Tutorials/PythonVisualize.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Visualizing data in Python\n",
    "**by [Richard W. Evans](https://sites.google.com/site/rickecon/), May 2017**\n",
    "\n",
    "A picture is worth a thousand words. In fact, most journal articles can be summarized by one good figure or one good table. This conjecture makes for a good rule for any researcher. \"What is the best picture or table that can summarize the story I want to tell with my results.\" This section will focus on using data visualization as preliminary a way for understanding and interpreting your data. This chapter is about using visualization for exploring your data. But the principles can be applied to the later steps of presenting your results. \n",
    "\n",
    "The standard visualizations of any data are the scatterplot, the line plot, the bar graph, the histogram (a particular type of bar graph), There are 3-D versions of all of these. Then there are ways to allow each of these methods to display more than three dimensions of the data. Finally, recent developments in D3 (data-driven documents) JavaScript visualizations for web browsers have made interactive graphics available to the common internet user via flyover display, toggle switches, slider bars, and other methods.\n",
    "\n",
    "We will focus on Python's `matplotlib` visualization package. But many other libraries exist in Python (e.g.scikitlearn, chaco, mayavi, bokeh), and many other programming platforms also have powerful visualization packages (e.g., R, Stata, SAS, MATLAB, Mathematica)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Some matplotlib preliminaries\n",
    "Plots in matplotlib are stored as `Figure` objects. The command to create a new figure object is,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1227d92b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# This next command is specifically for Jupyter Notebook\n",
    "%matplotlib inline\n",
    "\n",
    "fig = plt.figure()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can reference and change options in the active figure using the `plt.gcf()` function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.1. Subplot commands\n",
    "When you declare a figure using the `plt.figure()` command, you must then declare how many subplots will be in the figure. This is done using the `add_subplot()` command. You have to create one or more subplots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ax1 = fig.add_subplot(2, 2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ax2 = fig.add_subplot(2, 2, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ax3 = fig.add_subplot(2, 2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fill in the third subplot with a two-way line plot of some white noise. If we don't specify the axes of the specific subplot that we want, matplotlib will use the most recently created subplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1229583c8>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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/jBgxAiUlJWKHYhY8PDzQvHlzscNQ9rjVLaGanJys9y40/fv3x8KFC1Xu8MM5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\nEGJhKHETQoiF+X8r+JkQtnXsugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1229179e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "plt.plot(np.random.randn(50).cumsum(), 'k--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `k--` is a style option instructing matplotlib to plot the data with a black dashed line. The objects returned by `fig.add_subplot()` avobe are `AxesSubPlot` objects on which you can directly plot on the other empty subplots by calling each one's instance methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_ = ax1.hist(np.random.randn(100), bins=20, color='y', alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x122958a20>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax2.scatter(np.arange(30), np.arange(30) + 3*np.random.randn(30))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since creating a figure with multiple subplots according to a particular layout is such a common task, there is a convenience method, `plt.subplots()`, that creates a new figure and returns a NumPy array containing the created subplot objects. This is very useful as the `axes` array can be easily indexed like a two-dimensional array--for example, `axes[0, 1]`. You can also indicate that subplots should have the same $x$ and $y$ axis using `sharex` and `sharey` options, respectively. This is especially useful when comparing data on the same scale; otherwise, matplotlib auto-scales plot limits independently"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1229a93c8>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x122a3b128>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x122a76048>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x122aa2f28>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x122a7eba8>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x122b0deb8>]], dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ErCWL3wQG9mlsjbSX2w50Qq6QjWz3ejuJTsjWuVbRrEJQz20rWsWu+7Dts7lh4PV9HF+j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\nYGaWcf8fiv5/FT1ilzQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1228c1438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 3)\n",
    "axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.2. Colors, markers, and line styles\n",
    "Matplotlib can accept a single string argument that can encapsulate a subset of the options available in the `color`, `marker`, and `linestyle` options. For example, the following two commands do the same thing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x122bc9f28>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A7yiljtF45/+Ldji3ED6ruq6aPQV7eHBS6wRsYUFhrPrpKpIGJFncd/3R9QQa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\nUagFRN8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122b6a198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.arange(45)\n",
    "yy = 0.5 * xx ** 2 - 3 * xx * np.random.randn(45)\n",
    "\n",
    "plt.plot(xx, yy, 'go--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x122cec470>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A7yiljtF45/+Ldji3ED6ruq6aPQV7eHBS6wRsYUFhrPrpKpIGJFncd/3R9QQa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\nUagFRN8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122b80748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xx, yy, linestyle='--', color='g', marker='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.3. Ticks, labels, and legends\n",
    "The following commands show how to add a title to a plot, add axis labels, and set the minimum and maximum to be plotted on both axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 700)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZL5zFqoJVLLxhYaX3qnSHRBGROHyw7AOO+ecxLNqwaL9pZrY3icxeO7tK3YGT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\nERGRQP4/hEv8yuehwhkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122b80240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xx, yy, linestyle='--', color='g', marker='o')\n",
    "plt.title('This is the best plot ever', fontsize=20)\n",
    "plt.xlabel(r'$X$')\n",
    "plt.ylabel(r'$Y$')\n",
    "plt.xlim([10, 30])  # This gives the xmin and xmax to be plotted\n",
    "plt.ylim([200, 700])  # This gives the ymin and ymax to be plotted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding a legend to a plot is essential if you are plotting more than one series. In the example below, I plot two time series. Both series are with periods 1 and 50. Note that I put grid lines on the plot by using the `MultipleLocator` function from the `matplotlib.ticker` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122e00cf8>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wkoZX6GmgMmUVT2tDon0K9wJvqurBQE9gOTAemKWq3YFZ7mfDMIz0J41CT6OR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\nwTAMw6jClIJhGIZRxf8DidlplfOne74AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122d20160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.ticker import MultipleLocator\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "my_age = np.arange(3, 45)\n",
    "knees_hurt = 0.03 * np.arange(50) ** 2\n",
    "all_ages = np.arange(50)\n",
    "plt.plot(all_ages[4:46], my_age, marker='D', label='My age')\n",
    "plt.plot(all_ages, knees_hurt, marker='o',\n",
    "         label='How much my knees hurt')\n",
    "# for the minor ticks, use no labels; default NullFormatter\n",
    "minorLocator = MultipleLocator(1)\n",
    "ax.xaxis.set_minor_locator(minorLocator)\n",
    "plt.grid(b=True, which='major', color='0.65', linestyle='-')\n",
    "plt.title('My knee pain and my age', fontsize=20)\n",
    "plt.xlabel(r'Age')\n",
    "plt.ylabel(r'Pain units')\n",
    "plt.xlim([-1.0, 50])\n",
    "plt.ylim([-2.0, 80])\n",
    "plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose I wanted to change the tick labels on the x axis to highlight some key years (8, 28, and 41) in addition to the 0, 10, 20,... currently listed. And I want those three extra years to be labeled with the strings ('bt', 'mt', 'cr'). And assume I wanted the labels to be vertically oriented (rather than the current horizontal orientation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122a0c2b0>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZZwIQCoU44IADWLduXc33/fffn/Xrax/zww8/pH///hxxxBH079+fFStWALBjxw7OOOMM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\nYRgG8P8Bbo2si1HHSygAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122d39a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xtickvals = [0, 8, 10, 20, 28, 30, 40, 41, 50]\n",
    "xticklabs = [0, 'bt', 10, 20, 'mt', 30, 40, 'cr', 50]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "my_age = np.arange(3, 45)\n",
    "knees_hurt = 0.03 * np.arange(50) ** 2\n",
    "all_ages = np.arange(50)\n",
    "plt.plot(all_ages[4:46], my_age, marker='D', label='My age')\n",
    "plt.plot(all_ages, knees_hurt, marker='o',\n",
    "         label='How much my knees hurt')\n",
    "# for the minor ticks, use no labels; default NullFormatter\n",
    "minorLocator = MultipleLocator(1)\n",
    "ax.xaxis.set_minor_locator(minorLocator)\n",
    "plt.grid(b=True, which='major', color='0.65', linestyle='-')\n",
    "plt.title('My knee pain and my age', fontsize=20)\n",
    "plt.xlabel(r'Age')\n",
    "plt.ylabel(r'Pain units')\n",
    "plt.xticks(xtickvals, xticklabs, rotation='vertical')\n",
    "plt.xlim([-1.0, 50])\n",
    "plt.ylim([-2.0, 80])\n",
    "plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.4. Annotations and drawing on a Subplot\n",
    "Annotations and text can be added using the `text`, `arrow`, and `annotate` functions. `text` draws text at given coordinates `(x, y)` on the plot with optional custom styling.\n",
    "```python\n",
    "ax.text(x, y, 'Hello world!', family='monospace', fontsize=10)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(600, 1800)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZnuHxEBGJsx+LiDwsInVFpKmIbHaqN0NEbrR/zfRF2zx54oknGDp0KIsWLbL+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\nNm/ePCZOnMjBgweJj4/n4sWLdOvWjZ9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pmETO1e0pYAyAmd0PPA8My00MCDAV+L6ktfga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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122dbd0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from datetime import datetime\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "data = pd.read_csv('DataFiles/spx.csv', index_col=0, parse_dates=True)\n",
    "spx = data['SPX']\n",
    "spx.plot(ax=ax, style='k-')\n",
    "\n",
    "crisis_data = [\n",
    "    (datetime(2007, 10, 11), 'Peak of bull market'),\n",
    "    (datetime(2008, 3, 12), 'Bear Stearns Fails'),\n",
    "    (datetime(2008, 9, 15), 'Lehman Bankruptcy')\n",
    "]\n",
    "\n",
    "for date, label in crisis_data:\n",
    "    ax.annotate(label, xy=(date, spx.asof(date) + 50),\n",
    "                xytext=(date, spx.asof(date) + 200),\n",
    "                arrowprops=dict(facecolor='black'),\n",
    "                horizontalalignment='left', verticalalignment='top')\n",
    "\n",
    "# Zoom in on 2007-2010\n",
    "ax.set_xlim(['1/1/2007', '1/1/2011'])\n",
    "ax.set_ylim([600, 1800])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.4. Saving figures\n",
    "Good housekeeping in your file directories is an essential skill for any significant coding project. The directory of the main Python scripts can get cluttered with datafiles, scripts, modules, figure files, and other output files. It is good practice to save files to an \"images\" folder. I prefer to have that folder in the same directory as my calling Python scripts or modules. But in the following format, one can put the images folder anywhere to which the user's terminal can write. This code won't work in this Jupyter notebook.\n",
    "```python\n",
