{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
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Practical Work 4 : Second order ODEs and differential systems

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\n", "\n", "*Authored in 2025 for educational purpose by S. Cardonna, Q. Richard, V. Lleras & P. Azerad. If you identify any issues or have suggestions for improvement, feel free to contact me.* \n", " \n", "**Introduction** \n", "We now are focused on implementing harmonic oscillator (one of the first example of differential equation in physics degree), and then a differential system from epidemiology called SIR (*Sound, Infected, Recovered*).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
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Part 1 - Harmonic oscillator

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\n", "\n", "The harmonic oscillator is described by the second-order differential equation:\n", "$$\n", "y'' = -y, \\quad y(0) = 0, \\quad y'(0) = 1.\n", "$$\n", "To solve this using numerically, it is rewritten as a first-order system:\n", "$$\n", "\\begin{cases}\n", "y_1' &= y_2, \\\\\n", "y_2' &= -y_1, \\\\\n", "y_2(0) &= 0\n", "\\end{cases}\n", "$$\n", "\n", "where $y_1 = y$ (position) and $y_2 = y'$ (velocity)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Proof that $y(t)^2+y'(t)^2 = C$ ####\n", "To prove that $ y(t)^2 + y'(t)^2 $ is constant over time for the harmonic oscillator, we let $ E(t) := y(t)^2 + y'(t)^2 $. We then need to show that $ E(t) $ is constant, i.e., its derivative with respect to $ t $ is zero.\n", "The derivative is, using the chain rule:\n", "$$\n", "\\frac{dE}{dt} = \\frac{d}{dt} \\big( y(t)^2 \\big) + \\frac{d}{dt} \\big( y'(t)^2 \\big)\n", "$$\n", "$$\n", "\\Leftrightarrow \\frac{dE}{dt} = 2y(t) \\cdot y'(t) + 2y'(t) \\cdot y''(t).\n", "$$\n", "\n", "Using the equation of motion $ y''(t) = -y(t) $, we then just substitute $ y''(t) $ into the derivative:\n", "$$\n", "\\frac{dE}{dt} = 2y(t) \\cdot y'(t) + 2y'(t) \\cdot (-y(t)) =0 .\n", "$$\n", "We just proved that the quantity $ E(t) = y(t)^2 + y'(t)^2 $ is constant over time (this represents the conservation of energy for the harmonic oscillator)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Implementation of harmonic oscillator with RK45 ####" ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_ivp\n", "\n", "# Definition of the differential system\n", "# y[0] = y (position), y[1] = y' (velocity)\n", "# y\" = -y is written as y[0]' = y[1] and y[1]' = -y[0]\n", "\n", "def harmonic_oscillator(t, y):\n", " return [y[1], -y[0]]\n", "\n", "# Time interval (one period) and initial conditions\n", "time_span = [0, 2 * np.pi]\n", "initial_conditions = [0, 1]\n", "\n", "# Solving the system over one period\n", "time_points = np.linspace(0, 2 * np.pi, 100)\n", "solution = solve_ivp(harmonic_oscillator, time_span, initial_conditions, t_eval=time_points, method='RK45')\n", "t = solution.t\n", "y = solution.y\n", "\n", "# Plotting the results\n", "plt.figure(figsize=(12, 5))\n", "\n", "# Plot time evolution of y and y'\n", "plt.subplot(1, 2, 1)\n", "plt.plot(t, y[0], label='$y(t)$ (Position)', linewidth=2)\n", "plt.plot(t, y[1], label=\"$y'(t)$ (Velocity)\", linewidth=2, linestyle='--')\n", "plt.xlabel('Time $t$', fontsize=12)\n", "plt.ylabel('Values', fontsize=12)\n", "plt.title('Time evolution of position and velocity', fontsize=14)\n", "plt.legend(fontsize=10)\n", "plt.grid(True)\n", "\n", "# Plot phase space trajectory\n", "plt.subplot(1, 2, 2)\n", "plt.plot(y[0], y[1], linewidth=2, color='tab:red')\n", "plt.gca().set_aspect('equal', adjustable='box') \n", "plt.xlabel('Position $y$', fontsize=12)\n", "plt.ylabel('Velocity $y\\'$', fontsize=12)\n", "plt.title('Phase space trajectory', fontsize=14)\n", "plt.grid(True)\n", "plt.subplots_adjust(wspace=0.4)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We indeed obtain a circle in the phase plane $(y, y')$. Indeed, since\n", "$$\n", "\\frac{d}{dt} \\big(y^2(t) + y'^2(t)\\big) = 0,\n", "$$\n", "then\n", "$$\n", "y^2(t) + y'^2(t) = y^2(0) + y'^2(0) = 1.\n", "$$\n", "Here, of course, $y(t) = \\sin t$ and $y'(t) = \\cos t$." ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "image/png": 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FAHB3d0dwcDD69u2LyZMno0GDBgX2b9asWYFtVapUAQCkpaVZbN+xYwc++OAD7N27F9evX0dOTo75MQ8PD/P/+/r6olu3bti8eTOaNm2KXr16oUOHDmjRogXc3d0tau7Zswc+Pj5Yvny55PPx9vZGfHx8sc+7d+/e2LBhA/71r3+hb9++6NSpEx555BFUqlRJcv+qVauiWrVqBbY/8sgjWLZsGQ4dOoSePXsCAIQQWLFiBb766iscO3YMt27dQl5envlzrly5Yv7//fv3QwiBxx57rMBzfdiePXsAAAkJCZg5c2aBx5OSkpCXl4eTJ0+iefPmxc5BcRo1amTxdXpQSkoK5s+fj19++QXnz5/H3bt3LR5/8DlKSUhIwM2bNxEWFmZ+/T3o2rVrAGD+WsbHx+P27duIjo6Gv79/aZ6O2aFDhwBAcp3Zxx57DABw+PDhAo+1aNFCsp67uzsGDx6M+fPnY+vWrYiJiQEAfPHFFwCA4cOHW92XXq9Hy5YtreqrU6dOCA0Nxbp167Bo0SK4ud3/Mbd69WoAQP/+/c375r92kpOTJV87D85z/fr1zdu9vLwk3wecXZMmTVCuXLkC2x955BFs27YNhw4dQrNmzfD3338jNzcXWVlZkvN+6tQpAPfn/YknnrB4TOp1UJiiXtOtW7eGl5eXxWvnn3/+Mfcr9Rwe9uijjyI0NBTz58/HP//8gyeeeALt27eHwWBw6OUpnRUDM5GErl27YsuWLVbv7+vrW2Bb/g/q3Nxc87Zvv/0WL7zwAsqVK4euXbsiIiICer0eOp0OX331Fc6fP29R49tvv8W8efOwdu1avPXWW+axBg8ejHnz5pmXJEtNTUVOTo5kyMp3586dYp9Hr1698MMPP2DRokVYunQplixZAp1Oh8ceewwLFy5E48aNLfYPDg6WrJO//datW+ZtY8aMwccff4zw8HA89dRTCA0NhaenJwBg1qxZyMrKMu+b/3mVK1cutuf8pbnWrFlT5H7WPH9rFPacU1NT0aJFC1y4cAFt27ZFdHQ0KlSoAFdXVxw+fBgbN260eI6F1QCA48eP4/jx44Xul/9cSjJPxUlPT4eLiwsCAwMLPBYcHAydTof09HTJxwozYsQILFiwAF9++SViYmJw7949rFmzBpGRkYiOjra6r/DwcMnHQkNDzfvkc3V1Rd++fbFw4UL8+uuv6N69OzIyMvDDDz+gbt26aNq0qXnf/Pn++eef8fPPPxfaw8OvnaCgIMUDkZ+fHwDL76EHpaenQ6fToXz58lbv/+B+Jd3fGta+H+TP+65du7Br165C60l9zxb1entY/nOQ+hydTofg4GBcvnzZvC2/v6CgIKvG9fPzw549ezB9+nT8+OOP2Lx5MwAgPDwckydPxssvv2x1r2T7GJiJVDRz5kx4eXnhwIEDBdY3XbduXYH99Xo95s6di7lz5+Ls2bP4/fffsXTpUnz44Ye4e/cuPvvsMwD3Q7ROp8P169fL3GOPHj3Qo0cP3L59G7t27cKGDRuwbNkyxMTEID4+HhUqVDDvm5ycLFkjf3v+D9uUlBQsWbIEDRs2RFxcnMXaw0lJSQWCfv4YD/4wK0z+Lys//vhjgaNRSigsKC1btgwXLlzAnDlzMHXqVIvH5s+fj40bNxZbO/+59OzZE999912x+5dknqwZOy8vD9euXSsQGFJSUiCEkPzFsKjgGBkZiS5dumDTpk1ISUlBbGwsbt68ifHjx1sdOH19fZGSkiL5WFJSknmfB/Xv3x8LFy7E6tWr0b17d/z3v/9FZmamxdHlBz9v8eLFGD16tFX9AEU/Z7nkvz/kH219UG5uLs6ePYvIyEjzL+ZF7f/g9vz9fHx8EBoairNnzyI3Nxeurq5F7m8Na98P8ud9/PjxeP/9962uD5Rs7vPHSU5OLvCXMCEEkpOTLV47D75fPbx/Yc+tatWq+Oqrr5CXl4cjR45g69at+Oijj/DKK6/A398fffr0sbpfsm280x+Rik6fPg2DwVDgh9DVq1eLvbNWZGQkhgwZgp07d6JcuXLYtGmT+bFWrVrhxo0bhf6wLI3y5csjJiYGn3/+OQYNGoTk5GTs3bvXYp8LFy4UOCoOAH/++SeA+3+iBYAzZ85ACIHo6OgCN+rI3/dBzZs3h4uLC37//XeYTKYi+2zVqhUAIC4uzvonV4j80PDgXwWsdfr0aQD3f+F4mNRzlGIwGODr64v9+/cX+7wBoE6dOvD19cXff/+NmzdvFru/q6troc8t/2sldWvh/G0P/4XBGiNHjoTJZMLKlSvx5ZdfwtXVFYMHD7b685s0aYLMzEzs27fP6r4aNWqEBg0aYOPGjbh9+zZWr14NnU6Hfv36Wewn52tHbu3btwcAbN26tcBjf/31l/kmJflq1aqFsLAw7Nq1q8CR2Tt37mDXrl2IjIy0OFrfvn1782MP+/XXXwHcP+3AWocOHZK8o+DD7wctWrSATqdTfN6Lek3v3bsX9+7ds3jtNGrUyKLfBxX3Pezi4oLGjRtj4sSJ+OabbwDA4j2a7B8DM5GKqlWrhsTERIujFffu3cOoUaMKBKRr167h2LFjBWrcvHkTWVlZFnfsGjNmDABgyJAhuHHjRoHPSUpKgtFoLLa/P/74QzJQ5R/he/guYbm5uXjzzTctbtN75MgRfP311wgMDES3bt3MzxsAdu/ebXHe8qVLlzBlypQC4wUHB6Nnz54W55I/3E/+ud89evRA1apVsWjRIvzxxx8F9jWZTPjrr7+Kfe4AEBAQAAC4ePGiVfs/KP85PjzW2rVrzX+qLY6bmxtGjRqF8+fP44033pAMzceOHTN/Pdzc3DBy5EjcunULr732WoGv3a1btywCTEBAAK5fv4579+4VqDtw4EAA90+PefAUh1u3bpm/Bvn7lMSTTz6JsLAw/Pvf/8bOnTvRvXt3hIWFWf35+WNOmTLFYj4uXrxoPkf54SAM3D/KfPfuXXz00UfYvn072rdvX+DUjpYtW6JVq1b45ptvsH79+gI18vLysHPnTqt7lVOdOnXw6KOP4vfff8cvv/xi3p6dnY1p06YBAIYNG2bertPpMGzYMGRkZGDOnDkWtebMmYOMjIwC542PGDECADBt2jRkZ2ebt//yyy/YsWMHunTpInmNQmHS0tLw9ttvW2z79ddfsW3bNtSvX998rUdISAief/557N69G++9957kbb737t2LzMxMq8eW0rdvX7i5uWHRokUW1w9kZ2dj0qRJAIBBgwZZ7O/q6opFixZZ/FUjPT0dc+fOLVD/+PHjkkee87c9/H5Jdk7DCw6JbE5Ry8pJKepOf1JXbS9evFgAEKGhoeLVV18Vo0aNEjVr1hQ1atQQjRo1slih4dChQwKAaNSokejfv7+YPHmyGD58uAgKChIAxMcff2wx3rRp08xXqvfu3VtMmjRJDBs2THTo0EG4urpKruf6sEaNGonAwEDxzDPPiNdff12MGzdOtGzZUuD/10p+cDkuFLEOs4uLS4F1VPOXiWvSpIl44403RP/+/YW/v7947rnnJJdXu3btmjAYDObPGT9+vBg3bpx44oknhIeHh8Wyevv27RMVK1Y0X/X+2muvibFjx4pnnnlGVKpUyeobZHzyySfmlR/eeustMWfOHPPNMR68OYOUixcvCj8/P+Hq6ip69eol3njjDdG5c2fh4uJiXn3k4ZtbSD3ve/fuic6dO5tXaxk8eLCYNGmSePHFF82vkbi4OPP+d+/eNa/iUqtWLTFmzBgxYcIE0bNnT+Hj4yMOHTpk3nfixIkCgOjQoYOYNm2amDNnjsVNK/LXYQ4PDxdjx44Vr732mnmN4sLWYX74xidS8l+beGjlA2s8uA5zVFSUeOONN8SoUaPMN42RWtFAiPvLGLq4uAh3d3cBQCxbtkxyvzNnzphXvvjXv/4lXn75ZTF+/HjRq1cvUaVKFeHp6Wmxf1nuljh+/HgxcOBAMXDgQBEWFiaA+2u45297+IYdx44dE35+fsLDw0P0799fTJw40bx2sdTycRkZGebXSJcuXcTkyZNFly5dBADRokULyWXwhg0bJgCIevXqiYkTJ4r+/fsLDw8PERAQYNVqOUJIr8M8ZcoU8zrM3t7ekuswN27c2Lzk3IgRI8zrzOevk3z16lXz/sXdhbO4dZgrVqwoRo0aJd544w3zEnE9evQosBpN/koZwcHB4tVXXy1yHeZ///vfws3NTbRv314MHz5cTJ48WTz//PPCy8tLeHl5ib///tuq+SP7wMBM9AClA3NeXp5YunSpqFevnvDy8hIhISFi6NChIiUlpcAPhJs3b4qZM2ea7wro4eEhwsLCRExMjMWNFx4UGxsrnnzySREYGCjc3d1FSEiIaN26tZgzZ47kDSQetm7dOvH888+LGjVqCL1eL/z8/ESjRo3EggULCiwXlf/D4+LFi+KFF14QAQEBwsvLS7Ru3Vps3bq1QO3bt2+L8ePHi4iICPNd/ubMmSOys7Mlg6MQ95fWmzZtmoiKihKenp7Cz89PNG7cWEyfPr3AcnOXLl0Sr732mqhVq5bw9PQUvr6+wmAwiGHDhpnXni2OyWQSEydOFFWrVhVubm4WAbm4wCyEEIcPHxZdunQR/v7+onz58qJ9+/bit99+EytWrLA6MAtxf83gzz77zHyTFE9PT1G1alURExMjPv300wJ3crt37554//33RePGjYW3t7coV66cqFu3rhg/frzFLxa3b98Ww4cPF6GhocLV1VUy8C5fvly0aNFC6PV6odfrRYsWLSSXTSxJYE5MTBTA/RuilOSuk/lMJpN4//33RYMGDYSnp6d5bgtbYixfdHS0eTnIopYVTE1NFVOnThX169c3z1+tWrVE3759zcuw5StLYM4P5oX9k7pbYHx8vHjuuefMd8ds0KCBWLJkSaFLTaalpYmxY8eK8PBw4e7uLqpWrSrGjx8v0tPTJffPzc0VH374ofnOdhUrVhQvvPCC5J1HCyN1pz9fX1/h4+MjoqOjC73TX2Zmpnj33XdFs2bNhI+Pj/D29haRkZHi6aefFqtWrbK4E19pA7MQQmzcuFG0b99elC9f3jyHxd3pr27dusLDw0NUqVJFvPHGGyIzM7PA9+uJEyfEa6+9Jpo0aSIqVqwoPD09RfXq1cXAgQPF8ePHrZs8shs6IST+FkJEVAydTof27dtLnh9Ixbt37x68vb3RpUsX8/mijuq7775Dr169MG3aNMyePVvrdkhm586dQ2RkJAYOHIivvvpK63aIFMFzmImINJCYmAjgf+t1OyohBBYuXAg3Nzer114mIrI1XFaOiEhFycnJWLx4Mb7//nsAwLPPPqtxR8o4evQofvrpJ+zevRt79uzByJEjC11PmYjI1jEwExGp6OrVq3j33XdRo0YNfPbZZ+jevbvWLSniwIEDePPNN+Hn54f+/fuXeL1dIiJbwnOYiYiIiIiKwHOYiYiIiIiKwMBMRERERFQEnsOskry8PFy5cgXly5eHTqfTuh0iIiIipyeEwO3btxEWFgYXl8KPIzMwq+TKlSu8QpyIiIjIBl28eLHIZT4ZmFVSvnx5APe/IL6+voqPZzKZsHXrVnTp0gXu7u6Kj2cvOC/SOC/SOC/SOC/SOC/SOC/SOC/S1J6X9PR0hIeHm3NaYRiYVZJ/Goavr69qgVmv18PX15ffiA/gvEjjvEjjvEjjvEjjvEjjvEjjvEjTal6KO12WF/0RERERERWBgZmIiIiIqAgMzERERERERWBgJiIiIiIqAgMzEREREVERGJiJiIiIiIrAwExEREREVAQGZiIiIiKiIjAwExEREREVgYGZiIiIiKgIDMxEREREREVgYCYiIiIiKgIDMxERERFRERiYiYiIiIiKwMBMRERERFQEBmYiIiIioiIwMBMRERERFYGBmYiIiIioCAzMRERERERFYGAmIiIiIioCAzMRERERUREcLjD/8ccfePLJJxEWFgadTocffvih2M/ZsWMHmjZtCk9PT9SsWRNfffVVgX2WLFmCiIgIeHl5oVWrVti3b5/8zRMRERGRzXG4wHznzh00atQIS5YssWr/s2fPonv37njsscdw+PBhjB07FsOGDcOvv/5q3mf9+vUYN24cZsyYgYMHD6JRo0bo2rUrUlJSlHoaRERERGQj3LRuQG6PP/44Hn/8cav3X7p0KSIjI7Fw4UIAgMFgwF9//YV///vf6Nq1KwBg0aJFGD58OAYPHmz+nJ9//hnLly/H5MmT5X8SRERERGQzHC4wl1RcXByio6MttnXt2hVjx44FAGRnZ+PAgQOYMmWK+XEXFxdER0cjLi6u0LpZWVnIysoyf5yeng4AMJlMMJlMMj4DafljqDGWPeG8SOO8SHOkeRFCIC89HXf37kXaN+twb//+MtWrDSBxUukOGLhWqoSAkSOgb9cObqGh0Lm6lqkXW+FIrxc5cV6kcV6kqT0v1o7j9IE5KSkJwcHBFtuCg4ORnp6Ou3fv4ubNm8jNzZXcJz4+vtC677zzDmbNmlVg+9atW6HX6+Vp3gqxsbGqjWVPOC/SOC/SbHZecnPhEx+Pyqu+1rqTEsm9fh3X3p5Xos9Jb9IYKT2eRp63l0JdycdmXy8a47xI47xIU2teMjMzrdrP6QOzUqZMmYJx48aZP05PT0d4eDi6dOkCX19fxcc3mUyIjY1F586d4e7urvh49oLzIo3zIk3recnLyEDKnLnI2LxZ9bFtje+hw/A9dLjIfcK/+xYetWtDp9Op09RDtH692CrOizTOizS15yX/DIDiOH1gDgkJQXJyssW25ORk+Pr6wtvbG66urnB1dZXcJyQkpNC6np6e8PT0LLDd3d1d1W8MtcezF5wXaZwXaUrOi8jOxvWln+H6J58oUt+ZXHyul/QDLi6oueN3uAcFqdIHv4+kcV6kcV6kqTUv1o7h9IG5devW2PzQ0ZvY2Fi0bt0aAODh4YFmzZph27ZtePrppwEAeXl52LZtG0aPHq12u0Rkp0ReHm6uXoPkeSU7FYFkkJeHxEfbF9jsVbcuItZ9A52HhwZNEZE9cbjAnJGRgcTERPPHZ8+exeHDhxEQEICqVatiypQpuHz5MlatWgUAeOmll/Dxxx9j4sSJGDJkCLZv347//Oc/+Pnnn801xo0bh4EDB6J58+Zo2bIlPvjgA9y5c8e8agYR0YNETg6uvPkm0jf9qHUrVIR7J04gvmGjAttr/fkH3AIDNeiIiGyVwwXm/fv347HHHjN/nH8e8cCBA/HVV1/h6tWruHDhgvnxyMhI/Pzzz3j99dfx4YcfokqVKvjyyy/NS8oBwAsvvIBr165h+vTpSEpKQuPGjbFly5YCFwISkfMRQuDm2rVInjNX61ZIJqceedTiY7egINTc9ht0/LM5kdNyuMDcoUMHCCEKfVzqLn4dOnTAoUOHiqw7evRonoJBRBDZ2Yhv1hzgUlBOIyclBfENGlpsq755MzyrR2rUERGpzeECMxGRnFzu3kXiQ2GJ6Ey3bhYfR3z7Ldyi6mjUDREpjYGZiOgBIjcXp9q0Re6tWwCAmhr3Q/bhXK/7K3Tk39Cl5rbf4F65srZNEZFsGJiJyOnd/PZbJE2brnUb5EASO1neQTbqxHHoXFw06oaIyoqBmYicjsjOllwdgUgp8XXrmf8/4rvv4F2/XhF7E5GtYWAmIqeQfekSTkd31roNIpx77jnz//v364eQaVM17IaIrMHATEQO6/b233Hp5Ze1boOoUDfXrMHNNWvuf+DqiqhjRzW7tTcRFY6BmYgcyu3ff8elUQzJZIdycxFvqGv+MMp4guGZyEYwMBOR3buzZw8uDOKdN8mx5Idnnbc3og4d1LgbIufGwExEdsl09SoSH+uodRtEihN378IYZQDAc56JtMLATER2Q+TmIr5efa3bINLMg+c8R36/AV4Gg8YdETkHBmYisnlXJk3CrY2btG6DyKacfeZZ8/9znWciZTEwE5FNyrlxA6fattO6DYfmVbcu/Ho+C33TpnCvXBku5cpZFbpMJhM2b96Mbt26wd3dvdD9hBAQd+8i+9IlZMXHI+OPP5H+009yPgX6f/nrPFccORJBr4/VthkiB8TATEQ25cwzzyLLaNS6DbtUdeVK6Js1hc7NNt7adToddHo9vGrXhlft2vB76ilUfv89qz5X5OUh++xZJM2eg8y9exXu1HHc+Owz3PjsMwBA1NEj0BXxCw0RWc823lWJyKnl3buHhMZNtG7DppWPiUHYvLfhotdr3YoqdC4u8KxRA9VWflXoPsJkQtoPP/C25oWIb9AQABAyexb8n39e426I7BsDMxFpJnXlSiS/M1/rNmxK7X174errq3UbdkHn7g7/Xr3g36tXgcfysrKQ8t77uLl6tQad2Zak6TOQNH0GAMAQz7/eEJUGAzMRqS5/iSxnVmPLL/CIiNC6DYfl4umJkKlvIWTqWxbbc27exJnHuyE3LU2bxjSW/73HX8yISoaBmYhUIXJyEF+/gdZtaKLmHzvhHhSkdRsEwM3fH7X3xFlsy8vOxrlezyMrIUGjrtR3smUrAEDlxR/Bt3Nnjbshsn0MzESkqOyLF3G6cxet21BN+GdLUa59e63boBJw8fBA9Y0/WGxzllVaLr86BpcBeDdpgohv1mrdDpHNYmAmIkWkb92Ky2Ne07oNxdXc8TvcQ0K0boNk5laxosX5viI7G/ENG2nYkbLuHjpkPl2D5zkTFcTATESyuvbRR7j+yadat6GYWnG74ebvr3UbpDKdh4dlgHbgu04yOBMVxMBMRLK4MHwE7vz5p9ZtyO5Kv354dPKkIm/QQc5H5+pqEShz09Jw8l+tNexIfgzORP/DwExEZXL6iSeQnXha6zZkFWU8AZ1OB5PJhJObN2vdDtkB1woVUPPoEfMdENNXr0HKggVatyWL/OCc/31B5IwYmImoVM717oO7hw9r3YYsgt4Yj4rDhmndBjmQioMHoeLgQQAAU0oKEh+1/wtB4w11ATA4k3NiYCaiErk6cybS1q3Xuo0yi9y0EV61a2vdBjkB96Ag82kNwmQy34HPXuUHZ56qQc6EgZmIrHLzP/8x3y3MXtXcvg3uYWFat0FOTOfu/r/wLIQ5fNojnuNMzoSBmYiKdPfIEZx7/gWt2yi1yI0/wKtOHa3bICpAp9P9Lzzb8aobDM7kDBiYiUhS7u3bONmipdZtlErlDz+Eb1fnuVkK2b8HV93Iu3cPCY2baNxRyRmjDPDv2wch06dr3QqR7BiYiciCvf6ZWKfXI+rgAa3bICozFy8vc3i+s28fLgwYqHFH1ru59hvcXPsNIr79D7wbNNC6HSLZMDATkVmiHV6MVOefw3Dx9NS6DSJF+LRsaQ7P+ac+2INzvZ4HAEQdO6pxJ0TyYGAmIlybPx+116zVug2rhcycCf/e9nteNVFpmE/ZyMxEQtNmGndjnfj6/3+UecF8bRshKiMGZiInZm/rw0YdOwqdG9+2yLm56PXm8Hzq0fbISUnRuKPi1Z40GZfWr0fkWvv5xZzoQfzJQ+Sk7OXPu+W7dkWVDz/Qug0im1Trj50AgOxLl3E6Olrjbop27+AhGKMMqPFbLDyqVNG6HaISYWAmcjJnn+2JeydOaN1GsWrt3gW3gACt2yCyCx5VKsMQb7SLi3ZPR3cGwGXoyL4wMBM5iZybN3GqdRut2yhW1Inj0Lm4aN0GkV16cG3n8/0HIPPvvzXuqHDGKAO8GzVCxPp1WrdCVCwGZiInYA+nX/BoE5G8qn29CgBwZ/duXBgyVONupN395x8Yowyoc+ggXLy9tW6HqFA8jEPkwG5++61Nh+WKI0fCEG9kWCZSkE+bNjDEG1F7T5zWrRQqoUlTm36vIuIRZiIHZOvnMVZdsRw+rVtr3QaRU3GtUOH+ec42fBtuY5QB1daugb5pU61bIbLAwEzkYC6+NAoZO3Zo3YakyB++h1dUlNZtEDm1/Ntwi7w8xNetp3U7BZzv2w8AT9Mi28LATOQgbPmoUY0tv8AjIkLrNojoAToXF5teWcMYZUDlDz6Ab0xXrVshYmAmcgSnu8Yg+/x5rdsooMZvv8GjSmWt2yCiIuSvrGGLwfny2LG4DB5tJu3xoj8iOyby8mCMMthcWI7c8F8Y4o0My0R2JD84R504rnUrBRijDLj9229at0FOjIGZyE5dmTrV5s4/DHt3AQzxRnjVta2jVERkvfxTNer8c1jrVixcGv0qV9IgzTAwE9khY5QBt777r9ZtmJWPiYEh3gi/p57SuhUikomLpycM8UbU+vMPrVuxYIwyIOvsWa3bICfDc5iJ7MjtHTtw6aVRWrdhgecWEjk2t8BAGOKNyPhrFy4OG6Z1OwCAM493A8D3H1IPAzORnbC1P0VGGU9Ap9Np3QYRqaRcu7YwxBtx5plnkWW0jaBqjDIg6ugR6NzdtW6FHBxPySCycXl37thUWK5z+BAM8UaGZSInVf37DTZ1ZDe+QUNcmTRJ6zbIwTEwE9mwC0OGIqFZc63bAABU+WQJDPFGuHh5ad0KEdkAQ7wRUUf+0boNAMCtjZts6sACOR6ekkFko2zpzd+WjiYRke3QeXjAEG/EnX37cGHAQK3bgTHKgFpxu+Hm7691K+RgeISZyMbk3LxpM2E5yniCYZmIiuXTsqXNvFecat0Gp2Me17oNcjAMzEQ25Myzz+JU6zZat4Fqq7/mecpEVGKGeCOijh/Tug1knztnMwceyDEwMBPZCGOUAVkntD9CY4g3Qt/cNs6bJiL7o3N1hSHeiLD33tO6FRijDMjNuKN1G+QAGJiJNCZMJps4EnJy3tuoefSI1m0QkYPwe/IJmzhN42Tz5khe8K7WbZCdY2Am0lD6li2Ib9BQ0x70rf91Pyi7umraBxE5pppHj+D01Lc07SF1xQqbODBB9ourZBBpxBbevPNvPmIymbRuhYgcWG758qh59AgSNT5AYIwy8KZLVCo8wkykAa3DcsXhw3lRHxGpzhBvRO39f2vaQ7yhLnJu3tS0B7I/DMxEKsrLytI8LBvijQgaP07THojIebmWK6f5uc2nWrdByocfatoD2RcGZiKVZB46hIRGjTUbP2DwYM1/SBER5TPEG1HnwH7Nxr/x6VLND2CQ/eA5zEQqOPNUD2SdPKnZ+Dxnj4hskYuPDwzxRk2DqzHKwIMJVCweYSZSmDHKoF1Y1ul4rjIR2TxDvBHVN/+s2fjGKANEXp5m45Ptc8jAvGTJEkRERMDLywutWrXCvn37Ct23Q4cO0Ol0Bf51797dvM+gQYMKPB4TE6PGUyE7p+VRkzqHDsJgPKHZ+EREJeFZvbqmR3rj69bjxYBUKIcLzOvXr8e4ceMwY8YMHDx4EI0aNULXrl2RkpIiuf+GDRtw9epV879jx47B1dUVvXr1stgvJibGYr9vvvlGjadDdkrk5Wkalg3xRrh4e2s2PhFRaRnijag0erQmY59q3QbpW37VZGyybQ4XmBctWoThw4dj8ODBqFu3LpYuXQq9Xo/ly5dL7h8QEICQkBDzv9jYWOj1+gKB2dPT02I/f39/NZ4O2aHctDTE162nydhVPvmE5+IRkd0LHP0Koo4f02Tsy2PHIrFrV03GJtvlUBf9ZWdn48CBA5gyZYp5m4uLC6KjoxEXF2dVjWXLlqF3797w8fGx2L5jxw4EBQXB398fHTt2xNy5c1GxYsVC62RlZSErK8v8cXp6OgDAZDKpcpOI/DF4QwpLSs/L3cP/4HL//orULk6NI/+U+iYkfL1I47xI47xI47xIK8u8aHWzE9P5CzBGGe7fBVWpMfh6kaT2vFg7jk4IIRTuRTVXrlxB5cqVsXv3brRu3dq8feLEidi5cyf27t1b5Ofv27cPrVq1wt69e9GyZUvz9nXr1kGv1yMyMhKnT5/Gm2++iXLlyiEuLg6uhdxOeObMmZg1a1aB7WvXroVery/lMyRbFvjjT/D/6y9Nxj65YL4m4xIRqaHc0aMIW71Gk7H5/urYMjMz0bdvX9y6dQu+vr6F7sfA/ICRI0ciLi4OR44U/RvlmTNnUKNGDfz222/o1KmT5D5SR5jDw8Nx/fr1Ir8gcjGZTIiNjUXnzp3h7u6u+Hj2Qql50ep2r2GffQZ9m9bF71gMvl6kcV6kcV6kcV6kyTUvIjcXpxs3kbEz6ylxpJmvF2lqz0t6ejoqVapUbGB2qFMyKlWqBFdXVyQnJ1tsT05ORkhISJGfe+fOHaxbtw6zZ88udpzq1aujUqVKSExMLDQwe3p6wtPTs8B2d3d3Vb8x1B7PXsg5L1pd3KfE2sp8vUjjvEjjvEjjvEgr87y4u2u2ZnNig4aKrWfP14s0tebF2jEc6qI/Dw8PNGvWDNu2bTNvy8vLw7Zt2yyOOEv59ttvkZWVhRdffLHYcS5duoQbN24gNDS0zD2TfdMqLHNtZSJyVoZ4Iyq9/LLq48Yb6kLk5qo+LtkGhwrMADBu3Dh88cUXWLlyJYxGI0aNGoU7d+5g8ODBAIABAwZYXBSYb9myZXj66acLXMiXkZGBCRMmYM+ePTh37hy2bduGHj16oGbNmujKq2idmhZh2e/ZZ7kKBhE5vcAxr2pyW+34evWRl5mp+rikPYc6JQMAXnjhBVy7dg3Tp09HUlISGjdujC1btiA4OBgAcOHCBbi4WP6ekJCQgL/++gtbt24tUM/V1RVHjhzBypUrkZaWhrCwMHTp0gVz5syRPOWCnIMWYbnWrr/gVsTKLEREzkSr22onNG2Gmjt3wP3/cwU5B4cLzAAwevRojC5k0fMdO3YU2FanTh0Udu2jt7c3fv2Vi5jT/2gRlpU6d46IyN5pEZoT23dA5KaN8KpdW9VxSTsOd0oGkVKEEJqEZZ6vTERUNEO8ERVHvaTqmGef6oHMAwdUHZO0w8BMZAUhBOINdVUd0z08nOcrExFZKei111ArbreqY57v9yIy/vhD1TFJGwzMRMXQIixXW7MaNWMLnlNPRESFc/P3R5TxhKpjXhwxEulbtqg6JqmPgZmoCCIvT/WwXOfQQeibNVN1TCIiR6HT6VT/69zlsa8j7fsfVB2T1MXATFQIIQTi69ZTdcwo4wm4eHurOiYRkSNSOzRfnTIFN9etV3VMUg8DM5EELU7D4MV9RETyMsQb4abiTcaSZs5E2nffqTYeqYeBmeghWoVlIiKSX63ft6PyooWqjXd16jSk/8prUBwNAzPRQxiWiYgci2+3bqi5c6dq411+7TVk/v23auOR8hiYiR6g5jrLAUOHMCwTEanEPTgIUUf+UW288/0HIOv0adXGI2UxMBP9PzXDctXlyxA8YYJq4xEREaDz8FB12bkz3Z+AKTlFtfFIOQzMRFA3LNfc8Tt82rRRbTwiIvoftZedS2zfHrnp6aqNR8pgYCanp2ZYrvPPYbiHhKg2HhERSVMzNJ9s2QoiO1u18Uh+DMzk1NQMy1HHjsLF01O18YiIqGhqhub4ho0ghFBtPJIXAzM5LVXD8onj0Lm5qTYeERFZR9XQrPIqTCQfBmZySokNGqo2VpTxBHQu/FYjIrJVaoZmNQ/WkHz4U5ycToiKty6NMp7g3fuIiOwAQzMVhYGZnEpm3B74Hjqkyli81TURkX1RdfUMFf/SSWXHwExOI/f2bVwZMUKVsXhDEiIi+6Tm+3ftSZNVG4vKhoGZnIIQAidbtFRlLIZlIiL7pub7+I2Pl6g2FpUeAzM5BbWuTFbzDlJERKQctULzzc8+Q9bZs6qMRaXHwEwOT62LK3iBHxGRY1ErNJ95vBtEbq4qY1HpMDCTQ2NYJiKislArNMfXq6/KOFQ6DMzksOIbNVZlHIZlIiLHplZo5nJztouBmRzSnbg4iKwsxceJOnaUYZmIyAkwNDs3BmZyOMJkwoXBQxQfp87BA7zdNRGRE1HtnOann1FlHLIeAzM5nHgVFoOvuX0bXPR6xcchIiLbokZozoqPxz0jlyi1JQzM5FDU+FNW1eXL4B4Wpvg4RERkm9QIzWefeRZCCMXHIeswMJPDUCMsBwwZAp82bRQfh4iIbFvUsaOKj6HWPQSoeAzM5BBSV32tyjjBEyeoMg4REdk2nZsbasXtVnwcXgRoGxiYye7l3buH5HnzFB+Ht7wmIqIHufn7o+qK5YqPc/qJJxQfg4rGwEx2L6FxE8XHYFgmIiIpPq1bw6ddO0XHyE48jeyLFxUdg4rGwEx2TY0/VTEsExFRUap++YXiY5zu3IUXAWqIgZns1sl2jyg+RpTxhOJjEBGR/VPj4AovAtQOAzPZpZwbN5B7/bqiY9Q5sJ938SMiIqupEZp5EaA2GJjJLp1qq+z5YlVXrYSLj4+iYxARkeNR4y+Td48fV3wMssTATHZH6d+uPWvVgk/LloqOQUREjkmn06HOoYOKjnGu53OK1qeCGJjJriQ0b6H4GNV/3KT4GERE5LhcvL0R9v77io7BUzPUxcBMdiM3PR15GRmKjsEVMYiISA5+T3RXfAyGZvUwMJPdONmylaL1uSIGERHJSY2DMKakJMXHIAZmshNK/xZd688/uCIGERHJTunQnNjhMUXr030MzGTzbm3cqGj9Ci+8ALfAQEXHICIi5xV19Iii9XlqhvIYmMmmCSFwZdJkRccInTVT0fpEROTcdO7uqPLxYkXHuPntt4rWd3YMzGTTlL6rES/yIyIiNZSPjla0ftK06YrWd3YMzGSzTj/eTdH6USe48DsREalH6YM0PDVDOQzMZJOEyYTss2cVqx+27EvoXPjyJyIidSkdmi8MH6FofWfFxEA2Kb5BQ0Xr63knPyIi0oiSN8i68+efELm5itV3VgzMZHOU/pPSyQXzFa1PRERUFM9atRStH1+vvqL1nREDM9kUkZOjaP0aR/5RtD4REZE1aiq81Nzp7k8oWt/ZMDCTTYmv30Cx2uFffM6bkxARkc04Of8dxWpnnz4NIYRi9Z0NAzPZjPgmTRWtX+6RRxStT0REVCI6HcKWL1OsvNJLszoTBmayCSI3F+LuXcXqc71lIiKyRfoWLRStf3XGTEXrOwsGZrIJSl6gUOfAfsVqExERlZWSB3XS1q/nqRkyYGAmzSW/+55itd2Cg+Hi46NYfSIiIjnU3q/cwR2emlF2DMykudTlyxWrXWvnDsVqExERycW1nLIHdzJ27lS0vqNjYCZNKbnmcpTxhGK1iYiI5KbkqRkXR76kWG1nwMBMmsk+d06x2oFjX+MSckREZHeiThxXrLbSNwZzZAzMpJnTMY8rVrvSS/xNmoiI7I/OxQXlOnZUrL4wmRSr7cgYmEkTPBWDiIhIWvgnSxSrHd+goWK1HRkDM6lO5OUpVjtowgSeikFERHZPyVMzbnz5pWK1HZVDBuYlS5YgIiICXl5eaNWqFfbt21fovl999RV0Op3FPy8vL4t9hBCYPn06QkND4e3tjejoaJw6dUrpp+Gw4uvWU6x2xaFDFKtNRESkFp2LC7ybKnMH3JT3FypS15E5XGBev349xo0bhxkzZuDgwYNo1KgRunbtipSUlEI/x9fXF1evXjX/O3/+vMXj7777Lj766CMsXboUe/fuhY+PD7p27Yp79+4p/XQcTtbp04rV5qkYRETkSCLWrlGsNi8ALBmHC8yLFi3C8OHDMXjwYNStWxdLly6FXq/H8iLW+tXpdAgJCTH/Cw4ONj8mhMAHH3yAqVOnokePHmjYsCFWrVqFK1eu4IcfflDhGTmWM92fUKSu39NP81QMIiJyOFFHjyhWmxcAWs9N6wbklJ2djQMHDmDKlCnmbS4uLoiOjkZcXFyhn5eRkYFq1aohLy8PTZs2xbx581Cv3v3TBs6ePYukpCRER0eb9/fz80OrVq0QFxeH3r17S9bMyspCVlaW+eP09HQAgMlkgkmFF2j+GGqMZa2LvfsoVjtwzmyrnqstzost4LxI47xI47xI47xI47xIs4V5iW/QEDUVDOSlofa8WDuOTjjQDcavXLmCypUrY/fu3WjdurV5+8SJE7Fz507s3bu3wOfExcXh1KlTaNiwIW7duoX3338ff/zxB44fP44qVapg9+7daNu2La5cuYLQ0FDz5z3//PPQ6XRYv369ZC8zZ87ErFmzCmxfu3Yt9Hq9DM/W/tSeNFmRuifnvQ24uipSm4iIyBYo9TP0/OhXkBUerkhte5CZmYm+ffvi1q1b8PX1LXQ/hzrCXBqtW7e2CNdt2rSBwWDAZ599hjlz5pS67pQpUzBu3Djzx+np6QgPD0eXLl2K/ILIxWQyITY2Fp07d4a7u7vi4xUnUcFlbLo9+aTV+9ravNgKzos0zos0zos0zos0zou0ks5LTrNmOBfdWfY+qn28xKaOMqv9esk/A6A4DhWYK1WqBFdXVyQnJ1tsT05ORkhIiFU13N3d0aRJEyQmJgKA+fOSk5MtjjAnJyejcePGhdbx9PSEp6enZH013zDUHk+KyM5WrHZpbyNqC/Niizgv0jgv0jgv0jgv0jgv0qydF/cqVRTr4erIl1B1+TLF6peGWq8Xa8dwqIv+PDw80KxZM2zbts28LS8vD9u2bbM4ilyU3NxcHD161ByOIyMjERISYlEzPT0de/futbqms4tv2EiRupHfb1CkLhERkS0q7UGi4tzZvVuRuo7EoQIzAIwbNw5ffPEFVq5cCaPRiFGjRuHOnTsYPHgwAGDAgAEWFwXOnj0bW7duxZkzZ3Dw4EG8+OKLOH/+PIYNGwbg/goaY8eOxdy5c7Fp0yYcPXoUAwYMQFhYGJ5++mktnqJdyb50SbHaXgYuiUNERM6lQh/pxQbKisvMFc2hTskAgBdeeAHXrl3D9OnTkZSUhMaNG2PLli3mpeIuXLgAF5f//Z5w8+ZNDB8+HElJSfD390ezZs2we/du1K1b17zPxIkTcefOHYwYMQJpaWlo164dtmzZUuAGJ1TQaQXOtwK45jIRETmn0BkzkPbNOkVqCyG4RGshHC4wA8Do0aMxevRoycd27Nhh8fG///1v/Pvf/y6ynk6nw+zZszF79my5WnQK6Vu2KFab39BEROSsau/fj5PNm8teN95QV7HTPuydw52SQbbj8tjXFanLb2YiInJmruV8FKvNm5lIY2AmRVwe/4YidSPWK/NnKCIiInui1MGjeAWXgbVnDMykiPSff1akrncjZVbcICIisjeuAQGK1M3NyFCkrj1jYCbZxTduokjdKBtaWJ2IiEhrtXfvUqTuyeYtFKlrzxiYSXbi3j1F6uq44D0REZEFpW44Yrp8WZG69oqBmWSl1DqOvNCPiIioIJ82bRSpm9gpWpG69oqBmYiIiMiO1TmwX5G6WadOKVLXHjEwk2x4dJmIiEh9Lj7KLDN35smnFKlrjxiYyaYFjh2rdQtEREQ2T6k74GZfuKBIXXvDwEyyUOrocqWXRipSl4iIyJEodQfc0126KlLX3jAwk82q9vUqrVsgIiKyG0odZc5JTVWkrj1hYKYyO9WxoyJ19S24DiQREZG1lDrKfKpNW0Xq2hMGZiqznCtXZa9Zc8fvstckIiJydEpdKJ+bcUeRuvaCgZnKJPnd9xSp6x4SokhdIiIiKrmTzZtr3YKmGJipTFKXL5e9Zu2/98lek4iIyFkodZRZ5OQoUtceMDBTqd3Zs1eRuq7lyytSl4iIiEovvn4DrVvQDAMzldqFQYNkr1l7T5zsNYmIiJwNb/olLwZmKhWllphxrVBBkbpERERUdkrdd8HWMTBTqSixxEzNP3bKXpOIiMhZ8SizfBiYqcREbq4idd2DghSpS0RERPJJmjNX6xZUx8BMJRZfr77sNWv8ukX2mkRERM5OiaPMN9eskb2mrWNgJpvgUa2a1i0QERGRlbJOn9a6BVUxMFOJXHr1VdlrVv7wQ9lrEhER0X1RxhOy1zzT/QnZa9oyBmYqkduxv8le07drF9lrEhER0X06nU6RuiIvT5G6toiBmaxmunxZ9preTZrIXpOIiIgsRR09InvN+Lr1ZK9pqxiYyWqJnaJlrxnxzVrZaxIREZElnbu71i3YNQZmsooQQusWiIiIqAxqbpP/tMrUVatkr2mLGJjJKvGGurLX5ILqRERE6nGvXFn2msnz3pG9pi1iYCYiIiJyEoHjxsleMy8rS/aatoaBmYp174T8y9HUOfKP7DWJiIioaJVGDJe9ZkKjxrLXtDUMzFSss8/2lL2mi4eH7DWJiIiIlMDATEVS4mK/kBnTZa9JRERE1lHiRiapqx37dtkMzFQkJf7M4t+nj+w1iYiIyDpK3Mgkee5c2WvaEgZmKpLIzta6BSIiIpJZjditstd05CVoGZipULm3b8teU4k/AxEREVHJeISHy15TiSVobQUDMxXqZIuWstdU6n72REREVEK8+5/VGJhJNRHrvtG6BSIiIvp/hqNHZK+Zm5Yme01bwMBMkjL375e9pnfjxrLXJCIiIttx8l+ttW5BEQzMJOn8i/21boGIiIgUVnP7Nq1bsAsMzKSKqBPHtW6BiIiIHuIeFiZ7TSX+Sq01BmYqIHXVKtlr6lz4UiMiInIGjvhXaqYYKiB53juy1vN98klZ6xEREZF8+Ffg4jEwk+Iqv/eu1i0QERFRIZT4K/Dt336TvaaWGJjJwtVp07RugYiIiFRWoU9vWetdGv2qrPW0xsBMFtK+/U7WetV/+lHWekRERCS/0BkztG7BpjEwk6I8a9bUugUiIiLSQPqWX7VuQTYMzGR2felnWrdAREREGgn/4gtZ610eO1bWelpiYCazax98IGu9Wrt3yVqPiIiIlFPukXZat2CzGJhJMW4BAVq3QERERBq6e/SY1i3IgoGZAAB39u7TugUiIiLSWOSG/8pa71yvXrLW0woDMwEALgwcKGu9Ogcc77aYREREjs6rbl2tW7BJDMykCBcfH61bICIiIhuQd/eu1i2UGQMzISc1VesWiIiIyEZE/vC9rPUSmjSVtZ4WGJgJp9q0lbVerV1/yVqPiIiI1OMVFaV1CzaHgZlk51axotYtEBERkQ0RQmjdQpkwMDs5e38BExERkfyCJrwha73LY16TtZ7aGJidXMr8BbLWC//ic1nrERERkfoqDh0qa73bsbGy1lMbA7OTS125UtZ65R55RNZ6RERERFpjYCYiIiIixeXduaN1C6XmkIF5yZIliIiIgJeXF1q1aoV9+wq/i90XX3yBRx55BP7+/vD390d0dHSB/QcNGgSdTmfxLyYmRumnobi8zExZ67lXqyprPSIiItJOlPGErPUSmjWXtZ6aHC4wr1+/HuPGjcOMGTNw8OBBNGrUCF27dkVKSork/jt27ECfPn3w+++/Iy4uDuHh4ejSpQsuX75ssV9MTAyuXr1q/vfNN9+o8XQUldC0maz1amzZIms9IiIi0o5Op9O6BZvhcIF50aJFGD58OAYPHoy6deti6dKl0Ov1WL58ueT+a9aswcsvv4zGjRsjKioKX375JfLy8rBt2zaL/Tw9PRESEmL+5+/vr8bTsSv8xiIiIiJH5KZ1A3LKzs7GgQMHMGXKFPM2FxcXREdHIy4uzqoamZmZMJlMCAgIsNi+Y8cOBAUFwd/fHx07dsTcuXNRsYj1hrOyspCVlWX+OD09HQBgMplgMplK8rRKJX8MNcZ6eExbpsW82APOizTOizTOizTOizTOizR7mZcq69fh0gu9ZauXcfQoPIu4MYra82LtODrhQAvxXrlyBZUrV8bu3bvRunVr8/aJEydi586d2Lt3b7E1Xn75Zfz66684fvw4vLy8AADr1q2DXq9HZGQkTp8+jTfffBPlypVDXFwcXF1dJevMnDkTs2bNKrB97dq10Ov1pXyG8nFNT0eNt+fJVu/8mFeRVbmybPWIiIjINtSeNFnWeicXzJe1XllkZmaib9++uHXrFnx9fQvdj4H5AfPnz8e7776LHTt2oGHDhoXud+bMGdSoUQO//fYbOnXqJLmP1BHm8PBwXL9+vcgviFxMJhNiY2PRuXNnuLu7F3g8sUHhz680ah49Ims9pRQ3L86K8yKN8yKN8yKN8yKN8yLNnuZFzcyg9rykp6ejUqVKxQZmhzolo1KlSnB1dUVycrLF9uTkZISEhBT5ue+//z7mz5+P3377rciwDADVq1dHpUqVkJiYWGhg9vT0hKenZ4Ht7u7uqn5jqDWerX+zP0ztr4O94LxI47xI47xI47xI47xIc8Z5seb52lp+caiL/jw8PNCsWTOLC/byL+B78Ijzw959913MmTMHW7ZsQfPmxS95cunSJdy4cQOhoaGy9E1ERERkq+ocPiRrvazERFnrqcGhAjMAjBs3Dl988QVWrlwJo9GIUaNG4c6dOxg8eDAAYMCAARYXBS5YsADTpk3D8uXLERERgaSkJCQlJSEjIwMAkJGRgQkTJmDPnj04d+4ctm3bhh49eqBmzZro2rWrJs+xrHJv35a1Xp2DB2StR0RERLbD5f+v6ZLLmSeelLWeGhzqlAwAeOGFF3Dt2jVMnz4dSUlJaNy4MbZs2YLg4GAAwIULF+Di8r/fEz799FNkZ2fjueees6gzY8YMzJw5E66urjhy5AhWrlyJtLQ0hIWFoUuXLpgzZ47kKRf24GSLlrLWc7GBixiJiIiIlOJwgRkARo8ejdGjR0s+tmPHDouPz507V2Qtb29v/PrrrzJ1RkRERET2xuFOySAiIiIieUUdOyprvbw7d2StpzQGZicjcnNlrVd77x5Z6xEREZHt0bnJe1JCQrPiF1mwJQzMTiZ5/gJZ67n6+claj4iIiMjWMDA7mZtff611C0RERER2hYGZiIiIiIpVK2631i1ohoGZSi1y00atWyAiIiKVuPn7y1ov85C8N0RREgOzE8m7d0/Wel61a8taj4iIiJzH+T59tW7BagzMTiShcROtWyAiIiKyOwzMRERERGQV/772c1RYTgzMRERERGSV4GlTtW5BEwzMVCq19+3VugUiIiJSmU6nk7Ve5oEDstZTCgOzkxA5ObLWc/X1lbUeEREROZ/z/V7UugWrMDA7ieR587RugYiIiMguMTA7iZtrv9G6BSIiInIAQRMmaN2C6hiYiYiIiMhqAUMGa92C6hiYqcRq/fmH1i0QERGRRuS+8E8IIWs9JTAwU4m5BQZq3QIRERE5iOuffKJ1C8ViYHYCuenpWrdAREREJOn64o+1bqFYDMxO4Hz/AVq3QERERGS3GJidQFZCgtYtEBERkQOpvnmz1i2oioGZSsSnbVutWyAiIiKNeVaP1LoFVZUoMNvDVYykrCpLbP88IyIiIiI5WR2YV61ahYCAAIwaNQr79+9XsieyYS5eXlq3QERERA4m68xZrVsoktWB+bnnnsOSJUuQm5uLfv36oVGjRvjoo4+QmpqqZH9ERERE5ODOdOumdQtFsjow6/V69O3bF59//jkSEhKwZcsWBAYGYtGiRUr2R2WUff681i0QERER2TW30n5iaGgo+vTpI2cvpIALTzypdQtERETkgALHjcM1JzlwWqZVMtq3b489e/bI1QsRERER2YmKgwdp3YJqyhSYb9++jbZt2+KZZ56B0WiUqyeyUcFvvaV1C0RERGQjdO7uWregmjIF5oMHD2L16tU4duwYGjZsiCFDhuDixYty9UY2xr9Pb61bICIiIlJdmW9c0qdPHxiNRnzwwQf45ZdfULt2bYwfPx43btyQoz+yITq3Up/yTkRERFQkkZendQuFkuVOf25ubnjllVdw+vRpvPnmm1i2bBlq1KiBuXPnIjMzU44hiIiIiMiB3dq4SesWCiXrrbH1ej2mTZuGo0ePokGDBpgxYwaqV6+OJUuWICcnR86hiIiIiMiBXJ0yResWClXmwHzr1i3s2LEDixYtQv/+/VG/fn1Ur14du3btghACer0eY8eORd26dfHbb7/J0TNZyeXuPa1bICIiIrJ7ZQrMkZGRCAgIQKdOnfDGG29gx44dqF27NmbPno1ff/0VN27cwJkzZ5CQkIAmTZogJiYGy5cvl6t3KkbQ999r3QIRERE5sMoffKB1C6oo01VcBoMBAwcORPPmzdGiRQsEBwdL7le9enWsX78eI0eOxKxZszBkyJCyDEtW8v3nH61bICIiIgdWvlNHrVtQRZkC8+bNm0u0f4cOHfDFF1+UZUjSiM+jj2jdAhEREdkYZ1mLWdaL/orTrVs3fPfdd2oOSTIJnT1b6xaIiIiINKFqYPbz88Ozzz6r5pAkE/eQEK1bICIiItKEqoGZiIiIiMjeMDATERERkU0QQmjdgiQGZiIiIiKyCaaz57RuQVKZAvPevXvl6oOIiIiInNyNjxdr3YKkMgXm1q1bo3bt2pgzZw7OnDkjV09ERERE5ITuxNrmXaHLFJhXr16NWrVqYc6cOahVqxbatm2LpUuXIjU1Va7+qJREdrbWLRAREZET0LdqpXULiitTYO7bty9+/vlnXLlyBR9++CGEEHj55ZcRFhaGp59+Gt999x2yGdw0ce/ECa1bICIiIicQMHiQ1i0oTpaL/ipVqoTRo0dj9+7dOHXqFN566y3Ex8fjhRdeQEhICEaMGIG//vpLjqHISrb6Jw0iIiJyLPpmzbRuQXGyr5Lh7e0NvV4PLy8vCCGg0+mwceNGtG/fHi1atMAJHvlURdqqVVq3QERERE7AtXx5rVtQnCyB+fbt21ixYgWio6NRrVo1vPnmm4iIiMB3332HpKQkXLlyBevXr0dKSgoGDx4sx5CkIvewMK1bICIiItKMW1k+eePGjVizZg1++ukn3Lt3Dy1atMAHH3yA3r17o2LFihb7Pvfcc7h58yZeeeWVMjVM6gsYNEjrFoiIiIg0U6bA/MwzzyA8PByvv/46BgwYgDp16hS5f6NGjdCvX7+yDEkacIarX4mIiIgKU6bAvHz5cjz//PPQ6/WSj9+9exfXrl1D1apVAQAtW7ZEy5YtyzIkacCjarjWLRARERFppkznMA8dOhQbN24s9PFNmzYhMjKyLEOQDdB5eWndAhEREZFmyhSYhRAQQhT6uMlkgouL7AtxkMp0Op3WLRARERFppsSnZKSnpyMtLc388Y0bN3DhwoUC+6WlpWHdunUIDQ0tU4NERERERFoqcWD+97//jdmzZwO4f+Rx7NixGDt2rOS+QgjMnTu3TA0SEREREWmpxIG5S5cuKFeuHIQQmDhxIvr06YOmTZta7KPT6eDj44NmzZqhefPmsjVLRERERKS2Egfm1q1bo3Xr1gCAO3fuoGfPnqhfv77sjRERERER2YIyLSs3Y8YMufogIiIiIrJJJQrM+Rf35a+rLHWxn5T8/YmIiIiI7E2J1nyLiIhAZGQksrOzLT4u7p/alixZgoiICHh5eaFVq1bYt29fkft/++23iIqKgpeXFxo0aIDNmzdbPC6EwPTp0xEaGgpvb29ER0fj1KlTSj4FIiIiIrIRJTrCvHz5cuh0Ori7u1t8bEvWr1+PcePGYenSpWjVqhU++OADdO3aFQkJCQgKCiqw/+7du9GnTx+88847eOKJJ7B27Vo8/fTTOHjwoPnc7HfffRcfffQRVq5cicjISEybNg1du3bFiRMn4MWbehARERE5tBIF5kGDBhX5sS1YtGgRhg8fjsGDBwMAli5dip9//hnLly/H5MmTC+z/4YcfIiYmBhMmTAAAzJkzB7Gxsfj444+xdOlSCCHwwQcfYOrUqejRowcAYNWqVQgODsYPP/yA3r17q/fkiIiIiEh1ZbroLycnB5mZmfD19ZV8PD09HXq9Hm5uZRrGatnZ2Thw4ACmTJli3ubi4oLo6GjExcVJfk5cXBzGjRtnsa1r16744YcfAABnz55FUlISoqOjzY/7+fmhVatWiIuLKzQwZ2VlISsry/xxeno6gPt3PzSZTKV6flqxt36Lkv9cHOk5yYHzIo3zIo3zIo3zIo3zIo3zUjS15sXaccqUZMeMGYM//vgDx44dk3y8bdu26NixIz788MOyDGO169evIzc3F8HBwRbbg4ODER8fL/k5SUlJkvsnJSWZH8/fVtg+Ut555x3MmjWrwPatW7dCr9cX/2TKqLaMtR4+p9sRxMbGat2CTeK8SOO8SOO8SOO8SOO8SHOUeZEzd0AI1eYlMzPTqv3KFJi3bNmCAQMGFPr4c889h9WrV6sWmG3JlClTLI5cp6enIzw8HF26dCn0iLycEicVPP2ktLp16yZbLa2ZTCbExsaic+fO5nPxifNSGM6LNM6LNM6LNM6LNEebFzlzB3Q61eYl/wyA4pQpMF+5cgWVK1cu9PGwsDBcvny5LEOUSKVKleDq6ork5GSL7cnJyQgJCZH8nJCQkCL3z/9vcnIyQkNDLfZp3Lhxob14enrC09OzwHZ3d3e7+8awt36tYY9fBzVwXqRxXqRxXqRxXqRxXqRxXqSpNS/WjlGiZeUeVrFiRSQkJBT6uNFoVOVoaj4PDw80a9YM27ZtM2/Ly8vDtm3bzHcnfFjr1q0t9gfu/3kkf//IyEiEhIRY7JOeno69e/cWWpOIiIiIHEeZAnNMTAw+++wzHDp0qMBjBw8exOeff47HH3+8LEOU2Lhx4/DFF19g5cqVMBqNGDVqFO7cuWNeNWPAgAEWFwW+9tpr2LJlCxYuXIj4+HjMnDkT+/fvx+jRowEAOp0OY8eOxdy5c7Fp0yYcPXoUAwYMQFhYGJ5++mlVnxsRERERqa9Mp2TMmTMHW7ZsQcuWLfHUU0+hXr16AIBjx47hxx9/RFBQEObMmSNLo9Z64YUXcO3aNUyfPh1JSUlo3LgxtmzZYr5o78KFC3Bx+d/vCW3atMHatWsxdepUvPnmm6hVqxZ++OEH8xrMADBx4kTcuXMHI0aMQFpaGtq1a4ctW7ZwDWYiIiIiJ1CmwBwWFob9+/dj8uTJ2LhxI77//nsAgK+vL/r164d58+YhLCxMlkZLYvTo0eYjxA/bsWNHgW29evVCr169Cq2n0+kwe/ZszJ49W64WiYiIiMhOlHmB5NDQUKxcuRJCCFy7dg0AEBgYaHN3ACQiIiIiKg3Z7ihy584d3LhxAwCg1+tRrlw5uUoTEREREWmmTBf9AcDff/+Nxx57DP7+/qhfvz7q168Pf39/dOzYEfv375ejRyIiIiIizZTpCPPevXvRoUMHeHh4YNiwYTAYDADuLyf3zTff4NFHH8WOHTvQsmVLWZolIiIiIlJbmQLzW2+9hcqVK+Ovv/4qcGOQmTNnom3btnjrrbcc5raPzkoIwXPSiYiIyGmV6ZSMvXv3YuTIkZJ30QsODsaIESOwZ8+esgxBNiA3NVXrFoiIiIg0U6bA7OLigpycnEIfz83NtVjzmOzTXYkb0xARERE5izKl2TZt2mDJkiU4f/58gccuXLiATz75BG3bti3LEGQD0r77r9YtEBEREWmmTOcwz5s3D48++iiioqLwzDPPoHbt2gCAhIQEbNy4EW5ubnjnnXdkaZS0kyFxsxciIiIiZ1GmwNykSRPs3bsXb731FjZt2oTMzEwA99dhjomJwdy5c1G3bl1ZGqWS8f7Xv3CX548TERGRwoQQWreguDLfuKRu3br4/vvvkZeXZ3GnP567rK0KffswMBMREZHiclKuad2C4mS705+LiwuCg4PlKkdl5NW0mdYtEBERkRNI//lnrVtQXIkC84ULF0o1SNWqVUv1eVR6Lr7ltW6BiIiInEDKu+9q3YLiShSYIyIiSnUDi9zc3BJ/DpUNbzRCREREJI8SBebly5cziBERERGRIgLfehMntW5CQokC86BBgxRqg4iIiIicnU/nzsDevVq3UYAsF/1lZWXh4MGDSElJQdu2bVGpUiU5yhIRERGRE3ENCNC6BUllXvvto48+QmhoKNq1a4dnn30WR44cAQBcv34dlSpVwvLly8vcJBERERE5Pls99bdMgXnFihUYO3YsYmJisGzZMouFqytVqoSOHTti3bp1ZW6StJeXlaV1C0RERESaKFNgXrhwIXr06IG1a9fiySefLPB4s2bNcPz48bIMQTbi1qZNWrdAREREpIkyBebExEQ8/vjjhT4eEBCAGzdulGUIshFJ06Zr3QIRERGRJsoUmCtUqIDr168X+viJEycQEhJSliGoDO6FhWrdAhERETkwU1KS1i2ookyBuVu3bvj888+RlpZW4LHjx4/jiy++wFNPPVWWIagMkl7orXULRERE5MBSFi7SugVVlCkwz507F7m5uahfvz6mTp0KnU6HlStX4sUXX0Tz5s0RFBSE6dP5p3ytZAcFat0CERERObD0H3/UugVVlCkwh4WF4cCBA4iJicH69eshhMDXX3+NH3/8EX369MGePXu4JrOWXMq8aiARERGRKsp16KB1C4Uq8Y1Lbt68CX9/f/PHQUFB+PLLL/Hll1/i2rVryMvLQ2BgIFwY1oiIiIjISiGzZmrdQqFKnGpDQkLwzDPP4LvvvkPWQ2vzBgYGIjg4mGHZQT24zjYRERGRnNyCgrRuoVAlTrbPPfccfvvtN7zwwgsIDg7GkCFDsG3bNoYpJ5B18pTWLRAREZGDstW7/AGlCMxr1qxBSkoKVq9ejUceeQRr1qxBly5dULlyZYwfPx4HDhxQok+yAWd79NC6BSIiIiLVlercCW9vb/Tp0wc//vgjkpKS8Mknn6BWrVr44IMP0LJlS0RFRWHu3Lk4c+aM3P0SERERkQ3IPn9e6xZUU+aTjf39/TFy5Ejs3LkTFy5cwPz586HX6zF9+nTUqlULbdq0kaNPKqWwzz7TugUiIiJyQKe7xmjdgmpkvTqvcuXKmDBhAlauXIkePXpACIG9e/fKOQSVkPe/WmndAhEREZFdK/GycoW5cOEC1q5di2+++QbHjh2DEAJt2rRBv3795BqCSkHHFUuIiIjIxlV8aaTWLRSpTIH5+vXr+M9//oO1a9ciLi4OQghERUVh9uzZ6NevHyIiImRqk2yFEMKmr2IlIiIi+1Pp5Ze1bqFIJQ7Md+7cwffff4+1a9di27ZtMJlMCA0NxdixY9GvXz80bdpUiT7JRmRs347ynTpp3QYRERE5EBcPD61bKFKJA3NQUBDu3buHcuXKoW/fvujXrx86duzIm5U4iUuvjIYh3qh1G0RERKQhkZOjdQuqKnFgjo6ORr9+/fDUU0/By8tLiZ6IiIiIyIYlzZmrdQuqKnFg3rhxoxJ9kIJqbPkFp2Me17oNIiIichBp69dr3YKqeB6FE/DgxZdEREREpcbATCXmbOctERERkXKq/7JZ6xaKxcBMJXblzTe1boGIiIgchGdkpNYtFIuBmUosfdOPWrdAREREGjElp2jdguoYmImIiIjIaont22vdguoYmJ1Erb/+1LoFIiIiIrvEwOwk3CpVkrWeyM2VtR4RERE5H98nn9S6BaswMFOpJM9foHULREREZOdC37aPG6AwMFOp3Pz6a61bICIiIpVlnT0raz0XDw9Z6ymFgZmIiIiIrHLm8W5at6AJBmYnUvP37Vq3QERERGR3GJidiHtoqKz18jIzZa1HREREzsO7WTOtW7AaAzOVWkJT+3mhExERUdkIIWStV23VSlnrKYmBmYiIiIiKdXXqVFnr6VxdZa2nJAZmIiIiIirWrf9u0LoFzTAwO5na+/fLWo83MCEiIiJHx8DsZFzL+cha78KgwbLWIyIiItsj9/nLlRd/JGs9pTEwU5lk/v231i0QERGRwm7997+y1vPt3FnWekpjYCYiIiKiIl2dOk3rFjTFwOyEIjdtlLWeyMuTtR4RERGRLWFgdkJetWvLWu/C0KGy1iMiIiLbIff5y77d7O/22g4VmFNTU9GvXz/4+vqiQoUKGDp0KDIyMorc/9VXX0WdOnXg7e2NqlWrYsyYMbh165bFfjqdrsC/devWKf107EZm3B6tWyAiIiKFXPvwQ1nrhS18X9Z6anDTugE59evXD1evXkVsbCxMJhMGDx6MESNGYO3atZL7X7lyBVeuXMH777+PunXr4vz583jppZdw5coVfPfddxb7rlixAjExMeaPK1SooORTISIiIrIJN5Z+Jms9nU4naz01OExgNhqN2LJlC/7++280b94cALB48WJ069YN77//PsLCwgp8Tv369fHfB676rFGjBt5++228+OKLyMnJgZvb/6anQoUKCAkJUf6JqKTKJ0tw6eVXZKuXm3FH9iXriIiIiGyBwwTmuLg4VKhQwRyWASA6OhouLi7Yu3cvnnnmGavq3Lp1C76+vhZhGQBeeeUVDBs2DNWrV8dLL72EwYMHF/kbUlZWFrKysswfp6enAwBMJhNMJlNJnlqp5I9R2Fhejzwi63gnmzdHzaNHZK2phOLmxVlxXqRxXqRxXqRxXqRxXqTZy7yI7GxZ6+nbtinyOas9L9aO4zCBOSkpCUFBQRbb3NzcEBAQgKSkJKtqXL9+HXPmzMGIESMsts+ePRsdO3aEXq/H1q1b8fLLLyMjIwNjxowptNY777yDWbNmFdi+detW6PV6q/qRQ2xsbKGPyXvpH7B582aZKyqnqHlxZpwXaZwXaZwXaZwXaZwXabY+L7UnTZa13uEnnsBhK/KCWvOSmZlp1X46IfeljzKbPHkyFixYUOQ+RqMRGzZswMqVK5GQkGDxWFBQEGbNmoVRo0YVWSM9PR2dO3dGQEAANm3aBHd390L3nT59OlasWIGLFy8Wuo/UEebw8HBcv34dvr6+RfYiB5PJhNjYWHTu3LnQ55LYoKGsY9rLEebi5sUZcV6kcV6kcV6kcV6kcV6k2cu8qJ0V1J6X9PR0VKpUyXyGQWFs/gjz+PHjMWjQoCL3qV69OkJCQpCSkmKxPScnB6mpqcWee3z79m3ExMSgfPny+P7774v9ArVq1Qpz5sxBVlYWPD09Jffx9PSUfMzd3V3Vb4yixqv5+3YkPtZRtrHu/fEHynfqJFs9Jan9dbAXnBdpnBdpnBdpnBdpnBdpzjYv1j5XtebF2jFsPjAHBgYiMDCw2P1at26NtLQ0HDhwAM2aNQMAbN++HXl5eWjVqlWhn5eeno6uXbvC09MTmzZtgpeXV7FjHT58GP7+/oWGZXvhHhoqa71Lr4yGId4oa00iIiLSRsbOnbLWC3vvPVnrqcnmA7O1DAYDYmJiMHz4cCxduhQmkwmjR49G7969zStkXL58GZ06dcKqVavQsmVLpKeno0uXLsjMzMTq1auRnp5uvjgvMDAQrq6u+PHHH5GcnIx//etf8PLyQmxsLObNm4c33nhDy6dLREREpKiLI1+StZ7fk0/IWk9NDhOYAWDNmjUYPXo0OnXqBBcXF/Ts2RMfffSR+XGTyYSEhATzCd4HDx7E3r17AQA1a9a0qHX27FlERETA3d0dS5Ysweuvvw4hBGrWrIlFixZh+PDh6j0xO5KblgZXrlFNREREDsShAnNAQEChNykBgIiICIvbO3bo0KHY2z3GxMRY3LDE0UQdO4r4+g1kq3fyX615WgYREZGdy0lN1boFm+JQt8amktO5OdTvTERERCSDU23aylqvzqGDstZTGwMzyU7k5WndAhEREdkQF29vrVsoEwZmQuT3G2StF1+3nqz1iIiISD1y393PETAwE7wMBq1bICIiIhsR37CRrPXC3ntX1npaYGAmRfC0DCIiIgIAvyef1LqFMmNgJgBAuWh579DH0zKIiIjsj8jJ0boFm8TATACA8I8/1roFIiIi0picS80CgFcDeetphYGZFMPTMoiIiJxb5Lf/0boFWTAwk2J4WgYREZH9yLt7V+sWbBYDM5lFGU9o3QIRERFpJKFJU61bsFkMzGSm0+lkr8m1HImIiJyTIx2IY2AmRcm9liMRERHJL+faNdlrKnEgTisMzGTBkX4bJCIiIuuceuRRrVuwaQzMZEGJ3wazTp2SvSYRERHZLkc7AMfATIo78+RTWrdAREREhUjfskX2mo50OgbAwEwSDPFGrVsgIiIilVwe+7qs9Vz9/WWtZwsYmEkV5/r01boFIiIieogQQvaateN2y15TawzMJKl8166y1rt76JCs9YiIiKjs4g11tW7BLjAwk6QqH34ge02uyUxEROTYKr08SusWFMHATKrhmsxERES2w3T5suw1A8eMkb2mLWBgpkJFbviv1i0QERGRQhI7RWvdgt1gYKZCedWV/7ymK5Mmy16TiIiISkaJi/1q7twhe01bwcBMqrq1caPWLRARETk9JS72cw8Olr2mrWBgpiJFHT8me83ctDTZaxIREREphYGZiqRzdZW95sl/tZa9JhEREVkn488/Za/paLfCfhgDMxXL96kntW6BiIiIZHJx+AjZazrarbAfxsBMxar87ruy1zRGGWSvSUREREVT4p4IlRd/JHtNW8PATEREROQklLgngm/nzrLXtDUMzGSVqKNHZK95bfHHstckIiIikhsDM1lF5+4ue83rS5bIXpOIiIikKXE6pKNf7JePgZmsVumVV2SvmXXmjOw1iYiISB2OfrFfPgZmslrgq6Nlr3mmW3fZaxIREZGlS6+Okb1m9V82y17TVjEwk+aUuGKXiIiI/ud2bKzsNT0jI2WvaasYmKlElDhXSYkrdomIiOi+29u3y17TPTxc9pq2jIGZSkSpc5WEEIrUJSIicnaXXpb/GqSasVtlr2nLGJipxGrF7Za9Zryhruw1iYiInN29hJNat+AQGJipxNz8/RWpy6PMRERE8jrbo4fsNZ1lKbkHMTBTqYTMmS17TR5lJiIikk/2pcuK1HWWpeQexMBMpeLfq5fWLRAREVERTkdHy16z9r69ste0BwzMVHou8r98lLgLERERkbPJuXZNkbquvr6K1LV1DMxUaoYTx7VugYiIiCSceuRR2WtW+3qV7DXtBQMz2RweZSYiIio9U0qKInX1LVooUtceMDBTmSh1pSxXzCAiIiqdxEfby14zYOBA2WvaEwZmKhOlrpTlihlEREQldy8+XpG6wVMmK1LXXjAwU5kpdpQ5L0+RukRERI7q7NPPyF7To3p12WvaGwZmKjPFjjLXradIXSIiIkeUvmWLInVrbP5Zkbr2hIGZZBGl0IoZeVlZitQlIiJyNJfHvq51Cw6LgZlkoVNgTWYASGjUWJG6REREjuTyxImK1DXEGxWpa28YmEk2UceOKlI3+9IlReoSERE5ivRNP2rdgkNjYCbZ6NzcFKl7OrqzInWJiIgcgVL3L+DR5f9hYCZZRR0/pkjdax8tVqQuERGRPVPsvgUKXdBvrxiYSVY6V1dF6l7/5BNF6hIREdkzpe5bYFBoyVh7xcBMslNqXWbeMpuIiOh/ctPTFanr3aSJInXtGQMzyU6pdZkB3jKbiIgo38mWrRSpG/HNWkXq2jMGZlKEUhcK8JbZREREQNp//6tI3cDx4xSpa+8YmMnumJJTtG6BiIhIU1ffmqpI3UrDhytS194xMJNilDrKnNi+vSJ1iYiI7IFS1/REfPsfReo6AgZmUpR3o0aK1E3s2EmRukRERLZM5OQoVtu7QQPFats7BmZSVMT6dYrUNV25okhdIiIiWxZfX5lQW2v3LkXqOgqHCsypqano168ffH19UaFCBQwdOhQZGRlFfk6HDh2g0+ks/r300ksW+1y4cAHdu3eHXq9HUFAQJkyYgBwFf8NzNOFffqlIXS4zR0REzuTmf5Q7ZcItIECx2o5AmXsZa6Rfv364evUqYmNjYTKZMHjwYIwYMQJr1xa9PMrw4cMxe/Zs88d6vd78/7m5uejevTtCQkKwe/duXL16FQMGDIC7uzvmzZun2HNxJOXatVWs9r34eHhFRSlWn4iIyFYkTZ+hSN2oE8cVqetIHOYIs9FoxJYtW/Dll1+iVatWaNeuHRYvXox169bhSjF/vtfr9QgJCTH/8/X1NT+2detWnDhxAqtXr0bjxo3x+OOPY86cOViyZAmys7OVfloOo86B/YrUPfv0M4rUJSIisiVK/lVV5+IwcVAxDnOEOS4uDhUqVEDz5s3N26Kjo+Hi4oK9e/fimWcKD1Zr1qzB6tWrERISgieffBLTpk0zH2WOi4tDgwYNEBwcbN6/a9euGDVqFI4fP44mhdwNJysrC1lZWeaP0///bjwmkwkmk6lMz9Ua+WOoMZZVPDwUK22MMqDm0SNW7Wtz82IjOC/SOC/SOC/SOC/SOC/SSjIvubeUuaMfANQ8esSmvjZqv16sHcdhAnNSUhKCgoIstrm5uSEgIABJSUmFfl7fvn1RrVo1hIWF4ciRI5g0aRISEhKwYcMGc90HwzIA88dF1X3nnXcwa9asAtu3bt1qccqH0mJjY1Ubq1jz30HtyVMUKf3Lpk0Qbta/nG1qXmwI50Ua50Ua50Ua50Ua50WaNfNSe9JkRca+9ngMTm7erEjtslLr9ZKZmWnVfjYfmCdPnowFCxYUuY/RWPr1fkeMGGH+/wYNGiA0NBSdOnXC6dOnUaNGjVLXnTJlCsaN+9/dctLT0xEeHo4uXbpYnPKhFJPJhNjYWHTu3Bnu7u6Kj2etRIUCc623plp1lNlW50VrnBdpnBdpnBdpnBdpnBdp1s5LYoOGivXQ+t13FatdWmq/XvLPACiOzQfm8ePHY9CgQUXuU716dYSEhCAlxfIOcDk5OUhNTUVISIjV47Vqdf++7ImJiahRowZCQkKwb98+i32Sk5MBoMi6np6e8PT0LLDd3d1d1TcMtccrjiHeqNh5WKdbtETU4UNW7Wtr82IrOC/SOC/SOC/SOC/SOC/SipqXPAWvlaq1exfcbPjrodbrxdoxbD4wBwYGIjAwsNj9WrdujbS0NBw4cADNmjUDAGzfvh15eXnmEGyNw4cPAwBCQ0PNdd9++22kpKSYT/mIjY2Fr68v6tatW8JnQwAQ+f0GnH3mWdnrinv3IHJzoXN1lb02ERGR2hIaKnPzL4DLyJWUw1wWaTAYEBMTg+HDh2Pfvn3YtWsXRo8ejd69eyMsLAwAcPnyZURFRZmPGJ8+fRpz5szBgQMHcO7cOWzatAkDBgzAo48+ioYN7/8JpEuXLqhbty769++Pf/75B7/++iumTp2KV155RfIIMhXPy6Dclb7x9eorVpuIiEgtxrr1FKsdZTyhWG1H5TCBGbi/2kVUVBQ6deqEbt26oV27dvj888/Nj5tMJiQkJJhP8Pbw8MBvv/2GLl26ICoqCuPHj0fPnj3x448/mj/H1dUVP/30E1xdXdG6dWu8+OKLGDBggMW6zVRySn6zno55XLHaREREShM5OUBeniK1fbs9Dp1Op0htR2bzp2SUREBAQJE3KYmIiIAQwvxxeHg4du7cWWzdatWqYbONXkVqr5T8Zs0+dw4iL4/rShIRkV1S6vbXAFB50SLFajsyJgrSjCG+9KubFCdewT9lERERKUXJG5TU3q/MTcScAQMzaarmtt8Uq63kmw4REZHc8u7cUbS+azkfRes7MgZm0pR75cqK1s+9fVvR+kRERHJJaNa8+J1KScm/6joDBmbSnJLfxCdbtFSsNhERkVyU/Kto1RXLFavtLBiYySZU+XixYrV5agYREdmyu0eKv1NtWfi0bq1ofWfAwEw2oXx0tKL1M/7apWh9IiKi0jr3/AuK1eaay/JgYCaboeQ39cVhwyyWFCQiIrIFiQ0aKlY7aOJErrksEwZmshk6nQ6VXh6lWP14A29lTkREtqPG9BmK1q84ZLCi9Z0JAzPZlMAxYxStr+Rv8kRERNbKvXkTrllZitXnqRjyYmAmm6P0N7lHcoqi9YmIiIpz9tH2itUOemM8T8WQGQMz2RydToegCRMUqx+xaBHPZyYiIs0ovXpTxWHDFK3vjBiYySZVHDpE0fqnGzZStD4REZGUhJatFK3PUzGUwcBMNkvpuxJxfWYiIlJTzrVryEtPV6x+5UULeSqGQhiYyaZVW7Na0foZu7g+MxERqePUI48qWt+3WzdF6zszBmayafpmzRStf3HoMIicHEXHICIiUvqvmkr/VdbZMTCTzVP6TSC+fgNF6xMRkXNTOizX/GOnovWJgZnsRO19exWtz/OZiYhICckL3lV8DPegIMXHcHYMzGQXXH194V65sqJjMDQTEZGcctPSkLpihaJj8FQMdTAwk92oue03xcfI+PNPxccgIiLncPJfrRWtH3X8mKL16X8YmMmuKP2b9MXhI5CXna3oGERE5PiU/qtl5Q8+gM7VVdEx6H8YmMnu1PhN2SPNCQ0b8U6ARERUamqc4ucb01XxMeh/GJjJ7nhUUfZcZgCIN9RVfAwiInI8aoRlnresPgZmsktqvFnwIkAiIiqJG8uWKT4Gz1vWBgMz2S2GZiIishWmpCSkvPe+omOEL/uS5y1rhIGZ7FrNncov1p783nuKj0FERPZL5OYiscNjio9Trm1bxccgaQzMZNfcg4Pg88gjio6Rumw57p08qegYRERkv+Lr1Vd8DJ63rC0GZrJ7Vb/4XPExzj7VA3mZmYqPQ0RE9kWNU/eijCcUH4OKxsBMDkGN37wTmjaDyMtTfBwiIrIPaoTlWrt3QafTKT4OFY2BmRyGGr+Bx9etxzWaiYhIlbBc8aWRcAsIUHwcKh4DMzkMnU6H6pt/VnwcrtFMROTc1FpBKWjsWFXGoeIxMJND8axeHd7Nmik+DpebIyJyTmq9//MiP9vCwEwOJ2LNalXGYWgmInIul8eNV2UcXuRnexiYySGp9Zs5QzMRkXO48dVXSN+8WfFx6hw6yIv8bBADMzkshmYiIpJD+q9bkTJ/geLjVFu7Fi7e3oqPQyXHwEwOLer4MVXGYWgmInJMmfv34/Jrryk+TrkOHaBv2kTxcah0GJjJoelcXVFjyy+qjMXQTETkWO4lnMT5F/urMlb40k9VGYdKh4GZHJ5HRAQqDh+mylgMzUREjiH7wgWc7dFDlbG4IobtY2AmpxA0Xp0rmwGGZiIie5d96TJOd+mqylg1jx5RZRwqGwZmchpq/gbP0ExEZJ+yz53D6ehoVcY6Of8dVcahsmNgJqei5m/yDM1ERPblntGI0zGPqzJWjYMHAC4fZzcYmMnpnFwwX7WxGJqJiOxD5t9/4+wzz6oyVq3du6Bzd1dlLJIHAzM5JR5pJiKifOlbt+J8/wGqjBXxn/VwCwhQZSySDwMzOS01bz3K0ExEZJturPgKl8cov84yAARPmwrvhg1VGYvkxcBMTkun06HOkX9UG4+hmYjItlwa+zpSFih/Bz8AKNe+PQL69VNlLJIfAzM5NRcPD9TavUu18RiaiYhsgzHKgNtbtqg2XvhnS1Ubi+THwExOzy0gADV+Ve9Nk6GZiEhbar8P88Yk9o+BmQiAR7VqqLZ2rWrjGaMMEEKoNh4REd3HsEylwcBM9P/0TZsgbOH7qo0Xb6gLkZ2t2nhERM6OYZlKi4GZ6AF+3bsjaMIbqo0X37ARTFevqjYeEZGzYlimsmBgJnpIxaFDETBokGrjJT7WEWn//a9q4xERORORk8OwTGXGwEwkIXjyJFR4/nnVxrv61lQY6zdQbTwiImeQfeEC4lV+b2VYdkwMzESFCJ09C/59+6o3oAZHQYiIHNX1Tz/F6S5dVR2TYdlxuWndAJEtC5k+DS56b9z4cplqYxqjDHzTJSIqAy0OPvB927HxCDNRMYLeeAOBY8eqOqYxygCRl6fqmEREjoBhmZTAwExkhUovjUTIrFmqjhlftx6yzp5VdUwiInslhGBYJsUwMBNZyf+F51Flyceqjnnm8W441+9FVcckIrI3ppQUxBvqqj4uw7LzYGAmKoHynToh4tv/qDrm3QMHeDEgEVEhrs6YicRH26s+LsOyc2FgJioh7wYNUHPnTtXH5e20iYgsGaMMSFu/XvVxGZadDwMzUSm4Bwehzj+HVR833lAXpsuXVR+XiMiWaHW+sk+7dgzLTsqhAnNqair69esHX19fVKhQAUOHDkVGRkah+587dw46nU7y37fffmveT+rxdevWqfGUyIa5eHoiynhC9XETO0XjlAZ/fiQisgXZly5pcr5y8PRpqPrlF6qPS7bBodZh7tevH65evYrY2FiYTCYMHjwYI0aMwNq1ayX3Dw8Px9WrVy22ff7553jvvffw+OOPW2xfsWIFYmJizB9XqFBB9v7J/uh0Ohjijaof6chJSeF6zUTkdIyGuoAGp6ZFbtwIrzq1VR+XbIfDBGaj0YgtW7bg77//RvPmzQEAixcvRrdu3fD+++8jLCyswOe4uroiJCTEYtv333+P559/HuXKlbPYXqFChQL7EuXTIjQD98/fq71/P1zL+ag+NhGRmrS6+LnOgf1w8eF7rLNzmMAcFxeHChUqmMMyAERHR8PFxQV79+7FM888U2yNAwcO4PDhw1iyZEmBx1555RUMGzYM1atXx0svvYTBgwdDp9MVWisrKwtZWVnmj9PT0wEAJpMJJpOpJE+tVPLHUGMse6LkvNQ8egSJDRrKXrc4J5s3h3ebNqj82dJS1+DrRRrnRRrnRRrnRVpZ5yUnJQXnOkXL2ZLVavxzGLkuLshV4GvK14s0tefF2nF0wkEuu583bx5WrlyJhIQEi+1BQUGYNWsWRo0aVWyNl19+GTt27MCJE5bnpc6ZMwcdO3aEXq/H1q1bMWPGDLz77rsYM2ZMobVmzpyJWRI3uli7di30er2Vz4rsUe1JkzUb++SC+ZqNTUQkt1pvvgVdbq4mY/P91DlkZmaib9++uHXrFnx9fQvdz+YD8+TJk7FgwYIi9zEajdiwYUOZAvPdu3cRGhqKadOmYfz48UXuO336dKxYsQIXL14sdB+pI8zh4eG4fv16kV8QuZhMJsTGxqJz585wd3dXfDx7oda8XB42DHf37lOsflEid+6Aa0BAiT6HrxdpnBdpnBdpnBdppZkXIQRON2ykcGeFq3n0iOJj8PUiTe15SU9PR6VKlYoNzDZ/Ssb48eMxaNCgIvepXr06QkJCkJKSYrE9JycHqampVp17/N133yEzMxMDBgwodt9WrVphzpw5yMrKgqenp+Q+np6eko+5u7ur+o2h9nj2Qul5iVi5Enf27MWFYl67SjjbvgOA0q0TyteLNM6LNM6LNM6LNGvn5U5cHC4MHqJCR9LUvpiarxdpas2LtWPYfGAODAxEYGBgsfu1bt0aaWlpOHDgAJo1awYA2L59O/Ly8tCqVatiP3/ZsmV46qmnrBrr8OHD8Pf3LzQsEwGAz79aoc7BA0ho2kyT8Y1RBkQZTxR5rj0RkS3R8q6mfj16IIynYVAhHGYdZoPBgJiYGAwfPhz79u3Drl27MHr0aPTu3du8Qsbly5cRFRWFffss/1SemJiIP/74A8OGDStQ98cff8SXX36JY8eOITExEZ9++inmzZuHV199VZXnRfbNRa/XZK3mfPGGukhe8K5m4xMRWSM3LU3TsFz9l80My1Qkmz/CXBJr1qzB6NGj0alTJ7i4uKBnz5746KOPzI+bTCYkJCQgMzPT4vOWL1+OKlWqoEuXLgVquru7Y8mSJXj99dchhEDNmjWxaNEiDB8+XPHnQ45Bq7Wa86WuWIHUFSu4ZjMR2SQtgzIARB0/Bp2rq6Y9kO1zqMAcEBBQ6E1KACAiIgJS1zjOmzcP8+bNk/ycmJgYixuWEJWWlqEZuP9DqcqSj1G+UyfNeiAiyieysxGv4YV9gPrnK5P9cphTMojsgSHeiCofL9Zs/EuvjNb8aA4RkTHKwLBMdoWBmUhl5aOjEXXkH017MEYZcGvjRk17ICLnk3f3rua/tAeOH8ewTCXGwEykAZ2Hh+Zv2FcmTdb8BxcROY/EBg2R0KSppj3UOXwIlXgNEpUCAzORhrQOzcD9o80ps2Zr3QYROajc1FRN74CazxBvhIuXl9ZtkJ1iYCbSmCHeiKorlmvaQ/p336H2pMkQJpOmfRCRYzFGGcw3U9KSLRycIPvGwExkA3xat0bUieNat4HTTZvxNA0iKrPUr1fbxHtJ1VUrGZZJFg61rByRPdO5uGi+9Fw+Y5QBVVeuhE+rllq3QkR2xBaWisvHO52SnHiEmcjGGOKNCJk5Q+s2cGHgQBijDJJrlxMRPcwWlorLZ4g3MiyTrBiYiWyQf+/eiDp2VOs2ANy/vbYtHPUmItt085tvbOY9otratTwFgxTBwExko3Rubjb1xm+MMiB11ddat0FENiI3PR3GKAOSbGSVnSjjCeibNtG6DXJQDMxENs4Qb0TEf9Zr3QYAIHnePBijDMi5eVPrVohII0IIGKMMONmyldatmPEUDFIaL/ojsgPeDRvazAWBAHCqdRsAvKiGyNnYyntQvlpxu+Hm7691G+QEeISZyI4Y4o0o17691m2Y8fxmIudwedw4m/teN8QbGZZJNTzCTGRnwj9bCmEyIb5BQ61bMcv/QWpL51wTUdmlb96My+PGa92GhWprVkPfrJnWbZCTYWAmskM6d3ebOkUjnzHKAO+mTRGxdo3WrRBRGWSdOoUzTz6ldRsF8Jdy0gpPySCyY4Z4I+oc2K91GxbuHjwIY5QBKe+/r3UrRFRCOTduwBhlsLmwHPzmmwzLpCkGZiI75+LjY5M/SG58uQzGKAOuL/1M61aIqBg5qakwRhlwqm07rVspwBBvRMCA/lq3QU6OgZnIQdji0WYAuPbBBzBGGZD87ntat0JEDzElJd0Pym3aat1KAaHvvGOTBwPIOTEwEzkQWz3aDACpy5fDGGXAxZdf0boVIqeXdfYsjFEGJHZ4TOtWJBnijajwzNNat0Fkxov+iByQId4IkZ2N+IaNtG6lgIzt27mqBpFGMv78CxeHD9e6jUJFbvgvvOrW1boNogIYmIkclM7DA4Z4I64t/hjXlyzRuh1J+cGZN0AhUtal18bi9q+/at1GkfgLNNkyBmYiBxf46mgEvjra5page1C84f4RpTr/HIaLp6fG3RA5Dlv+vs/H73uyBzyHmchJGOKNqLl9m9ZtFCmhUWMYowy4Z+SRJqLSErm5MEYZbD4s+7/4IgzxRoZlsgs8wkzkRNzDwmCINyIxujNMly5p3U6hzj7zLID7/dp6yCeyFXd278aFIUO1bsMqPP2C7A0DM5ETqvlbLIQQ5lMhbJXpyhXzUbI6Bw/ARa/XuCMi22PrR5IfVPvvfXAtX17rNohKjKdkEDkpnU4HQ7wRtffEad2KVRKaNoMxyoBrNnoBI5Gacq5ds4vTLvJdezwGNY8eYVgmu8XATOTkXCtUQM2jR3CtezetW7HK9cUfm4NCbsYdrdshUlX+a//UI49q3YrVah49gpsdOmjdBlGZMDATEQDg5qOPoubRI1q3USInmze3u/BAVFK3f//dro4m54synuC5yuQweA4zEVkwxBvt4vzmB+X/eRoAwpd9iXJtbe82v0QlkXfvHhIaN9G6jVKpvX8/XMv5aN0GkawYmImogPzzm231boFFuTh0mPn/a277De6VK2vYDZH1RF4e4uvW07qNUotY9w28GzfWug0iRTAwE1Gh8u8WmJOailNt7O+obWKnaPP/14rbDTd/fw27ISrI3v6aIyVo0iRUHDxI6zaIFMXATETFcgsIgCHeiLvHjuPcc89p3U6pnGrdxvz/tXbvgltAgIbdkDNzhJAMAOWiOyH844+1boNIFQzMRGQ17/r1YIg34vaOHbj00iit2ym1B4+WR6xfB+9G9nXaCdmfvKwsJDRqrHUbsnANCEDt3bu0boNIVQzMRFRi5Tt0uB+ct/+OSy+/rHU7ZXLuhd7m//fv2wch06dr2A05knsnT+LsUz20bkNWXPWCnBUDMxGVWvmOjznEEed8N9d+g5trvzF/HLlzh3bNkN0RQqD2pMlInDRZ61ZkpXN3R5SdLTlJJDcGZiIqs/wjzpl//43z/Qdo3Y5szrbvgNoAEidNhnu1qqixZQt0Op3WbZENSf/lF1x+fZzWbSjCu3kzRKxerXUbRDaBgZmIZKNv0QKGeCOyz5/H6a4xWrcjK9P5CxYXavk9+yxC357LAO1k7uzbhwsDBmrdhqIqjnoJQa+9pnUbRDaFgZmIZOdRrRoM8Ubk3b2LhCZNtW5HEbc2bMCtDRvMH7v4+aH27l3Qubpq2BXJSQiBm998g+TZc7RuRRXhX3yOco88onUbRDaJgZmIFOPi7W2Xdw4sjbxbtxBfr77Ftmpfr4K+RQuNOqKSyrl502L5QWdRe08cXCtU0LoNIpvGwExEisu/cyAA8y2snYHU+dzVf/4JnjVqaNANPSgvMxMJTZtp3YamoowneEoRkZUYmIlIVfnBOeOvXbg4bFgxezueM92fKLDNp00bhC/9FDoPDw06cmwiLw+3Nm7C1SlTtG7FJriHhaHm9m1at0FkdxiYiUgT5dq1vX+6hsmE+AYNtW5HU3d270Z8Q+mbp9TY+is8qlZVuSP7k5uejsuvj8OdXbyhhpTIjT/Aq04drdsgslsMzESkKZ27u/mo87nefXD38GFtG7Ixp7t0LfQx/379EPj6WLiWK6diR9rIy8pC+k8/4epbU7Vuxa7wtAsieTAwE5HNiFh3/6YhznrxVUndXLMGN9esKXY/t5AQhM6eBZ+2bW1qFQ9hMiHr1Cnc+HIZ0jdv1rodh1Hl009Q/rHHtG6DyKEwMBORzXHz9zcfdb4yaRJubdykcUf2LScpCRdHjJS1Zv4NXch28GgykXIYmInIpoUtWICwBQsgcnMLLNtG5Oxq7twJ9+AgrdsgcngMzERkF3SuruajzlmJiTjzxJMad0SkjcDx41Bp+HCt2yByKgzMRGR3PGvWNIfnWz/+hCsTJmjcEZHCdDoYjCe07oLIaTEwE5Fd83vyCfg9eX9t46TZc3Bz7VqNOyKSD89LJrINLlo3QEQkl5Dp02CIN8IQb4R/v35at0NUKlHGE+bXMcMykW3gEWYickgh06YiZNr9NXvTY2Nx+dUxGndEJM29alXU3Pqr1m0QUREYmInI4fl27gzf/z/n2XT1KhIf66hxR+Tsqiz5GOU7ddK6DSKyEgMzETkV99BQ8wWDQgjEG+pq3BE5i9r798O1nI/WbRBRKTAwE5HT0ul05vAM8OgzySts4fvw695d6zaISAYMzERE/+/Bo88AcGPDBqS8+ZaGHZE98W7TBv889SS6de8Od3d3rdshIhkxMBMRFcL3ySfxl6srunXrBnd3d6Rv+RWXx47Vui2yEeU6dECVTz8xr2RhMpnwz+bNGndFREpgYCYispJvTFfzxYMAkHXmLM5066ZhR6Sm8M+Wolz79lq3QUQaYGAmIiolz+qRFqdwCCFwY+lSXPvwIw27Ijl41qqJyB9+gM7VVetWiMgGMDATEclEp9Oh0qhRqDRqlHmbyMtD6lcrkfLuuxp2RkXRt2iB8GVfwsXDQ+tWiMhGOdSd/t5++220adMGer0eFSpUsOpzhBCYPn06QkND4e3tjejoaJw6dcpin9TUVPTr1w++vr6oUKEChg4dioyMDAWeARE5Gp2LCyoOGWy+c1v+v1pxu7VuzSnV/H17ga9Fta9XMSwTUZEc6ghzdnY2evXqhdatW2PZsmVWfc67776Ljz76CCtXrkRkZCSmTZuGrl274sSJE/Dy8gIA9OvXD1evXkVsbCxMJhMGDx6MESNGYO3atUo+HSJyYG7+/hanc+QTOTm4uWYNkt+Zr0FXjsH3iScQOnsWXPR6rVshIgfhUIF51qxZAICvvvrKqv2FEPjggw8wdepU9OjRAwCwatUqBAcH44cffkDv3r1hNBqxZcsW/P3332jevDkAYPHixejWrRvef/99hIWFKfJciMg56dzcEDBwIAIGDizwmBACOcnJuDpjBu7s/EOD7myDTq9HtZVfwatePehcHOoPpURkoxwqMJfU2bNnkZSUhOjoaPM2Pz8/tGrVCnFxcejduzfi4uJQoUIFc1gGgOjoaLi4uGDv3r145plnJGtnZWUhKyvL/HF6ejqA+8sOmUwmhZ7R/+SPocZY9oTzIo3zIs0m56ViRYR+/HGRu4i8PORcvoJb//0v0qz8a5st8O3VC37P94JHjRrQWbGOcU5uLpCbq0Jn1rHJ14sN4LxI47xIU3terB3HqQNzUlISACA4ONhie3BwsPmxpKQkBAUFWTzu5uaGgIAA8z5S3nnnHfMR7wdt3boVehX/TBgbG6vaWPaE8yKN8yLNbueldi1ggQynduTlAUJAl5MDl///4SJc3SDcXCFcXACdDpDrSO+ZM/f/2TG7fb0ojPMijfMiTa15yczMtGo/mw/MkydPxoIFC4rcx2g0IioqSqWOrDNlyhSMGzfO/HF6ejrCw8PRpUsX+Pr6Kj6+yWRCbGwsOnfuzDtOPYDzIo3zIo3zIo3zIo3zIo3zIo3zIk3teck/A6A4Nh+Yx48fj0GDBhW5T/Xq1UtVOyQkBACQnJyM0NBQ8/bk5GQ0btzYvE9KSorF5+Xk5CA1NdX8+VI8PT3h6elZYLu7u7uq3xhqj2cvOC/SOC/SOC/SOC/SOC/SOC/SOC/S1JoXa8ew+cAcGBiIwMBARWpHRkYiJCQE27ZtMwfk9PR07N27F6P+fx3V1q1bIy0tDQcOHECzZs0AANu3b0deXh5atWqlSF9EREREZDsc6vLiCxcu4PDhw7hw4QJyc3Nx+PBhHD582GLN5KioKHz//fcA7t9kYOzYsZg7dy42bdqEo0ePYsCAAQgLC8PTTz8NADAYDIiJicHw4cOxb98+7Nq1C6NHj0bv3r25QgYRERGRE7D5I8wlMX36dKxcudL8cZMmTQAAv//+Ozp06AAASEhIwK1bt8z7TJw4EXfu3MGIESOQlpaGdu3aYcuWLeY1mAFgzZo1GD16NDp16gQXFxf07NkTH33EW98SEREROQOHCsxfffVVsWswCyEsPtbpdJg9ezZmz55d6OcEBATwJiVERERETsqhTskgIiIiIpIbAzMRERERUREYmImIiIiIisDATERERERUBAZmIiIiIqIiMDATERERERWBgZmIiIiIqAgMzERERERERWBgJiIiIiIqAgMzEREREVERGJiJiIiIiIrAwExEREREVAQGZiIiIiKiIjAwExEREREVgYGZiIiIiKgIDMxEREREREVgYCYiIiIiKgIDMxERERFRERiYiYiIiIiKwMBMRERERFQEN60bcBZCCABAenq6KuOZTCZkZmYiPT0d7u7uqoxpDzgv0jgv0jgv0jgv0jgv0jgv0jgv0tSel/xclp/TCsPArJLbt28DAMLDwzXuhIiIiIgedPv2bfj5+RX6uE4UF6lJFnl5ebhy5QrKly8PnU6n+Hjp6ekIDw/HxYsX4evrq/h49oLzIo3zIo3zIo3zIo3zIo3zIo3zIk3teRFC4Pbt2wgLC4OLS+FnKvMIs0pcXFxQpUoV1cf19fXlN6IEzos0zos0zos0zos0zos0zos0zos0NeelqCPL+XjRHxERERFRERiYiYiIiIiKwMDsoDw9PTFjxgx4enpq3YpN4bxI47xI47xI47xI47xI47xI47xIs9V54UV/RERERERF4BFmIiIiIqIiMDATERERERWBgZmIiIiIqAgMzERERERERWBgtlNvv/022rRpA71ejwoVKlj1OUIITJ8+HaGhofD29kZ0dDROnTplsU9qair69esHX19fVKhQAUOHDkVGRoYCz0AZJe3/3Llz0Ol0kv++/fZb835Sj69bt06NpySL0nxdO3ToUOA5v/TSSxb7XLhwAd27d4der0dQUBAmTJiAnJwcJZ+KrEo6L6mpqXj11VdRp04deHt7o2rVqhgzZgxu3bplsZ+9vV6WLFmCiIgIeHl5oVWrVti3b1+R+3/77beIioqCl5cXGjRogM2bN1s8bs17jT0oybx88cUXeOSRR+Dv7w9/f39ER0cX2H/QoEEFXhcxMTFKPw3ZlWRevvrqqwLP2cvLy2IfZ3y9SL2/6nQ6dO/e3byPI7xe/vjjDzz55JMICwuDTqfDDz/8UOzn7NixA02bNoWnpydq1qyJr776qsA+JX3PkoUguzR9+nSxaNEiMW7cOOHn52fV58yfP1/4+fmJH374Qfzzzz/iqaeeEpGRkeLu3bvmfWJiYkSjRo3Enj17xJ9//ilq1qwp+vTpo9CzkF9J+8/JyRFXr161+Ddr1ixRrlw5cfv2bfN+AMSKFSss9ntw3mxdab6u7du3F8OHD7d4zrdu3TI/npOTI+rXry+io6PFoUOHxObNm0WlSpXElClTlH46sinpvBw9elQ8++yzYtOmTSIxMVFs27ZN1KpVS/Ts2dNiP3t6vaxbt054eHiI5cuXi+PHj4vhw4eLChUqiOTkZMn9d+3aJVxdXcW7774rTpw4IaZOnSrc3d3F0aNHzftY815j60o6L3379hVLliwRhw4dEkajUQwaNEj4+fmJS5cumfcZOHCgiImJsXhdpKamqvWUZFHSeVmxYoXw9fW1eM5JSUkW+zjj6+XGjRsWc3Ls2DHh6uoqVqxYYd7HEV4vmzdvFm+99ZbYsGGDACC+//77Ivc/c+aM0Ov1Yty4ceLEiRNi8eLFwtXVVWzZssW8T0nnWi4MzHZuxYoVVgXmvLw8ERISIt577z3ztrS0NOHp6Sm++eYbIYQQJ06cEADE33//bd7nl19+ETqdTly+fFn23uUmV/+NGzcWQ4YMsdhmzTe6rSrtvLRv31689tprhT6+efNm4eLiYvHD79NPPxW+vr4iKytLlt6VJNfr5T//+Y/w8PAQJpPJvM2eXi8tW7YUr7zyivnj3NxcERYWJt555x3J/Z9//nnRvXt3i22tWrUSI0eOFEJY915jD0o6Lw/LyckR5cuXFytXrjRvGzhwoOjRo4fcraqqpPNS3M8ovl7u+/e//y3Kly8vMjIyzNsc4fXyIGveFydOnCjq1atnse3/2rv3mCiutw/gX+6KuCI3AUUEVIqKtwpUo2KEitgarWkUSa3ai1E0xsZStcZKwVZUSv8wGmmLJWlrSWu0mDQoYqQpFmnFtVZEKrDeYqRKERC8wvP7o+/O67iwwLLgrn4/CYl75syZZ549zD6SmbMLFiyQmJgY5XVXc20q3pLxnNDpdLhx4waio6OVtn79+iEiIgJFRUUAgKKiIri6umLChAlKn+joaNja2qK4uLjHY+4sc8RfUlKCM2fO4O233zbYtnLlSnh4eCA8PBx79+6FWMkS5l3Jy3fffQcPDw+MGjUKGzZsQFNTk2rc0NBQDBgwQGmLiYlBfX09SktLzX8iZmau+V5XVweNRgN7e3tVuzXMlwcPHqCkpER1XbC1tUV0dLRyXXhSUVGRqj/w3/uu79+Ra42lMyUvT2pqasLDhw/h5uamai8oKICXlxeCg4OxYsUK1NTUmDX27mRqXu7cuQN/f3/4+flhzpw5qusD58t/MjMzERcXhz59+qjarXm+mKK964s5cm0q+/a70LPgxo0bAKAqbvSv9dtu3LgBLy8v1XZ7e3u4ubkpfSyZOeLPzMxESEgIJk2apGpPTk7G9OnT4ezsjLy8PCQkJODOnTtYvXq12eLvLqbmJT4+Hv7+/vD19cXZs2exbt06lJeX48CBA8q4rc0n/TZLZ475cuvWLaSkpGDZsmWqdmuZL7du3UJzc3Or7+OFCxda3aet9/3x64i+ra0+ls6UvDxp3bp18PX1VX2wz5w5E/PmzUNAQAAqKyvx4YcfIjY2FkVFRbCzszPrOXQHU/ISHByMvXv3YvTo0airq0NaWhomTZqE0tJSDBo0iPMFwO+//45z584hMzNT1W7t88UUbV1f6uvrcffuXdTW1nb5d9NULJgtyPr167Ft2zajfcrKyvDCCy/0UESWoaN56aq7d+9i37592LRpk8G2x9vGjRuHxsZG7Nix46kWQN2dl8eLwNDQUPj4+CAqKgqVlZUICgoyedzu1lPzpb6+Hq+88gpGjBiBpKQk1TZLnC/Uc1JTU5GdnY2CggLVA25xcXHKv0NDQzF69GgEBQWhoKAAUVFRTyPUbjdx4kRMnDhReT1p0iSEhIQgIyMDKSkpTzEyy5GZmYnQ0FCEh4er2p/H+WLJWDBbkLVr12LJkiVG+wQGBpo0tre3NwCguroaPj4+Snt1dTXGjh2r9Pnnn39U+z169Aj//vuvsv/T0NG8dDX+/fv3o6mpCW+++Wa7fSMiIpCSkoL79+8/te+776m86EVERAAAKioqEBQUBG9vb4Mnk6urqwHgmZ8vDQ0NmDlzJvr27YuDBw/CwcHBaH9LmC+t8fDwgJ2dnfK+6VVXV7eZA29vb6P9O3KtsXSm5EUvLS0NqampyM/Px+jRo432DQwMhIeHByoqKqyiAOpKXvQcHBwwbtw4VFRUAOB8aWxsRHZ2NpKTk9s9jrXNF1O0dX3RaDTo3bs37OzsujwHTdatd0hTt+vsQ39paWlKW11dXasP/Z06dUrpc+TIEat76M/U+CMjIw1WO2jLli1bpH///ibH2pPM9b4WFhYKAPnzzz9F5P8f+nv8yeSMjAzRaDRy7949851ANzE1L3V1dfLSSy9JZGSkNDY2duhYljxfwsPDZdWqVcrr5uZmGThwoNGH/l599VVV28SJEw0e+jN2rbEGnc2LiMi2bdtEo9FIUVFRh45x9epVsbGxkZycnC7H21NMycvjHj16JMHBwfLee++JyPM9X0T++wx3cnKSW7dutXsMa5wvj0MHH/obNWqUqm3hwoUGD/11ZQ6aigWzlbp8+bJotVplCTStVitarVa1FFpwcLAcOHBAeZ2amiqurq6Sk5MjZ8+elTlz5rS6rNy4ceOkuLhYCgsLZdiwYVa3rJyx+K9duybBwcFSXFys2u/ixYtiY2Mjubm5BmMeOnRIvvzyS/nrr7/k4sWLsnv3bnF2dpaPPvqo28/HXDqbl4qKCklOTpZTp06JTqeTnJwcCQwMlKlTpyr76JeVmzFjhpw5c0YOHz4snp6eVresXGfyUldXJxERERIaGioVFRWq5Z4ePXokItY3X7Kzs8XJyUmysrLk/PnzsmzZMnF1dVVWP1m0aJGsX79e6X/ixAmxt7eXtLQ0KSsrk82bN7e6rFx71xpL19m8pKamiqOjo+zfv181L/TX5IaGBnn//felqKhIdDqd5Ofny/jx42XYsGFW8R9Mvc7m5eOPP5YjR45IZWWllJSUSFxcnPTq1UtKS0uVPs/jfNGbPHmyLFiwwKD9WZkvDQ0NSn0CQNLT00Wr1crly5dFRGT9+vWyaNEipb9+WbnExEQpKyuTXbt2tbqsnLFcdxcWzFZq8eLFAsDg5/jx40of/N9asHotLS2yadMmGTBggDg5OUlUVJSUl5erxq2pqZGFCxeKi4uLaDQaWbp0qaoIt3Ttxa/T6QzyJCKyYcMG8fPzk+bmZoMxc3NzZezYseLi4iJ9+vSRMWPGyJ49e1rta6k6m5crV67I1KlTxc3NTZycnGTo0KGSmJioWodZROTSpUsSGxsrvXv3Fg8PD1m7dq1qeTVL19m8HD9+vNXfOwCi0+lExDrny86dO2Xw4MHi6Ogo4eHhcvLkSWVbZGSkLF68WNX/hx9+kOHDh4ujo6OMHDlSfv75Z9X2jlxrrEFn8uLv79/qvNi8ebOIiDQ1NcmMGTPE09NTHBwcxN/fX959991u/5DvDp3Jy5o1a5S+AwYMkFmzZsnp06dV4z2P80VE5MKFCwJA8vLyDMZ6VuZLW9dMfS4WL14skZGRBvuMHTtWHB0dJTAwUFXH6BnLdXexEbHAtY6IiIiIiCwE12EmIiIiIjKCBTMRERERkREsmImIiIiIjGDBTERERERkBAtmIiIiIiIjWDATERERERnBgpmIiIiIyAgWzERERERERrBgJiIiIiIyggUzEREREZERLJiJiAhZWVmwsbHBpUuXzNqXiOhZwIKZiMgC6YtS/U+vXr0wfPhwrFq1CtXV1T0Sw2+//YakpCTcvn27R45HRGSpbEREnnYQRESklpWVhaVLlyI5ORkBAQG4d+8eCgsL8c0338Df3x/nzp2Ds7Oz2Y7X3NyMhw8fwsnJCTY2NgCAtLQ0JCYmQqfTYciQIUb7EhE9y+yfdgBERNS22NhYTJgwAQDwzjvvwN3dHenp6cjJycHChQvNdhw7OzvY2dmZvS8R0bOAt2QQEVmR6dOnAwB0Op3SptVqERsbC41GAxcXF0RFReHkyZOq/RoaGrBmzRoMGTIETk5O8PLywssvv4zTp08DMLwvOSkpCYmJiQCAgIAA5daQS5cutXkPc0fiSEpKgo2NDSoqKrBkyRK4urqiX79+WLp0KZqamto9/1mzZqn+2q0nIhg/fjymTJnS7hhERJ3FvzATEVmRyspKAIC7uzsAoLS0FFOmTIFGo8EHH3wABwcHZGRkYNq0afjll18QEREBAFi+fDn279+PVatWYcSIEaipqUFhYSHKysowfvx4g+PMmzcPf//9N77//nt8/vnn8PDwAAB4enq2GldH49CbP38+AgICsHXrVpw+fRpfffUVvLy8sG3bNqPnHxYWhtzcXNTW1qJ///5Ke3Z2NrRaLQoLCzuYSSKiThAiIrI4X3/9tQCQ/Px8uXnzply9elWys7PF3d1devfuLdeuXRMRkblz54qjo6NUVlYq+16/fl369u0rU6dOVdr69esnK1eubPd4Op1OaduxY4dBW1t9OxrH5s2bBYC89dZbqjFfe+01cXd3bzcvhw4dEgBy7Ngxpe3BgwcSFBQks2fPbnd/IiJT8JYMIiILFh0dDU9PT/j5+SEuLg4uLi44ePAgBg4ciObmZuTl5WHu3LkIDAxU9vHx8UF8fDwKCwtRX18PAHB1dUVxcTGuX79u9hg7E4fe8uXLVa+nTJmCmpoag35PCgsLAwDlVhIA+OKLL6DT6fDpp5929VSIiFrFgpmIyILt2rULR48exfHjx3H+/HlUVVUhJiYGAHDz5k00NTUhODjYYL+QkBC0tLTg6tWrAIDt27fj3Llz8PPzQ3h4OJKSklBVVWWWGDsTh97gwYNVr/W3V9TW1ho9lre3NwYOHAitVgsAaGxsREpKCt544w2MGjWqK6dBRNQmFsxERBYsPDwc0dHRmDZtGkJCQmBra9ple/78+aiqqsLOnTvh6+uLHTt2YOTIkcjNzTVzxB3T1iob0oGVTsPCwpSCOT09HbW1tUhOTjZrfEREj2PBTERkpTw9PeHs7Izy8nKDbRcuXICtrS38/PyUNh8fHyQkJOCnn36CTqeDu7s7PvnkkzbH7+gay52No6vCwsJQXl6OK1euIC0tDStWrIC/v7/ZxiciehILZiIiK2VnZ4cZM2YgJydHtcRbdXU19u3bh8mTJ0Oj0aC5uRl1dXWqfb28vODr64v79++3OX6fPn0AoN1v+utoHOYyYcIEtLS0ID4+HiKCjRs3mm1sIqLWcFk5IiIrtmXLFhw9ehSTJ09GQkIC7O3tkZGRgfv372P79u0A/luDedCgQXj99dcxZswYuLi4ID8/H3/88Qc+++yzNsd+8cUXAQAbN25EXFwcHBwcMHv2bJPjMBf9F7mcOHECSUlJbS51R0RkLiyYiYis2MiRI/Hrr79iw4YN2Lp1K1paWhAREYFvv/1WWfvY2dkZCQkJyMvLw4EDB9DS0oKhQ4di9+7dWLFiRZtjh4WFISUlBXv27MHhw4fR0tKi+sKUzsZhLm5ubhgyZAgaGxuxdu1as45NRNQaG+nIExZEREQWoqqqCsOHD0d6ejpWr179tMMhoucAC2YiIrIqCxYsQElJCc6fPw9HR8enHQ4RPQd4SwYREVm827dvIzc3FwUFBfjxxx+Rm5vLYpmIegwLZiIisnjHjh1DfHw8Bg0ahIyMDOXLW4iIegJvySAiIiIiMoLrMBMRERERGcGCmYiIiIjICBbMRERERERGsGAmIiIiIjKCBTMRERERkREsmImIiIiIjGDBTERERERkBAtmIiIiIiIjWDATERERERnBgpmIiIiIyIj/AfmsMiQNcSYZAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_periods = 1000\n", "time_span = [0, 2 * np.pi * num_periods]\n", "initial_conditions = [0, 1]\n", "\n", "# Solving the system over num_periods periods\n", "time_points = np.linspace(0, 2 * np.pi * num_periods, 200000)\n", "solution = solve_ivp(harmonic_oscillator, time_span, initial_conditions, t_eval=time_points, method='RK45')\n", "y = solution.y\n", "\n", "# Plotting the phase space trajectory\n", "plt.figure(figsize=(12, 8))\n", "plt.plot(y[0], y[1], linewidth=0.5, color='tab:red')\n", "plt.gca().set_aspect('equal', adjustable='box') \n", "plt.xlabel('Position $y$', fontsize=12)\n", "plt.ylabel('Velocity $y\\'$', fontsize=12)\n", "plt.title(f'Phase space trajectory over {num_periods} periods', fontsize=14)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe that the circle thickens over time: the trajectories do not close perfectly because the discrete scheme does not preserve the first integral. It gradually loses energy, whereas the continuous differential system does not lose any." ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_periods = 1000\n", "time_span = [0, 2 * np.pi * num_periods]\n", "initial_conditions = [0, 1]\n", "\n", "time_points = np.linspace(0, 2 * np.pi * num_periods, 200000)\n", "solution = solve_ivp(harmonic_oscillator, time_span, initial_conditions, t_eval=time_points, method='RK45', rtol=1e-5) # added precision\n", "y = solution.y\n", "\n", "# Plotting the phase space trajectory\n", "plt.figure(figsize=(12, 8))\n", "plt.plot(y[0], y[1], linewidth=0.5, color='tab:red')\n", "plt.gca().set_aspect('equal', adjustable='box') \n", "plt.xlabel('Position $y$', fontsize=12)\n", "plt.ylabel('Velocity $y\\'$', fontsize=12)\n", "plt.title(f'Phase space trajectory over {num_periods} periods', fontsize=14)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With enhanced precision, this phenomenon is reduced. However, it is worth noting that if the number of periods is significantly increased (e.g., up to 10,000), the same issue reappears." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Implementation of harmonic oscillator with symplectic Euler scheme ####" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Simulation duration\n", "num_periods = 10000\n", "T = 2 * np.pi * num_periods\n", "# Time step\n", "h = 1e-1\n", "# Number of points in the subdivision\n", "N = int(T / h)\n", "\n", "# Arrays to store position (q) and momentum (p)\n", "q = np.zeros(N)\n", "p = np.zeros(N)\n", "\n", "# Initial conditions\n", "q[0] = 0 # Initial position\n", "p[0] = 1 # Initial momentum\n", "\n", "# Symplectic Euler scheme\n", "for k in range(N - 1):\n", " p[k + 1] = p[k] - h * q[k]\n", " q[k + 1] = q[k] + h * p[k + 1]\n", "\n", "# Plotting the phase space trajectory\n", "plt.figure(figsize=(12, 8))\n", "plt.plot(q, p, '-', linewidth=0.5, color='tab:blue')\n", "plt.axis('equal')\n", "plt.gca().set_aspect('equal', adjustable='box') \n", "plt.xlabel('Position $q$', fontsize=12)\n", "plt.ylabel('Velocity $p$', fontsize=12)\n", "plt.title('Symplectic Euler scheme (implicit-explicit)', fontsize=14)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem is resolved, even with a very coarse time step. The implicit-explicit scheme preserves energy, even when simulating over ten thousand periods. Interestingly, it is only a first-order scheme, like the standard Euler scheme. The order of a scheme ensures accuracy but does not guarantee the preservation of the system’s invariants. Schemes that preserve the natural invariants of the system are called *symplectic schemes*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "

Part 2 - SIR System

\n", "
\n", "\n", "Let us now focus on implemnting the differential system from epidemiology called SIR (*Sound, Infected, Recovered*):\n", "$$\n", "\\begin{cases} \n", "S'(t) &= -\\beta \\frac{S \\cdot I}{N}, \\\\\n", "I'(t) &= \\beta \\frac{S \\cdot I}{N} - (\\gamma + \\delta) I, \\\\\n", "R'(t) &= \\gamma I, \\\\\n", "D'(t) &= \\delta I.\n", "\\end{cases}\n", "$$\n", "\n", "with the initial conditions:\n", "$$\n", "I(0) = 1, \\quad R(0) = 0, \\quad D(0) = 0, \\quad S(0) = N - R(0) - I(0) - D(0).\n", "$$\n", "\n", "This classical epidemiological system models the spread of a virus within a population. The variable $N$ represents the initial population size. The parameters $\\beta$, $\\gamma$, and $\\delta$ correspond to the rates of transmission, recovery, and mortality, respectively. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Proof that $S(t) + I(t) + R(t) + D(t) = N$ ####\n", "Let us define\n", "$$\n", "P(t) = S(t) + I(t) + R(t) + D(t),\n", "$$\n", "we then differentiate $ P(t) $ with respect to $ t $:\n", "$$\n", "P'(t) = S'(t) + I'(t) + R'(t) + D'(t).\n", "$$\n", "We replace the expressions for $ S'(t) $, $ I'(t) $, $ R'(t) $, and $ D'(t) $:\n", "$$\n", "P'(t) = \\left(-\\beta \\frac{S \\cdot I}{N}\\right) + \\left(\\beta \\frac{S \\cdot I}{N} - (\\gamma + \\delta) I\\right) + (\\gamma I) + (\\delta I)\n", "$$\n", "$$\n", "= -\\beta \\frac{S \\cdot I}{N} + \\beta \\frac{S \\cdot I}{N} - (\\gamma + \\delta) I + \\gamma I + \\delta I = 0.\n", "$$\n", "\n", "Since $ P'(t) = 0 $, $ P(t) $ is constant over time. From the initial conditions, we know:\n", "$$\n", "P(0) = S(0) + I(0) + R(0) + D(0) = N.