lab-1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning and Decision Making"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Laboratory 1: Introduction to scientific computation with Python\n",
    "\n",
    "In the end of the lab, you should submit all code written in the tasks marked as \"Activity n. XXX\", together with the corresponding outputs and any replies to specific questions posed to the e-mail <adi.tecnico@gmail.com>. Make sure that the subject is of the form [&lt;group n.&gt;] LAB &lt;lab n.&gt;.\n",
    "\n",
    "### 1. Basic interaction\n",
    "\n",
    "When you are programming in a Jupyter notebook such as this, you will observe blocks of text preceeded by `In [ ]:` and `Out [ ]:`. These are blocks where you can insert Python code (the \"In\" blocks), and whose result you can observe as you press \"Shift+Enter\" (in the \"Out\" blocks).\n",
    "\n",
    "For example, try that in the block below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, world!\n"
     ]
    }
   ],
   "source": [
    "s = \"Hello, world!\"\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since you are programming in Python, all your standard primitives are available. You can use conditionals, cycles, inputs and outputs, etc. You also have available all standard Python modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 radians correspond to 0.0 degrees.\n",
      "0.5 radians correspond to 14.32394487827058 degrees.\n",
      "1.0 radians correspond to 28.64788975654116 degrees.\n",
      "1.5 radians correspond to 42.97183463481174 degrees.\n",
      "2.0 radians correspond to 57.29577951308232 degrees.\n",
      "2.5 radians correspond to 71.6197243913529 degrees.\n",
      "3.0 radians correspond to 85.94366926962348 degrees.\n",
      "3.5 radians correspond to 100.26761414789407 degrees.\n",
      "4.0 radians correspond to 114.59155902616465 degrees.\n",
      "4.5 radians correspond to 128.91550390443524 degrees.\n",
      "5.0 radians correspond to 143.2394487827058 degrees.\n",
      "5.5 radians correspond to 157.5633936609764 degrees.\n",
      "6.0 radians correspond to 171.88733853924697 degrees.\n",
      "Please insert a number:\n",
      ">> 2\n",
      "Next square root: 1.4142135623730951\n",
      "Next square root: 1.189207115002721\n",
      "Next square root: 1.0905077326652577\n",
      "Next square root: 1.0442737824274138\n",
      "Next square root: 1.0218971486541166\n",
      "1.0218971486541166 is larger than 1.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "a = 0\n",
    "\n",
    "# Print a radian --> degree conversion table\n",
    "while a < 2 * math.pi: \n",
    "    print(a, \"radians correspond to\", a * 90 / math.pi, \"degrees.\")\n",
    "    a = a + 0.5\n",
    "\n",
    "a = input(\"Please insert a number:\\n>> \")\n",
    "\n",
    "for i in range(5):\n",
    "    a = math.sqrt(float(a))\n",
    "    print(\"Next square root:\", a)\n",
    "\n",
    "if a > 1:\n",
    "    print(a, \"is larger than 1.\") \n",
    "else: \n",
    "    print(a, \"is smaller than or equal to 1.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One important aspect that you should keep in mind is that a notebook such as this one essentially corresponds to a single Python file---and the same scope rules apply as in any other Python file. In particular, if you define a variable in a certain \"In\" block, that same variable will be accessible in successive blocks. Just make sure that you **run** the \"In\" blocks in sequence (by pressing Shift+Enter in each block)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variable s is accessible here: Hello, world!\n"
     ]
    }
   ],
   "source": [
    "print(\"The variable s is accessible here:\", s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Matrices\n",
    "\n",
    "In your scientific computation you will use three main python libraries: **numpy**, **scipy** and **matplotlib**. The first contains a large collection of numeric types and functions, particularly for matrix manipulation. The second contains a large number of scientific computation utilities (such as optimization sub-modules, etc.). Finally, the third includes plotting functionalities. \n",
    "\n",
    "Your work in these labs will involve some level of data manipulation which is done, essentially, in the form of matrix manipulation. In particular, you will use the vast number of matrix manipulation operations offered by **numpy** that, if used proficiently, render computations significantly faster.\n",
    "\n",
    "Matrices in **numpy** are represented by the type `numpy.array`. The array is initialized as a list of lists, each corresponding to a row of the matrix. There are also several commands to create particular\n",
    "matrices, such as the identity (`eye`), an all-zeros matrix (`zeros`) or an all-ones matrix (`ones`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 x 3 array of numbers:\n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "3 x 3 identity:\n",
      "[[ 1.  0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0.  0.  1.]]\n",
      "2 x 3 array of zeros:\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "4 x 1 array of ones:\n",
      "[ 1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "A1 = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "print(\"2 x 3 array of numbers:\")\n",
    "print(A1)\n",
    "\n",
    "A2 = np.eye(3)\n",
    "print(\"3 x 3 identity:\")\n",
    "print(A2)\n",
    "\n",
    "A3 = np.zeros((2, 3))\n",
    "print(\"2 x 3 array of zeros:\")\n",
    "print(A3)\n",
    "\n",
    "A4 = np.ones(4);\n",
    "print(\"4 x 1 array of ones:\")\n",
    "print(A4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now easily perform standard algebraic operations, such as matrix sum or products. You can also perform indexing, slicing, and other operations, as illustrated in the following examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 x 3 matrix:\n",
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "Vector with all numbers between 1 and 3:\n",
      "[1 2 3]\n",
      "Diagonal matrix built from the vector B:\n",
      "[[1 0 0]\n",
      " [0 2 0]\n",
      " [0 0 3]]\n",
      "A + I:\n",
      "[[  2.   2.   3.]\n",
      " [  4.   6.   6.]\n",
      " [  7.   8.  10.]]\n",
      "A * B':\n",
      "[14 32 50]\n",
      "inv(D):\n",
      "[[ -6.00000000e+00  -2.00000000e+00   3.00000000e+00]\n",
      " [ -1.00000000e+00   5.00000000e-01   2.22044605e-17]\n",
      " [  5.00000000e+00   1.00000000e+00  -2.00000000e+00]]\n",
      "Append matrix A to vector [1, 2, 3]:\n",
      "[1 2 3 1 2 3 4 5 6 7 8 9]\n",
      "Append [10, 11, 12] to A:\n",
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n",
      "Append [[4], [7], [10]] to A:\n",
      "[[ 1  2  3  4]\n",
      " [ 4  5  6  7]\n",
      " [ 7  8  9 10]]\n",
      "A[0]: [1 2 3]\n",
      "A[1]: [4 5 6]\n",
      "A[1, 2]: 6\n",
      "A[0][2]: 3\n",
      "A[1:2,0:1]: [[4]]\n",
      "A[:-2,::2]: [[1 2 3]]\n",
      "Vector with numbers between 10 and 1:\n",
      "[10  9  8  7  6  5  4  3  2]\n",
      "I[[3, 3, 1, 8]]: [7 7 9 2]\n",
      "I[np.array([3, 3, -3, 8])]: [7 7 4 2]\n",
      "I[np.array([[1, 1], [2, 3]])]: [[9 9]\n",
      " [8 7]]\n"
     ]
    }
   ],
   "source": [
    "# = Matrix creation = #\n",
    "\n",
    "A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "print(\"3 x 3 matrix:\")\n",
    "print(A)\n",
    "\n",
    "B = np.arange(1,4)\n",
    "print(\"Vector with all numbers between 1 and 3:\")\n",
    "print(B)\n",
    "\n",
    "C = np.diag(B)\n",
    "print(\"Diagonal matrix built from the vector B:\")\n",
    "print(C)\n",
    "\n",
    "# = Matrix operations = #\n",
    "\n",
    "# Sum\n",
    "D = A + np.eye(3)\n",
    "print(\"A + I:\")\n",
    "print(D)\n",
    "\n",
    "# Vector transpose and regular matrix product\n",
    "E = np.dot(A, B.T)\n",
    "print(\"A * B':\")\n",
    "print(E)\n",
    "\n",
    "# Matrix inverse\n",
    "F = np.linalg.inv(D)\n",
    "print(\"inv(D):\")\n",
    "print(F)\n",
    "\n",
    "# = Matrix concatenation = #\n",
    "\n",
    "G = np.append([1, 2, 3], A)\n",
    "print(\"Append matrix A to vector [1, 2, 3]:\")\n",
    "print(G)\n",
    "\n",
    "# When the axis to append is specified, the \n",
    "# matrices/vectors must have the correct shape\n",
    "\n",
    "H1 = np.append(A, [[10, 11, 12]], axis = 0)\n",
    "H2 = np.append(A, [[4], [7], [10]], axis = 1)\n",
    "print(\"Append [10, 11, 12] to A:\")\n",
    "print(H1)\n",
    "\n",
    "print(\"Append [[4], [7], [10]] to A:\")\n",
    "print(H2)\n",
    "\n",
    "# = Matrix indexing = #\n",
    "\n",
    "# Simple indexing\n",
    "print(\"A[0]:\", A[0])\n",
    "print(\"A[1]:\", A[1])\n",
    "print(\"A[1, 2]:\", A[1, 2])  # More efficient\n",
    "print(\"A[0][2]:\", A[0][2])  # Less efficient\n",
    "\n",
    "# -- Slicing\n",
    "\n",
    "# Rows between 1 and 2 (excluding the latter), \n",
    "# columns between 0 and 1 (excluding the latter)\n",
    "print(\"A[1:2,0:1]:\", A[1:2,0:1])\n",
    "\n",
    "# All rows except the last two,\n",
    "# every other column\n",
    "print(\"A[:-2,::2]:\", A[:-2][::2]) \n",
    "\n",
    "I = np.arange(10, 1, -1)\n",
    "print(\"Vector with numbers between 10 and 1:\")\n",
    "print(I)\n",
    "\n",
    "# -- Matrices as indices\n",
    "\n",
    "# Indexing with a list\n",
    "print(\"I[[3, 3, 1, 8]]:\", I[np.array([3, 3, 1, 8])])\n",
    "\n",
    "# Indexing with an nparray\n",
    "print(\"I[np.array([3, 3, -3, 8])]:\", I[np.array([3, 3, -3, 8])])\n",
    "\n",
    "# Indexing with an npmatrix\n",
    "print(\"I[np.array([[1, 1], [2, 3]])]:\", I[np.array([[1, 1], [2, 3]])]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several observations are in order:\n",
    "\n",
    "* The function `diag` can be used to build a diagonal matrix from a vector or extract a diagonal from a matrix. You can know more about this (and other) functions in numpy in the corresponding documentation or by using the help function. For example, to know more about the `diag` function, you can type `help(\"numpy.diag\")` in the Python prompt, to get something like:\n",
    "\n",
    "```\n",
    ">>> help(\"numpy.diag\")\n",
    "Help on function diag in numpy:\n",
    "\n",
    "numpy.diag = diag(v, k=0)\n",
    "    Extract a diagonal or construct a diagonal array.\n",
    "    \n",
    "    See the more detailed documentation for ``numpy.diagonal`` if you use this\n",
    "    function to extract a diagonal and wish to write to the resulting array;\n",
    "    whether it returns a copy or a view depends on what version of numpy you\n",
    "    are using.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    v : array_like\n",
    "        If `v` is a 2-D array, return a copy of its `k`-th diagonal.\n",
    "        If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th\n",
    "        diagonal.\n",
    "    k : int, optional\n",
    "        Diagonal in question. The default is 0. Use `k>0` for diagonals\n",
    "        above the main diagonal, and `k<0` for diagonals below the main\n",
    "        diagonal.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    out : ndarray\n",
    "        The extracted diagonal or constructed diagonal array.\n",
    "    \n",
    "    See Also\n",
    "    --------\n",
    "    diagonal : Return specified diagonals.\n",
    "    diagflat : Create a 2-D array with the flattened input as a diagonal.\n",
    "    trace : Sum along diagonals.\n",
    "    triu : Upper triangle of an array.\n",
    "    tril : Lower triangle of an array.\n",
    "    \n",
    "    Examples\n",
    "    --------\n",
    "    >>> x = np.arange(9).reshape((3,3))\n",
    "    >>> x\n",
    "    array([[0, 1, 2],\n",
    "           [3, 4, 5],\n",
    "           [6, 7, 8]])\n",
    "    \n",
    "    >>> np.diag(x)\n",
    "    array([0, 4, 8])\n",
    "    >>> np.diag(x, k=1)\n",
    "    array([1, 5])\n",
    "    >>> np.diag(x, k=-1)\n",
    "    array([3, 7])\n",
    "    \n",
    "    >>> np.diag(np.diag(x))\n",
    "    array([[0, 0, 0],\n",
    "           [0, 4, 0],\n",
    "           [0, 0, 8]])\n",
    "```\n",
    "\n",
    "* You can add, multiply, transpose, invert matrices much as you would in linear algebra\n",
    "* Indexing and slicing are quite powerful operations. For example, you can use a matrix to index another.\n",
    "\n",
    "The ability to leverage the powerful indexing and vectorization capabilities of **numpy** is key to producing efficient code. It takes some time to get used to this programming philosophy, but once you do, you will notice a significant improvement in the performance of your code. The impact of good vectorization in the efficiency of your code is illustrated in the following example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computation time with cycle (in seconds): 0.6074526309967041\n",
      "Computation time with numpy operation (in seconds): 0.003503084182739258\n"
     ]
    }
   ],
   "source": [
    "import numpy.random as rnd\n",
    "import time\n",
    "\n",
    "A = rnd.rand(1000,1000)\n",
    "B = rnd.rand(1000,1000);\n",
    "C = np.zeros((1000,1000));\n",
    "\n",
    "t = time.time()\n",
    "\n",
    "for i in range(A.shape[0]):\n",
    "    for j in range(A.shape[1]):\n",
    "        C[i, j] = A[i, j] + B[i, j]\n",
    "    \n",
    "t1 = time.time() - t\n",
    "\n",
    "t = time.time()\n",
    "C = A + B;\n",
    "t2 = time.time() - t\n",
    "\n",
    "print(\"Computation time with cycle (in seconds):\", t1)\n",
    "print(\"Computation time with numpy operation (in seconds):\", t2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Besides illustrating the importance of optimizing your code to take full advantage of its matrix manipulation capabilities, the previous example introduces several additional elements of the **numpy** syntax, such as:\n",
    "\n",
    "* The `rand` function from the **numpy.random** module\n",
    "* The `shape` attribute"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Activity 1.        \n",
    "\n",
    "Compare the time necessary to compute the cumulative sum of a 10,000 &times; 1 random vector using:\n",
    "\n",
    "* a for loop;\n",
    "* a vectorized operation.\n",
    "\n",
    "For the latter, you may find useful the function `cumsum`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computation time with cycle (in seconds): 0.012007474899291992\n",
      "Computation time with numpy operation (in seconds): 0.0\n"
     ]
    }
   ],
   "source": [
    "import numpy.random as rnd\n",
    "import time\n",
    "\n",
    "vetor = rnd.rand(10000,1)\n",
    "soma = np.zeros(10000);\n",
    "\n",
    "t = time.time()\n",
    "\n",
    "soma[0] = vetor[0,0]\n",
    "for i in range(1,vetor.shape[0]):\n",
    "    for j in range(vetor.shape[1]):\n",
    "        soma[i] = soma[i-1] + vetor[i, j]\n",
    "    \n",
    "t1 = time.time() - t\n",
    "\n",
    "t = time.time()\n",
    "soma = np.cumsum(vetor)\n",
    "t2 = time.time() - t\n",
    "\n",
    "print(\"Computation time with cycle (in seconds):\", t1)\n",
    "print(\"Computation time with numpy operation (in seconds):\", t2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Activity 2.\n",
    "\n",
    "Compute in 20 &times; 1 vector $y$ where the $n$th entry is given by:\n",
    "\n",
    "$$ y_n=\\prod_{i=1}^n\\sum_{j=1}^ij^3 $$\n",
    "\n",
    "You should use no cycles in your computation.\n",
    "\n",
    "**Suggestion**: Check the numpy function `cumprod`.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Insert your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Plotting\n",
    "\n",
    "The Python module **matplotlib** offers a number of plotting routines that are ideal to display scientific data. The following generates 100 perturbed samples from the function\n",
    "\n",
    "$$f(x) = 2x$$\n",
    "\n",
    "and uses these samples to estimate the function $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "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",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var 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",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py:3316: MatplotlibDeprecationWarning: The 'hold' keyword argument is deprecated since 2.0.\n",
      "  mplDeprecation)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create data\n",
    "x = 100 * rnd.rand(100, 1)\n",
    "y = 2 * x + 10 * rnd.randn(100, 1)\n",
    "\n",
    "# Estimate linear relation between X and Y\n",
    "\n",
    "X = np.append(x, np.ones((100,1)), axis = 1)\n",
    "\n",
    "f_est = np.dot(np.linalg.pinv(X), y)\n",
    "y_est = np.dot(X, f_est)\n",
    "\n",
    "# Plot commands\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y_est, hold = True)\n",
    "plt.plot(x, y, 'x')\n",
    "\n",
    "plt.xlabel('Input X');\n",
    "plt.ylabel('Output Y');\n",
    "\n",
    "plt.title('Linear regression');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider more carefully the piece of code above, where we included line numbers for easier reference.\n",
    "\n",
    "* On lines 5 and 6, the vectors *x* and *y* are created, using mostly functionalities that you already encountered in Sections 1 and 2. The novelty is the function `randn` which is similar to the function `rand` except on their underlying distribution: while `rand` generates random numbers uniformly from the interval [0, 1], `randn` generates normally distributed random numbers with mean 0 and a standard deviation of 1.\n",
    "\n",
    "* Lines 10-13 estimate a linear relation between *x* and *y* using the data already created. Do not worry about the actual computations, and simply observe the use of matrix concatenation in line 10, and the `pinv` function in line 12. The function `pinv` computes the Moore-Penrose pseudo-inverse of a matrix (see [https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse])\n",
    "\n",
    "* Lines 17 through 24 contain the actual plotting commands. In particular:\n",
    "\n",
    "  * The figure command in line 17 creates a new figure.\n",
    "\n",
    "  * The plot command in line 18 is responsible for displaying the continuous line in the plot. In here, it is used with its most basic syntax. However, the plot command has a very rich syntax, and you can type `help(\"mplotlib.pyplot.plot\")` to know more about this useful function.\n",
    "  \n",
    "  * To avoid subsequent plot commands to erase the existing plot, we turn on the \"hold\" option to True in the first plot command (line 18).\n",
    "  \n",
    "  * The plot command in line 19 plots the original data. Note how the line specification 'x' indicates that, unlike the plot in line 18, this data should not be plotted continuously but instead marking each data-point with an \"&times;\".\n",
    "  \n",
    "* Finally, the commands in lines 21 to 24 are used to include additional information in the plot, such as the labels for both axis and the title for the plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Activity 3.\n",
    "\n",
    "Recall the definition of $y_n$ in Activity 2:\n",
    "\n",
    "$$ y_n=\\prod_{i=1}^n\\sum_{j=1}^ij^3 $$\n",
    "\n",
    "Plot the value of $y$ against $n$ for $n$ between 1 and 20 (inclusive) using a *linear plot* (obtained\n",
    "with the command `plot`) and a *logarithmic plot* (using the command `semilogy`). Stack both plots together using the command `subplot`, and comment on the observed differences.\n",
    "\n",
    "What would you argue to be the usefulness of semi-logarithmic plots?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Insert your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Provide your answer here]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Activity 4\n",
    "\n",
    "A hospital is conducting a study on obesity in adult men and, as part of that study, tested the age and body fat for 18 randomly selected adults, with the following results:\n",
    "\n",
    "| **Age**       |  38  |  27  |  48  |  17  |  33  |  32  |  38  |  38  |  26  |  34  |  33  |  41  |  45  |  46  |  26  |  35  |  22  |  23  | \n",
    "| -------------:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|:----:|\n",
    "| ** Body fat** | 17.1 | 20.7 | 25.2 | 13.6 | 13.4 | 19.8 | 11.7 | 17.3 | 15.6 | 20.5 | 22.4 | 20.2 | 17.5 | 22.7 |  7.5 | 27.2 |  9.2 | 16.1 |\n",
    "\n",
    "Write down the data above as two row-vectors `age` and `fat`, and replicate the procedure used to generate the plot above to estimate a linear relation between the two quantities. Plot the relation that you estimated against the real data.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "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",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var 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",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAyAAAAJYCAYAAACadoJwAAAgAElEQVR4XuzdCfxlc/3H8RfG2LNUtrIbMdbGvpQkRguVpRHGUlpIi/6lwj9ahPZdSmUdJluG0kS0EGEsI4NkJxFKtmzj//iYc/tf192/39/93Xvu6zwek8z9ns853+f3mLnv3znf850LNwUUUEABBRRQQAEFFFCgRwJz9eg4HkYBBRRQQAEFFFBAAQUUwADiRaCAAgoooIACCiiggAI9EzCA9IzaAymggAIKKKCAAgoooIABxGtAAQUUUEABBRRQQAEFeiZgAOkZtQdSQAEFFFBAAQUUUEABA4jXgAIKKKCAAgoooIACCvRMwADSM2oPpIACCiiggAIKKKCAAgYQrwEFFFBAAQUUUEABBRTomYABpGfUHkgBBRRQQAEFFFBAAQUMIF4DCiiggAIKKKCAAgoo0DMBA0jPqD2QAgoooIACCiiggAIKGEC8BhRQQAEFFFBAAQUUUKBnAgaQnlF7IAUUUEABBRRQQAEFFDCAeA0ooIACCiiggAIKKKBAzwQMID2j9kAKKKCAAgoooIACCihgAPEaUEABBRRQQAEFFFBAgZ4JGEB6Ru2BFFBAAQUUUEABBRRQwADiNaCAAgoooIACCiiggAI9EzCA9IzaAymggAIKKKCAAgoooIABxGtAAQUUUEABBRRQQAEFeiZgAOkZtQdSQAEFFFBAAQUUUEABA4jXgAIKKKCAAgoooIACCvRMwADSM2oPpIACCiiggAIKKKCAAgYQrwEFFFBAAQUUUEABBRTomYABpGfUHkgBBRRQQAEFFFBAAQUMIF4DCiiggAIKKKCAAgoo0DMBA0jPqD2QAgoooIACCiiggAIKGEC8BhRQQAEFFFBAAQUUUKBnAgaQnlF7IAUUUEABBRRQQAEFFDCAeA0ooIACCiiggAIKKKBAzwQMID2j9kAKKKCAAgoooIACCihgAPEaUEABBRRQQAEFFFBAgZ4JGEB6Ru2BFFBAAQUUUEABBRRQwADiNaCAAgoooIACCiiggAI9EzCA9IzaAymggAIKKKCAAgoooIABxGtAAQUUUEABBRRQQAEFeiZgAOkZtQdSQAEFFFBAAQUUUEABA4jXgAIKKKCAAgoooIACCvRMwADSM2oPpIACCiiggAIKKKCAAgYQrwEFFFBAAQUUUEABBRTomYABpGfUHkgBBRRQQAEFFFBAAQUMIF4DCiiggAIKKKCAAgoo0DMBA0jPqD2QAgoooIACCiiggAIKGEC8BhRQQAEFFFBAAQUUUKBnAgaQnlF7IAUUUEABBRRQQAEFFDCAeA0ooMCwCzxfALTz5+HewE+BzwGHDzuc/W8oENfGYcA+wPE6KaCAAgq8WKCdv3A1U0ABBcosYAAp8+iOTt8MIKPj7lEVUGBABAwgAzJQnqYCCoyYQCcBZFFgGeDB4teInZSFB1rgFUD8ug94ZKB74skroIACIyBgABkBVEsqoMBACXQSQAaqY56sAgoooIAC/ShgAOnHUfGcFFCglwKdBJBGc0DiOf+9gK2A2cX8kA2BqP0H4JPArAad2g74MLAR8DLgXuDnwBHAQzX7xN2XycBbgVWBVwIPA38EjgSurHOMO4AVgLmBA4B9gXHAX4D1WkBX92s+4NPAa4G4E7Q48K9i/yWKPr4dWAl4GpgBfB04r8ExdgQOAtYBngAuBj4D7NFg/kS7/VgD+BSwNbBkcY5R+wvADXXO5S3AgcD44q5FmN8GXFDM9ansEn9f7gbsV/iFwT+Am4Gzge9V1W72CNbLC8d3AMsVfb+isPp1nfOLa+hOYBXgE8B7i/F8AJgCfBZ4qpf/wXgsBRRQIFXAAJIq6P4KKDDoAjkDSHzh/ihwVfGlMb7gr1YEibWAv9dgHVV8WY4v7BEe4pGddYsvuLcCmwP3V+3zQeCY4kvv7cC/i7YRCp4B3gbUfomtfHH/YTEp+nfF+YwFIgQ02yoB5EdFcIl+xXnFl+FtiseLon8XFl+m41jXAYsAmwALFsHkqzUHCaNvFmHt94XLxsBiwLnAnnUmcLfTj/hSfxoQYela4K/FeUW4exJ4MxDHq2wfAr4LPAdcWoS/eHQqQsyrgeq/I79SBID4sh814jG8pYEY1whQK7YRQF5V7LsycBdwWREitwTmAT4OfKPGqhJA/gREWPpt8fnriiB4ShHaBv2/Q89fAQWGSMAAMkSDbVcVUKCuQM4AEnc/diruYMTB4kvl1OL34ifw8dPqyrYL8DPgz8A7iy/L8Vn8uRw/QY+2se+uVfusXXxpr/1J/kRgGnB3EUgqfYpdK1/c4wvzGxrcBWh0aVQCSHwe5xHnU71F/64B4rzibsbXivOLNnGHJsLQ8sWdluhnbPHl+8bi/8fdn7g7EdsYoBKS4t9r3yDVqh8RAOIY0ffwjFBU2eI44RMBMM4rAl9scWch7kJEQIlwVdliDCIUVL7sz1/cSYn9IiBG+Ktscd6bFne6Kr/X6A5IhKsIiXHnIvpXOY8tgOlFcNqgCE+VWpWxDLM3VoXYuNN0dRHaok8RDN0UUECBgRAwgAzEMHmSCigwggI5A0i9n0avX3y5jTsPEQAqW/yEPr7Mxpf3ypfz6i/A8eUyPoufskd4aLWdDOxePNJ0fVXjyhf3eAys9k5Eq5qVAPKL4otzbfu44xCPH50J7FynWASBs4BvF3eGoskXgUOAHxd3Vap3izsgEaIWbhJAGvUj7qjEnZV4nC3uatRu3wI+Utz1iXOOLe5c/AeIR8iabfEoV9yJijGLu02ttnoBJIJXhITHikeo4tG56i3CW9wBOQ54X9UHlesz7jhVh6po8p3isTpf99tqRPxcAQX6SsAA0lfD4ckooMAoCOQMIDEP5MSaPsTjSPGoVMy5eE3xWeUL7S3FI1r1uh1fouMRofjpffx0vLLF40Xxe/FT+5gDEo9SxRZfjGM+RdyBiS/9la0SQOLYcQ6dbJUA8oHi7kTtvt8v5kRE8Imf6tdu8ThTzJO4vLhLEJ/HHY8IYrX9quwbYSYeDWt0B6RRP2KOTTw6FY85/a3OuURAOh2Ix95irklsMT8n7j78pJiDUW+OSKVUBKN4LOvowiLmiTTa6gWQeKzsBOAMIO5+1W7xuF7cTYo5JatXfRjXZzxet0DxqFj1fhG2ItwdXMwB6mRsbauAAgqMmoABZNToPbACCvSJQM4AEhOfL6rTr8pz/JV5AhEe4pn+draYlB13VmKLOyLxKFH1fIPaGjFRPr7oVrZKAIkvsPHT/k62SgCJuRO/qrPjL4t5Fa1qxlyMmPge201FEFuzwcT8mAPxsSYBpFE/4m5GfNZqq77DEIEtJvzH40yxxV2OuFMVAS6CQswNqWzx+FPML4nQF1s8vhVt4/fOrzlovQASE/jjRQFxFyru4tRucffnn8UdkgitlS2unQg/8Shb7ebCmK1G288VUKAvBQwgfTksnpQCCvRQIGcAibdgVeYNVHehNoDEBO2YgBxzEqrvbtTrdnxhvqSYGxI/5Y+fjv+g+BU/hY9HeqL+l4qf7De6c9DNn/fVb8Gq168IJTH/JP5ZPVm+th/xCFm8wSm21ADSqB8RruLuUHX4qucZlmFa2WJ+R9yNiQnecWemEpRifOLfK/M0on28pSzmcET7+Czmj8RW+whaNwEk3qoVbxWL8awNIBF26oVOA0gP/6DwUAookE+gm7+Q8h3dSgoooMDoC4xGAIlHeeKn2jH3I+5qtLPF40URQGKydLzit3aLn8RPanLnoJs/71sFkPgiH6+Fjceb4kt4O1urR7DizkM8RtZpkIq7LPF2rnjsq/b1xe2cV6VN3JmJx8ni7kg8AhePmTXaIkjGY10xnvFq5LgjFFuzR7Ci/bvqFIz5QDHHpN4jWAaQTkbQtgoo0PcC3fyF1Ped8gQVUECBDgRGI4DE6cVbjeIVthEs2pmbsVnxqth4ZCgmd1dvsSZHfAGPydSdfnFvRtUqgETgieDTyatgK5PQ49W+7685eNwFiGAWdwA67Ue8njheUxwTuKvvcHRwKfy3aZzXscUrj/dvUaBy5ynWHvlykwBSmYT+aPE4VWUNlUr5ymt+601CN4B0M4ruo4ACfStgAOnbofHEFFCgRwKjFUBiUbv44h53QWJxwfjpd/UWC9bFZOz4oh5bTFyPdULiEZ14VWtMYI8tHiGKx44qP1Xv9It7SgCJV9DGuh+xiF+8Nji+gFcvihd/x0Rwii3W2Ygt7lLEnZxw37ZqXY54pW986Y87KrF12o94Fe3M4pGp99RMxI968XjW9sWE+HuKNUpiUcZ4aUB1GIgFG+MuTIS8yuTumH8Rc0Ditckx16SyhX3c0Yk7ITGepxYfNHoNbyzKGHdK4phx7JhcHlu8xjcWPox69V7DawBpdpX6mQIKDJyAAWTghswTVkCBzAKVANJsUnj8VDp+tbMSejtzQCpdiNXO40turB8SASRe0xp/LseX9HgEKMJGTE6ubLFORvyEPxbVi8nu8c9YkC6+vMeX2zi/Tr+4N+NsdQck9o05EzGPJSZyx+rcEQLin/EoVLzZKYJTrDQer8mtbNULEcZE7pg/EhPz4w5O9CMm3te+Wasymb7Z31uxEns8PhULIMYdobjL9HjxZqwJwELF28LCujLpO0JArNoe9eONYvF4W8ztiH+PMBCPc1XeUBXhIx6BiwATtSJcxaT0+L14m1YlfDUKIPGGrnjzVlhFqKgsRBjzSWIM/6d4G1f1mNTOH6r+zDkgmf8wsJwCCvRGwADSG2ePooAC/StQvWhfo7P8XPFcf+4AEsd7fbGWQ6x6Hl9m45W99xZ3BmK+QPXK3fElNb68x12CeKTnkWJtiFhXI4LHYaMQQKIP8ejUAcUdm3isLO6MxAT7mM8Qb+2KOwe1a5nEPI9YvDDmwMQE8riTEK/HjTdExd2B2tf0thNA4lwivMV6GrFuRgSJCBjxWt54xW283eqc4i5JnGM8ahVvLov5F8sUvx8rlMd8lngNcmWtjngkLIJftI27PbE2SwSbWJAw7mJFMKy+M9IogMT5xZ2t6GesoRLnF/tdUSziWLuKfbQ3gPTvnx2emQIKdClgAOkSzt0UUEABBbILRMCKOygxL2bZqlW/sx/IggoooIACoydgABk9e4+sgAIKDKtA3KWIR5uq517EHI2Y0B13L2LF77iD4aaAAgooUEIBA0gJB9UuKaCAAn0uEIvyxWNtMfci3noV62tUHoOKR7ViPkU8vuWmgAIKKFBCAQNICQfVLimggAJ9LhATveNOR7w9Kua9xHyMmPcSk9ljtfAIJW4KKKCAAiUVMICUdGDtlgIKKKCAAgoooIAC/ShgAOnHUfGcFFBAAQUUUEABBRQoqYABpKQDa7cUUEABBRRQQAEFFOhHAQNIP46K56SAAgoooIACCiigQEkFDCAlHVi7pYACCiiggAIKKKBAPwoYQPprVGKF3IlArPgbKwO7KaCAAgoooIACCvSXwPzAisWb+2JNI7cOBQwgHYKNcPPdgFNG+BiWV0ABBRRQQAEFFEgX2B2Ykl5m+CoYQPprzDcDLj355JNZY401+uvMPBsFFFBAAQUUUEABbrzxRvbYY4+Q2Bz4oySdCxhAOjcbyT0mxMrAM2bMYMKE+L9uCiiggAIKKKCAAv0kcPXVV7P++uvHKcX/XN1P5zYo52IA6a+RMoD013h4NgoooIACCiigwIsEDCDpF4QBJN0wZwUDSE5NaymggAIKKKCAApkFDCDpoAaQdMOcFQwgOTWtpYACCiiggAIKZBYwgKSDGkDSDXNWMIDk1LSWAgoooIACCiiQWcAAkg5qAEk3zFnBAJJT01oKKKCAAgoooEBmAQNIOqgBJN0wZwUDSE5NaymggAIKKKCAApkFDCDpoGULIBsA8WLmNwIrAY8DNwBHAhdWcR0P7NWE71DgiBa8zWosB9zTxfAYQLpAcxcFFFBAAQUUUKBXAgaQdOmyBZAzgC2BM4v3Mi8M7AOsBewPHFOQbQqsUofvo0CEmHbe61wJIBFkZtfUOgt4oovhMYB0geYuCiiggAIKKKBArwQMIOnSZQsgsSLlVcBTVTQLANcCrwSWBJ5twLYg8HfgDmCdNmgrAWTeJjXbKPOiJgaQTsVsr4ACCiiggAIK9FDAAJKOXbYA0kjka8DHgWaPRu0OnAx8Aoj2rbZKABkLRMh5rM6dkFY1aj83gHQqZnsFFFBAAQUUUKCHAgaQdOxhCSCnAjsDixdBoZ7cr4GtgFcD97dBWwkgjwKLAE8C5wMHAbe2sX+9JgaQLuHcTQEFFFBAAQUU6IWAASRdeRgCyBrFI1jnATs1IHsVcFcRIN7WJutRwBhgBvA0sBlwAPDvYh7JnS3qLAPEr+ptdeCUGTNmMGFCZBE3BRRQQAEFFFBAgX4SMICkj0bZA8iiwGXAssC6QKNQ8OniTVm7ADGRvdttuyLEnADs3aLI4cBh9doYQLrldz8FFFCgC4GZp8P4HWDMfPV3fvYpmDUN1om/ItwUUGDYBQwg6VdAmQNIzMuYDmwEvBm4uAnXLGCpIqhUT2DvRjjuiMSdjQg9zTbvgHSj6z4KKKBAToEIH2ftC+MmwqSTXhpCInxMnQy3TIcdjzOE5LS3lgIDKmAASR+4sgaQmBg+Ddi6mPtxThOqDYErgO8DH0onJV7BG49xxTl0ujkHpFMx2yuggAIpAtUBozaENPss5Zjuq4ACAy1gAEkfvjIGkJiXEY9RbQ/sGXMqWjB9twgeGxdBJFV1ZjHZPd641elmAOlUzPYKKKBAqkC9oBE1K3c+Gt0dST2u+yugwEAKGEDSh61sAWRuYAowCfggcGwLorhLcV/x1qvxDdrGOh+xaOEjRdtotlDRNlZar97iuKcVx43jd7oZQDoVs70CCiiQQ6A6hKwcL0QEbru48aNZOY5pDQUUGEgBA0j6sJUtgHwdOBD4PfCjOjwX1Lxid8di1fSYhH50A84VgduB6onl6wEXxc/HgJuLt2DF6uqxlki8TSvuprTzKt/aQxpA0q9pKyiggALdCUQImTJpTvCILYLIblMbT07v7ijupYACAy5gAEkfwLIFkN8CWzZhiR9rRZvKFnNDYr5GPC71tw4CyNLFYoUxfyQmm8ddkruBc4EjgAe7HBoDSJdw7qaAAgokCxhAkgktoMAwCBhA0ke5bAEkXWR0KxhARtffoyugwLAK+AjWsI68/VagYwEDSMdkL9nBAJJumLOCASSnprUUUECBdgSchN6Okm0UUKAQMICkXwoGkHTDnBUMIDk1raWAAgq0EvA1vK2E/FwBBWoEDCDpl4QBJN0wZwUDSE5NaymggAKtBFyIsJWQnyuggAEk+zVgAMlOmlTQAJLE584KKKBAFwIRQsbv0PhtV3GXZNY0V0HvgtZdFCijgHdA0kfVAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFCifwMzTYfwOMGa++n179imYNQ3W2WVE+m4ASWc1gKQb5qxgAMmpaS0FFFBAAQUUKJdAhI+z9oVxE2HSSS8NIRE+pk6GW6bDjseNSAgxgKRfUgaQdMOcFQwgOTWtpYACCiiggALlEqgOGLUhpNlnGRUMIOmYBpB0w5wVDCA5Na2lgAIKKKCAAuUTqBc0opeVOx+N7o5kkjCApEOWLYBsAOwBvBFYCXgcuAE4EriwimtF4PYGfD8G9m2Tdi3gy8AWRftLgIOAP7e5f20zA0iXcO6mgAIKKKCAAkMkUB1CVt5qTsdvu7jxo1kZaQwg6ZhlCyBnAFsCZwJXAwsD+wARFPYHjinIKgHkHCD2qd7+ClzeBu044ErgYeA7RfuPAIsBGwG3tFHDANIFkrsooIACCiiggAJECJkyaU7wiC2CyG5TG09Oz0RmAEmHLFsA2Ry4CniqimYB4FrglcCSwLNAJYAcARzaJWMEl+2ANYC7ixrLATcC5wPdvHrBOyBdDoa7KaCAAgoooMCQCRhABnbAyxZAGg3E14CPAxEQ7qkJIBFCYnuyg1GMOysPAacBe9XsdwIwCXh58QhYB2UxgHSiZVsFFFBAAQUUGE4BH8Ea6HEflgByKrAzsDjwWFUAif8fYSK2ePTqG8D32xjRTYE/AvsBP6hpH78XNaJNO49yVe9uAGkD3yYKKKCAAgooMMQCTkIf+MEfhgASj0jFI1jnATsVI7Y88BPgbOAuYFng/fDCHYivAp9sMbJRJx7B2gE4t6Zt/F7MLYnAE3NRGm3LAPGrelsdOGXGjBlMmBCn4qaAAgoooIACCijwXwFfw1uKi6HsAWRR4LIiYKwL3Nlk1OYBflfcuVgNuLVJ28nAicBE4Nc17bYFpgPR5uQmNQ4HDqv3uQGkFP9t2QkFFFBAAQUUyC3gQoS5RUelXpkDSEw+jyAQb6R6M1C8IqGp8/bANOADwA+btPQOyKhcrh5UAQUUUEABBYZeIELI+B0av+0q7pLMmjYiq6CHvW/BSr8CyxpAxhZBYuviUah4JKqdbR3gOuAQ4EtNdnAOSDuatlFAAQUUUEABBUomYABJH9AyBpAxxfyMuJuxZ8yp6IBpx2LeRixEGAsSNtpavQVr1+ItWDHJvZPNSeidaNlWAQUUUEABBRTosYABJB28bAFkbmBK8RrcDwLHNiCK9UAeqPksHtm6tFi0cJWqtT3mBeLfHwHuq9onJpjHHJCYOB6v9o2tsg5IPPpVmfDeySgZQDrRsq0CCiiggAIKKNBjAQNIOnjZAsjXgQOB3wM/qsNzAXB/8farWKfjoiI8xFuwYj2PlYHPAEdV7VtZtDDW99i76vdfA1xRrAfy7eL3YyX0qBvzTm7uYngMIF2guYsCCiiggAIKKNArAQNIunTZAshvgS2bsGwFRJv3FoEjQsQSxdogVwPfKuaOVJdoFECiTcwZORrYotjhEuBTwMwuh8YA0iWcuymggAIKKKCAAr0QMICkK5ctgKSLjG4FA8jo+nt0BRRQQAEFFFCgqYABJP0CMYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzjvt91AAACAASURBVAoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQUUyCxgAEkHNYCkG+asYADJqWktBRRQQAEFFFAgs4ABJB3UAJJumLOCASSnprUUUEABBRRQQIHMAgaQdFADSLphzgoGkJya1lJAAQUUUEABBTILGEDSQQ0g6YY5KxhAcmpaSwEFFFBAAQXSBGaeDuN3gDHz1a/z7FMwaxqss0vacQZobwNI+mAZQNINc1YwgOTUtJYCCiiggAIKdC8Q4eOsfWHcRJh00ktDSISPqZPhlumw43FDE0IMIN1fUpU9DSDphjkrGEByalpLAQUUUEABBboXqA4YtSGk2WfdH3Eg9jSApA+TASTdMGcFA0hOTWspoIACCiigQJpAvaARFSt3PhrdHUk7al/vbQBJH56yBZANgD2ANwIrAY8DNwBHAhdWcbXbrpnw8cBeDRosB9zTxfAYQLpAcxcFFFBAAQUUGEGB6hCy8lZzDnTbxY0fzRrBU+mH0gaQ9FEoWwA5A9gSOBO4GlgY2AdYC9gfOKYga7ddOwEkQsjsmoZnAU90MTwGkC7Q3EUBBRRQQAEFRlggQsiUSXOCR2wRRHab2nhy+gifzmiWN4Ck65ctgGwOXAU8VUWzAHAt8EpgSeBZoN127QSQeYua6aMBBpAcitZQQIH+FvCtOv09Pp6dAvUEDCD/VTGApP8nUrYA0kjka8DHgVaPRrXbLo5TeQRrLBAh57E6d0I6HSEDSKditldAgcES8K06gzVenq0CIeAjWC+6Dgwg6f9ZDEsAORXYGVi8CAqN5NptVx1AHgUWAZ4EzgcOAm7tcmgMIF3CuZsCCgyIgG/VGZCB8jQVKASchP6SS8EAkv5fxzAEkDWKR7DOA3ZqQtZuu0qJo4AxwAzgaWAz4ADg30BMcr+zxfAsA8Sv6m114JQZM2YwYUJkETcFFFCghAJ+oSnhoNqlUgr4A4O6w2oASb/ayx5AFgUuA5YF1m0SCtpt10p8u+IuyAnA3i0aHw4cVq+NAaQVs58roMDAC/hIx8APoR0YAoEBeGTyqjse5rBpN7DjhFfz3i3iBagjvxlA0o3LHEBiXsZ0YCPgzUDx2oaXoLXbrl3tuCMSdzYi9DTbvAPSrqjtFFCgnAJOai3nuNqrcgn04UsjHv3PMxx0xkzO//PfX2R94+e3Y4Gx84y4vwEknbisASQmhk8Dti7mfpzTgKrddp1Ixyt43wZE7U4354B0KmZ7BRQYXAEDyOCOnWeuwCgInHX1PXz8Z9c1PPJtX3oLc8898l9tDSDpgz/yo5R+jp1WiHkZsc7H9sCeMaeiQYF223V6/JnFZPd441anmwGkUzHbK6DAYAr4CNZgjptnrUCPBe5++An2PeEqbr4/3vlTf3v3Rstx2PZrMv+8I3/3I87AAJJ+EZQtgMwNTAEmAR8Ejm1A1G672D3W+VgFeAS4r6i3UPHPWGm9eovjnlYcN47f6WYA6VTM9gooMHgCTkIfvDHzjBXoocBzs5/nGxf8he9e/NeGR33FwvNx0ns3Yo1lXtbDM5tzKANIOnnZAsjXgQOB3wM/qsNzAXA/0G67KLEicDtQPbF8PeAiYCpwc/EWrE2B3YG7gI2L43Q6QgaQTsVsr4ACgyXgW3UGa7w8WwV6KDDjzofZ9YeX88xzzzc86qFvXeOFyeZzzTV6X2ENIOkXxeiNXvq516vwW2DLJqW3AqJNu+0aBZClgVi0cMNisnncJbkbOBc4Aniwy+4ZQLqEczcFFBgQgQF4q86ASHqaCpRCICaUf+rMmfzy+hdPKK/u3EYrLcH3dpvAKxeZry/6bABJH4ayBZB0kdGtYAAZXX+ProACvRDow7fq9KLbHkMBBf5f4Oxr7uHAqY0nlEfLH+25AduMX6rv2Awg6UNiAEk3zFnBAJJT01oKKKCAAgoo0DcCMaH8fSdexU1/758J5d3gGEC6UXvxPgaQdMOcFQwgOTWtpYACCiiggAKjKhATyr954V/4zkXNJpSP5cT3bMz4ZXs/obwbHANIN2oGkHS1katgABk5WysroIACCiigQI8EZtz5T979w8t5+rnZDY94yFvWYN/Xje6E8m44DCDdqBlA0tVGroIBZORsrayAAgoooIACIyjw2FPP8qkzZvKL6yurFrz0YButuATf3f21LLnI/CN4JiNb2gCS7usjWOmGOSsYQHJqWksBBRRQQAEFRlzg59fcy8emXtv0OP06obwbHANIN2reAUlXG7kKBpCRs7WyAgoooIACCmQSuOefc1YobzahfNcNl+PwHXq3QnmmrrUsYwBpSdSygXdAWhL1tIEBpKfcHkwBBRRQQAEF2hV45rnZjDvk/KbNX77QWE5870asueyi7ZYduHYGkPQhM4CkG+asYADJqWktBRRQQAEFFEgWOO4Pt/HFX9zYtM7Bb1md971u5VFdoTy5o20WMIC0CdWkmQEk3TBnBQNITk1rKaCAAgoooEBXAg/8+z9s9KXfNN13wxUX53u7TxjoCeXd4BhAulF78T4GkHTDnBUMIDk1raWAAgoooIACHQm85/grueimB5rus8v6r+Yru6zbUd0yNTaApI+mASTdMGcFA0hOTWspoIACCiigQEuBK25/mHcde1nLdtd+dhsWW3Bsy3Zlb2AASR9hA0i6Yc4KBpCcmtZSQAEFFFBAgboC7Uwojx2/svM67LLBcipWCRhA0i8HA0i6Yc4KBpCcmtZSQAEFFFBAgRcJ/PiS2/nCebOaqiyx0FiuOuRNzD23XxPrQRlA0v+j8spKN8xZwQCSU9NaCiiggAIKKEA7E8qD6bwPb8Faryrv63NzXQoGkHRJA0i6Yc4KBpCcmtZSQAEFFFBgiAXee/yV/KbFhPKdJryar71reCeUd3N5GEC6UXvxPgaQdMOcFQwgOTWtpYACCiigwJAJOKF85AfcAJJubABJN8xZwQCSU9NaCiiggAIKDIFAuxPKv7zzOrzLCeXJV4QBJJkQA0i6Yc4KBpCcmtZSQAEFFFCgxAI/ueR2Pt9iQvniC87LVYduwzxOKM92JRhA0ikNIOmGOSsYQHJqWksBBRRQQIGSCTihfPQH1ACSPgYGkHTDnBUMIDk1raWAAgoooEBJBPY94UouvLH5CuU7TngVX3/XeiXpcf92wwCSPjYGkHTDnBUMIDk1raWAAgoooMAAC1x5x8Ps8oPWK5Rf87/bsPhCrlDeq6E2gKRLG0DSDXNWMIDk1LSWAgoooIACAybQ7oTyo3dam0kbLj9gvSvH6RpA0sfRAJJumLOCASSnprUUUEABBRQYEIGfXno7nzu3+Qrliy4wL1f/rxPKR3tIDSDpI2AASTfMWcEAklPTWgoooIACCvSxwAOP/oeNjvhNyzM894AtWPvVrlDeEqpHDQwg6dAGkHTDnBUMIDk1raWAAgoooEAfCrzvxKu4YNb9Tc/sna99Fd+Y5ITyPhw+DCDpo2IASTfMWcEAklPTWsMhMPN0GL8DjJmvfn+ffQpmTYN1dhkOD3upgAJ9KXDVHQ+zsxPK+3JsOj0pA0inYi9tbwBJN8xZwQCSU9Na5ReI8HHWvjBuIkw66aUhJMLH1Mlwy3TY8ThDSPmvCHuoQF8JxITy1Q49n+efb35aTijvq2FreTIGkJZELRsYQFoS9bSBAaSn3B5s4AWqA0ZtCGn22cB33A4ooEA/Cxx/6e0c3mJC+SLzj+Haz27rCuX9PJANzs0Akj5oBpB0w5wVDCA5Na01HAL1gkb0vHLno9HdkeHQsZcKKNAjgX88+hQbHnFhy6NNO2Bz1nn1Yi3b2aB/BQwg6WNjAEk3zFnBAJJT01rDI1AdQlbeak6/b7u48aNZwyNT7p46/6fc4zsgvfvASVcx/YbmE8rfsd6yfHPX1w5IjzzNVgIGkFZCrT83gLQ26mULA0gvtT1WuQQihEyZNCd4xBZBZLepjSenl6v3w9cb5/8M35j3UY9n3PkwOx3TeoXyWLNjCVco76ORy3MqBpB0RwNIumHOCgaQnJrWGi4BA8jwjXejx+yc/zNc10KPevvsc7MZ18aE8iN3XJt3b+QK5T0allE5jAEknd0Akm6Ys4IBJKemtYZHwEewhmesq3vq/J/hHPce9/rEy+7gs+fc0PSoi8w3hmsPc0J5j4dm1A5nAEmnN4CkG+asYADJqWmt4RDwS+hwjHOjXho+h3v8R6j37U4oP+dDm7Puck4oH6Fh6NuyBpD0oTGApBvmrGAAyalprfIL+Bre8o9xOz308bt2lGzThkA7E8p3WHdZvv1uJ5S3wVnaJgaQ9KE1gKQb5qxgAMmpaa3yCzgRufxj3E4PDSDtKJWvTaa3oM2485/sdMwfW/o4obwl0dA0MICkD7UBJN0wZwUDSE5Naw2HQKYvIcOBVcJe+ghWCQe1jS4l/vAhJpS/5n9/xXOzmy9R/qV3rs1uGzuhvI0RGaomBpD04TaApBvmrGAAyalpLQUUKLeA83/KPb7Netfl45ftTChfaOw8zDx8oiuUD+/V1bLnBpCWRC0bGEBaEvW0gQGkp9weTAEFBlagyy+gA9tfT/ylAm0G0Af/Axt8sfUK5T//0Oas54Ryr7Q2BAwgbSC1aGIASTfMWcEAklPTWgooUF6BxEdwygszZD1r8gjeh2cfyLk3PNwUZPt1l+U7TigfsosmvbsGkHTDsgWQDYA9gDcCKwGPA/Hy7iOB2h9/zAN8EtgXWA64GzgO+ArwXJu0awFfBrYo2l8CHAT8uc39a5sZQLqEczcFFBhCAef/DOGg1+lyzUsIfv/c2uz7zCd4mnkb+jih3EsnRcAAkqI3Z9+yBZAzgC2BM4GrgYWBfYAICvsDx1SRfR/YD/gpEK+/2BzYG4jf/1AbtOOAK4H48cp3ivYfAeKF4BsBt7RRwwDSBZK7KKCAAgooUBF49qknufyIbdhi7utf+K1GAeSId67F7huvIJwCyQIGkGTC0gWQCBFXAU9V0SwAXAu8ElgSeBZYG7iuCA4frWr7LeDDwLrAnD/JGm8RdrYD1ijunkTLuJNyI3A+sEsXw+MdkC7Q3EUBBRRQYPgETrr8Tr7w82s4Zt5vsvU817wQPGJ7/TzX85vnXst+z3yMMWPn53onlA/fxTHCPTaApAOX7Q5II5GvAR8vAsI9wBHAwcDKwO1VO8VjW7cVnx/ahDfurDwEnAbsVdPuBGAS8PLiEbBORskA0omWbRVQQAEFhkrgwcee+u+E8rE889/wUQkcgVEJJIybCJNOgjHzDZWRnR15AQNIuvGwBJBTgZ2BxYHHgOnFXY6l6xDeD1xT3N1oJLxp8dhWPML1g5pG8XvxGFe0ubzDITKAdAhmcwUU6KGAcy56iO2hqgU+dMrV/OL6+/77W/XCx7brLM93d5sAzd6QJqsCGQQMIOmIwxBA4hGpeATrPGCngiwer3oaWL8OYcwdiZlrc+7l1t+iTjyCtQNwbk2T+L1zisATc1EabcsA8at6Wx04ZcaMGUyYEFnETQEFFOgTAd861ScDMTyncc1d/+Sd36+/QvkOc1/Kt8d+74VHrdb7n2m8fLGXvRimOoTseBys081T0cNjbU87EzCAdOZVr3XZA8iiwGXAssUdjzsLhFuBuNOxWR2U+NMu5oqs2oR3MnAiMBH4dU27bYs7LNHm5CY1DgcOq/e5AST9wraCAgpkFnDdjcyglqsnECuUjz9sOk8/O7sp0BffsRZ7LHgFjN+h8SNWcc3Ommb48FLLLmAASSctcwCJyefxqFW8kerNwMVVXN4BSb92rKCAAsMm0ObCbz5zP2wXRnp/T778Tg79efM32M8/79z8+fCJjJln7vQDWkGBBAEDSAJesWtZA8hYYBqwdfEoVDwSVb05ByT92rGCAgoMo0CThd+c8DuMF0T3fX7osadYv40Vys/efzNeu3xM4XRToD8EDCDp41DGADKmmJ+xPbBnzKmow/Ql4DNN3oIVnx/ShLfVW7B2Ld6CFRPeO9mchN6Jlm0VUGB0BGoWfmPlrWC3qb5taHRGY+CO+qEpV/OLmf8/obxeB9669jJ8b3fnQg7c4A7JCRtA0ge6bAEk7stOKV6D+0Hg2AZEsc5HvOkqFhCstw7IesDMYt+YkL4K8AhQ/SdmTDCPOSAxcTxe7RtbZR2QuMNSmfDeySgZQDrRsq0CCoyOgAFkdNwH+KjX3v0v3vG9S1v24KpD38QrFva1uS2hbDCqAgaQdP6yBZCvAwfGQqjAj+rwXFBMPo+P4vW5HyhWQo8/FWMRw1g1PUJLhJfKtmKxVkis7xErpVe21wBXFOuBfLv4zVgJPdb/iHknN3cxPAaQLtDcRQEFeijgI1g9xB7sQz03+3nWPOxX/OeZ5hPKv/COtZi8iSuUD/ZoD9fZG0DSx7tsAeS3wJZNWLYCok1s8ajWQcC+wKuAe4HjgC8Xq6W3CiDx+TrA0cAWReNLgE9V3T3pdIQMIJ2K2V4BBXon4CT03lkP8JFO+dOdHHJ28wnl842Zmxs+54TyAR7moT51A0j68JctgKSLjG4FA8jo+nt0BRRoJOBreL02mgi0O6H8rP03Y4ITyr2WBlzAAJI+gAaQdMOcFQwgOTWtpYAC+QRciDCfZYkqffjUazj3ur817dFb1l6a7+9eb93fEkHYlaESMICkD7cBJN0wZwUDSE5NaymgQF6BCCEu/JbXdACrOaF8AAfNU84qYABJ5zSApBvmrGAAyalpLQUUUECBLALtTij//NvXZM9N490tbgqUV8AAkj62BpB0w5wVDCA5Na2lgAIKKJAkMOVPd3Hw2dc3rTF2nrmZ9XknlCdBu/NACRhA0ofLAJJumLOCASSnprUUUEABBToWePjxp5nwhXhrffPtzP02Y/0VXKG8lZOfl0/AAJI+pgaQdMOcFQwgOTWtpYACCijQtsBHTr2GaS0mlG+35tL8YLITyttGtWEpBQwg6cNqAEk3zFnBAJJT01oKKKCAAk0Frrv7X7y9jRXKrzzkTbxyEVco93JSIAQMIOnXgQEk3TBnBQNITk1rKaCAAgq8RCAmlK99+HSeePq5pjqf22FN9trMCeVeQgrUChhA0q8JA0i6Yc4KBpCcmtZSQAEFFPivwPtOvIoLZt3fVGTM3HNx0xe2Y8w8cyungAINBAwg6ZeGASTdMGcFA0hOTWspoIACQy5w10NP8PqvXNxS4cz9NmX9FZZo2c4GCijgI1g5roFeB5AfAscBVzQ4+Q2A9xe/cvRv0GoYQAZtxDxfBRRQoA8FVvz0L1qe1cQ1l+LYyfHXrpsCCnQi4B2QTrTqt+11AJkN7AFMaXDqk4rP5knv2kBWMIAM5LB50goooMDoC/z8mnv52NRrW57IhR/fklWXXLhlOxsooEB9AQNI+pXRbwFkf+CrwILpXRvICgaQgRw2T1oBBRQYHYFnnpvNuEPOb3nwTVZegtPev2nLdjZQQIHWAgaQ1katWvQigGwBvL44kS8CpwPX1TmxWM1oN+A+YFjvCRtAWl2xfq6AAgoowAdOuorpNzSfUB5MN39xO+YbM6wPFXihKDAyAgaQdNdeBJDDgPgV2/NAs2NG+IhHtFrPmEvvez9WMID046h4TgoooEAfCLQ7ofxL71yb3TZevg/O2FNQoJwCBpD0ce1FAHk58IoieMwCPgmcV3PqEUweB+5N79JAVzCADPTwefIKKKBAfoF2JpTHUe846q35D25FBRR4iYABJP2i6EUAqT7LrYHrgQfST72UFQwgpRxWO6WAAgp0JnDOtffy0dPamVD+elZdcpHOittaAQWSBAwgSXwv7NzrAJJ+xuWuYAAp9/jaOwUUUKChwLPPzWbVNiaUb7zSEkz9gBPKvZQUGC0BA0i6/GgEkHmBHYANgcWA2uVW43GsD6R3bSArGEAGctg8aQUUUKB7gQ+eNINf3fD3lgVihfL553VCeUsoGygwwgIGkHTgXgeQpYCLgDWAx4CFgEeARYu7MQ8DTwDDOnvOAJJ+TVtBAQUU6HuBux9+gtd9ufX7Vo5451rsvvEKfd8fT1CBYRIwgKSPdq8DyE+BnYC3V80FeRNwOXAQMBl4A3B3etcGsoIBZCCHzZNWQAEF2hNwQnl7TrZSoJ8FDCDpo9PrABKv2T25eBNWvB3rH8A2wG+Krkwt/hkrog/jZgAZxlG3zwooUGqBadf9jY+cek3LPl5w4OsZt5QTyltC2UCBURYwgKQPQK8DyH+ADwE/BuJP2Xj86h3AtKIrHwSOACKcDONmABnGUbfPCihQOoF2J5RvtOIS/OyDTigv3QVgh0otYABJH95eB5A7gWOAo4pTfxSI1dGPLv790OLuSMwJGcbNADKMo26fFVCgNAIfOuVqfnF93OxvvjmhvJWQnyvQvwIGkPSx6XUAORMYU8wBibP/ObAZ8BEgXu3xzWJuyBvTuzaQFQwgAzlsnrQCCgyzQLsTyr/wjrWYvIkTyof5WrHv5RAwgKSPY68DyHbA3sWveBzrNcAfikeu4lweAiYCV6d3bSArGEAGctg8aQUUGEYBJ5QP46jbZwXAAJJ+FfQ6gNQ743jcKlZIf64II/Eq3mHdDCDDOvL2WwEFBkLg3Ov+xofbmFD+6wNfz2pOKB+IMfUkFehUwADSqdhL2/dDAEnvRXkqGEDKM5b2RAEFSiLQ7oTyDVZYnDP2i6eK3RRQoMwCBpD00e1FAPk+8BPgqqrTXRB4EohVz93+X8AA4tWggAIK9InAAVOu5ryZTijvk+HwNBToGwEDSPpQ9CKAzAb2AKYUpxuv2H2gWP8jVkV3M4B4DSiggAJ9IfDXBx7jTV//Xctz+cLb12Typiu2bGcDBRQon4ABJH1MRyuAxAKEsQK6AeTFY+gdkPRr2goKKKBAxwJOKO+YzB0UGFoBA0j60BtA0g1zVjCA5NS0lgIKKNBE4PhLb+fwc2e1NJr+sdfzmqVdobwllA0UGBIBA0j6QBtA0g1zVjCA5NS0lgIKKFAj0O6E8rnmgtuPfKt+CiigwEsEDCDpF0WvAshk4NTidF8B/L2YA3Jxgy7EvJFh3Awgwzjq9lkBBUZcIOZ1xPyOVtusz09kwbGxXq6bAgooUF/AAJJ+ZfQqgNS+7SqO2+gNWPH7w/qnvwEk/Zq2ggIKKPCCwG3/eIw3fq31hPL3v35lDn7LGqopoIACbQkYQNpiatqoFwHkp12c5j5d7FOGXQwgZRhF+6CAAqMq4ITyUeX34AqUXsAAkj7EvQgg6Wc5PBUMIMMz1vZUAQUyCnx1+s189+K/tqx45n6bsv4KS7RsZwMFFFCgkYABJP3aMICkG+asYADJqWktBRQotcAzz81m3CHnt9XHO45yQnlbUDZSQIGWAgaQlkQtGxhAWhL1tIEBpKfcHkwBBQZRoN1HrG743EQWmm9YpxQO4sh6zgoMhoABJH2cyhZAFgY+AawPbAAsDZwA7F1DdTywVxO+Q4EjWvA2q7EccE8Xw2MA6QLNXRRQoPwCN973b978rT+07Ohb1l6a7+8efwW4KTDkAjNPh/E7wJj56kM8+xTMmgbr7DLkUJ133wDSuVntHmULICsCtwP3ATOAtzUIIJsCq9Th+2gRXOJvr6vbDCARZGpfG3wW8EQXw2MA6QLNXRRQoLwC7d7t8BGr8l4D9qwLgQgfZ+0L4ybCpJNeGkIifEydDLdMhx2PM4R0SGwA6RCsTvOyBZCI+bHOyL3Fq3yfaRBA6sktWKxPcgewThu0lTsg8wLPttG+nSYGkHaUbKOAAqUW+Pqvb+bbF7WeUH78PhvyhtcsWWoLO6dAVwLVAaM2hDT7rKuDDd9OBpD0MS9bAKkWiQd/OwkguwMnF49wfa0N2koAGQssAMQKV6kLKBpA2oC3iQIKlE/ACeXlG1N7NMoC9YJGnFLlzkejuyOjfNqDcHgDSPoo9TqAHFh8yf9H+qm3rNBpAPk1sBXwauD+ltWhEkAeBRYBngTidSwHAbe2sX+9JgaQLuHcTQEFBlNgpc/8gucbLUtb1aWZh2/Ly+aPG85uHQk4D6AjrtI1rg4hK8dXnFih8+LGj2aVDmBkOmQASXftdQCJOwRxV+KXzPkCfx7wXHo36lboJIC8CrirCBAxb6Sd7ajiMa+Ya/I0sBlwAPDvYh7JnS2KLAPEr+ptdeCUGTNmMGFCZBE3BRRQoHwCN/3932z3zdYTyieuuRTHTo73ibh1JeA8gK7YSrdThJApk+YEj9giiOw2tfHk9NIB5O+QASTdtNcBJP4miUnbuwKxEtSD8YW7mKdxXXp3XlShkwDyaeBIIF4FcUbCeWxXhJh6b96qLXs4cFi9YxlAEkbAXRVQoG8FnFDe46FxHkCPwfv0cAaQ7ANjAEkn7XUAqZxx3Effvggj8aU9wkIEkJ8CU4CH0rv2Qs1254DMApYClgWeSjx23BGJOxtRq9nmHZBEaHdXQIH+F/jmhX/hmxfe0vJEf7r3hmy1uhPKW0J12sB5AJ2Klau9j2CNyHgaQNJZRyuAVJ95vLUqJoDHnZF1i9AQj2b9pHhUq9tethtANgSuAL4PfKjbg1XtF6/gjce4YnJ6p5tzQDoVs70CCvSdwLPPzWZVVyjvj3GJx7BWmwhn7jvnlau18wB2Og7+Mt3XsPbHaOU9C8NnXs+qagaQdNp+CCBxJ2CPYrHANYB/FvNCIphcD+wG3NBFV9sNIN8tgsfGRRDp4lAv2mUmsDgQixF2uhlAOhWzvQIK9I3AKgf/kudmt55Rft1h27LoAk4oH/GBq54DEkHjZ3u+eB7Au078/2DiWhAjPhw9PYCP340otwEknXe0Akis1/GO4q7HBo4DIwAAIABJREFUNsDcwEXAj4GziwCyM/BV4G4gFg7sdGsngMRdili0MN56Nb7BAeJvyVi08JGibTRbqGj7eM0+k4DTgGOBD3Z6woABpAs0d1FAgdET+Mv9j7LtN37f8gS2Gb8UP9rTCeUtoXI2qP4Suso2MPtpuP13c46w0pYw91i49QLfiJTTvF9q+QKCER0JA0g6b68DSASJeNTqXcBiQLwpKt6GFXM/4i1UtVt8if8WEIGl3S3eRBW1I9R8DrgGiMeiYpsGxB2KyrYjcCYQk9CPbnCAyurq1RPL1ysC01Tg5uItWNG3eJQs+hF3U9p5lW/tIQ0g7Y6y7RRQYFQFnFA+qvztHzxCyKm7zwkaleAR/6wEkQgm7z7FNyK1Lzo4LX0F84iNlQEknbbXASRew/sf4OfFHI/fAM3u18dLqz9brM/Rbm9jJfMVGjTepwg8lY/PKeZrxONSf+sggCwNxGKFMX8kJpvHXZK4U3MucETxdq92z7e6nQGkGzX3UUCBnghM+dNdHHx2PBnbfPvJ3hvwxtXjvR5uoy4QAeS03eGvDQLIqtvArgaQUR8nT2CgBAwg6cPV6wCyf/GWq3+ln3opKxhASjmsdkqBwRWIOR0xt6Od7Y6j3tpOM9v0SqD6EawIGs/VPII1z9g5wcQVsXs1Ih6nJAIGkPSB7HUAST/jclcwgJR7fO2dAgMjsP13LuH6e2PqW/Pt+sO3ZRFXKG/FNDqfOwl9dNw9aukFDCDpQzzSAeT1XZ5i6xmNXRbu890MIH0+QJ6eAmUWuOuhJ3j9V4rVkpt0dO/NVuTwHdYsM0V5+uZreMszlvakbwQMIOlDMdIBJOZ8VM/xiOO1fkcjzJPetYGsYAAZyGHzpBUYbAEnlA/2+DU9e9eCKPHg2rXREjCApMuPdADZsuYUY7J2vG0q1smIV9XeWHwer8B9P/Aw8CkgJqcP42YAGcZRt88KjILAaVfcxafPaj2h/LT3b8ImK798FM7QQyYLuBZEMqEFFKgnYABJvy5GOoDUnuEXgbcDmwC1a2gsAlxWvDI33nw1jJsBZBhH3T4r0CMBJ5T3CLpfDuNaEP0yEp5HyQQMIOkD2usAcg/w9eJXvbP/BPDRLlcRT9cY/QoGkNEfA89AgdIJvP17l3Ld3a1fPuiE8tINPbgWRAkH1S6NtoABJH0Eeh1AngQ+DxzZ4NQPBg4FFkzv2kBWMIAM5LB50gr0n8DdDz/B677cekL5npuuwOffvlb/dcAzUkABBfpUwACSPjC9DiB/AmIRv3gE676a048F/S4vFgSMz4dxM4AM46jbZwUyCjihPCOmpRRQQIE6AgaQ9Mui1wHkDcCvgKeLBQlvLrqwOvBuYCywHfDb9K4NZAUDyEAOmyetwOgKTL3yLj51ZusJ5ae+bxM2XcUJ5aM7Wh5dAQUGXcAAkj6CvQ4gccabFXNANqo5/SuA/wEuTe/WwFYwgAzs0HniCvRWwAnlvfX2aAoooEBFwACSfi2MRgCpnPWSwErFv9wOPJDenYGvYAAZ+CG0AwqMrMA7v38p19zVekL5zMO35WWuUD6yg2F1BRQYSgEDSPqwj2YAST/78lUwgJRvTO2RAskC7U4o32OT5fniO9ZOPp4FFFBAAQUaCxhA0q+O0Qog2xTrgVTugNwGnANcmN6lga5gABno4fPkFcgr4ITyvJ5WU0ABBXIIGEDSFXsdQMYUk893AuLYjxVdWBh4HjgD2A14Lr1rA1nBADKQw+ZJK5BP4GdX3c1BZ8xsWfCUfTdm81Vf0bKdDRRQQAEF8goYQNI9ex1A/hf4HPCDYi2Qu4suvBr4DLAfEG2OSO/aQFYwgAzksHnSCqQJOKE8zc+9FVBAgV4KGEDStXsdQP4CxI/2dm5w6nEHZB1gtfSuDWQFA8hADpsnrUB3Ajsd80dm3PnPljtfd9i2LLrAvC3b2UABBRRQYOQFDCDpxr0OIP8BPlbcAal39nEH5BvA/OldG8gKBpCBHLYRPOmZp8P4HWDMfPUP8uxTMGsarLPLCJ6EpXMKtDuhfLeNl+dL73RCeU57aymggAI5BAwg6Yq9DiB/A04DPt7g1CN8TAJiVfRh3Awgwzjqjfoc4eOsfWHcRJh00ktDSISPqZPhlumw43GGkD6/dpxQ3ucD5OkpoIACbQoYQNqEatKs1wHkOGCP4lc8blW97VhMUD8JeF961wayggFkIIdthE66OmDUhpBmn43Q6Vi2c4HTr7qbTzqhvHM491BAAQX6WMAAkj44vQ4gSwGXA8sDtwI3Fl1YA1gFuBPYFLg/vWsDWcEAMpDDNoInXS9oxOEqdz4a3R0ZwVOydHOB2bOfZ+WDf9kW0x1HvbWtdjZSQAEFFOgfAQNI+lj0OoDEGS9WvPFq+5qV0GMdkKOB1kv8pve7XysYQPp1ZEbzvKpDyMpbzTmT2y5u/GjWaJ7rEB97lx/8kSvvcEL5EF8Cdl0BBYZEwACSPtCjEUDSz7q8FQwg5R3btJ5FCJkyaU7wiC2CyG5TG09OTzuae7cpcM8/n2CLo4sxabLPrhsux1E7xQv+3BRQQAEFBl3AAJI+ggaQdMOcFQwgOTXLVMsA0lej6YTyvhoOT0YBBRToqYABJJ27lwHk5cAzwL+L046X2r8HiGdKFgGuBr4DPJDerYGtYAAZ2KEbwRP3EawRxG2/9Jkz7uF/Tr+u5Q4nv3djthjnCuUtoWyggAIKDKiAASR94HoRQBYCTgcmFqd7FjAZmAa8qaYL9wKbAPHPYdwMIMM46s367CT0Ub0inFA+qvweXAEFFOhLAQNI+rD0IoAcCnweOBP4O7AXcCGwdfG63elA3A15J/Bd4ATg/eldG8gKBpCBHLYROmlfwztCsK3LTjr2Mv50+8MtG1732W1ZdEFXKG8JZQMFFFCgRAIGkPTB7EUA+TMwE9itON24+xEh4/AimFT34gfAm4EV0rs2kBUMIAM5bCN00mVfiLDPVnm/919PsvlRF7UczEkbLMfROzuhvCWUDRRQQIGSChhA0ge2FwEk5nwcBES4iC3Cxe3ADsB5NV2IBQi/B4xN79pAVjCADOSwjeBJ99mX9Gw97aNw5YTybKNqIQUUUGAoBAwg6cPciwAyu1j5fEpxujEZ/R/F/I/aHzfuDpwIzJPetYGsYAAZyGHzpDsWGOXHy86+5h4OnNp6QvkJ79mILVd7ZcfdcwcFFFBAgfIKGEDSx9YAkm6Ys4IBJKemtfpboMcT7J1Q3t+Xg2engAIKDIqAASR9pHoVQI4DLi9Od2HgG8DXgRtrurBp8Wpe74BMiCzipkDJBXrwiuHdfnQ5f7z1oZaQ1352GxZbcFif/mzJYwMFFFBAgULAAJJ+KfQqgHRyps/7CNYMJhhAOrlmbDvIAiOwyOLf/vUkm7UxoXynCa/ma+9ad5D1PHcFFFBAgR4LGEDSwXsRQLbs4jR/18U+ZdjFR7DKMIr2oTOBjAFk1YN/ybOz42cYzbc7jnprqyZ+roACCiigQF0BA0j6hdGLAJJ+lsNTwQAyPGNtT0MgwyNYv//LP9jzJ1e09HRCeUsiGyiggAIKtCFgAGkDqUUTA0i6Yc4KBpCcmtbqb4GESejPP/88K33ml231z7sdbTHZSAEFFFCgTQEDSJtQTZoZQNINc1YwgOTUtFb/CnT5Gt7Dp93A8X+8o2W/Zh6+LS+b3xXKW0LZQAEFFFCgYwEDSMdkL9nBAJJumLOCASSnprX6V6CDhQgffesxrH3moi37cuCbVuOjbxrXsp0NFFBAAQUUSBEwgKTozdnXAJJumLOCASSnprX6W6DFKu9rHjKNrZ+/nGmzN2/aDx+x6u9h9uwUUECBsgkYQNJH1ACSbpizggEkp6a1Bk7gD7f8g8k/bj2h/Mz9NmP9FRYfuP55wgoooIACgy9gAEkfw7IFkFjk8BPA+sAGwNLACcDeNVQrArc34PsxsG+btGsBXwa2KNpfAhwE/LnN/WubGUC6hHO3wRWICeUfOGkGv551f9NOvGqxBbj0028c3I565goooIACpRAwgKQPY9kCSCVY3AfMAN7WIoCcA5xRw/jXqlXbmwnHw+ZXAg8D3ykafgRYDNgIuKWL4TGAdIHmLoMp8KfbHmLSDy9vefJOKG9JZAMFFFBAgR4KGEDSscsWQOYDXgHcC4wBnmkRQI4ADu2SMYLLdsAawN1FjeWAG4HzgV26qGsA6QLNXQZH4Mmnn2Pbb/6Oux9+sulJf3TrcRy4zWqD0zHPVAEFFFBgaAQMIOlDXbYAUi3SbgCJEBJb829EL7aOR70eAk4D9qoZhnjkaxLwcuDxDofIANIhmM0HQ+DEy+7gs+fc0PRkJ2+yAp9/+5rMNVeZ/1gajPHyLBVQQAEFGgsYQNKvjjL/Td9OAHkMiDARWzx69Q3g+22wbgr8EdgP+EFN+/i9qBFtWj9f8uKdDSBt4NtkMATu/deTbH7URS1P9oqDt2bJl83fsp0NFFBAAQUU6AcBA0j6KAxrAFke+AlwNnAXsCzwfiACwFeBT7ag3amYO7IDcG5N2/i9mFuyM3BmkzrLAPGrelsdOGXGjBlMmBCn4qbAYAnEhPL/+dl1nHVNPAXZePvyzuvwrg3iiUU3BRRQQAEFBkvAAJI+XsMaQOrJzQP8rrhzEQ+f39qEdzJwIjAR+HVNu22B6UC0OblJjcOBw+p9bgBJv7Ct0FuBdiaUr770IpxzwObMNyb+U3NTQAEFFFBgMAUMIOnjZgB5seH2wDTgA8APm/B6ByT92rPCgAv855nnmPjN33PnQ0807clZ+2/GhOVds2PAh9vTV0ABBRQoBAwg6ZeCAeTFhusA1wGHAF9qwusckPRrzwoDKnDSZXfwvy0mlO++8fJ88R1rOaF8QMfY01ZAAQUUaCxgAEm/OgwgLzbcsZi3EQsRxoKEjbZWb8HatXgLVkxy72RzEnonWrbtmcDf/vUkm7UxofxPB2/NUk4o79m4eCAFFFBAgd4LGEDSzYc1gCwJPFDDtwBwKRCrm69StbbHvMW/PwLEAoeVLSaYxxyQmDh+T/GblXVAYg5IPKbV6WYA6VTM9iMmEBPKP3H6TM68unJ51z/Ul3dah3dt6ITyERsICyuggAIK9JWAASR9OMoYQA4oViOfG/gccA1wVkEV8ztmFm+/inU64h2h8e0q3oIV63msDHwGOKqKtrK6eqzvsXfV778GuKJYD+Tbxe/HSuhRN1ZCv7mL4TGAdIHmLnkFrrj9Yd517GVNizqhPK+51RRQQAEFBkfAAJI+VmUMIHcAKzSg2Qc4HnhvETgiRCwBxKNSVwPfKiahV+/eKIBEm5gzcjSwRbHDJcCnipDTzegYQLpRc59kASeUJxNaQAEFFFBgSAQMIOkDXcYAkq4yehUMIKNnP5RHPvnyOzn0539u2vfdNl6eI5xQPpTXh51WQAEFFHipgAEk/aowgKQb5qxgAMmpaa26Ak4o98JQQAEFFFCgewEDSPd2lT0NIOmGOSsYQHJqWuu/Au1OKD96p7WZtOHyyimggAIKKKBAAwEDSPqlYQBJN8xZwQCSU9NaXHnHw+zyg+YTyldbamHO/fAWrlDu9aKAAgoooEAbAgaQNpBaNDGApBvmrGAAyak5pLViQvmbv/UHbn/w8aYCZ+63Geuv4ArlQ3qZ2G0FFFBAgS4FDCBdwlXtZgBJN8xZwQCSU3PIajmhfMgG3O4qoIACCoyKgAEknd0Akm6Ys4IBJKfmENS675En2fTIWM6m+Xb5Z7Zm6UXnb9XMzxVQQAEFFFCghYABJP0SMYCkG+asYADJqVnSWjGh/JNnzOSMGc1XKD9yx7V590ZOKC/pZWC3FFBAAQVGScAAkg5vAEk3zFnBAJJTs2S1pt/wdz5w0oymvYoJ5dMO2IL5552nZL23OwoooIACCvSHgAEkfRwMIOmGOSsYQHJqlqDWE08/y/jPTm/ZkzP325T1V1iiZTsbKKCAAgoooECagAEkzS/2NoCkG+asYADJqTnAtY46/yZ+8Ltbm/bg3Rstx5feuTZzzeV/xgM81J66AgoooMCACRhA0gfMby7phjkrGEByag5YrXht7lZf/W3Ls/7tJ97Aiq9YqGU7GyiggAIKKKBAfgEDSLqpASTdMGcFA0hOzQGoFRPKY82Om/7+aNOz3f8Nq3DQdqsPQI88RQUUUEABBcotYABJH18DSLphzgoGkJyafVzrgln3874Tr2p5hrM+P5EFx45p2c4GCiiggAIKKNAbAQNIurMBJN0wZwUDSE7NPqvV7oTy4/bcgDeNX6rPzt7TUUABBRRQQIEQMICkXwcGkHTDnBUMIDk1+6TWJbc8yB4//lPTsxm/zMv4xUe2cEJ5n4yZp6GAAgoooEAjAQNI+rVhAEk3zFnBAJJTcxRr/euJp/noadfyu7/8o+lZXPyJN7CSE8pHcaQ8tAIKKKCAAp0JGEA686rX2gCSbpizwsgGkJmnw/gdYMx89c/52adg1jRYZ5ecfRqaWjGh/OQ/3cX//vzPTfu83xtW4VNOKB+a68KOKqCAAgqUS8AAkj6eBpB0w5wVRi6ARPg4a18YNxEmnfTSEBLhY+pkuGU67HicIaSDUb31H4+x10+u4J5/Ptlwr302X5HPvHkNxo6Zu4PKNlVAAQUUUECBfhMwgKSPiAEk3TBnhZELINUBozaENPssZ+9KVOuZ52Zz5C9v4ieX3t6wV8stsQA/3XsjVl1y4RL13K4ooIACCigw3AIGkPTxN4CkG+asMHIBJM6yXtCI36/c+Wh0dyRnDwe8VjsTyr/wjrXYY+PlnVA+4GPt6SuggAIKKFBPwACSfl0YQNINc1YY2QBSG0JW3mrOud92ceNHs3L2bkBrtTOh/PWrvZJvTVqPxRcaO6C99LQV6KGA89F6iO2hFFAgt4ABJF3UAJJumLPCyAeQSgiZMmlO8IgtgshuUxtPTs/ZwwGpFRPKT/nTXRzaYkL5Se/diNeNe+WA9MrTVKAPBJyP1geD4CkooECKgAEkRW/OvgaQdMOcFQwgOTW7qBUTyvf+6RXc/bATyrvgcxcFWgs4H621kS0UUKCvBQwg6cNjAEk3zFlh5ANI9V/+PoL1wti1M6H81YsvwPH7OKE858VurSEWcD7aEA++XVdg8AUMIOljaABJN8xZYWQDiH/pv2isLv3rg+x+XPMVyp1QnvPytpYCVQL+MMTLQQEFBlTAAJI+cAaQdMOcFUYugPjYwwvjFBPKPzb1Wn57c+MVyp1QnvOStpYCTQTizyXno3mJKKDAgAkYQNIHzACSbpizwsgFkCGe+BkTyqdccReHnN18hXInlOe8lK2lQBsCBpA2kGyigAL9JmAASR8RA0i6Yc4KIxdA4iyH7NWXt70wofxK7nr4iYZjtPdmK3LwW1yhPOdFbC0F2hLwEay2mGykgAL9J2AASR8TA0i6Yc4KIxtAcp5pn9aKCeVHnX8TP76k8Qrlr1psAU54z4asuuQifdoLT0uBkgs4H63kA2z3FCi3gAEkfXwNIOmGOSsYQLrUbGtC+dvXZI9NVnCF8i6N3U2BLALOR8vCaBEFFBg9AQNIur0BJN0wZwUDSAeajzzxDB+beg0XN5lQ/rpxr+Bbu76WJVyhvANZmyowggJDPB9tBFUtrYACPRQwgKRjG0DSDXNWMIC00IwJ5adecTcHn31905YnvGcjtlzNFcpzXpzWUiCbwJDNR8vmZiEFFOgLAQNI+jAYQNINc1YwgDTQjAnl+xx/JXc+5ITynBectRRQQAEFFFCgMwEDSGde9VobQNINc1YwgFRpxoTyo8+/ieOcUJ7zGrOWAgoooIACCiQIGEAS8IpdDSDphjkrGECAP976ILv9qPkK5Z9/+5pMdkJ5zmvPWgoooIACCijQhoABpA2kFk0MIOmGOSsMbQCJCeUH/uxaLrrpgYaeTijPealZSwEFFFBAAQW6ETCAdKP24n0MIOmGOSsMVQBxQnnOS8daCiiggAIKKNALAQNIurIBJN0wZ4WhCCDtTCjfa9MVOOSt4xk7Zu6cvtZSQAEFFFBAAQWSBAwgSXwv7GwASTfMWaG0ASQmlH/5Vzfxoz+4QnnOC8ZaCiiggAIKKNBbAQNIunfZAsjCwCeA9YENgKWBE4C9a6jisz2ANwIrAY8DNwBHAhe2yXo8sFeDtssB97RZp7pZ6QJIOxPKP7fDmuy5qSuUd3G9uIsCCiiggAIK9FjAAJIOXrYAsiIQP2K/D5gBvK1BADkD2BI4E7gaiOCyD7AWsD9wTBu0lQASIWR2TfuzgMYLVjQuXooA4oTyNq4emyiggAIKKKDAQAoYQNKHrWwBZD7gFcC9wBjgmQYBZHPgKuCpKsIFgGuBWD57SeDZFryVADJvG23bHamBDSAxofy0K+/mM2e5Qnm7g207BRRQQAEFFBg8AQNI+piVLYBUizQLII3kvgZ8HGjnEapKABkLRHh5rM6dkE5HaOACyO0PPs4+P72CO5qsUB4Tyg9+6xrMN2aeTj1sr4ACCiiggAIK9JWAASR9OAwgLzY8FdgZWLwIFM2EKwHkUWAR4EngfOAg4NYuh2YgAkg7E8qXXXR+TnjPRoxbKmjcFFBAAQUUUECBcggYQNLH0QDy/4ZrFI9gnQfs1AbtUcVjXjHX5GlgM+AA4N/FBPg7W9RYBohf1dvqwCkzZsxgwoTIIv21OaG8v8bDs1FAAQUUUECB3gsYQNLNDSBzDBcFLgOWBdYFWoWHRvLbFXdB6r15q3afw4HD6hXqpwASE8o//rNr+U2TFcq3WPUVfGvX9Xj5wjEFx00BBRRQQAEFFCivgAEkfWwNIHPmb0wHNgLeDFycyBp3ROLORoSZZlvf3gGJCeVTr7ybT7eYUH78PhvyhtfEfH03BRRQQAEFFFBgOAQMIOnjPOwBJCaQTwO2LuZ+nJNOSryCN17/G7U73UZ1DkhMKH/P8VcS/2y0xXodhzihvNNxtb0CCiiggAIKlETAAJI+kMMcQOItWbEeyPbAnjH3Ip3zhQozi0ns8SatTreeB5BnY4Xy6Tfzw9/f1vBcl1l0fk50QnmnY2l7BRRQQAEFFCihgAEkfVCHNYDMDUwBJgEfBI5tQhnrfKwCPFIscBhNFyra194qiHqnFfWibqdbTwPIdy+6ha/++i8Nz/Hw7cez12YrMtdcZb5MOh0i2yuggAIKKKDAMAsYQNJHv4zfLONNVIsBETI+B1wDLzwWFVs8bhV3KL4OHAj8HvhRHcYLgPuL36+srl49sXw94CJgKnBz8RasTYHdgbuAjav272SUehZA4lW64w6Jtwa/eNt81Zfz7V1f64TyTkbNtgoooIACCigwNAIGkPShLmMAuQNYoQHNPkCs3/FbYMsmfFsVbaJJvQCyNBCLFm5YTDaPuyR3A+cCRwAPdjk0PQsgs2c/zyE/v55Tr4jThp/usyFbOaG8y2FzNwUUUEABBRQYFgEDSPpIlzGApKuMXoWeBZDR66JHVkABBRRQQAEFBlfAAJI+dgaQdMOcFQwgOTWtpYACCiiggAIKZBYwgKSDGkDSDXNWMIDk1LSWAgoooIACCiiQWcAAkg5qAEk3zFnBAJJT01oKKKCAAgoooEBmAQNIOqgBJN0wZwUDSE5NaymggALDLjDzdBi/A4yZr77Es0/BrGmwzi7DLmX/FWhbwADSNlXDhgaQdMOcFQwgOTWtpYACCgyzQISPs/aFcRNh0kkvDSERPqZOhlumw47HGUKG+Vqx7x0JGEA64qrb2ACSbpizggEkp6a1FFBAgWEWqA4YtSGk2WfDbGbfFWhDwADSBlKLJgaQdMOcFQwgOTWtpYACCgy7QL2gESaVOx+N7o4Mu5v9V6CJgAEk/fIwgKQb5qxgAMmpaS0FFFBAAagOISvHOrvAbRc3fjRLMwUUaCpgAEm/QAwg6YY5KxhAcmpaSwEFFFBgjkCEkCmT5gSP2CKI7Da18eR03RRQoKGAAST94jCApBvmrGAAyalpLQUUUEABA4jXgAKZBQwg6aAGkHTDnBUMIDk1raWAAgoo4CNYXgMKZBYwgKSDGkDSDXNWMIDk1LSWAgooMOwCTkIf9ivA/o+AgAEkHdUAkm6Ys4IBJKemtRRQQIFhFvA1vMM8+vZ9BAUMIOm4BpB0w5wVDCA5Na2lgAIKDLOACxEO8+jb9xEUMICk4xpA0g1zVjCA5NS0lgIKKDDsAhFCxu/Q+G1XcZdk1jRXQR/268T+dyRgAOmIq25jA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFD4j8nfAAAadklEQVRAAQUyCxhA0kENIOmGOSsYQHJqWksBBRRQQAEFFMgsYABJBzWApBvmrGAAyalpLQUUUEABBRRQILOAASQd1ACSbpizggEkp6a1FFBAAQUUUECBzAIGkHRQA0i6Yc4KBpCcmtZSQAEFFFBAAQUyCxhA0kHLFkAWBv6vvXuBtayq7zj+jQwg0IcUFRCRl8gjONABQcDWYhOHpkhblA5FKJDSAgXFWsCCpEAaUEBqEESoY4EKVMqjYTSxaAt98Ko4IINlIJQ3FGmhCQri4ECbv7NOOB7Pa5+1zj6P/d3JhHjv3v+99mct7z2/u/da+wRgV2A3YBPgcuDwLlRrAScCRwKbA08AS4FzgVeGpN0JOAd4T9r/FuAk4LtDHt+5mwFkRDgPU0ABBRRQQAEF6hAwgOQrz1sA2RJ4BHgaWA7s1yeAXAQcA1wK3AbsnYJKfP3YIWi3Be4E/he4IO3/UeANwO7Ag0PUMICMgOQhCiiggAIKKKDApAQMIPny8xZA1gXeCDwFLAB+3COAvBO4JwWH49sYzwc+AuwM3DuA91pgX2CHdPckdo87KSuBrwMHjtA93gEZAc1DFFBAAQUUUECBugQMIPnS8xZA2kX6BZAzgVOArdMdk9ZxWwEPA/H9U/vwxqNezwFfAQ7r2C8e+VoCbAS8WLGLDCAVwdxdAQUUUEABBRSoU8AAkq/d1AByY7rLEXNEOrdngLvT3Y1ewnumx7biEa6LO3aKr8VjXLHPHRW7yABSEczdFVBAAQUUUECBOgUMIPnaTQ0g8XjVy2myeqfiXcDaQDym1Wv7IBCPYO0PfLVjp/jaDcCHgOv61NgUiH/t2/bAlcuXL2fRosgibgoooIACCiiggALTJGAAye+NpgaQh4C407FXF8KYkP5m4O19eA8F/gZYDHyjY7/3A3GHJfa5ok+N04HTun3fAJI/sK2ggAIKKKCAAgqMQ8AAkq/a1ADiHZD8sWMFBRRQQAEFFFCgcQIGkPwub2oAcQ5I/tixggIKKKCAAgoo0DgBA0h+lzc1gJwFnNxnFaz4/if78A5aBeugtArWCxW7yEnoFcHcXQEFFFBAAQUUqFPAAJKv3dQAEu/5iJWu4gWC3d4DsguwIvHGhPRtgOfTCw5b6jHBPOaAxMTxJ9MXW+8BiTssMVG96mYAqSrm/goooIACCiigQI0CBpB87HkMIMelt5G/DjgjBY3rE9WytmARy+celd6Efmt6E/oRwCXA0W20rberx/s9Dm/7+nbAt9L7QD6Xvh5vQo/3f8Sb0B8YoXsMICOgeYgCCiiggAIKKFCXgAEkX3oeA8ijwBY9aCJgXJa+Fy8qPAk4EtgsvT19KXAOsHqIABK7LATOBt6T9r8F+ERbyKnaQwaQqmLur4ACCiiggAIK1ChgAMnHnscAkq8yuQoGkMnZe2YFFFBAAQUUUGCggAFkINHAHQwgA4lq3cEAUiu3J1NAAQUUUEABBaoJGECqeXXb2wCSb1iyggGkpKa1FFBAAQUUUECBwgIGkHxQA0i+YckKBpCSmtZSQAEFFFBAAQUKCxhA8kENIPmGJSsYQEpqTrLWimtgx/1hwbrdW7F6Fdy3DBYeOMlWem4FFFBAAQUUqChgAKkI1mV3A0i+YckKBpCSmpOqFeHj+iNh28Ww5Ms/G0IifFx9KDx4Ixyw1BAyqX7yvAoooIACCowgYAAZAa3jEANIvmHJCgaQkpqTqtUeMDpDSL/vTaq9nlcBBRRQQAEFhhYwgAxN1XNHA0i+YckKBpCSmpOs1S1oRHtadz563R2ZZJs9twIKKKCAAgoMFDCADCQauIMBZCBRrTsYQGrlHvPJ2kPI1vusOdnDN/d+NGvMzbG8AgoooIACCuQLGEDyDQ0g+YYlKxhASmpOQ60IIVctWRM8YosgcvDVvSenT0ObbYMCCiiggAIK9BQwgOQPDgNIvmHJCgaQkprTUMsAMg29YBsUUEABBRQoJmAAyac0gOQblqxgACmpOelaPoI16R7w/AoooIACChQXMIDkkxpA8g1LVjCAlNScZC0noU9S33MroIACCigwNgEDSD6tASTfsGQFA0hJzUnVchneScl7XgUUUEABBcYuYADJJzaA5BuWrGAAKak5qVq+iHBS8p5XAQUUUECBsQsYQPKJDSD5hiUrGEBKak6yVoSQHffvvdpV3CW5b5lvQZ9kH3luBRRQQAEFRhAwgIyA1nGIASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD6oASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD6oASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD6oASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD6oASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD6oASTfsGQFA0hJTWspoIACCiiggAKFBQwg+aAGkHzDkhUMICU1raWAAgoooIACChQWMIDkgxpA8g1LVjCAlNS0lgIKKKCAAgooUFjAAJIPagDJNyxZwQBSUtNaCiiggAIKKKBAYQEDSD5okwPIZcBhfQhPBc7s8/1+x28OPDlC9xhARkDzkBkVWHEN7Lg/LFi3+wWsXgX3LYOFB87oBdpsBRRQQIF5FDCA5PdqkwPInsA2XQiPB3YDdgXuGiKARIh5tWO/64EfjtA9BpAR0DxkBgUifFx/JGy7GJZ8+WdDSISPqw+FB2+EA5YaQmawi22yAgooMK8CBpD8nm1yAOmmtz7wPeBRYOEA3tYdkLWB1fld8ZMKBpBCkJaZcoH2gNEZQvp9b8ovy+YpoIACCsy/gAEkv48NID9t+GHgCuAE4LwhA8g6wHrAC13uhFTtIQNIVTH3n12BbkEjrqZ156PX3ZHZvWJbroACCigwBwIGkPxONID8tOE3gH2AtwLPDBlAfgD8PPAS8HXgJOChEbvGADIinIfNqEB7CNk6/q8HPHxz70ezZvQybbYCCiigwPwIGEDy+9IA8prhZsDjKUTsNwTtp4EFwHLgZWAv4Djg+2kOyWMDamwKxL/2bXvgyuXLl7NoUWQRNwUaIBAh5Kola4JHbBFEDr669+T0BpB4iQoooIAC0ytgAMnvGwPIa4Z/BnwKiCV3rh2Rdt8UYC4HDh9Q43TgtG77GEBG1Pew2RQwgMxmv9lqBRRQoKECBpD8jjeAvGZ4H7Ax8BZgVQZt3BGJOxtRp9/mHZAMZA+dEwEfwZqTjvQyFFBAgeYIGEDy+9oAssbwXcC3gIuAYzNZYwneeIQrJqdX3ZwDUlXM/WdXwEnos9t3tlwBBRRosIABJL/zDSBrDC9MwWOPFERyZFcAGwLxMsKqmwGkqpj7z6aAy/DOZr/ZagUUUEABDCD5g8AAsuZOxdNp1asdu5DGez7ihYXPp/1ilw3Sfi927L8E+ApwCXD0CN1jABkBzUNmUMAXEc5gp9lkBRRQQIEQMIDkjwMDCBwAXAfEJPSzu5BuCTwCtE8s3wW4Kd5YADyQVsGKN6vHe0RiJa24kzJoGd9uvWcAyR/TVpgVgQghO+7fe7WruEty3zLfgj4r/Wk7FVBAgYYIGEDyO9oAAjekORvxyNR/DRlANkkvKoy5IzHZPO6SPAF8FTgTeHbErjGAjAjnYQoooIACCiigQB0CBpB8ZQNIvmHJCgaQkprWUkABBRRQQAEFCgsYQPJBDSD5hiUrGEBKalpLAQUUUEABBRQoLGAAyQc1gOQblqxgACmpaS0FFFBAAQUUUKCwgAEkH9QAkm9YsoIBpKSmtRRQQAEFFFBAgcICBpB8UANIvmHJCgaQkprWUkABBRRQQAEFCgsYQPJBDSD5hiUrGEBKalpLAQUUUEABBRQoLGAAyQc1gOQblqxgACmpaS0FFFBAAQUUUKCwgAEkH9QAkm9YsoIBpKSmtRRQQAEFFFBAgcICBpB8UANIvmHJCgaQkprWUkABBRRQQAEFCgsYQPJBDSD5hiUrGEBKalpLAQUUUEABBRQoLGAAyQc1gOQblqxgACmpaS0FFFBAAQUUUKCwgAEkH9QAkm9YsoIBpKSmtRRQQAEFFFBAgcICBpB8UANIvmHJCgaQkprWUkABBRRQQAEFCgsYQPJBDSD5hiUr7AXcesUVV7DDDjuUrGstBRRQQAEFFFBAgQICK1eu5JBDDolKewO3FSjZuBIGkOnq8oOBK6erSbZGAQUUUEABBRRQoIvAh4GrlKkuYACpbjbOIzYCFgOPAj8a54kaUHv7FObih8P9DbjeSV6i1vXpa12Ptc71OMdZtNa6PoFyZ3o9sCVwI/BcubLNqWQAaU5fN+1KfzKfBtgVuKtpF1/z9WpdH7jW9VjrXI9znEVrresT8ExTI2AAmZqusCGFBfylVhi0Tzmtta5PoJ4zOabrcTaA1Oesdb3Wnm2AgAHEITKvAn6AqK9ntda6PoF6zuSYrsfZD8X1OWtdr7VnM4A4Bhoq4AeI+jpea63rE6jnTI7pepz9UFyfs9b1Wns2A4hjoKECmwJHAZcATzfUoK7L1rouadC6Hmud63GOs2itdX0CnmlqBHwEa2q6woYooIACCiiggAIKKDD/AgaQ+e9jr1ABBRRQQAEFFFBAgakRMIBMTVfYEAUUUEABBRRQQAEF5l/AADL/fewVKqCAAgoooIACCigwNQIGkKnpChuigAIKKKCAAgoooMD8CxhA5r+PvUIFFFBAAQUUUEABBaZGwAAyNV1hQyoI7AYcArwP2Ap4EfgP4FPAP3bUWQs4ETgS2Bx4AlgKnAu8UuGcTd11WOstgUd6IH0p+TfVcNjr3gE4Ddg1LU36KvAQcClwMfByWyHH9bCq3fcb1tpxnefc7ej4uf1P6RvbAv/puC6PnCr2snZcj43cwsMKGECGlXK/aRK4FngvcB1wF/BzwBHATsAfA19oa+xFwDHpQ9xtwN7A4UB8/dhpuqgpbcuw1q1faDcAcUz7Fh8w7pjS65umZr0fOAH4d+BJIEJGjNffA5YBv+24LtZdw1o7rouR/6TQ2sCK9MegDYDOAOLP63Le/awd1+WcrTSigAFkRDgPm6hAfCj7NrCqrRXrAd8B3gS8GVgNvBO4B7gAOL5t3/OBjwA7A/dO9Eqm/+TDWrd+oZ0JnDr9lzVTLbwwheXtgQcc12Ptu05rx3VZ7pOBjwFXpf+2BxB/Xtdn7bgua221EQQMICOgecjUCpwHfDz9dS3+ghwfhk8Btu54PCge23o4fd8Py6N1Z6d1+y+0cI/tpdFKe1SHQNwViUcG353ujjiuxzdEOq0d1+Ws3wasBI4DtkiPG7YHEMd1fdaO63LWVhpRwAAyIpyHTaXA3wIfAjYEXgBuTHc5NunS2meAu4F9p/JKpr9RndatX2jhHo/ExRaPXn02Pe42/Vc0PS1cH4h/8YjK7sDn0x29bVKoc1yX66tB1o7rctZ/n+Y27ZnCR8x3ag8gjuv6rB3X5aytNKKAAWREOA+bOoGYVBqPYH0N+GBqXTxeFRN3Y1Jv5xZzR+IZ2bjt71ZNoJt1/HXzr4H4kPE48Bbgj4BFwGfSQgDVztLcvU9PH9BaAncmyxjfsTmuy42NQdaO6zLWv5nmMe2RHp9tubcHEMd1fdaO6zLWVskQMIBk4Hno1Aj8InB7+tAb8zoeSy2LFYTiTsdeXVoaE9Jjrsjbp+YqZqMhvay7tT4mUf8LEH/xfEda0Wk2rnKyrYxHBuPfRmmlt1hc4ZPAPzuui3fMIGvHdT7569MqhTcBf5jKdQsg/ryuz9pxnW9thUwBA0gmoIdPXCAmn8et+3hU5TeAm9ta5F/UynZPP+teZ/pA+svnUcBflW1OY6r9CXB2epwwnqF3XI+v6zutHdf51mekRT/ijxDP9gkgjuv6rB3X+dZWyBQwgGQCevhEBdZJH25/Pc39iCVg2zefKS7XPYOse51pYVqJLP6Cf1a55jSq0sbA95JfODqux9f9ndaO6zzrTdMCIDEX7JK2UrESVqxM+Gvp+/HYpuO6PmvHdZ61RxcQMIAUQLTERAQWpPdNxF/Yfx+4sksr4gNvLPvYaxWs+H58oHPrLzCMda8KB6T3tcSLIOOFhG7VBVoTRuP9NvGeG8d1dcNhj+i0dlwPK9d9v13SYh/9qsSLZGPhCsd1fdaO6zxrjy4gYAApgGiJ2gVel9aRXwIc3fGXtfbGxHyQWOmq13tA4pdjvBTLrbfAsNYxn+a/O8rEI1u3phdExgpO8RZ6t94C3Qxj73PSJP54gebl6VEsx3XeSBrW2nGd5xxzxvbpUuIgIH5+x0tiY8n0WDzEn9f1WTuu86w9uoCAAaQAoiVqF/hLIJ7V/lfgi13O/s00+Ty+dTEQ8w8uTR+G48V68db0eBwgwotbf4FhrWP1q5g0HRNN4wNFrIJ1WLr7FHehPi30QIGWYUw2j7D2BmAxEI8Y3pI+yMULNh3XAykH7jCsteN6IOVIO3SbhO64Holy4EHdrB3XA9ncYdwCBpBxC1t/HALxAe29fQrHX9xaKwbF40MnAfEI0GbAU8DS9Ffl1oe5cbRxXmoOa/0HKXBsB/xSeg9LLHUcb51fNi8YY76O+Itw3OWIeTNvAlYB9wNXp7t48b9bm+M6rzOGtXZc5zn3OrpXAHFcl/fuZu24Lu9sxYoCBpCKYO6ugAIKKKCAAgoooIACowsYQEa380gFFFBAAQUUUEABBRSoKGAAqQjm7goooIACCiiggAIKKDC6gAFkdDuPVEABBRRQQAEFFFBAgYoCBpCKYO6ugAIKKKCAAgoooIACowsYQEa380gFFFBAAQUUUEABBRSoKGAAqQjm7goooIACCiiggAIKKDC6gAFkdDuPVEABBRRQQAEFFFBAgYoCBpCKYO6ugAIKKKCAAgoooIACowsYQEa380gFFFBAAQUUUEABBRSoKGAAqQjm7goooIACCiiggAIKKDC6gAFkdDuPVEABBRRQQAEFFFBAgYoCBpCKYO6ugAIKNFzg3cDtwKvAlsATDffw8hVQQAEFKgoYQCqCubsCCijQcIEvAL8FbAj8BXBWwz28fAUUUECBigIGkIpg7q6AAgo0WGBd4Gngi8BWwM7Adg328NIVUEABBUYQMICMgOYhCiigQEMFDgT+DliYAsgNwJ7AHR0euwLnAXsAPwCuBz4PrACOAC5r23994BPAQemRrueBfwBOAZ5sqLOXrYACCsy1gAFkrrvXi1NAAQWKCnwN2Dzd+Vg73Q25Bjim7SxxR+ROYDVwIfAsEMFlA+CXOwLIOsDNwC7Al4DvAm8Djk3BZVE6vuhFWEwBBRRQYLICBpDJ+nt2BRRQYFYENk53JOLOxLmp0RelOxebAqvS1yKQHJBCxb3pawuAm4Bf6QggJ6Y5JL+aJra3LCKQfDud5+RZAbKdCiiggALDCRhAhnNyLwUUUKDpAh9PgSDuUDyVMPYCbgV+F4jgsRbwfeDfgH07wFqPb7U/gnUX8DKwXxfcqPEC8K6mw3v9CiigwLwJGEDmrUe9HgUUUGA8AvcAP053PNrPEEFheQoRm6THsi4APtrRjJiw/p2OOyA/BNbr09zHgS3GczlWVUABBRSYlIABZFLynlcBBRSYHYF4JOruPs2N+R5vBeJ3SqySNWwAeSnV/fMetX8E3DI7TLZUAQUUUGAYAQPIMEruo4ACCjRb4LNpYvihwCsdFL+QJpD/KXB+egQrQsPijv26PYIVc0RiMvv2zeb16hVQQIFmCRhAmtXfXq0CCihQVSAmkMecj3h8qjNUtGrF8rr/l1bHuhb4nSEnoccE83iRYefSvFE3fj+9Efifqg12fwUUUECB6RYwgEx3/9g6BRRQYNICHwCWpaV2L+7RmDOAeIwqltmN1bBiGd74byzD+1xahjfe9xHL6h4OXJ7qxIsNv5lWx4rgEndOYp5JvOQw3rYe7xw5ddIAnl8BBRRQoKyAAaSsp9UUUECBeROIYBDL6m6W5nd0u77WHJF4BOtjaeWqzwC7p5Ws4kWE8fLB24AlKVi06kQIiWMOBt6RAki8gDCW7Y3AE+8GcVNAAQUUmCMBA8gcdaaXooACCkyxQISY64BYuvf2KW6nTVNAAQUUGLOAAWTMwJZXQAEFGigQS+vGCletrfUiwp2A9pcWNpDGS1ZAAQUUMIA4BhRQQAEFSgs8BsRjV/cDG6YXFcb8kHjUKh7TclNAAQUUaLCAAaTBne+lK6CAAmMSiMnnsWJWzBuJbSXwubbJ52M6rWUVUEABBWZBwAAyC71kGxVQQAEFFFBAAQUUmBMBA8icdKSXoYACCiiggAIKKKDALAgYQGahl2yjAgoooIACCiiggAJzImAAmZOO9DIUUEABBRRQQAEFFJgFAQPILPSSbVRAAQUUUEABBRRQYE4EDCBz0pFehgIKKKCAAgoooIACsyBgAJmFXrKNCiiggAIKKKCAAgrMiYABZE460stQQAEFFFBAAQUUUGAWBAwgs9BLtlEBBRRQQAEFFFBAgTkRMIDMSUd6GQoooIACCiiggAIKzIKAAWQWesk2KqCAAgoooIACCigwJwL/D1IdaYSSymqwAAAAAElFTkSuQmCC\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py:3316: MatplotlibDeprecationWarning: The 'hold' keyword argument is deprecated since 2.0.\n",
      "  mplDeprecation)\n"
     ]
    }
   ],
   "source": [
    "# Create data\n",
    "x = np.array([[38],[27], [48], [17], [33], [32], [38], [38], [26], [34], [33], [41], [45], [46], [26], [35], [22], [23]])          #Criar vetor x\n",
    "y = np.array([[17.1], [20.7], [25.2], [13.6], [13.4], [19.8], [11.7], [17.3], [15.6], [20.5], [22.4], [20.2], [17.5], [22.7], [7.5], [27.2], [9.2], [16.1]])  #Criar vetor y, randn gera numeros normalmente distribuidos com media 0 com desvio padrao de 1\n",
    "\n",
    "# Estimate linear relation between X and Y\n",
    "\n",
    "X = np.append(x, np.ones((18,1)), axis = 1)\n",
    "\n",
    "f_est = np.dot(np.linalg.pinv(X), y)\n",
    "y_est = np.dot(X, f_est)\n",
    "\n",
    "# Plot commands\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y_est, hold = True)\n",
    "plt.plot(x, y, 'x')\n",
    "\n",
    "plt.xlabel('Age');\n",
    "plt.ylabel('Body Fat');\n",
    "\n",
    "plt.title('Linear regression');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}