    "from matplotlib.ticker import MultipleLocator\n",
    "import os\n",
    "\n",
    "plot = True\n",
    "\n",
    "if plot:\n",
    "    '''\n",
    "    --------------------------------------------------------------------\n",
    "    cur_path    = string, path name of current directory\n",
    "    output_fldr = string, folder in current path to save files\n",
    "    output_dir  = string, total path of images folder\n",
    "    output_path = string, path of file name of figure to be saved\n",
    "    xx          = (45,) vector, values of xx\n",
    "    yy          = (45,) vector, values of yy\n",
    "    --------------------------------------------------------------------\n",
    "    '''\n",
    "    # Create directory if images directory does not already exist\n",
    "    cur_path = os.path.split(os.path.abspath(__file__))[0]\n",
    "    output_fldr = 'images'\n",
    "    output_dir = os.path.join(cur_path, output_fldr)\n",
    "    if not os.access(output_dir, os.F_OK):\n",
    "        os.makedirs(output_dir)\n",
    "\n",
    "    # Plot line plot of xx and yy\n",
    "    xx = np.arange(45)\n",
    "    yy = 0.5 * xx ** 2 - 3 * xx * np.random.randn(45)\n",
    "    plt.plot(xx, yy, 'go--')\n",
    "    # for the minor ticks, use no labels; default NullFormatter\n",
    "    minorLocator = MultipleLocator(1)\n",
    "    ax.xaxis.set_minor_locator(minorLocator)\n",
    "    plt.grid(b=True, which='major', color='0.65', linestyle='-')\n",
    "    plt.title('Line plot of X and Y', fontsize=20)\n",
    "    plt.xlabel(r'$X$')\n",
    "    plt.ylabel(r'$Y$')\n",
    "    output_path = os.path.join(output_dir, 'xyplot')\n",
    "    plt.savefig(output_path)\n",
    "    # plt.show()\n",
    "    plt.close()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code won't work in this Jupyter notebook because of the line in which `cur_path` is set. This script is not being run from a traditional script and therefore cannot use that `os.path.split()` function. But lets go through some of the main principles in this code.\n",
    "* It is often wise to set a Boolean in your script (`plot` in this example) to allow yourself to easily turn the plotting on and off within your code. Sometimes your plotting is just a diagnostic that you don't need to run every time with your analysis.\n",
    "* Have your script intelligently choose the folder from which the plotting functionality is being called. This is the `cur_path = os.path.split()` line. Those lines check what the current directory is, check if a subdirectory named \"images/\" already exists, and makes that directory if it does not already exist. Then the `plt.savefig()` command saves the figure to that folder.\n",
    "* At the end of a script that creates a figure, make sure to include the plt.close() command. If you don't do that, the matplotlib objects can pile up in your computer's memory--regardless of whether the plots are open and visible on your screen--and crash your computer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. The Almighty Histogram and its Friends"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1. The cumulative distribution function\n",
    "All the standard univariate descriptive statistics (e.g., mean, standard deviation, quantiles, autocorrelation) are simply statistics derived from the cumulative distribution function (*cdf*). The CDF $F$ of a random variable $X$ is defined as fraction of the values of $X$ that are greater than some realization of the random variable $x$.\n",
    "$$F(x) \\equiv Pr(X\\leq x)$$\n",
    "The estimator for the CDF is the empirical cumulative distribution function (*ecdf*) defined as:\n",
    "$$F_n = \\frac{\\#\\{x_i\\leq x\\}}{n} = \\frac{\\#x_i\\in(-\\infty, x]}{n} = \\frac{1}{n}\\sum_{i=1}^n I_{(-\\infty, x]}(x_i)$$,\n",
    "where $\\{x_1,x_2,...x_n\\}$ is a random sample of $n$ draws from $F$ and ,\n",
    "$$I_A(x) = \\begin{cases}1\\quad\\text{if}\\quad x\\in A \\\\ 0 \\quad\\text{if}\\quad x\\notin A.\\end{cases}$$\n",
    "\n",
    "Because the data for the *ecdf* are discrete, the *ecdf* is a stepwise linear (staircase) function. The Figure below shows the *ecdf* of Old Faithful eruption durations lasting longer than 3 seconds. The smooth red dotted line is a fitted continuous *cdf*.\n",
    "![title](Images/OldFaithfulCDF.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2. The univariate probability density function and the histogram\n",
    "The most visually instructive transformation of the *cdf* is the probability density function (*pdf*). The value of the *pdf* at a given point does not have an intuitive interpretation. The *pdf* is the derivative or slope or rate of change of the *cdf*. But the *pdf* is good for describing what percent of the distribution lies between two values. The *pdf* $f$ is a function of particular values $x$ from the support of the random variable $X$ defined in the following way,\n",
    "$$f(x)\\equiv \\frac{\\partial F(x)}{\\partial x}.$$\n",
    "\n",
    "Scott (2015, p. 39) states that \"the empirical probability density function *epdf* is always a discrete Uniform density over the data, that is, the probability mass $n^{-1}$ at each data point.\" This means that the *epdf* is not continuous, nor is it continuously differentiable. It is simply a one-dimensional scatter diagram with each marker lining up along $n^{-1}$ on the $y$ axis and at each data point on the $x$-axis.\n",
    "\n",
    "A much more instructive representation of the empirical content of a probability density function is the *histogram*. It is more analogous to the discrete *ecdf* from the previous section. A histogram is an empirical estimator for the probability density function. A histogram $h(x)$ for a random variable $X$ is a set of nonoverlapping, contiguous intervals that include the entire support of $X$ that gives the count or frequency of observations in each bin. As such, a histogram $h(x)$ with $B$ bins is completely characterized by bin cutoffs $\\{c_1,c_2,...c_B, c_{B+1}\\}$. Let $bin_b$ be characterized by $x\\in(c_b, c_{b+1}]$ The specification of the count version of the histogram is the following.\n",
    "$$h(x) = \\sum_{i=1}^N I_{bin_b}(x_i)$$\n",
    "The bins need not have equal width, but that is usually the default for most histogram programming and graphical functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the penny thickness dataset `penny.csv`. Read it in to pandas. Reformat it to a Series with 90 elements such that each observation is a penny thickness. Create a histogram with 10 equally spaced bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "year        \n",
       "1945  penny1    51.8\n",
       "      penny2    54.6\n",
       "1946  penny1    53.2\n",
       "      penny2    54.2\n",
       "1947  penny1    53.0\n",
       "      penny2    53.0\n",
       "1948  penny1    53.6\n",
       "      penny2    52.2\n",
       "1949  penny1    53.2\n",
       "      penny2    51.6\n",
       "1950  penny1    53.4\n",
       "      penny2    51.0\n",
       "1951  penny1    53.4\n",
       "      penny2    54.0\n",
       "1952  penny1    53.4\n",
       "      penny2    54.6\n",
       "1953  penny1    50.6\n",
       "      penny2    54.8\n",
       "1954  penny1    52.2\n",
       "      penny2    54.6\n",
       "1955  penny1    52.6\n",
       "      penny2    54.2\n",
       "1956  penny1    54.0\n",
       "      penny2    53.6\n",
       "1957  penny1    53.6\n",
       "      penny2    55.0\n",
       "1958  penny1    53.2\n",
       "      penny2    53.2\n",
       "1959  penny1    56.8\n",
       "      penny2    57.2\n",
       "                ... \n",
       "1975  penny1    54.0\n",
       "      penny2    54.2\n",
       "1976  penny1    53.2\n",
       "      penny2    53.2\n",
       "1977  penny1    54.0\n",
       "      penny2    53.2\n",
       "1978  penny1    53.0\n",
       "      penny2    53.6\n",
       "1979  penny1    54.0\n",
       "      penny2    53.0\n",
       "1980  penny1    53.6\n",
       "      penny2    53.0\n",
       "1981  penny1    54.8\n",
       "      penny2    54.0\n",
       "1982  penny1    54.4\n",
       "      penny2    54.6\n",
       "1983  penny1    52.8\n",
       "      penny2    52.6\n",
       "1984  penny1    55.2\n",
       "      penny2    54.0\n",
       "1985  penny1    55.6\n",
       "      penny2    56.0\n",
       "1986  penny1    55.0\n",
       "      penny2    53.2\n",
       "1987  penny1    55.0\n",
       "      penny2    54.0\n",
       "1988  penny1    54.0\n",
       "      penny2    55.6\n",
       "1989  penny1    56.2\n",
       "      penny2    54.0\n",
       "Length: 90, dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import DataFrame, Series\n",
    "\n",
    "pennies = pd.read_csv('DataFiles/penny.csv', names =['year', 'penny1', 'penny2'],\n",
    "                      index_col='year', skiprows=[0, 1, 2, 3, 4, 5])\n",
    "pennies_all = pennies.stack()\n",
    "pennies_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  2.,   4.,   8.,  16.,  20.,  11.,  10.,  11.,   5.,   3.]),\n",
       " array([ 50.6 ,  51.44,  52.28,  53.12,  53.96,  54.8 ,  55.64,  56.48,\n",
       "         57.32,  58.16,  59.  ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N1gcdudcIfWY7JmuBtd3qU0nu71Hb3uIQ4LFJF7GMuX8W5v5Z3LLaR+k3Gf7SpXbsE/wz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\nY/BLUmP+H+5wy87uPNYfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122ed5860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pennies_all, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `plt.hist()` outputs three objects. The first is a list of counts in each bin (`n`). The second is a list of bin endpoints (`bin_cuts`), and the third is a list of patch objects. I have no idea what the patch objects are, but the `n` and `bin_cuts` are straightforward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a histogram with four equally spaced bins. Let's make the bin color green."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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klzL8EPT1VfU/i8y4aGPm6FtVdU5Vba2qrQzL63er6r8XGHUhxr2HgH8GLunGXwicwQb7\nMqqT5QRzdJjhxgEM5+r+xSQ8edzlMl/nAjcmgeFcf66qvpLkAeAZDP80BPhGVb19cTEXauQcLTbS\nhjLuPXQGcG2SA8DPgR2n8F964+boUeDvkpwG/C///62vzfJMUUlqhLtcJKkRFrokNcJCl6RGWOiS\n1AgLXZIaYaFLUiMsdElqhIUuSY34P81Zui0lB94aAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12303b320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bin_cuts, patches = plt.hist(pennies_all, 4, facecolor='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a histogram with 90 equally spaced bins. Note that there are only 90 observations in the `pennies_all` data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123060240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bin_cuts, patches = plt.hist(pennies_all, 90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cardinal sin of visualizations is not labeling your plot and your axes. We have so far committed that cardinal sin. We can label the plot and the axes by using the following additional matplotlib options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Number of observations')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PYI8/YD04qPC81myvDUG/gDRA4GhJ3T47xaHMLTSB9IX+FWnf3u8qzvciaTj8sv0VSP5R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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1231cfb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bin_cuts, patches = plt.hist(pennies_all, 10)\n",
    "plt.title('Histogram of penny thickness (mils): 1945-1989', fontsize=17)\n",
    "plt.xlabel(r'Thickness (mils)')\n",
    "plt.ylabel(r'Number of observations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now what if we wanted our histogram to be in frequency form rather than count form. The frequency form of a histogram is more analogous to the probability density function. It is simply a normalized version of the count histogram in which each observation is weighted by $n^{-1}$. We can implement this by creating a weight vector of $N$ elements, each of which is $n^{-1}$, we can then feed this directly into the histogram function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Percent of observations in bin')"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0srAlSdtKelTSJEmH1Xl+S0l3S5oladfSc3tLeiw/9q62OWZmtqCrkrjukfTh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\nyv8D+8HwX3VvMYMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12329c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_bins = 10\n",
    "weights = (1 / pennies_all.shape[0]) * np.ones_like(pennies_all)\n",
    "n, bin_cuts, patches = plt.hist(pennies_all, num_bins, weights=weights)\n",
    "plt.title('Histogram of penny thickness (mils): 1945-1989', fontsize=17)\n",
    "plt.xlabel(r'Thickness (mils)')\n",
    "plt.ylabel(r'Percent of observations in bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can verify that the percents in each bin sum to one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(n.sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It would probably be more instructive if the labels on the $x$ axis were closer to the boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Percent of observations in bin')"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RcUO+HUgaWdiWpO0kPSxpoqRRFa9vJekuSTMk7Vp6bR9Jj+TbPvU2x8zM5nV1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\nrrjMzKyruOIyM7Ou4orLzMy6yv8DHliIxCClll8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1230fcd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bin_cuts, patches = plt.hist(pennies_all, num_bins, weights=weights)\n",
    "plt.xticks(np.round_(bin_cuts, 1))\n",
    "plt.title('Histogram of penny thickness (mils): 1945-1989', fontsize=17)\n",
    "plt.xlabel(r'Thickness (mils)')\n",
    "plt.ylabel(r'Percent of observations in bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no universal rule for what is the optimal number of bins and what are the optimal bin cutoff values. Some of the principles for making these decisions are based on minimizing error and asymptotic bias between the true probability density function $f(x)$ and the estimator of the *pdf* $h(x)$. A great reference for many optional rules is Scott (2015, chap. 3).\n",
    "\n",
    "One of the most common of these rules is Sturges' number of bins rule for equal width bins. Let $k$ be the number of equal-width bins,\n",
    "$$\\textbf{Sturges' rule}:\\quad k = \\log_2 N$$\n",
    "rounded to the nearest integer. This rule is based on the property that the observation counts in each bin of histogram $h(x)$ are themselvess binomial random variables. Sturges' rule gives a frequency histogram of normal density with mean $(k-1)/2$ and variance $(k-1)/4$. This rule is good for distributions that should be normal. In our penny thickness case, $k$ should equal 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Percent of observations in bin')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SfgRb7uwWvl23XGu214agX0waIHCUpNk+N/VDmdvoHNIX+lTSsb3fVSz3Fmk4/BI9FUj+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\n5f8BWupK+MVJHL0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12369ccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_bins = int(np.ceil(1 + np.log2(90)))\n",
    "n, bin_cuts, patches = plt.hist(pennies_all, num_bins, weights=weights)\n",
    "plt.xticks(np.round_(bin_cuts, 1))\n",
    "plt.title('Histogram of penny thickness (mils): 1945-1989', fontsize=17)\n",
    "plt.xlabel(r'Thickness (mils)')\n",
    "plt.ylabel(r'Percent of observations in bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, from previous versions of this histogram, it is clear that the distribution is not normal. In this case, Sturges' rule oversmoothes the distribution and we don't see the richness between thicknesses 52.0 and 55.0. A histogram with the correct thickness takes a little exploration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3. The 3D histogram\n",
    "A 3D histogram can be used as an estimator for a bivariate probability density function. Load in Old Faithful geyser duration data file `geyser.csv`. Make a 3D frequency histogram with geyser durations in the current period `duration(t)` on the $x$ axis and geyser durations in the next period `duration(t+1)` on the $y$ axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>duration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>3.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>3.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>3.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>4.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>3.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>4.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>4.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>1.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>4.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>2.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>3.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>4.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>1.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>4.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>1.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>4.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>4.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>3.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>4.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>1.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>4.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>2.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>4.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>4.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>4.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>4.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>3.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>4.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>2.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>4.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>1.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>4.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>1.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>4.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>4.12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>107 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     duration\n",
       "0        4.37\n",
       "1        3.87\n",
       "2        4.00\n",
       "3        4.03\n",
       "4        3.50\n",
       "5        4.08\n",
       "6        2.25\n",
       "7        4.70\n",
       "8        1.73\n",
       "9        4.93\n",
       "10       1.73\n",
       "11       4.62\n",
       "12       3.43\n",
       "13       4.25\n",
       "14       1.68\n",
       "15       3.92\n",
       "16       3.68\n",
       "17       3.10\n",
       "18       4.03\n",
       "19       1.77\n",
       "20       4.08\n",
       "21       1.75\n",
       "22       3.20\n",
       "23       1.85\n",
       "24       4.62\n",
       "25       1.97\n",
       "26       4.50\n",
       "27       3.92\n",
       "28       4.35\n",
       "29       2.33\n",
       "..        ...\n",
       "77       4.42\n",
       "78       1.90\n",
       "79       4.63\n",
       "80       2.93\n",
       "81       3.50\n",
       "82       1.97\n",
       "83       4.28\n",
       "84       1.83\n",
       "85       4.13\n",
       "86       1.83\n",
       "87       4.65\n",
       "88       4.20\n",
       "89       3.93\n",
       "90       4.33\n",
       "91       1.83\n",
       "92       4.53\n",
       "93       2.03\n",
       "94       4.18\n",
       "95       4.43\n",
       "96       4.07\n",
       "97       4.13\n",
       "98       3.95\n",
       "99       4.10\n",
       "100      2.72\n",
       "101      4.58\n",
       "102      1.90\n",
       "103      4.50\n",
       "104      1.95\n",
       "105      4.83\n",
       "106      4.12\n",
       "\n",
       "[107 rows x 1 columns]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geyser_dur = pd.read_csv('DataFiles/geyser.csv', names =['duration'])\n",
    "geyser_dur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dur_t = geyser_dur['duration'][:-1]\n",
    "dur_tp1 = geyser_dur['duration'][1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a 3D histogram using matplotlib, you have to use the NumPy function `histogram2d()` and then port the objects into a 3D bar chart using matplotlib's `bar3D()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0.92,'Histogram by Old Faithful duration(t) and duration(t-1)')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6+KxWK7m5uWRnZ3PgwAF+/etfJ/TYOjs7+fnPf87IyAhbt25l//79nHvuucryK664ghtu\nuAGTyRQ2hliSJB566CHuv/9+nnvuORwOB+3t7Vx77bUMDg5y8803B7X52te+xr59+/jjH/+I2+3m\n5z//uS5ykzE8PIzL5aKoqAij0cgrr7yiTEyGwrRp0/yul14sW7aMTz/9lM8++wyHw8G9996rue2G\nDRv46U9/SktLCz09PUGz3cuXL1fcW7t37+aPf/xjxO1ZrVbS09MpLCzEbrdz5513+i2PdqyXXHIJ\n3//+9+nu7qarq4v77ruPjRs3ajqWc8891891ZjQaKSwsDNrfu+++y1e/+lXMZnPQNvReOzXMZjMX\nXHABmzZtwuFw8Pnnn/u5WwLxr//6r2zbtk2JDrnrrrv8SGz58uW8+uqr9PX10dbWxs9//vOI+x8a\nGkKSJIqKihBC8Nhjj3HgwAFl+bRp02hubg47mXnJJZfw+OOP8+mnnzI8PMztt9/OKaecQmlpadRj\nX7NmDV1dXX73i5Zx7fV6cTqdjIyMIIRQ/pfR2NjI0NAQq1evjtqHUBgzQn7jjTeU2eMbb7yRLVu2\nYLFYyMzM5M477+Skk04iLy+PnTt3cs0113D55Zfzla98hTlz5mCxWPjFL34B+Gagf/GLX3DxxRdT\nUlJCTk4OxcXFId0AMh566CGee+45cnJy+Ld/+zcuuuiihB7biSeeyOHDh5k6dSp33nknL774op8b\n5fLLL+fzzz+P6J8DX0jaM888wyOPPMLUqVNZtGgRDoeDv//970FuGfC9im7dupXbbruNwsJCDh8+\nzEknnaS7/3l5eTzyyCNceOGFFBQU8OKLL4b0c8u444472LRpE3l5efz0pz/Vvb9FixZxxx13sHbt\nWubPn69EF2jB9ddfz+mnn85xxx3H6tWrg5IqfvCDH3DgwAHy8vK47777uPTSSyNu7+qrr2bGjBnM\nmDGDxYsXByWuXHvttXzyySfk5+eHTODYtGkTy5Yt47jjjmPp0qWceOKJ3H777ZqO5YQTTiA9PZ09\ne/Yov917771ceuml5OXlKQ+TZ599lm9+85sht6H32gXi17/+NX19fUybNo1vfOMbXH311WHXXbp0\nKT/72c/YsGEDM2fOZPr06X4ugauuuoqFCxdSVlbG2WefzcUXXxxx30uXLuU73/kOJ5xwAiUlJRw4\ncIATTzxRWX7GGWcwd+5cpk2bFnJu5Oyzz+aee+7hwgsvpKSkhMbGRp599llNx52ens7ll1/ut/5N\nN93E73//e/Ly8pQosEC8/fbbZGRksG7dOurq6sjIyOCcc85Rlj/77LNcffXVpKWlaepHELTO/omA\nKIvxAqvVKoxGY8johPECu90usrOzlaiDFFKQ8eqrr4qvf/3rYZfv3bvXL3IphcShvb1dLFiwQDid\nzoRsz263i3nz5omurq5QizVxrCT0+VLHRXGhl19+mdNPP12J3d21axd79+4d8xRarXj44Yd55ZVX\nePvtt491V5IOIQQejwfwvYKP12uSQgpjDE03gt5qb+MC27Zt4/LLL0cIwapVq9iyZcu4vfHLy8sR\nQvDSSy8d664kFV6vF4/Hg9vt9qsNIEkSRqNR+RgMBgwGA5IkjdtrlkIKxwoT0kJOYfzA6/XidrsV\nq1iSJFwuF5IkKZOt8uuYGpIkYTAYMBqNmEymFFGnMNmhaVCnCDkF3ZAJdmRkBK/XC6AQqRBCIWQt\n2whF1FarlYKCghRRpzCZMHldFikcGwghFIs4kIj1Ilw7IQQHDx5k5cqVQfVD1K4P2f2RIuoUJhNS\nhJxCVKiJ+LPPPmPJkiVJI0J5u+rMMnUfPB6PbzZatW81QQf6qVNIYSIhRcgphIUcMeF2uxUStFqt\nEYnO4XDQ1tZGRkYGWVlZWCyWhBBjJIs6HFHLBB1qQjGFFMYjUoScQhBCEbHBEDmHyGazUV9fj9Vq\npbi4mIGBAVpbWxm0DbL94HaOm3kcq+auIisri6ysLDIyMpJO1LKf2+Vy0dDQwLRp05SCQimiTmE8\nIkXIKSgQQigRE1qJ2Gq1Ultby/DwMBUVFSxatAi3282gY5AfbP0BL73/Em7naDFyAZmmTAozC5k5\nZSbzp8/npHknUb2g2o+oE4FAoh4eHvY7HrfbHZSSmyLqFI41UoScgkLEsopDNCIWQjAwMEBtbS1C\nCCoqKpSqXx2DHVz/zPW8sesNvC6vf0MJ7B47dqudJmsTO5t38tSHT4GADGMGBZkFlE4pZU7BHA50\nHuCfFvwTOTk5ClFHezhEO0b52NR/A5eHImrZp62O+kglvaSQDKTC3r7EUCdzQPSICSEE77//Punp\n6ZjNZqVeNEBTbxP//vS/886H7yDciRkmEhKL5y3mtxf8FofDAaD4ptUWtRai3rdvH+Xl5WRlZenq\nQ2AstfzmIPuuXS4XeXl5qaSXFKIhFfaWQmjIEROHDh1i9uzZpKWlRSXirq4u6urqcLlcLF26VCHi\nA+0HuO6p69j16S7wJKiDApgKYpag093JkiVLlH47HA5sNhs2m43Ozk4cDgdCiCCizszMjMuilhHJ\nonY6nTQ0NAS5WeQ3DJPJlCLqFHQhRchfEoRK5rBarXi93rAkIYSgra2NhoYGcnNzWbp0KZ9//rmf\nWOlX7voKg/ZBMOP7eIERYnuXEkAxMFP909ENGQwGhXDVkEsiykTd3d2N3W73I2qn04ndbo/b9SFD\nTdTqED3ZovZ6vUHy8qnsxBSiIUXIkxyRkjkMBoPymxper5eWlhYaGxspLCzk+OOPx2KxKG3Vbi6P\nwwO9ARuQgAzAApghx5jjU2cwEP7FbRoQrF7lR8jhYDAYyMzMJDMzk6KiIr9jly3q7u5u5eHi9Xqx\nWCxBFnVg7HM0BIbZQXiLWl5fdhOlkl5SCIUUIU9SBBKxfHMHxumqCdntdtPc3ExLSwvFxcWsXr06\nqK5rYJuQ1qYA7KMfwIpKKscAGEf/moFSIIIMoBZCDgdJkhSi7uzsVHzIsrtBtqh7e3ux2+26iToU\nIUfrj5ZY6u7ubkwmE/n5+SGjPlKRH5MXKUKeZAgVQxyOCGRyHRkZobGxkba2NmbOnMmJJ56IyRR6\naARayLpf/72jH/ARc2RN1oRKbcmQJImMjAwyMjL8tArVRG232+nr68Nms+H1eklPTw8iar2EHKk/\n4UL0UkkvXy6kCHmSIJZkDiEEDQ0NWK1WZs2axZo1a6K+tsdNyH4d0LJK4gg5GlmpidqvD0IwPDys\nWNQtLS3Y7XZcLhdCCGpqavyIOtzDTCuiPUgDk15SRD15kCLkCQ45hrihoYEZM2YoN2AkOBwOjhw5\nQldXFzNnzmTJkiWaiTXQZaHX76oXiSLkeCxtSZKwWCxYLBY/Ka3e3l46OjooKCjAZrPR2tqKzWbD\n4/GQlpbmZ1FnZWVpJmqv1xvxekQiagif9CKEwGg0kp6eniLqcYoUIU9QBCZzNDc3M3PmzIg3mDq9\nec6cOUiSRGFhoS4rN9BCNhriIOQJHtUuSRImk4mCggIlMQZQSpDKFnVbW1sQUWdmZpKdnU1mZmaQ\neGmsrpBoSS+NjY2kp6dTXFysLJOJOVSIXgpjjxQhTzCES+YwGo1hLavA9ObFixcrhYJCRVlEgqZJ\nPa0YY5dFohGOOCVJIj09nfT09CCiHhkZUYi6vb0dm82G2+3GbDYrlrTD4SA3Nzdh/ZT7KIRQiFf+\nDgS5uoQQEV0fKbJOHlKEPEEQSpkjUsQEQH9/f8j05khtoiHQQo7XXxoNyZjUSxRiibJIS0sjLS2N\n/Px8v2Vqi1p+k6mvr1eIOjMzUyHsWBWNAx/Y0Sxq9YNf3SaV9JI8pAh5HCOSMkcgDAaDMhvf29tL\nXV0dJpOJqqoqJasuVJtjaiFPcCTyYaEmapvNRklJCbm5ubhcLux2Ozabja6uLo4cOcLIyAgmkynI\nR202myOSYjTftIxoRB2Y9CJPeBYVFaWSXuJEipDHIWJR5pAkia6uLlpbW8nMzGThwoVkZ2dH3I8k\nSfFbyMY4htAEd1lA9MiNWKDOnpSJOi8vz28dtesjFFEHWtSSJOHxeOKahA1H1C6Xi97eXgoLC1NJ\nL3EiRcjjCLI17HA4lJtIS8GftrY2ent7kSSJpUuX+qU2R0KsLouJGGWRDCQqDjkQWixZs9lMXl5e\nSKKWLeqenh4aGxtxuVwYjUZcLhcmkwm32+1H1PFCJvpQfVYnvah/k+c9Ukkv/kgR8jiAOoZ4aGiI\nuro6li5dGvX1U53eXFRUxOzZszWTMRx1c+iBHD4lw2SYGBZyMsgzWYQcz3bNZjNTpkwJclPJ8lsm\nk4ne3l6ampoYHh7GaDT6WdNZWVmkp6fr2r/X6w37YNaanZiKpfYhRcjHEKGSOUwmEx6PJ+zgC5fe\nvH///pj8wYHxqtGQUJeFBnwZLWQ5yiGRkCfhpk+frtQlAd94ki3qvr4+mpubGR4e9ivkFI2oY3GF\naE16qauro7S0VImdnuxEnSLkY4BIyhxGozGk1RotvTlcu0hIxKReXFEW45drNSGZLouxcoWYTCZy\nc3ODwuw8Ho/io+7v76elpQWn06kUclITtdvtTpjrKpCobTYbZrP5S6P0kiLkMYQWZQ45nliGy+VS\nsuoipTcngly1IGUhH0WyQvK0RkPohcfj0bxdo9EYlqhli1rWTZSFbwcGBvxSyBOhmyhb39EiP8IR\n9c9+9jNuu+22oOSb8YoUIY8B9ChzyH5dOb25r6+PsrIyqqqqIt5MgUSuBfFO6nk8HjwjiapKPzEx\n3nzIkZAIojcajeTk5JCTk6P8Vl9fr1jNQ0NDDA4O0tbWhsPhUCruBaq8aD0+LWnk6r8yZKL+wx/+\nwJ133qn3MI8ZUoScRERL5ggFu92Ow+Hg448/Zs6cOSxYsEDT4I11gi4WEvd4PNTX19Pa2hrfq6oG\nA9Pj9XDw4EG/GzrWxIhEYyL5kJO5XY/Hg9lsJjs7OyjU0uv1Kha11Wqlvb0dp9MJ4EfUskWdqP6p\n3+QmkusiRcgJhnpS4osvvlAINdqgUKc3m81mqqurdQ2kWMlVz2u32+2mu7ubgYEB5syZQ3V1NTnv\n50RvGAckSWL69OlB8bbqVOPs7GxdxXsShYnmQ04WIk3qGQyGsEQtiwcMDQ3R0dERUjfR6/XGbdlP\npHOZIuQEIVQyx8DAABB5QIRKb/7HP/6hexDJcaZ6oDUxRK4m197eTnZ2NmVlZZSXlwNgNiXZNycR\nMoxLnWrc3t7O0NCQUrxHJmj5k6xY6WQRMiSHRJLVVz2+aRmR5LjUuokul4s9e/YAPqJWF2WKppuY\nyMnGsUKKkONEJGUOOYQtcNDoSW/WimRM6o2MjNDQ0EBHRwelpaVUV1fT0dHhlzabZorDfRBHHHKo\nmhDqKmtDQ0O0tLQoBeZdLheNjY1MmTJFuaETqa33ZUakOGS9UBO12+2mr6+PFStWBOkmdnV1Bekm\nBgrcDgwMxH1fjTVShBwjtChzGI1GpZKX3EZWb46W3qzX+kqkD3lkZIQjR47Q2dmpRHbI5BUU9pbk\nKAs9iFRl7eOPPyYnJ4fh4WF6enrCqlXr8WMm00KeSIg3JTsc3G634obSopsoayc6HA62bdvGhx9+\niNVq5fe//z2LFi1i/vz5fjHYgXjjjTe48cYb8Xg8XHvttdx2221+y//2t79x00038emnn7JlyxbW\nr1+vLHvqqae4//77Abjrrru48sorYzrm8XM3TRDoUeaQY4NDqTdHyqiTSU/PIE+EhexyuWhoaKCz\ns5PZs2f7EbGMwLC3ZLssEhH2JqfpFhQU+N2Q6pt5aGiIzs5OxY8pTzjJ7g+LxRJyJn+iELI8t5EM\nJIuQtWxXjuIIJOrly5fz6quv8vTTT9PY2Mjrr7/Oxo0bOfPMM8Pu61vf+hbbt2+ntLSU1atXs27d\nOhYtWqSsM3v2bJ588kkeeughv7a9vb3ce++9fPjhh0iSxMqVK1m3bl1QRT8tSBGyRkRK5ggHg8FA\na2srXV1dQerNkSATuZ5BHk/YmzrWuaysLCQRB7aREZfL4hgj3M2sjgwYHByktbVVSYpQW9MjIyPj\nJuIjGpIVYQFjYyHrhZzwsmjRIm699dao6+/evZuqqioqKioAuPjii9m2bZsfIcvzJoHn8S9/+Qtn\nnHGG8lZ2xhln8MYbb3DJJZfo77fuFl8yCCGw2+1+LoloA1tOb+7s7KSoqCikenMkxEquel0Wcu2M\nDz/8UFOsM4SwkI1xWMjjtNr8yA/XAAAgAElEQVRbuMgAOSliaGiIvr4+urq6EELQ0tISNJE43og6\nWckmkLw3hXgn5QYGBoKKL4VDS0sLs2bNUr6Xlpaya9eumNu2tLTo6+woUoQcBupkjj179rBixYqo\n2T6B6c2lpaXk5+frvjmTHVM8PDxMfX09PT09GAwGqqurNd+sgZEZaebxRTzJRGBShNFoJCsrS9HU\nG4+heTKSScjJjN6I53zpIeRQ7hytxxVP20CkCDkAoZI55GiJcIQ8PDxMQ0NDUHpzXV2dbmKF2OpS\naLGqnU4n9fX19PX1UV5ezrx589i1a5euGzUwdjnZLouxVJ2OdZsmk0lXaF56enpQ4Z5kh2clk5CT\nhXhcFuALKVVbrpFQWlpKU1OT8r25uZkZM2ZobvvOO+/4tV27dq2eripIETLRlTnkGrKBiJbeHAux\nxtouklXtdDqpq6tTEjrU2X96J3oCXRYT2YccL6K9qusNzbNYLIpvemhoKGGheRBbrPCxRrwW8uDg\noGYLefXq1Rw+fJj6+npmzpzJli1beO655zS1Peuss7jjjjvo6+sD4M033+SBBx6Iqc9fakLWqswh\nW8gyAtWbw6U3y2FvepGoym0Oh4O6ujoGBweZM2cOCxcujNtKDNxPuik9ru2NFZIRYRCL7zRSaJ7T\n6WRoaIj29nYaGhqw2+0AcYXmyUiWhZxMzUO3261pEjwcBgcHNcchm0wmfvnLX3LWWWfh8Xi45ppr\nWLx4Mffccw+rVq1i3bp1fPDBB1x44YX09fXx8ssvs2nTJvbt20dBQQF33303q1evBuCee+4J0q/U\nii8lIcuhax6PJyiZIxRkYg2n3hwOJpPJL4lCK2IJYVO7LOx2O/X19QwODlJRUcGiRYsS9rqeUAtZ\ny6Se9OWo9iZJEhkZGaSlpWGxWFi8eLGyD4fDwdDQEDabTXdonoxEJm+okawIi0RsW48PGeDcc8/l\n3HPP9fvt+9//vvL/6tWraW5uDtn2mmuu4Zprromtoyp8qQhZSzJHKLjdbg4ePEhaWlpI9eZwGGuX\nxcjICJ9//jlDQ0MJJ2IZQZN6X2KXBSTeLx1KGVoOzQtcL7AMZqjQvOzsbNLS0pJa0jNZhByvD3lg\nYCCmWOBjiS8FIcsxxB0dHRQWFmoKXVOnN7tcLqZNm0ZVVZWu/Y4VIdtsNurq6nA4HMyfPz+q5R4P\nAif1LObYXyknOo6lLJQ6NG/atGnK7+rC8moFEHm7zc3NCQ3NSzYhx2shTwRCliRJEkIISZK+OqkJ\nWV0QXgjB4cOH/RIAwrUJTG/u7+/X7UKAYN+zVmglZJvNRm1tLQ6Hg8rKSgYHB6MeX7wY60m98V6g\nPhmEHI8lG66wfHt7O319fRgMhoSG5iXbZRGPhWyz2YKKF41HiKM3VM+kJGQtyhyB8Hq9ymRKYHrz\n0NCQMsGiB/FM6kXSuhsaGlJ82ZWVlRQUFCBJEocOHdK9L70ImtQzT4xJvWQgGYSczNKbmZmZQaFc\n8YbmjVeXhcxx4zWyRJKkqYBLCDEoSVIaIAkhPppUhKxHmUPdRq3eHCq9eSyjJSK1kycVXS6XHxHH\nCz3EEmghJ91lkUBuOlbuBT1Ilq833KRerKF5skU9MjKS1JTseOsgj7daI5IkGYQQXuA7wB5gG3A3\n8P8kSXp8UhCyHmUO+SYKp94cCuHikKMhVkIOjCm2Wq3U1NTgdrsVIk4UZILVOnADLWRJjK8BP5YY\nL6F0WqCH6KOF5skWdU9PD4ODg3g8HpxOZ9yheeH6EgvGcZF/uVNrgD9IkrQQmANUAQ9PaEKWn+SR\nYojVMJlMOBwO2trawqo3h2sXKyHHQ+SDg4PU1tbi8XiorKzUNEERS9lOvTerEEJJv24+EjoMKFEQ\nCFpbWxX/Zqyvx8mKlx1vPuRw8Hq9cadty6F5GRkZTJ06FfD5poeHhykqKoo7NC/U/mLF4OCgn+7f\nOII8EO1AKXAW8J4QolmSpJwJTchqgcNoF294eBin08mePXuUimZab+54LN1Y4HA4lEFdUVGheaZY\nr7Ur91HPhKXb7cZut7Nnzx7Ky8tZsWyF5raxwuPx0Nrais1mw+PxYLFYlAiDRFpjejGRfMjJDHsz\nmUwJCc1TH3e8D9D+/n5dMchjhVF3BcBv8bktcgE5rW9iEzJEJxR1enNaWhoLFy7UrSIQq4WsF7Kc\nk8fjISsri5UrV+pqr9faVbeJBnXRenVBoua65FrISPjVI1BntAVaY2pLLNRNnmhMNB9ysgg5nKtP\nb2ie0Wj0e8jGA71JIWMNIcSrkiT9FTDii3zLBC6e8IQcDqHSmw8cOBCTpZtsQu7v76empgaDwUBV\nVRVpaWns379f93biqYkcDmoZJ7lo/c6dO5Wbe6zjkNWvzYE1jOVJqL6+PpqamnC5XJhMJrKzs3E6\nnUptg0RVXJusPmQ9iCXKIlxontvtVq5hV1cXDoeD3bt3xxSaN97lmyRJOg64ApiPz42xE3hk0hFy\npPTmWIlVrzqzVvT19VFbW4vRaGTevHnKAHW5XAmZDNTaJhQhq4VNA2Wc1MhIi8+SSRQMBoNfaUwZ\ncqGe3t5eOjs7aWhoUNwe8g2enZ0ds9tjoviQj6Wqh1aoq+bZ7XbcbjdLliyJKTRPT2GhsYTkGzAm\n4DHgdXwRFhbgGmDiR1nIN0Qo9eZAjJXrIbB/gdZJb28vtbW1mM1m5s+fH0Qi8fisY7GQ1Q8bj8dD\nY2MjLS0tirBppBvOYorTQvYCkfgnTr4zm83k5+djsViUtw91tIDaGgP8LLFobo+UD3lsiF5vaN6W\nLVvo7OwkJyeHzz77jPnz50fNSoympzc8PMwVV1zBnj17KCws5Pnnn6e8vJyRkRGuvfZa9u7di9vt\n5oorruD2228Pu5/RJJARSZKGhBCb5d8lSfoceH/CE3J/fz8HDhzQpN5sNpvHnJBlcpUkSSHitLQ0\nFixYEHYWOBZilfelt538wPB4PDQ1NdHc3MzMmTM1T3rGbSFHI+QEQU2eoaIF4OgklOz2kH2bJpPJ\nj6TlV+ZjmTqtF8kk5GRsN1pSSKTQvPz8fB599FF6enp48MEHOXjwIK+99prftQ48hmh6eo8//jj5\n+fnU1NSwZcsWbr31Vp5//nm2bt3K8PAwn332GXa7nUWLFnHJJZcock8Bfc4G1gNOwClJ0lXAm4AL\n+CfgrQlPyJIkRVRvVsNkMmGz2WLeVyw3i5yq2tzcTHp6OosWLYra11hvyFhcFpIk0dbWRk9PDyUl\nJVRXV+vyscbtQ472/BjDUNJw0k0jIyOKJaZ+ZR4eHqaxsZHc3Fyys7MTUr94ok3qJauKXKx1LCRJ\nYu7cuRQUFHDmmWfy9a9/PWobLXp627ZtY/PmzQCsX7+eG264QeEDm82G2+3G4XCQlpYW5BtXYQpw\nCWAD0oEfAd8b/b0U2DbhCTkvL0+z1RuPy0K2dLWSlRCC7u5uBgcHMRgMLF68OOl59XosazlDsb29\nneLiYk3x2KGQmRZePXuywGw2k5eX5+eTFEKwd+9ecnNzcTqd9PT0KOn1mZmZftEe6enpuuSAJpqF\nnCyXxVhVetOip6deR/Z19/T0sH79erZt20ZJSQl2u51HHnkkbOKWEKIFX9wxAKMp0wX4zJJ0mATV\n3vQM3ngIWS4UFG2QyERcW1ur6K3NmTNnTIqcaPE9e71eWltbaWhooLi4mBkzZjB16tSYB7/BYPBZ\nsbHOeY4jC1kP5PooBQUFfv5JtdtjYGCAlpaWoJAu2QoPdc4nmmthPCpOQ+L19MKts3v3boxGI62t\nrfT19XHKKafw1a9+VbG2Q2F0Ym8xsBaYCrQBrwkhmiY8IeuByWSKWLQnEuSsu/T00MV01FXisrOz\nleJE+/fvj2mCLhZEspCFELS1tXHkyBGmTp2qpIrX1NTE5K8GONRxiKsevwqyADc+cvWMfrRCA5GP\nZz24wBs3nNtDVvi22Wx0dHRQV1enjCc1USfLBTDRCtRH0rDUAj0WshY9PXmd0tJS3G43AwMDFBQU\n8Nxzz3H22WdjNpspLi7mpJNO4sMPPwxJyKo6FquBTcAgsB04FbhEkqT/96Ui5Hgm9cJZ10IIOjs7\nqaurIzc3l2XLlvkFtcdaglPetp43gFCTekII2tvbqa+vp6CggJUrV/o9VGKZQGy3tfPPP/lndny0\nw0fCJvzftQT+5Cx/QpGvhl17hRfDWMz86YSe62MymUK6PYaHhxX/dE9PD/39/UiSRF9fX8wpx/H2\ndTxsN14LWY98kxY9vXXr1vHUU0+xZs0aXnzxRU477TQkSWL27Nm8/fbbbNy4Ebvdzs6dO7npppvC\n7Uo+UWcAnwgh7hj9/t+SJN0CfH3CE/JYuizUbYUQdHR0UF9fz5QpU1i+fHnI7KJY61nIRKnH+lBP\n6qkfFHl5eaxYsSKkPpmeGOtOaydX//fVvLX7rchWsIQv/yiw616CiVrDrt1eNybj+Buq8ZKRJElY\nLBYsFguFhYUANDQ0KFZzYMqx0WgMykbUY0UmgziTlQkZrw/ZarVGmlzzgxY9vW984xtcfvnlVFVV\nUVBQwJYtWwD41re+xdVXX82SJUsQQnD11VezdOnScLuSR3s/MEOSpALAI4QYAPIB2/gb5UlELGFh\n6rYej0exOI8cOcKUKVNClusM1S7W/cVCyJ2dndTW1mrqnxYLud/ezzee+gav/f01hDuOBBnD6McE\njKDZteH2uCH2t9ekIRnJQvJDOFTKcWAmW319veL2UBN1VlZWkIsnmWKkyUC8aiFCCF3to+npWSwW\ntm7dGtQuOzs75O9h+iTfaNuAE4D/BnZKkvRVoBe4Z8IT8liV2DMajXR1dVFTU0N+fn5UolO3GwsZ\nJyGE4p8sLCwMa7EHIlAjTw2P18M3nvoGL/zvC3hdsT3IguDGF4UpvzRocVloWSkKkvVqPZZxyOpM\nNvX6LpeLoaEhJSNRDu3MyMhQSNrr9SbtHCQD8RDyeH/4jFZ2uxo4DV/q9A+AXUII+4Qn5GTD6/XS\n1tZGY2MjmZmZQT7YaIhVeVorIcvafzU1NUiSxLRp01iwYIHm/cjiqKHQPtDOlhe2QCa+5E7ZSnVz\nlFC1wgM4QrTT4rLwjG0yj1aMh+JC6gQJ2e0hb0dWq7ZarbhcLj744IO43R5qJJP44nFZqJXkxxNU\n2nny5N5fRz8KJgUhB6pYRIOWG0kdHjZ16lQqKiqU/Hk9iMdCjuZKkIk4PT2dJUuWKD5HPYjksshK\nz/IRpm30o4YZX3RF2ugy2W8ceFo9+CzicMEtGi6bxzs2USqxYLxm6qlLXAL09PSwevVqxe1hs9n8\n3B5paWl+JJ2ZmRnVQh2vAqdDQ0PjshayrJ0nuy5kglavMykIWQ/kyblwVoGaiIuKipTwsM7OTt1k\nB4lTDVGjr6+PmpoazGazX+afw+FIaLW37PQIGYUj+KYmgjbI0Qk9L76k0EjQEvYmEuQumQBIRoif\n+p6P5vaw2Ww0NTVht9vxer1+Beazs7P9oj2SScjxFFkaGBjQPKE3lpAkaYMQ4gVJkiqBepVPWcGk\nIGQ9FrLZbFbUdtVQa+uFknQaaxmnUO0GBgaUMp2hamEkuvxmTJENciSF1nBvjVEWXxYcCzdIOLeH\nEEIpMG+1Wmlvb8fhcCjWd1paGh6PB5fLFbV4z1hiHJfe/JUkSXuBXwL/LklSMz4TxiNbypOCkPUg\nkFi9Xi/Nzc00NTVRXFzMCSecENJ6PlYyTuCLqaypqUEIEbGAUiLLbx5dAU0TbzFDAyHX1tVinGFM\nWL2I8YxkWMixblOSJMXtUVxcrPwuF5jv7u7G5XKxb98+xchRF2CKR3IrnofSeFULAZ4DvgGsBC4F\nrPgceg5JkkaAP0wKQo4lFtnj8dDc3ExzczPTpk0LS8SB7fQi1sQQo9GIzWbjo48+wuPxUFVVFXWQ\nxVp+c7wTcm5uLsPDw371ItSv0XKZzMmA8TBRGA1ygXlZXHjevHkAftEe6nKYcrSHWg0k0jHGO1k4\njtVC7gX+FWjGNwszA9+UeSZgFkJsnRSErAcGg4HW1lb279/P9OnTNRfViYdY9bYbGhqira0Nj8fD\nkiVLNKeAxuqyiHQDSJKEiLlQhQZo2HR2bjZlxWXKd7U6SE9PDw0NDYyMjCgTU/JnIlrTybCQk1nH\nQr3dtLQ0CgoKgsphqqM9At0egZJbMLZ1LMYSQoge4DeSJO0WQuyVJGkKYBdCKA6+Lw0hy4XXW1tb\nyc/P113dLBGuh2iw2WzU1tbidDopKCggIyNDMxlDclwWkuHYE3JglEU4dRCXy4XVasVms9HY2KjE\n42ZlZeF0Ounr62PKlCnj2ppOloV8rOpjSJKkCKCGcnsEPlTNZjMWi4WRkREGBwdjcnsMDAz4+cLH\nEyRJMo3+fRQowVes/k0hxKMwSQg50gB2u900NTXR0tLCzJkzqaysRAih+wkca9F4LanJdrud2tpa\n7HY7lZWVFBYWKpZEsvsYLjFELpYkpCQH2Scw7C0tLY3CwsKgeFy73c7AwAB9fX20tLTgcrn8/J2y\nlTYerOlkSDiNx9Kb4XT1XC4X3d3dId0egZJb4e57q9UasdraMcZs4GfAC8BPgDJ8E3wzhRATP1Mv\nHNxut2IRl5aWKgoY7e3tMRWpT0aQucPhoLa2lqGhISorK5k6daqyn1hcHYmKsujt7eXBVx7kd3//\nHSJd+LxdWgoFxYIkh73J1dfS0tKorKxUCETt72xqalLGhFzLOJSE08GOgzz+5uNUV1Vz5vIzY+5T\nJCRDwmk8EnI4pKWlkZWVRW5uLvPnzweOuj1ki7qjo0Nxe6ivlxz5MR5dFqqY49n43BS/GF1UI0nS\nAHA/TEILWRbnbGtr8yNiGcdCVy8QTqeTuro6BgYGqKys9BNilRErucbjshgYGOA3b/6GR955hP6e\n0SDjSIWCAkk6Ft48RmFvofydgRJOsnK1w+vg/vfuZ9cXu8ADv9n+GxBgNpgpmVLC/BnzqZ5XzVnH\nn8XSOWELy2jCRLOQk+H+CfQhq90eaqVxj8ejXC/Z7XH99dfjcrno6uqioaGB448/npUrV4bdV6xa\negCffvop1113nSJC8cEHH2gppzAA2CRJOg04iC/K4kSgByYJIYO/XH0oIpYhxyHHinh8fMPDw9TV\n1dHX10dFRQULFy4Mu61Y5Zj0wmAw4HK5+PXLv+aBtx6gs71TY8PRjzowRV120030pBC5TRSMVaZe\nYC1jr9fLzS/ezNPbn8YzHNAHCUbECI39jTT2N7L9i+3c99J9SEJiSsYUygrLWFa+jFMWn8I5K84h\nN1NbosKX3UIG7Vl6RqMxaC5h586dXHzxxZx33nn09vby6quvhiXkeLT03G43Gzdu5JlnnmHZsmX0\n9PREjNJSZel9JEnSNuCnQANQCXwBfAcmCSE7HA52794dUa5eRjwWciwlMcFH4gcOHKC3t5c5c+aw\nYMGCqDddrAkleuBwOPjj+3/kntfvoaW1Jf4NSvhI2o32xBANOBaZev/17n/x/Re+j8Oqz48vJEG/\ns5/+ln4+afmEp//+NAhIM6Yxq2gWz3/veeZNnxe+/QQIe5MxXuWbbDYbZ599dlhRUxnxaOm9+eab\nLF26lGXLlgHomkQUQjwFPCVJUgXQLYQYlJdNCkLOyMiISsQyEiHjpHUQulwujhw5gt1uZ9asWcyb\nN0/zjZFMQh4eHubA4QNc9fur2F+/PzFxxgIfCTvRt71xZCEDvLn/Tf7jif/Q/qagEa4sF7XTajnU\nfIjZebMj6uwlmpCTSZzJspDjcYVYrVZNmXrxaOkdOnQISZI466yz6Orq4uKLL+aWW26Jus9R+SaD\nEMIjhKgLXD4pCFnWN9OCRKiGRBssIyMjHDlyhM7OTsrKysjPz6e4uFiXlZIMQh4ZGaG+vp7u7m4K\nSwrZv2e/z6KVq7mZOEqsekjVA9jRJ92kA2OVOn3ez8/jb5/+TZurRQsEPunKytG/gMvp4uDBgwwP\nD2MymYIiPZKBL5tOn9fr1WRhx6Ol53a7ef/99/nggw/IzMzk9NNPZ+XKlZx++ulh96ea2At7p0wa\nQtaKWMPXIHossjyh2N7e7uc+6e7u1v0QiKeYfqh+NTY20tbWRllZGdXV1UcXeoGh0Y8aGaMfJ0cn\n9gLvPQFMw5cAao2xcxoOMRFx0FpcATt37fQdR6iHlBt9DxwJmINP4F2FqvIqlpb6Jv5GRkaCMtts\nNhuff/65H1HrUa0OBa0EFct2x5vAqRBCc6ZfPFp6paWlnHrqqYpb5Nxzz2Xv3r1hCVlVevM4oHU0\nSUReJpfjHIdCZTFiLGqfhnN3uN1u6urq2LlzJyaTiTVr1jB79mzFeoglyy8RFrLX66WhoYFdu3Zh\nMBiorq6mtLQUg8FwVC06HBz4NAzs+MprDuKbH7aO/pYLHI8v+TPJp37M6yHLD6luoB3owDcH7gST\ny+Q7Ny5Ch/8JYDqwjCAyBshIOyoaYDabyc/PZ9asWSxcuJBVq1bRONRIj6eHjIwMBgYGOHjwIB98\n8AF79+7l0KFDtLa2Mjg4qGtsTDQfcryEDNr4QK2l53K52LJlC+vWrfNbR9bSA/y09M466yw+/fRT\n7HY7brebd99918/3HKJf8kjZBBwXsPhxSZL+GSaJhTxWCCRkj8dDU1MTzc3NESM7YiHXSEoe0dp5\nPB5FZipiergB/QrRcoibeg4jHkLW4kMWY+NDjmpZOcEdqjK/HBZYCMwlopmTZgzt7mobbOPS317K\n3s/2+qx5IZGTnsOswlksnb2UNfPXcMrUU/B4PH4JE4Fx06Gs6YlGyPFs1263a3b9xKOll5+fz3e/\n+11Wr16NJEmce+65fO1rXwu7L0mSjgeWA0uANaPFhDz46lrMxfeYnzyErKcEp0x2egepbOl6vV6a\nmppoampixowZVFdXR3yix0rIeiGEwO12s3PnTqZOnRpUQjRoHwYJ4YnRHaB+ViSZkIV3fEvyKA+p\nKUR958xMy/T77va4uWHLDWx5ewvekaMnVUiCQdcg+9r2sa9tH7/f9Xsl9rkou4i5JXNZVbmKUxed\nSnFmMYODg4oYquybzsrKIicnh5GRkQlFyPFYyP39/bpKb8aqpQewceNGNm7cqHVXafjemwzA2cA5\nQDa+wNEXgX0wiQhZD7ROzgXCYDAoSs7Tp0+PSsQykh3CJoSgp6eHmpoaPB4Py5cv16SYEFedijEk\n5HFjIUeDBs7LMB91Wfz2vd9y95a7tYfWjcY+t1pbabW28u6hd/nP1/8TBOSm51JaUMq/nPwv3HzO\nzUpWW2trK93d3fT09PhZ0oHF5mNFMlyF8RD9eMzSAxBC7AJ2SZL0uBDis3DrpQhZA2QVkfr6erKy\nsqKW6gy3v2RAVg9JT09n6dKlHDhwQLN1YTAaYhcQVTdL8kzEmIW9xWuIa+Ami9nCP+r+wTWPXUNr\nc2ucOzy630HnIF8Mf0H/wX5uWXcLeXl5CjEdOHCAkpISzGazUnWtra0Np9Ppp3Atf5KlAqIV8URv\njNfi9KPhbhIwJEnSd/BNG49wVGnycSGEZ9IQciw1kaNBCEFraytHjhyhqKiIefPmYbPZdItCJsNC\ntlqtHD58GMBPPURPFInBGAeTjqGFPGEknKKdBwH/51f/h/c+fC+xtUAsQBVgBjPBY1OOhghVdc3t\ndiuRHm1tbdhsNjwej18N40RZ03oQ677GKyGPTuoJSZJewJcyXQPk4HNlpAnhew2cNISsB9EIWQhB\ne3s79fX1FBYWKr7Ynp6emHX1XK7YglsDw7VsNhs1NTW4XC7mzp0b9HqmJ1xuXBCyBrjc8QcGa3FH\nJN1lIeC97e/5JgCz8d2KRt/vuNBP0hJQgS/iZRRphuC3vkjzJSaTyc+ahuAaxuGs6WSpTsdD/OPV\nZQEgSVIWMCyECOt4njSErOcihqtnIYSgo6ODuro68vPzWblypZ/KdKxF6uMtbm8ymXA6ndTW1mK1\nWpk7d27YVE09NTDiejUdQwu5rq6O3e7dZGZmkpOT4xdRoAdJt/A0WMiAbwIw1HM9EzIyM3AMOY5G\nboTiUTn+e0bwIr2EHArhahjLitWyNS2XLJBLY+bk5GhSBImESawWAr70IJskSf8CfIYviHQIX/U3\nL0wiQtaDQAtZrv1bW1vLlClTWLFiRciqTcdCV8/pdNLc3Exvby+VlZUsWrQo4mDX47KYKIRcPqec\nVcevwuFwYLVa/SqxqVVCcnJyyMzMjJ144zX4NFjIEWEHhz1ggk+dlGMECvBZxWEuXaiwukRFQ6gV\nq91uN3a7neOPPx6n06m4PeQ63kajMUhmS8vcRrwhegMDA37p0OMMBnyj4AFgP76raAHqgOtgEhFy\nLD5kIQTd3d3U1taSk5PD8uXLycjIiNpOL2LxIbvdbhwOBx9//DEVFRXMnz9f0zHq2de4IGQN8AiP\nIvkTGGM6PDysvFp3d3fjcDiQJMmPpLXGpeqKOEnDl8no4GjYWxQekUQMUS1ylqCMuZFXTzcGvzUk\nSxbKaDQiSRIZGRlkZGT4lcZUW9MdHR3U1tbi8XiwWCx+JB1oTU9W+aZR9AFX4hsphfjunEx8+bDA\nJCJkPTCZTPT29rJ7t+81eOnSpWRmZmpql2xdPbXUlNFoZMmSJUGqCpGgx0KOK512nIS9hZKv93g8\nfhbb0NCQX0qy7PYISqLQwpUGoIij9T7kYSOAw/hsnnQgC19csvrSjUE49VgTcjiorWkZQgg/a1ou\nNK+2pk0mU1yupcHBwXFLyEIIjyRJecBpQK0Q4k1JkgqAYXmdLx0h9/b2Ultbi9frZcWKFboKusRS\noxi0WdZer5eWlhYaGxspKSmhurqa/fv36/ap6SJkYxyXX92tZIe9xZB2HkgGu3fvpqKiApvNxsDA\nAC0tLQwPD/tJOUU917JNMxximRzUJPDZO0586dbyJs341FeMJK0IE/jHOft1bxxUkNNiTXd1dTE4\nOMju3bujWtOhMDg4OAzSEA8AACAASURBVO6iLOSJeUmSTsTnmjgJ+BvwJnANPm2978EkIuRoF0qO\n1zWbzVRUVNDT06O7ulasgzqShayO6CgqKvKLcY6lwJCeNnrD9/wwwcLe5ImqrKwsv4kqtZRTWOTg\ns4RDEXHUHY/+dY9+cvAv5C8YTZpNDFzDrqSlSquRyCw9tTWdkZGBxWKhqqoKp9OJzWbDarXS2dmJ\n3W5XXFeyKyo7O9tvHA8MDOgSBh4LqCKl1gKfAI8Bl44udqDi4UlDyOHQ399PTU0NRqNRide12Wx0\ndHSMWR9CEbJ6IjEvLy8oogNil2TS2sZs+vIQMoR+oPpJOQX2JR3Ix2ftxkLGYTuC786rArrwVTOI\nF26gFd7ufZu89/PITsumNL+U48qOY1bmLMrnlVM0pSjqZrQimaU3ZbeFbE2rC82r1aq7urqor6/H\n7XbjdDr505/+xODgIB0dHUydOjXqAyMe+SaAxsZGFi1axObNm/m///f/ajk8O753pK/gK90FMFP1\n/+Qh5MCbbWBggJqaGiRJYt68eX5+2HhlnPQiUHm6t7eXw4cPk5WVFXEiMZbJQIPBoPnY4iJkNXlN\nktRpP0zjaMH9RCIwZE1PHfxQ51lwtCqd5+h6QyNDHOg8wIHOAwA8/M7DfnUwTpx3ImctP4vV81bH\ndBjHqvRmKLVqIQR9fX20tbXx97//nR/84AccPnyY888/n3vvvTfkduKRb5Jx8803c84550Q9JtWD\n63/