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February 21, 2021 21:03
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Populating the interactive namespace from numpy and matplotlib\n" | |
] | |
} | |
], | |
"source": [ | |
"%pylab inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from sympy import symbols, diff, sin, Function, Eq, solve, dsolve, lambdify\n", | |
"from scipy.integrate import solve_ivp" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Harmonic oscillator\n", | |
"t = symbols('t')\n", | |
"th, th_dot = symbols('theta theta_dot', cls=Function)\n", | |
"eqn1 = Eq(diff(th(t), t), th_dot(t))\n", | |
"eqn2 = Eq(diff(th_dot(t), t), -th(t))\n", | |
"# Numerical vector field\n", | |
"nvec = lambdify((th(t), th_dot(t)), [eqn.rhs for eqn in (eqn1, eqn2)], 'numpy')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[10, 0]" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"nvec(0, 10)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[Eq(theta(t), C1*sin(t) + C2*cos(t)), Eq(theta_dot(t), C1*cos(t) - C2*sin(t))]" | |
] | |
}, | |
"execution_count": 12, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"sol = dsolve((eqn1, eqn2))\n", | |
"sol" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[Eq(theta(t), sin(t)), Eq(theta_dot(t), cos(t))]" | |
] | |
}, | |
"execution_count": 13, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"# Simple pendulum has closed form solutions\n", | |
"sol = dsolve((eqn1, eqn2), ics={th(0): 0, th_dot(0): 1})\n", | |
"sol" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Numerical solution for [theta(t), theta_dot(t)]\n", | |
"nsol = lambdify(t, [eqn.rhs for eqn in sol], 'numpy')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[0.1411200080598672, -0.9899924966004454]" | |
] | |
}, | |
"execution_count": 15, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"nsol(3)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"tt = arange(0, 100, 0.1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x1185b4ac8>]" | |
] | |
}, | |
"execution_count": 17, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Phase portrait\n", | |
"x = np.arange(-2*pi, 2*pi, 0.6)\n", | |
"y = np.arange(-5, 5, 0.6)\n", | |
"u, v = meshgrid(x, y)\n", | |
"# Plot vector field (theta_dot, theta_dot_dot)\n", | |
"quiver(x, y, *nvec(u, v), pivot='mid')\n", | |
"plot(*nsol(tt))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Plot a few solutions with different initial conditions\n", | |
"quiver(x, y, *nvec(u, v), pivot='mid')\n", | |
"# Force finer timesteps\n", | |
"t_min, t_max = 0, 10\n", | |
"tt = arange(t_min, t_max, 0.2)\n", | |
"for y0 in [(0, 1), (0, 2), (3, 1)]:\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt)\n", | |
" plot(*solv.y)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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gwYPpq6++oj///JPKy8sb9f165dvdu3dJQUGBzMzMaPTo0bR69Wo6ceIEPX78mCoqKrjXBQYGUlZWViOtRCKh6OhoSk5OpszMTCoqKqKqqqomfZw4cYLWr19PUVFRMlXplpWV0aFDh0hZWZn69etHs2bNop07d1JMTEyrOolEQqmpqXTq1KlGVbp2dnZ08+ZNqf1mZWXRuXPnyNzcnNMOHDiQQkNDpWqrqqooNDSURo4cyWkVFBRo6dKlvKp0hUIh/fDDD2RlZUWzZ8+mQ4cO0dOnT6muro7Onz9P+/fvp4sXL5K/vz9FR0dTdnZ2o8rCrKwsWrduHVdF2cCBAwfI2NiYVFRUyMHBgRYsWEAHDx6kx48fU01NDfe6oKCgJtWVz549o/Xr19OgQYNIWVmZ7OzsaOnSpXTp0iXKz8/nXpeent5EW1hYSB4eHqSnp8dV+q5du5auXLnSaD6lp6dTdnZ2k+WxevVqWrlyJe3YsYN+/fVXCgwMpOTk5EbbXVxcHO3bt4/KysqkLt/XSUxMJBsbG1qwYAH9+uuvzVYfN0dJSQkFBwdzVbqKiopkbm4utUqXiKi4uJj++OMPGjRoEDdHTE1N6eLFi1K3j5qaGrp//z598sknnFZJSYlWrlxJxcXFUsddVFREJ06cIACkr69PQ4cOpYULF/Ka2/g7K08FAsElAFsAaAFYTUQftPb61gqU0tPT0a9fP6l91tbWoqqqCgCgpqaGTz/9FN7e3sjNzcWzZ8+4lpycjGfPniEtLQ26urqwtLSEqakpLl26BBsbG6xZswYzZsxodARVV1eHp0+f4t69ewgJCUFwcDCKi4vh7OyMwYMH4/fff4ednR22bt0KMzOzJmPLyclBcHAwgoKCEBQUhISEBNjb22Po0KFISUlBUVER9uzZg759+3KaysrKJgFWMTExyMzMRLdu3WBrawuhUIigoCDMnz8fa9euhYmJCaqrq2FpaYnq6mquNdChQweoqalxR57Z2dkA6jNipk6disWLF6O0tBSpqanIzMzkWkZGBve8rKwMXbp0QV5eHgBg6NChWLp0KcaPH9/oCLiiogKPHz/mQqoePnyIiooKDBw4EFlZWaioqIC3tzdmz57d7NFZVlYWAgMDERAQgICAAKSnp8PFxQVqamoICwvDDz/8gDlz5jSpBCwtLeVyaiIiIhAZGYn4+HiYmJiga9euuH//Pt577z189913cHBwAADs2rULBQUFePnyZbOtoqICCgoKXBxz165d8cknn2DBggW4cuUKQkNDUVhY2KgJhUJoa2tzlZ4REREQi8UYNmwY5s6di48++gjq6uoA6rNaIiIiGmWQ5OXlwc7ODg4ODoiOjkZZWRk2b97cbAJmZWUl7t+/zy2rx48fw8rKCsOHD4eysjJu376NvXv3Yvjw4Y109L9snobclNDQUEREREBPTw/Ozs7o3r07Dh48iNWrV2P16tVcSNuJEyfw7NkzZGdnIysrC9nZ2cjOzkZxcTF0dXXRtWtXdOnSBf7+/tDU1MSsWbPw2WefwdbWFgcOHIC/vz8qKytRWVmJiooK7nlDq62tbTROZ2dnfPvttxg1ahSA+m09ISEBT58+5VrDtmFhYQGJRILU1FRMmTIFGzZsgK2tbZP5VVhYiODgYAQGBiIoKAgxMTHo06cPevbsiWvXruGLL77A2rVrm03cLCwsxP3793H//n2EhITg8ePHMDIywjvvvIPz589j7Nix2L59O6ysrADUnwlkZGTg+fPnSElJQUpKSqPn5eXlMDMzQ2ZmJurq6jBhwgSsWrUK77zzTpO+X+dvqzwVCAQfABhDRJ8JBILhaMHYBQLBAgALAMDMzMwhLa35L9sWiUTIzMyU2u/WrVsRGRmJsWPH4oMPPkC/fv1avXRSW1uLFy9e4NmzZ/jjjz9w8OBBAIC6ujrc3Nywa9cuWFpaNqslIqSnpyMkJARBQUE4fPgwiAgdOnTAmjVrWpwQDRQVFeHevXsICgrCiRMnUFxcDAUFBXz22Wf45ptvWo1fbQiLio2Nxe7duxEdHQ0AUFFRwerVq/H11183umRARBAKhZzJNyTpHTlyBOfPn+dS8959911YWFhg1KhRKC4uhomJCUxNTRs9NphjZmYmtmzZgqVLlzba6fr6+uL333/Hw4cPERcXB0tLSy5p0MXFBba2tlBSUsLFixcxZsyYRmmO+fn58PPz48wpMzMTLi4uGD58OIYPHw5nZ2d06NABjx49gqWlZaMIgbS0NKxevRqRkZFITU2FlZUV7O3tMWDAANjb28Pe3h6dOnVCSEgIZ66v4unpCRUVFXTq1KlJa0hpDA4OxpkzZzB79myMHDmy1UsFRITKykrO5J88eYJ58+bByMiIS190d3eHvb19i++Rn5/Pmf22bdtQVlYGABg4cCC2bNmCd999t0Xtq0Z/7tw5Lnhr2rRp2L59O0xMTFrU1tbW4unTpwgNDcWFCxcQFBQEAOjSpQs2bdqEefPmtXh5o6qqCjk5OcjOzsatW7ewefNmqKuro2/fvhgwYACWLFmCzMxMvHjxApqamtDQ0Gi21dbWYtKkSRg3bhymTZuGHj16AACuXLmCjRs3IjExEXp6elwCZkPMrbW1NTQ0NHDs2DE4OzvDzs6OG1tZWRl8fX0RGBiIwMBAJCUlYcCAARg2bBiGDRsGV1dX6OjoICEhASoqKrCwsOC0IpEIZ86cQUhICEJCQpCSkoL+/fvD1dUVrq6uGDRoEIyNjbl1/fq6GTx4MKKjo9GjRw9YWFg0eTQzM0NFRQU2bdqE5cuXc5+XD3+nsW8B8B8AYgAdUH+N/QoRfdySpi0iBcrKyuTOSwkICIBYLEavXr3QtWtXmfIgQkJCcOHCBejq6nLN1tYWzs7OUrVZWVnw8vKChoYGtLW1oaWlBQsLC0ycOFHqGEQiEY4fPw4jIyMugvj11L7WyMzMbPOs95MnT3JH1k5OTjKN58KFCzh06BBn5E5OTrxzuEtKSnD27FkMGDAAffv2lTkrnQ/0BlkvL1684PJWZH2PtLQ0nDlzplG6ZsOjtPeqrq7GmjVrIBaLuf9JGBoaYvbs2VKXLRHh559/RllZGfT09LgsI1tbW16570+ePIGKigqsrKxkvl4uFouhqKjY5PM9f/4c6enp6NOnD6/8/FeJjY3FokWLOCN/5513eM8TiUSCqVOncmbu5OTEnW3xobKyEurq6nLPn9Z4K1kxrR2xvwrLimEwGAzZYVkxDAaD8X+UNv1qPCIKABDQlu/JYDAYDNlgR+wMBoPRzmDGzmAwGO0MZuwMBoPRzmDGzmAwGO0MZuyvkZ2d3ah6Uxby8vKQmpraxiNitCfe5PbiqqoqPHjwAHV1dXLpa2pq5O6b8e+iTe+K+bs4deoUrK2t4ejo2GzBzd69e6GiogJbW1vY2to2qlqUFr6zbds2HDp0CEOGDMGoUaMwatQo9OnThys2KCkpabEQJygoCHPmzIGpqSlGjx6NMWPGYMiQIdwX/JaXl7cYLpSZmYnPPvsMDg4OXDMyMuL+/vz5c3Tv3l2uAiMfHx+Ym5vDxsZGZu3Zs2cRHR0NGxsbWFtbw9ramndhWHBwMJYuXQp1dXWoq6tDS0sLy5cvh5ubm1RtdnY2xowZg8LCQigoKEBFRQVr1qzB/PnzpS4DoVCIOXPm4OXLl1xAk4WFBZYsWcIr2OvIkSMQCoVwdnZG3759m3xBc1FREVRVVZsteElLS0NhYSEXX/A6Bw8exL59+zB48GAMHjwYrq6uMDc35+ZXTk5Oo/X+KsnJyZg8eTKEQiFGjx4NDw8PvPfee9x8rKioaLEIRygUQl9fHzY2Nhg+fDhGjBgBV1dXbj6+fPkS2traLVaZPn78GMrKylxh3KvFN8nJyVBWVoa5uXmz2tYIDw9HcHAwhg0bhr59+8pU3JSWlobFixejY8eO3JfKW1tbY+zYsbyKuSZOnIi4uDgoKipCQUEBU6dOxYYNG3gVc61evRo3b96EqqoqVFVVYW1tja1bt8LAwEDquM+fP487d+6gR48eXDVqz549eYWH8eUf+WXWIpEIn3/+eYt/f/DgASIiImBoaAgPDw+MHTsWo0aN4jba7du348GDB4iNjcWzZ89gYGAAW1tb2NjYoGPHjti1axeWLFmClStXNrsiMjMz4efnh1u3bsHPzw/KysqcyR87dgyTJk3CwoULm52EQqEQwcHB8PHxwc2bN5GRkQE3NzeMGTMGUVFR0NHRwaZNm5oYTHFxMS5duoTw8HBEREQgOjoanTp14kw+OTkZiYmJ+P777+Hu7t5k4rq6uqKuro4r01ZXV+ceExMT4efnh759+2L69OmYOnUqunfv3mTsxcXFSElJQWpqKvcYHR2N+/fvAwAUFBQwceJEfP/99y3GL5SVlSE4OBj+/v64e/cuIiMjAQAODg7Yv38/nJycWlyvRISoqCjcuHEDPj4+ePjwIYgIffv2xfHjx1s0y4blHhERwWV6BAYGoqioCIqKili0aBE2bdrUqHoxNzcXeXl5KCgoQH5+PgoKCrgWFRWFR48eAaiPbpg6dSq2bdsGQ0NDAMC8efNw7NgxqKurw9DQkDMVQ0NDaGtrY9u2bXBwcMDChQsxffr0RmZbUVGBhw8fIiQkBPfu3cODBw+go6PDGf21a9dgYWGBzZs3Nzs3iQjR0dG4ceMGrl+/jvDwcLi4uMDDwwNEhKdPn+Knn35qtlKzqKgIwcHBuHv3LgICAhAfH48BAwZgxIgRMDIywrFjx/Dzzz9jyJAhTbRz587Fn3/+iezsbGhqasLc3JyrgO7QoQN+/PFHTJgwAZ6ennB1dW00P+Pj4xEfH4/y8vJGraysDC9fvsSvv/4KANDR0cHQoUPx5ZdfYtCgQc2u56ysLISFheHx48cICwtDYGAgampqoKamBk9PT3zxxRetVkAnJyfj5s2b8PHxQUBAAIRCIQwNDbFv3z5MnDixRR1Qf1Do5+cHPz8/3L59G4WFhVBSUsLq1auxYcOGZqtTiQhZWVlISEhAfHw8EhISEBUVxW1TampqmD9/PlavXg1TU9NW+wfeUuUpX6QZu1gsxg8//NDi3319fRESEoJ+/fph7NixGDt2bItH70KhEImJiYiLi0NcXBzu3r2Le/fuAahfqIsXL8aaNWu4jfZ1JBIJIiIicOvWLfz5559cloazszMOHTokNbAsNTUVN2/exM2bN3Hr1i3U1taiR48eOHLkCEaMGNGiTiQSITY2lguJ+v3335GbmwsAGDFiBLZs2dIoxiA4OLhRwFJVVRX3/O7duwgMDISmpiaGDBkCNzc3zJ07lzuTmTt3Li5fvozy8nKYmprCwsIC3bt3R/fu3aGhoYENGzZg7ty5WLFiRaNMDaD+8sD9+/fh7+8Pf39/REREwNbWFm5ubnBzc8Px48fh7u6O+fPnN7sjrKiowO3btzkzF4lE3NFoWloahEIh1q5d2yRyt6amBjdv3uSMPDw8HMbGxlyWR3FxMe7du4cdO3Y0e6bSr18/FBcXc6Xzr7aMjAycOHECkyZNwvz58zFkyJAmO1KhUIj8/Hzk5eVxO4nc3FwkJCTg7NmzAOpD2IYOHYrt27c3Cnx7FbFYjCdPnnCBc9euXUNtbS20tbWxYcMGLFu2rMkZw6sUFhbC19eXW35lZWXQ19fH3r17MWXKlFaPXIuKihAUFIS7d+/ixo0bSElJAQB8/PHH2LZtW7NnDrW1tcjMzERaWhrXHj58CF9fX+41Y8eOxe7du7mDh7179+Ly5cvQ0tLiojQamoqKCr766iv06tULH3/8MWbMmNHoyP/58+c4d+4cZ+YvX76Evb09Bg4cCEdHR1y5cgUGBgbw8vJC165dm4y3pqYGgYGB8PHxgY+PD/Ly8uDu7o4xY8ZAXV0d/v7+2LZtW6Oz+gbKy8sREBDAmXlaWhqGDBkCd3d3DBw4EF9//TUOHDjQKKOmga1bt+LSpUtISEjg4kusra3Ru3dvdOvWDZ9//jkWLVqEzz//nNdRfgP/amOXxrVr12Bvb99ssqI0Dh48iJycHHTv3h3m5ubo3r07unbtyivH+Y8//sCOHTugoqICFRUVaGhoYPXq1a0ehTaQmJiIefPmcdme1GFMAAAgAElEQVTTSkpKWLhwIaZOnSr1tLG8vBxr1qyBlpYWlx3SYGJ8MsYvXrwIMzMzODg4NPv62NhYqKmpwdTUtMnfc3Jy0KFDh2YnPgB8/fXX+P333+Hm5oYRI0Zg2LBhjS5zVVVVtZizcevWLXz44YewtbWFh4cHPDw8MHDgQG4HLRKJWvx8ZWVleP/99zFo0CAMGjQI77zzTiMjKi0tlfvUNiYmBl27dm3xM7fG3bt3kZKSgoEDB8La2lqmDPinT5/Cy8uLyyDq2LEjHB0dMXr0aKna4uJizJw5EwUFBRAIBFBQUOBSA6XN7bq6Onz++edIT0/nwrqMjY3h6enJaxleuHABhYWFsLOzg52dnUwZ45mZmSgoKED//v2b3Q5CQ0Nx7Ngxzsjt7OwaLdPCwsIWc2TS0tJgY2MDc3NzjBkzBmPGjIGrqyuX5Nra/CIimJqaokuXLnB3d4e7uztcXV25yzRCoRDKysotXhb09/eHUCiEtbU1zMzMGr2upKQERCTX/GrXxs745yCRSOQOFms4JTc2Nm7jUTEY/z+VtVu3bnLpKysrW01tfRvwNfZ/5T9PGf8c3iQtsuF0nMH4KxAIBHKbOoB/nKnLArvdkcFgMNoZzNgZDAajncGMncFgMNoZzNgZDAajncGMncFgMNoZzNgZjH8Zb+MWZca/i3/V7Y5EhIyMDF6FSWlpadDX129UHFNaWgptbW2pBUE///wzwsPDMXnyZIwcOZIraKitreWet4Sfnx+++eYbTJ8+HZMnT+aqylorhmhAIpHgypUrcHV1bVRs01rGjDSysrKarcjjQ2JiIgwNDeUq9ElKSkJubi4kEgnq6uogkUjQtWtXXnk12dnZePLkCXefe0VFBczMzDB+/Hip666iogJxcXFcEZmysjJUVFRgbGzMq1goOTkZ3bt351Ww9jpFRUXQ0dGRqo2JicGNGzcwevToRjlErRVzNZCeng43NzdMnz4dM2fORO/evQHwm18A4Onpib59+8LDwwNdunQBUF+dqaqqKteXLxcVFaFjx45y3faamZmJzp0788rveZ3s7GwUFhZyX9qtqakJNTU1Xp+htLQUjx49QkVFBVet3aFDB3z88ce8irlCQkJQU1OD2tpaCIVC1NbWYvTo0by+zD0xMRHa2towMDCQ+Uu/ZYKI/vbm4OBAfAgNDaX79+83aoMGDSJbW1v68ssvKSQkhMRicbPayZMnk5KSEvXp04fmzJlD+/bto0OHDpGjoyPdvn271X4TEhJo48aNZG1tTbq6uvTJJ5/QjRs3aObMmXTnzp1WtaWlpXTq1Cl6//33SVVVlUaNGkUnTpwgLy8vOnToEEkkkha1BQUFNGTIEFJVVSVLS0v69NNP6eTJk7Rs2TJatGgRFRQUtNr30aNH6eeff6ZTp07RlStXyM/PjyZPnkz9+vWjbdu2UUZGRqv618fy2WefEQDq3LkzOTk50YIFCygzM1OqViKR0Pnz5wkA1xYuXEhlZWW8+o6Pj6eOHTty2vnz51NlZSUvbV5eHvXu3ZvT6unp0ZkzZ1pd7kRE5eXllJSURBMmTCA1NTVydnamxYsX05EjR6i4uLjJ6w8cOEDjx4+nZcuW0datW+mXX36h48ePk4mJCX333XeUn5/fYl+RkZE0Y8YM6ty5MxkbG9Onn35Kv/32G02fPp32799PdXV1LWrFYjH5+fnRJ598QlpaWuTg4EC7du2iU6dO0Zdffkm1tbUtaiUSCe3du5fc3d1JVVWV3nnnHdqyZQtdvHiRxo0bRzk5Oa0uozlz5lC/fv1o8uTJtH79ejp58iT99NNPZGNjQ6dOnWq17waqq6spJyeH4uPjad++faSsrEwuLi60evVqunr1qtQ53vA57t27R6qqqtx67tatG129elWqlqh+btva2nLa4cOH85rXRERVVVX00UcfcVojIyPy9fXlpS0vL6e1a9cSAFJQUCBjY2OaMGECpaSk8NITEQEIIx4e+4829oEDB1Lv3r0btVc3+N69e9O2bdtIKBQ2qy8qKiI/Pz/asmULffTRR2RsbMxpR44cSWFhYVLHEBMTQ15eXmRjY8NpV61aRTU1NVK1+fn5tG/fPho8eDCnnThxIhUVFbWqq66upsDAQNq8eTONGjWK1NTUCADp6urSnj17SCQSNatbt24dTZs2jTw8PGjYsGE0YMAA0tPT4/pWUVGhdevWUUVFRRPt5cuXad68eTR48GDq3LkzKSkpkYWFBdevl5dXq+Oura2lO3fu0PLly8nMzIz09PTIyMiITExM6M8//5S6rIqKiujgwYM0ZMgQUldXp759+5K2tjadP3++VZ1QKKSAgABav349OTg4kIqKCllaWhIA+vTTT6mwsLBF7eLFi6lXr16kpaVFAKhTp05kYmJCAEhdXZ3mz59PERERzWqjo6Pp6NGj5OXlRXPnzqVRo0ZRjx49Gi3rWbNmUXJycov9i8ViCg0NpW+++YZcXFxIIBAQAHJ1daXY2Fipy6yqqoouXLhAH374ISkrKxMAcnFxodTUVKnakpISunDhAs2cOZN0dXUJAHXs2JHOnj3b4k4wKyuLbt++Tfv37ydPT0/y8PAgU1NT7jObmprSTz/91Oz82rt3L2fEysrKZGBgwK0nAGRnZ0fbt2+nrKysJlqJREKJiYl06NAhmj59OhkZGZG2tjYZGhqSqqoqbdy4UeqOv7y8nH755Rfy8PCgDh06kIODAykqKtLmzZtbPDhsoKKigi5evEhTpkwhDQ0N6t+/PwGgyZMntzq/wsLC6IcffqCpU6eSlZUVKSoqcp9ZT0+Pdu3aRdXV1a32/TrtwthfRyKR0LJly+jHH39sdYNpSbtq1Sry8PCgTz/9lNavX0979+7ldYRARHTmzBkyMzMjAwMD0tbWpoEDB9LTp095acPDw6lHjx6kq6tLysrKZGJiQoGBgby0ubm55ObmRm5ubjR+/HiaNWsWHTx4sNWjugYkEgl5enrSV199Rbdu3aLy8vJWP9/3339PV65cofj4eBIKhRQaGko//PADlZaWttrPr7/+Sh07dqQePXrQqlWrKDg4mMRiMR09epRKSkpa1SYnJ9O4ceOoQ4cO5O7uTidPnqTS0lIKCgqi58+ft6qtqamhjh07koWFBS1evJiuXr1KpaWl5O/vTwEBAa1qiYhCQkIoJCSEUlNTuQ3s1KlTtGfPnmaP0qVx7Ngx+vjjj2n79u1069Ytys3N5a0NCgqivn37kr29PQ0cOJCGDRsm9cyygZycHHJwcCBtbW0SCASkq6tLly5d4qWtqamhSZMmkZWVFVlaWnLrkO8Z0jfffEPTpk2jjRs30pkzZyg0NLTZM7Pi4mLKzs6mqqoqbscRERFBK1asoIiIiFbPqAICAkhHR4fGjh1LO3fupPDwcBKLxbRv3z569uxZq+MrLS2l6dOnk4aGBrm4uNCePXsoJyeH4uLiKCQkROrnmzdvHqmrq9PAgQNp69at9OzZMyotLaXTp09LPQvcvXs3zZ49m3bv3k1BQUFUWlpKL168IG9vb95nr6/D19hZVswbQERyXZcUiUSorq7mnWv+TyctLQ0VFRWwsbGReXkUFBTg7NmzmDZtWos55K3xJv9DaI8QESorK1FeXo4uXbq8UeTDP4WGLxaR55o0EWH37t348MMPmyST8sHX1xfW1tZvFE3QlrAQMAaDwWhn8DX2f//unMFgMBiNYMbOYDAY7Qxm7AwGg9HOYMbOYDAY7Qxm7AwGg9HOYMbOYDAY7Yz/M8ZeW1sr0+vj4+Nx7949LnBJJBLx1hYXF+PIkSOorq6WWQv8//t2gfovzZWXt3Era1sjkUhQWFj4tochlVfXGR9qamqQnZ3N/SzLepZIJNi+fTvy8vIA1M8vWdZ1REREo7kp7zwRi8Vy6f5plJWVQSKRyK3/J25n/5oQMJFIhE8//RT29vYYO3YsLC0tpWo2btyItLQ0jBgxAlpaWrh48SJ27twJExMTqdqEhAR89tlnMDQ0xLJlyxAZGYlJkyZh2LBhUrW5ubk4ceIE1q9fj8WLF0NPTw8KCgpYunSpVG1NTQ3MzMwwZMgQfPjhh3jx4gUUFRWxdu1aXiFPhYWFUFVVhaamJjw9PaGvr4///Oc/MhVYEBG2bt2K8vJyGBoacq1Pnz68go58fHzg6+uL/Px85OfnAwB2796NPn36SNUmJCTg4MGDSElJwfPnz1FaWopz585h6NChUrUFBQXYuXMnFxxWWVmJwYMHY/ny5VILderq6rB27VpoaWnB1tYWtra26NmzZ6vLPDY2FsnJyejZsycyMjJw+vRprFmzBgMGDJA61vDwcIwcORKDBw/Gxx9/jLCwMAwZMgRTpkyRqi0rK0NERAQXNvfhhx/Cx8cHe/fu5RVetnHjRoSEhGDGjBkYN24c9u/fj1OnTvEKe7t27RpevHiB/v37Izs7G76+vvDy8pK5+Ofs2bMIDw+Hs7MznJ2dYW5uzru47eHDh7h8+TJEIhHEYjHEYjEmTZqEkSNHStUWFhZi+/btSElJQWpqKjIzM+Ht7Y358+dL1YpEIuzYsQPJycnIyspCVlYWhgwZgp07d0oNbwOAvXv3IisrC9ra2tz3/b733ntyFeZJhU95als3WSIF3NzcyNzcnMzNzUldXZ3LlrCysqL9+/e3mvMQFRVFW7ZsIXd3dy5vRUNDg7Zt28YrsEgoFNK5c+fonXfeIQCkpKREhw8f5j32hw8f0tSpU0lRUZEA0PLly6XmUhARPX/+nH788UcaMWIEpx0wYACvCIORI0cSAFJUVGwUkjRixAg6efJki7k6RPXhSD4+PuTt7U2Ojo6NMkCOHz/eYkbNqxQWFpK3tzendXJy4h0+JpFIyMfHhzp16kQAyNzcnOLj43lpq6qq6OLFi2Rubs7lkezYsUNq9MKNGzfoq6++ohkzZlC3bt24cevq6tLXX3/dbO5JA1euXCFXV1fq0qVLo8CzkSNH0q1bt6SWnDfk47yaJbRw4UKqqqri9ZlTU1PJ09OTNDQ0CAB5eHi0GhvxKtHR0bRixQpuWffs2ZOio6Ol6q5cuULTp08na2trUlBQ4LaLBQsWSF3PDx8+pE8++YQ8PDyoT58+jZbZmDFjpMYDEBElJSXR999/z20XnTp1ogsXLvD6zET1wYLW1tYEgLS0tHjlGDUQGxtL7u7u3Jg3b94sdR035NwcOXKE3NzcOG3Pnj3p+vXrvPtuAH9XVgwAUwB3AcQBiAWwQppGFmOPiYmh8PBwCgsLI2tra3J1daUffviBYmNjpS7UBkQiEU2fPp2srKzI3t6eXF1dydPTU2oGSgNHjhwhAwMDbqUsX76cl8kRET148IDMzc25gKcPPviA98b3/Plz6tevH5mbm5OZmRn16NGDTp06JfVz19bWUn5+Pjk6OtLAgQPJ09OTfvvtN8rOzm5Vt2HDBhowYADNnz+f1q5dS506daKdO3fyCiqKiYmhGTNmkJqaGo0ZM4aGDBlC8+fP5xWWVlNTQydOnCBbW1syNzen+fPnk6OjI6+slbq6OpozZw6XdPjpp59Sz5496fHjx1K1RER79uwhT09P2r17N/3nP/+hnj170t69e3mvowa+/PJLsrKyorFjx9KqVavo8OHDzQZaNcfNmzepe/fu1KlTJ1JUVKQ+ffrw3qGlp6eTg4MDZ7IDBgyQmtLYQHl5OXl4eFDnzp1JIBCQmpoanT17lpdWIpHQxx9/TNbW1jRy5EiaPXs2eXt708uXL1vUxMTE0K5du+j06dO0a9cu0tXVpaVLl1JkZKTU/p4/f052dnakqalJU6ZMoaFDh5KHh4fUOU1UH7Z2+fJlcnV1JT09PVq5ciWZmpryznq6du0ajRgxgrS0tGjJkiXUtWtX3kmS3t7epKOjQx4eHrRp0ybS0NCgH374gdd20Rx/p7EbARjwv+daAJIA2LSmkScErLa2lndg119FTU0NpaSkUFBQEK8Evde1SUlJdOvWLQoNDf1rBvgKIpGo1aNNaaSlpUkN8HqVsLAw8vLyorS0NCIi3sZEVG9OgwYNoosXL5JIJKLs7GyZxn78+HFKSEggIqIXL17IHbCUmJjI64yqOeTVvY5EIqGqqiqZQ8iEQiElJSWRr68v3bhxg/dBTwNisZjy8/MpLi6O19msrO//OpmZmbzPTIjqP9/169e5g4ynT5/KdGDn7u5Ohw4doqqqKqqsrOS1Q2hg48aNtG/fPm5eNcw1PlRUVHBzo6CggHc8cEvwNfY2z4oRCATXAPxMRH4tvYZlxTAYDIbsvJWsGIFAYA7AHkBoW74vg8FgMPjTZsYuEAg0AVwG4ElEZc38fYFAIAgTCARhBQUFbdUtg8FgMF6jTYxdIBAoo97UfyGiK829hogOE5EjETnq6+u3RbcMBoPBaIY3NnZB/c2nxwDEE9GuNx8Sg8FgMN6EtjhidwXwHwBuAoEg6n9tTBu8L4PBYDDk4I0rT4noHgDZvx+OwWAwGH8J/yeyYoRCoVxZEGKxGHV1dSgtLZUrD6KsrAxEhLKyJv9L5kV5efk/MoeC0baUlpbKpSsqKgIAueZXw7ySt+83yVZh/PX8K4y9oqICZ8+e5SayLDx69Ai3bt3C+++/j9zcXJm0586dw4ABA/Dtt99i48aNMmnj4+Nhbm6OH3/8ER9++CFqampk0nt7e2Pfvn2YN2+eXEFg27dvR0REhMy6toKIkJKSgvPnzyMxMVFmbWxsLH788UfcuHFD5r7FYjGSkpIQFBTEa8coFApRUlIi105ULBYjMDAQGzZskNkk09LSMHbsWGzevBlr166Vqf/KykrY2Nhg1apVmDhxIrKysmTqe8qUKdi4cSPGjRsn8/opKCjAjRs3sGLFCrl2DE+fPkVJSYnMuteRSCTIyspCSkqKzNqMjAycPHkSx48fl3m9V1ZWwt/fHwcOHJA5XPBvg08VU1s3WStPjx49Svr6+qSgoECDBw+mrVu38o4UOHz4MBcHYGBgQL6+vrz7FYvFtGfPHi4OYMeOHTKN+969e6Svr08AaNKkSbyrE8ViMa1fv560tLQIAA0ePJjy8vJ49+vt7U2mpqYEgBwcHOjw4cO8qzFFIhFNnTqVunXrRj179iQbGxtasmQJ7/iF69ev0+jRo6lz584EgFatWsW7QjA1NZU++eQTMjY2JgA0ceJE3sssLy+PZsyYQba2tqSiokJGRka8sk+IiMrKysja2pq0tLTIzs6OxowZQ1u3bm01V6eB06dPk6amJpdbsm3bNqqsrOTd73fffUdKSkoEgBYsWCBTBWtqaioNGDCAAFDfvn15ryOi+qyYQYMGEQAyMjKSqVJ4x44dXISBoaEhnT17lvc6fvnyJS1YsIAAULdu3WjcuHHk5eXFuyIzICCARowYQRYWFqSsrEwODg68oxtKSkpo2bJlZGVlxS0zvtXVIpGINm3aRAMHDiRFRUXS1tam8PBwXtq6ujpatmwZ9e7dm8zNzcnQ0JBmzpxJRUVFvPSvgr8rUkCeJqux79+/n/T09AgADRw4kL755huKiIjgNZmqq6tpypQpZGFhQQYGBqShoUFr1qzhtdESEV26dImGDx9OHTp0IAB05MgR3uN+8uQJjR8/nnR0dAgALVmyhPcGkJCQQMOHDydzc3NSVlambt260ZMnT3hp79+/TyYmJqSgoEB2dnY0Z84cOn36NC/TOHr0KBeYpqOjQwcPHpQapNWASCSi/fv3cxu9p6enTKXnSUlJ1LNnTwJAgwYN4l1yLpFI6Nq1a9SjRw8uYCklJYV3v0uXLuV2ot26daMjR47wnh9isZimT59OysrKZGpqSs7OzrRkyRIqLCzkpf/zzz9p+PDh3I5w2rRpvEr6iep3ZnPmzCEjIyMCQO7u7ry1FRUVtGjRIurduzcJBAIyNDTkbe5CoZBGjRpFnTt3JjMzM+rduzetXLmSVwzEw4cPycbGhgCQpqYmLV26lOLi4nj1W1JSQl9++SUpKysTAJowYYJM0RO5ubk0dOhQAkBmZma8dwhE9Tuk6dOnEwBSV1ene/fu8dZev36dC6fr0KED7du3T+5IhnZl7OXl5XT06FGZ8h1aQywWy5ztUVNTQyEhIbRt2zZKT0+Xub9Hjx7Rli1bKDg4WCYtUf0ePzc3l3dGRVlZGQUFBckcZEVUn+Fx48YNmjp1Ku8wqQZu375N/fr1o+XLl9Py5ctlmrw5OTmko6ND69atIxcXF97G2MCsWbNoz549ZG9vL9PZDVH98t27d69Mht6ARCKhgoIC3ju/1t4nNzeX7ty5wzuc6lXt06dPaefOnXTu3DmZ+y4rK6PAwED65Zdf3vhz8MHPz4/27t0r0xkGUX2C54IFC2jZsmX0xRdfyDRWsVhMPXr0oDlz5tCIESN470wamDp1Kk2aNIk8PDzo1q1bMmkbMqKcnZ1l7vd1+Bp7m2fF8IFlxfyzEYlEvLLfX6dhUpWUlKBjx46887UbyM3NhaGhIYqLi9GxY0eZ+xeLxaiqqoK2trbMWsa/h5KSEl7fC/A6hYWF0NPTk2t+CYVCqKqq4uXLl+jUqZPMfYvFYkgkEqioqMisfRW+WTHM2BkMBuNfwlsJAWMwGAzG24cZO4PBYLQzmLEzGAxGO4MZO4PBYLQzmLEzGAxGO4MZOw8KCwvlzmwRi8XIyclp4xEx2hNisfiN9PKU1DdQVVX1Rn0z/pn8nzB2IoKPj49c2sTERMycORMXL16UWVtQUID//Oc/WL9+vVx9x8fHy9XvPwl5jYOI3siw/u7beN8kTGvLli34448/ZNbW1NRgyZIlmDBhAurq6mTW+/v7Y9q0aXLnnbzJ+vknkJaWJre2tLRUrmX+t8Gniqmtm6yVp0REN2/epOPHj8tcVUhEtHv3blJWVpYpDoCovtp05syZBIBMTExkKl+WSCTk7e1NAEggEFBkZKRMfdfV1VGPHj1ITU2NIiIiZNISEf3xxx+0YsUKevHihcxaiURCeXl59PDhQ7p06ZJM3yZPVD/2a9eu0ejRoyktLU3m/u/evUvOzs4UEhIiszYjI4O8vb3pp59+kkmXlJRE4eHhFB0dTfHx8TJVJqekpJC1tTWdP39e1uHSzZs3uRwjWef2L7/8wuXMnDhxQiZtVlYWl5myefNmmbRERL6+vmRgYECXL1+WWVtQUEBXr16lyMhIevnypczl9RKJhKKioujrr7+WqbS/gbi4OJo4cSLt379fZm1BQQF9/fXXtGDBApm1FRUVFBwcTAcOHOCd3fQ6aE+RAkT1eR4AqH///vTHH3/w1kkkEtq5cyc5OTmRqqoqnT17VqZ+k5KSaPbs2aSoqEgbNmyQSVtSUkIbN24kTU1Nevfdd2WawGlpabRy5Urq3r07mZqayrzRe3l5kUAgIEtLSzpz5oxMfW/dupUAkLa2Nvn5+fHWSSQSOnr0KGcYspprZGQkvf/++wSAxo8fL5M2JSWF3n//fS4fp7q6Wib99u3buawYHx8fmbS3bt0iAwMD0tPTo4ULF8pUKh8VFUVLliwhbW1tGjdunEzrqba2lg4ePEiGhoZkYmIi0w5YKBTS6dOnyd7enlRUVGQKASMiOnnyJFlZWZG2tjZ5eXnJVN6fmppKCgoKpKamRqtXr5YpPuL+/fvc/Fq8eLFMY05NTaXZs2eTgoIC9erVi3euDlF9zszq1atJQ0OD1NXVKSMjQ6a+9+3bRwoKCqSqqipTEOHrtDtjj4yMlOvo81Wqqqro/v37Mq3QBp49e0ZLliyReYUSEeXn59PKlSvJ399fZq1EIqHo6Gi6c+eOTLqcnByZza2BuLg4cnZ2ppiYGJm1v//+OwEgR0dHmfN4Ll26RABIQUFBrkyNYcOGkaqqqsxZK0REiYmJtHLlSrnyddqCiooKOnHihFxnZxUVFfTdd9/R4cOHZdZKJBIKCAigHTt2yB1MVV5eLtM2VVdXRz/++CPl5ubK1ZeZmRm5uLjInOsTExPDhb1dvXpVJm11dTWNGDGCANCWLVtk0hIRPXr0iHr27PlGpk7UDo39n4K8k5+oPv3w34Isl51epa6ujg4cOCCXQdXV1dGpU6do0aJFcvUtFArpl19+kUvbHqipqXnbQ/hbiI+P5x3z+zp+fn40ffp0ubbj5ORkWrZsmdzLWd4xvwpfY2dZMYw2h4hkDgB7lerqaqipqbXhiBiM/09NTQ06dOggl7aurg6KioptPCL+sKwYxlvjTUwdADN1xl+KvKYO4K2auiwwY2cwGIx2BjN2BoPBaGcwY2cwGIx2BjN2BoPBaGcwY2cwGIx2BjN2HhARsrOz5dbm5OSgsLCwjUfVvnkbt+G+Td4kCCw3NxfPnz+XW19dXS239t9Ke59f/2eMPTY2Fvfv35dZJxaLMXv2bFhaWsq18Xl7e8PU1BTR0dEya6urq+Hl5YWEhASZtW2FRCKRS1dcXIzQ0FC5tNXV1Th+/LhcWgB48uSJ3No3Qd7As7t378LR0RHl5eUya8+dO4euXbvi8uXLMmuzsrLw3nvv4bvvvpNZC9TfD/42k0tfvHghl46IcPjwYbn7vXTpktzbBRGhpqZG7r758q8y9t9//x1BQUFyaW/duoXt27fLrFNSUsKUKVPknsQzZsyAlpaWXNra2loEBAQgICBAZi0AXLhwAb/99ptc2qysLHz++edyJf8JhUJMmDABIpFIZi0RYdGiRcjIyJBZCwDXrl3D7t275dJGR0fjwIEDch3NPX36FLNnz5ZrgzcyMkJWVhZiY2Nl1np4eMDS0hJ5eXly9auvr4+YmBiZtQBw48YNfPHFF3Jpy8vLsXPnTpSVlcmsJSJ4eXkhODhYrr53794NPz8/ubQPHjzAxo0boaAgu3W+fPkSs2bNknunIBN8ylPbuskbKVBZWSmXrgF/f3+5y/p37dolV9ogUX0S3q5du+TSVlVVvZUyeX9/f6PMv/sAACAASURBVDp69Khc2pUrVxIAysnJkVm7Z88eAkAHDhyQWZuZmUl6enq0Y8cOmbVE9Vkiz58/l0tLVB/DIO8cjYiIoIsXL8qljY+PlzkQqwGhUEjLly+XS0tUH6wla2YLEZFYLKaEhAS5+nz06BEpKCjIta5u375NioqKtGTJEpm1WVlZZGJiQsOGDZNZS0R04cIF8vT0lEvbAFikQNtCRCgpKUHHjh3l0ufl5aFLly5tPKp/JgUFBfjtt9+wePFimatQs7Ky8NNPP2HUqFFwd3eXue/09HSIxWJYWFjIrH3bvEm5emZmJkxMTOTSvkmJ/dsiIyMDJiYmMs+v6upq7NmzB6amppgxY4bM/d64cQOVlZWYMmWKzFrgzSMJ+EYKMGNnMBiMfwksK4bBYDD+j9Imxi4QCN4XCASJAoHgmUAg+LIt3pPBYDAY8qH0pm8gEAgUAewD4A4gE8BjgUDwXyKKe9P3ZjD+KVyNzML2PxORXVINY101rHmvF8bbd33bw/p3EH0RuPMtUJoJ6JgA724E+sp3jZrBjzc2dgBOAJ4RUQoACASC8wDGAWDGzmgXXI3MwrorT1Etqv/y4qySaqy78hQAmLlLI/oi8MdyQPS/IqjSjPqfAWbufyFtcSmmK4BXbzrO/N/vGIx2wfY/EzlTb6BaVIftfya+pRH9i7jz7f839QZE1fW/Z/xl/G3/PBUIBAsEAkGYQCAIKygo+Lu6ZTDemOyS5kvuW/o94xVKM2X7PaNNaAtjzwJg+srPJv/7XSOI6DARORKRo76+fht0y2D8PRjrNv+NTi39nvEKOi3cW9/S7xltQlsY+2MAlgKBoLtAIFABMA3Af9vgfdsceYOWxGIxFixYgAsXLsil//zzz/HVV1/JVT5dVFSE/Px8ufp9m7zJmOUtcQfkz2tpjTXv9YKacuOiEjVlRax5r1eb9XHnzh1ERUXJFWewbds2fPLJJ3j27JnM2ujoaBw+fPivm2PvbgSUX9sBKqvV//4NeJPQtKSkJNTV1Ul/YTNUVlaiqKhI7r7/Lt7Y2IlIDGApgD8BxAO4SESyh17woLCwEG9S2DRgwAC5JrCSkhLOnz+PxET5rqmGh4fj8ePH0NbWllnr7++PsWPHyjWRKyoq5M7WAerHLS/r1q2TO+zoyJEjePTokVzakJAQ3Lp1Sy4tETWbuTLeviu2TOyDrrpqEADoqquGLRP7NPnHqY+Pj9w7lgMHDmDXrl1yfV/sixcv4O/vL1flaU5ODlasWCH3uL29vVvX9p0CjN0D6JgCENQ/jt0D9J2C27dvy5VFBADHjx9HSUmJXNp79+7h9OnTcmlzc3PlDk0DAF9fX7m1stAm19iJyOf/sXfeYVGc6/u/FxCR3kSlCYgUAWmCoMSGXdBoNEfTjBrLMdFYEo01ETVG/VpiiVHREGtOrKiosaGiIFV6k957h92F3X1+f3h2fhIps0uanPlc13Mxu+y97zsz7zzv7Ow89xKRFRENICL517oT6urqUFAg/7W5xYsXw8DAQC7t4MGDsXr1arm0/fr1w3fffSeXVlFREd9//z2UlGS/gUkgECAvL0+udgHg0KFDch88z58/x759++TSFhcX46uvvpLr7JXP5+Ozzz6DUCiUWcvj8XDv3r02233b2QhPvxqD7O+m4OlXY9q8G8bQ0BCqqqoytyvV7tq1Sy5t3759sWXLFrlsAbS1tfHFF1/AzMxMrrY9PT07X+fB7wIrE4Fval7+/e/dMNnZ2XIZxQEvLQXWrl0rl7a0tBSbN2+Wy664oqIChw4dktsmee/evX+NWysbQ5k/OuQ1AesqYrFYbm1MTIzc2pCQELm1TU1Ncmu7Sle217Jly+jw4cMkkUhk1r7//vs0cuRIys/Pl1n7/Plz8vf3p5qaGpm1fyclJSVyax89eiS3uV1paSnV19fL3fbfRUxMDEVERMg1vr777jvy9PSk6OhombWPHj2iKVOm0JMnT2TWEhFVVVXJ1Wcp4EzAON5UumqUxMHRERKJRC7b3X8CnFcMxxsLl9Q5/kze1KQuC91/DTk4ODj+x+ASOwcHB0c3g0vsHBwcHN0MLrFzcHBwdDO4xM7BwcHRzeASO0uISO4yZAByV9hxcLBB3ipfju7J/1RiF4lEKCkpkUsbEhKCdevWyVWJWVBQgNmzZ8tdoh8VFdWlSeWvpis+HhUVFXJVnP5TkLfvYrEYx48fl6saUigUYtasWXJ7GR0+fBixsbFyaQHIXT36d1BTUyP3sdTS0vLmrCubKqY/OrpSeZqfn08JCQlyadesWUNeXl5yVX5NmzaNANDq1atl1m/atIkA0MiRI6m2tlYmbWlpKfXu3ZsWLlwoV7/j4+Ppt99+k1kXHR0td/VmQEAAHTlyhEQikczamJgYmjVrFlVUVMisrayspI0bN1JZWZnMWrFYTHV1dV2qtk1PT6eFCxfKtd4nTpwgALRy5UqZ+3D+/HkCQGZmZvTixQuZtNXV1aSlpUW6urqUnJwsk5aI6Nq1azRjxgy5xqZEIqHq6mri8/ky6WJiYujs2bPU3Nwsc5s1NTU0YcIEmbcT0cv+fvTRR/Ts2TOZtUREwcHBclVTvwpYVp6+MYldIBDQ9u3bSUNDg9auXSuz/uLFi6Svr08LFy6k4uJimbTp6enE4/Ho448/psrKSpm0QqGQ+vTpQ8OHD6f09HSZtERE7777Lg0aNIiOHj1KAoGAta6lpYX2799PJiYmNGPGDJnbjYqKIh0dHXJ0dJS53L2hoYH09PTIxcWFQkNDZW