2019_08_06_Ajuste_Recta-Catedra.ipynb

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    "# GF5013 - Métodos Inversos Aplicados a la Geofísica\n",
    "## Prof. Francisco Ortega Culaciati\n",
    "## ortega.francisco@uchile.cl\n",
    "## 06 Agosto de 2019 \n",
    "\n",
    "## Ajuste a una Recta con Mínimos Cuadrados Simples\n",
    "\n",
    "\n",
    "En este notebook se ilustra el ejemplo de ajustar una recta a puntos de observación obtenidos a través de experimentos independientes. \n",
    "\n",
    "Se ilustra el concepto de error de ajuste\n",
    "\n",
    "Se muestra la importancia de realizar la inversión utilizando apropiadamente los errores observacionales, especialmente cuando haya observaciones anómalas con errores considerables. \n"
   ]
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   "source": [
    "\n",
    "# importamos paquetes de python que necesitamos usar\n",
    "import numpy as NP # para el manejo de arreglos (arrays, matrices)\n",
    "import scipy as SP # códigos de aplicación científica (algebra lineal, optimización, etc.)\n",
    "\n",
    "# las dos lineas siguientes son requeridas para poder interactuar con las figuras.\n",
    "import matplotlib\n",
    "%matplotlib notebook \n",
    "\n",
    "import matplotlib.pyplot as PL # códigos para hacer gráficos (muy similar a Matlab)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
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       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
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       "        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",
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       "\n",
       "    $(parent_element).append(this.root);\n",
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       "    this._init_header(this);\n",
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       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
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       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
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       "    this.header = titletext[0];\n",
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       "\n",
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       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
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       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
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       "        mouse_event_fn(event);\n",
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       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
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       "\n",
       "    function set_focus () {\n",
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       "        canvas_div.focus();\n",
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       "\n",
       "    window.setTimeout(set_focus, 100);\n",
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       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
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     },
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     "output_type": "display_data"
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SYrefvvtGHjbltXX008/HXNc5jfDhw8/5pxq1aplPoTXCCCAAAIIBEJg8mQb5SutXi1VqSL3e1R64QWpbNm44nXpIs2cKdWsGbvDWgZtu+0nBULAF88A/vTTT2rUqJFuvPFGde3a9Rj47XEPpL7//vu6+eabszw288lnn322e/j156df3Y6S/FWTmYfXCCCAAAI+F9i3Txo4UJo0yStI69bSlCleT2+2RbMgr1Mnb7Sv/X61Z/6s25ffkdmS+XGHLwLADu5hBfvKLsW33L3jVq6++OKL9Zvf/Ca7UyLbS5UqpfhzczyBnQgggAACCPhEYM0a6dprpW++kUq4/r6HH5aGDctlHGfBXtu2Pikp2cyPgPtIBCv97//+r957771IC+DxSvaN+6/CupXr1avn/iO5Vt9++22Opxw8eFB79+6N+crxBHYigAACCCBQxAI2XZ89qteypRf82biNjz+W/vjHXAZ/RZxfblc8AoELAN944w1VrFjRPaaQ83MKLVq0cE3ikzRv3jyNGzdOO9yESBe4p2N/+OGHbGtixIgRqly5csZXbfuvioQAAggggECSCNi0LldcId15p3T4sHT11dK6dQzcTZLqSapspKS7lFQ5Ok5mbLDH7Nmz1blz5yyPPOuss3TJJZe4OY3cpEZ5SPac4emnn657771XQ4YMyfJMawG0r2iy1kALAve4BRQrVaoU3cxPBBBAAAEEilxg4ULpuuske2yvTBnp+eel/v2zn9WlyDOYRDe039/WoBPm39++eAYwt5+ZJUuW6Ouvv9aMGTNye0rGceXLl1eDBg3csxLuYYlsUhn3X5R9kRBAAAEEEEgWAWvpGz5ccp1UsiYdm9bFfg26X2kkBLIVCFQAOH78eDVr1iwyYjjbEmezw1r2vvzySzfQiQkusyFiMwIIIIBAUQmkpeVqFO7mzVKvXtLy5V7G+vb1nv+z1T1ICOQk4ItnAPe5cezr3EMM9mVp06ZNkddbtmzJKJs157711lu65ZZbMrZlftGuXTuNHj06Y9Pdbir0RYsWRa610s2E2a1bt8jgjuuvvz7jGF4ggAACCCBQ5AKzZkl168pNZ+FFd/bT3tv2TMn9ylPjxl7w53oz9T//I40d6y3tlukwXiKQpYAvWgBXuXVqbFqXaIo+o2fB2sSJEyObp0+f7pq+09WzZ8/oYTE///GPf+j777/P2Jaamho51rZVrVrVjZZqqRUrVqhOnToZx/ACAQQQQACBIhWwIM81SET6cjPfeNs2b7ubjHn/5V00eLDcAEbvgPPPl6ZO9WLEzKfwGoGcBHw3CCSnwhT1Ph4iLWpx7ocAAggEWMC6fa2lzzVQZJncIMgNp7bTtb/6UF98YStgSUOHes//lS6d5RlszEaA39+SL1oAs6k/NiOAAAIIIBAcATeQMbvgz6breCW9n4b873M68L8pkcU5bHm33/0uOMWnJEUrQABYtN7cDQEEEEAAgawF4pY1jR60WyfrFr2m2fLmt/19k216fV5N9/hS9Ah+IpB3AV8MAsl7sTgDAQQQQAABnwnYmrtxaYkuUmOtiwR/pXVIz2uw3n32G4K/OCfe5l2AADDvZpyBAAIIIIBA4gVsGrJatSIzN6ephB7VQ2qrj7VVv9aZ+rtW6HwNrj1LKa2Zrizx+OG7IgFg+OqcEiOAAAIIJKNAyZLSqFFKTa+pdvqLHnYh4FGVlJvvQqt1rpqmrPUm+bPjSAgUUIAAsICAnI4AAggggECiBOaU6qJGFTZqkWv7q6Af9aauc+HfjapY+yTJTQHjFrpP1K24TsgFGAQS8g8AxUcAAQQQKH6BAweke+6RW7DA8lJG556brmmDv9AZJX4vVb9FbpkqiZa/4q+oAOWAADBAlUlREEAAAQT8J/DVV9K110rr13t5dwtV6bHHUnTCCS3cBvsiIZB4AQLAxJtyRQQQQAABBI4r4Bav0oQJ0h13SPv3KzKyd9Ik6fLLj3sqByBQYAECwAITcgEEEEAAAQTyJrBnj9SvnzRjhnde+/bSm29K1arl7TocjUB+BRgEkl85zkMAAQQQQCAfAitXSk2aeMFfKdcM88QT0rx5BH/5oOSUAgjQAlgAPE5FAAEEEEAgtwJHj0pPPy09+KB05IhUr540bZp7yo/H/HJLyHEJFCAATCAml0IAAQQQQCArgR07pN69pQULvL026OOVV6TKlbM6mm0IFL4AXcCFb8wdEEAAAQRCLPDBB1LDhl7wd+KJ0vjx0tSpBH8h/kgkRdEJAJOiGsgEAggggEDQBA4dkmxKlw4dpF27vCBw1Srpppsiq70FrbiUx2cCdAH7rMLILgIIIIBA8gts3Cj17ClZwGfp9tulp56Sypb13vMdgeIWIAAs7hrg/ggggAACgRKYMkXq31/at0+qUkV6/XXpqqsCVUQKEwABAsAAVCJFQAABBBAofgEL+AYOlGwyZ0utW0sWDNaq5b3nOwLJJMAzgMlUG+QFAQQQQMCXAmvWSE2besFfCfeb9ZFHpIULCf58WZkhyTQtgCGpaIqJAAIIIJB4AVvObdQo6b77JBv0Ubu21+rXqlXi78UVEUikAAFgIjW5FgIIIIBAaARsZO+NN0rvvecV+eqrpdde8577Cw0CBfWtAF3Avq06Mo4AAgggUFwC1r3bqJEX/JUpI738svSnPxH8FVd9cN+8CxAA5t2MMxBAAAEEQipw+LA0bJjUvr20fbtUv7706afSH/7A3H4h/Uj4tth0Afu26sg4AggggEBRCmzeLPXqJS1f7t21b19p5EjJVvcgIeA3AQJAv9UY+UUAAQQQKHKBmTOlW26R9uzxlnAbN0665poizwY3RCBhAnQBJ4ySCyGAAAIIBE1g/36pXz8v2LPg7/zzpXXrCP6CVs9hLA8BYBhrnTIjgAACCBxXYMMGqXlzaexY7/m+Bx6QFi2S6tY97qkcgEDSC9AFnPRVRAYRQAABBIpSwOb2e+UVacgQ6cABqXp1afJk6Xe/K8pccC8ECleAFsDC9eXqCCCAAAI+Eti9W+raVRowwAv+OjbepvUv/1W/a5Pmo1KQVQSOL0AAeHwjjkAAAQQQCIHAkiVS48bS7NlSaR3S8xqsP6+rpapXX+T1+86aFQIFihgWAQLAsNQ05UQAAQQQyFIgzTXuPfqo1LattHWrdKb+rhVq6cK/UUqJnrFtm9Stm0QQGBXhp88FCAB9XoFkHwEEEEAg/wKpqVK7dtLDD0tHj0rXn/iWVquZmmpt7EXtwUBLgwdLFjGSEPC5AAGgzyuQ7COAAAII5E9gzhxvOTcb2VuhgvTmA19q4v7uqqh9WV/QgkBrIrS+YhICPhfwRQC4ePFiXXnllapRo4ZSUlL09ttvx7DfcMMNke22L/rVsmXLmGOyevMnt3Djb3/7W5VxCznaz9n24AcJAQQQQCDQAjay9/bbpU6dJBv00ayZtNY1+F13jpvgLzfJ1oAjIeBzAV8EgD/99JNbdLuRRo8enS335Zdf7tZl3J7xNXfu3GyPtR3L3Vo+PXr0UO/evbV+/frIz+7du2vlypU5nsdOBBBAAAH/Cnz1lWTtA9FfJ3fdJS1bJp1xhiuTzfeSm5Tb43JzLY5BoJgEUtJdKqZ75+u21sJnLXWdO3fOON9aAP/9738f0zKYcUAWLyz427t3r95///2MvRZEnnzyyZo2bVrGtpxe2PmVK1d2SwPtUaVKlXI6lH0IIIAAAsUoYL/pJkyQ7rhDstU9qlaV3nhD6tAhU6bs2T6b5dkGfGT1q9H9/lGtWtKmTVLJkplO5KXfBPj9LfmiBTA3H6yPP/5Yp556qv7rv/5Lfd0K3Tt37szxNGsBvPTSS2OOueyyy9xfgu5PQRICCCCAQGAEbAm3nj29tXwt+GvfXvrss7jgz0prQd2oUV65LdjLnKLvR44k+MvswmvfCgQiAOzg/oSbMmWKFi5cqGeffVaffvqpm7H9dzp48GC2FbNjxw6ddtppMfvtvW3PLtn17K+GzF/ZHct2BBBAAIHiF7Cnepo0kWbMkEqVkp54Qpo3T6pWLZu8dekizZwp1awZe4C1/Nl2209CIAAC7j8H/yfrzo2mc845R+eee67q1Kmj9957z/23mv1/rNadnDlZb3j8tsz7R4wYoUceeSTzJl4jgAACCCShgE3p8tRT0kMPSUeOeD279nRPLsYHekGejRCx0b424MOe+WvVipa/JKxnspR/gUAEgPHFr+7+Y7UA8JtvvonflfG+mvvzL761z7qN41sFM05wL4YOHerWhhySsclaAmvXrp3xnhcIIIAAAsUvYB05bnyfFizw8mJtBK++KvfMdh7yZt3Bbdvm4QQORcBfAoHoAo4n/+GHH9xUTVvdH23ur7Zs0vnnn6/58+fH7P3www91wQUXxGzL/Mami7HBHpm/Mu/nNQIIIIBAggRsQIZ7ttuNyvN+5nLy5Q8+kBo29IK/E0+Uxo/3LpGn4C9BReAyCCSzgC9aAPft26eNGzdmOG5yI7DWrVunKlWqRL6GDx/uFu/uGgn4Nm/erAceeECnnHKKrr766oxz+vTp4x7pqCnrxrU0aNAgtW7dWk8++aSbC6qT3nnnHffX4gItXbo04xxeIIAAAggUg4Att+b+jZYt0xFN9gyeDdDI5rGeQ4fk/u2Xew7cO8GCwOnTpfr1oxfgJwIIZBbwRQvgqlWr3EO8TSJflnnrhrX3f/zjH92grZLasGFDJIizEcDXX399ZCSwjfKtWLFiRlm3bNkSmSMwusFa+qa7fx1ef/1199diQ02cONE9JDxDLVq0iB7CTwQQQACBohaw4M/W3M0c/FkecliL19oHrPMmGvzddpvcnK4Ef0VdddzPXwK+mwcwmXiZRyiZaoO8IICA7wWi8/DFB3/RgmUxD9/kydIf/iC5jiLXI+TN9WfjN0gI5CTA7+8AzQOYU0WzDwEEEEDABwI26ja74M+yb5Mz/7wW748/yvX4eIM9LPhzT/S4VZ285d18UFKyiECxC/iiC7jYlcgAAggggEDhC+Ryjd3Vfz0QWb930iTXiuF+i9nsXG4a2MgiHYWfSe6AQDAESgWjGJQCAQQQQMD3AjnM3GBlc+1/GqnBum/4pTp8xAv4pk71pujzfdkpAAJFLEALYBGDczsEEEAAgWwEbLJlG+0bN0m/Hb1TVXWF/qwhet4FfyXcevBel6+dQkIAgbwLEADm3YwzEEAAAQQKQyCbtXj/ot+pkdZrrn6vMqXT9NJLkg0WtkEfJAQQyJ8AAWD+3DgLAQQQQKAwBDKtxXtYpfSAHtMlmq8dqq76tfbq09UlNWBAlo2EhZEbrolAYAUIAANbtRQMAQQQ8KmACwI3f7xZbc7+XiNcCJiuEup7y1Gt+rqSGjTwaZnINgJJJkAAmGQVQnYQQACBsAu89ZbUuFlJLf9b5cj6vf/zP9LYcSVkS7uREEAgMQKMAk6MI1dBAAEEECigwP793gpwr73mXahlS8lG+darV8ALczoCCBwjQAvgMSRsQAABBBAoaoHPPpPOPVey4M8GAdu6vosXE/wVdT1wv/AI0AIYnrqmpAgggEDSCdjiHmPG2Brv0sGDkk0F+OabUrt2SZdVMoRAoAQIAANVnRQGAQQQ8I/A7t3SLbdIs2d7ee7YUZo4Uapa1T9lIKcI+FWALmC/1hz5RgABBHwsYMv+NmrkBX+lS0vPPSf9+c8Efz6uUrLuMwECQJ9VGNlFAAEE/CyQluat3du2rZSaKp1xhrR8uXTnnczt5+d6Je/+E6AL2H91Ro4RQAABXwps3Spdd503uMMK0KePNHq0VLGiL4tDphHwtQAtgL6uPjKPAAII+EPgnXfc3H6NveCvQgVvoMcbbxD8+aP2yGUQBQgAg1irlAkBBBBIEoEDB6Tbb5c6d5Zs0EezZtLatV5LYJJkkWwgEEoBAsBQVjuFRgABBApf4MsvpRYtvG5eu9tdd0nLlnnP/RX+3bkDAgjkJMAzgDnpsA8BBBBAIM8CNrffhAnSHXdItrqHTeti3b0dOuT5UpyAAAKFJEAAWEiwXBYBBBAIo8CePVK/ftKMGV7p27eXJk3yJngOowdlRiBZBegCTtaaIV8IIICAzwRWrPAGeljwV8o1LzzxhDRvHsGfz6qR7IZEgBbAkFQ0xUQAAQQKS+DoUempp6SHHpKOHJHq1pWmTZNatiysO3JdBBAoqAABYEEFOR8BBBAIscD27d58fgsWeAg9ekivvipVrhxiFIqOgA8ECAB9UElkEQEEEChSAVuuw9Zqs+iuenWpVSupZMljsvD++9L110u7dknlykkvvijddBMrehwDxQYEklCAADAJK4UsIYAAAsUmMGuWNGiQt05bNBO1akmjRkldukS2HDokDR3qrd9rGxo2lKZPl+rXj57ATwQQSHYBBoEkew2RPwQQQKCoBCz469YtNvize2/b5m13+zdulC644Jfg77bbpJUrCf6Kqoq4DwKJEqAFMFGSXAcBBBDws4B1+1rLn03iF59sW0qKJvddpD8culr79qWoShVvrr9OneIP5j0CCPhBgADQD7VEHhFAAIHCFrBn/lJTs7zLj6qg29JHa9Ju98CfS61bS5MnS7VrZ3k4GxFAwAcCdAH7oJLIIgIIIFDoAjbgI4u0Wk3VTKs1SderhNI0vOsGLVxI8JcFFZsQ8JUAAaCvqovMIoAAAoUkYKN9MyXrCH5eg3W+lusb/Zdqaas+Vls9fNsPWQ0IznQmLxFAwA8CBIB+qCXyiAACCBS2gE31YqN93bN+u3SKrtCfNcSFgId1gjprttarsVrV/s6bEqaw88L1EUCg0AUIAAudmBsggAACPhCwef7cVC8L0y9WIxfuzdXvVUYH9JIGaJa6qkrKv6SRI7OcD9AHpSOLCCAQJ0AAGAfCWwQQQCCMAocPSw+s6qL2KQu0XTVUX1/oE53nwr8xSqntWgZnzsyYBzCMPpQZgaAJMAo4aDVKeRBAAIE8CmzeLPXsKa1YYSemqO8tR/V8l+9V/t9utuccVgLJ4204HAEEkkjAFy2Aixcv1pVXXqkaNWq4x1NS9Pbbb2cQHnZ/tt53331q0KCBypcvHzmmT58++uc//5lxTFYvhg8fHrmWXS/6Va1atawOZRsCCCAQWIG33pIaN/aCP1u/d8YMaey4Eirfwc31YlFh27Z0+wa29ilYmAV8EQD+9NNPatSokUaPHn1MXe3fv19r1qzRQw89FPk5y81U//e//11XXXXVMcfGbzj77LPdUpfbM742bNgQfwjvEUAAgUAKuH86deutUvfu0p49UsuW0rp13vtAFphCIYBAjIAvuoA7dOgg+8oqVXZ/ss6fPz9m14tuRfLzzjtPW7Zs0a9//euYfZnflCpVSrT6ZRbhNQIIhEHA/tbt0UP68svIoN/Iur6uU0SlS4eh9JQRAQRMwBctgHmtqj3uz1nr1j3ppJNyPPWbb76JdBnXq1dP1157rb799tscjz948KD27t0b85XjCexEAAEEkkjAVnR7+WWpeXMv+LOnXuzv58ceI/hLomoiKwgUiUDgAsADBw7o/vvvV69evVSpUqVsEVu0aKFJkyZp3rx5GjdunHbs2OEWOL9AP/zwQ7bnjBgxQtbiGP2qzTpI2VqxAwEEkktg926pa1dp4EDJ/S2rjh2lzz6T2rVLrnySGwQQKBqBlHSXiuZWibmLtezNnj1bnTt3PuaCNiDkmmuuiXT9fvzxxzkGgPEn23OGp59+uu69914NGTIkfnfkvbUA2lc0WWugBYHW4phTsBk9np8IIIBAcQjYMr///d/S1q1eS9+TT0qDBrkuoMA1ARSHLvf0o4D9/rbGnDD//vbFM4C5+XBZ8NfdPc28adMmt07lwjwHZDaC2EYSW7dwdqlMmTKyLxICCCDgB4G0NK9795FHpKNHpTPOkKZPl5o180PuySMCCBSmQCD+/osGfxa8LViwQL/61a/ybGYte1+6J6Krx62HmecLcQICCCCQBAKpqdLvfic9/LAX/LnZsdxMCQR/SVA1ZAGBpBDwRQC4b98+Nz3BusiXqVkrn723Ub5HjhxRt27dtGrVKk2ZMkVp7k9ee57Pvg4dOpSB3M496JJ5Gpm7775bixYtilxr5cqVkWtYk/D111+fcQ4vEEAAAT8KvPOO3NRZkptCVRUqSG++Kb3xhlSxoh9LQ54RQKAwBHzRBWzB3cUXX5xR/ugzehas2YTOc+bMiexrbLOZZkofffSRm8O0bWTLP/7xD33//fcZe1Pdn8c93SSntq1q1apuDqyWbhb8FapTp07GMbxAAAEE/CTgxsDpnnvk/tj1cm1dvdOmSWee6adSkFcEECgKAd8NAikKlNzeg4dIcyvFcQggUNgCNqefm80qMrLX7mVj2dzEBTrhhMK+M9dHwH8C/P6WfNEC6L+PFjlGAAEEikbA5nGYMEG64w7JVvdwHRqR7t5s5s4vmkxxFwQQSHoBAsCkryIyiAACCGQtYEu49evnrd9rR7RvLze/qdxgtqyPZysCCCAQFfDFIJBoZvmJAAIIIOAJuLFratLEC/7cqpZ64gm5ie0J/vh8IIBA7gRoAcydE0chgAACSSFg8/k99ZT00ENysyBIdet6Az3cODYSAgggkGsBAsBcU3EgAgggULwCbnYr9e4tN9+pl48ePaRXX5Vb0aB488XdEUDAfwJ0AfuvzsgxAgiEUOCDD6SGDb3gr1w56bXXvJY/gr8QfhgoMgIJECAATAAil0AAAQQKS8Dms3fz1stG9e7a5QWBq1dLN98suaXRSQgggEC+BOgCzhcbJyGAAAKFL7Bxoze3nwV8lm67TXr6aalsWe893xFAAIH8ChAA5leO8xBAAIFCFHArW6p/f8mthKkqVby5/jp1KsQbcmkEEAiVAAFgqKqbwiKAQLILWMA3cKA3n5/ltXVruXXOpVq1kj3n5A8BBPwkwDOAfqot8ooAAoEWWLNGatrUC/5KuH+dhw+XFi4k+At0pVM4BIpJgBbAYoLntggggEBUwJZzGzVKuvde6fBhL+CbOlVq1Sp6BD8RQACBxAoQACbWk6shgAACeRKwkb033CDNneud1rmzNH6899xfni7EwQgggEAeBOgCzgMWhyKAAAKJFLDu3UaNvOCvTBnppZekWbMI/hJpzLUQQCBrAQLArF3YigACCBSagHXzDhsmtW8vbd8u1a8vffqpNGAAc/sVGjoXRgCBGAG6gGM4eIMAAggUrsDmzVKvXtLy5d59+vaVRo6UTjwx033T0qQlS7zosHp172HAkiUzHcBLBBBAoGACBIAF8+NsBBBAINcCb70lWcC3Z4+3fu/YsVL37nGnWx/woEFSauovO2wOGBsl0qXLL9t4hQACCBRAgC7gAuBxKgIIBFTAWuA+/thbbNd+2vsCpP37pVtv9YI9C/5atpTWrcsm+OvWLTb4s/tu2ybZdgsOSQgggEACBAgAE4DIJRBAIEACFmTVrStdfLHXV2s/7X0+g68NG6TmzaVx47zn+x54QFq82LtkjJoFmdbyZ3PCxKfotsGDCxyMxl+a9wggEE4BAsBw1julRgCBrAQsyEtQC5zFbGPGSOedJ33xhWSP8s2fLz32mFS6dBY3t2f+Mnf7xh9iF9y61Xs2MH4f7xFAAIE8ChAA5hGMwxFAIKACCWyB271b6trVG9V74IDUsaO0fr3Url0OdjYcODcpt8fl5locgwACoRUgAAxt1VNwBBCIEUhQC5xdpnFjafZsr6Xvueekd9+VqlaNuduxb6yJMDcpt8fl5locgwACoRUgAAxt1VNwBBCIEchty1o2x1kD4qOPSm3bej21Z5zhTfVy552Sret73GTrvtlo35SUrA+17bVrsz5c1jpsRQCBPArk5p+lPF6SwxFAAAEfCuS2ZS2L4+zRPeveffhh6ehRqU8fac0aqVmzPDjYPH821Yul+CAw+t4mDGQ+QM+I7wggUCABAsAC8XEyAggERiCfLXBz5njLuS1aJFWoIL35pvTGG1LFivmQsXn+Zs6UataMPdlaBm078wDGuvAOAQTyLcBE0Pmm40QEEAiUQLQFzkYBW4tbdOoVK2QWLXA2uOOee6TRoz0Fa+2bNk0688wCqliQ16kTK4EUkJHTEUAgZwECwJx92IsAAmESiLbAZbUSh3W//twC99VX0rXXeiN7jWfIEGnECOmEExKEZcGoPUxIQgABBApJgACwkGC5LAII+FQghxY4axScMEG64w7JVvewkb3W3duhg0/LSrYRQCC0AgSAoa16Co4AAtkKZNECZ0u49esnzZjhndW+vTRpkjfBc7bXYQcCCCCQpAIMAknSiiFbCCCQPAIrV0pNmnjBXyn3Z/MTT0jz5hH8JU8NkRMEEMirAC2AeRXjeAQQCI2ATeny9NPSgw9KR4546/faQI+WLUNDQEERQCCgAgSAAa1YioUAAgUT2LFD6t1bWrDAu0737tKrr0onnVSw63I2AgggkAwCCe8CTs1pMfNkKDF5QAABBI4j8MEH3tx+FvyVKye99po0fTrB33HY2I0AAj4SSHgAeM4557iJUN1MqAlMixcv1pVXXqkaNWq46bhS9Pbbb8dcPd0NzRs+fHhkfzn3r3Xbtm31t7/9LeaYrN68/PLLqlevnsqWLetm7G+mJbaIJwkBBEIrcOiQdPfd3qjenTulhg2l1aulm2/+ZSrA0OJQcAQQCJRAwgPAxx9/XAMHDlTXrl31ww8/JATrp59+UqNGjdyEqz/PuBp31aeeekrPuRXXbf+nn36qatWq6ZJLLtGPP/4Yd+Qvb2e4oXyDBw/WsGHDtHbtWrVyqwB0cHM5bNmy5ZeDeIUAAqER2LhRuvBC6dlnvSLfdptkgz/q1w8NAQVFAIEQCaS41jM3s1Vi06ZNm9xfzDfriy++0NixY3XVVVcl7AbWAjh79mx17tw5ck3LvrUMWjB33333RbYdPHhQp512mp588kk3bYObtyGL1KJFCzVt2lRjxozJ2Fvf/Utv1x1hM7rmIu3du1eVK1fWHjc/RKVKlXJxBocggEAyCkyZIvXvL+3bJ1Wp4s31Z4txkBBAIJgC/P6WCmUQiHWrLly4MNIiZy2BFliVsrkTMqU1tlJ6ApIFmzvc09qXXnppxtXKlCmjNm3aaNmyZVkGgIdcP89q169z//33Z5xjL+wadk52yQJL+4om+wCREEDAvwIW8LkOi8h8flaK1q2lyZOl2rX9WyZyjgACCORGIDYqy80ZuTzmu+++05/+9Cf313QVt6xlp2MCwFxe5riHWfBnyVr8Mid7b3nIKn3//fdKS0vL8pzo9bI6z1oGH3nkkax2sQ0BBHwmYH+D2nJu33wjlXAPw/zxj950LzYHNAkBBBAIukChBIDjxo3TXXfdpfZuqvzPP//cLZfk1ksq5GRdw5mTdQ3Hb8u8317H7z/eOUOHDnVrfrpFP39O1gJYm6aCKAc/EfCFgD30MmqU3CMjkg36qFVLmjpV7jlgX2SfTCKAAAIJEUh4AHj55Zfrk08+iXT/9unTJyGZzOkiNuDDkrXcVa9ePePQnW4IX3yrYHTnKaecopLuz/z41r6czrFzrWvZvkgIIOBPgV27pBtvlN57z8u/PUo8frz33J8/S0SuEUAAgfwJJHwUsHWtfvbZZyqK4M+KbM8bWhA4f/78DAF7xm/RokW64IILMrZlfnHCCSdEpn3JfI7tt/fZnZP5fF4jgID/BNxjyW42AS/4s7/jXnpJmjWL4M9/NUmOEUAgEQIJbwGMD6oSkcl97kntjTZHw8/JBn6sW7cu8nzhr3/968gIYJt+5swzz4x82esTTzxRvXr1ip6idu3a6eqrr9ZtNreDS9aV29tN83/uuefq/PPPj4xWtilg+ttQQBICCARG4PBhuXlC5Ub3S9b9a9O62KTONscfCQEEEAirQMIDwMKAXLVqlS6++OKMS0efw7v++us1ceJE3XvvvfrPf/6jAQMG6F//+pdsipcPP/xQFStWzDjnH//4h2zwRzT16NEjMk/ho48+qu3bt8smsJ47d67q1KkTPYSfCCDgc4HNm+X+EJSWL/cK0rev9PzzUvnyPi8Y2UcAAQQKKFAo8wAWME++OZ15hHxTVWQ0hAIzZ0q33CI3T6fcfJ1yrfySredLQgABBPj9XUjzAPLRQgABBIpLYP9+6c47vYDP8tCypTRtmlS3bnHliPsigAACySeQ8EEgyVdEcoQAAmER2LBBat7cC/5sZig3c5PcUuIEf2H5AFBOBBDItYAvngHMdWk4EAEEgiHgZhPQkiVyD+jKze/kTdKXwwzNNrjjlVdscJd04IDczADeih5u7BcJAQQQQCALAQLALFDYhAACxShgc7MMGiSlpv6SCZut2WZv7tLll20/v9q923vWzy0RHkkdO8oNDpObgP7nA/iBAAIIIHCMAF3Ax5CwAQEEik3Agr9u3WKDP8vMtm3edtufKS1dKjVuLFnwV7q09Nxz0rvvEvxlIuIlAgggkKUAAWCWLGxEAIEiF7BuX2v5s/7c+BTdNniw3ELe9n+5GZzUpo20dat0xhneVC82+MPW9SUhgAACCOQswD+VOfuwFwEEikrAnvnL3O0bf18LAl20lzrrEzexu/Tww9LRo3ITuktr1sit7hN/Au8RQAABBLIT4BnA7GTYjgACRStgAz6Ok+boSt14U1Pt3idVqCC9/LIXAB7nNHYjgAACCMQJ0AIYB8JbBBAoJgEb7ZtNOqAyukOj1ElzXPBXJtLaZ61+1vpHQgABBBDIuwABYN7NOAMBBApDoFUryUb72gR+mdJX+j9qqRV60YWAloYMPqply+TW/c50EC8RQAABBPIkQACYJy4ORgCBQhOwef5sqhdLLgi0oSATdKOaabXWq7GqaqfmDvurnn2+hE44IXIU3xBAAAEE8ilAAJhPOE5DAIFCELB5/twivnuqn6VemqqbXQi4X+XVrsxSrX9tlTr8vwsL4aZcEgEEEAifAINAwlfnlBiBpBZYWbOLepa5WpuUopIljur/3bxZ9750vkqUdi2EJAQQQACBhAjQApgQRi6CAAIFFbApXZ58UrroImnTppTI+r1L/1pC94/9DcFfQXE5HwEEEIgToAUwDoS3CCBQ9AI7dkh9+kjz53v37t5devVV6aSTij4v3BEBBBAIgwAtgGGoZcqIQBILzJsnNWrkBX/lykmvvSZNn07wl8RVRtYQQCAAAgSAAahEioCAHwUOHZLuuUe6/HJp506pYUNp9Wrp5puPmQnGj8UjzwgggEBSC9AFnNTVQ+YQCKbAxo1Sz57SqlVe+QYOlJ55RipbNpjlpVQIIIBAsgkQACZbjZAfBAIuMGWK1L+/tM8t53byyW6uvwlS584BLzTFQwABBJJMgAAwySqE7CAQVAEL+G67TXrjDa+ErVtLkydLtWsHtcSUCwEEEEheAZ4BTN66IWcIBEZg7VpF1u+14K+E+1dn+HBp4UKCv8BUMAVBAAHfCdAC6LsqI8MI+Ecg3a3nZqu73XefZIM+bKnfqVMlW/aXhAACCCBQfAIEgMVnz50RCLTArl3SjTdK773nFdOe8xs/XqpSJdDFpnAIIICALwQIAH1RTWQSgSIWSEuTliyRtm+Xqlf3muxK5n4pNuveve467/QyZaTnnpP+8AemdyniWuR2CCCAQLYCPAOYLQ07EAipwKxZiqzDdvHFUq9ekv2sW1ey7cdJhw9Lw4ZJ7dt7wV/9+tInn0gDBhD8HYeO3QgggECRChAAFik3N0MgyQUsyOvWTUpNjc3otm3e9hyCwM2bpTZtpMcfl+zZv759pU8/9SZ4jr0Y7xBAAAEEiluAALC4a4D7I5AsAtbtO2iQF73F58kiOkuDB0t2XFyaOVNq3FhavlyqXFmaMUMaO1YqXz7uQN4igAACCCSFAAFgUlQDmUAgCQTsmb/4lr/M2bIgcOtW79nAn7fv3y/16yddc420Z4/UsqW0bp3UvXvmE3mNAAIIIJBsAgSAyVYj5AeB4hKwAR+5ST8ft2GD1Ly519KXkiI98IC0eLH3uGBuLsMxCCCAAALFJ8Ao4OKz584IJJeAjfbNRUqvVl2vjJGGDJEOHJCqVfNW9GjXLhcncwgCCCCAQFII0AKYFNVAJhBIAgGbndlmarbmvKyS2767xjnq+kKbyKheC/46dpQ++0wi+MsKjG0IIIBA8goQACZv3ZAzBIpWwOb5s2U7LMUHge790vQL1fjQSs1+O0WlS3tz+737rlS1qncK3xFAAAEE/CNAAOifuiKnCBS+QJcukg3prVkz415pKqFHKz6tNiUWa+v3J+qMM7zRvnfe6a3rm3EgLxBAAAEEfCMQiACwrpukNsW1UMR/DRw4MMuKmDhx4jHH2rkHrE+LhEDYBSwItEn9PvpIqS/OVrtGP+jhvXfp6NEU9ekjrVkjNWsWdiTKjwACCPhbIBCDQD51s82mZZqb7PPPP9cll1zipqZwc1NkkypVqqSvv/46Zm/ZsmVj3vMGgdAKuO7gOXvb6saHpd27pQoVpDFu4Ict70ZCAAEEEPC/QCACwKpxDyE98cQTOv30092qBG2yrSFr8atmwxdJCCAQI2AN4ffeK734orfZWvumT1ek6zfmQN4ggAACCPhWIBBdwJn1Dx06pMmTJ+umm26KdPNm3pf59b59+1SnTh036LGWrrjiCq1duzbzbl4jEEqBr77yJnOOBn821cuyZQR/ofwwUGgEEAi0QOACwLffflv//ve/dcMNN2RbcWeddZbsOcA5c+Zo2rRpsq7fCy+8UN98802259iOgwcPau/evTFfOZ7ATgR8ImCLfIwf7z3bt369N7J37lzp2WelE07wSSHIJgIIIIBArgVS0l3K9dE+OPCyyy5zv7BO0Ls2P0Uu09GjR9W0aVO1bt1aL7zwQrZnDR8+XI888sgx+/e4NbDsmUISAn4UsCXcbDk3W7/XUvv20qRJUi7nhfZO4jsCCCDgIwFrzKnsFi4P8+/vQLUAfvfdd1qwYIFuueWWPH0MS5Qo4Za0an7cFsChQ4dGPiz2gbGvrbYuKgkBHwusXCk1aeIFf6XcE8Hu8VnNm0fw5+MqJesIIIBArgTcP/nBSa+//rpOPfVU/f73v89ToawRdJ1bwb5BgwY5nlemTBnZFwkBvwu4Rm89/bT04IPSkSPe+r3uaQi1bOn3kpF/BBBAAIHcCAQmALRuXAsAr7/+epWypoxMqY+bvKymm9h2xIgRka3WjdvS/aY788wzI8/zWbevBYAvvfRSprN4iUAwBXbskHr3lmst98rXo4f06qty3SHBLC+lQgABBBA4ViA2Ujp2v2+2WNfvli1bIqN/4zNt262bN5pskMitt96qHe43oT0D0MT1gS1evFjnnXde9BB+IhBIgQ8+UGQy5127pHLlvKle3IB5N2I+kMWlUAgggAAC2QgEbhBINuUslM08RFoorFy0EATc7Eh64AFvVK9dvmFDb26/+vUL4WZcEgEEEEhyAX5/S4FpAUzyzxrZQ6DYBDZulHr2lFat8rJw223e838sfFNsVcKNEUAAgWIXIAAs9iogAwgUnsCUKVL//pKb91xVqkgTJkidOhXe/bgyAggggIA/BAgA/VFP5BKBPAlYwDdwoDefn53oprh0K+RItWvn6TIcjAACCCAQUIFfRkYEtIAUC4GwCaxZIzexuRf82din4cOlhQsJ/sL2OaC8CCCAQE4CtADmpMM+BHwkYGv6jBol3XuvdPiw3DrX0tSpUqtWPioEWUUAAQQQKBIBAsAiYeYmCBSugE3rYstf2/q9ljp39tb2tef+SAgggAACCMQL0AUcL8J7BHwmYN27