x1bH4GvCxJEn3A/PwRV0Ak4iQwUfKg4OD1NTU4PV6qaqqCulPiieVOdbCROB7SBw+fBiTycTi\nxYsV7bZwiFV5enhYmzkXlw95DKMskpWAELyj0b9p+EpuZuKLpJCfW3J9rli3nY2vWL0h4HetCBxy\nQ/isay0PjRB1MB585UEkIZFryWV24WyWly/nurOvY2l5dKHW8VTpTZIkCgoK2LBhA7/85S/ZsmVL\n1GJj8cg3SZLESy+9REVFhWa3pyRJRiHE56MK0x58Vd9agRuEEO3yepOKkD/99FOcTidVVVUR/UiB\nFqsexFKYaGhoCLvdTk1NTZC1HgmxWsjR2shJJm5XHPU1xjLKYgwlnPxgH/2oYcYXQZGGz43hxUeU\n4c6BGG1TiY/cA2HCF40RqOAd6pDlfbjw3cr9Go8jAoQkGBge4LPmz/jM/hnuPDePlj8atV0yK71p\niXiKBPltOdKcTzzyTRkZGfz4xz9m+/btPPTQQ1H7M1o03zOqNP2FEOIRVV/zR8l68qVOz507V4sM\nd1zQQ8gOh4OamhrsdjtpaWkR5chDwWg06natRIqycLvd1NfX09XVRUVFBfl5cUx+jGWUxRgRsqYY\n4RFCE6ExxAdgNv61o4N3etSnbAr4XZ74kz8SPsu9g8ToIMr7ScPnz04PLg8aDh6PJy7du0jbjZXo\nnU5nxDwCNeKRb9q0aRM333xz1DdcGSr3zibgfqBdkiSLEMIJPAvcC+yCSUbImZmZCZM9CgctVuvw\n8DC1tbUMDAxQVVXF1KlT2bFjh25FYT3uB3WbwHPg9XppbGykpaWF2bNnU11djcFgIN2sL/XYD2Po\nQx6z4kLxeEZCWbVr49innKGn5qZCoBafhZ4+uo6H2BW+BUEPjJy06GVbYfzWQtb69hmPfNOuXbt4\n8cUXueWWW+jv78dgMGCxWLjhhhtC7kt1zxsZncIdJWPwvTcpAmiTipD1IJ4i9eH8z2oR0Tlz5rBw\n4ULlYshJJXoGW7xRFkII2traqK+vD6kcEhchj3Gm3qRFtIeAF18iyix8eV4ugkVYDfhI2sJRaSkj\n4a+LF1/0yJzgRTmWiUvIerL01PJNM2fOZMuWLTz33HN+68jyTWvWrPGTb3rvvfeUdTZv3kx2dnZY\nMga/Sb13gEskSfozvunc2fiu3uSLsoDY0qf1vnaFImS1uKksIhpI9HI9Cz2DLVYfstfrpbu7m8OH\nD5OXlxdWOcSSFod7ZzJbyGNXZTI8BD7bqZKjk4rhzpWX0EKzcv0L9ScNX/p1mGfxFIu2pIpkRVnE\nW5xea1JIPPJNceCnwG+ANaPfZwFXTdpJPT1IBCHLUk7Nzc3MnDmT6urqsIMp1ogJvS4Yu91Od3c3\nQgiWLVsWcYJkXBCyBjzyyiO88vYrrKxcyZnLz+S0paclRUX5mCAUyUr4iDjQWNX7XPKOfmSXhgSc\nGrlJdro2v6jb7U5KHHK8Lgs9adPxyDfJkKMwNOIaIcT60XTpdCFEW+AKk2RU60esscgyIbe0tEQX\nEQ1ol0zlabvdzuHDhxkeHiYzM5Nly5ZFbTNRfMiDjkH29OxhT9MefvvOb0FAVloWswpmsbx8Oacu\nOZWvrfoaeVlx1jA4Fhaym6ORGhHKagJjomiSl6HtHI5XC3m81rGQJCkdOEmSJJMQojfcepOKkJOh\nGqKGEIKhoSE6OzspKSmJKiKqRiwlOLX4kF0ulzKBOHfuXHJycvjkk080bV8tSa8bYyjhFAQJbCM2\nDnQc4EDHAbbs2gKP+QrrlEwpYVHpIk5eeDLnnXAe5cXlY9w5nRgGBvGR5cmELasJjAkhH+tJPb0T\n32qMZ0LG5+HPAH4qSdJWfOk8vUC/EEJJnp9UhKwHeghZLSJqMpmYPn068+fP17W/WF0W4dq43W6O\nHDlCR0cHFRUVLFiwAEmSFFXsaBh0DPK3L/7m8ymGi3uNhDG0kDVBgmHvMEf6jnCk7wivffoad/z5\nDkwuE4WZhZRklfDV2q9yzopzomenjaWFLFR/o/FbvK50DcfV2dTJ7v6jhX3kyniBEk7JIuR4MDg4\nyPTp0491N8IhHR/fHgecgY+gC/DFzSyXV5pUhJwMC7mvr4/Dhw9jsVhYunQpDoeDrq4u3X1LFCF7\nvV6am5uVcJw1a9b4+fKiWdVer5cbn7+R/37jv/EMe/zLR2pJTkC1voxkE5ie7csac6Npz27cdAx1\n0DHUwcevfcxDrz2EJCTyMvKYUzSHlZUrOWPZGXx12Vf9yXGs+qxnX2NgIZ+8+mSKc4qVMplqCSeT\nyaRUXnO5XElRYJmM8k2jiSGd+MpuRsSkImQ9iOZDtlqtHDp0CEmSWLhwoSIiOjIyMmZF6tVt1PJS\nRUVFYf3WkQb0w399mPuevy+07LzW5AS5QtlYErJWIpKVNaKEbgtJ0Ofso6+pj71Ne/ndO78b2+NR\nQ4/VOwaEnJ+RH7ZM5sjIiFIZz+Vy8dFHHyGECFIGiTVhxOv1TkpCHi29mYWPkNfjy9b78Wg5zmEh\nxMfyupOKkPVayA5HMDFpERFNVk3kQMj5+D09PRw+fJjc3NyQVeGi4Y8f/ZFvP/Ftejp7dLULmZwA\nvokoKWC9WKGBZCRJQnhE5Ff6dHxEPNFClsfSQo7m6/dCmjk8mZrNZvLz88nPz6e9vZ1Vq1bh9Xqx\n2+1YrVZ6enpoaGhgZGSE9PR0P5eHllrG8bpBxiMhq3IdvgJchG+Uyv7O5cCJ+GoiA5OMkPUgkCCd\nTic1NTUMDQ1FFBGNR8ZJr/K0XAOjqamJ4447Tnf95t1HdnPVb6+irq5OV7uwEPiGkxNfYoGMZBcX\nQvjIxM1RCx2O1pVIRnnMsYKeyI54fcjRJKa8+g/cYDAolrEMIYSftJZaGSRQWktNwImQbxpvtZBV\nWATsxpciffnobwZ8JaIUfOkJ2eVyUVdXp4iILl68OOKTfCx09RwOhxLClp6ezvLly6M3CsCtL9zK\nz9/4OWIkAQ5Rgc8n6yC0nzXZURaB9R5kP7ELsKmWRyryE237cUQAhoTWfoxRzgsQtU+SSMyTSJIk\nLBYLFovFr5ax2+1WXB6tra0MDQ0hhCAjI4OcnJy4JwnHo3yTiks6gHJgA0fNh7kEFGCdVISsx2Uh\nSRJ9fX188MEHzJkzJykiooHtohG5/HDo6+vzq4ERCz6p/QTROsqaJnylH2OpfyDXBA485LGIsnAC\nLfhXXDPhL6MUeA/Lfm95u3JRnnBv4oHbG2voeV7GS95R+M4gtD1Z46mUmJeX50eaXq9XURPv6elR\n5JtkNXHZ5aFFTdzlciW9uJheqML4ngWuAs4HGiRJ2o5PbfoB9fqTipDhqN81HGQR0ZaWFoCgKAUt\n248FkRJDPB4PDQ0NtLW1UV5ervnhEAl+WXhugiuUGcGYbcTj8PhGgTwhJu/Wg88iDvcMCSRkA4mz\n9tz4Cq53B/wu+4kjQfZ7y5BHuHpyUoz+nsPRWsKJdlPojbLQsn6SfcjGqHF3PiQy5E2tJm4ymbBY\nLFRWVvq5PLq6usKqicsujjGrma0DQggMBgPd3d0AK4H3gL3AQuAA8IkI6PikI+RwCBQRPfHEE/nw\nww+Trj0mI1wIW2trKw0NDWFTr+UHjF7rP2patAc8A6P9Ubu2ZWKOZkEHuixOxmfJWvF5xeS/0Uha\nvR0vPmFQtfqFXNMhXj+xYfQjE7EEtHG0AL36tB+LKItxQMgmjXSQzOL0MsFqVRP3eDy0tbWxc+dO\nwFe1rbS0NOr9Eqt80/bt27nttttwuVykpaXxk5/8hNNOCx3NJkkSO3fulIsWfXv056eEEGGLYkw6\nQg60kNUVz4qLi/1ERMfyqRoYwtbZ2UltbS1Tp07161Mg5LhivVXiYq5ToTVJJPDUGfC5RdSlEAbx\njbBAklZb3fJ2evCFyLtG25jxxUgnSkZJLhRfhc//XD/aD7kgz7G2kBO9bihEI2Tp2BKyFvmmQDVx\nIQQtLS10dXXxxhtv8M1vfpPm5mbuvPNONmzYELb/sco3TZ06lZdffpkZM2bw+eefc9ZZZylv26Hw\n0EMPUVVVBb6iQsuBuyVJahdCfCFJkvSlsZADRURXrVqlO1wsHGIp3Sm7LPr6+jh06BBZWVmsWLEi\nqs9LJnK9VeLCycGPKSR8pJqJr0aDDAdHCdqFT4e3T7Vcru/gwkee8rNKLpYTC8rw5UVF6uuxeOsd\nR1EWaZK2+OFkWsh6Y5glSaK0tJTzzz+f1157jVdffRUgYrZqPPJNxx9/vLLO4sWLcTqdyuR7KPT3\n9/PAAw/wox/9aAewQ5KkdYzqjAeSMUxSQtYqIhorZJLUQ8j/n70zj4uqXv/4+8zCDiruaaHiQq4p\nbpWWuWVaLlndrLSbXjVvlv7Ubnory6zM3NJySSsrs83c09R7U+tqgqgYLikggiKogMKwDDDL9/fH\ncA4zMAMzzKCIfF4vXszMOed7vmfmnM95zrN8Hr1eT1ZWFufPn3eqn17JfbkClUrlnk6FM3CGvByR\njC8WF8F1LO4JRyigtJvCi2KSlpXMHJ3FZqAeFtXZkuPqi8ax9it7ElXRh1wOh3qpnCPDymxwWtH2\nTSVzkMu6Nt1p32SdNbJx40Y6d+5cpqH3559/Mn78eD7//POpWELUbYH2kiQZsBSF2JT9VjtCloV2\nnCE9d0XqHbkZrCHnN+fm5uLl5UWXLl1c2ldFJDhVKlXlWsiyzm48FnKVm4HKWRwy7JGMGctpmUjZ\nrhFHBGVPoF1eX56XnFXSGtsz3IQl+SiN4tQ5GXLpuBttBl1GReQ03UE5V7tW5VwXcleNEWfhjuWt\n0+mc7hbiTvsmGadOneK1115jz549Ze5r5syZnDp1CizCp8FAErAYy1VTT5Kk+kIInbx+tSPkFi1a\nOO0b9qRIfUkYDAYSEhLIyMigZcuW1K9fv0IpbBXpGqJWq/H3dq2IxClIWEjMq+h1DrZp7SosxCyT\ntFT0Wr5207H4ie1UbrsNmVBrU1zAcoJiX7QPFm0tRz+bdZ5zRVsilRyvPLiaOljJLgsftXNxh6rY\nLcQVLWR32jfJ648YMYKvv/6a0NDQMvc1ffp0AL744osRzsyt2hGyKzKXsp6FJwlZTqtLSUkhJCSE\n1q1bu5XCVhGXRVJWEmt/W2shQ9nqc/di9sZCamUdihlLoUau1Wey7oWc++zsobj6eB6ApWpPdnHI\n81Rjsah19jaqRLhKsFXAZXErE/KNat+UmZnJkCFDmDdvHvfff3+F5loWqh0huwJPVt0JIUhJSSEx\nMZHGjRuX2T3E3X05wrXca4z+bDS/Hv7VQnzWri1X1dxkaLEQcUUPRaLYnaAtmkcdLC4LT0CLpUln\nybQ4NZZ559rbqIrgRlvI5Vztvhrn3FyVGdS7EeL07rRv+uSTT4iPj2fu3LnMnTsXgD179tCgQYMK\nzbvU3DwyShVCZYvUl9xOCEF6ejrx8fEEBweXK1pfkc7T5fmQjSYjL3//Ml/v/hpToQOWdaTm5oik\n1VgsbE+dIQKohaV4VI/7hCxhaf5ppHRanH/RPm4mGVeGy8Jd4aRyuM7ZuENFsiGcgbsWspw14Qwq\n2r7pjTfe4I033qjQHJ1BtSNkV6DVat0i5MzMTGJjY/H19XUqm6OiKWxlWchlSmqWB3skbcbic71K\nsXqalorrVcg6EaEUW+wSUBu81F5oVVrMBjOF+kKLPrMzqFM0Z3vBPYElaCgHGuU4lSvuEk+gKvqQ\nq7iFXJEAu4yqqPRWEdzWhKzRaCrUV89kMpGcnIyPj4+NVrIz+3PVCnAU1Nses51Jn08i/UrJ+uIK\nwrrLcQ6WdDQ5rUzmeussBmdIWsLSar5kI+Ai8ik0FVJoKmLVomCgl9oLjaTBbDJj0Bow5Vodux+W\nKrs8igNvcrl3SULLw1YDAywuDL+iuRuwWNeVVajpKsE6M49KJmST3nJey/oRjki3qnYLqSHkKghX\nXRauEHJBQQHx8fFcu3aN2rVr06FDB5fmVlGR+pJzfOnrl/j8P58Xi+i4K+6jwULEcgqoI3Kw7mKs\nx0KiXkXv5Uo4uVlnY6AC3XQKTYV4eXuRZ8yzjFcb1Bo1wkdgzjVbrHZ7XCDPrTyxopLuDWvNZ/lm\nc6MKRKqYy2L3X7sJjwynQUADWtRtwT1N72FAhwHc2ehOhaS9vLwqLQ/ZHWRlZdlU8N2qqHaE7Aoc\nidSXhNFo5Pz586SlpdGiRQsaNGjAtWsOG8c6REUJOT+/mEWMRiMn4k9YcmmhONXMm2IyLCkgXxbu\nwhIUs4azVqMe2xQ2PcW6FmWN4WBu/l7+5BbmklNglUvnj8WVkWN/GwWyVoWrZCp/X9aeq9qUtq5d\nxS3oshBmgd6kJykriaSsJPYl7GPJb0vQqrTU86tHs+BmtL+jPfc2u5f25vYUFhba7bdXEbjT3BSq\nvBay06h2hOxJC9lsNnPx4kWSk5O588476dmzJyqViszMzBvaxslsNtuII/l5W1Uz2Us1k0laj8Uq\n0mL5pWWSFFgCYk0d7NRdXQdnXBlW8FZ7YxImcgutDkL2N7samLuRwkBloTJcFu4WrZRX92GP8CUw\nCAOpuamk5qZy6OIh1kSuQY2a2j61uavOXdzd8G56t+5N9zbdCQwMJDAw0Cm5TGt4oltIDSFXUZQn\nwSnDUVDPWpCoUaNGpfrXlSWlWRYq2sYpOzubiIgIRYio7nH73UwUyCQtv7a+5wRikTgp69x3x6/q\nzDUoyf8kfLQ+6A1WZrYaCxm7a6G6A0+QujPf4Y22kD3Y1dqEiYz8DDJSM4hOiebbU98y47EZPN/5\nedLT08nLy0OlUimuDnsdQmzGc5OQ8/PzPS6RcDNQLQnZWdgjSDmFrVatWg5T2FwpPim5nStErtPp\niIuLw2AwKOJIZrMZP6+K1fsXT6Sc5ZVtZRrBV+2L3qi3JWOw+EllxTd3xITcwc3wIZdH4LLwfmWi\nIuMLLE9a9aFe7Xo0adJEbuqJ2WxW5DIvXbpEbm6uTVNUmaxlw6iiKW+y8VUZXbBvNGoIuYhYs7Ky\niI2NxcvLi44dO5YpclLZbZzy8/OJi4sjPz+fkJAQ0tLSlGCKJEn4+1S8LFqtVWMqLzrkjoVcFpmZ\nQX1VjSndhN5URMQmUKFCkiRMwlQshynDi+J8aJVl/UonJk9c156u1LsRNyZXpUD9sMiZFt3g6wbW\nVYhYhr+/P35+fjRu3FhZJncISUtLIyEhQUkFNZlMpKenExgYWCFlxhpCrqJw1mWh0WgoLCzkzz//\nxGAw0KZNG6cEStwpKCmLkK2Dh3ILp4KCApKSkoiMjCQgIICgoCCnVbnswWR0wkKvhPNadV2F+YoZ\nU77V/osyHMzWbFML2yIVI5DlYI6y4LzsI5czPaoCPB3UuxFWuyteuOZYgp9WaBjYUHmilEnZZDIh\nhEAIoXzm4+ODt7c3DRo0QKVSKfrgV69eJSsri+TkZEUAXvZJl9W52t3mqFUJ1eMoKoDCwkLOnTtH\nXl4ebdq0sZHVKw8VvRM76jxtNptJTk7m4sWL3HnnnfTo0QMo7qDQrVs3hBDk5OSg0+mcL6Cwh3Is\nLa9CL7gEhjoGfLW+aFQajAVG9Dl65xqmllwlD6RUCXO2kyaeKxWF8p9cMt0ICAP2O7erSoWrPuTy\n1nfXQnbmlM3CcgNUl/izDgbXAhwUxD370bO0atCKbqHdGHjPQPq372+jiCgTstlsVghaNlDkjI2Q\nkBDl+jIajWRnZ9t0rtZoNDbuDn9/f7KyspxWeqvqqJaEXBZhGo1GkpKSuHz5Mi1atODatWsukbE7\nKOmykEX04+PjqV+/Pt27d0elUiknruyLk18HBQURFBREy5CWFZ+EA05VGVX4ZfiRk1qcX5ZXaBVZ\n87fMwZqk83LyHCujGUGdqsZ03YQwu2nelew4Lbd0MmJLzJ6yIm+Gy6IqELLsDioZCJa//84U56rb\nQXZuNscSjnEs4Rif/udTAAJ8AgipH8I9ze6hb4e+PBr+KAE+xbK4BoOB2NhYCgoKFCEu+fxXqVQE\nBQVRu3Zt5VqQ2zhlZ2dz8eJFtmzZwqZNmxBC8Mknn9C5c2fCw8MdNn6oaOsmgHnz5vH555+jVqtZ\ntmwZDz/8sBNfqmuoloRsD9ZWaNOmTZXmpufPn79hc7AmZJ1Ox9mzZ/Hx8aFz586Kj1j2Ezu6qRz4\n6wCLNi7Cv4E/GklDYUEh+hy98ylRJUnLDEHZQegSdeSIspN9hRDlkrQ+V4/6qhpjmhGTwYO1yrJ+\ncSHFxR0lLel8INpzu3QLrrosnAnquQN3sjgEFoIuL5ZsLr2fnPwcTl08xamLp1j/v/UA+Gh9aFK3\nCa0atKJ1ndaMenAUndt2tjnnra1oa3cHoDQ6ValUzJw5kz59+rB8+XK8vLxYv349derUsen+IcOd\n1k2nT5/m+++/59SpU6SkpNC/f39iY2M9XiBTLQnZ+ocVQnDlyhUSEhKoX79+qRS2iorUy2O7mvdc\nUFBATEyMYhEEBAQoJ1xZRHwx/SLPLH2GYwnHSi8MAJVk6RKiRk1hfiH5unz7F7F8Xgvwy/VDn6RH\nZ6i4NqU1SaslNSJYYLxmtDzqyp2e3YX82OxMx+mqAk8TcmVbyOVVOZa3vcmJdYqQb8jn3OVznLt8\njl3s4uPfP2bpC0sZ12+cso58PVoTXkmSll/v3buX/Px8JkyYUOZ+3WndtHXrVp5++mm8vb1p3rw5\nLVu25PDhw9x7773OHbSTqJaELOPatWvExsYSFBREeHi43citrInsalRXDtA5G0wwGo1cvHiR9PR0\nOnbsSN26dW0sYkc3hPzCfP6x8h9sidpSZqDSLMzkFhQlH0tALVCrLL31VEJlIelsC0l7F3gjkgV5\n2Z5L9g3wDrBU2BViEYKXIQvWy3FIV0V+fLBYvjdSGMgT8HSWRWVbyOURvjOEXAE0rduUra9tJaxJ\nWLnrliTpq1evMn36dFQqFUuXLi13e3daN126dImePXvabFtWc9OKoloScm5uLidPnkStVtOhQwf8\n/R2nickZE64SspyLXB4hW7tKGjduTO3atQkODlZcF2VZxXM3zGXxz4spNNqTNSsfJrOpuAxZBVIt\niUDfQMznzagkFZJGosBYntlZNuyWO1ujZHk1FAvny2JF1oEjKPYTF+CZjtM3A65ayB4s2rALdwnV\nw4SsklRMe2wac/42x7UNsTyVbdy4kQULFjBnzhxGjBjh1JOqO62bnNnWE6iWhKxSqQgNDXVK/ckT\nmsj2YC9gJ5dix8TEUKtWLSVIV9IPtTFiI6988QqZuZkuz8sRgnyD0Ol16PSl3RMalQYfLx9Ukop8\nQ75TNwBvtTdGYbQtdwbniMiefIhMzj5Yun8UcnO6QHsKt5oPuTzCL29+LhBy09pN+WDoB9xV7y7i\n4uJcKre+cuUK06ZNw9/fn3379rkUkHendZMz23oC1ZKQ/fz8nGpACu5rItuDXGRSMmCnUqm49957\n0ev16HQ6Ll++TFxcHGazmcDAQJJzknl7y9skXE1AX+CZxnOBPoHkFuTaJWIZRrORnHxbC1ej1uCj\nLSLpwnxFJtNuubMnIEf31UBq0Wdyb74brWl8M0qnK9OHLPdCvEixTrRPiX26ayGbi84NLx+0ai0m\nswl9oR6zKJ64WqXmzSfe5NVhrwKWjIaSaW1qtZrAwECCgoKUcms58+inn35i0aJFzJ07l2HDhrls\nobrTumno0KE888wzTJs2jZSUFOLi4ujevbtL+3cG1ZKQK1OC03q7koSs1+uJi4ujsLCQ1q1bExgY\naDdzQo4Sy3fYq5lXefajZ/kj7o9S+/HWelusUbMRfaEe4aSp5K3xRiDIzi9Z+uYcjCYjOSZbkg7y\nDVL272X2KtYy9iSsD8+Ru8MPiwUtE7inNY09YZlXlbQ3udJRAjKK/qCYpOXv0wMWskCgL9SjL/Gj\n+Wh9CG8ezrop62hYu6Hyube3N97e3jZWrsFgUEg6KSmJkydPsmDBAjQaDX5+fixevJhevXpVyF3g\nTuumdu3a8dRTT9G2bVs0Gg3Lly+vFAlSydkOzUW4JR4ihRB2CzDsISkpCbVaTdOmjqTP7OPcuXME\nBATQsGFDpcP0tWvXlAo7uUKpLB+x0Wjk5S9e5pvfv7GxJMqChIS3xhutxmKF2KShFS338/YrDvB5\nAP5e/uQV5tm9GWjVWny8fEBYoucGDMUXfUXgTfnZFCVh7YtW437rprq4dwwAd2LRmC4LiUV/EhYZ\n1AbYdum2RjpwZQySFgAAIABJREFU0oX9q7AQrSsml6yXYV0lKVvOfkBZBmEGFgu8BLRqLR889wEv\nDnzRhYlYYDab+fHHH1m2bBnPPPMM/v7+HD9+nF69evH888+7PN5NhlN3kGppIbuCilrIsnB8UlIS\nycnJhISE0KpVK4QQiuVcFhkv27GMd356B32ha4/+AkG+MZ98Y3G0S5Ik/LR++HhZXAmeImOtSgsS\npf3EVjCYDBj0Vt/fzdAtt1fMcLPhrA9ZtmCzKC4Rt7Zc5SwVVyxkHyw3NleNSGuxfus5ym29yoId\nl0d4i3C2vLaF4IBgFycCqampTJ06leDgYPbu3UtwsOtj3IqoloTsyuOMVqslL8+19C8hBHl5eVy9\nepWmTZsqFXbOZE7sOb6HiasncjXrqkv7LAv+Xv7kFuTaEKdKUuGj9UGj1lBoLCTf4Fq6gp+XXynr\n2ym463+9JZ7BnICzMqT2iE7ubHLd6jNN0bolLVdrqIvW8eRNUQW0orToU0lY3TC8Nd4sG7eM5x54\nzuXdmc1mvvvuOz7++GPef/99hgwZUi1Eg5xFtSRkcE1gyJWgXlZWFmfPngWgcePGNG/e3KkKu/jU\neMavGs/h+MNO76s8+Gh9bFPbrGAW5lKEqpbU+Gh9UKvVFBgK7Ka8yfnE5ZKxu62jqjs87dc2UpzL\nDbbuBXm5N54jYzMW102I5a2UI5Udvygi5F5hvdj46kab8mhnkZKSwpQpU2jYsCG//fZbtRCcdxXV\nlpCdhbOErNfriY2NxWAwEBYWRkFBAYmJiaSnp1OrVi2HWR05+TmM+XgMu4/vBopKjb0spcYGk8Fl\nlwVY5Cp9vX1ddk2U6sqBJfLtrfZGo9Jgxuw4n1iGbNXlUqwfIZNz1WqzdnNR2Tcr+fuWSVr+LWT/\nr1x5JyvhuQIV0AaLq6QI5QWT1ULNvCfnMbLnSCST5FIVq9lsZv369SxfvpwPPviARx555Layiq1R\nbQnZUxaydcCuVatW1K1bF5PJhLe3N40bNyYjI4Pz589jMpnw9/dX8osDAwP593f/ZtXuVRjNxeML\nIcgrKGG5qiyWK8LS5NNgcuwMlfOJPRa0E5a0tzxD8Zw0KkvKmyRJlkCdPB85u0HedUkClsm5Bq6n\nvbkKa5ElGfZ8wFBM0HJ3brmxbUmYgYZAExfmYYYBDQfwzUvfUKAvQKfTceXKFfLy8tBoNMq1EBQU\nhJ+fX6mK1EuXLvHKK6/QpEkTfv/992rROdodVFtCdhaO8pCt++nZC9ip1WoaN25M48aNlfVzc3PR\n6XSs3LmSRXsWOZ2razKbShGsdbFGXn4evt6+5BTklJlP7Cr8vS2+55IazUaz0dZSlgNE5bmU5Qve\nHVQXQq+slkwCy+9hxPkqRnskbS4aQ7ak/YF2uKQnHWgK5JsR39C/TX8AAvwCqFu3uL2YnMKm0+k4\nf/48ubm5qNVq0tLSiI2NJS8vjy1btrBw4UIefvjh29YqtsZtT8glLWRZLPvcuXM0aNDA6YCdSqXi\nZMpJXlj+Ahcz7OT/uAi5WMNH64OkksjOzy5OMQP0hXqMpop1vZSJuFwrW66c81wG3e0DZyxkM5YU\nPzOW7xnKJ3IfXE8LtAcVFneHGYtF7E/ZZGx9PGYY3nQ4Xz39FRq1YwrRarUEBwfbZEgYjUYOHjzI\nf//7X65cuYKXlxdvvfUWGo2G/v37u3VI1QHVlpCdvdtauzYyMzOJjY3Fz8+PLl26oNVqnQrYXcq4\nxLPLniUqPspj81dLary9vG3cG6VSzLBEtL213piFmfzCfBv3SEl4a7ztWuN24Y+lKONW7fp8s+Fs\nloW1hIqgOINCdjFoKe4ino9nyFjelw+WDAoNFldUeXMF6pjr8OOTP3Jfi/tc3qXZbGbdunWsXr2a\nhQsX0r9/fyRJIi8vr0JNg6sjqi0huwKz2czx48cxmUyEhYUREBDgFBEXGguZsGoCO4/tRK1S4+/t\nT35hvqU3nBuQBXtK+prtocBYOlvCR+uDl8bLogCXn2spJtF6O+dCUVGssHYzGoxWF1TEh2yvW4qq\n6PMcittWyetWFAJL9kSw1fvyuoKp4Nlmz7L6ydUV2uWFCxd4+eWXCQ0N5cCBAwQGBirLyupfebuh\n2hKyMxaywWDg3Llz6PV6wsLClICdyWQqUxIT4L1N77Fw60K7QjxKTb/G4p92Np830DeQHH1OmYUY\nziDfkK/kHQd4B1j2L1kCgkZTOfNRASlFr32wBPLki1UuV65B+XA3qFcyaGevpZWc3SIH6srLcpF9\nxS0prWNRBhPUN9fnizFf0Ldt33J2UBpms5m1a9fy2WefsWjRIvr161fjKy4D1ZaQy4LZbObChQtc\nunSJkJAQpXmoMxV2Ww5vYfJnk7mee93ucrCq6bdKaVME5NVqCg22hRq+Wl8MZgPZ+orpTtiDn5cf\n+kK9EpwrqTEgz0ej0lBgLCiejzVJyAUK1rDWPjBgIQHrr8rdoNztFNRzdKxaLN+vo6CdvRRDmaTl\nQJ3s7rBerwWWnngl4eAmK5kkxoeNZ8nwJQ4mUjaSkpKYPHkyYWFhHDx4kIAA13OTnUGzZs0IDAxE\nrVaj0Wg4cuSIzXIhBFOmTGHnzp34+fnx5Zdf0qVLl0qZi7uotoRsj1Ctu4c0bNiQHj16IEkSubm5\nHD58GD8/PxtZTGut4xNJJxj98WjiUuMqNB8bAfki+Hv746XxwmQ2YSr0jA9No7LMuTyr3N581Co1\nWq2W/LLC9/YEf+Tuz/ai+TcDssV4M1ERC9leKpuzcFT2bMTypNO+jG3tnHqNzY1ZfN9iGng1ICoq\nSkldCwoKwt/fv0wr12w28/nnn7N27VqWLFlCnz59Kt0qLkuK85dffiEuLo64uDgiIyOZNGlSKWH6\nqoJqS8glkZmZydmzZwkICLAJ2AkhCA0NJTQ0lLy8PHQ6nZJlYTKZMKvNzN4+m0PnDnl0Po7yia3F\nevQG1zIpZN9zRVHhG4OZ4qCQC2lTdnGzidRTcKVST05lM+BZQX65wCOtnPWsLGSVUcW0e6Yx55Fi\n4XhH6Wv2ZDLPnz/Pyy+/TLt27Th48GCZzSFuFLZu3cqYMWOQJImePXuSmZlJamqqkrLqKlxt3eYK\nqj0h5+XlERsbi8lkom3btvj7+zsM2Pn7++Pv76/8UH+c+YNh84dVTNPBAYJ8g8jWZzvMJ7abSaH1\nxlvjjdlsKYcuqQwnlzu763uugQfhDCHnYyHhADyXPQEWgq2HRUEOkFTOlT2HakPZPm47IcEhNosd\npa/JJJ2YmMi8efP466+/uHbtGmPHjmXUqFEOOz97GpIkMXDgQCRJYuLEiaV669lr3XTp0iWXCTkj\nI4O6detWqrVfbQnZZDJx5swZrl+/TuvWrZW2Sc4E7GTcF3YfaWvTOBp/lE1Rmzh45iCxKbFk5WWV\nu21J+Hr5YjAaKlTYUWAooMBQfMXKEpzeWkvOVJbe9fk4nKfGt5SerUuoLhauu3DmmjVi+b6uYLGQ\nfSh+wqhYirnFZRFGcV4z9tsSWUNlVjE7fDav9n3V6d1oNBrq1KlDnTp1SEhIICsriwEDBjB06FBO\nnz7NokWLWLNmTaVoBpfEwYMHueOOO7h69SoDBgwgLCyMBx54QFnuqfZLc+bMwdfXl3/84x+0atXK\nrTk7QrUlZEmSqFWrFq1bt3ZaEtMRwluGE94yXHlvNpv5JfoXNhzYQFR8FJezLztUU9OoNGg12gpp\nVjiCSlIhEDZEXFbQ0Bl4qb1Awv1OIDWEbIGzPmR5vQJKW8k+RX9yOystjsc1A40AV7oKCWjn247t\nE7fTMKhh+euXgMlkYvXq1axfv56PPvpIIcGBAwe6PJY7kBs9NGjQgBEjRnD48GEbQvZU+6X33nuP\nlStXsnTpUh544AGeeuop9ydfAp7WpKoyyMvLUxqRWnd29sTjxvXr16lnrMfrg1/nzyV/kvFlBqlr\nUlkxfgXDuw0npH4IXmovAn0ClU4fnoK/tz8mYSqVeywH6XR5OoWMNSoNAT4BBPkGWQjXAQJ9Aik0\nFVpS+NxNa6shZAs8oWWRD2RiKVnXA7qi91lY8pLlKj8t0AGXyFhr1LLo/kUcfvlwhcg4Pj6eRx99\nlEuXLnHgwAEbAryRyM3NJTs7W3m9Z88e2re3jWAOHTqUr7/+GiEEERER1KpVy2V3hdxmbfLkyQwd\nOpRZs2aRmJjoqcNQUC07hgAcPnyY6dOnk5WVRVhYGOHh4XTr1o1OnTrh6+tb/gB2kJubS2xsLGq1\nmlatWpU7TlJaEhsObeC3U79x6uIp0nRpTncGKQnZT+wuvDReimynVq0lM89OI1V3eqv6Ub7mRVlQ\n4ZkOy+6cqZ7oGHIf5RdbRGB5RnXnZ1UDvctZ5yKWDiYAAsIDw9n2/DZq+7ku5GMymVi5ciXff/89\ny5Yto1evXi6P4UkkJCQwYsQIwOLXfuaZZ3j99ddZtWoVAC+++CJCCCZPnsyuXbvw8/Nj7dq1dO3a\ntcxx5R6YjvDvf/+bP/74g/379zs7VacswWpLyDIMBgOnTp0iIiKCqKgojh8/jkqlonPnznTp0oVu\n3brRunXrMn1dhYWFJCQkkJ2dTatWrdxSpHLVH+2tsfTTM5k9V1rqo/XBaDIqZdZy0NBkNpFXkIfI\nEhX/pX2x31XaWVQFQg4Grrk5h16U7xA8hMW6dYOQJW8JcW85B3sJaAJeBi/e6fYOf+/5dyUrwhXE\nxsbyyiuv0L17d+bOnVthw8ZZmEwmunbtSpMmTfj5559tln355Ze8+uqrNGlikaabPHky//jHP9ze\npzURZ2Vl4evri5dX8Z3VOsOib9++vPLKKwwfPtyZoWsI2R6EEOTk5HD06FGFpGNjY6lXrx5du3Yl\nPDyc7t2707BhQwoKCjh58iQGg4FmzZrRqFEjj0dYjUYju//czc5jOzkcf5jzV8+jL9SjQoVWo7Ur\nIl9RON1vL5uKd3eWy64rCk/kEFcFC/kByndb/IHFinbHQvYFepSzTircH3Y/Xwz7AnOBGZ1OR05O\nDiqVykYe0xFJG41GVqxYwYYNG/j444+57z7XdSwqgsWLF3PkyBF0Op1dQj5y5AiffPJJpex79erV\nrF27ltmzZ/PII4/YLJNJ+6uvvuL69etMmTLFGV6o6alnD5IkERgYSJ8+fejTpw9gIenU1FQOHz5M\nREQEq1evVvKQBw0axMiRIyutykij0TAkfAiDuwwmPT2dc+fO4V/Ln+jL0ez+czfRidGkXEspUyPZ\nGbiko+yuTsKtDk8cg7Nqb+7e38vZ3s/ox/vD32f8A+NLLSuZumadX2w0GikoKMDb25tp06Zx//33\nc/DgwRuWypacnMyOHTt4/fXXWbx4caXuSyZY2Tj9/PPP2bRpE1999RWtW7dW1jOZTKjVauWmJYQg\nJSXFo0babUfI9iBJEnfccQfDhw9n+PDhTJw4kZCQEMaMGUNiYiJbt27l7bffxmAw0LFjR8LDw+na\ntStt27Z12CnEFeTk5BAbG4uXlxf33HMPPj4+dLi7A2MeGqOsI/uj95/az6mLp0jXpTvlj/b39kdf\nqHct3c6dUG91IOQbBU98V464wAwDGw7kh+d+wEtj35ltnbomQy4CiYyMZMGCBcTGxhISEkJBQQEx\nMTF0715W62nPYerUqXz44YdKwM4eNm7cyO+//07r1q1ZsmSJTa6xs7B2UcjEGh0dTb9+/cjIyGDd\nunUcPHiQd955hwYNGnDgwAH++usvxo8fz4gRI/jrr7/IycnxmMF227ksnEFeXp5dBaq8vDyio6M5\nfPgwhw8f5vTp0wQGBioE3a1bN5o2beq0b04WN8rOzqZ169bUqmVPaMAxouKj2BK1xa4/Wi2p0ag1\nFXN56Kl4oYK3G9tC1XBZeMKH3Kf8VfxP+2MwGyjMKKz4fAOB8BIflRCOdxV//fUXL7/8Mg8++CBv\nvfUW+fn5HDt2jPr169OhQ4cKTtR5/Pzzz+zcuZMVK1awf/9+Fi5cWMplkZGRQUBAAN7e3qxatYof\nf/yRvXv3Or0PayK+fPkys2bNonPnzrzwwgukpKTw3HPP0aVLF8LCwvjll18IDAxk48aNHD16lMDA\nQMVy1ul0BAUFObPLGh9yZUMIQUZGBocPHyYyMpLDhw9z8eJF7rrrLrp160Z4eDjh4eHUrl3b5rHG\nbDZz6dIlkpOTPeqblv3R/435L3+c/YNzV85VLOXOnqiQs9BiqT67mbhFCNnrpJeiFqhRafDR+CAJ\niXx9PoYcJ7/EWkDnotdFwvHrRq1zOWAHlvNn6dKlbNu2jRUrVtCtWzeXx/AEZs2axbp169BoNOTn\n56PT6Xj88cf55ptv7K5vMpkIDg4mK6v8Aqn4+Hjq16+vGD/bt29n06ZN1K9fn9TUVBo1asSMGTNo\n2LA4FXDLli3s2bOHpUuXuvNEXEPINwNms5mEhAQiIyOJjIzkyJEj5Obm0rZtWyXV5uTJk/zf//0f\nzZo1sxEwqgzo8nR8+9u3bI3YSlxaHOk56eX7owupeOqamooHBD2FW4GQBfBn2ato1Vq8Nd5ggvy8\nfIx5dsr3agP3uCccD3D69Glefvll+vbty+zZs/H29i5/oxsARxaytRbF5s2bmT9/PhEREeWON2fO\nHEaMGEHHjh1JSEiga9euTJkyhbfeeovo6Gh++ukn6tSpwyuvvML58+eZOnUqWVlZrFmzhnbt2rlz\nKDWEXFVQWFjIL7/8wttvv01OTg716tXDbDbTuXNnunbtSteuXWnZsmWFrJqyIDdo1el0tGnTRnm0\nKtcfbaDibZvcTVu7XVwWZiDG9WG1ai1eKi+EUVCoL8Tsb2bUY6MqLBxvMBj46KOP2LFjBytWrCg3\nP9cdlJXGVlBQwJgxYzh69Ch169blhx9+oFmzZjaEPHv2bLp27aoUZmzbtg2NRkNwcDArV64kLCys\nzH3Lqa379+8nLS2NJ598ktmzZ7N161b+/NNyd9y4cSMHDhzgoYceolu3bqxfv54ZM2YAbosK1RBy\nVcK2bdsICAigb9++CCHQ6XRERUUpro5z587RuHFjxR/dtWtX6tevX6ETQI7+XrhwgZCQEBo3blzu\nOFHxUWyO3MzBswc5nXQafYbeqa7dpeAuGVYFQq4DOJa7dg59ylluBE66t4s6fnVY9vQyeoT1KDNt\nzRFOnjzJK6+8wsCBA3n99dcr3SouK41txYoVxMTEsGrVKr7//ns2b97MDz/84PY+rX3F8utvvvmG\nN954g6NHj1KnTh2GDh1Kjx49ePPNN8nMzGTZsmUEBAQwderUUtu6gRpCvpUghCA5OZmIiAglaHjt\n2jVat26tEPQ999yDn59fmeSalZVFbGwsQUFBtGjRosI+L6PRyO5ju/n58M9EnY0iMTURvd5zJeAO\ncbsQsgE4VbGhJUliQv8JLBi9QElbk3OLrWUxHWkXGwwGFi9ezK5du1i5cuUNEWtPTk7m+eefV9LY\nShLyww8/zNtvv829996L0WikUaNGpKWlVdgiLWnNrlmzhrNnzzJ58mSaNWvGxIkT0ev1fP311xw9\nepRx48axevVqunfvzuXLl2nUqJFbx2sHNYR8q8NoNPLXX38pBSzR0dEIIejUqZNC0m3atEGj0XDl\nyhXS09PJz8+nTZs2lZI3rcvTsengJvYc28Px+OOkpKVgMNzsCJ4d3GxCloAHy1mnEDjt+tBN6zZl\n62tbCWti//HcaDQqBK3T6cjNzUWr1SJJEseOHaNx48YsXLiQwYMH8+9//9umCq0y8cQTTzBr1iyy\ns7Pt+oTbt2/Prl27aNq0KQChoaFERkY6FJ0vCyWt2WXLlvHrr7/SuHFjrly5wgcffECzZs3o3Lkz\nc+fOZeTIkbz++utcv36dFStWKNt5WPe4hpCrG4QQ5ObmcvToUcWKPnPmjKVvX14e//rXvxgwYABN\nmjSp9A4NWVlZnD17ljyRR9TFKH478RunE0+Tdq1Ir+Nmnim3AiHnA2ecH1IlqZj22DTm/G1O+SuX\ngMFgID4+njlz5hATE4OXlxchISE888wzvPDCCy6P5yqcSWNr164du3fvtiHkw4cPU7duXZf2Ze0r\nXrRoEdeuXbMh2mnTphEQEMBbb73F7t27eeGFFzh9+jTBwcGVfc3UVOpVN0iSREBAAA8++CAPPvgg\neXl59O3bl3vvvZeePXsSExPD5MmTSU1NpXnz5oqgUufOnQkKCvLICVdYWEh8fDx6vZ527drh7+9P\nnx59ePWJYi3dqNgoNv+xmYOnDhKXHEdWdlbNrbwkhPOSqaGNQtk+czsh9UPsLi8Pp0+fZsqUKTz6\n6KP89NNPeHl5ceXKFafSxDyBgwcPsm3bNnbu3KmksT333HM2aWyyRGbTpk0xGo1kZWXZCOKXh127\ndtGlSxcaNGhARkYGX331FZGRkfTr14+VK1fStWtXxo4dy/PPP8/ixYv59ttvGT16NJMnT6agoEC5\nNjzgK3YLNRbyLY6rV6/SoEEDm8/MZjNxcXGKP/rYsWPk5+fTvn17haTbtWvn0uOqdaCwefPmNGzY\n0GmCv+H+aHczPWrjnuKdCouWRVnIA2JLf6yW1PhofVCr1JgxM2PoDF4d5rxwvDUKCgpYsGAB+/bt\n49NPP6Vjx44VGseTcGQhL1++nBMnTihBvU2bNvHjjz86NebVq1dZsGABc+fORavVMnXqVI4ePcqS\nJUvo0aMHmzdvZu7cuezevZv69evz8ccfc/ToURYuXFghl0gFUeOyqEExCgoKOH78uOKPPnnyJH5+\nfnTp0kXxRzdr1syudZCdnc2ZM2cICgoiNDTUI7nTleqPdpeQ3XVZOEPIuUAZ/XLb3dmO7TO307C2\n61rFAMePH2fKlCkMHz6cf/3rXx4p8fcEHKWx5efnM3r0aKKjowkODub777+nRYsWTo/bu3dv3nzz\nTQYOHMiRI0f44IMPGD58OCNHjsTX15dXXnmFK1euKJkb9gyZSkYNIdfAMYQQXL9+naioKIWkExMT\nadq0qULQLVq04LvvvmPQoEGEhYURGBhYqXM6f+U8P/zvB345+gvnks6RmZ2JMFfglLsVLOQcIL70\nx1q1lg+e+4AXB75YoV0XFBQwf/58/ve//7Fq1apKK3XOz8/ngQceoKCgAKPRyBNPPMGcObb+7cqS\nyLSG7DNev349Bw4c4OOPP0aj0bBs2TJiY2MZO3YsXbp0ISUlheHDh/Pll1/Stm1boHKbldpBDSED\nXLx4kTFjxnD58mVUKhUTJkxgypQpNusIIZgyZQo7d+7Ez8+PL7/88oakAlU1mM1mkpKSiIiI4Kuv\nviIiIoL27dtzxx13KFodHTt2rDQd3MLCQmJjYzEajbRp0wZfX9+K+aNvNiE7IxqvAxJsPwprGMby\nZ5dzZ6M7qVWrlt2UtbJw7Ngxpk6dysiRI5kxY0alWsVygDkgIACDwUCvXr1YunQpPXv2VNapDIlM\nWcjHOngHFj/1Tz/9xMMPP8ygQYPQ6/XKzWDMmDE0adKE3Nzcm9kFuyaoBxZFq0WLFtGlSxeys7MJ\nDw9nwIAByl0S4JdffiEuLo64uDgiIyOZNGkSkZGRN3HWNwcqlYrmzZtz9epVQkND+e677wgICODk\nyZNERETw9ddfExMTg1qtthH4b9WqlVvNLIUQXLp0iYsXLxIaGmrzKNmtdTe6tS7WVLhp+dGuwJlL\nz+qm4q3xZtm4ZYy6f5SSrpaQkEBubi4ajYagoCBq1apFUFAQvr6+pUg6Pz+fefPmcejQIb766it3\nS3ydghxgBksWh8FgqFRrMz8/nw0bNnDw4EFWrFihnG9yEK59+/bs37+f33//nbvuuou2bdsycuRI\nPvvsM+X88Pf3v9FWscuo9hZySQwbNozJkyczYMAA5bOJEyfSp08fRo0aBUCbNm3Yv3+/y323bgcI\nIcjOzrYR+I+Li6N+/fo2qnfOBv1ycnIU/3SLFi0q5J+28UefO86lzEsYcyvathmLYI87CQjewL3l\nrJMJJEKvsF5sfHUjAT7288YNBgM6nY6srCx0Oh16vR5vb28KCgpISEggODiY999/n7/97W9Mmzat\n0rVRrGEymQgPDyc+Pp6XXnqJ+fPn2yz/8ssvmTVrFvXr13dLIlOGXq9nxowZ+Pr60q9fP0U4Xibl\nmJgYtm3bRmxsLF9//TWAR6Ux3USNy6IkEhMTeeCBBzh58qSNZN6jjz7KzJkzlf5g/fr1Y/78+ZVa\n11+dIGdgyAL/UVFRpKWl0apVK0XxrkuXLjaP4CaTiYSEBDIzMyvFP510NYkNBzaw/8/9xfnRZif9\nGO4Ssg/Qs+xVvDK9+Hzo5zze43GXh8/Pz+fEiRO8//77nDx5ksDAQO6++27GjBmj9Je7kcjMzGTE\niBF8/PHHNg1G3ZXI/OOPPzCZTPTu3Ruj0YhGo6GgoID169dz6NAhRowYweDBg23cF9nZ2bz6qiUr\nZeLEiXTu3LmsXdxI1BCyNXJycnjwwQd5/fXXefxx24tgyJAhzJo1y4aQP/zwQ8LDw+0NVQMnYDKZ\nOHPmjKLVcezYMUwmEx07dsTf35/o6GjWrFlDSEjIDXmENJvNbPttG1sjthKfHs+5lHOO/dGVSchO\nCMeXB7mB76hRo5g6dSpqtZqEhAQMBkOZAjuViTlz5uDv768I8ZSEKxKZAKtWreKf//wnTZo0UXTH\nZUs4MzOTzZs3s2vXLlatWkWdOnVs8oeFEGzatAkfHx/69OlzM/3G1qjxIcswGAyMHDmSZ599thQZ\nQ3FSuozk5GTuuKPsnurOBAv379/PsGHDaN68OQCPP/44s2fP9sARVX2o1WratWtHu3btGDt2LADn\nzp1j3Lhx6HQ6WrZsyahRowgKCrJxdTRp0sTjiflZWVmcOXOGTs06MfTBocr4Dv3RntDSsAN3heP1\nej3vvvsux44dY/369TbkGxoaWqExK4q0tDS0Wi21a9dGr9fz3//+l9dee81mHWuJzG3btnH33Xc7\nNXZhYSFu3wuZAAAalklEQVRarZbz588zZ84cXn31VVatWqX8brVr16ZPnz6cPn2aXbt2MWrUKBsy\nliSJkSNHevBobxyqPSELIRg3bhx3330306ZNs7vO0KFD+eSTT3j66aeJjIykVq1a5fqPnQkWgiU/\nsmQS/O0KLy8vZs2axcMPPwxYfpv09HRF4P+bb74hOTmZkJAQJfUuPDycWrVqVciKNhqNxMfHk5ub\nS/v27UtZShqNhiHdhzCk+xDlM12ejg0HNrD3+F6i46NJuVqB/OiSUzXBiLtG8PXTX1f4ZhMREcGM\nGTN47rnnWLhwoVtBVE8gNTWV559/HpPJhNls5qmnnuLRRx+1yS1etmyZjUTml19+We64Qgi8vLwY\nMWIEwcHBLFq0iO7du7Njxw6GDBmiuC7uvPNOGjRoQF6eRbhbtpCrcsDOGVR7l8WBAwfo3bs3HTp0\nUC6G999/nwsXLgDw4osvIoRg8uTJ7Nq1Cz8/P9auXeuy/9hesNBRVVINHMNsNnPu3DnF1XHkyBHy\n8vIUgf+uXbvSoUOHcqUi09LSiI+P56677uKOO+5w60J12R/tBxS1nqtjrsOGpzZwb/Pyonz2kZeX\nx9y5czl+/Dhr1qyxabrpaTiTW+xIt9hTsJcFsX79ej788EP2799v0/9v586dLF68mP/+978e238l\nosaHfKPgKFi4f/9+Ro4cSdOmTbnjjjtYuHDhDUlJqm4oLCzkzz//VLqwnDx5Em9vbxuB/9DQUFQq\nFZcvX+bKlStIkkSbNm0qTeM3KjaKLYe2cPDUQWIvxtr6o/2BLvBYvcdYMmQJtWrVspuuVh7++OMP\nXn31VZ5//nlefvnlSreKncktrgzd4oKCArZu3cpDDz1E/fr17a7zt7/9jZYtWzJp0iR++OEHpk+f\nDsC7777L2LFjy3UxVgHUEPKNQFnBQp1Oh0qlIiAggJ07dzJlyhTi4sqol62BUxBCkJWVVUrgX6PR\nkJmZyVtvvUW/fv2oV69epT/Cms1mLly4wKXUS6QUpLD35F4SMxOZ+9xcWgS1UNLV8vLy8Pb2tskp\ndnSzyM3N5Z133uHkyZOsXr2aVq1aVeox2ENeXh69evVi5cqV9OjRQ/nc07rFYOny/NVXX9GpUyde\neOEFLl26xJkzZ3jooYcQQljElwoL8fHxITg4mHnz5jF+/Hjy8/O5ePHiTfl+KoAaQq5sGAwGHn30\nUR5++GGH/mlrNGvWjCNHjjgUNKkKj4y3IgoLCxk8eDB33XUXffr0ISYmhqioKK5fv15K4L8ilqoj\nZGdn89dff1G3bl2aN29ern9YVjqT84oLCwvx8/OjVq1a5OTk0KRJE06dOsVrr73G2LFj+ec//3nD\nfcXl5RZ7UrdYdk8YDAb279/PgQMHKCgoYMuWLUyfPp3x48cDlrS6WbNmceLECb799lvuuusu9w/0\nxqMmy6Iy4Uyw8PLly0qBxOHDhzGbzWXqu3p7e7N3716bR8ZHHnnE5pHx888/p06dOsTHx/P999/z\n2muveaTVza0MLy8vPvvss1I3JqPRyKlTp4iMjOSHH35g5syZSJJUSuDfVdIzm82cP3+ejIwM7r77\nbqdzqH18fPDx8VEqEYUQ5OXlkZWVxebNm/npp59IS0tjwIABaLVarl275vARvrKgVqs5fvy4klt8\n8uRJm9xiewacszc4nU7HkSNH6Nu3L2C5Qfn6+qLVagkODmbr1q3o9XrWrVtH9+7dle18fHwYO3as\n0gX7ZktkViZqCLmCOHjwIOvWraNDhw7cc889QOlg4U8//cTKlSvRaDT4+vry/fffl3nyOlOOunXr\nVt5++23A0oVh8uTJVb4c9EbA3lOCRqOhU6dOdOrUiQkTJig+0iNHjnD48GHmz5/P2bNnCQ4Otkm9\nK6sHoZxC17BhQ7p27eoWMUiShJ+fH0ePHuWXX35h6tSpjBs3jpMnTxIVFXVTS8Ll1LJdu3bZELI7\nusU+Pj58+umn/P777yQkJPD4448zfPhw1qxZw5IlS3jkkUcIDg7m4sWLCiELIfDx8VHIWAhRbckY\nsBygC381qGQYjUbRqVMn4e/vL/71r3+VWt6uXTtx8eJF5X2LFi1EWlrajZxitYLZbBapqaliy5Yt\nYtasWaJ///6iffv2YujQoWLOnDli586dIjU1VaSmpopvvvlG/Pbbb+Lq1asiNzfX7b8rV66IiRMn\nin79+omEhISb/VWIq1eviuvXrwshhMjLyxO9evUS27dvt1nnk08+ERMnThRCCPHdd9+JJ598stxx\np0+fLpYuXSqEEGL8+PHCz89PLFu2TFm+bds2ERcXJ4QQYvPmzWLixIkiIiLCI8dUheAUx9ZYyFUM\nlfHIWFWkEqsiJEmiUaNGDBs2jGHDhgGWR+LY2FgiIiLYvn0706dPJy0tjfvvv5+HHnoIjUZDu3bt\nKqymJoTg999/Z+bMmUyaNIkVK1ZUCavPmdzicePGMXr0aFq2bKnoFjuCKHpyGzBgAMeOHQMsQUFJ\nkoiJiQEsbqXHHntM2aZr165IknTbZiPVELILkMnwRrgHPPnI6IxvGiypRZ6USrxVoVKpCAsLIyws\nDH9/fxITE9m8eTPXr18nIiKC5cuXc+rUKfz9/W0E/kNCQsol1uzsbN58800SExPZunVrpQVkK1pJ\nGh0dXWqsd955R3nt4+PDhg0byty3TMTydVJQUEBKSgoAI0eOZODAgQwaNIh169YxevRom22bNm2q\nBAxvSzhrSosal4UCvV4vPvzwQ7Fnzx6PjltZj4zWyM3NFZ07dy71SLh27Vrx0ksvuTH76omCggJh\nNptLfW42m0V6err45ZdfxFtvvSUGDx4s2rVrJwYNGiTeeOMNsWXLFnHx4kWRk5MjcnNzRU5Ojvj5\n559Fx44dxaeffipMJlOlzjslJUUcPXpUCCGETqcTrVq1EqdOnbJZZ9++fWLIkCEe3a/1ceXk5Agh\nLOdc27ZtxY4dO5RlW7duFa1atRL79u0TL730kvjrr788Oo8qiBqXhSeh0+k4ePAgTZo0wdvbm8TE\nROXxviQqGgX29COjNUqmM1nnlsrYuHEjv//+u0ekEqsLHPUdlCSJunXrMmjQIAYNGgRYfvfExEQi\nIiLYt28fCxYsIDs7m9atW3P16lV8fX3Zvn37DUnbaty4sVL+L6vBXbp0qVRpv6chn/evv/66Erh7\n8skneeONN5gwYQLJycmARa7g1KlTzJ49m7///e83TRSpqqEmD9kJmM1mpk+fztmzZxFC4OvrS9Om\nTZk0aZLSPtxRfy65xLYq+Aih8qQSa2AfBoOBmJgYtm/fzuzZs2/KeXAjK0kvXLjAu+++i4+PD927\nd+eDDz5g2bJl9O3blyeeeILg4GA+/PBDateuDVgKUPz8/Nza5y0C5/yczprS4jZ2WezZs0c8/vjj\nIjU1VQghxKBBg8QzzzwjhBDiH//4h5gzZ44oLCwUQgjx7bffigsXLth9zBXC8qhrNBor/ZG1LLz9\n9ttiwYIFDpcbjUYRFBTk9HhGo1Hcc889dh9/8/PzxVNPPSVCQ0NF9+7dxfnz5ysy5RpUENnZ2aJL\nly5i48aNpZZlZWWJ7OxsIYQQO3bsEC1btnRpbLPZbHOeX79+Xbz99tuiefPmIjMzUwghxIIFC8SY\nMWPE1atXRV5envj73/8u3nnnHbFt2zZlu5t5LdxAOMWxVcNsq+I4evQoDz30kFLU0b59e9q0aQNA\neno64eHhSqeGadOmkZGRweHDh5kxYwazZ89WHl1NJhOSJKFWq20spcjISM6fP19qv8K1pxeHSEtL\nIzPT0iROlkos+YiYmpqqvHZFKhFg6dKlDte3LmT5v//7v1ISjTWoPJQnOxsUFKTkvQ8ePBiDwUB6\nerpTY8vnsiRJnDhxgri4OPz8/Hj22Wfp1KkTX331FQDTp0/HbDbz6aef4uvry8KFC+nduzebN2/m\n8uXLQNV5eqwKqPkmnICfnx8xMTFotVoyMjLQ6/WEhISQm5vL9evXadGiBZIkcfnyZQIDA+nUqRMX\nLlzgm2++oWXLluh0OoxGI+PGjaNXr14899xznDt3DrCQ7qJFizCZTMr+ZsyYwd69e5EkySOknJqa\nykMPPUTHjh3p1q0bAwYMUHzT27ZtA2DZsmW0a9eOTp06sWzZMqekEsGiHb1jxw6HKXJbt27l+eef\nByyFLL/++qvHbjQ1cAzhZCWp/Fs4U0kKcPbsWQClunHOnDmMHDmSN998k4EDB+Lv788TTzzB6dOn\nOXToEJIkMX78eKKjo7l8+TJ169alT58+fPjhhzRs2NCDR1xN4KwpLW5jl8Xu3bvFgAEDREREhFiy\nZIlo27atiI6OFtHR0WLo0KHiypUrQgghdu3aJe677z4hhBAffPCBkg0hIzs7W6Snp4tvv/1WzJw5\nUwghxNixY4Wfn5+YPHmyiIyMFCaTSZhMJmEwGGy2Lfl4WFUwcuRIceTIEYcR+5pClpuD//3vfwIQ\nHTp0EJ06dRKdOnUSO3bsECtXrhQrV64UQgjx8ccfi7Zt24qOHTuKHj16iIMHD5Y5ZnJyshg/frzI\nz88XQggRHR0t+vXrp7x/5plnxPz580VCQoJ47733xEsvvaS4RPR6fSUe7S2BmiwLT6F3794kJiay\naNEigoODue+++9Bqtfj5+VG7dm1SUlLw9/dn9erV9OrVSxFel1tAFRYWcvz4cebPn4/ZbCYgIIBD\nhw4xb948nnrqKSIjI7n77ruJiYkhICCAl156iX379gEQHx9Po0aN7DZqFEKUEua+kXX+P//8Mw0a\nNCA8PJz9+/fbXUe4oX1Qg4pDPg/LwuTJk5k8eXK5Y8mi8E2aNGH16tV89913SkPg+vXrc/36dRo1\nasTcuXMZNGgQTz/9NP369WPDhg1cvnyZli1b4uPjU601KDwGZ5lb3MYWcknk5OQoVsGsWbNEq1at\nxMyZM0VgYKDYuHGjSExMFBMmTBC//vqrEEKIiIgIMXr0aLF8+XKRkpIihg8frgQFlyxZIsaOHauM\nvW7dOjF48GAhhBA//vij6Nu3r2jbtq0YPny4yM7OFmazWVy7dq3M+S1fvlzJAa1MzJw5UzRp0kSE\nhISIhg0bCl9fX/Hss8/arDNw4EDxxx9/CCGEMBgMom7duk5b+mUFC9euXSvq1aunWH9r1qxx/4Cq\nMC5cuCD69OkjwsLCRNu2bcVHH31Uah2z2SxefvllERoaKjp06KDkIbuDuLg48dlnnwkhhDhz5oxI\nTU0Vffv2Fe+99564fv26ePTRR0VUVJQwGo1CCCGee+45ERkZKQwGgxLoroEQwkmOrSFkJ2Eymcok\nkrS0NPHjjz+KzMxMERkZKf7+978r+gRRUVFizJgxIikpSQhhydKYM2eOEEKIMWPGiCVLlijjTJky\nRSxZskQcP35cPPXUU2Lnzp1CCCGmTZsm5s2bJwoKCsS0adPEsGHDxLBhw8SMGTMUl4DBYBC7d+8W\njzzyiBBCiCtXroh169YpczcYDCIvL8/zX45wXGTgTiHLokWLxKhRoxwS8u1UyOJMoceOHTvEoEGD\nhNlsFocOHRLdu3f3yL579+4t+vbtKwYPHizi4uLE8ePHRceOHUVCQoL44osvxKhRo8S8efPEW2+9\nJTp16iRSUlKUbauim+0moSbLwpNw1K9LzjOuV68eTz75JLVq1aJ79+589tlnSklq165d0ev1DBs2\njClTprB7927FnXH8+HGGDh0KWG6OJ0+e5P777+c///kP3bp1Uzphq9VqcnNzycnJ4cSJE7Ro0YJP\nP/2U+Ph4vvvuO8DSYWLHjh28+eabgKXQY+vWrcrcjx07xjPPPFO5XxTYBAvHjRtHRkYGLVu2ZPHi\nxXzwwQdOjVFesPB2Q+PGjenSpQtgW+hhja1btzJmzBgkSaJnz55kZmbaZM84C+sAs16vR6vVcuLE\nCZYuXUrLli3p1KkTzz//PJMnT+aFF15g0qRJZGZmkpmZyb59+2z6Uda4p1yEs8wtbnML2RmUZw1k\nZGSI6OhosXLlSpGeni6EEGLw4MHi6aefFjt27BCXL18W7du3F1lZWeK9994T7777rrLt6NGjxfff\nfy9+/fVXMWHCBHHkyBEhhBCTJ08Ws2bNEkIIMWnSJDF79mwhhBC///67aNasmahfv76YNm2aSEpK\nEseOHRNTp0516M5ISkoS+/fvd/t78ATKCxauXbtWNGrUSHTo0EGMHDlSXLhw4SbM8ubg/Pnz4s47\n7xRZWVk2nw8ZMkT873//U9737dtXREVFuTS29TmcmJgohLA8ac2cOVNxswlhyS9/9NFHxYwZM0qN\ncZvkFbuKGgv5RqM8ayA4OJh77rmHF198UUkv+uKLLxg6dKgiFCS3+enfvz8RERGcP3+epKQk/vOf\n/3DfffeRkZGBSqVS2tbodDolB3jv3r2K+Hfv3r0JCwtj/vz5jBgxArVaTWhoKCaTSVHagmIL/8SJ\nE3z22WeKKpdcvm0ymW54mpp1sNARHnvsMRITE4mJiaF///5Kal11R05ODiNHjuSjjz6yqboD9wKo\n8raSJLF37146duzI3LlzGTx4MA0aNGDGjBkkJyezbt06AK5du8a7776LSqVSzhN5nJrAnRtwlrlF\njYXsMZRlScvL8vLyxDvvvCM6deokBgwYoFRavf/++4pVkpOTIx577DFx6NAhIYQQtWvXVgIply9f\nFh07dixlRd13330iJiZG2ZccjBk9erT49NNPy537jagydCZYWHJOrlQWhoSEiPbt24tOnTqJ8PDw\nUssrIzjmCRQWFoqBAweKRYsW2V0+YcIE8e233yrvW7dubePPtQfrc9FsNov4+HjRs2dPER0dLZKT\nk4UkSeKNN94QQgixc+dO0bx5czFp0iTx1FNPKU95NXAKNUG9WwXyRVHyvww5hzM7O1t8/vnnYvXq\n1UIIIQ4cOCD69OkjLl26JM6ePSvuvfdeZZtDhw6Jrl27CiGEQtL5+fmiXr16pQg1KytLdOzYUXlE\n3bZtm3jppZfErFmzxNtvvy0uXrxo9yayadMmsXz5cqVMtjLgyGVhTTSbNm0SPXr0cHrMkJCQMnOh\nKys45g7MZrMYPXq0mDJlisN1fv75Z5t5d+vWzenxDx48KIYMGSLS09NFZmam2LBhg+jSpYtYvHix\nCAkJUYLL69evF2+88YbQ6XRuH9Nthkoh5Jq/G/iHpZJSKmN5CPAk4AV0ABYBzYqWjQG2l1i/PxAt\nj231+cPAjqLXEvB34DwwAvgUWAlMBnYBSwFfq219AG2J/ajLmreL30Ef4Oei1+8AQ4tezwNOAX8C\n+4AwF8ZMBOqVsfxTYJTV+7NA45t8LvTCIu4VAxwv+hsMvAi8aPXbLQfOASeArg7Gkkq8fxL4GXjA\n6vf7Dnio6P1GIA4IKnl+3szvpDr+1RSGVGEIIcwlP5MkSRJFV4MQIglIKlp0QpIkfyAMC+GkAs0l\nSVqHhcguA72BTfJQVsO2LNoGoA7QCNgkhNgsSdIh4AKWi/ZfwAIgVJKk01iIa70QYr8kSQOBCCGE\nTghhogQkSVIXzbnUsnK+g/3A/qLXs60+nwXMcmUs62GBPZIkCeBTIcTqEsubABet3icXfeZ6yoKH\nIIQ4QDmKYUXnxUtOjGVhZUlqIoS4BNwLtAeiilapC+iAdpIkFQLpwI9AXolxSp2fNXAPNd73Wwzy\nxeQAMVisI4QQ/wG6AcuEEHHAKCxE9GPRumaZJIHWQFrR67pFf3Lkrz/wqxBiK5CAxSK9p2idQEAv\nSVJTYCfwqiRJf0qStEaSJJubvRDC5IiMJUlq5sShexL3CyG6AI8AL0mS9EDJKdnZ5pYX4JCsInxF\n33lM0f/FwAEsT0YIIa4CvwPdgTXAT0KI14UQxhs64dsQNYRcvfApFtKULWm9EEK2evoC3wohzoJC\n7DLJNMDyiAsW6zgQiC96fy9wrOj1XYA3FksxFNBjeZQNL9r+W+BxwBfoKkmSvyRJ4yVJOiZJ0reS\nJNn267HMUwuslSQpqOSyyoIQIqXo/1VgMxbisUYyYK3O3xRIuTGz8ywkSfKRJKkNWH5zSZJqFZ0b\niVjOl4+FEMnAViBckqT7itZdD0wCOhfd3G0IvQaVgxpCrkawtkKtLWlJkryBmUKI2BLry4+cO4E7\nil5rsPgQE4ve96P4UbYeFrI9A7QD0oUQ17BY0duEEH9hIbNsLP7tnkV/TwPbgaCi+Vhf2GaKibzS\nUXSTCJRfAwOBkyVW2waMkSzoCWQJIW6au6KikCTJF3gVGCtJUqOiJ4GvKf6t3wTqSpL0ohBiA5bf\nfJwkSX4AQohcIUSBJEmqove3/FNCVUcNId8GEEIUFFlEjrAHqFW07j5gYpFvESwBs0P/3965s0YV\nRVH4WxkR1GBAC4MgiKgQEIy9oH8gVRADgoUoDGIliBY2EnzUCWksrHyVKiJaKD4SgoKCINqkUzEg\nBEwKLZRlsffFa9ABmTETwvmqe2fO3LnMMOvss/Y6TB5vzXGzhCBX/vVu4Hkeryeq7A9Elb0NGLF9\nw/ZE3QOX1MgJZGNeYymqsE3ApKTXwAuimXlfUlNSM8fcI1YaM8SS/fh/vqeOI2mV7a/AA2KS3W/7\nKfAdOCBpTX72F4CTkjYTq4XHwLf6tYpXvHT86184FVYgKYK9thck9fztByhpC+E3PwIuE8J1G/gC\n7LA9K2kAGAMO2p6TtJ2okAeAU5VdkNdr2P4h6SowvViwC+2RPYJzxGRXNfz6gHHgrO0pSYPATWDS\ndtmn3mVKhVzAwUIe/ybG9YrV9nvbD3P8McKG6AUuphiLEN51Kcb7bM8AlwhR2Lnofasm3wbS+y5i\n3Bkk9RFxtR4iDrkWOAK8I5I2JySNAueBM4RfXOgyJfZWaEkrgcyu+zyx7K2aRs+Aj+lDNiVNENbG\nK2pRsqoSTz+3nxCKQudYTUT1DtueTx94BBiyPS7pDTBMxP7uwK/vpHu3XCiWRaFtWtkMKbi7iMbY\nW0mHiA0HR/P5IeC07b3Frugc2cgdA57Yvp6P3SI28ozanurm/RX+TKmQC23TQoyVVsh0njdsX5N0\nN8/3ELG6K9VLWAF53+VApiNeAoOSPmd07RMwRy3CVybB5cVPpIlhhwO29m8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12378f4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "'''\n",
    "--------------------------------------------------------------------\n",
    "bin_num  = integer > 2, number of bins along each axis\n",
    "hist     = (bin_num, bin_num) matrix, bin percentages\n",
    "xedges   = (bin_num+1,) vector, bin edge values in x-dimension\n",
    "yedges   = (bin_num+1,) vector, bin edge values in y-dimension\n",
    "x_midp   = (bin_num,) vector, midpoints of bins in x-dimension\n",
    "y_midp   = (bin_num,) vector, midpoints of bins in y-dimension\n",
    "elements = integer, total number of 3D histogram bins\n",
    "xpos     = (bin_num * bin_num) vector, x-coordinates of each bin\n",
    "ypos     = (bin_num * bin_num) vector, y-coordinates of each bin\n",
    "zpos     = (bin_num * bin_num) vector, zeros or z-coordinates of\n",
    "            origin of each bin\n",
    "dx       = (bin_num,) vector, x-width of each bin\n",
    "dy       = (bin_num,) vector, y-width of each bin\n",
    "dz       = (bin_num * bin_num) vector, height of each bin\n",
    "--------------------------------------------------------------------\n",
    "'''\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection ='3d')\n",
    "bin_num = int(9)\n",
    "hist, xedges, yedges = np.histogram2d(dur_t, dur_tp1, bins=bin_num)\n",
    "hist = hist / hist.sum()\n",
    "x_midp = xedges[:-1] + 0.5 * (xedges[1] - xedges[0])\n",
    "y_midp = yedges[:-1] + 0.5 * (yedges[1] - yedges[0])\n",
    "elements = (len(xedges) - 1) * (len(yedges) - 1)\n",
    "ypos, xpos = np.meshgrid(y_midp, x_midp)\n",
    "xpos = xpos.flatten()\n",
    "ypos = ypos.flatten()\n",
    "zpos = np.zeros(elements)\n",
    "dx = (xedges[1] - xedges[0]) * np.ones_like(bin_num)\n",
    "dy = (yedges[1] - yedges[0]) * np.ones_like(bin_num)\n",
    "dz = hist.flatten()\n",
    "ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color='g', zsort='average')\n",
    "ax.set_xlabel('duration(t) (mins.)')\n",
    "ax.set_ylabel('duration(t+1) (mins.)')\n",
    "ax.set_zlabel('Percent of obs.')\n",
    "plt.title('Histogram by Old Faithful duration(t) and duration(t-1)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4. The countour plot\n",
    "A contour plot is a 2D version of the 3D histogram. It is like a topographical map. The contour plot fits smooth level curves to the density data. Contour plots can also include color scale for monotonically increasing levels of the variables. [TODO: Add material here.]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. The scatter plot\n",
    "The scatter plot is usually first in line among visualization tools for 2D data. Let the $i$th observation of the two dimensional data be represented by $(x_i, y_i)$. A scatter plot places markers at each point $(x_i, y_i)$ in a two-dimensional plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The famous Fisher-Anderson Iris data is a canonical dataset of three species of Iris with five variables on each of the observations (sepal length, sepal width, petal length, petal width, species). We can creat a scatter plot of two of these variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'sepal width (mm)')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hgf0i4o+jrdf9FMzM2ldGP4XPdxJARNxM+rDPL/9Ew+9/B97ZyXbMzKw8o42S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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1236d2dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from pandas import Series, DataFrame\n",
    "\n",
    "iris_data = pd.read_csv(\n",
    "    'DataFiles/iris.csv',\n",
    "    names=['length_sep', 'width_sep', 'length_pet', 'width_pet', 'species'], skiprows=[0])\n",
    "length_sep = iris_data['length_sep']\n",
    "width_sep = iris_data['width_sep']\n",
    "fig, axes = plt.subplots(1, 1)\n",
    "plt.scatter(length_sep, width_sep)\n",
    "# plt.xticks(np.round_(bin_cuts, 1))\n",
    "plt.title('Sepal length vs. sepal width', fontsize=17)\n",
    "plt.xlabel(r'sepal length (mm)')\n",
    "plt.ylabel(r'sepal width (mm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could color the markers associated with different species with different colors. Note below that, with the colors, we are plotting three dimensions of data (sepal length, width, and species)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123275c88>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GUXyEYqcQJGanYBiGkT1+7RRsorkTMnr0aEQkvo0ePbrQIrULi5VgRJkgXHzn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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12395b240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length_sep_set = iris_data[iris_data['species']=='setosa']['length_sep']\n",
    "width_sep_set = iris_data[iris_data['species']=='setosa']['width_sep']\n",
    "length_sep_ver = iris_data[iris_data['species']=='versicolor']['length_sep']\n",
    "width_sep_ver = iris_data[iris_data['species']=='versicolor']['width_sep']\n",
    "length_sep_vrg = iris_data[iris_data['species']=='virginica']['length_sep']\n",
    "width_sep_vrg = iris_data[iris_data['species']=='virginica']['width_sep']\n",
    "\n",
    "fig, axes = plt.subplots(1, 1)\n",
    "plt.scatter(length_sep_set, width_sep_set, color='k', label='setosa')\n",
    "plt.scatter(length_sep_ver, width_sep_ver, color='r', label='versicolor')\n",
    "plt.scatter(length_sep_vrg, width_sep_vrg, color='y', label='virginica')\n",
    "\n",
    "# plt.xticks(np.round_(bin_cuts, 1))\n",
    "plt.title('Sepal length vs. sepal width by species', fontsize=15)\n",
    "plt.xlabel(r'sepal length (mm)')\n",
    "plt.ylabel(r'sepal width (mm)')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could plot four dimensions by doing a three dimensional scatter plot (sepal length, sepal width, and petal length) with colors for each species."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "length_sep_set = iris_data[iris_data['species']=='setosa']['length_sep']\n",
    "width_sep_set = iris_data[iris_data['species']=='setosa']['width_sep']\n",
    "length_pet_set = iris_data[iris_data['species']=='setosa']['length_pet']\n",
    "length_sep_ver = iris_data[iris_data['species']=='versicolor']['length_sep']\n",
    "width_sep_ver = iris_data[iris_data['species']=='versicolor']['width_sep']\n",
    "length_pet_ver = iris_data[iris_data['species']=='versicolor']['length_pet']\n",
    "length_sep_vrg = iris_data[iris_data['species']=='virginica']['length_sep']\n",
    "width_sep_vrg = iris_data[iris_data['species']=='virginica']['width_sep']\n",
    "length_pet_vrg = iris_data[iris_data['species']=='virginica']['length_pet']\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection ='3d')\n",
    "ax.scatter(length_sep_set, width_sep_set, length_pet_set,\n",
    "           color='k', label='setosa')\n",
    "ax.scatter(length_sep_ver, width_sep_ver, length_pet_ver,\n",
    "           color='r', label='versicolor')\n",
    "ax.scatter(length_sep_vrg, width_sep_vrg, length_pet_vrg,\n",
    "           color='y', label='virginica')\n",
    "\n",
    "# plt.xticks(np.round_(bin_cuts, 1))\n",
    "plt.title('Sepal length, sepal width, and petal length by species', fontsize=15)\n",
    "ax.set_xlabel(r'sepal length (mm)')\n",
    "ax.set_ylabel(r'sepal width (mm)')\n",
    "ax.set_zlabel(r'petal length (mm)')\n",
    "plt.legend(loc=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way to visualize all five dimensions of the Iris data is to use pairwise scatter plots. This method shows the scatterplot of each possible pair of variables. Pandas has a nice prepackaged graphical function that does this. Note in the figure below that there are only  6 unique scatter plots (either the lower triangle or the upper triangle)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "axes = pd.tools.plotting.scatter_matrix(iris_data, alpha=0.2)\n",
    "plt.tight_layout()  # adjust the spacing between the plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we wanted to customize our figure, we would simply use matplotlib's `add_subplot()` command. This matrix of scatterplots allows us, in a restricted way, to look at more than three dimensions at a time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure()\n",
