Simple Simulations/Mass-Spring-Damper with LQR Control.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">LQR Control of a Simple Mass-Spring-Damper <br> System with a Disturbance Force</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",
    "\t<img src=\"http://shared.crawlab.org/MassSpringDamper_SeismicWithDisturbance_Horiz.png\" alt=\"A Mass-Spring-Damper System with a Disturbance Force\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Mass-Spring-Damper System with a Disturbance Force</strong>\n",
    "</p>\n",
    "\n",
    "This notebook simluates a the simple mass-spring-damper model like the one shown in Figure 1. The system has both a position input $y(t)$ and a force input, $f(t)$. This system could also be used to model the position control of a mass via a Proportional Derivative (PD) controller.\n",
    "\n",
    "The equationof motion for this system is:\n",
    "\n",
    "$ \\quad m\\ddot{x} + c \\dot{x} + k x = c \\dot{y} + k y - f $\n",
    "\n",
    "We can also rewrie this in terms of damping ratio, $\\zeta$, and natural frequency, $\\omega_n$:\n",
    "\n",
    "$ \\quad \\ddot{x} + 2 \\zeta \\omega_n \\dot{x} + \\omega_n^2 x = \\zeta \\omega_n \\dot{y} + \\omega_n^2 y - \\frac{f}{m} $\n",
    "\n",
    "However, as we'll see below, we often will collect terms so that our ''motion'' variable are all on the left-hand side, like:\n",
    "\n",
    "$ \\quad \\ddot{x} = \\frac{k}{m}\\left( y - x \\right) + \\frac{c}{m} \\left(\\dot{y} - \\dot{x} \\right) - \\frac{f}{m} $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import the ODE solver\n",
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions defining the equations of motion and inputs\n",
    "We will first define the functions that define the equations of motion and the inputs. One \"trick\" that we will use is to define $y(t)$ and $\\dot{y}(t)$ as states. This allows us to specifiy an acceleration input $\\ddot{y}(t)$, which gets propogated to the $y(t)$ and $\\dot{y}(t)$ via the equations of motion (or state-transition matrix if we were solving in \"true\" matrix-based state-space form).\n",
    "\n",
    "So, we can then define our states as vector $ \\bar{w} = \\left[x \\ \\dot{x} \\  y \\ \\dot{y}\\right]^T $ and the inputs as $\\bar{u} = \\left[\\ddot{y} \\ f \\right]$.\n",
    "\n",
    "Then the system of first-order ODEs we have to solve is:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}} = g(\\bar{w}, \\bar{u}, t) $\n",
    "\n",
    "Writing these out, we have:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}}  = \\left[\\dot{x} \\right.$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\frac{k}{m}(y - x) + \\frac{c}{m}\\left(\\dot{y} - \\dot{x}\\right) - \\frac{f}{m} $\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\dot{y}$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\left.\\ddot{y}\\right]$\n",
    "\n",
    "Notice that the $\\ddot{y}$ in the last line is what we get to specify to generate the position input. In addition to allowing us to only specify one input that gets propograted to y and $\\dot{y}$, describing inputs in the acceleration domain is often preferrable. This is because representing a realistic input in this domain is often easier than in the position or velocity domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eq_of_motion(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",
    "    x, x_dot, y, y_dot = w\n",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\n",
    "\n",
    "    # Create sysODE = (x', x_dot', y', y_dot')\n",
    "    sysODE = [x_dot,\n",
    "             k/m * (y - x) + c/m * (y_dot - x_dot) - f(t, p)/m,\n",
    "             y_dot,\n",
    "             y_ddot(t, p)]\n",
    "    return sysODE\n",
    "\n",
    "\n",
    "def f(t, p):\n",
    "    \"\"\"\n",
    "    defines the disturbance force input to the system\n",
    "    \"\"\"\n",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\n",
    "    \n",
    "    # Select one of the two inputs below\n",
    "    # Be sure to comment out the one you're not using\n",
    "    \n",
    "    # Input Option 1: \n",
    "    #    Just a step in force beginning at t=DistStart\n",
    "    # f = F_amp * (t >= DistStart)\n",
    "    \n",
    "    # Input Option 2:\n",
    "    #    A pulse in force beginning at t=DistStart and ending at t=(DistStart+0.1)\n",
    "    f = F_amp * (t >= DistStart) * (t <= DistStart + 0.1)\n",
    "    \n",
    "    return f\n",
    "\n",
    "\n",
    "def y_ddot(t, p):\n",
    "    \"\"\"\n",
    "    Defines the accel input to the system.\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",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\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",
    "    \n",
    "    if t3 <= t2: # command should be bang-bang, not bang-coast-bang\n",
    "        t2 = np.sqrt(Distance/Amax)+t1\n",
    "        t3 = 2*np.sqrt(Distance/Amax)+t1\n",
    "        \n",
    "        accel = Amax*(t > t1) - 2*Amax*(t > t2) + Amax*(t > t3)\n",
    "    \n",
    "    else: # command is bang-coast-bang\n",
    "        accel = Amax*(t > t1) - Amax*(t > t2) - Amax*(t > t3) + Amax*(t > t4)\n",
    "\n",
    "    return accel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the parameters for simluation\n",
    "m = 1.0                      # mass (kg)\n",
    "k = (1.0*2*np.pi)**2             # spring constant (N/m)\n",
    "\n",
    "wn = np.sqrt(k/m)            # natural frequency (rad/s)\n",
    "\n",
    "# Select damping ratio and use it to choose an appropriate c\n",
    "zeta = 0.05                   # damping ratio\n",
    "c = 2*zeta*wn*m              # damping coeff.\n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 10.0\n",
    "numpoints = 10001\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",
    "x_init = 0.0                        # initial position\n",
    "x_dot_init = 0.0                    # initial velocity\n",
    "y_init = 0.0\n",
    "y_dot_init = 0.0\n",
    "\n",
    "# Set up the parameters for the input function\n",
    "Distance = 1.0               # Desired move distance (m)\n",
    "Amax = 20.0                   # acceleration limit (m/s^2)\n",
    "Vmax = 2.0                   # velocity limit (m/s)\n",
    "StartTime = 0.5              # Time the y(t) input will begin\n",
    "DistStart = 4.5              # Time the disturbance input will begin\n",
    "F_amp = 100.0                 # Amplitude of Disturbance force (N)\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp]\n",
    "x0 = [x_init, x_dot_init, y_init, y_dot_init]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAokAAAGaCAYAAABjfdmJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBz+P883O7LM2hZpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e77e080>"
      ]
     },
     "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('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "# plt.ylim(-1.,1.)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t,resp[:,0], linewidth=2, linestyle = '-', label=r'$x$')\n",
    "plt.plot(t,resp[:,2], linewidth=2, linestyle = '--', label=r'$y$')\n",
    "\n",
    "# If there is a non-zero force disturbance show where it began via an annotation\n",
    "if F_amp > 0:\n",
    "    plt.annotate(r'Force Disturbance Begins',\n",
    "         xy=(DistStart,resp[-1,2]), xycoords='data',\n",
    "         ha='center',\n",
    "         xytext=(DistStart, 1.05*np.max(resp[:,0])), textcoords='data', fontsize=16,\n",
    "         arrowprops=dict(arrowstyle=\"simple, head_width = 0.35, tail_width=0.05\", connectionstyle=\"arc3\", color=\"black\"),color = \"black\")\n",
    "    \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('MassSpringDamper_Disturbance_Resp.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forces\n",
    "We can also easily take a look at the forces acting on the system.\n",
    "\n",
    "The forces resulting from the position input are just the force from the spring, $F_{sp}$, and the force from damper, $F_{d}$:\n",
    "\n",
    "$ \\quad F_{pos} = F_{sp} + F_{d} = k \\left(y - x\\right) + c \\left(\\dot{y} - \\dot{x}\\right) $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Fsp = k * (resp[:,2] - resp[:,0])       # Spring Force (N)\n",
    "Fd =  c * (resp[:,3] - resp[:,1])       # Damping Force (N)\n",
    "\n",
    "F_pos = Fsp + Fd\n",
    "\n",
    "# Calculate the disturbance force over time by calling the disturbance force function\n",
    "F_dist = np.zeros_like(t)\n",
    "\n",
    "for ii in range(len(t)):\n",
    "    F_dist[ii] = -f(t[ii],p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAGVCAYAAADAJJRSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDMMwjET+f5dcUtMJREkhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121195eb8>"
      ]
     },
     "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('Force (N)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "# You may need to reset these limits based on the forces in your simulation\n",
    "ymax = 1.1 * np.max([np.max(np.abs(F_pos)), np.max(np.abs(F_dist))])\n",
    "plt.ylim(-ymax, ymax)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t,F_pos, linewidth=2, linestyle = '-', label=r'Spring-Damper')\n",
    "plt.plot(t,F_dist, linewidth=2, linestyle = '--', label=r'Disturbance')\n",
    "\n",
    "leg = plt.legend(loc='best', 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('MassSpringDamper_Disturbance_Forces.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation with the Control System Library\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{\\bar{w}} = g(\\bar{w}, \\bar{u}, t) $\n",
    "\n",
    "Expanding these, we have:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}}  = \\left[\\dot{x} \\right.$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\frac{k}{m}(y - x) + \\frac{c}{m}\\left(\\dot{y} - \\dot{x}\\right) - \\frac{f}{m} $\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\dot{y}$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\left.\\ddot{y}\\right]$\n",
    "\n",
    "We want to put this into the \"normal\" state-space form:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}} = A \\bar{w} + B \\bar{u} $\n",
    "\n",
    "where A and B are matrices, \n",
    "\n",
    "$ \\quad \\bar{u} = \\begin{bmatrix} \\ddot{y} \\\\ f \\end{bmatrix} $\n",
    "\n",
    "and, as before, the state vector, $\\bar{w}$, is:\n",
    "\n",
    "$ \\quad \\bar{w} = \\begin{bmatrix} x \\\\ \\dot{x} \\\\ y \\\\ \\dot{y} \\end{bmatrix} $\n",
    "\n",
    "***Note:*** It is more common to see the state vector written as $\\bar{x}$ instead of $\\bar{w}$ as we've written here.\n",
    "\n",
    "Looking at our equations of motion, we can then write:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}} = \\begin{bmatrix} 0    &    1 & 0   & 0   \\\\ \n",
    "                                        -k/m & -c/m & k/m & c/m \\\\\n",
    "                                        0    &    0 & 0   & 1   \\\\\n",
    "                                        0    &    0 & 0   & 0   \\end{bmatrix} \\bar{w} \n",
    "                        + \\begin{bmatrix} 0 & 0    \\\\\n",
    "                                          0 & -1/m \\\\\n",
    "                                          0 & 0    \\\\\n",
    "                                          1 & 0    \\end{bmatrix} \\bar{u}  $\n",
    "                                          \n",
    "where:\n",
    "\n",
    "$ \\quad A = \\begin{bmatrix} 0    &    1 & 0   & 0   \\\\ \n",
    "                            -k/m & -c/m & k/m & c/m \\\\\n",
    "                            0    &    0 & 0   & 1   \\\\\n",
    "                            0    &    0 & 0   & 0   \\end{bmatrix} $\n",
    "\n",
    "and:\n",
    "\n",
    "$ \\quad B = \\begin{bmatrix} 0 & 0    \\\\\n",
    "                            0 & -1/m \\\\\n",
    "                            0 & 0    \\\\\n",
    "                            1 & 0    \\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": 10,
   "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 diagonal, which will output each state independently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.array([[0, 1, 0, 0],\n",
    "              [-k/m, -c/m, k/m, c/m],\n",
    "              [0, 0, 0, 1],\n",
    "              [0, 0, 0, 0]])\n",
    "\n",
    "B = np.array([[0, 0],\n",
    "              [0, -1/m],\n",
    "              [0, 0],\n",
    "              [1, 0]])\n",
    "\n",
    "C = np.eye(4,4) # creates a 4x4 identity matrix\n",
    "\n",
    "D = np.zeros((4,2)) # no direct passthrough of input to output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can use the `control.ss` method to create the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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, $\\ddot{y}$ and $f(t)$.\n",
    "\n",
    "In this case, since we already have the funcitonal form define, we can use those funcitons to fill the needed arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "yddot_input = y_ddot(t, p)\n",
    "force_input = f(t, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t_resp, resp_out, states_out = control.forced_response(sys, t, [yddot_input, force_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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAokAAAGaCAYAAABjfdmJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXl8XNV5//8+s2i0eBlJ3vACtmyMMdgYyUDYkhJk0jRp\nVgHtt0nT5BsE+bVpv11it/12/XYhpm2StmkSmyZN0mYxUtJsJSE2hACBECxjDNjGRgJjeZOtzVpH\nM3PP749772g8Hmm2u86c9+s1L1uae899Zj46d555zvM8R0gpUSgUCoVCoVAo0gm4bYBCoVAoFAqF\nwnsoJ1GhUCgUCoVCcRHKSVQoFAqFQqFQXIRyEhUKhUKhUCgUF6GcRIVCoVAoFArFRSgnUaFQKBQK\nhUJxEcpJVCh8jBCiXQjRLYSQxqNbCNGV8TvP9LnKYW+3EGK7ECKacU6zEGJQCNFcwHVabbB9t2mz\n1WM7QZb3ftB4781/t9t03YL1UygU3kCoPokKhf8RQgwCUSmlSPtdFHgQaEv/vReYwd5moANoAFqk\nlD3G75uA3cCdUsp9eY5vHj9ksd0dQLOUcrWV4zqJ4eQ2Zbz3bejv/U4p5b0WX69g/RQKhTdQTqJC\nUQZk++BPe0560EnMaq/hUHQD+6SULSWML4F65SRezCzv/UWOu0KhqGzUcrNCUYYYy7Ztxo97Mpdw\nvYoRPdwHNBe7PCmE2GGtVRVFj9sGKBQK76CcRIWizDCice3mz1LKLWZEzXAed2fmoBm/N3PVmoQQ\nW438ta0Zx3QZjx0Z1zSf222Bk7bX+LdVCLHDyGeT6XmGQojWtOt1GP9vNl6TeVyH8XxrxuuLGmN0\nZeZs5vM+GMe1p+Xzbc94LmrYtDst57It7fmt6a8pLdexy9COjPFsf9+N1xcFLlpqnu0axntkvlZT\nC1Oztmz6FfL6Z9K52NepUCgKREqpHuqhHj5/oC/RyrR/JXouYvoxHcDutJ+7gB1pP7cZ520HzGXf\n7rRzzf9HjeO2Gj/vALpmus5s9s7w3HZj/B3Gz63Gz60Z50eN/zcZzzcbP7cbP0czxr3o98DWTDvy\neB/SX7t57fT3cXfG+7x9lmsMGq8vaugxmEUzy973jL+VrrT/D2b+veRzDWOMjszXbryvrbPol+/r\nn1Fn9VAP9bD/oSKJCkUZIfVcudXABbl4RoSmDf1D32QX0J5lKbpJ6su+dwJ3pp1rRsyajPF70qKW\nmeO2ZouKFclAlt81YUQMDVu3kfGaLeCC9yH9CSnlA2nX3kla5DaLHc9BSoNM7pdS7pF6pHcXEDWP\ns/t9l1K2GH8v9cA9GJFX8/k8r9Fsvj6D3ejO4ANSyj3G77Lpl/P1p71mu3VWKBQzEHLbAK9g3Jia\n0m5sCoUvkVL2CCEeyvi1uUSXnnNmVpq2Ap1pv99tjLMPUpWvqXON39dnPHevEMJ0pBqMY5soLsfN\ndFpnazWzB92pMV/HLsOJsJIL3oc0Mq/TDXp1tpRyn5TyTmPJuQ3YAmw2jsuWF5o+dua4F2hm1/tu\nOGidQogHgK1CiHYp5c606892jU7gbuAB4/kt6Nrky2yvH5zRWaFQzEDZOolCCPObvVkhuU3OXunY\nDDxoRFWG0POitmX5gFAo/MAOLoy4NBRw7t6Mn2c713xum4VfsMxI0mzj3Ynu3G4B7gK2CyGGDOfm\nAkznbYZxGme5Rub7ANkdPRMz79OM/pkPs7VPNmZzeJx+382IoHnPzOca9wOPGhHIHvSq9G0FXDOX\nw5e3zgqFwgbcXu+24wG0Z/6Mkdczyzltxr/RQq71tre9TSoUbtPU1CT16Zyd7u5uCciOjo7U73bs\n2CEBOTg4KKWUsqOjQwKyu7v7gnO7urokILdv337B7zs6OmZ9LnOcfOwdHByUgGxubr7o+rt37079\n3NraesF57e3tsq2t7YLXYb4uc6xsr6+1tfUiO2Z6H8yxMo9vb29P/c58n3fs2JF63nyfu7q6Zr1G\n5u/seN+lnPm93759+wVj5nONaDQ667XSxzH1y/Zas/0ul84KhaIk8vJxyi6SmCW/CinlTqNCr1Xm\n+NYtC+yrdu7cuUJNLJjjx4+zYsUK26+jKAwv6TIwMFvaFzQ1NdHW1saOHTtoa9NXKnfs2EF7ezvR\n6OzdcZqbm2lubub++++nubmZzZs3c88993D33XfT3NxMa2sr27Zto7W1lebmZvbs2cP9999PV1dX\nQfYODQ1x++23E41G6ejomPXYPXv20NnZmXot0WiU1av11oVTU1OpY6LRKE1NTanXYf6+vb2dffv2\nsXevHizs6elJHTcbQ0NDRKNRdu7cSXt7O0NDQzz00ENs37499TyQeu09PT2p53p6elI2pI+X7Rqm\nvVa/7zPR09PD/fffT1NTE+3t7anrz3aNnp4ehoaG2LZtG42NjUSjURoaGmhqarrgdc72tznb64fZ\ndVaUjpfuYVYxMDDAqVOnmJycdNsUT1FdXc0ll1xCQ0Mhi0qUXyQRfWknW2VjFxkRxoznL6rsy+fR\n0tJSiOdeFIcOHbL9GorC8YIuO3bsSEWGABmNRi+KvqSzdetW2draKpubm+XWrVuzjtPc3HxBJExK\nPcLX1tYmo9GojEajF0WX2tvbU8+1tramoni57G1qapLNzc2yqalJNjU1ya1bt15wbkdHR+r4pqam\nVBSttbX1gtfS3t6eOufQoUOyra0t9VrSx9u+fbtsampKnW9Gz6LRqOzo6Mj5PjQ1NcnBwUHZ3t6e\nunbme7F161YZjUZlU1OTbGtrk4ODg7K1tVVGo1G5e/fuC15Tc3Oz3L1790XXNaNuVr3v2d77aDR6\nwXvf3t6e9fzZrmG+z5kP833Lpl++rz+XzorS8cI9zErGxsbk/v375fnz56WmaW6b4xk0TZPnz5+X\n+/fvl2NjY+av8/JxynLHlWw5SELfTeBOOUMk0cgjSv9a24y+RdWskcXNmzdLMxqhUCgUlcK+ffu4\n88476ejoSEUOh4aGuOeeewAuiAYrFE5w9OhR5s+fz6JFi9w2xZP09fVx/vx51qxZA5DXzkpl2QIn\ni4PYBvTM5CAa7DOPMY7rZIZkc6OR7l4hxN5Tp05x/PhxQA/dHz58GID+/n7279+PpmlMTEzQ1dXF\nxMQEmqaxf/9++vv7ATh8+HDO80+ePFnS+aVeX52f/fz+/n5f21+u55va+NV+v5y/a9cu4vE4Cxcu\nTJ1/+vRpAG688cYLzn/22Wc9Z786H1544QVf2595/ujoaM70mUomGo0yMjKSev/yoSwjiekYOYqP\nArfnigpmObebHJvSOxFJ3L9/P5s2bbL1GorCUbp4E6WLM5hRw3379qXyOQcGBrj33ntTeY0mShNv\nUm66dHV10dzcjNEySZGBlJJ9+/bR0tICeUYSy65wJQvb0R29YhqwDqH3OHO1Dc7GjRvdvLxiBpQu\n3kTp4gyZBUazoTTxJuWoi3IQZ6aY96Ysl5tNjP1It8sczVeN/UezhVQHmH23AEeIxWJum6DIgtLF\nmyhdvIfSxJsoXRS5KFsn0Wim3ZnuIJobzGdhgCwb2+OBKCLAwYMH3TZBkQWlizdRungPpYk3Uboo\nclGWTqLhDO41HURji6zWtOebhBAdZk/FbEvRhpP5UK4opBOsX7/ebRMUWVC6eBO7dXnggQf4yEc+\nQrnnc1uJmiveROmiyEXZ5SQaezDvNv6f+XS98a+5aXwDRtsbqTfc3mr8bDqP2aKLjhOJRNw2QZEF\npYs3sVuXL37xixw5coSdO3cSCpXdLdQW1FzxJkoXRS7KLpIopeyRUooZHqZDuEdKWZ8ZJZRSPiCl\n3Gn8+0D2KzjPgQMH3DZBkQWlizdRungPpYk3UbooclF2TmI5Um7bJpULShdvonTxHkoTb6J0UeRC\nOYk+oLGx0W0TFFlQungTpYv3UJp4E6WLIhcqocYHHD58mHXr1rlthiIDpYs3qWRdpJQMbd3GxHe/\nR91vfYj5f/onbpsEVLYmXqZSdDmxzJsR02Unjhd97s6dOwHo7u5my5Yt9PT0sHv3bh588EFLd51R\nTqIPqKurc9sERRaULt6kknWZ+O/vMP71bwAw+m+fI3LLLVS/+VaXrapsTbyM0sWfdHZ2pnY1amlp\nYfXq1bS3t7N7927LtyVUTqIPUHkj3kTp4k0qWZexL38FgOCyZSRPnGDsq1/1hJNYyZp4mUrRpZSI\nnRdpbm5O/X/fvn3cddddAHnvgFQIKifRB5gbmCu8hdLFm1SqLsm+Pqa6uhA1NSzY9Q0QgslHH0Ob\nmHDbtIrVxOsoXfyJuVe6uW+61dHDdJST6APGxsbcNkGRBaWLN6lUXWJPPw1A1Q3XE1q1ivCGq2Fq\niqlf/MJlyypXE6+jdPE3e/bsobV1eiO5nh7r9/5QTqIPqITEYj+idPEmlapL7Ge6kxi5+Wb931tu\n0X//9DOu2WRSqZp4HaWL/9i3bx/btm0DYNeuXbS0tAC6gzg0dNHmcSWjnEQf0N/f77YJiiwoXbxJ\npeoSf0FvjFx13Wb9380tF/zeTSpVE6+jdPEfZrSws7OTjo4Ouru76ezspKen54JcRatQhSs+4Pjx\n46qflQdRuniTStRFxuPEjx4FIHzllfq/V18NQPyll5BSZtum1DEqURM/oHTxH21tbbS1taV+3r59\nu63XU5FEH7Bx40a3TVBkQeniTSpRl0R3N0xNEbzsUgJz5gAQXLqUQH092uAgyZOnXLWvEjXxA0oX\nRS6Uk+gDYrGY2yYosqB08SaVqEv80CFgOooIIISYjiYePOiKXSaVqIkfULoocqGcRB9w0OUbvCI7\nShdvUom6xA+/AkA4oxAhtGY1AAkbqh4LoRI18QNKF0UulJPoA9avX++2CYosKF28SSXqkjx2DICQ\n0T/NxPw50e2uk1iJmvgBpYsiF8pJ9AGRSMRtExRZULp4k0rUJWE4icHLLrvg96HVhpPociSxEjXx\nA0oXRS6Uk+gDDhxwv4WF4mKULt6kEnVJvPEGAKHLLr3g96lIYk+34zalU4ma+AGliyIXykn0AZWy\nv6bfULp4k0rTRRsaQg4NI2prCSxYcMFzwWXLIBJBO9OHNjrqkoWVp4lfULoocqGcRB+g+lh5E6WL\nN6k0XdKXmjN7IYpAgJDhCCRd3Ke30jTxC0oXRS6Uk+gDDh8+7LYJiiwoXbxJpemSOJZ9qdkkuHyZ\nflzvCcdsyqTSNPELShdFLpST6APq6urcNkGRBaWLN6k0XZJmPuKlMziJy3QnMXnCPSex0jTxC0oX\nRS6Uk+gDVN6IN1G6eJNK0yV5St9NxXQGMwl5wEmsNE38gtJFkQvlJPqA4y7mEilmRuniTSpNl+Tp\n0wAElyzJ+nxw+XL9uN5ex2zKpNI08QtKF0UulJPoA8bGxtw2QZEFpYs3qTRdTCcxMKOT6H5OYqVp\n4heULopcKCfRB6zL2GpL4Q2ULt6k0nRJRRIvmcFJTC03uxdJrDRN/ILSRZEL5ST6gP7+frdNUGRB\n6eJNKkkXmUig9Z0FIQguWpT1mOCSJRAMop3pQ8ZiDluoU0ma+AmliyIXykn0ASpvxJsoXbxJJemi\nnT0LmkZgwQJEOJz1GBEKEVi4EIDk2bNOmpeikjTxE0oXRS6Uk+gDNm7c6LYJiiwoXbxJJemSq2jF\nJLhksXH8GdttykYlaeInlC6KXITcNkCRm1gsRk1NjdtmKDJQuniTStJl2klcPOtxwUWLiANaX58D\nVl1MJWniJypFlz/4ry6ePnquoHNuunwBn/pAiyfGz6Szs5OBgQEaGhpoa2tL/e65555j+/btRY05\nEyqS6AMOHjzotgmKLChdvEkl6WJGBnNFEgOLjEhinzuRxErSxE8oXfzHvn37aGpqoqGhgV27dqV+\nv2vXLq677jrLr6ciiT5g/fr1bpugyILSxZtUki652t+YuL3cXEma+IlK0aXYiJ1Xxk8nGo3S1NTE\n/fffz9133536/Z49e3jwwQctv56KJPqASCTitgmKLChdvEkl6aKdMSOJuZebwb3l5krSxE8oXfxH\nU1MToDuF5lJzT08PDQ0NRKNRy6+nnEQfcODAAbdNUGRB6eJNKkmXpNHCJLhg4azHBQwnMXnGnUhi\nJWniJ5Qu/mTPnj0pZ9H8ubW11ZZrKSfRB6j9Nb2J0sWbVJIu2jk9WT7Q2DDrcanl5jPuRBIrSRM/\noXTxL+lOYkdHB1u2bLHlOspJ9AGNjY1um6DIgtLFm1SSLto5PZIYWLBg1uPcXm6uJE38hNLFn7S2\nttLQ0EBnZyc7d+5UkcRK5/Dhw26boMiC0sWbVIouUsrUcnMgx4d9YMECCATQ+vuRU1NOmHcBlaKJ\n31C6+JcdO3bQ1tZGU1MTra2ttuQjgnISfUFdXZ3bJiiyoHTxJpWiixwbg1gMUVtLoLZ21mNFMEhg\noR5tTJ4trJ+bFVSKJn5D6eI/hoaGqK+vT/28fft2duzYYdv1VAscH6DyRryJ0sWbVIouqXzEHEvN\nJsGFi9DO9KGd7YNlS+007SIqRRO/oXTxH9FolO3bt9PZ2UlPTw87duy4ID/RapST6AOOHz+uJrMH\nUbp4k0rRJXkuv6Vmk8AC/Titf8A2m2aiUjTxG0oXf9Le3u7YtcrWSRRCmO+i2eVym5RyKI9zzDto\nk5TyAbvsK4SxsTG3TVBkQeniTSpFF61fjyQGF+TpJDboxyXPOb/cXCma+A2liyIXZekkCiHapZQ7\n038GuoDVs50DIKXsNH5uFkLskFLea7e9uVi3bp3bJiiyoHTxJpWiS76VzSamM6kNOB9JrBRN/IbS\nRZGLsitcEUJcVOJjOIwNQojZasTvTXcspZT7AHtqyguk36hgVHgLpYs3qRRdpnsk5hlJNI7TXIgk\nFqOJ1DTO/+M/cfbOu5n4n4dtsEpRKXNFUTxl5yQCTcCOLM5ij/HcRRjHNmd5aiiHY+kIx48fd9sE\nRRaULt6kUnRJ7bZScE6i845BMZqM/utnGfn0Z5h6+mkG7vsYsb1dNlhW2ZTjXNE0zW0TPEsx703Z\nOYlGBLAlS/5hE7qjmI0mIFu+4gDZnUdH2bhxo9smKLKgdPEmlaJLodXNqZxEF5zEQjXRzp9n5PNf\nACC86RrQNEY+9Sk7TKtoym2uVFVVMT4+7rYZnmV8fJyqqqqCzik7JxFSjmIKIUQb0COl3DPDKQ1M\nF6ykMwRc9DVdCNEuhNgrhNh76tSp1Lex48ePp5qT9vf3s3//fjRNY2Jigq6uLiYmJtA0jf3796fC\n/IcPH855/vDwcEnnl3p9dX7282OxmK/tL9fzY7GYrdePxWKYuPn6zZzEfiM6kOv8xNy5AIweP+5p\n/QDOdnQgR0aouuEG6v79QbRIhNhPn2Dq2DHP//356fxDhw752v7M84UQdHd3Mzo6qiKKaWiaxujo\nKN3d3cTj8YLSDISU0kbT3MdYSn4UuH2m6mZjSXmHlHJ1xu870J3LbTONv3nzZrl3714rTb6Irq4u\nWlpach+ocBSlizexW5crrriCI0eOEI/HCYXcq/0707qFxKHDLPrxI4SvWp/z+MSxY5y56RaCy5ax\n5Bc/d8DCaQrVpP9DH2Zyzx6in7yfug9+gIH7PsbE93/A/L/6S+bc81EbLa0syvEeNjAwwIkTJ5hy\nYWchL1NVVcWyZctoaEjt8y7yOa8sq5sz2A7cmav9DXo0MZMo4Hpm7/r1uT8AFM6jdPEmlaKL2e8w\n0FCf40idVOFKfz9SSoTI6zPCEgrRRE5OMvnkkyAE1W+7A4Dqt/8yE9//AZO79ygn0ULKca40NDSk\nO0K+ZGJigpqaGrfNAMp0udlECLEV2C6lnCkX0WQvukOYSQOwL8vvHSUSibhtgiILShdvUgm6SCnR\nhvTvvYE892wVdXVQHUFOTiIdztsqRJOpF1+EWIzQuisILlqkn3/LLfpzXV2u7D1drlTCXPEjXtKl\nbJ1Eo+9hZ7qDOFOlshFl7MlSER2dJY/RMQ4cOOC2CYosKF28SSXoIicmYGoKUV2NyDPiIIQg2OBO\nhXMhmkwZVcxVLZtTvws2NhK6/HLk5CTxF1+y3L5KpRLmih/xki5l6SQazuBe00EUQkTTHUQhRJMQ\noiPDKdwO/EnaMc2A6w4iqP01vYrSxZtUgi7a4CAAgfr8lppNUm1wzjnrJBaiyZSR4x3ZfGGuXNX1\n1wMQe+4X1hlW4VTCXPEjXtKl7HIShRBNwG7j/5lPm3fUJvRG2Q0YrW+klDuNquVW9KXnJi/stgLQ\nmGcfNIWzKF28SSXoog3qS80iz6VmEzMv0ek2OIVoMvX88wBUZRRUVF27ifGvfY34Sy9balslUwlz\nxY94SZeyiyRKKXuklGKGh+kQ7pFS1mfmKkopdxrPdXpl32Yg1RZA4S2ULt6kEnSRBeYjmgQa9Z6K\n5r7PTpGvJsmBQbQzfYjaWoIrL7vgObOCWzmJ1lEJc8WPeEmXsnMSy5G6ujq3TVBkQeniTSpBl+nl\n5sKcxGCjXvVpVkY7Rb6aJI68AkBo7eWIwIUfT+G1ayEYJNHdjTYxYbmNlUglzBU/4iVdlJPoA7yU\nn6CYRuniTSpBl1Rlc6E5iUZrEG3AWScxX03ih3UnMXzFFRc9J6qrCV2+BjSNxCHvRFr8TCXMFT/i\nJV2Uk+gDynF/zXJA6eJNKkGXQtvfmJhOpXm+U+SrSeLIEQBCWZxEgLDR1y/uoeU4P1MJc8WPeEkX\n5ST6gLGxMbdNUGRB6eJNKkGX1HJzsU6icb5T5KtJ/BUjkrguu5MYWq1vipXo7rbGsAqnEuaKH/GS\nLspJ9AHr1q1z2wRFFpQu3qQSdCl6udlwKp12EvPVJHHkKADhy9dmfT6snERLqYS54ke8pItyEn1A\nIZtxK5xD6eJNKkGX6eXm+QWdZxa6aEPDlts0G/looo2M6LmS1RECSxZnPWY6kphrEy1FPlTCXPEj\nXtJFOYk+wEv5CYpplC7epBJ08dtycz6aJI69AUDo0ssuqmw2Ca1aCUKQeOMNZDxuoYWVSSXMFT/i\nJV2Uk+gDNm7c6LYJiiwoXbxJJehiRgILdhLTlpullJbbNRP5aJI8dgyA0GWXzniMqKkhuGwZJBIp\np1JRPJUwV/yIl3RRTqIPiMVibpugyILSxZtUgi7F5iSm9npOJJAOJsfno0nCcBKDl14263Gh1U36\n8T0qL7FUKmGu+BEv6aKcRB9w8OBBt01QZEHp4k3KXRcp5fRy8/zCchLBneKVfDRJLTevzOEkrloF\nQFJFEkum3OeKX/GSLspJ9AHrjd5gCm+hdPEm5a6LHB+HeHw6KlggbuQl5qPJ9HLz7E5icMVyABIe\nytvyK+U+V/yKl3RRTqIPiEQibpugyILSxZuUuy7FLjWbuNFQOx9NUsvNs+QkAoRW6M8nlZNYMuU+\nV/yKl3RRTqIPOHDggNsmKLKgdPEm5a6LGQEUBRatmAgXlptzaSLjcZInToAQhHJsSRa8VH9eRRJL\np9znil/xki7KSfQBXtrHUTGN0sWblLsu2mBxW/KZTC83OxdJzKVJ8swZSCYJLF6EyBFFCS3Xl5uT\nbxx3tEK7HCn3ueJXvKSLchJ9QGNjo9smKLKgdPEm5a6LTC03F+skOh9JzKVJ8tQpAIKXLM05lohG\nEXPnIsfGHHV0y5Fynyt+xUu6KCfRBxxWm9l7EqWLNyl3XbTz54HiKpshvbrZOQcrlybJkycBCF5y\nSc6xhBAEzWjicVXhXArlPlf8ipd0UU6iD6irq3PbBEUWlC7epNx1STmJ8+YVdb4bhSu5NElFEpfm\ndhIBQkZeYvJ4b2mGVTjlPlf8ipd0UU6iD/BSfoJiGqWLNyl3XbRhfbcVUaqT6OByc86cxJOngfwi\niQDBFf4qXkmePk3/R/43Z95yG6Nf/rLb5qQo97niV7yki3ISfYCX9nFUTKN08SblrossOZLofE5i\nLk2Sp/Jfboa04pVe70cSZSJB/299hMlHfkzi1VcZ/r9/zvi3vu22WUD5zxW/4iVdlJPoA8Yc3D5L\nkT9KF29S7rpoIyOAv5abc2lS6HKz6UwmT58uzTAHGO/sJP7iiwRXrGDu734cgOG//Tu0iQmXLSv/\nueJXvKSLchJ9wLp169w2QZEFpYs3KXddtGE9kuin5eZcmkxXNxfoJBrneRUpJaM7HgRg3tZPMHfr\nJwhv2IDW18fE977vsnXlP1f8ipd0UU6iD+jv73fbBEUWlC7epNx1SS03zy/SSTSqouXwMFLTLLNr\nNmbTRMbjaGf6QAiCixfnNd60k+jtSGL85ZdJHDlCoKGBml99J0II6j78IQDGv/FNl60r/7niV7yk\ni3ISfYCX8hMU0yhdvEm566Kd1wtXAnOLcxJFKKRHIaVEGkUwdjObJsm+PpCSwKKFiHA4r/ECixZC\nIIB29iwyHrfKTMuZ+O73AKh516+mXlvNO98JkQhTe/eSPHvWTfPKfq74FS/popxEH7Bx40a3TVBk\nQeniTcpdF3lez0kURUYSYTqaqDnkJM6mSfJkYUvNoDu6gUWLQErdyfQosZ8+AUD1296W+l2gro7I\nzTeDlEzuedQt04Dynyt+xUu6KCfRB8RiMbdNUGRB6eJNyl2XUvskgvNO4myaFJqPaBK8ZIl+/klv\n5iUm+/uJv/wyVEeIXH/dBc/VbGkFYPKxn7hhWopynyt+xUu6KCfRBxw8eNBtExRZULp4k3LWRSYS\nyLExCAQQJTTcNYtezCIYu5lNE+3MGYC88xFNvF68EnvqZwBErrseUV19wXORW24BYOrZZ13df7qc\n54qf8ZIuykn0AevXr3fbBEUWlC7epJx10cyl5rlzEYHib9+B6HTxihPMpomZlxdctKigMb3uJE49\n9xwAkZtuvOi54KqVBBYuROvvJ9Hd47Bl05TzXPEzXtJFOYk+IBKJuG2CIgtKF29SzrrIkdKXmsH5\n5ebZNNGMnMJAuTmJ+18AILxp00XPCSGI3HCDftyzzzpqVzrlPFf8jJd0UU6iDzhw4IDbJiiyoHTx\nJuWsixX5iOC8kzibJslz53SbFiwoaEwzJ1HzYBscOTVF3FgyrLomexFClZGnONXV5ZhdmZTzXPEz\nXtJFOYm4KBbjAAAgAElEQVQ+wEv7OCqmUbp4k3LWRZbYSNvEdDJNp9NuZtNE6zOXmxcWNKaXd12J\nHzkCsRjBVatSDnkmYaOCNf7iS06adgHlPFf8jJd0UU6iD2hsbHTbBEUWlC7epJx1mY4kzi1pHGFG\nEoeciSTOpkkqJ3FhgcvNS4zqZg8uN8eNpeaqTdfMeEz4qvUQCBA/cgQ5OemUaRdQznPFz3hJF+Uk\n+oDDhw+7bYIiC0oXb1LOumhW5SSmClec2b95Jk1kMomWWm4u7IMx5SSeOePYzjH5MmVEB6tm6XcX\nqK0ltGYNJBLEXfqbLee54me8pItyEn1AXQmtLhT2oXTxJuWsy/Ryc/YlzHxxOidxJk20gQHQNAL1\n9YiqqoLGFJEIIjofEgm0IWec3XxJHD0CQGjdFbMeF96wAXBvybmc54qf8ZIuykn0AV7KT1BMo3Tx\nJuWsi1bivs0mAcPJdDsn0cxHDBSYj2hiLlGbvRa9gJSS+Cu6kxheu3bWY6s2XA1MRx6dppznip/x\nki7KSfQBXtrHUTGN0sWblLMuKSdxrr9yEmfSJHlWb39TaD6iidlb0e09kNPRzp1DDg0h5s0jkKNB\neGjdOgASR444YdpFlPNc8TNe0kU5iT5gbGzMbRMUWVC6eJNy1kUaTmIp+zaD8820Z9IkWWIk0TxP\nO+Od/ZsTaVFEIcSsx4av0CON8aNHXNl5pZznip/xki7KSfQB64xvmwpvoXTxJuWsi2V9EtNa4Djh\nnMykiWZWNhfYI9HEi5HEuBEVDK29POexgYULEdH5yKHh1HvhJOU8V/yMl3RRTiIghGgSQrS6bcdM\n9Pf3u22C62hjY55LTle6eJNy1mXaSSytcEVUVSFqaiCZ1PeCtpmZNDGdu0J3WzExI4lJD+UkmkvH\nufIRQd95JXy5EU18xfkl52LmipyaYuyb32Tk3z5HorfXBqsUXrqHla2TKIRoFkJ05Hl4M9AhhJBC\niEEhxG4hRLOd9hWCl/ITnEZKyfnP/DOnrt7Iqas3MvgHf4icmnLbLKCydfEy5azLdHVzaTmJkJaX\n6MCS80yapCKJC4ssXFm0+IJxvEAhkcT04xJHj9pm00wUOle0iQnOtd3F0B9+gvN/fz99b21lqmuf\nTdZVLl66h5Wdk2g4h9uBu4GmfM+TUtYD9VLKeinlFimlZ/7yN87Sa6vcGf+vrzHyD/8IhmM4vush\nhv/qr122SqeSdfEy5ayLNjIClL7cDGl5iQ4Ur8ykSck5iYZzmezzUE5iz2sAeg/EPDAjjm5EEgud\nK+f//n6muroILFlC5JZbkGNjDNx7H9r4uE0WViZeuoeVnZMopdwnpdwG7CriXG+tZxrEYjG3TXCF\n5MAgw3/ztwDU//NnWPj970I4zNhXvsrU/v0uW1e5unidctbFqpxEcLZX4kyalB5JNApX+rwRSdTG\nxvTXFImktg3MxXQk0XknsZC5kuh5jbGvfBUCARq/8mUa/+urhDduIHnqFKNf2GGjlZWHl+5hZeck\nliMHjY3iK42xL38ZOTZG5C1vprbt/VRdey1z7vkoAOf/6dMuW1e5unidctVFatp0dXOJLXAgvXjF\nfidxJk3MFjiBop1Eo3DFI5HE5LE3AAitWIEI5PfxGl5jOomv2mbXTBQyV0a//GVIJqm9s42qq69C\nhMPM/4s/B2DsP77s2taC5YiX7mHKSTQQQrSmPbYKIaJu22Syfv16t01wHBmPM/blrwAw93c/nvr9\nnI/dB9URYo89RuKNN9wyD6hMXfxAueoiR0dBSkRdHSIUKnk8MV+/xTkRScymiUwk9KVuIQjU1xc1\nrohGoaoKOTKCNjFRqpklkzj2OgDByy7L+5zAksWI6mq0gQHHmpub5DtXtIkJxjs6Aaj7yEdSv696\n05sIb9iANjDA+Pe+b4uNlYiX7mHKSdTZB/RIKfdIKfcAncCMRS9CiHYhxF4hxN5Tp06lkkyPHz+e\n2nOxv7+f/fv3o2kaExMTdHV1MTExgaZp7N+/P1W9dPjw4Zzna5pW0vmlXt+N888+/EO0/n6Ca1aT\n3Lgxdb6IRpl8040AjH9zl6v2RyIRz75/lXx+JBKx9frpS0FOvv5xY2k2UVNjyftnLjcPvH7MdvsP\nHjx40flmtwI5dy4iGCzq+q+88gqyQXcwTxw44Prf38lfPKdrtHhR3uf3njhBcNVKAF59/HFH7T92\n7Fh++u18EHn+POFrruFgIn7B+x97x9sBGNy1y/X3v1zOHxsbc+T6eSGlLMsHesVyVwnndwPNuY5r\naWmRdvP888/bfg2v0f/x35O9S5fL4U99+qLnJp98SvYuXS5P3XSL1DTNBet0KlEXP2C3LmvXrpWA\njMfjtl4nk6mXD8repcvl6dveasl4w//0KX2ObX/AkvFmI5smU6+8or+eW95c0thn3vFO2bt0uZz8\nxXMljWMFA1v/WPYuXS5Hvvilgs47978/KnuXLpdj3/mOTZZlJ9+50v87H5e9S5fL85/7/EXPJfr7\nZe+Ky2Tvistkor/fahMrEoc+W/LyhVQkcWaGgM1uGwHe2sfRCWQyyeSePQDUvvvdFz1f9aYbCNTX\nk3z9dVfaRphUmi5+oVx10UaNyua5pRetwIUNte0mmyba4KBuR5FLzSZmXqIX2uAkj+lR2VABy80A\noVWrAEi89rrVJs1KPnNFxuNMPvoYANV33HHR88GGBiK33gLJJJO7d1tuYyXipXtYUU6iEGKTEOJ9\nQog/Mh7vE0Jssto4JzAaaWfbcmDAeLhOY2Oj2yY4SvyFA8jhYYIrVxJqWnXR8yIUonqL3vt88keP\nOG1eikrTxS+Uqy5yZBQAMXeOJeM5Wd2cTROrnMTAQrN4xf2G2gnDSSwkJxEgtHKlfr7DTmI+c2Wq\nqws5PExo9WrCq7N3lau+/XYAYj99wlL7KhUv3cPydhINx/DzQogk0IWes7fdeHQAXUKIpBDic0KI\nlXYYaxMDwL1Zfr8ZPVfRdcw8g0ph8qc/BaD6zbfOeEz12/RvtJOP/cQRm7JRabr4hXLVJRVJnGON\nk5hqpu1An8RsmmgDhpPYUGok0RttcOTUFMneXggECK1YXtC5ZiQx+frrNlg2M/nMldgzPwcg8pY3\nz3hM5C1v0Y994klkMmmNcRWMl+5heTmJQojPozuG9wICGAZeA543Hq8ZvxPAfUC3EOJzdhhcAA3Z\nfmlEDjvM6mWZpTeiEKIdeEhK2WOzjXlRV1fntgmOEntC/zY6603pxhshEGDq+edda+Raabr4hXLV\nZTqSWHr7G0hrpu1AJDGbJlYvN7vdBifZewI0jeDSpYhIpKBzpyOJr9lg2czkM1emTCfxTW+a8ZhQ\n0yqCy5ejDQ4Sf+kly+yrVLx0D5vVSRRCzBNCvIruHP4DsAV9V5IGKeUaKeVm47FGStkA1BvH/CNw\nnxDiiBDCmjtanhhOoBnhbBZC7DCcPpMmoJU0J1JKudNoe9MuhNgKRKWU2aKLruCl/AS70SYmmNr3\nPAQCRG66acbjAvPnE964ARIJpn7xCwctnKaSdPET5aqLNqo7iVZFEsslJzG1f7PLkcTEG8XlI0Ja\nG5z+fkfb4OSaK3JqiqmuLkDPBZ8JIUTqS33sqZ9ZZ2CF4qV7WK5I4j5gD7pj+MdSykellDN+7ZRS\nDhvHbEN3GH+Cw0u2UsoeKeU2KWWLlFJIKe+VUu5Me36P1Lfe68k47wEp5U7j3wectDkXXtrH0W7i\nBw5AIkF43bqcu0pEbr4ZgNjTzzhh2kVUki5+olx1kaMWRxJd3rs55SQ2ZF30yZtA4wJ9vP5zJY1T\nKsneEwAEC1xqBhCBAMGVunNp5jU6Qa65MvXCC8jJSUJr1xLMkScXuf56/ZznnrPMvkrFS/ewGZ1E\nIcQngO1SyvtmcwxnwnAY7wUeEEJ8tBQjK52xsTG3TXAMc7P4qpbmnMdGbtL7JcaeftpWm2aiknTx\nE+Wqi7lvs7BoKUpEnWumnU0TbUCvCyx5uXmh4SSeK6D3mw0kTxhO4vLCnURIq3DucW7JOddcmXpu\nLwBVhgM4G1XX6c1ApvZ2mW3kFEXipXvYjG37pZT/YMUFpJQPWjFOJbNu3Tq3TXCMqX26kxhuzu0k\nVrW0gBDEX3oZOTmJqK6227wLKEYXGYvpyzFCELnpRsdtrgTKdb6YkcSARZFEUV0NVVUQi9k+f7Jp\nog3q6eCB+tI2twosMJ3Ec0gpEUKUNF6xJMxI4tKlRZ0fMpYYk729ltmUi1xzJf7CAQCqmnM3Lwle\neimBRYvQ+vpIdHcTXrPGEhvtJH70KGP/9TWYmqLmve9JRUPdxkv3MNv6JAoh3GtgV2YU1B3dx0gp\n0yKJLTmPD8ydS2jt5RCPM/XSy3abdxGF6hI/fJgzb7mN/t/8EP0f/E3O3N5K/MgRm6yrXMp1vmhm\n4YpV1c1CTOcl2hxNzKaJVcvNorYWUV2NnJxEulTEBpA8qTuJoWXLijo/eOmlACTecG6pMddcmXrR\ncBI3bsw5lhCCqs1mNHFv6cbZzOSjj9H3trcz9u9fZOyr/8m5976f0Qf/3W2zAG/dw4p2Eo2ilk0z\nPO5BLxBRWICX8hPsJHniBFpfHyIazdofMRtVRsQx/vzzdpqWlUJ0SQ4McO43Pkjy+HFCTU0EV60i\n+foxzv36b5D00A2hHCjX+SJTzbStcRLBubzErDmJFi03CyGmo4kuNtROnjgJQHBZcZFEc5k62evc\n3+9sc0UbHCR57A1EdTWhyy/Pa7xI2pKzl0kcP87Ax/4/iMWoec+7mdN+DwDDf/XXTD7hfq9HL93D\nim2m/XlgEL0tTrbHF6wyUAEb8/gWVw6kljau3ZT3klHVtdcC08vUTlKILsN/+ddop09T1dLCoh//\niMW7H6HquuvQTp9m+C/+0kYrK49ynS/TkUTrGkakeiUO21tRm6mJ1LTU3s2BaGnLzQABIy8x6VJe\nokwmSZ46BUDwkkuKGsPsrZg87txy82xzZepFvZVN+KqrEKEZM9MuIHytvixt3su9ytCf/hlybIzq\nX/kV6j/7r8z/y79g7h/9of7cJ7Yh0/ZndwMv3cMKdhKFEJ9kul+iQO+RmPmwPxO6goi5/AfrFPGD\nBwH9ppQvVc2Gk/j8fltsmo18dZl66SUmvv1tqKqi/rP/gqipQdTUUP/Pn0ZUVzPxne8y9cILNltb\nOZTrfJnOSbQykqgvN9vdKzFTE3n+PGgaYs4cRFVVyeMHXa5w1s70QSJBYOHConM7g0ZOYqK3F6lp\nVpo3I7PNlfgB3dELX5O/wxJev17PEz9yBDk5WbJ9djC173lijz2GqKsjev/fpQISc3/344SuWEuy\nt5ex//wvV2300j2smEhiO9ANrJZSBoweiZmPBnQHUmEBBw3nqdyJv6znFYbXX5n3OaG1axF1dSSP\nHyfp8FJTvrqMfu7zANR96DcJGXlHoPdTq/vwbwEw8unPWG5fpVKu80Wa1c0WFa6Ac70SMzWZ3m2l\ntHxEk8ACvT2LWxXOCbOyucilZoBAXZ3+fsRiji2bzzZXpoxoYHjDhrzHC9TVEVqzBhIJ4h7aNSSd\nkX/7NwDqPvxbBI00BQARDDLvj7cBMLrzQWQi4Yp94K17WLE5iTuklLnq9LcVObYig/Xr17ttgiPE\nDx4CjG+jeSKCQcJX65FHpzv956NLsq+PiYd/CIEAc+65uBPUnPvuheoIk7v3kHjjDTvMrDjKdb5Y\n3Uwb0nISz9sbSczUZLqRdulLzXBhhbMbmEUrwWXFtb8xCV5qRBMdKl6Zba7ED+pf2qs2XF3QmKZT\nGT/wYvGG2USyr4/J3XsgFGLOR//3Rc9Xt7bq+eInTjC5e7cLFup46R5WjJO4B7guj+NUoySLiBS4\nxZMf0YaGSJ44oSdJNxVW82QuT8dfdvbbVz66jO96COJxqre0Zq16DC5YQM073gnA2Ne/YbmNlUg5\nzhepadPNtC10EoUZSbR5/+ZMTazabcXEbPScdMtJNIpWQiVEEgFCy802OM44iTPNFW1iguSxNyAU\nIrR6dUFjmk7llAe35xv/9rchmaT69rcSXLjwoudFIMCc3/oQgN4axyW8dA8rxkn8Y2CLEOLvhRCz\nbYmxvUibFBkcOODtJGAriB/So4ihdVcggsGCzk1FEl92tg1OPrqMf/d7ANT+2q/NeEzdB/6XfuxD\nDyGTSWuMq2DKcb7I8XGQUm/3UuD8mA2zaETavNycqUnSrGy2arl5ocuRxNRyc3Htb0yCDhevzDRX\nEkePgpSEVjcVnDMa3ujdSOJ457cAqL37rhmPqXnf+yAUIvbkU651nvDSPaxgJ9HYzu5+dGdxUAjR\nL4Q4mvFQPT0sxEv7ONqFGQUsZKnZxK1IYi5d4t09JA4dQsydS7Wxr2k2qq67juDKlWhn+lzbh7qc\nKMf5Mp2PaF0UEXCsT2KmJlZHEs2t+dyqbk5tyVdiJDFVvOJQC5SZ5kr88CsAhNeuLXjM8NVXG2Mc\ndr1KOJ3E66+TOHQYMW8e1bfdNuNxwYZ6Im9+MySTTHz/Bw5aOI2X7mHFVDffA3zS/BF9j+bVGQ9r\nZr4CgMYce2aWA6nK5mKcxMsvh1CIRE8PmoPbGeXSZfLhhwGovuMOxCzLB0IIat75DgAm/udh6wys\nUMpxvkznI1pXtALOFa5kamL5cvMCd6ubExZFElO7rjgUSZxpriSMJv+hK64oeMzAnDkEV62CeJzE\nq90l2Wclk7v3AFB92y/ljI7WvufdAEx873u225UNL93Dillu3obuHD4AbAFasjxmjuUqCuawR6vE\nrMSshCukstlERCJ6s1cpiR9y7r3KpcvEj34EQM07fyXnWDXv0I+ZePhhx9pflErs6WcY/vv7Of9P\nnyL+yitum5OiHOfLdD6iNfs2m5h9EqXNfRIzNUlVN1sVSTSrm8+6VbhiNtK2ZrnZqUjiTHPFnM/h\nIpxEgPCV+rZyXqpwnnjkxwBUv+2OnMdW37EFwmGmnttL0vhbdRIv3cOKcRKb0Kub/1hK+aiU8vks\nj05Ur0TLqKuz9oPBa0gpU984Q5cXvrwBUOVCXuJsuiQHBvWGslVVRG69NedY4Q0bCK5YoS8573N+\n95hCkPE4A7/3+5y78y5G/+1zjHzq0/S13sHIv37WbdOA8pwvZiNtyyOJ851Zbs7UxPLl5oYGEAJt\ncNDx1iXa6ChyeBhRXV1yjmXI3HXlxAlH8pNnmisJY7m5mEgiQHidt5xEbWhIT+UJhaj+pV/KeXxg\n7lwiN9wAmkbsp4/bbl8mXrqHFeMk7gOG8jguv33VFDnxUn6CHSRPnkKOjRFoaCDYUNyHhht5ibPp\nEnvqKZCSyHXXEaipyTmWEILq1tv1cx9/3CoTLUdKydAntjLR2YmorWXOx+6j9td/DaTk/Ce3M/IF\n9zdbKsf5kook2pWTaPNys905iSIU0seSMjW2UyRPnwYgcMklee8UNROipobAwoUQj+sNum0m21zR\nRkb0yGgkQmjlZUWNa0YgzdxGt4k98wwkk1Rtbkm1fcpF9e1vBfQ9np3GS/ewYpzETwLtQohcfz09\nRYytyIKX9nG0g0T3qwCELl9T9BgpJ/Ggc5HE2XSJPfkkAJE3544impjfcCc97CROfOvbjHd0Impq\nWNCxi/l/9n+p/8d/oP6z/wLA+b//pOuR0HKcL5pZuGJxJFHM16ub7e6TmKmJNmRtM21wr1eidvoM\nAMEliy0Zz9zDOXHc/r6p2eZK/BU9HzG8Zk3RlfQhI5KY8EgkMfb0MwBEbr4573Mit+tf2id/8rjj\nXSe8dA8rxkmMom+91yOE+KYQ4o+EEB/NeNxvHKewgDEHizHcIHHUcBLX5LeJfDZC6/RvrokjR5HS\nmRadM+kipST2U32T+MgsVc2ZVN10I1RVEd//git5MLnQRkYY/pu/BWD+3/w/qjZtSj1X+573MKf9\nHkgmGdy61dVWPuU4X+zYkg8gME93OuXweVtzYTM10cwWOBZFEgECqV6JzlY4J88YTuJia5zE0HI9\nr9HMc7STbHMl8UppS80AoVUroTpC8uRJ21MZ8iH29NMARG66Me9zwqubCK5ciRwacvyLr5fuYcU4\niTuBa9GLV+5C74e4I+Ox1SoDFbDO+FZWriRe1Z3E8JrCmramE2xoILBgAXJsLNWzzG5m0iX52usk\nT5wg0NBQ0D7UgdpaItdfD1ISe/IJq8y0jNHPfwHt3DmqWlqo/bW7L3p+3ratBJcvJ3HoMOMPdbhg\noU45zpfpSKK1TqIIhfQxpUw5onaQromUEm1Qz1gKFJleko1gqleis9tzWu0kmsUvZoNuO8k2VxLd\nen54uISVHREMEjbyy90uakv29+s5ltURqq69tqBzq42VoCnDyXQKL93Dit2W7zWg03h8K8tjvyXW\nKQDod6mhp1PEj5a+3Az6Ps4ACWO5xG5m0iX27LMAVL3pTYhAYVMscttb9DEe/2lpxlmMNjrK6Jf+\nA4B5f/5nWXOvRHU18/5E341z5NOfQcbjjtpoUo7zZTqSaO1yMzjTKzFdEzk+DlNTeqFHHvm6+TK9\n3OxwJNFYbg5Y7iTa/2U321xJvP46AKFVpZUVhM3VHZfzEqfMpebrrp+1FVk2IjfdBEwvVzuFl+5h\nxTqJrVLKu2Z5tKBHGhUW4KX8BDswv7mGLi9+uRkgfIXxzfWIM07iTLpM7d0LQOS6zQWPaebMxH7+\nbPGG2cD4roeQIyNU3XD9rK+r5l3vIrRmDckTJ5j4gTuNaMtxvpjVzVZHEgFEqsLZvuKVdE3sWGqG\n9OVmZ3MSzcIVy3ISjYbcCQciidnmiukkBletLGnskEcqnGPPGE5iAUvNJlXGObG9zznaGNxL97Bi\nnMQHpJSv53HcnUWMrcjCxo0b3TbBNrThYbS+PkRNDcGlpe1WEE5FEp355jqTLlPP6U5iVRFOYnj9\nesS8eSTfeMORD4l8kJrG6Je+BMCcj3501mNFIMCce9sBGP3CTsfyQ9MpdL4kz51j5F/+lf572hn4\nvd9n4vs/8Nz2iHJUX262JZJo9kq0scI5XROrK5tNphtqOxuF0exabj5pfyQxc65ITSNx7BgAocuK\nq2w2MSOJbjuJU137AKi6/rqCzw02Nur57pMxpp53Li/RS5/5MzqJM+3LLKX843wGllJ+K9dYivyI\neWhrI6tJ9UdcvbrgpdlMQg5HErPpkhwYINHdjaiuTm1PVQgiGKTqOv1mNvXzn5dsoxVMPfNzkq8f\nI7hsWV6NaGvf914CjY3EX3qJ+H7nM08KmS8TjzzCmVvfwvntDzD58A+Z6Oxk4L6Pce59bSRPnbLR\nysKwM5I4vdycT2ez4kjXJOUkWljZDO411LY8J9H4suxETmLmXNFOn4HJGIEFC0r+QjLdK/EVV74s\nAmjj48QPHYJgkHCRjpcbS85e+syf7VP5biHErlIvYIyhdmApgYMHnd2T2Enirx4FIFRC0YpJKpJ4\n5Kgju5Zk08Vcag5vugYRDhc1buTGNwEQ84iTOP7tbwNQ+/735dUSQ1RXU3tnGwBj3/imrbZlI9/5\nMvHwDxn4aDvy/Hkib76V+s/+C/P/8i8ILFnM1N69nPWQozgdSbTBSTQiiXb2SkzXZHq52doGGIEF\nCwFIOrg1n5Qy5SRalZMYqK9HVFcjz5+3vX9l5lxJ5SOuXFny2IHFixHz5iGHh9HOOltMZBI/cACS\nScJXXkmgtraoMcxl6piDxSte+syf0UmUUj4IBIQQzwkhZt4NewaEEG8VQhwFBqSU/16KkZXO+iL2\nM/YLqUjimtKKVkC/uQYWL0JOTJB0IKcjmy5Te7sAqNpc+FKzSeRNNwAQe8Z9J1FOTKT2k655//vz\nPq/2138NgInvfNfR/bQhv/kSP3SIgd/5OGgac3/34zR+/WvUvve9zGm/h0W7dxPedA3JN96g/6P3\nICcnHbB6dqQZSbRhuVnMM5zEIfsKV9I1SVU2W77cbEQSHSxc0QaH9CKcefOKdkIyEUKkLTnbG03M\nnCupfEQLnEQhROq+brY5cxqzdU1Vc2FVzelU3aB/aZ96/nnk1JQlduXCS5/5s67vSSnvRN9h5VEh\nxC+EEPcLId4nhFiZvoQshJhn/O59xjFHgd3Ao1LKj9n7EsqfSIEVWX4iVbSyuvRIIkB4rZEH40CF\nczZdpp57Tn/uusLzX0zCGzYg6upIvvZaKkrhFhM/3o0cGSG86ZqCWhSF16yhavNm5NgYEz/4Hxst\nvJhc80XGYgx8/HchFqP27ruYu/UTF1RrBxvqafzPrxJcsYL4/hc4v/0Bu03OiWZWN9uwXZe5NZ+d\nOYnpmtiVk+hGM23tjFG0YlEU0cQsXkmetDeSnTlXpiOJpeUjmphtdOJHj1oyXqGYeYRVzc1FjxFs\nqNed3ckY8Zec2azBS5/5OZPApJT3oi8XrwG2AR1ANzAohEgKIZLAoPG7DuOYRuAuKeV9dhleSRw4\ncMBtE2wjdVNqsmYXx1QbHAfyEjN1kYkEU8bvqlqKvymJUChV9OL2krMZRax973sLPtdccp743vcs\ntSkXuebL6L9/kcShwwRXrmT+3/y/rO18gg0NNOz4PAQCjP77F13fRUaafRJtLFyxc2kzXZPUcrPF\nOYmirg6qI8iJCbTxcUvHngmr8xFNnGqDkzlXEq+9DhjNsC0gtFbvWGH2wnUSKSVTXfrKTrgEJxGg\nanMLMJ1OZDde+szPq1JAStkppWxAdxYfQ29vk/kYBh4F7pRSNqQXrihKw0v7OFqJlZV0Jqk2OA5E\nEjN1Sbz6KkzGCF56aclRksj11wPTy9duIGOx1D7S1b/8toLPr/6Vt0MwSOzJp0gajoETzDZfzEpm\ngOj9fzdrZK7qmmuYc9+9oGkM/dmfOZLnOhPmkn3AjhY4ZuGKjcvN6ZrYFUkUQhA08hKdyoGzOh/R\nxHQSEzY7iZlzJWlhTiJA2NhFy43l5uTJU2hn+hDR+SUHIVJf2h26H3vpM7+gclLDWdwipQwA9cBq\n4+EAauQAACAASURBVFFvOIZ3KOfQehqN/l/lhnbGuko6k5CDbXAydYm/+BJAUVXNmVS1GN9cu9xz\nEmM/exo5Nkb4qqsIGfvJFkKwoYHILTdDMsnkD39kg4XZmW2+jHzmn5Gjo0Te+laq35x7y8S5v/9/\nCCxeRPyFA0x8//tWmpk3MhaDqSkIh8GGZahA1P4WOOma2OUkwnSFc9KhCmer9202carCOV0XKaWl\nhSswvUGCWaDoJPF9Ruuba6/NulpQCGaO+dTe5xyp1PbSZ37RPUeklMNSyteMh/ubM5Yxhz2ySbrV\npG5IFkURIS2S2P2q7b3uMnWZekl3Equuzn8rvpkIX7sJAgHiLx9Em5goebximHjkxwBU37Gl6DFq\n3vWr+ljfc87Bmmm+JM+dY+wb3wBg/p/m1cmLQG0t8/7ojwA4/8kHHEtcTyeVjzhnTskfdtlwYseV\ndE20AbMFjg1OYqORlzjgTPGKXcvNIYd6JV6gy9mzyPFxRDRKIGpN5Xlw+XKojqCdPmN7pXYmUy+8\nAFDwVnzZCDU1IaJRtDN9JHt7Sx4vF176zC+tMZ3CEepsSFb3AonX9aVmKyrpTALz5hFYsgQmY7ZX\nOGfqEjecxPCGDSWPHairI3zllZBIEDdudk4iNY3J3YaTmEdvxJmo+eVfhnCY2NNPk3RoCXCm+TL2\npf+AyRjVra36e5sntXfdqe8i88YbjP/3d6wyM2/szEcECJjVzeftcxLTNbEzkuh0hbN9OYnORBLT\ndZnejm+lZeOLYJBwk17w5vSSc2plZ0PpKzsiECBiRhOfsz8v0Uuf+cpJ9AFeyk+wEjtuSgBhI1k6\nfsTeJY50XaSmEX9Z720VtiCSCNPFL+aOAU4SP3AA7UwfwaVLS1o+D0SjRG69FTSNyd17LLRwZrLN\nF21sjNGvfAWAOb9dWMMFEQox93d+G4DRf/tc6QYWSHok0Q6EWbhi47Z8TuQkAgQWupSTuGSJpeMG\nL7lEH//UKVtXRNJ1SRWtWPilHdxZcpZSplZ2wleV7iSCs8UrXvrMV06iD/DSPo5Wknzd2qIVE6cq\nnNN1SR47hhwZIbB4EcFFiywZ3828xMmfPA5A9e1vLXmJs8aIRE7++MelmpUX2ebLxHe+ixwapqql\nJVUUVAg173k3weXLSXR3Ix3u+zgdSbTHSUy1wLFxudnURE5OIsfHIRSyJTIaNPdvdmhrPrtyEkV1\nte7wJhJofX2Wjp3OBfcwi/MRTUKXO1+8kjx5Ejk0RKChgeDSSywZ0yxecSKS6KXPfOUk+oAxhz+U\nnMLqJGkTc+cVuyOJ6bqY/bOs+tYKad9cu/Y5vq1V7MknAYi8JXdxRy6qt7QCMPnkk460Jsk2X8Y7\nOwGo/Y3/VdSYfQMDXHXwJdaeOsGrRsVpNBpl3rx5PPLII8UbmwfTW/LZs9ws6uogGEROTNiWc2lq\nkh5FtCW/0sFeiVLTSBoOXNCIYFqJueRs5x7u6XPFtvuxC05iKvXn6qss+zsLX3MNhELEDx9GM764\n2YWXPvOVk+gD1hl7YJYT6ZV0VuYkQlpvLpsjiem6pIpWLMh/MQledhmBxka0c+dIGq2CnEAbHdWX\nuIPB1L6lpRBcvJjwtdfCZIzYE09YYOHsZM6XxOuvM/WL5xA1NdS841eKGnPhwoXIUIhxKTHd9bGx\nMWKxGGuNLyV2Ic3lZpsiiUKI6eIVmz78TE3s2m3FJOBgTqLW3w/JJIGGBoQNVefBpfb3SkyfK7bd\nj11Ybk59abeg04RJoKZGTyXSNKaet3dPei995tvmJBq7rigsoN+hpRMn0QYGkKOjiPnzLd/Ddfqb\nq717OKfrMv3N1bqbkhDClbzE2NPPQCJB1aZNqUbLpVJjVEhPPmL/knPmfBn/9n8DUP32txed1xcI\nBPiND3yAYEZU4vLLL2fVKmsawc+E6bjZFUkEEPPt7ZVoapKKJNpQ2Qyk+iQmz9mfk2hXj0ST6V1X\n7IskmrroX9qN9J9VKy29RmjVKggGSb5xHOlQp4b4iy8C1uWHmziVAuSlz/ySnERjK75NWR7vB5os\nsrHi8VJ+glWkkqQvu9TyZadANKrv4Tw5aWu7glSelZSWVtKlk+rP5WBeohnti7z5VsvGNCukJ/c8\nantrovT5IqWcXmq+M/+9p7Px4Q9/mOqamtTPtTU13HvvvSWNmQ92RxJhetcVaVOFs6lJareVcogk\n2pSPaBJyYNeVlC6Dg8jz5xFz51q/E05VlZ53rmkkel6zdOyZsCP9B9KcxH32fmn30md+UU6iEOLz\nxnZ83UBXlsdDllmoYOPGjW6bYDl2JUmbhC+3f+cVUxft9Gm0/n5EdL7eF8xCUpFEB3deiT1hXT6i\nSWjtWoIrL0MbGLDd4U2fL1N795I89gaBJYuJ3HxzSeNee+21zE/rH5eIx7nrrrtKGjMfUpFEG9ti\npNrg2FS8kporNlY2w/RWf9rAgO1fRuxqf2My3VDbPifR1CWZVtlsR66omQLkxJJzcmCA5KlTiNpa\ny7Z7NbkgT9zGVSovfeYX7CQKIT4J3Mv0VnyvZXm43lxbCNEshOgo4Ph2IUSb8dhqp22FEovF3DbB\ncuxKkjYJGU21EzZuLG/qMmVEEauuutryG2wqWfrQodTWbHaSOHGCRHc3Ys4cqjZtsmxcIQQ1dxjR\nRJuXnNPny3iHEUV83/sQwWBJ4woh+MhHPkKVMc41Cxay2CYHIZ3pSKKNy82phtr2tMExNZlebrY2\nWmUiQiHdAZUydS27sN1JdKBXoqnL9P3Y2k4TJqE1el6iE8UrqdSf9esRAWsz6oJLlxJYsgQ5PEyi\nu9vSsdPx0md+Me9gGzAItBhb8a3J8mhAdyIdx3AOtwN3k+eStxCiHVLbDnYCe4QQO2w0syAOHjzo\ntgmWY+7ZHLTpppTKS7SxeMXUJb2SzmoCNTWEr1oPmkZ8v/1NtVNRxJtvQoTDlo5tLjlPPPJjW6u1\nTV3kxAQT3/8BALVtpS01m3zwgx8kEApRKwQfiFqTr5mLVHWzncvNNm/NZ2qSTC03W5uHnI5TvRKT\np0/r17PNSTR3XbHPSTR1satoxcTJCufpohXr78d6nrjZL9G+FREvfeYX4yQ2APdLKZ/Pcdy2IsYu\nGSnlPinlNmBXAafdK6XcmT4G0Gq5cUWyfv16t02wHLsat5qkljdsdBJNXaZ3WrE2/8Vk+qZkf38u\nO/IRTao2b0ZEoyRfe43Eq/Z9WJi6TOzegzx/nvDGDYSvuMKSsdeuXcull17KlJTcMTaBTCQsGXc2\n5Ki+3BywsXDF7q35TE3srm4GCJi9Em3OS0zanJMYaGyESARtcNC21lGmLnZtbGDiZIWzHUWE6UQ2\n21+84qXP/GKcxL3A6jyO80wkbjaEEFGgOctTQ0IITziKERvaK7iN3TmJocvN5eZXbcsdMXVJFa3Y\ndFMy82BiNuclSk0j9uRTAERutS4f0USEQlS3Gj0TbVxyNnUZ7/wWALVtbZaO/7u/93vcUV/P3GQy\nVRFqJ3JUTzOwNZJo7rpiUyTR1GQ6J9Ge5WZI25qv395eiZrNy80iEJjeecWmaKKpi+1f2s3l5p7X\nbP9iZVcRoYkTkUQvfeaHijhnG/CoEOIhKeVPZjnuNaCxOLMcpQkYyvL7AXTn0Zm9xGbhwIEDbLIw\nP8xttOFhtMFBRE0NsWgDtXmeNzw+xeOH+ogn8nP6hq//VeaeO827ek9QfWnubY4KHb/3RC9XLl3I\nladOE6qpIdQ0e3ZDoeMDzK8Lc2vzdEWd1LQZ82yKHf+2KxcTCgZIHDqMNjhIcOnSrAnfpY4P+u4r\nE52dTDzy49RWd1aOD/p82bBsGbHHH4dQiJp3v8vS8X/7t3+btqd+RuKJJ0m8epTwmtWWjp+JZkQS\nR6vqeKSr1/LxQc9JHInU8cRILeFn37B8/AMHDrBq7Xp+FFjC5JW3MWe4hlAe18l3fJh+/4cXbmDq\nyjFqXpskkuMaxYxvvv/DtauQVy5k3tkggRmuU8r4AKNX306ipoe6Z48R7q+yfPzeE70sX7ac4cBS\n5JVR5o3UXfBaSh0/nfM3vRdtcIi5jxwgaDQ9t3J8ADkVY7j6Mri6ifnna4m+dMrS8QFkIsrwhi2Q\nSHDps928dfMqS8cPBAT1iT5uu7El55hOUIyT2IIeTdwjhNgD9KBXNKezGrAv6cRaGtAdwkyG8IiT\n66V9HK0gcewYSSH4Quu9/PSTP+HTH2jh+tW53+qvP32MrzzZk/+FNr4bgEuefYVb83ASCx4f4IUR\n/nzpOq5fUpOzMKKo8YHPfKCZy5YsRjt9hkRPD2HjW7lV4//zB1u4Yc0CYj/7GWDkI2YpwCl1fDAq\npiMR4s8/T7Kv74ItDK0YH/T5MvHt/4ZkkuotrakPJKvGB4isWkXiiSdJ9k5Xnlo5fjrSyEncdTzB\nfxr5VlaOD/rWfN/bcAffrloHDx+yfPwVK1bo78/Kt8JK4KUxeCm/6+QzPqS9/4HVcPNq/Q6ex2sp\neHwT4/7CUyeBmSN9RY8PsORG/XEkAUeyv5aSxgd44RBc+179/0+eAC6spi55fJP179D//cVZYDpf\n1LLxTW76Df3fR47aMz7ADXfr/z78KvMb51s+/lvWNnDbjfmZYjfFOIk7AYlemLLF+H9FYRS6tAMs\nXbqU48ePs2LFCo4fP87Y2Bjr1q2jv7+f48ePs3HjRmKxGAcPHmT9+vVEIhEOHDjAihUraGxs5PDh\nw9TV1c16fm1tLV1dXUWfX+r1rT6/+/Gf8tjVd/DY4quJBCA5Ngg05jx/y/pVTMYTnD5zljlz5lBd\nXc3g0CDhUJg5c+YwOjpKPBGnPlrP5OQksZ8/S/0rL9HUuJ6urvqc9m++JMDpK+YyZ16UyclJRkdH\naWxsJKklGRwYpL6hnmAgSH9/f+r68rlnuOJMN+Etv2a5/aOjo6xecQlrF9Uw2LSa6tNniP3iOV4e\nHbXM/sTEeeoDY8AChvY8igAiN99sqf2XL6ye/vutqSG2cQOR5/YyuXsPx1uaLbM//f0/+U09Jbn6\n/e9jYmLCOvuNv59LjJy6sy++yKAx/620P/39TxotcO5YG2VqzjxL7M/8+1k4fz63v/IUsaXLqX7H\nOy21PxaL8frrr7Nl/SoGvvgl4gmN4HveQ/X8+ZbZn/7+R073MfXMMyRWrGDebbdZYv9Ffz+BIMnv\nfw8ZqYZ3vsNS+9P/fub19hJ/4QXia9Yw5003WGd/+t/PyCjisceQ8+cT/6W3WGp/+t/P3NdeI3no\nEPErrqB60ybr7E/7+0keOULoxRcRq1Yxvn69pfan//3UvtqNfOUwtWtXUR9YZ5n98UScxoYGbllV\nx/79+23//M4LKWVBD0ADXgV+PMujG0gWOraVD/Sl4q48jmsFBrP8fjewNdf5LS0t0m4OHTpk+zWc\n5NinPitv/dPvyhv+4kfyZ6/02XadkS9/RfYuXS4Hfv8PbBn/0KFDsv++j8nepcvl6Ne/Ycs1TEZ2\n7NRfyx/+kS3ja/G4PLF2nexdulwmTpy05Romo//1Ndm7dLk8+8EP2TL+K//zsOxdulyeuPIqqU1M\n2HKNsf/+b9m7dLk8d8+9toyfzok1a2Xv0uUyOTJi2zVie7tk79Ll8syvvMOW8Q8dOiS1eFz2Ll0u\ne5etkFoiYct1pJRy/Ic/1LX50G/Zdo3Yvn36+/W2t9t2DSmlHP36N/R5/3v/x5bxDx06JMe+8x39\n/froPbZcw2T0G/pr6f/t37HtGgN/8Ieyd+lyOfLFL9l2DSmlHDfuMWfv/nVbxnfoMz8vX6qYSCJA\nq5Ty9dkOEELY12nSWvaSfWm8AXBuL7RZqLOxia4bdJ4JMBWJcGNtjJvWLrTtOmGbK5zr6uqm2y3Y\nlCRtMr0dlD1/kvEDLyJHRwk1NRFceokt1zCp3qIXr8SeegptfJxAbb5ZqflR+/jj+r/v+lVEdbWl\nY5tMtyexr9ExgEwmkePjIATC4vcpHWEWrtjUJ7Gurg5taCh1rVJ7Vs5GoFFf+rOzutnuHokmZq/E\nRK89f2d1dXW2F62YmBscJI7YV+FsZ/ubdFKbHOzbh0wmLf979tJnfjHVzffmchAN7ixibMeRUg4B\nPUaVczpRKaXrRStQXjmJiaTGj4K6E/KB9fb2mQsZbU8SR47a0pdvWX09iZ4eCIcJr11r+fjphK++\nCiIREkeOpD5srST2lFHVfPNNlo+dSXDRIsLXXguxGLGf/tTSsWUiQXC3Pm1rLK5qTie41Nwyzb4e\ndjDdSFvMmWN5Y+B0AsbezdKmFjgrVqywfbcVk1R18zn7qpvN9jd29Ug0CS7Td3Cya9eVFStWOOYk\nptrgdL9qy244cmoqFRAI29xCJrh4McEVK5BjYyRs2NXLS5/5Bd91pJQPZv5OCLEyy3HfKs4ky8ja\nY0EI0SSE6MhwCrcDf5J2jCeqmk28tI9jqTzb3c/5UA3LB0+ycZO923sHGxoINDYix8ZInjxl+fgn\nfvI4AOErrkBUXVx5aCUiEqHK2Kppal+uFqWFE/vZ0/D/s3fm8VGd573/vefMogWEJPbFLALbbCYY\n8JrYiW3sptncOGDfJk3Tm9zgpNvtasdpbpO2nybXbtImXZIaJ22arg7YWXrjOAE7iXcbECCDANus\nEggEWpE0muWc9/5xlhlpjqRZzpz3mZnn+/mMsWbOe+aFn86ZZ54VKHp0Xa7U/lJppq/EX3gBZnc3\n9KVL3W/7pUCfOwfQNJjd3ZDJZMnex3SMxBJ7Ftw+iYODJflC1dHR4RqJeommrTi4zbRLaCS67W/m\nzyvZewBAyJm6cu5cSQyrjo6Okrcjc9AaGqDNmweMxmGU4DMt9eZbQCIBfelSaNNK1y7KIT0y1f/+\ntZQ+8wv+aiqEuF0IsceZ4SyEMIQQrwkhPujj/grZV4s9ceVhABuEEI86E1VsWmDlIbp3Kmk10j4u\nhNgshNgCK5x+f6Abn4ThAMaxBcXTrdYv/60n9yBkzyYtJU5T7dQbx3w/d+L11wGUPrTh4N6UfG7i\nKkdHEd+7x3qPm4MpqXOmr4zufsbXvmnp3ogfKskMWgcRCrlNm82e0oU1pV20UsqRfID1JUTU1ACp\nFGQs5vv5h4eHYbrTVkrrSRT19UBNFDIWK1kT6qDCzaKmxjJ6UymYF7p9P//w8HDJp61kkk4B8j/k\nnDhsh5rXBHQ/3rQJABAvQQoQpc/8goxEIcQ3YBV2bIRV5ew8NgHYKYT4um87zBMp5Qkp5YNSyo1S\nSiGlHD9NZbeUsklKeWLcuu32azullI8Ev/OJWblypeot+IJpSrx23PpAvSXRVdK8JAdnHFQpbkrN\n9tivUucjOrjD5X1u4ppo3Q+MxhFatQp6rhVvRRK68kroS5fC7Ovz7Zu4efkyRn/8NACg7kP3+HLO\nydBmOblvJfRYXU6Hm0uNcELO/f6HnFeuXJkxbaW03dGEENDtvMRSeRODMhIBQF9kpTakOv33Ll21\ncKH1bxSNltwrCmQOOfD/fpy0jcRI0F/aS+BJpPSZn7eRKIT4JID7ATwBK+9wI6y+iBvtn58E8Ckh\nxCd83GdV01NCT0WQnLg4hIGEiZlDvVg0N5i5t6GrS3dTitmzlMNrAjISneKV/ft9DT1l9kcMCiGE\n7yHn2I9+BDk6CrFxI0KLF/tyzslw+i+WckawO5KvhNNWHLQGZ+qK/0ZiT09POiexxOFmANCcvMSL\npTUSS52TCAAhJy+xBMUrPQfbrPdYsqSkOa8OriexBHl8ycPWvOOgPInhVasgamthnDoFw+fPaEqf\n+YX8VmyDVbxyr5TyCSnlfinlSfvPJ6SUWwF8yn4wPkApP6EY9p20wk1ruo4hHEBoA0hX1Pl9U5Kj\nozCPHweEQHhNMHM29TlzoC9ebCVLH/UvfO7mI77jHb6dMxeckHPsx0/7kgc38vh3AQCD7wgmr1Kb\nbXsSS2SIAJmexNKGm4HSjubr6OgILNwMANosKy/RKNFoPrPEc5sz0a9wjMRO3899cb+V3xxausT3\nc3vhpv+86fP9WEok2x0jMZj7sQiHEV7/NgD+d52g9JlfiJG4wat4JRM7vFu6rPEqY51dsFDutJ5K\nG4nB35T8rXBOHjsGYRgILV/uewuXyUjPcfYpRDs8jMT+/YCuI3rjDb6cM1cimzZBmzcPRkdH0TfZ\n1ImTSLy2B6K2Fis+FUw6setJLGG42aluDsKTKJzilRKEm9etWxdYdTOQWeHsv0dGxuPW3yUUCsQr\nmg43++9JXGTfE0tdtOLgpP+k3nwL0vSvS57R2Qk5MABt5sxAvLsO6dZk/qQASSmRfOstXHPNNb6c\nzw8KMRL3T1WcIoS4B4D/JZhVSjweV70FXzjcaX34rO06GthNSZs1C1pTE+TlyzDPn/ftvEH1RxyP\n38PlE6+9BqRSCK9bV/LiiPEIXUedPVc59r3vFXWu4e9aXsTa970XyXC46L3lgltFW8Jws2kXrgTi\nSWy0PImyBJ7EuGNYIahwc+kMeKPbKiDR58wJJESbboPjvycxftxKzQ+iaAWwviBoc+ZAxmK+tvVx\n8hHDa9eUtGBtPH4biak330T3O2/Dxfe935fz+UEhv+HbYRWnfFEIsV4I0QAAQogG++cvAdgB4L/8\n3Gg102670cudu66Zj/eefhVzL1+CviQYT6IQwvUm+tlUOxlwZbODW7yyZ48v54s/H1x/RC9q77G+\nb8b++/8V3EpGGgZGduwEANTdd29g10sQhSvSrnIMJifR9iSWoFdie3s7zF7Hk1jawhUAbuV5KbQJ\nqkeiQ8j2JBod/huJQ0esedChZUt9P/dEuN5EH4sJ3S/tAeUjOjj34+T+A760wor/4jkAwFAAX6Ry\npZA+idthFad8BsA+AH12G5w+++cHATwjpfyynxutZlaXuDFoUPzOu5bi47u/CaFpCNl5NkEQKkGn\n/8ShQwCAyDXBpgKEV62CaGiA0dGBlA95K6N2M+uaW28t+lyFEF6zBqEVK2D29LgNvfMl/vzzMM+f\nh75kMSI33hjY9ZIuXCmhkeh4EoM0EkvgSVy9enWw4eYS9kp0eyQGkI8IAPqidENtv3tYRi9ZXvCg\nIjtAOgUo6WNeoutJDCgf0UFvboa+bBnk6CiStsFdDM79eNZ731v0ufyiIF95RnHKIMa2wBmAVdRy\nl287ZBCNRlVvwRdSHZ2AlNAXLSp58+lMwnaFc9KnCmeZTCLZbt0QgvYkCl1H9KYbAQDxl14q6lxG\nVxdSR49B1NUhct0mP7aXN0II1P7K3QCAkSeeLOgcw//yHQBA/X33QQgR2PWizbS+7TvGTylwmmlr\nAYSb06P5/PckRqNRNdXNJchJDLL9DWD1yBQzZljFcj5WvZojI5AXuoFwGHoAPWsdQqXwJAZc2ZxJ\n1KfWZHJ0FImXXwEA1N/2rmK35RsFJ1TYfQWbADTBan/TJKVsnqqohcmftrY21VvwBbezf0ChZgf3\npuRThXPqzbeAeBzG/PluRWiQOFNR4i8UZyQ631qjb785UKN9PHVbPgQIgdiPnsq7lUTq9GmM7toN\nRCKo+8iHAQR3vWiNVti0FGMSHQL1JNq/y6UYzdd24EDaSGwsfbjZ6ZNYiupmw85tDspIBIDQIv8r\nnI3Tp61zL14MEQr5dt6p8LuhttnXB+PsWYiaGoRaSjvFy4vI9dcDAOIvv1zUeeJ79kKOjiK0ahUO\n219EKFB01q2UcsBufzPmziKEuL3YczMWlOY4FkPKuSkFVNns4N6UfKpwdietBFy04hC1p6LEX3qp\nqL9P/Oe2kfiud/qyr0IJXXEFau64A0gkMPKf+aUyD3/7XwApUXf3B9zwb1DXSxBGoutJrA/OSCxF\nuHlRUxNgmtYM6gC+kJSyT2LQOYlAusLZz16JQU5aySR0Vbp3rR/3Y8eLGFq1KpABDeOJ2i234i++\nVFT/2vhzVj5izbveSeozv5SlWTtKeO6qYmZAUzBKTfqmFKyRqM2ZA9E4A3JgAGZ38aOtnKKVaXZl\nW9CErr4a2syZMM+fR+rEyYLOIQ0Do88/DwCoede7fNxdYdR/7NcBAMP/+m8532jNwUEM/9fj1vqP\n/0/3+aCuFzF9OqBpkENDJZvfLJ0+iWVeuOL4DoPIRwTShStmb6/vM4/dnMS5c3w972Q4eYkpHz2J\nqVPOl/alvp0zF/SZM6E1N0MODflS4Rz0OL7xhBYvhr5kMeTAgPvZUAhO0Ur01ltJfeZPaCQKIe4R\nQjwuhFg67vkv5fB4HOn7AlMkR48eVb0FX1B1UxJC+NpUO/m6VbRyPoCwmRdC01xvYsKelpIvyQMH\nIfsHoC9dErgeXkTf9U7oSxbD6OxE7EdP5bRm6Fv/BDk4iMhNNyKS0Us0qOtFaFra+1YCwwoATGfi\nSiA5ifZYvgH/PYkn7KbNWnMwRqIIhSyDVErfc0bdnMR5pR9j56AvdDyJPhqJJ08BCD6yAwBhu7gs\n6UMnAseTGAm4aCWT6DtuAZDuFpEvRne3VXxTE0X0+utIfeZP5kn8JoAtsEbwZfIggAfsP70eD8Aa\nz8f4RH19veot+IKqnERgbFPtYpCG4VbS1djd9lXg5CWOvlCYkTj67LMAgJp3qg01OwhNw/RPWUOa\nLn/1q1M22jUHBzH02DcBAA1/8AdjXgvyehElDjnLIasFTpA5iaUIN9cmEtZ7BORJBErXK1GFkViK\nnMTUSSsKEWT7GwenCtkx8Iohaecgq0r/AYCaW6xpVYUaiaO7nwEARG9+O0RNDanP/MmyVbfZj0c9\nXtsPYPcka5cDuKeIfTEZUMpPKBRpGG7LlqB6JGYSvsofT2Lq+HHIWAz6okVYuFbdTSl6q/PN9XnI\nZBIizwbSsaefBgDU3HWn73srlLr77sXlv/t7pI69gdh//zfq7r57wmMv/81XIQcGELnpJter6hDk\n9aI1NsIAYPaVxkh0PIliWnmHm2fqIfQhaCNxJvDmmzAuXkJ4pT/nNIeHrWKimqhbDR4EpZi6oTOQ\nmAAAIABJREFUYjhGooJIghMaLtaTaA4NIfXWW0A47HonVRB5+82AEIjv3QsZi0HU1ua1fvSn1vx6\nZ549pc/8CT2JUsqdUsq7pJSnPF7eIqX8zCSPrbDa4TA+QGmOY6EY584BySS0eXMDHWPnELr6agAo\nupeVE2oOX7NWqS6hJUsQuvJKyMFBJF59La+1qZMnrdY3DQ2I3qymibYXIhrF9P/9uwCAgT//iwk9\nWsn2Ixj61j8BmoYZn/8/Wa8HqYvTGLoUnkQppZuTqAXgWRANDYAQkJcv+57H12MbJEG0v3Fw+1j6\nWOHsFK3oc+cGOtkjs1eiH5ixGIyuLkhdh67AIAmvXgUg3d+wUJKvvw5IifDKlRAKW8Xpzc0Ir10L\nxOOIv/JKXmvNkZF0fvjmOwDQ+swvdOJKbw7HccjZJ4btqQvlyMEzffhZ+4V0PqICLyIAROx+hqn2\ndshUquDzuJXNa9cq16Xmzs0AgNiuXXmtiz39E2v9HbcrbX3jRd2v/g+Er70W5vkLGPjTz2dVP5rD\nw+j9zd8CDAP1v/5RRDxmnAapi1PhLEthJI6OAoYBRKOBfAAKTbOKceD/aL6kPbpQTbjZx96CAfdI\ndNCamyFqayEHB33x9DqpP3LevEDb3ziEVqwAIhEYp8+4oycLIXHwIAAg/DZ1qT8ONXdYDV1Gf/LT\nvNbFn38eGI0jfO16N4VB9WdLJoVMXPmUlDLrDmKP5WvIOO6ZYjfHWKxc6VOsJGAMU+KP/2M/Hnr8\nAEbdJOmlSvaiNTVBX7wYcnTUCk8UiJP/Elm3TrkujpE4unt3Xq0kRn9shZpr3/3ukuyrGISuo+nL\njwA1UYzs2InLf/037t/NHB5G7//6JFJvvonQlVei4bMPeZ4jSF0co6cknkS3kXbpQ80OpZq60qRZ\nrUmCGMnnUIrRfMYFu0digPmIgFV853oTfQg5O0UrtXaEJWhEOIywD9Gd5EH7fqwwP9yh5t2/BACI\n/fSnU+ZUZ+IYlbV3pWeQqP5sySRvI1EI8UcTvHQfgFNCiB4hxB8Wty0mkx4fu+wHyZvnBzEYS2Jh\nUy3E6VMA1HkSAcv7BwCJtsLaFMhk0r0phdevV65LZONGaE1NME6dzrkgJ9XZaQ2jr4kiSqirfybh\nlSvR/NWvAkLg8l//DS5t2Yr+L/wZum/fjPhzz0ObNQvN39w+YQg2SF1K2SvRbX8zLbgk9lIVr4za\nxpXWpCDc7KeRqKBHooObl3i2+OIVpx1Zan6wxm4mfhSvOJ7EzO4GqgivXQt9wQKYF7qRPHAwpzVy\ndBQx+0t7zS+nv7Sr/mzJpJBw88NeT0opH5NSNgO4DsCnhRBfLGpnjAul/IR82HfSykrYsLTZbaQd\ndOPWTCLrrNBk0p67nC/Jo0chR0ehL1sGvblJuS5C193Ck9gPfpjTmpg9+q72rrsCyXMrlNr3vw/N\n39wOMWMGEq+8iuHHvgmjsxPh1asx64mdCK9YMeHaQHMSS2gkBtn+xkE4nsR+f1PKRx3jKujCFfht\nJDqexOCNRLfC+Uzxv99OZXN/Q8MUR5YOtw1OgXmJRm8fjNNnrEkr9uhVlQgh0t5EuzBwKkafeRZy\ncBDha65B2J4MBtD6zC/ESJw0W1dKeQJWRfT41jlMgawj8C2pEFpPWf3JNixrdr+5qujJ5eC0SEgW\n6ElM7GsFAEQ2bABAQ5e6e6wmAiNPfm/KkLOUEiM7n7DWbaWfMlz77ndj3ssvovGvv4yGzzyImf/y\nbcz+8Y8QXrF80nVB6uIaiSWY3xxkI20HzemV6LMnsc5uNh5Un0QA0GbNBgAYFZCTCKSHEDhfuIvB\nMRKX2K20VOB6EguscE6+bkd11q5VklfpRe0v/zIA60t7LiHnkSftL+0f/JUxz1P4bHGY9F/WzjHM\nHIYoAEghxNvgbSw228dv822HDOLxOGrzLKlXTcowceC09cF57RIrJAooDjfbRQ7Jw4chDSPvEU6u\nkbjRMhIp6BK5+Sbo8+fDOHMGiT17ELXniHqR2LsPqRMnoM2e7bbQoY42Ywbq77svrzVB6uLm8BWR\nfD8R5rCTkxicJ7FU4Wajz4oqBBtutj2JPobuVPRIdHDunU4RYDE4RqKxYH7R5yqU8OrVgBBIHjkK\nGY/nXZzlhHQpFK04RG68AfqiRTA6OxF/8SW3f6IXxqVLGH32Z4Cmoe7uD4x5jcJni8NUnsQ7AewE\n0ApgH4C9sIxD5+fxj12wvIjLAXy3NFuuPtp96EofNG+cv4zheAqLmmsxOz5o9Y5qbHQ9LyrQZ86E\nvmAB5MgIUidO5L0+0TrWSKSgi9A01N7zQQDA8L//56THDn/rWwCAunu3kvnmXQqC1MXx8slB/41E\nFTmJbrh5wL/wuZQSZo9tJAbqSSxdTqI+V4WRuNTaQ5GeRHNkBOb5C0A4jGMlmhSUC1pDg1XlnEgU\nlJcY37sXABDZsN7vrRWM0DTUbd0CABj57uQm0PC//TuQSKDmjtuzvnRQ+GxxmNRIlFI+IaVcIaXU\nAHwaticRwMkJHvsBPAHgQSnlp0u58WpitcImoYXS6pGPqKKz/3jckLNdgJIrRm8vjFOnIGpqELYr\nz6joUv+RDwOahtgPfgCjq8vzmJQz7i4UwrTf+I1gNxgwQeqiTbeNqqESeBIvO420g/ck+jmaT46M\nQKRSQE0UWoDeETFtGhCNQo6MwBwZKfp8UkrXk6gFOLfZwQ03nzlTVB9Lw+k0sXgxVnu0kAqSyIZr\nAQAJe2xjrkjTRGLvPusc100cPVFB3b1bASEQ+38/cn9fxiMTCQz/678CAOo//vGs16l8tgB55CRK\nKbcDuMv+/xUTPDZJKe+VUv5VyXZchUQVNgktlNZTtpG4rDk9I1RhqNkhsnEjACBhfwvNFSfUHF7/\nNtcLR0WX0JIlqH3Pe4Bk0h1VN57LX/0aYJqo/cD7oSsMMQVBkLqU1JNo90rTAs1J9H8WtZOvqQcY\nagbstjE+ehNlfz8Qj0NMn66k6Eurq4M2Zw6QTE74ZTAX0uP4lim/hzn53U6UJldSx45BDg5CX7gQ\noYULSrG1ggktXmxVKicSE96Ph//zv2Cev4DQVVch6hGSVq1LJnkVrkgpdwN4rER7YSagrS0/r5dq\nUoaJA2fsopWlzW54RFWPxEwi120CAMT37MlrXeLVV631mza5z1HSZdpvWY77oX/+tvsh4JA4dAgj\n//U4EAqh4fd/X8X2AiVIXTS7+XRJchIvBzeSz6EUfRLNXicfMbhQs4Nb4XyxeCMxXdmsrm2M80Xb\nKCIv0bk/6MuWKr+HRa4tzJMYf826f0euv873PfnB9N/+LQDA8L98B6mz58a8Zg4N4fLXvgYAaPjD\nP/Cc3KNal0wKaqady3FCiNvz3w7jBaU5jrlwrGsQI3EDV8ysw5yGGreyWcXM5vFE1q0DIhGkjr2R\nV9uS+EsvAQCib0+PsaOkS2TdOivMkUig7/f+ADKRAGAZGn2/878BKVH/sY8h1LJM8U5LT5C6uBNK\nhobyaqCbC24z7ekBtsBxPYk+Gom2J1GFkajPtsLCxsXuos9lKKxsdnC6Qzj31EJwO00sW6b8Hha6\n+iqIujoYp8/k1fQ8YX/Jj1xH00iMvO1tqHnPeyBHRtD/0Gfde4OUEgOf/wLMC90IX7seNe99j+d6\n1bpkUkgLnFzZUcJzVxUz7ckB5YLb+mapFV6ilJMoamoQedvbACndEPJUmIOD1szmUGiMJ5GaLg2f\n+xPo8+cjsXcvLn3koxjZsROXtt6H1BtvILRiBRo+84DqLQZCkLoIXYeoqwOkdMPDfmEqaaZtt8Ap\nQbg5yKIVByd30Ljgn5GoopG2g/NFu5g2OKnjVtFeaNky5fcwEQoh/Dar3Us+IeeE7UmMEjUSAaDx\nz78AMX064s88g/7PPIRUZycGv/glK6oTiaDpK1+ecP63al0ymdBIFELcI4R4XAixdNzzX8rh8TgA\ndWWsFcbRo0dVbyEvnHzEjctsI9H55krAkwjkH3KOv/oaYJqIrF8Pra7OfZ6aLvrMmWj+9j9BmzUL\niZdeQt/v/T6Sr78OfdEizPzOt8fsvZIJWhfRYIecfc5LlBXSAsfsVehJtA06c4ICgnwwncpmBY20\nHdKexMKMRCklkvZ0pvCVK0jcw5wv3olXXs3p+NSpUzDOnoWYMYNEE+2J0OfPR/P2fwTCYYz8+3/g\nwg03Yejr3wCEQNNX/8YdS+gFBV0cJuuD8U0AMwCcAJA5JPVBWBXOEzXVdl7LfZgsMyn1hCdjeNFY\nF8GMujCub5kJs68Psn8Aoq4O2uzZqrcGwAlRfMPNM5yKxMsvAwCiN9805nmKukTWrsWcnz6NoX/6\nZ6TeegvhtWsx7RMfd3PNqoGgddGmN8A8fwHy8iAA/5LolTTTdlvglMCTqMJInGN7Ert98CRSyEm0\n87qNAsPNZk8PZH8/xLRp0ObNQ30q5d/mCiT69rdj6O/+HvEXXszp+Phzz1vr3vGOvHvdBk3Nrbdi\n9vefxMBffgnJ9sMIr7gSDQ/88Zi0JS8ofbZMZiRusx+Pery2H8DuSdYuB3BPEftiMqCUn5ALn/uV\ntZBSIqRrSBy1RuCFWlomdK0HTfSG6wFdR6J1P8zBwSkNqNGf/9xaN246AVVd9LlzMeOhz6jehjKC\n1sUpLHHCw36hZCyf60msDCMxHW4u3pNIISdRt3slpk6fhpQy73uqM+M9dOUKCCFI3MOimzYC0SiS\nhw/D6O2DPkVawuhzzwEAat55axDbK5rI+vWYvePxvNZQ0MVhwnCzlHKnlPIuKeUpj5e3SCk/M8lj\nKwB1XTorDEpzHHNB1wRCuvWr5TStplQwoc2YYTXETqUQf3Hyb6+pM2eQOvYGxPTpWZV05aZLtRC0\nLpodbpY+VzgraaZdWwuEw8BoHHJ01JdzpnMSg22BA2SGmysjJ1FraoRoaIAcHi5okkzqzbcAwJ0T\nTOEeJmpr063J7ALBiZCplOtxLJepUYVAQReHQgpXtgPozeE4+sNhy4RhnxPigyRtJLZMcWSw1Lzr\nXQCA0Z/9fNLjRnc/Yx3/zndCRCJjXitnXSqZoHVxG2pf9neUnYqxfEII39vgqGyB42+42fYkzlcX\nbhZCuAWAqePH816ffMsyEkO2kUjlHlbzDitKM/r8C5Mel2hthbx8GfqyZQgR8rb5DRVdgAJb4Egp\nPe8emUUuUspnCt8Wk8lKe8JHOZI8TtNIjN5+GwAg/uzPIOXE6bOju3YBAGru3Jz1WjnrUskErYvb\nUNvncLOKnEQgYzSfX0Zin9VqSkl18+zZgBAwL12CLCL/ThoGzIsXAQC64tzq0ArLwHO8gvnghptX\nrABA5x4Wve1dAIDRXT+dtJVU7EdPAQBqf+muILalDCq6AAUYieOqmP/Ifu6TQggDwHEhhCGE+Lrv\nO61ienwcUB80ridxOS0jMbxmDbR5c2F0dSHZ6t3I1bh4EfEXXwJCIURvz277Wc66VDJB61KKhtrS\nMNyWOiLoQpxGOy+x35+MIdeTqCDcLEIha4azlK6RVwjmpUuAYUCbOTMrohA04assI9GpUs6HdLjZ\nMhKp3MPC11wDfdEimBe6J2xNJk0To46R+N73Brm9wKGiC1BYuHk5rArnrQBOCCGWIV3c8hkA1wG4\nXgjxRX+2yFDKT8gHaZowMkZAUUJoGuruvhsAMPLkk57HxL7/A8AwUHP7bZ7J1OWqS6UTtC6O5036\n2DYm00AUWinb2Waj+fz3UWkkAv6EnI1z1tQMfb76kZYh28BL5WkkmpcvW+P8olHoixcDoHMPE0JY\no+wAjD71lOcxidb9MLq6oC9YgPC164PcXuBQ0QUozEjcA2C3Pav5SQBb7Of7pZR/JaVsBXAvOCfR\nN9atW6d6CwVhdHVBjo5CmzXL7b9Gidp7PggAiP3gh5Dx+JjXpJQYfvy7AIC6D33Ic3256lLpBK2L\n5lQ3D/kXbpZDtpEYcKgZyOyVWLwn0YzFIGMxIBIJ3CPq4BSaFFPhbJyzZiVTmHteaLg55eQjtrS4\nrWMo3cNq7ekjI9//AWQymfX6yH/8h3XcB95PplNGqaCkSyFGotMax+FOWD0RtztPSClPAKAVXyxj\n4uMMmHLB7exPLNTsEF6zBqFVq2D29WHke98b81r8+ReQOnIE2uzZqNl8h+f6ctWl0glal1I001bR\n/sZBNPgXbnYaaYumRmUf7LrdBqeYCmfXk7jAvz6YhRJashiIRGCcOwczjwKH5LFjANLhaoDWPSyy\naRNCV10Fs7sbsR8/PeY1s78fsR/8EABQ/5GPqNheoFDSpRAjsWVcWxwno3+X84QQ4lpYvRQZH2hv\nb1e9hYKgWtnsIITA9E9bo8gv//3X3XnH0jRx+St/DQCY9omPQ9TUeK4vV10qnaB1caqbpY/VzaqK\nVoCM0Xw+hJud9jeJmtqiz1Uobri5KE8iHSNRhEJuSzHHO5gLycPWdRFes8Z9jtI9TAiB+o99FAAw\n9I//OKaAZejR7ZCjo4i+81ZS7dRKBSVdCjESTwoh3gYAQgg3DielfDbjmP8L4B+L3FugCCFahBDZ\nJawEWL16teotTEkskUJXf2zMc6kTdj4iUSMRsEIX+rJlME6exOCXvwIAGP6nf0Zi715os2ej/mO/\nPuHactClGglaF7eZdik8ifUqw80+GIl2PmKtwlw+N9xcVE4inXAzAISdkPMbueclJm3DI7x6lfsc\ntXtY3dat0ObOQfJgG0Z27ARgfY4MPfZNAEDDH/6hyu0FBiVdCjESPwPgWSHENwA8Zj/3CAAIIW4X\nQuyB5V3MbTBuiRBCbBNCbLEfD+SwZAOAHUIIKYToE0LsEkJsKPU+cyEajarewpT8xfcOYcvXnh9j\nKKZOWH28qIabAUCEw2j6q4cBITD0D19H97vfg4HPfwEA0PgXfz7pNJZy0KUaCVoXzWmBM1whOYk+\njuYz+ywjMTRrZtHnKhQ/ws0pQp5EAAg5Fc45ehKllEi2HwEw1pNI7R6m1dej4TPWtKiBz/4JLv/t\n3+HSr38MMhZD7Qd/xRqCUAVQ0qWQPok7AdwHaz7zbgD3SykfEkLcAWAnrOrnAQDPTnyW0iKE2Obs\n1d7vbiGE13jBMUgpmwA0SSmbpJR32kU4ymlra1O9hUlJpEy8+OZFGKZENJT+laIebnaI3nQTGv/6\nK0AkguTrrwO6jhmf/1PUvv99k66jrku1ErQuwm2B45+RmM5JDN5IdEfzDfjhSbTCzX2T9L4rNbov\nhSu0jMTwVVcBAJJHjuZ0vNHZCTk4CG3WLDf8DtC8h9Vt3YK6j3wEcnQUgw8/AuPkSYTXrEHjF/9S\n9dYCg5Iuk81unhAp5W6Mm91sN89W0+Mgm/ullBudH6SUrbmGkqWU/aXbVmFQmuPoRfvZAcSTJlrm\nTEPzNOsbkIzHYXR0ApqGkN1ugTL1925Fza23INH2OsJrViO0cOGUa6jrUq0ErYtjyEkfpySkcxKD\nL1xxcxL98CTa4eZpCq8VbY4Tbi7MSJSpFMzubkAI6PPUTVvJxPEGJg8fyul4N9S8ZmwYk+I9TAiB\nxoe/hOiNN2D0579A+MoVqP/4/4SmqDpeBZR0KchIHI8QYukEM54DRwjRCCt0PJ5+IcRm28AtK2bO\nVBeqyYXWk9YHwYal6V6CqTNnANOEvmQxBCHX+WTo8+ahNo8PAeq6VCtB6+LkJPo5u9lpzK2ibUx6\nLJ8f4WbLkzgthy9dpUKfPcvay8VLkIbhtn/JFePCBcA0oc2dAxEOl2KLeaMvXQIxbRrM8xdgdHeP\n8Q564RatjMt1o3oPE0Kg7p4Pos5uU1ZtUNKl4C6tTv7huEkrrwkhVKvaAsDLG9gLb+PRRQixOePx\ngG1wKufo0dxCCqpoPWUbicvSjmRnrmho+XIlewoC6rpUK0HrIurqACEgY7GiRr9l4nglNSWeROu2\n52fhyvlYbIojS4eIRKDNnAmYZkFTV6iFmgFrGEB4re1NPHR4yuOTdvjSWePA9zCaUNKlICPRLlrZ\nBWAjrNxE57EJwE7FY/maYRmE4+kHMJl53grghJRyt+1t3Algh9eBdlHMXiHE3q6uLrc7ekdHhytu\nT08PDhw4ANM0EYvFsG/fPsRiMZimiQMHDrhjd44ePTrl+kgkUtT6Yt9/svWvHz6Cg2csb8HccMxd\nP3jQuimFlrWU9P1Vrq+vry/r/Vfq+vr6+kDfv/PsWdebeGz/fl/+/rFLlwAAqK8P/N9P2OHmZE9v\n0f9+hm0kXtY1pb8/8SbL8E2ePZv/+lOnLC3mzCX1+x9euxYAcPGFFyZdPzIyguHXrDrS0Pr1Y95/\neHiY3PXL6y2CeP+ckFLm9QDwSQAmgO8C+BCAawEss//8ECzDygTwiXzP7ccDVmX1cY/ndwB4OM9z\nHQewYbJjNm7cKKuZ1pM98oY/fVp++B9eGPN8z2//ruxcsEgO/ft/KNoZwwRH18brZOeCRTLZ2enL\n+Xp+87dk54JFcviJJ305Xz6YiYTsXLBIdi5aLE3TLOpcF+78Jdm5YJGMHzzo0+4K49LHPyE7FyyS\nIz/877zXDn79G7JzwSLZ96ef939jRTC8Y6fsXLBIXvpf2yY9LnnypOxcsEieW7e+aD2ZiiInO6jQ\niSv3SynvlVI+IaXcL6U8af/5hJRyK4BP2Q9VeBXQNALId2p2PyzvqFIozXEcjxtqXjr2nzz1xhsA\ngNCVV2atqRQo61LNqNDFKTDxKy/RqZQW04LPSRThsBVCN03IIkcNOuHmC6OjfmytYHQ7JzJ19mze\naymGmwEgfI3lSUxOUQmbaLW825EN12ZNveF7GE0o6VKIkbhBSvnYZAdIKbdjivy/ErIXlkE4nmZY\nIeUs7Eba0uOlXniHrgNl2MeqSb/ZdzLbSJSGgeRbVpPXzBFQlQZlXaoZFbo4BSZ+tcFxei6qGMsH\nAMItXikuL9Gw+yQOKy74cJpgO02x88ExEkPEjMTQihUQ06fD6Oyc9O+VaLU+9iIbsj+S+R5GE0q6\nFGIk7p+qOEUIcQ8UjeWTVgubEx5FJ41y4srmXgD3ezy/CRMYlkGycuVK1VvwJJ40cKjTqoDMrGw2\nOjuB0Ti0eXPd6Q2VCFVdqh0VurgNtYf88SSqHMsHAFqj3Suxr/COYGYsBozGgZoorl6/3q+tFYS+\nwPIkGucK8CSepelJFLqOyHXXAQDir7064XHxV6zXvIxEvofRhJIuhRiJ22EVp3xRCLFeCNEAAEKI\nBvvnL8HK//svPzeaJw8DeMj5wZ6csjvj5xYhxA7HkJQevRHthtzflVKeCGC/k5JXkmmAHOocQCJl\nYsXcaZhRF3GfTx6zQs3hK69StbVAoKpLtaNCF2F7/JxJKcWispk2AGhNVmTAaWFTCE6oWW9qRm+v\n2oCMY+A5XsF8SHWcsc6xmE7vOofojTcAABKveBuJxsWLSB05AtREPaeV8D2MJpR0ybtPopRyuxDi\nTljj+R4EMD7PQQDYLaX8si87LAB7j9vsBtqNAFqklJmewhZYBS7NsNvl2GsesH92jEcv72LgdHR0\nkOqb5DBhPuKbVqg5VMGhZoCuLtWOCl0cT6JZZA6fgzuWT5WR2GwbiUUYd85aralJ+bUSWmgbiWfz\nMxLNgQHI/gGI2lpos2aVYmtFEbnBMhLjExiJ8RdfBABEb7gBoqYm63XVujDeUNKl0IkrW21P28MA\nMuOJ/QAenCpnMQjsvMiJXtsNoMnj+UdKuqkCWbduneoteNJzOQ4AuOnKsTfPpD10PlzBRSsAXV2q\nHRW6+N1Q2zE2VXkS9Wbr9ujMXi4E10hsblZ+rWhz5gChEMxLlyBHRz0NJi9SdgGBvviKrKIPCkTW\nXQNRX4/Um28i1dmJ0KJFY16PP/c8ACB6yy2e61XrwnhDSZecw812OLnB+VlKuV3as45h9UtsklI2\nUzAQK414PK56C5785p1X4asf3YgbV4w1ElNvHAMAhK6u7HAzVV2qHRW6OMacH55EGY8D8TgQCgE5\nGjN+ozU5RmIROYmukdik/FoRuu6O1DO6ci9eMc5YRmLoCpqjRUUkgprbbgMAjP7kp2Nek8kkYvZz\nNbff5rletS6MN5R0mdJIFEJ8w56q0gegz56s4jbLllIO2O1vip/hxHjSbs/dpEZDbRg3rpg15hu2\nNE2k3nwLABBaUdmeRKq6VDsqdHFb4PhgJJrD6VCzKu+VL+Fm28DUmptJXCuFVDinztDNR3Soefdd\nAIDYj58e83z8xRch+/sRuuoqhK++2nMtBV2YbCjpMqmRKITYA6svohj3uF8I8Ubpt8cAwOpx8zYp\nY5w9CxmLQZs92w1ZVSrlpEs1oUIXXz2JTqhZwUg+B19zEpubSVwrhfRKNDocTyJhI/GOO4BoFIlX\nXkHq9Gn3+ZHHvwsAqH3/+yZcS0EXJhtKukxoJAohPon02L3dsKqat9v/LwAsF0J8MYhNVjvRaFT1\nFnImdazym2g7lJMu1YQKXZym137kJEqFjbQd0uHm4qubteZmEteKYyQaeRiJqTPpnESqaA0NqLv7\nA4CUGPrWPwOwciljP3oK0HXU3XffhGsp6MJkQ0mXyTyJW2GFmJdLKe+SUn7KftwFqyr4ALx7CzI+\n0zZFR31KJG03eXj1KsU7KT3lpEs1oUIXpwWOH57EdPsblZ5E20js9cFIbGokca2EHCOxszPnNWlP\nIs2cRIf6T3wCADD8ne8gceAA+j/7OcAwUHv33W5ltxcUdGGyoaTLZEbiJgCflFKeHP+C3Vfwk/Ce\nbML4zBWEQx3jSR52jEQ67vJSUU66VBMqdHGbafswcUV1I23An3Cz0ZP2JFK4VvSlSwBgTEh2MqSU\npHskZhJZuwb1H/01IJnExfe+H/Fnn4WYPh0zHvrMpOso6MJkQ0mXyYzERkwybURK2QpAZFY8M6WB\nSr+kXHA9iWvWKN5J6SknXaoJFbr46kkcVtv+BsgwEosJN/dcAgDos2aTuFZCS2wj8eTW2rTZAAAg\nAElEQVSpnI43u7utyVFNTUrzQ3Nlxhc+j9p77gGEgL5oEWZ+59tusc5EUNCFyYaSLlNVN+fyNbJ5\n/BNCiBl2RTTjA0ePHlW9hZwwR0aQOnkSCIUQvnKF6u2UnHLRpdpQoUt6LJ+PnkSFRqKorwfCYciR\nEchYrKBzmJesqRHarJkkrhV94UKrV+L58zn9nVKnTlnrbA8kdURNDZr/7mtY8NYbmPvyi4hef/2U\nayjowmRDSZepjERZ4HmbYRW3MD5QX68ugT0fUkeOAlIidOWVEIQSb0tFuehSbajQxTHoTB8KV5xz\nqPQkCiHSeYkF9EqUqZQVqhYCWnMziWtFhELQ7WbTTpPsyUgdtyayhlqWl3RffiNqaiC03FogU9CF\nyYaSLlNNXHlMCLEX9ui6CdgihBj/+l0o3MBkxkEpP2EykocPA6iOUDNQPrpUG0pyEqelPYlSyqL6\nG8rBQQCAaFCbyaM1N8O80A2zr2/KsOV4zL4+QEpozc0QoRCZayW0dAmMU6eQOnUK4asmb/afOn7c\nWtOyLIitKYGKLsxYKOkylZG41X5MhIQ1mo8pIR0dHWR+aZ5uO4fHnn0LX/7IBiybPdbTUU2VzQAt\nXZg0KnQR0SgQiQCJhDUtpYhJKa4nUXEenNZoeRKN3l6E81xrXrLyEZ15x1SuldDSpYjjFzBOTV28\n4hiJ4eXl5UnMByq6MGOhpMtUPunxTbTzeTA+MWxPYKDAE6914GxfDOf7s3N6EnZlc6RKPImUdGHS\nqNLFr4ba5qBlJArVRmIRFc6Gk49oJ+BTuVbc4pUcKpzdcHMFG4lUdGHGQkmXqYzELVJKLd8HgHuD\n2Hy1sHLlStVbAADEEim0nx2AJoBrrhjb/UgaBlJHjgAAQlXQ/gagowszFlW6OHmJxTbUlpetcLPW\noNZI1JsLb6htXrponWO25Umkcq24bXDsopSJkMmkNZJPCISWLS35vlRBRRdmLJR0mcpI3F3gefeB\nvYm+0dPTo3oLAIC2M/0wTImr5zdgWs3YAFTqjTcgYzHoV1xR8eP4HKjowoxFlS6+eRLdcLP6nESg\nUCPRqWy2jEQq10pomZVf6HgJJyJ1pgNIpaAvXAhRWxvE1pRARRdmLJR0mcxIvF9KOVjISe0G3DyN\nxSc6cqjEC4LWU1bYacOyrK5HSBw4CACIXLs+0D2phIouzFhU6SJ8aoMjnXCzYk+iO5qvoHCznZNo\nh5upXCuhpUuBcBhGRwfMSUJ6qeNvWcdXcNEKQEcXZiyUdJnQSJRSPlbMiYtdz6RZt26d6i0AAFpP\nWR6FjUs9jMT9BwAA4fXVYyRS0YUZiypd3IbaRU5dIVO4UkROoml7QnTbk0jlWhHhMEIrrBzD1Btv\nTHhcst1Onbn66kD2pQoqujBjoaRLbs2UGKXE43HVW8BI3MpH1DWBty3ODicn9+8HUF2eRAq6MNmo\n0kWbZvU2K9aTaDotcGbMKHpPxaAVk5N40alutjyJlK6VsG34JXMwEit9vCglXZg0lHRhI7EMaLdb\ny6ikrSOdj1hfM7ZzkjkyguSxY4CuI3zNNYp2GDwUdGGyUaVL2pNYeOGKlNItfFHuSXTCzT0FhJt7\nHCNxNgBa14pjJKaOHpvwmHQ7r8o2EinpwqShpAsbiWXAagI3qtaTdj7iUg8v4qFDgGEgvHIltApO\n8h4PBV2YbFTp4o7mK6J9hYzFAMOwpmaE8+1O6C9OPqFZQBK9U7ii255EStdK6GqriXbymLeRaI6M\nwDh1qirGi1LShUlDSRc2EsuAKIERd07RykavopVWK9RcTfmIAA1dmGxU6eJHCxwq01aAdD6h0dMD\nKfMboDW+mTala8UNNx/xno+bHi+6ouLHi1LShUlDSRc2EsuAtrY2pe8/Ek/hyLlB6JrAOo98xMSr\nrwIAIps2Br01pajWhfFGlS5OeLiYFjhUilYAQNTWWg29EwnIgYGc15nDw5ZHtCYKYc+gpXSt6IsX\nQ8yYAbO7G8a5rqzXE/Zew2vWBr21wKGkC5OGki5sJJYBqsfzjMlHjI7NR5SmifhrrwEAojfdqGJ7\nylCtC+ONKl2EU7hSlCeRRvsbB8cT6LS0yQXHi6jPmu3OsKZ0rQhNcwvsEvv2Zb2e2LsXABCtgi+9\nlHRh0lDShY3EMmCmnRukijfPWx9cXvmIqSNHIfsHoC9ciBChX+wgUK0L440qXTSncKWInERz0PLY\nUfAkAumJKWb3xZzXuI20Z6ZTU6hdK5ENGwAAidbWrNcSeywjsRoiI9R0YSwo6cJGYhlw9Kh37kxQ\n3L56LrZcvxi/evPSrNfir7wCAIjccEPAu1KPal0Yb1Tp4jbTLqJPYnpus/qcRCBdnWxczN1INLov\nAAD0OXPc56hdK5GNtpG4b6yRaJzrgnH2LMT06QhddZWKrQUKNV0YC0q6hKY+hFFNvZ3Xo4qFzXX4\no/eu8nwt/oqVj1htoWZAvS6MN6p0cT2JQ0WEm52cRCLhZn2OZSSaeYSbjQuWkajNnec+R+1aiVx7\nLaBpSBw8CPPyZddzO/rcL6zXr7sOQtdVbjEQqOnCWFDShT2JZQCl/IRMpGEg8fLLAIDojdVnJFLV\npdpRn5NYGYUrQEZOYj6exPO2J3HeXPc5ateKNmMGItdtAlIpxH/xnPv86DPPAgBqNt+hamuBQk0X\nxoKSLmwklgGU5jhmkjxwEGZfH/Qli6EvW6p6O4FDVZdqR9ns5mnFVzdTaoEDAPps25OYh5Fodndb\nazPCzRSvlZrNmwEAsZ/8BICVSxr/+S/s16rDSKSoC0NLFzYSy4DhIhLhS8nos/a37ttuc6sYqwmq\nulQ7qnRxm2lXSAscANBmO57E/MPN+ty0J5HitVL7nl8GAMSeegpGbx9i3/8B5MgIItddh9DChYp3\nFwwUdWFo6cJGYhmwcuVK1VvwZPRnPwMA1Nx+u+KdqIGqLtWOKl2cnoByaAjSNAs6R7pwhYaRqM+2\nvIHmpTzCzRcsT6I2N+1JpHithJYuRfT224DROAY+9zlc/tu/AwDUf/TXFO8sOCjqwtDShY3EMqCn\ngLFYpcbo7kbyYBsQjSJy802qt6MEirow6nQRug5RVweg8NF88rIVbqZSuOJ4Es08PImmhyeR6rXS\n8Md/BOg6Yj/4IYzOToTXrEHtr9yteluBQVWXaoeSLmwklgGU8hMcYk89BQCoueWWqprXnAlFXRi1\nuogiQ87pcDORnMSMZtq5jOaTiQTM3l5A193ZzwDdayWybh2a/+HvEVqxAtFbbkHzP3+rKqqaHajq\nUu1Q0oVb4JQB69atU72FLGI/+CEAoPbuDyjeiToo6sKo1UWbNh3mhW6YQ0MoxNSgNnFF1NZCTJtm\nhdAHBiAaGyc93qmC1mbPGmNsUb5Wat//PtS+/32qt6EEyrpUM5R0YU9iGRCPx1VvYQzGuS4kXtsD\n1ERRc9edqrejDGq6MBYqdSm2oTa1whUA0OwK51xG85nns0PNAF8rVGFdaEJJFzYSy4D29vbA37N7\nYBR/+YNDONOTnVs1snMnAKDm9jugTZsW9NbIoEIXZmpU6qLVW9dDoQ21TWItcICMhtq2ATgZXtNW\nAL5WqMK60ISSLmwklgGrV68O/D3/7cWT+O/Ws3j+6NiqRmkYGP7XfwMA1P/ahwPfFyVU6MJMjUpd\n0jmJ+ReuSCnTE1cIeRL1+fMBAMb581Me6zVtBeBrhSqsC00o6cJGYhkQjUYDf8+X3rRCS9dcMWPM\n86O7dsE4dw760qWI3nJL4PuihApdmKlRqYvbUPty/p5EGYsBhgHURCEiEb+3VjCukdjVNeWxRpdl\nSGZOWwH4WqEK60ITSrqwkVgGtLW1Bfp+Z3qG0dk7gobaMNYsSieqSylx+Wt/CwCY9hsfg9Cq+9cn\naF2Y3FCpSzENtZ1pK1Qqmx30BQsA5Ggknjs3Zo0DXys0YV1oQkmX6v6ULxOCnuP4zCHLG3DjilnQ\ntfQkldGnn0ay7XVoc+ag7tc+EuieKEJpviaTRqUuws7RLcST6BatEMpHBAB9vhU6dgzAyTDOngWA\nrIklfK3QhHWhCSVdKrYFjhBiG4Be+8cWKeUjpVgTBDMz+o2VGiklnm6zPAbvXjfffd4cGsLA5/8M\nADD9d3+nansjZhKkLkzuqNTFKeQqpJm2OeAUrdDJRwQyw8055CSetT2JC8d6EvlaoQnrQhNKulSk\nJ9E29iCl3Cml3AlgtxDiUb/XBMXRo0cDe6+DZ/px+tIwmuojuH659YsqpcTA5/4PjLNnEV53TVWN\nrZqMIHVhckelLo4nURaSkzgwAADQZsyY4shgyTUnURqGe8z4cDNfKzRhXWhCSZdK9STeL6Xc6Pwg\npWwVQmwuwZpAqLdnwgbBt587DgC4Z9MVCOkapJQY/L8PY2THTojaWjR95SsQoUr9tcmPIHVhckel\nLk5VsllATqJJ1EjUZs0CQiGYPT2Qo6MQNTWexxnnLwCGAW3OHIhxifd8rdCEdaEJJV0qzpMohGgE\nsMHjpf6JjL5C1gRJUPkJP329C6+81YO6iI4t1y9CfM8e9Hz4Ixj6+38AdB1Nf/s1hFevCmQv5QCl\nvBEmjdKcxCKaaVM1EoWuu82xnRY3XhjnrHzE8aFmgK8VqrAuNKGkSyW6hFoA9Hs83wvLENzt05pA\neOGRR/HvXRpMPQRncqoEICHcnyGd5ywakyP4ndPPYpoRB6TMeGDMz1JK7G1aiv+84mbEtTDO1jUD\nQsNHDz2F2IbfxoidVyUaG9H8ta+iZvMdQf7VydPR0UHqYmYsVOriNtMeLsBI7LduQYKYkQhYIWfj\n7FkYXV0ILVnieUy6aGVR1mt8rdCEdaEJJV0qzpMIoBnp4pNM+gFMlA2a1xohxDYhxF4hxN6uri53\nGHdHR4ebS9DT04MDBw7ANE3EYjHs27cPsVgMpmniwIED6OnpAWDlHky2/vnzCexvWIyD9QvQZj9e\nr1+AQ/Xzcdh5TJuP9mnzccR+vNy0HGdPnkNy/wEkDxxE8mAbkm2vI/n660geOoTk4cNItrcjdeQI\nDidq8Nb0+eionwUJ4IMHnsKdz+2AHB6GMXsW6n/z05jxkx/jcFNjQfsv9u9Pef3w8HBZ779S1w8P\nDyt7/9M9Vn/RZF9/3usHOzsBAFrjDHL//gM1Vvg4dfbshOt7DltTIvSFC7LWnzlzpmx+f6pp/blz\n58p6/5W6vre3N5D3zwUhpZz6qDLCDg8/KqVcPu75HQBOSCkf9GONw6ZNm+TevXv92bwHw22H0Hai\nG4YUgBAQQkATcP9fCEBY/wHs/2+O6lg0LTTmebj/n/GA1d7m1OUUDAnUR3TMnx4GhIDW1ATdntnK\nMExupE6cxIVbboW+dAnmvfhCXmv7fv8PMPLdHWj88l+h/lf/R4l2WBgDf/lFDH39G5j+R3+Iht//\nPc9j+h/6LIa/86+Y8ed/hmmf+HjAO2QYJk/E1IdUZrgZsDyD42kEMJn5XMiaklO/bi2uWthT0pL4\nq0p25sqmp6e0ujCFoVKXSsxJBOCGmI3Tpyc8JmW/pi9enPUaXys0YV1oQkmXSgw374Vl3I2nGUCr\nj2sCw3EnM7RgXWiiUhe3mXYhOYmEjUTdNhJTkxmJJ04CAELLlmW9xtcKTVgXmlDSpeKMRCllP4AT\ndsVyJo1SSs8ClELWBMm6detUb4HxgHWhiUpdRE0NoOvAaBwykchrrWMkUixcCS2d3EiU8bhVuKJp\nCC3OTrjna4UmrAtNKOlScUaizcMAHnJ+EEKMqVAWQrQIIXaMMwonXaOSeDyueguMB6wLTVTqIoRw\nQ8759kqU/bYnsZGekagvWACEwzAvdMOMxbJeT505A5gm9CsWQUQiWa/ztUIT1oUmlHSpSCNRSrkd\nwHEhxGYhxBYAm6WU92cc0gJgMzLyEHNYo4z29nbVW2A8YF1ooloXbbo1e1kODua1jnK4Weg69EVW\naxuvvMTUyYlDzYB6TRhvWBeaUNKlUgtXHKNvotd2A2jKZ41KVq9erXoLjAesC01U66LNmAGjo8M1\n+nJBJpOQIyOArrt5jdQILV0C4+RJpE6fRnjlyjGvTZaPCKjXhPGGdaEJJV0q0pNYaUTHjbhiaMC6\n0ES1LlqjlcXiNMfOBdeL2NBgta4iSKilBQCQeut41mupEyesYyYwElVrwnjDutCEki5sJJYBbW1t\nqrfAeMC60ES1Lk7hidmfuyfROZZi0YqD4z1M2g17M0m2HxlzzHhUa8J4w7rQhJIubCSWAVTG8zBj\nYV1ooloXp/BE5hNuHqBbtOIQXmUbiUeOjHleGgZStuEYWuU92121Jow3rAtNKOnCRmIZQKWpJjMW\n1oUmqnUpKtxM2JMYuvpqQAik3nxrTHuf1KnTkLEYtHnzoDdnpXoDUK8J4w3rQhNKurCRWAYc9Qjv\nMOphXWiiWhfH0MuncMUc6B+zliJaXZ3VVDuVQup4Oi8xZVdihidJtletCeMN60ITSrqwkVgG1NfX\nq94C4wHrQhPVuhRmJNL3JAJpQzBx8KD7XKLVGkoVWXfNhOtUa8J4w7rQhJIubCSWAZTyE5g0rAtN\nVOtSULi5DApXACB6/XUAgMQrr7rPxV97DQAQueH6Cdep1oTxhnWhCSVd2EgsAyjNcWTSsC40Ua1L\nIdXN6cIVrxHydIjcdCMAIP6qZRiaQ0NIvn4I0HVENm6ccJ1qTRhvWBeaUNKlYptpVxLDw8Oqt8B4\nwLrQRLUuhVQ3l024edUqiBkzYJw5g+Rbx5FsbwcMA5FNm6BNEiJTrQnjDetCE0q6sCexDFg5Qe8x\nRi2sC01U6+LmJOYTbu7rs9Y20fYkCl1H7bt/CQAQe/JJxL7/fQBA7XvfM+k61Zow3rAuNKGkCxuJ\nZUBPT4/qLTAesC40Ua2Lm5OYjyex1zYSm5unOFI9dVu2AAAuf+1vMfqTnwKRCGo/8P5J16jWhPGG\ndaEJJV3YSCwDKOUnMGlYF5qo1kVMmwZoGuTwMGQymdMas7cXQHkYiZGbbkT09tvdn6dt+yT0efMm\nXaNaE8Yb1oUmlHQRUkrVeyhrNm3aJPfu3VvS9zBNE5rG9jw1WBeaUNDl3JprIPv7Me/gfuizZk15\nfNfadTD7+jCv7QB0Qo10J8IcGcHwv3wH2owZqLvvXghdn/x4Apow2bAuNAlIl5yGxPNvRxkQj8dV\nb4HxgHWhCQVd0m1wpg45S8Nw8xepF644aHV1mP7pT6H+w786pYEI0NCEyYZ1oQklXdhILAPa7YkG\nDC1YF5pQ0CWfCmdzYACQEqJxBkSoMhtOUNCEyYZ1oQklXdhILANWTzLuilEH60ITCrrkM3XFzUds\nop+PWCgUNGGyYV1oQkkXNhLLgGg0qnoLjAesC00o6JLP1BXHSNTLoGilUChowmTDutCEki5sJJYB\nbW1tqrfAeMC60ISCLgV5EpubSronlVDQhMmGdaEJJV3YSCwDKM1xZNKwLjShoIvrSbSbZE+G2WcX\nrVSwJ5GCJkw2rAtNKOnCRmIZMLMMWmJUI6wLTSjootl7MHNoiltOPRILhYImTDasC00o6cJGYhlw\n9OhR1VtgPGBdaEJBF22mZfCxkWhBQRMmG9aFJpR0YSOxDKivr1e9BcYD1oUmFHRxPIlGT++Ux6ar\nmys3J5GCJkw2rAtNKOnCRmIZQCk/gUnDutCEgi5asx1u7s3Fk+jMba5cI5GCJkw2rAtNKOnCRmIZ\nQGmOI5OGdaEJBV30WbaReGlqI9GognAzBU2YbFgXmlDShY3EMmB4eFj1FhgPWBeaUNDFMfjMvj5I\n05z02GoIN1PQhMmGdaEJJV2ElFL1HsqaTZs2yb1796reBsMwxDi3ag3k4CDmvd4GfZJQ8rmrV0EO\nDWF++6Gymd3MMEzZI3I5iD2JZUBPDhWSTPCwLjShoovrTZwkL9EcGYEcGgKiUYiGhqC2FjhUNGHG\nwrrQhJIubCSWAZTyE5g0rAtNqOii59Ar0bx40Tp29mwIkdMX+7KEiibMWFgXmlDShY3EMmDdunWq\nt8B4wLrQhIou6V6JE7fBMbotI1GbPSuQPamCiibMWFgXmlDShY3EMiAej6veAuMB60ITKrposyzD\nb1JP4qW0J7GSoaIJMxbWhSaUdGEjsQxob29XvQXGA9aFJlR0cXISjUuXJjwm7UmcE8ieVEFFE2Ys\nrAtNKOnCRmIZsHr1atVbYDxgXWhCRRc3J7F34nCzm5M4p7I9iVQ0YcbCutCEki5sJJYB0WhU9RYY\nD1gXmlDRxQ0324agF64ncVZl5yRS0YQZC+tCE0q6sJFYBrS1taneAuMB60ITKrroc+cCAIzu7gmP\ncXMS51R2uJmKJsxYWBeaUNKFjcQygNIcRyYN60ITKrpo8+YBAIzz5yc8Jp2TWNnhZiqaMGNhXWhC\nSRc2EsuAmXZuE0ML1oUmVHTR59mexPMXMNFkK9P2MlZ6TiIVTZixsC40oaQLG4llwNGjR1VvgfGA\ndaEJFV20+nqI6dOBeByyvz/rdWkYrpdRt72OlQoVTZixsC40oaQLG4llQH19veotMB6wLjShpIs+\nScjZ7O4GDAParFkQhBLVSwElTZg0rAtNKOnCRiIAIUSLEGKz6n1MBKX8BCYN60ITSrq4xSsXLmS9\nZpzrso5ZMD/QPamAkiZMGtaFJpR0qUgjUQixTQixxX48kMOSDQB2CCGkEKJPCLFLCLGh1PvMFUpz\nHJk0rAtNKOkyWfFK6uxZAIC+YEGge1IBJU2YNKwLTSjpElK9Ab8RQmwDACnlTvvnDUKIR6WU90+2\nTkrZJIRolFJmJw8pZnh4WPUWGA9YF5pQ0sUtXunKNhKNc+esYxYuDHRPKqCkCZOGdaEJJV0qzkgE\ncL+UcqPzg5SyNddQMkUDEQBWrlypeguMB6wLTSjp4uQkmlUebqakCZOGdaEJJV0qKtwshGiEFToe\nTz/lnMOp6OnpUb0FxgPWhSaUdHEMQCe0nInRZXsS51d+uJmSJkwa1oUmlHSpKCMRQAsAL29gL7yN\nRxchxOaMxwO2wTnRsduEEHuFEHu7urrc/IGOjg63dL2npwcHDhyAaZqIxWLYt28fYrEYTNPEgQMH\n3F+Co0ePTrn+1KlTRa0v9v15vfd65/hy3X+lru/o6CCzf22RlYA+fOxY1nrDNhx7QiFS/36lWN/e\n3l7W+6/U9ceOHSvr/Vfq+hMnTgTy/rkgJmryWo7Y3sJHpZTLxz2/A8AJKeWDE6xrAQAp5YmMnx+V\nUt451Xtu2rRJ7t27t+i9T4ZpmtC0SrPnyx/WhSaUdDFHRtB15dVAOIwFx9+E0HUAgJQSXavXQg4O\nYt7B/dArfHYzJU2YNKwLTQLSReRyEP92wDIOHQPR+RlAC5UK53g8rnoLjAesC00o6aLV1UGbMwdI\nJsdUOJu9vZCDgxDTp0MjNF2hVFDShEnDutCEki5kjUQ7pLsrx0dmaLjZ43SNAPIN8vcD2FTwX8BH\n2tvbVW+B8YB1oQk1XUJLlgAAjFOn3edSJ05ary1bCiFy+kJf1lDThLFgXWhCSRey1c1Syu0Atue5\nbC8sg3A8zQBavRbYoeXjUsrxd+pe+6Gc1atXq94C4wHrQhNquuhLlgB79iB1+jSib78ZAJA66RiJ\ny1RuLTCoacJYsC40oaQLWU9iIdgtbE54FJ00Sil3T7CsF4BXD8VNmMCwDJpohY/sKldYF5pQ0yW0\n1PIkpk64GS0wqsxIpKYJY8G60ISSLhVlJNo8DOAh5wc7r3B3xs8tQogdjiHp1RvRbsj93cw8RZW0\ntbWp3gLjAetCE2q6hFdZPc+SGSGkZPsRAEDoqquU7CloqGnCWLAuNKGkC9lwc6FIKbfb+YybYYWe\nW8ZNW2kBsBlWCLo/Y80D9s+O8TjphJYgoTTHkUnDutCEmi7hNWsAAMlDhyGlhBACiUOHrNfWrlW5\ntcCgpgljwbrQhJIuFdUCRwVBtMBhGKZ8kVKia801kAMDmLdvDxAO4/y69RB1dZh/7AgEtyBhGCZ4\nuAVOpeA0yGRowbrQhJouQgiE7UT0xIEDSOzbBwAIr11TNQYiNU0YC9aFJpR0qbhwcyVSX1+veguM\nB6wLTSjqEr35JiRefhnx554H7Iba0Xe8Q/GugoOiJgzrQhVKunC4uUg43MwwzFQk9rXi4gfuhjZv\nLiAlzAvdmPX9JxG97jrVW2MYpjrhcHOl4MxmZGjButCEoi7ha9dDX7YM5vkLMC90Q1+6BJGNG1Vv\nKzAoasKwLlShpAsbiWXA8PCw6i0wHrAuNKGoi9A0zPjcZwFNA4TAjD/5k6rJRwRoasKwLlShpAuH\nm4uEw80Mw+RKtU1aYRiGLBxurhR6evIdO80EAetCE8q6hJYtq0oDkbIm1QzrQhNKurCRWAZQyk9g\n0rAuNGFd6MGa0IR1oQklXTjcXCRBhJtN04RWRflL5QLrQhPWhR6sCU1YF5oEpAuHmyuFeDyueguM\nB6wLTVgXerAmNGFdaEJJFzYSy4D29nbVW2A8YF1owrrQgzWhCetCE0q6cLi5SIIIN8diMdTW1pb0\nPZj8YV1owrrQgzWhCetCk4B04XBzpRCNRlVvgfGAdaEJ60IP1oQmrAtNKOnCRmIZ0NbWpnoLjAes\nC01YF3qwJjRhXWhCSRc2EsuAK664QvUWGA9YF5qwLvRgTWjCutCEki6ck1gkPHGFYRiGYZgyg3MS\nK4WjR4+q3gLjAetCE9aFHqwJTVgXmlDShY3EMqC+vl71FhgPWBeasC70YE1owrrQhJIuHG4uEg43\nMwzDMAxTZnC4uVKgNMeRScO60IR1oQdrQhPWhSaUdGFPYpEIIS4COF3it5kF4FKJ34PJH9aFJqwL\nPVgTmrAuNAlCl0tSyndPdRAbiWWAEGKvlHKT6n0wY2FdaMK60IM1oQnrQhNKunC4mWEYhmEYhsmC\njUSGYRiGYRgmCzYSy4PtqjfAeMK60IR1oQdrQhPWhSZkdOGcRIZhGIZhGCYL9tJQ+PwAAAhzSURB\nVCQyDMMwDMMwWbCRyDAMwzAMw2QRUr0BZmKEENsA9No/tkgpH1G5H8bC1gUANtp/Piil7Fe1HyYb\nIcQOKeVW1ftgACHEAwD6Yd/LpJQ71e6IybiHNQKYCeBLfA8LHiHEBgAPed2rqHz+s5FIFOcidm6o\nQogNQohHpZT3q91ZdSOE2Cal3J75M4B9AJar2xWTiX3j3aJ6H4xlrMP6EnXC/lkKIZrYIFGHbbRv\nz9TA1om/VAWEfY+6z/6xxeN1Mp//HG6my/2ZxoiUshXAZoX7qXqEEI3jn7M1ahZCsDZ0aFa9Acb9\noNvjGIg2y9lAVM51Hhqc8Lq/MaVBStkqpXwQwOMTHELm85+NRILYF+sGj5f62RhRSguARz1upifg\n8W2QCR4hxBYp5W7V+2AAAA8DGBNaHmcwMmposT1ZmTSy8U4Dap//bCTSpAVWDs94euH9y8MEgP1t\nbqPHzbQFlqHIKMT+4GtVvQ/G/aBrtP9/ixBisxDiAfZWkeCTAPbZYWfYhsejarfEZEDq85+NRJo0\nI52wmkk/rCRjRhG2oegihNgC4AR7r0jQwp4qMjgfdI1Syp329bEdwDNqt8XY97DlAB4SQvRlPMfQ\ngNTnPxuJDFMgtlfkIQB3qN5LtWOHmblqlg7NsDyJrtHueOA5ZUYtQogWWIVdy2AZ7rsyqp0ZZgxs\nJNLFK/m+EUBP0BthJuRhAFs5l0ct9oceexBpcQJIG4YZcMqMeh6UUj4ipey3iyc2AniYjXdSkPn8\n5xY4NNkLO59nHM3gnCsS2Pk8D3N4kwSbATSO/5Bz+vNlVgkywSClPCGEmOhl/lKlCPsa2ZX5nJSy\nVQixFcCdADhtRj2kPv/ZSCSIlLJfCHFCCDG+4qyRc9/UY4dmdmYaiEKIzayNGryMQCHEw9x8Xjmt\nQojxeaItsD4EGVqcAEepSEDt85/DzXR5GFa+GwC3cpONEMXY38T3ZjQHzvJgMQwDAHjQfgBw72En\nuEhCHbaRcZ/HS1tg5ScywTJRT1cyn/9CSqnifZkcsD1WJ2C5nnksn2Ls3LfjE7zMUyQIYBvs98P6\n0NsJ4FH28KrDrv53eojOtHPgGIVkFNz1wK5Ax7jICFNa7M+S+2GlymyAZaDv85jmpfzzn41EhmEY\nhmEYJgsONzMMwzAMwzBZsJHIMAzDMAzDZMFGIsMwDMMwDJMFG4kMwzAMwzBMFmwkMgzDMAzDMFmw\nkcgwDMMwDMNkwUYiwzBVhxBisxBC5vk4Pu4cW4QQfXYvwLJBCLHN7pWXz5oHSrUfhmHowkYiwzDV\nSKaR9AiA5QA2Zjy3G0ATrHm2zoSQ8dMR7rfP4zXBgiRCiB0A7iyg8Xu/EOJ4vsYlwzDlDc9uZhim\nGnEMvkcyp4AIIZwJFK22IbVbCHEHgJMYa1gClpF4P4BHA9hv0QghHoU1uWHjlAePQ0q5XQixEcA+\nWAY1wzBVAHsSGYapZr401QG2sZh1nJTyhJTywXIYZ2aHxLchY5ZyATwIoMU2NhmGqQLYSGQYphrJ\n9BbmQrnPf34M1t+34L+H/W/1CIBtQogNvu2MYRiysJHIMEw1MhPA3lwPllK2AkA55uTZXsRG+GPo\n7rL/vN+HczEMQxw2EhmGqUZ2If9cwgcBK7dvXNXzw84BQoiHx722za6C3udUSAshttnHtgghdtgV\n0n2Z5xmPfZ5d9jn25Vlt7Bh0eyY49xZ7X87+HrD35bUfx7Delsf7MwxTprCRyDBM1SGl3O14B/NY\n84gdcn0QVvFG1nq7CGY5ACdP8X5Yod7dALYDaAHwqG3k7bOP+RKAXgAPeOX72c89CmCHlFLY7/+w\nXamcC5vtP7P2K4TYbO9vq33uO+2HZ1sf++/fb6/lkDPDVDhsJDIMw+SBlLLfLlbxDN/arzkG2QYA\nG+0Cl/th5fQBwMMAtkspt0opH4FlmAFWvp8b0s4oONktpdxun3+3fZ4ttpE3IePC470eh2wF8F3H\nYLaLce5E2sj1wjlPy2TvzTBM+cNGIsMwTOnYOa76eVfG/7sV0+OOyTS+nJDveA/jrnGvT4Tb23GC\nIp1mAPd6NAR/EEDPBOd0zsNGIsNUOGwkMgzDlI7xeYCOF67fw2jz8t61TPCa4yEsNuS7yz7XDjsn\ncZcdCm+1PZwMw1QxbCQyDMOUjola7HiFfscghMj01DmFL1IIIQHsyDhusorr3smOs0PYmcbgZlje\nSbfAxgPnPOT7QzIMUxxsJDIMw9Ak05BsklKKCR4T9nrMLDRB9lhBCCE22/mSTtHKIxnHT1T97ZyH\njUSGqXDYSGQYhiHIOONvk9cxOVYYO21rvI7d4RS/2BXfD0opm5Bu9zMm79D2Rjbax+dVHc4wTPnB\nRiLDMAxdnFBw1jg927jLpQ2O4xG8boLXvYpfdgNZBTVA2ljdnsP7MgxT5rCRyDBM1SOEaLSNLrcg\nxG52PVm+X8u4P71eWz7B81mh34znXK+h3XexFcBmu6hkmxBis93oegesFjaTIqXcCSuE7Nn7ENbf\ndZfjlbS9h4/B2xB0WvVMVVXNMEwFIKSUqvfAMAyjDLua9/+3dwc3DQNBFEC/O0gLiBIogVADJVBC\niqIEqCWUEHdgDrsEy5OAkBAK8Xtn73qPX7OrmbOhp7/Xm3//UcGbB8gxLbBtUqt7Y5KbJG+LNcln\nhXD5//00TceA2c/4mHZlPKZV+nYnKn0n9RY3z0ke5vObh2E4JLlPC6ZPff99Wuue3WKPTZJDWn9H\nY/lgBYREgBXok1u28/D5l+uB/8d1M8AK9Orf6w/G+R31djjbJHe/fjDgYgmJACvRg+LLN28tz629\n/ardDnB9XDcDAFCoJAIAUAiJAAAUQiIAAIWQCABAISQCAFAIiQAAFEIiAACFkAgAQPEOJ+d25Bv8\nX7MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120c96b00>"
      ]
     },
     "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('Position (m)',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'$x$')\n",
    "plt.plot(t, resp_out[2,:], linewidth=2, linestyle = '--', label=r'$y$')\n",
    "\n",
    "# If there is a non-zero force disturbance show where it began via an annotation\n",
    "if F_amp > 0:\n",
    "    plt.annotate(r'Force Disturbance Begins',\n",
    "         xy=(DistStart,resp[-1,2]), xycoords='data',\n",
    "         ha='center',\n",
    "         xytext=(DistStart, 1.05*np.max(resp_out[0,:])), textcoords='data', fontsize=16,\n",
    "         arrowprops=dict(arrowstyle=\"simple, head_width = 0.35, tail_width=0.05\", connectionstyle=\"arc3\", color=\"black\"),color = \"black\")\n",
    "    \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('MassSpringDamper_Disturbance_Resp.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 contorl 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",
    "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 $x$ and $\\dot{x}$ equally. We won't penalize the position input $y$ or its deriviative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Q = np.array([[ 1000,  0,  0,  0],\n",
    "              [ 0,  0,  0,  0],\n",
    "              [ 0,  0,  1000,  0],\n",
    "              [ 0,  0,  0,  0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this problem, we'll also need to slightly redefine our $B$ matrix to only include the input that will define our desired system states $\\mathbf{w_d}$. It becomes:\n",
    "\n",
    "$ \\quad \\widehat{B} = \\begin{bmatrix} 0  \\\\\n",
    "                            0  \\\\\n",
    "                            x_d  \\\\\n",
    "                            0  \\end{bmatrix} $\n",
    "\n",
    "We'll set R to something small, since we don't want or need to penalize the acceleration input to heavily. Since the revised $B$ matrix, $\\widehat{B}$ is just a column, the $R$ matrix becomes a scalar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B_hat = np.array([[0], [0], [0], [1]])\n",
    "\n",
    "R = 0.001"
   ]
  },
  {
   "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": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K, _, closedLoopEigenvalues = control.lqr(A, B_hat, Q, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we need to use the calculated gain matrix to implement the controller. To do so, we'll write:\n",
    "\n",
    "$ \\quad \\widehat{A} = A - \\widehat{B}K $\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}} = \\widehat{A} \\bar{w} + B_{dist} f $\n",
    "\n",
    "where $B_{dist}$ is just the part of the original matrix that operates on the disturbance force, $f$:\n",
    "\n",
    "$ \\quad B_{dist} = \\begin{bmatrix}  0    \\\\\n",
    "                                    -1/m \\\\\n",
    "                                    0    \\\\\n",
    "                                    0    \\end{bmatrix} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A_hat = A - B_hat * K\n",
    "\n",
    "B_dist = np.array([[0], [-1/m], [0], [0]])\n",
    "\n",
    "# C is unchanged\n",
    "\n",
    "D_hat = D = np.zeros((4,1)) # no direct passthrough of input to output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sys_lqr = control.ss(A_hat, B_dist, C, D_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this formulation, we are just looking at the disturbance rejection properties of this controller. \n",
    "\n",
    "*Note:* This notebook will be updated soon to include position response, as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t_LQRresp, LQRresp_out, LQRstates_out = control.forced_response(sys_lqr, t, force_input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAGTCAYAAABzkIUwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120ea13c8>"
      ]
     },
     "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('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "# plt.ylim(-1.,1.)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t, LQRresp_out[0,:], linewidth=2, linestyle = '-', label=r'$x$')\n",
    "plt.plot(t, LQRresp_out[2,:], linewidth=2, linestyle = '--', label=r'$y$')\n",
    "\n",
    "# If there is a non-zero force disturbance show where it began via an annotation\n",
    "if F_amp > 0:\n",
    "    plt.annotate(r'Force Disturbance Begins',\n",
    "         xy=(DistStart,LQRresp_out[-1,2]), xycoords='data',\n",
    "         ha='center',\n",
    "         xytext=(DistStart-2, 2.5*np.max(LQRresp_out[0,:])), textcoords='data', fontsize=16,\n",
    "         arrowprops=dict(arrowstyle=\"simple, head_width = 0.35, tail_width=0.05\", connectionstyle=\"arc3\", color=\"black\"),color = \"black\")\n",
    "    \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('MassSpringDamper_Disturbance_Resp.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To form some intuition about the LQR controller behavior, try changing the values in the $Q$ and $R$ matrices and re-running the code. For example, if you place higher weights on the 2nd state, which represents the velocity of the mass $\\dot{x}$, you should see a response that exhibits a higher damping ratio than for lower weights on the state. You can also add weights to the $y$ and $\\dot{y}$ states to limit its motion."
   ]
  },
  {
   "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": 24,
   "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": 24,
     "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\"))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}