{ "cells": [ { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML, display\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62 DM 2020" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : implémentation et comparaison de schémas\n", "\n", "Le déplacement $x(t)$ d’un système oscillant composé d’une masse et d’un ressort, soumis à une force de frottement proportionnelle à la vitesse, est décrit par l’équation différentielle du second ordre \n", "$$\n", "x''(t)+ 5x'(t)+6x(t)=0,\n", "$$\n", "avec $x(0) = 1$ et $x'(0) = 0$, pour $t \\in [0, 5]$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q1 [1 point]** \n", "Écrire le système sous forme matricielle. Calculer ensuite la solution exacte avec `sympy`. Afficher $t\\mapsto x(t)$, $t\\mapsto x'(t)$ et $x\\mapsto x'(x)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si on note $y(t)=x(t)$ et $z(t)=x'(t)$ on a $y(0)=1$, $z(0)=0$ et\n", "$$\n", "\\begin{cases}\n", "y'(t)=z(t),\\\\\n", "z'(t)=-5z(t)-6y(t)\n", "\\end{cases}\n", "\\quad\\text{i.e.}\\quad\n", "\\begin{pmatrix}y\\\\z\\end{pmatrix}'(t)\n", "{}=\n", "\\begin{pmatrix}0&1\\\\-6&-5\\end{pmatrix}\n", "\\begin{pmatrix}y\\\\z\\end{pmatrix}(t)\n", "$$" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "\n", "# VARIABLES GLOBALES\n", "t0 = 0\n", "tfinal = 5\n", "N = 50 #300\n", "\n", "tt = linspace(t0,tfinal,N+1)\n", "\n", "y0 = 1\n", "z0 = 0\n", "\n", "phi1 = lambda t,y,z : z\n", "phi2 = lambda t,y,z : -6*y-5*z\n", "\n", "def affichage(tt,yy,zz,uu,ww,s):\n", " \n", " subplot(1,2,1)\n", " plot(tt,uu,'--',label=r'$u(t) \\approx y(t)$',color=\"red\")\n", " plot(tt,ww,'--',label=r'$w(t) \\approx z(t)$',color=\"blue\")\n", " plot(tt,yy,label='$y(t)$',color=\"red\")\n", " plot(tt,zz,label='$z(t)$',color=\"blue\")\n", " xlabel('t')\n", " legend()\n", " title(f'{s} - $y(t)$ et $z(t)$') \n", " grid()\n", "\n", " subplot(1,2,2)\n", " plot(uu,ww,'--',label='Approchée')\n", " plot(yy,zz,label='Exacte')\n", " xlabel('y')\n", " ylabel('z')\n", " legend()\n", " title(f'{s} - z(y)')\n", " grid()\n", " axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution exacte est\n", "\\begin{align*}\n", "x(t)=y(t)&=3e^{-2t}−2e^{-3t},\\\\\n", "x'(t)=z(t)&=-6e^{-2t}+6e^{-3t}.\n", "\\end{align*}\n", "Vérifions-le avec le module `sympy`:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = z{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y(t)) = z(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} z{\\left(t \\right)} = - 6 y{\\left(t \\right)} - 5 z{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(z(t)) = -6⋅y(t) - 5⋅z(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\left[ y{\\left(t \\right)} = - \\frac{C_{1} e^{- 3 t}}{3} - \\frac{C_{2} e^{- 2 t}}{2}, \\ z{\\left(t \\right)} = C_{1} e^{- 3 t} + C_{2} e^{- 2 t}\\right]$" ], "text/plain": [ "⎡ -3⋅t -2⋅t ⎤\n", "⎢ C₁⋅ℯ C₂⋅ℯ -3⋅t -2⋅t⎥\n", "⎢y(t) = - ──────── - ────────, z(t) = C₁⋅ℯ + C₂⋅ℯ ⎥\n", "⎣ 3 2 ⎦" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : 6, \\ C_{2} : -6\\right\\}$" ], "text/plain": [ "{C₁: 6, C₂: -6}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = 3 e^{- 2 t} - 2 e^{- 3 t}$" ], "text/plain": [ " -2⋅t -3⋅t\n", "y(t) = 3⋅ℯ - 2⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle z{\\left(t \\right)} = - 6 e^{- 2 t} + 6 e^{- 3 t}$" ], "text/plain": [ " -2⋅t -3⋅t\n", "z(t) = - 6⋅ℯ + 6⋅ℯ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "z = sym.Function('z')\n", "edo1 = sym.Eq( sym.diff(y(t),t) , phi1(t,y(t),z(t)) )\n", "edo2 = sym.Eq( sym.diff(z(t),t) , phi2(t,y(t),z(t)) )\n", "display(edo1)\n", "display(edo2)\n", "solgen = sym.dsolve([edo1,edo2],[y(t),z(t)])\n", "# display(solgen)\n", "\n", "consts = sym.solve( [ sym.Eq( y0, solgen[0].rhs.subs(t,t0)) , sym.Eq( z0, solgen[1].rhs.subs(t,t0)) ] , dict=True)[0]\n", "# display(consts)\n", "solpar_1 = solgen[0].subs(consts)\n", "solpar_2 = solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(17,7)) \n", "yy = func_1(tt)\n", "zz = func_2(tt)\n", "subplot(1,2,1)\n", "plot(tt,yy,label=r'$t\\mapsto y(t)$',color=\"red\")\n", "plot(tt,zz,label=r'$t\\mapsto z(t)$',color=\"blue\")\n", "legend()\n", "grid()\n", "subplot(1,2,2)\n", "plot(yy,zz)\n", "xlabel(r'$y$')\n", "ylabel(r'$z$')\n", "grid()\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q2 [2 points]** \n", "Calculer la solution approchée obtenue par la méthode d'Euler Progressif avec $301$ points. Afficher $t\\mapsto x(t)$, $t\\mapsto x'(t)$ et $x\\mapsto x'(x)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On notera $u_n\\approx y_n=x(t_n)$ et $w_n\\approx z(t_n)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler explicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_n,u_n,w_n),\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_n,u_n,w_n).\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def euler_progressif(phi1,phi2,tt,y0,z0):\n", "\tuu = [y0]\n", "\tww = [z0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append(uu[i]+h*phi1(tt[i],uu[i],ww[i]))\n", "\t\tww.append(ww[i]+h*phi2(tt[i],uu[i],ww[i]))\n", "\treturn [uu,ww]\n", "\n", "[uu, ww] = euler_progressif(phi1,phi2,tt,y0,z0)\n", "\n", "figure(figsize=(18,7))\n", "affichage(tt,yy,zz,uu,ww,\"Euler explicite\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q3 [2 points]** \n", "Calculer la solution approchée obtenue par la méthode d'Euler Regressif avec $301$ points. Afficher $t\\mapsto x(t)$, $t\\mapsto x'(t)$ et $x\\mapsto x'(x)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler implicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_{n+1},u_{n+1},w_{n+1}),\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_{n+1},u_{n+1},w_{n+1}),\n", "\\end{cases}\n", "$$\n", "qu'on peut rendre explicite par un calcul élementaire:\n", "$$\n", "w_{n+1} \n", "= w_n + h(-6u_{n+1}-5w_{n+1})\n", "= w_n + h(-6(u_{n}+hw_{n+1})-5w_{n+1})\n", "\\quad\\implies\\quad\n", "(1+5h+6h^2)w_{n+1} \n", "= w_n-6hu_{n}$$\n", "ainsi\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\dfrac{w_n-6hu_{n}}{1+5h+6h^2},\\\\\n", "w_{n+1}=\\dfrac{w_n-6hu_{n}}{1+5h+6h^2}.\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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7q1fPV4+Hgy1ZsoS2bdseeP7HH39w/fXXExERQXJy8oHt8fHxVKpUiZCQkFzHp6SkEB4enmvb0KFDeeONNwgODuayyy7jpJNOYubMmSxZsoSePXseaNetWzd+++03XnvtNb7//nuAY3pdKbD83Gsc7j5lc9GGdoz++YGuv99AbM0qNDjhVK+jERERDyXs3ELFN3sSdtz1wJleh3NYxZWAMHlss0fYfugJjBkGDAOoVasWMwtxA5ona2l65pnU/eorOO88drdvzz+33sq+Ro0Cc/5yKCkpKXB/PuWcrmXg6FoGTkGvZaVKlTz/FX/Tpk34fD4SExNZuXIl3377LU899RTBwcGkp6ezfft2wsPDWbp0KTVr1swVb3x8PNWqVSM5OTlX0uDNN9/koosuYs+ePbz99tvcfffddO3alXvvvTfX8e3bt+eGG27guuuuo2LFiiQmJh543b179wIU6HWzJCcn6+90/uTnXsP7+5HCSM+kNZXhx5HMTAgFk9fbkLzoM6FwdN0KR9etcHTdCmbn1g2cC2zc52NvSb5u1tqALEBDYOlh9r0JXJzj+UogBjgJmJpj+73AvUd7rRNOOMEG2qKnnrI2PNxaY6wNCrL2+uut3bIl4K9THsyYMcPrEMoMXcvA0bUMnIJey7///rtoAimA2NhY27ZtW3vBBRfYRx55xNarV+/AvqFDh9pp06ZZa61NTEy0Xbp0sa1bt7a//fabtdbazz//3I4YMaLQr/3PP//YmJgYm5SUlGv70KFD7aRJkwr9unldV+APG6DP9bKy5Ode43D3KUc7d1HcjxTUig/usHZkRWvXzPA6lFJFnwmFo+tWOLpuhaPrVjC/z5pm7ciKduq7T3kdyhHvR4prGs7JwBX+KtPdgD3W2s3AfKCZMaaRMSYUuMjfttjt6toVFi6E445zvyC8/TY0awZPPQV5/PIkIiKlR/369Vm8eDGfffYZDz30EBs2ZPe2Hz58OO+99x4AUVFRzJs3j6VLl3LyyScD8NFHHzFs2LBCv/aYMWMYNWoUkZGRubYPHz6cjz76qMheVw7Iz73G4e5TSrytMQOxFeuyZ8rD2MxMr8MRERGPJO3ZBUBYeAWPIzmyQE3D+TEwB2hhjIkzxlxjjLnBGHODv8kUYC2wGngLuBHAWpsODAemAsuBz6y1ywIRU6G0bAnz58Njj8GSJdC3L9x7L7RoAd9951lYIiJSdDp27Ejfvn3JyKMYcWpqKkOGDMlVHDK/1qxZQ8uWLdm/fz9XXnllnq/bq1evgL+u5Ha4e4383KeUBpm+UJY0vpZKOxayaMYXXocjIiIe2ZvoT0BElOwEREBqQFhrLz7KfgvcdJh9U3Af/CVD9eou6QDw/POuN8SqVXDeeTBvHvinRxMRkbJj6NCheW4PDQ3liiuuKNQ5mzRpwooVK47Y5vLLL8fn8wX0deVQed1rWGvfyPH4sPcppcHxp9/I5r9eI3L202T2OY8gX3F1cBURkZIiOWm3exASecR2XtMn1JFMnw6TJkFkpFv+8x83R72IiIhICRESGs7m9rfSPGMVf/ww3utwRETEA4OPrwhAhq9k94BQAuJIhg2DTz+FxYuhYkVYvhxuucXrqERERERyaX/mDcQF1aHa/OdIT0/3OhwRESlmoelJAKQHR3gcyZEpAXE0F14IEybA2rXQqZMrTukvGiYiIiJSEviCQ9jZZQRNMv9l1/zPvA5HRESK2fyV68kMCsUGhXgdyhEpAZEfZ54JI0a4YRgnnQTXX+/qQoiIiIiUEG0HXo2tcTw1/ngeMtQLQkSkvMjItKyM3URyUMmu/wBKQOTfU0/BTz+5IRmhoa4eREqK11GJiIiIAGB8wZh+90P8Kjb8/K7X4YiISDGJ35tCJPtJD4nyOpSjUgIiv0JCwOdzyYfevWHhQrjzTq+jEhEREcnW8kxiw5rj++Upkvbu9ToaEREpBtsSUohiP4RFex3KUSkBUVC//AITJ0KXLvDyy+6xiIiISElgDKm976cO2/njyxe9jkZERIrB1oRkos1+gsKVgCh7LrgArrkG5s+H5s1h6FBYv97rqEREREQAaHrSYP4Jb0fr1WPZuXu31+GIiEgR27k3lSj2ExxR0etQjkoJiMIYMwaOPx527oT0dLjoIkhL8zoqERE5Bvv376d3795kZGQAEBcXx6effgpAamoqvXr1Cvj0hl68ppQDxhBx2sPUMLtZOOEZr6MREZEidkHn+rSqZgiLrOx1KEelBERhREa6YpRJSXDCCTB3Ljz4oNdRiYjIMRg3bhznnnsuPp8PgOnTp7NgwQIAQkND6d+//4HkQKB88MEHxf6aUj7U79Cf5VFd6brxfTL37fY6HBERKWJBKYkYDcEow9q2ha++gi+/hGHD4Omn4Y8/vI5KRKTE69Pn0OW119y+ffvy3v/uu27/jh2H7suPdevW0bt3bwAWLFiAMYb4+HgyMjJo06YN+/btY/z48QwePBiAWbNmMWLECCZMmECHDh1Yt24dQ4YMYfz48YV+3/369aNDhw506NCB8PBwPv/8cz777LMifU0p3xpf+BRRNpGgua96HYqIiBShN35eQ3pyoopQlnmnngpVq8ITT7j17beDtV5HJSIiB6lcuTKJiYkAvPzyy3Tr1o1du3bx7bffMmDAAIKDg1m7di0NGzYEoEePHnTp0oVJkyaxaNEiGjVqRJs2bZg/f36u8y5YsICbb76Z22+/nRkzZrBv3z6mTp3K3LlzD4nhp59+YtGiRVx//fWcffbZnH322fz7778Ffk2R/Apr0AlaDSFzzits2hjrdTgiIlJEpv4VS3BmSqlIQAR7HUCZcNNNYAzMmgVffAHnn+91RCIiJdbMmYffV6HCkfdXr37k/YdTqVIl9u3bR3x8PJs3b6Z79+7s2rWLsWPH8vzzz7Njxw4qV66c65iVK1fSokWLA899Ph+hoaEkJiYSHe0+4N966y0uu+wy9uzZw3vvvcc999xD9+7deeihh/KM4/333+e7777jiy++YPv27VSqVKnArylSEKm978P392SWfTqSOiPe8TocEREpAkmJu92DsIqw39NQjko9IALhllsgPt7dGd91FyQnex2RiIjkEBTkPu7eeustrrnmGqKjo1m8eDEZGRk0b96ciIgIknP83x0fH0+lSpUICQnJdZ6UlBTCw8MPPB86dCjjxo1j0qRJXHbZZfz000/079+fJUuWHBLD559/zvjx4/nss88ICQkhIiKClJSUAr+mSEGE1mrBytpn0WvPZBYvXex1OCIiEmAZmZaUpN3uSSnoAaEERCB07w7XXutmxVi3Dl56yeuIRETkIEFBQUyePJlzzjmHihUr8txzz3HDDTcAUKVKFTIyMg4kIdatW0edOnVyHR8fH0+NGjVyJQjGjRvH0KFDGTx4MO+//z59+/Zl2rRptG3bNtex33zzDa+99hpffvnlgWRCYV9TpKAanf8YGMOObx7FaqioiEiZEr83hcisbg9KQJQjTz0FVaq45fHHYds2ryMSEZEcQkNDGTRoEMHBwVSsWJG9e/dy5plnHtg/cOBAZs2aBUDLli3ZsWMHbdq0Yfbs2QDMmDGD008/Pdc5X3/9dbp3787pp5/O+++/z7x583jxxRcPGc5x5ZVXEhcXR/fu3enQoQNvv/024ApTFvQ1RQoqovpxrGt4Eb33/8jsubO9DkdERAIoYX8adSLS3JNSkIBQDYhAqVYNnnnGJSLWrYOHHoI33vA6KhER8Vu0aNGBx9dccw3XXHNNrv3Dhw/n+eef55RTTiEqKop58+bl2v/RRx8xatSoQr12fHx8ntuHDRvGm2++WSSvKZJT0/NGkjx6AjXnPwsndfc6HBERCZCmNaN5+6KW8BH+BESi1yEdkXpABNJVV8GyZfDf/8Jbb0EeY4BFRKRk6tixI3379iUjI+OQfampqQwZMiRXgchAaN++fbG/ppRPwdE1CO15K812zoC4P70OR0REAinFn3QIq+htHPmgBEQgBQVBSIibjjMiAu64Q9NyioiUIkOHDsXn8x2yPTQ0lCuuuKLMvKaUTyE9hkOF6uyd8gD7U9K9DkdERALgsz828NGvS92TUjAEQwmIovDOO7B3L0ybBlOmeB2NiIiICIRFs6PTLURums20bz72OhoREQmAhbG72bZ9h3uiBEQ5ddddUKcOhIW5XhBpaV5HJCIiIkL1PjewPbg2TRaPJj6xhE8WLyIiR7UtIZmaYalggiCkgtfhHJUSEEUhKspNxZmSAitXqhiliIiIlAzBYWT2vofWZh0/fTHW62hEROQYbUtMoXpwCoRGgzFeh3NUSkAUlXPPhdNOA5/PzYixa5fXEYmIiIhQq/sVbA5vQpd1r/Hv1t1ehyMiIsdga0IyVYJTSsXwC1ACougYA6+8Aj17wp498OijXkckIiIiAkE+IgY9QkOzhcQ547yORkRECslaS+1K4VQLUQJCAJo0gRkz4JprXDLin3+8jkhERESEyu3OJLP+SbRd9TqkJHkdjoiIFIIxhsnDe9A4OlMJCMnhuuvc+oEHvI1DREREBMAYggY+Cnu3ETvlOaymDRcRKb1SkpSAkBz27IH0dPj8c1i82OtoREQkh/3799O7d28yMjIAiIuL49NPPyU1NZVevXqRnp7ucYQiRaT+iWytcwpVFr3BTwuWex2NiIgU0OzVOxjy6m+k7tujBITkMGAAnH66e3z33d7GIiIiuYwbN45zzz0Xn88HwPTp01mwYAGhoaH079+fTz/91OMIRYpOtcFPUMGksOv7J0nLyPQ6HBERKYD1O/exaMNufGnqASEHGzMGgoLg++9h/nyvoxERKVeWLFlC9+7dDzxfsGAB/fr1A2D8+PEMHjwYgFmzZjFixAgmTJhAhw4dGDJkCOPHj/ckZpHiEFyrJVsan8/ZqVOYPGO21+GIiEgBbE1IBiAoNQnCKnocTf4Eex1AudG0KQwfDi+9BLfeCrP1IS8i5dBtt8GiRYE9Z4cO8OKLR2zSunVr1qxZQ0ZGBj6fjzvuuIPRo0eTmprK2rVradiwIQA9evSgS5cuPPfcc7Rp04aMjAzmK2ksZVydwQ+T+uIkIn57ioQeE6kYHuJ1SCIikg/bElOoXiEYk5qoHhCSh0cfhT59YM4c+PVXr6MRESk3goKCaN26NcuWLeOLL76gQYMGdOrUiR07dlC5cuVcbVeuXEmLFi0A8Pl8hIaGkpiY6EHUIsXDVKpLQvtrOd3+ypblv3sdjoiI5NO2hGSOy+r4UEoSEOoBUZwqVYJvv3XTcz7wAMycCcZ4HZWISPE5Sk+FotStWzd+++03XnvtNb7//nsAIiIiSE5OPtAmPj6eSpUqERKS/QtwSkoK4eHhxR6vSHGqcdrd2JUf03zJc9Cxh9fhiIhIPjSsFkmryCTYTalJQKgHRHGrUAEuuwx++cUlI0REpFh069aNBx54gHPOOYe6desCUKVKFTIyMg4kIdatW0edOnUOHBMfH0+NGjVyJSREyqTwSphed8LaGSyc+aXX0YiISD48cGYrRvSKcU+UgJDDOuUUt/7vf0HzbouIFIuWLVsSFhbG3QfNRjRw4EBmzZp1oM2OHTto06YNs2fPZsaMGZyeNYuRSFnX5RoSwusQ+tPDLIrd6XU0IiKSHyn+YaKlpAilEhBeOPVU6NgR4uLgvfe8jkZEpFwYM2YMo0aNIjIyMtf24cOH857//+KoqCjmzZvH0qVLOfnkk/noo48YNmyYF+GKFL/gMEIHPkzroPX8POE1rH4kEREpsbYlJNP1yR+Zu+Jft0E9IOSIPvrIrUeMgEzNuy0iUlTWrFlDy5Yt2b9/P1deeeUh+zt27Ejfvn3JyMjItT01NZUhQ4YcKEgpUh6Ed7iA+IqtOG/PO/zw13qvwxERkcPYmpDC1oQUwjP3ug1hUd4GlE9KQHilZUs44wzYtQueecbraEREyqwmTZqwYsUK3n777cO2GTp0KD6fL9e20NBQrrjiiqIOT6RkCQqi8tmjqGd2sPrbF0hJzzj6MSIiUuy2Jbr6VVV8KW5DeeoBYYw5zRiz0hiz2hhzTx777zTGLPIvS40xGcaYqv59/xpjlvj3/RGIeEqNDz6AmBh45x1IT/c6GhERERF8TfuwM6Y3V6Z/zo7tW7wOR0RE8rA1wSUeKgf5Z/MqLwkIY4wPeBUYBLQCLjbGtMrZxlr7rLW2g7W2A3Av8LO1Nmd1o77+/Z2PNZ5SpUoVeOUV+OcfGD/e62hEREREAKg6ZBSRdh91l7zudSgiIpKHrB4QUWa/2xBaThIQwInAamvtWmttKvAJMPgI7S8GPg7A65YN55wDTZrA9ddDQoLX0YiIiIhArdaYDpdif3+Tn+bM9zoaERE5SKPqkZzbsS6+1EQIqQC+YK9DypdARFkX2JDjeRzQNa+GxpgKwGnA8BybLfCDMcYCb1prxx7m2GHAMIBatWoxc+bMY488h6SkpICfM7/q9+tHk7feYsegQSx94glPYggkL69lWaNrGTi6loFT0GtZqVIlEhMTiy6gUiwjI6PQ1yY5OVl/p6Vo9b2P9MWfkzhlJKsaf0qzWqXj1zURkfJgcIe6DO5QFyaPKzXDLyAwCQiTx7bDzdt0FvDbQcMvultrNxljagLTjDErrLW/HHJCl5gYC9C5c2fbp0+fYww7t5kzZxLoc+Zb797wxRdUnzOHPg0aQOPG3sQRIJ5eyzJG1zJwdC0Dp6DXcvny5URHl54PxuKUmJhY6GsTHh5Ox44dAxyRSA6V6pJ+4o0MnvsCj0z8ipE3XO51RCIi4peZaQkKMpCaVKoSEIEYghEH1M/xvB6w6TBtL+Kg4RfW2k3+9TZgIm5IR/liDIwZA9bCxRd7HY2IiIgIABF9RrA/pAoDN77GLyu3eR2OiIj4dX/6Jx75ehmkJJa7BMR8oJkxppExJhSXZJh8cCNjTCWgNzApx7ZIY0x01mNgILA0ADGVPpddBg0awLx5sGCB19GIiIiIQHhFgvvfx0m+v/lx0nukZ2R6HZGISLmXkWnZmpBMVFhw+UtAWGvTcTUdpgLLgc+stcuMMTcYY27I0fQc4Adr7d4c22oBs4wxfwHzgG+ttd8fa0yl1ltvufWPP3obh4iIiIhfSJer2RvVkP+mvU/S/mSvwxERKffi96aQaaFmdJg/AVHR65DyLRA9ILDWTrHWNrfWNrHWPuHf9oa19o0cbd611l500HFrrbXt/UvrrGPLrYED4bTT4JlnYPdur6MRESnz9u/fT+/evcnIyAAgLi6OTz/9FIDU1FR69epFenq6lyGKeM8XQuQZTxCTFkvlFZ94HY2ISLm3LSEFgJoVwyEloXz1gJAAe/RRiI+HFi0gWb8yiIgUpXHjxnHuuefi8/kAmD59Ogv8w+BCQ0Pp37//gYSESLnW8gxocBLp05/kiznLvY5GRKRc25rgvidm94AoPQmI0jFZaHnSpQucfDLMng2jRsEjj3gdkYhIwNx2GyxaFNhzdugAL7549Hb9+vVj5043CdOKFSv44IMPGD9+PB999BEAs2bNYsSIEVSuXJmpU6cyceJEhgwZwr333sull14a2KBFShtjYODjBP+vP5umPMPqJi/TtGaU11GJiJRLtSuFc+VJx1G/SkSpS0CoB0RJ9Prrbj1qFGzZ4m0sIiJlxE8//cSiRYu4/vrrOfvsszn77LNZu3YtDRs2BKBHjx506dKFSZMmsWjRIho1akSbNm2YP3++t4GLlBT1OpPSYgjXBn3Da5N+9joaEZFyq3WdSjwyuA3Vwy1kppeqBIR6QJRE7drBoEHw3Xdwxx0wfrzXEYmIBER+eioUpffff5/vvvuOL774gu3bt1O5cuVc+1euXEmLFi0OPPf5fISGhpKYmEh0dOn5cBcpKmGnPULGP99ycuwbzFzZhT4tanodkohIubNnfxoVQn2EpCS6DaGlp0eaekCUVKNHu+6OH38MGzZ4HY2ISKn3+eefM378eD777DNCQkKIiIggOUetnfj4eCpVqkRISEiu41JSUggPDy/ucEVKpioNodsNnOv7lU8mf6NpOUVEPDDi00Wc/cpvbvgFlL9ZMKQIHH88XHghhIZCsDqqiIgci2+++YbXXnuNL7/88kAyoUqVKmRkZBxIQqxbt446derkOi4+Pp4aNWockpQQKc98vf6P9NBK3BP0IWnpSkCIiBS3bYkp/gKUCW5DKRqCoQRESfbEE5Ce7mpB7N3rdTQiIqXWlVdeSVxcHN27d6dDhw68/fbbAAwcOJBZs2YB0LJlS3bs2EGbNm2YPXs2ADNmzOD000/3LG6REimiMqH976dh4p9E/DvN62hERMqdrQnJ1KoYlqMHROlJQOin9ZKsSRO4+mp47TWYPBlWroSwMK+jEhEpdeLj4/PcPnz4cJ5//nlOOeUUoqKimDdvXq79H330EaNGjSqOEEVKl85Xw7yx7Pv2Pj7c1IhhfVt6HZGISLmQkWnZkZRCrYrhkBLnNpaiBIR6QJR0Dz4IQUGwfj2MGeN1NCIiZUrHjh3p27cvGRkZh+xLTU1lyJAhuYpSioifLwQGPkaFhLVs/PE1/t6U4HVEIiLlQnxSCpkW/xCM0tcDQgmIkq5BAxg2zBWkfPRR2LzZ64hERMqUoUOH4vP5DtkeGhrKFVdc4UFEIqVE89NIb9CD20K+5NlJv2Ot9ToiEZEyLzQ4iLtPa0nnhlVVhFKKyH33uWKU+/fDPfd4HY2IiIgIGEPwoCepTBJdN77Ld0u3eB2RiEiZV7lCKP/t04TjYyqqB4QUkTp1YPhwsBYmTICtW72OSESkQPTLaGDpekqJEdMe2/4ihgZ/z7ivZ5KcduhwJhERCZwdSSls2LmPzEzrEhBBIRBceuoEKgFRWtxzD0RHQ8+eUKuW19GIiORbeHg48fHx+tIcINZa4uPjD0wnKuK1oP4P4fMF81zVLwkOMl6HIyJSpn04dz09n5lBhvUnIMKi3XD9UkKzYJQW1avDXXfBAw/ArFlQty40auR1VCIiR1WvXj3i4uLYvn2716GUOMnJyYVKJISHh1OvXr0iiEikECrWwdfjNhr+/BRsnAcNunkdkYhImbU1IYVqkaGE+IKyExCliBIQpcltt8Err8BFF8G+fbBqFVSr5nVUIiJHFBISQiMlTPM0c+ZMOnbs6HUYIseu+y2w4H12fjGCMY3e4JEh7byOSESkTNqemEzNiv4fL1ISS1UBStAQjNIlMhJGjoSNG2HPHjdFp4iIiIjXQiPhlJFU3bOMhHkfMXdtvNcRiYiUSVsTUtwUnAApCaWuB4QSEKXNNddAs2ZQuTK88QYsWuR1RCIiIiLQ9kIyYzpyb+hnjJr0J+kZmV5HJCJS5mxLTKZWxawEROkbgqEERGkTEgJPPAE7d0JUVPbsGCIiIiJeCgoiaNBT1CSevvEf8+Hc9V5HJCJS5tx/Risu6FzfPUlJhLAobwMqICUgSqPzz4fOnV0y4t9/YcMGryMSERERgQbdsK3P4b8h3/LhtDns2Z/mdUQiImXK2e3r0KVhVfdEPSCkWBgDTz/tekEMHw4NGngdkYiIiAgA5pRHCAmCDxtOpVJEiNfhiIiUGbv3pTL/353sTUl3G5SAkGLTrx8MHAjPPgvbtsFPP3kdkYiIiAhUOY6gk26i9r9fQdyfZGZqqKiISCD8uX4XF7wxh3+2JkJGGqTv1ywYUoyeesr1ghgyBE49FZYv9zoiEREREeg5AiJrsuXzEVw0do6SECIiAbA1IQWAWhXDXe8HUA8IKUYdO8LFF7uZMCIi4JZbVJBSREREvBcWDf0fpPaeRdSI/Y4JC+K8jkhEpNTblpgMQI3oMCUgxCOPPw7p6dC2Lfz4I0yY4HVEIiIiJYYxpqoxZpoxZpV/XSWPNvWNMTOMMcuNMcuMMbd6EWuZ0+FSbO22jAz/hBemLFZBShGRY7Q1IYVqkaGE+IKUgBCPNG4M118Pv/8Oxx/vekHs3u11VCIiIiXFPcB0a20zYLr/+cHSgTustccD3YCbjDGtijHGsinIhzn1SWpmbuO81K94Ydo/XkckIlKqbU9MpmbFcPdECQjxzIMPuiEYderAccdBfLzXEYmIiJQUg4H3/I/fA4Yc3MBau9lau8D/OBFYDtQtrgDLtEa94PizuDn0a6bPW8T2xBSvIxIRKbVuO6U5D53pz48fSECUriKUwV4HIAFQsybccQc88gjMmQNNmngdkYiISElRy1q7GVyiwRhT80iNjTENgY7A74fZPwwYBlCrVi1mzpwZ0GALKikpyfMYjia84pl0sd/xbs3PWPZnycjrlIbrVhLpuhWOrlvh6Lod3swNUGPb77QG5v21nH2rkw7sK+nXTQmIsuKOO2DsWLj1VvjmG3jxRRg5EkJDvY5MRESkSBljfgRq57Hr/gKeJwr4ArjNWpuQVxtr7VhgLEDnzp1tnz59ChZsgM2cOROvY8iXkJU0mfU8TZo8wO5q7alcwdv7k1Jz3UoYXbfC0XUrHF233DIyLd8u2UzH+pWpX7UC/Pkv/A0n9uwPFescaFfSr5uGYJQV0dFuWs5589z6ySfh2We9jkpERKTIWWtPsda2yWOZBGw1xsQA+Nfb8jqHMSYEl3wYb639sviiLyd6joCo2mz57FYGPj+ThGQVpBQRKYj4pBRu+XghM1f6P8ZUA0I8d9ll0LUrfPQRDBkCjz0G/6jgk4iIlGuTgSv9j68EJh3cwBhjgLeB5dba54sxtvIjLBpOeZjaicvouX+6ClKKiBTQNn8NndxFKA2ERHoXVCEoAVGWBAXBmDGwZQvUrQvh4XDDDWCt15GJiIh45SlggDFmFTDA/xxjTB1jzBR/m+7A5UA/Y8wi/3K6N+GWYe3+A3VPYGTE50yYvZy/N+U5ykVERPKwNSEZgJrRYW5DSqJL7gaVrq/0pStaObquXeHKK+Gtt+D//g9mzID33jv6cSIiImWQtTbeWtvfWtvMv97p377JWnu6//Esa62x1raz1nbwL1OOfGYpsKAgOO1pKqbHc3v4Nzw4aSmZmfqRREQkP7J6QNQ60AMiodQNvwAlIMqmUaNc8cl58+D+++GUU7yOSERERATqd4F2F3Gl+YZ9W1azdkfS0Y8REZEDPSCqR+XoAREa5WFEhaMERFkUEwMPPABffw29ekG9ehqGISIiIiXDKSMJ8oXyVfPvaFqz9P16JyLihcu6HccX/z2Z0GD/V/isIRiljBIQZdVtt0GTJm69YYPrBTFtmtdRiYiISHlXsQ6m5wjCVk0hc/VMFsTu8joiEZESr3pUGCccVyV7gxIQUqKEhcHzz8Py5fDppxAX5wpS7tvndWQiIiJS3p00HCo3YPfEO7jw9V9ZErfH64hEREq0L/6MY86a+OwNSkBIiXPWWTBwIDz+ODz9NKxdCyNHeh2ViIiIlHch4TDwCaruXc11Eb/wgApSiogc0dPfr+CrhRuzN6QkQlhF7wIqpIAkIIwxpxljVhpjVhtj7sljfx9jzJ4cU1s9lN9j5RgYAy+8AElJ8P33MGwYjB4Ns2Z5HZmIiIiUd8efBQ17crvvM/7dEMenf2zwOiIRkRIpI9OyIymFmhXDsjeW1x4Qxhgf8CowCGgFXGyMaZVH019zTG31aAGPlcJq1QqGD4exY930nI0awcMPex2ViIiIlHfGwGlPEZKeyNNVv+Hp71ewc2+q11GJiJQ48UkpZFqomTUFZ2Zm+U1AACcCq621a621qcAnwOBiOFbya+RIqFYN7r3XzYwxcaLXEYmIiIhA7TaYE67m1P3f0ilsE5t27/c6IhGREmdbYgoANaP9PSDS9gK2VCYgggNwjrpAzj5zcUDXPNqdZIz5C9gE/J+1dlkBjsUYMwwYBlCrVi1mzpx57JHnkJSUFPBzliQxl19OixdeYNknn7C9Xz+CUlOJ2LiRvY0aBfy1yvq1LE66loGjaxk4upaBo2spAvR7ALPsS96u+RmmzpVeRyMiUuJsTUgGoFZWD4iURLcupwkIk8e2g6sILQCOs9YmGWNOB74CmuXzWLfR2rHAWIDOnTvbPn36FDbePM2cOZNAn7NE6dkTZs6k9Vtvwe23uxkxfvkFli51vSMCqMxfy2Kkaxk4upaBo2sZOLqWIkCFqtDvQcy3I0j963M+SOrCFScdR4hPtdJFRAB6Na/BrLv7Uj3K3wMiJcmtS2ECIhD/s8cB9XM8r4fr5XCAtTbBWpvkfzwFCDHGVM/PsRIgPh/873+wfTvcdZcbjhEfD//9L1hVnRYREREPnXAV1G6HnfoAo79ZwP9+Xed1RCIiJUaIL4h6VSoQHuJzGw70gCifs2DMB5oZYxoZY0KBi4DJORsYY2obY4z/8Yn+143Pz7ESQJ06wR13uETErl3wyCPw+efwySdeRyYiIiLlWZAPTn+OsP1bea72NMZM/4cNO/d5HZWISInwzeJNvD/n3+wNKQluXR57QFhr04HhwFRgOfCZtXaZMeYGY8wN/mbnA0v9NSBeAi6yTp7HHmtMcgQjR0KTJm5KzuHDoVs3uOkm2Ljx6MeKiIiIFJUGXaHdRQxK/IKGZisjJy/DqpemiAhfLdzIx/NylE4s5zUgsoZVTDlo2xs5Hr8CvJLfY6UIVajgpuTs3x+eeALefx+uuQb2q+q0iIiIeGzAI5gV3zK28gR6rajB1GVbOK1NjNdRiYh4amtCSvYMGFCqExCq7lMe9esHQ4fCc89BUpIrRtm0qddRiYiISHkXXRv63E2D+F8Z2TyW46pFeh2RiIjntiUmU6uiEhBSmj33HFSvDtdeC+npribE0KGwerXXkYmIiEh5duL1UL05Vye+yfHVQ72ORkTEUxmZlu2JKdSMDs/emJWACI3yJqhjoAREeVWlCrzyCixYAC+8AHv3wsSJcPnlkJbmdXQiIiJSXgWHwqCnYdc69v8yhhGfLWLpxj1eRyUi4omde1PJtBzUAyIBgsPd/5eljBIQ5dl558HgwfDQQ5CcDG++CXPnuik6RURERLzSpB8cfxbhc19k5crl3D9xCRmZKkgpIuVPjegw/nl8EBd0rp+9MSWxVA6/ACUgyjdj4NVXITQUrr8eLrjAzYgxejRMmuR1dCIiIlKeDXwCYzN5s/Yk/orbw/jf13sdkYiIJ0KDgwgP8WVvUAJCSq26deGZZ+Cnn+Cdd1zyoXNnuPNOVxtCRERExAtVjoMet1Nv43dcVy+OZ79fybaEZK+jEhEpVrNW7WDkpKXsTcnx3UwJCCnVrrsOevaEO+5wxSgnTIAZMyA4ILO0ioiIiBRO91uhcgPuzBxHekYaz0xd6XVEIiLF6o/1O3l/7npCg3N8dU9JhLCK3gV1DJSAEAgKgrfegn373BCMBg1cz4jMTJgyxevoREREpLwKiYBTRxG6cwVfnrCMO09t4XVEIiLFamtCCtUiQwnxHZyAUA8IKc1atIBHHoEvv3RDMQDefhvOOAM+/tjb2ERERKT8ankGNOnH8StepVZQIpmZltT0TK+jEhEpFtsTk6mRcwpOcLNgKAEhpd6dd0KfPnDzzbByJVx1FXTv7oZorFjhdXQiIiJSHhkDg56BtH1kTBvJRW/NZfQ0DcUQkfJha0JK7ik4QT0gpIzw+eDDDyE8HC65xA3B+OQTiIhwM2Ts2+d1hCIiIlIeVW8GJ92E76/x9I1Yw/9+XcfSjXu8jkpEpMhlZFpiKh3cA0IJCCkr6taFceNgwQK4/36oVw/Gj4dly+CWW7yOTkRERMqr3ndBxXoMS3yN6hE+7vlyMekZGoohImXblFt78uQ5bbM3pKdAZpoSEFKGDB4M//2vm5Jz6lQYOBBeeAGuvtrryERERKS8Co2E00bh276Mca0XsXRjAu/89q/XUYmIFDljTPaTlES31iwYUqaMHg2tW8OVV8K2bXDrra4eBLipOkVERESK2/FnQdNTaLXiZc5rFsTnf25QLwgRKbNWb0viuvf/4O9NCdkbU/yP1QNCypSICDf7xe7drhiltW77Cy9AmzYQF+dldCIiIlIe+QtSmoxUnoz8jK9u6k6wT7ezIlI2rY/fy7S/t5KSnpG98UAPCCUgpKxp2xaeew6++w5eesltGzAAEhPhrLMgKcnb+ERERKT8qdYEetxO2IovqRD3G8lpGSpIKSJl0rbEFABqVcxRhDIrAREa5UFEx04JCDmym25yyYa77oJFi1zvh88+g8WL3UwZGRlHPYWIiIhIQPW4Dao0hCn/x/0T/uTyt38nPinF66hERAJqa0IyANWjckzDqR4QUqYZ42bFqFYNLr4Y9u6F006DMWPg66/hzju9jlBERETKm5AIGPQs7PiHeypPJyklnce/Xe51VCIiAbU1IYVqkaGEBuf42q4ilFLmVa8OH3wAK1fC7be7bcOHw4gR0K6dt7GJiIhI+dR8ILQ8kxoLXuLObpFMXLiRn//Z7nVUIiIBExHio1WdgxINKkIp5UL//m4YxltvwXvvuW2jR7sClQD79nkWmoiIiJRTpz0FwDVJY2lcI5L7Jy5hX2q6x0GJiATGQ2e14oNruubeqCEYUm489hj07QvDhsGcOdnbp0yBxo3h77+9i01ERETKn8r1oded+FZ+w2tddlAjOoxd+9K8jkpEpOikJILxuaFopZASEJJ/ISHw+edQvz6ccw5s2OC2t2nj1meeCdvV9VFERESK0UnDoXpzWi58jC+v7UjdyqXzplxEJKeMTMvgV2YxcWFc7h0pia73gzHeBHaMlICQgqlWDSZPdkMuhgxx6wYN3LbNm2HIEIJSU72OUkRERMqL4FA4/TnY9S/mtzHEJ6Xw7NQVpGdkeh2ZiEihxSel8FfcHpJSDpp1MCWx1BagBCUgpDBatYKPPoKFC2HoULAWTjzRFaqcPZvjH3sM0jX+UkRERIpJ497Q5nyY9QLLli7i1RlreHvWOq+jEhEptG2JbmrhmtFhuXdk9YAopZSAkMI580wYNQo+/RSeeMJtO/98eOklUmrVAp/P2/hERESkfDn1CfCF0nP1Mww4viYv/PgP6+P3eh2ViEihbE1IBqBWxfDcO1ISlICQcuquu+Cyy+DBB2HiRLft5ptZPXy4G5O0ZQtkqvujiIiIFIPo2tD3PszqH3mmdSwhQUHc/cViMjOt15GJiBTY1gT1gBDJzRg3LeeJJ8Lll8Pixdn7tm2DTp3gttvcEA0RERGRonbiMKjVhiq/PMRDpx7H3LU7+Xh+rNdRiYgUWFR4MO3rV6Z61MEJiCQlIKQcCw93vR8qVYKzz86eBaNGDbj4Ynj5Zbj3XiUhREREpOj5guGM5yEhjvP3fswdA5ozoFUtr6MSESmws9vXYdJN3QkNPugru3pASLlXpw589RVs3QrnnYdJS3O9I557Dm64AZ5+Gh5/3OsoRUREpDxo0BU6XIaZ8wo3t02nZnQ4mZkWqx9DRKQsUAJCBOjSBd5+G379lZZPPw0ZGS4J8eqrcMUV8NBD8OGHXkcpIiIi5cGAR9w0dd/czu69yfxn7Bw++2OD11GJiOTblePm8dCkpbk3ZmZA2l4lIEQAuOQSePJJak2fDjfe6IZdBAW5xMTjj8PgwV5HKCIiIuVBZHUY+DjEzqHi8k/wBRke/2Y5m/fs9zoyEZF8WbElgeS0jNwbUxLdWgkIEb9772X9JZfA2LFw550uCREcDPffD9HRkJQE337rdZQiIiJS1nW4BI7rQdCPD/HsoBjSMy33fblEQzFEpMTLyLRsT0yhZvTBU3AqASFyiHXXXgvDh8Po0fDoo7l3PvYYnHkmvPCCN8GJiIhI+WAMnPkCpO2n/rzHufPUFsxYuZ0vF2z0OjIRkSOKT0oh00KtinlMwQlKQIjkYgyMGQNXXQUPPwzPP5+979FH4fzzYcQIuO8+zY4hIiIiRadGc+gxApZ8zlW11tL5uCq8O/tf9YIQkRJta0IKADUrqgeESP4EBcFbb7lkwx13uMcAYWHwySdw/fUwahQMGwbp6d7GKiIiImVXzxFQrSlBU0bwygUt+fT6bhhjvI5KROSwwkKCGNSmNo2qR+becSABUbH4gwoQJSCk6AQHw/jxMGiQSzh89JHb7vPB66/DAw+4ehDbtnkbp4iIiJRdwWFw5ouw619qL3qZCqHBpGZYlm7c43VkIiJ5al4rmtcvO4HmtQ7q6ZCS4NbqASFyGKGh8MUX0KuXm45z0iS33RhXD2LJEqhTBzIzXYFKERERkUBr1BM6XAqzX4KtfzNuaQqXv/07O5JSvI5MROQQhx0mpiEYjjHmNGPMSmPMamPMPXnsv9QYs9i/zDbGtM+x719jzBJjzCJjzB+BiEdKmIgI+PprOOEEuPBCmDYte1+1am59990uSbF1qzcxioiISNk28HEIrwTf3MZZjYPZm5LByEnLvI5KROQQ93+1lFOe//nQHUpAgDHGB7wKDAJaARcbY1od1Gwd0Nta2w54DBh70P6+1toO1trOxxqPlFDR0fDdd9CiBZx1Fnz5Ze79/frBihXQowesW+dNjCIiIlJ2VagKA5+ADb/TOfFHbj2lGd8u2cx3SzZ7HZmISC5b9yQT4svjq3pWAiI0qngDCqBA9IA4EVhtrV1rrU0FPgEG52xgrZ1trd3lfzoXqBeA15XSpmpVmDEDOnaECy6AN9/M3jdoEEyfDvHxcPLJMGeOd3GKiIhI2dT+ImjYkyZr3mdYp0ja1K3Ig5OWsnNvqteRiYgcsC0x5dApOMElIEKjIMhX/EEFSHAAzlEX2JDjeRzQ9QjtrwG+y/HcAj8YYyzwprX24N4RABhjhgHDAGrVqsXMmTOPJeZDJCUlBfyc5dXRrmXQyJG0fuQRqt1wA+vmzmX9FVe4mhBAhdGjafvAA4QMGMDcTz4hPar0ZvcCQX8vA0fXMnB0LQNH11KkmBkDZ75I0KvdCJp2P8+e/yIjJy1jb0o6VSNDvY5ORASArQnJHB+TxzCLlIRSPfwCApOAyGseozyrZhhj+uISED1ybO5urd1kjKkJTDPGrLDW/nLICV1iYixA586dbZ8+fY458JxmzpxJoM9ZXuXrWvbvD9ddR6N336VRhQrw0ktudow+fWDwYPjzT3oMGODaZmS4feWQ/l4Gjq5l4OhaBo6upYgHqjdl/XEX0GjpRxzf/hI+vb6/puUUkRIjI9OyIymFWhXDD92ZkljqExCBGIIRB9TP8bwesOngRsaYdsD/gMHW2vis7dbaTf71NmAibkiHlHUhIfDOO3DXXfDaa3DRRZDir0RdtSpkJR/ef98Vp9ys8ZkiIiISGLENzoXqzeHb2zFp+4lPSuH+iUvYsy/N69BEpJxLTc/kypMb0qVh1Tx2JikBAcwHmhljGhljQoGLgMk5GxhjGgBfApdba//JsT3SGBOd9RgYCCwNQExSGhgDTz8No0fDhAmuDkRCQu42ERGwaBF07gxz53oSpoiIiJQtNigEznwRdsfCz0+zeU8yn8zfwCNfa1YMEfFWRKiPkWe1plfzGofuzKoBUYodcwLCWpsODAemAsuBz6y1y4wxNxhjbvA3ewioBrx20HSbtYBZxpi/gHnAt9ba7481JillRoyADz6AX3+F3r1hy5bsfRdc4ApShoW5ff/7n3dxioiISNnRsDt0vAzmvEKb4Dhu6tuULxdu5Pul6nUpIt5JTssgOS0j750aguFYa6dYa5tba5tYa5/wb3vDWvuG//G11toq/qk2D0y36Z85o71/aZ11rJRDl10GX38N//zjZsFYvDh7X7t28Mcfrj7EddfB/PmehSkiIiJlyIDHILwyfH0rN/dtTJu6Fblv4lK2J6Z4HZmIlFMTF26k5YPfs3nP/kN3piRCWMXiDyqAApKAEAmI005z03SmpEC3bq5XRJaqVWHKFPjmG+jSxW3btSvv84iIiIjkR4WqcOqTEDefkIXv8sKFHUhKSWfUd8u9jkxEyqmtCckAVI/KaxrO0j8LhhIQUrKceCIsWABdu8IVV8B//5tdnNLngzPOcI///BMaNIDnn4fMTO/iFRERkdKt3YXQqDf8+AjNKuzl1Us6ce+g472OSkTKqa0JKVSLDCXEd9BXdWs1BEOkSNSqBdOmuRky3njDzYIRG5u7Tf36birPO+6AU045dL+IiIhIfhgDZ74A6Snw/T0MaFWLGtFhZGRadu9L9To6ESlnticmUzOvKTjT9oHNVAJCpEgEB7sZMr78EpYvh06d4IcfsvfXrAkTJ8Lbb7uaEG3bwvjx3sUrIiIipVe1JtD7Tlg2Ef75AWst173/Bzd8+CeZmdbr6ESkHNmakELN6LyGXyS6tRIQIkXonHNcAcqYGFcj4vHHs4dcGANDh8Jff7kExKpV3sYqIiIipdfJt0L1FvDtCExqEqe1qc3ctTsZ99s6ryMTkXLk4hMbcP4J9Q7dcSABoSKUIkWreXOYOxcuuQQefBDOPht27Mje37gx/PwzPPCAez59uitWKSIiIpJfwaFw9suwJw6mP8oFJ9TjlONr8czUlazamuh1dCJSTlzStQFnta9z6I6UBLdWDwiRYhAZ6WbFePVVNxSjdWuYMCF7v8/nhm0APPMMnHUWDB4M6/SrhYiIiORTg67Q9XqYNxYTO5dR57YlKiyY2z9bRFqGil6LSNHauTeVtduTsDaPoV8agiFSzIyBG290M2DUrw8XXOCWbdtyt/v6a5eEmD4dWrWCRx+F5GRvYhYREZHSpd+DULkBTB5OjXDLk+e0JTE5nS17dC8hIkXr67820W/0z8Tt2n/oTiUgRDzStq0bkvHkkzB5sksyfPyxm5oGIDQU7rwTVqxwwzVGjnTtRERERI4mLArOGgPxq+HnpzitTW1+uL0X9atW8DoyESnjZq3eQYOqFfL+/0YJCBEPBQfDvffCwoXQtKmrD3HOObB5c3abevXg009dsuKCC9y2r7/WsAwRkXLEGFPVGDPNGLPKv65yhLY+Y8xCY4wKCZV3TfpBx8vgt5dg0yLCgn0kp2Xw8vRV7E/N8Do6ESmD0jMymbsmnu5Nq+fdQEUoRUqAVq3gt9/guedg6lT3/L33sntDAHTt6oZvpKTA9de7No88AokqKCUiUg7cA0y31jYDpvufH86twPJiiUpKvoFPQGQNmDQcMtL4a8NuRk/7h6e/X+F1ZCJSBi3euIfElHR6HDYBkVWEMqr4gioCSkBI6efzwR13uOk427SBq66CAQPc85zCwmDePFeg8uGH3ewZzz8P+/MYYyUiImXFYOA9/+P3gCF5NTLG1APOAP5XPGFJiRdRGc58HrYugVkv0rVxNa46uSHvzv6XWat2HPVwEZGC+G3VDoyBk5pUy7tBShL4wiA4rHgDC7BgrwMQCZjmzd10nK+/Dg89BB07wtVXw2OPQR3/VDb16sFnn7lExAMPuMRFz57QpYu3sYuISFGpZa3dDGCt3WyMqXmYdi8CdwFHHFxrjBkGDAOoVasWM2fODFykhZCUlOR5DKVR/q9bJK1qdKf6zKf4I6kWJ0XW5/tIwy3j5/FY9wgiQ0xRh1qi6O9b4ei6FU55u26NMiwjOoWxeP7sPPc3W7eSGkFhzD7KNSnp100JCClbgoLgpptcTYjHH4eXX4ZPPoG77oL/+z83nSfAiSe66TyXLHFFLQEefND1irj88uwpPUVEpMQzxvwI1M5j1/35PP5MYJu19k9jTJ8jtbXWjgXGAnTu3Nn26XPE5kVu5syZeB1DaVSg69a5Nbx6Iidufh+GTqVW80TOe302P++pyjPnty/SOEsa/X0rHF23wtF1O0j8eNhf9ajXpKRfNw3BkLKpShUYPRqWL4fTT3dDLpo1g3HjICNH8ais5ENaGvz4IwwdCq1bu1k1MlRkSkSkNLDWnmKtbZPHMgnYaoyJAfCvt+Vxiu7A2caYf4FPgH7GmA+L7Q1IyRZVAwY9DXHz4fc36VC/MqPOacuwXk28jkxEyohFG3bz5s9rSExOO3yjlMRSPwMGKAEhZV2TJvD5565Q5XHHwTXXwAknuN4POQtVhoTA7Nnw1VeuVsQll7iExa+/eha6iIgExGTgSv/jK4FJBzew1t5rra1nrW0IXAT8ZK29rPhClBKv7QXQ7FT46THYuY4Lu9Snac0orLUkp+kHCxE5Nt/8tYnR0/4hxHeEr+cpiaV+BgxQAkLKi5NPdgmGTz6BPXvg1FPd7BhffgmZma6NMTB4MCxaBF98AfXru6QFuJ4U69d7Fr6IiBTaU8AAY8wqYID/OcaYOsaYKZ5GJqWHMa4gpfHB17cc+BHj/z5fzPCPFmBz/qghIlJAs1bvoEvDKoSH+A7fKCVBPSBEShVj4D//ccmEN9+EnTvhvPPctJzvvAOpqa5dUBCce64raNmggdt2xx2uN8V//gO//+7dexARkQKx1sZba/tba5v51zv92zdZa0/Po/1Ma+2ZxR+plHiV6sHAR2HdL7DgfQBa1anIj8u38dkfGzwOTkRKq+2JKazYkkj3w02/mUVDMERKqfBwGDYMVqxwPSIiIlzthyZN4MUXYe/eQ4954w0YMQKmToVu3VyPim+/LfbQRURExEOdroKGPeGHByBhE1ef3JCTGlfjka//Zu32JK+jE5FSaPYaN61vDyUgRMq44GDXo2HBAvj+e5eAuP121+vh4Ydh8+bstg0awDPPwIYNMGYMbN0Kixe7ffv3u14R6n4pIiJStgUFwVljICMNvhlBkIHn/9Oe0OAgbvlkIanpmV5HKCKlTNyu/VSPCqN1nUpHbqgEhEgZYYyrCTFzpqsT0bMnPPKIqwFxzjkwZUr2jBjR0XDLLbBqlUtWAEya5HpFtG4Nzz4LW7Z49lZERESkiFVrAv3uh3++g6VfEFMpgmfOa8fGXftZo14QIlJAN/Vtypx7++ELModvlJ4CGSlKQIiUOSed5GbC+OcfV/dh9mw44wxo1Mj1ioiNde2CgtxQDnDTfL71lpv68667oF49OOssSEjw6l2IiIhIUep2I9Q9Ab67C/buYGDr2vxyV1+Ojyn9FepFpPgdcfYLgBR/clOzYIiUUc2awdNPuyEXEya4QpWPPgoNG7qEw8SJkOafp7diRbj2WjfV5/Ll8H//B8nJrrcEwCuvwEcfKSEhIiJSVgT5YPCrkJwA390NQHR4CJmZlrdnrWN7YorHAYpIafDJvFgueGM2iclpR26Y4v8eoR4QImVcaKibKeP772HtWrj/fvjrLzdLRq1arnjld99lz6DRsiU89RRMm+aGdlgLr78Ol14KNWq43hTjxkF8vLfvS0RERI5NzeOh152wdAKs/A6A2J37eOb7Ffzf53+RmanaUCJyZDNXbmfT7mSiwoKP3DAl0a2VgBApRxo2hMceg/Xr4euvXTLhiy9cj4hateCqq9zMGCk5fvUwBpYscb0jhg+HZcvgmmvg8cfd/rQ0t18FLEVEREqfHrdDzdbwze2wfzcNq0fywJmt+Pmf7Yz7bZ3X0YlICZaRaZm9Zgc9mlbHmCPUfwAlIETKteBgOPNM+OAD2LbNJSPOPtvVjjjzTJeMuOIKN0wjIcHVizj5ZBg9Gtatgz//hJtvdueaMwfatYO6dV0C4+OPYft2L9+diIiI5FdwKAx+GZK2wrSHALisawMGtqrF09+vYOnGPR4HKCIl1ZKNe0hITqd7s6NMvwlKQIiIX1iYSzq8955LRnz7rZs54+uv3TCNqlXdrBqPPw7z50NmJnTqBI0bu+NbtXJDMnr1csdccolLYPzxBwAhu3dDYqJ3709ERESOrO4JcNJwWPAerP0ZYwxPn9eOapFh3PbpIjI0FENE8vDb6h0AnNyk2tEbZyUgQpWAEJEsoaFuOMY778DWrW5az7vugn374MEH4cQTXXLhootcm40boXp1uPpq+OQTl8CYN88lK9q3B6DBxx9D5cpwwglw663w+eewaZOnb1NEREQO0vc+qNoYJt8MqXupEhnKy5d0ZNS5bY88tZ6IlFuNqkdyWbcGVI8KO3rj1LLTA+Io1S5EpFBCQ6F3b7c8+aQbVjFtGkydCj/8AJ9+6to1agTdu2cvJ5wAXbocOM223r2p37IlzJoF//sfvPSSS1ps2+bqS/z4o5uFo1277GlBRUREpHiFRMDZr8C7p8NPj8Npo+jSsOqB3fFJKVTLz5cMESk3Tm8bw+ltY/LXuAwNwVACQqQ41KjhhldccokrOLlkiUse/PabS0x8+KFrV6kSdOt2ICGx77jj4MYb3b60NFi0yPWAyCpUc9NN8M8/ri5F69YugXHaaXDBBZ68TRGRY2GMmQ6MttZOybFtrLV2mIdhieRPw+7Q5VqY+zq0PAMa9gDgw7nrefr7FUy5pSf1q1bwOEgRKQm2JSYTEhRElcjQ/B2QkggYCI0s0riKgxIQIsXNGNdjoV07GDHCJSTWrnXJiKzlIVfIqidAkybQsWP20rVr9rl++MEVtfzzT1iwwNWRsNYlIKx1iYwGDVxyImtp0sQlLERESp5GwN3GmC7W2kf82zp7GZBIgZzyCKyeDl/9F/47G8Ki6d28Bk9/t4JbPlnIZ9efRIhPI6BFyru3f13Hu7P/5a+RAwkP8R39gJRECKuY/SNkKaZvISJeM8YlBZo0cbNnAOzaBXPnsvaLL2i8e7dLLkyYkH1M7douGdGuHRx/PAweDHffDdHRkJzs2iQkuCKYv/+ePeQDXD2KRx91+195BZo3h6ZN3RIVVWxvW0QkD7uB/sBLxpivgcu8DUekgMKi4Jw3YNxpMPV+OPsl6letwJPntuXmjxcy5sdV/N+pLbyOUkQ8Nmv1Djo2qJy/5AP4ExClf/gFKAEhUjJVqQKDBhEbEUHjPn3ctj173BCMhQuzlx9/dEMzstSp4xISxx8PLVvC7be7GTeqVIFVq2DZsgMFLlm5Eu6/P/fr1q4Nb77pphXdsgV++cUdf9xxrvZEGci6ikiJZqy16cCNxpirgFlAFW9DEimgBt2g+y3w2xhoeSY0H8hZ7evw66rtvDpzNSc3rcbJTfIx7Z6IlEk796aybFMC/zewef4PSklQAkJEilmlStmFLbOkpbnhGytWwPLlblmxwk0LmnP6Tp/PJREaN4bZs926cWM3U0daGuzcCWvWuCRF/frumFmz4D//yT5HRIQbzvHRR24q0RUr3NSi9etD3boQE6MeFCJyrN7IemCtfdcYswS4ycN4RAqn7/2wahpMHg43zoUKVXn47NYs3ZjAlj3JXkcnIh6avcZNv9m9aQESkeoBISIlQkgItGjhlsGDs7db64pVrlwJ69a5JEXW+quv3KwcB5+nTh2oVw+eftqta9WCZ591CYp9+2D3bnfOqv6q3t9/73pY5FSxouul0aiR2//TTy4xUasW1KzpltatXUJEROQg1to3D3r+JzDUo3BECi84DM55E97qB9/eARe8Q4XQYL6+uYem5RQp535bvYPo8GDa1q2U/4NSEiG8cpHFVJyUgBApi4xxvRLq1s17f1JSdkIiLg42bnTruDhXb2LyZNi//9DjIiLc/tq13ZCM//zHFbS0FtLTXf2J9eshI8P1oHjxxdxDRAD27oUKFVyhzc8/d0mJ6tVdYqN6dTdtqTEukbFnj9tetarrARIZqWEgIiJSOsS0gz53u2k5W54Bbc8/kHyYtGgjyWkZ/KdLA4+DFJHidkPvJgxsVZvgghSkTUmESvWLLqhipASESHkUFQVt27olL9a6QpgbNrhaEFu35l62bHGJhq1bYccOyMzMPnby5OzHPp9LKkRGuuRFaChceSVUruzO7fO55MeaNS4xAa4nR3Q0PPAAfPtt7rjq14fYWPf4tttg8WKXmKhUyR3TuHF2r4ypU905o6MhOprItWtdoc169bLfo5IZIiJSlLrfDiu/d70gjusOFWOw1vLlgo3MWRtP+/qVaVm7otdRikgxOq5aJMdVK+B0mhqCkZsx5jRgDOAD/metfeqg/ca//3RgH3CVtXZBfo4VEQ8Yk93zIKto5eFkZrrhGfHxh19273bLnj2uEGbW87x6WZx00qHbQkLckpjoCmxGRrrkx969rrdFerpbqlSBbdtcsmPsWJfc8OsC0KqV65URFuYSIZs3u7YVKrild294/nmXKLnpJnf+iIjspXNnuPhid8I3/T3Fw8PdEhbmZjLJSurMn+/OExrq9oWGZidKrHU9Q0JClAQRESnLfMFuKMYbPWDyzXDp5xhjeO6C9gwa8yu3fLyQSTf1ICJUQxNFyoPZa3awaXcy53SsW7DhWFnTcJYBx5yAMMb4gFeBAUAcMN8YM9la+3eOZoOAZv6lK/A60DWfxxa51FRITdWczCKFEhSUnaxo1qxgx6amukREYuLRl337XEIgax0Vlfv5/v1uGT360GEfWf7+GwYOzL0tJcXFALB6Nbz9du79WQkCa10S4p57XOJg7Vq3Lac6dVySw+dzPTAO1ro1dOvmkibvvpt9fp/PXccePaB7d/d+xo1z27P2BQdD377QpYtL5Iwfn73P53P7+/d3CZDt22HiRLcta7/PB6ec4v6MNm+GadNyHx8U5I6vV88lbmbPPnR/795QsybVf/kFpk9323Lu79HDJVni4lz9kaz9WUu3bi7RExcH//7rjjMme+nSxSVr4uJcjMZkHwtu6lmfz9UiiY/Pvn5Zbdq0cds2bXLXKCgo+9zBwa4HjDHu3ElJ2fvB7W/Y0D3essUNJ8p6XWOy66SAS3KlpmbvM8YlmGrUcI+3b3cJMcg+R1iYS5AZ42LPyICQEEzWeUSk7KreFAY8At/dBQvegxOuokZ0GM9f2J4rxs3j8W//5olzDtMjUUTKlPFzY1kQu4vzOh1mmHReUvdBahKEF6BmRAkWiB4QJwKrrbVrAYwxnwCDgZxJhMHA+9ZaC8w1xlQ2xsQADfNxbJHascPdM15yyXGHfC8RkSIWGppdnDKQMjKyExLJybB/P/N//ZUu7dq5hENKitue9ThrSUvLykjmvaSlZS9t2uQ+LiXFfbnct899+WzSxG3P2UNjxw747jv3uEIF13skM5P0DENqegipMxaS+tNS0ggmlcqkEUIaIaQS6tYfrCX9g1jSCSaNhqQT7H8c4h7/sYl0tpFOMBm0OrA/A59bT9lBOrvJwEcG7f3rHMt7e8ggiUyCyKCTf+0jkyD3ePReMllPJq0ObMu97COTZDIJI5MOB7ZbjP9xCpZUMqmIpf2BfVn7LWlY0smkGpbqB/ZlL+lYMrDUIJNaAAftz/CvY7DUwWIOaeOeH7ov67Fb18tjW/avFJZ6ee7LXtfP45hDjwe4peOf9NZnj0jZ1+U6WPEtfH8fNOoNVRvRq3kNhvVqzNhf1nLxiQ1oU5CCdCJS6mRkWn5bs4NTjq+FKUgP2I1/uHWdjkUTWDELRAKiLrAhx/M4XC+Ho7Wpm89jATDGDAOGAdSqVYuZM2ceU9BZ3ND13syfXzFg5yzvkpKSdC0DRNcycJJq1WJmVp0Jn88N44g8dPxdRoZh/34f+/cH+dc+kpPdOiUliJSUg9fucXJyEKmpbklLCyK1evbznNvT0gypqUGkmyDSMg3p6UFkZhb3MAyLL8jiC8rEWsjMcFtzfpWvGJVKsC+TlJQgkpN9B7ZnfWWPqb6X4KBMEhJD2Ls/hKyv2FltGsfswmCJ3xNB0r5Q/3ZcSsJk0qxOPAbL1l1RJO0PJQgLBozJJMSXQdOaOzBYNu2KZl9yKEEGCAJDJmG+NJpU347BsmFnZZJTQzDGgi8IgyUiOJXjKm8nCEvsziqkpAe7r//BPsASGZxM/Uo7MNayfmc10jJ8GAM2xLWLCt5L3UgX37qdNdyfT5DBhriPzIq+JGIq7ARgXXwN984N2NBQjLFUDkqgZsQuANburOEublAQNjQEgKpmN9Uj9mBDQmhwotG/cZHyICgIhrwGr50EX90IV30DQT7+b2ALTmpSTckHkXLg700J7N6XRo+CTL8JEDsXMFC/S5HEVdwCkYDI687Z5rNNfo51G60dC4wF6Ny5s+3Tp08BQjyy4GBISAgnkOcsz2bOnKlrGSC6lgWTkuJqZ+7c6dY5l7/+Wke1ao3YswcSEnIve/a4UR5797pzFERW7/ysUQ5ZPfJr1XJLWBj89Zfr9JCRkV2vc+BAV15jyxb44INDzzt8uBuxsGwZjBrl/p/KKicREgKPPgonnAB//unKUYSFuSWrHMW997rRFn/+CZMm5S5VERpquO46Q7VqQSxe7MpVZJXZyFoGDgwjIsJNlrJhg3v9kBC3XrBgPldd1QWfz40mSEpy24ODs69D5crVMSZ7NEzWKI1s9Q5907k0LdgfRCmlf+Mi5UilejDoafjqvzD3NTj5ZkKDg+jbwvUCXL45gUbVIwkPUT0IkbJo1uodAJzctFrBDoydCzVbQUSVIoiq+AUiAREH5JwTpB6wKZ9tQvNxbJGrUAGSkkKK+2VF5AisdcmBzZtdvcnt27OXHTsOfb5rV941LbM1IiLC1YCsUMGtq1d3w/7j4lwJi8zM7BEWnTvDmWe6bZdffujZ7r0XRo505QAaNHDJgchIV5oiOtrtv/hiV07hvvvc9qgo99qRkTBokCsJsXMnXHRRdh3MrHqXMTGuXWYmPP74wV/es3XuDNdff/h3PXDgoWUvcmrXzi2HvWqN3JLTnj178fnvj6tVc8vhhOi/VhGRbO0vdkMxpj8KTU+BmscDsGVPMkNe/Y1zOtblqfOO8J+yiJRaa7cn0aJWNDWjw/N/UGYGbJgH7S4susCKWSASEPOBZsaYRsBG4CLgkoPaTAaG+2s8dAX2WGs3G2O25+PYIle5MmzcqCKUIsUlNdV96Y+NdcvGjS7RcPByuIRC5coueVCjhksgdOjgftk3JnuCibp14eyzXd2/yy+HNWuSSUwMZ9s2d46rroJ33nHtw8LctqxamjVquHqKl1ziei6sWePOU6kSVKzo1s2auePq1nXlJLLOcbC6deG99w5/LapWhdNPP/z+wyUeRESkFDIGznwRXusGE6+Ha6eDL4TalcK5tmcjXp2xhk4NqnBhl/pHPZWIlC7PXtCevSnpBTto6zJITYQGecwSV0odcwLCWptujBkOTMVNpTnOWrvMGHODf/8bwBTcFJyrcdNwXn2kY481poKqWRNiY4NISTn8lwgRyb/0dFi/Hlatcl/e1693S1bCYfPmQyeQqFjR/eofEwNdu7oJB7Ke+3wuGbFvnxsusXGj++L+6KPu2ObN3WvlNGCA6zkArqdBlSq7aNs2hho1XPKidWu3zxjXCyEyMu8ZMYODXU+HwwkK0v8bIiJSAFE14KwX4dPL4Jdnoe99AIwY0IJFG3bz4KSltKpTUXUhRMqgyLACfv2OnevWDboFPhiPBKIHBNbaKbgkQ85tb+R4bIGb8ntscevRA/74w43PFpH8sdYlE5Yvd1/+V6/OXq9blz0LIbjhCQ0awHHHwamnusdZz+vXdz0KNm92M1uuWeOWXbvguefc8f36wYwZ2eerXBl69cp+PnKk61VRu3Z20qJ6jvo+b78NM2eupE+fmDzfS1RU4K6LiIjIUR1/lhuO8ctz0PxUqHsCviDDSxd15MyXZ3Hj+AV8fXMPKkVoHJtIWfDqjNUs35zAyxd3LNgMGLFzoGJdqFx2ekUFJAFR2h3vht+xc6cbgy0i2ax1dQ6WLs29LFvmCjdmiYpywxI6dIDzz3ePmzZ1S61arnfBhg2wYoVLWvz1F1x9tdt+xRW5CzFWrep6KFjr9o8cCXff7ZIV9eu7Ggs5XXppsVwKERGRwDntKVj3C0y8Aa7/BUIiqBYVxquXduLHv7cSGapilCJlxdRlWwgP9hUs+WCtS0Acd3LRBeYBJSDILqD288/6IiPlm7UuSTB/fvayeLEr8pilWjVo2xauvBLatIFWrdwQiJo1s4cwxMfDokXQpYubeeHll11RxqxZMMH1Yhg50iUbrr/e1Wto3NgtlSvnjqt37yJ+4yIiIsUtojIMfhU+GOKKUp42CoBODarQqYGrdp+clqFZMURKud37UlmycQ+39W9ewANjIXFzmar/AEpAAK7bNsC33yoBIeXL9u25kw3z53OgSGNwsJsdYfBgl3Bo08YtORMNWVatgldfhYULXeIhLs5tnzfPJSGOPx6uucatW7Z065zn6d692N6yiIhIydGkL5w4zE3L2WIQNMoeX/jP1kSuGjePZ85vT49m1Y9wEhEpyeasicda6NGsENNvQpmq/wBKQACuij648ewiZdmWLa6nz8yZbr18udtujEsKDBrkEgZdurjkQ/hBswQlJMD06TBnDsydCyNGQP/+rijkk0+65ELv3m4YRocO2cObTjnFLSIiInKQUx6B1dPhq5vgv79BeEUA6laOIDIsmFs+Wci3t/QgplKEx4GKSGHMWr2DqLBg2tWrXLADY+dAWEWo2apI4vKKEhC4X2LBsnlzAcbkiJQCmzblTjisXOm2R0e74qtXXgknnQSdOh1aiNFaN/NERIRLXAwY4Oo+ZM1e0aqVS0iA68GQmOjaioiISAGEVoBz3oRxA2HqvW5YBq5a/huXn8DZ/qKUnw47idBgzc0sUto0qh7JRV3qE+Ir4L/f2LlQ/0QIKlvDsJSAAEJCICTEEh+vBISUbhkZ8Pvv8M03blmyxG2vWNHNGnHttdCnj+udEJzHv/64OPjpJ9fL4aef4Iwz4I03XJKuaVNXXPKkk+DEE3PXaXD/horhDYqIiJRF9btAj9vh19HQ8kw3HANoUiOKZy9oz43jF/DklOU8fHZrjwMVkYK6tmfjgh+0bydsXw5tzwt8QB5TAsKvQoV0EhNDD1TdFyktdu+GqVNdDZMpU1wByOBg6NkTnn3WTWHZvj348kieZvVwADeU4qef3ONq1dxx/fu750FBMHFisbwdERGR8qn3PfDPDzD5FrhxLkS68eKnt43h2h6NWLM9ibSMzIL/iiointmemELFiGDCggvYiyFuvluXsQKUoATEAY0a7cXaUK/DEMmXLVvgs89cUuDXX13Ph+rVXY+FM86AgQMPnUkC3PCJFStg8mT4+mtYv97VPjEGzjrLHdu/vys6GaT7GxERkeITHArnvAFj+8C3t8MF7x34VeyeQS0JMoagIP1KJlKaPPL1MpZu3MPMO/sW7MDYORAUAnU6FU1gHlICwq927WSWLlXvBym5EhLgq69g/Hj48UfIzHSJgrvvhjPPdMMi8urlkOXzz+G++2D1ave8Uyc3M0VqKoSFwW23Fce7EBERkcOq3Qb63Q8/PgxLJkC7CwAI9vd62LR7P898v4LHhrQhOlxjH0VKssxMy+w18fRpXqPgB8fOhTodXI2YMkYJCL/IyHQ2bYI//4QTTvA6GhEnLc0webJLOkyeDMnJ0KiRSyRcckn2LBMHS011wzI++wzuvNPNaBEV5eo4jBjhejvUq1e870VERETy4eRbYOV3MOUOOO5kqFT3wK4NO/fx9eLNpGZk8uolnTD65UykxFq+JYGde1MLPo1uWjJs/BO6Xl80gXlMnaz9qlRJIzMTvv/e60hEYPFi+O9/4bzzTmbwYFeb4ZprYPZsWLMGHnvs0ORDZibMmuWOi4mBs892NSHWrHH7Bw2C775z+5V8EBERKaGCfDDkdchIg4nXQ2bGgV1dG1fj7tNaMGXJFt6etc7DIEXkaH5bvQOA7k0LmIDYvAgyUstk/QdQD4gD6tTZD2RPUyhS3NLS3BCLV16BX36B8HDo0WMnt99eiwEDDj/LREKCm+Vi715X+wFgyBC49FL3XLNTiIiIlDLVmsDpz8Kkm2DW89DrzgO7ruvZmAXrdzPquxW0q1eZExtV9TBQETmcX1ftoFnNKGpVDC/YgbFz3Lp+18AHVQKoB4Rf9eqpAKxTMlmK2ZYtrkdDw4Zw4YWwYQM89xxs3Aj337+c008/NImwaxe8+CJ07Ah9/TVtoqNdD56tW+Gjj1xBSSUfRERESqkOl0Kb82HGKDce3M8YwzMXtKN+lQien6ZfzkRKqhEDmnP/GYcZL30ksXOhWjOILGDPiVJCPSD8qlZNAdyXPpGiZi3Mnet6O3z+uev9cNppMHasWx+umOSyZfDCCy7BsH8/dOkCl13mhl8EBUGvXsX7PkRERKSIGANnvgAb/4AvroUbfoWIKgBUDA/h3atPpFqUZnATKak6NqhS8IMyM10C4vizAh9QCaEeEH5Vq7oeEPHxHgciZZq1MGMG9OkDJ58M33wDN90E//zj6jOcccahyYfkZNi3zz2ePx8+/tglHRYuhHnz4JZbNGWmiIhImRReEc4fB4mbYfLN7kbCr2H1SKLDQ0hOy2DKks0eBikiB5uxYhs//7O94AfuWAnJu8ts/QdQAuKAiIhMoqPhyiu9jkTKqqzEQ79+birMl15yPW5eeAGaNTu0/bp18OabjalXz/WMALjoInfM2LHQoUNxRi8iIiKeqHsC9B8Jy7+GP8YdsvvtWeu4cfwCvl+qJIRISfHi9FW8NH1VwQ/Mqv/QoFtgAypBlIDIISbGjccXCaSZM3MnHl5+2c1McfPNbmrMgy1b5gpINm0Kn31Wn9694cQT3b7wcKhcuRiDFxEREe+dNBya9Iep98HWZbl2XduzEe3rV+b/Pl/M2u1JHgUoIln27EtjSdzugs9+AW74RWRNqNo48IGVEEpA5FC1Kvz6Kyxa5HUkUhZkJR769nVDLF56ySUehg93iYTDuekmmDQJ7rgDPvlkLl984YZriIiISDkVFATnvAFhFeHzqyF134FdYcE+Xru0EyE+w38/XMC+1HQPAxWROWvjybTQo1AJiDmu94MxgQ+shFACIofq1V0PCCUg5FisWAGnnpo78bB2revxkFfi4ddf4ayzYNMm93zsWFi/Hp55BmrUSCne4EVERKRkiqoJ546FHf/A9/fk2lW3cgRjLurIqm2JjJy07DAnEJHi8NvqHVQI9dGhfuWCHZiwCXbHlun6D6AERC6N/T1dYmO9jUNKp4QEuPNOaNsWfv8dnn/+8IkHa2HqVDdrRa9erpjkihVuX/PmUK1a8ccvIiIiJVyTvtDjNljwHiz9MteuXs1r8Mz57bmxb1NvYhMRAJZu2kPXRlUJDS7gV+2s6XbLcP0H0DScudSt69arV3sbh5Qu1sL48S75sGULXHMNPPkk1KyZd/u0NNdDYsYMqFcPxoyBa6+FChWKN24REREphfreD//Ogq9vhbqdoErDA7vOP6EeANZalm9OpFWdih4FKVJ+fXHDyezZn1bwA2PnQkgk1G4X+KBKEPWAyCEmxq3XrPE2Dik9Fi6Enj3h8suhfn3X8+F//8s7+bB7t1uHhEDHjvDqq+7v2i23KPkgIiIi+eQLgfP+5x5PuAYyDv2i89avaxn86izmrdtZzMGJSFCQoUpkaMEPjJ0D9TqDr2z3EVACIoesBMS+fUduJ7JzJ9x4I3TuDCtXuqTD3LnZs1XklJAA993netgsXOi2jR7tjg8txP9NIiIiUs5VaQhnvwQb/4AZTxyy+z+dG1C/agWu/+AP1sfvLf74RMqpUVOW8+zUFQU/MDkBti4t8/UfQAmIXLISEPfcc+R2Ur5NmgQtW8Kbb7oZK/75xw27CDroX1N6OrzxBjRrBqNGwTnnuEKnIiIiIses9TnQ6UqY9SKs+SnXrkoVQhh3ZRcsMPTd+YXrDi4iBZKZaZnwZxwbd+0v+MFx88FmQoOugQ+shFECIoesBMTmzd7GISVTYqKr1TBkiOvNsGCBm+GiSpVD22Zmuqkz//tfaNHCFZn88EM3TENEREQkIE57Cmq0gC+vh6RtuXY1rB7JG5edQOzOfdz6yUKstR4FKVI+rNyaSPzeVLoXavrNuWCCoF6XwAdWwigBkUOVKm58/ssvwzLNYCQ5/PYbtG8P77wD997raj20b39ou4QEtw4KgqFDYeJE+Pln6FL2/y8RERGR4hZaAc4fBykJMPEG9wtIDt0aV+OZ89txTY9GGGM8ClKkfPht9Q6AQiYg5kDtthAWHeCoSh4lIHIwxk1/uHat61Yvkprq6jf06uWe//yzm+Hi4NoN1sLHH0PTpvClf1asG25wvSX0eS8iIiJFplZrOPUJWDMd5rxyyO5zOtajZ7MaAGzYqUJnIkVl1uodNK4RSZ3KEQU7MCMN4v4oF/UfQAmIQ2RNxRkb620c4r1ly6BrV1e/4eqr4a+/oEePQ9vFxsKZZ8Ill0CjRq7mg4iIiEix6XwNHH8WTH8ENv6ZZ5Mflm2h73Mz+WnF1mIOTqR8OK5qBQa3r1vwAzcvhvT90KBb4IMqgZSAOEj9+u4X6/XrvY5EvJKZCS++CCecABs3wldfuVkuovPoEfXuu9C6tesZ8eKLMHs2tG1bvPGKiIhIOWcMnP0yRMfAhKGuov5BejSrTova0dz80UJWbDl0v4gcm0cGt+HWUwrxS2TsHLeurwREuRQT48bvqwdE+ZSUBBdeCLffDgMHwpIlMHjw4duHhUH37rB0Kdx6K/h8xReriIiIyAERVeC8/8HuDfDN7W58aA4VQoN5+8ouRIUHc827f7A9McWjQEXKnt37Ugtf6HXDXDe1bsWYgMZUUikBcZCYGMjIgEqVvI5Eitu6dS6ZMHEiPPecm26zVq3cbayFV15x02sCXHQRfPcdNGxY7OGKiIiI5NagG/S5F5ZOgEXjD9ldu1I4b1/ZhZ17U7nu/T9ITc/M4yQiUlBD353Pte/9UfADrXUzYJST+g+gBMQhatd265EjvY1DiteMGW6mithYmDIF7rjj0OKRO3fCuefCzTfDDz+4/y+MUZFJERERKUF6joCGPWHKnbB95SG729StxAv/6cDgDnUI8ekmRuRYJSSn8VfcHlrVqVjwg3euhb3by039B1AC4hAx/p4vmzd7G4cUj6weDQMGQM2aMG8enHrqoe1mzYIOHeDbb2H0aJgwQYkHERERKYGCfHDuWxAS4epBpCUf0uS0NrW5urubmnPn3lQPghQpO35fu5OMTFv46TdBPSDKs6wExIUXuuk4pexKSYHrrnM9Gk4/HebOzXsGi9hY6NcPQkLgt99gxAhXJ0RERESkRKoYA0Neh61LYdqDh222dOMeej8zg0mLNhZjcCJly2+rdxAR4qNjg8oFPzh2DkRUherNAx5XSaWvUQfJSkDExrqaAFI2bdnikgpvvw333+9muqh4UK+p/fvdukED+PBDWLjQDdMQERERKfGanwrdboR5Y2HFt3k3qRXN8XUqcueExfy5flcxByhSNvy6ajsnNqpKWHAhqtHHznXDL8pR12olIA5Ss2b2n79mwiibshIJCxfCp5/C448f2qPhu++gcWM3vSa4HjEHJyhERERESrRTHoaY9vDVjbAn7pDdocFBvHHZCcRUCuf6D/5gw859xR+jSClmreWu01oyrFfjgh+ctB3iV0P9roEPrAQ7pgSEMaaqMWaaMWaVf10ljzb1jTEzjDHLjTHLjDG35tj3sDFmozFmkX85/VjiCYTgYKhRwz1WAqLs+fVX6NPHJZlmz3aJhZyshccec0MyatZ0i4iIiEipFBwG578DmenwxXWQkX5Ik6qRobx9ZRdS0zO59r0/SExO8yBQkdLJGMOprWsXrv7DhrluXY7qP8Cx94C4B5hurW0GTPc/P1g6cIe19nigG3CTMaZVjv0vWGs7+JcpxxhPQMTEQFgYrF/vdSQSSFOnugKTtWu7Wg4dOuTev38/XHIJPPQQXH65qwlx/PGehCoiIiISGNWawBmjIXY2/PJsnk2a1ozi9ctOoNNxlQvXjVyknPrx7638vSmhcAfHzgVfGNTpENCYSrpjTUAMBt7zP34PGHJwA2vtZmvtAv/jRGA5UPcYX7dIxcRAdDQ0aeJ1JBIoX34JZ50FzZu7XhD16x/a5qOP3JCMp56C996DiIjij1NEREQk4NpfBO0ugl+egX9n5dmke9PqjDq3HaHBQexLPbSnhIjkZq3l3olLeP3nNYU7QewcqHuC66lUjhxrAqKWtXYzuEQDcMQO68aYhkBH4Pccm4cbYxYbY8blNYTDCzExEBrqihNK6ff++3DBBdC5M8yYceiwipQUtx461PV6uPvuclUHRkRERMqDM56DKg3hi2shcethm21NSGbQmF/5YK66AoscyaptSWxPTKFnYYZfpO6FzX+5ApTlTPDRGhhjfgRq57GrQF/PjTFRwBfAbdbarH4qrwOPAda/Hg0MPczxw4BhALVq1WLmzJkFefmjSkpKOnDO1NRGbNnSgJ9++lnTLRZCzmvpta++qsOYMc3p1GkXDz64lL/+ysi1/5dfqvPqq015/vm/qFvXTXtRQkIHSta1LO10LQNH1zJwdC1FpNiERcOF78P/BsBnV8CVX0Nw6CHNqkeF0aRGFA9PXkbDahXo2ayGB8GKlHyzVu0AoHuzQiQgNv7parOUs/oPkI8EhLX2lMPtM8ZsNcbEWGs3G2NigG2HaReCSz6Mt9Z+mePcW3O0eQv45ghxjAXGAnTu3Nn26dPnaKEXyMyZM8k659KlMH48nHNOH/75B2rVCuhLlXk5r6WXnnoKxoyBs8+GTz+tQnh4zwP7rIUnn4SRI6FbN+jfvyu180qzeaykXMuyQNcycHQtA0fXsugZY6oCnwINgX+BC621h8w3aIypDPwPaIP7YWSotXZOsQUqUhxqt4XBr8AX18DUe11tiIP4ggwvXdyR81+fzY3jFzDxxpNpWjPag2BFSrbfVu+gUfVI6lYuxLjt2N8BA/W7BDyuku5Yf9+fDFzpf3wlMOngBsYYA7wNLLfWPn/QvpgcT88Blh5jPAGR9UU0IUEzYZRG1sJ998G997qikhMmQHh49v7kZFdk8oEH4NJL3bCMkph8EBGRgMhPwWyAMcD31tqWQHtczSqRsqft+XDyzTD/f7DggzybRIUF878rOxMWHMTQd/9gW2JyMQcpUrJlZloWbthN96bVCneC2DlQsxVElIgKBMXqWBMQTwEDjDGrgAH+5xhj6hhjsma06A5cDvTLY7rNZ4wxS4wxi4G+wO3HGE9AxORIiygBUbpYC7fdBqNGwbBhrv5DSEjuNk8+6Xq4PPEEfPBB7uSEiIiUOUctmG2MqQj0wv1ggrU21Vq7u5jiEyl+/R+Gxn3g2xEQ90eeTepVqcBbV3SmftUIQn0akyySU1CQ4be7+3HbKc0LfnBmBmyYVy7rP0A+hmAcibU2Huifx/ZNwOn+x7OAPEv6WWsvP5bXLypKQJReI0fCSy+5JMTzz+ddTPK++6BHDxg4sNjDExGR4perYLYxJq+C2Y2B7cA7xpj2wJ/ArdbavQc3LOqaVAWlOiKFo+sGwTHXcMKmvwl6/0L+PGE0qWF5/xJ7bRPLonmzSc2w7EncW+6vW2Ho71vhlNXrFpW4ls6pify9txLbiuD9lfTrdkwJiLIqKwEREqIERGny0kvw2GNwzTWHJh82b4Y77oBXX4UqVZR8EBEpSwJQMDsY6ATcbK393RgzBjdU48GDGxZ1TaqCUh2RwtF182vbCP43gJM3vglXTM6zKCW46QaHvjufjduSmXR7TyJCfcUcaOmmv2+FU5Kv2wNfLaF1nUpcfGKDgh/8+z8AtDp1KK0q1w9wZCX7usGxD8EokyIioFIlaN0aOnb0OhrJj/Hj4dZbYcgQeOON3MmHf/+Fnj1h8mRYudKrCEVEpKhYa0+x1rbJY5kEbM2qOXWEgtlxQJy1Nmua8Am4hIRI2ZZVlDJ2jitKeRjGGM7tVI9VuzIZ9sEfpKRnHLatSFmXlJLOJ/M2sGHnvsKdIHYOVKwHRZB8KA2UgDiM2rWhaVO44gqvI5Gj+e47uOoq6NMHPv4YgnP061mxwg23iI+HH390M16IiEi5ctSC2dbaLcAGY0wL/6b+wN/FE56Ix9qeDycNP2JRSoCz2tdhaJtQfl21g5s/WkhaRmYxBilScsxbF096pqVH00JMv2mtS0CU0/oPoATEYcXEuG77ew8Z/SklyezZcN550K4dTJqUu6DkX3+5ng/p6fDzz0o+iIiUU/kpmA1wMzDeXxi7A/BkcQcq4plTHoFGvf1FKf88bLOe9UJ4+KxW/PD3Vh79Wjk6KZ9mrYonLDiITscVYgaL3bGQuLlcJyBUA+IwYmJg6lSIioJ9+9ywDClZliyBM86AevVcL4iKFXPvr1oVWrWCt96C5oUoUCsiIqVffgpm+58vAjoXX2QiJYgvGC54F8b2hk8vg2EzIbpWnk2v6t4IC5zUpJDTD4qUcrNWb+fERlUJDylELZTYuW5djhMQ6gFxGDExkJTkHm/Y4G0scqh16+DUU6FCBfjhB6iZo6b5okWQkQH168PMmUo+iIiIiBxVharwn/Gwfxd8fiWkpx626dXdG9GydkWstfzyz3astcUYqIh3MjItTWpE0bNZIYZfgBt+EVYRarYKbGCliBIQhxETA6n+/3c1E0bJsnUrDBgAycku+dCwYfa+GTPcUIunnnLP85qGU0RERETyENMuR1HK+47afNrfW7li3Dxe/HFVMQQn4j1fkOH1y07gmh6NC3eC2LlQ/0QIKr8zySgBcRhZU3GCEhAlSWIinHaaq8/x7bduppIsc+fCWWe54qE33OBdjCIiIiKl1oGilG/Bwg+P2PSU42tx/gn1GDN9FWN/WVNMAYp44+d/trNmu+si7wsqxK+c+3fB9uXlevgFqAbEYdXOMZu4EhAlQ2YmXHklLF4M33wDJ52UvW/RIhg0yP25TZsG1TQsUURERKRwTnkEtiyBb26HGsdDvRPybBYUZHj6vHbsT83gySkrqBAazGXdjivmYEWK3p59adz+6SJa1Irm42GFTCBsmOfWDU46crsyTj0gDiOrB8R557lpHMV7TzwBEyfCc8+5ZEOWlBQYPNgVDJ0+PXfvFREREREpIF8wnP8ORNV2RSmTth2+aZDhhf90oF/Lmjw8eRkbdu4rxkBFisfz01aye18qD5x5fOFPEjsHgkKgTqfABVYKKQFxGFlfYk8+GU45xdtYBCZPhocegssug9tuy70vLAzefx9+/BGOU9JdRERE5NhFVoOL/EUpPztyUcrQ4CBeu7QT7w09kfpVKxRjkCJFb/nmBD6Yu57Luh1H6zqVCn+i2LlQpwOElu9/I0pAHEblyu6LbWwsrF7tdTTl2/LlLvFwwgkwdmx2YclNm+CTT9zj3r2hRQvvYhQREREpc2LawdkvQ+xs+OH+IzYND/HRvambGWD68q38/M/24ohQpEhZaxk5aRmVK4QyYsAxTK2Xlgwb/yz39R9ACYjDMsb1gpg2Ddq0cfUHpPjt3u2GV0REuOEXERFu+/btrmfKsGHusYiIiIgUgXYXuKKU88ZSe/P0ozbPzLS8NH0V13/wB7+vjS+GAEWKTlqGpUODytwzqCWVK4QW/kSbF0FGarmv/wBKQBxR7dqQnu5qDOhLbvHLyIBLL4V162DCBKhf323fvRtOPdVt//prqFHD0zBFREREyrZTHoFGvWn+z+vuV9wjCAoyvH1VF+pWjuCa9/7grw27iydGkSIQGhzEfacfz4Wd6x/biWLnuHX9rsceVCmnBMQRxMTA/v3usWbCKH4PPghTpsBLL0HPnm7bvn1wxhmwdKnrEdG7t7cxioiIiJR5/qKUqaFV4JMjF6UEqB4Vxvhru1ElMoQrxs1jxZaEYgpUJHDGzVrHb6t3BOZksXOhenOIrB6Y85ViSkAcQUwM7NnjHisBUbw++wxGjYLrroMbbsjePmkSzJ0LH38Mp53mXXwiIiIi5UpkNZa2udcVpfz8KshIO2Lz2pXC+ejaboSHBPHNX5uLJ0aRAFm9LZEnpyxn8qJNx36yzEyXgFDvB0AJiCOKiYEEf8JWCYji89dfcPXVcNJJ8PLL2UUnAS6+GJYscdOjioiIiEjxSYpu7IpSrv8Npt531Pb1q1bgm5t7csfAYyjeJ1LMrLU8PPlvKoT6uOu0AFS537ESkner/oOfEhBHkDUV5yOPQP/+3sZSXsTHw5AhbhaSL75wM5EAvPce/P67e9yqlVfRiYiIiJRzOYpSsnD8UZvXiA7DGMOa7UlcPHYu2xKSiyFIkcKbumwLs1bv4I6BLagWFXbsJ8yq/6AZMAAlII4oKwExcCC0a+dtLOWBta7nw6ZN8OWX2df/++/hmmvg2We9jU9ERERE8Bel7AXf3H7UopRZ9uxP46+43Vz29u/s3JtaxAGKFM7+1Awe+2Y5LWtHc2nXBoE5aexciKwJVRsH5nylnBIQR1C7tlsvXw7Tjz7rkByj1193s1o88wx09Q+RWrwYLrzQTYX6zjvexiciIiIi+ItSvgtRteDTy49alBKgU4Mq/O+Kzvwbv48rx80jIfnINSREvBDiM9zQuzGPDWlDsC9AX5Vj57reDznHlZdjSkAcQdYv8BMmuF4Qe/d6G09ZtnQp3HEHDBoEt9zitm3a5Ga8iI6Gb75xaxEREREpASKrwUUfwr74fBWlBDi5aXXeuKwTyzcnMPSd+exLTS/6OEUKINgXxOUnNaRLw6qBOWHCJti9XvUfclAC4ghq1oSgIIiKcsVLFy/2OqKyKTnZFZesWNH1cshKDo4ZA7t2ueRDvXrexigiIiIiB4lpn6Mo5f35OqRfy1qMuagjwT5DRqYt4gBF8u/Oz//iywVxgT1p7Fy3Vv2HA5SAOAKfLzsJAbBggbfxlFV33+16QLzzDtSqlb39ySdhzhzo2NG72ERERETkCNpdCN1ugnlv5qsoJcAZ7WL4+LpuRIeHsGd/Gnv2aTiGeOunFVv5/M84diSlBPbEsXMhJBJqq6BgFiUgjiImBhIToUYNJSCKwrffwksvwa23wumnu20vvggbN7oEUNu2noYnIiIiIkcz4NEcRSnzd8NsjMFay80fL+S8N2azcff+Ig5SJG/JaRk88vXfNKkRyVUnNwrsyWPnQL3Orm6KAEpAHFXt2rB5M3TqpAREoG3Z4ma9aNcOnnrKbXvzTbj9dnjrLW9jExEREZF88gXD+e9AVE349LJ8FaUEl4S4oXdjtiYkc86rv/H3poQiDlTkUG/PWsf6+H08fHZrQoMD+PU4OQG2LlX9h4MoAXEUMTEuAfH00/DJJ15HU3ZkZsJVV7neJR9/DOHhbrjFzTe7QpQPPuh1hCIiIiKSb5HV4T8fwr6d8OF57stXPpzcpDqf33ASQcZw4ZtzmLVqRxEHKpItPimFV35azaA2tenZrEZgTx43H2ym6j8cRAmIo4iJga1b3TSQLVp4HU3Z8dJLMHUqPP//7d13eJTF2sfx76SHAKFDaALSm3RpQiCgiAiiIKg0u0elCOoBPSpYXtGj2Bs2FARRREVUDkUjgvQioUoRAakiLRBIm/ePJyBKIG13n93k97muvbY9O3Nn2JB97p25ZxzUrevMhrjuOqhUCT76yFl+ISIiIiIBpHwjuP5D2LcOpt4EqdlbT1+7XFE+v6c1FYpF8tDnCSSnpns3TpEMJQuH8/pNTXj4qjqeb3zHYjDBzhIMOUMJiCzExDjf1u/eDePHw48/uh1R4Fu92ik82b073HWX89jIkXDkCHz+ORQv7mp4IiIiIpJbNS+HHq/Br/Nh+h2Qnpatl8VER/LJXa2YcHNzwkKCSE+3WKtdMsR7UtOcRFeH2mWoWLyQ5zvYsQjK1YfwIp5vO4ApAZGFmBjn+o8/4MEHYfJkd+MJdCdOOFtuliwJ77779y03v/7aqQchIiIiIgGs0Q3Q+QlY/wV8+2/IZiIhOjKUaqULY63lsRnreOTLtdqqU7wiJS2d7q8uZMLCX73TQVoK7Fqu+g+ZUAIiC6cTEHv3qhClJ9x/P2zaBBMnQqlSsGABJCVBdDTExrodnYiIiIh4RJsh0HowLHsb5j+X45cXCg9m0uId3DVpBUnJ2ZtFIZJdH/y0nfV7jlKphBdmPgDsWQOpSar/kAklILJQrpxzfXonjJ9/hhRtVZwr8fHwxhswbBjExcGqVdC5MzzwgNuRiYiIiIjHdXocGvaF75+EFROy/TJjDKOurMOY7vWYu2EfN76zmD+PJ3svTilQ9h89yYtzN9Oxdhni6pT1Tic7FjnXlZSA+CclILJwegbE6QTEqVOwcaO7MQWiEyfgttvg4ovhySfh4EG49lpnKcajj7odnYiIiIh4XFAQ9HgVqneGmffBhq9y9PKBravwxk1NWb/7KDe9s0TLMcQjxn67keTUdB7tVtd7nexcDMWrQNEY7/URoJSAyEJEBBQr9lcCAmD9eldDCkiPPQZbt8Lbb0N4ONx4o1PYc/p0KFPG7ehERERExCuCQ+H6D6BCU5h2K2xfmKOXd6lfjsm3X8qIzjUJDjJeClIKil2HTjDj593c0a4aVUpFeacTa50dMFT/IVMhbgcQCGJinAREzZrON/clSrgdUWBZtszZbvOOO6BDBxg9GmbPdpIRLVq4HZ2IiIiIeFVYFNz4Cbx3BUy5AW7+xtkdIJuaXvTXh+9Pl++kVOFwOtTWN1iScxWLF2LmkLZU9lbtB4A/t8HxA6r/cB6aAZENFSvCjh3OLDIlH3ImORluvdVJ4jz7rPPYTTc5yzBuu83d2ERERETERwqVgH7TIbwwTLoWDm3PcRNp6ZZJS3Zw24fLmbpsh+djlHztj8RTANQuV5RCYV78Hv50/QfNgMiUEhDZULeus+wiPR1mzYLevSFNxXizZexYSEhwik+CMyOpRg14+GF34xIRERERHytWCfp9BqmnYOK1kHggRy8PDjJ8dNultKlein9/lsALc37BZnOLTynYDiaeIu75H3jzh63e72zHIogsAaVqer+vAKQERDY0aOAUUfz1V2c7zmnTYPNmt6Pyf+vWOTMdbrgBrrgCOnWCu+5yOyoRERERcU2ZOs5yjKO7YXJvOHUsRy8vHB7CuwOb0btpRV6at5l/f7ZGSQjJ0nOzN3H8VCpxvli6s2Oxs/zCqGZJZvKUgDDGlDDGzDHGbM64Ln6e47YbYxKMMauNMctz+nq31c9YorZ2LTRt6txeudK9eAJBWpqz9KJoUXjpJRg5EpYvhy5d3I5MRERERFxV+VLoPQH2rIGp/SA1Z1tshgYH8WyvhgyJq0Gl4oUwOtGTC/h552E+XraTm9tUoUbZIt7tLPEAHNyi+g8XkNcZECOBedbaGsC8jPvn08Fa28ha2yyXr3dNvXrOdUIC1Knj7IyhBMSFvfIKLFkCL78MixbBCy/A4MHQs6fbkYmIiIiI62p1ge6vwLZ4+OIuZ61zDhhjGN65JoPjagCwZtdh9h876YVAJZClp1senbGOUoXDGZLxXvGqnYuda9V/OK+8JiB6AB9k3P4AuMbHr/eJwoWhalVnBkRICDRsqATEhezeHcHDD0O3btCmDQwa5Gxh+t//uh2ZiIiIiPiNxjdBpzGw9jP43yinWFgunEpN466JK7j29Z/YeiDRw0FKINt6IJFt+xN5qGttikSEer/DHYshJAJiLvF+XwEqr+U/y1pr9wBYa/cYY863qMYCs40xFnjLWjs+h6/HGHMHcAdA2bJliY+Pz2Pof5eYmHjBNmNi6rNkSSTx8cu46KKL2bGjEPHxCR6NIT+wFp55pj6QyoABy/jyywgiImozfPgaFi1Kcju8gJPV+1KyT2PpORpLz9FYikiB12YoJO6Hxa9B4TJw2YgcNxEeEswb/Zpyy4RlXPfGT7w7sNnftu6UgqtG2SLEPxBLiagw33S4YxGUbwIh4b7pLwBlmYAwxswFymXyVE72MWhjrd2dkWCYY4zZaK2dn4PXk5G0GA/QrFkzGxsbm5OXZyk+Pp4LtRkb62wj2bp1LH8d5tkY8oN334U1a+DNN6F3b2fq0d13Q0jIpS5HFpiyel9K9mksPUdj6TkaSxEp8IyBy5+E4wdg3uMQVRqaDMhxM5dUKsb0u1sz6P1l3Pj2El7q25gu9TM7hZGCYvXOwzSsEE3Jwj5KBiSfgD0/Q+shvukvQGW5BMNa28laWz+Ty5fAPmNMDEDG9f7ztLE743o/8DnQIuOpbL3eH9SvD6mpsGmT25H4r337YMQIuOSSw1SuDE8/7SznC/HiNrsiIiIiEuCCgqDHa3BxHHw1FDZ+k6tmLioZxbS7WlEnpihfrdnt4SAlkGzYc5RrX1/I+B+3+a7T31dAeqrqP2QhrzUgZgADM24PBL785wHGmChjTJHTt4HLgbXZfb2/OL0TRkKCs8zgsstgzBh3Y/I3DzzgbFd6yy3bGDgQJk+GU6fcjkpERERE/F5IGFz/IZRvDNNuht8W5aqZkoXDmXJ7S57v7azBP3wimfR0bdNZkFhreezLdURHhtK3eSXfdbxjMWCgUnPf9RmA8pqAGAt0NsZsBjpn3McYU94Yczp1WRZYYIz5GVgKfG2tnXWh1/ujWrWcb/LXrnVmiiUmwk8/uR2V/5g/HyZOdGZATJhQlePHYepUiIx0OzIRERERCQjhheHGTyG6EkzpA/vW5aqZyLBgIkKDOZGcyvVvLWLo1NUcO5ni4WDFX834eTdLt//Jg11qU6yQj2o/gFP/oUxdiCzuuz4DUJ4SENbag9baOGttjYzrPzMe322t7Zpxe5u19pKMSz1r7VNZvd4fhYU5SYi1GXM3mjRxdsLIZbHefCUlBe65BypXhuBgWLWqOK+9BnXruh2ZiIiIiASUqJLQfzqEFoJJ18HhHbluKjI0mGsaV+DrNbvp8uKP/Lj5gAcDFX+UeCqVp77eQMOK0VzfzIezH9LTYOdSqNzSd30GqLzOgChQGjRwlmCAk4D44w/4/Xd3Y/IHr73mJGYefdTZarNz570MHJj160REREREzlGsMvSbDiknYOK1cPxgrpoxxnB3bHWm/as14aFB9H93KaOmJ5CUnObhgMVf7Dp0gojQYMZ0r0dwkPFdx/vWQfIx1X/IBiUgcqB+fdi+HY4dcxIQ4MyCKMj27HESD1deCbfcAj/8AMOGbcb48PddRERERPKZsnXhhqlwZCdM7g2nEnPdVJPKxflmyGXc0a4a63cfISRYH1Tzq9rlivLdiPY0ruzjZRA7FjvXmgGRJSUgcuB0Icr166FhQ7j2WihWzNWQXHf//U6hyTvvdGpjtGwJhQopqywiIiIieXRRK+j1PuxeDZ8MgLTc13GICA3moa51+PSu1oQGB3H4RDJPf7OBxFOpnotXXGOt5dPlOzmZkkZIsAunuDsWQdGKUMyHyz4ClBIQOdCggXOdkABRUfDZZ9CunbsxuSk+3tnpoksXuOYamDvX7YhEREREJF+p3RWufgm2zoMv7nb2eM+DsBDn9Gf+5j8Y/+M2rnhhPj9t+cMTkYqL/rduLw9MW8P0lS6sjz+0HX6ZBdXa+77vAKQERA5UqQKFCv1ViBLgT78tm+ldpwtPVqzoJB7at4cOHdyOSkRERETynSb9Ie5RSPgEZv/HI1Xgu19Snml3tSI8JIgb31nCI1+s5bhmQwSkpOQ0npi5gdrlinB9s4q+7dxa+GoYmGDo8JBv+w5QSkDkQFAQ1Kv3VwLirbegZEnYu9fduNzw8svOUpTISAgPd7bgDA52OyoRERERyZfaDodL74LFr8HClzzSZNOLSvDN0Mu4rW1VJi35jSe/Xu+RdsW33ojfwu+HkxjTvZ7vl1/8PAW2fQ+dHoNoHyc/AlSI2wEEmgYNYOZM53bt2s71qlVOEcaC4vffYfRoqF4dNm+GadOgkpY7iYiIiIi3GANXPA3H/4C5j0FUaWh8U56bjQgN5j/d6nJF/XJUKl4IgP1HTxIVHkJUuE6V/N1vB4/z5vxt9GhUnkurlfRt54n7YdYoqNQSmt3q274DmGZA5FD9+rB/v3Np1Mh5rKDthDFihLMEY+BAGDwYrrvO7YhEREREJN8LCoJr3oBqHWDGYNg0y2NNN69SgnLREVhrGTZ1NV1ems/ibbnb/lN8JyXN0rJaSR7qWsf3nX/7oLNVbPdXnPemZItGKodOF6Jcuxaio6FGjYKVgJg3D6ZOhVGj4D//cZZiiIiIiIj4REgY9JkIMQ3h00GwY4lHmzfGMDSuBgZD3/GLGT1jHSeSVRvC38xdv48jJ1KoXqYwH97SgrJFI3wbwMZvYN3n0O5BKF3Tt30HOCUgcuj0Vpyn60A0aVJwEhDJyXDvvVCkiFOQU0RERETE58KLwE3ToGh5mHQdbIv3aPOXVivJrGGXMah1FSb8tJ0rX/qRLfuPebQPyZ0Dx05xz+SV3Pbhct5dsM2dIE4ega9HQJm60GaoOzEEMCUgcqhsWafw5OkExK23OjMBPFCM1++9/DJs3AjHjsGBA25HIyIiIiIFVlQpGDQTilWCSb1g7Wcebb5QWAiju9fj4ztaUqFYJOWiIz3avuSMtZbpK3fR+YUfmLNuHw9cUYvBcTXcCWbuaEjcC91fdWbkSI6oskoOGeMsw0hIcO537uxuPL6yb59TeDIoCDp2hOHD3Y5IRERERAq0ouXh5m/h4xth2q2QeABa3uXRLlpWK0nLjOKGJ1PSuHfyKu5oV40WVUt4tB+5sFe+28K4Ob/QpHIxnu3VkOplirgTyG8/wfL3oOU9ULGpOzEEOM2AyIX69Z0ZEKdnPaxb51zys1Gj4PhxKFoUPvhAdVZERERExA9EFoN+06H2VTDr3863016amrznyEk27TtKn/GLePyr9SQlp3mlH3GkW8uRpBQAejeryJju9fj0rtbuJR9STjrFT4tVho4PuxNDPqDTyFyoXx8SE2HHDuf+VVfBk0+6G5M3rVwJEyY4tz/8EMqXdzUcEREREZG/hEbA9R9C05thwQvw5T2QluLxbqqWimLW0Hb0b3kR7y38la4v/8jy7X96vB+BbQcSGbv0JHd/tAJrLTHRkQxsXYXgIONeUPOfhYNboNuLEBblXhwBTgmIXDi9E8bpZRj5uRCltTB0KJQqBT/8AFdf7XZEIiIiIiL/EBQM3V6A2Idg9Ufw8U2QfMLj3USFh/B4j/pMvv1SUtLSeWLmemxBKAbnI6lp6bz5w1aufOlHdh1Lp0ejCm6H5NibAAtfgktuhOpxbkcT0FQDIhfq1XOu166Fbt2gaVP4/HOnMGPp0u7G5mlvvw0LFsD48dCundvRiIiIiIichzEQ+28oXNrZpeDD7nDjJ1DI8/UaWl9civ8Na8ehE8kYYzh8IpmtB47T9KLiHu+roNj55wnu/mglCb8f4fK6Zela5ijXNKvkdliQluosvYgsDlc85XY0AU8zIHIhOhoqV/5rJ4zu3Z3rjz92LyZvSEx0Zj8EBcF117kdjYiIiIhINjS7Ba6fCHvWwHtXwOGdXukmKjyEisULAfDyvC30fvMn/u+bDZxMUW2I3ChWKBSA125swlv9m1Iswk9OVZe8AbtXwZXPeCWZVdD4yb9q4Klf/68lGA0aQKNG8Mknrobkcb17w8mTMGQIlNDvmoiIiIgEijrdoP/ncGwfvNsZ9nm3Yvzwy2vSt0Vlxs/fRtzzP/DKvM3sPpzk1T7zgxW/HeJfk1ZwKjWNIhGhzLi3DVc1jMEYF2s9nO3PbfDdU1DzSqh3rdvR5AtKQORS/fqwcSOkZNS3mTQJvv7a3Zg8adYs51K+PIwb53Y0IiIiIiI5VKUN3PKtc/u9K2H7Qq91VTg8hP/r2YCPbruUSiUieX7OL4yfvw1wdnPQrIi/O5Gcypiv1tHrzZ9Ys+sIuw45yRq/STyAUwzvq2EQFAJXPe8s8ZE8Uw2IXGrQAJKTYcsWqFPnr7oQ+cGJE9Cnj3P7q6/0uyYiIiIiAapsPbh1Nky8Fib2hF7vQh3vVVVvU70UbaqXYuefJ87s2LDpz3SGPjWXqy8pT++mFWlUqZh/nWj72ILNfzBy+hp2HUpiQKuLeLBLbQqH++Fp6eqP4Ncf4KpxEO0nxTDzAc2AyKX69Z3r08swAL78Eq65BtLTXQnJY5Ytg6NHoV8/Z4cPEREREZGAVayyk4SIaQifDIDl73m9y0olClG+WCQARcIMneuUZfrKXfR8/Sc6vzCfN3/YSlJywZsVkZ5uGTtrA6HBQXxyZyse71HfP5MPx/bB/x6Cyq2d7V3FY5SAyKXatSE4+K9ClADHjjlJiIXem93ldampMGIEVKgAb77pdjQiIiIiIh5QqAQM+BKqd4aZ90H8WGeKvQ9ULBLEuD6NWPZwJ8Ze24DoyFDenr+NkGBnFsSW/Ykkpwb4N5hZmLt+H0dOpBAUZHizX1O+HXoZLar6cZG5bx+ElJPQ/WWnIr94jB+mmwJDRATUqPH3GRA9e0JUFEycCJdd5l5subVzJ7RqBb//7tS0iIpyOyIREREREQ8Ji4K+H8FXQyH+aTi211nbHxTsk+6LRITSt0Vl+raozOETyYQGB5Gebhn43lJOJKfSo1EFejWtSP0K0T6JxxcOHDvF6K/W8fWaPQzpWJ3hl9c6s3OI39r4Naz/Ajo+AqVquB1NvqN0Th7Ur//3GRBRUXDttc5uGCdPuhdXbqSkOLte7N4NjRvDjTe6HZGIiIiIiIcFh0KP16DtcFjxvrMkI8X3H9yLFQo7c/upnvVpXb0Uk5fsoNsrC7jypR/5buM+n8fkSdZaPl+1i84v/MCcdfu4//KaDI4LgJP5k0fg6xFQtj60Gep2NPmSEhB50KABbN3qFG08rX9/OHIEZs50L67cePBBWLLEmYn21lsqPCkiIiIi+ZQx0Okx6PKM8233xJ6QdNiVUIKCDLG1yvDajU1Y+nAcT/SoR2iwObM65PfDScxZv4+UtMBaovHqd1u4b+rPVCsVxTdD23JvxxqEBgfAqeecRyFxH3R/xUlWicdpCUYe1K/vnLCvXw/NmjmPdewI110HxYq5GlqOfPIJvPiis7ypf39o3tztiEREREREvKzlXVC4NEy/E96/Evp9BkXLuxZOsUJh9G9Vhf6tqmAzMhCfrdjFuDm/UKpwOD0bl6d3s0rULFvEtRgvJD3dcuxUKtGRofRqVpEiESH0b1XlzG4gfm/7AlgxAVrdCxVUid9bAiAN5b9O74Rx9jKM4GCYNg06dXInptyYPh2KF3eWkDz9tNvRiIiIiIj4SP3roN80OLwT3r0cDvzidkQAZ7bp/Ffsxbw9oBlNKhfj/YXbufyF+fR64yfS031TQDO7th1IpO/4xdz90QqstcRERzKoTdXAST6kJMGMIVC8CnR42O1o8jXNgMiDiy92ilGenYA47cAB2LMHGjb0fVw5NWAATJ0Kzz4LMTFuRyMiIiIi4kPVYmHQTPioF7x3Odz4KVTyjynBocFBdK5bls51y3Iw8RRfrN7NwcRTBGWc2I+bvYmmVUrQtnqpHJ/sp6alc+xkKqdS0zmZksap1HROpaZxUckooiND2XvkJCt+O8Sp1IznUtI4mZrONY0qUC46gpU7DjF95S6On0rjm4Q9hIcE8Z9udb0xDN73wzPw51bo/wWE+XmRzACnBEQeBAdD3bp/3wnjtCuvhJAQWLzY93Flh7UwZgz06wfDhzs7egxVnRUREclnjDElgKlAFWA7cL219lAmx90H3AZYIAG42VobYCWlRSTXyjeCW2fDxGvhg6vh+g+g5hVuR/U3JQuHc2vbqmfuHzqezMTFv/Hyd1soVzSCJhcVIznVMqDVRbSrWZoNe44y7OPVfyUQMpIIz19/CV3qx7Bo20H6v7v0nH4m3Nyc2FplWL3zMPdMXnnO800vKk656Ah2HUri24S9hIc4SZJHu9WlTNEIr46BV+xZAwtfhkb94OIObkeT7ykBkUf168Pcuec+3rcvPPAA/PIL1Kzp+7iy8uKLTgJi1SrYtMkpmhkWluXLREREAs1IYJ61dqwxZmTG/X+ffYAxpgIwBKhrrU0yxnwC9AUm+DpYEXFRiWpOEuKjXjDlBqcQYeOb3I7qvIpHhbH4oTjmbdjPtBW72Lj3GBEhwZxITgUgMjSYKqUKER4STHhIEOGhQYSHBJ/ZBvPi0oUZfXVdIkKDzzwXHhJ0ZhvQ1tVLMvu+ds5rz2ojIsTZtrT7JeXpfol7NTM8Ii0VZtwLhUrC5U+4HU2BoAREHjVoAB9+CH/+CSVK/PX4jTfCv/8NkybB44+7F19mfvzRSY506QLx8c5sjauucjsqERERr+gBxGbc/gCI5x8JiAwhQKQxJgUoBOz2RXAi4mcKl4FBX8PUfvDl3c6OCG3v89st4sJDgunaIIauDc5dR12lVBRv9W923teWL+bUaTifohGhFI3I5ztBLH4N9vwMvSdAoRJZHi55pwREHp1diLJdu78eL18e4uKcBMSYMf7zf9bevdCnD1SrBqVKQVISvPCC21GJiIh4TVlr7R4Aa+0eY0yZfx5grf3dGPMcsANIAmZba2dn1pgx5g7gDoCyZcsSHx/vtcCzIzEx0fUYApHGLXcK0riZivdSOzGdsvPGsGvjCrZUvxVM7ur3F6Rx8yRvj1vkiT00W/4kh0peytr9xeCA9/ryJX9/vykBkUcNGjjX/0xAgLOl5YABsGYNXHKJ72PLzEMPweHDMG6cM0tjxAioVcvtqERERHLPGDMXKJfJU9kqZW6MKY4zU6IqcBj41BjTz1o76Z/HWmvHA+MBmjVrZmNjY3MZtWfEx8fjdgyBSOOWOwVu3GLjYPbDVFz8OhWLhUHPNyEkPMfNFLhx8xCvjpu1Tq2P0AhKDZxArIvbr3qav7/flIDIo/LloVixzAtRXncdXHYZVKni66jO76WXnKTIQw9BmTLwyCNuRyQiIpI31trzbn5tjNlnjInJmP0QA+zP5LBOwK/W2gMZr5kOtAbOSUCISAESFARX/B8ULgtzH4MTB6HPJIgo6nZkklerJsL2H6Hbi5CPkg+BIHfziOQMY5xlGJltxVmokP8kH6ZPh+PHoUgR2LULFi2Cp5+Govr/U0RE8rcZwMCM2wOBLzM5ZgfQ0hhTyBhjgDhgg4/iExF/Zgy0HQbXvAnbF8CEq+DYPrejkrw4thf+9x+4qA00GZj18eJRSkB4QIMGTgLC2nOf278funeHLzP7uOMj77zjzMZ47jk4dgwefBCaN4eB+n0TEZH8byzQ2RizGeiccR9jTHljzDcA1tolwDRgJc4WnEFkLLMQEQGg0Q1w41Q4uAXeuxwObnU7Ismtbx6A1JNw9cvOLBfxKY24BzRt6tRVWLXq3OdKlIBly2DCBF9H5Zg6Fe64w9nxYtQo+L//gz174GX9vomISAFgrT1orY2z1tbIuP4z4/Hd1tquZx33mLW2trW2vrW2v7X2lHtRi4hfqtEZBn4FJ4/Cu5fDhpluRyQ5teEr2DADYkdCqepuR1Mg5ekU1BhTwhgzxxizOeO6eCbH1DLGrD7rctQYMyzjudHGmN/Peq7rOZ0EgJ49ISwMJk4897mQEKfY49dfw8GDvo3r66+hXz9o2xY++wx27HCKTw4YAC1b+jYWEREREZGAV7EZ3DobipSDqTfBxzfBkd/djkqyI+kwfH0/lGsArQe7HU2BldfvwEcC86y1NYB5Gff/xlq7yVrbyFrbCGgKnAA+P+uQF04/b639Jo/xuKJECejWDSZPhtTUc58fOBBSUmD48MyXaXhDcjLcc4+z+8bMmU49ihEjnETJ2LG+iUFEREREJN8pVQPuiIdOY2DLPHjtUlgyHtLT3I5MLmTOo3B8P3R/BYJD3Y6mwMprAqIH8EHG7Q+Aa7I4Pg7Yaq39LY/9+p3+/Z16D7Mz2TW8YUMYMwY+/DDzWRLeEBYGc+bArFlOocnp02HGDGfXi5gY38QgIiIiIpIvBYc6xSnvXgSVmsO3DzjLMvZmUple3Pfrj7DyA2h1L5Rv7HY0BVpet+Esa63dA5CxvVWZLI7vC0z5x2P3GmMGAMuBEdbaQ5m90BhzB3AHQNmyZYmPj89T4P+UmJiYpzajogxFi7bm+ef/pFChcwtnX3YZjBxZlvLl9xMf771pENu2RfHjj6UYMOA3jIHff4fExBBuv7051asn06TJSq/2D3kfS/mLxtJzNJaeo7H0HI2liEiAK1EV+k2HhGkwayS81Q5a3wvtR0JYIbejE4CUJPhqCBSvCrGj3I6mwMsyAWGMmQuUy+Sph3PSkTEmDOgOnP2v/gbwBGAzrp8Hbsns9dba8WRUpG7WrJmNjY3NSfdZio+PJ69t3nQTvP9+WZo0KZvp9pYdOgDUYd8+2LQJ2rXLU3fn2LwZ+vaF4GB45pmqlMlIB91+Oxw5AnPmhNOkSXvPdpoJT4ylODSWnqOx9ByNpedoLEVE8gFjoGFvqB4Hcx6BhS/Bui+g2zio3snt6CT+afhzGwyYoaSQH8hyCYa1tlNGReh/Xr4E9hljYgAyrvdfoKkrgZXW2jMb51pr91lr06y16cDbQIu8/TjuGjAATp50Cj5eyN13Q9eusHKl5/peuRI6dYK0NJg7lzPJh++/d7bhHD4cmjTxXH8iIiIiInKWQiWgx2sw6GsIDoNJ18FntxGafNjtyAqu3avhp1ehcX+o5v0vYiVrea0BMQMYmHF7IPDlBY69gX8svzidvMjQEwjoRVOXXgo1aji1Hi7k1VehZEm46irYvj3v/f73v9CihVN48n//gzp1nMeTkpwtOC++GEaPzns/IiIiIiKShSpt4V8LnWUY67+kxdJ7YOWHvqtGL460VJgxGKJKweVPuB2NZMhrDYixwCfGmFuBHUBvAGNMeeCd0/trG2MKAZ2BO//x+meNMY1wlmBsz+T5gGKMs+3lY485W15Wrpz5cTEx8O230KaNMxNi4UIofs4Gplmz1umzTh245RZ45pm/tzN6NGzZAvPmObtgiIiIiHelpKSwa9cuTp486ZP+oqOj2bDh3NpT+VVERAQVK1YkNFQV7MXPhYRDh1FQ/zqOTxpEsRmD4eePoduLULqm29EVDItegb1r4PoPITIXJ1viFXlKQFhrD+LsbPHPx3cDXc+6fwIomclx/fPSvz86nYD46CMYdYEaJ3XrwhdfwOWXO8sj3n8/+30cPAj33w9Vq8KjjzpbgHbr9vdjVq6E55+HW2+Fjh1z9aOIiIhIDu3atYsiRYpQpUoVjDFe7+/YsWMUKVLE6/34A2stBw8eZNeuXVStWtXtcESyp3RNVjd6ktjoXTD7P/BmG7hsBLS9z0lSiHcc3ArxY6F2N6jbw+1o5Cx5XYIh/1CtGrRt62y3mdUsq/btna0xn3sue21bCx9/7Mx4mDTp/O2npsJtt0Hp0s7yDBEREfGNkydPUrJkSZ8kHwoaYwwlS5b02ewSEY8xQdBkANy7HOp0d4oivtkWti90O7L8yVr4aigEh0PXbJ5oic/kdQmGZKJ/f7jzTlixApo1u/CxV1zhXJ865eyi8ccfULSoc4mOhuuvdxIVhw7BjTfCrFnQvLlTaLJhw8zbHDcOVq2CadNyt7RDREREck/JB+/R2EpAK1wGer0Ll9wAX98HE7o6xRE7P+4UsBTPWPkBbP8Rrn4JisZkfbz4lGZAeEHv3hAW5syCyK5585wikgC7dsGiRfDJJ/DLL85j27fD/PnwwgvOc+dLPmze7CwB6dkTrrsuTz+GiIiIiIh4Wo1OcPdiaD0EVk+G11rAmk9VpNITju6B2Y9ClcugycCsjxef0wwILyheHLp3hylTnOUV2amT1LWrczmfunVh71640DJPa51dL8LDnZ02RERERPzVunXr2LZtG1dffbXboYj4XliUszNDg97OcoHpt8HPU+Cq56GEapzk2jf3Q9opZ/aDZkz5Jc2A8JL+/eHAAZg92zPthYdfOPkA8O67EB/v1H0oX94z/YqIiEjg+fzzzzHGsHHjRlf6nzBhAvfee+95n9+xYwdPPfUU7du392FUIn4opiHcNheufBZ2LoHXW8GCFyEtxe3IAs/6L2HjTIgdBSUvdjsaOQ8lILykSxcoWRI+/NA3/e3c6eyM0b69s/OFiIiIFFxTpkyhbdu2fPzxxx5pLzU11SPtnFa5cmUmT55M0aJFPdquSEAKCoZL74R7lkL1OJj7GIyPhV0r3I4sMBz4BWaNgi/ugXINodX5k5/iPi3B8JKwMOjbF955B44ccQpKesuxY842nNbC229DkNJKIiIifqHPW4vOeaxbwxj6t6pCUnIag95fes7zvZpWpHezSvx5PJl/Tfr7CcjUO1tl2WdiYiILFy7k+++/p3v37owePZr4+HgeffRRSpYsyaZNm2jXrh2vv/46QUFBFC5cmDvvvJPvv/+e4sWL8/HHH1O6dGliY2Np3bo1CxcupHv37jRq1Ij777+f1NRUmjdvzhtvvEF4eDjLli1j6NChHD9+nPDwcObNmwfA7t276dKlC1u3bqVnz548++yzAMyePZvHHnuMU6dOcfHFF/P+++9TuHBhVqxYwfDhw0lMTKRUqVJMmDCBmBgVkJMCJLoC9P0INnwF3zwA78RBi9uh4yMQoWTd36SecsZp+fvw2wIICoU63SDuMQjWKa4/06mqFw0Y4OxuMW2a9/pITXUSHevWwaefQo0a3utLRERE/N8XX3xBly5dqFmzJiVKlGDlypUALF26lOeff56EhAS2bt3K9OnTATh+/DhNmjRh5cqVtG/fnjFjxpxp6/Dhw/zwww/cc889DBo0iKlTp5KQkEBqaipvvPEGycnJ9OnTh5deeomff/6ZuXPnEhkZCcDq1avPHD916lR27tzJH3/8wZNPPsncuXNZuXIlzZo1Y9y4caSkpDB48GCmTZvGihUruOWWW3j44Yd9P3gi/qDO1c5siBa3w9K34bVLYcNMt6PyDwe3wuz/wLg68NmtcHQXdBoNwzdA7wmqnxEAlB7youbNoWZNZzcMby2LGD4cvvkG3nwTLr/cO32IiIhI7lxoxkJkWPAFny8RFZatGQ//NGXKFIYNGwZA3759mTJlCldddRUtWrSgWrVqANxwww0sWLCAXr16ERQURJ8+fQDo168f11577Zm2Tj++adMmqlatSs2aNQEYOHAgr732GnFxccTExNC8eXOAvy2piIuLIzpjCmjdunX57bffOHz4MOvXr6dNmzYAJCcn06pVKzZt2sTatWvp3LkzAGlpaZr9IAVbRFHo+l9o2AdmDIGpN0Htbk6tiOgKbkfnW6nJsOlrZ7bDrz+ACYbaV0Gzm6FqrKZ/BxglILzIGKcY5SOPONtoVqni2fZfecW5DB8Od97p2bZFREQk8Bw8eJDvvvuOtWvXYowhLS0NYwxdu3bF/KMi/D/vZ/Z4VFQUAPY82wNaa8/bTnh4+JnbwcHBpKamYq2lc+fOTJky5W/HJiQkUK9ePRYtOnfJikiBVrEZ3PkDLHoV4p9xZkPEPQLNb3NqR+RjEUl7Ye5oWDUJjh+A6MrQ8T/QuD8UKed2eJJLShd5Wb9+zvVHH3m23W++gWHDnO0+M5ZUioiISAE3bdo0BgwYwG+//cb27dvZuXMnVatWZcGCBSxdupRff/2V9PR0pk6dStu2bQFIT09nWsZ60cmTJ595/Gy1a9dm+/btbNmyBYCJEyfSvn17ateuze7du1m2bBkAx44du2DBypYtW7Jw4cIz7Zw4cYJffvmFWrVqceDAgTMJiJSUFNatW+e5gREJZMGh0PY+uHsRVGoO3z4I73aG3aucInD5SVqKU9th4rVcuuQuWPgSVGwON02Doauh3QNKPgQ4zYDwsipVoF07ZxnGQw95Zjvan3+GPn3gkktg8mQIzt/JTxEREcmmKVOmMHLkyL89dt111/HGG2/QqlUrRo4cSUJCAu3ataNnz56AM8th3bp1NG3alOjoaKZOnXpOuxEREbz//vv07t37TBHKu+66i7CwMKZOncrgwYNJSkoiMjKSuXPnnje+0qVLM2HCBG644QZOnToFwJNPPknNmjWZNm0aQ4YM4ciRI6SmpjJs2DDq1avnwdERCXAlqkK/6ZAwDWaNdHbKKFwOKrWAyi2hUktnW8/gULcjzbnDO2HlB7ByIiTuhaIV2F6lL1V7PlLwlpzkc0pA+ED//nD77c6shauuyltbe/Y4O15ER8NXX0HGzEgRERER4uPjz3lsyJAhNGzYkOeeey7T5ALAE088wRNPPHHBtuLi4li1atU5r23evDmLFy/+22ODBg1i0KBBZ+7PnPlXAb2OHTuemTFxtkaNGjF//vxM4xORDMZAw97Odp1rP4OdS2DHEtgww3k+JBIqNIXKlzoJiUrNIbK4uzGfT3oabJ7t1HbYPNt5rEZnaPoC1Lic335cQFUlH/IdJSB84Prr4fnnoUcPZ7nEffflbibE8eNw9dVw6BAsWAAV9PsoIiIiIlLwFCrh7JLR4nbn/tHdsGOxk5DYuQQWvAg2zXmudJ2/EhKVL4XiVT0zLTu3ju6GlR86l6O/Q+Gy0O5+aDIAilV2Ly7xCSUgfKBoUViyBAYNghEjYPFiePddKFIk+22kpzszKVatgi+/hEaNvBWtiIiI5DexsbHExsZm+lxiYqJvgxERzytaHupf61wAko/D7yuc2RE7F8Paz2HFBOe5qDJnzZC4FGIugZAw78aXngZbv3NmO/wyy0mOXNwRuoyFWlcG5rIRyRUlIHykaFH47DN47jkYORLWrnXu16lz4ddZC7NnwzPPwPffw4svOkswREREREREMhUWBVXbORdwvs08sOGvWRI7FjvFHgFCIqB8k7OSEi2cGRaecGwvrJoIKz6EIzsgqjS0GQJNBjo1LaTAUQLCh4yBBx6AZs2cIpItWsD770OvXucee+qUs3PGuHGwbh3ExMBLL8Hgwb6PW0REREREAlhQEJSt51ya3+o8dmzv3xMSP70C6S84z5WqddayjZZQolr2l22kp8Ov8c5sh03fQHqqkwjpPAZqd/P+bAvxa0pAuKBDB1i5Enr3di4jRsDYsRASAn/8AW++Ca++Cvv2QcOG8MEH0LcvhOl3VUREREREPKFIOah3jXMBSD7hLNvYudhZurH+S6dOAzgzFypd6lwqt8xYthH+9/YSD8DqSbDiAzj0K0SWgJb/giaDoFR1H/5g4s+UgHBJxYrwww8wfLhToHLZMqhb10k2JCXBlVc6z8XFuVsjRkRERERECoCwQlD1MucCzkyGPzb9fZbExowdbYLDoUITJyFRpq5T12HDV5CeAhe1gQ4PQ52rITTCvZ9H/JISEC4KC3NmOrRsCXfc4RSn7N/f2SVD216LiIhIbgQHB9OgQYMz9/v27cvIkSM90vbq1avZvXs3Xbt29Uh7IuLHgoKgTB3n0uxm57Fj+/7aaWPHYlj0mpN0iIh2duRoOghK13I1bPFvSkD4gX79oH17iIiA0qXdjkZEREQCWWRkJKtXr/ZK26tXr2b58uVKQIgUVEXKQt3uzgUgJQkObITStSE00t3YJCAoAeEnKlVyOwIRERHxqG9Hwt4Ez7ZZrgFcOTbHLzty5AgtWrRgxowZ1KpVixtuuIGOHTty++23869//Ytly5aRlJREr169GDNmDADLli1j6NChHD9+nPDwcObMmcOjjz5KUlISCxYsYNSoUXTr1o3BgweTkJBAamoqo0ePpkePHp79mUXEf4VGQvnGbkchAUQJCBEREZF8JCkpiUaNGp25P2rUKPr06cOrr77KoEGDGDp0KIcOHeL2228H4KmnnqJEiRKkpaURFxfHmjVrqF27Nn369GHq1Kk0b96co0ePUqhQIR5//HGWL1/Oq6++CsBDDz1Ex44dee+99zh8+DAtWrSgU6dOREVFufGji4iIn1MCQkRERMQbcjFTwRPOtwSjc+fOfPrpp9xzzz38/PPPZx7/5JNPGD9+PKmpqezZs4f169djjCEmJobmzZsDULRo0Uz7mj17NjNmzOC5554D4OTJk+zYsYM6dep4/gcTEZGApwSEiIiISAGQnp7Ohg0biIyM5M8//6RixYr8+uuvPPfccyxbtozixYszaNAgTp48ibUWk41tuKy1fPbZZ9SqpaJzIiKStSC3AxARERER73vhhReoU6cOU6ZM4ZZbbiElJYWjR48SFRVFdHQ0+/bt49tvvwWgdu3a7N69m2XLlgFw7NgxUlNTKVKkCMeOHTvT5hVXXMErr7yCtRaAVatW+f4HExGRgKEZECIiIiL5yD9rQHTp0oVbbrmFd955h6VLl1KkSBHatWvHk08+yZgxY2jcuDH16tWjWrVqtGnTBoCwsDCmTp3K4MGDSUpKIjIykrlz59KhQwfGjh1Lo0aNGDVqFI888gjDhg2jYcOGWGupUqUKM2fOdOknFxERf6cEhIiIiEg+kpaWlunjGzZsOHN73LhxZ25PmDAh0+ObN2/O4sWLz3n89KyI0956661cRCkiIgWRlmCIiIiIiIiIiNcpASEiIiIiIiIiXqcEhIiIiIgHnS7IKJ6nsRURCWxKQIiIiIh4SEREBAcPHtSJshdYazl48CARERFuhyIiIrmkIpQiIiIiHlKxYkV27drFgQMHfNLfyZMnC9QJeUREBBUrVnQ7DBERySUlIEREREQ8JDQ0lKpVq/qsv/j4eBo3buyz/kRERPJCSzBERERERERExOuUgBARERERERERr1MCQkRERERERES8zgRilWZjzAHgNw83Wwr4w8NtFlQaS8/RWHqOxtJzNJae4+mxvMhaW9qD7ckFeOnzSE7p9zF3NG65o3HLHY1b7mjccscfxu28n0cCMgHhDcaY5dbaZm7HkR9oLD1HY+k5GkvP0Vh6jsZS8krvodzRuOWOxi13NG65o3HLHX8fNy3BEBERERERERGvUwJCRERERERERLxOCYi/jHc7gHxEY+k5GkvP0Vh6jsbSczSWkld6D+WOxi13NG65o3HLHY1b7vj1uKkGhIiIiIiIiIh4nWZAiIiIiIiIiIjXKQEhIiIiIiIiIl5X4BMQxpguxphNxpgtxpiRbscTyIwx7xlj9htj1rodSyAzxlQyxnxvjNlgjFlnjBnqdkyByhgTYYxZaoz5OWMsx7gdU6AzxgQbY1YZY2a6HUsgM8ZsN8YkGGNWG2OWux2P+L+sPq8Yx8sZz68xxjRxI05/k41xuyljvNYYY34yxlziRpz+Jrufj40xzY0xacaYXr6Mz19lZ9yMMbEZ//evM8b84OsY/U02fkejjTFfnfVZ7mY34vQ3WZ13+fPfhAKdgDDGBAOvAVcCdYEbjDF13Y0qoE0AurgdRD6QCoyw1tYBWgL36H2Za6eAjtbaS4BGQBdjTEt3Qwp4Q4ENbgeRT3Sw1jby5726xT9k8/PKlUCNjMsdwBs+DdIPZXPcfgXaW2sbAk/g58XbfCG7n48zjnsG+J9vI/RP2Rk3Y0wx4HWgu7W2HtDb13H6k2y+1+4B1md8losFnjfGhPk0UP80gQufd/nt34QCnYAAWgBbrLXbrLXJwMdAD5djCljW2vnAn27HEeistXustSszbh/DOdmr4G5Ugck6EjPuhmZcVHk3l4wxFYGrgHfcjkWkgMnO55UewIcZ/+8tBooZY2J8HaifyXLcrLU/WWsPZdxdDFT0cYz+KLufjwcDnwH7fRmcH8vOuN0ITLfW7gCw1hb0scvOmFmgiDHGAIVxzjVSfRum/8nGeZff/k0o6AmICsDOs+7vQid64keMMVWAxsASl0MJWBlLBlbjfECaY63VWObei8CDQLrLceQHFphtjFlhjLnD7WDE72Xn84o+05wrp2NyK/CtVyMKDFmOmzGmAtATeNOHcfm77LzfagLFjTHxGf//D/BZdP4pO2P2KlAH2A0kAEOttfockjW//ZsQ4nYALjOZPKZvR8UvGGMK43yzMMxae9TteAKVtTYNaJQx7fFzY0x9a63qlOSQMaYbsN9au8IYE+tyOPlBG2vtbmNMGWCOMWZjxrcZIpnJzucVfaY5V7bHxBjTAScB0darEQWG7Izbi8C/rbVpzhfTQvbGLQRoCsQBkcAiY8xia+0v3g7OT2VnzK4AVgMdgYtx/mb+qM/GWfLbvwkFfQbELqDSWfcr4mTXRFxljAnFST58ZK2d7nY8+YG19jAQj+qU5FYboLsxZjvOFMmOxphJ7oYUuKy1uzOu9wOf40xDFTmf7Hxe0Weac2VrTIwxDXGWlvWw1h70UWz+LDvj1gz4OONvQi/gdWPMNT6Jzn9l9/d0lrX2uLX2D2A+UJALn2ZnzG7GWbZirbVbcOq21PZRfIHMb/8mFPQExDKghjGmakYxk77ADJdjkgIuY43bu8AGa+04t+MJZMaY0hkzHzDGRAKdgI2uBhWgrLWjrLUVrbVVcP6v/M5a28/lsAKSMSbKGFPk9G3gckCzcuRCsvN5ZQYwIKPyeUvgiLV2j68D9TNZjpsxpjIwHehfgL+F/qcsx81aW9VaWyXjb8I04G5r7Rc+j9S/ZOf39EvgMmNMiDGmEHApBbuwc3bGbAfOjBGMMWWBWsA2n0YZmPz2b0KBXoJhrU01xtyLU703GHjPWrvO5bACljFmCk512lLGmF3AY9bad92NKiC1AfoDCRm1CwAestZ+415IASsG+CCjynIQ8Im1VttHitvK4iwHAufv8GRr7Sx3QxJ/dr7PK8aYuzKefxP4BugKbAFO4HxrWKBlc9weBUrifIMPkFrQd6bJ5rjJP2Rn3Ky1G4wxs4A1OPWU3inIy0Kz+V57AphgjEnAWVbw74zZIwVaZuddOMXW/f5vgrHWL5aCiIiIiIiIiEg+VtCXYIiIiIiIiIiIDygBISIiIiIiIiJepwSEiIiIiIiIiHidEhAiIiIiIiIi4nVKQIiIiIiIiIiI1ykBISK5ZowpZoy52+04RERERETE/ykBISJ5UQxQAkJERERERLKkBISI5MVY4GJjzGpjzH/dDkZEREQKDmPME8aYoWfdf8oYM8TNmETkwoy11u0YRCRAGWOqADOttfXdjkVEREQKlozPIdOttU2MMUHAZqCFtfagu5GJyPmEuB2AiIiIiIhITllrtxtjDhpjGgNlgVVKPoj4NyUgREREREQkUL0DDALKAe+5G4qIZEVLMEQk14wxJYGV1tqL3I5FRERECh5jTBiQAIQCNay1aS6HJCIXoCKUIpJrGdMcFxpj1qoIpYiIiPiatTYZ+B74RMkHEf+nGRAiIiIiIhKQMopPrgR6W2s3ux2PiFyYZkCIiIiIiEjAMcbUBbYA85R8EAkMmgEhIiIiIiIiIl6nGRAiIiIiIiIi4nVKQIiIiIiIiIiI1ykBISIiIiIiIiJepwSEiIiIiIiIiHidEhAiIiIiIiIi4nX/D3HAGm0EBsMvAAAAAElFTkSuQmCC", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# VERSION explicite\n", "def euler_regressif(phi1,phi2,tt,y0,z0):\n", "\tuu = [y0]\n", "\tww = [z0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append( uu[i]+h*(ww[i]-6*h*uu[i])/(1+5*h+6*h**2) )\n", "\t\tww.append( (ww[i]-6*h*uu[i])/(1+5*h+6*h**2) )\n", "\treturn [uu,ww]\n", "\n", "\n", "# VERSION AVEC fsolve\n", "# from scipy.optimize import fsolve\n", "# def euler_regressif(phi1,phi2,tt,y0,z0):\n", "# \tuu = [y0]\n", "# \tww = [z0]\n", "# \th = tt[1]-tt[0]\n", "# \tfor i in range(len(tt)-1):\n", "# \t\tsysteme = lambda z : [ -z[0]+uu[i]+h*phi1(tt[i+1],z[0],z[1]) , -z[1]+ww[i]+h*phi2(tt[i+1],z[0],z[1]) ]\n", "# \t\tutemp,wtemp = fsolve( systeme , (uu[i],ww[i]) ) \n", "# \t\tuu.append(utemp)\n", "# \t\tww.append(wtemp)\n", "# \treturn [uu,ww]\n", "\n", "[uu, ww] = euler_regressif(phi1,phi2,tt,y0,z0)\n", "\n", "figure(figsize=(18,7))\n", "affichage(tt,yy,zz,uu,ww,\"Euler implicite\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q4 [1 point]** \n", "Calculer la solution approchée obtenue par la fonction `odeint` du module `scipy`. Afficher $t\\mapsto x(t)$, $t\\mapsto x'(t)$ et $x\\mapsto x'(x)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "\n", "# Bien noter l'ordre des variables dans phi\n", "pphi = lambda t,yy : [ phi1(t,yy[0],yy[1]), phi2(t,yy[0],yy[1]) ]\n", "\n", "yy0 = [y0,z0]\n", "uu,ww = odeint(pphi,yy0,tt, tfirst=True).T\n", "\n", "figure(figsize=(18,7))\n", "affichage(tt,yy,zz,uu,ww,\"Odeint\")" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : étude d'un schéma RK\n", "\n", "Soit le schéma de Runge-Kutta dont la matrice de Butcher est\n", "$$\n", "\\begin{array}{c|cc}\n", "\\dfrac{1}{3} & \\dfrac{1}{3} & 0\\\\\n", "1 & 1 & 0\\\\\n", "\\hline\n", " & \\dfrac{3}{4} & \\dfrac{1}{4}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q5 [1 point]** Écrire le schéma sous la forme d'une suite définie par récurrence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le schéma associé à cette matrice est semi-implicite ($K_1$ dépend de lui même) et permet de calculer $u_{n+1}$ à partir de $u_n$ par la formule de récurrence\n", "$$\\begin{cases}\n", "u_0\t = y_0 \\\\\n", "K_1 = \\varphi\\left(t_n+\\frac{h}{3},u_n+\\frac{h}{3}K_1\\right)\\\\\n", "K_2 = \\varphi\\left(t_{n+1},u_n+hK_1\\right)\\\\\n", "u_{n+1} = u_n + \\frac{h}{4}\\left(3K_1+K_2\\right) & n=0,1,\\dots N-1\n", "\\end{cases}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q6 [2 points]** Étudier théoriquement l'ordre du schéma." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Soit $\\omega$ l'ordre de la méthode.\n", "\n", "+ C'est un schéma semi-implicite à $2$ étages ($s=2$) donc $\\omega\\le2s=4$\n", "\n", "+ Si \n", "$\\begin{cases}\n", "\\displaystyle\\sum_{j=1}^s b_{i}=1&\n", "\\\\\n", "\\displaystyle c_i=\\sum_{j=1}^s a_{ij}&i=1,\\dots,s\n", "\\end{cases}$\n", "alors $\\omega\\ge1$\n", "\n", "+ Si $\\displaystyle\\sum_{j=1}^s b_j c_j=\\frac{1}{2}$\n", "alors $\\omega\\ge2$\n", "\n", "\n", "+ Si, de plus, \n", "$\\begin{cases}\n", "\\displaystyle\\sum_{j=1}^s b_j c_j^2=\\frac{1}{3}\\\\\n", "\\displaystyle\\sum_{i=1}^s\\sum_{j=1}^s b_i a_{ij} c_j=\\frac{1}{6}\n", "\\end{cases}$\n", "alors $\\omega\\ge3$\n", "\n", "\n", "+ Si, de plus, \n", "$\\begin{cases}\n", "\\displaystyle\\sum_{j=1}^s b_j c_j^3=\\frac{1}{4}&\n", "\\\\\n", "\\displaystyle\\sum_{i=1}^s\\sum_{j=1}^s b_i c_i a_{ij} c_j=\\frac{1}{8}\n", "\\\\\n", "\\displaystyle\\sum_{i=1}^s\\sum_{j=1}^s b_i a_{ij} c_j^2=\\frac{1}{12}\n", "\\\\\n", "\\displaystyle\\sum_{i=1}^s\\sum_{j=1}^s\\sum_{k=1}^s b_i a_{ij}a_{jk} c_k=\\frac{1}{24}\n", "\\end{cases}$\n", "alors $\\omega\\ge4$\n", "\n", "Calculons donc toutes ces sommes:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ordre 1 (=consistance): si la première somme vaut 1 et les sommes suivantes 0\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{j=1}^s b_j=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle i={}0\\quad \\sum_{j=1}^s a_{ij}-c_i=0$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle i={}1\\quad \\sum_{j=1}^s a_{ij}-c_i=\\mathtt{\\text{0}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Ordre 2 si la somme suivante est égale à 1/2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{j=1}^s b_j c_j=\\frac{1}{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Ordre 3 si les sommes suivantes sont respectivement égales à 1/3 et 1/6\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{j=1}^s b_j c_j^2=\\frac{1}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{i,j=1}^s b_i a_{ij} c_j=\\frac{1}{6}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Ordre 4 si les sommes suivantes sont respectivement égales à 1/4, 1/8, 1/12 et 1/24\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{j=1}^s b_j c_j^3=\\frac{5}{18}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{i,j=1}^s b_i c_i a_{ij} c_j=\\frac{1}{9}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{i,j=1}^s b_i a_{ij} c_j^2=\\frac{1}{18}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sum_{i,j,k=1}^s b_i a_{ij}a_{jk} c_k=\\frac{1}{18}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "\n", "from IPython.display import display, Math\n", "\n", "c=[sym.Rational(1,3),1]\n", "b=[sym.Rational(3,4),sym.Rational(1,4)]\n", "A=[[sym.Rational(1,3),0],[1,0]]\n", "s=len(c)\n", "\n", "print('Ordre 1 (=consistance): si la première somme vaut 1 et les sommes suivantes 0')\n", "display(Math(r'\\sum_{j=1}^s b_j='+sym.latex(sum(b)) ))\n", "for i in range(s):\n", " display(Math(r'i={}'+str(i)+'\\quad \\sum_{j=1}^s a_{ij}-c_i='+sym.latex(sum(A[i])-c[i]) ))\n", "\n", "print('Ordre 2 si la somme suivante est égale à 1/2')\n", "display(Math(r'\\sum_{j=1}^s b_j c_j='+sym.latex(sum([b[i]*c[i] for i in range(s)])) ))\n", "\n", "print('Ordre 3 si les sommes suivantes sont respectivement égales à 1/3 et 1/6')\n", "display(Math(r'\\sum_{j=1}^s b_j c_j^2='+sym.latex(sum([b[i]*c[i]**2 for i in range(s)]).simplify()) ))\n", "display(Math(r'\\sum_{i,j=1}^s b_i a_{ij} c_j='+sym.latex(sum([b[i]*A[i][j]*c[j] for i in range(s) for j in range(s)])) ))\n", "\n", "print('Ordre 4 si les sommes suivantes sont respectivement égales à 1/4, 1/8, 1/12 et 1/24')\n", "display(Math(r'\\sum_{j=1}^s b_j c_j^3='+sym.latex(sum([b[i]*c[i]**3 for i in range(s)]).simplify()) ))\n", "display(Math(r'\\sum_{i,j=1}^s b_i c_i a_{ij} c_j='+sym.latex(sum([b[i]*c[i]*A[i][j]*c[j] for i in range(s) for j in range(s)])) ))\n", "display(Math(r'\\sum_{i,j=1}^s b_i a_{ij} c_j^2='+sym.latex(sum([b[i]*A[i][j]*c[j]**2 for i in range(s) for j in range(s)])) ))\n", "display(Math(r'\\sum_{i,j,k=1}^s b_i a_{ij}a_{jk} c_k='+sym.latex(sum([b[i]*A[i][j]*A[j][k]*c[k] for i in range(s) for j in range(s) for k in range(s)])) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "D'après ces résultats, le schéma est d'ordre $3$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# import sympy as sym\n", "# sym.init_printing()\n", "\n", "# from IPython.display import display, Math\n", "\n", "# c=[sym.Rational(1,3),1]\n", "# b=[sym.Rational(3,4),sym.Rational(1,4)]\n", "# A=[[sym.Rational(1,3),0],[1,0]]\n", "# s=len(c)\n", "\n", "# B = lambda p : sum([sum([b[i]*c[i]**(q-1) for i in range(s)]) != 1/q for q in range(1, p+1)])==0\n", "# C = lambda e : sum([sum([A[i][j]*c[j]**(q-1) for j in range(s)]) != c[i]**q/q for q in range(1, e+1) for i in range(s)])==0\n", "# D = lambda z : sum([sum([b[i]*c[i]**(q-1)*A[i][j] for i in range(s)]) != (b[j]/q) * (1-c[j]**q) for q in range(1, z+1) for j in range(s)])==0\n", "\n", "# omega=0\n", "# for z in range(1, 2*s):\n", "# for e in range(1, 2*s):\n", "# if C(e) and D(z):\n", "# p=1\n", "# while B(p) and p<=min(z+e+1,2*e+2,2*s):\n", "# p+=1\n", "# omega=max(omega,p-1)\n", "# display(Math(f\"\\omega = {omega}\")) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q7 [2 points]** Étudier théoriquement la A-stabilité du schéma." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Soit $\\beta>0$ un nombre réel positif et considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=-\\beta y(t), &\\text{pour }t>0,\\\\\n", "y(0)=1.\n", "\\end{cases}$$\n", "Sa solution est $y(t)=e^{-\\beta t}$ donc $$\\lim_{t\\to+\\infty}y(t)=0.$$\n", "\n", "Le schéma appliqué à ce problème de Cauchy s'écrit\n", "$$\\begin{cases}\n", "u_0\t = y_0 \\\\\n", "K_1 = -\\beta\\left(u_n+\\frac{h}{3}K_1\\right)\\\\\n", "K_2 = -\\beta\\left(u_n+hK_1\\right)\\\\\n", "u_{n+1} = u_n + \\frac{h}{4}\\left(3K_1+K_2\\right) & n=0,1,\\dots N-1\n", "\\end{cases}$$\n", "\n", "L'équation $K_1 = -\\beta\\left(u_n+\\frac{h}{3}K_1\\right)$ \n", "donne \n", "$K_1=\\frac{-3\\beta}{\\beta h+3}u_n$ \n", "ainsi\n", "$K_2=\\beta\\frac{2\\beta h-3}{\\beta h+3}u_n$\n", "et enfin\n", "$$\n", "u_{n+1} = \n", "u_n + \\frac{h}{4}\\left( \\frac{-9\\beta}{\\beta h+3}+\\beta\\frac{2\\beta h-3}{\\beta h+3}\\right)u_ n= \n", "\\frac{(\\beta h)^2-4\\beta h+6}{2(\\beta h+3)}u_n\n", "$$\n", "\n", "Vérifions ce calcul:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle K_1=- \\frac{3 \\beta u_{n}}{\\beta h + 3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle K_2=\\frac{\\beta u_{n} \\left(2 \\beta h - 3\\right)}{\\beta h + 3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle u_{n+1}=\\frac{u_{n} \\left(\\beta^{2} h^{2} - 4 \\beta h + 6\\right)}{2 \\left(\\beta h + 3\\right)}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "from IPython.display import display, Math\n", "\n", "# pour ne pas effacer l'affectation de \"h\", ici on vas l'appeler \"dt\" mais on affiche \"h\"\n", "dt = sym.Symbol('h')\n", "u_np1 = sym.Symbol('u_{n+1}')\n", "beta = sym.Symbol(r'\\beta')\n", "sym.var('u_n,x')\n", "\n", "K1 = sym.solve(-x-beta*(u_n+dt/3*x),x)[0]\n", "display(Math('K_1='+sym.latex(K1)))\n", "\n", "K2 = -beta*(u_n+dt*K1).factor()\n", "display(Math('K_2='+sym.latex(K2)))\n", "\n", "u_np1 = (u_n+dt/4*(3*K1+K2)).factor()\n", "display(Math('u_{n+1}='+sym.latex(u_np1)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On note $x=\\beta h$ et on étudie la fonction $q\\colon \\mathbb{R}^+\\to\\mathbb{R}$ définie par $q(x)=\\dfrac{x^2-4x+6}{2(x+3)}=\\dfrac{1}{2}\\left(x-7+\\dfrac{27}{x+3}\\right)$.\n", "Le schéma est A-stable ssi $|q(x)|<1$. \n", "D'après les calculs ci-dessous on conclut que le schéma est A-stable ssi $h<\\dfrac{6}{\\beta}$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle q(x)=\\frac{x}{2} - \\frac{7}{2} + \\frac{27}{2 \\left(x + 3\\right)}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle q(0)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\lim_{x \\to \\infty}\\left(\\frac{x}{2} - \\frac{7}{2} + \\frac{27}{2 \\left(x + 3\\right)}\\right)=\\infty$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "On cherche les points stationnaires dans R^+\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q'(x)=\\frac{x^{2} + 6 x - 18}{2 \\left(x + 3\\right)^{2}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Le signe de q' est le signe du numérateur qui est une parabole. On cherche où elle s'annulle pour x>0\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q'(x)=0 \\iff x\\in\\left[ -3 + 3 \\sqrt{3}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle x=-3 + 3 \\sqrt{3}\\text{ est un minimum et}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle q(-3 + 3 \\sqrt{3})=-5 + 3 \\sqrt{3}\\approx0.196152422706632$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Conclusion: q(x)>0 pour tout x>0. Vérifions ce calcul:\n", "q(x)>0\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAACoAAAAOCAYAAABZ/o57AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB0UlEQVRIDb2W7U0CQRCGD0IBqB1oBxAqEDuA2IF0oH/5Z6ADtAKFDqAEpAOxA0MH+Dzn7uVyhFNAb5JhZudj592vOWrb7TYZDodvSZI04Q38GWQLKWlbw/rPg1yTc4NeGTVCJUH1KT6LldHv0UfwAP0pZ++hP8dxVbIOCHdqlgdZVjzELcti/sNXZ1KPc37g5KuwwAPTjg8XqDvqHTyE3gl2gZVRg51ZHVHNhU3JvUQ+wo47cBfuwy7ee6x/QZy2BHmHGMBpHuOx9kiMtT/AbsQF3MRmfFL351Ai2eLtkHcV5ATpo+zi82rot4MIOiVsPsprOLN9e9JFmGv3GRE3hlPASG3HATUxkEAE5mN0V8+QWYdgvHOl8G9CblFMMbyGeVIfujveQvZieyom/XZs0QxMCYjS+chzNz32dPcKwV7NzqlAndNdPZUEKbUB7T3Ok1dq+RdA9x1lvthPejyVOUCzj04+qZ4fVKEDJO5eVg6bx+uCbzNjTsHfPRVok/nkfeSHpAjMFiYo20+e7AY+TP0ZMfYzvq75pyRSCLLn2cxNEISTLmDv4oQYW48++5vf/eh/wb5zbNi8Y5K90dhX+AOWlvizPzfoLsq2JMVeas31Fx2vogF49TMKAAAAAElFTkSuQmCC", "text/latex": [ "$\\displaystyle \\text{True}$" ], "text/plain": [ "True" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "On resout maintenant q(x)=1:\n" ] }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ 0, \\ 6\\right]$" ], "text/plain": [ "[0, 6]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "On trouve q(0)=q(6)=1\n", "Conclusion: q(x)<1 pour x<6. Vérifions ce calcul:\n", "q(x)<1\n" ] }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0 < x \\wedge x < 6$" ], "text/plain": [ "0 < x ∧ x < 6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "from IPython.display import display, Math\n", "sym.var('x',nonnegative=True)\n", "\n", "q=((x**2-4*x+6)/(2*x+6)).apart()\n", "display(Math('q(x)='+sym.latex(q)))\n", "\n", "display(Math('q(0)='+sym.latex(q.subs(x,0))))\n", "lim=sym.Limit(q,x,sym.oo)\n", "display(Math(sym.latex(lim)+'='+sym.latex(lim.doit())))\n", "\n", "print('On cherche les points stationnaires dans R^+')\n", "dq=(q.diff(x)).factor()\n", "display(Math(\"q'(x)=\"+sym.latex(dq)))\n", "print(\"Le signe de q' est le signe du numérateur qui est une parabole. On cherche où elle s'annulle pour x>0\")\n", "sol=sym.solve(dq)\n", "display(Math(\"q'(x)=0 \\iff x\\in\"+sym.latex(sol)))\n", "minimum=sol[0]\n", "display(Math(\"x=\"+sym.latex(minimum)+\"\\\\text{ est un minimum et}\"))\n", "qmin=q.subs(x,sol[0])\n", "display(Math(\"q(\"+sym.latex(minimum)+\")=\"+sym.latex(qmin)+\"\\\\approx\"+sym.latex(sym.N(qmin))))\n", "print(\"Conclusion: q(x)>0 pour tout x>0. Vérifions ce calcul:\")\n", "print(\"q(x)>0\")\n", "display(sym.solve(q>0))\n", "print(\"On resout maintenant q(x)=1:\")\n", "display(sym.solve(q-1))\n", "print('On trouve q(0)=q(6)=1')\n", "print(\"Conclusion: q(x)<1 pour x<6. Vérifions ce calcul:\")\n", "print(\"q(x)<1\")\n", "display(sym.solve(q<1))\n", "\n", "\n", "sym.plot(q,1,-1,xlim=[-1,15],ylim=[-1.5,1.