{ "cells": [ { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 105, "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": [ "# 2022 CC corrigé\n", "\n", "\n", "- ⏱ 2H30\n", "- ✍ Deposer votre fichier .ipynb sur Moodle (dépôt de devoir)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve\n", "\n", "import sympy \n", "sympy.init_printing()\n", "\n", "from IPython.display import display, Math\n", "prlat= lambda *args: display(Math(''.join( sympy.latex(arg) for arg in args )))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 1 : étude d'un schéma multipas\n", "\n", "
\n", "\n", "On notera $\\varphi_k\\stackrel{\\text{déf}}{=}\\varphi(t_k,u_k)$.\n", "\n", "Soit la méthode multipas\n", "\n", "$$\n", "u_{n+1} = \\alpha u_n + (1-\\alpha) u_{n-1} +h\\left(2\\varphi_{n+1} -\\frac{3\\vartheta}{2}\\varphi_{n}+\\frac{\\vartheta}{2} \\varphi_{n-1}\\right).\n", "$$\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q1 [2 points]** \n", "Pour quelles valeurs des paramètres $\\alpha$ et $\\vartheta$ la méthode est zéro-stable?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le premier polynôme caractéristique est\n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}=r^2-\\alpha r+(\\alpha-1)=(r-1)\\big(r-(\\alpha-1)\\big)\n", "$$\n", "dont les racines sont \n", "$$\n", "r_0=1,\\quad r_1=\\alpha-1.\n", "$$\n", "La méthode est donc zéro-stable ssi\n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,1\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1\n", "\\end{cases}\n", "$$\n", "donc ssi $0\\le\\alpha<2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q2 [3 points]** \n", "Quel est l'ordre de convergence de la méthode?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On rappelle qu'une méthode est convergente ssi elle est zéro-stable et consistante. Nous allons donc étudier la consistance (puis l'ordre de consistance = ordre de convergence) pour les seules valeurs de $\\alpha$ pour lesquelles on a la zéro-stabilité.\n", "\n", "* On a $p=1$: c'est une méthode à $q=p+1=2$ pas. \n", "* La méthode est implicite car $b_{-1}=2\\neq0$.\n", "\n", "Pour que la méthode soit consistante il faut que\n", "$$\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=a_0+a_1=1,\n", "\\\\\n", "\\displaystyle\\sum_{j=0}^p (-j)a_j+\\sum_{j=-1}^p b_j=1.\n", "\\end{cases}$$\n", "\n", "De plus, la première barrière de Dahlquist affirme qu'un schéma implicite à $q=2$ pas consistante et zéro-stable peut être au mieux d'ordre $\\omega=q+2=4$. \n", "\n", "Pour que la méthode soit \n", "- au moins d'ordre 2 il faut qu'elle soit consistante et que $\\displaystyle\\sum_{j=0}^p (-j)^{2}a_j+2\\sum_{j=-1}^p (-j)^{1}b_j=1$,\n", "- au moins d'ordre 3 il faut qu'elle soit au moins d'ordre 2 et que $\\displaystyle\\sum_{j=0}^p (-j)^{3}a_j+3\\sum_{j=-1}^p (-j)^{2}b_j=1$,\n", "- au moins d'ordre 3 il faut qu'elle soit au moins d'ordre 2 et que $\\displaystyle\\sum_{j=0}^p (-j)^{4}a_j+4\\sum_{j=-1}^p (-j)^{3}b_j=1$." ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve\n", "\n", "import sympy \n", "sympy.init_printing()\n", "\n", "from IPython.display import display, Math\n", "prlat= lambda *args: display(Math(''.join( sympy.latex(arg) for arg in args )))" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★\n", "C'est une méthode à q = 2 pas d'ordre ω ≤ 4\n", "★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★\n", "La méthode est d'ordre ω ≥ 1 (= consistante) si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{0} + a_{1}=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle - a_{1} + b_{0} + b_{1} + b_{-1}=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★\n", "La méthode est d'ordre ω ≥ 2 si elle est d'ordre 1 et, de plus, \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{1} - 2 \\left(b_{1} - b_{-1}\\right)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★\n", "La méthode est d'ordre ω ≥ 3 si elle est d'ordre 2 et, de plus, \n" ] }, { "data": { "text/latex": [ "$\\displaystyle - a_{1} + 3 \\left(b_{1} + b_{-1}\\right)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★\n", "La méthode est d'ordre ω ≥ 4 si elle est d'ordre 3 et, de plus, \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{1} - 4 \\left(b_{1} - b_{-1}\\right)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# j = 0...p\n", "# q = p+1 # nb de pas\n", "# ω # ordre de la méthode\n", "\n", "CAS_GENERAL = True\n", "p = 1\n", "\n", "q = p+1 \n", "ordre_max = q+2 if q%2==0 else q+1\n", "\n", "print(f\"{'★'*70}\\nC'est une méthode à q = {q} pas d'ordre ω ≤ {ordre_max}\")\n", "\n", "\n", "if CAS_GENERAL:\n", " aa = sympy.symbols(f'a_0:{q}')\n", " bb = sympy.symbols(f'b_0:{q}')\n", " bm1 = sympy.Symbol('b_{-1}')\n", "else : # cas particulier\n", " α = sympy.Symbol('α')\n", " ϑ = sympy.Symbol('ϑ')\n", " aa = [α, 1-α]\n", " bb = [-3*ϑ/2, ϑ/2]\n", " bm1 = 2\n", "\n", "i=1\n", "sa=sum( [-j*aa[j] for j in range(len(aa))] )\n", "sb=bm1+sum( [bb[j] for j in range(len(bb))] )\n", "print(f\"{'★'*70}\\nLa méthode est d'ordre ω ≥ {i} (= consistante) si \")\n", "prlat(sum(aa).factor(),\"=1\" )\n", "prlat((sa).factor()+(i*sb).factor(),\"=1\")\n", "\n", "for i in range(2,ordre_max+1):\n", " sa=sum( [(-j)**i*aa[j] for j in range(len(aa))] )\n", " sb=bm1+sum( [(-j)**(i-1)*bb[j] for j in range(1,len(bb))] )\n", " print(f\"{'★'*70}\\nLa méthode est d'ordre ω ≥ {i} si elle est d'ordre {i-1} et, de plus, \")\n", " prlat((sa).factor()+(i*sb).factor(),\"=1\" )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans notre cas \n", "- la méthode est consistante ssi $\\vartheta=\\alpha$ car $a_0+a_1=\\alpha+(1-\\alpha)=1$ et $-a_1+b_0+b_1+b_{-1}=-(1-\\alpha)-\\frac{3\\vartheta}{2}+\\frac{\\vartheta}{2}+2=\\alpha-\\vartheta+1$;\n", "- pour que la méthode sois d'ordre au moins 2 il faudrait avoir $1= a_1-2(b_1-b_{-1})=1-\\alpha-2(\\frac{\\alpha}{2}-2)=5-2\\alpha$ ce qui n'est pas compatible avec la condition de zéro-stabilité.\n", "\n", "Conclusion: si $0\\le\\alpha=\\vartheta<1$ le schéma est convergent à l'ordre 1, dans les autres cas il n'est pas convergente." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q3 [3 points]** \n", ">Nous allons maintenant fixer $\\alpha$. Pour cela, écrivez votre nom et prénom dans la cellule ci-dessous et vous obtiendrez un choix pour le paramètre $\\alpha$. Pour $\\vartheta$, choisir une valeur qui garantie la convergence.\n", "\n", ">Vérifier empiriquement l'ordre de convergence sur le problème de Cauchy\n", ">$$\\begin{cases}\n", "y'(t) = t^2-y(t), &\\forall t \\in I=[0,1],\\\\\n", "y(0) = 2,\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\alpha=\\frac{5}{8}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nom = \"Faccanoni\"\n", "prenom = \"Gloria\"\n", "\n", "NUM = list(range(1,16))\n", "idx = sum([ord(c) for c in nom+prenom])%len(NUM)\n", "my_alpha = NUM[idx]/sympy.S(8)\n", "prlat(r'\\alpha=',my_alpha)\n", "my_alpha = float(my_alpha) # conversion en float" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Pour estimer les erreurs on définit la solution exacte (calculée en utilisant le module `sympy` ou à la main). \n", "- On calcule la solution approchée pour différentes valeurs de $N$. Pour le calcul de l'ordre de convergence on initialise la suite avec la solution exacte." ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle y{\\left(t \\right)} = t^{2} - 2 t + 2$" ], "text/plain": [ " 2 \n", "y(t) = t - 2⋅t + 2" ] }, "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": [ "# variables globales\n", "t0 = 0\n", "tfinal = 1\n", "y0 = 2\n", "\n", "phi = lambda t,y: t**2-y\n", "\n", "##############################################\n", "# solution exacte\n", "##############################################\n", "t = sympy.Symbol('t')\n", "y = sympy.Function('y')\n", "edo = sympy.Eq( sympy.diff(y(t),t) , phi(t,y(t)) )\n", "solgen = sympy.dsolve(edo)\n", "consts = sympy.solve( sympy.Eq( y0, solgen.rhs.subs(t,t0)) , dict=True)[0]\n", "solpar = solgen.subs(consts).simplify()\n", "display(solpar)\n", "\n", "sol_exacte = sympy.lambdify(t,solpar.rhs,'numpy')\n", "\n", "##############################################\n", "# schéma (initialisation avec sol exacte pour ordre de convergence)\n", "##############################################\n", "def multipas(phi, tt, sol_exacte):\n", " h = tt[1] - tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,len(tt) - 1):\n", " eq = lambda x : -x+my_alpha*uu[i]+(1-my_alpha)*uu[i-1]+h*(2*phi(tt[i+1],x)-3*my_alpha/2*phi(tt[i],uu[i])+my_alpha/2*phi(tt[i-1],uu[i-1]))\n", " temp = fsolve( eq ,uu[i])\n", " uu.append( temp[0] )\n", " return uu\n", "\n", "##############################################\n", "# ordre\n", "##############################################\n", "H = []\n", "err = []\n", "N = 50\n", "\n", "figure(figsize=(16,5))\n", "ax1 = subplot(1,2,1)\n", "\n", "for k in range(4):\n", " N += 20\n", " tt = linspace(t0, tfinal, N + 1)\n", " H.append( tt[1] - tt[0] )\n", " yy = sol_exacte(tt)\n", " uu = multipas(phi, tt, sol_exacte)\n", " err.append( norm(uu-yy,inf) )\n", " ax1.plot(tt,uu,label=f'Approchée avec N={N}')\n", "\n", "ax1.plot(tt,yy,label='Exacte')\n", "xlabel('$t$')\n", "ylabel('$y$')\n", "ax1.grid(True)\n", "ax1.legend()\n", "\n", "ax2 = subplot(1,2,2)\n", "ax2.loglog( H, err, 'r-o')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(f'Multipas ordre = {polyfit(log(H),log(err),1)[0]:1.2f}')\n", "ax2.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 2 : étude d'un système\n", "\n", "\n", "
\n", "\n", "Soit le problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\eta z(t),\\\\\n", "z'(t)=y(t)+\\eta z(t),\\\\\n", "y(0)=1,\\\\\n", "z(0)=1.\n", "\\end{cases}$$\n", "\n", "Pour fixer $\\eta$, écrivez votre nom et prénom dans la cellule ci-dessous et vous obtiendrez un choix pour ce paramètre. Cela fixera aussi le nombre de points $N$.\n", "
" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\eta=-1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "N = 15\n" ] } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve\n", "\n", "import sympy \n", "sympy.init_printing()\n", "\n", "from IPython.display import display, Math\n", "prlat= lambda *args: display(Math(''.join( sympy.latex(arg) for arg in args )))\n", "\n", "\n", "nom=\"Faccanoni\"\n", "prenom=\"Gloria\"\n", "\n", "L=list(range(-5,0))\n", "idx=sum([ord(c) for c in nom+prenom])%len(L)\n", "eta=L[idx]\n", "display(Math(r'\\eta='+sympy.latex(eta)))\n", "N = -15*eta\n", "print(f'{N = }')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q1 [1 point]** \n", "Calculer la solution exacte." ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "tfinal = 10\n", "\n", "y0 = 1\n", "z0 = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculons la solution exacte avec `sympy` par exemple:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\left(- \\frac{\\sqrt{3} \\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{3} + \\cos{\\left(\\frac{\\sqrt{3} t}{2} \\right)}\\right) e^{- \\frac{t}{2}}$" ], "text/plain": [ " ⎛ ⎛√3⋅t⎞ ⎞ -t \n", " ⎜ √3⋅sin⎜────⎟ ⎟ ───\n", " ⎜ ⎝ 2 ⎠ ⎛√3⋅t⎞⎟ 2 \n", "y(t) = ⎜- ──────────── + cos⎜────⎟⎟⋅ℯ \n", " ⎝ 3 ⎝ 2 ⎠⎠ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle z{\\left(t \\right)} = \\left(\\frac{\\sqrt{3} \\left(- \\frac{\\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{2} + \\frac{\\sqrt{3} \\cos{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{2}\\right)}{3} + \\frac{\\sqrt{3} \\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{2} + \\frac{\\cos{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{2}\\right) e^{- \\frac{t}{2}}$" ], "text/plain": [ " ⎛ ⎛ ⎛√3⋅t⎞ ⎛√3⋅t⎞⎞ ⎞ \n", " ⎜ ⎜ sin⎜────⎟ √3⋅cos⎜────⎟⎟ ⎟ \n", " ⎜ ⎜ ⎝ 2 ⎠ ⎝ 2 ⎠⎟ ⎛√3⋅t⎞ ⎛√3⋅t⎞⎟ -t \n", " ⎜√3⋅⎜- ───────── + ────────────⎟ √3⋅sin⎜────⎟ cos⎜────⎟⎟ ───\n", " ⎜ ⎝ 2 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠⎟ 2 \n", "z(t) = ⎜─────────────────────────────── + ──────────── + ─────────⎟⋅ℯ \n", " ⎝ 3 2 2 ⎠ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = sympy.Symbol('t')\n", "y = sympy.Function('y')\n", "z = sympy.Function('z')\n", "\n", "phi1 = lambda t,y,z : eta*z\n", "phi2 = lambda t,y,z : y+eta*z\n", "\n", "\n", "edo1 = sympy.Eq( sympy.diff(y(t),t) , phi1(t,y(t),z(t)) )\n", "edo2 = sympy.Eq( sympy.diff(z(t),t) , phi2(t,y(t),z(t)) )\n", "# display(edo1)\n", "# display(edo2)\n", "solgen = sympy.dsolve([edo1,edo2],[y(t),z(t)])\n", "# display(solgen)\n", "consts = sympy.solve( [ sympy.Eq( y0, solgen[0].rhs.subs(t,t0)) , sympy.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,solpar_2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On remarque que $y(t)\\xrightarrow[t\\to+\\infty]{}0$ et $z(t)\\xrightarrow[t\\to+\\infty]{}0$" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "func_1 = sympy.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sympy.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "tt = linspace(t0,tfinal,N+1)\n", "h = tt[1]-tt[0]\n", "\n", "figure(figsize=(12,5))\n", "yy=func_1(tt)\n", "zz=func_2(tt)\n", "subplot(1,2,1)\n", "plot(tt,yy,'-*',tt,zz,'-*')\n", "legend([r'$t\\mapsto y(t)$',r'$t\\mapsto z(t)$'])\n", "subplot(1,2,2)\n", "plot(yy,zz,'-*')\n", "xlabel(r'$y$')\n", "ylabel(r'$z$')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans la suite on notera $u_n\\approx y(t_n)$ et $w_n\\approx z(t_n)$.\n", "\n", "Pour l'affichage des solutions exactes VS approchées, on peut écrire une fonction qui prend en paramètres la discrétisation `tt`, les deux listes solution exacte `yy` et `zz`, les deux listes solution approchée `uu` et `ww` et pour finir une chaîne de caractères `s` qui contient le nom du schéma.\n", "\n", "NOTA BENE : on a juste fixé le nombre de points mais nous n'avons pas fixé la taille du domaine. On regardera la solution exacte pour choisir un $T$ final significatif." ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [], "source": [ "def affichage(tt,yy,zz,uu,ww,s):\n", "\n", " subplot(1,2,1)\n", " plot(tt,uu,'o--',tt,ww,'d--')\n", " plot(tt,yy,tt,zz)\n", " xlabel('t')\n", " legend([r'$u(t)$ approchée',r'$w(t)$ approchée','$y(t)$ exacte','$z(t)$ exacte'])\n", " title(f'{s} - y(t) et z(t)') \n", " grid()\n", "\n", " subplot(1,2,2)\n", " plot(uu,ww,'o--')\n", " plot(yy,zz)\n", " xlabel('y')\n", " ylabel('z')\n", " legend(['Approchée','Exacte'])\n", " title(f'{s} - z(y)')\n", " grid()\n", " axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q2 [3 points]** \n", "Calculer la solution approchée obtenue par la méthode d'**Euler modifié**. \n", "Afficher $t\\mapsto y(t)$, $t\\mapsto z(t)$ et $y\\mapsto z(y)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\text{(EM) }\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "\\tilde u=u_n+\\frac{h}{2}\\varphi_1(t_n,u_n,w_n),\\\\\n", "\\tilde w=w_n+\\frac{h}{2}\\varphi_2(t_n,u_n,w_n),\\\\\n", "u_{n+1}=u_n+h\\varphi_1\\left(t_n+\\frac{h}{2},\\tilde u,\\tilde w\\right),\\\\\n", "w_{n+1}=w_n+h\\varphi_2\\left(t_n+\\frac{h}{2},\\tilde u,\\tilde w\\right).\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "image/png": 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wbt06Jk+ezMyZM1m8eDFt27Zlx44dzJo1i+joaKZOncqsWbMIDQ3l7Nmz9O/fv8x5mWvi/Vef7s8q1qpXZ+IsuAFnt0PCZgwnNqO7rA27SDWzZ6uxE78bAthqDOAK2mdWc0frKom7pmbDSAZaFnvdAjhfVZX7DZrOb7ILTQ2worcZ5plmHP2fF/6DplXVKRSlTqiuR9QhISFFrWDnzp3j3nvvBSAyMpKhQ4cCEBsby8yZM1m9ejWBgYEkJiYybNiwotaxWw0bNoyuXbvi5+fHkiVLAK3fpq+vLxEREQQEBDBy5Eiys7PLLS88pkOHDkybNo0uXbqQlJTEvHnz8Pf3x9/fnw8++KDonMuXLycgIIDOnTszbtw4QGtpnDx5Mn5+foSHh5OTk1O0/4oVK+jWrRuBgYFMnToVg8FQqvzpp58uKm9EqvWeXZ4L18ueAu1adv6fqnflypWMGTMGgDFjxrBy5UoAunXrxj333INOp+PRRx8tSoLNzMwYPXo0AGPHji0qB4rKAbZt28Zjjz0GwLhx44r2i46O5sknnwRAp9Ph4OAAgI+PD4GBgQB07dqVs2fPkpmZyR9//MGoUaOK3ocXLmgN+Js2bWLGjBkEBgYyZMgQ0tPT6+QTHEWpNlJCyknY8QmZy0aQ928vWD4Etn2MztqBn5tO4ceQlawP/40XeZr/GnsWJcrWFjpm9W9fJWHUVMvyD8AMIcQ3wH3AdSllqcd5d2tYUHN+LPiI7PUPktbCSJKXgZbHc3jI26aqTqEota5wAENOvpa4FQ5gAO3/wN2SUnL27Fm8vLwAOHjwIJ06dSIvL49Tp07h7e0NaC2wwcHBzJ07t2igksFgYNeuXWXWu3TpUpydncnJySE4OJiHH34YgOPHj/P555/To0cPJk6cyMKFCxk5cmSZ5c8//3zRMcuWLWPhwoXs2bOHZcuWsWPHDqSU3HfffYSFhWFpacmcOXOIi4vD1dWVtLQ00tPTOXHiBCtXruTTTz/lkUceYc2aNYwdO5b4+HiioqKIi4vDwsKCadOmERkZSXBwcInySZMmERkZyfjx4+/6Z1wPVds9+9aW4OKaOVoXDdAprrmjNQDOtpYVHl+W1NRUoqOjOXz4MEIIDAYDQggGDhxYaiBdeQPripfb2tqWe67bDcyzsrIq+l6n01FQUIDRaMTR0ZH9+/eX2t9oNLJt2zasra0rrFdRGpTc65D4O5zcTP7/NmGRoXVDSjF6sFWGkto0lKf/OhGhb0L/Yoc1sdHz7s/HOXcth+aO1szq3/5PfTYWVyXJshBiJdALcBVCJAP/ACwApJSLgQ3AQOAkkA08URXnLW5wcFvw+hGPNaP4ppcVs5bnkvLRBzR97Z9VfSpFqTYVPaL+z0/HihLlQjn5Bl7/8QjDgppX6hF1WU6ePImPj0/RB31hspySklLU/aLQ8ePHad/+5l/qOp0OS0vLMh99z58/n7Vr1wKQlJTEiRMnaNq0KS1btqRHjx6A1mo3f/58Ro4cWWZ5YbLs5eVV1FczNjaW4cOHFyUtI0aMYOvWrQghGDlyJK6urgA4OzuTnp5eqjWvsAV98+bN7Nmzh+DgYO1nmZODu7s76enpJcqzsrJo0aLFbX+O9UlduGeXZVb/9iX+IIQ/3zq0evVqxo8fzyeffFJUFhYWRmxsLDt37iQxMREvLy+ioqKYMmUKoCWpq1evZsyYMXz99dfldtPp3r0733zzDePGjSMyMrJov759+7Jo0aKibhhZWVnlxtekSRN8fHxYtWoVo0aNQkrJwYMH6dy5M+Hh4SxYsIBZs2YBsH///qL3sqI0GEYDXNgPJ6ORCZshaSdCGsDSjjO2XVie34/rzf/CvUFd6e/fFHd7fZnVDAtqzrCg5tXSZaRKkmUp5aO32S6B6VVxrgq5d+C8RU+ueG7HoUc7rn67BufxT2BpahlTlPqsuh5RHzp0iE6dOhW93r17N1OnTsXa2rrEymCpqak4ODhgYWFR4vgbN26g15e8ecXExLBp0ya2bduGjY0NvXr1KqqrvNa8ilr5irfmlTcHrZSyzJa9W1vzCrthSCmJiIjgrbfeKrH/Rx99VKK8Pi2fXFl15p59i8JWoHd/Ps75azk0q4LWoZUrVzJ79uwSZQ8//DCLFi3i/vvvZ/bs2Rw6dIiePXsyfPhwQHu/HTlyhK5du+Lg4EBUVFSZdc+fP5+JEyfy7rvv4ubmxrJlywD48MMPmTJlCp9//jk6nY5Fixbh6Vn+ZCKRkZE8+eSTvPnmm+Tn5zNmzBg6d+7M/PnzmT59OgEBARQUFNCzZ08WL1581z8LRakz0i9AQjQkbEYmbEHkaJPznDBrza/5gwh54BG69uiPY65khpTlJsg1paa6YdSYMI9mRKXlw6tvI4aP4/K892kx/8PaDktRKqWmH1EDpKWlFT3mjY+PZ/369SxYsAAnJycMBgO5ubno9XoSExNp1qxZiWNTU1Nxc3MrlUBfv34dJycnbGxsOHbsGNu3by/advbsWbZt28b9999fNJ1XReW36tmzJxMmTGD27NlIKVm7di1fffUVlpaWDB8+nGeffRYXFxfS0iqaGU1r/Rs6dCjPPvss7u7upKWlkZGRUWZ5WlpaUTcVpXoVtg5VlbJGwv/9738nICCAuXPnlpsIv/HGG7zxxhsV1uXt7U10dHSpYz08PPj+++9LlR8+fHMNmOeff76o/7GPjw8//fRTqf1dXV3LjU9R6pX8XDj7h5Ygn4yGy0cAMNi4sTk/gPV5HflDdqKNzz0MDPDEp5MnmFvialfLcZs0uGTZw0KbXuiM+VXaDOlOyje/kL13HzZdGtRIdaURqo5H1AD9+/dn/vz5PPLII/j7++Pi4oKHh/b/KDw8nNjYWPr164evry8pKSn4+/uzZMkSunfvzpYtWxg4cGCpOgcMGMDixYsJCAigffv2Jaa76tChA19++SVTp06lbdu2PPnkk1y+fLnM8rJ06dKFCRMm0K1bNwAmTZpUNBPAyy+/TFhYGDqdjqCgIF5//fVyr7tjx468+eabhIeHYzQasbCw4OOPPyYkJKREeWHLoEqWFUVRKklKSPkfnNwMCZvhdBwU5GA0syTJLoBzPk/RPfwRhLsfP0QdIOQeF17xa4qbvdXt664FDS5ZtjJo/RU3Hj/I67ZbuGan4/I77+D1zUq1KpJSr1XHI2qAli1bcvDgwaLXr732WtH3M2bMYN68efTr1w87Ozt27txZ4tivv/66VDcG0Lo+bNy4sVT56dOnMTMzK/NRcnnl3t7eJVrkAGbOnMnMmTNL7RsREUFERESJsltb84obPXp0idkNyipviN0wFOjVq1e5/RozMzNrNhhFaQhyrsKp37Tk+GQ0pCcDcMPhHg67Dmb1tfZ8d82HGzl6HvJsRnfPAMyABY91qd24K6HBJcvuVg5IgxXH0xIx6zEVt0NzuLDzABk//0yTARWt7qoodV9VP6K+naCgIHr37o3BYECn05XYlpeXx7Bhw2jfvr2azkpRFKWxMRrg3F5TcrwZzu0GaURaNSHDszv2f3kO0aYv/4i+zre7k7i/tQuv9Pakv19TXO3qZgtyeRpcsqw3N0Nn8OBiThIEvYRD27dIO2vL5ffmYdenD2aWlrUdoqLUKxMnTiyz3NLS8o6nUyurlbiickVRFKUOuX7uZnJ8KgZyrwEC2SyIK4Ez+OWGH8tOu5BwLI8f+4XSycmBv/fNYVb/9rjUswS5uAaXLAPY65qRXnAcrB0RXR7F/cJKkqKzuPr117hMmFDb4SmKoiiKotR9+TlwJo7WJ7+EIy/AlWNaub0n+A6C1n1IsA9m4qpTnDmVjc5M0L11Eyb18qSVs7bWRTPH+j9PeINMlptat+J43nay87Oxue9v2J2KwfZ6a1IWLcZx+HB0ptWUFEVRFEVRFBMp4XK81nqcEA1n/oCCXJoLC/AJRQY+zgn7+/hvchNautjweCcvmucbaON2mSfDWhPu1xRn24b3BL9BJssBHm04ngQnryYS4O4HM3bjHv4/EocNJ2XxJ3i88H+1HaKiKIpSQ3Q6XYm5xMeMGVNq7uW7tX//fs6fP1/mrDCKUi9kp8GpLdqgvIRoyDCtbO/aHu6dCK37Enk4j2S9DxvjLnI2LQWdWSqP39cKAL2Fjs8nBNfiBVS/BpksPxp0L6uS4FzWWQLwAyHQ39MKh0H9uLpiBU6PPYply5a1HaaiKIpSA6ytrctcTroq7N+/n927d6tkWak/DAXaYLzCad3O7QUk6B3gnl7Qui+ydW9O3nCirYc2E9DqH37iSGoi3du4Mr13a8I7NsWpAbYgl8estgOoDq2atEIgOHXt1M3C5cNw89wH5uZcef/92gtOURRFqXXXr1+nffv2HD9+HIBHH32UTz/9FIAnn3ySe++9Fz8/P/7xj38UHbNr1y66d+9O586d6datG9evX+e1114jKiqKwMBAoqKiyMrKYuLEiQQHBxMUFFTm4iSKUuOunYXdyyBqLPznHljaH7bOBWEGYS/AX39FzkrgwP3zeetSN3ouOckD7//OedNCWI/5WrLr5X4sn9iN0cGtGlWiDA20ZVmHBRQ488uJw0wvXIuk00gsNjyPy8NPkrLie5zHj8c6MLBW41QURWlUNs6Gi4eqts6mneDBtyvcJScnh8Bi9/sXX3yR0aNHs2DBAiZMmMDTTz/N1atXmTx5MgBz5szB2dkZg8FA3759OXjwIL6+vowePZqoqCiCg4NJT0/HxsaGf/3rX+zevZsFCxYA8NJLL9GnTx+WLl3KtWvX6NatG/369SuxZLuiVLu8LG0hkMKZK1JPaOVNmkPHIdCmr9aKbO0EwJ4zV3l67laSr+Zgbibo0caVp3q3pYm1tjqrh61Zo0uQi2uQybK5zgxdgTuXc5NuFnZ+FDa/gUvLc1x1deXSf97FK3KFWqhEURSlgSuvG8YDDzzAqlWrmD59OgcOHCgq//bbb1myZAkFBQVcuHCBo0ePIoTA09OT4GCtb2aTJk3KPNcvv/zCDz/8wNy5cwHIzc3l7NmzdOjQoRquTFFMpIRLR24mx2e3gSEPzPXgHWrqe9wH3NojgQPJ11kffZ7AlrkMCtBmrmjjbsff+7YlvKMHjjaNNzEuS4NMlgEcLZqTavwdozRiJszAyg66jMNs+yLcJr3Fxbc/IOPXX2kSHl7boSqKojQOt2kBrmlGo5H4+Hisra1JS0ujRYsWJCYmMnfuXHbt2oWTkxMTJkwgNzcXKWWlGleklKxZs4b27f/cMvSKcltZKZCw5ebMFZmXtHL3jtBtitZ63Ko7WOgB2J90jfUb4tlw6CLnruVgoRM8GaZjUIAnbvZWfPFEt1q8mLqtQfZZBmhu64UUeVzKunSzsNtkQOLYtgDLNq25/N57yLy8WotRUZS6Iy4ujq1bt9Z2GEoNev/99+nQoQMrV65k4sSJ5Ofnk56ejq2tLQ4ODly6dKlo2XZfX1/Onz/Prl27AG0Z9IKCAuzt7UusYNm/f38++ugjpJQA7Nu3r+YvTGmYDPla14rN/4JPwuDdNvDfSfC/n8CrBwz9GGbGw7Rt0H8O8p7enLpWUHT4a98f5os/TtO+qT1zR3Vm9ysPMDNc/VFXGQ22ZbmNkw8HLsDByyfwtPPUCp28YdoOhGtbPGb5kzT1b1yN+hbncWNrNVZFqetycnIYMGAA0dHR6HQ6kpOTiYuLY/To0eTl5TFgwAB+++03zM3r5i3l9OnTPPTQQ+WuErhv3z6WLVvGokWLajgypSbc2md5wIABTJw4kc8++4ydO3dib29Pz549efPNN/nnP/9JUFAQfn5+3HPPPfTo0QPQVqyMioriqaeeIicnB2trazZt2kTv3r15++23CQwM5MUXX+TVV1/lmWeeISAgACkl3t7erFu3rrYuXanv0hJNXSuiIfF3yMsAoYMWwdD7JWjdF5oFgpkO0J5s7Dt7lfUHL7Dx0AVSsvLY++oD2FmZM3dUZzya6HEw9UNWKq9ufrJVgTCfjqy5AGfSTwM9b25waweAbWgoNveHkPLxxzgMHYKunP5nilLnXI6HVU/AqGXgXjP9IJcuXcqIESPQ6bQb8ubNmzl69CijR4/G0tKSsLAwoqKiePzxx6s9FpSv22kAACAASURBVCklUkrMzKruwVhQUBCfffZZldWn1C0Gg6HM8vj4+KLv582bV/T9F198Ueb+wcHBbN++vVR5YWtzoU8++eQuolQU4EYmnN56c1q3NNOsXo6toNNIrWuFT09tmrdb/Pa/K7y45iDnr+diqTPjL21dGRTgibmZ1n2onWkaOOXONdhuGL3atMHOwo4rxQf5FYp9H7E0HI9ZszBcv07qkiU1H6Ci3I28LIgcpS05GjlKe/0nJSYmEhYWBsDevXsRQpCamorBYMDf35/s7GwiIyMZOnQoALGxscycOZPVq1cTGBhIYmIiDz30EJGRkWXWP2zYMLp27Yqfnx9LTP/XTp8+ja+vLxEREQQEBDBy5Eiys7MrLO/QoQPTpk2jS5cuJCVp/6/nzZuHv78//v7+fPDBB0XnXL58OQEBAXTu3Jlx48YBWsI0efJk/Pz8CA8PJydHmxJpxYoVdOvWjcDAQKZOnVoisVqxYgW9evUqc5uiKMqfJo1w4QBsnQdfPATveMPKMbA/ElzawoP/gRl74OmDMPgD6DAY9A4YjZI9Z9L4149HiTuZAoCng54Onk2Y90hndr/aj88nBDOiSwv0FrravcYGoMEmy0IIvJp4cfJqYumNNq5wbjd6/RUchg4lbflX5CWfq/kgFeVOfT8dsq4AUvv3+xl/ukpHR8eiPpcfffQRISEhXL16lfXr1/PAAw9gbm7OqVOn8Pb2BiA0NJTg4GC+//579u/fj4+PDx07dizVulZo6dKl7Nmzh927dzN//nxSU1MBOH78OFOmTOHgwYM0adKEhQsX3rZ8/Pjx7Nu3Dy8vL/bs2cOyZcvYsWMH27dv59NPP2Xfvn0cOXKEOXPmEB0dzYEDB/jwww8BOHHiBNOnT+fIkSM4OjqyZs0a4uPjiYqKIi4ujv3796PT6YqS/sJtv/76a6ltiqIody3zMhz4BtZMpvsfE+CTnrD5n5BzDe6fBuN/gBdOw+Pfwn1TwbUNCIGUkt2n0/jnj0fo/nY0Dy/axortZ4i/kA5oLceFCXITvepqUZUabDcMgJPnbEB/ovSGTqNg0z9gx2Lcnnmf9I0bufLBBzSf+27NB6koxS0bVLrMb5g2OHXX53D0e60lAqAgF45+B9/ZwLCPISsVvh1f8tgn1t/2lA4ODmRnZ5OamsqFCxfo0aMHV69eZcmSJcybN4+UlBQcHR1LHHP8+PESo/11Oh2WlpZkZGRgb1/yUd/8+fNZu3YtAElJSZw4cYKmTZvSsmXLov6gY8eOZf78+YwcObLcci8vL0JCQorqjY2NZfjw4UXz144YMYKtW7cihGDkyJG4uroC4OzsTHp6Oj4+PkX9Vrt27crp06e5du0ae/bsKZoOLCcnB3d3d0DrarJnzx569eqFmZlZiW2KoiiVVpAHSdtvdq0onGvcxoWrTp3x6P6YNq2bvUepQ41GyblrObR0tgHg6W/2cyXzBmHt3JjdyZe+HdyxV4lxtWvQybKzZQsusIvs/GxsLGxubrDQQ9cnYOt7WPSfg/OECaR+8gnOERFYd/KvvYAVpSJb/n0zUS4kjVoCPezju662sO/vp59+yl//+leOHj3KwYMHMRgMtGvXjqtXr5Kbm1u0f2pqKg4ODlhYlLxB37hxA71eX6IsJiaGTZs2sW3bNmxsbOjVq1dRXbdOw1X4urzyWxd1KJxt4FblTfFlZWVV9L1OpyMnJwcpJREREbz11ltl1hMREcFLL71U6g8A5c5Udto15c6V9/9AqUVSan2NC5PjxK2QnwVm5tDyPujzqtb3uGln4n//HY/AXiUONxole0yD9H46fJECo5EdL/VDZyb4ZFxXvFxsVIJcwxp0stzKzosL2XD6+mk6unYsuTF4EsR9ADs/xWXyy1xbtYrL//kPrZZ/qW7qSu2pqCW43z9h4yzIz75ZZmEDD76jfW/rUqmW5LKYmZnxww8/8Pvvv5OcnMzcuXN5+21tTlwnJycMBgO5ubno9XoSExNp1qxZieNTU1Nxc3MrlUBfv34dJycnbGxsOHbsWInBUWfPnmXbtm3cf//9rFy5ktDQ0ArLb9WzZ08mTJjA7NmzkVKydu1avvrqKywtLRk+fDjPPvssLi4upKWllXvdffv2ZejQoTz77LO4u7uTlpZGRkYGXl5eRdsmT56Mvb19iW1K5en1elJTU3FxcVH31iompSQ1NbXUH6lKLchN12arKFwU5NoZrdzJBwIf1Wat8PkLWFX8h/ePB87z5vqjXEq/gaW5Gb3auTEowBOjlOgQ+DcvPbBPqX4NOllu79KaHdna9HGlkuUmnvDQB9CyGzo7O9yemsHFf/6LzC1bsO/Tp3YCVpSKdBkLCZvg+EatC4a5HtoNgKA/PwOFpaUlDz74IObm5jRp0oSsrCweeuihou3h4eHExsbSr18/fH19SUlJwd/fnyVLltC9e3e2bt3KwIEDS9U7YMAAFi9eTEBAAO3bty/RjaJDhw58+eWXTJ06lbZt2/Lkk09y+fLlcstL/Ti6dGHChAl066ZNpD9p0iSCgrT17V9++WXCwsLQ6XQEBQXx+uuvl3ndHTt25M033yQ8PByj0YiFhQUff/wxXl5eRduGDRsGUGKbUnktWrQgOTmZK1eu1Mj5Cv+oqw+qIla9Xk+LFi2qKCKl0oxGuLD/5rRuyTvBWACWdtpsFd2f0lqPne+poArJ8TQDMT8cYdS9LfBr5oCrnRWBLR0Z2MmTvh08sLNq0Gla/VE4DVNd/Oratau8U1u2bCn6/uejSdJvWSf50pa5tz3OmJcnTz44UJ4c8KA05uXd8XlrSvHra2ga47UdPXr0ziq6kSnlPD8p/+Gg/Xsj888HVwl79+6VY8eOLXf74MGD5bFjxypdX2JiovTz86t0eW1KT0+/7T5l/R6B3bIO3Edr8utu7tlVrT7dR1Ss1aPaYk2/IOW+SClXTZTyHR8p/9FE+1r8Fyl/fV3KxK1S5t+osAqDwSi3J6TI1747JIPf/FV6vbBOtnt5g1y1O6l6Yq4ijeH3X9E9u0H/yRLYwhWHve5cy08uf6cLB2BfJGLA27g//zzJ06ZxddUqnB97rOYCVZTKsrSFx1fdnGfZ0vb2x1SBoKAgevfujcFgKJpruVBeXh6DBg1Sy/sqitKw5OfC2W03W48vH9HKbd2hzQNay/E9vcHOrcJqDEbJpfRcmjlak2cwMvGLXRQYJb3bu+NtfpWnRvTCVrUg12kN+rfjbq8nwKMtl3MqSJZTTsDOT6BNP+x6P4BNcDApCz7GYcgQdHZ2NResolSWeweYXnphhOo2ceLEMsstLS157A7/uPT29i5zNb3yyhVFUaqdlFpOUNjv+HQsFOSAzhJahUC/17W+xx7+cJtFkQxGya7TadogvSMXcbKx4Jdnw9Bb6Fj+1/vwbWqPrZU5MTExKlGuBxr8b8hD34pdF3djlEbMRBlv7o5D4ZdXYMciRLtw3P/v/zg9ahSpn36G+7PP1HzAiqIoiqLUjJxrkPibaeaKaLhuWsjMpQ10Ga+1HnuH3tFTvJU7z/LeL/8jJfMGegszerd3Z1CAZ9GsMF29nKrpYpTq0uCT5d0ndNwwy+VS1iU87TxL76CzgOC/QvSbcOU41p38aTJ4MGlffIHTmNFYeJZxjKIoiqIo9Y/RAOf33ZzWLXk3SANYNdEG5v1lptZ67FS5gbwGo2RHYiobDl3gb2GtaeFkQxO9Bd18nBjYyZM+vu7YWDb4VKvBa/C/QS8Hb85kQOL1xLKTZdDmXP7tXdixGB56H/dnnibj559J/exzmr76Ss0GrCiKoihK1bl+Tms1TtgMp2Ig5yogoFnQzeS4xb1a41klGIySHadSWX/oAj8fuUhKZh7WFjrC2rnTwsmGQQGeDApQDW0NSYNPlv3c2vJ7hjZ9XPfm3cveydZVW1LSqgkAFs2bYxsaSmZMDPKVl9XcoIqiKIpST5gZbsDJTZCwRWtBvhKvbbD3hPYDtdXy7umtzU1fSQUGI2nZebjb67mancfYz3dgZa6jTwd3BnXypFd7N9WC3IBVyW9WCDEA+BDQAZ9JKd++ZbsDsAJoZTrnXCnlsqo49+34uTdHnrDi6JWTFe8Y/kaJl7ahPciMjib/zBksvb2rL0BFURRFUe6elHDlWFHXih6JsbA1D3RW4NVdm4u+dR9w7wh30PhVYDCyIzFNa0E+fBFfT3siJ4XgamdF5KQQAls6Ym2pu31FSr33p5NlIYQO+Bh4AEgGdgkhfpBSHi2223TgqJRysBDCDTguhIiUUub92fPfzj1udhjz3Em8nnj7nY1G7a/R1n2wCw3lEpAZG4ezSpYVRVEUpe7Iy4b//aR1rUjYAunntHLX9pxv1p+WYRO0RNnS5q6qX/J7Ap/8dorUrDxsLHX08XVncOebK5fe37ryrdJK/VcVLcvdgJNSylMAQohvgKFA8WRZAvZC689gB6QBBVVw7ttq5mhNF892nMs9dPudT26Cr0fBI8ux7DgUi1atyIqNxXnsn18hTVEURVGUKpByEqIe11qT9Q5wTy9o/YLWeuzYkoSYGFq27VXp6goMRrafSmPD4Qu8+KAv9noLrC10dG/jyqBOTQlr565akBu5qkiWmwNJxV4nA/fdss8C4AfgPGAPjJZSGqvg3LelMxOE+fgxf99msvOzsbGo4K/MNn3BsRVsXwwdh2IX2oNr332PzMtDWFrWRLiKoiiKopTn2AZYO1UbjPfoN9riILo7T2UKDEa2ndJmsfj5yCXSTC3Iw4OaE+ztzLj7vRl3v3fVx6/US1WRLJfVAUje8ro/sB/oA7QGfhVCbJVSppeqTIgpwBQADw8PYmJi7iiYzMzMUsckpWYAsCZ6DS2tWlZ4fAuXvrRJWMbhb+fgcTkKmW3kj2XLyK8jq5OVdX0NRWO8NgcHBzIyMmo+oErKyclhxIgRrFu3Dp1Ox7lz59i+fTuDBw9myJAhrFu3DnNzcwwGQ41dx7Vr11i1ahWTJ0+ukfNV5tpyc3Pr1Xu3Lo8zUZQyGQ0Q8zb8/h9tFotHvgLHij/Pb5VvMJKek4+LnRWJKVmM+3wntpY6+nbwYKBpkJ7eQrUgK6VVRbKcDBR/x7ZAa0Eu7gngbdPa2yeFEImAL7Dz1sqklEuAJQD33nuv7NWr1x0FExMTw63HrPsuFwDnNs70an2b+nIC4b0o/E8swOCQS4pZU9pev4r7HcZRXcq6voaiMV5bfHw89vb2NR9QJS1fvpxRo0bh6OgIwI4dO4iPj2fChAmEh4ezYcMGHn/8cTIyMmrsOlJTU1m6dCkzZ86skfNV5tr0ej1BQUE1Es+fVdfHmShKKTlXYc1kOPkrBI6FQe+Bhb5Sh+YbjPyRkMqGgxf4+ehFwtq58eGYINp62PPlxG7c5+OsEmTltiper7FydgFthRA+QghLYAxal4vizgJ9AYQQHkB74FQVnLtS/N1bI6Xg0O1mxACwdgR7D8jPQWdhxMY1n8wNq6o/SEWpJYcOHaJHjx5Fr/fu3UufPn0AiIyMZOjQoQDExsYyc+ZMVq9eTWBgIMOGDSMyMrLcelesWEG3bt0IDAxk6tSpGAwGdu3aRUBAALm5uWRlZeHn51e0vPWwYcPo2rUrfn5+LFmypKie5cuXExAQQOfOnRk3bhyzZ88mISGBwMBAZs2aVe65lHIVjTMxJb+F40yKq7VxJopSwsXDsKSXNj/yoHkwdEGlE+X3fjlO8JxNRCzdyfpDF+jVzo1hQc2Ltoe1Uy3JSuX86ZZlKWWBEGIG8DPaI72lUsojQoi/mbYvBt4AvhBCHELrtvGClDLlz567stq6OyGPOHE8NeH2O+9dAZkXKexJYts0hysHLSjYshjz3n+r3kAVpRb4+fmRkJCAwWBAp9Px3HPP8d5775GXl8epU6fwNs0GExoaSnBwMHPnzsXf378o+S1LfHw8UVFRxMXFYWFhwbRp04iMjGT8+PEMGTKEV155hZycHMaOHYu/vz8AS5cuxdnZmZycHIKDg3n44Ye5ePEic+bMIS4uDldXV9LS0khPT+fw4cPs37//tudSylSnx5koSpFDq+GHp7RBfE9sgJbdyt01r8BIXEIKW45dJsxe+/zWmQl6t3dnYCdP/tLWVSXGyl2rknmWpZQbgA23lC0u9v15ILwqznU3vF1tMea5cTbjzO133vw65OcUvbRteoMrByFr5Xs4qGRZqUbv7HyHY2nHqrROX2dfXuj2QoX7mJmZ4efnx5EjRzhx4gStWrWiS5cunD9/vqj7RaHjx4/T3tR/X6fTYWlpWWZ/3s2bN7Nnzx6Cg4MBre+zu7s7AK+99hrBwcHo9Xrmz59fdMz8+fNZu3YtAElJSZw4cYJdu3YxcuRIXF1dAXB2diY9Pb3S51LKVKfGmVS1+jT2QcVaNmE0cM+pL2iZ/APXHDpytOP/kZeQDQklz19glBxNNbDrooG9lwvIygdrc2gZINHFxBBoDoEewOVrbL9cI6HfsfryHqgvcUL1xNoolpvxbKJH5LuTemMHRmnETFTQ+6Tv67BxFuRnA6B3ykdnZSTTEIhDzYSrKDUuJCSEuLg4Fi5cyE8//QSAtbU1ubm5Rfukpqbi4OCAhcXNJWFv3LiBXq8vsR+AlJKIiAjeeuutUudKS0sjMzOT/Px8cnNzsbW1JSYmhk2bNrFt2zZsbGzo1asXubm5SClvu4JmRedSylSnxplUtfo09kHFWobMK7D6CUjeCt2m4th/Dt2LLUOdV2AkJ9+Ag7UFf5xMYd4vO7C3Mqe/f3OtBbmdK9tit6qfaxWrL3FC9cTaKJJlMzPBpJD7WHZ8K5eyLuFpV8Ga7V3GQsImOLYeDHkInQW27d3Jij+PNBoRZlXRzVtRSrtdC3B1CgkJYcKECUyfPp3mzbU+fU5OThgMBnJzc9Hr9SQmJtKs2c1J+VNTU3Fzc8PCwqJUsty3b1+GDh3Ks88+i7u7O2lpaWRkZODl5cWUKVN44403SExM5IUXXmDBggVcv34dJycnbGxsOHbsGNu3by+qZ/jw4Tz77LO4uLiQlpaGvb19idbsis6llKlonAlwDm2cyWO37FM4zmRrbYwzURqp5D1kr3gMXW4aL+Y9yY6D4czyvMzATp7EnrzC+oMX+fXoRUYHt+TlQR3p5uPM0gn30qONK1bmqouFUn0aRbIM8Bfvjiw7DonXEytOlgGGfgxJuyA9Gcz12I1+ivSX/0FufDzWfn41E7Ci1CBfX1+srKx44YWSCXt4eDixsbH069cPX19fUlJS8Pf3Z8mSJZw/f56BAweWWV/Hjh158803CQ8Px2g0YmFhwccff8xvv/2Gubk5jz32GAaDge7duxMdHc2AAQNYvHgxAQEBtG/fnpCQEEDrT/3yyy8TFhaGTqcjKCiIL774gh49euDv78+DDz7Iu+++W+a5VLJctvowzkRphPZ8iWH9c6QZHJma9zpHpDdcy+G5VQd4Yc0BbhRI7PXmPNDRg96+Wjcrc50ZfXw9ajdupVFoNMlyQa7W5/HU9US6N+9e8c6WtjB2NXzaB+zcse3ZG/gHWbFxKllWGqQPP/yQt956C1tb2xLlM2bMYN68efTr1w87Ozt27rz5FH7EiBEVdn0YPXo0o0ePLlEWEhJSNPBOp9OxY8eOom0bN24ss56IiAgiIiJKlH399de3PZdSvro+zkRpRApuwIZZsPdLdpsFMvXGk1zj5lSNBqPEUqdj6YQg1YKs1JpG06cg8ZIZ0qDn8JUTlTvAvQP0fB7SEjC3BitfX7JiY6s3SEWpYQkJCfj6+pKTk1MqIQUICgqid+/epaZiy8vLY9iwYUWD/RRFUe7Y9XOw7EHY+yWEzuSx7OdLJMqFcvMN9PH1UImyUmsaTcuyj6sdxjw3Tl5NrPxBbftD+gUw5GEX2oPUL77EkJmFzs729scqSj3QunVrjh2reAaOiRMnliqztLRUU7MpinL3TsfCqgna7FOPfEV++4ew+v0XsvNKz5HezNG65uNTlGIaTcuyj6stxhtunM86W/mDmvrDoLng0Bzb0FAoKCB7547bH6coiqIoSmlSwraF8OUQ0DvC5GgyWw/kr1/uJjvPgLlZydlvrC10zOqvnmAptavRJMseTawwM7iTUZBCtmlauEoxGuDCQay7dEFYW6uuGIqiKIpyN/Ky4b+T4ecXof2DMDka3NqzLSGVP06m8M7DnZg7qjPNHa0RQHNHa94a0anEqnuKUhsaTTcMIQRuVi1IA06nn6ajS8fKHbjrc9g4C7NnDmHbrRuZcXHVGqeiKIqiNDhpiRA1Fi4dgT6vQuhMcgok1sADHT3Y8nwvWjrbAKjkWKlzGk3LMsDc4Q8A2vRxleYdqv2b+Du2oaHknzlLXlJSxccoiqIoiqI58SssCYPrydpMUz2fZ/vpq/zlP1vYcSoVoChRVpS6qFEly5092mAmzDidfrryB7l3AFs3OPUbtqE9AFRXDEVRFEW5HaMRfnsXIkeBQyuYEgNt+vHDgfOM/3wnjjYWNHdSg/eUuq9RJcunU26gx434lJOVP0gI8OkJib9h6eWFRfPmZMaqrhiKoiiKUq7c61q3iy1vQqeR8NdfkE7eLP4tgb+v3EdgK0fW/K07LZxUi7JS9zWqZPladj7pGY53Nn0cgE8YZF5CpJ7ANjSU7O3bkfn51ROkoiiKotRnl49pi3r97ycY8A6M+BQsbfjl6CXe3niMQQGeLJ/YDQcbi9qOVFEqpVEly94uNhhvuHEpJwmjNFb+wPYPwtj/gqMXtqE9MGZlkbN/f/UFqiiKoij10dHv4bO+WstyxI8Q8jftCS3wQAcP3h/dmY/GBKG3UAuMKPVHo0qW3eytMDd4UCDzuJh1sfIH2rlDm75gocc2JAR0OtUVQ2nwcnJyCAsLK1q9Lzk5maioKEBbwa9nz54UFBTUaEzXrl1j4cKFNXpORVEqwWiATa/Dt+PBzRem/g7ePUjNvMHk5btJSsvGzEwwPKgFZrfMpawodV2jSpaFEHhYtwTg9PXTd3bwleMQ8w46WxusAwPVID+lwVu6dCkjRoxAp9NagDZv3szevXsBbQW/vn37FiXPNUUly4pSB2WnwYqHIfZ96PoEPLEBmjTjdEoWDy/6g9//d4VTKVm1HaWi3LVGlSwDtHVuDUBi+h32W75wEGL+DRcOYBfag9yjRylIS6uGCBWl5vXp04fAwEACAwPR6/WsWrWKyMhIhg4dCkBsbCwzZ85k9erVBAYGkpiYyLBhw4iMjCyzvhUrVtCtWzcCAwOZOnUqBoOBXbt2ERAQQG5uLllZWfj5+XH48GEAhg0bRteuXfHz82PJkiVF9SxfvpyAgAA6d+7MuHHjmD17NgkJCQQGBjJr1qxyz6UoSg05vx8+CYMzcTDkIxj8AZhbsffsVUYs+oP03AJWTgkhrJ1bbUeqKHet0SxKUmjRmJ6EfmN/Z3MtgzYjBpjmW+7LlQ/nkxX3Bw6DH6r6IJVG6eK//82N+GNVWqdVB1+avvTSbfeLjo4GYNGiRWzZsoUhQ4bw1FNP4e3tDUBoaCjBwcHMnTsXf39/gKIE+Fbx8fFERUURFxeHhYUF06ZNIzIykvHjxzNkyBBeeeUVcnJyGDt2bFFdS5cuxdnZmZycHIKDg3n44Ye5ePEic+bMIS4uDldXV9LS0khPT+fw4cPsN40ZqOhciqJUs/0rYd0zYOMCE3+C5l0B2HU6jXGf78CjiZ4vnuiGj6ttLQeqKH9Oo0uWzczM8HHwufNuGPYeWj+sxN/QP/YUOkdHsmJjVbKsNBjLly9n48aNrFmzhitXruDo6Fhi+/Hjx2nfvn3Ra51Oh6WlJRkZGSX227x5M3v27CE4OBjQ+j67u7sD8NprrxEcHIxer2f+/PlFx8yfP5+1a9cCkJSUxIkTJ9i1axcjR47E1dUVAGdnZ9LT0yt9LkVRqklBHvzyMuxcAt5/gZHLwO5my3EHzyYM7dycWQPa42pnVYuBKkrVaHTJcvLVbM5dscNo9b87P9gnDPYuR0gDtt27k/lHHFJKhFCDFZQ/rzItwNWlsNvF999/j4WFBdbW1uTm5hZtT01NxcHBAQuLklM93bhxA71eX2JfKSURERG89dZbpc6TlpZGZmYm+fn55ObmYmtrS0xMDJs2bWLbtm3Y2NjQq1cvcnNzK/V/q6JzKYpSDTIuwqoJcHYb3D8D+v0TdOYYjZIvt51mdHBL7KzMeWdkQG1HqihVptH1WdZb6Dh/xZ6reSlk5d/hgIN7wsBMB6knsQ0NxXAlhRvHj1dPoIpSQ9atW8fChQv573//i16vB8DJyQmDwVCUBCcmJtKsWbMSx6WmpuLm5lYqge7bty+rV6/m8uXLgJYgnzlzBoApU6bwxhtv8Pjjj/PCCy8AcP36dZycnLCxseHYsWNs3769qJ5vv/2W1NTUonrs7e1LtGRXdC5FUarY2R1a/+QLB+Dhz6H/HNCZc6PAwNNR+/nnj0dZu+9cbUepKFWu0SXLLraWWBmbAtzZstcAbcPhhdPg0RHbHmrpa6VhiIiIIDk5mR49ehAYGMjnn38OQHh4OLGm97evry8pKSn4+/vzxx9/ALBlyxYGDhxYqr6OHTvy5ptvEh4eTkBAAA888AAXLlxg+fLlmJub89hjjzF79mx27dpFdHQ0AwYMoKCggICAAF599VVCQkIA8PPz4+WXXyYsLIzOnTszc+ZMXFxc6NGjB/7+/syaNavccymKUoWkpNm5jfDFILCwhkmbtFX5gOvZ+Yz7fCc/HjjPCwN8eaxbq1oOVlGqXqPrhiGEoJldK86jTR/n5+JX+YN1N1vQLDzcsWrblszYOFwmTar6QBWlhhS23N5qxowZzJs3j379+mFnZ8fOnTtLbP/666/L7f4wevRoRo8eXaIsJCSkaOCdTqdjx44dRds2btxYZj0RERFERPw/e/cdHmWVPnz8e6alTHohCQkhtQHykwAAIABJREFUCYQiTSQgSICgImBZXdtaV9SVdRXLFtvuuqvu664ru5a1rD8sqGsv2EFEMCBNikgTQkkgBAjpZZKZTDvvHxMxhIAkmUlIcn+uK1cyz3PmnPsJZHLnmXPuc91R4/7UWEIIP3HZ4bPfM2Dn674bRhfPgZBowDetccbctRSW1/PkFady4anJnRysEIHR4+4sA/SPTgOtWl8RA2DHQt/bUA02rNnZ2Nevx1tf7/cYhehsI0eOZPLkyS2WYnM6nVx00UVHLPgTQnQzVYXw0jT47nX29L0Crnz7cKIM4PWCV2tevXGMJMqiW+uRyfKpKXGYdRwFra2IAb67ywe/g8LVWLPHo10u6prdcROiu7jhhhsOb0rSlMVikfJsQnRn+bkwJwcq8uHKt9iTfiUYfCnD1gPVeL2a1NhQFv12EmMzYjs1VCECrUcmyzdNzGBsn0Hsae3GJAB9xoLRAgVLCc3KQgUHU7dipf+DFEIIITqa1rDiSfjfz8EaDzNzYeD0w6ffWbuPnz29gldW7QHAKFtXix6gRybLAOmR6RTWFOLV3tY90RIKKWOgYCmGoCBCR4+WRX5CCCG6vgabryzcor/A4J/BrxZDrG/XW601jy/awd3vb+KMfrFcOiqlc2MVogP1yGTZ7vTw8To3Do+D4rri1neQMcm3/XV9BWHZ43EWFODaL+VyRNtorTs7BNEO8u8nuoXy3fDCWbDtY5jyEFz2MgSFAeDyeHlpi5MnF+/k0lEpvDRjNOHB5uP3J0Q30iOT5RCLkepq3+5kbVrk1/8sGHIRNNRizc4GwLZ8hT9DFD1EcHAw5eXlknB1UVprysvLD9enFqJLylvgm59sK4FrP4Dxd0CTDYG2Haxh1QE3d5yVyexLh2M29sjUQfRgfikdp5SaBjwJGIEXtNaPtNAmB3gCMANlWutJ/hi7rfpEpFGIr9by+OTxrXty8ijfX92AJUpjSkqibvlyon9xud/jFN1bSkoKRUVFlJaWdnYo7eJwOLptwvhT1xYcHExKirwlLbogrxeWPgJL/wlJI+AXr0HUj3WSHS4PwWYjw1Oi+PuEEC6fMqATgxWi87Q7WVZKGYFngClAEbBWKfWx1vr7Jm2igGeBaVrrQqVUr/aO2179oxModIS07c7yD2oOoCJ6E5Y9nprPF6LdbpSpx5WuFu1gNptJT0/v7DDaLTc3l5EjR3Z2GAHRna9N9GD2Kph3E+z8Ak69Gs77t2/DkUY7DtVy/dy13Dt9EBeM6E2vULmbLHouf/zvHwPs0lrna62dwFvAhc3aXAXM01oXAmitS/wwbrukx4fhaYhjd1Ubk+W1L8Jjg6HmANbx2Xhra7Fv2uTfIIUQQgh/O7TVN+1i91e+JPnCZ45IlFftLueS/67E6fGSHmftvDiFOEn4I1lOBvY1eVzUeKypAUC0UipXKbVeKdXpBVpHpkbT25rK3tZuef2DlCzf54JlWMeNBYNBqmIIIYQ4uW1+D14427cz34zPYPSvjpif/NF3+7nupTUkRATzwS1nMDQ5shODFeLk4I85Ay0VWWy+WskEjALOAkKAVUqp1VrrHUd1ptRMYCZAQkICubm5rQrGZrOd8HPGRMTwSVUJny/5nGBDK+dbai/jTeGUrXqbvMpEotPSODh/AVuHD29dP63UmuvrauTauq7ufH3d+dpED+Jxw5d/hVVP+/YLuPwVCE88osmW/dXc8dZ3jEmP4flrs4gMlYoXQoB/kuUioE+TxynAgRbalGmt64A6pdQyYARwVLKstZ4DzAHIysrSOTk5rQomNzeXE32Oe6+bT3I/oc+IPgyJHdKqcQAomUzS/m9JmjSJ0i1bKXvmGbJHjMAUHf3Tz22j1lxfVyPX1nV15+vrztcmeoi6Ml/95D1fw5iZcM7DYLIc1WxociRPXnEq04YmEmQ6eudOIXoqf0zDWAtkKqXSlVIW4Arg42ZtPgImKKVMSqlQ4HRgmx/GbpeHPvBVIGjzIr+MSVBTBBX5hGWPB62pX7XKjxEKIYQQ7bB/PfzfJChaCxc9B+fOPiJRtjs93PHWBrbsrwbgwlOTJVEWopl231nWWruVUrOAhfhKx72ktd6qlLq58fxzWuttSqnPgU2AF195uS3tHbu9YixJVGrFnuo9betgwHQIigBrHMHD0jBERmJbvoKIc8/1a5xCCCFEq337Knz2ewhLhBsWQu9TjzhdbmvgxlfWsbGoivH94mR+shDH4Jc6Z1rr+cD8Zseea/Z4NjDbH+P5S0ZcFPm1sW2/sxyZDMN9tZUVYB03jrrly9Fao1RLU7mFEEKIAHM3wIJ7YP1cyJgMl74EoTFHNCkoq2PG3DUUVzt47ppRTB2SeIzOhBA9unBieqwVlz2O/LbeWQao2gdrXwCvl7Ds8bhLSmjYudNvMQohhL8ppaYppfKUUruUUvceo02OUuo7pdRWpdTSjo5RtFHNAXj5PF+inP1buOb9oxLl/FIbFz+7glqHmzdnjpVEWYif0KN30EiLs+J1xrG3Zg1e7cWg2vC3w56vfW9z9Tkd63jfToB1y1cQPEB2OhJCnHy66kZS4gTsWQHvXucrC3f5q3BK8y0PfPrEhHLusCRumpBBmtRRFuIn9eg7y8OSI8nuewour5ODdQfb1kn6RN/ngmWYk5Kw9Osn9ZaFECezLrmRlDgOrWH1c/DqzyA4En61uMVE+Z11+yitbcBsNPDwz4dJoizECerRyXJanJXfjB8H0PZFfpEpENMP8n3vUoZlj6d+3Tq8DoefohRCCL/qkhtJiWNw1sO8mfD5PZA5FW5aAr0GHdHE69X8ff427n5vEy+taOMaHSF6sB49DQMgMTQV8JWPG588vm2dZEyCTe+Ax4U1O5uKV16lfu06wiZk+zFSIYTwi5NqIyl/60qbyLQ31mB7MUO3PIK1bg8F6VdTmHgprN5wRBunR/PC5gbWFHs4K9XE6KCD5OYWd3isHUli9b+uEicEJtYenyzf+cZODMGh7Gnrttfgm4qx/mUo3U5oVhbKYqFu+XJJloUQJ6OTaiMpf+tKm8i0K9adX8L79wAarn6XjMwpZDRrUlXvZOar61lTXM990wcxc2JGmys19ZjvawfrKrF2lTghMLH26GkYAOmxYWhnfNvLxwEMmAZ3F0DiMAwhIYRmZWFbIfOWhRAnpS67kZTANz952b/g9Ut90wBn5kLmlGM2rXG4+M+VI/n1pH5S0lSINurxd5bT4qw4D8SS355k2Rzi+2hkzc6m5NFHcR08iDkpyQ9RCiGEf3TljaR6PEcNfPgb2P4pDLsMLngSLEcv0tt5qJbU2FCirRY+vS0bk7HH3xcTol16/E9QepwVrzOeMnspda66tneUvxReuwRcdqzZjSXkVqzwU5RCCOE/Wuv5WusBWut+WuuHG48913QzKa31bK31KVrroVrrJzovWgFAaR48fybkLYCp/4CLn28xUc7NK+HCZ1bw6Od5AJIoC+EHPf6nKC3WlyxDOypigG/HpF1fwr5vCMrMxJSQgG25JMtCCCHaadsnvkTZUQXXfQzjboEWplS8vbaQG19ZR1qslZkTm89gFkK0VY9PltPjrNx8xlgACmraMRWj7zgwmCB/KUoprOPHU7dqFdrj8VOkQgghehSvB758EN6+BuIHwcylkHb0wnGtNY8t2sE9729mfP843rl5HAkRwZ0QsBDdU49PlkMsRm6fOA6DMrRvkV9QOCSPgoJlgK/esre6GsfmzX6KVAghRI9RX+FbxLf8MRg1A66fD5HNy2H7HKh2MHd5AZdnpfDidVmEBfX45UhC+JX8RAGltR7ig5PaNw0DfCXkvv43OKoJHTcOlMK2fAUhp57qlziFEEL0AAc3+u4m1xbDBf+BUde12Mzh8hBkMpAcFcJnt0+gT0yIVLwQIgB6/J1lgKcW76SkIrJ90zAA+p0JfcdDXRmm6GiChw2Tra+FEEKcuI1vw4vn+KZgXP/5MRPl4moHP392Jc9/nQ9AamyoJMpCBIgky/jKxzXUx7K3phCv9ra9o75nwIxPIbYf4JuKYd+0CU91tZ8iFUII0S15XLDgHvhgJiRn+eYnp4xqsemOQ7Vc/OwKCsvrGJgY0cGBCtHzSLLMjxUxnJ4GDtYdbH+HTl8JOmt2Nni91K1a3f4+hRBCdE+1h+CVn8E3z8G4WfDLjyAsvsWmK3eXccl/V+L2at7+9TgmDWi5nRDCfyRZprHWcoPvBaddi/wANrwOj6SCrZSQ4cMxhIdTJ7v5CSGEaMm+NTBnEhzYAJe8CFMfBmPLy4lKahxcP3ctiRHBfHDreIYmR3ZwsEL0TJIsA31jQ/1Taxl85X28btizDGUyYR07FtvyFWit2x+oEEKI7kFrkg58DnPPBVMQ/OpLGHbpcZ/SKyKYJ68YyXs3n0FyVMhx2woh/EeSZSDYbOTFa3IIM4e3/85y0ggIivTt6AdYJ2TjPngQ565dfohUCCFEl+dywMezGLjjv5CRAzNzIXFoi03dHi9//WgLX+WVADBtaCKRoeaOilQIgSTLh505OIGMqHT21OxpX0dGE6SN/7He8sSJANiWLm1nhEIIIbq8qn0wdxpseI09fS+Hq96BkOgWm9Y73dz82npeWbWX7wqrOjhQIcQPJFlutKukFpzx7b+zDJA+CSoLoKoQc2IiQYMGYcuVZFkIIXq0/KW++cnlu+GKN9mTfjUYWv41XGZr4Mo5q1myvYSHLhzCb6cM6OBghRA/kE1JGn21vZS1O80E9SrF5rQRZglre2cDpoL2gtkKQNikSZS/8AKe6mqMkbIgQwghehStYdXTsOgvEDcAfvEaxGVCcW6LzSvqnFz87EpKah08d80ozhmS2LHxCiGOIHeWG6XFWfE64wDYW7O3fZ3FpMO4W8AaC/iSZTwe6lasaG+YQgghupIGG7x3PXzxZxh8gW8hX1zmcZ8SHWpm2tBE3rxprCTKQpwEJFlulB4Xerh8XH51fvs7rCuHrR+C1oSMGI4xKkrmLQshRE9SvhtenALffwRnPwiXvQJB4cdsvnBrMbtLbSil+OO5gxmZ2vJcZiFEx5JkuVGfmFBwx6IwtH+RH8D2T+Hd66A0D2U0Yp04Aduyr9EeT/v7FkIIcXLbsRDmTIbaYrhmHmTfCcfZjnruigJufm09jy/a0YFBCiFOhCTLjYJMRnpHhhOs/LTIL2OS7/MPVTEmTcJTWYl906b29y2EEOLk5PVC7iPwxuUQk+YrC9dv8nGaa/7fp9/z4Cffc/bgBGZfOqKjIhVCnCBJlpt49YYxnJY0wD93lqPTICoVCnxTL8Kys8FolKkYQgjRXdmr4K0rIfcfMOIquGEhRPc9ZnOnR3PbWxt4YXkB143ry3PXjCLEYuzAgIUQJ0KS5SYy4sPoH5XB3uq9eLx+mC6RPgn2fA1eD8bISEJGnopt6bL29yuEEOLkcuh7eH4y7PoSzv0XXPQsmH96l72SGgd/PHcQD/xsCEbDsadpCCE6jyTLTew4VMuOohCcXicH6w62v8OMHHBUw1OjoGQbYZMm0bBtG65Dh9rftxBCiJPDlnnwwtngrIMZn8GYm447P7mosp5quwuLUfHmTWOZObEf6jjthRCdyy/JslJqmlIqTym1Syl173HajVZKeZRSl/pjXH/bV1HP4k0awD9TMfpmQ3gSVO6B1y8j7IwxgOzmJ4QQ3caa532l4RKHwa+XQerY4zbfXFTNz59dyd3vbQTAZJR7VkKc7Nr9U6qUMgLPANOBU4ArlVKnHKPdP4GF7R0zUHy1ln3l4/yyyG/hvWCvBDTUlRK09XHMvXvLVAwhhOgOKvfAF/dD5jlw3ScQfvyayF9tL+EXc1ZhMRr4wzkDOyZGIUS7+eNP2jHALq11vtbaCbwFXNhCu9uA94ESP4wZEH2iQ1FeKxYVxp7qPe3r7NvXfKWD3A7fY7cDtXMhYUOSqFu5Em9DQ7vjFUII0Um0hs9+DwYjnP84mCzHbf7mmkJ+9eo60uOsfHDLGWQmHLveshDi5OKPZDkZ2NfkcVHjscOUUsnAz4Hn/DBewFhMBlKirQSRQEFNO+8sL34AXPVHHnPVE6a+Qdvt1K9Z277+hRBCdJ6t83yL+c68HyJTjtu0rsHNU4t3kt0/jrd/PY5eEcEdFKQQwh9MfuijpVUJutnjJ4B7tNaen1rEoJSaCcwESEhIIDc3t1XB2Gy2Vj+nqQhDAyV10eSV5rWrn8SUK8jcOQej98c7yB5DEPuyLkV/9Rl5b7xOrcfd6n7be30nM7m2rqs7X193vjbRRvYqWHAv9B7pW8x3DC6PF4NSWINMvP3rcSRGBmOWOcpCdDn+SJaLgD5NHqcAB5q1yQLeakyU44BzlVJurfWHzTvTWs8B5gBkZWXpnJycVgWTm5tLa5/T1Jgz3LyxvYgnN6wj64wswixhbewpB94tgrwFh6diGAefy+DL/sG+FZVYdu3mtEmTWr0Cur3XdzKTa+u6uvP1dedrE2305QNQXwbXvOebhtGCWoeL37z2Lf3irTx44VDfLrFCiC7JH3/irgUylVLpSikLcAXwcdMGWut0rXWa1joNeA+4paVE+WQQajGRHpkO+KEixoXPgDX+x8ejbgAgLGcSrn37cBb4YRGhEEKIjlP4DayfC2NvgaSWd9srrnZw2XOrWJ1fztDkyA4OUAjhb+1OlrXWbmAWvioX24B3tNZblVI3K6Vubm//HW1veR1vr/LdCW53RQyLFa5+F+IGQEwGeJyAb+trAFuulJATQoguw+2ET+6AyD6Qc1+LTfKKa/n5sysoqrTz0ozRXJbVp8V2Qoiuwx/TMNBazwfmNzvW4mI+rfUMf4wZKFrDF9+5iRhs8E/5uF6DYdaRi/nMvXsTlJmJbelSYm+4vv1jCCGECLxVT0HpNrjybQg6eoqew+Xhmhe/QQFv/3osQ3rLXWUhugO/JMvdSUp0CCaDmQhjEnmVef7t3O303V0OCiMsJ4fyuXPx1NZiDJcSQkIIcVKryIelj8IpF8LAaS02CTYb+ddlI+jfK4zkqJ/e6loI0TXIstxmTEYDfWJCCfZmsLl0M1o3L+zRRvYqmN0f1r4A+OYt43ZTt2KFf/oXQggRGFrDp78Dgxmm/bPZKc0zX+3irTWFAEwaEC+JshDdjCTLLUiLDaWhrg+VDZXsq9330084ESFREJMGeb7ZKiEjRmCIjJR5y0IIcbLb/C7kfwVn/xUikg4fdnu8/OnDLcxemMeaggr/3VwRQpxUJFluwYDEcKzaVxFjY+lG/3U88DzYtwZsJSiTibDsbGxff432ev03hhCi21BKLVZKndvs2JzOiqdHqq+Az++D5CzIuuHHw043v/7fet74ppCbJ/XjX5eNaHUpUCFE1yDJcgvumz6Yz26+jFBTKJtKN/mv40HnAdpXexnfVAxPeTmOLVv8N4YQojtJB+5RSv21ybGszgqmR1r0F7BXsiTzT4x/dCnp937GGf9YzNTHl/FVXgl/u2go904fhMEgibIQ3ZUkyy34cMN+Jj66lJrqJN7ZspwPN+z3T8cJQyAq9fBUDGt2NhgMMhVDCHEsVcBZQIJS6hOllF/KKyilpiml8pRSu5RS9x6n3WillEcpdak/xu1y9qyADf9jR78Z3LrYyf4qOxo4UO3gYLWD68enc+3Yvp0dpRAiwCRZbubDDfu5d94m9lfZ8dhT8ZgOcN8H6/2TMCvlWxwy4fcAmKKjCRkxAttSSZaFEC1SWmu31voW4H1gOdCrXR0qZQSeAaYDpwBXKqVOOUa7f+Krod/zuBvg0zshKpXf7Dsbu8tz5Gmv5vMtxZ0UnBCiI0my3MzshXk4XL45xB57H5Ty4jQWMnuhn8rIDToX+ow5/DAsJwfH1q24Skr8078Qojs5XK9ea/0yMAP4op19jgF2aa3ztdZO4C3gwhba3YYvQe+ZL04rnoSyHXDeY+RXt7xw70CVvYODEkJ0BkmWm2n64ue1pwJgCCn074ti4WrY+BbQWEIOqFu2zH/9CyG6Ba31/zV7vF5rfcOx2p+gZKBpmZ+ixmOHKaWSgZ/TJFnvUcp2wbJ/wZCLIXMKvY9RCu5Yx4UQ3YtsStJM76gQ9jcmxtoThtcZizGkkF7+fFFc/7Jvkd/QSwgaMABTYiK2pUuJurRnTgsUQnSollaiNb91+gRwj9ba81MVHpRSM4GZAAkJCeTm5vojxjaz2Wzti0FrRmy8n3BMrIn4Gc7cXM7r4+b5qiO/SRYDnJfqaddY7Y61A0msgdFVYu0qcUJgYpVkuZm7pg7kvnmbD89P89j7YLLu5g/jB/hvkEHnwcY3oXAVKn0iYZMmUfPJJ3idTgwWi//GEUKIoxUBfZo8TgEONGuTBbzVmCjHAecqpdxa6w+bd6a1ngPMAcjKytI5OTmBiPmE5ebm0q4YvnsDqjbD+Y9zRtbPAXBsOYje/C1RoWaq6130jgrhrqkDuWhk8k90FuBYO5DEGhhdJdauEicEJlZJlpv54cXvHwu2caimgRBvBm7Td4wdYPTfIP3OBFMwbP8MGpPlqrffxr5uHdYzzvDfOEIIcbS1QKZSKh3YD1wBXNW0gdaNheYBpdTLwKctJcrdTl05LPwT9DkdTptx+PCBKgdDekfw0a3jMRll9qIQPY381LfgopHJfPPHs9nzyHm8du3lAGws8+PmJBYrZEyG7fNBa6xjT0dZLFIVQwgRcFprNzALX5WLbcA7WuutSqmblVI3d250neyLP0NDDZz/BBh+/PV4Q3Y6H8/KlkRZiB5KfvJ/QnJoBkHGIDaW+DFZBt9UDKcNag5gCA0l9PTTpd6yEKJDaK3na60HaK37aa0fbjz2nNb6qAV9WusZWuv3Oj7KDlawDDa+AePvgARfJT2n28uKXWVorTHKpiNC9FiSLB/HvG+LOO2hJWRGDWZTmR938gMYfjn8YSdE+qZ9hE2ahHPvXhoKCvw7jhBCiONzOeCTOyE6HSbedfjw22sLufqFb/i2sKoTgxNCdDZJlo+jX3wYXg3Rxv5sK9+G0+P0X+emIDCaQPvWV/9QQk6mYgghRAdb/hhU7IbzHwOzr/KR3enhP0t2MSY9htNSozo5QCFEZ5Jk+ThO6R1BiNmIuz4Vl9fF9ort/h2gYBn851SoKsSSkoKlfz9JloUQoiOV5sHXj8Gwy32Lrxu9smoPpbUN3DV1ID9VPk8I0b1JsnwcZqOBEX0iKSqOB2BjqZ/nLUckQ+UeX81lfFMx6tetx2Or8+84Qgghjub1+qZfWKww9e+HD9c4XPw3dzeTB8YzOi2mEwMUQpwMJFn+CaP6RpO330BCaCKbSv08bzm2H8QPgu2fAr5kGZeLupUr/DuOEEKIo333GhSuhHP+BmHxhw/vKrFhMRn4/TkDOzE4IcTJQuos/4TpQ5OIDwviu4bh/k+WAQaeCyuehPoKQkeOxBAejm3pUiLOOcf/YwkhhPCxlcIX90Pf8TDy2iNOnZYazYp7zsRikvtJQgi5s/yThiZHMmN8OqcljOBA3QFK60v9O8Cg80F7YOcilNmMNXs8tmXL0F6vf8cRQgjxo4V/BGcdnP84NJmT/G1hJS6PVxJlIcRh8mpwAoqrHRhdaQD+v7vceyRk3Qgxvg2zwiZNwlNahmPr9/4dRwghhM/uJbD5HZjwO4j/carFgSo7V8xZzb++yOvE4IQQJxtJlk/Ak4t38MhHNZgMJv/u5Ae+XaLOfwz6jAEgbOJEUEqqYgghRCC47PDp7yC2P2T/7ohTTy3ZCRquHdu3k4ITQpyMJFk+AaP6xlBrV6SHDwzMvGWtfeWLyndjiokhZPhwSZaFECIQls2GygLf9Atz8OHDBWV1vLOuiKtOTyUlOrQTAxRCnGwkWT4BWX2jAYg09Gdr2VbcXrd/B/C44PmzfAv98G1Q4ti8GXdZmX/HEUKInuzQ977X2RFXQfrEI049vmgHFqOBWyf376TghBAnK0mWT0Df2FBirRYabMk4PA52VO7w7wAmC2ROgbz54PX4SsgBtmVf+3ccIYToqbxe+PROCIqAc/7fEaccLg87S2zckJ1GfHhQJwUohDhZSbJ8ApRSjOobTeFBXx3OgEzFGHQe1JVC0TqCBg/G1KuXTMUQQgh/+fZl2PcNTH0YrLFHnAo2G/nstmxuOzOzc2ITQpzUJFk+QXdPG8gbM6YTFxIXmGQ5cwoYzJD3GUopwiZNpG7FCrTT6f+xhBCiJ6k9BIsegLQJMOLKI04VltdTbXdhMCiCzcbOiU8IcVKTZPkE9e8VTmqsleFxw9lUFoBkOTgS0rJhxxeAr4Sc12aj/ttv/T+WEEL0JJ/fC24HnP/EETWVtdbc/f5GLn52BVrrTgxQCHEyk2S5Fd5aU4jJncbemr1UOir9P8B5/4YbFwJgHTcOZTZjy5WpGEII0WY7F8HWeTDxDxB35OK9FbvKWZ1fwbVj+6KaJNFCCNGUX5JlpdQ0pVSeUmqXUureFs5frZTa1PixUik1wh/jdrT31hexNT8KgM1lm/0/QGw/3x1mwGC1EjpmjMxbFkKItnLWwWe/g7gBMP6OI05prZm9cDvJUSFceXpqJwUohOgK2p0sK6WMwDPAdOAU4Eql1CnNmhUAk7TWw4G/AXPaO25nGJUWTX5RDEZlZGOpnzcn+cGmd+GTOwHfVAxnQQHOwsLAjCWEEN3Z0n9CVaFv+oXpyCoXX3x/iI1F1dxxdiZBJpmrLIQ4Nn/cWR4D7NJa52utncBbwIVNG2itV2qtf5i3sBpI8cO4HW5UajROt4lka0ZgFvkBVO6B9XOhtpiwnMYScjIVQwghWqd4M6x8GkZeC2njjzq9Or+cjHgrF49M7oTghBBdiT+S5WRgX5PHRY3HjuVGYIEfxu1woxo3JwmnH5vLNuPxevw/yKDzfJ/zFmBJTcWSni5TMYQQojW8Ht87dCHRMOWhFpv89YIhfHjreExGWbojhDg+kx856mbrAAAgAElEQVT6aGlVRIvLipVSk/Ely9nH7EypmcBMgISEBHJzc1sVjM1ma/VzWiPJqrCXR1MXVMfbX75Nb0tv/w6gNacHJ1K/8n9stqUT1i+D0NylLP38c3RwcMCvrzPJtXVd3fn6uvO1dVvrXoL96+Di5yE05ohTTreX4moHqbGhRASbOylAIURX4o9kuQjo0+RxCnCgeSOl1HDgBWC61rr8WJ1prefQOKc5KytL5+TktCqY3NxcWvuc1lia7eVg/RDO/+BNgtKCyBkQgLGclxKyZg4540ZRFxxM4ZeLOc1kIjwnJ+DX15nk2rqu7nx93fnauiNLQzmsfBAyJsOwy446//a6fTz48VYW3DGBzITwTohQCNHV+OP9p7VAplIqXSllAa4APm7aQCmVCswDrtVa+3mv6I5lMRlIDU8lMigycIv8Bl8AqeOgrpTQ007DYLXKVAwhhDgBmTufB68Lzn/siJrKAHanh6cW72RkahT9e4V1UoRCiK6m3XeWtdZupdQsYCFgBF7SWm9VSt3ceP454C9ALPBsYy1Lt9Y6q71jd4bqehe3vbWBhOiBgVvklzoWrvP9vaEAa3Y2tqXLpGi+EEIcT94C4stWwVl/gZiMo06/umoPJbUNPH3VaVJXWQhxwvwxDQOt9XxgfrNjzzX5+lfAr/wxVmcLDzaxqaiKfsGp7HatocZZQ4QlIjCD1ZVDcARhkyZRu3AhDdu2BWYcIYTo6hpsMP8u6kJTsY677ajTNQ4X/126m0kD4hmTHtNCB0II0TJZBtxKBoPitNRoSsoSANhStiUwA+1ZAf/qD3uWEzZxAoBMxRBCiGPJ/QdU7yNv4C1gshx1em1BBfUNHv5wzsBOCE4I0ZVJstwGo/pGs684HoUK3Lzl3iPBGAR58zHFxRE8bJjUWxZCiJYc+A5WPwujrqcmcnCLTc4anMDK+85kWEpkBwcnhOjqJFlug6y+0eANJiGkb+DmLVtCod+ZsH0+aE3YpEnYN21C1dYGZjwhhOiKvB745A4IjYOzH2ixyf4qOwBxYUEtnhdCiOORZLkNRvSJ4ox+sWSEn8Km0k2BW3g36DyoKYKDGwmbNAm0JmhLgKZ9CCFEV7RmDhz8DqY/AiFRR50+WG1n8r9yeeHr/E4ITgjRHUiy3AbBZiNv3DSWqf1Pp8ZZw96avYEZaMA0UAbIm0/wkFMwp6QQsnxFYMYSQoiuproIlvw/6D8FhlzcYpP/LN6F1pppQxM7ODghRHchyXI7DIgaAhC4ecvWWLjkBRh5DcpgIOaX12LZvRv7xgCNJ4QQXcn8u33TMM7711E1lQH2lNXxzrp9XH16X1KiQzshQCFEdyDJchst31nGRY/vJMRoDdy8ZYChl0BUKgCRF1+CNySE8pdfDtx4QgjRFWz7FPI+g8n3QXRai00e/3IHFqOBWyb369jYhBDdiiTLbTQgIQy3VxFvyWRTWQCTZa1h49uwYyHGMCv27GxqF36Bs2h/4MYUQoiTmaMG5t8FCUNh7C0tNqm2u1i2o5Trx6fRKzy4gwMUQnQnkiy3Ua+IYPrEhOC1p7Kjcgf1rvrADKQUrHgCVvwHgPozJ4PBQOX//heY8YQQ4mT31cNQexAueBKM5habRIaYyb1rMr/JkbvKQoj2kWS5HbL6xlBcmoBXe9lavjVwAw06DwpXQn0F3uhoIqZNo+q99/BIGTkhRBsopaYppfKUUruUUve2cP5qpdSmxo+VSqkRnRFni/avh2/+D0b/ClKyWmxSbmvA69VEhpgJD245mRZCiBMlyXI7jOobTWWlb4V1wBb5AQw8F7QX1r3E6DW3EXPhJLx1dVS9937gxhRCdEtKKSPwDDAdOAW4Uil1SrNmBcAkrfVw4G/AnI6N8hg8bl9N5fBEOOv+Yza77c0N/PKlNR0YmBCiO5NkuR0mZsbzp6lZ9AlLDewiv94jISwRlv2L0Pp9hKy7l9Cs06j436totztw4wohuqMxwC6tdb7W2gm8BVzYtIHWeqXWurLx4WogpYNjbNk3/4XizTD9nxDc8k5835d7WLm7nLMG9+rg4IQQ3ZWpswPoylJjQ7lpYgZ7lp/Kiv0r0FqjWihf1G5KgTkEbIdQaKgrJWaAjaJ1B6n94gsizj3X/2MKIbqrZGBfk8dFwOnHaX8jsOBYJ5VSM4GZAAkJCeTm5vohxKMFOUoYs+ZvVMaOZsuhCCg5ehytNW9vsxMTbCClYQ+5uQGqge8nNpstYN8vf5NYA6OrxNpV4oTAxCrJcjuV2RoI9qRT7viY/bb9pIQH4AbMt6+B7RDQuFOg20GYaQ2WxAzK575M+PTpgUnShRDdUUsvFi1uQ6qUmowvWc4+Vmda6zk0TtPIysrSOTk5fgjxqEHgjV+A0UTctXPJierTYrMvthaz17aeRy8ZxpTRLbc5meTm5hKQ71cASKyB0VVi7SpxQmBilWkY7fT66kJe/sr3eyZgUzEWPwDNqm0odz0xGaU4Nm/G/u23gRlXCNEdFQFNM8kU4EDzRkqp4cALwIVa6/IOiq1l338EOxfCmX+CYyTKAO+uLyIxVHHxackdGJwQoruTZLmdstKi8TgSsBiCA1dv+awHwNxs9ylzKJEz/4gxMpIK2aRECHHi1gKZSql0pZQFuAL4uGkDpVQqMA+4Vmu9oxNi/JGjGhbcA0kjYMyvj9v0v1efxu+ygjEZ5VebEMJ/5BWlnU7tE4XRYCLalBG4O8unXQMDpoLph8L6CjLPwTB2BlFXXkHtl4tx7j255+YJIU4OWms3MAtYCGwD3tFab1VK3ayUurmx2V+AWOBZpdR3Sql1nRQuLH4I6koaayq3PHPQ5fFS73RjMhroFSq/1oQQ/iWvKu1kDTIxOCkcrz2VbRXbaPA0BGagC58Ba3zjxEINfc8AIPqqq1AmExWvyiYlQogTo7Wer7UeoLXup7V+uPHYc1rr5xq//pXWOlprfWrjR8sFjQNt3xpY+6LvjnLvkcds9s66fUx8NJcDVfYODE4I0VNIsuwHWX1jKC5JwO11s618W2AGsVjh6nepD+0DicPg639Dgw1zr15EnH8+VfPm4amqCszYQgjR0Twu+OROiOjtm6t8DA6Xh/8s3klabChJkbKttRDC/yRZ9oMbs9N5/ZrLgQBvTtJrMGvHPA3n/htsJZD/FQAxM65D2+1UvvNu4MYWQoiOtOppKNkK586GoPBjNvvfqr0cqmngrqkDpSqQECIgJFn2gz4xoYxMSSU5LDmwm5P8IPV0uGMjDL4AgOCBA7GecQaVr72GdjoDP74QQgRSRQHk/hMGnQ+Dzjtms1qHi2dzdzFxQDynZ8R2YIBCiJ5EkmU/+WTjAcJVv8DeWW4quq/vc42v4lPM9TNwl5RQs+CYewcIIcTJT2v47PdgMML0R4/bdP7mg1TWu7jrnIEdFJwQoieSZNlPFm4tJr8olkP1hyiuK+6YQTe+BU8Mh9I8rNnZWPr3o/zlV9C6xf0FRCdxuB2Uukopt5fj9sr25EIc17aPYfdiOPN+iDx+veTLs/rw2e3ZDEtpeetrIYTwB9nBz0+y+kYzf0dvrJGwuWwzidbEwA/a/2xfObkvH0Bd+SaxM2Zw8M/3U//NGqxjj7d7rfA3rTWVDZXkV+VTUFNAQXUB+dX57KnewwHbATSah955CIAISwTRwdFEBkUSHRRNVFDUkY+Dow4fjwqOItISidFg7OQrFKKD7P4KgqNgzE3HbVbvdBNqMTGktyTKQojAkmTZT7LSYvA6kjApM5tKNzGl75TAD2qNg+w7YcnfYM8KIi64gJLHn6Bi7lxJltvpww37mb0wjwNVdnpHhXDX1IFcNDIZj9fDftt+Cqp/TIgLqgsoqCmguqH68PODjcGkRaYRY8qkrHY4VbVhRFu9jMsMJiHaQ3VDNZUNlRyqP0ReZR6Vjspjlh1UKMIt4UQH+xLo5LBkMqMz6R/Vn8zoTJKsSRiUvEkkugnbIYhI9k3DOIaD1XamPr6Mh38+jAtG9O7A4IQQPZEky34yKDGcUEsQEYb0jpu3DDD2Fl8d0i/+jOGmJURfdSVlTz1NQ34+QRkZHRdHN/Lhhv3cN28zDl2OMWIPpeYS/rSyjKd21FDp3I/L6zrcNiY4hvTIdM7pew7pkemkR6aTEZlBojWRj787yL3zNuFweQEorYZFpUb+cfEwLhp79NvLdredKkcVVQ1VVDZUHv66qqGKSkcl1Q3VVDRUsKFkA/ML5h9+Xqgp9HDi3D+qP/2j+5MZlUlsiCx4El1QbTGEH/+duaeW7MLu8nBqn6gOCkoI0ZNJsuwnJqOBkalRlHnS+b48F5fHhdloDvzAllA4888w/w9Qup3oK6+k/P/mUPHyKyQ99GDgx++GHvliNd7YBVij1qKUF60V2hXDwbJeRJomMTgynbvOnEh6ZDrXvbCFLTvr+c6r8Xg0Lm8tZw0u5pmrejN7Yd7hRPkHdpeH+z/awkUjfcnyO2v3ERtmITEymKTIEBKtiSSFJbUY14cb9vPegkU85ZjNAyG3M25CBkm9qthVuYudVTtZXLiY93e+f7h9THDMkUl049dWsxVKtsG718Nlc6HX4MB9M4Vordri4/6f3FNWxztr93HV6an0iQntwMCEED2VJMt+NHfGGL4qquYPSxeyo3IHQ+KGdMzAI67wzV8OT8AERF54IdUffUT8nXdgionpmBi6MKfby7eFlSzcvouFRW9g67UMs9K4qsbgqjwdrzMetO9HZcKQBE6Ji+TUXpkAjOsXS7U9ArNBYTQYMBkVAxN8NWF/2E0sUxXxtPk/zHLdzk6dQq3Dt8jP4fJw9/tHlhq0mAzMmtyf28/KxOHy8PiXO0iMCKawoo4PvtnJp8a/kaTKebT+US7/7B/8ccogfpc2Cm+IDY+1lurKgxSX5FNWto/qyoPYKnfRULOWaoeb7xtgT4MmwmUirN6Nxa0xvHIx5l59CY6KwxQRiSHMijEsHEN4uO/r8HAM1jAM4WG+r8PCMIaF+c5brSijEUq2MXrNbXDKO5J4i/bxen1bW4clHLPJE1/uwGRUzJrcvwMDE0L0ZJIs+5HFZGBE/AjAtzlJhyXLBiOEJ/hKLlUVEjPjOqrefZfKt94i/pZbOiaGLuqFr/N5YslGnGFfYYlZgbK4ULZR2A6diXYd+YdGclQI/3ftkbv+3jNt0DH77h0VQkVVJXMtj5JEOXPNjzLF+SgxUdEABJkMrL7vLA5W2zlU4+BgtYPiagdDkyMAKLM1MHf5HsJslQwtL+C5yg9xlBnYZU/A61K8pP8KH0B+s3FDgdTGr1VoKAZrFN7QIBqCTdRZvVQ0HGR/vKbKYiDICaENhYQcKiRyv5lwp4HgBo253oXyevkphtBQDNRjtLgwLboYU9bPMCUkYYqPb/LRC1N8HIagoON3Jne7RX05eN0Q3vK7K4dqHHy66SC/mpBBrwjZrU8I0TH8kiwrpaYBTwJG4AWt9SPNzqvG8+cC9cAMrfW3/hj7ZOLxau5/v4gwYywbSzdy1eCrOjaARX+BDf8j6PbvsE6aSOXrbxB7440/naR0I8damFfvdLM6v5yleaUs21nG3BmjiY+EPMcHmNPeQVHPWX3O4fZRt7IpP4j75m3GjudwvyFmI3dNbV0t17umDiTogxuJoxqj0sRRzb8tz+Oc+iIASikSI4NJjAiChhqorUXXluA69D1VHxoxrF3L/KULcZXVAWAwebHEubH0cmMwazwmAx6zgXCLA2XSaDNgVtT0zab3jS+ys9ZLzGuTCdXFGIwmjCYzHkct5oYqzMqDCyg0m8gzB7E1sg8Ho6LY5amj0FWLRyuCXEbCXAYyVBz9TYmkmZJIMcaTSCTR7iCoq8e74X08hyrx2DXuOkXDlwtw13l8dwibMURGYoqPa5ZIN35Eh2Na+BtM7gMYXrsUNWuNb4v3tvJX4i13zTtW7UHf5/CW7ywnRASz4I4JxIf3nNc0IUTna3eyrJQyAs8AU4AiYK1S6mOt9fdNmk0HMhs/Tgf+2/i5WzEaFPsq6jFGpnXMTn7NDbsMVj4Fyx8j9vrrKZxxPTWffkrUJZd0fCyd4IeFeXaXL8ndX2Xnnvc38cxXO9lbbsfp8RJiNjImI4x3d77OJ3tfo7Khkpw+Ocw6dRYDY3zJcMZIX38tJd2tcZH+Crf5O0we34LAYOVimmEthrx7YORrAOh3b8C5diH1B7zUl1qoL7Xgrvf9WBojIwlJshA9zILZnE94lJ3mRS/qCMY04U5q6+3U1jmw2R30HnAaxshICouKWWsfjMVTj0l5MOJhumENZuX7/piBfi43/VxuptXnoUssGD0N1I/5NUXjfsXu0q3smn8Huy11rOIAbysTXu3bTthkMtE3LoJ+o4ro73KR4naT6PbQy1NN6pjfYDx1Fu4D+3DvWIu71om7xo670oa7ogp3aSn29d/iLi1tYcfJRJTRg/HtMzClDsQUE4MxLhZTTCzG2BhMsXGYYmMw/vA5Oto3FaQpZx28fhlUF/k+3/pN2xLvxn5C69vZjzhxtkO+z2FHL/Bzur1YTAYyE4699bUQQgSCP+4sjwF2aa3zAZRSbwEXAk2T5QuBV7Vvt4zVSqkopVSS1vqgH8Y/qYzqG81HBUlUG9ZTbi/v2IoEScN985dXP0forBsJGjSIipdfJvLii/Hd3O/eZi/MO5wo/6DB7aWgrJ4bstMZ3z+KIncuL22Zzbc7ShiXNI5ZI2cxPH74UX1dNDK51cnxYV4vGAyw+AFMHvsRp5TXjWP1Qupdr1G/bh31qzbiqfFNuzBGhRGaNZDQrNGE5kwnqH9/lMGXHX/74VMM2vA3QvmxvFy9DmL7yPsZddYsgoC4ZmGcMyQR/cAbVNtd7Kuws6+ynj+99RgPmV4hVB3Zz/2u63jfm4MFF8vGTGRAdAzLN2mKGu4kXTkZqxqIpA6HsRw1cAB7Q4LZsea/bAsys8gagm76/+vAPGIqckm0RJFYuoVEt4dE7SYpzENiiCbxlw8RN+oGjKU78H7wB9zlVTiL8vHawe0w4HYYcTU48epqXIVlOLbU4662gdvDUZTCGB2NKTYWY2wspthY7Ae+IcxdQ5AlBI+5Etv9lxJ/yYO+udZNPyyW4/4zFr18A3HVhwhG46gupuzlG0iZ+fZP//uLtjt8Z/nHZPmHd4v2V9mxWow8/PNhbf/ZFEKINvBHspwM7GvyuIij7xq31CYZ6HbJclZaNG9tSiE01rc5SU6fnI4NYPKfYMs81FcPEzPjOg7eex91y1cQNiG7Y+PoYB6vZn+V/Rjn3JwyII9/bHyO/bb9jOw1kkcmPsLoxNH+C6C6CHYv8X0ULINb18BZD8Bnv8Vlc1OzN4T6kiDqyyx4nQb4/GHMvXsTNnkKoaOzCM3Kwty37zH/qDntotsoKlmO4cASgnHiwExF8mRGXTTruGEppYgKtRAVamFYSiQPfzadJXWbONuwnmDlwqHNLPaMZEXYVD7+ZRaltQ3ERfvKcfWKDmddyiSW1zZQWttAmc1JvdPNzhnnYjQo/vThAd5TczEYnBQbjRSbjBQag/nIMprM0cNYV7iTb0NSqFe1ONWP5fb4/ikM254hyhhBktlGclQNSeFBJLo9xHk8WL1OQr0NWAzbiHLVEen1EuLVWJzgcRjx5DyK25KMfcMXGNa9g7vBjruhBHeBifqtXjx2qHQ3vQO8h8KPrjv6m2M2YbAoVJAJFWxGBZkxhliwpI2gomIfsdVrsZktOEKMRKXbidn/Fd9++BSnXXRbK/9ziBNW+8OdZd80jObvFtU5Pdw3bzOAJMxCiA7jj2S5pd/uzfdbPpE2voZKzQRmAiQkJJCbm9uqYGw2W6uf40+uei8eRzIKAx+v+xh2+7f/E7m+jN7n0StvMZtHnk90ZCS7Hn+MKs/Jv81yW//t9tV6eWlLSxt6eDGFbyGk1yLuX1FKH0sfftPrNwwOHkzd9jpytx9/rNC6QoZsnc3WIXdRb01tsU1E9TYG5j2Ntb4IgAZLDBUxp7Ln6yW4q0wkb0jDub0W7VWYw92YMyMpGXMJzv798cY2eddhzx7fx3EY+l1PXPl6dEMZOiiK/H7Xs6uV36/zUj38actMTjXcTW9dRpmO5M/emfwiTVOx6zuMwPJD2wAIAy4/nI8oIIgGj4Wvly0F4HXnRMaZv+Ns1pOmXSS6FKWewaxw38BNTivFVWdQWeYGN6DtNKgqwkKruWSwnUpPJcuLy9joraLAchCPqY4GQ0svE012Z9MKszZhrX6JIEMItbGayLNTCfIqQrwQ6tWcwkHCtRurUxPkBKNLYXSCajBQ5wwj2OPFGTYEo8tA3YED9HWVYHKCyQVGO5hqQB+sxlJfR5UzBKUVzkgPUel2QlUDfb97lNyoYa36notWsBX7du8z+xbvtfRukd3lYfbCPEmWhRAdxh/JchHQp8njFOBAG9oAoLWeA8wByMrK0jk5Oa0KJjc3l9Y+x5+01iwsWcf+kH5Uh1b7PZYTur5xWaAMTLCEUra3mNLHH2dsUm+CBw7wayz+1tZ/u0XfH6Lmu01cOy6J99btw+7yYAzbRlD8IozBB+kV1Jc/jnuCM1PPPPHpKM46eGYW1BcxZsej8JtVULH7x7vHI6/xTXmpTIOaRdD/Fuh3Jpa4gURu2EDKiy9hW7IEZ3AQUYMMRKcfIiglCW79ioz2zHsd9gm8ez0hl81lYhsWnOUAp2zYz70L7ud+x2z+FnwXD04f26bEI3n1Eu6qmsmioB8T77vdM0mOCiEnJ4eW/im9Xo2hMSk+UGWnst7J+f9Zzn/MTzLatAGbSVOpzHzNAJ7V5/KLMQk0eOpp8Nbj9DowGBuIi4B6Vz355RXUueqwaTsVXjsur4MN7gi8huNV8TAAeb4vRwK0tFDMCZhBa8we6FevebfcN13lH64r+Fcnvr50e7XFR1TCOHCMd4uOdVwIIQLBH8nyWiBTKZUO7AeuAJqXgfgYmNU4n/l0oLo7zlcG39veL84Yzd+/yeLDXR/i8XowHmfb1oAICvN9djcQPXUsZc+FUPHKK/T++8MdG0cArSmoYFeJjatOT2XKKQmM6zeZsCATGYkNPLnpATyWPSh3HJf0uZs/51zV+n+Dj26FulJAQ81+mJ0BnsbFaAnDOLzSLjoNrp2H9nioXbKEihcexL5xI8aoKOJuvZXoq6/C5D5E3cuXE3T1O+1fINZrMNy6ul1d+OZjzwBm8Fo7+rlr6kDum7eZ6513H64jjdl63KohhiZ3j3tHhRz+uLvq1ywy3E2Gs4wDOpLnnbeTEBXNw1PObFVM4x9Zwt11j3CGaQMW5cahTeR6TuUJ6+0suGMCuvENLd3kjS3fUgqOOH7BU8u5vf5pJhg2EcqP01VWRUxvVTyilWqLj6iE0TsqpMXpVb2jQjoyKiFED9fuZFlr7VZKzQIW4isd95LWeqtS6ubG888B8/GVjduFr3Tc9e0d92Q3OHoob7rfZFfVrsNVFjrcm1dgrC0m6ucXUfXue/T67Z2Y4uM7JxY/qXG4+OeC7bz+TSH94q1clpWC2WggLMjE9ortvLr3D1jDnPxu1AP8rP/PMBvasIvi0kdh+2c/JsfaC14PjPwlnPmnIxYfeR0Oqj/8iIq5c3Hu3Yu5Tx8S7v8zURdfjCHkh1/oMawd8xQ53az02A93o2cvtDC16lGSo0L4RxuqhrQl6T5eXw/Ou4WPvb8nljJqdQT/1Lfyl3NOIyr4xLdGvmfKaB6aN4sJ+vdEUcYBHcNf1W/4SxtiEq1gOwSxP242ctfUgUdsGQ9tK+MohBDt4Zc6y1rr+fgS4qbHnmvytQZu9cdYXcHOQ7Xc80YNQem+zUk6LVk+7Zfw7gxixlxB5ZtuKt54g1533NE5sfjBF1uLuf+jLZTWNnDThHR+O2UAZqPvDu/a4rXcvuR2rGYrr05/lX5R/VrXudZQsBRWPg27FrVw3gM7FsCFTwHgqaqi8s03qXjtdTzl5QQPHUry4/+/vfuOj6Ja/zj+ebLphYRAKAm9g3SRqggCUixgAdtVVLwWFPX+FMWr3uu1F7CBNBsgKCrSRAQUjChKkxIERIoIhEBCCaSSzeb8/pgNpCfAJpOE5/165bVlZne/k83OPDl75pw3CenXD/G+cOb6yR415Hy6P+Usugckvk7kORbdOZ8rZzeT/wy85OyH/fPQ86izYIy7ZfnMP6Nn/jbObxhHpZQ6HxfOUb0MNagehJcrHD+pQkxCDMOaD7MnSKshENUJ3+2TCO7dm8TPZlP93ntztHhWHH8fTeH+mb/RrGYI79/RibZ1zrQSLtu7jDE/jaFeSD0m95tMraD8Y7QW6cB6WPQoHNoCQTWg+dWwZzk4c3z96xMIff9HxoFYjk2fTuKcOZi0NIIu70m1u0cQ2PmSC2J4vtJyXkP1Ffhcd3K+3Uyynyc6ugEztZ9y6Us9BlnOXMUyWO9Dw+pBOLyE1lGhhTxYKaVKj1fxq6iz5ePwom2dqjic9Yk5YsPkJNlE4MoXISmOahcH4kpM5MSCBfblOUvGGNb+dQyA+tWCmDmiC1+PujRXoTz7j9k8/uPjtK7emukDp5e8UE5LhMR91vWAqlY3i2snwKNb4JZZ0GwAeLun0/X2Jy34MmI/2cDu/v05Pns2Vfr3p+HCBdSbMoWgLp21UFbqfCUfsi6D88/e9+RXMbz9/c4yDqSUUhZtWS4lnepXJeb3KFK9l3Di1AlC/WxqEanfDVpcTUDaH/i3acOxadMJGzbs9GQX5dXeIyn8e94Wftl9lPkP9qB93TC6Nzkz7YYxhvc2vceUmCn0qtOL1y9/nQDvErSYH98LqyfDxk+g4eVwy6dQrTE88Iv1z0W2we9hJnQmZUcCR3eFkxq7Ba+gPYQPH074HbfjU+ssW6+VUkU7PSFJ7XyLwgJ9OJnmzHe/UkqVBS2WS8nF9asyZW1dfLAmJ7k0ysZJQYZMRHxDCAhHej0AACAASURBVK/xLQcfe5zkH38kpHdv+/LkkXOGrsjVy+lYryrfbTuMr8OLl69rQ9s8X71mZmXy4uoX+WrnV1zf9Hqe7fos3l45/pTjt8OXd8HQj63RIwBiN8Cqd2D7Qmski9Y3QLccE3rkaRlO27GHQz81Jn17Ft7Vw6nx+F2E3XQTjhCdalepUpE9IUlI/pbl0AAf/jqSUsaBlFLKosVyKelUP5yHL72Cj/Z/SExCjL3Fsr9VbFa5tBPxtWpw7ONp5aZYzjtD18HEdA4mxtE6sgof3nkJNav451o/PTOdJ1c+yYr9K/hnm38yqsOo3F0gMlJg1lBrRr1ZQ63xkf1D4M8lsPsH6D4KOt8HoQX3j808fpyEN98icc4cHNWrUfvFF6hy7bXFTo2slDpP2S3Lwfm/tQkN8OGEtiwrpWyixXIpCQ304ZErWrNyYRNiEmzst5zN5UQ+7E1420jil60lbetWAi66yO5UBc7QBXA81ZmvUD6ZcZJRy0exMX4jYzqP4baWt+V/wgUPQko8YNwF8w0wYpnVitx9FPgV3DJsXC4Sv5xDwltv4UpOJnz4cKo/9CCO4GBPbKZSqjjJh8EvFHwD8y0KC/TVYlkpZZvy3XG1gjuR6qSadzNiEmJwZeUvCMuUwwcuvouw4PV4Bfhy7KlbrO4KNivpDF2HUw4z/NvhxByJ4fXLXy+4UF47FbYvgszsqa8NHNwEG2aCf5VCC+W0mBj2DruJQ889h1+zZjScN5eaY57UQlmpspRnQpKchnWqy4fDL8k1gYxSSpUVLZZL0bJth1ixMYwkZxIr9q+wOw50G4mjagRVGyZy8k8nR0bfYHVbsIkryxDgW/DMejln6NpzYg+3f3s7cSlxTOo7iQENBhT8hEuesoaeyvUip2D5cwWunnn8OHHPPsvem24mMz6eyLFjqTdjOv7Nyve04EpVSnnGWM6pSY1gejSprqPOKKVsocVyKTqemkFmUiuyTlXn8WVvMW/DAXsD+QZBaBQRrROpUj+VhDWG+AevtaW1xunK4v++2ERqhgtvr9wHwJwzdMUkxDD82+Gccp3io/4f0bV21zMrph2Hn8adGQ+5y31nhnvL5h4fOSfjcnF89mx2DxhI4tx5hN95J42+XUzo1VfpwVgpuyQfKrC/MkB8UjqLYg6SmJpRxqGUUkqL5VIzf2Msb333J+BFxrGeZPnu5+kl85i/Mda+UBtmQsIOxAsiuyYS1iSFoz8d5NBD/8BkZRX/eA9xZRlGztrAgk0HeWJAc8YObUeUuyU5KiyAV65vw5AOUfx04CfuWXYPIb4hzBw4k1bVWllPkHoMlr8Ab7WB5c/Dnh+t+/u/DM0H5hofmWYDoMOZLhtpmze7u1z8D//mzWk0fx41n3xCu1woZSdjrNEwCumGseNQEg99upGd8cllHEwppfQEv1JjnbhmFaDOEx3xrf4dJmwFbyy9yL6pWpc/B85UwBoprdbFJ3D4ZHF0+QaynniSyFdeRnx8Sj2Gw0toExXKZU2rc0e3BgD5pkxeuHsh/1n1H5pVbcbEvhOpHlAdMjMg+mVY+77VfaTVYOg5Gmq1PvPkg9+D97pYJ/cFRcDgCQBkHjtG/JtvcmLOV3hHRBA5bixVBg3SlmSlyoO041aXqQLGWAZrNAywzgOp1NJPWudcBEfYnUQplYMWy6Uk1wlqxpuMY5fhX3Mxh+L/BK6wJ1Sf5+Db0bkK5hrtkvHyMSQsWkTW8XiiJk7Fy8+vVF7+ZLqT2ONptKxdhYf7NC1wHWMM07ZO483f3qRL7S680/sdgnD3a3b4wN+/QNMr4fInzoyhnJNvENz25elxlo3Dn8TPPiP+7XfISkkh/O67qT5yJI7goFLZRqXUOUh2j7FcwOx9cKZYTqxkI2L8ctDJS698Q6ukVQzxXUt3NuGHky3SHGl1Da373g5VG9gdU6kLnhbLpSQyLIDYHAWzM7EzftVXUKXWz8D99oTq+A/Y/T3s+BYy061uCk2vpHqvi3B8PIlDq9aw/4a+1Pn4UxwRdT360sdSMrjjozUcPnmKlaN75z+xL347F68dxRtyFZ/s/YYBDQbwUruH8V3xMmyeDSNXW60twxeBdzFjHtdoCQ+uJm3TJg7dP4z0bdsI7NKFWs8+g1+TJh7dLqWUByS5p7ou5AS/sADrM19Zho+bvzGW/329lQ7pa/jK5z2q+KYRZ8KZ6erLcRPMAMc6Wm8dC1vHwrAZ1rdoSinbaJ/lUjK6f3MCfHIUhFn+ZJ3ojisghr9O/GVfsMHvWd0TEOvyusnQawxVJ6wh8pY2pO5OYN+If5J5/LjHXvLwyXRumvIrOw8n8/oNbfMXyhkpOGcN5cWgFD7Z+w23NryK11Id+E7oBKsnQpO+Z0a5KK5QxupycfDpp9l78y1kHjlC5Lix1Jv2sRbKSrmJyAAR2SEiu0RkTAHLRUTedS+PEZGOpRrodLFccDeMEH9vRCpHsZw9EdPgU1/zvs849ppaDD31H7qfepcXMm9ngus6rs54mUtPvc0+U4PD0VPtjqzUBU+L5VIypEMUr1zfhqiwAAQIDfBGTlyGr8OXaVun2Rcsu5tCRAvr0tfdHSGkFqH//ZI6r/2PU3vj2HfHHTi/eRlivoDzOPlv/7FUhk7+lYOJaUy7qzO9W9TIt07m/JH8X0AGi4ODeCQxiTE/TMVr7VRrSuqH1sP1U6BKZLGv5UpO4ciUqeweMJATCxYSfvfdNFq8mNCrdJQLpbKJiAN4DxgItAJuEZFWeVYbCDR1/9wLTCrVUMnuYrmQbhheXsJXD3TnH13qlWqMsvDU3BhuzPqW53xm8H3WxdyU8SzrTAtMnsPxAVODxa7OVD38K4vW/mFTWqUUaLFcqoZ0iGLVmCv469WrmH1vN9JOBRDpuJyFuxdyKOWQfcHc3RQK6vMbcu1N1J06FWfsQf5+/lMyZtwP7/eGv1ae00tNjN5NYmoGM+/pQrfG1XIvzEjFLPsPzyf8THSAH08dOcY9x48jXl7Q5xkYMhGqNS72NbJSUzn64Yfs7tePhLfeIqBDe2uUiydGa99kpfLrDOwyxuwxxmQAs4G83/MPBmYYy2ogTEQKbvb1hKRD4BsMfoWPStOxXlVq5JnVs6J5Zv4W/JwneNz7C1a62vCA81HSKHyblrk64Ssu1n83uwxTKqXy0mK5jLSsXYU7ujVg6/b2ZBnDJ9s+sTtSoYK6dqHetI/JIpi/VzXhVOwRmH4NfHoTHNuTe+X47fBe13yzAWaP3fzfa1ox78EedKgbdmbhhk9gSk94pQ7jt09jXnAg9x0/wa1J7mGhXE74dWKxObPS0zk6bRq7+l1J/Btj8b/oIhp8Ppt6U6ZolwulChcF7M9x+4D7vrNdx3OKmJAk2w9/xLNsq42NDB4wa/U+hjp+JFRSeSHzdrKKOQRvNE04bMLokr6qjBIqpQqiJ/iVoX/1a8bXmw/i5+zEl39+yb1t7yXUL9TuWAUKaNuWep/MYP+Ie/h7mYO6Dz1IwP7PwJV5ZqWMFJg11BqmbdZQeHAN+AaxYd9xJixez7uXZRGcsInGB9ZB7Hp44BerO0WWE/zD+LT91byfuJEbktN4MPHEmectYCKRnLJOnSLxyzkcnTKFzIQEArt1JWLUuwR2LN1ulUpVEgX1Sco7M1FJ1rFWFLkXq6sGNWvWJDo6+qwDtY/9E/BnUxGPHbsujfRM8E0IKHQdgOTk5HPKUBYMECbJOI2DnaZOrmV+XnAqK+/6XkS72nO192rbt6k8/17z0qyeV1FyQulk1WK5DIUG+PDkwBb899tL8a63hs/++Iz729k0MkYJ+DdrRv1ZM9l39wj2vbWMOuM/ISjCPRX0vAfg4EZIiQeMNfTTV//k187j+XT6e3zkNQ6+BBCru0eLq60WY4BOd7O0ehSv/jiaXnV78cyRk8jxJWdG6MgzkUg2k5FB4ty5HJk8hcxDhwjodDGR48YS1LlzWf1KlKoMDgA5h7upAxw8h3UAMMZMBaYCdOrUyWSPlX5WNqdCVCeKeuyXBzew/eDJItcBco3XXu4s+YZoV3uOmvyNJDtevopn5m9h5up9ue5v6dhPRmhj27epXP9e89CsnldRckLpZNViuYzd2LEOvZrdzAvrfmPW9lnc0eoOAn0C7Y5VKN969ayCecQI9j/wEFHvvE3IZT0gfhsk5Oh64coga+cyFm57jaOhnUluN4bgxt0gsiP4V8n1nGvj1vLUT0/RvkZ73uj5Bt5ZLnivC+bEASTHRCLZjNPJiQULODJxEs6DBwlo357IV14msGtXPXFPqbO3DmgqIg2BWOBm4NY86ywEHhKR2UAX4IQxJq5U0pyeva/obhihAT4VfjSMIF8H6zJasM7VIt/98zfG8tVvuWd4rS+HaSu7ofMLZRlTKZWH9lkuY15eQo0q/tzd+m4STyUyb9c8uyMVy6dmTep/8gl+TZty4KFRnFiyDE7mn7bbK8vJk96zmfDAtQT3ewoa9cpXKO84toNHfniEeiH1GH/FePy9/U+P0JEaWDfXCB0mM5PEefPZPegq4p55Fke1atR9/33qf/YpQd26aaGs1DkwxmQCDwFLge3AF8aYrSJyv4hkf9W1GNgD7ALeB0aWWqBTJyEzrdCRMLKFBfiQmOY8fT5ERfTSdW1weOXebzm8hJeua+Oe9dWVa9lVXr9aVy66rqwiKqUKoMWyTX77MxRXakM+iPkYZ1b5by3xrlqVetM+JrBDBw4+PprNx/qSanLP9Jdq/Pij9WOEBxU8FvKBpAPc//39BPkEMbnf5Nz9tWu0ZF3n8VCjJcbl4sTXX7PnqquJe+opvEKCqTNpIg2++Jzgyy7VIlmp82SMWWyMaWaMaWyMecl932RjzGT3dWOMedC9vI0xZn2phSlmjOVsoQE+uLIMKRmuItcrz4Z0iGLc0HanhxSt5i+MG9qOIR2ics/66nat41fWZTWHMM9OEqWUOjtaLNvkho518Enqw5H0wyzes9juOCXiCA6m7vtTCe7ZE995P7Jhe2PSjTUNbbrxYbmrA4/tbFPgY4+lH+P+7+8nw5XBlH5TqBVUwFeuWVmc/PZb9lw7mIOjn0D8/akzYTwNv/qKkN69tUhWqjI6XSwX3bI8rFNdfnqid+7JniqgnEOKjusVyJAO1iAjkWG5T1xsJvtp4bWflb497YiplMpB+yzbpGqQL6N7DublzYt497epXNP4Gryk/P/v4uUuYCcPuINeMZuIdYYT1egI8a5QJmQMJuDITtI2hWOcTusnM5P0tGQmrh9Po5Nx3NPyTsKX/sYx5+oz6zgzME4n4Qu/JvbgQXybNCbq7bcJubKfNeayUqrySj5sXQYX3We5apAvVQv51qoyeKxfMx6bs5nsXiZXO37FZYRWfW63N5hSSotlO93SuT4fbhxIfPrHLP1rBQMb9bU7UolkObx5r9vtpK73Z9D21fy13WoRepvxAOyNzv+YodlXFkyhwJFSRZCaNYkcO5YqAwcgjordeqSUKqEk93mDxZzgF38ynTkbDjCodW0aVK98kw2dTHdiDFQN9CExNYPrfNZwtHpXBnZrZ3c0pS54WizbyOElvDbgdu5ZsZD3Yz5gQMM+5b6rQbrTxaOzN5GcaZjU4UbW1mxJiDMVp5c3Xj4+3Nq9Ed1a1EJ8fDDeDqZs/YDoQ6u47+KRXNlkEHj7ID4+iK/70tvbunQ4iI6Opk0FGZpGKeUhSYetsdX9Qopc7UhyBq8v2UHDakGVrlg+dCKdscv+5LKm1Zlxd2fk4EZ4Pw66/dvuaEoptFi2XeeGETzZ7X5eXfcS6w+v55Jal9gdqUi7E5JZuTOB/1zdivAgX95YGsDBxDQiwwIY3b85/TqcmeRr3PpxTOMXRg18mKvb3mtjaqVUuZUUZ42EUUxDQVigdX5ERR8+riDPL9qK05XFi0NaWw0mW74ELx9rfHqllO20WC4Hbmg2hKlbJvHKLxP56rqPymXrcmpGJoG+3lwUGcqPo3sTEWKNhDGkQ8Ez4E7fOp1pW6dxc/Ob+Webf5ZlVKVURZJ8uNiRMMAaDQMgsZIVy5muLIL9vHm4T1PqVwuCnd/BminQ+noIDLc7nlIKHQ2jXPD39qddlWvYmbSej9atsjtOPnsSkrnyrZV8ttaaWSq7UC7Moj2LGLt+LP3q92NM5zHlsvhXSpUTSYeKHQkDINDXgY9DKk3L8vyNsTwWnUrTp79l1a6jRIb6Q1wMfHkn1GwFV79ld0SllNt5FcsiEi4i34nITvdl1QLWqSsiP4jIdhHZKiKPnM9rVlb/63UPYvyZsOF90srROKKb9idy4+RfSXe6aB2Zf4rWvH6J/YVnf36WS2pdwiuXvYLDS0/UU0oVIelQsSNhAIgIoQE+JKZW/GJ5/sZYnpq7haPpBgPEJqbxzrwfSZt+A/iHwq1fFNuHWylVds63ZXkMsNwY0xRY7r6dVybwmDGmJdAVeFBEWp3n61Y6VQPC6F/3Opz+G3nt+5/sjgPAj38mcOv7qwn282bO/d1pU6foYvn3I7/zaPSjNA5rzDu938HPUXQLtFLqAncqCZwpEBxRotWXPtqT566t+IePN5b+kWu2vmBSmSSvkpWeZBXKVSJtTKeUyut8i+XBwHT39enAkLwrGGPijDEb3NeTsKZXLbij6wXuiW7/xCHefLFrJn8fTbE1y/5jqdwzfR0NqgUx54FuxZ59/vfJvxn5/UjC/cOZ1HcSIb7aKqKUKobDz+qvvO4jOBlX5KrzN8Zy7YRVtHhmCT1eXcH8jbFlFNKzTqQ5iU1MP33bm0ze83mXpnKABzIegVqtbUynlCrI+RbLNY0xcWAVxUCNolYWkQZAB2DNeb5upRQRGMGgBtfgXeU34pLjbc1SNzyQsUPbMfu+rtQI8S9y3SNpR7jvu/sAmNx3MhGBJWslUkpd4Lx94dbPIT0RZt0I6ScLXC2720JsYtrpbgtPzd1S4QrmwyfTuWb8zznuMTzv/TGXO2J4OnMEu6t0sS2bUqpwxY6GISLfAwV1KHv6bF5IRIKBr4BHjTEF7xGt9e4F7gWoWbMm0dHRZ/MyJCcnn/VjypOOztZ8I/P4fMO7pP81ON/y0ty+LGOYu9NJm+oOmoc7CAU2rN5Z5GPSstJ499C7JGQmMKrmKPZu3Mte9p7T61f0964olXnboHJvX2XetnKhdjsYNgM+HQZf3A63fmkV0Tm8sXRHrm4LAGlOF28s3VHoiDzlUUSwH90aVeO6DlFMXbmH4VnzuNX7ByZkDmahV19e6d/c7ohKqQIUWywbYwqdVk5EDotIbWNMnIjUBgpsDhURH6xCeZYxZm4xrzcVmArQqVMn0+ssJ6mIjo7mbB9T3qz9cS0rD/xENb9/8Hi/9vj7nDlJrrS2z+nK4ok5MSzaE0vdevXo1atFsY9JdaYyasUoDmUeYnyf8Vwadel5ZagM711hKvO2QeXevsq8beVGkz5w7XiY/wAsHAXXTc417vLBxLQCH1bY/eVJWoaL15b8wb09GxEZFsBrN7YF4NJTK7lk/WwWuLozO+gOXhnQskIV/kpdSM53nOWFwHDgVfflgrwriDVu2IfAdmPMm+f5eheEEW1GsGTvEmZs/Yww/yo8dEXTUn29lFOZjJy1gR//TODxK5vxYO8mxT7mYPJBRq0Yxa7EXbzY48XzLpSVUhe49rfCiVj44UUIjYI+/zm9KDIsgNgCCmOHl2CMKbfDU+49ksL9M3/jj0NJtKwdwk2X1LMW/P0rl2z8N4mhrRg8aj6DvfVkaKXKs/Pts/wq0E9EdgL93LcRkUgRWexepwdwO3CFiGxy/ww6z9et1FqEt6BHVA+Ca/zKhOjtHDieWmqvdTLdya0frOGnnQm8en0bHrqiabEHno3xG7nlm1uIS45jYp+JXNP4mlLLp5S6gPR8HC6+E34aB+s+PH336P7NCfDJPQyln7cXd3ZvgIjgyjK2nxSd15LfD3HN+J85dDKdj++65EyhfHQ3zL4FQuvwe+unQAtlpcq982pZNsYcBfoUcP9BYJD7+s9A+fy3vxwb0XoEq2LvxitkPS99E8Wkf1zskeedvzGWN5buOD1F9WP9mtEkIpiHejehX6viJwaYt3Mez69+nsigSMYPGE+j0EYeyaWUUojAoHHW2MuLH4eQWtDiqtPdE3Luu0b3b376/k/X7uOFr7dx3+WNaO0wdm4BAAs2xfLI7E20rRPKxNs6UqdqoLUg5QjMvAHEC277kswt++0NqpQqEZ3uupzqVLMTbSPa8pfjF779vRM/7azHZU3Pb5SJ7DPKs0+UiU1M4+n5v/PK9W2KLZRdWS7e/O1NZmybQZfaXRh3+ThC/YqfpEQppc6Kwxtu/AimXwNzRsDwr6HuJQzpEFVon94BF9Vi49/HGb9iF9UDBO/Iw/RpWfw//56QtwFidP/m9GlZg0f6NGVk78b4ebtbxJ1pMPtWOHkQ7lwE1RoDWiwrVRHodNfllIgwovUIklyH6X1xHDsPJ9Hj1RXcuSTlnMYYjT+ZzovfbCv0jPKiJGUk8dCKh5ixbQa3tLiFSX0naaGslCo9vkFwy+dWy/JnN1ldF4oQEeLHmze1Z/a9XfF1wIjp63lh0bZSj1nQkHZj5sawfHs8/+rXzCqUjYHf58J7XWD/Grh+KtTtXOrZlFKeoy3L5Vivur1oHNqY/acW8cbSeqQ5s4AzY4wCp1ta4pPS2Xk4mdjjaRw4nsqB42nEJ53ikxGdERFeX7qDI8kZBb5OUWeU7zu5j1ErRrHv5D6e7fosw5oP8/BWKqVUAYIj4B9fwYf9YOb1MOL7Ymf669qoGs93D2C3ox5t64QB1mgUXl6caeH1kKR0J//7emu+Boh0Z9aZIe32r4Ol/4YDa6Fma7hjITS63KM5lFKlT1uWyzEv8eLuNndzOH0vGb65W0nSnC6emBPD8RSrAJ7569/c9sEanvgqhgk/7GL1nqNkZGaRmmHtyO/s3oBqQb75XgOsM80LsiZuDbcuvpWj6UeZeuVULZSVUmWrWmNr+uekw9Y4zBnFn8Tn7SXcd3ljujWuBsCb3+1g4Ds/sWrXkXOO4coy/B57ghm/7uXX3UcBOHzyFMdTnQWuLyf2wZy74cO+kPg3XDsB7luphbJSFZS2LJdzAxsO5KkfXse3ejRpKbnHPs5wZZGSkUnVIF+GdIiia+Nq1K0aSK1Qf3wcuf8Pah0VyrNXt8rVZxkgwMfB6AIGwv/8j895Ze0rNKjSgPFXjKdulbqls4FKKVWUOp1g6MdWf98v74KbP7X6NZdQjybVWbbtMLd9sIZr2kXyzFUt+XX30UJPFsyWlWV4d8VO1u89zsZ9x0lxNzzc1aMB3RpXo3FEEBEhfiQknTr9mBBSGem9gLu9l8Af3nD5k9D9YfAL9szvQillCy2WyzkfLx8CUvtwKnQujoC9uNIanF4WFRZw+izrRhHBNIooeodc3BnlAM4sJ6+tfY3Pd3xOzzo9ee2y1wj21R29UspGzQfCVeNg0b/gm/+Da97JNWlJUXo1r8HSR6sx+cfdTIzezbLf4zBAhssaNSM2MY0nv4ph/d/HAPD3dvDM1a3w8hIWbj6Iv7eD6zvWoVODqlxcvypR7m/iRISnB7XkqblbyHBmcItjBf/ynkM1SWJf3SHUu/Fla7xopVSFp8VyBfBEjzt4fvMSfKtFk3bgTqDwFuHiFHVG+YlTJ3gs+jHWHFrDXRfdxSMdH8Hh5dl+fkopdU463W1NWvLTWAitA5c/UeKH+vs4eLRvM4a0j2LA2ys5lZmVa/mpzCxmrt5HsJ83V7Socfr+pY/2zPctXU5D2kdS89CP1Fr7Eg3NATZ4tSbmsufo3bvf2W+fUqrc0mK5Ahh2cWNWJdzAisOf4AjeRk3vNjzRv41Hp0bdk7iHUStGEZcSx4s9XmRwk8Eee26llPKIK56Bk7Hww0tQJQo63HZWD29QPShfoZxNgM3/vRKH15kW66IKZQ79DsueptueaAhvDFd+Ssfmg0rc4q2Uqji0WK4gnu99H5vmfwN1Z5Am3nwW24xtGe1oF9GOthFtqRNc55ynfP059mdG/zgaX4cvH/X/iPY12ns4vVJKeYAIXPOuNWnJ1w9DSE1o0vesnqKwqbMjwwJyFcqFSjoEK16EjTMhIAwGvGa1ensXfAK1Uqri02K5ggj1C2XhkIXMWD4DU8uwOWEz83fN57M/PgMg3D+cthFtaRdhFdAXVbuIQJ/AIp/TGMMn2z5h3G/jaBrWlPFXjKd2cO2y2ByllDo33r4wbAZMGwRfDIc7v4HIkv+DP7p/8xKf6JxLRir8OgF+fhtcGdDtQWt67oCq57olSqkKQovlCiTUL5Q2gW3o1bEXAJlZmexO3M3mhM1sTthMTEIM0fujAXCIg2ZVm50uoNtGtKVeSL3Trc8ZrgxeXP0i83bNo2+9vrx06UvFFtdKKVUu+FeBW7+0xmD+dBiM+A6q1i/RQ0tyonMuWVkQ8zksfx6SDkLLa6Hf/yC8kae2RilVzmmxXIF5e3nTPLw5zcObnx4DOTE9kZgjMacL6K93f83nOz4HIMwv7HTxvCp2FRviN3Bf2/sY2X4kXqJDbiulKpAqtXNMWnKD1Z85K5Oah7bAhn3gckJWpvvSCa5M92UGQ1xOhrTLsWxvJuyxlp1Zz/34pDg4ugsiO1rTcNfvZveWK6XKmBbLlUyYfxg96/SkZ52eALiyXOw+sft0y/PmhM2sPLASP4cfb/R8gwENB9icWCmlzlFEc7hlNswYAl8OB6AlwB9FPMbLGxy+4OVjjdfs5QMOnzP3n77uYy0LqweXj4HWN4CXNioodSHSYrmSc3hZ3TGaVW3G0GZDAWuIOGMMYf5hNqdTSqnzVL87/Ot3SI4Hhw9r1m2gS/cehRfEOlqFUuosabF8AQr1C7U7glJKeU5wDesHSAuMs1qDlVLKQ/Q7JaWUUkoppQqhxbJS2g2nQgAACVxJREFUSimllFKF0GJZKaWUUkqpQmixrJRSFxARCReR70Rkp/sy36waIlJXRH4Qke0islVEHrEjq1JKlQdaLCul1IVlDLDcGNMUWO6+nVcm8JgxpiXQFXhQRFqVYUallCo3tFhWSqkLy2Bguvv6dGBI3hWMMXHGmA3u60nAdqCQKe6UUqpy02JZKaUuLDWNMXFgFcVAjaJWFpEGQAdgTaknU0qpckjHWVZKqUpGRL4HahWw6OmzfJ5g4CvgUWPMyULWuRe4F6BmzZpER0efXVgPS05Otj1DSWnW0qFZPa+i5ITSyarFslJKVTLGmL6FLRORwyJS2xgTJyK1gfhC1vPBKpRnGWPmFvFaU4GpAJ06dTK9evU6r+znKzo6GrszlJRmLR2a1fMqSk4onazaDUMppS4sC4Hh7uvDgQV5VxARAT4Ethtj3izDbEopVe6IMcbuDIUSkQTg77N8WHXgSCnEKS8q8/bptlVclXn7znXb6htjIjwd5nyJSDXgC6AesA8Yaow5JiKRwAfGmEEicinwE7AFyHI/9N/GmMXFPPe57LM9rSL9LWrW0qFZPa+i5IRS2GeX62L5XIjIemNMJ7tzlJbKvH26bRVXZd6+yrxtlVFFer80a+nQrJ5XUXJC6WTVbhhKKaWUUkoVQotlpZRSSimlClEZi+WpdgcoZZV5+3TbKq7KvH2Vedsqo4r0fmnW0qFZPa+i5IRSyFrp+iwrpZRSSinlKZWxZVkppZRSSimPqFTFsogMEJEdIrJLRMbYncdTRKSuiPwgIttFZKuIPGJ3Jk8TEYeIbBSRRXZn8TQRCROROSLyh/s97GZ3Jk8RkX+5/yZ/F5HPRMTf7kznQ0Q+EpF4Efk9x33hIvKdiOx0X1a1M6PKrSTvj5370OKOS2J51708RkQ6llW2ArIUl/U2d8YYEflFRNrZkdOdpUTHexG5RERcInJjWebLk6HYrCLSS0Q2uf8+fyzrjDlyFPc3ECoiX4vIZnfWu2zKmW9fnWe5Zz9XxphK8QM4gN1AI8AX2Ay0sjuXh7atNtDRfT0E+LOybFuObfw/4FNgkd1ZSmHbpgP3uK/7AmF2Z/LQdkUBfwEB7ttfAHfanes8t6kn0BH4Pcd9rwNj3NfHAK/ZnVN/cr1nxb4/du1DS3JcAgYB3wICdAXW2PR7LEnW7kBV9/WB5TlrjvVWAIuBG8trViAM2AbUc9+uUY6z/jv7MwZEAMcAXxuy5ttX51nu0c9VZWpZ7gzsMsbsMcZkALOBwTZn8ghjTJwxZoP7ehKwHatQqRREpA5wFfCB3Vk8TUSqYH2oPwQwxmQYYxLtTeVR3kCAiHgDgcBBm/OcF2PMSqydf06Dsf7hwX05pExDqeIU+/7YuA8tyXFpMDDDWFYDYe5pyMtasVmNMb8YY467b64G6pRxxmwlPd6PwpqyvcAp3ctISbLeCsw1xuwDMMbYlbckWQ0Q4p7lMxhrf5lZtjEL3Vfn5NHPVWUqlqOA/TluH6ASFZTZRKQB0AFYY28Sj3obeIIzM4VVJo2ABOBjdzeTD0QkyO5QnmCMiQXGYs0CFwecMMYsszdVqahpjIkDq+gCaticR+V2Vu9PGe9DS3JcKi/HrrPNMQKr5c4OxWYVkSjgOmByGeYqSEl+r82AqiISLSK/icgdZZYut5JknQC0xGoY2QI8Yowpj8duj36uKlOxLAXcV6mG+hCRYKz/kh81xpy0O48niMjVQLwx5je7s5QSb6yviiYZYzoAKVhfFVd47r6hg4GGQCQQJCL/sDeVqoxE5Ht3v/i8P2f17aEN+9CSHJfKy7GrxDlEpDdWsfxkqSYqXEmyvg08aYxxlUGeopQkqzdwMdY3rP2BZ0WkWWkHK0BJsvYHNmHt89sDE9zfoJY3Hv1ceZ9HkPLmAFA3x+06VPCvhHMSER+snfwsY8xcu/N4UA/gWhEZBPgDVURkpjGmshRdB4ADxpjsVqw5VJJiGegL/GWMSQAQkblYfRpn2prK8w6LSG1jTJz7azw7v9K9IBlj+ha2TERK9P7YtA8tyXGpvBy7SpRDRNpidZkbaIw5WkbZ8ipJ1k7AbKu3ANWBQSKSaYyZXzYRTyvp38ARY0wKkCIiK4F2WH3ry1JJst4FvGqsjsG7ROQvoAWwtmwilphHP1eVqWV5HdBURBqKiC9wM7DQ5kwe4e4b9CGw3Rjzpt15PMkY85Qxpo4xpgHWe7aiEhXKGGMOAftFpLn7rj5YJ3JUBvuAriIS6P4b7YPVF7SyWQgMd18fDiywMYvKr9j3x8Z9aEmOSwuBO9xn73fF6s4UV4YZsxWbVUTqAXOB240xZV3I5VRsVmNMQ2NMA/exZQ4w0oZCGUr2N7AAuExEvEUkEOiCPfvSkmTdh7WvR0RqAs2BPWWasmQ8+rmqNC3LxphMEXkIWIp1RudHxpitNsfylB7A7cAWEdnkvu/fxpjFNmZSJTcKmOXe+ezB+s+8wjPGrBGROcAGrBM8NlKxZnnKR0Q+A3oB1UXkAPBf4FXgCxEZgXWgGGpfQlWAAt8fEYkEPjDGDMKmfWhhxyURud+9fDLWSA2DgF1AKjbtH0qY9T9ANWCiu8U20xjTqZxmLRdKktUYs11ElgAxWOfufGCMKXBINLuzAi8A00RkC1ZXhyeNMUfKOmsh+2qfHDk9+rnSGfyUUkoppZQqRGXqhqGUUkoppZRHabGslFJKKaVUIbRYVkoppZRSqhBaLCullFJKKVUILZaVUkoppZQqhBbL6oIjImEiMtLuHEoppZQq/7RYVheiMECLZaWUUkoVS4tldSF6FWgsIptE5A27wyillCqYiLwgIo/kuP2SiDxsZyZ14dFJSdQFR0QaAIuMMa1tjqKUUqoI7v31XGNMRxHxAnYCnY0xR20Npi4olWa6a6WUUkpVLsaYvSJyVEQ6ADWBjVooq7KmxbJSSimlyrMPgDuBWsBH9kZRFyLthqEuOCJSDdhgjKlvdxallFJFExFfYAvgAzQ1xrhsjqQuMHqCn7rguL/CWyUiv+sJfkopVb4ZYzKAH4AvtFBWdtCWZaWUUkqVW+4T+zYAQ40xO+3Ooy482rKslFJKqXJJRFoBu4DlWigru2jLslJKKaWUUoXQlmWllFJKKaUKocWyUkoppZRShdBiWSmllFJKqUJosayUUkoppVQhtFhWSimllFKqEFosK6WUUkopVYj/B4GimCgvEQUOAAAAAElFTkSuQmCC", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# x0, y0, h variables globales\n", "def EM(phi1,phi2,tt):\n", " uu = [y0]\n", " ww = [z0]\n", " for i in range(len(tt)-1):\n", " uu_tmp = uu[i]+h/2*phi1(tt[i],uu[i],ww[i])\n", " ww_tmp = ww[i]+h/2*phi2(tt[i],uu[i],ww[i])\n", " uu.append(uu[i]+h*phi1(tt[i]+h/2,uu_tmp,ww_tmp))\n", " ww.append(ww[i]+h*phi2(tt[i]+h/2,uu_tmp,ww_tmp))\n", " return [uu,ww]\n", "\n", "[uu, ww] = EM(phi1,phi2,tt)\n", "\n", "figure(figsize=(12,5))\n", "affichage(tt,yy,zz,uu,ww,\"Euler modifié\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q3 [3 points]** \n", "Calculer la solution approchée obtenue par la méthode de **Crank-Nicolson**. \n", "Afficher $t\\mapsto y(t)$, $t\\mapsto z(t)$ et $y\\mapsto z(y)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\text{(CN) }\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\left(\\varphi_1(t_{n+1},u_{n+1},w_{n+1})+\\varphi_1(t_{n},u_{n},w_{n})\\right),\\\\\n", "w_{n+1}=w_n+\\frac{h}{2}\\left(\\varphi_2(t_{n+1},u_{n+1},w_{n+1})+\\varphi_2(t_{n},u_{n},w_{n})\\right).\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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6diY1J4+n1+0vtT1yet9qL+bbb79l6NCh9OzZExcXF06fPo21tTX79+/nxIkTuLm5MXz4cH799VfGjh1LTk4Offr0YfHixbzxxhu89957LFmyBI1Gw/Xr14mJiQHgwQcf5PHHHyc8PJzVq1fz0ksv8c033/Dkk08yZMgQnnvuOfR6PdnZ2aSlpXH27FkiIyPx8/PjkUce4ZdffmHChAnMmTOH5cuX06pVK06cOMHcuXOJjo5m+vTpzJ07l+DgYM6fP8+wYcMqnIe5tt9/DeVereI0rbqOs0BfyIkLydheO0jHjJ3k/28rFklHAUg1s+P3wu78pu9BTGF3rmH4zGrrYGWSmGtrNoxEoH2J39sBl0xVuff9M/lN9qRlAay9xwzzHDOSTtnjc/8MU51CUeqFmnpE3adPH2Mr2MWLF7n77rsBiIiIYNSoUQDExMQwZ84cNm7ciJ+fHwkJCYSGhhIREVFhnaGhofTq1Qtvb29WrFgBGPptenl5ER4ejq+vL2PHjuX69euVlhcf07VrV2bMmEHPnj25cOECCxcuxMfHBx8fHz744APjOdeuXYuvry89evRg4sSJgKFleOrUqXh7exMSEoJOpzPuv27dOgIDA/Hz82P69Ono9fpy5c8++6yxvAmp0Xt2ZS5nVDwFWvr1/Duqd/369Tz00EMAjBs3jvXr1wMQGBhIx44d0Wg0PProo8Yk2MzMjLCwMAAmTJhgLAeM5QA7d+5k/PjxAEycONG4X3R0NE8//TQAGo0Ge3t7ADw8PPDz8wOgV69enDt3juzsbP744w8efvhhgoKCmD59OpcvGxrwt27dyqxZs/Dz82PkyJFkZmbWyyc4ilJTjiSms/6n7axd9Aq/v3EvHdd0p+PmR+CPxVhY2nHGZzZpE37l91E7eZFn2VTY35goW1lomDvM0yRx1FbL8nfALCHEF0BvIENKWe5x3u0K9W/L9wWLub75PrLa6InvBJ1Oarj/+nbgMVOdRlHqVPEABl2+IXErHsAAhr+B2yWl5Pz587i5uQFw5MgRunfvTl5eHvHx8bi7uwOGFtiAgAAWLFhgHKik1+vZu3dvhfWuXr0aJycndDodAQEBxmTl1KlTrFq1iqCgIKZMmcLSpUsZO3ZsheV///vfjcesWbOGpUuXsn//ftasWcPu3buRUtK7d28GDhyIVqtl/vz5xMbG4uLiQmpqKpmZmZw+fZr169ezcuVKHnnkEb766ismTJhAXFwckZGRxMbGYmFhwYwZM4iIiCAgIKBU+ZNPPklERASTJk267de4Aaqxe3ZVLcFtHKyMA3RKautgBYCTjfamWpJLSklJITo6mqNHjxq/+AghGDFiRLmBdJUNrCtZbmNjU+m5qhuY16xZM+PPGo0GnU5HYWEhDg4OHDp0qNxTjMLCQnbu3ImVlVWV9SpKY1CgL+T4pUwSk65xv+0ZOBOFy/7NPFpo+J6e1qw1yW1HUdB9OA7dhoJlczoXHRsKIMx49+dTXEzX0dbBirnDPO/os7EkkyTLQoj1wCDARQiRCPwTsACQUi4HfgRGAGeA68DjpjhvSQ8G3AVu39Pqq4dZNtiRBWuSubZwAW36jQc1slhpIKp6RP1/P500JsrFdPl6Xv/+OKH+bW/7EfWZM2fw8PAwftAXJ8vJycnG7hfFTp06hafnX9/UNRoNWq22wq4KixYtYtOmTQBcuHCB06dP06pVK9q3b09QUBBgaLVbtGgRY8eOrbC8OFl2c3Mz9tWMiYlh9OjRxqRlzJgx7NixAyEEY8eOxcXFBQAnJycyMzMrbM0DiIqKYv/+/QQEBBheS50OV1dXMjMzS5Xn5OTQrl27al/HhqQ+3LMrMneYZ6kvhHDnrUMbN25k0qRJLFiwwPgeHThwIDExMezZs4eEhATc3NyIjIxk2rRpgCFJ3bhxI+PGjePzzz+vtJtOv379+OKLL5g4cSIRERHG/YYMGcKyZcuM3TBycnIqja958+Z4eHiwYcMGhg8fjpSSI0eO0KNHD0JCQliyZAlz584F4NChQ8b3sqI0BmeSsog6cZWLp/bgcGkHfQsPca/ZKRB6sLDGrl1fsjrNxM57OI7OnXCsIp8L9W9LqH/bGukuYpJkWUr5aDXbJTDTFOeqkmtXkpoN5rxVDPYPh5Ie+S2OJ05g5e1d46dWlJpWU4+ojx49Svfu3Y2/79u3j+nTp2NlZVVqZbCUlBTs7e2xsLAodfyNGzewtLQsVbZ9+3a2bt3Kzp07sba2ZtCgQca6KmvNq6qVr2RrXmVz0EopK2zZq6g1r3j/8PBw3n777VL7L168uFR5Q1gm+VbVm3t2GcWtQO/+fIpL6TramKB1aP369cybN69U2UMPPcSyZcvo27cv8+bN4+jRowwYMIDRo0cDhvfb8ePH6dWrF/b29kRGRlZY96JFi5gyZQrvvvsuLVq0YM2aNQB8+OGHTJs2jVWrVqHRaFi2bBmtW1c+mUhERARPP/00b7zxBnq9nnHjxtGjRw8WLVrEzJkz8fX1paCggAEDBrB8+fLbfi0UpS4V6As5cTmTXfEpPOpjjV1iDAUxXzPmaiwtRAYIyHD0JL/LU2i7DYMOfbAzb1Z9xbWgtrph1JqgFm34M7WA/GnhaH7+jaR33qHDorcQjm51HZqiVKu2H1EDpKamGh/zxsXFsXnzZpYsWYKjoyN6vZ7c3FwsLS1JSEigTZs2pY5NSUmhRYsW5RLojIwMHB0dsba25uTJk+zatcu47fz58+zcuZO+ffuyfv16Y2tcZeVlDRgwgMmTJzNv3jyklGzatInPPvsMrVbL6NGjmT17Ns7OzqSmVjUzmqH1b9SoUcyePRtXV1dSU1PJysqqsDw1NdXYTUWpWcWtQ6ZSPBK+ZF/fv/3tb/j6+rJgwYJKE+E333yTN998s8K6irm7uxMdHV3u2JYtW/Ltt9+WKz927K81YIqfmoChL/NPP/1U7ouZi4tLpfEpSkOQlJnLpoMX2Xv2Kvl/7iZAf5ABZkewjT4HSLpYOZHnNRi6DoNO92Bv16quQ65Q41ruGmhpYZhe6FxhEi3+9gzX9+4j641QyK+4VU5RGoq5wzyxstCUKjPFAIZhw4YRFRXFI488woYNG3B2dqZlS8PfUUhIiHHQkpeXF8nJyfj4+PDHH38AsG3bNkaMGFGuzuHDh1NQUICvry+vvvpqqemuunbtyqeffoqvry+pqanGgVCVlZfVs2dPJk+eTGBgIL179+bJJ5/E398fb29vXn75ZQYOHEiPHj2YM2dOldfdrVs33nrrLUJCQvD19eXee+/l8uXL5cpDQ0ONA64URVGUihXoCzmSmM6K38+yOz4F0s6h37sK963T+PD8GD4VrzPD4ge82rVADH4ZpkZjNvcMlo9+Cn7joZ4mytAIW5adNa4AfHloH/0f/htpa1aStOMCttH/h9mw1+o4OkW5fTXxiBqgffv2HDlyxPj7a6/99Xcya9YsFi5cyNChQ7G1tWXPnj2ljv3888/LdWMAQ9eHLVu2lCs/d+4cZmZmFT5Krqzc3d29VIscwJw5cypMhsPDwwkPDy9VVllrHhhmNig5u0FF5Y2xG4YCgwYNqrRfY3Z2du0GoygNVIG+kNWxCeyKT+VYwiW8848ywOwId9megNwLtAZcHdujuSsMOg3BzGMAWiuHauutbxpdsmxvYQt6W06nxyPMzXF99Q0uTJ1K2icrcPZ7CFqq/stKw2XqR9TV8ff3Z/Dgwej1ejSa0q3aeXl5hIaG4unpqaazUhRFaeT0hZIjiensik8BYFr/jphfO0H+7/9lljyEr1kc5tp8pLkVol0wdJ4JnYeice7c4CdaaHTJMoCNaE3KjUQAbPsHYxPUh+S9O7H/Yibmz0SBmaaaGhRFKTZlypQKy7Va7S1Pp1ZRK3FV5YqiKErd2nQwke8PX2bnmetY/rKF/mbHGGN/EvYcg+wrhpHArt2g03ToPBTRoS9YWFZXbYPSKJNlV8sOxOt2GkfHt3zpFeIfHElyTBqtHk+C5pWPSlYURVEURWlq9IWSE5cMs1UcOJ/G4kf9MaeQtLjfGXxpG69Y7sejIB6BBOkAboOh81DodA80b1P9CRqwRpksu9t7kJAXxclrl+nq2oZmnTrhOG4caZGROCbl0Kx5XUeoKIqiKIpS9/aeS2X59rPsSUgl60YBbbnGGPtT5H2+APPEGKbcyARhRoZdF0TPF6HzEGjj36Se0jfKZLlXG0+2XYP49AS6uhq+7bg8M4uM77/n6tvz6TCtLwRObfB9aBRFUZTqaTQavL29MTMzTAA1bty4cnMv365Dhw5x6dKlCmeFUZT6pGTL8a74FKYP7ESghxP5uhxaXPmd5S4n8L2xH7vsBLgBXGsH3qHQaQh0HMjB3YdNvthHQ9Eok+UhnXxYcBh0/DXdk7mjIy4zZpD0n/+Qbb4ZW2sn6D62DqNUFEVRaoOVlRWxsbE1MqvJoUOH2Ldvn0qWlXorJfsG/9h4xNhyDJIhjsnYH/wFduyh75876ae/AQWW4BYEQVMN3StcuqhGxSKNbp5lgDa2bWimacbZ9PhS5U6PjceiQweuHmuJ3PwPyEmpowgVRVGUupSRkYGnpyenTp0C4NFHH2XlypUAPP3009x99914e3vzz3/+03jM3r176devHz169CAwMJCMjAxee+01IiMj8fPzIzIykpycHKZMmUJAQAD+/v4VLk6iKDVBXyg5djGDj3fE8+Sne1nws+G9bW9lwfWMJF50i+O3Lhs46/w8q3TP4nnk/yDrCiJwKkz4Gl44BxO/hr4zoYWnSpRLaJQty2bCDI3elW+OHeSFwL/KhVZLy3/MJXHWM6Qdy8Ppl5dhtFo6VFEUpVZsmQdXjpq2zlbd4b53qtxFp9MRFBRk7Ibx4osvEhYWxpIlS5g8eTLPPvssaWlpTJ06FYD58+fj5OSEXq9nyJAhHDlyBC8vL8LCwoiMjCQgIIDMzEysra1544032LdvH0uWLAHgpZde4p577mH16tWkp6cTGBjI0KFDSy3ZriimUDyJAcALG4/w47HLZOUWANDZ2ZLhzf+EbV9hfiaK9Wn7IU2CpT10HGzod9zpHrBvV5eX0GA0ymQZwF7TlssF/ytXbjtkCNaBgSQfP4z93i/Q+D5ieMMoiqIojVJl3TDuvfdeNmzYwMyZMzl8+LCx/Msvv2TFihUUFBRw+fJlTpw4gRCC1q1bExAQAEDz5hWPFP/ll1/47rvvWLBgAQC5ubmcP3+erl271tDVKU2FvlASd7m4z3Eql9J1/PhsfwDsrS14zMuMYZZn6JqzB8sLO+BwBggzaNsLBr5QNDCvJ2gabepXYxrtK9bBzoNLBbu5mpVJS7u/bmpCCFq+OI+EMQ+RnNyHlk4d6zBKRVGUJqSaFuDaVlhYSFxcHFZWVqSmptKuXTsSEhJYsGABe/fuxdHRkcmTJ5Obm1uqFa8qUkq++uorPD3vbBl6RdEXSsyEIW9Zu/McC34+RWZRy7GHiw3B7jbknfoZbcJ2XoqPgmRDtwvs2kDXB4sG5g0Ca6e6uoRGo1H2WQbo6tIJISSxf54st82ya1fsx4wmdecl8jJVnxxFUSA2NpYdO3bUdRhKLXr//ffp2rUr69evZ8qUKeTn55OZmYmNjQ329vZcvXrVuGy7l5cXly5dYu/evYBhGfSCggLs7OxKrWA5bNgwFi9ejJQSgIMHD9b+hSkNUuk+x/vwf+MXTl01vLfaO1pzf/dWrB5hw5GQ02xr+SFvnnwA7fpHYO8qwzzHIfNhxi6YcwJGfQQ+Y1SibCKNtmX57jaefHIGDl35H2N8Asttb/Hss2Ru+Ymkt+fTbkCG4RFF2551EKmi1H86nY7hw4cTHR2NRqMhMTGR2NhYwsLCyMvLY/jw4fz222+Ym9fPW8q5c+d44IEHKl0l8ODBg6xZs4Zly5bVcmRKbSjbZ3n48OFMmTKFjz/+mD179mBnZ8eAAQN46623+Ne//oW/vz/e3t507NiRoKAgwLBiZWRkJM888ww6nQ4rKyu2bt3K4MGDeeedd/Dz8+PFF1/k1Vdf5bnnnsPX1xcpJe7u7vzwww91eflKPaUvlOQVFAJwJDGdCR/vLtVyfL9va5rlZ8LxKAafiWLwnxPJWrkAACAASURBVNFw9KLhYBdPuHuKofXYrR9orevqMpqE+vnJZgIBbT0BQaF5UoXbLVxdcZk2lWsffEiOdSE2GX+DadtAY1G7gSrKrUqKgw2Pw8NrwLV2+kGuXr2aMWPGoNEYJqGPiorixIkThIWFodVqGThwIJGRkTz22GM1HouUEimlMfExBX9/fz7++GOT1afUL3q9nqysrHJ9luPi4ow/L1y40PjzJ598UmE9AQEB7Nq1q1x5cWtzsf/+9793EK3SWJXtc7wnIYWp/TvSXQPuLjaM6N6avh0dCLY6j/OVGDizFVbvB1kIzeyh40AY+A9DguzQvq4vp0lptN0wrLVWtLVtQ564Uuk+TpMnY96mNVdPtkdePgp/LK7FCBXlNuTlQMTDcO2k4f95OXdcZUJCAgMHDgTgwIEDCCFISUlBr9fj4+PD9evXiYiIYNSoUQDExMQwZ84cNm7ciJ+fHwkJCTzwwANERERUWH9oaCi9evXC29ubFStWAIaWXi8vL8LDw/H19WXs2LFcv369yvKuXbsyY8YMevbsyYULFwBDguPj44OPjw8ffPCB8Zxr167F19eXHj16MHHiRMCQME2dOhVvb29CQkLQ6XQArFu3jsDAQPz8/Jg+fTp6vd5Yz7p16xg0aFCF2xRFUapSWChJyso1/hz0TjQPLI7hrc1xnEnKYkT31vR0c6RZbjLNT6znHf17jPq5P85f3A/b3zEkyf3/DlN+hn/EQ9hn0GuySpTrQKNNlgHcm3twMvVMpdvNLC1xnfM8N+IvkpHX1/DmTDlbixEqyi36dibkXAOk4f/fzrrjKh0cHIx9LhcvXkyfPn1IS0tj8+bN3HvvvZibmxMfH4+7uzsAwcHBBAQE8O2333Lo0CE8PDzo1q1buda1YqtXr2b//v3s27ePRYsWkZJimN/81KlTTJs2jSNHjtC8eXOWLl1abfmkSZM4ePAgbm5u7N+/nzVr1rB792527drFypUrOXjwIMePH2f+/PlER0dz+PBhPvzwQwBOnz7NzJkzOX78OA4ODnz11VfExcURGRlJbGwshw4dQqPRGJP+4m2//vpruW2KoihlFRZKjl/KYFVMAlPX7sP/zV+Z+uk+AMzMBE8Ee/BBmB875/Zj++hC3rGNJOjnB+i76wn47hk4vwu87oexqw3J8dRouOdl6NBHzWBRxxr1q5+R6Uh85i5ybuRj06zi7hXN7x9B2mefkbTjAs2HWWIW/SY8/EntBqooxdbcX77MO9SwPPveVXDiW0NrA0BBLpz4Br6xhtCPDIvsfDmp9LGPb672lPb29ly/fp2UlBQuX75MUFAQaWlprFixgoULF5KcnIyDg0OpY06dOlVqtL9Go0Gr1Vb4qHvRokVs2rQJgAsXLnD69GlatWpF+/btjf1BJ0yYwKJFixg7dmyl5W5ubvTp08dYb0xMDKNHjzbOXztmzBh27NiBEIKxY8fi4uICgJOTE5mZmXh4eODn5wdAr169OHfuHOnp6ezfv984HZhOp8PV1RUwdDXZv38/gwYNwszMrNQ2RVGUwkLJmWvZdGlpuOc9F3mI7w5fAsDd2Zr7fFrRr7MLSAnJ/2OqRRQcj4LNMYb7t0YLbv04a9ebTsOmgWs3tRBIPdWok+Uujp04ll3AngtnGdzZq8J9hBC4znuBPx8dT7IMw/WBlw0b6qBfqKJUadu//0qUi8lCQwId+tFtV1vc93flypU88cQTnDhxgiNHjqDX6+nSpQtpaWnk5uYa909JScHe3h4Li9JfQG/cuIGlpWWpsu3bt7N161Z27tyJtbU1gwYNMtZVdhqu4t8rKy+7qEPxbANlVTbFV7NmzYw/azQadDodUkrCw8N5++23K6wnPDycl156qUaWSW5KbnbaNeXWVfZ3oJheYaEk7komu+JT2RWfwp6EVDJ0+ex5aQiuzS155O723OPlSu+OTrTW3oCE3+DMxxAVBZmJhkqc7zJ0peg0BNyDQGvDhe3b6dTSu06vTalao06W/Vp34esLsO/SyUqTZQBrf3+ajxhB6te/4jh1NhYA6x6CzEuGfqEzd4NWrb6k1IKqWoKH/gu2zIX863+VWVjDff8x/GzjfFMtyRUxMzPju+++4/fffycxMZEFCxbwzjuGOXEdHR3R6/Xk5uZiaWlJQkICbdq0KXV8SkoKLVq0KJdAZ2Rk4OjoiLW1NSdPniw1OOr8+fPs3LmTvn37sn79eoKDg6ssL2vAgAFMnjyZefPmIaVk06ZNfPbZZ2i1WkaPHs3s2bNxdnYmNTW10useMmQIo0aNYvbs2bi6upKamkpWVhZubm7GbVOnTsXOzq7UNuXmWVpakpKSgrOzs0qYTUxKSUpKSrkvqYppFBZKTl7JopW9JU42WjYdvMjzGwyL1xS3HPfp6Ix1M3Mo1BNs9Sdc3AoboyBxH0g9NGsOHgNgwPOGBNlR3T8aokadLPdt7wV7IC658n7LxVyfn0NWVBRJ7y2kbYuNcCODUv1CH15T8wErSlV6ToCzW+HUFsMjPHNL6DIc/O98BgqtVst9992Hubk5zZs3JycnhwceeMC4PSQkhJiYGIYOHYqXlxfJycn4+PiwYsUK+vXrx44dOxgxYkS5eocPH87y5cvx9fXF09OzVDeKrl278umnnzJ9+nTuuusunn76aZKSkiotL/dy9OzJ5MmTCQw0TA355JNP4u/vD8DLL7/MwIED0Wg0+Pv78/rrr1d43d26deOtt94iJCSEwsJCLCws+Oijj3BzczNuCw0NBSi1Tbl57dq1IzExkWvXrtVpHMVf9uqz24nR0tKSdu3UksWmUJwcG2arSGF3Ucvxv0d3Z3zvDvS/y4X3w3rQ28OZNg5WkHkZzkbBd1EQvw10aYCANn4QPBs6D4V2d6tZthqBRp0st7RxQRRacyH7z2r3tWjbFqfJk0n5739xCsnFyqlEv9D//QQH1hmSFUWpS6M+go96Q0Yi2LSAUUtMUu2hQ4eMPz/xxBM88cQTpbbPmjWLhQsXMnToUGxtbdmzZ0+p7Rs2bODdd98tV2+zZs2MizqUdO7cOczMzFi+fHm5bRWVu7u7VzhH8pw5c5gzZ0658vDwcMLDw0uVlTz+73//u/HnsLAwwsLCytVRvG3EiBGqG8YdsLCwwMPDo67DYPv27cYvU/VVQ4ixMSlOjvWFku7t7EnX5TNikWFhIjdna4Z7t6JPJyeCOhvGP7hawejmp2HPcjgTDUnHDRXZtoQu9xmWk+442PCUT2lUGnWyLISgg50HWk3lj2FLcp46lfS1y7m63wa3obq/+tnnX4eo11WyrNQ9rQ08tuGv/vS11D3I39+fwYMHo9frjXMtF8vLy+P+++9Xy/sqilLvnbySyR9nSrccD/ZswZrHA3Gy0bJiYi982tobWo6lhJQzcPwTQwtywg4o0IGZBbj1NXSN6zwEWvqogXmNXKNOlgF6tfFk+4XtN7WvxtYG1wkPcHnlZjLPW2LvVjSoycLa8EehKPWBa1eYWX5hhJo2ZcqUCsu1Wi3jx4+/pboqaymurFxRFKUq3xy8yLs/n+JSuo42DlbMHeZJcyk5cSmTs9eyebCHYZzFK5uOse/PtFItx709/moJDulkBfG/wo4oQ+txxnnDBqdO0HNi0cC8YGhmWxeXqdSRRp8st7VxIzU3lT/TknBzrH7aJ/vn/kPq99tIOqzHrm0uZloLk/ULVRRFURTFtL45eJEXvz6KLt+waNDFdB1zvjyEuYC8n3dgoRHc260llhYa/jXKG0drraHlGKCwEC4fhMPRhtbjC3sMA/O0doaBecHPGhJkp7rvSqTUnUafLGsLWwHw0/+OMr33kGr3FxoNLd9ayPknnyLttC3OfRxN1i9UURRFURTTevfnU8ZEuVihBGEGCx/pQe+OzlhaGLqPebexh6wrcGgTnCkamHfdsFASrXtA8HOG5Lh9oBqYpxg1+mQ5sL0XHIFjSaeB6pNlAJvggVj5eJJ5+QzOj21Q08YpiqIoSj11KV1XYfkNPYzp2Q4KbkD8b4aW4zPRcPWoYQebFtD53r8G5tm2qMWolYbEJMmyEGI48CGgAT6WUr5TZrs9sA7oUHTOBVLKWpmLzdPJDaSGhIyEWzrOduhwrn3wIQU7VmE+6Glw7lRDESqKoiiKcquklKz4PZ7yy7JI3MUV7mt2FCI+hXMxkJ9jGJjXoQ8M+WfRwLzuULQok6JU5Y6TZSGEBvgIuBdIBPYKIb6TUp4osdtM4ISU8kEhRAvglBAiQkqZd6fnr47GTIMlrUi6ceGWjrMJ7s+1Dz4k57t12Ld2h36zaiZARVEURVFuScb1fJ7fcJitcVfp0a45iVeT6KU/ygCzIwwwO0IHs6J5vZM9wO9RQ9cKj/7QTE0Dqdw6U7QsBwJnpJTxAEKIL4BRQMlkWQJ2wrB8ky2QChSY4Nw3xVnbjsScs7e05Kplt65onJ3JTjPH/syvKllWFEVRlHogJfsGoUtjuZyey7/u68ik9KXIlM8x0xSQI5txUONLms9T6Kza0ue+R+s6XKURMEWy3BYo2WybCPQus88S4DvgEmAHhEkpC01w7psS5NaNDWf2kltwAyuLm1sdSZiZYRscRPbWn5AJfyBuZKupYhRFURSljjnZaBnWrRWjPPR0j5kOlw8jAqZCt1HYtO9NsLkWMCzyoiimYIpkuaKm2rJdiIYBh4B7gE7Ar0KIHVLKzHKVCTENmAbQsmXLW36zZ2dnlzvGKqcQSSGbtn1NG22bm67L0sUF+5w8cpMlZ77/iBSXst8Bal9F19dYNMVrs7e3Jysrq/YDMjG9Xt8orqMiN3Ntubm5jfa9qyj1Qc6NAt7afIIn+3ekUwtbXumWZFicqbAAHo0Ez+F1HaLSiJkiWU4E2pf4vR2GFuSSHgfekVJK4IwQIgHwAvaU2Q8p5QpgBcDdd98tBw0adEvBbN++nbLHtEh25dPNn5LpaMn4gJuvr6BHD06vXkN2qivdPVpCr1uLpSZUdH2NRVO8tri4uHq9lLJOp2P48OFER0ej0WhITEwkNjaW0aNHM3ToUKKjozE3NycrK6vWriM9PZ3PP/+cGTNm1Mr5bubaLC0tG9QyxfV5ULailHUmKYun1x3gzLVserS1p9P/VsPWf4JLFxj3uRqAr9Q4UwwD3QvcJYTwEEJogXEYulyUdJ6ieduEEC0BTyDeBOe+Ke7N3QDYevboLR1n7uiIpW93cgp8odfkGohMUeq31atXM2bMGOMS11FRURw4cACtVsuQIUOIjIys9ZjS09NZunRprZ+3sSgxKPs+oBvwqBCiW5ndigdl9wAGAe8V3d8VpVZ9e+giI5fEkpqTR8Sk7ow7/zr8+ip0fRCejFKJslIr7jhZllIWALOAn4E44Esp5XEhxFNCiKeKdnsT6CeEOApEAS9IKZPv9Nw3y0Zrg3mhE5evn7/lY22D+6M7coSCtDQo1Fd/gKI0MEePHiUoKMj4+4EDB7jnnnsAiIiIYNSoUQDExMQwZ84cNm7ciJ+fH6GhoURERFRa77p16wgMDMTPz4/p06ej1+vZu3cvvr6+5ObmkpOTg7e3t3F569DQUHr16oW3tzcrVqww1rN27Vp8fX3p0aMHEydOZN68eZw9exY/Pz/mzp1b6bmUShkHZRfNSFQ8KLukOh2UrSgA3x2+xLNfHMK7TXN+mtSOftvC4MQ3MPR1ePhTNY5IqTUmmWdZSvkj8GOZsuUlfr4EhJjiXLfLwaItKbqyvUOqZzugP8kffUTOPwdjHzYFgv5WA9EpSt3x9vbm7Nmz6PV6NBoNzz//PO+99x55eXnEx8fj7u4OQHBwMAEBASxYsAAfHx9j8luRuLg4IiMjiY2NxcLCghkzZhAREcGkSZMYOXIkr7zyCjqdjgkTJuDj4wMYWrGdnJzQ6XQEBATw0EMPceXKFebPn09sbCwuLi6kpqaSmZnJsWPHOHToULXnUipk0kHZdzrOpLY0hDERDSFGqPk4i2eustRLxnlqCbP7A4fPFpKPGSe6/5O0Aj/47bc6j9NUVJymVRNxNvoV/Iq1tXHjWv5JUnNycbK5uRkxACx9fNA4OJBzPscwhZxKlpUa8p89/+Fk6kmT1unl5MULgS9UuY+ZmRne3t4cP36c06dP06FDB3r27MmlS5dwcHAote+pU6fw9PQEQKPRoNVqKxz8FhUVxf79+wkICAAMfZ9dXV0BeO211wgICMDS0pJFixYZj1m0aBGbNm0C4MKFC5w+fZq9e/cyduxYXFxcAHByciIzM/Omz6VUyKSDsu90nEltaQhjIhpCjFCzcUbFXWVR9Bk+eyKQ5loNITveg23zoZUPhK2jh6N7vYjTlFScplUTcTaZZLmLUycOZ+azLzGBEM+uN32c0GiwCQoi+/etyHM7ETey1KTmSqPTp08fYmNjWbp0KT/99BMAVlZW5ObmGvdJSUnB3t4eCwsLY9mNGzewtLQstR8YWobCw8N5++23y50rNTWV7Oxs8vPzyc3NxcbGhu3bt7N161Z27tyJtbU1gwYNIjc396bmRq/qXEqFTDooW1FMoUBfyHu//o9l28/i3aY5ORlpNI9+Dk5thu6PwIMfgta6rsNUmqgmkyzf09GHDefAxjb1lo+16R9M5ubN5KaAVfxv0PUB0weoNHnVtQDXpD59+jB58mRmzpxJ27ZtAXB0dESv15Obm4ulpSUJCQm0afPX1IspKSm0aNECCwuLcsnykCFDGDVqFLNnz8bV1ZXU1FSysrJwc3Nj2rRpvPnmmyQkJPDCCy+wZMkSMjIycHR0xNrampMnT7Jr1y5jPaNHj2b27Nk4OzuTmpqKnZ1dqdbsqs6lVMg4KBu4iGFQ9vgy+xQPyt5RF4OylaYlKTOXZ9YfZHdCKo8GduD1vuY0+3IEpMbD8Heg91NwkwuKKUpNaDLJspdLZwDOZZ4jqG1QNXuXZhscDEDOteZYnf5FJctKo+Pl5UWzZs144YXSCXtISAgxMTEMHToULy8vkpOT8fHxYcWKFVy6dIkRI0ZUWF+3bt146623CAkJobCwEAsLCz766CN+++03zM3NGT9+PHq9nn79+hEdHc3w4cNZvnw5vr6+eHp60qdPH8DQn/rll19m4MCBaDQa/P39+eSTTwgKCsLHx4f77ruPd999t8JzqWS5YlLKAiFE8aBsDbC6eFB20fblGAZlf1I0KFtQy4OylabltW+PcyQxg4WP9GCM1SFY8xSYN4Pw78A9uK7DU5Smkyw7WzpjaWbLD3GHeKzrY7d0rLmLC5bdupGdk45LFzXxudL4fPjhh7z99tvY2NiUKp81axYLFy5k6NCh2NrasmfPX0/hx4wZU2XXh7CwMMLCwkqV9enTxzjwTqPRsHv3buO2LVu2VFhPeHg44eHhpco+//zzas+lVK4hDMpWGrfCQokuX49NM3NeH+lNRk4unnGL4bsF0LYXPPIZ2Let6zAVBTDNPMsNghACrWxJXPKZ2zreZkB/dGevom+jvuUqjcfZs2fx8vJCp9OVS0gB/P39GTx4cLmp2PLy8ggNDTUO9lMURblZ6dfzeHLtPp5at5/CQkkrrQ7P6CdgxwLwnwiTf1SJslKvNJlkGaCVlRv5mqvo8m59Dlbb/v1Bryfn501w8UANRKcota9Tp06cPHmSVatWVbrPlClTjIuSFNNqtWpqNkVRbtnhC+ncvyiGHaevcW+3loikY7BiEMT/Bg+8DyMXg8XNz1ilKLWhSSXLnRw6YmaexdHLl2/5WKsePTCzsyP7i/fhl1drIDpFURRFaZyklHz6xznGLv8DgA1P9WOS7T7EqhDIz4XHf4S7p6iBfEq91KSSZd+WdwGwJ/HW57IV5ubY9OtHzkUz5PldkJth6vAURVEUpVHKulHA8t/OEtzZhR9m9sHvxLvw1RPQyhem/wbtA+s6REWpVJNKlgPbeQGGGTFuh+2A/hSk67iRBsRvN1lciqIoitIYxV/LJl9fSHNLCzY+3Y9VYz1w/DoMdi6BgKkQ/j3YtarrMBWlSk0qWe7o0AFzM3PaupZfcexm2BinkHOA07+aMjRFURRFaVS+PpDIiEU7WBJtGFjf9vpJzD4eDOd3Q+gyuH8BmGvrOEpFqV6TmToOwNzMHDc7N+Izbm9ufYuWLWnm6Ul26iWc47eDlKp/laIoiqKUkJuv51/fH2f9ngv09nDisd4d4NDn8P1zYOsKT/wMbfzrOkxFuWlNqmUZwFq05o/zcRToC2/reNv+wVy/oEM/YYtKlBVFURSlhPMp13lo2R+s33OBpwd1IuJxf1x3vALfPA0desO07SpRVhqcJpcs25u35QbXOJt8ewP0bPoPgIICrh/5n4kjUxRFUZSGLetGPteybrAq/G5eCHLEfF0o7F0JfWfBhE1g41LXISrKLWtyybJ3i7sQopDdF24v2bX298PM2prsTZ/ATy+ZNjhFURRFaWDy9YVsOWqYktW7jT2//2MwQ2z/hP8OgMuH4aFVMGw+aJpUz0+lEWlyyXJA0YwYR5JuL1kWWi3W/fqSvf8Ectdy0KWbMjxFqTd0Oh0DBw40rt6XmJhIZGQkYFjBb8CAARQUFNRqTOnp6SxdurRWz6koSuWuZOQyfuUuno44wMHzaSAlloc/hTUjDIuLPPErdB9b12Eqyh1pcsmyT4vOAJxNS7jtOmyD+1OQdp28DKGmkFMardWrVzNmzBjj6n1RUVEcOGBYvVKr1TJkyBBj8lxbVLKsKPVH7Jlk7l+0g+OXMvlwnB/+ra3gu2fgh9nQcSBM3QatfOo6TEW5Y00uWbaxsKEZTuSZXbntOmz7G6aQy062V1PIKY3CPffcg5+fH35+flhaWrJhwwYiIiIYNWoUADExMcyZM4eNGzfi5+dHQkICoaGhREREVFjfunXrCAwMxM/Pj+nTp6PX69m7dy++vr7k5uaSk5ODt7c3x44dAyA0NJRevXrh7e3NihUrjPWsXbsWX19fevTowcSJE5k3bx5nz57Fz8+PuXPnVnouRVFq1srf45mwajdONlq+mxXEKA8Jn4yAg59B/7/D+C/B2qmuw1QUk2iSHYj8W3chKy/1to+3aNsWbadO5KRew/nMVjWFnGISV/79b27E3frqklVp1tWLVi9V37c+OjoagGXLlrFt2zZGjhzJM888g7u7OwDBwcEEBASwYMECfHwMLUXFCXBZcXFxREZGEhsbi4WFBTNmzCAiIoJJkyYxcuRIXnnlFXQ6HRMmTDDWtXr1apycnNDpdAQEBPDQQw9x5coV5s+fT2xsLC4uLqSmppKZmcmxY8c4dOhQtedSFKXmtHawJNSvLfNH+2B9aRd8Eg4FNyBsHXR9sK7DUxSTapLJsoe9B9+e+RYpJeI2k1zb/v1JW/cZhc07YaZLU9+glQZv7dq1bNmyha+++opr167h4OBQavupU6fw9PQ0/q7RaNBqtWRllV7kJyoqiv379xMQEAAY+j67uroC8NprrxEQEIClpSWLFi0yHrNo0SI2bdoEwIULFzh9+jR79+5l7NixuLgYRs87OTmRmZl50+dSFMW0DpxP41xyDk7AA75teKB7a9i9HH5+GZw6wrgIaOFZbT2K0tA0yWTZRrThesF1Np84yQPeXW+vjv7BpH7yCTld/oGdSpQVE7iZFuCaUtzt4ttvv8XCwgIrKytyc3ON21NSUrC3t8fCwqLUcTdu3MDS0rLUvlJKwsPDefvtt8udJzU1lezsbPLz88nNzcXGxobt27ezdetWdu7cibW1NYMGDSI3N/emvsxWdS5FUUxDSsma2HP8+8c43JytedFfQt51+P5ZOPoleN4Po5eDZfO6DlVRakST67MM4OXcCYB9l27/kbf13XcjrKzI+X0H5OWYKjRFqXU//PADS5cu5euvv8bS0hIAR0dH9Hq9MQlOSEigTZs2pY5LSUmhRYsW5RLoIUOGsHHjRpKSkgBDgvznn38CMG3aNN58800ee+wxXnjhBQAyMjJwdHTE2tqakydPsmvXLmM9X375JSkpKcZ67OzsSrVkV3UuRVHuXFZuPjM/P8AbP5xgkKcrXz8dhO2NJFgdAkc3wOBXDF0vVKKsNGJNMln2a9UFgP+lnr3tOsyaNcMmMJDsqB/hPx6gSzNVeIpSq8LDw0lMTCQoKAg/Pz9WrVoFQEhICDExMQB4eXmRnJyMj48Pf/zxBwDbtm1jxIgR5err1q0bb731FiEhIfj6+nLvvfdy+fJl1q5di7m5OePHj2fevHns3buX6Ohohg8fTkFBAb6+vrz66qv06dMHAG9vb15++WUGDhxIjx49mDNnDs7OzgQFBeHj48PcuXMrPZeiKHdOl6dn1Eex/Hz8Ki/e58XKSb2wv7yDXvufh/TzhkF8A+eCWZNMJZQmpEl2w3C1dsVMWnIx585aoGwG9Cf7t9/ISy9Ae3Yb+IwxUYSKUnuKW27LmjVrFgsXLmTo0KHY2tqyZ8+eUts///zzSrs/hIWFERYWVqqsT58+xoF3Go2G3bt3G7dt2bKlwnrCw8MJDw8vd97qzqUoyp2z0moYF9Aev/aOBLo7QuwHEPUGN6zbYzFlExQ9pVWUxq5Jfh0UQmCnaUta/sU7qse2f38AspMd1RRySqPj7+/P4MGDK5yKLS8vj9DQ0FID/hRFafhy8/W8+PURdscbvkRPG9CJwDZa2BAOW1+HbqM46P8flSgrTUqTTJYBOtp7oLVKpkBfeNt1aDt0QOvmRnaaK5zZCoW3X5ei1EdTpkwxLkpSklarVdOzKUojk5Ccw+ilf7B+zwWOJGYYClPOwsdDIO57uPdNGLsGvblV3QaqKLWsySbLAzy8uSHTyNVfv6N6bPr35/q5bAozkuDKERNFpyiKoii1Z8vRyzy4OIbL/8/efYdHWWUPHP/eqZnJpAcCSQiE3iFUlSKIKIquveva0d/a3dXV3XV11y67q4t10bWt2EVsCCoYiqggRXoNLQkJOlf5nQAAIABJREFU6WSS6XN/f0yAiCiEzGRSzud58oR55517zgskOblz33OrXLxy9XCuH9sVNs2B6ePBuReu+BBG3Sp7Cog2qc0Wy9kJ2QBsKjv2m/wAHGPHoL1+arOmQFzHcKQmhBBCNJlvtpbyfzNW0L29g89uHcP4HqmQ+xi8dREkdYYbFkDXcdFOU4ioabvFcnyoWH6+7s7+Y2UfPhxlsVBTlgxxaeFITbQxWutopyAaQf79REsVCIb+7x7fNYVHzhnAuzccT0aMF96+FHIfhUGXwLVfQGJWlDMVIrrCUiwrpSYppTYppbYqpe75hXPGKaVWKaXWKaUWhCNuY3SK7wTawM7qHY0ax2CzYR8xAueCBbDmfWkhJxokJiaGsrIyKbhaKK01ZWVlB/pTC9FSLNhcwsQnF1BQ6cJgUFw6MgtL+WZ48STY+iWcNhXOfh7Msj5ZiEa3jlNKGYFngYlAPrBMKfWx1np9vXMSgeeASVrrXUqpqO9HazaYsak0ytz5jR7LMWY0xY8+hve1KViunA4Dzg9DhqItyMzMJD8/n5KSkmin0ihut7vVFoxHuraYmBgyMzObMCMhjl0gqPn3vC08PX8LPdvH4fPX3Zi+/iOY9Tsw2+HKT6DzCdFNVIhmJBx9lkcAW7XWeQBKqbeBs4D19c65FJiptd4FoLXeG4a4jdY+phPbPTtw+wLEmH9+x//Rih0zFh59jJqyZCxbvpRiWRw1s9lMdnZ2tNNotNzcXHJycqKdRkS05msTbUup08Ptb69i8dZSzhuSyUNn98dmItQSbvGTkDEMLvofxKcfaSgh2pRwFMsZwO56j/OBkYec0xMwK6VygTjg31rr1w83mFJqCjAFIC0tjdzc3AYl43Q6j/o1Dl8cylLKm7Pn0TXB0qA4P6E1qSkplBW5id3wOUu+ng8qMsvBG3J9LY1cW8vVmq+vNV+baFuenreFpTvKefy8AVw4rBPKVQHvXAvb5sPQq+C0J8BkjXaaQjQ74SiWD9dH5tAFmCZgKDABsAHfKqW+01pv/tkLtZ4OTAcYNmyYHjduXIOSyc3N5Whfs/3HEtatmkffIZ04rlOfBsU51J5TJlI18wNM7irG9UyEjCGNGu+XNOT6Whq5tparNV9fa7420fpprams9ZEUa+GuSb25eEQWfTrGQ9EaePsyqN4DZ06DoVceeTAh2qhwTH/mA53qPc4ECg9zzhytdY3WuhRYCAwKQ+xGGZbeG4BavafRYznGjEF7fLhKrbDr20aPJ4QQQjRGlcvHDf9bziUvfofbF8BhNYUK5dXvwUsTIeCDqz+XQlmIIwhHsbwM6KGUylZKWYCLgY8POecjYIxSyqSUshNaprEhDLEbpUtCFwB+KNzY6LFiR44Esxln+g1w/E2NHk8IIYQ4VmsLqjjz6cXM37iX84dmYjUZQsXxnHth5nWQnhPqn5w5LNqpCtHsNXoZhtbar5S6GZgLGIGXtdbrlFI31j3/gtZ6g1JqDrAaCAIvaa3XNjZ2Y8VZ4jCTwPurV3D3cY0byxAbi33oUGqW/hie5IQQQogG0lrzzrLd/PXjdSTbLbxzw3EM7ZwMzhJ47yrYuRhG3ginPARGc7TTFaJFCMeaZbTWs4HZhxx74ZDHU4Gp4YgXTsnmTPa4CvEHgpiMjZtod4wZw96pU/G9dDnmURdDnzPClKUQQghxZL6A5vVvdzIyO5mnLhpMisMKBcvhnSugtgzOmQ6DLop2mkK0KG12B7/9Ojm6oCwl7CyrafRYsWNGA+D89rtQz0ohhGiGWuJGUuLX5ZU42ef2YTEZ+N+1I3j16hGhQnnF/+Dl00AZ4Zq5UigLcQzafLHcO7U7yuhmZcGuRo9l7dEDU4cO1FR2gG3zIBgMQ4ZCCBE+9TaSOg3oC1yilOp7yDn7N5L6jda6H3BBkycqjtonPxZy5tOLefjT0K1AKQ4rxqAPPr0DPr4ZOh8PU3IhfXBU8xSipWrzxfLQ9F4ArCz+WRe7BlNK4Rgzmpo8J9pZBoUrGz2mEEKE2YGNpLTWXmD/RlL1NcuNpMRPefwB7v9oLbe8tZLeHeO5fWKP0BP79sBrZ8APL8Oo2+CyDyA2JbrJCtGChWXNckvWv13om0vH1OqwjBc7ZgyV772Pq9SKfcsXkDk0LOMKIUSYNKuNpJpKS9hcpiE5lrmCPLvKQ15VkFO7mLigp4dNK79nT9UG+q17HJPfxca+d1FiHg2LFkctz2iSPMOrLefZ5ovlNHsaNpON6kBBWMaLPf54MJlwBgZht8tv8kKIZqdZbSTVVFrC5jINybGoys3Ta7/lhct7M6l/R9Aalr0EC/8CiVlw0Wz6pfU98kARzjOaJM/wast5tvliWSlFZmxnlhZsRGuNUof7OXL0jHFx2AcPxrm3hvYjp4QpSyGECJuj3UiqVGtdA9QopfZvJNX49WrimAWCmg9W5HP+kEw6JMTw1Z0nhro4+dzw2Z2wagb0OAXOfRFsidFOV4hWo82vWQYwBzuwuXwbxfs8YRkvdswYPBs24CvaAzVlYRlTCCHCpMVuJNWWlVR7uOK/33P3+6uZvzG0hNxkNEDlbnhlUqhQPvGPcMk7UigLEWZSLAM9krthMFexdk9JWMZzjB0DQM3fJ8Hnd4dlTCGECAettR/Yv5HUBuDd/RtJ1dtMagOwfyOppTSTjaTaqu/zypg8bRErdlUw9fyBnNw3LfTE9oUw/UQo3QoXvwXj/wQG+bEuRLi1+WUYAIPTevLRTlhesJGTe3c68guOwNq7N8Z2qdSUKhK3zYNgAAzGMGQqhBCN15I3kmpr3vx+F/d9tJasZDuvXzuC3h3iQ+uTv30WvvwrpHSHi2dAao9opypEqyW/ggKDOoS+yawv2xqW8ZRSOEaPwbnNia6pgGk5sFfewRRCCNEwvTo4mDygIx/fPCpUKHtr4IPr4Is/Q+/T4fp5UigLEWFSLAOd4zuDNrCremfYxnSMGU2wxoWr3AyVO2HGBaFvckIIIcSvWJNfxfSF2wAY2jmZaZfkEBdjhvLt8N9TYO0HMOGvcOH/wBoX5WyFaP2kWAYsRgsdYzPo3ckVtjFjTzgBFNTsiQkdqCmBj24O2/hCCCFaF601b3y3k/OeX8JrS3ZS7fYdfHLLVzB9HFTlw2Xvw5jfQyO7Nwkhjo4Uy3V6JXejyNX4La/3M+Z9ii3Vj3OPNXTA74bNc2DFG2GLIYQQonWo8fj5z2oPf5m1luO7pfDpLaNDs8law8J/wIzzISEztG11j5Ojna4QbYoUy3U62LPIq9zB1r1V4Rlw3gPEptXiLjfjd9f9NftqYd4D4RlfCCFEqxAIai6a/i3f7wnwh1N68spVw0mKtYCnGt65HOY/CP3Pg2u/gOTsaKcrRJsjxXKdNFsWQfx8uSVMN+JNeABHJwUoaorqZpfNdjj5b+EZXwghRKtgNCiuG92Vu4bHcPNJPTAYFJRugRcnwKbP4dRH4LyXwBIb7VSFaJOkWK4zpGMvANYUbwnTgJcTc9wEjNbgwaUYPU6BnMvCM74QQogWy+MP8JdZa5i1sgCAs3My6JtS12J042x48SSoLYXfzoLjb5L1yUJEkfRZrtMtMfTW1vaq7WEbU53zHLH/G07NbitagxpyZdjGFkII0TLtLq/ldzNWsKagiuRY68EndBDmPwwLn4D0nFC3i8TG9/4XQjSOzCzXSbAmYCaBvZ7w3eSHJRbHJbcR8Bhxl8fA9gXhG1sIIUSL89X6YiZPW8SOshqmXzGUOyf2DD3hqmTAmodChfLgy+HqOVIoC9FMSLFcT4olEzd7cPsCYRvTMfkiMBqpdnaFLV+GbVwhhBAty8aifVz3+g90Srbz2S1jOKVfh9ATxevhxfEkVfwIk/8JZz0D5pjoJiuEOECK5XqO69SbxIRKrKbw/bUYExOx5+Tg3G2Effngqgjb2EIIIZo/rz8IQO8O8Tx9SQ4f/N8JZKXYQ0+unQkvnQzeGlYNfgiGXyfrk4VoZqRYrqdXcnf2efdR7i4P67iO8ePx5Jfhu2wx2JLCOrYQQojma8m2Usb/I5fV+ZUAnDkonRizEQJ++OI+eP9q6NAfpixgX0KfKGcrhDgcKZbr6RLfBYDXf1ga1nEd48cDUL1wUVjHFUII0bzMWlnAqMfmk33PZwx8YC6Xvvg9MWYDNrPx4Ek1ZfDGubBkGgy7Fq78FOI7Ri9pIcSvkmK5nq6JXQFYuGN9WMe1ds3G0rkzzk/ehRfGgN8T1vGFEEJE36yVBdw7cw0FlS40sM/tx6gUU8Z0pUdaXOikwlWhbat3fQe/eQbO+BeYLNFMWwhxBFIs19MhtgMGLOyp3Rn2sR3jxlG7dhuB3Wtg5zdhH18IIUR0TZ27CdchN4gHtGba/K2hBz++DS+fCjoA13wOQ66IQpZCiIaSYrkegzKQYMqgOlCIPxAM69iO8ePR/gA1JQ7piiGEEK1QYaXrsMf3VlbD7LvhwxsgczhMWQAZQ5s4OyHEsZJi+RDpsVlgLmZ3xeG/6R0r+9AhGOLicFZ1gi1fhHVsIYQQ0ZcaZ/35Map4z/YYLP0PHHcTXDELHO2ikJ0Q4lhJsXyInkndMFgqKayqCuu4ymzGMWYMzu1edOlWKNsW1vGFEEJEj9sXAK2p3/QtR23hM+uf6G/Ig3NfgkmPgFE2zhWipZFi+RCjsvoCkJK0L+xjO8aPJ7CvFnfiJAiGb+MTIYQQ0fXUV1socXq54cSuZCTauMQ4n3esD+KIjcV0/Vcw8IJopyiEOEZhKZaVUpOUUpuUUluVUvf8ynnDlVIBpdT54YgbCdmJ2QBsr9oe9rEdY0aHdvPjeGjXM+zjCyGEaHqr8yt5cVEeFw7L5J7T+vDNcct41PwSlm5jib15EXQYEO0UhRCN0OhiWSllBJ4FTgP6Apcopfr+wnmPA3MbGzOSOsd3BhTPLV4S9rEP7OaXmwulW8EX3nXRQgghmpbXH+Tu91eTEmvhz5P7QtFaWPA49D8fLnsf7MnRTlEI0UjhmFkeAWzVWudprb3A28BZhznvFuADYG8YYkaM1Wgl1tCO7fu2o7UO+/iO8ePxbNqE7/ERkLcg7OMLIYRoOkGtOa5rCg+fM4AEqxE+uQ1siXD6VDAYjzyAEKLZC0exnAHsrvc4v+7YAUqpDOAc4IUwxIu4NFsWQVMxxfvCv3nIgd38iuNhS7OeZBdCCHEEMWYjD/ymHxP7psHyl6HgBzj1EZlRFqIVCcdtueowxw6dkn0K+KPWOqDU4U6vN5hSU4ApAGlpaeTm5jYoGafT2eDXHMpbFYvBUspxj35JSoyR83qaOSHd3Kgx60tp357yon3Y13zCd7G/gSP8ndQXjutrruTaWq7WfH2t+drEsQsENb9/dxVXHN+FoZ2ToLoIvvobZI+FgRdFOz0hRBiFo1jOBzrVe5wJFB5yzjDg7bpCORU4XSnl11rPOnQwrfV0YDrAsGHD9Lhx4xqUTG5uLg19TX2zVhawoywVU5ofZa6gzJ3C/zYE6NunL2fnZBx5gKNQfNppVMx4A7OzlHH9OkD7Pkf92sZeX3Mm19Zytebra83XJo7dy4u3M2tVISf1SQsVy3PuAb8HJj/ZoAkQIUTzF45lGMuAHkqpbKWUBbgY+Lj+CVrrbK11F611F+B94HeHK5Sbg6lzN+F1hRrGGywlALh8AabO3RS2GAd28yu2ygYlQgjRwmwvreEfX2xiYt80zhzYMbQr67oPYewfILV7tNMTQoRZo4tlrbUfuJlQl4sNwLta63VKqRuVUjc2dvymVljpIuCtK5ate39yPFwO7OZnnQQ5V4RtXCGEEJEVDGr++MFqLCYDD53dH+VzwWd3QmpPGHVbtNMTQkRAWLYS0lrPBmYfcuywN/Npra8KR8xISU+0UVAJQX8sRmsxvnrHw+XAbn7ff4+OSTzsom8hhBDNz2dr9rB0ezlPnDeQtPgY+PJ+qNwFV30Gpp9vdy2EaPlkB79D3HVqL2xmI0F3JgZbqMmHzWzkrlN7hTWOY/x4AmVluGfcBzu+CevYQgghIuP0AR15+pIcLhiWCcXr4NtnYPDl0GV0tFMTQkSIFMuHODsng0fPHYAt2A2jdS9xdi+PnjsgbDf37XdgN79P3oZVb4Z1bCGEEOGltaaq1ofRoDhzUDpK61BP5ZgEOOXBaKcnhIggKZYP4+ycDJ4//1wA+napDHuhDPV28ytOhK1fQjAY9hhCCCHC4/3l+Zz0z1y2l9aEDix/BfKXwSkPS09lIVo5KZZ/wYDUAYBic9XaiOzkB3W7+RXX4isuhaLVEYkhhBCicfbuc/Pgp+vp2i6Wzsn2gz2Vu4yBQRdHOz0hRIRJsfwL7GY77a3ZuI157KlyRyTGgd38CmOkhZwQQjRDWmvu+2gtbn+Qx84biMGgYM694HfBGU9JT2Uh2gApln/FkLTBxDjyQUVmiYS1azaWzp1xlqWBc++RXyCEaFOUUvOUUqcfcmx6GMadpJTapJTaqpS651fOG66UCiilzm9szJZq9poi5q4r5o6Te9KtnQO2fAXrZsIY6aksRFshxfKvGJs1DL92Ux3Ij1gMx/jx1BYECJz4t4jFEEK0WNnAH5VS99c7NqwxAyqljMCzwGlAX+ASpVTfXzjvcUI99NusxVtLGJCRwPVjssFbG+qpnNIDRt8e7dSEEE1EiuVfMbj9YABmb/kuYjEc48ahfT5qvl0CEVobLYRosSqBCUCaUuoTpVRCGMYcAWzVWudprb3A28BZhznvFuADoE2/7fXIOQOYcf1ITEYDLHwCKnfCmU9JT2Uh2pCwbErSWmU6MrGqBF5cOp+bhl6BxRT+3y0O7Ob38t+Jd34A5xx2LxchRNuk6nZJ/Z1S6ipgMZDUyDEzgN31HucDI38SVKkM4BzgJGD4ryao1BRgCkBaWhq5ubmNTC8ynE5ng3LbXBEg3qLoEBv6vh/r3MHQ5dMo7jCBTTv8sOPox4pUjtEieYaX5BlekchTiuVfoZSie3w/1ng2sWHPPgZ1Sgx/jP27+S38Er1pDioYAIMx7HGEEC3Sgd+etdavKqXWADc1cszD3ZF26NtaTwF/1FoH1BFuYNNaTwemAwwbNkyPGzeukelFRm5uLkeb2z63j3v+tZC0BCuzfndCqKfyyw9DTAIdr3iRjrEpUc8xmiTP8JI8wysSecoyjCM4PnMIBksZ3+Rtj1gMx/jxBJw+3PlOyP8hYnGEEC2L1vo/hzxerrW+ppHD5gOd6j3OBAoPOWcY8LZSagdwPvCcUursRsZtMR6dvYG91W7+/pt+KKVgxauQvxROfRgiVCgLIZovKZaPYEyn0DuQi/NXRCzGgd38Cm3SQk4IEWnLgB5KqWyllAW4GPi4/gla62ytdRetdRfgfeB3WutZTZ9q01uytZS3lu7m+jFdQ+8mVhfDlw/U9VS+JNrpCSGiQIrlI+ib0heFkc1VayMW48BufiVJUiwLISKqbg30zYS6XGwA3tVar1NK3aiUujG62UVXrdfPH2euJjs1ljsm9gwdnLu/p/KT0lNZiDZK1iwfQYwphq7xPTEllEQ0jmP8ePZO/QFf+mmYtZZvykKIiNFazwZmH3LssHcXa62vaoqcmgOF4uQ+aZzWvyMxZiNs/QrWfgDj7oXUHtFOTwgRJTKzfBSOzxjKTucmfEFfxGIc2M2vurMUykIIEQU2i5H7z+zHiOzkUE/lT++ElO4w+o5opyaEiCIplo/CoPaDcAfcvLkycv2WD+zm99WXsPPbiMURQgjxU25fgOte+4EVuyoOHlw4NdRT+QzpqSxEWyfF8lEY3C60OcmMVQsjGscxfjy1S5cSePUC8HsjGksIIUTItHlb+GpDMU63P3SgeD0smQaDL4PsMdFNTggRdVIsH4UOsR2wqWQKXRsJBCO3y55j/Hh0QFOz2we7IzeLLYQQImRtQRX/WZjH+UMzGduzHQSD8OntYI2HiQ9GOz0hRDMgxfJR6hrfDx2zgy17qyMWwz4kB0OcA2ehXbpiCCFEhPkCQe56fzXJsRbum9w3dHDFa7D7e+mpLIQ4QIrlo3R8xlAM5koWbtsasRih3fzG4iyKRW+WYlkIISLp/eX5bNizj4fO7k+C3RzqqfzV/dJTWQjxE1IsH6VxnYcB8H3hyojGcYwfT6A2gHtjHlTujmgsIYRoyy4c1okXfzuMU/t1CB2Y+yfwSU9lIcRPSbF8lPqm9MVssNC7S3lE4zjGjgnt5pd+EyR2OvILhBBCNEggqKmo8WI0KCb2TQsd3DoP1r4Po++UnspCiJ+QYvkomY1m+qf2Y1XJqojGMSYkYB8yBOf3P0Y0jhBCtFWvfLOdCf9aQGGlK3TA54LPpKeyEOLwpFhugB7x/VlTsp5v8/ZENI5j3Dg8mzbh+++VoW/iQgghwmJHaQ3/+GITQ7IS6ZgQEzq4cCpU7AgtvzDHRDU/IUTzI8VyAwxOG4TGz6cbf4honAO7+c3/AnYsjmgsIYRoK4JBzT0zV2M2GHjo7AEopWDvBvjm3zDoUsgeG+0UhRDNkBTLDXB8xlAAVhRHdilGaDe/LJyFsdJCTgghwuStZbv4Lq+cP0/uQ4eEmFBP5U/qeiqf8lC00xNCNFNSLDdAqi0Vm2pHvmsDWkducxIAx/iTqN1rIbBuLkQ4lhBCtAUrdlYyqnsKFw2vu3l65euhDaBOeUh6KgshfpEUyw3ULb4fQesO8kqcEY1zYDe/TcVQuiWisYQQoi34xwUDefG3w0LLL5x74cu/QufRMPjSaKcmhGjGwlIsK6UmKaU2KaW2KqXuOczzlymlVtd9LFFKDQpH3Gg4Ln0oBlM1W8p3RTSOfUgOBkcsztL24CyOaCwhhGjNFmwuoagmiFIKu8UUOig9lYUQR6nRxbJSygg8C5wG9AUuUUr1PeS07cCJWuuBwIPA9MbGjZZTuo0EIGjZGdE4ymzGMfZEnCUJ6M6jIhpLCCFaq73Vbm59ayWvr/ccPLh1Hqx5L9RTuV3P6CUnhGgRwjGzPALYqrXO01p7gbeBs+qfoLVeorWuqHv4HZAZhrhR0SOpBzaTjVV7I3uTH9Tt5ldWhnvVSgj4Ih5PCCFam/s/WofLF+DyPtbQAempLIRooHAUyxlA/X2Z8+uO/ZJrgc/DEDcqTAYTadaevL1mEbVef0RjhXbzM1D92IWweW5EYwkhRGsze80ePl9bxO0n9yDdUffjbuE/pKeyEKJBTGEY43CLvQ7bvkEpNZ5QsTz6FwdTagowBSAtLY3c3NwGJeN0Ohv8moZK8LQjaF7Dy598Qf8Ue0RjJXXtSvWuTfgXvsbmYkeTXF+0yLW1XK35+lrztbVmFTVe/vrRWvpnxDNlTFcWL8qv11P5EumpLIQ4auEolvOBTvUeZwKFh56klBoIvAScprUu+6XBtNbTqVvTPGzYMD1u3LgGJZObm0tDX9NQzi0BflzyFcUOHzdHOFZZ3nb2PvEEWXvWkj7lRHIXLIj49UVLU/zbRUtrvjZo3dfXmq+tNbOaDZw1OIPzhmRiMhpAB+HTO8DqkJ7KQogGCccyjGVAD6VUtlLKAlwMfFz/BKVUFjATuEJrvTkMMaNqdKf9m5OsjHgsR90P6eotlVC8NuLxhBCiNbBbTNx3Rl/6pscD0HHPV7Dr27qeyqlRzk4I0ZI0uljWWvuBm4G5wAbgXa31OqXUjUqpG+tO+yuQAjynlFqllIrsftERlhiTiF11JL92Y8Q3J7F2zcaSlYmzIAZWvsHwpbeE3koUQgjxM9VuH5e++B0rd1UcPOjcS9e8V6HzKBh8WdRyE0K0TGHps6y1nq217qm17qa1frju2Ata6xfq/nyd1jpJaz247mNYOOJGU9/kAZjtu/D6gxGP5TjpZGpL7QRWfoi9djfMuAC8NRGPK4QQLc2jn2/ku7xDVvrN/TPGgAfOeEp6KgshGkx28DtGk3sej0dXU+TKj3gsx/jxaH+Qmh21KDTUlMBHN0c8rhBCtCRLtpXy5ve7uHZ0NjlZSaGD2+bDmnfZlXWe9FQWQhwTKZaP0aB2oU0Iv96xNOKx7GoDBksQ525j6IDfDZvnwIo3Ih5bCCFaglqvn3s+WEOXFDt3TuwVOuhzwad3QnI3dmWdH90EhRAtlhTLx6hbYjcMOoYXl34d8VhqwYM4OrhxFlo5sETaVwvzHoh4bCGEaAne/H4Xu8preey8gdgsdRMLi/4JFdvhjCcJGi3RTVAI0WJJsXyMDMpAe0svKoNb8PgDkQ024QEcWZqAx4i7zBw6ZrbDyX+LbFwhhGghrh6VzRvXjuS4rimhA3s3wuKnQj2Vu54Y3eSEEC2aFMuNMCB1IMpSzPJdeyIbaMjlOMaOBaWp2mUDZYSekyBH7uoWQrRtHn+AMqcHo0ExukddS7hgED69XXoqCyHCQorlRjgpewRKaeZujfy6ZePF/yG+m4GqPDsBj4ZJj0c8phBCNHdPz9vKxCcXUub0HDy46o1QT+WJD0pPZSFEo0mx3Agndh4KWrFi74+RD2aJJeXefxD0G6jYmQxVuyMfUwghmrG1BVU8v2Ab43u1J8VhDR10lsAX94V6KudcHt0EhRCtghTLjRBniaODvTNxCZFvHwcQM+p0PL17U7Erg2D7AU0SUwghmiNfIMjd768myW7hvjP6HHziiz+H+tCf8aT0VBZChIUUy400utMwdlRvIKgjvzkJQO0pE/GXlLDv44+htrxJYgohRHMzfWEe6/fs46Gz+5Nor+t0se1rWP0OjL4D2vWKboJCiFZDiuVG6pc8gGpfNfO3rWmSeN4+fbD27kXZkw+gP76tSWIKIURzorVmS3E1kwd0ZFL/DqGDPjd8dickd4Uxv49ugkKIVkWK5UYakDoYgLdXL26agEqRcs01eMsCOOd/CVUFTRNXCNFqKKUmKaU2KaW2KqXuOczzlymlVtd9LFFKDYpGnr9EKcVTF+fwr4vqpbXon1CeF1q5EQQ4AAAgAElEQVR+YY6JXnJCiFZHiuVG6pmcjSEYy6bK1U0WM/600zC1T6V8gx2Wv9JkcYUQLZ9Sygg8C5wG9AUuUUr1PeS07cCJWuuBwIPA9KbN8pd9vmYPeSVOAKymus1HSjbB4idh4MXQdVzUchNCtE5SLDeSUor21l5UBLbiDzTNumVlNpN81TXUllhxzXkN/J4jv0gIIUJGAFu11nlaay/wNnBW/RO01ku01hV1D78DMps4x8PaWVbDHe+u4ok5mw4eDAbhk7qeyqc+HL3khBCtlinaCbQG/VMGUuRbwYr8QkZ0bpqfKYkXXkDpM9MoW1lB5sbPoP+5TRJXCNHiZQD1e0/mAyN/5fxrgc9/6Uml1BRgCkBaWhq5ublhSPHntNY8scyN0kFOaVd1IE6HPV/Re9cSNva6haJla3/x9U6nM2K5hUtLyBEkz3CTPMMrEnlKsRwGE7qM4KuiV5mz9fsmK5aNDgdJl1xK2Suv4I0bgqVJogohWoHD9VPThz1RqfGEiuXRvzSY1no6dcs0hg0bpseNGxeGFH/uze93saF8DY+eO4BzR2SFDjpL4JkrofMoel/8IL1/pVVcbm4ukcotXFpCjiB5hpvkGV6RyFOWYYTB+OwhGJSRxMSmvdku6bdXgtFE+etvNGlcIUSLlg90qvc4Eyg89CSl1EDgJeAsrXVZE+V2WHuqXDwyewMndEvh4uH1Uv/iL9JTWQgRcVIsh0GsJZZeST1ZXdp0N/kBmNPak3DGGVS+9w7+mX9o0thCiBZrGdBDKZWtlLIAFwMf1z9BKZUFzASu0FpvjkKOP5FgM3PpyCweO3cgan9RnJcLq9+G0bdLT2UhRERJsRwmnWL78EPRKsqcriaNm3LN1Wivn4q334Oa0iaNLYRoebTWfuBmYC6wAXhXa71OKXWjUurGutP+CqQAzymlVimlfohSumitsVtM/On0PmSl2EMHfW749A7pqSyEaBKyZjlMOtn6EGAmc7as4rKc45ssrrVHD2KPG0rFyqWkfPcyhgl3N1lsIUTLpLWeDcw+5NgL9f58HXBdU+e136yVBUydu4nCShcmo+KWk7pz64SeB0/Y31P5illgtkUrTSFEGyEzy2Fyes9Qgbxg57Imj53yf7cS8BipevtVCPibPL74ZbNWFjDqsflcNaeGUY/NZ9ZK2URGiF8za2UB985cQ0GlCw34Appnv9528GunZHNdT+WLoNv4qOYqhGgbpFgOkx7JWRiC8WyqaJptr+uzjxhOTPdMylf50BtmH/kFoknU/6EPUFDp4t6Zq4+5YN5feGff85kU3qLVmjp3Ey5f4CfHPP4gU+duAq3h09vBEgunSE9lIUTTkGUYYaKUor2lJ0WuLQSDGoOh6e7MVkqR8n+3UfD7u6heX0x8/yYLLQ7hDwTZWFTN6vwqHvps/c9+6Lt8Qe54ZxVT524i0W4mOdZCot3CDWO70j8jgcJKF8t2lJMcayHJbiEp1kKS3czctUX86cO1B8YLFd6hX8zOzslo8usUIlIKKw9/30dhpQtWzYCd38BvngZHuybOTAjRVkmxHEb9kwdRtPcHNpcV0rtd0xYwcadOwvzkvymfOZ/4C69v0titUf01k+mJNu46tdfPitJAUJNX4mR1fhXpiTaO75ZCcbWHM55efMhoQTC6IBADGNHAcV1TqKz1Ul7rJb/CRa03VASv2FXBbW+v+lk+qQ7LYQrvAI/P2XhsxfLeDfDe1XDBK9C+T8NfL0SEpCfaDrwbU1/fBG+oVVzWCTD48ihkJoRoq6RYDqMrhozlqzn/pcC1kd40bbGsTCaSr7yS4ocfpvaDp7Cfd3uTxm9N9i+fONws7lmD03lszkZW7qpkXUEVNXVF7vlDMxmUZaPKv4Mpp1WBeS/vrV6BRxVhsJSiDD4AdMCKQTsosHcgMTmRXtZEEq2JLN+3gbyNSdhscfzztzZ0wE7Ab8fnjaHaZeSJORsPm+ueKjfj/5HLOzccR/u4GEqqPdgtRmKtv/Kl7a2BGRdAVX7o803fh97WFqIZuOvUXj/5+gOwmY1My/gKdjhDPZUNsoJQCNF0pFgOo36p/TAZTPxY8iMTsiY0efzE886l9F+PU/bCM9gnXwMx8U2eQ2twuDWTLl+AqXM3cdbgdBblbcFvLCan/z4stjI8qohVrl2MfLP4wPkKRWJCB7wVCfgquhL0JaGMHsxmFwO6mImL8VLlrmJH1Q6qPFU4fc5fzMdqtBLXMwa/z44tYGRMYDdLXWMo9vTCTjp9O3YgNdYKwL++3MQ7y3bTvb2DARmJDMxMYGBmAjlZSQfGy3/1GlKriolB464qovTVa8ic8s6x/4Xt3cDwpbdA33dlllo02v53Sg59Z6fbj89AxlBo3zvKGQoh2hoplsPIarSSZMzm3TWLuXPonU0e32C3k3jeZMremIVn7nNYz7qnyXNoDfavmVSmSoz2nRgsJRgsJVRYSxj55j24HKHn97jA4XfQJb4LIzqMoEtCF7rEdyE7IZus+CysRuuB5RwFlS4yEm3cNeHnyzkAfAEfVd4qKt2VVHp++lHlqeLHwgJW5e+im3E9K2KgOn4xdkLLPVYZ4rl6bne6JXYjIS2d80cnsackhgWb9/LBinyyku0svGsc1JQw+9VHOalkHjEqNNMdg4/kgq9ZMWsaQ8aeCTEJoQ+D8ej+supmqe21MkstwuekPu3pnGKnd4d4bJa6/4uLiyCtb3QTE0K0SVIsh1l7Sy/WeuZQ5XKRYGv6/p/JN/6B8rc+ovy1GXQ88255u/IYOGKr8cZ9iTnxB5QKorVC+5KwBNM4r8dJZCdkH/hIiUk5uKPYYZydk8HZORlH3KvebDSTaksl1Zb6i+fkT7+I1MISYvCyx2BlVVoOFSPOZqu7hG2V25i79WP2BT2hkxUkZRoYa00ltf1o3t1YRLdZtzHK5yNGBX8yrl15yF41FVbdd/CgNT5UNI++HYZfB7XlMPdPB4vpmMTQ53UfQk0JCg01e+Gjm0ProI+FrKMWdZbvrODqV5bx/o3HM6xLcuhgdRF0b/p37IQQQorlMBvRcQjraj5l9ublXDJodJPHN6WmkjBuCFVfL6fdio8xDTu7yXNoidYWVLGjspBV1R9g6PwB5oDGVzESX+Vwgt522Ewx3H/ugOh1nljxBplF8wAfWkOaz8PE7UsJVlQTOPNFgoYaAp9dRlVtDXsNcZRhpTqgqAlU4XV/iNvlJ8+bSpFH43BDrFdj8QNmjcGkKTUmk505kG2VNdhsBmLtBhyxYKndiGPn+xhwYViyCCNODNqJwRzEYNYYrGZU0BvK0e+BdTOhYDmk50BiJxh8Wajw9bkh4AkV2Icj66hFPbvLawHISq7bsc9bA95qcKRFMSshRFslxXKYTe55HK9shQU7f4hKsQyQfMf9VM47i/J3Z9FeiuVfVe328dCc7/ho+xuYk5ZiMsL5Pc4ly3Am078up9BTt3ziMN0wIsrngrwF6L0b8Kb/htpn/0ZtfiyuUgs+lxGC+2ezK+DV8+v+bAISsAN2fGAyYXTYMDiSCNituOMV6/Y5ccWVstPmo9yssPgM2Dxg8+yjtrwWm8uALgO/J4DH78ezuIBqPquXmL3uYz+NwawxWoOYYgKYbEFMtipMSSswqfmYyttjGgSmyh8xfn4DypYQKqITsyChExz/O0jqAjOngHMvoKGmpHEz1CCz1C3crrJaYswG2sWF1uJTXRT6HNchekkJIdqssBTLSqlJwL8BI/CS1vqxQ55Xdc+fDtQCV2mtV4QjdnPTq10nDIEkNlasjloO1u49cUw4icoFy0mtrcVgtx/5RW2M1po3l69j6nfP449dgiU5yBnZZ3HTkBvIcISK4itHhinY0d4A5yxBr/8U98IPqV3xI7XFCldpDAHPdMCEMcaAPdVDfJYrNKsbY8I47GIM/U7BEOvA4HBgdMRicIT+rKzWny0R2b6ygL/PXMbHht/TgVJWGdtxnfl6Th5iJSa2lLyqPLZVbqPWX4sKGrF5IU0n0NuaSZwribUb/Nhq7WQZ4xnu2cLQ6u8w+IIEPAb8LiOuSgu+vTbUZi/ggO+eB54PBVcZGB0WTLG1mKxrMZmXYlphxmR0YsrLxWTRmGKMGGM8GNbNQu0rhItnQGwqVBWEZhcTMo484xzOWWq5eTEqdpbXkpVsP/j/11l386zMLAshoqDRxbJSygg8C0wE8oFlSqmPtdbr6512GtCj7mMkoZ+e4SpFmp0ujr4UezdFNYeUa69j57z5VM54heTrb4pqLs1NubucBxc9x5f5M1GOACemT+Ke42+mU1yn8Af7tRvgtCa4cyWunRXUrt5A7dcf4dq0Cx0wAHbMHVNxnHYC9mHDsQ0dimXZA6jNc8DvBlMM9DoFLni8Qensnx2/5/P7uM89ladMd/HApIk/mTXXWlNUU8S2qm1sq9x2oIDeWvkjNcNCXTuWAzP9sXT1pTLEV0GW30uKL8BObxb/CU7h96MG0N0cJEvXkuSuJlBagr+0FH9JCYGS0GdPaSn+tz6CQAD4aecWZdAYY7Zj+vR6jO3aYfLsxli1FlNMAGOcDVNKCsZ2HTBd9AzG9h0wlG8GrxPiM0K9eGtKaPQstdy8GDW764rlA6r3hD7HdYxOQkKINi0cM8sjgK1a6zwApdTbwFlA/WL5LOB1rbUGvlNKJSqlOmqt94QhfrNzQf/RPL7sG4pqiugQG523De1DcrBlp1D+n2kkXf5blC0uKnk0J0XOMp5c+iJf75mJJ+BhaOpJ3D/mNromdolc0I9uqncDXAn+GdfjMo+gdvFX1K7Pw10SBK1AKaw9upP4m9Oxj5mIbegwzGntfzpWxnPw7MjQjGlsOzjrmWNKKXTT4VXAVbxxmOeVUnR0dKSjoyOjMw4uJdJas7d2L9uqtpFXmcdDX3xNnrWI0lgP1cb9RWQZBh7lyXwI+h1oXyLjunUns3tHytvZqc7qTLekE+jXvjM5GVl0iLWx6u1/0nXpU5g8AfxuAwGPAbfbQrk9hwRHOwJl5XhKnAQqEtAHWvpVhz5ePBUAQ4wRk9mD0RrAFBPEaLViNJtDM/Cb5mNYfQ6G5I4YE1MwJLXDkNQeQ7ssjJ0Hoez2w9+keci/XaOXhoij9uDZ/THW3wW1um5mWZZhCCGiIBzFcgawu97jfH4+a3y4czKAVlksD24/GIBvC1ZwTs/To5ZHyuUXkv/g81S/8ijxv3skanlEW5Wnir8vep4vdr+PVl5O6Xwqtwz5HdkJ2ZENvOIN2DwXV3GAyrwEakssePetBFaiDJqYjFhSzhyIfcI52E4YjzHuCL/QWGLhsvcOrsVt4llOpRRpsWmkxaZxQvoJPP9xOgVFLjqqfJ6zTOMOLmeXyUZyfA0XH59AXkUBhc4i9tTms6pkOdW+agCW7AN2AsuAgANDIInevTLpHygjLeDDElRsD3TiE9MJPHLWMNo54ok1x2Iz2rB5wbrPjamqhmB5Of6ycgLlZfj37CRQtBv/5qV4qw34SwwEfQb0/rXdyzYCh9/YBYMBgxkM5iBGqxFDjAWDKYgK7sNosmKONdGuvxP/xtmYVrwBQ2T3uEgbvr8Dxn7OIjBawJZ0+BcIIUQEhaNYPlzfLH0M54ROVGoKMAUgLS2N3NzcBiXjdDob/Jpw8wZ96KCJ5xd+SlJheNcLN+j6OvQjIx72vjmLFb1PbvZt5ML9b1cbrGV22XwWORcQNLgxuQZyfrvTGaUy2LlyJzvZGbZYPxMMMvCd+9i3zoarNBGDKYitnZeELi6saYqVk18gGOM4eP7y5Uc/dr/HYH1x6COKJmcFeHUfbAlmcrbnCQAsPjinm4WhtWaGWvtD3f1ZJIA76KbCX8nO2nJ2uyoo9lTgVFXs9FawzhTPLpsLp3H/t4pK4HXuWvz64YNrhQELFmUlPj4Ga6KVQA8LtuGd6OrdTZz2YdQaQwDwGik3dMdqScXm9hDj8hDj9mDxBjEGrFg8ARzV5VjcHiyeABaPG4s7gMlrxuQ147dr2vV3Ygq4qfnsTyzblxnhv9m2bU+VixU7KxndI5UEmzl0sLoYHB3gV9o0CiFEpISjWM4H6i/2zAQKj+EcALTW04HpAMOGDdO/1pv2cI7Uz7ap2F/OptyQH/ZcGnp9FedNpOiVLxleu5vYM64May7hFo5/u1krC3jiix8pNX6FNWURGNwEawdwUfdruWfCeCymyP7CEKytpXLmh5T/9wWK98RgjvWTllNFQtdajGYNZjuc/g/G5pwR0Tyawjig76GbrhxD15BRj82noDI0Q/2ieRq3BaaQp1JIiA1y4/jQNuK1vlreWb6VgqoKavy1uHwu3IFaHHEwJNNOrb+Wb7YV4A1aqLTEogxeNKHfyD2YqVX70OwjGPvT39GtplpirUbASkXNwULMonzY8ACaTL+fdwqhVlt5Ul3BX5rB95fW7Pu8cm5/ZxVf3Tm2XrG8B+Lk5j4hRHSEo1heBvRQSmUDBcDFwKWHnPMxcHPdeuaRQFVrXa+8XxdHH9bXfsY+Ty3x1uh1o0j4v/speesLyl56sdkXy401a2UBf/r8AwxpM7CaavFV9yVYPpE/nnQS147uGtHYvuK9VMyYQcVbbxKsdmJL8dJ+Ygxx/TuhStaBX4duyus5CXIui2guTeloN135NXed2ot7Z65hiy+TM7yhGWqb2cgDk37a13pC51/fkGJ9n32cPm0Rxbj50no36ZRSqFOZ6H0QNzH87ax+uH0Bghq0hqDW9O4Qx4Q+oSJs2rwtBIIarTXT5m/lGfM0TjYsJ0b5cGsz8wI5/NdzAn85pqsUR2tXXY/lzKR63zedxZDSPUoZCSHaukYXy1prv1LqZmAuodZxL2ut1ymlbqx7/gVgNqG2cVsJtY67urFxm7sR6UPYsO1jPt/0AxcNHBu1PAzxKSRddB6lr83Es2UL1h49opZLpD288A0M6W8S9LTHvfsagu7Q2+UvL94RsWLZvWkT5a+8StWnn0IgQNyJo0iOX4z93D/AsGsg6IdnR6Kr8lGNuCmvNdtfEE+du4nCShfpxzhD3Tc9noxEGwWVcLX3bp4xT+Nm3624iCEj0cZvj+/yq6+/dcLBr40PVhRwV+WUUNGtSynVCdztn0J6YtPvytnW7CyrpUN8DDHmeluuVxdBl+j0rRdCiLD0WdZazyZUENc/9kK9P2ugTfUvO6PX8by2DRbsXBbVYhkg6cY/UPbu55S9/Arpj7a+G/201vx37X9xJ75BoKYbrvwrIBhz4PnCSlfY49UsXkz5K69Qs+RblMVIUk4iyQ+/iSUrCwJ+MO7/0rLCZe9R++qFxF72rrQe+wX7Z6gbq/4s9an1ZqnvOrXXMY1Tv+jGHNvgcUTD/axtnM8F7krphCGEiBrZwS9CerdLJ8HUAY8pL9qpYEpKIvGkoVR89CHtbvkd5vTWc4OSP+jn0e8f5d3N7+KrGoy78HwO/W8drtnAoNfLvk8+ofzVV/Fs2Yop0U67HA9JXSsxjjwJ0ut+mBsP+bJq34dlI55mnGxqEXHhmqU+OI6FUyufICPRxqNNvYtjG7WrvJZR3VMPHjiwIYkUy0KI6JBiOYLGZg1nSeEStNaH7+PahJLPGk/F7EVUTHuQ9o/9J6q5hIvL7+LuBXeTm5+Lt+xEOqvz2GV24/YFD5xzLLOKB9Rtmeyf+G8qvlpOxZtvESgtxdo1i44nBklovxXVdzKcfD+0kxnH5iJcs9ThWI8tGu6dG45DIT2WhRDNhxTLEdQ7qT+f5H3CxtKd9GnXJaq5WEZfRFzXh6mYvYiUvzgxOhxHflEzVu4u55Z5t7CmdA1/GvEn9L5RnJOTwdx1RY2eVQTAW4P3ufMp+6GaquevQvsh9oSRpEx9AntOP9SHN8Co2yDruPBfnBBtWOeUQ5YqOYtCn2WrayFElEixHEFxKnT39qwN30S9WMZgJOXSc6l+8H0q/zuNlNv+FN18GmH3vt3c+NWNFDqLuDvnES7pc7ANWzhmFQNOJ6W3/4byJQEUduKz3aQMVFgz1sGI4aFlFpe81djLEEIcYlNRNYu2lHDB0E4k2Pe3jasrlmWrayFElDTvXSpaOG9te3TAwqvLFzDqsfnMWlkQ1Xxs59yBPc1H+Yy30dNGhpYZtDBrS9dy+eeXU1pbgXPHtXyzOnw/QHUwSNVHH7Ht5HGUL95DQmcX3c4sJn14OVZrGWQMlU0RhIigb7eV8tBnG/AGDi6loroIDCawp0QvMSFEmybFcoTMWlnAAx9vJODOwmjfSUGli3tnroluwWxPJuXCM/Dv87FvxS6YcQF4a6KXTwMtzF/INXOvgaCF8i03MCB1EFMvGBSWsV1r1rLz0sso/OM9mM3VdJlYQvrISsy2ej+0t34FBuMvDyKEaJRd5S7sFiOpDsvBg85iiG3f7HcgFUK0XvLdJ0Kmzt2EyxcgUJuFwVqEMjpx+QJMnbspqnnFtqvAmuCndH0sgYpS+OjmqOZztD7Y/AG3zr+VFEsmhRuuo1/77rx2zQgc1satJPKXlbHnvvvYceGFeHfvpuNDf6PLk3/B1sH80xPNdjj5b42KJYT4dbvKa8hKtv/0hujqItm9TwgRVbJmOUL29/b17cvBkvo15uTFeEsmhb3nb4OseAO15QvaDw6QvyiZnXMddArMxdztDRhyefTy+hVaa5778Tle+PEFTkg/gepdl9K3vZHXrx1BXIz5yAP80rg+HxVvvUXJ088QdLlIvvJKUodbMK7+O0z6GrbPg02fg9/dKnfeE6I52lVe+/Mb/KqLIKlzdBJqBmbVbSnf6JuWhRDHTIrlCElPtFFQ6UJ72+Gv7o8l6Vu8ZSeSHp8cvaTmPQC+WhwdodPYMnYvTmbnnFiyDA9gaYbFsi/o4+/f/p1ZW2dxdrez+esJf8XnV/j8mvhGFMo1335L8SOP4NmyldhRo0i76bdYf3wMFn0DPU4FNJz1LDw7EqryQXbeEyLitNbkV7gY06PdT59wFkGnEdFJKspmrSzg3plrcPkCAAeW8wFSMAvRhGQZRoTcdWovbHXbtXpLx6OMHuyp30V3B7AJD4SWEwCxHbx0Hl9G0G9gxxcJuDc0r5v9anw13DLvFmZtncXkTleSt3EyHp/CbjEdvEu+gbz5BeTfehu7rr6GoNtD5rPP0OmGkVg/vxiK1oQK5EvfAUf70E57l70H7XqHPsvOe0JElFKKFfdN/Mm24/i9UFvWpnosz1pZwKjH5pN9z2f8/t0fDxTK+7l8AX7/7o9k3/NZs7hxXIi2QIrlCDk7J4NHzx1ARqIN7UlH1/TBnLyYU/onRS+pIZdDz1NDywoAWzvoPKEUpb3svOK31CxdGr3c6il1lXL1nKv5bs93XNH9D8z6uh9lTi9ef/DILz6MoMtFydPPkDd5Ms5Fi2h3+210/fQT4k46CbV9YWjW6nffQs7lP+120b4P3PRd6LMQIuJizEYSbPV+GT6we1/bWLO8pNDHvTPXhN6VBAJaH/a8gNZoaB43jgvRBkixHEFn52TwzT0nsf2xyUzOupygqmH6yjejm9RZz4aWFaAgrgPWS6bSZVI1ppREdl93PdXz5kU1ve1V27l89uXs2LeDm/s9witz0shKtjPjupEkx1qOPEA9Wmv2zZnLtsmTKX32WeJOPplusz8jdaQDQ/WuUGF8zgtwxYeQ0Hq2ABeiJfp2WxkPfrqefW7fwYP7i+VW3mN5/2zy9NVeXL4AiiAj1Ab+bnqF+ZY7edb8FGcalhDLz+95aQ43jgvR2kmx3ER+f+IpBGu7MmPj63gD3uglcujyguHXYL53JZ3ffhdrn97k33IrlR/MjEpqee48rvj8Clx+F3cNfJJ/fWQgPTGGGdcdR4rD2qCx3Js3s+uqqym4/XaM8Ql0/t/rZNz/e8zzb4WPboJl/w2daImV3slCNAPfby/j5W+2YzXV+7F0YEOS1juzvH9dckHdzd/nGxfwrfUW3rU+yAXGBezSaQw3bOZpyzOssN7IPaafb4gU1RvHhWgD5Aa/JtI+LobhiRey3PsYb63/gCsHXBLFZOqWF+xnS8IUo+l87SDynylkz5//TKCygpRrr22ylL7e9TXP7H2G9Lh0np/wPH5vMoM7reGpiwbTLu7oC2V/WRmlz79AxVtvYXQ46HD/X0m84ALU+pnw3Png98Ckx2HElP9v777DoyrTPo5/78ykQxICIUAIvUkTMCKiLkgRBBVeRQULyKKI4sqqq2LZVVdUVpS1rSKCigoqIouoIItgdBVlkRaadClJqCFAGklmnvePM0AqCTDJmUzuz3XNlSlnzvxOJnPOnTNPqcCtUUqdrd2Hs6gfEUKws8BY5qemuvbPNsvzVifz0Oy1uIxBcPMX52zGOuezwt2K5/Nu5Vt3F7IIIVAMndjMPc4vGe34infyB3CYyFPraRAVauNWKOX/9MxyJXr4D9fgyo5natJ08t35dscpJkBOEH9hEhFd4jkw6SX2vzgJU0qbOW96+YevuH/pA+RkxXJg8538uk1oWiecWXd1o25ESLnWkX/oEPv/8SLb+vTlyKxZ1GrroNlHr1Fr2DAkaRbMvQtiWsOYH6HbGJ3gQFVrItJfRDaLyDYRGV/C4yIir3keTxKRLhWdaXdaFvHRYYXvPL4PJMDTdMy/nDyjfLJd8vPO6Yx1zmdWfi+G5T7JfHd3sgghNNDBpJs689kLDyG9nyRADH0cq06tJzTQYW/HcaWqAa0YKlG7uEgGNx3Osfz9LNy50O44hYlAn6eRS0bRoMVyavW8gLR33yX1iScx+RVX2L/x01Le2/40rhN1yNr9Rw6kB/LwnKRyd1jJP3iQ/RP/wbY+fUmbMYOI3lfS7Eao124Xzi/vsGYobD8EBk6GkQuhTosK2xalqgIRcQD/Aq4G2gLDRKRtkcWuBlp6LqOBtyo6lzXGcgnFcngMOPzvS9CTE1cBdAvYyDDnd7ydP5DH8wX+s8UAACAASURBVEeR7/nSNy4qlBeu73BqmLgre/QmMyyOQcGni+WTbZa1k59SFUeL5Uo24aqbaFmrJdPWTcNtzm10hwojAgNeQjoNJTZ2CXUGX8LRuXPZO+7PuHNyvP5yO9J3MHXL45j8MLL3jAK3daDMd5syO6zkHzzI/hcmWkXyBx8Q0a8fzRd8TYNLDhMceBAwcCwF/j0GgsLg4lE6VbVSlq7ANmPMDmNMLvAJMKjIMoOAD4zlFyBKRCqsl11uvhu3MTQqemY5Y7/fjoSRXKCd8f2OuSSb2kzOvxEQQgMdvHJzJ34a36vweMoihHcczCUkEe3MKbQuHRVDqYrjf/+u+7gACaBfg1t4Y8MzfLvrW65qcpXdkQoLCIBB/0Lys4lp0RtHh77sn/Ace+68i4ZvvYmjZk2vvExqRiqjF4/G5Raydo/C5EcUery0Dit5Bw5weNo00j+djcnPJ/K666gz5m6CGjeGlTPgt6/hVAdKA9sWwyrfnaFQKRvEAXsK3N4LXFKOZeKA1KIrE5HRWGefiY2NJTEx8ZxCvXR5IG6zl8TE0wXfRanbyA2qxbpzXGdBGRkZ55ytIgQAJ0+X1JfD/OpuzQmsEX9uv8BB1NGtJCZuLfa8yJw4Orvz6OpO4htOT9aSnefi2S/WEnW0+HO8zdd+l6XRnN5VnXNqsWyDkLwuuE/U4bWVb9O3cV/E10ZjcDjhxhkgQnQXcIQFkvK3CewaPoJG70zFWafOea0+LSeN0YtHk5WXRY0j95CZV7vYMkU7rOTt9xTJsz1F8qBBVpHcqJG1wLFU+OoBMIUH8Ccv25q5UItlpU4qaYdTtHNCeZax7jRmKjAVICEhwfTs2fO8whWyIgOaXI431pmYmOiV9XiL+5uvT11f6L6EXeb0GfTHb+lb+hM3pMMaOErxiZLSckylbKOv/S5Lozm9qzrn1GYYNrjxokY4jvdiV8YWfkr5ye44JTtZwO9aRuRvDxH/xChyf/+d32+5ldw9e8783DPIzMvknm/vITUzldd7v85jvXsT5Cj8Z1iww0re/v3sm/Ac2/taHfcirhlI84ULaPD8c1ahfMxzoqtGLDToDI4iI2cEhkGfZ845r1J+aC8QX+B2QyDlHJbxmvlrU7h35kpyCs5W58qHzIN+OxJGXIETAi/mD+VT15XF7i/R+s85TBTL3cUnS9JRMZSqGFos2yAsyMmwtoNx50Xyxqopdsc5s9h2EN2UGtuep/Hz43AfPcrvt9xCzuazHwT/hOsE45aOY3PaZl7u8TKR0orBneN4cUjHUweIkx1aBtZ3sO/vz7K971Uc+eQTIq67lubfLKTBc54ied96mHkj/KsrZKVZzUfuWgJtBpyaoRBnCLTqD51v9eZvRKmqbgXQUkSaikgQMBSYX2SZ+cBwz6gY3YCjxphiTTC8ZdWuI/yw5VDhMZYzPX0P/HSM5Yf7tSY0sHA/iqAAzjyyRc4x2Pof0psOxOko/FwdFUOpiqPFsk1Gdm9JfloPNqSt5dd9v9odp3QhkXDbv6FWE0JXP07jyY8jAQ523XY7WStXlns1+e58Hv3hUZbvW86zlz1LampTrvrnDyzbdujUTIfv9w8nccQFdPtyulUkz55N5KDrrCJ5wgSC4uPhyC6YezdMuRz2LIcrHoLAAmdTCs5QGB4Dg97w/u9EqSrMGJMP3AcsAjYBs40xG0RkjIiM8Sy2ANgBbAPeAe6tyEwnh40r1CTt+MlvjfzzzPLgznG8cH0H4qJCEawTBXe0Dyrcoa+ozQshP4eYS2/B5TaEBztOPbfgqBlKKe/SNss2qRcZws1thvDN0e95Z907JNRLsDtS6cJrw+3z4L3+BP/3TzR56zN2P/gUu/84irhX/knNK68s9hTjcmHy8jB5ebjz8nhp2Qskbf+Wp9rfTcyuerw+5xuGNKhJh7SdZP6yDZOXR81ZH7P9558xxhB1/fXUHj2aoIYFdv5Hk+GNi60mIpfdD5c/AKG1Cr/wyRkKPxsJN75n3VZKFWKMWYBVEBe8b0qB6wYYW1l5dqdl0TymyGe1Gkx1PbhzXKECt8xOSes/h8h45h6oj8scZc6Y7lxQP+LMz1FKnTctlm309+s603jdSF5Z9QrrD62nfZ32dkcqXUR9GP4FrPqAwDYJNJ41kz2j72bv2PtwhBhwhmNc5lSBTJHJTAZ7LvAm8Caveu7f+9HpZUIdDiKHDKHO6LsIjPMcQHIzYed/oXV/iIyD/s9Dq6ut66UpOkOhUspnud2GPWlZ9GpTt/AD1WCq67OSlQbbl0C3e/lsVQrt4yK0UFaqkmixbLMhLW/i7bXTmJo0ldd6vWZ3nDOr1QR6/w0AZ0AGjV5+gsOP3oLreAYSAtJlGBIShgQGgtOJBAay4tBqlqR8T+e4BHo3uYZ/Ju7kaD48MrAddaNrnF42I4X8H54k4t6boW4cuPJg1Qz4/kXIPAR/XmcVyBffae/vQCnlVcdP5NMqtiYt69Yo/MDJM8vhdYs/qTra9CW489lRrz8blqbz9LVF55FRSlUULZZttur3bNL3XcJ3riVsO7KNFrWqwAxzbjfMGorjyO/UbZcPrhPgPAGtdlhNHzzmbp3LU8v+y9XdBzLsDxMRhJZxO7kwPopmTaJPry83E/71Rwx7rU57Vz4BP7wIaTugUXe4+aMzn0lWSlVZkaGBfPmny4s/cDwVwmqDM6jyQ/miDXMhujk/Z8UREniMQZ10n6hUZdEOfjb7Q6sY6tEHMcFMWz/N7jjlExAArfpBXqZVKAPk58CWhdYEIAc38+3yV3hm2dNcFt2eCS1uJu339YgId17RjIvrB1m9uvNyrML7i7GQeRDBQMYBmHevNZLFLbNh5AKI73rmPEop/3N8v1+3Vz4rx1IxO37g/aNdeHLeBmqFBfH9loN2p1Kq2tAzyzZzBAijurfn+V8uYYEsZOyFY4mPiC/7iXZb/WHx+zwTgCxvcQWPHF1B+xO5TF61kKCVC4g0Drbft5vmMTVgwV9g7cclr9d1wiqUu91jFeRKKb829YftLNqwn8/uvpSAgAKjYWTs89uprs9KXg6H3x9GDePg/axuGCD1aA6PzV0HoCNgKFUJzuvMsohEi8hiEdnq+VmrhGXiReQ7EdkkIhtEZNz5vKY/GnJRQ4IyewIOpq+fbnec8un9tDXhR0GBYWzoPob7MzfQuEYcb/aYzObL3+buvAd4v/6TNK3t6e3eYQhc9ZzV/rnoOsA6S73k7xW+CUop+21MOca+ozmFC2XwnFn2z2Hjys3thnn3UDttNQ/k3cPv5vSZ9uw8F5MWnf1490qps3e+zTDGA0uMMS2BJZ7bReUDDxljLgC6AWNFRHsmFBAe7OSWhPYEZ1/CF9u/YF/mPrsjla3LbdaZ3wITgOxo0YN79synVmg0bw/4kOSIP3Dr95Gk1OvDbX8cd/pg2KIPdL/PGiP56kklFt06655S/m/e6mS+XpdKcno2l01cyrzVydYDbpfVwa+6n1le+ixsmMvEvKEscHcr9nBKerYNoZSqfs63WB4EzPBcn8HJ0cEKMMakGmNWea4fxxoEX783KmJc75Z8fssTGGOYsWFG2U/wBQUmANlXM4a7Aw4hIkztOxVxRXLnjBVEhAQybUQCoUGOktdRQtGts+4p5f/mrU7msbnryHNZw0wmp2fz2Nx1VsGcdRiMy+rgV12tnAE/ToaL7uCz4BtKXESnt1aqcpxvsRx7cgpUz88zjvEjIk2AzsDy83xdvxMW5KRRREP6NxnAZ1vmcDj7sN2RyuaZAORITGtGxzUkIy+Tt/u+TaOIRkSEOunRui7TRiQQGxFy5vV4im6js+4pVW1MWrSZ7DxXoftONS0IiYLIeFj2OqTvtimhjbYtga8egOa9Wdvxrxw7kU+RRio6vbVSlajMDn4i8i1QUsOxJ87mhUSkBvA58GdjzLEzLDcaGA0QGxtb9oxGRWRkZJz1c3zFsROGr//XCuK/4vlvnufaWtcWW8bXti/HncPr0XVIzUrl3rr3krI2lZ2uVEKdQr9oOLT1MIlby15PWKtHaLNuIr+1eoSsZSsqPngl87X3zdv8efv8edvsVFoTgpT0bGu4uFs/g+n94KMhMGpR8dk6/dX+DTB7BMS0gRvfx33ARdsGkdzQpQFvf7+TlPRsGkSF8nC/1tq5T6lKUmaxbIzpU9pjIrJfROobY1JFpD5woJTlArEK5ZnGmLllvN5UYCpAQkKC6dmzZ1kRC0lMTORsn+NLPty5jO0nLmRZ9jKeGvgUEUGFZ2jype3LzMtk3NJxJOcl8+qVr9IjvgeTF2/hy7UpzL2nO7XCz2581MTwRj6zbd7mS+9bRfDn7fPnbbNTg6hQkksomE81Lah7AQydCR9dD5/cCrf/G5zBlZyycgWdOAwzx0JwDXJu/piQkAg6N4J593ZHRBh+aVO7IypVLZ1vM4z5wAjP9RHAF0UXEBEBpgObjDGTz/P1/N6oy5uSnvIHMvIy+OS3T+yOU6o9x/Zw24LbWLF/Bc9e9iw94nswb3Uyry3ZysVNahEVFmh3RKWUD3u4X2tCAwv3ZXAGSOGmBU2vgMFvwa6f4N9jrNEh/NWJDDqsew6yj5Bxw0wGf7iLf323DQDrMKqUssv5FssTgb4ishXo67mNiDQQkQWeZS4Dbgd6icgaz2XAeb6u3+rbth5x4c0Jd3Xgw40fkpWXZXekYn5O+ZmhXw/lQNYBpvSZwrXNr2XlrjQemZPEJU2jmTC4g+7clVJnNLhzHC9c34G4qFAECAtykO821Awp8oVnhyHQ9+/WDHbf/s2WrBXO7YLP76RGxk5y/286oxblsv1gBh0bRtqdTCnFeU5KYow5DPQu4f4UYIDn+o9QrG+CKoUjQBjZvSkTllxOeJO3mLNlDsPbDbc7FgDGGD7c+CEvr3yZZpHNuDb2cf7ywXFS0r9GBKLDAply20UEOXViSKVU2QZ3jjvV7jYnz8UNby3jgU/X8OWfLqfxyXHZAbrfD0f3Wh3+IhpCtzE2Ja4g3zwGWxaypcVo/rmyLst37uPVoZ24omWM3cmUUuh01z7ppovj+fj2m7k49mJmbJhBrivX7kjk5OfwxI9PMOnXSfSK78XQuElM+vowyenZGMBt4PgJl07BqpQ6JyGBDqbcdhEiwpiPVpGdW2CkDBHoPxHaXAPfjIeN8+0L6m2/vAX/exu6jeUfx/rwzYZ9/PWatgzqpJ33lPIVWiz7oBrBTi5pVpu7Ot7FgewDzNs2z9Y8+zL3ccc3d/Dlji8Z22ksL/d8mde+3V1s2KcT+W6dUUopdc7io8N4ZWgndh7KYM2e9MIPBjjghmnQMAHm3gW7q/gIpMZA0mzrrHKba+CqZ2kWGcDYK5sz6nLtyKeUL9Fi2UcZY1j0a01iAlvy7vp3yXfn25JjzYE1DP1qKDuP7uTVK19lzIVjCJCAMw/7pJRS5+jK1nX57yO9uLR5CROSBIbCsE8hIg4+vhkOlWNcSl+0bz18ONgq+hsmcLjfGxDg4PK4QB7u18budEqpIrRY9lEiwsGMXA7uvZzkjGQW7lxY6RnmbJnDyEUjCQ8MZ+aAmfRq1AuA9clHKa3/ns4opZQ6XzE1rSHivliTXPwMc3htuG0OiAM+ugEyShyx1Dcd3w/z/4SZcgXHdvzKM3nD6ZryIN0m/cz/dqbZnU4pVQotln3YqMubcjytJXWCGjN93XTcpnKGTcpz5zHhlwk88/MzdK3XlVkDZ9GiVgsAvk5KZciUZUSEOAku0pFPZ5RSSnlLjmc2v3s/WsnhjBOFH4xuBrfOhsyDMOsmyM20J2R55WXDD5Pg9S64V89ihvtqrsiZzHuu/hzIMuQbw++HMuxOqZQqhRbLPqxLo1p0aRRN9sGebD+6naW7l1b4ax7OPsxd/7mLTzd/ysh2I3mz95tEBlvDF2WeyOeZLzfQtn4Eix/syT9u6Hhq2Ke4qFBeuL6DziillPKKkx3+DmXmMu6TNbjcpvACcRfBkPcgdS18NhJc9jRVOyO322qX/HoCLJ0AzXoyLPBVns69laPUOLWYMfDqkm325VRKnZEWyz5u1OXN2JfSmjrBDZiaNBVjTNlPOkebDm9i2NfDWH9oPS9c8QIPJjyII8BBdq4Ll9sQHuzk49Hd+Hh0N2JqBjO4cxw/je/FzokD+Wl8Ly2UlVJe1T4ukgmD2vPjtkNMXlxC5+HW/WHgy7B1EXz9oFV1+ordv8D0Pla75PDacMfXMHQm/ztW8rTd2t9DKd+lxbKP69culruuaM7QViPYlLaJeenz+DnlZ47nHvfq6yzcuZDhC4fjNm5mXD2Da5pdA8DeI1lc/9YyXvqPdaBqHlODYKfjTKtSSimvuenieIZ1jedf321nU+qx4gsk/BGueAhWzYD/vlT5AYtK2wmzR8C7/eBYCgyeAnclciA6gcUb95far0P7eyjlu85rUhJV8ZyOAJ4Y2JY8V0tWHFrK0tSlLF28FEFoGtmUjjEd6VCnAx1jOtIiqgXOgLN7S11uF6+tfo13179Ll7pdeLnny9QJrQPAr7+ncfeHK8nNd9O1aXRFbJ5SSpXpqWvb0atNLBfUjyh5gV5/tSYtWTrBmrSk07DKDQiQnQ7/fRmWT4EAJ/R8HLrfx1FXEG//Zwvv/rSTwIAAnhx4AU9/ubHQ0Jun+nscraKjeyjl57RYriLeStzJip9v4viJ/sTWOcClbTPJC/yd7/d8f2oc5lBnKG1rt6VjTEc61rGK6Njw2FLXeSz3GI/+8Cg/Jv/ITa1uYnzX8QQ6AgGYvWIPT8xbR8NaYbwzPIEWdWuUuh6llKpIIYEO+ra19mUbU47RpE4YYUEFDl8icN0bcHwfzL8PasZC816VE86VDyvfg8QXICsNOt0KvZ4kO6Qu7y/7nbcSt3EsJ59BnRrwQJ9WNKkTTnCgg0mLNpOSnk2DqFAe7teawZ3jSEzUYlkpX6TFchUwb3Uyry7Z5ungEsr+A41ZdMTBC9ffwhu9GrA3Yy9JB5NYd2gdSQeT+HDjh6fGZY4Niy109rlt7baEOkPZkb6D+7+7n+Tjyfy121+5qfVNp15v75Esnpy3nm7NavPGsC5EhgXatOVKKXXageM5XP/WT1zdvj6Tb7oQKTiGpTMIbv4Q3r0aPh0Of1wI9TpUXBhjYOti+M+TcGgzNLkC+j0H9S8EYPe+47y46DeubF2Xv1zVmrYNTp8VLzjNt1LK92mxXAVMWrS5WE/w7DwXL37zG4M7xxFfM574mvEMbDYQgFxXLr+l/UbSwSSSDiWRdDCJxbsWA+AQBy1rtWTP8T0EO4KZ3m86XWK7AHAi30Ww00HDWmF8enc3OsRF4nRos3allG+oWzOEe3u2YPLiLXRuFMXwS5sUXiAkEm79DKb1gZk3wp3fQmTDs3sRY8CdD65ccOV5rueBO8/66cqDrMPWUHA7voPo5jD0Y9wt+/PV+n1sXPMb469uQ+t6NVnyYA+axei3ckpVdVosVwGl9ZJOPZoDwOZ9x6lbM5ha4UEABDmCrKYYMR1PLXs4+zDrD61n7cG1rDu0jpjQGP526d+oF14PgB0HM7jzg18Z17slgzrF0blRyT22lVLKTvdd2YI1e9J59quNtGsQyUWNi+yrIuOsSUve7Q/T+kKtJuDO46L0NNgYcrroPVkEu3ILF8TlnS01JAr6/wOTMJLE7UeZ9MZPbEw9xgX1I/hzn5aEBDq0UFbKT2ixXAU0iAoluYSC+WTv6fFzk0jae5RLmkbTr109rmoXS/3Iwj2ra4fWpkd8D3rE9yi2nh+2HOS+WatwOgKKPU8ppXxJQIDwz5s6ce0bP3LvzJUsuP8KatcILrxQbDsY9gl8P9E6U+wMJjfIDdH1rc53jkAICASH0/MzqMD1wNM/iy138hIMTS5jR0Yg46ev4n8702gUHcYrN3fiugsbEBBQyhSnSqkqSYvlKuDhfq15bO66kntPA89c145v1u9j0YZ9PDV/A0/N38CISxvzzKD2xdY1b3VygY4lIXRtEs0Xa1NoFVuTd4YnEB8dVmnbpZRS5yIyLJApt13EV0kpfL/5AC8v3lqssxxNLoMmX556zrrERHr27HnWr1V4n2mtf0Cb+gQ5A6iZf4IDx3J4dlA7br64EUFObbamlD/SYrkKONkRZNKizSSnZxNX8IAAdGwYRceGUTzSvw3bDmSwaMM+mnu+/juUcYJb31lO37axBDsDeDNxG9l51rTZyek5/HtNCu0bRPDp3ZcSHqx/DkqpqqFtgwi27D9e6ERCcno2j81dB+CVDnTzVicXW/9Ds9fy6rdbWPqXnsTUDGbpQz31TLJSfk6royriZO/pxDLOjrSoW4MWdVucun0kM5fo8CDe+n578eliPdKycrVQVkpVOZMWbS70jRtYnZ8fmZNESGAA/dvXZ++RLCZ8tYkjh3OYf2ANQY4AnA7hhi4N6dyoFsnp2cxesYcgZwDOACHQEUCgM4CerWJKXL/LGA5m5JLnMgQ5RQtlpaoBrZD8XMvYmnw8uhtpmbl0eXZxicukpudUciqllDp/pXV+znW5Tw0rl5PnZsehDI4dd5N8Io18lyHP5aZbs9pWsXwkm1eXFB/f+O3bLyp1/Zkn8rXJhVLViBbL1UR0eBBxZXQUVEqpqqS0zs9xUaH0a2eN9NOibg3+80CPUr+V69o0mh3PDyDfbRXR1sVQM8RZZudqpVT1oP8aVyMP92tNaKCj0H0FOwoqpfyfiESLyGIR2er5WWycSBGJF5HvRGSTiGwQkXF2ZC2Lt/ZpAQFCkDOA8GAnUWFBxNQMJsSzHt1nKqW0WK5GBneO44XrOxAXFYpgnX154foOOpOUUtXLeGCJMaYlsMRzu6h84CFjzAVAN2CsiLStxIzlUtH7NN1nKqVAm2FUOzrNqlLV3iCgp+f6DCAReLTgAsaYVCDVc/24iGwC4oCNlZaynCp6n6b7TKWUFstKKVW9xHqKYYwxqSJS90wLi0gToDOwvJTHRwOjAWJjY0lMTPRmVq/JyMjw2WwnVYWMoDm9TXN6V0Xk1GJZKaX8jIh8C9Qr4aEnznI9NYDPgT8bY46VtIwxZiowFSAhIcGcy8QflaGsYTd9QVXICJrT2zSnd1VETi2WlVLKzxhj+pT2mIjsF5H6nrPK9YEDpSwXiFUozzTGzK2gqEop5fO0g59SSlUv84ERnusjgC+KLiDWIMXTgU3GmMmVmE0ppXyOFstKKVW9TAT6ishWoK/nNiLSQEQWeJa5DLgd6CUiazyXAfbEVUope2kzDKWUqkaMMYeB3iXcnwIM8Fz/EdB5nJVSCj2zrJRSSimlVKm0WFZKKaWUUqoUYoyxO0OpROQgsOssn1YHOFQBcXyFP2+fblvV5c/bd67b1tgYE+PtML7sHPfZlaUq/I1WhYygOb1Nc3qX1/fZPl0snwsR+dUYk2B3joriz9un21Z1+fP2+fO2VSdV4X2sChlBc3qb5vSuisipzTCUUkoppZQqhRbLSimllFJKlcIfi+WpdgeoYP68fbptVZc/b58/b1t1UhXex6qQETSnt2lO7/J6Tr9rs6yUUkoppZS3+OOZZaWUUkoppbzCr4plEekvIptFZJuIjLc7j7eISLyIfCcim0Rkg4iMszuTt4mIQ0RWi8hXdmfxNhGJEpE5IvKb5z281O5M3iIiD3j+JteLyMciEmJ3pvMhIu+KyAERWV/gvmgRWSwiWz0/a9mZUZWtPO+ZnfvVso5VYnnN83iSiHSprGxnmfNWT74kEVkmIhf6Ys4Cy10sIi4RGVKZ+Qq8fpk5RaSnZ3r5DSLyfWVn9GQo632PFJEvRWStJ+dIGzIW21cXedy7nyFjjF9cAAewHWgGBAFrgbZ25/LSttUHuniu1wS2+Mu2FdjGB4FZwFd2Z6mAbZsB3Om5HgRE2Z3JS9sVB+wEQj23ZwN32J3rPLfpD0AXYH2B+14Exnuujwf+YXdOvZT5Ppb5ntm1Xy3PsQpr2vGFWFOOdwOW2/A7LE/O7kAtz/WrfTVngeWWAguAIb6YE4gCNgKNPLfr+mjOx09+poAYIA0IquScxfbVRR736mfIn84sdwW2GWN2GGNygU+AQTZn8gpjTKoxZpXn+nFgE1ah4hdEpCEwEJhmdxZvE5EIrA/1dABjTK4xJt3eVF7lBEJFxAmEASk25zkvxpgfsHb8BQ3C+ocHz8/BlRpKnYsy3zMb96vlOVYNAj4wll+AKBGpXwnZziqnMWaZMeaI5+YvQMNKzgjlP/b/CfgcOFCZ4QooT85bgLnGmN0Axhg7spYnpwFqiogANbD2mfmVGbKUfXVBXv0M+VOxHAfsKXB7L35UUJ4kIk2AzsBye5N41SvAI4Db7iAVoBlwEHjP08xkmoiE2x3KG4wxycBLwG4gFThqjPmPvakqRKwxJhWsAguoa3MeVbazes8qeb9anmOVLxzPzjbDKKwzeZWtzJwiEgf8HzClEnMVVZ7fZyuglogkishKERleaelOK0/ON4ALsE6OrAPGGWN87fjt1c+QPxXLUsJ9fjXUh4jUwPrP+M/GmGN25/EGEbkGOGCMWWl3lgrixPqq6C1jTGcgE+tr4SrP0w50ENAUaACEi8ht9qZS1YWIfOtpK1/0clbfKNqwXy3PscoXjmflziAiV2IVy49WaKKSlSfnK8CjxhhXJeQpTXlyOoGLsL5p7Qf8VURaVXSwIsqTsx+wBmu/3wl4w/Mtqi/x6mfIeR5BfM1eIL7A7YZU8a+ECxKRQKwd+kxjzFy783jRZcB1IjIACAEiROQjY4y/FF17gb3GmJNnrObgJ8Uy0AfYaYw5CCAic7HaMH5kayrv2y8i9Y0xqZ6v8ez6GlcVYIzpU9pjIlKu98ym/Wp5jlW+cDwrVwYR6YjVhO5qY8zhSspWUHlyJgCfWK0GqAMMEJF8Y8y8yokIlP99P2SMyQQyReQH4EKs9vSVpTw5RwITI7MpSAAAAyBJREFUjdU4eJuI7ATaAP+rnIjl4tXPkD+dWV4BtBSRpiISBAwF5tucySs87YKmA5uMMZPtzuNNxpjHjDENjTFNsN6zpX5UKGOM2QfsEZHWnrt6Y3Xg8Ae7gW4iEub5G+2N1e7T38wHRniujwC+sDGLKp8y3zMb96vlOVbNB4Z7evR3w2rilFqJGcuVU0QaAXOB240xlVnQFVRmTmNMU2NME89xZg5wbyUXyuXKifV3eoWIOEUkDLiEyt+nlifnbqz9PSISC7QGdlRqyrJ59TPkN2eWjTH5InIfsAirN+e7xpgNNsfylsuA24F1IrLGc9/jxpgFNmZS5fcnYKZnx7MD67/yKs8Ys1xE5gCrsDp3rKbqzPBUIhH5GOgJ1BGRvcBTwERgtoiMwjpI3GhfQlVOJb5nItIAmGaMGYBN+9XSjlUiMsbz+BSsERsGANuALGzYZ5Qz59+A2sCbnrO2+caYBB/Mabvy5DTGbBKRb4AkrD4804wxJQ6NZmdO4FngfRFZh9Xc4VFjzKHKzFnKvjqwQEavfoZ0Bj+llFJKKaVK4U/NMJRSSimllPIqLZaVUkoppZQqhRbLSimllFJKlUKLZaWUUkoppUqhxbJSSimllFKl0GJZVTsiEiUi99qdQymllFK+T4tlVR1FAVosK6WUUqpMWiyr6mgi0FxE1ojIJLvDKKWUKpmIPCsi4wrcfk5E7rczk6p+dFISVe2ISBPgK2NMe5ujKKWUOgPP/nquMaaLiAQAW4GuxpjDtgZT1YrfTHetlFJKKf9ijPldRA6LSGcgFlithbKqbFosK6WUUsqXTQPuAOoB79obRVVH2gxDVTsiUhtYZYxpbHcWpZRSZyYiQcA6IBBoaYxx2RxJVTPawU9VO56v8H4SkfXawU8ppXybMSYX+A6YrYWysoOeWVZKKaWUz/J07FsF3GiM2Wp3HlX96JllpZRSSvkkEWkLbAOWaKGs7KJnlpVSSimllCqFnllWSimllFKqFFosK6WUUkopVQotlpVSSimllCqFFstKKaWUUkqVQotlpZRSSimlSqHFslJKKaWUUqX4f6IhgUhm2H6lAAAAAElFTkSuQmCC", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.optimize import fsolve\n", "\n", "# x0,y0, h variables globales\n", "def CN(phi1,phi2,tt):\n", "\tuu = [y0]\n", "\tww = [z0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tsys = lambda z : [ -z[0]+uu[i]+h/2*phi1(tt[i],uu[i],ww[i])+h/2*phi1(tt[i+1],z[0],z[1]) , -z[1]+ww[i]+h/2*phi2(tt[i],uu[i],ww[i])+h/2*phi2(tt[i+1],z[0],z[1]) ]\n", "\t\tutemp,wtemp = fsolve( sys , (uu[i],ww[i]) ) \n", "\t\tuu.append(utemp)\n", "\t\tww.append(wtemp)\n", "\treturn [uu,ww]\n", "\n", "[uu, ww] = CN(phi1,phi2,tt)\n", "\n", "figure(figsize=(12,5))\n", "affichage(tt,yy,zz,uu,ww,\"Crank Nicolson\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Dans ce cas particulier il est possible d'expliciter cette récurrence en exploitant la linéarité des $\\varphi_1$ et $\\varphi_2$:\n", "$$\n", "\\text{(CN) }\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\eta \\left(w_{n+1}+w_{n}\\right),\\\\\n", "w_{n+1}=w_n+\\frac{h}{2}\\left(u_{n+1}+ u_{n}\\right)+\\frac{h}{2}\\eta\\left(w_{n+1}+\\eta w_{n}\\right)\n", "\\end{cases}\n", "$$\n", "ce qui donne le schéma explicite calculé ci-dessous par sympy:" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle u_{n+1}=- \\frac{4 h w_{n} + u_{n} \\left(h^{2} - 2 h - 4\\right)}{h^{2} + 2 h + 4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle w_{n+1}=- \\frac{- 4 h u_{n} + w_{n} \\left(h^{2} + 2 h - 4\\right)}{h^{2} + 2 h + 4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_n = sympy.Symbol('t_n')\n", "dt = sympy.Symbol('h')\n", "t_np1 = t_n+dt\n", "u_n = sympy.Symbol(r'u_{n}')\n", "u_np1 = sympy.Symbol(r'u_{n+1}')\n", "w_n = sympy.Symbol(r'w_{n}')\n", "w_np1 = sympy.Symbol(r'w_{n+1}')\n", "\n", "Eq1 = sympy.Eq (u_np1, u_n+dt/2*(phi1(t_n,u_n,w_n)+phi1(t_np1,u_np1,w_np1)) )\n", "Eq2 = sympy.Eq (w_np1, w_n+dt/2*(phi2(t_n,u_n,w_n)+phi2(t_np1,u_np1,w_np1)) )\n", "# prlat(Eq1)\n", "# prlat(Eq2)\n", "sol=sympy.solve([Eq1,Eq2],(u_np1,w_np1))\n", "\n", "prlat(u_np1,\"=\",sol[u_np1].factor(u_n))\n", "prlat(w_np1,\"=\",sol[w_np1].factor(w_n))\n" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# x0,y0, h variables globales\n", "def CN(tt):\n", "\tuu = [y0]\n", "\tww = [z0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append( -((h**2-2*h-4)*uu[i]+4*h*ww[i])/(h**2+2*h+4) )\n", "\t\tww.append( -((h**2+2*h-4)*ww[i]-4*h*uu[i])/(h**2+2*h+4) )\n", "\treturn [uu,ww]\n", "\n", "[uu, ww] = CN(tt)\n", "\n", "figure(figsize=(12,5))\n", "affichage(tt,yy,zz,uu,ww,\"Crank Nicolson\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q5 [1 point]** \n", "Calculer la solution approchée obtenue par la fonction `odeint` du module `scipy`. \n", "Afficher $t\\mapsto y(t)$, $t\\mapsto z(t)$ et $y\\mapsto z(y)$ en comparant solution exacte et solution approchée. " ] }, { "cell_type": "code", "execution_count": 101, "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", "pphi = lambda yy,t : [ phi1(t,yy[0],yy[1]), phi2(t,yy[0],yy[1]) ]\n", "\n", "yy0 = [y0,z0]\n", "uu,ww = odeint(pphi,yy0,tt).T\n", "\n", "figure(figsize=(12,5))\n", "affichage(tt,yy,zz,uu,ww,\"Scipy\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice 3 : étude de la A-stabilité d'un schéma\n", "\n", "\n", "
\n", "\n", "Soit le schéma\n", "$$\\begin{cases}\n", "u_0=y(t_0)=y_0,\\\\\n", "\\tilde u_{n+1/2}=u_n+\\frac{h}{4}\\left(\\varphi(t_{n},u_{n})+\\varphi(t_{n}+\\frac{h}{2},\\tilde u_{n+1/2})\\right),\\\\\n", "u_{n+1}=u_n+h \\varphi\\left(t_n+\\frac{h}{2},\\tilde u_{n+1/2}\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}$$ \n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">**Q1 [3 points]** Étudier théoriquement la A-stabilité du schéma suivant" ] }, { "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 $\\lim\\limits_{t\\to+\\infty}|y(t)|=0$.\n", "\n", "Le schéma appliqué à ce problème de Cauchy s'écrit\n", "$$\n", "\\begin{cases}\n", "u_0=y(t_0)=y_0,\\\\\n", "\\tilde u_{n+1/2}=u_n-\\frac{\\beta h}{4}u_{n}-\\frac{\\beta h}{4}\\tilde u_{n+1/2},\\\\\n", "u_{n+1}=u_n-\\beta h \\tilde u_{n+1/2}& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "d'où\n", "$$\n", "u_{n+1} = \\left( 1-\\beta h\\frac{4-\\beta h}{4+\\beta h} \\right)u_n\n", "$$\n", "\n", "Vérifions ces calculs:" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\tilde u=\\frac{u_{n} \\left(- \\beta h + 4\\right)}{\\beta h + 4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle u_{n+1}=\\frac{u_{n} \\left(\\beta^{2} h^{2} - 3 \\beta h + 4\\right)}{\\beta h + 4}$" ], "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 je vais l'appeler \"dt\" mais afficher \"h\"\n", "dt = sym.Symbol('h')\n", "beta = sym.Symbol(r'\\beta')\n", "u_np1 = sym.Symbol(r'u_{n+1}')\n", "sym.var('u_n,x')\n", "\n", "u_tilde = sym.solve (-x + u_n - beta*dt/4*u_n-beta*dt/4*x, x)[0]\n", "display(Math(r'\\tilde u='+sym.latex(u_tilde)))\n", "\n", "u_np1 = (u_n-beta*dt*u_tilde).factor()\n", "display(Math('u_{n+1}='+sym.latex(u_np1)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On note $x=\\beta h$. Le schéma est A-stable ssi $|q(x)|<1$. On étudie alors la fonction $q\\colon \\mathbb{R}^+\\to\\mathbb{R}$ définie par $q(x)=\\dfrac{x^2-3x+4}{4+x}$." ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dans R^+ on étudie la fonction\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q(x)=\\frac{x^{2} - 3 x + 4}{x + 4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Limites aux bornes du domaine de definition:\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q(0)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\lim_{x \\to \\infty}\\left(\\frac{x^{2} - 3 x + 4}{x + 4}\\right)=\\infty$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "On cherche les points stationnaires dans R^+:\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q'(x)=\\frac{x^{2} + 8 x - 16}{\\left(x + 4\\right)^{2}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "On remarque que le numerateur de q' est une parabole et on a\n" ] }, { "data": { "text/latex": [ "$\\displaystyle q'(x)=0 \\iff x\\in\\left[ -4 + 4 \\sqrt{2}\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "De plus q'(x)>0 ssi x est supérieur à cette valeur, donc\n" ] }, { "data": { "text/latex": [ "$\\displaystyle x=-4 + 4 \\sqrt{2}\\text{ est un minimum et}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle q(-4 + 4 \\sqrt{2})=\\frac{\\sqrt{2} \\left(- 12 \\sqrt{2} + \\left(-4 + 4 \\sqrt{2}\\right)^{2} + 16\\right)}{8}=0.3137084989847604>0$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Donc q(x)>0 pour tout x.\n", "De plus, on a q(x)<1 ssi\n" ] }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0 < x \\wedge x < 4$" ], "text/plain": [ "0 < x ∧ x < 4" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Conclusion: -1" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Math\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "sym.var('x',nonnegative=True)\n", "\n", "print('Dans R^+ on étudie la fonction')\n", "q = (x**2-3*x+4)/(x+4)\n", "display(Math('q(x)='+sym.latex(q)))\n", "\n", "\n", "print('Limites aux bornes du domaine de definition:')\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(\"On remarque que le numerateur de q' est une parabole et on a\")\n", "sol=sym.solve(dq)\n", "display(Math(\"q'(x)=0 \\iff x\\in\"+sym.latex(sol)))\n", "print(\"De plus q'(x)>0 ssi x est supérieur à cette valeur, donc\")\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)+\"=\"+str(float(qmin))+\">0\"))\n", "print(\"Donc q(x)>0 pour tout x.\")\n", "print(\"De plus, on a q(x)<1 ssi\")\n", "display(sym.solve(q<1))\n", "print(\"Conclusion: -1**Q2 [2 points]** Approcher la solution du problème de Cauchy suivant avec le schéma donné d'abord avec 120 points puis avec 130 points. Commenter le résultat.\n", ">$$\\begin{cases}\n", " y'(t)=-50y(t), &t\\in[0;10]\\\\\n", " y(0)=1\n", " \\end{cases}$$ \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour la A-stabilité il faut que $h=\\frac{10-0}{N}$ soit $<\\frac{4}{\\beta}$ donc $N>\\frac{(10-0)\\beta}{4}=\\frac{10\\times50}{4}=125$. De plus, le problème est stiff." ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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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", "\n", "def schema(tt,phi,y0):\n", " uu = [y0]\n", " h = tt[1]-tt[0]\n", " for i in range(len(tt)-1):\n", " u_tilde = fsolve ( lambda x : -x+uu[i]+h/4*phi(tt[i],uu[i])+h/4*phi(tt[i+1],x) , uu[i] )[0]\n", " uu.append( uu[i]+h*phi(tt[i]+h/2,u_tilde) )\n", " return uu\n", "\n", "\n", "t0, y0, tfinal = 0, 1, 10\n", "beta=50\n", "\n", "phi = lambda t,y : -beta*y\n", "sol_exacte = lambda t : exp(-beta*t)\n", "\n", "figure(figsize=(10,5))\n", "\n", "subplot(1,2,1)\n", "N = 120\n", "tt = linspace(t0,tfinal,N+1)\n", "h = tt[1]-tt[0]\n", " \n", "yy = [sol_exacte(t) for t in tt] \n", "uu = schema(tt,phi,y0)\n", "plot(tt,yy,'b-',label=(\"Exacte\"))\n", "plot(tt,uu,'ro',label=(\"RK\"))\n", "title(rf' $N$={N}, $h$={h:1.5f}')\n", "xlabel('$t$')\n", "ylabel('$u$')\n", "legend() \n", "grid(True)\n", "\n", "subplot(1,2,2)\n", "N = 130\n", "tt = linspace(t0,tfinal,N+1)\n", "h = tt[1]-tt[0]\n", " \n", "yy = [sol_exacte(t) for t in tt] \n", "uu = schema(tt,phi,y0)\n", "plot(tt,yy,'b-',label=(\"Exacte\"))\n", "plot(tt,uu,'ro',label=(\"RK\"))\n", "title(rf' $N$={N}, $h$={h:1.5f}')\n", "xlabel('$t$')\n", "ylabel('$u$')\n", "legend() \n", "grid(True);\n", "\n", "\n", "figure(figsize=(10,5))\n", "H = []\n", "err = []\n", "N = 130\n", "for k in range(7):\n", " N+=100\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu = schema(tt,phi,y0)\n", " H.append(h)\n", " err.append(max([abs(uu[i] - yy[i]) for i in range(len(yy))]))\n", " \n", "omega=polyfit(log(H),log(err), 1)[0]\n", "figure(figsize=(8,5))\n", "plot(log(H), log(err), 'c-o')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "title(rf'Ordre $\\omega$={omega:1.2f}')\n", "grid(True);" ] } ], "metadata": { "interpreter": { "hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90" }, "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": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }