{ "cells": [ { "cell_type": "markdown", "id": "ef674ab4-d343-474a-9b6e-a3888c353796", "metadata": {}, "source": [ "## MT09 - TP7 - Automne 2024\n", "### Schémas numériques pour les équations différentielles\n" ] }, { "cell_type": "code", "execution_count": null, "id": "83e13287-4134-4b33-93ba-8a6120ff85d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3fe9daf9-8d95-4546-9983-987fbaaa6b56", "metadata": { "tags": [] }, "source": [ "### 1. Croissance cellulaire\n", "\n", "Dans les exercices de travaux dirigés, on a vu le modèle différentiel continu de croissance cellulaire\n", "$$\n", "\\frac{d\\rho}{dt} = \\sigma \\frac{\\rho}{\\rho_M}(\\rho_M-\\rho),\\quad t\\in [0,T]\n", "$$\n", "\n", "où $\\rho$ représente la densité de cellules par unité de surface. À cette équation différentielle, on associe la condition initiale $\\rho(0) = \\rho_0$, $0<\\rho_0 \\ll \\rho_M$. On rappelle que la solution exacte s'écrit\n", "\n", "$$\n", "\\rho(t) = \\rho_M \\, \\frac{e^{\\sigma t}}{\\frac{\\rho_M}{\\rho_0}-1+e^{\\sigma t}}.\n", "$$\n", "\n", "\n", "Le module ```scipy.integrate``` donne accès à la méthode ```odeint()``` qui résout numériquement un problème différentiel :\n", "\n", "```\n", "y = odeint(model, y0, t, tfirst='true')\n", "```\n", "\n", "(voir l'aide de ```odeint()```). Ecrire une fonction\n", "```croissanceCell(y,t)``` qui implémente la fonction de l'équation différentielle de croissance cellulaire. Résoudre ensuite numériquement le problème différentiel et comparer à la solution exacte $\\rho(t)$.\n", "\n", "Pour l'application numérique, on utilisera les paramètres\n", "$T=20$, $\\rho_M=1000$, $\\rho_0=5$ et $\\sigma=0.7$ et ```t = np.linspace(0,T, 100)```." ] }, { "cell_type": "code", "execution_count": 5, "id": "526623a5-7281-4d52-a273-b2a21957284c", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "def rho(t):\n", " sigma = 0.7\n", " rhoM = 1000\n", " rho0 = 5\n", " rho = rhoM * np.exp(sigma*t) / (rhoM/rho0 - 1 + np.exp(sigma*t))\n", " return rho" ] }, { "cell_type": "code", "execution_count": 7, "id": "b3abacb2-af35-4f4a-b671-9b6f3678bd8e", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# function that returns ydot\n", "def croissanceCell(t,y):\n", " sigma = 0.7\n", " rhoM = 1000\n", " ydot = sigma*(y/rhoM)*(rhoM-y)\n", " return ydot\n", "\n", "# initial condition\n", "y0 = np.array([5.0])\n", "# final time\n", "T = 20.0\n", "# time points\n", "tref = np.linspace(0,T, 100)\n", "# solve ODE\n", "yref = odeint(croissanceCell, y0, tref, tfirst='true')\n", "\n", "# plot results\n", "plt.plot(tref, yref, '.-', label=\"odeint()\")\n", "plt.plot(tref, rho(tref), '-g', label=\"exact\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)'); plt.grid();\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "039b31c2-1318-4f52-8a48-380ef43cd036", "metadata": {}, "source": [ "#### Schéma d'Euler explicite\n", "Ecrire une fonction python ```Euler(F, y0, t0, T, N)``` qui met en oeuvre le schéma d'Euler explicite générique pour une fonction $F$ (à valeurs scalaires ou vectorielles), une donnée initiale $y_0$, un temps initial $t_0$, un temps final $T$, sur une subdivision uniforme constituée de $N$ sous-intervalles, avec un pas\n", "$h=\\frac{T-t_0}{N}$. Les tableaux de sorties seront le tableau des temps discrets $t$ et le tableau (ou matrice) $z$ des états du système $y_n$ aux temps discrets $t_n$." ] }, { "cell_type": "code", "execution_count": 10, "id": "9eaabc75-4fbd-473e-91f3-9102b2733031", "metadata": { "tags": [] }, "outputs": [], "source": [ "def Euler(F, y0, t0, T, N):\n", " d = y0.size\n", " h = (T-t0) / N;\n", " t = np.linspace(t0, T, N+1)\n", " z = np.zeros((N+1, d))\n", " z[0,:] = y0\n", " for n in range(0, N):\n", " z[n+1,:] = z[n,:] + h*F(t[n], z[n,:])\n", " return t, z" ] }, { "cell_type": "markdown", "id": "e5a14aa1-5d27-4dc3-be95-799d28da8de7", "metadata": {}, "source": [ "Appliquez la méthode d'Euler au problème de croissance cellulaire. On prendra toujours $y_0=5$, $T=20$, et $N=50$. Tracer la solution numérique $t\\mapsto z(t)$ et comparer à la solution de référence obtenue avec ```odeint()```. " ] }, { "cell_type": "code", "execution_count": 13, "id": "320268fa-31c1-4102-890c-b87006abf763", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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wduxYUlNTadeuHRs3bsTH558fho8//hgXFxcGDhxITk4O3bp1Y8mSJWYbU3777be8+OKLprvR+vXrV+LaR5WprG++ilK9enWgYNStcJTu4MGDt63TqlUrjh49apZgGY1G0tPTHfpOMiGqmtScVPZc2kPs5Vh2XtjLwaSDXM48V3xhRYVGCUKrhOGi1ERrDMNTE0aj6vW4K6Q+tasFMOf30yi3JDtfDDRPdmw1IgMV+2EunEOlJkRdunQxG324lUqlYtq0aaaJt8Vxd3dn7ty5zJ07t8QyAQEBLF++/E66WmEq482Xl5dX5I47FxcXgoKCaN++Pe+//z6RkZGkpKTwxhtv3LatV199lfbt2/P8888zevRovLy8OHr0KOvXr+eLL74ozzCEEFZSFIXT10+zJWELOy/uZNfFXZxIOVFsWY2xBq5KJFpjBFqlNlpjOFqlFuqb7q1Wq2DHK10J8//n7tUQP/cKTXaEsJTdziESFWfDhg1mE9ehYDL0iRMn+Prrrxk5ciRt2rShYcOGzJw502zdp1vdddddbN26lddff5377rsPRVGoW7cu/fr1K+8whBAWiE+NJ/psNL+e/p3t57dyLafozSfemlooefVwVeriaqyL1lgHDd5EBnrSoW4QbWpXo21kADFnUnh9rXmyc3MyBJLsCPsnCVEVt2TJEpYsWVLi840bN2bnzp1mx24e1StulK9t27Zs3LjR9LjwklmhhISEO+u0EMJiOqOO6LPRRMdHs/6v9Zy6dsq8gOJCmMdd+KibkXojEldDQzT4FdvWjAF30aHuP3cTRQRG0LmhJDvCsUlCJIQQTipTl8n60+v5Pu571p1aR+7hf/aJ0qg0uBga4W64C3djc1yNDVHnupELeAB3h/vToW4gX249U2Sic2RQ0YVcJdkRjk4SIiGEcCK5+bn8dOInVh1dxa9//Upu/j9JUJh3GH3q96FxtfvZc7wmu88W3Ujz6U6RjLm/rmm5j8hAz1Ln/gjhDCQhEkIIB6coCrsu7mLJwSWsOrqKtLx/VjSs5RNFv/qPEpEeRr2Gj7N8z0XmxtwAiiZDGpWKZ++vY7b2mb3d/SpEeZGESAghHNSN3BssPrCYL/Z9YTYnKMIvglZBD7PnWEPUOVGsT1bhplHIPRIHgFajou9dYYT5e/DFljOljv7I5TBRFUhCJIQQDiYuOY55e+ax7PAysvUFSz57aj15vMnjDG8xnIbV2nHfB1vQ/j33RwFyDSoCPLUM6xjJ4HYR1PApGAV6qn2EjP4IgSREQgjhEBRFYUvCFqbvmM6ms5tMx5vVaMYLbV9gcPPB+Lj5kKMz8OaPcWYToQvNeqI5XRubL7Ehoz9CFJCESAgh7JiiKPz616+8t/09Yi7EAKBWqXmk0SOMu2ccnWt3RqVSoSgKPx+6zPvrj3M5rej8IBUKdStgKyAhHJUkREIIYYcURWHDXxt4Y/Mb7E/cD4Cbxo1nWj3DKx1fobZ/bVPZwxdv8M7/jrH3XCoANf096NygOqtiz2P4ewfxgVHGSt0nSgh7JwmREELYmX2X9zF502T+iP8DAC+tF8+1eY4JHSYQ6lNwySsxLYcD51L55Ugiv8YloSjgodXwXJe6PHt/Hdy1GsZ1q0dCSjY1/Vw58OcflRmSEHZPXdkdEI7vxIkTtG/fHnd3d+6+++7K7o7diIyMZM6cOWUuP23aNJt+/4YOHcr06dNNj9u2bcuaNWts1r6wvYQbCQxZM4Q2C9rwR/wfuGncmNRhEgnjE/iw54emZOi7PefpOOMPxq44wPojBcnQoy1rsnlSF17sVh93bcHm1qF+HnSoGygjQ0KUgSREVdiIESNQqVSoVCpcXFyIiIjgueeeIzU11aJ23nrrLby8vDh58iS///57OfXW+U2aNMni719JSdfhw4dZt24d48aNMx178803mTJlCkaj8U67KmxMZ9Dx3rb3aPxZY1YcWQHAkOZDOPnCST7s+SFBnkGmskcu3WDqmiPcPGdarYLJvRuarR8khLCMJERVXO/evUlMTCQhIYGFCxfyv//9j7Fjx1rUxpkzZ7j33nupXbs2gYGBpVcohk6ns6qeM/H29rb6+3erefPm8cQTT+Dj42M69tBDD5GWlsZvv/1mk9cQtrHt3Dbu/uJu3tj8Brn5uXSJ7MK+Z/exfMBys3lCADFnUhiyYE+RNowKJKRkV1SXhXBKkhCVA0VRyNJllf1Lb0HZUr5u3Wi1NG5uboSEhFCrVi169uzJoEGDzDZmBVi8eDGNGzfG3d2dRo0a8fnnn5ueU6lU7Nu3j3feeQeVSsW0adMAuHTpEoMGDaJatWpUr16dwYMHm23qOmLECB555BFmzJhBWFgYDRo0KFIvMDCQ/v37F1vvo48+IjQ0lMDAQJ5//nn0er2pTF5eHpMnTyY8PBw3Nzfq16/PokWLTM8fO3aMBx98EG9vb4KDgxk6dCgpKSm3/T6tXr2apk2b4ubmRmRkJLNmzTJ7/urVq/Tr1w8PDw+ioqL49ttvi7SRlpbGs88+S40aNfD19eWBBx7g0KFDpudvvWRWWqxdunTh3LlzvPzyy6aRPijYTPeHH36gX79+Zq+v0Wh48MEH+e67724bq6gY17KvMfKnkXRe0pnjKcep4VWD5Y8u549hf9AqtJVZWaNRYd4fp3lq4W7Sc/VF2ippfzEhRNnJpOpykK3PxntG5dzemjk1Ey9XL6vqnj17lg0bNqDVak3HFixYwFtvvcW8efNo2bIlBw4cYPTo0Xh5eTF8+HASExPp3r07vXv3ZtKkSXh7e5OdnU3Xrl2577772LZtG2q1mmnTpvHggw9y+PBhXF1dAfj999/x9fUlOjoaRVGK1HNxceH//u//6N27t1m9zZs3ExoayubNm/nrr78YNGgQd999N6NHjwZg2LBh7Ny5k08//ZQWLVoQHx9vSngSExPp3Lkzo0ePZvbs2eTk5PDqq68ycOBA/vij+Emn+/btY+DAgUybNo1BgwYRExPD2LFjCQwMZMSIEQCMHTuWpKQk/vjjD1xdXXnxxRdJTk42taEoCg899BABAQGsX78ePz8/vvzyS7p168apU6cICAgo9rVvF+uaNWto0aIFzz77rCl2KLhcduPGDdq0aVOkvXvuuYeZM2eW9UdClJONZzYy4scRJGYmAjCm9RhmdJtBNY9qRcpey8zj5e8Pse3UVQCeaF2Lu2r5M+3no7K/mBA2JAlRFffLL7/g7e2NwWAgN7dg7ZLZs2ebnn/33XeZNWsWAwYMACAqKopjx47x5ZdfMnz4cEJCQnBxccHb25uQkBAAvv76a9RqNQsXLkSlUmE0Gvnss8+IjIxky5Yt9OzZEwAvLy8WLlxoSnRurQcFo1P+/v5m9apVq8a8efPQaDQ0atSIhx56iN9//53Ro0dz6tQpvv/+e6Kjo+nevTsAderUMcUzf/58WrVqZTbZ+OuvvyY8PJxTp06ZRqpuNnv2bLp168abb74JQIMGDTh27BgffvghI0aM4NSpU2zatImYmBg6dOgAwKJFi2jcuLGpjc2bN3PkyBGSk5Nxc3MD4KOPPuLHH3/kv//9L88++2yx5+d2sQYEBKDRaPDx8TF97wESEhLQaDTUqFGjSHs1a9bk/PnzGI1G1GoZIK5oOfocpmyawqd7PgWgUVAjFvVbRMfwjmblEtNyiE/JIiNHz1s/HyMpPRd3rZp3+jdjYJtwALo3qSErTAthQ5IQlQNPrSeZUzPLVNZoNJKekY6vj69NPqA8tZYNm3ft2pX58+eTnZ3NwoULOXXqlGki7tWrV7lw4QKjRo0yG4HIz8/Hz8+vxDb37dvHX3/9ZTZ/BSA3N5czZ86YHjdv3tyUDFlSr2nTpmg0GtPj0NBQjhw5AsDBgwfRaDR07ty5xL5t3rwZb++iI3hnzpwpNiE6fvw4/fv3NzvWqVMn5syZg8Fg4Pjx47i4uJiNyDRq1Ah/f3+z183MzCwyRygnJ8cstlvdLtaS5OTk4ObmZkoqb+bh4YHRaCQvLw8PD/kQrUgHkw4yZM0Qjl09BsALbV/ggx4fFHnProo9z9Q1R8xWmq5T3Yv5Q1rTMOSf94asMC2EbUlCVA5UKlWZL1sZjUYMWgNerl6V8he7l5cX9erVA+DTTz+la9euvP3227z77rumu5EWLFhAu3btzOrd/CF9K6PRSOvWrU3zaIxGI5mZmaY5Oze/9u3q3ax69eqm/998SQ8wjUIBpX7IG41GHn74YT744IMiz4WGhhZTo+By163Jxc1ztQr/X1wCcvPrhoaGsmXLliLP3Zw43ep2sZYkKCiI7OxsdDqdWcIJcP36dTw9PSUZqmBf7fuKcb+OQ2fQEeIdwuL+i+ldr3eRcolpOUWSIRWwYGgb6taQVaaFKE+SEAkzb731Fn369OG5554jLCyMmjVrcvbsWYYMGVLmNlq1asWqVatMk4eNRiPp6en4+t5+FOzWetZo3rw5RqORrVu3mi6Z3foaq1evJjIyEheXsv34N2nShB07dpgdi4mJoUGDBmg0Gho3bkx+fj579+6lffv2AJw8eZIbN26YvW5SUhIuLi5ERkZaFVtxXF1dMRgMZscKJ2YfO3asyLpGcXFxtGplPmFXlJ/c/FzGrR/HwgMLAejfsD8L+y00u43+ZscT04vsQaYAyRl5khAJUc5kEoEw06VLF5o2bWqaYzNt2jRmzJjBJ598wqlTpzhy5AiLFy82m2d0qyFDhhAUFET//v3Zvn078fHx/Pnnn4wfP56LFy9aVG/r1q289NJLt613s8jISIYPH87IkSP58ccfiY+PZ8uWLXz//fcAPP/881y/fp0nn3ySPXv2cPbsWTZu3MjIkSOLJBaFJk6cyO+//867777LqVOnWLp0KfPmzWPSpEkANGzYkG7dujFmzBh2797Nvn37eOaZZ8xGYbp3706HDh145JFH+O2330hISCAmJoY33niDvXv3lim2kuLdtm0bly5dMk0cr169Oq1atSqSxAFs377dNBdLlK8LaRe4f/H9LDywELVKzfvd3mftoLUlJkOZefl8sul0keNyB5kQFUMSIlHEhAkTWLBgARcuXOCZZ55h4cKFLFmyhObNm9O5c2eWLFlCVFRUifU9PT3Ztm0bERERDBgwgKZNm/LCCy+Qk5Nz25GfW+s1btyYkSNHllrvVvPnz+fxxx9n7NixNGrUiNGjR5OVlQVAWFgYf/75JwaDgV69etGsWTNeeukl/Pz8Shy9atWqFd9//z0rV66kWbNm/Oc//+Gdd94x3WEG8Nlnn1GrVi06d+7MgAEDTLfXF1KpVKxfv57777+fkSNH0qBBA/71r3+RkJBgdhnRUu+88w4JCQnUrVvX7LLis88+W+TS46VLl4iJieHpp5+2+vVE2WxN2Errr1oTezmWAI8ANgzZwKv3vlriZdX0XD1DF+3m0MU03F3UqP8uJneQCVFxVIqlC9dUUenp6fj5+ZGWllbkwzk3N5f4+HiioqJwd7dspdiyXk5yZM4eoz3Gl5ubS8OGDVm5cqXpzrdXXnmFtLQ0vvrqq9vWu/VnWa/Xs379eh588MEic5qchS1jXBm3kmFrh6E36mkZ0pI1g9YQ6R9ZYvm0bD3Dvi5Ihvw8tHz7TDsCvV1tegeZnEPHJ/FZ73af3zeTOURCOCF3d3e++eYbswUna9SoYbrMJ2xPURRm75zNpOiC7/HjTR7nm0e+wUNbckKTmqVj6Ne7ibuUTjVPLd8+054mYQW/sGVUSIiKJQmREE7q1qUHXnnllUrqifMzGA1M3DiRT3Z/AsBL7V5idq/ZqFUljxhey8zjqUV7OJ6YTqCXK9+ObkejEOtuJhBC3DlJiIQQ4g7k5efx1Nqn+O+x/wLwUY+PmNBhQonzhRLTcjh04QYzN5zkbEoWQd5ufDe6HfWDfYotL4SoGJIQ2ZBMxxKOTn6GLZObn8tj3z/G+tPr0aq1LH1kKU82f7LE8rcuuujj5sLKZ9tTT26pF6LSSUJkA4UTwLKzs2XBO+HQsrMLdkx3xkmbtpabn8uAVQP49a9f8XDx4Ocnf6Z7naJrXxUqbtHFLF0+Xm4lL3IqhKg4khDZgEajwd/f37SZp6en521XLb6Z0WhEp9ORm5trN3co2Zqzx+gM8RVurpucnIy/v/9tVyIXBcnQo6seZcNfG/Bw8eCXwb/wQNQDt63zV3JmkUUXjQokpGTLBGoh7IAkRDZSuLnmzTucl4WiKOTk5ODh4VHmJMrROHuMzhSfv7+/2Uaxoqhbk6F1g9fRNaprqfXWH04sckwWXRTCfkhCZCMqlYrQ0FBq1KiBXq8vcz29Xs+2bdu4//77nfYyhbPH6CzxabVaGRkqhd6g57HvH2PDXxvw1HqybvA6ukR2KbXe2gMX+S72AgBqVcHIkCy6KIR9kYTIxjQajUUfKhqNhvz8fNzd3R36w/R2nD1GZ49PFDAqRkb9PIr1p9fjqfVk/eD1dI7sXGq9uEtpTFl9BIDnu9blqfa1bbroohDCNiQhEkKIMpi6aSrLDi9Do9LwwxM/lCkZupaZx5hl+8jLN9KlYXUm9GiIRq2SREgIO+SYM0CFEKICzdk1h5kxMwFY2G8hD9Z/sNQ6eoOR51fs59KNHKKCvPjkXy3RqB17jpkQzkwSIiGEuI3vjnzHy7+9DMCMbjMYcfeIMtWbvv44u85ex8tVw1dDW+PnIZdThbBnkhAJIUQJtiRsYfiPwwEYd884Xu30apnqrd53kcV/JgAwa+Ddsgq1EA5A5hAJIUQxEm4k8Pj3j6M36nmiyRPM6T2n1GUVEtNy+P34Fd7+3zEAXnygHr2byTIGQjgCSYiEEOIWWbos+q/sz7Wca7QObc3SR5bedqNWKLotR+MQH8Z3b1ABvRVC2IJcMhNCiJsoisLTPz3N4SuHqeFVg7WD1uKhvf1dYcVty3HySgZXMnLLubdCCFuRhEgIIW4yY8cMfjj2A1q1ltUDVxPuF15qnfiUrBK35RBCOAZJiIQQ4m/rTq/jjT/eAOCzBz/j3oh7y1RPXczcItmWQwjHIgmREEIAV/KuMPzn4SgoPNfmOUa3Hl2mekajwqyNJ82OybYcQjgemVQthKjy9AY9H537iPS8dDrU6sCc3nPKXHf57nPEJqTi5aph2ah7yMtXZFsOIRyQJERCiCrvP1v/w+ns0/i7+/PdY9/hqnEtU72Lqdl88OsJAF7t04hWtQPKs5tCiHIkl8yEEFXaxjMbmbVrFgBfPvgltf1rl6meoii8vjaOLJ2BtpHVeKpd2eoJIeyTJERCiCorKTOJoWuHAtA7sDePNnq0zHXX7L/E1lNXcXVR8/5jd6GWfcqEcGhyyUwIUSUZFSND1w4lOSuZZtWb8XTo02WuezUjj3d+KViNenz3+tSt7l1e3RRCVBAZIRJCVEmzd85m09lNeGo9+fbRb3FTu5W57rSfj5KWo6dpmC+j76tTjr0UQlQUSYiEEFXO8avHTesNzek1h8ZBjctcd0NcEuuOJKJRq/jgsbvQauTXqBDOQN7JQogqxWA08PRPT5NnyKN3vd480+qZMtdNy9bz5k9xAIy5vw7NavqVVzeFEBVMEiIhRJUye+dsdl/aja+bLwseXlDqDvaFEtNyeGnlfq5m5FGnuhcvdqtfzj0VQlQkmVQthKgyjl89zpub3wTg414fU8u3VpnqrYo9z5Q1R1D+3q+sV5Ng3LWa8uqmEKISyAiREKJKuPlSWZ96fXj67rLdVVa4k71y0+atX22LJzEtp5x6KoSoDJIQCSGqhFk7Z5kulX318FdlvlRW3E72BkWRneyFcDKSEAkhnN7pa6f5z+b/AJZdKgPw99AWOSY72QvhfCQhEkI4NUVRGPfrOPIMefSo06PMl8oKfb/3otlj2cleCOckk6qFEE5t9fHV/HbmN1w1rnz24GdlvlQGcP5aNt/uPgfAp0/eTXVvd9nJXggnZdcjRPn5+bzxxhtERUXh4eFBnTp1eOeddzAajaYyiqIwbdo0wsLC8PDwoEuXLhw9etSsnby8PMaNG0dQUBBeXl7069ePixcv3vpyQggnk5GXwfgN4wGY0mkK9QMtu1X+o40n0RsU7qsfRL8WNelQN1CSISGclF0nRB988AFffPEF8+bN4/jx48ycOZMPP/yQuXPnmsrMnDmT2bNnM2/ePGJjYwkJCaFHjx5kZGSYyowfP561a9eycuVKduzYQWZmJn379sVgMFRGWEKICvL21re5lHGJutXqMuXeKRbVPXIxjZ8PXQZgSp9G5dE9IYQdsetLZjt37qR///489NBDAERGRvLdd9+xd+9eoGB0aM6cObz++usMGDAAgKVLlxIcHMyKFSsYM2YMaWlpLFq0iGXLltG9e3cAli9fTnh4OJs2baJXr17FvnZeXh55eXmmx+np6QDo9Xr0er3NYixsy5Zt2htnj1His09Hko8wZ9ccAD7u+TEuuJQYw60xKorCjPUFm7f2uyuUBtU9HS7+mznqObSEs8co8d1526VRKYqilF6scrz//vt88cUXbNy4kQYNGnDo0CF69uzJnDlzePLJJzl79ix169Zl//79tGzZ0lSvf//++Pv7s3TpUv744w+6devG9evXqVatmqlMixYteOSRR3j77beLfe1p06YV+9yKFSvw9JS7S4SwZ0bFyOt/vc7xrON08OvAq1GvWlT/xA0V849r0KgUXr/bQKB7OXVUCFHusrOzGTx4MGlpafj6+pZYzq5HiF599VXS0tJo1KgRGo0Gg8HAe++9x5NPPglAUlISAMHBwWb1goODOXfunKmMq6urWTJUWKawfnGmTp3KhAkTTI/T09MJDw+nZ8+et/2GWkqv1xMdHU2PHj3Qaove3usMnD1Gic/+fHP4G44fOo6X1ovlQ5cT7ht+2/I3x6jRuPDF/F1ABsM6RDK0T8OK6XQ5csRzaClnj1His17hFZ7S2HVCtGrVKpYvX86KFSto2rQpBw8eZPz48YSFhTF8+HBTuVvvGlEUpdQ7SUor4+bmhpubW5HjWq22XH4Yy6tde+LsMUp89iFTl8kbWwp2sn+r81vUCaxT5rparZZ1cckcT8rAx82Fcd0aOETMZeUo5/BOOHuMEp91bZaFXSdEr7zyClOmTOFf//oXAM2bN+fcuXPMmDGD4cOHExISAhSMAoWGhprqJScnm0aNQkJC0Ol0pKammo0SJScn07FjxwqMRghREWb+OZOkzCTqBdTjpfYvWVQ3L9/IRxtPAvDvLnUJ8HItjy4KIeyQXd9llp2djVpt3kWNRmO67T4qKoqQkBCio6NNz+t0OrZu3WpKdlq3bo1WqzUrk5iYSFxcnCREQjiZC2kX+CjmIwBmdp+Jq8ayhGbFngtcTM0h2NeNkZ2iyqOLQgg7ZdcjRA8//DDvvfceERERNG3alAMHDjB79mxGjhwJFFwqGz9+PNOnT6d+/frUr1+f6dOn4+npyeDBgwHw8/Nj1KhRTJw4kcDAQAICApg0aRLNmzc33XUmhHAOr//xOjn5OdwXcR+PNHrEoro5+TB/61kAXu7eAA9X2c1eiKrErhOiuXPn8uabbzJ27FiSk5MJCwtjzJgx/Oc//zGVmTx5Mjk5OYwdO5bU1FTatWvHxo0b8fHxMZX5+OOPcXFxYeDAgeTk5NCtWzeWLFmCRiO/8IRwFnsv72XZ4WUAzO4126IVqQF+v6wmNVtPvRrePN667HudCSGcg10nRD4+PsyZM4c5c+aUWEalUjFt2jSmTZtWYhl3d3fmzp1rtqCjEMJ5KIrCxI0TAXjqrqdoE9bGovqHL6Xxx+WCBGpyr4a4aOx6NoEQohzIu14I4fB+OvkT285tw93FnekPTLeo7qrY8zz2xW4MSkFCdD1LVx5dFELYOUmIhBAOTWfQ8Ur0KwBM7DCRcL/brzl0s8S0HKauOWJ27PW1cSSm5di0j0II+ycJkRDCoS3av4i/rv9FsFcwr3aybEXq+JQsjLes1W9QFBJSsm3YQyGEI5CESAjhsHL0Ofzf9v8D4I3738DHzaeUGua8irmTTKNSERkk2/MIUdVIQiSEcFifx37O5YzL1ParzehWoy2u/8vhRLPHahVMH9CMUD8PW3VRCOEg7PouMyGEKEl6XjozdswACrbocHMputXO7dzI1rFi93kAPnysGeeOH2Lgg12JCLJslEkI4RxkhEgI4ZDm7JrDtZxrNAxsyNAWQy2uv2znObJ0BhqH+tK/RSj1/RRC/WRbeyGqKkmIhBAO53rOdWbtnAXA213exkVt2WB3js7AkpgEAP7duY7FizgKIZyPJERCCIcz88+ZpOel0yK4BU80fcLi+j/su8C1LB3hAR481Dy09ApCCKcnCZEQwqEkZSbx6e5PAXi367uoVZb9GtMbjHz5955lz95XR1alFkIAkhAJIRzMjO0zyMnPoV3NdvRt0Nfi+usOJ3LpRg6BXq480absizgKIZybJERCCIeRlJnEl/u+BOD/Hvg/i+f+KIrCF1vPADDy3ijctbLBsxCigCREQgiH8VHMR+QZ8ugY3pFuUd0srr/l5FVOJGXg5arhqXa1y6GHQghHJQmREMIhpGSnMH/vfADeuO8Nq+4Mm7+lYHRoSPva+Hlqbdo/IYRjk4RICOEQ5uyaQ7Y+m9ahreldr7fF9fedu86ehOu4atSMujeqHHoohHBkkhAJIezejdwbzN0zFyjYs8y60aGCO8sebVmTYF9ZgFEIYU4SIiGE3Zu3Zx7peek0q9GMfg37WVz/1JUMNh2/gkoFz3auUw49FEI4OkmIhBB2LVOXyce7Pgbg9ftet3jdIcC07lDvpiHUre5t0/4JIZyDJERCCLs2P3Y+13OuUz+gPk80sXxV6gPnU1l74CIA/+5c19bdE0I4CUmIhBB2K0efw0c7PwLgtfteQ6O2bN2gVbHnGfB5DEal4PGJpHRbd1EI4SQkIRJC2K3FBxeTnJVMpH8kQ5oPsahuYloOU9ccQbnp2Gtr4khMy7FtJ4UQTkESIiGEXTIYDczeORuASR0modVYtm5QfEqWaWTI1KaikJCSbasuCiGciCREQgi7tPbEWs6kniHAI4ARd4+wuH5EgGeRYxqVisigoseFEEISIiGE3VEUhQ9jPgTg+bbP4+XqZXEbxxMzzB5rVCqmD2hGqJ+HTfoohHAuLpXdASGEuNX289vZc2kPbho3XrjnBava+GZnAgBD2kfQt3kYkUGekgwJIUokCZEQwu58FFNwZ9nwFsOp4VXD4vpnrmay/XQKKhX8+/66hBdz+UwIIW4ml8yEEHbl+NXj/O/U/1ChYmLHiVa1sWznOQC6NaohyZAQokwkIRJC2JVZO2cB0L9RfxoENrC4flZePqv3FSzEOLRDpC27JoRwYpIQCSHsRmJGIssOLwMKbrW3xtoDl8jIyycqyIv76gXZsntCCCcmCZEQwm7M3TMXnUFHh1od6BTRyeL6iqKYLpc91b42arXK1l0UQjgpSYiEEHYhS5fFF3u/AOCVjq9Y1cbu+OucvJKBh1bD461r2bJ7QggnJwmREMIuLD+8nNTcVKL8o+jXsJ9VbRSODj3SsiZ+HpatbC2EqNokIRJCVDpFUfh0z6cAjLtnnMWbuAIkpeXy29EkAIZ1qG3T/gkhnJ8kREKISvd7/O8cu3oML60XI1uOtKqNFXvOk29UuCcygMahvjbuoRDC2UlCJISodJ/s/gSAEXePwM/dz+L6unwj3+05D8CwjjI6JISwnCREQohK9df1v1h3ah1QcLnMGhuOJnE1I48aPm70ahpiy+4JIaoISYiEEJVq3p55KCj0qdeHhkENrWpj2d/7lj15TwRajfxaE0JYTn5zCCEqTXpeOl8f+BqAl9q9ZFUbxy6nE5uQiotaxeB2EbbsnhCiCpGESAhRaZYeXEqGLoNGQY3oWbenVW0s25UAQK9mIQT7utuwd0KIqkQSIiFEpTAqRubumQsUzB1SqSxfVTotW8/aA5cAGC77lgkh7oAkREKISrHhrw2cvn4aPzc/hrUYZlUbi3acJVdvpG51L9pGVrNxD4UQVYkkREKISvFZ7GcAjGo5Cm9Xb4vrf7fnPJ/+8RcAZ69m8f3eCzbtnxCiapGESAhR4c6mnuXX078C8Fzb5yyun5iWw2trj5geK8Bra+JITMuxVReFEFWMJERCiAr35d4vUVDoVbcX9QLqWVw/PiULRTE/ZlAUElKybdRDIURVIwmREKJC5ebnsujAIgDGth1rVRvFbdyqUamIDPK8o74JIaouSYiEEBXqh6M/cC3nGhF+ETxU/yGr2vjzrxSzxxqViukDmhHq52GLLgohqiCXyu6AEKJq+Xzv5wCMaT3Gql3tFUVhZWzBBOopvRvRItyfyCBPSYaEEHdEEiIhRIXZn7ifXRd3oVVrGdVylFVtxCakcvZqFp6uGp7qUBtvN/k1JoS4c3LJTAhRYebHzgfg8SaPE+wdbFUbK//e1f7hu8IkGRJC2IwkREKICnEj9wbfHvkWsH4ydVqOnnVHEgH41z3hNuubEEJIQiSEqBBLDy4lJz+H5jWa0ym8k1Vt/HTwEnn5RhoG+3B3uL9tOyiEqNIkIRJClDtFUUyTqce2HWvVvmWKovDdnoLJ1P+6J9yqNoQQoiSSEAkhyt3Wc1s5de0U3q7eDGk+xKo2jlxK43hiOq4uah5tWdPGPRRCVHWSEAkhyt2X+74EYEjzIfi4+VjVRuGt9r2bhuDv6WqzvgkhBEhCJIQoZ1ezrrLm+BoAnm39rFVtZOvy+fngZUAmUwshyockREKIcrX00FJ0Bh1twtrQKrSVVW38cjiRzLx8agd60j4q0MY9FEIIB0iILl26xFNPPUVgYCCenp7cfffd7Nu3z/S8oihMmzaNsLAwPDw86NKlC0ePHjVrIy8vj3HjxhEUFISXlxf9+vXj4sWLFR2KEFWOoih8te8rAJ5tZd3oEMCqvy+XDWobjlotk6mFELZn1wlRamoqnTp1QqvV8uuvv3Ls2DFmzZqFv7+/qczMmTOZPXs28+bNIzY2lpCQEHr06EFGRoapzPjx41m7di0rV65kx44dZGZm0rdvXwwGQyVEJUTVsfXcVk5fP423qzdPNn/SqjZOXclg37lUNGoVj7eqZeMeCiFEAbte5vWDDz4gPDycxYsXm45FRkaa/q8oCnPmzOH1119nwIABACxdupTg4GBWrFjBmDFjSEtLY9GiRSxbtozu3bsDsHz5csLDw9m0aRO9evWq0JiEqEpunkzt7eptVRuFo0PdGtWghq+7zfomhBA3s+uE6Oeff6ZXr1488cQTbN26lZo1azJ27FhGjx4NQHx8PElJSfTs2dNUx83Njc6dOxMTE8OYMWPYt28fer3erExYWBjNmjUjJiamxIQoLy+PvLw80+P09HQA9Ho9er3eZjEWtmXLNu2Ns8co8RXv5snUI1uMtOr7k5dvZM3+gsvbj7cKK7fvsZxDx+fsMUp8d952aew6ITp79izz589nwoQJvPbaa+zZs4cXX3wRNzc3hg0bRlJSEgDBweZ7IgUHB3Pu3DkAkpKScHV1pVq1akXKFNYvzowZM3j77beLHN+4cSOenp53GloR0dHRNm/T3jh7jBKfuR+Tf0Rn0FHPox6J+xNJJNHi19yfoiI1W4Ofq0LmX7GsP2NxExaRc+j4nD1Gic9y2dnZZSpn1wmR0WikTZs2TJ8+HYCWLVty9OhR5s+fz7Bhw0zlbl2xVlGUUlexLa3M1KlTmTBhgulxeno64eHh9OzZE19fX2vCKZZeryc6OpoePXqg1Wpt1q49cfYYJb6iFEVh0peTAJjYZSIPtnzQqtdetXgvcJ2nOtbl4W71rGqjLOQcOj5nj1His17hFZ7S2HVCFBoaSpMmTcyONW7cmNWrVwMQEhICFIwChYaGmsokJyebRo1CQkLQ6XSkpqaajRIlJyfTsWPHEl/bzc0NNze3Ise1Wm25/DCWV7v2xNljlPj+sSVhC39d/wtvV2+euvspq74v569lE3P2OioV/Oue2hXyvZVz6PicPUaJz7o2y8Ku7zLr1KkTJ0+eNDt26tQpateuDUBUVBQhISFmQ2w6nY6tW7eakp3WrVuj1WrNyiQmJhIXF3fbhEgIYb0F+xcAMLjZYKsnU3+9Ix6AtrWrER5g+8vUQghxM7seIXr55Zfp2LEj06dPZ+DAgezZs4evvvqKr74qWNdEpVIxfvx4pk+fTv369alfvz7Tp0/H09OTwYMHA+Dn58eoUaOYOHEigYGBBAQEMGnSJJo3b26660wIYTvXc66z+ljBKK61K1Ov2H2OJTsTAIhNSGVV7HkGtY2wVReFEKIIu06I2rZty9q1a5k6dSrvvPMOUVFRzJkzhyFD/tkccvLkyeTk5DB27FhSU1Np164dGzduxMfnn/2SPv74Y1xcXBg4cCA5OTl069aNJUuWoNFoKiMsIZzat4e/Jc+QR4vgFlatTJ2YlsPrP8aZHivAa2viuL9BdUL9PGzYUyGE+IddJ0QAffv2pW/fviU+r1KpmDZtGtOmTSuxjLu7O3PnzmXu3Lnl0EMhRCFFUVh4YCEAz7R6ptSbG4oTn5KFopgfMygKCSnZkhAJIcqNXc8hEkI4ln2J+zh85TBuGjeGNB9SeoVi+HkUnQCpUamIDJJ5REKI8iMJkRDCZhbuLxgderzJ41TzqFZK6eLtPHPN7LFGpWL6gGYyOiSEKFd2f8lMCOEYsnRZrDiyAoBRLUdZ1YaiKHy/t2Crjld6NaRVRDUigzwlGRJClDtJiIQQNvHDsR/I0GVQt1pdOkd2tqqNwxfTOHUlEzcXNU+1r13s5TMhhCgPcslMCGETiw4sAgpGh9Qq6361FI4O9WkWIsmQEKJCSUIkhLhjJ1JOsOP8DjQqDcPvHm5VG7l6Az8fugzAwDbhtuyeEEKUShIiIcQdW7S/YHTooQYPEeYTZlUbvx1NIiM3n1rVPGhfJ9CW3RNCiFJJQiSEuCM6g45vDn8DWD+ZGv65XPZ461qo1ZavXySEEHdCEiIhxB1Zd2odyVnJhHiH8GB963a1v3A9mz//uoZKVZAQCSFERZOESAhxR74++DUAw1sMx0Vt3Y2rq/dfBKBT3SBqVZMFGIUQFU8SIiGE1S5nXGb96fUAjGw50qo2jEaFH/YWJERPtJHRISFE5bDqz7mTJ0/y3XffsX37dhISEsjOzqZ69eq0bNmSXr168dhjj+Hm5mbrvgoh7Mw3h77BqBi5N+JeGgQ2sKqNnWevcelGDj7uLvRqGmLjHgohRNlYNEJ04MABevToQYsWLdi2bRtt27Zl/PjxvPvuuzz11FMoisLrr79OWFgYH3zwAXl5eeXVbyFEJVMUha8PFFwuG3m3daND8M9k6v53h+Gu1dikb0IIYSmLRogeeeQRXnnlFVatWkVAQECJ5Xbu3MnHH3/MrFmzeO211+64k0II+7Pj/A5OXz+Nt6s3TzR9wqo20nL0bIhLAmTtISFE5bIoITp9+jSurq6lluvQoQMdOnRAp9NZ3TEhhH0rnEw9qOkgvF29rWrjf4cuk5dvpGGwD81r+tmye0IIYRGLLpndnAx98803xV4S0+l0fPPNN0XKCyGcR0ZeBt8f/R6wfjI1wA9/Xy57ok0tVCpZe0gIUXmsvsvs6aefJi0trcjxjIwMnn766TvqlBDCvq06uopsfTYNAxvSoVYHq9o4mZTBoYtpuKhVPNqypo17KIQQlrE6IVIUpdi/6C5evIifnwx9C+HMCidTj2o5yuqRncLRoe6Ngwn0lrtShRCVy+Lb7lu2bIlKpUKlUtGtWzdcXP5pwmAwEB8fT+/evW3aSSGE/Th+9Tg7L+5Eo9IwtMVQq9rQG4ysPXAJkLWHhBD2weKE6JFHHgHg4MGD9OrVC2/vfyZTurq6EhkZyWOPPWazDgoh7Mvig4uBgo1cQ7ytWzdo9b6LXMvSEeDlSucG1W3ZPSGEsIrFCdFbb70FQGRkJIMGDcLd3d3mnRJC2Ce9Qc83hwpumrB27aFVseeZsuYIAKlZOlbvv8igthE266MQQljD6jlEw4cPLzUZUhTF2uaFEHbo179+5UrWFWp41bBqI9fEtBym/p0MASjAa2viSEzLsWEvhRDCchYlRI0bN2bFihWlri90+vRpnnvuOT744IM76pwQwr4UTqYedtcwtBqtxfXjU7Iw3vJ3kkFRSEjJtkX3hBDCahZdMvvss8949dVXef755+nZsydt2rQhLCwMd3d3UlNTOXbsGDt27ODYsWO88MILjB07trz6LYSoYFcyr7Du9DoAnm5p3dIakYFFd7LXqFREBskO90KIymVRQvTAAw8QGxtLTEwMq1atYsWKFSQkJJCTk0NQUBAtW7Zk2LBhPPXUU/j7+5dTl4UQlWHF0RXkG/NpV7MdTao3saqNSzdyzR5rVCqmD2hGqJ+HLboohBBWs2q3+44dO9KxY0db90UIYacURWHJoSXAna1MvSq2YO2hvneFMKRdJJFBnpIMCSHsglUJkRCiajmdfZrjKcfxcPFgUNNBVrWRkatn3eFEAJ7uFEXr2iVvEC2EEBXN6rvMALZu3crDDz9MvXr1qF+/Pv369WP79u226psQwk78fv13AB5r8hh+7tatRP/L4URy9AbqVveiVUQ1W3ZPCCHumNUJ0fLly+nevTuenp68+OKLvPDCC3h4eNCtWzdWrFhhyz4KISpRtj6b7akFf+hYu/YQ/HO5bFDbcNnIVQhhd6y+ZPbee+8xc+ZMXn75ZdOxl156idmzZ/Puu+8yePBgm3RQCFG51p5cS7Yxmyj/KDpHdraqjVNXMjh44QYuahUDWslWHUII+2P1CNHZs2d5+OGHixzv168f8fHxd9QpIYT9KFyZemjzoahV1v3KKBwd6ta4BkGykasQwg5ZnRCFh4fz+++/Fzn++++/Ex4efkedEkLYh/jUeDaf24wKFUPvsm4jV13+Pxu5DmorvxuEEPbJ6ktmEydO5MUXX+TgwYN07NgRlUrFjh07WLJkCZ988okt+yiEqCRLDi4B4C7vu6jtV9uqNjYdv8L1LB01fNy4v75s5CqEsE9WJ0TPPfccISEhzJo1i++//x4o2Npj1apV9O/f32YdFEJUDoPRYNrZvntgd6vbKbxc9njrWrho7ujGViGEKDd3tA7Ro48+yqOPPmqrvggh7Mgf8X9wIf0C/u7+tPNrZ1Ubl2/ksO30VQAGtpHLZUII+3XHCzPqdDqSk5MxGo1mxyMiIu60aSFEJfr6YMFGrk82fRJXg6tVbazedxFFgXZRAUQGedmye0IIYVNWJ0SnT59m5MiRxMTEmB1XFAWVSoXBYLjjzgkhKsf1nOusPb4WgBEtRpC4P9HiNoxGhe/3/bP2kBBC2DOrE6IRI0bg4uLCL7/8QmhoqCy0JoQT+e7Id+QZ8rg75G5ahrQkEcsTol1nr3Hheg4+bi70aRZaDr0UQgjbsTohOnjwIPv27aNRo0a27I8Qwg4UXi67o5Wp9xaMDvW7OwwPV41N+iWEEOXF6ls+mjRpQkpKii37IoSwAweTDrI/cT+uGlcGN7duxfm0bD2/xiUBMplaCOEYLEqI0tPTTV8ffPABkydPZsuWLVy7ds3sufT09PLqrxCinH19oGB06JFGjxDoGWhVGz8duoQu30ijEB/uqmXdZrBCCFGRLLpk5u/vbzZXSFEUunXrZlZGJlUL4bhy83NZfng5YJuNXAe2kY1chRCOwaKEaPPmzQDk5eUxffp0nnzySZlDJIQT+fnkz6TmplLLtxbd61i3GGPcpTSOXk7HVaPm0ZY1bdxDIYQoHxYlRJ07/7PT9ZAhQ3jggQeoX7++zTslhKgchZfLRrQYgUZt3UToxX8WbO58b/0gqnlZt36REEJUNKsnVQ8bNoxFixbZsi9CiEp07sY5Np7ZCMCIu0dY1cbyXedYvb9gI9fNJ5NZFXveVt0TQohyZfVt9zqdjoULFxIdHU2bNm3w8jJfhXb27Nl33DkhRMVZcnAJCgoPRD1A3YC6FtdPTMvhzR/jTI8VBV5bE8f9DaoT6udhy64KIYTNWZ0QxcXF0apVKwBOnTpl9pxMohTCsRiMBtPaQ8+0fMaqNuJTslBubVdRSEjJloRICGH3rE6ICidYCyEc3+/xv3M+7TzV3KvxaGPrNmxWbs2GAI1KRWSQ5x32Tgghyp/Vc4iEEM5j4f6FADx111O4u7hb1Ub0sStmjzUqFdMHNJPRISGEQ7jj3e6FEI4tJTuFH0/8CMColqOsaiNHZ2D1/osAfDzobkJ83YkM8pRkSAjhMCQhEqKKW3ZoGXqjnjZhbWgR0sKqNv53+DIZufmEB3jQv0UYarXMIxRCOBa5ZCZEFaYoCgsPFFwus3Z0CODb3QW31w++p7YkQ0IIhyQJkRBV2O5Luzl29RgeLh482exJq9qIu5TGoQs30GpUPNGmlo17KIQQFUMSIiGqsMLJ1E80fQI/d+s2YS0cHerdLJQgbzeb9U0IISqSJERCVFEZeRmsjFsJWL/2UGZePj8fLFiZeki7CJv1TQghKpokREJUUauOriJLn0WDwAbcG3GvVW38eOASWToDdat70S4qwMY9FEKIiiMJkRBV1Ff7vgJgdKvRVq0uryjKP5Op29WWFeqFEA7NoRKiGTNmoFKpGD9+vOmYoihMmzaNsLAwPDw86NKlC0ePHjWrl5eXx7hx4wgKCsLLy4t+/fpx8eLFCu69EPbjYNJBYi/HolVrGd5iuFVtHLhwg+OJ6bi5qHmsVU0b91AIISqWwyREsbGxfPXVV9x1111mx2fOnMns2bOZN28esbGxhISE0KNHDzIyMkxlxo8fz9q1a1m5ciU7duwgMzOTvn37YjAYKjoMIezCgn0LABjQeADVvapb1ca3uwpGh/reFYa/p6vN+iaEEJXBIRKizMxMhgwZwoIFC6hWrZrpuKIozJkzh9dff50BAwbQrFkzli5dSnZ2NitWrAAgLS2NRYsWMWvWLLp3707Lli1Zvnw5R44cYdOmTZUVkhCVJkuXxfIjywF4tvWzVrWRlq3nl8OXARjSXiZTCyEcn0OsVP3888/z0EMP0b17d/7v//7PdDw+Pp6kpCR69uxpOubm5kbnzp2JiYlhzJgx7Nu3D71eb1YmLCyMZs2aERMTQ69evYp9zby8PPLy8kyP09PTAdDr9ej1epvFVtiWLdu0N84eo6PF993h70jPS6detXp0qtmp1H4XF9/3e8+Rl2+kUYgPzUK8HCb2kjjaObSUs8cHzh+jxHfnbZfG7hOilStXsn//fmJjY4s8l5SUBEBwcLDZ8eDgYM6dO2cq4+rqajayVFimsH5xZsyYwdtvv13k+MaNG/H0tP3u3dHR0TZv0944e4yOEt9Hpz4CoKN7Rzb8uqHM9QrjUxRYeEgDqGjucYNff/21PLpZKRzlHFrL2eMD549R4rNcdnZ2mcrZdUJ04cIFXnrpJTZu3Ii7e8k7cN96d4uiKKXe8VJamalTpzJhwgTT4/T0dMLDw+nZsye+vr5ljKB0er2e6OhoevTogVartVm79sTZY3Sk+A4nH+bkwZNo1VqmD5xODa8apda5Nb7d8de5smsvnq4apg5+AB93u/41UiaOdA6t4ezxgfPHKPFZr/AKT2ns+jfZvn37SE5OpnXr1qZjBoOBbdu2MW/ePE6ePAkUjAKFhoaayiQnJ5tGjUJCQtDpdKSmppqNEiUnJ9OxY8cSX9vNzQ03t6Kr7mq12nL5YSyvdu2Js8foCPEtObQEgEcaPUJNf8vuDCuMb9W+grlD/e+uSYCPc+1m7wjn8E44e3zg/DFKfNa1WRZ2Pam6W7duHDlyhIMHD5q+2rRpw5AhQzh48CB16tQhJCTEbIhNp9OxdetWU7LTunVrtFqtWZnExETi4uJumxAJ4Wyy9dksO7wMsH4ydUpmHhviEgFZmVoI4VzseoTIx8eHZs2amR3z8vIiMDDQdHz8+PFMnz6d+vXrU79+faZPn46npyeDBw8GwM/Pj1GjRjFx4kQCAwMJCAhg0qRJNG/enO7du1d4TEJUlh+O/kBaXhpR/lE8EPWAVW18vSMevUGhcagvzWpat/eZEELYI7tOiMpi8uTJ5OTkMHbsWFJTU2nXrh0bN27Ex8fHVObjjz/GxcWFgQMHkpOTQ7du3ViyZAkajaYSey5Exfpy35dAwcrUapXlg8OrYi/y+ZYzAJxITGdV7HkGtZVRIiGEc3C4hGjLli1mj1UqFdOmTWPatGkl1nF3d2fu3LnMnTu3fDsnhJ06lHSInRd34qJ24emWT1tc/0YeTPvfMdNjBXhtTRz3N6hOqJ9zzSMSQlRNdj2HSAhhG/P3zgcKVqYO8Q6xuP7VXBWKYn7MoCgkpJTtdlYhhLB3khAJ4eTS89JZfrhgZern2jxnVRvKrdkQoFGpiAyy/ZpcQghRGSQhEsLJLTu0jCx9Fo2DGtO5dmer2jhw3fxXhUalYvqAZnK5TAjhNBxuDpEQouwURTFdLnuuzXOlLlhanNRsHbFXC+p9Prgl1bzciAzylGRICOFUJCESwoltP7+do1eP4qn1ZFiLYVa1sSr2InqjiiahPvRpHmpVUiWEEPZOLpkJ4cQKR4eGNB+Cn7vl6wbp8o0s330BgKc71pZkSAjhtCQhEsJJXcm8wupjqwHrJ1OvP5LIlYw8fLUKDzaz/O40IYRwFJIQCeGkFh1YhN6op32t9rQMbWlxfUVRWLQjHoB7Q4y4usivCyGE85LfcEI4IYPRYFqZ2trRob3nUjlyKQ03FzWdgovedi+EEM5EEiIhnND60+s5n3aeAI8ABjYdaFUbi7YXjA49cnco3s67ubYQQgCSEAnhlObuKdimZuTdI3F3cbe4/oXr2Ww8lgTA8A61bdo3IYSwR5IQCeFkjl09RvTZaNQqNc/f87xVbSyJScCowH31g6hfw9vGPRRCCPsjCZEQTmbennkA9G/Yn0j/SIvrZ+TqWRVbcKv9qHujbNk1IYSwW5IQCeFEbuTeYOmhpQC82O5Fq9r4fu9FMvPyqVfDm84Nqtuye0IIYbckIRLCiXx94Guy9dk0r9Hcqn3LDEaFJTEFk6lHdoqShRiFEFWGJERCOAmD0WC6XPZiuxetSmaij13hwvUc/D21PNqypq27KIQQdksSIiGcxC+nfiH+RjwBHgEMbj7Yqja+/nshxiHtIvBw1diye0IIYdckIRLCSXy651MARrcajafW0+L6m08ksyfhOhoVDOsQaePeCSGEfZOESAgnEJccxx/xf6BWqRnbdqzF9VfFnufpJbEAGBTYcjLZ1l0UQgi7JgmREE5g7u6ChRgfbfQoEX4RFtVNTMth6pojZsdeWxNHYlqOzfonhBD2ThIiIRxcSnYKyw4vA+Cldi9ZXD8+JQvjLVuVGRSFhJRsW3RPCCEcgiREQji4+bHzycnPoVVoK+6NuNfi+v4eRTcq06hURAZZPg9JCCEclSREQjiw3Pxc075lkzpMsupW+/8dTjR7rFGpmD6gGaF+HjbpoxBCOAKXyu6AEMJ6yw4t42r2VSL8Ini8yeMW10/N0vFNTAIAMx+7i/AATyKDPCUZEkJUOZIQCeGgjIqR2btmAzC+3Xi0mqKXvkrz9Z/xZOkMNAn15Yk2tWRlaiFElSWXzIRwUOtPr+dEygn83Px4ptUzFtdPy9az5M8EAF7sVl+SISFElSYJkRAO6qOYjwAY03oMPm4+FtdfHBNPRl4+jUJ86Nkk2NbdE0IIhyIJkRAOKPZSLFvPbcVF7WLVrvbpuXrTNh3jHqiPWi2jQ0KIqk0SIiEc0KydswB4stmT1PS1fBPWb2ISSM/Np14Nb/o0C7F194QQwuFIQiSEg0m4kcAPx34AYGKHiRbXz8zLZ6FpdKiejA4JIQSSEAnhcGbvnI1RMdKjTg9ahLSwuP7yXee4ka2nTpAXfe8KK4ceCiGE45GESAgHciXzCgv2LwBgcqfJFtfP1uWzYNtZAJ7vWg+NjA4JIQQgCZEQDuXjXR+Tm59Lu5rt6BbVzeL6K3af51qWjogAT/rfLaNDQghRSBIiIRxEak4qn8d+DsDr971u8bpBuXoDX2wtGB16oWs9XDTy9hdCiELyG1EIBzF3z1wydBncFXwXfRv0tbj+d3vOk5KZR01/Dx5tZfmdaUII4cwkIRLCAWTqMvlk9ycAvHbva1aODp0BCuYOaWV0SAghzMhvRSEcwBd7v+B6znUaBDawahPXhdvPciU9j2AfNx5rLaNDQghxK0mIhLBzufm5poUYp3Sagkatsaj+8l3n+GjjKQCSM/L48cAlm/dRCCEcnSREQti5rw98TVJmEhF+ETx111MW1U1My+HNH+NMjxXgtTVxJKbl2LiXQgjh2CQhEsKO6Qw6Zv45E4DJHSej1Wgtqh93KR3llmMGRSEhJdtGPRRCCOcgCZEQdmzxgcWcSztHiHcII1uOtLj+5pPJRY5pVCoigzxt0T0hhHAakhAJYady83N5d9u7QMG6Qx5aD4vqn7uWxX/3XgSgcEFqjUrF9AHNCPWzrC0hhHB2LpXdASFE8b7c+yWXMi4R7hvO6FajLa7/wYYT6AxG7qsfxAePNefctRwigzwlGRJCiGJIQiSEHcrSZTF9x3QA3rz/Tdxc3Cyqvyf+OuuPJKFWwesPNSbM35Mwf7lMJoQQJZFLZkLYoXl75pGclUydanUYcfcIi+oajQr/t+4YAIPaRtAoxLcceiiEEM5FEiIh7Ex6XjozYwruLHur81sW31n206FLHL6YhrebCxN6NCiPLgohhNORhEgIOzNn1xyu51ynUVAjhjQfYlHdHJ2BmRtOAjC2a12q+1h2qU0IIaoqSYiEsCPXc66bVqV+u8vbFq9KvWD7WRLTcqnp78HITlHl0UUhhHBKkhAJYUdm/jmT9Lx07gq+y+I9y66k5zJ/S8EGrlP6NMJda1kyJYQQVZkkRELYifNp50072r/b9V3UKsvenrM2niRHb6BlhD997wotjy4KIYTTkoRICDvxxh9vkJufS+fanXm4wcMW1Y27lMYP+woWYXyzbxNUKlV5dFEIIZyWJERC2IH9iftZdngZAB/1/MiihEZRFN5bdxxFgX4twmgVUa28uimEEE5LEiIhKpmiKEzcOBGAIc2H0CasjUX1v997kZ1nr6HVqJjcu2F5dFEIIZyeJERCVLJ1p9exJWELbho33nvgPYvqfrvrHK+uPgxAvkHhz79SyqOLQgjh9CQhEqIS5RvzeSX6FQDGtx9Pbf/aZa6bmJbDGz/GmR4rwGtr4khMy7F1N4UQwulJQiREJVq4fyEnUk4Q6BHI1HunWlT3z9MpKLccMygKCSnZtuugEEJUEXadEM2YMYO2bdvi4+NDjRo1eOSRRzh58qRZGUVRmDZtGmFhYXh4eNClSxeOHj1qViYvL49x48YRFBSEl5cX/fr14+LFixUZihBFpOel89aWtwCY1mUafu5+Za5rMCosiUkoclyjUhEZJJu4CiGEpew6Idq6dSvPP/88u3btIjo6mvz8fHr27ElWVpapzMyZM5k9ezbz5s0jNjaWkJAQevToQUZGhqnM+PHjWbt2LStXrmTHjh1kZmbSt29fDAZDZYQlBADTtkwjOSuZBoENGNN6jEV1F/8ZT9zldNxc1Kj/viFNo1IxfUAzQv08yqG3Qgjh3FwquwO3s2HDBrPHixcvpkaNGuzbt4/7778fRVGYM2cOr7/+OgMGDABg6dKlBAcHs2LFCsaMGUNaWhqLFi1i2bJldO/eHYDly5cTHh7Opk2b6NWrV4XHJcSRK0f4dPenAMztM9eiDVwTUrL4aGPBSOlbDzela6PqJKRkExnkKcmQEEJYya4TolulpaUBEBAQAEB8fDxJSUn07NnTVMbNzY3OnTsTExPDmDFj2LdvH3q93qxMWFgYzZo1IyYmpsSEKC8vj7y8PNPj9PR0APR6PXq93mYxFbZlyzbtjbPHaGl8iqLw3C/PYVAMDGg0gK4RXctc12hUeOW/h8jVG+lYJ4DHW4agUqkIivC1qA+WcPbzB84fo7PHB84fo8R3522XxmESIkVRmDBhAvfeey/NmjUDICkpCYDg4GCzssHBwZw7d85UxtXVlWrVqhUpU1i/ODNmzODtt98ucnzjxo14etp+jkZ0dLTN27Q3zh5jWePbfH0zf178Eze1G33UfVi/fn2ZX2NboorYBA2uaoXufsn8+uuv1nbXYs5+/sD5Y3T2+MD5Y5T4LJedXbYbTRwmIXrhhRc4fPgwO3bsKPLcrav6KopS6kq/pZWZOnUqEyZMMD1OT08nPDycnj174uvra2HvS6bX64mOjqZHjx5otWW/bOJInD1GS+K7kXuDZ794FoD/dP4PwzsML/PrXEjNZuq8nYCBqQ825ql2EXfS7TJz9vMHzh+js8cHzh+jxGe9wis8pXGIhGjcuHH8/PPPbNu2jVq1apmOh4SEAAWjQKGh/2xmmZycbBo1CgkJQafTkZqaajZKlJycTMeOHUt8TTc3N9zc3Ioc12q15fLDWF7t2hNnj7Es8b276V2Ss5NpFNSISZ0mlXnukKIovPHTcbJ1BtpFBTC8Yx3U6ordr8zZzx84f4zOHh84f4wSn3VtloVd32WmKAovvPACa9as4Y8//iAqKsrs+aioKEJCQsyG2HQ6HVu3bjUlO61bt0ar1ZqVSUxMJC4u7rYJkRC2djDpIJ/FfgbAvD7zcNW4lrnuij3niTlzDXetmg8eu6vCkyEhhHB2dj1C9Pzzz7NixQp++uknfHx8THN+/Pz88PDwQKVSMX78eKZPn079+vWpX78+06dPx9PTk8GDB5vKjho1iokTJxIYGEhAQACTJk2iefPmprvOhChvBqOBf//yb4yKkUFNB9GtTrcy1710I4cZ608A8EqvRkQGeZVXN4UQosqy64Ro/vz5AHTp0sXs+OLFixkxYgQAkydPJicnh7Fjx5Kamkq7du3YuHEjPj4+pvIff/wxLi4uDBw4kJycHLp168aSJUvQaDQVFYqo4j7e9TG7L+3Gz82PWT1nlbne5RvZ/HvZPjLz8mlduxojOkaWXyeFEKIKs+uESFFu3ZigKJVKxbRp05g2bVqJZdzd3Zk7dy5z5861Ye+EKJtT107x5uY3AZjdazY1fWuWqd6q2PNMWX3EtD1Hl4bV0cilMiGEKBd2PYdICEdnVIyM+nkUufm59Kzbk6fvfrpM9RLTcpi65ojZXmVzok/Lxq1CCFFOJCESohx9tuczdpzfgberN1/1/arU5SAKnb6SifGWAVLZuFUIIcqPJERClJOzqWeZ8vsUAGZ2n0lt/9plrvvzwUtFjsnGrUIIUX4kIRKiHCiKwjM/P0O2PpsukV0Y06bsm7euPXCR/+4vSIhk41YhhKgYdj2pWghHNXfPXDYnbMbDxYOFDy9ErSrb3x5HL6cxdc0RAF58oB5PtouQjVuFEKICSEIkhI0dTDrIK9GvADCzx0zqBtQtU70b2Tr+vXwfuXojnRtU56XuDdCoVZIICSFEBZBLZkLYUJYuiydXP4nOoOPhBg/zfNvny1TPaFQYv+ogF67nEB7gwSf/ultusRdCiAokCZEQNvTyby9zIuUEYT5hfN3/6zLfVTbn99NsOXkVNxc1XzzVGn/Psm/rIYQQ4s5JQiSEjaw+vpoF+xegQsWyR5cR5BlUpnq/H7/Cp7+fBmDGgOY0DfMrz24KIYQohiREQtjAVd1Vnvv1OQBe7fQqD0Q9UKZ6CSlZjF91EIBhHWozoFWt8uqiEEKI25CESIg7pDPomHVuFjdyb3BPzXt4p+s7Zap39momQxftJiO3YJ+yNx5qUs49FUIIURK5y0yIOzQxeiInsk7g6+bLigEr0Gq0pdZZuec8U/6+vR6gd9MQXF3k7xMhhKgs8htYiDuwaP8ivtz/JSpUfNP/mzLdYl+4T9nN3v/1hOxTJoQQlUgSIiGstOviLsauHwvAkyFP8mC9B8tU7/PNZ7hlmzLZp0wIISqZXDITwgpJmUk89v1j6Aw6+jfoz+Mej5ep3qrY8yzbda7IcdmnTAghKpeMEAlhIZ1Bx+PfP87ljMs0qd6Erx/+ukxbc/x86LJp3tB99YPQyD5lQghhN2SESAgLKIrC6P+N5s8Lf+Ln5sePg37Ex82n1HrRx64wYdVBFAUGt4vgvUeakZSeK/uUCSGEnZCESAgLvPHHG3xz6Bs0Kg0rH19J/cD66PX629bZcTqF57/dT75R4dGWNfm//s1QqQr2KJNESAgh7INcMhOijL7Y+wXTd0wHYMHDC+hdr3epdfYmXGf0N3vRGYz0ahrMh4/fhVr2KBNCCLsjI0RClMFPJ37i+fUFG7W+3eVtnm759G3LJ6blsPlEMu+tO06O3sD9Darz6ZMtcdHI3yBCCGGPJCESohS7Lu7iydVPYlSMjG41mjfvf/O25VfFnmfqmiMY/763PirQiy+fao2bi6YCeiuEEMIa8ueqELdxMOkgD614iJz8HB6q/xCfP/T5bXewL1x00XjTQkPnrmdxI0dXAb0VQghhLUmIhCjBoaRDdPumG9dzrtOhVgdWPb4KF/XtB1XXH0k0S4YAjAqy6KIQQtg5SYiEKMaRK0dMydA9Ne/h1yG/4uXqdds6Px28zIz1x4scl0UXhRDC/klCJMQt4pLjeOCbB7iWc402YW347anf8HP3K7G8oij8ekHFpNVx5BuhWZgvall0UQghHIpMqhbiJnHJcTyw9AFSslNoHdqajU9txN/dv8Tyunwjr66JY8PFggnTY+6vw6u9G3ElQxZdFEIIRyIJkRB/235uO/1W9uNG7g1ahrRk49CNVPOoVmL5G9k6/r18H7vOXkeNwrR+TRjWsQ6ALLoohBAORhIiIYAfT/zIk6ufJDc/l47hHfnfk/8jwCOg2LKJaTnsOnuNj6NPcf56Dl5uGobW0fFk2/AK7rUQQghbkYRIVHlf7fuK59Y9h1Ex8nCDh1n5+Eo8tcVPgl4Ve54pa46g/H0nmZ+HC9+ObMuZ/dsrsMdCCCFsTSZViypLURTe3vI2Y34Zg1ExMqrlKNYMWlNiMnT5RjZTVv+TDAFk5Obj66GtoB4LIYQoLzJCJKqkTF0mI38ayQ/HfgDgjfve4J2u75S46OLVjDye//YAtywxhFGB89dljSEhhHB0khCJKuds6lkeWfkIR5KPoFVr+ezBzxjdenSJ5aOPXWHK6sNcyyq62rRGpSIiwJNr5dlhIYQQ5U4SIlGlRJ+JZtB/B5Gam0qIdwj/feK/dIroVGzZzLx83v3fMVbtvQBAoxAfejcLYe7vf2FQlJvWGHLnQEUGIYQQwuYkIRJVgsFo4P0d7/OfLf/BqBi5p+Y9rBm4hpq+Nc3KJablEJ+SRUaOnvfWn+D89WxUKnj2vjpM6NkANxcNg9qGm60xpNfrKykqIYQQtiIJkXB659PO89Sap9h+vuBOsKfvfprPH/ocdxd3s3K37lIPUNPfg1kDW9C+TqDpmKwxJIQQzkcSIuHUVsWtYswvY0jLS8Pb1ZvPHvyMoXcNLTJ5OjEtx+x2egAVsPjptjQI9qnYTgshhKhwkhAJp5Sak8r438bzzaFvAGhXsx3fDviWugF1i5RNTMth8g+HzZIhAAW4lqmD4ArosBBCiEolCZFwKoqisOroKl7a8BLJWcmoVWpev+913rz/TbQa8/WCsvLy+WLrGRZsP0uu3likLdmlXgghqg5JiITTSLiRwNh1Y/n1r18BaBzUmAUPLzDdRVY4YToiwJMdp1OYFX2Kqxl5ALSNrEa7qEDmbzlzyx1kMldICCGqAkmIhMPL0efwye5PeHfbu2Trs3HVuPLGfW8wudNk3FzcgOInTAPUDvRkap9G9GoagkqlYkj7CNmlXgghqiBJiITDMipGvjvyHa/98Rrn084D0Ll2Z77s+yUNgxqayhU3YRrgxQfq8cID9XF1+WcHG7mDTAghqiZJiIRD2n5uOxM3TiT2ciwAtXxrMaPbDIY0H2K6g8