\n", "$$\n", "Thus, $ P(t) = N $ for all $ t $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Implementation of SIR with RK45 ####" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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48OBcY//zn//IYDBo6NChTrs/AABAcSKUgg06pQAAf2c2m7Vjxw69/PLLSk1N1YEDB3TXXXepT58+1r0Eb2bXrl1z+Fxnh1I//fSTUlNTrT/r1q2TJD300EO5xr3zzjtq0KCB0+4NAABQ3AilYMPRTqmLFy/q4MGDktjkHABKm0OHDunixYu66667FBERoapVq6p///7Kzs7WgQMHrONSUlLUu3dvlStXTiEhIXrsscd07tw5m2ulpKQoNjZW4eHh8vX1VcOGDbV582ZJ0p49e9S9e3cFBQUpIiJCw4cPV+Z1f0tSoUIFvffeezbX++mnn1SmTBlrOHajGo4fPy6DwaClS5fqjjvukI+Pj1asWGFX7QkJCWrXrp18fX3VuHFjbdu2TUeOHHFqKBUWFqaIiAjrz9dff63q1aurffv21jGXLl3SY489pnnz5qlcuXJOuzcAAEBxI5SCDUc7pSyBVIUKFRQWFubkqgAA7pSQkKBy5cqpbt26kqTffvtN48aNk4+Pj7VTJzU1Va1atVKNGjX0448/at26dTp8+LBGjhxpvU5ycrJatGihK1euaMWKFdq1a5eGDBmioKAg7dixQ7fffruaNGmixMRELVmyRB9//LFmzJhhPb9+/frau3evTW2jR4/W008/rapVq+rw4cNq2rRpgTXs3LlTkvTSSy9p4sSJ+uWXX1S9evUbnrd//3517NhR7du31549ezR+/Hj16tVLknJ1K02fPl0BAQEF/qSkpNzwe8/MzNSiRYv05JNPymAwWI8PHjxYPXr0UOfOnW94DQAAgJLMy90FoGRxtFPK8jfU1apVc3JFAAB3S0xM1IULFxQYGKjs7GxdvXpVvr6+mjt3rqKiopSVlaW5c+fq6aef1osvvmg9b9SoUTbBzsCBA9WqVSstXbrUeqxmzZqSpGbNmumJJ57Q1KlTJUk1atRQv3799PXXX2vChAmSpHr16tmEUmvWrNHPP/9svd6gQYM0aNAgTZ48Od8akpKS5O/vr08//VQxMTGSpK5du97wvMGDB6tXr16aMmWKpJwnzS5ZskS7d++Wn5+fzff1zDPP6F//+leB32lUVFSB70vS8uXLdf78efXt29d6bMmSJUpMTNRPP/10w/MBAABKOkIp2HC0U8oSSlWtWtXJFQEA3C0xMVGDBw/Ws88+q/Pnz2vEiBFq06aNNSxJTk7Wzp07dfDgQc2ZM8d6XnZ2tipXrmwd880332jHjh25rr9//34lJCRo0aJFNse9vb2Vcd3fktSvX1/Lli2TlLPP1ZgxYzRy5EiFhoYqOTlZ69at0+bNmzVr1qw8a5ByOqXuvfdeayBlz3nJycn67rvvrHsnWhiNxjyX7oWEhCgkJCS/r9Nu77//vu6++25rgPXrr7/queee07p161SmTJkiXx8AAMDdCKVgo6idUoRSAFD6JCYmasCAAapRo4Yk6a233lKDBg00YMAAxcTEaNeuXQoMDNS2bdtkNBptzvX19ZWU06Hk7e2dZ4jzyy+/yGg0qlatWjbH9+7dq/r161tf16tXT7/99psuXbqkr776SqmpqYqLi5OUEzaFhIRo27Ztua5vqcFSx/PPP299bc95SUlJ8vLysqlFknbs2KHY2Nhc502fPl3Tp0/Pdfzvny06Ojrf95OTk/Xtt9/qiy++sB5LSEjQmTNnbB4okp2drU2bNumNN95QRkaGPD09C7wvAABASUIoBRuOdkodP35ckqx/8wwAKB2OHj2q8+fPq169etZjdevWVfXq1bV48WKNHTtWRqNRV65cUVRUlIKDg/O8jtFo1LVr15Senp5ruZtlWWBWVpZ8/vrbkWPHjmnZsmVasWKFdZylhl27dmnChAmaOHGi/P39rde/ePGioqKicl3fIi0tTcePH7d5IIc953l4eMhkMikzM1NeXjn/6rRq1Srt378/z5DNGcv3PvjgA1WoUEE9evSwHuvUqZN2795tM65fv3667bbbNHr0aAIpAABw02Gjc9igUwoAcL2EhIQ8u5g6depkXUrXokUL+fr6ql+/ftq5c6cOHz6s1atXa+jQodbxLVu2VHBwsAYOHKh9+/Zp7969mjt3rg4dOqSWLVuqbNmyev7553X06FF999136tGjhx555BHddddd1msEBASoSpUqGj58uDw8PDRgwACb6wcFBalPnz751rBz5055enradDzZc17Tpk1lNBo1cuRIHT16VCtWrLDeO7/lezVq1CjwxxJu5cVkMumDDz5QbGyszbjAwEDVq1fP5sff31/ly5e3CQ0BAABuFoRSsGEJpQrTKWU2m62dUoRSAFC6JCYmqmbNmvK2tNL+pXPnzkpISNBvv/2mkJAQTZgwQWfPnlW7du3UpEkTjRs3zubhF+XLl9dXX32lQ4cOqXnz5mrbtq1WrFihChUqKDg4WMuXL9emTZv0j3/8QwMGDFCfPn30wQcf5Kqnfv36+vHHHzVt2jSbwCYkJESrVq3Sn3/+mW8NO3fuVO3atW32Y7LnvKioKL333ntasWKF/vGPf2jWrFnq06ePwsPDFRER4ZTv+XrffvutUlJS9OSTTzr92gAAACWJwWw2m91dhDulpaUpODhYFy5cUFBQkLvLKZKsrCytWrVK3bt3z7Wnh7127JCaNJGioqQTJ+w7JzU1VVFRUfLw8NDVq1cdvjeKjzPmCm4NzBXYg3kCezFXYC/mCuzFXIG9mCvFy96shU4p2HCkU8qydK9SpUr8jxsAAAAAANiFUAo2LKszCrOnFPtJAQAAAACAwiKUgg1HNjpnPykAAAAAAFBYhFKwYemUysyU7N1tLDU1VdKNH28NAAAAAABgQSgFG5ZOKUnKyrLvnN9//12SVKFCBRdUBAAAAAAASiNCKdi4/onf9i7hO3PmjCQpLCzMBRUBAAAAAIDSiFAKNq4Ppa5ds+8cOqUAAAAAAEBhEUrBhqfn//5sbyhFpxQAAAAAACgsQinYMBgkj79mhT2hlMlk0p9//imJTikAAAAAAGA/Qink4uWV89ueUOrs2bMymUySpNDQUBdWBQAAAAAAShNCKeRSmFDKsnSvXLlyMhqNLqwKAAAAAACUJoRSyMUSSmVn33isZZNz9pMCAAAAAACFQSiFXBzplGI/KQAAAAAAUBiEUsilMKEUnVIAAAAAAMARhFLIhU4pAAAAAADgaoRSyIVOKQAAAAAA4GqEUsiFTikAAAAAAOBqhFLIhU4pAAAAAADgaoRSyMWRUIpOKQAAAAAAUBiEUsilMKHUH3/8IUkKDQ11YUUAAAAAAKC0IZRCLoUJpS5cuCBJCg4OdmFFAAAAAACgtCGUQi72hlIZGRnKyMiQRCgFAAAAAAAKh1AKuXh65vy+USh18eJF658DAwNdWBEAAAAAAChtCKWQi72dUpale/7+/vK0JFkAAAAAAAB2IJRCLvaGUmlpaZJYugcAAAAAAAqPUAq5WEKp7OyCx1k6pYKCglxcEQAAAAAAKG0IpZBLYTulCKUAAAAAAEBhlbhQ6s0331RMTIzKlCmjli1bavv27QWOnzNnjmrXri1fX19VrlxZw4YN09WrV4up2tKJ5XsAAAAAAMDVSlQo9cknnyguLk6TJk1SYmKiGjZsqG7duunMmTN5jl+8eLGef/55TZo0Sfv27dP777+vTz75RGPHji3mykuXwm50TqcUAAAAAAAorBIVSs2ePVsDBgxQv379VLduXc2dO1d+fn6aP39+nuO3bt2qNm3aqHfv3oqJiVHXrl316KOP3rC7CgVj+R4AAAAAAHA1L3cXYJGZmamEhASNGTPGeszDw0OdO3fWDz/8kOc5t99+uxYtWqTt27erRYsWOnr0qFatWqUnnngi3/tkZGQoIyPD+toSrGRlZSkrK8tJn8Y9LPUX9XN4eHhK8lBGRrayskz5jjt37pwkKTAw8Kb/7m41zporKP2YK7AH8wT2Yq7AXswV2Iu5AnsxV4qXvd9ziQml/vjjD2VnZys8PNzmeHh4uPbv35/nOb1799Yff/yhtm3bymw269q1a3rmmWcKXL4XHx+vyZMn5zq+du1a+fn5Fe1DlBDr1q0r0vmnTzeRVFm7d+/TqlVH8h23e/fuv8af1qpVq4p0T7hHUecKbh3MFdiDeQJ7MVdgL+YK7MVcgb2YK8UjPT3drnElJpRyxIYNGzR9+nS99dZbatmypQ4fPqznnntOU6ZM0YQJE/I8Z8yYMYqLi7O+TktLU+XKldW1a9ebfhlaVlaW1q1bpy5dushoNDp8nWXLPCVJNWvWUffutfMd98knn0iSmjRpou7duzt8PxQ/Z80VlH7MFdiDeQJ7MVdgL+YK7MVcgb2YK8XLsirtRkpMKBUaGipPT0+dPn3a5vjp06cVERGR5zkTJkzQE088oaeeekqSVL9+fV2+fFn/7//9P40bN04eHrm3zPLx8ZGPj0+u40ajsdRMzKJ+Fm/vnN9ms6eMRs98x126dEmSFBISUmq+u1tNaZr3cC3mCuzBPIG9mCuwF3MF9mKuwF7MleJh73dcYjY69/b2VtOmTbV+/XrrMZPJpPXr16t169Z5npOenp4rePL0zAlRzGaz64ot5Xj6HgAAAAAAcLUS0yklSXFxcYqNjVWzZs3UokULzZkzR5cvX1a/fv0kSX369FHFihUVHx8vSerZs6dmz56txo0bW5fvTZgwQT179rSGUyg8y1fH0/cAAAAAAICrlKhQ6uGHH9bvv/+uiRMn6tSpU2rUqJFWr15t3fw8JSXFpjNq/PjxMhgMGj9+vE6cOKGwsDD17NlT06ZNc9dHKBXs7ZSyhFLBwcEurggAAAAAAJQ2JSqUkqQhQ4ZoyJAheb63YcMGm9deXl6aNGmSJk2aVAyV3TpYvgcAAAAAAFytxOwphZLDEkplZ+c/xmw2s3wPAAAAAAA4jFAKudjTKZWRkaGsrCxJLN8DAAAAAACFRyiFXOwJpSxL9yQpICDAxRUBAAAAAIDShlAKudgTSlmW7gUGBtpsPg8AAAAAAGAP0gTkUphOKZbuAQAAAAAARxBKIZfCdEqxyTkAAAAAAHAEoRRysSeUunjxoqSc5XsAAAAAAACFRSiFXOwJpa5cuSJJ8vPzK4aKAAAAAABAaUMohVzsCaXS09MlEUoBAAAAAADHEEohF0IpAAAAAADgaoRSyMXTM+c3oRQAAAAAAHAVQinkUpg9pXx9fYuhIgAAAAAAUNoQSiEXlu8BAAAAAABXI5RCLpZQKjs7/zGEUgAAAAAAoCgIpZALnVIAANiaOnWqWrVq5e4yAAAAShVCKeTCnlIAgL9r3769DAaDDAaDvLy8FBkZqQceeEA//viju0srFjt37lSjRo2cdr3s7GxNmDBBVatWla+vr6pXr64pU6bIbDZbx1y8eFFDhw5VlSpV5Ovrq9tvv10//fSTzXXefvttNWjQQEFBQQoKClLr1q31zTffWN/ftGmTevbsqaioKBkMBi1fvjxXLfaMsacWAACAwiKUQi50SgEArmc2m7Vjxw795z//UWpqqg4fPqzFixfLw8NDd9xxh7799lt3l+hyzg6lZsyYobfffltvvPGG9u3bpxkzZmjmzJl6/fXXrWOeeuoprVu3TgsXLtTu3bvVtWtXde7cWSdOnLCOqVSpkv7zn/8oISFBP//8s+68807dd999+uWXXyRJly9fVsOGDfXmm2/mW4s9Y+ypBQAAoLAIpZALoRQA4HqHDh3SxYsX1a5dO0VERCgmJkYdO3bUp59+qtatW2vixInWsSkpKerdu7fKlSunkJAQPfbYYzp37pzN9VJSUhQbG6vw8HD5+vqqYcOG2rx5s93nT5o0SfXr15e/v7/Cw8M1cOBAZWVlSZJMJpOmT5+umjVrqkyZMgoPD1ffvn1z3b+geyQkJKhdu3by9fVV48aNtW3bNh05csSpodTWrVt13333qUePHoqJidE///lPde3aVdu3b5eU05H8+eefa+bMmWrXrp1q1KihF154QTVq1NDbb79tvU7Pnj3VvXt31axZU7Vq1dK0adMUEBBg7WC7++67NXXqVN1///351nKjMfbWAgAAUFiEUsiFUAoAcL2EhAR5enqqYcOGNscNBoO6dOminTt3SpIOHz6spk2bqkaNGvrxxx+1bt06HT58WCNHjrSek5ycrBYtWujKlStasWKFdu3apSFDhigoKMiu881ms8xms9555x3t3btXCxYs0Oeff6733ntPkhQfH68lS5bo3Xff1YEDB7Rs2TK1a9fOev6N7rF//3517NhR7du31549ezR+/Hj16tVLktSgQYNc38306dMVEBBQ4E9KSkqu826//XatX79eBw8elJTTibV582bdfffdkqRr164pOztbZcqUsTnP19fXGuD9XXZ2tpYsWaLLly+rdevWeY5xhCO1AAAA2MPL3QWg5GFPKQDA9RITE1W7du08/yLC29tbRqNRkvTss89q0KBBmjx5svX9UaNG2YRKAwcOVKtWrbR06VLrsZo1a0qSunbtesPzDQaDXnzxRevrKlWqqHPnzjpw4IAkac2aNerZs6c6duxoff/222+3jh80aFCB9xg8eLB69eqlKVOmSJKqV6+uJUuWaPfu3Xl+/meeeUb/+te/8v/yJEVFReU69vzzzystLU233XabPD09lZ2drWnTpumxxx6TJAUGBqp169aaMmWK6tSpo/DwcH388cf64YcfVKNGDZtr7d69W61bt9bVq1cVEBCgZcuWqW7dugXWVBiFqQUAAKAwCKWQC51SAIDrJSYmqmnTpnm+d+DAAdWuXVtnzpzRt99+qy1btmjWrFnW97Ozs1W5cmVJOV1S33zzjXbs2JHrOsnJyVq3bp02b96c7/mWcTNnztTGjRt14sQJZWVl6erVq/rPf/4jSbr33ns1evRo/fzzz3rooYf04IMPqly5cnbdIzk5Wd99950SExNtajMajfku3QsJCVFISEhBX1+eli5dqv/+979avHix/vGPfygpKUlDhw5VVFSUYmNjJUkLFy7Uk08+qYoVK8rT01NNmjTRo48+qoSEBJtr1a5dW0lJSbpw4YI+++wzxcbGauPGjU4NpuytBQAAoDAIpZALoRQA4HqJiYnq2bNnruOXL1/WihUr9Nxzz+n48eMKCQnRtm3bco2zdNUmJSXJ29s7z4Bn586dNzz/999/V/PmzXXnnXdq9uzZqlixorKzs9WsWTPr0sIRI0bo3nvv1fLly/XKK69YA6qqVave8B4///yzvLy8VL9+fZv3duzYYQ2K/m769OmaPn16nu9Z7N27V9HR0TbHRo4cqeeff16PPPKIJKl+/fpKTk5WfHy89V7Vq1fXxo0bdfnyZaWlpSkyMlIPP/ywqlWrZnMtb29va8dS06ZN9dNPP+nVV1/VO++8U2BdhWFvLQAAAIVBKIVcCKUAABZHjx7V+fPn1aRJE5vj2dnZeuaZZ+Tr66uBAwfqtdde08WLFxUVFZXv/zcYjUZdu3ZN6enpucYYjcYbnv/VV18pOztbH3/8sQwGgyTpjTfeUFZWlk3QVatWLY0aNUrPPvusgoKCtHfvXlWtWvWG90hMTJTJZFJmZqa8/vo/w1WrVmn//v35dko5unwvPT1dHh62W3t6enrKZDLlGuvv7y9/f3+dO3dOa9as0cyZMwu8n8lkUkZGRoFjHFXYWgAAAApCKIVc2FMKAGBhWZ4VGRmpU6dOKS0tTQkJCXr11Vf166+/6uuvv1ZwcLBq1aqloKAg9enTRxMmTJC/v78OHz6s1atXa86cOZKkli1bKjg4WAMHDtTzzz8vs9msTZs2qVOnTmrZsuUNzy9fvrzS0tK0YsUK1a1bV1999ZXi4+NVsWJFhYWFaebMmYqIiFDz5s3l4eGhd955R+XLl7fuKXWjezRt2lRGo1EjR47U8OHDtWfPHg0cOFCSnL58r2fPnpo2bZqio6P1j3/8Qzt27NDs2bP15JNPWsesWbNGZrNZtWvXtm7Gftttt6lfv37WMWPGjNHdd9+t6OhoXbx4UYsXL9aGDRu0Zs0aSdKlS5d0+PBh6/hjx44pKSlJISEh1u4te8bYUwsAAEBhEUohF0/PnN/5hVJms5lOKQC4RVj2V6pVq5Y8PT1VtmxZ1a5dW/fee6+eeeYZhYSEKCsrS4GBgVqxYoXGjRundu3ayWw2q2bNmjbL3sqXL6+vvvpKI0eOVPPmzeXt7a1WrVrp0UcfVXBwsFatWqXRo0fne37Pnj3Vv39/PfHEE/L19dXjjz+uf/3rX0pOTpYkXb16VdOmTVNKSooCAgLUpk0bfffdd9Y9pUJCQgq8R1RUlN577z2NGTNG8+fPV4sWLdSnTx998MEHioiIcOr3+vrrr2vChAkaNGiQzpw5o6ioKD399NOaOHGidcyFCxc0ZswY/fbbbwoJCdGDDz6oadOmWTeWl6QzZ86oT58+Sk1NVXBwsBo0aKA1a9aoS5cukqSff/7Zuum7JMXFxUmSYmNjtWDBArvH2FMLAABAYRnMZrPZ3UW4U1pamoKDg3XhwgUFBQW5u5wiycrK0qpVq9S9e/ci/UvioUNSrVpSUJB04ULu969evWrtkCoN39utyFlzBaUfcwX2YJ7AXswV2Iu5AnsxV2Av5krxsjdr8cj3HdyyLMv3srPzft/SJSWxfA8AAAAAADiGUAq53GhPKct+Ul5eXiTMAAAAAADAIYRSyOVGoRT7SQEAAAAAgKIilEIu1y/fy2vHMUIpAAAAAABQVIRSyMXrumcy5rWvFKEUAAAAAAAoKkIp5HJ9KJXXEj7LnlJscg4AAAAAABxFKIVcbhRK0SkFAAAAAACKilAKuRBKAQAAAAAAVyOUQi6env/7M6EUAAAAAABwBUIp5OLhkfMjFbynFKEUAAAAAABwFKEU8mRZwldQpxQbnQMAAAAAAEcRSiFPliV8LN8DAAAAAACuQCiFPNnTKUUoBQAAAAAAHEUohTwVFEqxpxQAAAAAACgqQinkyRJKZWfnfo89pQAAAAAAQFERSiFPLN8DAAAAAACuRCiFPPH0PQAAAAAA4EqEUshTQaFURkaGJKlMmTLFWBEAAAAAAChNCKWQJ3tCKR8fn2KsCAAAAAAAlCaEUsgToRQAAAAAAHAlQinkiVAKAAAAAAC4EqEU8kQoBQAAAAAAXIlQCnmyJ5Ty9vYuxooAAAAAAEBpQiiFPNEpBQAAAAAAXIlQCnny9Mz5TSgFAAAAAABcgVAKeSqoUyozM1MSoRQAAAAAAHAcoRTyxPI9AAAAAADgSoRSyJMllMrOzv0eoRQAAAAAACgqQinkKb9OKZPJpKysLEmEUgAAAAAAwHGEUshTfqGUZT8pSfL29i7GigAAAAAAQGlCKIU85RdKWZbuSXRKAQAAAAAAxxFKIU/2hFJ0SgEAAAAAAEcRSiFPllDqr+2jrCyhlNFolIcH0wcAAAAAADiGVAF58vTM+f33p+9Z9pRi6R4AAAAAACgKQinkKb9QytIpRSgFAAAAAACKglAKebpRKMV+UgAAAAAAoCgIpZAny55SdEoBAAAAAABXIJRCniydUvk9fY9QCgAAAAAAFAWhFPLEnlIAAAAAAMCVCKWQJ0IpAAAAAADgSoRSyFN+oVRmZqYkQikAAAAAAFA0hFLIk2Wjc/aUAgAAAAAArkAohTzdaPmet7d3MVcEAAAAAABKE0Ip5Ik9pQAAAAAAgCsRSiFPhFIAAAAAAMCVCKWQJ8ueUoRSAAAAAADAFQilkCdLpxQbnQMAAAAAAFcglEKeWL4HAAAAAABciVAKecovlMrMzJREKAUAAAAAAIqGUAp5ulGnlLe3dzFXBAAAAAAAShNCKeTJstE5e0oBAAAAAABXIJRCnthTCgAAAAAAuBKhFPJEKAUAAAAAAFyJUAp5IpQCAAAAAACuRCiFPFn2lCKUAgAAAAAArkAohTxZOqXY6BwAAAAAALgCoRTylN/yvczMTEmSt7d3MVcEAAAAAABKE0Ip5Ik9pQAAAAAAgCsRSiFPhFIAAAAAAMCVCKWQJ8tG5+wpBQAAAAAAXIFQCnmiUwoAAAAAALgSoRTyRCgFAAAAAABciVAKeSKUAgAAAAAArkQohTxZ9pT6eyiVmZkpSfL29i7migAAAAAAQGlCKIU8WTql2OgcAAAAAAC4AqEU8pTX8j2z2UwoBQAAAAAAnIJQCnnKK5TKysqy/plQCgAAAAAAFAWhFPKUVyhl6ZKSCKUAAAAAAEDREEohT5aNzq/fU8qyybnERucAAAAAAKBoCKWQp7w6pSyhlMFgkJcltQIAAAAAAHAAoRTyVNCeUkaj0Q0VAQAAAACA0oRQCnkilAIAAAAAAK5EKIU8WVbnEUoBAAAAAABXIJRCniydUtdvdE4oBQAAAAAAnIVQCnli+R4AAAAAAHClQj9C7fjx4/ryyy+1ZcsW7d27V3/88YcMBoNCQ0NVp04dtWnTRvfee6+qVq3qinpRTAp6+p63t7cbKgIAAAAAAKWJ3Z1SX3/9tTp06KAaNWooLi5OSUlJqlSpkjp27Kj27dsrKipKSUlJiouLU40aNdS+fXt9/fXXrqwdLmTZU8pkkszmnD/TKQUAAAAAAJzFrk6pVq1aaefOnbrvvvu0dOlSde7cWUFBQXmOTUtL07p16/TZZ5/pX//6lxo2bKgffvjBqUXD9SydUlJOt5SXF6EUAAAAAABwHrtCqY4dO+rLL79UeHj4DccGBQXpwQcf1IMPPqhTp07p1VdfLXKRKH6EUgAAAAAAwJXsCqXi4+MdunhERITD58K9/h5KSYRSAAAAAADAeXj6HvJEKAUAAAAAAFzJoVBq/fr1eumll2yOzZ8/X9HR0QoPD9ewYcOUff1j23DT8bquh+7atZzfhFIAAAAAAMBZHAqlXnjhBe3cudP6evfu3Xr66acVFhamDh066LXXXtPLL7/stCJR/OiUAgAAAAAAruRQKLVv3z41a9bM+nrhwoUKCgrS999/r08++UQDBgzQRx995LQiUfw8rpsZhFIAAAAAAMDZHAqlLl++rKCgIOvr1atX66677pKfn58kqXnz5kpOTnZOhXAbS7fU30Mpb29vN1UEAAAAAABKC4dCqcqVK+unn36SJB0+fFh79uxR165dre+fPXtWPj4+zqkQbmPZV8oSSmVmZkqiUwoAAAAAABSd142H5PbYY4/pxRdf1IkTJ/TLL7+oXLlyuu+++6zvJyQkqFatWk4rEu5h6ZRio3MAAAAAAOBsDoVS48aNU2ZmplatWqXo6GgtWLBAZcuWlZTTJbVhwwY999xzzqwTbpDf8j1CKQAAAAAAUFQOhVJeXl6aNm2apk2bluu9kJAQnTp1qsiFwf0IpQAAAAAAgKs4tKcUbg2EUgAAAAAAwFUcDqX27dunUaNG6Z///Kc6deqkO++80+anU6dODl33zTffVExMjMqUKaOWLVtq+/btBY4/f/68Bg8erMjISPn4+KhWrVpatWqVQ/eGLctG5+wpBQAAAAAAnM2h5XsLFy5Uv379ZDQaVbt2bZUrVy7XGLPZXOjrfvLJJ4qLi9PcuXPVsmVLzZkzR926ddOBAwdUoUKFXOMzMzPVpUsXVahQQZ999pkqVqyo5ORk6/5WKBo6pQAAAAAAgKs4FEq98MILaty4sb755huFhoY6rZjZs2drwIAB6tevnyRp7ty5WrlypebPn6/nn38+1/j58+fr7Nmz2rp1qzUoiYmJcVo9tzpCKQAAAAAA4CoOhVInT57UiBEjnBpIZWZmKiEhQWPGjLEe8/DwUOfOnfXDDz/kec6KFSvUunVrDR48WF9++aXCwsLUu3dvjR49Wp6WROVvMjIylJGRYX2dlpYmKSdwsYQuNytL/c76HJ6eXpIMysi4pqwss/V78/T0vOm/q1uds+cKSi/mCuzBPIG9mCuwF3MF9mKuwF7MleJl7/fsUCjVoEEDnTx50pFT8/XHH38oOztb4eHhNsfDw8O1f//+PM85evSovvvuOz322GNatWqVDh8+rEGDBikrK0uTJk3K85z4+HhNnjw51/G1a9fKz8+v6B+kBFi3bp1TrpOR0UlSgDZv3qo//jinI0eOSJKOHz/Ovl2lhLPmCko/5grswTyBvZgrsBdzBfZirsBezJXikZ6ebtc4h0Kp2bNn66GHHtLdd9+t22+/3ZFLOIXJZFKFChX07rvvytPTU02bNtWJEyf00ksv5RtKjRkzRnFxcdbXaWlpqly5srp27aqgoKDiKt0lsrKytG7dOnXp0sUpS+wCA72Umio1b3677rjDrGXLlkmS6tatq+7duxf5+nAfZ88VlF7MFdiDeQJ7MVdgL+YK7MVcgb2YK8XLsirtRhwKpWbMmKHg4GDdcccdqlu3rqKjo3MtlzMYDPryyy/tvmZoaKg8PT11+vRpm+OnT59WREREnudERkbKaDTa3LtOnTo6deqUMjMz5e3tnescHx8f+fj45DpuNBpLzcR01mexPH3PYPCS0Shl/7W5VJkyZUrNd3WrK03zHq7FXIE9mCewF3MF9mKuwF7MFdiLuVI87P2OHQqldu3aJYPBoOjoaF26dEl79+7NNcZgMBTqmt7e3mratKnWr1+vXr16ScrphFq/fr2GDBmS5zlt2rTR4sWLZTKZ5OHhIUk6ePCgIiMj8wykUDhsdA4AAAAAAFzFoVDq+PHjTi4jR1xcnGJjY9WsWTO1aNFCc+bM0eXLl61P4+vTp48qVqyo+Ph4SdLAgQP1xhtv6LnnntO///1vHTp0SNOnT9ezzz7rkvpuNYRSAAAAAADAVRwKpVzl4Ycf1u+//66JEyfq1KlTatSokVavXm3d/DwlJcXaESVJlStX1po1azRs2DA1aNBAFStW1HPPPafRo0e76yOUKpble9eu5fwmlAIAAAAAAM5SpFBq48aNWrlypZKTkyVJVapUUY8ePdS+fXuHrzlkyJB8l+tt2LAh17HWrVvrxx9/dPh+yB+dUgAAAAAAwFUcCqUyMzP16KOPavny5TKbzSpbtqwk6fz585o1a5buv/9+ffzxx4QXNzlCKQAAAAAA4CoeNx6S2+TJk7Vs2TINHz5cqampOnv2rM6ePatTp05pxIgR+uKLL/Tiiy86u1YUs/xCKTaRBwAAAAAAReVQKLV48WLFxsZq5syZ1v2eJKlChQqaMWOG+vTpo4ULFzqtSLiHZU8pOqUAAAAAAICzORRKpaamqmXLlvm+37JlS506dcrholAyWDql2OgcAAAAAAA4m0OhVKVKlfLcdNxi48aNqlSpkqM1oYT4+/K9zMxMSYRSAAAAAACg6BwKpWJjY7V06VI988wzOnDggLKzs2UymXTgwAENHDhQn376qfr27evkUlHc2OgcAAAAAAC4ikNP3xs7dqyOHDmid999V/PmzZOHR062ZTKZZDabFRsbq7Fjxzq1UBQ/QikAAAAAAOAqDoVSnp6eWrBggeLi4rRq1SolJydLkqpUqaLu3burQYMGTi0S7mHZ6Jw9pQAAAADg5mI2m3Xt2jVlW7oMbnFZWVny8vLS1atX+U6cwNPTU15eXjIYDEW6jkOhlEWDBg0IoEoxOqUAAAAA4OaTmZmp1NRUpaenu7uUEsNsNisiIkK//vprkYMU5PDz81NkZKS8vb0dvkaRQimUbvmFUkWZcAAAAAAA1zGZTDp27Jg8PT0VFRUlb29vQhjlfC+XLl1SQECAdQsiOMZsNiszM1O///67jh07ppo1azr8ndoVSnl4eMjDw0Pp6eny9vaWh4fHDSe1wWDQNcu6L9yU6JQCAAAAgJtLZmamTCaTKleuLD8/P3eXU2KYTCZlZmaqTJkyhFJO4OvrK6PRqOTkZOv36gi7QqmJEyfKYDDI669NhiyvUbpZ9pQilAIAAACAmwvBC1zNGXPMrlDqhRdeKPA1SidLpxQbnQMAAAAAAGcjOkW+rl++ZzabCaUAAAAAAIDT2NUp9dFHHzl08T59+jh0HkqG60Op7Oxsmc1mSYRSAAAAAACg6OwKpfr27VvoCxsMBkKpm9z1oZSlS0oilAIAAAAA3Nw6dOigRo0aac6cOUUa4yp//vmn6tSpo+3btysmJibfcY888oiaN2+u4cOHF19xTmRXKHXs2DFX14ESyLLR+bVrhFIAAAAAANfq27evzp8/r+XLl9sc37Bhgzp27Khz586pbNmyLrl3cQdQv/32m6ZOnapvv/1Wv/32m4KDg9WwYUPNmjVL9evX17Rp03TfffflCqSGDRum5ORkffHFF5Kk8ePHq127dnrqqacUHBxcLLU7k12hVJUqVVxdB0ogOqUAAAAAAHCu48ePq3nz5urQoYMWLlyoyMhI/frrr/r888/l4+Oj9PR0vf/++1qzZk2uc7dv364ePXpYX9erV0/Vq1fXokWLNHjw4OL8GE7BRufIV16hlMFgkKflDQAAAAAAipnJZFJ8fLyqVq0qX19fNWzYUJ999pn1/dWrV6tt27YqW7asypcvr3vuuUdHjhzJ93p9+/bVxo0b9eqrr8pgMMhgMOj48ePWe40aNUohISGKiIjQCy+8YD3vo48+Uvny5ZWRkWFzvV69eumJJ57I936vv/66/P399cknn6h169aKiYnRHXfcoTlz5qhWrVpatWqVfHx81KpVK+s5mZmZMhqN2rp1q8aNGyeDwWB9v2fPnlqyZElhvsISw65OqTvvvLPQFzYYDFq/fn2hz0PJkVcoZTQaZTAY3FgVAAAAAMBeZrOUnu6ee/v5Sa74z8f4+HgtWrRIc+fOVc2aNbVp0yY9/vjjCgsLU/v27XX58mXFxcWpQYMGunTpkiZOnKgHH3xQGzZsyPN6r776qg4ePKh69erpxRdflCSFhYVJkj788EPFxcVp27Zt+uGHH9S3b1+1adNGXbp00UMPPaRnn31WK1as0EMPPSRJOnPmjFauXKm1a9fmW/+5c+d09epVpaSk5Llf1Pfff6+mTZvaHPPy8tKWLVvUsmVLJSUlKTw8XGXKlJEktWjRQtOmTVNGRoZ8fHwK+3W6lV2hlMlkKnQQYXlSG25elj2l/h5KAQAAAABuDunpUkCAe+596ZLk71+4c77++msF/K3g7Oxs658zMjI0ffp0ffvtt2rdurUkqVq1atq8ebPeeecdtW/fXg8++KDN+fPnz1dYWJj2799v031kERwcLG9vb/n5+SkiIsLmvQYNGmjSpEmSpJo1a+qNN97Q+vXr1aVLF/n6+qp379764IMPrKHUokWLFB0drQ4dOuT7GYcMGaL169erWrVqatq0qTp16qQ+ffqobt26kqTk5GRFRUXZnOPh4aGTJ0+qfPnyatiwoc17UVFRyszM1KlTp2667ZfsCqXySxNRulk6pa7f6JxQCgAAAADgKh07dtTbb79tc2zbtm16/PHHJUmHDx9Wenq6unTpYjMmMzNTjRs3liQdOnRIEydO1LZt2/THH3/IZDJJytlcvLAaNGhg8zoyMlJnzpyxvh4wYICaN2+uEydOqGLFilqwYIH69u1bYGNPkyZNdPToUW3evFlr167Vp59+qlmzZumLL75Qz549deXKFWsX1PV27NiRK5CSJF9fX0lSurta4orArlAKt6b8lu8BAAAAAG4Ofn45HUvuundh+fv7q0aNGjbHrg+TLv31YVauXKmKFSvajLMsXevZs6eqVKmiefPmKSoqSiaTSfXq1bN5gJe9/v7fwAaDwRpySVLjxo3VsGFDffTRR+ratat++eUXrVy58obX9fT0VPv27dW+fXu98MILiomJ0eLFi9WzZ0+Fhobq3Llzuc5JSkrKM5Q6e/aspP8tObyZ2BVKpaSkSJKio6NtXt+IZTxuToRSAAAAAHBzMxgKv4SuJKtbt658fHyUkpKi9u3b53r/zz//1IEDBzRv3jzdcccdkqTNmzff8Lre3t42ywQL46mnntKcOXN04sQJde7cWZUrVy7U+SaTSRkZGdZQqXHjxlq0aFGucbt37861NFGS9uzZo0qVKik0NNSh+t3JrlAqJiZGBoNBV65ckbe3t/X1jTj6DxQlA3tKAQAAAABKksDAQI0YMULDhg2TyWRS27ZtdeHCBW3ZskVBQUF64oknVL58eb377ruKjIxUSkqKnn/++RteNyYmRtu2bdPx48cVEBCgkJAQu2vq3bu3RowYoXnz5umjjz4qcOwTTzyhunXr6s4771R4eLiOHj2q6dOnS5KGDh0qSerWrZvGjBmjc+fOqVy5ctZzTSaTDhw4oJMnT8rf31/BwcGScjZG79q1q931liR2hVLz58+XwWCwBhKW1yjdrt9TKjMzUxKhFAAAAADAvaZMmaKwsDDFx8fr6NGjKlu2rJo0aaKxY8fKw8NDS5Ys0bPPPqt69eqpdu3aeu211wrceFySRowYodjYWNWtW1dXrlzRsWPH7K4nODhYDz74oFauXKlevXoVOLZJkyb67LPPNHv2bF26dEmVK1dW165dtWDBAlWqVEmSVL9+fTVp0kRLly7V008/bT136tSpGj16tKZPn64RI0bopZde0tWrV7V8+XKtXr3a7npLErtCqb59+xb4GqUTy/cAAAAAAMVlwYIFeR7v0KGDzGaz9bXBYNBzzz2n5557Ls/xnTt31t69e22OZWdnKy0tzfr67w90q1Wrln744QebY3k99G358uV53vPEiRN67LHHrPta5WfYsGEaNmxYgWMkaeLEiRo5cqQGDBggDw8PSdLjjz9u3fDd4oMPPlCLFi3yfKrgzYCNzpGvvEIpb29vN1YEAAAAAEDJce7cOW3YsEEbNmzQW2+95bTr9ujRQ4cOHdKJEycK3KPKaDTq9ddfd9p9i5vDodTly5f1+eef6+jRozp37pxNainlJJevvvpqkQuE+9ApBQAAAABA/ho3bqxz585pxowZql27tlOvbdljqiBPPfWUU+9Z3BwKpdavX6+HHnpI58+fz3cModTNj43OAQAAAADI3/Hjx91dwk3Nw5GTBg8eLH9/f61Zs0bnz5+XyWTK9cOT925+1290TigFAAAAAACcyaFOqZSUFM2YMUNdunRxdj0oQVi+BwAAAAAAXMWhTqkGDRrowoULzq4FJQyhFAAAAAAAcBWHQqkZM2borbfe0s8//+zselCCsKcUAAAAAABwFYeW77Vv315z5sxR69atVadOHVWuXFmelraavxgMBn355ZdOKRLuwZ5SAAAAAADAVRwKpT7//HM9/vjjys7O1m+//aaLFy/mGmMwGIpcHNzr+uV7mZmZkgilAAAAAACAczgUSj3//POqXbu2Pv/8c9WqVcvZNaGEyGtPKW9vbzdWBAAAAAAASguH9pQ6efKkBg4cSCBVyl0fSl27dk2S5OXlUI4JAAAAAABgw6FQqnnz5kpJSXF2LShhLPnTtWv/C6VYvgcAAAAAAJzBoVDq9ddf15IlS7R06VJn14MShE4pAAAAAADgKg6FUo899piuXbumRx99VMHBwfrHP/6hBg0a2Pw0bNjQ2bWimBFKAQAAAABKKrPZrP/3//6fQkJCZDAYlJSU5O6SbHTo0EFDhw4t9Hl//vmnKlSooOPHjxc47pFHHtGsWbMcK66EcChhCAkJUfny5VWzZk1n14MSJK+NzgmlAAAAAACu0LdvX50/f17Lly+3a/zq1au1YMECbdiwQdWqVVNoaGiRa+jQoYMaNWqkOXPmFPla9mrfvr2qV6+u+fPnS5KmTZum++67TzExMdYxw4YNU3Jysr744gvrsfHjx6tdu3Z66qmnFBwcXGz1OpNDCcOGDRucXAZKorz2lCKUAgAAAACUBEeOHFFkZKRuv/12d5fiMLPZrB07duihhx6SJKWnp+v999/XmjVrbMZt375dPXr0sDlWr149Va9eXYsWLdLgwYOLrWZncmj5Hm4Nlvzp+uV7bHQOAAAAACgOHTp00LPPPqtRo0YpJCREEREReuGFFyTldFX9+9//VkpKigwGg7WryGQyKT4+XlWrVpWvr68aNmyozz77zOa6JpNJM2fOVI0aNeTj46Po6GhNmzZNffv21caNG/Xqq6/KYDDIYDBYl9Dd6LqXL19Wnz59FBAQoMjISLuX1R06dEgXL15U06ZNJUmrVq2Sj4+PWrVqJUnKzMyU0WjU1q1bNW7cOBkMBut7ktSzZ08tWbLEka+3RLCr7eWHH35Q69atHbpBUc6Fe1mW79EpBQAAAAA3KbNZSk93z739/CSDoUiX+PDDDxUXF6dt27bphx9+UN++fdWmTRu9+uqrql69ut5991399NNP8vzrP2Dj4+O1aNEizZ07VzVr1tSmTZv0+OOP65tvvlHjxo0lSWPGjNG8efP0yiuvqG3btkpNTdX+/fs1ZMgQHTx4UPXq1dOLL74oSQoLCyvwumFhYWrfvr1GjhypjRs36ssvv1SFChU0duxYJSYmqlGjRgV+voSEBHl6elr35f7++++tAZWU89/gW7ZsUcuWLZWUlKTw8HCVKVPG+n6LFi00bdo0ZWRkyMfHp0jftTvYlTDceeedatWqlQYOHKh77rlHfn5+BY6/dOmSVqxYoblz5+rnn39Wurv+B4AiyatTilAKAAAAAG4i6elSQIB77n3pkuTvX6RLNGjQQJMmTZIk1axZU2+88YbWr1+vLl26KDAwUJ6enoqIiJAkZWRkaPr06fr222+tzTHVqlXT5s2b9e677+rtt9/WxYsX9eqrr+qNN95QbGysJKl69epq27atJMnb21t+fn7Wa97ouu+8846aNm2q999/X4sWLVKnTp0k5YRplSpVuuHnS0xMVO3ata05S3JysqKioqzve3h46OTJkypfvnyeD5SLiopSZmamTp06pSpVqhTuyy0B7EoYDh48qBdffFFPPPGEjEajWrZsqSZNmqhq1aoqV66czGazzp07p2PHjunnn3/W9u3bde3aNfXp00f//e9/Xf0Z4CLsKQUAAAAAcKcGDRrYvI6MjNSZM2fyHHv48GGlp6erS5cuNsczMzOtXVL79u1TRkaGNTyyx42ue+TIEWVmZqply5bW90JCQlS7du0bXjsxMdGmM+rKlSs2nVCStGPHjjwDKUny9fWVpJu2GciuhKFy5cqaN2+e4uPjtXDhQn355Zd66623dOXKFZtxvr6+atasmaZOnaonnnjC2uaGmxPL9wAAAADgJufnl9Ox5K57F9Hf9zU2GAwymUx5jr301+dcuXKlKlasmOd1LCFOYRR0XR8fH509e7bQ17RITExUz549ra9DQ0N17tw5mzFJSUn5hlKWe9+s+UuhEobQ0FANGzZMw4YN07Vr15SSkqI///xTklS+fHlFR0cTWpQi1y/fy8rK+usY/3wBAAAA4KZhMBR5Cd3Nom7duvLx8VFKSorat29v857JZFJaWppq1qwpX19frV+/Xk899VSua3h7eys7O9vu60pSuXLlZDQatW3bNkVHR0uSzp07p4MHD+Y53uLo0aM6f/68TadU48aNtWjRIptxu3fv1oMPPpjnNfbs2aNKlSopNDQ03/uUZA4nDF5eXqpWrZqqVavmzHpQgtApBQAAAAC4WQQGBmrEiBEaNmyYTCaT2rZtqwsXLmjLli0KCAjQ/fffrzJlymj06NEaNWqUvL291aZNG/3+++/65Zdf1L9/f8XExGjbtm06fvy4AgICFBISUuB1g4KCFBsbq/79+2vkyJEqX768KlSooHHjxsnDw6PAehMSEmQwGGw2Q+/WrZvGjBmjc+fOqVy5cpJyArUDBw7o5MmT8vf3V3BwsHX8999/r65du7rk+ywOBX9DuKXltafU31snAQAAAAAoKaZMmaIJEyYoPj5ederU0V133aWVK1eqatWq1jETJkzQ8OHDNXHiRNWpU0cPP/ywdZ+qESNGyNPTU3Xr1lVYWJhSUlLsuu5LL72kO+64Qz179lTnzp3Vtm1bmw6ovCQmJqpmzZoKDAy0Hqtfv76aNGmipUuXWo9NnTpVCxYsUMWKFTV16lTr8atXr2r58uUaMGBA0b84NzGYzWazu4twp7S0NAUHB+vChQsKCgpydzlFkpWVpVWrVql79+5OCY9++02qXFny9pa6dbtXX331ld577z3179/fCdXCnZw9V1B6MVdgD+YJ7MVcgb2YK7AXcyW3q1ev6tixY6patWquDbNvZZble0FBQTfsYHK3lStXauTIkdqzZ0+Btb799ttatmyZ1q5dW4zV/U9Bc83erIW1WMgXy/cAAAAAAChePXr00KFDh3TixAlVrlw533FGo1Gvv/56MVbmfCQMyJclfzKZCKUAAAAAACguQ4cOveGYvDZqv9mU7J41uNX1+VNWFqEUAAAAAABwHkIp5MuyfE8ilAIAAAAAAM7lcMKwb98+ffDBBzp69KjOnTunv++XbjAYtH79+iIXCPex7ZTK+usYoRQAAAAAACg6hxKGhQsXql+/fjIajapdu7bKlSuXa8wt/lC/UoHlewAAAAAAwFUcShheeOEFNW7cWN98841CQ0OdXRNKiOuX71k2OucxqwAAAAAAwBkc2lPq5MmTevLJJwmkSjmP62YHnVIAAAAAAMCZHAqlGjRooJMnTzq7FpQwBsP/lvBZOqUIpQAAAAAAgDM4FErNnj1b77//vrZu3erselDCWJbwEUoBAAAAAABncihhmDFjhoKDg3XHHXeobt26io6Oluf1GxAp5+l7X375pVOKhPt4eUkZGYRSAAAAAADAuRxKGHbt2iWDwaDo6GhdunRJe/fuzTXGYDAUuTi4nyWDysrK+us1oRQAAAAAAMWlQ4cOatSokebMmVPka/3555+qU6eOtm/frpiYmDzHPPLII2revLmGDx9e5PvdiEPL944fP65jx44V+HP06FFn1wo3YPkeAAAAAKA49O3bVwaDQQaDQUajUVWrVtWoUaN09epVd5dW4rVv39763Xl7e6tOnTpavHhxrnHTpk3TfffdZxNIDRs2TA888ID19fjx4zVt2jRduHDB5XU7FErh1mHJoLKzc0Ipo9HoxmoAAAAAAKXZXXfdpdTUVB09elSvvPKK3nnnHU2aNMndZRVZZmamy65tNpu1Y8cOvfzyy0pNTdWBAwd01113qU+fPjp27Jh1XHp6ut5//33179/f5vzt27erWbNm1tf16tVT9erVtWjRIpfVbFGkUGrjxo0aNWqUHn74YT388MMaNWqUNm7c6KzaUALw9D0AAAAAQHHx8fFRRESEKleurF69eqlz585at26d9X2TyaT4+HhVrVpVvr6+atiwoT777DOba5hMJs2cOVM1atSQj4+PoqOjNX36dElSRkaGnn32WVWoUEFlypRR27Zt9dNPP1nPfffddxUVFSWTyWRzzfvuu09PPvmk3TV06NBBQ4YM0dChQxUaGqpu3brZdd7ly5fVp08fBQQEKDIyUrNmzbrhd3bo0CFdvHhRd911lyIiIlS1alX1799f2dnZOnDggHXcqlWr5OPjo1atWknKCcqMRqO2bt2qcePGyWAwWN/r2bOnlixZcsN7F5VDCUNmZqYeffRRLV++XGazWWXLlpUknT9/XrNmzdL999+vjz/+mK6aUsCyfM/SKUUoBQAAAAA3D7PZrPSsdLfc28/oV6T9pvfs2aOtW7eqSpUq1mPx8fFatGiR5s6dq5o1a2rTpk16/PHHFRYWpvbt20uSxowZo3nz5umVV15R27ZtlZqaat0Le/To0fr888/14YcfqkqVKpo5c6a6deumw4cPKyQkRA899JD+/e9/6//+7//UqVMnSdLZs2e1evVqrVq1yu4aJOnDDz/UwIEDtWXLFrvPGzlypDZu3Kgvv/xSFSpU0NixY5WYmKhGjRrl+z0lJCSoXLlyqlu3riTpt99+07hx4+Tj46MGDRpYx33//fdq2rSp9bWXl5e2bNmili1bKikpSeHh4SpTpowkqUWLFpo2bZoyMjLk4+Pj2D9AOziUMEyePFnLli3TiBEjNHz4cIWHh0uSzpw5o1mzZumll17Siy++qClTpji1WBS/vy/fI5QCAAAAgJtHela6AuID3HLvS2Muyd/bv1DnfP311woICNC1a9eUkZEhDw8PvfHGG5JyupymT5+ub7/9Vq1bt5YkVatWTZs3b9Y777yj9u3b6+LFi3r11Vf1xhtvKDY2VpJUvXp13X777UpNTdXcuXO1YMEC3X333ZKkefPmad26dXr//fc1cuRIlStXTnfffbcWL15sDaU+++wzhYaGqmPHjnbVYFGzZk3NnDnT7tovXbqk999/X4sWLbLe+8MPP1SlSpUK/M4SExN14cIFBQYGKjs7W1evXpWvr6/mzp2rqKgo67jk5GSb1x4eHjp58qTKly+vhg0b2lwzKipKmZmZOnXqlE0o6GwOJQyLFy9WbGys9cu1qFChgmbMmKHTp09r4cKFhFKlAJ1SAAAAAIDi0rFjR7399tu6fPmyXnnlFXl5eenBBx+UJB0+fFjp6enq0qWLzTmZmZlq3LixJGnfvn3KyMiwhjrXO3bsmLKystSmTRvrMaPRqBYtWmjfvn3WY4899pgGDBigt956Sz4+Pvrvf/+rRx55RB4eHnbVYHF9V5I95x05ckSZmZlq2bKl9f2QkBDVrl27wO8sMTFRgwcP1rPPPqvz589rxIgRatOmjfr27Wsz7sqVK9ZOKIsdO3bkCqQkydfXV1LOPlSu5FDCkJqaavMl/V3Lli2LZe0hXC8ngzIrOzv7r9eEUgAAAABws/Az+unSmEtuu3dh+fv7q0aNGpKk+fPnq2HDhtbNuS9dyvkcK1euVMWKFW3Osywxs4QpRdGzZ0+ZzWatXLlSzZs31/fff69XXnlFkuyq4frPYlGY8worMTFRAwYMsH5vb731lho0aKABAwbYPGUvNDRU586dszk3KSkpz1Dq7NmzkqSwsLAi1XYjDm10XqlSJW3YsCHf9zdu3HjD9jLcHHIyqGvXvSaUAgAAAICbhcFgkL+3v1t+irKflJSzvGzs2LEaP368rly5orp168rHx0cpKSmqUaOGzU/lypUl5SyZ8/X11fr163Ndr2rVqvL29rbu8SRJWVlZ+umnn6z7MUlSmTJl9MADD+i///2vPv74Y9WuXVtNmjSRJLtqyIs951WvXl1Go1Hbtm2znnfu3DkdPHgw3+sePXpU58+fV7169WzuVb16dS1evNhmbOPGja17a1ns3r07z/2q9uzZo0qVKik0NDTfezuDQwlDbGysJk2apLJly2rYsGGqUaOGDAaDDh06pDlz5ujTTz/V5MmTnV0r3CBn+R6hFAAAAACg+D300EMaOXKk3nzzTY0YMUIjRozQsGHDZDKZ1LZtW124cEFbtmxRUFCQYmNjVaZMGY0ePVqjRo2St7e32rRpo99//127d+/WQw89pGeeeUYjR45USEiIoqOjNXPmTKWnp6t///42933sscd0zz336JdfftHjjz9uPR4YGHjDGvJiz3kBAQHq37+/Ro4cqfLly6tChQoaN26cPDzy7ydKSEiQ0WhUrVq1bI536tRJy5Yt09ixY63HunXrpjFjxujcuXMqV66cpJwnCR44cEAnT56Uv7+/goODJeVsit61a9fC/cNygEMJw9ixY3XkyBG9++67mjdvnvULMplMMpvNio2NtfnguHn9vVOKJyoCAAAAAIqLl5eXhgwZopkzZ2rgwIGaMmWKwsLCFB8fr6NHj6ps2bJq0qSJTQYxYcIEeXl5aeLEiTp58qQiIyP19NNPS8p5Ap7ZbNYTTzyhixcvqlmzZlqzZo01pLG48847FRISogMHDqh3794279lTQ17sOe+ll17SpUuX1LNnTwUGBmr48OG6cOFCvtdMTExUzZo15e3tbXO8c+fOmjt3rn777TfrSrb69eurSZMmWrp0qfX7mDp1qkaPHq3p06drxIgReumll3T16lUtX75cq1evLvDzOIPBbDabHT15165dWrVqlZKTkyVJVapUUffu3W0eOVjSpaWlKTg4WBcuXFBQUJC7yymSrKwsrVq1St27d3daeNSqlbRt2zlJIdZ70C1183PFXEHpxFyBPZgnsBdzBfZirsBezJXcrl69qmPHjqlq1aq5NrW+lZlMJqWlpSkoKKjAzqPSbuXKlRo5cqT27NmT7/fw9ttva9myZVq7dm2B1yportmbtRQpXWjQoMFNFUCh8P6+fM/T8jg+AAAAAABwU+nRo4cOHTqkEydO5LsHltFo1Ouvv14s9dDyggJdv3zP09OzyBvVAQAAAAAA9xk6dGiB7z/11FPFU4jsDKU8PDzk4eGh9PR0eXt7y8PD44bhhMFg0LVr1wocg5Lv+lCKZXsAAAAAAMBZ7EoZJk6cKIPBYA0lLK9R+uWs1suSRCgFAAAAAACcx66U4YUXXijwNUovOqUAAAAAAIArOLTl/Isvvqg9e/bk+/4vv/yiF1980eGiUHJcH0rxNAsAAAAAAOAsDoVSL7zwgnbt2pXv+3v27NHkyZMdLgolx/VP36NTCgAAAAAAOItDodSNnD17Vt7e3q64NIoZy/cAAAAAAIAr2J0ybNq0SRs2bLC+/uKLL3T48OFc486fP69PPvlE9evXd0qBcC9CKQAAAAAA4Ap2pwz/93//Z12SZzAY9MUXX+iLL77Ic2zdunX1+uuvO6dCuBXL9wAAAAAAgCvYnTKMGjVKQ4YMkdlsVoUKFTR37lw9+OCDNmMMBoP8/PxUpkwZpxcK98jJobL++jOhFAAAAAAAcA67UwZfX1/5+vpKko4dO6awsDD5+fm5rDCUDCzfAwAAAADA9Tp06KBGjRppzpw5Trnen3/+qTp16mj79u2KiYnJd9wjjzyi5s2ba/jw4U65b2E4tNF5lSpVCKRuEdcv3zMajW6tBQAAAABQevXt21cGg0EGg0FGo1Hh4eHq0qWL5s+fL5PJ5O7ySoT27dtbvyMvLy9FRkbqgQce0I8//phr7LRp03TffffZBFLDhg3TAw88YDNu/PjxmjZtmi5cuODq8nNx+Ol7u3bt0oABA9S0aVPVqFFD1apVs/mpXr26M+uEm9ApBQAAAAAoLnfddZdSU1N1/PhxffPNN+rYsaOee+453XPPPbp27Zq7y3Mrs9msHTt26D//+Y9SU1N1+PBhLV68WB4eHrrjjju0bt0669j09HS9//776t+/v801tm/frmbNmtkcq1evnqpXr65FixYVy+e4nkOh1IYNG9SiRQt9/fXXioqK0tGjR1WtWjVFRUUpOTlZAQEBateunbNrhRuw0TkAAAAAoLj4+PgoIiJCFStWVJMmTTR27Fh9+eWX+uabb7RgwQJJkslkUnx8vKpWrSpfX181bNhQn332mc11TCaTZs6cqRo1asjHx0cxMTF6+eWX7T5/9erVatu2rcqWLavy5cvrnnvu0ZEjR6zvf/bZZ6pfv758fX1Vvnx5de7cWZcvX7a5f0H3uHz5svr06aOAgABFRkZq1qxZN/xuDh06pIsXL6pdu3aKiIhQTEyMOnbsqE8//VStW7fWuHHjrGNXrVolHx8ftWrVSpKUmZkpo9GorVu3aty4cTIYDNb3JKlnz55asmTJDWtwNodShokTJ6patWr68ccflZmZqQoVKmjs2LG68847tW3bNt19992aMWOGs2uFG9ApBQAAAAA3L7PZrPT0dLfc28/PTwaDocjXufPOO9WwYUN98cUXeuqppxQfH69FixZp7ty5qlmzpjZt2qTHH39cYWFhat++vSRpzJgxmjdvnl555RW1bdtWJ06cUFJSkiTZdf7ly5cVFxenBg0a6NKlS5o4caLuv/9+JSUl6fTp03r00Uc1c+ZM3X///bp48aK+//57mc1ma803usfIkSO1ceNGffnll9ZMJTExUY0aNcr3e0hISJCnp6caNmxoc9xgMKhLly6aMmWK9dj333+vpk2bWl97eXlpy5YtatmypZKSkhQeHm7zkLoWLVpo2rRpysjIkI+Pj8P/rArLoZQhMTFRkydPVlBQkM6dOydJys7OliS1bNlSTz/9tCZMmKC7777beZXCLQilAAAAAODmlZ6eroCAALfc+9KlS/L393fKtW677Tbt2rVLGRkZmj59ur799lu1bt1aklStWjVt3rxZ77zzjtq3b6+LFy/q1Vdf1RtvvKHY2FhJUtWqVdWgQQO7zpekBx980Ob+8+fPV1hYmPbu3avMzExdu3ZNDzzwgKpUqSJJql+/vnXsje7RtGlTvf/++1q0aJE6deokSfrwww9VqVKlAr+DxMRE1a5dO889vr29vW32gU5OTlZUVJT1tYeHh06ePKny5cvnCrUkKSoqSpmZmTp16pT1MxUHh1IGLy8vBQYGSpLKli0ro9GoM2fOWN+vVq2a9u7d65wK4VYs3wMAAAAAuJvZbJbBYNDhw4eVnp6uLl262LyfmZmpxo0bS5L27dunjIwMa+BzPXvOl3KWyk2cOFHbtm3TH3/8Yd1oPSUlRd26dVOnTp1Uv359devWTV27dtU///lPlStXzq57HDlyRJmZmWrZsqX1vZCQENWuXbvA7yAxMdGm++l6Bw4c0G233WZ9feXKFZtOKEnasWNHnoGUJPn6+kpSsXfVOZQy1KhRQ4cOHZKU0yZ22223admyZXrsscckSStXrlRERITzqoTb5ORQWX/9mVAKAAAAAG4mfn5+unTpktvu7Sz79u1T1apVrZ9l5cqVqlixos0Yy7IzS8CSF3vOl3L2WKpSpYrmzZunqKgomUwm1atXT5mZmfL09NS6deu0detWrV27Vq+//rrGjRunbdu22VXj2bNnHfoOEhMT1bNnz1zHL1++rBUrViguLs56LDQ01LqyzSIpKSnfUMpSU1hYmEO1OcqhlKF79+6aP3++4uPj5eXlpbi4OPXr1081a9aUJB05ckTx8fFOLRTuwfI9AAAAALh5GQwGpy2hc5fvvvtOu3fv1rBhw1S3bl35+PgoJSXFutTu72rWrClfX1+tX79eTz31lM179pz/559/6sCBA5o3b57uuOMOSdLmzZttxhgMBrVp00Zt2rTRxIkTVaVKFS1btkxxcXE3vEe5cuVkNBq1bds2RUdHS5LOnTungwcP5lvT0aNHdf78eTVp0sTmeHZ2tp555hn5+vpq8ODB1uONGzfO9TS93bt351qWaLFnzx5VqlRJoaGheb7vKg6lDBMmTNBzzz0nz5y1XYqNjZWnp6c+//xzeXp6aty4cerbt68z64SbXL987/r1qQAAAAAAOFtGRoZOnTql7OxsnT59WqtXr1Z8fLzuuece9enTR56enhoxYoSGDRsmk8mktm3b6sKFC9qyZYuCgoIUGxurMmXKaPTo0Ro1apS8vb3Vpk0bnT59WgkJCRo8ePANzy9XrpzKly+vd999V5GRkUpJSdHzzz9vrXHbtm1av369unbtqgoVKmjbtm36/fffVadOHUlSYGDgDe/Rv39/jRw5UuXLl1eFChU0btw4eXh45Pu9JCQkSJIiIyN16tQppaWlKSEhQa+++qp+/fVXff311woODraO79atm8aMGaNz585ZlxWaTCYdOHBAJ0+elL+/v83477//Xl27dnXqP0t7OBRKGY1GlS9f3ubY448/rscff9wpRaHkoFMKAAAAAFBcVq9ercjISHl5ealcuXJq2LChXnvtNcXGxlpDmylTpigsLEzx8fE6evSoypYtqyZNmmjs2LHW60yYMEFeXl6aOHGiTp48qcjISOum5zc638PDQ0uWLNGzzz6revXqqXbt2nrttdfUoUMHSVJQUJA2bdqkOXPmKC0tTVWqVNGsWbNsHvZ2o3u89NJLunTpknr27KnAwEANHz5cFy5cyPd7SUxMlCTVqlVLnp6eKlu2rGrXrq17771XzzzzjEJCQmzG169fX02aNNHSpUv19NNPS5KmTp2q0aNHa/r06RoxYoReeuklSdLVq1e1fPlyrV692uF/bo4ymK9/ZuEtKC0tTcHBwbpw4YKCgoLcXU6RZGVladWqVerevbvTuppeflkaOXKOpGHq3bu3/vvf/zrlunAvV8wVlE7MFdiDeQJ7MVdgL+YK7MVcye3q1as6duyYqlatmmuj61uZyWRSWlqagoKCCuxIKk1WrlypkSNHas+ePQV+5rffflvLli3T2rVrC3X9guaavVmLXa0vd955Z6EKk3LWV65fv77Q56Fk4el7AAAAAADcfHr06KFDhw7pxIkTqly5cr7jjEajXn/99WKs7H/sShlMJpMMBkOhLnyLN2CVGizfAwAAAADg5jR06NAbjvn7ZvDFya6UYcOGDS4uAyVVTg6V9defCaUAAAAAAIBz3BoLKeEwlu8BAAAAAABXcChlSElJsWtcdHS0I5dHCXL98j02DgQAAAAAAM7iUCgVExNj1x5T2dnZjlweJQh7SgEAAADAzYd9nuFqzphjDqUM8+fPzxVKZWdn6/jx4/roo49UoUIFDR48uMjFwf1YvgcAAAAANw/LCpf09HT5+vq6uRqUZunp6ZKKtqrKoZShb9+++b43evRotWzZUhcuXHC0JpQgdEoBAAAAwM3D09NTZcuW1ZkzZyRJfn5+dq10Ku1MJpMyMzN19epVeXiwvXZRmM1mpaen68yZMypbtqw8c7pZHOL0lMHf31/9+vXTK6+8omeffdbZl0cxI5QCAAAAgJtLRESEJFmDKeQEKVeuXJGvry8hnZOULVvWOtcc5ZKUwWQy6dSpU664NIoZy/cAAAAA4OZiMBgUGRmpChUqKCsry93llAhZWVnatGmT2rVrx0O8nMBoNBapQ8rCqSlDWlqaNm3apJdeekmNGzd25qXhJjk5VNZffyaUAgAAAICbhaenp1OCg9LA09NT165dU5kyZQilShCHUgYPD498293MZrOio6P11ltvFakwlAx0SgEAAAAAAFdwKGWYOHFirlDKYDCoXLlyql69urp27UqAUUpcv6cUaTIAAAAAAHAWh5KjF154wclloKRio3MAAAAAAOAKRU4Zzpw5o+PHj0uSYmJiVKFChaJeEiUIy/cAAAAAAIAreDh64vr169WsWTNFRkaqdevWat26tSIjI9WsWTN9++23zqwRbkSnFAAAAAAAcAWHUoZly5bpoYceUnh4uEaNGqVatWpJkg4cOKCFCxfq7rvv1tKlS3X//fc7tVgUP0IpAAAAAADgCg6lDOPHj1e9evX0/fffKzAw0Oa9sWPHqm3btho/fjyhVCmQs3wvSxKhFAAAAAAAcB6Hlu8dPXpU/fr1yxVISVJQUJD69++vY8eOOVzUm2++qZiYGJUpU0YtW7bU9u3b7TpvyZIlMhgM6tWrl8P3hi06pQAAAAAAgCs4FErddtttOnPmTL7vnz592rqkr7A++eQTxcXFadKkSUpMTFTDhg3VrVu3Au8nScePH9eIESN0xx13OHRf5O36UMpoNLq1FgAAAAAAUHo4FErNnDlTc+fO1ZdffpnrvWXLlumdd97Ryy+/7FBBs2fP1oABA9SvXz/VrVtXc+fOlZ+fn+bPn5/vOdnZ2Xrsscc0efJkVatWzaH7Im88fQ8AAAAAALiCQynD66+/rrCwMD3wwAOKiopSjRo1JEmHDx/WyZMnVatWLb322mt67bXXrOcYDIY8Q6zrZWZmKiEhQWPGjLEe8/DwUOfOnfXDDz/ke96LL76oChUqqH///vr+++8LvEdGRoYyMjKsr9PS0iRJWVlZysrKKvDcks5SvzM/h9ksWUIpZ18b7uOKuYLSibkCezBPYC/mCuzFXIG9mCuwF3OleNn7PTsUSu3atUsGg0HR0dGScpbOSTmdNNHR0bp69ap2795tc47BYLjhdf/44w9lZ2crPDzc5nh4eLj279+f5zmbN2/W+++/r6SkJLtqj4+P1+TJk3MdX7t2rfz8/Oy6Rkm3bt06p13r9GlfWUKpxMREmXNSKpQSzpwrKN2YK7AH8wT2Yq7AXswV2Iu5AnsxV4pHenq6XeMcCqUsIZS7Xbx4UU888YTmzZun0NBQu84ZM2aM4uLirK/T0tJUuXJlde3aVUFBQa4qtVhkZWVp3bp16tKli9P2f/r1V8kSSt1+++3q2LGjU64L93LFXEHpxFyBPZgnsBdzBfZirsBezBXYi7lSvCyr0m6kRG0SFBoaKk9PT50+fdrm+OnTpxUREZFr/JEjR3T8+HH17NnTesxkMknK6do6cOCAqlevbnOOj4+PfHx8cl3LaDSWmonpzM/i6ytJOW13ZcqUKTXfEXKUpnkP12KuwB7ME9iLuQJ7MVdgL+YK7MVcKR72fsdFCqU2btyolStXKjk5WZJUpUoV9ejRQ+3bt3foet7e3mratKnWr1+vXr16ScoJmdavX68hQ4bkGn/bbbflWiY4fvx4Xbx4Ua+++qoqV67sUB34n+ufvufpWaIyTAAAAAAAcBNzKGXIzMzUo48+quXLl8tsNqts2bKSpPPnz2vWrFm6//779fHHHzuUPsbFxSk2NlbNmjVTixYtNGfOHF2+fFn9+vWTJPXp00cVK1ZUfHy8ypQpo3r16tmcb6nl78fhmOufvmcwEEoBAAAAAADn8HDkpMmTJ2vZsmUaPny4UlNTdfbsWZ09e1anTp3SiBEj9MUXX+jFF190qKCHH35YL7/8siZOnKhGjRopKSlJq1evtm5+npKSotTUVIeujcKz7ZSixREAAAAAADiHQ60vixcvVmxsrGbOnGlzvEKFCpoxY4ZOnz6thQsXasqUKQ4VNWTIkDyX60nShg0bCjx3wYIFDt0Tebs+lCphW5ABAAAAAICbmEOdUqmpqWrZsmW+77ds2VKnTp1yuCiUHCzfAwAAAAAAruBQKFWpUqUCO5Y2btyoSpUqOVoTSpDrO6UIpQAAAAAAgLM4FErFxsZq6dKleuaZZ3TgwAFlZ2fLZDLpwIEDGjhwoD799FP17dvXyaXCHTw8JJbvAQAAAAAAZ3MoZRg7dqyOHDmid999V/PmzZNHTnIhk8kks9ms2NhYjR071qmFwj0MBknK+usVoRQAAAAAAHAOh1IGT09PLViwQHFxcVq5cqVSUlIkSVWqVFH37t3VoEEDpxYJd2P5HgAAAAAAcK5CpQxXr17Vl19+qWPHjik0NFQ9evTQmDFjXFUbSgCTySTJJEkyGIzuLQYAAAAAAJQadodSZ86c0e23365jx47JbDZLkvz8/LR8+XJ17tzZZQXCvbKzs697RacUAAAAAABwDrs3Op8yZYqOHz+uYcOG6euvv9acOXPk6+urp59+2pX1wc2uXbt23StCKQAAAAAA4Bx2pwxr165Vnz599PLLL1uPhYeHq3fv3jpw4IBq167tkgLhXoRSAAAAAADAFezulEpJSVHbtm1tjrVt21Zms1mnT592emEoGQilAAAAAACAK9gdSmVkZKhMmTI2xyyvbYMLlCZZWVnWP5vNnm6sBAAAAAAAlCaFan05fvy4EhMTra8vXLggSTp06JDKli2ba3yTJk2KVh3c7n+Bo6eysw1urQUAAAAAAJQehQqlJkyYoAkTJuQ6PmjQIJvXZrNZBoPhb09uw83of6GUUTTEAQAAAAAAZ7E7lPrggw9cWQdKqP+FUl66biUfAAAAAABAkdgdSsXGxrqyDpRQhFIAAAAAAMAV7N7oHLem60OpzEy3lgIAAAAAAEoRQikUiE4pAAAAAADgCoRSKBChFAAAAAAAcAVCKRQoy5pEsXwPAAAAAAA4D6EUCkSnFAAAAAAAcAVCKRTof6GUkVAKAAAAAAA4DaEUCsTT9wAAAAAAgCsQSqFALN8DAAAAAACuQCiFAhFKAQAAAAAAVyCUQoFYvgcAAAAAAFyBUAoFyrK2R9EpBQAAAAAAnIdQCgVi+R4AAAAAAHAFQikU6H+hlJHlewAAAAAAwGkIpVAgOqUAAAAAAIArEEqhQIRSAAAAAADAFQilUCCevgcAAAAAAFyBUAoFolMKAAAAAAC4AqEUCkSnFAAAAAAAcAVCKRQoy9oeRacUAAAAAABwHkIpFIjlewAAAAAAwBUIpVCg/4VSRpbvAQAAAAAApyGUQoHolAIAAAAAAK5AKIUCEUoBAAAAAABXIJRCgXj6HgAAAAAAcAVCKRSITikAAAAAAOAKhFIoUJY1iSKUAgAAAAAAzkMohQKxfA8AAAAAALgCoRQK9L9QykinFAAAAAAAcBpCKRSIPaUAAAAAAIArEEqhQCzfAwAAAAAArkAohQLRKQUAAAAAAFyBUAoFIpQCAAAAAACuQCiFAmVZkyiW7wEAAAAAAOchlEKB6JQCAAAAAACuQCiFAv0vlDLq2jXJbHZrOQAAAAAAoJQglEKBru+UkkS3FAAAAAAAcApCKRSIUAoAAAAAALgCoRQK9PdQis3OAQAAAACAMxBKoUB0SgEAAAAAAFcglEKBLKGUhwehFAAAAAAAcB5CKRQo668Uymhk+R4AAAAAAHAeQikUyNIp5eVFpxQAAAAAAPj/7d17eNP13f/xV9qk6fnAsZyLyjjIGUZXmZf3sFC5mcqcoAyF4dRbARXZvZu5awM3fwoecIpDnE5lUxTFKZsHDgUBLwVBTiKCDJSTQCkFej6lzff3R5q0IUlJ2zRpw/NxXbnyzff7SfpOfRu71z6fTwKHUAr1qg2lLJIIpQAAAAAAQGAQSqFezlCK5XsAAAAAACCQCKVQL5bvAQAAAACA5kAohXpdOFOKUAoAAAAAAAQCoRTqxfI9AAAAAADQHAilUC9bzdQoZkoBAAAAAIBAIpRCvVi+BwAAAAAAmgOhFOrlDKWioiySWL4HAAAAAAACg1AK9aoNpZgpBQAAAAAAAodQCvUilAIAAAAAAM2BUAo+2e122e12SbWhFMv3AAAAAABAIBBKwafq6mrXMTOlAAAAAABAIBFKwSfn0j1JslqZKQUAAAAAAAKHUAo+2epMi2KmFAAAAAAACCRCKfhUd6YUoRQAAAAAAAgkQin45L58L1ISy/cAAAAAAEBgEErBJ2coZTabFRVlksRMKQAAAAAAEBiEUvCpbihlsTjOEUoBAAAAAIBAIJSCT+4zpRznWL4HAAAAAAACgVAKPjFTCgAAAAAANBdCKfhkq0mgCKUAAAAAAECgEUrBJ5bvAQAAAACA5kIoBZ+coZTFYnGFUhUVISwIAAAAAACEDUIp+FR3plRMjONceXkICwIAAAAAAGGDUAo+eQulyspCWBAAAAAAAAgbhFLwqe5G54RSAAAAAAAgkAil4JMzlLJYLIRSAAAAAAAgoAil4FPd5XvR0Y5zhFIAAAAAACAQCKXgEzOlAAAAAABAcyGUgk/eQim+fQ8AAAAAAAQCoRR8YqYUAAAAAABoLoRS8IlQCgAAAAAANBdCKfhEKAUAAAAAAJoLoRR88hZKVVU5bgAAAAAAAE1BKAWf6oZS0dG159nsHAAAAAAANBWhFHxyhlJms9ktlGIJHwAAAAAAaCpCKfhUVbNOz2KxKCJCslod5wmlAAAAAABAUxFKwae6y/cksdk5AAAAAAAIGEIp+EQoBQAAAAAAmguhFHwilAIAAAAAAM2FUAo+uUKpykpp2zbXZud8+x4AAAAAAGgqQin45Aql3n9fSk9Xb9N/JDFTCgAAAAAANB2hFHxyhVI5OZKkK4yDkgilAAAAAABA0xFKwSdnKGW22yVJ7U15kgilAAAAAABA0xFKwaeqqipJkqXmcRudlUQoBQAAAAAAmo5QCj65lu/VPG5rZ6YUAAAAAAAIDEIp+HRhKJVc5Qil+PY9AAAAAADQVIRS8OnCUCqpiuV7AAAAAAAgMAil4NOFoVRiJcv3AAAAAABAYBBKwacLQ6n4CkIpAAAAAAAQGIRS8MlWXCypNpSKK2f5HgAAAAAACAxCKfhkKyqSJJktjlgqtjRPkkEoBQAAAAAAmoxQCj5VVVZKkizt20uSIuzVSlIB374HAAAAAACajFAKPtmcoVRiohQXJ0lqq7PMlAIAAAAAAE1GKAWfXBudW61Su3aSpHbKI5QCAAAAAABNRigFn1yhVEwMoRQAAAAAAAgoQin4ZKuqkiRZoqOltm0lsXwPAAAAAAAEhjnUBaDlcoVSsbFScrIkZkoBAAAAAIDAaJEzpRYvXqy0tDRFR0crPT1d27Zt8zn2pZde0tVXX62UlBSlpKQoMzOz3vHwnyuUumD5Ht++BwAAAAAAmqrFhVJvvfWWZs+erXnz5mnnzp0aNGiQsrKylJub63X8xo0bNWnSJG3YsEFbtmxRt27dNGbMGJ04cSLIlYcft5lSNcv3mCkFAAAAAAACocWFUk8//bTuuusuTZs2Tf369dMLL7yg2NhYvfLKK17HL1u2TNOnT9fgwYPVp08f/e1vf5Pdbtf69euDXHn4qbLbJUnmmBgpKUmSlKAiQikAAAAAANBkLSqUqqys1I4dO5SZmek6FxERoczMTG3ZssWv1ygtLZXNZlObNm2aq8xLhq26WpJkiYuTEhIkEUoBAAAAAIDAaFEbnefl5am6ulodO3Z0O9+xY0d98803fr3GnDlz1LlzZ7dgq66KigpVVFS4HhcWFkqSbDabbDZbIytvGZz1B+p92GpmSkVER6sqOlpmSfEqVlWVVFJiU1RUQH4MQiDQvYLwRa/AH/QJ/EWvwF/0CvxFr8Bf9Epw+ft7blGhVFMtWLBAy5cv18aNGxUdHe11zPz58/XHP/7R4/zatWsVGxvb3CUGRXZ2dkBexzlT6tvvv1deZKQy5AilJOndd9cpMbEyID8HoROoXkH4o1fgD/oE/qJX4C96Bf6iV+AveiU4SktL/RrXokKpdu3aKTIyUqdPn3Y7f/r0aaWmptb73KeeekoLFizQunXrNHDgQJ/jHnroIc2ePdv1uLCw0LU5emJiYtPeQIjZbDZlZ2dr9OjRslgsTX89w5Ak9R86VKmDBkn/7/8pyVQkGdIPf5ipyy9v8o9AiAS6VxC+6BX4gz6Bv+gV+Itegb/oFfiLXgku56q0i2lRoVRUVJSGDRum9evXa/z48ZLk2rR85syZPp/3xBNP6NFHH9WaNWs0fPjwen+G1WqV1Wr1OG+xWMKmMQPxXqqrq2XUHMckJ8ucnCxJSjAVS4ZUWmpRmPy6Lmnh1PdoXvQK/EGfwF/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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Peak number of infected individuals: 233555\n", "Population conservation error: 6.984919309616089e-10\n" ] } ], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def SIR(t, y, N, beta, gamma, delta):\n", " \"\"\"\n", " Differential equations of the SIR model.\n", "\n", " Parameters:\n", " - N: Total population\n", " - beta: Infection rate\n", " - gamma: Recovery rate\n", " - delta: Mortality rate\n", "\n", " Variables:\n", " - S: Susceptible population\n", " - I: Infected population\n", " - R: Recovered population\n", " - D: Deceased population\n", " \"\"\"\n", " S, I, R, D = y\n", " dSdt = -beta * S * I / N\n", " dIdt = beta * S * I / N - gamma * I - delta * I\n", " dRdt = gamma * I\n", " dDdt = delta * I\n", " return dSdt, dIdt, dRdt, dDdt\n", "\n", "\n", "def SIR_scheme(N=1000000, duration=730, beta=1.5, gamma=0.00005, delta=0.5):\n", " \"\"\"\n", " Simulates the SIRD model and plots the results.\n", "\n", " Parameters:\n", " - N: Total population (default: 1,000,000)\n", " - duration: Simulation duration in days (default: 730 days, i.e., 2 years)\n", " - beta: Infection rate (default: 0.2)\n", " - gamma: Recovery rate (default: 0.1)\n", " - delta: Mortality rate (default: 0.01)\n", " \"\"\"\n", "\n", " # Initial conditions\n", " I0, R0, D0 = 1, 0, 0 # Initial infected, recovered, deceased\n", " S0 = N - I0 - R0 - D0 # Initial susceptible population\n", " y0 = S0, I0, R0, D0 # Initial state vector\n", "\n", " # Time vector for the simulation\n", " t = np.linspace(0, duration, duration)\n", "\n", " # Solve the differential equations\n", " solution = solve_ivp(SIR, [0, duration], y0, t_eval=t, args=(N, beta, gamma, delta))\n", " S, I, R, D = solution.y\n", "\n", " # Plot the results\n", " plt.figure(figsize=(12, 8))\n", " plt.plot(t, S, 'b', label=f'Healthy $S(t)$')\n", " plt.plot(t, I, 'r', label=f'Infected $I(t)$')\n", " plt.plot(t, R, 'g', label=f'Recovered $R(t)$')\n", " plt.plot(t, D, 'k', label=f'Deceased $D(t)$')\n", " plt.xlabel('Time (days)', fontsize=12)\n", " plt.ylabel('Population (millions)', fontsize=12)\n", "\n", " # Calculate R_0\n", " R_0 = beta * S0 / (N * (gamma + delta))\n", " plt.title(r'$R_0 = %.2f$' % R_0, fontsize=14)\n", "\n", " # Display final values for the populations\n", " plt.text(0.4 * duration, 0.95 * N, r'$Infected=%.1i$' % I[-1])\n", " plt.text(0.4 * duration, 0.85 * N, r'$Recovered=%.1i$' % R[-1])\n", " plt.text(0.4 * duration, 0.75 * N, r'$Deceased=%.1i$' % D[-1])\n", "\n", " plt.legend(fontsize=10)\n", " plt.grid(True)\n", " plt.tight_layout()\n", " plt.savefig('sir_plot.png')\n", " plt.show()\n", "\n", " print('Peak number of infected individuals:', int(np.max(I)))\n", " # Verify population conservation\n", " conservation_error = np.max(np.abs(N - (S + I + R + D)))\n", " print('Population conservation error:', conservation_error)\n", "\n", " return\n", "\n", "\n", "SIR_scheme()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the parameter $\\delta$ is increased, we observe that the epidemic stops! Although the virus becomes much more virulent, infected individuals die too quickly, leaving insufficient time to infect others." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 2 }