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      "from __future__ import division, print_function\n",
      "%matplotlib inline\n",
      "import sys\n",
      "sys.path.insert(0,'..') # allow us to format the book\n",
      "\n",
      "# use same formatting as rest of book so that the plots are\n",
      "# consistant with that look and feel.\n",
      "import book_format\n",
      "book_format.load_style('..')"
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     "source": [
      "This notebook creates the animations for the Multivariate Kalman Filter chapter. It is not really intended to be a readable part of the book, but of course you are free to look at the source code, and even modify it. However, if you are interested in running your own animations, I'll point you to the examples subdirectory of the book, which contains a number of python scripts that you can run and modify from an IDE or the command line. This module saves the animations to GIF files, which is quite slow and not very interactive. "
     ]
    },
    {
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     "input": [
      "import stats\n",
      "import numpy as np\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "# this code lets me animate the 3d covariance. to be honest I do not find it\n",
      "# very instructive or compelling so I am not using it for now.\n",
      "def plot_3d_covariance(ax, mean, cov):\n",
      "    \"\"\" plots a 2x2 covariance matrix positioned at mean. mean will be plotted\n",
      "    in x and y, and the probability in the z axis.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    mean :  2x1 tuple-like object\n",
      "        mean for x and y coordinates. For example (2.3, 7.5)\n",
      "\n",
      "    cov : 2x2 nd.array\n",
      "       the covariance matrix\n",
      "\n",
      "    \"\"\"\n",
      "\n",
      "    # compute width and height of covariance ellipse so we can choose\n",
      "    # appropriate ranges for x and y\n",
      "    o,w,h = stats.covariance_ellipse(cov,3)\n",
      "    # rotate width and height to x,y axis\n",
      "    wx = abs(w*np.cos(o) + h*np.sin(o))*1.2\n",
      "    wy = abs(h*np.cos(o) - w*np.sin(o))*1.2\n",
      "\n",
      "\n",
      "    # ensure axis are of the same size so everything is plotted with the same\n",
      "    # scale\n",
      "    if wx > wy:\n",
      "        w = wx\n",
      "    else:\n",
      "        w = wy\n",
      "\n",
      "    minx = mean[0] - w\n",
      "    maxx = mean[0] + w\n",
      "    miny = mean[1] - w\n",
      "    maxy = mean[1] + w\n",
      "    #print (minx, maxx, miny, maxy)\n",
      "    \n",
      "    minx = -9.57238091319 \n",
      "    maxx= 13.5723809132 \n",
      "    miny = -4.57238091319 \n",
      "    maxy = 18.5723809132\n",
      "\n",
      "    xs = np.arange(minx, maxx, (maxx-minx)/40.)\n",
      "    ys = np.arange(miny, maxy, (maxy-miny)/40.)\n",
      "    xv, yv = np.meshgrid (xs, ys)\n",
      "\n",
      "    zs = np.array([100.* stats.multivariate_gaussian(np.array([x,y]),mean,cov) \\\n",
      "                   for x,y in zip(np.ravel(xv), np.ravel(yv))])\n",
      "    zv = zs.reshape(xv.shape)\n",
      "\n",
      "    ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
      "\n",
      "    ax.set_xlabel('X')\n",
      "    ax.set_ylabel('Y')\n",
      "    ax.set_zlim([0,10])\n",
      "    #ax.set_ylim([-5,20])\n",
      "    #ax.set_xlim([-10,10])\n",
      "\n",
      "    ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)\n",
      "    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
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    {
     "cell_type": "code",
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     "input": [
      "import numpy as np\n",
      "import mkf_internal\n",
      "import matplotlib.pyplot as plt\n",
      "from gif_animate import animate\n",
      "import stats\n",
      "def mkf_animate(frame):\n",
      "    global ax\n",
      "    plt.cla()\n",
      "    var = (31-frame) / 3\n",
      "    plot_3d_covariance(ax, (2,7), np.array([[var,0],[0,4.]]))\n",
      "    \n",
      "    \n",
      "def ellipse_animate(frame):\n",
      "    \n",
      "    plt.cla()\n",
      "    cov = frame/15.\n",
      "    P = np.array([[2,cov],[cov,2]])\n",
      "    stats.plot_covariance_ellipse((2,7), cov=P, facecolor='g', alpha=0.2, \n",
      "                              title='|2.0 {:.1f}|\\n|{:.1f} 2.0|'.format(cov, cov))\n",
      "\n",
      "fig = plt.figure()\n",
      "#ax = fig.add_subplot(111, projection='3d')\n",
      "animate('multivariate_ellipse.gif', ellipse_animate, 30, 125)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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TLl9GKFqAU92D7i6ed6x3/N8hopryR1IYDETgSrgglVXgNCgbcjRnecL1jhpo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\nAUlERKTgf7zOyLeZdlfOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7effd7d90898>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='multivariate_ellipse.gif'>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "from gif_animate import animate\n",
      "import numpy.random as random\n",
      "from DogSensor import DogSensor\n",
      "import stats\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "from filterpy.kalman import KalmanFilter\n",
      "\n",
      "def dog_tracking_filter(R,Q=0,cov=1.):\n",
      "    dog_filter = KalmanFilter (dim_x=2, dim_z=1)\n",
      "    dog_filter.x = np.array([0, 0])   # initial state (location and velocity)\n",
      "    dog_filter.F = np.array([[1,1],\n",
      "                             [0,1]])  # state transition matrix\n",
      "    dog_filter.H = np.array([[1,0]])  # Measurement function\n",
      "    dog_filter.R *= R                 # measurement uncertainty\n",
      "    dog_filter.P *= cov               # covariance matrix \n",
      "    if np.isscalar(Q):\n",
      "        dog_filter.Q = Q_discrete_white_noise(2, var=Q)\n",
      "    else:\n",
      "        dog_filter.Q = Q\n",
      "    return dog_filter\n",
      "\n",
      "\n",
      "R = 5\n",
      "Q = .01\n",
      "noise = 2.\n",
      "P=20.\n",
      "dog = DogSensor(velocity=1,noise_var=noise)\n",
      "f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
      "random.seed(200)\n",
      "zs = []\n",
      "xs = []\n",
      "def animate_track(frame):\n",
      "    if frame > 30: return\n",
      "    \n",
      "    plt.gca().set_xlim(-100,100)\n",
      "    if frame == 0:\n",
      "        stats.plot_covariance_ellipse ((0, f.x[0]), cov=f.P, axis_equal=True, \n",
      "                                       facecolor='g', edgecolor=None, alpha=0.2)\n",
      "        xs.append (f.x[0])\n",
      "        \n",
      "    z = dog.sense()\n",
      "    zs.append(z)\n",
      "    f.update(z)\n",
      "    xs.append (f.x[0])\n",
      "    \n",
      "    stats.plot_covariance_ellipse ((frame+1, f.x[0]), cov=f.P, axis_equal=True, \n",
      "                                       facecolor='g', edgecolor=None, alpha=0.5,\n",
      "                                       xlim=(-5,30), ylim=(-5,30))\n",
      "    \n",
      "    plt.plot(zs, c='r', linestyle='dashed')\n",
      "    plt.plot(xs, c='b')\n",
      "    f.predict()\n",
      "\n",
