{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# [Chapter 5](https://github.com/Ziaeemehr/spikes/blob/main/docs/examples/chap_05.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### **Approximation and simulation**\n",
"\n",
"Code by : Abolfazl Ziaeemehr \n",
"- https://github.com/Ziaeemehr\n",
"\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# uncomment and run this line to install the package on colab\n",
"# !pip install \"git+https://github.com/Ziaeemehr/spikes.git\" -q"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import sympy\n",
"import sympy as sp\n",
"import numpy as np\n",
"from scipy.linalg import eig\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import display, Math\n",
"from spikes.solver import solve_system_of_equations\n",
"\n",
"sympy.init_printing()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\\begin{align*}\n",
"\\frac{dx}{dt} &= 2y \\\\ \n",
"\\frac{dy}{dt} &= -2x\n",
"\\end{align*}\n",
"\n",
"$x(0)=2, y(0)=0, h=0.1, 0.01, T=1$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{d}{dt}\n",
"\\begin{pmatrix}\n",
"x \\\\\n",
"y \n",
"\\end{pmatrix} =\n",
"\\begin{pmatrix}\n",
"0 & -2 \\\\\n",
"-2& 0 \n",
"\\end{pmatrix} \n",
"\\begin{pmatrix}\n",
"x \\\\\n",
"y\n",
"\\end{pmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left[ 2 \\cos{\\left(2 t \\right)}, \\ - 2 \\sin{\\left(2 t \\right)}\\right]$"
],
"text/plain": [
"[2⋅cos(2⋅t), -2⋅sin(2⋅t)]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# solving analytically and numerically using odeint:\n",
"A = np.array([[0,2],[-2,0]])\n",
"B = np.array([0,0])\n",
"X0 = np.array([2,0])\n",
"trange1 = np.arange(0, 1, 0.1)\n",
"trange2 = np.arange(0, 1, 0.01)\n",
"Sol, xvalues1 = solve_system_of_equations(A, B, X0, trange1)\n",
"\n",
"plt.figure(figsize=(5,3.5))\n",
"\n",
"plt.plot(trange1, xvalues1[0], label=\"x\")\n",
"plt.plot(trange1, xvalues1[1], label=\"y\")\n",
"plt.legend();\n",
"plt.xlabel('Time')\n",
"plt.legend();\n",
"\n",
"Sol"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 2, Solving with Euler method"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def system(t, x0):\n",
" \n",
" dxdt = -2 * x0[1]\n",
" dydt = -2 * x0[0]\n",
" return np.array([dxdt, dydt])\n",
"\n",
"def integrate_euler(ti, tf, function, h, x0):\n",
" x = np.zeros((2, int((tf - ti) / h) + 1))\n",
" x[:, 0] = x0\n",
" t = np.linspace(ti, tf, int((tf - ti) / h) + 1)\n",
"\n",
" for i in range(1, x.shape[1]):\n",
" x[:, i] = x[:, i-1] + h * function(ti + h * i, x[:, i-1])\n",
"\n",
" return t, x\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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0zJkzh/POO4+408zUO2vWLGbOnNnU3YiItH37loGzDsITIKKrp6OR1s5ioWuPftCjH5QfhP2r2LNxOc6SXIrWzmPu2q/xTx7GuHETGZQSp9YSItIqNKmeeN++fSxYsIBbb731tOtOnz6d4uLi+ldWVlZTdiki0jZVHILcDeZ71bKIqwVFQo9z6XrRg4w8+3IiIyIJpBLr3sV8N3cGf3rqn3y2fDPVdY7TlyUi4kFNqmmZO3cu0dHRXHDBBadd1263Y7fbm7IbEZG2L30RGE6I7GbWtIi4gY9/MMPHX8jwseexZ8sqNiyfT/b+vfge3sTuzzczsGYcCf3HQniiEmcR8UqNTlqcTidz587lxhtvxMdHcwiIiDRZSQ4c2GHeJHbVKIzSAqw2UvqNIKXvcIpy97ByydfU5e8kwZkN69+CkBi+LEogpttABiVFqumYiHiNRmcdCxYsIDMzk5tvvtkd8bRK48aNY+DAgTz99NOeDkVEWgvDMGtZADr1heBoj4Yj7YzFQnhcNyZdfVd9vxfyNlF5KJs9S5ewZuE83o0awKgxEzh3YBJ2H5unIxZp83Q/eWqN7tMyadIkDMOge/fu7ohHgMzMTC666CKCgoKIiorinnvuoaam5pTbVFdXc/fddxMVFUVQUBAXX3wx+/fvP2adxx57jFGjRhEYGEh4eLgbj0BETutQOhzeB1YbJJ/h6WikPfu53wsj76Si80i6xEYTbq0k9uBydsz7G/f/9Z889/VaCkqrPB2piDRCW7uf1IDtXsbhcHDBBRdQXl7O0qVLeeedd/jwww/53e9+d8rt7rvvPubNm8c777zD0qVLKSsr48ILL8ThONq5sqamhiuvvJLbb7/d3YchIqfyy1qWzoMhINyT0YiY/AKJ7HM2F/7mL1w35XYG9exGB7tBas0WqpY8y8y//43vV2/ydJQi0gBt8X5SSYuLOJ1OHnroISIiIoiJiWHGjBlNKmf+/Pls3bqVN954g0GDBjFhwgSefPJJXn755ZPOcVNcXMycOXN48sknmTBhAoMGDeKNN95g06ZNLFiwoH69mTNn8tvf/pZ+/fo1KTYRcZH8LVBWAD5+kDjK09GIHMvmQ4eUoYyd/DBTpj3I2GFD6Rxup6clk+EHP4b1b8OhdHKLKqipc3o6WpE2RfeTJ+fdPekNAxy1ntm3zbdRI6i89tpr3H///axYsYLly5czZcoURo8ezcSJEznvvPNYsmTJKbcvKysDYPny5fTt2/eY+W/OOeccqqurWbNmDePHjz9u2zVr1lBbW8ukSZPql8XFxdG3b1+WLVvGOeec0+DjEBE3c9RBxmLzfeIo8Av0bDwiJ2Ox4BvdnUEXd2dQSS6F25YQVJkOh/fC4b18ub6cBeVdGD1iNNeM6EJUsEYKFS/lqfvJRt5Lgu4nT8W7kxZHLSx50jP7HvM78yloA/Xv359HH30UgNTUVJ555hm+++47Jk6cyOzZs6msrGxQOXl5eXTq1OmYZR06dMDPz4+8vLyTbuPn50eHDh2OWd6pU6eTbiMiHpK9GqpKwB4C8UM8HY1Iw4TGEjX8Kqgsgv2rqMxcg7M0n+E12RxeuJbbF/WgW/9R3DS2B907hXg6WpFjeep+spH3kqD7yVPx7qSlFenfv/8xn2NjYykoKACgc+fOjSrrRENMGobR6KEnm7KNiLhRTQXsW2a+73Km+RROpDUJCIfUiQQkn8GU5NXsXLuQjRm5hJSso2rDFh5dn0JQ1+HcPrEfaUkRno5WpNXR/eTJeXfSYvM1s1RP7bsRfH2PXd9iseB0mm19G1OdFxMTw4oVK4757vDhw9TW1h6XMR8RExNDTU0Nhw8fPiY7LigoYNQotZcX8RqZy6CuGoI7msMci7RWvgH4poyhT/II+uRtInPjIjbuzCDgwDZqM3ZSteUsiD4PAjqcviwRd/PU/WQTHkzpfvLkvDtpsVgaXa3mjRpTnTdy5Egee+wxcnNziY2NBczOVHa7nbS0tBNuk5aWhq+vL99++y1XXXUVALm5uWzevJl//OMfrjkIEWmeysOQvdZ833U8WDUOirQBNl/oPJjE2IEkpu3k4LbFbN+5kxH2vbDiJYjuyWdFSeyrCmLy8CQ6BLX+a7q0QrqfBFr//aR3Jy1tRGOq8yZNmkTv3r25/vrrefzxxzl06BAPPPAAU6dOJTQ0FIDs7GzOPvtsXn/9dYYNG0ZYWBi33HILv/vd74iMjCQiIoIHHniAfv36MWHChPqyMzMzOXToEJmZmTgcDtavXw9At27dCA4Odukxi8j/SF8ETgd0SIaIrp6Opk157LHH+OKLL1i/fj1+fn4UFRV5OqT2x2qF6J5EduzB6P77IHMFHErHmbeFA8u+YFdFJJct7M3otIHcckZXukQFeTpikVanvd9PKmnxMjabjS+++II77riD0aNHExAQwK9//WueeOKJ+nVqa2vZsWMHFRUV9cv++c9/4uPjw1VXXUVlZSVnn302r776Kjbb0VmMH3nkEV577bX6z4MGDQJg4cKFjBs3zv0HJ9JeFe+Hgu3m075uZzd6NBk5tSNzBowcOZI5c+Z4Opz2zWIxE/MOyVCah7F3GaO6leG/7xBdSr8ne9VGblnZg67dBzD1zK4M6xLhFW3lRdqatng/aTEMw3Bb6SdQUlJCWFgYxcXF9ZneEVVVVWRkZNClSxf8/f1bMiw5Cf2diDSTYcDa16EkB2IHQM/zPRbKqc6/bcGrr77Kfffd1+ialrb+u3hcxSGMrBVkbV3B+n2FpBeWU2iEsdLZk/FjxjD9/D6ejlDaEN23eKdT/b009BysmhYREXcq2GYmLDZf6DLG09EIUF1dTXV1df3nk020Ji4SGIGlx3kkJp9B4v5VHNz5E+v3FtApdyWXWCogpxZi+nGwog4fm5WwAI2qJyLHU9IiIuIujjqzLwtA4ghzbhbxuFmzZjFz5kxPh9H+2EMg5SwiE0dydvYaRmWsIIBq2PEV7F3Kh3s78uz2IC4b2oWbR3chIUITr4rIURq+RkTEXbJXQ1Ux2IMhfpino2lVZsyYgcViOeVr9erVTSp7+vTpFBcX17+ysrJcHL2ckm8AJJ9BwJi7IeUssAdjVJUQun8RVzs+Z+Oyb5j4+HzufHMtazMPezpaEfESqmkREXGH6jLY96P5vsvYNjHcZku66667uOaaa065TnJycpPKttvt2O32Jm0rLuTjB4nDoXMalryNXB2wnH3ZufTM3MPOgztYtzmVazel0DepE3eOT+GsnieeW0JE2gevTFpaeGwAOQX9XYg00d4lUFcDITEQ08/T0bQ6UVFRREVFeToMaQk2H+g8GEvsAJLzt5CcsJzCglzWZmaxMW8na7K6sXZ3oJIWaRTdv3gXV/x9eFXScmQ4tZqaGgICAjwcjQD1w+D97wytInIKpfmQu8F8322Chjh2M81B1UZYbRDbHzr1JerAdiZ1+pHRh/LYsD+ffvavYc9hSBjGT/urWLTjAFNGJRMTptGh5FhH7lcqKip0L+lFXHE/6VVJi4+PD4GBgRw4cABfX1+smjHaYwzDoKKigoKCAsLDw48Zn1tETsEwYPcC88/oXhCe4OmI2jzNQdXGWK3QqTdE9yKocCejIpdCWQFk/gTZq1myKYjXsjoxe0k6Fw2I49YxXegTF+bpqMVL2Gw2wsPDKSgoACAwMFBzAXmQK+8nvWqeFjBrWTIyMnA6nS0ZlpxEeHg4MTEx+g8v0lAHdsDmj8DqA8OmQkC4pyOqp/lITky/i5czDDi4G/YuhdI89hwoY2VmKV8eimWNszsV+DOyayS3j0thTGqUrleCYRjk5eU1es4mcZ9T3U+22nla/Pz8SE1NpaamxtOhtHu+vr6qYRFpDEcd7PnefJ8wzKsSFpFWy2KBqFSI7AYH95CybykpHXM5q6SKVVk/8n5uNCvTU7kh/SAXDYjjP9cO8nTE4mEWi4XY2Fiio6Opra31dDjtnqvuJ70uaQGwWq2axVREWp+sFVBZZM5HkTjS09GItC0WC0R1g8gUOJROp71LuDA0l7EpNazKWsEbWZGMS+5Wv3qtw4nVYsFmVc1Le2Wz2fTwtQ3xyqRFRKTVqSqBzGXm+5TxGuJYxF0sFjNxiegKh9IJ2buEs/xzGZFUg1/1p5A+FBKG8/7aA7y8JJ3bx6Zw6aDO+Pmon6xIa6akRUTEFdIXms3DwuIhurenoxFp+36ZvBzcQ+DeH8yR+/Yth+w1bF4VQE5hLA99uJF/fbeL28Z25aohCfj76sm7SGukxw4iIs1VlAX5W82bqNSJGuJYpCUdaTaWdhP0vRyCo6Guhhn9D/N67zVMCNpDQVEpj3yyhTH/WMhLP+yhvLrO01GLSCOppkVEpDmcTtj9rfk+doA5maSItDyLBTp2NzvtH9iB394lDLcVkta5lA3563hxbzTflcTz1y+3s2F/Mc/+erCnIxaRRlDSIiLSHLnrzCYpPnbocqanoxERiwWie0JUdyjYis/epaTFHub5TkVsOniI5zNiuGnEsPrVD5XX4DQMooLtHgxaRE5HzcNERJqqpgIyfjDfdxkLfkFu29Un67N59JPNVNY43LYPkTbFaoWYvuZ8ST3OwxYYxsCONl4YWsCQgg8hfwsYBs8u3M0Zf/+emZ9tIbe40tNRi8hJqKZFRKSpMhZDbRUEd4Q4980NkV1UyR8/3kxpVR3JUUHcNLqL2/Yl0uZYbRA3EDr1hZx1WDKXQeVh2PopRuZPHMwMo6rWn7k/7uWNn/ZxRVoCt49NITEy0NORi8gvqKZFRKQpSnIgd4P5PvUc86muGzidBg+8t4HSqjoGJoRz/Ygkt+xHpM2z+UDCUBh+u9mU08cPS1kB/+y1k2/GZnFeYh21DoO3V2Yy/slF/Pbd9ezKL/V01CLyMyUtIiKNZRiwa775Z6c+EJ7gtl3NWZrB8vSDBPja+OfVA/Gx6bQt0iw+fpA82kxeEoZhsfrSw7+I53ttZcHEA1yQ4oPDaTBvXTZvrcz0dLQi8jNd/UREGit3PZTkmjc/KePdtpttuSU8/s0OAP7fhb3pEuW+PjMi7Y5fIHQ7G4bfZo78Z7HQzZrLs6nrWHRROb/qHcJvzuxav/r2vBLW7DvswYBF2jf1aRERaYyackhfZL5PPhPsIW7ZTVWtg9++u54ah5Oze0Zz7TD31eaItGv+odDzfEgYDhmL4MBOkmv28M+kfVDogMCR4OvP37/azsIdBxjZNZK7z+rGyJRILJqTSaTFKGkREWmM9EU/d76Phs5pbtvN7oIycooqiQzy42+X99fNkYi7BUWak1MWZ0P6QnPS2MyfIHc9dQmjiAnxw9dmYXn6QZanH2RQYjh3je/GWT2j9f9TpAVYDMMwWnKHJSUlhIWFUVxcTGhoaEvuWkSkeYqyYN0b5vvB10NYvFt3l1tcyf7DlQxNjnBJeTr/nph+FzmOYcDB3eZDivJCc1lAOPkdR/DcJh/eWb2f6jonAL1iQ3no3B6M7xHtuXhFWrGGnoNV0yIi0hBOJ+z6xnwfO8DtCQtAbFgAsWEBbt+PiPwPiwWiUiEiBfI2QMYSqCyiU+bXzEyI456hY3hpYzVvLN/HttwS9h/W/C4i7qaO+CIiDZG9GsoOgK8/dB3ntt3M+HQL323Ld1v5ItIIVqs5B9PwaZB8Bth8oSSHyJ3vMj1hG8vuG8yD5/TgyrSjDzGW7S5kbaY67Iu4WqOTluzsbK677joiIyMJDAxk4MCBrFmzxh2xiYh4h6pi6me+7zreHHXIDT7dkMOry/bym/+uIetQhVv2ISJN4OMHXcYcM9IYB3YQtulV7kzYhz+1ANQ6nDw8bxOXPbeM37y+mt0FmudFxFUa1Tzs8OHDjB49mvHjx/PVV18RHR3Nnj17CA8Pd1N4IiJeYNe34Kg1m4TFDnDLLnKKKvnjvE0A3Dm+GwkRmo1bxOvYQ8yRxuKHwJ7v4VAGZK2EvE3QZQyVEX0Z1iWCzEMVzN+az4Jt+VyRFs99E7oTF66mniLN0aiO+L///e/58ccfWbJkSZN3qA6PItKqHNgJmz8EixWG3AzBHV2+C6fT4Lo5K1i25yADEsL5YNpIfN0wiaTOvyem30WaxDDgULqZvBzprB8UBd0msLsuise/2cE3W8ymnn4+Vm4cmcQd47rRIcjPg0GLeJ+GnoMbdVX89NNPGTJkCFdeeSXR0dEMGjSIl19++ZTbVFdXU1JScsxLRKRVqKuGXfPN94nD3ZKwALzyYwbL9piz3j999UC3JCwi4mIWC0SmmA8zUieZ/d3KC2HDO3TL/4YXL+/KR3eMYniXCGrqnLy8JIPNOcWejlqk1WrUlTE9PZ3nn3+e1NRUvvnmG6ZNm8Y999zD66+/ftJtZs2aRVhYWP0rIUETpIlIK5GxBKpLISAckka7ZRfb80r4x9fmrPd/vLCXZr0XaW2sNohPMzvrxw81a2ULd8Gq2QyuXcc7Nw/i1ZuGcuPIJMakHn3wsWl/MbUOpwcDF2ldGtU8zM/PjyFDhrBs2bL6Zffccw+rVq1i+fLlJ9ymurqa6urq+s8lJSUkJCSoGl5EvFtJDqx93WwC0v8q84mqGzzz/S6emL+Ts3tGM/vGIW6dpE7NoE5Mv4u4VPlB2L3AbDoG4BdkjjgY08+snQEOllUz9vFFRAX78btJPbigXyxWqyaolPbJLc3DYmNj6d279zHLevXqRWZm5km3sdvthIaGHvMSEfFqTgfs+MpMWDr1dlvCAnDXWam8eH2aZr1vor1793LLLbfQpUsXAgICSElJ4dFHH6WmpsbToUl7FRQJA642H3YERkBNOWz/Ata+Zj4MAfYcKMff18regxXc/fY6Ln52KT/sPEALz/ct0qo0avSw0aNHs2PHjmOW7dy5k6SkJJcGJSLiUftXQVmB2Ua92wS37+6cPjFu30dbtX37dpxOJy+++CLdunVj8+bNTJ06lfLycp544glPhyftWWQKdEg2zyd7l0JJrll7G9OfYV3HsvjB8cxZmsFLP6SzObuEG15ZyaiUSP7v3J4MSAj3dPQiXqdRzcNWrVrFqFGjmDlzJldddRUrV65k6tSpvPTSS0yePLlBZagaXkS8WsUhWD0HHHXQ8wKI7e/yXZRU1fLnz7by4Dk9iA71d3n5J91vOzn/Pv744zz//POkp6c3aP328ruIB1WXQvoiyNtsfvaxQ5exEDeIgxW1PLtwD2/8tI8ahxNfm4Vlvz+bjiF2j4Ys0lIaeg5uVE3L0KFDmTdvHtOnT+dPf/oTXbp04emnn25wwiIi4tUMA3Z+YyYsHZLMNuhu8OgnW5i3LptdBWXMu2OUmoW5WHFxMRERESf9/kR9LUXcyh4CvS6C2IHmiIRlBeafueuJ7H4Oj1zUm5vPSOaf3+4ixN/nmISlpKqWUH9fz8Uu4iUalbQAXHjhhVx44YXuiEVExLPyNsLhvWD1ge7n1neadaXPN+Ywb102Vgv8vwt7K2FxsT179vCf//yHJ5988qTrzJo1i5kzZ7ZgVCI/C0+AtJsgdx2kLzaTl7X/hdj+xHcdx5NXDTimX8uWnGKueH45N45K5vaxKYQFKnmR9kuTAYiIgNl8Y/d35vsuY8wOtC6WV1zFH+aZzUPuGt+NtKQOLt9HWzFjxgwsFsspX6tXrz5mm5ycHM4991yuvPJKbr311pOWPX36dIqLi+tfWVlZ7j4ckaOsVuicBsNvO9r8NHcjrHwJctbxy8cYn67PobLWwQuL9zDmH9/zwuI9VNU6PBK2iKc1qk+LK6jtsIh4pc0fwoGdEBIDg280byxcyOk0uOGVlSzdXciA+DA+uH1Ui08i2ZrOv4WFhRQWFp5yneTkZPz9zT5BOTk5jB8/nuHDh/Pqq69ibcTfX2v6XaQNKt5vNkstKzA/h8aZNb0hnTAMg++3F/CPr3ewI78UgE6hdu6b0J0r0+Lx0US00gY09ByspEVEpGA7bJlnTgqXNgVCOrl8F3OWZvDnz7fi72vli3vGkNIx2OX7OJ22ev7Nzs5m/PjxpKWl8cYbb2Cz2Rq1fVv9XaQVcTohew1kLAZHrXkuih8CyWPAxw+H0+Djddk89e1OsosqARiWHMG7t41QE1Np9dzSEV9EpM2prTQ7xAIkjnBLwlLncPL+arMJ0h8u6O2RhKWtysnJYdy4cSQmJvLEE09w4MCB+u9iYjSUtLQSViskDIWOPWDPd+aDlKyVULANUidh69idy9PiuXBALG/+lMkzC3dzfr+Y+oTFMAwlL9LmKWkRkfZt17fm5G9BUZA02i278LFZ+eiOUby/ej/XDU90yz7aq/nz57N79252795NfHz8Md9poj5pdfxDoc+vIGaP2WSsqthsutqxO3SbiN0/lJvP6MKVQ+Kx+xytUfxqcx7z1mXzyIW9SYgI9OABiLiPmoeJSPtVuAs2fWCOEjboegjr7OmI3Ern3xPT7yJeyVFrTkqZtRIMJ/j4QZdxEDfomD53hmFwztM/sDO/DH9fK3eflcqtY7ock9SIeLOGnoPVg0tE2qfaStj5tfk+YZhbEpYV6QeZszQDp1NP/EWkkWy+kDIehtxkds6vqzGbsq77L5QdbQZpsVh45teDGd4lgqpaJ49/s4Pznl7C0l2nHshCpLVR0iIi7dPu76C6zBzaOHmMy4svqarl/vc28OfPtzJnaYbLyxeRdiI4GgbfAN0nmbUtJTmwZi5k/GBOhAt07xTCO78ZwdNXDyQq2E56YTnXzVnBnW+tJa+4ysMHIOIaSlpEpP0p3A15m8xmYT0vMJ9outiMT7aQXVRJYkQg16ofi4g0h8Vizu0ydCpEpYLTAXt/NJOX4v0/r2Lh0kGd+f6BsUwZlYzVAl9szGVbbomHgxdxDXXEF5H2pbYSdnxpvo8fAmHxp16/Cb7YmMtHP896/8+rBxBs16lWRFzAPxT6Xg4HdphNxcoLYd0bZkLTZSz4+BHq78uMi/tw5ZB4vtmcx/ie0fWbHyyrJjLY7sEDEGk6XUlFpH3ZNd8cLSww0rzIu1hecRUPz9sEwB3jupGWFOHyfYhIO2axQHRP6JAEe76H3I2wf7U5sEiP8yCiCwB94sLoExdWv9mB0mrOfnIRE3p3Yvp5vegYouRFWhc1DxOR9uPADsjf6rZmYU6nwYMfbKC4spZ+ncO4d0KqS8sXEannG2CexwZcDf5h5vDIG96BHV9B7fH9WBbtKKC0uo6P1mZz1pOLeH35XhwaJERaESUtItI+1JQfHS0scYRbRgvbnFPM8j0HsftY+efVA/C16RQrIm4W0RWG3mo2EQPIWQ+rZsOh9GNWu3JIAh/dPoq+nUMprarjkU+2cMmzS1mXebjlYxZpAs3TIiJtn2GYE7QV7oLgjjB4Ctjc0zp2c3Yxew6UcclA75vzReffE9PvIm1GUSZs/xIqf05EYgdAt7PB52hTMIfT4K0V+/jHNzsorarDYoHJwxP58yV9sVgsHgpc2jPN0yIickTeJjNhsdqg50VuS1gA+nYO88qERUTagfBEGHoLxA81m8Hmbvi51uXosOs2q4XrRyaz8IFxXD44HsMAH6tVCYt4PXXEF5G2rbIIdn9rvk8eAyGdXL6L15fvJS2pwzGdXkVEPMLmC6kToGP3o7UuG96BzoOh63hzrhcgKtjOk1cN4JphCfSICanffM+BMiprHPTtrPOZeBfVtIhI22UYsP0LcybpsM6QMNzlu1iZcYhHP93Cpc/+yN7CcpeXLyLSJOGJMOTmo31dstfC6legKOuY1YYmRxDqbw5KYhgG0z/axMXPLGXGp1soqapt6ahFTkpJi4i0XVkrzTbeNl/oeSFYXXvKK62q5f731mMYcMnAziRHBbm0fBGRZvHxg+6TYMA15hwvlYdh/ZuwZyE46o5bvbLWQXSIHacBry7by1lPLGbeuv20cPdnkRNS0iIibVNpPmQsNt+nnAWBrp8vZeZnW9l/uJL4DgE8elFvl5cvIuISEV1gyC0Q08+sgc78Cda+CmUFx6wW6OfDM78ezBu3DKdrxyAKy6r57bsbuOaln9iZX+qZ2EV+pqRFRNoeRx1s+xScDohKhbhBLt/F15tz+WDN/p9nvR9IiL9r53wREXEpX3/odSH0vcyc46XsAKx5FTJXmInML5yRGsVX947hwXN64O9rZUXGIc7/1xJWpB/0TOwiKGkRkbYofRGUF4JfoDlDtItHxSkoqWL6R+as99PGpjA0WbPei0gr0bGHOa9LVKr5YGfP97DhbXNyyl+w+9i4c3w3vv3tWCb27kRKx2AGJ3XwUNAiSlpEpK05lA77V5nve14Ifq7vZ/L68n0crqilb+dQ7pvQ3eXli4i4lT0Y+l4OPc41h4A/vA9WzYGCbcetmhARyMs3DOG9aSPrJ8ytrnMw/aONZGjwEWlBGvJYRNqOmnLY9rn5vvNgiExxy27un9id8EBfxvXoiJ+Pnv2ISCtksZhNZ8OTzOa0Jbmw5WM4uAdSJx4zISVAWMDRJrCzl2Tw9sosPlyTzW1ju3LHuG4E+Nla+ACkvdHVVkTaBsMw5ySoKYegKLPzvZtYrRZuHdOVbtEhp19ZRMSbBUbAoOshebSZyORtgtVzoSTnpJtc0C+Wsd07UuNw8p/vdzPxn4tZuquwBYOW9khJi4i0Ddlr4eBusPpA70vMYY5dqLrOwbMLd1NZ43BpuSIiHme1QZczYeDko0Mjr/0v7FsGTudxqydHBfHqTUN54brBxIX5s/9wJdfNWcHMz7ZQVatzpLiHkhYRaf3KCszOpAAp4yE42qXFH5lw7fFvdjB59k+as0BE2qbwBHNo5OieYDghfTFsfAeqjx/u2GKxcG7fWL69fyzXjUgEYO6Pe/njx5tbOmppJ5S0iEjr5qiFrZ+Asw4iux2d/dmFnl24m4/WZmOzWrhvQncsLh6NTETEa/j6Q+9Loef5x3bSP7jnhKsH2X34y6X9mDtlKMmRgdxzVmrLxivthpIWEWnddi/4eXjjIPMi6+KE4rMNOTwxfycAf7qkD2d27+jS8kVEvI7FArEDIO1ms+a6thI2vge7vzOHST6B8T2j+e5340iMDKxf9uaKfWQdqmipqKWNU9IiIq1X/lbIWW9eYHtd5PLhjddmHuZ3728A4JYzujB5eJJLyxcR8WpBkTD4RogfYn7OWgnr/guVRSdc3WY9+tBo2e5C/jBvM+f9awkfrtmvZrXSbEpaRKR1qjwMO78y3yeOhIguLi0+61AFv3l9NTV1Tib0iubh83u5tHxxnYsvvpjExET8/f2JjY3l+uuvJyfn5CMfiUgj2HzMIZD7Xm4Og1ySC6tfgQM7TrlZfIdAhiR1oKy6jt+9v4E731rL4fKaFgpa2iIlLSLS+jgdZj+WuhoIi4fkMS7fRVFFLQC9Y0P51zWDjnmCKN5l/PjxvPfee+zYsYMPP/yQPXv2cMUVV3g6LJG2pWN3GHIzhMZBXTVs/gh2LThpc7HEyEDevW0kD57TAx+rhS835XHO0z+weOeBFg5c2gqL0cL1dSUlJYSFhVFcXExoaGhL7lpE2opdC8xZ7339zYuof5hbdpN1qAIfm4XYsAC3lN/S2sv599NPP+XSSy+luroaX9/TD33dXn4XEZdwOiB9kdlUDCA01uy4HxB+0k027S/mvnfXsedAOQB3jEvhoXN7uj1UaR0aeg5WTYuItC4HdpgJC0DPC12asBiGQXZRZf3nhIjANpOwtBeHDh3izTffZNSoUQ1KWESkkaw26HY29LviaHOxNXOhcPdJN+kXH8bnd4/hxpFmv8DUTsEtFa20IUpaRKT1qDwM278w3ycMgyjXDq35yo97mfDkYr7dmu/ScsX9/u///o+goCAiIyPJzMzkk08+Oem61dXVlJSUHPMSkUaKSv25uVgs1FbBpvfNeV1OMBklQICfjZmX9OXzu8/g0oGd65fvLSzH4VQnfTm9RiUtM2bMwGKxHPOKiYlxV2wiIkc56n7ux1JttqnuOs6lxS/Yms9fvthKZa2DjMIyl5YtjXei683/vlavXl2//oMPPsi6deuYP38+NpuNG2644aSjFc2aNYuwsLD6V0JCQksdlkjbEhAOA687Oj/WvmXmZJQ15SfdpG/nsPq5rg6X13Dli8u5+sXlZB7U0Mhyao3q0zJjxgw++OADFixYUL/MZrPRsWPD5y1Q22ERaZKd8yF7jVv6sWzJKebKF5ZTUePg2mEJ/PVX/drkBJKt6fxbWFhIYWHhKddJTk7G39//uOX79+8nISGBZcuWMXLkyOO+r66uprq6uv5zSUkJCQkJreJ3EfFa+Vtgx5fmAyZ7CPT5FYR1PuUmy/YU8pvX11BWXUeQn41HL+7DlWnxbfL8KyfX0GuTT2ML9vHxUe2KiLSs/C1mwgLQ62KXJiz5JVXc8upqKmocjO4WyZ8u6asLpheIiooiKiqqSdseeRb3y8Tkl+x2O3a7vcmxicgJdOoDwZ3MUcUqDsL6N82+L3GDTzrp76iUKL66dwz3v7eeVXsP89AHG/luWz5//VU/IoP1f1SO1eg+Lbt27SIuLo4uXbpwzTXXkJ6e7o64RERM5YWw4+f5WJJGQWSKy4quqKnj1tdWk1dSRUrHIJ6bnIavTV39WpOVK1fyzDPPsH79evbt28fChQv59a9/TUpKyglrWUTEjYKiIO1G6NjDHGVs53yzH6Kj9qSbJEQE8s5vRvLQuT3wtVn4Zks+5zy9hIXbC1owcGkNGnV1Hj58OK+//jrffPMNL7/8Mnl5eYwaNYqDBw+edBt1eBSRJqurgS3zzAtehySXz8fy6rK9bMouJiLIj7lThhEWoNGmWpuAgAA++ugjzj77bHr06MHNN99M3759Wbx4sWpTRDzBx242DUs5y6xhydsE6/4LlUUn3cRmtXDHuG7Mu2M03aKDKSyr5pP12S0Xs7QKzZqnpby8nJSUFB566CHuv//+E64zY8YMZs6cedxytR0WkVMyDNj6MRRsB3uw2Y/FL8ilu6hzOJn11XbO6xvDkOQIl5btjVpTn5aWpN9FxE0O74UtH0NtJfgGQJ9LoUPyKTepqnXw3MLd3DKma/2DJMMw1Gy3DWvoObjZk0tOnDiRbt268fzzz5/we3V4FJEmyVoJu78DixUG/hrCNcJTc+nm/MT0u4i4UWURbPkISvPN83nKWRA/5KT9XP6XYRjc/sZaeseFcse4FHzUhLfNaZHJJaurq9m2bRuxsbEnXcdutxMaGnrMS0TklA7vgz0LzffdJrg0YflxdyEPz9tErePEcwmIiIgLBYTDoOshpi8YTti94Od+LnUN2nzp7kK+3pLHU9/u5MoXl7Pv4MmHU5a2rVFJywMPPMDixYvJyMhgxYoVXHHFFZSUlHDjjTe6Kz4RaW+qSsxmYYbTHI2m82CXFb27oJRpb6zhrRWZzF6S4bJyRUTkFGy+0PNC8yHUkX4u69+A6tLTbnpGtyj+efUAQuw+rMss4rx/LeHtlZknnYdJ2q5GJS379+/n2muvpUePHlx22WX4+fnx008/kZSU5K74RKQ9cdSZHe9rKiC4I/Q4r8FNCE7nUHkNN7+6mtKqOtKSOnDT6GSXlCsiIg1gsUDCUOh/tTnfVkkurHkVSnJOs5mFXw2K56v7xjC8SwQVNQ6mf7SJqa+vobDsxMOaS9vU7D4tjaW2wyJyQoZhDm2cu8G8oA2+EQJd0zm+us7B5JdXsHrfYRIiAvj4jtHtcg4AnX9PTL+LSAurPAybPjCHtLf6mA+oYvqedjOH02D2knSemL+DWofBoMRwPrp9lDrpt3It0qdFRMRlctaaCYvFYk4g6aKExTAM/u+Djazed5gQfx/mThnaLhMWERGvEdABBt8AUangrINtn5n9GE/zHN1mtXDb2BQ+ufMMesWG8ofzeylhaUeUtIiI5xVlwa4F5vuu41w6geR/vt/Nx+tzsFktPD85jW7RIS4rW0REmsjHDn0ug8QR5ufMn8xRxupqTrtp77hQvrj7jGOGql+4vYD9hyvcFa14ASUtIuJZVcXmhcpwQnQvSBju0uL7x4cRbPfhL5f25YzUKJeWLSIizWC1Qsp46HUhWG1wYKc5EWVVcQM2PVrDsjm7mGlvrOHiZ35kRfrJJzyX1k1Ji4h4jqMWNn/4c8f7aOhxvss63h8xrkc0Cx8Yx7XDEl1aroiIuEhMPxhwLfgFQlkBrH3d7KjfQBFBfqR2CuZQeQ2TZ6/gjZ/2uTFY8RQlLSLiGYYB2z83JxzzC4S+l4OPn0uKzjpUwd7Co2P5dwxRHxYREa8WnmAOwBIUBdVl5pDIB3Y2aNO48ADev20UFw2Io85p8MePN/OHeZuoqdN8XG2JkhYR8Yx9y6BguzlDcp9fmROQuUBxZS03vbqKS5/7kXWZh11SpoiItIAjE1FGdP15CPyPIHPFaTvoAwT42fj3NQN56NweWCzw5opMrpuzgoMaFrnNUNIiIi3vwA7I+MF8330ShLum6Vatw8mdb65ld0EZ/j42YsMCXFKuiIi0EF9/6HelObGwYcCe72HnN+A8fa2JxWLhjnHdmH3DEILtPqzMOMQ7q7JaIGhpCUpaRKRllebBtk/N953TIG6QS4o1DINHP93C0t2FBPrZmH3jEGLC/F1StoiItCCrFVInQbcJZj/HnHWw+YMGjSwGcHavTnx85yiuH5HEtLGuG41SPEtJi4i0nOpSc0IxRx1EdDEvSC4yZ2kGb63IxGKBf18ziL6dw1xWtoiItDCLBRKGms2HbT5wcI85slh1aYM27xYdwp8v7Yvt51HGquscvLliH05ni86pLi6kpEVEWsaRkcKqSyEwEnpfaj5Nc4H5W/J47MttAPzxgt5M6N3JJeWKiIiHdewBAycfO7JYeWGji/njvM38Yd5mbntjDWXVdW4IVNxNSYuIuJ9hmDMel+T+3F75CvNPlxRt8PryfRgGTB6eyM2jk11SroiIeInQOBh8g/nAq6rETFwON25Y4xFdI/HzsfLt1nwue+5H9h0sP/1G4lWUtIiI+6UvMjvfW23m0MaBEafdpKEsFguzbxzC78/ryYyL+2Bx8TwvIiLiBQI6wKDrICwe6qph47tQsK3Bm1+eFs+7vxlBdIidnfllXPLsj/y4u/E1NuI5SlpExL1y1kPmT+b7Hue7bKQwxy/aJfv72pg2NgVfm05pIiJtll8gDLjGbDLmdMDWT2D/6gZvPiixA5/dfQYDEsIpqqjlhldWMvfHDIwGDKksnqcrvIi4z6EMc6hKgOTRENPXJcU6nAbT3ljD499sV6dKEZH2xOZr9onsnGY2Pd71LexZ2KC5XAA6hfrz7m9GcNngzjicBk8v2EVhWcNGJRPP8vF0ACLSRpUVmBODGU7o1BuSx7is6L99tY1vt+azeOcBfjWoM92iQ1xWtoiIeDmrFVIngj0Y0hebtfk1ZWZtvtV22s39fW08eeUAeseG0iMmhI4h9hYIWppLSYuIuF5VCWx8zxxTPzwRelxgDl/pAm+u2MfLSzIAePLKAUpYRETaI4sFkkaBXzDs+AryNkNtFfS51KyNOe3mFm4d0/WYZT/uLiTE34f+8eHuiVmaRc3DRMS16qph03vm0MZBUdD3MnOMfRdYsusAj3yyBYDfTezORQPiXFKuiIi0UrH9zQFerD5wcDdseAdqKxtdTEZhOdPeWMOVLyznk/XZbghUmktJi4i4jtMBmz+CsgPgFwT9rgTfAJcUvSGriDveWIvDaXDZoM7cdVY3l5QrIiKtXFQ3s4O+jx2K98O6Nxo8CWV9EcF+DEuOoLrOyb3vrGfWV9uOGfBFPE9Ji4i4hmHA9s/h8F6zar7flRAQ7pKiiyvNUV5Kq+sYlhzBrMv7aWhjERE5KjwBBl1v9nMpLzQTl8rDDd48xN+Xl24Ywh3jUgB4cXE6t762ipKqWndFLI2kpEVEXGPP95C/FSxW6PMrCI11WdFhAb7MuLg3o1IieeWmodh9Tt/RUtqf6upqBg4ciMViYf369Z4OR0RaWnBHcy6XgA5QWWQmLmUFDd7cZrXw0Lk9+fe1g/D3tbJwxwEuffZH0g+UuS9maTAlLSLSfFmrIGul+b7n+RCZ4pJi6xzO+ve/GhTPG7cMJ9iu8UPkxB566CHi4tTPSaRdC+gAgyabCUx1Gax/E4ob10fl4gFxfDBtFLFh/qQfKOf15fvcFKw0hpIWEWmevM2we4H5vus4iOnnkmK/2pTLuf9aQn5JVf0yq1VNwuTEvvrqK+bPn88TTzzh6VBExNPsITBwMoR1NkcU2/A2HG5c4tG3cxif3nUGU0YlM/38nm4KVBpDSYuINN3BPbD9C/N9/BBIHOGSYuet28+db61ld0EZry7b65Iype3Kz89n6tSp/Pe//yUwMPC061dXV1NSUnLMS0TaGN8A6H8NdEgGR605DH/h7kYV0THEzoyL+9Q3SXY4DV7+IZ2qWocbApbTUdIiIk1TvP8Xk0f2gW4TXDIXy9srM7n/vQ04DbhqSDwPTOrhgmClrTIMgylTpjBt2jSGDBnSoG1mzZpFWFhY/SshIcHNUYqIR/j4mYPCRKWCsw42fwgF25pc3D++2c5jX27j6heXk1dcdfoNxKWUtIhI45UdgE3vg6PO7L/S0zWTR76yNIPpH23CMOCGkUn87bL+2NQkrF2aMWMGFovllK/Vq1fzn//8h5KSEqZPn97gsqdPn05xcXH9Kysry41HIiIeZfMxB4fp1Nt8yLb1E7NZcxOMTe1IeKAvG/YXc9EzS1mb2fDRyaT5LIZhtOgg1CUlJYSFhVFcXExoaGhL7lpEXKHikDkiS005hMbBgGvNp1nN9OzC3Tz+zQ4AbjuzK78/r6eGNXax1nT+LSwspLCw8JTrJCcnc8011/DZZ58d82/F4XBgs9mYPHkyr7322mn31Zp+FxFpIqcTdn4FuRvNh2zdz4G4QY0uJvNgBVNfX82O/FL8bFYe+1Vfrhyi2trmaOg5WEmLiDRcVYk5EktlkTkyy8DJLpk8sry6joueWUr6gXLuPTuV+yakKmFxg7Z4/s3MzDymT0pOTg7nnHMOH3zwAcOHDyc+Pv60ZbTF30VETsAwYNd8yF5rfk6dBPFpjS6mrLqO+99dz/yt+QDcPLoLD5/fEx+bGjA1RUPPwRo7VEQapqYCNr5rJiwBHcwOji6a7T7I7sNbt45gwbZ8rhuR5JIypX1ITEw85nNwcDAAKSkpDUpYRKQdsVjMRMXqYw7Tv2s+GA5IGNaoYoLtPrxwXRpPf7eLf3+3izdX7OOywZ3p2znMTYELKGkRkYaorYKN75izDNtDYMA15qzDzeB0GqzLOkxaUgQAMWH+SlhERMS9LBZIOQusNti3HHZ/Z/Z1aeTol1arhfsndqdnTAgBfjYlLC1ASYuInFpdDWx6D0rzwS/Q7MMSEN6sIh1Og4c+2Mi8dft5+ppBXDxAEwKKayQnJ9PCrZ5FpLWxWKDLWLDYYO9S2LPQTFySRjW6qPP7xR7zOaOwnOgQO0GaCNnl1PhORE7OUQubPzBnE/b1NxOWoMhmFVnrcHLvO+v4cO1+LBaLbjBFRKTlWSzQZQx0OdP8nL4Y9v7YrCIzCsu56sXlXD9nBcWVtS4IUn5JSYuInJijDjZ/ZM4i7OMH/a+G4OhmFVlV6+D2N9by+cZcfG0Wnv31YC4Z2NlFAYuIiDRS8mjoOtZ8n/FDsxKX0qpaauqcrM0sYvLsnzhcXuOiIAWUtIjIiTjqYMs8OJRujnHf70pzeONmqKxxMPX11SzYlo/dx8pLNwzh3L4xLgpYRESkiZJGQddx5vtmJC7948N5e+oIIoL82JxdwjUv/URBqSahdBUlLSJyLKcDtn4MB3cfTVjCE0+72alU1Tq4ce5KluwqJNDPxtybhjK+R/NqbURERFwmaeSxicu+5U0qpndcKO/dNoLoEDs78ku55sWfyC2udF2c7ZiSFhE5yukwZwsu3GUOCdn3cuiQ3Oxi7T5W+saFEWL34b+3DGNUSlTzYxUREXGlpJFHm4qlL4LMFU0qplt0CO/dNpLO4QGk/9zPZf/hCtfF2U41K2mZNWsWFouF++67z0XhiIjHHElYDuwwh4LsexlEdHVJ0RaLhf93YS++vHdM/RDHIiIiXidplNlBH2DP95C1qknFJEcF8e5tI0iKDCQi0I+wAF8XBtk+NXk8tlWrVvHSSy/Rv39/V8YjIp5wXMJyOUSmNKvIgpIqnlm4mz9c0Au7jw2LxUJCRKCLAhYREXGT5DPMIZD3/gi7F4DVCp3TGl1MfIdA3rttJHYfKyH+Slqaq0k1LWVlZUyePJmXX36ZDh06uDomEWlJR/qwuDBhyS6q5KoXl/P68n3M+HSra+IUERFpKcljzOZiADvnQ+6GJhXTKdSf8EC/+s+vLdvL5uxiV0TY7jQpabnzzju54IILmDBhwmnXra6upqSk5JiXiHiJI6OEHdjpsoRl38FyrnphOXsPVhDfIYA7xjWvPBERkRZ3ZALK+KHm5x1fQf6WZhX52YYcHv10C9e+/BNrMw+7IMj2pdFJyzvvvMPatWuZNWtWg9afNWsWYWFh9a+EhIRGBykibuCohS0fHdvpvpkJy+6CUq58YTnZRZV0jQri/Wkj1SRMRERaJ4sFup0NnQeDYcC2z81WCU00rkdHhiZ3oLSqjutnr+Cn9IMuDLbta1TSkpWVxb333ssbb7yBv79/g7aZPn06xcXF9a+srKwmBSoiLlRXA5s+gIN7zGGN+1/Z7IRla04JV7/4EwWl1fToFMI7t40gNizARQGLiIh4gMUCqZMgpp/Zz2XrJ+a1swlC/H157eZhjO4WSXmNgxtfWcninQdcHHDb1aikZc2aNRQUFJCWloaPjw8+Pj4sXryYf//73/j4+OBwOI7bxm63ExoaesxLRDyorho2vguH94LN15zpvpnDGtc6nPzmv6s5WF5D386hvPObEUSHNOzBhoiIiFezWKDH+RDd0+wHuvkjKMpsUlGBfj7MuXEoZ/WMprrOydTXVjN/S56LA26bGpW0nH322WzatIn169fXv4YMGcLkyZNZv349NpvNXXGKiCvUVMD6t6B4P/jYYcC1zZ44EsDXZuXpqwcyJjWKN28dQYcgv9NvJCIi0lpYrdDrYojsBs462PgelOQ0qSh/XxsvXJfGeX1jqHE4uePNtWQUlrs44LanUUMeh4SE0Ldv32OWBQUFERkZedxyEfEy1WWw8R0oOwC+ATDgGgiJaVaRVbUO/H3NhxVDkiN4/eZhWCwWV0QrIiLiXaw26HMpbHofDu8zWy0Muh6CGj9hsp+Plf9cO4gH3t9AaqcQukQFuT7eNqZZk0uKSCtReRjWvWEmLPZgGHRdsxOW77fnM+YfC9mSc3ToRiUsIiLSptl8zYFrQmOhtgo2vG1eY5vAx2bln1cP5M7x3eqX1Tqcroq0zWl20rJo0SKefvppF4QiIm5RXmgmLJWHISAcBk5u0lOhX/pyUy6/eX0NB0qreW3ZXpeEKSIi0ir42KHfVea1tLoMNrxr/tkEv3zYV1Zdx1UvLmf2knRXRdqmqKZFpC0ryTETluoy8+Q66DoIjGhWkfPW7eeut9ZS5zS4aEAcj/2qn4uCFRERaSX8As1m1v5h5kPBje+aNS/N8NmGHNZlFvGXL7bxzPe7XBRo26GkRaStOpRudrqvrTSrsQdOBntIs4p8e2Um97+3AacBVw2J5+mrB+Jr02lERETaIXuImbj4BUFZAWz+wJwDrYmuGZrA/RO7A/DE/J08/s12DMNwVbStnu42RNqi/C2w8X3z5BnRBQb82nwq1ER1Did//XIb0z/ahGHAjSOT+Ntl/bFZ1YdFRETascAIc+oAHz8oyjLncXE2rV+KxWLhnrNTefj8ngA8u3APf/58mxKXnylpEWlrslbB1k/NSbCie0G/K82TaTNYLRZ2F5jtde8cn8KMi/tgVcIiIiICIZ3Ma63VBwp3wc6voBmJxm/OTOHPl/QB4JUfM/jDx5txOpW4KGkRaSsMA3Z/B7sXmJ/jh0DvS8whGptcpHmStFot/POqgbx8wxAePKenRgkTERH5pfBE85prsUDuRsj4oVnFXT8ymX9c0R+LBeZvySO/tHn9ZdqCRs3TIiJeyumA7Z9D/lbzc9dxkDjCPHk2gWEYzFmawa78Mv52eT8sFgthgb5M7N3JdTGLiIi0JR27Q/dzYcdXsG8Z+AVDfFqTi7tqSAKBfja6RQcTGxbgwkBbJyUtIq1dbRVs+cic6MpihZ7nQ0zTR/Qqq67joQ828OWmPAAuHBDLmNSOropWRESk7YobCDVlkLEEdn9r9ieN7tXk4i7sH3fM5w1ZRfSICamf2Lk9UfMwkdassgjW/ddMWGy+0P/KZiUsu/JLufiZpXy5KQ9fm4U/XdKHM7o1b04XEXdLTk7GYrEc8/r973/v6bBEpL1KGg2dB5vNtrd9BkWZLin2p/SDXP3Scqa+vprKGodLymxNVNMi0lqV5MKm96Gm3Jzlvt9VZmfAJvp0Qw6//3AjFTUOYsP8eXbyYAYndnBhwCLu86c//YmpU6fWfw4ODvZgNCLSrlks0G2iWeNyYCds+gAG39DsiZ2dhoHVYmHJrkJunLuSV6YMJdjefm7lVdMi0hod2Anr3zATluCOMPjGZiUsT327k3veXkdFjYPR3SL5/O4zlLBIqxISEkJMTEz9S0mLiHiU1Qq9LoawzlBXbU4+WV3arCJHpUTx+s3DCLH7sDLjENfNXkFxZdPnhWltlLSItCaGAZkrzD4sjjpzDpZB14N/aLOKHZYcgc1q4c7xKbx+83Aig+0uClikZfz9738nMjKSgQMH8thjj1FTU+PpkESkvbP5Qt8rzLlcqkpg43tmAtMMQ5IjeHPqcMICfFmfVcSvX/6JQ+Xt43xnMVp4xpqSkhLCwsIoLi4mNLR5N1oi7YrTAbvmQ85683PcIEidZD7NaYLiylrCAnzrP+87WE5SZJALAhVv1VbPv//85z8ZPHgwHTp0YOXKlUyfPp1LLrmE2bNnn3D96upqqquP3jiUlJSQkJDQ5n4XEfESlYdh7etQUwGRKWYi08Rr9xHbcku4fs4KCstqSI0O5q2pI+gY0jofODb02qSaFpHWoKYCNrxjJiwWC3SbAN3PadJJzzAMnl+0hzP/sZCMwvL65UpYxJvMmDHjuM71//tavXo1AL/97W8ZO3Ys/fv359Zbb+WFF15gzpw5HDx48IRlz5o1i7CwsPpXQkJCSx6aiLQ3AR3MySdtPnBwj/kAspl1Br1iQ3nnNyPpFGqnW3QwIf5tv2+LalpEvF15odnhvrLIrGrufSlEdWtSUcWVtTzw/ga+3ZoPwP0Tu3PP2amui1W8Wms6/xYWFlJYWHjKdZKTk/H39z9ueXZ2NvHx8fz0008MHz78uO9V0yIiHnFgp9m82zAgZbw5n1ozFZRWERVkx2ptvZM+N/Ta1PbTMpHWrHA3bPsE6mogINysUg5u2pwp23JLmPbGGvYdrMDPZmXmJX24ZqieMIt3ioqKIiqqaSPtrFu3DoDY2NgTfm+327HbW2czChFpxTp2h5SzYfcC2LMQ/MOaNYcLQHTI0Qc3hmHwzZY8zukTg6WJk0t7MyUtIt7IMCBzOWT8YL4PT4Q+vzInqWqCD9fs5w8fb6Kq1knn8ACev24w/ePDXRuziAcsX76cn376ifHjxxMWFsaqVav47W9/y8UXX0xiYqKnwxMROVbCUKgqgv2rYdvnYA81RxhrJsMweOD9jXy4dj/3TUjlvgndmx+rl1GfFhFvU1cDWz+G9MVmwtJ5MAy4pskJy+cbc/jd+xuoqnUytntHPr/7DCUs0mbY7Xbeffddxo0bR+/evXnkkUeYOnUqb7/9tqdDExE5sZSzIbIbOOtg8wdm8+9mslgsDE4KB+DpBbt4b3VWs8v0NqppEfEmFYdg84dmPxarDVInmqOENcOk3jEMSerAGalR3HNWaqtu9yryvwYPHsxPP/3k6TBERBrOaoXeF8O6/0LZAbPf6uAbwKd5zVYnD08i+3Alzy3aw8MfbSIm1J8zuzetSbk3Uk2LiLc4uAfWvGomLH5BMODaJicsa/Ydos7hBMDPx8rbvxnBfRO6K2ERERHxBj52c0QxvyDzur/1E3A6m13sg+f04NKBcdQ5DW5/Yw1bcopdEKx3UNIi4mmGAXuXmk9a6qrNtq1DboLwxneSdzoN/rVgF1e8sJzHv9lRv9zXpv/qIiIiXsU/7NihkNO/b3aRFouFf1wxgJFdIymvcXDT3FVkF1W6IFjP052MiCfVVJgz5GYsOdp/ZeBksIc0uqiiihpufm0V/1ywE8OA0uo6WnhEcxEREWmM0FjoeaH5PmsV5KxrdpF+PlZeuD6N7p2COVxRw9ackmaX6Q3Up0XEU0pyYMs8qCoxn7KkngOx/ZtU1Kb9xUx7Yw3ZRZXYfaz85dK+XDlEwxmLiIh4veheUHHQfIC5cz4ERECHpGYVGRbgy9ybhpF5sIKRKZEuCtSzlLSItDTDgOw1sOd7cDrMmXL7XgbB0U0q7p2VmTzy6RZq6pwkRgTy/HWD6RMX5uKgRURExG2SRpt9Wwq2mQ8002407w+aoXN4AJ3DA+o/F1XUEBbg22rncFHzMJGWVFtlnox2fWsmLB27Q9qUJics+SVV/OnzrdTUOZnQK5rP7j5DCYuIiEhrY7FAzwvM5mK1lbDpA7Ofq4vsyi/lgn8v5Yn5O06/spdSTYtISynJMUcHqSwyhzNOOQs6p5knqibqFOrP3y/vT+ahCm4fm6LRwURERFormy/0uQzWvmbWumz7DPpe3qz7hCM27i8mu6iSZxfuoXN4IL8e3vom31VNi4i7GQZkroC1/zUTFv8wGHQdxA9p0onou235rNp7qP7zRQPiuHN8NyUsIiIirZ1/qJm4WH2gcBdk/OCSYi9Pi+fes1MB+OPHm/h+e75Lym1JSlpE3Kmm3BzKeM/3YDihYw8YcjOExjW6qFqHk8e/2c4tr63mjjfXcqDUddXGIiIi4iXCOkOPc833+5aZ/Vxc4L4JqVyZFo/TgDvfXMfG/UUuKbelKGkRcZeDe2DVHPNPqw90Pwf6/Ap8/Rtd1Ir0g5z/ryU8u3APABf0iyUswNfVEYuIiIg3iOkHCcPM99s/h7KCZhdpsVj462X9GJMaRWWtg5tfXUXWoYpml9tSlLSIuJqjDnYtMOdfqSmHoChzFJDOgxvdHOxgWTUPvL+Bq1/6iV0FZUQE+fGfawcx4+I++Pnov6+IiEib1XU8dEg27ys2f2h20G8mX5uV5yYPpldsKIVlNfzli63Nj7OFqCO+iCuVFcC2T6HsgPm5cxqkjDc71zVSYVk1E55aTFFFLQDXDkvg/87tSXignysjFhEREW9ktULvS8yO+ZVF5mA+/a4ylzdDiL8vc6cM5W9fbWPmxX1dE2sLUNIi4gpOJ+xfaXaYczrALxB6XABR3ZpcZFSwnbHdO7Ijr5THftWXtKQIFwYsIiIiXs8v0BxBbO1rcCgDMhabD0ObKSbMn6evGeSCAFuOkhaR5qo8DNu/hKJM83NUKvQ4D/yCGlVMeXUd//l+NzeMTCLu58mg/nJpXwJ8bfjY1BRMRESkXQqOhp4XwpaPIfMnCImF6J4u3cWrP2aQW1LF9PN6ubRcV1LSItJUhgG562H3d+CoNZuAdZsAsQMa1XfFMAy+2ZLPzM+2kFtcxd7Ccl64Pg0wq3BFRESknYvuZc73lrXS7JgfFGW+XGBzdjEzPjP7tsSFBXDjqGSXlOtqenwr0hRVxWZH+x1fmwlLeAIMvQXiBjYqYck6VMEtr61m2htryC2uIiEigKuHJrgvbhEREWmduo6HDknmfcfmD6G2yiXF9u0cxoPn9ABgxmdb+GZLnkvKdTUlLSKNYRiQsw5WzYZD6eZQxt3OhoGTIaBDg4upqXPy7MLdTPznYr7fXoCvzcKd41OYf99YxveMduMBiIiISKt0pGO+fyhUHDJrXAzDJUXfMS6Fa4clYhhwz9vrWJt52CXlulKjkpbnn3+e/v37ExoaSmhoKCNHjuSrr75yV2wi3qWyCDa+a9au1NWYE0QOudkcR72RQxnP/TGDx7/ZQVWtkxFdI/jq3jE8eE5PAvxs7oldREREWj+/IOhzGVhtULgLsla4pFiLxcKfL+nDWT2jqa5zcutrq9lbWO6Ssl2lUUlLfHw8f/vb31i9ejWrV6/mrLPO4pJLLmHLli3uik/E85xOyFr1c+1KxtHalUHXQ1Bkk4q8fmQSAxLCeeqqAbw9dQTdokNcHLSIiIi0SaGxZh9agPRFcHivS4r1sVn5z7WD6Nc5jEPlNUyZu5Ly6jqXlO0KFsNoXr1SREQEjz/+OLfcckuD1i8pKSEsLIzi4mJCQ0Obs2sR9ys7ADu+NDu/gdl3pcf5ENjw4YedToN3V2fxzZY8XrlxKFarWStjGAaWRtbQiDSHzr8npt9FRFodw4DtX0DeJnNY5LSbzGZjLlBQWsUVzy/nhpFJ3HJGF7ffqzT0HNzk0cMcDgfvv/8+5eXljBw58qTrVVdXU11dfUxgIl7PUQv7foTMFWA4wcfP7AAXN6hRTcG25pTwx483sTazCIDPNuZwycDOAEpYREREpGksFuh+DpTlmQ9Yt34CA39tNhtrpugQf76570yva7Le6I74mzZtIjg4GLvdzrRp05g3bx69e/c+6fqzZs0iLCys/pWQoJGRxMsdSodVc2DfcjNhiUqFoVOh8+AGJyxl1XX8+fOtXPTMUtZmFhHkZ+P/XdibC/rFujl4ERERaRdsvmb/Fh8/KN5vNhVzkV8mLCVVtbzx0z6a2Tir2RrdPKympobMzEyKior48MMPmT17NosXLz5p4nKimpaEhARVw4v3qS6F3QugYLv52R4CqZOgY/cGF2EYBl9vzmPmZ1vJKzGHIjy/XwyPXNiHmDB/d0Qt0mBqBnVi+l1EpFU7sAM2f2S+73t5o+5bTqe6zsElz/zI9rxS/nhBL24d09VlZR/htuZhfn5+dOvWDYAhQ4awatUq/vWvf/Hiiy+ecH273Y7dbm/sbkRajtMJ2Wtg7w/mqGAWC3QeAl3GgE/j/u0aBjy/eA95JVUkRgTyp0v6MK6HhjAWERERN+nYA+KHwv5V5jDIwTc1ahqGU7H72LhscGf++uV2/vLFNmLDArigv2dajTR7nhbDMI6pSRFpVQ7vg9VzzBqWI8MYp90EqRManLDU1DmpqnUAYLVaeOzSftw1vhvzf3umEhaRFvLFF18wfPhwAgICiIqK4rLLLvN0SCIiLSdlvHkPU1cNW+aBw3Wjfk0d05UbRyYB8Nv31rNq7yGXld0YjappefjhhznvvPNISEigtLSUd955h0WLFvH111+7Kz4R96gqhj0LoWCb+dk3ALqOhdiBjepov3zPQf748SbO6xvLAz/PJtsvPox+8WFuCFpETuTDDz9k6tSp/PWvf+Wss87CMAw2bdrk6bBERFqO1QZ9LoXVr0BpPqQvhNSJLinaYrHwyEV9yCmu4tut+dz62mo+umMUKR2DXVJ+QzUqacnPz+f6668nNzeXsLAw+vfvz9dff83Eia75UUTczlFrTsSUudx8CmGxmCOCdTnTTFwaqLCsmr9+sY2P1mUD8NHa/dx1Vjf8fb1rpA2Rtq6uro577733uKH3e/To4cGoREQ8wD8Mel4Em96H/ashPNFsOuYCNquFf18ziGtf/on1WUVMmbuSj24fTceQlusC0qikZc6cOe6KQ8S9DMOsVUlfCFU/D7sdnmBOzhQS0+BinE6Dt1dl8vevtlNSVYfFApOHJ/LgpJ5KWEQ8YO3atWRnZ2O1Whk0aBB5eXkMHDiQJ554gj59+pxwGw3FLyJtVlQ3SBxuTtmw/QsIjnZZ/5YAPxtzbhzCZc8vo7rWSVFFjfcmLSKtUvF+2P3d0Qki/UPNOVeiezWqKdjuglJ+9/5GNmQVAdC3cyh/ubQfAxPCXR+ziDRIeno6ADNmzOCpp54iOTmZJ598krFjx7Jz504iIo6fCHbWrFnMnDmzpUMVEWkZXcaa9z7F2eb8LYOud8n8LQCRwXZeu2kYdl8rsWENb6HiCs3uiC/itSoOmZ3R1v7XTFhsvmYzsGG/gU69G5WwAIQF+LE9t4Rguw8zLurNJ3eeoYRFxE1mzJiBxWI55Wv16tU4nU4A/vCHP3D55ZeTlpbG3LlzsVgsvP/++ycse/r06RQXF9e/srKyWvLQRETcy2qD3peArz+U5Lp0/haA5KigYxKW9ANlLTKHi2papO2pKYd9yyB7rTk5pMUCMf3MhMUe0rAi6px8vC6bdVlFzLqsHwAdQ+z865qBDE7sQHSo5lwRcae77rqLa6655pTrJCcnU1paCnDMXGF2u52uXbuSmZl5wu00FL+ItHn+YdDjAtj8IWSthA7JEJni8t18vjGH//fxZj6+czRJkUEuL/+XlLRI21FXbf7HzFphdrgH8z9o13Fmm84GqKip4+2VWcxekk5usTk55DVDExjwc43KuX01o71IS4iKiiIqKuq066WlpWG329mxYwdnnHEGALW1tezdu5ekpCR3hyki4r06dofOaeZcdNs/hyE3N/jhbUOVV9fx31uGuz1hASUt0hY46iBnHWQug5oKc1lIJ7PfSkSXBhVRXFHLa8v3MvfHDA5XmAlPdIidqWO6khLdskP6iUjDhYaGMm3aNB599FESEhJISkri8ccfB+DKK6/0cHQiIh6WchYUZ0FZAWz7DPpfA1bX9Q65emiiy8o6HSUt0no5HZC3Efb+CNVmExECI8xmYB17NrjPyqb9xVzz0nLKa8wJIpMiA7ntzBQuT+uM3Ucjgol4u8cffxwfHx+uv/56KisrGT58ON9//z0dOrhmxBwRkVbL5gO9L4U1r5gTametgKSRno6qSZS0SOvjdED+ZrPfSmWRucweAsmjIaZ/g0bIqKp11A9R3CMmhLAAXxIiArljfDfO7xuDj01jVIi0Fr6+vjzxxBM88cQTng5FRMT7BEVC6iTY/iVk/AAdkiA0ztNRNZqSFmk9TpSs+AVB0ihzJnvb6f85b8st4blFe9i4v4jv7h+Lj82Kn4+VD24fRWyYP5ZGjigmIiIi4vVi+sOhdCjYDls/hSE3gU/rGpBESYt4P0ed2Qws8yeoKjaX+QVCwghzNnsfv9MWsXrvIZ5btIfvtxfUL/sp/RBnpJodfePCW3ascREREZEWY7FA9/PMKSAqD8Oub6HXhZ6OqlGUtIj3qquB3A1m+8sjfVb8AiFhOMQNPm2yYhgGi3ce4LlFe1iZcQgAqwXO7xfL7eNS6BMX5u4jEBEREfEOvv7Q62JY/ybkbYKIrua8da2EkhbxPrWV5vB8+1eb78Hss5I4AmIHmJNENsDm7BKmzF0FgK/NwuWD47ltbApdotw/LJ+IiIiI1wlPgKTRsHcp7Pwawjqbc7q0AkpaxHtUHjYTldz1ZpMwgIAOkDgcOvU7bZ+Vmjonm3OKGZxojhjULz6M8T06ktIxmFvHdCUmTBNCioiISDuXNNrs31KSA9s+hwHXunQYZHdR0iKeV5wN+1fBge1gGOay4GhIHGkOXXya/0jl1XW8vTKT2UsyKKqs4cf/O4vIYLNz2StThqpzvYiIiMgRViv0ughWvwJFmbB/pdmaxcspaRHPcDqhcKf5H6U4++jyiC5mn5UOyaedZ6WoooZXl+3l1WV7Kfp5QshOoXYyCsvrkxYlLCIiIiL/IzACUif+YhjkZAiJ8XRUp6SkRVpWTYXZuT5nLVSVmMusNojuDfFDzZnsT+NQeQ3PL9rNmysyqfh5QsjkyEBuG5vCZYM1IaSIiIjIacX0h4O74cBO2PYZpE1pcL9hT1DSIi2jJAey10LBNnD+3F/FL9CcX6XzYLOjfQPVOpy8tmwfNQ4nvWJDuWNcCuf3i8VmVa2KiIiISIMcGQa5OBvKCyF9MaRO8HRUJ6WkRdynrgYKtkLOOijNO7o8pBN0HmLWrpyic71hGGzJKeGzDTlkFJbz0g1DAOgU6s9D5/YgJTqYcd07qgmYiIiISFP4BULPC2Dje2b/4sgUs6m+F1LSIq5Xmm+OAJa/2Uxc4OcmYL3M+VVC407ZX2V3QRmfbcjhs405pB8or1+eUVheP1zxrWO6uvMIRERERNqHyBRzsu6cdbD9Cxh6qzmni5dR0iKuUVsFBVvM/iql+UeXB3SAuIEQ0w/8Tj0/yrdb8/nntzvZmltSv8zuY+XsXtFcPCCOWA1ZLCIiIuJ6KWfB4b3m9BO75kPviz0d0XGUtEjTOZ1wOMOcVbVw19G+KlYbRKWa/VVOMQrYgdJqbFYLEUHmzPZ1Didbc0vwsVoYkxrFxQPjmNg7hmC7/pmKiIiIuI2PnzkM8rr/Qv4W6NjDfHkR3Q1K4xgGlOWbTb8KtkF12dHvgjtCzADo1MdsI3kCxRW1fL0ll0835LB8z0HuOTuV+yZ0B2B8z2j++qt+nNc3hg4/JzIiIiIi0gLCOpvztexbDju/hrD407aSaUlKWqRhKg6ZSUrBVnOEiSN8A8wkJaYfBHc6Ya1KeXUdC7bl89mGHBbvPECtw6j/LqPwaJ8Vf18bvx6e6NbDEBEREZGTSDrDHAa57ICZuPS57LTz5rUUJS1ycpVFcGAHHNgGJblHl1t9IKobdOoLEV3N5mAn4XAajH9iEQWl1fXLesaEcNGAOC7qH0di5IlrZERERESkhdl8oOdFsOZVc/6W/C0Q09fTUQFKWuR/VRwy+6cc2G7OrXKExWL2T4nuBVE9TjiqRJ3DybI9B/lxTyG/P7cnFosFm9XCmNSOrN53iIsHxHHRgDi6d2r4nCwiIiIi0oJCOkHyGZDxg9kpv0NSo+bTcxclLe2dYUBZARTuNF9lBUe/s1ggLAE69jQ7Y9mDj9vc6TRYk3mYT9fn8OWmXA6Wm0McX9Q/jr6dwwD40yV9CPSzaT4VERERkdYgcaR5X1iaBzu+hn5XeLyZmJKW9shRB0X74FC6WatSVXz0O4sVwhOhY3ezRuUEiQrAvoPlvLkik8835JBTXFW/PCLIj/P7xRD0ixG/gjT6l4iIiEjrYbVCzwthzVyzj0v+ZrP/sgfpbrK9qCwyk5RD6eY43I7ao9/ZfKBDF3OY4sjUE478VVZdR2WNg44hdgAyD1Xw0g/pAITYfZjUJ4aLBsQyulsUvjZrCxyQiIiIiLhNcEezmVj6Ytj1rdlNwIPNxJS0tFV1NVCUaSYohzOOHfELzBqUyG7mq0My2HzrvzIMg/2HK1mbeZg1+w6zeu9htueVcO2wRB77lZllj+wayZVp8ZzdqxPjenTE3/fknfFFREREpBVKGGE2EyvJ9XgzMSUtbYWjDkqyzWZfh/dBaS44HUe/t1ghNM4c7Ssy5YTDE9fUObnv3XWs2XeY/JJq/tf+w5X1731sVh6/coDbDkdEREREPOxIM7HVr3i8mZiSltaqrgZKc6Aoy6xRKck5OiP9EQHhZi1Khy7myA++AQAcLKtm7bYC1uw7jNMwePj8XgD4+VjZnF1Cfkk1PlYLfTqHkZbYgSHJHRic2IGYsONHDBMRERGRNiwo6mgzsd0LzPvKk/R5diclLa2BYUB1iZmYFGdDyX4ozQfDeex6fkFmchKeCOFJEBgBwO6CMlatO8CafWZzr19O6Bhi9+H/zu2JzWrWujxyYW9C/H0YkBCuJl8i4vUWLVrE+PHjT/jdypUrGTp0aAtHJCLSBiUMN6fDKM03h0Hue1mLh6CkxRvVVprNu0rzzESlNBeqy45fzz8UwuLNYYl/TlLKaxxsyy1hyM8JC8Cjn27mx90Hj9k0NTqYtKQODE7qgMNp1CctE3p3cuuhiYi40qhRo8jNzT1m2f/7f/+PBQsWMGTIEA9FJSLSxlht0OOCnyed3AEF2yG6Z4uGoKTFk47UoJQdgLJ881Wad+wQxEdYrBAcDaGdIawzhMVj2EPJLqpkzb7DrF2dy+p9W9mWW4LTgDV/nEBksDnS1xndOuJ0QlpSBzNRSexAWKDv8fsQEWll/Pz8iImJqf9cW1vLp59+yl133aW5oUREXCmkEySOgH3LYNc3ZsueE4w46y5KWlqCYUBNOVQchIpCcySv8gPmq7bqxNsEhENIrNl5PiQGZ1AMhs23vkbkrRWZ/Ou7VSfsMB8X5k92UWV90nL7uBRuH5firqMTEfEan376KYWFhUyZMsXToYiItD1Jo83RxMoLYc930OuiFtt1o5KWWbNm8dFHH7F9+3YCAgIYNWoUf//73+nRo4e74mtdaqugqggqD5uvikNmolJ56OTJicVq9j0J7sQhawe2lQawryaE/UUGufuqyCmqJLd4D3nFW5h94xDO7N4RMDvN55dUY7Na6BMXyuDEDvU1KXHhAS13zCIiXmTOnDmcc845JCQknHSd6upqqquPPvApKSlpidBERFo/mw/0OB/W/RfyNkN0b3NU2hbQqKRl8eLF3HnnnQwdOpS6ujr+8Ic/MGnSJLZu3UpQUJC7YvQOTifUlJmv6lKoKoHqYvPPqmIzWTlJYlLjcFJaXcdhRyAHnMHk1AazrzqI9IoAbpqYRlqXaAC+W53Fgx9uBPJPWE5u8dEhh8f36MjbU0cwICGMQD9VmIlI2zJjxgxmzpx5ynVWrVp1TL+V/fv388033/Dee++dcrtZs2adtmwRETmJsM7QeQjsXwU7v4Ght4KPn9t3azEMw2jqxgcOHCA6OprFixdz5plnNmibkpISwsLCKC4uJjQ0tKm7bh7DMGeEd1SbiUbdz6/aCrMTfG0F1FSYTbpqy80/a8rN7f5HndNJebWD0qpaMzGp9aVrYjwxnWIhIILv9tXy+6+yOUwwdSfIEf9+eT+uHpoIwKq9h5jx6RZiwwKIC/c/7s9Oof6abV5Emswrzr8NVFhYSGFh4SnXSU5Oxt//6FDsf/7zn/nPf/5DdnY2vr4n77d3opqWhISEVvG7iIh4hboaWPWy+fA+YSh0m9Dkohp6bWrWI/riYrPDeERExEnXcWk1/OF97Nq6hhXphwCwYAAGFsBiOLHgZHRKJAnhfuB0kFVYwtqMA1ipw+asw2bU1r8shkHP2FBiQs0L3oGyarZkn6AD/M+6dwohrkMQ+AWxu8TCh1tKyCr3YX+lHyUEUmIEUUIgNfjyt579uKaXmYgE1BVygHJC7D7E/iIBiQsLIDY8gGHJR3+7ockRfHHPmKb/PiIibURUVBRRUVENXt8wDObOncsNN9xwyoQFwG63Y7fbmxuiiEj75eMH3c+Fje/B/tVmM7HQOPfusqkbGobB/fffzxlnnEHfvn1Pup5Lq+HLCqjOWEnhjhM3nwKotsdBjTnhTXleCRnpeSddt1NYADGRHcDHn4KyGj7OrKYSO5X4UWnYqcCfcuxUGP78rl8aV4/sAVYr+bsLeX7Rivpy7D5W4sID6B5mJiWJEUdHUhiSHMGmGZMI8ddoXSIi7vL999+TkZHBLbfc4ulQRETah8gU6NQH8reYc7cMvhHcOGpjk5OWu+66i40bN7J06dJTrjd9+nTuv//++s9HquGbJDSWgO5jiPU7/IuFFsCCYbFgYMXevRNEhoDVil/HGsL8D+G02HBYfHFYfXFafKmz+uKw+OHsHw+dwwGwF5QS75dz0l33SOwEVrNpVp+4UF66Po248ABiw/yJCPI76dCafj5W/HzUpEtExJ3mzJnDqFGj6NWrl6dDERFpP7pNAEcNdB3v1oQFmtin5e677+bjjz/mhx9+oEuXLo3atjW1qRYRaUt0/j0x/S4iIp7jlj4thmFw9913M2/ePBYtWtTohEVERERERKSxGpW03Hnnnbz11lt88sknhISEkJdn9hcJCwsjIEBzg4iIiIiIiOs1qrPF888/T3FxMePGjSM2Nrb+9e6777orPhERERERaeca3TxMRERERESkJWlYKxERERER8WpKWkRERERExKspaREREREREa+mpEVERERERLyakhYREREREfFqjRo9zBWOjEBWUlLS0rsWEWnXjpx3NRLksXRdEhHxnIZem1o8aSktLQUgISGhpXctIiKY5+GwsDBPh+E1dF0SEfG8012bLEYLP3JzOp3k5OQQEhKCxWJp9PYlJSUkJCSQlZVFaGioGyL0bjp+Hb+OX8ff1OM3DIPS0lLi4uKwWtU6+Ahdl5pHx6/jb8/HD/oNWura1OI1LVarlfj4+GaXExoa2i7/YRyh49fx6/h1/E2hGpbj6brkGjp+HX97Pn7Qb+Dua5MetYmIiIiIiFdT0iIiIiIiIl6t1SUtdrudRx99FLvd7ulQPELHr+PX8ev42+vxe6v2/vei49fxt+fjB/0GLXX8Ld4RX0REREREpDFaXU2LiIiIiIi0L0paRERERETEqylpERERERERr6akRUREREREvJrXJS3PPfccXbp0wd/fn7S0NJYsWXLK9RcvXkxaWhr+/v507dqVF154oYUidY/GHP9HH33ExIkT6dixI6GhoYwcOZJvvvmmBaN1j8b+Gzjixx9/xMfHh4EDB7o3QDdr7PFXV1fzhz/8gaSkJOx2OykpKbzyyistFK3rNfb433zzTQYMGEBgYCCxsbHcdNNNHDx4sIWidZ0ffviBiy66iLi4OCwWCx9//PFpt2lr5z9vpmtT+7426bqk61J7vC6Bl12bDC/yzjvvGL6+vsbLL79sbN261bj33nuNoKAgY9++fSdcPz093QgMDDTuvfdeY+vWrcbLL79s+Pr6Gh988EELR+4ajT3+e++91/j73/9urFy50ti5c6cxffp0w9fX11i7dm0LR+46jf0NjigqKjK6du1qTJo0yRgwYEDLBOsGTTn+iy++2Bg+fLjx7bffGhkZGcaKFSuMH3/8sQWjdp3GHv+SJUsMq9Vq/Otf/zLS09ONJUuWGH369DEuvfTSFo68+b788kvjD3/4g/Hhhx8agDFv3rxTrt/Wzn/eTNem9n1t0nVJ16X2el0yDO+6NnlV0jJs2DBj2rRpxyzr2bOn8fvf//6E6z/00ENGz549j1l22223GSNGjHBbjO7U2OM/kd69exszZ850dWgtpqm/wdVXX2388Y9/NB599NFWfXFo7PF/9dVXRlhYmHHw4MGWCM/tGnv8jz/+uNG1a9djlv373/824uPj3RZjS2jIhaGtnf+8ma5N7fvapOuSrku6Lpk8fW3ymuZhNTU1rFmzhkmTJh2zfNKkSSxbtuyE2yxfvvy49c855xxWr15NbW2t22J1h6Yc//9yOp2UlpYSERHhjhDdrqm/wdy5c9mzZw+PPvqou0N0q6Yc/6effsqQIUP4xz/+QefOnenevTsPPPAAlZWVLRGySzXl+EeNGsX+/fv58ssvMQyD/Px8PvjgAy644IKWCNmj2tL5z5vp2tS+r026Lum6pOtS47jz/OfTrK1dqLCwEIfDQadOnY5Z3qlTJ/Ly8k64TV5e3gnXr6uro7CwkNjYWLfF62pNOf7/9eSTT1JeXs5VV13ljhDdrim/wa5du/j973/PkiVL8PHxmn/OTdKU409PT2fp0qX4+/szb948CgsLueOOOzh06FCraz/clOMfNWoUb775JldffTVVVVXU1dVx8cUX85///KclQvaotnT+82a6NrXva5OuS7ou6brUOO48/3lNTcsRFovlmM+GYRy37HTrn2h5a9HY4z/i7bffZsaMGbz77rtER0e7K7wW0dDfwOFw8Otf/5qZM2fSvXv3lgrP7Rrzb8DpdGKxWHjzzTcZNmwY559/Pk899RSvvvpqq3yqBY07/q1bt3LPPffwyCOPsGbNGr7++msyMjKYNm1aS4TqcW3t/OfNdG1q39cmXZd0XfolXZdOzV3nP695BBAVFYXNZjsucy0oKDguYzsiJibmhOv7+PgQGRnptljdoSnHf8S7777LLbfcwvvvv8+ECRPcGaZbNfY3KC0tZfXq1axbt4677roLME+WhmHg4+PD/PnzOeuss1okdldoyr+B2NhYOnfuTFhYWP2yXr16YRgG+/fvJzU11a0xu1JTjn/WrFmMHj2aBx98EID+/fsTFBTEmDFj+Mtf/tKqnmg3Vls6/3kzXZva97VJ1yVdl3Rdahx3nv+8pqbFz8+PtLQ0vv3222OWf/vtt4waNeqE24wcOfK49efPn8+QIUPw9fV1W6zu0JTjB/Mp1pQpU3jrrbdafXvJxv4GoaGhbNq0ifXr19e/pk2bRo8ePVi/fj3Dhw9vqdBdoin/BkaPHk1OTg5lZWX1y3bu3InVaiU+Pt6t8bpaU46/oqICq/XY05jNZgOOPtlpq9rS+c+b6drUvq9Nui7puqTrUuO49fzX7K78LnRkWLk5c+YYW7duNe677z4jKCjI2Lt3r2EYhvH73//euP766+vXPzKs2m9/+1tj69atxpw5c9rEsJINPf633nrL8PHxMZ599lkjNze3/lVUVOSpQ2i2xv4G/6u1j9LS2OMvLS014uPjjSuuuMLYsmWLsXjxYiM1NdW49dZbPXUIzdLY4587d67h4+NjPPfcc8aePXuMpUuXGkOGDDGGDRvmqUNostLSUmPdunXGunXrDMB46qmnjHXr1tUPq9nWz3/eTNem9n1t0nVJ16X2el0yDO+6NnlV0mIYhvHss88aSUlJhp+fnzF48GBj8eLF9d/deOONxtixY49Zf9GiRcagQYMMPz8/Izk52Xj++edbOGLXaszxjx071gCOe914440tH7gLNfbfwC+19ouDYTT++Ldt22ZMmDDBCAgIMOLj443777/fqKioaOGoXaexx//vf//b6N27txEQEGDExsYakydPNvbv39/CUTffwoULT/n/uT2c/7yZrk3t+9qk65KuS+3xumQY3nVtshhGO6irEhERERGRVstr+rSIiIiIiIiciJIWERERERHxakpaRERERETEqylpERERERERr6akRUREREREvJqSFhERERER8WpKWkRERERExKspaRERERHxYjNmzGDgwIGeDkPEozS5pIiIiIiHWCyWU35/44038swzz1BdXU1kZGQLRSXifZS0iIiIiHhIXl5e/ft3332XRx55hB07dtQvCwgIICwszBOhiXgVNQ8TERER8ZCYmJj6V1hYGBaL5bhl/9s8bMqUKVx66aX89a9/pVOnToSHhzNz5kzq6up48MEHiYiIID4+nldeeeWYfWVnZ3P11VfToUMHIiMjueSSS9i7d2/LHrBIEylpEREREWllvv/+e3Jycvjhhx946qmnmDFjBhdeeCEdOnRgxYoVTJs2jWnTppGVlQVARUUF48ePJzg4mB9++IGlS5cSHBzMueeeS01NjYePRuT0lLSIiIiItDIRERH8+9//pkePHtx888306NGDiooKHn74YVJTU5k+fTp+fn78+OOPALzzzjtYrVZmz55Nv3796NWrF3PnziUzM5NFixZ59mBEGsDH0wGIiIiISOP06dMHq/Xos+dOnTrRt2/f+s82m43IyEgKCgoAWLNmDbt37yYkJOSYcqqqqtizZ0/LBC3SDEpaRERERFoZX1/fYz5bLJYTLnM6nQA4nU7S0tJ48803jyurY8eO7gtUxEWUtIiIiIi0cYMHD+bdd98lOjqa0NBQT4cj0mjq0yIiIiLSxk2ePJmoqCguueQSlixZQkZGBosXL+bee+9l//79ng5P5LSUtIiIiIi0cYGBgfzwww8kJiZy2WWX0atXL26++WYqKytV8yKtgiaXFBERERERr6aaFhERERER8WpKWkRERERExKspaREREREREa+mpEVERERERLyakhYREREREfFqSlpERERERMSrKWkRERERERGvpqRFRERERES8mpIWERERERHxakpaRERERETEqylpERERERERr6akRUREREREvNr/B7S+HcwfOTXAAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t1, x1 = integrate_euler(0,1, system, 0.1, X0)\n",
"t2, x2 = integrate_euler(0,1, system, 0.01, X0)\n",
"\n",
"plt.figure(figsize=(10,3.5))\n",
"plt.subplot(1,2, 1)\n",
"\n",
"plt.plot(t1, x1[0], label=\"h=0.1\", ls=\"--\")\n",
"plt.plot(t2, x2[0], label=\"h=0.01\", alpha=.5)\n",
"plt.title(\"x\")\n",
"plt.legend();\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.plot(t1, x1[1], label=\"h=0.1\", ls=\"--\")\n",
"plt.plot(t2, x2[1], label=\"h=0.01\", alpha=.5)\n",
"plt.title(\"y\")\n",
"\n",
"plt.xlabel('Time')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align*}\n",
"\\frac{dR}{dt} &= \\frac{1}{0.02}(-R + S(P)) \\\\ \n",
"S(P) &= \\begin{cases}\n",
"\\frac{100P^2}{25 + P^2} & \\text{for } P \\geq 0 \\\\\n",
"0 & \\text{for } P < 0\n",
"\\end{cases} \\\\\n",
"P(t) &= 20\\sin(2\\pi10t)\n",
"\\end{align*}\n",
"$$\n",
"\n",
"\n",
"where $R(0)=0, T=1, h=0.004$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def P(t):\n",
" return 20 * np.sin(2 * np.pi * 10 * t)\n",
"\n",
"def S(p):\n",
" return (100 * p**2) / (25 + p**2) if p >= 0 else 0\n",
"\n",
"def system(t, x0):\n",
" dRdt = -1/0.02 * (x0 + S(P(t)))\n",
" return dRdt\n",
"\n",
"def integrate_rk4(ti, tf, function, h, x0):\n",
" x = np.zeros((len(x0), int((tf - ti) / h) + 1))\n",
" x[:, 0] = x0\n",
" t = np.linspace(ti, tf, int((tf - ti) / h) + 1)\n",
"\n",
" for i in range(1, x.shape[1]):\n",
" k1 = h * function(t[i-1], x[:, i-1])\n",
" k2 = h * function(t[i-1] + 0.5 * h, x[:, i-1] + 0.5 * k1)\n",
" k3 = h * function(t[i-1] + 0.5 * h, x[:, i-1] + 0.5 * k2)\n",
" k4 = h * function(t[i-1] + h, x[:, i-1] + k3)\n",
" x[:, i] = x[:,i-1] + (k1 + 2*k2 + 2*k3 + k4) / 6\n",
" \n",
" return t, x "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t, R = integrate_rk4(0,1, system, 0.004, [0])\n",
"\n",
"\n",
"t.shape, R.shape\n",
"plt.figure(figsize=(5,3.5))\n",
"\n",
"plt.plot(t, R[0], c='k');\n",
"plt.xlabel('Time [s]')\n",
"plt.ylabel(\"R\");"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 4
}