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q8 [2 points]** Implémenter le schéma et approcher la solution du problème de Cauchy suivant avec $N+1$ points et $N=8$. \n", "$$\n", " \\begin{cases}\n", " y'(t)=-6y(t), &t\\in[0;1]\\\\\n", " y(0)=1\n", " \\end{cases}\n", "$$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans chaque point $t_i$, il faut approcher $(K_1)_i$ en resolvant une équation. Si on utilise la fonction `fsolve` du module `scipy.optimize`, il faut initialiser `fsolve` avec une approximation de $(K_1)_i$. On choisira donc $\\varphi(t_i,u_i)$:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A-stable ssi h < 1.0\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve\n", "\n", "def RK(phi,tt):\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " k1 = fsolve( lambda x : -x+phi( tt[i]+h/3, uu[i]+h/3*x ) , phi(tt[i],uu[i]) )[0]\n", " k2 = phi( tt[i+1], uu[i]+h*k1 )\n", " uu.append( uu[i] + h/4*(3*k1+k2 ))\n", " return uu\n", "\n", "t0, y0, tfinal = 0, 1, 3\n", "\n", "sol_exacte = lambda t : exp(-6*t)\n", "phi = lambda t,y : -6*y\n", "\n", "print('A-stable ssi h <',6/6)\n", "figure(figsize=(10,5))\n", "N=8\n", "tt = linspace(t0,tfinal,N+1)\n", "h = tt[1]-tt[0]\n", "yy = [sol_exacte(t) for t in tt] \n", "uu = RK(phi,tt)\n", "plot(tt,yy,'b-',label=(\"Exacte\"))\n", "plot(tt,uu,'ro',label=(\"RK\"))\n", "title(r' $N$={}, $h$={}'.format(N,h))\n", "xlabel('$t$')\n", "ylabel('$u$')\n", "legend() \n", "grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : étude d'un schéma Predictor-Corrector multipas\n", "\n", "On notera $\\varphi_k\\stackrel{\\text{déf}}{=}\\varphi(t_k,u_k)$.\n", "Soit les méthodes multipas\n", "\\begin{align*}\n", "u_{n+1}&=u_{n-3}+\\frac{4h}{3}\\left(2\\varphi_{n}-\\varphi_{n-1}+2\\varphi_{n-2}\\right)&\\text{[P]}\n", "\\\\\n", "u_{n+1}&=u_{n-1}+\\frac{h}{3}\\left(\\varphi_{n+1}+4\\varphi_{n}+\\varphi_{n-1}\\right)&\\text{[C]}\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q9 [3 point]** \n", "Étudier consistance, ordre et zéro-stabilité de la méthode P." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "P est une méthode à $q=4$ pas explicite : \n", "- $p=3$\n", "- $b_{-1}=0$\n", "- $a_0=a_1=a_2=0$ et $a_3=1$\n", "- $b_0=\\frac{8}{3}$, $b_1=\\frac{-4}{3}$, $b_2=\\frac{8}{3}$ et $b_3=0$\n", "- La méthode est consistante d'ordre $\\omega=4$ car\n", "$$\n", "\\begin{cases}\n", "\\xi(0)=\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\xi(1)=\\displaystyle\\sum_{j=0}^p (-j)^{1}a_j+1\\sum_{j=-1}^p (-j)^{0}b_j=1\n", "\\\\\n", "\\xi(2)=\\displaystyle\\sum_{j=0}^p (-j)^{2}a_j+2\\sum_{j=-1}^p (-j)^{1}b_j=1\n", "\\\\\n", "\\xi(3)=\\displaystyle\\sum_{j=0}^p (-j)^{3}a_j+3\\sum_{j=-1}^p (-j)^{2}b_j=1\n", "\\\\\n", "\\xi(4)=\\displaystyle\\sum_{j=0}^p (-j)^{4}a_j+4\\sum_{j=-1}^p (-j)^{3}b_j=1\n", "\\\\\n", "\\xi(5)=\\displaystyle\\sum_{j=0}^p (-j)^{5}a_j+5\\sum_{j=-1}^p (-j)^{4}b_j\\neq1\n", "\\end{cases}\n", "$$\n", "Attention $(-0)^0=1$ dans les formules précédentes.\n", "\n", "Vérifions ces calculs ci-dessous:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge3$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge4$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega<5$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "from IPython.display import display, Math\n", "\n", "p=3\n", "bm1=0\n", "a0=0\n", "a1=0\n", "a2=0\n", "a3=1\n", "b0=sym.Rational(8,3)\n", "b1=sym.Rational(-4,3)\n", "b2=sym.Rational(8,3)\n", "b3=0\n", "\n", "aa=[a0,a1,a2,a3]\n", "bb=[b0,b1,b2,b3]\n", "\n", "cond=[]\n", "cond.append(sum(aa)) \n", "cond.append(sum([-j*aa[j]+bb[j] for j in range(len(aa))])+bm1)\n", "if cond==[1,1]:\n", " display(Math(\"\\omega\\ge1\"))\n", " for n in range(2,9):\n", " cond.append(sum( [ (-j)**n*aa[j]+n*(-j)**(n-1)*bb[j] for j in range(len(aa)) ])+n*bm1)\n", " if cond[n]==1:\n", " display(Math(\"\\omega\\ge\"+str(n)))\n", " else:\n", " display(Math(\"\\omega<\"+str(n)))\n", " break\n", "#print(cond) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Le premier polynôme caractéristique est\n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}=r^4-a_0r^3-a_1r^2-a_2r-a_3=r^4-1\n", "$$\n", " dont les racines sont \n", "$$\n", "r_0=1,\\ r_1=-1,\\ r_2=i,\\ r_3=-i\n", "$$\n", " La méthode est zéro-stable ssi\n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1,\n", "\\end{cases}\n", "$$\n", " ce qui est bien vérifié.\n", "\n", "- La méthode est convergente car consistante et zéro-stable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q10 [3 point]** \n", "Étudier consistance, ordre et zéro-stabilité de la méthode C." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "C est une méthode à $q=2$ pas implicite : \n", "- $p=1$\n", "- $b_{-1}=\\frac{1}{3}$\n", "- $a_0=0$ et $a_1=1$\n", "- $b_0=\\frac{4}{3}$ et $b_1=\\frac{1}{3}$\n", "- La méthode est consistante d'ordre 4 car\n", "$$\n", "\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p -ja_j+\\sum_{j=-1}^p b_j=1\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p (-j)^{2}a_j+2\\sum_{j=-1}^p (-j)^{1}b_j=1\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p (-j)^{3}a_j+3\\sum_{j=-1}^p (-j)^{2}b_j=1\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p (-j)^{4}a_j+4\\sum_{j=-1}^p (-j)^{3}b_j=1\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p (-j)^{5}a_j+5\\sum_{j=-1}^p (-j)^{4}b_j\\neq1\n", "\\end{cases}\n", "$$\n", "Vérifions ces calculs ci-dessous:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge3$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega\\ge4$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\omega<5$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "from IPython.display import display, Math\n", "\n", "p=1\n", "bm1=sym.Rational(1,3)\n", "a0=0\n", "a1=1\n", "b0=sym.Rational(4,3)\n", "b1=sym.Rational(1,3)\n", "\n", "aa=[a0,a1]\n", "bb=[b0,b1]\n", "\n", "cond=[]\n", "cond.append(sum(aa)) \n", "cond.append(sum([-j*aa[j]+bb[j] for j in range(len(aa))])+bm1)\n", "if cond==[1,1]:\n", " display(Math(\"\\omega\\ge1\"))\n", " for n in range(2,9):\n", " cond.append(sum( [ (-j)**n*aa[j]+n*(-j)**(n-1)*bb[j] for j in range(len(aa)) ])+n*bm1)\n", " if cond[n]==1:\n", " display(Math(\"\\omega\\ge\"+str(n)))\n", " else:\n", " display(Math(\"\\omega<\"+str(n)))\n", " break\n", "#print(cond) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Le premier polynôme caractéristique est\n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}=r^2-a_0r-a_1=r^2-1\n", "$$\n", " dont les racines sont \n", "$$\n", "r_0=1,\\ r_1=-1\n", "$$\n", " La méthode est zéro-stable ssi\n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1,\n", "\\end{cases}\n", "$$\n", " ce qui est bien vérifié.\n", "\n", "- La méthode est convergente car consistante et zéro-stable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q11 [2 point]** \n", "Calculer empiriquement l'ordre de convergence des méthodes P et C ainsi que de la méthode Predictor-Corrector associée aux deux méthodes P et C sur le problème de Cauchy\n", "$$\n", "\\begin{cases}\n", "y'(t) = 1+\\big(t-y(t)\\big)^2, &\\forall t \\in I=[2,3],\\\\\n", "y(2) = 1,\n", "\\end{cases}\n", "$$\n", " dont la solution exacte est $y(t)=t+\\dfrac{1}{1-t}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il est d'ordre $4$ car le prédictor est d'ordre $4$ et le corrector d'ordre $4$.\n", "\n", "On définit la solution exacte pour estimer les erreurs et on calcule la solution approchée pour différentes valeurs de $N$ pour les trois schémas:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Multipas P ordre=4.26\n", "Multipas C ordre=4.04\n", "Multipas PC ordre=4.12\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "\n", "# variables globales\n", "t0 = 2\n", "tfinal = 3\n", "y0 = 1\n", "\n", "phi = lambda t,y : 1+(t-y)**2\n", "\n", "sol_exacte = lambda t : t+1/(1-t)\n", "\n", "from scipy.optimize import fsolve\n", "\n", "\n", "def multipas_P(phi, tt):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,len(tt) - 1):\n", " uu.append( uu[i-3]+4*h/3* ( 2*phi(tt[i],uu[i])-phi(tt[i-1],uu[i-1])+2*phi(tt[i-2],uu[i-2]) ) )\n", " return uu\n", "\n", "def multipas_C(phi, tt):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,len(tt) - 1):\n", " temp = fsolve ( lambda x : -x+uu[i-1]+h/3* ( phi(tt[i+1],x) + 4*phi(tt[i],uu[i])+phi(tt[i-1],uu[i-1]) ), uu[i])\n", " uu.append(temp)\n", " return uu\n", "\n", "def multipas_PC(phi, tt):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,len(tt) - 1):\n", " u_tilde = uu[i-3]+4*h/3* ( 2*phi(tt[i],uu[i])-phi(tt[i-1],uu[i-1])+2*phi(tt[i-2],uu[i-2]) )\n", " uu.append( uu[i-1]+h/3* ( phi(tt[i+1],u_tilde) + 4*phi(tt[i],uu[i])+phi(tt[i-1],uu[i-1]) ) )\n", " return uu\n", "\n", "\n", "H = []\n", "err_p = []\n", "err_c = []\n", "err_pc = []\n", "N = 10\n", "for k in range(7):\n", " N+=20\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu_p = multipas_P(phi, tt)\n", " uu_c = multipas_C(phi, tt)\n", " uu_pc = multipas_PC(phi, tt)\n", " H.append(h)\n", " err_p.append(max([abs(uu_p[i] - yy[i]) for i in range(len(yy))]))\n", " err_c.append(max([abs(uu_c[i] - yy[i]) for i in range(len(yy))]))\n", " err_pc.append(max([abs(uu_pc[i] - yy[i]) for i in range(len(yy))]))\n", " \n", "print ('Multipas P ordre=%1.2f' %(polyfit(log(H),log(err_p), 1)[0]))\n", "print ('Multipas C ordre=%1.2f' %(polyfit(log(H),log(err_c), 1)[0]))\n", "print ('Multipas PC ordre=%1.2f' %(polyfit(log(H),log(err_pc), 1)[0]))\n", "\n", "figure(figsize=(8,5))\n", "plot(log(H), log(err_p), 'r-o', label='Multipas P')\n", "plot(log(H), log(err_c), 'b-o', label='Multipas C')\n", "plot(log(H), log(err_pc), 'c-o', label='Multipas PC')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "legend(bbox_to_anchor=(1.04, 1), loc='upper left')\n", "grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a bien\n", "- ordre du corrector $\\omega_{[C]}=4$\n", "- ordre du predictor $\\omega_{[P]}=4$ \n", "et donc \n", "ordre du predictor-corrector $\\omega_{[PC]}=\\min\\{\\omega_{[C]},\\omega_{[P]}+1\\}=4$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" } } }, "nbformat": 4, "nbformat_minor": 4 }