{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Matbplotlib Pyplot Library\n", "## Try me\n", "[![Open In Colab](../../_static/colabs_badge.png)](https://colab.research.google.com/github/ffraile/operations-research-notebooks/blob/main/docs/source/Introduction/libraries/Matplotlib%20tutorial.ipynb)[![Binder](../../_static/binder_badge.png)](https://mybinder.org/v2/gh/ffraile/operations-research-notebooks/main?labpath=docs%2Fsource%2FIntroduction%2Flibraries%2FMatplotlib%20tutorial.ipynb)\n", "\n", "\n", "The [Matplotlib](https://matplotlib.org/) (Mathematical plotting Library) is a Python charting package that allows us to render rich interactive graphics from Python data structures, including Numpy arrays.\n", "\n", "To use Matplotlib in your Notebooks and programs, you first need to import the Pyplot package (in this example we use the alias plt):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matplotlib modes\n", "\n", "We can use two different modes in Notebooks:\n", "- **Notebook:** This will create interactive graphics where you can zoom-in and move around the graph as well as export. You can use this mode for experiments, to interact with data directly in the book, but it is not recommended to use it for presentation.\n", "\n", "- **Inline:** This will create a static graphic with the selected properties. We will work with this mode in this course" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#We set the mode inline of matplotlib to get the result at the output of the cell code\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Main Concepts\n", "Matplotlib introduces the following concepts:\n", "\n", "- **Figure:** A figure is the canvas where we will plot our data. Note that a figure is not a graph, but the container that allows us to arrange one or more graphs for presentation.\n", "- **Plots:** Plots or axes are the actual graphs included in the figure. A graph has a **title**, a **legend** and 2 or more **axis**. \n", "- **Axis**: Conform the limits of the plot.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Creating bidirectional charts\n", "In this course we will work mainly with bidirectional charts, therefore we will create figures with one axe (or plot) and two axis. There is a convenient Matplotlib function for this exact purpose:\n", "\n", "- **plot([x],y,[fmt],[kwargs]):** This function takes an optional parameter x, a parameter y and optional parameters to format the line and pass additional formatting parameters to matplotlib. \n", "\n", "For instance,\n", "\n", "```python\n", "plot(y)\n", "```\n", "\n", "will plot the data in y versus the corresponding indexes. \n", "\n", "```python\n", "plot(x,y)\n", "```\n", "\n", "will plot y versus x \n", "```python\n", "plot(x,y,'o--')\n", "```\n", "\n", "will plot y versus x using a dotted line and circular markers\n", "\n", "```python\n", "plot(x,y,'o--', label='random data')\n", "```\n", "will plot y versus x using a dotted line and circular markers and create a label for y with the text \"random data\". Note that for the label parameter we can use expressions, for instance to write equations. For instance, using: \n", "\n", "````python\n", "label='$x_{1}=f(y,\\phi)$'\n", "```\n", "\n", "will create a label displayed as $x_{1}=f(y,\\phi)$\n", "\n", "Note that the plot function will not render the title or the legend of the plot. We need to use the functions:\n", "\n", "- **legend([kwargs]):** will render the legend, we can provide optional parameters to format the legend. \n", "- **title(label):** will render the title with the text provided in the label parameter.\n", "\n", "There are other signatures and many formatting parameters defined in the matplotlib library, but this is outside the scope of this tutorial. Check the documentation whenever you want to try to apply a different style." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Random data')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y = 200 + np.random.randn(100)\n", "x = np.arange(y.size)\n", "\n", "plt.plot(x,y,'o--', label='random data')\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot function allows us to effectively chart different lines into the same plot, just adding as many calls to the function as we want in the same code cell. For instance, in the example below we add two lines by calling twice the plot function with different data." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Random data')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y = 200 + np.random.randn(100)\n", "y2 = 100 + np.random.randn(100)\n", "x = np.arange(y.size)\n", "\n", "plt.plot(x,y,'o--', label='random data')\n", "plt.plot(x,y2,'*-.', label='more random data')\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Formatting the axes\n", "\n", "There are many different ways to format the axis. We will use the following convenient functions:\n", "\n", "```python\n", "plt.xlim((0, 20))\n", "plt.ylim((0, 15))\n", "plt.xlabel(r'$x_{1}$')\n", "plt.ylabel(r'$x_{2}$')\n", "```\n", "\n", " - **xlim((left, right))**: sets the limits of the x axis to the values provided. The limits are provided as a tuple of integer values, first the limit to the left of the plot (lower value) and then the limit to the right (higher value). \n", " - **ylim((bottom, top))**: sets the limits of the y axis to the values provided. The limits are provided as a tuple of integer values, first the limit to the bottom (lower value) and then the limit to the top (higher value).\n", " - **xlabel(label)**: sets the label for the x axis, using the text provided in the label parameter. We can provide expressions for instance to use equations in the labels (see example below). \n", " - **ylabel(label)**: sets the label for the y axis, using the same parameter as the xlabel function describe above.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$y=200 + 50·rand()$')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y2 = 200 + 50*np.random.randn(100)\n", "x = np.arange(y.size)\n", "\n", "plt.plot(x,y2,label='random data')\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')\n", "\n", "# sets limits\n", "plt.xlim((0,100))\n", "plt.xlabel(r'$x$')\n", "\n", "plt.ylim((0,310))\n", "plt.ylabel(r'$y=200 + 50·rand()$')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Filling areas\n", "\n", "The function **fill_between** allows us to fill the area between any two lines:\n", "\n", "**fill_between(x, y, y2=0, where=None, kwargs):** Fills the area between lines y (upper limit of the area) and y2 (bottom limit of the area), both versus x. Also, both y and y2 can either be a line or a numerical value. If a scalar value is used, a horizontal line crossing the y axis at the numerical value provided is used as the bottom limit of the area. The optional where parameter is used to provide an expression in x to limit the area in the horizontal axis. Additional parameters are used to format the area. For instance, in the example below, we set up the color of the area and its transparency.\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y_rand = 200 + 50*np.random.randn(100)\n", "\n", "x = np.arange(y.size)\n", "y_const = 50 + 0*x\n", "plt.plot(x,y_rand,label='random data')\n", "plt.plot(x,y_const, label='a straight line')\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')\n", "\n", "# sets limits\n", "plt.xlim((0,100))\n", "plt.xlabel(r'$x$')\n", "\n", "plt.ylim((0,310))\n", "plt.ylabel(r'$y=200 + 50·rand()$')\n", "plt.fill_between(x, y_rand, y2=y_const, where=x<60, color='green', alpha=0.5)\n", "# since y2 is a constant, the line above is equivalent to\n", "#plt.fill_between(x, y_rand, 50, where=x<60, color='green', alpha=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Note that in the last example, we are drawing the area between a line and a horizontal line and therefore we could just use y2=50 in the fill_between function call." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Drawing vertical lines\n", "In order to draw a vertical line, we use a different pyplot function:\n", "\n", " - **axvline(x=0, ymin=0, ymax=1, **kwargs)**: Draws a horizontal line at the scalar position x of the horizontal axis, the additional ymin and ymax parameters allow to set up the lower and upper limits of the line. Additional parameters are used to format the line.\n", " \n", "Similarly, the function **axhline** can be used to draw horizontal lines." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y_rand = 200 + 50*np.random.randn(100)\n", "\n", "x = np.arange(y.size)\n", "plt.plot(x,y_rand,label='random data')\n", "\n", "#Draw horizontal line\n", "plt.axvline(60,0,310,color='black')\n", "\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')\n", "\n", "# sets limits\n", "plt.xlim((0,100))\n", "plt.xlabel(r'$x$')\n", "\n", "plt.ylim((0,310))\n", "plt.ylabel(r'$y=200 + 50·rand()$')\n", "plt.fill_between(x, y_rand, 0, where=x<=60, color='green', alpha=0.5)\n", "# since y2 is a constant, the line above is equivalent to\n", "#plt.fill_between(x, y_rand, 50, where=x<60, color='green', alpha=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extra: Annotating a point of the graph\n", "As an extra (not needed to complete assigments, but used in the slides), we can annotate a point of the graph with the function annotate:\n", "- **annotate(s, xy, *args, **kwargs)**: Annotates the point xy with the string s\n", "\n", "See the example below:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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rrrnmGv7+7/+ebDZb3Xe7fYY5++yzeeyxxwB47LHHOHDgAABXX3013/nOd5idnQVgcXGRQ4cOrezLR0REnNQcy6itbVLKLVLKzVLKi6SUH/eX75dSXi6lfJ6U8o1SStNfbvjvn+ev39/rsZ+cyHJksbT8hqvI44czPD1XxPFn/Zs2beIDH/hA03Yf/vCH+ehHP8qVV15Z59T+8z//c973vvdx3nnn8ZWvfIWPfOQj1cE9zO///u9z880386Y3vWnZfYZ5wxvewOLiIpdccglf/OIXOe+88wB4/vOfz9/+7d/yG7/xG2zevJlXvvKVTE9P93UtIiIiPPbNFpbf6BnAs6LV7ss/czenjpl8452/eRzOyuMzP9nNP/5sH9e+fpi3X/7rx+08IiIiTgx2TOV4zefv5Z/fch6/+fxzj+u5RK12uyBXrjCRXTiu57BYrACwVCof1/OIiIg4MTia88aCB480h+M/03hWCJKy5WLax1fzWioFgqTZ0R3xzMF1JZbjLr9hRMQy5A0vfe5kGBOeFYLEtFwqtsCVx28AWCp6IbeZknncziGif/71/gO87NN34rhRUmZEfwSCJFeuHOcz6Z+TXpBYjovtSmw7huV0nz8xaBaLngDJngQ3zbOZHdM5JpcqHMpMHO9TiXiGUzA9QRIIlGcyJ70gMSxv5mg7MSz3OAoS37RVMKOZ7DOZ+YL3O87lT45om4jjR97wxqPVGhOms2XmC8fGAnLSC5JyIEhchYpzfLQBKWXVtFUwI/v6M5n5vGfPXoiCJiL6pOBrIqtl7f7gzVv5k5vvXZ2dN3DS92w3Kt7A7TjKwExbH/r2E8Q1h0/87qVdbV+sONiu5+wvmydPuPWzkTl/hrdQjARJRH/kfdNWeZUMJQtFk5w1h5SS1S6c/qzRSFxXxbT7F/3ZssX3H5/kJ7t2020OzlKxpgkZ1jO+Ev4ziieOZPjRk4NJoHRdWQvjLkZBExH9EfhGTCvW9ViyEgzLwbJjOHL1zenPGkECgmKlf9PW3btnsV2JYTld/0CLIUFiWsqq3DQRrfnyvfv5yHcfxbD7D7HMli2CyN/54vGtlBDxzCcwbVm2gu0O3uFu2i6WHTsmJv2TX5BUaoN9zuh/FnnHjhnAd953aSoLHO26VsJ2tOPmqzmZsB23q3yObNmiYEiWykt9HzPsuFw8CWL/I44vOd/Z7jg6pjN4Dde0HCwnEiQDwbBqgqRg9ndBTdvhrt1efSvXVbuOAgtMW6lkCdvWBjI7frZz3Q+e4pov37usdpcpWbgyxlKpfw1iLiRIMqVoMhDRH0HU1mqNCabtYjtqJEgGwSAFyQP7FymaDgm96AmSLjWSpZK33VCyhONEgmQQbJvI8uTkElkz23G7IG9nZgDhukHoL0DeiMK4I/ojyCOxHY2SNdjgDSklFVviOArGAHzDy3HSC5JynSDpLzziJ08dRVNd1q+dxXGVFWkkQkjSiQqOq1KsRIKkXyaWSlQsjdlCpuN2OT8kZq7Qv0Yyn/ceyFjMjsK4I/qmYNgI4QKCzIDDySuO67eTFeTKqz/ePKsESbEPQeK6kp/unGHt6AyjKQXXVanY3Wk4i6UKcc0mobv++8hR2w+G5bDo5+U8Pde+aaaUshoZM5cfgCApmMSEJBkvrVrsf8SzA9N2qDiSuO4JkMUBCxLTrk10ci0a2Q2ak1+QhJ3tZu9P/5OTWWZyJmvHjhBXvRDebqPAlooVNLVCQvPmCFEOQn9MLNWu36HFXNvtCqaN47tQ5gr9X/P5gklct0joDkYlCuOO6J0gYiuhexOcxQGPCaYVFiSRj6RvjDqNpPcL+pMdR4kJyYY1s6iK9yN163NZLFZQ1DJJ3XufiSJ++mIyU3voDncQJNlQptf8IExbhQq6ZpDQXCq2tiohmxHPDgL/SDzu3ZeZAdfgC497+QFEqy7HSS9IBuUjuWPHDGtHlzh1dAQlECTdaiSlCqpiENdc/30kSPphMqSRHFlq70QPC5KlAURZzeVNFLVEQpdR9F1EX+QbNJJMefVMW/k+fcPdcPILkkrtgvbqIzmyWGLPTIGx0cMktSRqzF3R/haLJppmoWueUIsESX9MZkoIIVFVk9l8+98gLEiy5f61h7mCga4a6JqN7eiUBxxpE/HsIRAk8bh3Dw3a3G3ag82fW46TX5BYDqriXdSS1VvI5v375gFYO+olIwamrW58JFJKlkoWulpBV73jR8ls/TG5VCYVr5BOGCwV2+eR5EKCJG/0V01ASslCoUJcN4lrDo6jUahEgiSiNwLTVqCRZMuDHezrNJLIR9I/huUQ17wLWar0Jkh+8fQCqbjFKWPe+6ogMZef5eZNG8cFTTOrGknUk6Q/JjJldD3PcNKmWNbbNpkKNBJNM/qOssoZNpYj0TUTXfV+9/lCsb+dRjxrCZIR04mgT9FgzU/1PpJIkPRNueIQU2xiMadaCXglSCn5xdPzjAwfZSwxClD1kZQqy//4QVa7rlbQfI0kuIkiemNiqYSuFxlK2piVJDmztcM9eDjTiRJGRe2rQ2ZQHkXTDOL+hGAhqrcV0SNVjSRuExMuhQEnuNb7SE4iQSKEOEMIcZcQYqcQ4ikhxAf85dcJISaFEFv9v9eEPvNRIcQ+IcRuIcRv9nJcw3aICRtVcTDs+oHEclz+9oc7mM62N1Hsmy0wX6gwNjKLElMAVhS1FWS1K5pBTICq2OSj5lY9YzkuszmTZLxEOlHBdnSO5lrX0cqWLQSSdNLEsvW+nONBMqKmeT4SiMK4I3qn5mwHTbUp9jDJ7UQ4/LdYWf3owmOpkdjAX0opLwBeBLxfCPF8f91npZSX+H8/AvDXXQNcCLwK+IIQQlnpQcsVBxGzUBWXRt/4npk8/3LfAf7iOz9r+/lfPL0AwNjITHWZEluBIPE1EjXmD0SqTSnKiu6Zo1kDV1IVJAAHFlpnt+fKNrrmkNBsbLs/53hQHiUeMlEuFiNfV0Rv5A2bWMwlrsbQVJsBu0jqnO2lYzBxPWaCREo5LaV8zH+dB3YCGzt85HXAzVJKU0p5ANgHXL7S45Yth1jMc7hbDYI5mBU8sM9l7+x8y8/fv2+eoaTJqWNadVmgkZSs5U1UQQn5ZNz7MXXVoRwls/VMkIyoxQtVQXJwsXW9rWzZQlO9BELb0cmZvfs0AtNWKu5UfSSRRnJyIKWsa/VwLCiYFrrqoAiFuOYwaGt3WCMpW6s/cT0uPhIhxNnAFuBBf9GfCCG2CSH+VQixxl+2ETgS+tgELQSPEOLdQohHhBCPTLUQBuWKjRJz0BRJxakfwIOoHilj/N1/Ptj0WceVPLB/geGhKUbiI9XlVUHShcoY5C+k4t5ndM3BjJpb9UyQjJiOG6R8QXKogyBRFJOkX5pmto/CjfMFE4FkKEHVR/JMjr6r2C4/3j7dV2+cpWKFfbP5AZ7V8eGu3bNc8cmfsn++9WRyNcgbNqpio8ZUdM0deJ+iQCMRwsGwVr//0YoFiRAi3YuJKfT5IeA/gA9KKXPAF4HnApcA08Bngk1bfLzpikgpvySlvExKedlSi2zjkuWgxBxUxcWyRd2PFWgkw+l5fr7LZiZf/1DsmMqRM2zWjM4RE7VLFQiSchdRYIt+wcak7n2duOZSsdW2kUYRnQmSEUfSLqmEBUgmM62d3tmyRUwxSfpCfLaPKKv5gklCt4mretVH8kwuJf+jJ6f5b19/jLv37e15H/9w517e8MX7BtJ59HiyZ6aA5Uju2b/zmB2zYNjElApKTEFXnYH3KTJ8LURTK00m/dVgWUEihIgJIf6LEOI2IcQssAuY9h3m/0sIcW63BxNCaHhC5CYp5XcBpJQzUkpHSukCX6ZmvpoAzgh9fBMw1Wn/roSJbP0mRsUhpjhoqovjqnVdDYPoqQvO2YvjqPzPn/yy7rO/eNqboawZnatbHvhIjC5UxqWSRVyz0RXPNKarDo6trUojm2cDk5kSyXiFtK6jxCRxvcJsrvWTkilX0JQKCd2Psuqj3tZcvuI52hUdVZHEhEPOeOaWSNk9402adhw9ssyW7TkwXyRbdtkzPzGo06pi2g6f+clu5vKr/5wEx5jM9N9qALy0gBvu2FPnp2gkb9oosYqvkTgDr5QQHDuuWcfEAtKNRnIXnsbwUeBUKeUZUsoNwK8BDwCfEkL80XI7EV73+a8AO6WUN4SWnxba7PeA7f7rW4FrhBBxIcQ5wLnAQ8sdJ2PUDxblkEbiOkpdD5FAI1k/luPU8QV+uLVIPlQp8xdPLzCaLnPKSKLhu4ASc+pitdvhFWw00QJBotnYUU+SnpnMlEnoJRKq95ukExWW2iga2VIFVfMEOcBsH/W25gteeZTw71gwTvygiVufmOJotvle2zvjDZr9XJMg2nHv7ELP+2jHrVun+Mef7eOf77934PtuZLYqSAZjpvvpzhk+f+devvvE4223yZUtFMUiJmJVjWSwgsRFINE1u8kSsxp0I0heIaX8/6SU23ytAQAp5aKU8j+klG8AvtXFfq4E/hh4eUOo798LIZ4UQmwDrgL+3N//U8AtwA7gx8D7pVy+SXq4IKKUEtNyfUHi4Lj13cJyhoUac9HUGFueO0vF0rn2h7/EsBwqtstDBxcYGppkWB9uOo6iOJj28j/OYqmCohpoMW8A0vyb5mQpr7FUrFRbhh4LjiyWUPVc9XoOJSyKRrNJU0pJzrDRlJogme+jlPxc3kDXjKqJU9ccTnTLVs6w+LNvPs61t/28ad1e37cx34eWNuX7q/bPd24utlKklHztFwcBmMiuvt9iNueNGTO5wWg/+2Y9Id3p3Aumhap4z42u2riuSsEc3JhgWA6K4qIqDnaDJWY1ULvYphv9fdltpJT30drv8aMOn/kE8Ikujl8lE2riYjkSR3ragypcHKe+PW7esNE0z+E1uqbAKWvn+e4j6/jxtv/kiueMU664rBmdQ4jmy6TGmsOJW7FYNFHV0ACkOkgZI2uU2TiyzIefAbzn64+iqQY3vfOqVT+W60qmswann1LGU3AhnbSYXBgmZ+ZYm1xb3bZUcbyKAqpFQg+irHqb8UkpmS9UOGV9baCJa/YJX0p+YtEbmJ6YqNcYDMvhyGJQvrw3aVgwbQp+WOmgBcljhzNsn/KSTLupHtEvs3nvvlgsDmawDQRJpkNDqbxhMzTifbcgUXlpgIUbTdtFiUnPpF/yJtBqrJvhvje6Mm0JIf5UCHFmeKEQQhdCvFwI8TXgratzeisnXLPG8O2EMcVGVVwcV6nTSLzICQs1piIEvOqFB/h/Ln6I4ZED3LPnKErMZXy0tdquKC7dlO5aKlbQ1Up14KvW2zpJQkePLBZ59NDSMXG4zhVMLEdWS2+DZ9pyHI2pbH1SYpDVrqoVVMVFCJdMqbdBqVhxMG0XXQsLEpeKdWIHTUwseddpPpugWKnZ/w7MF3F9ZbrXYpbToVL+4bL+g+DffnmQuOYihEPhGCTTBT6SfHkwE4NAkOTalEKSUlIwbVQ/jFyvVkoYoCCxXGIxB01xcI5B3/ZuBMmrAAf4phBiWgixQwhxANgLvBkvmfDGVTzHFZENFVUy/KiqwEcipULZqjdtxZSapBYCfmWj4NWXzfGGlz7ClVvuZOPYGlqhKi7L3eNSSjIlC02rqS7VZLYBd0Q7XmTLFkYlzlN9OG27JcghSYQESRACfLAhKTEsSIQAXbPI9ViGIshq1/XavVWtAGyfuL9jMMDbTpwnp2sO8WCgA7fnYpbTIb/LXG5wwnQ2b3Dbk9NsWLcfTXUoV3q37T+4f4Hf/OzdHfsQlStOVbMqmVqdD7UXLMdl/7wntNu1rTBtF8clZNoKqoIP0LRlO8RiLpoqm0z6q0E3guQq4PtSyiuBM4GrgS1SyrOklP9VSrl1Vc9whSyF1MmgF4mI1SoAh53pubJFLGaitIhmTsUVnrN+DF3RWx5HVVxsp/MMJmd4Hfp0tTYAaf4s5GQoJW85LiW/tMMDByZX/XjBwBjXa7PralLiQr15JcgRUhTv2sc1m2KPSlOQjKiqtQc9rg4+0mbQhDtJPnxouvp672wBgWQ4naNk9jYLDxzt6WSWXEnrq45ZmJsfOoLtSE7fsA9N6U+QPDGRYfdMkQcP72i7TaCNKDGLSiVJodLtOEfWAAAgAElEQVRf5NahhRKOr+4V22SUBz5FVfWLivqCJDPA/s2m5RITfrSqo666xaAbQfIG4FYhxBE8f8ZfAL8lhLiwn3yS1SJs2goEiVdrq7msSc7wMp8Ds9NKUBWJ7cQ6RkNUy6No4ZmsXwH4RPfUdkG4YumjR+Y6bDkYghySsVTtAU1XkxLrCzdWK//6s76E5lA2e8u/DQSJrtWERqCRFE/gUvITSyVSCQOQPHZ4trr86dkCQymDoYSNWenNPDeV8fa7djSLYabIm/1HPFmOy00PHmLDmnnOHE+gqU5fORBBVGa2Q8/ywD8ylM5gOzrzpf78PeEEzWKbPLOgza4S8zUSbfCTS9N2EDEbXXUBQb6PNuPdsOyTJaV8l5TyMrxEwT3AATwt5WHg0KqeXQ+E+xOXQ6YtrSpIws52C1XpzQbr+VzqnfeNLPrCQlNCgsSffSycBKatsCDZe3T1v89kpkRcs0knak7DVNxPSszWxwAH5xb3s9rjuk3Fqjdd3Hj/AZ440rpOV5g5v87WUKI26w4mBCdyKfmJpTLJRIahZIl9s7V7cM9Mnng8QzIusex4T+a5o1mDZNxiNG1iOzpHMv2HAN+xY4aZnMmGDbtI62l01cW0ei++EQiSTtW2g9Df4bR3HxxZ6leQeBqNqphttamg8q/SaNrq4JxfKabtEhM2muqdQ26A+27FSn6lt0sp3y+l/IKU8p14eST3rdJ59Uw+lCRW1UgUq1r6Pdy/OHC294KquLiu0tGmGmQ+q2qzIDkZ+rZn/MrGqlJhNhvvyb7supLP3rGHQwvLD8gTS2US8VoOCUAsJknoFeZy9ROCQJAkde9BSugOlq1Tsjz/Srni8PEf7uBTd9y97HE9H4kklagNDPFqBeDWIcW7j+b5p58/vey+V5OJpRLxeJF1owZz/u9jOy4H5oukkjmSDddkJUxly8T1MmNp737eN9e/ILl9+1FScZsz13vapaa62I7Sc0BDYEIqdOjHEZi2xoY9TWJiqT/Nat9sgXTCJBGv0O6wwRilKH6LCS0YEwaZ2e4gQhPo3Cr3JFmJIMkJIV4QvJFSPgqcN/hT6h2BrNrsodbcRYm5VR9JUFK5YruYtqzaKVdKVZA0aCRff+BQNVpmsegPZvHag3AyNbcK/BBjo7MYZpq98yv3k2yfyvIPd+7lc3c35zo0MrFUQtPyxJV43fJWSYneuUmSvosrrtl1g+bumTyuhLli614mYeYLJgnNJqHWCncuF2nzzYcO86nbdzGZO7rs/leDvGGRLduk4iXWjpQwzDRPL0xxaLGE7UrSyRxxzctfWCqt3C8wlSmjaXlGfTPj0/PLa3adcFzJvXvnGBmZZDzlhXFrfZYOCQbsXAezzmzeQAjJ2mHvd5zoMylx72yBRCJDXJWYdmuTeXBegW9kNfoUGZZDTDi+aavzNRgEKxEk78Ar5f5VIcSfCCH+GTihOjQJAaWQOhn0a9dUGTJteTdl8KP1rJHE/LyU0Cx8vmDyP76/ndd/8S6WimbVRxIUDQRPqAnhkj8G8fGrTcYXhuOjXuLVAwdXLkju3et99kimc+KZlJJJXyNp9GkNJS1Khl73W2TLXnVVTfHMYHHNRkqFxZIncXZOewKkm8Kb8wUTXTfrAi/iftBEu1LyQZ7G0XzrXimrTTUwIV5kfNg7lwcPTlYz2pPJLAndu14z+ZWZ56SUTPsayXDKuwf6zSXZPpklU7JYO3q02vdHV73Q1V7LCQXPeKfGTrM5k4RuMZL0ntF+yqS4ruTp2QKpZA5dk1h260KMwXnFNW/davQpMm2/6rkvpAqrnDTctSCRUu4FXozncD8Frwz8azp+6BgjhMQICxJfI1EVWXW2B20ngzpJvWokSguNJDCnzObgTV/+KUdzBrFQwUbvHP1GNidBT5Ksb9pav8YbLB85ONtp85bcv88TIIVlHqK8aVO2XBLxZg0glahgVlJkjdpgli17YddBaHfcT0qczdcLkkqbWWOY+UIFRS3VCZLlNJLAVNfJrNKKnGENpJxFkIwY14usHfEEyaOHZ3h6zhso1w5VqlWMZ1coSPKmTanikogbxDUbJWZXAyF65Z49cwgk42O1oI1+I46qpq0OHvu5gomulRlOxhDCZSbXu8l5MlPGsF1PkKgOdpv8jcBHEldrY8Cg+xQZloMSc6sT6NVut7siT5ZfXPHbUsq/kVJ+Tko5+CI7fSAEdQXKAkGihwRJoVKvkQR2ypWiKi6uVDDCeSm+IFk/foC9R+FrvziAHirYGKCrDiVz9Us7rzYZ//uOpisk42V2HV3ZbK5ccXj44KL/uvP1qOZyaM0PejpRwXFVpnI180q2bKGGcoSq9bb8QXOHL0i6qUM0lzfQQtUJvPPwfSQtfF2uKznimzdzRveD4Fze5PJP/JR/f7D/KrSBRjKcskjGbeK6ya6jBfbO5EknTEaSceK+RjK3wtIx0xnvO8e1EkJAOmkyl+9vEPz53jnGhgucMpKuLvPKGmkYPQqSvH9/FjsIktmcgaoW0RWNhF5hqY/s9sDRnkrm0FQHx2ldnDWI2kqEhgVddQZaKcG0XWIxt6qRZFdwH/ZC14LEz2L/ihDiM0KItwshXiCEiC//yWOHQFIJqZOmL0g0RVYvaHBTNTq8VkogmIqV+kx5gI2n7Oei5xzAdkFVjWqhvwBddTBO8J4k2yYyHF7oPMB4jaMcdEVh3WiZoxltRY7Rhw8uYjkSkMs+RAu+mVBTmx+IoaS37um5mhkpKCEfCJJEUG+rUEZKyS5fkDRWhG7EtB0ml8okE/XXIt4hjHs2b1brsK1kJvjooUUMy+XfHnqi68+0Y2KphBJzGUl613V8pMTUolK14ae0VEi4rkyQTPk5JLqfzzOcqpAtqj3nkuQMi8cPLTEyPEFaqwmSamDKMqVDXFe2nAwEVodSh3YPM3kDXTcQQpCKW2RLvT+XgSAZS5c7alN5067W+AvQtcGOCZ4gCTvbTxBBAnwd+CFexd/nAB8DnlqNk+oVIWSdOhmE/6pqaOCvCpL6ZKCVEpSSLzbkpYBn+3zBufM8b9NB0sN7qgUGA7zmVp1zUI43H7x5Kx/67j0dt8mWLHTVQlM01o2UKJWHOLjUvXP5/n3zKDHJyNASxjLXY6FQ65neyNiQN9Bsm6wpyJlyBVWpVLWIwLQ1VygxsVSumtIaK0I3sn+uiCNhKFXvA1BiLjHhtixYeXixNjAXKt2bTh/3Q5EPziT6zk+ZWCqTShgkNS/CbXykTLE8zL7ZPMlkDjWmVmuQzXcozTGZKfP7X/wF05ma+SuoJpxOet9tOFnpK5fkF/vmcSSsHZup839pXUQ45g2Lzdf/Jz98cn/d8qAMCbQXJI4rWSpaxP08r1TComw2FwDtlr2zeZJxi7GUjqa0r+ibN2w01a6rfaWrLhW79wi1RsLFamHlJtaVshJBsk9K+b2Qaet1UsrnrdqZ9YAQYNtq9ccrWw4x4aIpsVB7XO/C5sqBetnbLEptmZdS26cQ8JKL5njVJU7VeRgQ9/sPdMpBOd4slkwOLix1HNyzZcurZRVTfTu84IED3ZdKuXfvPGuGlxhOutiO2vEBDnI50onmB20kZRATDk9OLVaX5fw2uwHxkEYSmLVSyeyy5SN2H81Xtw0jBGiaRb5FKflwKPNKZoJbD2cAie3o3LFrV9efa8XkUhlNr0W4jY+UkDKGaXsRWxDq9Ngh5X/r4QyPHFriC/fVIv2nM2UEkpGUd28MJSt95ZL8fM88uupyypp6zUjzfQidEgpnciYF0+G2nfUl2w3LK0PivW59Dy8UTFwJcd3bfypuY1qJnrPb980WSCaypLSULwQF2Rb5G3nDQmkUJFp7U9hKkVJScaRfIiWwnKxucM9KBMnPhRB/LnpJAz9GeBpJ7ccoW16NrZiIocQkQrjVZlTBTDKh96YV1ART2LQVaCS1waXV5dJWof/AoCmaDkWzc8RMpmwRUwzUmMq479B95PBMV/tfKJjsmM4xMjJFQmPZciOBRpJuYUyNxWB0qMTh+ZqQyZVtNLX229Ta41Z8R7tkzXC2qSJ0I7tn8sSEZN1wswCLt/F1HQlpJN0KEseVbJvMsGH8CCD58Y7+cn2PLBVJxIvVScza4do5JROeUIzFJJpidSzcGCTV/nJ/Lapuyk9GTKpe8MFQ0vuOveSSSCm5Z88sYyOzjKfG6tYFGkmnUPlA62is7BwOpTXbCJIgGVHTPI0slahg23EWiiuPQJNSehpJIoumaKFzb76nC35Tq3BpJl11sG19IGOCaXvjTyzm+JYT2dG8NwhWIkguBN6L1x3xNiHEJ4QQb1yl8+oJIcB1dcqW92MENfmDH0yJudWQ4HwLh9dKqOalhMJ4c2UbgSSudZa1QSObE7VFqWE5WI7EqGh1VWMbyZRq5qNk3DMR7JhaPi8DvKZhAGtGZ6rlRjo9RPMFk7hmk9Ba/2DjIwZL+RSlSsnrJ+PU5wjFYhJVscmVbXZO5xhOGaQTsqkidCO7j+YZTpUYTqSa1nl27eZH6NBiiZioN6Uux56ZPOWKy7o1R1kznOfRg733TimaNkslm2SouOVwykTxqziMDYVKveg2uQ6FGzO+b+rwXLx6v05ny+h6kbjqSfVAkPSSS7J/vshkxmBsdLrJlxgMxu2q6ELNcR1EEAaEu1e2i7SfaxAkybi3j8NLK/8ec3mTvOGQTubrzr1VKfmCYXs1/mINgmRAfYpMf7LspRp4Y1W5srpRoisJ/329lPI84BzgWrzqvy9arRPrhZjf0j1wzpUrXix1YCdXQ82ovDpbDmqst3JhStXZXl9yRdNquQvtCNTYE7VOUzDLcxyN+Q4Je5lSpWo+EgLGR0tMLipdOV3v2ztPXHM4Zcys5guUO2okFXTNbPI3BawdLmPZCXbOTtYq/zbkCMU1i7wh2TGdI5lcIKkpTRWhG9l9NEc8sUBSTTati2sOptVs1z68UCKd8gaUbuP3t/r+keH0IpvWFZjPDnM4s/JwaqhFbCXitUmAELBmqIiqlhhL1a5hQrPpVCsw0EgqVpJfHvAy9aczZTStUGsuluw9l+SePV6479rRZt+aprQfjAMCzaPROhfWSNqFeAd1ttJx735P+YKkl1ySwNGe9M2GtUCB5oubM2rdEQN0zUbKGLkOZrxuCdrsiliQ/uC0Ne8NipVEbY0LId4LXON/7ltSyr9ctTPrASF8QVIK+UhidlXyq0qtGVUrh9dKUFs62200Zfl9VnuSlHqfda4mhdBsbiLTenCQUpJtMB+tGylTLA0zme1cwFFKyb375hgdmWFtao2fkyFYbFNuBDyNRFXLbasxr/FNNw8fmqorIR8mrjvkSipHFssMpTJV+3G+zcObNywmMwbDqXxLE6Xn62rWpA4tFkknvQiybk0KWw9nSGgOG0YFp6/LIWWMHz65p6vPNhLkdOha/YD4q889ysbTH2FIH6ouS+gOZqV9xFWmZKH4A9Iduw4hpWQqa5CIG9Vr0k8uyT175hhJGZw21jxB0LoIXQ0Se8sNUX+BxUEIB8tuHcgx63dEHEp665Jx73450kN2+15fkIykC/65t4+WyhtWtRdJQPBdOz0D3VI1bYla5vxqNzFdiWnre8B64JPA/wKyQoj+A94HSPCsBzOYsuUSi1l1Gonlz068go1W74KkTRFIRV2+E5lWzYo+sTUSgKk2s7Oy5WC7sk6QnLI2jyTGj3d0rjF1cKHEVMZgbGQGNaaGBGv76zHnC5LGwIWAwAew9ch8SCOpFyQJzSaT9+zwQ+lsy4rQYfb4WeCpVGtTh67ZTYKkYNosFi3SqQJCuNXgjuV4/MgSQ0MLjMSH2bCmgBKz+dnu9pUCOpXTCEr0jKTrtzljQ46rnp+suz8Tuo1lxduaVBaLFYZSeeK6wQMHFr3+M5ZLQq9t308uyfapLKn0UYbjze2sq4K+g2krEBimVR+sESyP6waOo7QM8Z7zzaVJzbseVY2kh3pb+2YL6KrDmpS3r0CbauXfyRt2kyDp5hloxVze5K5d9ZqrUa16HqQ/uF0l3vbDSgTJsJTy48CMlPKleE2tblyVs+qRQCMJfrxyxUYIu+oj0VRZ7WqY9+2U/QqScB5Jrst9BlnRg6z2OUjCIa1T2dY+kmrBxpAf4pQ1eWIxhzt2di6V8kvfP7J21HsAqq1GO4R5LhRM4nr7mWlcd0jGDfbOlKr2cqUh5yShe22OAYZTuVrWbxtBEkRsDaVam/d0zbNrF0NFD4Pcm2Si0LVtumDa7J0pMJSeR1M0lJjklLU5dk7SUlPYPpnlsr/9KZ/40aMt9zexVK7LIelEYw2yRhaLFRTV4PTxPEfmEhxa9K5JuEsl1OeSlCsOf/6trXzvsYlWu6xi2g5z+QrJeLHOzBMQ3BeFDuWEAu3ZsvU6YZivBtMYbSPzZnMmulYrfZPQbQQuM/mVP5dHlkqkEkVSerLu3Bud7VJKiqaDGqsX8tUxYYU9Sb7x4GHe8bWHmSvUIhYDjUTEgppeJ5YgCa6IKYRISin/gxOuRIr3P7BLGpbnIwlUcK8ZlWfDDxLWWt3A3RD4SMK1mnLlCkood6EdtQrA3nnuOprjscPHpyZTK8Kmrelca42kZj6q3fiqItmwJsdTE25HP8memTya4rJu2BP8tX4MrR8i03bIG05dq9tWrB0uM5NVqjXAklq9OSMIAdZVi7VDtZDwdjH2wXmOD7V+CL16W/UmucOLnuCN63lUxe3KNr1tIoMERtK1wWDTugLF8hCPHD5Qt61hOfzFLVsxbZev3DfJ3rlFGvFySEwS6vL5wnHdxnE1MuXWv/NSyURTTU5bW6BiJfjRdk/b1LT6CUaQSzKTy/C2rz7E9x6f5LN3dy4OPuVnyCcTrWfhSkwSE27HdruBwLDt+m6V1WCauNm21exs3kDVilVBIgQk4hUWCyuPcJpcKqOGCorWzHL1xy1VHCS01Uha+VQ6sVSqICUcXKpFSwY+kljVR9JfFeVuWMko+mkhxFrgW8C/CiH+FNi4OqfVG618JIF9FzwVz3EVbNf2ne12T02tIBT+GxYk/j6XI6zG3v7kNK/73/fz/m/84oTp/x2eAc62qT0UaCSKUn/jn7E+T7E8xGMTB9vu/+m5AulUgaG4l8W8XKvRxWJQbrvzQxYk3R1a9IRyQq8XZkFSYjqVYTg+VEvWahNZtetojqFUjuH4UMv1wSxyrhAWJN7rsSEbVXGWbccM8MQRzw+1ZqTmjzp9nff6h9v31W17wx172DNT4HlnPwRIPvSd5sHaq5Kcqyu3344g43+2TV+VpWIFXbU4da2nidy2zfN/DSXqr1mQS/L2G7fy8MFFEvECczk6JntWfTl6e+e2qtody+cE96rramTLte/gCRhJMm6110jyBrpWby5Nxi1yK+zdLqVkMlMiES9Xx5OqNtVgggwEXGMgSDCZWqm5O7AehJ+dIMVBiFqVYbePKsrd0JUgEULEgF+RUi5KKW/AK9x4BvC6VTuzHhB+1FbgnCtXbBSlNjiriludnQQ+kl4JBEk5ZAPPlbvrbxIMQHc8afG+mx6jYjvM5itkzf4qqA6KmiBxq6XwG6l2IGwoernRHwBv3ba37f6fni2gx5eqszd9GdPWQiHo69LZ5LBm2Eu6e+igl/OQ1FtrJOlUBl3RUdXmyLsAKSW7juZIJBfbOvhbPfyHFrzmW8MJtWvb9NYjSwynDMaHagP/aNpzaP9ga4FfPr2AlJIH9y/w5Xv2c8apB9nynBIXnT3FE4cUbttef62PLJVIxEtt/UlhAuE6k2sWJBXbpVhx0TST4ZRJQjeYWPQmbKMN0dBBCPCeoyXOe+59PPf0RQwjzUyhfVXnwJeTTrT/XZdrtxuuoj1XDCeC2miqi660LlUipWQub1az2gPScZuS2Tk5tpGc4RWxDIdbB3lrjV0Sg0mL0jBOVM27KzR3B4IpHNkWaCSqIv19u6vet70rQSKldPF6tQfv/11K+WEpZdclUoQQZwgh7hJC7BRCPCWE+IC/fK0Q4g4hxF7//xp/uRBCfF4IsU8IsU0Icenyx/D+B3HnZb9MQICqOLiuSsWu+E2tes/2jAm/RpQvSFzXt312sc9Aa9l3VOG09TOcs2kvjqOzVOq/XekgCG7OVKJErs0EKfBDNQ7Wo2mDZLzMvXtbJ6cVTZuprMFQslCdvVUb+7RR6+cK9fH+7Qh6Sjx5pIymNodhB4JkKO0JO7VDHaK5gkmmZDPUJmLL219zBeDDiyWSiSJJNdnWNm07LpZT05YeP5whlZqti6YSAq44/wiFsuTNX36A1/7jXfzFLU8wkq7wvLOeJK2n2fzcWRJ6iWtvfRLb31+54rBYtOoGtU4E1ySsVQUEjZZ01UIIOG3cuz+TeoWEVm82WzdaJBkvcP7z7mPL2bB2yEYS46np9gmqk5myJ5TSbTdBU92O7XbDjezmQzXDgqhMXZWAoFSpH0Rzho1pS3S9fuBOJVbeu32qWrK/dvwgf6OxyneQ36I0+ki6yJlpRWDaCzeuquWReM+mqjg4Tud8qX5ZiWlrqxDiWl876QUb+Esp5QV4+SfvF0I8H/gIcKeU8lzgTv89wKuBc/2/dwNfXO4AgWkr7995RoNpy9NIFPKmgeP2XkLeO1YQn10rQeDZPpf/sXTNYTid5/RTt3Pp+Y9zyqg3453MdE7mk1JSsd1Vr9HlBSK4pBImRbN16GStA2H9gyIEbFyX5/BcipzRPMs9MO8tSyVr37WWeNb69wg0knCDsFYMpw1iMYdShWoNsDBrhsuoSoWxYc88UzNtNf9me/xKxulk++S0YX8W/sSR2vc8tFBE03KextPGNv1f/+0RXviJn/D5O3ez+2ie2bzJyNBik2/tnNMyvPFlT3LBc55g/8I8U9kSZ511D2eOneKfv+SKCyaZz8W59oe/JGdYoRyS7gRJolpev3n7IIdE9eubnTbuh7bqhabmYkPJCr//0u284ByNuBpnJO19ZsfR9tnuE0tlUvEKKa29L0dXHSp2+yGnYFgIvHtwPpTdnjcsFKXiCxLINkxS5tpUk07GLSw7zmKpu8RaqAmSRhOdF3Zb/+wU2hSLVRUXgVsnGLsheA7D9cgCZ3tVI1HcVU+AXknI0hnAxcB7hRAPAtuAbVLKb3fzYSnlNDDtv877ocMb8cxjL/M3+xpwN/BX/vJ/k94o9oAQYkwIcZq/n7YoMYui6Q22huU2m7ZclSX/purHtOUdyw0lOAa2z+VvhJiA179kJ5ZroSvjlAreeUy1cWwHXP+DHdz4i4PEBMS1GONpjW+950VsHGttw++VgmmhKQ7JuEUhM4xhGyS1+oS8TMlCCElCa37IN63PsW9yAz/euYs3bXlB3bqgH0YqkQfWAN7MSYk5dU7+MPO+RjIU7xwBFRMwNlRiMTfcMgx7zXCZN738YQSjQDjyrvk+2HXUG0hG00WgOasdIJ2scNr4AnfvGKJYqRBXVCYzBptO85pvaaqL65tSk7Ha9ds3VyBvGNxwxz4++1PPBzIytACMNB1DVwVXnFfhsuc+xVQ2z4aRRJ2GdPapGXYcnuemX8I3H/gJm9Z45jE9ngeaQ2ob6aSRLBUDM4wBpKt+El0rtoxMDJvSAkGy62hzMEDAxFIJXS909OVoqku57AXItApiyRkW8XgZw0wzX6zXSJRYBd2fS+QbOgQGyYi6Vib8+6b8XJLDSxmes/bMtucVplqyP9mcG9IYpR2YjXWteQKmqc0azHIEGknYJGZY9aYt1a/7VVjFLokryWx/k69NnAVcD+wDLu/loEKIs4EtwIPAKYFw8P9v8DfbCIQrAE7QhXNfVT17ZcVxcWUtcgGCgUMw49trlC60h47HUtyqM7XWcbG7fQohamGHfvz60TahtuANpt946BDjY/OcefouRkcPMrFk8t1tD/XxDVpT8OPck3GbihVvWdU1W7aIa3bLLP7Txr1aVj9+qrle1L7ZAgLJmobaVZpqU2xjC18omKgxt6XQamTcN2/FYkbLwU5X9KqmUqsI3SzA9szkSeoWa4Y619C5+Jx5TCvOP937ENNZA8eVpOIFf/9OS9t03rA4df1hXvHCh1i/9jDDQ/OsH+38kCuK4Iy1I9WyJAFCwKteeJArLn6AM07fSaYySSJeqlZEXo7ARxIENIRZ8jWSuBZU+TVZN7ZIIn142SCVuOagaxUOLbQ/D0+Q5DuGyy/X3CpvWNUM/vlCuMaZRSykkTSaLwONpDGkPCiTspKWu5OZMkpMMtwgD3XVpdJQQqdWj69F7TbdIr9CR3+1nXDIJFbTSLz3QZh7ZgBZ8+3oJYlijZTyMeCxXg4ohBgC/gP4oJQy1+GGbLWiaaQRQrwbz/TF6CmjrFEcjAoYlcBOWO8jAZjxy2B7sdy9t1RRQlE5QTVhT2VtLqfRiaTfYGgq214juemBw1RsyfPOeoQLThunaBh8++4z2b/QX6/sVnhF5SxSca+n93wxz4ahDXXbZMoWqto6oTOuOYyP5nj8kNc0KvwbPz1XYChlMByvf+o0tb1TdaFQIa5XiKutnd5h1o6UYZK6EvLtCB6wcovs811H86SS2br+GK04bTzHcCrPTQ+UuPxMb0DztIG0FyXYUBRSSknesBlbY7NpXLBpfIaKU0GLrVv2u7VDiUku2KhwwcYCUuYxbANdGe/6s6piV00kYQJBEpgvhYDXXrGPbuv/jabLzOaa7wEAy3GZyZmceXpngecVOE1iOmaTVgzepGdktEQGWArVScn5wTRam4CKQJAMJ+s1gFQiSEpciY/EIBmvlewP0FWHXIM2VU2UbDE/GU5VyJbUttpXI1LKqhZfV6TSd7ZrIR8JrG5Pkl78HV/p9WBCCA1PiNwkpfyuv3hGCHGav/40IEjTnMAzpwVsAqYa9yml/JKU8jIp5WWp0RS6amNaohpNFYvVZptBlE5Q9bPXplbV/SmyLlMeetNykiDp6eoAACAASURBVPHODYZM2+HfHzjIKWvnOHM84X/Gsw1PZQZfZiVn2MQUk7Tvk5ho4bvJlS1UxWzyQwScsS7PUn6YvfP1P9m+2QLxuNdYKUxca98hbq5gomnNDcJaEWS4N0aTtSLmR9Y0Zp+7rvQ0kuTSsscUAi46e57FfIqv/XI3AMMpf6KiNmskQXnzcNSOrug9h6E3n48gqSW7itgKiGsW+XKzEF/ytZRUaHwUQjRpRe0YTVcolFJ1+R0BR7MGrmTZoABNcdrmgbiupOi3/BW41ZB0qJUhaWyxHTCbN1FiLim9fggMyqSsRCOZypTR9ULTdWmlTVUFidp8vUdSJmUj3XVfl1LFwfF3Ew7ZD/y2mhaEIgfX4AQSJFLK1/ZyIL/8/FeAnX4IccCtwFv9128F/k9o+Vv86K0XAdnl/CPgzWAqtlLN72g2bcFcPshL6C9vw3NiBYIkmGms3BGuKi6qYrPQJtT2B09MM1+ocMqGHaR1b4Yc85On5vODzz3J+0XlUgnvO7XSlJZKFWKKUVcKO8zG9TlA8P1tu6vLHFdyYL5IKplrmnEFjX1aOfYXCiaKUmpbsDHMmG/aEkp3ph1VcZrKjB9ZKmFYLkOp7h7o525cRFMr/HRHlpiQjKWCfbtIGaNYqXcCe+tOnF40cd1uKnoIsFj0fGVxtbf4mtG0QcVKcGixufjkRJBDEu/cL15TvXa7QUXvMEGPDVWpoGk2OcN7FryZuoOmWNXZeJMgyRkkWmi5Cd2rH7djsnun9+RSCV1v9hsF7SLCQrBg2i0jCqGWi3M40z5kOkzYMV8MVVAwbQchJGrMFyTBNeiyEnUvdJtHcr4Q4q/8cNx/8F9fsMJjXQn8MfByIcRW/+81wKeAVwoh9gKv9N+Dl6uyH88X82Xgfd0cRPMryeZN78aLhcLsggs6XwhKyPcX/eRF5cRwZa1TXq+NshJ6hWyp+bNSSv71vgOMDZU5a0P9w5ROVMh0fg57ouCbBQKT23QLQZItVdDUStuZ9PhoEV2rcOfOWvjnkcUSliNJJ5v3p/vNvlr1P5kreKUsupm1xzWHy87fzanr9y+7LdAy+zwY5BLx7gSJqrj8yhleJFgqUaqaOALTWThiKLhP+okYHDQJzcFoUbgxU6qga1ZXArwVgcN9e4sQ4CCHJBVf3rQFrdvt1tpl28S1mjA0bRfblSiK1bbV7HyhgqY1FwGNCThv0zz7p9Psmlm+t47luMzmTZItvkegTYXv6YWCia61NgkHUYB7Z7vr6xIuZVQO9cXxuiPWzGOBJWY1uyQuK0iEEH8F3Izns3gIeNh//U0hxEc6fTaMlPI+KaWQUm6WUl7i//1ISrkgpbxaSnmu/3/R315KKd8vpXyulPJiKeUj3RxHVWxsR6uWY26lkSwEgqTHplbh/bmuiuVYtZIMy5vxW5KM2xSM5p/jgf2L7JjOsWHDU6xNrqlbl05YlMz4wOPD86aXlR04HltpJJmGDoSNxARsWp/l6aMJCqY3aAQRW4lEs19HV+2Wzb5cV7JYrKDr3X/Hi87OsXnjKV1t2yr7PAhD1rXuj3nBWXMI4aLp2WoUkqoGM8GwIAnyCFa39elKSOgOVosqxoulCqra3ny5HKO+INnZInLLi3SSjKY7P4O1ckKtG0SBF3If15xqBeBq9rhqV3+DxuoFgUbdakA//8w5JIIb7lx+yAlMdAm92UTXSpuazhroWrGleXAo5QuSue7KJYX9IuHoMMN26gRJrYDk8TVtvRN4oZTyU1LKr/t/n8KL2Hrnqp1ZjwTqZGAPFKJ2hQNBslj0VL+42p9dWol5jZEs1yJXtlBibs9mgKRuY1S0ppIS/3r/AZK6wxkbpptm5ENJC9NMkTUGlxEfmAVUxfIjemTVMRnguL7pYJlZ9Zkbsti2zg+3e0WiA0Eylm4eRIPfrTE6J2dYOG5zvP+gCEfehY8JEF/BRCOdsLj8gn2ccsqTdW0LoN42nW+TR3A8iete7kRj4calYgVFKfeskQynTECyZ7Z54uDlkFik9c4zL7Xabrd1OXbwrA4J3cG0VBzXqYugbFXKCIJeOq016uFUhY3rFrh7Z4XCMpFO1RySFia6VtrU0VwZTSu2NAlXG4TNdfc8B5MSIRzMUHRYO43keDvbXeD0FstP89edUGiqjeOoVY0kiKX2Xnunu1R0vaZWSm9NrWr7c3BdBcux/JIMTs/VhJNxG6uhX7RpO9y5c4Z1409z+sj6ps+kEhVcqTCRHVzBx8AsoKqWl6+iV1gs1j+EecNCsrxDe+O6LEI4/OBJr/DgvtkCSd2qa6wUoGte1YG8WT+YzVez2ldPkFgNCW9BBN5KTZ8XnJnlRc9ZW31ftU0b9U5g6N8/N0gSmo3jaGSNes1zsWiiae3Nl8uhxCTphMHEYrPQnFwqE493ziGBUMZ3S0FSE8rxUEn/2vKaaasxxDtT8mqItePCc+apWDr/dH9nrWQqG3RXbDZtNWpTUkqOZg0SutHymsY1b3I2udTdvR5ozgm9jBVKfDVtFxFq6Bfch4UW+VKDohtB8kHgTiHE7UKIL/l/P8bLQv/Aqp1Zj3gJgYK5gvdjaGqzICmUvUGw10E/QFFcT5C4lh8lYrV1Pi9HkFEbfpgnl8q4EobTuZZROOmE94Ae6KHFaTsCc0HQljWp201lUto1jmpEU11OWZNj6yGvGvDTc0WSiVxTxBbUHrqFhqJ1835Wu6auzmxKU2TVzxWQMywEsuc2zAG1PJXaA9yrkFpNqvW28g2CpGTV9ZvphdG0yUK+2f9yZKmEphWW790TmGVKrft6gBeoofvl8Mt2uU7AxPwKwuHIPMsJaoi1/26nrc0znCpw84NTuG77+XJQwXg01bxNoAkEdbAyJQvTlsQ7+IWGkgbz+e7ujVqFYwPHqfkXg6rntT5M7fOlBsWygkRK+WPgPLwkxP8EfgJch1fE8cerdmY9EqiTQeZqMCOBWjy1RKD00dSqtj8vUz7QSJTY8k2t2pHQg0SomlobVJKN662dvoEgObQwONNWITSbA0/Alcz6aKpMm34frTjrlBzFcppfHNjH3tk8iUSmpc29Wrix3ChI/MSxZSr/9oqq1vxcAbmy1TayZiVoLWbTtT4ZJ5AgCSoA52raoOW4FE2nf0EyZFIqD9WZXx1XMp01SCbKy2o7atU81N5HktAkcb99dd4oVa9xcP0VxanmlUG4l0777yYEPP+seeZzaW7fubvtdpOZMgndIqW3v6eDOlhH/Uracb29IBlJWeRLeseqyQG1mnhGnVnYtF1iwm4QJJKSuXpacFdPil+08YFVO4sBEpQoqc5klfC62s3UT1Or8P6kjFG2KuT9/ia9m7aaI6SO+ILEy0toLoMSCJLDPXR0a0e9DV8nFbdZzCf5v+2deZQkV3WnvxtLZu3Ve6vVUtMtJFpIwggQSMYChDAYMAfhM4ABj9EYsJgZL3iOfWzsOWPMzJixx4yx8YJHgwHZxwg4DAINNqsExhgkkISQuiUktehW79WtWnOPXN78EfEyo7KyqjIrI6uyO+93Tp+ujMyMfBUVGTfufff9foVKoZ5JNBwIS8DKNe6Ld8xx76PP4LbvPsFCAXbubL3Qq+5Jklt8wbA6WyOr6GytlXD1eYqgGtQnQBe6tGFu7HtpbTpTrCQyP5ckVm/r6WzjAmcXI3bScNCKydEC1ZrHY2dOc90zwmaRqYVQAaAdPbDUCvX9bL3lvtaQesllyRRDaRjbQem7VeLqO1ZwNPTSWf5e+tLd09z/+G7ef+fjfPORgCHfZdtYmv9wwzNJRXOhJ+cKDKUKLUt0zS6Jp6OF0KGXy1I5HAjnlY6dmWSmMMvOpkXAzSwUyzhiGE5VFmUkYftvIyOxuoCFcu9mIjr+pojI9YQT7QeMMV9NfkjdYZV1pyP9Kr/FHAnQlgHValjf9mypxHwxwHPLa64nD0df5nggOTqTx3VqTI60HudQuoxIjRMJLkq0veahOmkqLLmVN5MpZeqBZC4KJGlv9Yv72HDAxGiGbz46DHiRxtbSjpXlXBKnsyUEw9jq1hprwgp5xleft2uZvBo2G46LQi4Uy6QSmJ9LEnsRnso0JoztXbu/ysV2NSaiTqSDp57mumeE207U1XKzwMp/WL/prj6O9RxJ+9LIqjI5ForhPm350HNrxKcHZu3v5gYrfr7v1Xjupcc5eGQbXzxwKFTQrfiMjSzwzheHGnLHZ/N4qUxLqwG/KZuyGcnY0PIlprHhEjXj8uOnn141kGQi/6OUH5bYs6UCjIWlLXEqSEwcpNeBpJ323+/Ffv5l4C8J1eDe10n773phy1ezuUgmwG8cTJGGZEo7BlSrYV0Ss0FAplDpam2A1duKCzcenckzOlxYIr1gcSSU9LbrYpLA3uXZ4zOUKlMzLlOZxup2W68eTrdXnnnGzgzlSnhRHl1mkd9yUvJnswHpVKUteZS14LtLvRrmC2XcJDLWFlaxoV9392XVJLFzJGdj5lZWe6ud8uVKtBJvtGtIWk1QN9MwiFp6jmdKFVJeDd/16hntdLYxR2IXB3tNcv6dlGafs+9p3viyA9z0ku/z+pd8B98r8Zn7Q/8XYwwn5woMp/MtbyAbqtbh55yaLyIYxoeX/97U15K00QJspfLT/uK5mGZnWDuWZRylE6GdW4148e8W4JXGmPcDrwJ+oSej6gJ7AZzLV3GcWn11p8WqASexsjg+mZopVfC72Kdd/DcVm9k+OpMnlVrZ6W50OGAu111mFcde9KyEQ0PELhZICp3V+S/eETYDuE6VLaOtM7b6HMmS0la4GHGtaxlWw3rUlCqxrKFQTiZjrasLxwNJuO++CiR1g67GMbDyKKkuA8noUIDjVOut39BwRtw0snpGu5xBFNigXMEVty6C+HQuDCS+25jj8t0a5YrU5/ls2W4k1d4duud4DHlDjKVH2HvBHE+cGmY6l2GhEArEDi0z5+E3tS6fni8wnC4z7C9/U1RfS3Jm9UBiz1ObedlsvlQJ238X/Q5ujVIPfdvb+aY4IrJZRLYCYow5C2CMyRF6jPQVNpDM58PSU3MXlf1yd2Nq1byv+UJAsVxb4sPcCb4XmnDZL7Mxhqemcwylcyte0EaHyuSL6cS8Bprv5holt8VlD89tf83M9skcKb9EOj3PaKq1JHujDNC8ArmE6+WXdSnsllZrPeajDrxusRfBQmyiN8x2+iuQeK4h5QdMzTcu1rb8M7yKdP9qiMD4SIFTc419H58NJ6hH0+39Tf1I0buZbDEUF/Ucrx4Mw0AS6WxFx9j3alRqHlVjO8Ds79Z5w8Mlu2ap1Txuv++HsRJda3kJe07noknu0wslUqn8ilplY8MBYDg8vbofSugbVKp/V63dbqkS3kQvHkutrgvYC9q5EkwC9wP3AVtE5AKoq/j2z4xhhC1tBRXBdZeqaNrn2zGgWv2zIkOdSLurXQn55RhKBczl7aLJILTvHFpZA2V0KCAIhhNblFjPSFKLM5L43M18oRwaR7W5UE0ErrviKXbtun/Z7CrMSMwSY5+nsyV8r9h1drAc9Zbw2OrzzCqr9jvbf8P8DMKMxEkg20marRM5Ts422nQbd+3dd5dtGg2Yy6YJoqzvxFyBoXS+LU95WN5uN1MK78hdx21kVdli5H7aKB96bpVatdGZN1cIIi+dzn+XnZszpPwSdz50PGZo1fo76joGR6r1QHJqroDn5Vb83riOYThd4tTc6uffgjXv8m1DQnh8i03OsGB1AZearCVFO+2/e40xlxhj9kX/n46eqgE/15NRdUF87sN1KkvWX9TNXhLISGz6+HTW1ly7u/jEZVJs6+/wKqJ2o9GixGNzySxKtO6INtuoB5KYp3coId/ZXfUlu+Z5ybM2LduMYDtLsk0tira01SvqnVVRAbkaKcomcX6E+1/skrdQTC5IJcn2yQLZ3Dgn5kPNsNlcgOdWGUp13xSwc3OWQmmM37nj+9RqhmMzeXx/oe0bkeXsdu0duSsuvh/eiMwVgkUBBuw8WMNqdjYfeumk1lAudRzYu3OOQ6eG69IvzYZWcTyvWs+mTi+EHV6rNeSMDZeYycqqTqgLdrLdrleJlbZaZSTLqSgnwZpvi4wxeWPM4SQHkwThhHpD+bf5zs+vl7YSzEhsIOlyn8PpMsWST6VWqQeSofTKvgijkX/C4YR8Saw7oi0Jpv0KQo2zmcbcxXyhjNtFq/NyNJcwiuUquaBGussW1JWwGWouCiTZuk5TMp/pu4svgguFSmJBKkm2TeYwOHz3cGhGNpMPSPmVNcujxHn2M6a4ZPcR7rh/jnf9/b9EE9SrX1At/jJ2u7aEJSI4Euq1LRSqLBQaAQbCyfb4RXQ+Wmi51nm3fVF56x/ufQrXqTExvPzv4XtVCmVDrlQhU6ySTq++an1iJCBfHF6ifdZMJvIEsjfP1iUxqNRwpDkjaW2ylhT9lV8nhK1NirN0pbmdAEtC66ih3RVdfLoU4rOOhLkgV19Dsml05YvO6HC0KHGmdU316HSeG/7kGzx5tr1AYycwbZAQCbWYbBcchPISrlvqyPOiHVIx4T1oLEbslc4WxEpb0SK2hYRl3uMdQ7WaIVeq9pWEvGXrZJhx3nskLDjM5gJ8rz0PmNUQgZdcdZYr9h3i7kczBFXD0FD7Lespr0a54i5ZHZ8plhcF5ZRfIVcyLBSDeoCBhlOlnUecjc7ftd4I7dwSlrdOz1cZGSoxtMKcR8qrUgqkrcWIlvGRgFIwzFR2eRXgeObc6A4LqNYM5apZJFYLS4Np0nQcSETklb0YSJLYDiCJre602AtHtza78X3NZq2RTHf1x+FIPG+umOHoTJ7hdJmxoZVNhOoe08sEkm88doYj03m+cPDetsaQLVYWlQUgzJTiMilzhaDrFc+tSHtViuV4IInmntYjkATR3WohmezSYjuGIOzeCjXK+i8jGUmXSadKPHwiPI9m8+Vl1XHXggi8aP8sL9j/GCJVRkfaL8UuZ7ebbQrKab9CPpD6HEn9/XVfmPD94Y3Q8l46q+EI7N0Zjt/3Myt7zrs1gopTd2VN+asH0LAFWHj8zPK+JHXlY7dcL21limWCyGZ3SWnLSton1JTTzFoykj9OfBQJU5dGaOqlhkYpYy0GVM3YVuK5yF1urV4klnA+Qjg5P8/RmTxD6ZVPUvsekVp94q+Z+5+ajcbY3sU4U6rgNHUVDacr5EuNO8L5fAXfT/6uOuVXKVe8+oTgtBVs9NozqVoLDfe4MHDYjCSxQGI7hmrVulprEmXVpBGBbRM5TsyEf+eZXAnfKyXeFPCcfQu8+cZ7uXxX+5lOXRk65utRrtaWdEoOpaqUAo9slFVb6uZWUflyJh90JUYJsG9XmOGnUrkVM/OUX6NcdTkRGQcNt1HaaqcFeKGudxeqjgs1sqVK3WZ3SUbi1jA4i5pKkuS8LG3ZLoa4za7F3oEmIZpXn6jNhydkt8HJSlWcnM9ydDpPKpVZtUYtAsPpEmeXWZT4wNHwZGzX1Ma6I8YvICPpMkF5iHw5T7FcpVSpdbVmZjlSXo1KpeFJYtsrR1dYCdwtXl0ZNQokkaiiXeCWxP5rUUmhbsfch6UtgO2bCuTy4zw1e5rZfNC1PMpyDPt+23a90NpuN1e/I2/8ndJ+laA8RFA1izKSZhn1cI6ku7/Bzi0ZNk/MMDx6rK2xW/WJiRbijs005OSXL0fHpYxEGpP6tkOwOSOxFsLH5tr3ou+EtvJWEfk4YAjbffeIyMfsc8aYd/RkZF2Qiom1NVMPJAm0NXpOuI9cMbwj6TY41Rf/zWY5NV9k70WtV8w2MzpUZqHFosQzC8W621+2TeVP647YPK5SMMK/+et7uXLXViC5yeg4Kb9CtTpGqVpilFEePDbHcKrC5tHe3e802n8XZyRJZKywuGMoE1nBhmXV4UT2nyRbJ3KA8C+HjpIpVtneg6xzLbQyiGrl65LyK5SC8Lg2l7bC95QoVUKpkG5Ls47A63/yEOXayuWx0LHV5+RcnrRfaSnu2MxIuowjVZ6aWb5jM7Moc/ZIeRXygalnJM3tv5Nj4bF75OQ0r3zWqkPomHYLoJ+I/Xw9cFvyQ0mOeGmrmQu2ZDg+U2TI636i2IkWnNWMk4harF3dfvBEDoO76hoSy9hQmVOzaYqV4qJSmM1GoLWEdFCpkQ8qbBppLAzLFCuMTiw+bpfvOUO2lGcqM8GTD2UAn6GhDElfDFNRCaNQLsAw/ODoLGOjZ5kYGk/0c+LUjY+i42NLBsNdlinr+49Nci4U4o0efRhIogn3bz4+BXiRqOHGY7/P84UibAq3ZRapVIffu3AtSXjjFW/Fr2edpXJ9MWISc3wisupC2bAs53FqoUA6VWwrExOB0eESUwvLz7naMqmtDPhejWIQtv6G+6gAjWucdat85HR7Nr6d0q767z/bn0UkE3/cj6wUSC7aPs+urVUcaa2+2SmeW6VccfDd7tVird7WE6fDkyCUj1+q+tvM6HBAaWoTc8V5LhiLB5I5XMdQM2aRH4Pl1m89yce/82O++96Xk/JSoTtiqcpkU0YyOlTmZc+ZBWYpVZ5gOltkYjh50UHfq2KMw1yhwKgXcPjpPJfsme7pKnB7kckH1oSqO8vkZvxYx1CmmEwJtFeMpCsMp4v88GgN8LoWbEwKv8nXA+K+OeEdOVCXSQE7D5WKfo4yklJQFxwNg2TvhTP9yKbg5FwJ38+2rdAwPhIwnwvnq1rNU2WaMueUF7okFqPvedj+2/j90n6VdKrE4bO9mW9cy1nSfzOFTdjSVvOEk8V13K4m2hbvK1qXkpBarONUOT4d7sdOuq3G6FCAMS7HZhdPzj3w1CyTY/N4bqXlyuATcwWmsxUeOPEksNgdcTnSXooLN00wlh5t99dqm7reVr7Ag8fC+vDEaG/uoCyuYwBDoWxVZpPxIrF4sY6huhdJQtlOL9g2mWd6IZSx6ZuMxI1lJBGt5pvSsXmteMnLBqJsMahriPWiNNsKe1N7bLpIKlVou3lhYqREoTjKfKF1N2Zdyigq0fteOKlfiHTdpMX88KbRImcWnFUXOq6FjgOJMea6xEeRMI21Ir23M7UKwM2dTmtBJFTbLVddXKfGppH2gt2IdUqMLUoMKjUeOj7H6OiZMO0tLz157Cryg6eejh4vdkdcb6wC8Ey+wA+OziEYtk70ZnLQUvdqiBZCLhQq+F04XTYT7xhaSDjb6QXbJxvtqb1ypeyUemkrpodWl/KJZXfxBgn7Hmj8DRaKpXpG0ov29VbYm6OgyrLijq3YNpmjUk1xz5HWk/l1m93opiRljb2CMNiKLL32bRorkc2PslBaXcerUzY+b+0BK5W2ksamzUnpJ9l5kpXk45upG1zF1pIcPDlPUDVMjk/ju9WWEhN2Ed4jp8K7/sV15/WnvkI3X+TBY3NMjOXZMpp85tOM61YpVcIL0kLUbJBUOc2PdQwtFMNWzXbFLjcCO08CMNKlYGNS1Bfcxex260E5FkisHD5A2muMPe4LM2ctENpU/u2WeEDrJJBcuDX8Lv/jgdbiIZlSBc+pkYrmeu2kfjYKtp679MZx01iBSjXF42dPL3muW9btjBaRj4nIGRE5ENv2ByJyQkQejP69Nvbc74rIIRF5TER+ppPP8lcpbSWJNbfyvbWbWsUZTkeTaP7K8vFx6pa7sUDywNEwO5kcn8Fv8mOw2Ls6K/Gd3eB1DjYjmc0H/ODYLCMjUy393ZMmlNgOf17o0umy1b4h7Biy/hH9pPzbTNi5FZKEYGMStMxIbGknFjDipa14ptKYbK/UvUjWLZDEqiJ+qv3V/CNDZSbHMnzvcOuM3Jpa2XMpFU3q5wLrDLv0b2cn3B8+ebbtcbRLu+2/lwM3AbsJ24BPAncaYx7t4LM+QWiK9XdN2z9kjPlg0+ddAbwFuBK4EPi6iDzLGNNWZGjMkTS6OHpFQwQymbt4G0iGh1aWj48zlKrgSJUnTjfG8MBTs4wNl9gxnubHbo1cENZG48HOZiCn5uxkZPh+J3JHXG/s3+2x0wUWCg4X7ppNbC5rJfyYg55VVE1qId6i0lbBr/tn9CtDqSojQwWKgZ+IYGMStJpsz0Q2s6lYdhefbI+XD+06knxQDVfsi2HIX597aD8e6FIFVnOEjHPx9gwHj1zA8bmnuWjTtkXPLRQWG6T5XuirM1+wGcnS/U2OhRnRwZPLr5hfK+04JP4O8CnCK/L3gO9HP9/eiUOiMeZbwMyqLwy5CfiUMaYUCUMeIrT3bQt/USDpLfZE6caLJI4tbbXb+gthnf+yi0/zo+MT/NU3HwLg/qMzjI6cYSw1FkpM1LxFdrIQGnIBzOfSBNVgiTviemMDycFj4TEdH+vtRLvFc2uUq2HAWiiU8buwTG4mPtGbKVb6zoukFTs25fC8bCKCjUlgz4u43W62FGpMxS2LU9F56zoVUrHtdV+YcpX5QkDKLyfWTLEa8dJWO4sR4+zetoAxDnc+/KMlzy1EdgT1QOJaY68w2LYqbY2ky7huhUNnkp93bOdovhO40hiz6CokIn8KHAT+qMsx/KqIvJ3Q7+Q3jTGzhJnPPbHXHI+2tcWW8TwX7jjKpolp4IIuh7cy9a6thMpBdlFiKB/f/hf52mefZCbj88GvGMaHhjg9X+KyvdO4jovnValWhwmqwaL2Q1vaKpZGOblwlkwxPPmsO+J6Y0tbx6ZdUl6NHZO9L01CmJHYjG2hWGZyU3JzRI2J3iDyIkleNTlprn32MY7OTjPs9279TifES1OWbAvLYseJ1lU45Rb2EWFDxVyXyr+d0pivrTCa6iwL2rE5i+tW+NqPTvAfX7L4ubiEPjS+Ow1vpKXfYRGYHC1wci75sl47v1mNsLzUzK7ouW74CPBM4GrgFPC/ou2tbgdbXt1E5BYRuU9E7svPhzVI36vxqudPcem23gYRSNZxEWwds8bIcGey8I7Aq15wjNHhBX7/86Gn9ER0YLeb2gAAGL9JREFUR++7NapVd4nyZ65UJZ3KA8KBU1NLTK3WG9epIVLDGGF8bIbJoWTW+qyGF2VsQaVMtpisOm98DcN8IZzIX49yXTcMpyvsv2Cyb8y3bEaRj9ntLsTcEeOk/PAC27zdc8POxdl8gOuV1i3bsoEklSow5LcvCwPh733Blnl+dNyhUl18fZkvBIsyZ/s5M3mrXt16n5vGSizkVpeo75R2zpTfAO4SkS+JyK3Rvy8DdwHv6ebDjTFTxpiqMaYG/B8a5avjwMWxl15EOC/Tah+3GmOuMcZcMzLZ+4nZZuqBJKF2wl1bF3jd9d9h77bO7wZ9r8bPXHM4dBR0qmyftPXSpV4E5WqNoGqYGAvXnjxyarplS+V6ItIoq42NnO2ZvW4znlujVnOZLRQidd7kAon9gmdLQdgR1oemVv2OSFi6yZUa963ZUljaaZ5vSvtVxFmqWuy5VUqVhvLvegVJW3LyvCxpt7NAAuE8SaE0wnefenLRduvFUv8ca1VtLS2WCySjRUrBCEdnz3Q8lpVoxyHxy8CzgPcDXwG+CvwBsD96bs2IyK7Yw58DbEfXncBbRCQtIvuAywjnZ/qOuiy9k8wFQgS2jaXb7thqZnykzGuufYxnX/ptto6EehJ2dW0uaNyFWMmU8dEw83lsamaJO+JGYOvhk+PJOD62g+eGMiYzked1khd7e37kShWyxUpfuiOeC3jeUqdJ11naFLF/z1k2b3l0qQ+RWyMoS2jYlVCHZTs4TrgMwfOza/Lv2b0t7MT8fw81B5LFmbOVkp/NV3DE4Dmtfz874f7DE8m2ALcrkVJj8ZxFx4jI7cANwDYROQ68D7hBRK4mLFsdAd4dfd5BEfkM8AhQAX6l3Y6t9cYuSHTdEtD5HUcv2DIesGW8kZ3Zu6JMcanoXSpVYChd5KnpIhcML3ZH3AjsndWm8Vlgx7p8pueGpa2ZaKIyLruRxL4h/OIXyslZ+A4avlelGMQ7DsuLzKss+y9+mv0XL83mfa9GqSoU8hV2jq5ve/uz9pwgcJ4Etnb83vGREqPDOb7zZOO8CSo1SpXaohue+ur/vMF1WsuqQKMF+ODJp3nT1R0PZ1nWrf3XGPPWFpv/doXX/yHwh+3uf6Ow60hSfSx7YdsfbWsghCZLAJ5TYXKkxNkFp+7jsJGTwWm/ip9aYNv42jKytRBKvbvM5cPjExcC7BbXMThSYz6fbJv4oLF1Is/RqU1kigXGh4ZDcdHx9o+l59bIFFOhBUIPrZtbce3lU6wliFgu3p7h8ePbmM4tsHV0oi4Ps0jhOFpDkytB2l8+kEyMlBCp8dhUsp1b69b+e75iO0r6WT/Jj61lsNhWX8cts2msRC4/xmyhuMQdcb153mUneeYz7mUstbpYZVJY05+z2fBuzU94QabrVlkohF81nSNZG/sumKVSTfG5Hz4MEFkWt5/d+V6NUmA1xM6tv8HubQvUah5fPBDet9cVKLylpS1jBEeqywYSxzGMDRc5NpvsOd4P7b/nNHt3zTBXmmHLWP+2dDY8nZdqFTlOwMRokUo1xVPT2UQ0w7ph5+YsOzdvWtfPtOWnqbqvdrI3Bb5bJVsIu4Qcp8RGLPY819m1dQHXLXPHg0d4ywteQLm6srhoM54bSoiA1RDrj8WW7bBrawbHqfKlg0e5+dpr6545cYVj65JocHCc5QMJwKaxItOZFNVaNbGbxo1u/z3nGUlXePH+yrq1qq6FhnlT44uXiwQb056p102PTgdL3BEHAZuxnVkI79KScM+M43k18qXwItav7oj9jucaLt4+x8FjHmcy4WLdTsRF7XcgfF+yra+9xnNr7Nw8z8PHDDVTa2nqZV0SgbYCSaE4xplscivc27n1tO2/TwBWinIPcCnwa4mNROkZfpPVKDSCSsqv1QOJYTBr+PYiczYTKaomnDB4bo2gHO40KQvfQWTfrjmOnN7Op+9/BOjsXPVjgeRc/Bvs2ZHh3ke38N3Dh8gUw2aC+Kp5+7hc8ZEVSlsQTrgb4/DwydPsmtiZyPi6bf/9UiKjUHqKncdZLMMdLZTyDKPDpcgIJ7mFlecSNpA8nQ271uLyGkkQv4jFRQaVzti9bR7XqfC5B8LWVbeDuSwvdtEdTvVlA+iKXLQ9bNO/44eHYsrHi88l2zovTmXVjATg4VPJiTe2W8N4FjAKfMUY81ljzD3GmKqIvDqxkSg9w965ZGJaRXYdyZAfroofG7EaPYMbSGZytZ6o8y4S7utTd8RzAc817N4+x8kZO9/UWdeWZfgcnKIaHwkYH8nyr0/MNbxImhQo6oFklYxkYrRAOlXg9EK70oer007X1q8DXyAsYx0QkZtiT38gsZEoPaPVHEm2VMF1avjR4sNNo9Eq+HOsoyUJbMY2m63hJuhF0rx/6G9Tq3OBS3Y1pIM6ERe182COVEl7/S1Rsxx7dmQ4PTvOUzPzQHgTGKdu6LeKfUbKq3Hji+7i2XuSawFuJyP5ZeAFxpg3EC4o/C8iYqVRzs2/yIBhv0RxrSKrnmoXH06O2jUUA5iRRF/AoBouLO1VRuL1oGw2aOzeNl9X9U530HJvb6Z8v0zK6w9V4065aPs8xjh8+cDpUPm4qeOqYZ+x/uXTdgKJa4zJAhhjjhAGk9dE7b8aSM4BHCfs5MiXGoEkV6rguY0yzsRoJA+yQaZWG0m87OG4pcS71mxG4rn9LyHf7/hejd3bwqykk+46W971vaBv5PE7ZefmLJ5b5mymdQnW99fP0K+Zdr4xpyMZEwCioPI6YBvwnF4NTEkWz61SiGkVZYsVnJjc9pbxMJD4/rnVGpkE8dJTUk6Xcfy6sGfyZbNB5Dn7zrB1y5OMptv/OzVUuvtfxn85HMdw4bawrNXK1yZVl6zvz4zk7cAihS9jTMUY83bgpT0ZlZI4fiSjbcmWKouMcbZO5rnxmvvYt2PwMpJ4V1Uvmg3qwp7uUp8MpXN2bM7xuhdOs2Vkc9vvaah0l87pv8GeHaGIYytfm/W0GG9m1dBsjDm+wnP/muxwlF7heVWC2DUyUyrjOAESq07u2WaAyfUf3AbjxgKJ7yffbFA3N2ohe66sjU6zRpt1ul5plVf2N7u3zQMGx1lagrVzof2akSjnASm3RlBu/LmzxXCOpN9NltYDRxp3cb3MSPR4bxyNhodzO5AMpys844IpUiNPLTmX6hmJ9OccSR0RuTH+v3Lu4Hk1ylWHmmn4Y8TnBgad+oR4QgZlrfatXiQbR7391y1s8Ei65+VXH+Onr1q6PdXnk+1xPtj0v3KO4HuheVO5Gl7MsqVkLWXPdRpZQ/KBpHE3rMd7o0inqrzwikfYuytZQ6eNopXnfF/PkSyD5ufnGL5bpVpLEVQDXPEpVWoDuWZkORpOlwEw3JN9ex0soFOS58o9OdbLLG0jsFLy0u+lLeXcxfeqVKuhb3suGFxdreWoB5IelrYcZ/Baq5X1YygVZbxuft0/+9xsqFY6xvqSB9WAYtXKUGupxWJbgHthUDacLgMG388CI6u9XFHWxNhwwI0veICR0QKwfg6joIFkYPDdKjXjkg9KVCs2kFTQpDTEzmM0C+ElwehQmdf+5H2kUhq4ld6yZ3sVaH99TVJ0Gkisylcm6YEovaXu214sgM1InDKQ3sBR9Q9ePSPpjTrvjkkYxDU6ymDQUSAxxrw0/r9y7uDHPEncqvVrD9BAEuK5VUQqpDxdMKgonaKlrQHBZiSZYgm/FgYSX02W6mzflGMqkz1nBf0UZSPRQDIg2IwkUyzjGyvDrSZLlv0Xn2XfhQG+o5PhitIpbc+0isjXReS5a/0gEfmYiJwRkQOxbVtE5Gsi8kT0/+Zou4jIh0XkkIg8JCLPX+vnKiF2DiBTLNXdEdX2dTEpN6USJoqyBjpp2flt4EMi8nER2bWGz/oE0GzN+17gLmPMZcBd0WOA1wCXRf9uAT6yhs9TYthVrwvFoB5IUlrFURQlAdoOJMaYB4wxNwJfBL4sIu8TkbaXABtjvgU0mwTfBNwW/Xwb8IbY9r8zIfcAm9YYvJQIu05ivlgiU6rgODXSnrb+KorSPZ2KNgrwGGGG8GvAEyLyi118/k5jzCmA6H+rX7AbOBZ73fFoW6sx3SIi94nIffn59V/Rea7gRRlJtlQmV6rgu1WVNFcUJRE6mSP5NnAC+BDhRf3fEdruvkhEbk14XK0K1S1nho0xtxpjrjHGXDMyqROly+EvCiRVPK9yThv8KIrSP3TStfXvgYPGmOYL+q+JyKNr/PwpEdlljDkVla7ORNuPAxfHXncRcHKNn6HQmGzPlSqIVHCdpZ7PiqIoa6GTOZIDLYKI5WfX+Pl3AjdHP98MfCG2/e1R99Z1wLwtgSlrwxFwnSr5oEauVMFx1K1PUZRkSOSW1Bjz49VeIyK3E5bCtonIceB9wB8BnxGRdwJHgTdFL/8n4LXAISAP/FIS4xx0PLdKsVzD1EK/9marTkVRlLWwbrUNY8xbl3nqFS1ea4Bf6e2IBg/Pq1IqQ1Au4zlq+6ooSjJokXyA8N0apTJUS2W8EfUiURQlGbS2MUD4Xo2g4kQ2uxpIFEVJBg0kA4Tv1ihXXArlmgYSRVESQwPJAOF7VYJy6Jym7oiKoiSFBpIBwnNrsUCiGYmiKMmggWSA8L0qxoR/cs1IFEVJCg0kA4Rd3Q7WZldRFKV7NJAMEFZvC8Bxgg0ciaIo5xMaSAYIP5aRpHw1tVIUJRk0kAwQXiwjSak7oqIoCaGBZICwvu0AadU0UBQlITSQDBB+LAtJp5YTclYURekMDSQDhBdlJCI1fEcFGxVFSQYNJAOEnWz33Ap/8bMf5o4P3FF/rlat8Sdv+BM++bufBOCxf32Mb3/y223v+xO/8QkOfe/Qom33fPYe/vFD/7ji+z7wmg+0/RmKovQnGkgGCNv+67pl/CGfM4fPUC6F60mevO9JxreN11+7/6f2c/3brm9731fdeBUHv3Fw0bYDdx/gqldclcDIFUXpZ3TKdYCwCxKdaDHipS+6lCfueYIrXnYFB+4KL/pHHzoKwINffpCTj53kte95LZ//o8+THklz8vGTZGeyvPLdr+SKl12xaN9XvOwKvvGxb1AJKngpj7nTc2SmM+x5zh6CQsCn/vOnKGQL1Co1Xv6Ol3P59Zcvev+RB4/wnU9/h7f9j7cB8E9//k9cuP9Crn711Zx87CRf/euvEhQCRiZHuOm9NzG+dRxFUfoDzUgGCJuR2MWIV914FQfuPkAlqDD14ykuevZFy743O5PlHR9+B2/7wNv4+q1fX/L8yOQIuy/fXS9vHbj7AFe+/EpEBC/l8fP/7ed5963v5uYP3cxXP/JVlndtXky1UuVLf/El3vT+N3HLrbdw9Wuu5u6P3t3pr64oSg/RjGSAsBmJOCUAdj5zJ3On53j4roe57NrLVnzv/p/ajzjC9r3byc3mWr7mqleE5a3Lr7+cA3cf4KbfvgkAYwx3ffQunnroKUSEzNMZcrM5xraMrTrm6WPTnDl8hr//rb8P91UzjG1d/X2KoqwfGkgGCBFwncoieZT9L97P1/7ma9z8oZspLBSWfa+Xapwqy2UTl19/OV/5669w6vFTVIIKu561C4CHv/4w+bk8t/zvW3A9lz97y59RCRarDzuus2i/9nljDDv27uCdf/XOzn9hRVHWBS1tDRhpv4LjNgLG8177PF76iy9l5yU7u953ajjF3ufu5Qv/8wtcdWNjkr2YLTKyeQTXczn8g8PMT80vee/kzknOHjlLJahQzBY5/MBhALZdvI3cXI5jB48BYanrzOEzXY9VUZTk0IxkwLjheY+zUD6O7a+a2D7BdW+8LrH9X/WKq/jM73+GN/7+G+vbfuKVP8Htv3c7t777Vi649AK27dm25H2TOya58oYr+Zt3/Q1bdm/hgssuAMD1Xd78/jfzpb/4EqVsiVq1xrVvvJYd+3YkNmZFUbpD2p30PBe4cP+F5q0ffivjae3oURRFWY6p7BQv3P1C3vG8dwAgIvcbY65Z6/76IiMRkSNABqgCFWPMNSKyBfg0sBc4ArzZGDO7UWNUFEVRWtNPcyQvN8ZcHYuK7wXuMsZcBtwVPVYURVH6jH4KJM3cBNwW/Xwb8IYNHIuiKIqyDP0SSAzwVRG5X0RuibbtNMacAoj+bzm7KiK3iMh9InJffj6/TsNVFEVRLH0xRwL8lDHmpIjsAL4mIj9q943GmFuBWyGcbO/VABVFUZTW9EVGYow5Gf1/BrgDeBEwJSK7AKL/dfGAoihKH7LhgURERkVk3P4MvAo4ANwJ3By97GbgCxszQkVRFGUl+qG0tRO4Q0QgHM8njTFfFpHvA58RkXcCR4E3beAYFUVRlGXY8EBijPkx8NwW26eBV6z/iBRFUZRO2PDSlqIoinJuo4FEURRF6QoNJIqiKEpXaCBRFEVRukIDiaIoitIVGkgURVGUrtBAoiiKonSFBhJFURSlKzSQKIqiKF2hgURRFEXpCg0kiqIoSldoIFEURVG6QgOJoiiK0hUaSBRFUZSu0ECiKIqidIUGEkVRFKUrNJAoiqIoXaGBRFEURekKDSSKoihKV2ggURRFUbpCA4miKIrSFRpIFEVRlK7o+0AiIq8WkcdE5JCIvHejx6MoiqIspq8DiYi4wF8BrwGuAN4qIlds7KgURVGUON5GD2AVXgQcMsb8GEBEPgXcBDyy3Bvy5fw6DU1RFOXcpFgpJro/McYkusMkEZE3Aq82xrwrevyLwLXGmF+NveYW4JbwAT/BOGc3Yqx9R8AIKTSqgh6LOHosGgz6sSiRoUQ2erTfGDO+1l31e0YiLbYtinzGmFuBWwFE5D4zb65Zj4H1OyJynynosQA9FnH0WDTQY9FARO7r5v19PUcCHAcujj2+CDi5QWNRFEVRWtDvgeT7wGUisk9EUsBbgDs3eEyKoihKjL4ubRljKiLyq8BXABf4mDHm4ApvuXV9RnZOoMeigR6LBnosGuixaNDVsejryXZFURSl/+n30paiKIrS52ggURRFUbrivAkkgyylIiIXi8g3RORRETkoIu+Jtm8Rka+JyBPR/5s3eqzrgYi4IvIDEfli9HifiNwbHYdPR40bA4GIbBKRz4rIj6Lz4ycH8bwQkf8UfTcOiMjtIjI0SOeFiHxMRM6IyIHYtpbngYR8OLqWPiQiz19t/+dFIFEpFSrAbxpjng1cB/xK9Pu/F7jLGHMZcFf0eBB4D/Bo7PEfAx+KjsMs8M4NGdXG8OfAl40xlwPPJTwuA3VeiMhu4NeBa4wxVxE27ryFwTovPgG8umnbcufBa4DLon+3AB9ZbefnRSAhJqVijAkAK6UyEBhjThljHoh+zhBeLHYTHoPbopfdBrxhY0a4fojIRcDPAh+NHgtwI/DZ6CUDcRwARGQCeCnwtwDGmMAYM8cAnheEHarDIuIBI8ApBui8MMZ8C5hp2rzceXAT8Hcm5B5gk4jsWmn/50sg2Q0ciz0+Hm0bOERkL/A84F5gpzHmFITBBtixcSNbN/4M+G2gFj3eCswZYyrR40E6Ny4BzgIfj0p9HxWRUQbsvDDGnAA+CBwlDCDzwP0M7nlhWe486Ph6er4EklWlVAYBERkD/i/wG8aYhY0ez3ojIq8Dzhhj7o9vbvHSQTk3POD5wEeMMc8DcpznZaxWRLX/m4B9wIXAKGH5pplBOS9Wo+PvzPkSSAZeSkVEfMIg8g/GmM9Fm6dsShr9f2ajxrdO/BTwehE5QljevJEwQ9kUlTRgsM6N48BxY8y90ePPEgaWQTsvfho4bIw5a4wpA58DXszgnheW5c6Djq+n50sgGWgplWge4G+BR40xfxp76k7g5ujnm4EvrPfY1hNjzO8aYy4yxuwlPAfuNsb8AvAN4I3Ry87742AxxpwGjonI/mjTKwgtGAbqvCAsaV0nIiPRd8Ueh4E8L2Isdx7cCbw96t66Dpi3JbDlOG9WtovIawnvPq2Uyh9u8JDWDRG5HvgX4GEacwO/RzhP8hlgD+GX6U3GmOYJt/MSEbkB+C1jzOtE5BLCDGUL8APg3xpjShs5vvVCRK4mbDxIAT8GfonwBnKgzgsReT/w84Qdjj8A3kVY9x+I80JEbgduALYBU8D7gM/T4jyIgu1fEnZ55YFfMsasqA583gQSRVEUZWM4X0pbiqIoygahgURRFEXpCg0kiqIoSldoIFEURVG6QgOJoiiK0hUaSBRFUZSu0ECiKIqidIUGEkXpIZFPzCujn/+7iHx4o8ekKEnjrf4SRVG64H3AfxWRHYSqzK/f4PEoSuLoynZF6TEi8s/AGHBD5BejKOcVWtpSlB4iIs8BdgElDSLK+YoGEkXpEZE09z8QemHkRORnNnhIitITNJAoSg8QkRFC34vfNMY8Cvw34A82dFCK0iN0jkRRFEXpCs1IFEVRlK7QQKIoiqJ0hQYSRVEUpSs0kCiKoihdoYFEURRF6QoNJIqiKEpXaCBRFEVRuuL/A/VSoJ+0ICRoAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "y_rand = 200 + 50*np.random.randn(100)\n", "\n", "x = np.arange(y.size)\n", "\n", "#Calculate minimum coordinates\n", "ymin = np.min(y_rand)\n", "xmin=x[np.where(y_rand==ymin)]\n", "\n", "# Calculate maximum coordinates\n", "ymax = np.max(y_rand)\n", "xmax = x[np.where(y_rand == ymax)]\n", "plt.plot(x,y_rand,label='random data')\n", "\n", "#Annotate minimum\n", "plt.annotate('Min Value',(xmin[0],ymin))\n", "\n", "#Annotate maximum\n", "plt.annotate('Max value', (xmax[0], ymax))\n", "\n", "#Add legend\n", "plt.legend()\n", "plt.title('Random data')\n", "\n", "# sets limits\n", "plt.xlim((0,100))\n", "plt.xlabel(r'$x$')\n", "\n", "plt.ylim((0,350))\n", "plt.ylabel(r'$y=200 + 50·rand()$')\n", "\n", "plt.fill_between(x, y_rand, 0, color='green', alpha=0.5)\n", "# since y2 is a constant, the line above is equivalent to\n", "#plt.fill_between(x, y_rand, 50, where=x<60, color='green', alpha=0.5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" }, "pycharm": { "stem_cell": { "cell_type": "raw", "source": [], "metadata": { "collapsed": false } } } }, "nbformat": 4, "nbformat_minor": 2 }