jRp5wZ8tVGPzmc+a5Q368FlRyC4CCCCAQBEJEAAWETS3QSDRAtbNO2yY1L69tH27ZHP6ffKJNGAAEzsn2prrIYAAAkEToAs4aDVKeUIhsHmz1KuXtHy5V9y+faXnn5fKlw9F8SkkAggggEABBQgACwjI6QgkXCAtTVqyxGvWq17dG8VRsmTGbd56S7KAb88eb/3esWOl7t0zdvMCAQQQQACB4woQAB6XiAMQKEIBe3hv0CApNfWXm9pwXje8d//lXTR4sDRunLerZUtp2jSpbt1fDuUVAggggAACuREgAMyNEscgUBQCFvx16ybZfC6Z07Zt2tB1uHrUaq8vUyspJUW6/37pkUek0qUzH8hrBBBAAAEEcifAIJDcOXEUAoUrYN2+1vIXF/xZKPhyen811yeR4K9atXTNny89/jjBX+FWCFdHAAEEgi1AC2Cw65fS+UXAnvnL3O3r8r1bJ+sWvabZ6hIpRUe9p4ljTlLVdhf6pVTkEwEEEEAgSQVoAUzSiiFbIROweVwypaW6UI21LhL8ldYhPac79a6uVNX/bMl0FC8RQAABBBDInwABYP7cOAuBxArYaF+X0lRCj+ohtdEibdWvdYa+0XKd78K/kW6P6xD++bjE3pyrIYAAAgiETYAAMGw1TnmTU8At2Jta7Vz9Tgv1sAsBj6qkemuS1qipmrnvkZEftWuzsG9y1h65QgABBHwnwDOAvqsyMhxEgXf+XFI37Vvqnvsrowr6US9rgAsAJ3tFtWG/lkaOlDLNB+ht5DsCCCCAAAJ5F6AFMO9mnIFAwgQOHJBuv13q3NkN+thXRs1O/5fWnNbxl+DP7mTzAM6cKXXxBoMk7OZcCAEEEEAgtAK0AIa26il4cQt8+aV07bXSZ595ORkyRBox4mSdUPLjHFcCKe58c38EEEAAAf8LEAD6vw4pgc8EbKq/CROkO+6Q9u+XqlaV3nhD6tAhWhC37FvbttE3/EQAAQQQQCDhAgSACSflgghkL2Dr9/brJ82Y4R3Tvr00aRKDe7MXYw8CCCCAQGEI8AxgYahyTQSyEFi5UmrSxAv+bCzHiBHSvHkEf1lQsQkBBBBAoJAFaAEsZGAuj8DRo9JTT0kPPSQdOSLVrStNmya1bIkNAggggAACxSNAAFg87vaI7VIAACLRSURBVNw1mQVsXV5bms1W57CJl90cffmdfmXHDql3b2nBAq/A3btLr74qnXRSMgOQNwQQQACBoAsQAAa9hilf3gRmzZIGDYpdl9emYRk1Ks/TsHzwgdSnj7Rrl1SunPTii9JNN3lzOuctUxyNAAIIIIBAYgV4BjCxnlzNzwIW/HXrFhv8WXm2bfO22/5cpEOHpLvv9kb1WvDXsKG0erV0880Ef7ng4xAEEEAAgSIQIAAsAmRu4QMB6/a1lj+boyU+RbcNHuwW63XH5ZA2bpQuuEB69lnvoNtuk2zwR/36OZzELgQQQAABBIpYgACwiMG5XZIK2DN/qanZZ86CwK1bvWcDszlq8mRvlK+19lWpIr39ttftW7ZsNiewGQEEEEAAgWIS4BnAYoLntkkmYAM+cpOyOG7fPmngQG8+P7tE69aSBYO1a+fmghyDAAIIIIBA0QvQAlj05twxGQVstG9uUtxxa9ZITZt6wV8J91/T8OHSwoUEf7mh5BgEEEAAgeITIAAsPnvunEwCNtWLjfZNSck6V7bdmvTsOJesR3jkSG8uv2++8U79+GPp4YfzPWNM5Lp8QwABBBBAoCgECACLQpl7JL+ALc1hU71Yig8Co+8t4nPH2cjeK66Q7rxTOnxY6txZWr8+Izb0rsF3BBBAAAEEkliAADCJK4esFbFAly7SzJlSzZqxN7aWQdvu9lv3bqNG0ty5Upky0ksvSTY7jA36ICGAAAIIIOAXgUAEgMPdg1cprpUm81e1atVyrINFixapWbNmKuuGaP7mN7/RK6+8kuPx7AyJgAWBmzdLH30kTZ3q/dy0SYev7KJhw6T27b0FQmxal08+kQYMOLbBMCRSFBMBBBBAwMcCpXyc95isn3322W65rQUZ20pal142aZP7hd6xY0f17dvXjdacrL/+9a/uF/kAVa1aVV27ds3mLDaHRsA+O23bZhTX4sFevaTly71N7mOj55+XypfPOIQXCCCAAAII+EogMAFgqVKldLxWv2jNWGvfr3/9a/cQv3umy6X6rjln1apVeuaZZwgAo0j8jAi89ZbcHwrSnj1S5crS2LGSredLQgABBBBAwM8CgegCtgr4xg3FrFGjhurVq6drr71W3377bbb1stw15Vx66aUx+y+77LJIEHjYnurPJh08eFB79+6N+crmUDb7XGD/funWW71gz4K/li2ldesI/nxerWQfAQQQQOBngUAEgC1atNCkSZM0b948jRs3Tjt27HDLcV2gH374IcuKtv2nnXZazD57f+TIEX3//fcx2zO/GTFihGsFqpzxVZuZfjPzBOb1hg1S8+ZynyXv+b4HHpAWL5bq1g1MESkIAggggEDIBQIRAHbo0CHSddugQQP3kH57vffee5FqfeONN7KtXhswkjml/7zea/z2zMcMHTrUdQXuyfjaakuDkQIjYB+BMWOk886TvvhC7pECaf586bHHpNKlA1NMCoIAAggggIAC8wxg5ros757Ot2DQuoWzSvasoLUCZk47d+6UPUf4q1/9KvPmmNdl3Lwf9kUKnsDu3dItt0izZ3tlc2OENHGi3MCg4JWVEiGAAAIIIBCIFsD4arRn9b788ktVj1u2K3rc+eef71p2XNNOpvThhx/q3HPPdS09NPVkYgnFyyVLpMaNveDPqv+556R33yX4C0XlU0gEEEAgpAKBCADvvvtu2bx+Nr3LypUr1a1bt8hAjeuvvz5SrdZ126dPn4wq7t+/v7777jsNGTIkEihOmDBB48ePl12HFB6BtDTp0Ue9GV+sN/+MM7ypXmyFD1vXl4QAAggggEBQBQLRBZyamqqePXtGBnDYXH4t3ZDNFStWqE6dOpF62759u7Zs2ZJRhzZSeK5byuFO95v+JbeUg40efuGFF5gCJkMo+C/cR0bXXSf3h4NXVvv7YPRoqWLF4JedEiKAAAIIIJDiBj+4R99J+RGwKWFsVLANDKlUqVJ+LsE5xSAwZ450442SPfdXoYI38MOCQRICCCCAQDgE+P3terrCUdWUEgHpwAHp9tulTp284M+tBKg1a7yWQHwQQAABBBAIkwABYJhqO8Rl/eorbzJn6+a15B7/1LJl0plneu/5jgACCCCAQJgEAvEMYJgqjLLmTcAecHBjfHTHHZKt7mHTutj0kG7qSBICCCCAAAKhFSAADG3VB7/gtoRbv37SjBleWd0c4W7FGLnpgYJfdkqIAAIIIIBATgJ0Aeekwz7fCrjZgNSkiRf8ufm99cQTcksFEvz5tkLJOAIIIIBAQgVoAUwoJxcrboGjR6Wnn5YefFBubWdv/d5p07zn/4o7b9wfAQQQQACBZBEgAEyWmiAfBRaw1f1695YWLPAu1b279Oqr0kknFfjSXAABBBBAAIFACdAFHKjqDG9hPvhAatjQC/7KlZNee02aPp3gL7yfCEqOAAIIIJCTAAFgTjrsS3qBQ4fklvDzRvXu2uUFgatXSzffLKWkJH32ySACCCCAAALFIkAXcLGwc9NECGzcKLcEoLRqlXe1gQOlZ56RypZNxNW5BgIIIIAAAsEVIAAMbt0GumRTpkj9+0v79kknn+zN9de5c6CLTOEQQAABBBBImAABYMIouVBRCFjAZy19Np+fpdatpcmTpdq1vfd8RwABBBBAAIHjC/AM4PGNOCJJBGzd3qZNveCvhPvkDh8uLVxI8Jck1UM2EEAAAQR8JEALoI8qKzRZTUuTliyRtm+PzNycflErjRpdUvfdJ9mgj1q1pKlTpVatQiNCQRFAAAEEEEioAAFgQjm5WIEFZs2SBg2SUlMjl9qlU3Rj2Wl670D7yHt7zm/8eKlKlQLfiQsggAACCCAQWgG6gENb9UlYcAv+unXLCP4W6mI10vpI8FdGB/RS33WyQwj+krDuyBICCCCAgK8ECAB9VV0Bzqx1+1rLX3q6DquUHtT/VXst0HbVUH19oU/UQgM+uEopR91xJAQQQAABBBAokAABYIH4ODlhAvbMn+v23aw6aqNFesyFgOkqob4aq0/VXA31mbR1q/dsYMJuyoUQQAABBBAIpwDPAIaz3pOv1G7Ax0x11S16TXt0kirr3y70u1Xd9VZsXm1gCAkBBBBAAAEECiRAAFggPk5OhMD+/dKdU9u4gM8t6+FSSy3XNPe6rr479vLVqx+7jS0IIIAAAgggkCcBuoDzxMXBiRbYsEFq3lwa++caStFRDdUILVbrY4M/W9jXZntm7pdEVwHXQwABBBAIoQABYAgrPRmK7MZ6aMwY6bzzpC++kKpVk+Y//Fc9njJMpVPiBnpY8Gdp5EipZEnvNd8RQAABBBBAIN8CBID5puPE/Ars3i117SoNGCAdOCB17Ch95sZ4tBveSpo5U6pZM/bSNvOzbe/SJXY77xBAAAEEEEAgXwI8A5gvNk7Kr8DSpVKvXt6A3tKlpSef9GZ/saXdIsmCvE6dYlYCiXT70vKXX3LOQwABBBBA4BgBAsBjSNhQGAI2zd9jj0mPPCIdPSqdcYY0fbrUrFkWd7Ngr23bLHawCQEEEEAAAQQSIUAAmAhFrpGjgK3qdt110qJF3mG9e0svvSRVrJjjaexEAAEEEEAAgUISiHa8FdLluWzYBebMkRo18oK/ChWkSZO8L4K/sH8yKD8CCCCAQHEKEAAWp36A722DO+64w3uczwZ9WFfvmjWStf6REEAAAQQQQKB4BQgAi9c/kHf/6is3mXNL6cUXveINGSItWyadeWYgi0uhEEAAAQQQ8J0AzwD6rsqSN8M2t9/rr0u33y7Z6h5Vq0pvvCF16JC8eSZnCCCAAAIIhFGAADCMtV4IZd6zR+rf3xvZa5dv1056802JldsKAZtLIoAAAgggUEABuoALCMjp0sqVUpMmXvBnM7iMGCF9+CHBH58NBBBAAAEEklWAFsBkrRkf5Mvm83v6aenBB6UjR6S6daVp07zn/3yQfbKIAAIIIIBAaAUC0QI4wjU5NW/e3M0rV1GnnnqqOnfurK+//jrHSp04caJS3Bqz8V8HbPgq6bgCO3ZIl18u3X+/F/x17y6tXUvwd1w4DkAAAQQQQCAJBAIRAC5yMwwPHDhQK1as0Pz5811r1BFdeuml+umnn3IkrlSpkrZv3x7zVbZs2RzPYac0b543t5+jVrly0muved2/J52EDgIIIIAAAgj4QSAQXcAffPBBjPXrbiiqtQSuXr1arVu3jtmX+Y21/lWrVi3zJl7nIHDokDRsmPTMM95BDRt6gV/9+jmcxC4EEEAAAQQQSDqBQLQAxqvusSGpLlWpUiV+V8z7ffv2qU6dOqpVq5auuOIK14Xp+jBJWQps3ChdeOEvwZ9rcI0M/iD4y5KLjQgggAACCCS1QCBaADMLp7vJ6Ia4mYcvuuginXPOOZl3xbw+66yzZM8BNmjQQHv37tWoUaNcgHOh1q9f7yYsznrG4oMHD8q+osnOC2RKS5OWLJHrG48M5Z2ytbX+MLCEfvxROvlkacIEuecsA1lyCoUAAggggEAoBFJcwOSm7w1OsmcB33vvPS1dujTSspfbkh11Q1qbNm0a6TJ+4YUXsjxt+PDheuSRR47ZZy2O9jxhINKsWdKgQVJqqvapvG7TaL2hGyJFa9VKmjJFql07ECWlEAgggAACIRWwBpzKlSsrUL+/81iXgeoCvt0tQTFnzhx99NFHeQr+zKxEiRKRkcTffPNNtoRDhw6NfFjsA2NfW7duzfZYX+6w4K9bt0jwt1aN1UyrI8FfCaVpuPvfwttnE/z5smLJNAIIIIAAArECgegCtkZMC/5mz56tjz/+WPXq1YstZS7e2TXWrVsX6RLO7vAyZcrIvgKZrNvXtfyZwwu6Q/fqKR1SGdXSVk3Rf6t1ylLprlpSl6skm+2ZhAACCCCAAAK+FQhEAGjdvlOnTtU777wTmQtwh01S55I175azeUpc6tOnj2rWrOlWqXDLVLhkXbktW7aMPO9nTcHW7WsB4EsvvRTZH7pv7pm/XakHdKPe1Xu6IlL8Tnpb43WzfqXdkj0oYC2e9mxg27ah46HACCCAAAIIBEkgEAHgmDFjInXSNi4wselgbrjhhsi+LVu2RLp5o5X373//W7feeqssWLRAsYlby2zx4sU677zzooeE6udHC9JcO996bVcN1+53QM9piP6gMUqJV7CBISQEEEAAAQQQ8LVA4AaBFGVtBOEhUlvCbfhw6fHH0133b4rq6wtN17VqqA1ZU7rnK2kBzJqGrQgggAAC/hAIwu/vgkoHogWwoAhhPX/zZqlXL2n5chNI0S3lp2rkT7e6sb9ZrKDiJs12I2skGwpMQgABBBBAAAFfCwRqFLCva6KIMz9zptS4sRf82Qw206dL4yaVVfmU/S4WjOv4jb4fOZIBIEVcT9wOAQQQQACBwhAgACwM1SS+5n4X3/XrJ11zjdxUNnIDYeQGv0g9erhMd+kiWWToBsvEJGv5s+22n4QAAggggAACvhegC9j3VZj7Anz+uRfoffGF18h3//02GloqXTrTNSzI69QpZiWQSLcvU79kQuIlAggggAAC/hYgAPR3/eUq97bWy6uvSnfeKR04IFWrJk2eLLVrl83pFuzFjajO5kg2I4AAAggggIAPBQgAfVhpecnybjeFX9++ki3yYaljR7k1kKWqVSNv+YYAAggggAACIRTgGcAAV7pbDjky0MOCP+vmfe456d13Cf4CXOUUDQEEEEAAgVwJEADmislfB9mqbo8+KrVp4y3eccYZ3mhf6wIuQY37qzLJLQIIIIAAAoUgQBdwIaAW5yVTU6XrrpMWLfJy0bu33PJ2ckvkFWeuuDcCCCCAAAIIJJMA7UHJVBsFzMucOVKjRl7wV6GCNGmS90XwV0BYTkcAAQQQQCBgAgSAAahQG9l7xx3e7C026KNZM2nNGsla/0gIIIAAAggggEC8AAFgvIjP3n/1lTeZ84svehkfMkRatkw680yfFYTsIoAAAggggECRCfAMYJFRJ/ZGNrff669Lt98u2eoeNq2LTe9i07yQEEAAAQQQQACBnAQIAHPSSdJ9toRb//7e+r2WRZvQ+c03perVkzTDZAsBBBBAAAEEkkqALuCkqo7jZ2blSqlJEy/4swU7RoyQPvyQ4O/4chyBAAIIIIAAAlEBWgCjEkn+8+hR6emnpQcflI4ckerWlaZN857/S/Kskz0EEEAAAQQQSDIBAsAkq5CssrNjh9SnjzR/vre3e3dvbd+TTsrqaLYhgAACCCCAAAI5C9AFnLNPse+dN8+b28+Cv3LlpNde87p/Cf6KvWrIAAIIIIAAAr4VIABM0qo7dEi65x7p8sulnTulhg2l1aulm2+WUlKSNNNkCwEEEEAAAQR8IUAXcBJW08aNUs+e0qpVXuYGDpSeeUYqWzYJM0uWEEAAAQQQQMB3AgSASVhlw4Z5wd/JJ0sTJkidOydhJskSAggggAACCPhWgAAwCatu9GjJJnp+9lmpdu0kzCBZQgABBBBAAAFfCxAAJmH1Va2Spv8ZsERaut2b4K9VK8km/SMhgAACCCCAAAIJECAATABiQi8xa5Y0aJCUmvrLZWvVkkaNkrp0+WUbrxBAAAEEEEAAgXwKMAo4n3CFcpoFf926xQZ/dqNt27zttp+EAAIIIIAAAggUUIAAsICACTs9Lc1r+bOH/+JTdNvgwZIdR0IAAQQQQAABBAogQABYALyEnrrEPfOXuds3/uIWBG7dKtlxJAQQQAABBBBAoAACBIAFwEvoqdvdgI/cpNwel5trcQwCCCCAAAIIhFKAADBZqr169dzlJLfH5e5qHIUAAggggAACIRQgAEyWSrepXmy0b3brvNl2mxTQjiMhgAACCCCAAAIFECAALABeQk+1ef5sqhdL8UFg9P3IkcwH6AnxHQEEEEAAAQQKIEAAWAC8hJ9q8/zNnCnVrBl7aWsZtO3MAxjrwjsEEEAAAQQQyJcAE0Hni60QT7Igr1Mnb7SvDfiwZ/5YCaQQwbk0AggggAAC4RMgAEzGOrfu4LZtkzFn5AkBBBBAAAEEAiAQqC7gl19+WfXq1VPZsmXVrFkzN2VeznPm/elPf9Jvf/tblSlTJvJz9uzZAahSioAAAggggAACCOQsEJgAcMaMGRrsVsoYNmyY1q5d63pNW6lDhw7asmVLlgLLly9Xjx491Lt3b61fvz7ys3v37lq5cmWWx7MRAQQQQAABBBAIikBKuktBKEyLFi3UtGlTjRkzJqM49evXV+fOnTVixIiMbdEXFvzt3btX77//fnSTLr/8cp188smaNm1axracXtj5lStX1p49e1SpUqWcDmUfAggggAACCCSJAL+/pUC0AB46dEirV6/WpZdeGvPRsvfLli2L2RZ9Yy2A8cdfdtll2R5v5x08eDASNNoHJ/oVvR4/EUAAAQQQQAABvwgEIgD8/vvvlZaWptNOOy3G3d7v2LEjZlv0jW3Py/F2nrUkWotf9Ku2TcxMQgABBBBAAAEEfCYQiAAwap4SnTD55w3Wux2/LXqs/Yzfd7zjhw4dGunutS5f+9q6dWvmy/EaAQQQQAABBBDwhUAgpoE55ZRTVNJNnRLf2rdz585jWvmitVKtWrU8HW/n2Whh+yIhgAACCCCAAAJ+FghEC+AJJ5wQmfZl/vz5MXVh7y+44IKYbdE3559/vuKP//DDD7M9PnoePxFAAAEEEEAAAb8LBKIF0CphyJAhkalczj33XFlwN3bs2MgUMP3794/UUZ8+fdwKazUzRgQPGjRIrVu31pNPPukW3uikd955RwsWLNDSpUv9XqfkHwEEEEAAAQQQyFEgMAGgTevyww8/6NFHH9V2t4TaOeeco7lz56pOnToRAJsPsESJXxo8rWVw+vTpevDBB/XQQw/p9NNPl80laNPJ5DZFZ9CxEcEkBBBAAAEEEPCHQPT3dvT3uD9yndhcBmYewMSy5O5qqampYiRw7qw4CgEEEEAAgWQTsMGctWrVSrZsFUl+CAALwHz06FH985//VMWKFY8ZUVyAy0ZOtb9OLLi0D2cYJpmmvAX9xCT3+dRvctdPQXNH/RZUMLnPD2L9Wsvfjz/+qBo1asT0DiZ3TSQ2d4HpAk4sS+6uZl3Khf2XgwV/YQgAo+KUNyoRzJ/UbzDrNVoq6jcqEcyfQatfm9M3zOmXh+LCrEDZEUAAAQQQQACBEAkQAIaosikqAggggAACCCBgAiWHuwRFcgrY5NZt27ZVqVLh6KmnvMn5OUxUrqjfREkm53Wo3+Ssl0TlKmz1myi3ZL4Og0CSuXbIGwIIIIAAAgggUAgCdAEXAiqXRAABBBBAAAEEklmAADCZa4e8IYAAAggggAAChSBAAFgIqFwSAQQQQAABBBBIZgECwGSuHfKGAAIIIIAAAggUggABYCGgFvSSL7/8surVq6eyZcuqWbNmWrJkSUEvmZTnjxgxQs2bN4+spHLqqaeqc+fO+vrrr5Myr4WRKSt/SkqKBg8eXBiXT4prbtu2Tdddd51+9atf6cQTT1Tjxo21evXqpMhbYWTiyJEjkfXF7b/fcuXK6Te/+U1kfXJbNSgIafHixbryyisjqyfYZ/ftt9+OKZatrmATS9jqClZ+m8Xgb3/7W8wxfnqTU3kPHz6s++67Tw0aNFD58uUjZe7Tp09kdSg/lTFzXnMqb+bj7HW/fv0i/36NHDkyfhfvfSJAAJhkFTVjxoxIQDBs2DCtXbtWrVq1UocOHbRly5Yky2nBs7No0SINHDhQK1as0Pz582W/PC+99FL99NNPBb94kl/h008/1dixY9WwYcMkz2n+s/evf/1LF154oUqXLq33339fX3zxhZ599lmddNJJ+b9okp/55JNP6pVXXtHo0aP15Zdf6qmnntLTTz+tF198Mclznrvs2X+bjRo1ipQvqzOsvM8991xkv33Gq1WrpksuuSSy5FZWxyf7tpzKu3//fq1Zs0YPPfRQ5OesWbP097//XVdddVWyFyvb/OVU3swnWeC/cuXKSNCbeTuvfSbg/mIjJZHAeeedl96/f/+YHJ111lnp999/f8y2IL7ZuXNnuvvPJ90FhkEsXkaZ3PqT6WeeeWa6C3rT27Rpkz5o0KCMfUF64VpH0i+66KIgFem4Zfn973+fftNNN8Uc16VLl3TXChqzLQhv7L/V2bNnZxTFtXKmu4Av/YknnsjYduDAgXS33Fa6C4oztvn1RXx5syrHJ598Evk37Lvvvstqt6+2ZVfe1NTU9Jo1a6Z//vnn6XXq1El//vnnfVUuMvuLAC2A7lOeLOnQoUOR7jFrBcuc7P2yZcsybwrk6z179kTKVaVKlUCWL1ooa/V0gYLat28f3RTIn3PmzNG5556ra665RtbF36RJE40bNy6QZY0WygW8+stf/hJpCbJt69ev19KlS9WxY8foIYH9uWnTJu3YsSPSih8tZJkyZeT+yAnFv19WZvs3zLrGg9rKbY8y9O7dW/fcc4/OPvvsaDXz06cC4VhiwieV8/333ystLU2nnXZaTI7tvf3DGuTk/ibRkCFDZL9AzznnnMAWdfr06ZHuIuseC3r69ttvNWbMmEi9PvDAA3KtI7rjjjtkQYE9KxXEZM+EWRDgWu1lKyfYf8+PPfaYevbsGcTixpQp+m9UVv9+uRaxmGOD+Ma1dsr11KhXr16qVKlSEIsoe8TBVqay/45J/hf4/+3dzUtUURjH8ceSFoK7NkIN7URBCHdGzKIR+gN8QRhwlm6chYjgIrCVYNCigRaB1Cbci4Eo4stKMAh1WggTJOg/YAQhlNP9HZiasUnozpj3HL8XJmdG751zPk8enzlvQwKYwBjqHWT1oeTo/HPV3w/h/vj4uO3v77vekhDqU68OR0dHFg332urqqlvgU+9nQnpOvQXqAZydnXXVUg+gFgQoKQw1AdQc3rdv39rCwoLrIdnd3XVzerUoIpfLhRTev9blfFt1HdovLQgZGRkx/Z/XIr4QDy3eevHihXsDez7GIdb3OtSJIeAERfn27duu16DyTrpStGhu3B+9gpXvhfA1n8+bhgs3Njbszp07IVSpbh3UgCqWWtmtd9G6aSFMoVBw99VbFNLR0dFh3d3dNVXq6uoKckFTpZIaGlMvkJIBrQ7VcNnExIRpxXfohxZ86Lhu7ZeSv+HhYdMQuBazhdr7p90o1H6lUqlf7Zd6dicnJ+3evXsu9vzjlwAJYILidevWLZccqBGpPvT4wYMH1U8FcV89A+r50+q59fV1t/VNEBX7SyUymYwVi0VTr1Dlph6ybDbrHmvIMKRDK4DPb+ujVZLRxPGQqllTF60MvXGjtllVXNUzFPqhrW+UBFa3X5rXrDc5IbZfimcl+SuVSra2tua2Owo1znozo1GaStulr+rZ1puelZWVUKsddL0YAk5YeDUPTr9oSgz6+vrcViHaAiZaGZywkjZeHC2G0FDZ4uKi2wuw0nMQrRp0e4g1/grJukJ7e/sf8xu1f5j2yAtx3qN6vvSHX0PA6iHRHEBtfaNbqIf2yNOcP/WSaJK8tnLStijRyuAgqvz161f79OnTr7qo10uJgBZuqc7a01Lxjla5u5vua/9HzYvz8biovkp+BgcH3ZDou3fv3HzPShsmD72h9+24qL6Kr9qq6kNbPCnp7+zsrH6a+74IRL0wHAkTePnypVteHzUg5d7e3mC3RYl+R9yWCee/vnnzJmERubzihLwNjNSWlpbKUXJbjhZ+lLWdUZT8XR5mAq785csXt61P9MeyHG3kXo42gi5He3qWT09PE1C6xosQTdOo+zsbzW90F496OsszMzNuOxjFPJ1Ol6Ne78Zf+IqucFF9o+S3roXaM53n43FRfevVh21g6qn481yLiupLsko5EUAAAQQQQAABBBoXqJ2s0vj1uAICCCCAAAIIIIBAwgVIABMeIIqHAAIIIIAAAgg0W4AEsNmiXA8BBBBAAAEEEEi4AAlgwgNE8RBAAAEEEEAAgWYLkAA2W5TrIYAAAggggAACCRcgAUx4gCgeAggggAACCCDQbAESwGaLcj0EEEAAAQQQQCDhAiSACQ8QxUMAAQQQQAABBJotQALYbFGuhwAC3gr8+PHDfXzdwMBATR1OTk7s7t279uTJk5rneYAAAgj4KsAngfgaOcqNAAKXIlAqlez+/fvuM4uz2ax7jdHRUdvb27P37997+RmvlwLFRRFAwGsBEkCvw0fhEUDgMgQKhYI9ffrUPn786JK+oaEh29nZcYnhZbwe10QAAQT+twAJ4P8W5/UQQCDxAvqI9EePHtnNmzetWCxaPp9n+DfxUaOACCDwLwIkgP+ixc8igMC1ETg4OLCuri7r6emxDx8+WGtr67WpOxVFAIHwBVgEEn6MqSECCMQQeP36tbW1tdnnz5/t+Pg4xhU4BQEEEEiuAD2AyY0NJUMAgSsS2N7etnQ6bcvLy/bs2TPT6uC1tTVraWm5ohLxsggggEBzBegBbK4nV0MAAc8Fvn37ZrlczsbGxqy/v9/m5+fdQpBXr155XjOKjwACCPwWIAH8bcE9BBBAwKanp+3s7Mzm5uacRiqVsufPn9vU1JQdHh4ihAACCAQhwBBwEGGkEggg0AyBra0ty2Qytrm5aQ8fPqy55OPHj+379+8MBdeo8AABBHwVIAH0NXKUGwEEEEAAAQQQiCnAEHBMOE5DAAEEEEAAAQR8FSAB9DVylBsBBBBAAAEEEIgpQAIYE47TEEAAAQQQQAABXwVIAH2NHOVGAAEEEEAAAQRiCpAAxoTjNAQQQAABBBBAwFcBEkBfI0e5EUAAAQQQQACBmAIkgDHhOA0BBBBAAAEEEPBVgATQ18hRbgQQQAABBBBAIKYACWBMOE5DAAEEEEAAAQR8FSAB9DVylBsBBBBAAAEEEIgpQAIYE47TEEAAAQQQQAABXwVIAH2NHOVGAAEEEEAAAQRiCvwEQfQ8LBt0kZMAAAAASUVORK5CYII=\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Primero creamos datos sintéticos con un cierto nivel de ruido\n",
    "# parámetros de la recta \"verdadera\"  y = a*x + b\n",
    "\n",
    "a_true = 1.234\n",
    "b_true = 1\n",
    "\n",
    "# creamos valores de x y estimamos los valores de y\n",
    "xMin = 0\n",
    "xMax = 15\n",
    "Nx = 15\n",
    "\n",
    "x = NP.linspace(xMin, xMax, Nx)\n",
    "\n",
    "# calculamos el valor verdadero de los valores de y (usando el modelo verdadero o real)\n",
    "y_true = a_true * x + b_true\n",
    "\n",
    "# simularemos los valores de y observados (y_obs), \n",
    "# agregando un ruido observacional que representamos\n",
    "# como un ruido gaussiano con desviacion estándar sigma_obs\n",
    "sigma_obs = 0.5\n",
    "ruido = NP.random.randn(len(y_true)) * sigma_obs\n",
    "\n",
    "y_obs = y_true + ruido\n",
    "\n",
    "\n",
    "# graficamos los datos observados con la recta real\n",
    "fig = PL.figure(1)\n",
    "s1 = PL.subplot(1,1,1)\n",
    "s1.plot(x, y_obs, 'or')\n",
    "s1.plot(x, y_true, '-b')\n",
    "s1.set_xlabel('X')\n",
    "s1.set_ylabel('Y')\n",
    "PL.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.21324323 1.19106586]\n"
     ]
    }
   ],
   "source": [
    "# buscar la solucion por minimos cuadrados par ajustar y = ax+b\n",
    "d = y_obs\n",
    "# si m = [a, b].T la matriz de diseño queda\n",
    "G = NP.zeros((Nx,2))\n",
    "G[:,0] = x\n",
    "G[:,1] = 1\n",
    "# la solucion por minimos cuadrados es\n",
    "invGtG = NP.linalg.inv( G.T.dot(G) )\n",
    "Gtd = G.T.dot(d)\n",
    "m_est = invGtG.dot( Gtd )\n",
    "[a_est, b_est] = m_est\n",
    "y_pred = G.dot( m_est )\n",
    "print(m_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# podríamos haber definido una funcion\n",
    "def minCuadSimple(G,d):\n",
    "    invGtG = NP.linalg.inv( G.T.dot(G) )\n",
    "    Gtd = G.T.dot(d)\n",
    "    m_est = invGtG.dot( Gtd )\n",
    "    return m_est\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a_est = 1.213 ; a_true = 1.234\n",
      "b_est = 1.191 ; b_true = 1.000\n"
     ]
    }
   ],
   "source": [
    "# y usar\n",
    "[a_est, b_est] = minCuadSimple(G,d)\n",
    "\n",
    "print('a_est = {:.3f} ; a_true = {:.3f}'.format(a_est, a_true))\n",
    "print('b_est = {:.3f} ; b_true = {:.3f}'.format(b_est, b_true))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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ltE645JUqLq3wV0Ia326A4dz0nvsTiv6roLQ3k/7u/J55ZVXzG26ZnDnzp148sknTbt13aP2jYkESIAEQpmALAdH796QteaQrSyBdneuwORrTZHm0jnY5svfwCRw/gtlvt76lsrbBeYnIwEN9ZIvH8TjImbS170pan3T61rOz0ktVDVq1MDo0aPRo0cPF7GkwbfV2taqVSuHIJIpY5cW6LkG3LYnFVtPP/20ealziV775Zdf8NBDD0EtdWohqxiPfqjjibYln3DQnS9UNNmTrOdDvXr1HKJQxdeuXbtQpEgRU0T3yNV2adBwtbjdKqkQmzNnjrFY2oXgunXrjLOGOrD4kh5++GETvFw9iwupJ7eXpBZRfSl7dWSRaXA888wzXkozmwRIgASCm4A6eDRporMkMf2QTb/w4ZAqQOtnId5/wFtvQf7IB3cnA7T1pBqIA6Nx/uxWMBV7zsl+rgGYEyke4KhRo8wUqVrNdN9ljQn4vdjmVRiq4LF7y2qzxDkDQ4YMgYaMUUufOH6gW7dupsXqxTtu3DizJZ+Glvnyyy+N8BLnESNydCpXxaRu8adToeIcYTxzxWnEuccej/VenUbWtjQSb2nnPW/Viqlb/KlIU4tip06djPiyV6RlZW2esRBOnjzZTLWqcNW2ekpquVQGuhe1WkC//vpriAOI2Rfa123XdEcanUbWWIqyZhHqaazte0v+uKmnr6zbM9sdqhe0OMwYrsrDLlo9tYt5JEACJBDMBGSDLzEGAFs3R+H19MPxzZQzEssXSJtOvvd0oweZFZF4XMHcxcBuu0xlMcWTQGyLSP2yEH/OnJu9gdX7V/MTOYlAsdq0aWNJOBPjiSvTuZYIIEuCQjuerF7A/fv3t2T3FeMlq965sjOI47o6kkhoF+P8kCFDBqtcuXKWhJJxXFfnEAksbYlFzDxDnyXWLmvHjh2mjDqByDZ/jvLuB+pkIf93WTLN63JJvWrFAmicNG6//XZLRJYlQtPk2Quq88Z7771nHFnU01jCwDg8n92dQPQeEWaWPk+dTbSd6twhU9n26owXsAhfx7keaBtat27tyFPnE2Uo4XAcTEXIWrI20ZI1iVaTJk3EuTu/eYaWkf2v4+VF7pfPnqPVPCABEiAB/xI4f96Sv8kxjh75sN/akqVyzIk4EYq3nX8f5qW22L6/vdwSctkST0S5M8WHgHyhy+LULGZ7OY3r5pzE29NYtQoXLuxinXIu49NxMu0E4lPbWCggCfjtsxeQvWOjSIAEgpmATNyYKV9ZlYNGtjmYnLYD0l06DQkGC5lGgkwLQdYYJXoXY/v+TvSHB8gDaFsNkIHw2gyd5q1SxetlXiABEiABEiCBQCegpiZd2SS+eUh97QKmZuiOZhe+AC5Jy8uUAaZNg0Tm/68bNH78xyKRjigAEwksqyUBEiABEiABEojx7G3TBtDl3ffhD/yQsR7uiPwrxtInuyqhf38No/AfKt3pSteSO4XZMo6PqiAbNPivHI8SRIBOIAnCx5tJgARIgARIgAS8EZBIXChRIkb8RUQAr3yQE3kzR0I8CiHxroCBA28Wf8m0Daq3PoRqPgVgqI4s+0UCJEACJEACyURAwr1Ct42XAAi4fOQUitxvSaQHifH3anbYZH932Qj95uVNOu2rlj9Prgn2vO7dITHEkqlXofVYCsDQGk/2hgRIgARIgASSlYBEuULlyjHGvaesBdgfcS+29piMYsVuNEtjv0jM2ZuSxHB1mfZ1L6AiUEJyQcsxJZgABWCCEbICEiABEiABEiABJSChYFGypMT2++kSPkvTBQtQDxmvnETEFImzarfieUPl6/amvpbz9hzmGwIUgPwgkAAJkAAJkAAJJIjAxYtAx45A48ZAgbM7sDNdaXS4Ojqmzl69INH5bx3exdftTX0tl6Aehf7NFIChP8bsIQmQAAmQAAkkGgHZ3ROlSwOff27hZYzA5pRlceel34DcuSFbHwH/+x+gHiC3SvZtUL3FAdR82WM+MbZBvVXTQvE6BWAojir7lCQE5s+fj+nTpyfJs/gQEiABEgg0AjqjK9vGmzB+susmaubYio9t3ZE66grw1FPAjh2SWdP3ZifzNqi+NzQ0SlIAhsY4shexEJAt7cwevLEUifOlDRs24OWXXzb7+97q5n79+smaGFkUw0QCJEACIULg1CmgYUOgSxfI3vFAnTrAlN8ehu3ttwHZTx4LFgA5c8a9txrnb/bsmDAxznfnyxeTzziAzlQSdEwBmCB8oXeziiWbmNn1lUo24ZY9cvHiiy/i9GnZqsePqVChQpB9g/1S46effipxpkrITkIZkDVrVtlc/CF88MEHjrqHS/DQiRMnOs59OdD+q4XPUzolf/natWtnrms/nJOn+3r37o0ffvjBuRiPSYAESCBoCagTrv6mXTTvMv6X4hWMf2M3NLKL0Xsa1FlVofwNjXdSkaeuxCtWxOwQou979jAIdLyBer6RO4F45hLWubVq1cKECRNw/fp1/Pbbb2jbti3OnDkTkNOd48aNQ8+ePTFixAgJO1BZfolekVmHHabd9kHU/Zr9mbJly4Zff/3V5yozZswIfTGRAAmQQDAT0PB7778fs3HHfdG/YUmaprj/qkzz/iCK8N11Ivr8aFPiNqiJ/lHx42glelv5gCQiECGLdXPL4t18YnKvKes3nnvuOSxZssTl6WfPnhWPr464/fbbkTlzZjz++OMS11MCezqlBTIFUFpWBqdNmxY5cuSQHXzkV52kKlWqYN++fejRo4fD2qj5J0+eRNOmTc1z06dPLzGjit1SdC5cuFC8zhobi9zdso/kgw8+aOp49913tUqT3KeA9fk6ffuqbEqpYk77qtO09mS36j3zzDOmffZzva7PK1WqlOnTnXfeKTsY9TdCWa/Zy7nf52kKePz48aatyjqPeLR17dpVqzBp2LBhpu9q0cwvC547d+6MyMhI+2W+kwAJkECSE9Bd2eTPPPr2tdAxegy2pSwVI/7U7KfTvikoJ5J8UBL4QI5YAgHG5XZdMHvhQtK/bhV6KbY+/PPPP/j+++9lm8b/9mm0pMInn3wSR48elb0dF2Hz5s14+OGHUa1aNej0qKZvv/3WCD4tt3XrVjMFqmJQ01zZ51HF5YABA3BE4jnpS9Ply5eNuPpG5hLUwqYCs2XLltD1dt6Sirf169cbQemtjKf8SZMmmSljrXvIkCGmLUs1TIGkjRquXpJaQbVt9vPF4s3WokULIx7VMqpTzzq1/L7+JJZkL+d+n7no9M+YMWNkhqSL6d8v4j6nQlnFqz2lkD+katFUBtrO5bJdkopVJhIgARJIDgJffx2zndvO1SfwTcr6GIPOSBN1OcbBQx095O88UxASkC9zpngSECuYSDpY+u6eLl26ZIlIsPTdniIjVYol/Uuf62tq3bq1lTJlSkusT5ZY7kz/tI9ilXJUIevZLLH6WSLYHHl6cNddd1kiikxe+fLlrebNm7tcdz4pWLCg9dFHHzlneTyuU6eO1atXL4/XNPPw4cNWuXLlTDvvvfdeS9s/c+ZMKyoqynGP5tWrV89xLlPF1mOPPeY414MyZcpYr732miNP+zxv3jzHuR5UrFjRGjhwoEvel19+aYkFz5Hn6b6+8pNZ1ig6yuTNm9d68803Hee3Ovjqq6+s7Nmz36qY47qnz57jIg9IgARIwEcC+vXVtWvMd9a9+MM6llr+1umXWJo0lnwpWPKH1seaAq9YbN/fgdfaxGkR1wDKNzaTK4GqVatCrVQXJbLnF198gb/++gsvvfSSo5Ba/HRKUkSJI08PRHjg77//Nnnbtm1Dhw4dXK7f6kREGwYPHgwRcDh06JBZz6dr+nQq1FvS6dOffvrJWMtWrVqFdevWQQSfabdaLtWa5ikVL17cJVvrOXbsmEue+4n2W618doufXtc2q+VSWem09a2SPkNEq7GWeiu7QhY8i9A06xjPnTtnppj1GRfEfBwbC2/1MZ8ESIAE4krgj51RaFLvErb/HbN+uf7LBZH9x7zARVlTreGvGNkgrkgDrjwFYBIOieqD5FjK5YMucaGgIsM+JalTkSoIda2bfV1ddHS0Wbe2cuVKl/v0RL1wNaVLl868x+WfoUOHQqyCxjtY1/9pO7rLxt9Xr169ZTVFixaFvnRq9ccff5Q4oRWhglDb7ik5T2nrdfXe1X7FlvS6crCvZXQuq+scfUm34qJrI8XqiRdeeMHw1jWK2h/1Or6mu6szkQAJkEAiElAT3/gum/Hy2CLIbf2LPDiLcWiP2nPF8e2dd4DmzSG/dhOxBaw6qQhQACYVaXmOaAwRNUn4QD89SqYwUbt2bRMORqYvzXo/Xf+nYWLsjg/uj1ILm4Y+ef75590vmfM0adIY65nzxTUSW0Cmas06O81XwbVr1y4UKVLEudgtjx944AFTRi1m8U0qENW655x0neOff/7pEMfO1+zHnu6zX9P3TJkyGWbKxpM43bRpk7H4qRi2Wy9lCti5Ch6TAAmQQKIQEN8+dHryAGaufRhtMR6j0AVRSIWMkL+lh+QLrFMnyNQPw7EkCv2kr9Tz/FjSt4NPDGAC6jWr3rU6LampevXqJgBy/fr1ZZefxRKuaa+Zen3rrbegAkaTikbdJUPff5cQ8ersoM4W9qTCcfXq1Waq98SJEyZbrY7qiKHTuHpPJ/ljo0IztqQxCtUyuXbtWuMIog4hrVq1knhUOX0K0uytbm2fijR9vj0G4jvy63fy5MnGY3jnzp2mjTpdrf22J0/32a/Z39UrWAWeWldV4G7ZsgUjR440l2UdpRGAeq4OOLLGEGPHjrXfyncSIAESSBQC6mv30EMWFq/NiFloZKx+6XAlRvzpE9U0qElmZeTXccwx/w1qAhSAQT18Sdd4jbX3+eef48CBA2a6VL1/K1WqZGIEivMFmjRpYoRgrly5TKNUNM6aNct4uOouGBomxtmbVz2AVTiq4FGxpultCSWgVrYnnngCer96+KrIjC2pGFXR9+yzz0Lb0VBC0+t0rIo39zWKsdXjfk0FmopRDcOigaU1abvUQ1nzxWkE4nwCDdkiDi2O2z3d57h440DXKGoQ7NGyh5IK66dkyyQVgpqUldapgax1Snvq1KkYNGjQjTv5RgIkQAL+JaArX2TpNR57TLbZ3bMaO/GgyL+5nh+iIlC+A6CRoJmCnoBNfUuCvhfJ1AFdoK9BhjUmnsbCc066aH+PRC4vXLiwESTO13hMAolJgJ+9xKTLukkgdAjoBItE2sLKZdfQT/7rg0FIAR8kwbRpkICrQQ0itu/voO5YHBpPC2AcYLEoCZAACZAACYQCAQmSAA2GsGwZcG/aA3g1zce+iT/tvERNYAp+AhSAwT+G7AEJkAAJkAAJ+ERAgyrI9uTi2AccPx4jAmdvuROpx38WE95FgvQbj0VPtdnEEUSWxUiYBU9XmRdkBOgFHGQDxuaSAAmQAAmQQHwI7N4NWa8N7Np8FpPRFacbtEfHqZVlmZLUVkTCu2iSCA1o1ChGBDqvEFPxp0nWL0P36WUKegJBYQFUb9G6detCQ5BovLb58+e7gNc8T68PP/zQpZzziXpiut+jTgdMJEACJEACJBBqBKZMUS9f0Xeb12FHipJoiSl4eUsbpE3pFl9U92yfPRu44w5XBGoZ1Pwbe7q7XuRZMBIICgugxnOTrbRMTDn18nRP9r1k7fnfffedCZzrqay9jL6rB+YyXQBxI8kWaPZDvpMACZAACZBA0BPQzQckPj6mTr6ON/E+3sEApFTXX3FQhDpzOO3z7uisijyJyWq8fXWvdl3zp9O+/I50IAqFg6AQgBqEWF/ekrvl7mvZuVqD7N55553ebjH5GsjY/d5Yb+BFEiABEiABEggSAhJi1Ez5Xt21FyvRAo9hbUzL1fV31ChI+ArvPVGxV6WK9+u8EvQEgmIKOC6U//33X3z77bfGAnir+zT2mk4ra6gWjWOngXdjS7ovrbqOO79iK89rJEACJEACJJDUBHTpni7Vk1CluLZrD3bYSsSIP9mJCDoXLAHtYxV/Sd1gPi9ZCIScAJw0aZLZbsvTfq3OhB955BGzq4PuZKEBjnXHhwoVKuDkyZPOxVyONSCvxv2zvzRIMBMJkAAJkAAJBAoB9eyV2PLo0UPEnyzve6h+IaStWxOyNRKwfXvMXr6B0li2I1kJhJwAHD9+vOxV3fyWwZd1SlnXCBYrVsxsbaZWQ00qIL2lPn36mKDPGvhZX7orBhMJkAAJkAAJBAKB5csh6+WBfxdtQq40p2W3IWDOXBvSTBkP2XszZt1fIDSUbQgIAiElANfI9jR//vkn2rdvH2e4GTJkMGLQviWXpwoiIiLMjh+664f95akc84KfgCdv86TqVXI+O6n6yOeQAAn4j4Ba+t58E6hZLQqtjgzGTyiPPyt3xIsvWBLtQp6jU7+y5p2JBJwJhJQAHDduHEqVKmU8hp076cuxru/7/fffxdkpvCOct2nTxhEeR51kChQogBdffBGnT5/2BaPPZQoVKmT2w/X5Bi8FV65c6Wive1gfnda/VdJwQLr/rntSz/LYHI/cy/OcBEiABPxKICpK9mhbGROcWd/13EOSLdVRubLMXg08iKWojsGyoVtqXEeW2+TrXaM+M5GAFwJBIQAjxY9927Zt5qX90D129Xz//v2ObqljxqxZs7xa/6pVqyZOT+L1dCP1llDoq1atMnVt2LBB4l42Ms4drVu3thcJ2/datWpBBdBe+cvyxRdfYOHChejcuXNA81DLr7bZ+XX77bfHu83qHa4WXyYSIAESSHICc+cC8iNZwlkAzZrFvOu55jsl+cqTH7BA7p/m4hdbcVTFSkBmsyBLoTBjBuSPmFNpHpKAK4GgEICbNm2SAJYPmZc2v2fPnub4nXfecfRmhnzYLXF9auplg+q///4bJ06ccJQ/ePCgKXvfffdJXMsGEvw8DdavX4+CBQs6yoTrgQofFUD5JPBnzZo18dxzz2HJkiUuOHQNZMeOHaEiS6fDH3/8cVlfLAuMndKCBQtQunRpsx4zR44chrNerlKlCvbt2yeLlHs4rHearw44On763PTp05sp+enTp+ulWyZth7bZ+ZUiRczHW62EZcuWlb+LGZA1a1Y8+uij5vkTJ05E//79Tbvt1kPN0+Q8DatCWM+/+uorCYVVEenSpUOZMmXw119/YePGjaaPGTNmhArn47oC+0bSazVq1ID2XR2HKsvP9C0al8Ep6ZKDSpUqGUYPPPAAli5d6nQ15vC1117Dvffea5hoaKO3335bFnfLnA8TCZBA6BFQkac7cch3lEs6dCgmX65fvAj5+wu0aXwBQ852xFw0xG2WzNLI31ts3QoJmqt/xFxu5wkJuBMIikUBKhhU3MWWVIzoy1vSL3HnpIIx2ZIEtvaaNPaS2ZfnRonYyqrAETHiSJ7K6q/BBCQNjfO97Bqe2ilYqI7Fk08+iWzZsmHRokVG3Hz66adQK6uKIs1XpxoV1m/KwpQvv/xSZiKumjxtylz5A6aBvXW8OnTo4Gjd5cuXzRS+Ch4VlVpHS4lXpaJHvbbjk65fv4769eub56iY1Hb8/PPPRtCpsP31119N/+wBwVWoeUt9+/Y109Y6Ld62bVsjVrWdw4cPN+KscePG0B8lY8aMMVWcP38ealEeMWKEOR86dCjq1KkDFX2ZZE1OtARjVUYqEPXHh1qxu3fvftPjtawKUw1Z9Msvv5i+aN6rr756U1lmkAAJBDEBnebt1g3yhXdzJzRPRN0vncegSfZn8NtvNtyGq2ic+XtY52U3LPm7Kb9oY7Zyu/lu5pDAzQTky5wpngTECqb/l1r67p4uXbpk/fbbb5a+35Ri/vfW/51vftWp41o8ffqby9jvq1zZtWyOHDeXdS1xyzMRLJbsiGKJtcxKmzat6Z/2cdiwYY57f/jhB0uEjyWCzZGnB3fddZclQtDklS9f3hJvbJfrzidiabU++ugj5yyPxyKYrF69enm8ppkrVqwwbdT2Or/EYmbuEauiuS5WQI91iKizRIzedE37PG/ePJMvSw5MHTId7ignYtLkKQt7kjBBlliU7ac3vYsYtUS4WTKlbq5JCCLDWrzJHWVlFxtTr/3ZjgtOB0OGDLFkratTjuthrJ8916I8IwESCCQC8vdM/gB4fEVL/mi8YKVDpBSJtvLksSzz52fNmhsHgdSRwG9LbN/fgd96/7QwKCyAN8tW5iQmAd1FRa1YF2WeQdcAqlXvpZdecjxy8+bN0HWZ2bNnd+TpgQgP6FS7Jl2j6WzdM5m3+CdKfv0OHjwYM2fOxCGZ7lDHHH3p1O2tknqAq1XMntSBRZNaI9Wx5YknnjDTsdWrV4da6uLj7FO8eHF79ciVK5c51jBC9qR5x44ds5+aY7UILpfYDBqgXPunTO1rV9XpSK2JOuVtTyKc7YeO99my/+bHEtV1t+zkrtzVqqmWRyYSIIEQI6DbrnlIp8TW1x5fGO/er1EfOwvURvNNPZEzpxZ+zMMdzCKBWxOgALw1I/+X0M0ZvSWdAnZOToLCOdsc31jj5sh3m+Z25MfxQAXX3Xffbe7S6UsVhLpW7t133zV5OnWpAkrX1rknXWOnSdfJxTXpFKlYBY3YUWGl7dApUZ22vVUqLLu52J/tXnbChAl4+eWXzVSvisu33nrLrLUrp2Hy45Ccp8F1TaAm9zxlY08qPHVNoIo3XVuqaytV4Nn7I7/h7EUd7/Z67Rk6Nay71Ch/FbE6Ra3LF5QVEwmQQIgR8BCFYo0IvOaYihLYjh0ojpw4gernNsGW4QXpfPoQA8DuJCUBCsCkpG1/lg8WLXtR49HlOLnFQVzqvUVVzpd17ZuGRNFwMLoO7eGHHzY7p6iVrVChQs5FHcdqLZPpUVmL/Lwjz/lAnW7UIuac1IpXTzYgb9GihclWMaXr5YoUKeJcLF7HdiciDeatImyabIKuAtBTO+L1AA83aX9GSyRWXfenSQOHOzsiqdOHWgMPHz5suGqZn376Sd8cae3atUY86lpKe1IHGiYSIIEQJCBOZjIlAJkCQZRlw/t4Ex/gVXm9jq74JKbDsh7bJn9bZOFxCAJgl5KSQIybZFI+kc8KOgLqhPPggw9i4MCBpu06jaoiSp0rdCs9dbBZt26dsaypx7YmFY3qdKHvOtWpzguyds1c039UOK6WyPQ61WsXRWp1VC9YrUvv6dSpkxGajptiOdCpV4375/xST1kNGaSiT4WVCif1ZtYpbbuo1HbYwwppO3TK2V9J+6MOMNoXDTWkO9Q4W0aVo3qht2rVyngiq2B0FnraDq1DRaJa/XR6XS2ysj7QX01kPSRAAoFEQGeAxKnsoHUHquEHzMKz2IBy/4k/bav8TUHRooHUarYlSAlQAAbpwCV1szX0ju6ZrFYsnaZU718NX6LesBqiRKcpVQja18apaNS4jBoKRgMta5gYFUH2NGDAAFNeHEdkHYtZyGLCm6h1Uac69X4N6aIi05ekQkqnpZ1fulZRw8n88ccfZts/bad6Hnft2tWIS61XtwPU8C06za3t8DXsjC9t0m0JNYC2Wh/Vm1mnoZ1jE2qYGhVzKjo1TI3uYPP++++7VK0WUQ2Xo21WjiqONQwMEwmQQGgSWJCqAUpk3I3fUQTrRfwVxc6YjurfyTlzIHG5QrPj7FWSE7CpL0mSPzVEHqhhO3RNlsbEc1+UryFN1LKka9PEmzZEesxuBAMBfvaCYZTYRhJwJSBfGXjlFciGBTH5pUtbWJz3eWQ7sAPyqw94+mnAfY24axU8iwOB2L6/41BNUBflGsCgHj42ngRIgARIINgJyCSFzKLIjh7bv8c9uBP1et8rswE2pEk5DpCZAgZ1DvYRDsz2cwo4MMeFrSIBEiABEghxAjr/JlvYo/zDV9B6ew98j9rYeE8zfPj+VXFQk86rxU+W3DCRQGIQoAUwMaiyThIgARIgARKIhYCsHJK1yMCOmb9hBZqhpIR50ZSlpoSncgonFUsVvEQCCSJAC2CC8PFmEiABEiABEogbAfWHe6ikhawzx2IzShnxZ8mWkFi4MGYRINeNxw0oS8eLAAVgvLDxJhIgARIgARKIGwE17H3wAVD70XMYtvcZjMWLSAfx/qhZE7Yd4uzx1FNxq5ClSSABBDgFnAB4vtxKJ2tfKLGMPwnwM+dPmqyLBPxDQMKUSjgoYNkyIJXIvqLZDsM6L0GdZftL2fIoxtnDP49iLSTgEwEKQJ8wxb2QfYsw3fvVOfhv3GviHSQQNwL6mdNk/wzG7W6WJgES8DeB778H2rW8imMnbBKbNDVGjkyNuypNh+38OZkLfsjfj2N9JOATAQpAnzDFvVBK8d7SvWl1hwpNGpDYfZ/XuNfKO0jAOwG1/Kn408+cfvb0M8hEAiSQfAR0G/M33gAWDP0LX4ujx/acNVBh1SDZiUjbdFfyNYxPJgEhQAGYiB8D3clCk10EJuKjWDUJOAio+LN/9hyZPCABEkhSArt3A02bWCi2eQK24iVkwEWUsvbBlvtVacdtSdoWPowEPBGgAPRExU95avHTrcl0+y/dl5aJBBKbgE770vKX2JRZPwnETmDqVOD1Tqcx7EJH2c13dkxh2W7Spvv43kbxFzs9Xk0qAhSASUBav5D5pZwEoPkIEiABEkhGApGRQJcuwJ7Jq7EWLVAAB2ClSgXbe+8BvXtzK7dkHBs++mYCFIA3M2EOCZAACZAACcSJwJYtMdu5/bvrLPbhaWTFWVh33w3btGlAmTJxqouFSSApCFAAJgVlPoMESIAESCAkCeh2bsOHA6+9BqjTR/78WfBvi+HIemQlbCNHAhkzhmS/2angJ0ABGPxjyB6QAAmQAAkkA4Hjx4HnnweyfjsF5ZEP2Z6pgi++ALJlay2t0RcTCQQuAQrAwB0btowESIAESCBACSxfDrzY7Cze+bczmmMaIrPegQyf74AtW7YAbTGbRQKuBCgAXXnwjARIgARIgAS8EtCADv36ASsHrsP3Iv0KYy8scfTL2OsFMQVm8XofL5BAoBGgAAy0EWF7SIAESIAEApLA3r2ynVvT66i6fiBWYYAE0o1CdKHCSDFN4r6ULx+QbWajSMAbAQpAb2SYTwIkQAIkQAI3CMyWcH7d2kVixrnaqIgfY3JbtECKTz4BMmcmJxIIOgIpgq7FbDAJkAAJkAAJJBEB3Vq7Uyfg2WeBw+cy4Er2OxCdMRMwZQqggZ0p/pJoJPgYfxOgBdDfRFkfCZAACZBASBD45RegbeNI7PrjuuzlnhV9+thQuftYpDh/CrjzzpDoIzsRvgQoAMN37NlzEiABEiABDwQ0tt/YscDU7hsx7Woz/JW2ONJ9MxuPV7NJ6axATnkxkUCQE6AADPIBZPNJgARIgAT8R+CUGPc6tovC3fM/xAq8jdS4jjsznkPK+w7JQ/L570GsiQSSmQDXACbzAPDxJEACJEACgUFgzRqgVtGD6Dy/BgajjxF/YgxEyhPHYrx8584NjIayFSTgBwIUgH6AyCpIgARIgASCl0BUFDBggGzpVnkuvj9SHI+L7S8KMV+POulr0iGxADZqBFAE2onwPcgJUAAG+QCy+SRAAiRAAvEncPAgUK0aMKjvJQy1eiAbThvxlxLRrpXqwkBN3bsDqhiZSCDICVAABvkAsvkkQAIkQALxI7BgAVCiBLBqFZAqYzr80eI9U9FN4s9evYrAAwcAnStmIoEgJxAUAnD16tWoW7cu8ubNK674NsyfP98Fe5s2bUy+XrO/ypUr51LG08mcOXPwwAMPICIiwrzPmzfPUzHmkQAJkAAJhBCBy5eBl7tGY1W9oah3ajxKlQK2bgWeqOOjX+SRIyFEg10JVwJBIQAvXLggv9JKYNSoUV7HqVatWjgi/1PaX4sWLfJaVi/89NNPeO6559CyZUts377dvDdu3BgbNmyI9T5eJAESIAESCF4Cf/wBPFXqCJ76pBaGojfGpnoJ62bsx913S5/y5PGtY76W8602liKBZCFgsyQly5Pj+VC18Kmlrn79+o4a1AJ45syZmyyDjgIeDlT8nTt3Dt99953jqorI2267DdOnT3fkxXag92fJkgVnz56VYPDcCig2VrxGAiRAAslJQL/pxo8HFnX5BmOvPI+cOIGoiHRIOfwjifvSETJ9FLO2r1AhQB0+PH01apl8Egpmzx5xDU6ZnN3hsxNIgN/fuOHmlECQgXD7ypUrcfvtt+Pee+9Fhw4dcOyYuO3HktQCWLNmTZcSTzzxBNatW+eSxxMSIAESIIHgJiC/0dHq2Uu42P4lzLlS14i/aw+WQMqtm2P2eVNhp0lF3fDhMcf2vJizGIGoxx9/TPFnZ8L3oCYQFFPAtyJcu3ZtTJ06FcuXL8fQoUOxceNGPP7447hy5YrXW48ePYpcuXK5XNdzzfeWtD791eD88laW+SRAAiRAAslPQFf1lC15Fb3mlMdLiFlGZHXvgdSb5UKRIjc3sEEDYPZs4I47XK+p5U/z9ToTCYQAAR9XvAZ2T3U6156KFi2K0qVLo2DBgvj222/l/1Xv/7PqdLJz0tlw9zzn64MGDUL//v2ds3hMAiRAAiQQgASiJYrLkCHA228D16+nwZosdfFAyqNIM20SbDLbE2vS74169WK8fdXhQ9f8VaxIy1+s0Hgx2AiEhAB0h55H/mdVAbhr1y73S47z3Llz32Tt02ljd6ug4wY56NOnD3r27OnIUktg/vz5Hec8IAESIAESSH4COpHz0nPHsHl1pG7kJg5/MgU86h2ksV6WfXxz+tZAnQ6uUsW3sixFAkFIICQF4MmTJyVU0wH50ebdo6t8+fJYunQpevTo4Ri2JUuWoEKFCo5z9wMNF6MvJhIgARIggUQmoMGWNd5eHC1w338PTGiyGCPPtsYR2x3YPvYntO6QRmZ3UkuDfRR/idw1Vk8CgUAgKARgZGQkdu/e7eC1Rzywtm3bhmzZsplXv3790LBhQyP49u7dizfeeAM5cuTAM88847inVatWsqTjDug0rqZu3bqhUqVK+OCDD8TSXw9ff/01li1bhh9//NFxDw9IgARIgASSgYButyZ/o6HbdNiTrsFTBw0vy3quXpXp3levINfwPpgJ8eyVlPWuHHio9r/iwMGZGjtGvpOAg4CGgQn0tGLFCg1Vc9OrdevW1sWLFy3x5rVy5sxppU6d2ipQoICl+fv373fpVuXKlU2+c+asWbOs++67z9x3//33WxIY2vnyLY8l/Itpk74zkQAJkAAJ+IGA/h22SYSymEAs/71rnr48/J3etcuyGj7wm7UVJRzlr3XqYskXhB8axCpCkQC/v+V/Jx1YhxrkQZwIMI5QnHCxMAmQAAnETkCnfQsVcrX8Od+hjntucfimfGnh5w6fYfCVHkiPS7iSOQcipkjAP9k9iokEvBHg93cIxQH0NsjMJwESIAESCBICuubPedrXvdlqr7ixF+/580Dr1kCbVlFoemWiEX+XK9ZAxB87KP7cufGcBDwQCIo1gB7azSwSIAESIIFQI+DjHrub115G0w4Wdu22IUWKVNj40lQ8UmAB0nYXL98UIRHeNtRGlv0JQAIUgAE4KGwSCZAACYQlgVgiNygPXa80QsI5X317BdpZKzAq3weYNk1D9N0pV7prESYSIAEfCVAA+giKxUiABEiABBKZgAZb1jV+HvbiPSYhXN7Ee+iEz1Da2oxo2NDpqzbIWt7Dbh6J3ExWTwKhQIC28lAYRfaBBEiABEKBgJe9eH9AVQzC6xLcpSdKYzMuZ8gG25w5FH+hMObsQ7IRoABMNvR8MAmQAAmQwE0ENM7fjb14ryEVBuAtnER2EX+9kBEXEFmmKtL+sR22Bv/Feb2pDmaQAAnckgAF4C0RsQAJkAAJkECSEhARuHflXlR94F80wDw0xmxE2VLhav9ByPjT0php4iRtEB9GAqFHgAIw9MaUPSIBEiCBoCYwaxZQslRKrP0tG0amew3nc9+NlBvWIc07rwM6TcxEAiSQYAJ0AkkwQlZAAiRAAiTgDwIXLwLvtt2DlTOP4izKo1w54PWpLZApTyMgXTp/PIJ1kAAJ3CBACyA/CiRAAiRAAslOYIfEb+53z1T0mVkCc9AQ73U/gdWrgcJ3yu4fFH/JPj5sQOgRoAUw9MaUPSIBEiCBoCGgm3t8MewcMrzaBUOip5h2RxctgTd7XQZSB0032FASCDoCtAAG3ZCxwSRAAiQQGgROnQL6VPkJ1XqXRDMRf1G2lLjw2gBk3bqCjh6hMcTsRQAToAUwgAeHTSMBEiCBUCWwZrWF9XXfx3vn+kmwlyiczVYImRdOQ4YK5UO1y+wXCQQUAVoAA2o42BgSIAESCG0CUVFA//5Alao25D33uxF/J2s3R5Z/tsFG8Rfag8/eBRQBWgADajjYGBIgARIIXQIHDgBtml3F8h/TmE6uaTIaDWrVQ/bWjUO30+wZCQQoAQrAAB0YNosESIAEQonANzMicbb1y3jp6in8nGEexoy1oUWLLNJFir9QGmf2JXgIUAAGz1ixpSRAAiQQdAQuizPviFabUH9WM9yLXYiGDb9N3oT8DcoEXV/YYBIIJQIUgKE0muwLCZAACQQQgd93RmNx9Q/R4+hbEtHlOs5kzIcM86Ygf3WKvwAaJjYlTAnQCSRMB57dJgESIIHEIqCx/ab/7xD+LV4D3Y++bsTfkccaIev+HUhdvXJiPZb1kgAJxIEABWAcYLEoCZAACZBA7ATOngWaNrFwzyv1UCV6OS6lSI8zQ8chz+qvgNtui/1mXiUBEkgyApwCTjLUfBAJkAAJhDaB9etF/DUF9u614XDKEZiRtydyL5mMdPffG9odZ+9IIAgJUAAG4aCxySRAAiQQSASio4FJ3bdiySe7sDe6MQoVAoZMr4C8j/wE2GQvXyYSIIGAI0ABGHBDwgaRAAmQQPAQOHIoGl9X/Rhtd72O5ySsc57axdB3ehFk0Qgv4vHLRAIkEJgEKAADc1zYKhIgARJIPgK6XceaNcCRI0CePEDFikDKlDe154epR5Hi+dZ44doSc+1IyToYOiknbEb83VScGSRAAgFEgE4gATQYbAoJkAAJJDuBuXNh5nCrVgWaNQP0vVAhQPNvpKtXgS+e+RbFWhRHVRF/l2zpcOSdMSi4ZR5sOXPYi/GdBEgggAnQAhjAg8OmkQAJkECSElCR16gRoHFcnNOhQzH5s2djd7Fn8PNjPdH+2MemxMEcJZBzyTTkeegB5zt4TAIkEOAEaAEM8AFi80iABEggSQjotG+3bjeLP334DUE4pcMqPPQw8NexmDne3U/3QL6DGxBB8ZckQ8SHkIA/CdAC6E+arIsESIAEgpWArvk7eNBj688jA16zPsCYU13M9dUV38K/3arj7oaPeSzPTBIggcAnQAtg4I8RW0gCJEACiU9AHT48pO0oho0oi474HGlxEf0a/oKlK1IhF8WfB1rMIoHgIUALYPCMFVtKAiRAAolHQL19nZKuApyLZ1ABP6EEfsEVpMF6lEOJriPEI9ipIA9JgASCkgAFYFAOGxtNAiRAAn4moKFe8uUDxOHjuJUNa1ARDTHPPGQ/8iMLzqJE/jMxIWH8/GhWRwIkkPQEOAWc9Mz5RBIgARIIPAIa52/4cKy3yuJf5EYDzDdt/AUPivw7gCy288DH4vnrIR5g4HWGLSIBErgVAQrAWxHidRIgARIIAwLXrgFvbGqA88iEotiJU7gNe1BQVgDuhC1/fkBCwKBBgzAgwS6SQHgQ4BRweIwze0kCJEACXgns3Qs0bQqsXw9Mx2eYXag3irzXAtlSXI51JxCvFfICCZBAwBMICgvg6tWrUbduXeTNm1f2Fbdh/vyYqQmle01+tr722msoVqwYMmTIYMq0atUKhw8fjhV+v379TF1an/2VO3fuWO/hRRIgARIINQIr+67ApPsHGfGn+/d+MLMwSu2Zg/TNn4lRhVWqcNo31Aad/SEBIRAUAvDChQsoUaIERo0addOgXbx4EVu2bMHbb79t3udKJPu//voLTz/99E1l3TMefPBB2eryiOP1yy+/uBfhOQmQAAmEJIGLZ67iu5Kvo9KAauh75Q10KbIc27YBjRuHZHfZKRIgATcCQTEFXLt2bejLU8oiP1mXLl3qcmnkyJEoW7Ys9u/fjwIFCrhccz5JlSoVaPVzJsJjEiCBcCDw5ze7cPXZZqh9eZPp7saSHfDRikeQOms49J59JAESUAJBYQGM61CdPXvWTOtmzRr7X7Ndu3aZKePChQujSZMm+Oeff2J91JUrV3Du3DmXV6w38CIJkAAJBBABK9rC8pYTcEfdh1BMxN9p223Y8c5slNn6mYi/DAHUUjaFBEggsQmEnAC8fPkyXn/9dTRr1gyZM2f2yu+RRx7B5MmTsXjxYnz++ec4evQoKlSogJMnT3q9Z9CgQVCLo/2VXz3jmEiABEggCAicOgUsvasTHp/SFhlxATuyVUH0lu0o3r9hELSeTSQBEvA3gZASgOoQopa86OhojB49OlZWOqXcsGFD4zxSvXp1fPvtt6b8pEmTvN7Xp08fqHXR/jpw4IDXsrxAAiRAAoFCQLf5LVkSmLC3Kq7LNh4/1hmIokeXIXtJ/ogNlDFiO0ggqQkExRpAX6Co+Gssq5f37NmD5cuXx2r981SfehCrJ7FOC3tLERER0BcTCZAACQQDgagr1zHmlX/Q7ZN75YcxsOnupvj9f2XxWL27gqH5bCMJkEAiEggJC6Bd/Kl4W7ZMftVmzx5nZLq+7/fff0cet/0w41wRbyABEiCBACBwZN0e/H57JTQcWRnZoo9DomNJpASgGMVfAIwOm0ACyU8gKARgZGSkhCfYZl6KTK18eq5evtevX0ejRo2wadMmTJ06FVFRUWY9n67pu3r1qoNwtWrVXMLI9O7dG6tWrTJ1bdiwwdShDh6tW7d23MMDEiABEghGApt7TkXGR0ug6LmfkA6XMO2NndDVLZkyBWNv2GYSIIHEIBAUU8Aq7jN/n1sAAEAASURBVKpWrerof8+ePc2xijUN6LxgwQJzXlIXuTilFStWoEqVKibn77//xokTJxxXDx48KJHvm5q8nDlzoly5chIIdT0KFizoKMMDEiABEggmApePncOOSl1Q9s8pptnbMjyKLN9MRY0q/LsWTOPItpJAUhCwWZKS4kGh+Ay1GKpHsDqFxOZxHIp9Z59IgAQCi8CeGeuRunUz5Lu6xzh6LCv/Dh5f9gbSpA+K3/mBBZOtCXkC/P4G+Jch5D/m7CAJkEAoE9Cf8OPHAxGdxqJF1B7sS1EIh4dMRa1eFUK52+wbCZBAAglQACYQIG8nARIggeQiIJMP6NQJmDlT1vdhBNIWyIbHlvRF+ftkU18mEiABEoiFQFA4gcTSfl4iARIggbAksGvgLPyQr5WIPwuyqyXeHJwZDfYMQ26Kv7D8PLDTJBBXArQAxpUYy5MACZBAMhKIPheJX6p1Q4lN43GPtOOlHLXRbGFTcWRLxkbx0SRAAkFHgAIw6IaMDSYBEghXAie+34TLDZuhxMVdiIYN8x94A++uaoQsOcKVCPtNAiQQXwKcAo4vOd5HAiRAAklFQLbx+LPdEGSpXR75RPwdtOXDd6+swDO/vifiL3VStYLPIQESCCECtACG0GCyKyRAAqFHQOPZby3VAY/8Kq6+kpZkaYSC332KJ8tnC73OskckQAJJRoAWwCRDzQeRAAmQQNwI7N4NVJBoLt1/bY8zyIKpj3+BSke+wn0Uf3EDydIkQAI3EaAF8CYkzCABEiCBZCZw8SKWvv8zGoyoAtkJE9mylcfakfvQvBnDuyTzyPDxJBAyBCgAQ2Yo2RESIIFQIHBx3TacqdMUj53diwLYhByVHpR9zoF8+Sj+QmF82QcSCBQCnAIOlJFgO0iABMKbgDh6HOz1EVI99gjynv0Dp3Ebej1/GsuXq/gLbzTsPQmQgP8J0ALof6askQRIgATiRMA6chT7Hm+DQn8sNvctSfs0Mn01Dm3rMr5LnECyMAmQgM8EKAB9RsWCJEACJOB/AmenL4LVRsTf1eO4hLSYVGIYGv/wArJlt/n/YayRBEiABG4Q4BQwPwokQAIkkEwEdHp3bMctyCrib4etOOa/uQmdtr5I8ZdM48HHkkA4EaAFMJxGm30lARIICALXrkSj34AUGDQIsFl9EJUrE57+phOalk4bEO1jI0iABEKfAAVg6I8xe0gCJBAoBCwLJwd8gqP/+xJDI1fBkinf9h1SovvH3ZA+vVMjo6KANWuAI0eAPHmAihWBlCmdCvCQBEiABBJGgAIwYfx4NwmQAAn4RuD4cRyu1RZ5t3yD7HLHi2knovykF9C4sdvtc+cC3boBBw/+d0HdgIcPBxo0+C+PRyRAAiSQAAIUgAmAx1tJgARClICfLXCXFyzBlSatkffSUVxBGnxS8EN0W9EJhQq78VPx16gRIJZCl3ToUEz+7NkUgS5geEICJBBfAnQCiS853kcCJBCaBFSEFSoEVK0KNGsW867nmh/XdOUKjrfuhbT1nkAWEX878QA+bb8RL+16WcSfzbU2FZ1q+XMXf1rKnte9O6DlmEiABEgggQQoABMIkLeTAAmEEAG7Bc55+lW7Z7fAxUEEqmbbWb0bck4eZgBNTN8Zx77dhJc/L47UqT0w0zV/7s91LqYVHjgQszbQOZ/HJEACJBAPAhSA8YDGW0iABEKQgB8tcKdOAQ0bArV/fAO7cDcGlPoaT+79BFXrpPMOTh0+fEm+lvOlLpYhARIIWwIUgGE79Ow4CZCACwF/WOBE+f35xiSULAnMmwccTV0A3374O976+WnkzOnytJtP1NvXl+RrOV/qYhkSIIGwJUAnkLAdenacBEjAhYCvljUv5aKWrcCFhi1x37lDKIqciLi7DmbMAEqV8vHPrIZ6UW9fnW62r/lzbqBN1gzqdS3HRAIkQAIJJEALYAIB8nYSIIEQIeCrZc293LVrONe1D2w1qiGziL8/cS9KP5kbW7ao+IsDG43zp6FeNKnYc072848/ZjxAZy48JgESiDcBCsB4o+ONJEACIUXAboGziy33zml+/vyuFrjdu3H6wUeR+ZPBSCFhnSemao8tn2/BgG8eRqZM7hX4cK5x/jTUyx13uBZWyx9DwLgy4RkJkECCCPg4N5GgZ/BmEiABEgh8AnYLnMbhU7HnPA1rF4VOFrirE6fB6tgRt127gFO4DYPv/Bwdvm+Ie+5JYFdVBNarx51AEoiRt5MACcROgBbA2PnwKgmQQDgR8NEC98cfwNt9UyBCxN9KVMYnHbbjvd/9IP7srFWMVqkCNG0a885t4Oxk+E4CJOAnArQA+gkkqyEBEggRArFY4KzzkRj/VUa8/DJw8WITHMqcAc2n1sHbT4lgYyIBEiCBICJAARhEg8WmkgAJJBEBuwXO/rjr13H59X64OOJzvHFpCy4iF6pXBz6cXBfuPiH2W/hOAiRAAoFMgAIwkEeHbSMBEkh+Anv24Hy9Fsj0yzqkldY0TzEDuQZ2wyuvACm4iCb5x4ctIAESiBcBCsB4YeNNJEAC4UAgeup0XGv3AjJdOYezyIy3c4xFs4VNUa5cOPSefSQBEghlAhSAoTy67BsJkED8CJw7h0vtX0K6WZMRITWsRQVMf3Iq3ptSCFmzxq9K3kUCJEACgUTA7xMYB2PbzDyQes62kAAJkIAXAv+0e9+IvyiJ7vdeqn7489NVGLmQ4s8LLmaTAAkEIQG/C8CiRYviyy+/9CuK1atXo27dusibN6+E57Jh/vz5LvVbEq+rX79+5nq6dOkkekIV7Ny506WMp5PRo0ejcOHCSJs2rUTsL4U1uhcoEwmQQNgSuHoV6N0bKDH7LSxFdbS9azUa7uiLth1T3bQ5R9hCYsdJgARCgoDfBeDAgQPRpUsXNGzYECdPnvQLpAsXLqBEiRIYNWqUx/qGDBmCYcOGmesbN25E7ty5UaNGDZw/f95jec2cOXMmunfvjjfffBNbt26V7TUronbt2ti/f7/Xe3iBBEggRAkcOIBTXd7GoxUsDB0KRCITFnRdik9/fRRFioRon9ktEiCB8CYg1jO/p3/++ceqWrWqlStXLuvrr7/2a/0yWta8efMcdUZHR1si+KzBgwc78i5fvmxlyZLFGjt2rCPP/aBs2bLWCy+84JJ9//33W6+//rpLXmwnZ8+etbQ9+s5EAiQQpARmzbIup8+q+35YXTDSypbNsubPD9K+sNkkQAI+EeD3t2UlihOITqsuX77cWOTUElhEfkKnSuX6qC26U7of0h4J0XD06FHUrFnTUVtERAQqV66MdevWoVOnTo58+8FVmefZvHkzROzZs8y71qH3eEtXrlyBvuzpnCwUZyIBEghSApGRuNalO1JPHmccPX5GGZwqUwvb5sRs+RukvWKzSYAESMAnAq6qzKdbfCu0b98+zJkzB9myZZNtLevdJAB9q+XWpVT8aRJro0thPdc2eEonTpxAVFSUx3vs9Xm6b9CgQejfv7+nS8wjARIIJgLyA/Byg6ZIu38XomHDYPRB1Nv98GXf1OCua8E0kGwrCZBAfAkkigD8/PPP0atXL4mUXx2//vorcubMGd/2+XyfOoc4J7EBG4cR5zz347je06dPH/Ts2dNRjVoA8+fP7zjnAQmQQOATsMaNR3SnF5A26hoOIB965vgSL8+tIuuAA7/tbCEJkAAJ+IuA3wVgrVq18PPPP5vp31atWvmrnV7rUYcPTWq5y+O0J9OxY8dusvDZK8mRI4f8yk9p7rHn6Xts9+h1nVrWFxMJkEBwEjh+HBg0oSg+iLIwDw3xdZ3P8OmX2WSmIjj7w1aTAAmQQHwJ+N0LWKdWd+zYgaQQf9ppXW+oInDp0qUOBrrGb9WqVahQoYIjz/kgTZo0JuyL8z16Xc+93eN8P49JgASCjIAsB5FlyRJNAPhobVmUT70Zx0bNwuRvKP6CbCTZXBIgAT8R8LsF0F1U+aOdkbJYe/fu3Y6q1PFj27ZtZn1hgQIFTDgXDT9zzz33mJcep0+fHs2aNXPcU61aNTzzzDPo2rWrydOp3JYtW6J06dIoX748PvvsMxMCRjyDHffwgARIIMgJXLyIqB69ED1uArpHbcQRFDNhXcbPKI7ixYO8b2w+CZAACSSAgN8FYALa4vXWTZs2QcLKOK7b1+G1bt0aEydOxKuvvopLly6hc+fOOH36NB555BEsWbIEmTJlctzz999/Q50/7Om5554zcQoHDBiAI0eOQANYL1q0CAULFrQX4TsJkEAwE9i+HVcbNUWa3b8jpfSjKpajXIdi+OgjIEOGYO4Y204CJEACCSdg04A5Ca8mPGtQJxCJNwiJJ4TMmTOHJwT2mgQCjUB0NDBiBKJeeQ0pr1/FYeRB5/ST0GxCDTRuHGiNZXtIgASSgwC/v4GgsAAmx4eDzyQBEghCAv/+i6iWbZBy6ffG6rcAdTGm1DiMmZ0ThQoFYX/YZBIgARJIJAJ+dwJJpHayWhIgARK4JYEjH04x4u8S0qIzRmP9619jwU8Uf7cExwIkQAJhR4AWwLAbcnaYBIKAgEQTwJo1kAW6kPhOMEH6YonQrAtZxo4Feo/qjv9hN2Zk74p3Zj4I8f1iIgESIAES8ECAAtADFGaRAAkkI4G5c4Fu3YCDB/9rRL58wPDhQIMG/+Xp0c6duPL2u2gdNQEzF6STjJT4ps4YzJ4ICUCvBZhIgARIgAQ8EeAUsCcqzCMBEkgeAir+GjVyFX/akkOHYvL1uiY1+Y0ejaiHSyNi3kw8tKAfUqcGhg0DFi6k+IuBxH9JgARIwDsBWgC9s+EVEiCBpCSg075q+fMUmEDzdLvH7t0h0dphdegI2zcLjaPHd6iFeYV64qfZkADvSdlgPosESIAEgpcABWDwjh1bTgKhRUDX/DlP+7r3TkXggQOIKlIUKc+cxBWkwasYgjMtXsLS0Skk7qf7DTwnARIgARLwRoBTwN7IMJ8ESCBpCajDhw9Jxd9OPIAq6X5G6cndMOlLij8fsLEICZAACbgQoAB0wcETEiCBZCOg3r5e0mVE4B30wyncJsFdXkTHhzZi8vYSsp2jlxuYTQIkQAIkECsBCsBY8fAiCZBAkhGoWBFQb19d6+eU/sB9KIf1eBd9UQS/4+/uo7BifXrZ99upEA9JgARIgATiRIACME64WJgESCDRCGicPw31ciPJij+T3sD72I6SyIljmPjmbgz9KAXSpLlxkW8kQAIkQALxIkABGC9svIkESCBRCGicv379EJ0iFdQOeE12q8wlwq9axI/Y/sUm1H7v0UR5LCslARIggXAjQC/gcBtx9pcEApXAtWtA376wBg9GCvH4/Qv3oKVtCp5pnwOffFIQKVKLhZCJBEiABEjALwQoAP2CkZWQAAkkiMDu3bCaNYNt40Zj+fsC7fBRgY8xbmZGlCuXoJp5MwmQAAmQgAcCFIAeoDCLBEggaQmcXrkNt4n4O42s6IjPkKLxs1j7KZA1a9K2g08jARIggXAhwDWA4TLS7CcJBBqBGzt+LF4M3P9mI/TEUDwSsR21vngWM2ZQ/AXacLE9JEACoUWAAjC0xpO9IYHgIPDjj4gu+wgGdD6KWrWAY8eAH4r3xNdbC6Bdu5siwQRHn9hKEiABEggiAhSAQTRYbCoJBD2B69eNl69VuTJSbNqIvGPeMl3q0gXYsAEoUiToe8gOkAAJkEBQEOAawKAYJjaSBEKAwN69QPPmwLp1xtFjElrh3azDMG8CUL9+CPSPXSABEiCBICJAARhEg8WmkkDQEpg+HdYLL8B27hzOIjNewFgcrtQUP04B8ucP2l6x4SRAAiQQtAQ4BRy0Q8eGk0CQEBg/HtAQLyL+1qICHrJtx/39mmL5coq/IBlBNpMESCAECdACGIKDyi6RQKAQUEff0ccb43H8DzPRGBPveAtfTk8F3faXiQRIgARIIPkIUAAmH3s+mQRCk0BUFDBzJo5Xa4Ln26XAt99mRBpsRZ36EdgyDsiWLTS7zV6RAAmQQDARoAAMptFiW0kgqQioiFuzBjhyBMiTB8Zkl9KHrdgOHABatgRWrcLIzMfw7bnuiIgAhg2LwIsvMrxLUg0fn0MCJEACtyJAAXgrQrxOAuFGYO5coFs34ODB/3qeLx8wfDjQoMF/ee5Hs2fD6tgRttOnEYkM2HMuuwnrokGdixd3L8xzEiABEiCB5CRAJ5DkpM9nk0CgEVDx16iRq/jTNh46FJOv193ThQtA+/bAs88a8fczyqAktiFdh5aQ3d0o/tx58ZwESIAEAoAABWAADAKbQAIBQUCnfdXyd2OLNpc22fO6dwe0nD1t2wY8/DAwbhyiJbrfQPRBncxrMXDm3fjsMyBDBntBvpMACZAACQQSAU4BB9JosC0kkJwEdM2f87Sve1tUBOoaPy1XpYq5ejnyOlLv+gdHcAdaYAqulKuCTdOBQoXcb+Y5CZAACZBAIBGgBTCQRoNtIYHkJKAOH76k/ftNqV9+AUp1Ko0G1myUwA48+kYVrF5N8ecLQpYhARIggeQmQAtgco8An08CgUJAvX19SFavXpj1Zwm0HlYCly8Dp3LXw1dTgGrVfLiZRUiABEiABAKCAC2AATEMbAQJBAABjc6s3r42W6yNsZ04gaiBg434q1MH2LGD4i9WYLxIAiRAAgFIgAIwAAeFTSKBZCGgcf401IumWETg/9ALHVJNlNh+wMKFQM6cMbfwXxIgARIggeAhQAEYPGPFlpJA4hPQOH8Szw933OF4lrh+mHQEuVETi/Hp3f/DqvUR6NEDSMG/IA5OPCABEiCBYCIQEn++C4nLoU0sFu6vLl26eByLiRMn3lRW772sC5qYSCDcCagI3LsXePttQ0InhBfiKRQXR488rWpiyxZx/igV7pDYfxIgARIIbgIh4QSyUaLNRjnFJvv1119Ro0YNiUv7rNfRyZw5M/7880+X62nTpnU55wkJhC0BmQ5e8HA/RKTeggXXamNyhs4YM9aGFi3Clgg7TgIkQAIhRSAkBGBOt0VIgwcPxl133YXKlSt7HSy1+OXOndvrdV4ggbAjoBbwoUNx+cUeeLVfeowcqRMEC8XaZ8NW2c7t7rvDjgg7TAIkQAIhSyAkpoCdR+fq1auYMmUK2rZta6Z5na85H0dGRqJgwYLi9JgPTz31FLZu3ep8mcckEF4Edu4EypYF3noLC+7tJeIvpvs9e9qwbh3FX3h9GNhbEiCBcCAQcgJw/vz5OHPmDNq0aeN1/O6//37oOsAFCxZg+vTp0KnfRx99FLt27fJ6j164cuUKzp075/KK9QZeJIFAJ6C7e4wZA6t0aUAiOx9HTkw8Wdd49i5aZAyCSJMm0DvB9pEACZAACcSVgM2SFNebArn8E088IV9YaSQ8hcSn8DFFR0fLdqYPo1KlShgxYoTXu/r164f+/fvfdP3s2bPQNYVMJBBUBCSeH9q1g/wSMs3+DrXwPCagWPXcmDwZ8DEudFB1mY0lARIgASWgxpwsWbIgnL+/Q8oCuG/fPixbtgzt27eP0yc8hcSyKFOmzC0tgH369DEfFv3A6OuA7ovKRALBSGDDBqB4cSP+riANuuMj1Ev5LXoMzo3Fiyn+gnFI2WYSIAESiAuBkHACsXd4woQJuP322/Hkk0/as3x6VyPotm3bUKxYsVjLR0REQF9MJBDsBKLz3IErZ69gD4qgGabhbKGSWD0dKFcu2HvG9pMACZAACfhCIGQsgDqNqwKwdevWSJXKVde2atUKar2zJ53GXSxmjn/++ccIv3YyDaYC8IUXXrAX4TsJhB6B48dNn44eBZ5olw+PXVyC0tiE+58rKZ9/ir/QG3D2iARIgAS8E3BVSt7LBfwVnfrdv3+/8f51b6zm6zSvPamTSMeOHXFUvgl1DcBDDz2E1atXixOkeEEykUCoEdBlvuPGAd27Y3Pvaag9+mmoFkyXrpTx9hWHefGYD7VOsz8kQAIkQAKxEQg5J5DYOuvva1xE6m+irM/vBE6dgvzaAebMMVXPRGM0wUyz/G+GxPYrUsTvT2SFJEACJBDwBPj9LVt5BvwosYEkQALxI7ByJVCihBF/122p8AqGoCmmo2tXQH1AKP7ih5V3kQAJkEAoEAiZKeBQGAz2gQT8QuDaNaBfP2DQIECmf3fb7kETaxr2ZCuNeeOBevX88hRWQgIkQAIkEMQEaAEM4sFj00nAIwG1/A0caMTfOLRFSWsLMlQqbRw9KP48EmMmCZAACYQdAVoAw27I2eFQJ7Alew1sydobi8+UxdwUz+Kdd8wOb0iZMtR7zv6RAAmQAAn4SoAWQF9JsRwJBCoBCUouMYxgHTqMjz+OCefS4cyHWJ/vWagxsG9fUPwF6tixXSRAAiSQTARoAUwm8HwsCfiFwLp1QPPmwN692Dx3H3oc/85UW79+TOSXbNn88hRWQgIkQAIkEGIEaAEMsQFld8KEwPXrkI2pgYoVjfjbl7Iwuh7vKzvVAJ98AsydC1D8hclngd0kARIggXgQoAUwHtB4CwkkKwGx9qFFC2DtWtOMyWiJrlGjkK9IZvwssf10i18mEiABEiABEoiNAC2AsdHhNRIINAIawK9kSSP+LqTMhOaYgtaYjCYdMmPjRoq/QBsutocESIAEApUALYCBOjJsV/gSiIoC1qwBjhwB8uSJmea1u/AWLYpzGXLj98gH0CRqKk5nKYyZnwGNG4cvLvacBEiABEgg7gQoAOPOjHeQQOIR0MV73boBBw/+94xcuYBRo3CxTiN075EB3x1eiiPIgzLlUmHFdKBQof+K8ogESIAESIAEfCFAAegLJZYhgaQgoOKvUSMTwNnlcf/+iyPPvoRq+Wri94OZYbPlx+uvx/iApE7tUpInJEACJEACJOATAQpAnzCxEAkkMgGd9lXLn2zd5iktx+Mi/jIhd24LU6bYUK2ap1LMIwESIAESIAHfCNAJxDdOLEUCiUtA1/w5T/veeNolpEUbTEALcfaog0XYMWYdxV/ijgRrJwESIIGwIEABGBbDzE4GPAF1+HBL21Fc/tuBaWiGYeiJhaiLnJf2u5XiKQmQAAmQAAnEnQAFYNyZ8Q4S8D8B9faVpBPA+hqMV1EGEtdF0k8ojx74GCn0yo1y5gL/IQESIAESIIF4EuAawHiC420k4FcCsqPHwdylMe1oFXwnk70rUVXCO0/GJ+iCTIiEeH4A+fLFhITx64NZGQmQAAmQQDgSoAAMx1FnnwODgE77dugADBiArw88jLaRP+IUIpAR50X6tZT/psS0U8Wfpo8/BuzxAGNy+C8JkAAJkAAJxIsABWC8sPEmEkgggYULgbZtgRMnsP/nI6h/fJNUGIFSd53G9Mincc+/P/73ALX8qfhr0OC/PB6RAAmQAAmQQAIIUAAmAB5vJYE4E7h0CejdGxg92tz6R9qSIv6myrENPXsCgwbdhjQpV3rfCSTOD+QNJEACJEACJHAzAQrAm5kwhwQSh8COHUDTpsBvv5n6h6fqhVcvv48sOSOwaBJQu7b9sSmBKlXsJ3wnARIgARIgAb8ToAD0O1JWSAIeCGzZAlSoAFy5gtNpc+O5y5Ow9HpNVK8OTJ5M514PxJhFAiRAAiSQiAQYBiYR4bJqEnAQKFkSZ4s9hh/SPYV7L+/A8pQ1ZboXWLyY4s/BiAckQAIkQAJJRoAWwCRDzQeFHYEffgDKlUN0ugwYMiQFPtg6D2eiMqJQIRsWTjeXwg4JO0wCJEACJBAYBCgAA2Mc2IpAIqD78urWbBqmRQMvS4y+OIVfuXwZ6NPHeO5ebNER9Y5+imXLtIOZ0Lgx8OmnQNasgdRhtoUESIAESCDcCFAAhtuIs7+xE5g7F+jWzXVfXg3DMny4b2FY1MFDHT3U4UPS1DkR+OFSNNKlS4GRI2Miv9jD+sXeEF4lARIgARIggcQjwDWAiceWNQcbARV/jRq5ij/tw6FDMfl63VuyZJu2MWOAUqWM+ItMlxNP4ht0vDQCxYqnwObNQLt2MRt6eKuC+SRAAiRAAiSQVAQoAJOKNJ8T2AR02lctfyrk3JM9r3t3QMu5p5Mngfr1gc6dAZn+XZf5Cdx9aQcWiQTs2hXYsAEoUsT9Jp6TAAmQAAmQQPIRoABMPvZ8ciAR0DV/Bw96b5GKwAMHYtYGupeS0C5YuxZRqdLgtTQf4bFzi3AtW27Mnw8z7Zs2rfsNPCcBEiABEiCB5CXANYDJy59PDxQC6vDhS7KXU0vgjX15IzPnxeiHpmPaspzYjpKoVAmYMgXIn9+XClmGBEiABEiABJKeAC2ASc+cTwxEAurt+//27gXepjr///j7OK4JuRRCqDzq5JLoImEUKWZqjKQk9Gt+xYyMUv0iXVRT0kUilGZ0k8t/iu4KkRhS43JSujAIDSONHHLLOfv//azdPu19HGeOc7PW2q/VY3fWXnuttb/f53fb53O+3/X9rPwstt/XX0vnnSfNnCnL79yihXTH3Iu1qlRzDR8uzZtH8JcfSvZBAAEEEDh6AvQAHj173tlPApbqxWb72oSP2DV/8eWzqbt16khr1ki//rW0Z4929LtDrXdcrv0HU71Dp0yJZoyJP4x1BBBAAAEE/ChAD6AfW4UylbyADedaqhdbcuZpsecWFNqY7o03esFfevUL1eS7+V7wZ/M/0tMJ/qJ4/B8BBBBAIAgCBIBBaCXKWDIC3bpJr7wS7emLf8caNSR7LFmirNTSerDSw2rx/Rx9X66Oxo2TLDtMtWrxB7COAAIIIICAvwVCEQAOdxdepbhemvhHrVq18pRfsGCBS9nWUuXdFM2TTz5ZTz/9dJ7782KSCFgQuGGDNH++ZGO6L7wgWZqX7du1veqpapW5WHftukOnpaXq44+jmV9ydhgmiRTVRAABBBAIsEBorgFs3Lixu92Wd78trzlSf56hmVvbrF+/Xl26dNENN9zgZmtOdhk8/u5SuP1Rxx9/vK644orcDmFbMgnYZ6d9++waZ8xeog9n79fV343RjzrWfW6kJ56QKlbM3oUVBBBAAAEEAiUQmgCwdOnS+m+9frGWsd6+k046SaNHj/Y2pbksvf/4xz/02GOPEQDGkJL1p13rZz1/FgC6SR9/+5vU782ntCMjVVWqSNMnyrufb7LyUG8EEEAAgXAIhGII2JpijZudeeKJJ6phw4a6+uqrtW7dusO20BJ3LVenTp0SXr/kkku8IPCnn35K2B7/ZL9L+JuRkZHwiH+d9YAL7Nwp9eolXXutMnv1Ub8bsrxgz4K/Vq2klSsJ/gLewhQfAQQQQOBngVAEgOe5nGwvvvii3nvvPT377LPaunWrWrdu7S7dctdu5bLY6zVr1kx4xZ4fPHjQXeq1PWF7/JMRI0a4XqAq2Y96ZPqN5wn2+uLFUvPm0tSpirgh4HGrL9Rf/hLxJgTfeaf04YdSgwbBriKlRwABBBBAICYQigCwc+fO3tBt06ZN1bFjR7399tte/V6wC/gPs9iEkfgl8nPut5zb4/cZOnSodrpeothjk90ajCXYAi7o1/33y7t9h5v8kVG9odqnLtKg7+7SCbVSNWeO9OCDUpkywa4mpUcAAQQQQCBeIDTXAMZXqqK7Ot+CQRsWzm2xawWtFzB+2bZtm+w6wurVq8dvTlgvV66c7MESEgH7DFx5pbRokVehD+pdq8s3jdMuVXaThKTnn5ebGBSSulINBBBAAAEE4gRC0QMYVx9v1a7V++KLL1T7MLf3Ov/8813PjuvaiVtmz56ts88+2/X00NUTxxLu1cqVvRQvB4+ppD9Vm6wLN72kfWUqa9Qo6c03Cf7C3fjUDgEEEEhugVAEgLfddpssr5+ld1m6dKm6d+/uTdTo27ev17o2dNunT5/slu7fv7+++eYbDR482AsUJ02apL/+9a+y87CEXGD3bikry6tkZrljNP6iV3T63pUa+59eOvVUL9ezbrlFKhWKfxkhb0uqhwACCCBQYIFQ/JrbvHmzevbsqdNOO03dXCLfsmXL6qOPPlL9+vU9mC1btmjjxo3ZSDZT+J133tEHH3zgrvtvrgceeEBjxowhBUy2UEhXLHOzTfRw6X7cR0YdOkgDxp2hf0ZOdn8gSMuXyyUHD2ndqRYCCCCAAAJxAilu8oNLfMZSEAFLCWOzgm1SSGUbTmTxp0BmpvToo9Ldd8tN9daPtU7Rqfs/19Yd5XTssdKECV7mF3+WnVIhgAACCBS5AL+/pVBOAinyTwonDK6AdfX17i3X3evVYfmpPdRh7dP6QeW83j6X9UWNGgW3epQcAQQQQACBggiEYgi4IBXnmCQQmDFDatbMC/6yjqmoe+tNUsu101zwV9Vd/ylZ6j+CvyT4HFBFBBBAAIFDBOgBPISEDaEQsJ4/d12oDhzQdw3OVoetU7RqUyMvrYulh3SpI1kQQAABBBBIWgF6AJO26UNe8bp1tfe+R/Ra2hDV2fB3rdrXyCUJl9LTCf5C3vJUDwEEEEAgHwIEgPlAYpcACFhql8cfl7uhs1dYlw1IjScO0u++GKFI6bJ6+GG5WwXK5YYMQF0oIgIIIIAAAsUswBBwMQNz+hIQcGl+ZDkfXXLviLuob1TvlRpy/zE24de7f69N9GjVqgTKwVsggAACCCAQEAF6AAPSUBTzMAJvvRWd6GHBX/kKGp16m267p4IX/PXoIa1YQfB3GDk2I4AAAggksQA9gEnc+IGu+t690u23S+PGedXIOPlMdd4xVYu/TFOFCtLYsdL110spKYGuJYVHAAEEEECgWAQIAIuFlZMWq8C2bdJFF0mff+69zYKWt6jTshE64HL7WdaXadOktLRiLQEnRwABBBBAINACDAEHuvmStPA1akhulu/BGjU1sNG7ar9slBf8DRggdy9ogr8k/VRQbQQQQACBIxCgB/AIsNj1KApYr1/FitFHqVJ69fIXdNvCFG3YfoKqVpUmTZK6dj2K5eOtEUAAAQQQCJAAPYABaqykLeq770Ynetx8s3bvjk747T6gpjbsOUHt2kVz+xH8Je2ng4ojgAACCBRAgACwAGgcUkIC+/fLu2eb3bbj3//W3vkfqW3zXXrxRcl1Amr4cGnePKlevRIqD2+DAAIIIIBASAQYAg5JQ4aqGpmZ0uTJ0r33St9841VtRduBav/RSGX8VMEu/9OUKVLbtqGqNZVBAAEEEECgxAToASwxat4oXwKvvirZJI/rrvOCvyyl6L4yD6jFwjFe8GdDvXY7N4K/fGmyEwIIIIAAArkK0AOYKwsbj4rAjBlS9+7Zb/29qqqD3lf6T2e5BC/7NOqGL/WHZ5qT2y9biBUEEEAAAQQKJkAAWDA3jipqARv2HTTIO+tBldJsddJlelNZKq00rdY09VSzd3dIWeul1NSifnfOhwACCCCAQFIJEAAmVXP7sLIHDkj33CPv9h2bN2uD6usaTdEStfYKe4Mm6gndooraI21ymxYulNq392FFKBICCCCAAALBESAADE5bha+kX38tXXONtGyZl9/vddfn11cvaqeOUxX94EK/G9VDf0us95Ytic95hgACCCCAAAJHLMAkkCMm44BCC0Qi0czNZ53lBX+RatU04fQn1VVveMFfK9f/t1LNDw3+7I1r1y7023MCBBBAAAEEkl2AHsBk/wSUdP13uOv4brxReuUV7513n3OhLv/hRc1fVtfN983SEI3UfbpHZXQwsWQpKd7t35j+m8jCMwQQQAABBAoiQABYEDWOKZjAzp3SmWe6a/k2KVK6tD76zZ/VcdZt2rM/VbVqudR//f6uDvcPi57bdRJmLxb82TJ6NBNAohL8HwEEEEAAgUIJMARcKD4OPiKBKlWkyy9X5smn6o42i9X6tTu84K9LF+nTT6UOw11mZ+sZrFMn8bSW+dm2d+uWuJ1nCCCAAAIIIFAggZSIWwp0JAcpIyNDVVxQs9P1bFWuXBmR3ATWrZPKlo0O37rXF7+/V7/ve1BffltJZcpII0dGs7/Yrd2yF0sJY7N9bcKHXfNnWZ9J/ZLNwwoCCCCAQOEE+P0tl2SNBYHiErDbuf3xj1LLlsp8b64efDhV991XQVlZ0qmnStOmeS8d+u4W7JHq5VAXtiCAAAIIIFBEAgSARQTJaeIE7Fq/AQOkl1/2Nu7/8aC6X7hTby2u5j3v3VsaN06qVCnuGFYRQAABBBBAoMQECABLjDpJ3mjJkmhuvw0bvGHbL6+6V+1mDdV3O0rr2GOl8eMlCwBZEEAAAQQQQODoCRAAHj37cL2zXbf30ENyY7ySW8+q30Cjz5miW6ec79XTjQJr6lSpUaNwVZvaIIAAAgggEESB+Evvg1h+yuwXAbul2/TpXvC387JealdppW59JRr8DR7sJn8sJvjzS1NRDgQQQAABBOgB5DNQOAGbRG55+ipUUGTKVH04ZqW6TO2tPe7WvccfL73wgtS5c+HegqMRQAABBBBAoGgF6AEsWs/kOduuXdL//I/08MNenW3exzUjmqr9X6PBX4cOUno6wV/yfCCoKQIIIIBAkAToAQxSa/mlrJ98Ep3osXatVK6clje7Tt0H1tb69dF0fX/+s/R//ycl5PbzS9kpBwIIIIAAAgiQB5DPwBEI2ESPRx+V7r5bOnhQkXr1NKXzZF3XtbY9VYMG0YkerVodwTnZFQEEEEAAAQRKXCAUQ8AjRozQOeec4/LKVdIJJ5ygrl276quvvsoT8/nnn3eXrqUc8ti3b1+exyXti5s3SxdfLA0d6gV/ey+7Uleckq5rJ7bzgr8ePaQVKySCv6T9hFBxBBBAAIEACYRiCHjBggUu7/AALwg86Lqihg0bpk6dOmn16tWqWLHiYZvDbt+WM1AsX778YfdP2hf27pXOO0/617/kQLWq31h1fOk6bfsuxeZ+aOxY6frro3NBktaIiiOAAAIIIBAggVAEgO+++24C+XPPPef1BC5btkzt2rVLeC3+ifUA1qpVK34T67kJWJR3xx3KevElPdp8ioaMiibza9Yseju3tLTcDmIbAggggAACCPhVIBRDwDlxd9qUVLdUqxa99VjO12PPd+/erfr166tu3br6zW9+44Yw3RgmS1TALJYvz9ZY23mgLoj8XUP+Gg3+7E5vS5dKBH/ZRKwggAACCCAQGIHQBYARl5dusMs83KZNGzVp0uSwDXH66afLrgN844033B0qpsqGfi+44AKtWbPmsMfs379fGRkZCY/D7hzUF7KyohM9zj1X6tJFeucdvfxSllq0TNFHy8uqalVp5kzpqafkzIJaScqNAAIIIIBAcgukuIDJZfINz2LXAr799ttatGiR17OX35plucCnRYsW3pDxmDFjcj1s+PDh7k5n9x3ymvU42vWEgV+2bIkm7rMEfm45qFQN0miN103e87ZtpZdfltzkXxYEEEAAAQQCK2CdOVWqVFFofn8XoCVC1QM4cOBAr0dv/vz5RxT8mVspl7TOZhLn1QM41M2AtQ9L7LFp06YCkPv0kLfeklyvqJe92RVxo+qqsT7zgr9SytRw99+8gTMJ/nzafBQLAQQQQACBIxEIRQBonZg33XSTZsyYoXnz5qlhw4ZHYuDta+dYuXKlateufdhjy7mkx9bTF/847M5BecHu4esCZ112mdzYtqw7+EVdq0Zaq691ugsDN2m+LtS9Kfer9K2DvHv9BqVqlBMBBBBAAAEEchcIRQBow76TJ0/WlClTvFyAW7dulT32WvqSn5c+ffq4FHYuh93Piw3lvvfee1q3bp0X+P3+97/3fvbv3z+2S3L8LFNG+uc/vbruUXn9TjPUVy/pgMrpt3pNK9Vc7bRQsisFrMdzoVtnQQABBBBAAIFAC4QiDcyECRO8Rmjfvn1CY1g6mOuuu87btnHjRm+YN7bDDz/8oBtvvNELFO06gLPOOksffvihzrXJD2FfLJiznj/Xo+kyYUvOKf3m59R5Wh9t0Yku9NunURqsP2iC3KuJi10nyIIAAggggAACgRYI3SSQkmyNQF5Eum1bNGvz8cd7gZ/dws3NbdFDD0VcJ1+K0rRa03S1mmlV7pTu+krlCLRz35GtCCCAAAII+FMgkL+/i5gyFD2ARWwS3tO5IW/17Sv9+99e79/m6+5Sj6GnaMkSq3KK/rfiFI3+8UZV1I+HGlhPocuXKJsKzIIAAggggAACgRYIxTWAgW6Bkii8y1/okiNKl14aDf4aN9bsBz9Rk99Ggz/LYDNtmvTsi+VVMWXPofd0s+DPltGjpdTU6Dr/RwABBBBAAIHAChAABrbp8lnwL76I3sf3iSe8A37qf5NuOu8TXXJbU5fORmrVSm7yi3TVVe7lbt2kV16R6tRJPLn1/Nl2e50FAQQQQAABBAIvwDWAhWhC319DYBf4NXK3btuwQapRQ98Mf05dxv9Gq1dHO/mGDJFLbC3ZROCEJTMzOtvXJnxYWhwb9qXnL4GIJwgggAACwRXw/e/vEqDlGsASQD5qb1HaNe+4cYo8+aReuuh59buttvbtk2rVkkubI3XocJiSWbDHRI/D4LAZAQQQQACB4AswBBz8NkysgUuE7W6Hkr3tP626qHvFd9V3SDT4s9v7fvppHsFf9pGsIIAAAggggEBYBQgAw9KyltfPxnQ7dpRc0mu5vIfudshq3lyaMTPFG+YdNUp6803JMsCwIIAAAggggEDyCrgxQpbAC6xZI11zjfSPf3hVyepxlUZOrK67RkhZWdKpp0Zn+bZsGfiaUgEEEEAAAQQQKAIBegCLAPGoncLu6OHu4uFuYxIN/qpW1faJr+qir5/RnQ9W9IK/3r2l5cslgr+j1kq8MQIIIIAAAr4ToAfQd02SzwLZTN1evaTp06MHuEkbs3u/pJ6319V//iMde6w0frxkASALAggggAACCCAQL0AAGK8RpHWbqVuzpuRm+v50zwO67d+3a8zvo0marbdv6tRoBpggVYmyIoAAAggggEDJCBAAloxz0byL5fWz7M3Vq0fPN3Kk1rfrq9890ELp6dFNdsOPEe7av7Jli+YtOQsCCCCAAAIIhE+AADAobbp+fXTI13L7zZ+vSKlUPTelvAYObKE97u5tNrP3+eclS/PCggACCCCAAAII5CVAAJiXjl9ee/ll6Q9/kHbtkqpU0a6Pv9CNY5p49++1IlpC55deit60wy9FphwIIIAAAggg4F8BZgH7t22kjIzoLI5rr40Gf23aaMXz6TqzVzT4s8sAbbh39myCPz83I2VDAAEEEEDAbwL0APqtRWLlWbIkOuRrQ78u0su65149Vnqohl1ZWnYpYIMG0YkerVrFDuAnAggggAACCCCQPwECwPw5lexelr15wADJgj8X6X0/5mX1HNtac+ZEi9Gjh/TMM9Jxx5VssXg3BBBAAAEEEAiHAAGgH9uxlBuZt4v6HntM7182Wtf8bxVt2yZVqCCNHStdf72UkuLHglMmBBBAAAEEEAiCAAGgT1vpQKPGGlbjOT12RbSAzZpFb+eWlubTAlMsBBBAAAEEEAiMAAGgD5tq7VqpZ8/sW/t6o8GuM1Dly/uwsBQJAQQQQAABBAInQADowyYbNiz71r6aNEnq2tWHhaRICCCAAAIIIBBYAQJAHzbdU09JkYj0+ONSvXo+LCBFQgABBBBAAIFACxAA+rD5jq+Wqf/3x4XSoi3RBH9t23qpYHxYVIqEAAIIIIAAAgEUIAD0W6PNmCENGiRt3vxLyerWlZ58UurW7ZdtrCGAAAIIIIAAAgUU4E4gBYQrlsMs+OvePTH4szf69tvodnudBQEEEEAAAQQQKKQAAWAhAYvs8MzMaM+fXfyXc4ltu/lmyfZjQQABBBBAAAEECiFAAFgIvCI9dKG75i9+2DfnyS0I3LRJsv1YEEAAAQQQQACBQggQABYCr0gP3eImfORnye9++TkX+yCAAAIIIIBAUgoQAPql2WvXzl9J8rtf/s7GXggggAACCCCQhAIEgH5pdEv1YrN9D3eTX9tuSQFtPxYEEEAAAQQQQKAQAgSAhcAr0kNTU6OpXuykOYPA2PPRo8kHWKTonAwBBBBAAIHkFCAA9FO7W56/V16R6tRJLJX1DNp28gAmuvAMAQQQQAABBAokQCLoArEV40EW5P32t9HZvjbhw675404gxQjOqRFAAAEEEEg+AQJAP7a5DQe3b+/HklEmBBBAAAEEEAiBQKiGgMePH6+GDRuqfPnyatmypUuZl3fOvFdffVVnnHGGypUr5/2cOXNmCJqUKiCAAAIIIIAAAnkLhCYAnD59um52d8oYNmyYVqxY4UZN26pz587auHFjrgJLlizRVVddpd69eys9Pd372aNHDy1dujTX/dmIAAIIIIAAAgiERSAl4pYwVOa8885TixYtNGHChOzqpKWlqWvXrhoxYkT2ttiKBX8ZGRmaNWtWbJMuvfRSVa1aVVOnTs3elteKHV+lShXt3LlTlStXzmtXXkMAAQQQQAABnwjw+1sKRQ/ggQMHtGzZMnXq1Cnho2XPFy9enLAt9sR6AHPuf8kllxx2fztu//79XtBoH5zYI3Y+fiKAAAIIIIAAAkERCEUAuH37dmVmZqpmzZoJ7vZ869atCdtiT2z7kexvx1lPovX4xR71LDEzCwIIIIAAAgggEDCBUASAMfOUWMLknzfY6HbObbF97WfO1/7b/kOHDvWGe23I1x6bNm2KPx3rCCCAAAIIIIBAIARCkQamRo0aSnWpU3L29m3btu2QXr5Yq9SqVeuI9rfjbLawPVgQQAABBBBAAIEgC4SiB7Bs2bJe2pc5c+YktIU9b926dcK22JPzzz9fOfefPXv2YfePHcdPBBBAAAEEEEAg6AKh6AG0Rhg8eLCXyuXss8+WBXcTJ070UsD079/fa6M+ffq4O6zVyZ4RPGjQILVr104jR450N974rV5//XXNnTtXixYtCnqbUn4EEEAAAQQQQCBPgdAEgJbW5fvvv9f999+vLe4Wak2aNNE777yj+vXrewCWD7BUqV86PK1ncNq0abrrrrt0991365RTTpHlErR0MvldYhl0bEYwCwIIIIAAAggEQyD2ezv2ezwYpS7aUoYmD2DRsuTvbJs3bxYzgfNnxV4IIIAAAgj4TcAmc9atW9dvxSqR8hAAFoI5KytL//rXv1SpUqVDZhQX4rTeofbXiQWX9uFMhiTT1Lewnxh/H0/7+rt9Cls62rewgv4+Poztaz1/u3bt0oknnpgwOujvlija0oVmCLhoWfJ3NhtSLu6/HCz4S4YAMCZOfWMS4fxJ+4azXWO1on1jEuH8Gbb2tZy+ybz8clFcMitQdwQQQAABBBBAIIkECACTqLGpKgIIIIAAAgggYAKpw90ChT8FLLl1+/btVbp0cozUU19/fg6LqlS0b1FJ+vM8tK8/26WoSpVs7VtUbn4+D5NA/Nw6lA0BBBBAAAEEECgGAYaAiwGVUyKAAAIIIIAAAn4WIAD0c+tQNgQQQAABBBBAoBgECACLAZVTIoAAAggggAACfhYgAPRz61A2BBBAAAEEEECgGAQIAIsBtbCnHD9+vBo2bKjy5curZcuWWrhwYWFP6cvjR4wYoXPOOce7k8oJJ5ygrl276quvvvJlWYujUFb/lJQU3XzzzcVxel+c89tvv9W1116r6tWr65hjjlHz5s21bNkyX5StOApx8OBB7/7i9u+3QoUKOvnkk737k9tdg8KwfPjhh7rsssu8uyfYZ/e1115LqJbdXcESS9jdFaz+lsXg888/T9gnSE/yqu9PP/2kO+64Q02bNlXFihW9Ovfp08e7O1SQ6hhf1rzqG7+frffr18/7/ho9enTOl3geEAECQJ811PTp072AYNiwYVqxYoXatm2rzp07a+PGjT4raeGLs2DBAg0YMEAfffSR5syZI/vl2alTJ/3444+FP7nPz/DJJ59o4sSJatasmc9LWvDi7dixQxdccIHKlCmjWbNmafXq1Xr88cd13HHHFfykPj9y5MiRevrpp/XUU0/piy++0COPPKJHH31UY8eO9XnJ81c8+7d55plnevXL7Qir76hRo7zX7TNeq1YtXXzxxd4tt3Lb3+/b8qrvnj17tHz5ct19993ezxkzZujrr7/W5Zdf7vdqHbZ8edU3/iAL/JcuXeoFvfHbWQ+YgPuLjcVHAueee26kf//+CSU6/fTTI0OGDEnYFsYn27Zti7h/PhEXGIaxetl1cvefjDRq1Cjigt7Ir371q8igQYOyXwvTiusdibRp0yZMVfqvdfn1r38duf766xP269atW8T1giZsC8MT+7c6c+bM7Kq4Xs6IC/giDz/8cPa2ffv2RdzttiIuKM7eFtSVnPXNrR4ff/yx9x32zTff5PZyoLYdrr6bN2+O1KlTJ/LZZ59F6tevH3niiScCVS8K+4sAPYDuU+6X5cCBA97wmPWCxS/2fPHixfGbQrm+c+dOr17VqlULZf1ilbJeTxcoqGPHjrFNofz5xhtv6Oyzz9aVV14pG+I/66yz9Oyzz4ayrrFKuYBX77//vtcTZNvS09O1aNEidenSJbZLaH+uX79eW7du9XrxY5UsV66c3B85SfH9ZXW27zAbGg9rL7ddytC7d2/dfvvtaty4cayZ+RlQgeS4xURAGmf79u3KzMxUzZo1E0psz+2LNcyL+5tEgwcPlv0CbdKkSWirOm3aNG+4yIbHwr6sW7dOEyZM8Nr1zjvvlOsd0Z/+9CdZUGDXSoVxsWvCLAhwvfayOyfYv+cHH3xQPXv2DGN1E+oU+47K7fvL9Ygl7BvGJ663U26kRtdcc40qV64cxirKLnGwO1PZv2OW4AsQAPqwDe0vyPjFgqOc2+JfD8P6TTfdpE8//dTrLQlDfXKrw6ZNm+SGezV79mxvgk9u+4Rpm/UWWA/gQw895FXLegBtQoAFhWENAO0a3smTJ2vKlCleD8nKlSu9a3ptUkTfvn3D1LyHrUvO76pk+P6yCSFXX3217DNvk/jCuNjkrSeffNL7AzZnG4exvslQJ4aAfdTKNWrU8HoNYn9Jx4rmro07pFcw9loYfg4cOFA2XDh//nzVrVs3DFXKtQ72BWptaTO77a9oe9hEmDFjxnjr1lsUpqV27do644wzEqqUlpYWyglNsUra0Jj1AlkwYLNDbbjslltukc34DvtiEz5sSbbvLwv+evToIRsCt8lsYe39s2wU9v110kknZX9/Wc/urbfeqgYNGnhtz/+CJUAA6KP2Klu2rBcc2JdI/GLPW7duHb8pFOvWM2A9fzZ7bt68eV7qm1BU7DCV6NChg1atWiXrFYo9rIesV69e3nMbMgzTYjOAc6b1sVmS7sLxMFUzoS42M7RUqcSvVWtX6xkK+2KpbywIjP/+suua7Y+cMH5/WXvGgr81a9Zo7ty5XrqjsLaz/TFjozSx7y77aT3b9kfPe++9F9Zqh7peDAH7rHntOjj7h2aBwfnnn++lCrEUMG5msM9KWvji2GQIGyp7/fXXvVyAsZ4DN2vQyyFW+Hfw1xkqVap0yPWNlj/McuSF8bpH6/myX/w2BGw9JHYNoKW+sUdYF8uRZ9f8WS+JXSRvqZwsLYqbGRyKKu/evVtr167Nrov1elkgYBO3rM6W09La281y9x62bvkf7bq4IC551deCn+7du3tDom+99ZZ3vWfsO8w87A/6oC151dfa176r4hdL8WRB/2mnnRa/mfWgCLheGBafCYwbN86bXu++QCItWrQIbVoU92/ES5mQ8+dzzz3nsxYpvuKEOQ2Mqb355psRF9xG3MSPiKUzcsFf8WH64MwZGRleWh/3yzLiErlHXCLoiMvpGdm/f78PSlf4IrjLNHL9N+uub/RO7no6I/fee6+XDsbavF27dhHX6134Nz5KZ8irvi74zdXCvs/suCAuedU3t/qQBiY3leBsS7GiBiVYpZwIIIAAAggggAAChRdIvFil8OfjDAgggAACCCCAAAI+FyAA9HkDUTwEEEAAAQQQQKBqzr5lAAADEElEQVSoBQgAi1qU8yGAAAIIIIAAAj4XIAD0eQNRPAQQQAABBBBAoKgFCACLWpTzIYAAAggggAACPhcgAPR5A1E8BBBAAAEEEECgqAUIAItalPMhgAACCCCAAAI+FyAA9HkDUTwEEEAAAQQQQKCoBQgAi1qU8yGAQGAFMjMzvdvXXXHFFQl12Llzp+rVq6e77rorYTtPEEAAgaAKcCeQoLYc5UYAgWIRWLNmjZo3b+7ds7hXr17ee/Tp00fp6en65JNPAnmP12KB4qQIIBBoAQLAQDcfhUcAgeIQGDNmjIYPH67PPvvMC/quvPJKffzxx15gWBzvxzkRQACBkhYgACxpcd4PAQR8L2C3SL/ooouUmpqqVatWaeDAgQz/+r7VKCACCByJAAHgkWixLwIIJI3Al19+qbS0NDVt2lTLly9X6dKlk6buVBQBBMIvwCSQ8LcxNUQAgQIITJo0Scccc4zWr1+vzZs3F+AMHIIAAgj4V4AeQP+2DSVDAIGjJLBkyRK1a9dOs2bN0iOPPCKbHTx37lylpKQcpRLxtggggEDRCtADWLSenA0BBAIusHfvXvXt21f9+vVTx44d9Ze//MWbCPLMM88EvGYUHwEEEPhFgADwFwvWEEAAAQ0ZMkRZWVkaOXKkp3HSSSfp8ccf1+23364NGzYghAACCIRCgCHgUDQjlUAAgaIQWLBggTp06KAPPvhAbdq0STjlJZdcooMHDzIUnKDCEwQQCKoAAWBQW45yI4AAAggggAACBRRgCLiAcByGAAIIIIAAAggEVYAAMKgtR7kRQAABBBBAAIECChAAFhCOwxBAAAEEEEAAgaAKEAAGteUoNwIIIIAAAgggUEABAsACwnEYAggggAACCCAQVAECwKC2HOVGAAEEEEAAAQQKKEAAWEA4DkMAAQQQQAABBIIqQAAY1Jaj3AgggAACCCCAQAEFCAALCMdhCCCAAAIIIIBAUAUIAIPacpQbAQQQQAABBBAooAABYAHhOAwBBBBAAAEEEAiqAAFgUFuOciOAAAIIIIAAAgUU+P96DowtrhUTcgAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# graficamos los datos observados con la recta real\n",
    "fig = PL.figure(2)\n",
    "s1 = PL.subplot(1,1,1)\n",
    "s1.plot(x, y_obs, 'or', label ='Observaciones') # datos sintéticos con ruido simulando observaciones\n",
    "s1.plot(x, y_true, '-b', label = 'Recta Sintética') # recta sintética (\"verdadera\")\n",
    "s1.plot(x, y_pred, '--r', label = 'Recta Estimada') # predicción de la recta estimada por mínimos cuadrados.\n",
    "s1.set_xlabel('X')\n",
    "s1.set_ylabel('Y')\n",
    "PL.legend(loc='best')\n",
    "PL.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' ****** ASPECTOS ESTADISTICOS DE MINIMOS CUADRADOS ****** '"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\" ****** ASPECTOS ESTADISTICOS DE MINIMOS CUADRADOS ****** \"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Aspectos estadísticos de Mínimos Cuadrados \n",
    "# Que pasa si uno de los datos es anómalo (outlier)?\n",
    "# agregar un dato anomalo (outlier)\n",
    "Ioutlier = [int(NP.ceil(len(y_obs) * 0.7))] # introducimos el dato anomalo\n",
    "d_con_anomalia = y_obs.copy() # comando copy es necesario para duplicar el array\n",
    "\n",
    "d_con_anomalia[Ioutlier] =  d_con_anomalia[Ioutlier] - 20\n",
    "#d_con_anomalia[4] =  d_con_anomalia[4] - 20\n",
    "\n",
    "\n",
    "# solucion por minimos cuadrados\n",
    "m_est_anomalia = minCuadSimple(G,d_con_anomalia)\n",
    "y_pred_d_anomalo = G.dot(m_est_anomalia)\n",
    "\n",
    "fig = PL.figure(3)\n",
    "s1 = PL.subplot(1,1,1)\n",
    "s1.plot(x, d_con_anomalia, 'or')\n",
    "s1.plot(x, y_true, '-b')\n",
    "s1.plot(x, y_pred_d_anomalo, 'g')\n",
    "s1.set_xlabel('X')\n",
    "s1.set_ylabel('Y')\n",
    "PL.legend(['obs', 'Recta Verdadera (True)', 'Ajuste Min Cuad Simple'], loc = 'upper left')\n",
    "PL.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}