xgVNh0/AqzN54skgwBdKgbZJYMCSGEqLokIRIOZfu57byz7R02nd0EgLerN1PvncrL7V/GQ1swspOty+e/+y7y9Y54Eq4Vv8+YTJgWQghxM0mIhN1TFIXNCZt5d9u7bEnYAoCL2oVRLUfxdpe3MRp8OXA+C2+3PDbEJfHt7vOk5RSsHu3noWVIuwiqebry/q8nZMK0EEKIYklCJOyWzqBj9bHVfLL7E3Zf2g2AVq1lVMtRvHrvq0T6R/LdnvO8tvaPIpfEagd6MureKB5vXQtP14If874tQmXCtBBCiGJJQiTsTnJWMl/t+4rPYz8nMTMRADeNG6NbjWZyp8mE+4Vz6koG//kxjm92nStSf8ajzRnYNhyN2nw1apkwLYQQoiSSEAm7YDAaiD4bzeKDi/nxxI/oDDoAangG06/e04xrN4bqXsH8fPAyPx7czvHE9BLbigzyKpIMCSGEELcjCZGoVCdTTvLNoW9YemgplzIumY63DWtLu+pD+GV3baJ3a4nefRQ4anpeq1HRLiqQP/9K4earZTJZWgghhDUkIRIV7kTKCX44+gPfxX3P8ZQ40/EAjwCebDaY9sGP8dfF6izZmVCk7t21/HmibS0ebBZKNS9XVsWe57U1cTJZWgghxB2RhEiUO4PRwImsE+zcspN1f60jLvmfJAhFg4exJd0iBhLmfi9b96TzS24WkFVsW6/2aUSHuoGmx4PaRnB/g+oyWVoIIcQdkYRIlIt9F0/z0/Fo4q5tY+v5aK7nXIfTBc9pVC645rfA03AvHob2aPDhyF9whOsA+HtqaVs7gE3Hr5TpcphMlhZCCHGnJCESNnEp/RI7zu9gc8Jmfjq+kaTseLPn3VRehHl0xJjTEkN2KzR4F2njsVY1eap9be6q5Y9GrZLLYUIIISqMJETCYmdSrvH7X7Ek5Rzh6LW97LywkwvpF8wLKWpclbq4G1rgYWyDm7ExxmwNAO5qFfpbdlnVqFRM6tXQLOGRy2FCCCEqiiREwkxiWg7xKVlEBXkR4uvOlawrHE0+yuErh9mftJ8tZ3dzMeMMqIy31FSjNUbibmyOu+Eu3I1NUd80ClTXx8jATg1oExVEs5q+/HjgUplGf+RymBBCiIogCVEVcnOyc3OSkW/MJ+FGAgt37mDBzhh0qovkqy+g0l4gx5BWtCEVqBV/3Iz1cTM2xs3YCFdjfTQqD2r6uXPxRq5ZcbUKhtU3MrhTJFqtFpDRHyGEEPZFEiIHUFIiU9YyeoOer/7cy3sbdqBXXcWgukLDmjnkcYXLmedJybmEQSnY+wvtTRUNgKLCRQlFq9TG1VgHV2M9XI11cSHAVGzM/XV4sHko9YO98XR1KTL3593+jfG6crhIn2X0RwghhL2QhKiSJablcjpNRWJaLhFB2iLPr4o9z9Q1RzAqBSMtMwY0Z1DbCBRFIUOXQVJGMkt2H2JRzEHyuYFRlUpEjTxQp3It5wo3dFfIzr+GghHc/ml3V7L566gUt78Tn5q4GMPQKuG4GmvTIqQJLSOCiQz0xMdNy2s/Hily59eITpG3nfsT5OnC+vVFEyIhhBDCXlSphOjzzz/nww8/JDExkaZNmzJnzhzuu+++SuvPqtjzTF6zk3wymX1iCX1b+FE7SMW1nDRSc1JJyrhGzNnzGFwyMaoyMZLB0F8yGPZrJnolHQX9P425/vPfG6nFvJjigosSiEYJwkWpgYsSQqhXBPUCoqgbUJdg71C+2ppQJNn5ekQns2RHrcbiuT96vb7I80IIIYQ9qTIJ0apVqxg/fjyff/45nTp14ssvv6RPnz4cO3aMiIiICu9PYloOU9cc4Yr2PfI0RwBYcKKYgkUHjbg5a1Ep7mgUP9T4o1F80SgBaJQAGlYPp35QOOG+NQnyCGPu78mgqE31NCoVf4ztapbM1AnyKTXZkbk/QgghnFGVSYhmz57NqFGjeOaZZwCYM2cOv/32G/Pnz2fGjBkV3p/4lKyCy2B4olLc//7XEw8XbzxdvPFw8cVd7cPlVA1qvFErXqjxQYMvE7u3pklwTWr7B6PCjYfn7uDmu9g1KhU/jjBPdmr5lb6mT1mTHZn7I4QQwtlUiYRIp9Oxb98+pkyZYna8Z8+exMTEFFsnLy+PvLw80+P09ILd1fV6vU0uAdXyc0Otguq6N1BRsDO7WgVbxt1PqJ+7qdwP+y7yxk/HTHOI/q9/E55oXcusrf/r38SszLv9GxPk6WLWzwF3h9Ihqhrnr2cTEeBJqJ97sXEEeboQFOFritUWCttx1ktnEp/jc/YYnT0+cP4YJb47b7s0KkVRlNKLObbLly9Ts2ZN/vzzTzp27Gg6Pn36dJYuXcrJkyeL1Jk2bRpvv/12keMrVqzA09M2u6nvvKJi1Vk1CipUKAyqY6RDcNHTcSMPruaqqO6u4O9WTENlLCOEEEJUNdnZ2QwePJi0tDR8fX1LLFclRogKqVQqs8eKohQ5Vmjq1KlMmDDB9Dg9PZ3w8HB69ux522+oJR4Enr2WwZqNOxjQ817CA31s0q690ev1REdH06NHD9M6RM5E4nN8zh6js8cHzh+jxGe9wis8pakSCVFQUBAajYakpCSz48nJyQQHBxdbx83NDTe3okMtWq3WpicrPNCH+n4K4YE+TvlDfjNbf+/sjcTn+Jw9RmePD5w/RonPujbLQl16Ecfn6upK69atiY6ONjseHR1tdglNCCGEEFVTlRghApgwYQJDhw6lTZs2dOjQga+++orz58/z73//u7K7JoQQQohKVmUSokGDBnHt2jXeeecdEhMTadasGevXr6d27dqV3TUhhBBCVLIqkxABjB07lrFjx1Z2N4QQQghhZ6rEHCIhhBBCiNuRhEgIIYQQVZ4kREIIIYSo8iQhEkIIIUSVJwmREEIIIao8SYiEEEIIUeVJQiSEEEKIKq9KrUN0JxSlYBf6sm4SV1Z6vZ7s7GzS09Oddn8aZ49R4nN8zh6js8cHzh+jxGe9ws/tws/xkkhCVEYZGRkAhIeHV3JPhBBCCGGpjIwM/Pz8SnxepZSWMgkAjEYjly9fxsfHB5VKZbN209PTCQ8P58KFC/j6+tqsXXvi7DFKfI7P2WN09vjA+WOU+KynKAoZGRmEhYWhVpc8U0hGiMpIrVZTq1atcmvf19fXKX/Ib+bsMUp8js/ZY3T2+MD5Y5T4rHO7kaFCMqlaCCGEEFWeJERCCCGEqPIkIapkbm5uvPXWW7i5uVV2V8qNs8co8Tk+Z4/R2eMD549R4it/MqlaCCGEEFWejBAJIYQQosqThEgIIYQQVZ4kREIIIYSo8iQhEkIIIUSVJwlRBfj888+JiorC3d2d1q1bs3379tuW37p1K61bt8bd3Z06derwxRdfVFBPLTdjxgzatm2Lj48PNWrU4JFHHuHkyZO3rbNlyxZUKlWRrxMnTlRQr8tu2rRpRfoZEhJy2zqOdP4iIyOLPRfPP/98seUd4dxt27aNhx9+mLCwMFQqFT/++KPZ84qiMG3aNMLCwvDw8KBLly4cPXq01HZXr15NkyZNcHNzo0mTJqxdu7acIri928Wn1+t59dVXad68OV5eXoSFhTFs2DAuX7582zaXLFlS7HnNzc0t52iKV9o5HDFiRJG+tm/fvtR2HeEcAsWeC5VKxYcfflhim/Z0DsvyuWCP70NJiMrZqlWrGD9+PK+//joHDhzgvvvuo0+fPpw/f77Y8vHx8Tz44IPcd999HDhwgNdee40XX3yR1atXV3DPy2br1q08//zz7Nq1i+joaPLz8+nZsydZWVml1j158iSJiYmmr/r161dAjy3XtGlTs34eOXKkxLKOdv5iY2PNYouOjgbgiSeeuG09ez53WVlZtGjRgnnz5hX7/MyZM5k9ezbz5s0jNjaWkJAQevToYdqvsDg7d+5k0KBBDB06lEOHDjF06FAGDhzI7t27yyuMEt0uvuzsbPbv38+bb77J/v37WbNmDadOnaJfv36ltuvr62t2ThMTE3F3dy+PEEpV2jkE6N27t1lf169ff9s2HeUcAkXOw9dff41KpeKxxx67bbv2cg7L8rlgl+9DRZSre+65R/n3v/9tdqxRo0bKlClTii0/efJkpVGjRmbHxowZo7Rv377c+mhLycnJCqBs3bq1xDKbN29WACU1NbXiOmalt956S2nRokWZyzv6+XvppZeUunXrKkajsdjnHencKYqiAMratWtNj41GoxISEqK8//77pmO5ubmKn5+f8sUXX5TYzsCBA5XevXubHevVq5fyr3/9y+Z9tsSt8RVnz549CqCcO3euxDKLFy9W/Pz8bNs5GykuxuHDhyv9+/e3qB1HPof9+/dXHnjggduWsedzeOvngr2+D2WEqBzpdDr27dtHz549zY737NmTmJiYYuvs3LmzSPlevXqxd+9e9Hp9ufXVVtLS0gAICAgotWzLli0JDQ2lW7dubN68uby7ZrXTp08TFhZGVFQU//rXvzh79myJZR35/Ol0OpYvX87IkSNL3cDYUc7dreLj40lKSjI7R25ubnTu3LnE9ySUfF5vV8depKWloVKp8Pf3v225zMxMateuTa1atejbty8HDhyomA5aacuWLdSoUYMGDRowevRokpOTb1veUc/hlStXWLduHaNGjSq1rL2ew1s/F+z1fSgJUTlKSUnBYDAQHBxsdjw4OJikpKRi6yQlJRVbPj8/n5SUlHLrqy0oisKECRO49957adasWYnlQkND+eqrr1i9ejVr1qyhYcOGdOvWjW3btlVgb8umXbt2fPPNN/z2228sWLCApKQkOnbsyLVr14ot78jn78cff+TGjRuMGDGixDKOdO6KU/i+s+Q9WVjP0jr2IDc3lylTpjB48ODbbpjZqFEjlixZws8//8x3332Hu7s7nTp14vTp0xXY27Lr06cP3377LX/88QezZs0iNjaWBx54gLy8vBLrOOo5XLp0KT4+PgwYMOC25ez1HBb3uWCv70PZ7b4C3PrXtqIot/0LvLjyxR23Ny+88AKHDx9mx44dty3XsGFDGjZsaHrcoUMHLly4wEcffcT9999f3t20SJ8+fUz/b968OR06dKBu3bosXbqUCRMmFFvHUc/fokWL6NOnD2FhYSWWcaRzdzuWvietrVOZ9Ho9//rXvzAajXz++ee3Ldu+fXuzScmdOnWiVatWzJ07l08//bS8u2qxQYMGmf7frFkz2rRpQ+3atVm3bt1tEwdHO4cAX3/9NUOGDCl1LpC9nsPbfS7Y2/tQRojKUVBQEBqNpkj2mpycXCTLLRQSElJseRcXFwIDA8utr3dq3Lhx/Pzzz2zevJlatWpZXL99+/aV/pdMWXh5edG8efMS++qo5+/cuXNs2rSJZ555xuK6jnLuANMdgpa8JwvrWVqnMun1egYOHEh8fDzR0dG3HR0qjlqtpm3btg5zXkNDQ6ldu/Zt++to5xBg+/btnDx50qr3pT2cw5I+F+z1fSgJUTlydXWldevWpjt3CkVHR9OxY8di63To0KFI+Y0bN9KmTRu0Wm259dVaiqLwwgsvsGbNGv744w+ioqKsaufAgQOEhobauHe2l5eXx/Hjx0vsq6Odv0KLFy+mRo0aPPTQQxbXdZRzBxAVFUVISIjZOdLpdGzdurXE9ySUfF5vV6eyFCZDp0+fZtOmTVYl4oqicPDgQYc5r9euXePChQu37a8jncNCixYtonXr1rRo0cLiupV5Dkv7XLDb96FNpmaLEq1cuVLRarXKokWLlGPHjinjx49XvLy8lISEBEVRFGXKlCnK0KFDTeXPnj2reHp6Ki+//LJy7NgxZdGiRYpWq1X++9//VlYIt/Xcc88pfn5+ypYtW5TExETTV3Z2tqnMrTF+/PHHytq1a5VTp04pcXFxypQpUxRAWb16dWWEcFsTJ05UtmzZopw9e1bZtWuX0rdvX8XHx8dpzp+iKIrBYFAiIiKUV199tchzjnjuMjIylAMHDigHDhxQAGX27NnKgQMHTHdZvf/++4qfn5+yZs0a5ciRI8qTTz6phIaGKunp6aY2hg4danYn6J9//qloNBrl/fffV44fP668//77iouLi7Jr1y67ik+v1yv9+vVTatWqpRw8eNDsPZmXl1difNOmTVM2bNignDlzRjlw4IDy9NNPKy4uLsru3bsrPD5FuX2MGRkZysSJE5WYmBglPj5e2bx5s9KhQwelZs2aTnEOC6WlpSmenp7K/Pnzi23Dns9hWT4X7PF9KAlRBfjss8+U2rVrK66urkqrVq3MbkkfPny40rlzZ7PyW7ZsUVq2bKm4uroqkZGRJb4h7AFQ7NfixYtNZW6N8YMPPlDq1q2ruLu7K9WqVVPuvfdeZd26dRXf+TIYNGiQEhoaqmi1WiUsLEwZMGCAcvToUdPzjn7+FEVRfvvtNwVQTp48WeQ5Rzx3hUsD3Po1fPhwRVEKbvl96623lJCQEMXNzU25//77lSNHjpi10blzZ1P5Qj/88IPSsGFDRavVKo0aNaq0JPB28cXHx5f4nty8ebOpjVvjGz9+vBIREaG4uroq1atXV3r27KnExMRUfHB/u12M2dnZSs+ePZXq1asrWq1WiYiIUIYPH66cP3/erA1HPYeFvvzyS8XDw0O5ceNGsW3Y8zksy+eCPb4PVX93XgghhBCiypI5REIIIYSo8iQhEkIIIUSVJwmREEIIIao8SYiEEEIIUeVJQiSEEEKIKk8SIiGEEEJUeZIQCSGEEKLKk4RICCGEEFWeJERCCKexZcsWVCoVN27cqOyuCCEcjCREQgiH1KVLF8aPH292rGPHjiQmJuLn51fh/VGpVPz4448V/rpCCNtwqewOCCGErbi6uhISElLZ3RBCOCAZIRJCOJwRI0awdetWPvnkE1QqFSqVioSEhCKXzJYsWYK/vz+//PILDRs2xNPTk8cff5ysrCyWLl1KZGQk1apVY9y4cRgMBlP7Op2OyZMnU7NmTby8vGjXrh1btmwpsT+RkZEAPProo6hUKtNjIYTjkBEiIYTD+eSTTzh16hTNmjXjnXfeAaB69eokJCQUKZudnc2nn37KypUrycjIYMCAAQwYMAB/f3/Wr1/P2bNneeyxx7j33nsZNGgQAE8//TQJCQmsXLmSsLAw1q5dS+/evTly5Aj169cv8hqxsbHUqFGDxYsX07t3bzQaTbnGL4SwPUmIhBAOx8/PD1dXVzw9PUu9RKbX65k/fz5169YF4PHHH2fZsmVcuXIFb29vmjRpQteuXdm8eTODBg3izJkzfPfdd1y8eJGwsDAAJk2axIYNG1i8eDHTp08v8hrVq1cHwN/fXy7ZCeGgJCESQjg1T09PUzIEEBwcTGRkJN7e3mbHkpOTAdi/fz+KotCgQQOzdvLy8ggMDKyYTgshKpwkREIIp6bVas0eq1SqYo8ZjUYAjEYjGo2Gffv2Fbn0dXMSJYRwLpIQCSEckqurq9lEaFtp2bIlBoOB5ORk7rvvvjLX02q15dIfIUTFkLvMhBAOKTIykt27d5OQkEBKSopphOdONWjQgCFDhjBs2DDWrFlDfHw8sbGxfPDBB6xfv/62/fn9999JSkoiNTXVJn0RQlQcSYiEEA5p0qRJaDQamjRpQvXq1Tl//rzN2l68eDHDhg1j4sSJNGzYkH79+rF7927Cw8NLrDNr1iyio6MJDw+nZcuWNuuLEKJiqBRFUSq7E0IIIYQQlUlGiIQQQghR5UlCJIQQQogqTxIiIYQQQlR5khAJIYQQosqThEgIIYQQVZ4kREIIIYSo8iQhEkIIIUSVJwmREEIIIao8SYiEEEIIUeVJQiSEEEKIKk8SIiGEEEJUef8PRMTJU71OoT8AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y0 = np.array([5.0])\n", "T = 20.0\n", "N = 50\n", "t, z = Euler(croissanceCell, y0, 0.0, T, N)\n", "plt.plot(t, z, '.-', label=\"Euler\"); \n", "plt.plot(tref, yref, '-g', label=\"Reference odeint()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "b2edd6b6-9894-4c1e-94bf-6fbfc712e1c0", "metadata": {}, "source": [ "Testez plusieurs valeurs de $N$, par exemple $N=10,\\ 50,\\ 100, 200$ pour observer l'évolution de l'erreur en fonction de $N$ et vérifier la convergence de la méthode." ] }, { "cell_type": "code", "execution_count": 16, "id": "ba825e2e-e89f-456b-8e62-395dc4b9eeb9", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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XQ4VCvJyJ8FIIKcOY2fKmakGUmZnJ8ePHLY9PnTrFnj178PX1pUaNGkyYMIFp06YRERFBREQE06ZNw9XVlWHDhgHg5eXFY489xqRJk/Dz88PX15cXX3yRpk2bWmadNWzYkL59+/LEE08wd+5coGDa/YABA2SGGbBgwQIWLFhww+cbNmzIli1bimwrHEQM0K1btyKPAdq2bcvatWstj81mc5Euy7i4uNsLWghRaRRF4VzGOfYk7rF8HEg6wPHLxzEpN77fWqhHKLW8axHuHU64dzg1vWoS5hVGdc/qVPesjpfeq8Qem1yjiS0nLhF1+DTrDyeRmP7feCAHDbSq4UPPRkH0bBhEDW8nfv/9d9rX8q2SxVChoW1r0KVeAHHJ2YT7V87QC3uhakG0Y8cOunfvbnlcOGZn1KhRLFiwgMmTJ5OTk8O4ceMsN2Zcu3at5R5EAB9//DGOjo4MGTLEcmPGBQsWWGbIAHz//fc899xzlp6NgQMHMmfOnErKUgghbMflnMtsP7edbfHb2HpuKzvO7yA5O7nYtl56LxoFNKKhf0Pq+9enrm9dInwjqONbB1eda7H7lCQ5M4/1R5L46/AF/j6WTLbhv6LL1UlLl4gAejYKonv9APzc/xvWYM8z6MoqxMtFCqFboGpBVFzvwtU0Gg2RkZFERkbesI2zszOzZ89m9uzZN2zj6+vL4sWLbydUIYSwS+fSz7Hp9CY2xW1i0+lNxF6Kva6NVqOlYUBDWgS3oGVwS5oGNqVxYGNC3ENue1yOoigcT8ok6vAF/jqcxK4zKVz9ZyHY05mejQLp2TCIDrX9cNZVrZsWispjtWOIhBBClL+MvAzWn1rPH8f/YN2pdRy/fPy6NhG+EbSv3p721Qo+mgY1xdnx9sd2FK7VWN3HhfiUHP46nMS6wxc4fanotOgm1Tzp2bDgUljjUE+7GAwtrJ8UREIIYeeOXz7OT0k/Mev7Wfx79l+M5v8uLzloHGgZ3JJu4d3oWrMrncI64efqV+4xLI85w5SV+ynuooCT1oFOdf3o2TCIHg0D5XKPUIUUREIIYWcUReHgxYOsPLySFYdXsO/CviLP1/apTb+6/ehTpw9danbBy9mrQuNJSMvhlWKKof5NgxnYvBqdI/xx08ufI6Eu+QkUQgg7cS79HIv3Lea7fd9x6OIhy3atRksTtyaM6jiKAfUHEOEXUalxnUrOKnJvnEIjOoTTsU7590YJcSukIBJCCBuWm5/LikMrWLh3IetOrkO5sj67k9aJ3nV6c3/D++lXux9bN2ylf9v+qtx4Msjj+vFHWo2GcP9bm4kmREWQgkgIIWzQ6dTTfLHjC77Z9Q2Xci5Ztneu0ZmRzUfyYKMHLZfC1J6SvuXkpSKPbemGgaLqkIJICCFshKIobIjbwKfbPuXXo79iVgqWjanhVYMxLcYwovkIavvUVjnKohRF4bstcQA83yOCDrX95IaBwipV3dt5inJz5MgROnTogLOzc5FFXau68PBwZs2aVer2kZGR5fr9GzFiBNOmTbM8btu2LStXriy344vKY1bM/HzkZzrM60CP73rwc+zPmBUzPWv35KehP3HyuZNM7TbV6oohKOgdOnohE1cnLY91rkXHOn5SDAmrJAVRFTZ69Gg0Gg0ajQZHR0dq1KjB008/TUpKSpmOM3XqVNzc3IiNjeWvv/6qoGjt34svvljm79+Niq59+/bx22+/MX78eMu2119/nSlTplgWoxXWL9+cz5L9S2j+ZXMGLR/E9nPbcXF04Zm2z3D4mcNEjYji3gb3onWw3psVLoyOA2Bwq2p4OtvvwrnC9klBVMX17duXhIQE4uLi+Oabb/j1118ZN25cmY5x4sQJ7rzzTmrWrImf363NGDEYDLe0nz1xd3e/5e/ftebMmcODDz5YZJmbu+++m7S0NP78889yeQ1RcRRF4dfYX2n+ZXOGrxzOgaQDeOo9eeXOV4ibEMec/nNo4N9A7TBLFJ+STdShCwCM6hiubjBClEAKogqgKApZhqzSfxjL0LaEj5sthVIcvV5PcHAw1atXp3fv3gwdOrTIwqwA8+fPp2HDhjg7O9OgQQM+//xzy3MajYadO3fy1ltvWZZaATh37hxDhw7Fx8eHgIAAhg0bVmRR19GjRzNo0CCmT59OaGgo9erVu24/Pz8/7r333mL3+/DDDwkJCcHPz49nnnmmyKDRvLw8Jk+eTFhYGHq9noiICObNm2d5/tChQ/Tv3x93d3eCgoIYMWIEycnFr9VUaMWKFTRu3Bi9Xk94eDgfffRRkecvXrzIwIEDcXFxoVatWnz//ffXHSMtLY0nn3ySwMBAPD09ueuuu9i7d6/l+WsvmZWUa7du3Th9+jQvvPCCpacPChbT/b//+z8GDhxY5PW1Wi39+/dn6dKlN81VqGtr/Fa6LujKwGUDOXTxED7OPrzT/R1OTzjNtB7TCHQLVDvEUlu89QxmBe6o60dEkEfJOwihIhlUXQGyjdm4T3dX5bUzX8nEzcntlvY9efIkf/zxR5FpuV9//TVTp05lzpw5tGzZkt27d/PEE0/g5ubGqFGjSEhIoGfPnvTt25cXX3wRd3d3srOz6d69O507d2bz5s04ODgQGRlJ//792bdvH05OTgD89ddfeHp6EhUVhaIo1+3n6OjIO++8Q9++fYvst2HDBkJCQtiwYQPHjx9n6NChtGjRgieeeAKAkSNHsmXLFj799FOaN2/OqVOnLAVPQkICXbt25YknnmDmzJnk5OTw8ssvM2TIENavX1/s92Xnzp0MGTKEyMhIhg4dSnR0NOPGjcPPz4/Ro0cDMG7cOBITE1m/fj1OTk4899xzJCUlWY6hKAp33303vr6+rFmzBi8vL+bOnUuPHj04evQovr6+xb72zXJduXIlzZs358knn7TkDgWXy1JTU2nTps11x2vXrh0zZswo7Y+EqERn084yce1Efjz0IwDOjs483/55ptw5BW9nb3WDuwW5RhPLYs4AMFJ6h4QNkIKoilu9ejXu7u6YTCZyc3MBmDlzpuX5t99+m48++ojBgwcDUKtWLQ4dOsTcuXMZNWoUwcHBODo64u7uTnBwMADffvstDg4OfPPNN2g0GsxmM5999hnh4eFs3LiR3r17A+Dm5sY333xjKXSu3Q8Keqe8vb2L7Ofj48OcOXPQarU0aNCAu+++m7/++osnnniCo0eP8sMPPxAVFUXPnj0BqF37v4GmX3zxBa1atSoy2Pjbb78lLCyMo0ePWnqqrjZz5kx69OjB66+/DkC9evU4dOgQH3zwAaNHj+bo0aOsW7eO6OhoOnbsCMC8efNo2LCh5RgbNmxg//79JCUlodcXrND94Ycf8tNPP/Hjjz/y5JNPFnt+bparr68vWq0WDw8Py/ceIC4uDq1WS2Dg9T0J1apV48yZM5jNZhwcpIPYGhhNRj7Z9gmRGyPJMmbhoHFgdPPRvNn9Tap7Vlc7vFv2y97zpGYbqebtQs+GQWqHI0SJpCCqAK46VzJfySxVW7PZTHpGOp4enuXyB8pVV7YbnXXv3p0vvviC7OxsvvnmG44ePWoZiHvx4kXOnj3LY489VqQHIj8/Hy+vG9/qf+fOnRw/frzI+BWA3NxcTpw4YXnctGlTSzFUlv0aN26MVvvfINKQkBD2798PwJ49e9BqtXTt2vWGsW3YsAF39+t78E6cOFFsQXT48GHuvffeItvuuOMOZs2ahclk4vDhwzg6OhbpkWnQoAHe3t5FXjczM/O6MUI5OTlFcrvWzXK9kZycHPR6fbELYrq4uGA2m8nLy8PFRWb6qO3fM//y9G9Psz+p4JzeWeNOPu//OU2Dmqoc2e1RFMUymHpEx5poHWRxVmH9pCCqABqNptSXrcxmMyadCTcnN1X+Y3dzc6Nu3boAfPrpp3Tv3p0333yTt99+2zIb6euvv6Z9+/ZF9rv6j/S1zGYzrVu3toyjMZvNZGZmWsbsXP3aN9vvagEBAZavr73TbmEvFFDiH3mz2cw999zD+++/f91zISEhxe6jKMp1xcXVY7UKv77Zitxms5mQkBA2btx43XNXF07XulmuN+Lv7092djYGg6FIwQlw+fJlXF1dpRhSWZYhi8lRk/l8R8F4PD8XP2b0msHoFqNx0Nh+z93O0ykcPJ+O3tGBoW3C1A5HiFKRgkgUMXXqVPr168fTTz9NaGgo1apV4+TJkwwfPrzUx2jVqhXLly+3DB42m82kp6fj6XnzXrBr97sVTZs2xWw2s2nTJssls2tfY8WKFYSHh+PoWLof/0aNGvHPP/8U2RYdHU29evXQarU0bNiQ/Px8duzYQYcOHQCIjY0lNTW1yOsmJibi6OhIeHj4LeVWHCcnJ0wmU5FthQOzDx06dN19jQ4cOECrVq3K7fVF2W2L38aIVSM4dvkYAGNajOH9Xu/j7+qvcmTlZ8GV3qFBLarh4+Z088ZCWAnb/1dElKtu3brRuHFjyxibyMhIpk+fzieffMLRo0fZv38/8+fPLzLO6FrDhw/H39+fe++9l7///ptTp07x77//MmHCBOLj48u036ZNm3j++edvut/VwsPDGTVqFGPGjOGnn37i1KlTbNy4kR9++AGAZ555hsuXL/Pwww+zfft2Tp48ydq1axkzZsx1hUWhSZMm8ddff/H2229z9OhRFi5cyJw5c3jxxRcBqF+/Pj169GDs2LFs27aNnTt38vjjjxfphenZsycdO3Zk0KBB/Pnnn8TFxREdHc1rr73Gjh07SpXbjfLdvHkz586dswwcDwgIoFWrVtcVcQB///23ZSyWqFxGk5HIjZHc8e0dHLt8jGoe1Vj7yFrm3TvProqhC+m5/HEgEYCRnWqqHI0QpScFkbjOxIkT+frrrzl79iyPP/4433zzDQsWLKBp06Z07dqVBQsWUKtWrRvu7+rqyubNm6lRowaDBw+mcePGPPvss+Tk5Ny05+fa/Ro2bMiYMWNK3O9aX3zxBQ888ADjxo2jQYMGPPHEE2RlZQEQGhrKv//+i8lkok+fPjRp0oTnn38eLy+vG/ZetWrVih9++IFly5bRpEkT3njjDd566y3LDDOAzz77jOrVq9O1a1cGDx5smV5fSKPRsGbNGrp06cKYMWOoV68eDz30EHFxcUUuI5bVW2+9RVxcHHXq1ClyWfHJJ5+87tLjuXPniI6O5tFHH73l1xO3Ji41jjvn38mbm97EpJh4uMnD7H96P73q9FI7tHL3/dbT5JsV2ob70Dj0xmMNhbA2GqWsN66potLT0/Hy8iItLe26P865ubmcOnWKWrVq4ex8/arON1Pay0m2zN5ztMb8cnNzqV+/PsuWLbPMfHvppZdIS0vjq6++uul+1/4sG41G1qxZQ//+6qyUXhkqMsc/j//JsJXDuJxzGW9nb764+wseavJQub5GSSrrHOblm7jjvfUkZxqYM6wlA5qFVthrXcvef04lv1t3s7/fV5MxRELYIWdnZ7777rsiN5wMDAy0XOYTFc+smJn29zTe2PAGCgptQ9vy45AfqeFVQ+3QKszv+xNJzjQQ7OlMn8bBJe8ghBWRgkgIO3XtrQdeeukllSKpelJzUxmxagSrj64GYGzrsXzS9xP0jnqVI6tYhYOph7evgU5rHb2lQpSWFERCCFGOTqWcot/3/Yi9FIteq+eLu7/g0Zb2P25r79lU9pxNxUnrwMPt7bcXTNgvKYjKkQzHErZOfoZvz47zOxiwZAAXsi5Q3bM6Pz/0M61CqsZtDgpvxHh3sxD83e27J0zYJ+nTLAeFA8Cys7NVjkSI21P4M2yPgzYr2m9Hf6Prgq5cyLpA86DmbH1sa5UphpIz81i9LwGAUZ3C1Q1GiFskPUTlQKvV4u3tbVnM09XV9aZ3Lb6a2WzGYDCQm5trNTOUypu952gP+RUurpuUlIS3t/dN70QurvfVzq94+renMStmetXuxY9DfsRTf2s3F7VFy7afwWAy0zzMmxZh3mqHI8QtkYKonBQurnn1CueloSgKOTk5uLi4lLqIsjX2nqM95eft7V1koVhRsvf/eZ8pf00BYHSL0Xw14Ct02qrTw2Y0mVm8tWBV+9FyI0Zhw6QgKicajYaQkBACAwMxGo2l3s9oNLJ582a6dOlit5cp7D1He8lPp9NJz1AZvbv5XV7b8BoAr3Z+lbe7v23zRXFZrT14gcT0XPzdnejftPj1AIWwBVIQlTOtVlumPyparZb8/HycnZ1t+o/pzdh7jvaenyjemxvfJHJTJADvdH+HV7u8qm5AKikcTP1wuxroHaWgFrZLCiIhhCgDRVGYunEqb29+G4D3erzHy3e+rHJU6jh0Pp3tcZdxdNAwvL1cLhO2TQoiIYQog9c3vM67f78LwIe9PmRSp0kqR6Se77bEAdCnSTDBXmVbtkgIayMFkRBClNLMLTMtxdCsPrN4vsPzKkekntRsAz/tOQfAaJlqL+yAbc4RFkKISrZo7yImrS3oDXqvx3tVuhgCWB5zllyjmUYhnrSp6aN2OELcNimIhBCiBL8f+50xv4wB4IUOLzD5jskqR6Quk1lh0dbTQEHvUFWbWSfskxREQghxE1vjt/LA/z1AvjmfR5o9woe9P6zyBcBfhy8Qn5KDt6uOgS1C1Q5HiHIhBZEQQtzAkeQj3L3kbrKN2fSt25dvB36Lg0Z+bS68Mph6aNswnHUy1V7YB3lnCyFEMVJyUhi4dCCXcy7Tvlp7fnzwxyp1B+obOZ6Uwb/HL+GggREdZKq9sB9SEAkhxDXyzfkM/XEoxy4fo4ZXDX55+BfcnNzUDssqLIwuGDvUs2EQ1X1cVY5GiPIjBZEQQlxjctRkok5G4apz5eeHfibQLVDtkKxCeq6RFbviAZlqL+yPFERCCHGVBXsW8PHWjwH4btB3tAhuoW5AVuTHHfFkG0xEBLrTsY6f2uEIUa6kIBJCiCu2xm9l7OqxAEztOpX7G92vckTWw2xWLHemHilT7YUdkoJICCGAVGMqQ1YMwWAyMLjhYN7o+obaIVmVTccuEncpGw9nRwa3rKZ2OEKUOymIhBBVnlkx8/GZj0nMSqRxQGMWDloo0+uv8d2VVe0fbB2Gm15WfRL2R97xQogq74MtH7A3Yy8uji788OAPuDu5qx2SVYlLzmLj0YtoNDCyo0y1F/ZJCiIhRJX2z5l/iNwUCcCnfT6lUUAjdQOyQt9tOY2iQLd6AYT7y+0HhH2SgkgIUWVdyr7EwysexqSY6OrTlZHNRqodktXJysvn/3acBQoGUwthr+RCsBCiSlIUhdE/jyY+PZ4I3wieqvaUzJwqxsrd58jIy6eWvxtdIwLUDkeICiM9REKIKmn29tmsProavVbP9/d9j4vWRe2QrI6iKJbB1CM61MTBQQpGYb+kIBJCVDlHLx1lyropAHzY+0NaBLVQNyArteXEJY4lZeLqpOWBNtXVDkeICiUFkRCiSjGZTYz+aTQ5+Tn0rN2TZ9o+o3ZIVmvBld6h+1tVx9NZFrYV9k0KIiFElTJzy0y2xG/Bw8mDeQPnybihG4hPyWbd4QuATLUXVYMUREKIKuPQxUO8vuF1AD7u8zE1vGqoHJH1WrT1NGYF7qjrR0SQh9rhCFHhpCASQlQJ+eZ8Rv80mjxTHv0j+jOm5Ri1Q7JauUYTy2MKptqP6hiubjBCVBIpiIQQVcKMf2cQcz4Gb2dvvhrwlVwqu4lf9pwnNdtIdR8XejQMUjscISqFFERCCLt3JPkIkRsjAfi076dU85TFSW9EURTLYOoRHWqilan2ooqQgkgIYdcUReHp357GaDZyd8TdPNLsEbVDsmo7TqdwKCEdvaMDQ9qEqR2OEJVGCiIhhF1bvG8xG+M24uLowpz+c+RSWQkKe4cGtaiGj5uTusEIUYmsuiDKz8/ntddeo1atWri4uFC7dm3eeustzGazpY2iKERGRhIaGoqLiwvdunXj4MGDRY6Tl5fH+PHj8ff3x83NjYEDBxIfH1/Z6QghKtnlnMtMWjsJgKldpxLuHa5uQFYuMS2XPw4kAjBK1i0TVYxVF0Tvv/8+X375JXPmzOHw4cPMmDGDDz74gNmzZ1vazJgxg5kzZzJnzhxiYmIIDg6mV69eZGRkWNpMmDCBVatWsWzZMv755x8yMzMZMGAAJpNJjbSEEJXklXWvcDH7Io0CGvFCxxfUDsfqfb/tNCazQrtwXxqFeqodjhCVyqoXd92yZQv33nsvd999NwDh4eEsXbqUHTt2AAW9Q7NmzeLVV19l8ODBACxcuJCgoCCWLFnC2LFjSUtLY968eSxatIiePXsCsHjxYsLCwli3bh19+vQp9rXz8vLIy8uzPE5PTwfAaDRiNBrLLcfCY5XnMa2Nveco+VmnrfFb+WrXVwDM7jMbjVmD0Vx8DraaY2mVJr+8fDNLtp0B4JH21W3ueyHn0LZVZH6lPaZGURSl3F+9nLz33nt8+eWXrF27lnr16rF371569+7NrFmzePjhhzl58iR16tRh165dtGzZ0rLfvffei7e3NwsXLmT9+vX06NGDy5cv4+PjY2nTvHlzBg0axJtvvlnsa0dGRhb73JIlS3B1dS3/ZIUQ5cakmJgUO4m43Dh6+PZgfI3xaodk9WIualh8XIuXk8LUlia0Vn39QIjSy87OZtiwYaSlpeHpeeOeT6vuIXr55ZdJS0ujQYMGaLVaTCYT7777Lg8//DAAiYkF17qDgoreJyMoKIjTp09b2jg5ORUphgrbFO5fnFdeeYWJEydaHqenpxMWFkbv3r1v+g0tK6PRSFRUFL169UKns8+1guw9R8nP+nyy/RPi9sbh6+LLopGL8Hf1v2l7W8yxLEqT37y5W4F0Hu0cwT3daldugOVAzqFtq8j8Cq/wlMSqC6Lly5ezePFilixZQuPGjdmzZw8TJkwgNDSUUaNGWdpdO2tEUZQSZ5KU1Eav16PX66/brtPpKuSHsaKOa03sPUfJzzpczLrIO3+/A8D7Pd8nxCuk1PvaSo636kb57Tmbyr74dJy0DjzSMdymvwdV9Rzai4rIr7THs+qC6KWXXmLKlCk89NBDADRt2pTTp08zffp0Ro0aRXBwMFDQCxQS8t8vvaSkJEuvUXBwMAaDgZSUlCK9RElJSXTq1KkSsxFCVIapG6eSlpdGy+CWsjxHKS28MtV+QLMQ/N2v/0dQiKrAqq8SZ2dn4+BQNEStVmuZdl+rVi2Cg4OJioqyPG8wGNi0aZOl2GndujU6na5Im4SEBA4cOCAFkRB25mDSQebunAsULN7qoLHqX3FW4WJGHr/tSwBkqr2o2qy6h+iee+7h3XffpUaNGjRu3Jjdu3czc+ZMxowp+K9Po9EwYcIEpk2bRkREBBEREUybNg1XV1eGDRsGgJeXF4899hiTJk3Cz88PX19fXnzxRZo2bWqZdSaEsH2KojBx7UTMipnBDQfTNbyr2iHZhGXbz2AwmWkR5k3zMG+1wxFCNVZdEM2ePZvXX3+dcePGkZSURGhoKGPHjuWNN96wtJk8eTI5OTmMGzeOlJQU2rdvz9q1a/Hw8LC0+fjjj3F0dGTIkCHk5OTQo0cPFixYgFarVSMtIUQF+P3476w9sRYnrRMzes5QOxybYDSZWbytYALKqE41VY5GCHVZdUHk4eHBrFmzmDVr1g3baDQaIiMjiYyMvGEbZ2dnZs+eXeSGjkII+2E0GS13pH6u3XPU8a2jckS24c+DiVxIz8Pf3Yn+TUs/+FwIeyQX2IUQNm/uzrkcST6Cv6s/r3V5Te1wbEbhYOph7Wqgd5Qec1G1SUEkhLBpKTkpTN04FYC3u7+Nl7OXyhHZhoPn04iJS8HRQcPwDnK5TAgpiIQQNu2D6A+4nHOZRgGNeLzV42qHYzO+iy4YO9S3STBBns4qRyOE+qQgEkLYrMTMRD7Z9gkA0+6ahqODVQ+LtBopWQZ+2nMOgNEy1V4IQAoiIYQNe3fzu2Qbs2lfrT0D6w9UOxybsXzHWfLyzTQK8aR1TZ+SdxCiCpCCSAhhk+JS4yw3YZzWY1qJy/WIAiazwqItBZfLRncKl++bEFdIQSSEsEmRGyMxmo30rN2Tu2rdpXY4NmPd4QucS83Bx1XHwBahaocjhNWQgkgIYXMOXTzEon2LAHj3rndVjsa2FE61H9q2Bs46mWovRCEpiIQQNuf1Da9jVszc1+A+2lVrp3Y4NuNYUibRJy7hoIFHOtRQOxwhrIoUREIImxJzLoaVh1eiQcPb3d9WOxybsnjbGQB6Ngyiuo+rytEIYV1kjqoQwqa8vuF1AEY0H0HjwMYqR2M7cvLhp70Fq9rLVHshric9REIIm7Etfht/nvgTrUbL1K5T1Q7Hpmy7qCHbYKJekDsd6/ipHY4QVkcKIiGEzXh7c8ElshHNR1Dbp7bK0dgOs1nh78SCX/cjO8pUeyGKIwWREMIm7ErYxW/HfsNB48D/7vyf2uHYlL+PJ5Ocq8HD2ZH7WlZTOxwhrJIUREIIm1DYO/Rwk4eJ8ItQORrbsmjrWQDubxmKm16GjgpRHCmIhBBWb9+Fffx05Cc0aHi186tqh2NTTiVnselYMhoUHmkvU+2FuBEpiIQQVu+dze8A8GDjB2kY0FDlaGzLd1viAGjorVDTT6baC3EjUhAJIazaoYuH+PHQjwC81vk1laOxLVl5+fy4Ix6ALsGKytEIYd2kIBJCWLV3/34XBYX7GtxH06CmaodjU1buiicjL59wP1fqe0tBJMTNSEEkhLBaRy8dZdmBZQC81kV6h8pCURQWXlnV/pH2YTjITHshbkoKIiGE1fow+kPMipm7I+6mVUgrtcOxKdEnLnE8KRNXJy2DW8qq9kKURAoiIYRVSsxMZOHehQBMuXOKytHYngVXVrW/v1V1PJx16gYjhA2QgkgIYZU+3fYpBpOBjtU7ckfYHWqHY1POXs7mr8MXABjVqabK0QhhG6QgEkJYnYy8DD6P+RyAyXdMlqUmymjx1tOYFbizrj91Az3UDkcImyAFkRDC6ny962vS8tKo51ePgfUHqh2OTckxmFgWU3Bn6lGyqr0QpSYFkRDCqhhMBj7e+jEAL3V6CQeN/Joqi1/2niMtx0h1HxfuahCodjhC2Az5TSOEsCrLDiwjPj2eYPdgHmn2iNrh2BRFUVgQXTDVfkSHmmhlrr0QpSYFkRDCaiiKwox/ZwAwof0EnB2dVY7ItsTEpXA4IR1nnQND24apHY4QNkUKIiGE1fj9+O8cvHgQDycPxrYZq3Y4Nmfhlan2g1pUw9vVSd1ghLAxUhAJIazGB9EfADC29Vi8nb3VDcbGJKTl8MfBREAGUwtxK6QgEkJYhd0Ju9kYtxFHB0ee7/C82uHYnO+3nsFkVmhXy5eGIZ5qhyOEzZGCSAhhFT7Z9gkAQxoPobpndZWjsS15+SaWbj8DwKiO4eoGI4SNkoJICKG6xMxElh5YCsDz7aV3qKx+25fApSwDwZ7O9G4cpHY4QtgkKYiEEKr7cseXGEwGOoV1ol21dmqHY3MKB1M/0qEGOq38WhfiVsg7Rwihqtz8XL7Y8QVQMNVelM3uMynsjU/DSevAQ+1qqB2OEDZLCiIhhKqWHVhGUlYSYZ5h3NfwPrXDsTmFvUMDmofg765XNxghbJgUREII1SiKwqytswAY3248jg6O6gZkYy5m5PHb/gRABlMLcbukIBJCqGbT6U3svbAXV50rj7d6XO1wbM7S7WcwmhRahHnTPMxb7XCEsGlSEAkhVFPYOzS6+Wh8XHzUDcbGGE1mvt9WsG7ZaLkRoxC3TQoiIYQqTlw+wS+xvwDwXPvnVI7G9izdfoYL6Xn4uDrRv2mI2uEIYfOkIBJCqOKzmM9QUOhXtx/1/eurHY5NWR5zhjd+PghAaraBVbvjVY5ICNsnBZEQotJlGbKYv2c+UDCYWpReQloOU1butzxWgP+tPEBCWo56QQlhB6QgEkJUuiX7l5Cam0odnzr0qdtH7XBsyqnkLBSl6DaTohCXnK1OQELYCSmIhBCVSlEUPov5DICn2zyNg0Z+DZWFl4vuum1ajYZwf1cVohHCfshvIiFEpYo+G83eC3txdnTm0ZaPqh2OzdlwJKnIY61Gw7TBTQjxclEpIiHsg9wFTQhRqQp7h4Y1GYavi6/K0dgWo8nMoq0FU+2n3tOQBsFehPu7SjEkRDmQgkgIUWkuZF7gx0M/AvBMu2dUjsb2/H4gkQvpefi76xnWviZ6R63aIQlhN+SSmRCi0ny962uMZiMdqnegVUgrtcOxOQv+PQXA8PY1pBgSopxJQSSEqBT55nzm7pwLwDNtpXeorPaeTWXXmVR0Wg3DO8iq9kKUNymIhBCV4pfYX4hPjyfANYAHGz2odjg2x7KqfbNQAj2c1Q1GCDskBZEQolLM2T4HgCdaPYHeUa9yNLYlKSOXX/edB2TdMiEqihREQogKdyT5CBviNuCgcWBsm7Fqh2Nzlm47i9Gk0LKGrGovREWRgkgIUeG+2vkVAHdH3E0NLxn/UhaGfDOLZVV7ISqcFERCiAqVY8xh4d6FADzV5imVo7E9a/YncDEjj0APPf2ayKr2QlQUKYiEEBXqx0M/cjnnMjW8atCnjqxbVlbzrwymHtGhJk6O8itbiIoi7y4hRIUqnGr/ZKsn0TrIvXPKYveZFPaeTcVJ68DD7eVSoxAVyeoLonPnzvHII4/g5+eHq6srLVq0YOfOnZbnFUUhMjKS0NBQXFxc6NatGwcPHixyjLy8PMaPH4+/vz9ubm4MHDiQ+Pj4yk5FiCrnQNIB/j37L44OjoxpOUbtcGzOgiu9Q/c0D8XfXWbmCVGRrLogSklJ4Y477kCn0/H7779z6NAhPvroI7y9vS1tZsyYwcyZM5kzZw4xMTEEBwfTq1cvMjIyLG0mTJjAqlWrWLZsGf/88w+ZmZkMGDAAk8mkQlZCVB1zdxT0Dt1b/15CPGT8S1lcSM/lt30JgAymFqIyWPVaZu+//z5hYWHMnz