{ "metadata": { "name": "Heat Equation - FD", "zanadu": { "authors": [ "Antoine Jacquier" ], "category": "7", "clearance": "Internal", "group_name": "IC MathFin Num Methods", "md5": "AD7EBFF9E7E786CF9DB6F0765C4104CA", "notebook_id": "662A3FB0-C43D-4B41-99F4-11AC9AE8A769", "python_name": null, "reviewer_id": null, "status": "WIP" } }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "Finite-difference scheme for the one-dimensional heat equation\n======\n***" }, { "cell_type": "code", "collapsed": false, "input": "from time import time\n# For sparse matrices\nfrom scipy.sparse import dia_matrix\nfrom scipy.sparse.linalg.dsolve import spsolve", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We consider here the heat equation on $[0,\\overline{x}]\\times[0,\\infty)$:\n$$\n\\frac{\\partial u}{\\partial t} = \\frac{\\sigma^2}{2}\\frac{\\partial^2 u}{\\partial x^2},\n$$\nwith boundary conditions $u(x, 0) = \\sin(2\\pi x)$ for all $x\\in [0,\\overline{x}]$ and $u(0,t) = u(\\overline{x},t)=0$ for all $t\\geq 0$.\nWe apply a finite difference scheme, explicit in time and with central difference in space" }, { "cell_type": "heading", "level": 1, "metadata": { "zanadu": {} }, "source": "Explicit scheme in time" }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "No vector notation" }, { "cell_type": "code", "collapsed": false, "input": "sigma,barX, T = 0.2, 1., 1.\nnx = 100 # Number of grid points\nnt = 5000 # Number of time steps", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": "start_time = time()\n\ndx = barX/(nx-1) # Grid step in space\ndt = T/nt # Grid step in time\nprint 'Ratio $\\delta_T \\sigma^2/ \\delta_x^2$ = ', (sigma*sigma*dt / (dx*dx))\n# Boundary conditions\nx = linspace(0.0,barX,nx)\nu = sin(2.0*pi*x)\n\nfor n in range(0,nt):\n\n\tfor j in range (1, nx-1):\n\t\tu[j] += dt*(0.5*sigma*sigma)*(u[j-1]-2*u[j] + u[j+1])/(dx**2)\n\n\t#Plot every pp time steps\n\tpp = 100\n\tif (n%pp == 0):\n\t\tif (n%(10*pp) == 0):\n\t\t\tplotlabel = \"t = %1.2f\" %(n * dt)\n\t\t\tplot(x,u, label=plotlabel, color = get_cmap('copper')(float(n)/nt))\n\nxlabel(u'$x$', fontsize=20)\ntitle(u'One-dimensional heat equation')\nlegend()\nshow()\ntemp = time() - start_time\nprint(\"--- Computation time: %s seconds ---\" % temp)", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Ratio $\\delta_T \\sigma^2/ \\delta_x^2$ = 0.078408\n" }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEiCAYAAAD+lrlwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXdYVMfXx7+7gHTpilJFxIIKlp8RjYqNYGwoNhRETWIv\nsWMLdhRbsIs1NhQ1ig01KhZERQVRAQFRelF6L7v3vH/wZuNKh4Vd5H6e5z4Pe2fmzJk7e88OU87h\nEBGBhYWFhaXRwBW3AiwsLCws9Qtr+FlYWFgaGazhZ2FhYWlksIafhYWFpZHBGn4WFhaWRgZr+FlY\nWFgaGazhZ6k2hoaGuH//PgBg8+bN+O2338SskTDKysqIioqq0zoePHgAPT29ctO5XC4+fvxYpzo0\nBOqjL1iqD2v4GyAnTpxAp06doKioiBYtWmD27NnIzMyst/o5HI7g75UrV+Lw4cP1VndVyM7OhqGh\nobjVqBPWrl0LBwcHcatRJpaWljh69KjQve+5LxoyrOFvYOzYsQNOTk7YsWMHsrKy8OzZM0RHR2Pw\n4MEoLi4Wt3osjZivBwQsEg6xNBgyMzNJSUmJLly4IHQ/JyeHtLS06NixY0RE5OzsTGPHjqXJkyeT\nsrIymZqa0suXLwX54+PjafTo0aSlpUWtWrWi3bt3V1jvyZMnSV9fnzQ0NGjTpk1kaGhI9+7dE9Rl\nb29PRESfPn0iDodDx48fJz09PVJXV6cDBw6Qv78/derUiVRVVWnu3LlCso8ePUrt27cnNTU1+umn\nnyg6OlqQxuFw6ODBg9SmTRtSVVWlOXPmCNIiIiKob9++pKKiQpqamjR+/HihcpGRkURElJGRQQ4O\nDqSlpUUGBga0ceNGYhiGiIiOHz9OvXv3piVLlpCamhq1atWKvL29BXKOHTtG7du3J2VlZTIyMqJD\nhw4J0nx8fEhXV7fcZ1aR7pW1e/78+aSnp0dNmzalbt260ePHj4mIyNvbm5o0aUIyMjKkpKRE5ubm\nZdZdUf/m5eWRo6MjqampUYcOHcjV1VWoHV8/OyIiR0dHWr16NRERpaWl0dChQ0lLS4vU1NRo2LBh\nFBcXR0REK1euJCkpKZKTkyMlJSWaN2+eSPuCRbSwhr8B4e3tTdLS0sTn80ulOTo6kp2dHRGVGGM5\nOTny9vYmhmFoxYoV1LNnTyIi4vP51LVrV9qwYQMVFxfTx48fycjIiG7fvl1mncHBwaSkpESPHz+m\nwsJCWrRoEUlLSwsM/9q1a0sZ/lmzZlFhYSHduXOHmjRpQjY2NvTlyxeKj4+nZs2a0cOHD4mI6MqV\nK2RsbEzv378nPp9PGzdupF69egnq5nA4NHz4cMrMzKSYmBjS0tIS6DlhwgTavHkzEREVFhbSkydP\nhMr9a2wcHBzIxsaGcnJyKCoqikxMTOjo0aNEVGJsZGRk6MiRI8QwDB04cIBatmwpkHPjxg36+PEj\nERE9fPiQFBQUKCAggIiqZvi/1f3WrVtVavfp06cpLS2N+Hw+7dixg7S1tamwsFDwvB0cHMqtt7L+\nXb58OfXt25fS09MpNjaWTE1NSU9Pr8xnR0Q0ZcoUWrNmDRERpaam0t9//035+fmUnZ1NY8eOJRsb\nG0FeS0tLwbMVdV+wiBbW8DcgTp06Rdra2mWmLV++nAYPHkxEJYb/37+JSoy3vLw8ERE9e/aM9PX1\nhcpu3ryZpk6dWqbcdevWCX5QiIhyc3OpSZMmFY74ExISBPk1NDTI09NT8NnW1pbc3NyIiMja2lrI\nUPD5fFJQUKCYmBgiKjEaXxv0cePG0datW4mIaPLkyTR9+nTBiPNr/jU2PB6PmjRpQqGhoYK0Q4cO\nkaWlJRGVGBtjY2OhtnE4HEpOTi7zWdjY2Ah0r4rhL0/3ytr9LWpqavTmzRsiEn7eZVFZ/377I+/u\n7l7hiH/KlCmCEf+3BAYGkpqamuCzpaUlHTlyRChPXfUFS+1g5/gbEJqamkhJSQHDMKXSEhMToaWl\nJfjcvHlzwd8KCgooKCgAwzCIjo5GQkIC1NTUBJeLiws+f/4MAFBSUoKysjKaNm2K2NhYJCYmQldX\nV0iWhoZGhXp+Xbe8vHypzzk5OQCA6OhoLFiwQKDHv3Lj4+MF+bW1tYXqzs7OBgC4urqCiNCjRw90\n7NgRx48fL6VHSkoKiouLYWBgILinr69foXwAAv28vb3Rs2dPaGhoQE1NDTdv3kRqamqFbf+ab2VX\ntd3bt29Hhw4doKqqCjU1NWRmZiIlJaVKdVbWvwkJCUK7kfT19avcnry8PMyYMQOGhoZQUVFBv379\nkJmZCfrKz2N58/y17QsW0cIa/gaEhYUFZGVlcenSJaH7OTk5uHXrFgYOHFipDD09PbRq1Qrp6emC\nKysrC9evXxfIys7ORlZWFvT09NCiRQvExsYKyufl5VXL+FWEvr4+3N3dhXTJzc1Fz549Ky3bvHlz\nuLu7Iz4+HocOHcLs2bNLbZ/U1NSEjIyM0HbCmJgYoR+y8igsLIStrS2WLVuGz58/Iz09HT///LOQ\nkaspFbX78ePH2LZtGy5cuICMjAykp6dDRUVFUG9lC6j6+voV9m+LFi0QExMjyP/130CJwc3LyxN8\nTkxMFNS5Y8cOhIeHw9/fH5mZmXj48CGoZNagUt1q0xcsooc1/A0IFRUVODs7Y968ebh9+zaKi4sR\nFRWFcePGQU9Pr0rb/Hr06AFlZWW4uroiPz8ffD4f7969w8uXL8vMP2bMGFy/fh1PnjxBUVER/vjj\njzL/46gO/xqKmTNnYvPmzQgJCQEAZGZm4sKFC5WWA4ALFy4gLi4OAKCqqgoOhwMuV/jrLCUlhXHj\nxmHVqlXIyclBdHQ0du3aBXt7+0p1LCoqQlFRETQ1NcHlcuHt7Y07d+5Uu61f616VdmdnZ0NaWhqa\nmpooKirC+vXrkZWVJZCjra2NqKiocn+AKuvfcePGwcXFBRkZGYiLi8OePXuEDLa5uTnOnDkDPp+P\nW7du4dGjR4K0nJwcyMvLQ0VFBWlpaVi3bp1Q3c2bN0dkZGSZetWmL1hED2v4GxhLly7F5s2bsWTJ\nEqioqKBnz54wMDDAvXv3ICMjA6Bk5PXt6Ovfz1JSUrh+/Tpev34NIyMjaGlpYfr06ULG5Ws6dOiA\nffv2YeLEiWjZsiXU1dWFpgq+rasqW/r+zWNjY4Ply5djwoQJUFFRQadOnXD79u1yZX1d18uXL9Gz\nZ08oKytj5MiR2L17t2C/+Nfl9uzZA0VFRRgZGaFPnz6YNGkSpk6dWulzUlZWxu7duzFu3Dioq6vD\nw8MDI0eOLDNvRW0sS/eK2m1tbQ1ra2uYmJjA0NAQ8vLyQtMxY8eOBQBoaGige/fuperlcrkV9q+z\nszMMDAzQqlUrWFtbY/LkyUI/Im5ubrh27RrU1NRw9uxZjBo1SpD2+++/Iz8/H5qamujVqxeGDBki\n1M4FCxbg4sWLUFdXx++//15Kt5r2BYvo4VAt/3edNm0abty4gWbNmuHt27dl5pk/fz68vb2hoKCA\nEydOoEuXLrWpkoWFRUQ8ePAADg4OQtN5LN8/tR7xT506Fbdu3So3/ebNm/jw4QMiIiLg7u6OWbNm\n1bZKFhYWFpZaUGvD36dPH6ipqZWbfvXqVTg6OgIAfvjhB2RkZCA5Obm21bKwsIgIdkql8VHnc/zx\n8fFCc8K6urqCRTkWFhbxYmlpWWpnD8v3T70s7n67jMCOMFhYWFjEh3RdV6CjoyO0cBQXFwcdHZ1S\n+dgfAxYWFpaaUd09OnU+4h8xYgROnjwJAHj27BlUVVWFTnJ+zb97nRv75ezsLPT506dPWLp0KTQ0\nNDB48GDs2bMHnz59qrZchmEQFhYGV1dXdOzYEQYGBlizZg0+f/4s9jZX9Vk05ot9FuyzKOuqCbU2\n/HZ2dujVqxfCwsKgp6eHY8eO4dChQzh06BAA4Oeff4aRkRGMjY0xY8YM7N+/v7ZVNhrCw8Mxbtw4\ndO/eHQzDwN/fH3fu3MHcuXNr5OOcw+HAxMQES5cuxZs3b3DlyhV8+fIFbdu2xdKlS9lFdxaWRkKt\np3o8PDwqzbN3797aVtOoyMvLw4IFC3DmzBksWbIEx44dg5KSkkjr4HA4MDc3x4EDB7Bq1Sps3boV\n7du3x4IFC+Dk5ARZWVmR1sfCwiI5sCd3JQgiwokTJ+Du7g4ej4fQ0FA4OTmJ3Oh/i66uLvbs2YOg\noCC8fv0anTt3ho+PT53WWVUsLS3FrYLEwD6L/2CfRe2o9cldUcHhcGo8X/U9kJycjOnTpyMqKgon\nT56EmZmZ2HTx8vLCvHnzYGVlBTc3NygqKopNFxYWloqpie1kR/wSwPXr12FmZoaOHTvixYsXYjX6\nADBy5EiEhISAx+OhR48eCA4OFqs+LJLJv/512Kv+LpH1HTviFx8Mw2Djxo04fPgwzp8/j169eolb\npVKcOHECS5cuxdatWzFt2jRxq8MiQTTGd1aclPe8a9IPrOEXE9nZ2ZgyZQoSExNx6dIltGjRQtwq\nlUtISAhsbW1hbW2N7du3Q0pKStwqsUgAje2dFTeiNPzsVI8YiI+PR+/evaGurg4fHx+JNvpAiWtm\nPz8/BAYGYuzYsUKBOlhYWBoerOGvZz58+IA+ffpg4sSJcHd3bzDbJtXU1HD79m0oKipiwIABglB+\nLCwsDQ/W8Ncjb968Qb9+/eDk5AQnJ6cG56ZCVlYWJ0+exMCBA2FpaYmkpCRxq8TCwlIDWMNfT/j7\n+2Pw4MHYuXMnpk+fLm51agyHw8GmTZswYcIE9O/fH4mJieJWiYWlFIaGhrh//36dyD579iwMDAyg\npKSEUaNGIT09vdy8UVFR6N+/PxQVFdG+fXvcu3evxrJECWv464GgoCAMHz4cR44cwfjx48Wtjkj4\n448/YG9vj/79+yMhIUHc6rCwCFFXC8/BwcGYOXMmzpw5g+TkZCgoKGD27Nnl5rezs0O3bt2QlpaG\nTZs2YcyYMUhJSamRLJFCEoIEqSJSQkJCSFtbmzw9PcWtSp3g4uJCJiYm9PnzZ3GrwlLPSOo7a29v\nT1wul+Tl5UlJSYm2bdsmMtkrVqygSZMmCT5HRkZSkyZNKCcnp1TesLAwkpWVFUrr27cvHTx4sNqy\niMp/3jXpB3bEX4d8/PgRVlZW2LJliyBI9veGk5MTxowZg6FDhyInJ0fc6rCw4NSpU9DX18f169eR\nnZ2NJUuWlMoTExMDNTW1cq9z586VKTskJETogKWRkRFkZWURHh5eKm9wcDCMjIyETr6bmZkJDkQG\nBwdXWZaoqXN//I2VL1++wMrKCitWrBCEnhQVRIToyAi8C3iB2OhIxEdHIT4mCtlZmSguKkRxURE4\nHA5U1DWgpq4BNQ0tGBq3hUmHTjAx7YzmLXVEurC8ceNGJCcnw9bWFteuXUOTJk1EJpul4SKq7xjV\nwZSNvr5+jebTc3JyoKKiInSvadOmyM7OrlJeZWVlwbpYbm5ulWWJGtbw1wEFBQWwsbHBuHHjRDZn\nl5+XB997t+B3/zZev3gKOXkFdO72Awxat0EHs25oqWcAFVU1yDSRhUyTJiCGQWZ6GjLSU5H65TM+\nhoXg5t/n8OeGlZCWkUav/lb4caA1zP9nAWkZmVrpxuFwcPDgQdja2mLatGk4efIkuFz2n8nGTl0Y\nbHGjpKSEzMxMoXuZmZlQVlYuM29WVla5easjS9Swhl/EMAyDKVOmQE9PDxs3bqyVLCLC6xdPcevv\n83jicwemZt1gaT0MM5asgbaObqXllVVUoWtoBADoZzVUIDM6MgK+927hqNtWxMdEwXrUOIyc4Agd\nfcMa6yotLY1z585h0KBBWLt2LdavX19jWSwstaWy/zZiYmJgampabrq7uzvs7OxK3Tc1NUVQUJDg\nc2RkJIqKimBiYlJm3o8fPyInJ0fgYTcoKAgODg7VliVyqr0qUEdIkCq1YsWKFdSrVy/Kz8+vsQw+\nn0+P7tykGWOHkMPPfcjzhDulfqmbxdP4mCja77qORliY0vLp9hT08lmt5CUnJ5O+vj6dP39eRBqy\nSCqS/M727NmT3N3dRS43ODiYmjZtSo8fP6acnByys7MjOzu7CvVYsmQJ5efn06VLl0hVVZVSUlJq\nJKu8512TfpCYnpPkL1FVOXPmDBkZGdGXL19qVJ5hGPK9d4smD+1L08dY06M7N4nP54tYy7IpyM+j\na56nadyA/9Hy6fYUEfquxrICAwNJU1OTXr16JUINWSQNSX5nvby8SF9fn1RVVWnHjh0ilX327FnS\n19cnRUVFsrGxofT0dEHazJkzaebMmYLPUVFRZGlpSfLy8tSuXTu6d+9elWV9iygNP+ukTUS8efMG\nAwcOxL1799C5c+dql4/6EI59W5zxOSkBs5c5o0ef/mI52VtUVIhr50/htPse9OhtiVnL/oCquka1\n5Vy6dAkLFy6Ev78/tLW160BTFnHT0N/ZhgbrpE3CSE9Px+jRo+Hm5lZto19YWICD2zZgweTR+KHv\nQBy9fBc/9B0gNncOTZrIwtbhV5y55QcVdXVMHdEft654VvuL9e9C79ixY8Hj8epIWxYWlprAjvhr\nCcMwGD58ONq0aYM///yzWmXDg99gs9MC6LdqjYXOW6CmoVlHWtac8OA32LZmCZRVVOHk8ieaabes\nclmGYfDzzz/D3NwcW7ZsqUMtWcRBQ31nGyrsiF+C2LRpE7Kzs7Ft27Yql+Hz+Th10A3Lpk/CxN/m\nYp3bYYk0+gBgYtoZBzxvossPvTFjjDX8fO5UuSyXy8Xp06dx9uxZXL9+vQ61ZGFhqQ7siL8W+Pr6\nYsyYMXj16hV0dHSqVCY7MwMbl85Ffl4uVm/bi2YtqlZOEngb4I+NS+agr9VQTF+0EjJVPKjl5+eH\nUaNGwd/fHwYGBnWsJUt90RDf2YYMO+KXANLS0jBp0iQcOXKkykb/w/tgzBg7BHqtWmPncc8GZfQB\noFPXHjj89x0kxEZh4dSxyEhLrVK5Xr16YdmyZRg3bhyKi4vrWEsWFpbKYEf8NYCIYGtrC319/SrP\n6z+6cxM71i7D/FUbMHDoqDrWsG5hGAbHdrvi3o0r2Lz/L7Rq07bSMkSEYcOGoWvXrtiwYUM9aMlS\n1zSkd/Z7QJQjfonZiCtBqlTK/v37ydzcnAoKCqqU/9KpI2TbtwuFB7+pY83ql9teF2lkr4707OG9\nyjMTUWJiImlra5Ovr28da8ZSHzSkd/Z7oLznXZN+YEf81SQsLAy9e/fGkydP0LZtxSNdhmHgvmMT\nnvjcgevhs2iho1dPWtYf7wJfYM38XzF7mTMGDx9daf6rV6/i999/x+vXr9G0adN60JClrmgo7+z3\ngihH/KzhrwY8Hg8//vgj7O3tMXfu3Erzuq5ahITYKGzadwIqauoi1YVhGKQnxyPjcwIyviQi80sy\nCvNzwC/mgeGX7JuXV2oKeeWmUFBWhUZLfWjpGUFBWaUSydXnU0QYlk2fiEm/zYPNxCmV5p8xYwYK\nCwtx4sQJkevCUn80hHf2e4I1/GLCxcUF9+7dw507dyr0PskrLsam5fOQk5WJDXuOQk5eodZ183k8\nRIcE4tPbF4iLeIeEiBDIKipBvbkuVJq1gIpGc8gpKUNKWhpS0jIgIuTnZCE/OxO5melITYjGl9hP\nkJGTg45xB7Tq1ANGnf+HZvqtRXJYLCE2Gkt+mYChYyZi0vR5FebNzc1Fly5d4OLiAltb21rXzSIe\nJPmdNTQ0xLFjxzBgwACRyz579ixWrFiB1NRUDB48GMeOHYOamlqpfF++fMH8+fPx6NEj5ObmomPH\njti5cyd69OhRbVkAa/jFwr8uGV69egV9ff1y8/GKi7F+yWwU5udj/Z4jkJWVq3GdfB4PYS8eIeTZ\nfXwI8IOati6Mu1hAz6QTWhp3gJJq9f6LICJkpiQjLuwNPr55gY9v/MErLoJp70Ew6/czWhi1q9WP\nQOrnZCz+ZQL6Ww+H45xFFeb18/ODra0t3r59C01NyTzDwFIxkvzOtmrVCkeOHMHAgQNFKjc4OBgW\nFha4efMmunTpgunTp4NhGHh4eJTK++nTJ3h5ecHOzg7NmjXDkSNHsHLlSkRFRUFRUbFasgB2cbfe\nKSwsJDMzMzp27FiF+YqLimjVnKm0YtZkKiys2sJvWaQmxtKdk3vIdYoVHV35Kz33vkCZKck1llcR\nn2M/0b0zB2jXjBG0e85oeuJ1mgryyg79VhVSv3wm+yE/0tnDeyvNu3DhQpo4cWKN62IRL5L6zkpK\n6MWyaNq0KQUEBNRIVnnPuyb9IDE9J6lfIiKidevW0dChQ4lhmHLz8Pl8Wr94FjnNdKCiwsIa1ZP4\nKZzOuy6nLZMHkvfRHfQ59lMNNa4+DMNQdEggnd/mRC72A+jW8T8p40tSjWR9TkogOysL8jxRsVvc\n3NxcMjY2Ji8vrxrVwyJeJPmdNTQ0LOUJ82uio6NJVVW13MvDw6PMciNHjiRXV1ehe8rKygJjXhGB\ngYEkJydHWVlZNZIlSsPPBmKphJCQEOzevRuBgYHlToMQEdw2rELK52S4up+u8onWf0mO/gAfj0OI\nDX+DXiMdYDPPGU3k5EWhfpXhcDjQb28O/fbmSP+cgGfXPXBg4UR0GTgCfWynVGtRWKt5C+w67okF\nk20hKyeHEeMdysynoKCAo0ePws7ODn369Cl3bpOlYWLZvup+nSriQWiCSOR8TX2EXvyarKwsODg4\nYO3atYIIWzWVJQpYw18BDMPgt99+w7p166CnV/5WzKNurgh9E4Bdf12EbDUMdm5WBu6fPYDQZz7o\nYzsFoxduQJNarAmICrVmLTFk2mL0tpmMh+cPY89cW/QaaQ+L4RMhLVO1H7XmLXWx49h5zLcfBTUN\nTfQZNKTMfH379sXo0aOxaNEiHD9+XJTNYBEzdWGwxU1NwiXm5+dj+PDh6NWrF5YvX14rWaKCddlQ\nAQcPHgQAzJo1q9w8F08ewcM71+F6+CwUlarWYQyfj+c3z2PfvLGQkpbG3D0XYDF8okQY/a9pqq6F\n4bNW4pfNRxATGoQDCyciKjigyuV19A2xaf8J7HBehrcB/uXmc3Fxwf379/HgwQMRaM3CUrXQi8rK\nyuVe5S2wVjdcYmFhIWxsbKCvr49Dhw7VSpZIqfbkUB0hQaoQEVFMTAxpampScHBwuXke3/Um275d\nKDEutspyU+Kj6YjTNDq68ldKjv4gClXrBYZhKNjvHm3/ZQhd2bue8rIzq1z22aP7ZNO7E0V9CC83\nz5UrV8jExKTKp6FZxI+kvbNfIwmhF4uKimjYsGFkY2NDPB6vVrKI2MXdesHGxobWrl1bbnro29c0\nwsKUQt8EVkken88nv6tnaIvDAHp6zaPeQiqKmvzcbLp2cAvt+PVn+vjmRZXLeV8+T+MH9qgwdnBl\nz5xFspC0d/ZrJCH04oMHD4jD4ZCioiIpKSkJrq9dlogr9KLE9JwkfYmuXbtGbdq0KXf0mRQfS7Z9\nu9CjOzerJC87PZX+cp5Nh52mUkpCjChVFRvhr57Qtqk/0Z2/dlNxUVGVyhzb7Upz7IaXu9U1JiaG\nNDQ06P3796JUlaWOkKR3tjEgSsPPHuD6hvz8fJiamuLgwYOwsrIqlZ6Xm4u5E0fAetQ4jJsyo1J5\nUcEBuLRrNcwsh6K/3QxISX0/6+k5GWnw2rcBORmpGL/MFapaFcfWZRgGaxfOgLyCIpw27ypzHvbP\nP//E1atXce/ePbGFn2SpGpLyzjYW2JO7dcgff/yB9+/fw9PTs1QaEWHtwhlQUFTEso07KzRMRIQn\nV07i6dWzsJn7B9p06y1yXXmF+SjKSkNhdhoKs1LBLyoA8fkghg8AkJZThLS8IqTlFCGn1hxyKprg\nVOBqoiYQEfy8TsPv6mmMWbgJrTp1rzB/fl4e5tmPxKBhozFhWulFcx6Phx49emDJkiWYOHGiSHVl\nES2S8s42FljDX0dERETAwsICQUFBZQZXOXN4D3zv3sKfJy9V6IqhuKgQV/dvREpcFCY4bYOKZsUj\n4arAK8xDxqdgZMWEISfpE3ISo1CUmwFZZQ00aaoOWWU1SMkpgMuVAkdKGiACryAPvIJcFOdnoyAt\nGcV52ZBXbw7F5gZQMWgPFf12UGrRClxpmVrrFxn0HH//+Qd6j5oMi+ETK/xRTE6Iw+wJw7F0w3b0\n7Ff6SL2fnx/GjRuH0NDQetnaxlIzJOGdbUywhr8OICJYW1vDysoKixcvLpX+/NF9bFuzBPvPX68w\n4HhORio8XJZARbM5bOavrdUWzdzkGHx++wSpEQHITYqCsq4JVA3bQ6lFKyhpt4K8enNwuFJVlscv\nKkB+aiKyEz8hK+Y9MmPeIz8tCWqtO0Oz/Q/QbNsdTZRrfogq/XMCzrksQUvjDhg2wwlS0uVPa715\n9RzOC37D/nPX0UK3tO8jR0dHaGtrY+vWrTXWh6VuEfc729hgDX8dcOXKFaxatQqvX7+GjIzwCDg+\nJgpz7IZj/e4j6Nzth3JlfI79iDMbFsB8wDD0G/dbhR48y6MgMwWJr+7h85vH4OXnoFmn3tBo9z+o\nGLSHlIxsteVVRnFuFlLDXyEl1B9pEYFQ1jFGi+6DoGVqUaP6CvNz4bltBQBg3FIXyMorlpv3wl+H\nccfrAvae9Sp18C0pKQkdO3aEr68v2rVrV209WOoecb+zjQ3W8IuYgoICmJqa4tChQxg0aJBQWmFh\nAebajcCQ0eMx2v6XcmXEhr3FuS1LYOU4H2aWQ6tVPxEhPfIN4p/dQPrHt2jeuQ+am/eDin57kc/J\nVwS/uAgpoc+R+PIusuIioG3eD7q9R0BBo0X15PB5uH5wCxIiQzBptRuaqmuVmY+IsH7xLMjLK2DZ\npp2l0nft2gVvb2/cvn2bXeiVQFjDX7+whl/EbNmyBc+ePcOVK1dKpe1c64TMjDSs3XWoXOMTEeCH\ny27OsJnvDJNuP1a5XmIYfAl+iqj750DEQKfnUGh3sYS0bO3999eWgowviH/ujQT/W1A16gyDvqPR\nVK/qJwqJCI8uHkPgvatwXLcfas3LDiyfl5uLWeN/xljH6Rg2dpJQWnFxMczNzbFx40aMGtWw4xR/\nj7CGv36/M7v+AAAgAElEQVRh3TKLkPj4eNLQ0KAPH0qfor17/W+ys7Kg7KzyT6m+fXybXKdYUUxo\nUJXrZBiGkoIe0bNds8l/70L6EvK8Qs+f4qS4IJdiHl8hX5cpFPTXespO/FSt8s9vetL2X36u0NNo\n1IdwGt6zA0WGhZRK++eff8jIyIg90SuBSJD5aBSU97xr0g+NfsTv6OiIli1bwsXFReh+zKcPmDfJ\nBtuPeKBNh05llg16cBP/nNwNB+e9aG5gXKX6MqPfI+LGERDDh9Fge6ibdG0Q0xj84iIkPPdG1MOL\n0GjTFUZWkyCn2qxKZV/fv45/Tu+B/ZrdaNGq7DjF3pfP49zR/Tjo6Q15BeH/eEaMGIE+ffpg6dKl\ntW4Hi+hgR/z1CzviFxHPnj0jHR0dgX/sfyksLKBfRg2iK2dPlFs28N412jbNmpJjIqtUV37GF3p7\n1pV8XaZQwqt7xDRQlw3F+bkUefsUPVpvR598PIlfXLVTu++e/ENbHQdT/IfQMtMZhqENS+eQ6+rF\npdLCwsJIQ0ODkpPrJhgNS82QIPNRCgMDgwr98deGM2fOCLlZSEtLq7TMv+4bVq9eXWNZ5T3vmvRD\nrXvO29ub2rZtS8bGxrRly5ZS6T4+PtS0aVMyNzcnc3Nz2rBhQ9mK1POXiGEY6tWrFx0/frxU2r4t\na2nVnKnlTr+8+ucKbf9lSJUCpTB8PsX6XadHGyZS5J1TxCvMr6XmkkFeaiK9Pr6Wnu6YSWkfqjbN\nFfL0PrlOsaLET2U7a8vNyaaJVr3o7vXLpdJ+//13mjFjRq10ZhEtkmz4DQ0N6e7duyKX++7dO1JW\nVhY4Vps4cSJNmDChwjJFRUVkZmZGFhYWtGbNmhrLkhjDz+PxqHXr1vTp0ydB40JChOdpfXx8aPjw\n4ZUrUs9fogsXLpC5uXkpr3n+vj5k268rZaSlllku6KE3bf9lCH2Ji6q0jpzkGHp5YCm9PLCUcpKi\nRaJ3eTDFhcTkZxOTl0lMTlrJVZhHDFN3/1kwDEOfg5+Rr8sUen95HxUX5FVa5q3vHXKdalWuZ9L3\n74JohIUpJcQKP6+0tDTS0tKiN2/eiER3ltojqYZf0kIvuri40PLly2nKlClCI35xhl6sleMYf39/\nGBsbw9DQEAAwYcIEeHl5oX379t9OJ9WmGpFTVFSE5cuXw93dHVJS/x2AykhLxdaVi7BiixtU1EoH\nMn///AFuH98Fx3X7oaljUK58IkKc3zVE+ZxHq4ETofPDkFpvyyQiIPsLkBYLykwCspJBWZ+B/Cyg\nIBtg+ICMLMDhAlwpgBiguBDgFwHSsoCCKqCoAY6SOqCiDY66HqCuB45s+fvsK4PD4UCrww9QbWWK\niBtH4O82D+3HLICaUdlrIgDQsfdgMDweTq6biynrD0BTx1Aova1pZ9j9Ogebnebjz78uCfpHTU0N\na9asweLFi9ntnSwVcurUKfj6+uLo0aMYMGBAmXliYmJgZmZWrowDBw5gwoQJpe6HhISgd+//3K8Y\nGRlBVlYW4eHh6NKlS6n80dHROH78OAICAjBnzpxayRIltTL88fHxQpGpdHV18fz5c6E8HA4Hfn5+\nMDMzg46ODrZv344OHTrUptpas2/fPrRv3x4DB/7nLoCI4Lp6EQYPH41uFn1KlYkMeo6r+zdh0ho3\nNNNvXa7swqw0hF50Ay8/B91mboOCZs3CzxERkB4Pin8H+vwB+PKpxKBrGICjog1otwXXpA8grwLI\nKQMycmUaQ2IYoLgAyEsHclJBOalAZiKY6AAgLQ6QUwZH2wRo0Q4c7bbgKFb/5K6MvBI6jPkdKaH+\nCD6/HS26DECrwfbgSpV9qrhzvyHgFRfh1Lp5+MXlKJpqCC8Sj3WcjqcP7uLcsf2Y9Ns8wf2ZM2di\n7969uHPnDn766adq68lSvziPqthvU1VZd/mlSOR8TX2FXpw/fz42btwIRUVFcDgcoXe0wYZerMqo\nq2vXroiNjYWCggK8vb1hY2OD8PDwMvOuXbtW8LelpSUsLS1ro16ZpKWlwcXFBQ8fPhS6f/OSB74k\nJWLdn4dLlYkLf4dLO1dj/HJX6BiX/6OVGh6A0It/ouX/rGA4YAK41fTESQwfSAoDRb0Cxb0FpKTB\n0ekIbmsLoOekGhllDpcLyCqUXGo6+LrHiBggMwmUGAaKeQ3yPw8oqIFj2BUcg67gqFbvR0uzfQ/0\n0DNByIVdCDy8AqYTlkJOtezDW10HjURedgZOrpuLaZsOC8X0lZKSwgoXN8wYa40evS0Fu6pkZGSw\nZcsWLFu2DIMGDRL6b41F8qgLgy1uqhMu8dq1a8jJycHYsWMBlAzmvp79qGnoxQcPHtQ+Wl21J4e+\n4unTp/TTTz8JPm/evLnMBd6vMTQ0pNTU0vPntVSlyixatEgQKOFfEuJiaISFKUWGld5xkhIfTa5T\nrSjsxeNyZTJ8Pn2860GPN02mtMjqz0EzKTHEf3aOeOcWE+/qRuK/vU1MRlK97+1n+HxiEt8T/5kH\n8c4vJd5lZ+K/+4eY/KzKC38jJ+rBBXq00Z6+hPpXmPfW8T/p8PKpVJhfen3gttdFmjy0LxV8lfbv\novyJE+XvuGKpH+rrna0JrVq1qnBXT3R0tFBwlG+vs2fPlllu5cqVQvPyHz58KHde/vfff6emTZuS\ntrY2aWtrC9YcbGxsqi2LSIIWd4uLi8nIyIg+ffpEhYWFZS7uJiX9Z8CeP39OBgYGZStSD1+iT58+\nkbq6OiUlJQnu8fl8mu8wmjyO7CuVPzs9hXbNGEEv75TeZfIvRblZ9Pr4Wnp5cBkVZKZUWReGV0T8\nD8+Id92FeJ7LiB/gRUxGUuUF6wmG4ROT8J74D48Q7/R84vscIia5eqEi0z8Fk+9mR/p0/1y5P2IM\nw9Dfbs50asN84vGKS6WtXTiD9mz+Q+j+kydPSE9Pj/LyKl9MZqk7JNnwS0LoxezsbEpOTqbk5GRK\nSkqi8ePH06JFiwRRthp06MWbN2+SiYkJtW7dmjZv3kxERAcPHqSDBw8SEdHevXvJ1NRUsJ3p6dOn\nZStSD18iBwcHcnZ2FrrnecKd5k4aWWp3T0FeLh1cbE/3zx0qV17O51jy2/YbhV9zJ/43Rqs8mKJ8\n4r/xLhnd39pJTFQAMfzS8TglCaYgl/jBd4l3YQXxbmz5f52rtluoIDOFXuxbTG9Ou5S764fHK6aT\n6+bS1QObS/1AZKSl0ug+5hT04pnQ/VGjRtHWrVtr1iAWkSDJhl8SQi9+y5QpU4S2c1Ym61tEafgb\nzcndN2/ewMrKChEREYI5tOiPEZhvPwr7z12Hjr6hIC+fz4OHy2Ioq2lixOzVZa5lpEUEIvj8DrT+\naTJa/q90pK5vocI8UMhd0PsH4LTsAE5na3DUdEXWvvqAGAaICQTz7jbAKwTXfARg0AUcTsU7lhhe\nMcK8DiArLgJmjmvKPPFbkJeDYyt/hZnlUPS2cRBK8713C/td1+Po5buCU71hYWHo3bs3wsLCoKGh\nIbpGslQZ9uRu/cI6aasBQ4cOxU8//YT58+cDAPh8Pubb22DwcFvYTJwilNf76A58jo2E/erdZfqU\nj3t2E1H3PGBqt6zCrYsAQLxi0Hsf0Lvb4Oh2AqfzEHCaNhdZu8QBEQHxwWACvQCGD25XG0C3U6UR\nyWJ9vRDrewWdJ6+Gsk5pFxeZKUk44vQLrKcthGkvYS+pG5fNhYqqGuat3CC4N2vWLCgpKWHbtm2i\naxxLlWENf/3CumyoJj4+PtSqVSshR1+eJ9xpvsNo4n8zZfHc+wLtnmNLeTmlFzQZhqEPt/6ip9tn\nUG5KQoV1MgxTMofv6US8u3uJSY8XTWMkCIZhiIkOJN7lP0qmrdLiKi2T/NaXHm2YSF9CX5SZnhAZ\nSlsmD6TYsLdC9zPT08i2bxd67f/fVGF8fDypq6tTbGxs7RrCUiMkyHw0Csp73jXpB4npubr6EjEM\nQz169KDTp08L7sVFf6LhPTtQbNRHobwfAp+S6xQrSk0obUj4vGIK9txJL/YuosLsjIrrTI0l3k1X\n4l3dQExS2e4JvicYPo/4IfeI57GI+H6niSko/xQjEVFGVCg93uRA8f63ykwPfeZD238ZQpkpwr55\nnty/TXZWFpSflyu4t3z5cvrtt99q3wiWasMa/vqFNfzV4PLly9S5c2fByJ7P59OCybZ0/vhBoXxf\n4qJoq+Ng+vTuVSkZvMJ8en3MmV4fX1uhrx2mKJ/4z8+VGMDQBw3WEVtNYQpyiP/0DPHOLSZ+ZMWu\npnO/xNOTrdMo6sHFMtMfXjhKh5Y4UFGB8PNev3gW7XddJ/iclpZGmpqaFBYWJppGsFQZ1vDXL6I0\n/N/1HD+fz4eZmRm2bNmCYcOGAQC8zp3Ercue2HvWS3AAqCAvB0eWT0XP4RPR3Uo44AevIBdBJ9ZB\nXqMF2o2eV+6hLEoIAfPkFDgt2oLT3RYcucYbJJy+fATjdwqQVwXXYhI4yppl5ivMTMXrY2ug0a4H\nWls7Cq0REBEu7lwFDpcL2983CNIy0lIxdUR/uBw8hXYdS47cu7i44PXr1zh//nzdN45FADvHX7+w\nc/xV5PTp02RhYSEYeSYnxtMIC1P6FPHf6JDP59OZTQvp6oHNpcoX5mSQ/57fKczrYLmjd6Ywl/i+\nfxHPczkxce9E3oaGCsMvJn7QTeKdXUj8sEfljv6LcjLpxd5FFHppT6lnXFiQTwcX29Pjv4UPa92+\ncoGmjRxIxUUlLqFzcnKoRYsW9OpV6f/WWOoOCTIfjYLynndN+qH+ArrWM8XFxXB2dsamTZsEo8Xd\nG1fDZuIUGBr/F0Lwoedh5OdkYcgvS4TKF2anI/DwSqgZm6HN8OllOlmj5AgwXhsADgfckc7g6JjW\nbaMaEByuNLidh4BrvRj0/gGYe3tBeRml8skoNoX5rxuRlxKP0EtuJW4r/p8msnKY4LQdT6+dRWTQ\nfz6gBo+whbpWM5w7dgAAoKioiNWrV2PlypV13zAWlu+B2v4KiQpRq3Lo0CEaNGiQ4POjOzfJfsiP\nVFj4386e0OcPaMevP1N2uvCJ24LMVHq6YwZ9vFf2iVOGX0z8V5eJd24xMTFVD7nYWGF4xcQPuEI8\nj8XExLwuMw+vMJ8CDq+kdx7biP/NYbqPb16Q6xQrSk/+bydVYlwsDe/ZgaI/RhARUWFhIRkYGJCv\nr2/dNYRFCAkyH42C8p53TfpBYnpOlF+i/Px80tXVpefPnxMRUXZWJtn26yq0FTAlIYa2Th5Uatvg\nv0b/0/3zZcpmslOId20T8e64EZNXfixeltIwSRHE81xO/OfniOGVjtzFKyqgwKNr6O2ZLaWM/5Mr\np+jAoklCi72eJ9xpwWRbwY/z0aNHqX///nXbCBYBrOGvX0Rp+L/LqZ6DBw+iW7du6NGjBwDgyC4X\n9Ow7AGb/6wkAKCoswHnXZbCcMB26Jh0F5Qqz0xF4ZBW0u/SHYf9xpeRS7Bsw1zeDY9gd3EHzwJFv\nWi/t+V7gNDcGd8QaUHYKmJuuoOwvQulSMrLo5LAavMI8hF7YKTTtYzFiEjRa6uGG+1bBvVGTpiI3\nOwt3vC4CACZPnozY2Fjcv3+/fhrEIrEYGhrW2ffg7NmzMDAwgJKSEkaNGlWpe2c3NzcYGRlBSUkJ\nHTp0QERERI1liYza/gqJClGpkpOTQ9ra2hQUVDIF8y7wJY3uY05ZGSU+MP51CnZx52qhaZzC7Ax6\nunMWfbx3rpRMhs8j/otLxPNcRkxShEj0bMwwDFPi+8djETGxpb2Z8ooKKODwKgq+sEtowbcgL5f2\nzBtLAXe9BPdC374mmx87CyKmnTlzRmhBn6XukCDzUQpJCb14+PBh6ty5M4WGlnj+/fjxoyCuboMN\nvShKRPUlcnV1pbFjxxJRiffQaTYD6e71vwXpL27/TXvnjRVyA1yUl03P3eZT5J1TpeQx+dnEu7WD\neLd3Vts9MUvFMEkRxDu/lPiBV0uFiOQV5tPLg8sp9O+9QkY8OSaStkweKBS3d/em1bR15cKScjwe\ndejQgW7evFk/jWjESKrhl5TQi3w+n3R1den+/fu1lkXEGv5yycrKombNmtG7dyXbKj2PH6KFU8YK\nDEfCx/e0ZfJAoSDpxQV59GLfYgq/5l5qlMikxRLv4griv7jQ6A5j1RdMbjrxbmwl3t09xBQKe+8s\nLsgts29e+9wgt9mjKD83m4iIcrKzaIzlf2s4Fy9epK5du7Kj/jpGUg0/UcmIvzJ//KqqquVeHh4e\nZZYbOXIkubq6Ct1TVlamgICAMuvgcDjk5uZGenp61KpVK3J2dhZ8L6sji0iCYu5KGnv37sXAgQNh\namqKz0kJOHXIDfvOXgWHw0Fhfi4ubFuBIdMWQ0vXEADALy7C21MbodhcH8ZDfxU+QBQdAMbvNDg9\nxoPb+gcxtej7h6OgCq71ItCzc2BubgV34FzBgS9pWQWYTV2LQPcViPLxRKsB4wEAZpY/Izo0ENcO\nbMKYRZuhqKSMuSvWY9c6Jxy5/A9GjRqFjRs34urVqxg5cqQ4m9eoub9iuEjkDHC5JhI5X1MfoRfj\n4uIAAP/88w/evXuH9PR0WFlZQVdXF7/++qtYQy9KzE92bVXJzMwkLS0twVzaHwt+o2O7S35NGYah\nCztX0ZW96wX5+TweBZ3cQG/PbhXyh88wTIm//PPLiPkSVSudWKoOwzAl/n7OLS7l36ggK438XH+j\nWL/rgntFhQW0f6EdPfe+ICi/9LeJgoA6ly9fJnNzc3bUX4dIkPkoRWUj/ppS1ihdSUmpzFF6QEAA\ncTgcevTokeDejh07aNSoUdWWRcTu6ikTNzc3WFtbo127dnj+6D4iQt9h4vSSQN0Bd72QHBWBIb8u\nBVDiDiDsyj4wxUXoMHYhONwS1w3E8EB+p0CfXoA71AkcTQOxtaexweFwwG0/ANwfp4LxOQgm8pkg\nTVZZDea/rEf0w4tIev0AACDTRBZjF7vAx+MgkqIiwOFwMH/VRpw9sg+fE+MxcuRIcDgceHl5ialF\nLOKksnjgMTExUFZWLvfy8PAos5ypqSmCgoIEnyMjI1FUVAQTE5NSedu2bYsmTZqUq1t1ZImcav9U\n1BG1USU9PZ00NTUpPDycCgryyc7Kgp49KllQSY7+QFscBlByTKQg/4dbf5H/3oVCEaGYwtySRdx/\n9hBTVL4jNpa6h0mLJ56nE/FfXxcasWcnRdGjjfaUEvafa4bXPtdpz9wxgsX6Y3u20Zr5vxJRSRQm\nMzOzUq63WUSDBJmPUkhC6EUiosmTJ9OwYcMoOzubYmNjqV27dnTs2LEaySrvedekHySm52rzJVq3\nbh05OjoSEdFf+3fRqjlTiYioqCCf9s4fRy//+S9mboyvFz3dPkPItTKTk0a8K2uJ//QMu4grITC5\n6cTzWk9837+I4f8X1jL9UzA92jCRMuP+21Z76c8/BNN4Bfl5ZDe4Jz1/7EMMw1DXrl3p77//LiWf\npfZIsuGXlNCLWVlZNGHCBFJWViY9PT3asGFDlWV9C2v4vyIjI4M0NDQoPDxccIw/IS6GiIiuH9pC\n57c5/eek7a0v+W52pLy0/4KaM+kJJaPLoJvsfLCEwRTlE++OG/H+cSOm+D9XG5/f+dHjTZMFwXAK\n8nLJbfYoevPIm4iInj64SxOtelFBQT5dvXpVyC03i+iQZMP/PSJKw9/g5/h3796NoUOHok2bNti3\nxRljJv+GFjp6eO//EOEvfTF81kpwOBxkRIUg7Mp+dHZcA3m1ktCH9DkSzK0d4HQZAW7nIZXOC7LU\nLxwZOXAHzgZHVhnMnT9BhbkAAC1TCxgOGI+g484oysmErLwCxi7eDO8jO5CeHI+e/QbCsI0JLpxw\nx7BhwyAjI4PLly+LuTUsLBJEbX+FREVNVMnIyBDM7T97dJ/srCyooCCfMlOSyXWKFUWHBBIRUc7n\nWHr8zdwwE/eu3JOjLJIFw/CJ7+9JvMvOxOSkCe5/uPUXvdi3mHhFJf8N+F45RYedphKPV0zxMVE0\n/IcOlJwQx4766wgJMh+NgvKed036oUGP+Pfs2QNra2sYGOhjz6Y1mL9yA2RkmuDy7rX4n/UY6Lc3\nR1FOBoJOrIPRT5OhYdIVAEBRr8A8PgZu/1ng6FYcLJ1F/HA4XHD/NxYcYwsw3q6grM8AAKPB9pBX\nb44Qz10ghoHF8ImQkZXDo4vH0FLPAKMmTcEB1/UYNmwYpKSkcO2a6PeDs7A0RBpsBK6srCy0bt0a\nvr6+CHh8F28D/LF5/1/w8zqNkGf3MXWjO8DwEXh4FdSNzWFkZQ8AYMJ9Qa+vljhZU9erq+aw1BFM\n2CNQ0HVwB/8OjlpLMLxiBB5dDRX9djAeMhVZaV9waLE9xi93RTODNnAcZonlm3YiJikFGzZswMuX\nL9kpPRHBRuCqX0QZgavBjvj37t0LKysraKipwOPofsxevhZJURF4/PcJjF6wHlwOF6EX3SCn1hyt\nBk8CADCh90FBN8C1Xswa/QYKt21fcLrbgrm9E5QSDa60DDrbr0JKyHPEP/dGU3UtDJu5Apd2rQGI\nwZzla7F70xr8PGQIeDwebty4Ie4msLCInQY54s/JyYGRkREePnyIyycOQEu7BabMWQT3pZPRe6QD\nzAcMw8c7p5EWGYQuv26ClEwTMG9vgcIfg/vTInCUNOq4NSx1DcW8BuN3CtwBs8Fp1hp5KQkIOLQc\nHcYvhrqxOa7u3wQ+nwebuX9g6a92+KHvQHCV1LF161Y8f/6cHfWLAHbEX780+hH/gQMH0L9/f/AL\nchDw/AkmTZ+Pu6f2Qku3Fcz6D0ViwH0kvX6Azg6rwJWWAfP6OijiCbjWS1ij/53A0TcHt880MPf3\ng5LCoaDZEqZ2yxB8fgdyP8fip6kLERMSiNBnPpi7Yj1OH3JD/359kZ+fj9u3b4tbfRYWsdLgRvx5\neXlo3bo1bt3yxr71yzFu6gy00tPBlT3rMWvXWRSnJeDNqY3o8ttmKDbTBwVeBcUEloz02cAp3x2U\nEArm0RFw+/0GTot2SHh5F9EPPNF91nYkxUbBY8sSzNp5FicO7kZRYQH0TLtj165d8PPzY0f9tYQd\n8dcvjXrEf/jwYfTs2ROx4cFoIieHXpaD4LV3PUbOXQMOrxBvz7ig/ZiF/2/0vUqMvvVi1uh/p3Ba\ntgfXcjqYh4dBCSFo2X0QtEx74e2ZzdAxbo/uVqNxZe96OM5ZBN/7t9G5Q1tkZGSwUbpYGjUNyvAX\nFBTA1dUVixctxNHdrpi3cgO8D2+DSfe+MGxvhrcnN0C/z2hotO0GCrgCig0qMfpyyuJWnaUO4Wi3\nBbf/TDCPjoISQtD6p8mQllNC+NVD6Dv2F+RlZ+C93z+YNm8p9m1xxooVK7BhwwZxq81Sh0hK6MXg\n4GBYWlpCVVUVenp62LhxY41liZIGZfiPHTuGLl264M1TH1j0GwRexmfERwRj8OS5CPHcAWXdNtDt\nPaLE6Me9KZneYY1+o4DTvE2J8X94BEgKQ4fxi5AZ8x5JL25j9IL18PE4iJ69fkRBXh5aqCkhNjYW\njx8/FrfaLHVEXU1DBQcHY+bMmThz5gySk5OhoKCA2bNnl5vfwcEBffr0QXp6Oh4+fIj9+/cLzpNU\nV5ZIqfaRrzqiMlUKCwtJX1+frl6+RCMsTCkm4j1tdRxMsWFvKfLOKXp5cBnxi4uIH+BVcsKTDZPY\nKGESw0pOZCeEUl5qIj3eaE+pEa/J7+pZOuw0lV77+9HY/t3owP59ZGVlJW51GzQSZD6EkJTQi0RE\nsrKyghghRERjx46lLVu21EhWec+7Jv3QYEb8p0+fhomJCfxuX8GEabPw6NwBdLMahSaFmUgMuI9O\nE52A4DugqFfsSL8Rw9E2wb9z/nJFWf+/02c7OvXsC2npJsiKDYOpWTc0Kc5FaGgo/P39xa0yi4g5\ndeoU9PX1cf36dWRnZ2PJkiWl8sTExEBNTa3c69y5c2XKDgkJgZmZmeCzkZERZGVlER4eXmZ+Kysr\n/PXXX+DxeHj//j2ePn2KQYMG1UiWKGkQoRd5PB5cXFywfOFc+Hh5YpTNSLwKeYKhjnPw9q+1MJ+6\nDtJRz0GRz9iFXJaSOf++v4J5cAiqA+ag1UA7BJ/ehOEzluPIqt8wZs5arFgwA/PmzBKEaGQRPfwT\n00UiR2qKu0jkfE19hF4EgF27dmHw4MHYvn07+Hw+nJ2d0a1btxrJEiUNwvB7enpCu3lzPL7xN6bO\nmgefswdgv2I7Qjy2wmT4DChmRpcczrJeAo6CqrjVZZEAOC3bg/vjFDD396HloHnISfiIeJ+zGOww\nD4889mPEOHvEx8Xg5cuXCAoKEhp5sYiGujDY4kZJSQmZmZlC9zIzM6GsXHqGIS8vDwMGDMCmTZsw\nceJEJCYmYsyYMWjWrBlmzZpVLVmiRuKnehiGwaZNm2BtaQHNZs0RF/AAFsMn4rPvBTTr/CO05Dmg\n4H9KpncU1cStLosEwdHtBG4vB9DdPWjTZxiKczOhijw01WwOPXVFvH3lj2kOdti8ebO4VWURMZIQ\nejE4OBjZ2dmwt7cHl8uFjo4Oxo8fj5s3b1ZblqiReMPv5eUFeTlZvHxwGwP6/YjiwkI0l+WBw5WG\nkbEJ6PU11g0DS7lw9M3B+cEOuL8PHYf/gsSXd9Bn0BAE+VyHnb0jvnwMgY+PD96/fy9uVVlESPPm\nzREZGVluur6+PrKzs8u97Ozsyiw3adIkXLt2Db6+vsjNzcWaNWtga2sLRUXFUnmNjY1RVFQEDw8P\nMAyDpKQknD9/XvDfZXVkiRqJPrlLROjevTv6dmmPllpqYOJDMHrKTKS8+gfdRzqCG3C5xOirtRST\n1iwNBSbiCej1VeSZ2eK1524odRuKJzf/xrukHEg11UQuXwonTpwQt5oNCkk+uXv16lXMmzcPWVlZ\nWLNmDRYtWiQy2R4eHnByckJqaioGDx6M48ePQ1W1ZIp51qxZAErcygCAt7c3Vq1ahcjISCgoKGDE\niJSpUgcAACAASURBVBFwc3ODnJxcpbK+RZQndyXa8Ht7e8NpySIYNOViaJ/uMDXvDvr4DN1G/gLZ\n4BvgDp4PjoaBmDRmaWgwofdBIXfxpWVPRPndRAxPEcWcJvj7xm08Co7Bi5cvYWhoKG41GwySbPi/\nRxqF4Sci9OnTB0bqsujZuR3k+fkwUQXa9x0KlagnJV4ZmxuLUWOWhgjzxhsU+RQfSRM5Gam46/sM\nuXJaiExKg7K2Ifbv3y9uFRsMrOGvXxqFr57Hjx8jPTkeKMhBVsx7mOqpQ699V6hE+4Hb71fW6LPU\nCG7nIeDod4GRdCZQlIe+fftChclGZkIULnqeQ0JCgrhVZGGpcyR2xG9lZQWF/C/o29EQ3U1NoCnH\nQVtlHrg9J4Fj0EWMmrI0dIgI9NwDzJcovHgXjiRSwofEVDwNiUYrcwvs2LFD3Co2CNgRf/3y3Y/4\nX7x4gbiIYLRpqY6WakqQz0+BSVMGnK6jWaPPUms4HA44P0wAV6U5upqaQJOfjiZ5qZDj5+LcqRNI\nTU0Vt4osLHWKRBr+TRvWo00zJbSUI+jL82FuoAmuqRW4bXqJWzWW7wQOhwvOj46QVlRBlw4m6NJa\nB2YGzWBu1AJ//vmnuNVjYalTJM7wv3v3DpFvXqJ76xboZtwCXdvoQqpNb3BNB4lbNZbvDA5XGtx+\n0yGvqIgO+lroZNgcxlpKOHP0ILKyssStHgtLnSFxhn/jOmd00VdDF311dDVshiaG5uCYDxe3Wizf\nKRxpGXAHzIFaU2V0aqEEM52m6Kyrhr1794hbtQYBh8Nhr3q6RIlEGf6PHz8i9u0zWLbThkXrZpDX\naw/ODxPYEHksdQqniTy4Vr+jhaY6+rRpjt5tmuPs4b3Iz88Xt2oSDRGxVz1fokKiDP/alcvwcydd\nWHfSQ1PdNuD2nQYOR6JUZPlO4cgpQ2rIEhi20IJ1Rx30M9bE/r27xa0WC0udUGureuvWLbRr1w5t\n2rTB1q1by8wzf/58tGnTBmZmZggMDCxXllT8O0y0MIZGSwNID54LDrdBOA9l+U7gKKpD+uelMNHR\ngL2FMbxPH0RRUZG41WJhETm1Mvx8Ph9z587FrVu3EBISAg8PD4SGhgrluXnzJj58+ICIiAi4u7sL\nfFmUxeIhndBMSxNNhjmBIy1bG9VYWGoER7UFZKyXoIuhFhYOaoe9O7eLWyUWFpFTK8Pv7+8PY2Nj\nGBoaQkZGBhMmTICXl5dQnqtXr8LR0REA8MMPPyAjIwPJycllyjPQUoH86HXgyCrURi0WllrBbdYK\nUgNmoX/7llAIvwU+ny9ulVhYREqtDH98fDz09PQEn3V1dREfH19pnri4uDLlyY5YBa4iG0iFRfzI\nGHZBfjtrTLZog9Pr54pbHRaWMrnpUv4MSkXUahK9qrttvl2NLq/c5gN/Cf62tLSEpaVljXVjYakt\nGj+OxcNHNzFapxA58RFQ0mkjbpVYWPDgwQM8ePAAic9uQE26uEYyamX4dXR0EBsbK/gcGxsLXV3d\nCvPExcVBR0enTHlr166tjTosLCKnj9NRPF9ri3bXNoOZ7AauAhvPmUW8WFpaootMMqRaxuDwmxwA\nQZWW+ZZaTfV0794dERERiIqKQlFREc6fP48RI0YI5RkxYgROnjwJAHj2f+3dZ1gUV9sH8P/S7Qoo\ngqgoikjXYI+KIhYsscUaFVtsUUPsghVFxV6ikth7w64oNhQFAUXpICJKkbr0vrtzvx945ZEASll2\nEc7vuviwM2dm7pnEe8/OaS9fonHjxlBTU6vMZRlGYmRkZOBdtxPi07KRedkWJMiVdkhMLSd4/xLy\nwS448TwUM+2PVOgclUr8cnJyOHDgAAYNGgQ9PT2MHz8eHTt2hKOjIxwdHQEAlpaWaNu2Ldq1a4c5\nc+aw+c6ZH86CZTbYcNMPKcl85N7aChJV7Oc1w1QW9zkYomfH8DAwGh8a6KNhw4r9Aq220zIzTHWy\nb/cu8J+dwzxzfSjrdIb8gIXgybDBhYzkUNInCO44wDMsGnY33+CC61soKyvXnGmZGaa6mbvgD9wN\njMftt5HI/BgIzv00q6gwEkOpsRDe34XAmCRc9o5Axz7DoKysXOHzscTPMGWgoKCAiXMWwyUwBm7v\n4pDz4TU4n2vSDoupBSiTD9H9XQiL5eNxcCxcQ+OxynZtpc7JEj/DlNHcefPxNiYdHuEJ8PmYBGHo\nc3AB96UdFlODUU46OJfdiOJnwPNDEjzC4tBz0C9o3rx5pc7LJsNhmDKqW7curOYuwvNrp6BaPxby\nMgRTmQeAQl3I6PSWdnhMDUP52eAe7EVStgihSbkIScyGb1QKHl60qfS5WY2fYcphwYIFCIjmIyg2\nDSGJufCNTALncx308ZW0Q2NqEBLmgXt4AJkiWbyLSYBveDSCovnoZWGJ1q1bV/r8LPEzTDk0atQI\nU2fOQUIeD4m5QKpsI7zLkAH38jwoOkDa4TE1AImE4J44Ih+y8AsMxJvwWITGZyAgMgmrVq0WyzVY\n4meYcvrzzz/xKuQj3P1C8NovEBn5hBjFFuDcjoHiw6QdHvMDI44DuR0Fx4ng89YPqYpq4OqpIlMk\nhy69+qJDhw5iuQ5L/AxTTqqqqpg0ZRoUmqhD1KA5Xod8RPT7YKRomIJ7chjE/yTtEJkfEBEHcj8F\nys2CX3g0FFsZICwsDE89feAVHIHVq8VT2wdY4meYClm6dCkee76F1xs/KDZWRWYjLQS73UFeB3Nw\nD/aDUj5LO0TmB0JEIK9LoLR4hGXKQLZuI7g+eQxRIw2ottKGgUlnmJiYiO16LPEzTAVoaGjg13Hj\nodKqPfwj4uDr8QwqppZ46+IEztAS3IM9oPQEaYfJ/CDozU1QfBjiGndAWvR7hPNzodmxE168cMdj\nT1/Y2FS+J8/XWOJnmApavnw5rru4IiU1FW26WeDhTSeo6veAv/sjwNAS3P3doKxkaYfJVHOc313Q\nJx9kdhiMD65OqGtojujwYLwKeg+dzj2g1VYbPXr0EOs1WeJnmApq06YNhg0bBhUtXTg5XUHzth3w\nPjYFMnJyCH8fBp5ef3D3d4GyU6UdKlNNcYEPQGHuEPScBn+nA2gzZCbunT2M9j8PQ3xcLK67PIGt\nra3Yr8sSP8NUwqpVq3Dm0lW01m6PvDqqCHr5GPWNBoAf+grxuTLgafcoqPnnpEs7VKaa4UKegoIe\nA+YL4H95PzR7DoOby20Y9h6C86ePw7BHfzRt2qxKFqRiiZ9hKkFXVxf9+vVDnWatcfnMMfSb/Adu\n/bMdHX61xnvnY8hUbg+eVmdwLntAuZnSDpepJriw5yC/u+ANtEbIvbOoq6qBVKqL5M+RSCMlNG/R\nEqcvOsHW1rbMKx2WB0v8DFNJNjY2cDxyDBbDx+DRo0doa9QVbrcvQ3f0Qvif3QJB217gtdAraPDN\ny5Z2uIyUce89QG9uQmbQX4h664bsxGho9B0PlxN7MGD6Xzh35AA6dusLBUVFDB48uEpiYImfYSrJ\nyMgIXbt2hUChATyePYJ2DwtE+L9CclY+NLoOhv+ZLSCjYeA1a1+Q/PNZ8q+tuA+eoNdXITPQGvzY\nKES9uAn9yatwy3EbulqOw+0b1zBg2Cgc+ucobGxsqqS2D7DEzzBiYWtri91792HqPGsc3mmPX/5Y\ni1uH7NH0p4FQUlZDyLW/gS6/gte0LTiXvSz510JchDfI+zJkBv6J7Hwhgq/sgcGkFfB/6Yrc7Eyo\n63fF84fOaNmxE7KzszFy5Mgqi4UlfoYRA1NTUxgYGCA+PRd5OTn48CkSBr0H4Y7jFuiOXoTsxGhE\nuV0Fr+t48FRbg3uwD5SfI+2wGQnhPniBvC5CxuJPCBUawO+kHdoNsYJQvi5cL/yDUYs34KDDRlgt\nWILtO3bC1tYWMlW4whtL/AwjJra2tnBwcMD8FetxeMcm9BplhaTojwhwfwjDKTaIcr+FpGAv8LpN\nBE+lVUGDL6v513jcB0+Q9yXIDLQGNWoO/3Nb0dSgB5oZm+HqnrUwmzAHgQEByEhLRT1VDSQlJWHc\nuHFVGhNL/AwjJr169YKWlhZ8g9/BsHNXXD71L8ZYb8L9E3uQk5cPw8mrEXJ1HzLjPhYk/6ZtCrp6\n5mVJO3SminDhniDvK5AZ+BfQWAPvbjpCVkEJ2oOm4pnTMdRp0AhGZkNxaNsGLFy9EZvt7WFjYwNZ\nWdkqjYslfoYRozVr1sDe3h6zrFfh+rmTIIU66DVyCq7tXY8GLdpBZ8Rc+J2yQ35masFrn+Y6BYO8\nWFfPGod79xz02gkyA63Ba6KBaPdbSPsUDP0JSxHzPhjezlfwy4I1uHDsEDoad0ZmPofIyEhMmjSp\nymNjiZ9hxMjMzAxqamp48tQNY6fOwiGHjeg54jcAgPvNM1Az6g0NUwv4n9oETpgPnulY8DT0C5I/\nG+RVY3DBT0C+tyAzaAl4TTSQFOyFT8+cYDRtLUQc4LRnDYb+vhxZuXm4duY45i1bAzs7O6xatQpy\nclW/MCJL/AwjRjweD+vWrcOmTZswdtpshAX5w8fzBUYv3oAX108j9kMItPpPQB0VdQRf3g0QgffT\nKPBamYBz3s7m9qkBuAAXUOADyAxeBl4jNWR8Dkew014Y/WaDOk2a4d6xnWjV0QT6PQfgkMNGjJ06\nCxGR0QgNDcXUqVMlEiNL/AwjZubm5mjSpAlu3rqNBSvXY7/9GtRvooohM5bgyi5bCPLzoDtmEfLS\nkxHucgo8Hg8ynUaAp9O7IPmzWT1/SEQE7s0N0Ds3yAxZBl4DVeSl8eF3ahM6/DIfDVvqIPjlE0T4\nv4LlrKV47eGGsCB/jJ85Dxs3bsTKlSuhoKAgkVhZ4mcYMePxeFi7di3s7OzQw8wCahqauHr2GIz6\nDoG6ti7uH98NWXkFGE6xQWKAB2I8nQEAMgYDwTMcAu7eDlBKtJTvgikPIg7keQEU5VeQ9Os1gTA3\nG74nN0Czx1A0M+yF9ORE3Dq8BWP+tIOsnAL2b16D+SvWwdfXDwEBAZgxY4bE4mWJn2GqwKBBg1C/\nfn1cu3YNC1dtxBnHfeAnxGPY7yvx/o0HQjxdoVCvEYyt1iHi4TnwQwsWa5fp0Ac807EFvX3i30v5\nLpiyIE4IcjsOSomGzOAl4NVpCE4khP/ZLWjYsgNa9RkDjuNwbe86dBk8Bi11jeB05iiaqmvgZ/PB\n2LBhA1auXAlFRUUJBl1NVKNQGEYsbt++TYaGhiQSiejwjk20eflCIiL6FPSGHKwGUho/gYiIUj8G\n0TO7yZQeHVZ4LBflT8Jz1sRF+koldqZsuPxcEj7YS8IHe4kT5BZs4zgKvLyb3p7YQCKhkIiInjkd\npyOrZpJQKKDE+Fga3l2PIj+8Jy8vL9LU1KTc3NwKx1CR3Mlq/AxTRSwtLaGoqIirV69iytw/8cbr\nBfxee6JVRxOYDhqNq3vWghOJ0Kh1R3QYOR++J+2QkxwHAOBpGkBmwB/gXpwCF+Yu5TthSkI56eDu\n7wRPqSFk+s8HT66gxh7x6Dyy4iNhMHE5ZGRlEf0uAB43zmKM9SbIysrhkMNGjBg/BS3baEuntg9U\nn2p2NQqFYcTm9u3bZGBgQCKRiB7duU7TR/QngUBAQqGAjq6eRU8vHy0sG+V+m9y3/055GamF27iU\nzyS8vJJEb24Rx3HSuAWmBFxaPAmv2JDo9bUi/12iX96lFw6zKC89mYiIcrIyaPecERTo/pCIiHw8\nX9C4fqaUnZVF3t7e1KJFC8rJyalULBXJnazGzzBVyNLSEnXr1oWTkxP6DRmBJiqquHbmGGRl5TDG\nehNe3r6AyOC3AFDYCOh7cgNE+bkAAF5jdchYrgRF+YJenARxQmneDgOAEj6Ac94Onv4AyHQeWTiD\nZkKAOyIeX4DJjI1QaNAERIQ7jtvQ1qgr9HqYQygQYK+dDeavXI86desW9uRRUlKSwk1UE9UoFIYR\nq7t375K+vj6JRCL69CGMhnfXo8T4WCIiCvF6SjtnD6Ws9IJaPsdxFHR5D705uoZEgvzCc3D5OSR8\nsJ+E93cRl5cllftgiEQfvEpse0l+71vQThPzvnDbqwfX6MCicZSXW1CjP3/0IC2ZMZ44jiMvLy+x\n1PaJWI2fYaqlwYMHo379+rhy5QpatWmHEeOn4OC2DQCADl36oGO3frj59yYQEXg8HjqM+gMy8ooI\nurQTxIkAADx5Jcj0nwdeQzVwd7ayvv4SRkTgfO+AXl2BzCBr8FoaFe7L+ByOgPMOMJi4HA00tAEA\n8Z/e4+HpAxi3dCsUFJWQEBuDc/8ewJ9r7AsH+a1evVo6tf3/v6FqoRqFwjBi5+zsTHp6eiQUCikn\nO4vGm3cl7xdPiYhIkJ9Hh5f8Ru43zxWWF+bnkc+/qynYaX+xd/ui4CckPP8XcZ+DJXoPtRUnyCWR\n678kvLmJuKyUIvsy4yPJbfMUSghwL9yWm51F+xaMoTePbhVus/1jBh0/sIOIiNzd3alVq1aV6snz\ntYrkTlbjZxgJGDRoEBo2bIhLly5BqU5dLLKxw1671cjLy4WcvAJ+XboFbleOISrUHwAKB3hlxH5A\n+L0TKPj3XUBG1wwyfWeDe/pvwZwwX+1jxIsy+eDuOgA8XsHArLqNC/flJMfh7bG10B5shab6PQrK\nE+HOP9ugqWMAk/7DAADuTx7gw7sQTJy1AACwbt062NraSr4nz9fE8pUjBtUoFIapEg8ePCAdHR0S\nCAREVFALPLZ/e+H+oJdPCt73p/2vVpmfmUYv9/xB4Q/OFjsflxZPwmvrSPTsaGEfckZ8uNgQEl5Y\nQiL/+8V+deWmJtGLbTMpyuNOke2vXK7R/oW/Ul5ONhHR/37dPXclIqJnz55RmzZtKD8/n8SlIrmT\n1fgZRkLMzc2hrq6OM2fOAAAW2tjh+rkTiIwoGKHbsZsZ9HsOwNW9a8FxHABAvl5DdJpphwQ/N3x0\nvVzkfLyGzSAzdBVAHLg720AZiZK9oRqKiAPn5wzO9V/I/Dy9YCqNr9a+zUtPxpujNmjR3RKa3S0L\nt38OD8HDMwcwfrkDFJTqAABOH94LPePOMO3VF0BBbX/NmjWQl5eX7E39l9i+diqpGoXCMFXmS40v\nLy+PiIgun/yXFk8dU1ijFAoE9O/K6eR66d8ix+WmJZH79tn06dm1YufkOI5EQY8K3vt/fF31N1GD\ncbmZBb2nbm8hLpNfbH9uejJ57JxLEY8vFNmelZ5Ku+eMoIDnDwq3hYcG0S89DSgpPo6IiB4/fkzt\n2rUr/MUnLhXJnazGzzAS1Lt3b7Rv3x7Hjx8HAIyaPB3ZWZm4f6OgNi8rJ4dxS7fC2/kKwnz+N2JX\nsaEKOs3ajOiXdxDpdr3IOXk8HmQ69oeM+QJw3lfAvTwHEgokd1M1BMWHgbu5qeCX1JCl4NVTLrI/\nPyMFb47YQM3EDFr9xhdu/zIPj27XvtDvNQAAIBKJsH3NMsxavBIqzdRARLCxscH69eslMt/+d4n1\nq6cSqlEoDFOlPD09SVNTs7APd0iAL4382YhS+EmFZT4G+tC2aRbEj40qcmxOSgK5O8ymj66XSzw3\nl5tFoieHSXh9A3EpMVV2DzUJJxKQ6PV1Ep5fQlzk2xLL5KYnk8euefTh4bli+55c/JeOrJxBwq9q\n8k5njtIfk38hkUhERES3bt0iAwMDEv7/3D3iVJHcWW2yLUv8TG0yfPhw2rNnT+Hnv7euJ7tlC4qU\n8bh9ng7+ObFwANAXualJ5LFjDn14VPR1wxccx5Eo9BkJz1kXNEz+f/JhiuPS4kh4y56E9/cQl5Va\nYpmclHhy3/57ic872NOVdsy0pHR+YuG2+M/RNLy7Hn18/46IiEQiERkbG9O1a8Vf04kDS/wM84N4\n+/YtqampUXp6OhERZWdl0USL7vTy6aPCMhzH0ZXdtnRll23xXiX/XwN9f+9kqXP4cOkJJLzrQMI7\n24hLi6+6m/kBcSIRifzvk/DcnyQKfEgcV/KXY1ZiDL3YOoM+uRVP2gmRH2jb1AEUFer/v/NyHK1e\nYFWkt9bFixepS5cuVTbXEkv8DPMDmTRpEm3cuLHws/eLpzSunyllZWYUbsvLzaHDS34jt6snih2f\nl5FKXvsWU8i1v4kTlfwKgeNEJApwKUhwfs7EicTbsPgj4lJiCmr5ztu/+YWYGfeJnttPo2hP52L7\nsjPTae/8UeTz8EaR7Y/v3qAplr0pL6+ge61AICAdHR1ycXER7018pSK5k/f/B0odj8djA1GYWiU8\nPBzdunVDaGgoVFRUAADbbKyhVKcuFttuLiyXlhSPf1dYYfjc1ejQpXeRcwhzs+F3ehMU6jeG3q/W\nkJEruZsgZSSC8zgH5KRBpudv4DVtW3U3Vk2RIBfkexcU9hy8TiPA69AHPF7J/VvSPgXD/4w92lnO\nQPNO/Yrs40QinNvyF5Sba8Jy1rLC7anJfEz/pT827TsK/U6mAIDjx4/j5MmTePLkSZEuoeJUkdzJ\nEj/DSNH8+fNRr149bN++HQCQnpqC6SP6Y/0eRxh27lpYLirUH+ft/4KV3WE0a6Vd5BwiQT4CLziA\nE+TDYPJKyCnWLfFaRASK8AZ5XwavhT54nUcWGYlaUxER8Ok1OO/L4KnpgGc65pv3nRj0EiFXD0Dv\nV2uodPip2P57x3Yh/tN7/LZmH2S/6qFjt3Q+lFWbYcHK9QCA3Nxc6Ojo4MKFC+jZs6fY7+uLCuVO\nsf3eqKRqFArDSMznz59JWVmZoqL+13vn6f079NvgXpSTXXQWzjePb9HuOSMoMy3lv6chkVBIwVf3\nk+fehZSbmlRs/9e4vGwSeTsVvP55e5s4QZ54bqYa4uLfk/DOVhJeX09cbOh3y0d7OpPb5qmUFvWu\nxP1e967QvgWjKTsjrcj254/u0cSBPYr8N9uxYwf98ssvlbuBMqhI7mQ1foaRslWrVoHP5+Off/4p\n3LZxyTyoNFUrrD1+8eDUfkQGv8XUDQchr1B0rhciQuSzq4j2uA3jaWtRX73NN69LGYngXjkBiR/A\nMxwCns7P4MlKeUSpmFDqZ3A+NwD+R/BMfgFPuzt4MqUPWyJOhPB7J5EY9BLGVutRV1WjWJlwX09c\n3bMWM+yPQEW9ZeH2jPQ0TB/RH7YOB2DStWDOntTUVOjo6MDV1RV6enriv8GvsFc9DPMDSklJgY6O\nDtzc3KCrqwsASEtJxoxfzLFu92EY/dStsCzHcbiyywY8HjDGejNkSkhm8X5ueHfTER3HLoaqbpfv\nXp+SPoF7ewNIiQHP0BK8dj3Ak1MQ3w1KEPEjwfndBeLDwNO3AK9j/+/eizAvG0EXd0KYlwPDSSsh\nX69hsTKJURE4vmYOxi3dAi2Doq9/tqxcDKU6dWG9bkvhttWrVyM+Ph5Hjx4Vz419g0Rf9fD5fBow\nYAC1b9+eLCwsKCWl+M9PIqLWrVuToaEhmZiYUJcuXUo9XyVCYZgf3vbt22nkyJFFtj17cJcmDexZ\n7JVPfl4u/btyOrmc2l/q+VI/BtNz+2kU8fhCmbsRcvHvSfhgHwnP/0UinxvEZad9/6BqgONEBYvT\nu+wl4cVlJApwIS6/bJPWZSfH0cs9f1CQ074iC998LY2fQLtmD6M3j28V2/fswV2aOLAHZWVmFm6L\niYkhZWVlioyMrNgNlVNFcmeFa/zLly+Hqqoqli9fjm3btiElJQVbt24tVq5NmzZ4/fo1lJWVSzjL\n/7AaP1Ob5ebmQldXF2fOnMHPP/9cuH3T8j/QqHETLFxtV6R8Vnoqjqycjp4jJqPL4LElnjMvnQ//\nM1ug2EgVHccuhpxinTLFQqmxoKCHoI+vwdM0BK99L6C5Tqk9YKSFcjNA4S9BIU8BeUXwdPuB17Yb\neKX0bPovfugrBF3ZC62+Y6HZa0SJvW5yszJxzHY2DH8ehN5jrIrsS03mY8Yv5li/x7HIr7I5c+ag\nUaNGcHBwqNT9lZVEa/wdOnSguLiCyYdiY2OpQ4cOJZbT0tKipKRvNzb9/5dPRUNhmBrh9OnT1L17\n9yI19LSUZBpr1rlw0Zav8T9H0fYZgwsX8i6JSJBPQVf2kseueZQR+7Fc8XA56SQKeEDCa+tIeGVV\nwa+A5CipLvrO5eeSKNyz4JfJmYUkenqEuPj35YqJE4ko/MFZcrOfSikfAkotJ8jPp+Nr5tJtx63F\nzs9xHK1ZOJMOOWwssj0oKIhUVVWJzy8+wVtVqUjurHCNv0mTJkhJSfny5QFlZeXCz19r27YtGjVq\nBFlZWcyZMwezZ88u8Xysxs/UdhzH4aeffoKtrS3GjBlTuP3Vi6fYZvsXjl57iIaNmxQ5JjYiFKfX\n/4GxS+zR1qj09/mxrx/hvfMxaA+aCnXTgeXqU05EAP9TQVfQjz6AjCx4rUzA0+gINGsHnnzVLShC\nREBmEijaHxTtD8S/L7imdlfwWnUCT758SxfmpScj+MoecMJ86E9cAcUGTUosx4lEcNqzBiKBAOOW\nbYWMrGyR/S43nXD+yN84fPkuFBX/F8Pw4cNhZmaGJUuWlP9mK0jsjbsWFhaIi4srtn3z5s2YNm1a\nkUSvrKyM5OTkYmVjY2Ohrq6OxMREWFhYYP/+/ejdu3excl/WofzCzMwMZmZm5boZhvnRPXz4EPPm\nzUNQUFCROdv3269BclIi1u48VCxpfwx4jUvbV2Lymr1o0a70HiRZCVEIOO+Aes1aocPIeZCvU7/c\n8RERkBwJivQFxYUC/EhAWRM81TaAckvwlFsCjZqDJ1v+GSiJCMhOBdJiQcnRoMRwIOEDAAKvhQF4\nmgaAuh54pYxT+J7EoJcIvfY3NLoOhlb/CcWS+ddx3Dy4GSnxMZhsu6dY76m4mGjMHTcE2/89h/Z6\nhoXbHz9+jFmzZiE4OLhKV9dydXWFq6tr4ecNGzZIrlePrq4uXF1d0bx5c8TGxqJfv34ICQn55jEb\nNmxA/fr1S/w2ZDV+hikwePBgDB06FAsXLizclpebgzljh2DynEWwGD662DEhnq645bgFU9f9Ce5E\nGgAAHQRJREFUDbXW7Uo9t0iQh/d3jyMp2BO6oxZApYNppWIlYR6Q8AHE/wQkR4GSo4GMBECpAVBf\nBby6TQCFuoC8UsGfjAzAiQr+RAIgNwOUkwHkpAEZiYCcYsEXR5MWQLO24DXVLjhPJUa9CvOy8f7u\nMSSHvYXeuL/QWKv0L0ciwr3juxAdGoCp6/+GYp2iXzJCoRDWVmPRq99ATJg5v3A7x3EwNTXFypUr\nMW7cuArHWhES7c65fPlyqKioYMWKFdi6dStSU1OLNe5mZ2dDJBKhQYMGyMrKwsCBA7Fu3ToMHDhQ\nLMEzTE0UEBCA/v37IyQkpEiniLAgfyybPQmHLt2FeouWxY7ze3YPLif2YNqGQ2ja8tt9+JPDfRHi\ntA9NtI3RfuhMyCnVE1v8xIkKau5ZyaCsZCA/BxDkAoI8gLiC5C8jC8jKA0oNwFNqANRpCNRvWuHa\nfGmSQrwReuMQlLWN0X7YbMgpffv8j887ItTrKazsDqNO/eLdOk8d3I233h7YcfRCka60p06dwqFD\nh+Du7l5lUzOURuLdOc3NzYt154yJiSFLS0siIgoPDydjY2MyNjYmfX19sre3L/V8lQiFYWqcuXPn\n0uLFi4ttv3DsEM2fMIwEpazZ+ubxLdoxcwglRn+/IVeQm0XBVw+Q2+apFOvzWKqNtuKWl55MAecd\n6IXDLOKHvSnTMY8vONK+BWMoI6XkhtkAH28a+bMRJcbHFtmelZVFmpqa9OLFi0rHXREVyZ1sABfD\nVEOJiYnQ09PD8+fP0aFDh8LtHMdh1dyp0NbVw+9/rS7x2NcPr8P1wr+w2ngIKhqtvnuttMgQvLtx\nGLKKStAZMQ/1m7cW231IGicUIOrFTUQ+c4K6qQXamE+ErMK3G4CJCE/OOyLo5WNYbTyE+o1VipXJ\nzEjH7NEDsWDlevxsPrjIPjs7O/j5+eHy5cvFjpMENnKXYWqQ7du3w83NDTdv3iyyPYWfhNljBmHF\n5p3o0susxGNfP7iOJxccMWXt/m++8/+COBFiPO8h4tF5qOiaoo35JNRp0kwctyERxHFIDPTA+3sn\nUF+tNdoNmY66TVt8/zgiPDp7EKHezzBtwyHUb1x8vBERYb31HDRuolJkdC4AREVFwcTEBK9evUKb\nNt9+vVZVWOJnmBokLy8Penp6cHR0xIABA4rs83n5HJuXL8Q/Tveh0rTkBO337B7uH9+NSTa7v9nb\n52uCnExEul1DzEtnNO/UD637joZiw+I14OriS8L/+PgCeDKy0B5iBeV2JmU6luM4uJzYgw9+Xpi2\n4RDqNSq5a+fVs8fg7HQBB87fLNJ1EwAmTZoEbW1t2NnZlXisJLDEzzA1zNWrV7F27Vq8efOmSPdO\nADi2zwH+Pt7YfuR8qQt4h3i64ubBzRi/wgGt9TqV+bp5GSn45HoFcW8eQ1WvG1r1HoX6atXnFZBI\nkIcEPzdEul2HjJw82phPhIpulzI3rIqEQlw/sAEp8TGYtHo36jZoVGK5EP+3WDl3Cv4+fwstWmkV\n2ff8+XNMnDgRISEhqFdPfI3j5cUSP8PUMESEgQMHYtiwYVi8eHGRfSKRCMtnT4KOvhHmLLEp9Rzh\nvp5w2mWLob+vgH6vAaWWK4kgKx0xXs6I9riDemqtof6TOZrq94BsFQ7a+pZsfiw+e91H7OsHaNii\nPTR7DoeyTudy9aTJz83Bpe0rwOPJ4NdlW6GgWHIbQEZaKmaPGYR5y9ei78ChRfaJRCJ07doVS5Ys\nwaRJkyp1T5XFEj/D1EDBwcHo06cPAgICoKamVmRfagofc8YMxh+rN6L3gCGlniM2IhTnNv+F7sMn\noueIyeXucigS5CMp2BOxrx4iPfodmhn0gqpedzTRNoKsfNXO5JmbmoAE/xeI932G3NRENDcxQ4vu\nliVOnfw9GSlJuLB1KVQ0WuOXBWuKLKTyNY7jYLPAChotWxebJwkAjh49imPHjuH58+cS7775Xyzx\nM0wNtWzZMvD5fBw7dqzYvmC/N1g1byoOnL0BTa3Sl1RMS4rDGbvF0NLvjMEzl0C2AqNrASA3LQnx\nvs+QFOyFzNgINNE2RJO2RmjUShf11duUuvxjWeVnpiEtMgQp798iJdwXeRmpaKrfHWpGvdG4rVGp\nI26/JzYiFOe3LEEn8xEwGzf7mwn72D4HvPXywM5jFyGvUPSLLSUlBR07dsTt27dhalq5AXDiwBI/\nw9RQ6enp6NixI5ycnNC9e/di+29cOIXr507g7/M3Ubde6VMx5GZl4tKOleBEIvy6xL7UBs2yEmSl\ng//OB6kfA5EeGYJsfizqqbVCXRUN1FFRRx3l5pCv2wBydepBTqkeeDKyIJEQHCcCl5+HvIxk5KXz\nkZfGR1ZCJDJjP4IT5KGBZns00TaCcjsTNNBoC55MxZL9F8Gerrh5cBOG/r4CBr0svlnW7YEz9m9Z\ng8OXnKGs2rTY/vnz54OIcOjQoUrFJC4s8TNMDXb27Fns3r0bnp6ekP1PrZeIsHPdcqTwE2G3/1iJ\nC7R8wYlEeHTuEALc7mP8CgdoaHcUW4zCvGxkxX1CNj8WOfxY5CTHQZidAWFeNoS5WSBOBJ6sPGRk\nZCEjrwDFhspQaKACxYbKqNesJeqra0GxUVOxvT4RiYRwvfAP3j65jQkrtqNFe/1vlv/4/h0WTx2N\nbY5noGtYvHeQt7c3hg8fjuDgYDRpUrkvTXFhiZ9hajAiQt++fTFhwgTMnz+/2H5Bfj6WzpoIfZOf\nSh3c9bUgj0e4dXgLzCfPx08Wo6T+rlrcMpKTcGXXasjIyWHMn3YlDsz6WlpKMhZMHIHJcxZiyKjx\nxfaLRCJ0794df/zxB6ZNm1ZVYZcbS/wMU8MFBQWhb9++8PX1hYZG8cbN1BQ+5o8fBqsFSzDwl5IX\naPlaYlQEruy2QeNmGhgx3xb1GjauirAl7v0bD1zfvwE/DRqNvmNnfrddID8/D8tmTkQHQ2PMX76u\nxDKHDx/GuXPn8PTp02r1JckSP8PUAra2tggLC8PFixdL3B8RFoo/p43BpgPHYNi563fPJxTk49HZ\nQwh4fh+/LFiDdp16iDtkicnNzoTLib14/9YDI/9Y9801Cr4gItivWIS83Bys3/NPia/JEhISYGBg\ngEePHsHQ0LCEs0gPS/wMUwvk5OTA0NAQ+/btg6WlZYllvJ67YsvKRdhz0gmttduX6bwf/Lxw/cBG\naOl3xiAr60o3/Epa+NuXuHlwM9oad8Mgqz+h9I1G7q+d+HsnXj59hD0nr0CpTsmzd06aNAmampoS\nW06xPCQ6O6e4VaNQGKbau3//PmlpaVFWVlapZZyvXaRx/bsUm03yW3Kzs+je8d20bZoFvX5wnUQi\nkTjCrVIp8Z/pwrbltGv2MArzcS/XsXevXqDx5l0pKSG+1DK3b98mbW3tbz5raapI7mQ1fob5QU2a\nNAktWrTA9u3bSy1z9p/9eHz3Bvaevor6DYrPL1+a2A8huO24FSKhABZTFkLbpHgXUmnLy8mG+43T\n8LxzCd2HTUCvkVMgX8oo3JK4PXTG7g2rsPvkZbRuW/KvooyMDBgYGOD48ePo37+/uEIXK/aqh2Fq\nkYSEBBgZGeHGjRvo1q1biWWICHs32SDiXQi2/XOm1FcZpR0b5PEIj84cRKOmzdF/0jy07CD999t5\nOVnwunsZHrfOoa1RFwyYshCNmzYv1zlee7jBbul8bPvnLDroG5VabuHChcjKyipx4Fx1wRI/w9Qy\nFy9exMaNG+Hj41PqOq8cx2Hrqj/BT4yH/aGTxWaY/B6RUAifRzfw/OpJNFBWRc8Rk6Hb1azCI2gr\nKi0pHq8fXMere1fQ1qQb+oydgWYtSx+pXJoQ/7dYMec3bNjzL0y6lt6Q7eHhgdGjRyMwMLDISmjV\nDUv8DFPLEBHGjBmDjh07YvPmzaWWEwqF2Lz8D+RkZWHj/iNQUCj/JGsikRChXk/hfvMsMviJMOo7\nBEZ9hnx3mcfKEAoECH/7Eq8fXEVksC8Mfh6E7sPGQ7WFVoXOFxLgi1Vzp2Dpxu3o1X9QqeVycnLQ\nqVMn2NnZ4ddff61g9JLBEj/D1EJxcXEwNjbG3bt38dNPP5VaTigQYMNfc0FEWLfrcLE5aMrjc3gI\n/N3uwd/tPuo1aoIOXfqirVEXaOoYQk6+cnP1ZKWl4IOfF0K8XPH+zUs0bdkGncxHwPDnQVBQqlPh\n8wb5+mD1/GlYunF7sVW0/sva2hpxcXE4f/58ha8nKSzxM0wtdebMGTg4OMDb27vUVz5AwejeDX/N\nRX5+Hjbu/bdc7/xLwolE+BT0BmFv3BHh/wr8mE/Q0O6IZq210VSzDZpqtkH9JiqoU78RlOo3gIyM\nLDiRCCKhAHk5WUhPikdqYixSE2LxOTwYMWGByMlIQ6uOJujQtS86dOmNBk1UKxUjAAS+eQWbP6Zj\n+aZd6Nnv23P1uLq6YvLkyfDz84OKSvVdhOYLlvgZppYiIowdOxZt27b9Zi8foOC1j4PNX4iNicSW\nQ6fK1dvne3Iy0xH9LgCJUR+QGB2BxOgIZKelIiczDblZmSDiwOPJQFZeHvKKSmik2hyNmjZH46bq\naN5GB5rtDaDSovU35xoqry8Nuau27kO33v2+WTYjIwNGRkY4cOAAhg4d+s2y1QVL/AxTiyUlJcHE\nxASnTp36btdDjuOw334NAny84fDvOTRRqXyt+ns4jgOIJNoo/ODWVRzcth7rdjl+syH3i99//x0c\nx+HIkSMSiE48WOJnmFru/v37mD17Nnx9fb87eyQR4cSBHXC56YTNf59AWx1dCUVZ9YgIF44exPVz\nJ7DV8QzatO/w3WOuXbuGJUuW4O3bt2jYUHy/gqoaS/wMw2Dx4sWIi4vDhQsXyjSZmMtNJxzcth4r\n7fege19zCURYtfLz87B/8xoEvn2NrY6n0az591fqioyMRJcuXXDz5s1Sx0RUVxXJneJ7kcYwTLWw\ndetWBAYG4sSJE2UqP3BEwYRu29csxaUTjj90BSwxPhZ/Th2LFH4S9p+9XqakLxQK8dtvv8Ha2vqH\nS/oVxWr8DFMDBQYGwszMDI8fPy7zbJKxMVFYt3g2mjZXx4pNu9Cw8Y81SZuv90tsXDIPo3+bgYmz\nFpS5gXj9+vV48eIF7t+/L9ZGZUlhr3oYhil08uRJbNmyBd7e3mjQoEGZjhHk5+OfXfZ45nIHtjv+\nLtO0ztImyM/HyYO7cMfpPFZt2YuuP5uV+VhXV1dMnDgRPj4+UFdXr7ogqxBL/AzDFDFr1izk5OTg\nzJkz5Vo8xP3JA2xfuxSDR47DtPnWle7vX1XCQ4Ngv3IR1NRbYOnGHSWukVua6OhodO3aFSdPnoSF\nxbf79ldn7B0/wzBF7N+/HwEBAXB0dCzXcT37WeDotYdIiI3BjF/M8erF0yqKsGJysrNxZM82/DV9\nHMZOmYXNf58oV9LPy8vD2LFjsWjRoh866VcUq/EzTA0XFhaGn3/+GVeuXEHv3r3Lfbzns8fYtWEl\n9Iw6YebiFdDUKv/EaOJCRHh05xocd26GsWl3/L7EpkwNuP81d+5cJCQkwMnJqVoto1gR7FUPwzAl\ncnFxwbRp0+Dh4QEtLa1yH5+TnQ2n00dw6YQj+lhYYup86wol3IriOA7uT1xw9p/9EAmFWGhjV+H2\nh6NHj2LHjh3w9PT8ofrrl4YlfoZhSrV3714cO3YML168QP36ZVuW8L/SU1Nw/uhB3Lp0Bt37mmPU\nRCvomfxUZbXmvNwcuN67jfNH/oaCoiImz1mEn80HQ7aCo3+fPHmC8ePH49mzZ9DVrRkD1ljiZxim\nVESE2bNng8/nw8nJqVJdF9NTU+B87SJunD+J+g0awmL4GPQyHwSNlq0rHSfHcfB/7YX7Ny7D7aEz\ndA2MMW76HJj27FupL5jg4GCYmZnh/Pnz1XY1rYpgiZ9hmG/Kz8/HwIEDCxdrr2xNneM4vHJ/Btd7\nt+Dh+gCNlVXRtbcZOugbQ0fPEBqttL77BZOdlYnojx8Q8MYbbzzd4ev9Ek2bq8Ni+GiYDxuFpmqV\n72aZkJCA7t27Y+3atbCysqr0+aoTlvgZhvmutLQ09OnTB+PHj8fq1avFdl6O4xDs64PXHm4ICw7A\nuyB/ZKSlQqVpMzRWUUXjJiqQk5eHID8f+fl5yM7MQEzUJ2RnZkCjpRY6GnVCp269YNK1h1iS/RdZ\nWVkwNzeHhYUF7OzsxHbe6oIlfoZhyuTz58/o1asXbG1tMXPmzCq7TkZ6GpKTEpDK5yMlOQkioQDy\n8opQUFREnbr1oNGqNVSaqlXZiNnc3FyMGDEC6urqOHHixA/fg6ckLPEzDFNm7969Q9++fXHw4EGM\nGjVK2uGInUAgwNixY6GoqIhz585BTk5O2iFViYrkzpr5JBiG+S4dHR3cuXMHlpaW4DgOY8aMkXZI\nYiMSiTBlyhSIRCKcOXOmxib9imJPg2Fqsc6dO8PZ2RlDhgwBx3HVfmHxshAIBJg+fToSExNx584d\nKFRibeGaiiV+hqnlOnXqhPv372Pw4MEQiUSYMGGCtEOqsJycHIwbNw5EhFu3bkFJSUnaIVVLbK4e\nhmFgbGwMFxcXLF26FLt37/4h29vS09MxZMgQNGzYENeuXUPdutVzYrnqgCV+hmEAAIaGhnB3d8fR\no0exePFiiEQiaYdUZlFRUTAzM4O+vj5Onz4NeXl5aYdUrbHEzzBMoVatWuH58+cIDAzE6NGjkZGR\nIe2QvsvNzQ3dunXDxIkTceDAgR9yMRVJY0+IYZgiGjduDGdnZzRr1gympqbw9fWVdkglIiIcOnQI\nY8eOxfHjx7Fs2bIa2U+/KrB+/AzDlOrMmTOwtrbGpk2b8Pvvv1ebxMrn87FgwQL4+/vjxo0baNeu\nnbRDkhq2EAvDMGL122+/wc3NDX///TdGjx6NmJgYaYcEZ2dnGBsbQ11dHa9evarVSb+iWOJnGOab\ndHV14eXlBUNDQ5iYmGDfvn1Safj9/PkzrKysMG/ePJw+fRq7d+9GnTp1JB5HTVDhxH/58mXo6+tD\nVlYWPj4+pZa7d+8edHV10b59e2zbtq2il2MYRoqUlJSwceNGuLm54erVq+jSpQvu3LkjkdezWVlZ\nWL9+PQwNDaGmpgY/Pz/069evyq9bo1EFBQcHU2hoKJmZmdHr169LLCMUCklbW5siIiIoPz+fjI2N\nKSgoqMSylQilxnny5Im0Q6g22LP4n+ryLDiOo0uXLpGBgQGZmprSzZs3ieM4sV8nISGBNm3aROrq\n6jRhwgSKiIgo3FddnkV1UJHcWeEav66uLnR0dL5ZxsvLC+3atYOWlhbk5eUxYcIE3Lhxo6KXrDVc\nXV2lHUK1wZ7F/1SXZ8Hj8fDrr7/C19cXq1atwrp166CtrY21a9fi3bt3lTq3QCDAkydPYGVlBR0d\nHURERMDZ2Rnnz58vsmRkdXkWP6oqnbIhJiYGLVu2LPysqakJT0/PqrwkwzASIiMjg9GjR2PUqFF4\n8+YNTp8+jT59+qB58+bo06cPevXqhZ49e6JFixal9q3PyMhAcHAw/P394eLiAhcXF7Rv3x5jx47F\nzp07oaKiIuG7qh2+mfgtLCwQFxdXbLu9vT2GDx/+3ZNXl65fDMNUHR6Ph86dO6Nz587Yvn07vLy8\n8OLFC5w7dw6LFi1CSkoK1NTUoKGhASUlJeTk5CA3NxcpKSng8/nQ1dWFvr4+Bg4ciD179kBdXXyL\nsDClqOz7pW+94/fw8KBBgwYVfra3t6etW7eWWBYA+2N/7I/9sb8K/JWXWF71UCkt+6ampggLC8PH\njx+hoaGBixcv4vz58+U6B8MwDCNeFW7cvXbtGlq2bImXL19i6NChGDJkCICCvrZDhw4FAMjJyeHA\ngQMYNGgQ9PT0MH78eHTs2FE8kTMMwzAVUm2mbGAYhmEkQ6Ijd8symGvRokVo3749jI2N8ebNG0mG\nJ1HfexZnz56FsbExjIyM0KtXL/j5+UkhSsko6yA/b29vyMnJ4erVqxKMTrLK8ixcXV3RqVMnGBgY\nwMzMTLIBStD3nkVSUhIGDx4MExMTGBgY4MSJE5IPUgJmzJgBNTU1GBoallqm3Hmz3K0CFVSWwVx3\n7tyhIUOGEBHRy5cvqVu3bpIKT6LK8izc3d0pNTWViIicnZ1r9bP4Uq5fv340dOhQunLlihQirXpl\neRYpKSmkp6dHUVFRRESUmJgojVCrXFmexbp162jlypVEVPAclJWVSSAQSCPcKvXs2TPy8fEhAwOD\nEvdXJG9KrMZflsFcN2/exLRp0wAA3bp1Q2pqKuLj4yUVosSU5Vn06NEDjRo1AlDwLKKjo6URapUr\n6yC//fv3Y+zYsWjatKkUopSMsjyLc+fOYcyYMdDU1AQAqKqqSiPUKleWZ6Guro709HQABatvqaio\n1MhF1Xv37o0mTZqUur8ieVNiib+kwVz/nemvpDI1MeGV5Vl87ejRo7C0tJREaBJX1v8vbty4gXnz\n5gGoueNDyvIswsLCkJycjH79+sHU1BSnT5+WdJgSUZZnMXv2bAQGBkJDQwPGxsbYu3evpMOsFiqS\nNyX29VjWf6z0n7bmmviPvDz39OTJExw7dgwvXryowoikpyzP4s8//8TWrVsL5x3/7/8jNUVZnoVA\nIICPjw8ePXqE7Oxs9OjRA927d0f79u0lEKHklOVZ2Nvbw8TEBK6urggPD4eFhQV8fX3RoEEDCURY\nvZQ3b0os8bdo0QJRUVGFn6Oiogp/rpZWJjo6Gi1atJBUiBJTlmcBAH5+fpg9ezbu3bv3zZ96P7Ky\nPIvXr19jwoQJAAoa9JydnSEvL48RI0ZINNaqVpZn0bJlS6iqqqJOnTqoU6cO+vTpA19f3xqX+Mvy\nLNzd3WFjYwMA0NbWRps2bRAaGgpTU1OJxiptFcqbYmuB+A6BQEBt27aliIgIysvL+27jroeHR41t\n0CzLs/j06RNpa2uTh4eHlKKUjLI8i69ZWVmRk5OTBCOUnLI8i+DgYDI3NyehUEhZWVlkYGBAgYGB\nUoq46pTlWVhbW9P69euJiCguLo5atGhBfD5fGuFWuYiIiDI17pY1b0qsxv/1YC6RSISZM2eiY8eO\ncHR0BADMmTMHlpaWuHv3Ltq1a4d69erh+PHjkgpPosryLDZu3IiUlJTC99ry8vLw8vKSZthVoizP\norYoy7PQ1dXF4MGDYWRkBBkZGcyePRt6enpSjlz8yvIsVq9ejenTp8PY2Bgcx8HBwQHKyspSjlz8\nJk6ciKdPnyIpKQktW7bEhg0bIBAIAFQ8b7IBXAzDMLUMW3qRYRimlmGJn2EYppZhiZ9hGKaWYYmf\nYRimlmGJn2EYppZhiZ9hGKaWYYmfYRimlmGJn2EYppZhiZ9hGKaWYYmfYRimlmGJn2EYppZhiZ9h\nGKaWqXnrlDGMGLx+/RqnT5+GrKwsPn78iCNHjsDR0RGpqamIiYnBhg0b0LZtW2mHyTAVwhI/w/zH\nhw8fcPz4cRw4cAAAYGVlhe7du+PkyZPgOA69e/dG586dYW1tLeVIGaZiWOJnmP/YuXMnHBwcCj9n\nZWVBWVkZ3bt3R3R0NJYsWQIrKyvpBcgwlcTm42eY//j48SO0tLQKP2tqamL69Omws7OTXlAMI0as\ncZdh/uPrpB8aGorPnz+jX79+0guIYcSMJX6G+YbHjx9DQUEBPXv2LNwWEREhxYgYpvJY4meYr+Tk\n5GD58uUICAgAADx48ADGxsZQUlICAHAchx07dkgzRIapNNa4yzBfuXv3Lnbs2IGffvoJcnJyeP/+\nPRo3bly4f8uWLaxhl/nhscZdhvkKn8/HsmXLoKqqChkZGaxduxbz58+HkpISFBUVMXLkSPa+n/nh\nscTPMAxTy7B3/AzDMLUMS/wMwzC1DEv8DMMwtQxL/AzDMLUMS/wMwzC1DEv8DMMwtQxL/AzDMLUM\nS/wMwzC1DEv8DMMwtQxL/AzDMLXM/wFxVH1oeuq9ngAAAABJRU5ErkJggg==\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "--- Computation time: 2.79689407349 seconds ---\n" } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Vector notations" }, { "cell_type": "code", "collapsed": false, "input": "start_time = time()\n\ndx = barX/(nx-1) # Grid step in space\ndt = T/nt # Grid step in time\n\n# Boundary conditions\nx = linspace(0.0,barX,nx)\nu = sin(2.0*pi*x)\nrhs = zeros(nx)\nfor n in range(0,nt):\n\trhs[1:-1] = dt * (0.5*sigma*sigma) * (u[:-2] - 2.0*u[1:-1] + u[2:]) / (dx*dx)\n\tu +=rhs\n\t#Plot every pp time steps\n\tpp = 100\n\tif (n%pp == 0):\n\t\tif (n%(10*pp) == 0):\n\t\t\tplotlabel = \"t = %1.2f\" %(n * dt)\n\t\t\tplot(x,u, label=plotlabel, color = get_cmap('copper')(float(n)/nt))\n\nxlabel(u'$x$', fontsize=14)\ntitle(u'One-dimensional heat equation')\nlegend()\nshow()\ntemp = time() - start_time\nprint(\"--- Computation time: %s seconds ---\" % temp)", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEdCAYAAAALugwIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "--- Computation time: 0.532827854156 seconds ---\n" } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Matrix notations, using sparse matrices" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We are interested here in solving the matrix system in $\\mathbb{R}^N$:\n$$\n\\textrm{Diag}(-2,1,1)\\mathbf{u} = (\\mathrm{d}x)^2(1,\\ldots,1)'.\n$$" }, { "cell_type": "code", "collapsed": false, "input": "N=1000 # Size of the matrix\ndx = 1./(N-1) # Space step size\nx = linspace(0.0,1.0,N)\n\n# Definition of the tridiagonal matrix\nTmatrix = [ones(N),-2.0*ones(N),ones(N)]\nnonzeropositions = array([-1,0,1])\niterationMatrix = dia_matrix((Tmatrix,nonzeropositions), shape=(N,N))\n\n### Schematic representation of the diagonal matrix\nfigure()\nspy(iterationMatrix)\ntitle('Tridiagonal matrix')\ndraw()\n\nrhs = -ones(N)*dx*dx # Right-hand side\n\n## Solving the linear system\nt = time()\nspSolution = spsolve(iterationMatrix,rhs)\ncomptime = time()-t\nprint(\"Computation time using sparse library: %s seconds\" % comptime)\n\n# In order to compare with the full resolution\nfullIterMatrix = iterationMatrix.todense()\nt = time()\nlinAlgSolution = linalg.solve(fullIterMatrix,rhs)\ncomptime = time()-t\nprint(\"Computation time using standard linear algebra: %s seconds\" % comptime)\n\n# Solution plot\nfigure()\nplot(x,spSolution,'k-')\ntitle('Solution of the matrix equation')\nxlabel(u'$x$', fontsize=14)\nylabel(u'$u$', fontsize=14, rotation=0)\nshow()", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Computation time using sparse library: 0.0011830329895 seconds\nComputation time using standard linear algebra: 0.0667409896851 seconds" }, { "output_type": "stream", "stream": "stdout", "text": "\n" }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAARUAAAEMCAYAAADqNyKxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niqFCRKpiqBCRqv4f0hbmViVwwDIAAAAASUVORK5CYII=\n", "text": "" }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEdCAYAAADn46tbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X1cjff/B/BX6SAVpRK60c05VJpulERoQxRr7pe7CiO7\nydxsX5ubqZmbkLvayBhjtL7D5KayLysz5T6MRFq1Om5DKkl3n98f++1MTjjqqs85p/fz8ejx6Jzz\nua7rdT5yvc/nuq7PuTQYYwyEEELIMzR5ByCEEKJ8qDgQQgiRQ8WBEEKIHCoOhBBC5FBxIIQQIoeK\nAyGEEDlUHIhMTk4ONDU1UV1dXafld+7ciUGDBgmc6tVOnDgBiUQCPT097N+//5Xt6/s+eTt+/Dhs\nbW15x6g3PT095OTk8I5BXoCKgxr6/fff0atXL+jr68PQ0BCenp44e/asoNuobQc7fvx4HD58WNDt\nKOKLL77AjBkzUFxcDD8/P7nXLS0t8euvvzZ6rrrQ1NTEn3/++dI2ffr0QUZGRiMlEoaXlxe2bNlS\n47ni4mJYWlryCUReSYt3ACKsoqIiDB06FNHR0RgzZgyePn2K48ePo0WLFg2yPWWYQ/nXX3/B3t7+\nha9raGgoRU5FvSxrZWUltLRU77+thoYG7wjkdTGiVs6cOcP09fVf+Hp1dTVbvHgx69SpE2vXrh0L\nCAhgjx49Yowxlp2dzTQ0NFhVVRVjjLFOnTqxI0eOyJZdtGgRmzBhAmOMMXNzc6ahocF0dXWZnp4e\nS01NZVu3bmWenp6y9idOnGCurq6sTZs2zM3NjaWkpMhe69evH1u4cCHr3bs309PTY97e3qygoOCF\nuTdt2sTEYjFr27Yt8/PzYzdv3mSMMWZtbc00NTWZtrY209PTY+Xl5TWWmzBhgux1XV1dtnLlStn7\n/P7775mFhQUzMjJiS5YsqdFHy5YtYzY2NszQ0JCNGTOGPXjwoNZcSUlJzNTUlK1YsYIZGxuzDh06\nsJ9//pkdOnSISSQS1rZtW7Zs2TJZ+1OnTrGePXsyfX191qFDB/bRRx/JMvfp04dpaGgwHR0dpqur\ny/773//K1h8eHs7at2/PAgICWFJSEjMzM2OMMXbjxg3Wtm1bdv78ecYYY1KplBkZGbFjx47Vmlcq\nlbIRI0YwY2NjZmVlxdavXy97rbS0lAUGBjIDAwNmb2/PVqxYIdsOY4xpaGiwrKws2ePAwEC2YMEC\nxhhjDx48YEOGDGHGxsbMwMCADR06lOXn5zPGGJs3bx5r1qwZa9myJdPV1WUhISFy6yssLGQTJ05k\nxsbGrFOnTuyrr75i1dXVjDHGtm7dynr37s0++eQTZmBgwKysrFhCQkKt748Ih4qDmikqKmKGhoYs\nMDCQJSQkyO3UtmzZwsRiMcvOzmYlJSVsxIgRbOLEiYwx+eJgaWnJjh49Kls2NDRUVhxycnJqtGWM\n1SgO9+/fZ/r6+uyHH35gVVVVLCYmhhkYGMjy9OvXj4nFYpaZmcmePHnCvLy82GeffVbrezp69Cgz\nMjJiaWlp7OnTpywkJIT17dtX9vrzOZ/3/Ov/vM9p06axsrIydvHiRdaiRQuWkZHBGGNs7dq1zMPD\ng0mlUlZeXs6Cg4PZ2LFja113UlIS09LSYosXL2aVlZXs22+/ZYaGhmzcuHGspKSEXblyhWlra7Oc\nnBzGGGPnzp1jp06dYlVVVSwnJ4fZ2dmxtWvXytb3/A74n/V/9tlnrLy8nD158qRGcWCMsW+//ZbZ\n29uz0tJS5u3tzT799NNas1ZVVTEXFxe2ePFiVlFRwf78809mbW3NDh8+zBhjbO7cuaxv377s4cOH\nLC8vj3Xt2pWZm5u/MFtQUBBbuHAhY+zvf++9e/eyJ0+esOLiYjZ69Gg2bNgwWVsvLy+2ZcuWGnme\nXd/EiRPZsGHDWElJCcvJyWGdO3eWtd+6dSsTiURs8+bNrLq6mm3YsIF17Nix1vdIhEPFQQ1dvXqV\nBQUFMTMzM6alpcX8/PzYnTt3GGOMvfXWW2zDhg2ytteuXWMikYhVVVW9sjg8O3J4vi1jNYvD9u3b\nmbu7e41cHh4ebNu2bYyxv3cWz35a/+abb9jgwYNrfT+TJ09mc+fOlT0uKSlhIpGI5ebm1przeS8q\nDlKpVPZcjx49WGxsLGOMMVtb2xrtb968Keuj5yUlJTFtbW3Zp9yioiKmoaHBTp8+LWvTvXt3tm/f\nvlqzrVmzhg0fPlz2uLbi0Lx5c/b06dMazz1bHBhjzM/Pjzk4ODBHR0e50dM/Tp48ySwsLGo8t3Tp\nUjZp0iTGGKtRKBj7e7T2spFDUFCQbOTwvLS0NGZgYCB77OXlxTZv3lyjzT/rq6ysZM2bN2dXr16V\nvRYdHc28vLwYY3//XYnFYtlrjx8/ZhoaGrK/adIw6IS0GrK1tcXWrVuRl5eHy5cv4+bNm5g5cyYA\n4NatW+jUqZOsrYWFBSorK3Hnzh1BM9y8eRMWFhY1nuvUqRNu3rwpe9y+fXvZ79ra2igpKal1Xc9n\n1tHRgaGhIaRSab0yPrv9Vq1aybafm5uL4cOHw8DAAAYGBrC3t4eWltYL+8jQ0FB2TF1bWxsAYGJi\nUuO9PX78GABw/fp1DB06FB06dECbNm0wf/583L9//6U5jY2N0bx585e2ee+993DlyhWEhIRAJBLV\n2iY3Nxc3b96UvS8DAwMsW7YMd+/eBfD3v5m5ubms/fP/fi9TWlqK4OBgWFpaok2bNujXrx8ePXpU\n4/zJi847FBQUoKKiQu7v8tl/3+f/rQC88O+FCIOKg5rr0qULAgMDcfnyZQBAx44da1w++Ndff0FL\nS6vGzuwfOjo6sp0aANy+fVv2+6tOMJqamiI3N7fGc7m5uTA1NX3t9/B85sePH+P+/fsKr+t1T4Za\nWFggMTERDx8+lP2UlpaiQ4cOr7We2rz//vuwt7fHjRs38OjRIyxZsuSVl9S+Kn9JSQlmzpyJ9957\nD4sWLcLDhw9rbWdhYQErK6sa76uoqAgHDx4EAHTo0AF//fWXrP2zvwN/75RLS0tlj2/duiXLFhER\ngevXr+P06dN49OgRjh07Bvb3kYlXvgcjIyOIRCK5v0szM7OXvm/SsKg4qJlr165h9erVsk9deXl5\niImJgYeHBwBg7NixWLNmDXJyclBSUoJ58+bB398fmpryfwpOTk748ccfUVlZibNnz2LPnj2y/+TG\nxsbQ1NREVlZWrTl8fHxw/fp1xMTEoLKyErGxscjIyMDQoUNlbZiCVxCNHTsWW7duxcWLF/H06VPM\nmzcPPXv2VPiTrYmJyQtz1mb69OmYN2+ebOd47949heZPKKKkpAR6enpo1aoVMjIysGHDhnplBYCP\nP/4YPXr0wKZNmzBkyBBMnz691nY9evSAnp4eVqxYgSdPnqCqqgqXL1+WXeY8ZswYLFu2DIWFhcjP\nz0dkZGSNnbqTkxN27tyJqqoqJCYm4rfffqvxvrS1tdGmTRs8ePAAYWFhCr+vZs2aYcyYMZg/fz5K\nSkqQm5uLNWvWYMKECa/VD0RYVBzUjJ6eHk6dOgV3d3fo6urCw8MD3bp1Q0REBABg8uTJmDhxIvr2\n7Qtra2u0atUKkZGRsuWf3RksXrwYWVlZMDAwQGhoKMaPHy97rVWrVpg/fz569+6Ntm3b4tSpU9DQ\n0JAtb2hoiIMHDyIiIgJGRkZYtWoVDh48iLZt29a6rWeXfV7//v2xePFijBw5Eh07dkR2djZ+/PFH\nhfvk888/x1dffQUDAwOsXr1abtvP+/jjj+Hn5wdvb2+0bt0aHh4eOH369AvbP7+ul6171apV2LVr\nF1q3bo1p06bB39+/RvvQ0FAEBgbCwMAAu3fvfmG//PNcXFwcfvnlF1mRWb16Nc6fP4+YmBi5ZTQ1\nNXHw4EFcuHAB1tbWMDY2xrRp01BUVAQAWLRoETp16gQrKysMHjwYAQEBNQr4unXrcODAARgYGGDX\nrl0YPny47LWZM2fiyZMnMDIyQq9eveDj41Mj98cff4zdu3ejbdu2skOcz4qMjISOjg6sra3Rp08f\njB8/HpMmTZK919fpYyIMDabox7dXSExMxMyZM1FVVYX33nsPc+fOrfF6RkYGJk2ahLS0NCxZsgRz\n5syp8XpVVRVcXV1hZmaGAwcOCBGJEFIPycnJmDhxIvLy8nhHIRwIMpumqqoKH330EY4cOQJTU1O4\nubnBz88PdnZ2sjaGhoaIjIzEvn37al3HunXrYG9vj+LiYiEiEUIIqQdBDiudPn0aYrEYlpaWEIlE\n8Pf3R1xcXI02xsbGcHV1rfVKivz8fMTHx+O9995TqZmshKg7OnzTdAlSHKRSaY1L4MzMzF7rMsNZ\ns2Zh5cqVtZ4UJYTw4eXlJXfFEmk6BNkb1+fTxcGDB9GuXTs4OzvTqIEQQpSEIOccTE1Na5y0ysvL\nU/ga5ZSUFOzfvx/x8fEoKytDUVERAgICsH379hrtaHhLCCF1U5cP3oKMHFxdXZGZmYmcnByUl5cj\nNja21q9OBuRDLl26FHl5ebLLE9966y25wvDssvTDsGjRIu4ZlOWH+oL6gvri5T91JcjIQUtLC1FR\nURg0aBCqqqowZcoU2NnZITo6GgAQHByM27dvw83NDUVFRdDU1MS6deuQnp4OXV3dGuuiEQIhhPAn\n2BfD+/j4wMfHp8ZzwcHBst/bt2//yuul+/Xrh379+gkViRBCSB3R5UEqyMvLi3cEpUF98S/qi39R\nX9SfYDOkG5qq3c2LEEKUQV33nTRyIIQQIoeKAyGEEDlUHAghhMih4kAIIUQOFQdCCCFyqDgQQgiR\nQ8WBEEKIHCoOhBBC5FBxIIQQIoeKAyGEEDlUHAghhMih4kAIIUQOFQdCCCFyqDgQQgiRQ8WBEEKI\nHCoOhBBC5Ah2m1BC1E1xcTGuX7+Ov/76C3fu3MHt27dx+/ZtPHz4EE+ePJH9VFdXQyQSoXnz5hCJ\nRNDV1YWRkZHsp0OHDrC2toaNjQ309fV5vy1CFEJ3giNNXnV1Na5du4YzZ87gzJkzuHz5Mq5du4bC\nwkJIJBJYWlqiffv2sh8DAwNoa2vLfjQ1NVFRUYGKigqUl5ejuLgY9+/fR0FBAQoKCiCVSpGVlYWs\nrCy0aNECtra2cHZ2lv04ODigefPmvLuBqKm67jupOJAmp7q6GhcuXMDRo0dx5MgRnDx5EkZGRnBz\nc4Obmxu6deuGLl26wMzMDJqawh15ZYzh3r17SE9PR1paGtLS0nD+/Hnk5ubC3d0dXl5e8PLyQo8e\nPahYEMFQcSDkJUpKSpCYmIi9e/fil19+gbGxMQYMGID+/fvD09MTRkZG3LIVFhbi999/R3JyMpKT\nk3Hjxg14e3vjnXfega+vLwwMDLhlI6qPigMhz3ny5An27duH//73v/j111/Rs2dPjBgxAkOGDIGZ\nmRnveC90584dHDx4EPv370dSUhLc3d0xceJEjBgxArq6urzjERVT132nYGPmxMRE2NraQiKRIDw8\nXO71jIwMeHh4oGXLloiIiJA9n5eXhzfffBNdu3aFg4MD1q9fL1Qk0gQxxnDq1ClMnz4dpqam2Lp1\nK4YNG4bs7GwcPnwYwcHBSl0YAMDExARTpkxBXFwcbt++jalTp+Knn36CmZkZJk6ciKNHj9IHJdLg\nBBk5VFVVoUuXLjhy5AhMTU3h5uaGmJgY2NnZydrcu3cPubm52LdvHwwMDDBnzhwAkF0B4uTkhJKS\nEnTv3h379u2rsSxAIwfycmVlZdi1axfWrVuHx48fIygoCAEBAbCwsOAdTTD37t3Djz/+iG+//RYV\nFRX48MMPERAQgNatW/OORpQY15HD6dOnIRaLYWlpCZFIBH9/f8TFxdVoY2xsDFdXV4hEohrPt2/f\nHk5OTgAAXV1d2NnZ4ebNm0LEIk3ArVu3sHDhQnTq1Am7d+/GypUrkZmZiQULFqhVYQD+/j8UEhKC\nixcvIjo6GsePH4elpSVCQkKQm5vLOx5RM4IUB6lUCnNzc9ljMzMzSKXS115PTk4O0tLS4O7uLkQs\nosakUilmzJiBrl274v79+/jtt98QHx8Pb29vaGho8I7XoDQ0NNC3b1/Exsbijz/+QKtWreDi4oJJ\nkybh2rVrvOMRNSHIJDgh/jOWlJRg1KhRWLdu3QtPuoWGhsp+/+eyP9K05OfnY/ny5di1axcmT56M\n9PR0tG/fnncsbkxNTREeHo65c+ciKioKnp6eGDBgABYvXgyxWMw7HuHgn6ve6kuQ4mBqaoq8vDzZ\n47y8vNc66VdRUYGRI0diwoQJGDZs2AvbPVscSNNSWFiIZcuWYfPmzZgyZQoyMjLQrl073rGURtu2\nbfHFF19g1qxZWL9+PXr27Al/f38sXLgQJiYmvOORRvT8B+ewsLA6rUeQw0qurq7IzMxETk4OysvL\nERsbCz8/v1rbPn9ihDGGKVOmwN7eHjNnzhQiDlEjFRUViIqKQpcuXfDgwQNcvnwZK1asoMLwAnp6\nepg/fz4yMjLQvHlz2NvbIzQ0FI8fP+YdjagaJpD4+HjWuXNnZmNjw5YuXcoYY2zjxo1s48aNjDHG\nbt26xczMzFjr1q2Zvr4+Mzc3Z8XFxez48eNMQ0ODOTo6MicnJ+bk5MQSEhLk1i9gVKIiEhISWJcu\nXZi3tze7ePEi7zgqKTs7m40dO5ZZWFiwPXv2sOrqat6RSCOr676TJsERpXPz5k3MmjULZ8+eRWRk\nJHx9fXlHUnnHjh3Dhx9+CFNTU0RGRqJz5868I5FGwn0SHCH1VVVVhaioKDg6OqJz5864fPkyFQaB\n9OvXD2lpaRg0aBB69eqFRYsWoby8nHcsosRo5ECUQkZGBoKCgtCyZUts2LBBbhIkEY5UKsX06dOR\nm5uLbdu2wcXFhXck0oBo5EBUUnV1NdauXYs+ffogKCgISUlJVBgamKmpKfbv34///Oc/GDx4MBYs\nWICnT5/yjkWUDI0cCDfZ2dmYNGkSKisr8f3338PGxoZ3pCbn1q1b+OCDD3Djxg3ExMTAwcGBdyQi\nMBo5EJWya9cu9OjRA0OGDMGxY8eoMHDSoUMH7N27F7Nnz8abb76JDRs20IcwAoBGDqSRlZaWYsaM\nGfjtt9/w3//+V/a9WoS/69evY+zYsbCwsMDmzZthaGjIOxIRAI0ciNJLT09Hjx49UFZWhnPnzlFh\nUDKdO3dGSkoKbGxs4OzsjJSUFN6RCEdUHEij+OGHH9CvXz/Mnj0bO3bsgJ6eHu9IpBYtWrTAqlWr\nsGHDBgwfPhxff/01jdibKDqsRBpUZWUl/vOf/2D//v3Yt28fnfBUIVlZWRgxYgScnJywceNGaGtr\n845E6oAOKxGlU1BQgEGDBiE9PR1nzpyhwqBibGxskJqaisrKSvTq1QvZ2dm8I5FGRMWBNIiLFy/C\nzc0Nrq6uOHToEAwMDHhHInXQqlUr/PDDDwgKCkKvXr1w4sQJ3pFII6HDSkRw8fHxCAwMxPr16zF2\n7FjecYhAEhMTERAQgDVr1mD8+PG84xAF1XXfScWBCGrjxo0ICwvD3r174eHhwTsOEdjly5fx9ttv\nIzAwEIsWLVL7u+6pAyoOhKvq6mp8/vnn2LdvH+Lj42lSmxq7c+cO3nnnHVhbW2Pr1q1o0aIF70jk\nJeiENOGmrKwM48aNw4kTJ2TXyRP1ZWJigqSkJJSVlWHo0KEoLi7mHYk0ACoOpF6Ki4vh4+MDxhiO\nHDlCs2qbCG1tbfz000+wsrLCW2+9hXv37vGORARGxYHUWUFBAd566y3Y2tpi165daNmyJe9IpBE1\na9YM0dHRGDx4MDw9PZGTk8M7EhEQFQdSJ1KpFP369cOAAQPwzTffoFmzZrwjEQ40NDSwePFifPTR\nR+jTpw8uX77MOxIRiBbvAET1ZGVlYeDAgZg2bRo+++wz3nGIEggJCYGRkREGDBiAhIQEODs7845E\n6omKA3ktV69excCBA7FgwQJMnz6ddxyiRMaOHYvmzZtj8ODBOHToEFxdXXlHIvVAxYEo7OrVqxgw\nYACWLVuGgIAA3nGIEho5ciS0tLTg6+uLAwcOwN3dnXckUkdUHIhCMjIyqDAQhbzzzjsQiUR4++23\n8fPPP6N37968I5E6oBPS5JUyMjLQv39/LF26lAoDUYivry9++OEHDB8+HL///jvvOKQOBCsOiYmJ\nsLW1hUQiQXh4uNzrGRkZ8PDwQMuWLREREfFayxJ+rl27hgEDBmDp0qUIDAzkHYeoEG9vb+zcuRMj\nRozA2bNnecchr4sJoLKyktnY2LDs7GxWXl7OHB0dWXp6eo02d+/eZWfOnGHz589nq1ateq1l//8r\nPoSISl5DVlYWMzMzY1u3buUdhaiwuLg4ZmJiwi5dusQ7SpNU132nICOH06dPQywWw9LSEiKRCP7+\n/oiLi6vRxtjYGK6urhCJRK+9LGl8t27dwsCBAzFv3jwEBQXxjkNUmJ+fH9atW4dBgwbh2rVrvOMQ\nBQlSHKRSKczNzWWPzczMIJVKG3xZ0jAePHgAb29vTJkyBe+//z7vOEQNvPvuu1iyZAkGDhxINw1S\nEYJcrVSfr+19nWVDQ0Nlv3t5ecHLy6vO2yW1++e7kgYPHozPP/+cdxyiRiZNmoTS0lIMGDAAJ06c\nQPv27XlHUkvJyclITk6u93oEKQ6mpqbIy8uTPc7Ly4OZmZngyz5bHIjwysrKMGzYMHTr1g0rVqyg\n7+ongvvwww/x4MED+Pj44NixY2jdujXvSGrn+Q/OYWFhdVqPIIeVXF1dkZmZiZycHJSXlyM2NhZ+\nfn61tmXPfa/46yxLGk5VVRUmTJgAQ0NDbNy4kQoDaTALFixAz549MWLECDx9+pR3HPICgt3sJyEh\nATNnzkRVVRWmTJmCzz//HNHR0QCA4OBg3L59G25ubigqKoKmpib09PSQnp4OXV3dWpeVC0o3+2lQ\ns2bNQlpaGg4fPkw3byENrqqqCqNHj0aLFi2wc+dOaGrSlKuGQneCI3W2du1abNq0CSdOnICBgQHv\nOKSJKCsrg7e3N7p3747Vq1fTaLWB0J3gSJ3s2bMHK1euREJCAhUG0qhatmyJuLg4/O9//8Pq1at5\nxyHPoe9WasJSUlIwffp0HD58GJ06deIdhzRBBgYGSEhIgIeHB2xsbDBs2DDekcj/o8NKTdT169fR\nt29fbN26FT4+PrzjkCbu7Nmz8PHxweHDh+Hi4sI7jlqhw0pEYQ8fPsTQoUOxePFiKgxEKbi6umLj\nxo145513aBKskqCRQxNTWVkJHx8fODg4YM2aNbzjEFLDsmXLsHv3bvz222/Q0dHhHUct0NVKRCEf\nf/wxrl27hoMHD0JLi045EeXCGMOkSZPw6NEj7Nmzhy5xFQAdViKv9O233+Lw4cP48ccfqTAQpaSh\noYHo6Gjcv38f8+bN4x2nSaORQxNx7NgxjBkzBsePH0fnzp15xyHkpQoKCuDm5obw8HCMGTOGdxyV\nRoeVyAtlZ2fDw8MDO3bswMCBA3nHIUQhaWlp8Pb2xq+//oo33niDdxyVRYeVSK1KS0sxbNgwzJs3\njwoDUSnOzs5Yu3Ythg8fjgcPHvCO0+TQyEGNMcYQGBiI6upq7Nixg76egKik2bNn4+rVqzh48CCa\nNWvGO47KoZEDkbNx40ZcuHAB0dHRVBiIylqxYgXKysqwcOFC3lGaFBo5qKmTJ0/Cz88PKSkpEIvF\nvOMQUi/37t2Dm5sbIiIiMHLkSN5xVAqdkCYyd+/ehaurK6KioujeGERtnDt3Dj4+Pjhx4gQkEgnv\nOCqDigMB8PcMaG9vb3h4eGDJkiW84xAiqA0bNiA6OhqpqanQ1tbmHUclUHEgAIB58+bhzJkzSExM\npJN3RO0wxjB27Fi0bt0amzZt4h1HJdAJaYLDhw9j+/bt2LVrFxUGopY0NDSwadMmJCcnY+fOnbzj\nqDUaOaiJW7duwcXFBTExMTVuLk6IOrp48SIGDBiA48ePw9bWlnccpUYjhyasqqoKEyZMQHBwMBUG\n0iQ4Ojpi2bJlGD16NEpLS3nHUUs0clADX331FY4cOYKjR4/S4STSZDDGEBAQAJFIhO+++453HKVF\nJ6SbqOPHj2P06NE4d+4cTE1NecchpFGVlJTAxcUFX331FX1B3wtQcWiC7t+/D2dnZ2zcuBG+vr68\n4xDCxdmzZ+Hr64szZ87QvdBrQcWhiWGMYfjw4RCLxVi1ahXvOIRwFR4ejkOHDiEpKYkOrT6H+wnp\nxMRE2NraQiKRIDw8vNY2M2bMgEQigaOjI9LS0mTPL1u2DF27dsUbb7yBcePG4enTp0LFUltbtmxB\nbm4uli5dyjsKIdx9+umn0NLSwrJly3hHUR9MAJWVlczGxoZlZ2ez8vJy5ujoyNLT02u0OXToEPPx\n8WGMMXby5Enm7u7OGGMsOzubWVlZsbKyMsYYY2PGjGHbtm2T24ZAUdVCZmYmMzIyYleuXOEdhRCl\nkZeXx9q1a8dSU1N5R1Eqdd13CjJyOH36NMRiMSwtLSESieDv74+4uLgabfbv34/AwEAAgLu7OwoL\nC3Hnzh20bt0aIpEIpaWlqKysRGlpKZ1YfYnKykpMmDABCxcuhL29Pe84hCgNMzMzbNiwAePHj0dR\nURHvOCpPkOIglUphbm4ue2xmZgapVKpQm7Zt22LOnDmwsLBAx44doa+vjwEDBggRSy0tXboUbdq0\nwUcffcQ7CiFKZ8SIEejfvz9CQkJ4R1F5gtxlXtF7BbBaTopkZWVh7dq1yMnJQZs2bTB69Gjs3LkT\n48ePl2sbGhoq+93Ly6vJTfg6deoUvv76a6SlpUFTk+YvElKbNWvWwNHRET///DOGDx/OO06jS05O\nRnJycr3XI0hxMDU1RV5enuxxXl4ezMzMXtomPz8fpqamSE5ORq9evWBoaAjg78qfkpLyyuLQ1Dx+\n/BgTJ07E119/jY4dO/KOQ4jS0tHRwffff49Ro0bB09MTxsbGvCM1quc/OIeFhdVpPYJ8/HR1dUVm\nZiZycnJQXl6O2NhYufsI+Pn5Yfv27QD+vhGNvr4+TExM0KVLF5w8eRJPnjwBYwxHjhyhY+m1mDNn\nDnr16oU9s/4HAAAc10lEQVRRo0bxjkKI0uvduzcmTpyI6dOn0yXwdSTIyEFLSwtRUVEYNGgQqqqq\nMGXKFNjZ2SE6OhoAEBwcDF9fX8THx0MsFkNHRwdbt24FADg5OSEgIACurq7Q1NSEi4sLpk2bJkQs\ntXH48GEkJibi0qVLvKMQojK+/PJLdO/eHTExMRg3bhzvOCqHJsEpuUePHqFbt2747rvv0L9/f95x\nCFEp/9w97sKFC032cCzNkFZTU6dORbNmzbBx40beUQhRSWFhYTh16hQOHTqk8MUz6oT7DGkivF9+\n+QX/+9//sGLFCt5RCFFZ8+bNw507d7BlyxbeUVQKjRyUVFFREd544w1s3rwZAwcO5B2HEJV25coV\neHl54ezZs03uy/kabORQXV2Nr7/+GlOmTMHZs2cBAHfv3kXv3r1fPyVR2KeffopBgwZRYSBEAF27\ndsWsWbMQHBzcpD5k1scri8O+ffvg7++Pp0+fIicnBwBw9OhRWFlZNXS2JuvIkSNITEykb1slRECf\nfvopbt++jR9++IF3FJXwysNKxcXFYIxBIpEgJycH2tramDp1Kjw8PDB58uTGytlkDisVFRWhW7du\n2LRpE7y9vXnHIUStnDt3Dr6+vvjjjz/Qrl073nEaRYMdVtLT00N8fDz69u0LbW1tAH9Pz37rrbdQ\nWFj4+knJS82bNw8DBgygwkBIA+jevTuCgoIwY8YM3lGUnkJXK+Xn58PGxgYAcP36dZSWlsLCwgKx\nsbENGq6pSU1Nxd69e7Fy5UreUQhRW6GhoTh37pzcN0eTmhQqDiNHjsSff/6Jn376CZcuXYKHhwci\nIyPpqxwEVF5ejmnTpmHt2rUwMDDgHYcQtaWtrY1vv/0WH374IR49esQ7jtKiS1mVxNKlS5GSkoID\nBw40yYk6hDS24OBgAJB9zY+6ohnSKiwzMxMeHh44d+5ck7sGmxBeHj16BAcHB+zYsUOtv/6fZkir\nKMYYgoODsWDBAioMhDSiNm3aIDIyEtOnT6f71teCigNn27ZtQ3FxMd25ihAOhg0bhs6dO9NFILWg\nw0oc3b17F2+88QYSExPh7OzMOw4hTVJubi5cXFxw6tQpiMVi3nEER+ccVNCECRPQsWNH+mI9Qjhb\nsWIFfv31VyQkJKjdBSF0zkHFJCcn4/jx41i0aBHvKIQ0ebNmzUJ+fj52797NO4rSoJEDBxUVFXBy\ncsLixYsxYsQI3nEIIQB+//13+Pv7Iz09Ha1bt+YdRzA0clAh69atg4WFBYYPH847CiHk/3l6emLQ\noEFYuHAh7yhKgUYOjSw/Px9OTk5ITU2FRCLhHYcQ8oyCggJ07doVCQkJcHFx4R1HEDRyUBGffPIJ\n3n//fSoMhCghIyMjLF++HNOnT0d1dTXvOFxRcWhER48exalTp/D555/zjkIIeYHAwEA0a9YMW7du\n5R2FKzqs1EjKy8vh6OiI8PBw+Pn58Y5DCHmJc+fOYciQIcjIyIC+vj7vOPVCh5WU3Jo1a2BjY4O3\n336bdxRCyCt0794dfn5+CA0N5R2FG8GKQ2JiImxtbSGRSBAeHl5rmxkzZkAikcDR0RFpaWmy5wsL\nCzFq1CjY2dnB3t4eJ0+eFCqWUsjLy8PKlSuxbt06tZtgQ4i6WrJkCXbu3InLly/zjsIHE0BlZSWz\nsbFh2dnZrLy8nDk6OrL09PQabQ4dOsR8fHwYY4ydPHmSubu7y14LCAhgW7ZsYYwxVlFRwQoLC+W2\nIVBULt599132xRdf8I5BCHlN69evZ2+99Rarrq7mHaXO6rrvFGTkcPr0aYjFYlhaWkIkEsHf31/u\nLkv79+9HYGAgAMDd3R2FhYW4c+cOHj16hOPHj8vuR62lpYU2bdoIEUsp/P7770hJScHcuXN5RyGE\nvKb3338f9+7dw549e3hHaXSCFAepVApzc3PZYzMzM0il0le2yc/PR3Z2NoyNjTFp0iS4uLhg6tSp\nKC0tFSIWd9XV1Zg5cybCw8PRqlUr3nEIIa9JS0sL69evx5w5c9Rmv6QoLSFWouhxdPbcGXMNDQ1U\nVlbi/PnziIqKgpubG2bOnInly5fjyy+/lFv+2ZNDXl5eSn+Dju+//x4tWrSAv78/7yiEkDry8vJC\nz549ER4ejrCwMN5xXik5ORnJycn1Xo8gxcHU1BR5eXmyx3l5eTAzM3tpm/z8fJiamoIxBjMzM7i5\nuQEARo0aheXLl9e6HVW6cqCoqAjz589HXFwcnYQmRMWtWrUKzs7OCAoKgpWVFe84L/X8B+e6FjRB\nDiu5uroiMzMTOTk5KC8vR2xsrNy1/H5+fti+fTsA4OTJk9DX14eJiQnat28Pc3NzXL9+HQBw5MgR\ndO3aVYhYXC1duhTe3t6yokcIUV3m5uaYMWNGk5rAKsjIQUtLC1FRURg0aBCqqqowZcoU2NnZyW7c\nHRwcDF9fX8THx0MsFkNHR6fG7MPIyEiMHz8e5eXlsLGxUfmZiVlZWdi8eTMuXbrEOwohRCBz5syB\nra0tUlNT4eHhwTtOg6MZ0g1gxIgRcHV1xbx583hHIYQIaPv27fjmm2+QmpqqMoeLaYa0kkhKSkJa\nWhpmz57NOwohRGATJkxARUUFYmNjeUdpcDRyEFBVVRVcXFzwxRdfYOTIkbzjEEIawLFjxxAYGIiM\njAy0bNmSd5xXopGDEti2bRv09fXp7m6EqLF+/frBxcUF69at4x2lQdHIQSCPHz9G586d8fPPP6NH\njx684xBCGlBmZiY8PDyQnp6Odu3a8Y7zUjRy4Gz16tXo06cPFQZCmgCJRIKAgAAsWrSId5QGQyMH\nAdy5cwf29vY4c+YMrK2tecchhDSChw8fokuXLkhKSlLquVl13XdScRDABx98gBYtWmDNmjW8oxBC\nGtH69euRkJCAhIQE3lFeiIoDJxkZGejTpw8yMjJgaGjIOw4hpBFVVFTA3t4eGzduRP/+/XnHqRWd\nc+Dk888/x6effkqFgZAmSCQS4auvvsLcuXNRXV3NO46gqDjUw/Hjx3H+/HnMmDGDdxRCCCejR48G\nAOzevZtzEmHRYaU6YozBw8MDH374ISZOnMg7DiGEo6NHj2L69OlIT0+HSCTiHacGOqzUyHbv3o3y\n8nKMHz+edxRCCGf9+/eHlZUVNm/ezDuKYGjkUAcVFRWws7PDxo0bMWDAAN5xCCFK4Pz58xgyZAgy\nMzOhq6vLO44MjRwa0XfffQcrKysqDIQQGRcXF7z55ptqc0k7jRxe05MnTyCRSLB3716aDU0IqSEr\nKws9evRARkYGjI2NeccBQCOHRhMVFYUePXpQYSCEyLGxscG4ceOwZMkS3lHqjUYOr+HRo0eQSCRI\nTk6Gvb091yyEEOV09+5d2NnZ4ezZs0pxv2kaOTSCiIgI+Pj4UGEghLxQu3btEBISgi+++IJ3lHqh\nkYOC/vk0cO7cOVhaWnLLQQhRfkVFRRCLxUpxlIG+W6mBzZo1C5WVlYiMjOSWgRCiOlasWIEzZ87g\np59+4pqDikMD+uuvv+Ds7IwrV66gffv2XDIQQlTL48ePIRaLER8fD2dnZ245qDg0oClTpsDExARL\nly7lsn1CiGpav349/ve//+HAgQPcMlBxaCDXrl2Dp6cnrl+/DgMDg0bfPiFEdZWVlUEikeCnn35C\nz549uWTgfrVSYmIibG1tIZFIEB4eXmubGTNmQCKRwNHREWlpaTVeq6qqgrOzM95++22hIgli0aJF\nmD17NhUGQshra9myJRYuXIiFCxfyjvLaBCkOVVVV+Oijj5CYmIj09HTExMTg6tWrNdrEx8fjxo0b\nyMzMxKZNm/D+++/XeH3dunWwt7eHhoaGEJEEceXKFSQlJSEkJIR3FEKIipo0aRL+/PNPJCcn847y\nWgQpDqdPn4ZYLIalpSVEIhH8/f0RFxdXo83+/fsRGBgIAHB3d0dhYSHu3LkDAMjPz0d8fDzee+89\n7hPdnhUWFoY5c+Yo1ZdoEUJUi0gkwqJFi7Bw4UKl2r+9iiDFQSqVwtzcXPbYzMwMUqlU4TazZs3C\nypUroampPHPy/vjjD/z222/48MMPeUchhKi48ePHo6CgAL/88gvvKArTEmIlih4Ker5qMsZw8OBB\ntGvXDs7Ozq8cdoWGhsp+9/LygpeX12smVdyXX36JTz75BDo6Og22DUJI09CsWTOEhYVh4cKF8Pb2\nbtDD58nJyYIcwhKkOJiamiIvL0/2OC8vD2ZmZi9tk5+fD1NTU+zZswf79+9HfHw8ysrKUFRUhICA\nAGzfvl1uO88Wh4Z06dIlHD9+HNu2bWuU7RFC1N+oUaOwZMkSHDhwAH5+fg22nec/OIeFhdVtRUwA\nFRUVzNrammVnZ7OnT58yR0dHlp6eXqPNoUOHmI+PD2OMsdTUVObu7i63nuTkZDZ06NBatyFQVIWM\nGDGCrVq1qtG2RwhpGvbs2cNcXFxYdXV1o22zrvtOQQ7ya2lpISoqCoMGDYK9vT3effdd2NnZITo6\nGtHR0QAAX19fWFtbQywWIzg4GN98802t6+J9tdKFCxeQkpIidzUVIYTU17Bhw1BRUYH4+HjeUV6J\nJsE9Z/jw4ejbty9mzZrV4NsihDQ9P/30E1auXIlTp041yodh7pPg1EFaWhpOnTqF6dOn845CCFFT\nI0eOxOPHj3H48GHeUV6KisMzQkNDMXfuXGhra/OOQghRU5qamli4cCHCwsKUet4DFYf/d+7cOZw9\nexbTpk3jHYUQouZGjx6NwsJCHDlyhHeUF6Li8P8WL15MowZCSKNo1qwZFixYoNSjByoO+Htew6lT\npzB16lTeUQghTYS/vz/u3buHpKQk3lFqRcUBwNKlSzF79mwaNRBCGk2zZs0wf/78uk9Sa2BN/lLW\nf+7X8Oeff0JPT0/w9RNCyItUVlbC1tYWW7ZsQb9+/RpkG3Qpax0tX74cISEhVBgIIY1OS0tLaUcP\nTXrkkJOTg+7du+PGjRt0Mx9CCBcVFRXo0qULtm/fDk9PT8HXTyOHOlixYgWmTZtGhYEQwo1IJMJn\nn32mdPeob7Ijh5s3b8LBwQEZGRlo166dYOslhJDX9fTpU1hbW+PgwYNwdnYWdN00cnhNERERCAwM\npMJACOGuRYsWmD17NpYvX847ikyTHDkUFBSgc+fO+OOPP2BqairIOgkhpD6Ki4thbW2NEydOoHPn\nzoKtl0YOr2Ht2rUYM2YMFQZCiNLQ09PDBx98gBUrVvCOAqAJjhwKCwshFotx5swZWFlZCZCMEEKE\ncf/+fUgkEly6dEnubpp1RSMHBX399dcYMmQIFQZCiNIxNDREUFAQIiIieEdpWiOHJ0+ewMrKCr/+\n+ivs7e0FSkYIIcKRSqV44403cP36dRgZGdV7fTRyUMC2bdvg7u5OhYEQorRMTU0xcuRIREZGcs3R\nZEYOlZWV6NKlC3bs2IFevXoJmIwQQoSVmZmJXr16CfKdbzRyeIU9e/agQ4cOVBgIIUpPIpGgf//+\niI6O5pahSYwcGGNwdXVFaGgo3n77bYGTEUKI8C5cuABfX1/8+eefaNmyZZ3XQyOHlzh69CjKysow\nZMgQ3lEIIUQhTk5OcHZ2xvbt27lsv0mMHAYOHIjx48cjKChI2FCEENKAjh07hmnTpuHq1avQ1Kzb\nZ3nuI4fExETY2tpCIpEgPDy81jYzZsyARCKBo6Mj0tLSAAB5eXl488030bVrVzg4OGD9+vVCRQIA\nnD9/HhkZGRg3bpyg6yWEkIbWt29ftG7dGgcOHGj8jTMBVFZWMhsbG5adnc3Ky8uZo6MjS09Pr9Hm\n0KFDzMfHhzHG2MmTJ5m7uztjjLFbt26xtLQ0xhhjxcXFrHPnznLL/v/opk7Z3n33XRYREVGnZQkh\nhLfY2FjWu3fvOi9f132nICOH06dPQywWw9LSEiKRCP7+/oiLi6vRZv/+/QgMDAQAuLu7o7CwEHfu\n3EH79u3h5OQEANDV1YWdnR1u3rwpRCxkZWXhyJEjmDp1qiDrI4SQxjZixAhIpVKkpqY26nYFKQ5S\nqRTm5uayx2ZmZpBKpa9sk5+fX6NNTk4O0tLS4O7uLkQsREREIDg4mG4BSghRWVpaWpg9ezZWrVrV\nuNsVYiUaGhoKtWPPnRR5drmSkhKMGjUK69atg66ubq3Lh4aGyn738vKCl5fXC7d19+5dxMTEICMj\nQ6FshBCirCZPnowvv/wSN27cgFgsfmnb5ORkJCcn13ubghQHU1NT5OXlyR7n5eXJfaPg823y8/Nl\nX5ldUVGBkSNHYsKECRg2bNgLt/NscXiVqKgovPvuuzAxMVF4GUIIUUY6OjoIDg7G6tWr8c0337y0\n7fMfnMPCwuq0TUEOK7m6uiIzMxM5OTkoLy9HbGws/Pz8arTx8/OTXa978uRJ6Ovrw8TEBIwxTJky\nBfb29pg5c6YQcVBaWoqNGzdi9uzZgqyPEEJ4CwkJQUxMDO7du9co2xOkOGhpaSEqKgqDBg2Cvb09\n3n33XdjZ2SE6Olo2/dvX1xfW1tYQi8UIDg6WVb8TJ07ghx9+QFJSEpydneHs7IzExMR65dmxYwc8\nPDwEvZsSIYTwZGJiglGjRr1y5CAUtZsEV11dDXt7e0RHR6Nfv36NkIwQQhpHRkYG+vXrh+zsbLRq\n1UqhZbhPglMWCQkJ0NHRQd++fXlHIYQQQdna2qJnz56N8pUaalccVq9ejdmzZyt8BRUhhKiSTz75\nBBEREaiqqmrQ7ahVcbhw4QKuXbuG0aNH845CCCENwtPTE4aGhnITjYWmVsVhzZo1CAkJQfPmzXlH\nIYSQBqGhoYHZs2dj7dq1DbsddTkhffPmTTg4OCArKwsGBgaNmIwQQhpXZWUlrK2t8fPPP6N79+4v\nbdvkT0h//fXXGD9+PBUGQoja09LSQkhISIOOHtRi5PD48WNYWloiNTX1lVPLCSFEHTx8+BDW1ta4\ncuUKOnbs+MJ2TXrksH37dnh6elJhIIQ0GQYGBhg3bhw2bNjQIOtX+ZFDdXU1bG1tsWXLFvTp04dD\nMkII4eP69evw9PREbm4utLW1a23TZEcOhw4dQps2beDp6ck7CiGENKrOnTujR48e2Llzp+DrVvni\nEBERQZPeCCFN1syZM7F27do6jQ5eRqWLw4ULF3Djxg2MGjWKdxRCCOGif//+0NDQwNGjRwVdr0oX\nh8jISHzwwQcQiUS8oxBCCBcaGhqy0YOg61XVE9IFBQWQSCS4fv06jI2NOSYjhBC+njx5AktLSxw/\nflzuVgVN7oT05s2bMWzYMCoMhJAmT1tbG9OmTcO6desEW6dKjhz+mTq+b98+uLi4cE5GCCH83bp1\nC127dpX7CqEmNXKIi4tDp06dqDAQQsj/69ChA4YOHYrNmzcLsj6VLA7r169HSEgI7xiEEKJUQkJC\n8M033whyrweVKw4XL15EVlYWhg8fzjsKIYQoFTc3N5iYmODgwYP1XpfKFQe6fJUQQl4sJCQEkZGR\n9V6PSp2QLigogFgspstXCSHkBZ4+fYpOnTohKSkJdnZ2TeOENF2+SgghL9eiRQtMmzYNUVFR9VqP\nYMUhMTERtra2kEgkCA8Pr7XNjBkzIJFI4OjoiLS0tNdaFvj7hj50IpoQQl5u+vTpiImJwaNHj+q8\nDkGKQ1VVFT766CMkJiYiPT0dMTExuHr1ao028fHxuHHjBjIzM7Fp0ya8//77Ci/7DwsLC7p8FUBy\ncjLvCEqD+uJf1Bf/aup90bFjR3h7e2Pbtm11XocgxeH06dMQi8WwtLSESCSCv78/4uLiarTZv38/\nAgMDAQDu7u4oLCzE7du3FVr2HzNmzBAirspr6n/4z6K++Bf1xb+oL/4+MV2fQ0uCFAepVApzc3PZ\nYzMzM0ilUoXa3Lx585XL/oMuXyWEEMX06tULurq6dV5ekOKg6L0U6nthFF2+SgghitHQ0MDy5cvr\nvLyWECFMTU2Rl5cne5yXlwczM7OXtsnPz4eZmRkqKipeuew/6IY+/woLC+MdQWlQX/yL+uJf1Bf1\nI0hxcHV1RWZmJnJyctCxY0fExsYiJiamRhs/Pz9ERUXB398fJ0+ehL6+PkxMTGBoaPjKZYH6jzoI\nIYQoTpDioKWlhaioKAwaNAhVVVWYMmUK7OzsEB0dDQAIDg6Gr68v4uPjIRaLoaOjg61bt750WUII\nIfyozAxpQgghjUfpZkjXZzKdunlVX+zcuROOjo7o1q0bevfujUuXLnFI2TgUnSh55swZaGlpYe/e\nvY2YrnEp0hfJyclwdnaGg4MDvLy8GjdgI3pVXxQUFGDw4MFwcnKCg4NDva77V2aTJ0+GiYkJ3njj\njRe2ee39JlMilZWVzMbGhmVnZ7Py8nLm6OjI0tPTa7Q5dOgQ8/HxYYwxdvLkSebu7s4jaoNTpC9S\nUlJYYWEhY4yxhISEJt0X/7R788032ZAhQ9ju3bs5JG14ivTFw4cPmb29PcvLy2OMMXbv3j0eURuc\nIn2xaNEi9tlnnzHG/u6Htm3bsoqKCh5xG9Rvv/3Gzp8/zxwcHGp9vS77TaUaOdR1Mt2dO3d4xG1Q\nivSFh4cH2rRpA+DvvsjPz+cRtcEpOlEyMjISo0aNUuvv3lKkL3bt2oWRI0fKrvozMjLiEbXBKdIX\nHTp0QFFREQCgqKgIhoaG0NIS5FSrUunTp0+Nu789ry77TaUqDnWdTKeOO0VF+uJZW7Zsga+vb2NE\na3SK/l3ExcXJvpZFXS97VqQvMjMz8eDBA7z55ptwdXXFjh07Gjtmo1CkL6ZOnYorV66gY8eOcHR0\nFPQey6qkLvtNpSqhdZ1Mp447gtd5T0lJSfjuu+9w4sSJBkzEjyJ9MXPmTCxfvlz29cTP/42oC0X6\noqKiAufPn8fRo0dRWloKDw8P9OzZExKJpBESNh5F+mLp0qVwcnJCcnIysrKyMHDgQFy8eBF6enqN\nkFC5vO5+U6mKQ10n05mamjZaxsaiSF8AwKVLlzB16lQkJia+dFipyhTpi3PnzsHf3x/A3ychExIS\nIBKJ4Ofn16hZG5oifWFubg4jIyNoa2tDW1sbffv2xcWLF9WuOCjSFykpKZg/fz4AwMbGBlZWVrh2\n7RpcXV0bNStvddpvCnZGRAAVFRXM2tqaZWdns6dPn77yhHRqaqranoRVpC9yc3OZjY0NS01N5ZSy\ncSjSF88KCgpie/bsacSEjUeRvrh69Srr378/q6ysZI8fP2YODg7sypUrnBI3HEX6YtasWSw0NJQx\nxtjt27eZqakpu3//Po+4DS47O1uhE9KK7jeVauRQn8l06kaRvvjyyy/x8OFD2XF2kUiE06dP84zd\nIBTpi6ZCkb6wtbXF4MGD0a1bN2hqamLq1Kmwt7fnnFx4ivTFvHnzMGnSJDg6OqK6uhorVqxA27Zt\nOScX3tixY3Hs2DEUFBTA3NwcYWFhqKioAFD3/SZNgiOEECJHqa5WIoQQohyoOBBCCJFDxYEQQogc\nKg6EEELkUHEghBAih4oDIYQQOVQcCCGEyKHiQAghRA4VB0IIIXKoOBBCCJFDxYEQQogcpfriPUJU\nSUpKCjIyMnDp0iX07NkTjx49QmJiIlavXg0rKyve8QipFxo5EFIHJSUluHbtGiZPnoz+/ftj7dq1\nCA4Oho6ODlq1asU7HiH1Rt/KSkgdlJWVoVmzZhCJRFiwYAFat26N//znP7xjESIYGjkQUgctW7aE\nSCQCAPzyyy/o378/AMhuZk+IqqPiQEgdHDhwAGvXrkVOTg4uXboEZ2dnAMD333/PORkhwqDDSoTU\nwbZt23Du3Dl06dIFZWVl0NTURKtWrTBy5EgYGxvzjkdIvVFxIIQQIocOKxFCCJFDxYEQQogcKg6E\nEELkUHEghBAih4oDIYQQOVQcCCGEyKHiQAghRA4VB0IIIXKoOBBCCJHzf5X//+tk2N09AAAAAElF\nTkSuQmCC\n", "text": "" } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 1, "metadata": { "zanadu": {} }, "source": "Example from the Lecture Notes" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We consider here the example in the lecture notes, namely the heat equation\n$\\partial_{\\tau}u(\\tau,x) = \\frac{\\sigma^2}{2}\\partial_{xx}u(\\tau,x)$ on \n$[0,\\infty)\\times [0,1]$ with boundary condition $u(0,x) = 2x\\mathrm{1}_{x\\in [0,1/2]} + 2(1-x)\\mathrm{1}_{x \\in [1/2,1]}$.\n\nWe first rewrite the explicit scheme as a function, taking the boundary condition as argument.\n\nAs seen in the lecture notes, the CFL condition, ensuring convergence of the scheme, is\n$\\mathrm{cfl}\\leq 1$, where $\\mathrm{cfl} := \\delta_t / \\delta_x^2$." }, { "cell_type": "code", "collapsed": false, "input": "def explicitSchemeHeatEquation(sigma, barX, T, m, n, BC, *extraArguments):\n dx = barX / (m-1) # Grid step in space\n dt = T / n # Grid step in time\n \n # Boundary conditions\n xx = linspace(0., barX, m)\n uu = BC(xx)\n rhs = zeros(m)\n for l in range(0,n):\n \t rhs[1:-1] = dt * (0.5*sigma*sigma) * (uu[:-2] - 2.0*uu[1:-1] + uu[2:]) / (dx*dx)\n\t uu +=rhs\n return xx, uu", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": "#############################################################################\n######## Boundary conditions in the example from the lecture notes###########\n#############################################################################\ndef boundaryConditionf(zz):\n uu = []\n for z in zz:\n if z < 0.5:\n uu.append(2.*z)\n else:\n uu.append(2.*(1.-z))\n return np.asarray(uu)\n#############################################################################\n#############################################################################", "language": "python", "metadata": { "zanadu": { "is_hidden": false } }, "outputs": [], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Convergence of the scheme" }, { "cell_type": "code", "collapsed": false, "input": "sigma, barX, T = sqrt(2.), 1., 0.001\n\nnx = 100 # Number of grid points in space\nnt = 10000 # Number of time steps", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": "TT = arange(0.01, 0.5, 0.05)\nplt.figure(figsize=(8,5))\n\nfor T in TT:\n xx, uu = explicitSchemeHeatEquation(sigma, barX, T, nx, nt, boundaryConditionf)\n plt.plot(xx, uu, color = get_cmap('afmhot')(T), label=\"t = %1.2f\" %T)\n plt.legend()\n\nplt.plot(xx, boundaryConditionf(xx))\n\ndx = barX/(nx-1)\ndt = T/nt\ncfl = sigma*sigma*dt/(dx*dx)\n\nplt.title(\"Solutions of the heat equation. CFL= %s \" % cfl)\nplt.xlabel(u'x', fontsize=12)\nplt.show()", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAeYAAAFUCAYAAADxkZ+xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYOhHYMTMwMDAwMDQj/D/AUAnSkDAfjIDAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Comparison with the true solution" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "The true solution has the explicit form:\n$$\nu(\\tau, x) = \\frac{8}{\\pi^2}\\sum_{n\\geq 1}\\frac{\\sin(n\\pi x)}{n^2}\\sin\\left(\\frac{n\\pi}{2}\\right)\\mathrm{e}^{-n^2\\pi^2\\tau}.\n$$" }, { "cell_type": "code", "collapsed": false, "input": "def TrueSolution(x, tau, nMax):\n temp = 0.\n for n in range(1,nMax+1):\n temp = temp + sin(n*pi*x)*sin(0.5*n*pi)*exp(-n*n*pi*pi*tau) / (n*n)\n return 8.*temp / (pi*pi)", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": "nx = 100 # Number of grid points in space\nnt = 10000 # Number of time steps\n\nplt.figure(figsize=(8,5))\ntau = 0.1\nxx, uu = explicitSchemeHeatEquation(sigma, barX, tau, nx, nt, boundaryConditionf)\ntrueSols = [TrueSolution(x, tau, 20) for x in xx]\n\nplt.plot(xx, uu, 'r+', markersize=10, label=\"FD solution\")\nplt.plot(xx, trueSols, 'ro', mfc='none', markersize=10, label=\"True solution\")\nplt.legend()\n\nplt.title(\"Solutions of the heat equation. tau = %1.2f\" %tau)\nplt.xlabel(u'x', fontsize=12)\nplt.show()", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAFUCAYAAADmsw94AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": "" } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Explosive scheme" }, { "cell_type": "code", "collapsed": false, "input": "sigma, barX, T = sqrt(2.), 1., 0.001\n\nnx = 100 # Number of grid points in space\nnt = 100 # Number of time steps", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": "TT = arange(0.1, 0.5, 0.1)\nplt.figure(figsize=(8,5))\n\nfor T in TT:\n xx, uu = explicitSchemeHeatEquation(sigma, barX, T, nx, nt, boundaryConditionf)\n plt.plot(xx, uu, color = get_cmap('afmhot')(T), label = \"t = %1.2f\" %T)\n plt.legend()\n\ndx = barX/(nx-1)\ndt = T/nt\ncfl = sigma*sigma*dt/(dx*dx)\nplt.title(\"Solutions of the heat equation. CFL= %s \" % cfl)\nplt.show()", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAeQAAAFCCAYAAAAg664KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9ukAAAAASUVORK5CYII=\n", "text": "" } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": "", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [] } ], "metadata": {} } ] }