    "\n",
    "width_pet_set = iris_data[iris_data['species']=='setosa']['width_pet']\n",
    "width_pet_ver = iris_data[iris_data['species']=='versicolor']['width_pet']\n",
    "width_pet_vrg = iris_data[iris_data['species']=='virginica']['width_pet']\n",
    "\n",
    "ax1 = fig.add_subplot(3, 3, 1)\n",
    "ax4 = fig.add_subplot(3, 3, 4)\n",
    "ax5 = fig.add_subplot(3, 3, 5)\n",
    "ax7 = fig.add_subplot(3, 3, 7)\n",
    "ax8 = fig.add_subplot(3, 3, 8)\n",
    "ax9 = fig.add_subplot(3, 3, 9)\n",
    "\n",
    "ax1.scatter(length_sep_set, width_sep_set, color='k', label='setosa')\n",
    "ax1.scatter(length_sep_ver, width_sep_ver, color='r', label='versicolor')\n",
    "ax1.scatter(length_sep_vrg, width_sep_vrg, color='y', label='virginica')\n",
    "ax1.set_xlabel('sepal length (mm)')\n",
    "ax1.set_ylabel('sepal width (mm)')\n",
    "ax1.set_xticks([4, 5, 6, 7, 8])\n",
    "\n",
    "ax4.scatter(length_sep_set, length_pet_set, color='k', label='setosa')\n",
    "ax4.scatter(length_sep_ver, length_pet_ver, color='r', label='versicolor')\n",
    "ax4.scatter(length_sep_vrg, length_pet_vrg, color='y', label='virginica')\n",
    "ax4.set_xlabel('sepal length (mm)')\n",
    "ax4.set_ylabel('petal length (mm)')\n",
    "ax4.set_xticks([4, 5, 6, 7, 8])\n",
    "\n",
    "ax5.scatter(width_sep_set, length_pet_set, color='k', label='setosa')\n",
    "ax5.scatter(width_sep_ver, length_pet_ver, color='r', label='versicolor')\n",
    "ax5.scatter(width_sep_vrg, length_pet_vrg, color='y', label='virginica')\n",
    "ax5.set_xlabel('sepal width (mm)')\n",
    "ax5.set_ylabel('petal length (mm)')\n",
    "ax5.set_xticks([1, 2, 3, 4, 5])\n",
    "\n",
    "ax7.scatter(length_sep_set, width_pet_set, color='k', label='setosa')\n",
    "ax7.scatter(length_sep_ver, width_pet_ver, color='r', label='versicolor')\n",
    "ax7.scatter(length_sep_vrg, width_pet_vrg, color='y', label='virginica')\n",
    "ax7.set_xlabel('sepal length (mm)')\n",
    "ax7.set_ylabel('petal width (mm)')\n",
    "ax7.set_xticks([4, 5, 6, 7, 8])\n",
    "\n",
    "ax8.scatter(width_sep_set, width_pet_set, color='k', label='setosa')\n",
    "ax8.scatter(width_sep_ver, width_pet_ver, color='r', label='versicolor')\n",
    "ax8.scatter(width_sep_vrg, width_pet_vrg, color='y', label='virginica')\n",
    "ax8.set_xlabel('sepal width (mm)')\n",
    "ax8.set_ylabel('petal width (mm)')\n",
    "ax8.set_xticks([1, 2, 3, 4, 5])\n",
    "\n",
    "ax9.scatter(length_pet_set, width_pet_set, color='k', label='setosa')\n",
    "ax9.scatter(length_pet_ver, width_pet_ver, color='r', label='versicolor')\n",
    "ax9.scatter(length_pet_vrg, width_pet_vrg, color='y', label='virginica')\n",
    "ax9.set_xlabel('petal length (mm)')\n",
    "ax9.set_ylabel('petal width (mm)')\n",
    "\n",
    "plt.tight_layout()  # Adjust the spacing between the plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These pairwise scatter plots allow you to start to see how the multiple dimensions (more than three) might work together. The plot above shows 5 dimensions of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Linked brushing* or *painting* is the use of a pointing device such as a mouse to highlight certain markers in one plot and have them automatically also be highlighted in the other plots.\n",
    "* A python library that only works with Python 2.7 to 3.4 is the `mpld3` package. An example of a linked brushing pairwise system of scatter plots using the Iris data is [here](https://mpld3.github.io/examples/linked_brush.html).\n",
    "* A page showing Bokeh's capability for linked brushing is [here](http://bokeh.pydata.org/en/0.10.0/docs/user_guide/interaction.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. The line plot\n",
    "The two-way line plot is the staple for visualizing time series data. It is also an alternative to a scatterplot when there is a clear order to the points in the data. The line plot connects the points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1. Line plot\n",
    "We did some examples of the line plot in the Section 0 on Python preliminaries. The `matplotlib.pyplot` package has a function `plot` for making two-way line plots. And you can stack them on top of each other in the same figure by simply calling one after another. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "my_age = np.arange(3, 45)\n",
    "knees_hurt = 0.03 * np.arange(50) ** 2\n",
    "all_ages = np.arange(50)\n",
    "plt.plot(all_ages[4:46], my_age, marker='D', label='My age')\n",
    "plt.plot(all_ages, knees_hurt, marker='o',\n",
    "         label='How much my knees hurt')\n",
    "# for the minor ticks, use no labels; default NullFormatter\n",
    "minorLocator = MultipleLocator(1)\n",
    "ax.xaxis.set_minor_locator(minorLocator)\n",
    "plt.grid(b=True, which='major', color='0.65', linestyle='-')\n",
    "plt.title('My knee pain and my age', fontsize=20)\n",
    "plt.xlabel(r'Age')\n",
    "plt.ylabel(r'Pain units')\n",
    "plt.xlim([-1.0, 50])\n",
    "plt.ylim([-2.0, 80])\n",
    "plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2. 3D surface plots vs. 2D level plots\n",
    "You can productively plot 3D surface visualizations in matplotlib. If you are working from the terminal on your computer or creating a D3 web manipulatable graphic, a 3D image is a productive summary of data. However, in print, a 3D image is often not ideal. If the image must remain static, level curves are often more instructive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we did with the 3D scatter plot, we will use matplotlib's `mpl_toolkits.mplot3d` toolkit. Read in as a NumPy array the `emat.csv` file. This 80 x 7 NumPy array contains relative estimates of hourly compensation by age (21 to 100) and income percentile (0-24%, 25-49%, 50-69%, 70-79%, 80-89%, 90-98%, 99-100%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "emat = np.loadtxt('DataFiles/emat.csv', delimiter=',')\n",
    "emat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "from matplotlib import cm\n",
    "cmap1 = matplotlib.cm.get_cmap('summer')\n",
    "\n",
    "ages = np.arange(21, 101)\n",
    "abil_midp = np.array([12.5, 37.5, 60, 75, 85, 94, 99.5])\n",
    "abil_mesh, age_mesh = np.meshgrid(abil_midp, ages)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(age_mesh, abil_mesh, emat, rstride=8,\n",
    "                cstride=1, cmap=cmap1)\n",
    "ax.set_xlabel(r'age-$s$')\n",
    "ax.set_ylabel(r'ability type -$j$')\n",
    "ax.set_zlabel(r'ability $e_{j,s}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we can't manipulate this graphic, then we might want to just plot the level curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "abil_pcts = np.array([0.0, 0.25, 0.50, 0.70, 0.80, 0.90, 0.99, 1.0])\n",
    "J = 7\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "linestyles = np.array([\"-\", \"--\", \"-.\", \":\",])\n",
    "markers = np.array([\"x\", \"v\", \"o\", \"d\", \">\", \"|\"])\n",
    "pct_lb = 0\n",
    "for j in range(J):\n",
    "    this_label = (str(int(np.rint(pct_lb))) + \" - \" +\n",
    "        str(int(np.rint(pct_lb + 100*abil_pcts[j]))) + \"%\")\n",
    "    pct_lb += 100*abil_pcts[j]\n",
    "    if j <= 3:\n",
    "        ax.plot(ages, np.log(emat[:, j]), label=this_label,\n",
    "            linestyle=linestyles[j], color='black')\n",
    "    elif j > 3:\n",
    "        ax.plot(ages, np.log(emat[:, j]), label=this_label,\n",
    "            marker=markers[j-4], color='black')\n",
    "ax.axvline(x=80, color='black', linestyle='--')\n",
    "box = ax.get_position()\n",
    "ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
    "ax.set_xlabel(r'age-$s$')\n",
    "ax.set_ylabel(r'log ability $log(e_{j,s})$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. More than 3 dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1. Plotting a time component with dynamic graphics\n",
    "[Here](https://sites.google.com/site/evanjmagnusson/) is an example of a gif that a researcher made of the time series of a three-dimensional object. Python's `PIL` package has the functionality to do this (e.g., `from PIL import Image, ImageDraw`). See examples [here](http://stackoverflow.com/questions/13041893/generating-an-animated-gif-in-python) and [here](http://stackoverflow.com/questions/34126016/trying-to-create-a-gif-from-a-set-of-images)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2. Brushing\n",
    "*Linked brushing* or *painting* is the use of a pointing device such as a mouse to highlight certain markers in one plot and have them automatically also be highlighted in the other plots.\n",
    "* A python library that only works with Python 2.7 to 3.4 is the `mpld3` package. An example of a linked brushing pairwise system of scatter plots using the Iris data is [here](https://mpld3.github.io/examples/linked_brush.html).\n",
    "* A page showing Bokeh's capability for linked brushing is [here](http://bokeh.pydata.org/en/0.10.0/docs/user_guide/interaction.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3. Using glyphs\n",
    "Glyphs, or images with many characteristics, can be used as scatter plot markers in order to incorporate more than two dimensions of data. You can use marker color, marker length, marker shape, marker size to encapsulate more dimensions of the data. Below is a rich example.\n",
    "![title](Images/glyphexamp.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4. Chernoff faces\n",
    "The Chernoff face is an interesting way to compare data visually in a way that simultaneously presents as many dimensions of the data as you want. Chernoff (1973) proposed using an image that associates different attributes of the image to variables in the data. For example, the size of the nose might represent the variable \"wind speed\", the color of the skin might represent \"temperature\", the openness of the eyes might represents \"time of day\", and the length of the hair might represent \"age\". The only limit to the dimensionality is how many characteristics you can put on the face. Also note that it is valuable that there be some intuitive association between the variable and the characteristic of the glyph. And, of course, the image could be anything besides a face."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](Images/ChernoffFaces.png)\n",
    "The above image represents data for lawyers' ratings of twelve judges. Each facial feature represents a dimension of the ratings. Because the features of the faces vary in perceived importance, the way in which variables are mapped to the features should be carefully chosen (e.g. eye size and eyebrow-slant have been found to carry significant weight)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5. D3 javascript visualizations\n",
    "D3.js or D3 or Data Driven Documents is a Javascript library for producing dynamic, interactive data visualizations in web browsers. D3 graphics are the future of visualization. These techniques have not yet become mainstream among researchers. The features available in D3 visualizations include slider bars, toggle buttons, flyover info, and dynamic time advancement.\n",
    "\n",
    "The *New York Times* graphics and data department have been the best at producing D3 graphical representations. My favorit example is [this graphic](http://www.nytimes.com/interactive/2015/03/19/upshot/3d-yield-curve-economic-growth.html?_r=0) that shows the user the ins and outs of U.S., German, and Japanese yield curve data (interest rates across different maturities at different points in time).\n",
    "\n",
    "D3 visualizations allow us to use objects like slider bars to envision more than three dimensions of data at a time. The [Bokeh package](http://bokeh.pydata.org/en/latest/) is Python's library for D3 visualizations. Below is a screenshot of an example. This [*Wall Street Journal* article](http://blogs.wsj.com/economics/2016/08/18/why-its-so-hard-to-get-rid-of-tax-loopholes/) has an example that my group at the Open Source Policy Center built using Bokeh.\n",
    "![title](Images/BokehSlide.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "* Chernoff, H., \"The Use of Faces to Represent Points in $k$-dimensional Space Graphically,\" _Journal of the American Statistical Association_, 94, pp. 807-823 (1973).\n",
    "* McKinney, Wes, Python for Data Analysis, O'Reilly Media, Inc. (2013).\n",
    "* [Python labs](http://www.acme.byu.edu/?page_id=2067), Applied and Computational Mathematics Emphasis (ACME), Brigham Young University.\n",
    "* Scott, D.W., Gotto, A.M., Cole, J.S., and Gorry, G.A., \"Plasma Lipids as Collateral Risk Factors in Coronary Artery Disease: A Study of 371 Males with Chest Pain,\" *Journal of Chronic Diseases*, 31, pp. 337-345.\n",
    "* Scott, David W., *Multivariate Density Estimation: Theory, Practice, and Visualization*, 2nd edition, John Wiley & Sons, Inc. (2015)."
   ]
  }
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