{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">LQR Control of a Simple, Planar Crane</h1>\n",
    "<p style=\"text-align:center\">Dr. Joshua Vaughan <br>\n",
    "<a href=\"mailto:joshua.vaughan@louisiana.edu\">joshua.vaughan@louisiana.edu</a><br>\n",
    "http://www.ucs.louisiana.edu/~jev9637/   </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <img src=\"http://shared.crawlab.org/crane_positionInput.png\" alt=\"The Simple, Planar Crane Model\" width=35%/><br>\n",
    "    <strong> Figure 1: The Simple, Planar Crane Model</strong>\n",
    "</p>\n",
    "\n",
    "This notebook simluates a the simple, planar crane model like the one shown in Figure 1. We'll be treating the trolley as the input to the pendulum system. This is fairily consistent with \"real\" cranes, where we can generally control the trolley location fairly well and are intersted in controlling the payload.\n",
    "\n",
    "In this case, we can more explicitly draw the model like that in Figure 2. Because we're saying that we can exactly control $x(t)$, the mass of the trolley doesn't matter. We're really just controlling the pendulum connection point.\n",
    "\n",
    "<p style=\"text-align:center\">\n",
    "    <img src=\"http://shared.crawlab.org/crane_positionInput_noTrolley.png\" alt=\"The Simpler, Planar Crane Model\" width=35%/><br>\n",
    "    <strong> Figure 2: The \"Trolley-input\" Planar Crane Model</strong>\n",
    "</p>\n",
    "\n",
    "\n",
    "If we are treating the trolley as the input, the equation of motion for the payload angle is:\n",
    "\n",
    "$ \\quad \\ddot{\\theta} + \\frac{g}{l}\\theta = \\frac{1}{l}\\ddot{x} $\n",
    "\n",
    "In order to simluate the system (in this case a single, second-order ODE), we need to write it as a system of first-order differential equations. To do so, let's define a state vector: \n",
    "\n",
    "$\\quad \\mathbf{w} = \\left[w_1 \\quad w_2\\right]^T = \\left[\\theta \\quad \\dot{\\theta}\\right]^T $\n",
    "\n",
    "We can then write the system in the form:\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = f(\\mathbf{w},\\ddot{x},t) $\n",
    "\n",
    "So,\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = \\left[w_2, \\ -\\frac{g}{l}w_1 + \\frac{1}{l}\\ddot{x}\\right] $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by simluating the system using a nummerical differential equation solver, which could be used for more complex *and* nonlinear systems. We'll then see how to simluate the system using some functions from the [Python Control Systems Toolbox](https://www.cds.caltech.edu/~murray/wiki/Control_Systems_Library_for_Python).\n",
    "\n",
    "## \"Standard\" Imports\n",
    "First, we need to import [NumPy](http://www.numpy.org), the standard numerical *toolbox* we use, and [matplotlib](http://matplotlib.org), the standard plotting library. Nearly all of our projects will import NumPy, and those with plotting will always import matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We want out plots to show up inline with the notebook\n",
    "%matplotlib inline \n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation Using an ODE Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We need to import the ode solver\n",
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eq_of_motion(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the planar pendulum system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "    \"\"\"\n",
    "    theta, theta_dot = w\n",
    "    m, l, Distance, StartTime, Amax, Vmax, Shaper = p\n",
    "\n",
    "    # Create sysODE = (theta', theta_dot')\n",
    "    sysODE = [theta_dot,\n",
    "             -g/l * theta + 1.0/l * x_ddot(t, p)]\n",
    "    return sysODE\n",
    "\n",
    "\n",
    "def x_ddot(t, p):\n",
    "    \"\"\"\n",
    "    Defines the accel input to the system.\n",
    "    \n",
    "    We'll make a call to our lab function accel_input()\n",
    "    \n",
    "    Depending on the desired move distance, max accel, and max velocity, the input is either\n",
    "    bang-bang or bang-coast-bang\n",
    "    \n",
    "    Arguments:\n",
    "        t : current time step \n",
    "        p : vector of parameters\n",
    "    \"\"\"\n",
    "    m, l, Distance, StartTime, Amax, Vmax, Shaper = p\n",
    "    \n",
    "    x_ddot = accel_input(Amax,Vmax,Distance,StartTime,t,Shaper)\n",
    "    \n",
    "    return x_ddot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This cell includes functions to generate the acceleartion input\n",
    "\n",
    "def accel_input(Amax,Vmax,Distance,StartTime,CurrTime,Shaper):\n",
    "    \"\"\"\n",
    "    # Original MATLAB/Octave premable\n",
    "    ###########################################################################\n",
    "    # function [accel] = accel_input(Amax,Vmax,Distance,CurrTime,Shaper)\n",
    "    #\n",
    "    # Function returns acceleration at a given timestep based on user input\n",
    "    #\n",
    "    # Amax = maximum accel, assumed to besymmetric +/-\n",
    "    # Vmax = maximum velocity, assumed to be symmetric in +/-\n",
    "    # Distance = desired travel distance \n",
    "    # StartTime = Time command should begin\n",
    "    # CurrTime = current time \n",
    "    # Shaper = array of the form [Ti Ai] - matches output format of shaper functions\n",
    "    #           in toolbox\n",
    "    #          * If Shaper is empty, then unshaped is run\n",
    "    #\n",
    "    #\n",
    "    # Assumptions:\n",
    "    #   * +/- maximums are of same amplitude\n",
    "    #   * command will begin at StartTime (default = 0)\n",
    "    #   * rest-to-rest bang-coast-bang move (before shaping)\n",
    "    #\n",
    "    # Created: 9/23/11 - Joshua Vaughan - vaughanje@gatech.edu\n",
    "    #\n",
    "    # Modified: \n",
    "    #   10/11/11\n",
    "    #     * Added hard-coded shaping option - JEV (vaughanje@gatech.edu)\n",
    "    #\n",
    "    ###########################################################################\n",
    "    #\n",
    "    #\n",
    "    # Converted to Python on 3/3/13 by Joshua Vaughan (joshua.vaughan@louisiana.edu)\n",
    "    #\n",
    "    # Modified:\n",
    "    #   * 3/26/14 - Joshua Vaughan - joshua.vaughan@louisiana.edu\n",
    "    #       - Updated some commenting, corrected typos\n",
    "    #       - Updated numpy import as np\n",
    "    \"\"\"\n",
    "\n",
    "    # These are the times for a bang-coast-bang input \n",
    "    t1 = StartTime\n",
    "    t2 = (Vmax/Amax) + t1\n",
    "    t3 = (Distance/Vmax) + t1\n",
    "    t4 = (t2 + t3)-t1\n",
    "    end_time = t4\n",
    "\n",
    "    if len(Shaper) == 0:\n",
    "        # If no shaper is input, create an unshaped command\n",
    "        if t3 <= t2: # command should be bang-bang, not bang-coast-bang\n",
    "            t2 = np.sqrt(Distance/Amax)+t1\n",
    "            t3 = 2.0 * np.sqrt(Distance/Amax)+t1\n",
    "            end_time = t3\n",
    "        \n",
    "            accel = Amax*(CurrTime > t1) - 2*Amax*(CurrTime > t2) + Amax*(CurrTime > t3)\n",
    "    \n",
    "        else: # command is bang-coast-bang\n",
    "            accel = Amax*(CurrTime > t1) - Amax*(CurrTime > t2) - Amax*(CurrTime > t3) + Amax*(CurrTime > t4)\n",
    "\n",
    "    else: # create a shaped command\n",
    "        ts = np.zeros((9,1))\n",
    "        A = np.zeros((9,1))\n",
    "        # \tParse Shaper parameters\n",
    "        for ii in range(len(Shaper)):\n",
    "            ts[ii] = Shaper[ii,0]  # Shaper impulse times\n",
    "            A[ii] = Shaper[ii,1]  # Shaper impulse amplitudes\n",
    "\n",
    "        # Hard-coded for now\n",
    "        # TODO: be smarter about constructing the total input - JEV - 10/11/11\n",
    "        accel = (A[0]*(Amax*(CurrTime > (t1+ts[0])) - Amax*(CurrTime > (t2+ts[0])) - Amax*(CurrTime > (t3+ts[0])) + Amax*(CurrTime > (t4+ts[0])))\n",
    "        +\tA[1]*(Amax*(CurrTime > (t1+ts[1])) - Amax*(CurrTime > (t2+ts[1])) - Amax*(CurrTime > (t3+ts[1])) + Amax*(CurrTime > (t4+ts[1])))\n",
    "        +   A[2]*(Amax*(CurrTime > (t1+ts[2])) - Amax*(CurrTime > (t2+ts[2])) - Amax*(CurrTime > (t3+ts[2])) + Amax*(CurrTime > (t4+ts[2])))\n",
    "        +   A[3]*(Amax*(CurrTime > (t1+ts[3])) - Amax*(CurrTime > (t2+ts[3])) - Amax*(CurrTime > (t3+ts[3])) + Amax*(CurrTime > (t4+ts[3])))\n",
    "        +   A[4]*(Amax*(CurrTime > (t1+ts[4])) - Amax*(CurrTime > (t2+ts[4])) - Amax*(CurrTime > (t3+ts[4])) + Amax*(CurrTime > (t4+ts[4])))\n",
    "        +   A[5]*(Amax*(CurrTime > (t1+ts[5])) - Amax*(CurrTime > (t2+ts[5])) - Amax*(CurrTime > (t3+ts[5])) + Amax*(CurrTime > (t4+ts[5])))\n",
    "        +   A[6]*(Amax*(CurrTime > (t1+ts[6])) - Amax*(CurrTime > (t2+ts[6])) - Amax*(CurrTime > (t3+ts[6])) + Amax*(CurrTime > (t4+ts[6])))\n",
    "        +   A[7]*(Amax*(CurrTime > (t1+ts[7])) - Amax*(CurrTime > (t2+ts[7])) - Amax*(CurrTime > (t3+ts[7])) + Amax*(CurrTime > (t4+ts[7])))\n",
    "        +   A[8]*(Amax*(CurrTime > (t1+ts[8])) - Amax*(CurrTime > (t2+ts[8])) - Amax*(CurrTime > (t3+ts[8])) + Amax*(CurrTime > (t4+ts[8]))))\n",
    "\n",
    "    return accel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the parameters for simluation\n",
    "g = 9.81                     # gravity (m/s^2)\n",
    "l = 4.0                      # cable length (m)\n",
    "\n",
    "wn = np.sqrt(g / l)            # natural frequency (rad/s)\n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 15.0\n",
    "numpoints = 15001\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.,stoptime,numpoints)\n",
    "\n",
    "# Initial conditions\n",
    "theta_init = 0.0                        # initial position\n",
    "theta_dot_init = 0.0                    # initial velocity\n",
    "\n",
    "# Set up the parameters for the input function\n",
    "Distance = 2.0              # Desired move distance (m)\n",
    "Amax = 1.0                  # acceleration limit (m/s^2)\n",
    "Vmax = 0.35                 # velocity limit (m/s)\n",
    "StartTime = 0.5             # Time the y(t) input will begin\n",
    "\n",
    "# Design and define an input Shaper  \n",
    "Shaper = [] # An empty shaper means no input shaping\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [g, l, Distance, StartTime, Amax, Vmax, Shaper]\n",
    "x0 = [theta_init, theta_dot_init]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Call the ODE solver.\n",
    "response = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vy90Tixd7upadj9S7ciVTXS7f9xodDJUQi8WCNkEZWltbgzZBGbQWDloLExV16F1hJch6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\nyjpJsKAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1157a4d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Angle (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t, response[:,0]*180/np.pi, linewidth=2, label=r'Angle')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "plt.xlim(0,15)\n",
    "# plt.ylim(0,10)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "# leg = plt.legend(loc='upper right', fancybox=True)\n",
    "# ltext  = leg.get_texts()\n",
    "# plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('Crane_AngleResponse.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What about Position?\n",
    "We can also include the trolley location in the state vector. We know that how the position and velocity are related to the acceleration input. The new state vector becomes:\n",
    "\n",
    "\n",
    "$\\quad \\mathbf{w} = \\left[\\theta \\quad \\dot{\\theta} \\quad x \\quad \\dot{x}\\right]^T $\n",
    "\n",
    "We can then write the system in the form:\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = f(\\mathbf{w},\\ddot{x},t) $\n",
    "\n",
    "So,\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = \\begin{bmatrix}w_2 \\\\ -\\frac{g}{l}w_1 + \\frac{1}{l}\\ddot{x} \\\\ w_4 \\\\ \\ddot{x}\\end{bmatrix} $\n",
    "\n",
    "The acceleration, $\\ddot{x}(t)$, is still the input to the system. The function from above can be used unaltered. It's recopied below to avoid confusion, but note that it is generally bad practice to have functions defined in muliple places in a script or notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eq_of_motion_withTrolley(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the coupled spring-mass system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "    \"\"\"\n",
    "    theta, theta_dot, x, x_dot = w\n",
    "    m, l, Distance, StartTime, Amax, Vmax, Shaper = p\n",
    "\n",
    "    # Create sysODE = (theta', theta_dot')\n",
    "    sysODE = [theta_dot,\n",
    "             -g/l * theta + 1.0/l * x_ddot(t, p),\n",
    "             x_dot,\n",
    "             x_ddot(t, p)]\n",
    "    return sysODE\n",
    "\n",
    "def x_ddot(t, p):\n",
    "    \"\"\"\n",
    "    Defines the accel input to the system.\n",
    "    \n",
    "    We'll make a call to our lab function accel_input()\n",
    "    \n",
    "    Depending on the desired move distance, max accel, and max velocity, the input is either\n",
    "    bang-bang or bang-coast-bang\n",
    "    \n",
    "    Arguments:\n",
    "        t : current time step \n",
    "        p : vector of parameters\n",
    "    \"\"\"\n",
    "    m, l, Distance, StartTime, Amax, Vmax, Shaper = p\n",
    "    \n",
    "    x_ddot = accel_input(Amax,Vmax,Distance,StartTime,t,Shaper)\n",
    "    \n",
    "    return x_ddot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to specify the initial conditions for all the states, which include $x$ now. I've also respecified all the solver and system parameters for completeness. This is arguably bad practice, if the same parameters as above are being used. This also means that anytime I want to change a parameter, I would have to change it in mulitple places."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the parameters for simluation\n",
    "g = 9.81                     # gravity (m/s^2)\n",
    "l = 4.0                      # cable length (m)\n",
    "\n",
    "wn = np.sqrt(g / l)            # natural frequency (rad/s)\n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 15.0\n",
    "numpoints = 15001\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.0, stoptime, numpoints)\n",
    "\n",
    "# Initial conditions\n",
    "theta_init = 0.0                        # initial angle (rad)\n",
    "theta_dot_init = 0.0                    # initial angular velocity (rad/s)\n",
    "x_init = 0.0                            # initial trolley position (m)\n",
    "x_dot_init = 0.0                        # initial trolley velocity (m/s)\n",
    "\n",
    "# Set up the parameters for the input function\n",
    "Distance = 2.0              # Desired move distance (m)\n",
    "Amax = 1.0                  # acceleration limit (m/s^2)\n",
    "Vmax = 0.35                 # velocity limit (m/s)\n",
    "StartTime = 0.5             # Time the y(t) input will begin\n",
    "\n",
    "# Design and define an input Shaper  \n",
    "Shaper = [] # An empty shaper means no input shaping\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [g, l, Distance, StartTime, Amax, Vmax, Shaper]\n",
    "x0 = [theta_init, theta_dot_init, x_init, x_dot_init]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Call the ODE solver.\n",
    "response_withTrolley = odeint(eq_of_motion_withTrolley, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now parse the output of the ode solver (which now includes the trolley position) to plot the position of the trolley and payload. We know that the horizontal position of the payload is defined by:\n",
    "\n",
    "$ \\quad x_{paylaod} = x + l \\sin{\\theta} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_resp = response_withTrolley[:,0]\n",
    "theta_dot_resp = response_withTrolley[:,1]\n",
    "x_resp = response_withTrolley[:,2]\n",
    "x_dot_resp = response_withTrolley[:,3]\n",
    "\n",
    "payload_position = x_resp + l * np.sin(theta_resp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QBEEQhAdoWdAXrFar2iZIidlsVtsE6SBNxJAuYkiX/pAmYkgXMVrUhZwrBcq5EqPFte5Q\nQ5qIIV3EkC79IU3EkC5itKjLoFsWZIyZAJg458W+XEfLgmLsdjuVqegDaSKGdBFDuvSHNBFDuoiR\nTJfBsSzIGFuqHEXKYfRwSS6ANYwxzhhrYoytZ4zleroPJbSL6erqUtsE6SBNxJAuYkiX/pAmYkgX\nMVrURWrnijG2lHO+UjmWAShVjgHhnCcBSOKcJ3HOF3DOyzxdQxXaxVRWVqptgnSQJmJIFzGkS39I\nEzGkixgt6iKtcyWKUHHOVwJIZowVeLqec97sy/2io6N9OX3IkJWVpbYJ0kGaiCFdxJAu/SFNxJAu\nYrSoi7TOFQATANEyYI3yXFCRaD1XKgwGg9omSAdpIoZ0EUO69Ic0EUO6iNGiLtJ6FMpSXp4gAmWC\nw8FyC2OsoNex3Is8LbS3twdg7eCloqJCbROkgzQRQ7qIIV36Q5qIIV3EaFEXaZ0rwOVguWCMLQRQ\n42EnYJnzHOW8tQDWiE5UEuVLGGMlzc3Nru2edXV1ri7cZrMZ5eXlsNvt6OjoQGlpKTo6OmC321Fe\nXu6qv1FVVTUorx82bJim7Q/F9SNHjtS0/aG63rm0rlX7Q3V9T0+Ppu0PxfVjxozRtP2huj49PV3T\n9ofq+jFjxkhjv7dophSDEn3aAOASX/OpGGPVABYNlNhOpRgIgiAIgvDA4CjF0IsVcDhIPjlWCs0A\n8gc6gXYLinF68MRpSBMxpIsY0qU/pIkY0kWMFnXRhHPFGFsOYAXn3FOulYkxJgrFNSqHWyihXUxc\nXJzaJkgHaSKGdBFDuvSHNBFDuojRoi7SLwsyxpYCKO7tWDHGCkR5V8rS4WKlZEPvx5vgSI5365zR\nsiBBEARBEB7Q/rKgUs+qxOkUMcaMvWtcKZGqNc7dgKIlQ8U5W+0p6kW9BcVosadTqCFNxJAuYkiX\n/pAmYkgXMVrURa+2Ae5QegSuV/6/79NJyn9NAAoAJMORVwXO+UplGbEZgNPpWubpftT+RozFYlHb\nBOkgTcSQLmIGmy5dPTac6rRCH8GQEB0Jnc6rH/JnMNg0CRaDUZf2Lis6emyIitAhPlov+j73iBZ1\nkX5ZMFzQsiBBEER/bHaOzXtP4Ivdx1F6oBHHW05v/omJisCkUQk4d/JwXJadhtFJsSpaSshAZ7cN\nxbvqsWlPAyoONaPJcnpVKDEmEtNGJ+L8qSOxYEYqhsVGqWip33jlHZJzpZCTk8PLy8vVNkM6zGYz\nUlJS1DZDKkgTMaSLGK3qYrdzfFx+BM99WY365tMOVYSOITEmEj02O051Wl2P6xgw/6xU3H/JZIxN\nHtjJ0qomoUbLunT22PDa5gN4a9tBtHacnhcGvQ6xBj26emxo77a5Ho+OjMB1eWNwz4UZHp0syXTx\nyrmSdlkw3FDOlZi6ujqZJrUUkCZiSBcxWtSl9sQp/Pnd71F5pBUAMDY5BtfmjsXcySMwcUQc9BGO\ndN2W9m7sONSMDbvqUbzTcXxV1YC7LzDhjvNNiHCzZKhFTcKBVnUpqTHjf97f6XLCzxo7DFfljMHs\njBSkGWOg0zFwznGirQslNWZ89v0xbNtvxlvbDuHTimP4+RWZuCx7tNvxtagLRa4UaFlQjN1upzIV\nfSBNxJAuYrSmy392HMWKDyvR2WPDiEQDfrJgChZMT/OYW3W8pQP/3rAf/9lxFACQb0rGn3+QjeT4\n/n3htKZJuNCaLnY7x3NfVOP5r6rBOTBpVDx+fsU05E1M9njtvvpW/O9/qlBW2wQAuC5vLH5xRSYM\nkRGC+0ilCy0L+kJubi4vK3NbwH3I0tHRgZiYGLXNkArSRAzpIkYrunDu+KJ89otqAMClM9JQeE0W\n4gy+LXB8U30SD7/9PZos3UgzxuCpO/KQnnJmnSKtaBJutKRLt9WOP7/7PYp31oMx4J4LMnD3hSZX\nVNMbOOd4v/Qw/v6fKnRb7cgZn4S/3nw2EmIizzhPMl20X4ohnFCFdjGVlZVqmyAdpIkY0kWMFnTh\nnOOJdVV49otq6Bjwq6um4U8/mOGzYwUAszOG4+X75yJrTCKONXdg6XPfYl996xnnaEETNdCKLp3d\nNvzytTIU76xHrCEC/7g9D/fNn+STYwU4KgFcn5+OVT+cjRGJBpQfbMIDL36HxlNdZ5ynFV16Q5Er\nBYpciZHsF4MUkCZiSBcxsuvCOcf/fbYXr22pRZRehz8vzMZF00YFPK6ly4oH3yzHdzVmJMVFoeje\nWRinRLBk10QttKBLj9WO5W9ux9Z9J5EcH4X/vS0PU9MSAx73WHMHfvpyCQ6Z2zElLQFP33UO4qMd\nESzJdKHIlS9ItJ4rFQZD/3yJoQ5pIoZ0ESO7Lq98fQCvbalFhI7hsZtyguJYAUCcQY8nbs3FrIwU\nNFm68f9eLkFDq2OFQHZN1EJ2Xex2jv9+73ts3XcSxthIPH3XOUFxrAAgzRiDZ+6ZhfSUWOw91oZf\nvb4dnT2O3YWy6yKCPAqF9vZ2tU2QkoqKCrVNkA7SRAzpIkZmXT6vPI6ni/eBMeDhG2fg3Mkjgjp+\nlF6Hx5bkYPrYYahv7kThG44vTJk1URPZdXnui2p89v3ppcAJI+KDOn5KvAFP3p7vWiJ87INd4JxL\nr4sIcq4UoqI0Wcws5KSnp6ttgnSQJmJIFzGy6lLT4Ci3AMCxI3BGWkjuE6tEsEYnxWD30VY8/mEl\nxo4dG5J7aR1Z5woAfLn7OJ770pGT98jiHGSOHhaS+4xOisHfb81DTFQEPqk4hre2HZRaF3eQc6Wg\n11PJLxFaqy0SDkgTMaSLGBl1OdXZg+VvbEdHtw2XzkjDLedOCOn9hsVGYcVNZyM6MgLrdhzFxv3a\na2cSDmScK4Cj7tmf3nE44g8UTMGcScNDer/JqQn4/fXTAQD//Gwvalt9b5mjNuRcKdBuQTFVVVVq\nmyAdpIkY0kWMjLr87ePdONzYjimpCfjNtWf51e/NVyanJuC3158FAHjq0yrsq28L+T21hoxzpcdq\nxx/WVqC924aC6am4dd6EsNx3/lmpuPP8ibDZOX73Vhla2rVV6JucKwVKaBcTFxfn+aQhBmkihnQR\nI5su678/hk8qjiE6MgL/s2gmoqP6F20MFQump+G6vLGw2oGH365wJSwTDmSbKwCw8vP92FvfhtFJ\nMXjomvA44k7uu3gSZqQb0dRhw4oPK6Gl6gbkUShQzpUYLa51hxrSRAzpIkYmXeqbO7DiI0fNoJ9e\nNhXjhof/y/xnl0/FuJRYVDecwtPr94b9/jIj01wBgNIDjXh18wHolA0PcdHhTZ/RR+jw8I0zEGuI\nwMbK4/i4/GhY7x8I5FwpUG9BMXV1dWqbIB2kiRjSRYwsunDO8diHu3Cq04rzpo7A9fnqJJXHROnx\nwPmjEKFjWPPtIew41KSKHTIiy1wBgI5uK/7nvZ3gHLjrAhOyxyWpYseY5FjcM8dRHuTJT6pwsq3L\nwxVyQM6Vgt1uV9sEKbFYKPG0L6SJGNJFjCy6OJvlJsbo8VCY8qzckRpjx23zJoJz4NEPdqHbSp+/\ngDxzBQCe/aIax5o7MDk1AfdcmKGqLXlpesybMgJtnVb8fd1uVW3xFnKuFKKjo9U2QUoyMzPVNkE6\nSBMxpIsYGXRpae/GPz7ZAwD4yYKpSBE0Uw4nmZmZuOdCE8alxKL2hAUvb6pR1R5ZkGGuAMDeY614\nc+tBMAY8dO1ZPre1CTbTpk3Dr6+ahtgox/LgV1UNqtrjDeRcKVitVrVNkBKz2ay2CdJBmoghXcTI\noMv/rd+LJks3zh6fhGtyx6htDsxmMwyREXjwWsfuwRc31eDAiVMqW6U+MswVm92xfGyzcyycNQ5Z\nY0JTz8oXzGYzUo0xWHbJZADAXz+qhKVL7u9scq4UKOdKjEw5ALJAmoghXcSorUvFoSZ8WHYEkREM\nhddkqboc6MSpSe6EZFyTOwZWG8eTn1RpajdYKFB7rgDAeyV1qDzSihGJBtw/f7La5gA4rYvT2TvR\n1oWXvpI72knOlUJsbKzaJkhJdna22iZIB2kihnQRo6YudjvHPz5x1E66bd7EoLcr8ZfemjxQMAXx\n0Xps22/G5r0nVLRKfdR+D7V19GDl5/sBAD+/PDPsuwPd4dQlQsfwiysdS6dvbK1FnVmeHLW+kHOl\nQAntYrq6tLEzI5yQJmJIFzFq6vLp98ccUYgEA24/b6JqdvSltyZJcVH44UWOhOl/fLJnSCe3q/0e\nev7LarS09+DsCUm4OCs4DbyDQW9dpo814sqc0eixcTz16R4VrRoYcq4UqEK7mMrKSrVNkA7SRAzp\nIkYtXTq6rXi62FFH6v6CyYg1yBGFAPprsnDWOIwfHofDje1Yve2gSlapj5rvoUMnLVj9zSEwBvz0\nskwplo+d9NXlgYIpiI2KwKY9J/DN/pMqWTUw5Fwp0G5BMVlZWWqbIB2kiRjSRYxaury6uRYnWruQ\nOToRV2SPVsUGd/TVRB+hw8+vcCz3PP9VNZosQzMHVs330D8/2wObnePqnDHIHJ2omh0i+uoyPMGA\nuy4wAQCe/NRht2yQc6VA7W/EGAzqbtmWEdJEDOkiRg1dGlo78ermAwCAn12eCZ1OnigEINZkzqTh\nmDNpONq7bNInK4cKtd5DpQfM2LTnBGKjIlw78mRCpMtNcycg1RiNmoZT+KRCvsrt5FEotLe3q22C\nlFRUVKhtgnSQJmJIFzFq6PLClzXo6rHj4qxRyBmvTmXtgXCnyQMFji/2t787hGPNHeE0SQrUmCuc\nczxdvA8AcNt5EzE8Qb4fSSJdovQ6LL14EgBg1cb90uXqkXOlQL0FxcjW60oGSBMxpIuYcOtyuLEd\nH5Qdho4By+ZPCuu9vcWdJlPSEnHpjDT02DhWKbvWhhJqvIc27TmBXYdbkBQXhZvmjA/7/b3BnS6X\nZY9Gxsh41Ld04p3vDoXZqoEh50pBr5cn2VMmUlJS1DZBOkgTMaSLmHDr8uzn+2Gzc1yZM0aa0gt9\nGUiTpfMnIULH8J8dR1F9vC2MVqlPuOeK3c5RtMERtbrrApNUmx56406XCB3Dj5Ro54tf1cDSKU9h\nUXKuFGi3oJiqqiq1TZAO0kQM6SImnLpUH2/Dp98fgz6C4d6L1O0HNxADaTI2ORY35I8F58C/lS/+\noUK430Prdx5DdcMpjBoWjRvy5Y08D6TLvCkjkD3OiOb2Hry25UAYrRoYcq4UKKFdTFxcnNomSAdp\nIoZ0ERNOXVZu3A/Ogevz0pFmjAnbfX3FkyZ3X5iBGGWr/a7DzWGySn3COVesNjtWfV4NALj3wgxE\n6eX9DhxIF8YYfrxgCgDgza0H0dIux05TedUMM5RzJYbyaPpDmoghXcSES5ddh5vxZVUDDJE63K1s\nU5cVT5qkxBuwcNY4AMBzX1SHwyQpCOd76KPtR3C4sR3pKbG4MkeuUh198aTLzHFJmDMpBe3dNryx\nVY46aeRcKVBvQTEy9LqSDdJEDOkiJly6OKMQS2aPR4qEO756440mt5w7ATFREdiy7yQqj7SEwSr1\nCddc6bHa8YJS7mLp/EnQR8jtCnijy70XOTZvrP5GjuiV3IqGEWp/I8Zikbd3k1qQJmJIFzHh0KXq\naCu27T+JmKgI3DpvQsjvFyjeaJIUF4UfnOOIWAyV6FW43kOffn8Mx1s6MXFEHC7JSg3LPQPBG11m\npBsxOyMF7V02vClB9IqcKwWq0C4mMzNTbROkgzQRQ7qICYcuL29yRCFuyE/HsFj5Uxy81eTWeRMR\nHRmBzXtPYPcQiF6FY67Y7Nw1X+443yRdgVkR3uri3MTxlgTRK3KuFKxWebZwyoTZbFbbBOkgTcSQ\nLmJCrUvtiVP4fPdxREYw3DxXzjpFffFWk6S4KPxgliN69ewQiF6F4z30xe7jOGRuR5oxBgumyx+1\nArzXJXtcEmYp0au3VO5RSc6VAuVciaE8mv6QJmJIFzGh1uWVrw+Ac+CqnDEYkaiNCLwvmtx67gRX\n9Krq6OCOXoV6rnDOXa2Fbps3QfpcKye+6OKKXm07hNaOnlCZ5BFtKBsGYmNj1TZBSrKzs9U2QTpI\nEzGki5hQ6lLf3IFPKo5BxxytS7SCL5okxxuGTO5VqN9D2/afxN76NiTHR+Hqs8eE9F7BxBddZirR\nK0uXVdUKscC7AAAgAElEQVToFTlXCpTQLqarq0ttE6SDNBFDuogJpS6vbamFzc5RMD0NY5O18wPR\nV01umTcBBr0Om/acGNRV20P9Hnppk6PI5i1zJ8AQGRHSewUTX3W550JH9GrNNwdh6VIn5YecKwWq\n0C6msrJSbROkgzQR406XgycteOmrGjz8dgX+/O73eHNrLRpah877LVTzpfFUFz4oPQwAuON87USt\nAN81SYk34JpcR6Tl5a/lqcIdbEL52VJ+sAnlB5uQEK3HDedoqyadr7rkjE9C9jgjWjuseK/kcIis\nGhg5GwmpAO0WFJOVlaW2CdJBmojprYuly4qPth/Bx9uPYG/9mZGGdQCeLt6HJXPGY+nFkxApcWXo\nYBCq+fLWtoPostpx/tQRmDQqIST3CBX+aHLrvIl4t+QwinfWY9n8SRidpJ1InbeE8rPlJWWH4OLZ\n4xEnaQ9Bd/ijy13nm/CL18rw5tZaLJo9LuwV6LWlcAih9jdiDAa5ixGqAWkixmAwoPFUF17dXIv3\nSw+7wvHx0XpcmDkSM8clwWbn2Lb/JL6sasArXx/A9tpGPHFrribKB/hLKOZLW0cP1n7rSPK983y5\nq7GL8EeTNGMMLpuRhnU7juLVzbVYfvXg+5ETqs+WPcdasXWfow7a4jnjQnKPUOKPLnMnD8fk1ATs\nq2/DuvIjuD7MvRPJo1Bob29X2wQpqaioUNsE6SBN+tPeZcWjq7dg4ZOb8PqWWli6rDh7fBIeWTIT\n6359MX5/wwxcmzcWN5yTjhU3n41VP5yN1GHR2Hm4Bf/1cgnaVNzVE2pCMV/e/q4Oli4r8iYmY3q6\nMejjhxp/NbldSdr/aPsRmNsGX45fqD5bnHWtrssbq8kfMv7owhjDHcp8eXXzAVht4c2rJudKgXoL\niqF+cf0hTc5ky74TuOVfm/Hhbgvau22YN2UEXlw2F8/cMwvzs1KF4fgZ6UasvHc20lNisfdYG/74\ndgVsdq6C9aEn2POls/t0DR8tRq0A/zWZODIeF2aORLfVjje21gbVJhkIxWfLoZMWbKw8Dn0Ewy3n\nTgj6+OHAX10uzhqFsckxONzYgc8rjwfZqoEh50pBr6cVUhEpKSlqmyAdpIkDS6cVf3rne/zi1TLU\nt3Rialoinrn7HDxxay4yRyd6vH7ksGg8eXseEmMisWXfSbz41eDcZh/s+fJB2WE0WbqRNSYR55iS\ngzp2uAhEE2fy/jsldYMu4hmKz5beddBGaqQOWl/81UUfocNt8xzz5eWvD4Dz8P2AI+dKgXYLiqmq\nqlLbBOkgTYB99a24a+VW/GfHURj0OvxkwRQsv8CIsyf49mU/OikW/73IUcPm+S9rsPdYayjMVZVg\nzpceqx2vbakF4IhaMSZ/6xIRgWhy1lgj8icmo73LhrXfHgqiVeoT7M+W+uYOrNtx1FEHTQM9J90R\niC5X5ozB8AQD9tW3Yeu+k0G0amD8cq4YYzmMsRsZY79SjhsZYznBNk6511LlKFIOjwkGyvkLlWO5\nN/ehhHYxcXFxapsgHUNdk08qjuKHq75BnbkdGaPi8fKPzsVt501EYkK8X+PNzhiOhbPSYbNz/M97\nOwfd8mAw50vvhrvnTx0ZtHHDTaCa3KEsh7617SA6u23BMEkKgv3Z8rqrDloq0lO0+7kViC5Reh1u\nnjsBwOkdk+HAa49CcaieYYzZAJQCWANghXKsAVDKGLMxxp5mjE0IhnGMsaWc85XKsUy5b6mnawCA\nc76Wc74WQDFjrMjTvSjnSgzlF/VnqGrCOccLX1bj4be/R5fVjmvOHoPn7puD8cMdH3yB6PJAwRSk\nDovG3vo2fLT9SLBMloJgzRctNtx1R6CanGNKxrTRiWhu78EHZerUMQoFwfxsaTzVhfcVbW4/T5u5\neU4C1eX6/LFIjNFjx6FmlB9sCpJVA+OVc8UYewYOp2YZAAagBcABANuV44DyGANwP4BqxtjTgRgm\nilBxzlcCSGaMFQxw6TLlPOc1ZQAGOh8A9RZ0B/WL689Q1MRm53jsw0oUbdwPxoCfX5GJ314/HdG9\nqjwHokusQY8fL5gCACjauE+1qsqhIFjzRYsNd90RqCaMMdx5gcNheG1LLXqsg6PDRjA/W97adghd\nPXbMmzICk1O1VQetL4HqEmfQY9EsR1PzcEWvBsziZowlAigDYALwOID1AEo458LumYyxYQDyAVwK\n4NeKE5THOfenX4EJQBFjbDXnvLnX4zXKc6L7GwHkCp5qZowVcM6L3d2M2t+IsVgsapsgHUNNE+dy\nnTO/6k8Ls3HRtFH9zgtUl4tHMJyVFIldTd14c2st7r1o0sB2HTsGyyuvgvuQL6kbNgxx994DXbzn\nJcxgje9OF1/G5xx4wX4WgDjcmp/mVcNdmfXxZq54Gn8mB8ZhBg61AO/9TxEu1Z1U5fUN5vg9Pd2w\nFxYGPL6FR2CNfSYAPRbu/xItf/44LPaHanxrYyNakpMDGv9yrsermImt+06i7E9PIIP1L7/ky/ie\n8LRFrgxAMYBCdw5Vb5RzNgDYwBh7BA6HrAzAZF8N45yXMcby+jhWgMOxcud6mgD0PR8AGuFwus5w\nrpQlxKUAMHr0aNTV1SE9PR11dXWwWCzIzMyE2WxGXV0dsrOz0dXVhcrKSmRlZcFgMKCiogLp6elI\nSUlBVVUV4uLiBt31I0aMQHl5uWbtD9X1drtd0/Z7e33DiZP4y/u78E1dJ6IjdfjRrATMnpDo9t8P\nwKf7jx01CjEbP4f5+RcQUVWFJamT8YerC/H65gO4ae4EdJ5qcXt99ZNPIe6VV339aIF94gQkXH21\nx3//mE8/Q9uTT/k8fnNKMiz5+a5/f2dnJ+x2e0D2bx97FvZfPgvG9hZcaN4Nuz0jbPaHQv8pV1+N\n8vLygO2/dvK5+L8L78GbTTGYs3YVdOBhsT9U88cA4MjUqQHb/072FWiflYezjlZh3Lq/41SY7AdC\nM3+iANe/wV/7dQAWzF6Mj2Zcitf2teMXn68U3Mmz/Xl5eV7ZzNxtTWSM/RpAM+d8lVcjubsBY/cB\n4JzzZwMZRxlrIYCHOOfCf50SKSvinGf0eXwNgBrOeaG7sXNycnh5eXmgJg46zGYzlR7ow1DRhHOO\nRz7YhQ/LjiAmKgL/e1secsYnuT3fF1045+j44AO0PvIYbIcdeSEsNhaGc8/Fb+beix3HLHigYLIr\ncVmEvakJ7e+/79sva6MRsddfD+ZFu6tgje9OF1/G/4U5Dd93R2PpyHbcfe8VYbU/FOM3Wiwe54o3\n41s5cOeJdDTY9PiD8TguTIsK++sbzPHb9ZEYedutAY3fyRlub0hHsz0CjyUfQ57h9PNqzP9gjN9u\naUdsXGzA45+wReCOhnTYATw34jDG6s9MP/ByfK+SHd06V7KhLPltAHCJIJrlPMdv5yorK4tTQ97+\nlJeXIycnJBtBNctQ0WTVxv147stqGCJ1ePL2/AEdK8B7XWyNjWgufAid69YBAPRTpyDhgQcQfdWV\n0MXE4Jv9J/HTV0qRFBeFd392AaKjIjyMKDeBzpfyg024//lvkRCtx3u/uFBzfeFEBPM9tOabg3hi\nXRUyRyfihaVzNFueAgiOLk49po1OxPMa18NJMOfLX97fiQ/LjuDa3DH4zXXT/RnCK0FDVn+AMbYv\nyEOuALDInWPVC1GhHSMA80AXxcYOviagwSA7O1ttE6RjKGjyXkkdnvuyGjoG/GXRTI+OFeCdLj17\n9+LEFVehc906sPh4GB9fgZHrP0Pswh9AFxMDAJiVkYKsMYlosnS7djtpmUDni5Yb7rojmO+ha3LH\nIikuClVHW/FtzYAf89ITqC49Vjte3VwLALjzAu3WQetLMOfL7edNhI4B63YcRUNL6Opb+u1cMcYS\nlfIMouM+uEk69/NeywGs4Jx7SvMvgcOR6ksyHLlfbqGEdjFdXYOvf1egDHZNvqk+ib9+vBsA8Our\nsnCel/WUPOnS9c03OHHdDbAdPozInJkYWfwZ4m69BSzizMgUYwx3XeAIPr+2Wfs7wQKZL86Gu9GR\n2my4645gvoeiIyNw0xxlJ9hX4atjFAoC1cVZB23CiDhcoOE6aH0J5nwZlxKHi7NSYbVxvL61Nmjj\n9sXfIqLPAGjC6bpTfY9/B8tAJel8bW/Hyl0pBiWqVSMo42AcaKcgQBXa3UFLpf0ZzJocbWrH79fs\ngM3Ocef5E3HDOd7XlxlIl57K3TDfeTd4ayuir7wSw9eugX6A2jXnTRkB08h4NLR24pOKoz79G2Qj\nkPnirGt1fb42G+66I9jvoR/MSkecQY+y2iZ8X+dpcUNeAtHFZud45esDAIA7zpuo6TpofQn2fLlT\naaH0XslhNFtCU4bJZ+eKMfYYTte7YnDUuOp7eNxZ6OW9CuAo/VCj/G3s7VgxxkyMsTV9nKkVAB7q\ndU6/XYIior1IkBuKZGVlqW2CdAxWTTq7bXjwzXK0dlgxb8oILJvv2yZfd7rYGptw8rbbwNvaEHP1\n1Uj+99OuJUB36HTM1UPu5a8PaLpqu7/z5eAgaLjrjmC/h+KjI7FwlsNZD2cV7mATiC5f7j6Ogyct\nSDVG49IZaUG0Sn2CPV+mpCVi7uTh6OyxYc03oWmh5E/kaimAagAZnHMd53yS4EiGl0lf7mCMmeCo\nq1XKGOOMMQ5HtGw9HMt/gGPpsQC98qyUAqLVjLECZXdhgVLdfUCo/Y0Yg8GgtgnSMRg14ZzjsQ93\nYW99G8Ymx+LhG2f4/MvXnS62AwdgP96AqLlzkfTk//ZbBnRHwVmpGJ0Ugzpze9g72gcTf+fLy5tq\nNN9w1x2heA8tmTMeBr0OX+85gerj/pRWVB9/deGc40XFqbxt3kSv6qBpiVDMlzuVncirvzkYkqLF\n/r4CRZzzAx7Ocbszzxs45zWcc+bmaFbOKeacJ/XNxVLa5RQrLXAe9+Z+7e39C4oRQEVFhdomSMdg\n1OTj8qP4pOIYYqIisOKmHCTERPo8hjtdInPPxsivvsTwN1/3agu1E32EDrcrHe1f2lQT1o72wcSf\n+XKsuQOfVByDjjkScAcboXgPJccbcE3uWACOaKcW8VeXrftOYu+xNqTER+Gas8cE2Sr1CcV8yRmf\nhJnjjGjrtOK9kuB33fDHuSoGcI4X52nqk5B6C4oZqn30BmKwaXLIbMET65wJ7NOQMcq/VhnudGGM\nITLDBKb3fafbVWef7mi/JYwd7YOJP/PlVWUpdMGMNIxNHnw7mUP1Hrp13gRE6BjWf38MRxq194PZ\nH10453hBSeS/5dwJMERqu3SJiFDNF2f06vUttejqCW4DcH+cqwcBLGCMPaK0x3HHCj9tUgW9Hx/8\nQ4GhUCzTVwaTJlabHQ+/XYGObhsWTE/FFTNH+z1WKHSJ0utc+UYvfqXN6JWvupxs68KHSvPqOwco\noqplQvUeSjPG4LLsNNg5XCUJtIQ/ujiT+BNjInFD/uD64eckVPNl7uThmJyaAPOpbqwrD+7GGZ+d\nK2UJ7lE4nKwmxpiZMbavz6G5YiO0W1BMVVWV2iZIx2DSZNXn1ag80opUYzSWX50VUF2cUOlyfd5Y\nJMZE4vu6ZmwPU0f7YOKrLm9sqUW31Y4Lp42EaWTgPc5kJJTvodvPmwjGgI+2H8bJNm2VTfFHlxeV\nqNWSOeMQO0jqoPUlVPOFsdMbZ17ZfABWW/DKvvizW/A+AI85/wSQBCCjz+G54qBkUEK7GGe/OOI0\ng0WTXYeb8crXNdAx4OEbs/3Ks+pNqHSJNeixRKnxpMU6Rr7o0tLejXeU/I+7LxicUSsgtO+hiSPi\ncWHmSPTYON7YWhuy+4QCX3XZdbgZ39WYEWuIwKLZ40NklfqEcr7Mz0rF2ORYHG3qwIZd9UEb1x+P\nohAOp+pxAAsA5AmOxcEyMFxQzpWYwZZfFAwGgyY9Vjv+8v4u2Dlw87kTvKrA7olQ6rJw1jjERkXg\nm2ozKo8EpdJL2PBFl9XbDqGj24Y5k1KQOXpYCK1Sl1C/h5zLqe9+V4fWjp6Q3iuY+KqLM2q18Jxx\nSAzwx5HMhHK+ROiYa9PIy5sOwB6ksi/+OFcmOHYLPsg538A53y441iJIta7CRXd3aAqJaZ26uuDv\notA6g0GTlzbVoKbhFMYmx+K+iycFZcxQ6jIsNspV0FRrdYy81cXSacXqbw4CgKtC/WAl1O+haWOG\nYVZGCtq7bVgbojpGocAXXfYfb8OmPSdgiNThprmDN2oFhH6+XDFzNEYkGFDdcAqb950Iypj+OFdl\nALwpgaup/cPU/kaMxWJR2wTp0Lom1cfbXDVxfnPdWYgOcHdRz/79MN95Nzo3bQqGeW65ee4EROl1\n+HJ3g6bqGHk7X97+7hDaOq3IGZ8UlEiizITjPeSswv3mtoOwdAa/jlEo8EUXZ9TqutyxSI4ffLX3\nehPq+dJ748wLX1YHZeOMP87VYwCWMsY8ucqa+nlJFdrFZGZmqm2CdGhZE5ud4y/v74LVxnFDfjpy\nJ4j6nPsw3rFjMN98KzqLizGqPrSFPocnGHCtUsfo2S+qQ3qvYOLNfLF0Wl272wZzrpWTcLyHcick\nI2d8Elo7evCWEhGUHW91qT7ehg276hEZwXDbPE3FMfwiHPPl+nxHA/DKI63YvDfw6JU/zpURjhY3\nNYyxNxljv2KM/bDP8SjEDZSlxWrVxi+bcGM2a27jZ8jRsibvlx5G5ZEWjEyMxk8WTAloLHtLC07e\nfgdsR48iKi8P3YsXBclK99x5/kQY9Dp8Xnkce4+1hvx+wcCb+fLWNwfR2tGDmeOMmJUxeEp9uCMc\n7yHGmGvJ+40ttWjTQO6Vt7o8+0U1OAeuy0vHyGGDPzAQjvkSE6V3RTtXfr4/4OiVP87VSgBnw5HU\nvhiOelZFfY7lAVmlApRzJWYw5BcFG61q0tLejX9v2AcA+NnlUxEX7f+2bd7ZCfO9P4R1dxX0kyYh\n+cUXcPhk6It8jkiMduVerfp8f8jvFww8zZe2jh68saUWALB0/qSAymFohXC9h/ImJiNvYjLaOq14\nc6v80StvdNl7rBWfVx6HQa9zOQODnXDNl+vz0zE8wYC9x9rwZVVDQGP5W3/gAIC1yvG24CgPyCoV\niI0dfFWQg0F2drbaJkiHVjV5pngfWjt6kG9KxsVZo/weh9tsaPx/P0P31m3QpY5CymuvICI5KWy6\n3H7eRERHRmDTnhOa2DnoSZc3tx1EW6dVcQQGf9QKCO97yBW92laLlna5f0R7o4vzR8UN56RjxCDr\nOemOcM2X6MgIl8O66vP9Ae0c9Ne5KuCcLx7gyEOAjZvDDSW0i+nq0lYRvnCgRU12H2nB+2WHEaFj\n+OWV0/yOjnDO0fLHh9H58cdgCQkY/uor0I915EGFS5eUeAMWznJEr1ZulD96NZAuLe3drohKsHZt\naoFwvodyxidhdkYK2rtseF2JEMqKJ112H2nBpj0nEB0ZMSh7TrojnPPlurx0jEyMRvXxU9gYQMN4\nf5yrxznntV6cF/oEjCBCFdrFVFZWqm2CdGhNE7ud468f7wbnwE1zxmPiCP+rfp/619OwvPAiEBWF\nlOefQ+S0aa7nwqnLbfMmIjYqAtv2n0TFIbmrtg+ky+tbDsLSZcXsjJRBv0OwN+F+D9033+G4rv7m\nEJos8kavPOmyUolaLZyVjpRBvkOwN+GcL1F6nWtTybNf7IfNz+iVW+fKXd9AzvmD3gzMOX/b01gy\nQbsFxWRlZaltgnRoTZP/VBxF5ZEWDE8w4J6L/K+fZFm9Bq2PPgYwhuSnnoTh3LlnPB9OXYxxUVgy\nx7FhuWhj4MmnocSdLua2LlddK+eX/1Ah3O+h6WONmDdlBDq6bXhZ4jppA+lSfrAJW/edRGxUxJDY\nIdibcM+Xq88egzRjDGpPWPDZ98f8GmOgyNUSxthb/pl2GmUM6Su2U/sbMQbD0Pl15C1a0qSz2+ZK\nYn+gYDLi/Ow91rnxczT/6tcAgGF//hNirrm63znh1uXmcycgIVqP0gON2LY/9Mn0/uJOl2e/qEZH\ntw3nTx2B6WM1tbk6YNR4Dy1VHNi13x7C0ab2sN/fG9zpwjnHPz/bA8BR780YN7Q6ioR7vkTqdfjh\nxY4fokUb9qGzx+bzGG49Cs75KgA6xth3jLGLfR2YMTafMbYPQCPn/FmfLQsz7e1yvtnUpqKiQm0T\npENLmry17SBOtHZhSloCLs8e7dcY1ro6NC5dBthsiP/xA4i/527heeHWJTEm0lXJ/J+f7Q1q09Vg\nItKl9sQpfKDkwP04wJIYWkSN99DUtERcMXM0emwczxTvC/v9vcGdLhsrj2PX4RYkx0fh1nkTwmuU\nBKgxXy7PHo1Jo+JR39KJ1dt832k6YLiGc74IjorsGxhj3zLGHmWM3cgYm9B7qY8xlqg8dqNyzj4A\n6wFs4Jz/yGerVIB6C4oZDH30go1WNGmydOOlrx1LIP916VTodP4lsdsbG8F7ehB7y81IfMh9VoAa\nuiyaPQ5pxhjUNJzCx+VHw35/bxDp8q/1e2Gzc1ybOwYTAsiB0ypqvYeWzZ+EKL0O63fWY9dhbxqN\nhBeRLj1WO54p3gsAuO+iSYj1M/qsZdSYLxE6hv+6dCoA4KVNB9DsY66ex7UwzvkyOJb1JsHRtHkN\ngGoATYwxG2PMBqBJeWyNck4KgMWc8/t9skZF9PqhN2G9ISVlaGwN9wWtaPLcF9Vo77Jh7uThOMfk\nv81RM2ciraoSSX99fMBdhmroEqXX4YGCyQCAlRv3ob1LvmLAfXXZXtuITXtOICYqAj+8aGjlWjlR\n6z2Uaoxx5er987O90uXqiXR5p6QOhxs7MH54HK7JHaOCVeqj1nyZPWk45kxKgaXLiue/9K0rhFeJ\nRpzztZzzZDicrI1wlFnoe7QA2ABgEec8uXdCuxag3YJiqqqq1DZBOrSgyaGTFrxbUgcdQ8CV2AFA\nFxPj8Ry1dCmYnoqsMcNgPtWN1yTcat9bF7v9dO7MredOQEqCdvL3goma76E7z5+IYbGRKD/YhE17\ngtOkN1j01aW1o8f1pf7jBVOgjxiaucFqzpcfL5gKxoC3v6vDIbP3PQ59eqUUJ2sB51wHIAlAhnIk\nKQ7VpVpzqpxQQruYuLg4tU2QDi1o8syGfbDZOa46ewwyRiWE5Z5q6cIYw/+7zBG+f3XzARxr7lDF\nDnf01uWj7UdQeaQVwxMMrkaxQxE130Px0ZG490JHrt5Tn1ahy49k5VDRV5eVG/ehpb0HZ09IwvlT\nR6hklfqoOV8mpybgqpwxsNk5/vnpHq+v89uj4Jy3cM4PKIf8ZZI9QDlXYrSSXxROZNek6miLoz1G\npC6shSnV1CVnfBIuOSsVXT12/OM/ckUWnbq0tHfjX0ruzE8vmzokc2ecqP0euvGcdJhGxuNwYwde\n+fqAqrb0prcue4614p3v6hChY/hVAIV/BwNqz5f7L5mM2KgInyKdFK5RoN6CYrTaRy+UyK6Js2r5\nwnPGYWQY22OorctPL5+K2KgIfFnVgK/3BNYXLJg4dfn3hv1oae9B3sRkFExPVdkqdVF7rugjdPj1\nVY4CuC9/fQCHG+XYLe7UxW7n+NvHu2Hnjk0b4Yo+y4ra82V4ggH3+lgjkJwrBWp/I8Zi8X6Neagg\nsybf1zVji7PQYJjbY6ity8jEaFek7ol1VejslmO5x2KxoOpoC94rrQu4/dBgQe25AgBnT0jGFTNH\no9tqx98+3i1FcrtTl3U7juL7umakxEfhviG66aE3MsyXxbPHY/HscV6fT86VAlVoF5OZmam2CdIh\nsyZFGx31exbPGY+kMBcalEGXRbPHYdKoeBxr7sALX/m2uydUZEyagr+8vwucA0vmjIdp5NArvdAX\nGeYKAPzk0imIj9Zj2/6TAfWRCxaZmZkwt3XhqU8dS9s/uXQq4qKH7vKxExnmS6Reh19cOc3ziQrk\nXClYrfJt4ZYBs9mstgnSIasmpQcaUVLTiPhovU/J0l1btuL4RfPR8fG6gO4vgy76CB2WX50FxoBX\nN9ei8oj66aD//mwX9tW3YUxSDO672P/2Q4MJGeYK4GgC/qNLHKU8/vpRJRpPqduU/eTJk1jxUSVa\nO6yYMykFl2enqWqPLMgyX3yBnCsFyrkSo/Zat4zIqAnnHCuVqNUtcycgMSbSq+u6d+6C+e57YN23\nD7aGwPKUZNEle1wSbpozHjY7x5/f/d6v1hXBYl99K9741lHc9DfXTUdMFEUhAHnmCgDckJ+OfFMy\nmtt7sOKjSlWXB9/dug9fVTUg1hCBh649a8gvHzuRab54S8icK6VKu2aIjY1V2wQpyc7OVtsE6ZBR\nk2+rzdhxqBmJMZGuIomesNbVwXz7HeCnTiHmmqsRd+cdAdkgky7LLpmM8cPjUHvC4krwDzddPTb8\n+d2dsHNg4ax05E1MVsUOGZFpruh0DL+7bjpiDRH4cncDPvWzUW+gNLR0Ys0uRxmRn16WiVHDPNeW\nGyrINF+8JSDnSml5kyM4fgDAFCQbwwIltIvp6lI3TC4jsmnCOcfKzx0OxO3nTfQqR8PW2AjzLbfB\n3tCAqHPPRdKT/wALsNabTLpER0bgDzdMR4SO4Y2ttfhGhcbO//xsD/bVt2G0MRoPFAy9/oEDIdNc\nARyV2392mSOv568f7UadD8Uig4HVZscf3q5Aa0cP5kwajmuHaCV2d8g2X7zBr09TxtgzStubagCl\ngmN10CwME1ShXUxlZaXaJkiHbJp8W2PGrsMtSIqLwsJZnuvB2NvbYb7jLlhraqCfNg0pz60CC0LX\nedl0OWusEfdcaALnwB/ersDxlvAVF924qx5rv62DPoLh9uzoIV3TSoRscwUArskdg4umjYSly4rf\nrt4R1uXk576oRvnBJgwz6PCHG6bTcmAfZJwvnvDZuWKMPQZgGU63vDkgONTPIvUR2i0oJisrS20T\npEM2TV78ytGc+ea54z3m9HCrFU0/+jF6tm9HxNixGP7qy9AlJg54jbfIpgsA3H1BBuZMSkFLew9+\ns3nXjJEAACAASURBVHoHeqyhj1AfaDiFv7y/C4CjYfbl52pvSSPUyDhXGGP43fXTMTY5Fnvr2/DE\nuvCUZ/h6TwNe3FQDHQMevnE6kuOHZkukgZBxvnjCn8jVQjgaNecpLW8mCY5kOJwvzUDtb8QYghDR\nGGzIpEn5wSZsr21CQrQePzhn4BosnHM0P/gQOouLwYxGpLz2KiJSg1fMUiZdnOh0DA/fmI1Rw6Kx\n63ALHv1gV0i/MJss3fjl62WwdFkxP2sUFs8eJ6UuaiOrJvHRkXh0yUwY9Dp8WHYEb2w9GNL77atv\nxe/XVoBz4L6LJ2H2lFEhvZ9WkXW+DIQ/HkUygEc559s9nFfox9iq0d4uR4Ve2aioqFDbBOmQSRNn\n1Grx7PEec63a/vYE2t94Eyw6GikvvYjIScEtCyCTLr0xxkVhxU05iI6MwLodR1EUogT3zm4bCt/c\njqNNHcgcnYg/3DADjDFpdVETmTWZnJqI310/HQDw1Kd7ULyzPiT3aWjpxK9e346ObhsunZGGuy4w\nSa2LmmhRF3+cqxI4mjV7osiPsVWDeguKUbunk4zIosnuIy3Ytv8kYqIisHjOwFEry8uvoO0fTwI6\nHZKeeRqG/Lyg2yOLLiIyRw/DI4tnIkLH8OJXNXh9S21Qx+/sseHXb2xHxaFmjEg04K83n43oqAgA\ncuuiFrJrsmBGGn68wLEJ4U/vVGDzXu97ynnDidZO/Pil73C8pRMz0o347XWOsguy66IWWtTFH+eq\nEMASxtjFHs6TpxumF+j1lHAqIiUlRW0TpEMWTV7c5Iha3XhOOobFuv9x0L1zF5p/+zsAgHHFY4i5\ndEFI7JFFF3ecO2UEHrzGkbvx1Kd78MKXwangbumyovCN7fiuxozk+Cj88458jOjV01F2XdRAC5rc\nNm8CFs8ehx4bR+Gb2/HF7uBUcK9v7sBPXipBnbkdU1IT8MStuTBEOhxxLeiiBlrUxR/nKg+O6FUx\nY+xTZefgD/scjwIwBtfU0EK7BcVUVVWpbYJ0yKBJ9fE2fLm7AVF6HW6ZO2HAc5lOh4hRo5D4+98i\n7pabQ2aTDLp44prcsUqUACjauB8rPqwMKMm9obUTP3r+W3xTbYYxNhL/d+c5mDDizPY2WtAl3GhB\nE8YYfn5FJm6aOx5WG8dv3irH61tqA8rZ232kBfeu2oaDJy3IGBWPp+7IP6PgrxZ0UQMt6uJPuGYl\nAA5HwvoC5f81DyW0i4mLi1PbBOmQQZOXNjkCw9fmjkFKwsDJnpFZ05Ba8m3IbZJBF2+4JncsoqMi\n8N/v7sS7JXXYf7wNv79hOsal+Gb/V1UNeOT9nWhu70F6Siz+fmsu0gVjaEWXcKIVTRhj+OllUxFn\n0OO5L6rx1Kd7UHmkBb++atqA0eK+2O0cq785iH+t34seG0f+xGQ8uiQHCX06KWhFl3CjRV2Yr144\nY8wOoEY53JEBYALnPCIA28JKfn4+LykpUdsMgvBIndmCJf/8GowxvP3T85FqpErO/lB5pAUPvlmO\nhtZOROl1uP28ibhpzvh+X3h9OWS24On1e/HFbke7oFkZKfjzD7JhDHOjbCK8bNxVj/9+byc6um1I\niovCsvmTcFXOGETqB/5hvuNQE/756R7sPOyoUHRDfjp+cUWmx+sIafGqEoK/zpWJc17r6TzOuWZm\nT3Z2NtfijoRQU1dXp8lkwlCitiaPvL8TH5QdwTVnj8FvlV1NMqC2Lv7Q0t6NJz/Zg3U7HP3/4gx6\nFExPxQWZIzElNQFJcVGwc6C+pQMVh5qxcVc9tu4/Cc4BQ6QO98+fjCVzxkOnc/95q0VdQo1WNTlk\ntuCxD3ahrLYJADAyMRqXzkjF3MkjMGlUPOKjI9FtteFwYwe21zbik4pjrubhyfFRKLw6CxdOc19u\nQau6hBrJdPHKufJnWXCZJ8dKYZEfY6sGtb8RY7GEtw2EFlBTk5NtXfjPjqNgDLj9/Imq2SFCi3Nl\nWGwU/nDjDFydOwbPf1GNkgONeL/0MN4vPez2msgIhstnjsZ9F0/CyETPxYe1qEuo0aom41Li8K+7\nzsH6nfV48asa1DScwquba/Hq5lq31yRE67Fw1jjcdt5ExHmo1K9VXUKNFnXxOXIlHISxCV46XNJC\ny4KEFnh6/V68/PUBXDRtJB676Wy1zRl07Ktvw+eV9SirbUJNwymc6uwBYwwjEgyYnJqAc0wpuHRG\nGi0BErDbOSrqHNHMnYebUXvCgo4eG/Q6hlHDYpA1ZhjmTh6Oi6eNcpXlIAYFIYtcOUZnbD6AFQBy\nlb8BR1/BRznn7/o7rlpYrVa1TZASs9msyW2woUQtTSxdVrxTUgcAuG2eXFErYHDMlcmpCZicmnDG\nY5zzgHq9DQZdgs1g0ESnY8gZn4Sc8Umux5zBCn/ny2DQJRRoURe/GzcDWA9HWQbW68gHsJYx9nTQ\nLPTNLhNjrMCfa7u7u4NtzqCgrq5ObROkQy1NPig9jFOdVswcZ8T09DMrnXAJfhwM1rkSaBPdwapL\nIAxWTRhjAc2XwapLoGhRF38aN98HR+Pmt+HIq8qDY3dgnvL3OwDuZ4zdGwwDGWO5jLE1Xp6eC2AN\nY4wzxpoYY+sZY7neXBgbG+u/kYOY7GxqOtsXNTSx2ux4c5ujz9mtfaJW7WvW4lhmFixvvRV2u3pD\nc0UM6dIf0kQM6SJGi7r4syy4FI6k9lWC57YDeJsxthTA/QCe89cwxSlaovxp8vY6znkSY8zIOW/2\n5X6U0C6mq6sLMTG01b83amhSvKsex1s6MX54HM6bMsL1eOeGjWj65a8Amw26+IQBRgg9NFfEkC79\nIU3EkC5itKiLP8uCuW4cKxec85VQcrH8hXNexjkvBODzz3FfHSuAKrS7o7KyUm0TpCPcmnDO8Zqy\nG+mWcye4tv13b9+OxmX3AzYb4n/yY8RcdWVY7eoLzRUxpEt/SBMxpIsYLerij3O1nTF2w0AnMMZu\nhCOKpRmioz1vqR6KZGVlqW2CdIRbk29rzNhX34bk+Chcnp0GAOiproH5jrvAOzoQu2ghEh8sDKtN\nImiuiCFd+kOaiCFdxGhRF3/b36xljK0AsBpADee8lTGWCMfy3RIAy+Fo8Bx2+iS05wJY6U0ki9rf\niDEYBm6tMhQJtybOqNXi2eNhiIyAraEB5ltvg72xEYb5F8P418cDTroOBjRXxJAu/SFNxJAuYrSo\ni88ehbLk9w6AB+EovdDEGLMBaFL+LgSwgXP+t2Aa6iVlcDh7xZzzYgBrAbhNhmeMLWWMlTDGSg4f\nPuzakVBXV+dqFGk2m1FeXg673Y6Ojg6Ulpaio6MDdrsd5eXlMJvNAByNJQfj9aWlpZq2PxTXb9++\nPWz3/7aqDt9WmxETGYErZwxH2aZNOHHr7bDV1aFnymTgkUfAIiOl0O/bb7/VxOsX7uu3bNmiaftD\ncf2OHTs0bX+orq+oqNC0/aG6fseOHdLY7y1+FxFVktZXABjW6+FmAIWecrJ8vE8ugFWc8zw/r68G\nsIhzXjbQeTk5Oby8vNyfWwxqtFhfJNSEU5M/vl2BTyuOYcmccfjZJRkw334nur7+GhETJmDEB+8h\nQqLXhuaKGNKlP6SJGNJFjGS6eLVM4PdaGOd8Jec8CUASHGUYkjjnycF0rIJEMxz1twZEr/e7nuqg\nRqIJLQ3h0qS+uQPFO+sRoWNYMnscmn7xS3R9/TV0I0Zg+OuvSuVYATRX3EG69Ic0EUO6iNGiLgEn\nGnHOWzjn2znnLb0fVyq4hw2lgKgoDNeoHANCuwXFOMOjxGnCpcmb2w7CZue45KxRiPu/v6Pj3ffA\n4uKQ8spL0I8fHxYbfIHmihjSpT+kiRjSRYwWdQllFre3hT+DRSMcxU37kg9HLtaAUEK7mLi4OLVN\nkI5waNLW0YMPlObBi2KacapoJaDXI/nZlYiaMSPk9/cHmitiSJf+kCZiSBcxWtTF7VqYUk5hCRw5\nVLW9Hn/Ui3FNAIwez/KOZNGDjDETHDlf93HOmznnzX13TCl5Yas55zWebhIVRY1YRaSnp6ttgnSE\nQ5N3S+rQ3m1DvikZ06YNR9Oc2Yi/915EX3BByO/tLzRXxJAu/SFNxJAuYrSoy0CJRs/CkaxeA+Ch\nXo8XAuBwn9TlfM6/THkFxXlaBqAAQC5jrAhAqbJbEXA4cAVwOF/NgCMPjDG2XPnbqDwmimb1g3oL\niqmrq9PkxA4lodak22rHW0qrm9vmTYTeNBwj3l4bsvsFC5orYkiX/pAmYkgXMVrUZSDnaqlyFAme\n2w6geIBrMwDcGIBdUKJNbmtlKaUWkgSPP+7P/aj9jRiLxaK2CdIRak0+rTgK86luTBoVj9kZ2knk\npLkihnTpD2kihnQRo0VdfC7FwBizAzD1Xip0c14j51y4pCcj+fn5vKSkRG0ziCGO3c5xy9ObUXvC\ngj/eOANXzByttkkEQRDEaUJWimElvNh9B2CRH2OrhtVqVdsEKXEWWSNOE0pNtuw7gdoTFoxMjMaC\n6akhu08ooLkihnTpD2kihnQRo0Vd/KnQfj/nvLXv44yxRKUFjvO8DYEaF04o50qMs2otcZpQavLa\nlloAwJI546GP0NYOVporYkiX/pAmYkgXMVrUxedPb8bYr9w8tQRALWPMzBj7ZWBmhZ/Y2Fi1TZCS\n7OxstU2QjlBpUnmkBdtrmxBn0OP6vLEhuUcoobkihnTpD2kihnQRo0Vd/PlpvEL0IOd8lZJjdQ6A\nHzHGHgnIsjBDCe1iurq61DZBOkKhie3YMby2+QAA4Pr8sYiL1l7HAJorYkiX/pAmYkgXMVrUxR/n\nasBkLmWXXxHEBT2lhSq0i6msrFTbBOkItiatf/0bdlx0JT7f5Wx1I1/1dW+guSKGdOkPaSKGdBGj\nRV0G/Hms5FCZej8EgDPGZkLsZCUr5y8NmoVhIjo6Wm0TpCQrK0ttE6QjmJqcevEltP3jSXx07i2w\ng+HKGWkYOUybc5HmihjSpT+kiRjSRYwWdfG09rAAjmVAE04XBWXw3E6GQVwfS1qo/Y0Yg8GgtgnS\nESxNOtb9By2/+z3aDHHYeNbFwP9v787jo6ruNoA/J/vCEhJAXBAIi4gbBrAurVbFqq1aRZbWBWut\n0PrWVq1K7Wttbd9W4VWrttYCrhVtFaq2tn1tAW3dkRAwSkxRAhiRdZKQZBImmcx5/5g7Ycj9TTIz\nmZl7z8zz/Xzywczce+fweHPz455zz9HA108dnZBjO4Hnioy52DETGXORmZhLrxWF1vpPWutxWuss\nAN/BgZnXt0T4Wg/gTwgumfOdZDY80dra2pxugitVV1c73QTXSUQmvjVr0PDd6wGt8e9rb8d+rXDy\nuDKMHzEwAS10Bs8VGXOxYyYy5iIzMZeoR81aS8vUAfiH1npcEtvkCK4tKDNtyYFU6G8mnbW18Fx9\nDeDzIXfuXPw5+3AAHbjs1DGJaaBDeK7ImIsdM5ExF5mJucTUF2YtObM0SW1xVE6OeU9npUJZmTnL\nr6RKfzLxb/8Mey+/EnrfPhR8+Xy8fel8NHg7MGHEQEwrN2ZBAxHPFRlzsWMmMuYiMzGXuCYRjWY7\npdRZsTfHOXxaUFZbW+t0E1wn3kwCTU3wXHElAjt3Iu+kaSh54H488/YnAIDLThsNpaJaVcG1eK7I\nmIsdM5ExF5mJuSRzFPfyJB474TigXVZcXOx0E1wnnkx0ezs8V38T/k2bkHPUBJQ9/hjerm/Ftr3B\npW6mH2PWUjcSnisy5mLHTGTMRWZiLhH7wpRSMxCcdX1B+CLNSqm7ojhuOYCSfrcuhTjmSmZiX3ey\nxZqJ7upCw/XfQ8e7a5E1YgTKnnoKWSUlePqFdwGYudSNhOeKjLnYMRMZc5GZmEtvA40eATAYQB2A\n28JeX4DgE4OR+jBC7+kI77sS1xaU1dfXG3liJ1Osmex/+R/Y/38vQw0ejKHPLEPO4YcZv9SNhOeK\njLnYMRMZc5GZmEtvxdU860uar2o9gFW97DsWwIx+tCvluPyNzOv1Ot0E14k1k7wTT0TR7Fkonnsl\nco86CgDw9JtbAZi71I2E54qMudgxExlzkZmYi9I6thtMSqkAgPLwrsII2zVYaw0aYerUqbqystLp\nZlAG2N7QhlkPvg6lFF644XRjZ2QnIspAUT15FM9AjyUAGqLYblYcx3aM3+93ugmu5PF4nG6C6/Q3\nkz++sw0BDZxr8FI3Ep4rMuZix0xkzEVmYi5xTcWgtW6W3lNKjQ7bbnX8zUo9jrmS1dfXO90E1+lP\nJo3eDvyl6lMAZi91I+G5ImMudsxExlxkJuYST7dg+NOCHq31PUqpawH8Luz1xVrr6xLRwFRht6As\nEAhwmooe+pPJklc+wmP/rsOp44fiviumJLhlzuK5ImMudsxExlxkLsslad2CYxF8YnAWgDql1Bgc\nGPT+QwDTAJyklPplHMd2DAe0y3w+n9NNcJ14M/H6/Fi+Jjhp6NwvlCeySa7Ac0XGXOyYiYy5yEzM\nJZ7iai2AVdaCzs8DmGm93qS1/l+tdRWA2TBszBVnaJfV1NQ43QTXiTeTFyvr0bLfjxOOLMHkUUMS\n3Crn8VyRMRc7ZiJjLjITc4mnuApN0RByDoJzWi0JvaC1rkNwIlFjFBSkz8DiRJo0aZLTTXCdnpno\nri741qyB7qVA7/AH8Ie3twEArkrDu1YAz5VImIsdM5ExF5mJucRTXPWchmG69efK0AtKqRMRnAvL\nGC7qz3WV/Px8p5vgOuGZ6EAAjd+9HntnzIT36Wci7vP3Dduxt8WH8SMG4pTxQ1PRzJTjuSJjLnbM\nRMZcZCbmEk9FsUUpdQIAKKUuDb2otX4lbJu7cfAAd9dra2tzugmuVF1d7XQTXCeUidYa++78Gdr/\n8hLUgAHIP/0L4vb+rgCWvbkFADD382OMX6A5Ep4rMuZix0xkzEVmYi7xFFc/BPCKUuphAEut1xYB\ngFLqLKXUWgTvZq1NTBNTg2sLykxbciAVQpm0Ll4M7yOPArm5KH1kKXLHjxe3f7VmFz5taMcRpYU4\nc9IhqWxqSvFckTEXO2YiYy4yE3OJed0NrfUKpVQTggPZVwFYqbVeqpQ6G8Bya7N9AF4BUJawliZZ\nTk56LEGSaGVlxvwvTJmysjK0/el5NP/8FwCAIfffh4IvfF7cVmuN378RvGt1+alj0mKB5kh4rsiY\nix0zkTEXmYm5xHWl11qvsiYTna21Xmq9tlprXRr2ZVQafFpQVltb63QTXOejZcvQeNMPAACD7vgx\nii6+OOK2b3+0Fx/tbEHZgDx8efJhqWqiI3iuyJiLHTORMReZibkk5J/R4TOzm4oD2mXFxcVON8FV\nOqqrUXjnzwG/HwPmz8PA+fMibqu1xuOv1QEAvn7KaOTnZqeqmY7guSJjLnbMRMZcZCbmEndFERpf\npZTqArBZKdWllHpXKXVJAtuXMhxzJTOxrztZ/Fu3wnPlVVBtbSi85GIMuv2/e93+3c0evF/fhMFF\nuZgxLf1z5LkiYy52zETGXGQm5hJXcWUNZl8JYAqCU8GHvqYCWKGU+m3CWpgiXFtQZuKaTsnQtXcv\n9l5+JQJ790JPm4Yh990L1cvdTq01HvnXZgDA5aeORlF++o/p47kiYy52zETGXGQm5hLzFd9aR3A+\ngBUAngVQB6AJQAmCE4d+DcC3lVLrtNaPJrCtScXlb2Rer9fpJjgu4PXCM/cqdG3ditxjj0XDj/8b\nqo87ne/WHbhrdelJR6aopc7iuSJjLnbMRMZcZCbmEs/CzWsBLAkNZI+wzTwA12qtp/WzfSnDhZsp\nkrblK9B4w43IPvJIDPvzC8gePrzX7bXWmP/Yu6j+pAnfOXs8rjo9PWdkJyLKQElbuLmit8IKALTW\nSwBUxHFsx/j9fqeb4Eoej8fpJjgu/+yzMPDmH2Doc39E9vDhfWaytq4B1Z80YVBhLmZ+LjPuWgE8\nVyJhLnbMRMZcZCbmEk9xtb6vQetKqRkwbPkbjrmSmdjXnWjZpaUYdOMNyLEGVfaWidYaj/7rYwDB\nsVbFGTDWKoTnioy52DETGXORmZhLPN2C8wA8DGAhgOcA1Gmtm5VSgxAcczUHwK0AFmit70lwe5OG\n3YKyQCDAaSp66C2TtXUeXP9kJQYV5uKFG0/PqOKK54qMudgxExlzkbksl+R0C1pdfs8juAzOOgCN\n1nQMjdb3CwCsNqmwAjigPRKfz+d0E1wnUiZaayx5JXjX6uunjMqowgrguRIJc7FjJjLmIjMxl3hn\naJ8F4NsAmnHwVAz7AMzXWn8pYS1MEc7QLqupqXG6Ca4TKZM3Nu3B+/VNGFKch9knj0pxq5zHc0XG\nXOyYiYy5yEzMJepuQavbD1rr5h6vD0awO7BOa70v4S1MkYqKCl1VVeV0M1ynvb0dhYWFTjfDVaRM\nugIacx9+C5t3t+LG8ydiTgYWVzxXZMzFjpnImIvMZbkkpltQKfVwWLdfozUTe/ckoVrrfVrr9SYX\nVgCXv4kkPz/f6Sa4jpTJP9/fgc27WzGipACXTDVvNuFE4LkiYy52zETGXGQm5tJrRWHNaTUPB3f9\nKQDzlVKbkt+81Glra3O6Ca5UXV3tdBOSLtDSAu9zyxFobu57Y9gz6fAHusdaXXvmOOTlZGahngnn\nSjyYix0zkTEXmYm5RPwtYM3EHlreZhWAJdbXKuu1sUqpX6aikanAtQVlJq7pFAvd3g7PFXPRdONN\naHv++aj26ZnJi5X12NHUjjHDinHe8Yclo5lGSPdzJV7MxY6ZyJiLzMRcenucaRaCXYFTtdZbwt9Q\nSpUAWI3gMjg/Sl7zUicnJ7Oe7IpWWVmZ001IGu33o+G6/0JHZSWyDzsMheefH9V+4Zm0+fx4/LU6\nAMB3pk9AdlZU3fFpKZ3Plf5gLnbMRMZcZCbm0lv/xVQEl7DZ0vMNrXUTgGsRXE8wqZRSFUqp5TFs\nP08pNdP6ujXa/fi0oKy2ttbpJiSF1hpNP7od+/+5EqpkMMqefgrZhxwS1b7hmfz+jS1o9Hbg2CMG\n4wtHDUtWc42QrudKfzEXO2YiYy4yE3Pp7XZNCYCIj89pratU0KCeTxAmglKqAsEJSYHg04jR7DPP\natuK0DGUUou11vP72pcD2mXFxcVONyEpWn51P9qefhooyEfZE48jd8KEqPcNZbKjqR3PvLUVAPD9\n8yZCqcy9awWk77nSX8zFjpnImIvMxFz66gtriOIYpQjOd9XNmp6hQWudHW/DtNZVAKqsImt6lLvN\n11pPCT+GUiqqfTnmSmZiX3dfvE8/g5Z77wOyslD60G+QPy229cVDmfx25SZ0+AP40nEjcNzIpN/E\ndb10PFcSgbnYMRMZc5GZmEtft2tiWxvngFJEORdEoljjwKTFopuiKbC4tqDMxDWdetP+z3+i6Ye3\nAQBKfvkLFJ53XszHqK+vR/UnjVj5wU7k52ThuunR3/VKZ+l2riQKc7FjJjLmIjMxl77uXC1VSlUC\naOplm5lKqZ7vfwnxF2bxKofczgYEi65Vve3M5W9kXq/X6SYkjG9tJRq+cx0QCGDgjTeg+Mor4jpO\nS2sr7n/9UwDA5aeNxogS10xu56h0OlcSibnYMRMZc5GZmEtfd65mIbhA8+IIXzrC+5cmqb29KYXc\njdkEQHzUwBr8XqmUqmxsbOyujuvr67sH0Hk8HmzYsAGBQADt7e1Yt24d2tvbEQgEsGHDBng8HgDB\nAXfpuP+wYcOMbn9o/45Nm+D5xtXAfh/yZ89C8Y03xP35m1oKUbO9GYMLsvDlowcb8fdPxf6hcRGm\ntj9Z++/fv9/o9idj/wkTJhjd/mTtP3HiRKPbn6z9J0yY4Jr2Ryvi8jdKqf7eytH9GXMV1o4KAEvD\nx1JF2G46gMVa67E9Xl+O4NI8C3rbf/LkyXrDhg39bW7a8Xg8Rj4GG65rzx7s+cqF6Nq+HQXnTEfp\nI0uh4px6Y19bB2Y/+Dr2tfvxkxnH4fwTMndeq57S4VxJBuZix0xkzEXmslwSsvzNTK11VqxfAGb3\nv/1xKRVeKwHg6WtHjrmSmdjX3dP+lavQtX07cisqMOTh38ZdWAHAw6s+wr52P04cPQTnHX9oAltp\nvnQ4V5KBudgxExlzkZmYS1+/ZXodp9SLdUjxgHYAlZDn3SpFL1NKhBQVFSW8Qeng+OOPd7oJ/VZ4\n0YVQBQUoOGc6svqx+Of79U14cd2nyMlSuPWCSRk/9UJP6XCuJANzsWMmMuYiMzGX3u5czY93/ipr\n4tE+55ZKJGti0zrrqcFwJVrrPotEDmiX+Xw+p5vQb1kDBqBoxiXIGjgw7mP4uwJY+NJGAMCczx2B\nMcMGJKp5aSMdzpVkYC52zETGXGQm5hKxuNJaL+3Pgfu7fxipqw9KqXKl1PIexdRCALeFbdPnU4Ih\nnKFdVlNT43QTXOGPb2/Dx7tacWhJIaYO4SLfEp4rMuZix0xkzEVmYi4RB7Q7TSlVjuDdr+kITqWw\nBMA6rfUS6/3pAJYDmKK1rgvbbx6AOgS7CMu11oui+byKigpdVdVn72HGaW9vR2E/utLSwZY9rbjq\nd2+jwx/AfVdU4MQjBmR8JhKeKzLmYsdMZMxF5rJcohoP4trViq2CKeITflZX3xDh9SXxfB6Xv5Hl\n5+c73QRH+bsC+PkLH6DDH8CFJx6OU8cPYxdyBJl+rkTCXOyYiYy5yEzMhRWFpa2NXT2S6upqp5vg\nqGfe2oqa7fswfFABvn/eUQCYSSTMRcZc7JiJjLnITMyFxZWFawvKTFzTKVE272rB0lc/BgD86KvH\nYEBBLoDMzqQ3zEXGXOyYiYy5yEzMhcWVJacfcx+lMxdN3BaRf/t2NP/vPejavTthx9zf0YXbl7+H\nzi6NiyoOx8njhna/Z0ImTmAuMuZix0xkzEVmYi4srix8WlAWWgbArbr27MHe2XPQcv8D2L9qdcKO\ne9//fYgte7wYNbQYN54/8aD33J6JU5iLjLnYMRMZc5GZmAuLKwsHtMtC68W5UcDrhWfuVejaZe0Z\n9gAAIABJREFUug25xx+Hwq9elJDjrnx/B/5StR15OVn4n1knoDDv4Luabs7EScxFxlzsmImMuchM\nzMW1UzGk2tSpU3VlZaXTzaAo6Y4OeL5xNXz/fg3Zo0dh2IsvIHvYsH4fd+ueVnxz6Tto83Xhlq8c\njUtPOjIBrSUiojSRkLUFMwbXFpS5cU0nHQig8Qe3wPfv15BVVoahy55KSGHV3N6JW/6wHm2+Lpx9\nzAjMmCYPonRjJm7AXGTMxY6ZyJiLzMRcWFxZOHeRzOv1Ot0Em+a77kb7889DFRWh7KknkTNmTL+P\n2RXQuGPFe6j3tGH8iIG4/eJjIq4d6MZM3IC5yJiLHTORMReZibmwW9DCbkEztD7yKPb95KdATg7K\nnngMBWee2e9jaq1x/8u1ePadT1BSlIvH5p2Cw4a4ZjZgIiJyD3YLxsLv9zvdBFfyeDxON6Fb219e\nwr6f3gkAGHLvPQkprABg2Ztb8ew7nyAnW+GXcyb3WVi5KRM3YS4y5mLHTGTMRWZiLiyuLBxzJXNL\nX7fvzbfQ+P0bAK0x6Ee3oWjmpQk57l/Xb8dDKzdBKeAnlxyHitHiOuEHcUsmbsNcZMzFjpnImIvM\nxFzYLWhht6AsEAg4Pk1F5+Y67PnKBdAtLSi+5psYfOdPI46HisXqjTtxx4pqdAU0bjp/ImafPCqq\n/dyQiRsxFxlzsWMmMuYic1ku7BaMBQe0y3w+n9NNQMdbb0G3tKDwggsw+Kc/SUhh9XL1Z/jx8vfQ\nFdD45hnlURdWgDsycSPmImMudsxExlxkJubC4srCGdplNTU1TjcBRXNmY+ifX8SQ3/4GKgH/evnL\nuk9x5/PvI6CBa744FteeOS6m/d2QiRsxFxlzsWMmMuYiMzEXdgtaKioqdFVVldPNcJ329nYUFqbH\nk3OBgMbiVz7Gk6/XAQDmnzUOV58xNubjpFMmicRcZMzFjpnImIvMZblE1XXC1YotLurPdZX8/Hyn\nm5AQbT4/fvHnjVi9cSeysxR+8OWjI04S2pd0ySTRmIuMudgxExlzkZmYCysKS1tbm9NNcKXq6mqn\nm9BvH+1swdVL3sHqjTtRlJ+Ney+viLuwAtIjk2RgLjLmYsdMZMxFZmIuvHNlycvLc7oJrjRyZPxF\niNO6AhrL12zDw6s+gs8fwJhhxfjl7MkYM3xAv45rcibJxFxkzMWOmciYi8zEXDjmysKpGNJL7WfN\nuPuljaj9rBkAcFHF4bjp/KNRkJftcMuIiMhgnIohFnxaUFZbW+t0E2JS7/HijhXv4RuL30btZ804\nZHAB7rnsRPzoq8cmrLAyLZNUYS4y5mLHTGTMRWZiLuwWtHBAu6y4uDjpn9GxYQNaH30Mg265GTlH\nHhnz/lprvF/fhOfWfIJXa3ahK6CRm60w86Qjce2Z41CUn9jTPBWZmIi5yJiLHTORMReZibmwW9DC\nbkFndG7ahD2XzIBu2ochD/0aRRdfHPW+2/Z6sXrjTqz+YCc2724FAGRnKZx/wmG45otjcWiJax7d\nJSKi9MCpGGLBtQVl9fX1SRtM2LVjBzyXXwndtA8FXzoHhRdcEHFbr8+PLXtasXlXK97b1oiqbQ3Y\n2XSgK3dwUS4unjISM6YdgUMGJ7eoSmYmJmMuMuZix0xkzEVmYi4srixc/kbm9Xrj2k9rjf2dXWhu\n70Rzeye8vi74uwLo7Aqgs0ujo6UVnnt/hf0DyqHPPQe5V12Fzrc+QYe/Cz5/AN79fuxt9aGh1Yc9\nLT7sabYvfzCoMAefP2o4zj5mBKaVlyEvJzVdu/Fmku6Yi4y52DETGXORmZgLuwUt7BaMj78rgC17\nvKjZvg8f7WzB9sY2fNbYjp1N7fD5E1ew5mYrjBpajDHDBuDYI0pw4ughGHvIQGRn9X+dQSIioiix\nWzAWfr/f6Sa4ksfjQVlZ2UGv7Wnejzc37cEbm/Zg3ZYGtHd0ifvm5WRhcGEuBhXloigvB7nZCrlZ\nCrpmI7J2bEduXi4GnnkGCgYPRF5OFvJzspCXk4Xc7CwU5+egbGA+ygbko2xAHoYPKkBOtjseOpAy\nIeYSCXOxYyYy5iIzMRcWVxaOuZLV19ejrKwMnf4AXvvPbrxU9SnWbPYg/IbnYUMKMenwwZh46CCM\nLCvC4aVFOKyk0PaUntYa+358B7zLnoAaNAjDnl+B3KOPTvHfqP9CmdDBmIuMudgxExlzkZmYC7sF\nLewWlLX7OvHXDZ9h2ZtbsWtfcAB5brbCyeOG4rQJw3DqhGEYPqggqmO1/OYhNN91N5CXh6FPL0P+\nqacks+lJEwgEOHWHgLnImIsdM5ExF5nLcmG3YCw4oP1ggYDGy9Wf4aGVm+BpDd7VGzOsGJdMHYlz\njz8Ug4tiWy7I+9zyYGGlFEoffMDYwgoAfD6fm1Zodw3mImMudsxExlxkJubimlLQaZyh/YCPdjZj\n3qNr8LMXPoCntQNHHToIC782GU9fdxpmnzwq5sLKV7kOTTffAgAY/LM7UXhh5CkXTFBTU+N0E1yJ\nuciYix0zkTEXmYm58M6VpaAguq6tdNYV0Hj6zS1Y8urH8HdplA3Iw7wvjsGFU0Yhqx9P5fk3bQK6\nujDg+u9iwDevTmCLnTFp0iSnm+BKzEXGXOyYiYy5yEzMhWOuLJk+5srT6sPtz72H9dsaAQAzpo3E\nf50zAYW5Wf3u69ZaI7B3L7KHDUtEUx3nsv5/12AuMuZix0xkzEXmsly4cHMs2tranG6CYz7cvg9X\nL34H67c1omxAHu67ogK3XjAJxfk5qK6u7vfxlVJpU1gBSEgm6Yi5yJiLHTORMReZibmwW9CSlxfb\nOKJ08crGnbjz+ffh8wdw/JEluGvOZJQNyO9+37QlB1KBmciYi4y52DETGXORmZgLuwUtmdgt+GJl\nPRb+tQZaA1+dcgRu/vLRyE3REjJEREQGYrdgLDLtacFlb2zB3S8FC6v5Z43DDy+cJBZWtbW1DrTO\n3ZiJjLnImIsdM5ExF5mJubBb0OKiwXJJ98xbW/GblZsAADd/+WjM/NyREbctLi5OVbOMwUxkzEXG\nXOyYiYy5yEzMhd2ClkzpFnyxsh53vxScM+T2i4/FBSce7nCLiIiIjMFuwVhkwtqCKz/YgYV/DRZW\nN50/MarCqr6+vs9t2l9+GXsuuhidmzb1u40miCaTTMRcZMzFjpnImIvMxFzYLWhJ9+Vv3q9vws9f\n+KB7jNXsk0dFtZ/X6+31fd8bb6Lh29cBnZ3o+nQ7cidMSERzXa2vTDIVc5ExFztmImMuMhNzYbeg\nJZ27BXc0teObS95Bo7cDM6aNxC1fORpKxT/jekjHBxux99KZ0K2tKP7WNRj8058k5LhEREQulZnd\ngkqpcqXU9Fj38/v9yWiO47w+P25+pgqN3g5MKy/DTedPjKkA8ng84uv++np4rpwL3dqKwosuxOCf\n3JExhVWkTDIdc5ExFztmImMuMhNzcX1xpZSap5SaaX3dGsUuFQCWK6W0UqpRKbVSKVXR107pOOZK\na427/rIRm3e1YtTQYvxy9gnIyY7tf7nU193V0ADPZVcgsHs38k49FUPu/xVUBj1taWL/fyowFxlz\nsWMmMuYiMzEXV3cLKqXmAYDWeon1fQWA+Vrr+b3sM1NrvUIpVaK1bor2s9KxW3DFu5/gnr99iKK8\nbDw+/xSMGhr746w913QKtLVh7+yvoXP9euQcfTSGPb8CWYMGJbLZrueyda5cg7nImIsdM5ExF5nL\nckmLbsH5ocIKALTWVQCi6vKLpbAC0m9Ae+1n+/DAy8GJ12676Ji4CisA8Pl83f+t/X40fPs6dK5f\nj+wjjsDQZb/PuMIKODgTOoC5yJiLHTORMReZibm4trhSSpUg2MXXU1M8Y6r6kk4ztHv3+/Hfz72H\nzi6NGdNG4pzjDo37WDU1wakbtNZoWvBD+FavRtaQISh7ehmyR4xIVJONEsqEDsZcZMzFjpnImIvM\nxFzcPBVDOQDp7lMDgkXXqkg79ii+KgAs6etOVkFBQTxtdKVfvVyL7Y3tmHDoQHz/3KP6daxJkyYB\nAFruuRdtf3wWqqAAZU8+gdxxYxPRVCOFMqGDMRcZc7FjJjLmIjMxF9feuQJQimAh1VMTgLJe9qsC\nUKe1XqW1XgVgBYDl0obWYPlKpVTlrl27ugfN1dfXd69l5PF4sGHDBgQCAbS3t2PdunVob29HIBDA\nhg0bup9iqK2tdcX+r/9nN/66fjtysoA7Lz0erc1N/fp8r9eLmod/h5b7HwCys9Fwyw/QNelo1/79\nU7F/IBAwuv3J2n/Pnj1Gtz9Z+9fW1hrd/mTsn5uba3T7k7V/fn6+0e1P1v65ubmuaX+0XDug3br7\ntFhrPbbH68sRLJ4WxHCszQBmWWO2RJMmTdIm3noM1+jtwGUPvYlGbwe+f+5R+Pqpo/t9zA0bNmDC\n1q1oWnAbBv/spyieM6f/DTXchg0bMHnyZKeb4TrMRcZc7JiJjLnIXJZLVAPa3dwtCATvXvVUAiDW\nSS+aAExF8K6WKC8vL8ZDuovWGov+WoNGbwdOHD0Ec6Kcgb0vI0eORNHkySi88EKo7OyEHNN0I0eO\ndLoJrsRcZMzFjpnImIvMxFzc3C1YiWAh1VMpIhRJ1gSi0q24BshdjN1yctxeZ/bu1Q934dWaXSjK\ny8aPLz4WWVmJmdCzrCzYA8vC6oBQJnQw5iJjLnbMRMZcZCbm4triyhqAXmc9NRiuxBpLJWkAIM2B\n1etdK8DspwVb93fivr8H+4ivO2cCDhtSlLBjh/qe6QBmImMuMuZix0xkzEVmYi6uLa4sCwHcFvrG\nmkR0Vdj35Uqp5aECTHoi0JqI9DmtdV1vH+SiCcpi9rvVH2Nviw/HHDEYM6Ym9vZpcXF882OlM2Yi\nYy4y5mLHTGTMRWZiLq4d0B5iFUd1CHYRlmutF4W9Nx3BJwGnhBdP1jI5TdY+CN8nElNnaN/4aRO+\n9cgaZCmFJ+afgvEjBjrdJCIionSVFgPaET5Du/DeKgBDhNf7LKZ6MnFtQX9XAAtfqoHWwNdOHZWU\nwqq+vt7IwYTJxExkzEXGXOyYiYy5yEzMxdy+sAQzcfmb59fWY9POFowoKcC3vti/ST0j3cH0er39\nOm46YiYy5iJjLnbMRMZcZCbm4vpuwVQxrVtwX1sHZj34Oprb/Vj4tck44+hD4j5Wy+IlaP3dYpQ9\n8RjyTjghga0kIiJKK2mxcHPK+P1+p5sQk6WvbkZzux9Tx5Ti9InD4z6O99ln0fyznyNgza7dU2gG\nWzqAmciYi4y52DETGXORmZgLiyuLSWOu6na34oXKemQp4IbzJ0Kp+Oa02r/6FTTdEpzofvD//Fy8\naxVaEoAOYCYy5iJjLnbMRMZcZCbmwm5Biyndglpr3PDUOqzZ7MElU0diwYXxLWjZsX499s6aA93e\njoHfux6DFtwqbhcIBIyepiIZmImMuciYix0zkTEXmctyYbdgLEwZ0P7mpj1Ys9mDAQU5mHfWuLiO\n0bm5Dp6534Bub0fRnNkYeOstEbf1+XzxNjVtMRMZc5ExFztmImMuMhNzYXFlMWGGdn9XAL9ZuQkA\ncM0ZYzGkOPb1ELt274bn8isQaGhA/llnoWTh3b12K5q+mHUyMBMZc5ExFztmImMuMhNzYXFlKSgo\ncLoJffq/9z7D1j1eHDakEDNPOjLm/QMtLfBcMRdd9fXIPXEyShc/DJWb2+s+kybF1+2YzpiJjLnI\nmIsdM5ExF5mJubC4srioP1fk6+zC0lc3AwDmnTUOuTmxtVd3dKDhW/PQuXEjsseMQdmTTyCrqO81\nCPPz8+NqbzpjJjLmImMudsxExlxkJubi7ooihdra2pxuQq/+tLYeu5v3Y/yIgfjSsYfGtK8OBNB4\n403wvfEGsoYPx9BnliE7ylXGq6ur42luWmMmMuYiYy52zETGXGQm5sLiypKXF/v4pVRp3d+JJ14L\nLp34nenjkZUV29QLbc/8Ae0v/hlqwACUPfUkco6MvkvRtCUHUoGZyJiLjLnYMRMZc5GZmAuLK0tO\njnuXWXz6za1obu/EiaOG4JRxQ2PeP3vECOQcPRFljz6CvGOPjWnfsijvcGUSZiJjLjLmYsdMZMxF\nZmIuLK4sbn1a0NPiwx/e3gYAuO6cCXFNGFow/Wwcsmol8j9/Wsz71tbWxrxPumMmMuYiYy52zETG\nXGQm5sLiyuLWAe1PvbkF+zu7cPrE4ThuZEnKP7+4uDjln+l2zETGXGTMxY6ZyJiLzMRcOEO7xY0z\ntDd6O3DJr17D/s4u/P7bp2DCoYOcbhIREVEm4wztsXDj2oJ/fHsb9nd24bQJwxwrrExc0ynZmImM\nuciYix0zkTEXmYm5sLiyuG35m5b2Tqx49xMAwDdOL3esHV6v17HPditmImMuMuZix0xkzEVmYi7s\nFrS4rVvw8X9vxuJXPsaUMaV46BvTnG4OERERsVswNn6/3+kmdGvv8OOP7wSfELw6yrtWgSRV9h6P\nJynHNRkzkTEXGXOxYyYy5iIzMRcWVxY3jbl6sfJT7GvrxLFHDMaUMaW9bqu1RuOtP8SOiZPge/fd\nhLfFxL7uZGMmMuYiYy52zETGXGQm5sJuQYtbugV9nV249IHXsbfFh3suOxGfP2p4r9s3L1yElgd/\nDVVYiOGr/omc0aMT2p5AIODaaSqcwkxkzEXGXOyYiYy5yFyWC7sFY+GWAe1/2/AZ9rb4MH7EQJw2\nYViv27Y+8QRaHvw1kJ2N0sW/S3hhBQA+ny/hxzQdM5ExFxlzsWMmMuYiMzEXFlcWN8zQ7u8K4Kk3\ntgAArvpCea+zsbf/7e/Yd/sdAICS/12EgrPPSkqbampqknJckzETGXORMRc7ZiJjLjITc2FxZSko\nKHC6Cfjn+zuwo6kdo4YW48xJh0TczvfOO2i4/nuA1hi04FYUz5mdtDZNmjQpacc2FTORMRcZc7Fj\nJjLmIjMxFxZXFqf7c7sCGk++HrxrNfcLY5CdJd+16vzwQ3iuvgbw+VB81VwMuP67SW1Xfn5+Uo9v\nImYiYy4y5mLHTGTMRWZiLiyuLG1tbY5+/r8+3IVte704tKQQ5x53qLiNf/t27L1iLnRzMwq+fD4G\n//xncS3kHIvq6uqkHt9EzETGXGTMxY6ZyJiLzMRcWFxZ8vLyHPtsrTWeeK0OAHDFaaORk23/3xJo\nbITn8isR2LkTeSd/DqW/fhAqOzvpbRs5cmTSP8M0zETGXGTMxY6ZyJiLzMRcWFxZcnJyHPvstz7a\ni492tmDowHxccOLhtvd1ezs8V18D/0cfIeeoCSh79BGoFI0RKysrS8nnmISZyJiLjLnYMRMZc5GZ\nmAuLK4tTTwtqrfH4vzcDAL5+ymjk59rvRrUuWYqOtWuRfeihGLpsGbJKSlLWvtra2pR9limYiYy5\nyJiLHTORMReZibmwuLI4NaB93ZYGfPDpPgwuysUlU48Qt8k7+XMoOO9clP3haWQfJo/HSpbi4uKU\nfp4JmImMuciYix0zkTEXmYm5cIZ2i1MztH/3ibWo3NKAeWeNwzfPGJvyzyciIqKocYb2WDixtuD7\n9U2o3NKA4vwczDrpyJR/fjRMXNMp2ZiJjLnImIsdM5ExF5mJubC4sjix/E3oCcGZJ43EwMLclH9+\nNLxer9NNcB1mImMuMuZix0xkzEVmYi7sFrSkultw045mzP3d28jPzcKLN56BIcXOTQVBREREUWG3\nYCz8fn9KP+/J14N3rS6ZMtLVhZXH43G6Ca7DTGTMRcZc7JiJjLnITMyFxZUllWOuPt7VgtUbdyE3\nW+Gy00an7HPjYWJfd7IxExlzkTEXO2YiYy4yE3Nht6Alld2CP/zjevzrw92YedKRuPkrR0P7/fBv\n3oycCROSvpxNrAKBgOPrLroNM5ExFxlzsWMmMuYic1ku7BaMRaoGtP9nRzP+9eFu5Odk4Runl0P7\nfPBcdgV2nzUdHe+8k5I2xMLn8zndBNdhJjLmImMudsxExlxkJubC4sqSihnatdZ44OXgTLMzpo1E\nWXEuGr9/A3xvvoms4cORM3580tsQq5qaGqeb4DrMRMZcZMzFjpnImIvMxFxYXFkKUrBW36qNO1G1\ntRGDi3Jx1RfKse+nd6L9pb9CDRyIocueQvbQoUlvQ6wmTZrkdBNch5nImIuMudgxExlzkZmYC4sr\nS7L7c1vaO/HgP/4DAPjO2eOR/fhSeB99DMjLQ9mjjyD3GHeePPn5+U43wXWYiYy5yJiLHTORMReZ\nibmwuLK0tbUl9fj3/P1D7Gn24ZgjBuOLa/+G5rvuBpTCkAfuR/5ppyb1s/ujurra6Sa4DjORMRcZ\nc7FjJjLmIjMxlxynG+AWeXnJm2vqbxu24x/VO1CQm4Wbm9bBe3+wsCpZeDeKLrowaZ+bCCNHjnS6\nCa7DTGTMRcZc7JiJjLnITMzF9VMxKKXmAWiwvi3XWi9Kxj7Jmophw7ZGfPfJtfB3aXyveT3OeO6h\nYGF17z0onjM74Z9HRERESWP+VAxWkQSt9Qqt9QoAq5RSixO9D5CcpwWrtjbgpqfXwd+lccEna3DG\ncw9BDRiA0sceMaawqq2tdboJrsNMZMxFxlzsmImMuchMzMXt3YLztdZTQt9orauUUtOTsE9CB7T7\nuwJYvuYT/HbVJnR2aZxW9y7mvvoIciYehdKHf4vcCRMS9lnJVlxc7HQTXIeZyJiLjLnYMRMZc5GZ\nmItruwWVUiUAGrXWqsfr6wAs0FqvSsQ+IeNHj9f33XEvdEAjoINzUgW0BvSB77XWwfcB5IweDTV8\nOKxNoBHcbl9bJ1Zv3IFPG9oBADOPKcUVzy5C0amnYOD134VK4tguIiIiSqqougXdfOeqHECT8HoD\ngAoAUqEUzz4AgB0dCr/YFsPjnnsbcGBYl90RpUX43rlH4fSJw4HZy6M/rsvU19cbOZgwmZiJjLnI\nmIsdM5ExF5mJubi5uCqFXL00AShLxD7W+Kx51re+NT8774M42ilaA+BPiTqYs4YC2Ot0I1yGmciY\ni4y52DETGXORuSmXl7XW5/W1kZuLq6TTWi8BsAQAlFKVWuupDjfJdZiLHTORMRcZc7FjJjLmIjMx\nF1c/LYjgnaieSgB4ErwPERERUUK4ubiqRLAo6qkUQFUC9yEiIiJKGNcWV1rrJgB11hOA4UoiPfUX\nzz5hlsTZ1HTHXOyYiYy5yJiLHTORMReZcbm4dioGoHvA+Vit9QLr+woE57Gab31fDmAhgGutwqrP\nfYiIiIiSydXFFdBdLNUh2N130FI21uSgywFM0VrXRbMPERERUTK5vrgiIiIiMklGT8UAxLfIcyYI\nrdEIILSU0IJQ1ysBSqnlWutZTrfDLZRStyI4n1wDEFzb09kWOS/sZ6gEwXn27sq0nyFrWMZt0s9K\nJl97o8gFyMBrb2+59NjO9dffjC6uwhd5tr6vUEotzvTxWUqpedYcYN3fA1gHYKxzrXIP6wIw0+l2\nuIVSajmCvwDqrO+1UmpIpvxCkFjF5pLwDKycXP0LIVGsn5E51rflwvsZee2NJpdMvPb2lYuwreuv\nv659WjBF5oefyFrrKgB9LvKczoQnLUOTrZZGswB2hpDmUstI1sV/bfiYRwQfKMnYwsoyTchAepI5\nLWmtq6yHip6NsElGXnt7yyWTr71RnC/hjLj+ZmxxZZ3IFcJbTel+IvehHMBi4Qe9Dn38iyITKKVm\nRjGtRyZZCOCgLsAehVamKrf+hR2uhEUnr7294LW3DyZdfzO2uELfizxnJOtfkFOEXwLlCP6QZyzr\nlyUno7VYvwRKrP+eqZSarpS6NVPuzvThWgDrrO7B0JPNi51tkmvw2ivgtbd3pl1/M7m4imdh6Ixg\n/ZB3U0rNBFBnyr8Ykqicd2UOEvolWaK1XmGdH0sArHa2Wc6zfobGArhNKdUY9hrx2hsRr729Mur6\nm8nFFUXBugtxG4CznW6Lk6zb0Rn/BFwPpQjeueq+4IVN5pvJ3TuhCY5nAhiDYMG5MuwpMKI+8dp7\ngInX30wvrrjIc98WApiVyWNFrF+UxvyLKYXqgAMFVZiM7t6xLNBaL9JaN1kDdacAWJjpRWcYXnv7\nlvHXXsDc628mT8XARZ77YI0XWWjSrdgkmQ6gpOcvxtDcTuFPPWUSrXWdUirS2xn7C8E6T1aGv6a1\nrlJKzQJwDoBM7+LhtbcPvPYexMjrb8YWV1rrJqVUnVKq5xM80SzynPasLowVPZYVmp6J2Ug/vEqp\nhZk06WEvqpRSPcdClCP4C5QOVgfemeG1tw+89h7M1OtvpncLLkSwTxtA99MIGXkCh7P+hVAZNimk\n7V8NRJYF1heA7p+hukwevG39EpwjvDUTwfFXmSTSnESZfu0Vc+G114w5rKKR8WsLcpHng1n925sj\nvJ3Rs24D3Re/+Qj+olwBYHGm/osyxHqiKTQPT5k1xiijhQ1G9sB6ohI97kakM+s6Mh/BLp0KBIvK\ndcLs4xl17e0tl0y+9kZzvljbGXP9zfjiioiIiCiRMr1bkIiIiCihWFwRERERJRCLKyIiIqIEYnFF\nRERElEAsroiIiIgSiMUVERERUQKxuCIiIiJKIBZXRJRySqnpSikd49fmHseYqZRqtCYxNYZSap41\nyWgs+9yarPYQUeKxuCIiJ4QXF4sAjAUwJey1VQCGILjQcWgpnZ5LY8y3jiMtNeNKSqnlAM6JY7bt\nJqXU5liLMiJyRsYu3ExEjgoVSovCl8tRSoWWiqmyCpBVSqmzAWzBwQUZECyu5gNYnIL29ptSajGC\ny7xM6XPjHqzlUaYAWIdgIUpELsY7V0TkpLv62sAqsmzbaa3rtNYLTFivz+q6nIewRa7jsABAuVWk\nEZGLsbgiIieE352KhisXZ43BUgT/vnH/PaysFgGYp5SqSFjLiCjhWFwRkRPKAFRGu7HWugoATBxz\nZN21KkFiCsSV1p/zE3AsIkoSFldE5ISViH2s1AIgOHapx1OEC0MbKKUW9nhvnvVU4boTlqYQAAAD\nf0lEQVTQE4dKqXnWtuVKqeXWE4eN4cfpyTrOSusY62J8ei9UCK2NcOyZVrtC7bvVapfUnlBBOi+G\nzyeiFGNxRUQpp7VeFbobFcM+i6yusQUIDuq27W8Njh8LIDQOaz6CXXKrACwBUA5gsVUcrbO2uQtA\nA4BbpfFM1muLASzXWivr8xdaT/5FY7r1p629SqnpVvtmWcc+x/oSp5ew/v5N1r7sGiRyKRZXRGQU\nrXWTNYhd7Gaz3gsVMhUAplgD3+cjOGYJABYCWKK1nqW1XoRgQQMExzN1dz2GDURfpbVeYh1/lXWc\nmVZxFFGPbswGYZNZAJ4LFZrWIP1zcKA4lISOU97bZxORc1hcEVE6W9HjacKVYf/d/QRij23Ci5ZQ\n11zPO1ore7wfSffcXBEG75cCmC1MhLoAgCfCMUPHYXFF5FIsrogonfUc5xS669MkFDvS3aLyCO+F\n7kj1t2tupXWs5daYq5VWl2WVdUeNiAzE4oqI0lmkqR6kLrqDKKXC7wyFBsRrpZQGsDxsu96eYGzo\nbTurqzG8iJqO4N2w7oH3gtBxXD+/F1GmYnFFRCQLL8CGaK1VhK+Ic3WFD0CHffkeKKWmW+PBQoPZ\nF4VtH+lpytBxWFwRuRSLKyIiQY+iaaq0TZRP7IWmT5C2XR4aFG89QblAaz0EB6adOGhclXX3q8Ta\nPqanLYkodVhcERFFFuqysy1bYxVF0UzHELoDNS3C+9Kg+FWAbaA9cKDIWxLF5xKRQ1hcEZHjlFIl\nVrHSPVDcmuSzt/FM5T3+lN7ruchx6HVbF13Ya913qax5s6oATLcGm89TSk23JvhcjuBUCr3SWq9A\nsKtPnLsKwb/rytBdMOtu1VLIBVRoyoi+nlIkIgcprbXTbSCiDGY9HRexWLDGI4VvH7pjFF54NSFY\n6JTAfjepCcAYAFt67AMcuCPV8/PrtNbdhZnVxjkIdu01IXhnKepFo62pFpYDOCd8fUGlVCOAsxEs\n6OZbx69DcAqJBT2OUQKgEcH5ubj8DZGLsbgiIkoBa6b36eFFWyr3J6LUYbcgEVEKWHebVsWwbE43\na1qG6QCmJLxhRJRwLK6IiFLEKrBW9jGWLNK+Y3ub9oGI3IPdgkREREQJxDtXRERERAnE4oqIiIgo\ngVhcERERESUQiysiIiKiBGJxRURERJRALK6IiIiIEojFFREREVEC/T8d0p9p0OFscAAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1181e0ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, let's plot the horizontal position response\n",
    "\n",
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t, x_resp, linewidth=2, linestyle='--', label=r'Trolley')\n",
    "plt.plot(t, payload_position, linewidth=2, linestyle='-', label=r'Payload')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "plt.xlim(0,15)\n",
    "plt.ylim(0,3)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('Crane_Position_Response.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simluation Using the Control System Toolbox\n",
    "We can also simulate this system using the [Python Control System Library](https://python-control.readthedocs.io/en/latest/). We'll first set up the state-space form of the equations of motion by writing our system of first-order ODEs in matrix form. Our system of first-order ODEs is:\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = g(\\mathbf{w}, \\bar{u}, t) $\n",
    "\n",
    "Expanding these, we have:\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = \\begin{bmatrix}w_2 \\\\ -\\frac{g}{l}w_1 + \\frac{1}{l}\\ddot{x} \\\\ w_4 \\\\ \\ddot{x}\\end{bmatrix} $\n",
    "\n",
    "The acceleration, $\\ddot{x}(t)$, is still the input to the system. \n",
    "\n",
    "$ \\quad \\mathbf{u}  = \\left[ \\ddot{x} \\right]$\n",
    "\n",
    "We want to put this into the \"normal\" state-space form:\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = A \\mathbf{w} + B \\bar{u} $\n",
    "\n",
    "where A and B are matrices, and, as before, the state vector, $\\mathbf{w}$, is:\n",
    "\n",
    "$ \\quad \\mathbf{w} = \\begin{bmatrix} \\theta \\\\ \\dot{\\theta} \\\\ x \\\\ \\dot{x} \\end{bmatrix} $\n",
    "\n",
    "***Note:*** It is more common to see the state vector written as $\\mathbf{x}$ instead of $\\mathbf{w}$ as we've written here.\n",
    "\n",
    "Looking at our equations of motion, we can then write:\n",
    "\n",
    "\n",
    "$ \\quad \\dot{\\mathbf{w}} = \\begin{bmatrix} 0    &    1 & 0 & 0   \\\\ \n",
    "                                          -g/l  &    0 & 0 & 0 \\\\\n",
    "                                           0    &    0 & 0 & 1   \\\\\n",
    "                                           0    &    0 & 0 & 0   \\end{bmatrix} \\mathbf{w} \n",
    "                        + \\begin{bmatrix} 0 \\\\\n",
    "                                          1/l \\\\\n",
    "                                          0 \\\\\n",
    "                                          1 \\end{bmatrix} \\mathbf{u}  $\n",
    "                                          \n",
    "where:\n",
    "\n",
    "$ \\quad A = \\begin{bmatrix} 0    &    1 & 0   & 0   \\\\ \n",
    "                            -g/l &    0 & 0   & 0 \\\\\n",
    "                            0    &    0 & 0   & 1   \\\\\n",
    "                            0    &    0 & 0   & 0   \\end{bmatrix} $\n",
    "\n",
    "and:\n",
    "\n",
    "$ \\quad B = \\begin{bmatrix} 0    \\\\\n",
    "                            1/l \\\\\n",
    "                            0    \\\\\n",
    "                            1    \\end{bmatrix} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've determined what the state-space matrices are, we can set up the system using the Control Systems Library. To do so, we'll first need to import the library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we'll first define the matrices. In this case, we'll set the output matrix, C, to be include $\\theta$, $x$, and well as the linarized prediction of the payload position $x - l\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.array([[0, 1, 0, 0],\n",
    "              [-g/l, 0, 0, 0],\n",
    "              [0, 0, 0, 1],\n",
    "              [0, 0, 0, 0]])\n",
    "\n",
    "B = np.array([[0],[1/l],[0],[1]])\n",
    "\n",
    "C = np.array([[1, 0, 0, 0],   # theta\n",
    "              [0, 0, 1, 0],   # x\n",
    "              [-l, 0, 1, 0]]) # x - l theta (paylod horiz position)\n",
    "\n",
    "D = np.array([[0],[0],[0]])\n",
    "             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can use the `control.ss` method to create the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sys = control.ss(A, B, C, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, the `odeint` method of simluating the system needed all of the input to be defined in function form. However, the Control System Library needs the inputs to be arrays. So, we need to generate the arrays for our inputs, $\\ddot{x}$.\n",
    "\n",
    "In this case, since we already have the funcitonal form defined, we can use those funcitons to fill the needed array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xddot_input = x_ddot(t, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_resp, resp_out, states_out = control.forced_response(sys, t, xddot_input)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot this response as we did for the `odeint` simulated version above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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djhOMDRd0AYuA0VajBhg9sKr6GiHELRWvTxeDNd9QIedFSsng/Q9ALkfLb/4G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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1190106d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Angle (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "# plt.ylim(-1.,1.)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t, resp_out[0,:], linewidth=2, linestyle = '-', label=r'$\\theta$')\n",
    "\n",
    "# leg = plt.legend(loc='upper right', fancybox=True)\n",
    "# ltext  = leg.get_texts() \n",
    "# plt.setp(ltext,family='Serif',fontsize=16)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# If you want to save the figure, uncomment the commands below. \n",
    "# The figure will be saved in the same directory as your IPython notebook.\n",
    "# Save the figure as a high-res pdf in the current folder\n",
    "# plt.savefig('planar_crane_angle.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As above, we can also plot the trolley and payload positions as a function of time. Since we defined one of our outputs to be the payload position, we can use it directly, rather than having to calculate it after the simluation like we have to do for the `odeint` case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UOjpG5jfIwSgvL1fbBOkgTcSoocsrO4+isc2KzPGxWDTL+3yIUCLSZdXVU2DQ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\nWFseUeROswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1181f9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, let's plot the horizontal position response\n",
    "\n",
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t, resp_out[1,:], linewidth=2, linestyle='--', label=r'Trolley')\n",
    "plt.plot(t, resp_out[2,:], linewidth=2, linestyle='-', label=r'Payload')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "plt.xlim(0,15)\n",
    "plt.ylim(0,3)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('Crane_Position_Response.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot matches the one above, as it should."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LQR Control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Control System Library also has several control design tools built in (as you might expect it to). Here, we'll design a [Linear Quadratic Regulator (LQR)](https://en.wikipedia.org/wiki/Linear–quadratic_regulator) for this system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The form of the control law for LQR is:\n",
    "\n",
    "$ \\quad \\mathbf{u} = -K \\mathbf {w} $\n",
    "\n",
    "where $K$ is a matrix containing gains. The gains multiple each state of the system via the state vector $\\mathbf{w}$. Hence, this is a *full-state* feedback controller. \n",
    "\n",
    "For this problem, since we have a nonzero desired state, we can redefine the control law to be:\n",
    "\n",
    "$ \\quad \\mathbf{u} = -K \\left( \\mathbf{w} - \\mathbf{w_d} \\right)$\n",
    "\n",
    "where $\\mathbf{w_d}$ is the desired final state of the system, written as a vector. Luckily, this reformulation does not change the solution of the gain matrix $K$ at all. So, we can still use the Control System Library's built-in LQR solver.\n",
    "\n",
    "The full derivation of the controller is beyond the scope of this notebook, but we do need to know that it is an (mathmeatically, not necessarily-practically) optimal controller. It is desined by picking the gain matrix to minimize a cost function of the form:\n",
    "\n",
    "$ \\quad J = \\int_0^\\infty \\mathbf{w}^T Q\\mathbf{w} + \\mathbf{u}^T R \\mathbf{u} + 2\\mathbf{w}^T N \\mathbf{u}\\; dt $\n",
    "\n",
    "For our purposes, let's ignore the $N$ matrix for now and concentrate on the $Q$ and $R$ matrices. These two matrices must be positive-semidefinite. The $Q$ matrix effectively penalizes states from deviating from the desired, regulated value. The $R$ matrix penalizes actuator effort. So, by changing the relative values within $Q$ we can value one state over another and by changing the ratio of values between $Q$ and $R$, we can balance performance and actuator effort.\n",
    "\n",
    "As a simple choice, here let's set $Q$ to penalize $\\theta$, $\\dot{\\theta}$ and $\\dot{x}$, with slightly more emphasis on $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Q = np.array([[ 100000,  0,  0,  0],\n",
    "              [ 0,  1000,  0,  0],\n",
    "              [ 0,  0,  1000,  0],\n",
    "              [ 0,  0,  0,  0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll simply set a low value for $R$, which will be a scalar value since there is only one input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "R = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can use the `control.lqr` method of the Control System Library to design the controller by simply passing it the system, $Q$, and $R$ matrices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "K, _, closedLoopEigenvalues = control.lqr(A, B, Q, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this problem, we want to regulate our states not about zero ut about some desired final state vector $\\mathbf{w_d}$. To so do, we need to define an augmented state-space system to implement this input. \n",
    "\n",
    "We saw that:\n",
    "\n",
    "$ \\quad \\mathbf{u} = -K \\left( \\mathbf{w} - \\mathbf{w_d} \\right)$\n",
    "\n",
    "and know that our system form is:\n",
    "\n",
    "$ \\quad \\mathbf{\\dot{w}} = A \\mathbf{w} + B \\mathbf{u} $\n",
    "\n",
    "We can subsitute our control law for $\\mathbf{u}$ into this equation to determine what the \"new\" matrices need to be:\n",
    "\n",
    "$ \\quad \\mathbf{\\dot{w}} = A \\mathbf{w} - B K \\left( \\mathbf{w} - \\mathbf{w_d} \\right) $\n",
    "\n",
    "We can now collect terms to find:\n",
    "\n",
    "$ \\quad \\mathbf{\\dot{w}} = (A - BK) \\mathbf{w} + B K \\mathbf{w_d} $\n",
    "\n",
    "\n",
    "From this, we can use the solution from the \"standard\" regular problem to find $K$, we can define:\n",
    "\n",
    "$ \\quad \\widehat{A} = A - BK $\n",
    "\n",
    "and\n",
    "\n",
    "$ \\quad \\widehat{B} = BK $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_hat = A - B * K\n",
    "B_hat = B * K\n",
    "\n",
    "# Given the size change of the input matrix, we also need to to modifiy the D matrix\n",
    "D_hat = np.zeros((3, 4))\n",
    "\n",
    "sys_lqr = control.ss(A_hat, B_hat, C, D_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to define the desired state trajectory, $\\mathbf{w_d}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set it to all zeros to start\n",
    "w_d = np.zeros((4,len(t)))\n",
    "\n",
    "# Now, fill the trolley position row with the desired final trolley position\n",
    "x_d = 2.0\n",
    "w_d[2,:] = x_d * np.ones((1,len(t)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t_LQRresp, LQRresp_out, LQRstates_out = control.forced_response(sys_lqr, t, w_d, X0=[0,0,0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oEPpPd8HmsMNitmDQH4DJZITN6UQoGERMklBcXIxwJIJgKIRSlwuGa5ejOxbH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11938a470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, let's plot the horizontal position response\n",
    "\n",
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t, LQRresp_out[1,:], linewidth=2, linestyle='--', label=r'Trolley')\n",
    "plt.plot(t, LQRresp_out[2,:], linewidth=2, linestyle='-', label=r'Payload')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "plt.xlim(0,15)\n",
    "# plt.ylim(0,3)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', ncol = 2, fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('Crane_Position_Response.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"border: 0px;\n",
    "        height: 1px;\n",
    "        text-align: center;\n",
    "        background: #333;\n",
    "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc);\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Licenses\n",
    "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n",
    "\n",
    "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsx.otf');\n",
       "        font-weight: bold;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsi.otf');\n",
       "        font-style: oblique;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunso.otf');\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "    }\n",
       "\n",
       "    div.cell {\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    h1 {\n",
       "        font-family: Computer Modern;\n",
       "    }\n",
       "    \n",
       "    h4 {\n",
       "        margin-top: 12px;\n",
       "        margin-bottom: 3px;\n",
       "    }\n",
       "\n",
       "    div.text_cell_render {\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width: 100%;\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    .CodeMirror {\n",
       "        font-family: \"Source Code Pro\", source-code-pro, Consolas, monospace;\n",
       "    }\n",
       "    \n",
       "    .warning {\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    }  \n",
       "  \n",
       "   \n",
       "    hr.style-end {\n",
       "        border: 0px !important;\n",
       "        height: 1px !important;\n",
       "        text-align: center !important;\n",
       "        background: #333 !important;\n",
       "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "    }\n",
       "\n",
       "    hr.style-end:after {\n",
       "        content: &#x269C !important;\n",
       "        left: 50% !important;\n",
       "        position: absolute !important;\n",
       "        /* Controls the whitespace around the symbol */\n",
       "        padding: 0px !important;\n",
       "        background: #fff !important;\n",
       "    }\n",
       "    \n",
       "/*  Center figures, etc\n",
       "    .ui-wrapper {\n",
       "        margin-left: auto !important;\n",
       "        margin-right: auto !important;\n",
       "    }\n",
       "*/\n",
       "    \n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This cell will just improve the styling of the notebook\n",
    "# You can ignore it, if you are okay with the default sytling\n",
    "from IPython.core.display import HTML\n",
    "import urllib.request\n",
    "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n",
    "HTML(response.read().decode(\"utf-8\"))"
   ]
  }
 ],
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    "version": 3
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   "file_extension": ".py",
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   "name": "python",
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   "pygments_lexer": "ipython3",
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