{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical diffusion\n", "Numerical diffusion is a common problem with advection of field data on an Eulerian particle grid (one that is fixed in space).\n", "The code below can be used to demonstrate numerical diffusion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting started\n", "Here we consider advection of a rock mass with density $\\rho$.\n", "\n", "$$\\frac{\\partial \\rho}{\\partial t} = -v_{x} \\left( \\frac{\\partial \\rho}{\\partial x} \\right)$$\n", "\n", "where $x$ is the spatial coordinate and $t$ is time.\n", "\n", "The upwind finite-difference solution to this advection equation is\n", "\n", "$$ \\rho_{n}^{i} = \\rho_{n}^{i-1} -v_{x} \\Delta t \\frac{\\rho_{n}^{i-1} - \\rho_{n-1}^{i-1}}{\\Delta x}.$$\n", "\n", "The code below calculates this finite-difference solution and produces a plot of the output." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setting up the problem\n", "First we can import the necessary modules and configure the problem geometry. \n", "We start by setting the spatial scale `xmax`, number of grid points `nx`, advection velocity `vx`, and time step `dt`. Then we can create the spatial coordinate (`x`) and density (`density`, `densitynew`) arrays." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['figure.figsize'] = [12,6]\n", "\n", "xmax = 0.25 # Length scale of problem\n", "nx = 30 # Number of points to consider along x axis\n", "vx = 1.0 # Advection velocity\n", "dt = 0.001 # Time step\n", "nsteps = 21 # Number of time steps\n", "\n", "x = np.linspace(0.0, xmax, nx) # Spatial array\n", "dx = x[1] - x[0] # Grid spacing\n", "density = np.zeros(nx) + 3200 # Density array 1\n", "densitynew = np.copy(density) # Density array 2\n", "\n", "# We initialize the density to 3300 between x = 0.05 and x = 0.10\n", "density[(x >= 0.05) & (x <= 0.10)] = 3300" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the solution and plotting the results\n", "Now we can calculate the finite difference solution and plot the results. Note that we plot only every 5th time step for the output. Note that if you make changes to the geometry of the problem (cell above) you will need to run both that cell and the one below to create a new plot." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CzlrrPKVU7fZavkCDi7c/99xzde9DQkIICQlpzTDFVcxgqObCxBHAHienaiZPNi32wYOdOfYpcIsGBwOc9YHcuBbFrtKVFFSeIq/yBPmVJ8irOEFe5Ym6r0tOHLowmQboAqU+Kfx6/XgslTVWqkvdn1Zc+LWlssZGdcGq3te1+8o3FNUl09R8Ogn5cDMG0z4QIYQQohFJSUkkJSWZPW6zCbVSyh2o0FoXKKXsgDuBxUqpQK11as0M9XjgYM0pnwOPADuBicCWetsTlFLLAB+gD/BDQ9esn1ALUZ+PjwXGucwLZ2NvuMGChx4yLfann1qQnNz5Yq9dm09y5R3wYJox+S0HPv4vXsGh+A7/nhNFJzhx9sT5P+u9P118Gjc7N7wcvPB29MbLzYu+jl54OQzEyzGMR9fvI7s89ZIZav/i60j7896WD1JrOHECDhyAgwfh4EGeyK9q4EcM8K407fMQQgghGnPxRG1sbKxZ4rZkhtoLWKOUssBYS/0P4Etgm1LKEVDAHiCq5vj3gA9qSj3OAJMBtNb7a2ay9wMVwCyp7RCtFRcXyfffx5CaGkttoUBgYAxxcbOv2dja7dj5ZBqMf/4mne071/H4V/vwcvTCy8H4utnnZuP7mm0eDh5YWTT+14D7qz244/f34N/lLJ7nINse0ssdWPPeWw2fUFEBqakXJM517+3sIDjY+OrfH4vBgzn3yy8X/YgBfYffavJnIoQQwjy2b9/O/PnzSU5OxsrKiv79+/Paa68xdOhQ1qxZw6pVq9i2bVubXPujjz7itddeY/fu3dxyyy1s2bLlgv27d+/mD3/4AwcOHOC6665j1apVDB48uE3G0hxZelx0Omlpx7j++niuv76awEAL4uIiCQjwM1vs6Oh4srKq8fbu2LHLq8r57OBnzHx6Jvkj8i/ZH5oWypb4LQ2c2XLH0tJYctsolmQZ6uqc53n7MO+rL/ErLb00cU5PB19f6N//guSZfv2gW7dLYv9lxK1UWFly0s0Nj9xcrCureH7H//ALCDBp3EII0Zl01BrqoqIievXqxcqVK5k4cSLl5eVs27YNT09PBg4cSHx8PKtXr+a7775rk+tv2bKF3NxcDh48yJYtWy5IqCsqKujbty9PPfUUUVFRvP3227z66qukpKRgZXXpRFFb11BLQi06Ha2ha1c4c8b457XmaN5R3t31Lu/vfp/+3ftT/p9y/tfzf5eUZYQXhbP2b2tNulZsRARzExIumUV+xdKSmEGDzifMtX/26QO2ti2KnZaeTsizz5IREWGcvS4podfq1SS9/DIB/v4mjVsIITqTxpK9Y2lpxEdHU20wYOHjQ2RcXKsnHEyJsWvXLsLCwsjNzb1k38GDBxkyZAiVlZXY2tpibW1Nbm4u5eXlLFy4kI8++ojy8nIeeOABli1bho2NDVu3biUiIoJZs2axdOlSHB0def7553n44YebHMd7771HQkLCBQl1YmIi06dPJzMzs26bn58f7777LmPHjr0kRod6KFGIjqCgALp0ubaS6YqqCj4/9Dkrd63kl+xfmDpoKlsjt9LPvR9pt6cR9lgYqYNT62qoA/cEEvdGnGkX1ZrqX39tsM65etQo+PZbk8JHr1hxPpkGsLMjY/p0olesYO3ixSbFFkKIzu5YWhrLw8KITU2t+w1hzPffMzsxscUJsakxgoKCsLS0JDIyksmTJzN8+HBcXFwACA4O5u233+a99967YIZ63rx5pKens3fvXqysrHj44YdZtGgR//d//wdAdnY2ubm5ZGVlsWPHDu69915uuukm+vbt26rPJzk5mUGDBl2wbdCgQSQnJzeYULe1Fi3sIkRHcuIEeHld6VG0j7S8NBb+ZyG9XuvF8h+WE3lDJJlPZvLqXa/Sz70fAAH+ASS+kUh4UTihaaGEF4WT+EYiAf6XWTZRWQnr18ONN2Jx7BjnLtp9DrDw8THpvgAySkrOJ9O17OzIKi5u+AQhhLiGxEdH1yXCYJzMiE1NJT46ut1iODo6sn37diwsLJg5cyY9evRgwoQJ5OTkNHrOqlWrWLZsGc7Oztjb27NgwQLWrVtXt18pRVxcHNbW1owePZpx48axYcOGFt9TrbNnz+Ls7HzBNmdnZ4qKilodyxxkhlp0OidOgKfnlR5F26moquDfh//Nyl0r+fnEz0wZNIVvH/mWYPfgRs8J8A8wubyDkhJ4/3145RXw8YG4OCL79yfmrrsunN0IDGR23OXPfmeXlfGGwcAPZ88ar1k/qS4pwfv0adPuQwghrgLVBkPDvyFMSICEhJbFoKGGrVCd1WDX4gb169eP1atXA3D48GHCw8OZM2cOCQ2MIScnh+LiYoYOHXp+DNXVF5RauLq6YluvNNDPz4+sVoynloODA4WFhRdsKywsxNHRsdWxzEFmqEWnk519dc5Qp+en8+x/nsXvNT9e+/41pg6aSuaTmSy9a2mTybTJ8vLg+echIAA2bYK1a2HbNrjvPvwCA5mdmMgr4eHEhIbySnh4q37dWN/Bc+eYcegQ/X/8kdzKSr565hkC1683JtUAJSVYrl7FAkmohRACCx+fhn9DGB5ufJioBS+L8PCGY3h7X9aYgoKCiIyMZN++fYBxtrk+d3d3unbtSnJyMrm5ueTm5pKfn09BQUHdMXl5eZTU/r0PZGRk4H0Z4xkwYAB7917YvnXv3r0MGDCg1bHMQRJq0el01pKPtPQ0Ih6PIDQylIjHI0hLT6OiqoJPDnzCPQn3MOydYRRXFPOfqf/hu2nfET4oHFurlj3gd1mOH4enn4bAQEhJgS1b4LPP4NYL29b5BQQQs3YtsVu2ELN2bauSaa012/PzmfDrr9y+eze+NjYcvvlm3goKIrR/fxJjYwlPSmL4h59g98y/sQ3txaKQEPTx4+a+WyGE6FQi4+KICQysS4hrf0MY2YrfEJoa49ChQyxduhSDwbjgVmZmJuvWrWPEiBEAeHh4cPz4cSoqKgBjgj1jxgzmzJlTVxZiMBjYvHlzXUytNTExMVRUVLBt2zY2btzIxIkTG7x+dXU1ZWVlVFRUUFVVRVlZGZWVxsUKQkJCsLS0ZPny5ZSXl/PGG2+glGLMmDEt/nzMyhzrl5vzhaxnL5rx9NNaL1lypUfROkfTjurAcYGahWieQ7MQ7TLGRXdf2F3ftvo2/cGeD3RxeXH7DGb/fq0jI7V2ddX6ySe1zsgw+yUqq6v1v06d0sN37dKBO3bot44f1+cqKxs9/uxZrbvYVGmnl9z10I826MXx8WYfkxBCdFSN5T7pR4/q58LD9V9DQ/Vz4eE6/ejRVsc2JYbBYNCTJk3SPj4+2sHBQfv6+uqoqChdVFSktda6vLxc33fffdrNzU13795da611aWmpXrhwoe7du7d2dnbW1113nV6+fLnWWuukpCTds2dP/cILL2h3d3ft5+enExISGr1+fHy8VkppCwuLute0adPq9u/evVsPHTpUd+3aVQ8dOlTv2bOn0ViNfcY1203OX6Vtnuh0wsPh7rthypQrPZKWi3g8ggTHhEta2407PY4vVn7RPoPYsQNeegm+/x4eewwefRTc3Mx6iZKqKtZkZ/Pq8eN0s7LimV69uN/dHUvVfEciJycYsuwO5rg+wKMWvqwZNYqwi3pXCyHE1aij9qE2t61btzJlyhQyMjLa/drSNk+Ii3TGGmpDoQEuzg27QHFZG3e00Bq+/BIWL4bMTJg7F9atM3vPwdPl5byZlcVbBgPDnZx4v18/Rjo7X1Jf1xQvL+hrP4zkbnmsW5rIb11c2HHLLQRc3AlECCGE6GAkoRadTmesofZx8oFyLpmh9na6vAdDLnZJ4/6//hW/nTthyRKwtIT582HiRGhg9ShTpJaUsDQzk3WnTvFg9+5sveEGgu0vfqa8Zby8wEcN46cTCfxl1Cj+/MMP/MbBgf8OGUJXS0uzjlsIIYQwJyn5EJ2Oq6vxGbrOVA3wzn/e4dGYR6m8vfKCxVdM6hddo8HG/VZWzB46FL/nnoO77oJWzBRfLC09negVKzCUluJja0tcVBSn3Nx4OSODrQUFzPTyYraPD542Nq2OnZ6WzoroFZQaSvnpqC1jHh3H+1YPczx8Fzo4mKlbt6KtrPigf/9WzXYLIURncq2UfFxJsvS4EPWUloKzs/HPzpJfHS88ztB3hvLmrW/y6fpPySrMwtvJm7in4kxOpqGJ5cHDw4lZa1pv6rT0dMJiYkidPLlueXDbv/8dt4kTmX/zzUz39MThMme909PSiQmLYXLqZOywo4QS3nZbz9bff8aB6AN4RfyJ4vvvZ+T11xPp6ckTvr4m3YsQQnRUklC3PamhFqKe7Gzjoi6dJZmuqq4i4uMIHr/5cR669SEeuvUhs1+j0eb/l9Eo/2LRK1acT6YB7OwonTqV25OSePw3vzEp9oroFXXJNIAddvwpdzJZ2/ez68Qu7ps+na6vvMInmzcz/OefGWxvT4irq6m3JIQQQpid9KEWnUpnq59+YdsLKKVYcNuCNruGRbduZm3cX5+htLTB5cGzS0tNjl1qKK1LputCY0fffX3JjM+kctRYOHIE/8xM1vbvz8MHDpBphusKIYQQ5iYJtehUOtOy4//N+C9v/vgmax9Yi6VFGz1UV1ZG5LFjxLi4mNT8vzFdrazOr2RYq6QEb1vTF5zR5zQlXBi7hBIs+ljQZVMXdgT8RLLzUnL+vJEx9i7M8fXlweRkSquqTL62EEIIYU6SUItOpbO0zMsrySP843DeHf+uscNHW9AaZszAr1cvZv/0k1mWB6/v17Nn+eHWW/FISLhgefDA9euJi4q6/GFXa1LmphCaE8q6XuvqkuoSSnjZej1R8VH85eG/cEvqLbj+LojjX9jwP+//8f9iixm5x4LHDh6WWkMhhBAdijyUKDqV6Giwtoa//vVKj6RxWmsmfjQRb0dv/nbP39ruQs8/b1wqfOtWs/eV/vXsWcbu3cuywEBuKSkhesUKskpL8a7p8hHg739ZcauKqzgQcYCKMxUM/GQghgKDsctHVinKzZb3N0eRX+BHj1d6sPuPu40/jAwfTmlUDKdyBpCdcJITx4upesCZO2f2xnGoo3T/EEJ0evJQYttr64cSZYZadCqdoeTj3Z/fJSU3hSVhS9ruIuvXw7vvwueft1ky/VqfPkz28CDA35+1ixez5fXXWbt48WUn02XZZewO2Y2lgyWDNw/G2s0a/wB/Fq9dzOtbXmfZR4spLfOntFQxzHsYP2X9ZDxx2jRs//0eveb24uZfbiJo80C2VBby82+T+aHfD6TFpFF8qI0XyBFCiGvU9u3bGTlyJC4uLri7uzNq1Ch27doFwJo1axg1alSbXfujjz5i5MiR2NvbM2bMmEv2W1hY4OjoiKOjI05OTsycObPNxtIc6fIhOpWOXvKRfCqZZ7c8y7Zp27C1Mr3OuEE7dsDs2fDNN2b/MPaePctdNcn0b3v0MFvcs/vO8ut9v+L1ey/8/uLX4KyyUuDhASdPwjAvY0I9IXgCTJ5sXJjm9Glwd6f/kG7c+/IAIg4e5DuCqPpnHrtDdtPFuwseD3vQ/bfdsfU1fvb1+1zb+tgSFReFf4C/2e5LCCGuZkVFRYwfP56VK1cyceJEysvL2bZtGzY16w5ordv0t4TdunXjySef5ODBg2zZsuWS/Uop9u7dS4CJJY7mIDPUolPpyF0+SipKmPyvybx0x0sEuwe3zUXS0uDBByE+HgYPNmvotkqmczfnsmfMHnq/0Bv/aP8m//L18jL+Nx7mPYyfTtTMUDs7w/jxkJBQd9y93brxJx8fptgdo9ervRlxfASBSwI5t/8cPw36id2hu9n5wk5ixsQQkhDCA0kPEJIQQkxYDOlp6Wa7NyGEaEtp6elEzJ9P6BNPEDF/Pmnp6e0a4/DhwyilmDRpEkopbGxsuPPOOxk4cCAHDx4kKiqKHTt24OjoiJubGwDl5eXMnTsXPz8/vLy8mDVrFmVlZQBs3bqVnj178uKLL9K9e3d69+7Nhx9+2Oj1x4wZw0MPPYRXI//wa62prq5u+YfNy6OrAAAgAElEQVTRhiShFp1KR06o526ey3Xdr2P6kOltc4GCArjvPliwAMaNM2votkqms97J4sDUAwz4eAAeD3s0e/wFCXXWT+fr3aZNg9WrjQ9i1ljo50d3a2vmpKSgLBWud7gS/F4wt564FZ8nfHh/5ftMTr+wz/Xk1MmsiF5htvsTQoi2UruwVkJICEkPPEBCSAhhMTGtSohNjREUFISlpSWRkZF8/fXX5Ofn1+0LDg7m7bffZsSIERQVFZGbmwvAvHnzSElJYe/evaSkpGAwGFi0aFHdednZ2eTm5pKVlUV8fDwzZ87kyJEjLb6ni91+++14e3vz0EMPcezYscuOYypJqEWnUVUFOTlgxnzPbD49+ClfpnzJyvtWts2vvyoqYOJECA01lnuYUW0y/boZk2ldrUl9JpXMVzIZsm0ILre5tOg8T09jQu3t6I2VhRWZhZnGHSEhUFgIv/xSd6yFUvy9f3+25OWx+sSJ89ttLOh+f3dsets02Oe6NEt6WQshOr6GFtZKnTyZ6BUtnxQwNYajoyPbt2/HwsKCmTNn0qNHDyZMmEBOTk6j56xatYply5bh7OyMvb09CxYsYN26dXX7lVLExcVhbW3N6NGjGTduHBs2bGjxPdX33XffkZ6ezsGDB/Hy8uK+++67YjPWUkMtOo3Tp8HV1djloyPJLMjkj1/8kU9/+ykuti1LHFtFa3j8cbC0hNdeM+sykfWT6UlmSqariqs4MOUAFacruHHHjVh3a/l/MC8vY528UucfTOzl3AssLM7PUt94Y93xTlZWfDpwIKN372agvT03OznV7bP1saWEkguS6hJKsPVuo9p2IYQwo8YW1krIziYhKallQbKzG4yR1YpFsvr168fq1asBYwlIeHg4c+bMIaFeGV6tnJwciouLGTp0aN226urqC7pruLq6YltvLQM/Pz+yLnNl39tuuw0AJycnXn/9dZycnDhw4AADBgy4rHimkBlq0Wl0xHKPquoqwj8O54lbnmBEzxFtc5HXX4ft2+Ef/wAr8/0MvOfsWcbu2WPWZLquk0fXmk4erUim4XzJB8BQr6HnO30APPIIrFsHF/1DEGxvzztBQTyUnMyp8vK67VFxUawPXH9Bn+v1geuJirv8HtpCCNFefGxtG1xYK9zTEx0S0qJXuKenWRfnCgoKIjIykn379gFc8htZd3d3unbtSnJyMrm5ueTm5pKfn09BQUHdMXl5eZTUG1NGRgbeZljZt/YBySvVflASatFpdMSWef+37f+wtrRm/sj5bXOBf/8bliyBL76AerOvptpz9ix37dnD8r59zZZMn913lp+H/0y3cd0I/nswFjat/+ultuQDuLB1HoCfn3F2+rPPLjnv/u7decTTk0nJyVTU/LrPP8Cf2MRYksKT+Hj0x/zT7p88/cLT0uVDCNEpxEVFEbh+vUkLa5ka49ChQyxduhSDwQBAZmYm69atY8QI4wSSh4cHx48fp6KiAjAm2DNmzGDOnDl1ZSEGg4HNmzfXxdRaExMTQ0VFBdu2bWPjxo1MnDixwetXV1dTVlZGRUUFVVVVlJWVUVlZCcD+/fvZs2cP1dXVnD17lqeffhpfX1/69+/f4s/HrLTWHeplHJIQl1q9WutHHrnSozjvu/TvtMfLHtpQaGibC/z8s9bu7lp//71Zw+4uKtIe27frDSdPmi3mmc1n9Pbu2/WJD06YFOeHH7S+8Ubj+6zCLO36kquurq4+f8CHH2o9dmyD51ZWV+t79+zRTxw+3OD+7A+z9Y9DftTVldUN7hdCiCulsdznaFqaDp83T4c+/rgOnzdPH01La3VsU2IYDAY9adIk7ePjox0cHLSvr6+OiorSRUVFWmuty8vL9X333afd3Nx09+7dtdZal5aW6oULF+revXtrZ2dnfd111+nly5drrbVOSkrSPXv21C+88IJ2d3fXfn5+OiEhodHrx8fHa6WUtrCwqHtNmzZNa631li1bdL9+/bSDg4P28PDQDzzwgE5JSWk0VmOfcc12k/NXWSlRdBovvABFRfDii1d6JJBbksuQlUN48943uS/oPvNfwGCA4cNh6VLjw4hmUn9meqKZZqaz3s0iLTqNAR8NwGWUaTXkx4/DzTdDbTmd71Jfvpv2Hb1dexs3lJSAr6/x4cRevS45P6+igpt27eI5f38iLvp1htaa3aN34zHVA+8Zpv96UQghzOVaWSlx69atTJkyhYyMjHa/tqyUKESNjlJDrbXmD5//gQeCH2ibZPrcOWPf5VmzOnQyras1qfNSyVxS08nDxGQajAu75OQYO7qAsexjV9au8wfY2cFvfwtr1jR4vqu1NZ8OHMiTqan8UlR0wT6lFH3+1oe06DQq8itMHqsQQghRSxJq0Wl0lBrqlbtWkpafxuI7F5s/eFUVhIcbF21ZsMBsYWuT6TfMlExXFVeRPCmZwu8LufH7G+na1zzLn1tbg4uLMamGBuqoAaZPNy5s00hrpIEODrzZty+/SU5m1+HDFyxocNr1DO4T3DkWe+V6lQohhLj6SEItOo2OsOz4vlP7iP42mvUPrsfGysb8F1iwAPLzYeVKs7XH211UVJdMP2SGZLr8ZDm7Q3djYWvB4MTWd/JoTm3rPKjp9HHiooR66FCwt4fvvms0xqQePQgrK2NUAwsaWM604uTak5zbf86s4xZCCNG022+//YqUe7QHSahFp3GlSz6KK4qZ/M/JLLlzCf3c+5n/Au+8Y+xg8a9/QZcuZgm5u6iIu/fuNSmZTk9LZ37EfJ4IfYKn73uaL4Z+Qbd7u9H/g/6X1cmjORe0zvMeyq6sXVTrerPRSp3vSd2Es19+ScnUqZcsaPDchnfw+4sfKXNSromaRSGEEG1PEmrRKWh95Us+nt70NNd7XE/kDZHmD/7NNxAdDRs3QrduZglZm0y/GRRkUjIdExZDSEIIDyQ9wJ0b7+Tjio9h6qX9R82lfkLdw74HzrbOpOamXnhQRAR8/rlx9cRGnGhkUYSs0lK8Z3lTZijjzOdnzDx6IYQQ1yJJqEWnUFRkXCjQweHKXP/jAx+zKXUTb4972/yJ5IED8PDDsGED9O1rlpC/1EumH+ze/bLjrIheweTUyXWrDdphR/ipcFZEt3zp29by9Dxf8gGN1FF37w533GFc7KYRjS2K4G1ri4W1BX1e60PKUylUlVaZcfRCCCGuRZJQi07hSpZ7ZBRk8Kcv/sS6B9fhbOts3uA5OXDfffDyy3D77ZcdJi09ve7hu3uffpqwTZtMTqYBSg2lFyzdDcakujSr5cvWtlb9GWqAYV7D2HVi16UHNlP20dyCBm5hbthfb8/xZcfNOXwhhBDXIEmoRadwpRLqyupKwj8O56kRT3GL7y3mDV5aCvffD5MnG5fVvkxp6emE1Xv47qs778Tqs8+48ZzpD93Z+tjWLd1dq4QSbL0vb9nalrgkoW5ohhrg7rvh2DHjDH8DAvz9SYyNJTwpCYe//53QzZtJjI0lwN+/7pg+r/Yh89VMygxlZr4LIYQQ1xJJqEWncKXqp5//7nlsLG2YN3KeeQNrbWz/5uMDcXEmhYpesYLUyZMvePju5MMPE73C9LKM8HHhxFvG1yXVJZSwPnA9UXEtX/q2teovPw7GBxN/PvHzhQ8mAlhZwdSp8P77jcYK8Pdn7eLFLImLo/sf/nBBMg1gF2iH90xvji44asY7EEIIca2RhFp0CleiZd7W9K2s3LWSDx74AAtl+v8qx9LSiI2IICY0lNjBgzm2f79xgRIL02Ibmnj4zhSVZyspfraY+SvmkxSexCehn5AUnkRsYiz+Af4mxW5K/bZ5AG52brh3defwmcOXHjxtGnzwAVQ0vVDL5B492JSbS24Dx/Va2Iu8b/Mo2FFg6tCFEOKqs337dkaOHImLiwvu7u6MGjWKXbuMZXhr1qxh1KhRbXbtZ555hqCgIJydnbnuuuv44IMPLti/e/duhg0bhr29PTfddBN79uxps7E0x+qKXVmIVmivko+09DSil0aTnp/OLyd+YfnC5Xg5mn7hY2lpLA8LIzY1FXvgHBDj78/s7Gz8AgJMil338F39pLrm4TtTHF1wFOdRzvSf0Z8bZ9xoUqzWqC350Pp8K+7aso9g9+ALD+7XD3r3hq+/Nq4u2QhXa2vu6daND0+e5DFf3wv2WTlY0ful3qQ8nsKNO29EWbRN9xIhhOhsioqKGD9+PCtXrmTixImUl5ezbds2bGyM6zBordus4xOAg4MDGzdupG/fvvzwww/cfffd9O3bl+HDh1NRUcH999/PU089RVRUFG+//TYTJkwgJSUFK6v2T29lhlp0Cu2RUKelpxH2WBgJjgn8N/C/FN9czAuvvkBaeprJseOjo+uSaQB7IDY9nfjoaJNjL/rTn7D5+98bffjucuRtyeP0p6fp81ofk8fXWg4Oxo4u9TviNVpHDcbSmWZ6UgNM9/Tk/fpT3/V4hHugrBXZ8Q3vF0KIK6H+OgDzI+aTnpberjEOHz6MUopJkyahlMLGxoY777yTgQMHcvDgQaKiotixYweOjo64ubkBUF5ezty5c/Hz88PLy4tZs2ZRVmZ8TmXr1q307NmTF198ke7du9O7d28+/PDDRq8fExND35ruVzfffDOjRo1ix44dAHz77bdUVVXx+OOPY21tzezZs9Fas2XLllZ/RubQbEKtlLJRSu1USv2ilPpVKRVTs32tUuqgUmqvUmqVUsqyZruTUupzpdTumuMj68V6RCl1WCl1SCk1tc3uSlx12qOGOnppNKmDU6F2TZUukDo4leilpie91QZDXTJdyx6ozsoyOfZeBwf8Jk/md0lJhH7yCeFJSZc8fNcalUWVHPr9Ifq90w9rV/OugthSF9dRD/NupNMHwKRJ8O23cOpUkzHHuLqSU1HBnrNnL9mnlKLP3/qQ9mwalQWVpgxdCCHM4uJ1AEISQogJi2lVQmxqjKCgICwtLYmMjOTrr78mPz+/bl9wcDBvv/02I0aMoKioiNzcXADmzZtHSkoKe/fuJSUlBYPBwKJFi+rOy87OJjc3l6ysLOLj45k5cyZHjhxpdiwlJSX8+OOPDBw4EID9+/czaNCgC44ZNGgQycnJLbo3c2s2odZalwGhWushwA3APUqpm4G1WutgrfUgoCvwh5pTHgWStdY3AKHAq0opK6WUK/BX4CbgFiBGKWXmHmTiatUeNdSGQsP5ZLpWF8gqND3ptfDx4eKeG+cAC29vk+JWVFcz/+hRXr/tNj5cvJgtr7/O2sWLLzuZBjg67yguoS50u9c8C8xcjovrqG/0upHd2bupqm6gZ7Sjo7Fbytq1Tca0VIpHPD15v36mXo/TMCfc7nUjPS7dhJELIYR5NLQOwOTUya1aB8DUGI6Ojmzfvh0LCwtmzpxJjx49mDBhAjk5OY2es2rVKpYtW4azszP29vYsWLCAdevW1e1XShEXF4e1tTWjR49m3LhxbNiwodmx/OlPf2LIkCGEhYUBcPbsWZydL0wjnZ2dKSoqatG9mVuLiky01sU1b21qztFa66/rHfIDUFuYqAHHmveOwBmtdaVS6i5gs9a6AEAptRm4G2h8ZQYharRHyYePkw+Uc2FSXQ7eTqYlvQCRcXHEfPklsXl552uoAwOZbWKHj/dOnMDXxoa7an7VZqrcb3I5s/EMw/YOM0u8y3Vx6zwXWxe8HLw4ePogA3oMuPSE6dMhKgqefPJ84XUDIj09GfHzzywJDKRLAw+D9n6hNz8O/BHvGd507dfVHLcihBCXpbF1ALITsklKSGpRjGyyTV5LoF+/fqyuKas7fPgw4eHhzJkzh4SEhEuOzcnJobi4mKFDh9Ztq66uRmtd97Wrqyu29Z7x8fPzI6uZ39Y+88wz7N+/n2+//bZum4ODA4UXrZZbWFiIo6Pjxae3ixbVUCulLJRSvwDZQKLW+sd6+6yAKUBtgv0GcJ1SKgvYAzxRs90HyKwX1lCzTYgmlZUZV0o0U87YqLin4vD+yduYVAOUQ+CeQOKeMi3pBfDz9WW2lRWv3HsvMaGhvBIezuzERJMeSDxbWcmiY8dYEhholodCKgtrSj3e7Ye1y5Up9ah1cckHGNvnNVpHPWqU8Rvlxx8b3l8j0M6O67p25YszDS853sWjC70W9CLlyZTLGbYQQphNY+sAeIZ7EqJDWvTyDPc061oCQUFBREZGsm/fPoBL/u1xd3ena9euJCcnk5ubS25uLvn5+RQUnO+ilJeXR0m9VWwzMjLwbuK3tTExMWzatInExEQc6i2XPGDAAPbu3XvBsXv37mXAgAYmXdpBixJqrXV1TcmHL3CLUuq6ervfArZqrf9b8/VdwC9aa29gCPCmUsoBaOhffN3ANiEucPIkeHiY3F2uWQH+AYyfMp6BKQMJTQslvCicxDcSCfA3rQsHAJ9+il///sRs3Ejsli3ErF1rcnePV48fJ9TFhaFm+mk8dW4qbmPdcLurjX9yaYGLSz7AuGJiowm1UsYWek30pK41zcuL1Y2UfQD4zPah5GgJZzY2nHQLIUR7iIqLYn3gepPWATA1xqFDh1i6dCkGgwGAzMxM1q1bx4gRIwDw8PDg+PHjVNS0JFVKMWPGDObMmVNXFmIwGNi8eXNdTK01MTExVFRUsG3bNjZu3MjEiRMbvP6LL77IunXrSExMxMXF5YJ9ISEhWFpasnz5csrLy3njjTdQSjFmzJgWfz7m1Kq+IlrrQqVUEsZSjf01Dyi6a61n1jtsGvBizfGpSqk0IBg4DoTUO84X+JYGPPfcc3XvQ0JCCAkJaegwcY1oz1USd5zdwcpXVnJrz1vNG/iNN+Cxx8wW7mR5OX87fpyf6v1azRS5m3PJ3ZTLTb/eZJZ4pvLygoufKxnmPYx/Hvhn4yc98ggMGgSvvgpdGy/XeKh7d+akpHCirAyvmtZP9Vl0saDPsj6kPJGCa5grFl2kGZIQov35B/gTmxjLiugVlGaVYuttS2xc69YBMDWGo6MjO3fuZOnSpRQUFODi4sL48eNZsmQJAGPGjGHAgAF4enpiaWnJqVOneOmll1i0aBHDhw/nzJkz+Pj4EBUVxdixYwHw8vLC1dUVb29v7O3tWblyJUFBQQ1e/9lnn8XGxoa+ffvWtehbuHAhCxYswNramk8//ZTf//73LFiwgP79+/PZZ5812zIvKSmJpKSkFn6CLafq17U0eIBS7kCF1rpAKWUHbAJeArwxJs9jah5crD3+TeCU1jpWKeUB/AQMxjgb/RNwI8aZ8Z+AoVrr/Iuup5sbk7i2fPqpceLxs8/a9jqGQgPXr7ieU8+cwsrCjD0sf/3VuEx2ejpYm6eUYtbhw9haWLC0j+lt7SoLKvnx+h/p914/3MKu/Ow0wObNsGQJfPPN+W2FZYV4vepFwYKCxv/73H03TJkC4eFNxv/DwYMEde3KvF69Gj1m7317cbndhV7PNH6MEEKYg1KKayH32bp1K1OmTCEjI6Pdr93YZ1yz3eS6yZZMvXgB3yqldgM7gU1a6y+BFUAP4Hul1M9Kqb/UHP88cKtSai+QCMzTWudqrfOAOIyJ9E4g9uJkWoiGtNey45tSNxEWGGbeZBrgzTfhj380WzJ9qLiYj3JyeNbPzyzxUp5Owe1etw6TTEPDNdRONk70cu7F/pz9jZ84fXqryj6a+gesz7I+ZCzOoOxEWaPHCCGEENCCkg+t9a8YZ5Uv3t5gdqC1PoGxjrqhffFAfKtGKK557bXs+FcpXzGu7zjzBs3Ph3/8A/Y3kQS20sKjR5nbsyfdzJCgn/nqDHnf5HWYUo9aDdVQw/kFXgZ5DLp0J8CECTBrlvG3AU20DrzVyQkNfF9YyAjnhrt3du3bFa/fe3H0z0fpH9+/1fcghBDi2iHFgaLDa48a6srqSr45+g1397nbvIHXrDGWIZjpBv5XUMAPRUU87mN6g5yK/AoOzzxM8HvBWDm2/zKtTenWzdjZpeyiyeGhXk10+gCwsYHf/Q7i45uMr5RiWhMrJ9by+4sfeYl5FO4sbPI4IYQQzbv99tuvSLlHe5CEWnR47VHysSNzBwEuAXg6mPFC1dXGco9HHzVLOK0181JTifP3x87S0uR4qU+m0m18N1zvcDXD6MzLwgJ69Gig00dTS5DXmj7dmFBXVzd52FRPTz7KyeFcVQOLxdSwcrSi9wu9OfL4EXT11V/fKIQQ4vJIQi06vPYo+fgq5Svu6XOPeYN+842x28TIkWYJ99np0xRWVTHFDD9dnNl4hvyt+fRe0tsMI2sbDZV93OB5A/tO7aO8qrzhkwCGDAFXV+Ny5E3wtrHhVicnPm5ixS8AjykeAJz84GSLxi2EEOLaIwm16PDao+Tjq5SvzF/u8cYbxtlpcyy6Ul3NgqNHWdy7N5YmxqvIq+DQHw/Rb3U/rBw6VqlHfRevlgjg0MWB3q692XdqX9MnT5sGNSt7NXlYC8o+lIWi79/6cvTPR6ksqmw2phBCiGuPJNSiQ6uuhlOnjAu7tJUTRSdIz09nRM8R5guang7/+x88/LBZwr2XnY2PjQ13m2G5yJQnUuj+QHdcQzpeqUd9DSXUYCz72JW1q+mTw8Nh40bjQ6FNGO/uzq/nznG0pKTJ45xuccJ1rCvHnj/W3LCFEEJcgyShFh3a6dPg5ARdurTdNTalbuLO3neat13eihUwdSrY25sc6mxlJbHp6WZZYvz056cp+F8BvV/quKUetRpqnQctrKPu1g3GjoX165s8zMbCgod79GBNM7PUAL1f7M2J905QfKS42WOFEKI1/Pz8UErJqw1ffmZqNdsYSahFh9Yp66dLSozlBrNmmSXc0uPHCTHDEuMVZyo4HHWY4NXBWNqb/lBjW2uydd6JZhJqaFXZR3x2NtXNLKpg42VDr3m9SH0qtflrCyFEK6Snp6O1llcbvtLT09v0v6Ek1KJDa+v66crqShJTE81bP/2Pf8BNN4EZVjE8WV7O68eP838BASbHOvL4EbpP7I7LaBeTY7WHxko+BnsM5kDOAUorS5sOMHYsx44dI3bcOGJCQ4mNiOBYWtolh93g6IibtTVb8vKaHZPvE74UHyzmzNdnWnobQgghrgGSUIsOra1b5u08vpNezr3wdvQ2T0Ctzz+MaAaL0tOZ6ulJgJ2dSXFyPsmh6Icier/Q8Us9ajVW8mFnbUffbn359eSvTZ5/LCOD5eXlzP3yS2KTkpibkMDysLAGk+rpLXg4EcDCxoLAZYGkzEmhurzptnxCCCGuHZJQiw6trUs+zN7d44cfIC/PuJiLiQ4XF7MhJ4e/mFj3VX66nCOPHqHf+/2w7NrxSz1qNVbyATDMq/k66vjoaGLz86mtYrcHYlNTiY+OvuTYhz082HjmDPkVFc2Oq9u4btgF2GF4w9DssUIIIa4NklCLDq2tSz6+TvnavPXTb74JUVFghoVXFh49ytO+viYvMZ4yO4Uek3vgclvnKPWo5elp7PDS0Posw7yHsetE050+qg0GLn4k1B6ozsq65Nhu1taEubmx/tSpZsellCJwWSA743byzIPP8EToE8yPmE96Wnqz5wohhLg6SUItOrS2TKhPnj1JSm4Kt/a81TwBT52Cf//buFKfiXYUFLCzqIgnfH1NG9I/T1H0cxEBz5teg93eunQxdng5ffrSfS3p9GHh48O5i7adAyy8Gy7vaWnZB0COTQ4f648Z8/EYHkh6gJCEEGLCYiSpFkKIa5Qk1KJDa8sa6k2pm7ij9x1YW5o2A1znvffgN78BE3tFa615JjWVRSYuMV6eU07K7BSC44M7ValHfY3VUQ/yGMThM4cpqWi8f3RkXBwxgYF1SfU5ICYwkMi4uAaPH+vmxvGyMpLPXZyGX2pF9AqmFEzBDmNtux12TE6dzIroFc2eK4QQ4uojCbXo0Nqyhtqs7fIqK429p83wMOLnZ85QUFXFVBN/kjjy6BE8IjxwHuFs8piulMbqqG2sbAh2D2bPyT2NnusXEMDsxERe+d3viLGy4pUJE5idmIhfIx1TLJViqqcn7zeUwV+k1FBal0zXssOO0qxmOo8IIYS4KnXcdYeFoO1KPqqqq9icupmXw142T8AvvgBfX7jxRpPC1C4xvjQw0KQlxk9tOMW5X88RvCbYpPFcaY21zoPzZR/DfYc3er5fQAAxH34IFhZw223QTPvBaZ6ejP7lF17s3Rtri8bnG2x9bCmh5IKkuoQSbL1tm74hIYQQVyWZoRYdVlGR8U8T1zNp0A+GH/B29MbXybQa5TpvvAGPPWZymNXZ2Xh16WLSEuPlJ8s58vgRY6mHXecs9ajVkoS6RcaNgy+/bPawoK5d6WNnx1e5uU0eFxUXxfrA9ZRgLDkpoYT1geuJiotq2XiEEEJcVWSGWnRY2dltVz9t1u4eBw7Avn3w4IMmhTlbWclz6el8PnBgq5cYT09LZ0X0CkoNpZSllPG7+3+H0y1OJo2nI/D0hMYWtxrmPYzlPyxvWaC77oI//hFKS8G26VnkaV5erD5xgv/n7t7oMf4B/sQmxrIiegVnD5yl7EgZz216Dv8A/5aNRwghxFVFEmrRYbVlh4+vUr5i8Z2LzRPsrbdgxgywsTEpzNLjx7ndxYVhTq1LhNPT0okJi2Fy6mTssKOEElYnrsYvza/TJ3heXrBjR8P7BvYYSGpuKufKz2Hf5eIGeRdxc4NBgyApqdke4ZO6d2duaiqnysvp0aVLo8f5B/izeO1itNb8NOQnnFOcIbDpYQghhLg6ScmH6LDaKqHOOZfD4TOHGdlrpOnBioogIcE4+2kCU5YYXxG9oi6ZhpqOE0evjo4TTZV8dLHswsAeA9mdvbtlwVpY9uFoZcWEbt1Ye/Jki8IqpfCd7SsLvQghxDVMEmrRYbVVy7xNqZsIDQili2Xjs48t9sEHMGaM8YFEE9QuMd77MpYYv5o7TjTWNq/WUK+hLa+jvvde2LjRuDx8M2rLPnQLjgXo8XAPCr8vpBVj0q0AACAASURBVORo4238hBBCXL0koRYdVlu1zDNbuzytjQ8jmtgq73BxMf84dYpne/W6rPNrO07Ud7V0nGhq+XGoeTDxRAsT6kGDoLwcDh9u9tDRzs6UVlfzU+2Tsc2wtLPEc5onhrdklloIIa5FklCLDqstSj6qqqvYlLKJu/s0XUfbIklJoBSEhJgUZuHRo8zt2RP3Jup1mxIVF8Vat7VXZccJR0fjzy2N5bWt6vSh1PlZ6mYPVUS2YuVEAO9Z3mTHZ1N1rqrF5wghhLg6SEItOqy2SKh3ndiFh4MHvZwvbzb4ArWz0yb0i/7eDEuM9/LuxW8sf8M393zDJ6GfkBSeRGxibKd/IBGMH21TddTXdb+OjIIMispaNpPc0oQa4BFPT/5x6hQlVS1LkO387XAe6czJD1tWey2EEOLqIV0+RIfVFm3zvjpipnKPzEz49luIj7/sEFprnjl61OQlxk8mnKTPkD48+KVpbfs6Kk9P4/dCUNCl+6wtrRnkMYhfsn9htN/o5oPdcQdEREBhITTTTaWnrS3DHB359PRpfufh0aKx+sz2IfWpVLz+4NXq1odCCCE6L5mhFh1WW8xQm61+euVKCA83adWZz8+cIb+y0qQlxnW1JmNJBr3mm2HGvYNqaoYaYJhXK8o+HBxgxAj45psWHT6tlWUfrnf8f/buPD6q6v7/+OtM9oQEsi9DliEgiFY2960JJQrWtqLVooCAX2sbFW2tLd3yjWna/tTaftuKxrZWQUHTVuvSyiKosS4FBAQXRCVkn0x2EpJM9vv7YxIImGTuvTPZ4PN8PPqoTO4596ZN8DNnPud9wtE6NRr/06h7jBBCiPFPCmoxJnV0QGMjDHG2hmG1rbV8UvsJlyZd6tlE7e3w+OMebUbsO2L8gSlTPDpivPblWnxDfZmUPsn0HGOd24LaSB816I7PA7gmKoo9R49S2qYvMUUphfVOq0ToCSHEaUYKajEmVVVBdDRYvPgT+mrhq6SlpBHg69kBLDz3HJx9NsyYYXqKviPGF3lwxLimaZQ9UEbijxJP6fYCt9F5CQai8+B4Qa0jEi/Qx4clMTGsN7BKHXtzLA2vNdBWNv5jC4UQQugjBbUYk4YjMm/zoc0sTPVCuscjj8CddxoeVlRczLI1a7j8rrv4XlYWd/v4eFQIN77dSGdtJ9HXRpueYzxwF503I2oG9qN2Gtt0tllMnepq/din70CYVXFxrHM46NGZSe0b6kvssljsf7Lrex4hhBDjnhTUYkzydv90j9bD1kNbWTTNw/7pvXuhvByuvtrQsKLiYjKys9mYlsZb116L85vf5AcPPURRcbHpRyl9oJTEexNRPqfu6jS4b/nwtfgyO242eyv36p/0q1/VnfYxLzSUYB8f/nPkiO7prXdYqfxLJd1tEqEnhBCnAymoxZjk7YJ6b+VeIoMjSZmU4tlEjzwCmZngaywgJysvj8IlS6DvJMSgIAqXLCErz9zx4M0fNXN091Fib9aXPjGeuSuowUQftYH4PKUUtxjcnBg8PZgJsydQ848a/c8khBBi3JKCWoxJ3j523CtxeXV18PzzcOuthodWtLUdL6b7BAVh17nZ7WRlvylj8l2T8QkyH7c3XrjroQaDJyYCXH45HDgAtbW6Ll8WG8tLtbU0dXXpvoV1tZWKh2VzohBCnA6koBZjkrd7qL0Sl/fkk/D1r7t2SxpkDQwE54nHg+N0khBo/HjwttI26v5VR0JmguGx41F0tCvxpaNj8GsMr1AHBMD8+bBli75n8PcnPTycv1dX675F5KJIOms7adrVpP+5hBBCjEtSUIsxyZstH/XOej6q/ojLki8zP0l3Nzz6qOmovNzMTBKeeeZ4Ue10kpqfT26m8ePBy39fTtyqOPzC/Uw9y3hjsUBMjCv5ZTBnRJ5BTUsN9c56/RNfdZXu+DzAcNuH8lFY75BVaiGEOB1IQS3GJG+2fLxa+CqXJ19OoK/x1eBjtmyByEg4/3xTw20pKVy8YgVzNm0i/YUXWFpQwLacHGwpKYbm6azvxLHOweTvmz+qfDxy1/ZhURbmxM9hj32P/kmvugq2bgWdbRyLIiI43NbGp62tum8RtyqOun/X0VE1xPK6EEKIcU+OHhdjkjdbPrYc2uJ5u8fata7VaZMxd81dXWwPDOSThx4iLsB8DnbFoxVEfSOKwMkevDkYh9xF58HxExMzUjP0TWq1QmIi7NgBl7o/7MfXYmFZbCxPVlZyf2qqrlv4RfgRfX009r/YSfl5ir7nEkIIMe7ICrUYczTN9fG+N1aoe7QeV0HtSVzeoUOwZw9861ump3i+tpbLJk70qJjudnZT8XAFiT9MND3HeKU36WNPpYEVajB0aiK4Mqmfrqqiq6dH9xjrnVbsj9np6dQ/RgghxPgiBbUYc+rqXOdueFB7HrPPsY+JgROZEj7F/CSPPgq33PLFlA4DnqysZKWH7xAc6xyEXRBGyMwQj+YZj4YlOg8MxecBzAwJITEggFcbGnSPmXDOBIJSg6h9UV+iiBBCiPFHCmox5nizf9rjuLyWFli/Hr77XdNTHHY6+bi1lasjI03P0dPVQ9lDZSStSTI9x3imJzovNSKVI21HqGkxkP184YVQUeE6rEenVfHxPOHuYU5ivVM2JwohxKlMCmox5nizf9rjuLxnnnH11xrcPNjfeoeDm2Ji8LeY/3Wrfb4W/zh/Jl4y0fQc45meHmqLsjA3fq6xtg8fH7jySkNtH0tiYtje0EDtUDl+J4m6JgrnYSfN+5v1P5sQQohxw+2/4ZVSAUqpnUqp95VSHyqlsntf36CUOqiU+kAp9bhSyqffmLTe6z9SSr3R7/WFvWM+U0qtGZ5vSYx33orMa3A2sL9qP5cnX25uAk07vhnRpB5NY73D4VG7h6ZplD5YetquToO+lg/woO3DQEE90deXqyMjecZAJrXFz4I100rFWlmlFkKIU5HbglrTtHYgXdO0OcBsYJFS6nxgg6ZpMzRNOwcIBm4FUEpNBB4BrtY07Wzg+t7XLcBa4ErgLOBGpdSMYfiexDjnrZaP7Ye3c1nSZQT5mex9fucdaGuDBQtMP0PBkSNM8vVlTmio6TkaXmugx9lD5NXmW0bGOz0tH2CyoF64EN54A9rbdQ8x0/YR/+14ap6robO+09jzCSGEGPN0fQataVpf8GoArqg9TdO0/keM7QL6gnFvAp7XNK2id2zfTpzzgc81TSvRNK0TyAe+4eHzi1OQt1o+PG73WLsWbr/ddbKISes8XJ0GKHugjMQfJqIs5iL7TgVxca7kF3fhGqaSPiIj4ayz4M03dQ9JnzSJmrIyrvrBD0i/+26WrVlDUXHxkGP8Y/yJ/FoklU8YK8SFEEKMfboqBaWURSn1PuAAtmma9l6/r/kCy4HNvS+dAUQopd5QSr2nlFre+7oVKOs3bXnva0KcwBstH5qmeRaXV1npOvRjxQrTz9DU1cXLtbUsjY01PcfRvUdp+aSF2KXm5zgVBAa6kl/q3RyEaJtko6WjBUez/hMNAcPxeSUlJTiff57NCxZQsHgxG9PSyMjOdltUW++0Yn/UjtatGXs+IYQQY5qug100TesB5iilwoAXlVIzNU070PvlR4E3NU17t9+cc4H5QAjwX6XUf4GBltcG/LfKfffdd+yf09LSSEtL0/OY4hThjYJ6f9V+QvxDmBox1dC4kqIi1mVl0fPOO1iioljZ0EDypEmmnuEfNTWkh4cT7e9vajxA6YOlJH4/EYu/7B/u66OOihr8GqWUa5XavoevnvFV/ZN/9atw/fXw+9/rujwrL4+GZcuORykGBVG4ZAlZeXlseOCBQceFnR+GX7QfdZvqiPraEN+IEEKIYVFQUEBBQYHX5zV0UqKmaU1KqQJgIXCgd4NilKZpt/W7rByo0TStDWhTSv0HmNX7ev9dVZMB+0D36V9Qi9OPN3qozcTllRQV8XBGBjmFhYQALUB2Rgart20j2WYz/AzrHA7uTTR/CIuz0EnD9gam/3m66TlOJX191F/60tDX9fVRGyqoZ82C1lb4/HOYNs3t5RVtbV/MJQ8Kwt7W5nZsX4SeFNRCCDHyTl6ozcnJ8cq8elI+ono3GqKUCgIWAAeVUrcCVwA3njTkJeAypZSPUioYuAD4BHgPmKqUSlZK+QNLgJe98l2IU4o3eqg3H9rMwqkLDY1Zl5V1rJgG18crOYWFrMvKMnz/z1tb+ay1lasiIgyP7VP2uzISbkvAN8zQ+95Tlp7oPIB58fPYXWlwY6JShg55sQYGgtN54otOJwmB7o+Ej7khhub9zbQcbDH2jEIIIcYsPZ8jxwNvKKX2ATuBrZqmbQLygBhgh1Jqr1Lq5wCaph0EtgIfADuAP2uadkDTtG7gTuBV4GMgX9O0T7z+HYlxraUFurogLMz8HI1tjbzveJ+0lDRD43oqKjj5DMIQoMc+4AcpQ1rvcLA0NhY/kxsaO6o7qH6mGutdss2gz7BG54Gh+LzczExS8/OPF9VOJ6n5+eRmZrodawmwEP/teOyPGP+5EkIIMTa5XfrSNO1DXD3RJ7/uN8SYh4CHBnh9CyCfX4tB9bV7KA8CLbYf3s4liZcQ7BdsaJzFaqUFTiiqWwBLQoKhebo1jfVVVbzirjdhCBUPVxB9QzQBcV44f/0UERcHZWXur0uamERXTxf2o3YSQg38f7dggWsTanOzawfkEGwpKWzLySErL4/X6+uJCQjghZwcbDoPAEr4bgK7z9mN7Vc2+QRCCCFOAbLTSYwp3mr3MBOXtzI3l+zeohp6e6hTU1mZm2tontcbGojx8+McN0XZYLqau7A/ZifxXvP916civS0ffRsTDa9Sh4bCBRfA9u26LrelpLDhgQf450MP0bp8OSnJybpvFTg5kPAF4TieMphGIoQQYkySglqMKZ4mfHgSl5dss7H6mmt4aOZMstPTeWjpUlMbEj3Nnq58vJJJaZMInmZshf1Up7flA+Dc+OFv++hzQVgYPkrxblOToXHWO10nJ2qaROgJIcR4J581ijHF04L6w+oPCfANYFqE+6SGgSS/+y7Zjz0Gl11mavyRzk5eqavjjzqSIgbS09lD+e/KOev5s0yNP5UZKqgTzuVPe/5k/CZf/Sr89reuY+d19h0ppVgVF8eTlZVcMnGi7ltNvGwilgALDdsbiMgwv3lVCCHE6JMVajGmeBqZt/nzzSxMXYgy04Rtt0NxMVx0ken7/72mhgXh4UT6DbrFYEjV+dUETQ0i7DwPdmWeovQePw4wL2Eeu+27ja/+TpvmOkXmgw8MDVseG8vztbW0dHfrHqOUOrZKLYQQYnyTglqMKZ72UG8p9OB0xM2b4YorwNf8BzdPOhysMvkNaJpG2YNlJK1Jcn/xaWjiRFcCTHOz+2utoVYsykJZk45djP0p5Vql1hmf1yc+IIBLwsJ4rqbG0LjYpbE0vtOIs8jp/mIhhBBjlhTUYkzxpOWjqb2J3fbdpKekm5tg0yZXD61JB1taKG5r48rwcFPj6zfVgw+EX2Fu/KlOKeMbE/fY9xi/kYmCGuCW+Hie1LuE3ssn2Ie4lXHY8yRCTwghxjMpqMWY4klB/drh17ho8kWE+J+cJq1DRwe89hosNHYYTH/rHA6Wx8biazJ7uvTBUpJ+lGSuXeU0YbSP2tTGxMsvh48+gro6Q8OujozkQGsrh08+8MUN6+1WHE866G7V3y4ihBBibJGCWowpDof5HmqzcXkAvP02TJ8OMTGmhndrGk9XVbHC5MM37mikraSN6BuiTY0/XcTF6Vuhht6C2uiJieDqoU5Lg61bDQ3zt1i4KSaGdXofsFfQlCDCLgyj6pkqQ+OEEEKMHVJQizGjqwsaGiDaRE2paZqroDbbP+1hu8e2+nqsAQGcFWJidRwoe6CMxB8kYvGVX8mhGFmhnhdvcmMimIrPA1gVH886h4Nug/e0rpYIPSGEGM/k395izKiqgqgo8PExPvbjmo/xUT5MjzR5EKeHBfWTDgerTK5OtxxsofGdRuJv8fBEm9OAkYI6PjSeQN9Aio8UG7/RVVfBli1gILUDYNaECUT5+fF6Q4OhceELwulp66Hx7UZD44QQQowNUlCLMcOTyLwth7awaOoic/3HRUWuftl580zdu6Gzk6319Swx2S5S9lAZ1jus+ISYeCdxmjESnQce9FEnJoLVCrt2GR56S1wcTxps+1AWhfUOidATQojxSgpqMWZ4EpnncbvHokVgcjPhs9XVLIyIINxE9nS7vZ3af9aScEeCqXufbvSmfPSZwhTuu+8+0lems+yuZRQVF+kffNVVptI+boqNZVNdHUc6Ow2Ni1sRR8O2Btor2g3fUwghxOiSglqMGWYTPo62H2VXxS7m2+abu7GH7R6eHDVe/odyYpfF4h/lb/r+pxMjLR9FxUX87cm/ceCMAxTYCtgYupGMOzP0F9Um4/Mi/Py4IiKC/OpqQ+N8w3yJuSkG+58kQk8IIcYbKajFmGG2oH696HUusF7ABP8Jxge3tsJbb7kOdDHh45YWKtrbyYgwfnR0V2MXlY9XMvmeyabufToyUlBn/S6LynMroe+9ij8Uziok63dZ+ia48EIoLYUK420Yq+LieMJg2weA9U4r9j/b6WnvMTxWCCHE6JGCWowZZiPzPIrLKyiAOXNg0iRTw9c5HNwcF4ePid5t+2N2IhZGEJQSZOrep6PoaFcSjJ5uioqmiuPFdB9/sDfpXAH29XW90dq82fBzXhERgb29nY9bWgyNC5kRwoQvTaDmOWMnLgohhBhdUlCLMcPMCnVfXN7CqSYPZPGg3aOrp4cNVVWm2j162nso/0M5ST+SY8aN8PFxJcHo6aawhlmh46QXOyAhzEC/usn4PB+luDkuzvDJieCK0Ct/uNzwOCGEEKNHCmoxZpgpqA/WHkTTNGZGzzR+Q01z9ciaLKi31NdjCwxkenCw4bGOpx1MmDWBCbNMtKmc5vS2feTek0vq/tTjRXUHpO5PJfeeXP03W7gQXn8d2o1vFFwZF8eGqio6e4y1b0R+NZKS8hLuWXgPd6ffzZplayguKjZ8fyGEECNHCmoxZpiJzetr9zAVl3fwoCtn+OyzjY/F/GZErVuj7DdlJP4o0dR9T3d6o/NsKTa2rd3Gtxq/haXAwjePfJNta7dhS7Hpv1l0NJx5pqvP3qAzgoOZGhTEpvp6Q+NKSkt43vk8GVszWFywmLSNaWRnZEtRLYQQY5gU1GJM0DTXwS5GV6i9cjqiiWK8tqOD7Q0NfMtA9nRxUTFrlq3hjtl38Hjt4xxJPmL4vsJYdJ4txUb+2nyuvPVKbrj9BmPFdB+TbR/gOjnRaNtHXlYey+qXEYSrtz6IIJYULiEvK8/UMwghhBh+UlCLMaGhAYKCIDBQ/5jmjmZ2lO/gK7avmLupB/3Tz1ZX89XISCb6+uq6vriomOyMbNI2pnHDRzdwbf213HfFfbLqaIKRpI8+i6YuYvMh45sLAdPxeQA3REfzZmMj1R0nN3MPrq2i7Vgx3SeIINrsbaaeQQghxPCTglqMCWb6p98oeoPzEs4jNCDU+A2bmlyn4H3FXDFu9KjxvKw8lhQukVVHLzBVUE9bxJZDW9A0zfgNZ892/bwcOmR4aKivL9+IjGRDVZXuMYHWQJw4T3jNiZPABAPvNoUQQowoKajFmGC2f9p0usf27XDxxRASYnjo/uZmajs7SQ8P1z1GVh29x+jx4wBTI6YS4h/C/qr9xm9osXjc9vFEZaXuYj4zN5P81PxjRbUTJ/mp+WTmZpq6vxBCiOEnBbUYE4wcO15UXMTSu5byxP89wZvr3zR2nHQfD9o91jsc3Bwbayh7WlYdvcfo8eN9Fk1dxObPPWj7MFlQXz5xIs6eHnYfParr+hRbCjnbcihYWsBz5z7Hc0HPkf1KNim2FFP3F0IIMfykoBZjgt6Wj6LiIjLuzOCZ0Gdov6ydTdGbjB0nDa4dkJs2uYokgzp7ethoIns6MzeTDREbZNXRC8y0fAAsnLqQLYVbzN10wQJ4910weFALgFKKlXFxPGngXUCKLYUHNjzA2vfWcveX7ybwLXnjJYQQY5kU1GJM0NvykfW7LApnFZo/Thpg3z6YMAGmTjX8nJvq611xaAazp5OTkrnO/zq2L9rOC+kvULC0gJxtObLqaEJcnGuF2mg7dFpKGnsr99LY1mj8pmFhcN558NprxscCK+Li+Ft1NW3d3YbHJv04ibIHy9C6TfR/CyGEGBH6IgqEGGYOB8yb5/66iqYKiDzpRSPHSYNH7R5PVlYa2ozYp+6VOpKTk7l207Wm7iuOCwpy/aehASIi9I8L9gvmksRL2H54O9fNvM74jfv6qL/+dcNDkwIDmRcayou1tSyJjTU0duLlE/GL8qPmhRpivqk/plEIIcTIkRVqMSbobfnwynHSr7xiqt2juqODgiNHuD462vBYe54da6bV8DgxMLNtH16JzzOTFAKsMtj20UcpRdKPkyi9v9RcSokQQohhJwW1GBP0FtS59+Ri22czf5x0bS189BFcfrnhZ9xYVcXXo6II1Zk93cdZ6OTo7qNE32C8EBcDM11QexKfN306+Pu7fn5MuCYqit1Hj1LaZjzZJfLqSHqcPTS81mDq3kIIIYaXFNRiTNDbQ21LsZGzJofofdGkF6Wz9OhSY8dJv/oqpKdDQICh59M0zXD2dB/7n+zErojFJ8jH8FgxMDPReQDTIqYR4BvAh9UfGh+slKvtw+QhL0E+PnwrJoanzKxSWxRJa5Io/X+lpu4thBBieElBLUZdayt0dMCkSfqur7BUsOyuZby+7nU2/HGDseOkX3nFVP/0vuZmjnZ382W9D9mru60bxzoHCd8x0JIi3DIbnaeUYtFU1yq1KR6cmgiuto91DoepFfKYG2NwHnLStKvJ9P2FEEIMDymoxahzOFwrjnpjnfdU7uHchHON36i7G7ZuNVVQP+lwsCI2FouB7GmAmudqmDB7AsHTjKWCiKGZbfkAV3ye6T7qL38Z9u937Yg04dzQUAItFt5qNJ40YvGzkHhvIqUPyCq1EEKMNVJQi1Fn9JTE3fbd5grqXbsgIQESEw0Na+/p4dnqalaYaffIs5OQKavT3ma25QMgPSWd3fbdNLWbWOkNCnIV1Vu3mrq3UurYyYlmxP9PPI1vN9Jy0HgethBCiOEjBbUYdUZOSaxtraXeWc/UCOMZ0mbj8v5dV8fZISHYgoLcX9xP8/5m2kraiPzayTl/wlNmWz4AQvxDuGjyRbx22FymtCenJgIsi43lxdpajnZ1GR7rE+yD9U4rZQ+Wmb6/EEII75OCWow6vQkfAHvse5gbPxeLMvGjazIub53DYfhkRICKvAoSbkvA4iu/Zt7mScsHeBifd9VVsGWLq4XIhFh/f9ImTeIfNTWmxlvvsFL7Yi1tZcbTQoQQQgwP+Te9GHVGCurd9t2cG2+i3cNuh+JiuOgiQ8Mc7e283djIdVFRhsZ1NXVR87ca4m/V+Y0JQzwuqKe5CmpT8XlJSRAbC7t3m77/qvh4U5nUAH4RfsStiqP8/8pN318IIYR3SUEtRp2RHmrTGxK3bIGMDDCYIb2hqorFUVFMMDiuakMVk74yiYAEY/F8Qp9Jk6C93ZUQY8b0yOn4Wnw5UHPA3AQexOcBXBURweetrXxm8htIvCcRxzoHnXWdpp9BCCGE90hBLUadkR5q0xsSTbR79GVPG2330DRNTkYcZkq53oSZ7aNWSrEw1YO0Dw/j8/wsFpbGxrLO5DcQYA0g6tooKh6pMP0MQgghvEcKajHq9LZ8VDVXcbTjKFPCpxi7QUcHvPYaLFxoaNjuo0dp6+nhsokTDY1rfKeRno4eJs03llktjPFW24cpF18MRUUePcCquDiecjjoNnmceNIPk6hYW0F3i7lebiGEEN4jBbUYdXpbPvZU7mFe/DyUwSxo3nkHzjgDYmIMDevbjGj0fn1ReYafUxjiSXQewHzbfHZV7OJo+1Hjg319KbnoInIWLyY7PZ2cZcsoKSoyNMXZEyaQEBDAtvp64/cHgqcHM/HyiVQ+7sH/CEIIIbzCbUGtlApQSu1USr2vlPpQKZXd+/oGpdRBpdQHSqnHlVI+J407TynVpZS6tt9rK5RSnymlPlVK3ez9b0eMN93dUFenr9YdyXaPtu5u8k1kT3dUd1D3Sh1xK4yngghjPInOA5jgP4ELrBfwetHrhseWFBXx8O7d3LtzJzkFBdy7cSMPZ2QYLqpXxcWZ3pwIkPTjJMp+W0ZPR4/pOYQQQnjObUGtaVo7kK5p2hxgNrBIKXU+sEHTtBmapp0DBAO39o1RSlmA+4Et/V4LB/4XOA+4AMhWShn7LF2ccqqrITJS315B0xsSDeRPFxUXs2zNGubdeSd+Tz1Ft8Fip/KJSqKvjcYv3M/4cwpDPG35APPxeeuyssipriak988hQE5hIeuysgzNsyQmhq319dR3mttcGHZuGMHTg6l+ttrUeCGEEN6hq+VD07S+regBgK/rJW1Lv0t2AZP7/Xk18BzQ/2/5K4FXNU1r1DTtCPAqYKypVZxyDEfmGS2oi4pcS+Dz5rm/tLiYjOxsNqalceBb36Jq8WIysrMpKi7WdSutW6PyT5VyMuII8UpBPW0RWw5tMRyf11NRcayY7hMC9NjthuYJ9/NjUWQkz1RVGRrXX9KPkyh9oBStx1wvthBCCM/pKqiVUhal1PuAA9imadp7/b7mCyyndzVaKWUFrgEeA/o3kVqB/sd7VfS+Jk5jevun7UfttHW1kTwx2dgNNm2CRYvA4v5HPSsvj8IlS1zHSwMEBVG4ZAlZeXm6blW/tR7fSF/Czgsz9ozCFE97qAHOjDqTHq2Hg7UHDY2zWK2cfPh3C2BJMP5m6hYP2z4mzZ+ET4gPtS/Xmp5DCCGEZ3SF62qa1gPMUUqFAS8qpWZqmtYX4Poo8Kamae/0/vn/gDWapmknC+FZLgAAIABJREFUbcoaaIfWgEsq991337F/TktLIy0tTc9jinFIb2TeHrur3cPwRr9Nm2DFCl2XVrS1HS+m+wQFYW/TdyKdROWNLE97qMEVn9fX9nFm9Jm6x63MzSV7xw5yCgsJwVVMZ6emsjo31/AzzA8Pp6azkw+amzlnwgTD45VSrlXq/1dK1DeiZDOsEEIMoaCggIKCAq/Pa+i0Ck3TmpRSBbhaNQ70blCM0jTttn6XnQvkK9ff6lG4eq67gHIgrd91k4E3BrpP/4JanNr0tnyYOiHR6YT//Ac2bNB1uTUw0DWmf1HtdJIQGOj+VsVOGt9tZObfZhp7RmGaN1o+wNX28ch7j3DPRffoHpNss7F62zYeysqi5513sPj6svrVV0m22Qzf30cpVvSuUv/f1KmGxwNELY7i8M8Oc+TNI4SnhZuaQwghTgcnL9Tm5OR4ZV49KR9RfZsHlVJBwALgoFLqVuAK4Mb+12uaNqX3PzZcfdS3a5r2MrAVyFBKTezdoJjR+5o4jektqE1tSCwogDlzIFxfgZGbmcnkZ591FdUATiep+fnkZma6HVv550pil8fiE+zj9lrhHTExrvb4ri7P5vmK7SvsKN9Bc0ezoXHJNhvZGzaQ89//kl1XR7LOn7OBrIyLY2NVFR095tI6lEWR9KMkSu8vNf0MQgghzNPTQx0PvKGU2gfsBLZqmrYJyANigB1Kqb1KqZ8PMPZYS4emaQ1ALrC7d56c3s2J4jTmcLjvodY0zdyGRINxebaUFNJXruRLr7xC+gsvsLSggG05OdhSUoYc19PRQ+UTlSR8VzYjjiRfX4iIgJoaz+YJDQjlvITzeKNowA/M3IuLcx0atH696WdIDQrizOBg/l1XZ3qO2KWxtHzUwtG9JnK1hRBCeMRty4emaR8Ccwd43W0umKZpt5z053XAOv2PJ051elaoK45W0KP1MDls8tAX9qdproL65Zd1D2nv6WFzQADv/eY3pJzcSz2Emn/WEDIzhJAZJ+c+iOHW1/ahNylmMH191F+b/jVzE9xxB6xaBatX69oAO5Bb4uN50uHg2uhoU+MtARYS70mk9IFSzvrbWabmEEIIYY6clChGlZ5iqG912tBmq08/dfUCnH227iGv1NVxVnCwoWIajp+MKEaet/qoF05dyOZDmw3H5x1z8cUQEgLbtpl+hm9GR/N2YyOO9nbTc8R/O54jrx+h9fNW9xcLIYTwGimoxajRNH0tH30JH4b0tXsYKMLXOxyGT0Zs+bgF5+dOoq6JMvZ8wiu8EZ0HcHbM2XR2d/JZ3WfmJlAK7rwTHnnE9DOE+PhwbVQUT3uQSe0b6kvC7QmUPVTm/mIhhBBeIwW1GDWNjeDvD8HBQ1+3u9JE/7SB0xEBajo6ePPIEb5p8ON2+2N24m+Nx+Inv0qjwRvReXBifJ5pN94I777rOkzIpFVxcTzhcJhfKQesq63U/KOG9krzK91CCCGMkSpAjBo97R6mNiQ2NcGuXTB/vu4hz1RX87WoKEL1nIHeq6u5i6qNVcR/28MGXmGat1o+wBWf51FBHRwMK1eCzoOABnLJxIl0axo7m5pMz+Ef5U/s8ljK/6/c9BxCCCGMkYJajBo9BXVpYym+Fl8SQg30KG/f7uppNXBIxnqHgxWxsfrvAVQ/U83EyycSmOg+p1oMD28W1AumLODdsndp7fSg/zgzE5588nj0okFKKVZ5eHIiQOI9iVT+tZLOhk6P5hFCCKGPFNRi1OjpnzYVl2ew3ePD5mZqOjtJN5AjrGmanIw4BsTFeaflAyAsIIx58fPMx+cBpKbC+edDfr7pKW6Oi+MfNTW0dnebniMwOZDIqyOx59lNzyGEEEI/KajFqNGzQr2nco+xExI1zXBBvd7hYHlsLD4GNjA27Wyi62gX4RlyKt1o8uYKNbjSPrYc2uLZJHfeCWvXun4WTbAGBPClo0fJuOce0u++m2Vr1lBUXGx4nqQ1SZT/sZxup/nCXAghhD5SUItRYyQyT7d9+1ytHtOm6bq8q6eHjdXVhtM97Hl2Er6bgLIYiPITXteX8uHBHr4TeLwxEeDKK107bnfuNDW8qLiYTzdu5N2FCylYvJiNaWlkZGcbLqpDZoYQdmEYjie9tIQvhBBiUFJQi1FTWTl0y0ffhsR5CfP0T2pwdfrVhgaSAwKY7i5qpJ/Ouk7qXq4jfpVsRhxtISGupJgjXjpz9ZzYc3B2Ofm87nPzk1gsroNe1q41NTwrL4+qpUuhLw89KIjCJUvIMrHZMenHSZT9poyeLnNHmgshhNBHCmoxahyOoVeoi44UEewXTNwEA6vHJto9jK5OVz5ZSeTXIvGLdHtYqBgB3orOA9emwIWpCz1fpV650pWFbiJTuqKt7Xgx3ScoCHtbm+G5Jl44kYDkAGr+5uH57EIIIYYkBbUYNe5aPgy3e9TVwUcfwZe/rOvyhs5OttbX862YGN230Ho07I/JyYhjibf7qD2OzwMID4frr4fHHzc81BoY+MWUEKeThEBzaTLJP0mm9P5Sj7KthRBCDE0KajFq3BXUhk9I3LoV0tIgIEDX5X+vqSEjIoIIP/0rzQ3bG/CZ4EPYhWH6n0sMK28X1AumLODt0rdxdpqLvjvmjjvgscegq8vQsNzMTFLz848X1U4nqfn55GZmmnqM8CvCUb6K+k31psYLIYRwTwpqMSqcTmhtdS3kDcbwCYlm2j0MZk/b8+xYb7eiDCSCiOHlrePH+0wKnMTsuNm8WfKmZxPNmgUpKfDSS4aG2VJS2JaTw9KCAtJeeIHQ55/nZ9/7HraUFFOPoZQi6cdJlPy/ElPjhRBCuCcFtRgVVVWuQmiwurRH62GPfQ/z4nVuSOzuhi1bdBfUn7W2ctjp5MqICJ1PDG3lbRx58wgxN+lvERHDz5s91H0WTV3E5s89bPsAV4TeI48YHmZLSWHDAw/wxh/+wNP338/vurro9qBlI+q6KDocHRx520u7N4UQQpxACmoxKty1exTWFzIxcCLRIdH6Jty1CxISIDFR1+VPORzcFBuLn0X/r0DlXyqJuSkG3wn6jycXw8/bLR/gpfg8gMWL4eBB+Phj01N8PTKSSb6+POXBuwaLr4WkHyZRen+p6TmEEEIMTgpqMSrcReYZ3pBooN2jR9N4uqrKULpHT2cPlX+plJMRxyBvt3wAzI6bzdGOoxTWF3o2kb8/3HabqVXqPkopfjNlCllFRR6dnhi7Ipbmvc00f9Bseg4hhBADk4JajAp3kXmGT0g0UFAXHDlCuK8vsyZM0D197Uu1BE0NIuSsEP3PJEbEcLR8KKVYONUL8XngKqjz812HvZh04cSJXDRxIn8oLzc9h0+gD5O/N5nSB2WVWgghvE0KajEqvBqZV1kJRUVw8cW6LjeTPW3Ps5Nwu0TljUXD0fIBXmz7SEiAK66Ap57yaJpf22z8tqyMmo4O84/y3QQ+/vfH3PuNe7k7/W7WLFtDcVGxR88lhBBCCmoxSoYqqHu0HvZW7tV/QuLmzZCRAb7ue5ubu7p4qbaWmwyke7R+2krLxy1EX6uzn1uMqIgIV2LMydHNnlowZQFvlbxFW5fxA1W+4I47XG0fHmwsnBYczE2xseSWmE/rKK8r50X1Il95+SssLlhM2sY0sjOypagWQggPSUEtRsVQPdSf1X1GVHAUEUE6EzgMtHs8X1vLZZMmEevvr/NJwf6Ynfhb4rH4y6/LWKQUxMZ6v+0jIiiCL8V+if+U/MfzyS691JWP/tprHk2TlZzMM1VVHGptNTU+LyuPZUeWEYTrJMYgglhSuIS8LOPHmgshhDhOKgQxKobqoTbU7tHRAdu3w6JFui43mj3d3dqN42kH8bcN0Z8iRt1w9FGDF+PzlHJF6K1d69E00f7+3JOYyE+LikyNb6toO1ZM9wkiiDa7F1bhhRDiNCYFtRgVQ7V8GDoh8Z134IwzQMfx4SVtbXzQ3MzXoqJ0P2d1fjVhF4YRlBLk/mIxasZ8HzXATTfBW29BcbFH03xv8mTebWxkZ1OT4bGB1kCcnNgb48RJYIK5Y82FEEK4SEEtRlx3N9TUDF4DGzoh0UC7x9MOBzfExBBgIHvanmeXqLxxYDii8wDmxM+hoa2BogZzK8InCAmBFStcx5F7INjHh1/YbPywsBDNYE92Zm4m+an5x4pqJ07yU/LJzDV3rLkQQggXKajFiKutdR057uf3xa9193Szz7GPufFz9U32yivw1a+6vUzTNJ4ymD3dtLuJztpOIhbqP01RjI7havmwKIv34vMAbr8dnngC2jxrsVgRF0d9Zyf/qqszNC7FlkLOthwKlhbwQvoL/PvMf3PTjJtITkn26HmEEOJ0JwW1GHFDtXscrD1I3IQ4JgVOcj9RUZGrOp/nPg3kv01NWIDzQ0N1P6c9z078d+JRPoOcjy7GjOFq+QBYmLqQLYe2eGeyqVNdP69/+5tH0/goxYOpqaw5fJiunh5DY1NsKTyw4QH+8Pof+OPePxJeGk51frVHzyOEEKc7KajFiBuqoDa0IXHzZtdmRB0tHH3Z00rpK447Gzqp/Wct8bfIZsTxYDgL6itSr+DNkjdp72r3zoRe2JwIsCgignh/f57wYGneJ9CHGetncOh7h2iv9NL3J4QQpyEpqMWIGyoyT88JiSVFReQsW0Z2VhY5hw9T4ibxwNndzT9qaliuI92juKiYNcvWsPr81WyYuAF7i93tGDH6hquHGiAyOJKZ0TN5q/Qt70y4cCHU18OuXR5No5TiwSlTuK+4mOauLtPzhJ0bRsJtCXz2nc8M92QLIYRwkYJajDhPIvNKiop4OCODezduJKe+nnvffpuHMzKGLKpfrqtjXmgokwOHTjIoLiomOyObtI1pLDm0hG+UfEMOvRgnhquHuo/X4vMAfHwgM9Mrq9TnhoWRNmkSv/PgSHKA5Kxk2kraqHqqyuNnEkKI05EU1GLEDdby0dXTxf6q/cyJnzPo2HVZWeQUFhLS++cQIKewkHVZWYOO0Zs9nZeVx5LCJXLoxTgUG+tKjunuHp75vRqfB3DLLfCvf0G1573Lv7LZ+EN5OVUeHElu8bcwY/0MCn9YSFu5ZFILIYRRUlCLETdYy8eBmgMkhiUSFhA26NieiopjxXSfEKDHPnBrRmV7O/9tamJxtPtjw+XQi/HLzw8mTXIV1cNhXsI8altrKTli/tjvE0REwHXXwV//6vFUtqAgVsTFcZ+H+dahs0Oxrrby6a2fSuuHEEIYJAW1GHGDtXzoOdDFYrXSctJrLYAlIWHA6zdWVbE4KooQHx+3zyWHXoxvw9n2YVEWrki9wntpHwB33AF5eeBB/3Ofnycn81xNDQdbTv7tMCbpx0l01nZS+fgwNaQLIcQpSgpqMeIGa/nQk/CxMjeX7JiYY0V1C5CdmsrK3NwvXKtpGusNZE9/9xff5amAp0489CJVDr0YL4Yz6QOGoe1jzhxITHS1fngows+PHyUm8hOTR5L3sfhZOHP9mRT9tAhnsdP9ACGEEAD4jvYDiNOLpg3e8rG7cjc3funGIccn22ysPuMMHpo2jR5/fywJCazOzSXZZvvCte83N9Pc3c1lEyfqerYJ+yZwY+qNFMwuoK2yjcCEQHJyc0ixpegaL0bXcBfUV069kts33U5Hdwf+Pv7emfTOO+GRR2DxYo+nWm21sraigrePHOHSSTpy3AcRclYIifcm8un/fMqsbbNQFslhF0IId6SgFiOqqckVcjBhwomvd3R38GHVh8yOmz30BOXlJB84QHZ5OQQFDXnpUw4HN8fGYtGRPa11axT9vIhLfnsJX1/0dbfXi7FnOKPzAKKCo5gRNYO3S99mvm2+dya97jq45x745BM480yPpgr08eGXNhs/PHyYd+fM0Z25PpDJP5hMzQs12PPsWO+wevRcQghxOpCWDzGiBuuf/rj6Y2zhNib4T/jiF/t7+mm4/nq3xXRnTw/PVldzs852j6oNVfhF+ckx4+PYcEfngZfj8wD8/eHb33atUnvB0thYnN3d/LO21qN5LL69rR/ZRbQeavXKswkhxKlMCmoxogbrn95T6X5DIpoG69bBypVu77O5vp4zgoNJdVN4A/S091B8XzG2X9k8WtUTo2u4Wz5gGPqoAb7zHXjmGdfHNx6yKMVvUlP58eHDdBo8kvxkwdODSf5ZMp+u+hStW1I/hBBiKFJQixE15IZENycksmMHKAUXXOD2PnqzpwEqH68k+MxgJl1mvu9UjL6RKKjPTTgXR7ODssYy701qtcKCBa5PX7wgIyKCKYGB/NkL/2NMvnsyKCj/o2cHxwghxKlOCmoxohyOQTYk6kj4OLY67WYVua6zk9caGrg+Jsbt83S3dFPyqxJsv/ripkYxvsTFDX/Lh4/Fx/vxeeCK0HvkEdenMF7wwJQp5BYX0+RhJJ+yKGY8OYOSX5XQ+qm0fgghxGDcFtRKqQCl1E6l1PtKqQ+VUtm9r29QSh1USn2glHpcKeXT+/pNSqn9Sql9Sqm3lVLn9JtrYe+Yz5RSa4bv2xJj1UAr1O1d7RyoOcCsuFmDD3Q64R//gOXL3d4jv7qaqyIjmejrfs9t+cPlTLxsIqFzQt1eK8a2vhXq4T6TZFjaPi6/3LVb9403vDLd7NBQroyI4Ddlnq+kB6UGYcux8cmKT+jp8qyNRAghTlVuC2pN09qBdE3T5gCzgUVKqfOBDZqmzdA07RwgGLi1d8hh4HJN02YDvwT+DKCUsgBrgSuBs4AblVIzvP0NibFtoIL6w+oPmRoxlWC/4MEHvvginH++6+NxN9Y7HLqypzuPdFL+23Jsv5DV6VPBhAmumtQLrchDunLqlbxe9Dod3eaP+v4CpVwRemvXem3KXJuNRysqsLe3ezxXQmYCPiE+lP9WWj+EEGIgulo+NE3r+6wvAFfUnqZpWv/PPHcBk3uv3aFpWmPv6zuAvgrofOBzTdNKNE3rBPKBb3j4/GKcGSiDWs8JiXo3I37S0kJFezsLwsPdXlv2mzIivx5J8PQhCnkxrgx3dB5ATEgM0yKn8W7Zu96deOlSePNNKC31ynRJgYHcGh/P/3p42Au4Wj+m/3U6ZQ+V0fxRsxeeTgghTi26CmqllEUp9T7gALZpmvZev6/5AsuBgZoKbwX6Phu1Av0/fyzneLEtThMDxea57Z8uL4f33oNvuH//td7hYFlsLD5u+qw7qjqwP2YnJTtFx1OL8WIkovNgGOLzwLXEvnw5/OlPXpvyJ0lJvFxXx0fNnhfBQSlB2H5t4+CKg/R0SuuHEEL0p3eFuqe35WMycIFSama/Lz8KvKlp2jv9xyil0oFVQF+v9EAVjmQxnWYGavnYXemmoNaZPd2taWyoqtKVPV3y6xJil8cSmBSo57HFODESSR8wTH3UALffDo8/Dm1tXplukp8fP01K4seHD3tlvvhb4/GL9qP0fu+sogshxKnC0EmJmqY1KaUKgIXAgd4NilGapt3W/7rejYh/BhZqmtbQ+3I5kNTvssmAfaD73Hfffcf+OS0tjbS0NCOPKcao9nZoboaIfmenODudfFr7KefEnjPwoL7s6XXr3M7/WkMDcf7+nBUSMuR1bSVtVG2o4vxPztf/8GJcGKmC+nzr+VQcraCiqQJrmBc/aDvjDJg9W/cGXD0yrVb+WFHBGw0NpOtohRqKUorpj09nz9w9RH4tktDZsplXCDG+FBQUUFBQ4PV5leZmS7xSKgro1DStUSkVBGwF7gcScK1Az+/duNh3fRLwGrBc07Qd/V73AT4FvgJU4uq7vlHTtE9Oup/m7pnE+FRSApdeCv2DB3aW7+S7r3yX97/z/sCD/vtfV+/0wYNu4/KWHjjAhWFhrJ48ecjrDt5ykABrALZc2Yx4qrn/fqirg9/8ZvjvdfWjV1P7bi1BvkFYw6zk3pOLLcULP1P/+hf86leu3HUvya+q4rfl5eycOxeLFw4vcqx3UPa7Mua9Nw+Lv6SvCiHGL6UUmqZ5/Bejnr8J44E3lFL7gJ3AVk3TNgF5QAywQym1Vyn1897rs4AI4NHeqL1dAJqmdQN3Aq8CHwP5JxfT4tQ2UP/0nso9Qx/oojN7uqmri1fq6rjRTfZ0y8EW6v5Vx+QfDF10i/FppHqoi4qLeO+F99iZvJMCWwEbQzeScWcGRcWebwDkqqsoKS8nZ+FCstPTyVm2jBIPNxbe0Pt78ffqas+fD4i9OZbA5ECKf1HslfmEEGK8c9vyoWnah8DcAV73G+T6bwPfHuRrW4DpBp9RnCIG7J+27+YC6yAnH/ZlT3/wgdu5/1FTQ3p4OFH+/kNeV5xVTOK9ifhNGvDHV4xzI9XykfW7LKrPr4a+Hzd/KJxVSNbvstjwxw0ezV1SWsrDTic5W7cSArQA2Tt2sHrbNpJt5lbALUrx4JQp/M+nn7I4OpoAi2erykopzvjzGeyetZuob0QRdl6YR/MJIcR4J5/ViREzUGTekAkfL74I550Hblo4QN9R40f3HKXxnUasqyVc5lQ1ErF5ABVNFceL6T7+YG8acFuIIeuyssipr6dvJ0AIkFNYyLqsLI/mTQ8PZ2ZwMHkVFR4/I0BAXABTfz+VgysO0t3W7ZU5hRBivDK0KVEIT5zc8tHa2cqh+kOcHXP2wAN0Zk8fdjo52NrKVZGRQ15X9PMikn+ejE+wj/6HFuPKSLV8WMOs0MGJRXUHJIQleDx3T0UFJ2+rDQF67J4X6/dPmcLlW7bwzh//SG1HB9bAQHIzM7GlpJiaL2ZJDDXP11D8v8WkPpjq8fMJIcR4JSvUYsSc3PKxz7GPmdEzCfAN+OLFFRWu7OlrrnE771MOB0tiYvAf4mPsI/85QuunrcTfGj/oNWL8i4yEo0ddiTLDKfeeXFL3p7qKaoAOSNmXQu49uR7PbbFaaTnptRbAkuB5sR5SW0vXP//Jc/PnU7B4MRvT0sjIzqaouNjUfEopzsg7g6qnq2h8t9H9ACGEOEVJQS1GzMkF9ZAnJOrMnu7RNJ6qqhryqHFN0zj808Ok5KRIIsEpzmKB2NjhX6W2pdjYtnYbS48uJb0onRmfzSD1ylRSklM8nntlbi7ZqanHiuoWIDs8nJW5nhfrWXl5HF2+/PjvVVAQhUuWkJWXZ3pO/2h/pq2dxsGVB+luldYPIcTpSVo+xIg5uYd6d+VuLku67IsX9mVPP/mk2znfbmwk2GJh7oQJg15Tv7meroYuYm8ausdanBr6+qiTk4f3PrYU27ENiB3dHVz814t59L1HueP8OzyaN9lmY/W2bTyUlUWP3Y4lPJzVO3eS/NZbYHJTYp+KtrYvvkkNCsLu4UEy0ddFU/N8Df+54z9s6dxCW0UbgdZAMnMzSbGleDS3EEKMB1JQixFzcg/1bvtuvn/h97944c6drqL6wgvdzrne4WBFXBxqkFg9rce1Om37pQ3l43n+rhj7RqqPuj9/H3+eve5ZLn7iYi5NupRZcbM8mi/ZZiN7Q7+0kI8/hvR0V0F92QBvQnWyBga60nP6F9VOJwmBnp8Y6vdDPx477zFWdq8kiCCcOMnekU3OthwpqoUQpzz5/FuMiJ4eqK52fRwP0NzRTPGRYs6KPuuLF+vMnm7t7uaftbUsGyLdo+YfNVj8LURdE2X+4cW4MlLReSebFjmN313xO5Y8v4SWjpO7oD101lmwYYOrDerQIdPT5GZmkpqf7yqqAZxOfNev5zurVnn8iI//9vFjxTRAEEEsKVxCXpb5dhIhhBgvpKAWI6K2FsLCoC8mep9jH2fHnI2fz0l50H3Z0zqOXX6htpYLw8KIDxhgUyPQ09VDUVYRtl/bBl3BFqeekYrOG8jyWcs5L+E8vr91gE9ePHXFFZCTA1dfDQ0NpqawpaSwLSeHpQUFpL/wAksLCvjJ3Xdz85EjFPcV2Sa1VbQdK6b7BBFEm92zdhIhhBgPpOVDjIiB2j0GPCHxpZfg3HOHzJ4uKi4mKy+PTbW1zJwwgaLvf3/A2K+q9VUETA4g/CvhXvgOxHgRHw97947e/R+56hHm/nku//j4H1x/1vXenfw734HPPoPrroMtW46/QzXAlpLChgceOOG1qPJy0vfv541Zs0hxsxF4MIHWQJw4TyiqnTgJTPC8nUQIIcY6WaEWI+LkhI9BD3RZtw5WrBh0nqLiYjKys9mYlkbD8uW8s3DhgLFf3W3dFOcUy+r0aWi0Wj76hAaEkn9dPndsuoPiI8Xev8GDD0JoKGRmuvYaeMFdkydzz+TJpO3bZ3qlOjM3k/zUfJy4xjtxss5nHUuvXuqVZxRCiLFMCmoxInQV1BUVsGvXkNnTWXl5FC5Z4jb2y/6YnQlzJjDxwone+hbEODHaBTXAvIR5rLlkDTc9fxOd3Z3endzHBzZuhPffdxXXXrJ68mTuTUwkbd8+ikwU1Sm2FHK25VCwtIAX0l+gYGkBP3niJxy96yiOp0d4l6gQQowwafkQI6J/ZF5TexNlTWWcGX3miRc9/TR885sQHDzoPHpiv7qOdlF6fymzXvUsaUGMT6PZQ93f9y/6PtsObyPnzRx+Of+X3p18wgT4179cSTipqa7fGy+4c/JklFKk79vH67NnM8Vg+0eKLYUHNpzYTtIyr4UPr/4Q5+dOUnJS5BMjIcQpSVaoxYjo30P9fuX7zIqdha+l3/u5vuxpN0eNxwUEHE8o6HNS7Ff578sJ/0o4E84ZPJtanLri4lyJMj09o/scFmVh/TXreeL9J3ij6A3v38Bqde05yMx0fbLjJXdYrfwoKYn0ffs47OFGRYCQs0KYu2Mu9a/W88nST+huk8NfhBCnHimoxYjo3/IxYLvHzp2uCuiii4acJ/iqqwh5+ukTYr9S8/PJzcwEoLOuk/I/lJOSk+Ldb0CMG/7+MHGiK1lmtMVOiGXdNetY/sJyaluH4YHmzoXHH4fFi6G01GvT3m61sqa3qC70QlHtH+vP7Ddmo3Vp7F+wn46aDveDhBBiHJHWdRPMAAAgAElEQVSCWoyI/i0fuysHKKh1ZE+/1tDAVn9/3jop9mtbTs6xlI/SB0uJ/mY0wVMHbxsRp76x0vYBcEXqFdz0pZtY9dIqNC9tIjzBN74BP/iBK06vqclr095utfLjpCTme6mo9gnyYWb+TCZdPom9F+2l5aCXs7qFEGIUqWH5C94DSiltrD2T8Ny0afDKK3DGGTDt4Wm8tOQlZkbPdH3R6XR9fL1/PyQmDjj+SGcn5+zezV+mT+fKiIgBr2m3t/Pel97jvA/OI8A6cDa1OD1kZMC998KVV472k7h0dHdw6ROXsvyc5ay+YLX3b6BprtaP0lJ4+WXw9d72mMcqKvh/paW8Pns2qSYj9U5W+WQlh398mJnPziR8vsRaCiFGj1IKTdM83twhK9RiRPS1fBxpO4Kj2cH0yOnHv9iXPT1IMQ1w5+ef8/XIyEGLaYCSX5YQf0u8FNNiTCR99Nd3NPkv/vML9jn2ef8GSsHDD0NXF3zfu4fKfNdq5afJyaTv28eh1lavzBm/Kp6Z+TM5cOMBKp8cQ/9HCSGESVJQi2F39Kjrv0NDYW/lXmbHzcbH4nP8AjebEf9eXc3uo0d5MDV10Guch51U/72axDWDF+Xi9DHWCmqA1IhUfn/l71ny3DAcTQ7g5wd//zu8/rqruPai7yQk8PPkZObv3++1ojo8PZzZb86m5JclHP7pYbQe+WRSCDF+SUEtht0J/dMnn5DoJnu6or2d1Z9/ztNnnkmwj8+A1wAUZxczefVk/KOMnxwnTj1jqYe6v6XnLOXCyRdy1+a7hucGkybBv/8Nv/61q8fKi27rV1R/7qWiOmSGKwHkyJtHOLDkAN1OSQARQoxPUlCLYdc/Mu8LCR9DZE9rmsb/HDzI7VYr54WFDTp/80fN1L9az+R7Bj+uXJxe4uNdP3dj0cOLHuat0rfI/yh/eG5gs8E//+n61Gf/fq9OfVtCAlleLqr9o/2Z9doslK9iX/o+OqokAUQIMf5IQS2G3aCReZoG69cP2u6RZ7fT0NXFT5OShpy/OKuYpDVJ+IbKOUXCZSy2fPQJDQjl2eue5a7Nd1HUUDQ8N7noIli7Fr72Na//D/HthAT+18tFtU+gD2duPJOIKyPYe+FeWj6WBBAhxPgiBbUYdn0FdV1rHbWttUyLnOb6wq5d0N09YPb0p62tZBcX8/SZZ+JnGfzHtGlnE0d3HyUhM2G4Hl+MQ2O5oAbX0eQ/ufQn3Pj8jd4/mrzPt74Ft93mKqpbvFugfjshgezeovozLxXVSilsOTZSclLYl76P+m31XplXCCFGghTUYtg5HK6e1r2Ve5kbPxeL6v2xGyR7urOnh+WffEJOSgpnDHEMOcDhnx0m+X+T8QkavL9anH7i4sZuy0efuy+8m4igCLILsofvJj/7GcycCcuXe/3oyFsTErgvJYX5+/Z5ragGiLs5jrOeO4tPln2C/c92r80rhBDDSQpqMez6VqhPaPdoa3MlEixf/oXrf1VSQoSvL5kJA686FxcVs2bZGu6YfQdrd66l7cttw/n4YhwKDXV1FPUlzIxFFmVh3TXrWL9/Pa8dfm14bqIU/OUvrmMjf/ITr0//P/Hx/MJm83pRPenyScx5ew5lD5VR+MNCSQARQox50nQqhl1fQf2vyt1cP/N614svveQ6Nvmk7OldTU3k2e28f+65qAFOTSwuKiY7I5slhUsIIggnTnKuyiFnWw4ptpTh/2bEuKDU8baP0NDRfprBxYTEsP6a9ax4cQXvf+d9okOivX+TgAB44QW48ELXCUu33urV6W+Jj0cB8/ftY114OOvWraOirQ1rYCC5mZnHTjE1KnhaMHP/O5ePrv2Ij7/5MUG/DOLPv/4zbRVtBFoDyczNlN95IcSYISvUYtj1xeadsEI9QPZ0S3c3yz75hLXTppEQMPDhLHlZeceKaYAgglhSuIS8rLxh/A7EeDRWo/NOtmDKApads4yVL60cnqPJASIjXXF6P/sZJRs2kLNsGdnp6eQsW0ZJkecbI1fFx3OXry8L77uPjWlpFCxezMa0NDKysykqLjY9r1+kH7NenYVDc/DzuT8nbWMaiwsWk7YxjeyMbIqLzM8thBDeJAW1GHYOB/hNqqGxrZHU8FRX9vSOHbB48QnX/aiwkAvCwrg+JmbQudoq2o4V032CCKLNLm0f4kRjOTrvZLnpudS21vKHnX8YvptMn07J73/PwytWcO/GjeQUFHDvxo08nJHhlaL6g+efp3vlSug7njwoiMIlS8jK8+zNriXAwrbgbdzcfrO8kRZCjFlSUIth1dEBjY1Q3L6HeQnzXG0cGzZ8IXt6S10d/66r4+GpUwedq6uxi/ZD7ThxnvC6EyeBCYHD9j2I8WmsJ3305+fjx7PXPcuv3voVeyv3Dtt91r3yCjk9PYT0/jkEyCksZF1WlsdzV7S1HS+m+wQFuV73UJt94DfSzjLnICOEEGJkSUEthlVVFcTEwF5H7wmJmvaFdo+6zk5u/fRT1s2YwSQ/vwHnaf6wmT3n7eGGtBvIn5J/rKh24iQ/NZ/M3MwR+G7EeDKeCmqAKeFT+OPCP3Lj8zfS3NE8LPfoqag4Vkz3CQF67J6naVgDA8F5UoHrdLK7pYW8igpau82fghhoDRzwjXTzzmYK1xTSViKfUAkhRpcU1GJY9UXmHeuf3rULurrg4osB12mI3/3sM26IiSE9PHzAOao2VrF//n6Ss5KZ//R8crbnULC0gBfSX6BgaYFsSBQDGg/ReSe78Us3ckniJaxct5Jldy0jfWU6y+5aRlGxdw6AsVitnJxI3QJYPvkEtm93veE1KTczk9T8/ONFtdNJan4+f73rLrbU12PbsYP7ioqo6TB+EmJmbib5qV98I/3DzT9E69DYPXc3Hy3+iIbXG4avD10IIYagxtpfPkopbaw9kzDv5ZddqV3vp0/mrVVvYfvpgzD5/7d37/FVVOf+xz/Pzg4BEggBVCDcAp7ihQqoP6s91YqK2p6qre3R1tBCjweoVbxVpB6LgByOl4pYuSsKKFhpbbVUa4UqqGgRKgEsF7klkdwQCUQSctvZ6/fHDCEkoSSZJJj4fb+Y18xeM/PsmbCYeZisWaun1z8usDgvj4c++YQPzzuPtjHH9iUdLYuy6xe72P/6fgb+cSAJ5yScjFOQFuqvf4XHH4fly0/2kdTPP7f/kyE3DyFySQTaAGXQf2N/VsxcQUrflECxM9PTmTFsGJN37SIeL5me2K8fY8eMoc+CBRAfD+PHw/XXQ0z9+3ZPz8hgwpw55JSU0KNaLx/bioqYlpXFS/v28aNTT+Xunj05/QT9zFeVkZ7BnAlzKMkpoW2PY3v5iBRG2Pv8XrJnZoNB8m3JdPtxN2Li1T+9iPxrZoZzrma3YvWN80VLXpVQty7z5sG7aXm83u9sPhubhfXsCWlp0Ls3n5SUcP6HH/LGOecwpFrfZiVZJWy5YQuxp8RyxqIziO1Ue1MQkePZuBGGD4ePPjrZR1I/w28fzpIOS7xk+ogySD2UyuInFweOn5mezsIJE4jm5BDq0YORU6bQJyXFG/jlz3+GRx6BffvgnntgxAho27jvJ+SVljIzO5t5ublckpjIuF69uDAxsVFiO+c4+NZBsmZkUfBuAd1GdCP51mTa9W934p1F5EtJCbW0CJMmwcfR19j/b79heZubYf58WLGCqHNcsXEjVyYl8cs+fY7Z58BbB9g6fCvJY5PpPb43Fgpcz+VLaO9eOPtsb0yTlmToyKGsSllVo/z8j89n3Qvrmv4AnIPVq+Hhh2H9erj9drjlFujUqVG/pjASYUFeHo9nZdEzLo5xvXrxnS5dCNXS/3xDFGcUkzM7h7wFeXT4Wgd6ju1J0rAkXU9E5BiNlVCrDbU0qbw8ONTRbz9d5WXE32RlURaNMq5378ptnXN88sgnbE3dypnPn0mf+/ro5icNdsopXg8zDWiye1Ild0yG6sdcBpv3bebC+ReyIG0BRWXVW0I3IjO4+GJ47TWvvcyWLdC/P9x7LzTCy4tHJITDjO3Zkx0XXMBtyck8mJHBWWvX8nRODiUBXmA8ol3fdvR/tD8XZl7IKd87hV3jd7H2zLVkzcgi8nmkEc5AROQoPaGWJnXddZBz6TVMHnIt3/7evZCdzT+jUYZu3MgH555LP7+brUhBhG0jt1GaW8rZvz+btr3UDZ4El5zsdXlebUDOL7T0jHSG3TaMXYN2HdOG+vUnX+fjyMfM+3Ae7+95nx8N/BFjzhvDV0/7atMfVGam1yD9+ee99tXjxsGAAY36Fc453j54kF/v2cP6wkJuS07mlh496Hycnn8aEr9gdQHZM7I58LcDnJZ6Gsm3JdN+QPuj7bM1CqPIl46afEiLcMEFsPv67uwoGUFS9n7K5s3jgg8/ZGzPntzcvTvgdYm3+fubSRqWxOmPn04oTr84kcZx/vkwe7ZXD1uS9Ix0Jjw+gZzPc+jRsQdT7p5yzAuJewr28EzaM8xfP59eib0Yc94Ybjj7BtrH1v0lvwb57DOYNcubLr7Ye4GxCX64m4uKmLZnD6989hnDTzuNu3r2hL17mTBnTqMMa16SVULO3Bxyn86l4CsF/Hbnb7kp7yavb2u/BxH1HiTy5aCEWlqEHgNyKB15Dp89dwo2fz7/0707m4uKeGXgQMyMvUv2svPOnfR/vD/dftztZB+utDLf+Q6MGuX9pqQ1ikQj/GXHX3jqw6f4e9bfuWngTYw5fwwDTx3YtF9cVATPPAPTpkG/fl5ifdVVZGZkeC88ZmcTSk4++sJjA+WUlvJkVhZz168n8vLLFP34x97gMX6XfCsmT25wUg1QUVLB3ZfdzdV/v/qYgWOKKWbVTat4ZMkjDY4tIi2D2lDLF140Cp+G/0Fq6b9hkQirzz6bBXl5PD1gAK7csf227aRPTGfQm4OUTEuTaEnDjzdEOBTm2gHX8upNr5I2Jo3O7Tpz9eKr+fdn/51FGxZRXN5EIwnGx3svK+7cCTffDOPGkXnWWcy46KJGHda8R1wcD/fvz1Xr1h1NpqFyWPOfPvEEmSUlDe57OqZtDMRR6yiMe1/cS9rFaey4fQe5z+ZyaP0hoqXRBp+LiLRuSqilyeTnQ2yff5CaVs6hm2/mJ9u2MfcrX6Hjp1E2fHMDpXtKOe8f56l/aWkyLW20xCB6J/Zm8tDJZNyZwb1fv5ffbfkdvab34o7X72Dzp5srt0vPSG+8QWNiY72+CTdtYmG3bkzeu7fmsOb33BNowBiAT0tLax3W/KPCQi5av56k1au5JC2NsTt2MD8nh7Wff17nkRmPNwrjKd87hb6T+9K2b1sOrjrIthHbWJ20mnWD1rF1xFb2TN/DgZUHKD9Q/i/jZ6RnMH74eO4Yegfjh48nIz2jHmcuIi1F+EQbmFkc8A7e6zFh4CXn3GQzWwycj/c++lpgjHOuwt/nSeBbeOMGjHTObfDLRwD3Aw6Y6px7rvFPSb4ocnMhvscHDHlpOz9/YBiXxcdzyaYY1qeuJ/l2dYknTa9bN68/6i+TcCjMdWdcx3VnXEfmwUzmr5/PsOeH0S+pH9/t9l1mz5pN+uB06AKUwZrb1gQfNMaMKNQ+rPmyZdClC5xxhjedeebR5ZQUCJ/wNnR0WPOqSXVxMd/q0oXFX/86+8rK2FRUxMbCQlYXFDArJ4ePDx+mV1wcgxISGJSQwDnx8QxKSKBXXBxWpWu+W6bcwv3v3s/wT4ZXtqFe3HsxU389laSUJJIuOzqCa0VJBYc3H6ZwQyGFGwrZ94d9FG0qItw5TMLgBBIGJ9BhSAcSBicQ1zuOzIxMJg6byA93/bAy9sQ1E9U+W6QVqlMbajNr75w7bGYxwHvA7UBn59xf/fUvAG875+aZ2beA25xz/2FmXwN+45y70MySgH8A5wIGfAic65wrqPZdakPdSixf7lg4J5HrT72Re0f+F2+s6s6+J3M4c/GZJF1e+zDjIo3p5Ze93hr/9KeTfSQnVyQa4dXtr/LzcT8n95zcGoPG3FBwA0tnLg30HZOHD+eeJUuOSaqLgMdSU5k4fTps2+ZNW7ceXc7N9brkq55sDxgACUd/c7X63Xf5zgMPUHDvvZVtqBMffZRXH3yQb1x8ca3HUx6N8vHhw2wsKmJTYSEbCwvZWFRESTRamVyfEx9P1/37uX3iJKIH2tO5IER+YpRw0mFWPj6tTu2zXdRRvLu4Msku3FBIYVoh0cNRnmvzHN/79HtN1j5bvZOIBHdSXko0s/Z4T6tvcc6tq1J+J9DFOTfBzOYCK51zS/11W4FLgaHAN51zt/jlc4BVR7arEsulxA9gxD2pTJw0IdjZVTF50hQWPbaETnTmIPmNGl+xa4+98LEldLHO7E8Kc2f8CL6ROFhd4kmz+uMfMxk1aiHnnBMlOTnElCkjSUnpc6Ld6iQ9PZMJExaSnd1yYh9v0BhbZcRfGU/3hO5079Ddmyd0p0eHHkc/+/NObTsd84T3iNXvvsMTV13OouJI5bDmI9qFufONN/nGxZfUfkDFxbB9e81ke/t26Nq1MtGevGYNP1i3joeSk8np3Jke+fncl53NS6mpTFxcv9EjPy0r8xJsP9FeNm0aB7///RpPvwe+9ho/HT+epHCYTuEwSeEwSbGxlcsdYmJq/TkcUfZpGbdeeiupW1NrrFvAAkafOprYLrHe1DWWcJdw5XKt5Z1jsZij35eRnsFdF9zF6M9GVz79fqrrU0xfO71RkuqWeu9p6viK3fpipxd93CgJ9Yl/1waYWQjviXJ/YFa1ZDoM/BgY6xclA3uq7J7ll1Uvz/bLaphVNJ2HHpkG0Cg/uMmTpvDmI28zq2R65YWnseIr9vFjzz4Su7CYWTFzKRifw3m9zgsUW6Su0tMzueuuGeTnT2bVKi/FW7NmIitWjA2cnKanZzJs2Ax27ZoMtJzYHUOJXiO9ak+or0m5lufuWkRuYS45h3LIPZRLbmEuuYdySctLq1zOLcylrKKMbgndaiTfL814iQ0/jbDxXeh2CPI6wM6LIxx+5hF+97VzaRPThthQ7LFJaLt2MGiQN1UVjcInn1Qm2MUvvMDZwOLsbMjOrtzst7//vTfwTIcO3hPtOkynJiRwhT/RqRMDDx3iYC3ts/cePMie0lI+KiriQHk5ByIRDkYiHPCn4ooKEmtJtKsm4KuLt3I9xTWeUG/ovYtTVg0kdKCCUH4F5FdAfgSXH6Esr4zDWw5Tvr+c8s/Kvfn+ciIHI4Q7esl1uEuY6dumM7pgdGXsdrRj9GejGX/peJ6Y9AShuBChuBAWZ4Tahio/V5ZV/9w2RCjsvVbVUu89LfnYFfvkxf423w4U64j6PqHuCLyC16Rji1/2FFDonLvb//wq8H/Ouff9z38DxgGXA22cc//nl/8KKHLOTa/2HW4lKymmmF+3n8FV594Y+CTfWL+UcYfH1rioNUZ8xa577Fvj72J34bZAsUXqavjwySxZcg9Ua4Rw1lmPce21EwPFXrZsMlu2tLzYL710Bztj/gzfT68cNIY/pHB6xTX84Ae/qVOMMooosjwKyaXQcii0XIosl3XLZ1Lx7VpGcHzTiL2sHRWUEbUIIRcmRCwxtDl27mor8+ZtZq9k/f5IjeYk30wM0+8/ryS+LEK7sgriSyO0L4vQvtyfl0X8deV+WblfXkZ7v/zSTklsfvrpGk+ozxw9ir8dOkRFKERFyIiaN68IhYiaURobS0H7eA52SKAgvgMFCe0pSEigID6ez9vHcyg+gVc++IDzPj6F+3NGViYEU3ssZM3gIrr+dCQVMTGUh8NUhEJEYmKI+MsGhCsixFREiamoIFxRQWxZBR0PRel00JFY4CifvpAHPx9X48f9WNwMLhnyE8IRiC03wuVGOFJlKjfCFUa4PEQ4YsREjHDEWwaIhKM8F1lIqrupxjX82Zjn+P6pw8EcziDqz13I4Y4sm78c8tZTuZ3DhRzLdr7A2NLRNWL/pu1c/uPMH+HAaxTqLfmf/eUq/xdz5qosHy17fdOL/KL41hrxp7WbxdWDarm31fJcskZW5H/XXzcs5Z7Dt9WI/Vj7mVw1+AT3zRM8/3wj7fixrxwS7J68/DixW2ou0dixhzK0+Z5QH+Gc+9zMVgFXA1vMbCLQ1Tk3uspmWUDVccl6Ajl++aXVylfW9j0LWQhAZukudhRtpl/SGfU5zBpio+Fau0UKR8NUtAk2xK1i1z12JzoHiitSH9nZtb8mV1ISpWPHYLGLi1tm7IqKTrDzTZg7ARJyoLAH5E8h2m9hPWLH05X+eL+wPOqjvNcoKvtnjaffCZln8z9xHwHeaIVRIlRQRgXlx8yjlBNx3vxoube8pOuHpEbzWXKAyuYkqUmw8bR4UvrcwCEch3A4HFSbO6K1lh+Zt3v4F/SfOpVd999/tI/rqVNJ2p/Hr342jpCLEoo6YqJRQtEo5ir8ZUeMixKKVhATdYRclJholISSKB0OFxDz6QHe27WD9/73J4xa8js650fJ7xwiO/Vb9J40gTuX/NbP0xxe3unw/3jJasiIhmL8JD6GipiQl9T78xdisymu5en3lo67STl3Bc4Mh3nJphlR/7OX4PrleOUY3joXIhSJYdvCPbT7vOY1PKv9Pt67ehMhB7gQODBnx0w4887HXw5FvTwl5H8uTi+t9f5QFoqwL/lAtWzW/Nz6aK5zJI+2WspwhmG1xjeMkg6lx1blWp4n1siqqmwT42JqjR0TjaG83fF7e7Favqe6mOjxY1fERU4coAGxW2ouETT27gPbyCzdxVKCvTdSXV16+egKlDvnCsysHXAF8LCZ/TdwJXBZtV2WAbcCS83sQuCgc26vmb0BTDWzRLzu+oYBv6ztO0cykmKKeaftGuavf7TBJ3fE/IRHa73w7IzZzvI3/0uxmyn2QfIDxRWpj+TkEF7qdexzzYsuCnHffcFib94cIj29pcY+FfIXc/SfY+PE/uCDy/jTH4pqPP2+fMhlVWIbEOtPdbfqj8n86Uf5DD6mOQn0XdOb3/9qRKDjHvL4RP703ns8NGrUMe2zhycl8uzjDwWK/UKnRFKemU/6/feT7SfrKVOn0rbgc+56+Q+BYs/s1Zup3Rdwf+5Pjz797r6A/Jj9zJg1M1Dsfs+cUes1fG80ixnPBqso/RJm1Ro7w3bx1p9vCRTbiz+t1vi7QjtYsfy/A8V+JuGx4983/3ZzoNjzE37dqu73X/TY/RKWcWPRjbSjHYtYFCjWEXXph7o7sNLMNgAfAG845/4CzAFOBdaY2Xq/CQf+unQz2wnMA37ulx8ApuD19PEBMNk5d7C2LyymmIfaTmPEPTVf5miIEfek8lBb7x9ZY8dX7OaNLVJXU6aMpH//iXhJNUAR/ftPZMqUkYrdBLGnT7+bXsWXw9wb4dmhMPdGehVfzvTpdweOveiJ2YTfSWTnNbB6JOy8BsLvJLLoidmBY9835yl+FWvMy87mrY8+Yl52Nr+KNe6b81Tg2JPmPc3pa9/nxlGjGHr77dw4ahSnr32fSfOeDhx7yvjxrO+RzqhLX+D2IQsYdekLrO+RzpTx4wPHbsn3h5Z67Ip9cmM3CufcF2oCXEr8ADdp4oOuMU2a+KBLiR/ghsRf1OjxFbt5Y4vU1e7dGS41dZIbOvQBl5o6ye3enaHYLTT22++86/qe+1XXaVBf1/fcr7q333m30WIvfXGpG5yU6C6Nj3ODkxLd0heXtojYT86Y6ZJSUlynwYNcUkqKe3LGzEaL3ZLvDy312BX75MT2UuHg+Wu9XkpsDuqHWkRERESaQ2P1Q62hx0VEREREAlBCLSIiIiISgBJqEREREZEAlFCLiIiIiASghFpEREREJAAl1CIiIiIiASihFhEREREJQAm1iIiIiEgASqhFRERERAJQQi0iIiIiEoASahERERGRAJRQi4iIiIgEoIRaRERERCQAJdQiIiIiIgEooRYRERERCUAJtYiIiIhIAEqoRUREREQCUEItIiIiIhKAEmoRERERkQCUUIuIiIiIBKCEWkREREQkACXUIiIiIiIBKKEWEREREQlACbWIiIiISABKqEVEREREAlBCLSIiIiISgBJqEREREZEAlFCLiIiIiASghFpEREREJAAl1CIiIiIiASihFhEREREJQAm1iIiIiEgASqhFRERERAJQQi0iIiIiEoASahERERGRAJRQi4iIiIgEoIRaRERERCQAJdQiIiIiIgGcMKE2szgz+8DM0szsIzOb6JffamY7zKzCzDpX2b6jmS0zsw3+9iOrrBthZtvN7GMz+0mTnJGIiIiISDM6YULtnCsFhjrnhgCDgW+Z2QXAauByILPaLrcCm51zg4GhwDQzC5tZEvAA8P+ArwETzSyx8U5FWrNVq1ad7EOQLyDVC6mN6oXURvVCmlKdmnw45w77i3FA2CtyG51znwBWfXOgg7/cAdjvnIsAVwHLnXMFzrmDwHLg6qAnIF8OuhBKbVQvpDaqF1Ib1QtpSnVKqM0sZGZpQB6wwjm37l9sPhM4y8xygI3AHX55MrCnynbZfpmIiIiISItV1yfUUb/JR0/ga2Z21r/Y/CogzTnXAxgCzDKzBGo+yQbvabaIiIiISItlztUvpzWzB4BC59zj/ufdwPnOuXz/86vAQ8659/zPbwLjgdOBS51zP/PL5wIrnXNLq8VXki0iIiIizcI5V9tD33oJn2gDM+sKlDvnCsysHXAF8HDVTTj26XOmv817ZnYa8BVgN7ALmOq/iBgChgG/rP59jXFSIiIiIiLNpS5NProDK81sA/AB8IZz7i9mNtbM9uC1g95oZk/52/8v8HUz2wSsAO51zuU75w4AU4B/+HEm+y8nioiIiIi0WPVu8iEiIiIiIkc160iJZna1mW3zB3cZX8v6Nmb2oj9gzN/NrHeVdff55VvN7MrmPG5pWg2tF2bWx8wOm9l6f5rd/EcvTaUO9eJiM/vQzMrN7Ppq6zSIVCsVsMFLZAoAAAOVSURBVF5U+NeKNDN7pfmOWppaHerFXWa22R90boWZ9aqyTteLVipgvajf9cI51ywTXvK+E+gDxAIbgDOqbXMLMNtfvhF40V8+C0jDa/Pd149jzXXsmr6w9aIPsOlkn4Omk1YvegMDgYXA9VXKk/De2UgEOh1ZPtnnpOnk1gt/3ecn+xw0nbR68U2grb/8syr3EV0vWukUpF74n+t1vWjOJ9QXADucc5nOuXLgReC6attcByzyl18CLvOXr8U7yYhzLgPY4ceTlq8h9eLyKuv0EmvrdMJ64Zz7xDn3T2p2v6lBpFqvIPUCdL1orepSL952zpX4H9dwdBwMXS9aryD1Aup5vWjOhLr6wC5Z1BzYpXIb51wFUGBmnWvZV4PCtB4NqRcH/XoB0Nf/9e5KM/tGkx+tNJe61Iu67qvrResRpF4AxJnZWjN738yq/8ddWq761oubgdePs6+uF61HkHoB9bxenLDbvEZUl4FdjreNBoVpvRpSL8zfJhfo7Zw7YGbnAq+Y2VnOucImOE5pXkH+zet60XoF/bvt7ZzLM7MU4C0z2+ScS2+kY5OTp871wsyGA+fh/aq/XvtKixOkXkA9rxfN+YQ6C69t2xE9gZxq2+wBegGYWQxeO6YD/r69TrCvtEwNqRcdnXMHnHNlfv3AObcer+3bV5r+kKUZ1KVeNMW+8sUW6O/WOZfnz9OBVXij+UrLV6d6YWZXAPcB1/hNAOq8r7RIQepFva8XzZlQrwNO93tmaAP8EFhWbZs/AyP85f8E3vKXlwE/9Ht7SMEbdXFtMxyzNL0G1wsz62pmIX+5H1692N0sRy1NrS71oqqqTyLeAIaZWaKZJeENIvVG0x2qNKMG1wsz6+Tvc2TAsq8DW5ryYKXZnLBemNkQYC5wrXNuf5VVul60Xg2uFw25XjRbkw/nXIWZ3YbX4D8EPOOc22pmk4F1zrlXgWeA581sB7Af7+Rxzm0xs9/hnUw58HPnv4IpLVuQegFcAjxoZuVABTDGabCgVqEu9cLMzgdexnsz/ztmNsk591W/CdCRQaQcGkSq1QhSL4AzgXlmVuHv+5BzbttJOhVpRHW8jzwKxAO/NzMDMp1z39X1ovUKUi9owPVCA7uIiIiIiATQrAO7iIiIiIi0NkqoRUREREQCUEItIiIiIhKAEmoRERERkQCUUIuIiIiIBKCEWkREREQkACXUIiIiIiIBKKEWEREREQng/wMHMr3pK3v3EAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for t in range(nsteps):\n", " for i in range(1, len(density)-1):\n", " densitynew[i] = density[i] - vx * dt * (density[i] - density[i-1]) / dx\n", " # Plot every 5th time step\n", " if t%5 == 0:\n", " plt.plot(x, density, '-o', label=\"Step {0:d}\".format(t))\n", " density = densitynew\n", "\n", "#plt.plot(x, densityOrig)\n", "plt.ylim([3180, 3320])\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What to do?\n", "Feel free to play with the time step, number of time steps, advection velocity, etc.\n", "You should find that numerical diffusion is problematic no matter what you do (other than `vx = 0`)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }