are not perfectly synchronized. Within a time point, some cells will have gotten \"further\" responding than others.\n",
    "\n",
    "The great contribution by Trapnell et al 2014 (Monocle) was to point out that using latent variable techniques, such within-contidion variations can be detected, and considered in the analysis in a meaningful way.\n",
    "\n",
    "I like to think of each time point in an single cell experiment as a **shotgun time-course**.\n",
    "\n",
    "Analogous to shoutgun sequencing, where we sequence fragments of a genome, and assemble them computationally to a genome. We can measure transcriptomes of samples, and infer based on their similarites, the process that would explain the data.\n",
    "\n",
    "Note that this is completely the same as clustering. In the clustering case, you measure a group of single cells, and you conclude that they are heterogenous within that group. By clustering, you are trying to explain the heterogeneity by assigning cells to sub-groups, thus improving the model of your data.\n",
    "\n",
    "The difference here is that clustering puts discrete values on cells, while latent variables (or \"_pseudotime_\") puts continuous values on them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### _Appendix_: What happens if we remove a slice, in terms of uncertainty?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mask = ~((XY[:, 0] > 3.5) & (XY[:, 1] > 0.) & (XY[:, 1] < 3.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HJOdak5OTuv76b2T6HO52415OHjFORzNfghotVHLECNndn5LUa2anmNkCSRdJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a39c4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*XY[mask].T, c='k', s=75);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m2 = GPy.models.BayesianGPLVM(XY[mask],\n",
    "                              input_dim=1,\n",
    "                              kernel=m.kern,\n",
    "                              X=np.array(m.X.mean[mask]),\n",
    "                              X_variance=np.array(m.X.variance[mask]))\n",
    "m2.Gaussian_noise.variance = m.Gaussian_noise.variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9GSZEyEmLUogwZLX6/w5rGBaiov7953vq1Cn+/vd/curUCdxuN+3bt2fChEmM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\niIiE+D8HtBzl1/mrYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a2972e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(8, 6)\n",
    "plt.scatter(*XY[mask].T, c=m2.X.mean, s=75);\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu, va = m2.predict(Xnew, full_cov=True)\n",
    "size = 100\n",
    "samples = []\n",
    "for i in range(mu.shape[1]):\n",
    "    smp = np.random.multivariate_normal(mean=mu[:, i], cov=va, size=size)\n",
    "    samples.append(smp)\n",
    "\n",
    "samples = np.stack(samples, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VVbcBfwTc95ztEfjeuq6bK3GASfL1aDW863z7O76F73jve1/wNUoK9pYdy8Yy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\nrOEveS6MPR50MO0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a87bda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*XY[mask].T, c=m2.X.mean, s=75);\n",
    "plt.colorbar();\n",
    "for s in samples:\n",
    "    plt.plot(*s.T, c='b', alpha=0.1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu, va = m.predict(Xnew, full_cov=True)\n",
    "size = 100\n",
    "samples = []\n",
    "for i in range(mu.shape[1]):\n",
    "    smp = np.random.multivariate_normal(mean=mu[:, i], cov=va, size=size)\n",
    "    samples.append(smp)\n",
    "\n",
    "samples = np.stack(samples, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2pxXzRcOsaZjXLdYFhIDgYb40TBcGFwLL2jKrLHvThtZ4tOqCZCxNF0XR9Yif\nHNE1efOb38JP/dR/z4kTd12ehg0Ijmwd50d/5O/wjW95OzsHNbvTikRJNkYZ9xwbkGWK/bmhaRy9\nImVzlONswAfBgw+9liPHTzIejkl0TtIbsXnfvdx3/0MInbJoDdY79mYNF6Y1WIFxHghsDDJObg04\nutFjPEjwLuA9GOtYtpZlbV/aX1gU3cEOy4jyBe9RTiaTAvhl4BiQAf+wLMuPPmv7E8DTQPfJBT9U\nluW5m3K00W3h/e//Pr7zO7+LD3/4Q1y8eJHhcMT7/qP/hIcePMlTp3dZ1pYAuADDfop3gV6umS4M\nUklEkKSJZDhImS1bsiRhY9DnPC1FDTpXrPdHIBRVY6jqliJP8B56SUKSCerGI4WjV2iKTLM2TMlT\nTdU4ZlXLsgmsD3PG/a5x88G8BboemllM5ImiW+Kw3KO8mmSe9wN/Vpbl/zGZTO4Ffhf46LO2B+C7\ny7KsbsYBRrenoujxwz/8XzznsX6RsDHKSVTLsrEkWtEaR69IWDSWe472mS4TpvOWWWM5OKhRSvDo\nEw9z7vQFAqqr94pgmmQcPXqCYjhm0QZcZdFSUpkWVXVXmgfzJU888gVS3fKGV93PW9/8DYTgEUIw\nKDT9Ql8usXfJsu5GmUoJBnmsxhNFN9PtNCp8MV4wUJZl+aFn/XgvcOqrniJWX1G0anWVEhAY200y\nnL64pDWWLNUcXSsoEs2XT+1xsDScO3uG00+dRiQ5wlqCb3DB4RvFGVtz3/1vJNXgfQAJrYGFMDx9\n9hSLvR3q2R6u3uPP/vLzfPQT/573vff9PHDvMaQQqzZbhvVRjqArdtCYLmg6FzhYdKPMIlPkaUwA\nj6Ib7bCMKK/6LCaTyaeAXwF+6nk2f2AymfzRZDL5uRt2ZNHL1lfKwsF0YTDu0oguMFsaamMZ9jMG\nuWb/4lmEzlFCdUtEZIpUCQhBQLB/sAOy6/xRJBopAqcunGF2sMCRoPsbpP0tdO8IF3aX/Na//jBa\nQt06dg5q9uctZy7OmS5bIKyCoqKbCOlUTXf/c7pon7P8JYqiCK5hHWVZlu+cTCZfB/wq8HXP2vQz\nwO8Au8BHJpPJ95dl+a+u9FpbW8PrOdaXrTvpfC+da2McTZjSs57huGBjmLGsLafPz9hZGPr9lNcM\n1/jdj19EZGsgEoI3qLQHPiDytFujaZcMeglN63De4ZxnOW0RQiCVIoSA6G3iggHnOHPmET73V5/l\nLW99K8aVFnd3AAAgAElEQVRCkBKRKAySNNEIKZACtkYF66OcZW2omq8k/PSL5JpGl3fiv+2d4k47\n35vhVky9TiaTXwDeRpcn81NlWf75s7b9JPBDgAX+vCzLn76efVxNMs+bgAtlWZ4uy/Jzk8lETyaT\nI2VZbgOUZfkrz3rux4A3AFcMlBcvzq7nWF+WtraGd8z5Pvtc69awt1tRtZYjwwJnLK4xBOfJhMDY\nbhQndUJAErwliK5urNAKb2q8bSGD4Dx1bZFSMFvOISiCFzjXgLcgFTgHwpMOT/CZLz3CXfe+hn6h\nqSpJr1I0uaatNFpJ6saitcQ2g8vH7rzH2oBrDLOrfHPfqf+2d4I76Xxv5gXBzQ6Uk8nkXcAryrJ8\nx2QyeTXwfwPvWG0bAv8d8GBZlmEymfzbyWTy1rIsP32t+7maqdd3Af/tasfHgP6lIDmZTEaTyeR3\nJpNJsnrutwJ/fa0HER0uIQRaG8gSzfogo7aWg3nD7qyGEBj1E/p5AkqwPl7DVHvY+gARDN5UtLNt\nqv2naOZnmS0rzj3zJFJ4nHd4AKVRMkVKgVCrouZCotIhQiY0YcCyaakb1/2BS4kUglQrEt213kq+\nKvNVSUmWfu22XFEUXbtbUBT9O4DfBCjL8mFgbTKZXLoCboEGGE0mEw0UdDOf134eV/GcDwBHJ5PJ\nHwL/BvjJyWTyo5PJ5PvKspzSZcD+6WQy+SO6keeHr+dAosOjahzGevJMoZXEmsD+rGHZOMKqjNzG\nMGWtn/KaV7+KtOij8xGBBNcucXbWTb/qHkEods+d5dyjnyYRkOui24mUeA/BtDjbEHyXmCOTAePx\nFrOlxXnPorHMFi2zRYtxnoNFgwdSHZeIRNEhcBy4+Kyft1ePUZZlA/ws8DjwBPAfyrJ89Hp2cjVZ\nrzXdHO/X2v6LwC9ez86jw8X5wGzZcrBKiunnCVJK8lwhdcqyckgFVe2wzjMoNMeP38UDD1q2z59n\nb/sUAYcQGpVpVJrjbYut9zHesPfMk2zc/QpqA/OdGQIIMhBsVzxdqJSN4ZD1I0fJkm6/bQtZIhn0\nEnanNdCNHke95MonE0XRi/YSzNBc3uFq6vXvA68AZsC/m0wmbyjL8vPX+qIxJz56UazzGOu7Sjm6\nvhyMxoOULNEkWjAImnllEKFlf9EyXTQ01nEwq1lWLeO1MaPxGk8w58K5syT5gGCWSKXBWly9g0zG\n7M8P2DCWo+MjUFuqusK0IIRBqpRRf8C9999PcF3BdGdhWGjWhzmJViwqiw+BAJzbWdLLk1h8IIpu\noluwPOQsqxHkyl3ApYI3rwEeK8tyD2A16/lmIAbK6NbwPqzaWq3K2IXAomoJdG+ORW273o+r1RYh\nBBZ1d69yumxpWk9rPMZ206DGeXTaJxtsopICq3NC8Hhh0b1j6HxEkq9Rm4pxMebY8buoakPT7CNZ\nYzw8wmg8pGoMTeuYL2p2DhLsIAXRrTwRSIpcMV9YslSyP284tt576X6JUXTI3YIR5ceB/xn44Crx\n9ExZlovVtieB10wmk2w1DfuNPLdYzlWLgTK6LmG1DvFSYRvjAz6ELrEmBJwDJQVKgrVdtZxhL6G1\nrushmQsWtWR9lHEwa9mZVZzPFb6ZEbxDpQMggAU12kAnA5yrGPUKMiWpvKXfzzgyPkmvSFkfZ9SN\nxVpPIiU60WSpoldoWhtoW0uqFYNCIYXB+4RESarGUmTxbRBFL0dlWf7JZDL5i9U6f8cqhwbYL8vy\nI5PJ5H8H/mAymRjgj8uy/NT17Cd+QkTXRUnJqJ8+57HxWo9cCpQUl0vD1a2lahzBBw4WDQroF5pz\nu0uWlWVYpGysZSwby0MP3s+pR7+AbxxSJwiVIZRC6pwgAoM05ciRMXVjyIQmIGicI/GGROaM1jOc\n8zggTxWJlmRKozLB+brhU3/0pzz22Jc42N9DBsODJzf5nve+j7e/9U0kMbknim64W1GZpyzLv/9V\nD33+Wds+CHzwxe4jBsrohkmTLjg9W5YorAuc312yP2+QAowLQCBLJEoJ5kuL0orxaJ1XvuqNPPr0\n6a5kHQ1KZ3hToXXC0ZP3Y4xDCIlSEFzA+kDTeqwPOBvIU4XxjsZ0o8jpsmZWWf7wkx/n4c9/Dpn1\nEbLAGMPnv/gwjz36CPXf+2/4jm/75tiGK4pusMOy3CoGyuimss6zP29YNoZepruydYuGnfPb/Mkf\n/xHnnjnAp+v0RiMeuOdBXvnq10E6ZHt3j2pxgEgL8l6PoxsbjMdDnLP4IJhXhkR1ayOVlDRtg1JZ\ntwSFQNsajHX084QL5y/y5fLLIBXBtgQtVpV9Epqg+Ve/+RHe9Ka3sDHOu6njKIpuiBgoo+gFeB/Y\nmzXszWqEEKSpYm/e8pm/+jwf++hvsagWKN1HprCY7bB79gle94Y38ZpXvYb96XEa51lWBucsAo1p\nWjySgEcBUivGwwzvAo2Bne0zPHXqDKZtEFqxvnac17/2AZ458zCm2kflQxASXAtBdOs0g+Ps+Yv8\nxWc/zxte/zqOb/RiR5Eoip4jBsro5hEgpGDczwgEqtrhvOeTn/gdprunQWqE1ITWI6QiqILyi3/F\nQw89RJJIrA+kiaINXaKQ1l1x9NZ5BAIBmNbRWsepc6e5+NSXELpACo3zLdPZgt29M/RVjUxyhEwI\ngJCSEDwq7RNsTdtMOXXuPPfe/wpcCGyN89hNJIpugDiijKIX0LQOLSXDXorzHi0lj3zxLzn1yH8A\nPMgEgkWmA5QeEERC08Lnv1By8v5XdjXR8QTAh0DrAnkqKZTEWIMxjqlr2d/bZ393jsw3Vlm4CYno\n4VzDfG67qdZ0iBCS4BpA4OwCnIHgSfMe999zD1VjSRPJojIAXSju/kNrGadlo+gaxUAZRS9AK0mW\nQKIFi9qicsnFC2eRaR+gG/3pAlzAiwofDLrYpAoe47o+kVpLKmHQAlobWLSWQZaQJQJjwBrPYlEh\nCEghce0M5yw66RNsRUhyWtlH99awi51uBGsqhAcpNc423H3PQww2jqO1QK9qwT672TN0SUm9PL5d\nouhaxEAZRS8g0fJyFmyWBJwP3HX8RNfxQ6iupVYIgCV4AWiEKlBkKODIKEdI2J9pEiXwAfYWDUkq\nCUJjbbf8BG9xIYBzeNt0b04B3jUkWR8vc06efIAzjx9Qzy4gfFdiLwjN2rDP+7/3/WSJpDGO/VlN\nlgiKNGG1JBTnAjEhNoquXQyUUXQNLi3qf893fTu/8Ru/wplzFwmuJaxKMyrdQ+gERc2rHryHfj9n\n0MtJtMA7QdW21K0nUQIpAopAkUqcB4JDCJD5mCAC0geC1F03EZVBsNx194TjW0c48/SXWG4/jdCK\n++6+m/e85z1sbhwhURJPYNlY9mYtyXrXlaRuLY3pMmmN9Sgpu0IKSqyWsERRdNjFQBndMiEElo3j\nB/+z/5wPfvCfs1guIASETiE4tE544+tex30nNtBaU2QS5wNZpqhaQWscUghCELigaJ3BBUk6KJhf\nWBISjU77q+DrkSpFSEF/0EMpwWBjnfWNb6bfSzkyLhgPUjbGPdaGKUWqaa0j1RIQ9DKNkgLrPN6H\nrguKC1j3lSnZdFYzrwyDIhZYj6LnE0eUUXSN6rZrv/W2t72T9bUxv/lbH+Opp8/g2zknTh7jNd/w\nLRw/+Uq0VtxztE+iBa3rwt5s2TAsNMMiJcsT9mc11W6LEHDXseO08xmLuiEEidTJKuPWo6TmyOYW\nrXFUbaCXSqSSzKoWrQS9tEEIaDJHmijW+hnGe1rrGRZdlm2WKka9FOv85XO45JB8DkTRTREDZRRd\no0RLfAg4F5i8+vX85H2v5GDe9ZEsCs0TZw7Ym7VkmWK2NGgpkYquqmwQBAT7lWFtNfWplSIET65T\n7nvgIU5dPMfi4jMEJxBaUmQ5R48dJc9yWusRBIwThNAFX6UlFw5qjAss6q6qUKo1/VzhArStRUqB\nFJJ5ZS4HSCm6KkRrgwzf2pfs9xlFt7tbUcLuVoiBMrpltJJo1b1xfAgMCk0/S5ktWxaNoZeneN8V\nKthfNMggSFKJc55RP2G28OwvDOcbh5ABAuRpRlUbFrVnfXicuzdP0pgWpRNGRYLSEus9wYP1UCQa\n77ulH4vKdOsyrWfUTxFC4EPAOM+8srTG0s8TxoOMRINWgmxVpk8IgVKH40MgiqIri4EyeklIIZBa\nsTFWJInE7QWOjCVrg5TtacXOfo33gcRJtBTUJrA2zMjShGXTYj0k2mFtwGcSHzTL2uIC6CSBIKit\nR4RAsA6dSBIlMSEwziTL1jCvzeV7kYtaM+5nFJletQFzLBuDtYG1QUYvV2RJfLtE0bWIU69RdIPk\nmfrKVGqiqFuHXBM0xnMwr3lmt6G1HmsVSghAEpynbTyN8wTnu6xXCVkiybMEoaGuDFVtsc6jvUAJ\ngzaOmYJekdLPE4Y9TfDwzO6SZdWSp5o0VQz7KUp31X8CgmXtqFtPqiVpImMB9Si6CjFQRtENkijF\n5qhgXneFzMeDjGLVJuuM8NSNwzlHr5egpSJtHdtthVSC0AYWjYMQ8EFigBPDlEE/4dFT+1gXkEoS\nrKUJ4GTgyTN7uGafXgJvfN0rGa+N0EqwtzAcSRTjVLM5TEm1pDGe1li0SvC+S0iqW0eexrZcUfRC\nYqCMohto0Eu6rh9W0guBAwI7BzWNExzdKAgIslUG6nTW0lpPCNDLW9qLFa1pEQGwnp1pw/6sZn/a\nrKZaU1ojmC1aqt2zVE0FWLBLnjr1OA/etcW7vvXbcM4znTeMioQL+zVaCYa9lCxRZFqidbdcxfkQ\nC6dH0R0kBsrottHLNW5pMMYjlcS5VRk8DfPK4oRg96DBes+gl0IIHM0zgg9c2INLPS6ny4al8d26\nSKlIVFeqrpruUqG7OdqgQEhcNeORx/bo9VLe/vZ3AYGmdTQ4KuM5FgIm1dRKcmScXy6cEEXRC4sj\nyii6wZTs7v/tzxvq1tLvaZSC2dJgXcA42xUdkIFeluJDoG4dWik2BjmOQK67xtB125IoRZFKlPDs\n7u5QOQ9SgUwBD0Ih9ADR7vOlh7/MN33TO0F09ySt91SVY1vUjAcZznl8CJzY7Mfi6FF0lWKgjKKb\noJclDApD3biuvk4ItMazqC3eecwqcQcPOpFc2FtSNRYhBHXj8AFOrPdIlGRZW5RWZImirupuQWZQ\nIDUED0p3L+Qy6uqAj//eJ3jP3/ouUq3IhULLLlNWCYEVYG3AOY/U8f5kFF2NGCij6CZZH+aAYL5s\nERJa48lSiXGOnb2GWWVYVC2JkiwWLa11IAStDdStZdk4goc07YJdbTwgQdI1bfZ21cDZgZkDjpD0\neOLUGU6fOY9zW2ytFRxZy6kqy2xpSFOB8z7Wd42iO1AMlNFtR0nZ1U8NoJRES433jn6hmW4anjg3\nZW9aMVsalsZhjCdPJcNCsagDTWtJlCbPE6TwKAdZkVJNK7pqAxqChWAAR3AOLzRapPzVFx5GZgP2\n5y0P3NUFRR8CEk0IMKsMSaL+xvRrCIE/+IPf59Of/hOqqmI0GvHud38n3/ANb34JfoNRdHuII8oo\nuonyVHcl44RACNidWmZLyz1HBwzyhNPbcy7uVaT7FfuLBh+6LFjrBM4GpPR4a0m0ZjTQvPm19/KJ\nT/4J6AEIB7bpgmU6RHiLbJcgJZWtGRSaqrZc3K9YVo5xX7MxyqlbR1JbtGopMoWxntY4vPf8ws//\nIx5++IsodWlaVvC5z32Gd7zzW/mxH/txtBKH5kMjiq7WYfmbj4Eyum31co3zhjzRpNowWxpmS9t1\nBCkSnPUoLRgNNDt7DTvTBuMdQQTqxlHXBiEk2ULR7ylOHL+PU2efQksJSkHT4l1AJjk664HQeN1n\nUbVordhf1MyXltom+K5iHmq17yKVXJw2bO8t+Hef+DgPP3YKla2zqkwLdDO9f/zpv+T4Pb/Pu9/1\nLopMASIGzeiOcVj+zmOgjG5bSkryVFGFrmj6dGnYnVVUjcM5T5oq/LLLUl1by6msh6YrYFA3nsYE\nrA+YqmFRSQbrGwwPLjJf1ggfcCEg7RSSDGQBCIb9LXZmLVIIjPOkWqHV/8/em8ZKdp53fr93PefU\ncte+3c2tuUh0SbJlWWNt1mbZsiQv8mxZHNjITAYZJHDmywT5knEQwB9sJBhgjAwGCAYwMpMAmXhG\ntjM2grHHHi+wLY9si9ZiUaJKpESRTbKX2913qaqzvVs+vHUvW7QWkiYpsvv8gMKtW3W66pxTt89T\nz/M+z//vuXbUIACtJb2L3BCJ66uAjJFHv/wVlN2A0K33fB0shUQi+ORDD/Hed7+XsF7fLK0axkwG\nbgtum0A5m80q4P8EzgEF8HPz+fzf3fT8DwE/D3jgN+fz+c+9PLs6cDtyUoI1UmFVnqc8XHS4ENnZ\nKNiZFiykwgfH2a2SutVoLbl+1GCNpO08nVeEkOj7xJm9e+me/hIxCWQxBjEBYUFAtTFiOimJMZdu\nrZaURiIT+JSQCZLP5s5N79hIiYlJ1MfXESllz63QAXE9gpIgeo5vXKIqFGJdRrbP6ZpNKd0yF5SB\ngVuR5yNY+ePAJ+fz+QeAnwB+4TnP/1PgbwHvBT48m83e8JLu4cBtz6jUWC3wgTxfWWm2pgYlxdqA\nWdP2CR8S47Gh6QNCSqSQTErDmY2CzUnWkx1PK87f+R1Uow1IARJURclkc4s7ds8SomBZOzqXmI4s\ne1sVxijKtaB62/Usm45VHWjbQO8FUpncICQ0CAVIiA58Df6Y0sCoNJRWrQ2gI03nWTaOo1XP4bKn\n6Qa7roFbj/zl8MXfXi18y4xyPp9/7KZfLwAXT36ZzWb3A9fn8/kz699/A/gg8MWXeD8HbmOUlIyr\nbMa8ObJcOLdB2weO6pa69UiZba+kECxXjt5li6yYQIvEyFg2xwU3Vh3eRcaTknJ0D2VxgUIJnJcs\nm54YI30U9D6gpEUKwda4oHeBg2VPVWi8TGitODuSjKYlMkTO3X2By08+DrIEu3FTkFySZMk997+J\ng0VLTjq//n/+QcRg4Fbk1RTs/io874WS2Wz2x8BdwEdvevg8sH/T71eBB16aXRsYeBaBQElBSDCu\nFHvbFVu15WjZc+nairKQWF2w2u8JPjIpDeNScvW4Z9E4khBYJYgerJL0JLo+EVXCaDBK0jlPFIEk\nBG3Xc/WwwfuEi4HDZUfXKYSWxMbTFZLRqML5yHe/5V1cubxP8p4cDRWYMaAZjQwf+OCPcbzqUUpi\nlMBqjTUSYyRN60mAMYMbycCtx20XKOfz+Xtms9lbgH8FvOUbbHZrnJWBVxU+ROrOMxkZehdZ1I6y\nMExHFq0kzkfkWuquc57+esQoxdakwmjD9aOWVe2AhFWClU/ElCiNJISQjaNbh/O50aa00DtB2zqO\nAKFy2beOgSIGOg9dLynLGiUFdrTNu977ER55+CGu7V8m9ksKHbn7nnv5if/sJ7jvnrMIIfAxEWMi\nJeh9pOlz+bW0eS6z7bNRdFXoQXR9YOBVxPNp5vlrwNX5fP7UfD7/7Gw207PZ7Mx8Pr8GPAPccdPm\nd60f+6bs7U1f9A6/FrmdjvflONZV47CVZTItOK49WsF4UjIZWZrOYyrLbjvmaNlxZqcipOwUcvmw\nxhrFznbFonbEkBAy4ZNHRoFUUFiLtlnRrsETY6BuwBQKIQu6EOi7PBbiYqJrYXNs0EpQt47zZ8aE\nmLjvgXv5gfd+N64+4ujogPvvu4fzZ88ghMBoyWRkUevgF0LEx8TRsmPUOqpSk5Ig1R0e0KVBCpHF\nFtT6p8w/v53cTn/HcPsd78vB7ZRRvh+4F/jvZ7PZOWC8DpLM5/MnZrPZdDabXSAHyI8CP/mtXnB/\nf/FX2OXXFnt709vmeF+uY/UhZ5HOB5xPXF11tKuenY2CZq3v6kNEpYSIiTNTS+d6Dm8E+i6yMQWr\nFMZC13ucz56SRkIrBCklrJVobVg1nrqPuBDYDzVWSaSSjApJFyK9S0gBW5VBl4qDo45JJfBIru4f\nc8fuhK2tbXqXuHJ1QdcHYkpoLTm7VWFN7niNKXG8ymMoQktSTHS1I8SIax1Gq78klydEdlOZVOYl\nP8ffitvp7xhur+N9Ob8Q3E6B8p8D/8dsNvtDoAT+wWw2+7vA4Xw+/3Xgp4F/TR4e+6X5fP7Yy7a3\nA7clWkmK9RqekpHOKRaNI8aEkAKrJUZLYozUbSAJmBQFxVkDJHof6Z2DJEFICq2IMSKFIEnou4gP\nidIqxpUmxp4QoWkDoUhUKlG3iZACeTIy0oaAaHpiTESnKEzkYCU4rnu2JgVaKZSWWZC9czRd4GDR\nsrtRMi5zx25KYG0+rhATZp1BCiHYHGd3lBgTISRCjLR9wKVAiHnU5GRcM5HLuSc8ez99ze/p2YdA\ngNXylrmQDbw6uVX+vp5P12sL/NQ3ef7jwLtfyp0aGHgupdX0vkcqyaTSLBvPjeOWSA4mSiuUgI2x\npneaFEHrHExWvSOESOcio1KBsITjyLJ2eB8JMeFTDoRaSFKCkLIjlxbg+4BPCRcCEBEyN+GsjMK5\nwGUhMVpQGsPT+yumlcJoRUqS0mQlniQExY2a6chyx86IcWWYjCyjtRRe5zwhRZyPlFazqPusBrSO\nciHErDOr5FqqLx+PVoLSvjjxAlHq0wx3YOC1ymw2+wXgXUAE/uF8Pn/o62zzvwDvms/nP/Bi3mOQ\nBxl4TSCloDCKpvOEkPJsf4y0LiIAGWBUKrRUWGPQKtE7j9EK1yfGlaWqIoVW7GyUdF1g1QVSSCQC\ndr1+6BIYrdDkdcQQE2WhET7hPfiQOFx1jIwCJQkx0bosldfqwEalOVpFNivwKdB02Q5sWhl8iNw4\n7rly0LA5tszu2SQmkAJiTKxaT4gRpQTHq8DmxCKlQAA+5HVSKQVtH4CEkjkrLNbB7uYv7yf3Bad3\nTjvtfEh0Ljyv8x5TthYbGHgxvNwZ5Ww2ez/w+vl8/u71DP+/4DmJ22w2eyPwPqB/se8zBMqB1wyF\nVRwsWlaNQ2vFpCoYlQmlBNYIUhT0LtCHSIwRowV150kxMR0ZvI/EECmNZmezpLCKZeupm47OZYFz\nIpSFwCpL3XuaPlC3Hi2hLCRdHwkBWh/QPmCUpBLgfCQliQuRrXGBLTRnxwUuRoKPFFZTlRrnPYfX\nHYeLjlXjeODOTbY3CqyWNL0npcSlayukFCgB00lBJLFqPE3nmI4MUkpAYNbrlXmOlPUth8ZvdoFK\n6VsHyRizKXbvAynl4xsYeKG8AqXXDwK/BjCfz784m822ZrPZZD6fL2/a5p8APwP87It9kyFQDrxm\nkEIwrWyWo/ORqtSUhTqVhEspEWOk6QPBRaQS+OgQKTEqFL2QNHislozLLHReWI0WiaOVRwmZRdWR\nRKHQKlFZaLpA7UD73MgjJMQEXRdIBlJMaCVwIbGsPVXhmFYapQVWGqyCrWnFeKRxPiCj4LDu8TFx\n8eqC1uexkLbNQglVaZmODC4mms7Tdp5F06OVRAhJ5wICgdGKpy/v8x/+w29y7do+QgjuvPNuPvyh\nH2Y0Ht8UNFkLMgBkQYXeBYzKknpSCpQ8WSuNdH2gc88GRiVz+Xhg4IXyCgTK88DNpdZr68ceA1j3\n0/w+8MRf5U2GQDnwmmIyMkTyBX1zZL9mZML5QN3lWcgzWxVnt0uaLnC06kDAYtnjF5Gmi2xMLEIk\nXEhIUTGqIoUV+BA5rh1N61FJgRQUMYGLILKdZWEkPqTT91ZakFKe3fQhcP24p+kjy5VnMtYoqSit\npjAaHwVFYdjWklXjOVq1OOeYjEqcDzR95OzWena09WyMDaPSsj0p2JwWWQw+SCqr+exnP8Uv/+qv\noETIFyQB169d5guf/wx/5+/8fe65cB8pJXLl9Nlun84F2t4jRA7uAFWhCDHRrwOklOK063ZU6lum\nKWPgluf0D3U2m20Df4+cdd7DX2HOfwiUA68phBBUNhs0ty4wXgertvc0XSDFhNGKzUnB5qRAacek\nMiyaHu8jRevpXMBIjVYKHyOTsaVykUXrmZQWIxWP3bjClcMFkYTGsDGdnq4XKi3RQtD7vI5pFISk\niCnSO08SkRCydutx26Olou4c25MOY7NQu0ggpCAmwcHK0Xloeo8PASFS7sglURrF7mbFqNQcLzuE\nlIxHmqbt+Niv/39IbbMBdeqRKWe8xMCv/Jv/i5/92Z8/PW8nHbQ+REgJ7wRWi9Nu2t55tJIYo6is\nwodcei1M1qcdGHgxvAJfsJ4hZ5An3AlcWt//QeAM8EfkiY0HZrPZP5nP5//DC32TIVAOvOawRtG6\nQO8ihYloJfOAvhQ0LpDI4xTHq45F4yiMYlJZep+zwuXK0fuIVJJKCLQUHLus9bp/2PMXjz5GWDS5\nyyYl+hi4trzO9u7dqEIjQqIcG4QKNMddbvgxBa1LxAiIRBsivVuhlSSEyFcvHuCaBdYmtifbfNd3\nPsje9oQzW5an92uuHzS4lNiosjKPUoK2iYQIl280FFohdd4fqyWf/dzDdGIbJRMq9YjYomKHJJCI\nHB4v+MSffZI3v/l78ghLenaEpHORzkf64xbnIy6sRRS0YloZYkp0rUdKsfbQHBh4cbwCgfK3yWuP\nv7gWx3l6Pp+vAObz+a8Cvwowm83uBf7liwmSMATKgdcoldUsG0fbByaVxBqFNYrSStRKEEmklGcT\nc2OKZ1Rolk3PjWUHMWVPSAUHq5ZV5wgx8chjXyGsHCDAt6DLfMNxcP0iZ++8D0QuX0YSSmYZPIeH\nlGc4WZc7Ow8uraBpgQDR0NQdzfIyV2/s831vfxtFURFCwido+8Co0iglObNhcWNoWkfbe2IKiKgY\nF4rGRY4XxyAl4PGiRKqCIDpU8ggisvB8cf4YF+5/E4LEqDIYnYO294FF3bFsHFIKdqa5sSnL6AV8\niKQE4zLPa8Z19+/AwAvl5Q6U8/n8E7PZ7M/XWuSBvzzn/5IwBMqB1yRmLTLgfMT5gFk39Fij2ZwI\nVu2ymqIAACAASURBVK2nd3G9nSKl3BgzLgybI8v+Uc3yyOFi4njR5Qy162lXddazw0HswIW8shFz\nKbU5vs6FC/fQuoBUuZO2dXntUipNqRIhgXAeD1CvzZyFyq8jImiJ94E/f/gR3vjgG1BSUxmB84mj\no56n4jEHC0sMORM8EVzwreNwwXr2QxFQiNAj0oqkN0CWpLBEpY4UA0VZohUYrWl7T90Gut5Rt47O\nRRKJylp2tyq2J5ZVG9bi7Xk28+ScLhuHXXZrn86vvfDFmHAhn+fBAWXgubwSa9vz+fxnnvPQ577O\nNk+QS7EviiFQDrxmqdbD+k33bKCEPAc5qQQrHDGBNRK7VvaJMXF+t6LrA0exZ1yAVYIUEk88dQTd\nYt0mqkAaIEDoIXnQYxqyaXQICWSi0AKlssBBIhF8QqZIUSqW3cG6fSCtXUXWOxiyb2W99BwuepQJ\ndPUC14MtFE0v8SkRU6TpEtNC4owmCVg0Hqlgc/ccz1xfgZkgwwLQJCGJApLIGfXsu97GxSsrQswy\nf50LGCPx6+7dmGSWxCvzem1p4HDRoVTOMmE9R7ku3S5bx7QyuQnIRzqXu2eFEIwKTWEVIebPQyuB\nNWoIngO3BEOgHHjNomTOtDqXL9rFTSozWknGleZw2XO4yCVGrSRCCsal5e6zEyZ1z0ZlIOXGldRd\n40uffhqhRfaWFAWoCqSFpEBIFILtacUTl65xcPWQbtVAiqiJYXdylmJUAAarJel6u5bNy0OOTZCQ\nCiolIHma6Pny40/meZPks48lCjG2XNg7S2ELOpfwDiobMVZidZ7VxEwZTTapVwcoXSFSBCTBTOmc\n4t577uGJqx1ae2KISLFuchqPmGxarh931F1uHlrUDh8SvQ9ImdAqfwEprKJ3IYvS145l7VjUPUbm\n86iVXL9GZFzmc9+7uM7yWX+ByZ/RzV9kBm4fbpVu6SFQDrymOZG2a/twql16Uo7tfcxrbAliiAgB\nI6uxVlEYRVUaepfHR5yP3Hf/A1QjQ9u1EGpQCZIBWeUMMyY2iimXLu2vjZrVaeYZVpGryyfZO3s3\nO2c2EYDW4FuPj+CkplIaKMhLKYpKFUCWxjPSgNRAIjWJJ568ws6ZM8So0Hq9fjmy7Iwk2ipikrzl\nTQ/yxUcf5fjGFbxbgFDocpuz517HuTvP8+nPfBbvWpyv2TtzJxcu3MvuVpnLpT6ihcD5wI1FS9Vp\n6tYjZA7i145qCqNpW0frIlEJDo5qvI8IBDsbJZsTy6rucSGyHFt2jCauO4ZKq3DhJGhGpMyfjzXP\nmmwP3PoMgXJg4FXAibRd24e1BFw6nf+TUjAqFBsjk5Vz4HTcYVRohGiphSDEgFVZvOAt3/lG/vSh\nP0NIQwptfpNYAwZdjdk7v8cXvvAFQEAKeT1TyCwOG1v2Lz/GXXe8M3fbqiltuEZCUHCSUeXML881\nJiAgUlg/JtfPC0ByY1UzKSuiF/TO03mH6y1S5vGUQGRj5y729u4h+BWVVWxt7fDIY1/hTz/1ObQM\nKECmlvkX/oL5F+d8eu88b33rW0kItqclnResmo6taYkUGqkEi1XHk089w8NfeITj40NiiuxOK+69\n935e9/o34Dk5v7kU3LnApOoodJYYrHuPURarFY5I6zx9mzV1nY9oCdZq9rZKtBoyzVsZKW+N0aIh\nUA685jkpETofkSILAtjnzP89t/QnpchhKiWs1mgt8THxkY/8CCTHZ/78k7h+gQCCKNk4N+N73vYu\nnrh4Ka9jKgVx/frS5FGSEMD1HOw/zc7eHaymGxwf5EAjVc4WcxBU6/se0GiZcH2PsQaIWfZHaugD\nopIoCSEkmi5Stzl4GyWRZPuuRimi0Cx7wdNXLnNwdAOkwmPweLSosNOKvnNcu7HPn37qz/iet7yD\n3gdcSFw76jD7DdORYVwanrn8DA899Gm00QhtkSSO2o7Pff4zHNy4xve+830cLDs2J7mT9mDRcLTU\nHC56jlY91giOlwWT0bN2YG5tVJ1ioukDWkna1nNud4w1cpjVHHhVMwTKgdc8Uois2BPTWubtW5d7\nepeFxQHUeg6ztIpxafiv/8ufxP3Ef8Lv/M5vsVw13H3/m6Dao+0cj3/lMSCAP5GSVIAHvQm6Ag9d\n12CL3CCjjCY4l9cghXi2o1YITgOnUCDc+rm1aCsRgiOtRzWkBJmyOPpJKVmbdUk5BlKAgKB2KxBT\nns1YFZ4q3y+A5oDjOvHkU5eId5zDec/RsstzpVJQFYZHv/wltNEEekAhkCQsURd8+Zmr3H31MuVo\nhy8+ccCoMHQ+cGPRsF4mRQiLj4EYNaPSEEJAIIlREiNZAKJ2rFrH9aPm1NS6MApjhu7ZW4mh9Dow\n8CpCyZx5PV9ciGil2N3USJEH69VNZSJVlnzwQz9G5yLLpmfVOIyueHxb8tSXn0FKTdSjvAYaVoAB\nXYAsQBi6LqK1guCRoYO0ymuaJ520yYLQQIQEWsh1V+xJaTZCZbGFRkmBEoJCpDyO0od1HBT4mFiP\nbpJigsavXyOXdfNrnWSxAswERMHF6wv6ZPAh670mBEYLjo5XdJ3FaYu8eV9IJCTSVHz281/hzd89\n4Xjl0UpkZ5Q+UVWaymislmiRrcjazq8bqQSlNUiZtWOtWUvm+UjdOUaFpu4Sos+jP1YrjM6fR9PU\nCCERylC3nunIDBnoa4QhUA4MvIYZFZqq4OtmLyc6qyEmfAjECGe2KnamJX/9R3+Iz3zqTwgCklCA\nRISeJGtwLUjD3RcukBBMKo0tJMRI26woy2KdWRoQfq38I2n6mqqo1h2yrEdJBNvlBpPK4pynDwlS\nbqQprCLFbDZNBCXWK5sacmFWkR85KTcHTmdThCXPYGqaLgfAkBJKCIyy9F1DUoKAIRCzeMH6VeL6\n9TqXiCkQgqfpIikmdrbzOElhskj9jWVL3Xk2qqz4sz0tKK1kXFqOVlnNaG+r5GDR43ykV5FpafBr\nvdneRT7+8d/nCw9/htXyABJsbO3xlre+k7e97R3ZguwWuQjfygyBcmDgNcyJs8Zz8SGyqB2wjmNk\nIfbNcfaG3JxOeP9738Pv/sEfIoUiyRKhDVlbPHDfhfspbJHtvKaKC+d2eezxI8piE+97tBHkwAUk\nS+N6KgHElpwSK4g9m5sb3H3nlK5LkARSSYLP8nNCCEpr8THhXUCKhNQSIiwqBc2JjdZJJlmufw95\nbXUd+oIPIAV9SEgSIbQoU0E4QOm0Ltz26CydQCAL0vtU8tVLK4LPlma9D0xKDSkRQ0JskZ1QOkct\noLCJVSOoCk3vA4fL7tSg+tx2yfWjnqbzCATTkaFSgo/9ysd4/KuPY23BZPNsPkYCn/jEH7JaLfj+\n7/8gWxN7y1yIB17dDIFyYOAmhFir/iiZ+3Xq/PiidmuLLcFHf+yjTDc2+fNPfZInn7pMUpatM3dx\n4b7v4sEH7iMJuH7Y4nxga+885ukrtE2NVorOe4iB6ByolqooKbYmSHIXK0ju3LuHMzubLFaBusv2\nWuPSIlPkqHbEkLPA0kqklSRyBpoSTLsNFs0Nni253lyiPAmcIKmydZjI+rT9ekurADsmxFy2jSgS\nKywJTaLxka1zOzifrb60EHRt4OmDGiVBS8kz13K5eFRqtjZKtiYFi7rnsYsHaKWQOaZz8eoxi7rk\nnr0x144jTecQApbHBzz6pc8znmzik8InhREOIRRlqfn0Zz7FO97xXnrvGRUmr2/ary2dD7w6uFW+\nyAyBcmDgJpSUTKp8wU0pndpPpZRVfWLMQeod7/g+fuhDP8jRwRLnAxf3G24cdYzHGpESWgquH3Uo\n7xF4FMf0vUSqEoSgKARS1kQhkL3iLW/5XowRdC7gfEJLxXQEHkXfudx8lCJWSJyK9J1n6T3W6LyK\nmCIuCorCEqab1ItDcuhb69aeIlHVFK3W65ppvQJ5IuUqoDKbNKtr66uDwjPCExBeUFYjorRYwMeY\njan7wHHTIxJonRhXFePKYI3AGMm4MutMsqfpW7SUXDg/wfnE5esrVrVDaYH3ec3yd3/vj5DFHm0Q\n+KQJaHwSKLVO8bXht37/43zv296O1ZrpyDCpDJuT4pX6Mxl4ngyBcmDgFieXOP/yf5HsxJHY3RkR\ne8/homM6NkCWqZuUBhAYo0lE/ri9htY2Vz3x67wxIhKo1OJXDTpc4+FHvsrxqidJzaSquPP8XUzH\nGzit8D6/ZzACmyS9jySfEFEQREJJQSkSAcl4UmLtGRZ1Q3AteIeooKRkd2eTtosEEj6Ac+DjCoLD\nkwgYtkYTtjfOsH94A9ckcsBVpNTRNA1PX3wSURnGZhtpFIiI9zniVkh89EihAUnbBUKIbI4NSgj2\nj2ueudZQf/WQyShL/126tgKRqLuAkZKLRwqXppjgcVgSAi0UFocSAaUVy7rJWrg6YbQkpvzF5la5\nMN8q3CqfxxAoBwZeIHItSSfXnpRloRk5g0CwObZYozi3M6Ltc5Ao44KAXg+DaKIoSaLIvTupx8XI\nnzz0F2gBRkAIgmbZ89ijN/jO2ZvYPXMHx3VLChIXc5Ati4q+8xgtSQKCzzOVbR9wIaCEZDSyGLlN\nSpGIyNsozcYk4WLi6KihXd4AdXIZiKTQctA43MY2k9EufpRY1A20AYqsJASRFD3L4wOKaovphkIl\nQRcifYCmjTjfsqwdXe85WLQIoHOe3ie6LrBwkeOlwIVA53NqGyN5PERaPAKJIEsWKFRyFLRIGel7\nx93ntvO4KYKTiuvJlOrAwEvNECgHBl4kq9YTY0KIbPs1KhTW5P9ShZFsTQpWref+u/Z44uLjIAxR\nFojUE+WEKCxBWPpmH2s2IXSI1CGVIVEgU+BLj/xH/ubf/EkKC6vGo5TIPpzKMD2v1kpDisNly/Gq\nZ1LlgBlCIqRs0nywdKwaT4gRnQKFsYx04uKTT62D5MlapiQ3/MDyeIEYTXNJtolQnMxlnqChCHTt\nEZubewSZ8DESuohzPQBHSnDUOEqliDKCh6LQTEaWygq0lrgg0ApKrYhAWSounHmQP/j4ZZJV5OnQ\nnKkrEREkUvS88x1v58pBQ9M5ut5QWpHHY9QQKl9NDBnlwMBtTlUoRoXGGIlWHufj6eMnJdtRAT/6\nYx/lF3/xfydEj0gSgYG4ypmT95SjCVIk0CNSKtZaBAohDCFaPvvwF7n73geYVBZIVIXA+5gFFqSk\nD9ngeVxaRqXBakHb+yyeDhTWcOM4NxdVVqOt5NKlq0gSEk9ErodAJGA5aQRKqckHaj3P5msnDTO5\nJxYSN44aJJqeOgdVJFQCfEXv+iyWcKLat+wYrTompaYaF1gpEFLgU6J3gRATCsHdd7+Oi5e+ilIj\n5Hq8pYkR1x3zgff9IEcrR9N6lBS0fRZsl1IOnbCvMm6Vz2IIlAMDLxKjFYXNXaRKCrzI85n2JhcT\naxRvfPB+/rv/5r/ll3/l33Dx6WcIaISuOLOziaTk8GiB8J4o9FqEwOXMiSzIXne5Y9aHgI95VlGZ\nnFkuhM9jGj7PISqdM89V69BGMi41hZI0nccYiRGSFBNt2yBUIqKICLKcniW39kRQCYklkUji5kzy\nZs3aCFbhUw++yXXj6iTzFOAanIFKVSgBIWZJ3FXtcS5wXDukUhQmj+r0fY9ziY2JZm9nl7uU5Mql\n6ziWxASF2ebNb/4+YrXDoxcPANicFByvHFpL6tad2n0NvDoYAuXAwMApVaEprfqGF4bXv/71/KP/\n8X/ixo0bXHz6GbZ2zrK7s82v/dov86lPP4YQEhk7oijIaj0ORIHzR9y7/Xruu2ODZd3hg2B7wzKp\ndC7FSkHrIl3vQEjazpMiLDtHSnkWsu5S9qFsAk2KGCUptWYVJUHq3FhEQLAgB8I8kiEps75PDCBP\nRAtOumjX6j9dm/9NlZt38oxoAAowQBMwRf7CEA2EGHE+5QBMRERBXXsWzTHB9QgTOTwOXLlmOLt7\nhrvuvR+pJXubVT7HRpFi/mISgbYLxNgCkpQSWgn2tkeDGMGrhCFQDgwMfA3P56Kws7PDzs4Oy8bh\nfOTDH/phPvnJT2JMQpAQeBJ6raADFsd/8bc/TNMlntxfEVNiUioQgs2xou5yNrU9mUBKrNaScWd3\nK6IDaxVSQNM7Do9b6i6ghOD81gP8/sefxuLJgS+/e14FBELLA3feT9t7nrx4EQqDJCDpCUhAk07K\ntaXh2ZKsWN96IEGlWHUN1WgTFRKFEbQiEkNuQIrJc9xeR0uJMjpntzbRI7l49ZDtBsZlCQn2tkp2\npwXWKvYPfe5y1SqbWZNQEto+0rnIzkaJUXLQjh14SRgC5cDAt4FRqVnWDoox73vPe/iPf/x7SK0R\nyZOEJoqC6Fb8yIc+RFEU+OQ4v1MB2Ry5bh2rtqftIyFk+yqjBIXVTCvLRrLZccQFtIDdzRKQ2M4h\nhUAK+I4LezzxxKMYrfFoAiM84IJgd3uH19+9zc6G4SEO+cpTl0i2wOBJKCIdXaeQ1Yh4ojR0uo6Z\n10bFad4IwUeqQqOUQIjsURli4Gi5Qki13h4EgoTKIgpKsahXKKW5ftwSQySGSFUaWhcwSpKCQMiE\nlApjFN4HLl2v8T4wGeU120llGPj2MNhsDQwMvGikEIwrzaJ2/NBHfpwzu7t84hN/yJUrl4lSc+bc\nHbz/3T/CB973HnzI2qdloRmXmv2jhsVBT916rJFMRwVaC4zKdlWJRN15Ysg/jRQIIbhzb0zTZDm6\nunN8+APv53N/Mebzj/wFx4sDkjhmY7LB3p0Psnvnvaz6QHsjcf7uBxhvbfKVx75K2ziE7Nmoptz7\nugtc3F9y5fgIIU/CpMglVViXc3s0ht55eh+xRjOyiumGxVjFavE0SdhTGfec1ybSOuD6fsXm5Bw+\neBa1w4XE3kbEaEnTR0SZs+UnnngC5Q4Zm8CZ83ej3/SdrDpPYTRntkrGpUGKbK82KPi8ctxWpdfZ\nbPaPgfeSFzD+1/l8/m9veu5x4EmetSz4qfl8full2NeBgVsKJXOzzbLxvPXt7+H93/8BehdYNQ4X\nIoXR+BBpuhzcvI9cvl6fzm4qIdicFqdrd9kuLNtwFVqyqB1KCaSQuBBIXTYw8S4P5rsQefs73sn7\n3vMeFssFpVXs7mwRQ+Spq0uWTU/be45WjnvO38f21hna1hGiQMqEQLDRafZvrBA2ItZOIxKXM0IM\nrunZvXNzvZYYCcFT+4RyCSmA4LEaApJIwmPWQXLdgRscWkpSVCQRcN5zY5kFDLoucfnadZ669DhG\nlGgpaXvP/vxRvjB/hL/xoz9GtbPF8arnaNkRQsRqxXScFXyskVgtMVoRU2Kx6int0Az0UnLbBMrZ\nbPYB4E3z+fzds9lsB/g08G9v2iQBPzyfz5uXZxcHBm5djFZURaLpcoCMMaGUZFJZ6s5Td7lDNAsJ\nxNNMdG+rREmJVuLUT/O5lIXBaklMiYNlS9N4WpdwPuBDdhdpe4/Rgr2drTzuUhp6Fzm7M2I3Vqxa\nx93APec3+fyX93nm6pLjtmfZOpqmZ1wV3LG3zf7+E1gL8TTQBfoezmydwxgBSROSJyWJEuCjoPGB\npEc43MnZWA+cxPUtQTXiuO4YFQohJJ2PNMeB5cphjeTJS09RiBESj0+aLoGWYKXnt3/nd/mvfuo/\np24dy8YjBIyKhDF5/vTEpaQwCaMFMUHd+SFQDvwlnk9G+QfAn67vHwKj2Wwm5vP5TeqQgyDGwMCL\npbQ6ezO6vLZ3MuLgQl7LS4m89qgFo/L5eTGWVhNjOr3oTyrDsnHUneNw0ZNiovOBbu1t6Tz0XrE6\nnU0MNH3A+cC41GxOS3Y2Swqj2D+ouXbU0JpsTv3AXZtcvVrw1OOPcn21wKeC0oz4jted58zeOXrn\nOao9TdMj1r6bhVF4FxgXGyy6QzSCuC5KrQduCHRIJtRdj5JZyq7vevqY6ISiuXGIECV+nYeq5PBR\ngbTEJOmObvD//NK/wrsOF2A0GvPG2YN853d9D8vGMa0M1iiMHsqxLxe3TUa5Dogn2eLfB37jpiB5\nwj+fzWb3A380n89/5iXex4GBW55RoYnRIYQ4DW5VofAhYo2iKhRGP/9M58T0+AQhBJPKUFqN1ToP\n96cs8m6UIEYIKdG5SEqJpsuCBd5HtJJrOb7sUnJmu8IYRdd7hBQcLz2m3OXCG3e4JyRCiCgt6PuA\nDwlbaLaFojSSpg3EkHVro4SdnU3qSw0+NCgl19mowaVAIQo2tzZoes9x3RECCAmFyaM47aon6xgo\nOhSCSJE6QjDUSBwjFr5kZC0jlSik45GHH+LwYJ8f+OAPY7VCSUGIiRdwagdeALdNoDxhNpv9DeDv\nAR9+zlP/M/DvgRvAr89ms789n8//35duFwcGbn2EEExH9mseU1KyMX7pDIqFEBidDaWX5GA6KvXp\n6/sQ17fEou7pXKDtHCEkhMhdtaNxQUgJHyKFkWilsKolJs/R0uFDwKisTFQag7WSUaFxPlC2iuko\nsKgddesRMRGj4NzeWY5XLXW9oCciUIzNFnvbFW2IaCQuBeKJlkECYxSV6Ikp4FF4NBGDIGFwNLVj\nNNph5SGmlontqIRnc2K59MQjuMVbqe66l84Fmi5n1p0LFGaImC8lt1WgnM1mHwH+EfCR+Xy+uPm5\n+Xz+f9+03W8Abwa+aaDc25u+8D19DXM7He/tdKzw2j3eELPjyDfC+8DBoiMlWDY9dRs4f24Df5oN\n5rXRwihcmHLv3ZFF03H5Wk3bB3Y3CzZGBSllofO28+zfaFAmB86rBzW9C7Rtz5WDFm0UVVnS+bw2\nWRpBHyIxglSSkVVYnd1cnnzmGteXPaxqqrHFZlkFeiY4FA6PsQpBDqJ1LNDBYVVB8IHxxi6ffOhP\n+Om3v+W0eWpZ94yMZmtasLuZx3Beq5/twEvP82nm2QD+MfDB+Xx+9HWe+xjw4/P53AHfD/zyt3rN\n/f3Ft9rklmFvb3rbHO/tdKxwexyvAJIPVJVluWhpnWdZO+rOMx0ZEIlCSpRVjHSJ9Iknriw4Omq5\ncaPJDTSVoWkd1487Qkpsj23uLi012yPD5shw7chy5fqKG8ue6CMhCGIKtG3Ia5pJIozh4jPPkAuu\nBsa7NHVLNyoRxFMhBJqEqSSRmEUUkmTZj/GxZ6Q6hEgsrjgenl+htNlvtG4dRitC74m9vy0+2xNe\nzi8Et1NG+RPALvCx2WwmyMWP3wM+N5/Pf302m/074E9ms1kNfHo+n//qy7e7AwMDrzSVVUiVx0mU\nlBQ2r5duTy1VoU8vhikljFaklFg2jsO6Z9X0xJQIIaEEOB/ZP2wZl7mLtTASpQRb0yo3NIVE7wS9\nDyAE1sjsYCIEi2VLj0NhEGtXzzQqCE0HGKjWOxwDDgEo5Fr8oEdAsPggUAoqIXjm2gqrJUrl5iIp\nBcerHq0Eu/G5bRgDL4bbJlDO5/NfBH7xmzz/z4B/9lLu1MDAwKuHLP6uMTqPo0BCSklp9emapg+R\nEBMhJqSSTMcF48rQ9iVNH0gpsbc9ou08h8uOECMhRA6WntJmS7LSas7tjHA+sGwc3merMOfzGMdq\ncUAFSByajoQmIAmVIdDRH3dgStTYEJoeXxUoFFmCQeGTRwiF8x0Pvu4B6s7hgqDuAtPSsLedx2yc\nixytOnyIz6vDeOAbc9sEyoGBgYFJZWgqk8dJEMSYOFr1X7ONUgKrJed2xkhJFgpIibrNHbSd8yQE\nZ9qew+OeZeOQqidFaF12QEkCNkaWrUmJErBsew6XPVcPOxwSiUYi8GupOw/rUKjAKFRVENFQCFIX\nkIVam4ZlIzGfAoUasbl5DkVko6wQeLY3LIXROBey7F7MWXFV6KHBZ2AIlAMDA8+fmHJJUgpQSqKk\nQKucaX6j7KEqdO4sdZoYI5WRWKWwRjEqFMvasX/UcNw4lEw0CbSCkdWMS0taCwFcOwCHIa+cPnvp\nCkTU2iIsZGXZvIOFoG86smiYgxDZ2d7lwdfdx8p5DlYOITVC5JETowQHC0dIid3dnPHWrSeERFV8\nY2eYgW/MrXLOhkA5MDDwvCmtOl3Pe74IIRiVGqMFdetp+0BhNed2NMumJybQdc84RoSUhJDwwXHc\nRLwLCCLWSHY3xlw9PIIOTudEAAikSkOl18XY7IDi0Ygqr2cmPCUFW7t7LDvHqnNcP6ipyiXnNyu2\nJjaLzXeOQkt6n5Vn294TY8THyKQ0L+i4BwZR9IGBgdsQIQQvNkkwWjEdSYSA3keUFBRGEEKi94GQ\nCsaVRsTEjUXHsgl4LVmuWhSCqhxBd5miKohI1FpAPaLompaNrfMYIzhaHhJxaCxZEM9TYNnd28GH\nxGrVM50U1J2naT298yQhObNd0PaBmAR3hYjRAiEU7XrGMvjIZGT/kpjDwDfmlcgoZ7PZLwDvIpcO\n/uF8Pn/opud+CPh5sjP5b87n8597Me8xBMqBgYFXDCmzsEIuxYYsDF9pLpzdoPdrPVsp0FJT2o4b\ni46yNCAkly5fYVRJCulzT6sIuKDxKKgMTdfgUkVZblHIxKpuKK1gc+ccMkmMFgQPtXP44xYhE1Zp\nYoSjVYMxZAF5F7h0fcnZacG00GglqTvPonG0LrA5sYyKwbrr+fByB8rZbPZ+4PVrLfI3AP8CePdN\nm/xT4EPAJeAPZrPZr8zn8y++0PcZvhoNDAy8opyUYkurCEkgpWRUGe7YHWG0ouk82kjO7Yx44M4N\n7tidcm53TN8dY1CkmA2mRUpImYXiNRpPi5IQQqILAluOsNUGbROo1z6ck7HGaIULia5L1H1/On7S\n1FmUHiIpwtWDhhASG2PL9jR38fYu8Mx+zcWrCzrnv92ncgA+CPwawDoAbs1mswnAWlb1+nw+f2Yt\nu/ob6+1fMENGOTAw8G1BCIgxB7rCKrSW3L035vqxZP+gpTCGwgjO7SiaVhPpKHQWEEhIvLDI6ChN\nS+80OgRGpSGEbGadUkIQ6UOgd4kQI6PKMioVpYG2jax6z/WjFTEGlsagFi1tV6GMwQjYnFjU8atb\neQAAIABJREFUeiQmW3JJlnXPouloO8+ZrQprFFIIqmK4nD6XV6D0eh546Kbfr60fe2z9c/+m564C\nD7yYNxk+2YGBgW8LpdWMikBcS9zmhlrB5rhkWXs6l5t4SBFtJBUBLcGIFmLAJ0uQoBMk4ZEyz0EW\nVQExy99NRhpILOqA95G+C3jvMUpjrUZbOK4Dy9oRq7wPKSWCAJEE149bJqVBKZiOCkqrqCqN6qFz\ngaf3V1SVZmtUDIHy6/Bt6Hr9Zm/4ondm+GQHBga+bVRFthiT6yahfGFN9K4ihIiQIosAeM/ZzYrD\n1iOkQsuTrFETYsALzdgaRoVFisjGVsW1gw7n82tMx5q+j6zaQHKRFPO85KjQlEYgdQ6QPgo6F/EB\nXOfYv/IMsV+ysTHiDd/xBlIqOL9TMt4Z4X3g6lFL3ThkyipC1XpNcyDzCgTKZ8iZ4wl3ktcjT567\n46bn7lo/9oIZPtGBgYFvG9lCLPtvZm9IiVKSUWkYVYa9zYrtaYHWmne+8/tI3Q0qWQMyd+ASCSh8\n6HndvfcyKg1KK2IArQV17zleORa1J4lEYQRFqSkKxdnNgjObI6yWeJ+wWrBVaWypOT66xiMPf5LD\nK49i/TUOLz/Kb/37X+PxRx/mzFZJVWgmI8vOtGBaWbQWHC57jpY9q/ZkrXPgFeC3gf8UYDab/TXg\n6fl8vgKYz+dPANPZbHZhNptp4KPr7V8wQ6AcGBh4dbGOMVWhKQudg6ZVmLLigx/8EbS2rJolfXdM\ncjcwIvGGB9+INYY+BEIf6H1gZNXawDqyrB2rukdIAQmUFAipOL9TsbddUVlD00eEkqRuxZceewJT\njkhmymFfENSE8cYm8y9+hk9/5tNA1q0Fwd52xc5GSWkVTe+pW89x3dN0/lSg4XYljxO9+Nu3Yj6f\nfwL489ls9sfA/wb8g9ls9nfXtpAAPw38a+APgF+az+ePvZjjGEqvAwMDryrSOlKGkOj6cDrkr6Wk\nKMa87wMfwSoIrsOjuX7ssnBBTPQBFiRcH7BGs1lZggscOoePCa3yHOeqDTT9khACZaHZGBvqxrFq\nHVeevoS2BS4blxCVIESP0Yn/n703jZUsPe/7fu92ttru2t3T3cMZkuIUSZGSKMlirASwA1mWFWdB\nDCQOlACJE+eDvwcInCAfAjiBYwRBlA9GAMNGDMRw7HiRgUAOJMOJLFkRtUsUl+KQnL33e2+tZ3u3\nfHirmzMjkkOKs/TtPj/gorurTtc9p6rOec7zvM/z/1fjQ/7lr/0GH/6+T9J0qeu1yguM2asUdRLr\n9nJ8EXrrmY6yJ0ah5rvl/TjuxWLxX73toc+/6blf4a3jIn8khkA5MDDwWCGEQIrkmVnvg9H5tqNu\nLePK4D24GClHYxQCow1vPAipC3VWIEXgYtvjo8f1giIzFNbjXBI2uDorqIqMs4sd985alJFkWiKV\nQvrAzjuKYPBKEFySLFBKEKMnBFivVvTW0dlkUl13DrqUpSoJdr//deuSgMJTGiRhkLAbGBgYeE+Q\nQjAdZfiQxMl7FygzxclBkTRZtaDrA611BCJSCpQSGC0wuaa3OY2NxBBQMiCloSoUty4auj5wvu05\nnhacHo7YthbvPNY5VIwoKUkrn4IQIAaBiKCERARF5wU2alablumkYFblRHjkaRkiGCVZ7TqkFPRW\n4EOyJxu4vAyBcmBg4LFDCJEsvRQ4H6mKjOkoI5LECoiw2vVsa4t1DqMlTSvIg2A2zqm7HusgIlFS\nUmjB1YOSXWOxPnJ/1VCaJHrgJORG4kNyuVQoohAYEfGkwCisJwSBVQGhx9xd9nQOiv1r2JC8OH0I\nSAFGCZRSaCnZ1JZRkYQOnjaGjHJgYGDgPSbGVC4VAsrcIIV4tGZ5PC2YVRlfv71iVBiUAOfgcKKJ\nccyq7ul6l8q4EfIsCRxkIeJ8xDpPiJEYoek8uZGAZDY9ZLV+QGYEVkmsVwQEPkZcH7hy8hzn64au\nSw07RaaYjDLKLDmR7DpHCJGqTOuWzge2jaPI4lM3azmIog8MDAy8x/gQedg4uqktkBR9HgbM5DQS\nyY1kVo14+e6GO2cWpQVXD5JpdN3a5IfZO2IE5yznD+5RO0fAoVCUWcH1GzfRMVKNR/Q+sN3dojQj\nVASHxPYtp9OC5577KHXjsNZzse0ZlZorrkIrRWsd3iXZu8koS6VYoyBC23uUFGRPkb/lkFEODAwM\nvMdoJZlUBu8jIaYfHyIxRKxL/9YylVc3tUOIyKru8QFmI5PEDKSglBpRCbbbhtfuvMZI5+QyA3RS\n4rGO11/6Mj/46U+ha8mkOqbrJ9y9fYcQA0Jpnrn6PCeHMzZtx7g0HIwzQKBkmvv0IWJ3jroPZEax\n3HQYLTmZFSDFo30ZuHwMgXJgYOCxJhlD/+HHQ0zNPrmWXGxTYFruFKPC4GKg7S3LTY9SmusnJbOJ\n4QtfeoOxzh/pwAL0ZMQYqITi3q1XufHcR5GZ5uzBhpOr1ykyTaEltfV0vWVSjhkXCq0kPkCWqeS3\nqSTbXY+RMBsbOhdoe0+ZKzKjkyvKU6baM2SUAwMDAx8gUgikEoyrjLLQFEZxse3ZNj0KSZYpwgia\nLrDcdnhvCN2Sqphhg6B2yWILAhGBJ+P2WcON52JqxpGCpne4AM4IrAOjNZNS0tpA3XXkWtNahxSC\nk2lOiFDmisNJzvm6Iy/03nUk7tdAny6GQDkwMDDwmKCk5HhWcv3Y0lvH+aqjdpajSQFTWO96zpY7\nIgqhgAgiRnoUHoUg0EVNJPDV15ccH1W0XUQJifceLwV5lsqrd5cNVZ4xKjWzsUljJETWjUUbwcgY\nms6TGcXhtECQ9GufRsPnoZlnYGBg4DFCSsHxrOBgnHHrbMuLr6642PQcTTOqXCNEgQesl/RO0EcN\nSCQRj6QnENHcW7V0Fg6nhiJXjMskoxdjpLUBISSZFvs/FUoLIrDctLSdZ2Ms295y82TMqNBsa/tU\nll1hyCgHBgYGHitiTJJ3EPi+mwc4F3j9wZamD/S9x8VAlY/xMRKRpPDmUWnaEosANNbCatMiY8+V\n4xl5ZogIjJLMJgXEZLFVKoHRIJXYl1fTmmTnHbJO22wbhw+RInt6Ol2fRIZAOTAwcKlxPrBrkirO\nctcSQsr8ylzz/NUpy13P3Qc1zkY+8rEX+P0/+D20GaNDQCKQ0eHxeCKeHBe2uOBpl7Bc3uf5Z445\nODolKsnVyjAyhq/eWrPctExKg5QRH9J+ZJmiNIoi13gfuXu2QwjB9ZPqg36bPhCelIzy6asFDAwM\nPFEI8chwhMJoplWGURIlJFIKMi2pKoNREaUNH59/Gi0FLvZ0sacjkmcZOS0HqmcsoEBhyAiUfP32\nObfu3Mf6QLCB0SiNhhgtWe967q92PFg2hBCocpN2CMHJQYEQ0FvH2arlwarBOv9BvlXvO++1e8j7\nxZBRDgwMXGqUlIxLw66xRGDXOjIjiRKiiygpmI0yiJFN0zMqKrJizr2zHU1nQcJmtaYyOUoJhPOA\nxDlPQKLIuHO2ZDyZcVvX9CHSWYsPcLZp6a1jVHpuHo/IM8l2Z/E60PaO41mZ5itdYNtY6tZxPC2o\niqdDLP1JOcYhUA4MDFx6kjBBRtM72r0Cz8EoI1YZZ+sOcJweSMpcsW0t7Bw+BKyLGCPo24ZMa5xL\nUnUhCFK4TNlqwNN1DedrwbrukUKCiOQ66bnGKHAxstlZeuuJRM43HVcOFOPSoKTgbN1i97OVSgmK\nbLj8XhaGT2pgYOCJQErBlcMqCQ74iBBgfQpak0pjfaBuHVqqlOlIiVQgoiASEULgg8B6sW/vCUgc\nSinwMDKek+OKi3XPZtuSGcnxSY4xmlGZkRuTOl97R9sLkKkBSAoeSelNywytnp4O2KdqPGQ+n/81\n4F8DFPBXF4vFP37Tc38K+O8AB/zTxWLxV96LHX2vCSGmxfinSIdxYOBJQwqRyrCtw7rAemupck2m\nFdYHrAtY7zFKcnVaspSS1joQGhc8PkQgBU4lJJqAEJ4eyEdTrh2WqCjpO0sQcHfZ8sLNGd//4QM2\ntWfT9JRCJg9Mk9R7eufZ7Pok7F5oxpV5amy3npTS6zt+WvP5/E8Cn1wsFj8O/DTwP79tk58F/l1S\nIP3T8/n84+/2Tn6vxBiJD5WVv8Xz28Y+OrkAztcNbzzY4pN0x8DAwCVB7IOl0YIQAuvagoBJaXju\n6oRnjsdcO644mmYcHpQcjDOunkxofcDH5CCiSBJ3QkpkFGgU611g8eoFLgSuHI/IZOS112/xy5/7\nfX7xF36R3XaDcwEfUhm4zFKAXu8sPkROZiWTUfbUBEl4upp5fgn43P7vS6Caz+disVjE+Xz+YeBs\nsVjcApjP5z8P/ATw5fdkb/+I7FqH94FRab5pyaPtH95JQts7eitY15bMqEcfVrN3Wv92NjkPg+rT\ndCIMDDyuZFoxKjNC7CHCbJzRWw8CjmclRaEQ5w22UFS5YbmuWXUOjUpjI0JA6Oii5aPPf4RNa9nV\nPXXnOX9wB7s9wxRTjAmsO/j5X/gFyoPrfOyjc7atY1xqlruGGAVH05LjWfFYXfwHvnPeMVAuFosI\nNPt//kXg5/ePAVwD7r9p83vAR97VPfwesS7gfCCElDVWuX5UXm17RwjQO48UoJSkbi1N55DA0SRP\nJwtpeFhKQbl/3be7lscY2dYWIQXTKnufj3JgYODtWJ9mKWOMdNaz3LT0PkKMjEtN0zkyrcgzhZCS\n55+7zht3luzWa8DhgqAqSp6//jyZUbS2Z9v1vHFnhW17xvkELQSZCgignByzuljz8quvIfgQ1hpm\no5yTg5JnjqqnMkg+Kcf8HTfzzOfzfwf4C8Cf/jabPXbvivPhkZ9dCJFd6wgxkmlJ03m63pFnmqrQ\nKZi2jq6zXDsePepK8yG9htpb5Dgf2NQWpb4RFHsXkvfcE/LFGBi47IR9lUjuzZNvnTU4l3wpN0pQ\ndzYp7kjBtMiIBxVaanaHE4oiI1jLqnZsGstMKspM0lnJ2cUGjabxgiwGjJeILHXaVlXO3Xv3OD65\nRms9WaY4OcifWnutp62Z56eAvwz81GKx2LzpqVvAM2/69439Y9+W09PJd7OP3zO7xu6zx7RQX7c9\ntYNqnFGRMxvnlLlmves58BEouX5lTJlplJL01mOKnqowlLlOTT/bDuDRY6ttRzkKSCE4nBYf6PF+\nkDxNxwpP1/FetmM93jfo7RrLrQdbZkDbOW7d3+J84MrxGOc9vfXUXSAPkZtlxv2VwvaeyXjEtt3g\nBZSFwgVF5dKoSEThPVghWFuDIAVkH8BbS1YotBJ0LrBqPUUpGFUZUjxct0uNR5lRT3QQfWoyyvl8\nPgX+GvATi8Vi9ebnFovFK/P5fDKfzz9ECpD/JvAz7/Sa9+9v3mmTd5WHZdHepSHgi10HIdB0gesn\nI9q6Y7vPEAmRzgVe7uyjdc2HLuqHk5ytloQQON90eJ8cAUalpm6/objR1h1KpnXOG8/M2K6bb7N3\nTw6np5P3/bP9IHmajveyHmuIkfWup951FJmiUKAFrOuOYD2jMqMymuB67rf9vioEKje0naXIJL0L\n9DbQNJbOepJXiEDiyGSgd4qlM2gVKIxHEpgWGiUktvd86ev3eTlfcuN4xKjM3tInUebqA5+nvGw3\nQB8E38kn9OeBY+Dvz+fz5BcD/xz4/GKx+CfAXwL+j/3jf3exWHz1vdrZhzwshb75C9fth3i/WbOO\n8xEXIiEGrA1UmeLVOw2t9fTWcXpYIaVAIChzhXOBVd89qiPHyF5dQ1N3qTu27x0IQW7yR52yD1FS\n4Hwylf123bYDAwPvHTHGpNYTocw0IUaIcPWoZF13NNaTZ4HrpwU+BMrM0PSWzGiEkAQFs1HBcpdc\nQUIELRUZAguIqEBEpBB0XtAGTUAwKTOOpiWjQnN/1VIYxbTK0UqmzFOAUgLr4hOTcX0rnpTj+06a\nef4G8De+zfO/Avz4u7lT70TdOtw+mysyhZKCXWexLlBkikyr/bpkJETorONi22GExEXPemvpvGO9\n63HOs20dh5Oc4ON+ODmpeeRGsGktIUSqQqOVSGuRIWKUpMgVk5FhU9tH+6ZUamt2PmWYT8tg8cDA\n48Zuf53ITLpO3LtoKHJFqQzTMufBusEHz93zluAjRgs2ddq+Ght8JwiIR2MeQiXHkWgPeOX+Bo+m\n7QRGR0RMij5N1/Hsc88iYso7rQ3kSnL9ZESIER8iMkTqbr+mWTzZmi9PTaB8HClzTdv7NDzsApmR\nSCFoO8/5qkWrVPt/mP7uWkvd9Hztq1/COzDViGp6hTJXgMC7yN2zhl3boaTkcFKgtKDtBIVJJ0Bu\nFCHdkKbu10KjpKTdf+EfYvaB8eG4yRAoBwbef+o23TgbLany1OHqvKfpIrNRzvWTCiUFbe94cNFg\nfUQrUAoykwTVXXyo7gNGS47GeboBPjpm08L5ZomPmhgkIXqg5+jgGF1MuLOsmfQ5MUTKUlNk6fph\nXdjbe6Vu+11j0Uo8sSNlQ6D8ANFKMioEy02H9Z66jTxUZOycp7PpCzkZ54wyxVe//NsgDT/8I59h\n3XiW5+e89PUXOTy+wtHhMVJG7p13hBBRStD1gbGSzMYZo8ogBBxOC+6e7ag7z7Q0NAKKQuN6sdd6\njDSdQ0lBmYP3ASXFE71QPzDwONJ0js4GlBKM9uLjnQvUnWNSJhPnqlBsG4dWafSrtUkjNsQ0V41w\nCCk4GhfEGNg2nvHIsK0jnQ2cHs0YjyqWq5q2ayjyCdeupG5ZrSR15+itp8oVZh8ER4V+JGoSeTqW\nZZ6qrtfHFSkFwgukBOvSAnuZSc6WHUsXWNU957e/xqe//+Ncf+Yab5xt6VYd295QnjzHrdtvkBcF\ndS9xIXAyqzgeS373Cy9iIxgFtg+88NHnWB9O2e4cDy4uqFf3qDI4PjrkYx97AXTKWiHNbvmQRkUy\nPQTJgYH3G+f3PQORfa9AYLPt0g12aciMRAiBUoLeBo4mOV1vudhYiBBNCnRVJhlXhigq6nbL+aqj\ntw5iZNs5RIQrp2Pu3IPgGlZrMHpG0OCtQmqJlorepYaiItOMCs2msaw2PUIIRidPj5zdZebSBkoh\nBGWu0wL7fl1x11ikEJwcSV67s+H+Rc9rd3ueeV5x68t3OVs2XGxaLpYbbj/YkCt47de/wEee/wiz\naUlTb/iD197g+z/1aWwQVIXk3lnLF196CfPqPbpmxfVrV/jBz/wQp0cjHty7wz//F7/EJz/xCbJi\nQoxw7aii7Ry98ygpHgkYxBiJpMag3EiMHjRlBwbeC0aFoe1TVrncduzaJCF3MEoNNT5EtBKMS83t\nBwEpJZk2SNkT8SiRSrLWRu4ukwFziLCpOwKgtaDQkjsPNuzaM0pVoAWE9oKXXrrDeHaN61eOeOHZ\nQ2aTgt577i8bykIzKQ31fn/GpSZ/wrWlh9LrY0BmktBxbwNaCY5nBU3nWG6hKAyv3LpLyEZ87gu3\n0yyk0jw4u4/zcHw4pbWRg3LE67cvuHXvguAbPvXJF7h1VlPmGUoaeheYHlzjtdde4caNmxycHHK+\n6liuO1zUPPexz/Arv/k7vPDCJzma5rx8e43zSSPyYGSYNn0q5bwJJQXmUr/zAwOPL1IKqsKQmVRu\nXW472t4hSBUfKVNJVkkFpAYbZSSzUYZ1nvvLFilT1+zFqiUCTdOz6RzCB/JM0zYbdu0WJStQIESk\nLBRFNuJsfcGmNPT+gFmlWNVJ6OTeRcPZugEkRSY5nhXf/kCeAIZA+ZhQ5hrnUjAal6krzbmQ5iRb\nx7Z1hEbifcTaFYejnMPDQ0KE1bZh1waq6YS2bfC+ZLlr0UgiHWcXit55dKa4cfMmr9++S1lWFJmn\n7exeiUPxzI3n+fpLX6e/+TyrbZ8W7IWgPy4pRgWSiNEKoyRaP7kL9wMDjxNaSaZV0nddbwW7zrGr\ne87XLacHJV3viKTGHyGTZGXdW9a7nrOtJZeRWjqMkUgtUEDrI4UULM8v0KLABbAOTJaWfmyQjKqM\n3fIuuXqOgKDKNbvGcvusRkq4dlhxOCmeika/IVA+JkghEMDd84aXuxWdDYQYCcDhbMq987scH0/Y\nth0Xq4DONM35jlFu9sLIFikk1ZUxL379Nl3T0wqBc5ELH6h7T2YEh6MCfOpmXW4blusOKQWHIaMq\ncpyFPFPkRqCkQgqBVopJqdFRPTGL2gMDl40qN+RGMXOBe0KkqtOuY9c4DkY5TW/JjU43xS4wLjRR\nKPq2Q2uJlIJplWOU4GzTEwX0sQeR4xDEAL2VeB2QAjIZaJpt0o7uLM5GNq3F9Z4QI1WmybRkXA6a\n0O8F8/lcA/8b8BzJ/vEvLBaLl7/Ftn8XaBaLxX/67V7zUgdK6wLrXcftsx1N7/E+UuaKMtNJYMBH\nXr99l6qUnB5MabY7nA+0naXvHX1vyTJDkUOZS1yAs3XKCKUU9NbhnENKyW7nqBsYne/IjUTISOc8\n95eBa4cK51Ona64LlAxcOayYjDK0VmxWzbd0LhkYGHhvefOsYpEp1rueXduzqQPWCYzWlIUi1J51\n3ROASWVQI0nbJfODMtcUmWC1szStxaOJMQ16ONIISe0UhQ44JF3w/MGXv8KzN28yHue0XQAB0ypn\n2yQVsLIwnJgn21HkA0oQfga4WCwW/9F8Pv9J4K8C/8HbN9o/92Hgi+/0gpcyUDadezT470OkKlIQ\nsi5Q5oZxpVltOjpruXbtCq+8/BrVZIKWMJ7krDYdfe9xztNe1AgRWB+M8DYgtMPa1LXqrCcAo0Li\nfEdVCqpCEXwkzwxFFmk6z7puEQYmowypBDEIdq0jN5L1rudi09F0jukoo8z1E31iDAw8zmRaUmQa\n5wKzKuNiY2k6y7aWEAJKCCajHJNp6m0PWIo8NeFcbAMRsAEEmjcPd3hAhIiRkSAg0rFanfP6rbs8\nf/2Ef/XHfgj2zX3Op+sGMWnRPsmNfR/Qte4ngL+9//s/A/7W2zeYz+cZ8F8DfwX4c+/0gpcuxQl7\ny5wYI7lJ4gAfuT7jozdmHE+T2sar9zb0zrHc9Oy6wJVnbiCkpqnXlJmiyiUIQdNGmt6zayIv39ny\noO3Y1BYXIyF4Ggu2h9ZGLtZLTo9nHI4zTg5KcqMpMoNA8Nqrt3j2xk2KTDEqDQdjw7QyIJIiSAiR\ns3XL7bOas1WLdf6dD3RgYOBdRymJEGBMKn1WhaLKk7zdqu7xHoILNHuRkkjqTg1EOusQMVAYydFk\nBvRoIMmWgDGgJfh2y9iUjArDwWzCxeqML3zx88QQ8T7QdB4pI1LJJ77K9AEZNz+yf9xbQoZ9OfbN\n/GXgrwPfkYDxpcsopUjWVkK89W7FaMXBpOD+KrWD3992tC5SaImSCqXGOHtMs92S5RXTALEUbGtB\nZwO7nUNTsuuALmCAsP9xbcukOOD267cJ3QE3b5wwrgz1bsfdO7eYTmeEKIgRzlctSqUAXhWGg0nB\nbtvR9UlDdtta6t4zqzKmIzNklwMD7yNSCAoj2dTpJnk6znj2yohN43j5zoq6DbRdx7bxeBcxGh4s\nW4QUyCioCk2/czz/3Cn1VxqWfUwa0SJihONsuSEAxwen2BCojENkJV996WWe+8jHkxCCBqMUdev2\nGa5KOrDDteC7Zj6f/2ckn+SHCb4Afuxtm8m3/Z/vA350sVj8t/P5/E/yHdhDXrpACXxLtZuqMHzi\nuQN+7+sP+PLLG+q2YzpK6jql14yLq9y9e4vd5oLj42OijHjv2O16JD2B7JHsnSe9OaMx+NZx9fQY\nJWestjXnX3yDMoNJpfnUC8+zbjzWOra7Huvjfk5LopRAZRoh4HhWYLRiW1uW246Lbcu26TmY5FRD\nOXZg4D0nxEjbeTob0Cr5VRqpmI1zOhs5mBRcPZCcbxRiZWnbjq7znG23BB9T30GVc761Sajg8AS3\n2tG1DTu7hm3P8WRMlBm1BUcaP8k0CJVzfn6fFz787N4TNwkj1F3SowXQe1OH9PM9ZVSPDe/1MSwW\ni78J/M03Pzafz/8WKav8/MNMcrFYuDdt8meBZ+fz+a8CM+BkPp//F4vF4n/8Vr/nUgbKt2Nd0n11\nPlK3luAiQkYyo3E+3U6cHpc0rSVT16l7y5e++BW2HTQoJCUORdLzSJ6VYf+3Zhs5OTzAaImPYDLD\nbDLi5KCkzDVSCI4zSd0FHqwbQhQoAUoLbB/YtJ5ZKTmalPv/oyiKis22Z9tYHixbylwxHWXkRj0R\nJ8fAwONGZz1tlwKUkoJJmRNjupA/lMI0UqKU5GQ2Ii8cFyvJtrFs255b95bcvvUKylsan1FNZlTj\nMaPcMCoylktPlgtCFBAjWkScE3RIch2QStG2LUWmSTkoHI4zRmWG82H/E/dmCh4heBQw9SUu0X5A\n17NfBP69/Z//NvD/vPnJxWLxs8DPAszn8z8B/MffLkjCExAoQ4hsG0cIgV1r2TWWzkWePR1zvu6w\nPqKE5P5Fw3rXsW0dD+7eYXp6ldIKznc9fe+JHoL3ZCiEhuD3+bgWrJuO8VghhaTvPXWXhNfzrCKG\n9IWejTQhQNNZXACJ4GBsqKqM1bahswEfocrTW14WmqlKoupN57Bur9SRqSFgDgy8i2wbu59tTv6P\nuVFsakuZa6zzPNgvl0yq7NF2J2XJbtuhleO1F7+Iy0ZolRNEBkKwWW/o6i0HJ9eQIrBbg4uSbQ9F\nljwtg4/4ACJGbN8yPbhK2zumoxylJBGR7L3214S4b+6xLuJC2Js+AHikFEwqg7xk14UPqOv17wE/\nOZ/Pfxlogf8EYD6f/5fA/7tYLD733b7gpQ+UUgrGpaHtHKvQs9xamrYnhECmJb13nO86pADrI6vV\nksnsgKoq2DWWiQ9sfFL0rwpDvWsRZLgISoD04AWcLXuKPHW6JePmljKTFFmGLgXjMiOGgHUOoQVa\nQZFnCJlMn6WQLNctba7Jc41REiEFRZacBR7qIzedp+s9mVHkmbp0J8bAwOPGw1Mo7rXn52L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mh0wGc/+xmO9mXU5bZj3fRIJSgLWNXJmm86NogoEFqQa4GSJPP2PjXzxADKwOlhSYhwvukYFYFM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\n2LSRwflMYpgXxNBzc1rjxwWrj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LoiEEIwS3fNracv57bP3nvd3ks+vOt0n57pPtOa6Z7u\nOf3+qqbmnL323r3e/e6znvU+7/P8/yyWHb1z9L2l9TUTVZCJBNyK8WTEuSnkqaA3Huc8f/75r5KM\n1uj6nt6AlIqNkWRShO/QF7/6Fd77F/8KTWNoh/aTujVXRNmVDPrGHohfk2s5LX83MVDeoxx3HRl2\nbfDekycqrCB7i1BiKIjRtJ0NzdZNaNS2NhguW2tJEkmaBTkw4x3bmyMkQdmkbhN2ZEPb9PQIimzE\nuBjhAWsdHjAm9KO1fcLOvGN9nKCUZHOSY4yjc5beprTLmtlUMco11ocKyKYVjDJHoZOg/ZkpilSB\nF2RZyLXVraVtDBY4WASN0CLTYWWQJyRS0Nuw12Sw7B82oeDIeaSQpIliUoS0dpqEwHkvWia9Ftre\nXlE/utrqGzR9V40JIhCJ4sLukgs7K4y19L3lcNWjlGfVWHYPG4xx9DaIRVgX0qjC2aE9A2gNzluc\nE4jhW1gkMBsXzA/m7F/awdozrE8sbe2oPv8Mo3HOg489ydNf+DyzUcZ9WxOKRNA2DdWzz/PE297J\n5f0OISHTiiJRZKkmUWErQkrBavibiZxOYqCMXOHIocF5QIB3IShureXszdvBtcFhnEFKkA50okhS\nRdc7kkQz74Ohc6IEXR/Mah/ZnlD3lrYN1bhSCUxvaAfbLGMMrnGkhWZ+cIgU62jtaIVhPE5QJtzB\n16uas9vbQRpMCGyiOViFwKeTsO94sOy4f3PEdJJheo/xhlVtaTtD74JWp8eHACwtIwUeRZpo7i9S\nhAxiBk1rOFh2bM4y+t6wkqHfD8IKNs80m2cmr+nz7roO5xx5fne1FDjvX5VrytHeuHPh9VIKPEEF\nydjrNy557+mtxdaW85cWPHNxibGWItf0xrBsWnDQGst82VK3lkSHdHsiIU8UDgmtxzmDEBLjJDqV\nTArFfG/J1hRGhebsbIPLC8eFS4fs73RkeQrJjHR2jsvzloff9CjCrTjY28G2kjQr+JZ3fQ+ekBLe\nWs9ZmwQvypeLCoTxnZIFVOQlxEAZuQYhBhd545i3HdY5ikwzLlLGBawGebBpniBkMLM1xjEbJXRW\n0Pc9woeLZJrAbC1hVCRYa9lf9HSdJUkE3uU4HyyQVq0hnbcs2448KWiW+0xmE2qnsKueXMHh/g5b\nm9uMR5q2D+0lWaKY5I5VpzCdo3eWvge8Z3/VM86CSIEleFyGCldLlinSJLSVWOPphMEZSNZSNic5\nRZawv+jwzmEs3LdRMB0ltL2j7YKazKLu2Z83WOdu6AzhXDCffmn66TOf+SOee+6rJEnwVGyalq2t\nc7z73d/5OszwyTSdoW6DIfErqeUcBUZjrwbI4xwJzXs8eaLJM4USoYBMKhH2DKXCWceXn9/n0rzh\ncNUzysPzsixh2S5pW4sxljQJBT1KS0apwouQvtcKsgRaI7HOM0sV922MuH9rxMF8wpe/9DnWpvfR\nGxglnrXpBENwDDk8nDMd52gleGh7wnS8Raoe5dy5Cfv7NVpJ8izhzCxllAXv1Ov12B6NXMRynmuI\nqdfIqUUryWyS4gh7mEWur9xBm0loJZFSkCUh7aSEwAON9SFl1dmQE3NBYzZNJZNc88AZz4t7K6z1\nCDzNICc3LlKUFIhDj800fjRmfjDHOkuPw2Q5b37kTThH8LvM4HDl6J2nyBMyrehyy7IOFZTzpueg\n6UhksEDamCSsjTO8AGc982Uf3FSERB1d4iRc2JWMi4RzZ0YkMlRM7h80SA+9dYzzhOk4JUkkB8uW\nZdPRNYZpkVyTinXe07SGtn+5VdfHPvYHZJnkPe959zWf+cWLF/nN3/wI3/d9H7jt83sj6kEsH7hu\nm8NJgVGKICivZagSXdQ93oeexyxRSBFSrsaHdGtXB0/Jxarn+YuHnN9Z4bwfvguKZWc4f2kZUubO\norSk0JJ+MFb2XlCkgtZ4msZhnQMBkzxha6Pg3FpB18HuYc/OHPYPz7O2eRYHtD0Y41i0c97y6JvZ\nmGXct1GwORujlcchmY4zhPWsjTOmI01vQ7EbBGWnl+KvRsrIMWKgjJxqtJJDz6ENwWmoAE2TUNjS\ndBZj4agZUSnBbJJzbnPEYR1WnamWLBtD13kObM8oS3jgzJj9RXA3WZOwM69pW0uiJdM8pR8MmjfW\nCrrWDk3coJTGe0drLM56/CBPJ71Hp5qxTPC+pmlCu4DwAuMcTdNx0VgOlh3TkUaJI3GBsK9Vt/ZK\ne0KRpeRpx95hw5lpDlKiZRfexzrWx0H0OksVzkHdWpxxLOqeySi50jTftIajGNIbd8Xbsu87dnYu\nvixIApw9e5YXX7zAzs5lzpzZep1m+Sqrpqcd+kghFKgcD4z6sGG+vFonfTwwan3Vb7Ed9FuFEExH\n6SBYH2TnlAzVzLuHNTsHLU0bDMEPm57OWsZ5EvYjW8PuQc28blEK8ixh2QQLtiJTeOex3jNfNRhj\nME7jcRRZgjGWC5eWHBw0LBvDxYsvsHVmGw/M53s47+l7SesNb3nwIdYmGfdtjtlcK3DWc2GvCb6S\nWpFOM4QQHKz6YFE3iOcn+sYr7dMRFm4dMVBGTj2JlqG60LprWiWKTJMmQeLOHGs7kUJgHaRKIXTo\nzZyOUpquY1lblk2PFAKlZKhmFIJpkdG0K+ywHzobDxJzIly8dw876t6C7cm1Aufoeo+Qoe+usxbb\n9rhEMc4TrPEgJHkqcc7RtBbTW7zzg9ydINGCcZYxyoNy0aI2QSmo6+k6T9OmNI1Das84D+m2rd7Q\n9Tl5qpEC+t6R5hphHHXjOVh1qCPLLwSplmglqDtD1xsmRconP/HveOc7v/m6n7X3nrc98QQf/+Qn\n+a73vR8hwv7u0eduXQi4QTji5pSD6tYcE8kPz3/5y4J1lbFBnMF76J1DSnFtKtVfPzAecWSBdSQB\nOMrD57Sse9ywIl/UHTv7NcvaDkViCusUadKRaBFMmJVk77AZnF0kWSqom56m7UOSwsNyuWS+qBGE\ndijvHA5BP52QJqGlwzrL3sEuWxtrFJkg04o3b5/DG8vSCFrj2N29yDe/7QHWxxkSsHim45SNaUGS\nKF7cXYabLkL2pMhCBXjb2StCHkeZhOCCcnoCQ+RaYqCM3BCtQmrVGPeyY0pKlIR0yCp679lcy9nd\nDatQ4zzOOUZ5SqJz8tRxuGo5WPQ0vbni/F6kmscenKEvrDhYtCRaUDcWIaFIE6aFYLdf0DaW2nVY\nb/FOkOcSKSUJIXgaD7kIrii9DTqi+bAHGFYCGtO7QbgdDkzLyAxGu9MUJSQ7hw2LVUdnepq+J1GS\nw1XPuEhxzmKNY3OWkqgwxudeXIQg7B2r1qLkUCWcacTgau+8J1GS3gTxeeOTKwHIOn9FGOIonbls\nYWfeIAfx+tyGHr3u2GrvSIs21RI9yL+9FOf91TTqDVgsFnz6jz+DdfBN3/gEW5sbLJouBMEhbXoU\nGDdmOWZwbvE+CIDjwRN6cld1H5ILeFKl2D2oaXsTWjDw1HXP+cs1dWfIcon1Yb932XQ8f3lJ11ka\n4zC9o20tnXEYY1nWQ3W0FxjvODhY0jc1RVGEVg519TtYH+5x7uEHybOELFHY1Xnecv86RSqxxmO8\npzGKPPUoKdn1nv3DhrPrI87MCuSw4s1SSaIkxRC4j/Yk7SB5eBwpGDIUPq4m7yLKsvxu4JeAH6+q\n6sPXOf4fAD9FkDD7raqq/s5J7xcDZeREEiVpe8vhqhuCY7iLfqmObGg3kUxHKVJeXcmkiUQJyQpD\nkYW9vMUq9LA1raGzjlUXLkrZZo4Qgm4ULpZJosgzxayQXDpouLxfs2odwnmMU5jEs71W4DPFvDFY\nAdNRStt5vAhpTykkzjqM8cwmWaie7QzGOFadwXjHGgkbk5z7z4zZ05qDZUNjHKu2x3tH3VpWdcd8\n2bJ7kHPuzBilYGksy0VLliq8h0mhOarz8EDbG/CwbDra3uLlmC88c5HZbI21kb5qEj1cxL0LBSuj\nLKEzhot7NRBkBcd5Gtpd/NV07nGnk+OtCtfMn5aDAtLVx6y1fOQjv0bv4BsefxytJZ//s0/w2dbw\nnvf+JWbTlEmR8lIOV92VDIIkyLU1XdiLtdZdSTcfLEKFdNcbvAjKTqu6C+0cUkDrOJh3rLqe3f2W\n/WUzrGYtWinqtqe1FpwI3x8tsd4jUew3+0wmY6QHElACJgk4YLY1ozu8zCP3P4qWkp3nHZkGvKcx\nntY6UhVusCSeSS5JZJhfYx2r2uCsZ11mpInizFpxzed51Hvs3FXVqyOTbwB5nb3Le507scIuy/JR\n4CeB37/B8QL4n4G3V1W1KsvyY2VZ/mJVVU/f6D1joIycSDpoaIa9quvfTR8Fz64PajtHaTvnPIfL\nniwN+4KzUUqa5Ch1JCfXsTsPe0mrxgxpUTDGkqeKItfgFTtecG5TkqaK+aKj7Sx1Z+it58J+g1Ye\nvMRpiXeDRVii6J1lWVush67tAUGShJWeEY626VnWgvmy5cJuS54KpJB0xiG8p8gVXS+pu5667dlb\ntORJzbMXDpmMNEpJFm041/VxxsU9R54oJuOEIklD1Wfv6DpLZy3T/Cyf+tzTPPHWlMVKIYWgyDRZ\nGlKpf/65P+Obv+UvsHe4YtlYjHEsW8PuoWRjkpMPn+Mo1+CDaLd1DufclXYMJQWJViQqFFU570m1\nHFKuAiHgX//ar/LY44/z4osXqP7sT0g1vP3tb6d3kn/7W/8fP/qhD9F2hs64K+WcTq54cWeFsS6k\nZ60JguMirM6yVLFYBTWdpnOD+pOlM6Fox9pwHq1zHNYerRVta8Iq20EmQ+pWqDBuNwjf66F4x3Xh\nxgYkxkBngvtHogalQ8ALWLU9befpsCxMwgt7brhJ8KRakGTh5inPBWt6xZsfOMN8FZSejmQYUx1k\nINveUmRXL5FHvce8ZIvyaIUd064v5w59Ji8APwL8k+sdrKqqLsvyyaqqVsNDO8CZk94wBsrIiWgl\nWRunN7ybtsfuqA9XXRCN7i1dH/Y2e+OYkLA+ySjSsH/kvWdSJMFjUiku7q04XLUoebTSdOz1HUUt\n8YMrRKokD5+bMX1zwqLp2TtouLBfs6y7IDvmJd56OmsRNqx8s0SjxyHw1bUF4ZBSkachPbpQfWh3\nQWCM4aDzg3Fz6GQfJyrkOZ2j6T3OwYE1SNmSJoI8S0IaVMDuvGGUhfEkB5LJOGOSKToT+gSNc8xr\nz9r6Gb7ytfM8/NB9KCWpW4dOJBfOn6dxM5653IJvkUqQq+C0UreGrqsZF5pxkVC3NkgGDoHPw5W5\nuLqvGEysi0QznWTBEQW4ePkyu0vLhU98hvKxN/PN73wXB4uW3//DL7JqeqazDT7xJ59nffPclZsd\nYx06U+zt1yRKhdVXO1icSYkUjs442j4ISOC40re6qhushTTT+OFxY0PatraW3hpSrXFSULdBxCJL\nARcGZmy4CShSjfeWPglqTGqYmlEWPCPxEqXArMI+NBI216ak9BSTFOHB2OAykyYCY6B2I5reDSlX\nx3SSUWSaZKjU7W5S81eIUPkduTuoqqoBKMvypOcsh+c8CTwCfOyk94yBMnJTvNLdtHPBQWSRyCsX\nnlSEC40xjvmyY/9wUGaBqysgJdgcDKSlgMkoZbFq+dqLhywaw2ysmOVpkNhLFFor7t9MuX9zxAOD\nW4ixnvmy47DumC96uj70Au7u79O3dSi+seCcZG19jVGaIZMgrpBqSdMHH01wSCnpe09rPQfGDELX\nEiUdznoSEfbFnPMw9En6YR93YTxKG5RQNG3PYZ5SZIpREgqUOuMoRpsgNdUXnyWRFo/Eedg+s8nW\nmXXOP/clJnnGw295FO/Btp6RUuhMoUXosRgXGiGGlZYD7x2GIaaLUGyyaAyX91cIKdnueoo0/Kl/\n/NN/Sl0b3v2t72Q60iEIW8Fjjz/O/t4hzz3/Al/+cs8TozPDTUjYI5Wdpu/Das9aj5aK8TSl7Xp2\n5j2LVR8C9rCCvLx7CHZJmoYqVeEd+XjCdG2dxSpo7XrnSKSkSCSrLlhkZVriekPde/JMMlaK8SSn\nyDSrWlMfHjDKIFWCLIHeKiapwwvIUo1fOc7McrQWPLj5OH/4qY9ydn2L0XjM4cqz7MJe83PPfI33\nve99bG+MKDKNFCJUXo/S0NIzSqmX7ev15xV5lZRl+deAnyBcVo6s63+mqqrfuInXPg78M+A/qqrq\nxA39GCgjr4mju2klQzXsKA+VFWvjLFRC1oZF0w/VoFxtOBNiqBIMvZbTUYIjpNuKLOHsxohxa5iO\nFOMiQxICg3VhP0wpxfo4HfbFPLNxQt3l7B+27Bw0PPvcC6RFxmS6gXUObS2NhQsX91hbn6K1RknF\nbKTIlQCn6IUg05J0KmlN2LOyLqQftYJEhwpLvAMp8cLjpQhFH1rS21DAZLzjYOXRnQ0rzCQUGSFA\neoEQGaONBxBCkCcC7x1fee4Z9uYH3H/2DIu257d/7xOMR1O2zj5Alio2pwWLvkc6KArNtEiC96EQ\nJDJUEtvhhqUzFoFnXCQwVOh6H7RJL166zFPvfAfGwP7SoiWMEokTnm40pjMWpKfrLQ6PVBJngjvG\n4bILvbGJQAnJ/qKhbg2tseAd3gXR+RfOXyLPCqbTCVkyCPQLwWrVMd/bZzxbo0gUjQmydgLAMaS9\nByk4C51USA922bCsFYvGsDKSqQGZBDeZzhl2utCKtFo1oVfSebyXNJ3jHU99Bxee+QIXLjxLZ8O1\nVMwK/uoHP8DZzSmT0cv3YiO3jtudeq2q6heAX/h6X1eW5UPAvwD+k6qqPvtKz4+BMnLbkEIwGSWk\nSdiDO9rLfGkatx9UdrrhgiwVPLA9ZtWYUKVqPFniYSjBN96zXDR4BM4ZlrXFeBAe1icZe3u7nNnI\nSbOCrvP0TgZbMWtJNqfM9w7Z2Nigt5aDpWOUJuR5QmbD+/TGk0jFdBTaEfJU0ztH1xpWnaXvPRIT\nWgUaS9P2ZFqHZnsJCBmKgGrPip5ES+YIpAKlgpWUJKSsHbC7c4nNMxscWqhfbEkSjRqfZb+pefFL\nL7CxscGFvZos1XTWYYxDK8E4SxgXCVKBFsFfM1GDvFsi0BKEVHgcy6YnV4oiz4LU3yq0bYih0OVg\nacMeYL7F/uE8yMpZz+GyZdVZ8jyktr337C06Vs2wmh5u5BMtaDpD1zTkGegElh00xjJ0+yCQ7M1X\ntC6lc254ncT2DuMtArAOhJB45cHb0KrSazph8M4xm83Y3btEotdBSdzg/NK2HYXq+LZvfpJUK7o+\n7E2PM80jZ5/CDd+zSZFwdqNAK3lDRaXIreMu2Le90Qn8Y+C/rKrqMzfzJjFQRm47L7WremkaN7Eh\nnQchjZinoVDGWMfhsmM1OEgESTkXLo5a0naWpoO2c+HC6Bx9pmmXl3nrW95C7z1KCJZLw6oNrQqt\nMfhWk2cSL8LKKMsUk1HCbJwhhOfCbh0KS7xG45FSsDnOYJJzuGzZW4QKThChctdA3QT920SB0pCo\nJBQ/+dA+4bwPQVJZUilRKqyol8uW6WRCIoKTsPMe7xxKwHRSUF+8hGRG3wF48iTBesNqFVoo5qs2\nVCMrQaI0iQ4FQs4r5ssOaxwCQe9DanPpZ7yw36G9p3OEz31I1y47h3AwKmZc2l1hCJXJTeuYkeOM\noW0dy84EhxkXMgnjXIOXZFpz0Mx503bBooHGBM3fcDMU0sRKjziYdyR5COihxsggvECI4XPBwSCq\nL4Wksx4hQwV2nivu23iYvb19+n4ZWpSEZWt7g3d/yzt45L4ZIHDWUXeGw0EkYZQnoRVokr0O3/jI\nEXeo6vUHgP8GKIGnyrL8G1VVfaAsy78F/A6wC7wX+LtlWR6la3+uqqp/faP3jIEycsc5ajNRSjDJ\n8ysl+VmiGGVhH80cCW2L0M/mfPCbbHvD/rxn97Bh77AJ1ble4rxEeYcQks21lKKVdL2n6RS+T1h1\nLcV4jFahV04g6K0l15pHzk24dNBycW/JwSKosixXijzTZKlmXDjmhw4nHHmmSdLQ/yd92CO0FrwL\nfZhCCFadw1vwicH0sPKh9y+XmrqpGRcFISg4tBQYoK4dbmnxesLFy3M216c0RtAmw7/pBcZYDB5H\naNXJE0tqJVo58rwgU4qWIBfYG8/eQUPdwd68RUp9JYWshKVuww3BwXxFsn2W8ztLnJQ475Be0LU9\nxgTFnUmR0DvNYtHR9gZjQMueJFEIPFInjArQJtzAyNBJQj8oG/auZaQnaAXWSbRK8TDsB1ukGiQN\nCb261rkrji1aabJUMB2fI89CCjpYajmeubCg7hzjwRVGChBDNfZsnDKLadZ7gqFv8mW9k1VV/a/H\nfv26HA1ioIzccaQUrI3Tl/UAPvvsM3zuc5+58rhznieffCcPPvjQNc97aBsOli2X9mvatufgRc/m\nNGHRmKERPFSoegy99yxq0GkSjHcVJKLHWcf+wiNkCMZaimHv1NMZ3JcSAAAa00lEQVQ0YUVqnGPR\nhBWYUoJUpehCkCdBjLvrg0eitWEF1dQG72rG4wJroGlrrAOdFkNxUUj17q9ACIMSkGchOHgPq9bR\nGzAGvGyHdpxQ8FSkCj/YSDFI5x0cNnigyBNS0eBlkP/LdULTGZZtz2S6waXLu5w7txEcXkzLshM0\nxg3BTND0Ftv3SCWwFhDhxkQQtHYR4BCkmSTPMhYrQ91bmt6y3ylWF3oEoX3FuZC+ViqkVU0Hgoyu\nDxXIqRZILUmUYJKnpKlC4lnWliwVTEY5o0yhhv1Li8e7kA7fWsuZTVL2Dlsu7q4GhaUVWxs5zsOk\nSCgyzbLu6a2L1miRV00MlJG7gpdexP70Tz/DfL7Ld33Xe655/NOf/mMODvb5xm98+zWPT4s0KMQo\nycPnJpydeh7cmrKsg66sUGFlumwM5597nvUz28yXHW0bTKp71yMQdCakeIUXqEQEZR8pkT5owkop\nGeWaQnt0ErRFhQTpPUpJggSAZ7FqyDIYFWMEEnLPdDzBGMvu/orReIQbhiz8sOJy4BqHkCErLQHX\ndUzGWbA9EyH4HCw6VolAS4VOJONck2lJMkoYOlvoTE/dhBYNIYOcX9gl9Ih0xHPndynycejFtJ7W\ngLc109mUZd3jhSATKqz6fAjEbTsUBvoQsPNsUKyxHtNbeu/J05z5YkWeFaHfEoI4AJAqsH7JZG2d\nUaLI84RZoVE6VMbqRFLXdhB68KRpSpErpoPYQm8SvPO0XQ9Ksmotq6am7YL92bjQTEYpiQz+oUoL\ntAwrYOe4orkbef24C/YobwkxUEbuOvq+49lnv8L73vddLzv21FPfwu/8zu9Slk+g1NW9TykFkzxh\nWRsef9s7+d3f/jd827e/G1C0zjJNYeNMzmf+5M/59rc/xHi2zc685vJ+y+WDVSis8ZCnYui3CwEn\nk4rxusZ1wa0k06HS1PnQr2edoO9CCjRTEo8E34GpSYox1oUtkNDZIRFKsDYbhfQsiiIvWDU1iSrw\nQO9DQJSEiuDGWxIrUCpIwQnC3l7TeRAG3QtWdY/WilwLjBP0vUEqgdCQ+VDw0vmjqAxCJ+hswnzl\n6V0dzI3zgtnaOjoJgUQpjxIaZ11QyQlbqDhr8ULS9Y5VY0F4tBYYG85tlGU467GmpcgzjA3iADgw\ntmZtNmU2zhgVCVrBsvPYZYPHM85TPILxSJOlKefWMtanOXjPojFX5rrIMhwuuNYIyLOUMypnfZwx\nGadIEYq6+kH6DoLIe9vbGChfZ2KgjERuEx//+Ef51m991w2Pv+tdT/HJT37sZf6NR3tWTW/54A9+\nkN/7vd+mMxZVzKjrFu073la+lQcefARjPJtrBevTmrVpyrLukUIGr0zvabujAhyJP2rk92BxNL3D\nW8faJGN33mBSjbFB63UjUzz/wiFb2zOMDWnCLAFkUHsxfWi5WCyXjKbrQbZNFDhbo4dVGBBStTYE\n0FUX/k2tBIkIykMSD1LROR+CrjdoGVZQUksyIciylFGqcAL6zuIA7xx1YzGDXyiEfTvnj9LOEoGj\na6BxXdB81YpESPIUnA99plILrHKD7qwm0cNqO005M8vZnx+yP1/QG0/nQ9HO9saELMspUkWiBfNF\nT2ss3jpUohACtjZyUqloejO41DiarkNKSZ5q1iYZo0xTpJpxoVFSBnUiH3p6R3mC96FVaS0JBWFt\nH4QvjH25ZnEkcjPEQBm562jbhtFodMPj0+mU5XJx3WOjIgiSj3LND//QD2GM4cKlHRadIM+KoB0q\nJV45Eq14aHvCA2dG9C4ICuSpCscBXBA735m3HCwbDhYd0gucE+hEsbk+YpQlYX+yMzgEo0zRzV/k\nwQfPsLPoWa6C7q2UCrxl0YaqXVcLHtwqMG6Ec47OjNjb3cHb4Fym8oKH1jZxDg7rjq5zODwG8Ebg\nCCtKSajJcR5QCi8hl6EqWAkPWLTUyCRUj/Y27DEmSpMogZeSpu3BOJrecFh3g+B5kL3TUqBywXSU\n0LcGpCSfSTKlUBKWjWNRt3R9SNHWbUdnJeiM9Y00iLkf7emmmnGqmRWaZWvQWrI+TSlyCT70WyoB\nF/eXKB10foOQQMLaOGU6DgIOWoYWGyUlaaKwVtL0oV1nkKCl6QxpkgY5P62GPl5/3e9MJPJKxEAZ\nuesQQmCtvSa1ehxjTAg81yE4PQSR6yxRaK158P5zrJqenXmLGTRIj6o3s0F4PbSaBPukUaZwPhj0\n1q1lc61g1fRcPqjZOegwrse5kPYLknGeNNXBsaN3rK9tslru8sDmFueBVWODzqhOyXNL2zj6RrK1\nPgqyfUPa9833rQ+KeYP5tXPoTNJ1hvmi46DuWNVhDM6E4hh/LLPlsAgjWHSWpeoQQoF3CBEqSIUM\nq8M8FaR6+NN3jnroMXQOjAl2W9NcMio0XkoKrSlyhRkqWK3xrEzoU9Ra4G1LvVrhnWa6PgEPrbEo\nLygKzSjVGOcHcQowLgS5cxspWxtFSKF6wXScMF+2NJ0lSxTnNsdsrxWsTbLg0DF4Y/rBtqu3DprQ\n/mFtqNo1h92VlWbTXdVqDXvgpyMN+EYipl4jkdvEU099G3/8x5/iXe966rrH//AP/4hv//b3XveY\nVhIpuKI/e8QoT8gzfcUzUavQb3hkoXR0QW06y6q1TIugMGRtCDTjIg2GzX5BbzTjXNM6eLELwaPr\nHcKGgNOQ89zXnuNRsYYfNEuXrSPzYY9zf+8i959709B7qUCGlGjrwl6aG/pFu97iWoEYVI2KJAEv\nQ7ELDttbvAx2YqbrQ1Wp8JgehAGpwr6eEAJJUDPSKQihWDYGZy04T++DKk6iYVQoUilCAZPSeOfZ\nX3YctgbhPakSODHYrOG4cP45xuN17tuaYK3h8s5FPIqz586BkGyvZRRZEoT1TdBt9RK0TChSjfCS\n3nlSDXUTejPPbkzYnGU8uD1hnOsgHD8YhgNXFJqM8VjrMM5jB1cT5/2VwjDr4gryTnNPBcqyLH8O\neDfBzeZvVlX1qWPHvgI8MxzzwI9VVXX+Npxr5B5hfX0DYzwXLlzg3Llz1xw7f/48UiaMxzdug9I6\nFJss6mD2e/THKkUwVFYSEq2G1dtVw90i0wgBdWs5rHsmhWY2TvH+yJhYsL1ehPaEXHH2zIQvFpqD\nRcey7lk1hixRHAjP+uYDfPHLz/DYI/eTpppm2VPXjgvzHdamY6bjYCmWJYreGJoenHP0NuzNiUEH\n1/UOKwReKKRyFKlgOkqp647DtqezwZ4ry8J5SkAUAuuGlaQXeMIqUYkgCn4kXq50EHHPJVhjkEKg\ndXA16Y3jcNVhXSiIyaQgE9DZsBfoteP8hRfY3toeDJQBmbC2vkHf9+zt7fDIQw+hlUIQvDPHeWgB\n0YlAC8XWRkaRJjRdz3xlaDqDJ5g+n90cMR7kEOvWYp2/8rsUAqkUyfWTCsCw5/rqv4KRyDW8YqAs\ny/J9wDdUVfWesizfRrAuOV6z74EPVFVV36ZzjNyDfO/3fj8f/egf8PTTn2djYx3vPQcHc7a2zvI9\n3/P+E1+banmNX+P1aLprjw3tgSHt6xzLxrJqDJNRkKYDT9uZsAqSYV+wyBNmoxQlJZMi9Coi4AE3\n4cxazqWNCeeffx7jOoYOBh564D7Wp1NGWYJUYlgxjTFuaLGwgHcsG0PbGerehb21YdXU45jlKUrN\n6DrDsulpWkOWKtJU4WyojW07A97RdZ7aBnUenA3BSECiQWtNpoL5c28T0kSQJgolBMITVHl6GypM\nlWbVdKSJIlWSncv7rK2tBaUjAfU8pFO1gulYcenSgiIRPLA1JksSlBKc3ShCiru3bE6z4HkpwHpP\nnnnWxinFYHw9LYIIQbAR8193ter1zKwjkVfLzawo3w/8K4Cqqp4uy3K9LMtJVVVH1RQx+R+5LXzH\nd3znECD3EUKwtrZ+U69LtGJ9ooIcnPf4IBM7OGFw7WP4q8eG/4cLvqPpDP3cMs51SKl2wXtSIVk2\nPS/uLoMQgbEoKRllmoNlDwK2ZiMyLdmYPs6oCKoyh0sDeIpcIxCDcowcWkdABhkarA9BeG2SoTQE\n3SDB5XnDpb0VvQli64/cP8PY0N+pZFgtdp1jf9kiJUEGsLPo1rKzu0vX1UMhT8GZzU20liSJQgvJ\ntNBsrRW0nWfnsGbVGjIUQomwr1lkHC5qEq2Y5Jr5znkm49mw5wsG0BLGmcB4yWg6YXFwgbNPnGOa\nJ0zHGR7YmzcIEQLyUWJUDV6la6MU62GUafQQGBNiO8cbmXsp9Xof8Kljv18eHvviscf+UVmWbwF+\nr6qqv30Lzy9yjyOEYH1941W9Vh7Zk7wKvE+pW8OqtYBHK8UoC2lPgEQHM2Vhwo7DojEY48h6R9Na\nVCIYFxmzkWQ6TihyTdP2HCx6jHNkSbDdMsaxqC3WWawNRSnWg5RhJZl6hRBB8T2RkKaKVIUCpP3D\nDmPNsHr2NMaGfUStGGUJXW9ZNg3PP/88m+sz7j+3RaElfdvw/Atf5K2Pv5WN9QltH9SEll3w4pyN\nUopMY3E4G1LZZ9YL9vcknQXrHXniuH8jobeCVAvWR4oil7S9ZW/hWa0suQ57xfurnsZ45oNt1bn1\nEamW5JkKfqVFqGbtjQP79a8eI5Hbzasp5nnpleengY8QhGZ/pSzLH62q6l+85jOLRO4gQghGeYKS\nklUb8qajLL1S9FNkmjPrBa4PxyZFyqLuWZ9kV/w4lZQUmT62mi3Ikppl0yMlrGkZKjldEE7Hh9VV\nomUQjffhmHPQGof3nnUbqnVVIoPs3tLSd8Gwej7vkBI2ZpJZmpGmli98qeKBB86Ra4VC0BkPOuOR\nNz/CF77wBd7+9idBKvIsvJ9SQZhcO0miFZuzlOWqx6IoigzdW6SSbE6C+s3aOGGSa8a5wHnBonHM\nCseXv/Qs733P95CojFUbVt91Z5gVKU1vUTrcxHgfbjrSRFG3Fq1ElJo7RdxLK8oXCCvIIx4ArhTr\nVFX1i0c/l2X5YeBJgs/XDdnenn59Z/kG514a72kca9MZ2s4yGQWx7uMcH++5l77wOtx/bsb5nSVt\nZ9BKMS40eaJDGnLYJw1OKEd9f+KKqfDOvOZw0TObBEk2gN7YsIo7WHH5oOZgYWj7HiPg8HCfsxtr\nnN3MGCWK1oSg2gxtFtONM3z1hYu86aH7kUqT5QrhBX1vEUoyKhI6J0hGKcp4xhsF65OM8SjlsYfG\n/Ma//R3OPPE441ySpxLroLeezjumY81bH7ufZd0zX3YkeZCjW58Ek+4jF5g0kWytFQDoLGGUJ1du\nRu40p/G7HHl13Mw38teB/wH4v8qyfAp4vqqqJUBZljPgl4APVlXVA98N/PNXesNLlw5f9Qm/0dje\nnt4z4z3tY90ddGOPeLXj9b1hcdhinWNfyuCSkmsSLQdlnrDC7MxVRZmut+wdNsEDs87QWgWlHi1J\nJeRacW42YpT0LGpJbzzPXLrE2bPncE6w6BxaBCGGiXRYYH2k+cozF1Dcz2LZ0HWKIgtmzxI4XPR4\nLEJItrfGrBYthx6apkcLyZPlN/DFpz9L9k1PYH2OtZ6LF17k4ovn+YEf/BG+9NXdYASNZ5QmjLVC\ne4/wDmcdprcsG89q0V75bPpxwuIu8Ik87d/l48QbglfmFQNlVVUfLcvyD8uy/APAAn+9LMv/DNiv\nqupXyrL8NeBjZVmugD+qqur/vc3nHIm8oclTzXTkmC87hIBF3bGoO8ZFco2Z8FE/Zdvbof8TslSS\npcHyS0k5VOrCuc0xEIS/69bgnGPvedjeSOiMH1w8HFKCFCr4bKaatcLz0PZ4qOwVOBxaSibjsHou\nMo0UgtlawaWLi/DehNRz+da38thb3sLHPvFxVnWNdYJHHn4TH/iB72DVWqyD6SgZ7NEEeRr6OUJK\nOqSlw01AEA84UtuJnB5OS+pV+CNxydcPf6/cqcG9d2d6r4wVXtt4rQuBsutDBWszqN5MRhrnBMaG\nICmEGPo9ATxrk4zspAZCYFH39MZx+fJFvvCFP+PRxx4FH97D+FCg0xnH+RdfZH3tDG9762OkOogL\nNL0BgrG2VhI57Jk+cN8a+3tL2i70mHoPozwoGFnrWDU9+8uePAlycdORZlwE67SudxSZIk/vjpTq\nzXAvfZe3t6e3LZotFovXFGAmk8ldEWnfON/cSOQUEdpJEiAEoixTHCw69g47RnlYhY3yhFRLEi1Z\nDopCN1MROso1bWd5+KEH+Owff4xREiyrIKjVeA94y1efPs93f/9fDEo3Ngi/T8cpiQ5C490gJt71\nQXzgYNmFatVUXXFbybSi8UGP9VyiaDpLP7S4KBlsy6TgFYN7JHI3EwNlJHKHyFIVNEsHYYSjfkrn\nPGvTBH1M69YOqcmbaaSXg8oQwAd/6N/jwx/+VUajjG/6pm9ECsGfP/00BweH/PAP/+iV50t97fte\nTY+GCt6gWiRo+3CubWdwHrrEopVklCp6K1BKcVTvdPTco9dG7j1Oy7zHQBmJ3EFGmWbhe5QUTIqC\nzli6PlhDHQXKIxupVH/9F50kSfjQh/4qe3u7fPrTn8J7zzve8RRnz95MjW5AK8koDw4eR3uKAs+q\nDeeqZNBrDX6eiiILAvF1Gxw90iTuO0be2MRAGYncQeSgSnOEVgLnerreIYUJjf+DwLt+DYUuGxub\nvP/93/+az1crOQROzbhw9MbSmSAzd3wfUgpxRZs1cu8SV5SRSOSWE5xKEhar/ortlxtcMJS6uy46\nybB/WngfTK5jxWrklBK/2ZHIXYYUgnGhkQJWjaEb9jBfKnZwtyBEbOuInG7iijISuQtRUoaVZd3j\nXLDJOi1prMi9w2n5zsbbwEjkLkWr4Ehy9HMkErkzxBVlJHIXkyYKpW6uLSQSuds4LSvKGCgjkbuc\nuP8XidxZ4l9gJBKJRCInEANlJBKJRCInEFOvkUgkErktnJY9yriijEQikUjkBGKgjEQikUjkBGLq\nNRKJRCK3hdOSeo2BMhKJRCKnirIsvxv4JeDHq6r68HWOvwP4BcADv1pV1d876f1i6jUSiUQip4ay\nLB8FfhL4/ROe9n8CP1FV1V8AnijLMj/pPeOKMhKJRCK3hTuUen0B+BHgn1zvYFmWZ4FxVVWfAaiq\n6sde6Q1joIxEIpHIqaGqqgagLMsbPeXNwF5Zlv8U+Abgl6uq+vmT3jMGykgkEoncFm73irIsy78G\n/ARhr1EM//+Zqqp+46TTIgTLHwZa4KNlWf56VVV/fqMXxEAZiUQikTckVVX9AqEo5+vhAvC5qqr2\nAcqy/H3gm4AbBspYzBOJRCKR08rLlrRVVX0VmJZluV6WpQS+BahOepMYKCORSCRyWxBCvKb/Xg1l\nWf5AWZa/Dfxl4O+XZfmR4fG/VZbltw9P+yngI4TK2F+vquqzJ47De/+qTuY14C9dOny9/807xvb2\nlHtlvPfSWOHeGu+9NFa4t8a7vT29bRuJ1trXFGCUUneFYkHco4xEIpHIbeG0KPPE1GskEolEIicQ\nA2UkEolEIidwU6nXsix/Dng34IC/WVXVp44d+z7gfwIM8G9eSTMvEolEIvcG90zqtSzL9wHfUFXV\newiNnf/7S57y8wS5oPcC31+W5dtu+VlGIpFIJHKHuJnU6/uBfwVQVdXTwHpZlhOAsizfAuxUVfVC\nVVUe+PDw/EgkEolETgU3EyjvAy4d+/3y8Nj1jl0E7r81pxaJRCKRNzJ3oo/ydvBqinlOOvu7Z2SR\nSCQSidwCbqaY5wWuriABHgDOHzt2fAX54PDYSYjt7elNn+Bp4F4a7700Vri3xnsvjRXuvfHeJk7F\n4ulmVpS/Dvz7AGVZPgU8X1XVEqCqqq8RNPMeLstSAz80PD8SiUQikVPBTUnYlWX594HvBizw14Gn\ngP2qqn6lLMv3Aj9LsDf55aqq/uFtPN9IJBKJRF5X7oTWayQSiUQibxiiMk8kEolEIicQA2UkEolE\nIicQA2UkEolEIidwW222yrJ8O0HV5+eqqvo/XnLsK8AzBP1YD/xYVVXnX/4ubwzKsvxZgoyfAv6X\nqqr+5bFjp04P9xXGe2rmtizLAvi/gXNABvy9qqp+7djxUzW3NzHeUzO3R5RlmQN/Cvzdqqr+n2OP\nn6q5PeKE8Z66ub1V3LZAWZbliKAL+5s3eIoHPlBVVX27zuH1oizL7wG+saqq95RluQn8EfAvjz3l\n54G/ROg//d2yLH95kAN8Q3IT4z01cwt8EPhkVVX/W1mWDwO/AfzaseOnam555fGeprk94qeBnes8\nftrm9ogbjfc0zu0t4XauKBvgrwD/7Q2OC05JMyrwu8DHh5/3gVFZlqKqKn9cDxegLMsjPdw38h/c\nDcc7PHZq5raqql869uvDwLNHv5zGuT1pvAOnZm4ByrIsgbdx7c3AqZxbuPF4B07V3N5KblugrKrK\nAW2Ylxvyj4Yv5O9VVfW3b9e53G6GAHF0F/YTwIePBY3r6eE++jqe3i3nFcZ7xKmY2yPKsvwDgvLU\nDx17+NTN7RE3GO8Rp2lu/wGhN/w/f8njp3VubzTeI07T3N4y7mQxz08DP0UQMniyLMsfvYPnckso\ny/JDwI8D/9UJTzs1d2wnjPfUzW1VVd8JfAj4Zyc87dTM7QnjPTVzW5blfwr8u0FhDE65jvVNjPfU\nzO2t5o4FyqqqfrGqqsvDyvPDwJN36lxuBWVZ/mXgvyPk+A+PHXo1erh3PSeM91TNbVmWT5Vl+RBA\nVVWfAXRZllvD4VM3t68w3lM1t8APAh8qy/KjhMzI3ynL8nuHY6dubjl5vKdtbm8pt7Xq9RjX3LmU\nZTkDfgn4YFVVPeEO5p+/TudyyxnG87PA+6uqOjh+rKqqr5VlOR0KI14gpLL+4ztwmreMk8Z72uYW\neB/wCPCTZVmeA8ZVVV2G0zm3nDDe0za3VVX9h0c/l2X5M8BXqqr6reHYqZvbk8Z72ub2VnPbJOwG\nAfV/QPij64HngV8lTM6vlGX5Nwh58hXwR1VV/de35UReB8qy/C+AnwE+T7gp8MBvAZ89jXq4NzHe\n0zS3OfALwJuAHPgfgS1OqdbxTYz31Mztccqy/O+BrxK+z6dybo9zg/Geyrm9FUSt10gkEolETiAq\n80QikUgkcgIxUEYikUgkcgIxUEYikUgkcgIxUEYikUgkcgIxUEYikUgkcgIxUEYikUgkcgIxUEYi\nkUgkcgIxUEYikUgkcgL/P5mt99EZUJxzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b1e8a790c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*XY.T, c=m.X.mean, s=75);\n",
    "plt.colorbar();\n",
    "for s in samples:\n",
    "    plt.plot(*s.T, c='b', alpha=0.1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}