      "animate('multivariate_track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0Gl1trVsRERGRTbaWUOt96lOUrr2WrgmNLOxYyMrcSlp7WmnNt9JV7Frjtrcf\n9twf9+CRH3+a8iitGc1w2SM/qlyPWBGSdnWXsMpuYdE06UiaumhdZXmv8stnCrTDRzOZRUREZLPj\n33UXxkMPYT/0ENaOU3jhjotYmVvZrzBbdt+Vx/LG3z5COdRO3mUZx337Lrat2ZZYKBbsGBaK990t\nLJLCMq0+GyxoOa+RQ8FWRERENjveL3+JSRBJaxcs4iv7ns3i3ady3/9+Cd+2K/UMw8AyLGzTDg7L\nJmSGuOS4T7J0YS3lUHvcFxZz8VUryXXN4MDd/hNCIbK3/gL7hP9ebacwjciOXAq2IiIiMnQuuACu\nvjrYhGETmHPm4PzpT9if+AQQxNPJLy/kwsO+w7x/Px2sLWsYGBhYpkXYDGNbNmErzPRttyWbLcdi\nn3vuKfCZz4zFMMax4tc/At8HxyExaTJGJLLJv7IMHQVbERERGRqLFsH//m9wzJoFp5220Y8yDAP7\n6KPxXRfvmGOw/vxn8H28qVPZe6u9K3V61y8UoKbGwvPKUwd83n8fJk6MVOqOu+66yitkHHroRvdP\nhoeCrYiIiAyNI46oljch1JZVtq195JHgB21tWIC1hlHWvBHj4/wFjwMAsCzIZg0+XDXU0REU1vLC\nmoxsmu0sIiIiQ+Oddwb3+fX1wfEhfzr1Lj7JQ8zjAGLkuJ3TKIWiRK65om/Fv/ylWv7f/x3cvsqg\nULAVERGRobFqa9vVhkkH0VlnwSdmn8jjHE4NHTzOoZzOHcGODFde2Xc3s298ozoN4aSThqyPMnA0\nFUFEREQGX+9dxr74xSFpcq+94J//hPI43rGn17LfadfB8ccHmz4YRt8R3jfeYOlJJzGhUBiS/snA\nU7AVERGRwffd71bLt9wyqE35vk9DA7S3Q3nlg9tuczn1VHD8/WDJkko9isXKi2OGYdDy7W8zbtdd\n9VfamykFWxERERl8t90WHC+9NGCP9H2/sqVuudzT41Nfb+O6BuVQ+/jflzBl+yL/biniuA4lvxTU\nx8dY9Y9pmERCEUrhEt25bmLhGLZta83azYyCrYiIiAydPfbYqNvKAbZ3iHVch6yTJefkyDt53l2Y\n55MfnQ6UR2A97nz2dyy3HRYvdnC84HB9NxitXaUSbK0IhUyBFqOFncbsxPia8YRCikqbE/2vJSIi\nIiPKh0diPc+jWCrSXeyms9BJd6GbTDFDvpSvHM/OqePmC4+hPEprRwv8zyM/4N/Z/rcbD8VJkSIS\nipCKpDQFtCWiAAAgAElEQVRauxlSsBUREZFh13tE1nVdMsUMXYWuytFd7CbjZMgUM3Q73eScHEWv\nCMCfbz6MZ357AOVQW79VC1+/6+Z+tRsyQzREG2iINjAmNoaEk2C3Cbth2zaWZQ3eLyyDQsFWRERE\nhkU5zLquS8kt0Z5vpyXfQluujc5CJ11OVyXI5kv5NT7jhYd26xNqdzzwVT5/1QNrbdPAIB6KUxup\nrRxj4mNoSjRRH6tn4cKFRKNRjdZuphRsRUREZHDZNqTT8Mgj8B//UQm0pVKJzp5OlnYvpTnbTHuh\nnbaeNtoL7RTc9S+51dMD/++Gz1IOtdt8/GH2PWF+36ZNm6SdJBVOkbSTQTmSoi5aR0O8gdpILZZl\nYVkWpmmSy+UUajdjCrYiIiIyeBYsgFIp2Ajhrrvw99mHUqlEV76Ld9vfZWlmKcuyy2jtacXxnA16\n9HVHX0Y51NZt+yZnXvoa8VA9sVCMuB2vBNl0JF05UpEUtmVjmmblUJAdPRRsRUREthTlADdtGrz5\n5tC0efTR1fKNN+J7HtmeLC8uf5GlmaUs6lqEh7fex4SMELZlY5vBceXxJ+P7wWqz4WiJW2YvYnzT\nfiTsBHE7TsJOkIqkiNvxPgFWQXZ0U7AVERHZ0rz11tC11XvHMYJNEOyQzbjkOGzLpjHWSN7N4/ke\nnl8NuAYGlmERskLYpk3YDGNbNmErzG9+OY7WJbWUR2uXregmah+EZVoYhtEnwJYP2TIo2IqIiGwJ\neu/8BcFmCWecMfjtlteLjUSAINjGIjF2aNwBz/NwXIcepwePINhWNk0wDCysYJTWsjGNIKh2dhrc\n+H2bcqidP9+jNlmrACuAgq2IiMiW4eqrq+U99hiaULtgQbV81lmVYnlqAEDYDxOPxtf6iN7b3QKM\nG1e9dsIJBtOna0kuqdJWyCIiIluCc84B04RQCF58cWjaXLIkaBPgxhvXWKU8bWBtR++R2AkTqgPA\n6TT85jdD8UvI5kTBVkREZEtw/fXguuBs2MoDm+Sww4I2e21fu7EuugiWLat+7uzc5EfKKKRgKyIi\nIiPa8uXwwx9WPy9cOHx9kZFNwVZERERGtPHjq+WvfhWmTBm2rsgIp2ArIiKypdppp2Di6gjW0FAt\njxkDt9wyfH2RkU+rIoiIiIx2uRzEP7TyQDQKhfVvWzuczjgj2LAMgr0lmpuHtz8y8mnEVkREZLRL\nJIJk+M1vVn92xx3V8h57DHybhhEcn/jERt2+YAHcfnv1czngiqyLgq2IiMhoduSR1fLFF1fLn/98\ntfzyywPbZu/1a6dN26hH7LRTtXzZZVBbu4l9ki2Cgq2IiMho9pe/VMtjxvS91vstrLlzB67N3mH6\nhhs2+PZUqlqeNAmuumoA+iRbBAVbERGR0czz1n7t9der5UMOGbg2339/o2897jjIZIKyYWzSo2QL\npGArIiKyJeg9DFoWiwU7kQGceOLAtVXekCES2aDbnnsOHnig+jmXG7guyZZBqyKIiIiMVo88Ui3/\n4hdrrjPQO5EtX14tn332Bt26777V8k9+EizcUOavY/ey8pa7IhqxFRERGa2OOgreeAN23hlOOGFo\n2hw3DmbNgrFj+z2/1vd9otHylAmfHXYo8dWvOhSLRQqFQuXI9+TJ5XNk81my+Sy5fI6enh4KhQLF\nYhHHcfDWNfVCRj2N2IqIiIxmO+4Ir702tG2edlpw9FIecfU8D9/3+xwf+5hBoWADYJo+D8x5i9dW\nFHFch6K36uwWcT0Xf9U/AAYGpmEStsIkw0nSkTQT0xOJRWJYljWUv7GMEAq2IiIiMuDKodXzvEqY\n7XF6yDpZck4uOBdzzHk8zFNPTQcMwOemp+7g7x+UcLxVodZzKHklHNfBY82jsWEzTG2klm1qtsE0\nTKbaUxVst1AKtiIiIhLI52HvvTdqhLd3iPU8D9dzyRQzdBW66Cx00lXoIlvMki1lyZfy5J08uVKO\nS8+8gHKo/cyl97LCeQ82YNpvxIowNj6WCYkJTKqZxKT0JIXaLZiCrYiIiMCrr8JuuwXlk06CX/96\nvbf4vo/rukGQdV06ejpoy7fRWeiku9BNxsnQ7XSTKQbnglvdwnfRy+O547zzKYfasdstYffDF6y1\nrd4iVoS6SB0N0QbqY/U0JZqYnJ5MLBwjFAphmnqFaEulYCsiIjIazZgBTU3w4IP9q/+Rj1TLd9+9\nzmDreR6lUjA9oDXXSnOumbZcG9POvpQl//kRXj10Z7JOdo1TB/5+7z789WdHEQTaVasZGC5HXvrL\ntbYXsSIk7SRJO0ltpJbaSC318Xoa443UxeoIWSEsy1KgFQVbERGRUenZZ4Ozaa57k4beksnq7ght\nbVBf3+ey7/uUSiVyhRzvdb7H8sxy2nraaO1ppb2nncOfeJ7JTzzPR38Y5YcPfrvPvffOPI4FT+26\n6lN5eS4fDJeZT3yvUs/EJGEnSIVTQZgNB4E2HUlTE6mhNlpLKpKqBFnTNLXcl1Qo2IqIiIxmW2/d\n/7rvvQcNDUF5yhTo6qpc8n2fYrHI+x3v8277uyzJLmFpdiklrwRA3dvB+rUG8MLRe1buu/GUr9L+\nQdOqT9VAa0cLXPbQTfR0x5icmkwsFAsOK0YqkiIdSVeOmB3DMIw+QVZhVtZEwVZERGS0+exnq+Un\nn+z/fb1HaLu7+1wqr2rwbse7tPa0ki/liVgRQkYI3/c55bJ7Vs2WhTmnf5prjvkGxVyUPqOz+DRN\n7OaXjz5JNBQlFppBzI6RsBMkwsERs2OYhrlaiFWQlf5QsBURERltHnqoWp48ecPu/fzn4d57gykM\nq5TXoI3aUfYatxet+VYyxQw5J4fruZS8ErUrOnEI8QO+zZVHXkTfQAv7HdzKT2YtxDItoqFtsQwL\nDLAtm2goSk20hkg4gmVZCrGy0RRsRURERhvX3fh777kH/ze/CdaeLZUqa9AWSgVyTo4epwcDg1go\nRsSM4HgOv/tNiif4Hr/mZN6nPPUhGKE97qsv88kvvYLjOjy/skjJK1F0i3h4hK0wiVCCSalJTExP\nZIfGHRRqZZMo2IqIiIxWyWS/qq1pDdquQlefI+fkgvVny4eb567vHsj8R6avesqlAFg4uIbJyT+c\nxbZ7fQDAwq41txu2wjREG0hH0kxKT9KqBrLJFGxFRERGm1VTB9Z+ubormOu6FEtF2nra6OoJQmx3\ncdUatL3ORa9Yuf/emcey4Kny8mDVKQchq8AF911LrH7t7SftJA3RhsoatFNqp9CYaCQUCmljBdlk\nCrYiIiJbiPKGCq7rki/mWZlbSWsuWKqro9BBV7GLjJMh62TxWXM4ffHRnVeF2vKrYj7J+k4u/N2P\n11g/YkVI2algqa5ILbXRWhrjjTTFm0hEEliWpXm1MmAUbEVEREa5cqAtlUqsyKzgg+4PaMu30dYT\nHF3FrrUG2YY3lhDL9fDBXtsC8OC1/0U51KYmLuTY797JlClBXdMwSdpJUnaqsv5seQ3a2lgtDbGG\nYNUD06yEWQVaGUgKtiIiIqNYeVOF1mwrb7e+zfLscj7IfEBnsXO991526JWYPvgGXPXETL57xKWU\nQ220tp3v3f8wsdBWxENxYqFYEGrDfdegjdpRrUErQ0bBVkREZJQrOAVeWfEKbT1tLO5eTK6UW2vd\nkBnCNm1s0wbTwHB98OHxH52AVyrHBp/fPPYvJo7dn7gdD9ahXbUWbXkkVmvQynBQsBURERktPvpR\nmDcv2D2spaXyY9uy2aVxF5pzzUxMTQzWn/VdPL+61a6BgWmY2JZN2AxjWzZvzb6ZHU88G4DXHx5D\nebT2/cUFmhr3xTAMrLo6jJ4e+MIXMG67TSFWhpWCrYiIyGgxb15wbm2t/MgwDMLhMGOtsTSlmirr\n0np+cC7PrS0H2/KSW4ZhYBy/F5x4Nj/ny7QxBvA56iifiVtFqwE2t2r095574Pbbh+o3FVkjBVsR\nEZFRzjAMQqHqf/L9dSwH9uER1yvC3+W64gUANNDKn/40pnrxpZeq5fPOG5jOimwCrYQsIiIy2kya\ntM7Lvee+fvjo7Z//hCuL3yFPnGN4mJajTu37oE99qlq++uqB6r3IRlOwFRERGQ1OOaVafuyxAXnk\nXnuVSx4HXPMJ+NOf+lb44IMBaUdkoCjYioiIjAb33FMt77jjJj+urq5aTqdNLr54DZXKUxpisU1u\nT2QgKNiKiIiMBvvtF5zNTf9P+w03QEdH9XPn2pa8bWoKzt/85ia3KTIQ9PKYiIjIaPDUUwP2qAsv\nrJb//vd1VFyxYsDaFBkIGrEVERGRCtuulnfdFfbffw2V8vkh64/IhlCwFREREQA++1kolaqfX331\nQxW+8AUwDIjHh7RfIv2lYCsiIiK0tMAf/lD9nM2uodK221bLRx896H0S2VAKtiIiIkJjY7V88slr\nGZS9/PJq+ZFHBr1PIhtKwVZERGRz1tISTA8wjI0Om70HYkMhmD17HZV7rwOmKQkywijYioiIbM4O\nPLBaPvjgDb79kUfg3Xernx1nPTcsWVIt956QKzICKNiKiIhszhYsqJY3YgS191TZX/yiHzfEYrDD\nDsEI8fvvb3B7IoNJ69iKiIhsoRKJarmxEc48s5839g7TIiOIgq2IiMhoMH78BlWfORNyuernlSvB\nX7VFru/7lfKaGIZROURGEgVbERGRzVXvrWyfeGK91cuBNZv1ueoqEzAAn5deKlIogOd5OJ6D4zoU\nvSIlt4RPNeQahoFpmNiWTcJOYFs2pmkSCoUUcmVEULAVERHZXF1/fXC+/XbYccfKj8sB1vO8Stn3\nfRzXIefkGFc3hnKo3WWPTrqSrzL3/SKO6wTB1nMoeSVKXjXY+viYhomBQdgKEw/FSYaTTK2dyrj0\nOOzeW5aJDBMFWxERkc3Z9dfj//CHeK5bCbKe55EtZukqdpEpZsgVc2SdLPlSnm+duhe+Xx5d9fni\nzbczb1k1zPZXTbiGnep3IuNk1jltQWQoKdiKiIhsZsrhtXwUS0W6il10FYKju9BNppih2+km5+TI\nlXLkS3mWLg7xxgtHUx6t/db/u4quYv/btQyLukgdTfEmxiXGMaV2Ck2JJo3WyoihYCsiIrKZcF23\ncnQUOmjNtdKWb6O7WA2yGSdDppih5Pcdff3JSefQsbQ6BWGfY//er9XBbNOmLlJHbaSW+mg9DfEG\nxibG0phoxA7ZWJal+bUyYijYioiIjGC+7+O6LrW1tazsWsnK7Eqac810FDpo72mno9BBtpRd6/0/\nOOZbFHJxgkAL4GNYDjt/8q9rrB8LxUjZKZJ2kmQ4SU24hrpYHQ3xBuqj9UTsCKZpKtDKiKRgKyIi\nMkJ5nofjODRnm3mj6w2K+SLN+Wbaeto45rLZvHz4rmQP3GW1+7JZuOHTl+K5IXoHWoB441K+dd+t\nAESsCPFQnISdCMJsOAiz6UiamkgN6XCaRCSBZVpYloVpmgqzMqIp2IqIiIxAvu9TLBZ5rfk13ut8\njxfef4FwbbhyfbenFrDbUwtwQg9w9V8uA2DlwiQ//eIFBGG2b6Dd7eA3+fr1c+lui7F1w27EQjFi\ndoy4HScVSZGOpEmH04RD4UqALZ8VZmVzoWArIiIyQvn4FN0iYTPMpNpJhJNhXN/Fy2aAILo277Q1\ny5+dzs8v/gSrB1qfk895i7POayZmx4iF9iM+OU48HIzS2iG7ElxN09SIrGz2FGxFRERGmPK6s5Zp\nscfYPcgVc0yJTsGMmjiuwzYfOw4DaKeGia++DReXN1uAcqC94RfvcsRRPXh4eF4Kz/focXvwfI+S\nXyJqRYlaUUIhRQEZPfSnWUREZBj13kCh9xJeOSdYezbn5OhxemjLtRE34jiewysLGniIL/F/fB2w\nyk8CfC77zR2kJ7WSd4v87t8OsGoLXAxsM9gxbLua7WjJtTB9wnQFWxlV9KdZRERksOy0Ezz/PCST\nlR99OMT6vk+P00NnobOyDm2mmKlsqFBeg/bZ+Ut57Edfp3nheELMpUR57VgfM1Tigj98n0Qi+EnG\n6duN8gYK6VCarRJbUROtYYeGHbAsC5HRpF/B9pprruGBBx7grbfeIhKJMGPGDK655hp22aXvm5hX\nXHEFt956K+3t7ey7777cfPPN7LzzzoPScRERkRHt/vthwQJIpfBPPx3v1lsrYTZbyNLW00ZnTxBm\nM04mWIvWyVQOz/cqj/r5l7/I8rcmrfpk4GLxSR5kG96idk5mrV0wMEiH09RH64M1aGMNTK6ZTGOi\nkVAopGAro06/gu2TTz7J1772NfbZZx88z+Pyyy/n8MMP5/XXX6eurg6Aa6+9lhtuuIE77riDadOm\ncdVVV3HEEUfw5ptvkuz1/1RFRES2CJ/7HBBMECj+9Kd0ZlppzjbTkm+hs6eT9kJ7sOWtk6HgFtb6\nmOuO/Tr59nrKGyuAT+2EFqbfOhcjBz59d1lIhBKV9WdrI7XURmsZEx9DU7yJWDiGZVlag1ZGrX4F\n20cffbTP59mzZ1NTU8O8efM45phj8H2fH//4x1xyySV89rOfBeCOO+6gqamJu+++m7POOmvgey4i\nIjJClf/qvxxF/7H4H7T3tNPa00roH8+x+wNz+efMz633Odd99nzyHenKk6bs+TZfuOHuVVfjhJI2\nSTtJKrxqQ4VV5XQkTU20hvpYPZFQpM8atAq0Mppt1Bzbrq4uPM+rjNYuXLiQFStW8LGPfaxSJxqN\nctBBBzFv3jwFWxER2aKUdt4ZmyDUvnbikTy//HmypSxNr73HGd/4FQDp1lnMvvH0tT7jB5/8JoVM\ngnKo/Y8T7+O0b7QRDW1NPBQnFoqRCCdIh9PBGrSRNKlICtuyKyFWI7OypdmoYHvuueey5557st9+\n+wGwfPlyAMaOHdunXlNTE0uXLt3ELoqIiGw+fN8ntGBB5fPfvn40rpPFNm12nPc2EETVbV59nzPP\n/Cm/nnUhtmkTMkPYpo1t2pxz4MkUesKUQ+13fjyf/Q9OM6FxR+J2sAZt3I4TDUX7rD+rdWhlS7fB\nwfaCCy5g3rx5zJ07t1//8uhfMBER2ZIYhkH5tS83HGa/CfuRdbK4nos3c1/eTt3G9j+/BwOY8O+V\nfPWU/+P1Ob/FtmzCVpi9pu5IsWhRDrUPPpTjY0d8hPfee4+pTVMr0wl6HyISMPzyRKB+OP/887nv\nvvuYM2cO06ZNq/z83XffZbvttuP5559nr732qvz8mGOOoampiVmzZlV+1tnZWSm//fbbm9p/ERGR\nESkUCmEXCoRqayurD5RDaOLWWxl77bWVObj5bbfl/YcfZtddt8d1y5st+Nx990tMm+ZV5uxOO/lk\nkm++SWaXXXjrV78ajl9LZFhtv/32lXJNTc1q1/s9Ynvuuedy//33rxZqAaZOncq4ceN47LHHKsG2\np6eHuXPncv3116/1mXvvvXd/m6944YUXNuo+2TD6ngefvuOhoe95aOh73kA/+AFssw18+csYQPyy\ny9hllx3xqit88fbbBtttt2fl8wsvvED6zTcBSL/2mr7vQaI/y0NjY7/n3gOka9KvYHvOOedw1113\n8Yc//IGamprKnNpUKkUikcAwDM477zyuvvpqdtxxR7bffnu+973vkUqlOPHEEze40yIiIqPeWWdB\nOg3NzZinf4Hef3+6bBmMG7eOezX9QGSN+hVsf/rTn2IYBocddlifn19xxRVcfvnlAFx00UXk83nO\nOecc2tvbmTFjBo899hiJ8jYoIiIi0tcJJ6yWUbu7+2xUVpXLVct77rmGCiLSr2Dr9f67kXWYOXMm\nM2fO3KQOiYiIbJaWL4d//QsOP7zft/Q71ALTvvKV6oenn96IDoqMfuZwd0BERAQIEt23vz3cvdh4\nkyfDEUf0e5rAh6v5/qpQ++ijwcVwuM/15BtvVD/E++42JiIBBVsRERl+oRBks3DddcPdk43nOP2u\nuqZQW3HUUdXn2Xblx8UxY4KCqf90i6yN/u0QEZHh57rV8qp3NzYrZ5xRLU+fvtZqvu9jGL1TrEep\n5FIqlXAcJzg++IByDb9UwrUsHMfh7SeewHNd/FJpUH4FkdFAwVZERIbfqnVeAfjud4evHxvr9tur\n5fnz8X0fz/Nw3WpobWsrrhpsLa9e6/FB6zLeb3+fd1vf5a3mt3htxWu86q3gxTeewl9V0/Q8rHCY\nfChPa3crhUIBt/f/ERCRio3aUldERGRAlUqb7RJWfnc3EIRQ1zAoFQqU3BJ5J0+ulCPn5Ghuz3PQ\nzntQDbU+97/yAE8tdih5JRzPwfGCsucHL2zP/evVfP3w/6H8rfzj7b/SzO7URevYa8JelU0fRKRK\nwVZEREaGbbeFd94Z7l6sk+/7lcPzvGBU9soriBHE1TfvvInmxc+Qc3Lk3Tz5Up6FH+S57JNnUAm1\nhsfMJ77Lv1rX05gFV86ZyeWHXMk9lx1LJhS02xBv0Da6ImuhYCsiIiPDv/893D1Yo94h1vM88sU8\nnYVOugpddBW66P7SEWS+sB9b33gHz2znkl32D3rcHgCWLUzxiy9eQDXUusx84nv9bjtlp7hz/iwa\nog38hxNl+sTppKIp7F4vlYlIlYKtiIjIGpTnyLquS2dPJy35FlpzrUGoLXbRXewm42TIOll8fP51\n0l7QEwzDvvPiBO664EsEgTYItYZV4vK/fn+dbYbMEDXhGmojtdRGaqmL1tGUaKIx3kjL8hZqE7WY\npqkRW5G1ULAVERHpxfM8SqUS2UKWJd1LaM42097TTluhjfaedrKl7FrvffmxafzhmhOoBloAH6wi\np/7ymj51DQzioTjJcJKUnSIZTpK0k9REaqiP19MQayBmxzBNE8uyeKfzHc2rFVkPBVsRERk+W28N\n778flPss5jo8XNcl25NlUcciPuj6gGXZZTTnmytTC9bmb7P35cnbP85qgRafXU/+JZ8/cyUxK0U8\nFCdmx0iEEiTtJKlIinQkHRzhNPFwHNM0K4dhGBqdFdkACrYiIjJ8yqF2BPB9H8dxeGn5S7TkW1jQ\ntoCiV1znPX/84cd56U/7snqg9bj2ngfYZieDfPcEJjRuS9yOEw/HSdiJYHQ2nMS27EqAVZAV2XQK\ntiIiMrLccgucc05Qfu012HnnIWvaMAy2Sm+FZVgk7SRZJ4vrubi+u2pzBQN8uOYbM5j69D9ZwB5U\nl4QPVjx44uUXGVMXIWbvGYzQhmJE7AiGYWBZ1mpBVkQGjoKtiIgMv97bxJ58cjXY7rZbsMbtICuv\nfGCaJlultmJ8Yjye55EtZim4BYpukZJX4tgjt+KNV5MAvMzWANTSTpeV5vGXXiKedHE9l85CD235\nNnx8wlaYeDhOY6KRMfExWJalQCsySBRsRURkePTehvZHP6qW0+lqeRB22Oq9Dm35XCwVyTpZsk6W\nnJMjV8yRK+VwXZeiV+S0ww6geVlq1ROCUPpJHuQ8/pe//+1QXN/lby1AS9+2yi+ITUxNZGV2JftP\n2p8w4QH/nUQkoGArIiLDo/c2tOed1/eabYPjBOWurr5hdwP1XofW931czyVbyNJV7KqsRZspBst2\n5UvBbmH5Up4et4eZR30NJ5tc9aTqrmFPcwAHMA8PeMo/eK1tp8NpJiYnMi4xju0btidiRzb69xCR\n9VOwFRGR4fHee8FUg0xm9WvvvguTJgXlsWMhn9+gR5fDrOsGUwO6Cl205doqGytknExwFINzrpSr\n3Pv47fszd/ZhBHNn+65wkG5q5fX4Tmy1qAUfePr4ffu0a2CQDqepj9ZTHw2W7NoqtRVjk2MJhUKa\nhiAyyBRsRURkeEyeDB0da742cWK13LPupbZ6K4fZUqlEW08bzdlmWnOtdBQ6aO9pp6sYhNqS13fe\n7u3fOJUlr21DNcj2DrRQM3EJ583+JQDjD2mhvDDZk+ccTWrVKgfpcDrYWCFay5jYGBrjjcTCMSzL\nUqAVGSIKtiIiMjLtvjvE4zBv3nqrlpfqKjgFFncuZmn3UlrzrbT0BLuFFb0inu/h+V5llYNbTric\nQleaNYfZ4Gja6Q3OvPE3mKaJ7xtEQ1Fu+cf/ccTMO6ld1sq+4/YlGUmSjqSpidRQF60jHAr3Wf1A\ngVZk6CjYiojIyPTSS2u99OGXv0qlEsu6l/FW61u81/Ue73S8Q3exm5JXouSVcD2XjsVJHv7Wj8Et\nv7zVO3BWw2zdtFc4+vvXUxupJWbUUh+uZ3xqPKlIsDtYOpLGmn0kRiTNgeEklmmttqmCiAwPBVsR\nERnR1raKQXexu/LiVyqU4uWVL9Oca2ZR5yLaetrIOTlef3Q/Xpl1DtW1Zj8cZgE89j/xMY760nzi\ndrCBQsg8hIgVCba3jdYzOT2ZmlhNZT1a7QwmMjIp2IqIyNA7+GB48EGoqVnjZd/3cV03mDO7llUM\nMk6G7mI32VKWhmgDteFaDNPgV9/5OC/MWdN8WSiHWcP0uPT2R9hl9wyWaWEZFqaxK7Zpk7AT2JZN\nLBSjLlZHY7yRsB3Gtm2FWJH/z96dx8lRFvgf/9Tdx/ScmclNDi5FcJXDAxUJXuB9sLKCAt4nrtd6\nYwRR12O9WHVdUBYRVv3pquuFqIso664LKIqgGAOBhEwmk7n67q6uqt8flb4mk2SSzCRzfN++nlc/\n1V311NP90uHrw1PPM8cp2IqIyOH3y19Cdzccdxzcey/QDLNBEFCpVRgtjTJSGmG0OErOzzXC7ORV\nDABGy6Mk7STvftI7aF/NAOpTDJKpKl/46Y9IdcTTE/zQJ1/ziaKIpJ2MA63pkHSTDKQG6E/34zke\ntm0r0IrMEwq2IiJyeB1/fLP+058SRRG1Wo2qX2WoMMRwYZjR0iijlVHGK+MEv/09b3jjVRjAh/5r\n416bvfb9T6UZancvz7VikLdef1XjnAeqBulcmg6ng4ybodvrpsPpoCfZQ1+qj95EL57jYZpm+0oG\nO3bA8uXxDmkPPQTLls3CDyMih0rBVkREDq+//KVRDVaupFIu8VDuIR4cf5Ch4hDDpWHGK+NEu6cN\nXC/nk3UAACAASURBVPqGq7Bozojdmz/dcjL1UPuol3+GF16UJ2knSdr9pOwUGTdDh9PReACsXlJO\nqjFndq/Lch11VPwahlOvuysic4KCrYiIHBERUPWr/H7H79mW28Z92fso1fbciOGHr30qz/nSzzCA\nV1/8ea76tzcCYGLiWA62afPOJ76Neqjt6C7yllcczYqBJCknRcpJ0eHEYbbD7cC27D0e/trvVIP6\nLmgAxxwzUz+BiMwwBVsRETkyDAMDg6STpNvr5vie4yn6RWpRLV4JgQgDg7HXrIMv/QyA5Q/s4tH9\nj8Y2bRzTwbVc3vnyE2iuehDxl/uzpOwn49nNFQxaXw94vuxrX9usn3zyjHx1EZkdCrYiInL43HVX\no2p84AO4rssJAycQhAGlaomCXyCIAsIoXtoLI96mNiIejzWAM446ozFSm80a3HarS320dvPmkIHM\nwPRHYqfjX/+1Wb/jjkNvT0RmjYKtiIgcPiedBFEE110HL3sZJuC6LlEU4bkeXVG8/FcUtc+ojS65\nhOjKKwHoes4LMG6+GYClS5vBdfVqg/XrZ/Efa1oZQWTOM/d/ioiIyAx72cvaDutTBSzLwrIsbNtu\nK9bnPtcYsTUf9SgMw+C009qD5oMPzlJfP/e5+PWmm2bpBiIyUzRiKyIi80PLKO7ERPusgPHxWbzv\nJZfERUTmPI3YiojIvNPd3aw//OF73cBMRBYZBVsREZlXWvd3ALjnniPTDxGZexRsRUTk8HDd+AGs\nl770oJuYmGjb32F2pyCIyLyjYCsiIodHfZOD668/6CaaUxAiznnYn2ZvCsK6dXEI/+pXZ+kGIjIb\nFGxFROTwSiYP6rJVq5r1r3E+P/rzCTPUoUl+/GPYsiWuX3TR7NxDRGaFgq2IyGJ0wglw3HGH736n\nntqs/+Y3B3z5gw/CQw/F9UfxOy7g6zPUsSk885nN+vOeN3v3EZEZp2ArIrIY/elPsGnT4dt0oHVt\nrpNOOuDL16xp1i/xvtg8uOaaQ+jUFFp/j1QKvvvdmW1fRGaVgq2IyGLz7Gc365535PoxTX197cev\nKLdscfuKV8zcjXp62o8LhZlrW0QOCwVbEZHF5oc/bNbL5cN7b8s6oNNvvRVGR5vHk3banVlPeEKz\nns3O4o1EZLZo5zERkcXke987Mvc9yET6pCc16xdc0PJBfz8MDx9anyb7wQ/g9tvhgQcgk5nZtkXk\nsNCIrYjIYvL85zfrmzc36wMDc25R2I6O9uOvfa3lYOfOeBrCTA/hnnoqvOhFM9umiBw2GrEVEVlM\nMhnI5eL6+vXxa/2BqZ6eWf53/dP37W+3T3Gdsltf/vJh64+IzA8asRURWUyy2TglzpEAuzfnntus\nv+tde34eRdE+y7ScfXY89UBEFgwFWxGRxe7445v1v/mbI9cP4sDqeSEQh1PTrPGhD/lUq1Wq1SqV\nSoVKpUK5XKZQKlAoFcgX8+SLeQqlAqVyqXGu7/uEYTj1jf75n+EnP4HTTmtP0SIyr2kqgojIYvfn\nPzenI/zhDzPbdl9fc1mDlpHU1tHVMAwb9auuDqlWE4ABRNzz0Gb+PFzFD3yqwe7XMH4NoqDRFoBh\nGJiGiWd5dLgddHqdrOpcRdJLYrWuxpDLwSWXNI9Xr57Z7ywiR4yCrYiItLvzTnjUo2amrd2hNgKC\nWq0RZIMwIF/NU/SLFPwCRb9I0S9yyZvOoB5q/+5tt3Lrtr/gh/4epRbWAOjcvI2/f9WXMYHLvvdW\n6OzENV16Ej2s61yHZVisdda2B9vOzma9rw8+/emZ+a4icsQp2IqILHSvelW8pMC+1qy9/35Yty6u\nf/WrhxRs66OvQRBgU4+psG18G9lKlmwlS76ajwNtrUi5VqZYK/LWJ76x3gKG6XP8c37O1vy+75Xz\nOjF33+M9536OT//8Cpall7EivYLVXatZ1bWqPdRO3pBi166D/p4iMvco2IqILHT11QMMY+8Pja1d\nC2Nj0N190LcJgoAgCAjDkFwlx2hplOPqnzk2t269lbyfJ+/HoTai2ZdPnvtmotCiHoM/8POPTOue\n0arm6KvrBzx22WMZ6Bhgdedqkm48BcE0Wx4nqVZbLp7bD9CJyIFTsBURWcjuuGP65x5EqA3DkCAI\n6O7pZig7xHBhmJHSCBOVCU47/x2N0drP/9PLGJ/46x7Xf/b81zM+OLD7KD57/XNuYMuWOGtPJWkn\n6XA6yDgZur1uQtPACuOQ+viuR2D19OwZaOv+/Gd42MPgF7844O8qInOfgq2IyEJ26qnN+gwubRVF\nEbVajYpf4cGJB7l3/F5qhRoj5RHGKmNUggrPveu+xvnjJx3Vdv0/v/xVjGxZufuoHn8jvL7tvOxt\nmxrnOaZDh9MRF7f52ul10ul10pvopfZfN2OeeSYG4B13HMa+Npo4/niN1IosYAq2IiKLxSmnzEgz\nURTh+z7bJraxeWwz2/PbuWPzHfQO9Lad97OXPZGnXndr23v/+oYLGfzT7rm8GPUWcZIlPvazLzE2\nnGBd5zqSdrJR6iG20+sk42ZwbRfTNONVEEwT44wzGi0ZExMz8h1FZH5SsBURWagcp1l/5SsP7Nrx\n8XhJrOuu2+OjKIoo+2U2jW5itDxKzs/hWA6e5cUPjhFhYPDbVz+T3736WdimzQ1veR6bbj9mdwst\ngdbz+c87/4uEnSBpn05yTZK0kyblpEg5KTzbwzTN9iBbX5qsVSIRPxx34YUH9j1FZEFRsBURWaj+\n5m+ac2yvvnr612UykN+9HMEUwdYwDBJOglOXn8pIaYR8Nc9ady0dmY5GsK27/O+P45Yft045AIiw\nnRr3bx/CtVwS9ulYZrxyQT3EWpbVWM1gyiA7Wam053tvfSt85jNw5plw883T/PIiMp8p2IqILFQH\nO6f2xS+Gr3wlrnd1wRT/et+yLDqTnaTdNGEYMmAM0N3dTRAG+KHPJW80+foN3cRhthloTTPg13+9\ng1pU476JgCAMCKMQwzBwTIe0m6bD7WBpeinpRBrbPsh/TG3fHoda0INiIouIgq2IiLT78pcbwTbK\nZonCkHB3iaIIP/AbGyrUy+CuQbyCx5c+uYL/uPoEJgdajIBP/uqz+KHPT7fWGruF1actmIaJYzqk\nnBRHdx7NruIuTllxysEH25Urm/X16w/6pxCR+UXBVkREGuo7g4WOg+P7AOx6/7vJveW1zc0V/Dzl\nWplSrdQoX//nZfzPDc9ij0BLyMabPwRAzt/7fcMoJONkWJFeQVeii+P7jm/fWOFAtF5nGLB588G1\nIyLzjoKtiMgiVt8lrL4ebbVWZbw8zsSW3/KIlSdhAEs++gl+fO4jGpsrlGrN+azj4/DZF3yAyYH2\n+zybZ/Ij/vDEY/ku5095bxMzXrLL66U30Utfso+juo5iSXoJtm1PvQ7t/txyC4Rh87i1LiILnoKt\niMhCct99cPTRMDoKPT17Pa2+5W0QBBSrRYaL8cYK4+Vxxivj5Ko5Tmg5//7s/VO2E4faegCNR2iH\nExmWlEtEwHff8azGuQYGKSdFxsnQ5XXR7XXTnehmSWoJ/al+kk6y8dDYtB4Ym8pzntOsP/TQwbUh\nIvOWgq2IyEJy9NHxa2/vlBsR1AOt7/sM5gcZzA0yWh5tlGw121jV4MpPX8R4dzfR2ql3JPvCK19B\nc5Q25G/+/nIe9SjofXlzRLdv6fp4lzA307a5Qneim55ED67tNnYJMwzj4ANtXTYLS5bAjTfCihWH\n1paIzDsKtiIii0R9Y4UduR3cN3YfOwo72F7YTraanfL8sUet3Wd7w/etpr5r2OPf+mFe9ndLSdrJ\nthm2p684Pd5YwcuQcTPYlt1Y0muva9Ieql27Zr5NEZkXFGxFRBaKRKJZf97z9vg4DEPGS+PcM3wP\ng4VBhopDlIPyXpuzDAvHdNqKbdk4psPLT3kZ9VDb21/kzc99HCesXErKSTXvZ1mctOyk/W+uICIy\nQxRsRUQWikqlWf/ud/f42DRNMm6GY/uOZUlqCeur6ynVSgRR0LZjmGEYmJg4loNjObimG79a8es7\nXreM1nm127faPPDAGtYNrMP43Od2vwvWN76B7bqz/rVFROoUbEVEFoJTT23Wu6eeE2sYBolEgjXO\nGlZ3rY7n2+7eIGGPYGuYmEb7vFfj97/HWLeCH32vvvFCxG23GXieRzabxXEcePvb4/LkJ8OLXjT7\n31tEpIWCrYjIQnD22c3tc8fG9nqaYRhtmx5EUzxg1npuywEAb+BzwCUAeJ7Rlqfb3HLLtLotIjKT\nDmKRQBERmXOuuCJeBWEfQXUq9RHZqcpkZTy+xwubx3ufnisickQo2IqIyP4tX84VvJ/trMSixr/8\ny5HukIjInjQVQURE9ssb2U5ADYOQz/NGXvvaLx3pLomI7EEjtiIisk933AHVKgTYvIEv8Fr+FbZs\n2fPEVAqSSbjrrsPeRxERULAVEZnfDAO+971ZvUXzAbGIK3hfXP3bv93zxFIpnnj7yEfOan9ERPZG\nwVZEZL7q6Ihfn/98+PnPZ+UWAwOtRwbdT39c/IDabbe1nzgx0az39c1KX0RE9kdzbEVE5qtCoVl/\nylNmvPmxMRgebh7HCy78ZMpzH/HiFzcPNm+e8b6IiEyHRmxFROajDRua9VRq7+cdgt7eZv2UU/Z9\nrjc62jzo6pqV/oiI7I+CrYjIfPSLXzTrrSO3M2Tyxgu3377v8/dc9VZE5PBTsBURmW++9rVZv0V9\nEzOA1sHYvWlsC+E4s9EdEZFpUbAVEZlvHv7wZn06qfMAtW461t8PPT1TnPT4x8cn7j75t7fdFk/C\nrVZnvD8iItOlYCsiMt+cckpz+9wpU+fBe9Wr2o937tzLiZ2dzfqKFTPaBxGRg6VgKyIiDV/+crO+\nz3m1P2lZHWFwcNb6IyJyIBRsRUQEALPlnwiuu/+VEFovSP1k6mXAREQOJwVbERHhS1+qr1Mbq1Sm\ncdHISKP6sPe/f+Y7JSJygKYdbH/5y1/y3Oc+l1WrVmGaJtdee23b5xdffDGmabaV008/fcY7LCKy\naBkGnHferDT9utc165/+9NTnRFHUXrq6GqshaLkvEZkLph1sC4UCj3zkI/nsZz9LMpnEMNr/jBmG\nwdOe9jR27NjRKD/60Y9mvMMiIotSd3f8+s1vwrveNaNNJ5MRzQW7arzpTTV836darVKtVqlUKpTL\nZUrlEsVSkUKpQL6YJ1/MU/zoR4iAEKhWq9RqNaLWoV8RkcNo2lvqnnPOOZxzzjlAPDo7WRRFuK7L\nQPvG4iIiMhMmJpr1j33sgC+vh80wDNtGXW+/PaJcdonHXCP+uvMB/rrLpxpUqQZV/MCnGsavfujH\n1xE12jOe90is5/+YarHKyh130ZvqZVnHMhJeYo8BEBGR2TbtYLs/hmFw6623snTpUrq7u3nyk5/M\nhz/8Yfr7+2fqFiIii9PxxzfricS0LomiqBFiwzAkDEMqtQoFv0DRLzbKE57wGOqh9rSnbeLWrf+D\nH8Yhth5m6yWIginvZWAwvmuck42TGSgN0OV14bmegq2IHHYzFmzPPvtsXvSiF7Fu3Truv/9+3v/+\n93PWWWdxxx134LruTN1GRGTx+ctfmvVSaY+P66OvrUHWD3xylRzZSjYu1SwFv0CpVmqUd57zEpqz\nY0Oe+d4buD97YF0zMOj2ulmxdAVru9ZydM/RdHgdCrUickQY0UFMhspkMnz+85/nwgsv3Os5g4OD\nrFmzhm984xu84AUvaLw/0fKv0zZt2nSgtxYRWVSWXnEFq773PQygBtx5222NzxzHwXEcXNelRo2J\n6gSFWiEufoFsJctEeSIupQkqQXOpg9FR+PYlX6I+Wvvq61877T5ZpkVfqo+B9AD9Hf10e930e/10\nO92Uy2XK5fKMfX8RkVbHHntso97V1bXH5zM2YjvZ8uXLWbVqFX/961/3es6pp556wO3efvvtB3Wd\nHBj9zrNPv/HhMe9/5+9+t7FtrR1FnByGBEFAGIZMlCfYVdzFYHGQ8co4E5UJstUseT9PsVaMr3fB\ndm36Ovvamr3qgg9QD7WJvoeoVlewdu3UXbAMiw6ngw6ngy6viy63i55kD32pPpYkl5BwEmzatImj\nH3a0Rmpn0bz/7/I8od/58DjY37l1gHQqsxZsh4eHeeihh1i+fPls3UJEZHHYPdWg5vtU/Apbs1sZ\nyg8xVh5jpDzCWGWMgl+YdnOXbbiU1ikI7/rW1W2fp+wUGSdDhxuH2bSTptPrpNPrpMuLQ61t2W3L\nO5bLZYVaETniph1sC4VCY+pAGIY88MAD3HnnnfT19dHb28vGjRs599xzWbZsGVu2bOE973kPS5cu\nbZuGICIiBy4MQ6rVKlvGt7B1YiuDhUEGi4OUanvOt92fT77wzcQrPcajte/81udZmV5J0k42SsbN\n0Ol1kvHi17SbxjItDMNoBFmFWBGZi6YdbG+77TbOOussIF4BYePGjWzcuJGLL76YL3zhC/zxj3/k\nuuuuY3x8nOXLl3PWWWfxrW99i3Q6PWudFxFZDIIgYOvEVraMb2FLdgtjlbG2+bKtDAwc08ExHWzT\nxrEcXNPFNm1uvPY4CmM91EPtx7/yKzacdjopJ0XKSZF20iSdJI7lNMJr/VVBVkTmg2kH2zPPPJMw\nDPf6+Y033jgjHRIRkXamabI8s5wgCuhN9lLwC1RqFcIoJNq9sYJBHD5Nw8Q13TjQWm4j2LqWyyuv\nPIbG0l6nVXjz+Y9thNbWAKsQKyLz1azNsRURkYM0Ogp9fbBqFWzdimVZpBIpjnaOblvaa2/Bth5M\nW0Oq61rUQ61lwW9+o3VmRWThUbAVEZlr+navYLBtG/zf/8FjHtOY21q3r5UaJwdWs23zdINabQb7\nKiIyhyjYiojMZY95zJRvT3e09RGPgNYMfOArl4uIzB/m/k8REZHDpnV49fnPP6Smvv1tuOee5vE1\n1xxScyIic56CrYjIXNI6pPqd7xxSU+ee26wfcwxcfPEhNSciMucp2IqIzBUtW0VyzDGH1NTkmQra\nwVxEFgMFWxGRuWLTJqiv/X0ISdRx2o81r1ZEFgs9PCYiMpfk84d0+Zln0rbqwcjIoXVHRGQ+0Yit\niMgC8X//B7fc0jzeuBF6e49cf0REDjcFWxGRBeKxj23W+/vhgx88Yl0RETkiFGxFRBaAyQ+L7dx5\nZPohInIkKdiKiBxJ73pXnEpd96CbqD9vVqeHxURksdLDYyIiR9LHPx6/+v5BXX7hhVAsNo9HRuLt\ndutb7rbWp2IYRlsREZnPFGxFRI6Um2464EtaA+vISMR115mAAURccEGVVCqiWArwA59qWKUaVPED\nnyAKCKOQiAii3YEWA9d2STtpUk4K27KxbRvT1L/ME5H5ScFWRORIecYzmvXf/GaPj+ujrWEYttWr\nQZVSrcSygX7qoTaR9Hn1Zf/Lrx6Mg6wftpTdwTaiffTWMAw8yyNpJ+lwOljfs541PWsUbEVk3lKw\nFRHZlw0b4FWvggsumNl2R0fbDqPTTiPaHWDDMCQMQ4IwIFfNka/kKfgFCn6Bol+k5Jd4ziPOIQ61\nACFX/PRK/md7HGSDKJh2NyzDYllqGWknjWsd/DxfEZG5QMFWRGRffvGLuLz0pe1PZdXnox7kk1rR\nypWNuv/pTxNWKhT9IrlKjmwlS7aSjUOtH4faYq1IqVaiWCtyxbPfTPzsbzxau/HmD5E7wCm6GSdD\nX7KP/mQ/KzMrWdO1hrSXxrb1jwURmb/0F0xEZG+uv37q97/xjWbdMCCZbH+Cay/q0wmCICAcH6d2\n8sl499zD71/wBLIP/jd5P0/ez7cF2oj24HzVm86nkstQD7WXXHX5tL6KZVh0eV10e930eD30JHro\nT/czkBpoBFpNQRCR+U7BVkRkb1760mZ9eLhZnzwftlSKA+769bB58x7N1MNsEARky1l2Fneyq7iL\niW9+lPHKOOPb/4ecn8MP9z3s+qnz3kBuZ3NebWbtPWTtiKk2F0tYCTrcDjJOhg6ngw63g55ED33J\nPnqTvaTcFKZpYlmWVkQQkQVDwVZEZDqWLGnWP/WpuKxcCdu3N9+/7754va2+PqAZaP2az47cDh7M\nPshoaZTR8igj5RGKtf2P8tZ95Jlvxy91UA+1ZnKCt13z/wBwTZeUk4oDbL24HXR6nY3S4XZgW/Go\nrGmaCrMisiAp2IqITKV1xYKenqnPeeih+NXzoFqN67tDLUCtVmO0MMqfd/2ZHYUdbM1vJe/nD7gr\nlz31vRA41EPt8qOHePvnf8qavhNJ2klSdoqUmyLjZhpB1rM9DMNQkBWRRUXBVkRkKrfe2qxPWsFg\nD5XKlG+HYcim0U0U/SIT1Qkc0yHtpImXko3nzhqGgYmJZVo4ptMoruXimA7n/c0LAYt6qD3zGUN8\n/ppRks4TG+vPOpbTCK71IFtvW0RkMVGwFRGZSqEQv/7gBwfdhGVZPPqL3yP1yU8SApW+XpIjo4TA\n/2z+FQCmEY+mWoaFa7ltZc2SlbSufvCud1W5/PJeDKOvEWI1Eisi0qRgKyKyL89+9kFfats21ic/\niUE85pocGcUgjqqnrTwNaB9VrdcNw8Bx6mfGofbrX4fzzvMOui8iIouB1nYREZlFxlvf2qzXXx0H\nz/PwPA/XdRvFcZzdxaY5/QDuvdfgvPM0Kisisj8KtiIis+lTn4o3cXjUo5rv1R80m8LkWQW7dsFx\nx81S30REFhhNRRARORx+97t9fjwy0r6iGBz0pmYiIouWRmxFRFoZRly8wzef9S9/UagVEZkJCrYi\nInX/8i/Neq12WG75jW/A8ce3v6dQKyJycDQVQUSk7vWvb9aHhmb9du99b8RHPwr1lQ8gxPcjfD8i\n2p1uo5aUG0XRHqsoTN6EQURkMVOwFRGZyuS5AYcgiuKgGoZho/7iF0d873suzVAbcN/Orfx1V4Vq\nUG2UWlgjjELCKGyEXMMwMA2TpJMk5aToSfSwJLUEz/MUbkVkUVOwFREBeMxjmvWlSw+qiXrwDMOw\nLcT6gU/BL1CsFin6RV749BX85e5u6qHWtGp87Y5v8autPn7oUw2r+EH8WgtrRESNcGtggAGWYZGw\nEvQl+hhIDXDy8pPpc/qwLOvQfwsRkXlKwVZEBOC225r1HTumdUnrSGw9yFZqFbKVLNlKllw1F4fZ\nWpFSrUSxVuRNT30eudFO6qHWTeV5zw//iXvHDqCvEbi2y0BqgGWpZazvWU9Xoquxla6IyGKlYCsi\nAvETW096UnvA3eOU9iAbBAH5ap5sJctEZYJsJUu+mifv58n5uXiU1i9SDeN1a694xjsJqknqoTYz\nMMzbvvGFaXcxZafoTfTSl+ijJ9HDiswKVnauxLVdbNvWNAQRWfQUbEVE6n71qz3eqofZIAgIw5Bi\ntchIaYTR0ijj5XHy1TjE5v08uWqOclCesukvve6lbaF2xSM28ep/vmGf3XFMh4yTodvrptvrpsvr\nYklqCf3pfjq9TizLUqAVEWmhYCsiMoX6yGytViNfyTNcHGa4MMxYZYzx8jjjlXEmqhMEUTCt9nbc\nezT1UNt30v/ytLf9pO1zA4OUkyLjZMi4GTqcDjqcDjq9TnqSPfQme0m76cYKCFoFQURkTwq2IiKT\nhGGI7/uMlcbYMr6FocIQo+VRRsoj5P38Abd32YZLaax+YJX4+yt/RtLuIGWnSNrJOMS6HWTcDJ1e\nZ6OknNQeQVZhVkRk7xRsRURahGFIuVLmnuF7eCj3ENvy2xguDR9wO7Zh41gOV776PJp74URc84uf\nsXLgcaSdNCknRdpNk3HjUVrbsvcIsQqyIiLTp2ArIotbPTh+8YvwutcRRRH5ap7R0iilWomknWQg\nORCvI0vLOrKYmIaJbdo4poNjOriWG7+aLq4Vl3f/eQ310dqf//cQJz/yDBJ2orGxQusmCwqxIiKH\nRsFWRBavT3yiWX/Tm+B1r8M0TbqT3Txu1ePIVrIU/XiprtYNEkzDbGySYJs2nuU1gmy9mIZJMulQ\nD7WeF/Dkxw5oJFZEZBYp2IrI4vXOdzbrtRoQj8a6brx8VjqRbqyKsDf1gDo5sJ5xRmtwNSiX9edW\nRGS26S+tiMgUDnWzg1tvbdanWEVMRERmgbapEZHF6aSTmvWjjprRpltnGbguPPGJM9q8iIjshYKt\niCxOf/xjs/7AAzPW7IYN7ceVyow1LSIi+6FgKyKL05veNCvN/uIXzbqmIIiIHF4KtiKyOF15JURR\nXGZI6xQEx9EUBBGRw03BVkRkBjzjGe3H1eqR6YeIyGKmYCsiMgNuuqlZ//73j1w/REQWMwVbEZFD\nNHkKwrOffeT6IiKymCnYisjiYhjw6lfPWHPPeU77saYgiIgcOQq2IrJ41Hcau/pqOProGWnyBz9o\n1jUFQUTkyFKwFZHF4xOfaNY3bz7k5lqnIFiWpiCIiBxpCrYiIgfh3HPbj2u1I9MPERFpUrAVkcWh\nderBwx9+yM19+9vN+te+dsjNiYjIDFCwFZHF4b77mvV77jmkplqnIJgmXHDBITUnIiIzxD7SHRAR\nmU9e+tL24yCY+rxoPzuaGa3pWEREZoSCrYgsDjO0de711zca5KtfDQmCOMS2FoAwDAmjkCAK2t4H\nsC0bx3IwDAPTNLEsS0FXRGQGKNiKiEyhNaDWg6nrmoAFRBhGjac8e5gHxypUahWqQZVKUKFai1/9\nwCeIgka4bWWbNkk7SdJJsiy9jBWdK3BdV+FWROQQKdiKiBAH2TAM24JspVah6BcpVAu84+9TwLL6\n2XzrD9/nlw9WqYZV/MCnGsT1+qsf+vu8X8pOcVz3cfiBz/LM8ln/fiIii4GCrYgsOvXgWg+xYRhS\nqVXIVrJkK1ly1RyFaoFSrUTBj1+/+/ULAQOIOOfv/x9/2PWng7q3Z3kMJAdYkV7Bqs5VrO1ei+M4\nGq0VEZkBCrYisqAt+dKXiE45pW1ENgxDCtUCE5UJspUsE5UJ8tU8uWqOnJ8jX81TqpWohvH+eTfc\nZwAAIABJREFUuJdteD/1UAs1HvP8Awu1CStBT6KHJYkl9CR66E/3s7pzNSk3hW3bmKYWqBERmQkK\ntiKyIEVRRPTqV7Pmy1+Gq68md8XljLzmAkZKI0yUdwdZP9cIs6Vaacp2rnjGPxDPq41tvPnD+723\nbdhk3Aydbic9iR66vC76kn30p/vpTnRjWzaWZSnQiojMMAVbEZn7uruhWgXXhVQKOjqgrw/+8R/h\nyU9uOzWKIoIgIAgCnC9/uTHO+qsXPJqxbf/NeGWcieoEtXD/W4Vd9pT3QuhQH61de8432bIF1q5t\nPy9pJ8k4GTJuhoyTocPtoNPrpCsRB9qMl8E0zUbRtAMRkdmhYCsic9/ERPxaKjXrmzbBmWe2LeMV\nBAG1Wg03kWgZY42D7e07bz+gW1624X3EfyLjUNu59i4ufuefSdhJUnaKlJ0i7aTJuHGQ7fK64jDr\ndZF203sEWYVZEZHZp2ArIvNXS1is1Wpki1n+PPJnHk8cRyEOtfcdv2yqq/cqnlNrUQ+1Z77wD5z/\n5s2sGngMaTdN2kmTdtONkVnP9hoBVkFWROTIUbAVkblvGpsrBEHAPbvuIVfJcefZp9D1wBDJbJGf\nPelYtr7+uXiGgWmYmJiYholrubimi2M5uKYbH1suLzjx2bSG2re8ZzNvfXsPKfsMkk4S27LbAqym\nFoiIzB0KtiIyt9RD4tVXwytfOe3LTNPkxIETGcoPUbzqKnb4JapBlc6JCU7v6gLAMuIHtizDwrEc\nPMvDszxc28WzPJb39AMm9VB79dU+F120tjECq5FYEZG5TcFWROaO005r1v/pnw4o2DqOQ6fVSUei\no7G0F8BWtrJ69eq2c+vhtDWs2rZBHGjjz37xC4MnP9k9pK8jIiKHl4KtiMwdt7c84HXPPQd8ef1h\nrVbj4+Mcc8wx+7xu8iDs3XfDCScc8O1FROQIU7AVkUVtcqjduRP6+49MX0RE5NBodXARmRte+MJm\nfWDgsNxSoVZEZGHRiK2IzA3f+U6zPjQ067ebHGqnsfCCiIjMcRqxFZG54aSTDstthof3HmqjKGo8\neFYv9V3M6iUMw8Z5IiIyt2jEVkTmhj/8YdZvsXNnxNKlQGOj3YhqNaBajRphtRpUqQU1giholNYQ\n61ouCTuBa7lYloVlWXs8sCYiIkeGgq2ILDj1kBpFEalUimq1yt13R5x8sksz1IbcM/gX7h6qUK6V\nqQQVKrUK1aCKH/qEUUgQBYRRSBiFjbZdyyVhJUjYCY7qOoq1PWtxXS0LJiIyFyjYisi81jp9oHUa\nQcEvUKgWGAlH+P6/FXj3a0+lNdRee8f13LotDrLVoEoliOsh4X7uCF1uF8f1HEc1qM721xMRkQOg\nYCsi88pUITZfyTNRmSBXzZGv5ilUCxRrRQp+gf+41uQ7n30JraF2480f4r7sgd3XwKDb62Z5ejnL\n0stY172O/nQ/juPMwrcUEZGDoWArIkfWCSfAS14Cl1465cd7PMwVBmQrWSYqE0yUJ8hWsuSqubj4\nOYp+kWKtSETET696DL++4RyaoTZg481XTLtrBgadbid9iT76knFZ3rGcgY4BHNvBsixtsSsiMoco\n2IrIkfWnP8EHPhCX3Q9p1cNsEAQEYcBEeYLR0ijj5XGylSx5P0+22gy0tai2R7M7/2gcVKj1LI9O\nt5Mer4dur5ueZA/9qX76U/0knETjgTEFWhGRuWfawfaXv/wln/zkJ/ntb3/L9u3bueaaa7jooova\nzvngBz/IVVddxdjYGI997GP5/Oc/zwnal1JE9ua//qtRjYCwZVmt0dIow8VhRkojjJfHGauMka1m\nyVfz05oH+8VLLqUZamtcdM2HpzwvbafJuJm20uV10ZvspS/Zh2u7jZUPtPqBiMjcNu1gWygUeOQj\nH8lFF13EhRdeuMdoxcc+9jE+9alPce2113Lcccdx+eWX87SnPY17772Xjo6OGe+4iCwAT3kKEEdP\nf+tWsvkxHso/xHBhmNHyKCPlEcbKY1TDA3tI67IN7yMOtRDPqY1DrWM6pJ10I8x2up1xkE100eXF\nJekmMQwD0zQ1MisiMs9MO9iec845nHPOOQBcfPHFbZ9FUcRnPvMZ3vOe9/CCF7wAgGuvvZaBgQFu\nuOEGXvOa18xcj0VkwYhoxs+7oiG2P7SdwcIgu0q7DjjM1n3nH59C/KctHq19979fycN7H07aTpNy\nUqTd3aHW66TL68K13cZorGEYjSIiIvPPjMyxvf/++xkaGuLpT396471EIsEZZ5zBr3/9awVbEdnT\nzp2NagDcseMOdhR2TGuagWVYeJaHa7l4ZvzqWi6e5XHZT55IPdQ+97xBnnvSY1mzYg1pJ41ne40A\n2xpmRURkYZiRYLtjxw4AlsZb+jQMDAywffv2mbiFiCw0z3oWEI/a/vI/Psvy9HJ6vB4qQYWICGP3\nWK5pmFimhWXEpR5gPdsjYSXw7LjuWR7r+lfTOq/2W9f1c++9oyztXNqYH6sgKyKycM36qgj7+ofI\n7bffflBtHux1cmD0O8++Rf0bf/GLGIZB8pZbWPPIZ+FHPlWrSjWsEhGvjmBgYBpmo9iGjWM6mJiE\nQUjox0uA1cIaj33CUUD94a6I2277Pb//fXz0u9/97oh8xcVmUf/3+TDRb3x46Hc+PA7mdz722GP3\n+fmMBNtly5YBMDQ0xKpVqxrvDw0NNT6byqmnnnrA97r99tsP6jo5MPqdZ59+491OOYWoZZmven2y\n+v9JnvwK8Mc/wsRE89y77jI58cT4t9XvfHjod559+o0PD/3Oh8fB/s4TrX/spzAja9esW7eOZcuW\ncdNNNzXeK5fL3HrrrZx++ukzcQsRWcDqD2zVVyKYqkx+wKvVSSc16wMDcOKJh/kLiIjInHBAy31t\n2rQJgDAMeeCBB7jzzjvp6+tj9erVvOUtb+EjH/kID3vYwzj22GO54ooryGQynH/++bPWeRGRybOd\nhoaOTD9EROTIm3awve222zjrrLOAeHRl48aNbNy4kYsvvpivfOUrvPOd76RUKvHGN76RsbExHve4\nx3HTTTeRTqdnrfMisrhdcEH78V5mMYiIyCIx7WB75plnEob7XoanHnZFRPbK86C6e43aQ0yiN9zQ\nrL/pTYfUlIiILADaH1JEDq/qwW28MNnkKQhXXjkjzYqIyDymYCsi805vb/uxpiCIiAgo2IrI4dTZ\n2awf5NyBP/4Rxsaax3fddYh9EhGRBUPBVkQOn1yuWT/IuQOtS3utXKmlvUREpEnBVkTmjcnzardt\nOzL9EBGRuUnBVkQOn2c+s/31AGhpLxER2Z8Z2VJXRGRafvjDg75US3uJiMj+KNiKyJzXOgXBMJrT\nc6MoIto9dFuvtx4DdHZ2Um1ZYqy+Ja9lWXtszSsiIvObgq2IzGk9PfU5BwYQUqkEVKtxgA2jkIpf\noRyUKdfiUgtrjRJGISPFEXY9tAsAz/ZI2AlSdoqB9ACe62Hb+jMoIrJQ6C+6iMwJ9RHWMAzj0BqG\n/PznEePjLnGojbjl93/h7qFmiK3U4lBbCSqNUgtrBFFAEAYEUcCOoR30D/RjYOBaLp7lsbJjJYP5\nQU5ZcYqCrYjIAqK/6CIy+wwDzj8frr++8VZ92kAYho0wW6lVyFfz5Ko5CtUCz3zmo6iH2t6BMTZV\n/5vKQ80wWw2qROz7KbKx0hhJPwmAF3r0eD0krARH9x6Naer5WRGRhUTBVkRm17OeBUB0ww1EQ0OE\nN95IGIYEQUC2mmWiPEG2kiVXzVH0i+T9PAW/wCtPvZA41AKEXPKNz7E1f3Bd6HQ7WZJcwrLUMo7q\nOorVXavxHA/LsmbkK4qIyNygYCsis6LxINePftRYV3DXt29gbGQz4+VxJsoT5Ko5stUseT9P3s9T\nCSoA/PulzwEs6qO1G2/+0AHfP22n6Uv2sX7tetYvW8/SjqUsSy8j4SawbVsPjomILEAKtiIyY1qn\nFoRhSK6co6/+GfCrB39FtpptlCAK9mjjsg3vI/7TFIfax533k2nd2zIsMm6GLreL3kQvPYke+lP9\nBLmAY1cei2VZmKap6QciIguYgq2IHJL6yGwQBPH0gkqW4cIww8Vhej/w8UawLXk2d43ctdd2Ljvr\nvRA5u4/iUAs1jj/7f6c8vx5kO93ORunyuuhOdrMkuYQOrwPTNLl76G5c19UIrYjIIqBgKyIHLQxD\narUahUqBocIQQ/khRsujjJRHGC2P8vZ//3Ejon7ixvdN2caHnv4uQj+x+6h+doSZGOf9P/rM7lFg\ncCyHDqejEWAzboZur5vuRFwyXgbbshujsvX1amu1mkKtiMgioWArInDeefDNb8blb/92v6e3Btr7\nx+9ne247w6VhdpV2UagVGudFLQWaS3oBfPTZb8Mvdu4+agZay8vz3h98gqCcpM/ro8PpIONk6PDi\nUFsPst3JbhzbaYTY+quIiCxeCrYiEgdagBe/OH6N9r6EVhRFVKtV7hu7jwfGH2BbfhuDxUHCKGw7\nB+Dyn1/a3AmsVgPg0+e9meJo/+4zm4HWsKpc+curSTtpEvYJeLaHZ8UbKiTsBJ7lEUYhBb+AZVr0\npftwHEdhVkREGhRsRRa7G2/c8z3DgE98At7xjj0+CoKAofwQD048yAO5B8hVc5iYjQBr7P4PEYTE\n69OapsmVr3gFux5cWb/B7tcI8Pn6776DaZo45kpcy40DbK3AeGm8sfxXOShjYLC2cy3rutaxpmfN\nrPwcIiIyfynYiix2Z58dj9CuWAGDg833/+Efpgy2hmGwJLWE9T3rWZJcQqlWouSXqAZVgiggjOIV\nEQAiIi59xWn8+bericNsa6Ct8Z27ftjYMazklyj6RYq1In7o73HfLreLtZ1rWZlZyfF9x+M6eiBM\nRETaKdiKSGz79vh1irBYX8YrCALCMKTsl/FMj4ybwbVcMk6GalhthNRyrcyH33Ic//vTY9gz0AZc\nccvH8EOfO3ftu0smJn3JPgaSAwykBzim5xiWpJdg27Y2VxARkT0o2IpIuygiuukmwqc8hdD3CcOQ\nSq3CWHmMsVJcJqoTTFTiDRZyfq6xsQLAv3/4dP7ys2cyVaDdePMVAPjh5Ju263Q7WZJYwpLkEvrT\n/SzvWE5fqg/HdrAsSyO1IiIyJQVbEQHaR2VrT3oiE7mdjJXGGC2NMlGJg+ypr/kgTlTjlk9cOGUb\nl224FDCpB9oOsuRJ87qvf4ilS/d+bwODDqeD3kQvfYk+epO9LE0vZSA9QNJNNjZXUKAVEZF9UbAV\nWawMg2j3DmFBEFALaoyWRtlZ2Mmu4q44zFYnGK/ED3ABvOS2TQBcuuEyPnTzxrbmLtvwfuqh9gTu\n5qO8h6fxfT426by6hJWIN1Twuulyu+hKdMXTDlIDpL20dgoTEZEDpmArsghFhhGPqZomI+NDDOYH\nGS4MM1oeZVdpF6PlUWpRre2a0z//YyAei7WAjRsuY8u6fq79yhv46LPfsvtdg6PYwl2chEHE5Ve+\nvnG9ZVhxkHW76fK66PQ6461vkz30JHpwbRfTNBtTDTQ6KyIiB0rBVmQRqW992/rY1a+3/pqdpZ3s\nKu2iGlb3eu2v33gO9x2/ktd8+DuN2bNr7x/mVRu+yGVspL4m7R85AZOICOg77YR4cwWng4yboSfR\nQ0+yh95EL2kv3RiR1TQDERGZCQq2IotEGIb4vo+VSDS2RXho7QB37rpz2m3seOojufypj+S9Z12G\ns3sPhwu5gXqo7Uo/REehBEAAnL7idDq9Tjq9Tjrcjim3vBUREZkpCrYii0AYhpQrZe7eeTentrx/\n9TWv3+s1k5mYeLZH0kryb7/5Eom7t/Ddl5/CzTyF+rq0O8yHwe6j4Ec/4sSlJyrIiojIYaNgK7II\nhGHIYG6QR699TGO09sGjBzANExMzfjVMbNPGNm0c08ExHTzLI2knG68JO0HKSZG0k5z4mFcSPywG\nEFKpRJjmOOF734v5iU/gnn22gqyIiBxWCrYii4BpmizLLCN72qPpvu13ANz346/z+LAWj6gaJpZh\nNUOtFQfbhJMgZcdB1nM8TCMeefU8g+ayXhFhaGIYu2fufvzjcRERETnMFGxFFgHTNEklUni//j9q\nu7e7PT2KiKKobVS1Xm99nVyOPrq97cFBY6rNykRERA47BVuRRcIwDGz70P4n/4UvwH33NY/PPx+W\nLTvEjomIiMwQrXwuItP2xjc26x0dcP31R64vIiIikynYisi0TJ5ukMsdmX6IiIjsjYKtyEJnGHG5\nc/rr1U7VRKsoOsQ+iYiIzAIFW5GFbMeOZv3Rjz6oJly3/VihVkRE5io9PCaykC1f3qw/4QkHfPkT\nnwi+3zz+8Y/bP492p9xo9woLrcet50xeWcE09f+pRURk5inYiixUraO1ALfeekCX33gj/Pd/148i\nnvAEeNrTQmq1ZogNw5BKrUI1qLaVWlgjiAJqYY0oinAsB8/28CyPnkQPSTeJ4zjawEFERGaUgq3I\nQtU6WnvWWdO+rB5azznHoL4Bg2VV+eGNZXZmixT8QlyqBYp+kVKtRCWo4Ic+fuDjhz61qEYQBgRR\nQESEYzq4potneQykBnjEwCNY1rkMy7Jm/GuLiMjipWArshj8/Od7/ag+8hqGIVEUEYQBqaQHjc13\nQ26851f88sESpVqJYq1IyY9fi7UiQRRMuxtdbhf9yX48yzvkryQiIjKZgq3IQvXRj8J73gPnnNP2\ndmuQDcOQaq1KtpJlojJBtpLl8etOJQ61ABGfvPUz/O9giVpUO+iu2IbNms41rM6s5vglx9OV7NI8\nWxERmXEKtiIL1bvfDe9+dzy1IAwJgqARZCcqE4yXxxkvj5OtZMlVc+T8HG940nmARX20duPNl5Pz\n93OffbAMi6WppaxIr2Bt91rW9azDczwsy9L8WhERmXEKtiIL0ORR2Xwlz67iLnaVdjFRniBbzTZK\nwS8QEfGdj2/AL3dQD7VPv+SGg75/0k6yLLWMgdQAyzuWs6pzFZ2JTmzb1kitiIjMGgVbkQWiHmaD\nICAIAybKE+wq7mKkOMJ4ZZzR8ihjlTGy1ewe1+7YAX/48RnUQ23HwE4e/8JNB3R/y7DoS/QxkBqg\nL9nH8o7lrMisIOEksCwL0zQ1SisiIrNKwVZkHmsNs37NZ7Q0GofZUhxmx8pjjFZGKdVKe23jPz91\nBr/7/gaaD4vVePs3vjit+1uGRbfXTW+il16vl/50P8szy+lN9mJbdiPQioiIHA4KtiLzUGNkNggY\nK48xmBtkePNdPH3DxawE/vNVT+GPFzxxv+1ctuF9xH8GmisgXHTNh/d5jWd59Hg99CR64lCb7GVJ\ncgl9qT6NzoqIyBGlYCsyT9TXl63ValT8CoP5QQZzg4yURhgqDfGaDW9orGWwdPPgPtv67Y0r+P7H\nXkUcaOuhNmDjzVfscU/DMEjbaXoSPfR6vXQluuhL9rEktYSeZA+O5WCaph4IExGRI07BVmQeCMOQ\nWq1GrpxjW24bg7lBdhZ3MlQcolArwI4d1P+FfwT85AN/u9e2LjvrPRC5tC7p9Yin38oTLr6JIIjD\nbMJK0Ol10ul20u11053opi/ZR1+qj+5kd9s0A4VZERGZKxRsReawKIoIgoBytczm0c08mH2QHYUd\nDJWGqIXNdWUvfcmXGuOuv9lwwh5tAGzfHnH1Sz9I+yhtyFt++A48y6PD7WgE2bSbJu2kSdkpMl6G\nhJ0gjEKylSwpO4VjO9o1TERE5hwFW5E5KooifN9nKD/EppFNPJh7kK25rXvu9DVptPbGS88lCsNG\nG1EU8fHnvgO/1EXrKG3Pqm1cesO36PROJGkncW033vbW9ggJGa+MsyW3hYJfIIgCXMsl42RYnVnN\n6atPx7ZtjdaKiMicomArMkfVajV25Hbwux2/Y9P4JvJ+fsrz3vSGrwJxqL3lGSdR9atUggqWYeGa\nLh95xuWASXOUNuK6O27ANm08ay2e7eGHPrlqjuHyMNlqdspVFIq1IrZpk7STWIZGa0VEZO5RsBWZ\no6IoYrg4jIFBxsngWR7VoIof+liGhYmJgcH13/8o0Y5BXv93H+cPl76S1aZDyk7xvpc8g+2bl9E6\nSuslynzz9p9SqjkUagWGSkPk/Tx+uP/txY7KHMW6rnU8vP/hOI6j0VoREZlzFGxF5ijLsjhhyQks\nSS5hfXU95VqZSq2CH/jx3Nso3oghJISe4/jZ75/EuiggIuL5Jz6byaO0b/t/n6K7v8Rvh4N933gS\n13Q5pvsY1nat5eH9DyfpJjW/VkRE5iQFW5E5yjRNbNtmacdSemu95Kt5Cn6Bkl+i6BfJ+TnKQZmc\nn6MaVqkGVa7+4Cnc8eNTaR2lBZ+NN38EgCCa/v0d02FFegUr0itY17OOo7qOwnVdbbggIiJzloKt\nyBzSupNYLagxUhxhqDDEruKueCexyhivfOwbMIErbt7Ydu2emy1EPOddV3Py2dsPqA+O6bA8vZwV\n6RWs6lzF6s7VJN2kph+IiMicp2ArcoTVVy5o3UlsKD/EcGGY0fIow+VhxspjBFHABzZc1hiLfeXL\nPseXr3szP75uBf/3lf1vtrA/STvJ8vRyliaXsqJzBUd1HkXSTWLbtkZpRURkXlCwFTlCTNPE933C\nMCRXyTFUGGJnYSejpVF2lXaxq7yr8VDXi95xLSfesaVtgkGpw+OyDe8FHFqnHpz49Ft54bt/RjTF\ntIPJI64GBj2JHgaSAwykBljZuZKVmZW4tqtAKyIi846Crchh1LotbkdnB/eP3s9QYagtzE5eaut9\nGy6bNMEAXvuJV3P1P/wLkzdbeO9NH6AW1ihV4/tExOnWNm1sM1531jAMurwu+pP9ja1xl6aXMpAe\naGy8oEArIiLzkYKtyGHQOne2UCmwNbuVe0fvpZQtMVwaJufn9npt69oGPpBOjFP7h05aR2k7VtzH\nCz93OVvGawS7V0aoB1sDA8u06PF6WNe9jvVd6xnoGGBZZhkDqQESTgLLsrAsS3NoRURkXlOwFZlF\n9UBbq9XIlrM8MPEAQ/khBouD3Hn/nSxZumTKa+qvURSx8afv47KnfZj/2nAsT7/5T1BuX8brSV94\nDom0z9Z8jTAK29pK2knWdK5hbdda+pP9LEktYXVmNcf2HUvCS2h0VkREFhQFW1l06oGxHjonM00T\nwzCmHfgmB9F6AQiCgFwlx5bxLQzmB9le2M7O4k5CQqpBda/XV2tVykGZci0u3avvJn/zw2lbxsvO\n8uSrngdAteVr9CZ6WdGxguUdy1mSXEKH00HaTWObNtlqlryfxzANbYkrIiILjoKtLAqtqw7UghpF\nv9go9TmtBgau7ZJxM3R5XY2NCOpBt7WteiiuFz/wqdQqjTAahRGe5bE1u5UdhR1sy21jpDwCRvMB\nLtM0CYKAKIrwA5+uX/+ed17+E17xrZdRCSqNcuPLfsDkzRaO/fBZrFgR98ezPJall7E8vZzlHcvJ\nuBmSdpKkk8SxHMYr4zyQe4CJygTH9hzLkvQSPMdTqBURkQVHwVYWrNbw6dd8dhV3MZgfZLQ4SqlW\nolgrUgpKlGtlIA62nuWRdtJ0eV0sTS/lqK6j6E52Y9t22zzZXCXHeGWc8fI4E+WJOITW4iDam+zF\nMRx2FHbw19G/cveuuzFNs9Fuwk7EI8KOyVhpjKJf5NN/dw2d8QAuXzn3Op56zZO558uvYvjWC5i8\n2cJT/u2Z9KeWsyy9jKXppfQmeknYiUaYDaKA8co4Q7khspVsvDMZcGz3sRzTcwzrutdp5zAREVmQ\nFGxlwWkdnc2Ws+zI72CoMMRIaYSdpZ2MlkcbqwXsjWmY9Cf6GS2NckzPMfQn+xmvjjNSGmG0NMpE\nZYKJ6gTZapZsNUstrAGwvnM9hWqBHfkd3LbjNu6fuB/HdEjZKRzTYaI8wQQT1MIaE8UJwkrIf1zw\nn23jsQC3vPynTN5s4fRXXMczX7aN3sSL4hBrJ0k4CRzTIefnGKuMcV/uvj1WVahvibuuax2P6H8E\nnudpXq2IiCxICrayYNQDba1WY0d+B9uy2xphdrg4TDWsTqsd13TpT/bTn+qnGlT5064/cVdwF6Wg\nxFhljPHqOJWgssd1aTtNX6KPrdmt/PzBn1OtVVmaWoplWFSDKhPlCcpBmUqtQkTEi677I5f8YrRt\nPPa3DHAqg0zebOG6O76OayXxrBNxLIdirchEZYKHig+Rq+b2GtS7ve54pLb3GNZ0rdGWuCIisqAp\n2MqCUA+0o8VRNo9tZjA/yLb8NiaqE9NuI+2kWZleSbfXTcEvMFYaY6w8xpbxLWSr2f/P3n3HR3rW\n997/3HV6Uy+rss3dBq+XAMbgGIiBJ+ADJCEhBR7C4xNDgFDCSWIICSUmyQk1Mc2YcpJQAmk+JM8B\ngoFgHIPNuqzt7U27klZ1NL3c7fwxO7PSrrRqozbzexu9dlZzz31fmh2hr37zu66LiBkhHogv+Da+\nqqioikpAD3BN6zVMFafIlrLMFGeYKk5RsAq4uISMEB2BDt7w42ng/Nq0ASYp08Ls1oPnvPgYf/Dx\nJ8lZCjPlGbJWlpyVw/GcS34tuqozEBmgL9LHVe1XEQ/EZUtcIYQQDU+CrdjSqpsdZItZjk4fZTg7\nzFB6iOnS9JLPETWj9IZ7Cekh0qXKklyn06c5njrOWG4MDw9N0egKdhEyQxdNJgNo8bXQFeqiNdBK\nxIgQMSNkShnS5TQFu4DnebXNEVQq/bb/+KNX8FvPeQNlIIjDhZstfOTHnyBn5Xhs4tIhdjYFhc5g\nJ32RPgZjgwwmBvEZPlmjVgghRFOQYCu2pGrbgWVZDKWGODFzglOZU5zNnV20f7Yq7ovTG+rFr/tJ\nFVOcyp3i8PRhDk0fougU5xzreA4ZK8NMcYZ2rb2yoYGi0R5opzvUDR6ky2l+OvJTksUkZbdcq96+\n7jf+ivbhKe7+0ccoO2WKbhFd07HKFqFgmlI+zOwqbaRzlHd+7XOkl9Y5UdPia6E/2k/aJ9YRAAAg\nAElEQVRvuJcdiR1E/BHZFlcIIURTkWArthzP87Asi5nCDAcnDzKcHeZE6sSSe2jjvjj94X50VSdV\nSjGaGeXQ9CGOJI9c8hyZcoZsOUt3uJv+SD/tgXZKTonpwjRThSkOTx/meOp4bSLZd97wQ4xZj//p\nfZ9i5KoeDNVgW3gbX/qlz3PhMl5/8v0PLPv5iJpR+sJ9dIe72dmyk5ZASy3QSpVWCCFEM5FgK7YU\n13WxLIszqTMcmjrE0dRRpotLazsI6AEGI4MEjSDJQpLpwjQHpw9yNHkU27MXfXzUF+Watmu4rOUy\nym6Zs9mzjGRHODR9iJHsSKVSPDLC995zhGqNdPbEsL/69FF+/a97mB4L8B+v/8Kce1WjwB9/5y9r\nmzXMZ3ZIVVBoC7TRHeymPdhOX6yPrnAXuq5L24EQQoimJcFWbBmO41AsFzk0eYgTMyc4PHN43tUJ\nLqSrOn3hPtr8baRKKU7OnOTJySc5kjxy0Ra08wnoAa5tu5bB2CCO6zCUHmIkO8KR5BGSpeRFx8+t\nwYIN/MIXbwZgeBiOvvdf5xzx8j/8IM98sY1te7iei+u5lTVzPbfW36tremUDCc2kO9xNd6ibjlAH\nfdE+WoItldYICbRCCCGanARbselVJ4hlChmenHiSk6mTnEifWLSXVkGhK9hFb7iXvJXnTPoMh5OH\n2T+5v7ad7aXois7lLZdzZeuVOK5DupTm6cmnOZo8iq4t0Lva04PLERRgPAi/dvfNtbsmRk2Ovvfb\nzJ4g9rZvvZOyW2Y0Y2E5FrZr43JxsG3xt7ArvosdiR0MxAboi/XN6aGVQCuEEEJIsBWbXLX1YCw7\nxoHJAxydOcpEYWLRx8XMGNtj2/Fcj7HcGKfTp3l07NElL//VG+7lhs4bMFSDvJXn+MxxHhp5iFQp\nRdSM8vB/fwINeNEXb77osdXPqYpKSKtspDBx1uTpO/+e2aH21s/+MkNpsFwLy62E2tnLeCko9IR7\nuKzlMnrDvSQCCbrD3WiqVtku1zBkYpgQQggxiwRbsWm5rkupVOJo8ijHksc4nDxM3s5f8jG6ojMQ\nHSDhSzBVmGIsN8ajY48ymhtd0jUN1WBv1176In3krTxD6SF+PPxjRrIjADz0R6foLJ6Pp//fvU/z\n+TdeVXu8qqgEtABBI4ipmliuxclHO3j4L/6a2aH257/4YiYzlbVxLxQ2wgxEB9ge205rsJWoGcWv\n+xkvjHP/mfvZGdtJPBCn19e7tCdSCCGEaBISbMWmVO2nfXLsSY7NHONY6tiimxK0+lsZjAxSsAuc\nTp3micknODR1CJfF+2gBWvwt3Nh7I4ZqMF2Y5icjP+HJySfntDzMDrUAN+2f5gvzhFnLschbeQ49\nFuPYR+aG2hd84YV4zG0d8Gt++qP9DMQG6Ah2EDJChMwQAGdzZxkvjNe+ftdzpfVACCGEmIcEW7Hp\nOI5DoVTgibEnOJo8yvH08Userys622PbiZpRJvOTnE6f5uGzD5MpZ5Z8ze2x7ezt3EvRKXI6fZrv\nnvwuqdLctoUj7zhVi6cl4FV/+1LCRpjuC8JstpwlVUpx4IHLKX9lbvvB8++9hepqCH7dz47YDvqi\nfXSHugmbYUJmCFM1mS5Nczx1/KLWCRWViBkh5otJG4IQQghxAQm2YlNxHId8Mc/jY49zJHmEU5lT\nlzw+4UuwI7qDgl1gKDXEo2OPcnTm6LKuORgd5FldzyJXzvHo+KP8ZOQn81aHZ3+zvP5rryEKlJ3y\nnDCbLqdxPZfhn/4c9le/xuxQ+9x7nk/QiNIX7aMv0kdcj5MIJwgaQQJ6gFQ5xZnsGZLF5IJV5r5I\nHz3hHny6T6q2QgghxAUk2IpNw7ZtcsUcj489zuHkYc5kzyx4rILCYHSQVn8rk/lJhtJD/GT0J+Ss\n3LKu2RHs4Oe6f46clePBkQd5dOzReY8L6kFsKt8ww1GdvJUnb+eZLk6TKqXmLBs2/MAt2P9YXafW\nAxxu/+c30x/9f+gIdRA0ggSNIOVCGTQYy48xXZxedC3dqBllMDrI7tbdGIZxyWOFEEKIZlTXYPun\nf/qnfOADc3dO6urqYmRkpJ6XEQ2oupzX42OPc2j6EKP5hSd7+TQfl8UvQ0HhTPoM+8b2cTh5eEXX\nvabtGop2kX1n910UahUUor4o7YF2fJqPl3+5D8d1yJQzpJNHKTiFi843/r1fxv7W/2R2qP3Ug/cQ\n8/08ASOAqZukSilG8iM8feJpOro6ljTOgB5gd3w3l7ddjt/0SxuCEEIIMY+6V2yvuOIKfvCDH9T+\nrmlavS8hGojneTiOQyqf4vGxxzk4fZDxwviCxyd8CXbGdpIupRnJjvDg8INL3nnsQiEjRHugnZnS\nDI+cfaT2eRWVhD9Ba6AVXdWxXZuslWUiP8FkfhJVUWutAKZm0h3qpifcw+Fv/DKnvvVqZofar/zs\nGyhqgrydZyI7Qap8vrpb3Xp3MQE9wFUtV3Fd53W0hdrke0oIIYRYQN2DraZpdHQsrQolhOM4zORm\neGzsMQ5MH2CqODXvcQoKfZE+OgIdTOQnOJ48zk9Gf0LZXXyjhYUU7SKO56ApGs/f9nwOTh1EV3WC\nRhBFUWqbMkwVpig7ZcJmmKvarqIj2EFbsI24P07UjGKoBv//569h3zdvZXaoffu/vZsnJv0Y+srX\nm50darsj3RiGIb21QgghxALqHmyPHz9Ob28vPp+PZz/72dx1111s37693pcRDcBxHLKFLI+PPc7T\nU08zXZq/8mqqJrvju9EVneH0MI+OP8rB6YOrv77nsH9yP89sfyY399/MiwZeRNktU7SKlNwS+XKe\nsltGQaHyPwVN0fBpPkzdRFcr3z5f/MvLeORfXsT5UGvz2n94PYrSVdkKd4VBNGbGuDxxOVd3XC2h\nVgghhFiCugbb5zznOXz5y1/miiuuYGxsjA996EPceOONPPXUU7S0tNTzUmKLcxyHfCnPE+NPcDh5\neMFQG9SDXJ64nIJV4HT2NA8OP8hkYbIuY1BQsBwLF5eIGcFQDQpWgZyVo2gXefXbP8vl+4co6gof\n/NYfkrWy5KwcjutQdstkrSz/dfevMfngxaG2M9RJyAyteLvb7mA3u+K7uKbjGhLBhIRaIYQQYgnq\nGmxf+tKX1m5fc801PPe5z2X79u18+ctf5h3veEc9LyW2MNd1KZVL7B/bz5HkEcYKY/MeFzNj7I7v\nJllMcjJ1kgfOPEDJKdVlDB3BDvZ07CFshilYBX50+kc8OPIgY7kxTM3E8zz+x/4hFMBve3zlwFeA\nStCO+WKYusn+T72d5COvZHao/bV/eB0doU7CvvCKQq2maOyM7WQgNsDV7VcT9ofRNE1CrRBCCLEE\niud53uKHrdwLX/hCrrzySu6++24AUqnzC84fOXJkLS8tNiFVVYlGo5zIneDA5AGeHHty3uO6I91c\n2XElM9YMh6cP86OhH81ZUmulor4oN3TfwLboNkpuiWQxyX+d+S8OT89dVeHh95+lt1CJrA6w7c+7\nAEgEEoSNMPs/9iGKR36B2aH2Vf/rV2n1t+JTfJTLy+/9TQQSXN15Nf2RfnoDveRzeSzLWu2XLIQQ\nQjSM3bt3127HYrGL7l/TdWyLxSIHDhzghS984bz37927d9nnfOSRR1b0OLE8a/E8e55HuVzm8ORh\npvPTJLUkPT09Fx3XG+qlO9TNWG6Mg+mDPDb9GKFwaFXXNlUT5eBL2Bn2s+0qi2w5y76xfTwx/gS2\nZ+Pz+eaOoXA+su782AA+QFVUTMPkqY9+hOLRmzh/hMWvfv11dIS2EfPHllypHRkZoaenB1VRGYgM\n0B/p57K2y2gLtmEYK59wJuaS/89YH/I8rz15jteHPM/rY6XP8+wC6XzqGmx///d/n9tuu42+vj7G\nx8f54Ac/SKFQ4PWvf309LyO2IM/zsCyLUzOnODJ9hMPJw3hc/GbBjugO4r44I5kRHj77MEeSq6/q\n90X6+Ltf/hKgcj6MLixEltv4PgEK/Ijnc/Yd3fMcdT7U/to/vJ72YMeyQm1V1IzWWg92tezCb/ql\n9UAIIYRYoboG2+HhYV772tcyOTlJe3s7z33uc3nooYfo6+ur52XEFlMNtaOZUQ5OHuRA8sC8W9bu\niu0iZIQYTg/zwPADDGeHV3Vdn+Zjb9de7rr1A5wPtcz6c345InyL2xY5uweU+Y1vvJH2UBdhc3k9\ntYZqcFXHVTyj/RlSpRVCCCHqpK7B9qtf/Wo9TycahOM4JAtJnhp/igPJA1juxX2jO6I7CBthhjPD\nfH/o+6te+aAv0sfezr28/fm/y5xK7W9vRzvxRpz9r4B0L5RDVL4NlFkf8Hx+yCRtHOCaC85crdQW\n+MXPvYmg20XYDCw51Coo9IR62BbeRsgJsad3j1RphRBCiDpZ0x5bIVzXJV/K89TP/g+5H3+LwvOv\nvuiYweggMTPGcGaYHwz9YFWh1lANntX1LHojvbzlxv8OaFTDqPrmF9DeB/5r74Xb7r3keYbO/Tlw\n7k9d1YmaUcJmmLg/DvkWruzrxmdUdiBbSiht9bfSH+lnW2QbOxI7GBseI+gPSpVWCCGEqBMJtmLN\nVCeLHZg4wM+/6P9FAW7jm3z4+39SO2YgMkDCl2AkM8IPT/+QicLEiq8X98W5qfcmDM3gLTfezvlK\nrIf6K6+lb/fpFZ/bVE18mo9WfystgRZMowPfElsHQkaIwcggPeEedrbsJBGorEt7LHtMQq0QQghR\nR/JTVawJT1HwVBU3HmPoG1+pvclvAu+75f1w+jR94T5a/a2MZkb50ZkfMZaffz3bpeiP9PPigRej\nKipvv+kOwKAWam++i74bH1rxuRUUgnqQbZFttIfa6Qp30d66eKg1VZNdsV3s7djLs3qexQ09N9Ae\nacc0TQm0QgghxBqQim0TmL1U8UK3L+Tz+XCciyd4AXPedl/oNlR+a9JLZQ49u53xRJCOZL4WcP/k\ndV8gH/wKf/e9j/PA8AOMZEeW90XNcm3btVzZeiU5K8f/eNHvUInP53phd/9v+l55z6Ln+PJHTvH6\ndw3Me1+Lv4Xt8e10hbuI+WOL9sP6NB89oR66gl0MxAfoi/XhM3zSRyuEEEKsMQm2DaYaVj3Pq912\nXIeyU8Z27QU/HNeZs/zWiewJlAkFhUr/qKqo6Kpe+dB0DNU4/3dVx6ed7zV1r7oKncoUq3/9vV/E\ndm0+/U/vhtOned/rvlALt8F8kYdGH+JM5syKv949nXvYGdtJupTmPS9/PdgRaqG2bR8Db37boue4\n5YFhXnAGTrzjFENBuPnPKgFXQaEz1ElfpI/eSC9h36V3AQvqQXrDvXQGO+mN9NIb7SVgBtB1XQKt\nEEIIsQ4k2G5x1QA7O8QW7SIFu0DRLlK0i5SdcuWYc8HVw7vo7xdK5VOU3Lnb156LuZXbijLn76qi\n4tf9+HU/XYcO1R6z/7Y9KNXK8LZtfPiHH+Jdt7wXnws2cCJ1YsVf++xQ+6e//nLcXBe1UOsfYeA9\nv7Sk89z7j3ZtrYOP31L5ljBUg75IHwl/go5gByEztGCojZpRekO9dIQ62BbdRk+4B9Mw0TRNWg6E\nEEKIdSTBdguaHWZt1yZbzpItZ+eEWBe39mfdrsv5MHxRFvagXC7jOu6cxu2Z4gy6qmNqJqZW6Tn9\n50e+wuHpw/zg9A/mOdHSXN9xfS3U/sU7rqZ89hpqoVZJM/Dh5y3pPH/1uaHaqrYe8M8v7q0E1XAv\nITNE1IyiadpFoVZFpTXQSlewi/ZgO/2xfjpDnei6LhVaIYQQYoNIsN0iZofZkl0iU86QKWUo2kUc\nz8H13LqG2JUwVZOyU54TFEtOibJTpmAV2Bnfied5jGRH+PGZH+N658dbDYIfuOsRfnx1gm//t50L\nXqcv0sfuxG5SxRSf+HCY1OOv4Pz6smUGPvqMJY/51Qe82iN//i0+tkW20eJvIWgEcTyHslsmZIRq\n4/NpPjqDnXQEOugMV1oOWgIt6LouPbRCCCHEBpNgu4nNDrMFq0CqlCJbzlK2y7i4OJ4zbxvBRlBQ\n8Kt+Dk0f4goqE8cczld5Q0aIbZFtTOQnuP/U/SRLSVRFRVM0dPX8y/D5R3I8/0iOd/3LGW794s0X\nXcen+djbuZe8ledr3xhl7LufYPb2tgMfu3zJY77/j0/VQrgLBJ51M2EjjE/3kSpX9qJO+BPomk7c\nF68E2mAH3eFueiI9hHyhWruBBFohhBBi40mw3YSqYdZxHVKlFDOFGQpWAYdKZXazhNnZglqQifwE\npzOnefN9t190/+WJy8mVcxycOsjZ3FkAXM/FwcFyLTRF4yvv/ilQiakGcP8bfsjr37mD09ee35J5\nT+cePDx+9ORJnvj0X3M+1NoMfOyyZY15PAzbs5VHv+rvXkHiXJV2LD+G67lc1XoV17VfR3ekm9ZA\nK92RbjrDnZi69M8KIYQQm5EE203iwlaDZDFJqpjCcq1NVZmdj67oKJ7CcHqYA9MHLrq/PdBe21ns\nsbHH5txXncjmei6v+Ys93Pu+x7hu3KmtnPC/PnqcnHKcl3/hZlRUesO9HDye477fnR1qHQY+tnvZ\n4/6d911HT6iH4HiSsBkmU84QMAJc31np3+2P9rMjsYOuSBdBMzhvr60QQgghNg8JtpuA61YmemVL\nWaYKU+TKORwcHG/+dWQ3m5AW4kTyBEdmjlCwC3PuU1G5LHEZ6VKax8Yfo+gUFzyPh8dvf+AZKCj8\n5I6foVKJriGvEvwTgQSKonD3b72b86HWZeBju5Y13oAeoDvUTcSMEDJCRC8bqEwYi/RWPmeG2BHb\nwY7EDsL+MIZhLHnbXCGEEEJsHAm2G8jzPFzXJW/lGcuOkbfylYlgGzwJbDn8qp9MKcNwdphTqVMX\n3d8d7kZTNMbz4xyaPjTPGS7m4fFzn9nDf7xlH3EbftZr4HkehmrwlhvfRKWDtxpqF55kdiFd1ekO\ndbMjvoPecC8dwQ6CZhBDMwgaQUJGCNuzcT0XTdUI+UKYpimBVgghhNgiJNhugGqgLdpFJnITZEqZ\nSqDaQoEWKtVYUzE5mj7KgakD846/M9hJ3srz1ORTc1ZBWIoX/80e4Nz6uXaBr//qV6juAm1SoEgI\n9x1w1y0a99627aLHa4pGzBej1d/KjsQOBqIDdIW6iPvjaKqG67n4dB8lp8R0cZpTmVMU7ALXt19P\nX6yvVqkVQgghxNYgwXYdVQNt2S4zkZ8gXUpjudaWC7RVIT3EaGaUk6mTJEtJAD57W2X72qIC77rv\nTcR9ccZz4wylh1Z8HQ+Pn/3OT2HWGgZ5QiiABrz3+w7v/f4pHODP/viXyd24HVM1CZthwkaY1mAr\nMTNG1BflObufjwL8/X13kWoPky5X/g2qOoOddEe6ifqjMjlMCCGE2GLkJ/c6cV0Xx3EYy45xLHmM\n6eI0Jbe0ZUOtqZhYtsVwZpjDycMA9D5UCa8KkAtotAfbsVyL0ewoJad0ibNd2r47qqFWAVye9/kX\nkDUVXCoNCdV7dOB9H/wmg7FBrmq/ir1de7mu4zoGY4P4DT+HnrofjUoY/s3b7mSqODUn1Coo9IZ6\nGYwNyiYLQgghxBYkFds1Vq3SFqwCI5kRCnYB27M3elirFtSCHJ46zOHk4Vo4/MO7vl2b0nXn136b\nK31xSnaJ4czwiq+z744HoTaNzKP9Pc+iYMMLP3k9CgpBI8j33vij2gvZ4/xmD1k7Cw4MZ4eZKEzw\nx698f218J3a0XXStjmAHPZEeqdYKIYQQW5QE2zXkui6u6zKeG2e6ML2l2w5m86k+0qU0Z3NnGc6e\nD60XvpiUc60DZbe8iqsZ1FZA+O29xOPn7/HwyFt5br7nuVzTfg1XHTG57uQYvZFebM/mdPY0U8Up\nAN53y/vn7Ij2t/f+7pyr6IpOf6SfwbhUa4UQQoitSoLtGmjUKm1VQA0wlB3i2Myx2ueUWoyt8Kt+\nDNVAUzRM1URTtNqatctbk/d8HN3zc3Pv6Qx1sju+m8HYIBFfhNhgjEk8RlLHSZaStXD6svd9tdau\n4AHfe9UNF12lP9LPQGxAqrVCCCHEFibBts48z8NxnIar0lbNrtaOF8bROLclrseciuh4bpygHmRX\nfBfxcy0JmqqhKZUPF3eZqyRU1vQN6kF2JXaxM76TlkALQSNIQA8wU57h0fFHSZVShM3KtrhQaUso\n+81alHaAH7/t5XPOHDEi9EX72B7fLtVaIYQQYguTYFtHrutiORZnUmfIWtmGqtJWBdQAp7KnOJk6\niV/1Y7s2qWKKvJWnRKVxoAScSJ3gbO4s3aFuusJdRM0oI7kRdFXHUA0MzcBQDYAFN6LY99ZvU62z\nPvdtf8wLBn+BnnAPQSNI0Ajiei7DuWFGsiO1jSEUFNKlNEE3SMgMAfC9O3+J7935S/NeQ0Fhe2w7\nu1p24TN9Uq0VQgghtjAJtnVQ3Qq3YBU4nTpN0SlumV3DlqNarZ3MTTKZnyRdSpOzcqRKKTLlDM/7\nzJ7zB7s2mXKG/ZP7ubr1al6y4yU8OvYoT4w/QcpK4dN8+DQfpmZiauacCm5AD9AZ7GSflaid7g2/\nsbN2/GRhkmOpysoSF7Y1eHg4OLXNLiJmBFVVF6zCdoe66Yv20RHqQNO0+j9pQgghhFg3EmxXqdpP\nmy6mGcmMUHbLDdV6MFtYDXMod4inp55mLDfGVGGKTDlzycc8NvYYmqJxZeuVPLvn2VzfeT2ThUny\nVp6iXcRxHSK+CAl/grAZJqhXdgIzNIN/mrUaXdktM5IbYTw/PmeJroU4OLXzR31RdO3iFgOf5qM/\n0s/ult2yGYMQQgjRACTYrkI11E7kJpjITWB51jInRm0dUS1KupTmWPIYT048yURhAsddvCrt4fHI\n2Uc4lT7FlS1X0h/tJ2SE5kwkM1SDkBEiYAQI6AFKTol0OT3rLC6PTzy+7DG7uJTdMjPFGSK+CKZW\n2R63GmC3R7ezI7GDkC8kLQhCCCFEA5Bgu0Ke52E7NsPp4coOYt7iVcStKqgFMTB4fPpxfnzmx5zN\nnV32OSbyE0zkJ/BpPsJGuBZi/bqfslOmYBUIGAH8mp+wL8z+73edf7CeX/HYPTxszyZdShMyQwT0\nAACtgVZ6I730RfvQdfk2EEIIIRqB/ERfgWqoPZ06TaacachJYlVhLYzjOAzlhjg0dYiD0wdXdb6S\nU6rsQla8+D4FhY5gBy1uCz/4yEeoThy7/Z/etaprVsNttpTF8zwiZoTB6CCXtV4mLQhCCCFEA5Fg\nu0ye52HZFkOpIXJWrqFDbUgLkSvnyJVyHJs5xv7J/Qse+8gd+wBIafCiu/cseNyleHiM5cfOTSKr\n/0QuB4dcOccViSsYjA0S98dlwpgQQgjRQCTYLsPsUJu1sg258kFVa6QVy7Y4kTyBqqgki0lOpk7O\ne+zn3v9YbfODT7z04q1ql2uiMMHsVXEVlLr1LneGOumJ9NARlFUQhBBCiEYjM2aWqNp+0Ayh1lRM\nYqEYR6ePMpGfIFVKMZQeWnA1gmeMnl8F4r5X9Nd5NC4+1XfBvmYrE9SDXNV6FYPxQZKlJBO5CVzX\nxfMac8KfEEII0Wwk2C5BLdTOVNoPGjnUaoqGX/VzOneap6aeImSGyFt5jiSPLPiYer+IHn3vF8/d\n8uh5wTfIW3kMxVjVOVVUrmu/jsH4IKqqknfzlQltEm6FEEKIhiHBdhHVJb0aeTex2cJamFOpUxya\nOkTWyqIpGjPFmUuuhDB7K9168Cavrp11229+nGQxieM66MrKO2cuS1xGf7SflkALOScHgOVZta2P\nXbcx1x4WQgghmokE20uohtqz2bMNv/oBVJb1minOcDp9msdHH6c33EveynN05uiSHl+/muf5tgPb\ntRnPjTNTnEFDW1FLQlewi92J3QzEBsg62Tn3WZ7FWHaMbDkr4VYIIYTY4iTYXoLruiSLSabz0w29\nTi2AruionspQaognp55EV3XaA+2VYJu8dLB99VvbKAE/3VavuYhza8B5O0+ylCRTzmCq5rLOFDJC\nXNN2DTsSOyh5pXnbSMpumeH0MCWrJOFWCCGE2MJkVYQFuK5L3sozlhmj7JU3ejhrLqSFOJE8weHk\nYTLlDD3RHizHYiQ7Qs7KXfKxQ1f3c+Nn6jNpbGho9t/O/zIxVZgiqAfx6350VV9S9VxTNJ7R9gy2\nJ7ajaVqtBeFCHh4lp8Tp9GkG44MYiqxtK4QQQmxFUrGdh+d5lO1zVTy3tNHDWXMBLUCymOR05jQn\nUicA6Ah1UHSKDKWHFnl0fU3e9SDVjRna7ryx9nnXcxnPj5MqptDRF21JUFC4tu1aBuODJPyJBUNt\n7fy4FOwCI5kRmUwmhBBCbFESbC9QXQHhTPoMRbtYt/VTNysVFROTM6kzPDX1VO3rbQu1UbJLjGZH\n13lE51c/6L+gCFywC8yUZsha2UVXSbii5Qp2JnayLbqNjJ1Z0pWrW++OZcck3AohhBBbkATbWaqT\nxUYzo5VlvWjcZb2qAlqAsdwYpzOV7YEBImYETdVIl9Kky+l1HtGl11iYLk6TLVcmgKkLvHy3R7dz\nWctl7IjvIOfkcFl636zlWUzlp0gX0xJshRBCiC1Ggu0snueRKWVIFVMNvwICVHpQVVRGs6NzVj5o\n8bdgudaSqrXf+919FzbG1sn8odJ2bZLFJNlyFkO9uGrbHerm6rar2ZXYRcEtrOjf0fIszmbPYjmW\nhFshhBBiC5Fge47neVjOuUDT4CsgVAW1ICOZEU6mT1J0irXPx31xLNdiLD92ycf3PzVEzIFH7prk\ni+99dNXjOfi53z93y0PtfmzB42ZKM2TKGVzXReP8trit/lae0f4MdrfsxsJa8b+jh0fJLTGaGZWW\nBCGEEGILkWDL+RaEsewYRafx+2qhsryX4ziczZ7leOr4nPtiZgzbs5nIT1zyHF/768la48AbPnT9\nqseU3/crVFsRnvkn/33B41yvsgxbupRGVysLe0SMCM9sfya7W3bjqd6qJ/05nuRACwQAACAASURB\nVEO6lCZVTEmwFUIIIbYICbbMbUFo5O1yZwtoAUazo5xIn8B2z79d79f8GKpB3sov2l9b/7Xilv5y\nTJfSlT5o1yGoBdnTsYfdrbsxdIOCU6jLaGzPZiw7Ji0JQgghxBbR9MG2GVsQNEXDcz0m8hOczpye\nc1/EjGC5FpP5yUXPU/+VXpe+Oa+HR6qUwrIt9nbtZWfLTsK+8KLLei2HtCQIIYQQW0vTB9tma0EA\n8Kt+xnPjnM6cnlOtBTA1E8dzFt2UAZYTQ5draVVz27W5vvN6did20x5qJ2tnF3/QckciLQlCCCHE\nltHUwdZ1XXLlXFO1ICgo6OhM5Cfm3XzBUA08r7IT11J4sIzFtBa27833U9uY4a2vWfT4sBHm1u23\n0hXuImyGsV17zX4xsT2b8dw4jutIuBVCCCE2sabdUtfzPDzPYzw33hRLe1X5VT9ThSlGsiNzVkKo\nMlQD13Mp2YsH272f2cMzH6jTUl9uuHaz/+pLnzPmi3Hr9lvpDnWTtbIcSR7hmo5rUFDWJNxWt9yd\nyk/REe6Q7XaFEEKITaqpg22mlCFv5Ze1gP9W51N9HM8fZygzf3isBtuifXHonc9jN/UvftCSLO3N\ngxZ/C7duv5XOUCdFp8ij449yTds19ER6CPlCFN2ljXu5bM9mujBNIpDAVEwJt0IIIcQm1JStCM1a\nrTUUg4JdYKowxUxpZv5jtHMV2yW2ItTfwr9kdAQ7eOmOl9IV7iJn59g3vg/HcxjJjjBVmMKn+tZ0\nZJZb2ZXMdZvnFyEhhBBiK2naYJssJinazTNhDMBUTabyU4zkRhY8ZrkV23oY+u4t5//im5r3mJ5w\nD7cOViq1qVKKx8Yfw/UqAXOyMEmykMR2bTRFm/fx9WB7NslCUpb/EkIIITappgu21c0YJnOTTVWt\nhcqmDNPF6UtulasqKh7euga3yX/8MNWJY3s+8bKL7t+d2M2LB19MR7iDqeIU+yf3z/mFxMNjNDfK\nVH4dqrZeZSk0qdoKIYQQm09TBtvpwjQlp9R01dpMKcNEfmLeSWNVRbuIruiEzfCCxwD89I59PHDH\nPhiqx+Sx+ausmqLxvN7n8YK+F9AR6uBs7ixPTT0177/baG6U6cI0pmrWYTwLczyHmeIMJbskVVsh\nhBBik2mqYFut1k4Xpptmea8qn+pjqjDFaG7hai1A3s6jqRpRX3TBYz73/sfQAD9w2+P1GN3FK+JG\nzSi/uPMXubb9WhL+BAenD3IoeWjBM6TLaaYKU+TLeQzFqMegFlSdSCZVWyGEEGJzabpgmyllKDvl\npqrWKigonkKykGQsN3bJYwt2AV3VifgiCx7zjNHzge6+V9RrVQSoThzrj/bz8l0vZzA2iKmbPDz2\n8KKBHGAkN7JuVdtUMSXr2gohhBCbTFMt91WdNNZs1VpTNUmX0kwUJhbtK85blYpti79lwWPq+dvQ\nvnd/k2p/beKWu9nbtZfrOq4j4U8wXZzmqamnlvzvNZ4fZ6Y4w7bYtqVuXrZitmeTKqVo1Vpl6S8h\nhBBik2iaiq3neZTsErlyrqnWrYXKMl8zpRkmChOLHpsqp9AUjfZgOyEjNO8xdd1KN3O+4vumPxxn\nT9ceWgOtnEid4InJJ5b1S0jezjNTmqFoVfqE15LjOSQLydrScUIIIYTYeE0VbJPFJM5al/I2IV3R\nSRfTTBYmFz3W9VymilOYqslAdOCSx9Ynzp2vdu5q2UXICLFvfB+nMqdWdLaJwgQzpZk177P18Cja\nRbLlrARbIYQQYpNoimDreR6Oe64vssnaEAzFIGflSJaSS950YTQ3il/zc1XbVQuuC+sB1irH1hHs\nYHb9N2tleWj0oQU3j1iKicIEqWJqzftsYW7VVgghhBAbryl6bD3PI1VKYbmrjWJbj6EaTOYnmcgv\n3oZQNZ4fp11tpzXYytVtV/PExBNz7t/7mT2rGlPEjLCncw9Geif/p/bZMvsn96/qvAAzxRlSpRSu\n56KirmnbiYtLtpzFcixUVZVeWyGEEGKDNU3FNlVovmotVCq2qVJqSf21sz01/hRRX5Q9XXvoCffU\nZSxhI8yzup7Fqy57Fdd2XMtfvvZ2qhPHXvI3b6vLNTw8JguTpIopDHVt2xHg3AoJpZRUbYUQQohN\noOErtp7nYbs2BbvQVEt8AaioOK5DupQmXU4v67ETuQlOpU+xLbKNW/pv4T9P/yenM6eXPQZN0RiI\nDrArsYveSC8BI0DICDGWH2P2y6+/jquGTRWmSJfSRP1RSiyt/WKlHM8hU8rQFmxb0+sIIYQQYnFN\nEWyz5WxTVmt1VSdbzpIsJVf0+GOpYwT0AJ3hTn5h8Bc4PH2YpyafWtL52gJt7ErsYntsOxEzQsAI\nYGom4/lxnp56moyVoc7rK9QkS0my5Sy6qq/5sl/VSWS2a0s7ghBCCLHBmiLYZkoZXK+5lviCShvC\ndHmameLKJ2M9OfUkg9FBdsR28Ezjmexu2c14fpzJ/CQzpRls18bzPAJ6gJgvRswfI2bGCJpBgnqQ\ngBEga2U5mT7J2dzZBdbRre+/TcEukClnKNtlNLQ1XwnD8Rwy5QwtWosEWyGEEGIDNXSwra4x2oxr\n10Jlma9MObPiim3VyfRJxvJj9D9e4h1/9Fk84G//8f3YA3sq7R0eqIqKruq1D9uzGc2NMjw1TM7K\nXXTOf33PG8/d8mi9fPWTxi6ULCXJWlkCZgDHXdtg63ou2VKWhD+xptcRQgghxKU1dLAFyJVzTdmG\noKDU2jAy5cyqz1ewC7zlj+5BpdI4MNKqE7SyqErl7XfLscjZObJWlryVX3RpsfH9N1CdOPbq//np\nVY/vQslikmwpS8QXWfM+WxeXXDlX+0VKqrZCCCHExmjoYOt5HhmredsQsuVsZcZ+nXpYZ79YTqZP\nrvJsa7sgx0xpptJnu8Y7kFU5nkOunCMaiK7L9YQQQghxsYZe7svzPLKlbHPuNrbKiWPzqW8dcm0m\njlVlrUql2nEd1HV4mbueS8bKyLJfQgghxAZq2GDreR6WY2E5zbcpA1SW2cpZOVKlVN3OuTZRdL7J\nZPWRLqfJW/kFd0+rJxeXolWUYCuEEEJsoIYNtgBFu9h0a9dWaYpWWx2g3lbb2HHPf/sEtY0Z7vxw\nHUY0v0w5Q8EurEuwrS77Ve2zFUIIIcT6a9hg63mVoNGMqyGoqNiOTcEqUHbLdTuvd+7j4I74Kk9k\n1m72P2d4dee6hKyVpWAV1q3P1vVcinZxXa4lhBBCiIs17OSxarBtxupZrVpr1bdae8d9t9fpTOvz\n+1S2nF23ii2cr9oGzaCsjCCEEEJsgIat2AIUrEJTVmyrwTZbzm70UBaxtv82OStHwS6g1Hna20Kk\nYiuEEEJsrIYMttWJY7a7dhOTNjNN0ShYBbLW5gu2P/nKc2u3zcjEml6rur5s0S6ue5+tEEIIIdZf\nQwZbkIljazVxbLWe+NpvUp049vq/f9+aXy9jyQQyIYQQolk0ZLBt5oljUJk8VrAK825lu/HWp9+1\nKlte/wlki+26JoQQQoi10bCTx2zPbsqqmYZGySmRs+q3lfDb3v4Nrj4+g0c9JpCt7cYMF8pa6zuB\nDMB2mrMFRgghhNhoDVuxbdZwsRb9tVccn0Gh3juPrc9ucJlyhoK1visjWJ7VlL9UCSGEEButIYMt\ngO3aTdljuxYrItTrRfKl136Ian/t3ts/XaezXlrRKZK387iuuy6rI3g07y9VQgghxEaTYNtgVEWl\n7JTJ2/m6nbNezQNWrrV2+/pXPLnKsy1dwS5Qdsqoytq/3D3Pw/Yk2AohhBAboaGDbTNSFRXLtSg7\n9dtxrGr1vyZszMut7JSxXAt1na5vO83Z3y2EEEJstIYLttX+2mYNFgoKtmOvSbCt368K67taRTXY\nrsduYB5e0/5SJYQQQmy0ugfbT33qU2zfvp1AIMDevXt54IEH6n2JRdlec7YhwKyKrVunYDs0hEsl\niv75nS9Z+Wke6j3/F3V9d+cqu2Vsx16Xiq0EWyGEEGLj1HW5r69//eu8/e1v59Of/jQ33XQTd999\nNy972ct4+umn6evrq+elLslx12fG/WakeAq2W8eKbX8/b1r1El/w7bv+iOrEsdv/5R2rPt9ylJ0y\ntmuvS48tNPfrTwghhNhIdf1J/9GPfpQ3vOENvPGNb+Tyyy/nk5/8JN3d3Xz60+szA76qWau1Cgq2\nVwm1m+852Lglk0tOqdKKsA6rIkDzvv6EEEKIjVa3YFsul9m3bx+33nrrnM/feuutPPjgg/W6zNJ4\nzRkuVNS6VWsnJ406jGi29d2YYbba5LF1qtgKIYQQYmPU7Sf95OQkjuPQ2dk55/MdHR2cPXu2XpdZ\nkmYMtQCKomA5FiV3dVu6njoFD/zB1/jBZ29d/OBlW/9tjstOpcd2vSq2QgghhNgYG7ql7iOPPFL3\nx6mqSlkpM5wbJl+q31quW0E0ECUYCjKZnGRiYmJF55icNHjgD74GqBz5t1/iyP3P45V/8+ZVjes/\n3v++c7c82q69f8VjW6mMnmEmMcOEO8GxsWNrfr1YMIY77lIuL145X+n3gFgeeZ7XhzzPa0+e4/Uh\nz/P6WMnzvHv37kveX7dg29bWhqZpjI2Nzfn82NgY3d3d8z5m7969y77OI488csnHeZ5HupAmkAo0\n3UL5ftVPppjBn/HT3t6+onO0t8MDuHBuE93+Qpm3v3GSv7/vyhWPKzt0HdWJY6/6s28CKxvbSiko\n+AI+ujq68LX41vx6PtXHle1XommX3sZ3sdeyqA95nteHPM9rT57j9SHP8/pY6fOcSqUueX/dWhFM\n0+SGG27gO9/5zpzPf/e73+XGG2+s12WWRqEp33ZWUOqyOcPt970ZKBEnyRADvIJ/457bVjMBcGP/\nLTy8SjuCJ+0IQgghRCOr62yad77znXzpS1/i3nvv5cCBA/ze7/0eZ8+e5Y477qjnZcQCVEXFdmxK\nzup6bAFeee9reZIruY1/JUMUULnnts+s8GwbN3Gsqrbk1zqsZSvhWQghhNgYdf0p/5rXvIaPf/zj\nfOhDH+L666/nwQcf5N///d/XdQ1bAE259FvAjapWsa3T5gw9jPFPvJoX8AMq4VTlnts+y6HvDyz5\nHENDs/9m1WVcK1FyS1jO+uw+JqsvCCGEEBuj7j+B3/SmN3HixAmKxSIPP/wwN910U70vsShd1Zuy\nalbbdayO2+lquHyPW6isZuABCv/5sTv52pt+f0mP//ZbPkm1v/Ylf/PWuo1rudarYqugoGsbOidT\nCCGEaFoNWVrSVX1dKnObjUqlFaEewfbF/7q/dvvgjji333cHs8NtZng399z2ySWcyazd6u9f9bBW\nbD3XstUVCbZCCCHERmi4YKsoCoqiNGU7gqJUdh6z3NW/5f8f18coAw7wyY//CgC33/cmoEw13IKP\ne2771GKjOvfnxq4tbLkWtrv2k8eqFdtm/MVKCCGE2GgNF2yrdK052xE8z8P16rAJQn8/b73vdt50\n3+1zPn37fW/FFx3lfLjVljipbGODreu567Jxh6IoGGq9d20TQgghxFI0brBt4reD1zrAve7v/pRr\nX/NlzofbyqSyU//VO+e4//jEK2ojCnWcXtMxLcar7LO85iuPKSjoavO+9oQQQoiN1JDBVlGUpq7Y\nrofn/OaD3PrXv8PsvtvvfPh9/O8/eV3tmBPfexnVJPnrn79rXca1IK8SbtfjNdGsPd5CCCHERmvI\nYAuVim2zhQvP89bl7faqgQEumlR29tHncc+rPnbuiM3z8nJx1yX0S8VWCCGE2DibJ3nUmambTVmx\nrUd/be9DQ/TvH1r8wHMqk8psau/1O0Huue1uNsvEMVi/0K8oCoYmPbZCCCHERmjIYKsoCn7dvy67\nTG0mHvUJb++569t8/OP7+Oxt9yz5Mbff97tgpjnfyDq7aumsekyrVa/nZjGGakgrghBCCLFBGjb5\n+XV/U+0ApaBUqpJ1eLtdZWVzrG7/5rvZ9pz7OR9uKxsz3Pyuv1j1mFbL8yqTx9ayiq+iEjACa3Z+\nIYQQQlxaQya/arXMp/uash1htVbTQPCyO78+a1JZRSY8xMhIPUa2uVXfKZBqrRBCCLExGjLYQiVk\nBIxA07Uj1DNUrbT2e35SWQmj+zFuuAF6euo2rBVZj7CpokqwFUIIITZQQ0/froWMjZ+7tOY8vMqu\na3WsUNurfPzt971101RqFSo70q1ln221YiuEEEKIjdGw5cza28JN1IpQDW+r8Qd3fBWo/C7w53e+\nZNVj2uhKbVW9Q/98ZOKYEEIIsbEaNthCpWKrKdpGD2Pd1CO8/cVnXssH7nwJOQWGn9Nfp5FtPAVl\nTXcdk4ljQgghxMZr2GBbrZqFzFBT9dnWo1o4/Jx+fuvzr6zDaDaPta7YqopKyAxJtVYIIYTYQA2d\n+BRFIewLN92yX83UfrFU1edlrXYf0xSNiBGRYCuEEEJsoIZOfIqiEDEjzdWOIMF2XvXoP77Uuf26\nH12T/lohhBBiIzV8sNVVvWkmkXl4qIqKpjZPkF8qTdVQFXVNVkVQFZWwGZZQK4QQQmywhg62cK5q\n64s0RTuC53nomo6pmRs9lE3HVE10VV+TYKuhEfFJG4IQQgix0Ro+7SmKQtgMo9H4VUwXF0M1MFUJ\nthcyNRNDNXA9d/GDl0FBwdRN2ZhBCCGE2ASaItj6dT+mbjZ8O4LneZVgKxXbi5ja2lRspQ1BCCGE\n2DwaPthCJdxGzWjDtyO4uOiqtCLMx9RMDK3+FVsNjagvKsFWCCGE2AQaO+mdoygKiUACXWnoHYRx\nPRdd0/Fpvo0eyqbj03yVVgTqF2wVFPyGn6ARlGArhBBCbAJNE2wNzSBshht6swYPT3ps56EpGoZq\n1D18aopGwp+QUCuEEEJsEo2b8i6gKAoJf6Kh17R1PVd6bOdRq9bWuQ3BUA1i/pgEWyGEEGKTaKpg\nG/aF8em+hp1E5uFJj+081mLimKZoxPwxNFWTYCuEEEJsEk0VbBVFIe6PN2zV1vVcDE0qthcyNRNd\n0+tasdWQNgQhhBBis2maYAvUgm2jTiKrrmMrk8fmMlWzrhPHVFRCZqhS/ZdgK4QQQmwaTRdsdVWv\nvIXcoFVbRVEwVKNhv76VqG7O4Hn1aUXQFI2WQIuEWiGEEGKTaapgC6CqKm3BNgzF2OihrInqBDKp\n2p7n03yVVoQ6VGxVVIJGULbQFUIIITahpgu21aW/GnVdW5lAdrF6Vmx1Racj1FHr2RZCCCHE5tF0\nwRYqVdvWYCuG2nhVW5lAdrFqsF1txValsn1uyAyhqk35rSOEEEJsak3507latW0JtDRc1VYmkF3M\np/rQ1dWvimCoBh3hDgm1QgghxCbVtD+hFUWhNdiKT2usdW1dz8Wv+wkb4Y0eyqagKRpBI4ipmauq\n2GqKRtQXxa/7pQVBCCGE2KSaOthqqkZrsLWhqra2ZxMwAoRNCbYAYSNMwAisug1BV3Tag+1SrRVC\nCCE2sab+KV3dZtev+1Eb5KlwPIeAHpCK7TlhM0xQD+J4zorPoSs6LYEWTN2Uaq0QQgixiTVGmlsh\nRVFQVZWeSE/DTCTz8FBVlaAexK/5N3o4Gy5shPEb/hUHWxUVv+6nPSTVWiGEEGKza/qf1KqqEjAC\ntAYapyXB8RxpRzhntRVbQzXoifSgqZpUa4UQQohNrumDLVTCbXuonYAeaIiWhGo7QsSIbPRQNlzE\niBAwAisKtrqikwgkCBpBqdYKIYQQW4D8tKbxWhJkAlmFT/MRMAJoqrbsyWPVFoSOkCzvJYQQQmwV\n8hP7nEZqSZAJZBVhY+VtCNKCIIQQQmw9EmxnaZSWBMdz8Ok+wmZ4S38dqxU2VzZxTFoQhBBCiK1J\nfmrPUm1J2Bbd1hAbNwT0ACEjtNHD2DARI7Lsiq2maISNMJ2hTgm1QgghxBYjP7kvoKoqfsNPb6QX\nUzU3ejgrVl0ZIWI27wSyiLm8iWMqKn7Nz7bYNjRNWhCEEEKIrUaC7TwURSHsC9MeasdQtuZkMtuz\nCRth4r74Rg9lQ+iKTtSMEtAD2J696PEKCqZq0hfrw9AMCbVCCCHEFiTBdh7VloS2YBtxf3xLTiaz\nPIuwGSbhT2z0UDZE3B8nbIZxWFq11lAMuiPdBIyAtCAIIYQQW5T8BF/A7CXAQkYIDW2jh7Qsjufg\n1/1EzeiWbqlYqYQvQdgMY7uLV2sNxaAt2EbMH5NKrRBCCLGFSbC9BEVR0DSNvmgfft2/5VYYcHAI\nm2Hi/uZrR6hWbBdrQ9AVnagvSke4sl6tBFshhBBi69paSW0DKIqCoRv0xfrwa1sr3NquXWlH8DVX\nO4KqqMTNOCEzdMlgqys6YSNMb7RXQq0QQgjRALZOSttA1c0b+uP9W2oZsGbts42ZMcJmGO/cf/PR\nFI2QEaI/3o+u6RJqhRBCiAYgwXaJauE21o9f82+JcGt7NkEjSMyMNcRWwUvV4m8h7Fu4DaG6Vm1/\nTEKtEEII0Ugk2C6DqqoEzWAt3G6FtgQHh6g/SlugbaOHsm7ag+3EfXEs17rovmr7QX+sH0OXZb2E\nEEKIRrL5k9kmUw23A/GBLRFuy26ZuC/eNMHWp/lI+Cvb4Vre3GAroVYIIYRobJs7lW1Ss3tuA3pg\nUy8FZrkWMX+MtkDblmifWK32QDsxX+yiNgRd0YmYEfrjEmqFEEKIRiXBdoWq4XZ7fDthM7xpN3Fw\ncVEVlZgv1hTLfrUF2oj5YnOqtYZi0BpsZSA+ID21QgghRAOTYLsKqqpiGiaD8UES/sSm3X637JaJ\n+WO0B9o3eihrSlVU2gJtRH1Rym4ZBQWf6qMn2kN3uFuW9BJCCCEanATbVapu4tAb7aUz3IlP3XzL\ngVmeRdwXb/hg2+pvJeqLggIqKgEtwEB8gIQ/IaFWCCGEaAISbOuguv1uW7CtskvZJptUZns2fsNP\ni7+FqBnd6OGsma5QF4lAAser7Li2PbGdkBlC0zQJtUIIIUQT2Dzpa4urhtuIP8JgfJCQEdpUfbdl\nt0xLsIXuUPdGD2VN6IpOV7CLtkBbbdUKn+FDVeUlLoQQQjQL+alfR9Vw6zf87EjsoCPYgU/1bYrq\nbckt0RpopTvUvelaJeqhK9RFW7CNlkALvdFemSQmhBBCNKGNT1wNSFVVNE2jI9yxaaq3juegqRqJ\nQKKh1rRVUNDQ6I/2syOxg7A/LP20QgghRJOSYLtGqpPKgmZw01Rvy265VrVtBCoquqLTHmxnW2Qb\n7aF2dF0qtUIIIUSz2jxNoA2qWj3sCHcQ8UUYyYxQtIvYno2Ht65jKbklEv4EncFODNWYd8vZrUBB\nQUXFp/sIm2H6on10hDpk4wUhhBCiyUnFdh1cWL3tjnQT1IPr3p7g4eHi0hpspTfcu67Xrodq24FP\n8xH3x4n6ouiqTmewk55Ij0wUE0IIIZqcVGzXUbV62xpsJe6PM5WfYrowjeVaF20Bu1ZKbonOUCd9\nkT5OpU+te9V4JaoVWl3VCRpBfLqvVpltDbTSEapUwyXYCiGEEM1Ngu06UxSl9tER7iARSDCVnyJZ\nSGJ5Fo7nrOn1Lc8iqAdpC7bRHmxnPD++ptdbDeXcf9VA69f9tUBb/bMr2MW26DZZq1YIIYQQEmw3\nSjXcmopJZ7iTlkALk/lJUsUUtmfjeM6aVVOLbpHOUCeD0cFNGWyrFVpN1fDrfgJGAFWpVGNnh9eI\nEaEj1EFrsBVN0zZquEIIIYTYJCTYbrBq/62qqnRHumkPtTNTnGGmOEPJLuF4Di5uXa9ZckvEfXE6\nQ50kfAmSpWRdz79SKioKCqZm4tf9c1oO5qvG9oR76Iv2yaQxIYQQQgASbDeN2QG3PdROW7CNbClL\nspgkW85iezau59atiltyS3SFutgR28HPxn9Wl3OuRLXdQFM0fLoPv+5HV/VLBlqAoB6kM9hJV7hL\nqrVCCCGEACTYbjrVFgXP84j4I4R9Ycp2mZniDKlSCsuxcHBWHXKLbpFEIEFPuIeT6ZNMFafq+FVc\nWjXMqkplQli1Ojtfu8FC+iP9DMQHpForhBBCiBoJtptUNeAC+FU/nUYnHeEOinaRTClDtpylaBcr\nrQqeu+x2BQ+PkluiN9rL7sJupkbXNthW2wwUpdJqUP1QFXXR6uyFYmaMnnAPPZEedF1ewkIIIYSo\nkFSwBcwOuUE1SMAI0O61Yzs2GStDtpQlV87VJpx5XmW92sUqukW3SMwXozvUTXeom9HcaH3Ge+6/\n6m1N1WpB1tCMWsCtfm3LNRAZYHtiu1RrhRBCCDGHBNstZnbIVVWVFr2FhD8BQNEuUrSLFOwCRatY\nm3zmVf/zvFrYrf5ZcAtsi25jV2EXY7mxJVd+q8F19u3Z7QWGZqCrOrqqz6nKVr+GlWrzt9EV7qIj\n1CG9tUIIIYSYQ4LtFjY75HqeR9CsVHMTJPC8SnCtht2yXcb2bGzHnvMnHoTMED3hHnbGdnIsdQwA\nQzNq7QMXXlNV1Is+ZofY6nGzH1MPmqLRH+lnZ8tOdF2Xaq0QQggh5pBg2yDme2t/dtid/bnZt23X\nxnIswkaYslOm6BbJWTls0ybuj1fOea51oBpi57vuQn+vp4HoAIPxQRKBhOwyJoQQQoiLSLBtYIv1\nsXqeh6Zp+AwfPs3Hle1Xkrfz7J/cj0Zl+a1LnXc9xX1xqdYKIYQQ4pKk7NXEZm/vaxgG3ZFuBmID\nbItsw/O8OffP/lhvmqKxM7aTK9quwGf4pForhBBCiHlJQhAAtXB7WetlDEYHifljGz2kmu3R7QzG\nB2kJtsiEMSGEEEIsSIKtqFFVlf/b3r2FNP3+cQB/f9U2p+bU5dQ50Wm5hbOyg6QXZpEdKKKo6EB0\norxJKK2gQnKR2OEiig5gEWFEdLitoILsMOzC7GQavwi9sMJhItZEO2zP7+JP4z+1afpdX7ff+wWD\n+fjd9uHhDX5wz/d5NCoNJsdPxjTDNKhCVEqXBEOkAaYYEzJiuQSBiIiI/rBgZwAACIhJREFUfJOt\nsS0sLERISIjXY/369XK9Pf0lYWFhiI+MR3p0OiyxlgE3i/1NsepYTIyZCGu8FWoVlyAQERGRb7Ld\nPCZJErZu3YqqqirPmEaj8fEKGot+LUmYMG4CIrQR+Ob+hn+6/vnrdUSGRcIca0a2PhuR4ZFcgkBE\nRERDknVXBI1GA71eL+dbkgIkScLXr18x2TgZfT/68NP907O/7d8QERYBS5wFWfosxETEsKklIiKi\nYZH1u91r164hPj4eVqsVe/fuhdPplPPt6S9yu91Qq9XITsiGOc6MzJjMAYc1+MP4ceNh1VkxLWEa\nEqISuK6WiIiIhk0S/79j/yhcuHABaWlpMBgMePPmDfbv349Jkybh7t27Xtd1d3fL8XFERERE9B+m\n1Q7cwclnY1teXu61ZnYwDx8+REFBwYDxZ8+eITc3Fw0NDcjJyfGMs7ElIiIiotH648a2s7MTnZ2d\nPt80JSVl0JvEfn2VffXqVaxevdozzsaWiIiIiEZrsMbW581jOp0OOp1uRB/W2NgIl8uFpKSkIYsg\nIiIiIhotWdbYtrS04MqVK1iyZAl0Oh2am5uxe/duREZGor6+njf/EBEREZHfydLYfvjwARs2bMCb\nN2/gdDqRkpKCpUuXoqKiAjExMXLUSURERETkk2y7IhARERERKSlgzyjlEb7+ce7cOZhMJmg0Gsyc\nORN2u13pkoKKzWYbkFuDwaB0WQHv8ePHWLZsGYxGI0JCQlBTUzPgGpvNhuTkZERERGDu3Llobm5W\noNLANdQcb968eUC28/PzFao2cB05cgSzZs2CVquFXq/HsmXL0NTUNOA65nnkhjPHzPPonT17FlOn\nToVWq4VWq0V+fj7u3LnjdY0/chywje2vI3zb29s9j+rqaqXLCmjXr1/Hrl27UF5ejpcvXyI/Px+L\nFy9GW1ub0qUFFYvF4pXbxsZGpUsKeD09PZgyZQpOnToFjUYzYF3/sWPHcOLECZw5cwb19fXQ6/Uo\nKiriITJ/YKg5liQJRUVFXtnu/0eMhvbo0SOUlJTg6dOnePDgAcLCwjB//nx0dXV5rmGeR2c4c8w8\nj15KSgqOHz+OFy9eoKGhAfPmzcPy5cvx6tUrAH7MsQhQhYWFoqSkROkygkpubq4oLi72Gps0aZLY\nv3+/QhUFn4qKCmG1WpUuI6hFRUWJmpoaz89ut1skJiaKqqoqz1hvb68YP368qK6uVqLEgNd/joUQ\nYtOmTWLp0qUKVRS8nE6nCA0NFbdu3RJCMM/+0H+OhWCe/SUuLk6cP3/erzkO2P/YAjzCV07fv3/H\n8+fPsWDBAq/xBQsWoK6uTqGqglNLSwuSk5ORnp6OdevWobW1VemSglprayscDodXtsPDw1FQUMBs\ny0iSJNjtdiQkJMBsNqO4uBgdHR1KlxXwvnz5ArfbjdjYWADMsz/0n2OAeZaby+XCtWvX0NfXh4KC\nAr/m2Oc+tmPZ+vXrBxzh+/r16wFH+NLwfP78GS6XCwkJCV7jer0e7e3tClUVfGbPno2amhpYLBY4\nHA5UVlYiPz8fTU1NiIuLU7q8oPQrv4Nl+9OnT0qUFJQWLVqElStXwmQyobW1FeXl5Zg3bx4aGhqg\nUqmULi9g7dy5Ezk5OcjLywPAPPtD/zkGmGe5NDY2Ii8vD9++fYNGo8GNGzdgNps9zas/cjymGts/\nOcJ3+/btnrGsrCxkZGQgNzcXL1688DrCl2gsWbRokee51WpFXl4eTCYTampqUFpaqmBl/03cY1s+\na9as8TzPysrCjBkzkJqaitu3b2PFihUKVha4ysrKUFdXB7vdPqysMs9/7ndzzDzLw2Kx4PXr1+ju\n7sbNmzexdu1a1NbW+nzNaHM8phrb0tJSbNy40ec1KSkpg45Pnz4doaGheP/+PRvbEZgwYQJCQ0Ph\ncDi8xh0Ox4DT40g+ERERyMrKwvv375UuJWglJiYC+F+WjUajZ9zhcHh+R/JLSkqC0WhktkeotLQU\nN27cQG1tLdLS0jzjzLN8fjfHg2GeR2bcuHFIT08HAOTk5KC+vh5nz57FwYMHAfgnx2Nqja1Op0Nm\nZqbPh0ajGfS1vzvCl4ZHpVJhxowZuHfvntf4/fv3ucWJH/X19eHt27fMrR+ZTCYkJiZ6Zbuvrw92\nu53Z9qOOjg58/PiR2R6BnTt34vr163jw4AEyMzO9fsc8y8PXHA+GeZaHy+WC2+32a45DbTabbZR1\n/nUtLS04ffo0oqKi8P37d9TV1aG4uBipqak4fPgwv44ZoejoaFRUVMBgMECj0aCyshJ2ux2XLl2C\nVqtVurygsGfPHoSHh8PtduPdu3coKSlBS0sLqqurOcej0NPTg+bmZrS3t+PixYvIzs6GVqvFjx8/\noNVq4XK5cPToUZjNZrhcLpSVlcHhcOD8+fNcLzdMvuY4LCwMBw4cQHR0NH7+/ImXL19i27ZtcLvd\nOHPmDOf4D+zYsQOXL1/GzZs3YTQa4XQ64XQ6IUkSVCoVJElinkdpqDnu6elhnmWwb98+z9+7trY2\nnDx5ElevXsXx48eRkZHhvxyPdusGJbS1tYk5c+YInU4n1Gq1mDhxoti1a5fo6upSurSAd+7cOZGW\nlibUarWYOXOmePLkidIlBZW1a9cKg8EgVCqVSE5OFqtWrRJv375VuqyAV1tbKyRJEpIkiZCQEM/z\nLVu2eK6x2WwiKSlJhIeHi8LCQtHU1KRgxYHH1xz39vaKhQsXCr1eL1QqlUhNTRVbtmwRHz58ULrs\ngNN/fn89Dh065HUd8zxyQ80x8yyPzZs3i9TUVKFWq4VerxdFRUXi3r17Xtf4I8c8UpeIiIiIgsKY\nWmNLRERERDRSbGyJiIiIKCiwsSUiIiKioMDGloiIiIiCAhtbIiIiIgoKbGyJiIiIKCiwsSUiIiKi\noMDGloiIiIiCwr8xV38/wGdz7gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7effd05c44a8>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='multivariate_track1.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}