/fsi08PNzytaIozJo1i1dffZXBgwcDsHDhQoKCgliyZAljx44lLS2NefPmsWjRInr27AnA4sWLCQsLY926dfTpU/yYhry8PPLy8iyP09PTATAajRiNxnLLsfBY5XlMa2PvOUp+xcsyZPHdvu8AeKzFY1b9/bHGc/hd9CnyzQqta3jTIMj1tmKzxvzKm73nKPnd/rFLolEURSn3Vy8njRo1ok+fPsTHx7Np0yaqVavGuHHjeOKJJwA4efIkderUYdeuXbRs2dKy37333ou3tzcLFy5k/fr19OjRg8uXL+Pj42Np07x5cwYNGsSbb75Z7GtHRkYW+9ySJUtwdXUt50yFsD/rLq1jztk5BDsF83nDz3HQWHWHtFXJN8PUnVoy8zWMrmeipZ/V/poWwuplZ2czbNgw0tLS8PT0vGE7q+4hOnnyJF988QUTJ07kf//7H9u3b+e5555Dr9czcuRIEhMTAQgKCiqyX1BQEKdPF9y3IzExEScnpyLFUGGbwv2L88orrzBx4kTL4/T0dMLCwujdu/dNv6FlZTQaiYqKolevXuh0unI7rjWx9xwlv+K9M/8dAJ674zkGdBxQUeGVC2s7h6t2nydz2wGCPfVMHtYZnfb2iklry68i2HuOkt+tK7zCUxKrLojMZjNt2rRh2rRpALRs2ZKDBw/yxRdfMHLkSEs7jUZTZD9FUa7bdq2S2uj1evT66wcx6nS6CvlhrKjjWhN7z1Hy+8+uhF3sSNiBzkHHY60fs5nvizWcQ0VRWLTtLAAjOobj6lx+g6mtIb+KZu85Sn63dszSsOo+7JCQEBo1alRkW8OGDTlz5gwAwcHBANf19CQlJVl6jYKDgzEYDKSkpNywjRCifBXemXpww8EEugWqHI1t2Xk6hf3n0nBydODhdjLVXojKYtUF0R133EFsbGyRbUePHqVmzZoA1KpVi+DgYKKioizPGwwGNm3aRKdOnQBo3bo1Op2uSJuEhAQOHDhgaSOEKD+ZhkyW7F8CwNjWsm5ZWRXeiHFQi1B83ZzUDUaIKsSqL5m98MILdOrUiWnTpjFkyBC2b9/OV199xVdfFfz3qdFomDBhAtOmTSMiIoKIiAimTZuGq6srw4YNA8DLy4vHHnuMSZMm4efnh6+vLy+++CJNmza1zDoTQpSfHw7+QIYhg7q+dekW3k3tcGxKQloOfxwo6PEe3amWytEIUbVYdUHUtm1bVq1axSuvvMJbb71FrVq1mDVrFsOHD7e0mTx5Mjk5OYwbN46UlBTat2/P2rVr8fDwsLT5+OOPcXR0ZMiQIeTk5NCjRw8WLFiAVit3zRWivH2962sAHm/5eIlj+URRi7eexmRWaF/Ll0ah5Td5QwhRMqsuiAAGDBjAgAE3nqGi0WiIjIwkMjLyhm2cnZ2ZPXs2s2fProAIhRCFDiQdYGv8VhwdHBnVYpTa4diUXKOJJdsKxkc+eke4usEIUQVZ9RgiIYRt+WbXNwDcU+8egt2DVY7Gtvyy5zwp2UaqebvQs6FM+BCisklBJIQoF7n5uSzatwiAJ1o9oXI0tkVRlP9Wte9YE8fbvO+QEKLs5F0nhCgXKw+v5HLOZWp41aB3nd5qh2NTtp+6zOGEdJx1DjzUNkztcISokqQgEkKUi8LB1GNajEHrIBMWyqJwVfv7WlbH21Wm2guhBimIhBC37dilY2yM24iDxoExLceoHY5NOZeaw58HC6fah6sbjBBVmBREQojbVjiYum/dvoR5ySWfsvhuSxxmBTrV8aN+sEfJOwghKoQUREKI22I0GVmwdwFQcO8hUXo5BhPLthesWya9Q0KoSwoiIcRtWX10NUlZSQS5BTGgnnWvam9tftpzjrQcI2G+LvSQqfZCqOqWbswYGxvL0qVL+fvvv4mLiyM7O5uAgABatmxJnz59uP/++4tdKV4IYX++2V1wuWx0i9HotPa7Cnd5UxSFBf/GATCqYzhaB7mrtxBqKlMP0e7du+nVqxfNmzdn8+bNtG3blgkTJvD222/zyCOPoCgKr776KqGhobz//vvk5eVVVNxCCCtwLv0cfxz/A0AGU5fRlpOXiL2QgYtOy4NtZNyVEGorUw/RoEGDeOmll1i+fDm+vr43bLdlyxY+/vhjPvroI/73v//ddpBCCOu0YM8CzIqZzjU6U8+vntrh2JTC3qH7W1fDy0V61oRQW5kKomPHjuHkVPI9Mjp27EjHjh0xGAy3HJgQwrqZFTPf7vkWgMdbyWDqsjh7OZuowxeAgstlQgj1lemS2dXF0HfffVfsJTGDwcB33313XXshhH3ZGLeRkykn8dR78kCjB9QOx6Z8tyUORYHOEf5EBMlUeyGswS3PMnv00UdJS0u7bntGRgaPPvrobQUlhLB+83bPA2BYk2G46lxVjsZ2ZOXlsyymYKq9rGovhPW45YJIURQ0mutnRcTHx+Pl5XVbQQkhrFtKTgorDq0A4LFWj6kcjW1ZtfscGbn51PRzpVu9QLXDEUJcUeZp9y1btkSj0aDRaOjRoweOjv8dwmQycerUKfr27VuuQQohrMv3+78nz5RHs6BmtA5prXY4NkNRFMu6ZaM6huMgU+2FsBplLogGDRoEwJ49e+jTpw/u7u6W55ycnAgPD+f+++8vtwCFENan8HLZ4y0fL7anWBTvn+PJHE/KxM1JywNtqqsdjhDiKmUuiKZOnQpAeHg4Q4cOxdnZudyDEkJYr10Ju9iTuAe9Vs/wZsPVDsemFE61f6B1dTydZaq9ENbklu5UDTBq1KgS29xonJEQwnYVLuR6X8P78HW58f3IRFFxyVmsj00CYJSsWyaE1SnToOqGDRuyZMmSEu8vdOzYMZ5++mnef//92wpOCGFdcow5LNm/BIDHWspg6rL4bstpFAW61Q+gdoB7yTsIISpVmXqIPvvsM15++WWeeeYZevfuTZs2bQgNDcXZ2ZmUlBQOHTrEP//8w6FDh3j22WcZN25cRcUthFDBysMrSctLI9w7nLtq3aV2ODYjMy+f/9shq9oLYc3KVBDdddddxMTEEB0dzfLly1myZAlxcXHk5OTg7+9Py5YtGTlyJI888gje3t4VFLIQQi2Fg6kfbfEoDppbvmtHlbNiZzwZefnU9nejS0SA2uEIIYpxS2OIOnXqRKdOnco7FiGEFTuRcoINcRvQoGF0i9Fqh2MzzGaFhYVT7TvJVHshrJX8iyeEKJXv9hUsydO7Tm9qeNVQORrbsfnYRU4mZ+Ghd+T+1jLVXghrdVsF0aZNm7jnnnuoW7cuERERDBw4kL///ru8YhNCWAmTYmLRvkUAjGk5RuVobEvhjRgfbBOGu/6WJ/YKISrYLRdEixcvpmfPnri6uvLcc8/x7LPP4uLiQo8ePViyZEl5xiiEUNmejD3EZ8Tj5+LHvfXvVTscm3HyYiYbYy+i0cDIjjXVDkcIcRO3/O/Ku+++y4wZM3jhhRcs255//nlmzpzJ22+/zbBhw8olQCGE+tZdWgfAI80eQe+oVzka21E4duiu+oGE+7upG4wQ4qZuuYfo5MmT3HPPPddtHzhwIKdOnbqtoIQQ1uNi1kVi0mMAufdQWaTnGvlxZzwAo2VVeyGs3i0XRGFhYfz111/Xbf/rr78ICwu7raCEENZjycEl5Cv5tA5pTdOgpmqHYzN+3BFPlsFE3UB37qzrr3Y4QogS3PIls0mTJvHcc8+xZ88eOnXqhEaj4Z9//mHBggV88skn5RmjEEIliqIwf898AB5t/qjK0dgOs1lh4ZY4oOBGjLKEkRDW75YLoqeffprg4GA++ugjfvjhB6BgaY/ly5dz770y6FIIe7D93HYOJR/CSePE0EZD1Q7HZmw8msTpS9l4ODsyuFU1tcMRQpTCbc0Bve+++7jvvvvKKxYhhJUpvDN1J+9OeDl7qRyN7Zh/ZVX7h9qG4eokU+2FsAW3/U41GAwkJSVhNpuLbK9RQ27cJoQtyzRksvTAUgB6+vVUORrbcexCBn8fS8ZBAyM7hqsdjhCilG65IDp27BhjxowhOjq6yHZFUdBoNJhMptsOTgihnv87+H9kGjKp61OXxm6N1Q7HZhSOHerZMIgwX1d1gxFClNotF0SjR4/G0dGR1atXExISIoMGhbAzhZfLRjUfhSZV3t+lkZZjZMXOc4BMtRfC1txyQbRnzx527txJgwYNyjMeIYQVOJJ8hH/P/otWo2VE0xHs+XuP2iHZhP/bcZYco4n6QR50rO2ndjhCiDK45fsQNWrUiOTk5PKMRQhhJb7d/S0A/SP6E+oRqnI0tsF09VT7O2SqvRC2pkwFUXp6uuXj/fffZ/LkyWzcuJFLly4VeS49Pb2i4hVCVDCjycjCvQsBuTN1Wfx1+AJnL+fg7apjUAuZai+ErSnTJTNvb+8i//UoikKPHj2KtJFB1ULYttVHV5OUlUSQWxD9I/qDueR9xH+r2j/UtgYuTlp1gxFClFmZCqINGzYAkJeXx7Rp03j44YdlDJEQdubqwdQ6rQ6j2ahyRNYvNjGD6BOXcNDACFnVXgibVKaCqGvXrpavhw8fzl133UVERES5ByWEUMe59HP8fvx3AMa0HKNyNLajsHeoT+Ngqnm7qBuMEOKW3PKg6pEjRzJv3rzyjEUIobIFexZgVsx0rtGZ+v711Q7HJqRmG1i1+8qq9p3C1Q1GCHHLbnnavcFg4JtvviEqKoo2bdrg5uZW5PmZM2fednBCiMpjVsx8u6dgdpkMpi69ZTFnyTWaaRjiSbtavmqHI4S4RbdcEB04cIBWrVoBcPTo0SLPyXRTIWzPhlMbOJlyEk+9Jw80ekDtcGxCvsnMoi2nAXhUptoLYdNuuSAqHGAthLAPX+/6GoDhTYfj5uRWQmsBsO7wBc6l5uDr5sTA5nK/JiFs2S2PIRJC2I/k7GRWHVkFwOOtHlc5GttRuKr9w+3CcNbJVHshbJkUREIIFu1dhMFkoFVIK1qFtFI7HJtw6Hw6205dRuug4ZEOMtVeCFsnBZEQVZyiKHyz+xsAnmj1hMrR2I4F0acA6NskmBAvmWovhK2TgkiIKm5L/BYOXTyEq86Vh5s8rHY4NuFyloGf9pwHYIysai+EXZCCSIgq7ptdBb1DQxoPwcvZS+VobMPS7Wcw5JtpWs2LVjV81A5HCFEOpCASogpLz0tn+cHlgFwuKy2jyczirQVT7Ud3kqn2QtgLKYiEqMKW7F9CtjGbhv4N6Vi9o9rh2IS1By+QkJaLv7sTA5qHqB2OEKKcSEEkRBVWeLnsiVZPSE9HKc3/t2Aw9bB2NdA7ylR7IeyFFERCVFG7E3azM2EnTlonRjQfoXY4NmF/fBo7TqfgKFPthbA7UhAJUUXN3TkXgPsa3Ie/q7/K0diGwlXt724WQqCns7rBCCHKlU0VRNOnT0ej0TBhwgTLNkVRiIyMJDQ0FBcXF7p168bBgweL7JeXl8f48ePx9/fHzc2NgQMHEh8fX8nRC2E9MvIy+H7/9wA81eYplaOxDcmZefy6t2CqvaxqL4T9sZmCKCYmhq+++opmzZoV2T5jxgxmzpzJnDlziImJITg4mF69epGRkWFpM2HCBFatWsWyZcv4559/yMzMZMCAAZhMpspOQwirsPTAUjINmdT3q0/Xml3VDscmLN12BoPJTPMwb1rKVHsh7I5NFESZmZkMHz6cr7/+Gh+f/34RKYrCrFmzePXVVxk8eDBNmjRh4cKFZGdns2TJEgDS0tKYN28eH330ET179qRly5YsXryY/fv3s27dOrVSEkJVhZfLnmz9pAymLgVDvplFV6baPyq9Q0LYpVte7b4yPfPMM9x999307NmTd955x7L91KlTJCYm0rt3b8s2vV5P165diY6OZuzYsezcuROj0VikTWhoKE2aNCE6Opo+ffoU+5p5eXnk5eVZHqenpwNgNBoxGo3lllvhscrzmNbG3nO0tfx2JuxkV8Iu9Fo9wxoNKzFuW8vvVpSU4+p9CSRl5BHg7kSvBv42972Qc2j7JL/bP3ZJrL4gWrZsGbt27SImJua65xITEwEICgoqsj0oKIjTp09b2jg5ORXpWSpsU7h/caZPn86bb7553fa1a9fi6upa5jxKEhUVVe7HtDb2nqOt5PfZmc8A6ODZgW0bt5V6P1vJ73bcKMdP92sBDW28c1i39o/KDaocVeVzaC8kv7LLzs4uVTurLojOnj3L888/z9q1a3F2vvGMjmu7/BVFKfEyQEltXnnlFSZOnGh5nJ6eTlhYGL1798bT07OUGZTMaDQSFRVFr1690Ol05XZca2LvOdpSful56Qz/dDgAU++eyp017ixxH1vK71bdLMe98WnEbdmGTqvhjeF34e+uVynKW1fVz6E9kPxuXeEVnpJYdUG0c+dOkpKSaN26tWWbyWRi8+bNzJkzh9jYWKCgFygk5L87xiYlJVl6jYKDgzEYDKSkpBTpJUpKSqJTp043fG29Xo9ef/0vPp1OVyE/jBV1XGti7znaQn4/7PmBLGMWDf0b0q12tzKNH7KF/G5XcTl+v71gRuo9zUIJ8XFXI6xyU1XPoT2R/G7tmKVh1YOqe/Towf79+9mzZ4/lo02bNgwfPpw9e/ZQu3ZtgoODi3SxGQwGNm3aZCl2WrdujU6nK9ImISGBAwcO3LQgEsLeKIpiGUw9tvVYGUxdCkkZuazed2WqvaxqL4Rds+oeIg8PD5o0aVJkm5ubG35+fpbtEyZMYNq0aURERBAREcG0adNwdXVl2LBhAHh5efHYY48xadIk/Pz88PX15cUXX6Rp06b07Nmz0nMSQi3bz21n74W9ODs6M7L5SLXDsQnfbz2D0aTQuqYPzap7qx2OEKICWXVBVBqTJ08mJyeHcePGkZKSQvv27Vm7di0eHh6WNh9//DGOjo4MGTKEnJwcevTowYIFC9BqZR0iUXUU9g4NaTwEHxe5j05J8vJNfL/tDCA3YhSiKrC5gmjjxo1FHms0GiIjI4mMjLzhPs7OzsyePZvZs2dXbHBCWKmUnBSWHlgKFFwuEyVbsz+B5Mw8gjz19G0SrHY4QogKZtVjiIQQ5WP+nvnk5ufSPKg5Hat3VDscq6coCvP/jQNgRIea6LTyq1IIeyfvciHsnFkx83nM5wA80/YZGUxdCrvPprIvPg0nRwcebldD7XCEEJVACiIh7FzUiShOpJzAS+/FsKbD1A7HJhT2Dg1sHoqfDd53SAhRdlIQCWHnPospuDP16BajcXNyUzka65eYlsvv+xMAGUwtRFUiBZEQdiwuNY7VR1cD8HSbp1WOxjZ8v+00+WaFduG+NKnmpXY4QohKIgWREHZs7o65KCj0rN2T+v711Q7H6uUZTSwpnGovN2IUokqRgkgIO5Wbn8s3u78BYFybcSpHYxt+O5DIpSwDIV7O9G4UVPIOQgi7IQWREHbqx0M/kpydTHXP6txT/x61w7F6igILtxT0Do3oWBNHmWovRJUi73gh7FThYOqxrcfi6GBz92CtdCcz4FBCBnpHBx5uK1PthahqpCASwg7tStjF1vit6Bx0PNHqCbXDsQmbEwt+Hd7Xsho+bk4qRyOEqGxSEAlhh2ZvL1im5oFGDxDkLmNhSrI3Po29lwpuWDlKptoLUSVJQSSEnbmQeYEl+5cA8Fz751SOxvotjznDg3O3oVBQEO2LT1U3ICGEKqQgEsLOzN05F4PJQLtq7ehQvYPa4Vi1hLQcXlm5H+Wqbf9beYCEtBzVYhJCqEMKIiHsiMFk4IsdXwAwof0EdYOxAaeSszArRbeZFIW45Gx1AhJCqEYKIiHsyA8HfyAxM5FQj1AeaPSA2uFYvbOXr+8J0mo0hPu7qhCNEEJNUhAJYScUReGTbZ8ABTdi1Gl1Kkdk3c6n5jD998MAV0YPgYMGpg1uQoiXi3qBCSFUITcnEcJORJ+NZsf5Hei1ep5s/aTa4Vi1fJOZCcv2kJptpGk1Lz4e0pSf/tzEkP7dqeHvoXZ4QggVSEEkhJ0o7B16pNkjBLgFqByNdft0/XG2x13GXe/I7IdbUs3LiQgvhRAvZ7VDE0KoRC6ZCWEHzqadZeXhlQA83/55laOxbtEnkpm9/hgA797XhHB/N5UjEkJYAymIhLADn8V8hkkx0T28O02DmqodjtW6lJnHhGV7UBQY0qY697aopnZIQggrIQWREDYu05DJVzu/AmBChwnqBmPFzGaFSf+3l6SMPOoEuBE5sLHaIQkhrIgURELYuG93f0tKbgp1fetyd8Tdaodjtb799xQbYy/i5OjAnGGtcHWSIZRCiP9IQSSEDcs35/Px1o8BmNRxEloHrcoRWae9Z1N5/48jALwxoBENQzxVjkgIYW2kIBLChv146EfiUuMIcA1gVPNRaodjldJzjYxfuhujSaFfk2CGt6+hdkhCCCskBZEQNkpRFGb8OwOAZ9s9i4tObiZ4LUVR+N/K/Zy5nE01bxfeG9wMjUZT8o5CiCpHCiIhbNT6U+vZnbgbF0cXxrUdp3Y4VumHHWdZvS8BrYOGTx9uiZer3L1bCFE8KYiEsFEfRH8AwJiWY/B39Vc5Gutz7EIGU385CMCLvevTuqaPyhEJIayZFERC2KB9F/bx54k/cdA4MLHjRLXDsTq5RhPPLtlNrtFM5wh/xnaprXZIQggrJwWREDaosHfogUYPUNtH/thf663Vh4i9kIG/u56ZQ1rg4CDjhoQQNycFkRA25mzaWZYdWAbAS51eUjka6/PbvgSWbDuDRgMfD21OgIde7ZCEEDZACiIhbMzMLTPJN+fTLbwbbULbqB2OVTl7OZspK/YB8HTXOnSOkEVuhRClIwWREDYkKSuJuTvnAvDyHS+rHI11MZrMPLt0Nxl5+bSq4c0LveqpHZIQwoZIQSSEDZm5ZSY5+Tm0CW1Dnzp91A7Hqny4Npa9Z1PxdHbk04dbotPKrzchROnJbwwhbMTlnMt8FvMZAK93eV1uMHiVTUcvMnfTSQBmPNCM6j6uKkckhLA1UhAJYSM+3fYpmYZMmgU1455696gdjtVISs9l4vI9AIzoUJO+TULUDUgIYZOkIBLCBqTnpfPJtk8AeK3za9I7dIXJrDBh+R4uZRloEOzBq3c3VDskIYSNkoJICBvw2fbPSM1NpYF/AwY3HKx2OFbjy00niD5xCRedljnDWuGs06odkhDCRklBJISVyzJkMXPrTABe7fwqWgf5ow+wI+4yM6OOAvDWvY2pG+iuckRCCFsmBZEQVm7uzrkkZydT26c2DzV5SO1wrEJqtoHnlu7GZFYY1CKUB1pXVzskIYSNk4JICCuWY8yxLNPxyp2v4OjgqHJE6lMUhck/7uN8Wi7hfq68c19TGVMlhLhtUhAJYcU+j/mcxMxEanjVYGTzkWqHYxUWbT3N2kMX0Gk1zH64Fe56KRKFELdPCiIhrFRGXgbv/fseAFO7TsVJ66RyROo7eD6Nd1YfBuCVfg1pWt1L5YiEEPZCCiIhrNSsrbNIzk6mnl896R0CsvLyGb9kNwaTmR4NAnn0jnC1QxJC2BEpiISwQpdzLvPhlg8BeLPbmzJ2CHjj54OcTM4i2NOZDx5sLuOGhBDlSgoiIazQjH9nkJ6XTrOgZgxpPETtcFS3clc8K3bF46CBTx5qga+bXD4UQpQvKYiEsDKJmYl8uu1TAN7p/g4Omqr9Nj15MZPXfjoAwPM96tG+tp/KEQkh7FHV/k0rhBWa9vc0cvJzaF+tPQPqDVA7HFXl5ZsYv3Q32QYT7Wv58uxdddUOSQhhp6QgEsKKnEk7w9ydcwF49653q/w4melrjnDwfDo+rjo+eaglWoeq/f0QQlQcKYiEsCKRGyMxmAx0D+9Oj9o91A5HVVGHLrAgOg6Aj4Y0J9jLWd2AhBB2TQoiIazEnsQ9LNizAIDpPaarG4zKzqfm8NKPewF4/M5a3NUgSOWIhBD2TgoiIayAoihMWjsJBYWHmjxE++rt1Q5JNfkmM88v201qtpGm1byY3LeB2iEJIaoAKYiEsAKrj65m/an16LX6Kt879Olfx4iJS8Fd78icYS1xcpRfU0KIiie/aYRQmdFk5KWolwB4ocMLhHuHqxuQiqJPJDN7w3EApg1uSk0/N5UjEkJUFVIQCaGyuTvnEnsplgDXAF7p/Ira4ajmUmYeE5btQVFgaJswBjYPVTskIUQVIgWRECpKyUkhcmMkAG91fwtPvae6AanEbFaY9H97ScrIo26gO1MHNlI7JCFEFSMFkRAqevfvd7mUc4lGAY14vNXjaoejmnn/nGJj7EX0jg7MGdYSVydZu00IUbmsuiCaPn06bdu2xcPDg8DAQAYNGkRsbGyRNoqiEBkZSWhoKC4uLnTr1o2DBw8WaZOXl8f48ePx9/fHzc2NgQMHEh8fX5mpCHGdY5eOMXv7bAA+7PVhlV3Ade/ZVN7/4wgAb9zTiAbBVbOXTAihLqsuiDZt2sQzzzzD1q1biYqKIj8/n969e5OVlWVpM2PGDGbOnMmcOXOIiYkhODiYXr16kZGRYWkzYcIEVq1axbJly/jnn3/IzMxkwIABmEwmNdISAkVRGP/7eAwmA33q9KFv3b5qh6SK9Fwj45fuJt+s0L9pMMPa1VA7JCFEFWXV/5L+8ccfRR7Pnz+fwMBAdu7cSZcuXVAUhVmzZvHqq68yePBgABYuXEhQUBBLlixh7NixpKWlMW/ePBYtWkTPnj0BWLx4MWFhYaxbt44+ffpUel5CrDi8gj9P/ImT1onZ/WZXySU6FEXhfyv3c+ZyNtW8XZg+uFmV/D4IIayDVRdE10pLSwPA19cXgFOnTpGYmEjv3r0tbfR6PV27diU6OpqxY8eyc+dOjEZjkTahoaE0adKE6OjoGxZEeXl55OXlWR6np6cDYDQaMRqN5ZZT4bHK85jWxt5zLGt+GXkZTPhjAgAvdXyJcM9wq/7eVNT5+2FHPKv3JeDooOHjIU1xdVTvZ0R+Rm2fveco+d3+sUtiMwWRoihMnDiRO++8kyZNmgCQmJgIQFBQ0dv6BwUFcfr0aUsbJycnfHx8rmtTuH9xpk+fzptvvnnd9rVr1+Lq6npbuRQnKiqq3I9pbew9x9LmN//cfM5lnCPIKYhm6c1Ys2ZNBUdWPsrz/CVkw0f7tYCG/tXzSdgfTcL+cjv8LZOfUdtn7zlKfmWXnZ1dqnY2UxA9++yz7Nu3j3/++ee6567tZlcUpcSu95LavPLKK0ycONHyOD09nbCwMHr37o2nZ/kN+jQajURFRdGrVy90Ol25Hdea2HuOZclvf9J+Vu9dDcDX931N3zrWP3aovM9frtHE4C+3YjRncWddPz4Y0QoHlVexl59R22fvOUp+t67wCk9JbKIgGj9+PL/88gubN2+mevXqlu3BwcFAQS9QSEiIZXtSUpKl1yg4OBiDwUBKSkqRXqKkpCQ6dep0w9fU6/Xo9frrtut0ugr5Yayo41oTe8+xpPzMipnn/nwOk2Li/ob3c0+DeyoxuttXXufvjV+PcCwpC393PR8PbYle71QO0ZWPqv4zag/sPUfJ79aOWRpWPctMURSeffZZVq5cyfr166lVq1aR52vVqkVwcHCRLjaDwcCmTZssxU7r1q3R6XRF2iQkJHDgwIGbFkRClLeFexby79l/cdO58XGfj9UORxWr951n6fYzaDQwa2gLAjyu/6dDCCHUYNU9RM888wxLlizh559/xsPDwzLmx8vLCxcXFzQaDRMmTGDatGlEREQQERHBtGnTcHV1ZdiwYZa2jz32GJMmTcLPzw9fX19efPFFmjZtapl1JkRFS8hIYNLaSQBM7TqVMK8wlSOqfGcvZ/PKioKBQuO61eHOCH+VIxJCiP9YdUH0xRdfANCtW7ci2+fPn8/o0aMBmDx5Mjk5OYwbN46UlBTat2/P2rVr8fDwsLT/+OOPcXR0ZMiQIeTk5NCjRw8WLFiAVqutrFREFaYoCk/99hQpuSm0CmnFhA4T1A6p0hlNZp5dupuMvHxa1/RhQs96aockhBBFWHVBpChKiW00Gg2RkZFERkbesI2zszOzZ89m9uzZ5RidEKWz9MBSfon9BZ2DjgX3LkCntd/r/zfy4Z+x7D2biqezI5881AKd1qqv1gshqiD5rSREBUrMTGT87+MBeKPrGzQNaqpyRJVvY2wSczefBGDGA82p7lP+t60QQojbJQWREBVEURSeWv0Ul3Mu0yqkFS/f8bLaIVW6pPRcJv2wF4CRHWvSt0mwyhEJIUTxpCASooIsO7CMn2N/RuegY/6986vcpTKTWWHC8j1cyjLQINiD//VvqHZIQghxQ1IQCVEBEjMTefb3ZwF4vcvrNAtqpnJEle+LjceJPnEJF52WOcNa4ayTSQxCCOslBZEQ5cysmBmxagSXcy7TMrglU+6conZIlS4m7jIfrzsGwNuDmlA30F3liIQQ4uakIBKinM34dwbrTq7DVefK94O/r3KXymIT03lq0Q5MZoX7Wlbj/lbV1A5JCCFKZNXT7oWwNVvjt/La+tcAmN1vNg0Dqta4mWXbzzBl5X+rtLYI8y5xXUEhhLAG0kMkRDlJzU3l4RUPY1JMPNTkIR5t8ajaIVWqXacvFymGAN769RAJaTkqRSSEEKUnBZEQ5UBRFJ5e8zRxqXHU8q7Fl3d/WWV6Rsxmhe+2xDHs623XPWdSFOKSs1WISgghykYumQlRDqIuR7Hi7AocHRxZ9sAyvJy91A6pUpy8mMnLK/YRE5dS7PNajYZwf7kRoxDC+klBJMRtijkfw9fxXwMw7a5ptKvWTuWIKl6+yczXf5/i43VHMeSbcXPS8nK/Bui0Dry26gAmRUGr0TBtcBNCvFzUDlcIIUokBZEQtyExM5EhK4ZgVIwMiBjApE6T1A6pwh06n87kFXs5cC4dgC71Aph2XxPLkhzd6gcQl5xNuL+rFENCCJshBZEQtygvP4/7f7ifcxnnqK6vzoKBC3DQ2O+wvLx8M59uiOWLjSfINyt4ueh4fUAj7m9Vrch4qRAvFymEhBA2RwoiIW6Boig8u+ZZos9G46X34pVar+Cp91Q7rAoTlwH3fr6FExezAOjXJJg3721MoIezypEJIUT5kIJIiFvwxY4v+Gb3N2jQsHjQYkyxJrVDqhDZhnxm/H6EhQe0KGTh767n7Xsb069piNqhCSFEuZKCSIgyWn9qPc//8TwA03tMp0+dPqyJXaNyVOUv+ngyU1bu58zlbEDDfS1DmXpPY7xdndQOTQghyp0UREKUwd7EvQxaNoh8cz4PNXmIyXdMJj8/X+2wylVajpHpaw6zLOYsAKFezgwMyWLS4CbodFVrGRIhRNUhBZEQpRSXGke/7/uRYcigS80uzL93vt3dfDHq0AVe+2k/F9LzABjZsSYv9KjD5r/WqhyZEEJULCmIhCiF5Oxk+i7uS0JmAk0Cm/DzQz/j7Gg/A4ovZeYR+eshft17HoBa/m68f38z2tXyxWg0qhydEEJUPCmIhChBliGLAUsGEHspljDPMP4Y/gfezt5qh1UuFEXhl73nefPXQ1zOMqB10PBE59pM6BmBs06rdnhCCFFppCAS4iby8vMY8uMQtp3bho+zD38+8ifVPKupHVa5SEjL4bVVB/jrSBIADYI9+OCB5jStXjWWHRFCiKtJQSTEDeTl5/Hg/z3ImmNrcHZ0ZvWw1TQMaKh2WLdNURSWbj/L9DWHycjLx0nrwPi76jK2ax2cHO33xpJCCHEzUhAJUYzCYujXo7/i7OjMLw/9QqewTmqHddtOX8piyor9bDl5CYAWYd588EAzIoI8VI5MCCHUJQWRENcorhjqVaeX2mHdFpNZYf6/p/hwbSy5RjPOOgde7F2fR++ohdbBvmbKCSHErZCCSIir2GMxdPRCBpN/3Mees6kAdKrjx3uDm1HDz1XdwIQQwopIQSTEFel56QxePpi/Tv1lF8WQId/Ml5tOMHv9MYwmBQ+9I6/e3ZChbcPs7v5JQghxu6QgEgJIyEig/5L+7Encg5vOjZ8e+ometXuqHdYt2xefyuQf93EkMQOAng0DeWdQU4K97OfeSUIIUZ6kIBJVXmxyLH2/70tcahyBboGsGbaG1qGt1Q7rluQaTXwcdZSv/z6JWQFfNyciBzbmnmYh0iskhBA3IQWRqNK2nN3CgKUDuJxzmbq+dfnzkT+p7VNb7bBuybaTl5iycj+nkrMAGNg8lKn3NMLPXa9yZEIIYf2kIBJV1nd7v2Ps6rHk5ufSrlo7Vj+8mgC3ALXDKrPMvHze//0Ii7aeBiDIU8+7g5rSs1GQypEJIYTtkIJIVDlGk5FJaycxe/tsAO6pdw9L71+Km5ObypGV3YbYJF5duZ/zabkAPNwujFf6N8TTWValF0KIspCCSFQpFzIv8OD/PcjfZ/4GYGrXqbzR9Q0cNLZ1h+aULANvrz7Eyt3nAKjh68p7g5vSqa6/ypEJIYRtkoJIVBnRZ6MZ8n9DOJdxDk+9J4vuW8TA+gPVDqvM1uxP4I2fD5CcaUCjgTF31GJS73q4OsnbWQghbpX8BhV2z2gy8vbmt3n373cxK2Ya+jdk1dBV1Pevr3ZoZZKUnssbPx/kj4OJAEQEuvP+A81oVcNH5ciEEML2SUEk7NqxS8d4ZNUjbD+3HYARzUbwWf/P8NDbxtpdCWk5nLqYxcHzacxef5z03HwcHTSM61aHZ+6qi95Rq3aIQghhF6QgEnZJURS+2fUNL/z5AlnGLLydvfny7i8Z2mSo2qGV2vKYM7yycj9m5b9tTat58f79zWgU6qleYEIIYYekIBJ2JzY5lqd+e4qNcRsB6B7enYWDFhLmFaZuYKWUlJHLz7vP8e6aI0W2a4DPh7ckzNf2ZsMJIYS1k4JI2I28/Dze++c9pv0zDYPJgIujC293f5sXOr5g1bPITGaFPWdT2Bh7kQ2xSRw4l15sOwWIT8mVgkgIISqAFETCLkSdiOLZ35/l6KWjAPSt25fP+39OLZ9aKkdWvOTMPDYfvciG2Iv8fewiqdnGIs83CPYgNjGDq66WodVoCPeXFeqFEKIiSEEkbNq+C/uYHDWZP0/8CUCwezCf9P2EBxs9aFVrd5nMCvviU9kYe5GNsUnsO5eGclW14+nsSJd6AXSrH0jXegEEeOhZHnOG/608gElR0Go0TBvchBAvF/WSEEIIOyYFkbBJ59LP8fqG11mwZwEKCjoHHePajiOyWyTezt5qhwcU3Dxx87GLbDiSxOZjyVzOMhR5vlGIJ90bBNC9fiAtwrxx1Ba9rDe0bQ261AsgLjmbcH9XKYaEEKICSUEkbMq59HN8GP0hc3fOJSc/B4AHGz3I9B7TqeNbR9XYzFf1Am2ITWLP2dQivUAeekc61/OnW71AutYPIMjTucRjhni5SCEkhBCVQAoiYRPiUuN4/5/3+XbPtxhMBT0tncI68WGvD+kY1lG1uNKyjWw4ksj3xx14a8YmLl3TC9Qg2INu9QPpXj+AVjV90Gmtd3C3EEJUZVIQCasWcy6G2dtns/TAUvLN+QB0rtGZ17u8Ts/aPSt9nJCiKBw8n86mowWXwnadSblynyAHwICbk5Y7I/zpVj+QbvUDpHdHCCFshBREwuoYTAZWHFrBp9s/ZWv8Vsv2XrV78VqX1+hSs0ulxpOea+SfY8lsOJLEpqMXScrIK/J8RKAbYdoMHu3bjvZ1AnBylF4gIYSwNVIQCatx+OJhFu5dyMK9C0nMLFivS+eg46EmDzG+3XjaVmtbKXEoisKRxAzLWKCdp1MwXXW7aFcnLZ3q+NO9QcGssEA3R9asWUOH2r7opBgSQgibJAWRUFVKTgrLDy5nwZ4FbDu3zbI9xD2Ep9o8xZOtnyTYPbjC48jINfLv8UtsjE1iY+xFEtNzizxfJ8CN7vUD6VY/kLa1fIqsIWY0Gq89nBBCCBsjBZGodJeyL/HTkZ/48fCPrDu5zjI2SKvR0j+iP6NbjGZAvQE4aZ3K9XUT0nI4lZxFLX83gj2dOZaUyYYjBQVQTNxl8q/qBXLWORT0AtUv6AUK85UbIgohhD2TgkhUioS8BD6L+Yw1J9aw/tR6TIrJ8lzTwKaMbjGa4U2HE+QeVCGvf+1Cqd4uOlJzivbs1PJ3o9uVAqh9LV+cdbKSvBBCVBVSEIkKkWnI5J8z//Dn8T/57dhvHLt8DA7/93zzoOY82OhB7m90Pw38G5TLaxpNZhLTcolPyeFcag7xKdmcS8nhZHImO0+nFmmbmmPESauhU11/ul25Q3S4v6wRJoQQVZUURKJcpOelszV+KxvjNrIhbgMx52KK9AJp0dK5Zmf6R/RnUINBRPhFlPk18vJNnE/NtRQ6BUVPDudSCoqfxPRczErJxyn09cg2dK0fWOY4hBBC2B8piESZmcwmYi/Fsi1+G1vit7AlfgsHkw6iULQaqeVdix61etC7dm/yj+bzwD0PoNPpbnjcbEP+leImh/jU/wqdc1e+vna6e3GctA5U83GhmrcL1a98dtNrefu3w0XuGq3VaKgX7HHL3wMhhBD2RQoicVPpeekcuniI/Rf2sztxN7sSdrHvwj7LshlXq+lVk67hXeke3p3u4d2p6V0TKJiFtebEGtJzjFy4WPRyVuHlrXOpOdet9VUcF522oNDxKSx4XC1fV/d2wd9dj4PD9TdrdNM7ykKpQgghbkgKIoFZMXMu/RzHLh/j2KVjHL10lEPJhziYdJCz6WeL3cfF0ZVmQS3pWvMOOoZ1pF1oO5y1/pZCZ+2+HM6lHizo7bmcxelkLTlbNpQYi4ezI9V9XC09PNUtvT0FhY+Pq+6W7k4tC6UKIYS4GSmIqgCzYiYpK4mzaWc5m36WuNQ4TqWc4lTqKeJS4ziZcrLYHp9CAa7B1PJqQLhnY3Kywth13ButEkJihpY9Ge7s3A/nUvaRYzTd8BhQUMT4ujldVeQUfK7m42rp9fF0vvEltdslC6UKIYS4ESmIVJaQlsuxNA0JabnU8C99MaAoClnGLC5mXSQpK4nEzCTi0xM5k3qO8xkJJGQkcCErkYvZiSTnJGJSbn7zQA1a9ASjU6qhMYXgaA5Dp9RAZ66BNsedC5fgwpW2V//QxF7ILHKcQA/9leLG1VLwBHvoOLEvhocG9sbLTQoSIYQQ1qdKFUSff/45H3zwAQkJCTRu3JhZs2bRuXNn1eJZHnOGySu3kE8mM48sYEBzL2oGaLicnUZKTgopuamk5aaRbkgl05BGpjGV7PxUck2p5JnTMVPymBsLxQEtPmgVfxzNgTgqQdd9aK75cdBowF3viJveETe9FhQ4kZx13aH/178hvRsFEeLtXOQOzoWMRiNZx8HVqUr9uAkhhLAhVeYv1PLly5kwYQKff/45d9xxB3PnzqVfv34cOnSIGjVqVHo8CWk5vLJyPxd075Kn3Q/A10eAI2U7jkZxwkHxQos3DoonOnxx1frh5hiAh1MA3vpA/J1DCXANwsNZj5veEfcrH27XfHa/UvgUbnN10hYZr5OQlsMd760vMrVdq9FwT/MQuRQlhBDCplWZgmjmzJk89thjPP744wDMmjWLP//8ky+++ILp06dXejynkrMwK+CAKxrF+cpnV1wc3XBxdMfV0RNXnRfuOk889d546b3xc/HDz9WXQDd/gtz9CfEMINDNGw9nnaUXp7gemvIS4uXC9MFNZbaWEEIIu1MlCiKDwcDOnTuZMmVKke29e/cmOjq62H3y8vLIy/vvvjfp6elAweWf8ljMs7qXHgcNBBheQ3NlwLGDBjaO70KIl/OtHVQxYzSabzu2mxncIoSOtXw4czmbGr6uhHg5l/j9KHzeXhdBlfxsn73naO/5gf3nKPnd/rFLolEUpQz39rVN58+fp1q1avz777906tTJsn3atGksXLiQ2NjY6/aJjIzkzTffvG77kiVLcHUtn4U+t1zQsPykAwoaNCgMrW2mY5Ddnw4hhBCi0mRnZzNs2DDS0tLw9PS8Ybsq0UNU6Nr71yiKcsN72rzyyitMnDjR8jg9PZ2wsDB69+59029oWfQHnryUwcq1/zC4952E+dnnnZONRiNRUVH06tXrpneqtlWSn+2z9xztPT+w/xwlv1tXeIWnJFWiIPL390er1ZKYmFhke1JSEkFBxa+urtfr0ev1123X6XTlerLC/DyI8FII8/Owyx/yq5X3987aSH62z95ztPf8wP5zlPxu7Zil4VCur2qlnJycaN26NVFRUUW2R0VFFbmEJoQQQoiqqUr0EAFMnDiRESNG0KZNGzp27MhXX33FmTNneOqpp9QOTQghhBAqqzIF0dChQ7l06RJvvfUWCQkJNGnShDVr1lCzZk21QxNCCCGEyqpMQQQwbtw4xo0bp3YYQgghhLAyVWIMkRBCCCHEzUhBJIQQQogqTwoiIYQQQlR5UhAJIYQQosqTgkgIIYQQVZ4UREIIIYSo8qQgEkIIIUSVV6XuQ3Q7FKVgFfrSLhJXWkajkezsbNLT0+12fRp7z1Hys332nqO95wf2n6Pkd+sK/24X/h2/ESmISikjIwOAsLAwlSMRQgghRFllZGTg5eV1w+c1SkklkwDAbDZz/vx5PDw80Gg05Xbc9PR0wsLCOHv2LJ6enuV2XGti7zlKfrbP3nO09/zA/nOU/G6doihkZGQQGhqKg8ONRwpJD1EpOTg4UL169Qo7vqenp13+kF/N3nOU/Gyfvedo7/mB/eco+d2am/UMFZJB1UIIIYSo8qQgEkIIIUSVJwWRyvR6PVOnTkWv16sdSoWx9xwlP9tn7znae35g/zlKfhVPBlULIYQQosqTHiIhhBBCVHlSEAkhhBCiypOCSAghhBBVnhREQgghhKjypCCqBJ9//jm1atXC2dmZ1q1b8/fff9+0/aZNm2jdujXOzs7Url2bL7/8spIiLbvp06fTtm1bPDw8CAwMZNCgQcTGxt50n40bN6LRaK77OHLkSCVFXXqRkZHXxRkcHHzTfWzp/IWHhxd7Lp555pli29vCudu8eTP33HMPoaGhaDQafvrppyLPK4pCZGQkoaGhuLi40K1bNw4ePFjicVesWEGjRo3Q6/U0atSIVatWVVAGN3ez/IxGIy+//DJNmzbFzc2N0NBQRo4cyfnz5296zAULFhR7XnNzcys4m+KVdA5Hjx59XawdOnQo8bi2cA6BYs+FRqPhgw8+uOExrekclubvgjW+D6UgqmDLly9nwoQJvPrqq+zevZvOnTvTr18/zpw5U2z7U6dO0b9/fzp37szu3bv53//+x3PPPceKFSsqOfLS2bRpE8888wxbt24lKiqK/Px8evfuTVZWVon7xsbGkpCQYPmIiIiohIjLrnHjxkXi3L9//w3b2tr5i4mJKZJbVFQUAA8++OBN97Pmc5eVlUXz5s2ZM2dOsc/PmDGDmTNnMmfOHGJiYggODqZXr16W9QqLs2XLFoYOHcqIESPYu3cvI0aMYMiQIWzbtq2i0rihm+WXnZ3Nrl27eP3119m1axcrV67k6NGjDBw4sMTjenp6FjmnCQkJODs7V0QKJSrpHAL07du3SKxr1qy56TFt5RwC152Hb7/9Fo1Gw/3333/T41rLOSzN3wWrfB8qokK1a9dOeeqpp4psa9CggTJlypRi20+ePFlp0KBBkW1jx45VOnToUGExlqekpCQFUDZt2nTDNhs2bFAAJSUlpfICu0VTp05VmjdvXur2tn7+nn/+eaVOnTqK2Wwu9nlbOneKoiiAsmrVKstjs9msBAcHK++9955lW25uruLl5aV8+eWXNzzOkCFDlL59+xbZ1qdPH+Whhx4q95jL4tr8irN9+3YFUE6fPn3DNvPnz1e8vLzKN7hyUlyOo0aNUu69994yHceWz+G9996r3HXXXTdtY83n8Nq/C9b6PpQeogpkMBjYuXMnvXv3LrK9d+/eREdHF7vPli1brmvfp08fduzYgdForLBYy0taWhoAvr6+JbZt2bIlISEh9OjRgw0bNlR0aLfs2LFjhIaGUqtWLR566CFOnjx5w7a2fP4MBgOLFy9mzJgxJS5gbCvn7lqnTp0iMTGxyDnS6/V07dr1hu9JuPF5vdk+1iItLQ2NRoO3t/dN22VmZlKzZk2qV6/OgAED2L17d+UEeIs2btxIYGAg9erV44knniApKemm7W31HF64cIHffvuNxx57rMS21noOr/27YK3vQymIKlBycjImk4mgoKAi24OCgkhMTCx2n8TExGLb5+fnk5ycXGGxlgdFUZg4cSJ33nknTZo0uWG7kJAQvvrqK1asWMHKlSupX78+PXr0YPPmzZUYbem0b9+e7777jj///JOvv/6axMREOnXqxKVLl4ptb8vn76effiI1NZXRo0ffsI0tnbviFL7vyvKeLNyvrPtYg9zcXKZMmcKwYcNuumBmgwYNWLBgAb/88gtLly7F2dmZO+64g2PHjlVitKXXr18/vv/+e9avX89HH31ETEwMd911F3l5eTfcx1bP4cKFC/Hw8GDw4ME3bWet57C4vwvW+j6U1e4rwbX/bSuKctP/wItrX9x2a/Pss8+yb98+/vnnn5u2q1+/PvXr17c87tixI2fPnuXDDz+kS5cuFR1mmfTr18/yddOmTenYsSN16tRh4cKFTJw4sdh9bPX8zZs3j379+hEaGnrDNrZ07m6mrO/JW91HTUajkYceegiz2cznn39+07YdOnQoMij5jjvuoFWrVsyePZtPP/20okMts6FDh1q+btKkCW3atKFmzZr89ttvNy0cbO0cAnz77bcMHz68xLFA1noOb/Z3wdreh9JDVIH8/f3RarXXVa9JSUnXVbmFgoODi23v6OiIn59fhcV6u8aPH88vv/zChg0bqF69epn379Chg+r/yZSGm5sbTZs2vWGstnr+Tp8+zbp163j88cfLvK+tnDvAMkOwLO/Jwv3Kuo+ajEYjQ4YM4dSpU0RFRd20d6g4Dg4OtG3b1mbOa0hICDVr1rxpvLZ2DgH+/vtvYmNjb+l9aQ3n8EZ/F6z1fSgFUQVycnKidevWlpk7haKioujUqVOx+3Ts2PG69mvXrqVNmzbodLoKi/VWKYrCs88+y8qVK1m/fj21atW6pePs3r2bkJCQco6u/OXl5XH48OEbxmpr56/Q/PnzCQwM5O677y7zvrZy7gBq1apFcHBwkXNkMBjYtGnTDd+TcOPzerN91FJYDB07dox169bdUiGuKAp79uyxmfN66dIlzp49e9N4bekcFpo3bx6tW7emefPmZd5XzXNY0t8Fq30flsvQbHFDy5YtU3Q6nTJv3jzl0KFDyoQJExQ3NzclLi5OURRFmTJlijJixAhL+5MnTyqurq7KCy+8oBw6dEiZN2+eotPplB9//FGtFG7q6aefVry8vJSNGzcqCQkJlo/s7GxLm2tz/Pjjj5VVq1YpR48eVQ4cOKBMmTJFAZQVK1aokcJNTZo0Sdm4caNy8uRJZevWrcqAAQMUDw8Puzl/iqIoJpNJqVGjhvLyyy9f95wtnruMjAxl9+7dyu7duxVAmTlzprJ7927LLKv33ntP8fLyUlauXKns379fefjhh5WQkBAlPT3dcowRI0YUmQn677//KlqtVnnvvfeUw4cPK++9957i6OiobN261aryMxqNysCBA5Xq1asre/bsKfKezMvLu2F+kZGRyh9//KGcOHFC2b17t/Loo48qjo6OyrZt2yo9P0W5eY4ZGRnKpEmTlOjoaOXUqVPKhg0blI4dOyrVqlWzi3NYKC0tTXF1dVW++OKLYo9hzeewNH8XrPF9KAVRJfjss8+UmjVrKk5OTkqrVq2KTEkfNWqU0rVr1yLtN27cqLRs2VJxcnJSwsPDb/iGsAZAsR/z58+3tLk2x/fff1+pU6eO4uzsrPj4+Ch33nmn8ttvv1V+8KUwdOhQJSQkRNHpdEpoaKgyePBg5eDBg5bnbf38KYqi/PnnnwqgxMbGXvecLZ67wlsDXPsxatQoRVEKpvxOnTpVCQ4OVvR6vdKlSxdl//79RY7RtWtXS/tC//d//6fUr19f0el0SoMGDVQrAm+W36lTp274ntywYYPlGNfmN2HCBKVGjRqKk5OTEhAQoPTu3VuJjo6u/OSuuFmO2dnZSu/evZWAgABFp9MpNWrUUEaNGqWcOXOmyDFs9RwWmjt3ruLi4qKkpqYWewxrPoel+btgje9DzZXghRBCCCGqLBlDJIQQQogqTwoiIYQQQlR5UhAJIYQQosqTgkgIIYQQVZ4UREIIIYSo8qQgEkIIIUSVJwWREEIIIao8KYiEEEIIUeVJQSSEsBsbN25Eo9GQmpqqdihCCBsjBZEQwiZ169aNCRMmFNnWqVMnEhIS8PLyqvR4NBoNP/30U6W/rhCifDiqHYAQQpQXJycngoOD1Q5DCGGDpIdICGFzRo8ezaZNm/jkk0/QaDRoNBri4uKuu2S2YMECvL29Wb16NfXr18fV1ZUHHniArKwsFi5cSHh4OD4+PowfPx6TyWQ5vsFgYPLkyVSrVg03Nzfat2/Pxo0bbxhPeHg4APfddx8ajcbyWAhhO6SHSAhhcz755BOOHj1KkyZNeOuttwAICAggLi7uurbZ2dl8+umnLFu2jIyMDAYPHszgwYPx9vZmzZo1nDx5kvvvv58777yToUOHAvDoo48SFxfHsmXLCA0NZdWqVfTt25f9+/cTERFx3WvExMQQGBjI/Pnz6du3L1qttkLzF0KUPymIhBA2x8vLCycnJ1xdXUu8RGY0Gvniiy+oU6cOAA888ACLFi3iwoULuLu706hRI7p3786GDRsYOnQoJ06cYOnSpcTHxxMaGgrAiy++yB9//MH8+fOZNm3ada8REBAAgLe3t1yyE8JGSUEkhLBrrq6ulmIIICgoiPDwcNzd3YtsS0pKAmDXrl0oikK9evWKHCcvLw8/P7/KCVoIUemkIBJC2DWdTlfksUajKXab2WwGwGw2o9Vq2blz53WXvq4uooQQ9kUKIiGETXJycioyELq8tGzZEpPJRFJSEp07dy71fjqdrkLiEUJUDpllJoSwSeHh4Wzbto24uDiSk5MtPTy3q169egwfPpyRI0eycuVKTp06RUxMDO+//z5r1qy5aTx//fUXiYmJpKSklEssQojKIwWREMImvfjii2i1Who1akRAQABnzpwpt2PPnz+fkSNHMmnSJOrXr8/AgQPZtm0bYWFhN9zno48+IioqirCwMFq2bFlusQghKodGURRF7SCEEEIIIdQkPURCCCGEqPKkIBJCCCFElScFkRBCCCGqPCmIhBBCCFHlSUEkhBBCiCpPCiIhhBBCVHlSEAkhhBCiypOCSAghhBBVnhREQgghhKjypCASQgghRJUnBZEQQgghqrz/BwrOywL2L0N+AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "t, y = Euler(croissanceCell, y0, 0.0, T, N)\n", "plt.plot(t, y, '.-', label=\"Euler\"); \n", "plt.plot(tref, yref, '-g', label=\"Reference odeint()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "0ba9aa89-764c-44f0-b7a7-2d6084fc76bc", "metadata": {}, "source": [ "### 2. Oscillateur non linéaire de Duffing\n", "\n", "Le système non linéaire de Duffing modélise un système masse-ressort isolé avec une loi d'élasticité non linéaire cubique. Les équations de la cinématique et de la dynamique autour de l'équilibre donnent\n", "\n", "\\begin{align*}\n", "& \\dot x(t) = v(t), \\\\\n", "& \\dot v(t) = - \\alpha\\, x(t) -\\beta\\, x^3(t).\n", "\\end{align*}\n", "\n", "Le terme $\\alpha x$ est le terme d'élasticité linéaire classique avec $\\alpha>0$ le coefficient de raideur du ressort. Le terme non linéaire\n", "$\\beta x^3$, $\\beta>0$, agit pour les plus forts déplacements et exprime une plus grande force de rappel.\n", "\n", "On peut vérifier que l'énergie totale du système (somme d el'énergie élastique et de l'énergie cinétique)\n", "\n", "$$\n", "E=E(x,v) = \\alpha \\frac{x^2}{2} + \\beta \\frac{x^4}{4}\n", "+ \\frac{v^2}{2}\n", "$$\n", "\n", "est conservée au cours du temps (système hamiltonien).\n", "\n", "Ecrire d'abord le système sous la forme vectorielle générique\n", "\n", "$$\n", "\\frac{d\\mathbf{y}}{dt} = \\mathbf{F}(t, \\mathbf{y}(t))\n", "$$\n", "\n", "où l'on précisera $\\mathbf{y}$ et $\\mathbf{F}(t,\\mathbf{y})$. Ecrire une fonction python ```Duffing(y,t)``` qui implémente $F$.\n", "Pour les paramètres, on prendra $\\alpha=1$ et $\\beta=12$." ] }, { "cell_type": "code", "execution_count": 19, "id": "5f77a176-60cb-4158-bbc7-85ac797be179", "metadata": { "tags": [] }, "outputs": [], "source": [ "# function that returns ydot\n", "def Duffing(t,y):\n", " x = y[0]\n", " v = y[1]\n", " alpha = 1.0\n", " beta = 12.0\n", " ydot = np.zeros(2)\n", " ydot[0] = v\n", " ydot[1] = -alpha*x - beta*x**3\n", " return ydot" ] }, { "cell_type": "markdown", "id": "eb5c0628-5ff4-4d94-9517-7d480384ee14", "metadata": { "tags": [] }, "source": [ "Intégrer numériquement le problème différentiel en utilisant ```odeint()```. On prendra $t_0=0$, $T=4$, \n", "$y_0=(x_0,v_0)^T=(2,0)^T$ et ```t = np.linspace(0,T, 200)```.\n", "Tracer les solutions numériques $t\\mapsto x(t)$ et $t\\mapsto v(t)$ obtenues. Tracer de même l'évolution de l'énergie totale $t\\mapsto E(t)$ et faites attention à l'échelle de l'axe des ordonnées." ] }, { "cell_type": "code", "execution_count": 22, "id": "d82c7fb8-e7ca-4947-b419-71240bcf2a32", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# initial condition\n", "y0 = np.array([2, 0])\n", "# final time\n", "T = 4\n", "# time points\n", "t = np.linspace(0,T, 200)\n", "# solve ODE\n", "y = odeint(Duffing, y0, t, tfirst='true')\n", "\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()\n", "\n", "x = y[:,0]\n", "v = y[:,1]\n", "alpha = 1.0; beta = 12.0\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure()\n", "plt.plot(t, E, '.-'); plt.grid();\n", "plt.xlabel('time t');\n", "plt.ylabel('E(t)');\n", "plt.ylim((49,51));" ] }, { "cell_type": "markdown", "id": "7d3b9136-7065-4677-b97b-9143f4600960", "metadata": {}, "source": [ "Tracer de même la solution $(x(t),v(t))_{t\\in[0,T]}$ dans le plan de phase $(x,v)$. La courbe fermée ainsi obtenue est dite une orbite." ] }, { "cell_type": "code", "execution_count": 25, "id": "3e3081a6-0eb7-4b1b-8fc5-95cee3abb261", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(y[:,0], y[:,1], '.-');\n", "plt.grid();\n", "plt.xlabel('x(t)');\n", "plt.ylabel('v(t)');" ] }, { "cell_type": "markdown", "id": "7a4e2a84-b2fd-4886-9d98-08ece9f06110", "metadata": {}, "source": [ "Appliquer le schéma d'Euler à l'oscillateur de Duffing avec $N=500$. Tracer les solutions numériques obtenues ainsi que l'évolution de l'énergie totale. Est-ce satisfaisant ? " ] }, { "cell_type": "code", "execution_count": 28, "id": "c49bf475-54a7-42ee-85a8-ccd109961c8e", "metadata": { "scrolled": true, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, y = Euler(Duffing, y0, 0.0, T, 500)\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()" ] }, { "cell_type": "code", "execution_count": 30, "id": "8d64568e-bf66-4400-9277-2213b3903796", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = y[:,0]\n", "v = y[:,1]\n", "alpha = 1.0; beta = 12.0\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure()\n", "plt.plot(t, E, '.-'); plt.grid();\n", "plt.xlabel('time t');\n", "plt.ylabel('E(t)');" ] }, { "cell_type": "markdown", "id": "1ec97e7b-bd9d-42e3-b7b8-3f3585c2ceea", "metadata": {}, "source": [ "#### Schéma de Runge-Kutta RK2\n", "\n", "Le schéma de Runge-Kutta RK2 (ou schéma d'Euler-Cauchy) du cours s'écrit\n", "\n", "\\begin{align*}\n", "& k_1 = F(t_n, z_n), \\\\[1.3ex]\n", "& k_2 = F(t_n+h, z_n+h\\,k_1) \\\\\n", "& z_{n+1} = z_n + \\frac{h}{2}\\left( k_1+k_2\\right).\n", "\\end{align*}\n", "\n", "Mettre en oeuvre ce schéma dans une méthode ```RK2(F, y0, t0, T, N)```.\n", "Appliquez RK2 au système de Duffing où l'on comparerea les solutions avec celles obtenues avec ```odeint()``` ainsi que l'évolution de l'énergie totale. Commentez. " ] }, { "cell_type": "code", "execution_count": 33, "id": "622dbff9-c7a7-42b0-a2d2-9276bd3b91fa", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def RK2(F, y0, t0, T, N):\n", " d = y0.size\n", " h = (T-t0) / N;\n", " t = np.linspace(t0, T, N+1)\n", " z = np.zeros((N+1, d))\n", " z[0,:] = y0\n", " for n in range(0, N):\n", " k1 = F(t[n], z[n,:])\n", " k2 = F(t[n]+h, z[n,:]+h*k1)\n", " z[n+1,:] = z[n,:] + 0.5*h*(k1+k2)\n", " return t, z\n", "\n", "T = 4.0\n", "N = 80\n", "t, y = RK2(Duffing, y0, 0.0, T, N)\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()\n", "\n", "x = y[:,0]\n", "v = y[:,1]\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure(figsize=(3,3))\n", "plt.plot(t, E, '-'); plt.grid()" ] }, { "cell_type": "markdown", "id": "0323a455-b410-4d74-8483-3e1573f43648", "metadata": {}, "source": [ "#### Schéma à variables décalées de Verlet\n", "\n", "\\begin{align*}\n", "\t& x_{n+1} = x_n + h v_{n+1/2}, \\\\\n", "\t& v_{n+3/2} = v_{n+1/2} - h\\alpha\\, x_{n+1} - h \\beta\\, x_{n+1}^3. \n", "\\end{align*}\n", "\n", "Les données initiales sont toujours $x_0=2$ et $v_0=0$. Pour \"l'initialisation\" de $v_{1/2}$ on utilisera ici simplement le schéma d'Euler explicite sur $v$ (sachant que l'on peut faire mieux) :\n", "\n", "$$\n", "v_{1/2} = v_0 - \\frac{h}{2}\\alpha\\, x_0 - \\frac{h}{2}\\beta\\, x_0^3.\n", "$$\n", "\n", "Mettre en oeuvre le schéma de Verlet pour l'oscillateur de Duffing. On utilisera une subdivision uniforme comme pour le schéma d'Euler avec $h=\\frac{T-t_0}{N}$. Tracer les solutions numériques $t\\mapsto x(t)$ et $t\\mapsto v(t)$ ainsi obtenues. On utilisera \n", "$N=100$." ] }, { "cell_type": "code", "execution_count": 36, "id": "4409d7d5-e980-40db-8004-962b7c2bbaf0", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 100\n", "t0 = 0; T = 4\n", "h = (T-t0) / N\n", "t = np.linspace(t0, T, N+1)\n", "x = np.zeros(N+1)\n", "vdec = np.zeros(N+1)\n", "x[0] = 2\n", "v0 = 0\n", "# Calcul de v_{1/2}\n", "vdec[0] = v0 - (h/2)*alpha*x[0] - (h/2)*beta*x[0]**3\n", "\n", "for n in range(0,N):\n", " x[n+1] = x[n] + h*vdec[n]\n", " vdec[n+1] = vdec[n] - h*alpha*x[n+1] - h*beta*x[n+1]**3 \n", "\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, x, '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, vdec, '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()" ] }, { "cell_type": "markdown", "id": "3d4f9f88-7a43-4812-97d7-f2a6eb876be1", "metadata": {}, "source": [ "Les variables discrètes de positions $x_n$ et de vitesse $v_{n+1/2}$ ne sont pas définies aux mêmes instants discrets, si bien que l'on ne peut pas définir strictement une énergie totale. On peut toutefois définir une estimation en calculant une valeur moyenne $\\hat v_n$ de vitesse aux temps $t_n$ par\n", "\n", "$$\n", "\\hat v_n = \\frac{v_{n-1/2}+v_{n+1/2}}{2}\n", "$$\n", "\n", "et définir une énergie totale approchée $\\hat E_n$ par\n", "\n", "$$\n", "\\hat E_n = \\alpha\\frac{x_n^2}{2}+\\beta \\frac{x_n^4}{4} + \\frac{\\hat v_n^2}{2}.\n", "$$\n", "\n", "Tracer dans ce cas l'évolution de $\\hat E_n$ ainsi définie au cours du temps. Est-ce satisfaisant ? \n", "\n", "Refaire le calcul et les graphiques avec $N=200$." ] }, { "cell_type": "code", "execution_count": 39, "id": "c54e2a69-acd3-41d7-8086-3940d2f25a8d", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vhat = np.zeros(N+1)\n", "vhat[0] = v0\n", "vhat[1:N+1] = 0.5*(vdec[0:N]+vdec[1:N+1])\n", "Ehat = alpha*x**2/2 + beta*x**4/4 + vhat**2/2\n", "plt.plot(t, Ehat, '.-')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "c0f2275a-17f0-4840-afb6-00a64e1dd5e3", "metadata": {}, "source": [ "C'est fini pour les TPs !" ] }, { "cell_type": "code", "execution_count": null, "id": "9c30b731-0740-430d-b537-fa92fd63e292", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }