kqdtran/hw7_julia Secret

## hw7_julia
{
 "metadata": {
  "language": "Julia",
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Installation Instructions (for non-VM users)\n",
      "\n",
      "* Download Julia at http://julialang.org/downloads/.\n",
      "* Install IPython and IPython Notebook from http://ipython.org/install.html. In Ubuntu, you can do `sudo apt-get install ipython ipython-notebook`. The version of IPython needs to be 1.0 or later.\n",
      "* Once IPython 1.0+ and Julia 0.2 is installed, you can type `julia` in the command line to start the Julia REPL, and install IJulia with: `Pkg.add(\"IJulia\")`.\n",
      "* Continue the installation with `Pkg.add(\"PyPlot\")` to install PyPlot, which is a plotting package for Julia based on Python's Matplotlib\n",
      "* If the commands above returns an error, you may need to run `Pkg.update()`, then retry it.\n",
      "* To start the IJulia interface, run `ipython notebook --profile julia` (a window will open in your web browser).\n",
      "* Execute the code below block-by-block. For example, there's a good chance the code in part n will not run without first running the code in part a.\n",
      "\n",
      "More comprehensive installation instructions can be found at https://github.com/JuliaLang/IJulia.jl, as well as https://github.com/stevengj/PyPlot.jl. If you are not using the recommended VM, stackoverflow and google will be your best friends."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Installation Instructions (for saasbook VM users)\n",
      "(borrowed heavily from the installation instructions in CS194-16: Introduction to Data Science http://amplab.github.io/datascience-sp14/setup.html)\n",
      "\n",
      "*Note: While you should also be able to set up a similar environment on your Mac or PC without needing a Virtual Machine, the course staff will not support such configurations - so you\u2019re on your own if you choose to go that route!*\n",
      "\n",
      "* Follow [the instructions available here](http://beta.saasbook.info/bookware-vm-instructions) to install VirtualBox, and the virtual machine image. The virtual machine image already includes most of the software necessary to run the code. We will install extra packages below.\n",
      "* Start up the machine. Enter \u2018saasbook\u2019 as the password.\n",
      "* Launch a terminal. (Third icon in the launcher on the left.)\n",
      "* Run `sudo bash setup.bash`. Make sure you are in the same directory as `setup.bash` before executing this command. Enter the same password again to install lots of packages.\n",
      "* Grab a coffee or something - it will take a few minutes to build/install these components. Also if you see warnings etc. on the screen, don\u2019t worry that is expected.\n",
      "* Once IPython 1.0+ and Julia 0.2 is installed, you can type `julia` in the command line to start the Julia REPL, and install IJulia with: `Pkg.add(\"IJulia\")`.\n",
      "* Continue the installation with `Pkg.add(\"PyPlot\")` to install PyPlot, which is a plotting package for Julia based on Python's Matplotlib.\n",
      "* If the commands above returns an error, you may need to run `Pkg.update()`, then retry it.\n",
      "* To start the IJulia interface, run `ipython notebook --profile julia` (a window will open in your web browser).\n",
      "* Execute the code below block-by-block. For example, there's a good chance the code in part n will not run without first running the code in part a."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Tips and Tricks\n",
      "\n",
      "* If you are new to Julia, I recommend downloading and playing around with the language. The syntax is a mix of the best of Python and Matlab, and is very easy to get used to. Speaking of Matlab, Julia is 1-indexed instead of 0-indexed like Python and other languages\n",
      "* I recommend http://learnxinyminutes.com/docs/julia/ as the quick tutorial to learn most of Julia's basic features\n",
      "* Use a semicolon at the end of a statement to suppress the output/printing\n",
      "* To make the plot small enough and fit into the writeup, use the `figure()` command. In particular, the code below used `figure(figsize=(5, 3))` to indicate that the size of the plot should be 5x3 inches\n",
      "* PyPlot is the porting of `matplotlib.pyplot` to Julia. If there are naming conflicts (like the function `hist()` which plots a histogram), use the full function call `plt.hist()`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Import the plotting package for Julia\n",
      "using PyPlot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Declaring some global variables for multiple uses\n",
      "N = 1000\n",
      "sequence = [2, 4, 10, 50, 100, 500, 10000, 100000]\n",
      "Qs = [0.4, 0.1, 0.25, 0.5]\n",
      "ks = [2, 10, 50, 100, 500, 10000, 100000];"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part a"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Returns the number of heads in n flips\n",
      "# rand() generates a random number between 0 and 1, that number is then rounded to either 0 or 1. \n",
      "# By summing them up, we essentially are counting the number of heads\n",
      "flip_coin(n) = sum(round(rand(n)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "flip_coin (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "heads = flip_coin(N)\n",
      "figure(figsize=(5, 3))\n",
      "bar([0, 1], [heads, N-heads], width=0.2, align=\"center\")\n",
      "xticks([0, 1], [\"Heads\", \"Tails\"])\n",
      "title(\"1000 coin tosses\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1064c6cc>)"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part b\n",
      "\n",
      "We simply call flip_coin m times. The result will be a list of the number of heads in m runs"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Simulates a flip of n coins m times\n",
      "flip_runs(n, m) = [flip_coin(n) for i = 1:m]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "flip_runs (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "plt.hist(flip_runs(N, 1000))\n",
      "title(\"Heads frequency in 1000 runs of 1000 coin tosses\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118f55ac>)"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part c\n",
      "\n",
      "* We repeat part b for every number in the sequence\n",
      "* `for i = sequence` is Julia's syntax for Python's `for i in list`\n",
      "* `$i` is the Julia's way to do String concatenation by evaluating `i`, much like Perl's"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i = sequence\n",
      "    figure(figsize=(5, 3))\n",
      "    plt.hist(flip_runs(i, 1000))\n",
      "    title(\"Heads frequency in 1000 runs of $i coin tosses\");\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x120f116c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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S0jq/hiHao+57j+K0tOV3381w48YNSJJU4zpCCF3btXkNY0REROCpp54yaZ37GTNmjOx25IiICAD6+5CWoc9vs2bNYG1tfd/X2rp1K65fv47Q0FD06dNHb9krr7wCV1dXpKWl4dKlS6Z0waA333wTWVlZWLt2rW7fro1169ahuLgYkZGRss8nAL2zquvXr8ft27cxbdo02dH9W2+9BWtra6xfvx6VlZVGvfazzz4rO5P24osvwszMzOC2MUQIUePyjz/+GACwbNkyNG/eXFfevHlzvP322wCAjz76SLaeof3A0dHRqHr37i8rV64EAHz44YewtbXVqztx4kQ89dRTSE5ONqptOzs7o+8KeSiGGCRJQlVVVbXL27VrJ/tAHTx4EACQlZVl8BTmL7/8AuDOKTh3d3dd+fr167F27VqcOHECRUVFeq9774fs2LFjMDMzw7PPPitr39ApwG7dusHDwwMpKSm4cOECRo0ahWeffRY+Pj4GE5O66NWrl6xM+54UFRUZfE/y8/MBQJc0FRcX47fffkPbtm0Nnjrt379/vcSqjSsnJ8dgXNnZ2bq47h1m8PHxkdVv06YNAOD69eu6skOHDgEAhgwZYlRMf//737FixQqsWrUKL7zwAgCgoKAAW7ZsQdeuXQ1uc1N16tTJ4B+Vxx9/HEIIXL9+Xe8Liwzv13Vl7D40YMAAtG7dGsuWLcOxY8cQEBCAZ599Fh4eHkbfx3/s2DEA0A3d3M3MzAz9+vXDZ599hqysLKNuVa3ODz/8gKVLl+LVV1/F008/Xet2gP99dgwN8d2rpv7Z29vD09MTGRkZOHPmDHr06HHf9gxtm2bNmuGxxx7T2zZ1of0eN/Sd3a9fPygUCmRlZenKxo0bhy1btuDpp59GaGgoBgwYgD59+uj2GS1T9peDBw/C3NwcGzZsMJjQVFZWIj8/H9evX4eDgwPGjBmDlStX4rnnnkNQUBD8/PzQp08fdOzY0aS+PxQJQm1cu3YNwJ2MrDqSJKGkpET3+8yZM/H+++/DxcUFAQEBaN26NVQqFYA7R9L3zrNw48YNqNVq3fj+3R577DFZmUKhwN69e/Hmm29i06ZNuiNZGxsbTJw4EUuXLoWVlZXpnTWgVatWsjLte5KWloa0tDSD6939nmiPAg31pbrXqA1tXBs3bqy2zr3bSsvQWRft2NvdyZ32SLV169ZGxdS+fXsMGTIEu3fvxrlz59ChQwesW7cOlZWV9XL2AKj+jJGh+OuT9uj93vF7LW353fHde4bgfuvU5jWMUV/73N2M3YdsbGxw6NAhLFq0CKmpqbozik5OToiKisJrr71233Ffbb+dnZ0NLteWm3pm5W5//vknJkyYgM6dO2PJkiUG69zvqPpupnx2jO1fdfvFvWr6jNTX50P7PW5o2zVr1gxOTk4oKCjQlT3//PPYvn074uPj8fHHH+vOKnp7e2Pp0qX429/+BsC0/eXatWuoqqqqdnsBd74Db926BQcHB/Ts2RMZGRl46623sGnTJnz22WcAgM6dO2PRokUYM2aMUX1/aIYYTKX9gvrxxx+h0WgM/lRVVWH8+PEAgD/++AMrV65E9+7dcfbsWXz66adYunQp3njjDbzxxht6Qwh3v0ZhYaHBHfXq1asG47K3t8e7776LixcvIjs7Gx999BG6dOmCxMTEep3syNApJu17snLlyhrfE+0kKtr6v//+u8HXqK6P2uzY0OQ5hr74tK+TmppaY1w1Ddvcj/aLJjc31+h1oqKiIITQJZmrV6+GSqVqsIsH/yraIbezZ88aXK49Y3P3KeLOnTtXu86ff/6J8+fPw9zcHB06dABwZ/jExcUFt27dMrifGHoNY1R36lS7z/35558Gl9flD+7dWrdujY8++gh//PEHfv75Z6xcuRJqtVo33Hk/2n29us9OXl6eXr3auHXrFrKzs3Hq1ClYWlrqJkdSKBS6GKdOnQqFQoGZM2fetz1TPjvauLX9uFd99K++1fQ9/ueff6KgoEB22n/YsGHYs2cPioqKsGfPHsycORMnT55EYGCg3rC1sfuLnZ0dHB0dq/3+034H3n1W6ZlnnsG2bdtQVFSE77//Hq+//jp+//13jB071uBwrCGPbILQu3dvAEB6erpR9c+dOwchBPz9/WVH8bm5uTh37pxsHW9vb1RVVSEjI0O2THuFf006duyIF198EQcOHICVlRVSU1ONirW2TH1PbGxs8MQTT1Tb/+r66ODgACGEwZktMzMz6xxXbWhfY/fu3UYfPQ0fPhyurq745JNP8M033yA7OxshISEP1JdbbWjH29PS0mTvRXFxMb7//ntYWVnhmWee0ZX7+fkBuHMF973S09NRVlYGX19fvaEyPz8/CCEMrrNz504Ahk9F14Z26mFD+9yvv/5q8DqluuratSumTZumOxt37/UqhmjvUtLeSXK3P//8ExkZGZAkqca7me7H0tISU6ZMQXh4uOxHe+V+3759ER4eDl9f3/u2p/3saLdZTbRxG/pu0N71oFKp9IZ1G5r2DG91Zxy8vLxQVVVlcDr09PR0aDSaareHSqXCwIEDER8fjwULFqCysrLa96mm/aV37966OyFMZW5ujt69e2PJkiW6axmM/VvyyCYIkydPhr29PZYsWWLwYhaNRqO3E2vH2DMyMvSOfG/duoWpU6ca3Lm0U3cuXLgQFRUVuvLCwkKDt8fl5OQY/ENbWFiIiooK3XBGQ/H29kbfvn3x5Zdf6i6wvNdPP/2kuxYBuNNHjUaDuXPn6v0xOX/+vG5nvJd2zPPe4Z09e/YgJSVFVn/UqFHo2LEj/vWvf1X74Tp48CDKyspq7mANvLy84Ovri6ysLN2FR3e7du2a3jYE7hytvvTSS/jjjz8wZcoUANC7naup6tChA/z9/XH+/Hn861//0lu2aNEilJaWYvz48Xr7Y1BQEJycnPCf//wHR48e1ZWXl5fjtddeAwDZGTDte/XWW2/pHcHn5OTgX//6FywtLett+lt3d3fY2tpi69atevtvWVlZvV1Me+rUKYNn07RnA4y5XuS5556Do6MjUlJS8MMPP+gtS0hIQE5ODv72t7/JxrNNYWlpiQ8//BCrV6+W/YwYMQLAnQvfVq9ejeDg4Pu2N3HiRNja2iIpKcngwdDdZxbGjRsHc3Nz/POf/8Rvv/2mV+/1119HcXGxrs5fRZs8XrhwweDyF198EQAwf/58ve+Y0tJSzJs3DwB0n3/gTtJQ01lj7QGmKfuL9kzO1KlTDZ59KSkp0V0LAtyZ8ry8vNyotmvyyFyDcO+RkKOjIzZt2oTnn38ezzzzDPz8/NC1a1dIkoRLly7h4MGDuH79uu5K8cceewxjxozBf/7zH3h4eGDw4MG4ceMG0tLS0Lx5c3h4eOhdqAIAYWFh+OKLL5Camoonn3wSI0eOxO3bt7F582b06tVLlgxkZWXhhRdeQK9evdClSxe4uLggPz8fW7duRVVVlcGr6+vb559/jkGDBmHKlClYuXIlevXqBXt7e+Tm5uLHH3/EyZMncejQIbRo0QLAnSurv/rqK2zevBleXl7w9/dHUVERNm7ciP79+xs8apo8eTKWL1+OpUuX4sSJE3B3d8cvv/yim5fi7rskgDvjfF9++SWGDBmC4cOHw9fXF0899RSaN2+OS5cu4ciRIzh//jyuXr1apyRq/fr1GDBgABYsWIDNmzejf//+EEIgOzsbaWlpOHv2LNq2bau3zpQpU7B48WJcvnwZPXr0qPMFXw3hzJkzWLZsmV5ZYWGhbp4GSZKwYsUK3f38wJ35I3x9fRETE4M9e/agS5cu+OGHH7B//3507twZb731ll57NjY2+PDDDxEUFIQBAwZgzJgxcHBwQGpqKn755RcEBwfL7ozp3bs3Zs2ahXfffRc9evTA6NGjUVlZiS+++AJFRUX45z//KXu/a6tZs2aYPn06YmNj4enpieeeew5//vknvv32W7Ru3RouLi4mjbsb8s033+DVV1+Fr68vOnXqhJYtWyI3Nxdbt26FmZkZXn311fu2YWVlhY8//hjBwcHo378/goOD8fjjj+Po0aNIS0uDs7Ozbkz7QaFWq/H5558jKCgIAwcOREBAALp3746bN2/ixx9/1DvD6OrqioSEBERHR8PLywshISFwcnLCgQMHcOjQIbi7uxtM0Ou6bWpibW2NZ555BhkZGRg3bhw6deoEMzMzjBo1Ct27d0dYWBi2bt2KDRs2oFu3bhg1ahQkScJXX32FnJwcjBkzBmFhYbr2YmJicOXKFfTp0weurq6wsLDA0aNHsW/fPrRr1043/m/K/jJo0CAsW7YM8+fPR6dOnTBs2DC0a9cOt27dwoULF5Ceno6+ffvi66+/BgC888472LdvH/r27Yt27drB2toaJ0+exK5du+Do6Ki7C+e+jLoZshr/+Mc/hCRJ4sknn5QtO3XqlBgyZIiwtrYWjo6OYvz48SI/P99gOx999JHo0qWLsLS0FJ06dRL//Oc/jY7BmJkU27VrV+1Mijk5OWLatGmiU6dOwtLSUtjZ2Ql3d3cxYcIEsXXrVr26paWlYuHCheKJJ54QlpaWom3btmLatGni2rVrYsCAAQbjqKysNDiTYkVFhWwehNzcXLFgwQLRp08f3cx5jz/+uBg2bJjYtWuX0e/J2rVrhUKhMDgPwqRJk+477XRxcbGIi4sT3t7ewtraWqhUKtGhQwcRGBgoPvzwQ717gYW4M5PirFmzdDMpuru7i3fffVecO3eu2vuLT548KYYNGyZsbGyEtbW1GDhwoEhPT68x9j/++EPMmzdPPPnkk6J58+bC2tpauLm5ieDgYJGcnKw3J8HixYuFQqGQzS8gxP9mnDQU17Vr18TcuXNF586dhaWlpXBwcBCenp7itddeq/Z5Cc8//7yQJEl88MEH1b6n1akuzpqm4TZmG95Ne8+4QqHQ/av90f5uqK1Lly6JyZMnC2dnZ2FhYSHatWsnZs6caXDWNq3vv/9eDBs2TDg4OAiVSiV69OghEhISarzveu3ataJnz57CyspK2NraigEDBogdO3YY1Tetmrb33ZYtWyY6duwoLCwshKurq5g7d64oLS0V7dq1k82DUNO+KIR8G50+fVrMmjVL+Pj46GZAbN++vQgODhYHDx40qT9HjhwRzz//vGjRooUuVkMzKQpR+3kQDNG+j7WZSfHkyZNiwoQJonXr1sLCwkK0atVKDBgwQHz44Yeyut98843w9/fXzaTYqVMnMXfuXIMzKRr6br1fnw1tz5r8+uuvYsSIEUKtVus+G3dvd41GIz744APh4+MjmjdvLqysrISPj4/Bz/yGDRtEWFiY6NSpk7C2tha2traie/fu4rXXXhMFBQW6erXZX7777jsREhIiXFxchIWFhWjZsqXw9PQUr7zyit5Mu998842YPHmy6Nq1q7CzsxNWVlaiS5cuYvr06eLixYtGvy+SELVLzXJzc9G5c2coFAq0b99eb2bA3NxceHp6wsHBATExMSguLsaKFSvQtm1bHD58WO/0kXZWraCgIAwZMgTp6en47LPPsGzZMsyZM6c2odEDIicnBx06dMCkSZN09xI/bDQaDTp27IiCggLk5eUZda87EVFTUOshhtmzZ8PX11d3Fefd4uLiUFZWhuPHj+vGynr16oXBgwdj7dq1uolqysrKsHDhQgQGBmLDhg0A7pyy1Wg0iI2NRURERL1ODkRU3zZu3IgLFy4gMjKSyQERPVRqdZFieno6Nm/ejISEBAghZLcWbd68GYGBgXoX0vj5+cHNzU2XCAB3rtQtLCxEVFSU3vrR0dEoKSnhM+HpgaU9w/XSSy/B2toa8+fPb+yQiIjqlckJQlVVFV5++WVMnTpVNoUtAFy+fBn5+fkGZ7jq2bMnjh8/rvtd+/9763p5eclmpyJ6kCxYsAArV65Ehw4dsGXLljpdVU5E9CAyeYjh3//+Ny5evKh7etu9tLdgGJopy9nZGYWFhbh9+zbMzc2Rl5cHMzMzODk56dWzsLCAWq3GlStXTA2PHiDt2rV+m7MsAAAgAElEQVQzOBnSw+Bh7RcRkZZJCcK1a9d0MwfefUvU3bT3iRp6+If2wRFlZWUwNzdHWVmZwRkItevXdF97Xl5etbNxERHRo8HZ2bnaqZupbkxKEF577TU4OTnh5ZdfrraO9j70eyeVAaCbuEFbR6VSVfvUrvLy8mrvac/Ly4OPjw/PMBARPeJcXFyQmZnJJKEBGJ0gZGdn48MPP0RCQoLezFjl5eWorKzEhQsXYGtrq9tIho7u8/LyoFardbc5Ojs7o6qqCgUFBXrDDJWVlSgsLNR7TOi97Vy5cgXr16//S6fkrE8zZsxAQkJCY4dRa009fqDp96Gpxw80/T409fiBpt2H06dPY9y4ccjLy2OC0ACMThAuX74MjUaDmJgYg1OTtm/fHjNmzMC7776LFi1aGJy++PDhw/Dw8ND9rp33+8iRI3qPCs3MzIRGo9Gra4i7u3ud5iRvTPb29k02dqDpxw80/T409fiBpt+Hph4/8HD0gRqG0QlC9+7dsWXLFr1bGoUQeO2113Dr1i28//77umdNjx49GuvWrUNubq7u6u49e/YgOzsbr7zyim79QYMGwdHREUlJSXoJQlJSEqysrDB8+PA6d5CIiIhMZ3SCoFarMWrUKFn5e++9BwAYOXKkrmzBggXYuHEjBg4ciOnTp6O4uBjLly9Hjx499B6+YmlpidjYWERHRyMkJAT+/v7IyMhAcnIy4uLiOEkSERFRI6nzw5okSZJNlNSmTRscOHAAs2bNwrx586BUKhEYGIj4+HjZU7oiIyNhbm6O+Ph4pKamom3btkhISKi3J6wRPaxKSkpw7Nixxg7DIBsbG3Tq1KmxwyCiOqhzgmDoueXAnWdbG3rOuyHaZ5E/Su5++ldT1NTjB5p2H7Kzs7F37154e3s3dijV+uWXX+6bJDTlbQA0/fiBh6MP1DAemcc9P2ia+oeyqccPNO0+FBcX/9//1gN40O7kOQ1g3F0xVq8pbwOg6ccPPBx9oIbBBIGoSXMHwCvQiaj+1ephTURERPRwY4JAREREMkwQiIiISIYJAhEREckwQSAiIiIZJghEREQkwwSBiIiIZJggEBERkQwTBCIiIpJhgkBEREQyTBCIiIhIhgkCERERyTBBICIiIhkmCERERCRjUoJw8uRJBAcHo2PHjrCysoJarYavry+Sk5P16k2aNAkKhUL24+5u+Ln1a9asgbu7O1QqFdzc3JCYmFj7HhEREVGdNTOl8sWLF3Hr1i1MmjQJLi4uKC0txaZNmzB+/Hjk5ORg4cKFurpKpRJr1qzRW9/Ozk7W5qpVqxAZGYmgoCDMnj0b6enpiImJQWlpKebMmVPLbhEREVFdmJQgBAQEICAgQK8sOjoa3t7eWL16tV6CYG5ujrFjx9bYXllZGRYuXIjAwEBs2LABADBlyhRoNBrExsYiIiIC9vb2poRIRERE9aDO1yAoFAq0adMG5ubmeuVCCGg0Gty8ebPadfft24fCwkJERUXplUdHR6OkpAQ7duyoa3hERERUC7VKEEpLS1FQUIDffvsN7733Hnbv3i0bDigtLYWtrS3s7e2hVqsxbdo0lJSU6NU5fvw4AMDHx0ev3MvLCwqFAllZWbUJj4iIiOrIpCEGrVmzZmH16tV3GmjWDCtXrkRERIRuuYuLC+bOnQsvLy9oNBrs3LkTH3zwAU6cOIH9+/fDzMwMAJCXlwczMzM4OTnptW9hYQG1Wo0rV67Utl9ERERUB7VKEGbOnImQkBBcuXIFycnJmDZtGlQqFSZOnAgAiIuL06sfEhICNzc3LFy4EJs2bUJoaCiAO9cgWFhYGHwNpVKJsrKy2oRHREREdVSrBKFz587o3LkzAGDcuHEYMmQIZsyYgZCQEKhUKoPrzJw5E6+//jr27NmjSxBUKhUqKysN1i8vL6+2La0ZM2bILmIMCwtDWFiYqV0iIqIHWEpKClJSUvTKioqKGimaR0OtEoR7jR49GmlpaTh79iw8PDwM1rG0tISjoyMKCwt1Zc7OzqiqqkJBQYHeMENlZSUKCwvh4uJS4+smJCTAy8urPrpAREQPMEMHf8eOHYO3t3cjRfTwq5eZFLVDAQpF9c0VFxejoKAALVq00JV5enoCAI4cOaJXNzMzExqNptpkg4iIiBqWSQlCfn6+rOz27dv49NNPoVar0a1bN1RUVKC4uFhWLzY2FgAwdOhQXdmgQYPg6OiIpKQkvbpJSUmwsrLC8OHDTQmPiIiI6olJQwwREREoLi5Gv3794OLigqtXryI5ORm//PILPvnkE5iZmeHSpUvw9PTE2LFjddcp7N69Gzt37kRAQABGjRqla8/S0hKxsbGIjo5GSEgI/P39kZGRgeTkZMTFxXGSJCIiokZiUoIwZswYrFmzBklJSbh27RpsbW3x9NNPIzExEX5+fgAABwcHjBgxAmlpaVi3bh2qqqrQqVMnLF26FLNnz5a1GRkZCXNzc8THxyM1NRVt27ZFQkICYmJi6qeHREREZDKTEoTQ0FDdHQjVsbOzw6effmpSEOHh4QgPDzdpHSIiImo4fNwzERERyTBBICIiIhkmCERERCTDBIGIiIhkmCAQERGRDBMEIiIikmGCQERERDJMEIiIiEiGCQIRERHJMEEgIiIiGSYIREREJMMEgYiIiGSYIBAREZEMEwQiIiKSYYJAREREMkwQiIiISMakBOHkyZMIDg5Gx44dYWVlBbVaDV9fXyQnJ8vqnj59GkOHDoWNjQ3UajUmTJiAgoICg+2uWbMG7u7uUKlUcHNzQ2JiYu16Q0RERPWimSmVL168iFu3bmHSpElwcXFBaWkpNm3ahPHjxyMnJwcLFy4EAOTm5qJfv35wcHDA0qVLUVxcjBUrVuCnn37C4cOHYW5urmtz1apViIyMRFBQEGbPno309HTExMSgtLQUc+bMqd/eEhERkXFEHVVVVQkPDw/Rtm1bXVlkZKSwsrISly5d0pV9++23QpIksXr1al1ZaWmpUKvVYsSIEXptjhs3TlhbW4vr168bfM2jR48KAOLo0aN1DZ+oSdJ+BoCjAhAP2A8/n/TX4N+ChlXnaxAUCgXatGmjd1Zg8+bNCAwMRJs2bXRlfn5+cHNzw4YNG3Rl+/btQ2FhIaKiovTajI6ORklJCXbs2FHX8IiIiKgWapUglJaWoqCgAL/99hvee+897N69WzcccPnyZeTn58PHx0e2Xs+ePXH8+HHd79r/31vXy8sLCoUCWVlZtQmPiIiI6sikaxC0Zs2ahdWrV99poFkzrFy5EhEREQCAvLw8AICzs7NsPWdnZxQWFuL27dswNzdHXl4ezMzM4OTkpFfPwsICarUaV65cqU14REREVEe1ShBmzpyJkJAQXLlyBcnJyZg2bRpUKhUmTpyIsrIyAIBSqZStZ2lpCQAoKyuDubk5ysrKYGFhYfA1lEqlri0iIiL6a9UqQejcuTM6d+4MABg3bhyGDBmCGTNmIDQ0FCqVCgBQUVEhW6+8vBwAdHVUKhUqKysNvkZ5ebmuXnVmzJgBe3t7vbKwsDCEhYWZ1iEiInqgpaSkICUlRa+sqKiokaJ5NNQqQbjX6NGjkZaWhjNnzuiGFrRDDXfLy8uDWq3WXdDo7OyMqqoqFBQU6A0zVFZWorCwEC4uLjW+bkJCAry8vOqjC0RE9AAzdPB37NgxeHt7N1JED796mUlROxSgUCjQunVrtGjRAkeOHJHVO3z4MDw8PHS/e3p6AoCsbmZmJjQajV5dIiIi+uuYlCDk5+fLym7fvo1PP/0UarUa3bp1A3DnjML27duRm5urq7dnzx5kZ2cjODhYVzZo0CA4OjoiKSlJr82kpCRYWVlh+PDhJnWGiIiI6odJQwwREREoLi5Gv3794OLigqtXryI5ORm//PILPvnkE5iZmQEAFixYgI0bN2LgwIGYPn06iouLsXz5cvTo0QOTJ0/WtWdpaYnY2FhER0cjJCQE/v7+yMjIQHJyMuLi4mTXFxAREdFfw6QEYcyYMVizZg2SkpJw7do12Nra4umnn0ZiYiL8/Px09dq0aYMDBw5g1qxZmDdvHpRKJQIDAxEfH683oRIAREZGwtzcHPHx8UhNTUXbtm2RkJCAmJiY+ukhERERmcykBCE0NBShoaFG1e3atSt27dplVN3w8HCEh4ebEgoRERE1ID7umYiIiGSYIBAREZEMEwQiIiKSYYJAREREMkwQiIiISIYJAhEREckwQSAiIiIZJghEREQkwwSBiIiIZJggEBERkQwTBCIiIpJhgkBEREQyTBCIiIhIhgkCERERyTBBICIiIhkmCERERCRjdIJw5MgRTJs2Dd26dYO1tTVcXV0RGhqK7OxsvXqTJk2CQqGQ/bi7uxtsd82aNXB3d4dKpYKbmxsSExPr1iMiIiKqs2bGVnz77bdx8OBBBAcHo0ePHsjLy0NiYiK8vLxw6NAhdOvWTVdXqVRizZo1euvb2dnJ2ly1ahUiIyMRFBSE2bNnIz09HTExMSgtLcWcOXPq0C0iIiKqC6MThFdeeQU9e/ZEs2b/WyU0NBTdu3fHsmXL8Nlnn+nKzc3NMXbs2BrbKysrw8KFCxEYGIgNGzYAAKZMmQKNRoPY2FhERETA3t7e1P4QERFRPTB6iKF37956yQEAPPHEE+jatSvOnDmjVy6EgEajwc2bN6ttb9++fSgsLERUVJReeXR0NEpKSrBjxw5jQyMiIqJ6VqeLFIUQ+P333+Hk5KRXXlpaCltbW9jb20OtVmPatGkoKSnRq3P8+HEAgI+Pj165l5cXFAoFsrKy6hIaERER1YHRQwyGJCcn48qVK/jHP/6hK3NxccHcuXPh5eUFjUaDnTt34oMPPsCJEyewf/9+mJmZAQDy8vJgZmYmSy4sLCygVqtx5cqVuoRGBmRnZ6O4uLixwzDIxsYGnTp1auwwiIjo/9Q6QThz5gyio6Ph6+uLiRMn6srj4uL06oWEhMDNzQ0LFy7Epk2bEBoaCuDONQgWFhYG21YqlSgrK6ttaGRAdnY23NzcGjuMGv3yyy9MEoiIHhC1ShCuXr2K4cOHw8HBAZs2bYIkSTXWnzlzJl5//XXs2bNHlyCoVCpUVlYarF9eXg6VSnXfOGbMmCG7kDEsLAxhYWFG9uTR8b8zB+sBGL7ltPGcBjDugT27QUSNLyUlBSkpKXplRUVFjRTNo8HkBOHGjRsICAjAzZs3kZGRgVatWt13HUtLSzg6OqKwsFBX5uzsjKqqKhQUFOgNM1RWVqKwsBAuLi73bTchIQFeXl6mduER5w6A7xkRNS2GDv6OHTsGb2/vRoro4WfSRYrl5eUYMWIEfv31V2zfvh1dunQxar3i4mIUFBSgRYsWujJPT08AdyZgultmZiY0Gg08PDxMCY2IiIjqkdEJQlVVFUJDQ/HDDz9g48aNePrpp2V1KioqDJ4mjo2NBQAMHTpUVzZo0CA4OjoiKSlJr25SUhKsrKwwfPhwoztBRERE9cukiZK2bduGESNGoKCgAOvXr9dbPm7cOOTl5cHT0xNjx45F586dAQC7d+/Gzp07ERAQgFGjRunqW1paIjY2FtHR0QgJCYG/vz8yMjKQnJyMuLg4TpJERETUiIxOEE6cOAFJkrBt2zZs27ZNb5kkSRg3bhwcHBwwYsQIpKWlYd26daiqqkKnTp2wdOlSzJ49W9ZmZGQkzM3NER8fj9TUVLRt2xYJCQmIiYmpe8+IiIio1oxOEPbt23ffOnZ2dvj0009NCiA8PBzh4eEmrUNEREQNi497JiIiIhkmCERERCTDBIGIiIhk6vQsBiKipobPJCEyDhMEInpk8JkkRMZjgkBEjww+k4TIeEwQiOgRxGeSEN0PL1IkIiIiGSYIREREJMMEgYiIiGSYIBAREZEMEwQiIiKSYYJAREREMkwQiIiISIYJAhEREckwQSAiIiIZoxOEI0eOYNq0aejWrRusra3h6uqK0NBQZGdny+qePn0aQ4cOhY2NDdRqNSZMmICCggKD7a5Zswbu7u5QqVRwc3NDYmJi7XtDRERE9cLoqZbffvttHDx4EMHBwejRowfy8vKQmJgILy8vHDp0CN26dQMA5Obmol+/fnBwcMDSpUtRXFyMFStW4KeffsLhw4dhbm6ua3PVqlWIjIxEUFAQZs+ejfT0dMTExKC0tBRz5syp/94SERGRUYxOEF555RX07NkTzZr9b5XQ0FB0794dy5Ytw2effQYAiIuLQ1lZGY4fP442bdoAAHr16oXBgwdj7dq1mDp1KgCgrKwMCxcuRGBgIDZs2AAAmDJlCjQaDWJjYxEREQF7e/t66ygREREZz+ghht69e+slBwDwxBNPoGvXrjhz5oyubPPmzQgMDNQlBwDg5+cHNzc3XSIAAPv27UNhYSGioqL02oyOjkZJSQl27NhhcmeIiIioftTpIkUhBH7//Xc4OTkBAC5fvoz8/Hz4+PjI6vbs2RPHjx/X/a79/711vby8oFAokJWVVZfQiIiIqA7qlCAkJyfjypUrCA0NBQDk5eUBAJydnWV1nZ2dUVhYiNu3b+vqmpmZ6ZILLQsLC6jValy5cqUuoREREVEd1DpBOHPmDKKjo+Hr64uJEycCuHNdAQAolUpZfUtLS706ZWVlsLCwMNi2UqnU1SMiIqK/ntEXKd7t6tWrGD58OBwcHLBp0yZIkgQAUKlUAICKigrZOuXl5Xp1VCoVKisrDbZfXl6uq1eTGTNmyC5kDAsLQ1hYmPGdISKiB15KSgpSUlL0yoqKihopmkeDyQnCjRs3EBAQgJs3byIjIwOtWrXSLdMOLWiHGu6Wl5cHtVqtu83R2dkZVVVVKCgo0BtmqKysRGFhIVxcXO4bS0JCAry8vEztAhERNTGGDv6OHTsGb2/vRoro4WfSEEN5eTlGjBiBX3/9Fdu3b0eXLl30lrdu3RotWrTAkSNHZOsePnwYHh4eut89PT0BQFY3MzMTGo1Gry4RERH9tYxOEKqqqhAaGooffvgBGzduxNNPP22w3ujRo7F9+3bk5ubqyvbs2YPs7GwEBwfrygYNGgRHR0ckJSXprZ+UlAQrKysMHz7c1L4QERFRPTFpoqRt27ZhxIgRKCgowPr16/WWjxs3DgCwYMECbNy4EQMHDsT06dNRXFyM5cuXo0ePHpg8ebKuvqWlJWJjYxEdHY2QkBD4+/sjIyMDycnJiIuL4yRJREREjcjoBOHEiROQJAnbtm3Dtm3b9JZJkqRLENq0aYMDBw5g1qxZmDdvHpRKJQIDAxEfH683zTIAREZGwtzcHPHx8UhNTUXbtm2RkJCAmJiYeugaERER1ZbRCcK+ffuMbrRr167YtWuXUXXDw8MRHh5udNtERETU8Pi4ZyIiIpJhgkBEREQyTBCIiIhIhgkCERERyTBBICIiIhkmCERERCTDBIGIiIhkmCAQERGRDBMEIiIikmGCQERERDJMEIiIiEiGCQIRERHJMEEgIiIiGSYIREREJMMEgYiIiGSYIBAREZGMSQlCSUkJFi1ahKFDh8LR0REKhQLr1q2T1Zs0aRIUCoXsx93d3WC7a9asgbu7O1QqFdzc3JCYmFi73hAREVG9aGZK5fz8fMTGxsLV1RUeHh7Yv38/JEkyWFepVGLNmjV6ZXZ2drJ6q1atQmRkJIKCgjB79mykp6cjJiYGpaWlmDNnjinhERERUT0xKUFwcXHB1atX0bJlSxw9ehQ9e/astq65uTnGjh1bY3tlZWVYuHAhAgMDsWHDBgDAlClToNFoEBsbi4iICNjb25sSIhEREdUDk4YYLCws0LJlSwCAEKLGukIIaDQa3Lx5s9o6+/btQ2FhIaKiovTKo6OjUVJSgh07dpgSHhEREdWTBrtIsbS0FLa2trC3t4darca0adNQUlKiV+f48eMAAB8fH71yLy8vKBQKZGVlNVR4REREVAOThhiM5eLigrlz58LLywsajQY7d+7EBx98gBMnTmD//v0wMzMDAOTl5cHMzAxOTk5661tYWECtVuPKlSsNER4RERHdR4MkCHFxcXq/h4SEwM3NDQsXLsSmTZsQGhoK4M41CBYWFgbbUCqVKCsra4jwiIiI6D4aJEEwZObMmXj99dexZ88eXYKgUqlQWVlpsH55eTlUKlWNbc6YMUN2EWNYWBjCwsLqJ2giInogpKSkICUlRa+sqKiokaJ5NPxlCYKlpSUcHR1RWFioK3N2dkZVVRUKCgr0hhkqKytRWFgIFxeXGttMSEiAl5dXg8VMREQPBkMHf8eOHYO3t3cjRfTw+8tmUiwuLkZBQQFatGihK/P09AQAHDlyRK9uZmYmNBoNPDw8/qrwiIiI6C71niBUVFSguLhYVh4bGwsAGDp0qK5s0KBBcHR0RFJSkl7dpKQkWFlZYfjw4fUdHhERERnB5CGGxMREFBUV6e4wSE1NxcWLFwEAMTExKCwshKenJ8aOHYvOnTsDAHbv3o2dO3ciICAAo0aN0rVlaWmJ2NhYREdHIyQkBP7+/sjIyEBycjLi4uI4SRIREVEjMTlBiI+Px4ULFwAAkiRhy5Yt+PLLLyFJEiZMmAAHBweMGDECaWlpWLduHaqqqtCpUycsXboUs2fPlrUXGRkJc3NzxMfHIzU1FW3btkVCQgJiYmLq3jsiIiKqFZMThPPnz9+3zqeffmpSm+Hh4QgPDzc1FCIiImogfNwzERERyTBBICIiIhkmCERERCTDBIGIiIhkmCAQERGRDBMEIiIikmGCQERERDJMEIiIiEiGCQIRERHJMEEgIiIiGSYIREREJMMEgYiIiGSYIBAREZEMEwQiIiKSYYJAREREMkwQiIiISMakBKGkpASLFi3C0KFD4ejoCIVCgXXr1hmse/r0aQwdOhQ2NjZQq9WYMGECCgoKDNZds2YN3N3doVKp4ObmhsTERNN7QkRERPXGpAQhPz8fsbGxOHv2LDw8PAAAkiTJ6uXm5qJfv344d+4cli5ditmzZ2PHjh0YPHgwbt++rVd31apVmDp1Krp3747ExET07t0bMTExeOedd+rQLSIiIqqLZqZUdnFxwdWrV9GyZUscPXoUPXv2NFgvLi4OZWVlOH78ONq0aQMA6NWrFwYPHoy1a9di6tSpAICysjIsXLgQgYGB2LBhAwBgypQp0Gg0iI2NRUREBOzt7evSPyIiIqoFk84gWFhYoGXLlgAAIUS19TZv3ozAwEBdcgAAfn5+cHNz0yUCALBv3z4UFhYiKipKb/3o6GiUlJRgx44dpoRHRERE9aTeL1K8fPky8vPz4ePjI1vWs2dPHD9+XPe79v/31vXy8oJCoUBWVlZ9h0dERERGqPcEIS8vDwDg7OwsW+bs7IzCwkLddQh5eXkwMzODk5OTXj0LCwuo1WpcuXKlvsMjIiIiI9R7glBWVgYAUCqVsmWWlpZ6dcrKymBhYWGwHaVSqatHREREfy2TLlI0hkqlAgBUVFTIlpWXl+vVUalUqKysNNhOeXm5rl51ZsyYIbuIMSwsDGFhYSbHTURED66UlBSkpKTolRUVFTVSNI+Gek8QtEML2qGGu+Xl5UGtVsPc3FxXt6qqCgUFBXrDDJWVlSgsLISLi0uNr5WQkAAvL696jJ6IiB5Ehg7+jh07Bm9v70aK6OFX70MMrVu3RosWLXDkyBHZssOHD+vmTwAAT09PAJDVzczMhEaj0atLREREf50GmWp59OjR2L59O3Jzc3Vle/bsQXZ2NoKDg3VlgwYNgqOjI5KSkvTWT0pKgpWVFYYPH94Q4REREdF9mDzEkJiYiKKiIt0dBqmpqbh48SIAICYmBra2tliwYAE2btyIgQMHYvr06SguLsby5cvRo0cPTJ48WdeWpaUlYmNjER0djZCQEPj7+yMjIwPJycmIi4vjJElERESNxOQEIT4+HhcuXABwZ5rlLVu24Msvv4QkSZgwYQJsbW3Rpk0bHDhwALNmzcK8efOgVCoRGBiI+Ph43fUHWpGRkTA3N0d8fDxSU1PRtm1bJCQkICYmpn56SERERCYzOUE4f/68UfW6du2KXbt2GVU3PDwc4eHhpoZCREREDYSPeyYiIiIZJghEREQkwwSBiIiIZJggEBERkQwTBCIiIpJhgkBEREQyTBCIiIhIhgkCERERyTBBICIiIhkmCERERCTDBIGIiIhkmCAQERGRjMkPayIiokdLdnY2iouLGzsMmdOnTzd2CA81JghERFSt7OxsuLm5NXYY1AiYIBARUbX+d+ZgPQD3xgzFgK8BvN7YQTy0mCAQEZER3AF4NXYQ9+AQQ0NqkIsU9+/fD4VCYfDn8OHDenVPnz6NoUOHwsbGBmq1GhMmTEBBQUFDhEVERERGatAzCNOnT0fPnj31yjp27Kj7f25uLvr16wcHBwcsXboUxcXFWLFiBX766SccPnwY5ubmNbZfUlLywF04Y2lped+4iYiIHnQNmiD07dsXL7zwQrXL4+LiUFZWhuPHj6NNmzYAgF69emHw4MFYu3Ytpk6dWmP7/fr1q9d460PHjm749dezjR0GERFRnTRogiCEQHFxMVQqFZo1k7/U5s2bERgYqEsOAMDPzw9ubm7YsGHDfRMEYCmA9vUbdJ18jcuXNzd2EERERHXWoAnC5MmTcevWLZiZmaFv375Yvnw5vL29AQCXL19Gfn4+fHx8ZOv17NkTO3fuNOIV/PFgXTSTB4AJAhERNX0NkiAolUoEBQVh2LBhcHJywsmTJ7FixQr07dsX//3vf+Hh4YG8vDwAgLOzs2x9Z2dnFBYW4vbt2xzPJyIiagQNkiD07t0bvXv31v0eGBiIoKAg9OjRA/Pnz8fOnTtRVlYG4E4ycS9LS0sAQFlZGRMEIiKiRvCXzYPQsWNHjBw5Elu2bIEQAiqVCgBQUVEhq1teXg4AujrVmwHA/p6ysP/7ISKih0fK//3cLbcxAnlk/KUTJT3++OOorKxESUmJbmhBO9Rwt7y8PKjVaqbpXMoAAAzOSURBVCPOHiTgwboGgYiIGoahg79kAOMaIZZHw1+aIJw7dw4qlQrW1tawtrZGixYtcOTIEVm9w4cPw8PD468MjYiIiO7SIDMp5ufny8pOnDiB1NRU+Pv768pGjx6N7du3Izf3f6eJ9uzZg+zsbAQHBzdEaERERGSEBjmDEBoaiubNm6N3795o2bIlTp06hdWrV8Pa2hrLli3T1VuwYAE2btyIgQMHYvr06SguLsby5cvRo0cPTJ48uSFCIyIiIiM0yBmE559/HgUFBXjvvfcQHR2NjRs3IigoCJmZmejcubOuXps2bXDgwAF07NgR8+bNw4oVKxAYGIi0tDTevUBERNSIGuQMwssvv4yXX37ZqLpdu3bFrl27GiIMIiIiqqUGOYNARERETRsTBCIiIpJhgkBEREQyTBCIiIhIhgkCERERyTBBICIiIhkmCERERCTDBIGIiIhkmCAQERGRDBMEIiIikmGCQERERDJMEIiIiEiGCQIRERHJMEEgIiIiGSYIREREJMMEgYiIiGQeiAShoqICc+fOhYuLC5o3b45nnnkG3377bWOHRURE9Mh6IBKESZMm4b333sP48eOxcuVKmJmZYdiwYfj+++8bO7QGk5KS0tgh1FFTj/9h2AZNX9PfBk09/odhG1BDafQE4fDhw/jiiy+wbNkyvP322wgPD8fevXvh6uqKOXPmNHZ4DabpfyibevwPwzZo+pr+Nmjq8T8M24AaSqMnCJs2bUKzZs0QERGhK1MqlZgyZQoOHjyIy5cvN2J0REREj6ZGTxCOHz8ONzc3WFtb65X37NkTAJCVldUYYRERET3SGj1ByMvLg7Ozs6xcW3blypW/OiQiIqJHXrPGDqCsrAxKpVJWbmlpqVtevS8BZDZMYLVyEFVVfyI5Ofm+NXNzc42qV1/Onz//f//7GsDpemgxF0B9xX8ntq+//hqnT9dHbMYxdhsoFApoNJq/ICLj1f/2rE/Gb09+Du72YH4OHux97eG9kP1BIAkhRGMG8OSTT8LZ2RlpaWl65adOncKTT/7/9u40JKoujAP4fy4pxphmjuGGWWlFWqkt5oKMUdiCRcsohZVB9kUNDQoisw9mELQhUlbQZCQUjKRQtNAifajMUaGFSitUzMkNM0vG9bwfYobXZmmcO+M91vODgTreE89z/o2drnfuDcfFixeRkZEx5ms6nQ7Lli2jswuEEPKP8/f3h1arNXsmmogj+RkEPz8/s//Q63Q6AL/CNzdHq9UajyGEEPJv8vPzo82Bk0i+QYiMjERVVRX6+vowbdo043h1dTUAICIiwuw8+ktBCCGEOI/kFylu27YNIyMjuHTpknFsYGAAarUaK1euREBAgITVEUIIIf8myc8grFixAiqVCocPH0ZHRwfmzp2L0tJStLS0QK1WS10eIYQQ8k+S/CJF4NcZg6NHj+L69evo6enBkiVLUFBQgDVr1khdGiGEEPJP4mKDQAghhBC+SH4NAiGEEEL4w80GQcwjn799+4Z9+/bBx8cH7u7uWLVqFerr651csSl7e7h69SoEQTD76ujomIDKf/n58yeOHTuGtWvXYsaMGRAEAaWlpTbPlzoHMfXzkEFNTQ2ysrIQFhYGd3d3zJo1C6mpqWhsbLRpvtTrD4jrgYcM3r59C5VKhblz50Iul8Pb2xuxsbE238yJhwzE9MBDBuYUFhZCEAQsWrTIpuN5yOFvIPlFigbp6ekoLy9Hbm4uQkNDoVarsX79ejx58gRxcXEW542OjmLDhg149eoVDh06BG9vb5w/fx5KpRK1tbUICQnhvgeDgoICzJ49e8yYp6ens8o10dnZiYKCAsyaNQsRERGoqqqCTCazaS4POYip30DKDE6ePInnz59DpVJh8eLF0Ol0KC4uRlRUFF68eIGwsDCLc3lYf7E9GEiZQUtLC378+IH09HT4+/ujv78fGo0GO3fuRFNTE44cOWJxLi8ZiOnBQOrvRf/X2tqKEydOQC6X2/R+5iWHvwLjQHV1NZPJZOz06dPGMb1ez0JCQlhsbKzVuTdv3mQymYyVl5cbxzo7O5mXlxfbsWOH02r+nZge1Go1k8lkrLa21tllWjUwMMDa29sZY4xptVomk8lYaWmpTXN5yEFM/Txk8OzZMzY0NDRmrLGxkbm5ubG0tDSrc3lYf8bE9cBDBuaMjIywiIgIFhQUZPU4XjIwx9YeeMwgNTWVrV69mimVShYeHv7H43nOYbLh4kcMYh75rNFo4Ovriy1bthjHFAoFUlJSUFlZiaGhIafW/v86xD62mjGGvr4+jIyMOLNUi1xdXTFz5kxjLePBQw5i6jeQMoOYmBhMmTL2pF5ISAgWLlyI9+/fW53Lw/oD4nowkPp98DtBEBAYGAgXFxerx/GSgTm29mDASwZPnz5FeXk5zp07B8aYTWcQeM5hsuFigyDmkc/19fWIiooyGV++fDn6+/vR0NDg2GKt1CH2sdWJiYnw9PSEXC7Hpk2b8PHjR6fU6gy85CAWbxkwxtDe3g6FQmH1OJ7X39YeDHjIoL+/H11dXfj06RPOnj2L+/fv49ChQ1bn8JaBPT0Y8JDByMgIsrOzkZGRYdOPpgx4y2Ey4+IaBDGPfNbpdFAqlVbnjucvl73E9CCXy7Fnzx4kJibCw8MDWq0WZ86cQWxsLOrq6hAYGOi0uh2FlxzsxWsGZWVlaGtrw/Hjx60ex/P629oDTxkcOHDAeHfXKVOmoKioaMzZQXN4y8CeHnjKoKSkBC0tLXj8+PG45vGWw2TGxQZBzCOf9Xq9iMdFO46YHlQqFVQqlfH3GzduRFJSEhISElBYWIgLFy44vmAH4yUHe/GYwfv375GZmYnY2Fjs3r3b6rG8rv94euApg9zcXKSkpKCtrQ1lZWXIysrC1KlTrfbAWwb29MBLBt3d3cjPz0d+fj68vb3HNZe3HCYzLjYIU6dOxcDAgMm4Xq83ft0Zcx3J0XXExcUhOjra5o96So2XHBxJygy+fv2KDRs2wMvLCxqN5o8/e+Vx/cfbgzlSZTB//nzMnz8fAJCWloakpCTk5OQgJSXF4lryloE9PZgjRQZ5eXlQKBTIzs4e91zecpjMuLgGwZ5HPjtiriM5o47AwED09PSIrm0i8JKDo0mRQW9vL9atW4fv37/j3r178PX1/eMc3tbfnh4s4eF9sHXrVvT29uLDhw8Wj+Etg9/Z0oMlE5lBY2MjLl++jOzsbLS2tqKpqQlNTU3Q6/UYHBxEc3Oz1Vp4z2Ey4WKDEBkZiYaGBvT19Y0Z/9Mjnw1fq6urM7lqvbq6GnK5HPPmzXN8wWaI6cGSz58/w8fHxyH1ORsvOTjaRGeg1+uRnJyMjx8/4vbt21iwYIFN83haf3t7sISH94HhtLQgWP6WyVMG5tjSgyUTmcGXL18wOjqK/fv3Y86cOcbXy5cv0dDQgNmzZ6OgoMDifN5zmFSk+Gzl7wz3EDh16pRxzHAPgZiYGOOYTqdj7969G/M5a8NnXjUajXGss7OTTZ8+nW3fvn1iGmDieujo6DD58+7cucNkMhnLyclxbuEW1NTUWLyPAM85GIy3fh4yGB4eZhs3bmSurq7s7t27Fo/jef3F9MBDBuZqGBwcZFFRUUyhULDh4WHGGGNtbW3cZiCmBx4y6OrqYhUVFayystL4qqioYOHh4Sw4OJhVVlayN2/eWOyBlxz+Btw8rCk1NRW3bt1Cbm6u8ZHPWq0Wjx49Qnx8PIBfdyq8du0ampqaEBQUBODXXbPi4+Px5s0bHDx40HjXrNbWVtTU1CA0NJT7HkJDQxEVFYWlS5fC09MTdXV1uHLlCgICAlBTUzOh/3sqLi7Gt2/f0NbWhpKSEmzZssV49mP//v3w8PDgOgd76+chg5ycHBQVFSE5OXnMhWIGaWlpAPh+H4jpgYcMNm/ejL6+PiQkJMDf3x9fv35FWVkZGhoaoFarsWvXLov185KBmB54yMASpVKJ7u5uvH792jjGcw5/Bal3KAZ6vZ4dPHiQ+fn5MTc3NxYdHc0ePHgw5pj09HQmCAJrbm4eM97T08P27t3LFAoFk8vlLDExUZI7gdnbQ15eHouMjGTTp09nrq6uLDg4mGVmZprdzTtbcHAwk8lkTCaTMUEQmCAIxl8bauY5B3vr5yEDpVJprPf3lyAIxuN4Xn8xPfCQwY0bN9iaNWuYr68vc3FxYd7e3mz9+vXs4cOHY47jOQMxPfCQgSVKpZItWrRozBjPOfwNuDmDQAghhBB+cHGRIiGEEEL4QhsEQgghhJigDQIhhBBCTNAGgRBCCCEmaINACCGEEBO0QSCEEEKICdogEEIIIcQEbRAIIYQQYoI2CIQQQggxQRsEQgghhJigDQIhhBBCTNAGgRBCCCEm/gP1IqOolP9VKgAAAABJRU5ErkJggg==",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1140524c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1095ac8c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x10727e2c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1036142c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113b080c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1134aecc>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1133ba6c>)"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part d\n",
      "\n",
      "We shift the center of the horizontal axis to the origin by subtracting half the number of tosses\n",
      "from the number of heads"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scaled_run(n, m) = [flip_coin(n) - n/2 for i = 1:m]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "scaled_run (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i = sequence\n",
      "    figure(figsize=(5, 3))\n",
      "    plt.hist(scaled_run(i, 1000));\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113f090c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1049a82c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x10674d4c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118a270c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118e548c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x11901a0c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x119725cc>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1193490c>)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part e\n",
      "\n",
      "We use a fixed horizontal axis for all plots in this part"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i = sequence\n",
      "    figure(figsize=(5, 3))\n",
      "    plt.hist(scaled_run(i, 1000));\n",
      "    xlim(-500, 500)\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113602ec>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x10497aec>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIO6ME+//zzULcAdHsEHdCDFRcXq7KyMtRtAN0aQQf0cA0NDaFuAejWCDqgh6mpqQl1C0CPQtABPUxtbW2oWwB6FIIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgtQ4FXWNjo372s58pNTVVcXFxCgsL05o1a4LWHj58WKmpqerXr59cLpfmzJlz3udolZWVKSkpSU6nUwkJCSopKen4ngAAEESHgq6mpkYFBQX67//+byUnJ0uSHA5HQF1VVZVuvvlm/fnPf9aKFSu0aNEibd68WXfccYfOnDnjV7tq1SrNnTtXY8eOVUlJiaZMmaL8/Hw99dRTl7BbAAB8rU9HiuPj43XixAkNHTpU+/fv16RJk4LWFRYWyuv1qqKiQsOHD5ckTZ48WXfccYdefPFFzZ07V5Lk9Xq1fPlypaen65VXXpEkPfTQQ2pra1NBQYEefvhhDRw48FL2DwDQy3XojC4yMlJDhw6VJBljzlv36quvKj093RdyknT77bcrISHBF2iStG3bNtXV1emRRx7xWz8vL0+NjY3avHlzR9oDACDAZb8Z5fjx46qpqdHEiRMDlk2aNEkVFRW+n8/++Zu1KSkpCgsL08GDBy93ewCAXuayB53H45Ekud3ugGVut1t1dXW+9+k8Ho/Cw8M1ePBgv7rIyEi5XC5VV1df7vYAAL3MZQ86r9crSYqKigpYFh0d7Vfj9XoVGRkZdDtRUVG+OgAAOqtDN6O0h9PplCQ1NzcHLGtqavKrcTqdamlpCbqdpqYmX10wCxcuDLhRJTs7W9nZ2Z3qGwDQfZWXl6u8vNxvrL6+vl3rXvagO3vJ8uwlzHN5PB65XC5FRET4altbW1VbW+t3+bKlpUV1dXWKj48/799TXFyslJSUy9w9AKA7CnYic+DAAU2YMOGi6172S5dXXXWVhgwZor179wYs27Nnj+/zd5I0fvx4SQqo3bdvn9ra2vxqAQDojC75CrB77rlHb731lqqqqnxjW7duVWVlpWbOnOkbmzZtmuLi4lRaWuq3fmlpqWJiYjRjxoyuaA8A0It0+NJlSUmJ6uvrfXdEbty4UUePHpUk5efnq3///lq2bJnWr1+v2267TQsWLFBDQ4OefvppjRs3Tg8++KBvW9HR0SooKFBeXp5mzZql6dOna9euXVq3bp0KCwv5sDgA4JJ1OOiKior06aefSvr6679ef/11vfbaa3I4HJozZ4769++v4cOHa8eOHfrhD3+opUuXKioqSunp6SoqKvK9P3dWbm6uIiIiVFRUpI0bN2rEiBEqLi5Wfn7+5dlDAECv1uGg+8tf/tKuutGjR+vtt99uV21OTo5ycnI62goAABfFY3oAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFbrkqDbvn27wsLCgr727NnjV3v48GGlpqaqX79+crlcmjNnjmpra7uiLQBAL9SnKze+YMECTZo0yW9s1KhRvj9XVVXp5ptv1qBBg7RixQo1NDRo5cqV+vjjj7Vnzx5FRER0ZXsAgF6gS4Pupptu0t///d+fd3lhYaG8Xq8qKio0fPhwSdLkyZN1xx136MUXX9TcuXO7sj0AQC/Qpe/RGWPU0NCgr776KujyV199Venp6b6Qk6Tbb79dCQkJeuWVV7qyNQBAL9GlQffggw9qwIABcjqdmjZtmvbv3+9bdvz4cdXU1GjixIkB602aNEkVFRVd2RrQY508eTLULQA9SpdcuoyKilJmZqZ+8IMfaPDgwfrDH/6glStX6qabbtIHH3yg5ORkeTweSZLb7Q5Y3+12q66uTmfOnOF9OuAb6uvrQ90C0KN0SdBNmTJFU6ZM8f2cnp6uzMxMjRs3Tj/+8Y+1ZcsWeb1eSV+H4jdFR0dLkrxeL0EHALgkXXozyrlGjRqlO++8U6+//rqMMXI6nZKk5ubmgNqmpiZJ8tUEs3DhQg0cONBvLDs7W9nZ2ZexawBAd1BeXq7y8nK/sfZe3bhiQSdJV199tVpaWtTY2Oi7ZHn2Eua5PB6PXC7XBc/miouLlZKS0mW9AgC6j2AnMgcOHNCECRMuuu4VDbo///nPcjqdio2NVWxsrIYMGaK9e/cG1O3Zs0fJyclXsjUAgKW65K7LmpqagLFDhw5p48aNmj59um/snnvu0VtvvaWqqirf2NatW1VZWamZM2d2RWsAgF6mS87osrKy1LdvX02ZMkVDhw7VH//4Rz333HOKjY3VE0884atbtmyZ1q9fr9tuu00LFixQQ0ODnn76aY0bN04PPvhgV7QGAOhluuSM7u6771Ztba1++ctfKi8vT+vXr1dmZqb27dun66+/3lc3fPhw7dixQ6NGjdLSpUu1cuVKpaen69133+VuSwDAZdElZ3Tz58/X/Pnz21U7evRovf32213RBgAAPKYHAGA3gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIO6OGCfRMRgP9H0AE9XG1tbahbALo1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDgBgNYIOAGA1gg4AYDWCDujhTp48GeoWgG4t5EHX3NysJUuWKD4+Xn379tV3v/tdvffee6FuC+gx6uvrQ90C0K2FPOgeeOAB/fKXv9R9992nZ555RuHh4frBD36g3/3ud6FurVPKy8tD3UKPw5zhSuFY65yePm8hDbo9e/boP//zP/XEE0/oySefVE5Ojt5//32NHDlSixcvDmVrndbTD4hQYM5wpXCsdU5Pn7eQBt2GDRvUp08fPfzww76xqKgoPfTQQ9q9e7eOHz8ewu6A7scYo8bGxlC3AfQoIQ26iooKJSQkKDY21m980qRJkqSDBw+Goi2g23rqqaf0xBNPhLoNoEcJadB5PB653e6A8bNj1dXVV7oloFs7cuRIwNjnn38egk6AnqNPKP9yr9erqKiogPHo6Gjf8vM5fPhwl/V1Kerr63XgwIFQt9GjMGftFxhqDj3zTIluueUWjRgxIiQ99SQca53TXeetvTkQ0qBzOp1qbm4OGG9qavIt/ya3263ExETNnj27y/vrrAkTJoS6hR6HOesso7a2r3T33XeHupEeg2Otc7rrvCUmJga9MniukAad2+0OennS4/FIkuLj44Ou8/777/tqAAC9l9vt7t5BN378eG3fvl0NDQ3q16+fb/yjjz6SJCUnJwddrz07BgCAFOKbUTIzM9Xa2qrnnnvON9bc3KwXXnhB3/3ud3XVVVeFsDsAgA1CekY3efJkzZw5Uz/+8Y/117/+VaNGjdKaNWt09OhRvfDCC6FsDQBgCYcxxoSygebmZv3kJz/R2rVrdfLkSd1www0qKCjQHXfcEcq2AACWCHnQAQDQlUL+pc4AAHQlgu4SzJ07V2FhYcrIyAi6/IMPPtDf/u3fKiYmRm63WwsWLAj6PYXGGD311FP69re/LafTqRtuuEEvv/xyV7d/xWzdulX/+I//qISEBMXExGjUqFGaO3euTpw4EbSeeTs/Hmv1tb1792revHkaM2aMYmNjNXLkSGVlZamysjKg9vDhw0pNTVW/fv3kcrk0Z84c1dbWBt1uWVmZkpKS5HQ6lZCQoJKSkq7elZD6xS9+obCwMI0dOzZgmVXzZtApe/fuNREREcbpdJqMjIyA5RUVFSY6OtpMmDDBrFq1yjz++OMmOjrapKWlBdQuXbrUOBwO80//9E/m+eefN+np6cbhcJiXX375SuxKl5swYYIZNWqUWbp0qSkrKzPLli0z/fv3N8OGDTMnTpzwq2XeLuwf/uEfTEREhFm8eLFZvXq1mTp1qomIiDC//e1vQ93aFXXPPfeY+Ph4s2DBAlNWVmZ+/vOfm2HDhpnY2Fjz+9//3ld37NgxM3jwYHPdddeZf/u3fzOFhYUmLi7OJCcnm5aWFr9t/upXvzIOh8PMnDnTPP/882bOnDnG4XCYJ5988krv3hVx7Ngx07dvXxMbG2vGjh0bsMymeSPoOqGtrc1MmTLF5OTkmGuuuSZo0KWlpZmrrrrKNDQ0+Maef/5543A4zH/913/5xqqqqkxERISZP3++3/o333yzufrqq01ra2vX7cgVsmvXroCxnTt3GofDYR5//HG/cebt/D766CPjcDhMUVGRb6ypqclce+21ZurUqSHs7Mr74IMPzJkzZ/zGKisrTXR0tJk9e7ZvLDc318TExJhjx475xt577z3jcDjMc8895xs7ffq0cblcAb/Ls2fPNrGxsebkyZNdtCehk5WVZb7//e+bW2+91XznO9/xW2bbvBF0nbBmzRozYMAAc+LECTNy5MiA/5O/+OILExERYZYsWeI33tLSYvr162dycnJ8Y//+7/9uHA6HOXz4sF9teXm5cTgcVv9L3eVymczMTN/PzNuFPfbYYyYiIsLvHwHGGLNixQrjcDhMVVVViDrrPlJSUszEiRN9Pw8dOtRkZWUF1F1//fXm+9//vu/nzZs3G4fDYbZs2eJXt3v3buNwOMzatWu7rukQ2LFjh+nTp4/5/e9/b2655ZaAMzrb5o336DqooaFBS5Ys0bJly/Stb30raM3HH3+sr776ShMnTvQbj4iIUHJysioqKnxjFRUVio2NVWJiol+t7Y8q+vLLL9XQ0KDBgwf7xpi3C+OxVhdmjNFnn33mO6aOHz+umpqagONJ+nrOvnk8SQqoTUlJUVhYmFVz29raqvnz52vu3LkaM2ZMwHIb542g66B/+Zd/UUxMjB599NHz1pz9Hs5gX1M2bNgwv+/39Hg8QQPT9kcVFRcX68yZM8rKyvKNMW8XxmOtLmzdunWqrq72HVMXOp7cbrfq6up05swZX214eLjfP7wkKTIyUi6Xy6q5/dWvfqWjR4+qoKAg6HIb5y2k34wSSsaYoE9OCObsY4P+9Kc/6ZlnntHLL7+siIiI89affbzQ+R5BdO7jhy7lUUWh0Jl5+6adO3fqn//5n5WVlaVbb73VN27zvF0OvXGf2+vIkSPKy8vT1KlTdf/990u6+PF0tiYiIkJer1eRkZFBtx0VFWXN3H7++ef66U9/qp/+9KdyuVxBa2yct157Rrdjxw717du3Xa8//elPkqQFCxboe9/73kUfiXL28ULnewRR3759/WrPPpbom3Xnbqu76My8nevIkSO6++67NW7cOD3//PN+y2yet8uhM4+16g1OnDihGTNmaNCgQdqwYYMcDoekix9P59Y4nU61tLQE3X5TU5M1c/v4449r8ODBmj9//nlrbJy3XntGl5SUpBdffLFdtcOGDdP777+vd955R6+99pr+93//17fsq6++0unTp/Xpp58qLi5O/fr1853yB3uUkMfj8Xv8kNvt1vbt24PWScEfVRRKHZ23cx07dkzTp0/XoEGD9Jvf/EYxMTF+y22et8uhM4+1st0XX3yhtLQ0nTp1Srt27fI75i52PLlcLt+VGbfbrdbWVtXW1vpdhmtpaVFdXZ0Vc1tZWanVq1eruLhYVVVVvvGmpia1tLTo008/Vf/+/e2ctxDfDNNjvPDCC8bhcFzw9a//+q/GGGPq6+t9n3U6V3Nzs4mNjQ169+Af//hHv9p169ZZdfdgbW2tSUxMNMOGDTOffPJJ0Brm7cIee+wx06dPH3Pq1Cm/8V/84he98q5Lr9drbrp65eLuAAACtklEQVTpJhMbG2s+/PDDoDVDhw41s2bNChhPSEgIevfgb37zG7+63/3ud93q7sFLsW3btov+N+zRRx81xtg3bwRdOx09etS8+eabfq833njDDB061EyePNm8+eab5n/+53989WlpaSY+Pj7o58Heeecd31hVVZWJjIw08+bN8421tbWZm266yVx99dWmra3tyuxgF/ryyy/N5MmTzYABA8yBAwcuWMu8nd/Zz9GtXLnSN3b2c3RTpkwJYWdX3ldffWXuvPNOExkZGXBr+7lyc3NN3759g34ebNWqVb4xr9fbIz4Pdilqa2vNG2+8EfDfsO985zvmmmuuMW+++abvw/a2zRtBd4mCfY7OGGMOHDhgoqOjTUpKiiktLTXLly83TqfTpKamBtQuXrzY9w0fq1evNjNmzDAOh8OUl5dfiV3ocnfddZdxOBzmoYceMi+99JLf64033vCrZd4ubNasWb6z3lWrVpmpU6eayMjIoB/Kt9mCBQuMw+Ewd955Z8Ax9dJLL/nqzn7Dx7XXXuv7ho9BgwaZG264IeAbPp599lnfN3ysXr3a9w0fK1asuNK7d0XdcsstAR8Yt23eCLpLdL5vRjHGmN/+9rfme9/7nnE6neZb3/qWmT9/vvnyyy8D6tra2syKFSvMNddcY6KioszYsWPNf/zHf3R161fMNddcY8LCwoJeKvn2t78dUM+8nV9TU5N57LHHjNvtNtHR0ebGG2/0+8aY3uLWW2897zEVFhbmV/uHP/zB/N3f/Z2JiYkxcXFx5r777jN//etfg2539erVJjEx0URFRZnrrrvO93aEzW699daAD4wbY9e88ZgeAIDVeu3HCwAAvQNBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALDa/wGBHUEx0Gr1nAAAAABJRU5ErkJggg==",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1138ee2c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1045d88c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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a3//+923aZk5OjnJyctraCgBJs2bN0ocffqhRo0aFuxWgS+IxPYAFQn0uDuArBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqBB0AwGoEHQDAagQdAMBqbQq6uro6/exnP1NaWpri4+MVERGh9evXh6wtLy9XWlqa+vbtK5fLpXnz5qmmpiZkbUlJiZKTk+V0OpWYmKiioqK27wkAACG0KehOnjypgoIC/fd//7dSUlIkSQ6HI6iuqqpKN954o/76179q1apVWrJkibZt26Zbb71VZ8+eDahdu3at5s+fr7Fjx6qoqEhTpkxRfn6+fvWrX3VgtwAA+ErvthQnJCToxIkTGjJkiA4ePKhJkyaFrFu5cqV8Pp/Kyso0bNgwSdLkyZN166236umnn9b8+fMlST6fTytWrFBGRoaee+45SdJ9992n5uZmFRQU6P7779eAAQM6sn8AgB6uTUd0UVFRGjJkiCTJGNNi3fPPP6+MjAx/yEnSLbfcosTERH+gSdLOnTtVW1urBx54IGD9vLw81dXVadu2bW1pDwCAIJf8YpTjx4/r5MmTmjhxYtCySZMmqayszP/zuT9/vTY1NVURERE6fPjwpW4PANDDXPKg83g8kiS32x20zO12q7a21v85ncfjUa9evTRo0KCAuqioKLlcLlVXV1/q9oBurbKyMtwtAN3OJQ86n88nSYqOjg5aFhMTE1Dj8/kUFRUVcjvR0dH+OgBSRUWFZs2aFe42gG6nTRejtIbT6ZQkNTQ0BC2rr68PqHE6nWpsbAy5nfr6en9dKIsXLw66UCU7O1vZ2dnt6hvo6rxeb7hbAMKmtLRUpaWlAWOnTp1q1bqXPOjOnbI8dwrzfB6PRy6XS5GRkf7apqYm1dTUBJy+bGxsVG1trRISElr8ewoLC5WamnqJuwcAdEWhDmQOHTqkCRMmXHTdS37q8oorrtDgwYO1f//+oGX79u3z338nSePHj5ekoNoDBw6oubk5oBYAgPbolK8Au+OOO/TKK6+oqqrKP7Zjxw5VVFRo9uzZ/rFp06YpPj5excXFAesXFxcrNjZWM2bM6Iz2AAA9SJtPXRYVFenUqVP+KyK3bNnivxIsPz9f/fr10/Lly7Vp0ybdfPPNWrRokbxerx577DGNGzdO9957r39bMTExKigoUF5enubMmaPp06drz5492rhxo1auXMnN4gCAjjNtNGLECONwOIzD4TAREREmIiLC/+ePP/7YX/fBBx+Y73//+yY2NtbEx8ebu+66y3z66acht7lu3TqTlJRkoqOjzahRo8xvfvObFv/+gwcPGknm4MGDbW0d6NbOvfdDvfh9QE/U2jxo8xHd3/72t1bVjR49Wq+++mqranNycpSTk9PWVgAAuCge0wMAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHWKCysjLcLQBdFkEHWGDWrFmqqKgIdxtAl0TQAZbwer3hbgHokgg6AIDVCDoAgNUIOgCA1Qg6AIDVCDoAgNUIOgCA1Qg6AIDVCDoAgNUIOgCA1Qg6AIDVCDoAgNU6Jeh27dqliIiIkK99+/YF1JaXlystLU19+/aVy+XSvHnzVFNT0xltAQB6oN6dufFFixZp0qRJAWMjR470/7mqqko33nijBg4cqFWrVsnr9Wr16tV6//33tW/fPkVGRnZmewCAHqBTg+6GG27QD3/4wxaXr1y5Uj6fT2VlZRo2bJgkafLkybr11lv19NNPa/78+Z3ZHgCgB+jUz+iMMfJ6vfryyy9DLn/++eeVkZHhDzlJuuWWW5SYmKjnnnuuM1sDAPQQnRp09957r/r37y+n06lp06bp4MGD/mXHjx/XyZMnNXHixKD1Jk2apLKyss5sDQDQQ3TKqcvo6GhlZmbqBz/4gQYNGqQPPvhAq1ev1g033KB33nlHKSkp8ng8kiS32x20vtvtVm1trc6ePcvndACADumUoJsyZYqmTJni/zkjI0OZmZkaN26cfvzjH2v79u3y+XySvgrFr4uJiZEk+Xw+gg4A0CGdejHK+UaOHKnbbrtNL774oowxcjqdkqSGhoag2vr6ekny14SyePFiDRgwIGAsOztb2dnZl7BrAEBXUFpaqtLS0oCxU6dOtWrdyxZ0knTllVeqsbFRdXV1/lOW505hns/j8cjlcl3waK6wsFCpqamd1isAoOsIdSBz6NAhTZgw4aLrXtag++tf/yqn06m4uDjFxcVp8ODB2r9/f1Ddvn37lJKScjlbAwBYqlOuujx58mTQ2JEjR7RlyxZNnz7dP3bHHXfolVdeUVVVlX9sx44dqqio0OzZszujNQBAD9MpR3RZWVnq06ePpkyZoiFDhugvf/mLnnjiCcXFxemXv/ylv2758uXatGmTbr75Zi1atEher1ePPfaYxo0bp3vvvbczWgMA9DCdckQ3a9Ys1dTU6Ne//rXy8vK0adMmZWZm6sCBA7rmmmv8dcOGDdNbb72lkSNH6uGHH9bq1auVkZGh119/nastAQCXRKcc0S1cuFALFy5sVe3o0aP16quvdkYbAADwmB4AgN0IOgCA1Qg6AIDVCDoAgNUIOgCA1Qg6AIDVCDoAgNUIOgCA1Qg6AIDVCDoAgNUIOgCA1Qg6oBuoqKhQeXl5uNsAuqXL+uBVAG1XUVGhxMTEcLcBdFsc0QFdnNfr/f9/ui+sfQDdFUEHdBvucDcAdEsEHQDAagQdAMBqBB0AwGoEHWCJysrKcLcAdEkEHWCJWbNmqaKiItxtAF0OQQdY5P9uRQBwDkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALAaQQcAsBpBBwCwGkEHALBa2IOuoaFBy5YtU0JCgvr06aNvf/vbeuONN8LdFtAlvP3227r++u+Euw2gWwt70N1zzz369a9/rbvuuku//e1v1atXL/3gBz/Qn/70p3C31i6lpaXhbqHbYc5a9ve//1319b5wt2EN3mvt093nLaxBt2/fPv3hD3/QL3/5Sz366KPKycnRm2++qeHDh2vp0qXhbK3duvsbIhyYM1wuvNfap7vPW1iDbvPmzerdu7fuv/9+/1h0dLTuu+8+7d27V8ePHw9jdwAAG4Q16MrKypSYmKi4uLiA8UmTJkmSDh8+HI62AAAWCWvQeTweud3uoPFzY9XV1Ze7JaBbKy8vV0VFRbjbALqU3uH8y30+n6Kjo4PGY2Ji/MtbUl5e3ml9dcSpU6d06NChcLfRrTBnLfv73/9+3k/vX7R+7ty5kqQXX3xRV111Vec01Y3xXmufrjpvrc2BsAad0+lUQ0ND0Hh9fb1/+de53W4lJSX5f6G7ogkTJoS7hW6HOWuNl1tdOWvWrE7so3vjvdY+XXXekpKSQp4ZPF9Yg87tdoc8PenxeCRJCQkJIdd58803/TUAgJ7L7XZ37aAbP368du3aJa/Xq759+/rH33vvPUlSSkpKyPVas2MAAEhhvhglMzNTTU1NeuKJJ/xjDQ0Neuqpp/Ttb39bV1xxRRi7AwDYIKxHdJMnT9bs2bP14x//WJ9++qlGjhyp9evXq7KyUk899VQ4WwMAWMJhjDHhbKChoUE/+clPtGHDBn322We69tprVVBQoFtvvTWcbQEALBH2oAMAoDOF/UudAQDoTARdB8yfP18RERGaOXNmyOXvvPOOvvOd7yg2NlZut1uLFi1SXV1dUJ0xRr/61a/0zW9+U06nU9dee62effbZzm7/stmxY4f+6Z/+SYmJiYqNjdXIkSM1f/58nThxImQ989YyHmv1lf3792vBggUaM2aM4uLiNHz4cGVlZYX8Vpjy8nKlpaWpb9++crlcmjdvnmpqakJut6SkRMnJyXI6nUpMTFRRUVFn70pY/eIXv1BERITGjh0btMyqeTNol/3795vIyEjjdDrNzJkzg5aXlZWZmJgYM2HCBLN27VrzyCOPmJiYGJOenh5U+/DDDxuHw2H++Z//2Tz55JMmIyPDOBwO8+yzz16OXel0EyZMMCNHjjQPP/ywKSkpMcuXLzf9+vUzQ4cONSdOnAioZd4u7B//8R9NZGSkWbp0qVm3bp2ZOnWqiYyMNG+//Xa4W7us7rjjDpOQkGAWLVpkSkpKzM9//nMzdOhQExcXZ/785z/7644dO2YGDRpkRo0aZf793//drFy50sTHx5uUlBTT2NgYsM3f/e53xuFwmNmzZ5snn3zSzJs3zzgcDvPoo49e7t27LI4dO2b69Olj4uLizNixY4OW2TRvBF07NDc3mylTppicnBwzYsSIkEGXnp5urrjiCuP1ev1jTz75pHE4HOa//uu//GNVVVUmMjLSLFy4MGD9G2+80Vx55ZWmqamp83bkMtmzZ0/Q2O7du43D4TCPPPJIwDjz1rL33nvPOBwOs2bNGv9YfX29ufrqq83UqVPD2Nnl984775izZ88GjFVUVJiYmBgzd+5c/1hubq6JjY01x44d84+98cYbxuFwmCeeeMI/dubMGeNyuYJ+l+fOnWvi4uLMZ5991kl7Ej5ZWVnme9/7nrnpppvMt771rYBlts0bQdcO69evN/379zcnTpwww4cPD/qP/Pnnn5vIyEizbNmygPHGxkbTt29fk5OT4x/7j//4D+NwOEx5eXlAbWlpqXE4HFb/S93lcpnMzEz/z8zbhT300EMmMjIy4B8BxhizatUq43A4TFVVVZg66zpSU1PNxIkT/T8PGTLEZGVlBdVdc8015nvf+57/523bthmHw2G2b98eULd3717jcDjMhg0bOq/pMHjrrbdM7969zZ///Gfz3e9+N+iIzrZ54zO6NvJ6vVq2bJmWL1+ub3zjGyFr3n//fX355ZeaOHFiwHhkZKRSUlJUVlbmHysrK1NcXJySkpICam1/VNEXX3whr9erQYMG+ceYtwvjsVYXZozRJ5984n9PHT9+XCdPngx6P0lfzdnX30+SgmpTU1MVERFh1dw2NTVp4cKFmj9/vsaMGRO03MZ5I+ja6N/+7d8UGxurBx98sMWac9/DGepryoYOHRrw/Z4ejydkYNr+qKLCwkKdPXtWWVlZ/jHm7cJ4rNWFbdy4UdXV1f731IXeT263W7W1tTp79qy/tlevXgH/8JKkqKgouVwuq+b2d7/7nSorK1VQUBByuY3zFtZvRgknY0zIJyeEcu6xQR9++KF++9vf6tlnn1VkZGSL9eceL9TSI4jOf/xQRx5VFA7tmbev2717t/71X/9VWVlZuummm/zjNs/bpdAT97m1jh49qry8PE2dOlV33323pIu/n87VREZGyufzKSoqKuS2o6OjrZnb//3f/9VPf/pT/fSnP5XL5QpZY+O89dgjurfeekt9+vRp1evDDz+UJC1atEjXX3/9RR+Bcu7xQi09gqhPnz4BteceS/T1uvO31VW0Z97Od/ToUc2aNUvjxo3Tk08+GbDM5nm7FNrzWKue4MSJE5oxY4YGDhyozZs3y+FwSLr4++n8GqfTqcbGxpDbr6+vt2ZuH3nkEQ0aNEgLFy5sscbGeeuxR3TJycl6+umnW1U7dOhQvfnmm3rttdf0wgsvBDwM88svv9SZM2f08ccfKz4+Xn379vUf8od6lJDH4wl4/JDb7dauXbtC1kmhH1UUTm2dt/MdO3ZM06dP18CBA/XHP/5RsbGxActtnrdLoT2PtbLd559/rvT0dJ0+fVp79uwJeM9d7P3kcrn8Z2bcbreamppUU1MTcBqusbFRtbW1VsxtRUWF1q1bp8LCQlVVVfnH6+vr1djiz7XkAAADIElEQVTYqI8//lj9+vWzc97CfDFMt/HUU08Zh8NxwddvfvMbY4wxp06d8t/rdL6GhgYTFxcX8urBv/zlLwG1GzdutOrqwZqaGpOUlGSGDh1qPvroo5A1zNuFPfTQQ6Z3797m9OnTAeO/+MUveuRVlz6fz9xwww0mLi7OvPvuuyFrhgwZYubMmRM0npiYGPLqwT/+8Y8BdX/605+61NWDHbFz586L/j/swQcfNMbYN28EXStVVlaal19+OeD10ksvmSFDhpjJkyebl19+2fzP//yPvz49Pd0kJCSEvB/stdde849VVVWZqKgos2DBAv9Yc3OzueGGG8yVV15pmpubL88OdqIvvvjCTJ482fTv398cOnTogrXMW8vO3Ue3evVq/9i5++imTJkSxs4uvy+//NLcdtttJioqKujS9vPl5uaaPn36hLwfbO3atf4xn8/XLe4H64iamhrz0ksvBf0/7Fvf+pYZMWKEefnll/0329s2bwRdB4W6j84YYw4dOmRiYmJMamqqKS4uNitWrDBOp9OkpaUF1S5dutT/DR/r1q0zM2bMMA6Hw5SWll6OXeh0t99+u3E4HOa+++4zzzzzTMDrpZdeCqhl3i5szpw5/qPetWvXmqlTp5qoqKiQN+XbbNGiRcbhcJjbbrst6D31zDPP+OvOfcPH1Vdf7f+Gj4EDB5prr7026Bs+Hn/8cf83fKxbt87/DR+rVq263Lt3WX33u98NumHctnkj6DqopW9GMcaYt99+21x//fXG6XSab3zjG2bhwoXmiy++CKprbm42q1atMiNGjDDR0dFm7Nix5j//8z87u/XLZsSIESYiIiLkqZJvfvObQfXMW8vq6+vNQw89ZNxut4mJiTHXXXddwDfG9BQ33XRTi++piIiIgNoPPvjAfP/73zexsbEmPj7e3HXXXebTTz8Nud1169aZpKQkEx0dbUaNGuX/OMJmN910U9AN48bYNW88pgcAYLUee3sBAKBnIOgAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAViPoAABWI+gAAFYj6AAAVvt/BCLQG6ccZvEAAAAASUVORK5CYII=",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1148836c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1093d20c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113b582c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x104a1f2c>)"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part f\n",
      "\n",
      "To normalize, the leftmost point corresponds to tossing 0 heads and all tails, whereas the rightmost point corresponds to tossing all `i` heads and 0 tails"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i = sequence\n",
      "    figure(figsize=(5, 3))\n",
      "    plt.hist(flip_runs(i, 1000));\n",
      "    xlim(0, i)\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118f056c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1197848c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118bd40c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x104b6b8c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1146a10c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x1073a4ac>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113cda4c>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x11c1170c>)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part g\n",
      "\n",
      "Comments on the three parts above:\n",
      "\n",
      "* **Part d**: As the number of tosses increases, the distribution moves closer to a normal curve\n",
      "* **Part e**: Since we are working on the same scale, the histogram gets bigger as the number of tosses increases, since the number of heads will also increase\n",
      "* **Part f**: The curve becomes tighter and tends toward the middle as the number of tosses increases. This makes sense because as we toss more coins, the chance of getting all heads or all tails decreases significantly comparing to say, when we toss 2 or 4 coins."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part h\n",
      "\n",
      "* We first define a function that generates a random number, either -1 or 1 based on the result of `rand()`\n",
      "* We then proceed to append the y-values to the list one-by-one. `push!` is Julia's syntax for appending an element to\n",
      "an array and modifying the first argument"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rand_one() = rand() < 0.5 ? -1 : 1\n",
      "\n",
      "# An n-step random walk starts at 0 by default\n",
      "function path(n, walk=[0])\n",
      "    for i = 1:n\n",
      "        push!(walk, rand_one() + walk[end])\n",
      "    end \n",
      "    return walk\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "path (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "title(\"20 random walks of 1000 coin flips\")\n",
      "for _ = 1:20\n",
      "    plot(path(1000))\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Y0ah2GntPWno9ZN05n8v70lJlGqLuGtV9vJ2JC3kX3NGQfmq12um9bUka+m2ok9c/t3/961/861//ws/Pj4ULFzJ27FhCQ0O56aabzvmjsDWiPnuWvyaLFy9m9uzZ9OrVi3Xr1jl6eKcTHx/Pjh07OHLkCP369XNKs1qtZGZm4unpSVxcXKPbbmiI7n//+x/bt29n2rRpLgvVCwoKmD9/fqPbaIi6H54TJ064TS8sLGywTEFBAd26dXNJLygocMrXktT1BH755RdGjhyJXq93MqALFy5k/fr1jp7o6T2H5557Dm9vb1JTU4mPj3dKy8/PP+dILcuWLeOVV15h/vz52Gy2Bu/ZFVdcwQ8//IDFYiE1NZW1a9fy9ttv87e//Y3Q0FAXQ3869e+Ju2fvYt0TX19foqKiKCgooLCw0OWDLC0tDcBp+LNr164ADTrNnKnMkSNHGl2mIeqMWF5enss0yOm05nehqTjbb0P9c1OpVDz66KM8+uijFBUVsWnTJlasWMHKlSs5cOAABw4ccDhIXorIHqgbXn31VWbPnk2/fv1Yv359g8YTTvVY1q5d65L222+/YTQaGTZsGJ6enhes17FjxwC45ZZbXNKaKuRW3bDphg0bXNJqa2vZtGmTi7x///4NljEYDOzevRutVuv2B6W5CQ8Pp3v37vz++++Oe1R3zxISEvDy8mLdunUkJycTHBzs8hF07Ngxunfv7mI8bTab22txNnQ6Hb/88guJiYm8+OKLPPXUU2fM7+npydChQ5k/f74j9Nr3339/1nb69++PEMLtPTl27Bh5eXnExsY6zT+3FKNHj0YI4fadWbNmDeD8IdOxY0diYmI4cuQIWVlZjSpTF5rul19+cZmzr6ioYPPmzfj6+jrNdzfE0KFDndo5E635XWgqcnJyyM7OdpHXnfPp71AdoaGh3HzzzXz11VeMGjWK9PR0Dhw40JyqNjvSgJ7Giy++yDPPPMPAgQNZt26dWweS+kycOJE2bdqwYsUKduzY4ZCbTCaeffZZAB544IEm0a3Ogai+UwxARkbGWX+IG8uwYcOIj4/nt99+c/mhXrp0KRkZGS495DvuuANPT0/efvttl2GZ5557joqKCkeei0FSUhLV1dW89dZbdOnSxTEUp9VqGTp0KF9//TUZGRmOOZz6xMbGcvToUUfPAeyOQPPmzePQoUPnFerMz8+PtWvXMnr0aBYtWuRwAKsjJSUFk8nkUq7uC9/Hx+esbUyfPh2Al156ieLiYoe8traWf/zjHwghuOeee85Z96bg/vvvB+xONfWHkLOysnjnnXfw9vZm2rRpbss8+eSTTgbxf//7H5s2baJHjx5O8/ZxcXFcffXVZGZm8s477zjVNXfuXKqrq7nzzjvRarVn1feuu+4iICCA9957j99//90lvf58fGt/F5oCq9XKU0895XQfMjMzeeutt/D09OSOO+4AwGw2s3nzZpfyFouF0tJSFEVp1LPcmpFDuPX45JNPmDt3Lh4eHgwfPpzFixe75ImNjeWuu+5yHPv7+/Phhx8yceJERo4cyeTJkwkKCuL777/n6NGj3HrrrUyaNKlJ9Bs/fjydOnXizTffZN++ffTt25ecnBx+/PFHxo0b1+j5sbPx8ccfM2bMGCZMmMAtt9xCx44d2b17N8nJyVx77bUuPYf27duzePFiHnroIfr378+kSZNo06YNGzdu5I8//qBbt24uXnvAGWMLNyWjR49m6dKlnDx5kgkTJrik1X05uxsWfeyxx7j//vvp168ft9xyC56enmzevJlDhw4xfvx4fvjhh/PSSavVsnr1aiZMmMBbb72FyWTi/fffB+xrfdevX09iYiIdOnTAz8+PAwcOsHbtWoKDg7nvvvvOWv/QoUN58sknee211+jZsycTJ07Ex8eHNWvWcODAARITE3niiSfOS/fTWbhwocMpps6BZNmyZY753sTERCdjPXToUGbPns2bb75J7969mTBhAmazma+++gqDwcDbb79NTEyMUxuzZ89m9erVrFq1iiFDhpCUlEROTg4rV67E19fX4XVcn3fffZdhw4Yxc+ZM1q1bR9euXdm6dSsbNmwgPj6el19+uVHnFxISwhdffMHEiRMZNWoUY8eOpVevXpSXl7N3717y8vLIyMgAWve70FRt9O7dm61btzJgwADGjBmDwWDg66+/pry8nNdee83xoV9dXU1iYiKdOnWif//+tG/fHpPJxC+//MLhw4e58cYbXUZ2LjnOZ+1LZWWleP755x2RNhqKKiKEEAcPHnREtAkODhZ33nmnKCoqcpv3o48+El27dhXe3t6ic+fO4u233z4f9c6befPmOdY5NhS9o6GQV5s3b3ZEDtJqtaJ3795i8eLFjY6aI8SptV/z589vME9ubq64/fbbRdu2bR1RiBYtWiSsVqtb/ebNm+eybrOOzMxMoSiKmDZtmkvajh07xLXXXiv8/f2Fv7+/GDNmjPjjjz/OWN/PP/8srr76akf0lc6dO4unnnrKbfSVkSNHNrgu7e677xYqlcoRfamx59MQBoNBeHh4CJVKJVatWuWUtmXLFsc9b2it7vLly0Xfvn2Fr6+vCA0NFbfccovYv39/g7qcy30wm83illtucdwHm80mfv75ZzFt2jTRvXt3ERgYKHx9fUXXrl3Fo48+KnJychp93kIIsWLFCjF8+HDh7+8vvL29Rc+ePcWCBQucIhGdTcezMXLkSMc1rP+vTubu+RLCfl0HDRokfH19RUBAgBg5cqT48ccfG2ynurpaPP/886Jz586OSECTJk0Shw4darBMbm6umDZtmoiMjBQajUZ06NBBPPbYY04hBBvLgQMHxNSpUx0RqSIiIsTIkSPFhx9+6JL3Qt+Fs/0WdOjQQcTGxjZa9zO9b+fyvNblLSgoEHfccYcICwtzRCI6PYayxWIRr732mhg7dqyIiYkR3t7eIiwsTAwdOlR88MEH5xRRq7WiCHHunyVZWVnExcXRvn17YmNj2bBhA8uXL3dZr5SXl0e/fv0ICgpi5syZVFRU8PrrrxMTE8O2bduchjE++OADHnjgASZOnMg111zDb7/9xmeffcbChQt58sknL/xLQSKRSCQXhEqlYuTIkU5Rn/7KnNcQblRUFIWFhYSFhbFjxw4GDRrkNt+CBQswGo3s2rXLsd5t8ODBjBkzhuXLlzsW8huNRv75z38ybtw4vv76awDuuecebDYbL774Ivfdd985LQORSCQSiaS5OS8nIo1G44hucqYO7DfffMO4ceOcFouPHj2aLl26OAwl2J1iSktLefDBB53KP/TQQ1RVVZ1xj0CJRCKRSC4GzeaFm5+fT1FRkdtIGoMGDWLXrl2O47q/T8/bv39/VCqVU2QLiUQikUhaA83mhVvn9u8uIkdkZCSlpaVYLBY8PT0pKCjAw8PDZb2lRqMhJCSE48ePN5eaEolEImkkDe329Fel2Qyo0WgEwMvLyyWtLki20WjE09MTo9HYYDQKLy8vR13uKCgocFqjJ5FIJJK/HpGRkQ2GUGwums2A1i1QdhcntG6ReF0erVbb4O4EJpOpwcXOBQUFDBw4UPZQJRKJ5C9OVFQUqampLWpEm82A1p2Eu95hQUEBISEhjmUskZGR1NbWUlxc7DSMazabKS0tddou6PR6jh8/zueff35Jh8ZqaWbNmuU2SITkzMjrdu7Ia3Z+yOt2bhw6dIg77riDgoKCy8OAtm3bltDQULd71m3bto2+ffs6jutiJ27fvt1py6DU1FRsNptTXnd069bNEYNScnZ0Op28XueBvG7njrxm54e8bpcGzRoLd8KECaxevdopVuS6detIS0vj1ltvdciSkpIIDg7mvffecyr/3nvv4evry/XXX9+cakokEolEcs6cdw906dKlGAwGx/zj999/T05ODgAzZ84kICCAOXPmsHLlSkaNGsWjjz5KRUUFixYtonfv3k7Bor29vXnxxRd56KGHmDRpEldffTW///47//d//8eCBQtkEAWJRCKRtDrO24C+8cYbji1tFEXhu+++49tvv0VRFKZOnUpAQADR0dFs3LiR2bNn8/TTT+Pl5cW4ceN44403XHYjeOCBB/D09OSNN97g+++/JyYmhsWLFzNz5swLO0OJRCKRSJqB8zagmZmZjcrXvXt3t/v+uWPGjBnMmDHjfFWSNJIpU6ZcbBUuSeR1O3fkNTs/5HW7NJD7gf4FkS/n+SGv27kjr9n5Ia/bpYHcD1QikUgkrQZruRWbyYYmzH1wnfqYzUWYzQUYjVnNr5gbpAGVSCQSSash7eE0qg5WMTDVNY766aSk2Dc1OXq0ubVyjzSgEolEImkVCCEo/akUy0kL5iIzmtCGe6EWS2kLauYeOQcqkUgkklZB9cFqLCctABQuK3TaLtNms2AyZVNTc5zKyn0cz/7InpAb7a6qFkH2QCUSiUTSKtAn61E0CgjIeDoDRaPQ7rF2ABw//i4ZGXOw2apPFbCoYepncNU7wKoW11f2QCUSiUTSKjAkGwgYGoB3nH3HrpLVJewcupMNygbyt//X2XgCFIXS7ql2sGXoRdBW9kAlEolE0goQtQLDBgPRj0UTOjGU7T22Y0g22BM9rBi9/ziV+UB3MHmj+d9s2v/QnvbePWB+y+ssDahEIpFILjqVuyuxGqzoknT4dvel5w892T9+vz2x62HQmuBoZzDo4KnXABhYOAx1oJrQG0KlAZVIJBLJX4v0p9LJfS0XAEWjEDA4AADdCB34mFAvexpr+B4wauGRt0EoAFyRcwWa8LOvFW1O5ByoRCKRSC4K1jKrw3gCqDQqVBq7WVIHqIl4N9duPAHF5gtmLzx8tMQtisO7nfdF0bk+sgcqkUgkkouC4TeD03Hbh9s6HasTDsOfu2EG19xFWYiaYfnDUHm1jr6fNKASiUQiaXEqdlSw/4b9eEV7MXCvPeqQOvCUSSos/IS8vDcJC5tM587v4uERgO1q0WqMJ0gDKpFIJJcNNpsZs7kQRfHAYtHj69sDRVEutlpOiFpB1YEqdo/eDQg8BxbhGeTpku/w4bsBCA6+Fk/PIABUfi2oaCNoPaZcIpFIJBdEXt4Stm/vxZYt0aSm9qKwcPnFVsmF7JezSe2TSm1ZLQzaTuXMm6iuPuKUp6Ym3/G3TjeqpVVsNNKASiQSySWM1VpJaupA9u+/mdLStdTWljvSjhyZztatXTGbiy+ihs6Urvkzhm2XI/DaU6AISkt/caSbzUVs2WIPzzdkSDre3jEXQ81G0ewGNDU1lRtvvJGoqCh8fX3p1q0bL774Ikaj0SnfoUOHuPbaa/H39yckJISpU6dSXNx6brpEIpG0RkpKfqCycgfFxf/FYEh2STcaj1BY+J+LoNkpqg5WUbm3kso9lVQdqALA49VXHOl1ehuN6RQUfOiQa7VxLavoOdKsc6D79u1j+PDhREVFMWvWLIKDg0lJSWHu3Lns2LGD//73vwDk5eUxYsQIgoKCeOWVV6ioqOD1119n3759bNu2DU9P1/FxiUQikUB5eYrTsZ9fP7y8omnT5maOHJkOQGXlnouhGgBF3xZxYMIBJ1mfX/tw0LuaWgt4ebXDYNhARcVOduwYgLd3LABhYZMvhrrnRLMa0BUrVmA2m/nxxx/p1q0bADNmzMBms/Hpp59SVlZGYGAgCxYswGg0smvXLqKj7V33wYMHM2bMGJYvX869997bnGpKJBLJJUlBwcfk5y8lPPxOTKYsqqoO0q9fCoqioFJ50abNzWRlPUdR0TcIIVrUoejYY8cImxLmslQFwGtAGZbdRcTHL0Or7cju3VeSk2OPLmQyZdK27aN07Ph6i+l6vjSrAdVqtQCEhYU5ySMiIvDw8ECjsUeR+Oabbxg3bpzDeAKMHj2aLl268PXXX0sDKpFIJG44cmQGAMHB16HRRFBTk4eHx6kAA56eOoKDryc/fynFxd/h7z8Ib+92jnSz+QRm8wl8fXuiKE03o2fKNpG3OI/ayloqd1cC4NffDwREzoik3LQOgJCQ8ajVAahUWoqKvnKUDwnkUSiYAAAgAElEQVS5HpWq9S8SadY50OnTpxMeHs4999zDnj17yM3N5auvvuL9999n5syZaLVa8vPzKSoqYuBA193HBw0axK5du5pTRYlEIrkkMRozHX8HBY0iKGgkERF3uOQLDBwOwIEDE/jjjxhsNosjLSUlgtTUPuTkvOJS7kLQr9cDUPJjCRU7K4j/KJ6BOwYycOdA2j7YFr0+GV/fPmg0bVCpNAQGJgL24We1WkdgYEKT6tNcNKuJj4qKYvPmzVx33XX069fPIX/22Wd54YUXACgoKAAgMjLSpXxkZCSlpaVYLBY5DyqRSCRATs7raLWdsFpLARVXXJGFRhPeYH612nnxZEVFKoGBQzGZToXQy8x8loCAKwgKGt0kOhqSDShqBXOBGQBdks6RJoTAYFhHaOitDllQ0Gj0+p/p0uXf+PjE4+Hh0yR6NDfNakBPnDjB2LFjAfjwww8JCQlh9erVvPzyy4SHh/PQQw85vHG9vLxcynt724cijEajNKASieQvR01NAWp1AKDCaExDo4kkK2seWm1HNJoI/P37Ow3JNkSfPr+Snf0SBsMGDIZkPD1DKS/f7JRnz56rGDlSXLDOQgj0yXrC7wqncFkh3u290cZqHelG4zFqavKcjHV4+FRqa6vw9+/fpEPJzU2zGtAXX3yR/Px8jh49SlRUFAA33XQTNpuNp556iilTpjjmSWtqalzKm0wm4NRcakPMmjULnU7nJJsyZQpTpkxpitOQSCSSFkcIwe7dIwgOHovJlElJyWpHWlXVXqqq9tKu3ZONqisoaDRBQaPZt+8Gjh//kMzMZ/H2jsXPry+xsS+zb9/1f7ZZi6J4XJDexjQj5nwzoRNCMR414tfXuQdsX7Li4Ri2BfDyiiA2tnH7kX355Zd8+eWXp9Xp6qjUEjSrAd20aRP9+vVzGM86xo8fz/Lly9m9ezfx8fHAqaHc+hQUFBASEnLW3ufixYvp379/0ykukUgkFxmTKROj8RilpT9hNB51yBVFjRBW4NT8ZmPR6ZIoKfnBUX909GxCQq6jV68f2bfvenJyFiKEoEOHZ89bb32yHkWtEDg8kN4/90bxcPb81euTCQgY9GfP+txx1znauXMnAwYMOG+dz5dmNaAWi4Xa2lq3cgCr1Urbtm0JDQ1l+/btLvm2bdtG3759m1NFiUQiaZXo9XXBBY46yYODx6LVdsFiOUlw8NXnVGdQUJLb46Cgq1CptGRmPouiaGjXbrbbeUijMR2ttqPbuqsOVSEsgqKvi/Af7I/a39W8CGHDYFhPZOTlsbKiWQeb+/fvz86dO0lLS3OSf/nll3h4eNC7d28AJkyYwOrVq8nLy3PkWbduHWlpadx6661IJBLJXw2DIRmttrPjeMiQDDw9wwgJGU+nTq/TrdunqFSuviNnwte3J15e7QkMHI6HR4BjGLW+J6wQZsrKUlzKlpdvZ+vWTpSVbXFJK1lTwvbu20ntk4phvYGgpCC37VdVHcBiKXIx5JcqzdoDfeKJJ/jmm29ITEzk4YcfJjg4mNWrV7N27VruvfdeIiIiAJgzZw4rV65k1KhRPProo1RUVLBo0SJ69+7NtGnTmlNFiUQiaXUIIdDrk4mMnEZJyRpstmq02liGDEm/IA9VRVExePABVCpvamurUav9HWl1nrDgwd69Yxg4cC9+fr2ora3m6NEH8PCwz2Xq9T8TGDjUqd6y38ucjgNHBLq0bTLlkJpq7zQFBAw773NoTTSrAe3duzcbNmxg7ty5LFq0CJPJRFxcHAsWLODJJ09NfkdHR7Nx40Zmz57N008/jZeXF+PGjeONN96Q3rcSieQvR0nJaiyWE+h0SQQGDsdmsy8HOX1Jyvng4eH7Z13+TvI6T9iiolVUVx/k6NH76NcvhYKCjzhx4lNHPr0+mQ4d5jqVrYs25DfAD7/efuhGOjt1AmRlzaunw5kdQy8Vmj3Uw+DBg1mzZs1Z83Xv3p21a9c2tzoSiUTSqikr28L+/TcAEBiY0GJrIus8YdXqQNLTH8diKaGg4GOOHXvUkUerjae8fAu1tVUOQ2yttFKxtYLO73am7QNtG6zfZMoBIDp6VvOeSAty6Sy4kUgkkr8AZWW/Of6+GAEFoqMfo3PndzAa0zh61NnZx3//IwhhoazMvobUWmlla9xWhFWgG+XP4cMzqK5Oc6nTZquhvDyFDh3mXRIxbhuLNKASiUTSitDr1wPQp8+6i9K+oii0aXOjs/CZBfgfeoSiWT1QyoMpOf4LQgjy12zCUlsI4YVYIvZQWPgxJ0585lJneflWbDYjISHjL3idaWui9UfrlUgkkr8INpuZsrLfiYt79aJ6qmo09dbuv/I0/DEUc54XorIGtvclP381Wl17MkMfgW8AizeHD9vDser1ycTGvuBUn16fjFodhJ9fnxY8i+ZHGlCJRCJpJZSXb8Nmq0anu7jLPEyZJrhmLXha8A5vQ9jTYeQszEFRK4id/WF0MseOPXKqgKcJkykTRVFTUbEVq7XSyeHJYEhGpxt5WfU+QQ7hSiQSyTlhMmU77WhyOjab2eEwc64YDMl4eATi79/v7JmbkFpTLaY8k+NYn6wHsxdU+RE0JoiQcSEABI8Npk3HaxqsJyJiOkJYKSvbdKru2irKy/9oskD1rQlpQCUSiaSR1NYa2b69J/n5bzeYJy9vCdu398Jmc43vfTb0+ovTU8tZkMOO/jsQtfZg8oZkA9rOWlQ+KtqMb4P/YH88wzwJGR9Cz7euOlVw/vME+iYREDAMRfEkOvpRNJrIP+Pd2ikr24wQloveq24O5BCuRCKRNBL7Eo5KSkt/ol272QAUFHwMqIiMtAd9KS39idracnJyFmKzWYiJeYK0tIfp2PFfaDRtGqw7Pf0Jyso20qnTkpY4FSdKfyrFUmShcnclfv390CfriZwWScycGEdIviHpQ/DwsRv28C92cmJFPlccuArPKFAUD2w2E2q1PzpdErm5iygs/A+9ev2IXp+MRhOBj0/XFj+v5kYaUInkEsVsLkZR1Hh6ui5al1w4NpuVmpo8tNoODlldfNqyst+x2cyoVBqys1/GZjPh7z8Am62GsrKNwKnAAULUcOLE53h7dyA8/E58fLq4tGW1lpGba1/e0dJDndYyKxWpFYB96LbmeA2WExZ0STqneLZqv1N/t3ukM/49Q/Fu5+2QqVT2oDdBQUmcPPl/WCzFHDgwCY0mDJ0uCUVxDip/OSCHcCWSS5QDB27hyJEZF1uNy5aCgo/Yvr0bVuupMHX2+LTx2GxGysu3YjRmYjJlYjYXkJrah507ByOEFa023lGmzjBmZ7/Etm3xlJdvc2nLYDi19tPHp3sznpUrht8MYANtvJbcN3LZf8N+AAITXMPx1eHXy4/omdFu0+oP1ZrNhVRU7LhsYt+ejjSgEsklQG7uv9iwQUVqaj+s1nLS0h6hrOx39PpfsNmsF1u9yxK9/idsNhObNuk4cuRerNYKysu3ER09E7U6iJMnv2Dr1ji3ZaOjH3ErB9i5cwgbNihkZDwDQEXFDvbvvwEvr2gSEytbtKdWsaOC/Tfsx6u9FxF3R2A5cco5qm649lzRajswfHg5Xbt+ihA1gO2ynP8EaUAlklaPELWkp88GBJWVu8nIeIb8/KUA1NaWU1m5q0X0qKkpoLa2qkXautgIUYvBsMFxXFDwESdPfgnUEhQ0Bp1uJMePv+9Ij4t7FT+/vvj7D6Jr188IC5tCTMw/6d59BTrdaHr1+hGdznloNidnITU1x9m92y739u7oCI/XXFhKLVhKTxnJg1MO2tvu4E3Q6FM7qPRZd2HrNdVqf0JCxgEK3t6xaLWxF1Rfa0XOgUokrZzKyt1Ox8ePv+v4W6XyxWCwb1DcnAgh2L17BMHBY+nc+a1mbas1UFm5G6vVgErli81m/2jIzn4RL69otNpO6HRJFBd/B0B4+F3ExDxJTMyTTnXExb0EQFjYbQCEhFxHevqT5OYucuTZsuVU7NjwcOdNopuDQ3ceQtQK+qy1G0irwT56ET4lHP/+/miiNLSf077B7cjOBU/PIAIDh+Pnd/nu6Sx7oBJJK0evT0al8mHYsEK8vTs45ImJVeh0iQ7HltMpKvqW3Nw3LqjtkpI1ZGW9hMmUidF4jNLSn9zmMxg2sXlzKAUF/7mg9hpDdfVRNm+OIDt7gZPcaq3k0KGpmM0nL7iNumuekHCChIRSfHx6UFOT53CGqXP0adfuCeLjP2p0vXFxC0lIKCUhodQp2k+nTkuIjLzvgvU+E7YaG4b1BvQ/6fnd/3c2KBuwFFmIXxZP5H2RKB4KQ44OIeqBqLNX1kh69/6Zjh0v7BlszUgDKpG0cvT6dQQGJqLRhDuGAnv0+BYPDx90uiTKyn7HbC7CbC5CCEFl5T4qK/eSmfk8WVnzL2iONC9vCdnZL1JSshoAo/Eo1dVp1NTkYzJlU1m5n8rKvezenYjFUsyRI9Mxm4uorNxLZeV+TKYcamryqazcjxCiwXas1grM5hMIITAa07FYSrBY9G7zHjs2C4vlBJmZ/3Rs82W/Tr9w4sRnFBV9C4DFYsBsLm70uda1DXZnocDARDw8fPH0DCI4+GrglIesj09XOnR4gbZtH0GlavxAnqKo8PQMwtMziKAg+3pKX9/eREbOaPTcp81iw5RtOqVzurFR5cq3lmMz2gCorax1yEPGhzja9vD1QFE13Rysh4e3wzv3ckQO4UokrZi62Kh1+y/6+nanb99fHelBQUlkZDzJzp1D0GgiCQub4hxiDais3EFAwJDzblsIM7m5i9BqO2M0prF37zXYbCbM5gK35VJSwtzK4+OXOdZKnk56+mzKy7cSF/ca+/Zdh1bbCR+frvTq9b1L3vo9zPLyreh0iQCOxfsGQzJt297PkSPTsFoN9O27vlHnW1r6E/v2XcfAgXswGH6nQ4fnHWkhIeM4fvw9hwFVFIUOHZ5rVL0NERIyjuLi/9Kv3+/ntOvK8XePkzEng4STCZT8vxIOTjnIFZlXOC0pcYc+WY86SI1V7/xBpWmjOS/9JbIHKpG0as4WG9XPry9qtQ6TKZPy8j8oLv7WKV1R1A0O8Ta2bUVRU1OTR2joBHx9+ziWbZxOp05vAw33Xupv01UfIQSlpT9RVbWPwsL/AAKjMQ29PpmcnEWcPLmK8vKtbN4cSm7uG1RW7iYu7jXUah0GQzIGwybS059Cr09GUdQUFa0kO3shev06yso2YbVWYrWWcejQnWfsker1PwGC1NTe2GxVTtc8KCiJYcNO4uXV8H6X50po6ESGDs1DrQ44p3KlP5Viq7aR81oOBycdhFrIX5rP5rDN5LxuDyGo36Bnc+hmCj8rdJQzJBvQjdKRWJnIcMNwEkoTSKxObLLz+SvSIgZ0586d3HDDDYSEhODr60uvXr14+23nUFiHDh3i2muvxd/fn5CQEKZOnUpxceOHXySSy43aWhMnTnyKWq1rMDaqonig043688iGwWDvbfn59aVdu38QFHQ1xcXfntNQ5ultt2lzE2Bf33f6ej6dbhT+/gMJD7+TqKh7HQ4jWm3nenrZcbf+EcBoTKemJheAoqKvHXKbrYqMjCfJynqeXbuGY7EUk57+D6CWNm1uQqcbRVHRd2Rnv0Bu7mtUVx8kImI6AJmZz1BbW4EQVgoL/0N+/jucOPE5+flLEKLWnRouHxqnX3O12v9Ml+ycURTlnOu0WWz2dZtA9gvZDnnua7lYiixkPJGBudjMnlF7sBRbODz1MAC1VbWU/1FOUFIQHr4eqAPVeAZ54qG9vIK7tzTNPoT7888/M378eAYMGMDzzz+Pn58fx44dIz8/35EnLy+PESNGEBQUxCuvvEJFRQWvv/46+/btY9u2bXh6Xr5j6BJJQxw+PJWiopVn3UMxJGQcBsNveHhoqanJo2fP/zr2c8zNfZP09MdJSQll5MiG5yDP1HabNjeh1/9KYGACiuLB8ePv4ePTAz+/XnTt6uw0FBIyDiGsDBq0F4BDh6ZitRoIC5vCoUN/o6amEC+vCKcy9qFXD7y922MyZeDn1w+rVY/Foqe2tozq6kNO+U/3hK2qt7Kmffs5FBT8GwAPDz9qays5dmymIz072+4ZGxv7olOdZnMRVVV78fRsg8VSjK9v71a5c0jF9gpsVTa08VqMR+xzn94dvDFlnQoEnxKa4lSmprCGqr1VCItAlySjVjUlzWpAy8vLmTp1KuPHj2fVqlUN5luwYAFGo5Fdu3YRHW2PbjF48GDGjBnD8uXLuffeexssK5FcrhQVrQRAq+14xnwREdMIDZ3EsWOPUli4nMDAKx1p9XuBaWmz6Nx58Tm3HRb2N0JCbsDDw8cxlKlSaXA3XNu+/fPExDztOLZ7qAqHQ5DBsN5luYZeb1+G4+8/hPz8JfTs+T88PYM5ePB2Skt/RAj7nF3Hjm+Qnv4kOt1oJ0/YOnx8euDt3Z6EBD1//NGOwMArKS9PwWp1dkbKzn6JgoJl9Ou3iZKSH/H0bOMwlgMG7MTDw6/Z12OeDSEEaQ+mEfVgFH69Tm0Lpk/W4xHgQbvH2nH0/qP0WNUDlVbFvuv30fHNjmQ+l4mtyu4o1PndzqQ9mMaWyC0AaCI0+HRt/Fyr5Ow0qwH94osvOHnyJC+//DIAVVVVaLVaVCrnkeNvvvmGcePGOYwnwOjRo+nSpQtff/21NKCSvxx14eM8PcOIifnnGfPahwL9iI6ehZ9fH6fYuH5+fQgLm8zJkyvIz19CRMSd+PsPOKe2Tx9qPNOwo90jVV3v2O6g4uUVgY9PDwyGZMLDp2A0pqNWBwECgyGZyMh7iYi4Cy+vKLy92wEQE/M0bdqMx2g8hsmUTVTUgyiKhsDA4YDdEzY6+nEslpOEhNyASuX1p946OnV6Cx+fLqhUPqSnPwFAu3az2bfvegDM5uNkZj6LXv8LanUgvr690GrjHW23NMYMI5oIDZZSC97R3pT8UMLx949jNViJ/ygeVGAttdrnMa/UEXpbKKYck2ObsZhnYoicHon+Vz2l/68U3WgdkTMiSXswzdGGpq3msoxHezFpVgP666+/EhAQQG5uLjfccANpaWn4+vpy55138q9//QsvLy/y8/MpKipi4MCBLuUHDRrEmjVrmlNFiaRVUhcbtX//lDPu4FEfP79e+Pn1cpIpiopu3b7g5MkVAOzYMZChQwtchlEvtO3GEBSUREmJfXeOPXtGo9V2RohaLJYigoKS8PHp4hSMIDDwCgIDr3CqIzr64XrnptCp0+tu26rv7Vvfa7lPn1/Zs8e+fMRg2IDFUoTFUoTReIyoqAea5DzPFXORmW1dt+Ed641Vb6Xndz3Zf6M9Hu3JFSepOV5DwNAATnx6AkuphbiFcXjqPIl7+VQYwbgF9r9DxodQsaOC3mt7o1KrCJ0YStGqIgAipjZ8zyXnR7M6EaWlpWG1WrnpppsYO3Ys3377LdOnT+f9999n2jT7A15QYPfmi4yMdCkfGRlJaWkpFkvDm9dKJJcLeXlLOXHCbugMhmS8vGLw9nYfa/VcUBSFxMRTE4VbtkSf0amoKduuj06XhMmUwfHj9jlKozENkykDRfEiIGBYk7bVEEFBoxk+3EBs7EuYzcdRlFN9CH9/14/45sZSamFL9BaERWA8asRSZGHXcOfQjGW/lZH7ai7mAjOiRpwxSlDUfVEMOTYEldr+097ty24klCaQUJpA20eazoNYYqdZDWhlZSXV1dXcddddLF68mJtuuoklS5bw97//nRUrVnDs2DGMRvtEuJeXl0t5b2/7uqa6PBLJ5UZV1UFMplyEsDm8ScE+LxgUNLrJhtw8PHzo0eObP49q/1wu4orZfILi4u8JCmr67ad0uisBhaKir5zkgYHD8PDQNmlbZ0KtDiQkZPyfbSfSvv3zhIZOJCxscovpACBqBdkvZiPM7p27ev63J9rOztfFM9QT354Nz88qKsVp2zGVWoVnkCeeQZ5y+LYZaNYhXK3WfvOnTHF2GpgyZQoffPABf/zxB1272jdZralx3b3dZDI51dMQs2bNQqdz9i6bMmWKS7sSSWuiqOhbDhyYAMCAATv+HE4sprr6CFVVe2nX7okmbS809BZCQydSVLSKyso9bvOkpNiH+XS6eU3aNthjo/r59aeycgd+fv2xWE4CHn8GHW9ZfH174uXVnpCQcY6NsVua7JezyVucB4BnuKc9wIEAYRHEPB1DmxvbEJAQ4PCq9evrh19fvyaNFHQp8uWXX/Lll186yQwGw0XRpVkNaFRUFAcPHiQ8PNxJHhZmj1Si1+uJirLHXawbyq1PQUEBISEhZ13GsnjxYvr3799EWkskzYNevwG9/ldstip8fXs67eW5Y0edY49wbMQcFDTKtZILpFu3L9FoIsjPX4qfX1+qqw8SEDCMmpo8IiPvceRrrv0bg4JGU1m5gx49VqLR2H8XVKozR9BpDhRFxeDBB1qkbWuZlV1X7qJqbxVxr8VRfbCa9s+1p3RNKQC+fXwZkDoAm9GGSqOitroWdaD9p1nTRsPwcrvTlEqjOlOcir8M7jpHO3fuZMCAMzvHNQfNakAHDhzIr7/+Sl5eHp07d3bIjx8/DkBoaChRUVGEhoayfft2l/Lbtm2jb9/LN5K/5PLGbC5CpdKgVts3Jj5+/B2KihpezgWg1Xbi5MkVaLXxTRr1pg6VSk1w8PXk5y8lI8Pew7UP53qg0YQC0K7dk83SNkBU1N9Rq3VotU07v3o+tNRSlZMrT1K1xz4HnfFEBgCKRqHqQBV4QI+VPVCpVaj87TNqKi/nmTW1v4y42lpp1jnQSZMmAfDxxx87yT/66CM8PT0ZOXIkABMmTGD16tXk5eU58qxbt460tDRuvfXW5lRRImk29u0bz9GjDwIghA293jUma6dOS/Dx6QFAdPQsR/i45uoBAo7Ysc7UkpOzED+/vnTs+Gqzta3VxtG+/TPNVn9rpGJbhYus4IMCaitq6fNTH3w6y7WZlyrN+mnTt29fpk+fzrJly7BarYwYMYINGzawatUq5syZQ0SEfb5lzpw5rFy5klGjRvHoo49SUVHBokWL6N27t8NbVyK5lLBYSqmo2IbJlI4QNqqq9mG1lji8PoWw0qXL+0RG3kdU1N+pra1GrQ6gqGgVBQX/dgkS0JR4ePiSkFDMli3RCGFFCGu9eLeTmq3dvyr6ZD0R90QQ+1IsW2O3YjPZHGkBw84tDq6kddHsYwPvv/8+MTEx/Oc//+G7776jQ4cOLF68mJkzT4XXio6OZuPGjcyePZunn34aLy8vxo0bxxtvvCHD+EkuSQyGjdgj8BRTVbX/z/0lvYmPX4ZK5UVFRSphYX9DURQUxcsRBCAkZBwxMc8QHDy2WfXz9AyhU6e30GgiqajYitGYwcmTXzRrz/evhMVgQVgFVfuqMKWbCHktBK8ILzq91QlNpIbj7xwnZHyIjEV7iaOIM23S18qpmzjesWOHdCKStCrS0h6huPh7zOYTxMUtxGBYR22t0WlRf2vi5MmVHDkyg6FDc895dxCJK/tv3k/l7kpHjNqEkgQ8g2VnoLm4WLZAzk5LJM2AXp9McPA1GI3ppKc/BkBs7MsXWauGCQ2dSHDwtU2+48hfEZvFhv5XvdOm1dJ4Xp7I/UAlkiamrGwz1dUH0emSCAxMcMgb2tOzNXA+W2tJ3FP0dZGT8ez1/3qdIfelhTHdHtSm5ngNtdXut4VrivovFaQBlUiaEKMxk1277Ov2goJGERx8jSPtYoSKk7QsJWtKOHSHffs1747exL4SS8jYkIusVdNQvr2crZ22UraljJ1Dd5L5fGaT1l+xu4KtnbZi2HhxgiKcD3IIVyJpQuo2tAbQaMLRaMIZPrwMUP25U4nkcqbs9zLH34P2DnJZ03kpU/qTPfBD3pI8anJq0P+kBzex/PUb9Oh/1RP30rmt9dX/rHe0o7vy0ti39PK5uxJJK0CvTwagZ8/vHTK1OgC12q+hIpLLBHORmZIfSgDot6kfHj4eKB6XT+ggQ7K9Z1j0lX13l6r9VRizjNQU2MOwVh2qonJvJdnzs8l5OYeKHa7rX0/HmGFE2Ox+rPpkvdP/xgwjrd3HVRpQiaSJEMK+t2W7dk/Sps34i62OpIVJCUuhan8Vnd/tTGBC4MVWp0mpNdZSllKGNt4el1zbxf7/nqQ97Bq2i5I1JWzvvp3UPqkYNtgN7Y6BO6gpdI1xXkfdNm4nPjuBzWyj7Hd7/RXbK6g6XMW2+G2c/Opk85/cBSANqETSRFRXH8FsLpBrKVsR+g16NodupvCzwmZro+DjAjZ4bHAcB41ueLuxS5XyLeWIGkHs/FgAwqaE4dPVB1OmCVOWiYKPXWOZAxjWn5rPNOWY2NJuCxnPZDjShEVQ+lMp5dvKsVXb7PXbIGteFsIq7MPErRhpQCWSJsJgWIeiqAkMHH6xVZH8yZ6kPViKLRyeepjKvZVU7q1E1J7/sKC52IzFcGp/4prjNRyZcQT+DC4UOSPSZQuy5sBaZsVcZD7v8qJWYMxsvMerPlmPZ6gnobeG0uGFDkTeE4ku6dQ8ZfE39v1l/Qb4ETEtgu4rugOnhn3BbhRr8mrIWZhD2eYyTn550lG3YZ0Bj0APQieG4hXj5RgmLvmxhJr8hnuxFxtpQCWSJkKvTyYg4IoWC1IuOTM2qw3q2crUPqmk9kkla17Wedd54JYDdoOJfch+S9stTunxH8a3yL6bR/5+hP037T/v8oWfFLKt6zbMxY0zwoZkA7pROhSVQofnOuDdzpuQ8SGotCrHsG7ndzszMHUgXZd1Jey2MNo+0tYxnwn2Hmgdu4bvovi/xWjjtVhOWCj4qADdSB2Kh+LYMFwbr8VS9OeG4610LlQaUImkCRDChsGwvlWv9fyrUfxtsVt59kvZpLRN4fhHx8mc534pRsmaEjaHbubkqlNzcGmPpFH2exnF3xSTvSCb6sPVjrQhmUNIrHIXpL/pEagNHc0AACAASURBVDaB/mc95X+UO/WGG0vpr6UcuecIwiwo21jmlFaypoSsl7IAKN9azubQzeS+kUv5tnKHYasj5NoQhp0YRtit9u0pTx+61iXpMGWYMGYZyXg2A8M6Ax3mdXDK0/bhtiieCjV5NY7663q2HZ47lbfqQNU5n2dLIA2oRNIEVFbuwWrVN2sQ+NaEudhsHxLdX4kp2+R2Yb3NbHP0OozppzwqjZlGl2FUa4WVyr2VWCutTbaY/sQXJwB7wHaVVoU6+NQyIvNxM0fvPUr2C9mUbS47Nbz7p0fovuv2YSm2cPDWg5hPmrGUWMhfmu8on/nPTErX2pd1xC6IRdtBi4dPy8S1rdxTad982waF/yk8Y+/MWvnndS23OmR7x+x1/F2/h2gpsZA1L4vsF7MxnzCza/guLMUW0v+RDrU4DdnWofZXE3lvJB1e7OAydK27UgcKlKwuIeflHABCxofQ/avuBFwRQOjEUCKnRxIw1B46ss4At7mpDTHPxNBmQhviFtmXwtQfCnZHYzx+mwO5ME0iaQIMhmRUKi0BAUMutiotQkpoitOxpq2GsMlhdHq9k0OWtySP7Jey6Z/Sn+29ttPz+54EDg9kW7dtdH67M1H3Rjny7h65m8qdlfYDBQYfGoxP/IVt81W+pRx1kJr+m/uTNjONkh9L6PF1D/ZctedUJmEfTqwj9qVY2j3Rzvlcw1PosaqHS/15b+YRODyQ9s+0vyA9zxVDsgGVVoXNaCN9djoqbxVtH3C/f+vea/ZSnlKOb09fBu0bZB/W/hPvOG8nw7S5zWbH3ykRzvfXq50X2k7u53a9Y7zp8GwHF7lnkCd+/f3IfTXXIfPr64d/f3/CJoU5ZCHjQqjJrcGnu/1+q/3VxC2wG86Yf8RQ+mMp+mQ90TOj3bZfsqaEI/cdcZvW3MgeqETSBOj1yQQGDnfsqnI5U783U4c530zeG3nkvZ3HoamHMJ80U/pTKbXltWzvuR0E7B+/n9xFuYga4ViUD/a5RIfxBBCwres2TLkmhBAcuPUAqf1S3bbbEJnzM7GctOA/0B6esG440bujNzFzYgi/K9xtudKf7R6hACE3noogdGDiAdQ6Nb1/6s3wsuGotCpq8mrc9sqaG32ynsDhgXhF25+1umUjANmvZFPy4/9n77zDo6i6P/7ZkmTTNw0SCBAgoUMINSQgEOC1YkfFF1ERO4gVEUSxACqiCOqLCioKYm+ogMAuvYQeekjvS0J2N9kkm2y5vz+GzGZJAogU8Zfv8+TJzp07t8zOzrnn3HO+56R8XLZVmkvFwQoyp2ey0WMjAD1W9aDdrHZUHq3k0KhD7taDOop0+7ntQSXdv/PZ2w1KCqI6rxqPZh4MLB+IQlm/jVZPt6Lvgb6Ntq9N0mJabyLnzRyKfy6ud74uecWlRpMAbUIT/iacThtm88b/N/uftS8srzZeaIe6C5C0J9IwfGnA8JWBsi1l9a7NmSWZ8kx6k2wubcxkmz0zm4qUCoq/L8ayz0Lxj/Vfng3BYXWQPSMbgLA7wwCXOTF/QT45b+RQcbCCyGci6fxVZwLiA/CNlRy/Ko9VYlpnArVkeqyNdwSwm+wUflooaX81kibn1+vSEmQ4bU7MG81ok7Qyx655k5nqwmoqj1WS9VIWefPyqM6v5uQfJ92uzX49W/6sTdLK313x98VkvZIFQOhtoYTdKt0z/z7+tHisBdHzool8smHt72yoNcsGDQ9C7dewwVOhUqDybdz8HZQUhMPsIGNKBnnv5Lmdq0tecTnQJECb0IS/ifLynTgclv838Z9GnRGvSC/iM+PpqetJxPgI/Hq6C5K8uXk4rU4UXpJWofRxvWq8O3pjL5X25uDU/pYK4nPiUfmrUAVIL9OqzCqyZ7le+uU7zm2fq2y7S3A3/6+kaXoEeaBpp5FewE6w7LaQPz+f5qOb02tbL/ru60uP1T2wGWwUfFIgee86oCrVXbibdCbKk8vhlMJ26OZD5zSmC4XyXeU4LA6CkoLw6+5H1x+6UlNYw7YW20julIywC8ybzWyL3MaB6w8A0n1VqF3anXeMN0oPJZ7NPOWy3LckM2vX77oSelMoaq2anht6otKoiJwQiX/P80s0EDgwEFWgipCR588H7N/XH6Wv9PyUbS/DUeHSlmvJK1pPaX3e7f8dNAnQJjThb8Jo1KFSBeDn9+/ISWv4ykD+h/mNnjfpTG4mvZgPYojbFkd8VjwoQKGWvCrVIWoGmgaSWJrIoLJBdPqiEwCtn2+NUqPEpDNRuraU1IdTCegbgO2EDYWnAkeZ9II0/Wmi+FtJ69QO07o5vJwJJp0JhVpB8DXBqDQuzabW5FkLYRPkzs3F8LXkbBSYGIjCQ0FNfo0sIAGU3q7XpK3YRt6CPDcz5/l4wp4PKlMr2ZuwF6WvUtZ8G+KMdVqdbseaVhoC4gPwaO5B4slE+h7oK58bVOnyHFb6KlEoFDS7u5m0mLkATlEqXxUDcgfQ7M5mZ6/cCJSeSrRXaVGoFQibYHv77TgqHNhKXffdv+/lySR0yQXozJkzUSqVdO9eP8XPkSNHuOaaa/D39yckJISxY8dSUtKwK3oTmgDgcFRhsaRgsaRQUXH0sozBZNKh1Q7+V5DF1xhqyJyeSdarWbJ3p9PuxJJioeZEDWU7y7Dss7iFNCg9lag0KjRtNES/G037d9oDEDQ0CJVGhUeQBwqVgrDbw2j9QmvCbg8jcGAgRp1R9gj1jfVl37B92E82vM/prHJSlVpFRWoFlgMWbCZbo6m1jGuNCKcg6D/uYRWdPu2EdpiWzks7y/ub6c+mkzU9ixpDDSpfFQHxkkeoKkBFpy+l+t1+7iZdt6wzCk8Fxd8UE3JdCOH3hwNg3mA+b8/hut7HtbDmWqk4XD9sI+3JNEByslGqpVe3R4gHUa9Fuea4pJPsbRw4MFA280bNiCJ6XjQewR5uBPcqbxU9VvVAO0xL3IY44FRqO/8L9yyr/dV/Oza29dTWdPikAwA2g7SIKfxUYj+KGB+Bpo3mb4/zfHBJf/F5eXnMmjULX1/fejc0Ly+Pq666iqCgIGbPnk15eTlvv/02Bw4cIDk5GQ+PpoS0TaiPw4fv4OTJ3+TjHj3+JDh4xCXr3+GowmzeSrt2b1yyPi8m6npfVh6pxLeLL1nTs8h5I8etXmPOM5GTInFYHWTNyCLkBnezncpbJXtXapO08n4ogGmdCYe54fySXq28ZGeYvQP24rA40ERpqEqtIm5rHIfvOkzYqDCi347GbrFLTkBO6sUterfzpufanoBERbe1+VZsJTaq0qrYGr6VIWIIISNDKNtZhjZJS/iYcMLHSEIy+D/BABR+UohpvYmgYUFETorEpDeR9lQa1hwr8ZnxaFr9tRd5rfexf19/eif3xlnjZHvr7QB0+7kboTeFynVrTkikBy0eaeHWRtSLUZg3mNG01xA+NhzjWiN2k53uv7qUlDPRCwZfHUzw1cF/adyXGtqBWrQDtRQtLsK82UzmC1L8rsJDQcdPOrJnz57LMq5LqoE+++yzJCQk0KdPn3qxS7NmzaKqqgqdTseECRN44YUX+Pbbb9m/fz+ff/75pRxmE64g1BWeAGbzRkymzaSnP3/R+05Le4pNm3wQovpfsf9pzXUxxaCS9jpPrjxZT3gCZxQUKo2K+Ox4mo9t2NMVTjmGnEo63ey/zahKkzS46PeiGVg2kKusVxH0nyCUPkpaPu4K0bCX2hE1Qt6b3Juwl+qcavLm5rHReyOb/TeDA1RaFb7dG2eEUigVkhm6zt7goVGHqCmqQVhFPeFbi9qFQ93/1kwrOGB76+3kL8xnS9gWN0/YxlDX+7h8p7S/W+sBDGDa5PKutZfZseyz0P7t9rSZXj9sptuKbsQsiAGg46KOdP2uftjNvwGx62LxCHMpU6eb5S81LpkA3bhxIz/88APz5s1DCFFPA/3hhx+44YYbiIx0eXsNGzaMDh068O23316qYTbhCkF1dSFWa+2LXSEnqy4pWUF29qvk5r5FTY3hL7crhAOLJYWaGgNVVRlYLAewWvPq1Ssr20le3jz52Ne323nN45+EWuLvVpNbEZgYiEln4sB1B+rV6/qj9HK2Zltx2pz1zgOo/Ro321VlVuHX0092MDqxTGL78e3hS8T4CMlE6aUk6pUoYubH0OKxFoTeHNpgW3VRd+8vaFhQgyETddHq2VbEvB9D5DPSO6f4+2LZy7MxARoxLoKoGVH4dvVtsN7xR49jK7Fx4Ib6960WtlIbtlJbPbNvVWaVW1ymebMrPMO8yQwOCLkxpMF5qTQqlB7S61zpqfxX5SGtC6Wnkth1sWiHaSXz+q+X93d3SUy4DoeDiRMn8uCDD9K1a/2VUX5+PsXFxfTp06feub59+7Jy5cpLMcwmXCEQQrBv31UIIWkw8fHZaDStyMt7n7S0iVSc2j4ymdbTrNmdf6nt7OyZZGW9XK988GA7CoXkVFFdnc+ePf3kc/7+/VEorvwXllFnxK+nH+3fbE/WK1I4RC1i9bGkP51O8LXBhN0ShqNKiu+MeiWKVk+3arzR02Az2WQiBXWAGlvxKUcQFcRtinNzXAmMDyQwXkoL1u2nbmTPzCbzxUzJmcR+Zm7Uc8mIEtA3gIC+0p5n3lz3RVJtUP/p8GrpRdTLUfKxdphWYjkKUlNT4M4r66x2NijIjtxzBOEQUriICuIz49ketR2TzoRRZyT05lCCrw0m9dFU7GY76kC15Pl8BjKD/0/w6+4nm+IvNy7Jr37hwoXk5OTw2muvNXi+sPDUZnBERL1zERERlJaWYrNdGk+3JvyzIYQgJeUaqqrSsFoz8faOQaORXuCn0+jVJrcGyM6ezcmTv5+1/dLShhdrFss+AGpqitm2zWUlSUwsJS5u41+exz8Nee/nYVhicDNN2k2SY0usLpagIUHEbYkj6pUoQGL5cVgcboQI5wLzBjOiWpD6UKosPBVqBQH9AlAHnHk933JiS1CBTzd34dbQfuxfTSk2qHIQfnF+eEV6Mcgy6JydXrzCvUgwJBCfHU/k09Jz0XFRR0AKuSj4qIAtYVtk06yz2olJb8K42ih7H2taafDv7c/J305Stk3af9UmacHpMuOe7vnchH8GLroGevLkSV566SVeeuklQkIajgWqqpJMGV5e9e3ZGo1GrtPkSNSEysrDGI1/ysd1yQt8fDoRGfkMNtsJlEovTCbdqWuOkZX1ElrtEEJCrgfAbrfgcFhwOqvQaFpjt5uprs6losI9ri8wcBBm8yaMRh2+vrFkZk6Tz3Xt+iMeHld+7kfhFKRNlDw8a02SAf0DUPoo5RACkJyAalEbUmLeZMZZ40TpeW5r8dNDUcLHhxOUFIRHyNl/2+oANdHzovHp4EPZtjI0URoMSw10/LQjlr0W8ubn0erpVpTvKf/LKcVU3irazW6Hvdx+xqD+Bsd1ymM1clIk6iA14feHkz45naIviyhaLOUhPXTHIQZkDaBsRxnOKpepuTb8QpuklSnvgpKC8G7vjVcrL04sO4FfDz8s+yxEPnV+ZAZNuHi46AL0xRdfJDQ0lIkTJzZax9tbetirq+vnfbNarW51GsKTTz6JVuu+Ch09ejSjR48+nyE34R+MulqlUulDaOhI+VihUBAd/TYAxcU/Uli4iIqKw+zcKW0bmM2bcTqrUSq9yMh4npMnf6OmxkBMzALS0p7C6ZRsv7Gxa8nImIZWO4j27eewf//VmEw67PZSCgs/AaBZs7sIC7vlUk37oqJupovAQZLJVOmpJPjqYJTeShSq+lqPaZ0J747eVB2romxHGdpB50ZpZ9KZ0LTXYE2XftcdP+p41r3KuoicIAmRWq/Y8HslL1lNKw2hN0r7pCHXnV/Q/t/1RK3LCasdopWFJyB7GBt1RtRBaokMHgi5XhprUFIQuW/m4tHcA58uPigUkpOTYYmBE19Le8Snsz79f8Xy5ctZvny5W5nJdGay+YuFiypAjx8/zieffMK8efPIy3PtMVitVmpqasjOziYgIEA23daacuuisLCQkJCQM2qf8+bNo1evf0cQexPODJNJR0BAArGx6xDChlrdcAC1VjsYQBaeAE6nlY0bNSiVvrKwBEhNfcjt2oCABHr21KNQSM9cUFASWVmvYbVmyec7dfryQk7rL8NR6SD10VTazW6H4SsD3tHehN0cdsZrCj4q4PjE4wibIOSmELr91A2FQiERD3gpGJA7AHWAGsNXBuwmO21ntiXnjRycNqfsoAKSR2jZzjJi5seQMTWDfVfto+/hvvh2PnMe1BpDDRUHK+i8rDMh14egUCv+kvC8klBXA475MIbjjx2nKqtKzqvZ+YvOCLtAHeiK2VR4SLkwa820fj38MGCQ2/urITL/VjSkHO3Zs4fevXtf8rFc1D3Q/Px8nE4nTzzxBO3atZP/kpOTSU1NpW3btrz22mu0bNmSsLAwdu7cWa+N5ORkevb8Z2wYN+Hvw2YzUVNzZnIMIRxUVdXP0yiEA5NpPcHBV6NSaRoVngAeHu5aSKdOS+TPdYWn+zXNiYn5AJXKG5XKWyZG0GqTcDorqKw8ikLhRefOSy8JaYLD6sCaJ2lqTruTqixpq6MqowqjzojhCwMnlp8ga0ZWPY7QWjhrnHKqrtRHUhE2yfnm5C8nqThQgTXXKpGTJwTiGebpRqRQ/G0xhi8MEnVdHdR6hAaNCEKtle7D8YnHzzgX4RRy4Lt2qBZ1oPovm0qvJLSe3Jrg64KJnhdNs7uaSTy87+dj3mImKCkIla9KFp4AKh8V0fOjafWMyyEr4sEIWRBfDtL6JpwdF/Ut0L17d3766Se3jW8hBC+++CIWi4X33nuP9u0l1pLbbruNJUuWkJeXJ4eyrFu3juPHj/PMM89czGE24RLi2LH7sdtN9Oypb7ROUdESUlMfZcCAfDw9XeELFss+7HbTOZO2N28+BoNhKYGBgwkPH0te3nwslt3yeV/fWEBQUSGx4SQkFDToTevv3wuVKhCHw0xs7Fq8vdue42z/HnJm5VCwsICEwgQKFxWS/lQ6vff2Zlf3XXi1kvwF8ubl4axwyhyhpwul4xOPU/hxfcsOQOaLmZKTihM5hVddIoXCRdJ1Rp2RwMRAubyWC9c72psWD7Ugc1qmy5u2EeTOzSVzaibqIDVeEf/+jDUewR70+L2HfKxpp5E9fRsThi0fcU9JpvZXE7c1ju1tthM68uxhPE249LioAjQkJISbbrqpXvm7774LwI033iiXTZ06le+++46hQ4cyadIkysvLmTNnDj169OD++++/mMNswiVAcfGPVFUdx2hch8NRzsaN3nTo8DF+frHs3z+MNm1eJDJyEgClpasRooatW8No3vweOnVagtWaye7dfVAoPAkI6HeW3iR07PgZ0dHzUakk3tBevbbicFScEpJKFAoPFAoVTmclCoW60VAUhUKFVjsEo3HNOfd9vrCV2kiblEbAgACyX5OI1C37LBhXG3FanezsLFlprJlWmXO2LkdofHq8mxAt/t49g4lXGy+q86rBgVsWi6CkoHpECrVtZ72UhU9nHzStNJz49oSbR2jrF1qj8lWR9mQaxx45Rvu323P8seO0f7u9TFZuXG8kY3KG1P9lDny/XPCK9JL3fX06nXueU89QTxKKEi4otV4TLhwuS/CaQqGo544dGRnJhg0baN++PVOmTOHtt9/mhhtuYM2aNU3et/8C5ObOJSNjCg6HZA50Oq0cPTqWlJTrsNlKSEt7EiGcCOHEZHJppwbDl1itmWRkvACAUumJUunZYB+nQ6lU4+ERhFLpIV/r4RGEWh2IWu2PSqVBqfRArQ5EpTrz/l3r1lOIiZl/zn2fL07+dhLDUgPHH3eZRI1rjW45H2sRPu4Uzdy1kvOLzWAjf2G+zPJVeawSu1lyVvGL86PNS22ozq4m4oH64WKqIJUcxF9LpADIeTMPjzpM1muSqbguF65CoSDkRslcXvhRIYalBgxfGsh9J5fKY5XYTDb2D3UlsO7ybZe/cXeuXMg8vMs7/+VQlCbh+c/FZflm9PqGzXddunRh1apVl3g0TbjYsNvLKS9PBkCl8sPhcCVPrqlxZf2wWFJQKFTYbMWoVP6ysDUaddTUFADQsuWESzhyFwID4wkMjL/o/Zwe5uEd403++/nYTXaUvkqcFU48IzyxG+20fqE1JT+XEDIyBFupjbItZWQ8m4HKR0Xze5qT3Em653329cEv1o/CzwtBAW1ebONm1lWoFezqsgtNW41MpJAzJ4fq3GoiJ0bK3qSlv7tiPuuaIb3buhxmcmZK7FC5b+bKYRm16PZzN3w7nXmh8m9FXR7eJvx7cOXTpzThHwUhnBw4cBO7d/fD4ZCcdczmzQhhR6FQExg4mEGDKujXz5U5pU2blwEVu3fHUVi4GIXCiwED8klMLMXPL47U1AcxmzfTtu1s2radeZlmdv5w2p2kXJvCnsQ9OKoaJkwHyT+gNhUXQL+j/Yh4IILqvGqUPkoSDYkkliYSnxNPwokEvKO86Z/en4gHIujwQQe5naLPiuSk1wDWHMl0aNKZ8IvzQ9NKw8CygcTnxhM1M0pm9bFmWmXB2OrpVvQ90Be/WD9673X3bmzII3RQxSC8o70l83AD6PpjVzdi9CY04d+AJttAEy4oLJb9nDz5KwAnT/6Ov39vTCYdnp4taNv2dXx8OqBS+eDj05GoqNewWPbQqtUz5OTMQggH+fnvodUOlT1sAwL6Y7HsBSA0dOQVSZlXvrOc0lWS9mZca2zQIcSaZ8VuslOdW037d9ojbAKfjj6yQAscFIjKVyXvbyr9pfug9pN+wnV5U8t3lssOQAAHbzzIYOdgjDojzUdLJlm1vxq1v5rQG0LJmpYl15VNsyqF3JdfrB+tp7TGmm0l7LawBpfdKh8VQf8JoiqtinZvtqP0z1JM6ySTsHaYtl5mliY04d+AJgHahAuKWvYfgIyMKVitOXh5tSAoKImICHdnsKioF+XPkZFPkps7B3BnFwoJGUlBwUIAfHyuzP2zWpJ2kEJAThegTruT3XG7UfmrQAURD0TItHb+vfzxbOF5Vi9Mo86Ifz9/OeSk5Ef3UKGKgxXU5NfU8wD17eaLVxsvNK00WFIsMpFCXSgUCtrNbnfWeYaMDKHosyLC7wun9eTW5C/MJ2tGFj1W9ZDzVzahCf8mND3VTbggqKxM5dixByktXUNg4GCaNbsbqzUTcFBdnXvW0JN27d6gbdvXAdxSg4WEXMfAgSYGDbJcsTygRp2RoBFBhI0Kq7fHCWDZY8FWYsOaaSWgrzsnrEKloH9qf1o82qLedbUQToFJbyL4muB65tbaJMQ5s3JQqBW8+turJCcnu9pXKuh3qB891/dkQN6As/LRngkh14SQYEiQvW9bPNSC/mn9L7vw/OijjwgLC3Ob94XG5MmT2bp169krNuFfhSYNtAkXBEVFSygsXARA27az0WhaceLEV/L5s+XLVCiUREQ8hNNpxd/fPVREra6vFf1TUFNSg0KtwEPr7inuqHBQlV6Fs9qJeYOZdm+2Qx2k5ti4Y5TvLse/t4sEoq5QbShG8EyEA9nZ4G+wYDfaCRoWhH9Pf4L+E4TxTyMe4R5EjIsg4/kMDn19iMLOhcz/cD6VNZWEhYVhs9no0KEDKl8VDgfklqhp2zg3xTmhrseoQqmQTcyXC0IIHnnkEQDuuOMOsrKyLngfhYWFzJkzh6KiIhISEi54+03456JJA23CBUFd021QUBJa7TCUSm8CAwfi69sdjaZ+EuDT4ekZRtu2r10Slp8LhUO3HuLY+GP1yg/cdIBdsbvY028Pwi7QJmnl/cXdfXZTXeRytjHpTPh09UHhqfhLe4VVVdCtG8x73Y7SW0lAfyk1V+zqWIKGBxF6UygKpYKAIQHcwR1MOiLF2f7++++0a9eOjh07ylrZkiXQqROUnJkk6opDamqq/NlsNp+h5vmjNqpAp9PJIURN+P+BJgF6AeGodHDk3iMUfFxAzps5Z7/gX4LjxydSVrYdhUKNShWIn18vvLzCSUgwEBurp1ev7Zd7iBcF9jI75q1mjGuMOO1Shg3TZhPpz6fLDjS18Ovhh6aNy3N1W+Q2akpqJA11s5nw+8JJLEkkcMC5aduVldChA1gssHabmsCBgW65J7ut6EbMghgADJ3cE4sXFoYCJ4AnWLZsGVdfPYcHHoCaGtiwwVUvIwPGjYMrMZOg3W5n/PjxfPzxx6jVaj788ENMJtNF0UB1Oh1qtZr8/HyOHz8zpWET/l1oEqAXCEIIChcVYvjCQOrDqWS9koWzxnn2C69w2Gwnyc9/H4AOHT4mOnqerEGq1f4olWpUqnNnXrmSUMsJ6yhzUPx9MXaznexXs8l961T8o0pKV9Xpy04yaXrXH06R2zsg6+UszFvNOKucBCUFnXPAfHo6fPgh1OZn2FPig89V7qZflUYlE8Dv95GIDAYmDmTZsmXAZ0AY8B7z5y/gzz+fk69bvlwSygBLl8Jnn0FyMpSVQUoKcrLyfyIqKipISUnBbDaza9cuFi9ezDvvvEO/fv246667UCgUjcagnw/MZjMpKSn89ttv3HPPPahUKj799FOOHatvkfgnory8HIPBQEZGBk7nv/9ddTHQJEAvEAoXF5I2KU0+dlY5KdtRdhlHdGlgMq2XP4eH30dExH2XbSyXGkadEc8WksPMkdFH2KzdjHGNaz+z947e9E7uTfiYcLks7NYwwm6XsqYUfFjA/hH7UQep8Yv1O6c+8/MhOhqeOyXzPHFQjYr0sMa9dDds38CwYcPYtHkTd999NxpNXSYiVxajdu3ghx8g6dR2tU7n+t+/P8TGwnXXndMwLwtuuukmYmNj6d27Nzqda0shKSmJoKAgevXq5Vb+dxEbG0tsbCwGg4GbbrqJLl268Oabb9KpUyc2bdp0wfq5WHj66aeJj4+nU6dOfPnl5c0udKWiSYBeINSjWlPC3sHvewAAIABJREFUvqv2UXHkH7xkvwAwGnVoNO0YNKjiivWSPV+YdCaCRjSeUHt3n90cvOUgwum+L9Z5eWf8+53y1nFIuSMbyrlZF/PmwcKFEFknp7IvdlawBX9sTPtoHUeOHKl3nd1uZ8OGDSSdkooGA1itLXj3XQcqlQB2nap5NUOHSjy7O3eCn59kzlWr4aWX4Ogp3ouNGyEsTPp/uZCamkp4eDizZs2SyxYvXsy6desASE9PZ926dajVkkY/bNgwQBKk69at+9v7lCtWrCAkJITs7Gy5bPDgwXISDICNl/MGnQOEEKxcuZKsrCxsNhurV6++3EO6ItEkQC8QyndJ8Xfdf+tO1IwomTT7+MTjCCGwHJBSStVyk54N1jwrFYcqGv2xV6VXuR07qhxU51djzbbitF0ac0x1dSEnT64gKGjEv9ZM2xhsJ20yJ2zPTS6KtsCBgXg0c3nklvxcQsVB90WUUq2ky/IuKDwkoRk0rGEhbLVKZtqsLJg2DR591HXuqtga5rEP/zYe9OhUyp69gSxZsqReG7t27aK8vFwWoOvXS+V33qlC6fbr17F48RC6nrIw15pq7723/rhKSuA//2lwyAAUFxdfNIcdgCeffBKDwcC0adMoLi4mJSWF8ePHu9XR6XRMmTKFadOmkZiYCEiCtLCw8G+bWG+88UZKSyVijMDAQObMmYNWq2XhwoWysF6/fj35+fkcPHjwH+lYlJqaSn6+i0bzjz/+YP/+/aSkpFBdXU1eXh7ff/89O3bscBv/0aNH3RYOlxvFxXARH7WzQ1zB2L17twDE7t27L+s4rHlWoUcvDN8Y5LKsmVlCj14k90gWuQtyhR690KMX29pvO2t7DptDrm/42lDvfNneMqFHL4zrjXJZ2vNpYkvEFrHRb6PImZtzYSZ2BjidTqHXI/R6hMHwzUXv75+GE9+fEHr0oiqnSgghRMHiArEpZJOwHLEIPXqxZ/Ae+TvMebfh78O8wyzWe64XFccrGjw/fboQYWFCgPvfXXcJcfzp42Jr5FbhdDrFzTevFVAtevUaVK+NmTNnCn9/f2Gz2YQQQjz0kBCdO0vnnntOaq9Nm2oBCECkp59062vfPtfn7Gz3cTidDd+b/v37i7vvvvsv3tFzR+/eveXxnv6XlZUlvLy8BCD27dvndp3FYhFqtVp88MEH5913ZWWlW39Wq7Venblz5wqNRiPX+fTTT8+7v4uFkSNHyuMLCQlxm9O4ceOEp6enfPzOO+8IIYTQ6XRymcViucwzkNC/vxB33335ZEGTBnoBYNRL+17aoS5HjtYvtCZ6XjQVByvcWGGs6Vay38jm6PijVB6vlMstKRa2hG0h7708LHtcZOslv5SQ3DWZI2OPyCtB459Sf6WrS9mRt4OwOWEc/+k4NYU1OCwOSleWcuyhYxfVfCyRJEjQaodetH7+iSgr20FWyfN4x3jjDMnh2LEHaX5fGPFZ8ZRtLQMldP2+K4mliQQOCpSznJyOgH4BJJYk4hPdsPa+erW0wq6LSZPgyy9xSyl28uR3gCd79/pgMrn3pdPpuOqqq9i8WU1YGHz8sWuP8403oLQUjh3z5NChQwDs27eesjIwmSRnothYyYGorAxat5b+//STdL1SCXWsqCxevBiVSsWOHTv4888/G3VM+fZbmD//zPe4MZSVlbFv3z7eeusttFp3x6mcnBzatGlDYmIiISEhdO/e3e28r68v8fHx57wPOm/ePBYuXMg999zD+++/T1hYGG+++SYAmzdvpry8HC+v+unZkpKSsFpdqeH+Kebcmpoahg8fjkKhYMWKFXK5r687wf/SpUupqamRj9etW0dqaqpsxQB46623eP7555k8eTKLFi3i4YcfvuSOSKWlkoPbV1/BF19c0q5duKTi+gLjn6KBHrn/iEjukVyvvDKjUtZC9OjFRv+NbsdHxh0R5Snlonx/udjScotcfuyRY271av8q0yuFEELsu3qf0KMXu/rvEi3mthABkwMarJ/2fNpFmW9FxVGRnj5N6PWIjIyXLkof/1TYzDaRsmWM0OsRB59ZJQ4fvlfo9YiSki3i+PEscei/h8SuPrvk+lmvZ4mNARtFdXG1qC6uPmPbFccrhPOUWmcyCaFUurS9jz4SYuZMITIyhKgpqRF69KLw80JRU1MjfH39hLe3ScBs8c4778htVFVVCY1GI+bOnSsUCldbP/7YcP/R0dHi9ttvF+Xl5WccZ2WluyZafWpanKYN7t+/XwghRF6edE0t+vQRIjhYCIfjjN3UQ3p6ulixYoUARGpqqrjvvhECEIGBgWLOnDlyPb1eL7788ssG23jppZdEcHCwcJylc7vdLrRabYNablhY2BmvdzgcIjg4WK7fpUuXvzbRiwS9Xl9vLm+//bYAxPDhwxvV6gMDA0WXLl0aPX/69/13YLMJkZl5bnV//LHuc9ikgV6REEJgXGeUg+TrwrutN5ooKfav28/dSDjhzlJS9GkRu3rsYlfsLmryXSu+goUF7I3eyxs3v+FW36gz4qxxYt5kxrujN+U7y7GZbPTMkvbgPHp44Bfn8uZsTPP5OzCbt5Gc3ImcnJn4+HSibdtXLngf/2Ts7r+bkzlrACi+4RoMBmnfcdeuMaSldaFwk8GNTUibpMVR5mBPvz0cHnW40XYrDleQHJOMca1kXdi4EZxO6NUL7r4bHnoIpk6Ftm1dDmvaJC27du2iosLCVVfZgCSefvppFi6UuIO3b9+O1WplyJAk6m7DDR7c8BiSkpL4/vvv3TSNhuDtDc2auY537IDMzEy3Ol5eXuh0OpxO6NsXXpdYGjEaYc8eSXtISTljN24oKCigY8eOTJo0icjISJo1M3LvvWsYMCAAg8HAs88+K9cdMmQIY8aMaXSOpaWlpJyl83379tXT5msxdOhQlMrGX51KpZLrr7+ekSNH8tVXX3H48GGKiorOYZYXF+trN8BPYfbs2TzwwAMArF27FoDmzZvL54+e8hwzm80cPiw9uzNmzGD06NENtn8hPJwXLYLOnc9tX1Onk6wilxNNAvRvwppppTqnukEKNjhFzaaEwMGBqDQqEo2JqPwapmZr87KLrSc/IJ+UdtKPvMWjLfCL8yP1wVQ2em3EWemk7SttwQmL5yzm6fKnyQvJ4/DCw8RtjUMdpEahVlC+WxKwFxJms8sc5eUVeYaa/z4IIagyp0O4Aezu36GXVyYaTSVpzY66Lab8+/ij8lNhzbRi3mzGbrHDU09BcjInvj1B3nwpmLM2/CXlPymU7y1Hp4M2bWDrVikWsy6MOqOcUmzdunUEBARw661BQG8gkMceEygUaQwdegfBwcEoFD0A+PVXyQQbHNzw/Hr3lnh0d+7cedZ7kZMjORN5e1v58MMj6PV6lEolmZmZVFRUkJiYiE6n48ABKCyUTL0ffCDNyemUvHs//xzuvx/effdDvv7660b7Ki4upmXLltjtdvLzM3j5ZU954fLJJ6PYu7cLqannlic2Pj4etVpNXFxcPaFfF7XkCID8/+OPPwZcXr1nwqJFi/juu+8YOlTa3pg/fz6PP/74ZXUo0ul0XH/99cyaNQsvLy8mTZpUzwxuMEikG4mJiXTs2NHt3D333INGo2H58uWAlGSg7j1auDCUiAg4Xy6JlSslRzmrFRqLAioqgvbtwccH3n8frr5aWpR5ezdc/2LjogrQnTt3MmHCBLp27Yqfnx9t2rThzjvvbJCt48iRI1xzzTX4+/sTEhLC2LFjKfmH84o57U4KFxeCErRXNSxAI5+MJPrdaJkr1UPrQfT8aLr92o3g64IJvCqQgIQAQm8JpdUzreiwsAOmvia+vvprhiQM4bdbfiPyqUiZpq0WQbdKL2l/qz+BKwPJ65rHN8e/oZxyot+LlkjEnWDeWH8pZzPZqCmRNF5LjYUUQwpl1fVjVu32cmpqXCw2NttJiot/BECrHUaHDh+fx127clF5uBJ67QGHEp+CWwBpEVG9Zpxcp6rXAQIHutiElB5KAgdLx8Iu2Pe/LMS8efDJJ+TOySXrlSxEdg5GnZFcvClEw+a7jvPLj06u6mPHyws8PaVnzZJioeZEjbz/CdJLcfDgwYwYoQJUwJ3AY0A08CZ+fvF88YUSjQZGjAD/M3Dd/ve//6XrKTfcWo2kMXh5gcmUjtW6ip9/VvDll6vo1asXYWFRpKX5kJBwLevXb+XTT137YhMmQLnkrM6QIfDee5IQfeWVtUyfPl1+edciNzeXAwcOMG3aNLksLg6iozMoKPgQgOLixVitGRQUfIDZvO2MY66pOYFKVS2HW02fPt3tvBCC9PR0QLqvSUlJzJw5k19++YW5c+dy7733MnXqVEaNGnXGfgA8PT3x8vIiPDycLl26MHv2bD788MNLRrKQn59PVZXLU7+iooJt27YRHx/P9u3bSUhIwPuU1Fm1ahXDhg2TLRc9evTg1VdfBeC3334jKioKAG9vb6ZMmSK3KYTgf//7Hy+88AITJz7HsWNjKCqCOsaAc8bJkyfdYoxrldmqqio3b+EFCySGrNqpJSWBVgu93XMoXDpcTPvwbbfdJlq0aCEmTZokFi9eLF5//XURHh4u/Pz8xMGDB+V6ubm5IjQ0VMTExIgFCxaIWbNmieDgYNGzZ09RU1PTaPuXew80fUq60KMXOzrtuKDtjvhihLh26bXi872fC8UMhSipKBElv5fIe5vJPZLFlDVTxJx2c+SyeS/OE8xARLwdIbezLWqbSH0itV77B24+IPYO2SuEECJhcYJgBqLbh93q1Tt6dLxITu4uH9d63WZnv3lB53ulIHd+rtC/lCSSN/cR+ri5Qr/KU+SvPyCiog6KP//0EJ8v6i4++6h3vevy/pcnNjffLL4J2y0UOMUKrhc1bboJvVL67sz+fcRi3931vG2ncliUp0j7kbXPmuyd/Y1BVFZWCi8vLzFv3jwhhBBRUUIEB1vqtQNCDBx4bnM0Go3ynlZKSkqj9VzeqI/LfUyePFkMGyZ9btmySsDCU+cy3cZy9dVCzJpVd3yvyX3Worra5Rlc+xcRESEmTFDJz+H27R3lz7V/VVXZjY55586e4siR+8Rzzz0nADFkyBC38ytXrhQKhUKkpKQIX19f8eabF+Y5nzBhgjyHv+MBfK5wOBwiIiJCTJ06VS5bvXq1AERAQIAIDAwUr732Wr3r7Ha7aNGihXj//ffrnevfv3+D+55ff/21EEKI998/KH+f/fv/9TGDh3y9QpEmunWzCyGEeP7550XLli3lff1bb3V/rouKpOufeuryyIKLKkC3bt0qu8/X4vjx40Kj0YgxY8bIZY8++qjw9fUVubm5ctnatWuFQqEQH3/8caPtXy4BWpleKbZEuJx+9g3fd/aLzhFWm1V4v+4t5myZI7JN2YIZiKlrp4rQt0KF7xRf4fe8n1C/qBbMQKimq8SToz8Wox7Viz+2/yEi30Q88xWixi651h8Zd0Qkd3M5N5344YTYpN0k9OjFevV6YSu3CWYg/znrxCU4nU6xdWsrodcjrNZ8kZb2rPySMpt3ntfcbDabeOCBB0Rqan2hfiUg5eYUsX5FsNCPv1v67r1/F3PZK0AIb+8y8e51r4u1a5ViwsMn3K5zOpzCVm4TL/UrECDEKNaIUawUP7NZfoYe53g9ofctW+RQmeTuyW4CtNpQLdatW+cm6MaNk66LibGLgQNr3NoaPfrc51n7cpw/f369c59//rnw8fGp8xLtJPcxa9Yr4pZb5osXXrhHaLWGOv0vEyNHhooRI74QgYHfioKCYrF9u3ROqbQL2Cq3d/vttwun0yk2bvxGTJ6MUKmk8u7dx4vQUKf4449YsX69+lT41NdCr0ekpT0nP5uFhZ/LY83LE2LsWMmBqbq6SOj1iC1bIoTdbhevv/66AMTzzz8vhBBi165d8hjuuusuAYidO8/vOT8dP/30kwCEWq0Wt912mxBCiDVr1oiXX365Xt3KynRx5Mj9wuFoXHE4G/bt2yfPJSQkRFxzzTXigQceEB4eHnL5li1bGrzWYrE06CB1++23y9cWFxeL0tJSER0dLR566CEhhBBTp9oFnBRXX60TIMSkSUI8+aQQixYJERoqxKk1nlizRoiXXxZiwgQh9uyRyioqKgQknnpWhggYI0CIBQuWn+ozRoSE1IjAQNez/MQTQpSVuca3bt2/UIA2hl69eok+ffrIx82aNRN33nlnvXodO3YUw4cPb7SdSyFAnXanqMyQXAgr0ytFeUq52J242907NqPyLK2cOzZkbRDMQOwukOYUPT/aTcid/nfrhu0CvV6sKTkhJv/cRSzStxNLDy8TWVVVomhpkfSyLZLcJE/30k15K0VoXtCIdo+0Ez5TfMSR4iPyOCoqjssvpby8D+TPBw7cJpzOv+g+eQrbtm0TgJg+fbpITU0V6enpf/+GnSOq7dVif9F+UVxRfM7XVKZXCqdDWlQ47U6xsfsX0n3oPUfo0IulbBNjyBIgxKusEN+E/yD0ekRCwi9i69b67d3Qu/I0DXObWM8aoUcvEih2O3cX2fL3dHT8UXnho0cvkrtLi6Jp06a5eYQuWyZdO3GiFLM5bJgQQ4cKMWKEEPn5536vVq1aJQBxyy231Dt3ugayePGnomvXHQKEWLasrfycjBz5v1NzKRcQLr79FrF8ub8ICmov3nrrLWG3S3GuHTsuEwqFXUycOFVu89dffxXvvddb6PWICRO6iaFDR4mYmHzRsWOy0OsRWVmzRGbmDOF0OkRm5quiqipHFBf/IvR6xP7914ry8v3iyJGj4p13hAgNzROrVh0QRUXL5bGdOPGD2LNntdxfWVmZiImJcZtXYGCgsNvt537TGoHT6RClpYfEE088IR5//HERHe0j9u7dK4YPjxUajVKUlZWJ6uoiYbOVC7u9Shw9+uCphcCSs7adn58vKircY4gPHz4snnzyyQa1RYVCIQDh5+d3RsteQ8jLyxPDhw93i2l97LHHRHR0tBBCiMREIcLDN4kBA+5v0AICQuzdK1lCao9vu02I/fuFWLFinYCPBBgFKAW0PFXndgHtBPzu1s7w4dL/LVtcC/7/N3GgQggMBgOhoRJ3Z35+PsXFxfTp06de3b59+7J3795LPUQ3FC0pIrlTMhVHK9jRfge7euyibItrvzBWH4t32wu3g63L1BGkCSK2eSwASVGNe0TqxurZ5SHtMY04cIi3Aj9gPIsZY2hB1PbteAyWNrxM603Yy+szIJ2cfJKVs1eyeOFi3v/0fXSZLi86KT2ZCo2mHTk5s+Xyrl2/Q6E4v8em1ktv8eLFdOjQgfbt218y78SJf0wkdmEsYXPCzql+TXENyZ2SMXwp7ctZ9llwRO8EhxoOduPQwHaMVfRnDc0ZocxgPB/SokhFYWEUcXE6EhIkR5taOJ2w7bgHrXDF/h7Ak0i+x4GC/QTy2muSf1EPPwuvP2uj5cSWAJxceRK7yU7PTT3xi/MjZKSU8kyn07l5hCYlSc4UI0dK3olr10p7SX/+CS0az8ddD1dffTUzZsxg/fr1OBwOubzuXhRA//79GTfufg4e7EefPpm0aJEpn+vVq/ZZuopRo6IIC4Pw8HJ+/DGd/fv3o1LBSy/Zyct7GyFUXHPNTPnaG2+8EadzDwC33XaQCRM28soriSxcKOWJraoaQ1TUyygUSqKipqPRtCI09EYiI5+htHQlu3bFUlTUidWrN/Ddd5F4eXUnNfUhNJq2ABw6dBtm89WoTvmBbdq0Sfa4bdWqFSB58qpUjedhPVecOLGclJRY9u5dh82WzCefVDJqVByPP76fO+5wsmnTJvbtSyI9/VmOHh1LYeEnABw9ei8lJb802q4QggEDBvDSSy/JZStXrqRLly7MmzePNm3aNHhNXFwc11xzDR4eHvXOnwktW7ZkzZo13H///XJZUlISaWlpHDmSy44dkJBgZc+e5Y22ERcHmze7jn/4QYozHjkyCXiIoUPVeHioiI0NBY4BbwKpKJXuG5z79knvssREhdtv7HLgkgvQZcuWUVBQwJ133glIyWgBIiIi6tWNiIigtLQU22XMp1S6uhRRI9jZ2d0zMeLBCAaaBxI0pHEu1L+Kbw99yysbXmFI1BBUSunHO6yd5PH32U2fUTalDOs0K6WTS0kdO4vi/AnkVFc32t57NgOfTlFj1Bkxb5aciXps68Gol0dR5u3uNNT2RFt0GS4BajTqCAjoS0jISKqr8/DyimTQIMs5891uztnM82uedyur9WwsKCiQyxrKjiGEYMyYMXTr1g2j0Vjv/Png+yPfy5/nbp3Ll/vPTJ5t0psQNsHR+45SsKiA3Y99CE8sIO9gb7YOjGPi5tY4hQIDGm65PYdwVhLPXXTfm0tcnI6HH57M1m++kRqbPZsDH2zkZJma1xTSPVHhJJnWLH10BpuHe1KBB0mJ1bz5JmzJ9qbt7LZEvxtNm+ltqMmvQemjJKBfAHFb4tjQfgMajYZt27a5hZyEh0tctyNG/P37lZSUhNFoZP/+/QghGDVqlMz1mpqaSmlpqRtBwC236HE6FYAChULN8OF6Nm3aR2joXh57zD2dXUrKnwgh2Lt3LxUVewkLq0ang8pKaXHx8MPQs6eQ6wcHG4iIyJKPN25sVW+8ixfD7t2JbmVTpgyRPzsc5QQHuzPh5+evo0WLFlx//fUUFxfz6aefsnTpUqBxT9vU1FQefPBBt4VFYeFiCgs/4/DhwzRr1ow33niD8ePHc/DgUo4cGYMQdjw8DuHrK4WCjB4tOb7cfz8kJz9DZeVhjMbVFBd/59aXybSJsrId/PrrNbIHcC2OHj1KTk4Oc+fO5bPPpL6vq+OFk5CQQFlZGc3qxhsB27Ztk+d4rqislCgd6/xsAWmRAR/QpUsr7Hbw9u5OdXUSq1Ztok0bydMa6pNmNPYKCQz04/nnyxk7diygA9oBKpzO5sAz+Pq+BUBJyamGH07n461mJq9YQe+6efguIS6pAD169CiPP/44CQkJ3HuKZLPWU6whRg+NRuNW51LDmmuldGWpW1ng4ECCrw2m7ay2qAMubOLnO7+XFhVDo1zMPtfHXM8LA1/gjq534O/lj5faC60mgPzsqey0t0GJk686d5brh1FKrJBW769mZ/Pl1XaObyjBsMyAZwtPjrU8RomihGfGPlOv/7Jfy9izew/7i/ZhPLkOrXYoQUHSC1riu/Wtd01j+N+u//HW1rfIMGRQWFiI1Wply5YtjBs3zq1eQ7FjaWlpLFu2jEOHDjFz5kz+2LmTlJSU8xKmxRXFnKg4gaXGxe707JpneWOLK8b2dF5hkEJFapH6YCq8KXkfbjw0hGnrmrvVHT4+CsWSJaiHDyQs5jbatz/AXXfNwa55F7vFAK++im7BITTKGu7sf5AnmufwCBkYCGXG/8KZsXYAvljoe/RLPNQCv2AVSrUShUoha5uBgwJReipReasY98A4qk8tnOoK0OrqAnx8KrkQ6N+/P97e3uh0Og4fPsz337sWIDExMQQFBeHpKWWisdvNDB78DVZrb6Kj36V9+3ew20vo0QPmzO0nX9e6teRN27JlMceOHWPDht9o3tyH//zHg19+gbIyb1at+oG77pLqz5mzqN64Fi9ezu+/V5KdLeUpNZvNHDhwkmnT4LnnrmP79v9y5EjfBucUFJREbOxatNohAFit22jTpg3e3hAUBCNHjiQhIYFp06bJsY5lZWWcOHFCbmPJkiUsWrSIPXuk31h1dQEZGdPIyZnFo48+SnFxMdOnv8CKFYspLr5Hvi4uDjp0kJjB6obZDhly9NRYsgDw8GhGt24SS1BJyW8cOPAcAQGr+eCDGQghyM7Oxmazuf1uxo0bx6N1iJJHjBjB22+/TWlpKSdOnJAXvcuXL8fLy6vBd+2ZoNdLTD9z59becymGd//+ECSPbwnffmtErX6OrVvX8s478M038MILcN99UiKEXr3gwQdh2TL46qsqrr/exdYUEFCJ2QxvveXFf//7IH37lruNwdt7PRUVk10FwQ/AXbksKc1kjr8/+J77u+lC4pIJ0KKiIq6//nqCgoL4/vvv5S+11pW6ugFNqpYOy/ssQT5PPvkkN954o9tfbazS+cJpd7K99XYc5Q5U/pI2GHpzKHHr4+jxRw88Qz3/Vvunw1jlemEntXX9wnw9fZk1bBY+Hi66N4tlHwB76EUnRTajmzfnqYCjtFYU8FvrKuYpnmGYxhUEntzCxollJwhKCkKfpcfP04+KmAqm3TUN4SOIz4kHYOpXUynrU8bEeSOxO0tQZfQlMPAqVCp/QkJuOOe5CCFkc/CEZyeQkJDAtm3bsFqtPPLwI0SqInluyHNMnDixQQFat2zu3Llc368fsbGxtG3b9pzHUIuRy0cSvyieGkcNex/eS4SfZOk4XHyYIksRRp2RHdE7sKRY3K6rm5YMtcsCkpx8jfy5M4fpyFGih7WBsWNhzRq0V7vc/CO772DXzl5gtaJLb02iahua4QN54j4bd8aVyyt0gKvYiMdjD0o8d3Xg38sfzxaehI50bXnURXR0NCDd8z17BpCZ+RIXAp6engwaNAidTuf2fdxVK93qYOfOWGy2P+nYMYnIyElERDyIQuGF2byek22kSaZo7qBdu9fx8Ymjd28FOp0OrfZDZs3yYfhwJWlpkgbdu7fLtJibO4433liKxRJAVlYbli6FFStK+e23Krp1EyxYAA899DA9eoRgMEBurhcvvLCUxx5LZsUKKURFpWrJtGm/IIQvWu0QgoKG0bOnnpCQkRiNOsaMGcNjj8GcORAaGopareb111+Xt5gmTJjgptnV3gudTocQgm3bWmKzGaiqSsPhkKxpt90macS1mlZBAQwcqCImxmXWr83lKo2xNbWv4l69thIaegMdOnyE1XoMm00KiGzevJBDhw7RrVs3FixYgE6no0OHDnIbtUQHb7zxBn/++SctWrRAr9ejUCiIj49n4sSJDX4Y19U0AAAgAElEQVR354Lar/+dd+DJJyWza2wsuCvp67HZOuNwOFi7dhO33gq33irF//r7S1aF3bslKsnRo0Gne4JDhzoDA4FqfvihmB07pKTuBw7488cfk/HxgYEDoWNHeP/9r+r0tQgv79UwbRp5nz0uZVr44IPzmtvfxYVVoRqB2Wzm2muvpaysjE2bNhEe7sqPWGu6rTXl1kVhYSEhISFntdfPmzePXr16nbHOX0VdPtoB+QMQdiEL0ouBjdmSOSzlkRS6NuvaYB2rw8Ejqak84rWZ7xV3oxPDuFss48iR9dzpOMCYsJ70aLOQlRn30NLyG6jHoAb2xkGSHr4LnkiPqnXc36EPRmUnvq78ml7v90ITonHr59W0m6DmY2rWxpDSJZ2fLHfzdsjNDY5pyb4lVDuqeaj3Q3LZ0ZKjFFmKUCvVbNuwDVOuiY8++oiQkBDaK9rzieMTgsqCKEwqZMGCBSgUCgICAvDz8+OVV17hkUceoXfv3lRVVckvBpCeIw8/H5Z//gW33357vbEIp2DL2HQ+LG/DwMlfUaUoITk/GYEgxDuEHs17MKzdMJYfWI5DONBn6um3WtKQdsXuon9Gf7zaeLGj5xqqpz8MqR0QJ4NRjJZMsU89pWP//iEALONu7uQbqsNaoVBmyWPwah2HzxZPKiOkOFurooBffw6GRfk81G0BjqQ5tB3UlrDn9vPaJ48zffr72O0Khqk2gAOJgujU9gaAQqWgf2p/lN5KiouL3cyoLVu2lBeilZVHqa7OwWhcDbzd4HdVUPARSqUP4eGSZuR01pCSch1C2AkNvZGcnNn06PEn/v5xgKTdvvbaayiVShISEvjtt9/wPy2QVAgn1dVSdo7AQMmEqlJpCAxMJD39KXoDXzKGz6338QQQEjKc4cP3UlHxuKw0KBT+3HTTm3Tpso2cHBVVVZHceutR3npLwdixo+ne/VluvvkmkpPXYjb/CDyGxQKrVjnZsSOL0zFtGrzyygzKy58iIMCHoiIvfv21kKFDXWPXapNIT3+K7t2T6dJFKvv66w8oLVXw2GOPnZqbYPXq1Zw4cYJXX01kzJg72LlzJ2q1Gp1Ox1133VinVwV+fsf59NP7adv2M7l06lSJM/j11yWT7+efS+nhEhNnk54ehlo9nuPHmxEb25yamhNoNO0A+OmnbDkzDkja24ABA+je3UJGxkx0OidDhoTw5ZcPEB//KSUlJcyaNYvJkyUtbf369dx///1yDtTz2c/dsQNuuEEizKjFDz9I2wQuCOBGYNWpe7adrVs/paSkgpkzX2T06NH069cPtytO3dfc3FwgCwjFy6uMykpQqaQtiJQUiTTBxweqq+Htt2OAcpShfXDOe5nqlkvB7gC1NK8BSw1sSzm/BcLfwUUXoFarlZEjR5KWlsbatWvp1KmT2/mWLVsSFhbWIPtJcnIyPXv2rFd+MWCxSAG6UVHggZO970tPTcz7Maj9L+5tstRY+OrgV7TVtqV78+6N1ttkNrPEYMDq5eAb8SAAcezFYNgNQJtWk1CrPDHYwxml+RoHUOLRn/3DOnJUd5irbpHyJd4asovAjh8zIHIAgSFSkH/s2li2Pb8Nn90+ELcXDnajdE0Fn131GR/t/ohrO9zGiPb1N9dmb55Npa2SwWG3UWzwoLzGzK6SnaiVam6NvJVvcyWN6ptvvuH222/HvN6MBg1Ve6tIiHVRG5aVlVFWVsaDD0rz6tO/D2PHj2XEQ09QabPjkZODzWjEXlHFqFGjGmR0WfHFcb5apuEbPFjXbDMnIl0mwKFth6JUKHk6/mniW8bzv13/Q5epo4POtYrPnJ6JdoiW6pjfICoborKpu12TkvJ/5J13eJTV1vZ/U9LbJCEJJCGEXlOpIaE4kSZVmoACHkVQsaAUEVFREUWxHAuIgFJFBQSpUlLoEFJIAiEBQkIKIXUmPZn2fH/syUxG8Lzn+673Pe93nbOua65MZp6yn2f2s9fe97rXvYZy4ABcfuprJtf9hgITzicOPNCOTh5LaLjfyKHKi/TufQl3jyoWL14AgLaHDm+lnNKqrQwatJ7dux8jI2MsTw2eAWM+gYsPigEoXBTk5OTw2WefWT7r2rWrzTaC9AX19dfQ6Uqxt7eFmSVJIj//fUCBwSGMQM9QqqsvoNWKPlFdLWJIN248xYABQlherVazfPlyjhw5wnvvvYen54Px/rq6dAA8PGLw8hpl+dzgPADMbbpIFCYUaPR6VCo1hYWf2iBuklTHokULAaGUlJj4N5qaXFCroajoBoWF9xk/fhxKpYLMzA1AM+BAXJwJk6ll0HwTMOLr+zjz5/dCofBApfI0XwecOCGcZ15eHkFBQZbQhNFonSifOLGWo0d1vPDCC8hkMrKysizwbXDwBXJzb2A0Gpk/fz47duzg7NmTBAZCU9MalMpNDB+eZ+M89Xo5M2asxWRqBN5FkvxQKHqhVAYTEPA3Onb046mn5nPnTilfffUmnTp5I5PJMBqNvPTSGubNg4AABT169KV//1Tq6uqYOhVCQqo4eRIGD9bS0JBLaGgQ6ekFmEwmy4SqBdoPDw+3hMJs+oNRoqmg6aEESIMBsrLE6s9g5h6uWSNeLc7Tw0M4Ng8PGaWl3wLPAHHAAWABzz+/l337vqSurs7iQM0V4KiqyjU7T2G7dm1jxw4ZKhW0awc3bsCYp5rZd0qPt0JOF2dnEhPlRERo6fzRV+w1Q9Ddquu4qfKAKnsubunywHX8K+x/FMI1Go088cQTXL58mT179jBw4MCHbjdlyhQOHz5MUStcIy4ujlu3bv1Tqh//HTZqlIAloqNh+bAKxu9oj2usJwELA/7nz71zFL9e/9UGun2YxZuZgr80W1fbfbhmea9Sif2d3aJxpZ55bGGwfgeFzibe/9uXNscK8+vFi/2t8QvPWE8eS34MpxB7CEun8VpPGtIbuHztMgAjd44kszTT5hjFNcXkVOZQWFNIjw7eDBngzmMx7Xln0hz6+wzHv0JQPzt1EbNqtVqNNl6LU3cnkECW/teEpLs+d5lx/nkaPl1H268+Rb/HlmDx53qTn/+UxsS/deMXhDhmWaaYvgd5BOHl5MW4rgKCjmgXwcIBC1F3VHMp6xK1qbWW+p2aUxoR7+z6oFLWndxQPvpIwcQJEmukN3GkGbZtg4dM8No89iFBMz7n7dcOPvCdtl7QEFscXps241iyJAm/0RFieXL1KlRW2uxz8eJFevTowaZNgqH5MChOo4nHyamb+diJD3zf2HgTne4eOl0ht9PD/nI7ncEK/UdGRuLhISZYf6WPq9XGI5c7ERZ2CrlcDGx1BgN/u2el/R4cIFa8p7VaVKohDz1Oa0tNFefq1UtApXZ2dkRHRzNu3DiELzgFpGIyKYFFQArwMfApZWWDUattWZtqtXAIOTnV9OzZkx9++AEXlz4229jZdaBNm0JKS0sthcnj4+Oxt7enTRvBaraz0xAZ2Zb58+fT2NhITc0JMjJi+OOPN7lzx4NBg6zHc3EJo23bsbzyyhIWLXobD48YAgOncfJkHDExWywTnJSUbly8WEj//i+yebPod1evihDN5s2wbFkNjz76Nt7eBoKDoU8fsLODjRuFxjBA//5igp+eLiYzJpPJMsGcMKH1KtlqLdkFLYpkre3tt8VYaGhF3H/ySVFgHQTT+9IlIbm3cSNERQUBp5gy5TNEgXYf9u0rtdzDFps9W+g6t6yIQ0JCWLJkCQcOTGbTJhgyBERZV4niv19k0PVkuiYlkVHVwIULMHdue0wB1vH4gyFRKDI84aI38M+RG/+77X/UgS5evJhDhw4xevRoKioq2Llzp82rxVasWIGzszOPPPII33zzDR999BHTpk0jNDTUhjb9P2kXLoi/165BQroDtdhx2+Xh8nz/7ecuFCdvSV35K4vT2A6sldHRjBiiwdm5N05OXXF0FOzEkA5zLduEIR6qktDv0KDikOfPTGEvaeUPlz3rkaAA13o29kxCJslwS7PCXon5iZb35fXlBH4h4ERZs8efD8OVV3dz52Ip+EDv4cKZPTLsEbSntbSd0xZdBzsuHb5HY2MjVVVVaLValqwUGmDT1kznXO9ICt3FhKtj9VmB7Rw9Chs3AKBq58Xcn8V13rx5k3WrLts24PIi+KSMcN0L3F10lzlhc2gubuZi8EXOuJ7h8YmP8/WbX4MJwk+H4xrpyqVSV7bSQazAf5/AvXJXNPV2XB+fyILnrwjyR16eqDa9a5eIewKHKipY+xA+/b0yN/q0L6RrFzHyyGRKCgs/pbDwM+rrrRMfrVbA99Lw4WS9KZGUFoFeL2Kwd+7cYfBg60p98ODB7NhhyyCWJBNabQK+vjNxdu5BVtYMqqsvUF7+G4WFYtWq0Yi0pBa7VXqOKk08SURxjmh02PF3XsGgu0dzs6BbKhQKhg8fjrOz8wMwXEPDTXJynqOq6iQeHjEW5wkCKblGCGM5THiUhi7ObnRydCReq0WhcCEmpobQ0LtERpYyZEgd/fqJiZlwiFBa+ogZoj3GK6+8QlRUFM7OzqjVasrKyqiufhSw3pOxY8NsVuS5ubmsWbOGbdtOMXcuREWJz8PDX6O5uZlDhw4xYsRIPvwwhv79S9m2bTq7d98lIkJcc+s4Z1RUFKmpWwAwGmHy5GDaty/k4EEZvXodIT1dTXw87N9vJf717ZtM375J9O5tnfSFhp6gc2crgtBiMTExlvcrV64kKCiIbdu24ezsTGVlJc7OzqhUQwGhiWz/EOqFu/sdFAoFCQkJvP/++xa49uDBg0ycOPHBHbBmF1Sftp2IHjsmyty12KZN1lJ2YWGCbBUTI8ZLuVwUJmiJhT75ZOuyhoOAz7lzx5v8/HyamwUZ6fhx+OILP/r378/ly5f56KOPaJkbd+4s0rheXdtEa9t6VUtzM+RHFfBbRQVL27dHEx3NdF9fKhb0oXi5LRrzr7T/UQeanp5uqT03Z84cm9fcVqXuAwMDOX36NJ07d2b58uWsW7eOcePGcfLkyf/rfKX/F/tzgfVMSTiEm73+8eozpyKHfG3+Pz74vXuCB/4XlpAn0jh6tOnB0+FP/+V21QYDKbV1/I0f6McVNnbrgpedHQqFE507r6VTp7WWbXv7P0aBLpZbDc/ggTVdZb1sCZ9r/KjCm2V3Cqmru2YDhZpMzZRW7kAud8Gjy0CKvIqIyItg1+RdoHfgaIq1gsWm1E2W913rzMxaj3wIFoOPQdeGg/v1+PTxwdTTm7fe+gSvirbcrHXEGOHJuRAjd39vJOtqDUhOOLo4csE/A2JV7HEuos5nBAQ9CQ0F5OZsJpIS7GsSsWtvduiNJrb/vJ3MokxeWfY+JbfEAO/vksVz3BHbNPhw8I3lGBtdkclkFHxaQPPdZgo9TKC3zlhvphmpS63jNwKI8zeAXxkHy1z4OrMt5ytGs9W7GqWDiYgIBKNCLoexYwGo0Ol4Nz+f9/LzKdfpKG9VR9FR5UibzoH4B8TQocO7BAevAiA3V0wUPmQFAFqt6AONPjrKRkCDspCywm1otVlmSr+w2NhYdu7caRHw1ukq0Ou11NWlYzBo8PRU4+wsGNmZmeMpLPyMvLyV1NamUl7+Kw4u4eww9/X4rA+pqbnIRfqzk6f4hpc4zTBApGVIkgm9vpJly6by1VefWRi3LXb//jZKSjaj0RxH5TjYUri03mhklxnn29ijLyoHMQlVe3oSb2ZRK5VueHkF4e7ui0LhgqtrHzp1+pimpt/ZuHEt/foF0NRUaSHvRLV4QMDNzQ13dwfOnj1Fr15r6dtXw4YNStatW8eePXsYZF4GvvXWW6xcmcH27ZCe3oy/fxVNTeI4hw4dIi4ujlOnzrFt2162bv2VtDQBH44dG8nhwz+RmnqGEydOoFarqa8/R3V1G3JyIDKyhqysx3FzE8+Nt3c0mZkQF/cRJ08+SUHBElxdI5HL7W0mFQqFI3L5g2PZihUrbP4vLCzk66+/ZsiQISiVSvOEwTaN79Kl4RQWOlNeHsHhw2KCsHDhLBobm3n33Xct2414SD6TvkpPXXqdJbugNdu8shIbPdqZM+Gpp6z6yQqFYOLOmCEYtpGRIh3nuefggw9gwoQwS3oiNACvAW+xYcMuTp9usujXZmdPJDp6NE5OTly7Jvqyr6+IXctk0GWauU3Z4sTHyzS0aWviywbxXI/z9kZl9gsqZwX+vnJaXfa/1v6lsg3/zfbfpT7x44+SJMMk7fdPlhQYhRxaR6OkVv/1PhcKLljUgLSN2odvZDJJUlCQJC1e/NCvb5TfsByjsqHyH7bxYHm5REKCtDPBX0pKCv0vr+naE9ekSwMvSbHr7aURCW9KJCTYvHomCHWhe/esyiJZWXOkhASkq1dHSD+m/Si93vd1aXfb3ZIkSdLQ2YmSzKVMatYJdZYZe2dIrEKasXeGFD39oqRU3ZN8PvGVYn6IkWTOZ82qIV9IE96dINkHpUizZpmkmf1rLGoivSZelxQYpX2cl3Z1TpTm7J8jceroA+1s89tqiVVIgZ8HSpN+niRNOLNDom9foa7SD4lutFIpeUUCpB3E2SiXdO4sFEvSx6ZLO/0TJFlcgrRmkFD1Wd75hASS9D1XJBf00rhxG6VTpxSSs3O1ZX8Hz3LJt69Z+mzmTEkaMMByz1q3tePFi9Lgf9AXGxryLGo4P54KlEhIkGYlzJMSTrtKRqNOKi7+zvL9xb0OUnw8Uvv2QkVm+fLlDxwvNXWIlJk5RSooWCedPu0kGY1N0v37P1mO0SJ51/Laf2G8JFslkzYfVkq/HBOf9UrcKnW4cEH6rKBAmp+dLR1I8DKr/ay27HfjxjMPnDslZZBV2vHlRyVp8GBJkiQpNi1NIiFBeiory2b7n+7fl0hIkEqamv7y/mg0kuTmJkn79tkqHiUkJPzlPn+2xsZGycHBwbzvQQkkqUuX36TevU9JcFtycXGxOXZgYKAESC4uSHFxSN99N0H69FOk1avF92fOnJEuXAiS4uOnSAsWKGzuZ0ICkp1dkE1fmzbtn26qxVq3p+W1du1aafbs2VLfvn2lvXv3SosXi/MlJ1uFZouLi6UhQ6xt2bnTz7J/QEDAQ8912uW0RdHqUvdLNjrera/jr275q69at1m27MHvTSaT5OvbToKlrY6XIcG7ElRaPvvwwzSprMx6rNutShfPvH5diryULIEkjf89V1IeOiepX9FanrOmh0gN/scoEf3/aPHx0M2+HtW9WnpRgzfNPDFPS+JZPdV1zbx89GXSSmwVkVpYswDrLqzD51Mfvk/5U3WS7GzBWz9+3OZjg8nEmIwMxmbdAbmY2Xs5/UWNqZY2arW0lWkI9R5I375X+PJLaJWaZ2MFnxRQ/ks5jVca2T0hizf4hHCs7V/qkcNNutGIo015srIykfrj6BiMuqOatI5ptL3fluvTrlOeEYFU70Ofd56i2dDM7+t+J1Yby4mnT3BzT3se1SvInnaDhDkJuCsnI+MnQM3Uo/PRFYRz7LiRI2lWwsKtkjYYkZOGCv9ciclzn6Z/yoOEhs8HPoWd3I6imiLUwWr2R8/i493bYfRo7Aod4WbrLG2xknPcU8XrT17E8RURy8rNlXF79V3m/xHIm479kX4LJG5Cd07sO8FaXxFvOuwnY+Gy5xg44CjZ2f1paLBWv2nWtGFa/i8Y1n4Eu3dbEvlqWgWJFEBeUxMXamqwO32aHx/CKr/c5MH7Wx8FIO1gEajVpC3dDaY6ll/bS0VVHHm3FRw6BE3ezchkospEt6goVrVSnNl2/z77rz5DdfVZNJpTNjCqn99MevUSpcEkyVZ9avWVQ0S0i6DE0BZfR6gwudNsUBBT9gML/Hy4e8CTUkTeadY9K/xYVm6bWlPbrEFTcwWjJEdRL8P121Nw6RJbcnOJM8fpezs72+yjNhOQEv6ixiaI1UxxMYwaZUVs4uLi+fbb4URECCjxYXbuHLzxhiACxsQ44uZ2CrncERgG6Ll9uz2VlXuAzly+XIqDgxuBgScIC/uaoqJn6du3L4WFVbi796Nbt0pCQwUX4umnISzMh+bmAsrL55Kba1UG2rz5BGPGHECvL8DNrQh7+zu8/rqAKU2mh7fzr6yhoYGIiAimTp1qURZSq9UcP36clJQUpk6dyqFDXYiOriIiwvq8+vv7M2uWlTcSEFCKl5cXFRUVlqoyre3OyjuY6q2NC1oeREN2A833mm1Asvh4US3nYXagFWeuFfpsMZlMxogRauztW6enhQCrEM+nC1DMW2+F29SU7SRoEiIFTqNhpI8nYWFw6D0VBlc98Y+nYSeToY2JweEf1GL9V9v/Py35XzCtVtCljxySCNcJSGMu+QRGfUGO23pMejve23mCb658w+bUzUiSRG5VLpUNlfyW/ZvlOKvPrqaioYIFhxfYskNbAujXrtlwvy9Ua/ijqoo7JmdoN54jM48+0LaipiaaWqmdxFVVEC5dxtt7DJJkz3vvCTp8WZmYw7U8Lzlnmoh7o5RcXNCa7JCleOCs78WL1d8TlqFjk0tHZncajxElmYSg0cRTV5dBdnY5BQWdUCq96NjxA4I8ghg7R8CUeXuryMkUcMqtlEBe+PEFGi81EvdlHFV1nSiXAgirr0TzrYYD+w9QXVPOCAxAKEevhAByNJVKagxWNrM+STw9yXIVJTjiWiPjkzfAR6mgl52O9x31vOscwBS/QKLaC+hN3VGNXC7nyfadYOBA9KV9gJcB6O2cRn8vMWgnJyfz+bxmBjmX0QsR4/n6nSYuG70ovOMC33bh3CYPhoUOg3w1dnbNdJzxA2PGbCVmyO+kpamxtzcQ2s3K33+h8hTK5QJu00RHIkkSvxaJJPgnfX15xN3q/A2SxDM5OZTrdGTU1WEwj6jfFBeTcOQq69fD/v2AJJGTWk99PRjyNlJWdojzl4xcaiXco1bLMLz5BFf276bu5jF0ujK+ys/AUyvYnkZjtYBRVWruNTeTWVdHtfMjIFNiZ+9P564bUTj24lgJXNVCuF84j4eLUlVpsn7k3tnHrqub2XcujeMfq/iAtzEhw6k53dIGk7EJna6UuroM6uoyOZ1/EAVG1smWoNjrh9wEmEzMMzMrOzk68kJAgLVTAn729vR2drYQ4Sz9vKjIku8N4OoqsXOniPFOmTIFH59h7N0ruFW//WazK3q9eH7ffx8++USkjKSkQEVFDGPGXAHcgR+Afty/n41MJvHLLy5Mn36YoqIRpKe/BKxk+PDxeHp64ukZi0x23hJnnDsXyspOAHKeeWYoiYkj+OOPuXh5vcrBg2p69xbQam3ti4wcecqS8nHtGv9X5uTkxMQBEzl14hQTJ07knVdfxUEmsxFw6NatB3Z2nsjltlD6J58EsGXjRzTUi+dz4cJP8fb2fkAsoe5aHQUfiji9nZ8dXb/tisMQMVkq2VLChXOS+Z7/dcH13FxR2xUEIWjkyIdvp1ar0elS+OSTFHr3bp3fnwg04KbSQFureMmePQK6LWxq4mpdHaV6PWqVitBQ4LqVX6GXJMp0D5Ke/jftP9qBdusmAuNVWhkRaHEMceTuwB9IH/UmeyreAedyNu8T+p7x+fEczz1O16+70ubTNiQVJ7H20bUPxC1zNa1mfvHx4iQArarBL0lqJaXV5SVK3WyZnAaTiYiUFNaaB6RynY7MhiYiScHTM5arV4Xzv3ED/PxEoeRu3SAjxUiPYY48Q3/m0Z/HiUYTr8H+9lC+eP0n2rwaxqjzcvq4t6OdvT13vd6hubmAxMSh9Ozpw5w52RiNyRaG4OLxQq0oAxUmkww731zIU/Pj/haqvj9wxfwum8QLiRbW9NMILc6fzaxYmUJ0/MCp48FLDJh2vrmcdFEylwEcQ+QD3xswmOvRI5m+JYix87Q4KxSM6zqOjqqO9PIRCXuBjo709hpqOTfA1w3VbBmyiZkzZ3LMXMsyJEfiC9Kxw8RWe1tt0OY8Z+TVUUj3w1m+eDaTJq23fJeVNpAbOi8ybvoAS5Fzh+5Y81EDLk7nYM5Bnju3gbZ2Cl5xr+PUlffw+NPT5HvhAmHJybxx5w4mSSIuIwMqKthz1IUWFr/JBJmZMMHjNEp5E2lpkJ4ueEo3b0JIiMQWt0UY/J8l+d5jXLjgh2uTlQAml4t8EJVKTcDFi4QmJ9MtOYvrsggy5NGsTk1h6PEsPrkJRgkmdJ9Aj8DpSHJ3LsqiQSsUdX4+VAZae4pozxuIeHoVnjzDFsDAhQttSU4OIzk5FKei5yjDhz8Yzdmm4QDkRURY2rTHLxKPy5ehSxfh0czWOg4KYDAYiIiIYO1aa/x+9+7dPP/88+I4e/aQmGi9qZf/xBNbulQ8vydPmvvA19bvjhwRLNvTp1sEQBIJDDTxwQewY8fQVkdR0q7ddAA8PQUbxs7OujTKyPiUGzf6UV/vgcFgz9q1W4mN/ZLaWgXr108118o8xLx5fkRFiTqpD9EG+YemK9cxdMtQBtYMpG/fvryzdSuJ771nE3d+WDZCXp54uf88lfqph9DpHMjKqnmgGLVeqyc5JNny/+B7gwl4MYA3PranRmlH/jv55H1YgK+vcGYPW+A1NoqfU6cTv8P27eJaH2YtjO1ly/px8KD19z58eDEdOnSg68Iy2JYE7jomTYKpU0FnMhGanMzU69exk8mI9vBg0iSg2TZ/tVtSEvWtFhb/2/Yf60D1egvvAYCoMAOlO0pZP9I8kMolCE6gNrsfSrmS7Ipsfrz6IxLWFaa6o9oi9r5h7AYUMgW7c8/y2Nm1nEz0whR/gqbHo2nooKD24DfM2T+Hsvoy0ppkUHUFjGIW9kxODh0uXqTCPLs6WlVFhV7Pqvx8fi4tJdE8ax9oX869ex35s+7+pEliIA7r92Cy9OK/u1C8cBrZd8JJUXpx67VcSjaV0PeGnPVVrpxgBFevWqecSUnBlvdVVbB55lAueLXDjyaWjfOD/CFwzA5kbQCrKs6rTOZgkjVto97UtEAAACAASURBVF2r+9SORoKdNbiho2ikCvpqQW5AH/0uxlpf9Mj5jO5MI4rrh+qRJImq41XUZ9aTKEtkxtUZXBl1hYsBFzmrOkv6yHR6JlhViS4MSUcG6Mv19B0yhIzUNOZ+Xcf0LEeKBssJdq2mptmRUGUVnQPLkCPx4ouvsfmzNIYP24d6lBWu1Okg7dosOtMiJfY5JkLoZg9aJXgtg0Z72JW5CzzCuV94lIFbBsL9Y7xoOsvJYAXz9Yk2pPpDlZVk1tejTU4GhYLQQ4eoqqqiqqqKr/bvpzXae+0aBB09TY7XKXTXH57y8R6ruIc/R/0zKLKLxCB3wyvNVvrsNdNq3jMsZM+NfWDfBrovZ/e035jYYyIKhQsn250hQ/4INBSglCtJOucilJFGDSFgxzz0KEkjgjw6Ui+zzf9UKPQUlHTFP0fB5ulLGXnkGuuffRaZUYLpg8js9JwV3ztxwrKfWqXiTlMT+WY2SWpqKhUVFRxvFeI4bc6VcHFxQSaTER8Pgwdb5eBcXMRqZdy4B1ekIIhArW3oUCsR0NX1wedDqZQoKRHEKw+PaGQyOzw91cTE1GJn1wYvryJLWk2L2E1FhUjwj4wUzkIulzNs2DAcHQX0Gxf30J/tL027JRWZQcZgBvMGb5BUHUNtXDuioqJoaGhAo9HYkMkkk0TO/BzO7arnMUqYRhE+TRK3rg0iIiKeVhLFADZM25jaGGRyGZIkIkv3DcILdj2Tx+xemr/UqW2dnvxfada0FOAG6NYtkLy8CoqLaxk7NphvLlwg9VE52Evw+wVcVt+g0WikV1ISWoOBO01NRLm7k5mczPnzi3ku88GUsvN/SmH737T/WAfaopjm5SXxqkceASM8iL8XT5B3EN+N/Y6RnUcydpQzSCHM7CqS4H+9bo0FTek5hch2kUzqMYk3Y97k6fCn6effj79XGFlmXI7nLQ21eokLgb9RFW7kRm4xh3KPsC1jNwbX7qC5wohGa2mCkro6dt26xfVaDW/fTrV8PvPGDeK1WjrISunmFcmKFaKHu7jAi9Y0ThuL7tFM587i/SH8SZTaISFDa7AjDxduLrhJ4D4BP33ECq5etWIxiYnWJ+jwYdi1W86RqjZEoCHwhxwwuAJRdPBsLUj9OAAHDcKBfsEXAHwzvJABvnV8yDVeqS3h0R650PVZ5FPv0n/ez9DtCGCNyVTgwNtvQuXBSpoLBfQjAWdeKiZ7eTmVJSaM1UaKTtaQlyCgnRn8SvNZMcutuVJLmbwLSCa6/paOIaeJ9lN8cesivo82VPFGUQGrwncwbdqXtPffybvvCtZgba0jb77pwTffQJOu3tKmXZiABvJ08HxUO/yChBDInsIMcOsKWmts+Wj2Pj45+wHfX3iPXjKTwLzq6iipr2fb+fPIExPpFhnJx6GhZsjQkwXjxnG1fgpXr7vy5d5AdKs/4YbJxOJmBa8+/i6HGfvQ37ha0ZlP71XyUfM01plexGROUelhjj3qsafUIFFr3xbajYO2o3D1sYqtn6wxMNLblyXha5jX7msqMwfw5Gwd6BT8/oMnmab3KXJ/jlc9g7kiCYRE3mTtG6dSnuBeQjC3PWs46VzOut69sbvlAOWO/MITVGOOIbdajg1TqZBhjYO2pIskJSVRWysmAJfM+PXp06fJzxf+d9QoKzu0JVZ35AiWVfzs2WLlFBsrtk9IEO9bKn8sXSqOGRIiGKVKJfz+O6xcCdOny/j9dzFxOX7cGTe3r2jffgklJa6AWJGmpoq/QUFWyVU7O6DewEuPvcSGpRtQKj0oKRHh8dOnbXMo/8oko0RdRh1lG28DMJShjGY0zSxhYMN0RnYaTdVtOa5KN65dE/FhgLr0Oko2lVC1+z5LybEcr7fTQMLCTnP6tIHiYnGvMjOh+JDo/z1396RGp6SqSnTNwkL4gF6W/cclWmF7SxvN4aGWn/GHH7CRoPwr27dvHyC0APbs+RF/fzeq9HrG37xps92u8lK2379PbisYP8bDgy83bODzzz9n06kjgAiTbDWL8MQ/RBO7uflfU9Xpz/Yf6UCPHRP0bIC8s41Mqr6LSq0iPj8edUc1C/ot4PhTx5k8oyfsTMFRNo8QX6EQFNE2go6qjuyZtge5TI6bgxtrYtfgqHRE3VFNrUHMrlVpMH/J67zaazXrx05i4Mc/oO23j0+uHQaFA7vVyzjpaqWZuzQ14bd8OX1S0iltshWwP1FZTph0ScS5zBURXn4ZvvnGuspzRMAafVzqOHfDgdu3rfvvJIigAAkHe4k0PDEBP6eGWr7PKHqWESO288QT6Zw5I1bnYAtFRaIlGA2gBeK4WyVUZ8YEVfPcc9YSYQtZSDjhKFVKFia0x+34bep71xOOFuNoEQcePsCBla+74+Kux6VLGt4drSvZwltGrk2yBpGu4MVsBjLzcAc+RjxALxJJSrUXoV0KGREs4DaDSg56iTHP29GWtqSZSVMDZ7SnemQVSkwMpIqu7bMY8oVIoRo06IjlPOu/7UDTpWoOHbJe86QhQ5hlb09Hc4mrX86W8HHgx3T0GwCR34mNzBCon4sf6aXpnLwj8MSyJa/DvHkEvPIKdV98wRejR2NKS2P6qFGM8fa2nMNeqeT05r2M+Vspv0/dYc2OB0wo2GH3Jqo+qehRYrj0tOU7g4dIkL9GCMex6vNmmz2MUiZDCRi6r0ARLK73TI1wUhq9ntTaWmK9vNjw5Jt899zz0OxOt2HWycDi2Dd5mRn8MMeH80QhKTyIftKJS1un04w9KYfGQprtylSX5kd3sjnGY/QlRSwHz50TkjWAp50dka6uljhofHw83bt3x2g0cvbsWcrLy8nIyGDHjh2EhPSlY0fhBNRqeOQRHmotcOLUqaJ8W58+ggBz6pRYDQJ88skgXn4Zzp4V0LjBIJzhBx+ION7t28K5jh0Lffs+z61bfQkNhW+/HU9trQqNRuScjh8v9gchqH62+xWqp1bTbW03tky4x+DBop21tTbI9V/a3Q/vkhyWTEV+IE7Y5hErUDD4x0Ek9U3l8MQ7hIRAYKBwaNp4cf8Cs60xUqeuTqiyQnF1raG0NJV+/YS2cGgopGzR0vbZtvjN8GslZiDSUopwZjlW9TPJaKvw1RIe2rEDpk8XFWT+GZs8ebJFbrNF4CGo1TLWqRVO/MYdkZ7iqlBgJ5ORVlvLby2oxGuvQWEhO3r2ZG7btsz09X0gjg5QVfUgj+RfYf8RDrQ1S69fP9tcp9TeSQC8XvU618qu2agB1bQT8EZqnavl899n/E7mC5l88GstrzutIy+wM+POnGHimXe5rmimt5ueCxfG8alpCb8OV5Ml78npnk9bjlnR9S0cjLUEK0Vsdf7Bg2xfswatmxsHzHGkUtryND/iY44b3mnWE0kqG8q6cilJou/rZaz6wERTXhN/cIZDnOOw7CwXJmdz5b6V/VhfD106SZTjyKjHZETHyMgZ2IEXiURb6kHwU0Lg4JZLNYmJ00jq7kFdzyqSk+Gbb4TQTsts8/HNKp5lLnCaFgXIyHaNHMhxY6nXUp6PFnGrSCJReiqJKhHEnzitllQz5JNuFoiJ9fRkQvcJlCwuoSitNwVZvmi1sGhgBdfxQGfulkMahlA0rxcSMgqNTlygDeOIoQCxDHDoVMs5M1J4Zbo1XhRBBGmk4dLHBXd/J65+GM4368fgMHapEEkwW5s2Ajt1avqJAys3cwmoBuadPUvi3bvsiY+Higpu3LLCSGfPnqVTsFhx09REv/0dGHlpJLOqZ8EN4C5wEsqTxaBRnJdnlXABhg5tHX+zWndnZ2piYqiKjma+GYdUIOKGYd7hPKs8ypaQqYziD2oTF9MzUOTeygF7mYyBf9KoNUgShurr4OSP0XyseI2GZ7Oz8Tp/HhMQ7awSDiGyCubmUeq134aN2bcv1Ga4cLp+DAnOh1BUNbCrz2IeLz5Gxc3OKPJdoUYJBvPKNNWToseEDm8uXdAfOMK8pq+5tTddSNbs2IHa05M4jYa3Vq7k5MmTPPvsswQGBrJ3715LLc5HHnmEpCRrOwYMgDZtBAtXoxGhhdhYcFdJfO+Ww416K2LwV6ZWCwJMC0M2IkLEDx/mmFeuFByD3btnsWBBAXl5zg9sI0NCVmolyCiSKlmen0z6hGu4O5vIfymbhlv/uDJO1TGrMEqA/CAy9BhaITIAnvpmVPHFjOMegTRw2OE8uUtyMSDD29SMJIdBBYPwfcKXuj2BgCvDhu3g6afn0tzcyOsvvkKnHsm8tMUTd3ehRXL8OKxbJ+ZqDQ2gi/DmfSfhRHOP1/HllwIub1nZm0wimeAvxKj+0j780J+3355GfHw8b+XmUm+++UdDQqg29/UIV1eqzTHNJe3b80b79iTl5KBrXSd4zhyLVrpapSKlthZtqxKX5eW/UVz8bywm/79tGzbATz9Bx462M8OvSMWecgy4s+/6dnprYUSdn5AcUShI0AqoIMtBy0/9X8TfzR83pT/HUptZ9bKS9Hbr2axWc8RkYnJxA+MK4jnjO4g/tszn7BYxoJlQcMFgq9Tja9TSdPoLQpoXsvGLL9C4uiIzmfilVQ+NqbvIFdf+1NEJR5oI5yqTTjqCTkZKn3yS6x3oGF+PAya6vdMeOx87PGI8cHQVzqfaYECnNDFytD2314vO36EDrFxpB4gk5PxiH9zz7aiJ0KK/0Ia8IXdRuHqybZsXGzeKdnzyiViRlvqkco97CL3LidhhYvPHzcjqlRSvLUaNmma7Ztrrg2l4SsV1QyOujQJWTB1tx4BEI4vd2lLZwY6ZeGFsNOLm5AYtRARHeOpjD758RM7ZbsEsWKTAWGPkdJIt67De3GW7U0OndhXseFKEq38Z18RgL3h8P0SoYjh2+RgVcwSLtuh2FsGdTlA2DoyNWSiAb7/144UXyii/r+CJWTMt8ivxW7ey2WDAvqmJYUoluLnhgJDTi4qK4vTZsygffQsaG5mblMS2JEHOOPHHCQL6BGDnaUf++XzbDmiGJ0fMmGauofhwczPPVha3b09nJyfcFQr6u7sjk8kY7OnPz4Zy5EYjQ9d9h+Mzr7AiKIjfykrIbtJz2XyOUKU7y7oE8NSNazb5FF2cnEipqyOlzqr9WpbuBG567J67i76blsTbp3Fygj/+gNGWRa0M4xVP9vTLZ2qXLmR3MtC5PIApK2DQIBmHmrqwaa0SetZAuoopP8nZnnEJigaxOSWELUTgvzGR93PfB5WK2LNn+bSwkDXbtwMQGxTEtWHD+PFHq4ast3cA770n3m/cCPZNNaBtws3HRwhWd+7MqlUQd7WAVaUltLFX8rE5ZlGu02Evl1Oh19O5VRWnYcNE7DQ4WECXBgM884yAgqOibGN8x45Zr72kRDzHe75q5Os9jri5y1i4EF55TNzHJqUCR4ORPvVm1KiyjiUBefgl36d0hwPG2cH4NdZj72uHqdGEY5AjMoWMpsIm6jPFMdy4hNvMAJp3xfMuE+jB9xThxVuMt7RpMTe5hBduZsdxEj/GcB+XcDcc2zuiUqu4u/ourrpBTJ78DQBVVX6Mn/Y1OI0lLfsZamvBzU2089YtLyZMELJ88+bBqws9aULOwfc0fJjjgqpaOP97ONGiYPXPOFC9XoskGTCZ6rl37yuGDRvEZ5+VsObXXyEqirFeXnSsrETp5YWnnR1D3d1Jq60FmYxV+fniIFeuCCbTihWwejUAr732Gjt37qS/XI5Jq+V0dTWPOjlRU1NDTs6U/7ph/0P2b78ClSQrFNk6h+mNURpC0NKXF2jbYzNrT8G1DeAz+FFYtQqDyUSiVktbvRON/nXIDB1ZFr2MkCl1TBviiPRrEqE//MAaMxb8W8BYtKldSJn3Ah87vWk9kXkMm3vsGK6NolMu/PEow2enkSGEH/Gsq6O7UaxyIm/eJLCsjLmTb/Mop3iR9XzKUjIIhVQVeOoguIF4jQZtvBa3AW50fK8jgS8F4hZuXYUsyMlh0rVrjB8vHhK1+uEPQE2qL0RocOhfDUoJKbSajZutA++zz8KyZXDuoggoBbvkYKeQ+FqRRuhUN7SJAk7xwYdX1a+y8WU5oyZXEJacTGczbbJsdT8WFUZze5KMRQWelERlcnf13QfaEjFUOPbVN4P4/kUtR9teISMDerg20Bbbmp1fO2fwaJg3BjvYMg/q3KB8iisrNyuZt1cQLh5b9hhZWVnMmBGGgwO07wGKiAq2b4e9e0vJzJTIvWEuzhwfz9W5c3msg2Dr/hkmGjRoEBs3biQ5JYVLT8/HYeZMtq1aZbNNWU4Z9dnW1dD5jPOWdAK7jV/RPLrin1LW6ubszLKgIJ4PCKCveWXZkkfZ7+ZNPOrrSdu1lsX+fmQ3tFp91SrJGBJJzX4/HJrvg2eICCKbIOdPNXX97e3Fc/HLRfQ9qkEuI6MZKhsqGTVKhAgAUOgwpXiS7epC2KZNGLx0jGnryYcfCkjz+2ltiZG3gS2doNd2JvcZS++lL4GiiWXvCAcRf9lZKHJlZRHT1IRCkixMlPAZM1C3ijdMmjSJOXOEhNz48TB/PvDSSwI2asET79whxuEKrmeWPvBbjc/MZGBKCl0uXyal1kqsapGgGzdOoIIgiPEuLsJ52tuL8lstJpdb2ah+ymZ8Xk/i1xfLOHwYxoyBt8ZoaULOM6po3sG2etKQYhGcLT6s4e1uhaSEJXOx3UWSeiZR8kOJtVRivUQYi5nDeN6oW06C3JNLDGArJzhFJw7gz22sqvs95NbrOUQ7CuTO+E4Q4QD3KBFzrttslbWbOfNTAEwRaVSZZ6orVsxm5cpZAHh5CSLlwoVgQE4mHsjTtUyuzmcLyWwhmY/JICJClBTr8k/otefk/I2srGloNCInW6G4JNjRK1bAjRt8rFDQs3t3TpmZ8jXZ2SCTEdRK/1meloZ9jx4QG0useXz99ddfWbRoER8tWoTDO+8Qr9GwcuVK1OpBD7ThX2n/lg705k2B/69ZI7QM7t8XUGRSkoAlqqrgCf1d2g2qwIFKumXvZWHrYjDHjpFWV0eN0chbAcEgh+U/a/HxgaJ4V9ia9NDzvr5wIbU/XWfXo4/iVl+PfNwgqBQrqOI2bSifOImq8eNZ9vPPNvtd3Kcg3E7E0lYbvuDY1VmUjZCYk/w7kyqP05k7OK+bxSf7NzC72yZ+109l0MerKNstanz+2UySxAmNhks1NQyK1TPr3C0G37lEhzAdMnsTeLTKpUpTQUATze9ngBFMDkboLh7UsjK4dQvc3H7i448/ZlTvUWyWlnH60esMiJajcFagidcgUwoIz+dxH5Jn2HLbHe45U3LDgWYUXMGT4vXF6Ep0FKwp4P4OAdOU/VrGeZ/z3N9yDzvzjOMDerMHobX7aadbHBiTi2bFV1TI26NFxfDNWqa+0BUFIt4HsLVHD/IHDaKjueQXwPvvv09kpAAVWizDrEi4dCl8XjsOXWMjj44ZQ8TTT1u2yW5oYNr16zZ5vY888og4UGkpzWYmoIeHB7GxsSiVSvR6PeXl5UJqzxduGW8RHR0tSvJVvseFgrM2hb3/K3v3XSujM9bsQNuGtOWaD9z4dT3eG4cIIQ6TgXaNdTBFwOYvfvsrzS1ECxlQ8mA1jns6HdubC8DJZNkMVThBXwahadTwxRdwNOMivOmGR5ptXOy5/rYa0XFx8FXiTmQT5zMseBhB3r4QdJ66ChVKuZHzugEskoliBi5BQbQrKsKhf39qgfjISK6aySFTgx7n3Nl9Qhu1XSO5U7LRG41w/DiXGxpYfPy4WFWfOsWhK1dY8uKLKE0mC6RXpdeTVFtrmSxsvX+fuTcEyxMEweizzwTY8OdYXliYkKf76O1mviSNOFMiRzhNHIn8bLiIZJC4MfMGlzpe4t739wg+lou+uwclFXLSUWEC2syyrYDTlFZLNNZcYqlZsMvrjlonDG1JIoveHE9vR3zEYh5/XEFh4U2qUkbzPgOYuWAvvTp/BDITKpOek10684RrDGfKPZhS3pegt0SamMLRzDBOfZAiKw+4x5EjY1m9upnw8AQiIhKxs2vi/v2X2bRJhDTs7Jro/uVqwt2zeXLK5zD0NPTMIuyFjzh6FFJTsWHontNq8Tl/ngPpL5J+Pw7f8+f57G4uGs0ptNpEcnKsN7hFJGFx3mV2bO+D3ZTx/D0zk5TaWgrck5hYvZ2w66ICkHzvXkxxcfQ2s7h3fv89Y82ymfv27ePEiRPorl/nZGEhx48fx91dxI579LDVh/5X2b+lA120SOgWvPWWgKOUSjG71GjERNbdyUjthRp8fa8/sG9e27Y05Oay7dYtXORyFtjVoCx15Lc7GlEXL0ILAYIxFno7F/sUJ44stxZRzm/XjvWTJtHuvh5TvSMeOz1xrtFyqXdvFCYjnnV15Ed4UNsNbrp25FW+pIQPWeAfyEL7coLDx1Mx0sjNpVDTDwzegs4X4/UdC73WsmDsB7jbV2I3Yxs4NKFSi8Gs0WikuLmZu01NJNfWojGIaMqnhYVsqSkmt6mJ13JvI718E568C22aQWkk9Kr12l0rXKBOARFaZs4ER0eY/IiOuronxfWOi6VBrqD5eIXFcWvjtfjN9iNoRRCeU72pMAiIqaVjNV+yOvh0VNz/1TqgZM8RQgRZT2Shr9Bzc/5NvmqlmPQTHejkpcM1Q0P7x71QpRzF+9FeeAR5YHclHpWjPV926cKBPn1YFRxMHxcXXM0w6O+/C9WYX375hYgIaD4Pty+24/IFD2ZfhQ88POg/fASVI0fz1uXLxLXKY9zZU6Q17C0vJ68VOzBLpcJGPgVRd3HVqlVs2rQJPz8/lEol27dvp9PUTsTnx/P222/z0jsv0aCrxGAycK7gHP+MVVcL9OrbbwXkGCBz5O32/tQW7+VEZ1DnAaoI5M0aZMlbkceXgN48iN6NgVVqaDb/Cn+0hfIHVcjzRgnyxlgvL2b6+oIqggZ9Az9f+xmFAq5UnaRDrY7Ye2dhVxDcdoHNHenlb3usRlM1hwt30DcwDJWjiu/GfQcdxQrEpacoKfd36VVSEDMZY3w8Up8+OMtkfD15Ml/Pns2Kxx7jgvIDKupNYGfE8ZkCsjrcJykzk5q6Oj6YPZvPp0+nqE0biI9ngrmI51Pp6ZiA09XV/FBSQmtX/01xMdtLSzltXqE6Ogr2rFwOa9eKuCqI8WHXLvF3ruIcYWbxDUeT9MAA2ZTfxM0FgkkaOEaEZmqwQzevC8ELXMl8qifpChWf0h0lEn2wlU/SJmjRvHdY3BO6ojPDo/n5kJSiYMwYCAx0wS28I1Xr3sbljefxndAbN4VwuqPf92bt10ratAEXLwVypbWFYQlhcKcTjmcW0MN/P7KMvrD6LQCcnY9SUPAOjo6N2Nk18+ST25k8+RvKysTvs2fPWdzD9sKsn+DZLfDEL5gmHILpe6jTZvEnYSkey8zEpL+PSrOBhNwvKNfr2ZJ33KY8nLP3ExTJuwMwaBDcK9rGmDEw6m8BnAjw55HUVGaymznOezGkpvCKQoHJnCv04rhxfNa5M22dnNi4cSOurq6Ulpai0WiQTCZufP89N27cICICmppccXTsxv+G/Vs60FYCHnz+ufjx/M3Vlbp2hZpLNZiaTLhpk9B1CrZsq3Vxoee2bbju28e3tbUMlsux69aN9gUa4TgBQsXDFZqby6grSXjs7UXbyzpeWZ9g04bBmraoKaX6YE/CnoklwNub0+Fh5I2344XPn2fnhu70lyfxFa8yZcobtJNeYfPw2Zz9/k8DrBEU9dD4TAZJO4HerS6u93U8osVD/F5+Pv1TUuhz5QozsrIseYhrWlUJ+bWyDMbdhwkl8F0KEX+/y0+jrccb1tAO0lUQqWH3bnB3h8W11uv6NMSfWebFsypWJSTAshvwGu1Fpw87kaZsot5k4nJkJMVRUdib5HDBm/BwQdpoQEkOrjh1tcamWkOeAD2o5VWsVPc+VSJZ1zPGVdAoY2MFFm3G5V8KDGSstzfvBgcjbzVFnjBhAosXL8bREXr3hLAUmDfmKG+s0PLqjp9YWV3N8bNnwdnZpvz0osBAnvSzriRaKPMXq6uZdP06REURGh6Os7Mzhw8fJjw8nJiYGJ5++mnGjx+PWq1m5syZPD7xceLz4hk2bBj2Efa42rvSzrUd8Xn/XJb9mTNisZWQIJiUX34pY88fE0nI/omsED86VIOTSyTDLhYgvbGT4i2xEHQWpk+GOn+42QsWRqAwyehV6QMLI0EnY2CdDz0drbCgu0zJwZAQRnp5gWtXULqTfE/Edc/cOkX+32GUFA+bO8Fz/Zlh7PBAW8O+C+NE7glLTnSQRxA/LpkKch3Vw/5u2a4fKWTjx/20NHQeHqT27UtiTAxGhYI1S5dyb0s5fJ4OK7JpelSQRuJzchi4YQNHzILyCSNG0NhKKWDBjz8SbG/PrKwslprZnF5KJRGurtbf8CGsTR8fgUjZ24t73VLMpfGPB0MLAHKaHvis0xOe9OoFq1bB6E2BuC6bRr/S9SwyhnOne1sqEBONNwghHQ8qPF0xVBkovt6FS3hxAGuOagtc3BJm2VxSQs/+/alu3x7UatoYzuBEATFPONIKKLExz+GedF7XFd1Hs8jurkJ6dR0hi1+zfD9z5icAKJVtmDXrAwAiIuJ54QUICTH3y0m/g1MTpp45aEcKpO3GlcM255EkiVqjkQjzZLe9PgmQiCSVBqzP9pLKEJbJhNTmRx8JpjTAYpfviPHLQi5p6MwdvOxqKcxN4KtWBLtZsbG8biaVBQQEWPKDnVri2r+IIvcDB9px5kwdX33VWtLzX2f/dg5Uo2ng6lUDE5a+gmyZD0WuB+jSBb78EkDilRP3KD5ZSUenXSjP/MGpoQH8HCLD2Lsnp69do9neHsncm4PNQdPBty5DcAO+76bAkwU8fuYMV55/nul9d/HTB16U7LnDm59HUtC/P8vNK5Sh+w10QMQ8L1a6oZDJmLDmY0Jf2cc74cv5Q3OAoiXxEwAAIABJREFUmpo2lna/9VYpzfrPsIu4Zs0hM4BzthNSsbVT6r0k7DdNosHgAZ8t4dL9DWxJfpYfVkHJ1BcJeWsRA8/vtZmJuykUDFe1gt0cTOCtI61XAalfeJG5359jz9mxsqe/gHT7VIOdEW/usaSFyLBtGwQEUOcCW58Dx46OXAwUzAvVcBU3GxqITktjlulXcg6dIrqXA7pxg+nd5EVcXBY7dizAydHIQvqysDmMkAxRPeVKT4Gdd98sZqrB7wXzqaYTm821sCMRDsyxIt2a06BWC7meigrx2dy5WPJ7WllsbCyhoSBXgmcawhOBZZRybbIdFKuio1lnJqM0DBlChKsrz928SZxGw5mW5O2XXuLyxYvcv3/fAi212LfffmtZ+ao7qimqKSJ2eyxxeXEM6zCM2E6x/9CBfvONGNg3b4YJEwC5Hq1WMEKPH5fIrhAr9tHPrKHG2RmdZw8SUs0KNZpO0DEegq2M37dmuFE1JJq0Ay441zvCpGi6/9aTVaWRMDEamuU86q1CLpPxiEolMLro3/nF2Il6XT3Gy+L3VRMHi24S+3kJpxae5/tW99okmbhbLZxOTJBVHPXpMeH8kZEMvjc4kXLS8nlvWTFS1n0cmpsZN+nv1EgSytZJkz1rYbhV4eQdPz+yg4Is/8+ZPx/nXbsAOF9VxaDMTNT5+TSYCVMdHR25O2gQW7qL/qSUyR7MG/zgAzh+nI4dRReKioLalFrOu8dRcKkTbWTn2EA104hgAJOJZjwxjCV65NcELRdtiTgfgccgD65cEUgXVVWQlES/1O9xdZV4RC1D00EFShkZeLBcHspsTTgGuRxdsztpiOexpVhT376C5NcCdx7XaGgymTir1cLQoQSxm37MR5aVxV/Zb7/BoSIVpiYrh+G1HzwYOdI2/u3p+Qh2dkVIkpIOHbKZPl1GQcHHNtvIZSa85FVIBgVu7d9g3tb13DOnI12vzmMnT7KSDzGgwJtyZvAz89hCOmGsU13kxzaXOEs0JUYrWuHVSu77HT7gwP8h772jo6zatu/f1PQyaYQkpAGhE0LvJTRBECyIqGCH24KiIChFqSJNEEVABJWiIlUQkTYJJZSENJAaIIUQ0hvpU/b7x57MZCje91rf+96P6/lO1iwyc+19Xftq+9z72Md5nJb4cSGUNGtmW9+tT+PW0CIjI9HpdPTu3ZsgyxLNtGkQFmYgORm2WZ6J/7b9r3Ggd+/KsI2DB1MwmdTsc/kK4VwIzz3J9u3ygXLxEJyOVXLzQBYh1bKHXlsTR8uqIJTDHkffgBrtVVbGgk2bAHg5QQYH5veXN/mxhATKehqpaFaJWm3ExacMH//+NHFx4Z2mTfm0SQhhF0w8xR0aWUau+UkG3nAKokLtxq6cQo7tNuLheQcYB8CuXRGEhvYnuO09tm6FpKNtOLIYEn6YwMwFezAn2qBQ7/OOVDvI2EtD1mSaVmwiNGcD4U6pvPxiEi+1/Rp1bjYUFhJQe4swcZPlOg9crnnS/Vg4EaoifChASy0Tblyj8TBvHG8YaONWzcQuOqkS0q4Md/9tGJDXxF8jOw7ffIjtCTc35VDvpf80VfBE4iUCuMNLiu8oLlzFrVtAtYqePW9SUvI9BQXf0q+/dC6JWY6czrB/Qfxf9idkTggBkwLILFQzdixMG1/GEMfTtHZegmLLFvDwkFPZ+tiD2Fg5Rdu8WS5uNbh/IFVi3hzeGE0BOH22uQErpJGl14Oj6ekMTEri7K1b6DQaVJZZrJNKRTd3ScwYlJpKjKUTPtapE46OjrjdFzYCoNVqcZQZn+kTLFWEYjJi0KfrrapVSXeTKKl+MBDcbJbEncJCmR4KgIAEUMtBWNxpAQZHOgd0prXuBba3H4JJpZLEsnoL0/PZiGksWSId8IcfgrtGjVZrERWoVnP+lJE4vQrKNbxeGcZ0BwfIzia4QVsqvXrx6slv6HNDOrat01rBqByORV2j0Ghg0vXr1rXh1FwZrtM7uDdDmtqLow5u3R0vJy9Olp3EElePWajQqSfRtlxFXq86qFbSp/DBYAA/jYaZDXIGd3ZzY4yvr12Z7qNGQaNGRDdg8O5r2xZXtZpIV1c+DQlhbmgoSRUVZNfUkH27AuPdcszzFlOx8GcMxQZcnQXV6dVcHncZwz0Jp3qN8OP9V/P5vPFynClBQwVKzGiunifw7QBC54bi3l0+G87OllCv48dBCDRFufSNusfatbA0swl1rzfl7dcqcHBVUIOaFLNEjJLR8fXXMlTWyUn69OXL5Rgmo7qaw8WSLasvLeWWRgPLlqCi9pE6gQUFUhv74w2uqL3k9fSa3ZQtO9UYDI6cOnWUqqqBODicBVf5bPr6vmS3j+95mQQ60yxiPVqHYARKKjLkzP+FgCmszJbC9VcyVxGIHEQl0AUTSiYhE2lcoD0HSmvYWWwL8QlqbYvRPOjQgGBpMQ+PXnTpIq/9+vXr8WroaS2mUqn48ssvmTVrFn/88QdthnSqzyhIcsoDxf9r9r/CgQoBffvCxx/DsWN1+Pg3kH8SUF0tT9MnqgqSPAmsZ5EAK08E0PHbHzgwaBD60lI6uLqiNZuJWfQWjUpKqPOA6NQkwk02jdseaUlcmov16ikUGtRq+WIEOjjwfp4XVAiO/OxG3XpJDnruY0/GjC8DAV/McGZGyzl8+ulI4BdgNS4upXz/fVu59nTShcbfzeIzPbxzvjtx2UMZOG0j69aBJk9L43vZmLyet7sGS+csYeNGSVJ0dKil1fLXaLfwbbY5vMaX5le4lx5O5b8imdJ2O1+ZX2aj4k3GIxfea7s4oVArKD9eytrpLvhoNPgtvU7Gj1Hg7k4vetMxCdTjO/PrWPjhFbi5TELDx6Jh1LULpJuK2caLaBUGWrc+i6NjJf367WTcuBbk50u4ZcaMp2nXTsJvJ0+C7zOyQ9QN1aFQKQibH8aNIi3Nm0tm5LItnvSomYRf1Z+Sltm3r4z+DgqSJ6rX2zqUL76Qi98NzMHBgbbhpXiVhaF4cbz9Q7NwIXTqxMBPPuHo1Kl0a5Bzst5GNhA8OFVWxpLwcCsb9t+Zm4MbrlobjBgdFk10WDQCwfHM4w+Uv/Tgcjx0+BGa/UlUlMBQp0SV3ZefB5+gTUsHJkYtQ5mnhjtOhHMTbwp5vKszH/f5mOnTpdKOR4Poqago+OmtU1xO07Jrh4nXXoMNVzbTrVs3uXHJErvz/VXVhVBDGGL0aK4+NeGBpt20EHX06Xqc1E4cHX8UB7U9gUypUDIgdAD6dD1PPWWD8LwChuFxz4KZpnqiy2+Npk5Fqzm2pN1xDg6MjbEtHxzv0IHnGqw/dysoQKlSQXQ0AxMTcaqp4XBJCW0t0K1SoWBuWBgvNmqEAPqmpKAflMiNlxK4ZnqP86de5rT/aXJ/zCW+ZTy1d2xohOd7fem+8Q1em2a51xoN7N8PWVk41N4h9NNQFMr7NO/0eqnO4ODAQC8Jbd7AjVEb/Vmx0ZOyctlZnMGbfBwIH+zC22/bqg8datOEDTt3jiqzmRZOTuwoKKBFfDzbx4+XChGPcKB+fvIZKq9QILp54z3Sm6SmTazbZ88eyPDhR+nSrQuD0n2oQ8N11yft9nGUQWx1+YaggIn4eI9A59kXtZsc4Cu0Bq5bQqDKKq9Y6xxmCFdoZf2eiAz2rjKbCXZwoLObG838htGs2ZdotUGsNwzlhtd8a3kfn9F4eQ2kY0clL7zwHBMnTnzo+QGMHz+efv360a5dOxZ//br197yZ/zPwLfwvcaDvvDeWG8Ej+OrbcjZt6k/zaKkwM7U5UCgZfr0G7cPH+xYUOvJdbxM+e/cyaP40jnTujFAqmeLiwl+VlUxwvU2y5ndKFuZwah8krZNxhj0t6cyuTpiAX+O7bLviwnHxId8VPsHg4wbe2PeGtT0l+hIUbkbC2t8hMCKR9//1AV+XtiEl0wHvPT6M122kT5+9RHVItrxEejp0sHWqN7PSScyLAvKBl4FvgDHs2AEHXq7D/e4pPN6KYVXpyw+9HiYTrF5eR8/u+Xa/BwWlofTbh1ZU4C6KeMVZwkHHjfeo7ehI2ttpnFAeJyoF8lU1CK2aqBFv8VyLuXy4HJ7PthGA3O/BzqfhM0s+4DbYPIBGY2DevDhWrz6EQmGitva2ddvq1X355JPv0GpnsyGgNdojvWm3vx0LFkgf2cYSEXBo50NyV9XrE4KEYdeuhS++oCoI4nbBqWFrKfigqxzGv/MOhrfGUxFYzafhT+Nz6hQHGlDlrfvIzpaUbQsTtKEN9/bmQDsZYF5pNhPt6flAmb+zgg8L6BPcB28nb9o3ak+IZwjhunD06Xou5F3g7QNvM//4fD4/8JMVXbYKoo96mW/ndoFnxmF8pSta91J8M96heZgFzo8qxZzszfLFRtJoTgah7A59+6HtqLcBloHMnbsqordPkooBJSVy2nvoELvatKG4l03ur8y/A4roaIodQsAsZ6Nrm0vm8+Jbl2h5+DsO3zpK7+DeDzjPeosOi+bcnXNU1FWwalUe8BU3b3ZHv0w6p5AKDbvf88UwugePdXGmfPhwyocPp9ny5bS/dYvhO56DU4/T67vODHJ3oKRXL4q7dOHESMvSwsCB+JeUkPfsswz+888Hjh/i6Ei4oyOlOTUEXxfkHlGRh1TREgZB4W+FiDqBuUrQgiX0Pt8I54GWZ+H99yU0W14uB28gYzkeslyAXi+9YK9eRJdIkV61ykyNwTa7/pAl7CGQl+hKQqpVoMlqNRZNWGv54GCya2sxHvRj9XqzfF5jY+0p5cgm1ptaDTtCW/CFexu+2llNk9YGO3GMpIoKcmnMaPaysyqMKU7HGck+3tAe4a9ez5LQqZPlNFfRrt1Bho19C99yicSNmpZEbZ2BRnXn+Mv5VUawn1OKaJKRBDzXlsdJw0bmiXR1pbmTE4V1dQQGvoO6VTxlZkGr4Mn06lVMr17FtG69A0/PaBwdDbz77mXMZnsUqd4KC/eTlWVLOhBsiCeLJjzGQWjXji4NMwn8F+0f5UBra2uZMWMGAQEBODs70717d2u80N/Z2bgbUHUAmv0Jupu4tU9Gp/VgSGMVvgVD8FXkMPmcJ+9ZJLDWz+9EkYcHx/o8jt7CvrxpWYdxK1hOvmklQgsmB1dq/KEqECYe+40l69cRpLpNUU9B2+1vsEi/im2X9mEQ8F3yd2SXZ1NXV0jRqeuI9gl0rFnFTOejPDF2JTpdHks8/PE5XM2rr9pyOz7zDHR0TadPlBSxnz//Z2qNvqygJVAPWR2AZmGYzXDEMlAeeuIkmXsr2bZNhjukpkJauR87r7W1iuQ/95z8/8oVeY5vvXsAd4XtBTVUpdDJycgv+fnENrM9uG0P2f4uGdCJotZyHeMVMuyue/XgSjYHKgi7ls/gfDkAOHRoE3V1jRgyRE9VlW203LLlj9a/Bwx4g+joz9i4qZQlX6k5d17J3LmWmD+L6evbMH269CrDhllhV0CSiSx2Y3UEBi8wugouPWGJR1qzhuJrW0EJJ5SdKDIaGXHxol37rYyN6GgepaI9SKfDSaHATaWitYvLQ8s8yhzVjswfMJ9Vj61CqZCvWnRoNPuu7WPRyUV8c/4bPo39lI9n14BPDWhMPDa2lPBxu2neN4Wx7V8EZ3cuFp+nrtMRcm8PgPAK8KuB5hWQrOOJpzUof/wBVyrRHv8bhq8Q+J/ZQ2vLQGdAxT777fHxaCor0Wk0LPSRYU57+/QjpW9f4ipqcSs8TBfjdfo51tDZzY1NhZVc0zbjcH460WEylVrVQ7JkRIdFW9nHJ0/GABb5xOtuDM0LwankJKCAajUDB4Lbnj24VVfD9u2UOsCfPnlgqiIlN4Xlp5fjoVajc3FBa4HKefppmDkTt7FjHzo7u1N+hygHQYdHwHxF+2yDKu+m+ag72WZTKBQygNTRUTLq6m2l1HouMxq5UFHBxYwMxOXLFAwcSNngwbRP/pFP55iZa7K958M1+3kydBuN2lylBhXF+Uq+3WhGCMizpL3Tl5ZaNWHXR0TQS+0FN11gUxjn1niR3X+ApGcny8F8To7Uuq1P9PT661Ka8Ku1Sn7YpiTpgBOlHQpIM1VQbjRSazbzo0Xhpxpnfs7PJ7XaTAVuBDp5o9No0FqWOZRKDSqVvMbNB46BOg3h7knsPnYQN+6xuboDlbgy0tubkIBJNA6eR5Rfb6Y3aUJnCwqwv6iIn/Pz2VdUxJWqajYX3MNFqaRdvga12tOSnk2Nu3s3AKqqLlBefl/KHYtlZ68kI2MeZnMdtbU5VJT8gdZ9IEO9A/mwSRMStA+yzP8b9o9yoC+//DIrV65k/PjxrF69GpVKxfDhw4mLi/v3ldOBQR/B5AgSxSHapkbx27nFlL/yOHsdnqXRPTNNSswE6Ow1J/VRnWli+Skgx0SYSQpPq6s1DND+xufMoDQKuu69y0sF20n4HvIHQ+Spx5lywB4yjEmP4a8Lo7jXawF0SMRcHkOwQT4QHTrEsmVvIOvWdeV+WxE5hqFRaZSdG0NMzHMPbFe1LpbTsyefJKnB78k/7uDX2AhO5OxlynQtE2u/Zo32A37/w3Zbf/4Z3nprBn9d70bTLotxoI4bNMfFNQoQPO10nX1FRRzqaCNydEkAVZ0J0tLIDPVCMcyGBSY4+rC+XwD3XATjW4wgMLc/m1qMZZjfPs6cGUN4+CsEBUVTXb2Nmpp0XF2jcHFph7//BEJC5lj3o1QKIiOPs2+fzLbRMAmxjw+kZOooattPxhu8847UIPOxka4aZvyta2Q/+zFZ+tabkyAPP/Lwt26rbXigPn0kzjlyJI8yrVJJtYV1OLmBpN9/av1D+/Ni+xet3weGDySzLNMuMQH3gmFDIoEL4uh+eh23ni9hUIueLM++i7LzRnBvC5/4wsbz8rNdPqPh5Z4yuH3CBBg37u/zaF2/DnfuMNIrjs4k0BiLVFo9Rdpkoj4P1qy2Q5h74wYnIiOJKimhymymt7OCuxcX0P6blvgbG6SP8YxiQOgAeiQl8Ul6+gOHbeHdwso+ltq3ltGdWcGS1k247bjeWrZ1pyI5i7MIVMSGgrlBD7XgxAJWnV1lfwBPT1i0SA6wbtyQmnMWMwszQSuDKNg2ja4JRnIaZGrp3HsTGuSA2tXpNu78hXZIt0dfP7AtTlsE0SMTEog8f572GRmse+IJRoaE8FbPnijvlTF3eDwT+BEHaogJfYU/DrvR8/vV5H6dB6GSef7u20p+/RX8LWnvRlsSibZ3cWFiQABP9nWA17tAgSPmfAeaZGkQLi6g1yMEBAZKXtyECRKc2bDBblwJwL32UtSkV3IyE69d45ucHAbrdFZh9nob18g+hrWhaV1cUaS1hahkcq8dogYHUoQkaT3n58cnEb1pEf4JKqWSJU2bktC5Mz+1sg1Ept28SZuEBNbk5PBEoStJLRIoOWrjASiVWhwdZXal0lL7aAYAk6masrLTmM3VlJef5cyZQAyGPAY2GcVv7drxZMN+4b9s/xgHGh8fz/bt2/n8889ZsmQJr7/+Onq9npCQEKZPn/73lXt3A7EdjhWC0kxRbR7vHg/mEgHUOmr587kIRu8RHH/3J6p+lS5omlmqdBR7uPLyRUnb7+b7ByrMGIWS7KzuNLqrJFlEURIFDqUmSiMbHLPZTYYnD2f/iv3cGX6HNr5tOJnxJ+X3zkq91Y6JgBGDIQ+FQs0nn9g7xtnDo6h77DfuVfvDwjkQnk638U9QWmpVr8Jj2V/MS7mF6Yu5bGrRgrFhP2KOnIxrg/30qWsKN0YRk3ybmqefpvjFF1m8soBLl2RwRlJSE+AYyUXd8KOAMtx5i6+pDD+Io2M4mjPfwJUrJHWCx3cbGBQ5lSW5U+gy+jMi9hzhI/XnuA9W0O6AhDKfXuDJ3PXNeM/Xn/vtqada8NprMjdlbW02oKT9np50rJOdXmjoXMLDJZXeaFSzcOGTtGxpL0oxbx4kxAsESo6HvfzIW37X8BsnYh1JSehDRd1FmoYtJeojSew5e8SP7Em+VPspSaAL7/IlOxpLBuvZ8gbQsIuLDLIcO/aRx2k4q9qUm8u6O3doce4cb1y79sg699vChZIskpYGA0LtxVdVZmdwbA+eBsraZ1DkEAauTYn3GM6h4mLMGnf8WzwIzTZ3cmL3uts0buzPZ599JnvOxERJ2Z0+HU6ftq+g14NazcIVzpygrxQ7LS+Hs2flgnNQkM0B//QTfetzd1lsTFBbssuzMZqNFOdYUCGzEbVXN6bma8iqrWVFdja+cXGcbpBuSqFQMDB8IMtOL+O3P39j0KAelJfLQ9d5JVPpngQfu8HHbiQVxwKw1k1e22PhoJ+gp3h6MaGeofK39EfkCqvX6rOsmxrNRp6b3Z/4RR+hX3GeUYfyicr7jU9WXGW93gnXSHc8SUZBHR2qJxHJVB7IE3i/rV0LH30E+/ax9IcfyGyAwb71/vucq6nhsFKJ2c0NvvySJmRT8IueVpfu02n9LsGaUPrjPbYZsEEInvTxIaFTJ4SQIjBWUwpI8mTNu+/iGxHBZ0NftW6qrARFxxLWHThAdpUMOVGqBTyRDVHSUf1VWcnmPJnMIdTRUbKugTcDAuz0lx9lwY+NxtwplXCnBG6rOmBAy47WrXn2vrjoeqvnCqgVCkos6J5fHkx8Wr5/xYfsE2Z07XoFL69hlJQc4/r1N6mokGjRrVszuZm8ECFqAaVd6kVPz/6AJJj9T9k/xoHu3LkTtVptt4js4ODAa6+9xpkzZ7hTn8vnYdb6HF69j+J4YySUgXeBjp4lZzgfKdlcC16aQJmngrlPPk+pWj44L226jFdZGQ5GA737LOZNvmG0RuaF3HN7Mv6bhzLwGCydHUfJ3RHU6aCsgw0mUIw4AmG3cHWuIPfdXIY0HUJBrh4UZnCtxL/HIIw4AUrc3W0Eldu3w1i0CNpUdyH4+QgKXW15LTWe/fDwsECZ4zMoiyri05IscHCgn9qbHatcIXUmlXzCOORo+YWsasIiSujf2g8HpRKdRkMTby/Gjn2Nc+dm4ug4HB+fGMpaSu+fY2qPS7WJX84molB0wlt7ifBjx5gZHMwkYymm1CRSSeVstZ527fIZwhEa154gp5cWzfwAgl72IyJCSavWEhW4erUzt2/3xcvrccLDP0CpBJ1OQqNuju3QfrYG1fofICMDxfU0Gjd+jeDgWQghmYBLlz5Lt26wdSvMmQOTJkGo8QbNSOOYuT8IgenGZSoqLlBRcYHCwn2Ulp4iLe1dzKKG0go5a3J174L6PbkgazDmc+O5AlSYSaIjPTiD19238FKr2ZKba1WmkY10eyR8C9g5A4A309K4Xl3Nd3fvkl3zYGwgwI2qKi4WVXP3LtTUyPPKzZVZMNxVjVgwYAHDWz3PT2P28nrzvTBIzoQqnILBUc4EEo2uxFuk6HKd5WwhoMwNtSXCN9rTk48/fo+8vDxmzZpFYWRvMJup27Idli2jZtU67Jqu10PXrqjHPo3Tx+/Lxri5yazIDg4Sxv7tNynT9MIL9LlwgdfLyujo6sq3EREMCbfpQJ68uAYyt/K4UwVGzw7ENRiUFBoMjLwPKh8QOgBKIf92PlE9oig0puPsYkKfrsdF48K2cevBoQJ9up6U3BQml/7Mwj7wc1voG9IXnZOOA89L6Pdi/kU7dSireXvL2fQvv8CFC1w8sZNRWxtRaRhKHkOpFQH4mBMZcPEcv6vryPz4Y5p4/ElzvkZNNar2LW1rHo8ylQpGjMCgUjHDkvPSQ2WfY7TQaGTH669zIT6eCy1boh7ZnxjLfWzj7ExHV1dQgcPXkr2cnmQPPQ7z8kKrVFIfreLiIifYwZF1kKxj8pAhFHp6MnumhdgVUA0IbrS8y5suLmzooGTObBPdv8xE9Wa6ZNQ3ME+1mgVhYQQ7OvJ5eDjvBwWh02hQ/M07AODlMxClUwUeLRLIV3dDo1DYZRW63xpptSxv2pSV7sGE3wSlCWb+bDvX+owy9aZUOuDl9RhlZcfJyVlHbu73GAxFZGUtJqfiMyjxRKuwxc0GecyzEjc1SiWfhjwYn/zfsH+MA01OTiYiIgJXV1e737tY0julpPw9V/nLl3/kjTdy8EvzonBNCRnNtFQ6ORGRdfuBsp3zrtJ2WwaPnztHJ1U8WvdinmUHwdyG+C48faQCZizhmb21hDS7h/GF3zm9G6qa1NGy5RY8PQcgRu6CTa/BL+OoqyohOiyaMVlNoUDCCbl536GmmttVgrIy29rUhAnTOXoUXtz6Ii03tcTV15Zpvv8lCavpvM3wagao5MMf6eLCpbNazGYF4A9BM/iFyfyAhnHEcrhy9APn6OPjyYwZi5gyZTCFhTdYFNmTcqMLvy07Renw4ax//HFmztxBWBi430xgUXg47vdRQZt1lVDTxdw/aJ+cSO8+Oai8NSgUMGyYnitXuvLmmwkIcZz27X9Ho5GjTiencJydW+OdbyH9HDoklfxbtkRz9hLh4Qtp21ayYnW6Ms6ehRdegPnzZYQJej3Rihj0aU3g0CGubm3D+fORnD8fyV9/jSIlpQ9ms32mi9TUASQ0/hhnZ3td0hJtZ/zJQ4mgl6uZjbm5PH/lCv+p6UtL8dNoSHnI7CTmIQH66dXVNI+Pp/3Fc3QdUWMnUn7+vPRbs/vOJif8faaU+LA+SAOjc2iisXTEwn4dsYUlcHxJeDgDd3WizSc9cFYqGenjQ34DxZC2I/JJJ5SyDyV8Ub5Xz1tvWjrPekWG6GgZM/HZZ9J5NrToaAmBRsqBltpsZkObNiR27swbAQEEugcS5R9FlH8UCCNBxYeY1+bh6uJlRqOdk4sOi5ZLLMDrF16n1ZpWbErehD5DT9+Qvjzf7nkmdpzIb9d+I2p9FCYVzBkIgeHtUSnldWnt25r94/aTVZbFrZJbDz0u0dFSeiwykqgB42hxR679Z/IiYMaTVKLVaipMJkLT0nA6+yMBWPLXWUQ1/q117Uo8o5XsAAAgAElEQVRCA/gzLzCQnxYssCvy3BNPELlxI5Fr1/L8rVvoS0tp5ezMX127WpnOUWFamHEFbrhCmZqTHTqgVSikoAVyvKPRSFGYmTPhhcccUF12tzsOffJhy1mU0fnWmWaFqzPDhp3jcrvbmBwfXJM+FRVFI8t64YzgYJr/J+cMuLl1BWTZklsd6e7ujst9g4f7bWqTJrTtmMnG1+G3A970q5D1NT4aKlIqMBTZE4Y8PW3PU0mJntLSWNvGlA64ZMkBjkrpSXbnvhTusZEan7gvxOm/Zf8YB3r37l0aPwRGqP8t52HMN4u9outPkFsdXbrfYn5sV0bO+ZbdoV/jVlHNYzvlusL6FStQmM2MP3yY316QcjrfLVvGp4p51v2Uxw2GmZ+h7JwA7vfw/OIN6GW//qrTDcDR0X60U+McT0+XngSE5kFiJ7ttWUWCUaMFTzwBjz2m5e2J73MxfhF9XpAzsDEt3+da+CWG8id/VVbyZXY2yRa6+IYIyWgbqNPVI3AAtHqhBMc/Qgge+SkAze7cl4K+3k6dYvjx47gA55q24vi2EdSn2QMrF4Fly7JYm3CUrQcPMmz4cEY+8QQODlpG+OdiRs0g8QejkKISKRUVCCGIitLTr180JSVyDeZ+69QpgeD9HrLRDaWhTsi2Nm78Ci1bbsZoLKW6OoOMjAUUF1sad+wY09w34Hj9AhW7DlHQ/+Gn97DHt6rqEl5ej+OUBTmGQLoYPenVqxil0oVAIQdTewsLH6j3KNOXlMiUYq6uJFsYiu8FBtLG2ZkJV6+iiI1FERuL16lT7C0osHOq2Z3vEP37NTy8zbTaeBWG57D3pTiWZ2WRUlFBfoO41aE+fqjqinCtvWMVcQhxcOAVy/OfvkvH4cOQelLLzMSe3NiqISUlhaVLl+Lp6Ule3k90o4iQ2mw2KZX4Ge7w5s5ozLUG6NYNior+Pp3G/Xm9rl59QD087tU4jk44ikqhIjosmg5ubujUavp5eFDdpw/lvXvzS+vWmIDo1FTMFieakZIBvwH+gDPUmmrZf30/JzNPWtMERodFc+eeDWUqnl5MwhsJdsfvGyKZsM2+akbOvRyWxi2l0fJGXCm4wsakjazdr+QsW7nDSLJ4jmpTJAqlmVr8SPO/wW+nltP966+t+9Pm5vLhpYsST3a/zzk9yjQa9Lt24VZVRempUzjExjIuNpaStm2p7NPngeJ7CwvZcPeulcGtLy1Fbcl52ahbJQgFPxl60NvTk8JevQixkKP0einwUO/foqPBFCBhX8W3FrWFZ+6AUoHbB6mo3eQ2tdHI4txcShugLK/5+9PZzY1R3t60cXHhaHExcx+yXv13plRq8NL1g0pXRkwI4oVDKm7OuPm3derybJrbjY7UUH66nNC5oXRM6AgCzgSf4c43d4jzjaPkWAkuLm3QaPxQKNRUVqZy6dIzKOoThqV2RGx9nl69igm/mQTmB2Hg/wn7xzjQ6upqa+aKhlYfmF59XzaJhtY9PBaAJgFZ1I1TEJrryYgD0OIvFR5OSibe2spLhw7x/pGtTP1lOwEmyRid2m4fXq6Dadp0FZmpvSgv02EIyYC2loTOwbchwkYccXJqjoNDIGFhi9HphuDh0V9uGHSU8199Cc1vUHWtKZ661dSoWnM+F76cCuVlMqNVbW0dvQfUUFg5C7PZRtqZENiCNq5yZDrlxg2+z83FRankJX9/Pg8P5xlVAPv2SZ7IrFnwxUQ3vu7QlC7r3qVQZ4mnswQ5k5kppU0uXID583H66is+ASYAlT9st7tu9QItajXcufwh6SmJDB82jDmzZ7NhwySMhmyMOhlvOoUvAYE+J4eqqssYDHn4+0fzqMgOVV4pyoOHZZbiBslzrZRBwNt7BKCgqOh3MjPnk529mprqLEzHj9C87DyzWERl6g5reaXSfrQcEfEtjRo96L1LKnKoctFyVtOV6OXL0Wh0eHr2Yxy/EGAZfccVPHwWev3KFa7v3EnBX3/x+9WrxN+7Z+38Il1dWRQWxntBQXS8bwZXYjTy5KVLbG84WBh3G0beRfH6Ta6E58KH18HTYJWcq7eWFToWhoUx2VvNzCaNcVKpWBwezvKmTXmpUSOangph3VRXLEtYzP5AzcKFJzGZTIwePZqoqAHAOgq4RzXwmtnMXaC3IZbCf82SU1+QPfKjLDhYRuJHRkpat0XJp6E5aZzwcvJi1WOreL/7+6gUCr5s1ox5YWE4qlS4qdUMt8ygYktL2ZWby4ULFxgwZgxotUR2sJEI9l/fT7Wx2upAB4TZHPiOMTvQOenQquzhTXcHm5NbGreUGUdnkF+ZzzM7nmH6T9NpdX04NQSSxgfcYhImXPAfKbPfZLbJ4lBRPDlVObzgYLtHy/MLKa9n9P4bqzaZuFBRwe579+ifm4vHkSPS03XsiKePD84qFTGRkQzw8KBTg0wwINcEK00mzpaX86q/P7VCMLGDNwHhJnZvV1FRYUtnZzLJ16QhIahnT1B2LoEqFWJXIBRrrLKiZS5aPt62jbd376bH3bvsbyBEsLxpU6Y1acJwLy9OlpVRlJHBvMxMFmZmcq+BAlSNyfTQJYmb1dXcsMTBBIfMhJ/eBbOKFh8Xc3vpbcrOlD1QB0CYBXc32shmlX9VYq424z3SG6dQiaqYq8ykvZ2GodBA6qBUarNraRr6BS1abLLWczH2ga0v0ChoLGUxZRgyHCg7Jn1B0f4iau/Kdeja3Ptigv5L9o/JB+rk5ETt/YFRQI3lpjo1yO13v61ZAyoXR5wUNdSgR1t3DE8+5JPV3XAt6Yd21JOolQa63b1ApbPcz4qBEazRD+HrLsPYuhUq3r/BuGbbubBRsiONZgVqpQVC1T/OjZA/oL2s6+DgT2TkIe7cWUdZ2QkYqEeLJGDMbLKN1L1lcBB4CCPb38K9qahItNK3nVQqTkZF4WphQa61MOU0SiUzgoOtS3Tz5oHM7uNu+YDb9dNS/y0mRsbEtG0rA8wazG7qKVjRQHxUFDk5OZjXrKH4+eeBHsBxBoWkkPMCBHTvTssWaiorZVxVh6afcvm8zN047uIB9ImNGTdWi0KhwcPDFjNoZ/UUQYD6teuJE2WnPGuWbJ+DAxqNDlfXjty+vQQhjJSVnSAxvgOBj5USuhme8NjFack5ouNESFpbRXjzJeTmbqGuLpuAgNcICHgNg6EQrdaP5OQCGjc+QHFdOjrvOpLoyKzTq0AIdLqBlKbP4qjrJFrXudL7Uh4ZndwIcbNlbklJSWF3VBTzgQIPD0ZapBzrCREKhYKZlrWW0T4+bKn3aA3scEkJ/NxEkj7GykFN6WMPrt+HOTqSX22gckEEu9c0opEWVnYaZd0+1NIJ1tXB3cVhIKRua+PGcoxUWKjH3z+IZs2a4eERDeyx238AMpOe3w/LLD8EyHCMv7N587Am4vwbe6frO9a/x/vbk8nc1GpcVSoqTCaevXZNilusXQt//sm8kSNZUbyCiroKknOT0TnqiGwknaqfix/dArvRJ7gPz7R+5pHHfqPjG2xI2sCuK7usv10uuMzA9IEPlFUpqghe1pfcPxPRDNJwIO0A3yVbNCI7bwIXyT/47OLvfN7xyQfq32/PXr7M75ZY4glOTpJ8dfUqDcVp++t09NfpICqKjOpqwiwp/fp7ehJXVoZBCN4NCmJ3YSECGDFIxbffyntaHwKakiK5YA0BA2dncO5VSsU5L6hToVRjl3p7wUv2qkIA/woIYKpFTzZap2N+ZiY+9Tk3gZNlZQy3QMqfZWWxLieHuz17WtW47tTW0szS/mtduxLh2Zs7Qe4EYpv5JfdMpntmdxyD7Z+t2ytukz4rHbVOTds9bUnpn4Jap8Y1Ui7ReY/0pmi/fVz2+fbnaTKjN8Ezgrl6VQ6MNReH4XCoN0F7W5G3JpH4iHhi3WI55nIM810zBMh95V188F38b9g/ZgbauHHjh8K09ZnIA+rV4B9ib78NT74xglcWNWXFoloWL6ujX9Nw3HJdULz9NYaCZpzeCbrm2SQMlR2mU28jQkgM/8UX4aC2G++Ot2lwBq1VoDE1QqFwwDFiIB3fEoR9lMbNG9OJjVWQmjqYoqLfUVbbZ5BP/aoMzmPvPJ+CUZtGUFlZaYUTS0rsQw5cVCoKGwSxh1o6u9sNlnDvR9kAGdoRGSlHwmfOQEXFA5J21vrAT1u3cuPGDYa0akW7w4fZ2uhrruTJzrpbLxVP37vHrQKbdqmfazjt972MwgBDymI42bo1xQnrcb8Eqh9+hqlTHzyQHX3QYu++K3uEmhrJ/LSYTicZuwqFGpOpAoMoobgLXJ4Jpxvkb3VLgw2T1+C9JY+OGTPo1k1CUFVVVaxcqcPN7VO2bDHx9VZPdJRiQkkqkTSyQJee7v1R59XQqpMtZOW7xJe4dGmsdb0uNjaWYUCxmxtBv9rCTMIt92LlSqn4cvEiPOXrK4P6e/Vi5ple8JYtjZTikgd93TY/9B74/CBh+eFeXrx+pAeNrvg9TMPBavHxElBQq+UEsmPHc8BUQE9oaDQKhYLiYuk8PvzwQ5xJtdZNA4zAMKBXcLAdivPrr7/+xwLcq1atYufOnf9RWYCCnj0bVgYfH5o+9xyjRo3i8PjDnHjlBI5qRwaEDbCucQLEvBTD4kGLH7rPc+XlTL1xg7WPr+WjXh+RXZ6Nm9aNqT2m0jazLbN3z6Y2pJZfe1gGwEojHkP8cWruSq+CXrQf1Z67FQ3CbxInQdxIqC3gz6J8Eu/d4920tIcTlCz2ewMhjug2beR7lp/PxkGD+N7ST+0uKGCF5aUNdXKivHdvynv3xkujQV9Sgr9WS2tnZwZ4erIwMxNzf9nxJyTANzIUHL1eOsyuloi3H3NzWXH7NpVNyiFZDuZa+MqZdYBaLQes91mrjAy+btxYikHEx9Pd3R2nOhukqgAev3hRJrMGDhUXU2Aw0PH8eQyWUK+YBhrCLeLjUcTG8uJjxRz50H4yUxpjzwUoiS3h1nSJsjgEOeDe3R2loxLPAZ4oVNI5t9nVhsYT5fJExAb5ThhLjaR/nM7tZbdh6J84TjmCYfMAPKM9ce1g48b0v9efnd/uZJHl3wf7P+C1jNcecdf+39o/xoFGRUVx/fp17t0HfZw7Vx9H2eGRdWsPjCBofTuKcmyziavPJ0PTmzDiAA5lbjQ6rkLTKw9FhwI+j+xCi963cHEpRautAm6ib1OEzkKILayF3LfNGFR5+GoHcS9ShaoOfPTVFMQvo6wMsrKOUlBwALENMk+quHhRsi0BaJC8YMQzI6A1XKq4irOzsxVOLC19MGbPW6NhXUQEQ3Q6FoTJxtSrmU2fbpvUPWD12UmO3UfxHz8eduyAgQMpnjsXX6CFwYCrqyvROh0pQrAxr5AFua9jMECTIGiquEnKnZ8BaNdOKrt4HUvC/TI09UzH1amMQpcrOCdB/rRpUkIvLU1CxhcuyE6lPhzCxcXWC2zZItmeXl528Yo6nez8fbSDUNVKQKS8rYy1rbcFn/5MNU70uHIZx4XrUH/xNRqNJ9y6RYxezw8/bOOXX3Zx4sRJ4gySdJZdHYJxpuWZiY3F9eA1Ir6Wnc6uT2SAezJRFBT8SlWVDJs4eCCVpqjYOngwdRaoN3zpFi5ckLOCDz6QmqP1RHFPjQadRsOZIxq44kZQXBBhaY1oU1XLiVWfyxxZs2ahSklhT6tWzAjUMdrJg0a7m/JOYCBxR9QMjFY8kgRcUyNlfj094fvvJcIK64EvgBTKy6NJSoKzZ1syaNB8Jk+ezM+/tSc8XJJaFvd8n/XKzvwJnD571ipKkp+fz5w5c5g1axaZmQ/PPlJvGRkZzJo1i+XLl/9tuZycHCorK7l48SIl+fn8eJ+e6S21mhKDAUe1I65aV1Y/tprpPe3D05w0TqiVD4Ji5UYjCzIy+CI7m1Pl9xgRMQKQMbaz+85m+S+ybf5d/dnbYy8bB2yk/NNyQuZIEpvaTU3/0P4oLAzmgWEDOfvqSeJf1kNJEleNjqzOuslXd+7Ypa8DKK8tJ78ynyLLoFSBXAN3atpUwkkaDYtcXa1Zj1bcvs28jAyMFifkppa86QsVFewtLCTa0xNFvXg/8F3jKzQdXAGORt6eYuJwcg07d8oQ5XptgMWZmUy7eROhhJ6Onry+soylzcOZGRzM6ogIwi2OsbmTEwM8PAgvK2ProkWofv5ZDmA2bMDhyhV6WyRMHy8utoZ+DE5N5VRpqZXxfaGyki15eWRUVz80iw0KcH7Rh+CZwbTeIVPK5W/Px1hmg4NTo22DuNa/tkbpoKTZ6mYET7cpLis1SppMbUL4knD8J/ijdLa5olszbkGdAzWpaipSKtBFS6nPlj/KkaZCo8BnlA+hC0IfbN9/28Q/xM6dOycUCoVYvny59beamhrRrFkz0aNHj4fWSUxMFIDYyQQRzwZxK6qdiPlTK2J+CBYrfu8l9GMnipgYROx2TxETg4iJQeza1ViAWYwZs0L07btDRET8JEAhnJ4dKjbuR0z7CfHeVqzlY2IQJ4+5CCHHeeLqNESnToiePRHvv49wVCL8QUwB8Ub//gIpsS4Acebbb4UQQuy6vEswF5FZmimEECIra4U4ftxRmEw1//a6vPSSEB06/JtC+/fL9gUFCdG+vRAajRCpqfZlqquFcHAQ4osvhBBCZFRXC2Ji5OePP0TH7k525/xizKvil7w8IfLzhQCRvvdJcfKE7Tr2/W2h6LRunfW6WD9vvSXEU0/JNkyfLo/drp1te79+QvTubW2W0VghTuhdRG404q85iIT19td+/vzRAoQ4xgDbPpRKIa5cEUKtFpuHDxeACAoKEoDwWLVK/HLQX2yZ0EuAEOW4PtDGQhCTJ08W/oe3ipgYRHb2GlFdbRBtuSAEiKHbjgliYsTg+cuFCYWI4KrdLpo3t13Wqip5WVu0kKfs5yfEiBHbrM/A6dOn5bNw5rSIi2ss9u+fKUCIq1flaXz33aNv65gx8ngjR8rvZrNZBAcHN3jGsqxtOnfOvm6PHj1EdPQYAYus5T/88EMhhLB7RgFRV1f30OPX1tZayyiVSlFaWvrQcvXt8vDwsN/3K6/YnrGYGLEnP//RJ/s31vLcObv9/FVeJvyW+Ylvz38rzGaziCFGxBAj8rbniUGbB4lJ+yc9dD99NvURk/+YbPfb6+d2CPTHBH/+KoiJERvu3LHbPn73eNFpfSexMz9fEBMjsqqrRXxZmSAmRpz+6CNx69lnre26VFEh1LGxgpgYcbaszLqPnomJ1jLf5eQIIYS4Wllpd058c17wyi3B7lMCpVksWSLrZtfUWMs0OX1amM3mB85rzq1bol18vO0Hs1mIxo1lfwDybxBfPvWUCNq1S5iio8Wa7Gz748fECOV93/3j4sSUtDTxxtWrdr+fafAcpE1NEzHEiDNNz8hDm2z3o2BvwX98j1NHp4qNjTda655tftb6d3VWtbXc1devipShKdbvJ1xPiBhixHrWC0AkJib+x8f8v2H/mBlo165dGTNmDB9//DEzZszg22+/JTo6mqysLJYuXfq3dd24RiXNqEp+kqIX17L52B3aqM/h2fE7MCoQfraRlJfXXVa++wn9PDNo3/MX5q18kTd/EDhGHiLcFe5WwZc34Pe78OxZ2HALjMpKzhybTGmYM1/9qiIxERITYM8uqDFDLtAv0Ie1wcFMmz4NgDgg9No1JkyYQGffzihQsObgPPw+cWJzWhZmcw3l5WcffkLA0aMwd3g8+i3ZRPtelOuc9RhPAzuXfY6ZdX/KGLXsbHjrLcm4rBdXrTdHR+jVyzr7q9cIbe/iQvGgQRz6I8OueCqRnDh1ipuD5VTQI8sHo8l2HU+7dyWxRQsKGsSC7e/RgyXFxTKvksFgW8QJsiEDCAFxcVJ/FahOPYjvgUp89dDqc+j4DmgL4NYNKRB0/ryGmJho2g7Ptu3DbKZo8mQwGhn/xx/0V6nIzs5G6ziHivAOXN05iK1bZwDv4osNlgc47edClFJBdFISuZpAZqvW8tniNUyZsplo9Kwc/QyHApT0+u0Wf8ydjhLBYGyQ9qpVcsJdn0ktLEwu6X76qRXRw2DQ06JFCyorKwkJuY2TE2zc2JP4+LuMH78UuEHLljK6pH4CePSovMVqtVzG/uYbCR6AVJlZtWoVy5YtIysrC7VaTUBAc8AmFt7RhiADMhONXr8DmEWzZoMZM2YMer2evIes256vJxkBiYmJ+Pr64uvry+ef21Jcmc1mQkNDKW8oRAEsXboUpVJJVlYWZffFzPLDDxT26EFN376EOzqiLy3lQkUFbzfI5vLvbOXt21ytsg9ZirtXwVcvJlLkNZiUvjK8rfWO1vg968f+cfv5atjDdVEPjz/MiiEr7H57LawjKJTg4Isa+9yhQggO3TxE4t1EDhTk0NTRkdnp6fxgkcPbPGEC4W++CciZ6fyMDIxCPJBC7XSDazbQMvNs4ezMJUuIHiDTuE3IBJ0BmlVYX516GFUJ1tnr/fZJSAhnGz4ACoVN51mtlqmqgHf27OHq7dso4+J408vLmrqv3qoa5OMEyK2rI9rTk7URERRblivKeveme4MsBfX5iGtu1pD5eSZJ3aRQTfaKbA6GHnygrQ0tMSeRdw++ixCCsqVlTHptEuvmrQPA92lfXCJdcGruRJZzFm/sewOT2UTzNc1pu7etdR89C3rSq7gXHU48GqH8f2n/GAcKsHnzZqZMmcKWLVt47733MJlM/P777/Tu3ftv67kjIbgCBnA+8C8SrptwcDBS1tVMeoItPmjlFy6YzQo6PLmQ1k+vp1XXg/g7m3k2BHpb1KDiz8pOacV1KKiFn25DlREOnxzKz5VDWJMl6eG1BptqmFIBPQcPQxUTw5SBg5nr708n4Ivt29myZQs7N++ko3MLDh7fRK2hhtknvwSFJyV3bFhvfmU+F/IucD3NRHExzJsnmHewK7fNQUQf+QhzYSGJ37zNhRM7uJB2ilqjJFytT1zP4otrKG9vYU1GRz8Y41dv0dEy7ZKFfbesaVM+Dw9Hp9Hgo/MjImIdjo7tScnvyiXacLiqijStlqtNmlC8dD9KhWTBruADjEg49I/33pP7VihY+cwzzHn1VdLqseb6+7ZunY1SeOKEdKKffIIx9SyZhydQ3kY+iEqD/Pj8BmvXy+Xcfft2kJMTi3nRRDJaDOENviWTYLwbaCQfBkCNseubmNwEvc5fJs03CliPk2c6/YlBzwAOM5hn8r/CJ/IZgq5IdnWcqSVrk9qwfn01/RV6PnhPqv4YzvqjtsBw0ewGEoFJNG8uZdw2boRvv8XKjG2uvIm3NwQpU7iatJ8hQ4bg7OzM9etjad9ehgx98AGUlgYAtvCQBQvkeGfwYOmUTSa4dCmPt9+uAGrw8rrAE0+kMGvWLGbMmIFSqWTz5s2sWrWEl16S4jmbNtlCnGy3umHIyiCGDRtGYmKiFYqdPHkya9euBeR7d+nSJe7du8fAgQMpLCyksLCQTz+VYVLr10u5vdLSUnbv3m3dq8FgYMaMGQ9/1oAtmzfj7eCAg1JJtE6HvqSEjXfv8k1ODn80UEAXJplSrC6vDmOFEVONiZrsGqqyqplxRYZKdHZzY7dLcxDwa34+n2fnsvVYJmWnpNPO7eOAEAJHtSMalcauHWYhuFVd/dBt3X3D0QkZNtbboZI/ioqsbNTLBZfJr5SM3cNFBTR3cmJzXh7fWLga6xoMRjq4urK9oIAArZYhOp3VEWda9qVVKJgZHExoAzJkaxcXPgkJQXufU2w3LZc2HeSzpy8tpb2LC182a8aUhgPRBqZWKnG+Pyaz/v6/9JJVKET500+4DBgAtbUozp7lXwEBPO3jQw93d3a0bo2DUsmZqCirk1cCfT09USkU6CzLFe73PWjew72tqd3SP07n3nkJBc82zObzOPsco8XVxRRXF2Mym0gvSWdD0ga+iv+KK4VX2HJ1C0a1kT2KPQTND6LxxMaELwonaFEQn538jO+Sv2PH5R0otUpUjrZzVTmq0Og0qF3+h/iw/9X57v9lq4dwE1UqcZYfRQwxov8z/YV6HuLQHxICbLkCEfN9iIiZ8LIY8PQAEfNVGzuIsP6z/SDi+x8RhA0UzMXus2QronfrdNGBeVZ4SmH5vwMIJYgZXl52MOF7Op0dnHXES/6eppP73LZYK5J+8LCei/V4A2bbwYUqDKIMN7FulH2bXt37qoTOVgYL5iJmRiNqm4VJ+OZRdvq03OnZs48u4yLh6h+GDhXExIirTZqINU88ITYMHy4uLncWl74JFFs3bxbaw4eF+uhREfjrr8Lg6CiqsrKEw7FjVpinws/vwX2vWGF3jRK/Qpzcb/tuauwnqv0V4siwNkKlUliv3bRpiKqqGyI1VRbdxMtCgLjZYF90mGQ99mlNF9GpkxBTp04V4CAUipoGh80VIMRq3rGHr1oWi7iw1tbv7s6Fogw3kUiwKLLc4/r2uLqa7e5RZ+KFANGd0yKDYLEMxJ49e4TBUC5iYhBvvonQauvrv/QA6v3gp7WASQLGPAC3du3a9T96N6qrq611tNpEce1ahvW7Tqezlhs2bNgDx2j4GT16tBBCiEGDBglA/Otf/7LWjYuLsyvr5OQkDh8+LAYNGiQmTbKHUX/KzRXExIjAuDjrNT5ngTlzNuaIWG2sOB1yWlyddFXcmnNLnPI9JWI8T4hxb8iyJVmVIlYdK75cdcFaf8ybEuLb5yq/f5Od/dBrsTU3V6hjY8XdmocvmbyfliacD2wUQ3+fZd230WwWq8+uFtoFWhH4VaQgJkY8nppq3d7i7Fnr3y9dviympqUJYmLEi5cvixVZWcLx+HFRYzKJ73NyhCImRhQ9AiYXQoiSujrrvgJPnRDExIhXr1yR7/fp02JKWtp/dM/tLCtLri3ExAjRp48Qky3QtckkhI+PELNm/W31t65dE/2Tk/+jQxmrjVa4NYYYEesfa+2n7t67ay03fBi52DcAACAASURBVNtwMXTLULExaaPQLtCKgBUBdn1as9XNBHMRR28etdYZ8dMIuzKHbxx+aBusvuD/rxDu/yc7cgTdq1J1JDksGaOApCqoMML1ezDq5l2y/+hP3yt9ITnKrur5NEdy83zxcwRl4kDc02/DjxKyUx6fh7IigCNbmpF6uQ8pfEoQMAfZYzgAi4EWtKKm2F5PdW+DEeGrwCDLgLtZCRQugbrjdZSFlLFgf38U8xqMQPsthA8CwTMdBWa6hhWgiLjH78PtT3lTyiaU85Vklclp8Oe9YcsPH/ytLB2dO4Orq4RxY2NlOquyMkk2KiyUWGSlVB8aMGYMu+fMocXt2+g7duRg9+5M1szn/dr3eGbHDtwrKjCqVNzx9cXp4EGcb96ktkG858+/y9n19Js32Zabi19cHMsbsDPrPODziLdQzrFRULNiJxK/SbDesRFdunQlJeVVmjeH1FRnHB3DrTM5PXJ0/X/Ye++AqM616/s3hc4AgyBFAUEFFBVRFBUVBZWoQY0taozdJJpiNImxxt6iscQSoyaKvZsYe0HsXRA7Ir1KG/rADDPfH3uYYSw5ec57cs77nu9Z/sOe2W22e+/rvq9rXWv92uIr+rEbgI4tDAzmlyoX8vMhODgYqESrvQLkIxZPBwSpvJsEUdHDYAA9ucVcbrdqgqgK6NeBUePq0Ns/gymibdgD/sCXQDVwqdQPGcUsYgaduEQ4ggDEdTrgQSrh1CEjowe3bsXyww8bef/9HVRVuQLb8PbuDdzHx2cqq1YZd5YcP66ld+/3gMcIZCFDD2wNQv9MDKEWzM3NKSkp4cqVYqqqWpGV5aH/rk4dw0zGy8vrtW3XrFnD8ePHjY534sQJRo0axcaNG7GyssLT05Ndu3Yhk8nIzc2loqKCnJwcunfvzh9//MHaV+ylakgzGbWYoJd0s7SC0wVoq7RUplSS9XMWKQtSUOWqQFFNu9uQHxyM8mIxWrWWpjcNrPfW9yDWHwboOlqiXyG9ZFRW0uD6dYY/eYJaq32jchQIKk+jxQ85fc+Q3o0tLSUqOYrW7mFk+AnuKymVlUh1z1fmw8UAfOPmxhYfH32rU6idHaF2dig1Gm4UFxOlUBBgbY29iQlvg52JCROVx+FKL+prhNLG/txckpRKUisr/8c2egC4uQmMty5d4MwZwXAehJ7srl3/3HgAWN2oESd1Vn7/CBJzCcGFwVSaV3Lb6zY/r/wZiUh4/9VfWZ+88jwq1ZVcSLpAdHI0vz/7narqKjJLMo1IY70b98bR0pFuO7rxIEeQgzwWf8zoWJdS3iIa8x/Cf0cAtbWl3ldeNPyhIbOuCimdXamwLkHolSoWV3HHM4Yuj7vAsXd5+msw5as+g9uBWC2dxZ3bQmuD+70QgmkIyS5wcTaaWx+jSQjjXIMipJRhjjkNgZpGiC6A1MyMPkTQj8G8xJ8qILZ/f7KKi7FEMG/65ZXTrVMBo05BkQq+u/e6uTI2mbiGjmGH30I+WVbE5WW23NOVVBpbv7767o6r0Ihhz+N9xOXE8TTvDW0kIGiDdewo6IXOmydIuq1YQdWxnaj/2Ae7d6OSgWpAd9w7dOC9K4IEYaOePTncqRPRLVpzpmUbtgF5tYyl1bWPoasPbXnwgOtFRSxPS2PC8+fkqlR8o1SSuGQJ2okTyTJ34oDpIJYNHE6clxcPZotJzlzIyzILzpy/Q8cuXbFy6kVgIMTEaCkoKKCwsBB/f7gkD2MxYRwu/ZpTnqHc8fKhLFho0Tj35Vf81HQdycnQtGkvHBzaAQuASfTrZ0jnH2IAj1VunNO14TwJcCEqIADbdFvGDDDls89g1jIZE7cHUyU1Z0GnMFYhPDABPGEJw5nBEiYyi5FuxpZ7zcknct5LNs0r59ixj7GxGYql5ShgJPHxg7CxOYOLy1HGjjVkuXv3Bk/PBI4f/41X0apVKzZt2sSiRYv+1HD4VVhbW9O+vQx7+xqC9iEgjLS0/cTFCeniOXPm8M477+i3adGiBePGjaNHjx7MnDmToUOH6m4dE3r1EkZx5eXlJCcns2HDBrp06YKDgwPm5ubIdKUDc3NzTF4JGM5mZvjpZHV26Pp2LigUKNOU5J18xae1Fpo9AOm9Cl7uFVKpllfLGVm3Ll/WdSXgAdxqC5YWwsv6clERWbV6yZenphoJvr+RVYqgpdrDswtolJAgBP6DWYmczHhCifso/aD0YVkZ8xs0gOStlKT/AUm/MkxugVQsJkwuZ7q7O/0dHWlhbY29VMr5wkK9ktWbUK2pJi4njricOE7FH4bqCuyzD2EjEaOsruZ4fr4+jfpPoaaUY24uPPs1CAsT+qNe6XggP19QV3nxAhOxGPN/INVXG4nqRNa+s5btXbazJ34PQfWFHvdqbTVzLsxhR9wOKtQVVFZXcvSZwUpvlP8oAJysnJjVeRZO1sIAN2JPBNHJ0QDUt6nP0SHCNpdS3xxAs0uy//K5/ivx3xFAAaumVrhNceNrv/HULYWHxXA6B7old4OVEOMu6NZlVKqZcPkqBxVlMHU5bR3eoV07X9QVFnDfn1aiVqC9CBfmQ5kTJJWCcy4rRSuZwAScgFYIjeoRQFjPXkSYCDfLY1ajpj51Dx+mqqqKC/7+1J44thMbX+7Br94LkYYXcWObaCoHxzD+mT+97xeRqYSZTUzZ1Br2WxpubBOxCUPf+Ybpj+w5n3kF/43+NFnfhLMvzvJGSKVCu0l0tJAtXLiQuO8hIWkKjBnDkxnweLZIL7kHEPqKpNvC4cMxBXze1AJx6RKcP0+MXE6wTiuwpJasWMN27Sj6bAAXdG1JR4OD8f/lF5aHjqS6GgYNqqC4uJhHPj58kCqndWsL8vIqaNu2LSNHjkQkAondcxaYb+CJr4bKb9Jp88tGYry9Wb1uHd8nrWfjcaGO7etrRl7eBeAisIvDh7sAgt6EEgs6c5+we/dYvHkzl1q04GJLf74KlfPLL9C4seCsNXi4KaahnemdZOy+8qlOQzWMy7ilXSITYxnKvbmhzDnzCaDl4kUJcrlBHKB16ySeP3+BTCYQperXh6NH4dKl12cFz58/5+7du4wfP54ZM2bg6en52jp/hpoJx9atAP2Bc1RW+uLvL7iGOTo6cvLkSfbv34+NjQ2XL1/G0tISqVTKwoULcahlFdX1DY3If3VGDPBunTq0trZmuLMziz09uZKv4Ib7DbQlGrT+Fli1MPitPm8ECY0FEfJ77e5RcLwACx8LqlIr+cnMk7kKJ0zLITFQQk5wMIf8/MiqqsL1+nU9QSmhVt+rp7m5EbHnVdTIBJJxGApuszT5BZWtNvIQndtIkdAC0lpSACnbEUjQOwhYK9T7zcRiFnt5YSuVIta1qWzNziZDR8R5ExZdXoT/Rn/8N/qTWJiITx0fricep/jGSNTAvMR4AmUybF8tcP+fIjTUyL5OjyFDBNnHRo0ErsRfRGlVKb7rfTne8jiqAKHdJ7RBqF4QY8OdDYz/Q7CCc7AU7qdWLq3o4NaBkS1HYiox5ea4mzhYOjC65WgAUopS6Bop3G/XxlwjwieCtT3Xcj3tOuWq8ldPgRPPT/zPrsG/CP81AVSPn34idWoWYTe70vVGV55feA6lEHs0Fg0aYhrGwCjYFrSNn/mZknslBKUMQTrgIKIKW9qatKVPRBSzPkpkKluwTE9i/r75NNA2oA3tOMBspo3JI757dyZYWKBcsBmVytDzpqAlroAEaFWLcHECC25qttK9XQSrxgri7+3SQaSRwMpUPH5J5uiagfzWRsSI+iZcbABjtb9RVW1IeX0S/hwPj9k4+YPiansKHveheL4K1Go6xRjrQh54fICGPzbksxOfGX2ufvn6SE2khoIWVWjEIKoG6w3n4ZNPoHVrKC8n2NYWE5GI9+zs6JmURHrdurS3sSFm4ECSa5pfy9Ph2Uqci09AdixVcjm1eZb1Mfg0ynPEjJ42zegczhb1Ytcuw3JcgwbcKhdDn9tw5AiJvr780awZ058+JT13H0qlN6jFAntRh85ffMmhjHY0aEAtcQJzoAQoRhj6wMGDQmAp0xnDhcbEUGppSZGVNfapg8jJ2Wt8gXSMRo2FJU6kkVTLUM4RMEfL758MRQ4E+p3hCb54kYQnyTTmOZMnQ0ZGAFKpFqkUBg92ICNDzcmTXfn0Uy1PnwrnExUVRevWrSkvL6e4uJji4mIavTJ4+WdQm5BZm9C+cEkV4RvGsONYEg8fDiQ9PR2bt2jC5pblMvnyZNJz0yksLOSj6R9BBHQJ7fKXz2OhpyenJd5cdbxK+1ap9N1hSMf2XlyB5Kw3B+440es4fLoeJq4z3t5tihtIoDCqkMKoQiQ2Es6OaIeZWExIrSAVev8+Cy4t5XxBLjbZR7G8OZi8B/NJVCpJfoskqJ25Hdlf6Z4NxT0wNTzTvhYWUJoE5Wn8emMZAFsitui/Vyhfn9mGyuWk61K+nWqxVmtwLvEcc6LnGH02t8tcYV/lyVBVSL5G/NbZ6z+L1KJURj9aTKV7PSP7On74QRj81nje1hbN/ge4nGIIxJ+3/RwQtI33DNhD23rG/sddG3TFTGJG9Mhozn14jo7uHcn7Jg8PO6HEMLndZOZ1MVbDcrN10+9TpVFxNVXQJy+tKmXEkRFsvLOR9bdfsYz7N+G/L4BKJJg5OhPetScXTl3QN4oXq4rZINnAoSChYKJVarnKVVDDi69fQIUlzmOcsamyIelSPC6PouhJIz7MD6LTU0Ek2oW6tOILNh+qQ8KA+WRPX0vhjUoQw93WAmU7HqHGGjVuHNLvDI70iuE7gRGcu+HKV7/EUmAmIjQJxJmtEZXUY/7CcGQyBa5ZWrq+wR/2q3afU9/WnTp1ItCYVkPWdeT7j2Kuy5+GJcHIWAiUCDfb5nubSSxMZP3t9VxJiaKyMouKR+e5KLrLj23h15YQ1UDYtuVkQAQiLbjvhoabhBmjplULqiTFWKWksFOl4tvCLLrXsUJSXc175eVYWFlRN6QxP/62HnJOQfYfZDdOgXrGszUpKn5iIt9g3I405MED3tcVAbNNLNl6wgkcHGi3bBk14ndfZ+QKSgLffAM9erB040ZUpb8LX9bMKDQwMD4R/+D21Jj51EyMvLzgm2+sAWNm8sCB0LBhKV82W02AqyuWaiUWlOOtieHJk6HGF1/HIBZ17oS5e33eZRdJXo1RR0ZSJRLxEvh040oUQMSgLeQ2N6TL5nU+rv/7xx9FrFkD/fuP1llXRqNQnMCqsgBNbCzXoqIIDw/HwsICmUymT4n+n6KGAN2mrYYu7z+gzzBdoKh/gzO5W5m9bzcLF2t4lJFH7sMcgf78Cn57+hs743ay8+lOTK1MKWxWCK2h0v4fa5BmZEBFhcAWTRoXjypPBQXVjNkqfL/mC6iwhA+Tn3FFU0qFJahMwcpSSuOd3pi2NqXu0Lo4jXBCFihDEaVAEaXALsQOmblwrRUlqUJ6FaEWOvfZNZRIKM48Rbkyl5KXl0GreWsdFMDJ2okV4T9C5UujzxtZWuLgFgGKGPY92oejpSOjA0brZ0tbY7YateW8KHhBmC7wNTeXvNG1pPsOg1KIv5M/c0Lm0KtxL0NNUCFkb8L+2fTtW7D7wW623d9GZIQb2qjz5JTmULpiMXz9taAbWYOa4KrVwsOHBknOV1BWVcauB8LId8d7OxjafCgzO82ko3tHpGIpewbsIcwzTBCvGHuDbzp8w5p31iAzk2FhIjCSZWaG+1wkEjG53WT6+fYj2C2Yw4MNk5AmDk1wsnIiKimKFwUvOPPiDDvidjDh+IR/6TX6n+C/L4DqEFZLidnW1hYLCws+PvkxeW5CkT5UHkoaaRSbGHq0PGZ6gAS8irwovyo8aEMw9ghcwUPsi0pp+Uk76n03lofbFcgCZfjM7cQudlEsbo0W6LxlC/op1ciRXLfrr9vDVLQkEV0lJyzenOqn77FkSW/c3YWg43JGQkBdQ9uOlxX42SA82IBM1gqJSEZhbS6UiwumJuZse+rL7TutXuuD67QtjBNXAriZ2409E7RM6gVj+8EOnba3pBI6DBQCqO1jw3b5FnE8iu4KDRsyuHt3gkJ7MX7oB3x8/Difd+9O5csn3Oy2leb9DuKQUSv9KHoOZckQF4e0uor9DMaaMnpxEm8MwbVBr17sbdeO76uqBO2yvXvhwAFutDUetRqhoADIBI8U+F5oIwioskfVvg3iWi+qiAjBuev6dUGE38QEvcciCLZiCQnWrH4wCdNz54hwcaMtt5AiDB5Uqlp1uYAAcHVFFBHBu+9C3S598HwRj3TECKTh4ZyWSvSz7fbt92M3/AHVZlDuBt0lBj+z8eOFNt26dT1p3FggRD148C5a9/qIAwL4Pi/vf5QS/avw9haycnY9f6Dt1hYc9Xbh3DnAU/g/SxFHoWkeSfvdvhS1CRFepq8gKllYd9r5aVgttuLAc4HgVFOnehs0GmjTxmASry40qphzIwjuDBFMJNIqKwUlHF9f3nNwoJe9PX/4HCXsvTDq/VoPibkEeaicwnOFFF0rwi5UCC4pihS813njV3EP1EJ6T+M2HNRlUKK739SlSMoS31oHrcFNWSg0ma1f9rGw4Fh+PnkaMf2chVlSV8+uiEVifu0riJ5POTOFjXeE/sWrqVdptLYRxYWPoDydmEcb2Ba7zegY6lpGEqc+OEXsJ7HM7TKXcUfH6b9rZVIJqhL8zP7cp/N/iqgk4f/xY8cb7FfFErq5I1/X09kY1q0raCYHBAjagkVFQr9W8+ZCneENvbt99/Zl14NdDG8xnOEthmNvYc/C0IX6diEvuRfnRpzj3IhzBNUPok29Nnwc+PGfnqPMTMaR949wZcwV3mti0CgWiUSEeoay++FuvNd58/WZ1+/Tfzf+awOov78/crmckJAQsrOz9QzB3G9yKZhawJnvzrBs2TJuqG6gEWs4OOQgLXu0pMy9jC/5kkCM/R/DZ4br/27ZcwRtPwjiN+lZTC+/5EiynJYtO3NffB8bjS1lNDBs2L07bNmisyPTAgLr8Zy2L0FZaqyuTMDil0v4Lgbfp/2ot7kA+/p9ONERjnWUsDukFTcmGF7mIpEEO/tQFEEmgkVDQYHQkPrypRAVoqMJPSekYd6v1TZ2M1cINjEKCJTDscBJnGwHWz401J1qc7K1InD88S4B4cauJdblatavWoVYqaT8tJDGKlNDoToLsUYENeXOe58gW7UKdUQ/PvtAQWEhrBVNZR2fcZQIWhHD0rQ0fG/eJPmcMQnnNej6MVGrhYfb2Ra2Jem/fs/XhmiFgupaD/g77wg9mnXrQlL9XOY+TqNJE4FkrFBA377Gh4hs0oQTwV8RGCiw/xSKWjUgiQTi42HCBFavhpO1+sPFv/3G9g6eWFrCH38I8msFbeHaYSgIs8PhwgEqFqygpASkV6IF5jMQETFZsJOrBFGZkFYcCnSorSP7L4JIBON/Wc3JaoN03tLM7jSLOA/VUnC/Cg2Pc/hAFY2Uz+Dnn9GuXAWjRnHy2nYWXlrIhRfn37jvmsD6Njx4IPTxF+3MZF3nNJRJSu6GeNPijCD0ca8V7G3alM3e3vpaeVe5nD1Nm7LV15fTL06jVCs5/XQLCQlfYRdqhypPhbZSizxMmOWdTzqPRqthz8M9cK0fKO6DeV0oimNmp+kovlWwvd92qgvvsDMnh/5XdhmdY4FKxYdPnlCoUnEg11h4Y3Qti8XhbkIDf5inYXBe30Z4yI49P0bgpkA6bhUGvz9c/wHujoO0fVxKvURcThyOyx1Zc2MNMVnC7PLUB6cIbxSuFxQ48NjAupbkRcPN9zn0aBeRsZE4Lnf8P2agVqoruZJq8CaeHgqPixP4ORA2tBXEF06eWsfC2SHCM7dihTDqq8ErfsEgXHsAP0e/1777OxDqGUpqUSoarYYkRZJ+xr6z/85/y/FfxX9tAJVIJKxZs4Z58+YZMwSl5sgt5EgkEvr06cMBDvCj5kfW713Ps2fPOJ5kSLmtN1vPQ9MnxI0qw1nWmKnDhRdQy6SWLNu1DFu1MMo6VQznztkwdPEYtFJ4NiSSC6JQbtt1g19+4epNKY8fw5gxhtFkFFMxQU1HRnPteTnOZ6HuCw9EVlY4OX2Ar9csApvtoHHDJVibG+uKyuWhFDXVUr1gFpWWStQoqZC+FPKWRUXU3/ojoxtA/3qwNUHYJkYBVRp4oBDRRg5WVmsIlMMPTaRCUAKyO0NlQAO0EjEl3sbXs6Btc16+4r2rPnOEjAo4mQ3VIvB+2ojAFH++cB4Amkqq7e2hooLMTDh3rj3veHzCi7wIMlVdMStqgFV5OYpHj9h54AAcP84boUEoEFaI4YCJoLA0Z7n+a9nTH+lqZ0dRdTUxJSUUqdXk6lJRMhnkVlXxXVISS7MEfVJLS3hDSQozsRhLExnW1s2wsGjEy5d7KC2NQ6vVBW8rKxCLMTF5xdTEzIxho2R8/rnQIWRr25GmTQ8gcw2jziChdcB89jdYv0wUbIMWL4bCQnoFtsU1Hyqjhd2k24BSChZq4xnavwrfXphstHwu8RwPS67QtHIMSCtpb3OK92qRt0VfTYHISNacX8TsC7PJqchlda2Bg5NFfaa0mcHllMvkluWSW2YceGogZAK1hKQm0+yyIIqw+GIdrlfIcZxRn+aj6hNoJcO/XKhbNDa3oJ5OfEGlTNXPcE882Up6+krwi0NkKsLE0QQrP2HwVzOrOvj4IGhV1FEKg6sedRyZ2GYitua2gn5uoaCSc0Rdj3slxRTo9G2P5eezMyeHPbWs6FpZW7PJ25uJrq70c3BgkacnEV6dmNFxBoOaDtKvd2KYQF458fwEd7Pu6j/f92gfaCoBDVFJUfTa1Yu88jy+PP0l5xLPYWVipbdyqxEUAMGVZnbn2dzOvAXVFWyN2cqo30eRV55HyLYQ4nLiUFUbzCK0Wi0vCl6QW5ZLkfLN1mI1Ii3X0q5Roa7g53cFYYykWq+VT3tpuf9RH+beXMqCRxvI8a5H3OaFlNUmU0dFoapWkaJIIbMkU29s7mnnyYTAf08atfbgBWBR6CIWdF1APbOyf8vxX8X/NXZmfwc+/PDDP/3ex8eHBN2/GtzkJoMZDMDu4t2YmAp3UN+cYBpsqMPWLlsZeMPYbunhsA+4efM66emfgDqWsr0SZnMekzKIKTa0KsyYIRBYPDwgJsaHTOwJ5Qg1VQ7xijVgLsN0wQI8PY1d7mvDzi4UrUhNkb8Jz2M7A2IqKhIIavUICysrigLKGOUEJsVABAwugehMuPuiHirrDFrbhwHnCZDD8ewiDi9YTeiAELbK4FtJfTRh7mQ3uYSNLvtVEubOrAk27H8KecIECmV9E0yuJTG8Fscl8fcUzvTqTciUk5yc6U6+r5py4Z1FZGR91OqlbNqks90SHWNd27aE3bxJE932Pe3tsZJIqLhmx/HGOjLDpJZI19yn/a9tuXxHDUPvgK/ggWqSd4mSnCPYq5diJRYTpVCwIi2NtMpKruqkzepeu6Y/v7ulpQT9BeNkO7tQsrI2kZt7EE/PhXh4zHzrutXVFXh5PaZ58wCUylT8/c8hFptRt+5A8FUCOpeIhg0FIX2tFi5eJHToUOIAzfciKmy0eH4Cs27CnMuXoVevtx7vn0HtlGEdizrkVxgyGvu/+oJOm/cQllTy2nZVErisegESMNGKGX9PQ/OgCLrbnSVn4Q22N8ihYsBigrYE4SJz4eqYq6/tIyoKOntW4JgkDGqSsaQAM97tCzdvNmJ2W0FJacIEU0w3yLCosoN2oNFUsTe6OQplKT51fLiWFc8oF4h71hXbrtewcJEjEovQarWcTzqPTx0fnuU/o6G8IQd7L6DtvXusDhyKq5UQZOUWcih6oD+v1nfvYSISURUSomfnLtFJiyUEBdGwlmLQkWYG6bhFYYuMfl9zp+YcGnyIAfsH6D9zsXYhqzSLMM8wxgaMZdjhYUbbHI0/SmePzvo0Z80AAATGaYW6ggWXhOf/wcsHRtv6b/RnYuBE1vcWSDMHHx9k6KGheNh50K5+O3b1N55dAzitEFpDJCIJcnM5ga6Br60D0PKS4Tydhwk1z87JcLFrpEDjjopiQ1stM6JmIDc3+LVeH3sdW/M3jEr/BnjKPWnq2BR7C3vuZt5lVMtRSJR3OXToX/vM/FX8185A/wpEIpFOr9SDFi1a8Nlnn3GPe/QV92Vtr7X64Ang4WRHa9dA0pulI1MKs9nJ78+l1/ReVLrfYKOziGNZm4ixqKalNAsxalQqQddUvw8PQfv0l18AREThwmgPD4yqXjX5wXPnSLf+kBybvkKxrBYE53ZH4uK6U1GRQEVFPKChsPQSdO5MYRsJtlXeyO9AZV1oJ6vDSw3MsM6ACjm/b3oPu1iYMlzG8Psw4E4IblNA89wKyfkrSLpHcHLw98i/Bfm3cHF6NZfTY/GXw4DNHem9oSOPhqqwS4TJ12D8HTCvhh6VVYQcOQLl5byb1ARxwzTWrfMFplBWdoEDB2oJA2i1hN98iC8685qAAFbb+GGxsgkd5x8hPmIULcJtWDPejvxOwfQONIdkQ7rZRZNPeq9PkYgkXEmJppOdHecKCzlTWMiN4mIUKpV+hgEY6ZP+nJnJjuy3943JZK31fxcUnHnregkJk7l82RKtthJf3220a5eMWFzLFN7c3EB0EnYmUGH37NF/pBZp8R8Haks45SvVkzd2P9jNhtuvax/XYMb5GVxKucQfz/7Acbkjvz19vX+0BoefCEQMsUhMfkU+EpEEE7EJ1qbWjFzblW73S1gYAnubgcVM6NI6lm+6izGbDc0SW3Pk+yN8fr4PyeqZNNmegmbpSyipR95DfyyQk6RI4kb6jdfYqGo1PLhQybykW/rP7mFgldZ0Sp06raXq3eFUxY4j7ehpHJc78sfDDdzOL8VMLMYjYxTPS1QodByXoikhePwoQ6vVcPL2YLJLs/ku5DtECDWyljIZ+cHBHZe2eQAAIABJREFUNLGyqn06VEwv5FHLxvpllVbLtBcviFIokIpEpFdW4m5mprev+6sI8QhBhIgPW3xIwdQCjg8TsikN7BpwK8Pw2+eEzMFMYsbdzLv62WdaURrPC54jFUvxsPXAS+6Fn6Mfda3qIhaJUWmEe3h9LwPLdMOdDfr/79MnfqRaW01iYSKnE06j0RqYzQDDDhmCYrW2mq6eXY1SwbvDN5M9Kd1omxoRBIBLDcAx5ysudfWC6GhOJ5yiXFVORkkGSYok/Bz99L2b/y7cHn+bCyMvkPN1Dlbk8eDBfyZ4wv/PAyiApaUlK1euZOnSpUyePJnFixezYuMKpn439bV1F4XNZ8LYCYgtxagtpMSpXagwq0WLj/iYmKbnsVabMuP92goaWlwR1rO2Fuw7p06tQNytCY4pKTQC9rdtS4XUjfInJajuJ1La/ROSyoaQXDKIqrCBRsxIkUiEqenrN21hYRSa6VMpam2Cnc8Q5G59AOhSqxAvVjoQE9WLlpNBriphh25CqBHBrKdCGkQT2pUvz05FYQEKC9iZnMEjRRkBcmhR355zeTfYrjv8yjOw6Cw03oCuM1JA+OVCyqoLyTL3xdyhPZBHYa1g4g40Qjheb+BQnobDeyXs/BWmpX9O49IUjpl/yLhxYGMiZeRImPWdBh4vgMK7LK1nQ13LOgS6BhKVFEWonR1nCwspVKvRAFuzs/XKNONcXPT6pFqtlvnJySytETJ+A5ycPsDBQZhRlJc/e034vLIyC6UylfT01frPrKyaIZW+QeXCzq5mxCQE1CFDoJbX6DU3eK6bFN92rqb4ohCwl11dxvyL898oun474zZLrixh/sX59Nnbh7zyPN7bZ2wIXTult/uBoNb0vp+gljU2YCwqjYrSqlImHsulq66cPHQgKE1AGn6JFcEabMptWLZrGXbldkRcmcRLbTckCjmNqrJxJQO0EkRP2mCltEJWKuPy5cv6801OhkMrn/Cu9p7+nIo+rI/1R6bofMo5dEjo3T93LwFa7AKHWArbfUpeeR79jkwmphCa22hwKhFShVlmXwgbmqpITJ3Cy5f7OP38IFKRmB7uzVkZvpIvgoR1ZG/onTSXmtPUrh7i52ugUpiFL9NlLMbojMFD5XKDYLtaLfyQfwB7C3tmdprJ1OCpyC3k+DsLrNrs0mzW3FzDjI4z6NWoF+ENw/Gr64dKo9IH0AvJFwCI7BfJih4rEIlEiEQiVoevZmWPlfpjuNu6Izc3DD7e2/cecTlxHMs3kNTyK/I5+vSoXp0sRZEi1IVrIbRBqP6YrjJXDqedxsrSlrU91xLgHMDEwIn0b9LfaJu88jx6iHaiKiniUrJxf2jN7/h3wtLEEqlYisxMRnz8f46BC/8bQAHo378/PXv2xMvLi+nTpzN+/HiCgoJeWy+8UTgDWw7EPtweWZg9ohfvIlIa08zjOwuzhrB9drR2FsgxIeSynZsk3hCEpcViWLbMgmFbBGFvDbA6q4Sb6u3cKv+Zqy1TucMWqrGigvpcK/zF2J4ecHYerf9bLLbE2roVCkUUJS1MqRYrkbv0xu6jnxGLLfCoNxixWni5d7Edy91S49/mVAIdEw3LsY6Gl4/MVMa+dEG6sL2zJ16iq1Rp1OxRwTOdEYtjJcTVIq2W14PwZ7c4sg8Wpf+G8rNBgM7ckBigEV1xp/ZYuf+kD8k4cgs/DEQFN2sFOvEanJ2h38exkBsFcV8z0EuQ7gv1DNUHUAALnVjFlBcvGPHkCQ3Nzdns40OYXM6VoiIelJWRWVXF4/Jysivf3IIhkVjRrNlBWrQ4jUqVQ3m5gUil1WqJje1MbGwXwzWSBSES/cmjNGaMIJfYvbshPdukCXc3bOBcA906GqgWablS9IDc9GfE5cSRU5bDkzxjEldGcQZttwgs5RoCRw3Kqgx1oIg9EUw8MRGA6+nXkZvLGdJsCFYmVszqPEtPvnAvglADHwsTsQnXzGcA8Pv3v7/2UxQEcJpwUpyDaMMt1saf4dvfvmLjpg1Yv2NN3pE8SkvhA8+rRF1uSr160QC4fuLKmfdXcbh5OH37CqXgGzcEP/hC2zcTke4rRLSSw5iBm3E2MWHBzipcXARSS27ufp48GUaMAvxsTXgY05IPGrrTrG6zN+6rNr5q0BhuGOqYEmCWhwcyiYSIWu5CbNkCTZoIbNQ/wcHHB1lyZQm2ZkIaUywS813Id9xIv4EWLW3qteFEwgk6/NqB2Gyde4yD4KUZlRRFS+eWDGs+TC88ADC0+VAmtZukX47YE0Gh0lgIwn+jPzkW1QRkga+uBP3e/vfwWO0hSOfpAiXAzXE3MZWYEuYVRnRyNAu6LuDdxu9y8PFBQiND+aztZ9z7+B7re6+nr09f7MztSPnSIJRSqaniVkMzyqorCHAOoJVLKyykFkR4R/CfhEoldFXUq/f5f+T4/xtA/wk03dOUNod8Kbg4jLyZqQxPKYdVKaCRUGVruOm6iHKYzhMmBeQhAVLb3+Dg1OOclZ8l/3i+kNP18qLYywtxmv3bDwg8ut2Lb6d+qx+hbtlSRLB3PJ23DKVDs3gaNvwelSqXjIy1SCQ2WFu3wux2Ah3/+BjojmZpLsdzIjljoqWAkZRTT2+PNmk1nN4LOVZg3bYX269GYyYx4+XXL2lcx5Dyau05nvqm+chNBKeaeF+3184zZp2EHJ3EbPgLw+c2nq2AOnTr1oL33rtPmKgNMcAHnxheZGtvBfEAgZ1Z9cNayMyEQYNQqioY9dsoIu9HYmliSf7UfCxNhMga6hlKbnkup+6vwyJ9Hx1tbalvJqRRyzQaAsT5fPzHx3SxtUGp0eBfy7rrz3oCAWxthSB9+7YfmZmbSU5eiFKZREVFAkplEubmXgQHFxAQ8BfYkVu2CP5kNWo+YWE0GzOGJZ5APLxzD+pKIcoTos9sAoRU2pZ7W3D9wZW50XPJTX1C/VWvO3JsjtgMQMMfG/LjzR/54doP3Mq4xe4Hu1l8eTEvy14S6BpIH58+ZH2VhVtKIS+/h+IlIrolwe7msLPvdgBUGhUVmlLMiuvq9++K4NqiRkQ27fEiCWl2BrcIYlSMiC5PW+Nc5IpII6Jg9lGsZSKm1ZvOu+eO0v55e3Z02kGAawAb7mzgWf4zeu/ujWCdK0DcMIoAp9b09hKuTZhOcbFSq6WVbtLlqa1LlnkUnTv/RFp5CP2vwY4UiFWAv61A1ikoMDT/p6QsIT//zcS0pd2WMrrlKLjcEypzaWNjg5u5ORnt2/NeLeUlTp8WXM0vXyYyNhKrxVaEzqxP2agPYNky+O03rqReYfDBwVRrq/W1zIWXFiKZLyG/Ih+pWGqUHahJsVostmD6uenC4K/B22dx+d8Yyxx+UfI62/XMDri7CSxqtXH+dOcnRv8+mhZOLSifUU7bem3J+yaPksoSiiuLCfUMpbWrUKq4nXnbaH/Dmg8j9ctU3G3dKZ5WzN4BgrDI2nA5NmopV3sf4upVX3ImJtK9YXf+U3j6dBzl5Y9p1Ggtzs4j/yPn8L8B9J+A2EyM2FSMjY0Ie2sZfXpaQJE7ZArF+c8bCXZH72bVowc5yGMM7D6H5VaYKEx48K6OHLB8OZIlSwjAWOReSgE/sprD7AMgly7ELz9Pc6A5sHT+fFJWRKLedZKipWvITbHBOlFK2fW92Fl1QiyWwk8/IV6xmj2rc3BQl9Dt/PeUzt5ONr3JafAxL7p2pahePabrWk+yrCSUNb/Gb88O0sGtA45WjuwZsIfO9VuypccU7O27IRJBgG7SfbS+G1OA2BEjyHCUkxgB0o49eRQ6DKUuxTtGKVCEmkW0B1bTs6eY2bMseM/2BpqQECSdzAkb8fo1rhqkm6kdPMih4yuIvB/J2ltr6eTeCXsLw2Cjg1sHTCWmzIqaSXXKNqbWd+FELRFsZeZxNt3bhLokHpQG+yk/S8t/2BMokRhqaPHxH5GSsoD8fENqXi7vjomJHLHY9E2bG8PUFMzMhKn0ihW8HDuEQlUhIg8JPpLGTJ3SlZZ14Ly3iKhnp/Gp40OwezCrbqwiqzSLeRfnMWWboZ61r+sGRvqPZFLQJMYEjAEgpyyHSacm8fXZr6lTpsVGCTOjBALUYD+BGCczk8Ho0chL1cgqhSBWr8fnDPJ+Hz9LP7yyvTCvNKdHvJClUHdwYC79iELDLyJPNNRFiSHIlNGQagzErNwntpTihSxjvp4rcN37OuUag/zaiecnsBGfElqJRBokjS7QzcqdF/HCjOl8LpiJQVxlg7xyJ2p1GHm3p4NDPC/ViYw5mUuhCn5NhhK14X5UKIQAVl7+jOTk7/Qp9oqKF0apcLFIzLJuy3Awt4YXG/i2nnCzyqRSQ/q2ulqQuwQqtm1h7/JReKWVM+J4BlaRu2HaNFi5kl67DPW3qOQolGolsy8Y+kg7uL29LWnp1aWkFae9OQ36Qhh92lvac2zoMTp7dKa3phFz1z9iW4s5mCGlYQF8cQNWB4GlCprV0n+YfFpgXQe6BBoJFkQlRWFlYkUb1zZ80PwDfftJUqEhDSESifTiBjIzmZ7stM8hm5DEaixWrMF8+25klw313X83KiuzyM4WSiMODhFv9En9d+B/A+i/AHqJ0GcRkOfDw4ShbGmaabROpenrNRlNpQb690c2eDAdzDvwrOEzGq1pBOJ8SqxGcYTfWctG/fqTWME1PIkDNgDxqzTEsZQ6y5fjHdCWwLFq2owDzzVFoNWiPiu8UC4tiCaXupjGP0Khk7PLsg+lcdOm/FZLUPpaYCNwU5DCFf1D7V3Hm4tjYxjb/gdkslaYmrrSz28kduZ2nLqVivbLL2kZGYlLdg5Z39aljmMfth7ZxZm5wsz1l6VP6GfRCqtm6ZiYDKdnTwiwfo61IoM2335LTFEMUV7wfWtD/XBVO7ikNPRUXPjVoOj06svG0sRS/5KqUisxK31Gc2trTjZvjoVYTGqOYFo+5OD7iO+OBU0Vn7i66v0p/xFqp4a02irS0pZjYdEYsdgSB4d/Mn311VeE3/yMDr90oJpqjvzwO127RtG7yTju19FylKeEeoa+NjPZqRXSf0MewOAUa7b128bqd1YjFonp6G7smXt6vykbak3AhrcYblio9bs1iPFb+T6ZyzNZuGkhv2z8hZNLTjLl2BQAwq740eXnoSwglOyWQp1QYWIQulDYd0NMJSbiVOKd41FrHbjzin3CM1djZSqAi5/34vC0W7j4P0Jlmkv4nCM8WWj4vlIDrqW9GDzwA7p1O8fRtcIAgC+8UTsYFDEspBYEOvlibR1ARUUCZWWPuXXLF61WTVHRFcrKHnHzZuPXZqOOVo4Cazg3GtPi+6+dH7GxoFCg9fHB4tDvnNwNDzbCqFqram9cp6RKeH4a2DUgKimK62mGmmQ9WT29WDoIbiOmElMa2Ruo6xKRhE4enV4/di092t7evbk46iLHzjggV8LIeAvS1puR8CO4lsCiEFC2aUX/56+/Y/r49DFaPp90Xs8AtjK14sqYK4hFYiMm8Kuokc4DCE3Uwpo1wsI/cHT5O6FQGNLT5uYef7Lm34v/DaD/Ajg4QHExFP4xjYIl9ygoEPHNRmEWpBarqRZVk3HiBfcCBUbdD32F/sDiG4IK0uMPHuOidOHAiwP4zfSjj/Vw5nzrTUycwL4NxyDikE1PnjKVEN7Hkh6U4kMVxhRyy1NPqGrXGWluNiqkDOR3njCdDCJIYhwiUTVV91RM1E7kSLFOiWnjRsw+Nyh7LBrfng0bhNJdzfs2KSmFzZvDGB/0E62iW5GelI5WG8qmTSAWmxAU9IKdO8dy+DDE5MTq93Xk23ukpZ/nxIfhqA5+Dj6C+feYgq08fPkQqVjKtN6l+E7sgSIjkZUDXIhKiuJewhXuORvX6F7tAwP0gUYqlrL7wW5GHBlBJ5k5gwq2EZcdg1QsJUmRhEZdhlvcRzTOP07k4fYkvox5qzZqDRo1WoWHhxDARSIplZXpODoOoEOHbOrU6f2n274Nww4NIzY7liRFEi7WLvg6CMK9PZuMRSuCTMtqOls31g8WFocu1m/bQe3CjmdNX3t5nR9xnmHNhyFChH05tEytom+qBdMvQa94ML9yA2bNQj1oFE+ShlC1YjMoFJRGZ6LKU5E8Nxm7BON6frVFNSKRSC8F2C7cFCt/KxSDlwqpzYICCoMmYBvqSFuneWzpaWyubbHhJR3pSclyEYqTLSmeVkxFi/0EpcOpRjDu6GgGdnkf02rokCZss8rbcE0HeRhqgL5ujjRzaKFfdk7+AjtzOzq6d6R927u0aHEKENLtNdBolNy+3QzQUlj4urZrY/vG1Lepz4nnJ/jwyIcUVtQaUEVFgakppc19X9sOQCWCp7ZCe9CByr6s77We9OJ0QreHYmduR943eST6/4r/OgPz/F7WPXK/zuXhhIcUTC3AVeZK23pteZ7/nC9OfmGYJZ/RMb91erSRsZFsvbhGUAeSSmHaNBxzhXr3VV0VxbxHT6Y8scHa1DAQ3d1/N9HJ0XomcI2Qgv4ZKijArnUwrSvkrwXQ3LJcPjzyIeturROMrHU1/i61nsV/GECLiqBlS3j//TeqGP1VlJfH8+zZeLRaIVWmUFzhyZMPsLDwoVOn/0z/Zw3+1gB6/vx5xowZg7e3N1ZWVjRs2JDx48eT/ZYWgmvXrtGxY0esrKxwcXFh0qRJlJX9Zy/QX4VMBna2EuTWlsjl0DzYj2cjnjF76Gw2hG9g7JVRXO13kF86HKC4h4YyqzKeHn1K7J1YXu4Wci8xxFBcUUxJRyW3NXfJtczl8+8+B1N4gsAKTmcQ2fQknU/0x1YgOJvUkHLEL/MxvSUojuxkOF1II4cePEeYVTj1EkaqAxnIVax51r8/DBvG8NAP4TZwF5QJlXz6aRI7d8IJndHBzp072bZtB3PmzCXqlPDwHD/emZkzBalMrdaab78VbqmuXS3hdwMJZfbhAkK2naHFdwaF8K0JwstldMvRaMUQEdIHO1dP2ri1IyopiiEnRnOmoRBAjw35g+86f0eAi3GqG2BMwBjmhsyld+PebLy7kR1xO5h3cR7b72/V778GaUUpfHVmCsXKfHg87x+mcUUiCa6uE/Dw+A4HB6GWZWcXilRq0O9MUaRQrioXGswrKymv5T6j/z9SKojLieNJ7lMjZmRrt86k68hMjeu2o74uGxx07BTt6wUxs9NMxjv3Ym2TrwhLhJ1tlyLtHi68vGq9lEwlpkwLnsbqwFlEykcj1oJ1UQWLo2Bjgq9exCH/YCo59CAjPYhqE2uy97+dILN56mbicuKo517JokXw0Udg19WOlxcLiX3xhNisFBSXFSjbq0g6sBE/tRU/d/uZ587P2dthL23G90c651ssZ83D9mYssofxmEdfITwB/vCBrWaPWWv3hA6pYKFrVR33yIeV3QT/TZtmBpHyrJIsunjqHFOK6pO9dy6TvH9kZqeZSCSWmJrWNTp3X99Io+XCwiiqql6iVhukO2uk4Y7FH2Nn3E7W3Vqnr1FWnD6OVqNBeeMy2cbdMAAs6QxbOpgjrYaeK36nk7mP/jtHS0fqWNaheu2PtPz1JHYV4FgKpXlZZJZmYiY1Q24hZ1X4KqYGT2Xh5YWsvbWWJEWSQEs+pDM4/e03iIvj0P65XNqxEKqrKRhoGGBcdofTjUBuLudFQANMXxYQIjc8HwqlgtU3V7P5rlAjv5x6mQp1hTAwq66mau5sePyY0Dv5HHt8hLt3j5FWlEa5qpzVN1azM24nn5/8nLTiND72HY5LMTTLFwvM8iVLBJmpgwffev9w4ADcvy+wzk+cENq4Cgrevv5bkJ0dSVbWFkpKBEZ3TduKtXVLJBLLP9v0b8ffGkC//fZbLl26xIABA1i7di1Dhgxh//79BAQEkJOTY7RubGwsYWFhKJVKVq1axbhx49i0aRODBg16y97/74ZYLObjyI859NMhDrcT+vAOqzex27UIeUkYd9zvcOvgLaYtNLiSFFAgeKTpMmQfH/uYn01+5nHyY45YPMRdHPnacQpNCrjeaDAqqZSW9vZoa5FkCrGjtEsEilfqqy5zW+r/9jcLwnHzZpDJMDM1wy/ZT+hH0XwG+AJ5+oFmlO6P73WWHiYmJiQk2JKXJ0hl3qpVEgkKAvr0geFC6nDYQzCpRbt9OtBgjTWu1ThMJaZ83C2cx7mPOfL0CLHZsRRUFBDlCc5l0Lvai3ld5+lHwrVRz6Yec7rMoZtXN/1ny68Z1IomBE7ARGyCjZmxiIKkuvwvpXHNzJzx9JyHg0NfpFI7PbkIoEJVQbOfmhHwcwBNNzQl6NZVvktKem0f3mu98d/oT9MNTfSfWZracAxv3G/cQKWTK+zq7kX7TPBccQbpsuUs7Pgddm060fOTHzizR4pn2ECBkZ2aComJRsdorrThiz6LePdSNhp3N5S6jJ5bXLI+4Nak8FNW53PZ6jKZGzIx9zT0PbZLbYdEJuHRvEfsE+3Df6M/n56YyIwZ4OkJtz1uo0nX8Dj4MY+DH6Mp1TAqZxQ+53pQMGo6ezvu5aNPPuLp+KeIpVLBM013DxAYCIcOEdrUuG8vLAnCRkCWNVgvWsnk6DJ6NOzBzVzhftNqtXTe1pn0knTMpebU+e0GKOVYxH9ISIMQ/X6cnITj2NqG4Ow8AmtrgSQjldpTXv6Ye/eCSEiYZHTs0AahpBQJxL/vor9jyeUlVFWUwqWLiNRqHNMLcC5DuJdrocwEVrZS0iIHrFQgu3ZHP/sbGzAWTbWasjPHEQMhyXB6J6w9LTKa6Q32G8yCSwv0PZ1RSVFCOuvWLSFL8+QJ+PtzdEky6yPzSLOBHjLDoLTbCOjQqAuFykL8YsZTKRXxbpETTlZOOFs5s/iKkLmokVtcfHkxIkQ0dWwKixZhulYgEYYmQbGmgsBjEfivb0ad7+vot63B9PHbyVwJUrVG0MMcqGMMDxok0KnfhNovhHffFWajw4a9ed0/QU1tW6GIQqvVUl0tpM0dHfv/2Wb/FvytAXT16tUkJCSwZMkSxowZw6JFizh27Bg5OTmsW2fsVTRjxgzq1KlDdHQ0H330EQsWLGDdunWcOnWKs2ff4m35/wBcZa4kT0rWLzewasbvq7sS4xlDi9QWTPt9Gi+cXpB1K4vi4mJMWhnEG5IUSVRVVxFbGMuhnBzkxwUVFJFUhBglwe2X4jPSF2dxa64cOsSDggIeSaVo5XKuSENYPjmLCXtDKKQVIpHwgo77NI71Z9bzDu+AE8yqnIU0wVA7uXv3Lr179wGSoGcVONfn7NlCCgrKuXzZUN8BUKmKjZbXrhVm4gqFwJcBBAWTLl2M1kv5dDhL3nd9jSEozhQT2SOSQdcGcfj7w8gT5dzw0N2ifn4EznZibvRc4wtcXg4jR0JmplF9dMw9GBUDZTPKCHAJIH9qPrnf5DKo6SCkYikbem2gWl3Cmawnb+y1fBPq1h1Gu3apRqPe6+nXKa0qJT4/nnJVOem5dzn9SlBWVavILa8ldSeV4WzrxeDwI+AoDCTulJSg1WpRmbXhx9O63/zHH9C0KdKiEhoWQoK3Ax+e/pjioJZoJRJOfNVHYITWzHg3bgSNhsorF8lo78dVN9BKpfp0KyIRheLWvAp5NzkdizvSsbgj5m7mtM9oT9PhTfXf/xr7qyCTB5x1OEu1qBpXhSuuCldKzUqJd4kH4InYFREiejXsQ2P7xoam/toDiowM2rUfjLnYDKnutINThH5Yp8a6gd2sWYzOc+dUwilsl9oini8moSCBx7mPefn1SzKe1CM0VODxODkJcQbAx2crwcEF+PsL74tWra4RHFxAmzaCl6dSmUxBwWmj/++a4FmDqKcnyPV0wkIF6tq8lL59BU3kIUPIbddcX1aoXyxcY9XZ0zS2F+r+P1xaRnazBjhUgEoMu6veJSAbeieaYLtsDT/MDSepMAmtVsu9LGFWNTQOzNfUsuSaO9fovCzVAkP7bj2wmQbW0yF7RoGeIVtpAlfctIT+8YiELxII8wojvTgdqVhKYmEiyYpk7mbdRYtwzOwDQnYm1gk61mqJdsosRqlW4lAG2w+DiRrEGnCr/airVAZ5NTD0Ob+KqCgKhtXqT05LE9LSr1gZ/hnU6mKKi28j0ohYfWsLq04KKfqmTQ9Qt+7gv7yfvwt/awDt2LHja5916tQJe3t7nj41kESKi4s5d+4cw4cPx9rakMMfMWIE1tbW7K/VeP7/IjzsPFjWbRl9fPowwH0C5Phzr8Twgnrm+oyorCjEZmKqtdXYW9gzN2Su/vuopChkMhm23Zxxn+mO3xE/Go9XYrJwKg49HKiIryCgSWdMTU3Zu+4ACRNW8r16Lu/0M6csQUo5DfD80hrrSdZ8tfErZs6cichchG1zoXb6aLCh99LMzIx+wRGYyE0gCGhVSVraYj7/PBKNpoqBA7cQFhbGmDHnEbw2YblusrdvnxArjbRmpVKIjKQwuBVXFn7E0jAzlrcs41TyWbp7dUdSKKE0rhRRvIgzU8/QM7YnE89MxK7cjpmHZ1JSa9o6b99Lvj87j4q7NwXx/MREYWa1fTscPEiTIlPmd5nPuf+PvfMOj6La3/hntmTTNtkljSSEJJTQQgudUDc0KSp2FFFUsKIoCoKCIEVREbDrRURAEKyIoLSE3mtoIYSEFtJ7z272/P44m90sCYhey733x/s8+2QzO3POmdmd+Z7zLe8bs5S3t7nw/tFAe7mLXqfHRe3C5B6TWThoIfdF3oeCQlbWfs6UlpJ7FXNRXUjOS0aj0ZNWlGavuayVfJG5iROFOWTUkIaqyZEKgKWI9IJk1sV/AljBXMiK5D2cyDzB1ydXcf8wK1YF2LfPno0JsNwvneXxy/n4zFfkRzZh8JpTeHy5gtTFNkKHr+XDVFdUyvZGGj4e5CPLZ+rVo0IXTI62B+XWQBq/0xhFK62Dpp6G8JnhaPQaNHo5kdLoNfQM68lj7R+z9333N9ITtCd/DwmsTc2MAAAgAElEQVTBjnv3WNgxrGr5HZ29vJlXTXPxdPNm0ZFFnMg8IWdTM5z1HXUxA3hv0EKWlbaha5Eso1kzegOqr1fZ97nveSlUUFjheHIn5iRSUFGATueQaMvMhHG2PC+VSmPLitba/ndBqzWi0wXj7i7vt8rKNEpK4ikvv8SlgktOmpzhudBz9X6CM2TG8C+N4e2eapLu7c/x/m0Q8+eT9+xY3tIfp+cFaVwisuHELR0o//FbLEeP4FUOAw7mEZQgqfDO9u+A+w8yc9u3oJJ7v0+k+YqNrDi+gnN58rvt49aC93Z7MXKpzBsovfUWTvVpBS+/zMUwR8Z5bLhMVurUwsS6sVsxuhkJ8Axgbr+56F30xIZDyL7TuF68Yo9zPtT2IRQUvjv1nf1aLj2yBFXyeSwK3H0PDL8XxtkWkRHZ4GKBuxM1PBgPgXgQWSFv6IL6Rh4fbpvg1/Qg/vILFBRwbtfPpO3aANnZknLt3Dl+CK+onWU/d64sUYuPlwQx5eVSsPbSJSmZVFgImZkIIUhPXwJU4bNO8PHpJL5MlLMlH59b+I+A+JtRVFQkXFxcxBNPPGHftnPnTqEoivjmm29q7d+zZ0/RoUOHOts6dOiQAMShQ4f+svH+2di5UwgZvLKKOOJEHHFiztQ5otHCRmJD0gbBdMSpzFMiOTdZuMx0Ee0+aSeaf9D8mu1VZFaIOOJE2tI0Ed0pWqxjnVjt+pP4hW0i93CxvY/cc7kCyYcgABETEyOuLL4i4ogTOww77O1VmavEtnrbxMPBDwumI3gap+MGDrQKIYS47z55HvfdJ4/r00f+P3/+9c8/8J1A2e50xPhfxtvHV9drtX61YDpiYWeqL5rzS6MRIjxcvq/+u3u38z4XLlxzLO0/iRLKx/3Fh5cvi8HHjomBR49ec98jaUcE0xFbU7aKJu81EePWjxNCCNFtUTfR5uM2Qvu6VnjPj5DntrCj+Dojw37s7O2zhWaWh/28a76Grhkv1DPdam2f8qzjHApdEBVqRIcxjs/f7K12Os+Di2cLq0pl/3/Q835i5PcjhRBCWEc+6HRdK0+nioJ9BWKry1ZRcrbkut/XsfRj9j5PZ50WTEesHbdW7Gm6V3xn2CyGDBsmWLvIvo/PqpeEy7vNBNMR8/fMF8LPz/n7aNvW3vbBwzHCc5ZGzNw209HhunX2fVXTal+vpUeXCiGEOHDA0WSbNtc9BSGEEElJk8T+/ZFi61at2LOnkYjbZnBq1/cl59/W0QBEmycR+y/vt+/z7u53BdMRUWPlPie+/VgwHTH8HsdxqZ6O91kGnRArVjj/PkEUaxD9P+8jPj34qVDPcP4eK/18BK/J/n48/aNoOL+h+OCNO0Wli0b0nNlIWK3WOs+vzFwmuj7qaOdixlmhm6kTcSlxosOnHYTvW76C6YiQd0NE5JNyH9MoxMX8i0I/Ry++O/Wd6P6EVgx6ALE4ShHZtw0Ql/VyHF+1VYnL3ipx8PIBwXREfqc29n6yXa9xb37xhRCKIqLfai6Yjtg+4S4hGjSovV+nTkJMner8O+nTR4gOHURq6r9EXBwiLg6xqbsci2YGYuNW71rn/0/Zgr89C3fBggWYzWbuvfde+7a0tDQAAmtIB1Wjfv36XLlypdb2/1ZER1dzgCrwa0965Pegxf0tSM5LZuDygXhSnwuHmhNuDCf7pWxejn6ZhOwErhTVfQ1c/GRmZM7POUw6MQl33PEr1+OKlWNRjgLpvWec4xQmk4nA0YE0X9ocS76F+CHxWCutHGx3EGuulQHuAyRbjR9wN9APmA4FVU9y9rVkYmPhuedg2bLq9uTfmBhIL05n1A+jKKks4al1T6HMUBi+ajivb3udtOI0+xiKr9QWbgZABwtvWYhfkR/n7zvPxMEaVtWllmSxSPegRuNwE9aUA5Oq1df4JqBfoxi0BUd5OjGR9bm5xCZv5tXYabX2S85Lpv2nMo7c58s+JOUmyQSL9ePYc3kPT3V8iqyXsqnwsZUj5B1kQ+ZlOn7WkS5LB7P49DqsHo0BGHsQRh4D9DK7M/HSJqqqyog5B5lvweTL4YyNGsvXflqsaoVUo4a2j8PaXV9wKNgxpo2hzolKHgu/YZ91Kdv5hTQG0Wd/Fm8+mMklj9GURDmLH2hbh+LVqJLo7Gjcm1w/CaNNQBuOPC6zwWdskyvJTrM6URrXhAdWqHnuXx+SO3AUwXpJ8JCTFktlYSKKoiFnyvNwlTwYJ06QdXoRFy++w8HUnRRbLM6lSYMH25V5igfvJH9SPrkTcyl7pYy2AW3t8byOHWWS54IFUu85Px+5mhk1Si5LZ82CwEA4K0UJwsNnERW1Hy+vLpSXJ3O6RvLYuoaQ6mDNw6yCTmMgOcgNH3cHM9GPZ2Ss8mh9sHh50uquJznyuZYDQY5jg2r8pDdOHSG9CAA1NG49LFCxdxfrz65niJsjs9iiwDcBOWBzHS+NX8rFgos0HP4Qqswsfp10/Jr1jq4aV9bPdxSChpxOZV3Rrfzy/FBWzU7kgy+zUaEwLGIYphSoUMPX8y4Q4h1C6gupDG8+nKHaSH5tCue9BD5rNhIXLtvql2Rlc5gVjVqL0dXIe7Nv5dwtXahS4Mt2dQ4HRo8mJdSbXaUJaFQaent8i8eoywz6pAciqMYFO3AAZs60/04EYNm/FQ4dwv0uWcuqzYM9WskYZREwYGsBz6x/5hod/724YQMqhKC8vPyGXtfC9u3bmTFjBvfeey99asTFymylBDqdrtYxrq6u9s//VxAdLYU5ln+jJuGShg6+jkSI4itBvP++vEkyLunpHdoHgM8Pf16LKLoaRpORrNVZ6Mv0dX4e+VOkPQHoyy+/5LXXXuPhhx8GwGeofEDkrs8l5ZUUSk9K95X/OX8ea2pz4bUCbN744SmNuDjnIub8HCLbHaUgKQchBLffn82k6fm0agXfnfrOngn78UHJYvNjwo9O7jLFqqD/UY43xS+Fw2GHOdD4AG5L3YhYGEGPJ2SHYrXgFt1QnhsEVd51K6mUjLy31jYxezZlkc0o/fXnOo6QMIWbqCzPglw5uTCnfs+cHbM4li6L/ZLLyrAKweQtk2sdm1eWx/oNH9jbSTYrlPv1x8ddFuV/c+QjDqUdYn/KL4iTu9GXVtE6Hd6O0/BBfIgUbVY0JGZL9/nmZeBXCnMWpTAkYgjJVWY29FERnGfhzgS4vdODzDbNthOV72gIuUEO957LsQ6UE4wVV84wiUm7IKNkGOdL7yL3BcmF66lPoTWT5MTjiy+o8lBxqdp9dvy4dKlVu9VqoG1AWxp6N+TrE1/TzC8Sf70/sRUF6L20xPg3wKjV8ssDMlXbPfMQ9YsELsbezKyeu8TEkL5UMh1RVUXFJzNISHqJX9Mq8NC60Smok/PF7dcP3Nxw2yFVPoxuRlw1rnbaRmGLYXq5mbmjwwWsVvj+7XOIDRvljO6NN2DqVEhPt4uDq1Qa1Go3fIvaQ5WU9wOY6QHdFoKLbT5yuD7sDZZGrlyYWZfoqB+tJmEf0fYB1EZ537S7ZGaMOZLP7mlClacjXffz90YzfEeWrJl86imniZxVpdA/wcyaM2sYmW1jlpo4kWcGw7wa87/vT3+PSlHRK7QXam+DPRxxLRj1fiwYI8vnxNKltH/vG+b+WELji0XcexI6FuqZ0eY5xiQbyW7XFD/fhoAMbyiKQr/HZOLQ632gVAux93WmdQb4l8D2xmqWHltKr9BerE76kdndq5h/Twizesrs/8t6sKjgYo1bNNYoL/I9rh0QKih1gQ3pO0lsX5vBDKDcDwpagcbGuWHYU4wuC9q8BHGDmhNTI4H3wwMfOmpuz5+/Ic7ivwI3bEC3bduGu7v7Db0SExNrHZ+QkMDw4cNp06YNixYtcvrMzSYdVFEHN2l5eTnu7tf/4YwfP55bb73V6bVy5crrHvNPQqWSscJqsfd2zRwk0Rx7iO3b5XOsaVM4vldm1VVnCNYFg8lRv1cMmDFTiIx3XGxxEd9hvsTGxjJy5EhGjRrF9OnTCbLNArVGR9LSpXdsxXhqUFvV3FXivHLRWDS0vtgatQU+cI3D/flTHI08SuaqTJ7efgdJLR5DpXJk/dXMhK2JxsbGzEmew61rb6XIrYhHnn6ECQ9P4I0xb9DxgY4EPR7EhFsnoA3Qcn7aeZ6b/BxN1T1Q7dtPlUZNxzHyQZfUsj5mFw0xwZsR/v5SMgzAYODDfl586JlA7rpvEda6Jx49G9pWjCemQMFJyD+GQNDu03Yk5F+h+f79LMvIsK/+az7Abj0Die/LuFmTek2Izc9HOTaenFIZGypOlokV3S/Cufcg/5WTxH8CXiUWvM9d4jaNH3eYlgDgq3Wuv+ztKflcj1bIp/ptqXrUKjVTek5hcNPBbBm1BbWrK57+Dlq/Uho6tVFCKEU0pwoPUrkDA4dYf3schUNt5R7HjvHOpUtE7d0LISFSZ7VtW/m6ine5utwDINGlGasyM4nNz6evwYDKtiJqHdCaV29ZwqxY2L1YTbcCR7bxydUrCQoJ4Vdbu9pTl5mXCD9ege4h0XamGztcXKBnT9jizPVbLaZcrUPJRx8RMrAlzTnNQ3MiKHrcVse8wEHy7xSry8+nwYBPCfxVzbFCd0aWwqsvgbEGOUKj8SPp2XE4O9IHY7FaeGv3W3QO7szaEVIqoYFXA5YNX4Yydqz9mGmaGMauOos65bzccNddPPr0Itx27LWPk2qt0SFDUFkFU2wVOtFJFTI7de5cXJ4ex+Egueqv1uzsGNTxd0mFWUc/zI8tVSiLF1PvqrXM08Ut8G0RRWRiHsG31ZZ6jIp00PLtCoEtrmmY2t8Brq5kdm3Du3vfJbcslxOZJ/ii6iBZj45AF1CfvQ1kEtiIqS25801Hxv9PtsqeRxKdRRZedd9HoQ76j3YkL1o7tOHUa2C4SrO71VseaCzB7LakMLjBnfS4qMBxYAV079ed/gNM3Boezvg77+SfwA3rgbZo0YIlS5bc0L71bcoG1bh06RIDBgzAaDSyfv16PK6SGap23Va7cmsiLS3N/rC/FhYsWECUTf/xvwVNHRSzsjRqVhloyqDcQDHyOQYyaS04IpiMkgxejXuV19Z+yq5HdtGlhWMWZ+hlADXscfFnWllTtHhjvtuMq5srpStKGa0ejdVq5Zln6nZ79CzryQ43R83dgMkDWP7ecvwf8ydrXxYDjgyg79cmhm0dCkhyiKBCB53bwrcWsuM2efys7bOIS3F2m+ZOzOW2r28jYnUE0x+fTr0h9Tix5gSllJKpz+S9Qe8xcfNE+ob3Ra1ySCnpgnWYM2Riz8y3ZhJ/uJzI9Bw2uVuZ1O9ZFp9YjpsFirUZxEzrxKbHd6EuKmZX1mHGrezHLeHw4h5IObCJ8C4DuRoeLvJ3+HosPDLvGXo8Audtc5kWm/4Ffr3ZeCmZOTN20cCvCaG7TnAs5xRRn0UxMAnUApLfg4zTA3n5pRf5ZHU687tBgp+jj4FJtboFYHVmJpV338GmLToOfiIN/ISXnmfe2/Px/uhzMhfIFalZBdEXrFBZKQ0L0pCkPXoc7WsRZL3UjbK3Q8mmFx6uX5O+dgj6AZ6cF6MQaEBlocLqTxA/saNNOy4MGsTnYWGUffMNVpWKrGoffE0cOABeXrLeb9cuCAmhY4NeLDm6BGGIYoQt7fWhCGfV9UmH8vHcC1DF47EnyfF0J2xcKcXbvwJDO+6d8izHvLcTuN1Cr0pYfAQ+mOdTu3+QRnzmTKfz7hXaC7WiJjYllsa7TsH48QCcRiYIeeVcVT705psy43P8eHYmxdEtNhF1RSXqPc154/szmGpUAQmfehxdGYQuyIJh/EpaAX7vhXC58DIjW4+09x0THiPdqJMnw5NPwjPPyFXmp5/KZBiQRrtLF1nTWRNz5siZ8zpZ3lL+OuisG+EFWZ89f+B8ZvSZgYeLB5cK5GS2LuKQ68EUbuJXo/OEcVF7GFIZyqjP9jk2XpUZD6BWqSmaXETY/FAGjMqFwkvEDP4QMpfg+usjcOoIOy46nhNt67clfXc6seHw+CFIOZDKfUY5iX23K5w3QOkscLNsId9Xj9XTg3oPp/NtS0mkUayzUKkCFyuoDsUTVSPXbvuv0OEJ0B0vofFLgoqqCkw9RvLk5O8oCfan3iNyQhIV6EO+Dqb9DFf5Mf4W3PAKNCAggFGjRt3Qy6uGaHFOTg4DBgzAbDazYcMGAgJqy3BFRkai0Wg4cMCZ1LiyspKjR4/Srt21HO3/vZg48SrdZIsrlBtZvtw5xhEbCyvvdKymqzwvcc/SJ6iwOFbrGi8NpaOb8HlZCBa0TPp0MpZWFoobFWONsGK1rcCadmrKicwTdrmjaqhd1bTd3BZvkzdLXluCWWMm00v+QBMGJ/BGqzfsxhNgZ/OdTse3SW4jgxfA1Lip5JXn8cEtHxATHsNPt/6Ee747rzd8nQc2P0DG7Aysp61UHq3EqliZcfcM7mp5lzSi3Z0l5FqubIkhxrE6y9ucR9bPZRjdjPRvdStVaii2ef3jsg+w+vS3YDRyy3cydX5HqIwrHV3xLmeya9PJAcTeuZap2yG4CGbGAs1t4tn5R6DsCpU/L6HnBUH4wSQyPn6XvZtW0zZD4e5kR7ghYNMmHvnmfcYehoeOAgIiM6B1Ogx3JKxSVc8oV0etWuGyejWe5WbWZj5G6CXpLcgb+TAXQ0Jgzhz8bG6s87f4oJSUUPHlPEdD586hXfwWSpXgXMv9JPO4/F5GVdG4S08823qQhQnqZUEnWRd8vFsVu9u1YG9pKfkDBuCWkcHUGsZzd7t2xLdubTdWFBXJrMjZsnQq07szhNxP/XpBVH/ZMQbnlbPnU+Pt7++LiyM2qiPFHl6QsQmqKuih3klhVwu6HHjFds2nbbGQWFpKytVhmpgYWW9Y45ngpfOiY1BHVp9aXasusxopj75AlZs7VlcdZ7rYZqkLF9JjXTzqMmngmuxKkJR0NaDMeQOvRkPIy49DuLig6HT2Vbcp3ISXzosFgxYwvqvtHBUFjEbHTVwzdLVjB1TXY69YIePyw4dLY9u5s537U1dt52wrc7VKjdFNClU3MjZitmk2Y6LG1Hme10KbgDb8q5+BdU1hwX1hmOe+QdG4sfj0r3G9hgyBbt3qPN7TxZNAL8eCpVdoL9DrWTBwATq1c4gtt0z6VLc1UuFXCpPWF3DnV4cxu2h4K8aFyDwtbm9LUgzv7CKM59PZ/xmgOO7b+NDaYbuEL5/AqoOiNq5UVUGqWt4MrboMw6UKjBczWdPgJQDeSvuWzzrCuetrcfxl+EuTiEpKShg8eDBpaWmsX7+extUutqvg7e1Nv379WL58OcU14i/Lli2jpKTkv5ZM4XqoV0/mSqxZAx4ecsU5bhw88AC0siXM+PpKWkxrVgR85YjFXHRdz1PrnnJqb4tXA86hp0sX8Iys4fKu9uy5QM/vetL649Z2uaOaMMYYWTBuAV8qkqyh6jbpPrTkWND1dPzIq5qo2dV8F0WuRWiba0msn0j9gvoE5TluOjeNG49FPcbmUZtpsbQFhzsfhn6gWBSKDhZxsO1BLLkWDs86TEDbAAL1gYzpMIYuDZxl1twj3Gm3uR3B4xzZMwkPJ5C9Jpu+4X25Gvd/fz8bz22085N+/sAqToS5Y968keYfNmfHhR21jumb6nAfNilz48MeT0LgUMjeBQceImr7CvvngeOn8ORDb3L0Y4FfbgU5bo52Xl0lY63Pl7Xh6f1w/GOI/wRaZ0J60yAICECdkSkzr0wm+Okn8rz7ID66i2IaQdOm9Pb359dq14MNuffIVYxu7BQKl02RlE9NmuDximSXKS9yUM3d9sYbtD50lKxucmDqzueg+24w5uI5czXfGT7kVGkpDTQazGrHSj85JITo+fNp99575F52Fleuji0lVir4NBrOMtVj9EV6GBq71bgANWs9be4V1379wNAW0tfjljiH1iRQ0BqqHF1juZJJs/37abRvH9k1Sn9o317WQ11FFxcTHsPOM5sdG2x5E2X1ginFjfDP30VdVoqqvIJRy2u79Yqvxft/330YjSYn+bphEcMwuBqIbiiJM57p/Azt6l81me971e+wfQ3SkqAgGDFCruK//14WSavVDqq+avS8igsX6Taf0nMK4cbwawy4bqgUFe1bxjD0AcgZMxLtxJd5fvSnuAy9zbHTTz/JxLtroJq5S6vS2t3HwV7B7HzEMXEO9Q5l7q65ACx/JxmrznFh94aqydBWsqKFmcz7nCc6na5IYiKvctCbVUzr5vwcOvzQQNpfWgK6NtClC+4WaJQHXYK7oFKp7fWnt87+lgl7HIuN/ff35p/AX2pAH3jgAQ4cOMBdd93FyZMnWb58uf21pgbNG8Ds2bPJzc2ld+/efPLJJ7z66quMGzeOgQMHMmDAgL9ymP8obr0V0tIkmcc82yLj0CHp1j1wQOZ1T58OnB0Mb+TT0iqLh1efcq6NXZ42hU6PL+L8XfV5cdOL9A7tzf2t74eu4DrTFaY497v3cm32kJXH5Ur3gdYP8PTCp2n8jmPCo2ugIzo3mr4no1ny6Xf0vNSTroe7cvfhu0ENu1rsouDlAjs/qU4jH2y5G3KpuFy37ua4Z8ax/eHflgJrMr8J0bkO9p/8Hfn4uvtS+HIhhS8XUv6KY/Y/cLl01X5z9zfc0+oeEtoEcs8pmLDLkQQCUFBewJT5Q2HQIIS/P2XTptA1qYzHIhrzWVIlVGaDsGA6W0JsB+eQRDVaPQXGSbAlXBaam1WgOxzPB7847xewZjMkJdkfWpbILpxmMhlI91wag0no+gN93bzYbAtFbHn3XZYc+oKyGqHNqm0bnZJRKo3A0faoPK2wdigX4/1YxyB0oTI+V9KrAc8N7QdfPQBqK67FcmAlbm7sbdkSs78/H8fH02LRIjSKggC2AquTklh06hR5L78MGzaw9dlnicvL42XjeTRUMY2ZpLURzhmhcXEIlULGgXck9ykw5J57eK6pnBSVZW5nED9z3vdu9jXyI1OvIn/aNLR796KzGU6/3bvRbtvGR6mp0tD06VPLgPZo2INutlC9Zcc2WTOYm0vpqfM01zkTfez7HPY0gEwft2oHCTtDoEwDB6PqS5eqi4uMT3p5OcnXlZdfsst6XTd5JyjIRoSdJ2/aXbukoezfvxZTlB0ajXTzBgbKWbNX3clxfxTVbt+YRjXcvzExMlW5uFgmYVwHz3d9ntyJuRROdiZK6RjUkYKXCyiaXERMuCRqaOXXigDfUIiOxmxr9peQCrvebPC/mpGTniL7niXVAu6a9wuXX0ylaYM2/BIB3i/L+8g4CTqGbqDcUk6BcRr+T32PRQUvV3Ri+2jbvbtli2QzSknhqX2CbhdBg5rcfc5C338X/lIDeuzYMRRFYfHixbXcvM8//7zTvu3bt2fz5s24ubnxwgsvsGjRIh577DG+vR7X4v8I9HpwdQWtbTGk00nvUFiYFGVYZasv/2a5N+/0XwhlBkoqSzidJWfKZy/nkNnsDQ4EjiGjRCZNmMJNDG4i3UvlVQ4D0zdMzphjU2KxCivJeclklmSSXpxuJ3GYN2AeGrWGoCeCcG8lHx7G/ka0Ri0qFxXBvl4YfA2o3dQYA43oO+op+K4AtzI3Pmr2EVPCpbXO35lP6WmHjFXzL5sTPC4Yz/aeNFnQBJ2Xzi61dD0oagWtUUv7PXJ2X7BT8rfqdXqZQZivsP2O7YRkhRCQL0MEtzSRhdZ9H5U37TubYHuyfBhbhZXPtr3LU6/JVb3SoAFud8qHvktpBWPe3oh/sZwld7wCu7p2ouvzLdgcDvuC4WhYIMcnT2bSne9S7u3NrzZxjax7r1JnadcOXnwRpXlzqEEQkuPamwwGkI7kNU3lTtKXZaFZlc+6Ll2Zc//9DGvRgkcLQ/iZIfz4oUwW0sWepGqF9BDktHMhbcGLuJ6+A2NfX/CUxA6uVKBqfwju/4onW2s5rookPeA+e98DXS9gII+TLzyFduFCosPDqXRxoae3N03c3FiZmcnkrCxm5KTxfmvZb5/336ewqIgojtjbSYg3UVwcT3HeESoO/AqrVlHSTMu5ynmU3N+DqhmvQJMwJnZ6kCC99E4cywetezRTTa58MbozkyIjcTWb6XbSkTliEYKnz54lx2wmNToa6+7d0tjYknBiArvzUnIAme7wrddlaQDLyvDxrGCuSdai/CsKu3eg22X4sWFZdWUIg87ByUeH4Tp9lpy1RkeDnwxa15Svu3BhtpOs13Wh18t4sdEIbm4yJvraazXouOqAv780sjt3yvMrvkZJ1x/AvZH38krPV+jeoBtlZTWMuLe3dHf9BhRFsWc+Xw0vnSSsr+neBlBNncae6Y9xeOwwlrSTK0YAi9XCRye/AW9vzI/cTfGbY7CaeqD3CWLl3aswhfWmSX14uf8D5LtBdWHltgu7yHMRHAyEIUdLcSkqJSE7gYtpZ+yr0Eb58MF6eLbxCMYdqDXUvwd/a9Xpn4z/RiKF34uxY2Vt8ZNPyv8tFiE8Gx23F3fnl+WLFz//tlbB+Z5Le0RqYarTtt5f9BZCCHHnqjtFj8U9xPJjy4XmdY0IXxAuwheE20kcaqIyr1Js128Xmd9lXnOM5yafq0WCUHzCQeJwoN0BkfB4wp9yPVI/TRVxqjhhzjfbtx3ueVjsCt5l7y/g9QDHAWVl9gLtno+7iHJzuXhr51tiZ0iNYu6FC4WoqqpV5D10hPzbZvF8weuugneaCs83vEWTXVvFE2fOCCGE6HJgr2g33ktYNGohjh1zHL9q1TXPIWFMgn2se4M2OV23CW8dEMTF1Xq9/0I/e9tX7vUScSPGiJ31t4utuq3i4vyL4qsdUfai8+pX9bGHCgtFWdl5+/bvtgaJ06cfFkIIUWW1itDdu8W8ixfF2IQE+zGj4x4UP272dhAzvPOO2LW7odizJ9ypj0t3Oq7Xhfsc2/fsaSwuXHhLbN/uJU6m/pU0/ZcAACAASURBVHLV71MlWPGiULZsEZne3mLDU0+JYfHxtc651eLFknggNFSIajKVoUOFALGqpWxr49kNQjRsKIS3HGuFGuE1u56YEXCrg1TAC2FVFMd38+GHQpjNQnh5CTFzptN3k5g4TsTFIY4eHfin/F6viyVLhFAUIUJDhXj88T+9+fT05WLrVo0oL0/709tOK0oTbrPcxMakjU7brVaraPJeE/HGjjeEzxN3CaYjvEc/IIQQYts2DxEXhzh58j77/llZP4m4OERRcaL999F4YWPR9uO24tuT34pZPeV3Vu7vI5iOWNkKYekQJYRWaydTOb7yPXFIBub/94kUbuL3oZqyrPqvWg2m1g5WgR0Xd/DrmViwSpfJvAHzKHi5gK4NuhKkD6Lw5ULyJuWROzGXTQ9KjlBTuImdF3cy8oeRWKwWUvJTSMlPob5nfbu0VjW0Bi3dUrvhO9yXa8G7Z+00+wORjilh+z3tafp+01r7/BEYTAawSjcugKXQQsHuAipTHfGzHZU7ODfJRoHn6gq5uVS5uxGdVMmbO99k4uaJRNvcgJNjYGEnK6hUfBg7l3ZPOwJ0Dx5XuOAN8ReeB2s5Hw35mCvPX6KfbyCxeXkUFFZgeqWMx0bsQ8nJkaUgJSXSnXdP3TydVz69Qtq/0lA0ck0UPq+10+dDJxYzKU9eazWgsblJV0Q5qMuulHWDlfdjTq9CVAj0fbwZL95hY/AhmnXOYChrGYR01x6IiiJKr3fSTKwnrtg5YVWKwsnOnXmuQQOi9I7VVicO4K0u4OPDq8nx9uaXF19Ee/oirQ7eSu/BOrqMgMC10OA7x9gLapxKefk5kpMnUlVVSGbi1bRrVjBEIVQqkrt2pf/Ro3zXqhW50dFc7tYNre2cT4aFUeTmhseFCzKukZUFP8tYc6ptqM8uGCiJ9QukV6LAV0/qixfo8/X3GMllW1RDQgrB2rYN5UV5WDt3hqeflu6ewsJaJTtSvm4qeXkbSEl5jT8bM2faVcpk30JI2jv7xj8P8ju2OGln/lmo71mfjBcz6N+4v9N2RVE49sQxXur+EjmfrYR9z1BQL5Zz517BapVekszMr8nIkLST+fmx6HSheLg3oXhyMQUvF/Ba79c4lnGMu765i5RW0nuhy8xBa4EB50B15KhMhNJowGIh8sdd/FO4aUD/wzFkiMyYv6XGMyjGpKD+USa3LNr/Faeta2lW/iBTekxhdLvRTqojep0eg6sBo5vRXm93tSh1NUzhpjqZTjR6zXUV340xRgx9DHV+FvlTJGpXNSrtn/NTc2vshq6hjvzYfMmVuSQdrlIPS52VyqW3LlGZYTOqRiOqPn2454ya71ZNJyJbbs5s0ITP27ozfuPz5JTm8PX5tdTr1ItFtrrae04IYsOxM8M82rQ3ep0ek8FAYlkZ/1p9lgEboctywM32RHd3l+68q2DON1McX0ziE7JGutGbjQifE47f3f6ETg2l9c8O6zP0lRLmNmrEB02b8mNkJNNCQ3naNIJT97uTYYKinxxk3HkGmOORSVaVwiC/RgS6+1OCJxU2nuIONYxiq1YOa1dZmUZpqcxM9lCrqSg7yx2eGYw15DA7WEcz5DijdLFoAqTbr/UU0I9biFJWgVs6NKvB3pPeH8x9o2jUaC5qdW2354yWEBUo47sGzxBwC6SeRkOLoUNR9uxBu3cvxtxcgnU6unl5Ua+ggMiyMnQ1+Ynfe8/+9vY+j9MsC0Yfce7n4MdT8XTxpEcvNap6RlIayIQYdb/+uHoaUF2dsNPJUfyQnAxCqPHxka74Cxdep6pKhiCEEJSVnePfQUkJvP56jdMICXHUs50/75yI9W9CCEFenkPF5K/Atdzb7lp3Ll9Sy0n92SG4eqdx6ZKzusvp0yOorMwgLy8Wo1E+dzxcPHDXulPf05FzkNO9HebuMkHo4aNQrxwUq1VKvVUT/K9a5Vhh/M24aUD/w+HhIXMdanJJmExQdXQE/f0fYs25r6nyvMQtTQcxO2Y2RjfjtRuzoZmPQ7sw0j+SSP9IvHXeDIsYdp2jrg2Vi4o2G9ug9dcS8VkE3j3kijTgoQB8h1175fpHoCgKRpORvNg80j5PI+k5WWhZ3bf/CIcuZP5WB12bYoqh/eUq4j+BMx+AUBRSDF8yOlbWxvq+7cvOizsxhZs4NXE0SQ3kBd9iS4I0eEfgopar/D42A5m8UVri4vfTSRp/jYJPG/ZH7OdgW4fUXP3R9QmdHIqiVgh/PRyfIT40/VA+TFUFVUxs2JAngoMZ4uPDjPBwHggMZPtzt7HlKQcl3NkmsLcrvJ0qM2e72JJRRtpKxXp7eztNfPz87iAkZBIeHpEoitb+YC0qOsr+/c04eTiKEfl30T21OyqsZClBlGV+QlaMJJJwdVYgtCNlRX8SpoC3fz8aNpxI9+4OSjlFkZO2+9o+waGxh+jZsCcDmgzGRVHYFxWF18CBchUWHQ22+vGhPj6smT2b+GeewcVisScAVSehAIR/8QMJH8LE3ZL9plQD/R+EqP6SuVylkgmya9MelbHIITYdzZoz0aZN7YkHWVnQvLkkMtLrHTXlBQW7AcjJ+Yl9+yKcY4q/Ezt3ShKo7duloIk82aHSc6FS/bZA9e9AWdlZKitTcXNrZjekfyfi4mSlT8KGnrTWO8xMp06n7O93765PSUk8BoNjQj81dioDljuSRoe3uZd+6jUUa2HefgMVLmoyqslffvjBUTDf6Z+oAv0dRAo38Z+DVq1k3sOmZW3Axg8wdkDtso5rQVEUSqaUYK4y4+HigbnKjMVqcVKz/71QaVV0OdcFtbua+g/Vp6qkCrVe/dsH/gEYTAbSl6ST/Z00YFp/rb1vRaWQuTITRaOQF5uH/73SoFp79SWRF/HiFCmMwSwMcKKSYfWH8Z76PXuiVe/Q3nRt0BVleCW8/yEfvX2Kd+r74+niSL7ws9VKtq+x+sn+PpuID52JBaphNVsxZzlWUt2udENbT1trv6Ang1BcFBLHJFJxpQJdkHMSikfIXJatOcMkYNK3Lqwf2IH6exyZpzpbduUXzZrxXpMmeKprX//w8FmEhb1GfPwAzp59mrNnn65zzDpdKC0MfcjO+JLLd4O6DMKX2D5MTITFiyVRwa5duIafhjObMBpt9YxqV3r0KAIEKpWOqqoSNBpp3Dc+uBG1oqZcKOg1GpklVxNXrvCCjw+qY8dQKisRGg2KxeK8j0bjYPYBTjZw4Z7bKinWQYCno87cZIKnnw5h0pNZVK7RE3kODh+O4YO8fBRhdZqVxsVJo7ZhAzz0kJoePYrYuzeM+HhnF+W+fY3p1i0Vne765C41YbEUcPbsM+zYMR9XVy+mTx/Mrl1byMp6GWvUXO6dbYHevaUBffTRG273esjLi0VRNISGvkJCwijKys7j5hb2p7R9LVgs8MQTMGmSPJX27aFZIw+6uAdSUJFN205HaP7ZAB5v/Rg9NA42OqPR8exad9ZRrnf2mbP4a5sw+kosO0LhlqR89gS15JT/KR7Js61Eg4Ph8OGbBvQmbhyKInUQsw6NgYY76NusEy0a+v32gTXgrnUH2zO8OuX834XGU7ajuCioXP4654ahr1wB5v4qC7nbbGhj79v3Tl/KksswZ5rJj3WsQIvMjUhniD3ztRqWdAu3aW9jVdUqhjQdQreQbvJ6PPMsNGiIV+MW1CwysBRaKD9fzvqCcNySUnB9LQjzvAws+RaslVbM2WbMOWY8Ij0wZ5tRuajI+VnWcmrqaQibFoYusO7sTEVR8B3mSyKJ5MflE/CAM+lIX6MfJw6f41wjaB/pg4+njrhO7Zh+/jxTw8Ls+2lUKozXKFVQqTSABr2+CwUFzoQYXl5dKSo6jBCVGI0mwsPnUFWZhhBmDDNegPzP5YOqaVNJCuDqCl274lvVkrKyZAyGPo4xaDxr9OmoEazO7LRPHxRFuuBmz5b8lXFxqAMCJAMRoJhMWE6fRnPpkmOgjzwCn30m3/frR/jciXQ5MZfnujiLZVd79d76WH/Vdm86dQKlRNZau7pSQzReLog1Gk90ukAslqvYhIDLl+fTuHHdNJXVyM+XodmmTaGw8BcyMpaTm9uXiRMFHTpIikI/vzeZPn0Effq3IcBkgi+/lJ1fJ1xyo8jP34Je3xkfn6GAQn5+HFZrF9RqPa6udXPR/rs4eFDSk7q6prJpUz1GjpSp0F3rCw7kCH7Y/haXCy8zddcitg96nKqyT3Fza4ZOJ+u8z+eft0u8ARxJP4I6ORhr5DIOp7txS1IZa/KGsO62U9x2BnzLoFy4oDz9AjRoUOeY/mrcNKD/pRg9GiZM0KP9/gdiK397//8luDZwxS3CjbLEMlquaom+neMBqTVoaTS7EVnfZ5G2KI3yi+W4NnQlf2tBnW0pWoVh2cPYFbSLn0b8hEqxGZ6ICEkXdRUOdzlMaUIp1cU37R5tiPnWQA51OETh3kKO9paajk0/akr6l+lUXKygMk1+Qd0zuqPSXH9i4RLggkekB3mxebUMaLBOR+ejCnHRApNRuup7GAxs/gNMXT4+t3D5soPdqEGD8TRpMh+zOZ+9exvi4zMUna4+bdvWSG75wcFGRXCwLNUAtCoDjRrN/t1jsOOee+SrTRtpwQICZJmHRgPDhqFp0oRDO3fSOiEBF5BJAT/+KF26Y8bQHNgc1b9WsxF1OwSopk319ZXzgNdek902awZnzkiB7pYtoX790Zw7N8F+XFmZO25upZSW1ub6rqvvrCy4/XZ4801pnQcNehEvL2ex9enT2xIRkUXBNyapk1nd+b8BIazk5cURHPwkWq0RT88ozp2bgMUi++7Vq9KumfpnIjYWFMVKnz6dKC8fjck0G7M5jyB9Ol+lWTl0aZN9314rN7F4gBu9QmTYqLKqkvCFMl6yY/QOHv3pUWJTYtm4bymukT8z/mc1FlSsL3uA4vKv8C27QoIP+G7Yjt5aDB7/jCm7GQP9L8Xzz8u67cLC3973fxHGGGlAqlejV8PQ2wAK5MfJVWhebJ498zVyVWOi86LpWdoTry5etE1pS8LTCQ7jeQ0IIShNKHXa5hriimdbTzRGDakfpdq3n33qLEX7iuzGE/hN42kfu8lA+uJ0dvntIm9Lnr3v+EHx+KQLjrSHvnUkKv0eGI0x9OiRT3R0LtHRuTRu/A4AWq2Bbt1S8fUd/m+1/4dgMknX8BtvyPeJiVLJZMEClixfTtdffpFizWFhrN+3j7n9axvNmlAUmbgTGlo38U52tiQpURSpejZligyJVq9Gg4Of55FHchk2LJehQ/MYOrSQr756mdzcbQhRVbtBG8xmh4rbjz9CTk4sFovGyXgOG+aQFlm1qiGXw1o5d25DYeE+kpIm8HtQUnIciyXHHls0Gk124wlw4EBrrNa6yU3+HcTGQqNGx/H1TWPkyDm0bLmMgoLtKIqVw1kuZJanMr33dNzMQWBM5olDZUzYm0xZmaDT7fvt7XQO7owpzMQnhz4hWfsz3S6BR1UVGqzc2iqFey43okqBmb3B15yFrqoMsXvPdUb21+GmAf0vRTUVp2vtWuf/Fwh+JpjG8xrj4lc3N5vWR4tnO0/yYvOoKq+icFchDV9uSMNXGlJveDBagxa1mxqDyUB+XD7umusr/gCUnpLGU+Whwivai1bfy3IiRa1g6GMga1XWNY9tv7P9NT+7GtWTA3O2mWP9jmHOM5OzNoe8jfIhePftYfY47L8DjcYbrdaIVmtEUdQ1tuuvm3X9l6FmSUnfvjKDTqUCrZZeAQEcUanYYDaTWlHBO/n5zLh4kcprKO1Uw90d3n1XeomrF6518KgDkta2WzeHDfv5Z4WUFCOzZhnp2tVA165q9u4dihAFXLmykqSkCwCUlZ2zS6yBpKqrRkDABSorz/HLL4/Yt4WH76VHDyOXL0uGFFfXMg6c/Imydo7OrVYLxcXxnD8/k8uX36W8/CqKxesgLy8WlcoVLy/Jd2s0OmeolpWdIS3tC6cx/7soL4d9+yqZNm2JfVtKyijy8mJxdQ3HnN0LgCFNh2E91w+ASiusSfqeNz9NIb5InveEiE+5csnFqVJgyAWHh2nWyeE8fsXKYfcQDrdqg9n2O1V21qbp/Dtw04DexH8lPFp6EPLC9WM5BpOB/Nh8CvcUYi234neXH41mNXIqqTGajFhyLRTH/zYTTF5sHopWITozmqidUfgNd8SdqyXlvHt402KFQ8pLU09D8yXN8Y6+cUkq717O++6qt4sTt50ApMt5fKuwG27rvwq9ejneX1WfWb3iHhQfT4M9e9hdUECZ1cq+G3DB3HGHfM2ZIysf4uIk2+DVnm9fX9nt1q2Ske82G33smDGwebPc5u8vk1XOnn2Qy5fDyM4+zb59EWRn/wDAL7/AyJHyuKQkaNcuDqtVYdmyVykv96ZFi5WEhnax7XePvWTmxImDzD1goip2K1RVcf78VA4ebEturkyq+T21nPn5sXh5RaNWy9m1cO9CMR68zlQU1xa28T9JVtbq6zXzu7B3L4wdO46GDReg0zlqjrOyvsNgMNHddxhKYQNIb0dF/FCocGQWvL4sFsJj4fTtfP/KWFq0gGCzI7FobEFTKkIddeSNTu4mtmQEl0/2Z1tDF44oNz45/bNx04DexP8sjCYjFZcrSPssDY2PBo/WtWnMvLp6oXJVkb4knT0he0iefO0yhfzYfLy6eaF2r53dancpxxgIGBEgXcQlPel6oSsBo2orEF0PWoOWHoU9iPwpstZnPQp7/K62/qtgMMiYRGFhrexc36tW3BVCoFEUYvPznbafKinh8TNnsP7G6urLL+VD30alS6nNM28ySR6MGiWnTiVkffo4j+PEiZaAldzcDZSUnCI7+3EURa6KGzeGqKhYkpLa4+0dQu/el/D3dxZ/b9XqO1JSxtKkSSxbMKEuyMPSLoJLyW867XejtZxms4UrV7axerWJaoGbncUW7mE1cfTlYKCDg/zUqfsoKjpyjZZuHKdOSYdBnz6SdtXbuzudO8s4cWVlKkajiSn9nkG8n0Cnjio4dRepEy7T/LtSSGsPTddBgz20cDORkiJXs9HtfWFOIVlnx6I/ehjd5AmUxDrk2M4H96D4uImhIyt4fsCSf/sc/ihuGtCb+J+Fd09vFI1C5teZGPsaUVS13ZIqnQrvHt6kLkyl4nIFF9+8iKXIUmu/svNl5G7MxWiqu87Wvbk7Ya+HEfio1LbVGrSo3dVoPK9PQnEtaPQa6t1SD+NAR39tt7RF7frXlAb9x0Cvl6868HPr1nS31br6abUMqVePH7KyyLJl7JZUVTHnwgU+S0tjTXZ2reMzKysptJXE6HTypdc7KGxByni6uzvcsFdpemMywbhxOzh82HmFnJ0dS3r6F4SEfEZ4+Al27oSKilT69VtHTo6JtWvBza22a1yl0hIQMITAwPOkhchz05xIxn8zqEsgf/sg9n9+D9lZW27I5bpv32p0uiJ2fxPJV+tzSC4rY39SEpoSASjEFpQRFeWIN54+PfI32/wtPPkkhIScwd29ALXai8aN38HdvSnu7jIZymDoKw2nuXoCqxDko2fNt26EWgZAix9BU8ltbZyvacfKBHy/smVbm0x49OkEEybAgw+iGzYALvTErFVj7rKS6bz6b5/HH8FNA3oT/7PQ6DXoO8uHcbWLtS7U1BwFKNjhnLFrrbSyL3wf1lLrNdtRFIWwqWG4hvx5QWmVRkWbdW1wCXKh6QdNr2m8/79giI8Pu6KiGFyvHkN8fOhnNHKspAT/3ZLs4Lbjx/nKVh96x8mT7LhqdTowPp7nkq5PeOHi4lAXmzu3lieZTp0gJaUHEyZs4cQJ6Q0oKjJgNieRni7p6WbPjqV7dyt79jRApcpl7FgTzZ0ZMp3QuXMvqqpUzJ0/nJIA+UhuMRd6DoXbX/uVictXU//rS7/JhJST8wsWywNghRUpj5Pxw3M03rePEaNG8cvnnzMnPJztBQW4eXagadMPAbBY8q/b5o2gqKiYpUubo1ZX0b79dnuNrI/PMPT6juh0gWg0DplGmw46ERHw2WR5gQM8Anh4cEu0WulKDyKVAzhIQ2jSRCZ+vPMOLF3KoNt0uKn1NKvXkt2qN1nb9c9jcfo9uGlAb+J/GtVGp9rFer19wmaE4RLkQl6sI2OxqryK/S0dM3avLn+u9NRvQVErdEnsQtCTN164/7+O7yMj+TQiwl7KA/DupUtsucpgbi9wTIQyKis5WlzMhtzc31zJVRvNutjhXFxkqNbLC0aP3kKrVrm89toZrFYFs/kyFouG0NBYSkqO24/x9q6t91kTvr4G9PoO+PikcHBp3UlRhkNw4EDdbtxii4Vnj6/l+PHBNPwKGq6AoKp0XvnqK0TfvkSePUv73bsxGQwUV1XxcWwR//rXk0RE/IvKyitUVFy57vjqws6dkjAhK6uYadMcmqUeHg5KyvDwWbRr55AQrJZpfOcdRzs9GvZAq9JiCjfRrJlCTg5cuQKJn9SI+ZaU1KqNHTRIitiE1bPVf7b56nefw5+Bmwb0Jv6nETgmkLCZYbg1vbZsmr6DntCpoQQ9HoSxn5GcNTkUxxdTHF9M2r/SKD8nWYoiPo34SwkirgW1h7pO9/P/V+hUKlxUKlq4uzPaRv834ZxcnTVydWVNpIwd/5idTXZlJWdLS/k8LQ2AtMpKzpSW1t2wDaNGwbRpztrYNTFlilQs8/Bwwc/PSFiYP0lJMiPp119HY7FsIzdXimY3bjzPiVTiWvD1ldZauMDueY79i5FuT12iC3GxW+o8dlNeHo1zXkVVCaFLodHntfdxz8jAf28qepWad7fmM2uWgsUiE5hOnfqcqqrrZzNfjY8/hrfego0b12IwSHd58+bLKLBUEV9czIniYhRFjVrtuO+qZRprEmS5a91575b3mNBNluroM8+h1YLHPttk4fvvnYPQNaDXwydDP0Hhn7s3bhrQm/ifhmtDV8JeDbtuHLKaj9YlwAWjyUhZUhkH2x7kYNuDJD0rXX4ebTwIGntzFfifBEVRWNy8OWE1arl2R0Vxq68v8xo35mBREX67dxOxfz+vpKTgplKhrSPx6GrUrw8zZlxbd7pHD3j4Ycf/d98Ne/cO5dy51qSnj6aqqpDU1PcwGGIICXnhhs6lXr0hKIoLen0nDINuJfaR5eRhYHCHTHZPXos+r5Lu9TdjtdZePcfm5+NNAV6nQG0rO066ipnHqtHy9qCtFO0wcKFeHlVV0LdvAAUFARQUTOOnn964oXGCJEuqLvU5eVK6z729e1O//kgi9u+n7cGDtD54kCXp6TfU3hMdn6BDUAc4elS6ardtk8Hn8eNh+PXrkRt6N2TH6H+mhAVuGtCbuAkn1EXMoGgUOhzo8A+M5iZuBCaDARVwsWtXAmzZunURTTR2c6OLlxdPnz3LhtzcWp//UYwYAfPmTeP22/fy+ecdUas9qai4bOcGvhEYDD2Ijs6mffsdNG/+BaGT76chF4nu7073l2V5z4Cncjm1uXY5y97c8zTkIomHO2O2Le8WDxzIr2cusOLjHNy0RSQaumAiFo4YILIAXKpIToaMDEmjV1a20d6eEPDw+EqG7T5NocXClCmwaJGcWMyZAwkJkJ4uySkiImJJSXmQtm03YbZayaqhnvPImTM037eP7MrfoEorL5d+8eolf58+kgfx6gD0NRDdMJqf7//5hvb9s/G3GtAxY8agUqkYNqxu1Y/du3fTo0cPPDw8CAwM5LnnnqOkpOTvHOJN/D+Ha0NXQqeF4tHWA69uXhhiDETtjfpHXLc3cWMY36AB85s0IaTGSrStpyf3+TuUeWIMBr5p2ZIutgzfQfHxf+oYjEYNPj7u6HRavL2lwaupMnIj0Gj0qFQ6VCoXGjVWmDxbz9ixyICrDd7Tn+R0fAFnz8ZTWZlFenk5jZLWo0IQeqSAn7p3Z/pDD7Hyllvo0ziYW+6tR4XFk1XZJvoSR72DVozlBcSMk/WzM2euxGpVcHc/Y1/drosv5cviy/xcmcG7O3N5Y14VYyZXABeYNs3Mp59K4zlmTBphYacwGgdzscLCClsCV70atE9nysr44norUSEkge6OOlaRNeuCfwOB+sAb3vfPxN/2VDh48CBffvklrq6udbrTjh49SkxMDOXl5cyfP5/HHnuMzz77jLvvvvvvGuJN3AQA4TPC6XS0E1G7o2i3uR36DnWXVdzEfwZae3ry7FUuS5WisKJFC5q4ufFGeDib27WjuYcHt/j42Pcx/waL0R+Fj88wtNoA9PqOf7gNRZGx1vDq/JwxYwAI2ZOI1zQDqalt2b3bn7PLlrFi1EKKDjYg6sQ5NnfowIyHH6ZR48a4qtUYjRAVBbGY8CGXw5f78u3s2Xj3zcPLC4zGCD777FcMhgxOnDjNnoIChuXth5EXAZixJh8eOo/LR7tZvDiSO+54n4ULoXVruP12uRqO7NiT8H37eDghAYCM7t1Z3MwhmXis+DokJStXSkLialTHO7Va8L5x8pF/Cn8LA68QgmeffZaHHnqIzZs317nPlClT8PHxYevWrXh6yiB6WFgYY8aMYdOmTfT/Dd7Lm7iJm7iJmlAUhWMdO9pl3gBijEY2tWlD//h4DhYV0e0veEgHBY0lIGCkTfnmT8LHH3Pl0FqCDqfjuwPO2kpBPFe/gdoqaLBIhxYLg/vezyeUEFMjQzkmBhYc6orV1Y3Q8hQCj6YyWJvEx/Ee3OcfQHl5NAcPatl3+lfG5kY599s+DyrUtPI7gjvFPPXUBK5caQSt+7BDt5JoTTPOujmXbmlUKkYHBjJcq6W4Z08OBwUhNm1CqSuovG2b7SCbRJ23NxQUOApz/8Pxt6xAly1bxqlTp5g1a1adKeSFhYVs3ryZkSNH2o0nwKhRo/D09GT16j+PcuombuIm/v/AXa1GfZXHq4/BgJda/ZvJRH8UiqK6oczb3wW1mtSpa7G48X/t3X1YU1e2P/DvCSGQAEFn3AAAG3BJREFUhPeAgYACTqEgqGDptKItgraKji+tRaW1WC3q47RqO/da52rrGzpcf1NbrTpV0bH+0F9/ttrajp1WL4N1fGkREPANClpAEETQgEIMIbDvHycJhAQJ1ADK+jxPHvVkJ9lZ+rA85+y9FoT1ANcEiGqAkGx+/2P4L9eglCgwcdJTWO3rizd0q5MBYOFCYM1f7CB4jt+3KtJoMPLyZcwrzodYDLi4SFB262loXA5gMK7BH79ilPIWnvnZCRh0H6KA23gBrZ1U1q9/CXmzLiKYZeOfTUNwoIrvtD7WxQWn2yxddjlyBD4FBZiSno7Szz9HfkEBlMXFfNmnCxf4h/6E6uef+SW6AsEjVeTb6meg9+7dw/Lly7FixQrI5eZLml28eBFarRYREcaXPGxtbREWFoacnN9ebooQQgD+DCnKxQXpSiVW+vp2/oI+ImxSBOb4foEDBTOQtv7vSPo3X6BeNRCQlAGuL8cANgKs8fc3et3gwXwhfUj/AOTnQ6tWIyYnBz+Gh+N2UxOO3bmDf3sH4A3swx4k8i9yBfAsEI0TWI21iMRPKIc3fMB3HHJnV6FAJc5jBM7cuoXZcjlSg4ONPhfnWvdP++kKBFc7O/PtatpuJUpNBZ56NBfpWf0MdN26dZBKpXj33Xc7HFOp26Pl5WV6I9jT0xMVFV3f6EsIIR2JcXHBmbo6qJs7bkvWXcmlpfjudmsj7jqtFq/n53e4GjX73j14nDmDv924YfZ5PVtbYOfPL4O5umCNvLVP67lYfiWt2coPbb39NlBQAGF0NP6jsBCffPIJck+dwsnaWuRhuNmXREo0iATfKiwdMfgj+ApGe8En71zw+19DzO3VTE8H3nzT6JBHXZ1x8gT4Qrqd+EdNDTzOnMGR6o47HvUGixMoYwxqtdqih16h7i/pr3/9K2xtO27gel9X9djOzs7kOXt7e8PzhBDyMMS4uqKRMfz0kBvqqpubsa60FJvL+fZjRSoVtt+4gf1VVdhy4waaGcOdpibcabPdI/7KFdQ0NeGtoiLk1dfjQn09GjtY4OTgbANuTDRsvuRboe19fSJW532CK1P/q9M9kxAI+BZxMTGQZGRg8ddfoyklBWlKJS5gGL6rfhmFV8OhUkVDIuFrD66W/AMAIBR5o9p5PvJhfJa5avAwTJHJsMjb2/izSkuBa9eAiRPxWWoqTphr+j58OJQrVqBF0bq/WtvSggv19bil0eDX+/cNt/ymXLqEmqYmvHT58oO/Yw+z+BLuyZMnEWPhvpyCggIEBgZi6dKlGDVqFF7q5C9WrLth3Nho2uRVrVZD0kElCr133nkHLu32fcXHxyM+Pt6i+RJC+pdQqRTutrZIr61FtOvDqzH88927ULe04HRdHfLq6xGWlWV4bn0p3z/0/L17aGYMPwznz/pqta3NC/Tj53l6Yk9HBXRjYoCvv0bGsGH4Z8InyJzyO7h/+zJg6XqoNj/Hfc+exa8LFyI1KARffXIYFWLggK4q3qlTjhDVbAMARIz4Cf+wH4ht5eW4cHUohuEi5PI5eG/QIPOfceIEv5Q4KgpDbG3x3MCBqN62DfmXLiHs2jWM+fhj7H3jDQzLykJKVRXm6O7ZflBSgv++zq8AFnIcUoOCMNXd3eit9x44gK8PHjQ6Vmul+9mdsTiBBgcH47PPPrNorKenJ9LT03Hs2DF89dVXKCkpMTyn1WqhUqlQWloKNzc3ODo6Gi7d6i/ltlVZWQmF4sEVYDZv3owRI0Y8cAwhhOgJOA7RLi5YX1qKEIkEs3TrM1YXF+N5FxejVawdudnYiPd+/RWfBgZCamODKw0NiM7LgwCAuqUFybqE2ZY+idpxHNTNzahuakJ1UxO2BQTg7aIiw7i/37yJWDc3vNJmL6uB7lLt9+HhSBzhir9XddjAxryAAMDHBy03byL4+nV8sWYNIn/4AXGfG5ectbPzgUrFb02xt+d77451dcUwbMJqHw+sGGzabg8A31B17ly+MIJMht8DqBk1Co7PPovQ5ma4//gj6iUSrCkpQRNjeKOgAD52dhjr6mp06VvLGOLz87Fad586JTAQ8wsL4R0bi29fe83oI8+fP4+neuE+qsUJVC6XIyEhweI3vq77X8TLL79s8lxFRQX8/f2xefNmLFmyBKGhoRAKhcjMzMQrr7xiGKfRaJCbm4tZs2ZZ/LmEEGKJaBcXfFldjfj8fES7usJeIMD60lJMbWiwKIEerqlBalUVwhwc8IKrK6brLi/629tDqdXioO5+3VgXF/xp4EBMuthaYL6RMZyuq8MZ3SXkmR4eYIzh7zdvIke3bzLuyhXkSST4nVgMadsCskFByPjP/8S+3/8ey5ydIe1qhzuOAzZtgqaxEfYJCYg7eZKv4D54sNGwkJDDKCpaAm/vt1o/WiLBKr8AzPH0NN2mo9HwJYr0Z7htVuQ6CoWAUAgpgD0REZh55YohPgAwLi8P2qgolJm5Crm2tBQetraY5+WF94uLsb+qCqOdnSGx6f3WflZbhTt27FgcOXLE6BhjDAsWLICfnx9WrlyJUF3RZ2dnZ4wbNw779+/HBx98YNjKkpqaioaGBiqmQAh56Np2c/E8exbfhoaiBcCPtbVoZsxk+0t76Uq+a4++kL3efIUCmXfv4nBNDd739UWSblVs2vDhGJeXBwBwt7XFxIsX0cQYfOzs4C4S4W0fH7zt44ML9fUYrruUOzwrC887O+Nk28r2HIf/M2cOfJqajBNrV8yYAXuAr5wP8At+2iVQqXQIwsKM9+1zHIcP/PzMv+eWLcD69Xx1IQCYMsX8Rw8YgH8pldhVWYnB9vb4VbduJvvePdRqtTgVFoYlV69C09KCy7oFR9EuLhBwHGJcXZFaVYUqjQbHhptf+NSTrJZABw4ciIEDB5ocX7p0KeRyOaa0C+6GDRsQGRmJqKgozJ8/H+Xl5fjoo48wfvx4vPjii9aaJiGkn3pSIsHlp59GSGYmAH6hipDjoNRqITx5Eqt9fU22hOi1MIYTZu67rRw0CO8NHIhPKypwuKYGY9uszRjr6ora0aMh5DjMLSjAl7ozMG9d/V69YQ4OyHnqKYRnZwPg27KpmpuxqLAQo5ydcbupCSdqa7G4/cKd7lCpgFGj+ASamPjb3uvYMUC/KOvbb4EOSrYCfCx2VVZi4+DBkNjYYNLFi/i4vBwSgQC/d3LCmfBw2HIcjt6+jZcuXzZcEQjWrYc5rlSiXqvFmNxcDLS3h8LM7b+e0OMFPjvqihEeHo60tDSIxWL86U9/wu7du5GYmIhDhw718AwJIf3FEKkU/9GmDODTbW4mri0tRcbdu7hlZvtJXn09lFottgUEYKyLC0Y7O2OKTIZlgwaB4zjMGjAAKwcNwqh2lY6chUJIbWwQo0usQo4z3T8JvpbvnwcNgq3u5+WakhL836oqLCwsxIriYii1WqMz6G4Ti4EXX+QTaCd9UjtUXQ1kZrZWFbK3BzqpHDdJJsN/DRqEibrG6GKBAP//1i085+wMkUAAsY0NhAIBJspkWDFoEOI8PAAAi7294avbrbHn5k1k19fjSE1Np1uArIVjnXWX7cP0N46zs7NpEREhpNu4H38EAOwIDMTG69dR3GY7HgCwMWOM/ryprAwfFBdDOXq0UalASxXfv4+gc+fwY1jYA8sJ1mg08Dh71uS4WCDo9mebOH4cGD8euHwZGDKk669ve1IUHg74+PBnoF0wPi8Px5VKbBw8uOOVvToVjY3w/ukn+NjZoVx/z7SwEFi4sMdzQY/UwiWEkL5M9dxzULe0wEUoxBuenmhobobszBnD89UaDTxEIhSqVPhrWRnK1GqMdnbudgLzF4v5lanCB/8Idm93eRfgz1p/y2ebGDWKr9KQnt71BNq+LdzZs8YJ1UJjXV1xXKm0aPGWws4OQRIJClQqvC6Xo0StRm91BKUESgjp98Q2NhDrFuTYcRzsBAL8v+BgrCstRYFKhR9raxEskeDDsjLs09V+Te7g/qilOkueekeHDsXHZWV4d+BAZN27B397e/g+zFqxUinw7LPAl18Cr73G16K1lP6ybUAAsGpVt2vYJsjlaGhuRriDZTWEY1xcUKBSYaKbGzxFIpyursYH3frk34YSKCGEmBEvlyNeLseTGRmY98svqG9X9u+h3IO0wCSZDJN0bdgmtWnH9lCNHQusWcP3T+tKUYL0dOB3v+Mvof4GnnZ2WNuF/5BMlsmw9+ZNxLi6YoBIBCd3915JoNQlmBBCHiDG1dUkeTrb2GCEhWdLjwR98+q6On4/p6XS040qG/WUCTIZqiIjMcDMJe6eRAmUEEIeIKbNVpRJbm74NjQUm594AsKHdQ+yL3juOX4hEcCvqLVEZSVw5UqvJFDA8kvg1tT7MyCEkD4s2sUFEoEAX4SEWO8Sam8TCoHvvgNkMv6sctSozl9z4gT/qwXdVB5Xj9F/oQgh5OFzF4lwMzLy8U2eejY2wJgxfAK1RHo6EBICdNDnuT+gBEoIIZ3oC5cLe0RMDL8VxZIWkr10/7MvoQRKCCGEFxPDLyIyU7zBSHEx/6AESgghhIC/JOvhAYwbB7TpHmPk5s3WwvPtKjT1N5RACSGE8DgO0DW3xuTJQEOD6ZitW1t/32aFcn9ECZQQQkirN97gfy0tBSZONH2+gG+yjTlzemxKfRUlUEIIIa3efRdYu5b//b//zZf68/fnm263tPDbV5YtA3bv7t159gGUQAkhhLTiOD6JBgTwf1apgJIS/tjBg4BSCfzhD/ze0X6OEighhBBjjo6mK3G/+AJ49VX+98880/Nz6oMogRJCCDHl7g7cvcufcU6aZPycrql1f9cjCTQtLQ0xMTFwcXGBk5MTIiIi8MUXX5iMO3v2LEaPHg2pVAovLy8sXboUDeZWgRFCCLE+R0d+pe3OnfzWlpgYQNd8nPRAAt27dy/Gjx8POzs7JCcn48MPP8Tzzz+P8vJyo3G5ubkYO3Ys1Go1Pv74YyQmJmLXrl2Ii4uz9hT7nc8//7y3p/BIorh1HcWse/pc3Ly9gf/5H+Bf/wKionp7Nn0Hs6Li4mImFovZO++80+nY2NhY5u3tze7du2c4tnv3bsZxHDt+/LjZ12RnZzMALDs7+6HNuT+YPHlyb0/hkURx6zqKWfdQ3Lqmt3KBVc9Ad+zYAcYY1q1bBwCor68HY8xk3N27d5GWlobZs2fDoU2PvYSEBDg4OJi93EsIIYT0Jqsm0LS0NAQFBeHo0aPw8fGBk5MT3N3dsWrVKqNEevHiRWi1WkRERBi93tbWFmFhYcjJybHmNAkhhJAus2oCLSoqwvXr1zFv3jwkJibi8OHDiI2Nxfr167Fy5UrDuMrKSgCAl5eXyXt4enqioqLCmtMkhBBCuszinbCMMTQ2Nlo01t7eHkDrJduNGzdi2bJlAICXXnoJd+7cwZYtW7By5UpIpVLc17XOsTOzNNre3t7wfEfy8/Mt/RoEQG1tLc6fP9/b03jkUNy6jmLWPRS3rum1HGDpzdITJ04wjuMsevzyyy+MMcakUikTCASsrKzM6L327dvHOI5jp06dYowx9uWXXzKO49jp06dNPjcuLo4pFAqzc6qoqGAKhYIBoAc96EEPevTjh0KhYBUVFZamtIfC4jPQ4OBgfPbZZxaN9dRV81coFLh27Rrk7TqWDxgwAACgVCoBtF661V/KbauyshIKhcLs53h5eSErK8vs6wghhPQfXl5eZm8DWpPFCVQulyMhIaFLbx4REYGrV6+ivLwc/v7+huP6e5oeHh4AgNDQUAiFQmRmZuKVV14xjNNoNMjNzcWsWbM6/IzeCBohhBBi1UVEM2fOBADs2bPHcKylpQV79+6FTCbDU089BQBwdnbGuHHjsH//ftTX1xvGpqamoqGhgYopEEII6XM4xsxszHyIXnjhBaSnp2P+/PkYNmwYjhw5grS0NOzatQuJiYmGcTk5OYiMjMSQIUMwf/58lJeX46OPPkJUVBS+//57a06REEII6TKrJ9CGhga8//77OHjwIO7cuYOgoCAsX74c8fHxJmPPnDmD5cuX4/z583BycsKMGTOQnJwMqVRqzSkSQgghXWb1BEoIIYQ8jqidGSGEENINj2QCbWxsxPLly6FQKCCRSPDss88iLS2tt6fV4zIzM/H2228jJCQEDg4O8PX1xcyZM1FUVGQyNj8/HxMmTICjoyNkMhkSEhJQU1Nj9n337NmD4OBgiMViBAYGYtu2bdb+Kr1qw4YNEAgEGDp0qMlzFLdW58+fx5QpUyCTySCVSjF06FBs3brVaAzFy1hWVhamTp0KhUIBqVSK4OBgJCUlmRSH6a9xa2howOrVqzFhwgS4ublBIBBg3759ZsdaI0a1tbVYsGABPDw84ODggJiYmK6Vju3RXacPyaxZs5itrS177733WEpKCouMjGS2trZmCzE8zqZPn84UCgVbunQp27NnD1u/fj3z9PRkDg4O7NKlS4ZxZWVlzN3dnQUEBLCtW7eyv/zlL8zNzY2FhYUxjUZj9J47duxgHMexuLg4tnv3bpaQkMA4jmMbN27s6a/XI8rKyphEImEODg5s6NChJs9R3HjHjh1jIpGIjRw5km3evJnt3r2b/fnPf2bLly83jKF4Gbtw4QKzs7Nj/v7+bOPGjSwlJYXNnTuXcRzHpk6dahjXn+NWXFzMOI5jfn5+LDo6mnEcx/bt22cyzhoxam5uZpGRkczBwYGtW7eObd++nYWEhDAnJydWVFRk0fwfuQSakZHBOI5jmzZtMhxTq9XsiSeeYJGRkb04s5539uxZ1tTUZHSsqKiI2dvbs9mzZxuOLVq0iEmlUqOKUGlpaYzjOLZr1y7DMZVKxWQymUkrpdmzZzMHBwemVCqt9E16z8yZM9m4cePYmDFjWGhoqNFzFDdeXV0dk8vlbPr06Q8cR/EytmLFCsZxHLty5YrR8Tlz5jCO41htbS1jrH/HrbGxkVVVVTHGGMvKyuowgVojRgcPHmQcx7HDhw8bjlVXVzNXV1f26quvWjT/Ry6BLlu2jNna2hr1DWWMseTkZMZxHCsvL++lmfUdI0aMYBEREYY/DxgwgM2cOdNk3JNPPsnGjRtn+PN3333HOI5j33//vdG4n376iXEcx/bv32+9SfeCkydPMqFQyC5dusSioqJMzkApbrxPP/2UcRzHCgoKGGOM1dfXs+bmZpNxFC9jSUlJjOM4VlNTY3R8+fLlTCgUMpVKxRijuOllZmZ2mECtEaO4uDjm5eVl8p4LFy5kUqnU5MzWnEfuHmhOTg4CAwON+oYCwNNPPw0AyM3N7Y1p9RmMMVRVVcHd3R0AcOPGDVRXV5u0igP4mLW93q//ffuxI0aMgEAgeKxi29zcjMWLF2P+/PkICQkxeZ7i1iotLQ1OTk4oKyvDk08+CUdHRzg7O+OPf/yjocEExcvUvHnzIJfL8eabbyIvLw9lZWU4ePAgduzYgSVLlkAsFlPcLGCtGOXk5GDEiBFm31OlUqGwsLDTuT1yCbSystJs6T79sf7e+uzAgQOoqKgwVIF6UKs4Ly8v3LlzB01NTYaxNjY2huSrJxKJIJPJHqvY7tixA9evX0dSUpLZ5ylurYqKiqDVajFt2jTExsbiq6++wrx587Bjxw7MnTsXAMXLHIVCgTNnzqCgoADh4eHw9fVFfHw8lixZgk2bNgGguFnCWjF6GLnE4lq4fcX9+/c7bHumf76/KigowFtvvYXIyEjMmTMHADptFacfY2tri/v370MkEpl9bzs7u8cmtrdv38aqVauwatUqyGQys2Mobq3q6+uhUqmwaNEibN68GQAwbdo0aDQa7Ny5E+vWraN4mVFVVYXY2FgAQEpKCmQyGY4ePYoNGzZALpfjrbfeorhZwFoxUqvVvzmXPHIJVCwWm+1LqlarDc/3Rzdv3sSkSZPg6uqKQ4cOgeM4AK3xsCRmYrEYGo3G7Pur1erHJrbvv/8+3N3dsXjx4g7HUNxa6effvnpYfHw8du7ciZ9//hlBQUEAKF5tJSUl4caNGygsLDR0lJo2bRpaWloM1djo31nnrBWjh5FLHrlLuF5eXmZPrfWn+R21Pnuc1dXVITY2Fnfv3sUPP/xgaCcHdN4qTiaTwdbW1jC2ubnZZG+VRqPBnTt3HovYFhUVISUlBYsXL0Z5eTlKSkpQUlICtVoNjUaD0tJSKJVKilsb+vk/qC2hfgzFq9Xp06cRHh5u8n0mT54MlUqF3Nxc+ndmAWvF6GHkkkcugYaHh6OwsBD37t0zOp6RkQEACAsL641p9Rq1Wo3Jkyfj6tWrOHr0qOFMQM/b2xseHh7IzMw0ee25c+eM4hUeHg4AJmOzsrLQ0tLyWMT2xo0baGlpwZIlSzB48GDD49y5cygsLIS/vz+SkpIobm3oF2SUl5cbHW/bllChUFC82mlqakJzc7PZ4wCg1Wrp35kFrBWjsLAwnD9/HqxdNduMjAxIpVIEBgZ2PrlO1+n2Mfp9oB9++KHhmH4f6MiRI3txZj1Pq9WyKVOmMJFIZLJsu61FixYxiURidg/Vzp07Dcfu37//2O0za6+mpoYdOXKEffPNN4bHkSNHWGhoKPPz82PffPONoQgFxY2Xk5PDOI5jr732mtHx+Ph4JhKJWGVlJWOM4tXe7NmzmZ2dHSssLDQ6Pm3aNCYUCilu7TxoG4s1YqTfB3ro0CHDserqaubi4sLi4+MtmvMjl0AZY2zGjBmGSkQ7d+5kkZGRTCQSsVOnTvX21HrU0qVLGcdxbMqUKSw1NdXkoaev4vHEE08Yqni4urqy4cOHm+x1+tvf/mao4pGSkmKo4pGcnNzTX69HRUVFmRRSoLi1evPNNxnHcWzmzJls+/btLC4ujnEcx1auXGkYQ/EylpeXx8RiMZPL5SwpKYlt376dxcbGMo7j2IIFCwzj+nvctm7dypKSktiiRYsYx3Fs+vTpLCkpiSUlJbG6ujrGmHVi1NzczEaOHMkcHR2NKhE5Ozub/KenI49kAlWr1WzZsmXMy8uL2dvbs2eeeYYdP368t6fV48aMGcMEAgHjOM7kIRAIjMZevnyZjR8/nkmlUubm5sZef/11duvWLbPvm5KSwoKCgpidnR0LCAhgW7Zs6Ymv06vGjBljUkiBMYqbXlNTE1u7di3z8/NjIpGIBQYGmv1+FC9jGRkZbMKECczJyYmJRCIWFBTEkpOTTQpR9Oe4+fn5Gf3c0v9MEwgErLS01DDOGjFSKpUsMTGRubu7M6lUyqKjo1l2drbFc6d2ZoQQQkg3PHKLiAghhJC+gBIoIYQQ0g2UQAkhhJBuoARKCCGEdAMlUEIIIaQbKIESQggh3UAJlBBCCOkGSqCEEEJIN1ACJYQQQrqBEighhBDSDZRACSGEkG6gBEoIIYR0w/8C1yjtd3qWDaUAAAAASUVORK5CYII=",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x11472f2c>)"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part i\n",
      "\n",
      "* Instead of (n, k) where n is the number of tosses and k is the sum so far, we use (n, k/n)\n",
      "* Every value is normalized between -1 and 1\n",
      "* Like in the earlier plots, as the number of tosses increase, the deviation is smaller"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "title(\"100 normalized random walks of 1000 coin flips\")\n",
      "for _ = 1:100\n",
      "    plot([k/n for (n, k) = enumerate(path(1000))])\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x106dbfcc>)"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part j\n",
      "\n",
      "* Plot how frequently the fraction of heads is less than `q`\n",
      "* The optimization trick we're using here is based on the fact that a run of length 1000 contains a run of length 500 as a prefix\n",
      "* Hence, we can use earlier values that we computed for smaller number of coin tosses in computing the number of heads in larger number of coin tosses"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "identity(x) = x\n",
      "\n",
      "# runs and tosses are the number of runs and tosses respectively\n",
      "# q is the threshold which we're interested in finding the fraction of heads smaller than\n",
      "# func is the function we want to apply to the vertical axis values\n",
      "# For this part, that function should do nothing (identity). For next part, it's the log function\n",
      "function multi_toss_runs(runs, tosses, q, func)\n",
      "    runs_table = Dict()\n",
      "    for k = 1:tosses\n",
      "        runs_table[k] = Float64[]\n",
      "    end\n",
      "    for _ = 1:runs\n",
      "        heads = 0\n",
      "        for k = 1:tosses\n",
      "            heads += round(rand())[1]\n",
      "            push!(runs_table[k], heads)\n",
      "        end\n",
      "    end\n",
      "    \n",
      "    # Computes the frequency of the fraction of heads is less than q\n",
      "    # Code explanation: for every run whose fraction of heads is less than q, give that run a 1, otherwise 0\n",
      "    # Then sum up all the values to get the number of runs that satisfies this requirement, and divides\n",
      "    # it by the total number of runs. Repeat for each of the k tosses\n",
      "    return [func(sum([heads/k <= q ? 1 : 0 for heads = runs_table[k]]) / runs) for k = 1:tosses]\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "multi_toss_runs (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "for q = Qs\n",
      "    plot(multi_toss_runs(10000, 1000, q, identity));\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x113c722c>)"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part k\n",
      "\n",
      "When you increase the number of tosses, it gets less and less likely that the fraction of heads will be smaller than a small threshold (like 0.4 and below)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "for q = Qs\n",
      "    plot(multi_toss_runs(10000, 1000, q, log));\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x101f892c>)"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part l\n",
      "\n",
      "* We sort the ratio to clearly indicate the fraction of m runs in which R <= q\n",
      "* We also return the quartile values (25th, 50th, 75th) for part n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function q_curve(m, k)\n",
      "    res = [flip_coin(k) / k for _ = 1:m]\n",
      "    sort!(res)\n",
      "    first_quartile = res[m * 0.25]\n",
      "    second_quartile = res[m * 0.5]\n",
      "    third_quartile = res[m * 0.75]\n",
      "    return res, first_quartile, second_quartile, third_quartile\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "q_curve (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "title(\"Ratio of heads as a function of q\")\n",
      "curve, _, _, _ = q_curve(10000, 1000) # don't care about the quartile values here yet\n",
      "plot(curve, 1:10000);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x11bb418c>)"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part m\n",
      "\n",
      "* The curve is more straight as k increases, i.e. there's less deviations across runs"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "firsts, seconds, thirds = Float64[], Float64[], Float64[]\n",
      "\n",
      "figure(figsize=(5, 3))\n",
      "title(\"Ratio of heads in k tosses as a function of q\")\n",
      "for k = ks\n",
      "    curve, first_quartile, second_quartile, third_quartile = q_curve(10000, k)\n",
      "    plot(curve, 1:10000)\n",
      "    \n",
      "    # Save the quartile values\n",
      "    push!(firsts, first_quartile)\n",
      "    push!(seconds, second_quartile)\n",
      "    push!(thirds, third_quartile)\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0xfedb2ac>)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part n\n",
      "\n",
      "As k increases, the quartile values becomes closer and closer to 0.5. This suggests that the heads/tails distribution tend toward 0.5/0.5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Ignore k = 2, so we start indexing from 2. Recall that Julia is 1-indexed\n",
      "function plot_quartiles()\n",
      "    plot(ks[2:], firsts[2:]);\n",
      "    plot(ks[2:], seconds[2:]);\n",
      "    plot(ks[2:], thirds[2:]);\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "plot_quartiles (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "title(\"q quartile markers as a function of k\")\n",
      "plot_quartiles();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0xfe8fecc>)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Part o\n",
      "\n",
      "* The log-log plot seems to offer the most insight since it's a rather straight line comparing to the other plots"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Computes the gap between the 0.75 marker and the 0.25 marker\n",
      "gap = thirds - firsts\n",
      "\n",
      "function plot_quartiles(plot_function)\n",
      "    plot_function(ks[2:], gap[2:]);\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "plot_quartiles (generic function with 2 methods)"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5, 3))\n",
      "title(\"Linear-linear plot\")\n",
      "plot_quartiles(plot);\n",
      "\n",
      "figure(figsize=(5, 3))\n",
      "title(\"Log-linear plot\")\n",
      "plot_quartiles(semilogx);\n",
      "\n",
      "figure(figsize=(5, 3))\n",
      "title(\"Linear-log plot\")\n",
      "plot_quartiles(semilogy);\n",
      "\n",
      "figure(figsize=(5, 3))\n",
      "title(\"Log-log plot\")\n",
      "plot_quartiles(loglog);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "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