Example 5.3.4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.4 Poisson distribution and Charlier Chaos\n",
    "\n",
    "$$ f(k;\\lambda) = e^{-\\lambda} \\frac{\\lambda^k}{k!}$$\n",
    "\n",
    "When $\\lambda=1$, $k\\sim poisson(1)$; when $\\lambda=2$, $k\\sim poisson(2)$;\n",
    "\n",
    "$$ \\zeta \\sim Poisson(\\lambda)$$\n",
    "\n",
    "[Wiki - Charlier Polynomial](https://en.wikipedia.org/wiki/Charlier_polynomials)\n",
    "\n",
    "<font color = red> ** By the following formula:**</font>\n",
    "$$ C_n(x;a) =\\ _2F_0(-n,-x;;-\\frac{1}{a})$$ \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "C_0(x,a) &= 1\\\\\n",
    "C_1(x,a) &= 1-\\frac{x}{a}\\\\\n",
    "C_2(x,a) &= 1-\\frac{2x}{a}+\\frac{x^2-x}{a^2}\\\\\n",
    "C_3(x,a) &= 1-\\frac{3x}{a}+\\frac{3(x^2-x)}{a^2}+\\frac{-x^3+3x^2-2x}{a^3}\\\\\n",
    "C_4(x,a) &= 1-\\frac{4x}{a}+\\frac{6(x^2-x)}{a^2}+\\frac{4(-x^3+3x^2-2x)}{a^3}+\\frac{x^4-6x^3+11x^2-6x}{a^4}\\\\\n",
    "\\cdots\n",
    "\\end{align*}\n",
    "$$\n",
    "<font color = red> **If by formula from Wiki with [Laguerre](https://en.wikipedia.org/wiki/Laguerre_polynomials)**</font>\n",
    "\n",
    "$$C_n(x;a) = (-1)^n n! L_n^{(-1-x)}(-\\frac{1}{a})$$\n",
    "\n",
    "$*$<font color = blue> ** Need to swith the sign in odd terms** </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Laguerre Polynomial\n",
    "$$ L_n^{\\alpha}(x) = \\frac{(\\alpha+1)_n}{n!}\\  _1F_1(-n;\\alpha+1;x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "C_0(x,a) &= L_0^{(-1-x)} (-\\frac{1}{a})=\\ _1F_1(0;-x;-\\frac{1}{a})=1 \\\\\n",
    "C_1(x,a) &= (-1) L_1^{(-1-x)} (-\\frac{1}{a}) =(-1)\\frac{(-x)_1}{1!}\\ _1F_1(-1;-x;-\\frac{1}{a})= x-\\frac{1}{a}\\\\\n",
    "C_2(x,a) &= (-1)^2 2! L_2^{(-1-x)} (-\\frac{1}{a}) =2 \\frac{(-x)_2}{2!}\\ _1F_1(-2;-x;-\\frac{1}{a})= x^2 -x-\\frac{2}{a}x +\\frac{2}{a}+\\frac{1}{a^2}\\\\\n",
    "\\cdots\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red> $**$ When $\\lambda=a=1$, switching the sign seems enough if we look at the first two polynomials in both definitions, but when $\\lambda=2$, swithing the sign will not be enough since $1-\\frac{x}{2} \\neq -(x-\\frac{1}{2})$, besides $1-\\frac{2x}{a}+\\frac{x^2-x}{a^2} \\neq -(x^2 -x-\\frac{2}{a}x +\\frac{2}{a}+\\frac{1}{a^2})$ even when $\\lambda=1$.\n",
    "\n",
    "If the author uses the polynomial chaos as the second one, then I will not get the second error plot correctly.\n",
    "\n",
    "So I think when the author was solving the differential equation system, he used the first definiton. But when he made the first plot, he switched the sign on purpose (for some unknown reasons), and when he made the error plot, he still used the first definition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Bell Polynomial](http://mathworld.wolfram.com/BellPolynomial.html)\n",
    "\n",
    "The $k$-th moment terms of $Poisson(\\lambda)$ form Bell polynomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `mpmath.hyp2f0(a, b, z)` - For Charlier polynomial\n",
    "\n",
    "Gives the hypergeometric function $_2F_0$, defined formally by the series\n",
    "$$\n",
    "_2F_0(a,b;;z)=\\sum_{n=0}^{\\infty} (a)_n (b)_n \\frac{z^n}{n!}\n",
    "$$\n",
    "This series usually does not converge. For small enough $z$, it can be viewed as an asymptotic series that may be summed directly with an appropriate truncation. When this is not the case, `hyp2f0()` gives a regularized sum, or equivalently, it uses a representation in terms of the hypergeometric $U$ function [1]. The series also converges when either $a$ or $b$ is a nonpositive integer, as it then terminates into a polynomial after $−a$ or $−b$ terms.\n",
    "\n",
    "P641\n",
    "$$\n",
    "C_n(x; a) = _2F_0(-n, -x; ; -\\frac{1}{a})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mpmath as mp\n",
    "mp.hyp2f0(-1,-0.5,-1)  #mp.hyp2f0(-1,-1,-1) gives me error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Char((1,1))(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from math import factorial\n",
    "from scipy.stats import poisson\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Char(params):\n",
    "    '''\n",
    "    The first 4 (degree from 0 to 4) Charlier polynomial\n",
    "    Follow definition on P641\n",
    "    '''\n",
    "    n = params[0]  #degree\n",
    "    a = params[1]  #parameter value\n",
    "    if n==0:\n",
    "        return lambda u: 1\n",
    "    elif n==1:\n",
    "        return lambda u: 1-u/a\n",
    "    elif n==2:\n",
    "        return lambda u: 1-2*u/a+2*(u**2-u)/(2*a**2)\n",
    "    elif n==3:\n",
    "        return lambda u: 1-3*u/a+3*(u**2-u)/(a**2)+(-u**3+3*u**2-2*u)/(a**3)\n",
    "    else: #this actually means n=4\n",
    "        return lambda u: 1-4*u/a+6*(u**2-u)/(a**2)+4*(-u**3+3*u**2-2*u)/(a**3)+(u**4-6*u**3+11*u**2-6*u)/(a**4)\n",
    "    \n",
    "############# Charlier Chaos ###############\n",
    "def inner2_ch(n,a):\n",
    "    '''\n",
    "    n is the degree of charlier polynomial\n",
    "    a is the parameter of Poisson\n",
    "    '''\n",
    "    return (a**(-n))*factorial(n)\n",
    "\n",
    "def product3_ch(i,j,l,a):\n",
    "    #compute \\Phi_i*\\Phi_j*\\Phi_l\n",
    "    '''\n",
    "    a is the parameter of Poisson\n",
    "    '''\n",
    "    return lambda x: Char((i,a))(x)*Char((j,a))(x)*Char((l,a))(x)\n",
    "\n",
    "def inner3_ch(i,j,l,a):\n",
    "    #compute <\\Phi_i\\Phi_j\\Phi_l>\n",
    "    inner = 0 \n",
    "    for k in range(11):\n",
    "        inner += np.e**(-a)*a**k*product3_ch(i,j,l,a)(k)/factorial(k)\n",
    "    \n",
    "    return inner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_system_ch(y, t, P, a):   \n",
    "    #P indicates the highest degree\n",
    "    #a indicates value of lambda\n",
    "    dydt = np.zeros(P+1) \n",
    "    for l in range(len(dydt)):\n",
    "        dydt[l] = -(sum(sum(inner3_ch(i,j,l,a)*ki_ch[i]*y[j] for j in range(P+1)) for i in range(P+1)))/inner2_ch(l,a)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = 4\n",
    "a = 1\n",
    "\n",
    "ki_ch = [a,-1*a]+[0]*(P-1)\n",
    "sol_ch = odeint(ode_system_ch, [1.0]+[0.0]*P, np.linspace(0,1,101), args=(P, a)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def y_determ_ch(x):\n",
    "    return np.e**(-x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color = red> Need to put $(-1)^i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
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       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
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       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
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       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
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       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
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       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
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       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\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",
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       "        stop: function(event, ui) {\n",
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       "            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",
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       "\n",
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       "\n",
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       "        var fmt = mpl.extensions[ind];\n",
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       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
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       "\n",
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       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
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       "    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 overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    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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voPldhWCz9dMkN88Xyo3vTZHjtcdRs5UMbhzD2ySwkACJEACaUAA3bPw0LVkwD0YSCCBBNhv5w928m4F5++5YtdeqVvL3XWXyH33iWyxs4O3dO8lj+x9gtw3cKKU5+tSMxr22KmjnDGunxy5W08pzNOBhQwkQAIkkEIEYm0hlgyP0L9/f3nllVd0AYeRydCcpG5DrPfIreB0yGlSv7nkb1zmCUD3TjZtErn/fpE77xRZs8akVnXoJG9OPFGu3+lAWVdoPYAlbfLkxDF95Iy9+srgbu1dbR5JgARIIKkJxBIOrdnoK6+8Ul588UVZpRP0unTpIu10t6fvsK4rQ0wCsd4jBSAFYMyPJs6MzBWADlB5ucijj4rcdpvIggUmdYfuPPL1oSfIDUMPl2nZHVxJ2bN/RzltT3oFg0AYIQESSFoCsYRD0jaYDYtKINZ7pAAU4YJuUT8ZJsZNoE0bkcsuE5k7V+Tpp0XGjJEsHS+4+4tPyDNF8+Xh8/eUQ4d3l5zsLJm6eKNc/Z8Zsuef3pbfvfgN9x+OGzILkgAJkAAJkEDzEmAXsD+e9ABG8sN6We+8Y8cJPvywaD+FKbHh7fflo+mL5NbafrJsU0Ww1m59SuSUsX3lmFG9pLhQdyhhIAESIIEkIBDLc5QETWMTGkEg1nukB5BdwI34jKIWpQCMiiVK4gEHiHz4odTecot8ctx58u/Pl8pbs1ZJVY0KRg2FedlyxMieZoHpcQM6cV3BKAiZRAIkkDgCsYRD4lrAOzUHgVjvkQKQW8E1x/fFazREoKpKZPRokZkzJfuMM2S/3l1lvyFdZeO3c+WlpRXyxKxNMn9NmTynW9DB+ncukpP26CMnqvUs0S5mBhIgARIgARIggWYlwC5gfzjpAWwMvwrt+i20y8SYaocfLjJ5suy46CL55uTz5IllO+SVr1fI1soak63DBmWCCsVTxvbRPYi7czmZxrBmWRIgAV8EYnmOfF2UlRNOINZ7pAeQXcB+P0YKwKYSLCsT2WsvkVmz7BVydU3yU06R8h/9WF7N6yXPTFsqny/aELx6cWGuHL17L+MZHNWXW88FwTBCAiTQIgRiCYcWuRkv2mIEYr1HCkAKQL8fHQWgH4K1tSKvvy7yl7+IvPde6EoHHijys5/J4nEHyLNfrpD/Tl8mKzeHJo4M7NrWrC2IXUd6dWAXcQgcYyRAAs1FIJZwaK7r8zqJIRDrPVIAUgD6/QIpAP0SdPWnT7drCT7zjEiN7QKWYcNEfvpTqTnzLJm8stwIwde/WSkVVSocNWRpF/E+gzrLCaP7yOEje3AfYseSRxIgAd8EYgkH3xf2cQG06bTTTtOOk1lSpOut9ujRQx544AHBziAM0QnEeo8UgBSA0b+Y+FMpAONnFV/JpUtF7r5b5G9/E9m82dbp3Fnk8stFrrhCtnTsIq/NXKlicHlYF3FRfo4cPqKHHD+mt4rCLmbdwfhuyFIkQAIkUJdALOFQt2TiUtCmd999VyZNmmRWSrjnnnvkpZdekrfeeitxjUixO8V6jxSAFIB+P2UKQL8EY9XHPsMPPWS3mlu82JbSGcTy5JPBGks3bJPnMXNYu4gXr98WTO/WvkCO0fGCx2kX8YhexVxSJkiGERIggXgJeIVDQUGBlFfrrkctGNrktmn076pp06YZjyC3g4v9YrzvsdAzCZECkAIw9lcTXw4FYHycml6qulp080uR228XueMOkXHj7LWw7dy334oceaTsyM6W6Us2yQsqBl/WWcSbtumyM4EwpFs7IwQhCPt2KnLJPJIACZBAvQS8wqE2p1b2ekonrbVgmHLGFCnKa9zvqHPOOUc6aw/JHfjdyBCVgPc9UgCGI9JRVAw+CFAA+oDnqyq6hHXsi1xyiciDDwYvVVldKx/MW2vE4P9mrxacu7DHTh3lWN1x5Mhde0rndgUumUcSIAESqEPAKxySUQDeeOON8vLLL+vGS++Y8YB1HoAJhoD3PVIAhn8UuvYGAwmkIAEd/CwdO4qcfnqo8atWSb7uQ3zo8IFm/+HN5VXy5jer5MUZy+XTBevli+83Gvv9y7Nk38FdTDfxD0Z0l/aF3IIuBJExEiCBSALonoWHriUD7hFvuO222+S5556Tt99+m+IvXmgsV4cAPYB1kDQqgR7ARuFq5sJbt4r+9rPTgXHpq6+23cTHHCPy4x+LTJwYzFtdWiEvz1ghL361QmYuD0wu0Sr5udly0LBuZi/ig3buxsWmwZGBBEhAYnmOWhvN7Toc5kkdCw3x1xF/BDPUSyDWe+QYwPQbA3iFfgm/UOuppgPE5CdqH6nFCsjXvkTpp7ZO7Vm1a9RCi87pST2BArAeOAnPOvVUESwj48Juu4lcdZUIJo+0Cf11vXBtmYrBlfKSegYXrFURGQhtdSbxIcO7y1G79ZL9h3aRgtwcl8UjCZBAhhGIJRxaE8OyZcukb9++MnDgQGnfvr1pCiaoTJnSst7J1nxmv/eO9R4pANNLAOp//eVxNYjAT9QuVbtIbbjaErXIcKYm/FPtArVP1YaqPaL2tNpP1eIJFIDxUEpkmdmzRf76V5HHHhPR7mATsIzMxRebZWT0t2ewNTt27JBZK0tVCK6QV1QQLt9UHsxrrzuP/ECXlTlyt56yry4rA08hAwmQQOYQiCUcModAejxprPdIAZheAhB/Ak1Xu9zz2aoakBfU4NWLDPdowi5qB3sydEsKwTTT/Txp9UUpAOuj05p5GzeK/OMfIvfeK/L997YlOerRO/546xWcMCHYPYxMiMGvlm4ynsFXZ66Q1aXbg60vaZOnYrC7HKGTRzB2MC+HYjAIhxESSFMCsYRDmj5u2j5WrPdIAZg+AjBfv164e05We97zJd+l8VFqB3jSXPQ0jeg0UjlM7XO1gWqvqj2qdrNatICpo97po/DBL9usCxYXF0MLMiQdAewqojPljFfQu93c7ruL/OhHIuedJwJh6Am1tTtk6uIN8qouOP26TiJZuyVcDB6m3cRH0DPoIcYoCaQfgVjCIf2eNL2fKNZ7pABMHwHYSz/h5Wr7qqE714VrNXKu2jCXEHFUBSDw+mEyDGZE36+GLuRY4XrNuC4ykwIwkkiSns+caXcZeeIJkXLt7sUYwa++CvMERra8xonBryEGV8q6sspgEXQTHwoxOLKnTBjShRNIgmQYIYHUJxBLOKT+k2XWE8R6jxSA6ScA99FPe7Ln8/6Nxs9W29mT5qITNfJvtd+qoft4sBo8hn9Xu0EtWqAHMBqVVEvbsMHuMtK/v8hJJ9nWY+eRi3TIKOyQQ6KKQojBzxdtMEIw0jOICSQH7dLdbEc3cVhX7kucat8E20sCEQRiCYeIYjxNcgKx3iMFYPoIwKZ0AX+k3+1nar/wfL9nafxvau3UQisIewpERDkGMAJIyp5irOAPf6i+YnUW60broruL1BcgBrGuIPYlfkO7iVfpMjMuFOiEkQOGdjWTSA7epZt0KMLnyUACJJBKBGIJh1R6BrZVl/TQ/ZMXLVokAwYMEC4EHf5F5IafpuwZ+uW+UDtUzTsGEOcvqkULRZoYKfJ0wJjpDkaXMEMmEThMh4JiTCDGBjrxh27ia3T+0IUXiuy6axiNnOwsGTegk7HfHTVcZizbZIQgPINLdI/it2atNoZy4wd2NpNIDtNZxd2LC8OuwxMSIAESIAESaA0C6SR0TlWAj6tdpoZu4EvUdO0PGaH2vdpjahgn6GYEX6/xn6mhnOsCxhhACElcK55AD2A8lFK1zMMP6yJBF9jW76cTw6+80s4izo/t0XNLy7z5rQrAb1fJnFXatewJu/ftYMXg8B4yWPcpZiABEkhOArE8R63d2sP0j9VVuutRtv6hirUA7777bhk1CnMdGaIRiPUe2QWcPl3A7r1jAscv1XqqfaP2U7UP1RDeV1usdp4aAryfboxgb42vVdPpoiZtkx7jCRSA8VBK1TJTp4rceqvonksimE2M0L27XVMQexB71hS0mXV/Ll63Vd5UIfiG2pdLwj+rgV3bmkkkh+rYwdH9Ogq8hQwkQALJQSCWcGjt1m3atEk6dOhgmvHCCy/IH/7wB5k+fXprNytp7x/rPVIApp8ATPRHSAGYaOKtcb8VK3RqkM4NevBBkZUrbQvQTXz00brqpC47eaiONHDdxvW0b42OE3x79hrtGl4ln363XiprQiMQOrfNF4wXPETF4H5DukobnVTCQAIk0HoEvMIBu23swJCQFgxZultRVlbj/gh89NFHjQdw2rRpLdiy1L609z1yDGD4u2zc1xZel2ciFICZ9BVUVemIUh1Set99It41BQcN0n1nLhU5/3yRLl3iIrKlokren7tWBeFqeW/OGimtqA7WwyQSLDgNMQhRyHGDQTSMkEDCCHiFQ35trcwds0eL3nvY9C8kG3ubxxHOOecc/RX0nin5xhtvyIgRI+KolZlFvO+RAjD8G6AADOfR2DMKwMYSS5fy2HLuAV1H/JFHREpL7VNhbODrr4scdFCjnrJKPYFTdXkZTByBIFy2MdzTsGvvEiMED965u4zoVazORv6zbRRgFiaBJhDwCodkE4DuceABfPrpp+W1115zSTxGEPC+RwrAcDj8L0k4j8aeUQA2lli6ld+6VVeT1OUk779fZP58nWak84zaBSZ3YOHpfv1ESkrifmpMIpm7eou8o13FEIPYnk6TgqFb+wI5cFg3XXOwm0xQL2HbgnSZyB98REZIICkIeIVDsnYBA1Qb7TpetmyZdMae5wx1CHjfIwVgOB4KwHAejT2jAGwssXQur7+EpU8f+4RQbdhpZOFCkZde0h2nD27Sk2MbOnQRvzNntXw0f51sqwxMRtGr5euexHsN7CQTIQh37iYDurRt0j1YiQRIoC6BWMKhbsnEpWDiQllZmfTq1cvc9Pnnn9fVq34kS5cubfT4wcS1unXvFOs9chKInQnbum+HdyeBdCHgxB+eZ906Ma47CME9PGOH5swR6a2TznX5hnhCV/X4nbJnX2Pbq2tkysIN8m5AEC7dUG5EIYThDa/Mkv6di4wYPFDF4F66RmFhHieSxMOYZUggVQhg29ETTzxRd7IsN8vAdO3aVV555RWKv1R5gUnWTnoA/b0QegD98Uvv2hB/CxboJoODQ885bpzdaeSMM3QFSl1KZuzYUF4jYugqXrB2q/EOvjd3jdmirlp3J3GhMC9b9hnURQVhV5k4tJv0U3HIQAIkED+BWJ6j+K/AkslAINZ7pAeQy8D4/T4pAP0SzKT6GzeKjB8vMndu6KlHj7ZCEIKwGJ9T0wJmFX/y3TozsxiCcHXp9rALoXsY29PB9tadSbjMTBgenpBAHQKxhEOdgkxIagKx3iMFIAWg3w+XAtAvwUyrD6/gh7o2+d/+JvLssyKVlZYAln847TS7yPRee+m/zKY75+EdxA4kWGYGYnC67lns9Q7m6zIz4/p3kv2HdlHrKsO6t2cXUqZ9h3zeBgnEEg4NVmSBpCIQ6z1SAFIA+v1QKQD9Eszk+hgn+PjjdpFpLCvjwsiRVgiedZZIp04utclHeAc/XbBePpi3Vj5QUbh8U/gyM5hZjMWnIQgxs7hzu4Im34sVSSBdCMQSDunyfJnyHLHeIwUgBaDffwMUgH4Jsr6dLPLJJ1YIPvOMSEWFpaK7D8hFF4ncc0+zUbJjB8tUDK6TD1UQTlm0XiqqQjuS4EZYa3DCEPUOqijcY6eOnEzSbPR5oVQiEEs4pNIzsK34dVohixYtkgEDBgiXgQn/IriIWDgPnpFA4gmgu3fCBGt33SXy5JNWDM6YEb7FHLqPdRN46dmzyW3EVlODu7U3duGEASr+amTa4o3y4fy1Zkbx7JWl8u0Kaw9+sFCwK8k4nVEMzyBE4S49uBB1k+GzIgmQAAkkEYGmDzRKoodoxabQA9iK8NP61hB72OAdXcD6l6sJGDt44IEip54q8tRTLfL4WHcQk0kgCD/W5WXW6Lk3YM/i8YM6m63qIAr7duLsYi8fxtOHQCzPUfo8YWY8Saz3yC5grgOYGf8C+JSpRwBeQe/6gXgCCEDdk1TaehZ8hlCMXGrGx9Ni3cHjRvc2hu7i+WvKjBD8WEXhZwvXy/qtlfLK1yuN4TZ9O7WRfXW5mX1UDI7X2cWoz0ACJEACJJD8BOgB9PeO6AH0x4+1G0sAC0ljz+GBA23Nzz8XwazhffYRufBCkVNOCW1F19hrN1C+srrWbE0HD+GnC9bJl0s2hc0uRnXMKIaHcB+1vQZ0lpKivAauymwSSE4CsTxHydLa3//+93L99dfLTN1yciQmjjFEJRDrPdIDSA9g1A+GiSSQtAR23jm8aVOniuTojh+ffmrtqqusCDz/fDum0MdyMuE3Ut0ZGA+IMYE/PXSolG2vlqmLNgi8g5N1lvEsHT+IfYxhj3y62Kxkgwkl8AxiUeo9tV477l0ciZXnJNBoAtN1eMhnn32mW43rXuMMJNBEAvQANhFcoBo9gP74sXZzEFi5UuSxx0T++U+R+fNDV8QOJBCC55wT2qM4lNvssQ3aPYxuYngHP/1uvSxctzXsHjnZWTKyd4kuRN3JLEa9p65FSEEYhognSUTA6zkq0Bn51ZXhs+Wbu6m5+dlxrce5fft2mThxog4DfkqHBB9otoKjBzD22/C+R84CDudEARjOo7FnFICNJcbyLUcA4wHhCXzoIREsJ6ObxpsAL+Chh1oxeOyxIm3atFwbPFdeXVphPIPwDk5WYbhkwzZPrjounSBUz+BeKgrHqiAsLmSXcRgknrQaAa9wyMnKk7/9+IMWbcsldx0geQUN79/9q1/9ynj+rrzySunfvz8FYANvxfseKQDDYXEZmHAePCOB1CUAobfvvtawnAx2Gnn4YTt55K23RGAlJTbt+ONb/Dm7FxcGJ5TgZliAeooKQXgJP1u4wQjCGUs3CezBDxeK6kEZrl3GGDu4l4pCeAg76qxjBhIgAUtg8uTJMlWHfdx8881EQgK+CeivXAYfBOgB9AGPVRNEALOEH33U2pIlIth1xI0lRJcxtqHr3TtBjQndxgnCKSoGsSD14vXhHkKUxKQSjDnE+EFsX9ejpDB0AcZIoAUJeD1HydIFDOH317/+VeeB2T+Mli1bJt27d5d//OMfMmnSpBakkbqX9r5HegDD3yMFYDiPxp5RADaWGMu3HgEsIYNJI5g17AJmDcNTiN1GrrjCpbbKcdXmCiMEp+jEEkwuwRI0kQHLzsAzCDEIUTiwS9u4xk1FXofnJNAQgVjCoaF6icxnF3DDtGO9R84C5izghr8eliCBdCGQnR0u/iAIN22yW9GNHx96ym+/FVm/3s4iRp0EBXj3jh3V2xhuub5su0zVXUrgHZy6eIPMWlEqSzeUqy2X56YvN63qpF3EY3W7OojCsf076jZ2JWa2coKazNuQAAmQQMoSoAfQ36ujB9AfP9ZOBgLffy86qlx3Bg/8OjjvPNtdjB1Izj7bGmYUt3LYUlEl03XtQXgHP1dB+JWOHcTahN5QmJctu/XpoIKwowrDTjKmX0euRegFxHjcBGJ5juK+AAsmBYFY75EeQP2VnxRvKHUbQQGYuu+OLY9F4Cc/sTOJt2wJlYCHEGIQ29Bhe7okCNura+Sb5aW6l7F2GauncNr3G2TTtqo6LRvavZ3soV5CiEEcB7DbuA4jJtQlEEs41C3JlGQmEOs9UgBSAPr9bikA/RJk/eQksE0nZLz4osjjj4u8+abdgg4txeDzI4+0YvCII0R0fbRkCbW1O3TtwTIVhBCDG+ULtUURaxGireg2HtOvg4xWQQhRuHvfEinK54IIyfIek6UdsYRDsrSP7YiPQKz3SAFIARjfFxS7FAVgbDbMSRcCWGj6X/+yYvCrr0JP1bGj3XUEnkFsRee6kEMlWj22TscRTocYXLLRHGcs21yn2xjrEe7co70Rg2N2UmHYt6Ps1LmIk0ta/e21bgNiCYfWbRXv3lgCsd4jBSAFYGO/pcjyFICRRHie3gR031F54gmRJ5/Uhf3sRAzzwFhepm/fpH92jBn8ZsVmIwaxl/F0FYYrdfZxZOioexjDQzi6bwcZpd5CjCssacNFqiM5pfN5LOGQzs+cjs8W6z1SAFIA+v3eKQD9EmT91CRQUyPy/vvWK7hhg8hLL4We42c/s5NKsAVdkowXDDWubmzl5nIVhJvkSxWDX+rEkpnL63oJUWtQ17ZGFI6CKFQbpl7DvJzEzZKu23KmtCSBWMKhJe/Jazc/gVjvkQKQAtDv10YB6Jcg66c+AWxB57p/V68W6dXLjhmcN09kyBD7fN4ySf7EmFwye+UW4yXETGNY5DZ2eISC3GyztzHE4O4QheolxDqFWY5Fkj8nm1c/gVjCof5azE02ArHeIwUg1wFMtm+V7SGB1CPgFTzYZ1h3KhCMFXTiD0901lkiVTpD98wzRQ4/PKkmj0QCL8jNMR4+CDsXMJYQW9ah23jGMisKt1RUm4kmmGziArqO0V0MQbh7nxLZVa1be+5e4vjw6I9A//79BbtZYGeSbTpRa/jw4YK9gffBGNx6wgsvvKB/l/WScePG1VOqebJGjRol2LKuTQN7jl900UVy7rnnyn777RfzxnfeeaecccYZ0q1bN1PmgQcekPLycvnpT38asw4z4ifAZWDiZxWtJD2A0agwjQS8BDZvFv0NLlJZaVM7qLA66STR3+wi++8vkpPjLZ0Sccw4XrR+qxGF8BBicslsXai6siZ8XUI8TE9d4Ho3FYIQhjju2rtEOhRxj+Nkf9GxPEet2W4IwFdeeUVGjhxpmvGiztSHiHpTZ+rv5d3hJ6KR5+nanmPHjpUf/vCHETkNn9bocI+cVvo3Gvm8Dbe2bolY75EeQHYB1/1aGpdCAdg4XiydiQTQ/fvll3biyL//LbJiRYgCuouxtuDpp4v+FyrUlRwqkTIxdB3P0a7jr42HcLM5fre2TPD4kaFfpyLjHdxNxSAE4Qg1TjKJpNS651GFw9atjW8UlkrKDSwzVF0tsn27CHbYacBDFu1G0QTRtddeK/N1T++nnnpK/u///k/effdd/VurUrf73lngMfv000/VAX+WbvldJF26dDEiEN63x3WJp3t0C8gq9cy3b99e7r33XiMsH3nkEfm3/juF123WrFly9913yzXXXCN77rmnTJkyRRYtWiRXXXWVzvnqa/YlXq6Twf785z/LaaedZpqMIRBbdA3Rdu3aCdp7/vnnG4G6UlcTuPDCC+W3v/2tKTdx4kT5+c9/LkcddZTZy/j22283exxDcGJvY4jaP/7xjzJw4EDj9US74MksKyuT2267zVwD931CJ6VlK094HPHseE5viPoetQAFILuAvd8J4yRAAi1BQP+DIGPGWLvlFpGPPhL9r5XIf/5jxeAdd4jAsNsI/iMCMahdW6kW0HVsun61+/fs8bb1Zdur5VudVPK1egjRdYwJJt+v32bGFGJc4atf6xI7gYClZ0YGBCFE4Ujd1q5Eu5QZkoiAippGh2eeETn5ZFvt+eft0kkHHGAnUTX6YnUrQJhBGN16661GdH3++eem0A033CDXXXed3HXXXXLMMceEeQA/+eQTI/I+/PBD0538kf6bPFOHZ8yYMcPU/fjjj/Vvti91FEdgDK+mLtGZ/u/rxK9Vq1bJoEGD5OqrrzbiEvc77rjjggIwsoWbdLtJiNC1a9fqP/HBRhD27t07rBiuNXv2bNNNDUG6XUUyPJoPPfSQblX+bNDjied04dFHHzXPjWcpLi6WjRs3mmdx+Tw2TICrnzbMiCVIgASaiwC6kvQvf2PqWTCLTGONQcwi/u470T/5rcEb+NlnKdk97EXVriBX9hrY2ZhL36y7lWApGojCmcutKMQexxCGMK8oxKQSCEEIwxG9is2xSzv1KDGQQIDAjoCLGeIIXi0IJgR4ASHUogV0HUPsebuNIdBQB2HChAlh4g9pJ6uIhacNYwnhSYToQ9hjjz0E3j142jA+MTJAWCJ07drVePPgQYwUgAcddJCco6sGHH300TJp0iQZOnRo5GXqnKMr/PLLLzfiD5kdsS4pQ6MIUAA2ChcLkwAJNBsBdI2pZ8KYduvIyy9bzyB2HunRI1z8Yd1BCMcIz0GztSWBF4JXb9/BXYy5227cWmlEITyE3xgrNV5CCEPY69+sckWlR3GhEYPoNoYoHN6zWPp05OzjIKCWjOA7bWzw7pZz/PGifZi2C7ix14lRfurUqcZDBmF13333CcRUQwGi8YILLpA//OEPUYui+zYyeMUdxgS6czc+sBrd21GCK4cslI1W7rnnnpMvvvjCeBiP0B2G0PXrupSjXJJJzUSAArCZQPIyJEACPgjgPzjo+oVhXUGYC/ofNjOLGOOosMxMCqwt6Joe77Gjbk+335CuxlwdeAq/VU8hvIUzdc9jxLG13arSCmPvzFnjikpxYa4MVzE4Qr2FRhRqfFDXdlynMEiomSJt2/q7EL5hNx7Q35VMbXjy7r//fnnjjTfkf//7n2Ac3d57723GwWGWMEThiBEjjJdsMyZjBQI8bfC4XXzxxWYsX21trUyfPt10E7syiTpCEC5evNjcGxNV1q1bJ+hWhgBE16633d42oVsbgheeSJRDVzPGMjpB6i3LeHQCFIDRuTCVBEigtQhA4HlFHsSgdkmZfYe96br8hRk3CK+KdkmlW4CncB/1FMJc2KpjCmevhBgsNZ5CHOev2SKluiTNZws3GHNl83WR6qE92skuPdRLqIJwF/UUwjjZxBFKzeNJOoMey8Bs1QkpWAbmtddeM6IPXbG///3vTbeuW4sSS8RAAJ6t2zWepzOB/6PjbjETGJNAbrzxRjn22GMFky4w7u5I3eMbAizRAffHRBGM4ctVcYyu4ocfftg0A5NNkIeJHZgE4g14phU6oWz8+PGSl5dnyrz99tt1JoF46zAeToDLwITzaOxZsVbQP1A2B8chNPYCLE8CJBAnAYxPys+3hXUguukOVs+FWUbm4IPtbGKMS/KKxDgvncrFsL0dRCDE4CyYCkQsSbNFxWK00LtDGxWC7YOCEKJwJ52VnK17IjOECMSaPRoqwVgqEIj1HjkLmMvA+P1+KQD9EmR9EmgKgfXrRf7+dxHMsMQSMy6ge+3QQ+2sS4jBDB0YjjFeyzaWW1EIQagGcbh8U7kjFXZsk5djtraDMNxZPYbY5m5ntUxerzCWcAgDx5OkJxDrPVIAUgD6/XgpAP0SZH0S8EsAW85hSZmnnxaZOTN0Ne0WkkMOyXgxGAKi3RU6rnD2KisIsWYh4nNXbZHt6kWMFrCINcSgE4QQhxhbmK/b4KV7iCUc0v250+35Yr1HCkAKQL/fOgWgX4KsTwLNSWDOHCsGIQi9YhCewRNOsCKxOe+XBteqqdVdTXRyCbyEEINzVBTO0SM8iNFCrnYVD+jS1grD7u11nKH1FvbtmF7dyLGEQzQmTEteArHeIwUgBaDfr5YC0C9B1ieBliIQKQax9RyWk0HA2mlYf/Cww9JyAol9SH8/SyuqZJ4RhFvChCH2QI4W0I08pHs7GdINHsN2MhTiUA1eRDcpIVq9ZE2LJRyStb1sV3QCsd4jBSAFYPQvJv5UCsD4WbEkCbQegblzrejT7bFM+Pprkd13F8GyHrrshC5q1nptS6E7Y2zhys0VMnf1FiMOrcdwi2DLO0xGiRba62LYg1UYDlVhCIHohGH34oKkFoZOOGA7M2wzxpCaBMrLy80yMwMGDAiuXYgnoQBMv63grtD3+gu1nmrfqv1E7SO1WKGDZvxJTfuGBMuI64JjcrXaa2oMJEAC6UJg2LDwJ9E1w8z2dLqfaZj403XRdFVd212MPIYwAvDk9dJZxLADh3UL5lXX1Mr3urXdfBWGc1eVyTwc1RZr1zJmI3+5ZJOxYAWNtNe1C4d0sx5DCMPBiKvHsFeSeAyxtAieFztkYGmSVPRienlnYhx/sOD94d3hfTKEE0inef+6o7w8rgYR+InapWoXqQ1XW6IWGbCeBMqtUbtRbZkafuNvUZuhFk+gBzAeSixDAslKQPccNesLon0LF4runRVq6bhxIieeaMUg9ilmaDQBeAUxvhCCEOJw3uoys2TNYt3yDmMPo4W2+TkySMXgYJ1sYo5GJLaTfrpUTa6ubZjIUKa7dixbtkxHDERvayLbwns1jQDEX58+fcw+yd4r0AOYXl3AU/TlTle73POSZ2v8BbVrPGkueplG4C1En1CVS2zkkQKwkcBYnASSlgAWnH5c/4b8739FPv7Ydhm7xu62mxWCEIS6sK66FFwOj00gsL26Rr2D24LCEF3I360pM2Kxqia62MLC1v27FJlZyPAWwjAjeWDXtlKUn9uEVsRXxS2UHF9plko2AvD8RdsdhAIwfQQgvHnb1E5We97zAd6l8VFqB3jSXBTdvPob39Q7Vo9r1Z5S+7NajVq0UKCJMBfaa2QZF4J2OHgkgTQhgIWmn9dfJbpHqbz3nv5G8PxKgDcQM4qxAwm8hNmJ9UqlCeGoj1GFrmT1Dn6nC1tDEBoLiMOKquhjDHEhdBvDWwhBOEgF4UBzbCfJPs4wKgQmJoQABWD6CMBe+sUsV9tX7VPP13Otxs9VixgAZEroehHSX+1JtfvUhqjdqwbR+Ae1aOF6TbwuMoMCMJIIz0kgjQhg0elXXrGewbfeEkG3sQu6/ZZMm+bOeGwhArXaXYxFrBcExOCCtVtlgQpEnK/fWhnzruhOHgBB2MV6CiEMB+oSNi3tNYzZIGYkDQEKwPQTgPvo1zXZ84X9RuNnq6GbNzLM04RCtQFq7s/7n2kc3cKYRBIt0AMYjQrTSCBTCGzRIcJvvGE9g6++KnLmmSL332+fHl5C3WfV7ERy9NGio84zhUqrPudGFYAL16kYXLPVzEZeqKJwoQpETEqJNc4QDcbyNFjP0Bm8h4j36dgm4WMNWxVght6cAjB9BGBTuoA/0O8eY/8O8Xz/kzSOrmEIvdh/VoYqFGuUewGHeDBGAplDAJ5ACMIuXewzf/KJyIQJIiUlOrVM55a5fYu9E00yh06rPykmoCxREQgvISaiOGG4UOMb6vEaYqFrTDiBGOzvEYiI9ywu5J7Jrf5mm6cBFIDpswwMxNoXaoeqeccA4vxFtWhBf1vLGWoYwOMGlwzV+Eq1eMSfFmMgARLIWAIF+ncizIXu3UV+pp0I2HXEiT/MHsWyMj21UwF7Ex+rw429M41dXR6bnQC2q3OTRSIvDq/hovVbZZF6CuE9tAJxqyzWNIw1hEiERYYCveZOnYukf2frOdxJj5iYArHYvT3FYSQvnic3gXSayuaWgblMkU9Wu0TtYjWdsiffqz2mtlztGjWEvmqz1B5Ru1ttiNpDan9V+5NaPIEewHgosQwJZCoBLEDtFp92DDCLGEIQNnYsJ5E4LklwxFjDVaUVRhB6RSHWM4Q3sTrG0jVoemGeisNOba1AVEHohCK8iVg3MUc9iwzJQ4AewPTpAnZfFdYA/KWa/rkt36j9VO1DNYT31RarnafmwniN3KGGmcIQh/9Uq28WsGaHBQrAMBw8IQESqEPge/3780XtiHhBV6T6UH8deWcU9+olgvGCEIMHHhi+KHWdCzGhNQlgsWtMRIEwhCDEWobwGCK+VPdNrm+8YV5OlmCvZIhCeA0hCm28SMccFql4zGnNR8vIe1MApp8ATPSHTAGYaOK8HwmkMgGsNfiaDjOGIMRkEl1oOBiwLd0PfiByzDE6de1segaDYJI/guVrVqg4hCj83ohCKw4RX7qhXCo1P1bAkpI9dGxhX4hCNYjDfioUzVHjndrmcxeSWPB8pFMAUgD6+HxMVQpAvwRZnwQylQAmh2CNwZdesrYcnRAahuholHnzbBw/V65UhdBDf1uzCzEEJXVi8AyiW/n7gNfw+w3anWyE4jbTrVymW+XVF9rpXsoQh/06tTFeRIhDeBORhhnL9B7WRy92HgUgBWDsryO+HArA+DixFAmQQH0EMFlk+nQrBDt1Evnxj21piETdh1YwweT990V6967vKsxLMQLYYg4zkjG+EIZFsE08cIRwbCh0a19gxGBfFYMQhRCHfQJiEUvdJHr7vIbamyz5FIAUgH6/RQpAvwRZnwRIIDaBL3Rxg332EYEohIfQ7Try4IOim5uKHH64SOfOseszJ6UJVFTVyDIdX7jUiEM71hBxiEQct1bq2pP1BEw8gQg0olAFIsYb9lVxiCO8h9216zlTJ6dQAFIA1vNPJ64sCsC4MLEQCZBAkwlgrcH580XGjLGXqNXxZFhWBmsNQhBCIB51lLXhw9lV3GTQqVUR3sON26qMEFy6EYJQhaI5bjOicbkKx/rGHuJpseYhZij3VoMghDDsrUd33kPFY57uwZyOgQKQAtDvd00B6Jcg65MACTSOwFZdn+7GG0Vefllk5szwuv37ixx5pDXOKg5nk2FnWNJmzZbtKgZVHKotU4FovImIqzjEpJX6lrUBLqxcgwkqThTi6BWMiBfl67qXKRgoACkA/X62FIB+CbI+CZBA0wlgiRlsSYe9it99N3yf4jZtdJ8j3egIgvCII3TlUyx9ykAClgAmp6zWMYZY2gYi0QlEnDvDbioNhQ5FecZj6IRhrw6FRiS6867tCpJy9xQKQArAhr7thvIpABsixHwSIIHEEIBn8J13rCCEKHSzit3dV62yk0ncOY8kUA8BeBDXbYUH0XoL0aVshKE7qlDcUlH/DGZcHt3M6EruVQLvYaH0VK9hL5zrsWcgraRNXsKXuqEApACs5/OPK4sCMC5MLEQCJJBQAphV/PXXITGI2cTTpoWacNppIijzu9/pXkm6MwkDCTSBQGlFlelKRncyBOKKzRVh55jFrDqywVCUnxMUiVYsFuq5CkQIRhWLEIrFhbnNKhIpACkAG/wwGyhAAdgAIGaTAAkkAYGqKpG8PNsQeAoxq7iyUjfD1N0wd9nFpn/5pUh5uchee4nkcGeKJHhrKd8E7J6CcYgQiBCHK3F08c2IV5hlcOJ5UIhEJwYxexlxiEUc3XljFs2mAFTvbDzgWYYESIAESCCFCTjxh0coLLRrCmJbOu8+xTffLPLMMyIdO4ocdpjIpEl2mZnuugYhAwk0gQDWIERXLyxWwFI3KyEOVRCuVEEIryFEok3Tc03HbOdtuuTNgrVbjcW6Vn5utorBAulZrEvcQCBqHOIQQhGTWRCHoRwDPYB+vwF6AP0SZH0SIIHkIHDppVYAbtoU3p7Ro0NicO+9Q57E8FI8I4EWI1Cu4g/CEB5Ec1TBuMqIRiscMZllXZl6tOMMnXV7vU75NfL2r/WPHJEStdI4q6ZVMe4t5O91UgD648faJEACyUSgWgf1T5ki8vrrdq9iLETtDcX6Kw8zi7EANfYt7tfPm8s4CbQaAcxYhhCEQSRCIBrzpK3evD24NmLtdl0e585T0F4KwFZ7a6l9YwrA1H5/bD0JkEB9BFavFnnrLSsIcVy/Prz0iy+KHHNMeBrPSCBJCbjFsyEMF65YK0fvORgtpQBM0veV7M2iAEz2N8T2kQAJNA+BGt12DB5BeAfffNPOKl6xQqRLF3v922+36VdeSVHYPMR5lRYkwEkgutB3C/LlpUmABEiABNKFAGYGjxsnct11Ip9+ar2BTvzhGeENhJfQu/4gBOK//y2ybl26UOBzkEDaEOAs4LR5lXwQEiABEkgggfbtw2/2wAN23CB2HnEBovCKK3S6oQ43x17GmF186KF2/+KCAleKRxIggVYgwEkg/qCzC9gfP9YmARJIZwKPPSbyl7/YRam9z1lUJHLAAVYMQhBiMWqIRAYSSBABdgFzGRi/nxoFoF+CrE8CJJD+BFauFHn7bTtGEEdMLvGGnj3t7GKIQcwyxjkDCbQgAQpACkC/nxcFoF+CrE8CJJBZBLAF3cyZIv/7nx0ziAWpKypCDC67TOT+++05lqXB7iSR3c2h0oyRQJMIUAByEkiTPhxWIgESIAESaCIBdPXutpvI1Vdbj+DGjSLvvCPy61+LjB1rxwm6S3/+ud227rjjXAqPJEACzUSAk0CaCSQvQwIkQAIk0AQC2JruoIOs3XRT+AWwKDW8gPn5oXR4EM85R2TUKJGDD7ZiMpsLWoQAMUYC8RHgqNv4OMUqxS7gWGSYTgIkQALNQWDRIpHt20P7Fs+dG4rj+liK5sADrRiEkBysi/tyQklzkE/ra7ALmGMA/X7gFIB+CbI+CZAACTSGwJo1Ik88YSeVYPzg1q3htfv2DXkUIQj79AnP5xkJKAEKQApAv/8QKAD9EmR9EiABEmgqgaoqEYwTxBjCd98VmTxZpLIy/GpDhlhBeM89Irkc9RQOJ3PPKAApAP1+/RSAfgmyPgmQAAk0F4Ft20Q++cSKQQjCadNEamtFhg0TmTMndJf77hPp0cOuQ8gZxiEuGRSjAKQA9Pu5UwD6Jcj6JEACJNBSBDZvFvngAzuG8OST7V3gNezY0XYdz5hhJ5EgZ+lSkXbtbF5LtYfXTRoCFIDqEE+at8GGkAAJkAAJkEBzEigpETnmmPArlpWJnHeeyFdfiYwcGcq79lqRJ5+0s4snThSB7bcfBWGIEGNpRoCzgP29UHoA/fFjbRIgARJIDgJYUgbdxt6A2cS7727FILau239/uy6htwzjKUmAHkB2Afv9cCkA/RJkfRIgARJIFgLYsg5dxu+/bw1LzngDBOGuu9p9jCEIsfxMp07eEoynCAEKQApAv58qBaBfgqxPAiRAAslKYMUKESw140ShdyIJ2vz44yJnnWVbv26dnYHcq1eyPg3b5SFAAcit4DyfA6MkQAIkQAIk4CEAMXfaaXZv4tmzRVatEnnmGZErr7TjB+EFdOHhh0V69xa59FKXIoJdS2AMJJCEBDgJJAlfCptEAiRAAiSQhAS6dxfBbGI3o9jbxGXL1KWSHb5LyeLFdiIJxg5iQgmOu+xiy3nrMk4CrUBABzQw+CDALmAf8FiVBEiABNKKAJadgcevQwf7WI8+amcce/Qqt3kAAD9rSURBVB8SYwYnTLCCEKJwzBiRvDxvCcYTQIBdwBwD6PczowD0S5D1SYAESCBdCWBh6ilT7DjCjz4S+fRTkfLy8KctKhLZe28rCiEMx4+36xGGl+JZMxOgAKQA9PtJUQD6Jcj6JEACJJApBLAI9fTpIhCDsI8/FtmwIfzphw4V8c4+3rQp5FEML8kzHwQoACkAfXw+pioFoF+CrE8CJEACmUoA29RhcgmEoDNMLHnkEUukpsYuM9Oli12Wpm/fTCXV7M9NAUgB6PejogD0S5D1SYAESIAEQgS2bxcpKLDn8ARi0gi2qNu4USQnx6b/5Cci8+eL7LuvtT33FEFXMkPcBCgAuRVc3B8LC5IACZAACZBAixNw4g83GjbMCr9580LiD+mvviry3Xcir72GM/0vuS7oMXq0yD77WEGII5akYSCBeghwFnA9cOLIogcwDkgsQgIkQAIk0IwEpk0T+eQT222MiSVYsDoy9OtnBSHEIGy33Tjb2MOIHkB2AXs+hyZFKQCbhI2VSIAESIAEmoUAlp1ZssQKQohBCMOvvxbB+EJveOwxkbPPtimYeILxhV27ektkVJwCkDuBZNQHz4clARIgARJIMwLYn3innUTOOEPknntEvvxSBDOH33lH5IYbRCZNsrOIsbyMC5hk0q1b3V1LqqtdCR4zgIAOHGAgARIgARIgARJIGwLt24scdJA1PBS8gRCKLnz/vY0NGOBSrBdxxAgRTCjBuoTOsPsJQ1oS8HwRafF8V+hT/EKtp9q3ajpVSnSxpQaDbvYo/1J7Ue24BkuHCrALOMSCMRIgARIggVQhgFnF6D7GziQITz9t9z22Z6Gf/fuHxOBee9nJJt6JKqGSKRVjF3B6jQE8Vb++x9UgAnUQhFyqdpHacDUdIBEzqO/clF+oRx0YQQEYkxQzSIAESIAE0pOAW5Pws89EnH2rfhSIRG/IzxcZNcqKQgjC008P9y56yyZxnAIwvQSg7rcj09Uu93xzszX+gto1njRvFIsqfaD2sNp+ah3U6AFUCAwkQAIkQAIZTqC0VOTzz+12dk4UrlsXgoKxh4sXh86feMJOLMH6hFi7MIkDBWD6rAOof5LIHmo3R3xvb+m5zn+PGX6nOWvV/qkGAdhQKNACMBd0oAUDCZAACZAACaQhgWId5XTIIdbwePAGLtTOMohB7HFcUhJ6aOT96Ed2AgqWqdkD/0nWAC9iWZnI7ruLFBbaNP5MCgLpMglE98kRePNWR1DFeY+INHeqf6LIhWrqy447wJN4XdylWZAESIAESIAE0oUAJpIMGmTtzDPDnwoi78gjRWbMsGsOutw77xT5xz/sGoQQgePG2YkmmGyy887hC1y7OjwmhEC6CEAHS/8ECQuY5BKZhgLw3KmvWi5W8/iz9az+cJNm3+4pguss85wzSgIkQAIkQAKZRwAzj9EFHBmwRR32MkbXMTyDMBfQTQxPoVcUolvZO2PZleWx2QlAIKVDQBfwNrWT1Z73PNBdGoeH7wBPGqJI+1KtBieBkB046nx5Gaa2IHBe30H947JZgxTDVc5AAiRAAiRAAiQQTgDdw1h6BuMJYVOninzxhcjWreHlcAax+DsdnYXuZATUbQFByDGA6TMGsFI/E/2a5FA1rwDEOZZ2iQxzNGHXiMQ/6nl7tR+rLY3I4ykJkAAJkAAJkEBTCEDA9e9v7ZRT7BWwE8lsnafpBCFEIXYwgaewTZvQXZB+wgkiP/iBjtb/ZyidMd8Ecn1fIXkugK7Zx9XgX56sdolaP7UH1BB0HxxZroZxfBVq36h5w6bASWS6twzjJEACJEACJEACfgnk5IiMHGntggvs1Sr0P80QgRCLLkAALtf/dK9c6VLsETONe/WyXchjx4qMGRNa0zC8JM9iEEgnAfi0PmNnNfUdm4WgIeSOUFO/swkQg7WBOA8kQAIkQAIkQALJRACzhDEe0BvOPddOKoFgdAFiEPseIzz7rD3iJ3Y2gRjEuEIYRWGITZRYVpQ0JsVPgGMA42fFkiRAAiRAAiTgnwA8hRCAmFCCsYSwBTGG7UMUQghCEF54od0DWVvAMYDptRC0/4+q8VegAGw8M9YgARIgARIggeYlgK3tpk8PF4VYs9Abli4V6dPHpJQ+8oiUnH8+4iVqpSYxw36kUxdwhr06Pi4JkAAJkAAJkIAh0LGjyMEHW3NInCiEh3DePJHevV2O7hH2QiieoTF2Aft78fQA+uPH2iRAAiRAAiSQcAKlTz8tJaedhvtmrAfQrX2XcPi8IQmQAAmQAAmQAAm0CoFJk1rltsl0UwrAZHobbAsJkAAJkAAJkAAJJIAABWACIPMWJEACJEACJEACJJBMBCgAk+ltsC0kQAIkQAIkQAIkkAACFIAJgMxbkAAJkAAJkAAJkEAyEaAATKa3wbaQAAmQAAmQAAmQQAIIUAAmADJvQQIkQAIkQAIkQALJRIACMJneBttCAiRAAiRAAiRAAgkgQAGYAMi8BQmQAAmQAAmQAAkkEwEKwGR6G2wLCZAACZAACZAACSSAAAVgAiDzFiRAAiRAAiRAAiSQTAQoAJPpbbAtJEACJEACJEACJJAAAhSACYDMW5AACZAACZAACZBAMhGgAEymt8G2kAAJkAAJkAAJkEACCFAAJgAyb0ECJEACJEACJEACyUSAAjCZ3gbbQgIkQAIkQAIkQAIJIEABmADIvAUJkAAJkAAJkAAJJBMBCsBkehtsCwmQAAmQAAmQAAkkgAAFYAIg8xYkQAIkQAIkQAIkkEwEKACT6W2wLSRAAiRAAiRAAiSQAAIUgAmAzFuQAAmQAAmQAAmQQDIRoABMprfBtpAACZAACZAACZBAAghQACYAMm9BAiRAAiRAAiRAAslEgAIwmd4G20ICJEACJEACJEACCSBAAZgAyLwFCZAACZAACZAACSQTAQrAZHobbAsJkAAJkAAJkAAJJIAABWACIPMWJEACJEACJEACJJBMBCgAk+ltsC0kQAIkQAIkQAIkkAACFIAJgMxbkAAJkAAJkAAJkEAyEaAATKa3wbaQAAmQAAmQAAmQQAIIUAAmADJvQQIkQAIkQAIkQALJRIACMJneBttCAiRAAiRAAiRAAgkgQAGYAMi8BQmQAAmQAAmQAAkkEwEKwGR6G2wLCZAACZAACZAACSSAAAVgAiDzFiRAAiRAAiRAAiSQTAQoAJPpbbAtJEACJEACJEACJJAAAhSACYDMW5AACZAACZAACZBAMhGgAEymt8G2kAAJkAAJkAAJkEACCKSbALxCmS1Sq1D7Qm0/tVjhYs34SG1jwN7W4zg1BhIgARIgARIgARJIawLpJABP1Td1p9qf1EarQdy9rtZPLVqYqIn/UjtQbbzaErW31HqrMZAACZAACZAACZBA2hLISqMnm6LPMl3tcs8zzdb4C2rXeNJiRXM0A97AH6o9FqtQRHqxnm/WIMXFiDKQAAmQAAmQAAkkO4HS0lIpKSlBM/GjNNnb2xLtSxcPYL7C2UMNHjxvwPk+3oR64kWal6e2oZ4yzCIBEiABEiABEiCBlCeQm/JPYB+gix7gwVsd8Tw47xGRFuv0Zs1YroaxgLFCgWbAXGjvIjySAAmQAAmQAAmQQKoQSBcPoOO9w0UCR3RxR6ZFFDGnv9Sfp6udoIYJJLECupI3e2xZrIJMJwESIAESIAESIIFkJZAuAnCdAq5Ri/T2ddO0SK9g5Lv4uSZcq3aY2teRmRHnN+k5xgs46xORz1MSIAESIAESIAESSHoC6SIAK5U0ln05NII4zj+NSPOe/kJP/k/tcLVp3owY8e2ajsGizrbEKMdkEiABEiABEiABEkhaAukyBhCAb1d7XA1CbrLaJWpYAuYBNYTH1DDGz80IRrfvDWpnqC1Wc97DMo3DGEiABEiABEiABEggLQmkkwB8Wt9QZ7XfqfVU+0btCLXv1RAgBmtNzP7AotGYPfysJw3R36tdjwgDCZAACZAACZAACaQjgXRaB7A13g/XAWwN6rwnCZAACZAACfggwHUARdJlDKCPz4BVSYAESIAESIAESCCzCFAAZtb75tOSAAmQAAmQAAmQAD2A/AZIgARIgARIgARIINMI0AOYaW+cz0sCJEACJEACJJDxBCgAM/4TIAASIAESIAESIIFMI0ABmGlvnM9LAiRAAiRAAiSQ8QQoADP+EyAAEiABEiABEiCBTCNAAZhpb5zPSwIkQAIkQAIkkPEEKAAz/hMgABIgARIgARIggUwjQAGYaW+cz0sCJEACJEACJJDxBCgAM/4TIAASIAESIAESIIFMI0ABmGlvnM9LAiRAAiRAAiSQ8QQoADP+EyAAEiABEiABEiCBTCNAAZhpb5zPSwIkQAIkQAIkkPEEKAAz/hMgABIgARIgARIggUwjQAGYaW+cz0sCJEACJEACJJDxBCgAM/4TIAASIAESIAESIIFMI5CbaQ/M5yUBEiABEiABEkhPAjt27JDK2krZVrVNtlVvk/KqcnP0xsury2X9xvXpCaART0UB2AhYLEoCJEACJEACJNA8BGp31ArEmBNrOG6t2lpHsHnzIeS856jvvQbiNTtqGmxgTXnDZRq8SIoXoABM8RfI5pMACZAACZBAIghU1VQZgba1WkWaE2s4es89As2IuUA+PHFBcadpxiOnYq0lQ0FOgRTlFkmb3DbG2ua1tfG8NpK9PVtm6/8yOWRl8sM3w7MX6zU2a5DiYkQZSIAESIAESCA5CMDDBqFWVlUWFGwQa06YId3FcXQCzcVxhEfNnVfVVrXIg2VnZRuhBrFWlGcFG44QbC7NCTmkx0qD0AvW12vlZOfEbG9paamUlJQgHz9KYxZM4wx6ANP45fLRSIAESIAEUosAxrBBdEGcGYFWqcIMok2PTrBBkHnjTqBFHuFla4mQn51vxVlApEUKNXPuEWouPzIdQg5p8NRlZdEf1RLvqr5rUgDWR4d5JEACJEACJBAHgZramjChZgRcpfWwObEWK82JO+et2yE74rhj/EVysnKM0ILYciKsba4nrunt8toZ75krg3znhXNpzsOWl50X/81ZMmkJUAAm7athw0iABEiABFqaADxuFTUVpptzS+UWKVPRtqVqizlH3Ik2c1SvHMoYD1xEXnN729AtCuEFYeYEWLt8jasww9F5z0x+voq5KOlOwNHD1tJfUWpenwIwNd8bW00CJEACGU8grLs0INy8Is6IOYg6dKcG8p2o8wq56h3VzcYyNztX2ue1N6Ktfb49OpGGozEIOY/XzZU3aQFxB28bu0Wb7bXwQlEIUABGgcIkEiABEiCBlieASQVOpMHrFhRvKtoQRxrySytLwwScy0PXaXOJN+NxC3jR4GFzoiwYVy+bS/MKO+OVC4g5pOfn5Lc8ON6BBJqBAAVgM0DkJUiABEggEwlgWRCIMyPIAqKttCr8HHlBAeeEXUDcYbJDcwSIN3jWIMBgzsvmFWwmPSDsINpceXjdkIcuVXrcmuNt8BqpQoACMFXeFNtJAiRAAs1MABMX0D3qRJw7GtG2vTR6ukfwYexccwSIL4iy4vziMAGHc6+YcyLOm444u0ub4y3wGplGgAIw0944n5cESCCtCGyv2S6lAbHmBNzm7ZuNV86d4+jKOI8cjhB/zRHgRXPiDSLNG8c5PHFe8eZNa6tdq5xV2hxvgdcggcYRoABsHC+WJgESIIFmJ1BRXWG8bRBuXrEWTcBF5kMA+g3woEGkFRcU1xFvTszhCPN66oyo067X+hbc9ds21icBEmgZAhSALcOVVyUBEsgwAhgPt7lSBVzAGxcUc+p9C8Y1z1vGiTlsXu8nZEmW8bBBkBmhFhByTrR5hR3SXDl3zMvhum5++LMuCaQiAQrAVHxrbDMJkECLEMDWWegWdYLNHSNFHdJdnjv6ndCAxXqdIKsj4ryCLiKOOhgnh4kQDCRAAiQQLwEKwHhJsRwJkEDKEPB64+BxixRs5jzgrXMCDuUwLg4isKnBeeIg4EoKSup641S8leRrukfEuXIYR8dZqE0lz3okQAKNJUAB2FhiLE8CJJAQAm6Hhljirb50v944MyYu0J0KgeZEm/fohBvEnEuHN46euIR8HrwJCZCATwIUgD4BsjoJkED9BCDksE0WBNum7ZusN87jfTNCLoaXzs/YOK83rkNBB+uR84g1iDYj7pynTr12HQo7GK8dF/Ot/50ylwRIIPUJUACm/jvkE5BAQgh4x8c571s08RYUeZ4ZrX52a8jNyjVdpk7EOW+b62Z1HjrnkUM5eOXojUvIZ8GbkAAJpCgBCsAUfXFsNgk0lUB1bbUZ6xZNvAWFXcAjh8kPbgwdZqz6GR+Xn50vTpw50Qah5oSdE3Q4ujQcuchvU98065EACZBAbAIUgLHZMIcEkpqAWwA4lpCDYIsm6LC/qp8AQeYEnPO6mXPtSnXCzYk5b7nC3EI/t2VdEiABEiCBZiRAAdiMMHkpEmgsAW+3qhNsbm04J95cutcTB8+c3224sHSIE3BBT1zEuDgn6JzAg7Dj+LjGvmWWJwESIIHkI0ABmHzvhC1KMQKY5LC1aqvdwcGz5ZYTck7AmfNAPsQczv0uO4IZp87b5o5er1tYmmeyAwQft99KsQ+NzSUBEiCBZiRAAdiMMHmp1CWAcXFllWXB/VOdWHP7prqFgGOd1+yo8fXw3mVH4HXzCjcXh2jzToBAOawdx2VHfKFnZRIgARLISAIUgBn52tPvobHwL8a2QaBByEHAYUcHnEcz430LlEc+PHh+AzxqwS5V7SqFYIN4MxYh3lw5d2S3ql/6rE8CJEACJNAYAukmAK/Qh/+FWk+1b9V+ovaRWqxwombcoDZIbYHab9SeV2NIEAGMgcOivRBtEGEQbca85/DMqVhDGSfqwuJaBxMimiMU5RaF76kaIeTMVl0eYWfOA2UKcwq5k0NzvARegwRIgARIoMUJpJMAPFVp3akGEfiJ2qVqr6sNV1uiFhnGa8LTav+nBtF3vNozahPUpqgxRCEAwVZRXWEW9i2vKjdHLPIL8batKnDUcxc36YF8xJ1ByLkyO2RHlDs1LQldopjcAGEGQxyeuPZ59hzeuHb5mqZHJ95MOU3DkePimsadtUiABEiABFKLQFZqNbfe1kK0TVe73FNqtsZfULvGk+aiEH/FapNcgh7fUNuodronrb4o6m/WIMXFiLZewEQE7JoAcVZZU2k8YvCKYabo9urQ0aWhnDHNxxFeOJSFqCuvUdNzZxBqLo5jS4ScrBwjzNrmqoBTMQbhhqMTdIhDxAXzAvlO5OGIsrnZ6fQ3TUuQ5jVJgASSgQB+Z+NvX/PnL+IabNxGgn8YB8tofqCcK2xrobyWDp64C+F6trI3L3gNZJk6tqIr49pl7mEvbS7o8m0jw9ti8sytzA9XNXj9WHW96a6tqGyvFyAQ2UZ3i0DlYLZJN2d4cNtMHIM3MY8RSN8hW8q2yO4T0PknJWqliGRaSJf/Wubri9tD7eaIF/iWnu8TkeZO4QG8w50Ejm/qEd3GjQrPXn+vFBXYNc4Cn5/Wd/8g8RHbVHyI7szGa83HadJMHj7WWtFUk25img6vm/7UYyheg/Io6yxwj8iGh9rjyfHIfm9+thZpq1ak+VlSqFfEM3U0FYPlgnWzJCc7Wycg5EpujpoKuGwVX7nZOUaE5Zh4rpZBmtfy7HlO4Kjj5vJy8s21RGe0mpCFTbw06DEQqXvUjNqs7bI5q1JtQ5R6uIK3PuJIwyEU1wcwaTYvkO7Jz0K+qefJ0+vapCzZoRHT2mA5e7nIn/q66oZoaVHeY9S6da+m30P9icHsYCRKeU0K/sKMUi6YFIzgGvYk7P5h+fY+wSRPwVCaLWN+BhLx7yIYgmnBFHdbNDiYGIwFI4FigTLBZBepp64rEry+JgTTcMfASbCd7txbyHtfT3rotq6SfQRz5pJChYJNCD1o8K6mHaGirnKweRqxaaEywST7EK5K4Ih7BL8Bd0PNC9XH7x6XEUj3JHiippD3WibP1LUXcGXd0XvhYFrgVuY6aAfOPZkmatLtNd17CSumhWy9QP2wTPcMSES+uZiNBy6J+0Wt74oGygVK2ZsE03DRUH1zYf5odQLllf7Hfbf6Q/hsQLoIwC7KIUdtdQQPnPeISHOnSG9MedQrCBjiCO3xY8OmkVKeD+nUMiEgi8wDtswdmveq+L1XHbCmXTnwm9P+ym3aJViLBEiABEggnID7exep5o9XHANF8DcuTuz/PekmNZTu6nrqmSRX16W7cjYTuTbgvu4kcAzeN5huI+an/jB/tIeq172OpthronAw20Ri1S3f7v7Lastn4s90EYDu3Tnl4M7xKUSmuTwcI/MaKo+u5Ou8F0C8bfk0aVOt3jL1fol6s+DJ8n50tnzgH5E5CcVdOfvN4qf9xxEsoV+1/UyRHsi3pex3rmn2f/gHEMq39/T8jHxSkxVIDOYF/34NVTR5wQI2PTKtwXNPffPneuDy3noad3dXv5p9M+6vZtcaUzdwLVc3cBr0CATK2NvgOq6AXgRxc+pJ96bhPnpuqwTK2BPXAnO078qbZC7qTdB4tLSIIjiNUsw8f52idQtm1U2KfsFoN/FcPyvKM4ayvTex8dB9vXmhGqFYZHnkuDruGCodvR3echHXc15X8+9Nr6MeafNvAOmI418Ijq6cJz8L3mZNt+VdvUDZYB0tg39fOaF8ew/cK8de15R198DRXteU03rmdwHuY9JdvueIa3vzAufBNFzD3cPEcd9Amqubo2nmo7Rfpo1rG/XUpiAejIWiJj+Q7g4xyukVLM/QZZBkrxWoE8wKRpCvJ/b/pryNexICZc1BywZObR2bGKxn7md+4L3ZZPNT48GagXSXb38nBsqiXLCejQTPkefu7ikXWT9wez1EqR+8mLuPp522uOXhmoM03Mv+CKTag7mU/ghUc7cL8kQpkxdZ35wjM7xu2HPYW2T8z9JS7fW9PrMxpIsAXKevEQuxRXr7umlapJfPvfFVjSyPejep3Y5IIMADuOzMk0qleNZ92oJKmzz0cJEDr9W5yLu7cjymMAHT9VRbq++3xsoXxNV21KogqdXPDqIRaRBSSK/ROEoGywXqIt9bxtVFeXTz6/VNHVwvMs3cz97DlAvme+o2lKb3M9fFEW3T8jvQhnqPthyeM1gX93HnYGKuFeNYXR3Kx/MFyu+oUR8x7utJc3ni6uiRIU4CEIkqBCUvzxxNPDe3bjwXf6TadB27IVm5gfKR6YEyWXn6nwhvecRx3cjykdfxljH3wXVwP3dvHN11Auma5y2DsuLKo6732RD3CK44KbEYCZCAh0DwDwxPWqpGp2jDv1DDLGAXZmnkRTV47iLD05oAAXeEJwOzhjepne5Jqy8amgRSu1nkg5tFvnrK/MfcVNr5KCsEu4+o7xrMIwESiEEgKC6dUISARByCuBrHwHlANO6AaPTmoYyKzZB41fIoY64DcWvzrCANXAt5Ws9eC2mectVV4cLVlPWmBa4XvAfq6/3c9cx9kabtQptxxDMg312rStMhqgP5Nt222fyBEINVxiVD9HpEohXAAWEJMewRuN54nXIqco0YjagTFL8QoUbwqgiFaDWiOBA39w8I2KCgRXlPHYhjVz8QN+0OlA+KddQxbbDH4LMhHV5fhmYlAA9gSQnmf2TuJJB0EoCn6ot8XO0ytclql6hdrAb19b3aY2rL1ZwYxOSQD9Ww9h9E4rFqf1SboAYxGU8ICUA3C3jdd1YIznxW66vHB2HE8SIH/Fqk2872nD9JgARIoAkEvII4JGQhIK1ADB6NmAyIXwjJoBAOiE0IWSOUXT13DVvWilbE1ZwANiJVywfSQmVcXXs0ohbCGkIWAhdxr8ANxIPp5np63UB5c09NsyLdCuUmoEqvKvB2GlEZEIdOKHpFo4t7BG1QREaKWyNIA9cKE7QQzkhX06MRzoF40OtrhDW8tSgDIRyo4+4fVj4gjnEtLYdrmvIoY9qpdV26y8MxAYKXAjA4siBt/q3A+/dLtZ5q36j9VA0iD+F9tcVq56m5cJJGIPoGqi1Qgxh8Ti3eUFcAuppr5ugdtcd4FlahQdB/wCOOE9lfm9d9uE3iTxIgARIggXoJmCEYRtCGRGFQJEI8QshWwQurAhSmQtJ6dj1xlHMC1lwLYjVQxwhPrRMsExCtSIcQjfTQohyGL6A+rmnqBdpm8qxoNemmTZrnEbdez669J65nryN4DgY7hlGFoBWjHpHphCwEJISjEa8BUWmEafxDGrbo+xt2s/ba0QPIL66JBGILQHfBVapDIQTnvOJSRHY5Rj2Cv9IRiyNDaYyRAAmQAAlkPAEjaCE8A2LSiNCAyAx5YwOC1olYFaLWo2pFq6njhK4ZghAoj7hLxz2Md9aTZ+6jYtTUiRC3TqSiDgStCmOvaA4KYi1Xx7vrvL7B58A9tFwrCt4yvf+47+bje0M/cEauA5hOXcCt8YujYQHoWgUh+OEt6hFEb3MgDDtSPYJXi/TGEoYMJEACJEACJJBZBILeTwhMGIRpUCgGxt86YQrBG2vogqsbOAaHPTjPL65hJp5ZEVxaukUG/QodhhSAmfXFNd/Txi8A3T1X67yUD2/VnYqf15TAGMGBB6oQ/LnITvsa17cryiMJkAAJkAAJkEDzE+AYwPQbA9j8X0n9V2y8AHTXWztX5OM7RL5+RnWgusIR+u4tsp96BIccSiFoifAnCZAACZAACTQ7AQpACkC/H1XTBaC788bFIp/8VeTLJ3TcxHab2k0nLu/7Y5GRJ+gMqTxXkkcSIAESIAESIIFmIEABSAHo9zPyLwBdC7asEvn0bl3J8BGRyjKbWtJXZPwPRcacLdKCW825JvBIAiRAAiRAAplAgAKQAtDvd958AtC1pHyjyNR/6kqED4hsXWtT23QUGXuhyDhd2rB9d1eSRxIgARIgARIggSYQoACkAGzCZxNWpfkFoLt8VbndVQRewY2LbCr2Gd5N17uGV5CLSjtSPJIACZAACZBAowhQAFIANuqDiVK45QSguxnWWprzqu0eXva5SxUZrBNF9r5cZNBB+ha5mk8IDGMkQAIkQAIkUD8BCkAKwPq/kIZzW14AetuwRHeom6wewdlYVDqwhEzXna0QhGcwr423NOMkQAIkQAIkQAJRCFAAUgBG+SwalZRYAeiatmGhjhF80M4cdhNG2nQS2eM8kT11rGBJH1eSRxIgARIgARIggQgCFIAUgBGfRKNPW0cAumZWbBaZ/rgVg5uX2NSsHN1q7iidMHKpLiy9D7uHHSseSYAESIAESCBAgAKQAtDvP4bWFYCu9di3ce5rIp//TWTxRy5VpLvuNTzuYpFdT+YyMiEqjJEACZAACWQ4AQpACkC//wSSQwB6nwJ7Dk/9u8iMp3U/RZ1JjFCgzRx1hl1KputQm8afJEACJEACJJChBCgAKQD9fvrJJwDdE2E9QewuMu0hEYwZdGHA/ioELxAZdqRIri4rw0ACJEACJEACGUaAApAC0O8nn7wC0D1Zba3Iwvfs4tLzXtfJw3qO0LaryOizdJeRc0U6DbBp/EkCJEACJEACGUCAApAC0O9nnvwC0PuEm5barea+1IkjZatDOVhLEEJw2BH0CoaoMEYCJEACJJCmBCgAKQD9ftqpJQDd09ZU6aQR9QZ+8bDIgnddqkhRF5HdT1MxeI5I12GhdMZIgARIgARIII0IUABSAPr9nFNTAHqfesMiXUrmMbvtXNmqUE7fvW0X8YjjdBJJ+1A6YyRAAiRAAiSQ4gQoACkA/X7CqS8AHQEsJfPd/6wYnPemjhXULegQ8tqKQASOOpPrCloi/EkCJEACJJDiBCgAKQD9fsLpIwC9JEpX6jIyT+ks4id1BvGCUE5HnSyy++lquu1cx/6hdMZIgARIgARIIIUIUABSAPr9XNNTADoqO3aILNX9h7GczLfPi7ht55C/0752vOBw9Q4WAgMDCZAACZAACaQGAQpACkC/X2p6C0AvncqtIrNeEvn637qszAeao+IQIbfQzh7eTb2Cgw8Wycmz6fxJAiRAAiRAAklKgAKQAtDvp5k5AtBLavNyFYK608iMf4msmxfKKeqs4wVPENntFJE+e+rXlRXKY4wESIAESIAEkoQABSAFoN9PMTMFoKOGLuIVX4rM/I/asyJb17gckQ47iYw8UfchPkn3JB4RSmeMBEiABEiABFqZAAUgBaDfTzCzBaCXHmYRL3pfPYMqBme/LFKlXcYudN1FhaCKQXgHOw9yqTySAAmQAAmQQKsQoACkAPT74VEARiNYuU0E287N/K9dWqamMlSq5+5WCGJpGc4kDnFhjARIgARIIGEEKAApAP1+bBSADREs32Q9gt+oGFz0YWh9QdTrvYcIZhEPP4ZisCGOzCcBEiABEmg2AhSAFIB+PyYKwMYQ3LpOxaDOJP7mOZHvP1ExWBuq3XOUCsFjrbGbOMSFMRIgARIggWYnQAFIAej3o6IAbCrBLautGIQgXPxxuBjsppNGdjnaGiaQcDZxUymzHgmQAAmQQBQCFIAUgFE+i0YlUQA2CleMwvAMznlFF5t+oW43ccf+IjsfZcUglpbJzolxESaTAAmQAAmQQHwEKAApAOP7UmKXogCMzaZpOds26AQS3YsYM4kXvCNSXRG6TlEXXXR6kgrCI0UGTtR9ituE8hgjARIgARIggTgJUABSAMb5qcQsRgEYE00zZGwv01nEb6t38FUrCrdvDl00r0hF4IFWEA79gUi7bqE8xkiABEiABEigHgIUgBSA9XwecWVRAMaFqRkK1VTZiSMQg3NeEyld5rmo7jiCGcXDDhcZqtZ9pH7Z3IXEA4hREiABEiABDwEKQApAz+fQpCgFYJOw+ayEHUhWfS0y9w273iB2I/GG4t4iQw5VU8/gwANE8tt6cxknARIgARLIcAIUgBSAfv8JUAD6Jdgc9UtXqhCEGNSxg4s+0F1IdCFqF3LyRXba1wrCwSoKuwyhd9Cx4ZEESIAEMpQABSAFoN9PnwLQL8Hmrl+lk0awrMx8FYMQhJu+D79Dh34iEIKDDxYZsL9IQfvwfJ6RAAmQAAmkPQEKQApAvx85BaBfgi1ZH13F6+bb7ejm/8+OIfRuS5edK9J3L5FBB1nDYtTZ2S3ZIl6bBEiABEggCQhQAFIA+v0MKQD9Ekxk/cqt2kX8kZ1ZjCVmNiwMv3ubTnbMIGYXD1KDt5CBBEiABEgg7QhQAFIA+v2oKQD9EmzN+hsW2bUGv3vXLkBduSW8NZ0GWUE4QCeSoLu4SAUiAwmQAAmQQMoToACkAPT7EVMA+iWYLPWxzMzyL1QQvieyUG3ZNN2ersbTuiyRHrtaQdhfxeBO4zl+0EOHURIgARJIJQIUgBSAfr9XCkC/BJO1foUuOr34EzureOEHImtnh7c0S7ek6z1GpP9+6h1Uw1hCLjcTzohnJEACJJCkBCgAKQD9fpoUgH4Jpkr9LatsNzGWmcE4wsjZxZhQgsWoseRM/wlWEBa0+//2zj3Yj6ug45vc5tGb103TPJomTUqhaZXSokChKgRGO4ia4aVFnMEZtcgw6IDjY4qDja9p/cOKCCN2RDNSBP5gppZhKihDB5S2Imgf9qGUpEnaPJrHzfPm5nHj97u752azd3+/u/vbe3/Pz5n55jz27O5vP2fz+33vOXvO9srV8TkhAAEIDBQBDGD/GMDlunM/IW1J7+AHFP+GNJrm85Ef5vpD6VZpvXRAul/6mJR535hyzQMGsDmf/t06ujMxgtu/mSw7c9GbSXTZ7iFcq1nFG26Joqus1/MMYf/eDVwZBCDQYwQwgP1jAB/UvbdOen96D96reIf0c2k+H+ldYbEB3Kb4KWmD9GnpcendUtmAASxLqp/rebkZ9wh6/UEPGzs+IoOYD6t+KDGCwRCO+G8PAgQgAAEItJsABrA/DOD1unFs4tTFEj2a3kROPyxdJz2blk0X/bwq3Cf5vWFnp6ucbscAlgQ1cNXcQ/i8bsHnZQh3Kj7wv1MRLNXfLFfp2cH1ul3Xvy55h/GQhpIJEIAABCAwqwQwgFHUD782mo4ZD9sG8+eb5pG0TGNvpQ3gMtU9KjUzfwu03QphSUgQQ+AiAl5D0LrxtqT4+P4o2qVbdKduTRvCPY/pbtsdRU9aX0rqzNPfHuv0HKEnlKyTIVz3GoaNL4JKBgIQgAAEZopAPxjANYKhX9cpwWXeViasUCU///c301S+Q9vvnKYOmyEwlcDiVVF0vZ5IsBy8KLWXmtn1H5JM4a7vRNG4Hj/1M4VWCCtekfQO2gxeKXkYmV7CQIcYAhCAAARaJDCnxf3asdtWnWQ6s/Va1fFEjl+WNknZoHeARZ+R7s4WFqQ9jPs16bC0RdKCcA1DUQ/g7iNHjkRLl/owBAi0SGBiQkvNPHPBDO6WMTz4/akHmzesySWvTmYcx6ZQPYZLr9TDHN38X3nqZVACAQhAoJMEGALu7mcAL9fNYTULO7TxvdI90oiUDZ4B/BHp77OFubSHcL8qnZR+VjolVQl2ffJ/GMAq0KhbksDJQ+olVM+gewlfUG/hC99TL6GfUsiFxasTQ7j2RxTLHDrmrSU5SGQhAAEIXCCAAexuA3ihpZqnwiQQPTgV6ZcyDk77OcDrpGfjkqn/2LzZ/I1Lb5NsAqsGDGBVYtRvnYB7CT2ZxGbQxtCGcN//5N5Ykh5+ZIPMoIygewuv0HI0V9wYRZfm/0Zq/aOwJwQgAIFeJoAB7A8D6HvwQWmt9OvOKNwraV2OyWVgNEYWfV16n2ST6J6/f5GGpXdIeiBrMryk1LnJXPMEBrA5H7bONoHT+rtl7xMyg99N9OJ/RdGh54rPetnLEjPo9QltCNe8ip7CYlKUQgACfU4AA9g/BvAy3aufkLak9+wDij8keRjYYaO0XXqz9JC0WfqGVBSuVuGOog0FZRjAAigUdZjAmB5n9Sxj9xDaEO75b/1P2Fn8oZZppvIVMoLBEDq95Ap9M8wprk8pBCAAgT4ggAHsHwPYqdsRA9gp8py3GgE/T2gj+KLkeM/jmvbkv4kKwrAmxbt3cM0NiVa/Uk/jajby0LyCyhRBAAIQ6D0CGEAMYN27FgNYlyD7d47A2GgyfOzeQstDyX7G8HzBExBD86NopR6ptSm0IVz9w4kWTTdPq3OXx5khAAEINCKAAcQANro3ypZjAMuSol5vEDgzplU1n5YZVA+hDeHeJ5OJJqePFX9+z0C2GfT6hNZq6XKtyDTfj9cSIAABCHQnAQwgBrDunYkBrEuQ/bufgGcfj+5IzWBqCD37+LDKovMFn1/PD3rCySpN0A9aqfSKl+vdQ+pJJEAAAhDoMAEMIAaw7i2IAaxLkP17l8D48WTx6n0yhe41tCnc/5QWVDpYfE1z9eKhy67RULJ6CG0MHXtYOTaGC4r3oRQCEIDALBDAAGIA695WGMC6BNm/vwicV4+g33tsI+g3mzje71gGsdEw8py5UbR8YzJ0vPLaNJY5tDFk7cL+uj+4Ggh0CQEMIAaw7q2IAaxLkP0Hg4CN4dEXElP4ktZmtyF0bPkdyI2CnzG83KZQs5D9XmTH1rL1UTR3qNFelEMAAhBoSgADiAFseoOU2IgBLAGJKhBoSCDuMdyXGkPNQD6QmkK/B/nYnoa7RUMaMl6h4eRY6il0b6HlIWbPTGYdw8bs2AIBCEQYQAxg3f8GGMC6BNkfAo0InDoaRQf/T6bQsjlM037TybnTjfaKogX6b+lJKLEplCG0KXTe8juSMYeN2bEFAgNCAAOIAax7q2MA6xJkfwhUJTChdQr9ZhP3Eh6UGYzjNH1kl45WNDM5PcmCZTKCetlPbAgVL3c6jf0GlLlzq34a6kMAAj1IAAOIAax722IA6xJkfwjMJAGvY+jlaWwM3VNoc3hou/SD5BnEZue6ZGEUjWxIJqR4UoqN4WRe5fMXNdubbRCAQA8RwABiAOverhjAugTZHwLtIpA1h34Nno1hHMscjqrnsOgNKNnPtmhlaghlBm0MR/Qe5eVpetk6rXHIUjZZXKQh0M0EMIAYwLr3JwawLkH2h0A3EDh3JoqO7E56D20K3Ytogzj6fJI+1WSmcvz550TRkjWJKbQx9CzlEWmZ0nGsNG9H6YaW5jNAICaAAcQA1v2vgAGsS5D9IdALBPze5GAGD8sU+hnEWGn6zMnpr2J4RWIM3VtogxjHTqdatIpnEKenSA0IzAgBDCAGsO6NhAGsS5D9IdDrBLyUjd9+YoM4aQxtEDWs7Ekpjhstgp299rnzomjp2sQQLr0yk1ZZnFeZTSQTVbLUSEOgJQIYQAxgSzdOZicMYAYGSQhAoICADaKHkG0GPcwcK03bHHqBbK95eH6iYOdc0ZDepezZysEgLlV6iQ1iJl6soWjeuZwDRxYCFxPAAOpr4mIk5CAAAQhAYEYJeN1Bv9LOWnND8aHPnU1MoM2gDWIcK+04pE/oFXte/zDuaVRvY7PgCSt+JtFmcVIhr7eruMx1eJtKM4psg0BfE8AA9nXzcnEQgEBPEBjSV7Eni1iNwlmZv+N7ZQhfTI2hY/UcHnMc0spPaELLiZcS7X2i0dE0/qM1D4NRdK/hEhlDx4v1LKLNY0j7dXzztEQOAQIQ6CsCGMC+ak4uBgIQ6FsCHtb1DGOrUZjQMPLYocQQHpNZ9NDypPTKvTitcvcmesj5uMqs6LFGR0zKvYC2jaHN4GL1HDq2eYzzKo/TacxyOM1ZshUCXUJAYxOEGgR4BrAGPHaFAAQ6RMBDzicPyBDaJEruWTyWmkEbwrhMJtHlzV67V/TxF8os2hB6VrPNYpxW7AksIR3HemfzQg2LM6mliCJls0yAZwB5BnCWbzEODwEIQKALCXjIOX5GUEO9zUKYwHLcZjAYRKXdg3hcw8wuC2kPO3v42RNeLL+FZbowV5/DxnBYZnBRiJV23u9tXhTSNo9KX7o8iobmTXdUtkMAAiUIMARcAhJVIAABCAwkgewElpXXNkdgszh2OHn20GbQpvGEehnD84iTscukcZnECfVEBmPZ/OgXtrqHMTaNNoypbAxD2sbxUinE3sas6Av8SEEgJYAB5FaAAAQgAIH6BGwWbbqslZumP97Z8WT9xNgYyhB6LUUbQw9Nx7Hyk2VK21xG6ZI67mH0+53LhvlLkt7DYZnBSXOYpm0QL5JnbKvMw9MYx7KEqdeDBDCAPdhofGQIQAACPU/Ak0W88LVVJkyckwkcTUyhjWEsG0ZNevHEF8exbBbTdDCNXojbOqIFuquEeYtkBjOGMCznY3PotONsOi5TD6V7KZkMU4U0dTtAAAPYAeicEgIQgAAEKhLwmoV+TtAqGzwr+tRo0nsYG0X1IgZz6PKiMptM9zC6t/HMiURei7FquOTSxAjaDAbZIC5YeiEflyvvWdYL0/J4u9LzhrVUD/M0q2KnfnkCGMDyrKgJAQhAAAK9RMAzjMOw9Ipryn9y9zaOH02Mow2hexJjI5lLhzLHNo1jkp9tdDg7pucbLc2kbiXMkeG1KQyG0PFFaQ1rh+3xNuUXZOX6yjOM3Qr9gdgHAzgQzcxFQgACEIBAaQLubQzPBZbeKa04aR5lCm0ibQyDbCbjsly5TeOptMzbvUbjeQ95u8dSqhOGNNQeG8PFSeznIUN+fihL4wWKXRaXh1j1Q55eyTot0XX7YgC7rkn4QBCAAAQg0LME6phHX7RnU58+LqOoZxZtCoNhDCbR5S7Lbo/LXB62aX8PXzuc82Qb60CSr/WvhqSDGZyv5yODWYzTzoeyfFrD2XFdldtExmnHzktelojQdgJQbztyTggBCEAAAhBoQMDP/YWh3LITZIoOFfdEBlOoODaVNo6pubRZDEYzxN4W0nGc5k/bTMqYWmFCTdE5Wy0b0ltughmcL2MYm8RgFp13Ws9UxtuUDnXieml9pyfzqhvn05h3Xhe2DAawEAuFEIAABCAAgR4mEPdEjiSzletehifT+JnGYBBtDm0KY9lQZoziZLm322SeTOq5R3Jym8u0j4e5Hfy2mTGr5nB3crSp/3oY3AYyawrPsqA4BnDqrUIJBCAAAQhAAAKBgCfThGHeSO+BnongoW4bv2AKz6Sm0IYxTsswOj4j4+k6DctUx+Y03k9xvE+6X9xrqQ/rYXDLk3VCGHeP5mAHDOBgtz9XDwEIQAACEGg/AQ91e61EyzO1ZzrYYJ49lTGQMoc2ijaUNomHD0bR3b8w02ftqeNhAHuqufiwEIAABCAAAQhMS8AGMx721dBvkcE8quchBzyoX5cAAQhAAAIQgAAEIDBIBDCAg9TaXCsEIAABCEAAAhAQAQwgtwEEIAABCEAAAhAYMAIYwAFrcC4XAhCAAAQgAAEIYAC5ByAAAQhAAAIQgMCAEcAADliDc7kQgAAEIAABCEAAA8g9AAEIQAACEIAABAaMAAZwwBqcy4UABCAAAQhAAAIYQO4BCEAAAhCAAAQgMGAEMIAD1uBcLgQgAAEIQAACEOgXA7hcTflZ6Ugqp0ekMkHvi4kelPxm6LeX2YE6EIAABCAAAQhAoJcJ9IsB/Ec1wk3SW1M5bRNYJnxYlWz+CBCAAAQgAAEIQGAgCFzSB1d5va7Bxu/10qPp9dyu+GFpk/RsWlYU3ajC35JeK+0pqkAZBCAAAQhAAAIQ6DcC/WAA36BG8dBvMH9uo0fSslsUNzKAw9r2eelD0l6pTFigSlYIS5w4evRoyBNDAAIQgAAEINDlBPjdjqJ+MIBrdJ/tL7jXXOZtjcJfaMO3pX9qVKGg/A6V3ZkvX79+fb6IPAQgAAEIQAAC3U/gMn3EgezF6WYDuFWNMsVs5e4lD906FD3D58kdReWuv0V6i/RqZyqEu1T3nkx99wDultZJxzLlJNtPgLZoP/NGZ6QtGpHpTDnt0RnuRWelLYqodKYstMWhzpy+82ftZgP4SeH5wjSIdmj7q6TVBfVWqmxfQbmLbP6ukUadyYQvKf0taXOmLJscV8bKB5u/gfwLIg+iC/K0RRc0QvoRaIvuaQt/Etqje9qDtuietuCT9DABTwJxT9/rMtdwc1q2KVOWTXpo+JU5+Ri/KV0tlQ1LVdH7OSZ0lgBt0Vn+2bPTFlkanU/THp1vg/AJaItAovMxbdH5NpiRT+B1/B6TPBPYelz6shTClUo8I2VNYtgWYhu5t4dMyZgbqCSoNlSjLdoAueQpaIuSoNpUjfZoE+gSp6EtSkBqUxXaok2gZ/s0fojzPsnDsJbTI1IIG5WwwdssNQqtGEDPCN4qZWcGNzo+5bNLgLaYXb5Vjk5bVKE1+3Vpj9lnXPYMtEVZUrNfj7aYfcacAQIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAKzT+CDOsV26ZT0XeknpGbhXdr4lOQFox2/QyLMDIEqbXG7TulFvQ+n+lfFzZYB0mZCBQJV2iJ72Pco4xn392cLSdciULUtvELCp6Q9kr/XnpbeJhFmhkDV9viwTvusNCbtkvya0oUSoR6BN2p3Lwf3olR2lY83qa5/5/3/4gfSByTCgBK4Tdd9Wvo1yQtOf1w6Ll0lFYU3qPCsdId0XRqfUXyzRKhHoGpbfE6n8xfxTZLb4u+kUclrQhLqEajaFuFsG5TYLX1Tuj8UEtciULUt5uts35G+Iv2Y5Db5celGiVCfQNX2+CWd0mbjvdJG6VbJhsUmkFCPwE9r9z+R3imVMYB+CcQJyb/z/r33775//92pQxhAAo/qmv86d91PK39Xrixkv6jEgyGTxv+s+PO5MrLVCVRti/wZhlTgNSLfl99AvjKBVtrC/P9N+lVpm4QBFIQZCFXbwj0az0nzZuDcHGIqgart4Veefj13mD9X/lu5MrL1CJQxgH+mU/j3PRs+rczD2YJ+Ss/tp4uZ4WvxX8o/Kn0td1znb8mVhax7APP1v9qkftiPuDmBVtoif8RhFfhH71B+A/lKBFptiz/QWV6SPlPpbFRuRqCVttiiA/oHzUPA+6QnpY9KNuiEegRaaQ//UeTfmfB4ysuU9nC8e2gJ7SXQ6Pf7NfoYffkH0yXt5dtTZ7tcn9Zfiv6SzAbn12QLMmmXV6mf2ZVkEwKttEX+cHer4AXJzwISWifQSlt4qNE9fze1flr2LCDQSlvYYLxF+pxko/EKyWbQvwV/JBFaJ9BKe3xBp1sp2QjOkdwOHnXy9xWhvQQa/X67Tdy2e9r7cWb/bL4wQnMC7jrOBv8nzZdlt+e3TVc/uy/p5gRaZfu7OuwvSpulUxKhPoGybbFEp7pPul06UP+0HKGAQNm28K5zpf3S+6Vzkh94Xyv9joQBFIQZCFXaY7PO9/vSB6VHpZdLfynZbPyxRGgvgaK28yfIl7f3U83S2TCAjcH6x8pfkPnevlUqy/fyhaPsrVg/7EfcnEArbRGO+NtKeIjrJ6XHQyFxywSqtsU1OtNGybPxQrAJcfCEqU3Sc84QKhOo2hY+gY3FGcnfbSH4uSd/z3kI83QoJK5MoJX2sMn7rPS36dmeULxIulf6U2lCIrSHQKPfb39PHWzPR2jvWcIXcXvP2htn8xeh/zr+qdzHdf7bubKQfViJfP1bm9QP+xE3J9BKW/iI7tX4mPRW6T8lQn0CVdviGZ3yBsnDv0EPKP2NNL9LMaE1AlXbwmf5d8m9TNnv/muVtzH08QitE2ilPYZ1urzJszn3yJFFaB+BRr/f/u3wH02EASNwm67X/6l/Rbpe8tT849IGyeEfpLviVPLPLYr818LvSdelsW+cmyVCPQJV28LDvuPSuyT3bgQtVppQj0DVtsifbZsKmAWcp9JavmpbrNdpjkl/Jdn4/YzkEQ0PQxLqE6jaHlt1Sq9O8B7paskdCN+XvigR6hHwd334o9NDuB9J81elh/Vvt3/DQzD/E9I9kn/v/bvv33//hhAGlICfzdgh2Uy4R/CNUggPKbEtZNL43Yrd6+Eb52npnRJhZghUaYsdOqX/0+e1VWWE+gSqtEX+bNtUgAHMU2k9X7UtPNvxEemU9Jz0UWlIIswMgSrt4cew7pRs+sakndKnpBGJUI/AZu2e//53fpvksE16SMqGNynzPcm/99ulD0gECEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAQEcJ/D8iDKpVXTXs+AAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x15103c2dd8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.ylim([-0.4,1])\n",
    "plt.xlim([0,1])\n",
    "\n",
    "x= np.linspace(0,1,101)\n",
    "\n",
    "for i in range(P+1):\n",
    "    plt.plot(x,(-1)**i*sol_ch[:,i],label=i)\n",
    "#    plt.plot(x,sol_ch[:,i],label=i)\n",
    "\n",
    "plt.plot(x, y_determ_ch(x), color='r', linestyle='-.',label='Deterministic')\n",
    "plt.legend(prop={'size': 8})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error plot\n",
    "$$\n",
    "\\bar{y}_{exact}(t) = \\hat{y_0} e^{-\\lambda+\\lambda e^{-t}} \\ \\ \\ \\ \\ \\ \\ \\ \\bar{y}(t) = y_0\n",
    "$$\n",
    "So \n",
    "$$\n",
    "\\epsilon_{mean}(t) = \\left| \\frac{\\bar{y}(t) - \\bar{y}_{exact}(t)}{\\bar{y}_{exact}(t)}\\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\sigma_{exact}(t) = \\hat{y_0}^2 e^{-\\lambda +\\lambda e^{-2t}} -\\hat{y_0}^2 e^{-2\\lambda +2\\lambda e^{-t}} \\ \\ \\ \\ \\ \\ \\ \\ \\sigma(t) = a_1y_1^2 +a_2y_2^2+a_3y_3^2+a_4y_4^2\n",
    "$$\n",
    "The coefficients $(a_1, a_2, a_3, a_4)$ in $\\sigma(t)$ can be obtained by code below.\n",
    "\n",
    "So\n",
    "$$\n",
    "\\epsilon_{variance}(t) = \\left| \\frac{\\sigma(t) - \\sigma_{exact}(t)}{\\sigma_{exact}(t)} \\right|= \\ldots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red>This is $\\lambda=1$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_1 = 1 #value of lambda\n",
    "allcoeff_534_1 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_534_1[0,:]=a_1*np.ones(4)\n",
    "allcoeff_534_1[1,:]=-1*a_1*np.ones(4)\n",
    "y_534_1 = np.zeros((5,4))   #row 0 stores y0 for each P from 1-4; row 1 stores y1 for P from 1-4;...\n",
    "#h = unif_icdf([-1,1])                          #index k follows uniform distr\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_ch = allcoeff_534_1[:,i]\n",
    "    y_mid=odeint(ode_system_ch, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, a_1))[1,:]\n",
    "    y_534_1[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`expect(func, args=(mu,), loc=0, lb=None, ub=None, conditional=False)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "2.0\n",
      "6.0\n",
      "24.000000000000004\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Char((n,1))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    print(poisson.expect(g(i), args=(1,), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "############# lambda = 1 ################ \n",
    "a_1 = 1\n",
    "\n",
    "mean_534_1 = y_534_1[0,:]\n",
    "mean_exact_534_1 = np.e**(-a_1+a_1*np.e**(-1))\n",
    "error_mean_534_1=np.abs((mean_534_1 - mean_exact_534_1)/mean_exact_534_1)\n",
    "\n",
    "\n",
    "sigma2_534_1=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_534_1[i]=y_534_1[1,i]**2+2*y_534_1[2,i]**2+6*y_534_1[3,i]**2+24*y_534_1[4,i]**2\n",
    "    \n",
    "sigma2_exact_534_1 = np.e**(-a_1+a_1*np.e**(-2))-np.e**(-2*a_1+2*a_1*np.e**(-1))\n",
    "\n",
    "error_var_534_1=np.abs((sigma2_534_1-sigma2_exact_534_1)/sigma2_exact_534_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color = red>This is $\\lambda=2$\n",
    "$\\downarrow$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_2 = 2 #value of lambda\n",
    "allcoeff_534_2 = np.zeros((5,4))   #store ki value/ column 0 stores ki when P=1; column 1 stores ki when P=2\n",
    "allcoeff_534_2[0,:]=a_2*np.ones(4)\n",
    "allcoeff_534_2[1,:]=-1*a_2*np.ones(4)\n",
    "y_534_2 = np.zeros((5,4))   #row 0 stores y0 for each P from 1-4; row 1 stores y1 for P from 1-4;...\n",
    "#h = unif_icdf([-1,1])                          #index k follows uniform distr\n",
    "\n",
    "for i in range(4):\n",
    "    P=i+1\n",
    "    ki_ch = allcoeff_534_2[:,i]\n",
    "    y_mid=odeint(ode_system_ch, [1.0]+[0.0]*P, np.linspace(0,1,2), args=(P, a_2))[1,:]\n",
    "    y_534_2[:,i] = y_mid.tolist()+[0]*(4-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.49999999999999994\n",
      "0.4999999999999999\n",
      "0.7499999999999998\n",
      "1.4999999999999996\n"
     ]
    }
   ],
   "source": [
    "def g(params):\n",
    "    n = params\n",
    "    return lambda u: (Char((n,2))(u))**2\n",
    "\n",
    "for i in range(1,5):\n",
    "    print(poisson.expect(g(i), args=(2,), loc=0, lb=None, ub=None, conditional=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "############# lambda = 2 ################ \n",
    "a_2 = 2\n",
    "\n",
    "mean_534_2 = y_534_2[0,:]\n",
    "mean_exact_534_2 = np.e**(-a_2+a_2*np.e**(-1))\n",
    "error_mean_534_2=np.abs((mean_534_2 - mean_exact_534_2)/mean_exact_534_2)\n",
    "\n",
    "\n",
    "sigma2_534_2=np.zeros(4)\n",
    "for i in range(4):\n",
    "    sigma2_534_2[i]=0.5*y_534_2[1,i]**2+0.5*y_534_2[2,i]**2+0.75*y_534_2[3,i]**2+1.5*y_534_2[4,i]**2\n",
    "    \n",
    "sigma2_exact_534_2 = np.e**(-a_2+a_2*np.e**(-2))-np.e**(-2*a_2+2*a_2*np.e**(-1))\n",
    "\n",
    "error_var_534_2=np.abs((sigma2_534_2-sigma2_exact_534_2)/sigma2_exact_534_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color = red> The error of mean plots when $\\lambda=2$ is a little different "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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 overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    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"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a11db5f98>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlim([0,5])\n",
    "plt.semilogy([1,2,3,4],error_mean_534_1,'-bs',label='mean($\\lambda=1$)')\n",
    "plt.semilogy([1,2,3,4],error_var_534_1,'-rs',label='variance($\\lambda=1$)')\n",
    "plt.semilogy([1,2,3,4],error_mean_534_2,'-.b^',label='mean($\\lambda=2$)')\n",
    "plt.semilogy([1,2,3,4],error_var_534_2,'-.r^',label='variance($\\lambda=2$)')\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}