InverseSensorModels.ipynb

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  "signature": "sha256:60743108a8dc9c1e24fd74a6addccdf709efb04fbccf58443c5e101a45f192db"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import matplotlib.cm as cm\n",
      "import matplotlib.mlab as mlab\n",
      "\n",
      "from IPython.html.widgets import interact\n",
      "from IPython.html import widgets\n",
      "\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Inverse Sensor Models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Gives the probability $P$ of how a sensor reading $z$ might be, with a given sensor pose $x$ and an environment $m$.\n",
      "\n",
      "$P(z\\mid x,m)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def normalize(P):\n",
      "    return P/np.max(np.sum(P))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "2D Mixture Density"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Good tutorial video:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import HTML\n",
      "HTML(\"\"\"\n",
      "<video width=\"500\" height=\"260\" controls>\n",
      "  <source src=\"http://ais.informatik.uni-freiburg.de/teaching/ss13/robotics/recordings/rob1-07-sensor-models.mp4\" type=\"video/mp4\">\n",
      "</video>\n",
      "\"\"\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<video width=\"500\" height=\"260\" controls>\n",
        "  <source src=\"http://ais.informatik.uni-freiburg.de/teaching/ss13/robotics/recordings/rob1-07-sensor-models.mp4\" type=\"video/mp4\">\n",
        "</video>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "<IPython.core.display.HTML at 0x10b060450>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$P(z\\mid x,m) = \\left(\\begin{matrix}P_{hit}(z\\mid x,m) \\\\ P_{unexp}(z \\mid x,m) \\\\\u00a0P_{max}(z \\mid x,m) \\\\ P_{rand}(z \\mid x,m) \\end{matrix}\\right)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = np.arange(0, 10.01, 0.01)   # Entfernungen"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Measurement Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sensor readings are normal distributed around the true value with standard deviation $\\sigma_z$ and mean $z_{exp}$.\n",
      "\n",
      "$P_{hit}(z\\mid x,m) = \\frac{1}{\\sqrt{2 \\pi \\sigma_z^2}} \\cdot \\exp{\\left(-\\frac{1}{2} \\cdot \\frac{(z-z_{exp})^2}{\\sigma_z^2}\\right)}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "varz = 0.05 # Variance\n",
      "zexp = 5.0  # here is the obstacle\n",
      "\n",
      "Pzx_hit = 1.0/np.sqrt(2*np.pi*varz) * np.exp(-1/2.0*(zs-zexp)**2/varz)\n",
      "Pzx_hit = normalize(Pzx_hit)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Unexpected Obstacles"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There might be measurements before the beam hits the real obstacle.\n",
      "\n",
      "$P_{unexp}(z \\mid x,m) = \\lambda \\cdot \\exp{\\left(-\\lambda \\cdot z\\right)}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lamb = 0.5\n",
      "\n",
      "Pzx_unexp = lamb * np.exp(-lamb * zs)\n",
      "Pzx_unexp[zs>zexp] = 0.0\n",
      "\n",
      "Pzx_unexp = normalize(Pzx_unexp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Random Measurements"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is a random distribution, that the measurement is somewhere.\n",
      "\n",
      "$P_{rand}(z \\mid x,m) = \\frac{1}{z_{max}}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Pzx_rand = np.ones(len(zs)) * 0.01\n",
      "\n",
      "Pzx_rand = normalize(Pzx_rand)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Max Range Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The beam can get lost and is responding with the maximum value.\n",
      "\n",
      "$P_{max}(z \\mid x,m) = \\delta(z_{max})$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Pzx_maxrange = np.zeros(len(zs))\n",
      "Pzx_maxrange[-2:] = 0.03\n",
      "\n",
      "#Pzx_maxrange = normalize(Pzx_maxrange)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Resulting Mixture Density"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Pzx = Pzx_hit + Pzx_unexp + Pzx_rand + Pzx_maxrange\n",
      "Pzx = normalize(Pzx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(12,6))\n",
      "ax1 = plt.subplot2grid((4,4), (0,0), rowspan = 2)\n",
      "plt.plot(zs, Pzx_hit)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('Measurement Noise')\n",
      "plt.ylabel(r'$P(z \\mid x,m)$')\n",
      "\n",
      "ax2 = plt.subplot2grid((4,4), (0,1), rowspan = 2, sharey=ax1)\n",
      "plt.plot(zs, Pzx_unexp)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('Unexcpected Obstacles')\n",
      "\n",
      "ax3 = plt.subplot2grid((4,4), (0,2), rowspan = 2, sharey=ax1)\n",
      "plt.plot(zs, Pzx_rand)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('Random Measurement')\n",
      "\n",
      "ax4 = plt.subplot2grid((4,4), (0,3), rowspan = 2, sharey=ax1)\n",
      "plt.plot(zs, Pzx_maxrange)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('Max Range Measurement')\n",
      "\n",
      "ax5 = plt.subplot2grid((4,4), (2,0), colspan=4, rowspan = 3)\n",
      "plt.plot(zs, Pzx)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('= Mixture Density')\n",
      "plt.ylabel(r'$P(z|x,m)$')\n",
      "plt.xlabel('z [$m$]')\n",
      "\n",
      "for ax in [ax2, ax3, ax4]:\n",
      "    plt.setp(ax.get_yticklabels(), visible=False)\n",
      "    # The y-ticks will overlap with \"hspace=0\", so we'll hide the bottom tick\n",
      "    #ax.set_yticks(ax.get_yticks()[1:])\n",
      "    ax.text(-1.5,np.max(Pzx_maxrange)/2,'+', fontsize=20)\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.savefig('InverseSensorModel-MixtureDensity.png', dpi=150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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btp/KSu+dbm1t7bAtXcfTk6Z1Tulb0zqnVH9O2WPzGzQthCNPoSquu7yNwwaB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\n6xY/lHWeOQ6xzL2hTgl4Q4nuKoaSOOEfATpjLGdlnWdSVJRr4pnMSFQ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       "text": [
        "<matplotlib.figure.Figure at 0x10be07150>"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fit the model with real data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![ibeo Lux](http://www.mechlab.de/wp-content/uploads/2012/02/ibeoLUX.jpg)\n",
      "\n",
      "Maximize likelihood of the data:\n",
      "$P(z \\mid z_{exp})$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ibeo2XYZ(theta, dist, layer):\n",
      "    '''\n",
      "    Berechnet die kartesischen X,Y,Z-Koordinaten aus polaren Koordinaten des IBEO Lux Laserscanners unter der Annahme er ist perfekt horizontal ausgerichtet.\n",
      "    \n",
      "    Input:\n",
      "        - theta: Horizontaler Winkel\n",
      "        - dist : polarer Abstand\n",
      "        - layer: Ebene\n",
      "    '''\n",
      "    # Ibeo Lux hat 3.2\u00b0 bei 4 Ebenen vertikal\n",
      "    oeffnungswinkel = 3.2\n",
      "    ebenen = 4.0\n",
      "    \n",
      "    # aus Ebene den Vertikalwinkel berechnen\n",
      "    phi = (layer * oeffnungswinkel/(ebenen-1) - oeffnungswinkel/2.0) * np.pi/180.0\n",
      "    \n",
      "    X = dist * np.cos(theta)\n",
      "    Y = dist * np.sin(theta)\n",
      "    Z = dist * np.sin(phi)\n",
      "    \n",
      "    return np.array([X, Y, Z])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('kalibrierungtisch2.txt', delimiter='|')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.head(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th># &lt;Zeitstempel&gt;</th>\n",
        "      <th>&lt;Ebene&gt;</th>\n",
        "      <th>&lt;Echo&gt;</th>\n",
        "      <th>&lt;Winkel&gt;</th>\n",
        "      <th>&lt;Radius&gt;</th>\n",
        "      <th>&lt;Xwert&gt;</th>\n",
        "      <th>&lt;Ywert&gt;</th>\n",
        "      <th>&lt;EchoPulsBreite&gt;</th>\n",
        "      <th>&lt;Scanflags&gt;</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1350996337947</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.872665</td>\n",
        "      <td> 184</td>\n",
        "      <td> 118</td>\n",
        "      <td> 140</td>\n",
        "      <td> 160</td>\n",
        "      <td> 68</td>\n",
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        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1350996337947</td>\n",
        "      <td> 1</td>\n",
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        "      <td> 0.872665</td>\n",
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        "      <td> 139</td>\n",
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        "      <td> 208</td>\n",
        "      <td> 68</td>\n",
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        "      <td> 1350996337947</td>\n",
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        "      <td> 0.863938</td>\n",
        "      <td> 187</td>\n",
        "      <td> 121</td>\n",
        "      <td> 142</td>\n",
        "      <td> 160</td>\n",
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        "      <td> 143</td>\n",
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        "      <td> 204</td>\n",
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        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1350996337947</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.855211</td>\n",
        "      <td> 189</td>\n",
        "      <td> 123</td>\n",
        "      <td> 142</td>\n",
        "      <td> 184</td>\n",
        "      <td> 68</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "   # <Zeitstempel>  <Ebene>  <Echo>  <Winkel>  <Radius>  <Xwert>  <Ywert>  \\\n",
        "0    1350996337947        0       0  0.872665       184      118      140   \n",
        "1    1350996337947        1       0  0.872665       217      139      166   \n",
        "2    1350996337947        0       0  0.863938       187      121      142   \n",
        "3    1350996337947        1       0  0.863938       221      143      168   \n",
        "4    1350996337947        0       0  0.855211       189      123      142   \n",
        "\n",
        "   <EchoPulsBreite>  <Scanflags>  \n",
        "0               160           68  \n",
        "1               208           68  \n",
        "2               160           84  \n",
        "3               204           84  \n",
        "4               184           68  "
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Let's see how they are collected, line by line"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@interact\n",
      "def integratemeasurement(t = widgets.IntSliderWidget(min=1, max=5000, step=1, value=40, description=\"\")):\n",
      "    #print t\n",
      "    f = (data['<Ebene>']==3) & (data['<Winkel>']>-0.015) & (data['<Winkel>']<0.015)\n",
      "    angle = data['<Winkel>'][f].iloc[:t]\n",
      "    distance = data['<Radius>'][f].iloc[:t] /100.0\n",
      "    layer = data['<Ebene>'][f].iloc[:t]\n",
      "\n",
      "    plt.scatter(distance,angle, s=50, alpha=0.1)\n",
      "    \n",
      "    plt.axis('equal')\n",
      "    plt.xlabel('z [$m$]')\n",
      "    plt.ylabel('$\\phi$ [$rad$]')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FSCtTrr8H/iTBTBfjptLOC22bz+DH7E7iXUxQaK6sBuIvOlEy+T72SWYK+1/A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\nIiIiIiIiIiIiIiIiIvH5//36o5Ov8xp1AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106956d90>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timestamps = data['# <Zeitstempel>'].unique()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=[]\n",
      "y=[]\n",
      "for i, timestamp in enumerate(timestamps):\n",
      "    \n",
      "    #f = (data['# <Zeitstempel>']==timestamp) & (data['<Ebene>']==3)\n",
      "    #f = (data['# <Zeitstempel>']==timestamp) & ((data.index%467.0)==0)\n",
      "    f = (data['# <Zeitstempel>']==timestamp) & (data['<Ebene>']==3) & (data['<Winkel>']>-0.015) & (data['<Winkel>']<0.01)\n",
      "    \n",
      "    angle = data['<Winkel>'][f]\n",
      "    distance = data['<Radius>'][f] /100.0\n",
      "    layer = data['<Ebene>'][f]\n",
      "    \n",
      "    # 350. Punkt jedes Zeitstempels nehmen\n",
      "    [xe, ye, ze] = ibeo2XYZ(angle, distance, layer)\n",
      "    \n",
      "    x.extend(xe)\n",
      "    y.extend(ye)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(x,y)\n",
      "plt.axis('equal')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "(2.1400000000000001,\n",
        " 2.2600000000000002,\n",
        " -0.040000000000000001,\n",
        " 0.019999999999999997)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1069961d0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(6,3))\n",
      "plt.hist(x, bins=5, align='mid');\n",
      "#plt.axvline(np.mean(x), alpha=0.6, c='k')\n",
      "plt.xlim(0, 5)\n",
      "#plt.title('Histogram of real ibeo Lux Sensor measurement')\n",
      "plt.xlabel('z [$m$]')\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.savefig('Histogram-ibeoLux-InverseSensorModel.png', dpi=150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x108840150>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Actually, the sensor is so good, that all assumptions are not necessary. It basically just detects the obstacle with a very narrow normal distribution. In case of a deterministic grid, you even do not have to assume a normal distribution, because the discrete cells can't determine the difference.\n",
      "\n",
      "Like so, it is implemented in Hornung, A., Wurm, K. M., Bennewitz, M., Stachniss, C., & Burgard, W. (2013). OctoMap: an efficient probabilistic 3D mapping framework based on octrees. Autonomous Robots, 34(3), 189\u2013206. doi:10.1007/s10514-012-9321-0"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Multivariante Gaussian for Sensor"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sensors scan a 3D environment, so we have to take a look at a multivariant gaussian sensor."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Range for Sensor Readings"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = np.arange(0, 10.1, 0.01)   # Entfernungen\n",
      "ts = np.arange(-1, 1.1, 0.01)   # Winkel"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Standard Deviations for Angle and Distance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calcmultivargauss(sigmaz, sigmat, dxy, txy):\n",
      "    P = np.zeros((len(zs), len(ts)))\n",
      "    x = np.zeros((len(zs), len(ts)))\n",
      "    y = np.zeros((len(zs), len(ts)))\n",
      "    for i,z in enumerate(zs):\n",
      "        for j,t in enumerate(ts):\n",
      "            x[i,j] = z * np.cos(t)\n",
      "            y[i,j] = z * np.sin(t)\n",
      "            P[i,j] = 1.0/(2.0*np.pi*sigmat*sigmaz) * np.exp(-0.5*((z-dxy)**2/sigmaz**2 + (t-txy)**2/sigmat**2))\n",
      "            \n",
      "    return x,y,P"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@interact\n",
      "def plotmultivargauss(sigmaz = widgets.FloatSliderWidget(min=0.01, max=5.0, step=0.01, value=0.3, description=\"\"), \\\n",
      "                      sigmat = widgets.FloatSliderWidget(min=0.01, max=1.0, step=0.01, value=0.2, description=\"\"), \\\n",
      "                      dxy = widgets.FloatSliderWidget(min=0.0, max=9.0, step=0.1, value=4.0, description=\"\"), \\\n",
      "                      txy = widgets.FloatSliderWidget(min=-1.0, max=1.0, step=0.1, value=0.0, description=\"\")):\n",
      "    \n",
      "    x,y,P = calcmultivargauss(sigmaz, sigmat, dxy, txy)\n",
      "    \n",
      "    plt.contourf(x, y, P, cmap=cm.gray_r)\n",
      "    plt.scatter(0, 0, s=250, c='k')\n",
      "    plt.plot([0, 10*np.cos(np.max(ts))],[0, 10*np.sin(np.max(ts))], '--k')\n",
      "    plt.plot([0, 10*np.cos(np.min(ts))],[0, 10*np.sin(np.min(ts))], '--k')\n",
      "    plt.xlabel('X');\n",
      "    plt.ylabel('Y');\n",
      "    plt.xlim([0, 8]);\n",
      "    plt.ylim([-4, 4]);\n",
      "    \n",
      "    return plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3705lZSWDBg1i69atpmOJiMVsmxGMB3KB2+r/QDOCxGzfvp1LLrmE9evXk5+f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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1069a2f50>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigmaz = 0.3  # Entfernung\n",
      "sigmat = 0.2  # Winkel\n",
      "\n",
      "dxy = 8.0  # Sensor Reading Entfernung\n",
      "txy = 0.0  # Sensor Reading Winkel\n",
      "\n",
      "x, y, P = calcmultivargauss(sigmaz, sigmat, dxy, txy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "3D Plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,6))\n",
      "ax = fig.gca(projection='3d', axisbg='w')\n",
      "\n",
      "ax.scatter(0,0, s=100, c='k')\n",
      "ax.plot_wireframe(x, y, P, rstride=50, cstride=5)\n",
      "\n",
      "ax.set_xlabel(r'x [$m$]')\n",
      "#ax.set_xlim(0, 8)\n",
      "ax.set_ylabel('y [$m$]')\n",
      "#ax.set_ylim(-4, 4)\n",
      "ax.set_zlabel('P')\n",
      "#ax.set_zlim(-100, 100)\n",
      "ax.view_init(elev=45., azim=180.)\n",
      "plt.savefig('InverseSensorModel-3D.png', dpi=150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i/q8BAOap1wNcgLlEIEu6cpLnWVYLD7WzICtQXyyrQfdv4AQrT93cojfZ4zmH\nkUnBKubf3Tc3hSqGxGplCGpXb78wEHHqPQ9ZVgk3JFaJmsKbAcWBxGplqRexyrYuB18zD1JrgHnS\ntfnWSrew81o5vdZLN5bXsioLfC5Cfy2rQf60PmLVOurfIUdMAt/xIdjquaXXr4ohsVoZgiyrxfxS\n/cqc78crVgstEwRAYpWoE6iDqwz19uDPWFVPvAaIjswPOZUj7IqEh3IXB1lPK+Kz2gerrx7LLTJT\ngKLBPPU6AICSbpNah8RqZRioWC0kRp1y57iFlgkCILFK1BiFHkTu9dTJlY+6cgPo2gH+9j8gGYN5\n2o32Oo+1kum5KUxzCApdVZFoAJ79As7B8oR0YTcAlhbP5ilfglQj4CvngO1YWXodq5S6uEerEK/I\nDCoLEqsOXtFbSLxalkXfKZGBxCpRUwSJVXIFKD/1JFbFa/eCmTqsGRcB4w6wV3oFoNsK6bVyBoWH\n8lpP3e3V3zirXtxW4GJC2l3utaw6Ar1hDKzjrwQAiHm/Kr2OVQ5ZVsuH+3cfJFaDKOST6hWnfueh\nvpxwILFK1BRBDyJyBSg/dSNW2zZDzP0lAMA84+bs+kCf1dxrzrdeusVq5eOs5gri0sUqS/bmlrkE\nunn6VyEB8Df/AmxaUno9qxByAyg/bhcAv3Z1JkEFCU5vWbFlIQRNsiLyILFK1BSlJAaoeWFVRdSL\nWFWe+C8wU4dUw5D7n5wtCHQD8FpW++kGUCafVdaHCVY5yQx07wSrbH3k+OlAw1gwaUF9/Oul17MK\nIbFafoJcAAqVc85zBGgxNwA/X1hnHYWvIhxIrBJ1A7kBlJ+6EKuWCb52PoB08Hy3IPQKSbdY9Vov\nvYH33eVBFqAga6kHVonQVbrHsuoV6LHd9v8ty4Ckx2WghiCxWn4KDdV7y91tzhjLE6/ecjfe7d3L\n8Xi8tvseomyQWCVqCm/H5i0DSKwSufD3nwZzD+93bc9+9lor3f6d3vvIaz0t1Q2gv6GrvA9pq7DP\nap6LgvuceWLVJaxd18SkabsD1CgkVstPsYQAfmI2SHw62zrLhdwHnP+6rtP3SQAAlKGuAEH0lWQy\niXg8P02k03Emk0noekC2IaLPGIaBjo6Ooa5G35ESo+f8PGdVz9a1MNAIABAdHQi5ypLd7ehJXyeL\nd2C8uyzWlSkDgNGmkXnbT8R60Osqi/T2QnXO19WFlKftJqT/e9tUdHVirHPMRAIxV3mouwsj058t\nKXP2jfaIUqoiAAAgAElEQVR0osl1nK7ODpghuzzauSdTF7s+HZn68M6tGOcq43PvQtthnwFE7T0a\nHGEVi8XQ29tbZGuiFJw+Vdd1pFL5L2SFxGwhn9UgQ4OUkoQpUZDa65GIYY83jZ9fOQ0dlZ9atFhr\nGxZC3fouJBNg6Vn5rHtX1tfOzH2pYcmYq8xjdU0l89JJZj4bem72HneZZRZsO+967nInyLvPc9wA\nrNwyj4uCtFzlnmgA0jQyZaJ7V3Y9ExAdW6CteAqJwy/xrW8tQL//8lOsTYMsq8467zKJU6IvkFgl\nao5QKARVVfPWG4aBWCwGzjmampp89iT6imVZ6O7uBgA0NzcPcW36TujN++wPkWagtw0A0CB7EU5f\nC4tHc7bXmJG9TpErZENC5rSBcD2gw5oCxV0WiWQ+N0TDiBRoO2+bsli2PqFQCMJ9zFC2u2aM5eyr\nKrkP/caGCGS6XGW5/rQNkVCmPnyba4RCqIBhonnR7xA65fNAjQmJ7u5uWJaFhoYGKAo92spBLBaD\nYRiIRqN5fa6u65kRrmI+qd7P9DJB9BX6RRM1hxACQLBvmrMNMTDcFpNaa1O25R2I1XMhtQZA0TLr\nRW874NxDHn9Slkpkr9P70DX1nDZwl3Jp5pRxVyFnHKxA23nblLl25IzlHtPlz8o8+zKPP63gHDJd\nzlO5LjMcMlMfHm/PFpg6ZNNE8O0roK5+GdZh5/nWudpRFKXm7tVqxRGVQoj8e7WCLzPe5AJkgSVo\nghVRcxTquCjzSWWptTYVaV9Vc+ZXcofJY23Zz3mhq9xD5qWnNM2bqOU+Zl9CV5WattU7wcoMyGCV\nyvXfdNeHudqCSQvmrP8EAIiX7uhbfNgqgCZYlZ+gaABB/YFfJiu/fZxl7383teh+RJQfEqtEzUEp\nVwePWn3wsx0rId5/ClIJwTz9q4DLush63WLVG7oqKINVQFIAr3+r+/brQ+iqoHSrudbTPoSu8iYF\ncAtrd1sAMI+9DDI6CnzDYrB1r5ZW5yqBxGp5cftMFxOrhXy5neVSRaqfaKXEAARAYpWoQSgxwOBS\ni35mYs4dAADrhGuApgm5oZ16XUPfaeEmRdpNICApQGB4qKCA/f1Nt9qH0FWBGazSltXMNbotq72e\nCA+cZ6yryou3l17vIaaW7s1aoViq1VIsps5nR8x6Jw0WErLubSgxAAGQWCVqkFLEKg0dlY9aE6ts\n11rwdx6DFCqMj/93jlUVAFiOWE0Lt0h6spJbrHrvob5YVt1CtlzpVj3RAILr5pMUIDzC/u+2Jnss\nq0jFYZ52I2R4BPja+WAfvVFavasIsqyWh2IJAXKiX3g+F7K6uo9bqNy7P4lVAiCxStQZlBig/NSa\nWBVzbgeTFqzjrwJG7wsYnsxTcZc10RFuYTt6BNNdwjZPEHqH2l2Wp6CkAGVKtxpovS0lg1XEEatu\nN4BcyyrTE0B0JMxZNwIAlOd/UqzGVQG5AJSfUhMCuLd11gdZXf3EaaHjAuQGQNiQWCVqDnIDGFxq\nSayynavBlz4CyRUYZ3/TXumJQcr83AAcq2NffFYRYFl1t5W07PKOFrAt74CtmZety+pXwDYtBdo2\n2ZZTq7DPas45+mRZta8pc40uscrinZ5z2McxZ91kW1fXvAK2fiGqHRKr5ScTb7hAmxaMOewZxi8m\nTr3n8YpTEqsEQKGriBqllIgARHmoGbFqGlB/c7Y9q/34q4AxU+31acuqDDWBJbuBRFd2H49l1e0G\nwIq6AbjK3dZKPQ62a01mUTz5DSh/uQbMxzKq3XNB9nCMA03ZnFls90dAsgcINabP4XYD8KZb9ViP\n3X6pGTeA9DW6RW/aypxpG8ey3DAa5mk3QJlzB9T7PgX9xxuy+1chJFbLTzE3gL7O+Hdwi1O3sHWW\n3ee1LIv6cgIAiVWiRnE6Ni8kVocvfOnDYOmMTNZ+x2bWs5QtMmXTeFuQxTttscdYZoa91BohGbcz\nWpmGnW40LUYl42DSyp9g5b7/El3gr90HseJZsPWvgbmsubxrByRjkCMmQjZNACIjwNe9Ztdz+iwg\n3gnW3Qp0bQfr2pHZT7z9D/B3n4ScehKsGRcCPXvcJ8+tS7puTl1zXA/SYtXXspoW7nLEBLDW7hxB\nbu0/094m2QM+9y5YF96CaoXEavkpFgkgSKD6HccrRv2W3ccily7CDYlVoq6oGStgDVErbSrm/zrz\nmbVtzhY4AizUCKk12LFUk932hCPHyigUQIvalkw9Zk+4cmbxqxF7XYBfKH/3SYh3n8wsW817gXdu\ns09/4a12+Cwtm9UqdHMYAJD6zxdz6smX/B3qI9fbhx8xCejeCb7uVXBvGCmvH6xTN6euvj6r6Ulk\nPpZVjJgAtK4DM5IZGcx3rc5sprz5IPQLfli1Wa1IrJafUsNWubctZERwl5UqTt3llBiAIJ9VoiYh\ny+rgUQtilW1YBL5teXbZNQyfiQaghoHISPuzM7HIsTJyBVDTqU4dcefcQ1p6vSN62zZBPP1dsNZ1\nrgpwmDM+gdQVv0fyfzbB/Ph/Z4rkyMk5QrUgSghy1N6ZRfOEq6Df1oLUNX+BedS/Q3KXbSHRBeXR\nr4LtTAtKx5Lr1NURq5YF5lx/KD2JzLlmQwfTeyG5gIyOyT0OctuQdW4Df/+Z4tdA1A1BLwCF+teg\n1Kre+QTFlt0Zs8hvlSDLKlFXkFgtP1UvVqWE8vT/y1nFdn+UXXBEphKCjDSDdW4Fi3faFkQnHJRQ\ngFAU6EFWrDqWVUdopuJQHrwKfNkT9lC7C+uQc2B8+fHs+b0TrPpwLTmfG0bDOvqzsI7+LJSHr4NY\n/IB9fADi9d9DvP57mIddAJZIT5RyxKpz/6eFqlQj2TirzjU7+4SbbSEP5EROyGlDAOLZH9juCKL6\nHhtkWS0/QZZVd5m7r3W3P+c8R2R6vxvvcb3LjLHM8U3ThKJU331HDB5kWSVqkkJO/96hI2LgVLtY\n5cv/Bb5hEaRQM+tY+5bs57TPqm1ZTfttOkLNmbQkVEitwd4+Y1m1H7SSifT6GMQ7j9lW1GMug2ze\ny1ULj0jqp1hlQdEA3CVKCObJX4RUwxAfzAbr2JqzR8Z66kQ30KKA0z7pMtabboOIS6y6Iye0Z10p\npNDAd60BX/Tnkq9lMCGxWn5KEatBApRznlPutpT6HddPrBaKEEAMP0isEnWFu4OrVnFVa1R1exo6\nxNPfBZD28UzD4h22/ymQtS4qYci0G0AmZJNjZeRq1iqZFnhs9wa7aM+G7OlOuxH6D1fCuPqBrPgD\nfGb6u7Nb9TeDlafMcw7j0t9C/9FaGOd8GzItlnnbJrtw19qca4EWBZR0fT2WVRlpBhTHspoW9lKC\ntbdkT5aOBKA8/2N7glqVQWK1vPj5lropJGS9bgB+bgGFlr3i1r1MiQEIsqsTNQnnHPF4PFBAxWKx\nghZYonScB0UqlUIsFiuy9eASWngvQrvXwxw3PTfDE4D49nWwxk2HFuuECsBgKqCoEACSHbugx2II\n9cagAkhJBiFC4ACSOzdAXfQglLceBABbCDIOJk10nfkdW/jFYlAsE46tyNQTOW0TSiYznaueSCDp\nabdQ+r+3PdW4XR8ASKWSiLvKG5KJzPkgLXtfFgVO/xZGLfgtkOzJRANQn/oWkhuXIHn0ZQgBsJQI\ndNPu8FPxGOKxGJT2HdAAmFojTAgIAKlYJxKxGJDoQsgdczaVQGq/E6FuWgxr9k8QP+9HJX0/g0U1\n36O1iLtf7e3tzStPpezfmiNI/cJcecWqIz4Lbev8d5/b2YbEKkFilahZDMMI7MScDpUoD5ZlIZn0\nBsYfOnhsN0bO/TkAoPPjP8DIp24GABhjp0HZvQ7mni3QR+wLHu8GAJhchVRCCAEwe/YgmUxCJG2r\nqwkOcA0qgIbHrgc3EhlrZWqvI6Ds2QCW7ILe2wUp05LRNTRpGXpO2yhG9t4zUknoXbsh2jZAdG0H\ndyUl4IsfgBUZCatpEozRU8D07DFMw8g5ZiTlanvvd5GOBpDc/1SE1y+AZAKhdx+Dtvxpe3MRgiHt\nB7+px5FMJsG67VSrptZoC3kAZrzHbpc9tguAMXoqRPtmMD2GzjO/i7F/vhjhhb9D9xGXwhyzf9Hv\naLAxTZOGjMtM0G/eLVa9ltEgy6ojQp193WLVb/9kMgnDMMhvdRhD3zxRkzDGEAqFoGlaXlkymYRp\nmtA0jTq3MmCapi1ghEAoFCq+wyARee7n4MkupA46G+LwC8Ee+TwAQE48BNi9DhG9A0o0Co3ZQ5Yi\n0gSZHs4OmXEgGoXGbSuO1rMDYvNiAAA3EkgdeBaMA89E5NnvQUgrE7Kp+f1H7fisyR7wRHY4XG1d\njbEPXw1mxAFDB2/bmCkb8fz30Dw7dwKYw8hnvpGzLF2eWdFljyC8ZQmghiCVMMT2FZkyJk2Meu0u\nQGuADDXY8WEBiLTvQOLMb0LsWpkRq0rrKoT3HGjXlUlEo1Goli3UecNoKNGmdJmJaDQKoaejJTRP\ngkx2gcX2QJt8CPRjPwdt6d8w6qVb0fuFR6smlBX95suL85vnnCMcDueV+1lbAX9B6i13W04LRXXx\nE680Sja8oV81UbP8/e9/x1VXXZW33jAMmKYJxhg9uMpMtbQn37AY2tKHIIWK1L/9HIqVAJMWZKgR\nGLUPAED07IJUFIh0ClEmREbUKZuXgL92N8T7dmxU9cPZmWNLxqGumQt1zVz7ONuzIbEiL9zqX594\nB/ial33LWB98fRlcsVvj7eBblhbcNvzKL/LWqevteKyRuXcAcCU0MFPQ3nvC3mbVHLDmieBb38+c\n0xEFwkxCURSI2G77gCMmAt27gNgeKHo3Up/4MdQV/4K6+iWEVr0A8/CLSr62SqLrabEuRNXco7WM\n2yc1qD2LCUg/0dkXnP16enowceLEfh2DqA/oV03UJFJK/PWvf8WVV17pW+b3megf1daebNsKhP58\nKQAgdfrXYI2dlgmzJNUIkA7Gryz9G8TqlyFa3gUAaAt/lzmGsmoOsGqO//H7EmqqBKTQIENNAOcA\nEwDj4F12Ha0RewGQ9iQsywTTe/IzZQ0Av2vhu9dBe+6HmWX17Ucyn5U3HwTbutzO9AUAvW12vQGg\npxVy/IHQz/shQk/9N0IPfxnx8KOwpp1atvoOFIoCUn760p4DFaVeLMvCU089hZaWFvz4xz/OiyhA\nDB8C7yxJv3qiCii1A2xtbQVgW1allBBC0NBRGXDiHA65pdoywds3Y+TvzgWPt0MygdT+MyHaN4G3\nbx6wyJTIdojmiEmwGsdD3fYezFH7gem94LFWxE7/L0QX3gPmikea2Z8r0A86G1Z0DCJvP5RZHzvv\nVsRn3pCz7djvjwMA7P5Ja8760LuPo+nx6zPLicM/BTCO0Iezfc8JAD0f/x4aX74NUo3CHD0Fys4P\nkZpwKLgeg2jflHdt/UWCwWqeDHPMVCib3gQ3dUglhPYbXoE1ZmpOdITBxvnNc85J0JSBYr95Zz5A\nKBSCruuZtg+HwxkXgUgkglQqlZlX0NjYiFgsltk2Go3mLcfj8cx5GxoaYBgGpk2bhra2NrS0tGDy\n5MmD1wjEkMAKPPDJskrUDd4JVTTZorxIKQdn0pplQNnzEZRdq6G0robSuhZK6xooez4Cs7LnZ9KE\ntn5B0cNJcDBYMEZMgujanhFtxsh9YTbvhdCmxeg68ztglomm+XfaVWgYi56T/gOjnrgB+qQjIDq3\nQou1Ij51FrQPnoPaujrnHFZ4JFpvXACrcRzCH/wrR6yahl6w3bzrFU9K1+Tko9F7wpfAzu/E2PvO\nhdKxOafcbBiH3kM+gcaXb4MZHYXkfidB2fkh4kd+FtqGhRmx2nvc56FPOhyjnvkG9ElHgBkJqK1r\n0u0DGCP2htrVAgkGViC+K4OE6GyB6MyGtGJGEqN/fQok4zBHT4Ux7kCkxh0IY9yBMMYfBGPsNEDk\n+5VXCsuyKCFIGenrb97d9l4rt5/ty7vOWXb/nzBhAtra2rB582YSq8MYEqtE1ePXyc2ZMwcbNmzA\npZdemleWSCQgpUQoFCLLahkwDAOpVApCCN8JbQOB9bZDbFsOsX05xLbl4NtXQLSuATNLf0BKocKK\njoHo3mEvaw1gegzmmKnouf5FRJ7+NrTl/4To3pURqpbWiJ5vvYPIEzcDmxZDGTkpk7lKMgF1+3KE\ne3cBAISqZe6jUc/8F8Se9fnXIU00L/4dmBEHdyUkAICGdx9BZONCe5hfWjmxVMc9eAnAOCTjABdg\n3bty9o2ufgHhtvWAGgE3c4UsAIhYK0Y/dJldB6FCqLZ1U7USCG18PbtdtBnqaPtBz0aMR+zzj6Lp\np4dCdO8AA6B02QLUnHIiYlc9hIYHLoWyZSmsyCjwuB29wGocB5bo8nVTYNKCsmc9lD3rEV71fPa7\n4QLWmANgTpoBc6/D039HQDaOyzvGQHAseIqiQFWHzsJbL0gpkUjYlvxIJD9VsK7rME0zR5D6idNi\nYjRovZQSlmWhsbERALB9+/aBXhZRw5BYJWqSbdu2IZlM+oqneNye5RwKhShIeBlwrCsDFqu97eBb\n3kn/LQNvWQbevrn4fkjHx+dKXvD91Kk3IHXxz6Asvh/i8ZshIyPthAAAeLIH4U1vQF2ZnjwlTRgH\nngllzStgqV6EW5ZASQtPbe1cwAkpxQVgmgi/+BO7LD0xCYCvUAUAluxG+PV7fcvE7vUQu/33UzYu\nDrxudcMbwIY3ArdR0tZT0bYR4nXbLzf8yi/ALAOSq2BWCur6V6H0pMV3RwvCW5eC96ZDV+1/CviG\nxYA0ITa/hcjK58DTLgc83g4ZagRL9sA8+UtInfs9KHP/F9rsW3LqIBkHpJXnasAsE6J1DUTrGiA9\nmQ0ArBGTYO1zFKy9j7b/73sMMAABK6WEYRjgnJf9hWo44harqqrm9aPOqJXXkupddlNs20Ji1xHL\nLS2uJBXEsIPEKlGTbN++HdOmTctbT27W5adf2YEsE2z7CoiNb4Jvegt84xLw3etK27VhLOR+x8Ga\ndBisiYfAmngIoCcQ/u05mW3MvY+CaFkG1tFiTwCK7bHX738KlA+eszfqaUXor5/PXsfIvSFa3rOv\nRVoI33N+pkxZ/kzmsxMxwBHGbn9PK9wMOe4AiC3v5NRZqhGkLrgFUCOQ0kLoia9nylLHXAbz2Cts\nEcwEwBjCvz0XAJC48UU7Nau0J1iJD56HujArevULbwUiI4FUHMrcu8B7ci2v5uSPgXVuBe9pzamr\nU3fHbUK0LANalgEA+M5VCN+dbUu+dQXkqH3A2jaCWSa0x7+aiTELAOb006GseBaItdlhuzrt1K7m\nvsdBbF6Sac/El5+EHLk3+I6V4DtWgu34EHzT0sxkMje8azv4B9uBD7JRGKzR+8Ha7zhY+x0Pa78T\nYO195JD6wQ5n3PFT3XFQHZyRhkIWUsAWp97lQtsWWnb8WQGyrA53SKwSNcn27dsxc+bMvPVuYUVW\n1fJQkljVe21R+tEbEBveAN/4FpgenElIMgE54WBY+x4Na68jwLa+D3XJXwEtguTn/mTnrAeAZAzh\nX55qWwrVKFiqFywtzvimt6DOvhXiXdv6KVa9lDm+t7a8I9cyI7VGQKhg8XYYx34OUo1AXfRHWJNm\ngLtjmsIeAuc9rUh9+pcwj/wUot8a7Tm4AmPWTU6DAS6xijFTYR10lm8bWAfk3sPu1K4AYJzyH9lU\np2/8CfCI1eSXHwffuRrhey+E1TAGPC3aM/vvexyUzUtgHH0pZGQU1Nd/B6lGIbVIZluW7ARL5qZQ\ndfutig/tqAlixb+AUAPE2vn2Noku+3KFaofG+scNSPz3YpiTDoMJAEYS4V+eBnRtg3H4RbAOPAts\n6/u2ZX37Bzn+x4CdKpa3bQKWPW4fVwnD2vcYWPufDHPqybCmngiER/i2Y1WnBK5ROOcZ62mhtKpB\ngtNrKfWKVe98Aj8xa1kWJk+ejHnz5mHWrFn9vxii5iGxStQkO3bs8I27VyhnNVFm9Dj4xsUQ6xaA\nr3sNfNMSMBk8mU1yAWaZMA+YidQnboO11wxAdQUcN1PgOz6E2PI2tKe+Cf3y3wOxPdAe+gL4rtWQ\nkZFAsgdAVnjyrh3gL/88cwjm8etMHf5Je9g/2YPEtY9C7n0UwrcfAZaKA3oPoNpDjKkzbgaLtUFd\n9Ecg0ZUz0cj42L8DWgT8rb+CdWwF27k6MzSePVEc6gu3AaleIJU7a18sexy8ZRlgGra/qqudQvde\nALB0SCuhAB5/V/W5W+w20qIZge6Gde0E25Oe8b/vsUiNPxDqgt/Yy0AmW5Z52AUwDzwD6uu/A4x4\njhjt/c4y8Fg7wr85ExIMxrFXQF36t+w5LLtNeec28Ffuyqznu1bbRzFTsBrHg3ftQOj3lyD5xceB\n5glQX7gNfPsKWGP2h37FH4FQY7bihg6240Ooc+6AsuJfvm4EzEhAfPQ6xEevQ0U6GsHeH4M17TSY\n006Dtf8pGSFPYrX8BLWpE3Gh2FC/m0LbOhZcP/EqpcSePXswY8YMMj4Mc0isEjXJrl27MGHChLz1\n/RqyJgKR0o4DqrS8A+Wj1yDWzAPfuChwEpTUGmBNOQHWlBNhTj0B1r7Hgu9cjdBvz4VYvxDGrtXA\nfse6TwLWvgXm0Z8F3/oelCV/A/9gdk5qUscXNbMLbKuncdDHIdbOzwx9m9PPAP/odTBThxx/ILDi\nWQCAdfDZgKJBRkeBdcZtYZSy/ZvZjg8h1tkB9b1+tGLVHCBhxx3VnvsB8NwP8q6XWQbUOT/1bQve\nuhZoXetbJtYGRzNQX78vsDxy1ynZ86x8EXzDotxzp10vxHv/hNSikI7fb/q6JRfAuOmwxjPIhrFg\nsd2w9jrMLmMc5mEX2C4AACRjMA86F8qqF7LuBunzMMcftuUdRG/d336xiHfY4veYy8A6tkKOm2a7\nQgCAooF174L4wD62fu0/YE47DXzz2+Cb3oLYuBj8o0VgrixhDBKiZRlEyzKo838FyYTtNjD9dFgH\nnAaMPQyghABlw3nh94uu4HUDcLsMOHjFqHe5kJjlnOe4EHR2dmLMmDHlvDSiBqE4q0TFuPbaa/Hc\nc89h/PjxWL7czgL0zW9+E88++yw0TcMBBxyAP//5z2hubu7zsWfOnIk5c/KDuieTSSQSCWia5juL\nlegDXTsgVr0EueIFaOvm5aQX9SIjoyCFAt7TCqt5MhJfWwA0T8rbTiy6H6HHboJUQkid932wWBv4\nlrfBW97LESaZ48LupMypJ8Pa+0ior90La8LBkFojhE92p+Sl98A8/mqE/m8WxJa3IZUQmJGEjDQj\nddpN4O2bIN59sqiLQiGs8Ahg1D6Q4OC7VsOaeDD41uVgkEid9S3IcKNtre3ZDXXeL8FMHcaMi2Ce\ncLVtPRQKwDjCv7MzPyWu+5dtbbVMezLS+09DWWKHvdLP+Bowcm8gFQfT41BeuQvMSMCc/DHwHR/A\nGjsdjHOgc1tmslRfkVyFefRnIEfvB7HkIfD2LZBKGMxIwBq9LxLfXwm+ei7C930yvy3G7A/ZvBfE\nRwuROv5qsK7tGTcMvweL1BpgTT7SdvsYuQ+0F28DS3RBP/d7MM71SUfb24nwb84E37kKMjISUqgZ\n31w/LK0BqQNOAzvsfJgHnw05et9+tQlhk0gkkEwmEQqF8lKuSinR1dWVWXYEph+OOHX+O9t6l4UQ\nME0z7/+nP/1pvPFG8CRDon6gOKvEoPOFL3wBN910E66++urMunPOOQc/+9nPwDnHd77zHdx+++24\n4447ynZOsqwOAMsC3/ouxAezwT98wZ6UUwAZHgFz2ixY02fBnD4LcsIhQLIH4XvOA295F+E/fhqJ\nG1+wfQyNpD37f8Mi8E1vQaoRsFQc2rO5FkrZNMEe5t3rcCgL7wNLdttCdb/jkbzpJYjFD9rVHLk3\nWDwrbKUaBkslILkCvnMNxANXZHw/nTBLLN4JLT27P+9a0ilJM8taFPpn7gbfvARSCcE89UYob/we\n6st3wjztRqTO+37O/pFvjQGMBFJnfxPQoq6CEdD+9T3IMVNgHnaBf5MfeGbOMttpx29NzboJxkW3\n5ZQpC34DGAkkb5id9ecFoLzxR2iP3wzj+GugX/BDOwtV+2ZY006D+vT/A+/ekRH93mtlVgrK0r/n\n1iEdCYDF2qH96TOQ46ZDRprB4p2wQk3g6exWUqiQTePtz2OmInXZvdD+fAWU5U/b6xQNxulfsyda\ntbwL3tECscH2ac60tdAgNi8FXr7TtsTve6zdhkYSoQevAN+5CtaY/ZH46stA43iw3evB170KsXY+\nxNp5YLGsSOd6DKGVzwMr7dBZ1oRDYB52PsxDz4c15YSsVZcoiSA3APcELPe2fji+r17LqbvcHR/X\nOZZlWQUjvhDDDxKrRMU49dRTsXHjxpx1Z599dubzCSecgCeeeAJ9JRaLFbSakljtI4YOvnY+xIpn\nIVb8C9wT59NBgkE27wXeuRWSceiX/K89w91NuAmJL/8T4V+fCb71PYTvPN6eHb7lnbzYnJIJMGnC\nGrUvUp/6Oax9j4V0LLF7NkCZm817z1vXAVJCrHoRAKCsfjldp/RQdNpHlFkG1Pn/51t/c6/DYR18\njm1BXPo3iI1vwjjwLIi1r4BJC9aYqdA//UuEf/8pwDRgHnMpzGOyMXxlyPaNdGKx5qBogJEAjGSu\nWHXEkdWHxBSOPyv36Zodf1xvkH0nPmy4ERgxEcbZ384Uqc/9CACQ/OKj0Gb/ODNxzJh+BpS182BN\nOBipWV8Fb9to3web3srsy5LdUFyz9QFkhSoAsWs1sMsW12LVHBhnfwtsxwfZ/Q0dxiHnQF6QDnPV\n0wq++R2oz34fYseH9j1g6hArX4RYaX+3kiuwJn8MLNEB3roOsnEcktc9AzTZLj9y3DSY46bBPOla\n8A9fROiBy8AMHVbTRLCe3WAyG9qM71wJvnMl1FfugoyMgjnjQpgzPgHzoLNyvyfClyA3AAAFxaoj\nZOICBnQAACAASURBVN3zB9z+qF4R7HUpcC/v2LEDe+21V1muJ5FIYNasWUgmk9B1HRdffDFuv/32\nvO2++tWv4vnnn0c0GsUDDzyAo446qiznJwYGiVViyLj//vtx+eWX93m/bdu2+U6uAmiCVUnocYhV\nL0G8/xTEB7OzeeA9WE0TYB16PnqmnIrElFPQMGYSwi/fAXXO7dAe/gp0MwXzhGuAVAJ8wyJ7stXa\nBWBt9oQf3r4lM2HImngIzCknwZpyvG3lUqMI/9+p4O2bwT9aCPNwe1gcRhLhP1xiWwHT/pWstw2R\nb48G82R38r6OWBMOhvGxf4ccPw1s90fQnv8xzL2PgnXw2Uid/e3MZC6+ynYfUdbMhWQMqVOvR+qC\nWwEtmp7ZrtvCUwllD6412P/Tvp45ONt5g+U7grMvYtURBl4roJRZwe+uF5AV0D4CzJmxb005EYmv\nvwb15Z9DeflOKGvn2YcNN8E88Rp79r71fSiv3AWxcg7EhjeQmvWfsKacCNa6DmL5MznhurxtLzYs\nQuS/R2Zm+FtCAzd1hB/4HOLffc+eCNU4DnzHB7ZQDTUhcfM8QA2Db3zL9lPdsAhs6/u57h09rQg9\neCXMabYF39r/FCDUCLHiOWgPXglm6kid9EUk/+0u9LS3IrRpERo3LYT48Pkc32MWb4ey5CEoSx6C\nVCMwDzkX5hEXwzz0/MwkLSKXYpPWvALVoVDkAAchRE5WLO/27uVt27Zhn3326WPN/QmHw5g3bx6i\n0SgMw8DMmTOxcOHCnKgys2fPxrp167B27Vq8+eabuP7667F4cXAsZGJwILFKDAm33XYbNE3DFVdc\nUXxjD9u3by8oVsmyWgAjaQvUJX+HWPUSWMrHQgiXj+j005H84mOAFkWiq8tuV8aQOu/7kEoI2uwf\nIfSPG2DN+xVY26acvPWSC5jjDwHfvd4WE8ddidRlvwM830ny839H6LfnQV1wNyRXgVAjlDf+AN5l\nZ6JyJwBwhKoEYM64CNaU4yHVKEL//AYkVyDHTUfi+meBEfZ9wZ2JS078UwDQe6G+eBuEM+EqOhr6\ntY/YAsgh3AzEdgPxTiA9xA0AMmQLQT9fV6lotoXX0HMTlWbEqpG3T0Gcbb2W1fRkNskVO66sC+ZY\nVh1BnamYBNJiFeERgFCROu/7MA6/CKE/fdYelt+0BNqj/wn9op8AkZEwPv5N8K3v21XZ5xiYR/4b\nAMCYeR1Cv7sIvGUZmGVAv+AWQAmDb1kG8e7jYNLKCUXlZNti3TsR+Z9DkDrly4ASgvqi7dqgX/EH\nyImH2Jc2ZirMYy5FCoDy3I+gzb3Tznw1/mDw1jW2C0HLu/akKqHCGnMAeOsaMGkhNfN6pP7tTvvl\nRosiMf0shI69BKmLfwbtb9dCec9OROCOlctScSjvPwXl/adsN48Dz4R5zGW2cA152nAYU4pl1cEt\nQAvFZC20HLT9nj17yiZWASAatX/HTgau0aNzQ9A988wzuOaaawDYI38dHR3YuXOn72ReYnAhsUoM\nOg888ABmz56NuXPn9mv/7du3F+w8yLLqwrLA178G5Z1/QLz3VIEJTAzWATNhHv5JmIdfBNa6FqEH\nPgexdj5C916I5BcfBRAC02NQPpgPdeWcjGUSsMMXAYC11+Ewp58Oc/rpsPY/GQiPAF+/EKH7Pgl1\nyUPAqH1sX08pwXZ/BL5xEfiGNyEbx4J17YA275eeevlP0jFmXo/UJWkXgWQM+Oc3AMaQ+OabOdZI\n2WwPHbIuO5A4Xzsf2qM3ge/5KB3wXsI86jO5QhW2Ly6L7QaLd2b8MQFkLau+bgDpySdeV4d0fVgf\nLKuZRAReseq8DHitqgDgCGivZTXZAyYtSC2aE1xfTj4Sxslfgjb7R5CMQ1n8Z/APX0DqkrtgHvFJ\nsE47iL8c4ZogF25C8mvzEb51OljnNphHfQZyzFS7SpMOhTb7R3nVyrhpxNuhucKLyeho+4WhZzes\n/U+CHH8QwBiU1/9gC1XGoV/9EMwjPmnH792wCGLtAvB1C8A3vw2xa1XmWMqyR8ESHTAOPhds8gmQ\n4WbIeBfCf70GYtUcSCUE/Yo/wNz/FIgPZkN5/2nwNfOyYdaMJJQPn4fy4fOQWhTmjE/AOPpSOy7u\nME9I4Las+iUGKNWa6vVv9eK3r+PH2tPTgwMOOGBA1+HGsiwcffTRWL9+Pa6//noceuihOeVbt27N\nEcd77703WlpaSKxWASRWiUHlhRdewJ133okFCxbkzTAtlUJuAO5wKMPZssp2roay5G8Qbz8Cns42\n5EVqDUid8XUYJ38x14I4ah8kbnoZoT9+GmLTW4j87BiIMdOgbV2WE8NUNk2ANWofe3IMAOPoz8I4\n879yzmEdMBP6VQ9Ce+AKqHNut0NRde0A696ZWxdXTFN3SCTZMAapYy6D9upvIZUwjFk32cP5DqEG\nWCMmgXdtB2vfAjlmSvaYjljt3Abt71/OTCKyJh4K4/CLob10e14oLACQ6YlLLN6ZYyV1rJYs4eMy\n4QhIr4tAxme1L5ZVx2fV4wbgxG5V838zTrxXqTXmrk9PQpPh/GgbLB0SzDjtBvCNb0FseguhBy6H\nMeMisLTrhtOGGfRe8M5ttiV7ZPaBbpxhJ0BQ5/8arLcNqZnXQSx/BtwRvci+eEgwsN62zJA8YH/P\n1uj9wLfYE/r0T/+fLVQBQIvCOugsWAedBfHWX6FteRuQgDn5SLDYHvCOFihLH4ay9GFMYAL65I9B\n7doG3rUdsmEMktc+aicTAGCedC3Mk64FetshlvwN2pzce4DpvVDeeRTKO49CNo6DcdRnYBz3OcjJ\nR+aNCgwHivWhhQwCjth0b+cWq+5lR8h6/V+dc+u6XlbLKucc7777Ljo7O3Huuedi/vz5OP3003O2\n8Yrq4fwsqSZIrBIV4/LLL8eCBQuwe/du7LPPPrj11ltx++23Q9f1zESrk046Cffcc0+fjrt9+3bM\nmDEjcJth18EkuiCWPQ5l8YO+IZ0AwJx6Esxpp0FZ9hj47o/sYdVJh2WFAWD7J374PGRkFNC+BSy2\nB6HYHnv4fb/jYR56PsxDzoHc6wiAc4hFf4b2+E32zP5UEsY53wFr3wy++hV7xva6BZnZ52KrnepU\nNoyFOfVESK0RyntP5MRrdWasp879fzBOvxlQI1CXPQ7WvRPGcZ8DtNyJdXLcNKBrO1jr2hyxCjWS\niTqgLP27HSrr7G/DOOPr4Gl/Tb8g+4iOtP/H23PXOwHt/dwA0gKSGUl/N4CAeLR5ONt6xKrjryp9\nxKqTKCFvCNsJZ+Vck/t46bio1qTDkLrop1Be/wPU2T+yA/Snt8mxLANgu9fb68dMtUNwOQgFxilf\nti21QkPqkz9F6pO3Qyy+H9pT385154C047cecTEABr7hDfCuHRCuzFvac7fAXP0yrOmnwzzwDMhx\n06Esuh/a418FAOjn3wLj7G/ZVvqdq+wJWh++AL7+dYRa3s4cR0ZHQayeCxlqhJx0WEZw8q3vQ5v7\nC7B4B6wRk2AcdyXElqXga+ZnXppYTyvU1+6B+to9sCYeBuOEq2EccxnQODa//esY90x9JxFAoe2C\ncPrjQtZZt3j1bjdlypT+VD2Q5uZmXHjhhVi6dGmOWJ08eTK2bMkm5mhpacHkyZPLfn6i75BYJSrG\nww8/nLfu2muvHfBxC/msDjsXACnBNy2Bsvh+iGWP21mZPFjjpsM47nMwj/4s5Oj9ANiWMO0f10N5\n758IPXA5Uid8HnLUPlDefwp82/Ls4ZUwZKQZvHsnIFQYM6/LmSEPAOZJX4AOCe3xm6G9+BOor96d\nH7y/aQKsERMzYtU46jNgsT1Q3nkkZ6jfio6GNf0MpM75DuSk7PCcud/xUFb8C3zTWzDHT8899rhp\nwPrXwFvX2UH/AbCWZdCe/EamPcx9job+ufsh0/vK9Mxyr4UXsIeogazlMbPeyZTkZ1lNZ8HyZq7q\n3wSrtLDzDkE7362aHwXDmSAnPROFnGtwrimnLB31QTaOB7iAcep1MA+/COqj/wkl7eYR/s1Z0C+5\nK5MSlu+yExtYnu8AAHjawm7t/bGMpdmceR0Sh5wP9YX/AV87HzztksGkBeW9f8I85DwYx10J9ZW7\n7IgMEw8FEl22tXT5M8DyZ+xjRkaCp+8p/bwf2EIVABiDnHgIjImHwJp4KLQtb4PpvbAaxoAZSfDW\ndeBzfgp1zk9hjT8Q5hGfAvQYlNfuBZOW7Zd91QP/n73zDJCqvLv479YpW9hdlt47SJEiiEoXFFCQ\niCJWDBbsPWJiCYoae0XBisYCIqCA0qR3UXrvvbOwfcotz/vhmbmzs4v6JjF5Ne+eLzC3t5059/+c\n/zmQWgkbIP8I+pqJMpCixN+BenQT5pThGN88jtOyP/Z5f8Rt2PX/RbX155qsfq6y+nOf/zfLxv9N\nTU0lMzPzf3/AP4OTJ0+i6zoZGRmEQiG+++47/vrXvyYt079/f0aNGsXgwYNZsWIFGRkZ5RKA3wjK\nyWo5fncwDIPKlSsTiSRrBOP2KEKIMvP+qxApwFw7Ed+KD9FLWAXFEffSFIpKpHk/wuffLslP/Joo\nJtE+IwlGQhhbZ2J8/1FiXV8a0bP6YjW/FKtRd4Rm4pv6CCkrP8T32VBCx3cS7v4g6ul9GFtmYWyd\nhb5nmVc9VUK5CM3AatILu2E3rAZdcCs1AkXBP2sk/gWvYSwZnXy8MeN+FJWCK0ZJslPy/tVsKyt+\nu1cQaXVF8slm1UcH3CNbiOYcJDD7GcwfP0ERAqGZKE6UUOd7sCrU9rap+DIJAOQfLfOcqL4K6ICT\ndyxpnqr6CQAilFdmHUPzoQFWcR52iXmGAB/g2pEy68TVpWX2b0UxAFsoSfO0ojwCgKv5yqxjFsvh\n/qjqxym5/zxJxp1AZtl18iRxjAYqJtYJZGN1e4D0rbMRmol6ZBP+ty4m2uoPhHqPQDmyBQA7q36Z\n7fl3yeQsq2bb5HmpVQkPHEX6q3Io3jVTUGPVaW3LTLQtM+V1aHctxZe/DqqKemov+q5FGDsWYmyd\n6RFVAGP2syjb5mI1uQir2cW4lRpj/vAxvil/QnEdQi0uo/iKt1A1HX3XQsxN32Bsno56fHtSLK9V\n7wKK+7+Ea6QnnjVfFpEON+OzogSObUVxrGRfWieKvnYi+tqJOBUbEDl3CNF21yKCvw6Z+i0iTlLj\nDUklYdv/gLylFH5Ow1oSv2Zy1ZEjRxgyZIhXKb7++uu58MILeecdmRI3bNgw+vbty/Tp02nYsCEp\nKSmMHTv2V9t/Of41lJPVcvxm8XNv5CW/RA4fPpw0TwhBOBwuvcrvHlrOLlJWjiWwZjzqGbr5I3Uv\noLjt1YQbXUjaklGkLH2bwIJX0LbNIffyN3HTa+DfMp3A+i8xdy8poROVmlE3kMGpK9/FqhezcnEB\n1ybS52nszDqkzxpB4Ltn8S0ahRpJpNcIFKI12mJn1CawdbqMOY0UUdDoIoRmEFg8huDa8RhHSlRt\nkUP+0aotOH31x2R9fj3Gsc2w9ivCLQYknZdbpRVBQNv3fZn7KjLqEgT0rd+RvvoL1GghQtUpPPcm\nFKuYlFWf4J7YnbyenkYFRUMtyiFcmJfUtKT7KuAHnLyjSesoio8KSCuo0scQ0HySYBblJc0Tjry+\nrhX5yeex9HQzIiuolps8zyiUhM3V/WXWSYuRuYgawC4xT82Vrgq2r0KZdSrEyGrIzMQtMc9/XMaz\nhhtdiF3lLFKXvoW5/iuMzTOwM2UiVDizXtlrsFf6s4aqnl32nPYuRzuxAyetKidunUXmpNvx7V2W\npGX1rfoMdd9KQq2vInT2FYhGF1Nh+3xMK4RQVMJN+6AW52Du/wFjzzKMPctg5ghcfwUvWa3wgrso\nuPARECrYLtTpDHU6o7e5jqxxQ9BKhCMYe5ZS4eVziNbuQHGrKwg374cSKSTj6/vw7V0KQHHba8nv\n+SjmvuUEV4/Dt2MuxP5mtJxdBKc/QWDW04RaDaSow1Dsqs35b4VlWUl2U6VR2jGgJBE9U7Tq/xal\nu/X/FbRs2ZLVq1eXmT5s2LCkz6NGjfrV9lmOXw/lZLUcv3vEE04cx8FxHFRVRf9vyQgXAmPXQvxL\nx2Bun1N2tu4j3H4I4Y434WbLrlkTiPR9EqfZxaROvBPzyHoqvd0DVM1rkhKaSaRJL6JnD8Sq3oq0\nSXdj7F1OxU+vobj3CMLnD4vJDFZgbpiKf8t0j9yqkXyEohFt2oto8/5YjXsgUqSWz9q7grTPbsC3\nayGVX20Hruut5xoB3Mw66Me3ogCRs6+gcMAr6GaQaPsbML55hJQNk3HbDko+ybrtEaqGfmwLpogm\n9KOOje+U1FHqudJTM9q4J0V9R+JWaoR/6Rh5PfL2Y5VKwXHTq6LlHcIfzsHNqutNVypIeYkROp2c\nnKPL81Mi+Zi6lqQpVfzyeAw3iltiHT1md6W6zk+m8JSerhHT95qBpHmGiBEFX2qZddSYPZWWno1a\ncp1wTLOaXiV5nWgxaug0QjPQM6olWWH58mJ6vcqNiF70Z3I7XE9w1pP41n+FcWK7XObkDhxVJEi+\n62IeipGAeh3LHF/KRmkfFWl7NUZWDQqHTsKd8VcCy98FwK7UCDX/KMbJHRhzniZtzjPyWXVthJlC\nwVXvYjW9GJBNY8bO+Ribp+PbNC0pAjiw9guUcB5Wy/449TuDpmOumUDqFCkJsau2oOCqd9FO7cW3\nfhLm5hmY+1di7l+JmP6o3L5r4aZkU/iH17Ca9cYARKvLKGp1GaHcQ/hWfoR/+btedVhxogTXjCO4\nZhxWvfMJnX+bPNb/krSsX/pOjUZj3yelyGnJQsOZiGrpaaU/HzhwgN69exMIBMoEy5Tj/yf+S37R\ny/HfiDN9yVmWRc+ePZkxY0aZeeFwGMdxMAzjn3Ya+M3AjqKt+RJjwRte6lDJSpSbWhml8ASKHcG3\nbRZKiz64tUo0nRWeRD++CSVGKBThgOMg/BWwLnwI+7w/QjATDeQQ9p0z4NsnMBa8Qcr0xwj88BGE\nC6ReNb7PCtVx65wrm6aKT2Ec24Lb+zG0bNmtqxxaj759VkJ3VkqrqVoh1ONbEaqBNeB5nAtuJRD/\nUeswGDH9UYyd8wk4RcmNLIEAbo2z0Q6sJuX4BtyG3dDWTcaY9Qzq8e3eYuHrPsJteyXxOqlaXfp4\nGqf3lE08y6oNeYcIFB/DrdHMm6xVlOeiF58os44IZKCEcgkQgUBieFKNNTCZbgS1xDpqUGpINWH9\nZOJa6em6VE9iBFKStqUJSQrUQHryOkKgxJrB/FnVk9wCjGLZtKRn1UxaR8mXoQ0ioxaBlOSmLPP0\nXrmfqk3lOoFGODd+SnjnEnxv90ZBEFg2Bt+Wb7F6PYLT/lqUEztQQ7m4Farjq9YoWctpR/Btkr62\nSsfrYscRQFz5KpEG52F+cSf6iR1Jx6AgEtpdRSOwaz5mZnXcOu0hEECp2w5zwStymN6XitO0l/R7\nPbWXlFWfwKpPEMGKuGmV0I5Jmyu7/XVEB76GzwxAnbNx2lxGKFyA9uM4jNnPopZstjP8+HO2Y0Q7\nJlLVAPXoScxtMz2i6qZVTkp8i1d83ewG2F3vxm5/XZmGwN8botEooVAITdPO+AxbloUQIkkicCYi\nGp/2U/+WXjcjI4Pjx4/j8/lwXff/Tx9COX4S5WS1HL8rHD16lMqVK59x3n9Fg1WkEH3FWPQFb5a1\nnVI07DYDsTvfiVvnHNT9qzAn3Il6eAP+9/6A3foK7HZXoa+ZiLbuq0QVNa0KTp32aDsXo4TzMOa/\nisiu5xm+Ayg5e8EI4qZWRi08LiNOATe9CsXNB2C1vAxf486gqii5hzHHDkY7sAr/691xG3RCyT+K\nemyLtz23cmPsphdBRk3UXYvRNs/wtH/2+Tdhd0oeeiO1Em7jHmhbv0NfP0VaapWAW/98tAOr0Ze+\ni/rVw96+3Ir1QDMkaS3VYCSqNAFAPbqV0hAV68Ke5fK8S/QLiQqy81fNLWv5JVKzUUK5KIUnECkl\ntHT+dPlvOD95BS/ZKjl562cRX7a0n2q8ghhILzM9TtpK21rFnx+RkdzNrJzcI6dXrFNm92qM3MWv\nXRzClyKlIunVIJiJenQzvgl34s55EadOB0Deo9JNR9rWOSjhPNzqLRFVmibNc9oOwjp9EPPbxxOn\n36gHTrNeqAXH0LbPQz20HmPZ+xjL3sfNboBbsR7a7qUoVgi3cmMiQ79AVG4MQhDZvRJ9/VSCm75G\nO7UXLUbWXX8FRDBLOkbUaJU41/0/YMx9EbXwhEy1atwD9dB61NwDmDOeQsx6Bqf5JdjnXI22dQ7G\n8g/k9rIbEL3iddzG3VGObsZY9DbaD5+jOFL7qp7chTnpPowZT2F1uVM+679TXesvpVjFo1RLV1ZL\norQMoKRk4KdIa2pqKsFgkOLiYnJycqhUqdK/diLl+N2jnKyW43eF/9r0qlAu+uIxspu+dCe6ouK0\nHojV71lERsL70q3djvD9S9Dnv4ox6xmv+QNiSU9NL8I+byjOWb1lg1X+EXzjb0fb+h2+j6/DbnMF\nbu1z0NZOTsqEd1OyZSJR8SmUUD52pcbYNdvhi2d2BzOwOw1DmTESNfcAWjy6U/djt+qP0/kO3Nrn\noG6fhzn5AZnxrijYzfuib5qOvmIsdte7PFP5OOzWA2XK1pqJyWTVCoMth8H1DdPkMWbWwur5ME6H\n6zG+/Svq8e1o+1bintU7cd0y6yB8qbLrv+B4kp+sW6kxIMlZyfqvmxWrEp/aJxOgSg5nplWFEztR\n8o4kEa+EN2up+xbr3D+TS8NPIb6sKNX1H3dYEIFkGyolpj0V6WX/JuKxt25MaxqHF+QQuwYeHAsl\nRlbdaslm6dr+H+T0hl2IXvMe2tpJ0jv3+HbUU3vlQq4rbbR8Cb9Xbc0EAOw2pRrjAIpyMOa9Iuc3\nvwRtyyz0HfNQj2/FGvAC1qVPoxzZiL7kHfTVE1BP7kKN2We5qZWwOg1LnLei4FZvhXViD8oPUs8u\n/OkIMwU1/wjqwjcwFr6BW70ldttBKCd3Y6yQyzl1zyV6zfuI7PoySGPHPPTlY9E2TEPfMFU6EyD/\nDu2ud2P1ftyrmIqqZxEdNAr6jsCYORJ9xUeeVZdSfApz5kiMea9gX3ArVre7Ie331Vn+v02xKk1G\nS34Hl163NFkt/Tk+LU5WDx06VE5Wy1FOVsvx+8JPBQJA4kvwd0VWi09jLHoLfdGoMrZIbiATBYES\nykVf8yVYYax+zyAqxRJd8o9iLH0Pfdn7SV6lIKMyo5f9LbmalV6NyM2TMaY8jL7kXfQ1E2FNjNz6\nUnFaDcBuNxi3YRewwpiT70f/4TMypj5IZNcCRMcb0Dd+g7Z2csIuSdXAn45SfBrFDqOv+RLFdSFa\njL55ujyWKk2JXvmmrLx9dhP6qvEY344gesPHScfstOyPmHgv6u7FKKcPIgw/+vIPMZaM8WymBBC9\nTEoI0KU20q13Hix4HXX3suRrq6pSPrB7KeqB1clENkbG4hILD6mVEb40SQ4LTyQHJsQqlErugaRV\nREyyoBSeTN5WfAj4TKlXP4X4sqWGj+PbjmuDvemn98eOrWbydhwb5eRuOS+7ftIsT1ZSipAqRzai\n2BGpffYnV3DV3bLpyK13HqgaTttBOK0Hoq0ajzn+tpgd1WS07fNjlfPbEL5UtI3fysNpc2WZUzW+\nex4ldBqnUTeiQ79AObwBc8KdaAdW4/v4OpyGnaXGefUX3vMt/BXACqEWnsA3+UHEtMdwWvbDPvty\nUjZ8i//HTwCwm/clOvgdWQXe+z3aqvHoayaiHt6AGbOlEijY7QZjDXoLjFglW1Vxm/TEqtwEJZyH\ntn1+4voIF33FWBAuduc7EFnyJUDJO4Lx7RNe8ITwpSKMgCctUKJFGPNfRV8yBvv8m7C63+/FAv/W\n8UuV1fj8M1VL4/i55quf+iyEwDCkfduhQ4do3br1P3H05fhvQjlZLcfvCj8XtVoyIeU3j3A++sK3\nMOa/WiZv3s1uiNXzQZy2g8F10Be+gTH3ZfSN09C2zMRuNxjFsdHWTvKG+t2arbE63QaKijntUTlE\n/1JH7Av/hNXzISkv+OFT9OUfekP8cQgU7A43YF06MjGU7EshevW7RCqfRXDmk/g2TYNN07x1nFrt\ncNpfKytmKRVR969CXzRKBhPEq7tGEOui4dhd7/GIpdX3SbR1X6GvnYjV435EzRI/QoEKOM0vQV83\nGXPsYNSjW1BiMaNu9Zbg2HL4P5jpbQ/AqX8BQlFR966AcEGSHMCtey7a7qVoOxclkVW3ZlsA1P2r\npQ9qvCFGUXCrNUfbuwL18HrcJj1jO7E9k3xt6xzQfLLyXHQK5dBaua0ts/GNvgQiRfKexl4+lJM7\nCfy5ijT8dx0QiVpu4MFUUFTpyaoZEJWVVfOzmyGYIZOzfCkosXum7liI4UQRwUxEMAt1jyToIq2K\nlBDErotybCuKE5XNY77kZCt1X6xKWqtt0nRt52I5PZb4lLhYDtr2BfIyNOpaYkMaIr2q9EjNqIHI\nqIW2dwXG3JfQ57+GW7M1ihXCqXee5/Ebh3L6APrS9xCKQrT/36Rnao1WRO5dIF9Qpj+JtnMxGosR\ngH1WX+xu90jP10iBfIZ+HIe2a7GXOgWy+hnuei+i30ivKu7W64hb+xxEWmWM2c+hCCem/xYYq+Q2\n7I5/xDl3CCK1EvqS0RgzRqJEixD+dKy+IxApFdGXvou2eynGwjfRF7+N07IfIpiNvupzlGgxQjOx\nu9yB1fNh8KWirZ8iZQaH1stztkIYC0ehL3kXu/PtWD0e+M2HDPxS5Gr8u/bnCOgvkdczfRZCkJGR\nwY033kj9+skvW+X4/4mfLUGJf9Zvohzl+DfhiSeeoEOHDvTo0SNpuhCC/HypGUxPT//tVlejIfSl\n72DMfRklnjAUg0ipSPSSp3A6XF82wSjvCOaEuzxfSogN9Te/BLv7vbj1SugFi09jTnsMPeafcOyQ\ntQAAIABJREFUKvzpYIW86pRboTpOB5nIo68ajz73RRTXkRXQwe/g1mglc9S//wh12xyU0j82VZrE\nKqUXyAmhXIwFb8rqcKTQawRza7YmfPfcMlpKY8ojGAvfxGnai8itX8uJdgRt3dfoc15EK6F9dZpe\nhNX1LtzGPdCXvY856T6cJhcSGTY1aZu+N3uh7VlG5NoPk4IL1B0L8I++BLdyY8LDVycN6/ufaYGa\ns4fw3XNxK9ZBzdmHcmqfJCV7V8gKoy9FDrUXnSxzHX6LECnZcmjcdVCPbcGp1hy7+32IzNqIrLpg\nRwn8rSXCl0bo6YNJSVS+t/qg7VpE5NoPcNoN9qarOxbiH90Xt2J9wn9Zn3QNzXG3ov/wGVavR7D6\nPI66Z4V8aVn3dcIFIrOWbMZqc6WXsmWOvw195SfYba4kev1HySfhOvjeHYC2fZ73LAndh33+zVgX\nPugNpSsH12JOvNeL/C0Jp0Fn7HOH4LQagHJqL+b427zlrE63YXe5E23tJPTv/46aE6tAKxr40zzJ\nhX32H4j+4UVITzRZKQfXYMx/A23txIT/KuDUO5/o4DGJUQ/vhgjUdV9jThleRoMuzFTsbvdIeUCp\nSvZvCfn5+QghSEtLK1MIiDdgxXEm/9R4ClZ8nqZpOI7jfdZ1Pcmz1TRNotEol19+OcuXL//3nlw5\nfnNQfuLHu5ysluNXx9ChQ/n222+pXLkyGzbIIbdTp05x1VVXsW/fPurWrcuECRPIyCgbA/lLuOWW\nWxg2bBhnnZU8hOm6LgUFBSiKQnr6b/CL33XQfvwcY8bIM/xoBVFiw7/CXwGr+73Yne/wKoTq7qUY\ns59D2z5PLhPzRQUZlxm97DncxiXIu2OjbZiKPvtvaEc3Jw6hQnWsS56SpKEESVH3/Yg57hbU49sR\nKGD4E9pJzSTc5GLs9tdhWgUY0//qNR/Z7QYj0quhL/8AJdZc5DS7mGiXO/FNuBP19AHsDtcTHTwm\n+VoUniTwTAuUSAGRwWNQj2xC//FzlFjkZtyIPdr/b9jd7kmsV5RD4MlG4EQJD1/jJVIB6EvfxZx0\nP06DzkTuTBB6HIvAkw1RCk8SvvVrMFNQjm9HPbEDbf0U1Jw9CFUr41xQGkJRIJCBUnwaoWo4LQcg\nUitCMBPhS8P49glAEBk6AVIqSs2pEcD/0rkodoTiJ3bIirAqba+CD8lntPilfBAuODa4FoERDVGi\nRYTuXwKajhINQaQA30fXoEQKiV70F3nvi0+jFOWgbfwGxQrJlKpQbhKBOvN5aCjCwU2vhtNmIKJS\nI9zKjRFmEP/r3UAzCT25G0poY81PhqCvmYjVazhWnyeS7+NTTVDsMKE/r08iatqaifg+GZL0rApf\nGna7wTgNu+D7ZAgoKuHhq8sQPGP6CIw5LyKCWUSuG4u+8pMS1foA9rlDwLHQV4yV4RcpFbEufoxI\nVn20Hz4jsPkblJgPsdD94ES96m908JjkvxXXRd08HXPKX1BydiXcNrLqYl30CE7bQUnNbuq+HzCm\nDEfb+33seiZCA5y652L1fBi32cWS0Fth9OUfYMx9KZEYZqaUGUkRKRWxej2Cff7NSSMGvxUUFBTg\nui6pqallIldt26aoKHE+cWIKyRGqQghvXul/4+Q1/tkwDCzLYuDAgSxbVkraU47/epST1XL8x7B4\n8WJSU1O54YYbPLL68MMPk52dzcMPP8zzzz/P6dOnee655/7hbffr148xY8aUieBzHIfCwkJUVSUt\nLe0n1v6/gbp9HubE+1FPJg+/uxm1sHo/itPuatT9P2LMeBJt5yJAVsjs1pejHtmEFtMLCl+qbNTo\nfAfanuUY3zyGGmuisZv3xbr4MbTdS9AXjkKNaxl96bhVm6IeXCO7xlOyifZ/Fueca+QPqmOjbZ6B\nvng02s6F3rEJVcc+5xoKej5KxEjD7/fj8/kgWowx/Sn0xW9LO6wYnEbdsHo/JjWNSBsr/xs9UKwQ\nkavexjl3SOLEwwWY427xmqW861GjFdb5t4AdxvfVn3ArNSL8p5VJP+DmF3egf/8xdrvBRK/9ILFy\nKE8Sp0gB4WHTIFAB5fAG1MMb0TZOQ809+LP3SASzcCvWRWTVSRBwO0Lkhk9w63aUEgBNx/9MS9Sc\n3YTvXSCtlGLwP98O9dhWQvcvQdRqk5g+shnq6f2E/rIhSTsafEBWGItfKUFcosUEH6mE0ExCL5zy\nKphK3hECTzZEBDJkNTQ+/fQBAiObIvzphEYekNMLj6Mc3Yr/ncuktvKCW1GKclBO70fN2YNS0qLp\nDHBTK+G0GoCo3gK3WguE7sP/WhdJLB/diMis5S1rTHsUY/5rOGf1JnLzpBIXU+Ab1Qttz3KiPYcj\nKjdCX/Y+2t4VSfty6l9AZOgXSZ3y6uaZ+N8fKNPXbvsGNyY7UA6tl02EG79J7AYFp/21RAc8D4EM\nr8pnOmHSFr+KsfRdmYwW31+d9jIy+Ow/eARU2/gtxuQHUHMPIhQVt1Zb1Jy9KEUxjXBaFazOt+Oc\n1Qdj3ivoq7+ITa9MtM8InBaXSEK66C3vZcup2Ra3bge0DdO8F1OnVjusvk/gNuqBtnEaxoynPOcF\n79pn1MQa8AJOy/6/qSjXwsJCHMchGAx6OtI44kWCOOLEE5KJa8l5pSuspUmrpmnk5+dz2223MWdO\nWW/pcvx346fIarlmtRy/Ojp37lzGyHnq1KksXCjJ0JAhQ+jWrds/RVZPnz59xorsb7G5SjmxE3PK\nI2ibkz1hhS8dq8/jsuM99qPp1utI5I4ZqDsWYn79MOqRjRhLpWm60P3Y3e7G6noPpMhEF6f15TjN\n+6IvGoXx3Qvom6ajbZqeqAxlN8Ducid2+2vBl4pyfDvml/ei7VqEb9ytOMs/xKndDn39FI/ICd2P\n07gb6oldqCd2YKz8O6l5R7F7P41SrRHK0S0YC95AWzUuiagKfwWsS0cmaSBFjVZEB76Kb/xtmJMe\nIFyjNUqkAH3lJ9JWq0R1yanZBmvga7i128kfaTuKu+Qd1BM70Oe/lsiCB6yeD6P9OA591Xjsc2+U\nrgOH1qEeWI3IqoNyZCO+d/r95Fu4U7kJolYbWU3MboA+9yW0wxuweg3H7npX4t7FjlU9vB6n9eWJ\n9ZtciLpsN+rWOUlk1a3eAvXYVtRD63FqtZFOAo4lLa5O70c9vAlX1aRmtUQVVzm+w6u2KnkyiU2k\nZoMTBc0ERUE5tC62j5ZJJEbd+p08poZdE5Xy9GpyCF44OE17YQ18xVs+Xu10M2pg9XsOJWcX6omd\nKIfWox5ejwKohSdQl72XuI/EJB1ZddDWTsKt1Q63Vhspl1j0lrwnFz+adI21lX9H27MckZqN3eM+\n8KfjnHM1ypFNGF/9CT32UqTtXkpgRAOcFv2wO1yHyG6A77Ob5Tb7POER1fjzZPV7BnXfD6gFxzzN\nqfbj55hWCKv7/ShVW6AWnSTlu6cw18lKrJtZG7d6S7Sdi9D2/YC27wfElEewWw9EPbETbdsc7xmM\nXvmmfNGwwtLjeOEo1CMbMaePQEwfIeUImikdAXr+yRv5sHsNx+5yp3TzmPsS2sHVaAdlSIJbsR7W\nZc/jNO/r3Tun1WU4LS5F+/EzjG+e8Bqx1NyD+D66BqdBZ6IDnkfUOLvsA/x/gDPZU8VR+vu25Ocz\n6VtLbqd081bJz4cPH6ZmzVJNg+X4f41yslqO/wiOHTvmNUZVqVKFY8eO/cIaP40zEdLfVHNVpBDj\nu+fRF74pq5nEdHexf5VIPtrGabiVG8kGnnil7Ph26SMa79aODTEqdhht1XjcrLo47a+VjTgAodOy\nSzw2DBm/KsKXht35DuzzhnrLisqNidwxHX3ui1JSsHeFV+lys+tjXzAM+5xrJBl2HfSl72LMeApz\n22wq7VqEW7E+2rHNseNSsM++HKvTbZhzX0LbKhuLIrd+jVv3XO8yOB2ux976HfraSfhf6+JZ+oDU\n+Dl122POfx318HqwihNETDeJDnwV/5h+GLOewW3YRTb9xKyknLP6oG+Ygu+dfjIhSyQP4SvICqHb\nuDtutRayYWrzTIxl70Ewg+g17yf2ZQTQPhyEvvAN7BIOA3b76ySx/uEzrPNvlgEM+cc8Uqgv/0CS\n/OLTKOFclGPS2N786iGYMhys4iRpge+jwZwJgefKdjmreYcJPpyFUFQwg8RG0VGPbcH3dh9pXxXI\n8Dr0hS8VddMMSKuMSK+KvvLv3jl4EAJj7ktyes/hOG0SBNwcezXK4fXYZ/8B+9whqEc3ox7eiLpr\nMepp6Xyg5uzBnCZJqUAB3URxLJwGnaUmOnZvlGNbMb+WLxfR/s8lazGF8CzSrE63oZ7Ygbp9nme5\nJlQdxbWl3rTHg8n39OgW/KMvQSk4hlOnA9H+z2J8/7F8cVk7CX3tJMzKTUnLPSgjd3U/Vq+Hsbvf\nJ18IwwWyEWvJGNSjmzGWSGmKUHXszndg9Xs6oRM3/DjnXAuKhjn1EVmZLnEOcQmGiDfyuS7a5pno\nP36WcMmIyS3UnD3oS9+RDWglmgnVfStl5TVGVEt+R2i7FuN/pRP2eUOl7KKkp+//AX7OEeCnGq7i\n/483S/3csqW/u+NktVatWpSjHHGUywDK8W/B3r176devnycDyMzM5PTphA9lVlYWp06d+qnVzwjX\ndenatSuzZs0qMy8Skfnrpmn+ZFrQvx1CoK37CmPKcNS8w0mJU3brK7C63o2+/mtpNRX7UXNrtMI6\n72bUw+ulBs91ZCW18+1Y3e9D270MY+ZTqEfjJvj1sbrcKauOKz7yuuWdphdhn/2HWIe0lBK4VZoS\n7fcMbtOLUHcuxJj/mldJghJVs/RqWJf9Daf1FQkS51hoy8diTB/hRVoKRcU+51rsnn9K6AwdC/PT\noejrJiN8qURumYxbsw3a+inoP3yCtqOEtEAzsDvdjn3eUE9vanzzOMa8VxDBLML3zJUG7zEYXw/H\nWDQK4UvDadhZVlBLmfULpNelW/scWdl1LMyv/yS1tg8sQVSL5bWH8wn87WyUguPJDUSRYvwvd0Q9\nuQu7zZWyuz33IMqpA6iH1vyilvXnIFQdUGSEpz9N6kAVWUX1/EKzGyQcAsIFqKFcuZ6ilLEj+4f2\njYJb82zZWJVRU8o3vv8IkZJN6JE1XoVe3T4f/5hLEWYK4UfWej6+Su4h/C+0RwnnEb34L4gKNVAP\nrEY7sArl4DpPh+rtL7USTu32aPtWohSdxG59hWycKiFl8L3RXeqYz7mG6DWyequcPoD2/d+lK0YJ\nP1qn7rnY7a/HaTMQ5dR+/GMuQSk8idOoK5GhX3qNWkruIfT5r6Evfdd7GXKNAFav4Thd705q7lM3\nz5SjFrFrX1JP69Q7H7v7fThn9UHdu0LqUg/I6qhTsw32+TejbZuLtv4rFCEQqo5zzjU4ddpjLHnH\ne8F0s+piXfwX6Wqx9B2M+a95em677VU4jbqhxyrPEBs1OfcG7PbXYqz4CG3F2KQXWxHMInrJSJxz\nb0iKxf1P4pe+W+MNWIqiYJomkYiUXpimiW3b3qhXIBBIasby+/2Ew+Ezfh43bhypqanceuut/9Kx\nHzhwgBtuuIHjx4+jKAq33nor99xzT9IyCxYs4LLLLvNcBwYOHMhjjz32L+23HP88yjWr5fiPojRZ\nbdq0KQsWLKBq1aocOXKE7t27s3Vr2WShn8PJkycZOnQo48ePLzMvFAoRjUYT2sr/MJScvZiT7kOL\nDc3G4VZvSfTylxOd8wChPPRl72EsfAulMBHXGNfgWX1HJMU84rpoaydKnVvOnqTt2y36YV00HFEz\nppMUAm3DNIxpjya6nH1piYqPGcRufx125ztkzvrkB9AOrALAadiF6KVPo+1Zhr7oLa+q5popKK4t\nPTiz6hC58bPE/gAcG/PzW9DXTJC+q5ovqcHFadrTG7516p1P5JbJCXsp18H34SC0zTNxM2oQGfKZ\nbH7aPh91+3zU/CNJ5ysCmbj1zsWp3ARj+Qey6ejix7Av/rO3jDnhLvQVY3FrnE343gWyWlp4EmP+\nazK9y0zBrd0OJWcvSu6BX+zyF7qJqNQYkVYZkVYZddcS1NyD2B1uwGnaU1Y6XRf/ewMQZgqhx7fJ\n89N0jJnPYMx+tkxz0pk0q/EmMavjUKxBb0oSGy3C/1JH1FP7iFw3FpFaSaZo7V2JufANRDAL56ze\nsvJbcAzl+I7/VQiBm1EDkd0A9dAGlNBprA7XY/Ud4XXa+97pj7Z9Hs5ZfYjc9KVHOrXlY/F9eZcc\nDr/gFkk29ywvo4UVKRVxGnfHadQDt2ZrfJ/dJN0J6nQgcvv0hI+sHcH8u/TvFYEKOI26oW2bixIp\nlNvRfIBAcaI4TXoS+eP4JA9a5fgOfB9dg3p0M0I1EGYANUYORWqlmN60N8asZz29q1ulKdE/vISo\n1BB9yRj05WNR4i9kvlRv3256NaxLRuC0u8YjisqxbRhzXkBb9UUSYXfTq2Jd/Kh08tBK6DqLcjBm\nP4e+5J0y0hm7823Sbq6El69ycC3mVw95ZDYOp955RK94PfHy9R9EXAtsGAbBYLDM/DhZVVUV0zQ9\nwun3+7Esy9Owxk3+4/i5zy+//DI9e/akd+/e/Cs4evQoR48epXXr1hQWFtKuXTu+/vprmjVLRCwv\nWLCAV155halTp/7Mlsrxn0K5ZrUc/6fo378/H3/8McOHD+fjjz9mwIAB//A2fi4Q4P8svcp10Be9\nJX0ZreKkaqoIZmK3uRK3VMwk/nTcqs1lhGVhYrKCQNsyS+pNL7gl0XhihVBO7StrOg+op/eh5h3B\nqdFaEgpFkfq44lOyc7/wJEqkAAG4NdsQueZdqCqdFAQQuXcB2sq/Y057DG3nIjlcHz+1So0oPPcW\niloNJNUtIvjZjWgHVuN/40KiV7yG0+EGKMpB/3GcHMoHWYl0i3Gz6mH3uE/6sAYyUE7uxvfWxWh7\nlknJwC2TPY9Jq8udKIc2oOYeIvB6t6TzEylZ0uA+nI9T42wid84Gv/QNdRt1w/f+5Rizn8Gt1Ub6\nqLou1nk3yyHWQ+vwP98GJRryQgVAmrR7jWyqhptZG6XgKIoVwm49EKfFpYjMWghFw/9mDxAQvmO6\nNxyrL3gdc+pfwLVwWg9MPArpVVHzj6IUn0KkyHsn0mM2S/m/LHvxlomtI4elFdRT+xCaidNqgCdT\nMPbLFwy7w3VY/f8ml7cj0i3BChG+5St53XMPoG6fj7FiLEIzEJm1ZbNV7iEoUaU2Vn6CsfITaX0V\nzJCpY2YK0a53S5mJoqHuXYk5+X4AooNGSUkKgG3he28A2o4FCCMoZQmFx9HXTJTBE/F7GczC6nF/\nYrg9Uohv7NXSoiqQSfj2b+RQeaQIbf3X6PNfRzu6KXF9TuxEXzQKp/11iArV0DZ+i/n5zSjhfGlN\ndv0n5AWqEtg0lfSV76EeWi9jU2c8JauUZhCr92PSaSNGKK1+z2BdMAzfuFtQdy1JkGR/Onb3e6Vz\nRomKplJwDOXU/oTDATFpT9Fp1Jw9ONGihJNCpAh91Xi0DVPLSFWE4cet3BhSk5OZRHYDnNZXoOTs\n9V7UBKDtWY7/lQuwezyI1evhsnG8/0acyfi/9Pwzff8qinLGz78kCwDZm1C7dnLy2j+DqlWrer8Z\nqampNGvWjMOHDyeRVTizxKEcvy2UV1bL8avj6quvZuHChZw8eZIqVarw1FNPcdlllzFo0CD279//\nT1tXzZw5k2XLlvHII4+UmfdzHav/LihHt2COG+ZVJuNwqrdEKc5FjSUdCd2P0/ZKrE7DIJAhKyeb\npb2SW6UZ0f7PoESK0Oe9gnZwjVzHl4rd8Y+4adUwFr3p/XA5jXtg9X4M9dB69O+eT0yvfQ7WRX9B\nKTyBMeeFxDBzhRqI7Pqoe5ajuLb8we5+P3a3e2Nm87sw5r+KtvJTFDcx7Oxm1CB6/SfkZZ+VsK0R\nNsbkhzBWfCiXqVgP5fRBbz2RUhE3q653PaweD8hqXYycKDl78I2+FPXUXtz0qri126PtWeZ1Ucch\ndB9Wl7tw2l6JqNYCJe8wvjd6yGpm875EbxyX0I5+OwJz7osI3YdboxXqsW3esGvSNn2puFWaIlKz\n0TfPRKg6kVu+wm3YGTQDbcXH+CbcgVu1GeGHVnoExffOZWjb5hAd8CJ2lzti930zgRfaI1KzZeU2\nlIcSysWY9ijawbVYHW5AVGqIYoVRDm9A3zgNN7OWtExybfmCs0qODtjtBscarHTUvStQj23Dadxd\nOhAYfpT84xiL38LNqkt00ChZxQ1m4vvgCtSjWwjfNs2zYtLWTsb39+txq7Ug/KfvvXP3je6LtmMh\n0T5PYPcaLsn/oXX4R/dFiRTiNO4B0WIZwhCrMCZdOzOIW7U56tHNKNEi7PbXE706ZkcmBOaEO9G/\n/1gSzru/Q1RpinJiB9q6rzHmvewRQG97/nScBp1Rj2xCPbUXkVqJ8LApiYYiIdAXvI7xzWMoQsjG\nsqIc1HgDmqIiKtbznnG71QDpcepL9byWM4oP4vv4OtTj2xP7VVScNldg9XgAUb0l2FE5VD9bJmkJ\nRcGt2xEl/5g3KuFWqI594UO4VZthfPc82o4F3rNudb8Pp1F3GYKwXvoFi2AWVpe7ZJrbsvc9L2W3\nchOsHvchKtbHmPqXxGhG/QuIDnwVVB196bvoPyR0r25aFURGzTLfL9IPeUxSg9+/E7/ktBK3tlJV\nlUAg4FlZBYNBotGo56GamppKUVGRV4UNBoPeZ0VRSElJ8T4PHz6c0aNHk5KS8qudx969e+natSub\nNm0iNTURlLFw4UIuv/xyatasSY0aNXjppZfKWCOW4z+HchlAOX73+PDDDykuLmbo0KFl5v2cF+Cv\nDtdBn/8axoynJAEkpv3MrEX0itelz6LroG6ZjbH0nSRpQFwnJ3xp0hHgglsTw4ZCoO6YjzHvlaSY\nRwCnSjOsy1/CbdQtMTEaSvg4lhqGdbMbYPV8CKfd1aAZKMd3YHzzOPpGaRclUivhZtVB3b9KHo+i\n4LToh9P4QoxFo1BP7EAoKkXn3UZB94dIy6yEGi1E/+Fz9LkvouYfjZ0PuPUuwO56p6zoagb6svcx\nJj+A4sqO9Mi1H0pCuGk62qrxaFu/Sx5CrVgf56yLcRp0xljwOtre73HTqxK5fTqiShMg1mAz6iKU\n4lM49c6XBHzvijJpXCCHb91abVAKc9D2fY+bVUcS0FhF1vz8ZvQfx2G3uJToUGlFhB3F/2wL1NxD\nRK77GLdGS5TcAzKFaPmH0tqqTntZoS04jpJ3+Oe/PP8DEIBIqwrplRFpVVCObEbNO4TdeiB2+2sR\nmbVQCo7jH32JtLd6fItX9TMm3oux7H2cxj1kwIKigG3hf70r6qF1ONVbIirWRz24xrNBKwk3s7a0\nKSs+jb51NsIISKupWPqVknsI3+i+qCd2yheyPo/LbvzNM2UKWYlzcOt3wm5/DU6LfqD7ML+8y0uk\nivZ+XBJs4aJum4O+aAzattmJ6n8gE7v7fdgdb0SkVCQ/9xQpS0eTtvBlmeCVUQOr+/1o+39EWzPR\n07U6NdugFBzzCLDTqCvRfs/Kyq7rom2YgjH7uTJxvMJfAavbPfLFpUTzmLrvR4yvHkLb/0PS8k6d\nDtgXPohzVt9EhdZ10X78FHPaY7JRq4R2FiSBtTsNkxZWmoG6ZznmhLtQj20t0YilYHe7F6vvE//2\nKusveViXJKt+v98byi9JVuNktLi42Fu2JFmNf47PHzlyJG+//favdg6FhYV069aNxx57rMyoXkFB\nAZqmEQwGmTFjBvfeey/bt2//iS2V49+NcrJajt8N/pGh/KNHJWkqaV3175QCaKf2kT75LswDyT9K\nobOvoOCS5xCloi0BfBunkv7NcNRQosHMDVak+JwbCLW/AbdEQo6ad4i0WSPwx6JNS8oKwk37UNzp\nLqxa7bzlzV0LSZ31FMaxxHApQKTuBRRd+AhW7eTqi3/VZ6TNfjKh60Mh2uhCCnqPwMluKBeyQqTO\nf5HgsjEowsXOqI1VtQW+3QtRY5ZTTiATRQjUcC7CCJDf5xnCba/2tI3G7iVkTLgFNXQa1wiguI4X\nDQvg+tJQIwUIzSTvitFEzroEACVSRMbn12PuXYaTkk3uoHfRC45h7lqEuWMuWgmNL4AwAljVWqGf\n3IFafIpIo57kXvuJZ8qe9W5vjONbKe4wlIJLnpXXOP8oFd+8ADVaRGHX+xG6Hz1nF8a+FehnIGY/\nB9eXhpNRCxGoANFizMPrcNJrEG7RXwYDWGFSl72N669AYa/HEZoGikaFr2STR94f3gDhoDgOKYte\nQ8s7SNE5QxCp2ShWCN+22egnd2JVboYIZqKE89HyDqLGUpb+t3DSqhKt1wmnYj2EbpI652+AQs4d\n83AqyxeClIWvkTrvOZz06uTcMU9WcYG0r+8nuGYcrpmKVa0VxtENqJGC5O0HMog26km0QWfs7EZU\nmHg7+ul9WFVbcPqG8YgUKfkw9iwlY9yNqJECXDMVJVqUGFJXNIQRQI0W4hpB8i9/03suAHybvyV9\n6oOooVxcMxVhBtDi3fS6j0jD7mgnd2GclM4Mxe2uo/CiJ6RbAaDmHiB1zrP4N07xjPxdI0BR1wcp\n7nRnki2YfnQTKfNewL8tuZnTzqpHYa9HiTS7xFteP7aF4JK38G/4qsxwf6RBNwr6Pp342wKUopME\nVo8juHIsWv5hb7prplB40ROE2g+hDOwIqbOfJvj9+0nE1qrSjPzL38Ku+u+rBMajVuHM36/x795/\nhaxqmuY1YDmOw+jRo3nqqad+leO3LItLL72UPn36cN999/3i8vXq1WPVqlVkZWX9Kvsvxz+GcrJa\njt8N/hGyefjw4V9e6NeAEATWfUn6jEdRo0VJJDKOSL1OhFpfRahZHzCCYBWTNvd5UmI/MHZmHcKN\ne+HbsxTjuKwuCUUj3KwPxe2uwzi0ltTFr6NaIfkj2uluQk0uJuWHjwiunYDiyC7bSJ08zO1RAAAg\nAElEQVTzCDfvh2/rLPy7Zbe9k1aNgvNvRwvlkvL9+6gRSUbDDbpR2P1hhG6StuAl/Ful/ECoBkIz\nUGONUKGWl5Pf89EEcRaC4A8fkTb3WY+gAkRqdaD43JsIN+2NYoep8O2fCWyYLPfVtA+5l76AfmoP\ngXVfEtj4dRKpsbPqUdThj4Sb9cVNqUSFb/9McM3nCBQKLvorRR1vAQTGvuVkTHkQPXd/mevsGiko\nVjEKgsKOt1LQ81FZtc3ZRfZ7fVEjBeT3eISizpIM6kc2kP3+JSiuTfHZg1DsEPqxreg5u3427clJ\nrYyd3QinQg30E9swD68j3PBCCrvej5taCf3garIm3U60ZjtybpIvFtqpPVR+8wKc1Cocf3BN7KTD\nVHumPkLVOfrYXlBkda3ak7Lr/shfE89v5VfboeUf4fg9K3AypV4v+92LMY5s4OSNX2HVkbZgGRNu\nJrBlOnm9nyLctDda4UmC339AcMMkrOxGWDXbouUfRju5Gz0/2T2hJATgZNXHqtIUN5BFcO04FNch\n59pxRBtKj9PAmvFkTH0AoZnk/PErrBptwHVIWfY26XOlVtY1U5KeEe8aplQir9+LRBr1AFUnsG4i\nFaY+iOJahJv25vTlo1Cjxfi2ziRl5Vj041sSFVPdT/isSwm1HoRV/WzSZ40guGacfM4aXUjeZa/h\nBjLw7ZxPcOVY/LsSIxFCMynofA9FXe7zrrdSfIq0+S8SXPWJTL3S/QjhosZeoCL1OlHQ/U8IfwVS\nF7xEYLNsxhK6n6L2Q7Cz6pO6fAz6KdngGK3ZjuJWV+DfMQf/jrlyWUUj3OIyCjveinlgJWkLXkYN\n5yFUg6LzhhFu1IPgmnEENk71/pbtrHqEG12Ib/dijBPbAChuPYj8i59E+CuAE8W/7TsCa7/At3Ne\n0jPrVVk1k4IL/0JRx5u98/2/gKqq+Hw+r+M/EAhgWVaSDKA0WY1/Lk1Wv/76a26//fZ/+ZiEEAwZ\nMoSKFSvy6quvnnGZY8eOUblyZRRFYeXKlQwaNKiMT3g5/nMoJ6vl+N1j8ODBPPvss1SqlNyU4Lou\nxcXF3tv7r45wPv5J92GsnZg0OXrOddgtLsFYNxl9wzTPRkr40rAbdEY7tA417xBC1Yh2vYdor0fA\nCMiO/T3LMJa+i75xahl7JKt5PyIDnpeWQzEo+ccwlozGXPaep2kDWVmMXvgnol3ulNsGKD6NuWgU\n5pLRZfWCRgDrvJuIdr0X4UvBnP8K5sI3UeyIbKjp/gBuZk3MxW+jxczohaKBcFEQuJm1CV/+Kk7T\nXt429VXj8U9+ACVaWCa61ImlIOkx3V303D8Suex5aSkkBOa8l/HNlBUUp3ITlKIc1KLkRjKh6rJD\nvv11uNVboq+ZQGD8MABCV7+H3fYqALTNMwiOvQqBgtXmStRwHuqBNailqrEQsy6N+Xra9Ttht74C\nt1IDtO3z8M1/Fbve+YTukMRePbSelNc6IQIZFD6+XR57uIDUEXXBdSgcsRuCWeC6pD5RCyVSQOFf\ndyFSK4EQclo4n8I/rYJABRAuqSOlRVfhY9tA1RCKSurTTVAci4Jnjkp/Vcci9dFqKE6UgpEH5bCz\nY5E6op7c3p83ILLqgBCkvNAG9eRuim+aiNP0IgD8n96IsW4y0fbXY7e7GjVnN9qmbzE2z5AernBG\nwi6CmTg12+BWqIaxegKKYxG+chRWhxvkdd42h8CHg1Bcm/AlI7G63oN6bAv6mi8xF41KSo0COXTu\nZtT0mqWine8gcukzUqvr2Jizn8E372XveUH3Jek04/6rQjOJXDoS64LbvKqmuvd7/F/ehXZ8W9Ky\n8nlqjNX5TrBC+L57DiWUi1A1rPNuJnLRnwEFc/Hb8u/EG2mIEUDdh9VxKNHuD3hNcjgWxooPMWeO\n9EYmQBJa69wbiHa5W96PGJTCk5jfPoH546fJ10NRcJpeRPT8W3Aa95TyAMfCXPgm5nd/k64bKdk4\ndc9F27McNaZ7FaqO3aw3Vtur0Pcsx1jydtIPuN2kJ+HB78jn7ldGnFQGAoEyMquS378+n+8n3QDO\npFn9KbL6448/0q9fv3/5uJcsWUKXLl1o1aqVVwR59tln2b9fjqAMGzaMt956i9GjR6PrOsFgkFde\neYWOHTv+y/suxz+HcrJajt89unbtyjfffPOT+dT/jqhV5dA6fB9chZp7IPFDFsgketXbOK36JxYM\n5aKvmSTTe/b/6E0WminNvXs+BCWG+wEIF2BMfhDjx8+SJgt/urSXuuBWz48Ux5b61OlPooTzkiqO\nbmZt7K53y8z0mP8k+Ucxvv2rbNgoMWxoN78Eq9/TSX6mSs5ejCnDk6IsAdyUbIra/5Hi9kNId/Lw\nfXEHaozA2m2uJHrZ86jHt6Mvew9t/ZRk0//qrWRDUG0pWdC+/xhz0v0odgSnVluiV7+Penwb2rpJ\naBumJREcN6MmTvNLcBp3l7nwm75F+NKI3PqVF+ca78gXqo7V9S6UUD7a3uWeH23y9ZQEUYkUSEP5\ny19BVGmCtmMBvg+uRPgrEPrLOtmZHS4gMLIZSug04Ttn4TboBID/pfNQD68neulI3GrNUQqOY3z3\nvOwAb9AZEaiAEspDPbAKJVos9+naMhzgH/waFYoiXzw0UxIszcSt015KDZwo+tY5Mjb30qekVjX/\nCL4Jd+GmVyP8hCS/yvHt+J9vC6pB+NFN0j81Woz/uTaouQeJXPkmTvtrpRXT9BHoW2YhjCAYAZTi\nnDLH5FZqiFvvPNwK1TEWvIFihbC63YvVX0orlKObY6b9x3HqnS89gnctRts0IylmWKg6zll9cM7+\nA06d9vi+vFu6CKgaVt8R2N3vj4ULbMP88m7U3UsT7hoouGf1xjr/Ztw652LMeBJ9+fuyCatSQ6JX\njiK/QgP8qz4ldeWHXoOj90w26Ex04CuIEkPmyumDGNNHoK0en3Sf7BaXYg14IUE+7QjaqvEY819H\njRNjYt8HMV9Xu9s9nn5UOX0Afdn76N9/VMbFw27el+hVoz03DA9FOegLR2EsGoUSTVg6uVXPkl6s\n7QYnuQeoOxZgfn5Lkqezm1aZ8KObk+y9fg0UFRVh2/YZG1iFEF5jm2EYWJZsuCztsxqXAZypwSpO\nVhcuXMgdd9xB3bp1WbRo0a96DuX4faCcrJbjd49OnToxe/bsMtMty6K4uBhd13/VympJghWHCGZi\nXfRn7A7XJ6fzIK11zE//iHZgtaSHZtD70RGKitvsIml03rwv6u4lmF/cgXr6gKyYdLsXt0oT9OUf\nJmWoO00uxGl8Ifqq8Z49lNO4B9FLn0Y9uBZj/quoJ6RGT6RUxO44FCFcjCVjUKJFXgc0uh9t1XgU\nJyqntb8O66I/I9KrSEI450UvdjUOu34nTvf6K061FrKxwrHRF76JMesZFCvkJWzFz89pdjEEMtHW\nfoniWLiVGxO59kMZYQko+1fJLvaC42WH97MbyKYlK4RbszWRmyZKr1nHwvzsZplwZKYQuW4sihNF\n3T4ffe0klFLaTaEa0uUglIubUVNup3oLlJO78L/UEcUKERnyqcyHFwLfuwPQts3B7vhHov2eQT25\nC33OS+gbpuCmV0NUaYxy6oC0DhP/XECA11RnpkgSoagoBbLaK9IqS2soK4oSyT+jvOQf2Y/Iqi3t\nqXIPoebsxmnYBavvk7iVGmIsfhtj9t+k/+z9i2U4wa4l+N7uDShE7pmHW/sc6drwwSDUY1uk3tOx\nyni3CiMoCWeTHrhpVfB/ciNK0UmcRt2kL6sZhFCutKbauQihGbgV66GV7M6PnavwVyBy46eeq4Fy\nfDvmZzfJvyNFwWkl75W26RsvKCGeECVUHbvH/Vi9HgHDT2FhIZzYSebcpzFKxxynVJROGBfcCtFC\njDkvoi/7QP5NqBpO64FyFGDVF3Ja7EVTpFZCX/a+57zhZtbC7no3TuMeGLOeQV/3lZye3RD7vBtR\n965E2/hNQhcbC/5QinIw5rwg/3ZSs4kOfA2nRT/ZOPbDp2gbv/V03cIIgB1BES5upUZErv8oKQEL\ngGixjIWd8ZTX8OhUb0XkoWSP1l8DxcXFWJZFIBDANM0y8/PypIuEruvesL9hGDiO45HVkj6q8VGw\nwkI58hMnrytXrqRnz540btyYbdu2/ernUY7fPsrJajl+9/gpsvpLptX/MOxIkkUTxIaNS3TtCt2H\n0/QinDZX4JzVB23DVMyJ96JEi3AzaxO99n3cOh3Qtn6HtvITtE3Tvcqj0H0eAXZqtiE6eLS00olB\nObgWY+m7aKu/QLESCS9uoALWZS/itL8m0Qziumgbv5G2V6U6ke1G3bEufwkR83lVTh/E+O45tJV/\nl0lZqiYraXET9KrNsHo8iFKcizH7WekXqqiE2l4L/Z8CBMbiMdLgvITFkZtZi+jV70kbqNjxSxP4\nrZJMXHAraCbamgle93X8mjqNu2Nd8Toiu4E0eH/vctSc3ZJo3jwJUa05yoFVmBPuQju8oQyZ84aI\njQDRQW/hnD0ArDD+17uhHt+O3Xog0es/BkXxTPdFMIvI1e+h5B9G3bUUffUXSKr384h/Gbr1zkNk\n1UEoKsaPnyP8aUSvGo0IZqLuXIz53XPYzS8h+j/snXeYU2X+xT+3JpnCDAx96HXoZei9d5AqWGgW\nEEWxt8WyVnRV7CKgIKCIAtJ7ld6H3jsMvU1NctvvjzeTSRhYd111dX9znkd5kntzc1vunPf7nu85\n93wFmgf9u/tRd0zHd/d4rDp3ATlDAbKSpKyyTfENmw9GJtrs59E2TsBoPASrRg9xXWY9Iyy8qncX\ng6EbychHVv9L1dusc2dW7YpdsRV2XGlRvbx2Oiy0QPvpabQ1X2DnKYz3ybUQmR/50ApcU+4LTKVr\nYTZnwfsgrgz+vp9hl2mMdP2MuJYXDuBEF8L7wAyc4rWQrp1Fm/2sqMSHVPydyPyYtXrjuCLRfv5c\nDFpueV/dh3whm8Q4mgez4X2YzYbjeGJwFrxBxIZxSLaBo0ditH4ap2AF1JWjgzMejuYB2wwSX7NW\nb4z2I4OzGNLVk2izX0DdPTv8+ApXxmj1hPBeDTH+l/fMF936oQEfsopVoztmk4ewSzXITvK6fAx9\n2iPBlDlH8wQHAo4kY1dohVl/AFaVzkgXD+Gacp8YNCg6Rtc3MRveh3JwGcqO6eKZEqIVtkrVF0EV\nDQb94r3w78Lr9eLz+XC5XLjd7hzLs4IBFEUJTvurqoplWcHmrJsTq25FXk+ePEm1atWIjo4OVmtz\n8f8LuaEAufhLIzU19bZV09Bu1P8YKedxTbwb5cSm7IpYRD5894zHLlYLdddslB3TkY+vQ90zF3XP\n3DCdnFm9B/6+nwYtgqwqnYSlU9ol1OUfiIpnSKVWsk2Uo2sxY4oGTeedYjUxq3dH3r8Uycie4pMz\nb6BPfwzr2BqMxkNFxVKWsQuWu6V9jXJ0DSx/T/hKFq6Mk7cY/j6foBStjj7/ZaF99aWJ5KwqHfHf\n+VkwTcdM7Iuy6E309eOI2DYZJ+l7MZUe0KNaxWpjl0hE3fkT8rXTuL7shtHmWczWT+IUq4n30WXo\nkwaiHlqOtibbgsaOK41Vuy94U1DXfoF6aCXSzKfw3fMVTsHyeEesxPXVnSgnN+Ee3QTHnQc5xIdV\nQkyTm4l3YTUegl2kKq5J/VH2LUSb/zJ2mcY4eYvhG/w97g+boybNwImME2lNp7bi6BFIGVdxf9WL\nm+Eg4RRKwC5YAen6GZTT27BK1heDidhi6NOGoSbNwEpoG7BTclCOrEa+fhY7rhROsVpiqn7pKFHt\nDqR0OYFUqNBggpuRtcyJLiS0nK4o5EvCR9Sq1B67XDOkG+eQr5/B0SMCRNgt/GEPr8Iq0xjf0DlI\n18+gzX4edd9C7MKVsQslIF8+gpS8N1gZVvfMhYCFGQipinT+IOqKDyDzBtqaL3AUDf/Ab4V0Jf0q\n+ty/IWVexypVH9+Ds5GuHBUV+fXjgveEfOUY7s87ChcBw4tkerELJeB78CecfCXAl442f2TQk9Ss\nNwA7rhTq9h+RL+xHWzsmuE9Wybr4Bn0HMUWFVdzaMcIqzpcmZDI1eyNfPIxybA3az5+hrvlcyCYC\nvy1/4t2YXV8LSm+sCi3RZj6Juv3HbHKouTFaP4vZ5ukwL2B15Uco+3NGOqNoOAXKB4mqdOEA6tqx\nqFu/zQ4TCNyjuPJgVe0SRlTxpiAf+RmskN+/kYkjK5h17sXs8Dec2Pjs6xJfHe8Ta0Ts8Mav0Gc9\ngzbvpaA2HoS/slWzl6gKh3z2t0YWf7hd/SrL7D90uW3bOV6HInRZ1mfj4uKQZZnU1FQyMjJ+m+JD\nLv4nkFtZzcVfAgcPHuStt97iiy++yLHst4palc7uxDW2B3LqhWwNWNFq+AZ/jxNXKnzdG+dQ1o9D\nW/VJMFoURHOVVbWzaNip2FokDtk26uqP0ea/gmSb2HGlsIsnohxcgRSws3IUDatqF8yavVD3L0bd\nPBlA6Dt7f4yUegFt7Zgwz1arRB2cyPzCt9SxhI6x06vYxWujrfoQJWlGkEiYVTphVe6EuvXbYJSj\nHVMMJ0/BYAa644rCbDYco8Wj4InFPncQZc6LuA8uytYNahEYbZ7BbP20aAwJEBl18ySxzbgy2CUS\nUQ6tCJr9B0m/5sbf432s+gNBkpAPLhPVuvQr2HlLYLR6EuVMkkj8CTSVANjuPNg1e2EltBXetZsm\nCjLVf5LQDfszcI3pinJiI3aB8hhtn0M+m4S8dxHK5Zw+rFnX1ipRF6t6N+x8JXHNeAIp/Qq+e77G\nSuwLKefxvFEFyfSS+cxmnCJVkA8sxT22O3Zcabwv7AJZDka7+ls9hVX3bqTUi7i+6AKOjb/XB0i2\nhbx/MeqBpVgl62KXbQq2hbbqIwCMFiPEdPzp7SiHV2GVbohVoyeO5kGf/SySPwPv4O9xCpRFPrAc\n15znRQTqA6LZz/Vxa5QTG/H1GyOiPlPO4Xm9MtgG3me24BSuhHx4Ne4vOgkv1D6fIKdfRtm3SGhF\nufUfATu2mCBbJRJR13yBcno7dqFKeIcvgch8Qj4wvheSLw2z2h2Y9e5BObgCJWkGcojnr6NHYVXr\nglWqIdraL0SlVY8Umu9avQFQds5Cn/ZwQIsdMnvhisZMaIdyYT/y+X3iPq52B0aP94QGF1DWj0ef\n93JYpd9bqhH+bqNQSyWCPwN17ZdoK0cH70e7aDXwpQWji+2i1TAaPSg0tkkzgtP3ZpXOmK2eFAOA\nuS8iXz8bmA1ojWT6UI6tzf4tlmmC2WQoduHK6DOfCCakmVW7Ydbph7pnLsrOWdlE2RWFVbEt0oUD\nKBf2iwFYq6cwOowUZNgykY/+LHTwN/8e4quLpLWavXM8l34vZM1e3U5qlRXKcnNCVSiFCNWzArhc\nLny+bOKeVWktXbo0Pp+PQ4cOUb58+d/xqHLxZ0SuDCAXfzjefvttpkyZgizLVKtWjQkTJvxqMrlq\n1SoWLFjAq6++mmNZlvj/dnqqfwXy3oW4Jg8Mm1ZzNA9mYj+sat2wyzcPq17KB5fhmjQIKfMadt4S\nWNW6IR9bF0ygAnA8sVgJbZEuHUU5Iwih0WQYRpfXhXbR8KLsnY+6eTLyweXhtjSSgtF8OGbn14Jp\nTQDSpaOo68eKPPPAvooo1Zr4+43FKZqdHS5dOYG66iPUTd+E627deTA6voLZ8D5QdeTT29EWvhYk\nwo47D3ZcGeSzOwXJlBXssk2Rrp4KJvtYZZvh7z4qmDqkrP1SkAZ/tvuAXaQKRpOHsCq2QZ/3EmrA\nTcGs2gV/n08gqgDygSXo3z+EnBresW8XKI8TkRfl5GZx3to8g9HhZZAktDnPo63+VLgs9P0CJzIO\nZd9C1M2Tc3aiE9Ld3fZ57IQ2SOf345o6BMcVhffpjThxpbMTrGKK4n0+CVyRaDOeRFv3JWal9lgN\n7xfTwwv/LlKfilZHMn1I18+E3TN/BBzVLeJgXdEoZ7bjKBpGx5dx8pdD3j0bbdv3ItVp0Ldgmbjf\nb4h8fh/+jq9gtn0W0i7j+UddpNSL+Lu8jlWxDfLRNegLXhOODjeZ1EOgE732ndhVu+JIEq4pg0U8\nbe2++O8aC7IiYofnPI/kOFjxNQRRv9lU3xODv+dorNp3gi8V/adnULeIbnmrYmv8vT5EPrEJdd3Y\n4LUXx+zCaP0UZrsXRQPWxcNoc/+Gunc+IJLa7MIJKEfWBHWfVtFqyDeSgyTVKt0Qo+PL2OWagW2J\nhqk5L4a5TziyipXYF6PlEziFQyI5r5zENXUI8rG12QM31YVZ9x7MxkNxilYNOUgHZfn76IvfDPMW\nhgCprXev0Ey7osAy0Za+g7p0FJJjYxWujFOsFsqBJWFBH3bhStkEteAfT+CymlgVRQlLf8pC1jP4\nVsgiraESAchJXrNkAvXq1aN///4MHz6cokWL/vYHk4s/NXLJai7+UJw4cYJWrVqxf/9+XC4Xffv2\npVOnTgwceAvD638BU6dO5dy5czz00EM5lmWN6iMjI1HVf1/Zoq4fjzbjiXCy6IoKs31yXFFYFVpj\nVekkKi2L3xSG+VU64b97vLAkQpBJJWkGatJ05HPZRv0OEnZCG4yWT4gOcznE0cAyxNTt2jE5fpBW\nqfqiKatWL9HQlXkdffYLwUqmo7qzLbNkBatqV1HhKdsUbFMQiMVvig51QhwEClfGaPWkqG4FpjXl\nvQvQp4/IjrUEjPhapPX8BHfpWtmOBIvfFMk7koRdviVkXA+S8VBLJCeqAP4e/8CqGaigbZ+GPuNJ\nUUFzReFE5LtlOpJZtQv+eyeAHoGy4Wv0GY8j2ZZwILjrS6Srp9FnjLhlZTBYEc9fFn/3d7FLNcD1\n3f0o+xZhF62G97EVQkc6aQDqzplYpRvhe3ihiHQd0wX58lHsotVFvv3FgzmiYG+FrIekE1caJzI/\n0vXTyCnnsUrWwy5WEyn1Auqu2dj5SmE2GASygj7vJQD8XV4XxGnHdJRzezAT2orkqIsHUA6vFslZ\nBcohZVxDunQkB4m87T65Y7ALVRTE6dQWnOiCeB9ehJO/HPrkAai7ZmGVaYLv4YXg2LjGdkM5vBqr\nRB18Q2Yhn92FNucFlLM7b3uOrWK18Pf9HKdwZaGvXStmPfwdX8Zs86yoIE9/DG3TNzn2z44phuRP\nExpY1Y3R9Q3MJsKSSt6/GH3GE8hXT4qjDTRTgbhv7dhionJvmziuKIzWT2M2fxQ0N97kQ0TMeAzX\n8TXZpDIiH/473hF6YUm6pc47OKiRNczWT2K0fgZ0D/Kpbahrx4j0q6zmp5DfnFntDvy9R0N0IdHw\ntHsO6ubJwVjWUBi178S48/PwTn3HQT65BXXVR6KCGvIMsguUw6rZC7NmL5wiVXJs74/EL0WuZs1u\n3QpZZFWWZWzbzkFes17ruo7P56N3796sX7/+9z6kXPxJkUtWc/GH4urVqzRs2JCNGzcSHR1Njx49\nGDFiBG3atPlV23v//fcpUqRIjqg8+M+iVtWVH6LP/VvwtSNr+O8ei1WzN/LZJJQ981H2zkdO3p3j\ns1b5lvh7vIdTOCHHMmXjRPTpj4tGj5A/biB0iWaNHli1euPEFBUOAic24UgyZqunsCq2Qt06FWXn\nzGwtnOYRueXJu5HTL4tKU7sXMFuMQD61BXXtl2H2UXZcaTAyg13CZtUuGB1eQjm0HHXVJ+GdzU2G\ngS8NbfUnSL5UQRAi47KnTaMLYbZ7XlhjqS5Iu4z+3YOi+pN1TKoHs+lDmM0eAe8N9B8fQzm2Tpyn\nhLb4e45GSrskGl32zA02BDmqC7POPVj1B4gu8OkjRHNNfHV8A78Vsar7l+CaeLfQ94U0pATPJ2BV\n6oDZ4jGciLy4x3RBSr+CWedu/P2+BF8K7tHNkC8fxax1J0a7F5CP/ow+5wVB4m+6PmHbDjge2DFF\nsSp3xNEj0Vd/jKPqAfJXBtfEe1GOrcU3YBJWzV6oqz9Bn/288Ia98xOk5N143msgptGfE00+NzdY\nub7ojHJ4Fd4hs7AT2qItegNtydsYLZ/A6PoG8rF1uD9th12gPN7HliPdSMb9eUekjGsYDe8HWUE5\nuBz58tEwl4YcxxM4VkfR8Hd8GbtyB9SN36D9/KkgtE+sw4ktijZ3JNrK0Th6BL4hs0GSUNaORd3x\nY86qa+CaOLKGv98YrDr9hPZ70kCUY2uFLVXXN7HKNUfd+h3qhq+yXTIAq3wrzNZPYheuhD77OdQd\nogJvx1fH3+dToWtdNw5t5YdBj2ER89sQ370TIG/xYKVUXfwWytUTYp2IfJB5PRAC4BKDuHyl0NaO\nQQ64EjiRcRhNHsKs0R19xWjUrd+J747MDxF5s502JAm7UnuMxkOxy7dC3TQBbd7IoIbWLlEH+dTW\nbL9W1Y1VrStm3XuRz+0RlnOWH7twJXz9J4HpQ02ajpI0M2zAZucpglXnLkFQ42uEpWr9NxFqTxUT\nE5Njuc/nCzZP3axvvZmkZr2++V9VVbl06RLPPPMM8+fP/4OOLBd/NuQ2WOXiD0W+fPl46qmnKFGi\nBB6Ph/bt2/9qogpw7tw5atWqdctl/0mDlV0om2g6koxVo7uwE7IN7OK1sYvXxuj4EtL5fbgm3IN8\n6VCwCqMcXonn3UTsAuVFI1XVztjFaqPN/Rvaui8BMBoPweg2CuniQdSkGULTd+U42toxaGvH4EiS\n8ImMKoB/wORg57O/XDPo8R7Krp9QN01CObYO5bBI6XEUHbP+IDGVqurYZRrjL9MY6cY51DWfo64Z\nE9TjOZKEVaUTRpc3cAqWxyxaFbPJMJRtU9FWCNsrfe6LwXNgVWiF/45ROIUrY+2ah3vxG2jn96DP\neAJ1xWishHYoR9dke00GnA0kMxNl50zs4rWxavTA9/AiYf01728oB5bifrtaNkFFVI2kKyeE9u/I\naqz6A7Dq3oM3vjquifcgn92F+/1GWBVbI59JChLULMssq1J7rFq9kS4cQl/2DiAyfpkAACAASURB\nVOr+RdiV22M2HoLvgZm4vuiEuvU7IcWo1lXIMdadQN3xA+qOH8LuAcn04nhisIvWQEo5h3zpMFap\nBvj7TwR/Ju53E5HSLmG2eRYnbzGUMzvEOTi3D6tUfaxK7VCOrUXZvwSrZi/sgDQiy5P2326wAqSz\nwqbMjq8OgLJfuGBYCW3FQOLEZqSMa0Kj2/sj0bC2bRoAvkcW4+QrhTbjcdS987Fji+EUKIecvDs4\nAJEsA9e8lyBQ4XWQAhrKfShbvxVEVVbxDfwWu0wjlKSZqDtnIuFgNHoQu1wzlJ0/iWpg1rWxDbR5\nI1H2zkM58rPQIucpLO7rMo2Qzu9DObJaDBAkGSd/GaTLx1APr0A9vCJIsh0tAqP9i6JaqqjIB5ai\n7pieTVQDhFs5vgH3p+2wEtoG7klBQM24smS2eQ6l7l1I106izRVNXdqqj7N/97HFMVs8FuZNbHR8\nGRwbZcePQhqQfln81hoMxmzxKE5c6eDnzWpdkK6fQV3zuYjAPbRCXJ9itbAaDMKs1TvYZGkntMEq\n3wLXxLuRz+/H/X6DsOAMO6YoVs2eWDV7Y5eo86chqLeD4zg5UgZDX9+OrN7uddb6tm2TnJxMfPzv\n1yiWi78ucslqLn4XHD16lA8//JATJ04QExNDnz59+Pbbb7nnnnt+1fbOnTtHoUKFcrz/nxb/ndhi\nWOVbIh9fj2T6UHf8iLrjRxw9ErtcU6yKbbDia+Ca8YQgqlEF8N07ESnjCsreBSj7FiNfOoy86iO0\nVR8FbX0cWRVT4I2HiO+Jr44RXx2j06vIp7ahzX4O5cTGIIGT0y6hf/+QmPar1QunaHVwRWKXrIe0\n+lOxDSRw50Hy3kBb9yXaui+xyjcXdjXVuiFdPCimK40AGchTGPlGMuqe+ah75mNVbI3Z5CHRXV6q\nAU5MUQhUjrIgn9iIunEiZovHMCq2Ja1kE6IOLyVy0SvI104hbxgPgB0Rh9HpZax6A4Rn7KznkM/v\nwzWpvzCF7/CSsL5SdCTIJqpRBfD1+Ri7Wjek5N3C4urcXlyftMZs8yxG/YGYde9GWyGqaFmd405U\nQcyEtijH1yNfOY5ycjNm66exEvtBZD702c+hz3gC/JnYpRtgVuuKum2a8BYNcSMQ5xHsUg2wKrVD\nPr4B9cBSnLwl8Q2djZR+BffbNcS1uXQYu0IrrJo9UXdMR105GqPn+5h170U5ukYMNmLjIWCBpOyc\niS7JEDCBl89sxz0qEYyABCPjKp7nC0IIUfE8Gyc0yb5AhXV8b3BHI10WTgDKpkkoh1ag7MuKyVWQ\n9y1CWy2Il1mvf9CWS/LewCrbTBDDs7tQ9i3EkRV8Q37CKZggpvoPrcQqWRerShfkI6tQDq1CEj4I\nqFu/RQ0JqLAqtReOA5unoE8bhuTYGK2exOj8GtL5fWgnN4uGwTxFsCq2Rjm8Gvn6aeSA76ijujET\n78KJKSrkKPNeEulMcaXx3z0Ou3RDYfU19UHka6ezq8GKhuRLRTq5BX35P4Kd+XZcaVGhrdIZZcd0\ntPkvB+7Jr4L3Vkb7l0mpfAe6OwJP+mXUTd/cckreiS6AVboh6BHIh1eJmYlQb9Q8hZHSLiNZftSd\nM7HLt8CKiQ9qo+UDS4KE03FFgT8TybGQMm9gFU8MElXpwsGALGgG8tWT4j3bwokuiFm9B1atXtil\nGopmxT8xJEkKVkazEqdCEfr6ZiJ7cxEh6/XNZNVxHJKTkylevPhvvv+5+OsjVwaQi98F06ZNY+nS\npYwfL8jN5MmT2bhxI5999tmv2l6bNm344Ycfcnj8ZWmpJEkSxvW/FoZXNEgdXCamU0P0pllw3Hnw\nd/67sF4KaFSxTOTjG8QU5NZvg96NICqgdrlmWFU7Y1XuhJO3GHhT0b97AHXPPBzAbHCfiJfc9VNw\nyh5Eg5FdKAHl4DIxLR5XBv+9E7CL10Y+vFLo4kIjXhU9qKmz42vg6zcGJ756tmfrtmnZ67pjwJcm\nHAQi8ommk4IV0FaOzm6yklX81XuSXqEd0dunoB1ZFXg/O07VLlQJo8NIrOp3CHuhTRPFdGdI5zII\nnaFVviXK7jkiCUySMZsMxej4Cqg62vxXUVd/Ipq5yH4oOZpoQpNwsMq3xNd/AqhuXJMGoBxYgqO6\n8N89HqtcU7Q5L6BtnXrby2uWb4nVYBDysXVo68biRObH+8QanMh8uN9rgHzluGji6vQq6vL30Oe/\nInSv3d5COb4BbeWHYgAQVwrpevJtZQN/NBxFx4mNF41eloFRf5CY2l/2D5TT2zCaDsPo8R7qmjHo\nPz2FE5mfzGc3g6ziHt0U+epJ0bhToyfKtu+FROPm7yCgUa3UQThTXDqIa+I9SN4UrJL18N3/A6hu\nYe2VRVS1iKBLRug1Nevei7/He6BoaMvfQ13+HpJl4EQVwKzZC/nkVpTTW8M+5+iRGO2eFxITRUc+\ntBxt4evZvqkh96RZoi4p9R7Ec2oD7u1Tg9fJKtMYo+UTSN4UtLl/Q045JwZ/nthsR46bvFGly8fQ\nf3hEWMBBmD9yMImrXn+sSu2QLh/FNXkQcvLuwLIOyFdPhsmHnMg4zGp3CIJatmm4bv0vgH/WG3Bz\nipXjOMGGq5u7/m9+res6fr8fSZL45ptvKFSoEIMGDfr9DygXf0rkalZz8Ydi586d3HPPPWzZsgW3\n282gQYOoV68ejzzyyK/a3u0CAX6pS/XXQrpxDvngUpSDy4XFVAgBc2QFu2Q9rIptsCu2wZEV3ON7\nIaVewM5fBqt6d+Rj65FPbgoza7cLVxLVmrRLIrWn/0TsSu0CCy3kY+tRkqaj7pyFFNqh7M4juurr\n3oNToFz2TmZeR131Mdqqj8LDAwpWwKzXH7POXdkRr+lX0Ra/gbrh67AUIKtmT4yWI3CKBVKmzu5C\nW/GB0MuGVACDhKHhgyi7ZqItGRXU2tnxNfC3fBzlzE7UdV+GaUod1S2srlqMAMcWiT8/f4pkW6Ii\nV6ElyrF1waqT2C8Zs8EgjO7vIZ/YIFwa0i5jx8bjH/gtdrFa6N8PRd32vVj/Ft3rVvFEzFZPIV06\nhL7gVVFhvO8H7IS2uMb1RDm4DLtYTbzDlyEfW4trbA/xuYQ2yCnnkZL3/NNmJkfRREpXbHHsso2R\nz+5CPr8Ps2oXrNp3ov78GcqJTfg7/R2rZk9cX/dFPr8P78MLsUvUIeJ5EZuZMeoS0tWTeN6tgxNV\nAO+IlciHV+P64RHsghUwOr6MvHch2tZvsfOVwi7TCPnkFuRLh29rzh/cRxC+sXGlUA4sR7INfP3G\nYtXph2tcD5SDy7GK18Y3fCny2Z24vugsYlSbDRe+pKs/uXVVkgB5TWiLb9BUpKsnhHTj4kEcV7TQ\nrVbtgrrodXFvhg7gogsJacfxjUFnCbP+IPxd3wBXFOq6sWgLXw9O+UPAiaDBYOzyLVDXfB7UQjtR\nBcS9VW8A6rbvhVNDxrWwfc2yn7JLi6x36cJB1NWfom6ZHPI7kDET+wqXjpDfi7r9B1FFPZsUdt3N\nRg9gtHk26EkMIl5V2TYN9edPw6273DFCu1qzF3aFlmFhAn81/DuRq5IkBRuuIiIiyMzMDFZSPR4P\nmZnZz4jQsIBRo0bRvXt3WrZs+R/t6+nTpxkwYAAXL15EkiSGDBnCY489lmO9xx57jIULFxIREcHE\niRNvKzXLxR+HXM1qLv5Q1KhRgwEDBlCnTh1kWaZ27doMGTLkV2/vNvdvjqmk3wpOTBGsegOw6g0Q\nRPJMEvLBZSgHliGf3IxyfIPwK130ejD60S5QAd/g77Itb9IuoexbiLJnAcqBpWG59Y7mRtm7ACBo\ni2WXa4pdqAJy8l6U9Muis151I3lT0Je9C8vexS5WM1gJkw+vQlv5kTBfz1tCaAsPrUC+eAh93kto\nC17FTmiHmdgP+dRW1HXjgs1CTkxRlFNbg7IHq1R9zMZDsap1wyrfQmgkvTeCxETyp6PsXYBTKAGr\nbn+sxH6om75BXTIK+exO3FMGB4/NqtQes25/lO3TUPfMRV/0OuqmiRidXxPTuKUaov84HDnlHHJW\nQ0tsMcx69yKf34+6azbahq+Rr5/F1/dzvE+uR5/UH+XEJlwft8bJWxw50EQDIOFgxxTFbPE4OCba\n3JEop7dhn96G0VlYTWnL38P1zb34hs7F3/5F3GeSkM8k4Xm1DHhTgqN2NcTHFgJEqc5d4M6D9vNn\nOFoEmc9tRU45j/vjVkiWD3+/MSh75uP65h6kjGtYNXuJ6d8Tm5AyruDkL4MTWwzO70Pypooo0iyE\nRvLGFMGJK420e444j+WaYdXogRKoVprNH8VsMhT3P+oB4B/wDVbZpnjeqY2UdgmjwWCQFEHETJ+4\nbhcOIF84EPw61/dDcGY9E3RkMDq8jHTpKK7xvYUVVb3+GHeMEqQwQFSNts9hxxRDW/WRCBgIbEs5\nsBT3O7WRUs5nNw8N+g4nuiD61AdRtwttsFWxNVbpRqjbpiFfOhRsYnLceUSXfr3+wgFgzotBLbRV\nvjlGwwdECEfSdLT142D9OPE5TyxGqyeFe4AegXxktagIB4hqsCKrebDLNsaOr4Gye67o6g8h31Z8\nDaTMG8hXT6BtnYqk6JgJ7YS2fM+87O5/T14xiDm7E/niIdR1Y3HyFMFMvAt11yyUpBlhEcmO5sGq\n2hWrdh+siq1vGdjxV0TW9P3N5v5wa81q6OtQz9XbyQKA30wGoGkao0ePpmbNmqSlpZGYmEjbtm2p\nVCnbjmzBggUcOXKEw4cPs2nTJoYNG8bGjRv/yVZz8d9ELlnNxe+GZ599lmefffY/3o7f77+tJdVv\nml51O8gKdolE7BKJIrnImyL0eVnkNUCc5EuH8LxbB7twJaF1TWiDVbMPTnRhlIPLxf7mKQKOjZx6\nAXn9OLT144K2WHZ8NdT1XyGnnMPOUwT/4KnY8TWQD60QncO75yGfSUI/kxRsjAFEpGjfzwO+jQbK\n/iUi4nXfwuB/ELCiqtsfo/eHoLmRLh1BXTcWdfMUlBObhCNBSLXOX6YpKc2eJOrUOlwbvhIE/as+\nYvq/5QgcbtN17s/EiSmM/77vMQ+vRp/9HHLyblxTBuPMfAoyrmZP9QeIvpR5A6IL4W/3N6xdP6H/\nOAJl/2I879bFbDAIx5NPVFAdC+nqCVEVrtIRJ19Jkdt+Ixnl4FJ8AyaLtKkpg9FWvA+WD7PBA8hH\n16Kc2Ijr07ZhFVPJmyK2FV8N+cpJpMxrmNW64u87BtfkAeK6yRpG93eRz+9HObQCbfMUjPYvYhes\niHzxoGisqtBS6ElPbIQb53FixR9c+eha5MOrcAIuDfLeBRBiYK9s/Q45eU/wXMiHVqIcDDTS5S0B\nGTeC945VqR3y6e3I5/fhROYXMb9bpiClXcIuUhWjzydoi98SutD46ngfXiS6+jd+LTTYhRJEk1Xg\n+yVfGu5x3bOb/ApXwmj2MOqK0ejzA9ZaPd7HbDhYeOFePiLSluoPQvKlouycFayuOwhdsbLlO9St\n3yHfOIujR2B0G4XZYDDKjh+QMq8GjlMGx0HypuCaNgxn7kikjIDzRP6yGN3eEnGjybvAyMg5/ec4\nIMtCP7rqY5TT28TbeiT++oNILdeOqI1f4t6/AH3OiyKMI6uKqkdg1u6H2WSIiDi2TNR5I0UK1qZv\nUAM2W44kYVVsg1mvP1bVLqC5wfSjzXoGbf149Pkvi+1mBRhoHiELqNlLaH1D7an+R/BLKVa3WvdW\n799MbENfX7lyhRIlSvyHewqFCxemcOHCAERFRVGpUiWSk5PDyOqcOXOCVor169fn+vXrXLhw4Za9\nEbn47yNXBpCLPz1OnjzJc889x9dff51j2S9lVv/ucByky0dRDixDObgM+cjP4cECqgtMPxKO8GQd\nMAUU7Z/aYjmuKIxmj2Al9sMpWCF7geFF2fot+tyXwhJ7QGjyrJq9MGt0F56PjoO68kO0Ba8G7ayy\nYMfXEDKB2neKiNfMG+hTh6DsmZ/9x1eS8VfuTFqdQaiVWqE5ftSNE1BXf4J8/Wz4dxcTjgny2Z3C\nXijzung/oS1Gh5fAsdGnPYJ8PlsHbMeVwXfnp5C/rIjBDJi7WyXricAAw4tr8oAc8gCnSFWkCwdE\nJa9IFXwDv0XKuIrrqzuR0i9jF6mKb/BU0dG+9N1bkuksNwEi8grHAFnBN2wBjjsP7g+bIVkG3iGz\ncPIWx/2P+uBYeJ9Yi+RNEXGirmj83d5G2TUL9eAy7OhCOLHxyOf25ggl+K3gyIogV2lXkK+fxipZ\nH7PBQLSFryGnnMd370TsUvVxj6qFZHrxDl+Co0fg/rAFkm3ifWgeTnRB3B+1RPKnY1bvARJC92zn\nNHN3ALPxEIxWT+H69n5hQeWKwjdgEk6RaoFK90YhiSlcBfn8/jBJgh1dEP9d43AKlEWfPiKbcJdt\nir/Px+BLFwT43J5s7998pfH3+QgnpqiQi2TpX/UIzCbDMCu2Rl/6DsqR1eH7Gpkfo+kwzMZDsNwx\n+A6uJXLLBNx7ZmWTVMAu1wzfvRMhTyHwpgqHgy2Tg4luwe1JEkaLx0UgRyClTdk9V3gnH1md3Vil\n6FiV2gmCWqWTGCz+DyPLnkrTtFvGoN64IZ5Juq4jSVJQlxoVFUVmZmbQUzUyMpL09PSgjVVERETw\n9bBhw5g1a9Zvut8nTpygefPm7N27N0wq1rVrV1544QUaNWoEiL6Id955h8TExN/0+3Px7yFXs5qL\nPz3+nan8c+eET2joLfpbSwF+FUw/+umt6EdX4jqyCu18eIKPlacovrLN8Zdtga9MU5yIvESs+5zo\npW+IBqNAlSu4ubiy+Cq2w1uxHdgWeX8cgpxxFTNvSTLqDEQ/sxXXoeVIgbxxR5Lxl6iP5M9APyes\nkzJq9iOzZl/ce2fj2T0L2SvIpKPo+Eo3Rrl2Ei2gH/SWbwOyiuvQ0qARu1EwgYy6g/CXbUHUinfw\n7Pkp7JhsT14y6g0mvd59IKtEbviSiI3jkEPSrABs1Y1ZMAHtwl7RVKO6SWsynPRGD+E6soo8C/6G\nknZBNL4E/g/ZmlQrJp7rPT/D8cQSO+1+1CtHsV3R3Oj+IWa+0uSbfFfw8zfrTc3YEqQ3eADPrhno\nyTsx85fjyuBZRK77nKj1n2NF5ufKkEV4ds0gevnbWJEFSO3wGhGbv0Y/vQVbiwDHQTbDPV5vBUeS\nsSPikDOuIDk2/vjaSL5UtMuHMfOWwihWG8/umQBkVuuJen4f2qUDmHlLYkUXRj+1SZyvyIKBbVj/\n7OsC19KFo+rIvlSMggmkNXuC6BWjUK8eJ73+/aS1eJq4sR1Rr50gs3ovUjq/Q97JfdHPbMOMK0t6\n3fuI2D4JLTANH9xu4Fza7hiu3fUNkm0SM/0hlPTLWNFFuH7nOBzNQ8z0h9AuH84ZIJDlU+uOJbXd\ny2RW60nE1olErR6N7L0h9KJFqqFcOYYc4qEqBY4po+5A0ps8iqO6iNg6iYiN41DSwi3AvOVak9Lh\nVfQz24nYMhH97I7gvvvLtcBRPbgOLBT3UJ54jEKV0E+sQw5oq20tAm+VbmRW74n78AoiN4wBxH1v\nRxdGP74uSMQdWcVfphmZVe/Al9ABx/0fNHX+xfBLz9qs5f8KWc3IyAh6rGbFrNq2zUsvvRRsyv0t\nkJaWRosWLRg5cmQOj+6uXbvy/PPP07hxY0CQ1XfffZfatWv/Zt+fi38fuWQ1F396/DtkMzk5+Xfc\nk98OctolXEdXox9bjevozyjpIc0XkowVWxz1mqgepjV+hLQmj+I6ugrXoaW4Dy0PEkvI/iPuL1SF\na/0mYscKP0LJl4b74GLce2fjOrIqWClzALNQZdIbPIg3oYNwATC9uA8sxpM0DdfR1WGVVG/lLqS2\nfAYrrixyyjkitk0hYtuU4D6HpvykNRmOUbAiURvHoZ8JTMOqbjJq301G9d5EbP6aiF3Twx4w3ood\nSGnzIig60Utfx7M/UE3NUwRvQie0k5vQL2STe1uPJLXlM/jLNCf2p0fRzu/BkWTSGz1MWqOhxMx7\nDs9+oft1ZDWsQuhIMpmVu2IUq02e5W8jmV4yqvcmpf0rxH1zJ9rF/fjja3H13qnk/X4wrpMbsKIL\nYeSvgOvkhltWG8U+RSH703BUF+mJA3Ad+xnt0kHS6w7GV64l+aYOwIouzMUntpFvcl9cx9dytd9E\nJNNH3ulD8SZ05FrfryjydxEjee6VZPLMf4HIrd9wo8NrGMXrkn9cR4z85bn8yGryj22Pdm431+/4\nCOXGGaJX/QMzJh5vle5EbJuE7EvF1iORbxP56kgy/uL1UFLPoV47iVGwEpcHzyLvjGG4j6zAjCnG\nlftmE7lxLFEbvsSRFFJbPoNy/TQRSdNuOqcKOBYS4CvViOs9PxPkfuW7SJYfM18Zrvf4GOXKEWIW\nvRp27xr5yuAr3wr34eWoV4UHsK9MM1Lav4rtiiJ6xT/w7JoeNsjIrNiO9KaP496/gIitk5B9ooHH\nKFSZtIZDUdIuE7X6fWTjpnQ2dywZtfqSUXcQVt6SKNfPELnmoxzH4ytRn8xa/fBW7oKjRyL5M3Ad\nWkrk5q/QTm8NkarI+Es3JrNKN7wJHUXYQC5ui5sbrCIjI/F6vViWlYOcKoqCx+MJvh43bhwvv/zy\nb7IfhmHQpUsXOnbsyOOPP55j+UMPPUSLFi3o168fAAkJCaxevTpXBvBfRi5ZzcVfFp999hnR0dH0\n7Nkzx7L09HRs2yYiIuLfTq/6w2HbyOf2BO2xlBMbwjul3THCN7Via6wKbXBiiiIf34C+6DXUE+HC\nf0fRsco1x6zcUWg3Y4uJhpfJA0UKlR4pbJ+ckCnLhDaYNXphlm2Ka+6LaEkiKejmaFmrVH2Muvdy\no2x7yLhC/h8eQDkfbuVlVmiN0XgIVkI75BMb0VeORj0g3BqCpFaSMWv3BUVD3fY9kuUPdF73w9/2\nBaRrp3BPexj5WshUvzsPZrU7UE5uCpq8G7X74ev0d/T1Y9FWjhaVuijhVypnZMehOq5o/I2Hopzf\nh7pvgZje7/4+TsEKuL/ug+RPx6jRE3+bZ/F82RU57ZLwyPSl3dauyUxohxOVH23rd9h5CpPx3A48\nn3dEOZuEr/t72LFF8Uy8G6tQAplPbSLijYrIKefJeHI96rap6Ks/wdfub1jlmhLxeQeskvXIfHQ5\nUU+LyMq091Jxf3MP6u45eO/9Brw3cE9/DKPWnfi7vU3k38viqG7SXz+F+6s+qEdW4+05GicyP57J\n/bHzliDjma14PmqGcuEARtVuoKioO0Xl9lYPeMeVB8mXguOKJuPBn9B2/Ii+7kscRcN77wSwHdxT\nH0QyvZhlm2CVb4n+82fhjhiuaBxXNHKKGDQaDe/H1/Z59OXvoa0fKzSweYtjlm+Bum9RWIe8HVUQ\nX++PsIsnoi1/D23TBFFpl2SR3KRHoW39VtwvIcdglWmCv+UTWBXbCJ/bdV+i7J0fHlGarzSX+4zF\niitD3hOrxDT/kdXZPr96ZFCmY1Zsg7f3xyhntqMmzUTdtyjEbkvCLlEHI/EurOrdcaIL3OJM/v+C\nbdukp6cjSdItnVf8fj8+nw9VVZFlOcwNwOv1BlOsQiurN5PVJUuW/OpI7lA4jsPAgQOJi4tj9OjR\nt1xnwYIFfPrppyxYsICNGzfy+OOP5zZY/QmQS1Zz8ZfFyJEjadSoES1atMixLCUlBcdxiI6O/n2b\nrH4P+NKQj6xBObAE5dDKYLRjFuyCFXD0SJQzO0RzVOunwZ0HZe+CnLZYMfFIN84KglXtDvx3jwXD\nG+ymlo+uCUmQElO7jurG3/N9rPoDkY+vF96tSTODf8wdRReaXNvAccditHgU+eoplO3Znq12vpKY\njR7ALpSA/tMzYV36IJwBjFZP4uQtibrsXdTNk0Smu6QI8/uAvjU0ItSs1Qej48soSTPQlowSCVMR\neTET70I+vhHlzPbs446Mw6rcCXXfQqFZDSQmKQeXoS19BwCjxePYRaug/zAcyfTlkAk4koRdqDLy\nxYNItom/48sQkQ99xuM4EfnIfHojrq/7opzZITrj42vgmng3dmwxvM9tx/NmFaS0S3jvHoe69XvU\nQ8sxK3cAWUXdMw87b3HswpVQ9y/B0dzYpRoEu9Kt8s2RTycheW9glm2GnHoe+eIhrHLNcaIKoCZN\nxypeG6PdC7i/6oOjusl89QjuLzojn92Jv+cHAOgzn8TOVxLviJW4P2yBfO0URtvnsWOL4fpxuCBf\nRQLa0hBZQfbAQsF/x9tIpoE2fySS42A0uA+z0X3CP/TSERxXNGa1biiHVyHfyNYtW4USsBPainS2\nG8miCav5YxiNHkRb8T7qxgkimSrkGjvuPGBkBkiqhFWzF0b7kSL2d8UHKLtmhZPQ6EL4u7+HnH4J\ndd3YoMNBljeqXbQ66urPkNMuiHtL0bJ9hVWXsI+q1x+7fEvkPfNxTR0iBnU3VeStkvWEBrVGT5zY\norf40f7/Rag9VZ48eXLMhPn9fjIzM1EUBUmSgj6rHo8Hn88XRlazNKpZZPXs2bPs37+f8+fPM2zY\nsP94X9euXUuzZs2oXr16cD/feustTp0SDYFDhw4FYPjw4SxatIjIyEgmTJiQKwH4EyCXrObiL4v7\n77+fRx55hISEhLD3f+nh+VeDdOWEaNI6uBzl8KpgzjiIP8p22cZYFVpjJbQRDgMHFosmrX2Lwv7g\n2jHxIv61SqegLRYp59EWvY66aVIYCXD0SKwqHbFq9RFRnpaBsu179MVvIqVezN5mbHHM+gOF16sr\nCnXzJNR143KQUzu2GP4OL6GcSULdNDHouWqVqo/Z6kkwvGgzn0QOxH6KbPgW+Ht+gLZtKuqqjwWh\nVN2YLUdgVu6Ia+qQYJVVnAsNJ19x5MtCZ2tVaIW/y2vos55DObYOR1Yxur0FGdfQlr5z6yYrTyxW\nlS4oO2cEvEUfwS5WC9d3D4iY0YcXoi17F+XA0gDhfhr3Z21xFA2jxQi0ZJfFuAAAIABJREFU9eOR\nMq9jRxVESv/XdKW/BRxJwokqiJx6AUfzYDQbjrbmcyR/Or6BU1D2L0bdPBmrWC38fb/A/WkbJF8a\n/m5vgW2hz3tJ2HHV7ivutdtEwBqNhmCXqIM+Y4QIpShaDd+dn6Gt/DBYtbXzlURKvRSsRoK4/r67\nvkQ5kyTOvTdFkNdGD2I0fRh93siwpCjHFY2/y+s4BcoKknooK1JYw0rsh1W+JdqSt3MO5PIUwWx4\nP2ZDYZmmbvseddM34feJOwaj7bOBSNVo5COrUHdMF01lmdkSBatYLUFQa/bCyfefd6L/LyOriepW\nz9usgBZZlpEkCcsSv4lQH1UQGta0NDGTkyULmDRpEsOHD6dt27a39NPOxf8f5JLVXPxl0blzZ8aP\nH09MTEzY+7Ztk5oqmjJuXvaXh2UKP9eDy5D3LUJO3hVWSXWiC2KVb4V07STK8Q2iqadsE6SLh5FT\nzmWv54oSXo+SEiQZZpVO2CXro+yZG0wBAlHtsso1RT6zE/n6mUADVhP0y4eQr58R60gSdjkR8eq4\nItGnPRwknsFdz/JsLdsUbePXqGu/zJFq5XjyYucriRIwXBcd3w9h1uyNtuID1CyJQmg1Lis7XnVh\ntH0OJ3959JmPI6VfwfHkxd/rA+QjP6NtnHDLU+pE5sdo+ADa+i+FH2rF1hhNHsI18W4ky8Df+e9I\nqReFn2pkfvxNhqEvfzdInn8ptcqRZOxS9ZGPbwRJwmz+WCAAwcTX51P0n55CMn14B3+Pe4LQyXmH\nzhEep5YfX9/P0Gc8iWT68Dd/HG3dF0imD6tUA+TT28IkI7f8/kBQgSMpGK2fQt32PfK1U5i1emNV\naC1soiQJ/93jUfYtErHCmgejxQjULZNzuDxkwazWDbPuvejTR4jkJ1cU/jveQfJnoi18FcmXdtN1\nym4StBLa4e8wEuXgchEQkOUUUaQqUuol5JuapRxXFGbD+zAbP4ScvCuHN6pYJxp/r9GgR6JsmYyy\nf3F2h35UAXxFaqCf2IBspGNHFRD+w0fXhQVt2EWqYNbsLQhqgbL/9LzmIhupqanYtk1UVFQO2VXo\n81iW5aCtYFZCVRayNKtAsNK6dOlSevXqRe3atdm2bdsfdDS5+DMil6zm4i+LJk2asHjx4n86ko+O\njv4v7d0fhPQrKIdWCvJ6YFkYIQXhT2lV7y6IqeYWXqs32WI5CO9Os/EQrKqdcQpWENXcpOkiu/zs\nrux1JRlvQkcy6vTHU7Ud8rE1IRGv4fZMVqEEjC5voBxeibp5StBWy4kqIDxSbRtt9SdBk3UIVMZa\nPIZVsi7aitFB6yrHFYVdog7yya1IIW4Cdlxp/He8g7p7DuqWKeK9QpXwd34Vbf1XKDfpZYPH4YnF\naP4o6sYJyNfPiNja7u/gmvYwUtolrLLNMOvcjT5tmOgWj68upspvQQwdd55ATK2N0eA+cX5TL+Dr\nOwZ1w3iUU1vx3T0edcPXKMfX4xv0Hery91BOb8f78CJB7K8cI/P5HXhGiaScjLfOEfFiERw9Au+T\n6/GMqimSuvpPwv1Ja7G/fT7GPaYLdt4S+Ht9iHt8T0Hq6g9G/fnTwHHmRc68mnOfJQW7aFXhr+rY\n+Lu+jXxiI+ru2YL03TUWbclbIiY0Ih/+FiPQ1nx+24qrVao+Rutn0JaOCg50zKpdMRreL6qm57Ib\n5BzVhV26IfLZXcHBilWuGUbbF5AuH0FbMTqYYpW1r2ajB3HyFBTX69pp8X7AG9Wq1hVtyVsoJ7eE\nH2Mg3tSq1x+rYlu8h9bi3joFz+6Z4TMOBSti1eyJWas3TqHwWZpc/Gv4VyNXQ6FpGoaR/Xu6OcEq\nKiqKXbt20aRJE4oVK8bp06d/vwPIxZ8euWQ1F39Z/NFRq396OA7S+X2iUWv/UuRj68KIoOOKwirX\nHLtcM+Sds1BPiMorkhQWoWoXKB+UC8hH16Ivel183p0nXIIQVQCzRg9RhVI9uCbeFaZZBEEczbr3\nYFa/A/XQStR1XyKfu6kpq1QD7GrdRBUvkObleGIFeS7VAH3u35AvZKd82bElMKt1Rd05M0jOzZq9\nsKp0QVvyJvKlI2IbISlQgKgWNrwf9eAy5AsHRCWw65uoGycK/a8nL/7Or6HPfwkp83qwIhl2igOV\nQqt4bdAiUI6txSrdCCuhDfrC10QwQpOhuGY8jl24MmbjIegzHhepUxVaoS94FbP+IJAk1I0T8N/x\njkg6OrkZ7+CpuCfcBUDmo8vxfNIaO18pjE6v4poyCKtyR+z46mhL38Fo8hBS+hXUHT9itHsR+cQG\nlEMr8bd7EeXoWpSjP4t1biSj7p6DVbQaRORDObI6hw0ahFRfNQ++bqPQl72DfCMZu0A5jNZPo88d\nKbS/eUtg1roTbf24ME9fR3WD5RMNVDFFMTq8JAIlNn+D5Dg4EfkwE/uJQVXIlLydr6QgypcPo/38\nWVBiYucrhdlwMPKRtagHw9PD7PxlMRs/iFmlC+qBJaibJyGfSQpfJzIOX/9vkFzRKEnTUXbODKsQ\n2zHxWHXuEo1bRavBX1wq9N9GRkYGhmHg8XjQdT3H8iyZQCgURQlKAuDWldbLly9Trlw5dF3H6/X+\n5SVdufj1yCWrufjDcP36dR544AH27t2LJEl8/fXXNGjQ4Fdty7ZtWrRowaJFi3IsyxL0386k+v8N\n/JnIx9YK8npgeRjhg4BFVtXOWDV6gGmgHF6Jsm8xUmZ4jroDmIn9MHqOxrl6Envz93j2zUENrX5l\n+W7mKYLR9S3kM9tFp3+g29uRFeyKbbEjYlG3/4jkWOG2QoUrYzYaghOVD3XNF0FD9tCmp9CObScq\nP0bzx5C8KairPxXNVoqOXaQy8tk9SE7ApiuQaCVdPYWSvAtHkjCbDENKORc0lzcaDEY+tU0s56YK\nrKzhFCgryK3qwt/j/eC0ve+Od9BWjkZOOY+/4yuCNF05jr/b26irPkZOOYfR9BHUdV8i2SZm6Uao\nx9fjyCqOFoHsS8nxff8Mjh4JtoVkerFK1kM+vQ1sG6P5Y+irPxLku/t7uKY9hBMZh7/DSFwznhCV\n0jtG4frhEWG31OtD9Hkjkbwp2PnLIl07E/TjzbreEiKgwazSCW3NZ0iOI+JRiyeirfgAyTbFoCa+\nBuru2SEm+zJ2fHXkS4eR/OlCB9v4Qey4MmirP86uioY4TYSSZzu+OkazR8GxUNePD1Zpgw1fgFW9\nB4Do+A9Gn8Zi1uqDVbYJ+oK/I185FiZBALBi4sms3AXq9EMuVTeXoP6GyMzMxO/343a7cblyxshm\nNbyGIksSkBW5enOlNUvTWrx4cSzL4uLFixQokOu+8P8VuWQ1F38YBg4cSPPmzbnvvvuC1c9fqym9\ncOECQ4cO5bvvvsuxLCtRRdd1PJ7/vXjDXwvp+lkRBXtwOcqBpTkbtUrVF/Gg7li0VR8jXz8V9nlH\n0bHKNiW9XGv8FdsRhQ999rMox9aFrWfnLSGmVat3R045j7JlSs5mr8KV8Xd8GeXsTtQNXwUrao47\nD2at3kgXDqMeW5P93ZKEVaMXVrlmQnZwSkz52nmKYCXehbJrNvKVo9nbjysNip6dKV+pPXb+sgHi\naGEXqYpVsALqzp9yBAUAmKUbIV85LiJu42tgFa6Ctu070ZzTcgT6wtdwFA1/p7/jmvuimHIuVR/1\n2Lpbhg/8MwQ1t6Fk3BUtutKl20TX/sK2rBJ1xRS/6cXf4SWRIOZLxWj1JMrWqcgp5zArd0TypaEc\nXYMTkRerWC2UQytuaddlVWqPlHEd5aQIJjDqCys0NWlm8Hw7qgv5woHsAUhMUczEfqg7ZwWn9e3C\nlTEaPYByZifK1m/DO+6L1cIuUQ9154ygjtTx5MWs3z+7oerk5rBQCLtiK9HNX6A86p55wnkgtHKb\npzBWjR5YNXuTmr8KZsDOTtO0f/mc5uKXkZUYeLtnbpamFQiS05v/vVWl1ev10rFjR3744QfKlSt3\n23jtXPzvI5es5uIPwY0bN6hVqxbHjh375ZX/BSQlJTFmzBg++OCDHMuyRvn/tajVvwJsS+TJZ8XB\nntoSJgUAQU7NegNwImJRjq7NYYvlRORFyrgmKq8N7wfNI6Zbb2QHM9j5y2KXqIOyb2GwAzxMclCs\nJmbiXTh6BOrW78IiLh0kobWNiEXZOStIbKyKbbDKNkHd/mNYVKsD4IkNNuvY8TUEud00Ccl7Q2gc\na92Jumt2juoxCIJoVu+OunUKkuNg1uyFfCYJ+fJR7MKVsWOLox5YjBORFztPEZTz+25bGQ2VV1gl\n66Oc3IQTkQ8rvibq4RUYLR5DXf0JSApGm2fRl7yF0fpptOXvAeDv/i76rGcxGg9B3TULKfUi/rbP\noS99B6t4baT0q8hXT2CWaoB6YiOOJAFKsKIcti9kVUpLg5GJnHIeq1QDcEA5uREnuhBm5Q5om74B\nwKjdF/XAUqSMqzkrza4ozJq9g+fQ0TyY9QeJmOCsargnFjJvhBF2O640Zt3+yGd3ouyZI6QBkoRV\npQsAyr4F4fdF0eoY9QeCrKBu/wHl+PrsfQjYSjmqB6taV+Rze5DP78teHpkfs0Z3rJq9sMs0Blk0\n/KSnp2Oa5m2nqnPx6/FLs1lZmlYIb7IKfX1zpVVVVZKTk3nllVd+86jVXPz1cDuymjt8+R/H5cuX\niYyM/MMqj8ePH6dAgQIMHjyYnTt3kpiYyEcfffSrp+mTk5MpXLjwLZdljaX+cv6qfyRkBbtkXeyS\ndTHbvwCZ11EOr84mr9dOIVl+tA0i4tAuUgWz0YNYiguS9+I6ugopQxA+CVD2L8Kq3Al/n09B01F2\nzUXd9RPy5aPIl0XF09EjMBo9iFOyHvLhVag7fkQ+k4R+JglH0XHyZF/PrAqhenCZ8Gxt+TikX0Xd\n/n0gPGEZjhz+mJIQWkWz1p0oe+chn92JfHYnZqX24EtHPbYWbdPEHKfCKlYLFA3l5GbUbd9hJd6N\nkjQDNWkGVulG2JaBfH4f0pXjgrxlXEMJOXZHdYGkIBkZmBXbiC51x8JsNOT/2rvz+CjKbG/gv1o6\nnXRnD9lIAgGSkLAlgUBERBSEgAouMBquKAKOiNcFr58ZxzuOKHfG3Y8zV16XQa+D44igDsKwZASV\nOIjAKLgAImEJJOkshOxrd1fV+0d1VbrT3dk61Z10zvcPJanuqieVTvXpp85zDnQH3gA4HmJkMtia\nYogjpwBFn4Mt+Q7SsBS59JJt5pRpqOj4WRoq1XPGNFZBCgwFe0k+j0LKLAR88YrceSw0Xv7e1GXg\njn4IWK2wjr8B/IldDuMCAPay3CFKAuTFTZYWeVV8QiZ0hzfJt+yn5IM/9pGcajB8IqTAMPDnDnSM\nq71JPYdCYjakiBHgv3pDDj6NUbBm3gKu+DBYpU6u7RwxNRcQULBe/h4XAGv2EogRI8D/8ElHbVT7\nGemmajlVwVbiTAowyjOk6fPAVJ6SUxNa68Ef2ypvD4qAMGkRrFmLIabMAjjntzDKd9SOcm7dzWOx\nLKsGq51/D0qQan/dFgQBkiTBZDIhMTFRw5GTwY5mVv2YJEkYO3Yshg0bhoCAAAQHByM8PBxRUVGI\njo5GXFwcYmNjERMTg8TERCQkJHh8zG+++QbTp0/HwYMHMXXqVKxduxahoaFYv359n/b31ltvwWKx\nuOxqosyg0O2+PpIkMJeKwCmB69l/OS5UUme29BBGzQBbcRJsY0egJemDIaTNBtN8WU0RkHSBYCwd\nJZ7E4RNhnXQTpMBQ8Mc+cry9GxgG69RlkPgA8N9vU2u2SnygrVj+MbBNjrVehbGzwRV9CdbWslOM\nzYAQPx788X/YCv4796YXxi0AV3wYTHO13CVs9JXgT+4BAAgjpoAtP6kGS+rzAIDXg7G2Q4wcKc9U\nNlbJRfGP75SfO+lm8N//HUJyLtiKU2Da6mGZdhd0R96FdcJCcCd2AQwjNwE49xWsY6+Tg/LYdDVw\nE0ZOA3fhCKxp14E/vQ9i/HgwtSVg2hpgmbIUum83w5r9C3DffQSwPIS0OeB/KoA1fR64M1+CsbbB\nMvk26I5uhRQYAjE8EVzFT3JDB8HsfKuf00FMmgLO1hHNOvY6cGXfg2m6BCkwBELKNeBO7AEjWV3k\n9fIQJtwIpuYCuNJj8vkPjYeQPhfc+UNgL9nVOA2KgDAqVy4Z1d5oe2wchKwlkFgOum/eV/OcAduH\npKnL5Dq/x3eCu3CkY186A4TMm2DNWgIxbTbAdz1b2l1eJem77iqwKGkCgHx732KxqMFp51xVnudh\ntVrBsix27tyJ6upqPPbYY975QciARWkAQ1BFRQVGjx6NrVu3oqysDA0NDaitrUV9fT3q6+vR2NiI\n1tZWNDY2wmKx4Jtvvul+pz045vTp03H+vBxMHDhwAM899xx27tzZp/39z//8DyZMmIC8vDynbV3V\n/CN9YG0He/5rcKf2gT2116EMESAXfBcTswCWB1t12vGWLAApJk0OPg2R4IoPyWWu7FeSK4uzgocB\nfKBauxUAhOQrICZlg634yaGupsTyEEZOBVtbCrZOXrQjhsZDTL4C7MUj6spvp8DKEAEhIUturgAJ\nYlgCpLB4dSGPGDkKTE2xU86pxAdCMkTIOazh8kwPW1cKIWmKPEspWmBNzwN/6p9yUfzWerk5QMxY\nsFU/Q9KHALbgzNP5PfW2fmAY2LZ6iMPGgK0+K5eEik4FV34cQuo1YM8Uyj/TqBngzh2AZIySf4ZL\nZyAZh8mdomw5sva/CylqJNjLxfJzh0+SO6rZck6FMTPlmr12H04cnm8cBmHMVWBLj4GtkdvlSsEx\nEGPHgi0+4rCQSxiZC3HEZPnDzpkvOxZZhcYBYOTarZ3OlxRggDDuerlYf8Y8QNfzNB8lYKL0oP6n\n1FJlGAahoaFO25V1BACg1+thsVjUVAC9Xq8GskBH8MowDDZu3IiUlBQsXbrUOz8IGbAoWB2CLl68\niBdeeAEbNmyA1WqFKIpq/+a2tja15d23336L//7v/0ZxcbGaU+SJq6++Gm+99RbS0tLw1FNPobW1\nFc8//3yf9vWf//mfWLZsGTIzM522DepWqwNce3s7zNUXYbjwFYLOFcoLcpo6iqpLDAvoQ+QcUUb+\noGDfxUmMToWQkQfJGAX+338DW33GYf9KcMo0VsmLspQFR/bF5e1aYUrB0RBG5oK9dFpdWCPxesBq\ndsyZjEmDxHDgbBURxGFywXc1RcEYBTRfdli8I7ee1UOKTJYDTl0QxLAEcNVnIIbEghHMchOB4RPB\nmX6Uf16WdwjIXJFYHRjRAjEoHGxrXUfury6o47a3MQpM82WIwTFgm6ogBkWCba1xWU7Lef88AAaM\naIGQkAmu7HtIAUZIwdFyKkJEEpjWRjBtdRCjRoFprJJX7tutypcASIZIsLY6qGLECEj6YHC2DyLi\nsBRIAUHgHOr1MrZZ546Wu+LwiXLer9I8guUB0Wpr5Wr3O+X1ENLnQYxIAld+HOzZA47bMvIgZC+B\nkDEf0Bu7/PndoWBVO911DbRYLGrB/8DAQFgsFjUtoHN9VfvOVuvXr8eyZcswY8YMj8a3cuVK7Nq1\nCzExMfjxxx+dtu/fvx833XQTRo8eDQBYvHgxnnjiCY+OSfoX5awOQSNGjMCGDXLRcGV1pZIOYE+v\n1yM/X+6o0x+fT1599VXccccdMJvNGDNmDN55x3VHoZ4oLy9HbGys0/clSVLHSjlq/U+SJIjBMbBM\nzgd35d2AKIIxfW9LGfgM7Pmv1VlTRhLk2+uxaYAkga0sAnupyKFFprqIShcoVykoPgTOtmBIHDVd\nnq21C1wAQApPgBA/wRagFoE/sVMujRWXAebSGbU5gcSwcrBUc1ENZMXYDKClpiNItZVQYpQ2r7aO\nVAwkiDFpYKtOg6n6GWJ0qjz2y2fV/FOJD4QERg3YGEkA7FYzSzqDnBcalQz2cjHE+Algy49DGjYK\nTNVpICAIaK0DBNuiKPumCko+boCc0y2FxgKtNRCHTwRXchRC4mRwpUftxqIHrO1yfqjdCnuu7Hs5\nZJckOVANGw6mvkIOloelqB8WxOgUMNXnAEhyzVRrmxqoSjoD2Fq5MoRkiIAYlgiuXP6ZpQCjfJ7K\nfpB/fmsbJIaDFJ0C5vJ58LbZVTFyJMT48WCrzqhpAYwkyiv6k3Pl3//JPeCVDyGcDsLYPLl+7oQb\ngEDn2bre6i6vkvQdwzDqwihlhb89+ztcSttV++d23pfCZDJhxAjPW92uWLECDz74IO666y63j5k1\naxZ27Njh8bGId9HMqh/rLphrbW0FwzADevZh1qxZ2LVrl9PMaXe3o4hnup2damsEd+ZLtUSWEhQq\nxIgkMM01zrefuQCIY66CGJ4Aps4E7uy/HDtbBUVATLLdMrY1ApAYBmJCFgCALT3WMSvK6SCFJ6m3\nriWGhRiXAbbmQkdtT7uGARIgzwYrOZThiWDqy8FIAsTQODBN1XJdUWOUUwtZ5fnybflQsG0NECOS\nwNaWqLOjEifnUjKCuaMklSESTEuNuk8pKMKhQoFazgoAOB0gWAAuQP4/y8uVBgSz2qhBDBsuF/FX\ngldbEO62WoHt+BIYSGHxagUHMWIk2Frb7Xtb6oJ6Xu3yjiVdIKRhKWAqT6nBsRg1Sj5vtplVCXJu\nMvhAuS2sMlNqjIKQkCmv4m/syD2WWA5i6jVygDpxEWCIcDHyvqP6y9rqactVg8EAs9kMq1V+3QQH\nB6t38wDAaDSiuVm+PixZsgSFhYX9UrKquLgYCxcudDuz+vLLL+Mf//iHx8ch2qCZ1SHI1e9cFEWU\nlpYiOjoaQUFBuHDhAmJjYwdswOouLYFmVbXV7fkNDJEbDUy4ARYAzOXzcq7rz/vkagO1HS0TJU4H\nKSIJEKxgai+CO/05lLc4ufyR2XYjnwHbWgv29GfyjNuIHPl7Zd+rC3oAW9Bpu5XOXD4n3/qOSAJT\nVQTO1jVL0gfLrVGVQFUfCrQ3yAGkXl4YwtaVQmI5SEGRYBsqIDEsJDBOgaoyc4oAIyRzsxyoBoaC\nrS2BGBoHtqFCDVzFqGQwl4shBYXLx2J5OQhUZkE7LeRiJNFhIRsjWOR9N1dDDIkFW1/aUWEgPAFs\nXRkk4zA5UNUFAe3N6nlkWus6xqrs31aWCgwDtt4kt4y1tIGtvQApwACJC+hY0R8YBrTVdwSqAUbA\n3CzPEjMsxJg0MA2VHdUG+EB5EZckqrPOEstBSJwCcDzYku/An/7c9jtjII6ZCSF7CayTbgKCh7l+\nXZEBT1nVL4qiU7Da0+tx51nXoKAgr9RWZRgGBw8eRGZmJhISEvDSSy9h3Lhxmh+XeI5mVocIJej7\n8MMP8fnnn4NlWWRkZKC5uRlz5sxBTk6Oy9s63tCbY1ZV2do02i6WDMPQ4ioNKCVlWJbtfT6wYIGu\n5Bvoir5AwOl94CtPONRtFQNDIQUEg20od8g3FULiIESNBtNWD77iZEdHK7v8R4fDhMYDLAfObqGW\naJu5VAvW64LACFYwokUOmIyR4GzBqJJLCjgu0OqY7WQg8QFgre3qbKqSPmBfX1ViOFunrt41Cegp\nZY9yZye7/9qCXDHACNbc3DFGlpcfIwpumw2IQRFgbTO8oiFSXigmyT+LpAsEq+QQQwmEO+qpCqHx\nkBgOfH2pwz7l2WG9Qy6vZcQ0tE28Ge3jF0IKcU7n0QJdG7TV3bVBmUkNCgqCxWKB1WoFwzAwGo1o\naWlR34sMBoM60/rII4/ggw8+6JfxdTWz2tjYCI7jYDAYsGfPHjz88MM4ffq0i70QX6GZ1SFO+f3r\n9XosWLAAdXV1+O6778AwjFMO60CmXAgVkiQ5fY/0H+WNv3cYWBOnojVxKnDtr8E2X0bAuS+hP1sI\n/dlCcE2VgK2rlgTbjJ5oBddYAc62+lzUGWCNHAWuvhSsQ296PayhCWCbqsCpaQKsvECpsVINwCSW\ng8TqwNpmMkV9KBhzM7jmy7YgVK8GqvKIbT8vFwBWMKsLnBhrO0Q+UJ5N1QWBtbSqDQ+U+FtZWKYG\n17b9qTOmAKB0nAoKB2d3XAAQAsPBtdVBZHVgRVs7UzUAdpxRcDiGaIXE8nKgqjPYgmm9mssr8nqw\n1nZIrA4QLQ77YVtr5bQFUQBrSxNQqg4w5mZ5mySBES3yjC0AITgWbEuNet5FnQFCaDy4hnKwlhZ5\n/0I7zMOz0DZ+EVrHL4QYZlcOz8t/p3Rt0FZ31wb7ua7u5r1SUlL6bVxdsS+3tWDBAtx///2oqalB\nZGSkV45P+o6C1SFCCVaTk5ORkZEBnU6Hu+66CxcvXlSL7vvqlrq7C9mpU6fw/vvv49FHH3XaZrFY\nYLFYwPM8danRQFtbG0RRhF6v93x2ymAAou+AJfcOWCQJbMUJ8Kc/B//zPvDFhxyDUS4A4PVg2xvB\nVtpu6QOQDFHyqvS6UuhqbDmqukA5J7O+I8iV66PaFk+JgjzLyOvBttuCY9sCJdYu31JZsQ4wtkA1\noKMXPcuDtbbJ/7e02oJEJTh1EZjagkVlsRMgB+PKz8i6WOGv/N2xogVSQDAYc5Nc7N4qyPu2jcc+\n+FX+UpU8UtbSIgfR1nY1mGat7R3jYRhIYB0CYEaQ0y8kPgiMtVWu7KALAkSh4+fnA20LuiRwTZVy\nfmpoPNDWANbcrLa+FYZPhGXiLTBn3gopKhkA4KvEIkEQ0N7eDoZhqA2zBrq79irXjq4CVOU1ryzW\nGjlypGbjtVdZWYmYmBgwDIMjR45AkiQKVAcJClaHCOUW/8cff4xDhw7hyiuvxA033ICcnBxfD80t\nk8kEs9nssuC/MmPC8zw1BNCAUg+R5/n+zyUbkQ1pRDYs1z0Ki7kF7Nl/dVQZqPoZsFtwpeaytlwG\nbKmYkjEKEsOBbaoCY9fyVW3xqgSigSFg2hoBs23lOavrqCBge44aqEpiR9CpBGoM2xEc2oJChwBV\nSRewlaiSWF7dP2wzsxLDglFmkVneacEZAIdatMrYGbtAkxHMHWNTUixkAAAgAElEQVRR9qvM7sI+\ncBXUYFopT8XYZlYZ0QJAcCwHpjzX2qp+Xy2ppQ8F097QsYhK2Q6AUWZWYzPkRVLZiyHFpAEYGG8o\nLMuqwSpdG/qfJElqfVRX51eprSpJksPMq30FF/tAVhAEDBvWPznMS5cuRWFhIaqrq5GUlISnn35a\nbUSwevVqfPTRR3j99dfB8zwMBkO/pR4Q7VHO6hCzYcMGhISE4MKFC2hra8PYsWNx5513Dsg6pX/7\n299w6dIl3HvvvU7bWlpaYLFYqP+3RpQVv0aj0SsLHxRMbQnYnz9TW60ybY3qNjlPlHUo2eSKxAfK\nwadd0AlJ6riFbl9n1L4GqP2/0bOi/h2BK6emAzjuh3FKD+hqP07PcbFf+woCjJt9OO3TYT/uxgpA\nCfhhyxXmdA7dvcSoURAm3wZr1mJI8eN7cIa8jyqFaMtqtaK5uRkcx7lMIVM6iOl0OgiCoAasBoMB\nra2tar6rwWDAxo0b8etf/xq33nortm7d6u0fhQxAlLNKIAgCMjIyMGfOHADAV199hQMHDgzIQBWQ\nZ1aTkpJcblMugAN17P7C26khUkQShCvuhnDF3XI+5cVv1CoD7MVvHAJV59aqHKDTO7WMtV+c5RCo\ngQHsg1O7hUhObUrRscCJgdRxK119rt3tdYf9SHb/ds9VXipc7FcCo+6/I7h1vW+HfdotAJMXUtlm\nXiVRnaWVqxYIHfm6ohUQrRAjRkDIWgxr9mJICVnAAK/AQXVWtdXd+VWuyZ1TAVzNrIaGhkIQBNTW\n1jrviBA7FKwOIc3Nzdi+fTu++OIL3H333ZgxYwZmzJjhsyoA3SkvL8fUqVNdbqPSVdoaEOeX5SAm\n58rF5Of/FmipBVe0vyN4rXNcjQ5JcAxUGc4xuLWbNbR9p8sAsiNAtf+/5PR99TZ8p+d13k9PdPdc\np0Vc3fzfee/KP+0CblFwODeMYIEYNhxC5i0Qsn8BcUTOgA9Q3Rmo17bBrLtg1X67/WNcpQQoDV+q\nq6tBSFcoWB1CmpqaEBcXh6CgIGzatAnh4eG48sorMX36dF8PzSV33auAjgsfvRFpY0AEq50ZIuQA\nKvMW+bZ+5Sm5G9bP++TuV3a3q5XZzo6vWYdA1d3teYccUDfDcLe9c/Da+euecPdc56DV9Rhcfd9p\nFlj9t/IdW8AaHA3rhIUQcvIhJk8HBuldiwH1mvVDnYNRd12sOgezrr5WFvdeunRJq+ESP0HB6hBi\nNBoxdepUREdHo6qqCjt37oROp8P06dMhCEK/1CQUBAE5OTlITEz0uEtIZWWlejGzZ3/Rozem/jco\nbp8yDKS4DFjjMmCd9YBc6P78QdtCrX1gbc0B1IfDblYH7m/Pd3U73WWHqE7buwp27c9qd6/a3s7M\ndjU2dz8fAwmSIRLCpJtgzV4CccxMgPWPuqRdtQQlnumu5aqSBtD5OiIIgsPXoigiJiYGAFBRUdFv\n70HEP1Gw6qcaGhqg0+kcSreEhoZiypQpYFkWWVlZmDdvnrqtvy4Sf/rTnzBu3Di15Z4nLBYL9Hq9\n0/ftZ/3ojUhbg+b86gIhps2GmDYbFjwDpr7c1gp2H7ifPwfTUqM+tDcLp7rjbmazJ4/tid6kEPR4\nn4GhECYugjVrMcS0a+U2r4T0Asuy6uKpzusGOl8z7ANb+68FQQDDMBg5ciR+85vfULBKujQ47/OQ\nbv35z3/G3r17ATgGd5GRkQgPD1fLeVy+fBmtra1u99MbpaWl2L17N+655x5NZ+docZW2BmQKQC9J\nYfEQpt0J852b0Lr+AtrWfgnzgichjJ4hL8TqxkD5yT0Zh8PsrM4A6+Tb0L5yK1rXF8O89E2IGfP8\nNlClRVba6mnealePlSQJlZWVmDZtGu677z6/qOqSnJwMg8GAkJAQxMXFYcWKFWhudi5XR3qPZlb9\n1NatW5GZmYmJEydCFEVERUXBaDSqdfGU/7/xxhvIyclBXl6ex7fMHnnkEbz44otoaGjwePxtbW1u\nL17+EEwRL2JZiCOmQBwxBda5jwFtDeCKCsH+9E9wpz8HW3PB1yPUhMQHQhi/AELWYggZeUCAwddD\n8hoKVrXVk2BV2cayrENlAPuZVpPJhMTERO8M2gsYhsHOnTsxe/ZsmEwm5OXl4fe//z2effZZXw9t\n0KNg1U9NmTIFf/3rX/Hee++hvb0dPM8jODgYERERiI2NRXx8PLKzs/Hkk0/ik08+AeDZytmdO3ci\nJiYG2dnZ2L9/v8fj72pxFQWr2vL78xsYCmHiQggTF8ICgLl0Vs5zPbUXXNF+h4Vag43E8hBSZ0HI\nuQPChBsA/eBppawFCla1YV+eyhX7a0fnO2BK8CqKYpflCQe74cOHY/78+Th+/Livh+IXKFj1U6+/\n/jpef/11AHLuZ2VlJUpKSnDx4kUUFxejuLgYX3/9NXJzc5GZmQnAs+Dk4MGD2LFjB3bv3o22tjY0\nNDTgrrvuwrvvvtun/fWkEgClAWjD74PVTqToMbBGjwGuWg1YzWCLD8kLtX74BGz1WV8Pr1sSw0JM\nvRbWKbdBmLAQCArz9ZB8bqi8dn2lL2kArp5rMpmQlZWl0Sh9QzknJSUl2LNnDxYvXuzjEfmHLv+i\nqYPV4GW1WsEwDFiW9fqFu7CwEC+99JJH1QA+/vhjnDlzBg8++KDTNqVDSmBgoMsFWMQzFosFLS0t\nbjvUDCmNVeBOfw7u+E5wP3+mtk71NQmAmHwFrFOXQZi0CDBG+XpIAwp1uNOWco3geR5Go9Fpu3KN\nBuTOVS0tHfWP9Xq92s75iSeewH333ee2nnZPrFy5Ert27UJMTAx+/PFHl4956KGHsGfPHhgMBvzl\nL39BdnZ2n4/XleTkZFy+fBk8zyMsLAw33ngjXn75ZXqf6gXqYDXEuGqRqfRqVj6DKCs5tWin6WmA\nbDKZaGbVx2h2CkBIDIQp+RCm5Mu1XU0/gju5B9z328CajjuUwNKaBECMnwBh+gpYM28BQlz/fRDK\nWdVab2dWO+ewKsrLyzFy5EiPxrJixQo8+OCDuOuuu1xu3717N86cOYOioiIcPnwYa9aswaFDhzw6\npjsMw2D79u2YPXu2JvsfyihYHSKUfFT7gs1a9XyfNWsWZs2a5dE+ysvLkZqa6nLbULtN7W10ft1g\nGEgJk2BNmCQv1GpvBltUCP7oB/Ksa2udJocVI0bCOn0VhJylkMKHa3IMQnqjv4LVuro6DBs2zKOx\nzJw5E8XFxW6379ixA8uXLwcA5Obmoq6uDpWVlW4nQ8jARMGqn6utrUVxcTGys7NhtVrBsqyaGlBT\nU4PIyEhfD9Gl8vJylw0BAAqmtEbnt4f0RogTrod5wvUAAKbmIrijW8F/uxlM1c9gPJjVk/ShsFxx\nN4SZayBFjuivEQ8ZNLOqrd4ssOr8ffttISEhmt8hKysrc1jElZiYiNLSUgpWBxkKVv2Ucov/66+/\nxrJly/D3v/8d11xzDQDAbDbjhRdegCAIWLdu3YDs8lJdXY24uDiXtfnsW63Sm1H/sz+ndH57TopI\ngjjnUVjmPAoIVrBn9kP35f8DV1QICOZua6ZaRECatAjWG56CFJNmt2P6HfRV5/70pH/Yn1NRFLt9\n/1C22/9fkiS1g5XWOr8GBtr7HekeBat+imVZSJKE66+/Hi+88ALuvfderF27FrGxsdi4cSPa2tqw\ncuVKAPLFxledQ7q6aMTHx6v/NplMTtv7o0sWcc9sNquLJEgfxE8Dbp8GhmHwxNrVyCnbgRVjgYBO\nf2qlTcDSzwDLyGn4+Mn/J/8t9kOtYkKvYW/o7jrc1YeFlJSU/h6Ok4SEBJSUlKhfl5aWIiEhQZNj\nnT9/XpP9EgpW/RrDMBBFEffccw/q6urw4IMPIiUlBcuWLcOvfvUrBAYGUos7QjQmSRLGTrkKa7bs\nwJoD8vfWjgPONQI7Ot5D8XD+dPA8TzOBxK+4ulOjzKwmJydrfvxFixZhw4YNyM/Px6FDhxAeHk4p\nAIMQBat+Srm1X19fjyeffBL79u3DAw88gGPHjqGpqUkt5+LrQNXVG7MgCJg9ezb27NnjtM1qtaK5\nuZnKKmmISoP1vxkzZoDjOAiCAAD440nnxyxcuBChoaFeHpl/6q60EvFcc3MzrFYrDAaD2hHRXkND\ng5qG0fk6bzabUVlZ2S/Xl6VLl6KwsBDV1dVISkrC008/rbYTX716Na6//nrs3r0bKSkpMBqNeOed\ndzw+JvE+Clb9lHJrf8mSJRg2bBg+/PBDpKen4+jRo3jqqaewcuVKvPTSSx6vxNRCVVUVoqJc142k\nxT/ao3Pc/8aNG4fXXnsN9913n8sPaM888wwmTZrkg5H5N5ql1k53i6xYloUgCC6D1b/+9a/47W9/\ni1/84hfIz8/3aBybN2/u9jEbNmzw6BjE96hQpZ9SZkw3bdqEt99+GxMmTADP85g2bRr++Mc/4ty5\nc7h06RKAgXdB76oSANVY1R4Fq/0vICAAS5Yswa5du3DTTTeB4ziwLIs5c+Zg27ZtWLlyJc0A9iN6\n7Wqvp+Wr7Gt7K4Grchu+trbWCyMl/oBmVv1cYmKiw9eiKCItLQ0fffSRWrZqoF3YTSYTla3yoYH2\n4cVfBAYG4uqrr8bUqVNx8eJFAHL/8JCQEHo99zMqXaW9nsysAs6/A/tg9fLlyxqOkPgTClaHGOUC\n4q2SIX3Rk+5V9OauPTrH/Y9hGBgMBrXSBeWoaoOCVe31ZmbVniiK6vW9qqpKwxESf0L3UsmAU1FR\n0e3MKqUBaIdmrwkh3ekuWO1qZlWZLKmoqFAXHRLSFXrHJx4pKSnBtddei/Hjx2PChAn43//9X4/3\nSd2rfIvOMRnsaGZVez3tYtX5eiIIAgRBQHp6Onbt2kW/I9IjlAZAPKLT6fDKK68gKysLTU1NmDJl\nCubOnYuMjIw+77O8vLzbNACaWSWE9MRA7NDnD+yDUVfnWFnk27m2qiRJKC8vx5QpU5CXl+fdQZNB\ni97xiUfi4uKQlZUFAAgODkZGRobLblO9UVNT47Kkln0JFHrz0Q6dYzLY0WtXe/bn2NXsaOffgX1w\nazKZkJSUpO0AiV+hYJX0m+LiYhw7dgy5ubke7UeSJJczp/YXRHoz0gbdkiP+glIBtOcuLxXoOlgt\nLy93qlRDSFcoWCX9oqmpCUuWLMGf/vQnjzpLdfXGQourvIs+EJDBjIJV7fW0IgDgGNiaTCaMGDFC\n+wESv0Hv+sRjFosFixcvxrJly3DzzTd7tK/6+nqEhYW53Ea3p7VH55gQ0lM9XWRl/1gA/RasFhQU\nID09HampqXj++eedtu/fvx9hYWHIzs5GdnY2fv/733t8TOIbtMCKeESSJKxatQrjxo3D2rVrPd6f\nyWRyWwOWFldpj4JV4i9oZlV7fZlZBeTrfHJyskfHFgQBDzzwAPbt24eEhARMnToVixYtclrcO2vW\nLOzYscOjYxHfo3d94pGvvvoK7733Hr744gv102tBQUGf90fdqwgh/YGCVe25K/zfeTvgGKwyDONx\nQ4wjR44gJSUFycnJ0Ol0yM/Px/bt250eR79//0Azq8QjV111ldsLVV90VWOVuldpjz4QEH9Bwar2\nulpgBbheZCVJEiIjIz2+xpSVlTlUFEhMTMThw4edjnfw4EFkZmYiISEBL730EsaNG+fRcYlvULBK\nBpTy8nK3t4dogZX2KFglhPRUbz8QKMGquwmJvhy7K5MnT0ZJSQkMBgP27NmDm2++GadPn/b42MT7\nKFglA0pFRQWuvPJKlxc/+5lVmi3Rhv15pXOsPTrH2rG/RU3nWRvdnWN3H37HjBnj8bETEhJQUlKi\nfl1SUuJUDiskJET994IFC3D//fejpqYGkZGRHh+feBcFq8QnuvpU/Morrzh83bnJQEtLiyZjIh2s\nVisaGhp8PQy/R+dYe+3t7Whvb/f1MPyaKIpdvpY7B7L9UWM1JycHRUVFKC4uxvDhw7FlyxZs3rzZ\n4TGVlZWIiYkBwzA4cuSImoJABh8KVgkhhBCiKUmS8O2332Lz5s0YPnw4br31Vo/2x/M8NmzYgLy8\nPAiCgFWrViEjIwNvvvkmAGD16tX46KOP8Prrr4PneRgMBnzwwQf98aMQH+gy6UOieyfEy2bOnIl/\n/vOfTt+XJEn95B4aGko5lRppa2tDe3s79Ho9AgMDfT0cv1VfXw8AbmsKE8+1t7ejra0NAQEBCAoK\n8vVw/FZDQwMkSUJISIjL9QTKa91oNGLz5s247777MG/ePJfXeUIYN2/utFKFDAr2uU8UqBJCukPV\nALyjp7VWRVFUa2hfunTJO4MjfoOCVTJgtLa2Qq/Xu9xGq9S9g84zIaQ3etrFSpIkNVitra31zuCI\n36BglQwYXTUEoO5V3kHBKvEXNLPqHb2ZWY2NjQUgV32h3wvpDXrnJwNGRUWFejHrjIIoQkhvULDq\nHT3tYiWKIoxGIwIDAzFhwgSq6kJ6hYJVMmCYTCa3wSp1r/IO+lBA/AUFq97RXRcr++2NjY2YOXMm\n/v3vf8NoNHptjGTwo2CV9FlBQQHS09ORmpqK559/3uP9dZUGQN2rvIOCVUJIb3T3ocA+WDWZTP1S\nY5UMPfTOT/pEEAQ88MADKCgowMmTJ7F582b89NNPHu2zvLy822CVgiht0Xkm/oJmVr2jNwusKFgl\nfUXBKumTI0eOICUlBcnJydDpdMjPz8f27ds92mdXwSotsCKE9AYFq97R3XnmOE7dbjKZkJSU5LWx\nEf9B7/ykT8rKyhwuOomJiSgrK/NonxUVFYiPj3e5jWb8vIPOM/FHFLBqp7sFVvYTDCaTCSNGjPDK\nuIh/oWCV9IkWwUxLS4vbpHtaYOUdFKwSf0GvYe+wP8/dfSiorq7ul2C1J+slHnroIaSmpiIzMxPH\njh3z+JjEtyhYJX2SkJCAkpIS9euSkhLNcpHsL4D0BqQdmn0i/oZSAbRn31XQ1Xm2397e3o6RI0d6\ndLyerJfYvXs3zpw5g6KiIvz5z3/GmjVrPDom8T0KVkmf5OTkoKioCMXFxTCbzdiyZQsWLVrU5/1Z\nrVa3+ajUatX76DwTQnqqu0VWCqPRCIPB4NGxerJeYseOHVi+fDkAIDc3F3V1daisrPTouMS3KFgl\nfcLzPDZs2IC8vDyMGzcOt99+OzIyMvq8v8rKSkRHR7vcRourvINSAIi/oZlV7+hpF6vIyEiPj9WT\n9RKuHlNaWurxsYnv8L4eABm8FixYgAULFvTLvqhsFSGkv1Gw6h3dLbJSDB8+vN+O1Z3Ov3N6/xjc\naKqKDAhdNQSgxVXeQR8KiL+iYFVb3XWxUq4p/bGuoSfrJTo/prS0FAkJCR4fm/gOBatkQCgvL3fb\napW6V3kHBavE39Br2Tu6m8G+cOEC3nrrLY8bxwA9Wy+xaNEivPvuuwCAQ4cOITw83O37CxkcuvxL\nlujjKOlnvXnzqKqqAiCv/pQkCSzLUsCqIVEUIYoiGIZRC3kTbVitVgBy7jfRDl07vKO7a8enn36K\nZcuW4YorrsDXX3/t8fH27NmDtWvXQhAErFq1Co8//jjefPNNAMDq1asBQK0YYDQa8c4772Dy5Mke\nH5doj3ETJFCwSryqN8GqyWQCAFgsFuh0Oq2GRGwkSaKZKOKX6LXtHe6u1cePH8e8efMwZswYnDlz\nxgcjI4OFu2CVPtYTr3L3+ef222/Hyy+/jJCQEKdt1113HU6dOoVPPvkEOTk5Wg9xyHr//ffx8MMP\nIz8/H6+++qqvh+PXwsPDAQB1dXU+Hol/W79+PTZs2IDHH38cjzzyiK+H47cuXLiAmTNnIjw8HD/8\n8IPT9uTkZABATU2Nl0dG/AUFq2RAMJlMiIiIcDn7UVVVhaamJkRFRdEMq4ZaWlpgsVjAsiydZy+h\n86wtnudhNpvR0tJC51pDsbGxaGhogNlsBsdxTikXyuLZ2tpamM1mBAQE+GKYZBCjYJUMCPn5+Vi5\ncqVT4WZJktQaeg8//DDdytNQRUUFAODgwYO4/vrrfTyaoYHOs7aqq6sBAB9//DGOHDni49H4N57n\n0dbWhvnz57vMxVZyWaurq/ulhBUZWihnlQxoDQ0NCAsLg9FoRFNTk6+H49fWrVuH9evXY926dXjq\nqad8PRy/RvU/veONN97AmjVrcO+996oLcIg2UlJScPbsWfz8889IS0tz2t7S0oKgoCCacCBdcpez\nSssjyYCmzPZR2RHtKR8GgoODfTwSQvqH8lqmD7raU67RyjW7M4PBQIEq6TNKAyADWkREBF555RXK\ncfKCG2+8EdHR0bj66qt9PRS/RzOq3jF58mQ888wzmDhxoq+H4vdWr16NxYsXY+TIkb4eCvFDlAZA\n+uxXv/oVdu7ciYCAAIwZMwbvvPMOwsLCfD0sQgghhAxClAZA+t28efNw4sQJfP/990hLS8Ozzz7r\n6yERQgghxM9QsEr6bO7cuWqJktzcXJSWlvp4RIQQQvxdTU0N5s6di7S0NMybN89tveLk5GRMmjQJ\n2dnZmDZtmpdHSfoTBaukX/zf//0fleEhhBCiueeeew5z587F6dOnMWfOHDz33HMuH8cwDPbv349j\nx45R6bJBjnJWSZfmzp3rcnXnM888g4ULFwIA/vCHP+Do0aP4+OOPvT08QgghQ0x6ejoKCwsRGxuL\niooKXHPNNTh16pTT40aNGoVvvvkGUVFRPhgl6Qt3OasUrBKP/OUvf8HGjRvx2WefITAw0NfDIYQQ\n4uciIiJQW1sLQK6sERkZqX5tb/To0QgLCwPHcVi9ejV++ctfenuopJfcBatUuor0WUFBAV588UUU\nFhZSoEoIIaTfuLur94c//MHha4Zh3NZv/eqrrxAfH49Lly5h7ty5SE9Px8yZMzUZL9EWzaySPktN\nTYXZbEZkZCQAYPr06Xjttdd8PCpCCCH+LD09Hfv370dcXBzKy8tx7bXXukwDsPf0008jODgYjz76\nqJdGSfqCZlZJvysqKvL1EAghhAwxixYtwqZNm/DYY49h06ZNuPnmm50e09LSAkEQEBISgubmZnz6\n6adYt26dD0ZL+gPNrBJCCCFk0KipqcFtt92GixcvIjk5GVu3bkV4eDhMJhN++ctfYteuXTh37hxu\nvfVWAIDVasUdd9yBxx9/3McjJ92hBVaEEEIIIWTAog5WZNBYuXIlYmNjHfp597QINOk7KqDtPQUF\nBUhPT0dqaiqef/55Xw/H7z311FNITExEdnY2srOzUVBQ4Osh+Y0PP/wQ48ePB8dxOHr0qMO2Z599\nFqmpqUhPT8enn37qoxESf0DBKhlwVqxY4fRm0tMi0KTvqIC2dwiCgAceeAAFBQU4efIkNm/ejJ9+\n+snXw/JrDMPgv/7rv3Ds2DEcO3YM8+fP9/WQ/MbEiROxbds2XH311Q7fP3nyJLZs2YKTJ0+ioKAA\n999/P0RR9NEoyWBHwSoZcGbOnImIiAiH7+3YsQPLly8HACxfvhyffPKJL4bm9yjzR3tHjhxBSkoK\nkpOTodPpkJ+fj+3bt/t6WH6PXtvaSE9PR1pamtP3t2/fjqVLl0Kn0yE5ORkpKSn0IZj0GQWrZFCo\nrKxEbGwsACA2NhaVlZU+HpH/YRgG1113HXJycrBx40ZfD8dvlZWVISkpSf06MTERZWVlPhzR0PDq\nq68iMzMTq1atojQiLzCZTEhMTFS/ptc58QSVriKDTldFoEnfUQFt76DXrja6KiK/Zs0aPPnkkwCA\n3/3ud3j00Ufx9ttve3uIg1ZP2m73BL32SV9RsEoGBaUHtFIEOiYmxtdD8jvx8fEAgOjoaNxyyy04\ncuQIBasaSEhIQElJifp1SUmJwwwU6Zu9e/f26HH33HNPrwIs0vNza6/z67y0tBQJCQn9OSwyhFAa\nABkUlCLQANwWgSZ919LSgsbGRgBQC2jbV2Mg/ScnJwdFRUUoLi6G2WzGli1bsGjRIl8Py6+Vl5er\n/962bRu9tjVinxe8aNEifPDBBzCbzTh//jyKioqoygjpM5pZJQPO0qVLUVhYiOrqaiQlJWH9+vX4\nzW9+g9tuuw1vv/22WgSa9J/KykrccsstADoKaM+bN8/Ho/JPPM9jw4YNyMvLgyAIWLVqFTIyMnw9\nLL/22GOP4bvvvgPDMBg1ahTefPNNXw/Jb2zbtg0PPfQQqqurccMNNyA7Oxt79uzBuHHjcNttt2Hc\nuHHgeR6vvfYapQGQPqOmAIQQQgghxOeoKQAhhBBCCBl0KFglhBBCCCEDFgWrhBBCCCFkwKJglRBC\nCCGEDFgUrBJCiBewLIvg4GD87ne/69PzZ8+ejaCgIKp9SwgZcqgaACGEeAHLsjhz5gxGjx7d531s\n2rQJb731Fv71r3/148gIIWRgoGoAhBAyyNH8ASFkKKJglRBC+ujFF1/EkiVLHL730EMPYe3atT4a\nESGE+B8KVgkhpI/uvPNOFBQUoL6+HoDc/WvLli1Yvny5j0dGCCH+g9qtEkJIH8XFxWHmzJn48MMP\ncc8996CgoADR0dHIzs7u9rknTpzA4cOHcfz4cVx11VWQJAnbtm3D3XffDYvFgvfffx/r1q1DSkqK\nF34SQggZuGhmlRBCPLB8+XK89957AID33nsPd955Z4+eV1JSgqysLHz33Xe49dZbsXjxYhw+fBij\nR4/GggULEBwcjNOnT2s5dEIIGRQoWCWEEA/cdNNN+OGHH3D8+HHs2rULd9xxR4+eN3/+fOzduxfL\nli0DAJw9exajR49WqwUcOHAAV155pWbjJoSQwYKCVUII8UBQUBAWL16M//iP/0Bubi4SExN7/Nx9\n+/Zh3rx5AIC9e/ciLy8PAHDw4EFkZWWhrKwMpaWl6uPdVHUhhBC/RsEqIYR4aPny5Th+/Hi3KQD2\npadEUYTFYlGD26NHj+LGG28EAHAch5iYGJw4ccIh+KXSVYSQoYiaAhBCiIdKSkqQnp6OyspKBAcH\nu3xMUFAQ9Ho9Hn74YTz99NO9PsbcuXNx+PBh5ObmYu/evU9cYgkAAABUSURBVJ4OmRBCBhx3TQEI\nIYR4hgXwRwBv+XoghBBCCCGE2DMCaALwI4AEH4+FEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBC\nCCGEEEIIIYT4k/8PUr1GtS3pOS0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1072567d0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "KONOLIGE Ansatz"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Is ja alles ganz nett, aber l\u00e4sst sich schlecht implementieren. Deshalb Ansatz von Konolige, K. (1997). Improved occupancy grids for map building. Autonomous Robots, 367, 351\u2013367. Retrieved from http://cs.krisbeevers.com/research/research_qual/05-konolige97.pdf\n",
      "\n",
      "1. The range error becomes proportionally larger at increasing range.\n",
      "2. The probability of detection becomes smaller at larger ranges.\n",
      "\n",
      "A mathematical model for target reflection in the 1D case is:\n",
      "\n",
      "$$p(z=D|C) = \\frac{\\alpha(z_i)}{\\sqrt{2\\pi} \\delta(z_i)} \\cdot \\exp{\\frac{-(D-z_i)^2}{2\\delta(z_i)^2}}$$\n",
      "\n",
      "where the target is at distance $z_i$ from the transducer. In this model, $\\alpha(z_i)$ is the attenuation of detection with distance, $\\delta(z_i)$ is the range variance (increasing with distance).\n",
      "\n",
      "Example: For a Polaroid Ultrasonic $d(z) = 0.01 + 0.015\\cdot z$ and $\\alpha = 0.6(1-\\min(1; 0.25r))$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = np.arange(0, 10.01, 0.01)   # Entfernungen\n",
      "ts = np.arange(-1, 1.01, 0.01)    # Winkel"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D = 5.0 # Sensor Measurement"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = 0.01+0.15*zs\n",
      "a = 0.1*(1-np.min((np.ones(len(zs)), 1/10.0*zs), axis=0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(9,3))\n",
      "plt.subplot(121)\n",
      "plt.plot(zs, d)\n",
      "plt.xlabel('Distance in m')\n",
      "plt.ylabel(r'$\\delta(z)$')\n",
      "plt.title('Range Error')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.plot(zs, a)\n",
      "plt.xlabel('Distance in m')\n",
      "plt.ylabel(r'$\\alpha(z)$')\n",
      "plt.title('Detection Attenuation')\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rJxNr4U8AlB5/Kp7+E/B1uVJyFQrTMGPMoBCGY/19P66lT+DYUpYwuh6ePmPx\n9p8gCaOFMCpXI7wZE/H2Hotjc1muwr3U/88duJc+IbkKRVLTO2ZQRGC2+AWz1MdS+DPuD+9j853n\n4tz8FliseHreRN7kTXiGP5iwHUGzvD7CXGrtfWl34etxPfl3rqdw1BxKTmpXJ7kKzfY5M1N9zFSX\nWMmVQSGq4snHtXImrpxMLL4iCIC30xV4ht5H4Lh0vUsnhIiFLQV/p8vxd7xMy1U4Dfu+NSG5Ckfj\n7TeeQJNWepdUiFpnirgaiZURtcJfjHPty7hWTMN6+DcAfGcNxzPsAUqbt9O5cKIyEjMoYmXbtxZX\n1nQcXy0CIGi1abkKb5dchSJhSMygEPFQWoJj8wLcS5/Amn8AAH96L4qHPygJo5NPG+Bc1DKYDuA3\nVKqrVYBHx3KJWlCa3pOi9J4UH9yhOoWfL8S55R2cW97Bd/Z5KlfhKd31LqYQcRdLzGAbYBRwF3A/\nKifgYMAVx3IlNbPFLyRMfQIB7Lnv02hab+ovnIQ1/wAlzdtTMOYdCv/60ZGOYMLUJ0pmq0+cXAe8\nDtwKOIGvgQ3AL8DZwEzgWVSOVFEL9HxfBk5qq+Uq3Iin500EU1w4vvyERrNG0OCli0jZubTauQrN\n9jkzU33MVJdYVefK4HXAEOBnYBuqcSwGUlGN41VAPio59M74FlOIWhQMkrLrM9yLHiHlx22ASjlR\nPPR+/O0vBavMs0oi9YB7gP+hOoPH4gKuBM4C/lvL5RI6CBx3CsUjn8Qz6G6cq1/CuXYu9m9WYf9m\nFSXN2+MZMBH/OSMlV6FIeNGMKYc2jhuq2LescfydOmwcJVZGxMq2f4OWMFqdGQYaNad40GR8Xa+R\nhNEJqoYxg81RJ7wlYbdfAryv/d0UdYWwTCvUCkq6knawDnjyca6bhyvnxfJchce1xpMxAV+XqyRX\noTCEWNrAaC55pAKPUHVHEFQMzTxgc5TPPwL4CtgF3Bvh/qbAp8BW4AtgTJTHFeKYrIe+pP780TTK\nHI59bw4Bd2MOj5hC3l0b8PUYIx3B5HWAozuCoNqqadrfzYAHQu6LtiNYVXsHMEO7fxvQOeT2xsC7\nwJfADtRa7aKuuRrhzbidvHu2UnTJs5Qel47tt2+o/587SX2yM87sGeDJ17uUQlRbNJ3ByhrHS0L+\nbhp2XzSNow0VdzMCaIsaZg6frjUe2AJ0AgYAz5AEk17MFr9gpPpYf99PvX+No9H0vjh2fEzQXo/i\nAXeSP3lzyXwxAAAgAElEQVQL3ozbo1o5xEj1iQez1aeWWFGhMU8D24FB1Xx8NO3d+aiY7NOBvwKZ\nIfdNR63VfjbQAdUpNDVDvy/tLnw9xqhchVfOoaT5OVquwimkPtFRy1X4c4WHGLo+MTBTfcxUl1jV\nJBjqWGfK0eiOmpW3D/ADbwMjw/Y5ADTS/m4E/ErkjqkQx2Qp+An3B/fR6JluOLe8DdaUkITRDxB0\np+pdRGFsacCLqBCY+4Ep1Xx8NO3dxcBr2t/rUFcDm6FGZ/oBr2j3lQB51Xx+URtsKfg7Xk7BhCwK\nxryDv3VvrJ483MufIfWJjrj/ew/W3/frXUohqlSTzmBNz5RbUPEK4vfabaHmAO2AH1HDJhNjKmmC\n6du3r95FiCtd6+PJx7X4UVKfPhfXmpcgUIK30xXk37mO4pFPEmzYrNqHlNcnKT2i/X5U+92gmo+P\npr2LtE9LoDUqjvFVVAjOHFQst6kl1PvSYqHkzKEU/vUj8m/5BN/ZI7CUeHCtnUujp8+l3ju30L/N\ncXqXMq4S6vWpgpnqEquadAZreqYczbz8v6HiBU9GDRW/AMjCkaJq/mKc2c+T+mRn3MufweIrwnf2\nCPJvX8nhUbNk5RBRXaHjSI8Df1Tz8dHmIQkP+g6iQmO6oNrbLkARcF81n1/UkdJTelB03QLyJubg\n7XQFAM6t/yJ1el/qv341tm/X61xCIY5Wk/i70DPl+6n+mfIPqFl4ZVqhzoRD9ab8THwP8A0qr9fG\n8IONGzeOtLQ0AFJTU2nfvv2R3n5ZPECibGdmZiZ0+XWtT2kJa1/5B87NbzGosVo1ZGmgHd7u19H7\n8psTrz51sJ3o9cnMzCQ3N/fI53/YsGHUgdXV3D+a9i58n5babRZt37JJfO9SSWdQ2kHjbGfv/g1a\njKb/sL/hzJ5J5txX6fzjpwz48lP8rXuzpOFQSlt2oW+/foYob7K9PqHboTGDRihPLOVfsGABAGlp\naTG1gfFcsqk31WsgU1D5CAejhoHXo4KqQwOjn0XFxvwDFTuzCRU8/VvogcyWUiEnJ8dUl63rpD6B\nAPYv/ot78WPYft0DQMnJHSge9gAlZwwGS/ze6vL6GFsNU8u0Rs3UfSvK/ZsCl6KGbo8lmvbufNSk\nufO1MkyjfNZwNnATKjRnCuAmbEaytIPGtmrJRwwObsO5Zg5WbcZxSfNz8GRouQptNbk2U/fM9PqY\nqS4QWxsYzc611TgCnIdq8GzAy6jhl7HafbO1Y72KGpK2avcvCD+I2RpBUQ1HEkY/TMqPnwNQevxp\nFA+7H/85l0jC6CQUh7WJT0W1Q98Dn6FSuYQO8zZATQgZhMo3OJ3ohoGrau+gfMZxEXA95Wm6OgJz\nUUvi7dHuqzCJRNrBBOHJx7l+Hq6cTKwFhwAtV2H/Cfi6XAl2WcxL1ExtdQah9hrHuJBGMDnZvl2v\nEkZ/swrQEkYPnozvXEkYnczi0Bks0xG4EOiGmrBhQ83kPQhkAQupfuxgrZF2MMH4PTi2vI0r63ls\nv30DQKBhMzx9bsXbYwy4Gh378UJUoraSTgPsRQ1JZKPyC/4HWAwsAxahJnako2YWT6MOO4JmZLac\nR/Guj/XgDuq/fg2NZo3A/s0qlTD6vCnk3b0RX/cxtd4RlNcnaWxDxSxfAvwFdWVvuPb32xioI2hG\nZntfHlUfuwtf9zHk37mOwqvmUtK8PdaCQ9T7dAqpT3TAteiRo3IVGomZXh8z1SVW1Q1SsFE+oUOI\nOmX97VtcS6fi2PovLMEgQXs9PH1vxdtvvOQJFLWtAHWVMIg6Gb6S8rx/QsTOloK/w2X4219KytfL\ncGVNx/7NKtwrnsWV8yLerqPx9h9PoEma3iUVJlbdoZQlwFBUJ3IS6kz5F1Qcn24LtcvwiLlZCn7C\ntfwZnOvnYSn1E7TZ8XYfg2fgnTHlCRTmFsdh4lDpwHOovKelqJRXV8X5OWpE2kHzsH27HlfWdBxf\nfgJA0GrD1+FyPBm3Eziprc6lE0YXSxtY3SuD7wNNgHe07UdQM3uHApOBp6p5PCEq58nHlf08rlWz\nsPiKCFoseDuPwjPkPgLHnaJ36URyuRV4DJX8uT7QXN/iCDMrPaU7Rde9SfHBHbiyn8ex7V2cW/+F\nc+u/8J01HM+ASZSe0kPvYgoTqe5Uy1zgZlSOq09RiVi3oWIFv41v0ZKX2eIXql0ffzHO7BmkPtmp\nPGF02/NVwugrMnXvCCb965OcslF5/vahVlyqr2tpkoDZ3pex1CdwUlsOX5FJ/t2b8PS6mWCKC8dX\ni2g06zwazL6AlJ1LIKhPiL6ZXh8z1SVW1b0ymK39gBoefhc1dLwHtcC6ELEr9ePY9CbuZU9hzT8A\ngL91H4qHP0jpKd11LpxIcp2Ataj10UGtLyxEnQg0SaP44ifwDLob5+qXcK6Zi33fGuzz1iR0rkJh\nHDWNq2kIjEIlQJ2HCrKucxIrk+ACAexfvK8ljN4LaAmjhz9IyemD4powWphfLcUMnoyaOLIJ2A0c\nD/xfnJ+jRqQdTCKefJzrX9NyFR4EoPS4dDz9b5dchaJOYgbDFaASoQpRfcEgKV8vw734kbCE0X9T\nZ7mSMFoYx4+oPKqjADvS7gk9uRrh7T8Bb6+bcWx5B1f289h+3Uv99+/EvXSqyrLQ43rJVSiiJt+2\nBmS2+IVI9bF9u44Gcy6i4bwrSPnxcwKNmlN06XPk37Eaf4dLDd0RTIbXR0RUhEonMxvI17kspme2\n92Wt1Mfuwtf9L1quwpdVrsLCn6j36T+0XIUPYyn4Kf7Pi7leHzPVJVYSYCDqlPXgDtyLH8Hx5acA\nBNxN8AyYhLfXTWB361w6IYRIQFYb/g6X4m9/CSm7PlO5Cvfm4F7xHK6cTLxdr8Hbb7zuk++Ecekd\njDWC8rU65wJPRNhnACq/lx01aWVA+A4SK2N81t/24VoyFce2f6uE0Y76ePrcgqf/BBnKEHFVSzGD\nhiftoAhl279B5Src8TFQlqvwMjwZEyVXocnpETNYEzbUouxDgB9QaRs+AL4M2acxaqm74ah1kZvW\ncRlFDVkKDuH67BmcG147kjDa0/16LWH0iXoXTwghTKk0rRtF175B8aEvcWU9j2Pbv3FuVT++s4bj\nyZhIaXpPvYspDELPwKzuqFl5+1BpGt4GRobtczXwHqojCOrKoOmZIX7BUpyHa9EjpD51LmsXzoVA\nCd7OV5J/1waKL56a0B1BM7w+ocxWH2EOZntf6lWfQLOzOXzFi+TfvRlPr78StLtVrsLZ56tchV/F\nlqvQTK+PmeoSKz2vDLYAvgvZ/h4IT6l+Omp4eDkqjc10YH6dlE7ExncY55q5uLKmYS3+AwD/KT3J\nv+0ZAs3O1rlwQgiRnAJNWlF88VQtV+Hs8lyF+9ZQclI7PBmT8LeXXIXJSs9XPZpTETvQBRgM1APW\noBK/7grfcdy4caSlqYW8U1NTad++PX379gXKe/2Jsl12m1HKE9V2oIRBzn24lz1J9k6V96pP374U\nD38Qz34v2bt+pW8z4vd8Om6X3WaU8iR7fTIzM8nNzT3y+R82bBgi8YW+P83AKPUJNmiKZ9j/4cm4\nHee6ebhyMkk5uJ0G79xM6ZJH8fSfgK/LVVXmKjRKfeLBTHWJlZ5B1j2BKahJJAD3AwEqTiK5F5XQ\neoq2PRe1DN67oQeSwGkdBQLYc/+De8njIQmjO2oJowdKwmhR52QCiRDVUOJVuQqzZhxpwwMNTpRc\nhQksljZQz5jBjahh4HTAgUrm+kHYPv8F+qImm9RDDSPvqLsi6iMh4heCQVJ2LqHhzIE0ePtmbL/u\npbRpGwqvfoWC25ZRckb5yiEJUZ9qkPqIGI0AvkKNbNxbyT4ztPu3AZ3D7rMBW4APa6uARmK296Vh\n65PixNftOpWr8OpXKDm5w5FchY2ntq80V6Fh6xMDM9UlVnoOE5cA44FFqEbuZdRM4rHa/bNRDeen\nwOeoq4ZzSILOoNHZ9q3Fvehh7PvWABBIPZniwffg63K1xJsIEVk02RPOR63xfjrqxDcTNYJSZiKq\n/WtYB+UVycZqw9/+EvznjCRl13JcWdNCchW+iPfca/D2nyC5Ck3KFEMpMjxSN2wHtuNa/AiOrxYB\nWsLogXfg7XmjJIwWhmHQYeJewEOUh8Xcp/2eGrLPLNRkuXe07a+ADOAQ0BK1/vujwJ3AReFPIO2g\niDeVq3AGjh3/A7Rche0vxTNgkuQqNLBEyzMoEoRKGP04jm3vlieM7nsrnn7jJZ5EiOhEkz0h0j4t\nUJ3B54DJgHzgRJ1RuQrnU3zoK1zZz+PY+m+c297Fue1dfGcOwzNgkuQqNAnpDBpQ6MxOPVnyD+Ja\n/gzO9a9hCZQQtDnw9BiDZ+BdBBucEPVxjFKfeJH6iBhEm8gt/GzeAlwI/ISKFxxwrAebKatCZmZm\nQpffTPUJNDuLxc2vwtJgMENK1uPcMJ8X/72YTssX06d3TzwZk1jxsxssFkOUt7rboTGDRihPLOVf\nsGABAGlpaTFlVDDaUEpMzDY8oveXs6U4D2f2DFyrZmPxHyZoseLrPArPkHsJNEmr9vH0rk+8SX2M\nzaDDxNFkT5gFrEAl4Ac1TDwAuB24FhVn7UJdHXwPuC70CaQdNDYz1cdS+Avr5j7A0LxFWD15AJSc\n1FbLVXhJwsWOm+m1gdjaQKM1mDExWyOoG99hnGvm4Fox7cgH3Nf2AoqH/U0SRouEYdDOYAqwE5Uz\n9UdgPXAVR08gGa/97olatz18DC4DuBuJGRRG4C3Auf41XDmZWPMPAFDa5BSVq/DcqySWXCcSMyhi\nU+rHsfEN3MuewlqgEkb7T+1H8fAHKE3rpnPhhDCFaLInfIzqCO4GioDrKzlW9dcOE6I2OBvi7Tce\nb6+btVyFz2P7dQ/1/3s37mVP4ulzC96eN0hseQLQM8+gqESd5TwKBLBvfY9Gz/ak/vt3YS04SEmL\nThTc8B6FN70ft46g2XI4SX1EjD4BzkSlj3lcu2229lNmvHZ/R2BzhGNkARfXYhkNw2zvS1PX50iu\nwrUUXv0qJSd3VLkKF/1T5Sr89J9YCg7pV9gqmO21iYVcGUxGwSApO5fiXvwwKQe+AKD0hNMpHvo3\n/OdcLKuGCCGEqD6rDX/7kfjPuZiU3StwrZiGfe9K3FnTcK3K1HIVjidwXLreJRVhTPGtL7Ey0VMJ\no/+Jfd9aoCxh9L1qLcoEC/oVIhKDxgzWOmkHhRHZ9m/ElTW9PFehxYqvw2V4MyZS2rydzqUzJ4kZ\nFJWyHdiOa9HDOHYuBiBQ7zg8A8oSRh97QXIhhBAiFqVpXVWuwp924sqegWNLea5C/5lDKR5wh+Qq\nNAC9YwajWasToBsqAPuyuiiU3uIZv2D99Rvqvf1XGj7fH8fOxQQdDSgeNJm8yZvx9rutTjqCZovH\nkPoIUfvM9r5M9voETjyTw396gbzJm/H0HkvQXg/7ziU0mn0+DWedh/3LRRDUZ26U2V6bWOh5ZTCa\ntTrL9nsCtUZx0g39xMqSfxDXZ0/j3PB6SMLo6/EMvLNaCaOFEEKIeAk2bknxRY/jGXQ3ztUv4Vwz\nh5Rv19Hg9asoOakt3v4T8XW4VMKW6pienato1uoEmAT4UFcHP0IlW61AYmXKWYr/wJk1A9fq2Vj8\nxSo+o8soPIPvI9Ckld7FE6LWScygEAnEW4Bz/eu4cl4MyVWYhrffBLxdr5ZchTFItJjBaNfqHAkM\nQnUGJb9WZXyHca5+CVfW9PKE0e0upHjo3wg0O0vnwgkhhBAROBvi7Xcb3l434djyL1xZM7D9uod6\nH0zG9dmTePvcgrfHDQTdqXqX1NT07AxG07GbhrpiGERdxay0p5u0a3KW+ln78kM4N7/DoCa/A7CU\nDni7Xkvvy29MvPokwLbUx1jbmZmZ5ObmHvn8x7IupzAesy0RJvWpQooTX7dr8Z17NfbtH+HKmk7K\nD1txL3oY14ppeHvegKfPLQQbNovfc2rM9trEQs+hlGjW6txLeRmbAoeBm1GxhUeYbXgkqjdmIID9\n84W4lzyG7bd9AJS06EzxiAcpaTOg1stYHWb7oEl9jE2Gic3BbO9LqU81BYOk7MlSuQr3ZKubUpz4\nzr0aT7/xBI5vHbenMttrk2hrE0ezVmeoV4EPgYXhd5itETymYJCUnUtwL3qYlIPbAS1h9LD/w9/u\nIkkYLZKedAaFMBfbd5tUrsLtHwEqV6G/w6V4MiZS2vwcnUtnPIkWMxjNWp0ihG3fWup9+g9Svl0H\naAmjh9yHr/OVMvNKCCGEKZW2Opei0a9XyFXo2PYejm3v4T9zKJ6MSZS07qV3MROa3nkGo1mrs8z1\nRLgqaEbhOY9sB76gwbxRNJp9PinfriNQ/3gOX/AIeXdtxNd1tOE7gmbL4ST1EaL2me19KfWpucpy\nFTZ86YLyXIWBQLWPa7bXJhbG7kUkOesve3EvfRzHNpVNJ+hogKffODx9x4Grkc6lE0IIIepehVyF\na+bgXP3SkVyFpc3OxpMxEV+Hywx/ocRITBFXY7ZYGUv+AdyfPY1jw/wjCaO9PW/AM+BOgg2a6l08\nIQxNYgaFSDLeQpwbXse18oWwXIXj8Xa9JulyFSZazKAIYyn+A1fWdJyrXzqSMNp77tV4Bt8rCaOF\nEEKISJwN8PYdh7fnjTi2/lvlKvxlN/U+uAfXMi1XYc8bJVfhMegdMygAfEW4VjxHoyc748qaTta3\nxfjaXUj+pFUc/tPMhO8Imi0eQ+ojYhTNWuwztPu3AZ2121oBy4HtwBfA7bVbTGMw2/tS6lMHUpz4\nuo4m/441FF4zj5IWnbAW/YJ78SOkPtEe9ydTsOQfPOphhqxLHZMrg3oq8eHcMB/X8qexFhwCwH9a\nBkXdLqLosht0LpwQIo6iWYv9fNRkutNRqzFlovKx+oE7gK1AA2ATsITK03AJkdysNvznXIy/3UVa\nrsLp2Pdk4cqegXP1bHxdrsLTf0JccxUmOukM6iEQwLHtPVxLH4+YMLq3vqWLOzMl8wSpj4hJd2A3\nsE/bfhu11GZoh+5i4DXt73VAY6AZcFD7ASjUHnMyJu8Mmu19KfXRgcVCSZsBFLYZgO27zbiypmHf\n8T+c6+fh2PA6/vaX4MmYmBh1qWXSGaxLwSD2rxbjWvwwKQd3AGUJox/A3+5CSRgthHlFuxZ7+D4t\ngUMht6Wjho/Xxb+IQphXaasuFI1+HetPX2u5Cv+F4/OFOD5fiP+MIXgGTKIkvVfSfg9LZ7COpHyz\nBveif4YkjG6hJYweddT0d7MtjSP1MTaz1cegolmLHY7O8BD6uAbAu8BE1BXCoyTtGu0JsC31Mc72\n4T/NZEmDwThy32dowTJWrVgKK5ZS2uwselz/d/xnDiNn9WrDlLeq7ZycHBYsWABAWlpaTOuzm6IL\nbOSUCrYfc3Evehj710sBCNQ/Hs+AO/H2uB7sroiPMduXs9TH2MxWH4OmlolmLfZZwArUEDKoySYZ\nqCuDduAjVKL+aZGewMjtYCzM9r6U+hiTpeg31s19gKF5i7AW/w4QkqvwUrDZdS5h9SXa2sRlRqAa\nNxswl4qNI8A1wD2oshYAtwKfh+5gxEbQ+ste3Esew/G5WjQl6GyAp+9tePqNA2dDnUsnhHkZtDMY\nzVrs56OW6Dwf1Xmcpv22oGIJf0VNJInIiO2gEAnDW6gmdOa8gDXvRwBKG7cqz1XoqKdzAaOXiHkG\no5lhtxfoD+ShOo4voRpIQ7LkH8C97CkcG98ISRh9I54Bd0jCaCGSVzRrsX+M6gjuBopQS3AC9AFG\no06Ct2i33Q98WhcFFyIpOBvg7Xtrea7C7BnYft5FvQ/vxfXZU3j7jMXb8ybT5irUO89g6Aw7P+Uz\n7EKtQXUEQQVNt6yrwlWH5fDvuD+ZQurTXXGunwfBAN6u15B390aKL3y0Wh1Bs+U8kvoYm9nqY2DR\nrMU+Xru/I7BZuy0H1VZ3Qk0e6UwSdATN9r6U+hhXhbqkOPB1vYb8SaspvOY1Slp01nIVPqrlKnwo\nYq7CRKf3lcFoZtiFuhF19mwcviJcq2bjzJ6B1ZOvbjrnIoqH/o3AiWfqXDghhBBCVJvVhv+ci/C3\nu5CUPdm4VkzTchU+j3PVbHznXoWn3wQCTU/Vu6RxoXdnMNoZdgADgRtQQyZHqfNZdKV+Bjv24Prs\nabK//gmAPv0zKB72IFnfHoavf6av1hms7vHLbjPCLKV4bEt9jL2d6PXJzMwkNzf3yOc/lpl0wnjM\nMDkhlNTHuI5ZF4uFkjYZFLbJULkKs6dj3/4RzvWv4dgwH3/7kXgyJlJ6coe6K3At0DvIOpoZdgAd\ngIXafrvDD1KngdOBUpUwesnj2H7/FoCSll0oHv4gJW0y6qYMQohKGXQCSa2TCSRC1A3rz7uO5Cq0\nlPoB8J8xGE/GJEpa99Y9V2EsbaDeMYMbUUsvpQMOYBRqAkmoNFRHcDQROoJ1JhjE/uWnNHw+g/r/\nugXb799SeuIZFI5+nYJxS+LaETRTLAZIfYzObPUR5mC296XUx7iqW5fACadz+PLnyZu8GU+fWwk6\n6mP/ehkN51xEw1kjsO/4BAKBWipt7dB7mDiaGXZ/B5qg1ukENdGke10WMuWb1VrC6PUAlDZuiacs\nYbTVVpdFEUIIIYQBBFNbUHzho3gG3oVzzRycq18iZf8GGsy/htJmZ+HpPxFfx8sSIlehKYZSamt4\nxPbj51rC6GUABOo3xTNQSxid4oz78wkhak6GiYUQuvAV4Vz/uu65ChMxz6AhWX/ZoyWM/g+gJYzu\nNx5P31slYbQQQgghjuaoX56rcNu7uLKmR8hVeCNBd2O9S3oUvWMGDcWS9yP1/nMHjZ7riePz/xBM\nceLpO468yVvwDL6nzjqCZorFAKmP0ZmtPsIczPa+lPoYV9zrkuLAd+7V5E9aQ+Ho1ylp2aU8V+HU\nDrg//juW/APxfc4akiuDqITRrqxpOFfPwVLiIWix4u06muLB9xBsbMgc10IIIYQwMqsVf7sL8be9\ngJS9K3GteA777ixcK2fiXP0Svi5X4ul/uyFyFZoiribmWBlvIa7Vs3FmPx+SMPpiLWH0GXEupRCi\nLkjMoBDCqGzfb8GVNQ379o+wBIMELVb851yMZ8CkuOUqlJjBaJX4cK5/DdfyZ7AWqoTR/jYDKB7+\nIKUtO+tcOCGEEEKYUWnLzhRd85qWq/B5HFvewZH7Po7c9/GfPgjPgDt0yVWYXDGDgVIcm9+h0bM9\nqPfhvVgLf6KkZRcKbnqfwhsXGqYjaKZYDJD6GJ3Z6iPMwWzvS6mPcelRF5WrcIaak9B3nMpVuOsz\nlaswczj2HR/Xaa7C5LgyqCWMdi9+BNuhLwEoPfFMioc9gL/t+bpnCxdCCCFE8gmmnkzxBY9UzFX4\n3UYazB9N6Yln4smYiK/j5bWeq9AUvaBjxcqk7F2lEkbv3wConD8qYfQVkjBaCBOSmEEhRMLyFeHc\nMB/XypkhuQpbarkKR0eVq1BiBkPYftimEkbv+gwoSxh9F94eYyRhtBBCCCGMx1Efb59b8Pa4ISxX\n4X0qV2HvsXh73RT3XIWmixm0/ryb+gtuoNHMgdh3fUbQ2YDiIfeTN3kT3j5jE6IjaKZYDJD6GJ3Z\n6iPMwWzvS6mPcRmyLhVyFc7XchX+invJY7WSq1DvzuAI4CtgF3BvJfvM0O7fBlQ6w8OS9wP1Fk6i\n0bReOHLfVwmj+92mJYyenFArh+Tm5updhLiS+hib2epjYDVp76J5rKmY7X0p9TEuQ9fFasXf7gIK\nxi2h4Kb/4m8zAIuvENfKmaQ+2Zl6Cydh/WVPjZ9Gz2FiGzATGAL8AGwAPgC+DNnnfKANcDrQA8gE\nekY6WOrT3VTCaKsNb7drKR40OWETRufl5eldhLiS+hib2epjUDVp76J5rOmY7X0p9TGuhKiLxULJ\naf0oPK0fth+24loxDfv2D3FueB3HxvkqV2HGJEpbdIzp8HpeGewO7Ab2AX7gbWBk2D4XA69pf68D\nGgPNIh3MUuLB134k+ZNWc/iy6QnbERRCmFKs7d1JUT5WCJEkSlt0ouiaeeTfsU5NKrGm4Mj9L41m\nDqTBK5fHdEw9O4MtgO9Ctr/Xbqtqn4i9vPzxn1F09asETjg9roXUw/79+/UuQlxJfYzNbPUxqFjb\nuxbAyVE81nTM9r6U+hhXotYlcEKb8lyF/W7TchUuj+lYeqZfuBwVB3Oztj0aNTQyIWSfD4GpwCpt\neylwD7A59EDz58/f3bx589NqtbRCiIRw4MCBPddee20bvcsRJtb27l4gPYrHSjsohABiawP1jBn8\nAWgVst0KdcZ7rH1aardVYMCGXwghQsXa3n0P2KN4rLSDQoiElALsQZ31OoCtwNlh+5wPfKz93RNY\nW1eFE0KIOKpJexfNY4UQImGdB+xEBUffr902VvspM1O7fxsg6fWFEImqJu1dpMcKIYQQQgghhBDJ\nzWyJWFsBy4HtwBfA7foWJy5swBZUcHyiawy8i8rvtoNKcl4mkPtR77VcYAFg/OV5KnoFOIQqf5nj\ngCXA18Bi1GtmdmZqB83YBoK0g0Ym7WCCs6GGTNJRAdZmiKM5Ceik/d0ANSyU6HW6E3gTlSQ30b0G\n3KD9nQKk6liWmkoH9lLe8L0D/EW30sSmH2qVjtBG8ElUxgFQHaOpdV2oOma2dtCMbSBIO2hU6Ug7\nmPB6AZ+GbN+n/ZjJ+8BgvQtRAy1R6TEGkvhnxKmoRsMsjkN90TZBNegfola4SDTpVGwEv6I8Mf1J\n2raZmb0dTPQ2EKQdNDJpBzV6r01cE9EkcU1k6aje/jqdy1ETzwGTgYDeBYmD1sDPwKuoPJdzgHq6\nlqhmfgOeAfYDPwJ/oL6wEl0z1JAJ2u+IKxaZiJnbwXQSvw0EaQeNTNpBTSJ3BoN6F6AWNUDFZEwE\nCnUuS6wuBH5Cxcnomdw8XlJQsztf1H4XkdhXYE4DJqG+cE9Gveeu0bNAtSCIudsJMG/9zNAGgrSD\nRlR/lgsAAARoSURBVCftoCaRO4PRJHFNRHbgPeAN1BBJouqNWmv1G+AtYBDwuq4lqpnvtZ8N2va7\nJHaqo67AauBXoARYiHrNEt0h1LAIQHPUF7GZmbEdNEsbCNIOGp20gyZgxkSsFlRD8ZzeBYmzDBI/\nVgYgGzhD+3sK8IR+RamxjqjZmm7U++414DZdSxSbdI4OnC6bUXsfJg+cxnztoFnbQJB20IikHTQJ\nsyVi7YuKK9mKGlbYgkobkegyMMcsuo6oM+JtqDPIRJ5FB2q2WVlKhddQV2QSyVuoOB8fKm7uelRA\n+FKSJKWCxkztoFnbQJB20KikHRRCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhKhaJvCA3oWIUT+iWNBbCCGOQdpAIYSp7QMOA/nA78AqYCyxrbm5D7U0kxBCJIp9SBso\nhEhy31DeeDUELgL2Aq/EeKzBcSqXEELUBWkDhRBJL7QhLNMNKAXaatvzgIe1v5sCH6HOoH9FrWlp\nAeZrjzkMFAB3a/v/GzgA/AFkhRyz7LgvaMfLB9YCp4bc3w5Yoj3PQcqX5bKi1mbcDfwCvAM0qaR+\nA1DL+ZTZB9yFWnbpD+BtwFnJY8egrhI8q9V3N2rB8+uB/aiFw6+r5LFCiMQgbaC0gUIkvUgNIcC3\nqKESgFeBf2p/P46Kn7FpP32qONYYoD5qbcjnUOuSlpmHasi6asd6A7UmI6gz9APAHYADaAB01+6b\nCKwGTtaOOwtYUEn9BlCxIfwG1eCehGo8d4TUM9wYwA/8BdXYPwx8DzyvPe9QVANer5LHCyGMT9pA\naQOFSHqVNYRrKD8LDW0I/wG8D5xWjWOVaYxasL5hyHFfCrn/POBL7e+rgE2VHGdH2PM0Ry3obY2w\n7wCObgivDtl+AtWwRzIGtSh4mfZa+U8Iue0XoEMljxdCGJ+0gdIGmlKkN4MQ1dUS+C1kuyyY+inU\nUMFiYA9w7zGOYQWmavvnoRohUMMsZQ6F/F2MOvsFaIWK24kkHfgPatjid1TDWAI0O0ZZQh2s5Dkj\nCS8fwM/VeLwQIjFJGxi5fCBtYEKQzqCoqW6o4YecCPcVomJhTgMuBu4EBmr3BcP2vUbbZzCQCrTW\nbo9mlt5+KsbOhN83AjXEUfZTDzWkUl3hZRZCCGkDRcKTzqCorrKGqRFwISpmZT6wPex+tPvbaLfl\nowKmA9p9h6g4dNIA8KLOrusDj1XyvJH8DzX0MREV3NyQ8niZWdqx0rTtE1ANbixiSR8hhDAXaQOF\n6UhnUFTXh6hGbT8qRuYZ1GyxMkHKzx7boGa3FaACmF9AzZADFVj9AGrY4k7gdVQQ9g/AF6gYnNCz\n0CBHn5WWbReggpMvQp3tfo2KfQGYDnyAGqbJ147bncod68w3UhmiKZ8QwjykDYz+PmkDhRBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYSoK/8PFNzr\nVhhHACAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107256e10>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The effect of F is to make the no change for cells everywhere but in the vicinity of the range reading r = D\n",
      "F = 0.0001"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# probability Density\n",
      "p = a*np.exp(-(zs-D)**2/(2.0*d**2)) + F\n",
      "\n",
      "p = p/np.max(p)\n",
      "\n",
      "plt.plot(zs, p)\n",
      "plt.axvline(D, c='k')\n",
      "plt.ylabel(r'$P(z|x,m)$')\n",
      "plt.xlabel('z [$m$]')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.text.Text at 0x1087fbe10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8NaCz80REREREpLguw53bWA98JeBYgjQZeBx4DVgLfCbYcAJn4Z7k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\nERERERERERERERGRsPr/kJXygS/GnU4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b155090>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Probability that no range reading was received at a distance less than D:\n",
      "\n",
      "$P = 1- \\int_0^D p(r=x|C)\\mathrm{d}x$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# probability that no range reading was received at a distance less than D\n",
      "P = 1.0-np.cumsum(p)/np.sum(p)\n",
      "P[zs>D] = 0.0\n",
      "\n",
      "plt.plot(zs, P)\n",
      "plt.axvline(D, c='k', alpha=0.2)\n",
      "plt.ylabel(r'$P(\\neg z|x,m)$')\n",
      "plt.xlabel('z [$m$]')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.text.Text at 0x10b0f3f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b173b90>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sensor probability density\n",
      "spd = P*p\n",
      "\n",
      "spd = spd/np.max(spd)\n",
      "\n",
      "plt.plot(zs, spd)\n",
      "plt.axvline(D, c='k', alpha=0.5)\n",
      "#plt.ylim(0, 0.01)\n",
      "plt.ylabel(r'$P(z|x,m)$')\n",
      "plt.xlabel('z [$m$]')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "<matplotlib.text.Text at 0x106980310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2vP3vZPZuoXDUh2I9MMmnWNRLsYgoFvEpYYizWl9eAMCB2dfUXI5yg3oY4hcl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\nRERERERERERERERERERERERERMRX/x+qmPf0hXvKFAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b0503d0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,5))\n",
      "ax1 = plt.subplot2grid((4,4), (0,0), rowspan = 2, colspan = 2)\n",
      "plt.plot(zs, p)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('Measurement Noise')\n",
      "plt.ylabel(r'$P(z \\mid x,m)$')\n",
      "\n",
      "ax2 = plt.subplot2grid((4,4), (0,2), rowspan = 2, colspan = 2, sharey=ax1)\n",
      "plt.plot(zs, P)\n",
      "plt.ylabel(r'$P(\\neg z|x,m)$')\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('No Range Reading')\n",
      "\n",
      "ax3 = plt.subplot2grid((4,4), (2,0), colspan=4, rowspan = 3)\n",
      "plt.plot(zs, spd)\n",
      "plt.axvline(zexp, c='k', alpha=0.5)\n",
      "plt.title('= KONOLIGE Inverse Sensor Model')\n",
      "plt.ylabel(r'$P(z|x,m)$')\n",
      "plt.xlabel('z [$m$]')\n",
      "\n",
      "for ax in [ax2]:\n",
      "    plt.setp(ax.get_yticklabels(), visible=False)\n",
      "    # The y-ticks will overlap with \"hspace=0\", so we'll hide the bottom tick\n",
      "    #ax.set_yticks(ax.get_yticks()[1:])\n",
      "    ax.text(-1.5,np.max(P)/2,'+', fontsize=20)\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.savefig('InverseSensorModel-KONOLIGE.png', dpi=150)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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072S03M0hW2PnM8R1tR/SbTw7izwiwDVI3M9C4ElgEfK+re/baRYjjdinSBD0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\nbsj49XbyYmshUDt5sUV5sUHFjkg+adxK8YzJAGw/+RdQtFf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       "text": [
        "<matplotlib.figure.Figure at 0x10b322450>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "LANGERWISCH Error Bounding Box"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Langerwisch, M., & Wagner, B. (2013). Building variable resolution occupancy maps assuming unknown but bounded sensor errors. Intelligent Robots and Systems ( \u2026, 4687\u20134693. Retrieved from http://www.rts.uni-hannover.de/images/2/24/Langerwisch13-IROS.pdf"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Simple Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The error afflicted dis- tance will be the interval [d], having w([d]) as the maximum assumed error bound. The laser beam is assumed to spread in width with an angle of \u03d5b. Together with the angular position of the scanning mirror \u03d5m, the beam angle results in [\u03d5] = [\u03d5m \u2212 \u03d5b/2 ,\u03d5m + \u03d5b/2 ]. Now, an outer boundary of\n",
      "the possible locations of the real object reflection can be calculated in the sensor coordinate frame:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$[p'] = \\left[\\begin{matrix}d \\cdot \\cos(\\phi) \\\\ d\u00a0\\cdot \\sin(\\phi)\\end{matrix}\\right] $"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wd = 0.04 # maximum assumed error bound for distance measurement\n",
      "phib = 0.01 # rad\n",
      "\n",
      "d = 1.0     # m\n",
      "phi = 0.8   # rad"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@interact\n",
      "def plotmultivargauss(wd = widgets.FloatSliderWidget(min=0.005, max=1.0, step=0.005, value=0.05, description=\"\"), \\\n",
      "                      phib = widgets.FloatSliderWidget(min=0.01, max=1.0, step=0.01, value=0.01, description=\"\"), \\\n",
      "                      d = widgets.FloatSliderWidget(min=0.0, max=10.0, step=0.1, value=1.0, description=\"\"), \\\n",
      "                      phi = widgets.FloatSliderWidget(min=-1.0, max=1.0, step=0.1, value=0.6, description=\"\")):\n",
      "\n",
      "    p = {}\n",
      "    p['p1'] = ((d-wd) * np.cos(phi-phib), (d-wd) * np.sin(phi-phib))\n",
      "    p['p2'] = ((d+wd) * np.cos(phi-phib), (d+wd) * np.sin(phi-phib))\n",
      "    p['p3'] = ((d+wd) * np.cos(phi+phib), (d+wd) * np.sin(phi+phib))\n",
      "    p['p4'] = ((d-wd) * np.cos(phi+phib), (d-wd) * np.sin(phi+phib))\n",
      "    \n",
      "    plt.figure(figsize=(10,5))\n",
      "    plt.subplot(121)\n",
      "    [plt.scatter(v[0], v[1], s=10) for k,v in p.iteritems()]\n",
      "    plt.plot((0, d*np.cos(phi)), (0, d*np.sin(phi)), c='r', alpha=0.5)\n",
      "    plt.axis('equal')\n",
      "    plt.xlabel('x [$m$]')\n",
      "    plt.ylabel('y [$m$]')\n",
      "    plt.title('Error Bounding Box')\n",
      "    plt.scatter(0,0, s=50, c='k', label='Sensor')\n",
      "\n",
      "    plt.subplot(122)\n",
      "    [plt.scatter(v[0], v[1], s=100) for k,v in p.iteritems()]\n",
      "    plt.axis('equal')\n",
      "    axlims = plt.axis()\n",
      "    plt.plot((0, d*np.cos(phi)), (0, d*np.sin(phi)), c='r', alpha=0.5)\n",
      "    plt.axis(axlims)\n",
      "    plt.title('Error Bounding Box (Zoom In)')\n",
      "\n",
      "    plt.tight_layout()\n",
      "    #plt.savefig('InverseSensorModel-Langerwisch-BoundingBox.png', dpi=150)\n",
      "    return plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hBsVLKeJZbNuOJ9gZtcMHjhyh7Oc/J/Lss7zw1lvEx4yh+bbbrB74Wt0fJcy2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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bb5f3d0>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Including Beam Width"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Moreover, the width of the laser beam has to be considered, because it actually never starts with beam width 0.\n",
      "Therefore, we displace the origin of the beam virtually to behind. The distance [d] is extended by"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@interact\n",
      "def plotmultivargauss(wd = widgets.FloatSliderWidget(min=0.005, max=1.0, step=0.005, value=0.05, description=\"\"), \\\n",
      "                      phib = widgets.FloatSliderWidget(min=0.01, max=1.0, step=0.01, value=0.01, description=\"\"), \\\n",
      "                      d = widgets.FloatSliderWidget(min=0.0, max=10.0, step=0.1, value=1.0, description=\"\"), \\\n",
      "                      phi = widgets.FloatSliderWidget(min=-1.0, max=1.0, step=0.1, value=0.6, description=\"\"), \\\n",
      "                      wb = widgets.FloatSliderWidget(min=0.01, max=1.0, step=0.01, value=0.01, description=\"\")):\n",
      "\n",
      "    dd = 1.0/np.tan(phib/2.0) * wb/2\n",
      "    \n",
      "    p = {}\n",
      "    p['p1'] = (((d+dd-wd) * np.cos(phi-phib)) - dd*np.cos(phi), ((d+dd-wd) * np.sin(phi-phib)) - dd*np.sin(phi))\n",
      "    p['p2'] = (((d+dd+wd) * np.cos(phi-phib)) - dd*np.cos(phi), ((d+dd+wd) * np.sin(phi-phib)) - dd*np.sin(phi))\n",
      "    p['p3'] = (((d+dd-wd) * np.cos(phi+phib)) - dd*np.cos(phi), ((d+dd-wd) * np.sin(phi+phib)) - dd*np.sin(phi))\n",
      "    p['p4'] = (((d+dd+wd) * np.cos(phi+phib)) - dd*np.cos(phi), ((d+dd+wd) * np.sin(phi+phib)) - dd*np.sin(phi))\n",
      "    \n",
      "    plt.figure(figsize=(10,5))\n",
      "    plt.subplot(121)\n",
      "    [plt.scatter(v[0], v[1], s=10) for k,v in p.iteritems()]\n",
      "    plt.plot((0, d*np.cos(phi)), (0, d*np.sin(phi)), c='r', alpha=0.5)\n",
      "    plt.axis('equal')\n",
      "    plt.title('Error Bounding Box')\n",
      "    plt.scatter(0,0, s=50, c='k', label='Sensor')\n",
      "\n",
      "    plt.subplot(122)\n",
      "    [plt.scatter(v[0], v[1], s=100) for k,v in p.iteritems()]\n",
      "    plt.axis('equal')\n",
      "    axlims = plt.axis()\n",
      "    plt.plot((0, d*np.cos(phi)), (0, d*np.sin(phi)), c='r', alpha=0.5)\n",
      "    plt.axis(axlims)\n",
      "    plt.title('Error Bounding Box (Zoom In)')\n",
      "\n",
      "    plt.tight_layout()\n",
      "    \n",
      "    return plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fD+H663vOuplOR7jzzjr++Mdabr55F/PmJavuO83q8Q2A7T0zxXKpHpdqgfz1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\ndlDa2tr40NixxO+5h8jOnRCPk5g1i9S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       "text": [
        "<matplotlib.figure.Figure at 0x10b045590>"
       ]
      }
     ],
     "prompt_number": 35
    }
   ],
   "metadata": {}
  }
 ]
}