W1_Intro_to_Python/1_Python.ipynb

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    "EE 502 P: Analytical Methods for Electrical Engineering\n",
    "# 1: Python for Analysis\n",
    "## Prof. Eric Klavins, Electrical and Computer Engineering\n",
    "### 25 September, 2019\n",
    "Copyright &copy; 2019, University of Washington\n",
    "\n",
    "<hr>"
   ]
  },
  {
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   },
   "source": [
    "# Course Structure"
   ]
  },
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   "source": [
    "**Instructor**: Prof. Eric Klavins\n",
    "**TA**: Victor Cannestro\n",
    "\n",
    "**Goals**: To make mathematics fun. To flex your brain muscles. To remind you of things you might have forgotten, but will need for the rest of the PMP program. To point you toward where you can learn more. \n",
    "\n",
    "The [Canvas page](https://canvas.uw.edu/courses/1319727) will have\n",
    "- The schedule\n",
    "- The homework assignments\n",
    "- Your grades\n",
    "- A discussion thread for each topic.\n",
    "\n",
    "**Schedule (Tentative)**:\n",
    "- 9/25: Python for Analysis\n",
    "- 10/2: Sets, functions, relations, and reasoning\n",
    "- 10/9: Calculus Review\n",
    "- 10/16: Differential Equations\n",
    "- 10/23: Transforms\n",
    "- 10/30: Linear Algebra\n",
    "- 11/6: Linear Differential Equations\n",
    "- 11/13: Probability\n",
    "- 11/20: Machine Learning\n",
    "- 11/27: Topic TBA\n",
    "- 12/4: Review\n",
    "- FINALS WEEK: Final homework/project due Friday of finals week. Worth 2X regular homework\n",
    "\n",
    "**Grading**: 10 homeworks worth on unit, one take-home final worth 2 units for a total of 11 units.\n",
    "\n",
    "**Homework Schedule**:\n",
    "- Wednesday: HW $n$ assigned\n",
    "- Following Wednesday: HW $n$ due before class, HW $n+1$ due\n",
    "- By Sunday: HW $n$ graded\n",
    "\n",
    "**Office Hours**:\n",
    "- 5-6PM: Wednesdays in CSE 236 (Eric)\n",
    "- Saturdays and Mondays, 6-8pm, Online (Victor)\n",
    "\n",
    "**Text**: None. Readings will be assigned from electronic sources. \n"
   ]
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   "source": [
    "# Python and Jupyter Installation"
   ]
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    "To run the code for this course, you will need access to the following tools:\n",
    "- Python version 3.4 or greater\n",
    "- The [Jupyter](https://jupyter.org/index.html) notebook environment\n",
    "- Basic Python libraries: [Numpy](https://numpy.org/), [Scipy](https://www.scipy.org/), [Sympy](https://www.sympy.org/en/index.html), and [Matplotlib](https://matplotlib.org/).\n",
    "- For lecture 9, you will also need [PyTorch](https://pytorch.org/). \n",
    "\n",
    "## Anaconda\n",
    "\n",
    "The [Anaconda Distribution](https://www.anaconda.com/distribution/) is the easiest way to install Python, Jupyter, NumPy and a number of other Python libraries. Once installed, to add more libraries you use the `conda` command. Use this option if you have a Mac or a PC and currently do not have any version of Python on your computer.\n",
    "\n",
    "## Pip\n",
    "\n",
    "If you install (or have installed) Python directly using the distribution at [Python.org](https://www.python.org) you will also get `pip`, which you can use to install additional libraries. You will need to then install Jupyter, numpy, scipy, sympy, and matplotlib using the `pip install` command. Use this version if you are running Linux or are a more advanced Mac user. \n",
    "\n",
    "## Docker\n",
    "\n",
    "Python is notoriously annoying to install and it is easy to get multiple conflicting versions on your computer. To avoid all that, those of you computer savvy types may want to use Docker to run Python and Jupyter. You can find python stacks [here](https://github.com/jupyter/docker-stacks). \n",
    "\n",
    "## Online\n",
    "\n",
    "The easiest way to run Jupyter is to use [Google Colab](https://colab.research.google.com), where you can run all these tools for free in the cloud. You get what you pay for, and it is a bit clunky, but it is good enough that some classes use Colab exclusively."
   ]
  },
  {
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   "metadata": {
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   },
   "source": [
    "# Jupyter Basics"
   ]
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    "- You should be able to enter and run code in a cell. Note you can type Shift-Return or Shift-Enter to evaluate a cell.\n",
    "- Code is evaluated in the order you run the cells in a notebook, and not the order the code appears in the notebook.\n",
    "- The cell type can be switched to `Markdown`, which allows you to enter formatted text. See [here](https://www.markdownguide.org/cheat-sheet/) for details. Also, open any one of the Markdown cells in this notebook.\n",
    "- Sometimes Jupyter gets stuck. To cancel the currently evaluating cell, use the `Stop` button in the menu. To really stop things, choose `Kernel->Restart`. \n",
    "- More resources on how to use Jupyter are [here](https://jupyter.org/documentation)."
   ]
  },
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   },
   "source": [
    "# Python Documentation"
   ]
  },
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    "## Basics\n",
    "\n",
    "- Python [core documentation](https://docs.python.org/3/). Go year for basic tutorials, syntax, data structures, and control statements. You work through do the [informal introduction](https://docs.python.org/3/tutorial/introduction.html#) at your earliest convenience. \n",
    "- [W3Schools](https://www.w3schools.com/python/) also has a nice tutorial.\n",
    "- Numpy and Scipy [documentation](https://docs.scipy.org/doc/). \n",
    "- Matplotlib [documentation](https://matplotlib.org/).\n",
    "- SymPy [documentation](https://docs.sympy.org/latest/index.html).\n",
    "\n",
    "## Debugging\n",
    "\n",
    "When trying to figure out how to do something in Python, Google and [Stackoverflow](https://stackoverflow.com/) are your best bets. For example, if you search for \n",
    "\n",
    "> python get every other element in list\n",
    "\n",
    "You get the very helpful response [here](https://stackoverflow.com/questions/8865878/skipping-every-other-element-after-the-first):\n",
    "\n",
    "```python\n",
    "def altElement(a):\n",
    "    return a[::2]\n",
    "```\n",
    "\n",
    "More generally:\n",
    "\n",
    "<img src=\"https://i.pinimg.com/originals/53/be/34/53be34c987b10821f7c10b9d88436b92.jpg\" alt=\"drawing\" style=\"width:400px;\"/>"
   ]
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   "source": [
    "# Python's Syntax"
   ]
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    "Python's syntax is similar to many other languages. Here, we just highlight some idiosyncrasies.\n",
    "\n",
    "## Colons\n",
    "\n",
    "Python code has seemingly useless and extraneous colons after control statements, function definitions, and class definitions. For example\n",
    "\n",
    "```python\n",
    "if x < 1:\n",
    "    x = 2\n",
    "    \n",
    "def f(x):\n",
    "    return x+1\n",
    "    \n",
    "class Cat:\n",
    "    def sound():\n",
    "        return \"meow\"\n",
    "       \n",
    "```\n",
    "\n",
    "## Whitespace and indenting\n",
    "\n",
    "Where other languages, like `C` use curly braces to denote blocks, Python requires you to indent to show hierarchical relationships. For example, the above three lines illustrating colons, also have indented second lines. The third line of the class definition is also indented to show the return statement is part of the method definition. You will get errors if you indent incorrectly. "
   ]
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    {
     "ename": "IndentationError",
     "evalue": "unexpected indent (<ipython-input-1-b715671b1829>, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-1-b715671b1829>\"\u001b[1;36m, line \u001b[1;32m3\u001b[0m\n\u001b[1;33m    y = 2\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mIndentationError\u001b[0m\u001b[1;31m:\u001b[0m unexpected indent\n"
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   "source": [
    "if True:\n",
    "    x = 1\n",
    "     y = 2"
   ]
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    "## End of line\n",
    "\n",
    "The end of a line usually terminates a statement. You can use the semicolon to put multiple statements on a line.\n",
    "\n",
    "```python\n",
    "x = 1\n",
    "y = 2; z = 3\n",
    "```\n",
    "\n",
    "Also, in jupyter notebooks, the result of the last statement in a cell is printed when the cell is evaluated. To avoid this, use a semicolon after the last statement."
   ]
  },
  {
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   "source": [
    "x = 1\n",
    "x;"
   ]
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   "source": [
    "## Long lines\n",
    "\n",
    "If you have a long line of code, you should break it up to make it more readable. You can use the backslash to continue a line:"
   ]
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   "source": [
    "x = 1\n",
    "\n",
    "if x < -1 or \\\n",
    "   x > 2 or  \\\n",
    "   x is 0:\n",
    "    print(\"hello\")"
   ]
  },
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   "source": [
    "## Comments\n",
    "\n",
    "Comments start with a hash `#` as in\n",
    "\n",
    "```python\n",
    "# Here is an if statement\n",
    "if x < 1: # test\n",
    "    print(\"x is less than one\") # body\n",
    "```\n",
    "\n",
    "You can also put comments in a function definition to make documentation for the function."
   ]
  },
  {
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    "ExecuteTime": {
     "end_time": "2019-09-23T20:18:40.129133Z",
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   "source": [
    "def f(x):\n",
    "    \"\"\"\n",
    "    This is a function that takes a single argument x and returns its negation. \n",
    "    \"\"\"\n",
    "    return -x\n",
    "\n",
    "?f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "hidden": true,
    "id": "6paSQ3QbH0T4"
   },
   "source": [
    "You can put the question mark in front of any function to get its doc string printed out (if it has one). For example,"
   ]
  },
  {
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   "execution_count": 2,
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    "colab_type": "code",
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "?np.linspace"
   ]
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   "source": [
    "# Python's Types"
   ]
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    "Types\n",
    "---\n",
    "Like any language, Python supports numbers, strings, booleans, arrays, hashes and a special type called `None`. Python also allows the user or application developer to define custom types, called *classes*, whose values are called *objects*. Although we may not define our own classes in this course, we will have many opportunities to work with classes and objects defined by other oprogrammers."
   ]
  },
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   "metadata": {
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    "hidden": true,
    "id": "zO-DSOdVH0UO"
   },
   "source": [
    "**Numbers**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "colab_type": "code",
    "hidden": true,
    "id": "ApOATKjIH0UP"
   },
   "outputs": [],
   "source": [
    "1"
   ]
  },
  {
   "cell_type": "code",
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    "id": "N0rqf0uwH0UT"
   },
   "outputs": [],
   "source": [
    "-0.00748"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "id": "RW1KAVXNH0UV"
   },
   "outputs": [],
   "source": [
    "4.2E-3"
   ]
  },
  {
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   "execution_count": null,
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    "colab_type": "code",
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    "id": "XOFpDLmQH0UY"
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   "outputs": [],
   "source": [
    "0xABC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-24T16:13:22.287380Z",
     "start_time": "2019-09-24T16:13:22.260826Z"
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    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "z7tcsZxuH0Ud"
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   "outputs": [],
   "source": [
    "3 + 4j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "k-TtujkiH0Uf"
   },
   "source": [
    "**Strings**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "cHvs8YbEH0Uf"
   },
   "outputs": [],
   "source": [
    "\"Hello World\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "UKHVd7BCH0Uh"
   },
   "outputs": [],
   "source": [
    "\"EE447\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "5IQgXwIpH0Uj"
   },
   "source": [
    "**Booleans**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "uKrBAEABH0Uk"
   },
   "outputs": [],
   "source": [
    "True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "nyGoEesbH0Um"
   },
   "outputs": [],
   "source": [
    "False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "X525ZaQcH0Up"
   },
   "source": [
    "**Arrays**, a.k.a. **Lists**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "Mu9yop5SH0Uq"
   },
   "outputs": [],
   "source": [
    "[1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "GZOuNCtFH0Uv"
   },
   "outputs": [],
   "source": [
    "[\"A\", \"B\", \"C\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "CwQMawYGH0Ux"
   },
   "outputs": [],
   "source": [
    "[1, [2,3], [\"A\", [ \"B\", 1.23 ]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "yKdDN5lOH0Uz"
   },
   "source": [
    "**Hashes**, a.k.a. **Dictionaries**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "d5n0ZJpqH0Uz"
   },
   "outputs": [],
   "source": [
    "{ \"x\": 1, \"y\": \"ECE447\", \"c\": [2,3], 4: 5 }"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "QG6Zm1CiH0U2"
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   "source": [
    "**None**\n",
    "The object `None` is of type `None` and doesn't do anything. It is used when methods need to return something, but there is no actual value to return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "0i7hefFmH0U3"
   },
   "outputs": [],
   "source": [
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "rN4d7VGqH0U6"
   },
   "source": [
    "Variables and Assignments\n",
    "---\n",
    "\n",
    "A variable can be assigned to any value, or to the value of another variable. Variable names must start with an alphabetic character or an underscore, and can contain alphabnumeric characters or underscores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "colab_type": "code",
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    "id": "YQU_sy7WH0U7"
   },
   "outputs": [],
   "source": [
    "x = -2.5E-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "colab_type": "code",
    "hidden": true,
    "id": "Jaap-cdkH0U9"
   },
   "outputs": [],
   "source": [
    "y = x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "id": "eZ-juDOvH0VA"
   },
   "outputs": [],
   "source": [
    "z = [ x, y ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "qAh9AC9aH0VC"
   },
   "outputs": [],
   "source": [
    "[x,y,z]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "jiEGkVD4H0VH"
   },
   "source": [
    "Above, the assignment to z makes a *copy* of x, so that reassigning x does not affect z."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "pXOQ0H_RH0VK"
   },
   "outputs": [],
   "source": [
    "x = 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "yGl_L5smH0VM"
   },
   "outputs": [],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "uayTskYPH0VP"
   },
   "source": [
    "Operators\n",
    "---\n",
    "Operators take one or more values and return new values of the same types, or of different types. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "LWZslunwH0VQ"
   },
   "source": [
    "**Numeric Operators**: +, -, *, /, %, ^"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "RCsDohXxH0VQ"
   },
   "outputs": [],
   "source": [
    "1+2*4/(5%2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "HRm5RzGjH0VS"
   },
   "outputs": [],
   "source": [
    "2**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "9oTeErN5H0VT"
   },
   "source": [
    "**Comparison Operators**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "uV4JX4KhH0VU"
   },
   "outputs": [],
   "source": [
    "2 < 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "Ms59Qm_bH0VW"
   },
   "outputs": [],
   "source": [
    "5 >= 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "7TWg0fwwH0Vc"
   },
   "outputs": [],
   "source": [
    "5 == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "nZMPJnjgH0Vk"
   },
   "source": [
    "**Boolean Operators**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "iy-o7zysH0Vk"
   },
   "outputs": [],
   "source": [
    "True and False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "HdFjHg_UH0Vm"
   },
   "outputs": [],
   "source": [
    "True or False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "DKQedyqoH0Vo"
   },
   "outputs": [],
   "source": [
    "not True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "n8F9uMXMH0Vw"
   },
   "outputs": [],
   "source": [
    "2 < 3 or 3 < 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "yD8D3R45H0Vx"
   },
   "source": [
    "**Array Operators**\n",
    "\n",
    "Arrays can be index with brackets.\n",
    "* `a[i]` returns the `i`th value of `a` (starting at index `0`)\n",
    "* `a[i:j]` returns values `i` through `j`, with `i` inclusive and `j` exclusive\n",
    "* A negative index starts from the end and goes backwards\n",
    "* Leaving out an index means 0 in the first spot means 0 and in the last spot means max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "vOFXxdC4H0Vy"
   },
   "outputs": [],
   "source": [
    "a = [\"a\",\"b\",\"c\",\"d\",\"e\",\"f\",\"g\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "5El7EbNSH0Vz"
   },
   "outputs": [],
   "source": [
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "M53UXOhlH0V1"
   },
   "outputs": [],
   "source": [
    "a[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "OCYu_IKQH0V4"
   },
   "outputs": [],
   "source": [
    "a[1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "8VfzYaKeH0V8"
   },
   "outputs": [],
   "source": [
    "a[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "1IDDNHG8H0WA"
   },
   "outputs": [],
   "source": [
    "a[-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "WugFqHkvH0WC"
   },
   "outputs": [],
   "source": [
    "a[-5:-3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "v6jXdVARH0WE"
   },
   "source": [
    "**Strides**\n",
    "The syntax `a[i:j:k]` returns every `k`th value from `i` through `j`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "U_JBe8q1H0WE"
   },
   "outputs": [],
   "source": [
    "a[0::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "hE1tdSzOH0WG"
   },
   "outputs": [],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "GODVlJobH0WH"
   },
   "source": [
    "**Matrices**\n",
    "Note that matrices, which we will use frequenctly, are just arrays of arrays of numbers. The main confusion is that in moth engineering and math textbooks, matrices are 1-indexed, but in most programming languages they are zero-indexed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "TDL62JwPH0WH"
   },
   "outputs": [],
   "source": [
    "m = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "IDpt_2E5H0WJ"
   },
   "outputs": [],
   "source": [
    "m[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "WnTquuMZH0WN"
   },
   "outputs": [],
   "source": [
    "m[1][2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "dD_ZiCy6H0WQ"
   },
   "source": [
    "**The hash accessor**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "9ynk7ogUH0WQ"
   },
   "outputs": [],
   "source": [
    "h = { \"x\": 1, \"y\": \"ECE447\", \"c\": [2,3], 4: 5 }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "oF2mMv9vH0WS"
   },
   "outputs": [],
   "source": [
    "h[\"x\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "NL6nwcrnH0WU"
   },
   "source": [
    "Array Methods\n",
    "---\n",
    "Arrays are used in many ways in Python, so a number of built in functions are defined to deal with them. These include:\n",
    "* `len(a)` - return the length of the array\n",
    "* `a.append(x)` - append x to the end of a\n",
    "* `range(n)` - return somerthing that acts like the array [0, 1, ..., n-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "6o5RGsuMH0WU"
   },
   "outputs": [],
   "source": [
    "a = [1,2,3]\n",
    "len(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "jmb5ybNMH0WX"
   },
   "outputs": [],
   "source": [
    "a.append(4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "wmz81DGRH0WY"
   },
   "outputs": [],
   "source": [
    "b = range(10)\n",
    "b[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:10:42.902251Z",
     "start_time": "2019-09-23T21:10:42.897306Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "ENG55DuwH0We"
   },
   "outputs": [],
   "source": [
    "# A list comprehension is a way of making a new list\n",
    "\n",
    "a = range(10)\n",
    "b = [x**2 for x in a]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:12:29.988582Z",
     "start_time": "2019-09-23T21:12:29.984057Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "uGny5DZ7H0Wg"
   },
   "outputs": [],
   "source": [
    "# You can add some control to choose which elements to use\n",
    "c = [x for x in a if x%2 is 0]\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:12:49.127207Z",
     "start_time": "2019-09-23T21:12:49.122791Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "s3wh2y45H0Wh"
   },
   "outputs": [],
   "source": [
    "# You can contatenate arrays together\n",
    "# Note that a is a range, not a list, so we convert it to a list first\n",
    "list(a) + b + c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "vfpFi7QCH0Wj"
   },
   "source": [
    "# Control, Functions, and Classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "PD6iieKZH0Wm"
   },
   "source": [
    "Control Flow\n",
    "---\n",
    "Python includes standard control flow keywords like `if`, `for`, and `while`. Note that in Python, the code inside a control flow block is started with a `:` and *must be indented* (which is dumb, but that's Python)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "UNNKDSsHH0Wn"
   },
   "outputs": [],
   "source": [
    "s = \"two\"\n",
    "x = None\n",
    "if s == \"one\": \n",
    "    x = 1\n",
    "elif s == \"two\":\n",
    "    x = 2;\n",
    "else:\n",
    "    x = 10000;\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "jnuwsw-5H0Wp"
   },
   "outputs": [],
   "source": [
    "x=0\n",
    "for i in range(10):\n",
    "    x = x + i\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "bpDaIjf4H0Ws"
   },
   "outputs": [],
   "source": [
    "x = 2\n",
    "while x < 100:\n",
    "    x = x*x\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "9ElhBCbbH0Ww"
   },
   "source": [
    "## Functions\n",
    "\n",
    "A function is a way to encapsulate a certain calculation or algorithm. Use them as often as possible, especially if you find you are repeating yourself. A good acronym to remember is DRY = \"Don't Repeat Yourself\". It is the opposite of WET = \"Write Everything Twice\" or \"We Enjoy Typing\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "zxE3oyM_H0Wx"
   },
   "outputs": [],
   "source": [
    "def f(x,m,b):\n",
    "    return m*x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "b6VqwVETH0Wy"
   },
   "outputs": [],
   "source": [
    "f(1,2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "hec3yg7WH0Wz"
   },
   "outputs": [],
   "source": [
    "def sum(start, stop):\n",
    "    s = 0\n",
    "    for x in range(start,stop+1):\n",
    "        s = s + x\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "EOF01bJSH0W0"
   },
   "outputs": [],
   "source": [
    "sum(1,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "fwHQkWhTH0W1"
   },
   "source": [
    "## Keyword arguments\n",
    "\n",
    "You may encounter (oir even define yourself) functions whose arguments have defaults. These are very useful because the *order* of the arguments does not matter, so you can't accidentally call such a function with the arguments reversed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "HvNOP9COH0W2"
   },
   "outputs": [],
   "source": [
    "def another_sum(start,stop,step=1):\n",
    "    s = 0\n",
    "    for x in range(start,stop+1,step):\n",
    "        s = s + x\n",
    "    return s    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "VxFG_YbHH0W3"
   },
   "outputs": [],
   "source": [
    "another_sum(1,10) # returns 1 + 2 + ... + 10 = 55"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "5HswCKb-H0W6"
   },
   "outputs": [],
   "source": [
    "another_sum(1,10,2) # returns 1 + 3 + 5 + 7 + 9 = 25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "HYpgoM8CH0W7"
   },
   "source": [
    "## Classes and Objects\n",
    "\n",
    "Classes are ways to include data and code that belong together. For example, here is a very simple fraction class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "jJD8lOCzH0W8"
   },
   "outputs": [],
   "source": [
    "class Fraction:\n",
    "    def __init__(self,a,b):\n",
    "        self.numerator = a\n",
    "        self.denominator = b\n",
    "    def to_decimal(self):\n",
    "        return self.numerator / self.denominator\n",
    "    def recipricol(self):\n",
    "        return Fraction(self.denominator, self.numerator)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "3smQyqDUH0XA"
   },
   "source": [
    "To construct new `Fraction` objects using the Fraction class, we call `Fraction` as though it were a function. And to access the methods in a fraction object, we use the `.` operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "hWTDg9t3H0XB"
   },
   "outputs": [],
   "source": [
    "x = Fraction(2,5)\n",
    "y = x.recipricol()\n",
    "y.denominator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "iZK_VyU6H0XF"
   },
   "outputs": [],
   "source": [
    "x.to_decimal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "P7ijKcC_H0XG"
   },
   "outputs": [],
   "source": [
    "y.to_decimal()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "iiyvbUEjH0XH"
   },
   "source": [
    "You can get a list of all the methods in an object using the `dir()` method, as in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "96gChROtH0XH"
   },
   "outputs": [],
   "source": [
    "dir(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-24T18:24:35.568548Z",
     "start_time": "2019-09-24T18:24:35.560101Z"
    },
    "colab_type": "text",
    "hidden": true,
    "id": "Jrh1gjBKH0XL"
   },
   "source": [
    "## Exceptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T20:36:39.777205Z",
     "start_time": "2019-09-25T20:36:39.770193Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "gs60P5lIH0XM"
   },
   "outputs": [],
   "source": [
    "# Some code might not work, but you may wish the surrounding code to keep going. \n",
    "# To do that, surround your code with an exception handler. For example,\n",
    "\n",
    "del(x,y) # undefines x and y\n",
    "\n",
    "try:\n",
    "    y = x \n",
    "except:\n",
    "    print(\"x was not defined, so it is being set to 1\")\n",
    "    x = 1\n",
    "    y = x\n",
    "\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T20:38:45.987124Z",
     "start_time": "2019-09-25T20:38:45.976004Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "O_TR5rVeH0XP"
   },
   "outputs": [],
   "source": [
    "# If a function you write encounters a problem, then you can throw a custom error instead of \n",
    "# letting Python handle it. For example,\n",
    "\n",
    "def recip(x,y):\n",
    "    if x == 0:\n",
    "        raise Exception(\"The recipricol of %d/%d is not defined.\" % (x,y))\n",
    "    else:\n",
    "        return y/x\n",
    "    \n",
    "print(recip(1,2))\n",
    "print(recip(0,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "tsbx1GOzH0XR"
   },
   "source": [
    "# Importing Libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "-Psaz0jqH0XS"
   },
   "source": [
    "Importing Libraries\n",
    "---\n",
    "A library or *module* is a set of code, usually includeing functions, but also including new types of objects, that is not installed in Python by default. We will use a few libraries in this course. One of the main ones is `numpy`, which includes lots and lots of numerical methods. The following line of code imports the `numpy` library and calls it `np` so that you don't have to type as much later. Note that `np` is an object, so it is a number of functions (or methods) in it that are accessible via the `.` operator.\n",
    "\n",
    "Note that you only need to import a library once (unless you restart the Jupyter notebook)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T20:54:07.220385Z",
     "start_time": "2019-09-23T20:54:07.206242Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "HpAY5KJDH0XT"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 29 -2.0179709498623337\n",
      "3 34 0.5137337325055111\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.5183308014670234"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "r1 = random.choice([1,2,3,4,5,6,7])\n",
    "r2 = random.randint(0,100)\n",
    "r3 = random.gauss(0,1)\n",
    "\n",
    "print(r1,r2,r3)\n",
    "\n",
    "from random import choice, randint, gauss\n",
    "\n",
    "r4 = choice([1,2,3,4,5,6,7])\n",
    "r5 = randint(0,100)\n",
    "r6 = gauss(0,1)\n",
    "\n",
    "print(r4,r5,r6)\n",
    "\n",
    "import random as qwerty\n",
    "\n",
    "r7 = qwerty.random()\n",
    "\n",
    "r7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "Mybr-n1TH0XW"
   },
   "source": [
    "# Numerical Computation with Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "iO3jNy5KH0XX"
   },
   "source": [
    "One of the most useful Python libraries for scientists and engineers is [Numpy](https://numpy.org/devdocs/user/quickstart.html), a suite of methods for dealing with floating point numbers, arrays, vectors, and tensors. \n",
    "\n",
    "To start using numpy, we have to import it. As is customary, we call the imported object `np`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T20:56:39.083513Z",
     "start_time": "2019-09-23T20:56:38.959789Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "nXfVpI-QH0XZ"
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "1uVKaEuvH0Xb"
   },
   "source": [
    "##  Arrays and matrices\n",
    "\n",
    "The basic object that is manipulated in Numpy is the array, which is initialized with a list of numbers. The cool thing about numpy arrays is that, unlike basic Python lists, they can be used in complex mathematical expressions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:01:05.107054Z",
     "start_time": "2019-09-23T21:01:05.095909Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "wEOaJIfeH0Xc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 10, 18])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,2,3])\n",
    "y = np.array([4,5,6])\n",
    "x*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:01:24.270920Z",
     "start_time": "2019-09-23T21:01:24.263944Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "JMiX5A2VH0Xf"
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can't multiply sequence by non-int of type 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-10-7ba4458e1857>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# This gives an error though\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'list'"
     ]
    }
   ],
   "source": [
    "# This gives an error though\n",
    "[1,2,3]*[4,5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:25:30.665765Z",
     "start_time": "2019-09-23T21:25:30.660308Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "avEYlLGmH0Xh"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can make matrices as well and manipulate them as you would in math.\n",
    "M = np.array([\n",
    "    [1,2,3],\n",
    "    [4,5,6]\n",
    "])\n",
    "\n",
    "M.T # Transpose the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:05:03.917878Z",
     "start_time": "2019-09-23T21:05:03.910000Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "EDVgyg6LH0Xi"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "        [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]),\n",
       " array([[1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.],\n",
       "        [1., 1., 1., 1., 1.]]),\n",
       " array([[0.75349893, 0.22341524, 0.79369037],\n",
       "        [0.15727465, 0.83341978, 0.04969642],\n",
       "        [0.88569111, 0.75622641, 0.4265519 ]]))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# There are a number of constructors available\n",
    "\n",
    "x = np.zeros([5,10])    # 5 rows, 10 columns\n",
    "y = np.ones([10,5])     # 10 rows, five columns\n",
    "z = np.random.rand(3,3) # square matrix of numbers between 0 and 1\n",
    "\n",
    "x,y,z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:08:37.280353Z",
     "start_time": "2019-09-23T21:08:37.274621Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "dExs-pEjH0Xj"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.]),\n",
       " array([-6.28318531, -3.14159265,  0.        ,  3.14159265,  6.28318531]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# linspace and arange are particularly useful\n",
    "\n",
    "s = np.linspace(0,10,11) \n",
    "t = np.arange(-2*np.pi, 2*np.pi+0.01 ,np.pi) # its \"a range\" for \"array range\" not \"arrange\"\n",
    "\n",
    "s,t "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:13:35.919161Z",
     "start_time": "2019-09-23T21:13:35.911543Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "zpZJ3qIsH0Xk"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.50936683, 0.78357305, 0.96386399, 0.41410563, 0.44615534],\n",
       "       [0.44584593, 0.75899068, 0.4507131 , 0.35439104, 0.7276961 ],\n",
       "       [0.51190992, 0.17816762, 0.28373614, 0.3772171 , 0.19461247],\n",
       "       [0.77089416, 0.83130729, 0.22638443, 0.23015951, 0.32465889],\n",
       "       [0.39333848, 0.40399917, 0.10091366, 0.22849863, 0.33831517]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can reshape arrays if needed\n",
    "\n",
    "a = np.random.rand(25)\n",
    "a = a.reshape(5,5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:27:54.731674Z",
     "start_time": "2019-09-23T21:27:54.722998Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "MduJVseMH0Xl"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 4.]\n",
      " [7. 7.]]\n",
      "[[4. 4.]\n",
      " [2. 7.]]\n",
      "[[0. 4.]\n",
      " [7. 7.]\n",
      " [4. 4.]\n",
      " [2. 7.]]\n",
      "[[0. 4. 4. 4.]\n",
      " [7. 7. 2. 7.]]\n"
     ]
    }
   ],
   "source": [
    "# You can also stack matrices\n",
    "\n",
    "a = np.floor(10*np.random.random((2,2)))\n",
    "b = np.floor(10*np.random.random((2,2)))\n",
    "\n",
    "X = np.vstack((a,b))\n",
    "Y = np.hstack((a,b))\n",
    "\n",
    "print(a)\n",
    "print(b)\n",
    "print(X)\n",
    "print(Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "Q7JnA1VHH0Xl"
   },
   "source": [
    "## Operations on numpy arrays\n",
    "\n",
    "You can treat numpy arrays like vectors and matrices, and apply numpy enabled functions to them.\n",
    "\n",
    "The math functions in numpy include trigonometric functions, exponentials, logs, roots, powers, min, max, argmin, argmax, etc. Full lists are all over the Internet. For example, [here](https://www.geeksforgeeks.org/numpy-mathematical-function/) one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:20:03.560798Z",
     "start_time": "2019-09-23T21:20:03.554648Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "W1JzaOu4H0Xm"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  2.  4.  6.  8. 10. 12. 14. 16. 18. 20.]\n",
      "[  0.   1.   4.   9.  16.  25.  36.  49.  64.  81. 100.]\n",
      "[ 0.          0.84147098  0.90929743  0.14112001 -0.7568025  -0.95892427\n",
      " -0.2794155   0.6569866   0.98935825  0.41211849 -0.54402111]\n",
      "[ 1.          2.36787944  4.13533528  6.04978707  8.01831564 10.00673795\n",
      " 12.00247875 14.00091188 16.00033546 18.00012341 20.0000454 ]\n"
     ]
    }
   ],
   "source": [
    "t = np.linspace(0,10,11)\n",
    "\n",
    "print(t+t)\n",
    "print(t*t)\n",
    "print(np.sin(t))\n",
    "print(2*t + 1 / np.exp(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:20:31.481332Z",
     "start_time": "2019-09-23T21:20:31.474392Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "kvsBEPmXH0Xm"
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "only size-1 arrays can be converted to Python scalars",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-070b04f68a54>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmath\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: only size-1 arrays can be converted to Python scalars"
     ]
    }
   ],
   "source": [
    "# Note that math functions don't work.\n",
    "\n",
    "import math\n",
    "\n",
    "math.sin(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:21:22.742167Z",
     "start_time": "2019-09-23T21:21:22.737145Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "F3uiPmAhH0Xo"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.        ,  2.58578644,  4.26794919,  6.        ,\n",
       "        7.76393202,  9.55051026, 11.35424869, 13.17157288, 15.        ,\n",
       "       16.83772234])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can make this work with your own functions\n",
    "\n",
    "def f(x):\n",
    "    return 2*x - np.sqrt(x)\n",
    "\n",
    "f(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:25:51.585292Z",
     "start_time": "2019-09-23T21:25:51.573261Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "FKtSkJIVH0Xp"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[14]]\n",
      "[[1 2 3]\n",
      " [2 4 6]\n",
      " [3 6 9]]\n",
      "[[0 0 0]\n",
      " [0 0 1]\n",
      " [0 0 0]]\n",
      "[[ 2 -1  0]\n",
      " [ 1  0  1]\n",
      " [ 0  0 -2]]\n",
      "[[ 5]\n",
      " [ 5]\n",
      " [-4]]\n",
      "[[-1.   2.   1. ]\n",
      " [-0.  -0.  -0.5]\n",
      " [ 0.   1.   0.5]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix algebra\n",
    "\n",
    "x = np.array([\n",
    "    [1],\n",
    "    [2],\n",
    "    [3]\n",
    "])\n",
    "\n",
    "A = np.array([\n",
    "    [-1,0,2],\n",
    "    [0,1,1],\n",
    "    [0,-2,0]\n",
    "])\n",
    "\n",
    "B = np.array([\n",
    "    [0,1,0],\n",
    "    [0,0,1],\n",
    "    [1,0,0]    \n",
    "])\n",
    "\n",
    "print(x.T@x)\n",
    "print(x@x.T)\n",
    "print(A*B)\n",
    "print(A@B)\n",
    "print(A@x)\n",
    "print(np.linalg.inv(A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "nZFAmKkxH0Xq"
   },
   "source": [
    "## Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:45:43.596232Z",
     "start_time": "2019-09-23T21:45:43.591337Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "H3LNuTCNH0Xq"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can use a list of integers as indcies into another array\n",
    "\n",
    "i = np.array([0,2,4,6,8])\n",
    "x = np.arange(1,10,1)\n",
    "x[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:47:38.107386Z",
     "start_time": "2019-09-23T21:47:38.102244Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "fg9cCvOpH0Xs"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]\n",
      "[9 8 7 6 5 4 3 2 1]\n",
      "[8 9]\n"
     ]
    }
   ],
   "source": [
    "# You can use python indexing\n",
    "\n",
    "x = np.arange(1,10,1)\n",
    "print(x[2:4])\n",
    "print(x[::-1])\n",
    "print(x[7:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:56:44.309696Z",
     "start_time": "2019-09-23T21:56:44.304278Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "3XxVBlneH0Xs"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.  4.  5.  6.]\n",
      " [ 7.  8.  9. 10. 11. 12.]\n",
      " [13. 14. 15. 16. 17. 18.]\n",
      " [19. 20. 21. 22. 23. 24.]\n",
      " [25. 26. 27. 28. 29. 30.]\n",
      " [31. 32. 33. 34. 35. 36.]]\n",
      "[ 4. 10. 16. 22. 28. 34.]\n"
     ]
    }
   ],
   "source": [
    "# You can slice things up \n",
    "\n",
    "A = np.linspace(1,36,36).reshape(6,6)\n",
    "\n",
    "print(A)\n",
    "print(A[:,3]) # Can't do this with python lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T21:57:05.719989Z",
     "start_time": "2019-09-23T21:57:05.714699Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "3Sr-LRxOH0Xt"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False  True False  True False  True]\n",
      " [False  True False  True False  True]\n",
      " [False  True False  True False  True]\n",
      " [False  True False  True False  True]\n",
      " [False  True False  True False  True]\n",
      " [False  True False  True False  True]]\n",
      "[[ 2.  4.  6.]\n",
      " [ 8. 10. 12.]\n",
      " [14. 16. 18.]\n",
      " [20. 22. 24.]\n",
      " [26. 28. 30.]\n",
      " [32. 34. 36.]]\n"
     ]
    }
   ],
   "source": [
    "# You can use Boolean expressions\n",
    "\n",
    "condition = A%2 == 0\n",
    "B = A[condition].reshape(6,3)\n",
    "print(condition)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T17:40:49.570865Z",
     "start_time": "2019-09-23T17:40:49.567064Z"
    },
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "cj270iW7H0Xw"
   },
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "VQ3Cy9wuH0Xw"
   },
   "source": [
    "We will almost exclusively use [matplotlib](https://matplotlib.org/) for plotting in this course. For more examples, see [these examples](https://matplotlib.org/gallery/index.html) at the matplotlib website."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T20:45:40.978661Z",
     "start_time": "2019-09-25T20:45:40.968914Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "JOqPQg_nH0Xx"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "hidden": true,
    "id": "KtS3MPjYH0Xy"
   },
   "source": [
    "## Plotting functions of one variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T22:08:55.685232Z",
     "start_time": "2019-09-23T22:08:55.498362Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "IxnVvPB6H0Xy"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b69da96da0>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69da96d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To plot basic 1D functions, use code such as the following\n",
    "\n",
    "t = np.linspace(-2*np.pi, 2*np.pi, 1000)\n",
    "fig,ax = plt.subplots(1,1)\n",
    "ax.plot(t,np.sin(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T22:11:18.271322Z",
     "start_time": "2019-09-23T22:11:18.083268Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "DPk6NBUnH0Xz"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69dd6c5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To make the plot look nice, we fix the axes, label things, and make a title\n",
    "\n",
    "fig,ax = plt.subplots(1,1)\n",
    "ax.plot(t,np.sin(t))\n",
    "ax.set_xticks(np.pi * np.array([-2,-1,0,1,2]))\n",
    "ax.set_xticklabels([\"-2$\\pi$\", \"-$\\pi$\", \"0\", \"$\\pi$\", \"2$\\pi$\"]) # See Latex notes below\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"sin(t)\")\n",
    "ax.set_title(\"A fundamental trig function\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T22:14:17.251647Z",
     "start_time": "2019-09-23T22:14:16.915647Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "-idVdXgLH0X1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j9yyKHmKbseIAbLjX/qWzYi2MmTa0WGMxbFwDzaVw+z8gbeWgLicqWnjknVO4q+S8dncG02KHNhblTXq+s+40pQ1d/HFFOndOGOxdVFdX8/7776NQKLjzzjsdLks0NzezadMm6uvrufXWW5kwYcKgPqZaPc3/zAdBwHdVApr4oZcVLc09tHxYgrmmC+9lsXhMDR38NlRWsPH5nwOw+MlniBk/cUitjsYGtv/5D9SdL2HuQ48zftGtg/q01OrZ8toZbFaRuQ8kEZMxtPfX1Wpk9z8LqCvvYNqdcYxfMNjj7y0v5+KaBxGNRkJ+9zs8b144pJa5vp5LP/oxhuxsAp55Bv/HvjWoz4WOCzy++3E6TZ38euqvh75vgCZDEz87/DNO1J3giYwn+Hbatwd/SbWUwzvLoKcNbn0NUlfa3a5r0TfCJ49D+T6Y+UOY+/8G9atuNXD3P47T0t3L75anckfm0MaiRd/Ljzblsa+4kcdnx/DTRYmD+rW3t/POO+/Q1dXFkiVLGD9+/JBaBoOBLVu2UFJSwpQpU7j55psH9bN29tL0j3wsbUa8l8WinRQ8pJbNYKZt83l6ClrQTg3Be1nsoH76tlY2Pv9z2uvruGnNt0hfsBhBNjhcwditZ/c//ofS44dJm7eI+Y8+MahfT5eJT189Q3u9gWl3xpF2UziCbPC8enssHPyghNKTDSROC2HufYmD+lna2qh66GH0332S5PR05H5+/CH7DxS3XpOkXxQRTSZEiwVBoUAYYilTRMRoMWITbajkKpQyZX9bom8iP5n0k0FjrmbLli1861vfIjTU/vlsbW1l/vz5rF27lnPnzhnGjRtXBM6X6emjpKREdcstt4wdaenSy8vLIggCDz30UNMPf/jD5qvbV65cGTV+/PjuZ599tmmo8f/uuS63Ak8KgrABe+BJhyiKdYIg7AT++6oAlIXAz/6vJpXgm8B7S97ju3u/y08P/RSdSsf0sKu8i9rTdk/OZwzcu2n4fZLARHh0D6y/Gz55DJQaSLry5X2utoNH3jlFkKea9x6ZTOgw+ySxAR58/MQ0Hns3hx9uykWjlLM07cqeQ319PevWrcPd3Z01a9YMu0/i7+/Pww8/zEcffcS2bdtQKBSkp6f3t5vru2l6Mx+ZRk7At1KH3SdR+LsR+FgqLeuLad9SjqBRoB1/xeNsqa1m0+9+gVKtYeUvf4dP8GBD2IdXYBB3/eoFtv/pRfa9/QZypZK0eVcMRnujgS1/OotMLuP2H2TgE+x4OUvnq+G2p8eze20hRzeXoVDKSJ1z5eHAVFVF1YMPARC14QPUcXEOtZTBwUSu/SeXfvYsTa+8gkyjxveBB/rb67vreXTno1hEC2/f/DZJfo7zGga4B/D3+X/nV0d/xetnX8dd4c6alKsCizvr4L3lYOmBh7+AkHSHWngE2u/Bz74Ph16y31+zftTf3NBp5N63TtBlNPPR41NJC3d8T/h5qHnrgSx+tbWANw5UoFbIeWbBFW+/u7ub9957D4PBwJo1a4iIiHCo5e7uzqpVq9i5cyfHjx9HoVAwf/78/nZrt5mmt/KxdpoI+FYq6igvh1oydyW+9ybR8cUF9IdqERQyvJdeeYAz6vVs/u9f0tXcxIr/9zwRyakOtTRaD275/k84vCGEk59uRKZQMO/hb/e39xrMbP3zWTqaerjlu+lEJDnevlC7KZj/UDKeAW6c2l6JXC4w+56EfiNs1eup/tZjmCoqkPv6ovAfZvtCEOzGTSbrX9q82tiJiPRaehFFEY1Cg1wYZIdG5OzZszz33HN8+9v21/voo4+SlpY2qJ+zZXpc4ciRI8VRUVHm2tpaxdy5c+NTUlKMixcv1sPggqzOcsMYOkEQPsDunfkLglCDPZJSCSCK4t+Bz4ElQBlgAB663NYqCMLzQPZlqef6AlP+r/BUefL6/Nd5cMeDPLP/Gd5d/C4JvgnQUQPrVoLWD+7/BHROZCRX6+Dej+xP6B8/Bo/sguBUGruMPPh2Nl5uSt5/dDIhXiPvJbmrFLy1Jot73zrBDzaeJcLXjbRwb7q7u1m/fj0qlWpEI9eHSqVi1apVrFu3jq1bt+Ln50d4eDjWbjPN7xYiKGUEPJaGwnfkPUFBKcfv3iSa156jbWMpCi816hgvjN16Pn3xOQRBYOUvfjusketDoVSy9KmfsPWl37LnrdfxCQkjIjkVU4+Fz/6Si2gTWfb0+GGNXB9yhYyFjyTzhcXGoY/O4x3kTkSSL7bubqqfeALRZCLyvXeHNXJXXqOS0Bd+j9jbS8PvX0AVHY3HzJkYzAae3Psk3ZZu3l38LvE+I++XKWQKnp/+PEaLkZdPvUy4RzjzxswDcw+sXwmGVnjws+GNXB8yOdzyJzAbYd9vwW8spCyn12LlsfdyaNb3su7RycMauX4pmcBzt6XQa7Hy573niQv0YFl6KBaLhQ8++ICOjg4eeOCBYY3cFS0ZixYtwmKxcPjwYfz9/cnIyEC0irS8X4iltRf/h1KGNXJ9CDIBryXRiBYb+kO1KAPd0U4Mxmazsu3V/6btUg23/+TXwxq5fi1BYMbdD2C1WMj57BP8wiPJWLgE0Say65+FtF7qZskTacMauau1Jt0Sjc1i4/TOKnyCtaTPi0C02bj0ox9jLCoi/C9/oUZz5TM0kudlbmjA0tSEMigYRYA/oihSo6+hs7eTCF0Enmrn9gSvpa2tjeho+1aaxWJh165d/PznPx/Uz1WPzhmioqLMAGFhYZalS5e2Hzt2TNtn6IYqyOoMN8zxAlEUV4uiGCKKolIUxXBRFP8piuLfLxs5RDvfEUUxVhTFVFEUT101dq0oinGXf97+OuavVWr567y/4qH04IcHfoihtws2PwoWI9y72Tkj14dKC3evA403bLgHa08HT31wFn2vmbUPTnTKyPWhUcp54/4J+GnVfPu9HNq6e9m8eTPd3d2sXr3apYg3pVLJypUr0el0fPjhh3R3d9P6YQnWzl787k9yysj1IShk+D2QjMJXQ8uGYixdJna8/hqdzY0s+8HP8QlxPkKwz9h5B4fy2Wsv0tXSzL73iulsMbL48VR8nQhM6EMml7Hg4WR8gt3Z+eY5utqM1P3yV5gqLhD22qtohtmjHPwaFYT+4UXUCQnU/vBHmGpq+f3J33O+/Twvz37ZKSPXPy9Bxu9m/I5U/1T+35H/R01XDez4GdTn25fDQ8c7rYVMBsv+AhGT4dP/gpZyfre9iNzqdl65K4Pxkc5HswqCwG+XpzIxyocfbcyltKGLvXv3UlNTw/Lly10K+hIEgSVLlhAdHc22bdtoaGigY1clpgud+NwRhybW+XtVEAS8b41FHedN25YyTDVdHNu0gapzecx79AnGpGW4pDXr3geJyZzIvrf/Tl1ZCae+qKSqoIWZd41lTIqfS1pTboslOt2fo5vLuFTWTuvatei//JKgn/4U3dybnNYCUAQGIvf0wtxQj1XfTYuxhc7eToK0QaM2cgDx8fEcP34cgFdffZWlS5f2G76rycnJKSkuLi689me0Rq6zs1PW1tYm6/v/L7/80jMtLa0/umeogqzOcMMYum8Cge6B/PfM/+Zi50X+8Nn9UHUMbnnVqSi3QeiCYeX/QkcNJe98l2MVLfx2eSoJwa4fZ/D3UPPXezNp6OrlxXe2UlFRwZIlSwgJcT18WqvVsmrVKrq7u9n23sf0lrbhfUsM6kjXP1QyjQLfexKxGcxUvXGE8lPHmXXvw4QluF6iRO3uzm0/eBZTTw+f/OFlynIamHJbDKFjXQ9dV2kULH48FavFxu5XDtGxfTsB3/su2qlTXdaSubkR/uc/gdVKwTPfZsv5T3g09dGBy9tOolFo+MPsPwDw7K5vY8l5G6Z/H+JvdlkLpcZ+f8lVdKx/iHXHKnh0RjSLxrleB02lkPHXezPRqhX8+v29HDt2jIkTJzJu3KCt9hGRy+WsWLECjUbD5g0b6ThQhXZyMNrMkSMyr0WQCfiuTkSuVdL4Xj4nP9lIyuz5pN409N7qcMhkchY/+QM8fPz47NWXOLmtlPhJQaTMcv3IhiATmPdgMh5+Gnb/I5dLf3od3aJF+Nx3r+tagoAyLBRBpcJUW02TvgGdSoefxnnjOxSrV6/m9OnTxMXFkZeXxyuvvHJdegC33npr9IwZMxIvXLigDgoKSnv11Vf712dnz54dV1lZqaypqVFMmTIlMSEhITkzMzNp4cKF7StWrOgE6CvIet999zkdbdmHZOi+YiaHTObBmNvYrC/nZNJCSLtr9GKRk2kb/wTJ9Vv4UUwlK4YIKHGWjAhvnpgahKKhCJ/QKDIzM0ce5ICQkBBmTZpOcX051WF6tJNdN5h9qEI90MwMRNWsICN+AZlLHEcpjoRfeCSTlt9DU2U+nr4XhwwocRbvIHemLA6lrklO08RV+H1rcECJs6giI9H94Hto8sp4oDSEb6d/e+RBDgjzCOPnmU9zRn+R9WHx9oCS0eIZSs/Nf8SrJZefee/hR4sSRi0VqNPw3C0JhHQUInPzZOFC141JH1qtlluX3EJjWzO5HtV4LR392S25VonnsmjosJIZMp+5Dz8+ai2N1oMFj3+PzuY6ROsxZq1OGDF60RFqNwVz7xmLvtPKhcQVhPzm16PWEuRylGFhYLbg3wWhHqGj1urDx8eH48ePU1ZWxnvvvYebm+vnE69l27ZtF5qamvIsFsvphoaGvKeffro/yOTAgQNlUVFR5uTkZFNJSUlhSUlJYVlZWcGLL75Y39dHp9PZ2tvbz/r5+TldWbwPydB91YgiT5TnEG6x8ryie8DZFdelRJ68tJBywvh29xv2fZXr0PJvKwBBYEtLEEazbdRaAMkNQfiLOo72FmIa4qyPKxzN30SbqYFE5cTBZ+9cpKNlLDJFKJ31u+g1dF+Xlv+Xa/FuP895vzn09lzf+7U2qpK8aIGlO5oRWlx+IB3A0tIjzDD08LobNPa2XZfWi9Up7LRm8ZDlI9Td1569cw1VUzE6mYmdXWHUX3NW0VVCqt2IswaTa7tAW9f1vV+5hbup6MojRp2O0HF9f8fWOh/kqjR6u3LobKweecAwaI5uJbxmP9V+U2hpvz7D1C4z0qEFD4OIzPhvVxf1X45k6L5q8jeiqTzCz2NWUKmv5v2i90cttbOgniOVei5k/Qp5x0U49pdRa50/f54LFRWMmzidig4bf9tfNmot4/k2TEVtzB8/my59F4cPHx61VtW5XM5nH8WcKUPssdL5ZdWoterK2ik/3Uz6zffT29PN8Y83jFqrJy+Pzq1bmJRhw2QSOb6lfNRaBS0FfFS6kcb/Wg4mC01/+Z9Ra9FQgHDmXZ4NX4xZtPHSqdEf4C1v0vPe8YvkjfsJckTYOTjYwFlaW1s5fvw4iePSaJN58dvthaPWsrQZ6Tpcw+yEKcgVcr744otRa3W1NJO9ZTPdsUZkajkdn18YtVZ3Ry+nvrhI3KTb0Hjo2Pf2G4z2eJaltZXmv/2N1LBW3HRKDm88P3otm8V+INzHA0GhwFxXN2qtbyqSofsqsfTC3uchJJ0Zs3/NrPBZvJX/Fh29g7NBjITZauPFHSXEBXowZ/FK+zGDQ6/Yz0K5iNVqZffu3fj6+rLi5lncmh7KPw5V0NjpuocoWkXaP6tA7qshYWkmaWlpHD16lPZ215+6RZuNg+veRucfQNpdt+A+PhD90UtY2kcxL1Hk6MdluHupmLlqGuPmLODMjs9oq780Kq3GP76E3M+PmCcfIHVOGAWHL9F6yXUPURRFXsp+CR+ND2sW/RSfe1bTvmkTxtJSl7UA2P0rUOuImPcb1qSs4YsLX1DYMjqj8uIXxbgp5Ty0dDbMeAYKP4Xq7JEHDsHevXuRy+UsvXkB37kpjp0FDRyvaBl54BB07qwEBEJuSWLOnDmUlZVRUVExKq0jH76PKNqYdt99eM6NxFjShrF0dF5w9mcXsJltzFiVyoxV91NTdI6yU8dHpdX819ex9fQQ9uOnmXRrDHVlHVScHfJY2MhaPc3YRBuBHsEogoOx9fRgHSIDzX8ykqH7Ksn5X+iognm/ApmM743/HnqTnrXn1rosteFkFReau/nZ4kQUchnM+7U9gvPway5rnTlzhqamJhYsWIBCoeAHC+KxjRC/AAAgAElEQVSxWEX++qXrXp3hbCOWBgNei6MRlDLmzZsHwKFDh1zWKjl2iIaKMqbfdR8KlQrPhWMA6Nx10WWt8tNN1Fd0MnlZDEq1nOmr7kOuUHB4/Tsua+n377cf9n7yO8g9tGQtiUKpknPyM9e9geN1xznVcIrH0x7HU+VJwBNPINPpaPzjKDyxiv1Qthtm/gDcfXlw3IN4qjz585k/uyx18kIruwob+K85sfh7qGHqd8DdH/Y977JWTU0NBQUFTJs2DZ1OxyMzognyVPPKrlKXPQtTTReGs03oZoah8FYzadIkPD092bt3r8taTRcvUHBwLxmLbsUrMAiPaaHIfTV0fF6BaHNNq62+m8IjdaTMDsM70J3UuQvxCQnl6EfrEG2uLYeaKitp+/BDvFeuQB0bS/L0EHxCtBz7uByb1UUtq4lWYyveGm/7mTkvL2QajT19mOTV9SMZuq+KvjyWUTMhdi5gP0y+NGYp64rW0Whw3hMzmq38eV8Zk6J9mZt4+TC1fxykr4bst6DTeS/FYrFw8OBBwsPDSUxMBCDKX8vKrAjWn6yips3gtJZoFenaV4UyRIvbOHtUl5eXFxMmTODMmTO0tjof9WuzWjny0fsEREaRNHMOAApvDR7TwjCcacTc4Lz3JNpETn52AZ8QLYlT7YExHj6+TFh6G6UnjtBc7bzhFEWRptf+hGrMGLxXrADAzUNF+rwIyk830lTtfNS0KIr8z5n/IVgbzIp4u5bc2xv/bz1K96FD9OTlOa2FKNrPvXmGwyR7QIWnypNHUh/hSO0RTtW7luXn1d2lBOrUPDz9csi42gNmPgMXDsCFgy5p7du3D61Wy7Rp9ow/GqWcJ2+K42RlK4fON48weiCde6uQuSvQzbYHXikUCmbPnk1tbS2lLnrBRzeuR+3uzpTbVwH2Iy1eC8dgrjdgLHTN2zy57QIKlYyJS6IAe67VqSvvpbmqkpJjrj3kNf/tbwhKJQFPPnlZS8aU22LoaOqhNHtwzs3haOqxe4GBbvbvCUEQUAQGIppMWEexyvJNRTJ0XxU5b0N3E8z75YC0Sk9kPIHFZuHdgnedltqYU0NTVy/fnz92YPTU7B/bqx0cetlprby8PDo7O5k9e/YAre/Ni0MQBP5nn/NeneFsI5YWI57zB+bqmzlzJjKZjAMHDjitVXr8MO31dUxdeQ8y2ZXzprrZ4QgKGV37nU98UJHbRFtdN1lLxiC7Kq1S5pLbUGrcOPHJR05r6ffvp7ekBP8n/gtBeSVtUsb8CNTuCk5uc96rO1R7iLzmPB5PexyV/EqKP++7VyP38qL5b393WovKQ1CTDTO+bz8acJnViasJcAvgb7l/c1oq52IrxypaeGxWDG6qq876Zj0CulDY9zuntWpra6moqGDq1Kmor8rOcdfECMK83Xh5t/NenemSHmNRKx7Tw5BpruSyyMjIwMfHhy+//NJprebqi5RlH2P8omVoPK4knnZLC0Dh70bn3iqntdobDJSdbiR1Tjhuuit/x8SpM/GPGMPRjeux2ZwLojJVV9Px2XZ8Vq0akP0kOt0fvzAPcr64iLOOmMlqosPYgY/aB6X8yr0q0+mQubnZvToXvc1vKpKh+yqwmODY63ZvLmLSgKYIXQQ3R93MxtKNTu3Vma023jhQzvhIb6bGXHMWxicKMu6F0++BfuT1fKvVyqFDhwgJCSHummweIV5urMqK4OPTtU7t1Yk2ka4vq1GGaNEkD8wCodPpyMrKIi8vb8js9IO0RJGTn27ENyyCuKwpA9rkWiXaScEYchuxtDoxL1Ek54uLeAW4ETdh4FkrN50nGQuXUHz0IK2XRjacoijS8sY/UIaF4blkyYA2tbuS9HkRVOY103JJP6IWwD/z/0mINoTb4m4bcF3uocVnzQPov/wSY1GRU1ocehm0gTD+vgGX3RRu3J98PyfrT1LQ7DB94AD+Z18ZvloV90y+5viFUgPTn4Lq41B1wrlpHTqERqNh4sSB+UjVCjnfuSmO3Op2jjm5V9f1ZTWCWo7HtIEZceRyObNmzaK+vp7ycueCgk5+uhGlWkPm4oH5TwWZgG5OBOa6boxFzq1AnN55EblCRvrcgRleBJmMKXeupq2ulvJTzr1fLW/9E0Emw/ehhwZqCQJZS6JobzBgMTlnNFt67O+rn9vA74l+r85sxtrZOdTQ/zgkQ/dVcG4TdF2yH94dgofHPYzBYuDDkg9HlNp69hI1bT18Z07c0Gdhpn0XrL32JcwRKCwspK2tjVmzZg2p9ciMaMw2G/97tHJELWNxK5bmHnQ3RQypNWWK3WD1ZVMYjgtnTtFUVcmk21YMmUzXY1Y4CAJdh0Y2TtWFrTRVdZG5aKA310fWLbejUKrI3rp5RC1DdjY9Z8/i+8jDA7y5PsbNDkOhlJG7Z+Sw8nPN5zjdeJr7ku4bkFC3D9/77kPm4UHLm2+OqEVtjn1/bup3QDn4PNOK+BV4KD14u2DkpEDnajv4sqSJR2ZE464aIgNg5v32uohHR973a2xspLi4mMmTJw/w5vq4IzMMfw8Vbx0a2Qs2NxnoOdeMx7RQZG6D55WamoqHhwdHjx4dUau9oZ7iIwdJW7AYN93gRAbu4wOQ+2ro2j/y37Gr1UjJiXqSZ4Ti7jk48f7YyVPxCgzi1LZPRtQyNzTS8fHHeN1xx5A1C2PHB+AT7I6pxzKit2mxWWjrbcNL4zVgtaAPmYcHMrUaa3OztFeHZOiuH5sNjvwJgsZB3LwhuyT4JjAjbAbritZhtDj2UkRR5K3DF0gI0jEvyUFpHf+xEL8Yst+05zochuPHj+Pn50dCwtAHgaP8tSxKCeb94xfR9w6fOk5/uBa5lxq3lKGTzXp7e5OSkkJOTs6gmnbXcmrbx+j8A0icPnvIdoWXGvfxgXRnN2DtHv48Vu7earReKhImD53Rw93Lm+RZN1F0eD+GzuG9zda1byP388P7jjuGbHfzUJE4LYSSk/V0dwyuhXY17xa8i4fSgzvGDq0l9/TEe+VKOnfuwlxfP2Sffo79FdRekPXwkM06lY67Eu5i98XdVHcO/+X99pFK3FVy7psyZugOKi1MfBSKt0Pz8MvafQmYJ08eujyVRinn/ilR7CtupKxx+L1N/dFLIBPwmD50ftO+31NRUUFd3fDn/c7s2IYgE8haunzIdkEuw2NaKKaqLkwj7Lnmf1mDKOIw+YBMJmfC0uVcKi2itmR477xtwweIFgt+jwz9dxRkAhkLIrFZRcy9w3t1rcZW+9lYzdCfR0EQkPv7YzMasXWP7jyp1WrlqaeeIiUlhdTU1FFHvgKUlZUpJ0+eHB8TE5MSFxeX8vzzzw/5BWcwGITU1NSkhISE5Li4uJSnn366/4Zobm6WL1q0KCY6OjolJiYmZc+ePU7n9pMM3fVS8SU0Fds9rWGyETyY8iCtxlZ2Vu502OfUxTaK6jpZMy1q+MwG074LhhY4u95hl9raWmpra5k0aRKyIbymPh6bFUOn0cLGU46/IE2X9PRWdOAxLRRB7nheU6dOxWQycfr0aYd9mqsqqS7MJ2PhUuQKxznFdTPCwGLDkON4c769wUBVYSsps8KQKxy/xszFy7CazeTt2eGwj6mmBv2BA/isuguZxnHOzvR5EdisIvlfOvY26/R17Lq4y+5pqRwXJvW5914QRdrWD1NRqqseCrfYlyw1jtOs3Zd0HzJBxvpix/dEi76XbXmXuDMzHC+3wV5mP5MeA7kKjr/usIvBYCAvL4+0tDTchykAev/UMagVMt486NirsxktGHIacU8PGLYCfVZWFiqVimPHjjnsYzL2ULB/D/FTZuDh6zgNljYrCEEtR3+k1mEfi8lK4dFLxGQEoBsmj+u4OQvQaD04te1jh31sJhPtH23EY84cVMPk/4yfGIQgg55Ox4e+baKNNmMbHioP1ArHBYzlXl4ICgWWZtcCgvq4uvDq9773PV5/3fH9MBJKpZKXX365pqKioiA7O7von//8Z2BOTs6gN1Wj0YiHDx8uKSkpKSwoKCjcu3ev5969e7UAjz32WMTChQs7L1y4UFBYWFiYkZHh9DkkydBdL6fW2sOyU4YpiglMCp5EtFf0sMuX7x67iE6jYPn4EbL2j5lmz1Sf/RaOdq5PnDiBSqUaUE5nKMZH+pAR4c37xy86XOLQH7mEoJShnTh8vsGwsDDGjBlDdnY2Ngeb4Gd3fY5cqWTcTQuG1VIGa1FFeaI/XucwFDz/QA0yuUDyjOHfL7/wSMakjSd313aslqE917YPPgCZDO9Vq4bV8g50JyrVn8Ijl7Bahn6NfcbmnsR7htVShYehmzeX9o8+wubIC875X7BZYOIjw2oFuAcwP3I+W8q30GMZ2tPfkF2NyWLjgakOvLk+PAIhdQXkfQi9Q3s8Z8+exWKxMGnSpCHb+/DVqrgjM5xPz9bSYRjaO+/OaUA0WYesTXg1bm5uZGRkUFBQQLcDL6Xo0H56Dd1k3HzLsFoyjQLthCAM+c1YHRiV86ca6O22kDpn+HyWSo2G1PmLKM85QVfL0Eala8cOrC0t9oebYVCo5CjVcnp7LFgdZC/qMnVhsVnw1QxfMUGQyZD7+mLT67H1Dr8CcS19hVefeuopwF54taxs9EkmxowZY54xY4YBwMfHxxYbG9tTVVU16KlGJpPh5eVlAzCZTILFYhEEQaC1tVV24sQJ3fe///1msBtEf39/p9Mo3TBlev4t6aiFks9h2vdgmCcrsC8lrEpYxQsnX6CgpYAUv5QB7Y2dRr7Ir2PNtKih904GitmXsbY9BdUnIXLg0pFer6egoIDMzEw0w3gnfdw7OZIfbcrjxIVWplwTAGPtNmM424h2YjAy92G8gMtkZWWxefNmKioqBgXA9Bq6KTy4j8Rps3D3HLncise0UFrXF2MsbcMtceCH2mS0UHy0jtjMQLRew7/3YPfqPnnxN5w/eZTEabMGtNmMRjo2bUY3fz7KoJGTB4+bFUZlXjMVZ5sGVSM3WU18WvYpcyPnEuIxcg5Qn/vup2v3Hjq3b8f7zjsHNlrNcOptiJsPfrEjat2VcBc7Knew48KOQdXILVYb645fZHqcH2ODnEgMnvUwnF0H+RsHLZnabDays7OJjIwkOHjkJND3To7kg5NVfHymhoemD8yAL9pEuo/VoYrQoYoYeV4TJkzg5MmT5Obm9h9n6NcSRc7s2EZgVCyh8YkjanlMC0V/7BL6E3V4LRho/EVRJH9/Lb6hWqcSg6fNW0T2lk3k79vFtJWDH3Ba161DFR2NdtrIicGVlyNOe/Qm9H97hd6igYVXe6xGZKJIi8KNkcJpRFHE1mNAUCiRqex2RZ2USPCzzw47bs+ePVRXV5ORYa/y0Fd49VpGU6anpKREVVhY6D579uwho7osFgvjxo1LrqqqUq9Zs6Zx7ty53UePHnXz9fW1rFy5MqqwsNA9LS2t+80336z29PR0KqxU8uiuh9Pv2D2qrIdG7gssi12Gm8KNj0oGh7uvP1mFxSZyv6O9k2sZtwJUOvuxhmundfo0Vqt1xKftPm5JC8VTo2DdicHptwynG8Eq4jHFucTNSUlJuLm5kZOTM6it4MA+zL3GEZ+2+3BL8UOmU9F9bPC5wdIT9ZiMVtJuci7RdXTGBDwDgsjft2tQW+f2z7F2dOBzz/AeWB8Ryb7o/DQUHBo8r71Ve2nvbWfF2BVOablPmogqLpb2jzYObizaBvp6+1KiE2QFZRHrFTvk/bWnqIFLHUbWTI1ySouwCRCcCtlrB60alJWV0dbW5vT9NS7Mi/RwL9afGBzS31vWjqW5Z1CkpSOCgoKIiIjg1KlTg1YNagrzaampImPRUqeSGiv83VCP9cFwqmHQqkHDhU6aqrpInRPulJZ3UDBR6Znkf7kLm3Wgo9GTn48xNw+fe+4ZMvjqWmQyAbW7gh69Ga5ZzLCJNmw2K0qZAmeyYwqCgCBXgMVyrdSw9BVePXv2LGfPnmXhwoX9Ru9qXC3T09HRIbvjjjtiX3jhhWpfX98hjZRCoaC4uLiwqqoq7/Tp09rs7GyNxWIRioqK3L/zne80FRUVFbq7u9t+8YtfOF1q44bx6ARBWAT8CZADb4mi+MI17a8CfcWa3IFAURS9L7dZgfzLbVWiKI4+Bb6zWM2Q8479adsnyqkhOpWOJdFL2F6xnWcmPIOX2u7VWG0iH2ZXMys+gCh/J/dX1R6QttK+T7fo9/ZIOexP22fOnCEqKoqAgACnpNxUcu6cEM77xy/SrE+2Z8rA/jTYnV2PKkKH0onCpWC/STMyMjhx4gRdXV3odLp+rbw9XxAcF09w7FintAS5DO2kYLr2VWFpNQ6od1dw+BL+ER4ERTtXHkiQyRg3Zz5HN66jo7Eer8Arn5G2jz5EFReL+6SJwyhcQSYTSJkZyvFPK2hvMOAddGWPanPpZsI8wpgSOmUYhavmJQh437mCxhdfpPf8edRjr3pvct4G70j7Peak1sqElUOuGmzIribES8O8JCfL3fStGnz2tD3qMzzryrRycvDw8CApyflySvdMjuQnm/M5dbGNiVFXvPPu7Hpk7grcUoepqH0NWVlZfPLJJ1RWVhITc6WyQd7enai1WodBTkOhzQqidX0xvWXtaOKv1OErOFiLUiMnfpLz5YHSFixm60u/o+LMKeKyrqyytG/chKDR4LX8tmFGD0SjVdJrsOD9/R+h0V5ZSanT19HT20aUTzwKmXNf31a9HlNlJcrwcBRO1p/8VxRe7e3tFZYuXRq7cuXK1jVr1ox4mt3f3986Y8aMrm3btnk9+uijLUFBQaa5c+d2A6xatarthRdecNrQ3RAenSAIcuCvwGIgGVgtCELy1X1EUXxaFMUMURQzgL8AV+/89vS1/Z8YOYDzu+xP2w4i4RxxV8JdGK1GvrhwJVHt0fJm6jqMrMoauRLzACY8ZE8LlnsleXFVVRVtbW2MH+9CIU7sy0tmq8imnCtBFqbqLiyNBrQTXatRNmHChH6D20dD+XlaaqpIneta+Za+fUHD6StBKc01XTRX60maFuJSOZKUOfNAEDi3f0//td7ycoy5eXjfucIlrcSpIchkAgWHrgQzVHVWcaL+BHeMvQOZ4PxHy+u2ZaBU0r7pqiMQ7VVw4RBk3GevCu4kfasGm0o39V+r7zBysLSJOzLDkA9xBMMhqStB5WHfh76MXq/n/PnzpKWlIZc7P69b00PRqRWsv2rVwGYw01PYgntGIMIwwUTXkpycjJubG6dOXckGY+zWU3byGInTZqNUjbyU3Ydbsh8yrYLu7CuRryajhbIz9mVplcZ5XyA2cxIePr7k7f68/5qtp4fOzz/H8+aFyHXO15JUuSmQyWUY9Vf2NW2ijY7eDjxVnk4bOQCZVougUmF1IXPRV1141Wazcffdd4+Jj483/vrXv3YYYXbp0iVFc3OzHECv1wv79+/3TEpKMkZGRlqCg4NNubm5aoBdu3Z5JiQk/NsFo0wCykRRrBBF0QRsAIZ7/FkNDBOq9n9A7gf2A7xjXfviTvJNYqzPWLaWb+2/tjmnBk+NwvGRAkeEpNmXmE5fybpy5swZVCqVS0/bAHGBOiZG+bApp6Z/ean7ZD2CSoZbuvNP2wD+/v5ERUVx5syZfq1zB/aiUKpImDrTJS2FtwZ1rDfdpxv7l5eKj9YjkwuMHSE45lo8/QOJSs/k3P49/ZksOj75BBQKvJbdOsLogWi91ERn+FNyoh7r5fyEm89vRi7IWR43dFi7IxS+vuhuuomOrVsR+0oe5X4IiJB+t0taOpWO+ZHz2XlhJ71WewDCx2dqsImwYoKLD1JqHYy7Awo+BZM9+CM/Px+bzTbkMtZwuKsULB8fxvb8Ojp67F/ehrNNYBVxz3Lt76hUKklPT6e4uBiDwZ7CrvTYYSxmE+PmOOf99iEoZLiPD6KnsAWr3v7el59uwtJr7U8n5ywyuZxxNy2gMvcM+lb7Ye6uPXuw6fV43T70MROH8xIENB5KTEZLf9CT3qTHKlrxVrtWTFgQBOQ+PtgMBqeDUr7qwqu7d+/2+PTTT/0OHz6sS0xMTE5MTEz+8MMP+zfq+wqvVldXK2fOnJkQHx+fPH78+OSbbrqpc/Xq1R0Af/nLX6ruvffemPj4+OS8vDy33/72t07XlbpRDF0YcHV8e83la4MQBGEMEA3su+qyRhCEU4IgHBcEwbVvmdFgaIWSHfYnXrlrq7+CIHBb7G3kN+dT0VFBp9HMjoJ6lmWEolE6/4TcT/pqaCyE+nx6e3spLCxk3LhxqFSOw7QdcUdmOGWNevJrO7D1WujJa8ItLQCZ2vUV7oyMDNra2qiursZiMlFy5ABxk6aidnf66Es/7hOCsLYaMVV2YrXYKDlZT3SaP27DhKI7IvWmBehbmrmYewbRYqFjy1Y8Zs1C4ed6ReaEKSH0dJmpLmjFarOyrXwbM8NmEuju4gML4L3iTqxtbXTt+9K+J5a73p5px8fJPduruDX2VrrMXeyv3o8oimw6VcPEKB+inV0Wv5r01WDuhqLPAPveTWhoKIGBrr/GOyeEY7LY2HHO/v3UndOAMlSLKtTxEQyH00pPx2azUVBgzwZzbv9u/MIjCXJyWfxqtBODwCpiOGPPR1t8rA6vQDeCY5xbFr+a5FlzEUUbRUfs6fDaP/4YZViY08viV9O3ZNnn1bX3tqOQKdAqXf87yi8vWTqb//KrLrx6880360VRzCktLe33+latWtV/sLWv8OrkyZN7ioqKCktLSwvPnz9f8NJLL/Ubs2nTpvWcO3euqLS0tHDPnj3lAQEBTkdd3iiGbqj1FEd7p3cDm0RRvPpFRoqimAXcA7wmCMKQIWqCIDx22SCeamoaXUkMAAo+AZvZ5aftPpbGLEUuyNlWvo3P8+owmm3cmTnK6uHj7gSZAnI3UFBQgNlsdnnZso8lqSGoFDI+Pl1LT0ELosmG1sWn7T6SkpJQKBTk5eVRnnMSY7eelNlDH6gfCbcUPwS1nO6cBi6ea8GoN5M4bXRVzWOzJqPReVJwcB/dR45gaWrC6/bRPRtFpvii0SopOVFPdkM2TT1NLI1dOiot7fTpKIKC7B5m9QlorbAbmVEwKXgSQe5BbC3fyumqNiqau1npqjfXR8QU8B4DuR9QV1dHQ0ODy95cH+nhXsT4a/n4dC2mS3rMtXq0E0Z3fwUHBxMQEEBubi4ttdXUnS8hZc78UVXWVgZpUUboMJxupKOph0vn20mc6tqyeB8+IWGExCVQdHAf5tpaDMdP4HX77U4FoVyLQilDqZFj7DZjtprpMnXhrfYe1bxkSiUyrRZrR8d/ZKaUG8XQ1QBXfxLDAUcp+u/mmmVLURQvXf5vBbAfGPKbXhTFf4iimCWKYpazgRpDkrsBApPtUWmjwN/Nn2mh09hWvo1Np6uIDdCSEeHackQ/7r725dP8TeSePYufnx/h4aMzml5uShYkBbEt9xLdZxqR+6hRjXH9qRZArVaTlJTEuXPnyN+/Bw9fPyJThz/T5wiZSo5bqj89+c2UHLmEu5eKyOThzxA5Qq5QkjBlOuU5J2ja/DFyb290s50PXhigJZcxNiuQC7nNfF68A61Sy5zwOaPSEuRyPJcuRX/kCJYj/wtKLSQ7H7wwYF4yObfE3MKR2iOsP1WIm1LOkrTRPRggk0HaKrhwgNzso8jlcsaNGzcqKUEQuH18GCcutNJ4rBbkAm4ZrnuGfVrp6enU1NRwavcOBJmM5Jk3jTzQAe4ZAZjruinfVwUCDjPtOEPSrJtoqqrkwgfrQBTxWj76RSaNVonVYqOj256z0tVly6uRe3sjmkzYDMNnVPomcqMYumxgrCAI0YIgqLAbs63XdhIEIQHwAY5ddc1HEAT15f/3B6YDoy9vPBIt5VBz0u7NjeLJqo9lsctoMDRwpvEUKyYMnT/SadJW0aHXc7GqirS0tOvSun18GNZuM71l7binB1yXVlpaGkajkfKKcpJm3jSgSoGraCcEIZqsmM+3MTYrCJl89Ldu4vTZWHp7qTh9Es+lSxFGsczbR/yUYKwWGxWnm5kXOQ+NYuRzi47wXLoELBa6du2E5GX2yNpRcmvsrVhFK3uqdrAgOQiPUSw/95N+N1ZRJC//HAkJCcNmQhmJ5ePDEICevGY08T7ItSOfzXREaqr9QfNcYSFj0saj9fYZYYRj3NMCQABDbhPhCT7DZkIZiYSpM5HJ5RQdPYhb1gRU4cMfOB8OtZsCBDB2m3FTuA2bCWUk5J6eIMiwdvznle+5IQydKIoW4ElgJ1AEfCSKYoEgCM8JgnB1FOVqYIM40PdOAk4JgpALfAm8IIriv8zQtf/9d7SUeEDqXdelc1PkTSgFNxSeeSzLcO4MkUPiF1EoTwMgJSVlhM7DMzshgKUqDYII7qN82u4jJiYGtVKJWec76JC2q6jGeGLTyAmRC4MOabtKWEIyWnctlzw0duNyHQRFeaL0ERnTkMrSmNEtW/ahSU5GFepPZ7kAadd3f8V6xxKhjcfslsOt6dd5f/nFcsF/Pgaz2G9cRkuErzsrg71x67XhluZakNO1eHl5ERYchF6hdjnI6VrkOhVCmAf+ZhtjJ1zffe/u6UXk2ESqseCxeNF1acnkMhRqGQqzuv840mgR5HLkOi229jZEs2uZUv7duWHO0Ymi+Dnw+TXXfnnNv389xLijwPV9+lygO7eE7vM++LoHOHVg0xFquRpl7zg03oUEel7nn0Gp4Zw6k+CeZvy9RhFwcLWUXMZytYYLJjN+vhpG/7xtL6+iNRtp1XmjCxrl0tllBJlAs1xGkFKGf/D1bYwLMhnhNhmlnu4QGzPygOG0BIG60GJCChIZpxnd3tXVWp6JGpr3qTC7JVzXew+g6c1E7raB2NDr/1Ir0ExERQdxo1856+dOd3eMdFHpo+T6HsvAw9KLqNLgETE49N1VmhVy/OQCXkGj91j7iLDJqFQq0EeP4frMOcnAWtoAACAASURBVFiUvciMStzF65+XXCNg6xIRTSYE5ei9w383bgiP7t8J3bd+jbXHiuHkyevSKW/S09yQhE3o5mTd9Wm1tbVRa1AyTiyC8n0jDxgGS5uRkC4ruzDxZYnzVdGHoru9DWNlGQgC58+fvy6tHr2JksYeZICx0PnzQENh7ezEv7AUURAoyx65rNBwdPR2sF+1DQGBytzrmxcmA566IkCgc+fu65LqtVg5X2E34vtr9ozQe3isVitFTTYSKEdZuu26tESrSFiDkWP/n733DJIrO880n5O+MrO89y7LoOBNAYUG0ADakGyxSUo7ooaroGIUlKgNBRmr4P7QSruxmgiSE6GgYlaa2OWP1WgkDhUjSjPUaNQUm2x2owE00EABVXDlbZb3LsukN2d/3Lxl09zMQovNFt4IBMnMvIcnb5283znf+33vS4ifDB6iIAyQkQiuvmcADB9CWR8UQYPeiU0iQHjwcH9HKSVZDx+jB0b6ew41FsCGcCGFJOg9vImqTroxF5nQ2bT39H0S8CLQpQj7lSsIq5WNdw5KSaWCt7vmCLsbsBpsCR0NtKCnR/kxHTUvKD1Ph4DnmfLweWwV/Lhbc5tKTAy130Xn3cRmtW6XgacL55MlVoMSMo14uw73gNx87wZZmx5y8gvp//DWoca6PX2bZcsM1iI9o48PtzFg5F3MGZtYHFVs/PjHh5vX4BKb7iyqbU38bPxwa9XpdOLz+zlaoDv0+vI7XeAOMVVi4e3uuUNVAM4M9uFZWaIkP4/e3t5DjbUwtsHamp9IiQ1P11JcIXEt8PX1IScmqSyvZvjBh5rdx2OOFfLhD/vQmcHvCR1qXgS9iLAPYU2fy/xFxYtAlyJ0FguZ166y+e67yDhK+FrwT11ztFYX8WrVK9yYvEEwnNh3LRF6enqoqKggt+UaDP4EQumnqrzdyxgrMzl1vJj3+xfxanQ7joXB+3coqKji2PHjjIyM4E9RQX03hjsXyCm2Yj9dhG/YRSSOEr4WbPzkJ5gqKjhy/XWm+3txu9bSHuvdiXcpthbT0lrJ7IgrqU9dQvT8d7AVkvXLX8TX00NgKrkxaDz8qGuOPJuJX2n6LL0rvUxtpj9Wb28vZrMZx5mXYbEXltM/nXueLSHMempaS3EuuxlcSOwHlwgD9+5gMJk5c/48LpcrqU9dIox0LqIzCHIvlRHZDBIYT9+Ze+Ptt8Fg4Mgbn8Oz7mJmIP2SgY2AMg+b3YKMSAK+9J85+KJFKJbnkH/+BcOLQJcGMj/9GcKrq3g6DwoXa8HwwiaDC5t89ngpn675NBuBDdrn0kuhLS8vs7CwoJR8t/wyBDbTTl+GXD6CM1tkHM3ns8dL8QbD3Eozfbm5sszMQB9NL12hpaWFcDjM0NBQWmO51/3MDrlwnCtSquMiEm/vSlpjhdbWcN+/T9Ybn6HhwksgJaOdD9IayxP0cG/mHq9Vv4bjbBFI5eSZFgJuGHoHWr5A5qc/DcDmu+mlHH3BMO/1LfCZYyV8plZR7kn3VBcKhejv76e5uRnDsWi7Q5qnOhmO4O1dIaMln9dPlKETSmYjHUQiYYYffEjdmVaOHVcqjdPNGsiIZOTxIlUt+WSeKACDwNubnoeblJLNn/wU26WXcFy5isFoYqj9w7THWvevYzPayMgwIYTA7z1EoPO6FEk3vTb293karyYyVN2PL37xizV5eXknGxoaDlC4oVCII0eOtFy/ft0R69p4eBHo0oD95SuIjAw23olv5JkIP+6eQwh443gpF8sukmnM5Kfj6Y01MKBYeBw5cgRqXwZLtmLUmQbU4JFxNJ/ztXnk20xppy+HH94DlFLryspK7HY7fX3p7WzHu5aREhxnijCW29HnW/B0p/cg2nr/JoRCZH7mMxRUVpNTUro911RxZ+YOgUiAV6teJb/MTm6JNf305dA7EPLC0V/BVFmJubmZzffSC3R3hpfxBsP80rFSyu3lHC84zs8m0gt0TqcTv9+vVPNmlSkN5H3pBTr/2AbSGyLjWD6FmWbO1+bxdk8Sd/U4mB3ox7PuorHtElarlbq6Ovr6+tJKX86PbeB2+XGcLUJnNmBx5CqCCWmM5evrIzg7S9anPo3JkkHt6XMMP7yHjOPPmAj+sJ9AOECWOQuhE5gyDAQ8ofRStEGfooubwmnueRqvJjJU3Y+vfOUry2+99VbMtMG3v/3tYofDkXIj4ItAlwZ0GRnYr15l8933kOHUU3vv9C5wrjqX4iwLJr2J61XXuTV1i2Ak9XTcwMAApaWlZGdng8EEzW/CwNtppS99vSsYiqwYC60Y9Do+fayE9wcW8QVT/46jne3klVeSV1aBTqejpaWF4eHhtNKXzqfLZBVYyCuzIYQgoyUf/6iLSBppnM0bNzCUlWJpaUEIQcP5l5jseYbPHdMaKyHem3iPPEseZ4rOAFB/tojZYReeBO7QcdH/I7AVQpXiV5b5+mt4nzwhlIaCz89658m0GLhQpzTVf6r6U/St9KWVvuzv78dsNu+4BBz9ZVjoSSt96etbQRh1mBsUjuizx0sZWdxiKI305UhnO3qDgdpTZwFF6HltbY35+dQD59izJXQ6Qc1xRQYu41g+YZef4Ezqa2Lrxg3Q6bBfvwZAY9sl3GurzAymvslT05aZJqVwxGw1EIlIgv406AR/VG3Loq1F4Xkbr8YzVI2FN954Y6uwsPDAj3t0dNT4zjvvZH/1q19NeZf7sWkv+EVD1qc/xeZPf4r38WOsrdp17KZWPfTPbfB//NKOMeT1yuu8NfoWTxef0lqifazNzU2mp6e5fn2XIkTLFxTDTOdtaNQuOB3eCuAfWyfz+o5AzS8dK+VvHkzywdASnzqqXSnCt7XFVF8PrZ/bEbJtaWnh4cOHDA8Pp6SsEfCFmB5c3eMLltGSz9adGXxDa0oqUyMiXi/ue/fI+dUdpwJH60U63vp7xh53cCQFZQ1/2M8H0x/wRu0b6KON8I4zRXT+eBzn0yWOvZxCk3AoACPvKUEkOlbma6+z/P/8v2zeeJ/cLyV2Pd8zVDjCe/0LvNJchDHaVP9q1av8+0f/nttTt/lyy5c1jxWJRBgaGsLhcGAwRB8VRz4PP/0DGPgnuPwNzWNJqaSbzQ256EzKd/z0sRL+6K1e3u6eo1GLGeyusUY626k6fgpThlJy39zczD/90z/R19dHaWlqrSxjz5Ypa8zBHDUWthzJBzGMt3cFU0Vq1YmbN97HeuYMhjxlk1F39jx6o5HhB/eoOJKaosxmYJPxn3gZWuzefi3oD6PTC/QpuD0oFyri1xh7KKi0c+XXGhN+/KMwXo1lqJrKV/ja175W+Z3vfGd6fX09ZeWJFye6NGG78jLCaFREeFPAe/2KQ8XrLTuB46WylzDpTLw/mRq3Njg4CCg/8m3UXVPy8EM/iXlNPPj6V0FCxtGdrp8LdXlkWgzc6E8tHed80oGMRHC07rgpV1VVYbVat+esFZO9q0RCkrqTOwHNVJ2FzmbA25caT+f+8EOkz0fmq69sv1bqaMSem8fww/sJrjyI9tl2PCEPr1Xv/PjzymxkFVgYTzWtOnEX/BvQtNO8bm5swFhdlXL68tHEGmueIJ/atb4qsypx5Di4OZXaWp2ensbtdu9dX9nlUHpKKXpKAcFZN+F1PxktO+LZRZkWzlTlbv8mtGJ5aoL1hXkc53Y8/2w2G1VVVSnzwGvzblwLHmp3rS+9zYi5Njtlni4wNYV/cBD7qzuariZLBtXHTzH66EFKKcdgOIgv5MOo36vaI3QQCaeaupQgI4omrkZ8FMarsQxVtc7nBz/4QXZBQUHoypUrHs1fYvf/dzoXvQDo7TasFy6wdfMmxf/772u+7t2+BRxF9j1K8lajlQulF7g5dZPfb/19zbJbAwMD5Obm7lWSN5ih/rrirvDZ/1uzTJm3dwV9jhlj2c68jHod15qKuDGwQCQi0Wn0MhvtaMeWm7fHYFWn09HQ0MDg4CDhcFizl5nz6RIWu5GS+p2Ui9AJLM35eHuXkeEIQqMc2OaN99FlZWE9t2MiKnQ66lsv0nvrPYJ+H0aztt/euxPvkmnM5ELJjsGmEIKaEwX0fjBL0B/GaNa48Rx4GwwZyiZl11iZr73G6n/+PuGNDUW+SQN+1reASa/jatPek+61ymv8Vc9fse5f16ywMTg4iE6nw+HYx/s3vQG3/hi2lsCu7UTt7V0GAZYjezVKXz1SxHd+OsjcupfSbG1CAKMd7SAE9bvMTQGampr42c9+hsvlIkejwejYMyWY1e6zoso4mo/rR06Cix6MRdoatTdv3ADYs5ECqDtzHufjDlamJymo1OZGoaYtr/5a0x7ZL+9WgM0VH7klNu3ry70M61NQ2AxGbff4ozBeVbHbULW1tVWTp9zdu3ft7777bk55eXm23+/Xud1u3Re+8IXaf/zHfxzTcv2LE90hYL9+jcD4OH6npnvNuifIg7FVXm85KGF1veo6M1szjLi05cF9Ph9jY2M0NzcfDIxNvwSbszD3TNNYEX8I38ia4hKwb6zXjhSxvBXg6bQ2fbxQMMjYs8fUnzl/QLG9qakJn8/HlMay+XA4wkTPCjUnCg4E2YyWfKQvjN+5HufqvZChEFs3b2K/ehVh3Ft11nD+IqGAn/GuJ3Gu3jevSJhb07d4ufJljPsq2GpPFBAORZjq19h0LKVyOqp/5cBDKOv11yEUYuv2bY1DSX7WN88lR/4BbctrldcIyzB3Z+5qmxdKoKuurj5o0dL0BiBhWHv/p69vBVNN1gFty9ejjuepZA1GOtspdTQe0LZsamranrdWjD1borAq84C2pSWa2UilunfrxvuYGxsxVVXteb3urEJHjD7SLgyxGdjEpDcd0LY0Zyh/V783BT7ftw56E6Sgw/q8jVfjGapqnc93v/vdmYWFha6ZmZnu733ve862trZNrUEOXgS6QyEzyo1t3dSWEro1tEg4InntyMFAp6rea00vjYyMEA6H96aVVDR8ChCa00u+wTUISTKOHvRku9ZYhF4neK9PW3ppqucZQZ+X+tYLB96rr69Hr9drfhDNDrkIeEPUxTB+NTfkIIw6zelL75MnhF2uA7ttgIojxzBbbTg1Poi6lrtY969zrfLagfdKG3IwZRgY79KY9prvgo1paD6ouWk5cQJ9YYHm9TUwv8nUqjcmn3q84Dj5lnxuTd3SNNby8jLLy8ux11fJCcgq17y+QitegvMeMloO/h0dRXaq8qzc0Ji+3FheYsE5sictriI/P5/8/HzN68uzEWB+bOPAaQ7AkGPGWG7HN6BtwxJaW8Pz6BH2GOsrM6+A4joHo4+0tbFEZARPyLNdhLIbOr0Oo1lPwKOxICUSBv+mUoSSgkD78zZeTWSoCjvGqwCf+9znai9fvtw8NjZmLi4uPvGnf/qnh1VRe5G6PAyMZWWYjxxh8+b75P/WV5J+/md9CxTYzZyOYclTaC3keMFxbk3d4ndO/E7SsQYGBrBarVRWxvAZsxVA5QUYfBuu/2HSsXwDq4gMA6bqgymtbKuR8zV53Ohf5Pc/E+Ohtw8jHe0YLRlUHT1oyWM2m6mpqWFoaIhPR3vFEmHs6RIGo46KIwcteXQmPWZHDr6+VeTnZdJ07+aN9xFGI7bLB8V/9QYD1SfPMPakExmJJPUO+2D6A/RCz0tlLx0cS6+j+mge493LyIhEJEv3DrwNCGg8KP4rdDrsL7+sVPcGgwdOovvxs94FhCCmU71O6LhWeY13xt8hGA4eOInuhxos1FPS3okJ5VT39G+UsnVj4pOCuhnJiGGtJITg1SNF/JcHk3gCIaymxI8kNVg4Wttivt/U1ER7ezs+nw+LJfG8xruWQbKHn9sNS3Mem+9PEnYHk7osbN28BZEIma/GdjivP3uBez/8GzzrLqzZidOq/rAfszSTZYqdrjZnGNhy+QmHIsmLUvwbgEy5SVw1Xn1eUA1V471/+/bt7VTWj370o4QntTfffHPzzTffTKlU98WJ7pDIvH4N7+MnhNYSq2sEQhFuDy7x2pGiuFzX9crrdC93s+hJnMYJh8MMDw/T1NSELt5DuekzymlhfSbhWDIi8Q2tYWnMRehjz+u1lmIGFzaZXEnMA8tIhNFHD6g9eQZDHOubpqYmVlZWWF5OfOKRUjLWtUxlSx5GU2wuIqMln/C6n+Bs4uItKSWbN25gvdiG3h5b9Lru9DncrjUWx5M3xd6evs3potNxH0Q1JwvwbgZZ0KKuMfi2simxxd602q9eJbKxgedJ8rTqe/0LnK7MoSgz9gP+WuU1toJbdCx0JJ/W4CAlJSXxua6mN5RKvrEPko7l61/FWGLFkB+bH3r9SDGBUIQ7w8lPwaOdD8gtqyCvLLbnYlNTE5FIRFMpvPPZEpn5FvLLY6+JjOY8kOAbSq6cs3XzfQwlJViOtsR8v+7seZAS5+Pk994X8qHX6ckwxL5fpmj6MqCledy3DkIPpsOJvf+i40WgOyTs11+BSAT3B4l/8O3OFbb8oZj8nIrrlUoqNFl6aXp6Gr/fT0NDQ/wPqRV8SaovgzNbRLaCWJrjG5m+Fj0hJKuOWxgbxe1aO1AksBuNjUpZc7L00uqsm601PzUJrFwsR/IUr67+xOnLgNNJcGqKzFcOppVU1J4+B0Ik5VHmtuYYXhvm5Yr4tkNVLfnodIKxZOnL9WllMxIjbanC9tIlMBqT8nRLm366Z9Z5pTm+xUxbaRsWvSXp+nK73UxNTcU+zamouaJU9w6+Hf8zQMQXwj++kXB9tdaq1b2J11fA52W6r5v6s+fjfqayspKMjIyk6ysUCDM9sEbtiYK42QBjuR2d3Zh0fclAAPeH9xT+N85YRTV12PMLkqYvg5Eg/rCfTFNm3LH0Rh16gy65SoqU0bRl1qG8Mz8JeBHoDgnL0RYMRUVs3ryV8HM3BxcxG3RccsR/cNfn1FNuL+fO9J2EYw0PD6PT6XaaeGOhoBFya5XqywTwDqwq1XCN8YVeq/NtNBbbkwa6saedIAQ10SbeWMjJyaG4uDhpGfhEj/JwqWo5yBuq0NtNCo8ymHjHvfWBcj/tL8cPTtasbEodjYw9SbzjvjOjjHW1Ir4rucVmpLQhOzlPNxQt5oiRtlSht9uwtZ5LGuhuDymN5dea4gc6i8HCxbKL3Jq6lbDUfWRkBCnl9qYkJgxmcLwKQz+FBKofvmEXRCSWxviBTq3ufX9gkUgC0eLJni7CodB2k3gs6HQ6GhsbGR4eJpxAzGFmyEU4GKH6WPz1JXQCS1MeviEXMkFJv+fxYyIeD/ar8deXEIL6sxcY73pCKBBfUODp4lMiMkKmMX7/nhCKSkrQF04s8hz0QCQEZm0Vu59kvAh0h4TQ6bBfu4b7zh1kggV8e3CJtrp8LMb4JcFCCC6XX+bB/AMC4fhjDQ8PU1VVlZiDEEI51Y3dBn98hQff4CqmysykHMSrR4p5OLbKpi9+tdfY00eU1DmwZiUuX29qamJychKPJ34qdLJ3hfxyO/bcxJ5ZlqY8AtObhN3x5+W+8wEmRz3GssQGpHWnW5kfHU4o8vzB9AeU28upzU7sf1Z7opDVWTcbywnUikZuQE6VsilJAPvVqwRGRglMT8f9zM3BRQozzRwtS/xQu1JxhTn3HGPr8WmQkZERbDZb8sbrxs/A5pxyKo0D3+AqwqLHVJ248VpLde/Ykw6MlgzKm2OnB7en1diYtLp3oncFg1FHWWNi7srSnIf0hQhMxE9Db31wR+F/L8TPZADUnz1PyO9nqjf+/bo7cxeBwGZMnGo0ZRiQUhJIpJLii875RaD7+AQ6IcRnhBCDQogRIcQfxHj/N4UQS0KIp9F/v73rvX8jhBiO/vs3/7wzB/vVl4m43XiePo35/uSKB+eym2tNyXuOLpdfxhvy8njxccz3NzY2WFhYONjbFAsNr0M4AOOxS8rDmwGC01tYmuLvtlVcaywkFJHcG42dxvFubjA3PEjNqXMx398zrYYGpJRxRWID3hBzI+sJd9sqLE25IME/HDs4RdxuPB2d2K8kdzivPaOUgY89jS3W7Qv5eDD3gJcrXk5a/KLOfTKed14ooGxCHK8lTSvZryqnx61bsU91oXCEO0NLXGssTDqvy2WXgZ2T6X6o/FZ9fX18/ldFfbQxevRGzLeljPK/DblJex2vNhaiE8qGMN5YY08fUXXsJHpD4k1ZfX09QghGR0fjfmayZ4XyplwMCTaeAJaGHNALJfMRB1sf3Mbaeg6dLXFwqmg5hsFoYuxZfDH4uzN3MelN22o78WAy6xFCEPAkSF/6N8BoBf2LmsOPRaATQuiB7wJvAC3A/yyEiLVt+zsp5anov7+IXpsH/FvgAnAe+LdCiH9WwyXrhTYwGHDfiR1Qbg8pxSWJ0koqzpecx6gzcnc69lgqyZ6Qn1NRdVFZ6COx1TVUkj0Rf6LiTHUudrNhO0W2H+NdT0DKhGklFeXl5VgslrgFA1MDq0QikupjyedlqshEZzXETV+6HzxEBoPYXz5YbbkfRTV12HPzcD6OzdN1zHfgC/sS8nMqsosyyMy3MBmvD2uqHQJb4Hg96VimmhpM1dVx05dPplxs+EKa1lepvZT67Ho+nImtqD87O4vX69W2kcosVloNRmIHuuCcm8hGQNmMJEGO1cTJypy462t1ZorN5SXqTiffSFksFiorK+OuL9eih/UlL1Ux2mn2Q2cxYK7JittmEJydJTAyik3DRspoMlNx9DjjT2NvYhfcCwytDWHWJ3f+FjqB0aLH740j8hwOKqlLjdqWn3R8LAIdSoAakVI6pZQB4G+BL2i89tPAu1LKVSnlGvAuEJ/0+Aigt9uwnjnD1t3YwenW4BJVeVZq8pMrLFiNVs4Wn+XD2dgPouHhYbKysvaqocSD0aIUDcQLdAOr6DJNe9RQ4g6l13HJkc/twaWYP6zxJ51YMrMocSQPwDqdjvr6+m0uaD8me1YwWfQU1yX/kQqdwNyYi29oLSZfsXXnA4TVSsbZ5AFYCEHtmVYmup4QDh1Mhd6evk2GIUOTHqkQgqqj+UwPrBEOxeCwht8FnVFxnNAA+7VreB48IBIj3XtrcBG9TnC5QVu70aXyS3QudOIJHhxLDQ719fWaxsLxGkw9UKr79kHdfCTi53bj5YZCnk27WHMfTNs7n3QCJOR/90zL4WBubo6trYNpe3XzoWUjBWBpzie06CG0erC/eYf/Tb6RAqg9eYa1uRlcCwfFp+/NKi4a+5vE48GcYSASjhAOxlhf/mj1vflflpN4PHxcAl05sDuhPh19bT/+lRCiSwjxQyGE2kCm9dqPFLYrl/H39xNc3Nsa4AuGuTe6wrWm5GklFZfLLzPiGmHevffHEA6HGR0dpaGhQfNYOF6DtTFY2ZvGkeEIvuE1LE25mse62ljEjMvL6NLecn4ZiTD27DE1J06jS5Jy2Z6Ww8HW1hYLC3sLXKSUTPSuUtmSh16jtJelKY+IO3hAbV5Kifv2B9ja2tDFaXfYj9rT5wh4vcwODRwY6870HS6UXNC04waoaskj6A8zPxpDvWXkPai+CGa7prHsV19WqvseHKzauzmwxNmqXLIztPmMXS6/TDASpHOh88B7w8PDlJeXY0uShttGw+tKwUOMNgPf4CrGMhv6LG33/mpTIVLC3ZGDRTzjTzvJr6giq0Cb5Jh6Io2VvpzoWSGn2Ep2oTZpL0uzciKN1Waw9cEHGMvLMSUqDNsFNVCPPzt4qrszc4eijCKMOm1/R9O2SkqM9KVvQ9G2NGr7jp90fFwCXawn7f7t+Y+AGinlCeA94D+ncK3yQSF+RwjRKYToXErD/iQR7JcV7sP94V5vs87xNbzBsCZ+TsXlcmWs/XJNk5OTBAIBbWklFQ6VR9krGB2Y2ET6wkqvkEa83KicGPanlxbGRvFurCsl+hqhnhj2p5dWZty4XX5NaSUVloYcpc1gcG96KeB0EpydTVhtuR9VR08idLoDD6LxjXFm3bPbfxstqGjORacTTO5Xb1mfgcU+TWlLFRlnzyIsFtz39opPL2z46Jvb4Fqz9vV1pvgMGYaMA+vL4/EwMzOjLS2uoqJVKXbYlzWIeEMEJjc08b8qTlbkkJ1hPLC+Al4P0/19Ka2vkpISbDbbgfUVCoSZGXJRdVT7vAwFGehzzPj28cCRQAB3ezu2l69o3izmlpaTVVjM+D6eLhQJ0T7bzqXyS5rnpTfo0Bt1BH37ClKkVPg58+HaCn5exqvf+ta3ihoaGo46HI6j3/zmN4tSvT4WPi6BbhrYLfFRAczu/oCUckVKqZqZ/UfgrNZrd43x51LKc1LKc4WF2h8MWmBubkZfWID7zl6S/9bgIia9jrY67Q/uuuw6SmwlBx5EmtoK9iO/HnJrDjyIfEOroBOYHdoVEypyrTiK7AceRNttBSfPaB4rKyuL4uLiAw+i7bRSCoFuu81g34471bQSgNlqpayxmYl9upf3Z5UAE0sNJR5MFgOljmwmevfxO+rfokF7oNOZzVhbW3F/uDelrRZvXGvUkMqOwqw301rSemB9qaeflDZSeiPUXVV4ul1paN/wGkS08b/bQ+kEVxoKuD20Nz0+0fOMSDhErYZCJxW70+ORXe0P220FKawvIQSWxlz8I3vbDLydnUiPJ6WNlBCC2lNnoq0SO+nxrqUuNoObKW2kQFljAf++NoOgB2RY6Z87BH4exqsdHR2W73//+4WPHz/u7+/v7/3pT3+a093dbU7FuDUWPi6BrgNoEELUCiFMwJeAt3Z/QAixu9b580B/9L+/A3xKCJEbLUL5VPS1f1YIIbBfuqxYwezq37k1tMSFuryk0kb7x7pcfpn2uXaC4Z0fw8jICNXV1ZjN2lJn23C8pqSWdpmx+oZdmKoy0VlSq8i62ljIA+fKHjNWrW0F+1FfX8/k5OQeM9aJnhUKKu3YclL7jpamPAJTe9sMtLYV7Ef1idMsjI3i2dhJOd6fvU+FPbaVCQAAIABJREFUvYLKrBiSawlQdTSflekt3Ou7DGdH3lW0IguTS6rthu3SS9unVBW3hhYpzjJzpDQ1LuZy+WWmNqeY3Jjcfm14eJiMjAzKUrxfOF5T1PGXd3ojfYNriqxcZWrzermxkKVNP/1zOwpP408eRdsKjqQ2LYcDr9fL3Nzc9mta2wr2w9yQg/SHCUzvzEtrW8F+1Jw8S9DnZXawf/u1uzN30Qs9bWWxpc3iwZRhgP1tBmpbQQytTK34eRmvdnd3Z5w5c2YrMzMzYjQauXTp0ubf/d3f5aRi3BoLH4u6UyllSAjxdZQApQf+UkrZK4T4JtAppXwL+F+FEJ8HQsAq8JvRa1eFEN9CCZYA35RSapSOf76wXbnM+v/4H/h6e8k4cYLpNQ8ji1t8qTW1hyMoZeA/HPohT5cUM9aNjQ0WFxd5/XXtp4BtOF6Djr+AyftQd42wO0hwdousV6uSXrofVxsL+U93x2h3rnCtqQjv1ibzw0Nc+J+0m4NuT8vh4N69e9suDAFfiPnRdU69nvq8LE25bN6YxD+8hvVUERGPB09HJ7lf1m40qqLmxBnu/df/wmT3U5ovXSUYCfJw/iGfrftsymNVHc3j/j+MMtW3SvPFUqUaznkbjv5Kymkl+6VLLMK2eWw4Irk7vMxnjpVo52yjUNsM7s7c5dezfn27rcDhcCRvK9gPtc1g5D0obFLaCobXsDhykmt97sPVRiXTcntoiZayLKWt4Jm2toID09qVHi8vV2h7rW0F+2Gpj6bHh9YwVysnJfeHd5W2AmtqPFjVsRPo9HrGnj2m8ugJQPk7nCw8SZYpixl2ZPtufu/PWZxIkDKUu8xYjdG/WyDau2mKLSFWVF3H9d9MrKf78zJePXXqlPeb3/xm+fz8vN5ms8l33303++TJk26t18fDx+VEh5TybSllo5SyXkr576Kv/VE0yCGl/EMp5VEp5Ukp5XUp5cCua/9SSumI/vurn9d3sL30EgjBVjR9+cGQQqqnws+puFB6AYMwbKeX1Px4SmlLFTVXlAq/aBm4f9QFEswNqXdhnK/Nw2LUbacvp3qeIWUkpbSliqqqKoxG43bKbGbIRSQiqYwh/psMpopMRIZBUeIAPJ2dyGAQ2yXtnIeK4noHZptt27ana6kLT8iTUtpSRX65HWuWaafNYLpD4U8cscV/E8HkcGAoKmIrmr7snllnwxfickPq66syq5KqzKrt9TU/P4/H40ktbakip1I5nUZTsqElL5GNAOaG1E5NAMVZFppLMvkgur5c87NsLi9Rc+J0ymPZbDbKysq2TyIby17Wl7xprS+d1YipInO7XzO4uIh/eCSt9WXKsFLe1MJ4tF9z2btM/2p/ymlLAIRSebydupRSSVtqLAqLh5+X8eqZM2d8v/d7vzf/yiuvNF6/fr2hpaXFo7rbH8a49WNxovukwJCbi+XEcdx37lL4ta9xd2SJsmwL9YXaKut2w26yc6LwBO1zioK40+nEarVSXBxfKzMuzHalwm/kBnzqW/iHXYpaRUXqqQ2LUU9bndJmwOdgovsppowMSh2J1T1iwWAwUFtby/DwMFJKpvtXMRh1lGpoK9gPoRNY6rMVHkVK3PfuI0wmrOe0laPvhk6np/rYKSa6niCl5P7sfXRCx/nS+BqLceclBFVH8xjrWlbMa0dvKjbRdfElxBKNZbt0ia3330eGw3wYrU58qV4737Qbl8ov8Q/D/0AgHDjcRgqUwP3wP0LAs120YXGk1856tamQv7w7xpY/xES34qlYfeLgQ1bTtBwO7ty5g8fjYXpA2QRVxnDD0AJzQw6bN6eIeEN47iucre3iQbsgLag5dZY7f/M9tlZXeOBSKmljbaSSnbwA3Ot+3C4/+eV29MENpco6v0FzRW8s/DyNV7/xjW8sf+Mb31gG+PrXv15eUVERSOX6WPjYnOg+KbBfuoy3q4vgmot7oyu85IgvGpsMbWVt9K/0s+Zdw+l0Ultbm3paSUX9q7DYi1yfwTe8hrkuJ65bQTK83FCIc9nN9JqHye5nVB5VUjHpwOFw4HK5WF1dZWpgjbKGnJ0UTIowO3IJr/sJLXtx379Pxtkz6JJYtcRD9cnTbK2usDozxf3Z+xwrOBbXrSAZqlry8btDLE1sgvMWlJ9Nu5HXdukS4fV1fH193B1epqU0iwJ7ipxtFBdLL+IL+3i29Ayn00lRURGZmWnyOvWvQNgPk/fwj7jQ51sw5KV37682FBIMS+6PrjDZ/ZTMgkJySlLkDaNwOBxIKRkfH2dqYBVbtonckvRK7i2NURWeURfue/fR5+ZijuXXpwFqBmSi+yntc+1kmbJozktvrG03A19I6Z8TOjAdrq3g52m8OjMzYwAYHh42/fjHP875rd/6rdXDGre+CHTPGbaXLkIkwuDPbuPyBLmcQMQ5GS6WXkQiuT1wm62tLe1NvLFQrzgjhLrvEXb5lZL8NKEKU3/QOYhrYY6qY+nttmGHR+nvGWJtzk1FClV6+2GJVpB6n07jHxzEdjH1VKOK6uNKqmzg0T16VnrSSluqqIj2YU33zMHMI6hN/TSnwvaScoJw3b7Do4k1zU3isXCu5Bx6oef+9H0mJyfTP82BosKjNyFHPsDvXN/+W6SDszW5WIw6PhxaZLL3GdXHT6W9WSwvL8dkMjE6Osr0wBoVR/LSHstUmYkw6/EOreG+dw/bxbak3oXxUFhVQ0Zm1nagu1B6IansVzwYjDp0OqG0Gfg3FVcJcbhH+8/TePXzn/98fX19/dE333zT8Wd/9meThYWF4WTXJ8OL1OVzRsaJEwirlfmbdyDnOi850ksrARwtOIrNaOPZoJK+OdSDqPg4ZOTh75kCStLi51Q0FtspsJvp6ewkH6g+nn6gy8vLIysri4G+IaCSiiPpz0ufb0GfY8bzVBE/TjetBJBdVExuaTm9j+4QqY9wsTT9sTIyTeRX2JnqmuKsDEPdtbTHMuTlYWlpYfHmBwQaqhO6YSRDpimTowVH6RrpoiJUcbj1ZbJC5QUCA6NIfxhzmmlLALNBT2tNHj1dvVx0uw+1vvR6PdXV1YwMOzFtHaeyOf15Cb0Oc30Ovr4lQktLWA+xvoROR9Wxk4x1PWbePs9vH/vt5BfFGyvqZhDwhpA6PyKOt2Eq+Hkarz569OiAx1Ky65PhxYnuOUPlhcxdj2kstsc1wdQCo85Ia3ErazNr5OXlxTfB1AKdDmpfxjdrQJ9jxpCf/ryEEFxy5LM11octN4+88tgmmFrHqqurY35pBkumgYLy9HkFIZS+wNAK6HJysbSkVo6+H9UnTrMxOkWmzsbxwuOHGquiOZf5GUlInwWVqXN9u2G7dAlDfw/ZkQDna9I/AYPiUeeed6PT6aiurj7UWNRexbekpHct9YfTWLzkKIBZpV2h6thBt/pUUFdXx/rGGmGd71AZA1DECSJbYYStEPtL6Z/yAaqOn8S3vk6225ByW8F+GC16IhFJCNML2a8YeBHoPgKYz7dRsDrHa4WHNzu8UHIB+5ad4so0ilD2QdZcxR9oxFKpSzt9o+Kl+jyKNqfIdRw99Fi1tbWEIgFya0XK5ej7oTTAG7G1fRqRJm+oovrEaUQowiV5TLMsUzxUNOUSjuiZy/kVxcvtELBduoQuEuaXxQIZcdzXtaKttI1CbyH2Anvq/Zn7UXcVf+QkxvwgOuvh7tel+gIqvNOYiiqxZh9ig8dOJsRY5E25P3M/LNFMiLn5MsbywykNqin/5s1iqjJTb6nZDVO0HzZAJhjS38R+UvEi0H0EGK9WjBcub4wfeqw66jBIA57s+N5tWhGwXERiw5yRfuOniqNmNxkRH6s5iX3ZtCDXFg3i2TGLtFKCzqQ0yxprUq+23A9RlUtESBzrhzsFAJSVBtARYprDnQIAPI0t+PRGLq3Ht6HRikZ7I7n+XNxZmluS4iKSd4KAbMaScfh5NeSbKPPPs5ZzyFMmkJebjy5iRGQ9h/WVpSfiWcZYrV2lJR4yCwtxW8M41vMPvVnU6wUGESAobf/i3cRj4UWg+wjwQSiLdZONcmfPocfyLfiQSPoj/ck/nAT+BSsQwez52aHH8o4r83kaOjwfsDYRRB+0su4/vP6o9+lDwq5J0GmXxIqHztUnLOX4Mc4cPgiYZu5QbBxiei2JmakG3J/apCe/jvKx3kOPNTs1i0AwwEDyDyeBf8IN6J/L+pof7EMvIzwJFSZ0Q9eChbFNjP4c1v2Lhx7L19NDaLEfdAWJ3b01YGB1gJl8D+ZZL5EEbuiaEPRiFB4CYeOh5/VJxItA9xHgrnONiZoWAg8fHPqH5XQ6kVmSBysPiMgYdhwpwDfiwmhbQz/9HkQO98Oa6H5KKLuYD+eCBMOHm9fUwCp2QwEzs1OEQgmMJDXAc/8+0jtNcCFAJHC479g+185WiRHX+BR+zyGDnfMWFbZhFufC+BK4oWvB3eElBkub0E2METqkOLnT6UToBd2hbhY9i8kvSAD/iAuhj2B2vw9rE4caa6LnGegNdIfzGV85XDZjun8VUzAXr9/DYcXc3R/eI7w8CCFBcPagBVAqaJ9rZzbfR8QXYMF5yCxLYBOTUBRRgodc959EvAh0zxnr3iDd0y7EmfOEFhcJjI2lPZbP52NmZoayqjJWfasMrw2nPVbEHyIwtYGl2qx4h809S3usUCDATH8vhU3H2PKH6Jp2pT1WOBxR1OTLqwmFQkxNTSW/KA5kOIy7/QGmCjOEJYHxjbTHisgInQudFDU3ImWE6f5DnM6lhLHbVNSZQMLsUPr3S0pF9kt/VkmduR/ENonVCqfTSUlFCVJIHswdtABKBb6RNUwVZoQIKe7ph8BE91MK65sI6YzbjfHpYmpgjfJiRYbvMAr8AO779zEUKKlBfyz7pRTQPteOpU454U/2pP97VCazidGobKoD+90MXuBFoHveaHeuEJFQ+ymlV2q/rUoqGB8fR0rJ+aNKlZ6qkpIO/OMbEAHzqSblhUM8iGaH+gkFA5xtu4AQ8OFIHBdtDVhwbhDyhzl6qgkhBGOH2Rj09BDZ3MTW1gh6gW8ktuu4Foy4RnD5XZw4eQWD0cRkT1faY7EyAhszFJ9swWDWMxXHrVoLxpbdzK77aLh8Fl1mJp4H6a+J9fV1VlZWON50nBxzzqHWV2jdT2jRi+VoOdiLFT3PNOFZd7E07qTx9BnKsi3cG00/0PncQZYmNqhrKSc3N/dQgS68tYX32TNsF05hKLLiG01/w+IP+3my+IRztRcprK5lovtp2mMRiYB/C53FjsGkJ+g7XFbkk4gXge4548ORZawmPSfPH8VYUYG7Pf1A53Q6MRqNnGg4QW127eECnXMd9AJTczUUtSgKHWliovspQqfjyJlTHC3LimmUqRVTA6sIATVHiykvLz/Ug8ityjJdasNcnYV/OP0HUce8ohF+ofIiZU1HmDrMjjt6r/UN1yhvyGF6IP0ArJ5uLjcWYz1/Hnd7+qew3bJfF0ov0D7Xnnaq3T+i3GuzI1dpiB+7vce2JxWop5uaE6e55Cjg3ugKkTR5p5mhNaSEiiN51NXVMT4+TjhNPszzsAPCYWwXL2KuzyYwvo6M5R6vAU8Xn+IP+7lYdpGqYyeZHeonGPAnvzAWgm4U8dpMTBY9QX847fv1ScWLQPeccXdkmfO1eZgMOmwX2/A8eIhMk3caHx+nsrISg8FAW2kbjxYe7bHtSQUB5zqmikx0Jr3yIJpsh6BmBZ09mOx+SqmjCVOGlUuOAp5MruEJpPcdZwbXKKzKxGIzUltby8zMDD5fevNy32/H3NyMIS8PsyOH4Jyb8FYg+YUx8GjhEWW2Msrt5VQdO8nS5Pge256U4LwFOVWQV0tFcy6uBQ9ba+l9x3bnKuU5GVTnW7FduEBwaorgzEzyC2NNy+nEZrNRVFTEhdILLHoWGdtI70Ttd66jsxowltiUhnj3kmIumwamersxW20U1dVzyVGAyxOkby69NPT0wBpGs57i2izq6uoIBALMzsa0q0wKz4MHCJOJjNOnsNTnIAORPbY9qaB9rh2DMHC2+CzVx08RDgaZHUiz4Mwf5QpN9u02g6D/8OnL52m8qiIUCnHkyJGW69evx1QPf/bsmbm5ublF/We320+r5qtf/OIXa/Ly8k42NDQcTfX/90Wge46YW/fiXHJvy35Z29qIbG7i60v9B+92u1lcXKSmpgZQ+p28IS/PllI/WUT8IQIzm5hVseS6qxDywXTq/I7f42HBOUrVcaWJ91J9AcGw5OFY6um4UCDMwvgG5Y1Kb1JdXR1SSiYmUi9kiPj9eJ8+3fYGM9crvVf+sdSDU0RG6Jzv5FyJwoOpVipTvd0pj0UkDGN3ttVQtuXA0jjVSSl5MLbChVpFxsrapnzXdHg6KSVjY2Pb+qltpUrDcvtselkD/9g6ptpspQ9SFaxOM2sw1ddN+ZGj6HT6bcHqdHm6mSEXpY5s9Hrd9m8p3Qe2u+MhGadOoTObld+SSJ+nezD3gOOFx7EZbcp31euZ6EkzfRnYBKMVdHoMZqWv8nmkL5+n8aqKb3/728UOh8Mb7/2TJ0/6Vb3Mnp6ePovFEvnSl77kAvjKV76y/NZbb6VVqPAi0D1HqFzVS/VKoLO1KQ8P9/3UHx7qw179cZ4rOYdA0LHQkeCq2Aio/Jwa6KovgdCnxaPMDvYhZYSKI8cAaK3Jw6TXpfUgmh/bIBKS2yaYFRUVGAyGtB5Evq4upN+P9YLCZ5oq7AiTLq0H0ahrlDX/Gq0lrQCU1DdgyshgqjeN9OXsU/Cvb+tb5pfZycg0phXoRpe2WN4KbLvVmxsa0OflpcXTLS0tsbW1td1MXZlZSbm9nIfzqQfNkMtHeNWHuTa6vrIrIN+RVqDbWltlbW6GyhZFiaYoy0JjsZ0PR1PngT0bAdbm3NsbKZvNRklJSVrrK7yxgb9/AOt5ZX3prEaMZXbF8ipFbAQ26F3p3d5cmCwZlDY0M9mdxvqKRCDgUfQtAZ1OYDTrD12Q8ryNVwFGR0eN77zzTvZXv/pVTQ+Lt956K6uqqsrf2NgYAHjjjTe2CgsL04rgL7QunyPanSvkWo00lygSPIb8fMxNTbjb71PwvyS329iN8fFxDAbDttuzqm7eMd/B75783ZTG8jvXQScwRQ0jsWQpCvpjt4H/K6Wxpvq60ekNlDUqSusZJj2nq3Jod6Z+opsZWkMIKI0KABuNRqqqqtJ6ELk7OkAIrGeVRnGh12GqyVa+e4pQ+Tk10On0eiqOHEuvIGVc8Sak9mVlXjpBeVMu0wOrSClTahS+H73HaqATQmC9oPB0qY41Pj6uTGuXIn1rSSs3p24SkRF0KYgCq/fYvNteqfZl6PpvEA6BXvtjZrpPOTWrgQ6UjePfdkwSCEUwGbTPazbK0ZbtEjCvra3l4cOHBINBjEbt6i2ezkcgJdbzrduvmeuy2bo3iwyGESkYuT5eeExERrbXFygyZ/f//gf43HtbFlw/GiUwm6C1RYYg6AVDBHTKZiASihAOR1g064GDa8JUZiPnc4kF4j8K49Wvfe1rld/5znem19fXNd2sH/zgB3m/+qu/mn6l2y58bE50QojPCCEGhRAjQog/iPH+/yaE6BNCdAkhbgghqne9FxZCPI3+e+ufd+Y7aHeucKE2H90uGSvrhfN4nzxFBlLjiiYmJqiqqkI1HQTlQfRs8Rn+cGqktX9sHVNllJ9TUXsFZh7v5Pc1YqqvmxJHI0bzjsxQW10+vbPrrHtT4w9nh1wUVmViztj5jrW1tSwtLeF2p9a35nnYgbm5GX32zsPWXJdNaNFDeDO1e9+50EmprZRy+47EU+XRE6zNzbC5muLJdfwuFDSBfaeBvbwxF/d6gPWluBmcmGh3rlCabaEyb8c52nahjdDCAoFo4NI8rfFxsrOz9+intpa0su5fT7mNxe9cR2RE+TkVNZeVlNp8aqeUqb5uTBlWCmt2AvDF+nx8wUjKbSyzQ2sYzHoKq3e0H2trawmHw0xPT6c0lufhQ4WfO7mju2muz4GwxD+RGn/YMd+BSWfiROGJ7dcqjx4HKZkZSFEEQO2H3eV8oMroHaZx/Hkbr/7gBz/ILigoCF25ckVTU6TP5xPvvfde9m/8xm+kX7m1Cx+LE50QQg98F3gdmAY6hBBvSSl3k1tPgHNSSo8Q4neB7wD/OvqeV0qZvsT5c8D0mofpNS+/dXmvJJbt/HnWvv/XeHt6sJ7R5sLt8XhYWFjglVde2fP6+ZLzfL/v+3Qtde3ZDSZCxB8mML1J5tXKvW/UXIY7/x6m2jW7XQe8HhacI5z/whf3vN5Wl89/uDFM5/gqrx7RpskZCoZZGNvg+LW9eoFqqnZiYoKWlhZNY0UCAbxPn5Lza3vnpZ4w/GPrWE9oc+GWUtI538mViit7XleFhad6u2m5cl3TWIRDMHkfTvzrPS+XR1O1s0Mucoq0+YZJKXngXOVKw15/Q1uUp/M8eIA5hl9YvLHGx8dxOBx7xmotVtZU50InTXlNmsYCJdCZVX5ORXXULXv8rpI90Iipvh4qovycCoWTVAL9uRRErGeGXZTVK/yciqqqKoQQjI+Px/RXiwdPRwcZJ0+i26UHaq7NAp3C06ViMtsx38HJopOY9TtjlTqa0BuNTPV2U9y641qe7OTF8rDiKF6442UnI5Ll6S0sdiOZaXoCPm/j1bt379rffffdnPLy8my/369zu926L3zhC7X/+I//GLP66Yc//GF2S0uLp7Ky8rn0SnxcTnTngREppVNKGQD+FvjC7g9IKW9KKdXdQDuQvmT+R4AH+9JKKqznzoEQeB5q5z7283MqThefRid026k1LQhMRPm52n1q8pUXQGdQHkQaMTPYj4xE9qSVAE5X5WAy6Gh3as8yLDg3CIci2/yJirKyMoxG43ZqTQt83d1Inw/b+b2uAKbyTIRJnxKPovJz54r3ahkWVtVgsWem1tg79wwCW8qmYhdyiq1kZJmYGdK+WR1dcrO85aetbu+D3lhdjaGkJKU2g6WlJTwez4H1VWovpcJekdL6Crn8Cj+33xU+sxgKGlNaX27XGmuz01TsW185VhPNJVkppce9mwFWZ93b/K8Ki8VCaWlpSusrvLmJr79/m59ToTMbMFVkprS+NgIbDKwObG8qVBhMJsoampnqS6HgKRKBgBtMe90KRJSnO0xByvM2Xv3ud787s7Cw0DUzM9P9ve99z9nW1rYZL8gB/O3f/m3er/3ar6XfcLoPH5dAVw7slsSYjr4WD78F/GTX/7YIITqFEO1CiF+Od5EQ4nein+s8rBTQfrQ7V8ixGmkq3rvo9Dk5mJuaUgp0+/k5Fbt5Oq3wO117+TkVJpuy007hQTTd141Or9/m51RYjHrOpMjT7fBzex+Qer2eqqqqlB5EnocPFX7u3N7gJPQCc21WSjydWuyz/8QsdDoqjx5nsueZ9l6ziei93RfohBCUN+YwM+TSPJa6ibhQu3cjJYTAduECngcPkBFtPV3qvd0f6ED53p0LnZrl5tSq1gOBDpTvPXFfOdlqwFQMfk5FW10enROrBDT2ran83P6NFCjfe3p6mmBQW6rd8+gRRCJYWw9mUcz1OQSmN4loDCqPFx4jkdsVvbtR0XKcxXGn5r/jTv/cQWsro0VPKKhwdengeRuvJsNu49XNzU3d3bt3s7785S/v2UF87nOfq718+XLz2NiYubi4+MSf/umfahba/bgEulgseswngBDiy8A54E92vVwlpTwH/DrwZ0KImOd9KeWfSynPSSnPFRZqS2VpxYOxVc7X5O3h51RYz7fiefxEM0+3u39uP86XnOfZ0jN8IW19WH7nOqYKOzpzDP635nJKPN1UXzcl9Y0YLQfTIanydLPDLgoqMzHHsHOpqalhcXFRM0/n6ejA3NiIPoZfn7kuh9CSl/CGtnvfMd9xgJ9TUXX0JJvLS6wvLmgaKxY/p6K8MRe3y6+Zp3swtkpJloXq/IOpTmtbG+G1NfzD2ri18fFxsrKyyM09GARS5en8oy6EZR8/pyJFnm66rxtTRgZFNQcNYNvqUuPpZoZcGEy6Pfzc9rRqalLi6TwPOxBGIxmnDvrimetzIBJVHtKAWPycCpWnC4U0ct3b/XMH7/12P12a1Zeq8erIyAh//dd/TUZGRvKLNOLNN9/cvHnz5p4Sztu3b4/U1NQEATIzMyMul+tpfn7+nsn/6Ec/GltaWuoKhUKPFxYWur7xjW9oJsw/LoFuGthNIlUAB7o6hRCvAf8n8Hkp5XZFhpRyNvqfTuAWcPqjnOx+zLi8TK56DqQtVdjOn0f6fHi7k6clVH4u1m4blAdRMBKkayl5BaDCz21hrovj51VzWcnvTyUvTw/4vMyPDis/xhhoq8snIqFDQz9dKBhm3rlxIK20Pa1dPF0yyEAAz+MnB9JKKnZ4uuQPSJWfay1pjVnBWHlMeThpSl+GQ8pppuZSzLd383Ra5tXuXKGtLi/mvGzRlgqPBkdotU+xpqYm5lhqylZr1iAwto65Niu2j+Bunk4Dpvp6KG9Wesr2YzdPpwWzw2uU7uPnVOzm6bTA8/Chws/F2OCZqzPBILaVYZIhFj+nQuXpwloL1wJbYMxQKIh9MJgUz8nACzkw4OMT6DqABiFErRDCBHwJ2FM9KYQ4Dfx/KEFucdfruUIIc/S/FwCXgLQt19PBg+iPL16gS4Wni8fPqThdFOXpNPTTKfycjJ1WgpR4utkoP6f2z+3HqUrtPN3CWGx+TkUqPJ23pwfp8+0p+94NY5kdYdZr6qeLx8+pyCurwJqds10CnxDzz5TTzL60pYpUeDrnspulTT8X4qwvY1kZxspK3A+Tr4nl5WXcbnfc9ZUKTxda9xNa8cXfSGUWKyfasTtJx3K71lidmYqZtoTUeDrvVoCVGTdlcdZXKjxdeGsLX19f3PUljHpMlVmahAk2AhsMrg3GXV8qTxfSklKNw89tz0u/3mQPAAAgAElEQVQIjBZ92ie6Txo+FoFOShkCvg68A/QD/1VK2SuE+KYQ4vPRj/0JYAf+2742giNApxDiGXAT+ON91ZofOdqdK2Rn7PTP7YfK07k1BjqDwUB5HPfiTFMmLXktPJxLPpbSP8dBfk5FCjzdlMrPNR2J+f42TzeWPNDNDrtAQJkjdgBOhafzRB/u+/k5FQpPp62fTt08xOJPQHl4VLQcZ6q/Jzm3pt7T6tiBLhWeLl6h025YW1vxdnYm5XcS8XMqzpee18TTBWL1z+1HzWWl8jQJT6e6Q1S0xN5IgXaebm5YmVd5Q5wAjHaezqvyc3EyBqB8/+DsVlKe7snCkwP9c/tR0XKcSCiU3J9O5edMB/k5FUaznnAoQjhNPc5PEj4WgQ5ASvm2lLJRSlkvpfx30df+SEr5VvS/vyalLJZSnor++3z09XtSyuNSypPR//xP/9xzfzC2yvna2PycCuv5VrxPnhJJkpZIxM+paC1ppXu5G28oMb/jH4vqW8bi51Ro5Omm+3oornNgssTP1Ss83UZSnm5maI2CCntMfm57Whp5Os/Dh5gbGzHE4JtUmOuyCS17CW8k7j/snO+kxFZChT1+QW/lkWNsrSwn5+nG7ypVh5nx2y22ebrFxH/HducKxVlmamLwcyqsra2E19eT8nSJ+DkV54rPsRHYYGhtKOFY/rF1hEWPsTQGP6ei5rKSYktiCzXV14PRkkFxbUwJREA7TzcztIbBqKOoJs4GD+08nfvhQ4WfO3mQn1NhrssGmZynS8TPqVCpgYAvCXcbiP5ezfHv/fPUvfxFR8qBTghhi/a9vQAw6/IysRKfn1Oh8nS+BDyd1+tlfn6e6urquJ8B5cSRjKeLBMIEpjYT77ZBE08X9PmYHx2Km1ZS0VaXj0zC04WDEeadG3HTltvT0sDTyWAQz5MnMavhdmObp0twqpNS0rnQSWtxbH5OhXriSJi+DIcU0ew4aUsVKk+XKH2p8nMXavMTzku9B54Eupdq/1w8fk6FeuJIlr6M2T+3H+o9GE+cvpzu66a8uSUmP6dC5enuJ5EDmxlyUVKfjT6BiopWns7T0YnlxAl0CYoxzFWZoBdJswYdCx2cKDwRk59TUepoAgFBb5JA598CQ2x+ToXK071IX2oIdEIInRDi14UQPxZCLAIDwJwQolcI8SdCiIaPfpofXzwYU/m5xI2sWni6ZPycijNFZ9ALfUJdwm1+bn//3H5o4OlmhvqJhMNJA92pyhzMSXi6hfENwsHIHlmmWNDC03l7epBeb8K0EkR5Oktins657mTVt5q0ET+/ooqMzKzE/U7zXeDfSBrocoqtWLNMzCQoSBlf8bC46U+6kTJVlGMsK8PTET84JePnVJTYSqjMrEwY6MIbfkLL3uQbKXuRwtMlWF+edRcr05NJ19c2T5cgPe5zB1mZ3dreRMSDFp4uvLWFr7c3Lj+nQuHpMhPydNv9c0nWl8FkQm8wJj7RySg/F6OtYM+8RFT30v+iIEXLie4mUA/8IVAipayUUhYBV1Aat/84WvL/LxIPnKtkWQw0l8RPk4A2nk7tn4vHz6mwm+y05LfQOd8Z9zPb/FyC9A2giaeb7utB6HRx+TkVCk+Xm/BBNDO0pvBzSQKdFp5um59rjc2pqRA6hafzOeMHFPWhHo+f2x5LCCpajiV2HE/Cz+0eq7wxh9mhtbg8XbtT20YKlFOdp7Mz7lha+DkVrSWtPFp4FJen29a3TLaRgqQ8nXovkwU6UO7Do4k1/KHYp5TZYRdI4hai7JlWEp7O+/ix4j+XZCMFyn0IzmwSiRNUtPBzKgxGE0G/Pz5PF/CQjJ9TYbToCR+in+6TAi2B7jUp5beklF1S7qx6KeWqlPLvpZT/Cvi7j26KH2+0O1c4X5uPPlH6JopkPN34+DgVFRWaxGbPlZyja7krLk/nd65jKs9EZ9ag8paEp5vq66akrgFTRnK5qmQ83eywi4IKOxZb8u+YjKfzdHRgbnBgyEseBMx1OYRXfIRcsXm6jvkOiq3FCfk5FRVHjrOxtMjG0mLsD4zfhfyGhPycijJV9zIOT9fuXKEw00xtQQIeLArr+VbCa2sE4qjMa+HnVLSWtCbk6fzOdYRZj7Es+cM2GU831deN0WyhqDaJ3BW7ebrYp6eZoTX0Rh3F8Qqwdk8rCU/n6egAo5GMGBqP+2Guy4ZI1CkkBjrmOzDqjBwvSB7M9SbltxH3VKfycxoCncmi2vb8y05fagl05UKI7wgh/rsQ4i+EEF/fLagMIKVMzw30Fxxz617GVzyadtuQmKdT+Tktu21QGsdDkRBPFw96WEUCir5l0rSSiporcXm6oN/H/MgQFXH65/ajrS4vLk8XDkaYH11PeprbnlYCnk4Gg3geP8bamny3Dbt5uoOnum1+Lk7/3H5URnm6mOnLSFg5vSRJW6pIxNPt9M8l5udUqClcd4z0pcrPVVdXaxpLLYH//9l70+DGsuww87vYCXBfQYIkwJ3JXKoqk2RmVmZVd6vVcndIcsu27JYdDmtkW4qYGDtm5LDDssL2j4lRhD0TCvmHZc/IY8uyZ8aLWppReyyN5S6pa8skk8zKyo2Z3EBw33cCxH7nx8MFSRAg3nvIanVX5RfBYCYI3HxAPt773vnuOafQ7t7YnA4/pyji6Rafa37OesEGLEU2n66Ap1uZ3sPbWYXVXnxqK+bpwg8eUHb16oV+TuHwV4JFFAxfjq+Pc63hGi5b8dqTVptdc2uFPF3sUPNzOrpC2BxWbSwTG1JedeNVn893tbe3d6C/v3/gypUrBcNDhZ737W9/uzIQCFxpb2+/8su//MteI/+2noXu94BJToouvwF8IIT4dZW/9kVFz7bv01zk6RYWFgB9YSXQ8umswprXo8TnDyAlcehd6NqGwWLPG75cmXpJOpWkrUD+XC5vXODp1ucPSCYK58/lcpGni05MICORov5EYW/2IMpseT2dXj+nqG/z4yqvyB++1OnnFBd5uvntCOsH5+tbFsLe2orN682GdE+j188pvB4v7RXtefM1Uwdxkps6/JziAk8XOdhne2nhXH3LQlzk6aLhBFtLxf2c4iJPlzoKE31W3M8pLA4rjtbyvBtSDuOHvNh5ofv80nLgXPnv6GSm/1wRP3dmLJN1Lz+Lxqvvv//+VKap6oXt1HOfl0wm+cVf/MX23//935+ampp6/ju/8zu1Dx8+1F2xWs9CZ5VS/ksp5XvAjpTy59GcXQj4Db3/0OeR0bltKlw2LjUXD5PAxZ4uFAphtVqL+jmFx+7hct3lvAud8nNOHeEb4EJPtzTxNOPn9HUSUJ7ufp6FTlUBaenWNxFd5OnUZ1hsx6VCebp8V9zKdeYW2i08loXWS5fz39GF8te3LDjWBZ6uUH3Li8ZyDw0RGRs7N5YRP6dQni6VPns3oKrM6F7o4JSnOxv8OfFz+i6koLCnW53R/JzehQ4Ke7rjR48gldJ9foH2ecSXjkjHzx7Xo42Mn9N5foHWjDWvp4tHgLSusKVC1b1MG/B0n0Xj1VL43ve+5/H7/bGBgYG4y+WSf/bP/tmdb3/727r/o/W06fmuEOJvSCn/KZn6k5kE7/9FCHFxos3nnJHgDjc7anX5OYV7eIi9//jbpONxLA5H9nEjfk4x6B3k3zz/N0QSEdz2E38Wm9vH7qvA4jLQhSlwFz76Nc3TnbpaXJx4RlNHF063vnYyoN3h/pP3ptiPJKg6lSu3PLVLna8cV7n+9xgIBHjvvfcIh8N4PCeeKvJgDEd3F7Y6fYsAaBNRdGKb5F4UW/XJxeDYesbPVehviNF66SozYyMcbm9RUXeqtmzWz+mPrLT01jA9vsH+xjHVTSef80hwm/pyJ10Nxf2cwj00yMF/+k/E5+Zwdp7UjAyFQlRUVFCrw2cqhrxD/M707zC1O8WlupNIU9bPNeufbAnchfF/qXm61pMNP4vPn2JzOmnq1L95+1ZnHb/5cYgnS/sMnWrbszy1h7VI/ty5wwoEuHfvHouLi9lu65ApFG6z4X5LfzVBZ0cVh99bIj5/gKvnJGqh/NxF+XO5OMrKYBd+//f/M5tbpy4aU3Hty/GI/CWCzyPTkmQijc1uQVgEXq+Xb3zjGxe+5rNovArw1a9+tUcIwc/93M9t/u2//bcL1qrMfd7i4qLD5/NlNze0trbGR0dHdZ+Aeu7o/hZQJYQYB1oyHQD+shDi14FX0v31h5H1gyhzW2HdYUtFPk9n1M8phrxDJGWSx5snkl93/lwuefLpND83qTuspFCe7kHoxNOlkpqfM3K1Dfk9nUwmOX740NDVNuTPp5NSMrY2ptvPKfLm06VTMH9P992cIp+nk1IyOrdTsL5lIbL5dKfCl3rz53LJerqcNJZYcB9noBJh1T9WIU+39OIZvj59fk5RyNMtT+3i7ajEZqDbdyFPFxkb0/ycgQs8RyDTny4nfDm2NqbbzynsThdCCNLJnJBjOgXCgt5FDk4asaYNNGJ91Y1XAT7++OOXExMTL/7wD/9w+l/8i3/R+Ad/8Ad5F6p8z8u3k1gIofsNFT27Mjstf0UI8WvAjwJvAjXAM7QCy19IjIaVFMrThUdHcd/QGlIuLCwgpTS80J32dLdbbgMQX9D8nK5t36dRnm7uw2wj1tXpSVLJZMFCzoV4s13zdPdnt/nagLbzcGP+kGQiXbCQcyGUp5ubm8s2Yo1OTJCORHRt+z6N3ZvxdMF9PNe145rbn2MnulOw/mAhGvwBnG4Piy+ecUk1YjXo5xSnPd3ld7TQ9cJOhNX9aMH6loVwBALYGhqIjI1R8zNaw1ejfk7R5GnCX+lnfH2cn738swCkDjU/5xk0tBfgrKe7+4uA5ue2FkL0v/2uoaGUp7sf3OZvflW7E4xFND839OP6m6lCfk+XDoc5fvaMur/6Vw2NZXHasPvO5tMpP/fzV3/e0FjCYsHucvH20CD1re3agzINq0/BUwdVxtpx7q5HkClJbYu+6MCrbrwKoLoT+Hy+5I//+I/v3b9/3/ONb3zj3FbvfM979913j5aXl7MhsKWlJUdLS4vuTZC6K6NIKSOZclz3pZS/KKX851JKY73tP0eMBHeocNoYaNEfJoGMp+vtPZPYq/xca6uxk9dj92j5dOsn+XSx4D4IcBoI3wAZT3cd5j/OPrQ48QwhLPj6LhsaymnTPN3oqQ0D6m5F745LhfJ0p+/o1GaeQvUtC5HP0ynHqXejgMJiseK7dJmliVMbUkKZz86fv2NBweMSgpYcT6cupG7r3Ihyeiz30BCRBw+yY+ktRJCPwabBM57uwv5zxQjc1SrGZPLpll88BzAcMQDtru6ThRNPtzKzb9jPZQ8rEGB5eTnr6SKPPoVksmghgnw4O6qILx4iE9pxZf2cwfMLNE+XPO3pTPi57FhOK8lESrene9WNVw8ODiy7u7sW9ec//uM/rrx27dq53TaFnvelL30pHAqFXC9fvnREo1Hxu7/7u7V/7s/9Od3rj5lal//YxGs+d4wGtxk26OcU7uFhjh99mu1PNz8/b9jPKQa9g2fqXsaC+9h95cb8nCInn25p4imNBv2c4lZnHROrJ/l0K1O71Pk8lJU7irzyPH6//0w+XXhsDEdnJzYTPQWdnVVn8unG1sdodDfSVtFW5JXnabt0hd3VZY52MyHa0EdQ1w2VzYbH8uXk040Gd6gvd9DVYHxScw8PkdzcJJFZ4Mz4OcWgd5DD+CHTe1oNTUP5c7nk5NMtvniKzeHE21W4vmUhcvPpVqZ2sdosNHUYvMDjfD5dZGws4+eK58/l4uysgpQktqDN8+Nr44b9nMKRSWvI7r40kD+Xi13l0+lMM3jVjVeXlpZst27d6u/r6xu4fv36pR/7sR/b++mf/uls0qFqvFroeXa7nV/91V9d+PrXv97b09Nz+ad+6qd2BgcH9TXlRN9mlNfksHEQJbgV5meGjU+OoE1Eu//233L87BmWgQFWV1d5911j4RvFUNMQv/nsN3m8+ZjhuiHii4eU39G3c/Mcgbvw4a/C4ijJ9ndYnZnkra//pKmhbnbWIr+r5dN9pa+B1dl9Lr3dUvyF+Q7rlKe71NvL8fhDKn/yJ0yNpUK6sbl9rG82ML42zq2WW4bclULdiSxNPKX/9l3Nz135M6aOK9ufbnqPqsYyXfUtC6E8XXhsDLvfTygUoqOjw9RYp/vT9df2EwvuGfdzCnWnG/oQWm+w9PwpLX2XsNqMX+Dd7NAW7dHgNkOBWpan9mgy6OcUpz1dR0eH1n/u8mUsHv2bgBTOQCUI7YLA1VXN2NoYV+uvUmYz3rhUebrE8TEuT3mmvqVLV/7cubEcVhCCeDR1YTF1hWq8+qoYGBiIT05OFuwq8/7772e3dBZ63re+9a39b33rW8XbkORB1x2dEOI3hRD/Sgjxm0B75s//Sgjxr8z8oz/sjMwZy5/LRYXcIg8eZP1csULOhTjt6eILh5qfMxNWgjN1L1enX5JKJAr2nyuG6k83OrfN5vwhyXjaVFgJzubTRV+8JB0OG96IorA3exAuG7HZPeYO5tiObhva9n2axkAnjrIybYv82lOI7WvJ9yY43Z9uceeYlf2o7vy5XBydnVjr6oiMjbG9vc3R0ZGpsCWcrXuZOoqT3DCQP5dLRZPW0WH+Y44PD9hcCOkq+5WPGo+Dfm8FI8EdYsdJthYPDftfxWlPl45EOH761FTYEsDismFv0fLpjuJHTOxMmApbwomni0ePNT+XKF7fsvBYArvD8oXtZKD30uBfn/rzXeC3Xv2h/PAwEtzW/JzO/LlcbDU1mqd78IBQZ6cpP6cod5RzqfYS42vj/JXNnzTn5xQOD7Ronm5xt1vzc/368udyyfanC+7wdasW+jTq5xQ2m422tjbm5+eJrK4B+vPnctE8ndYoc3xtDjDu5xQWqxVf3wCLE89gILMBzKCfyx6XEPh6qlmZ3mMnqO26NnshdZJPN87KnPYezS50oH0+353/brZWqMPoRqfTBO7Ck99m6bnWeeOi/nPFuNVZx38YW2Rxchcp0V2IIO9hBQKMjo5y+PChaT+ncHZUcTSywuTKJ6b9nMLhKuNod4d0LIxFpgs2WtU3lo3wfox0Wl7YUuzziK47Oinl++oLOMz5+ytBCPF1IcSkEGJGCPFLeX7uFEL8h8zPR4UQgVM/+3uZxyeFEH/qVR1TIUaC2wwGarBZzbfzcw8PE3n0KaG5OXw+Hw6HcXelGPIOaXUvg7vm/ZwicAeWH7L0/DENgQ4tZGKSmx11PF/ZZ+HlLrUtHsoqzL/HQCDA+vo6O2NjOAIB7I2NpsdSdS9fzD2lscycn1O0DlxlZ3mRyOQHUNtlys8pfL3VHO3GePh8kzqPg+5G85+9e2iQ5Ooqcy9eUF5ebsrPKVR/uo0XCwiHFYfP/HHhvwPxQ5bGv5fxc72mh7rVWctxIsWTR2tYbAKvCT+XPSy/n1QqRXBkBKxWygzkz+Xi7KyCpGTuxUtsFpspP6ewK093lInYOYyHU7NjZetefvG6GZiZqS/uHGqCTH+7Xwe+AQwAf1EIkXsr8deAXSllN/BrZDbFZJ73M8Bl4OvAP/ss++VtHEQJbhrPn8vFPTxEPJFgdXW1pKtt0DYMWJKCxOKR+bCSInCXZDLFyvSk6bCS4lZnHaRhdXb/wm7PelCh3fmlxZKutuFUPt3cPoPeQVPuSqE+o6WXL7SLhBJQFfdXp/e5aTB/Lhf30BASmF9YMJw/l4u6I4nP7eMIVCJKuMBTqReLL57T0tuPzcQGLMVwJrVndWqfpkAlNof5X/usp1tYwHXlMtZy8wuK8nSJ0KFpP6d2zGY9XfQ44+fMf16ap/t8N2JNp9MCOLe11PAZK6W89UqO6CzDwIyUMiiljAP/HvhmznO+yUnI9NvAV4X22/tN4N9LKWNSyjlgJjPeZ8JoiX5O4R4aYquhHklpYSXQ+tMNRDsRKZ1tUy6i7RZr0WpSyZTh/Llc3mqvxietyERaV9uUi/D5fNisVtYrKkte6OzNHqRL0LHfXFJYCaCxowu7w8Hivt20n1PUeN04PHYqDpIln1/O7m4iLS2Ek0nT/lfh9Xi55OzFs+co/UKqwstxZS+bW4clhS0Baj0OLteXI3fjJYUtAcrKyvA2NbGaShvOz8zF4rZjbSrDu1llOD8TNGe4vb2NlBKLxYLd6SKeMJdWcBrN01mJf047GaTTabG5uVmFluN9Bt0xLiHEP5ZS/t1ij5nEByye+vsScLPQc6SUSSHEPlCXeXwk57Umtx0W59l3F/lq3MFlg/lzudhqatju68MipWk/pyh3lPOV9NukSeMMlDgROctZtPYBEl+/sfy5XFx2K8PlbjhImvZzCpvNhtdmZ7OxwbSfUwiLYLfhmGtrvXiL9J8rhtVmo6W5kqW1KtN+LntcQiAanbSFYgwHzIcaQdvIsHddC7+VeiEF8A2rlhTvKCE8qFh2vQGs0XaptPML4HZVOYJ9mrpKPO8Bn9PJJ3W1OK5fL3ms3aZj+tY7qGnQXw1F0draytLSEpubmwDEDveJRWOsH3gQq/lbaeklcpQgFUvh2nJgv6AD+0Wsra3ZUqlUffFnft9JA8+SyeRfz/2BEZnzNSB3UftGnsfMkC+uklvepdBz9LxWG0CIXwB+AbRQhRls4STXEjZT+XO5bHq91G5vYy8hrKR487iPWdcSjfYkrhKzRhaPa2l0reHS0eqkGIGUlS1LnJSj9PfYuL3FUnU1iYpyzAdwNJ57ZnkncRlvunjPuGK0eQ75KOYhIsoxnnF4lmW7pF5a8JrYQp7LpteLa3OTqgL9D43wxnEfxyLKvHuVPkpbVBaPa7GJZbzl+XsDGiGQtrGDZNMFgRLHatzaIm21suP1UtplGTxzz/K27OJyTH8NT4Xdbj+TnL3w7/4Bv/3/POLP/Pf/A51vlHZh9uv//hmbH2zwV/7WDTq7zd0FDwwMPJVSlnYg32eKzmRCiP9WCPEU6BNCPDn1NQc8eUXHsQSc3hHQCqwUeo4QwgZUATs6XwuAlPI3pJSDUsrBBhPJxgA/8aMd2BKSndX8zUD1EovF2AQa19Y4fnZBt2odyESa+t0KnrineLJZ2n9JMpFgdTNCm3sXlgp3Q9dDOpXGtpNg0ZZmPHS+35oRZCpFzZOnIES2pZHpsaTkv/ABAPG5/I0ydZNO05rU0n6WXz4vbSxg9Eg7r1ZnSis6JKVkJZWiYXOT4/HCnej10rhZyYQ7yPjWw5LHWlo7ornsENtS6Xla1q0Yq9Y0Y4ulnV8AVU+fgpQsrK+XPNZ30bpYiEXdOc0FaY49xyoki8HSznuA0UiEez1204vcDyt6Ltn/L+Ange9kvquvG1LKv/yKjmMM6BFCdAghHGibS76T85zvAD+b+fNPA38kNWP7HeBnMrsyO4AeoLQZ+gJaMlXJV/L0DzPCwsICEmjY2CQyVtpEFFs4wJISPPPM5O0fZoS1mUmSyRStnsO8bXuMsLlwRDqRZtUh8/anM0JscpKapSWsFzTK1EvoIMQjnpF0pAs2ytTN5gu8llVsNuvZcmAmWNyJMBE+Bqclb386I+zu7nJ4fEzj4VHetlBGSIUTsBknVL2ebWlklujRERuLi7TVWU5KppkkHk2yuxwmXGVjJHi+0a8R0sfHyEefUm+1lnx+RRIRxvYfsl95nLc/nSFSSewro3gb3GcLiJsgkUrzMLRjuD7v5wE9C92BlDIkpfyLUsr5U1/ZM0uUsqWLbNufvwH8F+AF8B+llM+FEP+jEOJPZ572L4E6IcQMWkeFX8q89jnwH4EJ4P8D/jsp5WdmWyvrXZTXOEueiEKhEBaLhZbqqryNWI2g6lvGfZa8/emMsDTxDITA1+kveSJS9S2r/RXZJHuzhB88wJpO01qgUaYRxtbGSAuJpd1d+kQU+hirkLR0d+fvT2eA0bkdENDYVZW347gRVH3Ldq+35AupeOZiwBIoY3x9nLTU39csl6WXz0FKWvv6tEoyafO/qquz+8i0pKGzioehHRIG+q3lcvz4MTKRwN/SwtLSEsncrgEGeLz5mKRMIvxlxEMHyBKOi9XHED+irbeX9blZYpGI6aGeLe8Tjqe4abIQwQ8zeha6PxZC/E0hxBmpJYRwCCF+RAjxW5zcaZlGSvn7UspeKWWXlPJXMo/9w0whaaSUUSnln5dSdksph6WUwVOv/ZXM6/qklH9Q6rFchNYos4aV6fONMo0QCoXw+XxU3bhB5JNPkAndhbjPEZ/bx95SzlXfGzzZfEI0aT5csjjxlIb2AGXdd2B5PFNI1hwr03vUeN1c76vj2fI+h1Hz7zHyYAx7ezsdvb2sra1xfJyn+7JOxtfGaShroLq3meTWMan9ElzR/EdQ1U7btSE2F0IcH53rTqKbkeA2NW47vVfqOdqJcbBl/j2GQiHcbje+62+RWFggsbZmeqxYcB9ht9De18tebI+ZPfMNOJcmnmK122m+8VWtksya+YuDlaldLBbBG281Eo6neLZs/qIl8mAMLBa6BgdJJpMsLy+bHmt8fRyrsNI80IFMpIkvl7CBJNPWqPXm15DpNCuFq2gVRe0Yf31Hl5+vAyng3wkhVoQQE0KIIDAN/EXg16SU//ozPMYfOFp6qzk+TLC7am4RiMVirKysEAgEcA8PIyMRos/N+R2ZSBNbOMDZUcWQd4hEOsHTLXOTRyqZYGXqpZYbFnhHa/C4ZO4OMZ1KszKzR0tvDbc660ilJePz5u5SZDpN5OFD3MNDefvTGRpLSsbWxxj0DuLq0rYcmA5fSqnd9Qbu0Hr5KkiZrchvhtE5rVB4a58WHi8lajA/P4/f76f8prZ5+XS3DKPEgns4ApUMtmj7D0oJXy5OPKWlpx9bd6a267z5qMHy1B6NgUpu92q+fbSEqEHkwQNcAwMEerUE9lKiBuNr41yqvURlj1bUoKSoQegjqO+l5Y1bWKy2kqIGo8Ftui3tHr0AACAASURBVBo8NFQ4zR/PDylFF7rMndQ/k1LeAfzAV4HrUkq/lPLnpZSffuZH+QPGSQFecxP34uJitv/c6QK8ZogvHkBSq2/5VtNbWIT58OXazDTJeEybtNtvaQ0eTU5Em4tHJKIpfL3VXG+vwW4VjJr0KLHJSdL7+3iGh/H5fFitVtML3fzBPFvHWwx5hzJ1L63mJ6LNSYhsgf8O3q5ebA6n6YloaTfC4s4xtzrrqG324Cq3s2IyfLm3t8fe3h5+vx9nXx+WykrT4fFUOEFiLYKzswpfuY8WT8uZtlBGiIaP2AzNaflzlS1Q22naA8ejSTbmD/H1VtNQ4aS7sdy0B07HYhw/eYJ7eBi3243X6zW90EWTUZ5uPWXQO4i13IGtqYTweCqptTUK3MXudOHt7jXtgZOpNGOhXcP9DT8vGNo/LqVMSClXv8h96AAq68tK8nTKz7W1tWGrq8PR3XWmI7QRTvefq3RU0lfTZ3qhU5N0a/9lcFVC8xumJyK1Waelp5oyh5U3WqtNT0TqbsQ9NITdbqetrc30RKQ26ww1DWl1LwNV5iei+cxnE7iDzW6npbfP9EKnLgJuddYhLIKWnmqWp82fX6DlzwmrFffgoOkNKcrPqUIEg95BxtfGTYXtl19OIGX6pOJOINPxIW3cYa1l/Jwq5Hyzo5axuR2SJnzY8aePkfE47mHtotPv97O4uGjK0z3ZfEIincgWInB2VBEP7ZvzdGuPIX6YrSbTNnCVteA08WPjkaSJ1QOOYqUXIvhhRfdCl9nV+JeEEL8shPiH6uuzPLgfVFSjzOUpc54uFArR0tKSrW/pHhri+OFDpIlfrFhwH3uzB0um9caQd4gnm0+IpYx7p6UXzzQ/V5FJCg7c1UKXCeOuaHl6l+omN54qLUxyq7OOp8v7HMWMv8fwgwfY29qwN2t1JP1+v2lPN7Y2Rn1ZPf5KrVqIs7NK83QHJjxd6GOo9EGNlvPUOnCVzfk5okfGnczo3DbVbjt9TVrRXl9vNYfbUVOebn5+HpfLRWOmHqh7aIjE/AIJE9vmlZ9ztGrHNdg0yG5sl9m9WcNjLSo/19OvPeC/C9E9WDd+l7I8vYfFIvBmKrXc6qwjHE/xfMV4ukjkwQOwWHDfuAFoFwhmPd34+jgWYeGtRi1Z39lZhYyb9HTqItOvLXStA1eQ6TTLky8MD5W9kOr44m1EAWN3dL+HVm4rCYRPfX0h8fXUaJ5uzdjV1Wk/p/AMD5OORIhOGBPNmp87xNl5kt465B0ino4bzqdLJRMsT06c7fbsv5vxdMZCVem0ZHV670zbFOXpHhr0dDKdJjI2fqYaSiAQQEppOJ9OSsn42rh2N5fZKJyte2n0rk5KbSLy34HMWG0DmqdbMpFPNxLcYShQm60qr0parZi4qwuFQvj9fiwW7ddb3amYiRrE5vZx+CsRmSoa6k7FTBrL0sQzmrv7sKkC5qo2qImowcrULg3+ChyZAuZqJ6GZqEFkbAxXfz/WCm0xz9ZVNREeH18fp6+mj4pMlwHT5xdoF1J13Vp7I8DXewmL1WoqzWB0bpuOeg+NlcYrtXweMLLQtUopvyWl/J+llL+qvj6zI/sBp+VUo0wjLC4ukk6nzyx0ahI36lHii4eQTJ+pb3m96ToCYXjDwNrsDMlY7Gx9S+XpDE5EW4uHxKMpWk/VH7zur8ZmEYYnotjUlObnbp7UH2xtbcVqIt9p/mCezeNNBk+V/bK3lCOcJjzd9gyEN84UcvZ292GzO1iaMHaRsbx3zMJOhNunwkq1zR6cHpvh8OX+/j67u7tnzi9Xfz+WigrD51c6kiCxFj5zfvnKfTR7mg2Hx2ORMBtzs2cvpKpatbthgx44Hk2yETrE13dyfjVWuOhs8BjekJKOxTj+9FPcN08qDrrdbpqamgyfX7FUjMcbj8+cX9ZyB7ZGE54ulYSF+2fqp9pdLrxdvYbD46m0ZHRuJ9us9ouIkYXunhCitCq/nyOqGsrwVDsN5zud9nMKW309js5Owx4lFtzT/Nyp+oOVjkr6a/sNX3Grq8QzjVbLqsF7zfBEtDyZ8XOn7ujcDhtvtBn3dGpyPn1HZ7fbaW1tNXzFnfVzpwo5a/3pTHi6nLASoHm6vn4WnxsLxY1mPpPT/kRYBL6eGsMbUtRncrqQs/J0Rhe62Nw+SHCeqiMphGCwaZCH6w8Nhe3P+TlF4I72WRrwdGvBfdJpea6R763OOsOeLtfPZQ8rEGBhYcGQp3u6+ZR4On6ukLOzs8p4Pt3aE4gdZP2conXgCmuz01ozVp28WD3gMPrF9XNgbKG7C3yS6fn2RAjxVAjxqkqA/dAhRGbDwNSeoV945eeczrNbfN3DQxw//MSQp4sF97F7T/ycYtA7yOONx4Y8XTZ/riKnaG/gLiw+gIT+3LxcP6e42VHL06V9wgY8XdbPtbScPaxAgNXVVaJR/cc1vjZOfVk9gcrAmcdNebr5j6G8Ceq6zjzcOnCVjfmgIU83EtymqsxOv/dsU82W3moOtqIc7uh/j6FQCKfTidfrPfO4e3iY+Py8IU+X6+cUQ94hdqI7BPeDBV55noXnT7DabDT39p39QeAdzdNt6A/3Lk+d9XOKmx21HMaSTKzq93S5fi57WBlPt7KSt5pgXsbXxxEIbjSdHUvzdCljnk5dSOUsdG0DVzP5dPo9XTZ/7guYKK4wstB9HehGK+78E8CPZ75/YfH1VnN8EGdvXZ+ny+fnFJ7hYdLhMNEX+k7gEz93vsDuUJPm6Z5u6gtxZP1cvrY8gbuQimnJ4zpIp9KsTu+du9oG7Yo7acDTZf3c8PluBX6/35Cnk1IytjbGYNP5/nOGPUo2f+5u1s8p2i4Z93QjQS2slNv1OevpDNzVzc/P097envVzCjOeLjZ71s8pVGjOSPhyaeIpzb392B05OVyq44OBKjwrU7s0Bk78nELdsRhJY4k8eIDr0iWslWcv8FTRdyPhy/H1cXpreqlynv2dNOXpQh9BXQ9UnL1gaenTPJ2R8OVIcJv2WjfNVcb74n1e0FPUWQma58BTtF4/zzJ/L6243w85aiLSm2aQz88pjHq6rJ/rOr+gKE+nN3yZ9XP5Gq223waE7oloa+mIeDSVtz/YDX+NIU+X9XN5+oMZ9XTKz+XrP2dvNujpdoJwuJK3LY+3u9eQp1N+Ll9Yqa4l4+l0nl+Hh4dsb2/nPb+ynk5nvqaWPxfOeyHVWt5Kk7tJdz5dNHzExlww//lV3QbV/mwFkGIoP5evv2FTpYvOeo/u8ysdi3H8+HHe/oYej4fGxkbd51cilTjn5xSapyvTf35l/dzdcz9yuMpo6tRfbi6dloyFdrj1Bb6bA30J43cz3yuklJWnviqklKU3p/ohpqqxDE+VQ/cVdz4/p7A1NODo6NB9xZ31c4Hz/wVVzir6avt0b0jJ6+cUZdXgvap7Isrn5xQep42rrVW6Nwzk83MKh8OBz+fTPRE9WNPGGvaen9SENePp9FZIUc4yz0Rkczho7u1nUWdibz4/lz0ui6Clu1q3Bz6dP3duLKsV940b+i+kVP5cnoVOCMGQd4ixtTFdYfuCfk4ReEf7THV4ukJ+TnGzs5YHoR1S6eLHVcjPZQ8rEGBxcZFUqng9zufbz4mmogUbrTo7qzOeTofmKODnFG0DV1mfnSahI2w/uX7IXiTxhSz7dRojeXR/XghRkfnz3xdC/K4Q4q3P7tB+8NHy6WpYntbn6Qr5OYV7eJiIzny63Py5XAabBnm8+Zh4qngvsoJ+ThF4R8unSxZ3WMvTu9R4z/s5xa3OOh4v7hGJF3+Phfxc9rAMeDpV31Llz+Xi7KwiuXlM6kBH77bQx+BpgPrevD9uG7jKRihINFzcyRTycwpfb41uTzc/P4/D4Tjn5xTu4WHioRCJ9Y2iYxXycwrl6eb254qOdS5/LpfAHTjehc3iYftCfk5xq7OOw2iSFzo8XdbPDeZfnAKBAIlEQpenU2HcXD+nUJ4usaLD0xXwc4q2gaukUymWp4p/XupC6ovs58CYo/sHUspDIcRd4E8BvwX8r5/NYf3w4OutJrIfZ3/j4l1QF/k5hXtoiPTREdEXLy8cK1vfsjP/VS1oE1EsFSta9/JCP6cI3IFkFJYv7kWm/Fy+sJJCr6e7yM9lDyuTT7e4uFjwOaD5uQdrDxjyDp3zc4qsR5krEiaUUrv78L99zs8pVD6dnv50hfycwkgaSygUor29HavVmvfnKkSnJ3wZC+7jCJz3cwp156InfLk08ZTmnlP5c7n49efTFfJzCnXnoid8qepbqvy5c4eV2bmqJ2owvj5Od3U3Na78575K0YgFdYShC/g5RUvfJYTFoiufbiS4Q2tNGa01pbYE/uHGyEKn7t9/HPjnUsrfAwqcuV8cTjzdxRP3RX5OkfV0RSai2MJJfctC3Gi6oXm6IhsGLvRziqynu3giOvFzhRfgG/4arJbidS8v8nOK1tZWLBZL0Ylo7mCO7eh2Xj+n0O3p9uZhf/FMflMu3u5erHY7i88vnogu8nOKel85Tret6Pl1dHTE1tbWmbSCXFyX+rGUlxcNX17k5xRtFW00uhuLnl8X+jlFjR+q24ueXxf5OYW3ykWgzl20P91Ffk7h8XhoaGgoen4l0gkebTwqGLYEsFbo9HQX+DmFo8yNt7OnaHhcSsmDL2j/uVyMLHTLQoj/DfgLwO8LIZwGX/+5pKqxDHelo+iGgYv8nMLe1IgjECg6EWXrW3YUnoiqnFX01vQW9XQX+jmFuxa8V4pORFk/11N4oSt32rjqqyp6xa1cZT4/p9Dr6cZWtbHy+TmFsAqcgcriE5HalJNnI4rC5nDQ0tNfdMPARX4ue1yZupfFGv2q/LmLLqT05tOd+LnC/496PV1RP6fw3y3q6Yr5OcWtzjoezG1f6OmK+TmFyqe7yNO92H7BcfI470aU0zg7q4nNFfF0a48v9HOK1stXWZuZIhErHNKe3jhiJxz/woctwdhC9RfQGqN+PVPUuRb4O5/JUf0QofWnq2alSN3LYn5O4R4eJjI+jrzgFysW1PrPWcryh28UQ94hPt389EJPV9TPKfyZfLoLPN3y1MV+TnGrs47HS3scxwu/x8jYxX5OEQgEWFlZIRYrfFxj62M0uhtpqyh8kQHaRFTU081/DGW10FDAN2Vo1eHpivk5RUtPNfubxxztFp7UQqEQdrudliKfl3toSPN0G4U9XdbP+covHGuwaZDt6Dahg1DB5xT1c4rAXYhsw2bhsH0xP6e42VnLQTTJy7XCnq5Q/ty5w9Lh6VT4tpCfUzg7dHi6rJ8rHDEAaLt0hXQqycpU4c9LXUze/gIniit0L3RSyoiU8nellNOZv69KKf+w1AMQQtQKIf6rEGI68/1cXEII8aYQ4r4Q4nkmWf1bp372r4UQc0KITzNfb5Z6TEZp6a0hfIGn0+PnFMU8nUykiC8cXBhWUgx6B4mlYjzbyh/i0OXnFIG7kDyG5U/y/vh0/7li3OysJZGSfLKQPxwn02kiD8aKXm1DcU+n8ueGvcMF/ZzixNNdcFcX+kjzc5aLf3XaLhf3dMX8nEJPGsv8/DxtbW0F/ZxCj6dT/ecK+TlFtu7lBeHLon5Ooe5gLqjCU8zPKU48XeHwZWR09EI/p9BT93JsbYyOqg7qy+ovHEtXPl2m/5yqb1mIlr6Bop5uNLhDS5WL1povbv6c4gch9PhLwHtSyh7gvczfc4kAf0VKeRktcf2fCCFOxy/+jpTyzczX970/ngqlFPIoevycIpvYW2Aiii0cQkrmzZ/LZbBp8EJPtzYzXdzPKfxva9/n84cvT/efK3pcGU9XKHwZm54mVcTPKdra2i70dMH9IDvRnQv9nOKk7mWBBWVvUXN0RcJKAM3dfZqnK+BR9Pg5RV2r5ukKbUgJh8NsbGzoOr9OPF3+cyJ1FM/0nyv+/9he0U5jWWPB8LguP6eo8UNVW8E0Fj1+TtFSXYa/zl3w/EpHo0X9nKK8vPxCT5dMJ4v6OYW1woGtoazw+ZVKwvzFfk7hdLsvzKeTUjI6t83NzrqiF3hfBH4QFrpvou3gJPP9p3KfIKWcOnUnuQJsAA3ftyMsQnWTm7JKR8GJSI+fU9ibmnD4/QU9yun+c8WoclbRU9NTMHF8UY+fU7hroamwp1OL/EV+TlHhsnOlpbLgRBQZLZw/l4vD4aClpaXgRKTy5/QsdEU93dwH2veOLxUdS3m6Qlfcys/d7iq+0FksguYL8unUe+/o6Cg6lrDZLsyni81p4T49EQMhBDe8Nxhfz9+fTrefUwTuag40z1h6/ZziZkctD+Z2SOfxdMefPkYmEroiBnCxp5vYniCcCHOz+WaeV57H2VlFrFA+XU7/uWK0XrpS0NNNrR+xdRTXdX59EfhBWOiapJSroIVDgcaLniyEGEbb7Xm6IdavZEKav5bZJPN9RXm6QnUv9fo5hXt4qKCniwX3sPvKsRQJ3yiGvEM83nhMIpU49zPdfk6h6l4mzzuslak9XX5OoeXT7ef1dHr9XPawLvB0Y2tjeD1eWstbdY2Vzac7zOPp5j4Adz00XtI1VuvAFTbm8nu6keDZ/nPF8PVWs79xTHjv/Hucm5vLLvh6cA8PE5+by+vpYsG9TP7cxX5OMeQdYvN4k/mD86E93X5OEbirdWzfnDz3I+XnmnVEMkA7v/aPE7xcOzz3M71+TuH3+4nH46yurp77mZELKdA8sIwV8HR5CoVfRNvlq6SSSVanz39e92a3AHj79UIHfJ8WOiHEd4UQz/J8fdPgOM3AvwV+Tkqptmf9PaAfGELbIPN3L3j9LwghxoUQ45ubmybfTX58vTWE92Lsb571dEb8nMI9PEz68JDY5NkTWPNzh7rCSoqhpiGiqSjPts+G0FLJBCuTL/T5OYX/DiQisPLozMNG/JziVmcd8VSaRzmezoifUwQCAdLp9DlPl5ZpxtfGdfk5hfpsz93VSaktdB3vFMyfy6Vt4CpSpll+eb7PoF4/p8h6uunzd3Vzc3P4/f6ifk5xkafL5s9Z9U0NQ02F+9MtPn9CS09/cT+nyObTnQ9fan6uErtT33u82Vk4n65Y/lwu6nc3X9RgdHWU3ppeal36djZe6Ol0+jmFr+8yQljyhi/vz2r1Lb/o+XOK78tCJ6X8USnllTxfvwesZxYwtZDl3Q4mhKgE/jPw96WUI6fGXpUaMeA3gYKBdynlb0gpB6WUgw0NrzbyqUJ2ueFLI35OoUJ2uW17YvMZP6cjrKRQO8FyPd3azDTJuE4/pygwERnxc4rBQA0WcX4iMuLnFG1tbQghzk1Es3uz7MZ2dV9tQ8bTOfJ4uu1Zrb5lx7u6x2ru6c94urMTkRE/p6hrLcdRdr7u5cHBAdvb27rClgrXpX4sHs+5hS51FCe5rs/PKfyVfurL6s95umj4iI1Q8Gz/uWLUBKCy9dyGlGz/OQPnl6+6jLbaMkbnzp5fRvycory8nPr6+nPnVzwV59HGowvTVnIp6OkM+DmF0+2msaOLpRwPnEpLRoLbr+/mTvGDELr8DvCzmT//LFon8zMIIRzA/w38Gynlb+f8TC2SAs3v/YkUmq7xuimrsJ/zKEb8nMLu9WJvbz+3YSAW3AOLPj+nqHZVa54uZ6Ez5OcUnjpoHDg3Ean3nK+QcyEqXHau+KoYyal7acTPKZxOJz6f79zOOKNhJVB1LyvP77yce1/7rsPPKWwOB809fec8nZ78uVwsFkFLd9W5fLq5Oa0El5GFTthslA3eOH9+qfy5Lv0XUkIIhpqGGF876+mWXz4HKc828i0+WMbTfXTG0534Of3nF8CtjjpGczydUT+nyOfpHm9qrbD0+jlFXk9n0M8p2i5fZXX6JYn4SUh7YuWAg2jytZ87xQ/CQvePgK8JIabRWgD9IwAhxKAQ4n/PPOcvAO8C/02eNIL/UwjxFK2zQj3wP31/D19D83Q1rOR4OqN+TuEeHtLqXp5KoI0F97H7KnT7OcVQ0xCfbnx6xtMtPn9CvRE/pwjchYURODXW8qTm59yVxgrl3Oqs49OFPaKJk8kj/GAUe2urbj+XPaxAgOXlZeLxE7c2vjaOr9yHr9xnaCxnZxXJjRxPN/cBVPqgttPQWG0DV9mYCxKLhLOP3Z815ucULb017K1HCO+fTGpzc3O4XC6amvSFuxSe4WHiwSDJUyH8WHAf4SieP5fLoHeQjeMNFg5PWiYtPs/4ue6+C16Zh8AdCG/C1lT2oeXJTP6cgQUYtPDlXiTB1MaJpzPq57KHFQgQj8dZW1vLPvZg7QEWYSmaP5eLs7NK83SrpzydQT+naL10RfN0UyeaQ/m51wvdCX/iC52UcltK+VUpZU/m+07m8XEp5V/P/Pn/kFLaT6UQZNMIpJQ/IqW8mgmF/mUppYHuhq8WX281R7snni4ajbK8vGzoalvhGR4mvb+f9XTpeIr44iEuA2FLxZBX83TPt7WcrmQ8zsrkC9qvvGF4LAJ3z3i6VCrN6sye4att0HbGxVPpbD6dTCaJjD7Ac/uW4bH8fv8ZT5eWacbWx3Rt+84l6+nUXV06rYVrO97V7ecUytMtvdACDVJK7s1uc6ujTrefU6jQnbqrk1IyNzdHR0fHuf5zxVChu9Phcc3PVen2cwpVEeR0+HLBqJ9TqDuaU7t7l17u0NSp388pbnZo3mxk9iR8GR4ZwXX5sm4/p8hX9/LB6gMu112mwmFsrOz5NXvq7jz4PtT36fZzCl//AEJYWHpxEjW4N7tNT2M5jRUuQ2N9nvkTX+g+T7T2a79YSy+1iXt+fh4pJZ2dxu4C4Hx/uvj8gWE/p8j1dCtTL0gm4uYWupwCvBtzByRiKVr7jS90g4FaLOKkUWZ0YoL04SHuW8YXuvb29jOebnp3mv3YPsPN+v2J4sTTZRa6jQmtaocBP6do7unH5nCy8PQxAPPbEZb3jrnTbfxqu76tAofLmg0V7+7usr+/b+pCyjUwoPWnG9F0d+pQ+Tnj51dHZQd1rrrshpTIwT6boaC586umQ7tzzpxfsUiCzYVDWvuMn19ttW5aa8qyiePpcJjjJ0/wmDi/KioqqKury55fkUSEJ5tPDPk5hbXCga3JTXQms9Al41p9y079YXGFy1NOY0dnVkXEk2nGQjuv/VwOrxe6V0hVYxnlNU6WXmq/WMFgEJvNRmurvq3tp7E3N2NvayOc2TAQm9kDq8ARMD4R1bhq6K7uzi50C88eIywWY35O4amHhkvZnLKlyV0Q4DMxEVWV2bncclL3Mnxfm3TNTEROp/NMPl3WzzUZczGgeTpHoPJkw4DKnytSlikfNocDX/8A80+1OgYfZ8JKd7ovrqKRD4tF0NxTnd3wZMbPKYTViufWTcIf30NKqZ1fgKtb/4aP7Fg5dS9VMev2qyaKFAmhXUxlPJ2WsnNyEWmUmx11jM5tk05LIuPjkEziefu2qbFOe7pHG49IyqSphQ7A1ZXpT5dIay2wEhHo/LKpsVovXWF1epJkPM6TpT0i8dTrsGUOrxe6V4gQgtb+GpYmd5FpSTAYpL29Hbs9f8+4YriHh4iMafl00Zk9HO0VWAyGbxSq7mUinWDh6WOau/twuk1uPe78kubpElEWX+zQ0FaBy2PuPd7qrOXRglb3Mnz/Ps6+Pmx15n5JOzo6WFpaIhqNMrI6gr/ST3N5s6mxzni6uQ+0O41q/RuKTtN+5Q22lxY42t3h45ktmqtcdNR7TI3l66lhd03zdHNzc9kdgWZw37pFYmWFxOIi0Zk9LG4b9hZjfk4x2DTIRkTzdAtPP9Uq7Hf1mBqLjncgvAGbkyy92MHmtNLUYa7H853uOnYjCSZWDwjfu49wOCh7y1wbzUAgQCwWY3V1ldG1UWwWG282mqs46OyuzrbbIvg9EJYLC4VfRNvlq6QSCVamXnBvdhsheN2xIIfXC90rprW/llg4yfzUOpubm6bClgrPrduk9/eJPHpGYuUIV7fxuybFkHeI4+Qxny6MszY7TftVE2ElRedXIHlMPDjK+twBbZfMH9ed7nriqTRjk6scf/KJqbs5RVdXF1JKgqEgY2tj3Go2P1Y232l2V9tlaiJsqfBn7mzmnz7m/uw2d7rrTZdlUiHixYntrJ8zO5bntlbW7ejeCLGZPZxd1QiD3lChdh6OrIyw8OwxbZevYtGZ13eOzi9r34N/zNLkLi3d1ViL1N0sxN3MnfPHM1uER0You34di8ucu1J3zsFgkAerD7hWfw233dzForOzCiyZSM3c+9ByHcqM300DtF66irBYWHj2mHuzWww0V1Lj+cJ3UDvD64XuFaMmoifjWpJwSQtdZlPG0QcTILWrQLMoT/dg7A+RMm3OnygCd0BYWR17Qjolae0z3wZkuKMWh9XC5Hsfa21TTGxEUbS2tmKz2Rh/Ps5x8rikhc7hy3i650GtbUoJC11joBNXeQVPHoyxG0mY8nOK+tZyXOV2pp4uEA6HTYUtFY6OADavl8joU1L7MV31Uwvhr/TT7GlmbPJD9tZXSzu/qtuhtoujFw/YXYuY8r+KxkoXvU3lfPI4SGxyEs9tc2FL0PLpvF4vUzNTvNh5YTit4DQWlw1HawWxqW1YGjfl5xROt5vmnn7mHj/ik4W9134uD68XuleMp8pJbYuH+YUQLpcLrzd/l2A92Orrcfb1EQsdIZxWHK3GdnedptZVS39tP8vPn2FzOPWXZcqHswJah1iaPsBqs9DcbdwbKtwOG9f91cRGR8Bmwz1o3Kkp7HY7fr+f+dA8FmExlD+Xi7BaNE83l9maXsJCJywW2i9fY3XiCUjJ213mQo3aWFp4PBQy7+eyYwmB5/Zt4iFto7IZP3d6rFvNt1jJJC/7zfi503R+maVpLSWjlIUOtKhB6qHmp83s6D1zWJ2dLC8tI1LCtJ9TOLuria+ESaddhvIz8+G/+gYbczOI2HFJ59fnldcL3WeAr6+a3eN1AoGAI3X8AgAAIABJREFU4W3fuXjefhtkLQ5/OcJaWhXy2823sS4e0NzXj82kN8zS+WUWt714A25sDpMhqgzv9DTQOvcc++UrWMvNuavsYXV2kjpMca3iGlVO8wswaBN/8qiMVM1NKL+wBGtR2q++iQzv8UZlgqbK0rZ9t12q5Si9TWVFFTU1pS0Cntu3EBUBLB4L1rrSjut2y21q1gXOygpqfeZ8ZpbOL7MU6cNVpnVZL4W73fVcXpsk7SnHdflyaYfV2YlMS5rjzVxruFbSWK7uGpCCmLgObebvDgH8V98CKWmPLTPU8brRai6vF7rPgOo2K2lrjFqTGyFO43rzNhZPIxZ74SaSernuuUz1kR3pN3/lrjj2fontZAetDRd3CtfDnSYH3XtLrHUbqKJRAG+bdgd9zVLaJATg7NAW3WjFT5Q8VnOmFNaws/TPq6W3ioRjj2p3aYsvQNnwTWz1fQjrbsntXIYaB2nedpFuryp5LBm4y1L8Gq3126a9oeJmZx1vbs6w3nkZYdYbZmhvbyct0gyIARzW0jyYo70CIeJEy74G9tIuMrzdvSStDt6wbFDuNFZQ4ovA64XuMyAitMnMemRup9hpLOVaompiqfQ2ezXr2oQRqi590Vw6DADQaincdFMvgaVJrEhGa7pKHmuBBWKWGNXh0hdze+IpFnaJJk2kYeQwG3Wxb6ug8VT1ELOE43tISxJbpLQ7VgCSboTDQ2LpcclDya0jyuJWQjUXNBbVyd6Bk3C6jlZL/nZCRnBsrOKN7PCgxrwvV+wn99lyblEbLv2uSRxv4hBPiCX0dcO4iKOEZNHZTHM4fwPiLzqvF7rPgIXFeezCxfZcsuSx4gsRZCpM5MEflTzW6sRzUk7B/eSTksdamjrAYY3RuPOdkseKjoyQsDv5vVhN3jZHRhhdG2Xbvc3+6n7JY4ngH+GyPia2VobM09fMCPdnt1ku8xFdmCSdPt+ayAizs1qHqvCik1QqXeTZF6OSlo/H/wvpPG2OjLDwTFssHzimiSQiJY2lii60Rv5fiJZ2YRa+dx+A/+xoYz9yvl2VEe6t3GOjbIPEfoKjoxKLMM19gMvyWAuP75f22d+f3WLB1QoHW+xvrJd2XJ9DXi90r5h0Os3c3ByNtT62Fg6JlfCLJdNaIq+1MkHsxQuS2+bDXlJK5p89xtXZwuxBkPVwab8MSy938LXEsexOw15pdynhkREi/VdZOEwQ2i5tghxZGcHd5Obo8Iitra2SxmLmPZwNB6QjSRKr4eLPv4CPZraw+PqIR8JsBGeLv+ACZmdnqa1qIB21sj5X2iIQm9nDUi5JH2xy/Ki0qMH8009xNdSy74zxycYnJY21+GKHiiqotKycKyJulPDIfdJ19Sx6GrgfLO2cuLdyj2iV1uhUJeybJvg9nC7tXMhWSTHJB9Nb7FQFALLFCV5zwuuF7hWztrbG8fExvX3dSMm5tipGSKyFSYcTlF3VXF94ZKTIKwqzu7rC0fYWfW9m8p1WzY91sHXMwVaU1muZYsnB902PlVhfJx4MUveOliz70Yz5iWgjssHs/iyXe7UNB+rOxxRHm7D2BNeA9h5jM/m7e+vhMJrg8dI+fZlE5VImolgsxuLiIr39PQgBSy92ir+oADKRIhbap+xyI1ithEfumx4rlUyyNPGM7jeGsFvsjKyYP7/SacnK9B6tA40IexnM/rHpsWQ6TeT+CFV33sbjtJV0fqVlmpHVEa50XsHlchEMBk2PhZQQ/B72bj8Wjy1bmcbcUJIPpjYZuNRNeU3t64UuD68XuleMOvnfGBrA5rSWNBGpk7/i3QEslZWE790zPdb8U60I8+Dwj1HrquX+qvlJLRtWutEP5U1aZQeTqLBS64++i6+6jI+nzU9Eo6ujANztvktNTU1pE1HmPVkvv6PVJZw2PxGNBndIpSVvXw3Q0B7IhvjMEAqFSKfT9PX30OCvzP5fmCE2fwBJietSI2XXrhG+b/6cWJ2ZJBGL0nntBtcbr5d0fm3OHxKLJGkdqAf/2yWdX7HJSVJ7e5S/fZtbnXV8PGM+KjK5M8lOdIe3fW/T0dHB7Oys+fD4ThAOlhCdX8LZVU10ds/0WKHtCEu7x7zT10j71TdZePb4TNeT17xe6F45s7OzNDY2Ul1TRUt3NYslTETRmT1sDWXYat14bt4kfO+++V+Gx59Q1dhEbbOPm803GVkZMT3WwsQ2nmonNc0erYpF8HtahX8ThD/8EGt9Pa7+fu5213NvdouUSR82sjpCtbOavto+Ojs7CYVCZ/qHGWL2j6CsBprfxNVTQyy0TzpubqwPpjcps1u54a+h/eqbLE9OnOkfZuiwZmex2+20tbXR1l/D2twB8WNzLjg2swcWgbOjCs/t20SfPiN1YC4UOv/kU4Sw0Hb5GrdabjG1O8XWsbmLloWJbRDQ1l+rnV9bk3CwYmqso4+04tCe229zp7ueua0wS7vmwuP3VrQLzdvNt+ns7Mw2vTXFzHva964fwdldTfogTjLT9cQoH05rrZbe7anHf+0toocHbMyXGFb9nPF6oXuFxGIx5ufn6e7uBqDtktY/7HAnangsmUgTn9vPVkPxvH2b5OoqiZzmonpIJRMsPntC4I0bCCG43Xyb7eg2U7tTxV+cQzqVZvHFLu2Xa7Ut5J1fhsgWbDw3PJZMpQh//DHld+4gLBbu9NRzEE3ydNn4rj0pJSMrI9xsvolFWOjq6iIej7O8vGx4LKTUFrrOL4PFiqunGpKSeMjcIvD+1CZvd9XhtFnxX32TVCLB8gvjnxdoC10gENCKhV+qRaYlyybvNqOTuzj8lVicVq3QcTptOjwe+nSc5p4+XOXl3G7Wqo+oO2yjLDzfprG9grIKx6lyYN8zNVb4w49w9vVhb2rkbs9JOTAz3F+5T09NDw3uBrq6tB3CpqMGM9/V6qfWdWVL+0WnzF0UfzC1RXutG3+dJ1uRZv7JI3PH9Tnl9UL3ClFhJbXQtQ9opXgWnhu/6ouF9pGJNK5MeS3P26ouofHw5fLLFyRiUQJvamXAbrdoE5EZT7eeuYNQ7y07EakrVANEnz8ntb+P5x2tK8CdTOmij6Y3L3pZXqb3ptk43shOsoFAACGEOU+38QKO1qDrRwBwdFSBVZiaiEJbYea3I3yprwGA1oErWO12Qo8fGh5rd3eX7e3t7CTb3FmFzW5h0UR4PHUQJ7EaxpXpOlH2xhtYyssJf/hRkVeeJ3Kwz1pwhsCb1wHor+2n0lFp6vyKhhOszx3QfjlzfjVdAXe9KU+XOgoT+eQTyt/Retz1NJbTVOnkAxPh8Ugiwicbn/B2s/Z7WFNTQ3V1tbmFLhnT+ht2/ygAtloXtvoyU+dXIpXm/uwW72QW8fKaWurb/K89XQ5/4gudEKJWCPFfhRDTme95Sz0IIVKnuot/59TjHUKI0czr/4MQ4k+smunMzAx2u5329nYAaprdlNc6WXhufCKKTu6CTWSLC9vb27H7fIQ/Mr4DLfT4IRarjfbLWtKy1+Olo6qD+yvGPcrCxA7CIk4KOVe2QONl7QrVIEcffghC4LmjTR515U6u+Cp5f8r4QvfRsjZB3/Fpm1rcbjc+n4/p6WnDYzGbSeXo/AoAFocVZ6DS1IaUDzKL9pd6tYXO7nTRNnCVuUfGFzo1qaqFzmq30NJbzeKEifMrM6m6Mg1zhd2O5/Ztjj76yHBIe/7JI5CSjje0Cymrxcqt5lvcW75neKyll7tIyclCZ7FA11dg9j3D4fHI6IjWlueudiElhODdngY+nNokaTAt4+H6QxLpBG+3vJ0dq6uri2AwSDJpMHS8cF9ry5NZ6ABcfTXEgvvIhLHw+KOFPcLxFO/0NGQf8197k+WXz0lEjUeSPq/8iS90wC8B70kpe4D3Mn/Px/Gp7uJ/+tTj/xj4tczrd4G/9tkebmFmZmbo6OjAZtMqEwghaL9cx+LLHVJJY79Y0akdnB1VWDLltYQQlH/pXcIjI6TjcUNjhT59iK9/AEfZSaX12823ebj+kFjKmCtaeL6Nt6MSp/tUCbGer2m/vAbzncIffoTryhVsp8pYfaWvkYfzu4bznT5a/oiemh68npPaot3d3aysrBAOG0wNmP0jqO8905bH2VNDYi1C6sDYZ//+5CaBOi2spAi8cYOdlSXD+U6zs7NUVlaeacvjv1LH3nqE/U1j3ik6tYOlwo69+eS4PO/cJbm6SnxmxtBYoU8fUlZRSVNnd/axu767bBxvGA6PLzzfxlFmoylwqq5rz49pjW9XjIXjjj78EOF2475+0pbnK/2NHESTPFo0Fu69t3IPp9XJ9abrJ4fV00M8Hs92tdfNzHfB6jjppk7mgiOZJho0Frb/cHoTq0Wc6T/X8eYQqUSCheel58t+XvhBWOi+CfxW5s+/BfyU3hcKrc7QjwDfNvP6V8n29ja7u7vZsKXCf7mORDTF2qz+Ezi5GyW5cYyr92z1Bc877yAjEY7Hx3WPdbSzzeZCiMAb1888fsd3h2gqysM1/XcWkYM4G/OHtF/OqQrR8zVIJ7V2IzpJ7e9z/ORJNqyk+HJfA2kJH87ov6s7ih/xaP0Rd31nx+rp0fqhzRiZuBNRLW8rE7ZUuHoyHsXAXV0smeLe7Hb2bk7R8ZZ252MkfJlOpwkGg3R1dZ0pr6XufOaf6b+rk2lJdHoPV2/tmbHK39UKVx998KGBsdKEnjzCf+0txKm6rur/4sNlA2NJycLzbdou1WCxnpqaur4KCJj5r4bGCn/4EZ5btxCOkyDPne56rBbB9yY3dI8Fmp+70XQDl+2kVFdHRwcWi8V41GDmPWi/Dc6TGp7OziqwWYhNGosafDC9xZtt1VSVnVx4+i5dxu50Mfep8ajB55UfhIWuSUq5CpD5XqiAn0sIMS6EGBFCqMWsDtiTUqrYwRLgK/QPCSF+ITPG+Oam8fDYRajJNHeha+2vwWIR2k4ynWTDSjlduz03byIcDkMTUeixlribu9ANeYdwWp18sPyB7rGUC8qGlRRtN8FZCdP6J6Lw/fuQTmfDSoo322qoKrPzvUn9/z+jq6MkZZJ3fGfHam5uxuPxGFvoFu5DMnpuobM3e7B47FpIWSfjoV2OE6msn1PUNPuoamwyNBEtLy8TjUazYUtFdaObqsYy5p/pP7/ii4fI4+S588vu9eLs6eHoI/3n10YoSGR/j46M/1U0uBu4VHuJD5f0j7WzEia8Hz9/fnnqwHfd0PkVnwuRWF4+dyFVVWbnRnuNofNrLbzG7P5sNmypcDqd+P1+Y+fX/jJsTJwJWwIIuxVXV5UhT7cX0TqKKz+nsNnttF99g7lH4yVXB/q88H1Z6IQQ3xVCPMvz9U0Dw7RLKQeBvwT8EyFEF5Cv2mvB/1kp5W9IKQellIMNDQ2FnmaKmZkZamtrqa09e7fjcNlo7q4ydMUdndzFWu3E1lB25nGL2417aIijD/QvTqHHn+CprqHBf7adS5mtjGHvsKGJaGFiG1e5nYa2nHZBVrvWT2vmu9qORR0cffghlspKyq6dLeRstQje7W3ge5ObpHWmGXy4/CGe/5+994yO4zzvt6/Zjl303hvRK0mAnWCnCimZkm0V23Jky4ntuKXaifPm79iJk+M4xYmdxCWSbclNXSJVKZEEK0iwEyA6QPTesYvtu/N+GCxJAFtmF46LxOscHlI7s7cGi9l5nvt3N7Vh2bRnhULKvuzs7MQtN77T8S4otYtkJZDG4+gKY7C2TyO65F3XifZxNEoFG3MXP7gFQSC7soq+xms4HfIk2o6ODgRB8DrfMKs0jsH2aZwyyx+s7dMgeB/LY6ipwXLxEm6Zcq+vjRRIXt218WvM2eVJ2p5YdmaJlz6S+XfB4CWYl7egzy8s1oatW5cd216YQNPQHGNGeTEsT/x36UIHkmowNjbG7KxMxaZrIWlryUIHoC2IwTlhwTkpr8zgRPs4osgyxQAgZ3UVc+OjTA0NyLuu9zi/kYVOFMU9oiiWeflzEBgVBCEFYOFvr5qCKIpDC3/fAI4Da4AJIFoQBE+77nQgtIKbFeB0Ounp6VnmzXnILI1jctCEaTpwPEx0urF1zqArjPHaAT58+zbsN25gHwh8A7vdLnobrtwsK1hKTXoNfcY+emZ7Al+XW6S/eYrMkljv3eTz9sLcoJSxGMiWR1batAlBtbzT+o6CBCZMNpqHAz8gRVHk9OBpNqZsRK1YPnooPz8fi8XC0JDM26L9bWmR0ywfF6QrikW0OLH3y3twn2gbZ31OLHrN8p8xZ00VDpuVobZmeZfV3k5GRgZ6/fKJ1lllcbgcbtldeKzt02gyIlDol39e4dtqEB0O5uvllQZ0X71EUm4e+qjli2ZNeg0u0SU76amveZLYVAPhMV46+eftBcRbC0UATKdOo8nORpOxfFzQjgUP+4RMr+7EwAlSDCnkRS//fnu+87Lly84jEJEKicsbOXsyrOV6dcdax4gzaKhMX/7Z56yuBqD7ivwwx3uZ3wXp8hDw+MK/HwcOLj1BEIQYQRC0C/+OB7YAzaLkl9cCH/b3/v9r+vr6cDgcPhe6rLKFMgMZ8qWtdw7R7loWn/PgScWX49WNdHZgnTfdTPteikfqkxNHGe83YjE6lstKHjw7VBlxFFtHB86xsWWykodtCzvU2tbAcZTOmU5GzaPL4nMePDEtWQ+iyS6Y6oKCu70e1uXHgELA2hrYOx+etdA2avS62wbIKK1AqVLJki/n5uYYGRm5GXNcSmpBNCq1gl4ZZSwukx3HgPHmQ3Up+rVrUej1su4vm3meofYWsiurvB4vjy8nUhMpSzWwW50Mdc549+YAUteAPk6WfOm2WjGfP3/zu7KUkpRIEiO0HJeR3Wtz2agfrmdb+javm8WEhASioqLk3V8uJ3Qdh7zd4MWWKk6HMlYnSx53uUVOtI+zvTABhZeNZ2RCInHpmXfidAv8Lix03wL2CoLQAexd+G8EQagWBOHJhXOKgYuCIFxDWti+JYqiZyv8V8CfC4LQiRSze+o3evVIuzmlUkl2drbX47GpBgzRWln1dNb2aVAKaH1M7dZkZ6POzGReRpyu++pFBEHhc9pzekQ6uVG5nBwI/FDra5K6Vfh8EEWlSWUGMh5EphNS0oo3WQkgIUJLRXqUrAeRR1bytdAFVWbQflj6O/8ur4cVYSq02ZGyFjqPt7DNx0Kn0YWRVlQqa8ftufaCggKvx1VqJWlFMbLidLbOGRBvlRUsRdBo0G/axPypwGUGvY1XEd1unxsplULF5tTNnBk6g1v0Lx0Ptk3jdoq+N1IKhbSZklFmYL5wAdFm87mREgSB7QXyygwujlzE4rSwLd37hHlBEMjPz6e7uztwmcHABbDNSgudD1u6whhsXTOIDv/XdaVvmhmzg91FST7PyV5dxWDLdezW0DquvJf4rS90oihOiqK4WxTF/IW/pxZevyiK4h8u/LtOFMVyURQrF/5+6rb33xBFcb0oinmiKD4kiuLK5l0Ef/20tbWRk5ODRuO9hE8qM4ilv2U64FgVW9sU2uxIFD6GJwqCQPi2hTKDAGNVui6dJ7WwiLAI33PxatJquDh6MeBYlZ7G27pV+CJ/D/SdA5vRry1T7XG0JcWok5N9nrOjIGHhy+w/nf/04GnyovMWlRUsRXaZQcdhiC+E2Byfp+iKYnGMmHHO+I/vHGkZIy06jIIk39Oxc1ZXMTnQx9yE/wW9o6ODqKgoEhN9D1rNKo1jbtzCzKj/36O1dQqFQYXaz9Tu8JqtOAYHsQfozn/j0gW0BgMpeYU+z6lJr2HCMkHrVKtfWz0NE2h0SlLz/cwRzNsrq8zAVHscQadDv369z3N2FEplBlcDlBmcGDiBTqljfbJvW3l5edjtdvr6AkzxaH8LFKpliU63oyuMRXS4sfX4j/kdbR1DpRCoKYj3eU7ummpcTid91++UGfzWF7rfdyYmJpiamqKw0PeXHST50m5xMtLp+wZ2TllxjJh9ykoewrfVIFqtmC/49gbmJsYY77nBqqoNfm1tS9+G0+3024R3ftbGaPccOZUBEnjy9oLb4bddk3NqCsvVq0Ts9P1lB9hRlIhbxG8Xi3nHPJfHLi/LtlyKrDIDmxF6zkCBd2/Og65oIY7ix6uz2F2c7hxnb0mS30nbOWvWAXDjsu/htU6nk66uLvLz8/3aulVm4NurE11uLK3T6Ap9xFkXuFlmUHvc5zlut4sbl8+Tu2YdSi9xVg+eBA6P5+31utwi3Y2TZJbGoVT5eSSt2gUI0PGOb1uiiLG2FsOWLSh0vqd2b82Xygxq/ZQZiKLIyYGTrE9Zv6isYCk5OTkolcrAqkHbW1L8V+d7YK6nzMAaoNtNbesY1dkxROqWx1k9pBWVoNaF0X1l5cORf9+5s9CtkPZ2qSDWl6zkIaM4FqVKQXeD7we3tUV6SOlKfMg3C+jXr0fQam9KgN64cUm6uXOrfO9EAdYkrsGgNviNo/Q2SteVXeF79whA5kbpS9z2ts9TTCdOgttN+M6dfk1VpkcTo1f7jdOdHjyN0+30KSt5SElJITw8/ObvyitdtdIiXXCPX1uqhDApjuKnWfeZzgmsDje7i317YACxaelEJ6fQdcl34kdPTw8OhyPg/RWVEEZ0kp7e677vL1vPHKLVSViA+0udmoq2qAjjMd/Dfofb27AY5wLeX/Fh8ZTGlfqVx8d6jVjm7IHvL0McpFdLnrcPbK2tOIeHidjl//6KClNTnRXD0Rbf99eN2RsMmgbZnr7dry1PmYHfhW6yCybaoeBev7YUGqm3qqV50qd0PDhjoXXEyK4i//eXUqUmq7yS7iuX3vdlBncWuhXS1tZGcnIyUVG+d2kglRmkF8XQfW3c501naZlClRiGOj7M63EPCp0Ow+bNmI4d82mr61I9MSmpxKam+7WlVqrZnLqZU4OnfNrqbpggIlZHXNryTMRFKNVSfKv9LfAxRdtUW4sqMRFdaYl/UwqBXUVJHGsdw+FD7q3tryVaG72srGApCoWCgoICOjo6fMdROg6DNkqqCfSDIAiEFcUuxFG8/4xHW0cJ16rYkON/QREEgVXVG+m/fg27xbvk2NHRgUql8hn/vZ2cingG22ew+ZhmYG2elNrK5XuPz91OxK5dWK5cwTnl3bPounwehVK5rH7OG9vTt9Mw3uBzmkFP4wSCIMmvASncJ0mXs96bdRtra0EQCN/uf3EC2FuSROuIkT4fw349i3MgxQCgsLCQiYkJ38N+295aONH/RgogrDgO14zN57Bfz+Zvl5/4nIdVVRswTo4z1rOCkVXvAe4sdCtgfn6e/v7+gLKlh5zKeOYmrEwNLb+B3RYnthuzAXfbHiL27MYxOIitrW3ZMbvFTH9TA7lVG/zKXR5q0moYM4/RMrW8NMBhdzHQMkV2ZbwsWxTuk+Io/cu9FLfdzvzp04Tv3CnL1t6SJGYtDi50L3/YOtwOTg6cZFv6NlQK39KZh6KiIux2u/ep0G63lESTt0tarAOgK5LiKFYv3W7cbpEjLWNsL0hA40+GWyCvagMup/NmPdrtiKJIe3u73/jv7eSsTsDtEunzIl+KooilZQrdqmgUWmVAW+G7d4Hbjem4d9Wg62I96SXlaPUBNj/ArsxdiIic6Pduq/vaBCl50ejCA3/2FN0n/d32ptfDpmO1hFVUoIoP4B0Cd5VIcd13mke8Hj85cJKCmAJSwlMC2vI8A1pbfcQi29+GxBKIyQ5oS1ccCwI+5ctjrWNkxupZlRD4s8+tWo8gKOi8EPog3PcCdxa6FdDR0YEoirIXuuxy6cvXfW35rs/aNgVuEV2xvIUufMcOEASMR5bXFfU0XMHldLIqgKzkYXvGdhSCgqN9y20NtE7jdLjJCSQrecjbAwo1tL6x7JC5/jxus5nwnTtkmdpWEI9WpeCd5uU9IS+NXsJoN7Ir03+sz0NOTg5qtZo2LxsDhq6AaTSgbOlBmxOFoFHclJpvp3FwlnGjjT0l/mUlD6mFxegiIum8uHxjMD4+zvT0dEDZ0kNSTiRhkRpuXFue3OIcM+OasgaUxT3oSkpQJSdjPLb8npgeHmRqsD9g/NdDQUwBaeFpHOtfLoXOTVqYHDTd/G4EJKEA4vK83l+O0VGs168TvkvePZEZp6cwKYJ3vdxfM9YZroxdCSiLe4iOjiYlJcX7QmeZht46KPQvW3pQRmjQZERg8VKOZLY7OdM5wa6iRFmbRX1kFGlFJXRdCH0Q7nuBOwvdCmhrayMiIoKUlMA7PgBDtJbE7Ei6vTyILM2TKMLVaJZ2HfGBKi6OsLVrMR5d/iC6cek8OkM4aYX+5UEPsbpY1iau5Vjf8gdRz7XxwNlwt6OLhJxt0oNoiRRqqq1F0OkwbNwoy5Reo6ImP553m0eXyaq1fbVoldqbY3kCoVarycvLo7W1dXmXlJZDUjacj/q5pQhqBbqCGCmOsqR7y5GWUZQKgZ2F8hY6hVLJqrXr6L58AdcSWbWlRfKwi4qK5NlSCOSUx9F7fRLXkvR0y8KEg7Bi/4lOHgRBIGLXTubP1OFe0gW/69J5ANkbKUEQ2Jmxk3ND55h3LFYzPPHfnEqZCx1A0X5pzI1lccakJ3kmUHzudu4qTeJCzxRT84uze48PHMclutid6b0UwOtlFRUxMDCA0bgk67jjCIguSe2Qia4kDsegCefs4szqE23j2Jxu7i71nWW8lFXVGxjv62Fm1Lvn+n7gzkIXIp5suIKCAnmS3gI5lfGM9RqZn7l1A4tON9a2aXRF/rPhlhKxeze2lhbsA7fiFVI23AVy1lSjUAaWqDzsztxN50wnvXO3BrvKzoZbStF+mO6G8Vu7W1EUMR4PnA23lLtKkhmcsdA0dKsbiSiK1PbXsillE3r18k4hPi+rqAiTybS4S4ooQstrkF0jTRSXSVhZPG6jA3v/4ofau82jVGXFEK2XPy1qVdUGrPOmZV1SWlpaSE9PJyJC3uYHJPnSYXUxsKSgIaCVAAAgAElEQVS7hrV5EnV6OMpIrWxb4bt2I1oszNct9ga6LtWTkJlNVGLgGJGHXZm7sLvtnBlcPGaqu2GC6CQ90Unyf48U3Sc1EV8yGspYewx1RgYaH40bvLG3JAm3KMmBt3O07yhJ+iRK40pl2/IoO8uSntreBEMipHqvN/SGJ4SxVDV4u2mEWIOGddny79W8amlj2XXx/Stf3lnoQqS7uxu73S5btvTgkQBvz760dc8i2lyy43MeInZLEo3pNnlpqK0Fi3GOVdXyZCUPHgnwdvlytHdOXjbcUjw719vkJVtLC86hYSJkypYedhcnohBYJC+1TbcxPD/Mzkz5O3fgZor+IvlyvFXqhlJ8f1C2dEWxoBSwNN76PfZPmWkdMbInQLblUrIq16BUqxfJl9PT04yMjFBcvLxVlD/Si2JQaZV0X72lGriMduz9RsJkyuIeDOvXoTAYMNXe8vQtJiODrc1B319rEtcQrY1eJF/aLE4G26aDv7/SqqWFo/X1my+55+cxnz1HxC558V8P5WlRJEfqePe2OJ3ZYaZusI49WXuCspWUlER0dPRi+dJplxbkgrukoneZqBLCUMWH3fTEAexON8daxthTnIhKKd9WdHIK8ZnZdN5Z6O4QLM3NzWg0Gq9Ndv0Rm2ogMl63KE5naZ6U5DC58uACmqwstPn5i+J07efOoFJrZGXD3U5qeColcSUc7b1lq+vyOAqlcLOFmWwiU6Td620JA3NvHwalkvDd8qUgkIaxVmXFLIrT1fbVIiAETPteil6vJzs7e/GDqOV1QJC80CBQ6FTo8qKxNE3clFXfuj4MwD2l8qRsDxpdGFnlq+m6eO6mLc81BrvQqdRKskpj6b42cVNW9cR65MbnPAgaDYZtNRiP1SK6pAzTzgtnEd1uVlXLk59vXpdCxfb07ZwcOInDLTWy7rk2jtslsmpNkA3WFQop3tVxRJrWjdRtR7Tbg76/BEFgT0kiJ9snsC5k0Z4ePI3dbQ9KtvTYKioq4saNG9g8zRxu1IJtDoo/4P/NXmzpiqXsXrdVkrTruiYw2pzcUyZftvSQt24jgy3NmOeCm3f3XuHOQhcCLpeL1tZWCgsLbw5ZlYsgCOSsTmCgdQqb2YHoFrFcn0RbEIOgli81egjfsxvzxYs4p6cR3W466s+QvXrtoiGrctmduZuGiQZG56WYWNflMdKLYtEZZGTDLaVon9RtfnYQURSZO/w2hg0bFg1ZlctdJcm0DM/RPyWlgR/rP8bqxNXEhQW5ACPJS+Pj40xOLkhCLYcgYz1EBP/wCCuLxzVtw7GQRftG4whlaZFkxgX/2a+q3sjs2OjNNPCWlhaSkpKWTcOQQ05lAuY5O6M9ktxraZxAFR+GOjn464rYvQfX5CSWK1I3kvZzZ4hMSFo0ZFUuuzJ3YbQbuTQq9V/svDxOeIyWpBzfnXt8UnQf2I3QLZUAzL19GGV8PPqq4DZ4IN1fFoeLUwvNCY70HSFGG8OaxDUB3unlsoqKcLlct5oTNL0qla3kBqc+gHR/4RJvNic43DSCQaNk86ogPWAk+VIU3X6bE7yXubPQhUB3dzcWi4XSUvn6/e3kVSXidol0X5vA3jOH22hHXxHa2KCI3XukNPBjtQx1tGGanqJgo/cef4Hw7GBr+2sZ7zNinLSSVxXiOKPihQlMLYewtbXh6O0j4m55yR5LuatUigW9dX2YntkeWqda2Zu1N7TLWvCQmpqaYLoHRhqCli096EriQADL9QkGps1c659hX3lw3pyH/PWbUCiVtJ89hclkoq+vT3YSylKyyuJQKARuXBnHZbJj65ohrFxmecgSwnfsQNBqmXvrbawmE32NVynYuCUkW5tSN6FT6jjSewS7xUl/8xSr1sjLHlxGzjbQREDzQdxmM6aTJ4m8ay9CEHFpDxtz44gKU/Nm4zB2l51TA6fYmblTVtnKUjwTJlpaWiTZsu0NadOnkh+z9aDJiEAZpcHcMIHLLfJu8yg7ihLRhbAhTsxZRUR8Ah31ZwKf/B4k+N/kHW7KlkuHYMolKTuSiFgdnZfGSMowSLJlUfA7dwBdaQnq9HTm3nqLLtMkSrWa3LXysuGWkhuVS3ZkNkf6jpBpqpay+AK1/fJFQgEklcH1l5mbt4NCQcSe4KQgD1lxBsrToni9YRgxqgkg5IUuKiqKjIwMmpqa2KZulF701GYFidKgRpsThaVpgrf1Upbj/hAXurCISDLLV9N29hRhBWVA8LKlB51BTUZJLB2XRqlI04MIYXLT95egDDcQvn07c+8cZmLLetwuF4UhbqTCVGFsS9/Gu73v8iHhCVxON6uqgotn3kStkxaQltcwqe5BtFqJuFteechSNCoFd5cm8WbjCPcNzGJymIKWLT0olUqKi4tpaGjA3nEMjXUWSh4I/EYvCAqBsPIETGeHuNwxwYTJzj1BZFsusiUIFGzYwtXDr2OdN6Ez+O51+l7kjkcXJB7ZsqCgALU6BEkP6abLq0qkv3kKc8MEuqJYWUW8vmxF7tuH6exZ2s+eIrtyLVovM8vk2tqbtZeLwxdpvzhCenFMaLKlh9IHEfvPY3zzdfTr16OKC15q9HB/ZQoNA7O81vUWaxPX+m3iHPCySksZHR1l/MqbkFzht4lzIMLK43GOWbh4eYjS1Eiy4gIX8fqicONWZsdGuXzhArGxsSQlyc9qXEp+dSKmKRuzF0Yl2TIl9OuKvPceXOMTtLzzpiRbrvI+LkgO9+bcy5R1ikt17RiitSSHIlt6KPsQWGeYe/kXKOPi0FcHL1t6uK8iFZPNyc8aDxKhjmBjSnAxyEWXVVaGw+Gg/dw7oI2EVcHLlh7CyiX5suVkH1qVgp0B2n75o3BTDS6nky4vNZvvde4sdEHS29uL2WwOWbb0kFedSIwCxHlHyLttD5H79zGjVUmy5YYtK7K1L2cfMaYU5qfsrFob+pcKgLIPYptVYe8dIPJu/82SA7G/IhWFZpReYxd3Z4cmgXooKZHqC5vGnFD+0IpshS20rUodtoYsW3rIW7cJtGEMjY5SXl4emqS3QE5lAmEqBe5BU8iypYfw7dtx6sMY6O4KWbb0sDVtK1FCDDMdTlatSQiqnGYZuTtxq6IxnW8gYu+ekGRLD5tXxRETDlcnT7Enaw8aZfBSo4esrCzCww009U9JSTMq+SUdS9FkRKCI0mDoMbKnJIlwH1NN5JCcV0BEfALt53w32H6vcmehC5J3X3kRhYDPIatySciMICdCjUsgZNnSg7aggLGsdAQCN3EORF5MHtXzu3ALbnJXhyhbeojNxTidDUDE3tCkRg9p0WFkZLaDKHBX9soWzcjISLKiFVynALH0wRXZUkZqmYzTshcV+0LIhrsdXXg44QXSBqqsrGxFtjRhKkqzwhEAXdnKNlIKvZ6Z6jW4EclfF7qnA6BT6bhb+BCCW0HW6pXd96g0mFiP6HATuUdeNxSfppQKKgtGcGFlV8bK7i+FQkFpWiTt7nSs+aHFfz0ICoHJdANrXAoeKA7dwwdJsUlevZ7G6XkGensDv+E9xJ2FLkg0CgWq6XFcAWbBBcQNyUqBEbsbu93/jLpAiKKboXAtCbPzKE3+55EFtOUWyR6vYCCqlUkx8IRv/9clMtutQp9kQ6WYC/yGALbQX8NpzmHGGPoOecEYZY4GJohjzBb6zt3Dm24bGShJtazs9whgDQtHYZ3HORt4uGsgkhVgcomMG/3P9JPDULiWMJuDyKmVp6dnjVZg0kxzI+z6im3N3VCh1LrQR6/883LrL+F2hjM3nbViW6XORlyoaHOszMsHeMtpQ4PAesfKH9dWQySiLgxVgEG47zV+6wudIAixgiC8KwhCx8Lfy/LPBUHYKQjC1dv+WAVBeGDh2E8FQei+7Zj/VvYrZN+BB9AO967Y/bd1zaB0uhm0u+m8tLzXXjD0XW/AYreRNm3EeNj3iBw5DHfNgFFNe/xF3up+a0W2LFeu4hibIyrbDNdfXpGt9ul2phwDOI2VvHZteEW2GL1O8fxpBOD69ZU9bDvHTPx8eg6XAixXA09E98fk5CTTRhMa0ywtp46vyJZzxoZywsKQGzovrWzDYpqeYnCon3STlbnXXw/8Bj+Y5+yYboj0JjVyuNf3uB05uGZmMF1oIioPhJaDK7JltBtpmq5HbVnDGw0r+z5inye992WiNC6ut3jprRoEVoeLp2+MM6sRsDf6HsEkB6fTyY2+fkrLyknODj0u/fvIb32hA/4aOCqKYj5wdOG/FyGKYq0oiqtFUVwN7ALMwO3TF7/sOS6K4tX/y4tNzFlFXHomTSd9z+qSw/ylUYQwFfb4MFrPrawHXcvJY2j1BjJSM5h9fXmz22BoPTeCWqsksgDe7PbeIV4us68dQtDpiNhYDg3PLet9GQyHug6hUqhYHVPDwauDK5uv1fgC4QoHudmZNDQ0LO99GQSvXBnAIoCqIAZzwziiK/Tr8iy6+bk5tJw5gcvpCNmW+eoYiCDkR9N1eRyXM/SfsfX0cURRpKCyGuPbh3FbLCHb6rg4iuiGlNV6jvUdCzjZ3h9zb7+N6HAQubdGGoNjDd3bPNp3FLvbzra0u6htHQ842d4vLa+jcM5TWrCKrq6uwJPt/XCsdYx5hwuxNA5b58yy3pfB0NHRgdVqpbKyMmQbv6/8Lix0B4CnF/79NBAoF/fDwFuiKK5MowsRQRAo2baLobZmZkZC8yzcVieWpkn0lQkUbk5ltHuO6ZHQvgwOq5WO82cp2LiF2A8cwNrQgK2rKyRbTruLrktjrFqTwN35d9Ex3UHHdICpyT4Q7XaMb75FxO7dKNc/Jg2dHFw+ikYODreD12+8zo70HTy8toieSTOXen0PPvWL2y15l6t2sbpqHbOzs/T09IRoSuTVK0PU5CcQW52M2+TA1hnadYmiSGNjI5mZmazZuQercY4bV3xPkA9ky3x5FE12JLlb07DOO+hZgTfQfKqW5LwCMh55BPf8PMYjRwK/yQft9SPEZ4Rzb9UuzE6z14kZcpk9eAhN3ip0+z8LTotUnB0ib954k/TwdD69fgd2l5vXrg0FfpMvGp6F6Ewqt96D2+2msbExZFOvXhkkPlxL/q4sEMF8OXTvvKGhAYPBEHQ3p/cCvwsLXZIoisMAC38HSvV7FPjVktf+URCEBkEQviMIgs8AjiAInxYE4aIgCBfHx0OXmYq37gBBoPlUbUjvtzRMgNONfm0iBeuTEBQCrWdD8+o6L5zFYbNSUrOLqA/cDyoVMy+HJhN2N0xgt7oo3JjMPTn3oFKoeLUztIeH6eRJXLOzRB34AJQ+AKowuPqLkGzVDdYxZZ3iQN4B9pWnoNcoeeHiQEi26D4Bs/1Q8QhFRUVotVquXg1NBLjQM8XgjIUPrk2TGnLrVJivhPYgGhgYYGJigsrKSrIr1mKIjqHpeGiLgGPAhHPMgn5tIhklsRiiNLTWhbYpG+/tZry3m5Jtu9BXV6NOT2f2lVdCsjU9Ms9Yr5HCDclUJVWREZHBK52h2bL39WG5coWoDxxASK+G+MKQ769h0zDnhs+xP3c/ZWnRFKdE8uKlEO8v4wjcOA4Vj5CUnExqaipXFrrKBMuEycax1jEeWJ2KNkGPJjsS8+XlkzzkYLFYaG9vp7y8HOUKslN/X/mNLHSCIBwRBOG6lz8HgrSTApQDt4v7XwWKgHVALPBXvt4viuKPRFGsFkWxOiEh9IzCiLh4MksraDlVG9JNN395FFVCGJqMCAxRWjJLY2k7N4zbHbytppPHiExIJK2oBFVcHOHbtzN78BCiI3jZq61+hPAYLWkFMcTqYtmZsZPXul7D4Qre1uzBgyjj4jBs3gy6KKn7yPUXwWEN/OYlHOw6SKwuli1pWzBoVewvT+H1hiHMdh/Twv1x5Wegi4ai+1Cr1ZSVldHc3IzVGvx1vXx5EINGyV0lyQgqBfrKeCxNk7h9TPj2x+XLl29ej0KppLhmJ91XLoTUm3D+8iioBPQVCSgUAoUbU+htmmI+BNmr+VQtCqWSwk01CAoFUQcOMH/2HI7h4BfOtnMjCALkr0tCEAQOrDrAhZEL9Bv7g7Y1e+g1EASi7r8PBAHWfEwa9jsRvALxape0mXswX8rA/XBVOtcGZmkfNfp7m3caXwDRDRWPArB69WpGR0cZDuHzeuXyIE63yCPrMgAwVCXhHLcsm5ghh+vXr+NyuaioqAj6ve8FfiMLnSiKe0RRLPPy5yAwurCAeRYyf1vih4FXRFG8+eQVRXFYlLABPwFWll8vk5Jtu5gZHWawtSmo9zknLdh75tCvTbpZj1S0MYX5WTsDrcFljs2OjdDbeJXS7bsRFjqjR3/wQVwTE5hOBZcsY5q20nd9koINyTdrmz6Y/0GmbdPU9gfnuTrGxjAeqyXqgQMInl6gqz8qxVB8TIb2xYx1htr+Wvbn7ketkIrXP1yVzrzdxVuNQXrB5ilpJE/FI1JnDaQHkdPppLm5OcCbF2O0OnitYYj9FSmEaaQdsmFdMqLDLcXHgsBms9HU1ERpaSlarSRIlG7bhdvlovX08aBsiQ43lmvjhJXEodBJn33x5hREt0hbfXCfl8vpoOnEUXLXrkMfGQVA1AMHQBSZPXgoOFsuNy11w2SVxWGIkn7GA3kHEBA41BWcLdHlYuallzBs2ojaMwuy4hEQlHD1l0HZcotuXu14lQ0pG0gLTwPggdWpqBQCLwXr1YkiXHoa0tdDvFR+VFZWhlKpDNqrE0WR5y72szYzmvwkaUxTWHk8glqBOcjkNVEUuXTpEomJibJnZ77X+F2QLg8Bjy/8+3HAX/rUR1giW962SApI8b2V5yzLoGDDFrR6A9feDS4z0XR+BBSgv60YO6ciHq1eRUuQ8lLD0cMICJTvulVAHb5tG8q4OGZfCU6+bD49hAiUbk29+dqmlE0kG5J5uSM4W7MvvwwuFzEP3VaMnbMNItMljyoIXr/xOk63kwOrbjn/63NiyYrT88KlID2BhufBZYe1f3DzpfT0dOLi4oJ+EL16dQiz3cXHNtxKRdekR6BOC2e+fiQoT7+pqQm73c7atbfmlcVnZpOUm8f140eCsmW+PoHb7MSw7lZNX3SSnuTcKFrrhoOy1XH+LJa5WSr33JqMrcnIQL9uHTOvvByUrZ6GCcxzdkpq0m6+lmxIZlPqJg52HsQdRLq76eRJnMPDRD/y6K0XI5Kl6fbXfgUu+R71ueFzDM0P8aH8D918LS5cy66iRF66PIg9mCSentMw2QHVT9x8Sa/XU1RURGNjI06n/Ou63DdN55jppjcH0sSMsLJ4zNfGcdtdsm0NDQ0xMjJCdXX1ior9f5/5XVjovgXsFQShA9i78N8IglAtCMKTnpMEQcgGMoATS97/C0EQGoFGIB745m/gmlHrdJRs20VH/RnZ8pLocGO+MEJYcRyqqFuhRKVaQeHGZG5cGZctL7mcDq7Xvktu1Toi4m4VBAtqNVEHDmCsPY5jVN7Oz+1y03xmmMySWCLjw25dl0LJA3kPUDdUx7BJ3iIsulzMPP8C+o0b0WRn3zqgUEoLTNcxmJSXLOMW3TzX9hwVCRUUxt6a+ycIAg9XZ3DuxhSdYzJlHFGUFtnUNZB8qxhbEASqqqro7+9nZESexyOKIr+s76M0NZKK9KhFxwzrknGMzOMYMMm7LiTZMj4+noyMjEWvl++6m/HebobaW328cznz54ZRxYehXbV45FPxlhSmR8wMd8qXQhvefYuoxCSyKhZ38Y9+6MM4evswnz3r453LaTo1RHiMlqzSxUXiD+Y9yPD88LKBrP6Yee55lAnxyyeJr/04GIehXX6JzSsdrxCljbo5j9HDRzZkMmGycbgpCC/40k8kWbx0cT7dmjVrsFgsUiNxmTx3oR+9Rsn+itRFrxvWJSNaXViuyc8xuHjxImq1+n0rW8LvwEIniuKkKIq7RVHMX/h7auH1i6Io/uFt5/WIopgmiou3fqIo7hJFsXxBCn1MFEX5T5gVUrn3XlxOJ9dr35V1/s3d9sbl8kH59nTcLpHm0/KyvTov1GOenaFiz/JGtjGPPgIuFzPPPSfLVk/jJPMzNkpv2217eCBP+tK+0P6CLFvzZ87gGBoi5pGHlx+sehwUKrjwlCxb54bP0TPXw6OFjy479si6DDRKBc+cldnhYeACjF6HNR9fdmjNmjWoVCrOnz8vy9SV/hlahuf46IbMZTtk/eoEBLUCU728jcHIyAgDAwOsXbt2ma3imh1owvRcPSyvds0+PI+9dw7DbfKzh/x1SWj1Khpq5clxk4P99Dc3Ur77npuyuIeIe+5BGRvL1C/kyYSz4xb6m6co3pKKYsnA0N2Zu4kPi+eXrfJsOQYHMZ04QfSHPoSwtNdswb2SanD+R7JsTVgmONp3lPty71vW8mt7fgJZcXqeOdsjyxamcWg+JEn06rBFh3Jzc4mLi5N9f82aHbx2bZj7K1KXtfzS5ESiStJjqhuS5VFbrVauX79OWVkZOp1O3s/yHuS3vtD9PhOXnkl6SRkNR95ClFGLNX92yOtuGyR5KaMklqaTg7hcgW01HHmLiPgEsivXLjumycwkfNs2pp97Hrc9cD1Q06lBDNFassuXN11OC09jR8YOXmx/EaszcMLG9HPPo4yNJcLbAMyIZCg5AFd+DvbA5RTPtj5LrC7Wa2/L+HAt91Wk8NKlAYxWGcky574vzQWreGTZobCwMCoqKmhoaMAio0bsl/V9GDRKDqxevjFQ6FSEVSZguTaO2xz4uurr61Gr1axZs3z2mUYXRtmOPbSfO8P8TOCyhflzQ6BSYKha3ipKrVFSvCWVG1fHMU0H/j02Hn0bhVJF2Y49y44pNBqiH34IU20t9oHBgLaaTw8hCFCyZfkGT61U83DBw5wePE3vXOBNy/SLLwIslsU9KFWw7lNSZu1YYC/4hbYXcLgdXjdSCoXAxzdmcaFnmpZhGV19rv4c3A6o+oQXWwrWr1/P4OAgg4OBP6/nLvZhcbh4fHP2smOCIBC+ORXH8Dz2vsBqRkNDAw6Hg+rq6sA/w3uYOwvdCqncu4/ZsVG6r17ye559yIS9z4hhY4rPRrblO9KZn7XTfdV/zdN4Xw99169RuedeFArvqcIxjz2Ga3IS49v+ZZzpkXn6mqco2ZKybLft4eMlH2faNh2wgNze24vp2DGiH3oIQeOjtda6PwLbrJSd5och0xAnBk7wofwP+Wyw+/jmbObtLl6+HODhMTsIzQclaUvrfTzJunXrcDqdAUsNxoxWDl0d4sG1aT4b7EZsTUN0uDEFSP6Yn5+noaGByspKwsLCvJ5Tedd+3C4nDUf9/x7dVifmK+PoK+JR6L1PnCjfnoYoilw/6f/zslvMXD9+hPz1mzBEex+UG/PIIyAIzDz3rF9bDpuLplOD5FQmEB7j3aN4qPAhVAoVz7b6t+W22Zh5/gXCt21DnbZ8kwFI8rhSCxf+168tu8vOc23PUZNWQ3ZUtvfrqspAp5ahGrgckkqRXQMJhV5PqaysRKPRBPTqnC43T9f1siEnlpJU75Md9KsTEXRKTHX+1R+32019fT2pqamk+fq83ifcWehWSP76TYTHxXPxNf8JG6ZTgwgaBQY/EwGyyuKIiNPRUOs/yeLS66+i0mqp2Huvz3MMWzajyc5m6uf+a4uuHu1HqVRQtj3d5znVSdUUxhTys+af+ZVLpp5+BkGlIuZjH/X9P8zcKM2pq/+R304pnofeQwW+pwtUZkRTmRHN02d7/JdmXHgSEGH9p32ekpKSQkZGBufPn/fbKeVnZ3txuN08scV3CyV1sgFtfrQkL/lJZrh06RIul4v1630nCsemppFduZaGd9/y2yllvn4Y0e4ifHOqz3Mi48PILo+n+fQQTofvZIbGY+9gm5+n6j7fvRvUKSlE7N7NzPMv+O2U0np2GJvZyeq9mT7PiQ+L566su3i181W/nVJmDx7ENTlJ7Cc/6fMcDPHS+J6rv/LbKeVwz2EmrZM8VvyYz3Oi9GoOVKbx6pVBpuf9KCNNr0q1mZu+4PMUnU5HZWUl169fx2TyHV050jLK4IyFT27J9nmOQqvEUJWEpXEC15zvmH57ezuTk5Ns2rTJ97W/T7iz0K0QpUpN1b4D9Dc3Mtzpva+dc9qK+doYhvUpPnfbIMklFTvTGe6cZbjL+5fUNDVJy+njlO3YS1h4hE9bgkJBzGOPYW1owHzhgtdzzHN22s6OULgpGX2k7+bGgiDwWMljdM50Uj/ifZaVc3qamZdfJvL++1En+qn5FwTpgTDWBB3veD1l1jbL8+3Pc1fWXaSE+0+HfmJLNjfG5znS4iPxxmaSkgQK90GM/2a9mzZtYnp62mepgdnu5GfnetlbnERugv/BlRE16biNdsw+kgYcDgfnz58nNzeXRH+fF7B23wFM01M+GxSITjfG00No86LRpPu+JwAqdqVjMTpo89F2zuV0cumNg6QXl5GS59078RD7+B/gmp1l5sWXvB53u0WuHukjKSeSlFVRXs/x8LHij2FymHzGgkW3m6mf/BRdSQn6DQEqiDZ+FhzzPmPBoijyTPMz5EblsinV/yLwqZocLA4XT5/t8X6CKELddyG+APL9Tz3YsGEDLpeL+nrv3yFRFHnyVDdp0WHsCTCpIHxzKogixtO+vfO6ujqioqJujqV6P3Nnofs1ULH7brR6AxcPeffqTKcGAYHwrYHlg9KaNHQGNZff7vF6/MrbryG63VTtC1xrH/2hD6KMi2PiBz/0erzx+AAul5s1e3zvtj3cm3Mvcbo4nmx80uvxmWefRbRaif3E416PL6L8wxCVCaf+zatX92zrs8w75vnD8j/08ubF7C9PITNWz3/Xdnr3Ni8+BZZp2PKnAW0VFRURHx/PqVOnvNp68dIAM2YHn94WuIWSNj9aSho4NeDV1tWrVzGZTGzdGnhad3blWhKzV3Hh4Iu43cs9MfOVMdxGOxHbfHvlHsyoVoAAACAASURBVNILY0jMjuTy4V7cXmLB7WdPYZwcp/r+Dwa0pa+qIqy6iskf/xjRSyy4++o4cxNW1vjx5jxUJFSwPnk9Tzc9jc213EsxHT+Ovbub2E89EThFPqVSKjU4+99gX+4hnhw4SetUK58o/URAWwVJEewtSeInZ3qYt3kpD+g+CSMN0uZN4f9xGh8fT3FxMefPn/faoODsjUku9k7z6W25qHyEETyo4sIIq0xg/tyw11jwwMAAfX19bNy48X3ZCWUpdxa6XwOaMD2Vd+2j/Xwdk4OLZUfXvIP5CyPoVyegig48XkatVVK5O52exkkmBhYHm81zs1w5/Ab5G7cQnRy48FMRFkbsJx5n/swZLEv67dnMDhqPD5BTEU90UuCJ5Fqllk+WfZL64Xoujy7uWekymZj66dOEb9+OrqAgoC2UatjyJamTRW/dokMWp4VftPyCmrSaRSUFvlApFfzxjlVcG5jldOeS2KbdDHXfg9wdkLEuoC2FQsHWrVsZHR2lo2Nxhw2b08UPjnexNjOaqizvcavbEQSBiG3pOEbMWJsnFx1zuVycPn2a9PR0cnICd5EXBIENDz7E9PAQHfWLPy/RLWI8OYA6RZJL5diqvjeLuQkrHRcWe8Fut4v6V18gNi2D3DXykhfiP/MZnMPDzL722rLruvBGD1GJYeTInGv46YpPM24Z59WOxW3nRFFk4n++jzotjci7ZQ7drfkLME/A5WeW2fphww9JC0/jvlX3yTL1uR2rmLU4+NX5vsUHRBFOfBvCk7wmOXlj27Zt2Gw2r7G67x3tJCFCu6h2zh+ROzIQ7W6vsboTJ06g0+kW1Wa+n7mz0P2aqNp3ALVGS93zi2Nixtp+RKebiB3ybl6Asu3pqHVKLr7Rs+j1C4dewmmzsfnDfmJgS4j5yEdQREUx8f0fLHr9yrt92MxO1t8vf1zHw4UPE6uL5fvXvr/o9amnn8Y1O0v8F78o2xZrHgNDApz41iKv7rnW55i2Tcvy5jx8cG0ayZE6vnd0iVd3+WmYH4ftPrvCLaO8vJyoqChOnDixyNaz5/sZmrXy53sLZRfd6lcnoooPY+7dXsTbYojXrl1jdnaW7du3y7aVt34TManpnHv5uUVenfnyGM5xCxG7lpc6+CK7PJ64tHAuvd27KLbZeuYkkwN9bPrwR5aVFPjCsHUrupISJn70o0Vt57qujDM5aGLd/hwUMqeIr09eT2VCJU9df2pR2znTsWNYr18n/nOfu9VpJxBZmyFzsyQr3tZ27uzQWRonGvlU+adudtoJxJrMGDaviuOHJ28sbjt34zj0npYWVbW81P2UlBTy8vI4d+4ctttmWl7smeLsjUk+sy0XnVqeB6ZONqArjsV4ZmhR27n+/n46OjrYsmXLzU4773fuLHS/JvRR0VTd9wDt504zeqMTAOeMFdPZIfRrk1AnBvaaPOgMalbvzqDryjgj3VKsbn5mmquH36Bo63bi0uUvmsrwcOI+8TimY8cwX5Y8MfOcnWvHBsirSiQ+QEzndsJUYTxR9gTnhs9xaVTKMnXNzjL106eJ2LuHsLJS2bZQh0HNX0rST6fUvHjWNsv/Nv4vW9K2sDZJ/k5Uq1Ly+Z2rON8zxbHWhfZbNiOc+nfI2io99GSiVCrZvn07g4ODtLS0AGCxu/iv2k425MSyJW95CYYvBKVA5J5MHCNmLAvTAxwOBydOnCA1NTWoKfUKhZLNH/4IE309N2fViU43c0d6UaeHE1YWxHUpBNbtz2Z6xEzrWanez+V0UvfCL0jIyqFwY2A59aYtQSD+i1/A0dvH9AtSfM3tFjn/2g1iUgzkr5M/FVsQBD5b+VmG54d5vv156Wd0uxn/z++iyc6WGoQHw86vwtwgnJeke7fo5rtXvkuyIXlRpx05/MVdBYwbbTx1qlt6QRTh2Deluj0vJQX+2LFjB2azmbq6ugVTIt8+3EacQcNHNwSWeW8nck8WosWJ8cQtJenYsWMYDAY2bNgQlK33MncWul8j1fc9iC48gtPPSnLJ3Lt9IEDk3uAnFq/em0lYpIa6lyQv5eyLv8LldLDpwx8J2lbs44+jSkxk9J//Wep793YPLrsrKG/Ow8OFD5OoT+RfLvwLbtHNxI9+hNtoJP4LQXhzHqqfgJhsOPJ34HbxVONTGO1G/mztnwVt6tH1meTGG/inN1twutxw+jswPwZ7/z5oW6tXryYhIYEjR47gcrn4SV0340Ybf3m3fG/OQ1hFAqokveTVOd2cO3eO2dlZ9u7dG7Stwk01JOXmc/q5n+Gw2zDVD+OasRF1d3bQtnLXJJCcG0n9oRvYrU6u177D7OgIWx75uGxvzkP4jh3o161j4r/+G5dpnrZzw0yPmFl/n3xvzsOW1C1sTNnI9699n1nbLHNvvIGtvZ34L35BvjfnIWeblCBy8t/APMUbN96gabKJL635ks+SFV9UZcVyd2kSPzx5gwmTDVrfgMGLsP0roArOa0pPT6e0tJS6ujrm5uY43DTK+e4p/nRvAXpNcD+jJi0c/ZpEjKeHcM7Y6Orqoru7m61bt6LxVeLzPkT59a9//bd9Db8VfvSjH33905/2nW4eCiq1BoVSybV33iQ5Jgd3nZHwLWnoK4KflKBUKVBrlVw/MYhaM039y09Redc+Smp2Bn7zEgS1GmVkFDO//BWWhFWcPmGheGsqxX5S0X2hVqiJC4vjV62/Intaje5bTxL14APEPOylE0ogFEpJvrzwJIP6KP6m7Rn25+7n4cLgbSkVAkmROn52rpcc9RTFZ/5cSjPf+JmgbQmCQHR0NOfPn8el0PD3x0bYUZjIZ7evCsmWKlaHqW4IM3YOnnubvLw8ampqQruu5FSuvv0aWoUezXkRbVYEkXuygl7oBEEgNsVAw7EB3E4z5w/+D0m5edR85PGQbGnz85h+5hkcopLjF7XEp4ez5cN5IdkqjCnk580/RzBbSfuHZ9BkZ5P0N38TWp/G5HKo/z4Wh5k/6XuV7MhsvrrhqyHZKkmN5CdnerBZ5tlx+UsQkQL3fUe6j4MkJSWF+vp65s0W/q3eSHyEln/+YHnQGwMAdVo4prohHCYrr157F61Wy4EDB/7PklC+8Y1vDH/961+X137md4Q7Ht2vmTX33E9cehbmw8Mo9CoidwUnRdxO8ZYUopP1nPzlk2jDw9nysO+an0BEPXAATXExp98YRqNTsPFA6MMX9+fspzK+Asu//TeCVkPinwXvgd2k9IOIGev55rX/Qiko+OKaEDzDBe4uTWJ9TiwRJ/4OURBg99dCtpWfn09ubi6nTh5H7bbytftCT9HWFcaiK4nj2OlanE4ne/fuDdlWZlkFq6o3Yj01jmhzEv2BVSE36k3OjWLV2kQuvv4stnkTu5/4bMi2wsrLibz/fi4dn8BidLDt0eC9Xw+FsYUcyDuA/alf4BwbI/lr/y9oL/MmicWw9g94suN5Rs2jfHndl1EIodlalRDOxzdmEXX5f2CmF+79tpRYFQKxsbFs2LCBa1evMD81yv+3rzhgpqUvVDE6ImrSuNBwmYmJCe655x7US9ujvc+5s9D9mlGqVOzZ+gTRygSGY/pRhAUpt9xuS6kgPX8Ap7Wf5Px70IX7r93yh6BUYnrkr5k2ZFOsaiUsPHRZQxAEvjq1mdJOOxfvz0cVHx/4Tb5QKDhc/SintSq+qEwk2ZAc+D1+rus/y3vYQz2Hoj8O0fJjmd5sxRRtwu1y81DCOOkx3juXyGWiTKRDMczayELi4uTH07yxbfdj5BjKGFJ1owoi9uuNvDUOnJZrRCasJz4ze0W2xI98nv7UbWTaW4hPN6zI1he097Cv3sWV9bFoyssCv8EPLVUf5amoCD7g0lAVX7kiW19Z4+LzqoMcV2/Fnhm8V347mWXVzIsa7g4fYOuqwJm8/nCsMXBZ3U2mIpH8HPmx3/cLdxa6XzOOkXm4ZMUUNseJ0z+nv6khZFvTw4NcfftXRCYWMtydRn9LcPPqbmd23My5sxYSdHPEHPrPoOfV3Y5jaAjVf/6UqaIUvp3VyPH+4yHbGjYN8w/NP6ZUE8tH205LjXFDxThKyum/ZTS8hD8f2Maha/IaZHtj0mTjG+/0MKjPxTk9SEND6L9Hs9nMm8cPE2eIpnwkmfnzoU2TB3CbHdgOj+IMc1HX/grX3gluvt/t2Mxmap/+HvqoBKy2ahqOhThVG6nVV+0rQxjCILv+SaZ+/OOQbbktFkz/7x8R46L5zy2z/KTpJyHbsjqt/O3FbxOjieArAzfg5LdDtoXTjv71z4E2ir8wfoz/ONIesim7081XX23lmmIVKoeJY8eOhWzL5XLx6muHUGpUbDHnM+ejBvf9zJ2F7teI2+Zi8letKHRKsj9fQ3RKKm98718xz84EbctutfDad76FSq3mw3/zV8SmhPPuj5tCmhLttLt458kmFAqBe76yA11+HkNf/nJIU6LdNhsDf/pn4Haz+j+eJD+2kL8987chTYl2uB381am/wul28s93P4UydS0c/LzsMT6LcDnghU+AfZ7Yjz3J6qx4vvpSA13jwQ+zcLrc/OlzV5mzOPnyx+8jMzOT119/nVGZY49ux+1289JLLzE/P88HP/IQ+rxYZl+/gX04cFPrpYhukamXOnAZHaR8cg2Zqys5/sz/3szyDc6Wm3d++F2MExN84C++Qk5lKnUvdzJyI/iJ5qIoUvuzFuYmLOz547XE7NnO2Hf+42aWb7C2Rv7+H7B3d5Pz7X9je9E+vnfle5wfltf5f6mtf6z/R9qn2/lGzbeIKn9UqnvrCnFROfw3MNqI5sH/Yk91Gf9zvItjrcHfEwD/9GYLV/tn+NKDNaxbt46zZ8/S2ip/HNPtHD16lIGBAfbft5+kzblSPLhB/hif9wN3FrpfE6JLZOpXrTjHzMQ+XIguPpL7/uQr2EwmXv32P+Dw0gnBF263i7f/+ztM9PWy/0tfJiYlkXv+qAyHzcWb/9OA3Sp/gKPoFjn6dAtjfUb2fKKYyNRo0r77n4gOBwOf/wIuo8x5biw8hL72NawNDaT887cwZOfynR3fQRRFvnTsSxjtwdn6et3XuTJ2hb/b9HdkxebBw09Lgf1nPypNA5dvDN76CvTVwQe+izqllP/66Bo0KgV/9PRFKUsuiOv65hstnOqY4JsPlFGSGs1DDz2EVqvl2WefxRjk53XkyBG6urq49957SUtPI/bhQhRhKiZ/et1vn0JvzB3uwdo0SdS+HLSZUdzzuT8jLCqaV//1m8xNBDfVvO7FX9J+7jQ1H/sEaYXF7H68mPAYLW//sJG5icATHG7n0tu9dFwcY+OBXNILY0n55j+gTktj4Et/gr1X5hilBaZ+/GNmX3mF+M9/nvDNm/n65q+TFZnFX574S7pnu4Oy9cvWX/Jq56t8uuLTbMvYDvv/VWq6/OITsqYbLOLCk1Kj6M1fhKJ9fONAKSUpkfzps1flTTe4jecu9PHTuh6e2JLDfRWp3H333aSkpPDKK68wNBScCnH16lXq6uqorq6moqKCqH05aDIjmH6xHXu//Hv1vc5vfaETBOEhQRCaBEFwC4Lgsx2DIAj3CILQJghCpyAIf33b6zmCINQLgtAhCMJzgiD8xnNqRZeb6RfbsbZOEf1AHroCSW9PzM5l/598hZGuDg79+z9htwZ+gLjdLt75wffoOF/Htsc+SfbqKgBiUw3c/YdljPebePP78hY70S1y/BetdF4aY9MDq8iplLI/tTk5pH3n37F2dND/2T/GZQrsXYhuN6P/8E1mDx4i/ktfJHIhoSIzMpN/3f6v9Mz28Jl3P8OcPfCX3i26+faFb3Oo6xCfq/wc+3L3SQeiM+Hhn8FUN/zsQbDI8IRFEd75W7j4Y9jyJ1AhZWymRIXxoz+oZmjWwh88dd5/U96bpkT+7Z12flrXw6e25vDwQoeKiIgIHnnkEUwmE8888wzz8zI+L1Hk+PHj1NXVsW7dOqqqpN+jMlJD3CdKcVucjD91HZdMD32uth/jiQEMG1MI3yJly+ojo3jwK1/DYbHw4j9+DdPUZAArEhdee5lzLz1L2c69VN/3ICDVbu774wqcDjcH/+OKrFE+AA21/dQfvEH+uiTW3i2V0SgjIsj4wffB5aLviU/hkDGaBmDql79k7F/+lYh77yH+C5+Xfka1nu/u/C6CIPBH7/yRbOXghfYX+Nb5b7ErYxefq/yc9KLGAB95Vppu8LMH5CsHV38Jb34Z8u+GPd8AQKdW8sOPV6HXqPj4U/V0jslTDg5eHeSvX26kJj+er+4rAkClUvHoo4+i0+n4+c9/ztiYvE1LU1MTBw8eJDs7m3vvlRq8CyoFcY8VowjXMP7j69iHfmPjOX+3EUXxt/oHKAYKgeNAtY9zlEAXkAtogGtAycKx54FHF/79A+CP5fx/q6qqxF8HTqPt/2/vzoOjrPM8jr+/hECAhIRwCOGKaBA5Ao4cgsoiMDMoCs54MTXiMesq7njsuqyIOiO77iiD7qAWSumK47ijMI4XFqDIGZAFFJQrEI6EKyE0IZCkk076ePq7f3Q7ZUma0Bmg0833VZUquvupXz6/5CHffp7+HXps3nY9PG2NVq44WO8x21d+of99x036zrRHtPKYK2JbHneVfvjcb/XF28fruvffrfeYgg2l+uqUFbrgvzZqxTFPxLZqq3266NWtOueBFbphYaEGg8FTjqn87DPdeXlfLbxpgnoPHIjcx6oqPfzQQ7rzsj569Pez6m1r5cGVOuidQXrzJzdrUUVRxLaqvFU6dfVU7f92f31+4/P1tqW7P1f9j/aqr1ypeqwgYlta51b94B9Vn2mruniqaj1trSpwac6TS/QfZq3UgtKqiE15vAH91798qz2nLdInPtyqjnNqW4WFhfrss8/q7NmztbS0NGJbPp9PFy5cqM8884x+/PHH6jjOKcfU7jupxb9Zp0ee36jew5FzBX2Onvhojx6etkaPz9+lwcCpuQ7v3K4v33Wrvv7gPVq6d3fEtgJ+ny6fN1dfvH28fjp7pgb8/lOOKS2q0NcfXa1/fHytlhZWRG4r4Oja9/fonAdW6JK52zQQOLWPnm3btWDwEN199TVas2lT5D76/Xp01izdeVkfPTTlQXW83lOOKSgv0BHvjdCRC0bqV6VfRWzL7/j1pc0vaf+3++uUZVPUGzi1LT2arzozO/RVuCpiW+oEVFf+LnR+/WmiqrfmlEP2utx65bNfaO6Mpbp697GITQWcoL6yfI9mP7FI73j9/9TjDZxyTFlZmb7wwgv63HPP6e7dkX+PjuPomjVrdMaMGTpv3jytq6s75Rh/ea0e+d0GLf7tOvXsKIvcx0YANmmM60a0X6Kn2SrlfBKR1cBUVd1Uz2vDgRmq+tPw4+nhl2YCZUBnVQ388LjTGTx4sG7adMq3OmNOtQ/Pt8dwrz5M0OuQMeESUodGXn+y6JuvWfTyLFBl8E0/Z8CYn5CWGRqtWFvtZtealWz46C94PR5G33s/A398Q8S2Dmw/zrJ5+QSDyqCxPeh3bdbf9vqqq/Gz5ysXm5bsx1sTYMStlzJwdOTRh9VfrqPkscdQr5fMe+6h3R23k5wVumJw3G6qFi2i7LXXcE6cpNO/TyXz7sjzrNYfWc+0NdPwBDzcefmd3HbZbXRNDS1kXeWr4vP9n/PGtjcoqy3jkSse4Vf9T7NA74F18P7k0Aonw6aENtRslx16zeuGHR9B3u+h6giMfjq0DFOEtjYdOMGUP2+mstbP3cOzmTy8Jz3bh0YF1ngDLN5Wyssr9nKkspZHRufw6JiciPOZiouLWbBgAR6PhyFDhjB06FAyMzMREXw+H/n5+eTl5VFRUcHIkSMZNWoUzSIMjfcVuyl/ZydOtZ82wzqTOiKL5h1aISIEfQ61+eW4lx8kUF5H6shupI/LjriX4bEDRXwy61mqT5STO3YcV4y7icyu3RAR/N469n29gfUfvMfJ0iNcOf5mRv7yXppFmGdVXlLN4te24T5RR99rshh4XXfadWmNiBDwO+zfcpyvF+/n5FEPudd1Y8Stl5IUYWi8t7CQw1MexF9cTPotPyfzrrtomZMT6qPXS/WqVZTNmYNvXyEZv5hE5+nTI+5luL9yPw+vfJiDVQeZeMlEJvedTO92vUM/e8dHXnEec7fOZe/JvdyScwtPDnsy8sTw8kKYPwmO74HcSTD816E5dyIQ8IV21sibCUe3w6Bfwvg/RFzm61C5h396ZxO7XW4mDsrivmt60b9r21CuQJC8PWW8smIv20squXlQFjNvyY24zFdFRQXz58/H5XLRr18/RowYQZcuXWjWrBmO41BYWEheXh4lJSX069ePiRMnRpwYHqjwUv6/O/GXVNOqf3tSR3ajRbe0iOfQmRKRzaoaVzu5xkuhuxUYp6r3hR9PBoYBM4ANqnpp+PnuwGeq2uB45MYWupMf76Wu4AROlQ8UWl6aQcaNvUju3PBw6spjLlb96X8o3LQBgDbtMpFmzaguDy0P1bVPP0bf+wCdshue4+Y+UceXf91L0behD51bp7egWTOhusILCl0uSeea23Po1LP+zRu/z+9y4Xp+Ju6lS0GVpI4dkORkAqVHQZWUgbl0fvppWg0Y0GBbrhoXs7+ZzeKixQC0T2lPi6QWuDwughqkf/v+TB82ndyOuQ22RfWx0G3J7X8FDUKbTqFVKKpKQo+7DAzNZepxVYNNlVd7eW5JAZ9sKcEJKh1SW9CyeRKllbUEFS7v0pYZN/VlWK+Gh/7X1NSwfPlytmzZgqrSunVrkpOTqaqqQlXp1KkT119//Rkt2Bz0+Kn8/AA1m1wQVJq1aY4kJ4XOr6DS/KLWZIzv9bfb4afj9dSw9r232b5yGUEnQKu0tiSntKL6xHGCjkNmVjdG3XUfF5/Bgs2+2gAbFhaR/2UJwYCS0iaZ5JQkak56CQaV9E6tuOa2HLIHNDy1JFhTQ9krr3By/gLU5yMpPZ1mqan4XS4IBEju0YOLpj1e/670P+Dxe5i7dS7zC+bjdbykt0wnNTkVl8dFIBiga2pXpg6eypgeYxqex+fzhIrZxjcgUAspGZCSDu5ScHyQ3j20sk6/n0V8E/WdOr/DnJX7ePPLIur8QdqmNCe9dTKuSi8+J0jntilMv6EPEwZmNZjL7/ezdu1a1q9fj9/vp2XLlrRq1Qq3243jOKSlpTF27Fhyc3MbbEsDQdx5xbjzDqO+IJKSRFLblnS4qy/NOzRuyowVukjfRGQ5UN8EqadUdWH4mNVELnS3AT/9QaEbCvwnsP4HhW6Jqtb7F1lE7gfuB+jRo8eVB6P8oBxCn5UEjtfSPDOFlD6ZtOga/dy2E0eKKdr8FccPH0KDDu26dOXiKwZzUa/o579UuDwc2H6c8iM1qBP6A5Q9oAMduqdGPWHXd+gQ7pUr8e7ZC06A5O49SB15LSkDBkTdVrG7mBWHVlBYUYijDlmpWVyddTUDOw6MfiJxxaHQkkuuHeAEIPNi6HUddB/a4B+gHyqpqGVZ/lF2lbrxOUG6t2vFyN4dubJnu6hzVVVVsWvXLo4ePYrjOGRkZNCrVy969ox+pZJApZe6neX4S2tQn0NSRgopvTNokZ0e9Tvw6hPlFG7eiGt/IQGvl7QOHek5YBDd+vaPuCN9JJ4qH0Vbyig75Cbgd0hrl0LX3u3o1qdd1LkC5eW4V6ygbkc+wdpakjt3pvWwYbQZfhUS5SoeFXUVLD+0nJ3lO6kN1NKpdScGXzSYEVkjSIp2pRLPCShYBCXfgK8G2maF1ke9ZAwkRTcPttLjZ2n+UbYWV+DxOXRMa8mQ7ExGXdaR5CgnhNfW1lJQUEBJSQler5e0tDR69OhBTk5O1KueBOsC1OaX4zvsJljtI2PCpSSdZg/K07FC93eIt1uXxhhzIYrHQhfzUZdn6GsgJzzCsgUwCfg0/MHoKuDW8HF3AwtjlNEYY0wTFPNCJyI/E5FiYDiwWESWhp/PEpElAKoaAB4ClgK7gPdVNT/cxDTgMRHZB7QH5p3vPhhjjGm6msyty/PNbl0aY0z07NalMcYY08RYoTPGGJPQrNAZY4xJaFbojDHGJDQrdMYYYxLaBTvqUkTKgOiXRmlYB+D4OWj3fIn3/BD/fYj3/BD/fYj3/HDu+tBTVTueg3bPmQu20J0rIrIp3obefl+854f470O854f470O854fE6MPZYrcujTHGJDQrdMYYYxKaFbqz741YB/g7xXt+iP8+xHt+iP8+xHt+SIw+nBX2GZ0xxpiEZld0xhhjEpoVunNERB4Wkd0iki8is2KdpzFEZKqIqIg0vI10EyMiL4hIgYhsE5GPRSQj1pnOhIiMC583+0TkiVjniYaIdBeRVSKyK3zePxrrTI0hIkki8q2ILIp1lsYQkQwR+SB8/u8K79N5QbNCdw6IyHXARCBXVfsBL8Y4UtTCu7X/GDgU6yyNtAzor6q5wB5gegPHx5yIJAGvAtcDfYFfiEjf2KaKSgD4N1W9HLgK+HWc5f/Oo4S2A4tXLwOfq2ofYCDx3ZezwgrdufEgMFNVvQCqeizGeRpjNvA4EJcf4qrqF+F9DAE2AN1imecMDQX2qWqRqvqABYTeMMUFVS1V1W/C/3YT+gPbNbapoiMi3YDxwJuxztIYItIWGEl4X05V9alqRWxTxZ4VunOjN3CtiGwUkTwRGRLrQNEQkQlAiapujXWWs+RXwGexDnEGugKHv/e4mDgrFN8RkWzgCmBjbJNE7SVCb/CCsQ7SSL2AMuCP4duvb4pIm1iHirXmsQ4Qr0RkOdC5npeeIvRzbUfo9s0Q4H0R6aVNaIhrA/mfBH5yfhNF73R9UNWF4WOeInRL7d3zma2RpJ7nmsw5c6ZEJBX4EPgXVa2KdZ4zJSI3AsdUdbOIjIp1nkZqDvwIeFhVN4rIy8ATwG9iGyu2rNA1kqqOjfSaiDwIfBQubF+JSJDQunNl5ytfQyLlF5EBDJKzTQAAAfpJREFUwMXAVhGB0C2/b0RkqKoePY8RG3S63wGAiNwN3AiMaUpvMk6jGOj+vcfdgCMxytIoIpJMqMi9q6ofxTpPlK4GJojIDUAK0FZE/qyqd8Y4VzSKgWJV/e5K+gNChe6CZrcuz41PgNEAItIbaEGcLBCrqttVtZOqZqtqNqH/OD9qakWuISIyDpgGTFBVT6zznKGvgRwRuVhEWgCTgE9jnOmMSeid0Txgl6r+IdZ5oqWq01W1W/i8nwSsjLMiR/j/6WERuSz81BhgZwwjNQl2RXduvAW8JSI7AB9wd5xcUSSSOUBLYFn4ynSDqk6JbaTTU9WAiDwELAWSgLdUNT/GsaJxNTAZ2C4iW8LPPamqS2KY6UL0MPBu+M1SEXBvjPPEnK2MYowxJqHZrUtjjDEJzQqdMcaYhGaFzhhjTEKzQmeMMSahWaEzxhiT0KzQGdOEhFee/+dY5zAmkVihM6ZpyQCs0BlzFlmhM6ZpmQlcIiJbROSFWIcxJhHYhHFjmpDwqv+LVLV/jKMYkzDsis4YY0xCs0JnjDEmoVmhM6ZpcQNpsQ5hTCKxQmdME6Kq5cA6Edlhg1GMOTtsMIoxxpiEZld0xhhjEpoVOmOMMQnNCp0xxpiEZoXOGGNMQrNCZ4wxJqFZoTPGGJPQrNAZY4xJaFbojDHGJLT/B+IVNhT1y2avAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69dfeb550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You can overlay many plots\n",
    "\n",
    "fig,ax = plt.subplots(1,1)\n",
    "for theta in np.arange(0,2*np.pi,np.pi/4):\n",
    "    ax.plot(t,np.sin(t+theta),label=\"$\\\\theta$ = %0.2f\" % theta)\n",
    "fig.legend();\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"sin(t+$\\\\theta$)\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T22:16:02.790058Z",
     "start_time": "2019-09-23T22:16:02.572201Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "22AAqCz6H0X2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b69e0a6f98>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69df24710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You can use different markers\n",
    "\n",
    "t1 = np.linspace(-2*np.pi, 2*np.pi, 100)\n",
    "t2 = np.linspace(-2*np.pi, 2*np.pi, 10)\n",
    "fig,ax = plt.subplots(1,1)\n",
    "ax.plot(t1,np.sin(t1))\n",
    "ax.plot(t2,np.sin(t2),\"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T22:20:44.457266Z",
     "start_time": "2019-09-23T22:20:43.934555Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "0guorhaDH0X2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69df1f710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You can make a grid of plots\n",
    "\n",
    "t = np.linspace(-2*np.pi, 2*np.pi, 1000)\n",
    "fig,ax = plt.subplots(2,2, figsize=(10,6))\n",
    "ax[0,0].plot(t,np.sin(t)); ax[0,0].set_title(\"sin\")\n",
    "ax[0,1].plot(t,np.cos(t)); ax[0,1].set_title(\"cos\")\n",
    "ax[1,0].plot(t,np.tan(t)); ax[1,0].set_title(\"tan\"); ax[1,0].set_ylim(-4,4)\n",
    "ax[1,1].plot(t,np.exp(t)); ax[1,1].set_title(\"exp\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "hidden": true,
    "id": "L9BpWgKOH0X4"
   },
   "source": [
    "## Plotting functions of two variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:06:02.293217Z",
     "start_time": "2019-09-23T23:06:02.285964Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "6qFsqSpfH0X6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [0 1 2]\n",
      " [0 1 2]]\n",
      "[[3 3 3]\n",
      " [4 4 4]\n",
      " [5 5 5]]\n",
      "[[3 4 5]\n",
      " [4 5 6]\n",
      " [5 6 7]]\n"
     ]
    }
   ],
   "source": [
    "# To plot functions of two variables, you need a meshgrid\n",
    "\n",
    "x = np.arange(0,3,1)\n",
    "y = np.arange(3,6,1)\n",
    "\n",
    "X,Y = np.meshgrid(x,y)\n",
    "Z = X+Y\n",
    "\n",
    "print(X)\n",
    "print(Y)\n",
    "print(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:06:21.788448Z",
     "start_time": "2019-09-23T23:06:21.348892Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "m1YmbTynH0X8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69f57c320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import\n",
    "\n",
    "fig = plt.figure(figsize=(10,6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Make data.\n",
    "X = np.arange(-5, 5, 0.25)\n",
    "Y = np.arange(-5, 5, 0.25)\n",
    "X, Y = np.meshgrid(X, Y)\n",
    "R = np.sqrt(X**2 + Y**2)\n",
    "Z = np.sin(R)/(1+R)\n",
    "\n",
    "# Plot the surface with face colors taken from the array we made.\n",
    "surf = ax.plot_surface(X, Y, Z, cmap='coolwarm')\n",
    "\n",
    "# Add labels\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "hidden": true,
    "id": "6JmEE945H0X9"
   },
   "source": [
    "## Plotting 2D arrays of pixels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:11:39.708028Z",
     "start_time": "2019-09-23T23:11:39.432497Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "DLHgZIALH0X-"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69f57cef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.random.rand(200,200)\n",
    "plt.imshow(data,cmap=\"gray\")\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:16:31.222075Z",
     "start_time": "2019-09-23T23:16:31.013228Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "5_RyA3NYH0X_"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x1b69e0741d0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69dd6c400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,np.pi/2,0.1)\n",
    "y = np.arange(0,np.pi/2,0.1)\n",
    "x,y = np.meshgrid(x,y)\n",
    "z = (np.sin(x**2+y**2)+1)/2\n",
    "p = plt.contourf(x,y,z,cmap=\"Oranges\")\n",
    "plt.contour(p,colors='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:31:01.701441Z",
     "start_time": "2019-09-23T23:31:01.484910Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "ocsdHilNH0YD"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69f5db8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-50,50,101)\n",
    "y = np.linspace(-50,50,101)\n",
    "x,y = np.meshgrid(x,y)\n",
    "z = (x**2 + y**2)%150\n",
    "fig = plt.figure(figsize=(6,6))\n",
    "ax = fig.add_subplot(111)\n",
    "p = ax.imshow(z,cmap=\"winter_r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "sRDo32LcH0YG"
   },
   "source": [
    "## Making arbitrary shapes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-23T23:41:18.968710Z",
     "start_time": "2019-09-23T23:41:18.964846Z"
    },
    "colab_type": "text",
    "hidden": true,
    "id": "sztRRAZlH0YH"
   },
   "source": [
    "See [here](https://matplotlib.org/3.1.1/api/artist_api.html) for a list of all the shapes you can make."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T20:45:43.152583Z",
     "start_time": "2019-09-25T20:45:42.938917Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "wWMY1SsyH0YI"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.2, 1.2)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b69f5a50f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.patches as pch\n",
    "\n",
    "face  = pch.Circle((0, 0), 1, facecolor='yellow', edgecolor=\"black\")\n",
    "left  = pch.Circle((-0.4, 0.3), 0.1, color='black')\n",
    "right = pch.Circle((0.4, 0.3), 0.1, color='black')\n",
    "\n",
    "mouth = pch.Arc((0,-0.1), 1.1, 0.9, angle=0, theta1=200, theta2=340, edgecolor='black',linewidth=5)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.add_artist(face)\n",
    "ax.add_artist(left)\n",
    "ax.add_artist(right)\n",
    "ax.add_artist(mouth)\n",
    "\n",
    "ax.set_aspect(1)\n",
    "ax.set_xlim(-1.2,1.2)\n",
    "ax.set_ylim(-1.2,1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "vQwNID1QH0YL"
   },
   "source": [
    "## Making animations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "AxAoU9VoH0YM"
   },
   "source": [
    "To make an animation, you basically draw a picture over and over with different value for the locations of elements in the picture. For example, to animate a bouncing ball, we define a position $(x,y)$ for the ball and a velocity vector $(v,w)$. Using the equations of motion for a falling object, we then have\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\frac{dv}{dt} & = & 0 \\;\\;\\;\\;\\;\\;\\;\\;\n",
    "\\frac{dw}{dt} & = & g \\;\\;\\;\\;\\;\\;\\;\\;\n",
    "\\frac{dx}{dt} & = & v \\;\\;\\;\\;\\;\\;\\;\\;\n",
    "\\frac{dy}{dt} & = & w\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "where $g \\approx -10$ is the force due to gravity.\n",
    "\n",
    "To make the ball bounce, we have updates say that whenever the ball reaches a horizontal wall, the horizontal velocity gets negated. Actually, we set \n",
    "\n",
    "$$\n",
    "v \\leftarrow - \\gamma v\n",
    "$$\n",
    "\n",
    "to decrease the energy of the ball. The constant gamma is called the coefficient of restitution. Similarly, when we hit the ground, we do\n",
    "\n",
    "$$\n",
    "v \\leftarrow - \\gamma v \\\\\n",
    "w \\leftarrow - \\gamma w\n",
    "$$\n",
    "\n",
    "The code below shows how to animate this in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T20:49:41.073963Z",
     "start_time": "2019-09-25T20:49:41.061495Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "bWq5Vn50H0YM"
   },
   "outputs": [],
   "source": [
    "# We need the animation library to do animations\n",
    "from matplotlib import animation\n",
    "from JSAnimation.IPython_display import display_animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:11:53.327962Z",
     "start_time": "2019-09-25T21:11:41.673595Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "Fe0dfRVhH0YN"
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Circle' object has no attribute 'set_center'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-42-1a3ef775744d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     46\u001b[0m \u001b[1;31m# Build and display the animation\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     47\u001b[0m \u001b[0manim\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0manimation\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFuncAnimation\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0manimate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mframes\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mframes\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minterval\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 48\u001b[1;33m \u001b[0mdisplay_animation\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0manim\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdefault_mode\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'loop'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\JSAnimation\\IPython_display.py\u001b[0m in \u001b[0;36mdisplay_animation\u001b[1;34m(anim, **kwargs)\u001b[0m\n\u001b[0;32m     84\u001b[0m     \u001b[1;34m\"\"\"Display the animation with an IPython HTML object\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     85\u001b[0m     \u001b[1;32mfrom\u001b[0m \u001b[0mIPython\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdisplay\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mHTML\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 86\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mHTML\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0manim_to_html\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0manim\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     87\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     88\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\JSAnimation\\IPython_display.py\u001b[0m in \u001b[0;36manim_to_html\u001b[1;34m(anim, fps, embed_frames, default_mode)\u001b[0m\n\u001b[0;32m     74\u001b[0m             anim.save(f.name,  writer=HTMLWriter(fps=fps,\n\u001b[0;32m     75\u001b[0m                                                  \u001b[0membed_frames\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0membed_frames\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 76\u001b[1;33m                                                  default_mode=default_mode))\n\u001b[0m\u001b[0;32m     77\u001b[0m             \u001b[0mhtml\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mread\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     78\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\animation.py\u001b[0m in \u001b[0;36msave\u001b[1;34m(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs)\u001b[0m\n\u001b[0;32m   1252\u001b[0m                 \u001b[1;32mfor\u001b[0m \u001b[0manim\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mall_anim\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1253\u001b[0m                     \u001b[1;31m# Clear the initial frame\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1254\u001b[1;33m                     \u001b[0manim\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_init_draw\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1255\u001b[0m                 for data in zip(*[a.new_saved_frame_seq()\n\u001b[0;32m   1256\u001b[0m                                   for a in all_anim]):\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\animation.py\u001b[0m in \u001b[0;36m_init_draw\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m   1790\u001b[0m         \u001b[1;31m# artists.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1791\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_init_func\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1792\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_draw_frame\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnext\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnew_frame_seq\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1793\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1794\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\animation.py\u001b[0m in \u001b[0;36m_draw_frame\u001b[1;34m(self, framedata)\u001b[0m\n\u001b[0;32m   1812\u001b[0m         \u001b[1;31m# Call the func with framedata and args. If blitting is desired,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1813\u001b[0m         \u001b[1;31m# func needs to return a sequence of any artists that were modified.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1814\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_drawn_artists\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_func\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframedata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1815\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_blit\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1816\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_drawn_artists\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-42-1a3ef775744d>\u001b[0m in \u001b[0;36manimate\u001b[1;34m(i)\u001b[0m\n\u001b[0;32m     41\u001b[0m         \u001b[0mw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mgamma\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mw\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     42\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 43\u001b[1;33m     \u001b[0mball\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_center\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     44\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mball\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     45\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'Circle' object has no attribute 'set_center'"
     ]
    }
   ],
   "source": [
    "# Constants\n",
    "g = -10         # Force due to gravity\n",
    "r = 0.25        # Radius of ball\n",
    "dt = 0.05       # Integration step size\n",
    "frames = 200    # Number of frames to animate\n",
    "gamma = 0.9     # Coefficient of restitution\n",
    "k = 0.95        # Coefficient of friction\n",
    "\n",
    "# Variables\n",
    "x, y = 1, 1.75  # positions\n",
    "v, w = 1, 0     # velocities\n",
    "\n",
    "# Drawing\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(0, 2), ylim=(-0.1, 2))\n",
    "ball = pch.Circle((x, y), r, facecolor='yellow', edgecolor=\"black\")\n",
    "ax.add_artist(ball)\n",
    "ax.plot([0,2], [0,0])\n",
    "ax.set_aspect(1)\n",
    "\n",
    "# Animation function. This gets called sequentially, once for each frame\n",
    "def animate(i):\n",
    "    \n",
    "    global x, y, v, w # Try commenting this line out to see what happens\n",
    "            \n",
    "    w += dt * g        \n",
    "    x += dt * v\n",
    "    y += dt * w\n",
    "    \n",
    "    if x <= r:\n",
    "        x = r\n",
    "        v = -gamma*v\n",
    "        \n",
    "    if x >= 2-r:\n",
    "        x = 2-r\n",
    "        v = -gamma*v\n",
    "        \n",
    "    if y <= r:\n",
    "        y = r\n",
    "        v = k*v\n",
    "        w = -gamma*w\n",
    "    \n",
    "    ball.set_center((x,y))\n",
    "    return ball,\n",
    "\n",
    "# Build and display the animation\n",
    "anim = animation.FuncAnimation(fig, animate, frames=frames, interval=20)\n",
    "display_animation(anim, default_mode='loop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "BuhdghE2H0YN"
   },
   "source": [
    "# Symbolic Computation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "hidden": true,
    "id": "n8Q_ZFJlH0YN"
   },
   "source": [
    "Python includes symbolic mathematics package called sympy in which you can have symbolic variables and symbolic answers to mathematical questions. This saves you a lot of pencil pushing for solving systems of equations and integrals, for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:23:49.196124Z",
     "start_time": "2019-09-25T21:23:49.192015Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "tFpffL0XH0YO"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "# Note there are so many functions in sympy that it becomes annoying to write, for example\n",
    "# sympy.sqrt(2). So we just import everything. This can be dangerous, because there might be\n",
    "# name conflicts, so be careful.\n",
    "from sympy import * \n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:26:19.200451Z",
     "start_time": "2019-09-25T21:26:19.195007Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "7qC1NztuH0YO"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4142135623730951\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(sqrt(2), sympy.core.power.Pow)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sympy returns symbolic numbers rather than floating point numbers. \n",
    "\n",
    "print(math.sqrt(2))\n",
    "sqrt(2), type(sqrt(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:26:08.642111Z",
     "start_time": "2019-09-25T21:26:08.637531Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "VyFqlTP5H0YP"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, sympy.core.numbers.One, int)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Integer(1)\n",
    "x, type(x), type(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:27:19.791967Z",
     "start_time": "2019-09-25T21:27:19.782395Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "w2ezuCA5H0YS"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( x^{2} + 2 y + z, \\quad x^{4} + 4 x^{2} y + 2 x^{2} z + 4 y^{2} + 4 y z + z^{2}\\right )$$"
      ],
      "text/plain": [
       "⎛ 2             4      2        2        2            2⎞\n",
       "⎝x  + 2⋅y + z, x  + 4⋅x ⋅y + 2⋅x ⋅z + 4⋅y  + 4⋅y⋅z + z ⎠"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can also work with unknown quantities\n",
    "x, y, z = symbols(\"x y z\")\n",
    "expr = x**2 + 2*y + z\n",
    "expr, expand(expr*expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:27:49.849832Z",
     "start_time": "2019-09-25T21:27:49.844239Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "nDROdD48H0YT"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$z + 5$$"
      ],
      "text/plain": [
       "z + 5"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can substitute in actual numbers for the variables\n",
    "\n",
    "expr.subs(x,1).subs(y,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:29:58.557609Z",
     "start_time": "2019-09-25T21:29:58.552077Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "TTtOmND9H0YU"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 8.0, sympy.core.numbers.Integer, float)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can get a numerical result too\n",
    "\n",
    "a = expr.subs(x,1).subs(y,2).subs(z,3)\n",
    "a, float(a), type(a), type(float(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:31:24.200946Z",
     "start_time": "2019-09-25T21:31:24.187471Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "eTOAFO36H0YU"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left \\{ x : - \\frac{4}{5}, \\quad y : \\frac{4}{5}, \\quad z : \\frac{2}{5}\\right \\}$$"
      ],
      "text/plain": [
       "{x: -4/5, y: 4/5, z: 2/5}"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can solve equations\n",
    "\n",
    "result = solve([\n",
    "    x + y,\n",
    "    x + 2*z,\n",
    "    y + 3*z -2\n",
    "],[x,y,z])\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:31:48.168646Z",
     "start_time": "2019-09-25T21:31:48.162343Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "61vwB7VvH0YW"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{66}{25}$$"
      ],
      "text/plain": [
       "66\n",
       "──\n",
       "25"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The result of solving a set of equations is a substitution rule. \n",
    "\n",
    "expr.subs(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:33:44.207580Z",
     "start_time": "2019-09-25T21:33:44.202511Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "XIvJ7oZIH0YW"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$8$$"
      ],
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can solve limits\n",
    "# This one requires L'Hospital's rule, but sympy figures that out.\n",
    "frac = (x**2 - 16)/(x - 4)\n",
    "limit(frac,x,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:45:49.187430Z",
     "start_time": "2019-09-25T21:45:49.181835Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "KpUfUCEdH0YX"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$2 x e^{x^{2}}$$"
      ],
      "text/plain": [
       "     ⎛ 2⎞\n",
       "     ⎝x ⎠\n",
       "2⋅x⋅ℯ    "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can find deriviates\n",
    "expr = exp(x**2)\n",
    "expr.diff(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:46:51.545198Z",
     "start_time": "2019-09-25T21:46:51.243243Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "egayWmRAH0YY"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{e^{x}}{2} \\sin{\\left (x \\right )} - \\frac{e^{x}}{2} \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       " x           x       \n",
       "ℯ ⋅sin(x)   ℯ ⋅cos(x)\n",
       "───────── - ─────────\n",
       "    2           2    "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can integrate\n",
    "expr = sin(x)*exp(x)\n",
    "integrate(expr,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:42:44.510346Z",
     "start_time": "2019-09-25T21:42:44.501229Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "Dh8PKjyKH0YY"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{d}{d t} y{\\left (t \\right )} = - \\lambda y{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "d                 \n",
       "──(y(t)) = -λ⋅y(t)\n",
       "dt                "
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# You can define differential equations\n",
    "t, l = symbols('t lambda')\n",
    "y = Function('y')(t)\n",
    "dydt = y.diff(t)\n",
    "expr = Eq(dydt, -l*y)\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:44:21.088017Z",
     "start_time": "2019-09-25T21:44:20.932866Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "CC33gDE5H0Ya"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$y{\\left (t \\right )} = C_{1} e^{- \\lambda t}$$"
      ],
      "text/plain": [
       "           -λ⋅t\n",
       "y(t) = C₁⋅ℯ    "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And solve them\n",
    "sol = dsolve(expr, y)\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:44:40.841057Z",
     "start_time": "2019-09-25T21:44:40.836437Z"
    },
    "colab": {},
    "colab_type": "code",
    "hidden": true,
    "id": "NW9C1LtHH0Yb"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$y{\\left (0 \\right )} = C_{1}$$"
      ],
      "text/plain": [
       "y(0) = C₁"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And manipulate the solutions\n",
    "sol.subs(t,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "heading_collapsed": true,
    "id": "keJss5ozH0Yc"
   },
   "source": [
    "# Typsetting Math in LaTeX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T21:48:17.607747Z",
     "start_time": "2019-09-25T21:48:17.599301Z"
    },
    "colab_type": "text",
    "collapsed": true,
    "hidden": true,
    "id": "CcFLEo3GH0Yc"
   },
   "source": [
    "\n",
    "- Jupyter notebooks consist of \"cells\" that can be either `Code` or `Markdown`. You can choose which one by selecting the cell and using the menu at the top of the window. \n",
    "\n",
    "- A `Markdown` cell uses the [markdown language](https://github.com/adam-p/markdown-here/wiki/Markdown-Cheatsheet) which is very simple. See the link in the previous sentence for details.\n",
    "\n",
    "- Images can be included in Jupyter notebooks with Markdown as long as you have a URL for you image. \n",
    "    - You can make a diagram in [Google Drawing](https://docs.google.com/drawings)\n",
    "    - You can get a URL for it by clicking File > Publish to the web ...\n",
    "    - Then put your image into a Markdown cell with the syntax `![](https://url.of.your.image)`\n",
    "\n",
    "- Equations can be put in Markdown as well using [Latex](http://tug.ctan.org/info/undergradmath/undergradmath.pdf). Latex code is separated by dollar signs. For example, to write a differential equation you can, you can write \n",
    "\n",
    "    ```latex\n",
    "    $\\dot x = x^2 - 2x$\n",
    "    ```   \n",
    "    which will appear as\n",
    "    \n",
    "    &nbsp; &nbsp; &nbsp;  &nbsp; &nbsp; &nbsp; &nbsp; $\\dot x = x^2 - 2x$\n",
    "        \n",
    "    in the notebook. Use one dollar sign for equations within paragraphs, and two dollar signs, or a latex directive like `begin` for an equation on a line (or lines) of its own.\n",
    "    \n",
    "- Here's a more complicated example\n",
    "\n",
    "    ```latex\n",
    "\\begin{align}\n",
    "    \\int_0^\\infty f'(t) \\; dt & = \\lim_{s \\rightarrow 0} ( s F(s) - f(0) ) \\\\\n",
    "    f(\\infty) - f(0) & = \\lim_{s \\rightarrow 0} s F(s) - f(0) \\\\\n",
    "    f(\\infty) & =  \\lim_{s \\rightarrow 0} s F(s)\n",
    "\\end{align}\n",
    "    ```\n",
    "\n",
    "    which produces\n",
    "   \n",
    "\\begin{align}\n",
    "\\int_0^\\infty f'(t) \\; dt & = \\lim_{s \\rightarrow 0} ( s F(s) - f(0) ) \\\\\n",
    "f(\\infty) - f(0) & = \\lim_{s \\rightarrow 0} s F(s) - f(0) \\\\\n",
    "f(\\infty) & =  \\lim_{s \\rightarrow 0} s F(s)\n",
    "\\end{align}\n",
    "    \n",
    "- And another\n",
    "\n",
    "    ```latex\n",
    "\\begin{align}\n",
    "    \\begin{align}\n",
    "        \\begin{pmatrix}\n",
    "            A & -BK \\\\\n",
    "            LC & A - BK - LC\n",
    "        \\end{pmatrix} \\begin{pmatrix}\n",
    "            {\\bf v} \\\\\n",
    "            {\\bf v}\n",
    "        \\end{pmatrix} & = \\begin{pmatrix}\n",
    "            A{\\bf v} - BK{\\bf v} \\\\\n",
    "            LC{\\bf v} - (A - BK - LC) {\\bf v} \\\\\n",
    "        \\end{pmatrix} \\\\\n",
    "        & = \\begin{pmatrix}\n",
    "            (A - BK){\\bf v} \\\\\n",
    "            (A - BK){\\bf v}\n",
    "        \\end{pmatrix}  \\\\\n",
    "        & = \\lambda \\begin{pmatrix}\n",
    "            {\\bf v} \\\\\n",
    "            {\\bf v}\n",
    "        \\end{pmatrix} .\n",
    "    \\end{align}\n",
    "\\end{align}\n",
    "    ```\n",
    "\n",
    "    which produces\n",
    "   \n",
    "\n",
    "\\begin{align}\n",
    "\\begin{pmatrix}\n",
    "A & -BK \\\\\n",
    "LC & A - BK - LC\n",
    "\\end{pmatrix} \\begin{pmatrix}\n",
    "{\\bf v} \\\\\n",
    "{\\bf v}\n",
    "\\end{pmatrix} & = \\begin{pmatrix}\n",
    "A{\\bf v} - BK{\\bf v} \\\\\n",
    "LC{\\bf v} - (A - BK - LC) {\\bf v} \\\\\n",
    "\\end{pmatrix} \\\\\n",
    "& = \\begin{pmatrix}\n",
    "(A - BK){\\bf v} \\\\\n",
    "(A - BK){\\bf v}\n",
    "\\end{pmatrix}  \\\\\n",
    "& = \\lambda \\begin{pmatrix}\n",
    "{\\bf v} \\\\\n",
    "{\\bf v}\n",
    "\\end{pmatrix} .\n",
    "\\end{align}\n"
   ]
  }
 ],
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