7b3d2d+vbtSzdu3JBZ+/XXX5Oamhpt2LCBqqurWeskEgn9/PPPpK6uTo6OjjIn11u3btGgQYPI1dVV5u3V2NhIRkZGNH78eLnK3EeNGkUWFhZylbl/8803pK+vT0ePHpV5Qvr111/JxMSEpk+fLvNJQGRkJDk5ORGPx6PCwkKZtBKJhMaMGUOmpqZ08OBBmffVokWLSFVVlQ4dOiSz9vTp08Tj8eizzz6T+STtxYsXpKurS25ubpSWliaTVkq3S+xSBAIB5eXlyaSRSCQUFhYm1wxPRLR37166e/euXNqrV6/Snj175DqLKyoqojt37nTJW4KI5GqbiCg8PJzmzp0r11nstm3bCABt3rxZZv3JkycJADk7O1NRUZFM2oaGBurXrx+NGzeOhEKhTFqil5P4+fPnZdZ1ZR/dvXuX7t+/L5c2NTWVFi9eLJffS0NDA33zzTdUVVUls1YikVB5ebnMuldpaWmh69evy7Xt0tLSSEdHh44fPy6z9vnz5wSADA0NKT4+XiZtc3MzGRkZkbKyslwT6d27d8nLy4saGxtl1hJ148T+dyBvYiQimc6y/4nIe2mipqaGTp48KZc5VWNjIy1atEhu47WnT5/KPYm/afydJnF/NykpKXJPqGvWrKFHjx7JpT1+/DhFRUXJpSV6OaHKC9vEzpmAcfwjeZONmjj++byp44szAeN4o3kTDzqON4fuPr6699pxcHBw/A/CJXYODg6ObgaX2Dk4ODi6GVxi5+Dg4OhmcImdg4ODo5vxP5fYk5KSUF5eLrOOiBAUFITs7GxIJBKZ9Tdv3kRRUZFcXjXNzc24d++ezLo3jb/j1ts/g4qKCrl0ISEhqKyslMtr5/bt26itrUViYqLM2pqaGjx+/Bi1tbUya4GXHippaWlyaTn+JNjc7P5HR1cKlEpLS+nkyZN06dIlmbUXL14kNTU1Wrx4scyFDd9++y0ZGBiQhoaGzF4RgYGBpKGhQXp6enTs2DGZtPX19TR+/HiysrKiTZs2yaQlIsrJyaF169bRyZMnWb1eIpGQSCSSu/Dj6tWrtH//fkpOTpb5PaKjo+mjjz6iwMBAmQu7Kioq6IcffqDw8HC5Kk6lSCQSqqiooMTERJn7UFxcTAsXLqS3335b5qK28PBw0tDQICsrK/L395dJGxcXR7169SJTU1NasWKFTFo+n08jR44kc3NzcnBwkHmfPX/+nJydnemTTz6RSUf0clsXFBTQ7du3WVcYJyYm0s2bNykvL0/mvhYWFtK8efPozJkzMtsBCAQC2rBhAwUEBFBpaalMWolEQhkZGVRWVtalYkeiblZ5Wl9fT9999x0NHTqUeDweAaCFCxey1otEIlq/fj0BIADk4OAg00F75coVRjt69GiZfDFSU1NJQ0ODANDAgQMpMzOTtbaiooKGDh3KtH3gwAFWOrFYTDdv3iRfX19me7m7u7PSSiQSCggIIC0tLVJUVKSePXuSmZkZ5ebmstK3tLTQlClTCAAZGRnRvHnzZDI+2rVrFwEgTU1N+uijj2Qypvrll19IQUGBevbsSR4eHnTo0CFWB39LSwvt3buXTE1NqUePHgSAnJycWCeOpqYm2rZtG6mrqxMA6tWrF+Xk5LDud1xcHOno6BAA0tHRoZSUFNba6upqGjBgAKOV5aRDJBLRzJkzmfG1detW1uvM5/Npw4YNpKSkRADIwMCAdZn8w4cPadSoUaSlpUUASFVVVabxNW/ePAJA2tra5OXlRUFBQay0REQ3b94kHo9HPXv2pKlTp8pk5SC1MeDxeOTh4UEHDx5kvb1CQkKoX79+zH5ydnaWKRdI6VaJneilc9+ZM2do9uzZpKWlRX5+fqx0IpGIduzYQbNmzaJly5bRtm3byN/fn7VBVGxsLGlpadGYMWNo//79Mu2Muro6srW1pUGDBtGmTZsoLi6O9UAoLCwkX19f8vHxoS+//JJOnDhBkZGRrLTNzc0UFRVFx48fp3//+9/k4eFBCxYsYN1vIqLc3Fzy9vYmANSjRw+Z/EQaGhpoyJAhBIBsbGwoKyuLtVYikdCMGTMIAJmYmMjshic1aQJA69evl0kbExNDEydOJAA0YsQI1rrffvuNvvvuO1qzZg0tWLCAZs6cSdnZ2ay0KSkpNHDgQJowYQJt2bKF7t69S3V1day0YrGYpk2bRn379qVly5bRkydPWFtASCQS+vTTT8nc3JwWLlxIv/zyC+szUbFYTCdPnqTVq1fTypUracWKFbRixQoqKChgpSd66dK6du1a0tHRIRMTE5n8n8RiMX3++ecEgBQVFencuXOstUREW7duJQDUs2dPmf1e7t+/z0xmsvoglZSU0KhRo5i2ZfW8IurmlgItLS0oKCiAubn5H9irtgkNDYWtrS10dHRk1kZHR6NXr14YNGiQzFoiAo/Hk1nXHmKxGIqKijJpJBIJjhw5gp49e+KTTz6RSVtaWooZM2Zg+PDhmDNnDpydnVlr6+rq4OvrC0dHR2hra8PPz0+mtgMCAvDgwQNMmDAB77//vkxaAHj48CFqa2sxbdo0mbWyUlpaCn19fZn3DQBkZGQgPz8fI0aMkFnf0NCA8vLyv+QY6ojGxkYEBgZizpw5Mo13IsI333yDhoYGzJ8/H3Z2dqy1EokE06dPh6OjIzIzM3H27FmZ+nz06FE8e/YMjY2NOHPmDJSVlVlrRSIRNm7cCHNzcyxevFimdgH2lgJvZGLn+GuR11ejurpargkRePmFnra2ttwTnFTP0b2pq6uDpqamzLra2lpGJ8/46srYBl7+OErPnj1l1rFN7Epy9Yrjfwp5fTW6MvClSVneTy1cUv/fQJ6kDgBaWlpdarcrYxuAXEldFv7nbnfk4ODg6O5wiZ2Dg4Ojm8Eldg4ODo5uBpfYOTg4OLoZXUrsPB5vN4/HS+XxePE8Hu8Kj8fjvrHi4ODg+Jvp6hn7XQD2RDQYQDqAdV3v0j8faRGAvMjjBcLBwRaBQPB3d4Hjb6ZLiZ2I7hCRNEs9A2Dc9S51THV1NcLCwuTSPn36FGFhYWhqapLZVOvSpUsoLy/HhQsX4Obmhrt377LWRkdHIy4uDvfu3cPIkSOxdetW1lqhUIhDhw5BLBYjODgYly5dkqnfJSUlXTIQE4lEaGlpYfXa4OBg3LlzB6mpqWhqapKpnYiICOzatQs3b95EXl6eTBNneXk5YmNjUVBQAD6fL1O7v4eIUFBQgObmZpm1NTU1Mhe7SMnMzERQUBByc3OxefNmXLt2jbU2Pz8f9+/fR1RUFHx9fTF79mzWWpFIhKNHj6KhoQFHjhzBO++8I9O2z8rKQmBgIICXxUayaKXbuqysjNXry8vLUVFRAYFAIPOJVV5eHnbu3InAwEBkZGRALBaz1jY2NuLEiRP47bffkJmZ+WacmLEpT2UTAK4D+IDNa2W1FEhNTaXdu3fTiBEjSFFRkWbOnEn+/v50+fJlVvqamhpasmQJAaDBgwdTz549afDgwaxtBQ4cOEA8Ho9MTU3J2tqaTp48ydpo6sGDB6Surk6mpqZkZGRE33//Petflk9OTiYnJyfS0tKivn37kpmZGe3evbtTnVAopMuXL5Ovry8pKirSuHHjaNWqVbRq1aoOdSKRiA4cOEBubm5kYWFBWlpaZGRkRJWVlaz6W15eTl5eXoz3iKWlJaWmprLSSiQSptQbAOnp6VFwcDArrUgkonXr1jFaVVVV2rhxIyv7BoFAQPv27aM5c+aQi4sLqaurk6OjIxUVFbG2fygtLaWvvvqKNDQ0yNLSknx8fGjgwIEUHR3NSh8UFETa2tpkampKqqqq9MEHH1BMTAwrbVpaGpmampKJiQlpa2vTli1bWI/rqqoqGjduHGlpaZGWlhaNHDmSLl26xKpMvqysjJYvX049evQgJycnsrOzI0VFxU7NvB4/fkx+fn7k6+tLffv2pR49elBQUBClp6cTn8/vUJuVlUUeHh4EgBQUFEhLS4sCAwNZrSsR0fnz5xk7ABUVFTp69Chr7ePHjxk/HyUlJVqwYAG1tLR0qhOLxXT06FEyMzOj3r17k4aGBpmYmMhkv/Aq+KO8YgDcA5DYRkx75TUbAFzBfytZ23mfRQCiAESZmpqyXpHKykrat28fjRkzhtkpLi4uNGPGDFq5cmWn+suXL5OhoWErAzC2G1UsFtOaNWtaJSq2SY6I6NKlS6SsrEwASF1dnRISEljpJBIJHT58mFRUVJi2/fz8WCWa+vp62rBhA9nb2zOeKc7OzrRhwwY6ePAgq/bv3LlDDg4OjE+MhoYGeXt7s/JtEQgE9OGHHzIHwOzZs2Uypjpw4ABz4M6aNYv1NiN66SwpNZYyMjKiDRs2sPL2qampoV27djHjRE9Pj5SVlUlDQ4Oam5vb1UkkEjp9+jQZGRkx+0lDQ4P8/f0pNDS0U1MssVhMfn5+zH5SVlamqKgo1usbGxtLBgYGBIB4PB5du3aNtTY9PZ2srKyYfn/66aesdC0tLbRnzx7G2A4A9e/fn+7du8dqQqmurqbDhw/T4MGDCQCpqamRra0t6erqsup/c3MzbdiwgdlmlpaWtHnzZkpPT2fV/1u3blGvXr0IAHl5edGdO3dYT+DJycnUv39/xsdo3759VF9fz0obGxvbalIyMTGh+fPnszY/k8I2sXfZUoDH430MYDEAbyJi9flbXkuBmpoa3LlzB01NTfj44487fX1zczNSUlKYywkikQgikQhDhgyBurp6h1oiwrFjxxAeHo6BAwdi4MCBsLKywsCBA9GrV69O237w4AG+//57WFtbY9CgQbC1tYWtrS2rSrnc3FyEh4ejV69e6NWrF1RUVKCtrQ17e/tOta9SW1uL8PBwZGdnY9GiRTJVcYrFYgQEBKCurg7Tpk1DWFgY3nnnHaioqHSqJSLs2LEDFhYWSE5OxpEjR7B37158+OGHrNr++eefIZFIkJ6ejsOHD2PlypXYsmULK21GRga2bduG+fPn48SJE8jOzsbjx49ZaYVCIc6dO4f6+np8+umnKC4uhrExu6uL1dXVyMzMRGZmJry8vGBkZNSp5sGDBwgPD0efPn1gYGAAAwMD9O/fH3369OlUm5KSgjVr1sDY2Bj29vZM6Onpserrrl27oKamBhMTEyYsLS1Zj5HGxkaUlpaitLQUZWVlGDlypEzVvkSEyMhInDlzBrt27WI1rl4lODgYQUFBGD9+PM6dOwcHBwesXr2alfbp06d4+PAhNDU1sXPnTri6ujKXkzqjuLgYmzZtwrvvvotdu3YhPj4eWVlZneYT4KU1h7+/PwQCAXM599///jd69+7Nqm3gL/KK4fF4EwHsBTCSiFj/egXnFfPmQF0wI5Maj0mvibKZEH+vraioQFlZmUxGaq8annWl/xz/bOQxtvu9VigUIiUlBU5OTnK1m5OTAzMzM5naltd7CfjrEnsGgJ4AKv/71DMiWtKZjkvsHBwcHLLzl5iAEZFlV/QcHBwcHH88XOUpBwcHRzeDS+wcHBwc3QwusXNwcHB0M7jEzsHBwdHN4BI7BwcHRzfjjUvsXfFp+L3/h0QiYe05IZFImOW8vDx89913YHvL5qvakpIS7NmzBydPnmSlFYlErfooEomQl5fHSguAtc9LVyAiVFZWorGxUSYPDikJCQkICwtDeno6Kisr5XqPPwr6/5XSMiOPv4yUV8c1ESEmJgZxcXGstK/2t7q6GocPH8a6dez8+H5/DLx48QJHjx5l2euurbO0/T+b3NxcRERE4MWLFzKPr7q6OmRmZqK0tBRNTU1dMv/7K3kjEnt2djYOHDiAcePG4fvvvwefz28VnVFUVIRPPvkEAQEBCAoKwubNmzF+/Hjo6uoiKyurQ61YLIafnx9u3LgBf39/jBo1CjY2NoiJiWFVHHHx4kUcO3YMFy9ehI+PD8zNzfHkyRP079+/U21YWBh8fX2RmJiI77//HlOnToWenh7mzp3boU4gEODy5cuYPn06du7cicLCQqSmpiIiIgL3799vU9Pc3IyAgACsW7cOc+bMgaenJ0aPHs3KzIvH4yE0NBTm5uZQUlJCjx49YGZm1um2lWJsbIzt27fD2toa+vr6UFVVxcOHD1lpc3JyMHHiRPTu3Rv6+vrQ09PD9u3bWWlbWloQHx+PU6dOYdWqVfD29sZ7773HSvsqeXl5WLt2LebPn4+0tDTcuXMH/v7+2LRpE5KSkjrUEhFOnz6NLVu24Pbt21i6dClMTU0xceJEVmZ34eHh2L59O+7du4f33nsPxsbGuHbtGoYM6fRWZ+Tl5WHmzJlIS0vDtm3b4OTkBBcXFzx69KhTh8icnBwsXboUW7duRUREBE6dOoV169bh7bffRk5OTpsasViMuLg4/PDDD/jggw/g4uKC6urqTvsJAI8ePcKwYcNgbW2N/v37w9DQEA8ePGCl7dOnDwICAmBlZQV9fX0oKSnhyJEjrLSqqqo4deoUDA0NoaamBiUlJXz88cesJiSRSIRDhw7ho48+woQJE+Dk5ARPT0/U1NSwartLsPEd+KODrQlYYWEhzZkzh/GkaCsMDAza1dfX19PmzZtJVVWV8S5xdXWlpUuX0qlTpygtLa1Dn4jCwkIaPXo0ASBFRUUaM2YMnTx5kmpqajrtu1AopOXLlzPeEE5OTrR//34qKyvrVFteXk4LFixoZYg1c+ZM+uGHHzrsc0VFBS1btoy0tbVbbaNevXqRgYEBWVpakouLC4lEojb1BQUFtHz5curZsyejNTMzIx8fH1q7di2dPn2aKioq2u13SUkJTZ48mfEuGTJkCO3cuZOysrI6XWexWEzbt28nBQUFUlBQIGtra9q5c2enplJEL/1Dvv32W8aXR1tbm2bPnk1nzpzpsL98Pp9OnTpFQ4cObbW9evfuTU5OTuTj40OLFy+mqqqq17QSiYSePHlCs2bNIkVFRUarr69PLi4uNH36dPr8888pMTGx3faLiorI19eX0dra2tLatWspNDS03X30avuHDx+mHj16kIKCApmZmdGWLVtYeY9IJBI6c+YM46ujqalJH374IQUGBnZqxJWamkoff/wx49vE4/HIzMyMJk2aRKtWraJjx461uc0lEgmdP3+ePD09W21rJSUl6t27N1lZWdHQoUM7NPXKzc2ladOmMVpjY2OaN28enTt3jkpLSztd77Nnz5KamhopKChQ37596csvv6SkpKROdUREDx8+ZDyB1NTUaM6cOXT9+vVOzQD5fD7t2bOHdHV1mX5bWVnR+++/T/v27aMnT56wNgUk+gNNwP6MkNXdMTs7mw4ePEjjx4+nPXv2EJ/PbxVt0dDQQN988w3NnDmTRo0aRfb29jR16tQOTZ1e5datW9S7d29mZ9jZ2bEaPEREOTk55O7uzmi1tbVZu/UlJyeTj48POTo6kpWVFRkbG8vkQicQCCgkJIS+/fZbmjhxIq1evZq1VkpRURGtWLGCNmzYQOHh4XTixAlatWoVTZgwodMDQZpwfvzxR7pw4QLNmjWLVFVVyc3NjYKCgjpt++7du7Rv3z66ceMGzZgxg3r16kW+vr508+bNTrXJycnk6+tLSUlJtGvXLhoxYgQpKyvThAkTOjV6ioiIoLlz59LXX39NKSkpdO/ePQoICKDt27e3eeCJRCKKjY2lM2fO0Nq1a2nKlCnk6enJatInIgoMDCRzc3PS1tYmHR0dMjIyoufPn7PSNjQ00Pvvv8+MLwUFBbp06RIrbWVlJf3rX/9iDN7U1dVp1apVrIyw+Hw+nTt3jrZs2UIfffQReXl50YQJE0ggELBqW0pqaiqtW7eORowYQcXFxZSSkkKhoaEUFBTE6iTg6tWrNG/ePAoLCyM/Pz966623SFlZmZYvX96pNjk5mdasWUNhYWG0aNEi0tTUJHd3dzpy5Ein26C8vJxmzZpFGRkZtG3bNrK1tSU9PT1asmRJp+aA1dXVtG7dOtq8eTM9evSI9uzZQ7Nnz6YBAwbQ3bt3O+23FLaJvcsmYPLQFUsBkUgEJaUuFcx2ikQiQVpaGtTV1aGpqQl1dXWZPCkSEhJARNDV1YWOjg5UVVX/Nr+SrvhSNDc3Q1lZucvtNjY24ubNmzAzM4Obm1unWnrF36W8vBxnzpxBc3Mz1q5d26lWLBZDQUGB0VdVVSE+Ph6jRo1i1e+urPPv+/5nUSy1RwAAIABJREFUkZaWhsrKSujp6UFfXx/a2tqsx6dQKAQRQVlZWe5x8UchvdYtj9/L7/NAfX09qqqqWF3ifHUf8fl8XLlyBTExMfi///s/Vlrg5eVHIkJcXBwuXLiAb775Bj169OhU39LSwup17fGXeMXIC+cVw8HBwSE7bBP7G/HlKQcHBwcHe7jEzsHBwdHN4BI7BwcHRzeDS+wcHBwc3QwusXNwcHB0M7jEzsHBwdHN4BJ7F8jKykJ+fr7c2oiIiD+4RxzdDaFQKJcuPz8fN2/elLvd4uJiubUcfz9vRGIvLCzE0aNHcevWLbn02dnZeP78OfO4pqYGISEh+OGHH7BkyZIOPU0EAgFyc3MBvCxeefDgAVavXg1bW1sMHjwY9+7da1dLRMx7SyQSPHv2DOvXr4eDgwMGDx6Mq1evdtjv4OBgpohDKBQiIiKC8Z6YNGlSh32+cuUK6+1FRCgtLcWjR49w7NgxrFq1Cp999hkrsySJRILDhw/Dw8MDzs7OsLOzg6enJ0pLS1m1fevWLVhYWEBLSws6OjowMjJiPeGlpKRg4cKFmDFjBsaOHQt3d3f4+/uz0kqprKzEb7/9hm3btmHnzp0yaaVkZWXh3LlzrZ4jIlRVVSEpKQllZWXtasViMaKjo5nHOTk5+PnnnzF//nxYWFhg4cKFHbYt9WUhIiQmJmLbtm0YMmQIrK2tcebMmQ61qampzMRRW1uLwMBALFu2DDY2NrCwsEBFRUW72hcvXrQa+0SE8vJyRERE4D//+Q+Kiora1OXn5+Ps2bNYtWoVKx8iALh9+zbWrl2LBQsWYNq0aXjrrbcQExPDShsXFwd3d3fo6emhd+/eMDAwwPnz51lpS0pKMHv2bFhZWWHAgAEwMzPDF198wcoITCAQ4OnTpzh79iy2b9+OTz75BHPnzpV7opaVf2yBUlZWFn7++WfcuHGD2YmjRo2Cjo5Om6+/dOnSaxV/OTk52L59OwICAvD222+jsbERCQkJKC4uhqWlJRwcHODg4ID58+fD2Nj4tfd8+vQpPvnkE4wePRqlpaW4e/cu+vTpgylTpmDy5MkYOXIkevbs2WZ/CgoKsGjRIqiqqkJbWxs3btyAoqIifH19MXXqVIwZMwYqKiptauPj47F27VpERkZi9uzZiIiIQFxcHPr16wd3d3cmRowYwWhEIhGCg4Nx7tw5XL58GXV1dRg1ahQ0NDTQ2NiIxsZGNDQ0MMuJiYkwMDAA8LIy9NixY9i3bx/zCcTQ0BDu7u6wtLTEgAEDMGDAAFhaWsLExKTNyt9bt25h6dKlyMnJgZKSEoYNG4bx48dj/PjxcHFx6bC6sLy8HEuXLsXFixcBALa2tnj77bcxbdo0uLm5dVghmZSUhBUrVjBJZuDAgRg5ciRGjBiBESNGtFuJWFlZifXr1+P48ePMgWptbQ17e3v06dMHBgYGMDAwYJadnZ2hpqbWansHBQXhxx9/xG+//YbBgwdjwIABKCoqQnFxMUpKStDc3AwDAwPs3bu3TXOxZ8+e4bPPPoOmpiZMTU3x8OFDlJeXY/jw4Rg1ahRGjhwJNze3NithGxoasHbtWiQmJsLNzQ1Xr15FVVUVfH198fbbb2P8+PGt+vsqfD4f3377LQ4ePIjly5fj3r17iIqKgqOjI8aOHYtx48Zh2LBhr41PIkJISAj27NmD69evY/To0VBTU0N2djays7MhEAhgamoKc3Nz7Nq1C66urgBeTl7Hjx/Hzp07mYlIX18fw4cPh6amJjQ0NKCpqcmEp6cnXFxcmHbFYjECAgKwadMmFBcXQ0FBAe7u7vDw8GDC1NS03YrfpqYmbNiwAd9//z2ICMbGxpg6dSqmTZuGUaNGdVhp3NLSgt27d8PPzw9CoRC6urqYMGECJk2axJjPtQUR4d69e9iyZQuePn3KrLOnpyfs7OyYsLGxQa9evdpt//e88ZWnEokEMTExuH79Oq5fv47nz59j1apVsLOza/P18+bNY3ZsdXU1Nm7ciGPHjjF2qG+99RYWLFgABwcH2Nradrgx6+vrsX79ehw+fBhEBHNzcyxfvhxTpkzBwIEDO+w3ESEgIAArV65EbW0t1NXVsXLlSkydOhUuLi4dJqn8/Hxs2rQJp06dYpLN8uXLMW7cOLi5uaFPnz7taktLSxEUFISHDx8iODgYBQUF+OCDDzB27FioqalBTU0N6urqzPKAAQNeS9AtLS349ddfsXv3bgwdOhRubm7IyMhAZmYm81dagu3j4/NaH5qamuDn5wdVVVVYWlrizp07uHv3LgQCAby9vTF+/HhMnDixzUmUiPDrr78iLi4OI0aMQGBgIAIDAwEA06ZNw7Rp0zB69Og2J1IiQmBgIPz8/LB37148efIEjx8/RmhoKHR1dZkkP2/evNfKuTMyMuDv74+ffvoJM2fOhKOjI8rKylBWVobS0lJm+eLFi7C1tQXw8pPb999/j6tXryI2NhZNTU2wsbHBqlWr0K9fPyYMDAzanARLS0vx1VdfISAgAACgoaGBdevWYdSoURgyZEinJechISH4+OOPmU+Dn376Kd555x14eXl1qr19+zY+/fRTRjt9+nS89957GDNmDHR1ddvV1dfXY8uWLfj555+ZM3kPDw8sWrQI5ubmMDc3h5GRUYd2Hy9evMDZs2dx5swZqKurY8WKFairq3st3n77bbz77ruv6RsaGrBnzx6EhYVhyZIlePbsGZ49e4bIyEhoamrCw8MDvr6+mD9/frvbzd/fH4sXL8a1a9dw7do1FBQUYNKkSZg6dSomT57c7oljWloalixZgt27dyM4OBg3b95EaGgonJycMGnSJEyePBlDhgx57fgmIjx8+BB+fn6wtraGm5sbkpKSmCguLoaFhQX27dvX5jH1e974xP57CgoKUFVVhcGDB7N6vVgsRnFxMfLy8pCXl4eGhgYsWLCgUx+PlpYW/PDDD8jOzoZEIoFYLEaPHj3g5+cHTU3NDrVEhAsXLuDWrVvg8XhMfPnll7C2tu60z6WlpSgsLER5eTnKy8tRVlYGR0dHeHt7s1rnV/uRmZmJkpISeHl5yaSV6vPz82Fqavra8+Xl5VBVVYW6unq7eoFAwJztERGSk5Nx584d3LlzB15eXtiwYUO72lc9QCQSCaKionD16lVcvXoV+vr6ePz4cYftKikpMfqWlhY8f/4cjx8/RmxsLE6fPt3u/m9ubkZubm6nE/fvEYvFSE9PR1xcHGbMmNGpzwwR4f79+ygoKEBDQwPq6+vR0NCA+fPnY8CAAZ229/TpUxw6dAg8Hg+KiopQVFTEhx9+yGqM5Obm4vLlyxAIBEzY2Nhg3rx5rNcXePkJKzk5GXl5eXj//fdl9pyh//rNu7i4yOWrU1tbCy0tLeaxSCRCYmIinj17BgUFBSxatKhd7e89Zl68eIFr164hMDAQKSkpKC4ubndykkgkkEgkzP/r6upw79493Lp1Czdv3sS9e/eYyb8tSkpK0Ldv31bP1dTUICUlBaampjAyMup03btdYufgqKur63Ry5eCQl8bGxnYvX3XGq+ZgfyZsE/ufa5PIwfEHwiV1jj8TeZM68OcndFl5I+6K4eDg4OBgD5fYOTg4OLoZXGLn4ODg6GZwiZ2Dg4Ojm8Eldg4ODo5uBpfY/wC6csuotICKg+PPgM/n/91d4PgbeCNudywrK0NDQwMsLCzk0rf3A9hSj5QXL17Aysqqw8rOV6mpqcGTJ0/w6NEjPHr0COPHj8e2bdtYaevr6/HkyRM8ePAAwcHBUFNTw6NHj9rsG/D6bVQSiQS5ublISEhAZmYmVq5c+ZpWKBSivLy8zQrP9nj1fSsqKlpV8rZHS0sLzpw5g9zcXFRXV6O6uhpEhMOHD7Mq5vr1119x8eJF8Pl88Pl8iEQiHD16FDY2Np32NzU1FUlJSSgtLUVJSQlKS0vh6+vLqnrvVZqbmxEbG4uamhqMHz9eJq2UqqqqDqs2ZUVaIBYZGYnIyEioqalh06ZNrLR8Ph9Pnz7F/fv3ce/ePWRnZ6O0tJT1D0aXl5cjLCwMYWFhCA0NxenTp18rVAM6v+dbLBZDIpG8VglbXV2N0NBQTJw4sdM+ERGys7NRUFDQKlasWMEqF4SGhuLHH39EY2Mjmpqa0NTUhHXr1mHixImdanNycnDs2DHU1NQwFbGjR49u83hrj5qaGqSlpTE/Pv7555//ZT8g/o9M7FJDo+vXr+PGjRt49uwZdu7c2enOnDx5ciurgOjoaOzcuRNz5syBqakp0tPTXwuBQABLS0scOnSoVWInIvzyyy8wMDCAo6MjQkJCmESelJSEwYMHY8SIEdiwYQPeeuut1/oSGRmJ1NRUzJw5E6GhoQgODsaDBw8QFRWFQYMGYcyYMfj6669b+b1I271z5w6OHz+O48ePIzExEfHx8UhISEB8fDwSExNBRLC3t8fgwYMhFouhqKiIlpYW3L9/H//5z39w5coVbNiwAba2tmhqagKfz2cGtnSZz+fjiy++gKqqKjZu3IjTp0+jvr4eADB8+HDU1NTA1NSUCQMDg9cGZY8ePTB58mRs2rQJ/v7+ICL07t0bK1aswPDhwzF8+HBYW1u3OUHweDy8++67UFZWxueff478/HwoKytj5cqV8Pb2hre3NxwdHds9EIyMjBj7g4aGBgAvK3eTkpIwZMgQuLq6Qltbu01tYWEhDhw4gKdPnyI6OhoCgQDvvvsu8vLyoKenBz09Pejq6jLLbVWTSo3Wjh8/DnNzc8ydO5epGG4r5s+fj88//7zVfr58+TKys7Mxb948JolHREQgMjISdXV1cHFxgbu7e5vjKz8/H4GBgViyZAmio6OZRB4aGgoLCwt4e3tjw4YNGDVq1GsJtKSkBFu3bsXu3buRmZmJ0NBQhIaGIiwsDDk5OXBycoKnpyeWLl3aqsReLBYjKCgIhw4dgre3N956663Xkm5hYSEKCgpQVFSE48eP47333sPt27cZq4u4uDjY29ujrKyMsbhQV1dn4lXrCyUlJZSVlWHbtm24e/cuAEBVVRUtLS1wdHSEo6MjHBwc2q2CHjZsGCQSCT799FPEx8cD+P9mfGPGjIGHh0e7lcJmZmaYOXMmli1bhtDQUGabFxcXY8SIEfDy8mp3fNXX1+Prr7/GgQMHGCM9Jycn8Pl8WFpaMvFn1mX8IytPExIScOTIEdy4cYMxpfLy8uq0XPvXX3+Frq4uHj58iB07djCDgcfjwdTUFFZWVq9F//79Xxv4cXFxWLZsGUJCQmBsbIzS0lK4uLhg5MiRGDlyJIYPH96qpPlVKisrsWHDBhw7dgxGRkYoLy+Hubk5xowZgzFjxmDkyJHQ19d/TSc1Dfr6668RFhYGBQUF8Hg8WFpaYvDgwYwjpIODA8zMzFolvMzMTKxevRpBQUHMpR1bW1vo6upCVVUVvXr1avPvkiVL0K9fP8bc6cCBA7hy5Qp8fX2hra3N2DFI94GxsTGT6BcsWNBqUoqLi8PKlStha2sLQ0NDPH36lFmPYcOGYfjw4Rg2bBjc3Nxe8+lpaGjA1q1bUVRUhFGjRuH+/fu4f/8+xGIxRo8ejbFjx8Lb2xsDBgx4bZIoKyvD9u3bcfHiRaxfvx5RUVGIiopCSkoKzM3NMWTIEAwZMgRubm5wdnaGhoYGgJfl9T///DN++ukn5OTkYPLkyVBRUUFlZWWraG5uhrq6OvT09HDq1Cm4urpix44dOHLkCKqqqgC89HoxNTVF79692w1ra2sYGhoCAB4/fow1a9YgPDwc6urqEAgEsLe3h7u7O9zc3ODm5gY7O7s2P2W2tLRg//792LJlC9TV1cHn86GhocFsozFjxrRbms7n87F3717s2LEDQqEQvXr1goqKCoYNGwZPT08MGzYMrq6uUFVVbaWrqqqCv78/fvjhB8bpVFVVFSYmJjA2NoaxsTGMjIyYZWno6+uDx+MhOTkZ58+fx7lz55CVlYWBAwdi0KBBjDGd1JxOuszn87FkyRIcOXKE6cPjx4+xadMmCAQCTJ48GXFxcYiLi0NOTg4sLCzg5OTEJHsnJyeYmJgwWpFIhEOHDiEwMBCLFy/GgwcP8ODBAxQXF8PLy4s5NtsyqyMinD9/HuvWrcPu3bvx7NkzPH78GHFxcbCzs2N8iN56663XPvHn5ORg37598Pf3x6RJk6Cnp4eMjAxkZGQgPz8f+vr6GDhwIJPop0yZ0sr8rC3YVp6CiLocAFYDIAD6bF7v6upKbJBIJBQbG0tbt26lx48fs9IUFxfT8ePHac2aNTR9+nRycHCgVatWsdI2NTXRV199RUpKSvTf9SF3d3eqq6tj1Vd/f3/S09NjtHp6epSRkcGq7YcPH9KiRYto4sSJNGjQINLU1KTg4GBWWil1dXUUFBREq1evpv/85z8yaaXk5OTQkydPWj0nFoupuLiYwsPD6eLFi7R3716Kiop6TSuRSKioqKiVLjExkY4ePUpz584lS0tL6tGjB33xxRdttl1TU9PqvRISEmj//v3k4+NDGhoaZGpqSp999lmb2qysLGppaWEeNzQ00JMnT2j//v30wQcfkI2NDSkqKlJFRcVr63b//n16+PBhm+vT0NBAubm5FBMTQ9XV1UREJBKJKCEhgU6cOEGLFi2iTz75hCQSSZv9+n1bP/zwA7m6upKpqSn17NmTDAwMqLS0tFMtEdGjR4/Izs6OGV+Kiop0//59Vm0nJyfT2LFjSV9fnxQUFAgA7du3j3W/X7x4QRcvXqSNGzeSj48P62PqVSQSCYWHh9PBgwc7fJ1IJCKhUNimPi4urtVztbW19OTJEzp8+DAtXLiQ3N3dycvLq833le4/KTk5OfTTTz/Rhx9+SIaGhqSlpUVTp06l2tra17T19fXU2NjYqt1bt27RunXraPjw4aSsrEzW1tYUGRn5mraiooLCw8NbPcfn8yk5OZmuXbtGe/fupX//+9907dq19jfKfwEQRSxybJfP2Hk8ngkAfwA2AFyJqH0T5//yV3vFEJFMJb8SiQSNjY2or69HfX09zMzM2rXnfRWxWMxc6pBe1+vXr59c11+JCC0tLZ1+SnnTKC0tRV1dncxmWyKRCJGRkcjKysL7778vV9v19fXMGfs/ASJCQ0MDFBUVXztLbovGxkbw+XwIBALmewldXV2ZvksBXo7vuro68Pl89OvXT97u/2OR9XiXal68eIGQkBDMnz9fZn1TUxMiIiLg6OjYrkPkH8FfZgLG4/EuAtgKIBDAkH9iYufg4ODoDrBN7F36ipbH400DUEhEcSxeu4jH40XxeLyo8vLyrjTLwcHBwdEBnd4Vw+Px7gHo28a/NgBYD4DVPWJEdAzAMeDlGbsMfeTg4ODgkIFOEzsRjW3reR6P5wDAHEDcf69HGQOI4fF47kRU8of2koODg4ODNXLfx05ECQAMpI95PF4OWF5j5+Dg4OD48+AsBTg4ODi6GX9Y5SkRmf1R78XBwcHBIT//SEuB3yPPfal/BU1NTXj+/DkiIiLQu3dvfPDBBzJpo6KiEBYWhsrKSuzatUvm9iUSCfLy8tC/f/8/ZPs0NjYiJycHdnZ2nb5WJBKhpKQExcXFzN+amhqsWLGC9Q86FxUVoaqqClVVVaipqcHatWtZ/aAv8NLjpaCgALm5ucjLy4ODg0OnVXvt9aWysrLNauB/AgKBACkpKaisrMTYsW1+3dUmfD4f0dHRCA0NRWRkJM6dO/eab0tn7SYmJiImJgY+Pj5M1WxX4fP5UFFRYT1eiQhVVVXIyspCVlYWvL29We2r6OhoZGVlMRXEVVVVmD17Ntzc3DrVlpSUICcnB2VlZUzY2NhgxowZrPr8at+LioqQm5uLYcOGyaTtKv/YxJ6eno4bN27gxo0b2L9/PwYPHiyTnogQHBwMAwMD2NvbA3hZQFRQUIDs7GxkZ2cjJyeHWc7OzsamTZuwePFiAC8TR3l5OZNoxGIxUlJSEB4ejoiICERERCAxMRFmZmZwd3dvtdOlO1SqJSJkZWUhLCwMz549Q1hYGOLj42FhYQEPD49WpflisRg3b96Ej48PM/jr6+sZM6HU1FRmOT09HYqKisjLy4OGhgYePHiAX3/9FZ988gk8PT1bvae0sOXVKCgoYDxtYmJikJaWho8//hgrV66EoaEhdHV12z0AJRIJrl+/Dj8/P5SUvPyu3M7ODqqqqnB1dYWjo2O7RTdSqwR/f3/85z//AQDo6OhAVVWVKW/v3bt3u/v24cOHWLp0KVJSUpjntm3bhqqqKjg4OHRo5iYUChEdHY2nT58y8eWXX2Lu3LnQ1tZmVYgGvLRBuHTpEng8Hj766CMAL/czn89nJqvfx6BBgxiTsubmZiQmJjKTERGhsLAQ8fHxiIuLQ3x8POLj45GWloZ+/fph/PjxrRL773/xvri4mPF8efr0KWJiYtC/f38MGzYMY8eOhUgkYhJ7WloaLCwsmMcNDQ2Ii4tDTEwMYmJi8Pz5cyQlJaFfv35wcXHB8OHDYWhoCKFQiCtXrqBPnz4YPXo00++qqiqUlJS0Gb6+vujbty9jeqerq4uAgACoqqp2ONFIJBIcP34cmzdvRllZGQDAwMAAe/bsga2tLWxsbDo0Ievfvz8CAgJw5MgRiMViKCgoQCQSISsrC56enjAxMWl3bCsrK+PSpUs4ePAghEIhAOC9995DY2Mj3N3dMXDgwHY9jCorK7Fjxw6Eh4cjMTERNTU1TG7o378/+vXr95cYgf3jvGLCwsKwfPlyvPp/tgcbAISEhCAlJQV79+5FXFwc3n33XVRWViI7Oxt5eXlQVlaGubl5m2FpaQlVVVVcuHAB69atw5w5c9Dc3IyIiAhERUVBVVUV7u7uGDp0KNzd3TFkyBDo6em1aj8uLg6rV6+GiYkJrKysmGTO5/MxdOhQeHp6wsPDAx4eHq20QqEQp0+fxs6dO9HS0oJJkyYxCby4uBimpqawtraGjY0NrK2tmeXKykocPHgQly9fZrxLjIyMIBQKmQQu9Y/h8Xjo1asX4xGioqKCdevWISIiAmfOnEFTUxOsrKzQ0NCAkpISKCkpwdDQEP369YOhoSET0seDBg2CtrY2Dhw4gJ07d2Ls2LHg8XiIjo5GXl4ebG1t4eLiAldXV7i6usLJyem1gzEsLAwrV66Erq4urK2tERoaiufPn8PMzAzDhg1jYtCgQa0OCLFYjF9++QV+fn6oqanBuHHjkJCQgJSUFGhra8Pe3h4ODg5M2NnZQV1dHfn5+QgICMCpU6eQkZEBANDV1UVdXR1EIhFUVFSgra0NHR0daGtrvxaWlpZ48uQJLly4gIaGBlhZWaFHjx5M8hYKhVBVVYWuri5jJCZdHjt2LKZPn45Tp05h69atcHBwgLm5OZPEpZ4xgwcPZsLBwaHVOCkuLsamTZtQWFgIHx8fJpkXFxdjyJAhzPby9PR8bYLLy8vDli1bcP36daxZs4ZJ4i9evICFhQWcnZ3h4uICFxcXODs7M2fGmZmZOHbsGH766SeUl5fDy8sLQqGQSd5isRgGBgbo27dvq9DR0UFWVhZu3rzJ+A0pKChAIpEAAJSUlKCmpgZVVdU2Y8SIEXjvvffwf//3fzh27BgsLCxgZGSElJQUFBQUwNjYGLa2tkzY2NjA1tYWvXv3ZpJ2Wloa1qxZg+zsbEyZMgVhYWGIjIyEtrY2PD09mXBxcYGKikqr7ZWbm4vNmzfj4sWLWLlyJWPSRkSM/5DU38fIyIhps7q6GidOnMDBgweRl5cHJycnNDY2Ii8vDxKJBKampujfvz8TZmZmzLKxsXGHE95fVnkqD51VnjY3N+PRo0e4fv06goKC8NNPP8HKyqrT983Pz8eOHTtw//591NXVAQA+/PBDTJkyBebm5jAzM2u103/Po0eP8OWXXyIyMhIAYG1tDR8fH7i7u8Pd3b3DSx5FRUXYuHEjAgICQETQ09ODr68vk8jt7OzatSm9fv06li1bxhgs9ejRA+vXr8egQYNgbW2NgQMHtnv2S0RIS0tj3P2Cg4Oxd+9eeHl5tUrgKioqUFJSarf/tbW1OHXqFMzNzeHj4wOxWIyysjIUFRWhuLgYRUVFTEgff/TRR4xjYVVVFbKzs+Hq6grg5eCOiYlBdHQ08zc7OxtWVlZwdXXF+PHj8eGHHzLrkJyczFwC4vP5iIqKYpJWaGgompub4eHhwSQub29v5izs8uXLmDlzJhQUFNDS0oL09HQkJCS0iry8PJiZmcHBwQEHDhyAiYkJwsLC8PPPP2PWrFnw9vYGn89HTU0NqqurUVNTw4T0sfQsuby8HKGhoYiNjYWPjw8zMenp6UFHR+e1BAG8vHR19uxZ+Pn5ISsrCwBgYmKCuXPnMknc0tKy3THyqoFXY2MjevbsiSlTpjAGa87Ozu2eAJWVleHbb7/FkSNH0NzcDAD417/+BQ8PD7i4uMDJyaldp8HCwkIcPnwYkZGRiI6ORnV1NebOnYs5c+YwCVxfX79DC16po+Ivv/wCFRUV7Nixo5Xj6KvxqsVu3759MW7cOGYdHjx4gNmzZwN4+SkjLS0NKSkpSE1NRUpKClJSUvDixQtoamrCzc0Nt2/fZvoQFxcHR0dHAC+N1BISEhhHy7CwMBQWFsLZ2ZlJ9FOmTGFOQuLi4jBgwACoq6uDiJCZmcm4cEZERCAmJgY6OjpMov/Xv/4FS0tLiEQiXL16FWpqapg0aRIkEgnKysqQm5vLRE5OTqvH8+fPx/79+9vdlm90Yn8VIoJAIHjNEbAzTWFhIZKTkwGAlc92bW0tfvvtN5SVlTFWqxoaGtixY0enH51EIhEuXLiAvLw85nqeUCjEgQMHWPtGtLS0IDc3FxkZGcjMzIS3tzcrX/K2+lJdXd3hpYy/i5qaGjx//hwxMTHo2bMnPvvsM1Y6IkJGRgaT5NPS0hAcHCzT9wr19fVITExEQkICZs+e/YdYpjb2P8zFAAAO5UlEQVQ1NSEtLQ3Ozs6dvlYikaC8vJxxy8zPz0dZWRnWrVvXru2sFCJCUFAQYmNjUVVVxUw03333HaytrTttOy8vD1lZWa0m5bFjx2LSpEms11XaD6m/+6uX+mR9jz/z+7KWlhZmXaWXi9hQUlLCXCYNCwvDhQsXWP8+Q0tLC5KSkphE//HHH2P48OEy952IWl0ya4tuk9g5ODg4OF7yl3jFcHBwcHD88+ASOwcHB0c3g0vsHBwcHN0MLrFzcHBwdDO4xM7BwcHRzeASOwcHB0c3g0vsfwBEhOLiYua+eVm1OTk5uHv37p/QM9n7IisCgQAvXrzAw4cPmYpCNu1UV1cjJSUFDx48wLlz51BTUyNz22KxGLm5uSgtLZVZ+yYiFotl1kjH16VLl5jyeFlpaGhAY2OjXNo/AiJCSUkJBAIBa41QKERubi7CwsJw+fJlpiiMLc3NzcjJyUFISAhiY2Nl7TJDS0uL3Nqu8I/1isnJycH169fx9ttvw8TERGa99Aep2/vxYiJCeXk5Uywijbfeegu+vr7tvq9IJEJ6ejpiY2OZiIuLQ21tLd577z2cPHmywz5lZGQwnhzSaG5uhpubG7y9vSEWi9stUCAilJWVITMzE5mZmcjKymL+/vTTT8jOzoalpSUsLCw63T7SAz4yMpKJd955B8uWLetUW1tbi40bN+LChQtMUh03bhx0dHRgY2PToQWESCTCgQMH4Ofnh9raWgCAqakpVFVVMWTIkFal2W1x7do1HDt2jFlvIsKtW7egoaHB6gehpcVOISEhCAkJwaxZszB58uROdb+nrq4O+fn5rAzTpD9aXVNTAx6PB2Nj4w4LdWpra5GamtqqojI1NRUNDQ0oLCzssJ2cnBxER0e3CqFQCGdnZwwdOrTDH74WCARITU1FYmIikpKSkJiYiMTEROTl5eGXX37BlClTUF1d3alRG5/PZ4r8SkpK0NjYiIKCAkgkEnzxxRedbq+Wlhb4+/vj2bNnjDdS79698ejRI/Tr16/D8UFEuHTpEj7//HMUFRUBAFRUVODv7w8igoWFRYf6qKgoLF26lKk+B4Ddu3dDTU0NAwYM6LBYsbq6GlFRUYiLi2Nyw/Tp07F169ZO1/mP5h9VoBQZGYkrV67g+vXrSExMhLKyMt5//32ZKtWEQiEMDQ1x5coVpjT398k7Pz8fBQUFEIvFMDIygomJCRPe3t6Ij4/H8OHDYWdnx5gySXdUYmIi1NXV4ezsDEdHRzg5OcHJyQnW1tZQVFTE9evXwefz8c477yAlJYXx45D+VVJSYvw4pGFpaYna2lr8+OOPiIqKws6dO1slbulyVlYWmpubYW5uDgsLC5iZmUEsFiMrKwsxMTGoqanBmjVrIJFIIBAIIBQKW8Wrz9XV1aGoqAjV1dXMmbaysjIMDAzQp08f9OnTp9Xy7x/r6urizp07+PrrrxEVFQUnJyeUlpairKwMVlZWcHBwaOXXYm5u3uqgqKqqws6dO3HgwAHY29tDSUkJsbGx0NTUZLxlpGFsbNxqDDx79gw7duzAtWvXoKWlBXV1dRQVFcHExAQ2NjaMn470r6GhIXg8HuLj47F06VI8ffqUeS9ra2vo6OhAU1MTWlpa0NTUfG1Z+lhNTQ1JSUm4e/cugoKCMG/ePNjY2LSyH2gvJBIJ1NTUMHXqVAwaNAg6OjqYPn16q8QtXS4tLYWZmVkr/xPpck5ODsLCwrB06VJkZ2e3SuDSkwRnZ+dW28/KygqKiooIDw/HkSNHcPToUWRlZTGJW5rEMzIy0KdPH9jb28Pe3h52dnawt7dHS0sLzp07h7Nnz+Lrr7+GtrY2k7jbisbGRqipqUFRURFNTU2MV5GlpSXMzMwYv6KOAnjpI3Tnzh2UlZVBR0cHjY2N6NGjBwYMGABLS8vXwsjIiBljTU1NOHz4MHbs2AFdXV0YGxsjJiYGCgoKrx1/AwcObGWJIBQKcfz4cXz77beoq6uDi4sL4uLiIBaL4eDgAEdHRyYGDx7MVA43Njbi3LlzOHToEOLj45n3U1dXh7GxMYyMjNr8a2xsDH19fVbmYG9k5WlVVRVu376N69ev49atW+Dz+di6dWuHPhRSysvL8fjxY0RHRzN+GP369UP//v1bJe5Xo0+fPszGFAqFOHbsGL799luUlJTA2NgYRUVFsLS0ZJK3NJG3ddbw4MEDrF+/HuHh4TA1NUVZWRk0NTVfG0RmZmattFlZWdi/fz9OnDiBpqYmAC+dDi0sLDBgwAAMGDCAWbawsICxsTGzPaKiovDrr7/i7t27zMfFpUuXQlNTEyoqKujZs2eraOs5AEhKSsL58+fx6aefwsbGhknQpaWlbS6XlZVBIpFAX18fixYtgoeHB5SVlTFu3DhUVlYypfsJCQnMslgsZhKFNNnb29tDLBYjNjYWU6ZMgUgkQkpKSqtkFRsbC3V19deSvYmJCRITExnjtIaGBqSnpzNneNIz3vT0dPTo0aOVeZp0uwcGBuLQoUPQ1tZGXV0d6urqUFtb2+ZyRUUFsrOzUV9fz1yycnV1hY2NTZtmYb+P5uZmHDp0CIcPH/5/7d1/aNT3Hcfx50vj77kFnWMkisYwN50uTtKyUTdWO0a3lNb/dP5gPxBc2UKFymit+0NQkE22FSZCbBVlwjJqu43p1E6nJJAm27rF2KrLpZKYeIsOkQSMyf1474+7C0ljft2p39zX9wOO5C65L+8Px/d1n88nl/eXrq4upkyZwqRJk/rfgAaG95IlS4a00IhEIuzcuZPq6mqKioro6ekhFosNCvHy8vIhIQWpgNy1axenT5/ub6k8e/bs/uZoA4N8YAuMSCRCZWXloJ4rZWVlLFy4kHnz5o14mzFjBvF4nAsXLlBdXc3x48epqKigoqKiv9NoT0/PqLeSkhJWr15NR0cH27dvp6Ojg0gkMujW0tJCJBIhkUj0nzOZsF+3bh2nTp1i48aNJJNJWlpaBq2WM3kxsAHaqlWrWLp0KbFYjIMHD7J161amTp1Ka2srjY2Ng27Xrl1j8eLFQ8L++vXr7N+/n/Xr17Ny5Uo6Ojpob2+/79fMyqK4uJji4mLWrl077MomL4N9oFgsRm1tbf+MazSZ5k+ZTnmNjY1s2rSJDRs2jPrcmzdvsmPHDurq6mhvb6erq4vNmzdz4MCBEVuDQmr5unfvXo4cOUI0GqW3t5eysjJOnDjRP1McjplRV1fHpUuX+mdsN27c4OTJk2PuSz5wDGfPnu0Pzmzcu3fvvg2sPi6ZTHLnzh06OzuZPn06JSUlI/6+mdHW1jYk8KdNm0ZDQ8OIz43H41y5cmVI2M+aNYuWlpZht9oyEokEbW1tgwL/6tWr7Nu3j+XLl9Pd3T2uXuzxeJyLFy9SW1vLzJkz2bJly6jP6enpoaqqiqampv7VV1FRETU1NRQUjLwbmkwmOXz4MLt376a9vZ14PM6cOXM4d+4cK1asGHWWd/78eaqqqvqbTEWjUc6cOcOaNWvGtBLObO80NDRQX19PeXn5mM6pj4vFYjQ3N7Ns2bJxP3csMvvwAwO/ra2No0ePjnoOtra2Dgn7rq4uampqKC8fOUO7u7tpamrq35JtbGykqamJPXv2sG3bNhKJxKgT00wfoUzYFxYWDmrlPVDeB3uQuru76ezspLS0dFzbQJk/CkajUUpLS8cUksMdZyJeWORBy3aciUSC5ubmrJqkTRS9vb0UFBSMaTWakUwmuX37NtFolKKioiEto8eir6+Pu3fvUlhYOO7nPi4y11OYO3duVudwIpEgFotlff6PxIPdOedCxpuAOefcY8qD3TnnQsaD3TnnQsaD3TnnQsaD3TnnQsaD3TnnQiaQjztKugW0PoRDfxr430M4bhB8LBNTWMYSlnHA4zWWhWY26pXqAwn2h0XSP8byGc984GOZmMIylrCMA3ws9+NbMc45FzIe7M45FzJhC/aqoAt4gHwsE1NYxhKWcYCPZYhQ7bE755wL34zdOecee6EMdkmVkq5I+kDSz4OuJ1eSXpZkksbeOHyCkfSL9GtyUdI7kvKqb6ykZyVdlRSR9ErQ9WRL0gJJf5P0Yfr8eCnomnIhabKkf0n6c9C15EJSoaS30ufIZUlfzeV4oQt2SU8DLwBlZvZFYF/AJeVE0gLgW0Bb0LXk6F1guZl9CfgP8GrA9YyZpMnAfuDbwDLgu5IezhUjHr448LKZLQO+Avw4j8cC8BJwOegiHoDXgVNm9gWgjBzHFLpgB14E9ppZL4CZ3Qy4nlz9CvgpkNd/DDGzM2YWT999Dxj+qsoTz5NAxMw+MrM+4HekJg95x8yiZvZ++vtuUgEyvst1TRCS5gMVwBtB15ILSZ8Cvg68CWBmfWZ2J5djhjHYlwBfk1Qv6YKkJ4IuKFuSXgA6zKwx6FoesB8Cfwm6iHEoBq4PuN9OnobhQJIWAV8G6oOtJGu/JjXpSQZdSI5KgFvA4fS20huSRr4m5yhGvuDiBCXpr8Bn7/Oj10iNaQ6pZeYTwO8lLbYJ+vGfUcayg9Q2TF4YaSxm9sf077xGajvg2KOszQ0m6RPAcWCbmXUFXc94SXoOuGlm/5T0jaDryVEBsAqoNLN6Sa8DrwA/y+WAecfMvjnczyS9CLydDvIGSUlS/RduPar6xmO4sUhaQeqdvDF9XdD5wPuSnjSz/z7CEsdspNcFQNL3geeAZybqG+0wOoAFA+7PTz+WlyRNIRXqx8zs7aDrydJTwPOSvgNMBz4p6bdmtingurLRDrSbWWbl9BapYM9aGLdi/gA8DSBpCTCVPGwQZGZNZvYZM1tkZotIvfirJmqoj0bSs6SWzc+b2d2g6xmnvwOfk1QiaSqwHvhTwDVlRalZwpvAZTP7ZdD1ZMvMXjWz+elzYz1wLk9DnfQ5fV3S59MPPQN8mMsx83LGPopDwCFJl4A+4Ht5NjsMq98A04B30yuQ98zsR8GWNDZmFpf0E+A0MBk4ZGYfBFxWtp4CNgNNkv6dfmyHmZ0MsCYHlcCx9MThI+AHuRzM//PUOedCJoxbMc4591jzYHfOuZDxYHfOuZDxYHfOuZDxYHfOuZDxYHfOuZDxYHfOuZDxYHfOuZD5P+mAW/bmELXEAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Simple pendulum\n", | |
"eqn1 = Eq(diff(th(t), t), th_dot(t))\n", | |
"eqn2 = Eq(diff(th_dot(t), t), -sin(th(t)))\n", | |
"# Numerical vector field\n", | |
"nvec = lambdify((th(t), th_dot(t)), [eqn.rhs for eqn in (eqn1, eqn2)], 'numpy')\n", | |
"quiver(x, y, *nvec(u, v), pivot='mid')\n", | |
"# Draw critical points\n", | |
"crit_pts = solve((eqn1.rhs, eqn2.rhs), (th(t), th_dot(t)))\n", | |
"for pt in crit_pts:\n", | |
" scatter(*pt)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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Ws4ldX33O3u++xt3Lm5GPPkVoQuJVHbO2rITls16n4nQ+XQcNof8dd+Pm5d2qY81NRnZ8sZgDq77DKyCQkY8+RXBM3FWN11BZwfLZr1N6/ChdBw2l/513XzBB/i9TYyNbFs8je/1qfIJDGP34s1f97L3i9EmWv/UadWVlJA4ZQfqkqbi0skpmY20NWz+dx+GtGwmIiGLko0/h1zH0qsZbX1HOirf/SenxoyQOHk7G3b9vdcJpqKli04KPOLZrG0FRMYyc8fRV/7RRdCSHFbP/SZPBQOrY2+g9/vZWf09RV17GxgUfcDJzD6Hx3Rg+/Y9XfXqm6sxpls/+J9XFhfS6ZQJ9J9yJSn3lb9hyYr8BlJ88wYp/v0FdaQn9Jk2h1y0TkFp5BaVLkbd9M2s/nINCoWT49CeI6tn7svopOpLDyjlv0lhTTb/br168J/btZvW7s3A47Ax9cAZxfftfVj9ncrJYOecNTI0NDLr7DyTePOKSrqbVGkIIstZ9z8YFH+Cq82DUjGfoGN/1svo6sXcXa95/G6vZzKB7HqDbTUPbPF6AY7u3s+b9txEOwZAHHqFz2oDL6ufozq2s+/AdHA4Hw6c/QUxq3zaOFITDwd7vvmbb5wvxCghkzBN/vqw3aSEEuZvXs+Hj91ColAx76PGrE68QZK9fzcb5H6Bxc2PEI08SkdijzfqXqzveICzNTaz5YA5Hd2yhU/eeDJ/+x1afmV6MzWJh08IPObR2FR1iuzDqsafx1AdcUZ8mYyNrP3yHYzu3Ep7YgxHT/3jBqZFLZbdZ2bp4AZkrviGgUxSjH3/2is8Em+rrWPXOTE4f2k9c3/4MeeBRtG1UftnS3MTaD98hb/tmIpKSGfHIk1f82hnralk5503OZB+kc7+BDPnD9Dab+rJazGxeOJdDa1cSFBXDqMeexTvwyubJDZUVfDvzVcpPHidlzHj633F3m03NNDcY+P7dWZzcv5fYPukMfXDGFb92tWUlrJj9T8pPniB5xFgGTLm3zaa+zE1G1rz/b47t2tbm/2+cJSf2G0jLWd8qNs7/AFcvb0bPeIaQzvFX1Gd9RTnfzXqV8pMnSBkznvTf3YVS1TbbFv73rGTkI08Rntj9iuNdPvt1yk4co/uw0Qycen+bfHSFlrO+Pcu+ZPuSRXgHBTH68T9d8dRM1ZnTfDvrtavyacvhsLPnmy/Z8d9P8QoMZPTjfyKw05Vdzaq6qJAVs1+n8szpH/4eprZZQrNZrWxa8CGH1q4kpHM8o2Y8g4fflX1RWXIsj+WzX6eprpaBd/2e7kNHtdmnF5vVypZPP+bAqu8IjIxh9ONX/gZXeuIoK2b/E0NVJf0mTaXX2NuuyqdZObHfgMpP5bN81mvUV5aT/ru7SB0z/rL+OE4e2Muqf7+JEILhDz9BdGqfqxAtVJ45zfK3XqempIjet04kbeLkyzpbO7pzK2s/mAPA0GkziO3dr61DBaDocA7L3/4n5sZGBt37AN1uGnZZyeLwlg2s/fAdNK6ujH78WULju12FaH+YV377XzQb6i87uQkhyN6who0LPkCt0TJi+h/p1OOieeGyHNm2ibUfvoNSrWbEw08QmZx6yX0IIdi/chlbPp2Hh5+e0Y//6aqtxjq+Zwer35uNcAiGPfTYZf3dORx29n23lO1LPkHn68eoGU/TIbbLVYi2hZzYb1DmJiNr3nubY7u3E5mcys1/mN7qZVoWUzNbFs3j0NqV+IdFMObJ5676l1pWk4kN8z8gZ+MaOsTFM2rGU62e7jE1NrJ50VxyNq4lODqOkTOevuIzp4tpqq9j5Zw3Kcg6QJf0DAbd+yCuutZtwmoy1LPh4/c4unMrHeO7MmrGM5e9HrnV8RrqWf2ftzi5fy8xvdIYOm0GLu6t+1K2qb6ONR/MIX/fLsK6JjJi+pMXXAHVVmpKiln+1mtUFpxqWZU0aQoal9btZjZUVbDuo3c5dWAf0al9GPbQ461+rpfr3E+Koxg45X5UrVzxZqisYNW7Myk6nENM7zSGPjCj1V+YXy45sd/AhBAcXL2cLYvmISmVpE24g6ShIy+4akE4HBzZvpltny+kobqKniNvod/vpl7T3Y3OszWlkt7jJ5E0ZMQF47VZrRzesp5tn3+CqaGB1FtuI23i5DabKroY4XCwe+l/2fHFYrQ6HemTppCQMeSCUz82q5Wsdd+z66vPMDc10fe239Hr1onXbJmfcDjIXPENWz9bgJunF2mTppAwYPAFx7eaTRxas5JdXy/BZjGTfsfd9Bx5y1WZGjgfm8XC5kVzObh6BTo/PQMm30tcn/QLxmtpbuLA98vZ/c0XCOGg/x330GP46KvyxfH52G1Wtn62kMzlS/EOCqb/nfcQ0yvtguObm4zsW/4N+777GoVSwaB7HiRh4OBrEm+7T+xFRUXo9XpcfljDWlxcjMPhIDT06i4Tu1T/e33TkydP4nA4iI5u2c1ptVqRJAnVeZJaXXkZG+a9x6kD+3DRedC53wDCuibhFRDUchHr6iqK8nLJ274ZQ2UFARFRDLr3ATp2Trhmz++nakuLWffRu5zJOYSrhyexffsTntgd3+AQJIUCQ0U5BTmHyNu2icbaGoJjOzP4voeueP74clUWnGLDvPcpOpKDm5c38QNuIqxrEp7+ASAEdeWlFOZmcWTbZprq6+gY35XB9067bjtby04cY8O89yk9cRRP/wDiB9xEx85d0fn5Iex2astLOZN9kLxtmzEZG+nUvScDp/7+qi+dvJCSY0dY99G7VBacwisgkPgBNxEa3w2dnx671UpNSREFhw5wdNdWzEYjkT17cdM9D1y3jU+nsw6wacGHVBedwSc4hISBgwmJi8fdxweb1UpNcRGnD+3n6I4tWM0m4tIGMGDyPVe8IOFStLvE/tZbb+Hm5kZCQgKHDh1izZo1rFmzxln4y2q1Mnv2bKKjoxk5ciShoaGsX7+e1NRUkpOTiYuLo1OnTs7+Tpw4QVRUlDPpfvXVVyQnJzvbzJo1i6qqKuLj44mPj+fAgQO8/fbbuLm5OYuLHT58GIVCgSRJuLq64u7ujq+vL/7+/uj1eoqKiigtLcVsNjNkyBCCgoKora3lrbfeIiQkhBEjRuDq6sqcOXNIT09n0KBBJCcnY7VaiYyMJCwsDIPBgKWqggPff8fJg/uw/VDv5ac0/kGkjBxLn+Gjmb9gAV9//bXzgt1NTU18+eWXqFQqlEolrq6uWK1WNBoNWq0WtVqNRqMhJSWF6OhooqKiiIyMJCIi4rxvNq1RdDiHA2tWcDJzDzbLufEqlCrCuiXRc+QthCf2uGZnZRcihKAg6wAHvv+O04cO4LDbznlcoVQRmZxK96GjCOuW9KuI98S+XRxas5KC7IPOsgpnqTRaIpNT6TFs9GUvu2xLDoed/H272b/yW4rycn8er1ZLTGpfeowYQ3D01d0b0RoOu528HVvIWreK4rzDP3tc4+pKTK80egwfc11KbdzQid1qtfLEE0+c87PMzEzKy8upqamhvr4eaKnlotfrUSqVFBUVodPp6NmzJy4uLmzatAmHw0GHDh1wOBwUFhY667v4+PhgNBpxOBz06tWL4OBgdu7cSW5uLqGhoYSEhGAwGDh8uOWFVSgUeHh4OMeNiIhAo9Fw7NgxAEJCQvD29ubYsWPO2jJKpRKFQuG8r1Ao0Gq1NDc34+7uTufOnfHz82P9+vUolUoSEhLQarUcPHgQs9mMSqXCarXi6uqKWq0mJiYGf70eY0UZTXW1hIeH4R8cQs6pArbv2gW01J7RarVUVVUBOKtOni3REB0djZeXFwcPHsRut+Pj40NSUhJ5eXmUlZUBLQXXnnvuOSZNmnTZid35OppNVBacpr6yHBwOdH56AiIiL7iz8XqzmJopzz9OY001klKJztePwE5Rv9oCYyZjI+X5J2hqqG/5G/XTE9Apus1WE7W1JkM9FadPYqytQalW4x0QhD4sotVz2tdaU30d5SdP0NxgQKFS4RUQSEBE1DWbMjyfGzqx22w2XnvttQs+vnLlSnbu3ElYWJjzrDYrKwtoSfYBAQEUFxcDEBkZ6UzcDocDHx8foqKiOHLkCEaj0dnn2YJfKpUKT09PLBYLjY2NBAcHk5iYiMViYcuWLbi7uxMaGkpzczOnTp0CQKfT4e/v70zEGRkZ+Pr6smnTJnJycujduzdxcXEcPnyYTZs2AeDi4oK3t7czoer1ejp06EB2djZCCMLDw4mLi2Pbtm00NTUhSRJ+fn6YzWYaGhqccUuShBACX19fwsPDUalU7N27F19fX2fce/fudY7Z2NiIm5sber2eoUOH0rVrVzIzM8nJyeH555/n1ltvRXGN5mJlMtmluaET+8UsW7aMHj16EBYWBsA777xDZWUlnTp1IiIigtzcXD7//HO0Wi1arRar1UpZWRnu7u7OuuVny9mGh4cTGxtLbm4u+/bto7a2lkGDBpGQkEBRUREvvfQSffv2ZeTIkQQGBrJo0SLS0tJIS0sjOTkZf/8ftybX19fj5fXjBpU9e/aQlJSEVtvyJeYnn3yCVqslJSWFTp06sXjxYpYtW+asZ9PQ0MDWrVtxcXFxJleFQkGHDh3Q6XS4ublRXl6OWq3G3d2doUOH4ubmxp49e3jjjTfIyMhgyJAhqFQqXnjhBQYNGsSQIUNIS0vj0KFDxMfHExcXh4uLi/O7CYDTp08THh5+3acZZDLZL2vXif1qcTgc55ytVlRUoNFo8PZuXU2V66WysvKcuX+LxYIkSah/pR/JZTLZ5WltYr9+k0W/Qv87BREQcO2+7b4SP/3UALS68qRMJmuf5MlUmUwma2fkxC6TyWTtjJzYZTKZrJ2RE7tMJpO1M3Jil8lksnZGTuzXwfVYYiqTyX47bqjljqdPn8ZisRAbGwvAG2+8QVZWFpMnT+amm25i2bJlvPvuu0ycOJFJkybh4uLC6tWr6dOnD8HBwc5+Ghoa8PD4sVRrcXExISEhQEvSPXLkCOHh4c514QcPHsRgMGC323E4HBQUFADg5uZGQ0MDJSUlBAcH07t3bzQaDQ6Hg/r6evr06YNCoeDrr7/m9OnTTJw4kdDQUObNm8fcuXO5/fbbmTx5Ms3Nzfz9739n5MiRDB06FFfXljKnJpPpnI1EVVVV6PU/lvDNz8+nU6dOzmWaOTk5KBQKdDqds5RAUVERRqORxsZGiouL8fb2Jjo6GrPZTF1dHXa7ndtuuw1PT095g5JM1k78qjco7dmzB7vd7rz/pz/9ia1bt6LVaomNjSU5OZnS0lI2bdqEVqtl7Nix+Pn58dlnn1FXV0e/fv04c+YMp06dIjg4mDFjxmA0Gjl27Bi+vr5MmTKFwMBAXnnlFUwmE3feeScZGRk8//zzfPvttwQFBTkT5/bt2wFQqVTccccdLF68GLvdjlKp5OGHH2bBggUYDAYAPD09sVqtOBwOwsLC8PLyoqCggKqqKjp06MCtt96KTqfjvffeo7m5mQEDBuDh4cG2bdswGAwMHz6crVu34ubmhr+/P+PHj6dLly4sWbIEo9HIAw88QGRkJM8//zzbt2+nX79+9OnTh9zcXBYvXuz8ffXq1Yu9e/cihECpVDJ9+nTmz5/vjHPIkCHk5eVRWFiIu7s7ISEhTJs2jUcfffSK68TIZLK21y52nvbq1eucuigApaWlzmJcOp0OSZKcbSIjI7Hb7RQUFCBJEoMHD8ZgMLBnzx4AEhMTqayspKysDCEEarUaDw8PGhoanMW6ALy8vKivr8fNzQ2FQoGPjw91dXW4u7uj0+morKzE3d0dg8GAt7c3JSUlKBQKbDYbkiTh7e2NxWLBaDTi4uJCQEAAzc3NVFZWAi01W1xdXamtrQWgd+/eWCwWDhw4AEC/fv2w2Wzs3bsXh8OBn58fFovlnN/F2eqMZ3+mUCgICAigsrIST09PdDodRqMRd3d3GhsbCQwM5OTJk864z34S8PLyoqSkhJtuuolXXnmFPn2uztWWZDLZlWsXif1/CSF47LHHiIyMZPTo0URFRfHEE09w4sQJgoKCCAoKIj8/n23btmGxWDCZTISFhVFTU4PRaMRoNBISEoKPjw9+fn54enpSWFhITU0Nffr0YfTo0Zw4cYJXXnkFf39/7r77biLYmhXfAAAgAElEQVQjI1m4cCE7duxgzJgxDBgwgGeeeYaQkBDGjBnDrbfeSkNDA1lZWQwYMIC0tDRUKhUvvfQScXFxjBs3DrVazVNPPYXRaCQpKYmkpCQ2b97M559/jkqlQqVSodFoOH78OA0NDTQ1NREbG4tSqXRO/wgh8PT0pHv37nTp0oU1a9aQmZlJbGwsd911Fz4+PsycOZOsrCzGjx9Peno6H374IUePHmXkyJHcfvvtzJs3D51OR//+/Rk+fDjR0dF8/PHHREZGMnjw4KvwSstksrbULhP75frpxS4sFgtms/mcOfafOnz4MG5ubkRERABw6NAh9u/fz/jx4/Hy8sJms1FdXU1gYOBVi9dut9PY2IjVaj1nTv2nLBbLOaUDDh48SF5eHmPGjMHd3Z36+no2btzIsGHDnHP2MpnsxiYndplMJmtnWpvY5eWOMplM1s7IiV0mk8naGTmxy2QyWTsjJ3aZTCZrZ+TELpPJZO2MnNhlMpmsnbmhE7vFYiE7O5vdu3c7f3b69Gk++eQTLBYLAFar9ZyyBGaz2fnvtljqabPZqKmp+cU2drudiooKjEaj82eHDx/mo48+wmQyOZ/Lzp07nTGdjf+n41wJh8Pxs128cjEymax9umHWsVutVu677z5KSkrw8vLi1ltvRavVMnv2bI4ePUpUVBSPPPIIy5YtIzc3F4PBwCOPPEJzczOzZs1izJgx3HLLLezbtw9fX18effRRdDodU6dOJTk5mcmTJ+Pr68tf//pX1Gq1cyfr/v37qayspKamhoqKCux2O5GRkVRUVJCfn4/dbuemm25CrVbT2NhITU0NVquVTp06ERISwsCBA9m1axcrVqwgMzOT8ePHM2XKFF555RVqa2uprKzk0UcfpbGxkffffx9/f3/uu+8+JEli06ZN3H777fTo0YOPP/6YkJAQpk+fjqurK0888QT+/v707t2b1NRUFi9eTH5+PjabDZvNRnl5OTqdjrKyMk6dOoUQgvT0dIxGI8XFxVRWVtKlSxcSExPx8PDA09OTkJAQRo4c+bNrv8pksl+H1q5jRwhxzW89e/YUrXXTTTeJiIgIERERIdzc3AQgAOHm5ibUarUAhLu7u7jjjjtESkqKAIRGoxHPPfecuOWWW4QkSQIQgwcPFmlpac77gFCr1UKj0QhAKBQKER0dLTp06OB8PDo6WgwdOtR5f/To0eLf//63UKlUAhApKSniX//6lzMurVYr+vbtK7y8vJzH/HQ8lUolunfvLsLCwpxxPvXUU+fEeffdd4tx48Y5xwgMDBRBQUHOPrRarYiNjRWBgYHnPI+4uDjn/bS0NPHiiy86++zXr5/46KOPhIeHhwCEv7+/ePDBB4Wvr6/zmLvuukuUlJS0+nWRyWTXHrBPtCLHXvEZuyRJocBCIPCHJPGBEGL2Lx1zKWfsubm5mM1mhBBMnToVX19fxowZw/Dhw3nllVfIysrCzc0NNzc31Go1OTk5VFVVATBp0iS2bdtGcXExAMOHD+f06dOYTCbsdjsajQaj0YjD4UClUtGjRw/8/Pz4/vvvCQoK4vjx44wbN44DBw4QFhZGTk4OAQEBhISEkJmZSW1tLenp6bi5uZGZmcnYsWNJSkpi4cKFADz+2B8ZPWYUY8aMpqqqiri4OOLi4sjNzWX37t00NDTQ0NBA//79OXr0KOXl5QDcdttt5ObmUlxcTENDA5GRkSgUCux2OzqdjqCgIGpqaigpKaG+vp6AgAAmTJjARx99RK9evTh48CCdOnXCx8eH4uJiqqur8fX1JTExkS+++IKIiAgGDRpESUkJpaWl/Pvf/6Zv374IR8vfgqS4Mcr33mjxymRX6pqVFJAkKRgIFkLslyTJA8gEbhVCHL7QMZc7FVNfX3/B2ik/ZTKZKCkpoaioiMjISPR6PQUFBZw+fZrAwEC6d+8O4HzD+GnN8+PHj5OVlUVhYSFTp07Fz8+PefPm8cUXX/D000+TkZHBiRMnWL16NbfddhvBwcHk5eURExODUqkEIC8vj86dO7N+4RGO7irFy9+VqOQAug8Ow0WnPidWh8OB0WhEoVDgcDg4deqUs8569+7dMZvNVFZWYjKZiI6Odh6Xn59Pc3MzQgi6du2Kw+Fg7ty5rF69mieffJK0tDQyMzN58803mTZtGv3796egoAB3d3f8/f2BlvrtcTGdOby9lGO7y6gqbkQ4wCfIjeieASTeFIrW9ddVvtdqsZOzqZhje8uoKTXisAv63x5D4qDQ6x2aTHbVXbdaMZIkLQPmCCHWXqjNb6VWzKmDFZQXNFBR0EDhkRq0ripuuqsLkd39r3doAFQUGFj9YQ6GKhMB4R6ExPogKSXKT9VTfLQOVw81g++JJzzB73qHCkDJ8TrWfpxLY62ZoEhPgqO9UaoUhHf1IyjS63qHJ5Ndda1N7G16OiZJUgTQA9j9yy1/G7RfzMZnzVqCIiPpmjGWfTXRrHovm34Toul+c9h1je3UoUpWf5SLq4easY91J7SL7zmPVxQY2LDwCMvnHCLjzjgS+odcp0hbHNtbxvp5R/DQuzDuyWQ6xHhf13hksl+zNkvskiTpgK+Ax4UQhvM8/gDwAEBY2PVNateKLj0dhdaF5qwszLNfpnvHcI4Pe4HtX55AUkgk3XR9pg8KD9fw/Yc56Dt6MHp6Iq4emp+1CQj3ZMKzKXz/YQ6bPj2KQqmgS1rweXq7+k4erGTdvCMER3kx8qFuaN3UFz9IJvsNa5N1bZIkqWlJ6p8KIb4+XxshxAdCiBQhRMrZOd727m2fTO6O38a/pvlT+o8HkewWOi2cTmhH2P7Fcc7kVl/zmOrKm/j+g2x8At0Z82jSeZP6WSqNkhEPdiO0iw+bPs2j5HjdNYy0RXVxI2vn5hIQ7sGo6YlyUpfJWuGKE7vUcgWLucARIcTMKw+p/eim70ZyYDKn6k/xWMNcXp/mjyo6nMgvnsHbW8GaubkY68wX76iN2Cx2vv8gB0kpMfLhbri4XzxJKlUKhv6+K556V1Z/lIOp0XrRY9qKpdnGqvez0bipGDGtGxqXX9cXuTLZr1VbnLH3A6YCN0mSdPCH28g26PeGUm+uZ1bmLKz2HxPfLdG38Gr/V1kxfgX/SP8HOfYCHhtbgzLYly473sRmsbPhkyPXbAfo7u9OUV3cyJB7E/D0a/1VlVzc1Qy9PwFTo5VNi/OuWbzbvz6BobKZYb9PwN1Le03GlMnagytO7EKIbUIISQiRKITo/sNtZVsEd6Ow2q3M2DCDTw5/wrHaYz97XCEpGBM1hsUjF2NyV/G3sSZcGkvpbNjGmdwajuwoveoxVhQYOLTuDPH9OxDe9dJXufiHedBrTCfy91eSv7/yKkR4ruJjtRzeWkLS4FA6xPhc9fFksvbkht07bjKZcDgcQMsad4fDQX19PdCym9ZgMGC1WmlqanIe87+1UtrKq3teZX/Ffl7u9zIJ+oQLtov0juTDIR9y2svC0lv0BOz5DF+3JnYuzaem8sfYTSaTs4YM4Hyel8vhEGxclIerp4a0cVGX3U+PoeHoQ3Vs//I4VrP94gdcJrvVwaZPj+Kpd6HXmMirNo5M1l7dEIm9sbGRRYsWUV3d8mXjrl27WLVqFaNGjaKiosK54/KFF17gtddeY/fu3URHRzNz5kwmTZqExWLh+eef57XXXuPpp5/Gbrdjt9t5+eWXycvLu+j4DoeDw4cPs2DBAme9mN27d/Pyyy8zb/M8vjj2BVM7T8W33Jft27c7j7PZbPznP/9h7ty52Gw2lixZwsznZ+K9y5vPwoo400VP6Oa3aG608NoTH1FeXk7Pnj2ZM2cO48aNw2QyUVBQwIsvvsiCBQsQQtDc3ExWVtbPioSd1dzczNGjR6mrq8Nms7F7927e/MtHVBU20v/2WMqrSlm8eDHr16+/5NdBoZAYMCmWxlozmatOX/LxrZW9uYi68iYG3BGHWqu8auPIZO3VDVEEbO7cufz5z3+murqatLQ09Ho9W7ZsoaamhqCgIObNm0d2djbPPPMMAO+++y7R0dFMmDABg8HAXXfdhY+PD++//z4mk4mRI0cSERHBF198QWVlJQMHDmTq1KksWrSIU6dOodFoUKvVREVF0dDQQGZmJg0NDTz77LOcOHGC9evXU1dXx73T7mV/0n6sDVaO/uUonWM6c+rUKdzc3AgLC6OmpoaysjJMJhOxsbE8+uij7Nq1i08//ZSQ+0KI7u7DnA9gY8exEJpBvmIt6Tf34qGHHqKqqoqhQ4fS0NDAzp07AUhPT+fpp5/mySefpKCggISEBBITE6mpqaG8vJwzZ85QXl7O5MmTaWxsZNOmTTQbzfzz/q9ostXznzXPUlhYSEZGBo2NjdTX12MymVAoFLz66qv87ne/o+W78F+2bv5hju8rZ8pLffHwdblo+0thMlpZ9MJOAiI8GTuje5v2LZPd6NrVxawtFgtCCBwOB2azma5du9K9e3ciIyOx2+1MmDCBbdu2kZ6ejlarZfr06ezcuZP+/fuj0+lYuHAhDQ0NJCcnExYWxurVq1m+fDlNTU2oVCoaGhr4z3/+w9atWykoKMBoNPKXv/yFrl27smnTJhoaGnjnnXcYM2YMa9eupa6ujsmTJ2NNsWLT2jj5zkky+mfg5uYGQFVVFSqVijfffJOwsDDc3Nyw2+0sWbKE2tpaUlJSqF9WT5mwsqKHigFFa7DbLTTku7Bjxw769OlDUFAQa9asQZIkgoODCQwMpLi4mAceeIDq6mqsVitGo5GAgACMRiN79+6lpqaGjz/+mLvvvpu1a9dSX1/Ps/e/jgoXvt75njOpd+zYkezsbI4fP05AQACrV6/mjjvuaFVSB+g9tmV6ZO+KU23+Wu//vgBzs4208Zc/ZSST/dbdEOvHpk6dikajYeTIkQQHn3+TzNma61arlb1797Jz504+/PBD9Ho9e/fuZcOGDUyfPp3k5GTsdjuHDx/m6NGjjB49GhcXF/Lz89myZQv79+/n73//O4sXL2b37t1MmTKF3r17k5SUxOjRo3nyySfZunUrz73+HJNWTyKiMYIuqV1YtGgRarWap59+mptvvpnhw4djsVi4+eab8fDw+FnSdDgcfLz7Y95zfYsRx9V0th9BHZVBhXo3r7xyD4mJiZSUlLBv3z68vLwYOHCg89h//etfJCUlcfPNN7NmzRp8fFq+XPzrX/+KzWbjjjvu4KmnniL3UB4d1N3IKdjNbVNHoPzGzLfffsvmzZuJiIjAbrfzf//3f2g0F17Lfj4evi50HRBC9qZiegwJwyfI/ZKOv5DGWhNZG4vo3DsIfUePNulTJvstuiGmYq4Vq9WKWt2yttvhcCBJEjU1Nfj5+eFwOKisrESv12M0Gnn5wMtsLtrMZ4M/I8I/wlkA7FLYHXYmfDeB1G2VjF7VxO6b3iA4zo/R05Muua+6ujq8vb1xOBzU1dXh5ubGvhUFHFpbzG1/7kFgmDe1tbX4+raUDmhqanJ+wrgcTQYLn7ywk4hufgz7fdfL7uenti45Rs7mYia/1AdPfeuXY8pkvxXtairmWjmb1AEUCgWSJOHn5+e8HxgYiFKppEpUsfr0aqZ0mUJUUNRlJXUApULJ48mP82XnOvBUEWncT0F2NeWnf1aR4aK8vb2dcfr6+iIJFUe2lRPZw5+gcB8kSXImdeCKkjqAm6eGpEEdOZFZQU2p8eIHXESTwULuthJiewfKSV0mu0JyYr8M83LmoVVqmRI/5Yr7GtBxANEB8XzfV0vArkVoNC3zzFcqZ3MRlmYbPYeHX3FfF5J0cygqtYIDq6883kPrz2C3OUgedvXilcl+K+TEfonKjGUsz1/O+Jjx+Lr4XvyAi5AkiXu73suSLrUo3FVEWI9w8mAlNSWXfxZsNds5uK6QsARfAsI9rzjGC3HVaYhP78DRPeUYqpovux+T0Ur25mKikwPabL5eJvstkxP7JVp8ZDECwd0Jd7dZn0PCh+Dv05GdvTwJ2DYflVpi/5rLPws+vK0EU6OVniMi2izGC+l+cxiSBAfXnrnsPrI3FWE12a9JvDLZb4Gc2C+BxW7hmxPfkBGaQQddhzbrV6VQcWfnO1nYuQKNo5kIl1KOXeZZsN3q4MCaAjrEeNMh+urXLPfwdSGuTxCHd5TSZDj/pqlfYjHZOLS+kIhEPfqOuqsQoUz22yMn9kuwrmAdteZabo+9vc37Hhs1FqOXlsLUUIK2fYwkwYHLOAvO21WKsd5CzxHXbq46eWg4DpuDQ+svPd6cLcWYm2zXNF6ZrL1rV4m9srLynMqDRqORmpqaNuv/i2Nf0FHXkT4d+lxRPzab7Zz7BoMBW6ONIRFDWBBfhaa2mDDfBo5sL8VY3/qyvg67g/2rCwgI9/jZFZGuJu9AN6J6BpC9uRiTsfVlfW1WO4fWFdKxsw9BneRL28lkbeWGTexCCFau/LGIZHZ2NpMmTWLFihUAFBUVMXnyZP7+978722zfvv2yaqQAnKw7yb7yfdwWexsKSYHVaqWwsPBnMf0vk8mE2fxjcq6srOShhx6iqKgIaLl49vjx4/nHP/7BxNiJZAWaqAjwwHXTezjsDg6uK6S8vJzGxsaLxnh8XwWGKhM9R0Q4N0RZrVZKSkrOadeWb3Zn9RwegdVkJ2tjUauPyfth+kaeW5fJ2tYNk9i///575s2bR0VFBQAzZ87k1ltvZcGCBTQ3N/O3v/2NjRs38vjjj9Pc3Mzs2bNZtmwZc+bMIT8/H7PZzNixY5k4cSL5+fkAfPzxx7zwwgvOPh0OB8XFxWzfvp1ly5Zht9sxm83Mnz+fu1+9GwmJ0Z1G8/nnn5OamopK1bJxNzs7myeeeIKVK1dy8OBBDhw4QO6hTOq+fIzaD8cxISORzMxMhBC88cYbfPTRR9xzzz2YzWbefPNN1q9fzzvvvINvky/+Kn++CK4huPIUfoFmcrYU889XZ5KWlsapUy1b+Pfv38+6des4fvy4swpkc1Mzm7/IwaJowC9Cg8PhYPHixfTp08e5Pn/Hjh2MHDmSrKwshBCcOXOGr7/+2vlmeCX0HXV0StKTtaEQS7Ptou3tdgf715whsJMnIbHy9UtlsjYlhLjmt549e4pL9cgjjwhAdO/eXXz77bfin//8p0hNTRVarVYsWbJE5ObmijvvvFMoFArx2muviaqqKvH0008LFxcXMXHiRJGXlyemT58uQkJCREJCgjAYDOL3v/+9UCqVIjExUSxfvlxMmzZNACIkJETs3r1bvPrqqyI4OFgAYuAnA8W4xeNEcnKyAMRf/vIXsXXrVpGamioAcfvttwuHwyEmTJgg0kKVouwZXyFe9HTeDjzkLWbOnCmWL18ubr31VqFUKsXs2bNFZWWleOKJJ4RGoxFTp04Vr297XfT6T4LYHxsn3k4ZLOZMWy+eu/8tERYWJoKDg8X69evFv/71LwGIqKgoMX/+fPG3v/1N9O5ys5jz4HrxzfwN4ttvvxXdunUTgPjHP/4hNm7cKAYNGiQAMWnSJNHQ0CBSUlIEINLT04XBYLjk1+N8yk/XizkPrheZ35++aNsjO0vEnAfXi1OHKttkbJnstwDYJ1qRY2+YxH7gwAFx+vTPE4bRaBTbt28XVqtVCCFEXl6eePjhh0VZWZkQQoji4mLx8MMPi3379gkhhHA4HGLv3r1i+/btoqioSJjNZmdfu3btEr169RJFRUVCCCFef/11AYixfxgrus7vKu6bdZ8AhF6vF/X19aK5uVkEBASI0NBQUVNTI4QQYv0nbwrLi37CMbuHEDlLhdj13o8J/sPBzrGKi4vFm2++6Tzu9OnT4p577hHf7/ledJ3fVWz+wwSR1S1RfPzXVeKDxzYJk9EiHA6HqK2tFcePHxfz5893PufPP18i/jThPfHvR1YKs8ki/v73vwtAdOzYUTQ1NYn9+/cLSZKEu7u7KCwsFEII8ec//7lNk/pZ3759QMx9aouwmGwXbGO3O8SnL+4Un720WzgcjjYdXyZrz1qb2NttrRghxDmFt2w2m3Pq5JcYjUbc3Vs2yTQ3NzNr1iwsaRa+LfyWlWNW8v7s9/Hx8WHGjBkAnDx5kqKiIgYMGADWZni3L9gt8MBm0P1w0W5rM7wS1PLvO/8LscMuOL7ZbGby6slEn7Fy95xjuPz5dVbu1NFrTCdSR3U67zEnD1aw6r0cMqbEkZAeQlNTE6+99hpRUVHcfXfLevs1a9Zw4MABnn32WaDlC1tJkvDwaNtiW6Un6vj6jf2kT4whaXDoedsc3VXKuvlHGPr7BGJSAtt0fJmsPWttrZh2m9jbisPhYPjXw4nziePfg//tvEjHeSsibnsL1r0Idy2DyIxzHys5CB/8UKHx/+p/ccy52XN5K3MWX37WAa0+gNx+z1ByrJbJL/XFzfPccR12B5+/vAch4I6/9kKhbPnaxGKxoFQqz6ljY7fbL7uuzaX4ZtZ+akqMTP5bH7Ru514w22a18+mLu3DVaZj4pxQkRetKBctkMrkIWJs5UX+CUmMpg8IGAaBUKs+f1K3NsG0WxAz9eVIH6NAdVD8Ut9r/yS+OOShsEEgSxf1jac7MJLWfDpvVwa5v8n/WNmdLMbVlTfQdF+VM6gAajeZnSfxaJHWAfrfF0NxoZc/yn9drP7iukMYaM33HRclJXSa7SuTEfhGbCzcD0D+k/y83zF0KpjpIm3HhNo/sbfnvt4/8YledPDsR6hHKmtiW67Uqdq4h6aZQjuwo5UxutbNdfWUTO785SVi8L52S9Bd/MteIf5gHCf1b6rWXnKhz/ry6uJG9K04RlRxwTdfZy2S/NXJiv4jNRZvp6tcVfzf/X264fyHoYyEi/cJtvH8y59x04bXkkiQxoOMA1lmy0KYkU//td6SMjsAvRMeaubmUHK+lrryJ5XOyUColMqZ0bvXVj66VvuOi8NS78P372ZSfMlBd0siKd7JwcVMz4Hex1zs8maxdkxP7L6g11ZJVmcWAjgN+uaGxCs7sgoTxcLEEm/7Hlv+ufu4Xmw0IGYDZbqaqfzyWkyexHz/KiGnd0LqrWfrmAT59cRdNBgsjH05s8+uOtgWtq4pRDyeiVCn48vV9fP7SHqwWO6OmJ/7sewKZTNa2bohL410v+8r3IRD07dD3lxseXwMIiBtx8U4HPA3bZsKhz2DcexdslhKUgovShW2xdkaq1dR/u4yg557j9udSOb6nDKvFQUxKADqfX19SP8snyJ1Jz/fi2N4yHHZBTGog7l7a6x2WTNbuyYn9F+wr24erypUEfcIvNzy5CdwDILgVl7TTtO7KRRqlhm7+3dhtzOX2jAwMK1YS+MwzaF1VdB3YsVV9/Bq46NQkDjr/skeZTHZ1tKupGCHEOXVRxA/b5g2GS7/UHEBmeSZJ/kmoFeqfPXbOMtGifRDa6+LTMGd5/pCYS7OAljX2R44cob7+x2WQDoeDbr7dyKvJQztqKPbqaow7d17yc7gey1llMtn1dUMn9pycHHb+kOwsFguTJk2iW7duzt1Xf/zjH4mMjHTWhmlsbGTGjBlUVlb+Yr9CCAxmA8dqj9EzsCf5+fkcP37c+XhJSQnffPNNy52mGqjJp0QZcsH+LBaLs6KjEIJtppiWB/YvxOFw8Ic//IGEhAQKClourrF161ZiYmJwq3bDIRwcj/MAnY66Zd/+Ytz19fVUV/+4aqawsJBVq1Y571ut1h/j/kFz8+Vf+Ugmk/063VCJfenSpWzZssV5f+XKlcyaNQtoWbd9++23U1NTQ21tbcsl5+69F61WS2lpKdCyq3TLli1s3brV2cd7773H2rVrnffz8vL405/+xNHaowgEYeowRowY4bxYtNls5rbbbsNut7ccUJYNwI5TTc4+Vq1axdKlS533lyxZwuuvvw60rHipCRsOgDjwCQqFgoceegi1Wk15eTkAcXFxSJKEvbhljGxDHllurtStWYPjh6Jf+/bt47PPPnOekVdXVzNq1Ch0upaLVTQ3NzNu3DjnahkhBI888sg5b1CrV6/mrbfeutSXQSaT/crdUIl92LBhLVv3f/DMM8/w4IMPOpPshAkTePnll53ldBMTE5k/f74zsQcGBrJ58+ZzpiemTZvGkCFDnPdzcnJIS0vjWO0xAN7927uUl5ej17esE58xYwa7du0iKKilRMDJzJYywB26/RiXRqNh2LAfywZMnTqVBx980Dnu2CnTAJBsLUn6/9u78/io6nv/468zk5lMVpKQhDUBQgIIQcISFFARUAtqVcQNxValXJdi61KpS7WKy621P7V6xV5XrLeKVAuVRSmggkCAACGQkISE7HvIJJlJZsksn98fIUeiCEGWQPg+H488knPmzPd85wx8zpkz5/s+48eP580339QLe2xsLF9++SXORif9QvtR0FjAVS+8gLG1lZZNm/TXcvXVV+uFe+HChRgMBgIDAxER7rnnHnbu3Kn38+233+att94iPj4eaPsU8dZbb3Xop6Io3URnAmVO9s9PCQHrLL/frwdrtWsPBDseT256Ui5Zconk5+fL3//+d73tjIwMueeee6SgoKBt3pdPiO+ZaGmw1h/fCtqDwQ7THtDVzul0yvx18+W65deJv7VV8i64UMofeviIzXk8HqmoqBAREZ/PJ3v27JFf//rX+mt3OBzy+uuvy549e/TneL1eFcKlKGcROhkC1u2uitE0jcjIyA7zevU6/qCpElsJA8MHkpiYSGJiot52SkoKb7755nfrayxBixxAROSJj6Ts37/j1S4Wi4XEyEQ2VWzCZ9QIu/xybKtW4Xe5MFg6XuYYEBBA375t92E1GAyMHDmS//mf/9EfDwoKYv78jiNeT1fEgKIop9dZdSrmdKpuqe7cDasdVgg5xqjUo/H7jvpwn5A+eMVLvbOe8BnT8TscNB/2HYGiKMr3nZTCrmnadE3T8jRNK9A07dGT0WZX8vl91Dhq6BPS59gLO60QfOSjda/P/+PPC8w1aTUAACAASURBVIlt+91ce9TmY4Pblqtz1hE8fjzGyEjsX3x57H4pinLOOuHCrmmaEXgDmAEMB2Zrmjb8RNvtSs2eZnziI8rSidMrzgYIOvKt3RKf+IKBj66ioaX1hw/2OHR5pK3iqM3HBLV9Gqhz1KEFBBB2xRXYv/kGv7pMUVGUH3EyjtjHAwUiUigircAS4NqT0G6XcXrbimZQe8zu0Xjd38XxHqbM+t3lj/d/nPHD54Ud+jRgrzpq80GmtrbdvrYbYofPmI44HDRvVKdjFEU5spNR2PsBZYdNlx+ad9ZqL+yWgE7ksIgPtB9uxrxqu/73poKDP3ye4dD31v6j3/jZpLWNevX4PQAEjxvXdjpmzZpj901RlHPSafvyVNO0/9I0bYemaTuONfKzqxkOFWq/HOUceTsRMPzw6hLDsbZse9uGo1+YZDzUtrd9B2AwoAUEIN6j7xAURTl3nYzCXgEcnvLU/9C8DkTkLREZJyLjYmJO4CqS0yDQ2JZA2H7646g07YhH3VEh36UYXjmy9w+f52s7Aj9WYf/+aSHn7t146+oIu/yyY/dNUZRz0sko7OlAkqZpgzRNMwO3AEcPNTmJvIcdudrtdu65554OeSjz5s3jmWeewXVoKH59ff0xs2L0InqoqNbWdrxyJSsr67uJwHC8joYftJESF0F0aFtx/383pvzg8brSvEMri0REmDlzJo8//jhud9vOZPXq1XzyySfUN7dlv4Sa26ICgkaOJO7ddwidMvUHbXq/dxSfk5PTYbp9RK6iKN3bCRd2EfEC84E1QA6wVESyT7TdIzl48CDfvwl2SkoKBw+2ncMOCQnhnXfe0UO/ALZt28a+ffuwHBrQs2TJEn75y1/qw/tra2tJT08//PWQn5VPgCGAOmfbDuChhx7qEEPwxBNPfFfsA8Mp3Z+lB3hB2w6mpaWFHX+4jOI/XUWQ2cinn37aoQ1jY3HbH1GD0TSNzMxMysrKCAxs2xm05+A4pW3nYvKZeP7559FMJkInTcITYOSrr77qsC2+n/uyYMECGhu/uzXdG2+8wb59+/Tp7OxsSktLj7itFUU5e52Uc+wislpEhojIYBF5/mS0eSQ2m43y8vIO8+699149x8VgMJCamtphhGX//v157rnn9OmgoCBeeeUVPWOlublZz5KBttGlL/35JXoF9aK6pRpoCx87PNQrPz+f558/9DItPTC02njggQf0x4ODg1mxYoU+LSIkJiZ2uH1dVPuFNCFtfY+Pj+eZZ57RH4+MjOSvf/0rVS1tfQt0B3LjjTfqj7e2tlJcXNxhW7zxxhsdAs5ycnL08DGA6upqfv/73+vTfr+fe++9V0X7Kko3c1ZFCiQkJJCQkNBh3r333tthetGiRfpRL7QdXSclJenTs2fPJijou8sTj9Tmxx9/zNz/zKW6pRqv18vPf/5zDId9GxoUFERVVRUulwtLeF96WQ4wa9YsPB4PJpMJo9HILbfcoi/fHkVwRIeK/VNPPdWhH3feeScJCQl8m/4tgcZARiWO6rBjCA8P56677urQ1EsvvcSIEd/dFCQiIoKamhq9X/Hx8ZhMJhobG4mIiCApKYl//vOfZ9z9UhVFOTFaVxytjRs3Tr5/SuVM80zaM6wpXsPmWzb/oPD5fL7vclbWPQ1bXoc/1B7x6pgf9XSPQ7+bjrrYb776DSW2Ev593b+Po/dt/H5/hx2SoihnN03TdorIuGMtp/7X/4ihkUOxt9r10zGH6xCeFRHfdlXMMQYa/VQ51hyGRg39Sc9VRV1Rzk3qf/6PGBY1DIC8hryjLxjTthw1+46+3OGaDl0NGhh+1MWsLivVLdUMjzqrExoURTnNVGH/EUMih2DQDGQdzDr6gr1Htv2uyux847s+aPudcutRF8upb7tccXhPVdgVRek8Vdh/RLApmPOizmNHzTG+CwgMg6jBULW7841v/Vvb7/H/ddTFdtbsxKgZVWFXFOW4qMJ+FON6jWNv3d5jj0CNnwDFm46Zra5zH/rCtOfgoy6WXp3OiJ4j9MFJiqIonaEK+1GM6z2OVn8re+r2HH3BwVPA1QiVnThqd/5wlOqRtHhayDqYxfg+4zu1vKIoSrtuV9j9fj9+f8fwrtbWI+Shd8KYXmMwaAa2Vm09+oIJU9oSHvNWH7vR9c+2/b7w1x1mi4geewCwq2YXXvGS2jv1eLutKMo57qwv7B6Pp0OWy5o1a3j66adpbm4GIDc3lzlz5nQYSr9jxw58vmOfNgk3hzMqehQbyjbo89rjCzoI6QkJl8KepeD/8URIEYEd7wJQknBrh9GsW7duZc6cOXoOzcbyjRj9Rnq6enZ4vsfjOWa/AaxWa4dpp7oxh6KcM866wl5eXt4hhOv3v/89t9xyiz4s/uWXX+bZZ5/lpZdeQkRYtGgR//znP1mwYAEOh4MDBw4wdepUnnzySb2NtLQ00tLS8Pv9bN++nZaWlu9WWNB2yWOlvRJo23H87ne/04+us7Ky+Mtf/kLrebOgqRRv/jocDscPhul/+eWXvPXCw/r0Ewv/xPXXX69HD/zv//4vn332GY8//jgOh4Mv9n9Bw+4G7pt3H83Nzfj9fu677z4+/PBDvQ2Px6PvaBYvXszu3d+dClq+fDlPPvmk/mllz549zJ8/H5vNBkBjYyNr1qzRQ8cURelGROS0/4wdO1aOl8vlkueff17CwsLk97//vYiIfPzxxxITEyN333231NTUSGZmpmiaJnfffbc0NjaK3W6X8PBwueyyy6SkpET8fr9MmTJFxo4dKx9++KE0NzfLU089Jb1795b58+eLiMiqVaskODhYpkyZIi0tLbJh7wZJXpwsk349SXJzc8XhcEhUVJSMGDFCdu3aJSIiP//5z2VAv95if6a/eN+ZLo899pgYjUaZO3eu+Hw+efnllyUhIUHkj+EifwyXAytfEbPZLPfee69UVlaK1WoVi8UiM2bMkMrKSsmuy5bkxcmSMidFNm/eLF6vV+666y4ZOnSoLFy4ULxer7z55psSHh4ul156qYiI7N+/XywWi1x22WWydetW/bWPGjVKMjMzRURk4sSJ0rdvX/nXv/4lIiJPPfWUhIWFycMPPyxer/e43xNFUU4vYId0osaeNYW9ncvlktLSUvH5fJKWliYej0d/7L//+79lw4YN+vT//d//yd/+9jfx+/0iIlJQUCCbNm3Spw93eGH797//LQsWLNCnxy4aKwMeHiAffvihiIg89NBDAsg111wjLS0tkpOTI4GBgfLZI5e1Fe99K2T9+vUd11W8WS/s7733nuTn5+vtv/POOx36+fjKxyX5/WSpba4VERGHwyHNzc0/6HNNTY1s3rxZn37uueekV69eUldXJyIi999/vwByyy23iMvlkn/9618CyGWXXSYNDQ3i8/lk1qxZ8s4773Ry6yuK0pW6bWE/mu8fdbpcrp/cls/n0/9+Ys0Tcv7i86XeUS8iIrm5uXL//fdLeXm5vsymTZuk1dkismiiyJ8Hi1iLv2uspV4v6lL07Q/W5XA4Okxft/w6uX317cfdZ7fbLQcOHNCn9+3bJ4888ojU1rbtILxer7zwwgsd+t3c3HzEHZ2iKGeezhZ2FQLWCXnWPG5YcQN/uOAP3DzsZuAoAVt1efDu5WAKhsuehrpc2PRK22Mjrocb3+/Uup644AluGXbLUZftDBUEpijdhwoBO4mGRA4hMSKRVUWr9Hk/WixjhsIdq9pyYJbd/V1RH3njMYs6wKrCVQRoAfxs4M9ORtdVUVeUc9BZlcfeVTRN46qEq/jrrr9S0VxBv9B+R39C75Fw31ao3AWVGTD8Ogg99n1efX4fq4pWcVG/i4i0RJ6k3iuKcq5Rh3OdNGPQDAA+P9DJ27kaDNB/HIyf16miDpBek06to5arBl/1U7upKIqiCntn9Qvtx8S+E/ls/2d4/d5jP+En+GfePwk3h3Np/0tPSfuKopwbVGE/DjcNuYkaRw3fln977IWPU62jlq9Kv2Jm4kwsAZaT3r6iKOcOVdiPw+S4ycQGxbJ0/9KT3vZn+Z/hFS83Db3ppLetKMq5pVsU9j179ujZKH6/n9WrV1NYWKgP61+9ejVFRUU0NLQlK7a0tLBhw4Yfbe/HGDUjs4bMYnPFZoqaio77+SLSIWvm888/x+Px4PF7+DTvU4aah2Ivs+v9TEtLo6amBrvdrj+nqqrqBzkwiqIohzvrCnttbS3vv/8+//rXvwD45JNPmDBhAk8//TQiwlNPPcXcuXNJSUlh7969/P3vf2fOnDmMGTOGtWvXUl9fz7Rp0/j1r3/NK6+0XYqYk5PD/fffz/Lly/WdgYjwzjvv8Pbbb1NSUgK05a/sem8XAVoA7+99n9zcXN577z2ys7N/kCjp8/morq4mOzsbgMzMTC6//HLefvttABYtWsRtt91GQkIC7299n1pnLVvf3MqECRPYtGkTubm5XH311UycOJEXXngBEeH9999n+PDhbNu2DWjLisnOzuaPf/wjW7Zs0XcAS5cu5cEHH2TLli34/X4yMjJ45JFH+Oabb/B4PDQ1NVFcXIzdbv9Bpo2iKN1AZ0Yxneyf4x15arfb5U9/+pNccMEFommaADJ37lxZsGCBAALI6NGj5YMPPtCnp0+fLt9++61YLBYB5Pzzz5f09HQ577zz9GUeeOABmTJlij49YsQICQwMlICAAAkMDJTzzz9fkpOTBZAhQ4bIb37zG5k9e7b0ub2PjHhnhMx7cJ789re/FUDCw8Nl8uTJcvXVV0uvXr3EYDAIIHPmzJG77rpL7/ewYcNk8eLF+jovmHCBTPm/KZK4MLFt+oILZM+ePRIfHy+ABAcHy6effipXXHGF/pyxY8dKcnKymEwmAWTixIkyaNAgAWTAgAEya9YsueaaawSQfv36yW9/+1t59NFHBZAePXrIjTfeKLfffrsAYjabpU+fPvLggw+qEaiKcoaju408tVqtfPHFF6xcuZLVq1eTmppKVFQUvXv3pnfv3rS0tPD6669z4YUXcs011zBp0iRmzpxJREQEN9xwA6mpqbz88ssEBwczbNgwBg8ejMViwWazkZGRwa5du7jyyiu5+eab+cUvfkFGRga9evVix44dTJw4kbKyMqZMmcIHH3zAVbdehf9OP+Z9Zjb8cYOeJmk0Gvn73/9OWFgYjz/+OFlZWVx55ZVMnDiR+vp66uvrKSsro6CggAkTJjBx4kTcg9x82PAh2gqNW8bcwowZM5g7dy4mk4lp06ZxwQUXkJ6ejtPp1N+0mJgYJk2axF//+leWL1/OzTffzF/+8heuuOIK9u3bR0JCAl988QXXX3892dnZXHTRRaxevZp77rmHjz76iJ49e/LVV1+Rn5/PnXfeid1uZ/bs2Xz00Uen6B1XFOVk6OzI07PiiP37WltbpbCwsMO8jRs3SmNjoz69ZcsW2b9/vz7dmaPR9qwZt9stTz31lKxevVpERLKysmTatGly9913S3V1tRQUFMj4J8dL8rvJ8uZHb4rf75cHHnhAHnnkEVm7dq3e1ocffii7d+/u0IfKykq9L62+Vpn2j2nysyU/E5+/LZumtLRUGhoaOr0tDhw4IOvWrRMRkbq6Ohk7dqwsWbJEvF6v7N+/X372s5/JNddcIytWrBCn0ykTJkyQhQsXyhtvvCEiInl5eXLVVVdJZWVlp9epKErXoLsdsXeFw3NWGhoaiIz8bjRoflU+t66/lSlxU/jz5D8jIthsNnr06NHp9v+R8w/+tP1PvD71dS6Nu/Sk9NlmsxEeHq5PNzY20qNHDzRNO+LrAHC73QQGBp6U9SuKcuqorJiT4PCcle8Xw6Q+Sdw+/Ha+KP6C9Op0NE07rqLe4Gpg0e5FTOgzgcn9J5+0Ph9e1AEiIiL0og4/fB2AKuqK0s2own4C5p0/j/6h/Xl6y9M4vZ2/9ZyI8OzWZ3F4HSxIXdCh8CqKopwoVdhPQFBAEM9MfIZSeyl/Tv9zp5/3+YHPWVuylvkp80mMTDyFPVQU5VykCvsJGt9nPL8a+Ss+3f8pS/OOPSJ1d+1uFqYtZGyvsdwx4o5T30FFUc45Krb3JJifMp9cay7PbX0Ok8HEzKSZR1wusy6T+V/Np3dIb1659BWMBuNp7qmiKOeCEzpi1zTtJU3TcjVN26Np2jJN0yJOVsfOJkaDkVcufYUL+1zIU1ue4tm0Z2lwNeiPt/pa+SD7A+aumUu4OZy/Xf43lbeuKMopc0KXO2qadgXwlYh4NU17EUBEfn+s552uyx1FpMMXkyKCz+cjIODUfFDx+Dy8uutVPtz3ISaDifNjzifQGEhWfRZN7iYu6X8Jz056lihL1FHb8fv9eL1ezGbzKemnoihnp85e7nhCFU5E/nPY5FbghhNprzMaGhrIzc1lwoQJAGzcuBGLxcKIESNIS0ujurqaa665hpUrV/LnP/+ZefPmccUVV5Cbm8tzzz3H9ddfT48ePZg7dy7r16/H7/czYsQIysrKuOiii9pfF8uWLSMsLIyEhATi4uJYs2YNhYWFjBw5kuTkZBwOB83NzfTs2ZOePXtiNpsxGU08kvoI1yddzz/z/smuyl04TA4m95/M2KCxWGoselH/4osvGDx4MA0NDbz99ttMnjyZqVOnsmnTJhYuXMicOXMYNmwYo0ePZtGiRURERDBmzBgGDhzIsGHDaGlpwWQy8e233zJ69GjCwsIwmUwsX76cqqoqRowYwfDhwykpKSEnJ4fExEQSExPp2bOnugpHUbq7zoxi6swPsAKY05llj3fkaW5urrz00ktyySWXiNFolBtuuEFee+01ufzyywWQUaNG6ZkngMTHx0tycrI8+OCDYrFYJD4+XgYOHCiPPfaYJCYmSnR0tERGRkqfPn1k2LBheoZLbGysRERESFhYmJx33nmSlJQkgGiaJqmpqTJr1iw9ryUhIaFDfktoaKjMmjVLZs6cKcOHDxeTySS33367bN68WebMmSNGo1EmTZokU6dOlaioKNE0TQYNGiSxsbFy7bXXislkkvj4eBk6dKg899xz0rdvX+nXr58EBwfL1VdfLampqQJIcnKyhISESFhYmAQHB0tSUpKEhobquS8jR46UK6+8Uu/XkCFD5I477tCnIyIi5OKLL5Y+ffpIVFSUBAcHy/33339c74eiKF2DTo487UzBXgdkHeHn2sOWeQJYxqFTOz/Szn8BO4Ad8fHxnX4h9fX18sorr8jUqVMlICBAABk0aJAEBgbqxSolJUXuvPPODmFeb775phiNRgEkKipKHn74Yf35gEyZMkUv3IBcfPHFMnPmTImOjhZATCaTRERESM+ePfUwrnvuuUduueUWASQwMFDuu+8++cMf/qCvJykpSS655BIJDg4WQEJCQvT22/s1btw4fToxMVFef/11PTCsT58+smjRIgkKCtKXmTx5coc2pk+fLrfddptERUUJIP3795f+/fvrr81oNMq0adPkoosuEkAsFovcf//98tRTT3VoY/78+RIWFqbvECZNmiSvvvrqif/LUxTllOlsYT/hSAFN0+4A7gamiYijM8/5qefYGxsbWbVqFQcOHOCqq65qyzL3eFi6dCk2m43hw4eTlJREeXk5a9euJTk5mfPOO4/g4GCcTicREREEBQURFBREdHQ0Q4cO5eDBg2zdupXGxkbmzJmDy+Xitddeo1+/fowePZodO3bw7bffMmfOHD799FMWL17MzJkzue2221i6dCmffPIJDzzwAK2trUyYMIF3332X2NhYEhMTSUlJYdq0aeTm5tLU1MSHH35IYmIiffv2JTY2lj179rB27VpGjRpFcnIyJpOJtLQ0Bg4cSFxcHHFxcQwYMIDAwEBqa2upqanB5XIxffp0XC4Xy5Yto6amhgceeACv18vChQtJTk6moaGBf/zjHwwdOpSbb76Zjz/+mE8++YR58+YxaNAgXC4Xr776KldffTVNTU288MIL7Ny5k6amJubNm3fc74uiKKdHZ8+xn+iXp9OBl4HJIlLX2eedDVkxctgXryKC3+/HaDTS2NhIeHg4IoLRaKSwsBCz2UyfPn0wGo0/eO7p5vP5OvSjvd/FxcX6Ds1oNOJ2u7FarfTp06dDJo6iKGeu01XYC4BAoP7QrK0ics+xnnc2FHZFUZQzzem6KkaNh1cURTnDqM/fiqIo3Ywq7IqiKN2MKuyKoijdjCrsiqIo3Ywq7IqiKN3MWVfYvV5vh+nW1tYffbyoqIhnn32WvXv3AlBWVsazzz7LJ5980uH5RUVF+rTP58NqteJwOPD7/QBs3bqV7du3c+DAARobG+nMJaLfX+Zo/WxtbWXNmjXU1tYCkJ+fz6OPPsqSJUv0Pm3cuJFly5Z1aKO9f+3r2759O5mZmZSWltLc3ExpaSmlpaVYrVY8Hs8x+6woSvdwVuSxFxUVsWLFClasWMH06dO57777KC8vZ+HChUyaNIn+/fuTlpbGRx99RG1tLU888QSrV68mPT2dMWPGYDabefjhh9mwYQOxsbE888wzPPfccyxdupSsrCzi4uKYPn06xcXFlJaW4vf7KSsrw+l0YjKZGDZsGIC+g4iKiqJ3797U1NQAbUX10UcfJSwsjN27d5OZmcm1117Lo48+yo4dO3j11VcZPnw4V199Nfn5+fztb38jMDCQWbNmsXr1alasWEHPnj2566672LBhA+np6SQmJpKQkMB9993HkiVLcDgczJ49m4KCAjZs2MCePXtwOp3Exsbidrtxu9307NkTp9PJ/v37AejVqxd9+vRh9+7dAFgsFmbMmIHBYKCmpoba2lrmzp3LggULuuBdVRTlVDnhSIGforMDlCorK/nd737Hxx9/fNTlRo4cSV1dHdXV1QQEBDB58mRaW1v59ttvMRgMnH/++RgMBnbt2gW0FTiPx4PP59PbMBqNHaYHDhxIY2MjjY2NGAwGJkyYgN/vJy0tDaPRyOjRowkKCuLbb78F0Eej2u12ADRNw2QydThSj4mJobm5GafTiaZpjB8/Hq/Xy86dOzEajYwbN46wsDDWrVsHQO/evTEYDFRWVup91DStw9G+2WzG5/PpfR81ahRer5fs7Gy9zcjISL788ks0TSMuLo7g4GByc3MBCA4OZsyYMaSmppKamsr48eMZPHjwMd8bRVFOv9MyQOlU69u3Lx999BEvvPACK1euZNmyZRiNRkJCQqivr6e+vp7Q0FDy8/NpaGi7scWQIUOoqqpi3759APTo0YPg4GCam5tJSkrC4XDw4osv0qdPHzZu3MjGjRuZMWMGjzzyCPn5+bzwwguMGTOG0aNHk5mZyfvvv4/b7Wb27NmsWrWKgIAAhgwZwjXXXMPXX3+NxWIhLi6Oxx57jPz8fJYsWUJxcTETJ05k2rRp7N69m9zcXFpaWnA6nVgsFoKCgoiLi6O5uZns7Gyg7VOA1Wpl27ZtBAYGEhgYyI033khQUBAHDhygsLCQm266iUceeYR169axePFiEhMTufvuuykvL+e1114jIiKCadOmsW7dOmpra2lqauKyyy5jy5YtBAYGMnToUObNm8eOHTsoLS3FYDDw8MMPk5ycTHp6Om+//TavvfYaaWlpXfaeK4py4s7oI/Yj8Xq9+o0yfD4f+/fvJywsjPDwcEJCQti7dy8BAQFERkYSGRlJUFDQMXNbvp+V0tra2uEmF4c/brVaWbZsGdOmTWPgwIEUFhby3nvvMWLECGbPng1AaWkp5eXlTJw4UW+jfTtrmoaIsG3bNoxGI9HR0fTs2ROj0YjJZMJkMnU6Z8bj8WAymY64baDtFFZsbCwhISEUFRWxePFixowZw7XXXovT6WTFihU4HA7uuOOOTq1PUZSudVqyYn4qlRWjKIpy/Dpb2M+6q2IURVGUo1OFXVEUpZtRhV1RFKWbUYVdURSlm1GFXVEUpZtRhV1RFKWbOScKe35+vj56E2D//v1kZGR0YY+OzO/36yNVRYRdu3Zx+GWhfr+f6urqruqeoihnibPiOvaKigpWrlxJfHw8M2bMAODAgQPY7XZSUlL0ZdLS0qipqWH37t1cfPHFfP3112zevJmqqioeeughcnNzyczMpLKykvnz5xMQEEB5eTlFRUXY7XZSU1PJzs7Ws1fcbjcBAQFUV1fT2tqK0WgkLCyM1NRUvF4vNpsNu93Oyy+/zIABA0hPTyc9PZ2xY8dy44036gORWlpamDZtGgA2m43y8nKioqKoqKjA5XKxdu1aMjMz2bBhA3PnzqW8vJzNmzfjdru59957aWpqIj8/n61btzJo0CBmzZrFxo0bCQoKora2luDgYA4ePEhFRQVerxdN0wgNDSU0NBSXy4XP58Pv9/Pggw9iNpspLi6mqKiI6667jltvvfXkv8GKopwSZ/0ApcLCQj744ANWrlypZ7xceumlmM1mcnNzKSsro2/fvni9Xj29sH2kaV1dHUajkUGDBtG/f3+2bduG2+3GZDIxdOhQPaURIDQ0FKfTqWetBAQEYDAY9CPnwMBAUlJSqK6upqSkBE3TGDp0KFarVU9jDAsL0zNiDr0+AIqLizl48CDDhw8nODiYiooKampqOiQ/Go1G4uLiiI6OJicnB7/fT3h4OKmpqWzbto26ujpEhOjoaKxWa4dER5PJpKc2WiwW+vbtS319PU1NTWiaxujRo2lqauLAgQNAWyhYU1MTLpcLgJSUFEaNGsWIESP0n/j4+E6PfFUU5fQ667NiBg4cyM9//nOg7bRERkYGVquV7OxsvQgHBwfrSYUA0dHRnH/++axevRqn00llZSWapmGz2QBwu91ER0cTEhJCTk4OdXV13HnnnYwcOZLt27ezcuVKfvazn9G3b1+Ki4vZtGkTPp+PXbt24fV6CQwMxGKx0Lt3byIiImhqaiIgIIDLL7+clpYWdu3aRV1dHdnZ2WiahtPpBKC6uhqHw6EX1KSkJEaPHs2KFStwOp3Y7XaSkpLwer24XC5czDXafQAAFHdJREFULhdZWVkdIoKvv/56YmJi2L17N9988w233XYbqamp5OXl8e9//5vo6GgMBgM+nw+TyYTVaqWurg6TyaT3e9KkSXg8HjZv3kxDQwMWi4WWlhbS09NZunQp+/btw2AwkJKSwsaNG1WBV5Sz1Bl7xP595eXl1NbWEhMTQ2lpKYWFhaxcuZLevXvj9/vx+XwUFhYSExOj5604nU5uvfVWjEYjdXV11NXVMWnSJC688EJEhH379uFwOEhNTQXasmeqq6vp16+fvl6Xy0VgYCBVVVVERkaSkZHB119/zX/+8x9+9atfERERwZo1a1i+fDnXXHMNTz75JBs3biQnJ4eWlhauvfZaVq5cSVJSEna7HbvdzrZt2wgKCsJsNmMwGKivr2fcuHGYzWa9sN90002MHTuWkpISsrOzCQ0NZcqUKQA4HA6KiooYMWKE3s+mpiZ69OihT9fX15ORkcHWrVu54oorsFqtrF69ms8//5yZM2fyi1/8gjVr1vD111+jaRpffvklfr+fkpISiouL9XUpinLmOOtPxZxtRITm5mbCwsK6uitHJSI4nU6Cg4M7zFNH54py5lNZMaeZpmlnfFGHtn4eXtTb5ymK0n2owq4oitLNqMKuKIrSzajCriiK0s2owq4oitLNqMKuKIrSzZxThf37l3Z6vd4u6snxaR/opCiK0hln7MjTw9XW1tLc3ExCQoI+7/s3bm4nItTU1LB//3569+5NTk4OGzZs4JtvvuHqq68mNTWVr776inXr1tG3b19WrFjB119/zerVq9mxYwdTp06loaGB+vp6ysvLiY2NxeVy4XQ6cbvd3HHHHTgcDmpqaqiuruahhx4iOTmZ5uZmtm/fTkREBGPGjNH70tDQQFRU1FFfn8/nIzc3l+3bt5Oens748eMJCgpi/fr1rFu3jpSUFF588UU2b97MypUrKS0tZeHChZSVlVFSUsLWrVuJjo7G6XTicDhoamoiNTUVt9uNzWajpaWFl156iaCgIPLy8sjLy2P06NFccsklJ/eNUhTljHBGDlASEbKyslixYgUrV65k69atvPjiiyQkJFBQUMCyZcuYMmUKERERVFZWkpaWhsvlQkQoKCjA7XZjNBoRERISEvD7/dTW1uJwOIiNjcXn83Hw4EEsFgsOh0Nfb0REBBaLRU9QDAkJYdSoUWRkZOB0OgkJCSE2NpaSkhL8fj8BAQEkJCTQ3NxMdXU1fr+fBQsW0L9/fzIzM1m/fj2zZ89m7Nix2Gw2li1bRmhoKJqmceDAAQoLC7HZbGiahtlsJjg4GLvdjsvlYujQoXg8HsrKytA0jdbWVjRNw+v1EhkZSXNzs54TAzBmzBiysrJobW0lPDycxMREcnNzcTgcmEwmgoODaWpq0pefN28eo0aNIjExkaSkJOLj44+4o1QU5cxxVo883bt3L2+++SYrV66krKwMgOTkZCoqKmhoaNCXM5vN+Hw+fD4fAQEB+P1+IiIisFqtxMTE0NDQQEBAAC6XSx+Ec/jrHThwICaTifr6eqxWKwMHDsRoNNLY2EhDQwN+vx+j0YjJZMLlchEQEEBiYqIeX2AwGEhMTNRzWfx+f4dgrh8TEBBAUFAQdrudyMhIbDYbYWFhNDY2YrFYaG1tRUT0voaEhGA2m7HZbPh8PhISEggJCaG+vp7a2lpCQkLw+XwdwsxiY2P1ZMqAgABGjhyJ3W6nqKgIj8ejt+F2u/Usm0GDBpGYmKgX+3nz5mGxWH7am6woykl3WkPANE17GPgLECMiB0+0vZEjR7Jo0SLeeOMN9uzZw0cffaQ/lp+fT25uLiEhIezatUtPOxw4cCC1tbVYrVagLbv8hhtuwGq1UlpaSlVVFRs2bCA+Pp5vvvmGr776iuuuu06P0923bx8ej4dRo0YBbadHampq8Pv9lJWVUVhYyMaNG4mNjWX//v20tLRQV1dHYmIizc3NbN68mZ49ezJx4kRiYmLYsmUL+fn5+P1+hg4dSk1NDXV1dcTHx9PY2KinS5pMJgYNGqQnRYoIH330Ec3NzezevZvMzEwee+wxZsyYgcPhYNWqVURGRnLZZZcBbbkxlZWVJCYm6s/fvXs3JSUlZGVlkZGRQVpamh5cVlJSQu/evRk1ahTh4eFs3LgRt9vN9OnTefzxxykoKKCgoIBt27Zx3333nehbqShKFzjhI3ZN0+KAd4BhwNjOFPaTkRXTfkTb3NyM3W6noaGBvn374vF4cDgctLS0EBcXpwdjiQgejwez2XxC6z18/aWlpRiNRvr374/T6WTz5s20trZy5ZVX6svZ7XY9asDr9VJeXk5gYCCtra04nU5cLheDBw8mLCwMj8dDY2MjJpOJiIiIk9LPw/uraRoul4utW7fi9/uZOnUq0BawduDAASZPnnxS16koysl12k7FaJr2KfAs8G9g3Okq7IqiKOea0xICpmnatUCFiGR2Ytn/0jRth6ZpO+rq6k5ktYqiKMpRHPMcu6Zp64DeR3joCeBx4IrOrEhE3gLegrYj9uPoo6IoinIcjlnYReSyI83XNG0kMAjIPHTFSX9gl6Zp40VE3XFZURSli/zkq2JEZC8Q2z6taVoxnTzHriiKopw651SkgKIoyrngpA01FJGBJ6stRVEU5ac7K8aQn+g9OVtaWti5cyfbt28nPj6eGTNmkJ6eTlpaGq2trdx3331kZ2djNpvZt28fTqeT3NxcUlNTaWhowGq10trayoIFC6ivr6e0tJSSkhKmT59OXFwc0HaNenNz8wlff97Y2MjevXsJCwsjLi6OtLQ0tmzZgqZpPP/881RUVJCdnc3OnTtJSUlhy5YtDBkyBKvVysGDB6mqquLGG2+ksbGR2tpaamtruffee+nbty9ut5u8vDzCwsIYNGjQCfVTUZQz1xkZKQCwf/9+Vq5cycqVK3n11Vc5//zzERHWr19Pv379OO+88wBobm5m3759OBwOioqK9FGTxcXFVFVVERERQXV1NbGxsYSEhGCz2airqyM8PByTyaQHZwUFBXVIURw+fDgtLS2UlJQA6CFbLS0tAISFhfHLX/5SH6a/a9cuPv30U8aOHYvD4WDJkiVcdNFFTJw4EYC6ujrKy8uJjIzEarVSW1vL1q1bKS8vp6CgQA8Cq6+vJywsDLPZTH19PXFxcQQGBmKz2Th48KAeGdAuPj6epqYmPQcmLi4Og8Gg9zssLIz4+HjsdjsVFRX4/X4WL17M6NGjGTBgAOHh4SfhHVUU5XQ4a7Ni0tLS+M1vfsPhj5vNZvx+Pz6fDxHBYDDoUQJHYjKZiI6OxuVy6UP3LRaLHhQGYDAYOuSxHEtwcDDh4eHYbDYcDgdmsxmLxYLdbtfbMBqNHQqvyWQC2uIJ2vtrMLR9reH3+zEYDAQFBeH3+/U8m169emG322lubgbacmWOFi98eHvtfQgICMDn8+H1egkKCiI2Npa6ujocDgeaphEVFUVra6ueVTNgwAAGDBjAwIED9b/bp6OiotTNrhXlDHFas2JOpgkTJrB582Y2bNjAihUrWL58OQMGDGD37t16sbv44ospLCzUA8ISEhIwGAwUFBQAbUW4sbFRPwIPCQnhzjvvxGazUVhYSEZGBkuWLGHo0KHYbDY+++wzrrjiCi666CJEhIyMDEpKSjCZTFRVVZGTk8POnTv1hMiIiAhsNhvBwcGEhIRw8OBBRITY2Fi8Xi9NTU243W48Hg+apumFv1+/fvh8Pj09MioqisDAQCoqKvR+R0VFYTabcblceL1eXn/9dQYMGEBOTg7r16/ngQce4NJLL8XhcLBx40Y8Hg+JiYm0tLRQWFjIjh07sNlslJSUYLPZyMvLo6SkBIvFgtlsRtM0YmNjMZvNHDx4kOrqapqamqivr8fj8WC1Wlm+fDklJSWUl5ezf//+DnHJiqKc+c64I/bvExFcLhcWi4Xy8nK2bdtGRkYGffr0oba2lurqampqarjwwguxWq3U19cD8Je//IW6ujoKCgo4cOAAM2fO1M+Htx+t9uzZ8ye/htraWnbt2sXOnTsZPHgw5513Hlu2bGHLli0YjUb+9Kc/sWXLFsrLy8nKyiI+Pp49e/YwbNgw/bx9S0sLd955J1arlcrKSqqrq3n00Ufp168fbrebrKwsIiIiGDx4cIftcbxH0DabjdzcXIKDgxER0tLSSEtLIyQkhIULF7Jjxw7S09MpLCzk3Xff1Z/n9XoxGAz6pwJFUbrWWXsqRlEURTmy05IVoyiKopx5VGFXFEXpZlRhVxRF6WZUYVcURelmVGFXFEXpZlRhVxRF6WbOuAFKp5KIUFlZid1uZ9iwYYgIhYWFFBcXM23aND1CoKGhgSFDhlBdXU1VVRX19fXceOONBAQE0NraSnFxMb179z7lw/F9Ph9GoxGPx8O+ffuoqqpi+vTpAHg8HrKyshg0aBBVVVV6P6+//nrsdjvl5eWUl5czYcKEDvd99Xq9+ohYRVG6pzP2Ovbi4mJWrFjBddddpw8s8vl8OJ1OQkNDj/gcEaG2tpby8nKKiorYuXMnu3fvJigoiKamJnbu3IndbichIYGAgAAKCwvxeDyEhobqN8YGCAoKwuPx6EP5Bw0aREREBFarlbKyMnr37s3q1atxu92kpaWxadMmXnzxRX2EZvuI2PZ+t/ftSAOLvF4v+fn5ZGRkUFFRoefO5OTkEB0dTWRkJHv27EHTNMLCwggPD6empgaHwwHQIV6hV69eNDc363k2ffv21Ufc5uXlkZeXx1dffaVGkirKWeqsHKCUnp7OsmXLWLFiBVlZWZjNZm677TZaW1vZv38/ubm5TJgwAb/fj81mo7S0VD+KttlsuFwu4Lt8FU3TMBgMBAYG4nQ69aH9ZrOZ1tbWDutuL7oi8oPMF03TCA4O1gtmexZLe3vt+StGoxG3201TUxMXXnghFosFh8NBaWkp0dHRaJqGzWajvr6e1tZWvF5vh8wbi8WC2+3WYwgCAgLweDz64yaTSc/MORKj0YjJZNK3g9lsxmAw6NPtIiIi6N+/PwkJCcTFxdGvXz/69+/f4XdISEgn3klFUU6nszIrZvDgwSQnJ1NUVERZWRkOh4N9+/axa9cuvcClpaUREBCAzWbD5/MRGBiI2+3GaDQCEBgYqBdtEdHDsMxms77cpZdeSo8ePaivrycnJ4dZs2YRGhpKS0sLe/fuJTg4mICAAOrr6ykrK6OxsbHDjsDr9RIWFobf76elpQURwW63d1hm27ZtGAwGvQhXV1d32HkA+o7H7/djNBr1AtwedDZo0CD9tVZWVjJr1ixiYmLweDxkZmYybNgw+vbtS01NDXl5eVitVjweDw0NDXqfTSaTHoBmMBiIiYnBYDCQn59PXl4esbGxhIWF6Tslq9WK1WolIiJCL/SvvPKKnqapKMqZ74wq7FFRUdx6663ceuuteDwevvnmG4xGI9XV1ezZs4dt27bpp1u8Xq9+rryhoYGqqip8Ph9JSUnMmTOHiooKcnNzaWxsZM2aNURGRlJeXs7atWuZOnUqAwYMANqKqNvtxmKxHLN/Pp+Puro6du7cSVVVFRUVFWRmZpKenk5MTAyjRo1i06ZNHDhwgPDwcEaNGkVRURG1tbUYjUaCgoL0LJshQ4aQkJBAdXU1JSUlhIaGsm3bNiorK9m+fTvp6en84Q9/0E+bHDx4ELfbTb9+/Tq9Pdu/DygoKCA3N5dt27ZhNBoJDw9n586d7Nmzh5CQEG699VYyMzPJzMzUY42bmpqoqKigvLycmJiYn/BuKorSVc6oUzHHq70IDR48GBHRw7TOO+88AgK+22ed6I06OuPwdbjdbkpLS0lKStIfdzgcBAcH4/F49PCylJQU/ZOGzWbDZDIRFBR0Svt5OI/HQ1VVFfHx8T/op6IoZ56z8hy7oiiK8uNUCJiiKMo5ShV2RVGUbkYVdkVRlG5GFXZFUZRuRhV2RVGUbkYVdkVRlG6mSy531DStDig57SvuGtHAwa7uxBlIbZcjU9vlyNR2aTNARI45YrBLCvu5RNO0HZ257vRco7bLkantcmRquxwfdSpGURSlm1GFXVEUpZtRhf3Ue6urO3CGUtvlyNR2OTK1XY6DOseuKIrSzagjdkVRlG5GFfZTSNO06Zqm5WmaVqBp2qNd3Z+uomnae5qm1WqalnXYvChN09ZqmpZ/6HdkV/bxdNM0LU7TtK81TdunaVq2pmm/PTT/XN8uFk3TtmualnlouzxzaP4gTdO2Hfq/9Immaeau7uuZTBX2U0TTNCPwBjADGA7M1jRteNf2qsssBqZ/b96jwHoRSQLWH5o+l3iBh0VkOHAh8OtD/z7O9e3iBqaKyCggBZiuadqFwIvAKyKSCDQAc7uwj2c8VdhPnfFAgYgUikgrsAS4tov71CVEZCNg/d7sa4EPDv39AXDdae1UFxORKhHZdehvO5AD9ENtFxGR5kOTpkM/AkwFPj00/5zbLsdLFfZTpx9Qdth0+aF5SpteIlJ16O9qoFdXdqYraZo2EBgNbENtFzRNM2qathuoBdYCB4BGEfEeWkT9XzoGVdiVLidtl2adk5dnaZoWCnwGPCAitsMfO1e3i4j4RCQF6E/bJ99hXdyls44q7KdOBRB32HT/Q/OUNjWapvUBOPS7tov7c9ppmmairaj/Q0T+dWj2Ob9d2olII/A1MAGI0DSt/UbG6v/SMajCfuqkA0mHvs03A7cAn3dxn84knwO/PPT3L4F/d2FfTjut7c7n7wI5IvLyYQ+d69slRtO0iEN/BwGX0/b9w9fADYcWO+e2y/FSA5ROIU3TrgReBYzAeyLyfBd3qUtomvYxcCltCX01wB+B5cBSIJ62pM+bROT7X7B2W5qmXQR8C+wF/IdmP07befZzebucT9uXo0baDjyXishCTdMSaLsAIQrIAOaIiLvrenpmU4VdURSlm1GnYhRFUboZVdgVRVG6GVXYFUVRuhlV2BVFUboZVdgVRVG6GVXYFUVRuhlV2BVFUboZVdgVRVG6mf8PNKcJk/iSqawAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Plot a few solutions with different initial conditions\n", | |
"quiver(x, y, *nvec(u, v), pivot='mid')\n", | |
"# Force a finer timestep\n", | |
"t_min, t_max = 0, 10\n", | |
"tt = arange(t_min, t_max, 0.002)\n", | |
"# Starting at the bottom (theta = 0) with different velocities. \"Unbounded\" perodic orbits for high velocities\n", | |
"for y0 in [(0, 0.1), (0, 1), (0, 1.9), (0, 2), (0, 2.1), (0, 4)]:\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt, method='Radau')\n", | |
" plot(*solv.y)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Starting at rest (theta_dot = 0), \"bounded\" periodic orbits except at critical points.\n", | |
"tt = arange(t_min, t_max, 0.00001)\n", | |
"for y0 in [(0.0001, 0), (1, 0), (pi-0.3, 0), (pi-0.01, 0), (pi-0.0001, 0)]:\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt)\n", | |
" plot(*solv.y)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x11cd2a390>" | |
] | |
}, | |
"execution_count": 24, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Orbits near the critical points\n", | |
"tt = arange(t_min, t_max, 0.00001)\n", | |
"for eps in [-0.2, -0.1, -0.01, -0.001, 0, 0.001, 0.1, 0.2]:\n", | |
" y0 = (-2, eps + np.sqrt(2 + 2 * np.cos(-2)))\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt, method='Radau')\n", | |
" plot(*solv.y, label=eps)\n", | |
"legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 25, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"/Users/dai/.pyenv/versions/3.6.5/envs/lab/lib/python3.6/site-packages/matplotlib/figure.py:98: MatplotlibDeprecationWarning: \n", | |
"Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n", | |
" \"Adding an axes using the same arguments as a previous axes \"\n" | |
] | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x11cd7c588>" | |
] | |
}, | |
"execution_count": 25, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Orbit at the critical point x0 = pi is subject to numerical instability. Radau solver seems the best.\n", | |
"# The actual orbit should approach (pi, 0) but never reaches it. Otherwise, the solution at (pi, 0) is non-unique.\n", | |
"tt = arange(t_min, t_max, 0.01)\n", | |
"# Initial point on the critical orbit.\n", | |
"y0 = (-2, np.sqrt(2 + 2 * np.cos(-2)))\n", | |
"\n", | |
"for method in ['LSODA', 'BDF', 'Radau', 'RK23', 'RK45']:\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt, method=method)\n", | |
" subplot(121)\n", | |
" plot(*solv.y, label=method)\n", | |
" subplot(122)\n", | |
" plot(*solv.y, label=method)\n", | |
" xlim(np.pi-0.1, np.pi+0.1)\n", | |
" ylim(-0.1, 0.1)\n", | |
"# Critical point\n", | |
"subplot(122)\n", | |
"scatter(np.pi, 0, c='black')\n", | |
"legend()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Hypothesis: almost all orbits (except for those starting at critical points) are perodic \n", | |
"# when projected down to the cylindrical space [-pi, pi] x Reals.\n", | |
"# \n", | |
"# Note that periodic vector field are not sufficient, constant vectors and helical orbits.\n", | |
"# \n", | |
"# Approach: conservative systems. Find an invariance over orbits, I(x(t)) = C.\n", | |
"# For simple pendulum, define I(x, y) = -2 cos(x) + y^2 - 2 (+2 so energy = 0 at the \"boundary\")" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 223, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from sympy import series, cos" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 333, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# Energy can range from [-4, oo)\n", | |
"energy = 0\n", | |
"# 0 ≤ y^2 = energy + 2 * np.cos(x) + 2\n", | |
"# (- energy - 2) / 2 ≤ np.cos(x)\n", | |
"x0 = np.arccos(max(-1, (-energy - 2) / 2))\n", | |
"xx = arange(-x0, x0, 0.01)\n", | |
"yy_plus = np.sqrt(energy + 2 * np.cos(xx) + 2)\n", | |
"yy_minus = - np.sqrt(energy + 2 * np.cos(xx) + 2)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 39, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<a list of 21 text.Text objects>" | |
] | |
}, | |
"execution_count": 39, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Contour plot of energy\n", | |
"xx = arange(-2*np.pi, 2*np.pi, 0.01)\n", | |
"yy = arange(-1.5*np.pi, 1.5*np.pi, 0.01)\n", | |
"xx, yy = np.meshgrid(xx, yy)\n", | |
"zz = -2 * np.cos(xx) + yy * yy - 2\n", | |
"cs = contour(xx, yy, zz, levels=8)\n", | |
"clabel(cs)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 364, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Draw iso-energy orbits explicitly\n", | |
"for i, energy in enumerate([-4, -2, -1, 0, 1, 2, 4]):\n", | |
" x0 = np.arccos(max(-1, (-energy - 2) / 2))\n", | |
" xx = arange(-x0, x0, 0.01)\n", | |
" yy_plus = np.sqrt(energy + 2 * np.cos(xx) + 2)\n", | |
" yy_minus = - np.sqrt(energy + 2 * np.cos(xx) + 2)\n", | |
" color = i / 6\n", | |
" plot(xx, yy_plus, color=cm.jet(color))\n", | |
" plot(xx, yy_minus, color=cm.jet(color))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 313, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Eye\n", | |
"plot(xx, yy_plus, c='black', linestyle='--')\n", | |
"plot(xx, yy_minus, c='black', linestyle='--')\n", | |
"# Starting at rest (theta_dot = 0), \"bounded\" periodic orbits except at critical points.\n", | |
"for y0 in [(0.0001, 0), (1, 0), (pi-0.3, 0), (pi-0.01, 0), (pi-0.0001, 0)]:\n", | |
" solv = solve_ivp(lambda t, y: nvec(*y), t_span=(t_min, t_max), y0=y0, t_eval=tt)\n", | |
" plot(*solv.y)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 95, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0, 0.5, 'period $T$')" | |
] | |
}, | |
"execution_count": 95, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Periodity\n", | |
"# Suppose the initial state is at rest (theta_dot = 0) and theta(0) = theta_0\n", | |
"# Then the periodicity is 4 * F(e) where modulus e := sin (theta0/2) and \n", | |
"# F is the complete elliptic integral of the first kind\n", | |
"from scipy import special\n", | |
"# Using m = e^2\n", | |
"theta0s = arange(-pi+0.0001, pi-0.0001, 0.00001)\n", | |
"m = np.sin(theta0s / 2) ** 2\n", | |
"axvline(pi, c='black', ls='--')\n", | |
"axvline(-pi, c='black', ls='--')\n", | |
"plot(theta0s, 4 * special.ellipk(m))\n", | |
"xlabel(r'$\\theta_0$')\n", | |
"ylabel(r'period $T$')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 94, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"/Users/dai/.pyenv/versions/3.6.5/envs/lab/lib/python3.6/site-packages/ipykernel_launcher.py:17: RuntimeWarning: invalid value encountered in subtract\n" | |
] | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0, 0.5, 'period $T$')" | |
] | |
}, | |
"execution_count": 94, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# At m = 1, there is a singularity for F (integral not defined), i.e., theta0 = ±pi.\n", | |
"theta0s = arange(pi-0.1, pi, 0.0000001)\n", | |
"m = np.sin(theta0s / 2) ** 2\n", | |
"\n", | |
"subplot(211)\n", | |
"axvline(pi, c='black', ls='--')\n", | |
"plot(theta0s, 4 * special.ellipk(m))\n", | |
"xlabel(r'$\\theta_0$')\n", | |
"ylabel(r'period $T$')\n", | |
"\n", | |
"# To compare the more numerically stable ellipkm1 near m = 1. Seems the same\n", | |
"subplot(212)\n", | |
"theta0s = arange(pi-0.000001, pi, 0.00000001)\n", | |
"m = np.sin(theta0s / 2) ** 2\n", | |
"# plot(theta0s, 4 * special.ellipk(m))\n", | |
"# plot(theta0s, 4 * special.ellipkm1(1 - m))\n", | |
"plot(theta0s, special.ellipk(m) - special.ellipkm1(1 - m))\n", | |
"xlabel(r'$\\theta_0$')\n", | |
"ylabel(r'period $T$')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 92, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0, 0.5, 'circumference')" | |
] | |
}, | |
"execution_count": 92, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Relatedly, the circumference of an ellipse of eccentricity k (can only be in [0, 1]) and semi-major axis a = 1\n", | |
"k = arange(0, 1, 0.001)\n", | |
"# Circumference of a unit circle (k = 0)\n", | |
"axhline(2 * pi, ls='--', c='black')\n", | |
"# Two line segments of length 2 a\n", | |
"axhline(4, ls='--', c='black')\n", | |
"# Ellipse\n", | |
"plot(k, 4 * special.ellipe(k ** 2))\n", | |
"xlabel(r'eccentricity $k$')\n", | |
"ylabel(r'circumference')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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