{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# On Browniam motion and Diffusion coefficient\n", "\n", "> In this notebook we perform a mini Brownian motion simulation in 3D and check that the mean squared displacement (the variance of the instantaneous position) follows the theoretical equation\n", "> \n", "> For a general introduction on Brownian motion simulation see [Theory - Introduction to Brownian Motion simulation](Theory - Introduction to Brownian Motion simulation.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\langle|\\vec{r}(t)-\\vec{r}(t+\\tau)|^2\\rangle = \\sigma^2 = 2 D N \\tau$$\n", "\n", "- $\\vec{r}(t)$ position at time $t$\n", "- $N$ number of dimensions ($N$=3 for 3D simulations)\n", "- $D$ diffusion coefficient\n", "- $\\tau$ time interval." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.4494897427831779" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = 1\n", "t = 1\n", "N = 3\n", "sigma = np.sqrt(2*N*D*t)\n", "sigma_1d = np.sqrt(2*D*t)\n", "sigma" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_trajectories = 100\n", "n_time_steps = 1000" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.random.seed(1)\n", "\n", "dx = sigma_1d*np.random.randn(n_time_steps, n_trajectories)\n", "dy = sigma_1d*np.random.randn(n_time_steps, n_trajectories)\n", "dz = sigma_1d*np.random.randn(n_time_steps, n_trajectories)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x, y, z = np.cumsum(dx, 0), np.cumsum(dy, 0), np.cumsum(dz, 0)\n", "\n", "r_squared = x**2 + y**2 + z**2 # squared distance form the origin\n", "dr_squared = dx**2 + dy**2 + dz**2 # squared delta-distance " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a consistency check we fit the diffusion coefficient from the simulated data:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitted diffusion coefficient: 0.99889 , True value 1.00000\n" ] } ], "source": [ "D_fitted = dr_squared.mean()/(2*N*t) # Fitted diffusion coefficient\n", "print('Fitted diffusion coefficient: %.5f , True value %.5f' % (D_fitted, D))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **NOTE:** To fit $D$ we are averaging the squared distance covered at each time step in each trajectory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we plot as a function of time:\n", "\n", "1. the squared distance $|\\vec{r}(t)|^2$ for all the simulated trajectories (*light blue lines*),\n", "2. the mean squared displacement $\\langle |\\vec{r}(t)|^2 \\rangle$(the variance of the distance), (*red line*)\n", "3. the theoretical mean-squared-displacement (*dashed black line*)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0t4qx+O6hnh4T5IODqrRKJeU662ZL4yiiqc+tEI/r+GZn9TE52VgL5D8D+tnq\nqs7F8LBaMNw/mVRl3sxd1mmXGdFySkXkfwfwGQAZEfG/9jKA/97uBepus28A+B3nXF68X0HdLbYl\nPq2bb74ZBw4cAADkcjkcOnTodFon/2jh/c56T2yX8Zyv90eOHNkW4/mFX9D3hw/r+xtvHEe1Cjz4\n4ATGxvQ9P+/vB37xF/X9978/gdlZ4D3vGYdzwAMPTKC3d/35X/taff/ooxN45pn1n199tb5/8MGt\nu/943O73Qx9q/Pyqq/T9j3+s79/whnGsren9LS/bfP3DP0xgbU3Pl0jo+WZngQMHxvHqV+v+S0vA\nG99o+zun59u9G3jkkQkUCmr5fPe7E3jppWMdTwbYNEYjIrc75249q5OLJAF8C8Ddzrn/XN/2NIBx\n59xk3S12v3PuahG5FQCcc7fX97sHwGcBvFDf59X17R8F8Dbn3Cfr+3zOOfdg3dI66ZwbazKOEKMJ\nCNjmYLGgDwbCX/96jaVMT2v8IJVSC4d0+6dO6bZCQZMAmtXBzMyoBdGq+dlWx2cAdRHOzel1o60D\nCgUdswjws5/pfe/fr5bJzIzGmNbWtLfNCy/ofTun+x07pq6wV7xCEwI4jwsLGpeiG3FgQPefmlIr\ncWFBz3P8OPCa12xhjAZKqtkHACLyMRH5w3ayu0RNly8DeJJKpo47AXy8/vrj0Gw2bv9IvV30FVAm\ngoedc5MAlkTkhvo5PwZtXRA914cA3NfG/QQEBGxDlMut4yOrqyp4q1Wju/ddP2QqbhZjqVY16L6R\nW80n4NxKsPFYs/tmNT+JPNklk+4tFnxms6owCgVNLJiZsdTvSkXPzeB/LtfIqFAq6T2L2HzG453v\nV9OOovkigFUR+TkA/yuAn0ED8pvhrQB+DcA7ROTR+uN9AG4H8B4ReQbKLnA7ADjnngTwdQBPArgb\nwC2eGXILgC8BeBbAUefcPfXtXwYwIiLPQsk/z8ry2kmIuo12MsJcKLbLPJRKGj9gLAawNsjRGpJm\nDMtMHIgqi3xeBTCFbjNwhf/AAxNnPf6zRaWiY4wWZIqoYshkzIqbnlYLiNlq+bxac4uLFrdh5p6I\nfk7l29urSilVj+X09Og1y2VVPlRUPKaTaCfsVXHO1UTkAwD+q3PuSyLyG5sd5Jz7IVorsne3OOY2\nALc12f4IgOuabF8D8KubjSUgIGD7o1xWYcgiRhENfBOLiyYcmxVbrq01ZqERvnJpRsTppxhvVbFm\nuazj9Ws5kkE+AAAgAElEQVR9FhZUsTDFmc3Kenp0PxEdZ1+f3lOxqEkMTM8m/LqcWk3vL5drdM31\n9Bjj8/S0Wk7FoiqZRMJaC3QK7Vg0+XpiwK9B3WhxAGfRjidgO4AByYAwF8T5nof5eV2NO9e42o66\neERM4LI4k4jFjKfLVzS12uarc5+O/53vHD+HO1kPuuSimJ3Vmh+fm61Wa6zQX17WuVlYUCXBmAyg\n89DXpwqkVLLz+HU2VLCtUsQ519yHVmIsdn64zj4MYA3Ab9TjJfsB/KfODiMgIGCnYnFRV+WFgq3m\ngfXNyTIZjTWQAZkFiYAxN2ezjRbM1JQqEiYB+I2/ymXrPEl0OkYzPa1JBlSCgLm2gOatqU+c0MeL\nL6pCck6VTDZrr0V0LpaXtbCzWrX+MwMDapW88pXNiTiJWMyU+fPP6/W4vdPY9JTOuZPOuT9wzv2g\n/v5F59wdmx0XsD2xXfzx2wFhLhTncx5qNSsOjNZ1+BZLtaor8FRKK/h7eqxokfEXv6cLQWuCZJm+\nEJ2eNuoW7tPJuahWzTJgjMm59hua0UopFk25Dgw0cqMtLGhciwWs1aoqm0svVcU6MLC+3YCPdNqs\nQ7+XTafRUtGIyAP152Wvs2bosBkQENAx+Lxb0TbDUUXDlGVmaVFpLC5akzC2MwY2r4L30d9/bplW\ns7OqQJaXVfjPzxtHG1GpqIvQjzv51/fB9gDxuCkaslfncjoHpZLed6rOaJ1ImKKgCy2ZbGwV7aNQ\n0PEuL1uMa25OEzA63SahZTKAc+6t9ecm1HQBFyrOtz9+OyHMheJ8zsPMjApgxiB8cOXvtwgAdN/V\nVQ1YFwoWzK7VrAkYV+pEs3bPPiisz2YuSiUdQyql111etlgSoFl08/N6P87p2Pv7G+Mz/f3WoyaT\nUXfbyooqFd6/r1gZk6rVGil4iGxWn33WBB+nTqlCLpf1mrQEmYixZYpmMyoX59zcRp8HBATsHHDV\n3YxheCPQookqBr9PCvm6mAklYvsnEnr8c8+psH/lK82ltpFFU6upoKfyOpdss7U1FfrFoioYxoQ4\nXs5JVHESVArZrL3mXAwNqXWTTmu8ZXnZmJlZS5RM6oPn9GMvVE4rK2pJkbqnUrEkAcZxGOfpBg3N\nRjGan0AZl38CYAZaw/Js/fUjnR9KwFYgxCUMYS4U5zoPdFk1C2xvhMlJiw0sLJhwLZWAp59WK+Cf\n/kmFZDzeGH8hQSQ5vVjMyOB5VFhGFSAzvFikyXN/5zsTTd1MrZDPW5yHygtoVJrRmAfHTCUQdRlS\nSYqogh0cVCWWSgEHDpgVUyxqbObqq/UcV12l731mZl67UNB7nZ+3WMzqqjFhDw6qUhsYaO5mO1e0\nVDTOuQPOuSsA3Avgl51zI865EQD/vL4tICAgoKEd8ZmgULDal3TaWgDMz+v2tTVd4dNC8EFKfDbx\nqtWMgiWqZIaGGotAOWbW6uzebRYCizvbRT7fmLnGLLhoS+lUykgrn3sOePZZLUSNjovHZjL6uYha\nai+8oC6zRELPUS7rZ6w7ymR0DqP0OiLrr7GwYI3knFMlw/Nks6qAorU554p2Etne4pz7Nt845+4G\ncGNnhxGwVQhxCUOYC8W5zoO/Ao4K2Fbg6pqrc7qwSiWrlGegm0LVB2s9arXGivdicf2KPJNZr6io\naDiWWk2Pu/HGcZRK7SlNKjRfsWWzal0wQy6dVsHNWpdyWZ/JrMxuodG5icf1vubmzI04P2/KAdDt\n2awVffop1D6isS9i1y6NxTDms2uXXrdZ3c25oh1mgBMi8n8A+EsAAuBfQ6n6AwICAhoE+8yMNtDa\nrK9LuWxuM8AypkiBUixa7AFoHkN5/nmzJpJJJZw8caJxPM2OW1vT63J8p07pMSTTLJUs+yoKdrMc\nHDQFk0xa/U4sZqnUIyNWzc/r+u6/SmW9W41WHRkOEgk990sv6b1lMmZ5ra6qBUMlvbjYvKI/FtMx\n+gqkWm1kIGASQiy2xa4zDx8FsAvAXwP4/+qvP9r5oQRsBUJcwnCuc8HVN6DuiGjx34WCc52HqKuK\nlf4b4dQpnTO/4LJUUgE6Pa3b4nF1Hw0Ors+CKpcbXVyXXGJpv6xZicfXJxnUatbThYqGn09OGmV/\ntKaHWFy0wD+Py2RUSe3bp24qxlzYIZSxm4UFY0em28+3QhYXdVzlcmOKcjZrNT/Hjzfee1+fKa+N\nEhpGRnQBMDys4y6XG5Ue74WKr9M9eTY9nXNuFsCnOnvZgIALHwx+791rAoMuk52EqKKh8iiXm2eh\nOYfT7ikRnT8qiHRaj2NcJZk0occVeTJpcRsKyETCVuiZjL1mEL2vT7+jZ5+1eEl0bNGU54UF675J\n0ALz2xkw9TgeV6XA9tMspsxmdZxsZUDL58QJ/ZwuMDII9PWZS4yZbIxJMZBPPrLLLtMxDAyoIvJb\nOfugUk0kdHzMTEulGjP0cjlVuJ3+DXeBbCBgOyPEJQydmgt/9Rst0rsQcK7z0Ipev5Wvn8WVgFos\ne/eqYOvpsc8oSBnDmJuzNs+rq8bNlcupQqLgpBDv61PFMTdni4DZWRXSpNeP9n+pVICf+7lxzM/r\ncfPzZl0BJuRLJcuYi3a5BPT6s7M6vtVVs6BIGkqXGrPmlpY02M9xcg6WljRu0tNjdDI8rlTS8VOp\nUBluFl+Jx/V4Jg+wTYHPczY2tn5uzhVb2LQ0IODixNycCbelpUYaD/J3bRUr8PkA4zEMfBOtfP0U\npJmMuYdYg/PTn+p59u5Vd1k2q6t6P/D+0kuWpZbLqXVDrrNYTIXwzIwF3mdnVUhHLS8G29NpVVYz\nM2pVMLjuB+qPHze3VyLRWHCZSDRaPbTAlpfNRTU/r+NlYzb2z1ld1fGzNgZQl5qvvFdX9RyplMWy\nfAJSoFHRbGSNiKhy9xVStHamXF7fsuBcESyaHYYQozGcy1xEs5J6esxdQwFULjenItlu6EQdDXun\n+GilaBYXdY56e00ox2K6PZPR1TSJIWMxE/izsyqEKbwvv1znvFDQRz6viqlSAZ55RgX00pIqiJmZ\nRnfX8LCOYX7e0oOdA376U5sLjn9hQd1eZABgptvwsB7H6zAlmK40MjGvrTX+PrJZVbCVivG8MQEA\naFQ6CwsW72ILgX377DwEKWjayfrzz89jqWiqVUt/7iQ2Ygb4E++tg2acnX7vnAtxm4AdC/4x43Fd\nofpV63Sn+H/eixmtOlduVGFeLJqrC9BnnwKfRJm7dxtdis/5xfoQFjEyhjEyonUqPjtAodAogCsV\nVRjxuBY3plKW7pxM6rZTp2wx4btG83kT9IWCKZlSyawrZm/Rysjn9RrZrG5jyjZbMpPqn661UskU\n8NqabuNYMhk9x9hYo6IBjCWhGZaXLd5VKjUe66c0z3WJ72Uji+aR+iMN4PUAnoEyAxwCsMPCnRcP\nQozGcC5z4VOE+CmlsZgKFl/Ibne3WSdiNNFU5lSq0erjfHFeyKTsWzR0++zZY/uzoJPHMkVYRIWl\nX2MjosLfp3HxWzwzAWFpSc/huzcZb3nDG8ZPn4tjpRuJMSQKZZ6P9TuAWmXPP6/uPbrURkfV1UYl\ns7RkLtZMxlxshYIlk7BYE9BjczlzCy4u6tijmXicw8XFRuutWtXrzc4CTz2lysT/zfruuG4tijYi\n1fwfACAinwTw8865cv39FwH8sDvDCQjY/iB5I7A+CO7Xg5wp79eFCj/TaWzMsq64ui4WVbgND5tQ\nrdUs5gBYQSMVkH9sMmk1LQzk87qVitWSTE5a7Q0LHmMxtU5WV1X48vtZXbXakVLJXFgECyNFjOqF\ninNuzsbQ22v3TmVF1yAtL8Z1Uim9f2aUsZslYEWVqZTe68CAxb2qVZ3XlRU999iYkXD6oBuPqc9s\nKbC4qOfwExuSSVU+7OEDNBaxdhrtxGhyAAa89/31bQEXIEKMxrDZXESFD+HXb0T/7KQAYU3IhYBO\n1NHQokkmLR2XbismCMzNaRxjZsao6X1LJxbTlbzv5ioWG1sCZDK6umeMJR435ZRO6/t8XpXLCy9Y\n35rJST032ZABay8wPa37r6wAjz46cTpjjfdTLOpYGZQH9BpkNqBrLZ+3pmYcC5Mc/CJOpi+znwzH\nnsuZ+47xqejcAvo+Gg8D1jMAkE1gackYron5ef0OeG9Ao6LpdHpzO1lntwP4iYhM1N+/HcDnOjuM\ngIDthWJR/4xsqOUHc8tl/bM3qxwn/1ShYAJtu7vOzgWkb4kqXNLYU8DTijh50lb5i4sa3N+7V88x\nNGQKxHe79fdbDxfWftBq8jPDhoe12yStB1pDLLDcvVvHmcupe46s0MvLOo61NRXKzz2nn+Xz+p2v\nrurzpZeawCYh5fy83svoqBVxLizovbAIlTEX3yryXY19fXoffX3r41p+vU80JhMN6gN6j4WCJUGk\nUnofPi8as9/87zAWM+LN3t7zkN7snPtzEbkHwJvqmz5db+kccAEixGgMG80FV9p01ayuWrC3VlOh\n0co1lk43Wj2FQvOsrO2Cs/1NkKYeWC/wKODLZeDJJ61fDIWcT6NPK0DEBDKLDwErfgTMpdSK+HJ0\n1KwlQBUPBfzysn4H2ayt/pnttbqqY37968dx8qQes7Zmx4+M6NhGRnQ7v2Ou/Pfs0djM/LwxEoyO\nqqKlQmDSyOKizsGrXqXX3bOn0bLwY0eViilTPrMj5tSUzgfTsXks5w9Yf85mtEDVqo5redniRp3G\npq4zEYkBeDeAn3POfRNASkTetMlhAQEXNKho/CyehQXj6Noo/uK7HfhHZ5Oqiwmzs5alFJ2PTMY4\nxWo1dU3NzOg8pNMqCKl4aTX6ZJJ79phwXF62xmjsnUL4c0qXWzarFfOMYwwM2HdC9xzhx3zoxlpY\nUBff/LyOeXFRx8tCR0DHceiQEWfSghscVDocwJQXedXiceNCA4yxYGXFrKahIY3BMDUeaGxKBhiF\nDMcfhU8fQ8VCxUryUR9Mv2e69UYcdWeLdk75pwDeAuM3W65vC7gAEWI0hmZzQX8+s4hacV5t5MP2\n/6i5nAnMSmW9W2g74Gx/Ez4lTJQbi8WUvFdme508qYqDLYlF9P2JExbTAHQ7U3iZKjw0ZJbC6KgK\n6QEvekxFMzxs1Pd0n2UyWndDl9DgoGWQ0eKJxYDHHps4rRBIRMmaH2axUent3q2PSy6xYtGhIbNc\nWJhJZRjlJGNVPqlrVlaModlf4PiZeXv2WBdPzmsz+PNSqajSZfaa3+yNr/N5VbC+Mu0k2lE0Nzjn\nbgFQBE531mwrn0ZE/kxEpkTkcW/b50TkuIg8Wn/8kvfZZ0TkWRF5WkTe622/XkQer3/2BW97WkS+\nVt/+oIhc3s64AgJagStw/tGpeHz4NRKbIZ22WM7Skq3qCd/9dKGBCjUaOwBUaPb06FxSmA4MqCVA\nizCZ1HO8/LJ1d4yuxv0Kdc45U4BZ1EmQWy1KGJlIANddpw3CMhm1wtiGoFbT8b/iFRorSqcbs7B6\ne3W/mRkdY5Qnbf9+VTxUQs4ZhQ6zznwGAX/eWnUk9Vmt/eMASzbxs/eagQp7YcHcaUwG8N1pfiyG\nLZyb0QmdK9pRNCUROX1pERkD0K4T4M8BvC+yzQH4Q+fc6+qPu+vnvQbAhwFcUz/mT0VOh1G/COAT\nzrmDAA6KCM/5CQCz9e1/BODzbY5rxyLEaAz+XDBO4Pv+WbfgkzeOjjZ2MGyFXM5qH/jHpfDwhQNb\n7J5Js62zwUZuO38eFhdNsW5WV8HVcJSanvxdrN4fGrLMMJJUcm7n5y3QDzQKVZ96Jp02upooGLOg\nsCep5iWXqDJiUS1g881alrU1i9Nceinw678+jl27jGF51y4t0CyVrOixVtPXvjXBhAhu271bn5lt\nBjQWp/IYMk77KBSsONXnM+OcM9ZFRdPsO2LGGjPh/OZnUUXHAlRmunUD7Zz2T6AtAnaJyG0AHgDw\n++2c3Dn3AwDzTT5qlodzE4CvOufKzrljAI4CuEFE9gLod849XN/vKwA+UH/9fgB31F9/A8C72hlX\nQEAUU1MqYP2VJJmE02n9ww8Otp/26fd/j2adUXiWy5YCfTbcUpWKupwYKG+FYlHvbTPCRSpaCtKZ\nGZ2XVojybREUfHSd9ffrGHp7jb14cFDvnSv6alWJI/258qvUBwfNWohiakofUWV66aUacGflPWCZ\nVz53GpMQAFV8zBoEdPuuXTrXbCmdz+vnnHfGWPy5yGR0QfKKV2i8iIrHH//srGaxjY5a3c7amvXH\n6e9fr8QnJ20elpb02s0s4njc6nr6+xvnlQsfPx16aEgt71qt8zxnwCaKpp4I8DyAT0OVywkANznn\nvn6O1/1tEXlMRL4sIszF2QfguLfPcQD7m2x/ub4d9eeXAMA5VwGwKCKRZqYBPkKMxsC5aLVqz+V0\nFU1q9WZNpc4GXIlOTzd2SzxT0ApaXW19/PKyBZVbueg4D76SXVpqTzGR+oWxDMCsw6NHVWhOTanQ\n7etThXHtteZOS6UsfbxV3RI50aanNcbjgy2f2QzMB6lWUim11FZWVIiShmV62hie6Q598MGJ09Q0\nAwPGTECaFjZWY/1NsWgFkVGGCNbH9PXpeU6caBw/3bPscUPrir+J+XmdP3++gUbXFi2WKHz+MlpU\nRE+P/q79bLVMxly8W95h0zlXE5H/6pw7BOCpDl3ziwD+Q/317wH4A6gLrKu4+eabceDAAQBALpfD\noUOHTrsM+EcL73fWe+Jb35pAuaxtfAcHVdhUq8Devbr/I4+o8LnppnGkUmd3vZkZPX86Ddx/v35+\n4436+UMPTaBWA/7lvzyz8V9/vb4/fHgCPT3AO985jmzWPn/Tm8axtGTNvN7xjnH09a0/35EjRwAA\nN9xg56tUgDe+cRyZDHDffRMQ0fP713/Na8YRi+n8nTwJ/LN/No59+/Tz6Wlg3z6dr0cfnUA2C7zv\nfePo7wf+4R8mMDsL7NkzjnhcP9+zB9i/X8//ve/p/L/mNfr+hz+cQG8vcNVV+v6739XxvOc945id\nBe69dwLpNHDddeMYGdHxx2LAW94yjpUVHX9vL/DWt46jVgN+/OMJlErA1VePI58Hnn56Arkc8Cu/\nMg7ngCNHJpDP6+fT03q+1VXg7W/X/Q8f1uu/5S3jWFgAvvOdCaRSevzysn4+Ogq89rXjKBaBZ56Z\nwOKizie/75UV4HWv0/ff//4ETp0C3va2cRQKwBNP6Pd5443jqFT09yICvPnN9v3Mz9v3/53vTGBo\nCHjXuxq/n4MH9f3DD0/g6NH2/g/f+tYEXn75WMv2z2cLcZukwIjIfwLwIIBvuM12bn78AQB3Oeeu\n2+gzEbkVAJxzt9c/uwfAZwG8AOB+59yr69s/CuBtzrlP1vf5nHPuQRFJADjpnFvnyRWRsxl6wA4B\nqeGjtTGFgq4qe3p0NTowYI2mzhRk9t29e707qr9fV6ZjY+0nGZDWxR9rJmP+dkCtGdZTEPG4uXGI\nUklX7aQ4GRlRTqxaTVf2uZy6iViDQhw7ZmnMMzNqrezfr+9/+lOrpGecZM8ePXc6bZbB/Lzuxx4o\no6O6ivezrlhAyDkk9u3TRIKpKUsd5qo8kzELiUWlzPpjDQqD9cPDetzgoN4n+dIWF5VdgAWlTDIY\nHDTamuVlfR4bUxcb3YO9vY3f+dycWQosHOXnbB3N73HPHiUK5e+Ev4t83qy25WXLPBsb0/v107Zr\nNW1tMDOjv1m6xTYL9HNMykwtcM51pNy4nRjNvwXwdWhSQL7+WNrsoFaox1yIDwJgRtqdAD4iIikR\nuQLAQQAP14tDl0TkhnpywMcAfNM75uP11x8CcN/ZjitgZ4KuimhPEaCxLoPcXWdLOshU2HjcMocA\na/DlX68dMHOtVGoMmvvg2sr3zzNovrCgn09PqzDyYz2plArNkRHdh/UyFNzFou4bJW+kf59ZWrw/\nxjmAxvRlVqIzg4yB7SgDMWtsoqCLjvfqp+X68RIRY3+uVi1exLYE1aqOjxmHVKbDw8aN5heNAnrs\n9HSju4/tCioVY48AdP4qlcZCTJ/Z228BznP4oMuTnTUBXRjt26dKrxljM1ktmLZNF2a76+2NYnNn\ng00VjXOuzzkXc84lnXP99cfAZscBgIh8FcBhAK8SkZdE5DcAfF5Efioij0HpbP5d/TpPQhXakwDu\nBnCLZ4bcAuBLUPboo865e+rbvwxgRESeBfC7AG5t8753LEKMxjAxMXH6T9qsR3qloqtvFuT5ac9n\nCr9GxPeZszskM9ucM4r8jUDlMTenVgsVj5+9RuHGXvEEe9WzOdjhw+pKIg0Lz816julpE8LOWddK\nkk76sZnVVe0FwwrzV75SFSznl3PADo8jIyowSR7ZLI5EZRCFr2io0AAVvtG4RDqt9zE3Z/tSkS4u\nqhKpVoEHHpg4Pc5sVsdOVgAq5ny+MUUdMLYIfgfT06ZoKPCpCFdXjeCSSimZtHTwUkktNX4HvBa/\nT3K97dpl8+gvNDiPa2v6ORUsP2sHZ7LoaQdtddgUkSGohXH663PO/f1mxznnPtpk859tsP9tAG5r\nsv0RAOtcb865NQC/utk4AgKaoVYzl0UrRcPumKSb73R1vy+A2cud7i7fDdYM1WojnT27efb2mnXB\n1blvrTGrrK/PhCEFEDm8yFHmB9iLRbV8qIioaJgUUC7rcXNz1ieGSpSszj5TAse0Z48prmgGXU+P\nueeioBsMUGFLYU0LcWjIxki25v5+3c4eMgsLeiz5yJyzfi+FQqNlwjoT0unUamqtsDAz6paKLhZ6\nemzMPpkoM/MSCWOiZjuE/n5VhHQ1suuoj2LROMxWV63SX8RqjU6e1Nf5vCriVmnMPT26AOl0bdem\nikZEfhPApwBcCuBRAG8G8CMA7+zsUAK2AqGOxnD11eOnX0dTkFlDQkVAF8pGiqZUMk60zRAtnqNl\n0G7GD/dPJk0BFov6WFoydwwzi3whuLxsmWpDQxp0TiRUQNHNQiuGLihSqSwuWh0RhXgyqUI5lzNW\nhVRKFSVjXLQQWiGbbVQye/boGDh+zvvYmL6mFcLV/p49Oh7/GrQgODepOgV/PK6xpFOn9Dy0RKpV\nTYjw3XsDAzoOzkM6bYzSr3ylKetW9zY83LiY4TxyXFQKzMjr7dVeNuWyfjeZjKUxLy0Z8aZfk8Os\nv5MnLVbHufBpa5aWrAX2cIvc3OFhS6/uJNqxaH4HwBsB/Mg59w4RuRpt1tEEBGxX+Cu2KH8WYKtR\nCp143FajbFJFXi5idlb/xCR+3AjRplVR37mv+OiyqVRUUKZSFuDmqn1x0c5BJZPJNCoYrsABFXh+\n10Zer6/PhAwbbA0P6z2RPgZQoTk/bzxirI8hxQ7dTa2KLJkW7WPXLhVy7FDpJy341fW0LKamdPvQ\n0Pr5jIJMzz09eo9kYN6/v9FC4zU4R9msKSJf0LO2qrfX3HEM2DO5A9B5YauCWMySLlIps6LIQMAW\nC3TTVqtqyYyMWFr03Jwex7lhYgJjYvw+Uym952zWev+0u4ihZddJtJMMUHTOFQBARHqcc08DeFVn\nhxGwVQgxGkWlorGJPXuau818QkM/cFssqtBfXrbVKGCuH+Ds3Gu+QqAi8VsJU/HNzKjVUKmY0GUN\nCFfVvn9+ZsbOxf4ktNSqVRVsjz02gUTCiCx9/zypZJJJFaB039RqemwuZ/xjrM0YGgKuvLL1vXI8\nsVij9ce4iV/FDtiKHjCl4MdtWikz/3jnVChznkT0/fCwXa9UAn70o4nT1ovPeByLWauIgYHGanry\nmfX2muvOj3MND9sYWa/Cz0dHlT2Blgc53XI5c6H6/GOsOyKa8cz5NDpcANCCYXHpRoiyHnQC7Vg0\nL9VjNH8D4F4RmQdwrLPDCAjYWpAEsZXlQXdUImGuEhFdcQ8OmhDiH9J3+5w6dWapyoC5nQBzr1Ah\nUDAwEM+UXMaOkkkVLiwq5Xn6+qyQkvcxMKAKZXm5Md2V3SoZhyF8Piz2eaFLi1Qy09NGpU+hGA3G\nE2RBBvS8UQLHZvUbvH8WudKtxPiZX3gYBQXryIgmRfixFLIEMJmCFDbNvrdMRr9T32VFiFh8jQKd\nbALNwP2JqBurt9e+f7rFGMPhnBO+kunrswJPukGZZALod8/iUoILEH5fzz9vi4lOop1+NB+sv/xc\nvfnZAIB7Wh8RsJ0RYjSKSkUL5FqBaaa7dln9RDZrXQnpMmNQOIq5OT223aZnsZi5Ufz2xrSomDVF\n98f0tAV1h4eNiuS4x6HBfZnZxCr3xUVznTmnvwmmKjNjiati1rjQNTcwYG47nptpyqyUp+srirU1\nc72l041ZWrGYHre83Bjz4LkBVeYUyvPzxsrcCuyACVh9S7N5Z3Mz57Sos9nYBwYa0459AU+FQgXd\n26uCulXRY/T3Ev2N0HVGcE6uvLIx443tovfssVbNdM357i/+DjIZ/YzfXyxm3HbZrI755Em9Rqd7\nJ23qOhORy/gA8DMARwC0QSsYELB94Qv0KJhiTN86m09FA/jctxnVR6kEPPpoY53JZmDwlwKKtO2V\nigobf5WZSqmg9dOFmUbrXCNflV/vksmYy80XZrRuuNplwJz1LXSNRe+5WDQ3GFmZW2U1+St8tnuO\njo+dIbn//Lx1fYy61GiVNkO1qoqB7s1WwW/A3F2plM1NFH6hK/cjoudeWWmMmTQbG6AKYu/e9Z9T\n0fjjoEXNz5ieTvqcXE7nPZEwxcLj+Vvg76lQaCwWZYO6Z55RpeNnxXUK7cRovg3gb+uP+6DK5u7O\nDiNgqxBiNJZR9qMfTTT9nIFYPy0WMN+6/yes1UxI0ucP2D5+9f5moH+eyqNW08p01r0wxbq/31h9\n/VgA/feplAohX9lwBZvN6rFLS5oYUKvpb4IxkHhchfPBgxabodCrVCz+w4LNfN6q8gFViCwGjcKP\naaVSliVH+O0YarX1rAZ+HxeimaIplxv7tVBAbwSSpkZ/E0yEAPQ+Wcjqo1VqfCvwt0XlEQVdd/5C\ngG6PL3MAACAASURBVNv8RQjPtbKi3wPHwd9eMqnfFS1iFtNGjwf090KLljVVnUQ7BZvXOueuqz8O\nQls6P9jZYQQEbB2iGWU+GAfhKp2+dBI7Rt0aMzONZIc9PcY0DFi/eqJQsGK9VhCxlsFc0bMvDi0X\nwk+rpRKk68qvgYnH1SpJp/V4noOprHNzRnL5ilfY/VLpch8SUvb06H0w5bunx87bLKPMx9CQCry5\nuUZFHHUXRRUl54VFrsB6BUIXHqvx21Ey/jWi+zJLjWhl8dCVSqtnI6oXxoJawXfxUcHwms3iR88/\nb/v4jdaGhsx9SMXrzzct02pV6YR812mniTXb/Ar8wbmfALihs8MI2Crs9BgNA8oA8O53jzd8RlcN\nBTSFTiajgoTZXX56KeGvsskmwOC4n8U1P79+JU9QoZTL1neEY2YraBb1cVx+HIDuMFaaF4u67759\njWzC/r0tLSlZJavOk0kr+KRQK5f1XJWKruiZecesNgoov/lXs7ok3vNGriUKWQrGoSFVkBxPOq3n\npmURZdTO563wk9lm7cbJKhUlzjwbDA5askFvb2tFe+rU5u2SRWwBwf18BcPPGNMjawN7/lSr+vuM\nxSwVn+cZGDAX7PKyWi5zczqvPF+5fB6yzkTk33tvYwBeD6XqDwi44OAHdKN/9pkZqxb3P/etBloE\nrE2Idk9ksynAYij5vLlfGDcoFjW4WyzqOaNdPMfGrGUvizJZQFirWfsCHyKWbdTXZz1SfKVGwby6\najQnJ05YUzLSlZD2PhbTbXTTsZnbyoqlO+dyKpxmZ03ozc01WgIrKzqve/aspzeJxXQ7Y0xPPGHt\nkv2iy2j3zWiwfXVV54tWKK/TTgYVBWyrbLl24HeuZMW/r+TyebMkNxPkuZylYpdKjffq/y4TCaMS\nuuSSRhaDyUldEPT2mnvzssss0+zkSf1e2Kbhkkus4HYzq/tM0Y5F0w+gr/5IAfgWtElZwAWInR6j\n8f/40bmgNUCwRsL/k5MJt1zWlTZX4BSCMzONyowswvR9M06xsmK9YqJKBtA/Ol0huZwK4ksvVQuF\nAqxZQzXfChsctBUrYLGF3l4VUtdeq8f88IcTmJuz5Af2XmEqMC0QCsdsVs9FN2I+r9aDn0iwuLie\ncJKuPc5xMqnnIetwImHpz2QU8O9tI8vEL1r1U803Y3NgHxsqp4cfnmi9c5vwY2w+/PloJ6uL9ThR\nhRpdIPn70LU5MwO8+KLFg9JpZTJglh3nq1TS38kll+j2kyd1LqK9fc4V7aQ3f66zlwwIOH+gsIxm\nMAH6h0yl1O1Qq6krJLryZB0DYxalkloZfp/56P7sxkjLgpZQKz6pvj5VQswCO3VKFQ1XpkBz4eln\nYdE/zw6OtBB8kBqGtS9MfWUxJ+llfvYzHS+TEBIJFZR0AVIhiABXX63nYGzJH5uItU8GNKstOqZK\nxWqEfKuAMTNfSflg9ltvr85VuawP0q60ApuOcfyb0ei3A54jGothBiOtlTMFa52YsZfJWPU/oK9p\njRYKeu8i9jsmXQ2/32JRv9e+PrOMmPByPrjO7gLgYO2XG147597f2SEFdBMhRmN/Un8uKBgzmUaO\nr1aprrRQoucm0mkVKAx4M22X7iCmlUbdXyRtJLnhvn22uvSzu6KKhoV97E1CUshiceO6iKEhbYjW\n22vC2ffhU4nk8401GiKqKEg7w7bXfgthPzuvVDJFkUxal9Eo6JLkMbOzqni4L106rfru8JqplFqf\nk5NmSVHI+nPmV8knEp35f/iKxr9WqaSPKKFpu2CvnL17G12go6OWDQhoLdWLL+q8DQ/rePr6LPWd\nFjYXM36WG4tSzyQtvx20wwzwPIDdAP4SqmA+CmAKwF93digBAd1Hs8wioLFHfLNgv494vFFAUaDw\nHMPDFrTu79dVInnQ0mkV7qSlp+CjG4pjS6VUoPjp1PG4KT4W8VEos3A0nVY3SDKpyqVWM3/8gQN6\njmi/k0RCFQrjG2QZWFpSC8aPjzA+xfbE5OciLQ5rjvJ5i+MAVlyYyVj8iIwD/nfjW0HOqcBkmjnP\nyzlgvIvWF8eXTKrw5fWKRfu+qKD88xDNCjrPBlFGbEAXG+Q7A3SuGbeLYn7emJt90Jpjski5rNYu\n+xzNzuo1SBSaTFoiyNycXm9mRs9Nlm0q/YEBnTvS33TaddaOTn2rc+7Dzrm7nHN31qn/f8E5933n\n3Pc7O5yAbmOnx2h8Xz/nwnd3RVe9zdCKDn5tzVKc/ZoPcoMBqjwYJC8UrPaGq0r/2j6zMwkyKajo\nh/ebYjnXuM/u3da9kbGglRXtnklrzDmNSxSLxupMavnpaX1cdhlwzTW6iqZ7jq4/JgwwNXppybKX\n/CQEunzoFuvt1bGcOGFxEr8BmD+vS0v6WFy02Ba7c87P61h8KyKVsrnzs/eIatXiSoDxsw0MnPv/\no1IxFmUqmkrFqHDasWIKheaCnve4vKzKgXNH5frCC7ZYYMsEv7fRc89ZZ1HOAdPv83k9J2OAnXAh\n+mjHosmKyCudc88BgIi8AsAGhN8BAdsXhcL6lStXimNjuircLPPIVwY9PZal4/cu8eFfj3ERupqS\nSSM+jO67smLpws1W28wquuQSi2P4tT6TkypcfLoYFmauremq/2c/s4D52poqxWTSfP1MXhgcNL//\n/v1m+TEVl++ZGkvKnNFR41zr7TUiz5UVm/e5Ob326qqeK5s1JuRiUb+TqOCbmbEeOJWKKZQoV1mz\nRQP5wAAb/2bJBgQz+VotRnju1VVVgn6BpZ+OTiW0tqb3SOvOV4qMT5HFwmdjWF42BUJizWpVFxHO\naUYja4mIkyetrmZhQb/HuTlbxORyFtvbcq4zaAfM+0WkXhaEAwD+TWeHEbBV2GkxGvb8IJ06YM/k\n+CLXFt1PG/FnARY8ZVdIv+I66g4CdL9USp8pMEdHLb0YMMFJYecLeWC9YKtWdQXO1T67gNK9trCg\nwsi3rPxCTRJaVqvAddeNY25O52FszJQFM+YAYyXwYyws6lxdtZgB7yGR0ELCqSngDW8wKnxafT7Z\nI+M++bxR2IioEOTKfni4kSng1Cl1SS4vm0IibY7//UUVlM+KDVj/HUCTCH7hF8bXf4EeFhYswB4F\nLTjyjjE+t2+fNdEDVLFxX7ZtYEtv3wpki+7FRZyOoTEjkPVZXFiQZYA0QIwFct79HkSLi8bQ3N+v\nCob9fdhobqPeQWeDdrLO7hGRqwBcDU0EeLre2TIgYFuDq3qgkReMIKcZoH8wKot2fPUUGlHOq2bW\nUDyuriff2hkeViHAgD/HQ/hp1iwU9VGpqDCgK4kxIV6DWV6plDXDouXFrCf/ftn9kvsDqgxfesn2\nobuL9DClkp6L1DRUYlzxVyqqBKamGjPGooqmWLS+OhSkdMMRdBH57/37pELlPPhz7ydQRDndaAkA\n9ltp1dmU+7H41P+uV1asMDKft/qj/n47L/vXFArr3XkkOmXdVLms5+Si6Phxoydi8S4tOTY1Gx21\nuhm2dSAHGlOWOV9XXGFxOLaUyGQsxf9c6omaoaXHUETeJCJ7dWJdEcDPAfg9AP+PiGxAURewnbGT\nYjS+n7tctkwapjZ/+9sTpz/v7ze3WruV5AT/lBv9OaMutWTSruOnklIgsB3A3r260vaPZ7oyYFYV\nEw/8/Wo13e+Nb9T9FhbUiioULHZTqwH/9E8Tp1Nf19Y0AA9YkzVS4FerKuQonJaW9FwzM8ZxRoF5\n8KDV2kxN6We8TzYDY9yCq212DaVLkKnA+/c3EldSOTDTbmVFLYNisXla7p49dnylomOJ/haIw4cn\nmn5/tZrFRIBGa4tWB12J/f3WTI/0L/G4WqC+4uMihygUbAEB2BjJysAsOSoidg0FdL5YA8Pvi6nr\na2v6OXn7qMwYi+vpUUv20kt1TCwi7iQ2Ck39NwBrACAibwNwO4A7ACwB+O+dHUZAQOfhZ/34SofW\nS5QloFI5uz/Y8HBzV8pmYCDdH9vsbCOzQDOlRzccoEKUfFVAY8YTec9I7c+0Wl6HRaFs/csAe6lk\nqdHptAr61VV9cFXMFfnioioUn9TRr7nJZo1HrVhUJcJzM8bC8QJ63pkZjS2RnYDJEkwmIJccxzI6\nanGGVszDtGbX1lSYMjOtWUwtWju1sKBuQDa843gnJ/Ve6e7ifQGqIA8etKZtvpVMDju6Rvv7G7MB\nWXuVz+v3xAzFqSlTVFQ6/B0sLuoiYnjYuO7YtvnFF83K6unRMXO+6P7k/Kys2GKhk9jIdRZzzpGC\n7cMA/ptz7hsAviEij3V2GAFbhZ0WoyGKRROyLBy88cbx05/Td3+22TZnagUBtuJk0WeUrbhVwLlS\nMSEVTTsmYy+VxOioubF277ZssKUlFXD79wNXXjmOo0c1VkFF09MDPP20npsulWLRhKZ/v4mEpR6n\n0yok6aqky0xEj83l9BpkkmZKNwUglQSD7nv36n6plApaxhD8wk9m+lWrKpRHR9d/jxwLFQXbLERd\nWDfeON7gXuN80G3nu/tKJcvcIhtCJmPtHkhQyTR053TcTH5gfx/GZqh0YzG9Dyp3Flz6rRWY/DA1\npckgMzPGydfbq2NJpdTKoWKJxSxtmokXl11mNTZAY7+gTmIjiyYuItRr7wZwv/dZO0kEAQHnFfzz\nUPj6oIDJZq1xFHDmRXTngmj75mhRZaux+PfiJw8w9fiJJ6xPCXnSxsY09vCKV5iiSiRU+bBFMRMc\nmBFHzM9bmmw8roJKRAU6s5MYdE4kdN9nnrEVNYX22JglKXDlf8klKgRnZ3UO/JV/JmMr9HhcBTiF\n+GWX2X5XXWXtmVu5zwAdD5MuEgmdAxaA+tflbyOftxjJ2poF3pmAQDfn/LxZI0xnHxxc3y+H1g2t\nuWrVeO7oJqPyYEEvoIqgr8+SHHI5m+elJU1rJgsBrTTnNK4zM6OZhexFQ2t4YEDHSEW3d29jGn4z\n5oxzwUZ/q68C+L6I3AlgFcAPAEBEDgJY2OC4gG2MnRSjYQYZ6z9SKQvCl8vAT34ycZok0qf699Fp\nFlsf0TTcKHGiv5L20azifnVVhaY/XpIyzsxYXQXbIA8PW8bYd787cbrGBjBSTArZ5WW1dpiGu7ys\nMYi+PlUUu3ebFTE0pPseO6YClIK2t9csthdesAwnFoMODurY0mlLh/aVHdOFOUYG1Sk0abHE4+u5\n4+haZMJCNmuuUs4llfzhwxOnFZBfH0VF2tfXWMDKmp5aTefE7xxaKqnFeO21+jukpUly0krFFF1v\nr35PLLqkUqO78MABPf/AgAXuyVn2j/+ocxOPGzs0LSc/jZyp67mcdZBdWLBW3NmspaZ3esHV8nTO\nuf8bwL8H8OcAft45RyNTAPx2OycXkT8TkSkRedzbNiwi94rIMyLyXRHJeZ99RkSeFZGnReS93vbr\nReTx+mdf8LanReRr9e0Pisjlbd95wEUPumX8GhP+GQETFmtrJpz8P1ipZAHWbiDKRkyf+fCwCm6f\nSRqw7C66N9izhuzJKys6XtbmMNWZ90RaHN9ddPy4PioVVRqAtUIgASYzzMgjNjCg1x0etup00pfQ\nReOcNQ2jcGZq88CACk2/dYBfCU+FtLyswrBctnnwG7atrel4mBHHLpkU/oBeY3JSrQQWUV55pe5L\nRcquo0wYYD0QP+d8scqe1gD39Qtlx8ZsscIiVca4jh/X+2A9E2lg2M6AnVSnpnQuLrtMx9TXp+dM\nJMx9Njio12JMikWbPj2S/7sH9L537bI0cyogJobQldsNq37DUzrnfuSc+2vn3Iq37Zl6T5p28OcA\n3hfZdiuAe51zV0E7dt4KACJyDTQWdE39mD8VOe0J/iKAT9Qbrx0UEZ7zEwBm69v/CMDn2xzXjsVO\niNFQIPvcW4D+8fwEgHe+cxyACq7ZWRVI+bwJJAblN+qW2GkMDlpGFmAWSj6vAp3bEwmLMbD/ST6v\n7iCmp3JlXas11kWwp/3+/brvtdeOI5WyYkkK1mpVM5HoBlpdVdcbM5X8hlq1mqVNsyCVrju65dhH\nhhQ3UaZlKlv2mclm9Z6OHm1MmCgW1TVHeh/A3IIscJ2a0rnw+94sLZnS861JWpLpdGPcDtD7LhR0\n3LQkALMWAYsRcTvnY3FRM9VOnGi0QlnP5DMGsJ6G1DTptBVisv3y7KwxcdPqYfyMLjH+LmgZDgwA\nl19uiRmvepXdw/y8/SeOHtXvgokgzRjFzwVdjbU4534gIgcim98P4O3113cAmIAqm5sAfNU5VwZw\nTESOArhBRF4A0O+ce7h+zFcAfADAPfVzfba+/RsA/kt37iRgO8Lv90HCwtVVW40vLakgInklGWpZ\nNzAzo39EXwgwABsF00LHxlqPh5X8Z1KD0KqXPVf6Pq8XtyeTOg4qQF+Qc/U6NGTZWczk8htmsZcM\n2zqnUipMn3pKrSnGIPxCy3Ta3C/k7iJYKDg0pMfMzur1lpZ0fHv26H4cQ7QlA3ndABXMl1+ugm9u\nTu/dn1NaG9G4FgUslZ+fPsyVP2NWfkyGY4omdDAtmQ3FOK+5nMWDVldVYbPIlDh61Hq7XHqpJTyk\nUnp9MiszVZnp2nTpXXGF3iOTHvJ5nbPZWf3t0mpjkSoVH5kRcjmLp/X02OKiUDAmh0LBFiis9yEB\n54kT6Ci2MPR5Grudc+xIPQUl7ASAfQCOe/sdB7C/yfaX69tRf34JAJxzFQCLocZnY1wsMRrn1E3E\nJmIzM1YlzxoH/oEZ1CWdyfKyPg4fnsDCgrUzblWoubioqz+erxm4gvVb5bYD3/Ig/BRdCiD/ulyB\nU5AylfWVr7QV9cqKruqpjHyGgN27TQkNDQHPPTeB/ftVIB46pIJs1y5rmUwFwxU0r8HA+6lTligQ\ni6nSeO1r1cJgWwF/1U3LhYqGBJiABcWTSUvz5T3G47agAEzp+RgdbSxGJXgMWzQkEs0TMA4fnjj9\nmguSaJU8xzoy0shVRyXvnBa60vVI7rH+fnNxks1hZEStsV27VLnu22eKhL/HYlHnYW1Nz3n0qC04\nikW9Z8ZuBgf1sWuXKqDLLgNe/Wr9LmkZFQqmQNNpHcvx4xpX61ZM8rxmjznnnIh0MdxquPnmm3Hg\nwAEAQC6Xw6FDh067kSh8w/vt/35+HnjggQmkUuryyeeB731vAmtrwPXXj2N1FXjoId3/zW8ex0sv\nqfBQ4TCOYlELFLkanJnRxl+lEnDTTeMYGQHuukuPv/HGcaysAEeO6PE33qgtj3/wg/XjK5V0PADw\nt387gd7es7/f731PA9LveMc4SiV9Pz+v1y+VgL//+wlks8DVV+t47rprAomEfp5K6f7ZLPDWt47j\nhReUNFMEeP/7tR3AfffZ+QoF4PjxI/jpT4HLLx+HiCZJVKvqWqxWgb/7OyXdfO1rxzE5CTz99ASW\nlvT9sWPAU09N1BWdnv9b35pAPK7HDwzo/M/OAr/8y/p9/fjH+v0dOjSO4WGdTxHgbW/T8Tz44ASS\nSeCaa3Q+uP973zuOclm/fwD42MfWz186DTzxhH4f76636v7JT3RB8ZrXjKOvD7j33gn09wO/+Iv6\n+X33TaBS0d9PpaLzt2eP3k8iofeTywH/4l+sv97AAPD97+v7N71pHGtr+nt66ik9PpnU95dfri2z\nBwb0+1PLYhw9Paroy2U9PpHQ7yuRAN71rnHEYpqsMTWl40+n9Xr9/cDrXqff16OP6viuuWYc+/bp\n/Lz0kp5PRK//4os6v8Wizke5rGntySRw4oSO58kngRdfnEC5fKxpq/FzgbhuptUAqLvO7nLOXVd/\n/zSAcefcZJ154H7n3NUicisAOOdur+93D9Qt9kJ9n1fXt38UwNucc5+s7/M559yDIpIAcNI5t865\nISKu2/cZsDWgSc+6jYUFc9GwhoM1IkND5pefmTE/v7+CZo2Jc7oSvPJKq6SuVtUCotsBsPTaKFjo\nRrSiMWkHq6t6X6ytyeUsljE5aSvW6Wndvnu33s/QkBXx0bLjSn5kxFKZAbNCCPrzT53SVffMjK7U\nmRVFkku2GojFdGXNgs143DqATk3ZeWk9kLAU0M+zWV1BX365rroXFoxHje5OFizyr0v3G9/v34+m\nmJnReaJbct8+m4uhIT0nv3dmYEUTPoaHzW0Xj+u1N3KJMq7BjLtcTuf0+HHNOrvkErNACwXdj27F\na681kkwW6TKJI51W62hqypInTpzQe6frc2gIuO66RtepjxMn7P57e6330syMnn9w0LjOkknlpnvi\nCeCXfkngnDuLCrH1OB+uszsBfLz++uMA/sbb/hERSYnIFQAOAnjYOTcJYElEbqgnB3wMwDebnOtD\n0OSCgIsMq6tWhU0wNdMniqQbhP1LGGthCjA/Y9+TVMrYhZkmS/caA9m53Pre9c3QyqXWLnxmZbJA\n85pcXTKgu7iotRHFogpwBtmZQktqGIKxAGaDMUOMfUwAU6S09EZGLEuNQtdnfn7yyf+fvTeNkSy9\nssPOe7Hva+6ZlVlbVlVXNXtnd3NNDpcZYTQiCY8lWIAg2iMB8sAeS4ANjQADsmGBsA1YEAwLxkAe\neCxZGs9gZqRZxJ3NJNnN7up9qcrKqsys3DMjMvZ9eRHx/OPGyfuiWE12kUn2cDo/oFCZkREv3vve\n9+797r3nnCvfwVoNjfC9BpuETWcLgHhcjmUYkv5kupGkU54/03w8jvN6KOLJQR0zYJT8yc8zNerz\nKdwd0L459zaxc5In34v2Hef13toJycGNxuhcMf3ZbovTKRSU20SIeKulwqsUZuVaODjQeksqpVpr\n7zZiMbnHPp+2vG40ZO1TYHV8XOZhdXUUpHES42fqaAzD+H0APwBwyTCMXcMw/nOIlM1nDcO4A+CX\nhr/Dtu0VAH8IYAXAVwH8piMM+U0A/xeANQDrtm1/bfj67wJIGYaxBuAfYohgOx3vPn4RazSNhua1\nAfmfHA3nzyymEtVEY0LIMKB8j1gMWFlZBiAPK9nR9xpKv1/7lRAhdL9BNjkN9o/qU3+/kcuJASBa\njvBk1iUA5b0ASvajo7h3J8vmZLOzChxghMauk6z9MDVIA0RpHCoOHx3J+zkP1aoY6FxOfr90Sf7f\n31foMYfLJTvow0N9bXxcIgSi0xhpttsa2QDauOvy5VEQBnfhHJ2ORjHZrMzd2Jh2lyQnh3PkjEz6\nfflsqyUO8Ac/WAagMGPWgKho/W6DXB2uuUhE1QH4ORbeuTHgoM7b5KTeK/YSuncDwpbczrXudiuJ\n9F79NG6AkkkFdVCJgDWcRkPbRoyPy3y8Hx02f+IxbJJ2v/GZd3n/lwF8+T6vvwbg4fu83gHwN3+a\nczwd7+8gmulHDctSaXPK2APK+Pf7xUBdvKi8GTofy9LujE8/LQbl8FAL4c4Htt//4QcVkAee0GJG\nA4RQc2c9GIxqT/04PoLz74T68rvYpRIQI0Lnd6/zokYZd/POXXm/r/DfbFbO3+mMyuVRfg2g124Y\n4jAiEWXrEzZLo0wkH9OVVCRmqg0Qw8k0EPkmgG4Yrl3TnTsbbjmjB6Y3CbtmO2TneqHzdP4OiIPh\n2uA5cU75eSdqkRI2waDK/DuJi7WavE7OElOLhBlz7thCIhZTuHCtpk6d10fkGqV1gkE18rdvy3Ei\nEZkr05T1HI/L/UynJbVF3hDXMCDvO3NGHWS3q0AMdkIleo08LCcJdn9f3vNeorgHGadSMh+w8ZeJ\nR0M9J2cK595BpAxz6oCiikj+q9fl4aOGFolygMJDDUPey4jANKXYTvJmMjlqsAA5JlNwlFdnyoH1\nGO4GKS3ClJuzTfO9gwKJZJoTFg3o7p6fdbvVMfLh9/s1pcJ0x/6+GEevVyVQSFAlgZMGhLUcjk9/\nemlEgodw52JR+6BQ2ZpOngx7SpX4/aM1qkhE2xiYprYxvnNHZX/GxuTcczl5XzQq72E7gnsdtWH8\n8KbEmS5Kp8VQc52026MpTSdCjTUVXi8d9Sc+sYRXXlHy5cSE1pzoyOm4MpnRYxJ55vfLtVQqgsCj\nE2bUyyj5mWcETp7JyGuFgq4n1ra4Ljj3tZrUEWs15QSVy6p4Uamo/pllybpoNCQyZM1rZ0ejYyoU\n1GrA66/LXHC9nOQ4dTSn4+c6KM4YDKqx4wN477AseQgta7T4z0IrH2Y+xAcHKq3CSMMp5U7ynlOY\nEVCCHIuilAgh54HnmUiMpidYnCVzPhwebaD2boO7+40N3fWHwyrDD4w6Ghq4w0Nlb7OZFQf7z3e7\nYihyOSnOcx6dTd+40+coFuU6KhWNCCMR5VawCRrlUwxDjLDPJ99BeftwWM+JfVOyWVWNpsYZm5yN\njyvjnXBjFvy93tFzfLcIkQ4wmdRzZ5GfdQ8SWp3DKaAaiaiBN00VoWQ0cu/gPeZwpjwBnXfbFrAD\nJXcYpSSTWqOiszAMeR+jxEhENz7c2BDGHIlI9E7hTPZdohPmxieTkbUZDMrcUxWbqgrOJnCU6Dk6\nUij7SY73AwxwOt7H8X7XaNi3xFlsfDejTCl7Ks0CauwoxkjlYzKcWVzmAxQOa2tg7nTTafn/ueeW\nAahBC4XEmUxNaZolGBQHRNFBZx6+XJaHt9uVNAQdjZMHQ6fjrF04NcyYkgkG5fj1+mh+3LljdoIE\nPB51phS5BEZbBZMl70xn8Zo44nGB97KwX6ups6hWVd+MEVq5rEg+OkFqoQEyT7Oz8r5GQwvNfr8i\n17JZ1fUKhxVwwethB0leU60mMv10ek6nQTAIX2Pk2+3KxoM1PM5zoyFAikZDU0+876Yp0GFGJh6P\n9n8xDDHEzvtIR8Z+PNWqElzJ2E+lxLHk84IeY9qxUpG1yhoLHRXP814HwHXP+04lh3BY+WOcr3Zb\nlRHIP9rfV5WD3V2tFVUqMj+UNkomZQNw0o7mNKI5HT+z4YRQcsdN1IwzdUNxxHsHDWSlIkxpGk6m\nxdhPhfpSTk0uw1DEEWXqAd1FU2KD9QeO+0GXaQBJPKzVxDgyMmC6jLt2IqcYMVmWwnSTSe2jk8tt\nCwAAIABJREFUAqjxmpmRz1IrjEbYGbXw+omac9ZyqA5w5oxqZ1Grjdc+NiZzxnRava7KwZTdYdTA\ne8JivcejdS2nYnS9rmKYNLBsyMXIKxbTOoVTDRnQHTqP6azzeL2qQkAJ/r09TWvlcmI0GX0ymmXx\nn5uZmRl5TzarqaZiUc7L69X0K6BdQ9kUjPePPWRYlyG4ZH9fgQA06k6RUHNIYGV0UijINUQiWgcK\nBlWmxu1W6R3TlPey/sdIKpeT+xaJKNDC65XPBIOqhE1Qgc8n72u3tUUBNyvVqkZ85bKm605adunU\n0XzAxs+zRkOVZErDh8Mq/+EsXDeboxIerZaqzvKhZVdIv1/1y27dUgTP0ZGKNlKEkFEF2wA4kUck\nYD7I4C610RBDx14vgIpHttval8U5D4D8rVSSc+Xf83nte8K+94w4trfl/1RKznd3V5FDlJnvdGQ+\nTVPy8EwdAcJzSaXkfWfPymcJ3Y7FdCf75JNLIxpehHvze4JBRSXRqYZCUm+hnAo/S9QXDTIjDkaf\n6bRqsbGVNRW2gdF1QV4N72OppA6KKDY6wXx+FDZt26rlRmi38/iM+Ih8o4rCmTNLI3B2Dm6QDg/1\nmIBGI0wp3htx0fmwDre5qZGDM9U1Pa2bACo3Ex3Yasn/i4sSjR0eymuXLsl79vdlg0FxUEZujPYp\nzkq+EAVI43GFgV+8KPf9zTdH1+BJjVNHczp+ZoO8iFpN/rEbJHkOpim7skpFjC8L2aWS7ORoBJxp\nrE5HjrG2pjs2woqTSc17ExQA/LAEPyAGr1rVSOu9DHIc2m2VijdN+V4WT7kjdQ7uKH0+2VFSY43X\ny7qPs05FxwiI4SJ6yjCUh0HH7BRhBBSZ5RQGpc7W+Ljm55NJMVrsddLryfkvLMjrTBsROk51Z+d8\nsJ2y08DSmPN6CCEmqZRGsF5XcixTj+ybws9R0ZjHJdJwf3/UubZaso7IryK8mzU8RjqhkEZ/TNux\nbTYjKDrkqSm9NtaQmMZlW2Q6/sFgtGMnz52AiJkZ4O23FTBCEMXNm/La/LzWqmo1mf/dXRUNDYdl\n47C6qmjAnR3l0rTbWrezLLkmv1+ek1hM5ouSOTMz8v2Ep1OAk+2gKxVxYic5Tms0H7Dx86zRODsm\nAmLYCbP1+1WlNxCQ1zc3hQhYrYphpiPgbpeGlC112WSKxejJSW2INRho46n7AQ3cbuDtt5cfOBc9\nP68cB0CuwYnQ4fc5G0eRWOqsHzHdQuNSKslrExNyTBpXOhW2ZSYHJRKRXTgNHol/1GObmdG6CKDS\n8QQysPYVCMg8WJYYG69XHUKppDWPe1FIdHqMqLgZYISzt6f3pVhU58sOlAQ+MP21tydGlPDetTW5\nvkJBI4Z0WhzD4aEqHzBVSZgza1LVqhhXOphMRvvQUDmCyDrOQzQqcjB+v0ZekYj24gmF5LtKJflM\nu61R6OSkrA1C6rlJcLm0ORrnttORaPXgQDlThCFHIpoyY2+Yy5flvjebCr2u1eQYjErp0DgnjCQ7\nHfkeogfHxgSsQLWLRkMVu1kv4ro+yXEa0ZyOn8mwbZXv4IPEugwlMLgLdO7O9/cVKeP3i1FxFpQZ\nnbTbynRmOoUdA1stNQbvBpt+N+LljxuE3zKVcu/xnamZyUmF7zJyoeP1eJTQF4tpym12VueM10TZ\ne37O75drNE0lOTIiYWqGhWLLUomeXE534SQPkvhoWdrEjN9D7kqjoa8DmhIF5PuZ76eBq1S0URmR\ngV6v3CfWRbJZudfkMlGUtN1WvtT2tgiF0lFFo2I0iaZie+jFRTkGWflca4mE1rkYOZGMypTc0ZH2\neKFT4vmWy3IM1kzI4He7teYSCGikwAZo3a5GUvv7Gp36fFq/i8W0xnf2rJxPo6H1qXJZBTu5zshh\nsizZUB0d6cbG5RIHzeeO50BFZzrTQEAi1kZjVMB0bU2uaWJC5oPIuZMap47mAzZ+XjUapi8o98EH\nwrI0ZHdCbmMxfZCYWqIDotw/C7es30xMjCr1MhfulIuhUeaO3TQVzru4+JPNxb2dMJ2DqT+S6Ki4\nOz6uqZdLl9S4cpAHMz8vRo3yOEyZFQq6c/Z6dZfKmgQNLBni+bwq9hIFx+gjHtfox+cDvvjFJWSz\nchw6znubfvF1oqUYORH+TcUA7tyZ9mT6iHUcOgQWnknmfOMNlZ3p9eQ4BFqYpmp7ERrPVtXJpMry\nMCIolRQQQiBCrycOytkEjOAOv19RXU88sXQMMDBNBVMQlu9MlzkBE4DUT0gCJTHS5dJW1EyZkdnf\naCifiI6Zcj0syrOVNSMUr1c+t72tKgHz8xIVcmPFFGg2qwRTn0/uOVW5iXys1WQub91SOSO2ejjJ\ncZo6Ox0nPlgwp5wIC5wslnLXy9FoqCw6C9FMrzBFsrqqhpvomnRa3sMce6WinAYOy5IHmAgrppmc\n5/qTDPb4uHdwZ8+IgbtGv18e8itXxEEGAppGY/qs15Pr3N+X62DdhVpgjP5I6HM2H6OBYz2iXtfU\nZSwmhojGY2tLRRbJdQG0YyMg318oyPnzGppNiZiY8gmHNWo9OlLElmlqPY3pHs4BDX0kog2/3G6N\n6AjtHQxkLt54QzYXfr/8vdmU9XL2rDgfvpeGnJ0/Wf8bDOR9TE1xPti7BtC56XRkLpiCIpCFfWUI\nVafApc+nyDauSyIc2fuG8HdCwhcWgMce0w1YJCKv87ubTbkPicQocMLvl7/RUR8cyH2h48hkxPlQ\nRsmp72dZeu+JWPR4lBbAepwz9fig7S5+3Dh1NB+w8fOo0ZBXwR2tsw7iLPQC+jD3emIAqKdFHa+z\nZ8V4OXPQ1aoYaspvpFKjjos7Wj5ozt0Zd9aBgOhaOeHDDzKSyVG9LQ7yR5zcjXpdzodINbL8u11t\nMcyCPwcJhXTUJDDathSB2aSKEdvOjhJBOd9M27hc8h6CDsieZ37/Bz9YPj7327eF1Fcsjjphdnik\nsQ4ExEguLqpRJUx5ZkYiBkAMdCIhqKazZ+U4uZx8/8GBFvspk8JodHJS1gKdJR0XWyCzjwvXysSE\n3HfKtDzyiNx/8lzYOIyCnCSPstZEwukbbywfS/Ds7Mjn9vZUgJJpKqbhyDkhCZIABDoe1qzYlpmK\nzaap+mpMbXGDlEhI6iocVlgz08HctLGu4uTUkEfWbqsuH58pOkeqaJNjQ0fd6ehzSHTlSY7T1Nnp\nOPHBgrPTcMbjikyigi13T0wztdsqVR8MivGgfhj1paJRjVCuXFEj1Wqp8wEURHDzpnx+YUE+RzFK\n8kGYv/9RnTMfZDDXz/QHO1u2WvLQFwpyLUQoMW3jdisUFdDIhFBpIqTW1+VftSqGdmxMZXYqFZl7\nfn82q4XpXk+MV7MpToQ7+Hxe5r9UknvBGgNl9mkIy2U5F0ZxlYqCDdixkZpfU1Mq2UOjSk5Jtyvn\nT+JpuazSMjScTukXl0t+5rGrVU3TUWGaxpu1vE5HZXvYQI3RjWlqJECHyTVJKRhCund31cEMBjJv\nTDuyVQO5TQSvsLa4vy/fSc4SU7/Fory30ZBjTU6Ofkc6Lf8z7clWA06u2dycPjP9vtRXOh1db2Nj\n2qSuXpcI1jTltbNnlRR8cKCK0SSnshb0bp1ff9Jx6mg+YOPnUaPhrogtgVm0p1Eh+oeLnDtxhuvs\nFkgyG3XMuEujPtre3iihkcaAuk+Hh4rsKhYVSUVn9OyzMhdkov8oEcwHGTRGhYKmahoNMT6sdTSb\nMi+sRwQC2l2R/JJ2W86t3dYd/htvaN8QkuxIxFtZke9+7DFJOxHmvLsrP1NRmFIjrGmdP7804pR2\nduS4/b4IXzqh2U5FB6bUeJ8IRWetJ5FQ7hKVoSnz0mgogZPKCuPjirJqtQSc0GwCN27IORWL6pAi\nEbnWgwP53YlIJNw5HFZ4Nom8R0cyl0xt1uuaiguFpBnYyoo4C4ILgsFRyDhBFi6XfNfOjsobNZvy\nHdz8eL26Idjf13tHR+12S8orn9ceRoSNB4MqphkKScfSdlu7mZbL4mRItqVGWSql5E5nK24+ByS+\nckOXyynE/eJFiWqp9HBS4zR1djpOdLAvBndQrCs4ByXS+30h/bEwyaJ9LDYqtBkKSeqBuWyvV97j\nRI4xj0+UE+VhAD2Oz6fQYGCU73JSHQWZqiKHiPBkJ9Sb7G4aS/I/iOCq1ZSIR8PEJmjUJKMO19aW\nfB8LykdH4nDIXq/V5HOso7AgTWkepuWcxpSF9FJJ7g8L9um0pMUoy8NidbOpIASPR+ebLYrZ6Ovw\nUP4RsUUmfy6nMiumKfetUlEUIaMzZ/Q5Pq51Eq4Z9iEqleRnOi/T1NrR2Jh8D9O6VGDgOebzMueV\ninJqyL5fWVElADpsKmMTkOJUed7dVWg2UWtE/zFKvXVLI1F+nrVNriVugqgFR5TbvdI3Fy/KeuOm\ngUCASkVJnJWKRJRUo7Btua+BgHJ5ZmZGm9edxDh1NB+wcZI1GichkGNnRxY/c9kcRM2wgVMgoIKH\n7bYYnelpeTjSac2/E1lDIzs2JnUBFn4B2fkuLMjPrEc4AQHsxMj0Dcebby5jakol5d/LuDd3zeIw\nDY2z+Rb73jg10KizRqQd9asoIUII8va2sLTv3hWn89ZbwAsviBHisV97Td7v8YgBmpnRegGvO5+X\nv7O7Jgv6rZYY8XIZ+KM/Wj6WCqI4aDot50cHMzmpYp2DgRhwtmxwthtg6pApM8OQc7h1S757fV1V\nhKtVmTsCOhoN5VJVKnIe4bA6sHpdYcGUk2GtaGJidAPBtF0goCk11h5o9Ol4GfHk80A2uzyCsON3\nEjjRbCoyrFgUR89jMoJxXl+vJ+e6uSmOh6x+8lRWV5Uzs7Mj585InW0CikWNjpluI9PfsuQ+zszI\n/4mEyjHxs6mUbNRiMVlXdOzceNGJOXsSnXRD4tPU2en4iQeROURCsRYB/DAAgKE46zbM/R8eymIv\nFMSYTE1p/YSFYQoAkjDHIny9Lt/NnfHU1GhqjA6NhuN+BU4axlZrlGTJUS7LQ0dtMz64jNIYqdRq\nmlcntDeRkIefOltsd0Cn2WyKcaGTazRkfjY3FY5MGZJYTAwCU5H1uqLNkkn5LhajCZBYW1OSJlNL\nhiHXkMspq55RAN/TaikHCBDn4PFo/SaV0vtOxr+T4EeEFzch+byKRlIvjRBoEhR5T8kZooad1yub\nCNb12OLa5ZL1wAikWFQIdK8n80vU296eRhBsYc2UIyOwQEDOb3JSeTwHB6powciG6d+ZGTkWo8te\nT14jArJQ0AI/1w173RCBuLqqsvx37ijniRuUvT1t1UBODLXk/H6576zlsRssNdDyeZm7+XlNbVar\n4uyqVZlTqnJfuiQbGqZ4ef9Ocpw6mg/YOKkajZO0l88r2xqQhe9soctUiVOFmQ8ge8Qw/cOHnoNG\n3DS1sRkNCaD6ToA6JxYyk0k5D6csyP3mgqg0KvpyONsUsFgKqDwJWd7Oc7VteWh9Psn7u91isJpN\nrbHQSZGdT2FJwmMbDfmOWk0NNPWuKIXCdgbdrszF1pa87/x5heICcl+oM0eHms3K6zMz8v1Xry5h\nb08dpd8v33vjhswf2zmzdQAFM0n6ozhjICDH8/vld55jKCTHYfTD4zNqobApi9mMQIiKIkqOqDJG\nQEyldjrisKenVdeL72FKcnNTPkv5feqKzczI+VGi/9y5peN2E/2+ws3ZmA1QdQB2ayV3K5FQDgqj\nasOQY1DZgOjJGze0cywNPuHpHo+qLTsJmOQIVSoSxafTKvs/O6vN01i7Y3Q6OzsK9GDtik3rvF5g\namKAy8k8ui99C6Hrz6HY9ON/+DE24EHGqaM5HT/RYE6Zu0PWJACBttJZMH1AYh+Nej4vv4dCqpRL\nljUgBt7ZqMwJVya8k5Bo53DWg+5N39EY3svmZ++Sex0Nmd7k4jD1B6jGFA0FkV2sTwFiOFi8ZfG5\nXBaje+mSOAeSHZnyYnqFpDrm1lnYZR2jXFZtrrU11ZOzbeDqVRWdZCvojQ1NAbGgv7+vwAzCzInQ\nOjwUQ5bLKXQ4nwd+7ddGIxXe92hU7tn4uKTJyKZnMZq1kGBQDN/amrYOpmZXpyMpHsrrE4lYLGo9\ni02/jo5UVoXpuYUFOc7+vp4700SAnAP5WgcHsrFhqojqy+ThpFIKO87ntQ4TjyuZtNNRx0XQSrWq\npGOCIKiQXK/LRuArX9HGZem01sTYOpr3iGhEdolNpXQj0O/LfeFGglEV1+/MjEaibHR3cCDz3esB\nXnTh2j3AWTOP6bdeRvDGdaRQPJY0Cp5GNKfjpxnLy8s/dVTDXTegfV5sW8N7RhhM//Az6bSSM6ki\nHArpQ8TcNh8oGkQ24iLngrvkePyHz8005XuYRuIgjJhoL+dcMP3Gfix0emSDA4rSevhhrStwDiid\nkstpDYX5cEYczgZilECpVtWIONNqhLgyNUL0GeHY/b6m+UolMSisi5DjwVQKd8Jer0rEOBFK/T6w\ntbWMmZklZDISFdCZORFkLMIzBVQsapqKdZR2W9I9nI/DQzmneFwiQP7e68n3kGxKFBejmulpRSAS\nRRYMqhgkI6NcTiNew5BIcndX1azZO4eSL8mkGmmSH0MhBY5MTACvv76Mj31sCaGQvI/puVZLItRi\nUdFbJO2y9sX7ceuWogVZn+N83rwp59vtarTV6ynCzqlkzYiXpFjypkIhTVePj6t8E9NwTPWy5vXQ\nQ0PQRGeA+e4a5ra+j/k3/xQwgFgUGNiA1wN0oN9x5yclmL3LOHU0p+OBB3e0waCKAjJSIYmSxVVy\nC2IxFfwDtL7A4iU7EN7bA56j1xuFXDYaYpDv13KWfe6dI5kcRQc5h7PborMjJ+tNZHrH44ryMU2N\nbvhZ1k24Q61W5TyZEiMDnpEPBUY9HnmdxofKzmwU5vWK0WFDNhZ9qQbA40QicozdXXEKsZi8lkho\nky32iqGYJBn0CwsqC1MuK7psf1/O4dw5ef311xV0UKvJ+UxO6vXQkTllVphyojGmfEunI9cUjYrz\nZlM01rA8Hr0GFqhnZxXZxfQPxS0LBblOpupWV5UkmUzK+3mOXKdUrHA2pWMPHp4vIc28Hoq5hkLi\nFJk+pFSQs50z0XyhkK4DQDhgJJMSRcmNEAViGQGyFTTTl16v3JdWC0hFunAN8shvxzBuZ3Gu/w66\npQYuWkWMrxTgumEhtOLClC+C8K0bGFR3UOpZ2Op30TAsfCqQxLlYADCAju2DHQqj17BwfW4CeHX5\nhx+Wn3CcOpoP2PhpoxnqhDEVRql2l0sViNl4CdCHk+93pgJiMQUHOAmT99ZSUqn74/qZX36vg8KO\nHEtLS7Bt7XzIFgOAijtyN0pgAQmOhYLutMNhuUYWoElGbTa19zvfQ72z1VX5HqbD6JgASa94PJJS\n2tiQuZ2dHZW3TyZV7wzQKIpOkKS7WEzmjwV0RkTPP6/KA37/Et56S40jrwuQ+0kp/f19RV51OnLc\nYFAiCbbPZrosm9UiNFUbqM1GIz49rYV/Os1+X6VYCBbweOT+eDzi6AxDDDH/zjrY+rpyStbWFElF\nx0IgCQEWrBPF49pe4MKFJSSTmuqbnZV57HQkGiHYg/e925Vz2d2Ve8V0J9FwXANTU5oinJ/XtByj\nRbacYGqvWWwj6HXBrtbwaGgPnptvIngzi0jSg2xsEZ28G4GV13G+9Co61TZK3R7aLgvBuAfxngeG\nAVwaytV468CflLfxdrMCDB22yw24XcDZCxdw/tPPovTwJ9C+9AgyebeANl77f4F/87vv/eH6MePU\n0XyABx/u9zqYDuAukHUCpj6cRp991+l8yNxnTYHsbO7Q2QCLXSYTCU1RORFsjI7YMOxBhtutKRNe\nN/vDAPKgT0yosyRJNJVSo0D1ZJIVaRwffRT46lfl/UdHmuKhrDuRYYWC9CWJRuU6CH8uFGQ+SXpk\nR8mzZ7XgzQZZFy/quTebYigJvmDaa3xc7gGdBgmzBBaw/tHpaPqL6cJIRNjndAjkjNAo3rmjqanF\nRXWgV6/KHL/+urL8CYV2tmFm4y8KrdJZsNMnU3bc3Y+PKzGRUcb8vNZBmMakU6E0fygkDoBOIZWS\n8yDUfHJS55UFfduW1BfJrUyj8n4A2l+H65ntkJ2KA3S829tyrLU1+f7tW008UVvGWWziqBPDUfgc\nzEEPF//iu0iUN9Hr2fAYfQS7JbhMoNdXJ2R1AV8ImOp+G3cKBTzfKONPYKHUtdDp2zAN4NcHM7hm\npuB2DzlOraFyQt8DA4DhNlELT8GKJhE8k8bNT/0tnPu1v3a8CfN6xaGa5n0gmD/FOHU0H7DBugSL\nxw/SH5xdLM+cUb5HtapGxedTmRXCOJ0ggX5f1W/jcYliuNOmoQyFNBVFBA1rIcyxAxoZPcjgdfZ6\nYiC+8x2pTQBi/OgccjkxEHwfeRxURyZJkNLulgVcv65In05HdrfsFEqekLOHyPS07HJZjN/dle89\nf17mi86IwAA2dvvwh8XYGoYw6Dc2tEbBXH4komrOgEYUu7vqyBklpNOi73X16hIWFhQFx7oZjS4b\npmUyWvxmC2KCMqpVcQAUsQwGVVWAXUQpTElWPTcvpinpJIIY6KzHxpRrRVkfqkpQ+4t1hXpdzp06\nY3QOgYBEE+vrMu/BoPbzyeXk2DMz8r6trWWEw0vH/Y7KZV2rFOh84QVdy05pHiLheC6l0lActtVF\nYH8d577+J3hm+xV43QN4vcCYBTw0fDZyvTbW0EK510WpZ6FkdVG2LHwknMaTgRQCQaA/ANrDTUKp\n18XOoAF7APRcosg6sIFCx8La+U/CN5FAOLmHI/Mi3iqdQWnvT2E1X0UjPoOWGZJUbRNYXS3hiSc0\noi8U2CTt4oM9XD/u2TvRoz3AMAxjC0AVQB+AZdv2hw3DSAL4AwDzALYA/E3btsvD9/8TAP/F8P2/\nZdv2N4avPwHg9wD4AXzFtu3/5ud7Jb+Yg/WHoyN5iMiheLdRLssCtCx5eGi8slkt6nMHSGFBp3rs\nxITWP8JhMUxMuTmH83e2x2W6615EWaulxWTneToROE5UmtPRsFhNJd9qVUl5bEzV6wFPPqkEPe7w\nr1xRKQ/DEGPP4izZ+YQTU8eqWpVd8O6uKgNUKmIYWXMguZIIODLcw2ElTJJwybSjz6f/E4lHwc6N\nDRVdbDYVlksEF2tZoZB8lpER01d0kHSmRDAxIojHVYttfV0lZFg/iMVkbZEJT44IyZnUCGMtw6lO\nEAzKvex0gFdeUS0yEnvpxOnEYjH5HsoUlcuC7Ot2xfnduKHSPlevKlmYEVwuJ3Uotmtg6rBYVLg1\n+/XYNtCrt7GS8WA+XMDDg7cQuHsTZc8Y3O0AZmsriN++jnJgHEY/j/aggVK7g/VBFxUjgMuhiBBK\nh/WlXh+42a3gm+WsCsH2AY8byFkd5McWUIguoBObwFx7DWa9Ap8ZQqMVQzs+iZYrjHqlj07XQHHy\no3jmmS/hQx8CDi4A/TpQfwmozgQw2AXiviRidgKtVgKhUBKGsXDcqI4pUrn2xR9tEB5wvJ8RjQ1g\nybZtpyD1bwP4pm3b/6thGP94+PtvG4bxEIC/BeAhADMAvmUYxkXbtm0A/yeA37Bt+2XDML5iGMav\n2Lb9tZ/ztfzCjKWlpePWsxydjvZ1ebeOlIeH8pC6XJIaoUghyZgsVAMqgc4eKsmkymA4mdrvJZKi\n5LmzORqgn2UDLEKNnbI0jcb9HQ2bok1OLiGfl3MPhaRuwmiL+lAUxSTZj4KehGGzbkFYq2lqD3f2\nS2EPHNZrWOOq1YT9z6jAqWjMPiTcrdu2clPKZSX/7e+rM6bz42cpV7Ozo43FKFVDMUzDAJ5+euk4\nFUq+Bx0BgQ2UxpmdVR061ny6XXUgmYykiag+zLXAWlMgIFEbO1eSlU/NMEANPwmS5bLCtAHlyTDd\nRTBKICD1IkrfUESVEjlUFN/Zke87OBhd9yI+uXQMRafD8fmGUXWjgeBLf4bPP/cS/NlN1Kwu+jYw\nn/Kg3x+SSYcK1svVAr6WeQem2z5uATHoA89GUricPodB2A07mUJjp4x+y8LA5ceRO41uLI1ue4C+\n4UYsauNbiWfwxsR/ecxTm7zEBnJvo3f9X8JlCxTZ7Q7DMJIIh2OYm9P1Z5qS3lxcfAKBwBMAZBO1\nuqpAisNDjRYDAdUePMnxfqfO7q0Q/A0Anxz+/P8AWIY4m88D+H3bti0AW4ZhrAN42jCMbQAR27Zf\nHn7mXwP4AoBTR/Mug6gpQOGqhAKzux/F/ZyfYe8Uy9L2utPTqtJrWcryp2giMErm6/V093o/aPL9\nBqOZe3u/OJ0h+9C8l2HbYnB2dhTtw/4prDUxcqLxZQ1pe1seTHIw6nWJUFhnovOmdtVjjyn/hCnE\nQECufTAQwxYMynGINrt7dxTiappipC9elGNsbyt5kCALEgOJGKPsO3vNUAGbUQhTJESsXbign+H9\ncrvl98VFqclkMrqbpzhmMCifpZhnpyObECeplu2c2S6AToD6bq2WstlZ53O5ZC52drR5l9crqUL2\nKyqVRrtcUohyclI+QxVw29a6YiIh37e7q2oSJMAerjdwbuU5TOTvwnQZiBlVBAc1eNtVJP6/Mu7W\n63i7voMXuxbyHQvlnoVu38ajvgT+dm8OBgDXUMhyYANe24W+bcNtALCBgdePGqJ455FfwbV/9D8h\nl5PvpWr2zs4tFK7/C9gWMBg+TwETKNWqML2qBnB0JPf4qafO4dq138L580ksLibQaPiRyci9vnxZ\neTtUhQgEZFPCGuPCguqgdTpyb6n0QZj9SY73O6L5lmEYfQC/Y9v2vwIwYds25dyyAIaZe0wDeMnx\n2T1IZGMNf+bYH75+Ou4zGg3ga19bxkc+soR0Wne17LLH4VQyJoKIToKwUkANg22Lk1lYkGMxx09C\nJvPqgMqevNfBOomz5QDw3qIhGnfKdNy+rbv7QgFYW1vG5z+/hH5fzpkQ6HpdHry1NTFDyj9MAAAg\nAElEQVRqBwejjdssS3Z9N2/K/5cuqdZVoaA776MjVTxmCwRqt9G5cF6ptsu56nTkWOPj2keG8OdG\nQ50U54JzXS6LM2LTOEJ/2SOepEM2EGu3pVb11//60jFRsNvVtZHNijGcmVGO0sQE8PLL8nM2K/cm\nlZKUHgEQXq/8XK3K+TjToCQ8er1aPCfHB9BeOKw3EdZ84cKoA2Hqk06f8HiivQCNNr1ecZr1OuA2\nBwj3DoG178KTv4lwbQULhS2s9S1U+hb+q9QiXC6piXg9wMAEqrUqXmuW0esDpiH5ewNA1edBNnEF\neaQBVxUuvwet+BTuJjs4yH0H8dkwCiUTlulFp2MAtg97e5Kqmp1VCHw8Po6pqafg8SQQCCTh9SZx\n/nwCxWLyuEUzpWiaTWBtLYzLl6/C45FjhcMSKZZKck9XVxVkEo3qBoqAlkJB+DX7+/L3qSlZz/2+\nSh6d5Hg/Hc1Hbds+NAxjDMA3DcNYdf7Rtm3bMIwTC+C+9KUvYWGovBiPx/Hoo48eQ30pNPlX+fdi\nEbhyRX5/551l+Hzyd78f+PrXl9FqAZ/+tPz9q19dRrsNfPzjS2i1gG99axmVirS5TaeB731vGZ0O\n8NhjS5idBV55ZRmZDJBILOHoSAx4oQA8+aR8/tVXl+HxAJ/9rKRolpeX0e/r9/2o87csOX44/MN/\nX1xcQq8HvPyy/P6rv7qEQAD4xjeWkcvJ9dq2/F20s5YwGIhhpRSKRCry90cfXUI4DHzzm8uwbeDx\nx5fgdgO3bi2jWpXjWRbwwgvLw7TTEmIxYHV1GQcHwMMPy99v315GowG4XHK+Kysi1Pj000tIJOR4\ne3vA9PQSzp4Fvv/95SGzfWmonLs8jLiWhtpny0MejRAJ335br3d6Gvjud+V+ffSjcj/u3JHfz51b\nQjQq8xePSzuAwUDu3+6u/F0iqzfxgx/I+UuUI5+PxSTNur4u9/PXf13+/sILyyiVgPl5mf/NzeVh\nVLM0LLIvY2sLmJlZQrEoYAOvV9bDwQFw9+4yJidlPtpt4MUXl3F0JMdLpeR8JfpZQqMh83lwADz7\noacwtvcO1n/wAg4a07h85QtY2Hoe+88vo1K28agdw5Sxh79oNLEzOIOw+yGcza/Bk1+FZXjwkdo1\nhLolbG99B3m7hre7JQwGQH4grNwE/HCZNq4384ABfDSShtsNfK+cR3HQlQ2GJ4j9SAxGPAZP4Ax2\n+lNYS//SsCna0nCTsIxOpAbbHkPXFQV8JXiNMMbGnsbExCSuX18ecsqWhu0DZP1NT/+9YQfMZQwG\nJQwGjyCVAsplWf+Li0tYWwM2NmR9Tk/L8/jCC8uYngY+8YklTEwA3/62NPR76ik5n+VleV4/8xlZ\n38vLy0MC7BJKJVm/zz/P+tQy8vmtB6INvJdh2CedjPtJTsIw/imAOoC/D6nbZAzDmALwHdu2LxuG\n8dsAYNv2/zx8/9cA/FMA28P3XBm+/p8B+KRt2//gnuPbfxmu8/0ati27ymJRUjBkxhN6Sx0ppkbY\n6vfgQIlqbIIVCslOjNwT25ad1Kuvyk6I6RwqAVCteHxc/rawoBL3sdj92yFzDAaSVrn3fewKyJ0+\nU0kUAwwGZbfLHuyZjHyOzPm33tJaETtUhkKy4+31BGnV60mem8oH2azMxd278jNrR7OzMi+sFZCj\nQQg12/ACUrdgG+uXX5b5P3dO5rpYFCgzGfDswTI5qbBv1ktY/E8mtUV1o6HkTNZM2F/+8FB2rE4m\n/+6urAX2IiFxMxaTc3jnnVHC6pUr0puGAIxkUj67vi5rq16XuaYQJms27KXDlF2jIefI6Ne2RYWa\nRXnWjy6daaGzsYfuQR7eYgYzrXVM774Iq9eGz3ZJVGxIwXwwANZKLfyb4hZaZg9Wzz6WDpr0BPB3\nfRfhckvx3TCGkF+zjd+p3cHgWL/MQAMhGLEFfPGZ30LHK8zIxeqrmHvnP+K1h38d/2LtO2jbXoTD\nxhDyHUCvN4lr134bV66IoWbUUKvZCAR6SCY9CATk2WL30ulpRWtSjfnuXeUKkQBLNCdrooRjs5fN\ns8+OrsPpaU1JkhRMSHujIaAIw5D7Ro03rp2VFVUWYHT9e79nwLbtB8g/vPt4XyIawzCCAFy2bdcM\nwwgB+ByA/xHAnwH4uwD+l+H//2H4kT8D8O8Mw/jnkNTYRQAvD6OeqmEYTwN4GcDfAfC//3yv5i/H\nID+BpD4WMsPhUc4J9azYg525eTZyyuVkYTMXT7Ii+3mMj2vqiP1TDEPC7/V1bSm8uKjpLaoOU5OK\nx71XW4yj3x+Vn3emyajtxEFhSdaa/H7tqklZGLY9puowpUHCYWXkM1fv88lDzY6GvC52xHS59Lg0\n+AIHlblgq2GfTwvN8/NynfzMwYE2GXvnHbkOqgf7fPI9qZS8j/Lvt2+raGcspsi/TkccPWG2lDUx\nTe3hQ1QWu3vSac3OivMgUCGXU5ADWwXTYRYK4mDJW6EGGO8npVnYVZJ6ZTxHv185SZ0OsHLTRq/a\nhD8ZxFx7HcbuDibSfcTWXoVv/SZ8KOK5Uh7lnoVyv4u6baFoWUi6vfiHY5ckBTQkZJomEAu4UOlb\nQF9Ts6YL6LgtxGKazusP0VwJjx9Wyw/b60PZSCHrn0fL9sHnM7F16bNoNk14vcD22JOwz/0DzM/b\nuBI6j3g8gcnJJMbHE9jd9ePwUEUq/X6twwUCBsplD1otqdW53WLMiU7sdlWx/OZNeb6od7e5qeth\ne1vuNSVl6JhIDC0UNOVINQaiCO/c0S6jrMdUKnqOTMM5U7xXr6q+3EmO9yt1NgHg3xuyItwA/q1t\n298wDONVAH9oGMZvYAhvBgDbtlcMw/hDACsAegB+0xGi/CYE3hyAwJs/kECAdlsNDfkr1aoaU8KQ\nX3ppGZ/73BK83lEFZIpj7u1pSom9NVgopMEnJJrIqcNDrSvwYWYr5lxOaznckdfrKunuHNRMOzyU\n7/N4tIHX4aGCFaiaS8TS3bvyWaJmCC8+d04iA14H6z1kyt+6tYwzZ5aOjSK5G9QgI4qNYAiS8Obm\n5D3xuEJ5qYxAWX42lZqbk79lMopMc9YxSIJki4NoVPuTEJ01NydOh71MGIFls4oui0ZlbojAqlTk\nmqh7RWd6+7bCqum4NjaWEYstHbdMLpe15sHCu2lqd0oSK3m/eC2xmHye0QyFUBMJIBbqwvX9fw/j\n7ito7+ygX9hCZWChhwH+k9gZ+H1DflIP6PSAvgf4XuMIvd6o+vYRDBTPPYHx7A24jQ7a7jD2p5/C\nIBpBtfX76HQBX6+JYOMIfa8XpVAQRwuPohlfgB2L47CbQikwjcPwRZRf/z+QTgcw60sg0UhiMEii\n213FYCDre3tbFabTaQNTUx875opRWonRGtsiB4MyJxcuyIYN0G6pxaJEHc3mqGwO7x25RZQfoqrA\nxIT8u3NHo042veN9Zd2K3WypnEBEZiwma5VAlkJBolqPR6N/ShPd27fpJMb74mhs294E8Oh9Xi8C\n+My7fObLAL58n9dfA/DwSZ/jL9ogyqvRGO3DvrurrWVJhqQ8OaAyGv2+kgm5az46koIhe9DHYhL6\nM+JgZ0MuzmRSd7OBgCzw1VXZWXc6qpBLwxWJSJrK65XFX60qjNcZadGYt9uKoonHNTI6OtLoiNL6\npinFfO7mGK0xkgmFlFxJ1rhlycPLh25tDcdpj50dDOsq4sC4kyUUlE6eDoOOiKgvGmdyZiYmtLBd\nryuMmgX6SERJmCSmEjlGwqVlyc88LpFVhDyvrkrUwv4k7AdDIcr1dRXbZKRx966KdpIXQ8kd8lDY\nCrheB3z5fZxfu44nmivYN8PwXN/D47EYMpUAAuNhFApA3NtCYOtN/N/byzANdVAA4DYNfDFiw3QZ\nsHoiiwIf0O+5ANOHXsgP2x+A5Qmi6wmh4J3EXzzx32HpGRe6Oxm8uDsLf9gtKKvb66jXywCiiESS\nSKUSeOihBHav/Br29oLHAq4+H9DbBJ588r/GtWu6GWq1gPX1Etpt8/i9XCPsAzQ2po6+35ffbVvR\nf9xwcG5tW37mpqzXU9UBQAVIqRBBzT9usthO2+/XzVYkoikyboqI+jMM4X5lMtoplN0y2ZenVpOf\n2QOHvZiiUVkHh4dqH05qvN/w5tNxAoPpHyKV2KyJ0GPyDeJx4FOfWjrO/3LnRHQQZUiYepuZkWPb\ntqY+GIWkUmpkmbdPpUTdeHtbzmF1Vd5PhjbTWawVUEBxfFzSBU4FYsKXCTEmVJO6UM89pzUj6nux\n34qTD+T1SkSwsiLnkE4rB+jcuSVks1qLWV0VR5pOq4Q/ZdyZ8mCagWzyTEZFIufnFenW72uKrVqV\nnSRRVBS/HB/XCLDRkHM+PJTPHx6qkjKdLFN5lqWcJhI52fqY0Vy5LOefych37+xol8pSSbuUCiJu\nCfv7QL1m42rvLUytfh9JFOEyB/A9cQ3RtSIqVRMdt0x2LLeOZhv4g8zLaJcP0DJ6cLltGKash2en\nrmG+Z8KfAaZ7QKcL2AMgaLrQNfqAIYit/gDo9GxkLBdCM0/A6wPaoTRqV5/G9fo17HznnwE4Ouax\n2DZgWwG02zWs701i/3ABuRLQGxrfZ575J5ifDyOXcx+3KD5/XtYRr52pJRJPTVNqY+zHc+nS0nHD\nMdbdul1FyJF0aprakZJRH/vF9PtyTIkW5fOM7Ag7Z32GMP9OR5+9VErbd09NyTpLJuV5KRS0tTkR\ngd2u/JxIyLncuKE1UWq81WpyDDZ2Y18abkxJyM1k5P97KQ4/7Th1NH8FBvtucBfc7WoxnpIerCew\n90q1KrDcXE6L6nRMpilGMxaTz1Mqnikmtlxm9LGxIYYwnVauBiG97NPBVFQiIbts9uzw+cQJAHIe\nTGs99JDu7vf3tSFWtyuOjA8IIw46VMuSY5AXxKIo8/Qs3m9uqiBiryd5chb6Kb3e68kxHn9cGfes\nZ1BmhgTLuTmdb6bquPtn50SPRwwQDVWrJQbDMCTypPxLNqtEQRbu3W45b59Pm2NNT4tjZyQWCIh0\nDaXiuSut12w06kA0YGG6l0Eyf4j5+gG6Azf6DQNpTxeTvV0cbnwLh/UMVqwuOh6B+pa+aeG/n34I\nka7rWJCx2wV8FtAq76M26MFlAi4ohLkOC0mvT9KC3aGh9gBxtwcHgQjyvjlYLj/qngS87gG+88v/\nGNNnFtFqyRoOBgHPLjA//9cQiQwwPZ3AYJCE253A4aH/WDSTkSujZ58vftzHaDCQegMg954aaIzo\n6MRrNeWXUGSUrSQODhQKvrcn1zYxocZ+fFxTqtSoYwqWUO6JCTH83a6ALzwelSPq9VRdgbWzRAL4\n3OfkZ8KaGRWn0xp9h8NK8OVGkmoYfDYyGW1nzVQgHVgmo+oIvG6mU0lJOMlx6mh+QYazOyV/JwSR\n9RTWQagyTLHATkfC73Yb+OM/Xsb58wKLvHFDyXeFgizkaFTrPFevag2AgoMsML/+ujxcXq8WJ9lU\naTBQJM3cnCoDeDyK0adMPFnfd+5onSWZ1J71h4fyjw6EKQj26SiXdYfKKI2KBGfPyt8PDhSRZdui\nVSXoumV8/OOymyfjn+CJoyN9SNfWZFdJMU0q7FIynl0PucNk7YPEzUhE5XYefVSO9c472qxsYUHT\nHJScoXoDFQMmJuR6CgUVAaWsz8qKnO/0NOD32ei1ezjTugPfwSoC+y+ju3kTjW4VjUEXZauDT/om\nETLdx9HU9WYe4740/ri+iordhekC3ERj2UDN7iJqBI5Vpl1uwGsAMZcXdbsHOxSG7RqgHYiiHwhj\n+1OfxyA9D0+1gOLLG2j4U6hNLaLa34HfU8WUlUCvl4BhJDEzk8T49Myxzhz7+Vy4APj9HznuR0NS\nLZuLEYwSiciun7wdqi4/9ZT2vOl2Jd1JQ8tais8nDpq8pvFxgf6n01LDnJlRAEskIk7F59NGbEwn\nplJyzlS/mJ3VmgnbMjvZ9ufPK8eJ4Iu331ZR05deUtWCsTG5PpJgmaojQdnrFQfGbpmdjjhFy5Lr\nYS2N6Wn2EWL9kURXdujkJuavRI3mdDzYaDS0EyB3LFxoZOybpix85n7DYVlw5bKmdNjjnA2+iBwS\nqXh5KHo9heQSwTYxIYudjPntba2nENVEfbNgUDsqTk4q8evcOXmt3ZY0DptNBQJKcuTnqCzMwiuV\noKmj5nQ2gApAMqLo97XmsrKibGf2H/F4tKmaUyer2RSjz2umeOPGhpzrwYG8t1wWI8Z5I6quXpf3\nM08fDGrEQkJdLCbHqddVHWB6Wo4zPS0GjARI29b2vAsLw66Rd0pI3LyJeGMH3t4etnMZzA38uBz0\nwWM18dH8bTSrfbg9wL8s3EGmK4gPqkybJvCIN4mI6Ua3q+ff7wNRw4syejDG0+iE42hVe3BZLezF\nZ5BOXkW2n0Y3lMCYvwYrU0ArkEbW6MCdjCAajcLnS2IilcDe4q+gHl8QUMdHZT4eewxYvDuq2Ex0\nHjtdRqPyv9st10qiLEmGNMput6wTv1/ed+WKNsojMKLfl88TKpzJKJnTMOQZoBgoU7mDgap0F4uy\nxqNRTSFHo7IWmk0cAyeIVqTOHKNXAnII7y6V5L2xmLYZiEZVEigYVGj39eta50yltKdONCrfy+ev\n09HNINN0FAllB9JiUfXqmOYj/J/R1cWLup45L6QlnNQ4dTS/QIMwRqr3MqJxNm6i4WfBlTUUFidT\nqaVjTgibSxmGNiDz+8U4stkWOSA0uj6f9lynXP+FC3KcfF6cAo0xnZffr/BJtgyoVNSYM900Oanv\nI0CBqSJGEIahPB82g2KRmg6KhpzQa7aTHgyU5+DzAc88I/l4HodcIaK5Mhlt6EWUEY/LnSE5PYAq\nWhNwQK0yFvBtW88NkDkvFhVlB6hWmcslBsW2gWjEhv3GW3juz/85CtuvId/ooGH30IcN2wa+FDuH\nM9HwceHeHxg6DtODQ7t9rDhgw4AdCGAzeQ62ewJ2o4HkhSSumjYOii4UcQmHRhETMx5ks0BreN//\n9OLfQTr9MSQSQw244X33refwyxNAIhHH1JTnWDWCqR7WAs+fVyhttyuGmz1geG6xmLYpJnPd65X0\nLlsSt9uy4QEkZehyKdCFu/BwWFWvKapaKknEzEjJNOUcmLIiIMS2gc99Tkiqr74q7w+HZZ2Ojcm6\nXF/Hsa4ZU2flMvDEE7Khe+01ud71dTlfKpBzLcTjWudkinlnR0EK3IC43TJX+/uSjXC5hHvlVOzg\n5osisqz5cfO5ualz0Wqp9A/T4WfOyDxcuSLR8uqqOmmngO1JjFNH8wswuHN3osUoZcKe5DTIbInM\n9rrUU7p7Vz5HrggRXHRGgEq7k7BF8UIWx+t1eSjIwyCCiqmNjQ1xFu22omficXnoUik5Bza+Gh9X\nw5BOi7jk5KTqijl733g8koLLZMSI8djkuzA9SG4O5ySd1vRFsajtj7lzzGTUmczOjkY+6bTURgxD\nEUDO3ilOdWpGfoR1U9reshSF5nbLtW1tKaeoVruLu3f3UC4X0e+X0O0W8d3lIv72Jz+BM4MQwrkS\nvKUsZvNvIlnbxmulbWy36xjYot/Emkm5b8EeOrtjNF1yGn1/BNlCHlYkCcsXlrn0u/Dahf8UmZnP\nYH9fjAyjhvTB6/DV9hCJJJFIJOD1JuH1JnBw4D/m9nCtxWLAM8+MHeveAUpUrVZljrkOSZydmpK1\n43KJsaPhM02ZM7dbXme3TTqnqSndOPEZuHhRnIZty3qh0a/XVYeNcizOlgKFghzv6lWtUzLyrdVU\n6JMRSaWiXUDv3NH6Sqkk/1er4ogODnTjls3Ka8GgCqgmEko8bjS0/5BpKvyZ631sTDdalgX8wR9o\nnZMp1Z0dcWiM0pj2OjgQB8INDcU4+cz2egp3ZjpuMJD3EaYO3L/R4E8zTh3NX/LBfvHOweJ2Pq8E\nTBY233pLjSEgu+y9PSWHdTqi75XJqMoweRvdLvDII5pmIUZ/Y0MW5d6eHO/wUArkbKVL0lckolpW\nh4eqH9Zsynddv679bNjDg7BNPoAXL8r7LUvOg8VS7l5LJS2yUmtLRAlVQyuREAfCVsPVKoaSKfK+\nSkWOf3S0jGh0CYAY0bEx7VrJyIJkUCK+qCJMuPb0tApRSstjC6lEHp3iLvqHm3jru7uYSZ3HtYfj\nSJZrCN4tobIvYdH38i/hYGcd6HYR8A0Q6LYRa1UxU/wOPhxLod0CYIhYo8sNRF0e2AAsfxh1/xha\nth+G34e3L3wEXoxjMDmFwYVLwMQEfIkgCt/4Oqx3lpFKJdHtJjA2lkQ6nYBlLQKQ+1WriYTMpz+9\nhHj8cZRKj2NzU9bLwoKmaDodRQzyXk9OarSZycj8UrOs0VDFaDp7KhAcHamunEjyiNGcmdG1s7sr\n9546cGTDkxfEqJ3tBe7eVRh7Nqu9ggYDOSfWAvkeosmc5EhRUVjGxYtLx1Bh1maKRTkHKjUcHGgk\nGwjIM0Kosm1rnyeXS9Z+LCbp49u3tZbEbqCNhlzvxASOu3uSOFwuyz0gOpPgHapQm6acUz4vn2OL\n6XBYNnhHR1qrYT8dn0+dqGkqaIY8NHZhPclx6mjep8EHgGStdxtU4D13TiGIdChEjLjdsttirrda\nVXkJclKYNhJBPuWdMKI5OtJiZLWqi28w0N3WrVua2hgMxNAPBnJ+u7sq48Idps8nDyCL5DRCW1sS\nQTCEr9VkZ0lV48lJKYg2GhLOz8xISoLHSKcl1GcdhDu9TEa+c35ejlWpKAOb0jqEc2ezyivhw8X0\nm9cr81GrKXLO77Mx5q9gbasNGD5cHWtjeu9ljLfLcAc8sLNHeGP7m1j99jq2+m0YJo45I48FpzF/\nJy358RYwMTR2R90MdspHIt7YGUYpABqmBZepxDyvF/BG/Ug89DEcbeTQdIXh9RowjSgmJpKoJJ/F\nS6FPiBHNAaEmEMkD58//Mq5e/eVjxxoIaA2L/eg5d2trmrpkSomFcrLRCVgIBJRzRRQTgSCWJf9P\nTSlYg+uIu+Xxce37Q8a6acr3EIhBkq9lKWjl8mX5R0HSO3cUaRgMyucoaMoIJpfTuh+jK56XMz3Z\n76vjIBSdaSSmSNttcQZs01AsatScy8lajcXk/AhS2NlRBY7NTXmGqBxNMjDbWcRi8p3ttrYOF828\nUSAK64AzM3Iu3NRJ+wB5ljY25BjJpPKivF557qjwwY1jpaKOJpPRFOZJjlNH8z4N6m95vT98U5mO\nIJO725UFzTrF3p7uGonNd7lUBt3nk4cum9Xd+MWL8kDOzS0dN4iilDgRa3zYSMAk5JLGgth7clfO\nnpWHYmNDvm9iQh4GEixpxFZX5bgXLsj3ZrP6wPDcueO9cUMjKnZl5M6X0irkmZCvQmhno6G7Mhad\nu105BpFuRHIlk0A4vDSScisWAV+vgbnsLSStA7hXv4rD/Oto2G00+y3s9brw2jY+7p7EUmQcXp9C\naZsNoNDP4e6gfeww+gNpYJXvdNFsDneJhjrreN9z3ChjMJCoZdAHcp0+6oExYG4O+chZVKavYPpz\n17DoauML1wvo9xO4fDmBdNqNGzfEOLNPDY16Pq8AhL09mYupKUXpNRpibLa3gVBoCZubYnTKZTGS\n3ACFw3LftrbkvjEqYAtoaqPRKfF1ptGmplTb7u23R/ucUHOvUpG/b2zI782mzFEoJLUSQO4/Vcad\nUkaWpdphTF2RbMn0K9n3hiGbEK6pM2fk71Rk8Pvl+djbU8N/dCRpW5IsyaNhKopRIR2Caco1854Q\niECuG8EwXJ9EhHU6ykU7e1Z5bYQgM2Vo2/Isk9vGPjoXLij8mc9NLKZoSdaWBgNNadfr2s6bQJkb\nN+TZIP/opMapo/kZDeb07zdY1Of7SO4jcZK945mO8fnEsJKQSGQY+8CwCBuLaX1ie1uOT2gke9yz\neE2CGKVOpqbkgWQbZqJ22JaWD1M0KlELWeSMOsJhWaBbW6OFeTauYuHS65WH0+tVOZX5eRW/ZJ8U\n5oudzGxA5rRaFXg1Na2iUTUu3a4Y1m5XeSetFh1pGY36NgKVVUTKb6LnLaBsWZjqj+Oj/hhS9W3E\nW4fweGxYFvBiK4f1Xua4/sIdb9ttHTvneh3AsAA/1vfCaMv7rC7Q9YTRdnlx2z2N6/5PYuxcBFYw\nhkEojETzAP3KDs6M5eDzxJDwB5CcnkJv5lE0Eh/CH3eCx6CFQAA4XAV6vRACgdQxyW9vT3PpDz2k\nmwTWrJpNNUQEf3CHT7FQyuBQXYH3LBSS+3nunHYB5b2KRJRXcnQkPxPpV63KZ3Z3xZHRYfn98t1E\nkNEIUyOMUGHn7psRC8Ea+/taN2Ttjg3pDg60dsRUc6ejrHgWzZmK5VwxAnICOppNlfDPZrXG4ZSI\nsW2tQ1Hrrd2WdOPUlKaj6fwoUptIKLKNXBo6p7k5zVik04qyZMO4qSmNwslbMwyZF0rlMM3c78v8\nswEdkWarqxKdGobSDpyNzwoFRQCe5Dh1ND+DQVY2w29CjjmoMQbow8eHndEEQ/BqVXYwt2+rdpjP\nJ4uIi4OFQxYkyQZPJtVhsbPjnTvLePrppREWMguJR0cqS0GtJUY0jGR8PnlYjo6kgB8M6k7vpZc0\n1URCprNHPHd1hIOm07KwL16UY9++rY3EnNBRtjnmA1OrjYp6NpsW2u0iCoUSwu01+Hw2BvbjcLWA\ny82X8XTnCIHbh9gtv4FXOjdgo4+6AeyabYyZfox5Eng8PYeuDXSHKS/DACKG5zhqAjBkvhtomF24\n3MCOeRa7qYeAcBjTqTb2rAGy+88jX5uE6RlDIJBEu51A1bOA4tTjOHNGo4GZc8M8eVmchGEA5eE9\nqKxrV0sCDjodWUvptMzXrVtiYMj4Z7qTtQrWme7c0boFCbKEu7KQvru7jMFg6TgypJHy++V+rK7K\nsZ3tupma5I7d5dJW1IRos39OtyvrcW9PIbls00wkWDAo38W1XK1qG+V4XI7PFoKHvyAAACAASURB\nVM1M83BtALqpOH9eW3FnMvJ6KiXnns+rcyEXh5EDz2llRXg0THW53cCLL8p1Ub+OsPZcTvkujAh2\nd7WD6+ysqmm73YqU9Pm0ORsVBs6dk3+bmwr+mZ1V3UG/X+4bnRjTjYwG33pLRXRNU9574YKsD6YK\nx8aUP8OokY6OzfZYO2W305Map47mhAeVbfmzc5EwwqH4ZL0uxoJESzLeEwnNl/p8qnDMQuD0tBbF\nWZjtduV4b76J4zQNd62A/I38kf19JSPyPbduiaPY3tYUAFUEKISZTuvuiREWuTO3bun3Uj2WrOmx\nMUW4UOk5nZYHgA6FjtAJrTQMIBTqI9DJYK6bQ/CghIRdxHj/EBeqryNj7eIrRhF1dODudzHb68Dt\nBhY9MfyqZx7mvjzYhiFpLAyqeHXQh2FCUla2Mtn9AZmTat1EOTSNXPQCVjpx3Dr8NtxhvxzDdMPj\niaEcPYfVxG8glPDCNIcCnX6g3R7g49f+Hu7cMUcMoc8nxuHWLSXdUr7E65WH2u+X9+7taY6ehojq\nBiTgbmyIsdvbU9LdnTuqYcZidz4v7z97Vo/j8YhBq1ZlfRWLcgySRJnyqtXkXGnYTVPTNeykahg4\nJnHSQTDNxFoIC+FspscaBMm4JGJS3Zp1FSpHT0wAH/6wrL8XXxRH2u2qigIh3ZGIkGHZBZXoRsKG\nZ2dlvjknTJtxo7S5KX/b25P52txUCLbfr+i1o6NRp8PNFFO//b6cI4Es4+Myr3QuRDZyA+r1KieO\n2QtCkt98U+1IoyH1KcL1azVxcnS0rM8S7GAYcgxqofEeLSxoWp7qBYzqKhX5eyYzmnU5iXHqaB5w\nNBpy8xhxMLfLwbCdaR/WIpgyYkGaqDAaBxblfT453iuvKNmLC4rIKXI8+FDF4/K9a2ua6qLIH3u0\nkPUeiSwd72qoACzNveThqlY1vUGNLaao/H45f9ZCyAugnAULzpTEYAtZKiLzwdrZUaOXzwsa7dFH\ngXp5H5XMt1E9KsNTuAXDygDVXTw26OILnnn0hnPrdgO9AVA3LRidPPxD7SxQ2sW0EBjuqI2hgXW7\ngPGgB6YF9Nx+NH1xuPx+5Ps22p4I/vTsP8Keax5b/TlU296hxE4Tk+GrOHs2iUuXElhbSyAWcx8X\n1J0RnhghE2trWjwvFrV2dnioPXi8Xk09MRVDJBXnmlEvIxuCQkhwZUqG2mlMKcXjqibQ7apDIxGV\nO386KCkgLx0DQ5wtCgBxHJTUoXEjORBQ8AZJq16vdvhkmorcomef1dohkVGWpb2NpqZkZ05uDIUm\n63X5Xq9X5jKbVS4WIxYKnHKjxJQcoewbG7rZcopbEg7P9PXExNLx3Nq2CFSurmqKkk6FzpHIQyo+\nr6yo8Sf/KptV0i5bCSQS6txNUySQ6CDm51Xokw630wG++12tCbKPEtsQkBzKe05VcGfq2O+XZ5WZ\nBIpyMmVK9YDFRU1Vn9Q4dTQPMAjXBJRZzpuYy41CAsmspTz4nTvyQLAwyJtO3gv5B263CuWZpqYQ\nnGTFzc3R3iO9njxQgYCGw92uGPRkUovlpZKmIWiwMhkxgoxMyInpdNSIEYRAOCb/Rq0lFqApvMmC\ncTDYQ7WaRXl9DTPWa+iv7OKoWUeiZ+DZ0EUkw100GwN0Sw3MvLiBRwZF/G5pQwiotqSwTBfQNAJi\nQC01kP0+EB54JSoxxdEMbKBjmdhAGEfmJIL+JnYDi9hynYcrnUBnMo3C1nOodadgGEnE46KfZbmT\neA5TKBe03bHsaINIJJ45jka5m2SO3rbVwNOQUR2bKTdyeNhIjfl19m5JJDTN5PfLgx6Lyb2rVsWI\nEajAh5+ET8r0UGetUpF0yeqqnGs6rRGvyyWcGcJ+CcqIx5XDQmVuzm+no8202I+n05FjTE1JtEIu\nCmtuzO8PBrKb5zPAAvrYmOqxTU+LsSXBk/14qlWZFwpJMtVTq2m0T96HyzUqV8SeLVNTMmdsZ9xs\nqhYYEZTT0/I5bsiYhqYSBdO08/NyXnfvisOORuWaCUOmU+KmikKypZI+F3w2Gc2cO6d/DwZl7otF\n7RNFvpJlyTG5OZROq0owJkXhyhUp5K+sAB/6kKLakklF4NFWEBRDvT+2Lgfk/pAwepLj1NE8wHAW\nDpk773ZlR0YIJRVUAe1qmc0qmYrSLiR/cXfPFJXHo9Bi6iNRwZicBO5OyDlgJDQzo7Id7AlP9u+r\nrxJJtozxcUHWEKlD9VZAFnEgoLtvdkZsteRcabx6vS5ahT2YhytYDB7g2tgE0OqgWHPDHPQwjiO4\nOyv4D4ffRs1u445rmK2ygTGPDxdDUmS3ekBnyD0IeTzHKRpAHIcxAGruLnKpyyi6xpEfJJHrJ7Hl\nOo+iN4Hdvf8W6NmwEYflmkbdmsLAGMc/m/8CYjHjWCz08iWZ20fGn8b2Nht5LWNq6upxA6luV+4f\nU0Y0qC6XGMdcTubzscdknk1THlJKgjBN5nIpmx1QQiNraqyPPP641FsyGZlTpg5ZWC+VFH4KqLFg\nJEBoeTAoxvDzn5d7/c1v6maEfeTDYbmHW1tijExTzs/rlVbCZ84sHTtT1u0AJTBSJ44bCRbNmX56\n9FHVpdvbE+c3PS3OhogycrCY3gE0hTcY6HkyLUWFBaIwp6flXkajwpa/eVMVCHge3ARRoDIS0Wsn\niOb2bY02CXBxueR5XFtbRrO5dIwIY73DNMW5sB+MbUttjc8p718oJGtme1v+UfXg6acV6MD6Yjot\nx+50VIWjWJTrZWqLena8BkZ1ExPyszO1SpHW6WndFBaLinAjYIYbY26q2HBtclJTooysT2qcOpoH\nGE4UGB++27e1cyDDcoaw1GMyDGWgz82JoCLzzBSbpGgk+RzcBTH8ZjqEjcj4gBEE4PVqyMzFE4uJ\nAcpmVb2ZSsGNhjwIhKgyPy/F+wHSaenJEbGKcGf2cKG+hWvbb+EHL30d/lYZnV4Lvl4PNoCWy4OP\nFa9IZNMXPojHA1iuHr6KttQ3elr4rA0sWD0blmVIDcUE+hbg63vQG7gA2Bj0B2i4YugEkqjHH8If\nffjLiEY9xzl6jwdYmAXOP/s7yOWiqNdNuFyy6ySrnNfLlsdkaKfTiqIjO5upvDFBFWNrSwxXpaIk\nT0Cjj3ZbkUs0YKYp94bN4yYnf5iTw7qUacpulNFNMilIOhaamTIj052KutxoUE+Lhf5kUn7f3BzK\nz0RVTZsOiehBSg7xOIStf+xjMh/PPCOvvfSSzKdpKl+EXJlaTSX2CUQIh9WQ7u4qv4RRH1FgVKZg\niwWi0DjOn5d/FL3knBPkwGjo6aflHNnVlengoyPZ1fO+s2bI+kkqpbUoEowpGUT9L7dbN4ClktxL\nRhKA6rFR5Xl/XyNJot/Y6+byZVXtJjJyZ0eeTdZ0p6fFCc/OKlqQNShGd263rK1LlzQDQsSl2y1R\nDXs9kUdXr+u1T09rHSce1/Yas7OK4AOUz3SS49TRvMdhWbKggkHt8bC6KjtXamrNz8vrhOlSFobM\n91xOCnxra7JwGMIyjF5bU8gyICTFclkWKhFW7CfidmvfFb9fc8FkLvv9wvLP57URlhhY4dFYnQEG\nVhe99ndh2YdI9TbQXMnj6M1NJDxl/P2JR+AqF+DudRAKAa02UGv18dX6LmwAJgB7WBup9nuoVm0E\n/Aa8PqA75MYEfS54DAOWYaAZSKHtjcJ0Gej2TPzHuS9hqzIr4oKeFo6MCWQjF9DsPY9uN4hGI4le\nL4FYLI6pqOc4ostkVGgykwG63fgxNDUSkXtwcKAP0diYGBMWvQ8ONK2ZTC4d57LLZZnT1VXt43H3\nrrK9vV5xIo2Gyq/v72utinU6KgRzTZDQSF4RwRcej5zLrVty3tSXc+bZmWoJBmWX32qpkyDUlSKP\nOzvAN74h30W9LEJemdaimsHcnBorMTRLx029KGZJWDnFHbtd+U6PZ7TYTXVkppUYIZNUSAAKa4Y0\n0OS4MJKYmNB+MVQSYAsIpyoABR8nJ+X/Z55RfTs2f/P55D6wgV0goPwuPi8LC/K8sXZJJN7MzNKw\nFbOcO5Fw0ahCmhnZbW3J+WQy8j7WbpzqyYuLsvZ2d0cVFkg4dbv1vJ96Srk1RHtGo/JvYUHOm+Kd\n4bDK83Duzp/XJnjr69pag51Aq1VZo7WaRtvNpkTVjGpIr5ibO1n7eepo3sOwbSnO12qS7iCMsVYT\nA8BUC4X0LEvCehbcolG5cevrWnycmtK0x1tv6a6ZyCx2TiQLn5BJSoRzR51IKEmt07HRbrdQLJYQ\n8R1ip3EHudU12OVd/A13EpHmkSj49i0E7TrsQR//W+MduNwShdBg2ybg9qQw6JjoGUB9qK/mNVwI\nmi40+n3xNIaJjieEmh3G16Ofhc+bwEy6Azd6KBopVIOTyHv+HDV/Gh17AmNjSZhmEtVCAt/yLMI1\n4UEwqOmkkB9I+38J4TCOuwmSW8RmUTQ2NAA0VMWiQqaTSbkfhYLsblk74+758FD+zp46rG9xbhkB\neDzD3is+Zcjn87qDZoTB7oZONemJCU3pkGlPrhN75zA/DkgkwoZWlBNhOpaoLar5sq+Kz6dkylJJ\nomvuxJn6oGGlAgN3z5GIOoZMRrXIXn1VogSijih2yrbZnY7MLx1aICD3oliUeWFdgwTEM2dUhoX3\n6soVFZAk+ZitvxldMEJMpeQYxaKc59mzWh+sVOS7SUAk54TzTe7Y9rYCYljPcbuVWc9W3YzcaMS9\nXkmPcfNB6gFrlqxtcmPo98u8FIvyvLNe2utJ/YRtltmemc87I65gUDYA4bDy0dimo1qVuTtzRiMn\nOnLyxjY2VBOOZOiFBfmdKFWmWankTbkqEk/ZS4dgkJMap47mRwzu1jY2tGZBxjxRMSzqDwaSxyfS\nY3dXd3LFouz4GMJGIlr4p04YHQmL3ZRLDwQk1SaG1oJpFtHpFOHzXUKraQCZLK4ZNzGBLMYGGfz5\nrX8NPzowB01sDMSB2DYQ9DwEv+nGO3Yej3rSYvjcBmJeD+oDS7oNGpo+K3YtRG0fGl0fDnAWRf80\ncmMXcaf0NeRaFbi8HsTGxgAjjfHxJFb8X0SlkvwhTbBW9xPotYGgTxcxlWe5iy6XtUUzoMgmquSy\nIGqaozpNfHDYQOpeaXjKjrCfCBUNaKTrdalXMfVAY5rLKcOdYIhuV3bA4bDu/EioczamIomOhM6D\nAyXZsecK0XdUNSDXSOpGupsnWdO2xRgypUI9LSIWea5ET3U6Mq+plNbYmGplenZ1VdZkJAK88Yb0\nKNrZEQPHCI61Mh5ja0t+Z1sB1u64A9/dFcdHWXw6NvJePB75O+VZIhHZfK2ual3z7Fk5NhUuwmE5\nHiO7ixc1WiXDnw6NaLr9fZXboSQOwQzk5tAgz83Ja4Qsr60tI5lcOq4R3b2rxEZAFbip88daF9d9\nMCjGnZsPv18yFuQNUd8vHle+GSNDpsjOnBFHdPOm/KNIJzcoTMMGAsDzz+v6SSa1pw/tCKHwgNy/\naFQ2GoSV///tnWmQXNdVx3+np3tmWtOzSLO1pBl5VFqQ5RQ2sh0pLpsIrIBYKglJCkJVEgrK4RPF\nVkWC84V8oYpQARJI8YUkrmBMoAjE5VTFxI6NCwgu24klLFu7LVkzYy2zrz1LT18+3Pef+0aWF4Vp\njzV9/1Uj9fr6vfveu+eec/7nfxS2VJF0un/TaiIamjfB6Gjg1re0+JWY6M39/SFhqqSt5LmnpsIE\n2dHhv698ivTJLlwIrKV0Z0ERDurrwVyF4bNfxuZeplIeZnFplnpboNlNcl/DeyiWZ2hamlyeFCoO\nnl2cZSIzT1mV7MnKZ3xxkZxlqSSrcFfxDK28a2Qcx1ymgMvVU87lGbeNPLjnD7gwcScXx/OUKxnP\nhhmGcvkOWtoa2LKllXI5Q339ynbHKvhSvxkV9Uk6plQKob1czocPFE4Q0jdyWuJfcWTltRSnlvxK\nY6PfliZcGSbJxatR1tycn2Dq6kIx3/h4aMer2gYlb+XJaFGgOL7Ok7S25PlINFFaXtqmGH1qg6Dj\nkAaXWgurqC8t1a7e7spDaLXb1BQMqphuqlXat89PWsrtnToVZOQlCqliSgi1MG1tfnyUFzl71k9a\nah+9ZctKD1ONvyAUNGp7yoFJmUDXQ0NDkCY6dMhv+9SpoADe3BzaUmtSVQhMxafy6js6/D6o5YKk\nVeQpbdoUJk4x4RQak9ilWKRSzRD7UyrLqgcrFn2IamYmFLGK6lwue2Ml2rgS/un2FG1tIeoh73bH\njlAoq7bgmvDTCxORBORtqu9MmgYtMoFyWadPB1235mZvhKVgvXNnEBTNZLznl763VhPmVnuL70KY\nmbue41Scub/fhzSKRZ/vUGOuJ5/0IQbVHiguq8prxWDV26RU8hetjz2/hHOXmZwcpVQaxZWHaVga\n5NaNH2Pz0gLtlSE22RibFy/QPfsKD5VeZNgls7AD9Vv/1bodFGlaZpQ459/+l8VXGHTTVJxRyjQx\nRYEZK7A5/wlyG+9iaLGNEnkyGxppaK5nfv6/WViYpKFhE3V1XhZ+cnIjzc1ZZmZCvF9sKK0stYrS\nRdnZ6S9khZvkpUhlN58PjzWhqt+HYsaS0xGzqa4uFMzJg1BXT4VXXnst1CJAoOtWKoFmXF+/sp1v\npeIXDX19oZBtYsIfaybjtymjIDrs6Kg/h+PjIVwm70LNqbQfCtkoZJfP+wlHlGD1A4IgZy/2k/Ih\n2nZXV8g1jI+H3ihpdWwtNGQ8Ojv9/m/dGhhIit2LoqyWC5qU5C01NvrwjaTqFcLUJCahSRkcGVGF\nhkXnVchIhb3btnnv4MqVIFE/NxfaUZdKfn+0bXlEGzf6MRAxRmxAkQpEZVYYanAwtBtvb/cTrVhU\nSqyrgFEelrTulB89f97vh0gIoms3NPjzqBya5JrU9rxY9IZSEjB79/ooh67drq7Q9lxEHeXw6upC\nGE8sMrEUe3pCXghC/lDKy7oXVYKgBZbqr2T8pe6hnNeOHf77LS0hf6kQZFsbfPrThnNuVfhn0aO5\nCuWyj1HLJVfYQYn/I0d8hTIopOFobS2RyYwyOTlGqTRGqTTKhvzdbGvOUBi5QO/sIA0LUxQqkxwp\nPcyMu0y7LVDPAvWVeVzF8eHZ49yUKfiJG59QrzhoquQYZs5bF/PhLYDZzCIZgxkKnKts51TmZiay\n7RyxFxhbush8bhsu08HCwkafFyncTI52ykk1cHMDVEpQLt+9vFqWN7Ww4I1mWq9NPcUVxhH9Up6I\ntNNk9GRYtapUrknihpIiTzPidKPl80GNdts2P5meO7dS402Gpr09MGRUDDc1FW4YNYlT+E3tqrV9\nNZ0Cz1SSmoFvqRDqKtQNUQsHhQYbG8OKUrJDs7MhCSsjoDzUli1+HyTzvnWrn+xkCCT7k8/7iUgT\nqxSXm5oCA0yEA8n1azWsrqQTE36i6+z0f3Nzfv8zGb8fkkaSFNHoaCCcTEwEarA8HRVBTk35z+/Z\nE5h9vb2BwVhX58+Xzsf0tDc4kk6Sl6rGXtp+V5f/PUnjK0rw8sthQSKPra0tyOEsLgYm4LZtQZJH\nr83MhKZ2pZI/5snJEPrTAmr/fn8+lpZCL6LbbvOfl3xOf3+gC+v+kHFVuBv87736alhUqc+Swmai\nlk9MhPyVvBaxRotFf56y2dAxs709hNYnJz3ZQOSVkRF/zeh+k9qzwrMqtC6X/XfPnfPbGRgI5REK\n3/X0rO68ui48GjM7DHwJqAO+6pz7wlXvv6FHo0Kw2Vm/kjlzxl8gklqpVBa5cmWU4eEWnMtTmnVs\nXLhMMTtMW2WUcxMPUaqcIZcpU+8WyLkFspUFPprr5RbLhgQ7fnJ41L3K2crEssKvmlcdsl5uyW5c\nzpE4523LdxnneZtmyerI5eqoz7Ywz2YW63+FhcZ7GCxtYsllluttIBSFLSz4i0uxbn9DP0W5fHB5\nAhT7RzF/bSMdwpPbr1yGVk2K1SveLY9BISOFx9SkTQlwFRBqIk8Xk8mIaCJRLYUKTiuV0DtEx6Rj\nUf2PGFIyetpfeVzKlZ048RT5/MFlD0XhMK18R0ZW5mKKxbBSB/+ZtN5YR0eY/JwLelbd3SFP0dfn\nb+IzZ/wEqp4nov6q8lyrbsX5VTuVZpU1NYXxGh31E4YkVVRHpVj91q1+n9MLgdZW/9unTj1FoXBw\nmTYuar2UfsWyFNtJyr/SCWtsDHlHGf2hoTDmY2Nhtbxrlz9HykdpEm5rC3UhKj6VR6SqfB2/xrq7\nO3jQCnfl8/635XVPTweDp+NQy2KFOcXeymZ9TVGxeHB5YbVvn98PrwkXiio7OgLFvK/PP758OShW\nS6Q0vShS7dX+/Z5Rqve91FJoC6FrurMzzFO6N7JZf92dPBlCwBLDrFT8vvh6oNA2YHw86KzJuPb3\nB69N9V8HDvjrRN7VgQPRo1mGmdUBXwEOAYPAc2b2iHPuxLU+L6kJ9a8YHPQeyhNP+Bv18uCTlCef\nJVe5SKZ8iUxlgmxlgbvcrbzHZelhgALTXvLE4HHXzyl8rCR9RubmJ5iz9lD4lIS9CpZbzqcI8zRy\nyjq5wk8zQRtX6rqYyHVyrv4nmMrMksmUMNtINtvK3JyPEdXnvFXdUAhGQjL6ihGbBQXdkRH/W9PT\nR8nlDi57MFqpqgg1nw/eiRL2KlqTRzM2FsKEkgkZGQn5q1wuNK1qbw8JfNWuQHD3m5pC7qa5OYSC\nlFuRSOC2bf4zorHKI/HtqYNhlQy8bkrRV7Wi003k82NH2bbtIBA8jlIprOpUmCnvdmgo7Lv61qge\nRcV6XV2BeSVKsUIVahA2NBS8Pxlc6b2pRkT5QREmpqf9tmUMFUqRAOLoaMi/dHQE1pZoraOjfmLu\n6vLb1X77ifoofX0HWVoK31U3StFcJSE0MxPClJrA03kThVNFEtC5Khb9b2rs5Z1JZ01GwCxUv99+\nu78njx4NfXCkdCEdNYVc0+02WlpCIaz64igcJ6JDR0cw6KIgv/wyHD9+lDvvPLg85seO+XHT9apz\nUCgEZfTW1mBkmppCHlILJBGINm3y2xgY8Nfp7GzoCqowmHQRVbwpqre8n+bmlUZFGms9PUGj7PTp\ncN0rLNbdHUKAw8P+/vR07qBOohykmIWriRve0ADvBc46584DmNk/AR8CVhiaxx57gokrlzj3Yj+n\nX7jIhpGbsVc3kp0YoXlxhPdXRmh3wzzPSxxn9HU/spNZ9hCWGC75p0Bu5WsJJllkxm2g3/XSTy+j\nbGLStXCRIYa4xDzdzLGVWbZSrtvC09mN6HQ0NAQXvFJuXc6DqHJcoSZdwDIuzc0rV8SajFQP4dV0\nx5fDXvX1/nuaWLRCBn8Bqu+FPAlpXmkVp3yNkuySNDELCeMNG4Jr39fn93V4OMi1VCr++7t2+Rte\nN6bUEUQzVeK3WPShJrPQm6SlJTSjkvCjqJ+ik0pyX4KhlQoMDo7T3e2/o7yIttHfH3r1iIpbLgct\nuitXgoZXsejPy5UrPrwqb1D1NRMTQQ1AE29ra2CNycBL/FIV+pIAErFBoTFNRlKRkGRKoeDHHYJH\nks/73xobC4Y73cjM1wSN84EPBKaWiCw9PcEg5nLBOE1NeeOmPEd/v//N7dv95Hvxoj9fkovJ5fy5\n1wJF9WM9Pf5xmh2msZufhx/8wH9/926WWyNIm0skjHTCXyv4ri5vhJSjkzhpPh9yTyIwpBXRfT3K\nOPfeG3IkFy/6/c7n/X7s2BHCVPKMtYhTIejYWFAwUBhYNUEDAz5k1d0d8oY6v8ofFYthESKCjRYF\nOqciIIhBKTKJwry6DhYXvVFTGcb0dAhba3GjGqeRkVDTo0jMamE9GJqtQH/q+QCw/+oPffHwb5Nx\nQZJ0P09zB92v21hzynCkMc3i8uNJWrhEkSE6Oc0lXuYEGVpZooNFisxR5GluY5I7WennrIRCBY1J\nHkRV3DIMmiiVL9DErjCVbmJRE5Uz0HuayCVlo4lPLBcx3VQhnsmsZMApD6FEvmoNpP2lJKpc/b17\ng8GTXtYrr4SbTYyxxkY/ISkco0lV0iTKvegmVJ5M8e3ubr/9m24KjDQpEksoMF2kKCVljYW8JXkx\nGkPlN5S7UHjupptCvY32T8V3ksyRdyZ2Wjbrj1F5IomVygNYWgoFkzqf8hbUD6a3N5AfRJsW9Vp1\nPgoFbtkSvJh0clhFqx0dIW+h60aT3TPPeCOpkJ88FiWa0/UhovS2twcDvnt3UAQvl/1ELwMtL3hp\nye/nzp3ewExNhXCbcicqVlRuRddtZ2cI6ShXo7yYQptq+tfc7I2n2GUih4yP+++JAqxrQZT7nTv9\nZ3/0I/8ZNRvbs8d/Tr17pI4tLzytcaZFXaGw8tzq+pPitHrdSLB2+/agAqBeOTLEEknVwlHhao2V\nohdLS8GYFAqhTAHC+YTQ0C0Nhd17e4OxEgtvtbAeDM3bSjKljQysNBxpNNHAHI3M08AcDcyzAaOV\nS+zjUT7CRTYzTAfZrCUXUgUzS/6S30pYH931YWUiAwFhhagQjOK0V/9pgpfY39Wrn3Shl/IGiu3L\neORy4fP5PHz72+f51KdC7kaJVE1Qqv9Qclo3pcT/1GtESVUZjKYmP3HpolYVu+LX8oo04SgZrclb\noouSzJBnJEZOegLUGGQyoXhV46tQT5rBpDYLqi9QWPHEifPcd18wFPPzfgJQvF6rPf0v70o1EFpF\ny5Co1UGhEM6vDMjSUvBApbMlz1UyJAq/icmoCUqMJYVfVA+i7SkPIAOv/ZDHIQq01CoUdtTE/cAD\n55fpzEruq2hPBkD5PIXQtECRd9zVFWi7ynFptS9KvzxC5TlEPti+PSyMtHBQIbKUFGR4xMKSV6Jj\n0/hlMr63jMJNy5OEC/U58mAHB8PrOl9DQ+eXKcla/EC4ByRQK3UHsSiVk1TeS/lA7btq6urq/D2h\na1P3lIyXGgBC0LRTFEP5KJ033e861qv1ydIG5s2Qzu1CkE9aTdzwZAAzAoJYhwAABY1JREFUOwB8\n3jl3OHl+P1BJEwLM7MY+yIiIiIg1wGqRAdaDockCp4B7gdeAZ4FffyMyQERERETEO4sbPnTmnCub\n2e8A38MTsb4WjUxERETEuwc3vEcTEREREfHuxttMF92YMLPDZnbSzM6Y2WfXen+qDTPrNbP/MLOX\nzOxFM/vd5PVNZva4mZ02s8fMrC31nfuT8TlpZj+3dntfHZhZnZkdMbPvJM9rcizMrM3MvmVmJ8zs\nuJntr+GxuD+5R46Z2T+aWUOtjIWZfd3MLpvZsdRr133sZnZ7Mn5nzOzLb/nDzrl1+YcPo50F+oAc\ncBS4ea33q8rHXARuSx4X8Lmrm4E/Bz6TvP5Z4M+Sx3uTcckl43QWyKz1cazymPwh8BDwSPK8JscC\n+AbwW8njLNBai2ORHM8rQEPy/J+B36iVsQDuAX4KOJZ67XqOXVGwZ4H3Jo+/Cxx+s99dzx7NciGn\nc24RUCHnuoVz7pJz7mjyeBpftLoV+CB+oiH5/8PJ4w8B33TOLTpf8HoWP27rAmbWA/wi8FVCQVPN\njYWZtQL3OOe+Dj6v6ZyboAbHApgEFoENCZFoA55EVBNj4Zz7L0ikTAKu59j3m9lmoNk592zyub9P\nfeeaWM+G5lqFnFvXaF/ecZhZH37l8gzQ7Zy7nLx1GZYrVbfgx0VYb2P0V8AfAek651oci+3AkJk9\nYGbPm9nfmVkTNTgWzrlR4C+AC3gDM+6ce5waHIsUrvfYr359kLcYk/VsaGqW5WBmBeBfgd9zzk2l\n33Pe132zsVkX42Zmvwxccc4d4Q3kGWplLPChsn3A3zrn9gEzwB+nP1ArY2FmO4Dfx4eCtgAFM/tE\n+jO1MhbXwts49h8L69nQDALpzte9rLTC6xJmlsMbmQedcw8nL182s2Ly/mYg0cN93Rj1JK+tB9wF\nfNDMzgHfBH7WzB6kNsdiABhwzj2XPP8W3vBcqsGxuAP4H+fciHOuDPwb8D5qcyyE67knBpLXe656\n/U3HZD0bmh8Cu8ysz8zqgV8DHlnjfaoqzMyArwHHnXNfSr31CD7hSfL/w6nXP25m9Wa2HdiFT/Ld\n8HDOfc451+uc2w58HHjSOfdJanMsLgH9ZrY7eekQ8BLwHWpsLICTwAEzyyf3yyHgOLU5FsJ13RPJ\n9TSZMBcN+GTqO9fGWrMgqsyw+AU88+oscP9a7887cLx34/MRR4Ejyd9hYBPwfeA08BjQlvrO55Lx\nOQn8/FofQ5XG5f0E1llNjgVwK/Ac8L/4VXxrDY/FZ/CG9hg++Z2rlbHAe/evAQv4HPZv/jjHDtye\njN9Z4K/f6ndjwWZERERERFWxnkNnERERERHvAkRDExERERFRVURDExERERFRVURDExERERFRVURD\nExERERFRVURDExERERFRVURDExGxijCz9qQtwREzu2hmA8njKTP7ylrvX0TEWiDW0UREVAlm9ifA\nlHPuL9d6XyIi1hLRo4mIqC4MwMwOppqvfd7MvmFm/2lm583sI2b2RTN7wcweTeTr1VzqKTP7oZn9\nu/SoIiJuNERDExGxNtgO/Ay+F8g/AI87534SKAG/lIij/g3wUefcHcADwJ+u1c5GRPx/kF3rHYiI\nqEE44FHn3JKZvYjv2Pi95L1jeAn73cAtwPe9biF1eI2qiIgbDtHQRESsDRYAnHMVM1tMvV7B35cG\nvOScu2stdi4iYjURQ2cREe88rtmI7SqcAjrN7AD4PkNmtre6uxURUR1EQxMRUV241P/Xegyv72jo\nnHOLwMeAL5iZ2j68r5o7GhFRLUR6c0REREREVRE9moiIiIiIqiIamoiIiIiIqiIamoiIiIiIqiIa\nmoiIiIiIqiIamoiIiIiIqiIamoiIiIiIqiIamoiIiIiIqiIamoiIiIiIquL/AEpPei22Yey2AAAA\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "time = np.arange(r_squared.shape[0])*t\n", "\n", "plot(time, r_squared, lw=1.5, alpha=0.1, color='b')\n", "plot(time, r_squared.mean(1), 'r', lw=3, alpha=0.7)\n", "plot(time, (2*N*D)*time, 'k', lw=4, ls='--', alpha=0.6);\n", "xlabel('Time')\n", "ylabel('Squared distance')\n", "grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that the simulated $\\langle |\\vec{r}(t)|^2 \\rangle$ follows the theoretical trend $2\\,D\\,N\\,t$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }