bungee_jump.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DhRAsoXW6oBE"
      },
      "source": [
        "# Example: Bungee Jumper Problem\n",
        "Here is an example of how python is used to solve problems numerically. Here we will use the popular libraries NumPy, SciPy, and Matplotlib. This example is based on the text found in the textbook \"Applied Numerical Methods with MATLAB\" in Chapter 1, but here we are using Python instead of MATLAB."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "bQRe5uWZ6pFK"
      },
      "outputs": [],
      "source": [
        "# load modules\n",
        "import numpy as np \n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#from google.colab import drive\n",
        "#drive.mount('/content/drive')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "##### Finding the analytical solution\n",
        "\n",
        "First, let us find the velocity of the bungee jumper using the analytical solution. \n",
        "\n",
        "\n",
        "We use the Eq.1 which is a differential equation\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "(1)\\qquad        \\frac{dv}{dt} = g - \\frac{c_d}{m} v^2\n",
        "\\end{aligned}$$\n",
        "\n",
        "Solving analytically yields\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "(2)\\qquad        v(t) = \\sqrt\\frac{gm}{c_d} tanh(\\sqrt\\frac{gc_d}{m}t)  \n",
        "\\end{aligned}$$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4hgVpa2l-SP8",
        "outputId": "8e7705b1-7076-4119-9ef7-23f44068fe78"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "velocity = 18.710954739084887 m/s\n"
          ]
        }
      ],
      "source": [
        "# Define variables, parameters, etc.\n",
        "g = 9.8  # gravity \n",
        "cd = 0.25\n",
        "m = 68.1\n",
        "t = 2\n",
        "\n",
        "# calculate velocity using analytical solution:\n",
        "v = np.sqrt((g*m)/cd) * np.tanh(np.sqrt((g*cd)/m)*t)\n",
        "print(f'velocity = {v} m/s')\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "##### Analytical solution using Python Functions and Classes\n",
        "\n",
        "Here we will use Python to get the answer numerically. Defining functions and classes is a fundamental part of Python coding. Here we will define a few functions and classes to make our code. A class is a special Python object which is a user-defined blueprint for defining objects. These can have special functions within a class.\n",
        "\n",
        "\n",
        "I will define a Python \"class\" object called \"bungee_analytical\". This will take a single input - the mass. \n",
        "In addition there are some static variables defined within the class such as gravity. I define a class function \"get_velocity\" to return the analytical velocity."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yZp2czkp6pNb",
        "outputId": "1394b34d-5c31-49de-e4bf-4217da8edab4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "18.729188845697273"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# How you might use python classes and functions to create your physical model:  \n",
        "\n",
        "# Here is an example of how to define a function in python\n",
        "def func(x): \n",
        "  a = 4 \n",
        "  return a*x**2\n",
        "\n",
        "\n",
        "# Here I will define the \"bungee_analytical\" Python class. \n",
        "class bungee_analytical (): \n",
        "  def __init__(self,mass=80): \n",
        "    self.mass = mass     # kg\n",
        "    self.g = 9.81       # m/s**2\n",
        "    self.c_d = 0.25      # kg/m\n",
        "\n",
        "  def get_velocity(self,t):\n",
        "    g = self.g \n",
        "    cd = self.c_d\n",
        "    m = self.mass \n",
        "    return np.sqrt((g*m)/cd) * np.tanh(np.sqrt((g*cd)/m)*t)\n",
        "    \n",
        "\n",
        "# test the model\n",
        "m = bungee_analytical(68.1)   # assigne the object to a variable\n",
        "m.get_velocity(2)             # use the subfunctions of the class variable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G-Yz2iCDwP9O",
        "outputId": "4a9881ea-151c-496a-ebad-af2fe3de8d0f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "time\t\tvelocity (m/s)\n",
            "[[ 0.          0.        ]\n",
            " [ 1.          9.69390882]\n",
            " [ 2.         18.72918885]\n",
            " [ 3.         26.61481921]\n",
            " [ 4.         33.11182504]\n",
            " [ 5.         38.21539929]\n",
            " [ 6.         42.07622706]\n",
            " [ 7.         44.91452141]\n",
            " [ 8.         46.95749513]\n",
            " [ 9.         48.40575664]\n",
            " [10.         49.42136692]\n",
            " [11.         50.12817751]\n",
            " [12.         50.61747935]\n",
            " [13.         50.95496525]\n",
            " [14.         51.18714999]\n",
            " [15.         51.34661086]\n",
            " [16.         51.45599493]\n",
            " [17.         51.53096657]\n",
            " [18.         51.58232304]\n",
            " [19.         51.61748925]]\n"
          ]
        }
      ],
      "source": [
        "# here is how we can use the class to model the bungee jumpers velocity as a function of time. Will use some list comprehensioin to get the time and velocity. \n",
        "\n",
        "model_analytical = bungee_analytical(68.1)\n",
        "\n",
        "t = [i for i in range(20)]\n",
        "v0 = [model_analytical.get_velocity(i) for i in t]\n",
        "\n",
        "print('time\\t\\tvelocity (m/s)')\n",
        "print(np.column_stack((t,v0)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Here we will plot the analytical solution. Visualizing and plotting results is very helpful. Firstly, it allows you to make a sanity check on your model. Apply your basic knowledge to insure that your model is producing reasonable results. This is even more importantly in numerical solutions. Secondly, it helps communicate your results to other, e.g. the TA grading your work."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "g8XB2opC6pSX",
        "outputId": "77668aa2-1804-4eb2-ca76-09d2f8a35dd5"
      },
      "outputs": [
        {
          "data": {
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74YiISJ1lzjNsjFSQmU0H+vXr16/a5vvNnzM6GKcAlMAr7/XxySefcMkllzBlypQjerdL7aLvDimNrg8pTkpKCjNmzACY4ZxLKbhPt6dF6ogVK1awYcMG/vSnP9GtWzfOP//8QIckIiIhRLenReqIW265hQsvvJCkpCQmTZoUdL3hRUQkuKmlUaSOqK7HJ0REpG5QS6OIiIiIlElJo4iIiIiUSUmjiIiIiJRJSaOIiIiIlElJo4iIiIiUSUmjiIiIiJRJQ+6IiIiIFOCcIzfPkesceXmQ613P821zvm3OQZ5z5OUv8wq8d0fud973uXml7M8rckzve+ccJycn0SqhXuB+MHpV/AVMB5y/r5tuuskVddNNN/ld/5FHHjmi/oABA/yu/+KLLx5Rv0ePHn7X/+STT46o36JFC7/rL1iw4Ij65fn5bd68uVDdzZs3l6t+UQsWLPC7bosWLY6o/8knn/hdv0ePHkfUf/HFF/2uP2DAgCPqP/LII7r2dO3p2tO1V6PX3scff+x3/aO7dHVfL93mPl+0xX38y2b3wU8b3U0PPOl//Z793F8+XOTum/yr+9O7v7g7J/3kel52s9/1W542wJ35zHeu79Pfut5jvnG9npjmmpx8gd/143tf49re91mhV70OPf2un3TubUfUj2rWwe/6TQY+fET9pCbNauram+6K5DxqaRQREanF3pq7jszsPDKyc8nMzmX1stV+1921P4vTnviGrNw8snPyOJSbR9ryBX7XX7fzAMPfLFw+/ZfNftffuPsgb/+wodC2vanpftffl5HNmp0HCm3LyM71u74UpqRRRESkGh3KyWVH+iH2H8phf2YO6Yeyy1V/0Ms/QP1EX+K3f/f2ctV/+OOlhePZttXvurnOsW1fZqFtrlxnD21hZkRHhBEeZoSbERZm7AkPI8PP+i3iY2jbsiFhZoQZmBlpUeFk+Vm/e5sE2nVpTlgY3mMYkwI4A6x5WiqlosxsOtCvX79+1TZN2969ewFISEioluNLaNP1ISXRtVE52bl57DmQxd6MbNIzc3xJ3/5DhdcPZOUU2V9g/VAOuXm17/dseJgRGW5EhYcRFRFGVHgYkd5lVEQYkQW2e9aNiPAwIsOM8LAwIsKMiHDzLg+vh4d5y4QbkWFhvvOEh4UdUb7gvkjvesF9+a8wswJJH4USQN+y4H5vebMAZmcBlJKSwowZMwBmOOdSCu4L+pZGM5sADCmlyArnXOcS6g4CRgBdgXBgOfA6MN45l1fFoYqISJDKy3OkZWSz+2AWew5ksftAFnsOZrHrQP56NnsOHt6++0AW6Zk5gQ67VNERYdSLCicmIpx6UeFHrMdEhhETGU5MZDj1Ij3r9bzrMZHh5GUfIircSGgYR1SEERUe7kkEvUlfdEThBDB/W2S4J5mTuifok8YCZgOritlebDu7mY0FRgKZwDdANtAfeAHob2ZXOOf0YIOISIhxznEgK9eX/O0+UDjZ8y0PeJLE3Qey2Hswi0A1+EVFhBEXHUFsTASx0Z5XnPd9A+/2uOjD6/WiwgsldwWTvfxldEQYYZVM3NQSLeUVSknjK865Cf4UNLOBeBLGbUBf59xK7/ZmwHfApcBtwHPVE6qIiFRURlYuW9Iy2Lo38/Byb4bnfVomW/dmcCCr+v/mDzNIrB9FQv1I4mIifYlebMFEL8ab+PkSwcgjksKoCA2JLLVDKCWN5fGAd3lffsII4JxLNbMReIbJud/M/qXb1CIiNSc7N49taZme5C8tgy3ehDD//da0DPYcLF9HEX/FxUSQ1CDK86ofRaL3fWL9KJIaRJLUIJqkBpHe9SgaxkRWujVPpDapdUmjmbUGTgKygPeK7nfOzTCzzUAr4DRgTs1GKCJSO+XlOXbuP8QWb2vglrQjE8Lt6Yeoiv6X0RFhNGoQRVJslC/J8y0bRNGo0LonEYwMV4ufSGWEUtJ4ppl1BWKBVGAW8HUxLYXdvculzrmSesXPx5M0dkdJo4hIuWRm57J25wF+T01n1fb9rEzdz8rt6WzYfZDs3MpnhBFhRvP4GFrG16NFQgwt4uvRyrtskeDZnlA/ss72bhUJlFBKGq8vZttvZna1c25xgW3tvMv1pRwrf6TQdsXtNLOhwFA/4+oGkJOT43uouKqlp/s/kKnUPbo+pCSVvTYysnNZvyuD1bsOsnpnBmt2HmTNzoNs2ptZ4U4lBjSOjaRZXDTNG3pezeKifO+bN4ymUYNIwkpMCB1kHyQtraKfSvLpu0OKk5NT8qgBoZA0/gIsxNMDej3QEOgB/A04EZhmZj2cc/lDzMd6lwco2X7vMq6E/clAv4qHLCISOg5m5bJ210HW7Mxgza6DrN5xkDW7Mti8N7PcAzkn1IvwJoRRNGsYTXNfchhFs7homsbpNrFIqAr6pNE592yRTQeAKWb2NTADz3OJD+DpDQ2eP2ShcoPWr/Me2x/dgPiIiIhqH7ZAwyJIaXR9SEnyr430zGzP7eTt+723ldP5PXU/m/f6O7+Fhxm0TapPx6ZxdGoWS6emsXRqGkf7Jg1oEB30v1akCH13SEERESX/Hw7Z/93OuSwzexL4GLigwK789vbYI2v55O8rtm3eO7TPBH/iyJ8Rxp+yIiI1wTnHpj0ZzPhtO8tTD7AhLZuVqelsTcssu3IBYQbJjRp4E0NPgtixaSwdmsQSExleTdGLSLAK2aTRa7l32arAtnXeZdtS6rUpUlZEJGTl5jl+T01n/rrdzFu7mwXr9hwxX3BpIsKM5MYNPC2GzeK8y1jaNW5AdISSQxHxCPWksZF3ub/Atp+9yy5mVq+EHtQ9i5QVEQkZh3JyWbQpzZsg7mbB+j1+TXkXGW60bxxLR+8t5aO9CWLbRg00ALWIlCnUk8Yrvcv5+RuccxvN7Cc8nWWuAN4sWMHM+gGt8cwWM7eG4hQRqbC0jGx+Wr+H+et2M3/dbn7dlEZWTunzEsRGR9C1ZSxdW8XRLbkJHZvG0bZRfXVCEZEKC+qk0cy64Unwvig4T7SZRQB3eF8A/yxS9Uk8A3s/ZWZznHOrvPWaAuO8ZcZoNhgRCUap+zKZt3a3N0ncw/Jt+8ocELtxbDSntEukZ3ISPZOT6Nw8jv3p+wB1dBCRqhHUSSOeoW8+BHab2e/AJjzD5JwAtATy8EwV+GXBSs65yWY2HhgBLDazaUA20B/PkD0fAS/U0GcQESmRc47VOw74WhHnr9vNxt1l92Zu37gBJycfThLbNqqvwa5FpFoFe9L4K/AccAqeji3d8Qylswl4HRjrnFtYXEXn3EgzmwWMwtO7ORxPx5nXgPFqZRSRQMjOzWPpln0syO+0sn4Puw9klVonzKBLy3hvgpjIyclJNImLrqGIRUQ8gjppdM6tBe6qRP2JwMQqC0hEpAKyc/OYs3oXn/26hS+XbmNfGZ1WYiLD6N4mkZ7JifRsl0T3oxKJ1fiHIhJg+hYSEakGObl5/LBmN1MWb2Hqkm3sOZhdYtmE+pGc3DaJU9p5WhGPbxmv3swiEnSUNIqIVJHcPMePa3cxZdFWpi7Zxq4Sbju3iI/h1HZJ9GyXxCnJSXRoEktYmJ5HFJHgpqRRRKQS8vIcC9bv4bNFW/h88TZ27j9UbLkW8TFceEILLuzagm5tEtRpRURCjpJGEZFyystz/LxxD5/+upUvlmwldV/xiWLTuGguOKEFF53Ygu5tEtWaKCIhTUmjiIgfnHP8snEvUxZt5fPFW9lSwjzOjWOjueCE5lx4Qgt6JicpURSRWkNJo4hICZxzLNm8j88WbeGzRVvZvLf48ROTGkRx/vHNubBrC05t14hwJYoiUgspaRQRKcA5x29b9/HZoq1MWbSVDbsPFlsuoX4k53VpzoCuLTmtfRIRmp5PRGo5JY0iUuc551iRms6URVv5bNFW1u48UGy5hjERnNvF06LYu2NjzeMsInWKkkYRqbOyc/P45JctvPT9GlakphdbJi46gnOOa8aAE1vQp2MTjZ8oInWWkkYRqXMys3N5d8FGXpyxptjnFBtEhXP2cc0Y0LUlZ3RqTExkeACiFBEJLkoaRaTOSM/M5u0fNvDqrDXs3F944O16keH0P7YpA7q2IOWYpkoURUSKUNIoIrXe7gNZvD57LW/MWXfEvM9JDaK4oXcy1/VKJr5eZIAiFBEJfkoaRaTW2pqWwcvfr2XSvA1kZOcW2te8YQw3923P1ae0oX6UvgpFRMqib0oRqXXW7TzAv2es5v2fNpGd6wrtS25UnxEpHfhj91ZER+gWtIiIv5Q0ikitsWzrPsZNX82URVvIK5wr0rl5HKPO7MgFJ7TQ4NsiIhWgpFFEQt7C9XsY990qvlm+/Yh9J7VNZNSZHTjzmKaYKVkUEakoJY0iEpKcc8xatZOx363ihzW7j9jf9+gmjErpwCntkpQsiohUASWNIhJS8vIcX/2Wyrjpq1i0Ke2I/ed1ac7IMzvQtXVCzQcnIlKLKWkUkZCQnZvHp79uYdz01azavr/QvvAw44/dWjEipT0dm8YFKEIRkdpNSaOIBLXM7FzeW7iJF2esZtOewrO3REWEcXXPNtx0RnvaJNUPUIQiInWDkkYRCUrpmdm88+MGXpm5lp37DxXaFxsdwbWnteWGPsk0jYsJUIQiInWLkkYRCSrOOd5buIknPl/G3oPZhfYl1o/kht7tuL5XMvH1NXuLiEhNUtIoIkFjy94MHvhgMTN+31Foe/OGMdzUtz3XaPYWEZGA0beviAScc47/zt/I/05Zxv5Dh+eGbp1Yj9vO7MilPTR7i4hIoClpFJGA2rTnIA98sJiZK3f6tpnB0NOTuefcY9SyKCISJPRtLCIBkZfnmDhvA09+vowDWbm+7e0aN+Dpy7vSMzkpgNGJiEhRShpFpMZt3H2QeycvYu6aXb5tZjC8TzvuPucY6kXpVrSISLBR0igiNSYvz/HWD+t5aupyDhZoXezQpAFPX34iJ7VNDGB0IiJSGiWNIlIj1u08wL3vL2Le2sPzRIcZ3Ny3A3ed3YmYSLUuiogEMyWNIlKtcvMcE+as45kvl5OZnefb3qlpLM9ccSLd2iQELjgREfGbkkYRqTard+zn3smLWLh+j29beJhxa7/23NG/k4bREREJIUoaRaTK5eY5Xpu1lr9/tYJDOYdbFzs3j+OZy0/khNbxAYxOREQqQkmjiFSpVdvTuWfyIn7esNe3LSLMGHlmR247syNREWGBC05ERCpMSaOIVImc3DxenrmWf077nawCrYvHtWjIM1d0pUtLtS6KiIQyJY0iUmkrtqVz7+Rf+XVTmm9bZLhx+1mdGJHSgchwtS6KiIQ6JY0iUmHZuXm8OGM1z32zkuxc59t+Qqt4nrmiK52bNwxgdCIiUpWUNIpIhSzbuo8/v/crS7fs822LCg/jzrM7cUvf9kSodVFEpFZR0igi5ZKVk8e46at44dtV5OQdbl08sU0Cz1zelaObxQUwOhERqS5KGkXEb0s2p/Hn935l+bZ037aoiDDuPudohvdpp9ZFEZFaTEmjiPjlnR/X88jHSwu1LvY4KoGnLz+Rjk1jAxiZiIjUBCWNIlIq5xz/nLaS579Z6dsWHRHGPecew7De7QgPswBGJyIiNUVJo4iUKCc3j4c/XsKkeRt9245v1ZB/XdODdo0bBDAyERGpaUoaRaRYmdm53DbxZ6YtS/Vt63t0E8YP7kGDaH11iIjUNfrmF5Ej7D2YxY1vLGDh+j2+bZd1b8VTl3fVQN0iInWUkkYRKWTL3gyGvDaPldv3+7bd0q89953bmTA9vygiUmcpaRQRn99T07n+1Xls25fp2/bwgOO4sU+7AEYlIiLBIOTuM5nZE2bmvK8/l1JukJnNNLM0M9tvZgvMbJSZhdxnFqkJ89bu5vLxc3wJY2S48fw13ZUwiogIEGItjWbWE7gXcECJ98nMbCwwEsgEvgGygf7AC0B/M7vCOZdb/RGLhIYvl27j9kk/k5WTB0CDqHBevO5k+nRqHODIREQkWIRMq5uZRQMTgFTg41LKDcSTMG4DujrnBjjnLgU6AcuAS4Hbqj1gkRDxzo/rGfH2Ql/C2Dg2mv/e0ksJo4iIFBIySSPwGHAccCuQVkq5B7zL+5xzvtGInXOpwAjv6v26TS11nXOOf379O3/5cAn5k7wkN6rPByNO5/hW8YENTkREgk5IJE5mdirwJ2Cic+7TUsq1Bk4CsoD3iu53zs0ANgPNgdOqJ1qR4JeTm8eDHy7huQKzvHRtHc/kEadzVKP6AYxMRESCVdAnjWYWA7wB7AbuLKN4d+9yqXMuo4Qy84uUFalTMrNzGfHOT0yat8G3re/RTZh002k0jo0OYGQiIhLMQqEjzN+AY4CrnXM7yyib381zfSll8n9Tltgl1MyGAkP9jK8bQE5ODnv37vWzSvmkp6dXy3GldijP9ZGWkc2d7y/jl02H61zYpQmjL+hIdsZ+9pb0p5aEJH13SGl0fUhxcnJyStwX1EmjmZ0O3AV85Jz7rx9VYr3LA6WUyR+xOK6UMslAPz/OJxIytu07xMh3l7Jm5+HMcMiprbgzpS1hpkG7RUSkdEGbNJpZPeB1YB+e3tB+VfMuXSVPvw6Y4WfZbkB8REQECQkJlTxt6ar7+BLaSrs+fk9NZ9g7S9iadnjQ7ocuPJbhZ7Svgcgk0PTdIaXR9SEFRUSUnBoGbdIIPAEcDdzgnNvqZ538tvbYUsrk7yuxXd45NwHP8D5lMrPpqFVSgtj8dbu5ccJ89mV6bjlEhhv/d2U3Lj6xZYAjExGRUBLMSeOlQB4wxMyGFNnX2bscYWYDgFXOueF4WggB2pZy3Dbe5bpSyojUCl8u3cYdk37mkAbtFhGRSgrmpBE8vbtLa8Vr730leNd/9i67mFm9EnpQ9yxSVqRWmvjjBh76aLFvDMbGsdFMGNZTYzCKiEiFBO2QO865ZOecFffCMwQPwD3ebd28dTYCPwFRwBVFj2lm/YDWeGaLmVsjH0SkhjnneHba7zz44WIN2i0iIlUmaJPGSnjSu3zKzDrmbzSzpsA47+oY51xejUcmUs1y8xwPfriEZ6dp0G4REalawX57utycc5PNbDyeKQMXm9k0IBvoDzQEPgJeCFyEItUjMzuXOyb9zFe/pfq29T26CeMH96BBdK37ry4iIjWsVv4mcc6NNLNZwCg8z0SGA8uB14DxamWU2iYtI5vhk35kwfo9vm2Xdm/FUwO7EhVRG28oiIhITQvJpNE5N5QyZmxxzk0EJtZEPCKBVNyg3bf0bc9953UmLEyDdouISNUIyaRRRDxW79jPkLcWkZqe5dumQbtFRKQ6KGkUCVG79h9i6OvzfAljZLjx9ytO5JJurQIcmYiI1EZKGkVC0KGcXG55ayEbd3tuSdeLDOPl63tq0G4REak2ekJeJMQ453jgg8W+Ti8GjLn4GCWMIiJSrZQ0ioSYcdNX88FPm33r/3NmMv06JQUwIhERqQuUNIqEkKlLtvLMlyt861ed3IbrTmkZwIhERKSuUNIoEiKWbE7jf/77q2/91HZJPP7H4zHTsDoiIlL9lDSKhIDUfZnc+MZ8MrJzAc9c0v++9iQN3C0iIjVGv3FEglxGVi7D31hA6r5DAMTFRPDKkJ4kNogKcGQiIlKXKGkUCWJ5eY4/vfcLizenARAeZowffBIdm8YGODIREalrlDSKBLF/Tvudzxdv860/enEXDa0jIiIBoaRRJEh99PNm/vXtKt/60NOTufa0tgGMSERE6jIljSJBaOH63dw7eZFvvd/RTXjowmMDGJGIiNR1ShpFgszG3Qe5+c2FZOXmAdCpaSz/GtSdiHD9dxURkcDRbyGRIJKemc3wNxaw60AWAEkNonhtaE8axkQGODIREanrlDSKBIncPMed//mFFanpAESFh/HidSfRJql+gCMTERFR0igSNJ74fBnfLt/uW3/yshPomaw5pUVEJDgoaRQJApPmbeDVWWt96yNSOjDwpNYBjEhERKQwJY0iATZn9U4e/miJb/3cLs245w/HBDAiERGRIylpFAmgNTv2M+Ltn8jJcwAc36oh/7yqG2FhFuDIREREClPSKBIgew9mceMbC0jLyAagaVw0r1zfk/pREQGOTERE5EhKGkUCIDs3j5Hv/MTanQcAiIkM45UhJ9M8PibAkYmIiBRPSaNIDXPO8dePlzJn9S7ftn9c2Y2urRMCF5SIiEgZKn0fzMwaAM2AxkA9YBew0zm3rbLHFqmNXpu9jknzNvjW/3TO0VxwQosARiQiIlK2cieNZhYODAD+AJwBHAcc8dS+maUBs4GZwHvOubVFy4jUNd8t387fpvzmW/9jt5bcdlbHAEYkIiLiH7+TRjNrC9wGXAc0oZhEsYgE4ELgAuAJM/sOeNk5927FQhUJbSu2pXP7pJ/xdpSmx1EJjBnYFTP1lBYRkeBXZtJoZk2Ah4GbgSjv5l/xtCIu8L7fCewBMoFE7ysZ6Ol9nQn0B84ys4eAvzjnPq3KDyISzHbuP8QNE+az/1AOAK0S6vHidScTExke4MhERET8409L4xqgAbAWeAOY5JxbWUr5Hd7X78BXAGYWjeeW9iDgYuAjM7vHOfePSsQuEhIys3O55a2FbN6bAUCDqHBeHXoyTeKiAxyZiIiI//xJGjcBTwLvOOdyK3IS59wh4H3gfTPrCNzP4VZLkVrLOcf97y9i4fo9AIQZ/GtQdzo3bxjgyERERMrHn6TxOOecq6oTOudWAcNND3JJHTD2u1V89MsW3/qDFxzLWZ2bBTAiERGRiilznMaqTBhr4rgiweLzxVv5+1e/+9avOaUNN/ZpF8CIREREKk6De4tUg0Wb9nL3u7/41nu1b8RjlxyvntIiIhKyqmWSWzNrDJwMRAMznXO7q+M8IsFoW1omN725gMzsPADaNW7A+Gt7EBmuv9FERCR0Vei3mJmdZmYTzey+YvZdi6fH9RTgA2CDmQ2qXJgioSEvz3HHpJ9J3XcIgIYxEbw65GQS6qvfl4iIhLaKNn1cC1wF7Cu40dsz+jUgFsgBDgH1gQlmdnwl4hQJCW/OXce8dZ6G9fAwY/y1J9G+SWyAoxIREam8iiaNfbzLogN034LnlvcMoBGeWWHe9W67s4LnEgkJG3Yd5KmpK3zrI1M60Ltj4wBGJCIiUnUqmjQ2B3KBzUW2Xwg44BHn3H7nXBaQfwu7XwXPJRL08vIc972/iIxsz1CmRzeL1ZzSIiJSq1Q0aUwC0gsOm2NmSUBnPLesZ+Zvd86tBw4CrSsRp0hQmzhvA3PX7AI8A3g/c/mJREdoikAREak9Kpo0HgDizazg0/35LYlzixmDMQtPy6RIrbNpz0Ge/HyZb/3mvh04sU1C4AISERGpBhVNGn8DDBhYYNtQPLempxcsaGaxQDywtYLnEglazjke+GAxB7I8fxN1aNKAu87uFOCoREREql5Fx2l8F+gFvGRmfYAWwEVANvDfImVPx5NgrqxokCLB6t0FG5m5cicAZvD05ScSE6nb0iIiUvtUNGkcB1wK9AVuxZMUAjzmfYaxoKvxtEB+W8FziQSlrWkZ/O9nh29L39i7HSe1TQxgRCIiItWnQkmjcy7bzPoDg4DT8HR++cI5933BcmYWCdQDPuHI4XlEQpZzjgc/WEz6oRwAkhvV509/OCbAUYmIiFQfv5JGM7OinVucc7nAW95XsZxz2cA1lYpQJAh98NNmvluxAzh8W7pelG5Li4hI7eVvR5jtZvammV1lZvHVGpFIkNu+L5NHP13qWx/SK5lT2iUFMCIREZHq52/SmIhn6sCJeBLIb83sT2am+3FSpzjneOijJezL9NyWbpNUj3vP038DERGp/fxNGpvgSRrfBfYDKcDTwG9mttLM/mFm/c2soh1rRELCp4u28tVvqb71pwZ2pX6ULnsREan9/EoanXN7nHMTnXPXAE3xJI3/AFYAHYC7gK+AnWb2XzO73syqZNJdM7vdzN41s2VmtsvMss1sh5lNM7NrzcxKqTvIzGaaWZqZ7TezBWY2yswqOj6l1GE79x/ikY+X+NYHn3oUp3fQ3NIiIlI3lDt5cs7lOue+d87d45w7jsNJ47dADHAF8Dqw1czmmNmDZta1EjHeB/wRyADmAO8Dq4Cz8HTC+bC4JNDMxgLvACfjmdbwa+Bo4AVgspmp14KUyyMfL2XPwWwAWiXU44ELjg1wRCIiIjWn0i1uzrm1zrnnnXPnAI3xJI1vAbvwDMfzOPCzma03s7FmdoGZRZfjFFcDic65Hs65i5xzVzvnegEnAKnAJcCQghXMbCAwEtgGdHXODXDOXQp0ApbhGWPytsp8bqlbvli8lSmLD09q9ORlJxAbrdvSIiJSd1TpbVrn3H7n3PvOuaF4ZonpBTwJLAbaACPwjNd4XzmOOcs5d6CY7UuBsd7Vc4rsfsC7vM85t7JAnVRvDAD36za1+GP3gSweLnBb+qqT29D36CYBjEhERKTmVVvS5Dx+dM495JzrhidpHAl8DhysotPkeJeZ+RvMrDVwEpAFvFdMXDOAzUBzPC2hIqV69NOl7NyfBUDzhjH8ZYBuS4uISN1TY/fXnHObgX97X5VmZu3wTGEIhWeb6e5dLnXOZZRQfT7Qylt2TlXEI7XT17+l8vEvW3zrT152Ag1jIgMYkYiISGBUOmn0DrPTEc9YjqX+Ni06zWA5zzMM6Oc9R2vgdDwtpU865z4sULSdd1l0DuyCNhQpW/RcQ4GhfobWDSAnJ4e9e/f6WaV80tPTq+W4Urp9mTk8+MGvvvUBxzehe/Ooavt3rihdH1ISXRtSGl0fUpycnJwS91U4aTSzDsDfgIsBfzq2uMqcD+hN4Q4vOcDDeIb+KSjWuzziOcgC9nuXcSXsT8aToEod9sy0tezY7+kt3bhBJPf0L/ZvDBERkTqhQkmcmXUBvgcSAMPzTOFOILfKIivCOTccGG5m9fC0EA4DRgNXmtkFzrn8e4j54za6I4/it3XADD/LdgPiIyIiSEhIqMQpy1bdx5fDvluxnU+XbPetP3FZV9q2CO7OL7o+pCS6NqQ0uj6koIiIklPDirb8PYXndvQK4CZgtnOuMkma37zPKf4G3GNm24C/4xl78TJvkfz29thiqlNkX7Ft8865CcAEf+Ixs+moVbJW2ZeZzQPvL/atX3xiS/7QpXkAIxIREQm8ivaePgNPS95A75A4NZIwFuN17/IiM8t/nnKdd9m2lHptipQV8XliyjK27fN0yG/UIIrRF3cJcEQiIiKBV9GkMQ9Id879VpXBVMBePM82RgBJ3m0/e5ddvLeyi9OzSFkRAGau3MF/5m/0rT92yfEkNYgKYEQiIiLBoaJJ4xKgfilJWU3piydh3IvnmUqccxuBn4AoPLPTFGJm/fD0vt4GzK2pQCX47T+Uw/0Fbkuff3xzLuzaIoARiYiIBI+KJo3P40nWbqzCWI5gZmeY2eDiph00s97Aq97VV51zBTvhPOldPmVmHQvUaQqM866Occ7lVUfcEprGfLGMzXs9Q3sm1o/ksUuOD3BEIiIiwaNCHWGcc++Z2UnA/5lZPPBP51xVzfJSUAc8zy2+YGY/4WkdjPNuP85bZgqeoXcKxjfZzMbjmTJwsZlNA7KB/kBD4CM8nWdEAJizeidv/7DBtz764i40iSvPFOkiIiK1W4XHTXTO3W9macD/Ag+Z2Tpga+lVXP9ynmYG8DiejjdH4xnQ2/Akj+8DbzvnPirhZCPNbBYwCk/v5nBgOfAaMF6tjJLvYFbh29JnH9uMi09sGcCIREREgk9Fx2k04Fk8CZnhGdz7GO+rJOXuYe2cWwv8tQIh5tefCEysaH2pG56euoINuz0N5Q1jInji0uPxXOIiIiKSr6ItjXcCt3vffwtMA7ZTjYN7i1SH+et288bcdb71v17UhaYNYwIXkIiISJCqaNJ4M56Ww4edc09UYTwiNSYjK5d7Jy8if5TRlGOaMLBHq8AGJSIiEqQq2ns6GU+rYtF5n0VCxj++XsHanZ4pyuOiI3jyshN0W1pERKQEFU0adwIHnHOZVRmMSE35acMeXp211rf+lwuPpUV8oIcdFRERCV4VTRo/BxqameZXk5CTmZ3LPe/9Sp73tvQZnRpzVc82pVcSERGp4yqaNI4GUoF/m1lc1YUjUv2e+2Ylq3d4bks3iArXbWkRERE/VLQjzNHAg8A/gbVm9m9gMaWP04hz7vsKnk+kSizatJeXvl/jW7//gmNpnVg/gBGJiIiEhoomjdM5PO6iAQ/4UcdV4nwilXYoJ5d73ltErve+9Gntkxh8ylEBjkpERCQ0VDSJ20AFBusWCaSx365iRWo6APUiw3l64ImEhem2tIiIiD8qOvd0chXHIVKtlm5JY9z01b71e887hqMa6ba0iIiIvyraEUYkZOTlOR78YDE53tvSPZMTGdIrObBBiYiIhBgljVLrTVm8lV83pQEQFRHGUwO76ra0iIhIOZWZNJpZ+6o+qZmFmZl6IEi1y8rJ45kvV/jWh/VOpn2T2ABGJCIiEpr8aWlcbmZvmNkxlT2ZmUWa2c3ASmBoZY8nUpaJP65nw+6DACTUj2RkSscARyQiIhKa/Eka5wHXAUvN7Dszu8XMGvl7AvM408xeBLYA44EmwK8ViljET+mZ2Tz/7Srf+m1ndiS+XmQAIxIREQldZfaeds71MbOLgSeAfkBfYKyZrQQWAovwzEW9B8gCEoBEoB1wMtAdaIBnPMdsYCzwuHNuR1V/GJGCXpyxht0HsgBolVCP63q1DXBEIiIiocuvIXecc5+Y2afAecBwYABwjPd1TSlV83sbrAFeA153zpU6a4xIVUjdl8krsw7P/PLnc48mOiI8gBGJiIiENr/HaXTOOeAL4AszSwLOBHoDpwAtgMZANLAbT8vjCmA2MMs5t6CK4xYp1bPTficzOw+A41o05JITWwU4IhERkdBW0cG9dwPve18iQWXV9nT+O3+jb/2BCzpriB0REZFK0jiNUuuM+WIF3nG8OaNTY87o1CSwAYmIiNQCShqlVpm/bjfTlqX61u87r3MAoxEREak9lDRKreGc44nPl/nWL+3eiuNbxQcwIhERkdpDSaPUGl8u3cbPG/YCEBUext3nHB3YgERERGoRJY1SK2Tn5vHU1MPTBV7fqy1tkuoHMCIREZHaRUmj1Ar/mb+RtTsPABAXE8GoMzVdoIiISFVS0igh78ChHJ6bttK3PurMjiQ2iApgRCIiIrWPkkYJeS/PXMPO/YcAaBEfw9DTkwMbkIiISC2kpFFC2vb0TF76/vB0gXefczQxkZouUEREpKpVaEYYM4sA/gD0Adp5j7Mc+FhTBkpNev6blRzMygWgc/M4LuvROsARiYiI1E4VShqB9UBz7/v8+dkc8KCZzQBGOeeWFVtTpIqs2bGfSfMOTxd43/mdCdd0gSIiItWiokljC+BnYA6wEYgGegFnAynAAjO7yTk3sSqCFCnOM1+uINc7X2Cv9o1IOVrTBYqIiFSXiiaNfZxzc4puNLOjgLHAhcBbZtbcOfePygQoUpyF6/fwxZJtvvUHLuiMmVoZRUREqkuFOsIUlzB6t29wzl0EjACygWfM7OFKxCdyBOccY744/PTDgK4t6No6IXABiYiI1AHV0nvaOfcicCawExhtZo9Ux3mkbpq2bDvz1+0BIDLcuOfcYwIckYiISO1XbUPuOOfmAv2AVOCvZnZXdZ1L6o6c3Dyemrrctz741La0bdQggBGJiIjUDRV9pvEIZlYPaFXk1RJPR5nmwDPAs1V1PqmbJi/cxKrt+wGIjY7g9rM0XaCIiEhNqOg4jY9xZIIYX0Y1DSQulXIwK4d/fP27b/3Wfu1pFBsdwIhERETqjoq2ND6EZ1zGkrqrZgFbgc3AFu9ycwXPJQLAa7PWsj3dM11gs4bR3NinfYAjEhERqTsqmjT+CmzicEJYaOmc21k14Yl47Np/iH/PODxd4P+cfTT1ojRdoIiISE2pUNLonOte1YGIlOZf365i/6EcADo2jeXykzRdoIiISE3Sc4YS9NbvOsA7P673rd93XmciwnXpioiI1CT95pWg98yXK8jO9UwXeEpyEmcf2zTAEYmIiNQ9SholqP26cS+fLdrqW79f0wWKiIgEhJJGCVrOOZ4sMF3g+cc3p8dRiQGMSEREpO5S0ihBa/qKHfywZjcA4WGaLlBERCSQlDRKUMrNc4z54vB0gYNOOYr2TWIDGJGIiEjdFtRJo5lFmll/M/s/M/vBzLaaWZaZbTazyWaWUkb9QWY208zSzGy/mS0ws1FmFtSfW+CDnzaxIjUdgAZR4dzRv1OAIxIREanbqmzu6WrSD/ja+34bsBA4ABwHDAQGmtnjzrm/Fq1oZmOBkUAm8A2QDfQHXgD6m9kVzrnc6v8IUl6Z2bmFpgu8qW97msRpukAREZFACvYWtzzgfaCvc66Fc26Ac+4q59wJwNVALvCwmZ1ZsJKZDcSTMG4DunrrXQp0ApYBlwK31eQHEf+9PnsdW9MyAWgcG81NZ2i6QBERkUAL6qTROfetc+5y59zMYvb9F5jgXb22yO4HvMv7nHMrC9RJBUZ4V+/Xbergs+dAFuOmr/Kt33V2JxpEB3uDuIiISO0X6knTz96lb045M2sNnARkAe8VreCcm4FnnuzmwGk1EKOUw9jvVpGe6ZkusH3jBlzVs02AIxIREREI/aQxv3fE1gLb8ufFXuqcyyih3vwiZSUIbNx9kDfnHp4u8N7zjiFS0wWKiIgEhZC972dmzYGh3tX3C+xq512up2QbipQteuyhBY5dlm4AOTk57N27188q5ZOenl4txw02T075nazcPAC6torj1FYx1fYzrU3qyvUh5adrQ0qj60OKk5OTU+K+kEwazSwCeBuIB75xzn1aYHf+YH4HSjnEfu8yroT9yXh6bksNWb5tP58v3eFb/5+UZE0XKCIiEkRCMmkE/o1n+JyNHNkJJj/TcJU4/jpghp9luwHxERERJCQkVOKUZavu4wfS2PdX+N6fc1wzzjzhqABGE5pq8/UhlaNrQ0qj60MKiogoOTUMuaTRzJ4DbsQznE5/59y2IkXy29tLmz4kf1+xbfPOuQkc7pldVjzTUatkpcxcuYOZK3cCEGZw33maLlBERCTYhFQvAzP7P+AOYAeehHFlMcXWeZdtSzlUfpfcdaWUkRqQl+d48vPD0wVe1bMNHZuW9NSAiIiIBErIJI1m9jRwN7ALOMc591sJRfOH4eliZvVKKNOzSFkJkI9/3cxvW/cBUC8ynLvOPjrAEYmIiEhxQiJpNLMxwD3AHjwJ468llXXObQR+AqKAK4o5Vj884zpuA+ZWS8Dil8zsXP7+5eHpAoef0Y5mDWMCGJGIiIiUJOiTRjN7HLgP2IsnYfSndfBJ7/IpM+tY4FhNgXHe1THOubyqjFXK5+0f1rN5r2cozaQGUdzcV9MFioiIBKug7ghjZhcDD3lXVwG3lzAMy3Ln3Jj8FefcZDMbj2fKwMVmNg3IxtPjuiHwEfBCNYYuZTiYlcPY7w5PF3jHWR2Ji4kMYEQiIiJSmqBOGoGkAu9P9r6KMwMYU3CDc26kmc0CRuHp3RwOLAdeA8arlTGwJs3byJ6D2QC0TqzHoFNL67ckIiIigRbUSWN5hr4pof5EYGJVxSNVIysnj5e/X+Nbv6VfB6Iigv5JCRERkTpNv6mlxn348ya27csEoHFsNFec1DrAEYmIiEhZlDRKjcrNc/x7xuFWxuFntCMmMjyAEYmIiIg/lDRKjfpiyVbW7vRMC94wJoLBp2q6QBERkVCgpFFqjHOOcd+t9q0POT1ZPaZFRERChJJGqTHTf99RaPaXYb3bBTgiERER8ZeSRqkx4wu0Ml59ShuSGkQFMBoREREpDyWNUiPmr9vNvHW7AYgMN246Q7O/iIiIhBIljVIjxhWY/eWy7q1pmVAvgNGIiIhIeSlplGq3dEsa363YAYAZ3NJPrYwiIiKhRkmjVLvx0w8/y3jBCS1o3yQ2gNGIiIhIRShplGq1ducBPl+81bc+ol+HAEYjIiIiFaWkUarVizNWk+c871OOacLxreIDG5CIiIhUiJJGqTZb0zJ4/6dNvvWRKR0DGI2IiIhUhpJGqTavzFxLdq6nmbFnciKntEsKcEQiIiJSUUoapVrsPpDFxB83+NbVyigiIhLalDRKtZgwZx0Z2bkAHNuiISnHNAlwRCIiIlIZShqlyu0/lMOE2Wt96yNTOmBmAYxIREREKktJo1S5iT+uZ19mDgDJjepzwQktAhyRiIiIVJaSRqlSmdm5vDzzcCvjrf06EB6mVkYREZFQp6RRqtTkhZvYkX4IgOYNY7i0R6sARyQiIiJVQUmjVJmc3Dxe/P7wlIHDz2hHdER4ACMSERGRqqKkUarMZ4u2snF3BgCJ9SO55pSjAhyRiIiIVBUljVIl8vIc46cfbmUceno7GkRHBDAiERERqUpKGqVKfLN8OytS0wFoEBXOkNPbBjgiERERqUpKGqXSnHOM/W6Vb33waW1JqB8VwIhERESkqilplEqbu2YXv2zcC0BUeBjD+7QLbEAiIiJS5ZQ0SqUVfJbx8pNb07RhTACjERERkeqgpFEqZdGmvcxcuROAMINb+3YIcEQiIiJSHZQ0SqWM++5wK+NFJ7bkqEb1AxiNiIiIVBcljVJhq7anM3XpNt/6iBS1MoqIiNRWShqlwsZPX+N7f/axTencvGEAoxEREZHqpKRRKmTTnoN8/Mtm3/rIMzsGMBoRERGpbkoapUJe/n4NOXkOgNPaJ9HjqMQARyQiIiLVSUmjlNuO9EP8Z/5G3/ootTKKiIjUekoapdxen72WQzl5AJzQKp4+HRsHOCIRERGpbkoapVz2ZWbz1tz1vvVRZ3bAzAIYkYiIiNQEJY1SLm/NXU/6oRwAOjRpwB+Oax7giERERKQmKGkUv2Vk5fLarLW+9REpHQkLUyujiIhIXaCkUfz27oKN7DqQBUCrhHpc0q1lgCMSERGRmqKkUfySnZvHS98fHsz75r7tiQzX5SMiIlJX6Le++OXjX7aweW8GAI0aRHHlyW0CHJGIiIjUJCWNUqa8PMf46at86zf0aUe9qPAARiQiIiI1TUmjlOmr37axescBAOKiI7iuV9sARyQiIiI1TUmjlMo5x9jvVvvWr+vVloYxkQGMSERERAJBSaOUaubKnSzenAZAdEQYN/RpF+CIREREJBCUNEqpxhV4lvHqnm1oHBsdwGhEREQkUII+aTSzY8zsTjN728yWm1memTkzu9yPuoPMbKaZpZnZfjNbYGajzCzoP3cwWLh+Dz+s2Q1ARJhxU9/2AY5IREREAiUi0AH4YQRwZ3krmdlYYCSQCXwDZAP9gReA/mZ2hXMutyoDrW0K9pi+pFsrWifWD2A0IiIiEkih0OK2BHgGuAroCMwoq4KZDcSTMG4DujrnBjjnLgU6AcuAS4Hbqi3iWmD5tn1MW7YdADMYkaJWRhERkbos6FsanXOvFFw382uu4we8y/uccysLHCvVzEYA04H7zexfzrm8qoq1Nhk//XCP6XOPa07HpnEBjEZEREQCLRRaGsvFzFoDJwFZwHtF9zvnZgCbgebAaTUbXWhYv+sAn/66xbc+8swOAYxGREREgkGtSxqB7t7lUudcRgll5hcpKwW8+P0a8pzn/RmdGtO1dUJA4xEREZHAC/rb0xWQP5Dg+lLKbChSthAzGwoM9fN83QBycnLYu3evn1XKJz09vVqOW5zt6Yd4b8FG3/r1Jzerts8lVaMmrw8JLbo2pDS6PqQ4OTk5Je6rjUljrHd5oJQy+73Lkh7USwb6VVVAoeTt+VvIzvU0M3ZtGcfJR8UHOCIREREJBrUxaczvKeMqcYx1+NFL26sbEB8REUFCQkIlTlm26j5+WkY27/+S6lu//exjSExMrNZzStWp7utDQpeuDSmNrg8pKCKi5NSwNiaN+e3tsaWUyd9XbNu8c24CMMGfk5nZdGpJq+R/52/gQJZn6MpOTWPp37lpgCMSERGRYFEbO8Ks8y7bllKmTZGydV5Obh5vzDn8GOiNfdoRFubX8EYiIiJSB9TGpPFn77KLmdUroUzPImXrvKlLt7F5r6ezeaMGUfyxe6sARyQiIiLBpNYljc65jcBPQBRwRdH9ZtYPaI1ntpi5NRtd8Hp11lrf+8GntSUmMjyA0YiIiEiwqXVJo9eT3uVTZtYxf6OZNQXGeVfHaDYYj4Xr9/Dzhr0ARIWHcd1ppd3ZFxERkboo6DvCmFkPDid6AMd5l0+Y2Z/zNzrnTivwfrKZjQdGAIvNbBqQDfQHGgIfAS9Uc+gh47UCrYyXdGtJk7joAEYjIiIiwSjok0Y8Sd6pxWzvVFol59xIM5sFjMLTuzkcWA68BoxXK6PHpj0H+WLJVt/6jWcUO965iIiI1HFBnzQ656ZzeOzF8tadCEys0oBqmTfmrPNNGdi7YyM6N28Y2IBEREQkKNXWZxrFD/sP5fCfeYenDLyxj1oZRUREpHhKGuuwd+dvJP2QZ47J9k0akHK0BvMWERGR4ilprKNy8xyvzzncAeaG3hrMW0REREqmpLGO+vq3VDbu9gzmnVA/koE9Wgc4IhEREQlmShrrqFdnrfG9H3TKUdSL0mDeIiIiUjIljXXQok17mb9uDwCR4caQ05MDG5CIiIgEPSWNdVDBKQMHdG1Js4YxAYxGREREQoGSxjpma1oGUxYVGMxbw+yIiIiIH5Q01jFvzFlPjnc071PaJXF8q/gARyQiIiKhQEljHXIwK4dJ8zb41oerlVFERET8pKSxDnl/4SbSMrIBaNuoPv2PbRbgiERERCRUKGmsI/LyHK/NXudbH3Z6MuEazFtERET8pKSxjvh2+XbW7jwAQFxMBFec3CbAEYmIiEgoUdJYRxQcZmfQKUfRIDoigNGIiIhIqFHSWAcs3ZLG3DW7AAgP02DeIiIiUn5KGuuAgq2M5x/fnJYJ9QIYjYiIiIQiJY213PZ9mXz66xbfugbzFhERkYpQ0ljLvfXDerJzPYN5n9Q2ke5HJQY4IhEREQlFShprsczsXN7+Yb1vXa2MIiIiUlFKGmuxD37azJ6DnsG8WyXU4w/HaTBvERERqRiNu1JLOed4bfbhDjDDeicTEa6/EUTEP/v372ffvn0cPHiQnJwcnHOBDkmqWG5uLgBbt24NcCRS1cyMiIgI6tevT8OGDYmNja2S4ypprKVm/L6DVdv3AxAbHcGVPTWYt4iUzTnH9u3b2b17d6BDkWoWFqaGhNrKOUd2djZpaWmkpaWRlJRE06ZNMavcTHBKGmupgsPsXHlyGxrGRAYwGhEJFfv27WP37t2YGY0aNSIuLo6oqCglGLVQTk4OABERSgVqm7y8PLKyskhPT2fXrl3s3r2bmJgY4uPjK3VcXSm10Ipt6cxcuROAMPPcmhYR8ceePXsAaNasGYmJGm1BJBSFhYURExNDTEwMERERbNu2jT179lQ6adSfjrXQawVaGf9wXHPaJNUPYDQiEkoyMzMBaNiwYYAjEZGqkP9/Of//dmUoaaxldu4/xIe/bPatDz9Dw+yIiP/yO7yEh4cHOBIRqQr5j5ZURWc2JY21zNs/rCcrJw+AE1vHc1Jb3V4SERGpqyrb+aUgJY21SNHBvG/o065KLxYRERGpu5Q01iKf/LqFnfuzAGgRH8MFJ7QIcEQiIiJSWyhprCWcc4U6wAw5PZlIDeYtIiIiVURZRS0xe9Uulm9LB6BeZDjX9DwqwBGJiEggJScnY2asW7euRs5nZgF7JGrdunWYGcnJyQE5f2lq+t+hOilprCVenbXG9/6Kk1sTX1+DeYuISNUYOnQoZsaECRMCHYoEkAb3rgVWbd/Pdyt2AGAGw3prmB0REalZy5YtC3QIUs2UNNYCr80+/Cxj/87NaNe4QQCjERGRuqhz586BDkGqmW5Ph7g9B7L44KdNvvUb+6iVUUSkuv3444/cc889nHzyyTRr1oyoqChatmzJ5Zdfzg8//FBsndGjR2NmjB49mtTUVG655RZat25NdHQ07dq14/777y921o709HReeukl/vjHP9KxY0fq169PbGws3bt3529/+xsZGRl+xeyco1OnTphZiTECXHbZZZgZ48aN8z0r+MYbbwAwbNgw37OLRW9Xl/ZMY3Z2Ni+99BJnnnkmSUlJREdHc9RRRzFgwADeeeedQmXXr1/Pk08+yZlnnkmbNm2Ijo4mKSmJM888k4kTJ/r1Wf21YsUKhgwZQtu2bYmKiiIuLo7k5GQuvfRS3n///SPKO+d46623SElJITExkZiYGDp06MCoUaPYuHFjuc5d1rOOKSkpmBnTp0+vwCerHmppDHET520gM9szmPdxLRpyWvukAEckIlL7/eUvf2H69Ol06dKFU045hejoaFasWMH777/PRx99xKRJk7jiiiuKrbtx40ZOOukknHOcfvrp7Nu3j1mzZvHUU0/x22+/8cknnxQq/+uvv3LLLbfQtGlTjjnmGE4++WR27drFjz/+yEMPPcQnn3zCjBkziImJKTVmM2PUqFH8z//8D+PGjeO11147oszmzZv59NNPiYuL47rrruPQoUMMGTKEWbNmsXr1anr37k3Hjh195Qu+L8mePXu48MILmTt3LtHR0fTu3ZumTZuyZcsWZs+ezZIlSxg8eLCv/FtvvcXDDz9Mhw4d6Ny5M71792bTpk3MnDmT6dOn8+OPP/Lcc8+Ved6yLF68mN69e5Oenk7nzp256KKLMDM2b97Ml19+SUZGBgMHDvSVd85x7bXXMnHiRCIjI0lJSSEpKYl58+Yxbtw4/vOf/zB16lR69uxZ6diClnNOr0q8gOmA69evn6sue/bscXv27Dli+6HsXNfzf792be/7zLW97zP3/sKN1RaDBK+Srg+Rilwbv/32m/vtt9+qJ6Ba5IsvvnDbtm07Yvsnn3ziIiMjXVJSkjtw4EChfY888ogDHOCGDx/uDh065Nv322+/udjYWAe4WbNmFaq3ceNG980337jc3NxC2/fs2ePOO+88B7gxY8YcEUvbtm0d4NauXevbtnfvXhcbG+uio6Pd1q1bXXZ2dqE6Dz/8sAPcqFGjCm0fMmSIA9zrr79e4s8k/7MVdfHFFzvA9erVy23evLnQvoyMDPf5558X2jZv3jy3ZMmSI47z+++/uzZt2jjA/fDDD4X2rV271gGubdu2JcZX1LBhwxzgnnjiiSP2paenuzlz5hTaNnbsWAe4Zs2aFYovJyfH3X777b7zZ2ZmFqpX3L9Dadvz9evXzwHuu+++8/szlaQ8/6/zzwtMd0VyHrU0hrDPFm1he/ohAJrGRTOga8sARyQidUHy/VMCHUKFrRtzYZUc57zzzit2+0UXXcQVV1zBxIkT+e6777jwwiPP16ZNG55//nmioqJ824499liuu+46xo8fzzfffEPv3r19+1q3bk3r1q2POE5CQgLPP/88Rx99NJMnT+a+++4rM+74+HjfeSZMmMCf//xn377s7GxefvllAEaOHFnmsfzxyy+/8MknnxAbG8vHH39MkyZNCu2PiYnh/PPPL7StpJa6Tp068fDDD3PzzTczefJkTj311ErFlpqaCnDE+QFiY2Pp1atXoW3/93//B8Djjz9Oly5dfNvDw8P5+9//zkcffcT69euZPHlyoZbT2kRJY4hyzvFqgcG8r+/VlqgIPaIqIlJTdu7cyWeffcaSJUvYu3cvOTk5ACxZsgSA33//vdik8ayzzqJevXpHbM/vSLJly5Yj9jnnmD17Nt9//z2bNm0iIyOj4B0vfv/9d7/jvu222xg/fjwvvfQSd999t2/7Bx98wLZt20hJSeG4447z+3ilmTp1KgCXXHLJEQljaTIzM/nyyy+ZP38+O3bs4NAhTwPJ1q1bgfJ93pKccsopfP7559x66608/vjj9O3bl+jo6GLLbtq0iTVr1hAWFsZ11113xP6oqCgGDx7MmDFjmD59upJGCS4/rt3N0i37AIiOCGPQqW0DHJGISN3x4osvcvfdd3Pw4MESy+zbt6/Y7UcdVfzkCw0bNgQ4ojNMamoql112GXPmzCn3uYpz3HHHcfbZZzNt2jS+/PJLLrroIgDGjRsHwKhRo/w+VlnWr18PlK9n9dy5c7nyyivZtGlTiWXK83lLcs899zBz5ky++eYb/vCHPxAdHU23bt3o168f1157LSeccIKv7ObNmwFo0aJFic+OdujQoVDZ2khJY4gq2Mo48KTWJDWIKqW0iEjVqapbvKFqwYIFjBgxgoiICJ555hkuuugiWrduTf369TEzHnzwQZ588klfK2BRYWHluys0fPhw5syZQ+/evRk9ejQnnngiCQkJREZGkpWVVWLrWGluv/12pk2bxr///W8uuugili5dyvfff0/Lli354x//WO7jVZWDBw9y6aWXkpqayo033siIESPo2LEjcXFxhIWF8dVXX3HuueeW+LMtj/r16zNt2jR+/PFHpk6dyuzZs5k7dy4//vgjTz/9NI8++ih//etfAXznK23Gm6qIqaC8vLwqPV5VUNIYgtbtPMC0Zam+9Rs0mLeISI2ZPHkyzjnuuOOOQs8E5lu1alWVnevAgQN8/vnnhIeH89lnn5GQkFAl5xowYADt2rVj6tSprFu3jrFjxwJw8803ExFRdalB27aeu2ArVqzwq/z3339PamoqJ510Eq+88soR+6vyZ5vv1FNP9T0fmZWVxcSJE7npppsYPXo0V111Fcccc4zvmdItW7Zw6NChYhP1tWs9jTmtWrXy67z5z7Tu37+/2P35rbTBRA/BhaDXZ68l/w+alGOa0LFpbGADEhGpQ3bv3g14OrQUtWPHDr7++usqO1daWhp5eXnExcUdkTACR4xx6K+wsDBuvfVW8vLyeOaZZ3j77beJiIjg5ptvLrZ8foKT/9ymv84991wAPv74Y3bu3Flm+dJ+tkCVj9NYVFRUFEOHDuW0007DOceiRYsAT2ek9u3bk5eXx9tvv31EvezsbF9sKSkpfp0rP7lcvnz5EfuWLFlS7nEfa4KSxhCTlpHNews1mLeISKDkP5/35ptvFmolSk9P54YbbmDv3r1Vdq5mzZqRmJjI3r17j0iYpk6dyj/+8Y8KH3vYsGHUr1+fcePGkZ6ezqWXXkqLFi2KLZuf4JR3qsDu3btz0UUX+Y6f35ElX2ZmJl988YVvPf9n++233xZKpvLy8njssceYPXt2uc5fmnHjxhXbArpmzRqWLl0KHG4pBXydhh5++OFCseXm5nLvvfeyfv162rZty+WXX+7X+fv37w/A008/XegZzY0bNzJ06NASb3d/+OGHdO7c2Ve/JilpDDH/mbeBg1m5ABzTLI4+HRsHOCIRkbpl2LBhtGnThp9++on27dtz2WWXcemll5KcnMyCBQu44YYbquxc4eHh/OUvfwFg8ODBnH766QwaNIhTTz2V888/v1Dv5/JKTExk0KBBvvXSOsBccsklhIWF8eyzz3Luuedy4403+p61LMuECRPo2bMns2bNon379pxzzjkMGjSIlJQUWrRowYgRI3xle/TowUUXXcS+ffvo1q0b559/PldffTWdOnXi8ccf5957763w5y3qpZdeonPnznTo0IFLLrmEwYMH079/f4499lj27NnD1VdfzSmnnOIrP3LkSK655hq2bt3KiSeeyHnnncc111zD0UcfzbPPPktiYiLvvfee38+Yjho1ijZt2jB//nyOOeYYLrvsMs466yyOPfZYGjZsyOmnn15svbS0NFasWMHq1aur5OdQHkoaQ0h2bh4T5qzzrd/Yp12pD+WKiEjVS0xMZMGCBdx8883ExsYyZcoUFixYwGWXXcZPP/1U4q3VivrTn/7E5MmTOe2001i6dCmfffYZ4eHhvP322/ztb3+r1LHPPvtsALp06UK/fv1KLNetWzf++9//0rNnT+bMmcNrr73Gq6++6tfQN0lJScycOZN//etf9OjRg3nz5vHBBx+wdu1azjjjDMaMGVOo/OTJkxkzZgwdO3Zk+vTpfPPNN3Tp0oVZs2YVO6ZiRf3v//4vt9xyCw0bNmTOnDlMnjyZlStX0q9fP959990jbv2bGe+88w5vvvkmp556Kj/88AMffPABeXl5jBgxgl9//bVcs8EkJiYye/ZsBg8eTE5ODlOmTGHTpk3cc889TJ06lcjIyCr7rFXFqrq3T7Axs0HACKArEA4sB14HxjvnKt01ycymA/369etXbfND5t/q+H79Qe6Y9DMAjWOjmHXfWcREhlfLOSV05F8fxT3vJHVbRa6N/NuPxx57bDVEJMEkJyeHyy+/nI8//phx48YVavGT2qU8/69TUlKYMWMGwAznXErBfbW6pdHMxgLvACcDM4GvgaOBF4DJZhYyGZdzjldnrvGtDz61rRJGERGpsIULF/Lpp5/SqFEjrr/++kCHIyGg1g65Y2YDgZHANqCvc26ld3sz4DvgUuA2oPKznteAXzan8+umNACiIsK49jQN5i0iIuU3fPhw9u/fz+eff+7rYNKgQYNAhyUhoNYmjcAD3uV9+QkjgHMu1cxGANOB+83sX1Vxm7q6vTP/8LRSf+zWkiZx5R/MVURE5NVXXyUsLIy2bdvy0EMPVdk801L71cqk0cxaAycBWcB7Rfc752aY2WagFXAaUHb3rwDavDeTb3/f5Vu/QcPsiIhIBeX3ZSjvmIsitfWZxu7e5VLnXEYJZeYXKRu0Ji3cSp63v1Kfjo3p3LxhYAMSERGROqdWtjQC+U1xpc3Bs6FIWR8zGwoM9fNc3cDzF1tVDuiab/+hHD74ZZtv/eruTavlPBK60tPTAx2CBKmKXBu5ubmEhYWpFaoOyJ/bWP/WtZ9zjry8PL/yh9Kuh9qaNObPq3eglDL5w/jHFbMvGSh5wKoa9O3vuzmY7fmP3a5RPU5vnxDYgERERCRkVOXQirU1acwf8bqiP6l1wAw/y3YD4iMiIqplnLzr+sTTKj6adxZs4Q/HtyIpMbHKzyG1g8ZplJKU59rYtm0bzjnMjPBwDetVm+W3KEVE1NZUQMBz98DM8DdPKe16qK1XSv49mdhSyuTvO+L+jXNuAjDBnxPlD+7tf2jlY2acdFQ8Jx0Vr6RARKpdTEwMGRkZ7Nu3j0T9kSoS8vLntY6Jian0sWpr0rjOuyxtMMP8eZ7WlVJGRKROSUxMJCMjg9TUVHJycoiLiyMqKgoz07SlIiHAOYdzjqysLNLT09m5cydAlfwRWFuTxp+9yy5mVq+EHtQ9i5QVEanzGjZsSGZmJrt372bnzp2+XzhS++Q/66Y/Bmq/pKQkGjas/MgrtXLIHefcRuAnIAq4ouh+M+sHtMYzW8zcmo1ORCR4mRnNmjWjTZs2xMfHExkZqaSilsrLy/P1oJbaxcyIjIwkPj6eNm3a0KxZsyr5f1xbWxoBnsQzsPdTZjbHObcKwMyaAuO8ZcaEwmwwIiI1LTY2ltjY0h4Ll1CXP/yKnpcXf9XapNE5N9nMxgMjgMVmNg3IBvoDDYGPgBcCF6GIiIhI6Ki1SSOAc26kmc0CRuHp4RwOLAdeA8arlVFERETEP7U6aQRwzk0EJgY6DhEREZFQVis7woiIiIhI1VLSKCIiIiJlUtIoIiIiImVS0igiIiIiZVLSKCIiIiJlsvxphKRizGwT0Co+Pp5u3bpVyzlycnIAiIio9Z3dpQJ0fUhJdG1IaXR9SHF++eUX0tLSADY751oX3KeksZLMbC8QH+g4RERERKpQmnMuoeAG/XlReWuBdsB+YFU1naMbnsQ0Dfilms4hoasbuj6keN3QtSEl64auDzlSRyAWT35TiJLGSnLOda/uc5jZdDwz2vzinEup7vNJaNH1ISXRtSGl0fUh5aWOMCIiIiJSJiWNIiIiIlImJY0iIiIiUiYljSIiIiJSJiWNIiIiIlImJY0iIiIiUiYljSIiIiJSJiWNIiIiIlImJY0iIiIiUibNCBMaJgDTgXUBjUKC1QR0fUjxJqBrQ0o2AV0fUg7mnAt0DCIiIiIS5HR7WkRERETKpKRRRERERMqkpFFEREREyqSkMciZ2SAzm2lmaWa238wWmNkoM9O/XR1lZhPMzJXyWh7oGKV6mdkxZnanmb1tZsvNLM/7b3+5H3X1nVKLVeTa0HeK+Eu9p4OYmY0FRgKZwDdANtAfeAHob2ZXOOdyAxiiBNZsYFUx27fWdCBS40YAd5a3kr5T6oQKXRte+k6RUilpDFJmNhDPl/s2oK9zbqV3ezPgO+BS4DbguYAFKYH2inNuQqCDkIBYAjwDLAAWAq8C/UqroO+UOqPc10YB+k6RUilpDF4PeJf35X+5AzjnUs1sBJ6xte43s3855/ICEaCIBIZz7pWC62bmTzV9p9QBFbw2RPyiZ1iCkJm1Bk4CsoD3iu53zs0ANgPNgdNqNjoRCTX6ThGRqqCWxuDU3btc6pzLKKHMfKCVt+ycGolKgs2ZZtYViAVSgVnA12olkmLoO0X8oe8UKZWSxuDUzrtcX0qZDUXKSt1zfTHbfjOzq51zi2s8Gglm+k4Rf+g7RUql29PBKda7PFBKmf3eZVw1xyLB5xfgDqALnmulJTAA+BU4DphmZq0CFp0EI32nSGl+Qd8p4ge1NAan/CeXNTG4HME592yRTQeAKWb2NTADzzNpD+DpCSsC+k6RUug7RfyllsbglO5dxpZSJn9feillpA5xzmUBT3pXLwhkLBJ09J0i5abvFClKSWNwWuddti2lTJsiZUUA8mdu0K0kKWidd6nvFCkvfaeIj5LG4PSzd9nFzOqVUKZnkbIiAI28y/2llpK6Rt8pUlH6ThEfJY1ByDm3EfgJiAKuKLrfzPoBrfHM7DC3ZqOTIHeldzk/oFFIUNF3ilSCvlPER0lj8Mp/juQpM+uYv9HMmgLjvKtjNH5W3WJm3cxsgJmFF9keYWZ34+kBCfDPmo9Ogpy+U+QI+k6R8jDn1JkuWJnZODyTz2cC04BsoD/QEPgIuNw5lxuwAKXGmdkfgQ+B3cDvwCY8Q6ScgGeYjDzgAefc04GKUaqfmfXgcKIHnmFR4oCVeK4NAJxzpxWpp++UWq6814a+U6Q8lDQGOTMbBIzC8x84HM9Dya8B49UiUPeYWTvgTuAUPJ0aGuEZRmUTMBMY65xbGLgIpSaYWQrwXVnlnHNHTDys75TarbzXhr5TpDyUNIqIiIhImfRMo4iIiIiUSUmjiIiIiJRJSaOIiIiIlElJo4iIiIiUSUmjiIiIiJRJSaOIiIiIlElJo4iIiIiUSUmjiEgJzCzFzJyZrQt0LFXNzBqZWZqZrS46hVwFjjXY+3N6pqriE5Hgo6RRROokMxtqZqPNrFugYwmQv+CZPvDJKpg68D/AKuA2M2td6chEJCgpaRSRumoo8AjQrZQyB4EVwOoaiKfGmNlRwEhgI/BGZY/nTTrHADF4fqYiUgspaRQRKYFzbp5zrrNzrn+gY6lio4BoYIJzLruKjjkJOABcb2aNq+iYIhJElDSKiNQhZhYBXO9d/U9VHdc5dxD4BIgCrq2q44pI8FDSKCJ1ivdZRgf082563duJwxXt9FJaRxgzm+7dN9TMGprZ095OJRlmtsbMHjOzmALl+5vZl2a208wOmNn3ZnZGGbHGmtmDZjbf22kl08xWmtnzZtamgj+CC4DmwFLn3G8lnDfKzO40szlmttfMss0s1cx+NbOxZtarhGO/610Oq2BsIhLEIgIdgIhIDcsAUoEkIBLY592Wb0c5j5cI/Ah0xnN7NhxoBzyM53nJi81sJPAC4ID9QH3gDGCamZ3lnJtd9KBmdizwBdDWuykHOAR0BG4HrjWzi4qrW4Y/eJfF1vO2RH7F4aTaAWlAI6Ap0NX7fm4x1fOP2dXMmjvntpUzNhEJYmppFJE6xTn3X+dcc2COd9OdzrnmBV49y3nIRwADznDOxQKxwE14kryLzOxh4Fk8HUUaOefigWQ8SVcU8M+iBzSzeOBzPAnjR0APoJ73+O2At/Akq++bWUI54+3tXS4sYf8gPAnjQeA6oL5zLhHPM5BtgduAX4ur6JzbAWzwrvYpZ1wiEuSUNIqIVE4DYIBzbhaAcy7LOfcK8KZ3/2PA2865B51ze71l1gPX4GnF6+ntzVzQPXgSy4+By5xzPzvncrx11znnrseTVDYDhvsbqPd2+Qne1UUlFDvNu3zTOfe2cy7Te95c59wG59xY59yTpZwmP6E81d+4RCQ0KGkUEamc95xzq4rZPq3A+yOSLG/imF/v+CK7h3iX/3TOuRLOO8m7PMffQPHcXs4fyHtnCWX2eZctynHcgvKPW9H6IhKk9EyjiEjlLC5h+3bvMpPDyWFRqUAnPLeaAfB2cMkfIPs9M8sroW6Ud1meDjEFh8LZU0KZL4D7gEvM7BNgAjDDObfLz3PkH1fD7ojUMmppFBGpnK0lbM+fZSW1lNbC/DKRBbYVbKFrgucWdHGv/ESzfjlijS7wPqu4As65GcBf8T6TCbwP7DSzZWb2dzPrVMY5Mr3LeuWIS0RCgJJGEZHgUvB7Od45Z2W8kstx7N0F3ieUVMg59zhwNPAA8CWeW9adgT8Bv5nZ9SXV5XAy62/LpIiECCWNIiLBJbXA++Oq+NgFn2NMLLEU4Jxb65wb45w7D8/wRGcC3+N5rGmcmTUtoWr+cUt6ZlJEQpSSRhGpq/KfFbSARlGEc24thxPHy6r42Ls4nMy1K0e9XOfcdGAAkI2nx/jJJRRP9i6XVyxKEQlWShpFpK7K7yWcEMggSjDBuxzpHeS7WOYRX85j549PWWzSZ2ZRxW33yuLwc5jRRXd6Bwbv5l2dWc64RCTIKWkUkbpqqXd5WQUSr+o2BliDp0VvhpkNMbPY/J1m1sbMbsIzQPel5Tz2LO+ypEHM3zSz183sXDOLK3DOZOANIAbPDDrFJYUnePcfAH4uZ1wiEuSUNIpIXfUWnpazPnh6B282s3VmNquMetXOOwj4ucAyPD2oJwBpZrbLzA7imXXlJaA7ngHCy+M9b52+BRPRAmKAocBU7zn3mNkBYC1wFZ6Wxlucc8U9s3ihd/l+/mDkIlJ7KGkUkTrJObccz8DYU/HMrdwczzR5rUurV1O8A4Z3B0YC3+Hp+dwQz1A4i4B/4Znu761yHncd8A2eIXEuKabI/cC9eH4ua/CMBxkOrAZeB3o450o659Xe5avliUlEQoOVPHyYiIjURmZ2OZ4WxynOuQFVdMwT8CSzK5xznavimCISXNTSKCJS93yAZ47oC8ysqob1+bN3ObqKjiciQUZJo4hIHeOcy8MzcLcBD1b2eGbWDhiEp/PLfyt7PBEJTpp7WkSkDnLOfWFmdwMNzCyikh1XWgF/w3O7W888idRSeqZRRERERMqk29MiIiIiUiYljSIiIiJSJiWNIiIiIlImJY0iIiIiUiYljSIiIiJSJiWNIiIiIlKm/wfG2pbQYGTf5gAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 691.2x518.4 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Apply your model to find velocity for seconds 0 through 12\n",
        "# Define model parameters, i.e. bungee jumper mass (in kg)\n",
        "model = bungee_analytical(68.1)\n",
        "# Use a simple loop to collect the data \n",
        "t = [i for i in range(20)]\n",
        "v0 = [model.get_velocity(i) for i in t] \n",
        "\n",
        "\n",
        "# Some plotting resources.\n",
        "import seaborn as sb\n",
        "sb.set_context('poster')        # set figure style \n",
        "fsz = np.array([6.4,4.8])       # figure size. \n",
        "\n",
        "# plot the results\n",
        "fig, ax  = plt.subplots(1,1, figsize=fsz*1.5)\n",
        "ax.plot(t,v0, label='analytical solu.')\n",
        "\n",
        "# decorate the figure to make plot professional\n",
        "ax.axhline(y=model.get_velocity(np.inf),ls='--',c='k')  # add terminal velocity\n",
        "ax.annotate('terminal velocity',[0.5,model.get_velocity(np.inf)+2],fontsize='x-small')  # annotate the graph \n",
        "ax.set_ybound(upper=60)        # set bounds \n",
        "ax.set_xlabel('time (s)')      # set x label \n",
        "ax.set_ylabel(r'$\\nu$ (m/s)')  # can use latex style with the r'$<latex here>$' \n",
        "ax.grid(True,alpha=0.2)        # add gridlines\n",
        "ax.legend(loc=4)               # add legend\n",
        "fig.tight_layout()             # expands graph to borders (exp. when printing)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "##### Finding a Numerical Solution with Python\n",
        "\n",
        "Here, we will use Scipy and some other libraries to solve the bungee velocity numerically. I use a finite-difference approximation to find the velocity. We will learn this method later in the semester, but you might want to remember what a deriviated is (i.e. $\\frac{dy}{dx}$ = $\\frac{\\Delta y}{\\Delta x}$). We can rewrite Eq.1 as an approximation by \n",
        "<br />\n",
        "<br />\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "    (3)\\qquad \\frac{v(t_{i+1}) - v(t_{i})}{t_{i+1} - t_{i}}  = g - \\frac{c_d}{m}v(t_i)^2\n",
        "\n",
        "\\end{aligned}$$\n",
        "We can rearrange Eq.3 to yield: \n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "    (4)\\qquad         v(t_{i+1}) = v(t_{i}) + [g - \\frac{c_d}{m}v(t_i)^2] (t_{i+1} - t_{i})\n",
        "\\end{aligned}$$\n",
        "\n",
        "<br /> \n",
        "<br /> \n",
        " \n",
        "\n",
        "\n",
        "Below I will use a loop to iteratively solve the problem. The loop will caluclate the velocity at the given timestep, using the previously found velocity to solve. This is a boundry defined problem, i.e. we know that the inital velocity is zero. Understanding this is critical to finding a solution. In other problems, it will be necssiary to know initial conditions to enable a numerical solution. Furthermore, we can calculate the model error since we know the true analytical solution. The results/data is passed to a Pandas DataFrame Python object to facilitate plotting, analysis, etc."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "rnQijFfNUxdO",
        "outputId": "b15f95be-1f26-4202-90ab-9c7c26730cb6"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_26035/2499770028.py:25: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  err = 100 * np.abs(v-v_analy)/v_analy\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>time</th>\n",
              "      <th>v_num</th>\n",
              "      <th>v_anly</th>\n",
              "      <th>rel_error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.0</td>\n",
              "      <td>19.613300</td>\n",
              "      <td>18.729189</td>\n",
              "      <td>4.720499</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.0</td>\n",
              "      <td>36.402213</td>\n",
              "      <td>33.111825</td>\n",
              "      <td>9.937198</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>6.0</td>\n",
              "      <td>46.286283</td>\n",
              "      <td>42.076227</td>\n",
              "      <td>10.005783</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8.0</td>\n",
              "      <td>50.169627</td>\n",
              "      <td>46.957495</td>\n",
              "      <td>6.840510</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>10.0</td>\n",
              "      <td>51.302813</td>\n",
              "      <td>49.421367</td>\n",
              "      <td>3.806950</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>12.0</td>\n",
              "      <td>51.591747</td>\n",
              "      <td>50.617479</td>\n",
              "      <td>1.924766</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   time      v_num     v_anly  rel_error\n",
              "0   0.0   0.000000   0.000000        NaN\n",
              "1   2.0  19.613300  18.729189   4.720499\n",
              "2   4.0  36.402213  33.111825   9.937198\n",
              "3   6.0  46.286283  42.076227  10.005783\n",
              "4   8.0  50.169627  46.957495   6.840510\n",
              "5  10.0  51.302813  49.421367   3.806950\n",
              "6  12.0  51.591747  50.617479   1.924766"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import pandas as pd\n",
        "from scipy import constants\n",
        "g = constants.g\n",
        "cd = 0.25\n",
        "m = 68.1\n",
        "\n",
        "v_init = 0 \n",
        "t_init = 0 \n",
        "t_final = 13 \n",
        "h = 2 # 1e-4   # stepsize --- try changing this variable to see how it effects the solution and error\n",
        "\n",
        "time = np.arange(t_init,t_final,step=h,dtype=float)\n",
        "vel  = np.zeros(time.shape[0])\n",
        "model = bungee_analytical(m)\n",
        "\n",
        "data = []\n",
        "for i in range(time.shape[0]): \n",
        "  del_t = time[i] - time[i-1]\n",
        "  if i == 0: \n",
        "    v = v_init\n",
        "  else: \n",
        "    v = vel[i-1] + ( g - (cd/m)*(vel[i-1])**2 ) * del_t\n",
        "  vel[i] = v \n",
        "  v_analy = model.get_velocity(time[i])  # Get analytical solution\n",
        "  err = 100 * np.abs(v-v_analy)/v_analy\n",
        "  data.append([time[i],v,v_analy,err])\n",
        "\n",
        "columns = ['time','v_num','v_anly','rel_error']\n",
        "data = pd.DataFrame(data,columns=columns)\n",
        "data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can plot our results and compare with the analytical solution. It is not a perfect approximation, but we can see that the results are close to the analytical solution. While the analytical solution wasn't terribly difficult to obtain, for many other problems a analytical solution will not be so easy to find and a numerical approach will have to be taken. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 568
        },
        "id": "WbvKBwTuhBeU",
        "outputId": "6da4d75d-ef00-4303-d931-41414ee6d6ff"
      },
      "outputs": [
        {
          "data": {
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48sorP94vTkRERCTKFI4EgClTpvCrX/2KBx98kNtvvx2fz8fy5cu54IILcDgc/OEPf+Dhhx/mN7/5Dffffz8AkyZN4vzzzx/wzX8su/jii/ntb3/L9773Pe677z4SExNZsGABf/rTn5g/f/5J339WVhZlZWVs3LiRGTNmMG/evH41aWlpvP766/zoRz/iueeeY/369djtdvLy8rjkkkuG7X1xOBxs3ryZ73//+zz77LP87ne/w+1289nPfpbvf//7EYtjQGgo4aWXXspjjz0W3pdo2rRpfPaznx3ycRITE3nmmWf4zne+w9e//nW6u7u57LLLIsJRamoqn/vc5/jVr34V3ixWREREZDSyTnSi+1hlWVZzWlpaWnNzc7SbQltbG3BsKJOMbuPpen7lK1/hl7/8Jfv374/YfHYsGU/Xc7zQNR1bdD3HFl3PsSWWrqfb7cbj8XiMMe6BzmvOkYicFI/Hw5NPPsnVV189ZoORiIiIjA8aViciH8uOHTt45513WLt2LW1tbdxzzz3RbpKIiIjISVHPkYh8LM8//zzLli1j9+7dPPzwwwPOrRIREREZTTTnSHOO5DTR9RxbdD3HHl3TsUXXc2zR9RxbYul6as6RiIiIiIjICVA4EhERERERQeFIREREREQEUDgSEREREREBFI5EREREREQAhSMRERERERFAm8CKiIiIiMhpEAgE2LRpE+vXr6ehoQGn08nSpUspKysjLi4u2s0bkHqORERERETklKqtrWXevHksXryYN954g+7ubrZu3crixYuZN28etbW10W7igNRzBASDQfbv3z/o+YkTJ5KcnAyEEvDBgweHvL+cnBwSEhIA8Pl8HD58eMj6SZMm4XQ6Aejq6qK+vn7I+ry8POz20KXr6OgY9slVUFCAZVlAaBOuoe7fsiwKCgrCtz0eD01NTYPW2+128vLywrebmprweDyD1judTiZNmhS+XV9fH94YbCAJCQnk5OSEb9fW1tLR0TFofXJyMhMnTgzfrq6upqura9D6lJQUJkyYEL59+PBhfD7foPVutxu3+9ieYQcPHiQQCAxY297eTnp6esSGZ0M9zwAyMzPD9cFgkAMHDgxZn52dTWJiIgB+v59Dhw4NWZ+bm0t8fDwA3d3dHD16dMj6vs+1zs5OampqhqyfMmUKNlvo/1yGe64BTJ06Nfx1S0sLjY2Ng9bGxcWRn58fvt3c3MxQmzc7HA4mT54cvt3Q0EBra+ug9cc/1+rq6mhvbw/f7v26929BUlISWVlZ4fPDPddcLheZmZnh20eOHMHr9Q5an5aWRnp6evj2oUOH8Pv9g9anp6eTlpYWvl1VVcVQm3z3fa4ZY6iqqhq0FiArK4ukpCTgxJ5rff8Oer1ejhw5MmT95MmTcTgcQOjvYHV19ZD1+fn54f91bG9vp66ubsj6vs+11tZWGhoa+l3TXjabjSlTpoRvD/dcO/7vYGNjIy0tLYPWx8fHk5ubG7493N/BxMREsrOzw7dramro7OwctP7459rRo0fp7u4etD41NZWMjIzw7eGea8f/HTxw4ADBYHDQ+gkTJpCSkhK+PdzfwZN9zR3u/o9/zR3uuabX3JF9zQ0EAvzpT3/ipZdeoq2tDZfLFe5pOHLkyKCvuQAZGRmkpqaGb+s1N9JIvubW1taycOFC9uzZw5o1a1iwYAF2ux2n08mGDRu47777wqEpLi6u32vu8U7la+5Qf6+A0IvieP4AmgEz1Mfzzz9vetXX1w9ZC5ht27aF68vLy4etf//9940xxrS2tpqXXnpp2PrDhw+H73/Dhg3D1nd3d4frH3/88SFrXS6X6WvNmjVD1hcUFETUr1ixYsj6c889N6L+1ltvHbJ+4cKFEfU33HDDkPU33XRTRP1ll102ZP1Xv/rViPrZs2cPWX///fdH1Ofm5g5Z/1//9V8R9Q6HY8j6p556Klzb0tIy7LXdvHlzuL6ysnLY+rfffjtc//bbbw9bX1lZGa7fvHnzsPUtLS3h+qeeemrIWofDEfG7+elPfzpkfW5ubkT9/fffP2T97NmzI+q/+tWvDll/2WWXRdTfdNNNQ9bfcMMNEfULFy4csv7WW2+NqD/33HOHrF+xYkVEfUFBwZD1a9asiah3uVxD1j/++OPh2u7u7mGv7YYNG8L1hw8fHrb+9ddfD9e///77w9aXl5eH67dt2zZsfX19fbj++eefH7a+r1/84hdD1mZkZETUP/DAA0PWFxUVRdTfeeedQ9bPmzcvon758uVD1i9evDiifvHixUPWL1++PKJ+3rx5Q9bfeeedEfVFRUVD1j/wwAMR9RkZGUPW/+IXv4ioH+5afdzX3NbWVvOPf/xj2Pre11xjjHn99deHrddr7uD1p/s1t6ioyGRlZRnAzJ0712RnZw9Z/9Of/jTi/vWae+zjdL/mlpaWms7OTtPR0WHa2tpMWVnZkPUlJSUGMH/4wx+MMVF5zW02g2QD9RyJiIiISMz5zGc+w3e/+13WrVvH7bffPuTIjljV+4Z7qB6vXq2trXg8HowxQ4506HX48GGSkpIwxgzbe26MYefOneH2DDeqyefz8de//jVcP9zogo6ODv72t7+Fb//zn/8csj47O5umpiaefPJJrrnmmiFrR5plhhh2MR5YltWckpKS9v777w9aM1LD6tra2ujq6hqyyxvUxT/ahtX1/XnVxR9Jw+o0rK6XhtVpWF2vj/ua29bWhs/nG/I1CDSsLlZfc7du3cqXv/xl1qxZw6c//WlaW1tJSUlh0qRJBINBfvOb33Dbbbfx3//931x66aUEg8Hw37jeN/BpaWm4XK6IN/TH9wr0PleNMbjdbpKSkggGgwQCgfD7td77Pv4jPT2d+Ph4jDH4fD6qq6sj2nD892VkZIT/rnm93iFf4yD03O/9u9bd3T3kcwFCf5d7X3M7OzuHfe73vbbt7e1DvibabLaI17i2trYhnztxcXERz4Wvfe1rdHV1sWrVKiD0b82yLKZOnUpBQQEJCQl8+tOfJjExkZdffnlEh9WdddZZtLa2eowx7oG+V+HIsprT0tLShnrhGym9T7q+c1Rk9NL1HFt0PcceXdOxRdczdvn9fnw+Hz6fL+LrvrfvvPNO3nrrLTZs2IAxJnw9e/8D0OfzceONN3Luuedy3333RfPHGRGWZYU/bDbbkLdP5tjp+r6bb76Zbdu2cfDgQZxOZzj49P779Hq95Ofnc+WVV/L000+P6O/W7Xbj8XgGDUcaViciIiIiwwoGgycUdI4/diL/EV9bW8ukSZMG7bXsHQ0w0H9mx3pQ+DjfN9otW7aM5557jmeffZZly5b1O79u3Tpqa2tZunRpFFo3NIUjERERkXHG7/cPG26Ov30i82aGY1kWDocj/GG328PB54033mD69OkkJSXR3d1NXFwcqampWJaFz+ejtraWK664gksuuaRfqJDYUlZWxty5c7n99tsxxrBkyRIcDgderzc8h2zu3LksWrQo2k3tR+FIREREZJTqnf/yUYPOqZhWERcXFxF0+oadwW4PtvHnv/3bv7Fx40ZeffVVli1bFh5W1zvX8bnnnqOuro5ly5aF54BJ7IqLi2Pjxo0sXryYW265hdmzZ1NQUMD27dupra1l7ty5bNy4MSY3gtWzS0RERCQGBAKBEw43vbeHWjzjRPX25gwXbPrettvt4cUAToXR3NMgA8vKyuKNN95g8+bNvPDCCzQ2NnLllVeydOlSFi1aFJPBCBSOREREZBQLBAJs2rSJ9evX09DQgNPpDG8aGq03X8aYjzQ3p/f2sJtTnoC+vTknGnZioSdmNPc0jGfGGFq6/DS1e2lo99LU7qWx47jP7VnUn3UzzR0+Pn9hAdfMnxHtZg8p6v8aLMu6HNg2yOkzjDG7+9ReBPwncC7QAjwLrDDGDL7OpIiIiIxJtbW1LF68mO3bt4ffTL/22ms888wz4TfTfZf//TiCweCAiwwMd/tkWZbVr6dmqKBzOnpzRtpo7WkYK4wxdPoCNLZ7aWr3hcNNv9DT7qWpw0tju4/mDi/+4IkP0TzSPPjy27Ei6uGoj58Afz/uWHhjDMuyzgZeAXYCdwJ5wDeB6cB1I9RGERERiQGBQIDFixezc+dO1q5dy3XXXYfD4SA+Pj48DGvx4sW88cYbxMXFhXtzPurcnFPVm/NRhqz1zs0ZjwsNxMXFcc011zB//nxAS7OfjG5/gOYOX0/Y6RtufDR19Ak94bDjpdt/cs/3eLuNCclO0pOdZCQ7SU8KfXY5wJ3k4NxpE4e/kyiLpXD0J2PMC0OcXw00AJcbY9oALMvaDzxiWdYVxpitI9BGERERiQGbNm1i+/btrF27lhtvvJEjR47Q1dVFfHw8559/PitWrOC+++7jpz/9Keeff/4JLyk9nKF6bQa7PZp7cyQ2BIKG5o5jPTZ9A03kUDYfje3dNLX7aOs+uR5Mu80KhZwkJ+nJjoiwk57kZIKrz+2eukTnwL17o2kfslgKR1iWlQJ0GmP8xx1PBRYC/9UbjHo8AfwYuBFQOBIRERkHuru7efTRR8nIyGD69On87W9/o7OzEzi2aegFF1yA2+1m48aNnHPOOf3uw2azfay5OeOxN0dOLWMMrd3HzdPpM1RtoHk7zZ0+TibbWxa4Ex19wk6fz8mOAcNOSvz4fL7HUjj6DeAC/JZlbQO+YYz5Z8+5Mwm19e2+32CM8VqW9S7Q/69eD8uy+u8WFikNjiXaaOro0NSpsUTXc2zR9Rx7dE1HD6/Xi8fjobm5GY/HQ2dnJw0NDRQXF9Pa2gqE9u1JTEwkMTExvCjBOeecQ0JCAgUFBf3m73yU+SvBYJDu7m66u7tP148oxxlN/z47faHha009H82dx77ue7u5w09Tp4/mDt9HmqczEFd8XCjsJDlwJzlIP+5rd5KD9CQ76UlO0pMcpCbYibOdaNAx4O+m3X/qnu+j6XrGQjjyAs8DfwTqgbMIzSV6zbKsucaYPUBuT+3RAb7/KDBvJBoqIiIip5/P5wsHIY/HM+Abq7S0NHbv3k1eXh6ZmZnYbDYsywrvi+Pz+airq2PevHlMnBj78xwkNvgCwVDQ6QkxTX0CTSjg+GiMCDw+uk7BPJ30pJ5wExFy7AMEntCHI05DNU+XqIcjY8xfgb/2ObTBsqzfE+oluh/4ApDYc26gCNvV5/xA9+8e6vF7epbSYmkMZCy1RU6erufYous59uiaRp/f78fj8dDU1ERzc3O/0RyJiYnYbDbS0tJwu92kp6cTCAS47rrreOeddyI2De29nmvXrmXHjh08+OCDusaj2Mlcu0DQ4OkcYn5Oz8IEje3HzrWe5DydOJsVGqKWPPA8nb7zc3rPJzrGz+Ibo+HfYtTD0UCMMe9ZlvUycGXPoc6ez/EDlCf0OS8iIiIxLhAIhIfJNTU10dbW1m+xBJvNRmpqKm63G7fbTWpqasTCBldffbU2DR1HjDG0dfvDS0w3tnf3n5/TNwR1hJaZPsnRa7iTHH3m5vSfpxMZdpykJozPeTpjSUyGox4HORaOeofT5Q5Ql0ufJb9FREQktgSDwXAYam5upqWlpV8YsiwrIgylpaUNucqbNg0dWwJBw8HGDipq26ioa2PX4SaOerpp6Q6EQ48vcLLzdOyh3po+CxJkDLDsdG/wSUt0YNfwtXEnlsPRdKCu5+sdgB/4BPC73gLLspzA2cDTI946ERERGVAwGKSlpSUiDB2/X5BlWbhcLtLT08Nh6KMGGW0aOvp4/UH2N7Szt6YtHIT21rSyr74d70eYu+Ps3U8novfGQUZyfCjcRPTyOHEnOYi36/kgw4t6OLIsa6Ixpu64Y5cAnwTWAhhjPD3D7G62LGt1n+W8bya0wt3/Hck2i4iIyDHGGFpbW8Nzhjwez4Cbp7pcrvCcobS0NOz2k38bok1DY1OH18+Hte1U1LVGBKGqhg4CQ4x1c9ptTM9MZmpGAvnpieSku45tKjpO5+nIyIp6OAKetSyrg9CiDPXAbOC2nq9X9qm7t6fmVcuyHgXygG8AfzTGvDyiLRYRERnHjDG0tbWF5wx5PB4CgUC/uuTk5Igw5HA4otBaOZ08HT721raGwk9tG3t7Ph9uHno6eLIzjsIsF4VZKT2fXRRlucjPSLG3E7IAACAASURBVCLOZo2qTUNlbImFcPQCoRXpvgGkArWEhsmtNMYc6C0yxvzDsqwFwIOENn5tAR4BVox4i0VERMYRYwzt7e0RYcjv77+qV1JSUnjOkNvtxul0RqG1cqoZY6hr7Y4IP71f17cNvRdOepKDoqwUZvSEn94glJuWoJ4fiUlRD0fGmJ8CPz3B2teAi09vi0RERKQ3DPV++Hy+fjUJCQnhOUNut5v4+IEWlZXRIhg0HG7u7BN+jvUItXQNvcR1TmpCOPgU9glCE1x6TsjoEvVwJCIiItHX2dkZnjPU3NyM1+vtVxMfHx8eJud2u0lISIhCS+Vk+QJBqhp6VobrCUB7a9vYV9dOp6//8MhelgVTMpIonOiKCEIzslykJmjIpIwNCkciIiLjUFdXV0QY6u7uPzzK6XRGhKHExEH3XJcY1OUL8GFdqOfnwz5D4vY3tA+5LLYjzmLqhGSKsl2hIJSdQuFEF9MnJpPg0IpvMrYpHImIiIwD3d3d4TlDzc3NdHV19atxOBzhIXLp6ekkJSVFoaXyUbV2+cK9Px/2mQ90sKkDM8TWQImOOGZkJVM40UVRdgozJrooynYxJSMJh/b3kXFK4UhERGQM8nq94V6hpqYmOjv7rx5mt9sjFlBITk7WJPkY1tDWHbEgQu9HdUv/oNtXaoKdop7en8IsF4U9PUKT3YnYbLreIn0pHImIiIwBPp8vYgGF9vb2fjVxcXERYcjlcikMxRhjDEc9XceFoNC8oKaO/oti9DUxJb6nF6gnBE0MBaGJrnhdZ5ETpHAkIiIyCvn9/ogw1LsvTF82m420tLTwnKGUlBS9SY4RgaDhQGNHxKpwvUPi2r2DL4oAkJeeGA4/x4JQCmlJWhRB5GQpHImIiIwCgUAAj8cTnjPU1taGOW5Cic1mIzU1NTxnKCUlBZtNc0eiqdsfYH99RzgA9c4L2lffjtcfHPT74mwWBROSIvYGKspKYfrEZJKcevsmcrroX5eIiEgMCgQCtLS0hOcMtba29gtDlmWFw5Db7SYtLU1hKErau/18WNfG3po2KuqODYk70NhBIDj4qghOu40ZEyP3BirMcjF1QjJOu66lyEhTOBIREYkBwWCwXxgKBiN7FizLIiUlJSIMxcVpaeWR1NTuDYef3iD0YW0bh5v7L3jRlyvezow+Aaj3c156EnFaFEEkZigciYiIRIExJhyGmpub8Xg8/cIQgMvlCs8ZSktLw27XS/fpZoyhtrW7JwC1UtHTI/RhXRv1bf03x+1rQrIzIgT1DofLTtWiCCKjgf7CioiIjABjDG1tbeE5Qx6Ph0Cg/8T75OTk8JyhtLQ0HA5Nsj9dgkHDoaZOKupaQ71AtceGxLV2+Yf83ty0hIjw0/t1RrJzhFovIqeDwpGIiMhpYIyhvb09Igz5/f3fcCclJUUsr+106s31qeYLBKlqaA8HoN5lsvfVt9HlG3xRBJsFUzKSeoJPSng43IwsF654vYUSGYv0L1tEROQUaW9vD88Z8ng8+Hz996VJTEyMCEPx8fFRaOnY1OkLsP+w59jCCD3LZFc1dOAfYlEER5zF9MxQz0/fIXHTMpNJcGhOl8h4onAkIiLyMXV0dETsNeT19p+PEh8fH54z5Ha7SUhIiEJLx6Zg0PDuoWY276hmy86j7G/oZPAIBEnOOGZMPNb709sTNCUjCXucVoYTEYUjEREZZwKBAJs2bWL9+vU0NDTgdDpZunQpZWVlw6781tXVFR4m19zcTHd3d78ap9MZnjPkdrtJTEw8XT/KuOQPBHmrspFNO6vZvLOampb+1yAt0RGxIELvx6S0RGxaGU5EhqBwJCIi40ZtbS2LFy9m+/btzJ49m4KCAl577TWeeeYZ5s6dy8aNG8nKygrXd3d3R4Shrq6ufvfpcDgiwlBSUtJI/kjjQpcvwOsV9WzaUc3Lu2po6ogcrliSncInizM4vyCNMwuyyHQ5tTKciHwsCkciIjIuBAIBFi9ezM6dO1m7di3XXXcdDoeD+Ph41q1bx+23384111zD73//+/AS252d/feusdvt4SFy6enpJCUl6Y34adDW7efV8lo27ahm2+5a2r2RK/vNyXdTVprDotJspk900dbWBoDLpTlcIvLxKRyJiMi4sGnTJrZv387atWtZtmwZbW1t+Hw+Ojs7mTdvHt/85jdZtWoVa9eu5cILLwx/X1xcXMQCCi6XS2HoNGlq9/Lyrho276zmz3vr8fqPrSRns+D8aRmUleZwVWkOk9warigip57CkYiIjAtPPvkkWVlZ3HTTTdTW1rJ7927a29vDc4IuueQS3G43L7/8MldffXV4mFxKSorC0GlU09LFlp3VbNpZzd/2NRLos6qcI87iksJMymbnsOCMbCaoV0hETjOFIxERGRdqa2uZPn065eXl1NfXh4fM2Ww2UlNTSU9Pp7i4GGMMc+bMiXJrx7YDDR1s2nmUTTuq+ceB5ohziY44PjlzIotKc/jkzCxSE7QJroiMHIUjEREZ84wxpKSk8I9//IPq6mrsdjsZGRlMnjyZSZMmYbPZ8Hq97N+/nyuvvDLazR1zjDHsqWlj045QD9Guoy0R51MT7CyYlU1ZaQ7ziydqbyERiRqFIxERGdM6OzspLy/nggsuYP369bz66qt87WtfC68qZ7OF9rdZt24dtbW1LF26NJrNHTOMMbx3yMOmHaEltyvr2yPOZ7riWVSaTdnsHC6cPgGH9hkSkRigcCQiImOSMYZDhw5RWVlJMBjk/PPPZ/bs2Tz00EMUFRWxZMkSHA4HXq83vFrd3LlzWbRoUbSbPmr5A0G2729ic88eREc9kUuf56UnUlaaQ9nsHM6Zkk6c9hwSkRijcCQiImNOe3s7u3fvprW1FYD4+HiKi4t55ZVXWLx4Mbfcckt4n6Pt27dTW1sb3udouI1gJVK3P8BfKxrYtKOal3bV0NjujThflOWibHYOi0pzKJ2UqsUtRCSmKRyJiMiYEQwGqaqq4sCBAxgTWvVs8uTJTJs2Dbs99JL3xhtvsHnzZl544QUaGxu58sorWbp0KYsWLVIwOkHt3X7+tKeOTTuq2bq7lrZuf8T5s/LSWFQaCkSFWa4otVJE5KNTOBIRkTGhpaWF8vJy2ttDc1sSExMpKSnB7XZH1MXFxXHNNdcwf/58AFwuvXk/EZ4OHy/vqmHTzmr+vKeO7j57EFkWzJ3auwdRNnnpSVFsqYjIx6dwJCIio1ogEKCyspJDhw4BYFkW+fn5TJ06NbzYgnw8ta1dbNkZ2pT1jQ8b8B+3B9FFM47tQTQxRXsQicjop3AkIiKjVlNTE+Xl5XR1hSb+u1wuSkpKSElJiXLLRq+DjR1s3lnNph3V/P1AE+ZYHiLBYePy4izKZof2IEpL1B5EIjK2KByJiMio4/f7+fDDDzl69CgQWo576tSp5Ofna8L/R2SMoaL22B5EO49E7kGUkmBnwRnZLCrN4bLiiSQ6NS9LRMYuhSMRERlV6uvr2bNnD15vaFW0tLQ0SkpKwvsWyfCMMfzzsCcciPbVHb8HkZOFs0JLbs+bPgGnXcMTRWR8UDgSEZFRwev1snfvXurq6oDQwgrTp09n0qRJ6i06AYGg4e39jWzaWc2WnTUcbu6MOD/Znciinj2IzivQHkQiMj4pHImISMyrrq6moqICvz+0ZHRGRgbFxcUkJCREuWWxzesP8tcP69ncE4gajtuDaPrEZK6enUNZaS6zJ2sPIhERhSMREYlZXV1d7Nmzh8bGRgDsdjuFhYXk5OREuWWxq8Pr5889exC9sruW1q7IPYhmT06lrKeHqDBLC1eIiPSlcCQiIjHHGMORI0fYt28fgUAAgIkTJ1JUVITT6Yxy62KPp9PH1t01bNpRzZ/21NHli9yD6BMF6eFNWfMzNDdLRGQwCkciIhJTOjo6KC8vx+PxAOB0OikuLiYzMzPKLYstda3dvPRBaFPWv1bUR+xBZLdZzJsxgbLZOSyclU1WioYfioicCIUjERGJCcYYDhw4QFVVFcFgqOcjNzeXGTNmYLfr5QrgUFMHm3fWsHlHNdurGiP2IIq327iseCJls3O4cmY2aUnag0hE5KPSq42IiERda2sr5eXltLW1AZCQkEBJSQnp6elRbln0VdS2hTdl/edhT8S5lHg7V5yRRVlpDpeVTCTJqZd1EZGTob+iIiISNcFgkP3793Pw4EFMTzdIXl4e06ZNIy5ufG42aoxh55GW8B5EFbVtEeczkp1cNSubRbNzuGjGBOLt4/P3JCJyOigciYhIVDQ3N1NeXk5nZ2i/neTkZEpKSkhNTY1yy0ZeIGj4x4GmUCDaUd1vD6LctITwHkSfKEjHHqdNWUVETgeFIxERGVF+v599+/Zx5MgRACzLoqCggClTpmCzjZ83/V5/kL/tawhvylrf1h1xflpmMmWzcygrzeGsvDTtQSQiMgIUjkREZMQ0NDSwZ88eurtDQSAlJYWZM2eSnJwc5ZaNjE5vgD/vrWPzjmpe3lVDy3F7EM3KTQ0Fotk5FGW5FIhEREaYwpGIiJx2Pp+PiooKampqALDZbEybNo28vLwxHwBaunxs213Lph3VvFpeR6cvEHH+vIJ0ynr2IJoyQXsQiYhEk8KRiIicVrW1tezduxefzweA2+2mpKSExMTEKLfs9GloO7YH0esV9fgCx9bcjrNZzJs+gUWzc7hqVjbZqdqDSEQkVigciYjIadHd3c2ePXtoaGgAwG63M2PGDHJzc6PcstPjSHNneMnt7fsb6bMnK067jflFoT2IFpyRhTvJGb2GiojIoBSORETklDLGcPToUfbt24ffH5pTk5mZSVFREfHx8VFu3am1r66NTTur2byjmvcORe5BlOyM44ozsikrzeHykokkx+slV0Qk1ukvtYiInDKdnZ2Ul5fT3NwMgMPhoKioiKysrCi37NQwxvDB0RY29+xBtKcmcg+i9CQHC2dlUzY7h4tmZJLg0B5EIiKjicKRiIicNGMMhw4dorKykmAwCEB2djaFhYU4HI4ot+7kBIOGdw42hTdlPdgYuQdRTmoCi0pDm7KePzVDexCJiIxiCkciInJS2traKC8vp7W1FYD4+HiKi4uZMGFClFv28fkCQd7c18imnUfZsrOG2tbIPYgKJiSF9yCak+fGZhvbK+6JiIwXCkciIvKxBINBqqqqOHDgAMaEVh+YPHky06ZNw24ffS8vXb4Af9lbz6aePYg8nb6I8zNzUsJ7EJVkp4z5JchFRMaj0ffqJSIiUdfS0sLu3bvp6OgAIDExkZkzZ5KWlhblln00bd1+tn54hM07qtlWXkuHN3IPonOmuMN7EE3NHB8b1YqIjGcKRyIicsICgQCVlZUcOnQIAMuyyM/PZ+rUqdhso2euzVuVjfx/r5TzRmVTvz2ILpiWQdnsHK6alUNOmvYgEhEZTxSORETkhDQ1NVFeXk5XVxcALpeLkpISUlJSotyyE3fU08kPXtzNhveOhI8542xcWpTJotk5LDgjm4xk7UEkIjJeKRyJiMiQ/H4/H374IUePHgXAZrMxdepU8vPzR828m25/gEf/UsnPt1WEh86dOSmFZRfkUTYnn5SE0b2inoiInBoKRyIiMqi6ujr27t2L1+sFIC0tjZKSEpKSkqLcshP3yq4aVm38gKqG0PyoTJeTu8tmsqjEjc2ycCkYiYhID4UjERHpx+v1snfvXurq6gCIi4tj+vTpTJo0adT0FlXWt7Pq9zvZVh76Gew2i+UXTeWOBUWkJjhoa2sb5h5ERGS8UTgSEZEI1dXVVFRU4Pf7AcjIyKC4uJiEhNGxOEF7t5+fba3gsdf2hRdbuKQwk/uvm0VR9uiZHyUiIiNP4UhERADo6upiz549NDY2AuBwOJgxYwY5OTlRbtmJMcaw/t0j/OCPu6hpCW3ampeeyHeuncWi0uxR0+MlIiLRo3AkIjLOGWM4cuQI+/btIxAILVaQlZVFYWEhTufoWLltx2EPKzfs5O2qJgDi7Ta+cnkh/3rZdBIccVFunYiIjBYKRyIi41hHRwfl5eV4PB4AnE4nxcXFZGZmRrllJ6ap3cuaLeWse+sAwZ7tiq6encO9155BXvroWTRCRERig8KRiMg4ZIzhwIEDVFVVEQwGAcjNzWXGjBnY7bH/0hAIGp5+s4o1W/bg6fQBUJTlYuWSUi4uHB3BTkREYk/svwKKiMgp1draSnl5eXi1toSEBEpKSkhPT49yy07Mm/saWPn7D9h1tAWAlAQ7/2dBMTfPK8ARZ4ty60REZDRTOBIRGSeCwSD79+/n4MGDGGOwLIu8vDymTp1KXFzsz8s56unkBy/uZsN7RwCwLLjxvHzuKish0xUf5daJiMhYEJPhyLKsbwEPAu8ZY84+7txFwH8C5wItwLPACmNMx4g3VERklGhubqa8vJzOzk4AkpOTKSkpITU1NcotG163P8Cjf6nk59sq6PCGFoyYk+9m1ZJS5uS7o9w6EREZS2IuHFmWlQN8B2gf4NzZwCvATuBOIA/4JjAduG4EmykiMir4/X727dvHkSO9vS0WBQUFTJkyBZst9oegvbKrhlUbP6CqIfT/X5kuJ3eXzeTT5+Zhs2lpbhERObViLhwBPwTeBmzA8f8luBpoAC43xrQBWJa1H3jEsqwrjDFbR7KhIiKxrKGhgT179tDdHdrzJyUlhZkzZ5KcnBzllg2vsr6dVb/fybbyOgDsNovlF03ljgVFpCY4otw6EREZq2IqHFmWdT6wFPgE8JPjzqUCC4H/6g1GPZ4AfgzcCCgcici45/P5qKiooKamBgCbzca0adPIy8uL+Y1Q27v9/GxrBY+9tg9fILQ29yWFmdx/3SyKslOi3DoRERnrYiYcWaFX7J8Ba40x7w7wAn4mofa+3fegMcZrWda7wDmD3G/zMA+dBoRXbYqmjg5NmxpLdD3HltFyPevq6qioqMDv9wOQlpZGUVERiYmJtLf3G60cM4wx/GFHLQ9t3UdtqxeAyWkJ3LVwBleWTMCyrFP+d3q0XFM5MbqeY4uu59gymq5nzIQjYBkwC7h+kPO5PZ+PDnDuKDDvdDRKRGQ06O7upqKigsbGRgDi4uKYPn06OTk5UW7Z8HZVt7J6UwXvHAotzR1vt/EvF+XzxXn5JDhifxU9EREZO2IiHFmWlUJortEPjTEDhR+AxJ7P3QOc6+pzPoIxZsiljHp6ltJcLtcJtvb0i6W2yMnT9RxbYu16GmM4evQoH374IYFAgMTERDIzMykqKiI+PraXt25q97JmSznr3jpAMDSCjqtn53DvtWeQl540Yu2ItWsqJ0fXc2zR9RxbRsP1jIlwRGh1Oi/w0BA1nT2fB3q1T+hzXkRkXOjs7KS8vJzm5tDoYYfDQVFREVlZWVFu2dACQcPTb1axZssePJ0+AIqyXKxcUsrFhZlRbp2IiIxnUQ9HlmXlAl8H7gOy+8w1SgCclmVNBTwcG06XS3+5wJHT2lARkRhhjOHQoUNUVlYSDAYByM7OprCwEIcjtldye3NfAyt//wG7joaG0KXE2/n6wmKWzSvAERf7S4uLiMjYFvVwBGQDTkKbvj44wPnKnuM/APyEVrL7Xe9Jy7KcwNnA06e9pSIiUdbW1kZ5eTmtra0AxMfHU1JSQkZGRpRbNrSjnk5+8OJuNrzXu98S3HhePneVlZDpiu3hfyIiMn7EQjiqBD41wPHvA8nA/wH2GGM8lmW9DNxsWdbqPst53wy4gP87Iq0VEYmCYDBIVVUVBw4cwJjQBJ3Jkyczffp04uJid9GCbn+AR/9Syc+3VdDhDQAwJ9/NqiWlzMkfckqoiIjIiIt6ODLGeIAXjj9uWdbXAb8xpu+5e4G/Aq9alvUokAd8A/ijMeblkWiviMhIa2lpYffu3eGlUJOSkigpKSEtLS3KLRvaK7tqWLXxA6oaQu3OdDm5u2wmnz43D5sttvdbEhGR8Snq4eijMMb8w7KsBYSG2f0YaAEeAVZEtWEiIqdBIBCgsrKSQ4cOAWBZFvn5+UydOhWbLXbn51TWt7Pq9zvZVl4HgN1msfyiqdyxoIjUhNieEyUiIuNbzIYjY8zlgxx/Dbh4ZFsjIjKympqaKC8vp6urCwgtf1pSUkJKSkqUWza49m4/P9tawWOv7cMXCA39u6Qwk/uvm0VRduy2W0REpFfMhiMRkfHI7/dTUVFBdXU1ADabjalTp5Kfn0+f1TxjijGG9e8e4Qd/3EVNS2grurz0RL5z7SwWlWbHbLtFRESOp3AkIhIj6urq2Lt3L16vF4C0tDRKSkpIShq5DVE/qh2HPazcsJO3q5oAiLfb+MrlhfzrZdNJcMTuQhEiIiIDUTgSEYkyr9fL3r17qasLzdGJi4tj+vTpTJo0KWZ7XZravazZUs66tw4QDI2g4+rZOdx77RnkpcdumBMRERmKwpGISBRVV1dTUVGB3+8HICMjg+LiYhISEqLcsoEFgoan36xizZY9eDp9ABRluVi5pJSLCzOj3DoREZGTo3AkIhIFXV1dlJeX09QUGo7mcDgoLCwkOzs7yi0b3FuVjdy/YSe7jrYAkBJv5+sLi1k2rwBHXOyuniciInKiFI5EREaQMYbDhw9TWVlJIBDaFDUrK4vCwkKcTmeUWzewak8Xq1/cxYb3jgBgWXDjefncVVZCpis+yq0TERE5dRSORERGSEdHB7t376alJdTz4nQ6KS4uJjMzNoejdfsDPPqXSn6+rYIObyjIzcl3s2pJKXPy3VFunYiIyKmncCQicpoZYzhw4ABVVVUEg0EAcnNzmTFjBnZ7bP4ZfmVXDas2fkBVQwcAmS4nd5fN5NPn5mGzxeYiESIiIicrNl+VRUTGiNbWVsrLy2lrawMgMTGR4uJi0tPTo9yygVXWt7Pq9zvZVh5aOc9us1h+0VTuWFBEaoIjyq0TERE5vRSOREROg2AwyP79+zl48CDGGCzLIi8vj6lTpxIXF3v7/7R3+/nZ1goee20fvkBobe5LCjO5/7pZFGWnRLl1IiIiI0PhSETkFGtubqa8vJzOzk4AkpOTKSkpITU1Ncot688Yw4b3jrD6xV3UtHQDkJeeyHeuncWi0uyY3WdJRETkdFA4EhE5Rfx+P/v27ePIkd5V3SwKCgqYMmUKNlvsLXW947CHlRt28nZVaDnxeLuNr1xeyL9eNp0ER+z1bomIiJxuCkciIqdAQ0MDe/bsobs71PuSmppKSUkJycnJUW5Zf03tXtZsKWfdWwcIhkbQcfXsHO699gzy0pOi2zgREZEoUjgSETkJPp+PiooKampqALDZbEybNo28vLyYG5IWCBqefrOKNVv24On0AVCU5WLlklIuLozN5cRFRERGksKRiMgQAoEAmzZtYv369TQ0NOB0Olm6dCllZWU0NDSwd+9efL5Q0EhPT6e4uJjExMQot7q/tyobuX/DTnYdDe2xlBJv5+sLi1k2rwBHXOwN+RMREYkGhSMRkUHU1tayePFitm/fzuzZsykoKOC1117jmWeeobS0lO9973ukp6djt9uZMWMGubm50W5yP9WeLla/uIsN7/XOg4Ibz8vnrrISMl3xUW6diIhIbFE4EhEZQCAQYPHixezcuZO1a9dy3XXXYbfbaWxs5Je//CU/+tGPWLFiBc8++ywzZ84kPj62gka3P8Cjf6nk59sq6PAGAJiT72bVklLm5Luj3DoREZHYpHAkIjKATZs2sX37dtauXcuyZcuoq6tj165deL1eFi5ciGVZPPDAAxw+fJg5c+ZEu7kRXtlVw6qNH1DV0AFApsvJ3WUz+fS5edhssTUPSkREJJZooLmIyACefPJJsrKyuOmmm+jo6ODdd9/F4/EAkJ2dzYoVK8jKyuLJJ5+MckuPqaxv54uPv8WX175NVUMHdpvFly+ZxtZvXs5nP5GvYCQiIjIM9RyJiAygtraWwsJCgsEg77//Pn6/H7vdzllnnUVGRgYAhYWF1NbWRrml0N7t52dbK3jstX34AqG1uS8pzOT+62ZRlJ0S5daJiIiMHgpHIiIDyMrK4pVXXuGdd96hq6sLm81GaWlpOBh5vV4qKiq48soro9ZGYwwb3jvC6hd3UdMS2l8pLz2R71w7i0Wl2TG3lLiIiEis07A6EZEBfP7zn6euro7169djWRZnnHEGqamp4fPr1q2jtraWpUuXRqV9Ow57+Oz/vMEdz7xLTUs38XYb/2dBMS/feRlls3MUjERERD4G9RyJiBzHGMOUKVMoKSnhxz/+Mbm5uZx11llAqMdo3bp13H777cydO5dFixaNaNua2r2s2VLOurcOEAyNoOPq2Tnce+0Z5KUnjWhbRERExhqFIxGR4+zdu5empiZ+8IMf8N3vfpc77riDRx55hIKCArZv305tbS1z585l48aNxMXFjUibAkHD029WsWbLHjydoU1ni7JcrFxSysWFmSPSBhERkbFO4UhEpI/KykqOHAltmDpnzhz+/ve/s3nzZl544QUaGxu58sorWbp0KYsWLRqxYPRWZSP3b9jJrqMtAKTE2/n6wmKWzSvAEafR0SIiIqeKwpGISI/Dhw9TVVUFQE5ODtOnTwfgmmuuYf78+QC4XK4Ra0+1p4vVL+5iw3uhsGZZcON5+dxVVkKmK7Y2nRURERkLFI5ERIC6ujr27t0LwIQJEygpKYlaW7r9AR79SyU/31ZBhzcAwJx8N6uWlDIn3x21domIiIx1CkciMu41NTWxa9cuAFJTU5k1a1bUVnt7ZVcNqzZ+QFVDBwCZLid3l83k0+fmaRNXERGR00zhSETGtdbWVnbs2EEwGCQpKYkzzzxzxOYS9VVZ386q3+9kW3kdAHabxfKLpnLHgiJSExwj3h4REZHxSOFIRMatzs5O/vnPfxIIBIiPj2fOnDk4HCMbRNq7/fxsawWPvbYPXyC0NvclhZncf90sirJTRrQtIiIi453CkYiMS16vl/fffx+v14vD4WDOAIFHngAAIABJREFUnDnEx4/cIgfGGDa8d4TVL+6ipqUbgMnuRO5bfAaLSrWJq4iISDQoHInIuOP3+3n//ffp7OzEZrNx5plnkpQ0chuo7jziYeWGnWzf3wRAvN3GVy4v5F8vm06CY+SH9ImIiEiIwpGIjCvBYJAdO3bQ1taGZVmUlpaSmpo6Io/d1O5lzZZy1r11gGBoBB1Xz87h3mvPIC995MKZiIiIDEzhSETGDWMMu/5/9u48Psrq3uP458xMVrJCwpawZSEhCWERUWy16rXV1v26K+BasVZvre292qut1trFVmu1VlvFBUQtWve6VC3q1SqbINlDgJCwBUgg+zoz5/6RkAYJkGWSyfJ9v155BeY5z5lv8iQwvznnOSc/n8rKSgBSUlIYNWpUnz+vx2t5flUJ97+3kaqGFgCSR4dx9znpfC0pps+fX0RERLpGxZGIDBubNm1i797W1eASExMZO3Zsnz/n6uJ93PVGLvm7qgEID3JxyzensnDeJAKcjj5/fhEREek6FUciMixs3bqVHTt2ADBhwgQmTJjQp89XVtXIr97O540NO9sfu3hOPP9zRioxYf238IOIiIh0nYojERnydu7cydatWwEYM2YMCQkJffZcTW4PT35azCMrNlHf7AFgxoQofn5OOjMnRPXZ84qIiEjvqTgSkSFt7969FBUVATBy5EhSU1P7bJnsf+bv5p6/51FSUQ9ATFggt52RygWz43E4tDS3iIjIQKfiSESGrMrKSvLz87HWEhERQXp6ep8URsXlddzzZi4fFrbez+RyGK48YTI/OC2ZiOD+3VRWREREek7FkYgMSbW1teTk5OD1egkNDWX69Ok4nb7dQ6iuyc0fV2ziyU+30OJpXZv760kx3HV2Gsljwn36XCIiItL3VByJyJDT0NBAVlYWbreboKAgMjMzCQjw3QiOtZY3NuzkV2/ns7u6CYC4qBB+etY0Tk8f22fT9kRERKRvqTgSkSGlubmZrKwsmpubcblcZGZmEhwc7LP+c3dWcfcbuazZuh+AIJeDG09OYtE3EggO8O3IlIiIiPQvFUciMmR4PB6ys7NpaGjA4XAwffp0RowY4ZO+K+tbePijYv62fhfe1hl0fDtjLHecOY346FCfPIeIiIj4l4ojERkSvF4vOTk51NTUYIwhLS2NyMhIn/RdXF7HFU9+wc6q1il0yaPDuPucdL6WFOOT/kVERGRgUHEkIoOetZaCggL272+d6jZ16lRiYnxTuBSUVTN/8WrKa5sICXDw49NTWThvEgFOh0/6FxERkYFDxZGIDHqbNm1iz549ACQkJDBu3Dif9PvltkqufGo1VQ0tRAS7+Mtl05mXMt4nfYuIiMjAo+JIRAa1kpISduzYAUB8fDwTJ070Sb+fb67guiVrqGv2EBMWxOOXZzB1dJhP+hYREZGBScWRiAxau3btori4GIDRo0eTmJjok35XFOzme8vW0eT2EhcVwrLrjiM22PqkbxERERm4NGleRAal8vJyNm7cCEB0dDSpqak+2V/ozQ07uX7pFzS5vSTEjODFG+YxJcY3K96JiIjIwNajkSNjzFQgHRgNWGAvkGOtLfJhNhGRTlVVVZGXl4e1lvDwcDIyMnA4ev9ez/I1pdz+SjbWwrRxESy9Zi6x4UE+SCwiIiKDQZeLI2PMNOAG4EJg7IGH2z7btja7gReBv1hr832YU0QEgLq6OrKzs/F6vYSEhDB9+nSczt5vvvrkp8X84u95AMyaGMUzV80lMjSg1/2KiIjI4HHU4sgYkwjcB5wPNACfAH8BNgMVtBZII4Ek4HjgOuBmY8wrwG3W2i19E11EhpvGxkaysrJwu90EBgYyY8YMAgMDe9WntZaH/lnEHz5oHfg+IXEUTyycw4gg3ZIpIiIy3HTlf/88IBu4CnjFWlt3pMbGmBG0ji79oO3c4F5mFBGhpaWFrKwsmpqacLlcZGZmEhzcu39erLX88q18Fn/auqjDadNG88jlswkO6P1IlIiIiAw+XSmOLrLWvtHVDtuKpyXAEmPMuT1OJiLSxuPxkJ2dTX19PQ6Hg4yMDMLCerestsdruePVbP66ZhsA58wYzwMXz9DmriIiIsPYUYuj7hRGnZz7ek/PFREB8Hq95ObmUl1djTGGtLQ0oqKietVni8fLD5d/yd+zdgFw2dyJ3HteBk5H71e7ExERkcHLJ5PqjTEu4Fxa7z1601pb5ot+RWR4s9ZSWFjIvn37AEhOTiYmJqZXfTa2eLjxuXWsKNgDwPUnJfCTb/tmGXAREREZ3Lo9f8QY81tjzJoOfzfAB7StUgdkty3iICLSK5s3b2b37t0ATJkyhfHjx/eqv9omN1c9vbq9MPrRN6eqMBIREZF2PZlcfwatK9YdcDZwEvA74PK2x27vZS4RGeZKS0vZvn07AHFxcUyaNKlX/VXWN3PF4lWs3NI6CvWzs9K4+T+SVRiJiIhIu55Mq5sAdNzs9Wyg2Fp7O4AxJh24wgfZRGSYKisrY8uW1l0AYmNjSUpK6lV/e2oaWfjkagrKanAY+M0FmVw8Z4IvooqIiMgQ0pPiKBBwd/j7KbROqztgCzCuN6FEZPiqqKigsLAQgOjoaKZNm9ar0Z3t++uZv3gVWyvqCXAa/nDJLM7M1D9RIiIicqieTKvbBsyD9lGiBODjDsdHA7W9jyYiw01VVRW5ublYawkLCyM9PR2Ho+dLa2/ZW8vFf/6crRX1BLkcPL5wjgojEREROayejBz9FfipMWY0kA5UA293OD4L2OyDbCIyjNTV1ZGdnY3X6yUkJITMzExcrp4vqJm3s5qFT62ivLaZsCAXi6+cw/EJo3yYWERERIaanrwl+2vgGVpHjyyw0FpbCWCMiQTOAf7Z1c6MMXOMMa8aY0qMMQ3GmDJjzLvGmBM6aXuCMeZTY0x9W7uHjDGhPfgaRGQAaWpqIisrC7fbTWBgIJmZmQQGBva4v3Wl+7n08c8pr20mKjSA5797nAojEREROapuvy1rrW0Crm37+KoaWu83qu9Gl4ltOZ4AdgFRtC7o8H/GmG9ba98HMMbMpLXoygVuBeKBH9M6re/s7n4dIjIwtLS0sGHDBpqamnA6nWRmZhISEtLj/j7bVM51S9dS3+whNjyIZdceR8rYcB8mFhERkaGqS8WRMWYb8Frbx0fWWk9n7ay1XqCqOwGstcuB5V95vsdoXdjhB8D7bQ//CqgATrbW1ra12wo8YYw51Vq7ojvPKyL+5/F4yM7Opr6+HofDQUZGBmFhYT3u74O83dz4/Dqa3V7iokJ47rrjmBwzwoeJRUREZCjr6rS614HzaC1U9hhjnjXGnN9XU9qstfXAXlpHkTDGRADfBJYeKIzaLKV18YeL+yKHiPQday15eXlUV1cDMG3aNKKjo3vc3+tf7mDRsi9odntJjB3B3743T4WRiIiIdEuXiiNr7U3W2gnA8cDjwBzgZWCvMeZ1Y8xVxpheTeg3xoQbY2KMMSnGmF8BGfz73qXptI5yrf1KrmbgS1oXgRCRQaSwsJCKigoApk6dSmxsbI/7en5VKbcs/xKP15I2LoLli+YxLrLnU/NERERkeOrWPUfW2tXAauAnxphU4HxaR5SeBLzGmE+BV4HXrLWl3czyNHBB25+bgT/TOpUO/r1v0q5OzttF29LinTHGVB7leSMBamv9v/p4fX13btWSgU7X8/CKi4vZvn07ABMnTiQiIqLHv4NPf76NB/7ZumHszPgIHr10OsG0UFvb4rO8oOs5FOmaDi26nkOLrufQMpiuZ483ELHWFlhrf22tPQ6YCPwQ8AD3A8XGmHXGmDO60eXPgW8B1wD/AoKAgLZjB94CburkvMYOx0VkgNu+fXt7YTR27FgmTZrUo36stTzyUXF7YXT8lCgevzyTiOCeL/8tIiIiw5tPXkVYa3cAjwCPGGOiaV097jxap8a928U+soFsAGPMMlqn0D0DXAg0tDUL6uTU4A7HO+s36kjP2zayFNmbm8B9bSBlkd7T9fy33bt3U1ZWRkhICLGxsaSlpWGM6XY/Xq/lF2/l8fS/Wgeov5U2hocvm0VwgNPXkQ+h6zn06JoOLbqeQ4uu59AyGK6nz99itdbup3WhhKW96KPFGPM6cKcxJoR/T6frbGv7ccDOnj6XiPSPffv2UVBQAEBUVBTTpk3rUWHk8Vp+8koWL65tHX06f1Ycv7swE5ezxwPhIiIiIkAvptX1gxDAAOFADuCmdSGIdsaYQGAmrYsyiMgAVV1dTW5uLtZawsLCyMjIwOHo/j8/zW4v//XC+vbCaP7xE3ngohkqjERERMQnevSKwhhzuTHmX8aYPcYYTycf7m70dcgSVW1Ld18EbLPW7rHWVgEfAAuMMR3H4xYAYcBLPfk6RKTv1dfXk52djcfjITg4mMzMTFyu7g9aNzR7uP7ZtbyV3TqQfMM3EvnFuRk4HN0ffRIRERHpTLdfoRhj7qR18YTdwGfA/l5mWG6MaWzrqwyYAFwNxAOXdmh3R1ubj4wxi9uO/wh4x1r7QS8ziEgfaGpqIisri5aWFgICApgxYwaBgYHd7qemsYVrl6xldfE+AP779BS+f0qSr+OKiIjIMNeTe45uBD4CzrDW+mKt3GXAQuC/gGigElgJLLDWfnygkbV2nTHmNOA+4EGgGngC+IkPMoiIj7ndbrKysmhsbMTpdJKZmUlISPcXltxf18yVT68ma3sVAPecm87CeZN9nFZERESkZ8VRBPCijwojrLVPAU91se2nwNd88bwi0ne8Xi/Z2dnU1dVhjCEjI4Pw8PBu97OnupH5T65i4+5aHAZ+e+EMLjwmvg8Si4iIiPSsOFpP69Q3EZFDWGvJzc2lqqp1pGfatGlER0d3u59t++qZ/+QqSirqCXAaHr50Ft+e3tmClSIiIiK+0ZMFGe4EbjDGzPJ1GBEZ/DZu3EhFRQUAycnJjB49utt9bNpTy0V//pySinqCAxwsvvJYFUYiIiLS57o9cmSt/dgYcy2w0hizEtgKeA5tZq/1QT4RGUS2bNnCrl2tq8lNmjSJuLi4bveRs6OKK59aTUVdM+FBLp66+liOnTzS11FFREREDtGT1eqOA5YAAcCJbR9fZQEVRyLDyPbt2yktLQVg3LhxTJkypdt9fFGyj6ueXkNNo5vo0ACevfY4MuIifR1VREREpFM9mVb3ENAMnAuMtNY6Ovlw+jamiAxke/bsYdOmTQDExMQwderUbvfxSdFe5i9eTU2jmzERQby4aJ4KIxEREelXPVmQIRO421r7pq/DiMjgs3//fvLz8wGIjIwkLS0NY7q3Mes/csu4+fn1NHu8TBgZwnPXHs/EUaF9EVdERETksHpSHO2hdeRIRIa5mpoacnJysNYyYsQIpk+fjsPRvQHpV9dv58cvZeHxWpJGh7Hs2uMYGxncR4lFREREDq8n0+qeAuYbY3pSWInIEFFfX09WVhYej4fg4GAyMzNxubr3z8KzK0u49cUNeLyWjLgIXlw0T4WRiIiI+E1PCpxPgbNoXa3uUaCYQ1erw1r7f73MJiIDVFNTE1lZWbS0tBAQEEBmZiZBQUHd6uOxjzZz37sFABw7OZonrzqWiOCAvogrIiIi0iU9KY4+6PDnxbSuTNeRaXtMizKIDEFut5vs7GwaGxtxOp1Mnz6d0NCu3x9kreX+9wr504ebATgxOYbHF8whJFD/ZIiIiIh/9aQ4utrnKURkUPB6veTk5FBbW4sxhvT0dCIiIrpxvuXnb+ay5PMSAM5IH8tDl80kyKXCSERERPyvJ5vALumLICIysFlrycvLo7KyEoDU1FRGjuz65qxuj5fbXs7m5XXbAbhgdjz3XTAdl7Mntz6KiIiI+J4WVRCRLikqKqK8vByApKQkxowZ0+Vzm9wefvDCl7ybWwbAlfMmcdfZ6Tgc3VvyW0RERKQvHfUtW2PMf/S0c2PMaT09V0QGjuLiYnbu3AnAxIkTiY+P7/K5Dc0evrv0i/bC6PunJHL3OSqMREREZODpynyWd40xK4wxZxljjnpjgDEmwBhzvjHmY+Dt3kcUEX/asWMHJSWt9wiNHTuWhISELp9b3djCwqdW8X8b9wJw2xmp/Pfpqd3eJFZERESkP3RlWt0s4PfAG8BeY8wHwGpgM7CP1tXpRgLJwPHAfwBRwHvAzD7ILCL9ZO/evRQVFQEwatQoUlJSunzuvrpmFj61ipwd1RgD95ybwYLjJ/VVVBEREZFeO2pxZK3NAb5ljJkH3AicC1xG50t4VwOvAI9Za9f4OKuI9KP9+/eTn58PQEREBGlpaV0e8SmramT+k6vYtKcWp8Nw/0WZnD+r61PxRERERPyhywsyWGs/Bz5vm1p3DJAGxNJaJO0FcoD11lpvXwQVkf5TU1NDTk4OXq+X0NBQpk+fjtPZteW2SyvqueLJlWzb10Cg08EfL5/F6elj+zixiIiISO/1ZClvD63T6lb7Po6I+FtDQwPZ2dl4PB6CgoKYMWMGAQEBXTq3aHcN859cxe7qJkICnDy+8BhOTI7t48QiIiIivqGlvEWkXXNzM1lZWTQ3N+NyucjMzCQoKKhL52Zvr2LhU6vYX99CeLCLZ64+lmMmdX0fJBERERF/U3EkIgC43W6ysrJoaGjA4XCQmZnJiBEjunTu6uJ9XPvMGmqa3IwcEcjSa+aSERfZx4lFREREfEvFkYjg9XrJycmhtrYWYwzp6elERER06dyPN+5l0bNraWzxMjYimGXXHUfS6LA+TiwiIiLieyqORIY5ay35+flUVlYCkJKSwqhRo7p07rs5u7j5hfW0eCyTRoWy7NrjmDAytC/jioiIiPQZFUciw9ymTZvYu7d1k9bExETGju3aynJ/+2I7//O3DXgtTB0TxrJrj2N0RHBfRhURERHpU90ujowxEcC3gFSgEfintXa9r4OJSN/bunUrO3bsAGDChAlMmDChS+ct+Wwrd72RC0BmfCRLrp5L9IjAPsspIiIi0h96MnK0AwilddNXAGuMeRe4zlq7y2fJRKRP7dy5k61btwIwZswYEhISunTenz7cxO/+UQjA3CkjefLKOYQHd22pbxEREZGBzNGDc/4KnASMA9KB3wCnACuNMck+zCYifWTv3r0UFRUBMHLkSFJTUzHGHPEcay2/eaegvTA6OSWWJVfPVWEkIiIiQ0a3iyNr7Xettf+y1u621uZba+8AZgMNwEfGmKk+TykiPlNZWUl+fj7WWiIiIkhPTz9qYeT1Wn76eg5//ngzAGdOH8fjC+YQEujsj8giIiIi/aInI0eHsNYWAMcDm4EPjTETfdGviPhWbW0tOTk5eL1eQkNDmT59Ok7nkQsct8fLj17awLKVpQBcdEw8D182i0CXT/75EBERERkwfPnqxgK3AU7gXR/2KyI+0NjYSFZWFm63m6CgIDIzMwkIOPKUuCa3hxufW8er61sXbbjqhMncd0EmTseRR5pEREREBqOerFZ3HRAPTPjK5xEHmgCxvgooIr3X3NzMhg0baG5uxuVykZmZSXDwkZfdrm92s+jZL/ikqByA/zo1iR9+c+pRp+CJiIiIDFY9Wa3u8Q5/9gK7gXxg+1c+RGQA8Hg8ZGdn09DQgMPhYPr06YwYMeKI51Q1tHDNM2v4omQ/AP/7nVSuPymxP+KKiIiI+E1PiqNL+HcBtNNa6/FtJBHxFa/XS05ODjU1NRhjSEtLIzIy8ojnlNc2sfDJ1eTtqsYY+OV507n8ON1GKCIiIkNft4sja+1LfRFERHzLWktBQQH797eO/kydOpWYmJgjnrOrqoErFq9iy946nA7D7y+ewbkz4/ojroiIiIjf9WTkSEQGgU2bNrFnzx4ApkyZwrhx447YvqSijsufWMWOygYCXQ7+dPlsvpk2pj+iioiIiAwIKo5EhqCSkhJ27GhdYS4+Pp5JkyYdsX1hWQ0LnlzFnpomQgOdPLFwDl9LOvIok4iIiMhQo+JIZIjZtWsXxcXFAIwePZrExCMvpLBhWyVXPr2ayvoWIoJdPHPNXGZPjO6PqCIiIiIDioojkSGkvLycjRs3AhAdHU1qauoRl95etaWCa5espbbJTUxYIEuvOY608RH9FVdERERkQFFxJDJEVFVVkZeXh7WW8PBwMjIycDgOv8/zh4V7uOHZL2hyexkXGcyy644jMTasHxOLiIiIDCwqjkSGgLq6OrKzs/F6vYSEhDB9+nScTudh27+VtYtblq+nxWOZPCqUZdcdR3x0aD8mFhERERl4VByJDHKNjY1kZWXhdrsJDAxkxowZBAYGHrb9i2u2cfsrWXgtpI4NZ+m1cxkdHtyPiUVEREQGJhVHIoNYS0sLWVlZNDU14XK5yMzMJDj48IXOU58Wc8/f8wCYMSGKJVcfS1To4QspERERkeFExZHIIOXxeMjOzqa+vh6Hw0FGRgZhYZ3fM2St5ZEVm3jg/dbFGo5PGMniK48lLEj/BIiIiIgcoFdGIoOQ1+slNzeX6upqjDFMmzaNqKioTttaa/n1OwU8/n9bADg1dTSPXjGb4IDD35MkIiIiMhypOBIZZKy1FBYWsm/fPgCSk5OJjY3ttK3Ha7nztRxeWF0KwFmZ43jwkpkEOA+/ip2IiIjIcKXiSGSQ2bx5M7t37wZg8uTJjB8/vtN2LR4vP3pxA29s2AnApcdO4JfnT8fpOPy+RyIiIiLDmYojkUGktLSU7du3AxAXF8fkyZM7bdfY4uGm59fxQf4eAK79+hTuPHPaETeEFRERERnuVByJDBJlZWVs2dJ631BsbCxJSUmdtqtrcvPdpWv5bHMFALeclswP/iNZhZGIiIjIUag4EhkEKioqKCwsBCAqKopp0zofBaqqb+GqZ1azvrQSgDvPnMZ1Jyb0a1YRERGRwUrFkcgAV1VVRW5uLtZawsLCyMjIwOE4dEGFvTVNLHhyFQVlNRgDvz5/OpfOneiHxCIiIiKDk4ojkQGsrq6O7OxsvF4vISEhZGZm4nId+mu7o7KBBYtXsaW8DpfD8OAlMzl7RucLNYiIiIhI51QciQxQTU1NZGVl4Xa7CQwMJDMzk8DAwEPaFZfXMX/xKnZUNhDkcvDY/NmcmjrGD4lFREREBjcVRyIDUEtLCxs2bKCpqQmn00lmZiYhISGHtMvfVc2CJ1dTXtvEiEAni688lnmJo/yQWERERGTwU3EkMsB4PB6ys7Opr6/H4XCQkZFBWFjYIe3Wl+7nqqfXUNXQQmRIAEuumcvMCVF+SCwiIiIyNKg4EhlArLXk5eVRXV0NwLRp04iOjj6k3eebK7huyRrqmj3EhAWx7Lq5pI6N6O+4IiIiIkOKiiORAaSwsJCKitb9iZKTk4mNjT2kzT/zd/O959bR7PYSFxXCsuuOY0rMiP6OKiIiIjLkqDgSGSC2bNlCWVkZAJMmTSIuLu6QNm9u2MkPl3+J22tJiBnBsuuOY3zUofciiYiIiEj3qTgSGQC2bdtGaWkpAOPHj2fKlCmHtPnr6lJ+8mo21sK0cREsvWYuseFB/R1VREREZMhScSTiZ7t372bz5s0AxMTEkJycfEibxZ9s4d638gGYNTGKZ66aS2RoQL/mFBERERnqVByJ+NG+ffsoKCgAICoqirS0NIwx7cettfzhgyIe+mcRACckjuKJhXMYEaRfXRERERFf0yssET+prq4mNzcXay1hYWFkZGTgcDjaj1trufetfJ78tBiA06aN4ZHLZxEc4PRXZBEREZEhTcWRiB/U19eTnZ2Nx+MhODiYzMxMXK5//zp6vJY7Xs3mr2u2AXDuzPHcf9EMApyOw3UpIiIiIr3k91daxphjjTF/MsbkGWPqjDGlxpi/GmOSOml7gjHmU2NMvTGmzBjzkDEm1B+5RXqqqamJrKwsWlpaCAgIYMaMGQQGBrYfb3Z7+cFf17cXRpfNncjvL56pwkhERESkjw2EkaPbgK8BLwFZwFjgJmC9MWautTYfwBgzE/gnkAvcCsQDPwYSgLP9kFuk29xuN1lZWTQ2NuJ0OsnMzCQk5N9LcTe2eLjxuXWsKNgDwKKTErj926kH3YckIiIiIn1jIBRHvwcut9Y2H3jAGLMcyKa1cLqq7eFfARXAydba2rZ2W4EnjDGnWmtX9Gdoke7yer1kZ2dTV1eHMYaMjAzCw8Pbj9c2ubn2mTWsKt4HwI+/NZXvn5KkwkhERESkn/h9no619rOOhVHbY0W0jhBNAzDGRADfBJYeKIzaLAVqgYv7Ka5Ij1hryc3NpaqqCoBp06YRHR3dfryyvpkrFq9qL4zuOjuNm05NVmEkIiIi0o8GwsjRIUzrK8IxwIa2h6bTmnVtx3bW2mZjzJfArP5NKHJ4Ho+Hd999l9dff52KigoCAwM5+eSTSUpKwul0kpSUxOjRo9vb76lpZMHi1RTursFh4DcXZHLxnAl+/ApEREREhqcBWRwBVwBxwB1tfx/X9nlXJ213AfMO15ExpvIozxUJUFtbe5Rmfa++vt7fEaSXKioqWLRoEdnZ2SQnJxMXF8fatWt5//33SUhI4IEHHiAqKqr9521nZSPXPZdF6f4GXA7DfedN4/TU6AHx8ygH0+/n0KNrOrToeg4tup5Dy2C6ngOuODLGpAJ/Aj4Fnm17+MAd602dnNLY4biI33g8HhYtWkRRURH33Xcfp5xyCnv37mXbtm2sXLmSpUuX8stf/pLly5fjdDoprqjnumVZ7K5pIsjl4A8XpnFi0ih/fxkiIiIiw9aAKo6MMWOBt4D9wEXWWm/boYa2z0GdnBbc4fghrLVRR3nOSiAyLCys+4H7yEDKIl331ltv8Y9//IMlS5Ywf/58iouL2bVrF+Hh4Vx66aUkJydz9dVX869//YvJM7/OVUs3UFHXTFiQiyevnMNxCSqMBgP9fg49uqZDi67n0KLrObQMhus5YIojY0wk8A6t09y+Zq0t63D4wHS6cYec2PrYzj6OJ3JUy5YtY/To0Vx22WWzzytqAAAgAElEQVRUVVVRWFgIQGRkJGlpaaSkpHDbbbfx2IvvUrLaSXWjm6jQAJZeM5fM+CPW8CIiIiLSD/y+Wh2AMSYYeBOYCpxlrS38SpMcwA3M+cp5gcBM4Mv+yClyJHv27CEpKQlrLXl5eVhrCQkJYfr06TidTgIDA4mfcxo5sadQ3egmNjyI5dfPU2EkIiIiMkD4vTgyxjiB5bQuqnCRtXblV9tYa6uAD4AFxpiO43ELgDBaN5AV8avRo0dTVFTEhg0baGpqwuFwkJaWhsvVOkD7TtZ2ytMuwjoDiY8O4W83zCNlbPhRehURERGR/uL34gh4ADiH1il1I40x8zt8nNeh3R1ALPCRMeYGY8y9wCPAO9baD/o/tsjB5s+fz969e3nllVcAmDp1KqGhoQC8/uUOvv/8lxhnAGNC4KUb5jFp1Ah/xhURERGRrxgI9xzNbPt8dttHRyXAawDW2nXGmNOA+4AHgWrgCeAn/ZRT5IjmzJlDSkoKDz74ICNHjmTGjBkALP1sC3e9kYfF4KrZxRs/uZwxkVpgUURERGSgMdZaf2fwK2NMZWRkZGRl5dG2Q+p7B/a2GQwrecjB6uvr+eKLLygvL+enP/0pubm5ZGRkEHrMuewe27oNV0BlKe/+77kkThzv57TSE/r9HHp0TYcWXc+hRddzaBlI1zMqKoqqqqqqw61oPRBGjkQGNY/HQ25uLh6PhzFjxrBmzRpWrFjBA+8VsiUkBYDUKHjprmsID+lsNXoRERERGQhUHIn00saNG6mrq8MYQ3p6OiEhIZRHp7Olbebct9LG8MfLZxHkcvo3qIiIiIgckYojkV7YsWMHu3fvBiAxMZHIyEg+21zOPX/PA+C01BgevWI2LudAWPtERERERI5Er9hEeqi6uppNmzYBrct4x8fHs21fPd9/bh0eryVlzAh+dU6qCiMRERGRQUKv2kR6oLm5mdzcXKy1hIaGkpKSQl2Tm+8uXcv++hZGjgjk4YsyCA3UVDoRERGRwULFkUg3WWvJy8ujqakJp9NJRkYGxjj48UsbKCirweUwPHrFbOKigv0dVURERES6QcWRSDcVFxdzYOn31NRUQkNDeeTDTbyTUwbAXWencXzCKH9GFBEREZEeUHEk0g3l5eWUlpYCMGHCBGJjY/lHbhm/f38jAJfNncj84yf5M6KIiIiI9JCKI5EuamhooKCgAIDIyEgSEhIoLKvh1uVfAjBnUjQ/PycdY4w/Y4qIiIhID6k4EukCj8dDTk4ObrebwMBA0tPTqWpo4btL11LX7GFcZDCPzT+GQJd+pUREREQGK72SE+mCr2706nC6uOn59ZTuqyfI5eDxBXOIDQ/yd0wRERER6QUVRyJH0dlGr796u4BPN5UD8NsLM5keH+nPiCIiIiLiAyqORI6gs41eX1q7jaf+VQzADd9I5NyZcf6MKCIiIiI+ouJI5DBaWloO2eh1fel+7ng1B4BTUmL579NT/JxSRERERHxFxZFIJzrb6LW8roVFz35Bs8dLQuwIHrpsFk6HVqYTERERGSpUHIl0ori4mP379wOQkpKCIyCI65/9gj01TYQHuXhi4RwiggP8nFJEREREfMnl7wAiA03HjV7j4+OJjY3lxy9lsWFbJcbAw5fNIjE2zM8pRURERMTXNHIk0sFXN3pNTEzkqX9t5eV12wG47YxUTkkd7c+IIiIiItJHVByJtPF4POTm5h600eunm8r55Vt5AJwzYzyLTkrwc0oRERER6SsqjkTaFBUVUVtbizGGtLQ0dla3cNPz6/FayIiL4L4LMjFGCzCIiIiIDFUqjkSAnTt3UlZWBkBCQgKukDC+u3QtVQ0txIQF8viCOYQEOv2cUkRERET6khZkkGGv40avsbGxxMXFs2jZFxTtqSXAaXhs/jGMjwrxc0oRERER6WsaOZJh7cBGr16vl9DQUFJTU/nDBxt5P283APecm8Gxk0f6OaWIiIiI9AcVRzJsfXWj1/T0dP6Rt4eHV7SOIi04fhKXzZ3o55QiIiIi0l9UHMmwtXXr1oM2ei2t9vCjFzcAcNyUkfzs7DR/xhMRERGRfqbiSIaliooKSkpKgNaNXl0jovju0rU0tHiIiwrh0StmE+DUr4eIiIjIcKIFGWTYaWhoID8/H2jd6HXCpMlc+fQatu9vICTAyeMLj2FUWJCfU4qIiIhIf9Nb4zKseL3egzZ6TUtL41dvF7Byyz4A7r9oBunjI/2cUkRERET8QcWRDCsbN248aKPXVzfsZsnnrdPrbj41iTMzx/k5oYiIiIj4i4ojGTa+utHrpkovP309B4DTpo3mh6dN9Wc8EREREfEzFUcyLNTU1By00aszPIYblq2jxWNJHh3Gg5fMxOEwfk4pIiIiIv6kBRlkyPvqRq+TEpK4bPEaymubiAh28cTCOYQHB/g7poiIiIj4mUaOZEiz1pKfn09jYyNOp5O0tDTueD2P7B1VOAw8cvlsJseM8HdMERERERkAVBzJkLZ161b27WtdiS4lJYXnvtjN61/uBOB/vzONk6bG+jOeiIiIiAwgKo5kyOq40WtcXBx5++E37xYA8J+z4rj261P8GU9EREREBhgVRzIkddzoNSIiAiLGcPML67EWZsRH8qv/nI4xWoBBRERERP5NCzLIkNNxo9eAgAAmJE7lksVrqWl0ExsexF8WzCE4wOnvmCIiIiIywKg4kiGn40avKanT+J9X89myt45Ap4O/LDiGsZHB/o4oIiIiIgOQptXJkLJr1672jV6nTJnCk2v2sKJgDwD3np/B7InR/ownIiIiIgOYiiMZMmpqaigqKgIgJiaG9fucPPbRZgCu/tpkLp4zwZ/xRERERGSAU3EkQ0LHjV5DQkJwh4/jtpezADghcRR3fGeanxOKiIiIyECne45k0Ou40avD4WDs5GQue2o9jS1eJo4M5U+Xz8bl1PsAIiIiInJkKo5k0CspKWnf6HVKYjK3vlrAzqpGQgOdPLFwDtEjAv2cUEREREQGA72dLoPavn372Lp1K9C60etjq8tZs3U/AL+/eCYpY8P9mE5EREREBhMVRzJoNTY2kpeXB7Ru9Pr5XhfPryoF4JbTkjkjY6w/44mIiIjIIKPiSAalr270Whsylnv+ng/AGelj+a9Tk/2cUEREREQGG91zJINSUVERNTU1GGOIHD+ZhctycXstKWPCeeDiGTgcxt8RRURERGSQUXEkg86uXbvYtWsXAGPjJvDDN7awr66ZqNAAnlg4hxFB+rEWERERke7TtDoZVDpu9Dpq1CgeWrmfvF3VOB2GRy+fzcRRoX5OKCIiIiKDlYojGTS+utHrh7sDeDunDICfnjmNE5Ji/JxQRERERAYzFUcyKFhrKSgoaN/odY8jlgf/uRmAi+fEc+UJk/0bUEREREQGPRVHMiiUlJRQUVEBQODIOH7y9yKshdkTo/jFeRkYowUYRERERKR3dOe6DHgdN3oNj47lR++UUtvkZmxEMH+efwxBLqd/A4qIiIjIkKCRIxnQGhsbyc9v3b8odEQYD66uZmtFPYEuB39ZcAyjI4L9nFBEREREhgoVRzJgHdjotaWlhYCAAN7dGcCnm/cBcN8F05kxIcrPCUVERERkKFFxJANWx41eN7dE8tTn2wG4/qQEzp8V7+d0IiIiIjLUqDiSAamsrKx9o9f6wGju/WAbACcmx3DbGan+jCYiIiIiQ5SKIxlwamtr2bhxY+tfgsK4a8Vumt1eJo8K5ZHLZuN0aGU6EREREfE9FUcyoLjdbnJycvB6vTgDAvnD2jr21DQTFuRi8ZVziAwN8HdEERERERmiVBzJgGGtJT8/n8bGRowxvLzF8OWOWoyBP1wyk6TR4f6OKCIiIiJDmIojGTBKS0vbN3r9siqE13JbV6b78bdSOC1tjD+jiYiIiMgwoOJIBoR9+/ZRXFwMQFlLCA+vLAfgzMxx3Hhyoj+jiYiIiMgwoeJI/K7jRq91ngB+/a/9eLyWtHER/O7CTIzRAgwiIiIi0vcGRHFkjBlnjPmNMeZDY0yNMcYaY04+TNtzjDHrjDGNxphSY8xdxhhXP0cWH+m40avbGh78op6qRg8jRwTy+MJjCA3UpRURERGR/jEgiiMgBbgNiAeyDtfIGPNt4DVgH3Bz259/BjzYDxmlD2zatImamhq8XsuzBW427WvG5TA8esVs4qND/R1PRERERIaRgfK2/BdAjLW2whhzHvDqYdrdD6wHTrfWegCMMdXAT4wxD1tri/onrvhCWVkZO3fuBOCjXfBxSSMAd52TzvEJo/wZTURERESGoQExcmStrbHWVhypjTEmDUgD/nKgMGrzKK1fxwV9GFF8rONGr/n7LEuy6gC4/LiJLDh+kj+jiYiIiMgwNVBGjrpiVtvntR0ftNbuNMZs73D8IMaYyqP0GwmtL9b9rb6+3t8R+oXb7Wb9+vU0Njayp8Hy0BdejDHMnhDBf586aUBcC18YLtdzuND1HHp0TYcWXc+hRddzaBlM13MwFUfj2j7v6uTYLmB8P2aRHrLWUlhYSGNjI3XNXv6cbWn0GMZGBPHghekEOAfEYKaIiIiIDEODqTgKafvc1MmxRqDTu/ettVFH6rRtZCkyLCysd+l8aCBl8bWSkhIaGhoIDAziibwGdjUYggMcLL7yWCaNifR3vD4xlK/ncKTrOfTomg4tup5Di67n0DIYrudgepu+oe1zUCfHgjsclwFq//797Ru9vraxnnV7Wx//7YUzyIgbmoWRiIiIiAweg6k4OjCdblwnx8YBO/sxi3RTU1MTeXl5AKzcVscbWy0A3zs5kXNmaEakiIiIiPjfYCqOvmz7PKfjg8aY8bTuj/TlIWfIgNBxo9fNFQ0sznFjjINTU0fz42+l+DueiIiIiAgwiIoja20uUABcb4xxdjj0PcALvOyXYHJUmzZtorq6mn21zTyyrgG3cZEQO4I/XDoTp8P4O56IiIiICDCAFmQwxtzZ9sdpbZ8XGGO+DlRaax9pe+y/gTeAfxhjlgMZwE207n20sV8DS5fs3r2bnTt30uz28NgXVez3hBIe7OKJhXOICA7wdzwRERERkXYDpjgCfvGVv1/T9rkEeATAWvt3Y8x/AncBfwT2Avd2cq4MALW1tRQWFmKtZdn6fWysD8HhgIcvm0Vi7MBfrUREREREhpcBUxxZa7s0v8pa+xrwWh/HkV5yu93k5ubi9Xp5r3AfH+8JxDgNt5+Ryikpo/0dT0RERETkEIPmniMZPKy1FBQU0NDQQPaOal7Y6MU4XZw7czzXn5Tg73giIiIiIp1ScSQ+t23bNsrLyymrauDRdbUQGEpGXAT3XZCJMVqAQUREREQGJhVH4lMHNnqtb3bz0OflNAREEhMWxOML5hAc4Dx6ByIiIiIifqLiSHzmwEavHo+Xxz/fyU4bRYDT8Of5sxkfFeLveCIiIiIiR6TiSHyi40avr3y5i/U14Rjj4J5zM5gzeaS/44mIiIiIHJWKI/GJzZs3U11dzeebK3i9xIFxBbJw3iQumzvR39FERERERLpExZH02u7du9mxYwfF5bUs/rIWZ0g4xyeM5Kdnpfk7moiIiIhIl6k4kl6pq6ujsLCQqoZmHvpkF+7QUcRFhfDoFccQ4NSPl4iIiIgMHnr1Kj3mdrvJycmhucXNHz8qYX/gaEIDXTyxcA4jRwT6O56IiIiISLeoOJIeO7DR69KVpWxsjsI4XTxw8QzSxkf4O5qIiIiISLepOJIeKS0tpby8nA/ydrNilxNHUCj/dWoS35k+zt/RRERERER6RMWRdNuBjV4Lyqp5NqsKV9hITps2hltOm+rvaCIiIiIiPabiSLrlwEave2oaeejjbRA5juTRYTx4yQwcDuPveCIiIiIiPabiSLrswEavtfWNPPjBJupHjCcqNIjFV84hPDjA3/FERERERHpFxZF02ebNm6mqquIv/7eFbXYkzoBAHrl8FpNGjfB3NBERERGRXlNxJF1yYKPXNzfsZNVeB86QCP73O9M4MTnW39FERERERHxCxZEcVV1dHRs3bmR96X6WZ+/HFTmG/5wdx7Vfn+LvaCIiIiIiPqPiSI7I7XaTm5tLaUUtj3xcgmvkBGZOjOZX50/HGC3AICIiIiJDh4ojOaLCwkL27K/mgfc20hIRx5ioETy+4BiCA5z+jiYiIiIi4lMqjuSwtm3bRtnuPTyyoog9Jprg0DD+vOAYxkQE+zuaiIiIiIjPqTiSTlVWVrJlyxaWr9lG9j6DK3wUv/rP6cyeGO3vaCIiIiIifcLl7wAy8BzY6PWToj28mbePwLGJXPO1KVx4TLy/o4mIiAxJ1lrKy8tpbGzE6/X6O47ftbS0ABAQoH0Uh4L+uJ4Oh4Pg4GBiYmJ6dV+8iiM5iNfrJS8vj4Id+3j8kxICYhI4MXk0//udVH9HExERGZKstezYsYOamhqCgoJwOnVfr8ull6hDSX9cz5aWFmpra2lqaiIuLq7HBZJ+8uQgW7ZsoWTXXu5/rxAbFceUMdE8cvksXE7NwBQREekL5eXl1NTUMGbMGEaOHOnvOAOCx+MBUKE4RPTX9dy3bx+7d++mvLyc2Nie7cWpV7zSbs+ePRSXlPLg+xupckYRERnN4ivnEBUa6O9oIiIiQ1ZjYyNBQUEqjER6aeTIkQQFBdHY2NjjPlQcCdC60WtBQQFP/6uYoiqLK3IMv79kJlPHhPs7moiIyJDm9Xo1QiLiI06ns1f37ak4kvaNXt/N3smHRfsJGDWRW7+ZwunpY/0dTURERESk36g4EgoLC1lTtIsln5cSEDOJ78yI5+ZTk/wdS0RERESkX6k4Gua2bdtG7uZt/OGfRZjIsaRNGsP9F83A4ej5EogiIiIiIoORiqNhrLKykrzCIu5/r5B6ZxixY8byxMI5jAjSIoYiIiIyuJ188smcfPLJPu3TGMPdd9/t0z4PeOaZZzDGsHXr1j7pvzN98fXcfffdvdpnyN9UHA1TTU1N5Obm8uiHRWyrsQSNiuNPV8xmwshQf0cTERER8ZuVK1dy9913U1lZ6e8oA9pvfvMbXnvtNX/H8DkVR8OQtZa8vDxeXFXMqpIqAmImctc50zkhMcbf0URERET8auXKlfz85z/vtDhqaGjgzjvv9EOqgedwxdGdd95JQ0ODHxL5huZPDUObN2/mnxuKWb52GwGxk7lsXhIL503ydywRERGRAS04ONjfEQY8l8uFyzV4SwyNHA0ze/bsYWXWRv704SacEaOZmzqJe85LH9RzQ0VERGRgKikp4cYbbyQlJYWQkBBGjRrFRRdddMh9NQfut1m5ciW33HILY8eOJSIigvPPP5+9e/ce1Pb111/nzDPPZPz48QQFBZGYmMgvfvELPB7PYXNs2bIFYwwPPvjgIcfef/99jDG8/fbb3H333fzwhz8EYMqUKRhjDroPqLN7dLZt28bVV1/NuHHjCA4OJikpiR/84Afd/h50VVlZGVdffTXx8fEEBQUxbtw4zj333IP6c7vd/PznPychIaHL3yOAq666ismTJx/y+FfvIzLGUFVVxZIlS9q/R1dddVWnbQ/kueeee46axxjDLbfcwssvv0x6ejpBQUGkp6fz7rvvdu+b1AuDt6yTbqurq2Pthhx+914hTc4QJkyYxGPzZxPk0sZzIiIiA43b42VXVaO/Y7QbFxmMy9m999XXrFnDZ599xqWXXkp8fDxbt27lscce4+STTyYvL4/Q0IPvdb7xxhsZNWoUP/vZzyguLubhhx/mpptuYvny5e1tnnnmGcLCwrj11lsJCwtjxYoV/OxnP6O6uprf/e53neZISEjga1/7Gs8//3x78XPAc889x+jRo/nWt75FfHw8mzdvZtmyZTz44IPExLTechAbG9tpvzt27GDu3LnU1NSwaNEiUlJSKCkpYfny5Tz00EM9+h4czQUXXMCWLVu48cYbGT9+PGVlZbz//vuUlpa2FzbXXXcdS5Ys4dJLL+XrX/86n3zyCT/72c8oLS3liSee6NbzdebZZ59l0aJFHHPMMVx//fUAJCYmHrb99ddfz9KlS7uU5+OPP+all17ixhtvJCwsjIcffpgLLriA0tJSRo0a1evsR6PiaJjweDxsyMrmwfcK2FPnITw+iSeunMPocA0Pi4iIDES7qho58bcf+jtGu0/+55RuL9x05plncuGFFx702Nlnn828efN4+eWXWbBgwUHHRo8ezTvvvIPX621/7OGHH6aqqorIyEgAnn/+eUJCQtqP33DDDdxwww08+uij3HvvvQQFBXWaZcGCBdxwww0UFRWRnJwMtN5D9Morr3DVVVfhcrnIzMzkmGOOYdmyZZx33nmdjqJ0dPvtt7N3717Wrl3LzJkz2x+/9957e/w9OJLKyko+++wzXnzxRS666KL2x++44472P2/YsIElS5Zwww038NhjjwHw/e9/n6ioKP7yl79w8803k5mZ2eXn7Mz8+fO56aabSEhIYP78+Udsu2HDBpYuXcqiRYv485//fNQ8+fn55OfnM2XKFABOOeUUZsyYwQsvvMBNN93Uq9xdoWl1w0RBQQFPflRA9o5qAmIm8duLZ5MZH+XvWCIiIjKEdSxiWlpaqKioICkpiaioKNatW3dI+0WLFh00JevEE0/E4/FQUlLSaZ81NTWUl5dz4oknUl9fT0FBwWGzXHLJJQQFBfHcc8+1P/bmm29SU1Nz1Bf4nfF6vbz++uucd955BxVGwEFfQ3e/B0cSEhJCYGAg7777LnV1dZ22efvttwG49dZbD3r8wIjZgeP95cDz3XLLLV3Kc/rpp7cXRgCZmZlERESwZcuWPk7aSiNHw8D27dv526d5vJW9C1f0eL73zQzOmxXn71giIiJyBOMig/nkf07xd4x24yK7P9ukoaGBX//61zz99NPs2LEDa237saqqqkPaT5w48aC/R0dHA7B///72x3Jzc7nzzjtZsWIF1dXVB7XvrM8DoqKiOOuss3jhhRfa7xt67rnnSE5OZu7cud3+2vbu3UtNTQ0ZGRlHbNfd78GRBAUFcd999/GjH/2I559/nhNOOIGzzjqL+fPnt0/9KykpweVyHTLNLSkpCZfLdVCh2R+6m+erPwPQ+nPQ8WegL6k4GuKqqqp49/MNPPHpFpyh0fzHMdP4nzNS/R1LREREjsLldAz6/Qdvvvlmnn76aW655RbmzZtHZGQkxhguvfTSg6bOHeB0dn4f9IGCorKykm984xtERERwzz33kJiYSHBwMOvWreO2227rtM+OFi5cyLnnnsvatWtJSEjgnXfeOWhKWl/o7vfgaG655RbOOeccXnvtNd577z1uv/127r33XlasWMGMGTN6lfVwC3QdbSEHXzraz0BfU3E0hDU3N/Pp6nU88I8CPI5AUqYm8/Cls3A6tDKdiIiI9L2//e1vXHnllTzwwAPtjzU2NvZ4g9WPPvqIiooKXnnlFU466aT2x4uLi7t0/re//W1iYmJ47rnnSE1NpaWlhSuuuOKgNl1dwTc2Npbw8HBycnKO2M7X3wNoXWDi1ltv5dZbb2XLli3MmDGD+++/n2effZZJkybhdrvZvHlz+71V0LqVi9vtZtKkw2/fEh0d3Wmuzkabuvp96pgnNfXfb9B3JY8/6J6jIcpay7ovs/j1Wznsb/QQHZfI4qvmEhka4O9oIiIiMkw4nc5D3vH/4x//2OORiAOjCh37bG5u5tFHH+3S+QEBAVx66aUsX76cZ599luOOO46kpKT/b+/O46Mq7z2Of36EkCAhi0AQkE1oQRovboiyasNWjAuKLShCWLyCVaRyBRdUVETApRQVUUFBULBaBAuyChS1qIhWBC+yiLQqEtYAAgEnz/1jZnKzkn1OJn7fr1dekzznzHN+Mw/DnN95lpNjnxo1agAUmrxUqVKFa665hgULFvD555/n2JY9vrJ8D44dO5bnBqtNmjQhLi6OEyf8Kxv27NkTgMmTJ+fYL7h63pVXXllg/c2aNSM9PZ2NGzdmle3evZu33347z741atQoUoIXjGfKlCnFjscL6jmqpHbs2MGf3/0X29OOUq1OY565uS3NE2t6HZaIiIj8gqSkpDB79mzi4uJo1aoV69atY+XKlSVekrldu3YkJCQwYMAAhg8fjpkxe/bsYg25uvnmm3n22WfZvXs3zzzzTJ7tF110EeBfAa5Pnz5ERkZy1VVXZSVN2Y0fP57ly5fTsWNHhg4dSosWLfjPf/7DvHnz2Lp1a5m/B1u3biU5OZkbbriBVq1aUa1aNRYsWMD3339Pnz59AGjdujUDBgxg6tSpHDx4kA4dOvDBBx8wd+5cBg8ezHnnnVdg/X369GH06NH06tWL4cOHc+zYMZ5//nl+/etf51k84qKLLmLlypU8/fTT1K9fn6ZNm9K2bds8dbZu3Zr+/fvz/PPPc+jQoWLF4wUlR5XQ3r17eWnJev6xdS8RsYmMvvYSks+t63VYIiIi8gvzl7/8hYiICF577TVOnDhB+/btWblyJd27dy9RfbVq1WLRokWMHDmSMWPGkJCQQL9+/UhOTi5ynZdccgktWrRgx44dWQlFdhdccAHjx4/nueeeY+nSpWRmZrJz5858k6OGDRvy8ccfM2bMGGbNmsWRI0do2LAhKSkp5fIeNGzYkL59+/Lee+8xZ84cqlatSsuWLfnrX//K9ddfn7Xf9OnTadq0KTNnzuStt96iQYMGPPLII9x3332nrb9WrVq8/fbb3HXXXYwaNYqmTZvy+OOPs23btjzJ0ZNPPsktt9zCmDFjOH78OAMGDMg3OQJ48cUXadKkCa+++mqx4vGChWpyU0VlZofi4uLiSjPus6wcPXoUgJiYmBLXcezYMWYufI9xizZDVA16Jbfj2RsvLPK4UCk7ZdGeUnGoPSsftWnlEs7tGZzPUdHmXngpOOSsoMn5pXXeeefRuHFjFi1aVC71S07l3Z7ZFfZ5io+PJz09Pd05lwUexzcAAB1FSURBVO89bTTnqBLx+Xys+HA9Ty3bgqtSldZJv+HJG85XYiQiIiIS8NFHH7Fp06Zi3XxVfjk0rK4S+fzLzTy64HN+OunjrKYtmT7oMqpXK/8MXURERKSi27RpE59++ilPPvkkjRo14rrrrvM6JKmA1HNUSfz73/9h7Bvr+O7gcaJr1eeFwR1pEF+98CeKiIiI/AK89dZbDBo0iMzMTF577TUiI7WCr+Sl5KgSSE9PZ+Kb/+DTXQeIOCOBcTd1pu05JVsFRkRERKQyGjt2LJmZmXz11Vd06NDB63CkglJyFOZOnjzJjL//g79t+A8WGU3/HpfS71JN6BQRERERKS4lR2HMOcfitZ/wl+VboEoEl110Pg9f+19ehyUiIiIiEpaUHIWxzzZt4cE3PyHjZx+Nmv6KFwe1o1pVNamIiIiISEnoTDpM/fDjHu6euZq9RzI448y6vDz0t9SOifI6LBERERGRsKXkKAwdO3aM+19Zxle706kSFcPkId1JahDndVgiIiIiImFNyVGY8fl8TH5zFUu+/B6LiOT26zpz9fkNvA5LRERERCTsKTkKM/NXf8xzKzYBRvJlFzH6yvO8DklEREREpFJQchRGNny1jTFz1+HLdDRv3oypgzoQUcW8DktERETkF2XmzJmYGd9++2251H/55Zdz+eWXl0vd+Smv19OkSRNSU1PLtM7ypuQoTOzZd4A7XlhK+vGT1Eyoxat3/I7YaN3ZWURERES8s2XLFsaOHVtuiWKoKTkKAxkZGQx//u98s/coEdWimfbHqzinTozXYYmIiIj8It18880cP36cxo0bex2K57Zs2cLDDz+cb3L09ddf89JLL4U+qFJQclTBOed4bM4K/vG/P4BV4d4bu5Lcqp7XYYmIiIj84vz0008AREREEB0djZmmN5xOVFQUkZHhNdJJyVEFN2/Vp7z03pcAXN25DX/s+huPIxIREZGKzufzsXjxYvr27UtycjJ9+/Zl8eLF+Hy+kMYxduxYzIydO3fSv39/4uLiiIuLY+DAgRw7dixrv2+//RYzY+bMmXnqMDPGjh2bp87t27fTp08fYmNjqVu3LhMnTgRg69atdOvWjRo1atCoUSPmzJmTp84DBw5wxx13cPbZZxMVFUWLFi2YMmVKjn3WrFmDmfHmm29y7733Ur9+fWrWrAkUPEdn8eLFdOrUiZiYGOLi4mjXrh0LFizI2r5w4UKuvPJK6tevT1RUFM2aNePRRx8tcbusWLGCDh06EB8fT0xMDC1atOC+++7Lsc+OHTvo3bs3CQkJnHHGGXTo0IE1a9YUWnfu9z0o+zyimTNn0qtXLwCuuOIKzAwzy6o/vzlHRYkn+P5+9NFHjBgxgjp16lCjRg169erF3r17i/LWlFjVcq1dSmXD17u4f/ZqHPCbX53DlIGddYVCRERETistLY2UlBTWr19PYmIizZs3Z9WqVcybN482bdqwaNEiEhMTQxrT9ddfT7NmzZgwYQKfffYZ06dPJzExMSuhKYnevXuTlJTExIkTmT9/Pvfccw/x8fE8/vjjXHfddVxzzTVMmzaN1NRUOnToQJMmTQB/70/nzp3Zs2cPQ4cOpUGDBqxevZo777yTgwcP8tBDD+U4ztixYznjjDMYPXo0R44cKTCeGTNmMGTIEFq3bs39999PzZo12bBhAytWrODaa68F/Cf9MTEx3HXXXcTExLBq1SoefPBBDh8+zBNPPFGs179582ZSUlJo3749jz32GBEREWzbto0PPvgga589e/bQvn17/xSN4cOJjY1lxowZdOvWjeXLl5d60YdOnToxYsQIJk+ezH333ce5554LkPWYW3Hjue2226hVqxZjx45l586dTJ48mdtvv5033nijVHGfjpKjCmrPgXT+e8pCjp30cWZCArP/dBXRkRFehyUiIiIVmM/nIyUlhc2bNzNr1iz69u1LZGQkp06dYu7cuQwbNoyUlBTWrVtHRETozivatGnDCy+8kPX3/v37mTFjRqmSo/bt2/Pcc88BMHDgQOrXr8+wYcN46aWXGDx4MABdunShZcuWzJ49mwceeACAp59+ml27dvHFF1/QtGlTAG699VYSEhKYMGECw4cPJyEhIes4p06d4v333yc6OrrAWNLT0xkxYgTt2rVj1apVREVFZW1zzmX9/vrrr1O9evWsv4cOHcrQoUOZOnUq48aNy/G8wqxYsYLo6GhWrFhRYFtOmDCBPXv2sG7dOi699FIABg8ezLnnnsvIkSPZsGFDkY+Xn3POOYfOnTszefJkunbtWmiyVdx4EhMTWbJkSVbnQGZmJlOmTCE9PZ24uLhSxV6QsBtWZ2ZRZjbRzH4ws+Nm9pGZJXsdV1k6depnbpm8gO8P/kTVyEheHnEt9ePP8DosERERqeCWLl3K+vXref755+nfv3/WfI/IyEj69+/P1KlTWb9+PcuWLQtpXEOHDs3xd8eOHdm/fz+HDx8ucZ1DhgzJ+j06OprWrVsTERFB//79s8pbtGhBfHw8O3fuzCp766236Ny5MzVr1mTfvn1ZP926dePEiRN8/PHHOY6Tmpp62sQIYPny5Rw9epR77703T4KTfdRP9sToyJEj7Nu3j44dO3Ls2DG2bNlSrNcfHx/PTz/9xNKlSwvc591336Vdu3ZZiUjweampqXz22Wf8+OOPxTpmaRU3nltvvTXH+9exY0d8Ph+7du0qtxjDsedoJnA9MBnYDqQCS8yss3NunYdxlZjP52Pp0qUsXLiQ/fv3801kY3ZXqQMYj6b24NJfneV1iCIiIhIG5syZQ2JiIn379s13e9++fRk1ahRz5syhZ8+eIYurUaNGOf4O9swcPHiQ2NjYMqkzLi6Os846K88CAHFxcRw8eDDr723btrFx40bq1KmTb72557QEe5dO55tvvgEgKSnptPtt3ryZMWPGsGrVqjyJYXp6eqHHye4Pf/gD06dPJyUlhXr16tGlSxd69erFtddem5VQ7Nq1i/bt2+d5bsuWLbO2n3VW6M4zixvP6f7dlJewSo7M7BKgD/An59zkQNmrwCZgItDJw/BKJPu44KSkJKo3u4TdUf4Pa8zxPVz5m9COCRYREZHwlZaWRvPmzQtcIaxatWo0b96ctLS0kMZV0LCv4JCzguZUn26hgvzqLOw44B+a1aNHD0aOHJnvvr/5Tc7Fr7L39pTGoUOH6Ny5M7GxsTzyyCM0a9aM6OhoPvvsM0aPHk1mZmax6qtevTpr165l9erVvPvuuyxdupTZs2fTtWtXlixZUm7DJkO5qEdR2rOshVVyBPQGTgHTgwXOuRNmNgN4zMzqOed2exZdMeUeF9ygVRsG/uXv4PPR6MwYNs96nJSUD0M+LlhERETCU2JiIqtWreLUqVP5JkgnT55k+/btJCdXrBkJwR6BQ4cO5Sgvj+FTzZo14/jx43Tp0qVM6wTYtGlT1sIPua1Zs4b9+/czf/58OnX6/+v52Yf8FVeVKlVITk4mOTmZp556ikmTJjF69GjWrFlDcnIyjRs35uuvv87zvGDZ6e7TlJCQkKc9Tp48ye7dOU+1i7NYWGniCZVwm3N0AbDFOXc0V/kngAHnhz6kkss+LrhrSi/unL6Ckz4fdc+MY/H4IUx99hlPxgWLiIhIeOrXrx9paWnMnTs33+1z584lLS2Nfv36hTiy04uNjaV27dqsXbs2R/nUqVPL/Fi9e/dm7dq1+S5nvW/fvhL1SnTt2pWYmBjGjx9PRkZGjm3B+oIXurPXf/LkyRK/xv379+cpO/98/6nwiRMnAOjZsyf//Oc/+eSTT7L2SU9PZ+bMmVx44YWnHVLXrFmzPO3x4osv5uk5qlGjBpA3sc1PaeIJlXDrOaoHfJ9PeTCFrZ97g5kV1lJxAEeP5s63yt/ChQtJSkriqquu4qY/v82+wz8RFVmVqUN7UL2Kj6uvvpqkpCQWLFiQ4wqDhIfs92+Q8Kf2rHzUppVLOLfnqVOnqFq1apkMV+ratSsXX3wxw4YNwznHjTfeSGRkJCdPnsxare7iiy+mS5cuIRkeFRwq5vP5chwvv/JBgwYxadIkBg8ezIUXXsj777/P9u3bs/YP7ldQncGkI7/X5ZzLKh85ciQLFy6ke/fuDBw4kNatW3P48GE2btzI/PnzOXToUI72yH7sguKPiYnhiSeeYNiwYbRt25bf//73xMbG8vnnnxMVFcUzzzxD27ZtSUhIYMCAAdx+++2YGa+99lqOuIPHOd1rCXrkkUd4//336dGjB02aNGHv3r1MmzaNs88+m8suuwyfz8fdd9/N3Llz6dGjB7fffjuxsbG88sor7N27l9mzZ5/2PR00aBC33XYb1113HV26dGHjxo0sX76c2rVr53g/k5KSqFq1KhMmTODgwYNERUVxxRVXZC0X75zLqr808WR/P3KX527rn3/+ucTn9uGWHFUHMvIpP5Fte9jYv38/jRs3JjIykruuacvwF5Yw4qpLaN3E/48pMjKSxo0bc+DAAY8jFRERkXAQERHBO++8w9VXX01qaiqjRo2iefPmbN++nbS0NC6++GLeeeedCjlc/4EHHmDfvn387W9/480336R79+4sWrSIevXqlelxatSowerVqxk/fjzz58/n5ZdfJiEhgRYtWvD444+X+L255ZZbSExMZNKkSYwbN45q1arRqlUrRo0aBUCtWrVYuHAhd999Nw8++CAJCQnceOON/Pa3vy3R4hgpKSl8++23zJo1i3379lG7dm06derEQw89lLXMdd26dVm7di333HMPU6ZMISMjgwsvvJAlS5YUuuz2kCFD2LlzJ6+88grLli2jQ4cOLF26lG7duuXYr06dOkybNo3x48dzyy234PP5WLlyZb730ipNPKFi5TmhqayZ2Sbge+dc91zlrYDNwBDn3Ixi1nkoLi4urihdgWWtb9++rFq1iu+++47IyEh+3HeAmOhqxMTEAP6u1oYNG5KcnMzrr78e8vikdIJXLILtKeFN7Vn5qE0rl3Buz+C8mrKcb+Hz+Vi2bBlz5swhLS2NxMRE+vXrR/fu3StkYpRbsFcgHGKVwoWyPQv7PMXHx5Oenp7unIvPb3u49Rztxj+0Lrdg2Q8hjKXU+vXrx7x585g7dy79+/cnJrpaju0VdVywiIiIVGwRERH07NkzpMt1i1QG4bYgw7+AlmaW+7JQ28DjFyGOp1R69OhBmzZtGDZsGLNmzeLUqVOAv8do1qxZDBs2jDZt2tC9e/dCahIRERERkdIKt56jt4D/AYbgvwksZhYFDAQ+dM6FVc9RREQEixYtIiUlhdTUVJKSkmjcuDHr168nLS2NNm3asGjRInUpi4iIiIiEQFglR865j83sTWCSmdUDdgADgMZAqpexlVRiYiLr1q1j2bJlLFiwgAMHDpCcnBxW44JFRERERCqDsEqOAvoDjwYeE4CNQE/n3IeeRlUKwXHBweW6w3EyqYiIiIhIuAu75Mg5dwK4O/AjIiIiIiJSJsJtQQYRERGRSqVKlSohuSGryC+Bz+ejSpWSpzhKjkREREQ8FB0dTUZGhm76LlJKBw4cICMjg+jo6BLXEXbD6kREREQqk9q1a5ORkcGePXs4dOiQFmMCnHMAmJnHkUhZCEV7+nw+MjIyqFmzJrVr1y5xPUqORERERDxkZjRo0IB9+/Zx4sQJMjMzvQ7Jcz///DMAkZGRHkciZSEU7RkZGZmVGJUmCVNyJCIiIuIxM6NOnTpeh1FhHD16FNAKvpVFOLWn5hyJiIiIiIig5EhERERERARQciQiIiIiIgIoORIREREREQGUHImIiIiIiABgwXXHf6nMLBOwuLg4r0MREREREZFylJ6eDuCcc/l2Eik5MvsZfw/aYa9jAYIZWrqnUUhZUXtWLmrPykdtWrmoPSsXtWflUpHaMxbIdM7le0ujX3xyVJGY2SEA51y817FI6ak9Kxe1Z+WjNq1c1J6Vi9qzcgmn9tScIxEREREREZQciYiIiIiIAEqOREREREREACVHIiIiIiIigJIjERERERERQMmRiIiIiIgIoORIREREREQE0H2OREREREREAPUciYiIiIiIAEqOREREREREACVHIiIiIiIigJIjERERERERQMmR58wsyswmmtkPZnbczD4ys2Sv45KSMbM2ZvacmX1lZj+Z2b/NbJ6ZNfc6NikbZjbKzJyZ/cvrWKRkAp/TxWZ20MyOmtkXZpbqdVxSMmb2KzN7w8y+C/y/+5WZ3WNmUV7HJgUzs3pmNsHMVpvZkcD/q5cXsO/VZvaZmZ0IfK8+ZGZVQxyyFKIobWpmtczsbjN738z2mtkhM1tnZjd4FHYeSo68NxP4EzAHuBPIBJaY2WVeBiUlNhq4DliJvz1fBC4HPjezcz2MS8qAmZ0FjAF+8joWKRkz+x3wIRAJPACMxP95behlXFIyZtYA+ARoCzyL//t0A/A4MN3D0KRwLfB/Z54NbCxop8BndgFwALgj8PuDwJ9DEKMUT1Ha9DLgMWA/MA64HzgO/NXMHghFkIXRUt4eMrNLgI+BPznnJgfKooFNwA/OuU5exifFZ2btgE+dcyezlf0K+BKY55xL9So2KT0zmwk0wn9hKd45d763EUlxmFkcsBX/Z/FOr+OR0jOz0cAEIMk5tzlb+VvANcAZzrlTXsUnBTOzmkA159x+M7sWeBu4wjm3Jtd+m4ETwCXOOV+gbBxwL9DSObcttJFLQYrSpmbWFMh0zu3KVmb4L1JdBtRyzh0PbeQ5qefIW72BU2S7uuWcOwHMADqYWT2vApOScc79M3tiFCjbBmwG1HMUxgIXM/oBd3kdi5TYjUA8/qvOmFnNwJeyhK/YwOOeXOU/4v9+9YU2HCkq59wR59z+0+1jZq2AVsALwcQoYCr+c9jryzFEKaaitKlzbmf2xChQ5vD3CFYHmpRfhEWj5MhbFwBbnHNHc5V/Ahigq9KVQODkqy6wz+tYpGQCbfgMMMs5p7lG4asLsAXoaWb/AQ4DBwJj5CO8DU1K6B+Bxxlm1trMGprZTUAqMNE5l+ldaFIGLgg8fpq90Dn3A/Bdtu0S/s4KPHp+rqTJbN6qB3yfT/nuwGP9EMYi5ecmoAH+cbUSnvrjv3p5rdeBSKk0xz+3aCYwCfgcSME/Rj4aGOFZZFIizrnlgXkK9wFXZ9v0oHPuUY/CkrITHEGzO59tu9F5UqVgZmcCQ4A1zrm9Xsej5Mhb1YGMfMpPZNsuYczMWgLPAR8Asz0OR0ogMIZ6AjDBOZffF7SEjxggAbjHOTcxUDbfzGKA28xsnHPO86uWUmw7gTX45zfsB64EHjazvc65aV4GJqUWPA8q6FzpjBDGIuXAzKoArwFxwHCPwwGUHHntOJDfUqPR2bZLmAqsbLYYOAjcoOEdYWsMcBJ42utApNSC/6fOzVX+GnADcAnwbkgjklIxsz7AC8CvA0OtwJ/wVgGeNLM3nHMHvYtQSin4mS3oXEnnSeHvGaA7cJNz7kuvgwHNOfLabv6/yzi7YNkP+WyTMBBYFWsJ/ish3Z1zP3ockpRAYFGUEfh7/+qaWRMza4L/S7la4O8ED0OU4gn2/OWevB/8W20Zfm4DNmRLjILeAWoArUMfkpSh4Ge2oHMlnSeFMTN7CP9neJRzLvdFK88oOfLWv4CWgSEd2bUNPH4R4nikDASWY/878GsgxTn3tcchScnVBaoBE/EP3Qn+tMW/+uBO/PNVJDxsCDw2yFV+duDR87HuUmx1gfwW04gMPGqETHgLLoBzcfZCM6uP/3OrBXLClJn9ERgL/Nk596TH4eSg5Mhbb+H/D3xIsCBwR++BwIf5XAmTCi6w4tUb+Nfqv8E595HHIUnp7AR65fOzGfg28PurXgUnxfZm4HFwsCCwEuEQ/Df21ec1/GwFLjazZrnK++JfxrvAm4tKxRe4d9UW4L9zrSg5DMgE/uZJYFIqZvYHYAr+Ic0jPQ4nD11R8ZBz7mMzexOYFBi+swMYADTGvwyphJ+n8K+Y9HfgTDPrl23bUefcAm/CkpJwzqXjv/dCDmY2AvhZ7RlenHMbzOxV4F4zSwQ+wz95vzv+YR2HPQ1QSuIJ4HfAh2b2LHAA/wqEvwOmOefSvAxOTs/MxgR+Dd4H8GYz6wAccs49Gyi7G/8wyWVm9gaQBNyO/95HW0MasBSqsDYN3DPwVfyLp7wH3JTrdnMrnHO5hz6HlPnvuyReCQzBehT/zSUT8F/lus85t9LTwKREzGwN0LmAzbucc01CF42Ul0A7xzvndC+yMGNm1YAH8F+IOgv4Bv+wjhc8DUxKLHCyNRb/PW9q4e/xfQV4IteNQ6WCMbOCTkJzfF+a2bXAQ/hPuPcCLwOPOud+LvcgpVgKa1MzS8X/+SzIFc65NWUeWDEoORIREREREUFzjkRERERERAAlRyIiIiIiIoCSIxEREREREUDJkYiIiIiICKDkSEREREREBFByJCIiIiIiAig5EhERERERAZQciYhIBWNml5uZC9wssMIyszfM7MMSPO9OM9tvZgnlEZeIiJSckiMREQk5MzvfzMaaWROvYykJM2sP/B4YU4KnvwBkAA+UaVAiIlJq5pzzOgYREfmFCfQKvQJc4Zxbk2tbFaAacMo55wt9dIUzs2VAonPughI+/0HgPqCBc25/mQYnIiIlpp4jERGpUJxzmc65ExU4MWoOdAVeLUU1c4AoILUsYhIRkbKh5EhERELKzMbi7zUCWB2YX+TMbGZge545R9nLzOw2M/vazE6Y2ZdmlhLY5zwzW2pmhwNzeqaYWWQ+x/+Vmc02s91mdtLMvjWzJ8ysRhFfQm/AgHfzqbudmS0xsx8D8X1vZu+a2aXZ93POfQN8DdxQxGOKiEgIVPU6ABER+cWZD9QD/hsYD/xvoHxHEZ77RyABmA6cAIYDb5vZDcBLwFxgAdANuANIA8YFn2xmFwGrgEP45/58D7QO1NPezDo7504VEkPnwPO3Zi80sxbACuBH4C/AHqAu0CFwjI9y1bMO6GdmMc65o0V47SIiUs6UHImISEg55zaa2Tr8ydGK3HOOClEfaOWcSwcws1XAF/gTrt7OufmB/aaZ2Qb8ydS4bM9/GdgNtHHOHQkWmtl7gTpuAmYWEkMrYKfLO2m3O3AG0Nc590kRXssO/N/DLYANRdhfRETKmYbViYhIOJkZTIzAn2gBh4EfsiVGQR8AZ5lZDPiH3QH/BbwORJlZ7eBPYN+f8Pc4FaYOcCCf8mBc15hZdBHqCS7EkFiEfUVEJASUHImISDj5Jp+yg8DOAsoBagUezw08PgzszfWTBtTAPwyuMA7/nKPc5gEr8a9Cd8DMVpnZaDNrXEA9wTq0bKyISAWhYXUiIhJOClrB7nQr21mux6eApQXse7CA8uz2AmfmLnTOZQBdzewS/EPsOgGPAGPN7Ebn3Nu5nhKsY28RjikiIiGg5EhERLzgRW/JtsCjzzm3shT1bAI6mVkV51xm7o2B+UafAJhZQ+Bz/POecidHzYGf8a9aJyIiFYCG1YmIiBeCq7Pl6YEpR5/jT2yGmtk5uTeaWVUzK0o8a4Ca+BdmyP782vns+x0F9DQBlwIbtFKdiEjFoZ4jERHxwnogE7jfzBLwL4aw0zn3cXkd0DnnzOxm/Et5bzSzl4HN+FeYaw5cB9xL4avV/Q2YCPTEn2wFjTGzbsAi/HOgDLgKaAlMyl6BmTXDv0rd/5TuVYmISFlSciQiIiHnnPu3mQ0CRgPPA5HALKDckqPAcf9lZhfgT4KuBoYCR4Bv8SdF7xWhjp1mtgy4mZxJzwL892/6Pf6FHY7jH8p3CzAjVzX9gAwKT8RERCSELO9tGkREROR0zOwy4J9A1+LOXwos8/0NMM85d1d5xCciIiWj5EhERKQEzGwe0Mg5166YzxsBPAg0c84VZXU8EREJESVHIiIiIiIiaLU6ERERERERQMmRiIiIiIgIoORIREREREQEUHIkIiIiIiICKDkSEREREREBlByJiIiIiIgASo5EREREREQAJUciIiIiIiIA/B8t2v8/xW3YQwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "import seaborn as sb \n",
        "sb.set_context('talk')\n",
        "fig, ax = plt.subplots(1,1,figsize=(12,8))\n",
        "ax.plot(data.time,data.v_anly,label='analytical solution')\n",
        "ax.plot(time,vel,alpha=0.25,c='k')\n",
        "ax.scatter(time,vel,fc='w',ec='k',label='numerical solution')\n",
        "ax.axhline(y=model.get_velocity(np.inf),ls='--',c='k')\n",
        "ax.annotate('terminal velocity',[0.5,model.get_velocity(np.inf)+2])\n",
        "ax.set_ybound(upper=60)\n",
        "ax.set_xlabel('time (s)')\n",
        "ax.set_ylabel(r'$\\nu$ (m/s)')\n",
        "ax.grid(True,alpha=0.2)\n",
        "ax.legend(loc=4)\n",
        "fig.tight_layout() \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Here we can plot the position (i.e. the horizontal position) and the velocity. We see that the velocity quickly saturates as it approaches the terminal velocity becoming constant. Correspondingly, we see in that the position with respect to time (i.e. $\\frac{dx}{dt}$) becomes linear. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 416
        },
        "id": "Qt31AxmrfcT1",
        "outputId": "e69651a0-4ec5-4fe7-f53a-92378abf408b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "   time           x        vel\n",
            "0   0.0    0.000000   0.000000\n",
            "1   2.0    0.000000  19.613300\n",
            "2   4.0   39.226600  36.402213\n",
            "3   6.0  112.031026  46.286283\n",
            "4   8.0  204.603592  50.169627\n",
            "5  10.0  304.942846  51.302813\n",
            "6  12.0  407.548473  51.591747\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light",
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "t = data.time.values\n",
        "v = data.v_num.values\n",
        "\n",
        "x = np.zeros(len(v)) \n",
        "for i in range(v.shape[0]): \n",
        "  if i == 0: \n",
        "    x[0] = 0\n",
        "  else:\n",
        "    delt = t[i] - t[i-1] \n",
        "    x[i] = x[i-1] + v[i-1] * delt\n",
        "    \n",
        "data2 = pd.DataFrame(np.column_stack((t,x,v)),columns=['time','x','vel'])\n",
        "print(data2)\n",
        "\n",
        "fig,axes = plt.subplots(1,1)\n",
        "axes.plot(data2.time,data2.x,label='position (m)')\n",
        "axes.plot(data2.time,data2.vel,label='velocity (m/s)')\n",
        "axes.grid(True,alpha=0.2)\n",
        "axes.legend()\n",
        "fig.tight_layout()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "bungee_jump.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.9"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}