{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last Updated On: 2021-01-28 10:34:35.127594\n" ] } ], "source": [ "from datetime import datetime\n", "print('Last Updated On: ', datetime.now())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_TP1 EDO : calcul approché VS formel." ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul approché avec la fonction `odeint` du module `SciPy`\n", "--- " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'ECUE M62 n'est qu'une introduction aux méthodes numériques d'approximation d'EDO en utilisant Python comme langage commun de programmation. \n", "Nous allons étudier, programmer et tester plusieurs méthodes numériques.\n", "\n", "Cependant toutes ces méthodes (et bien plus) se trouvent déjà dans le module `SciPy`. \n", "Bien sûr vous devez toujours faire un peu de programmation avec Python pour les utiliser et une compréhension des fondements de la méthode numérique que vous utilisez est toujours indispensables. \n", "\n", "Voyons sur trois exemples comment utiliser la fonction `odeint` du module `SciPy` pour approcher la solution d'abord d'une EDO ensuite d'un système d'EDO (ce qui inclut les équations différentielles d'ordre 2 ou plus)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Principe d'utilisation de `odeint`\n", "\n", "Le principe d’utilisation de `odeint` (pour intégrer numériquement des équations différentielles) est le suivant: pour avoir une estimation numérique de la solution du problème de \n", " $$\\begin{cases}\n", " \\mathbf{y}'(t)=\\boldsymbol{\\varphi}(t,\\mathbf{y}(t)),\\\\\n", " \\mathbf{y}(t_0)=\\mathbf{y}_0\n", " \\end{cases}$$\n", "avec $\\mathbf{y}(t)=(y_1(t),y_2(t),\\dots,y_n(t))$ le vecteur des fonctions recherchées, dépendant de la variable $t$ et $\\boldsymbol{\\varphi}=(\\varphi_1,\\varphi_2,\\dots,\\varphi_n)$ une fonction de forme quelconque, on donne comme argument la fonction $\\boldsymbol{\\varphi}$ (qui doit avoir deux paramètres, même dans le cas autonome, avec $t$ comme deuxième paramètre), la condition initiale $\\mathbf{y}_0$ et le domaine de temps qui nous intéresse (qui commence à $t_0$). Elle retourne un tableau `Numpy` (même si $t$ était une liste). \n", "\n", "Notons que la résolution de $y''(t)=F(t,y(t),y'(t))$ passera par celle du système différentiel\n", "$$\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=F(t,y_1(t),y_2(t))\n", "\\end{cases}$$\n", "avec \n", "$y(t)=y_1(t)$, \n", "$y'(t)=y_1'(t)=y_2(t)$ \n", "et \n", "$\\varphi_1(t,y_1(t),y_2(t))=y_2(t)$, \n", "$\\varphi_2(t,y_1(t),y_2(t))=F(t,y_1(t),y_2(t))$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 1\n", "\n", "En guise d’exemple, considérons le problème de Cauchy $y(0)=1$ et une équation logistique simple de la forme\n", "$$\n", "y'(t)=\\frac{3}{2} y(t) \\left( 1-\\frac{y(t)}{6} \\right). \n", "$$\n", "On crée alors la fonction $\\varphi$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# def phi(y,t):\n", "# return 1.5*y*(1-y/6)\n", "# ou \n", "phi = lambda y,t : 1.5*y*(1-y/6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction `odeint` peut être appelée avec au minimum trois arguments: \n", "- la fonction $\\varphi$, \n", "- la valeur $y(t_0)$, \n", "- le vecteur $t$ (qui commence à $t_0$) où la fonction $y$ sera évaluée.\n", "\n", "Elle renvoi un vecteur `sol` contenant l'évaluation de la solution en les points du vecteur $t$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "y0 = 1\n", "tt = linspace(t0,5,201)\n", "sol = odeint(phi,y0,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution peut alors être tracée simplement " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol)\n", "xlabel('t')\n", "ylabel('y')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NB: le nombre de points en lesquels les résultats sont évalués n’est pas (du moins directement) relié à la précision des calculs internes (ne pas imaginer que cela fixe le pas de la méthode, en particulier)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Champ de vecteurs\n", "\n", "Bien qu'il soit trés rare que l'on puisse résoudre explicitement une équation différentielle donnée, on peut souvent avoir une idée de l’allure des graphes des solutions en observant le champs de vecteurs associé. \n", "En effet le graphe d'une solution de l'équation $y'(t)=\\varphi(t,y(t))$ est par définition tangent à son vecteur vitesse $(1,y'(t))$ et donc au vecteur $(1, \\varphi(t,y(t))$. \n", "La connaissance de la fonction $\\varphi$ en chaque point $(t,y)$ permet donc de représenter facilement ces vecteurs tangents même si l'on ne connait pas les solutions. \n", "Et si l'on en trace un grand nombre, uniformément répartis dans le plan $(t, y)$, on obtient une représentation\n", "du champ de vecteurs associé à l'équation différentielle qui permet souvent de deviner les graphes des solutions puisqu'il s'agit des courbes qui sont tangentes en tous leurs points aux vecteurs de ce champs de vecteurs. \n", "Il est alors intéressant d'y superposer la solution numérique obtenue avec `odeint`.\n", "\n", "La fonction `quiver` du module `matplotlib` permet de tracer un champ de vecteurs.\n", "Utilisons-la pour obtenir celui associé à notre équation différentielle.\n", "La courbe rouge est la solution déterminée par `odeint`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "\n", "# quiverplot\n", "# define a grid and compute direction at each point\n", "g1 = linspace(0,5,21)\n", "g2 = linspace(0,8,21)\n", "T,Y = meshgrid(g1,g2) # create a grid\n", "DT, DY = 1, phi(Y,T) # compute growth rate on the grid\n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M==0 ] = 1 # avoid zero division errors \n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "\n", "plot(tt,sol,'r')\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "title('Champ des pentes');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’un système d'équations différentielles d'ordre 1\n", "\n", "Considérons deux espèces: une proie (des lièvres par exemple) et un prédateur (des lynx par exemple). \n", "Ces deux populations sont représentées par $y_1(t)$ et $y_2(t)$ des fonctions continues du temps $t$. \n", "Si on suppose qu’il n’y a aucune autre intervention extérieur, une modélisation possible pour ce genre de système a été proposée indépendamment par Alfred James Lotka en 1925 et Vito Volterra en 1926:\n", "$$\n", "\\begin{cases}\n", "y_1'(t) = y_1(t)(a-by_2(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_1(y_1(t),y_2(t),t)] \\quad\\text{équation équation des proies}\\\\\n", "y_2'(t) =-y_2(t)(c-dy_1(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_2(y_1(t),y_2(t),t)] \\quad\\text{équation équation des prédateurs}\n", "\\end{cases}\n", "$$\n", "soit encore en notation matricielle\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(y_1(t),y_2(t),t)\\\\\n", " \\varphi_2(y_1(t),y_2(t),t)\n", " \\end{pmatrix}.\n", "$$\n", "\n", "On suppose qu’à ce jour il y a $y_1(0)=2$ unités de proies (une unités = $1000$ animaux) et $y_2(0)=1$ unités de prédateurs et on se demande comment vont évoluer les populations de ces deux espèces. \n", "Pour les simulations on prendra $a=2$, $b=1$, $c=1$ et $d=0.3$. \n", "\n", "Soit $\\mathbf{y}(t)\\stackrel{\\text{déf}}{=}(y_1(t),y_2(t))$ le vecteur des deux fonctions inconnues. \n", "On commence par créer la fonction vectorielle \n", "$$\n", "\\boldsymbol{\\varphi}(\\mathbf{y},t)=(\\varphi_1(\\mathbf{y},t),\\varphi_2(\\mathbf{y},t))\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# yy est une liste a deux composantes\n", "pphi = lambda yy,t : [ yy[0]*(2-yy[1]) , -yy[1]*(1-0.3*yy[0]) ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En faisant varier le temps sur l'intervalle $[0;20]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$ on écrit" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "yy0 = [2,1]\n", "tt = linspace(t0,20,201)\n", "sol = odeint(pphi,yy0,tt)\n", "sol_1 = sol[:,0] # [y_1(t) for t in tt]\n", "sol_2 = sol[:,1] # [y_2(t) for t in tt]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_1$ et $y_2$ en fonction du temps $t$ peut être obtenu par " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol_1,tt,sol_2)\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "legend([r\"$y_1(t)$ proies\",\"$y_2(t)$ prédateurs\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_2$ en fonction de $y_1$ peut être obtenu par" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "Y1,Y2 = meshgrid(linspace(min(sol_1),max(sol_1),21),linspace(min(sol_2),max(sol_2),21))\n", "V1,V2 = pphi([Y1,Y2],tt) \n", "r1=sqrt(1+V1**2)\n", "r2=sqrt(1+V2**2)\n", "quiver(Y1, Y2, V1/r1, V2/r2) \n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons la fonction\n", "$$\n", "E(t)=dy_1(t)+by_2(t)-c\\ln(y_1(t))-a\\ln(y_2(t))\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est une intégrale première du système, c’est-à-dire que si $(y_1, y_2)$ est une solution alors l’application $E$ est constante:\n", "\\begin{align}\n", "E'(t)\n", "&=dy_1'(t)+by_2'(t)-\\frac{c}{y_1(t)}y_1'(t)-\\frac{a}{y_2(t)}y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1'(t)+\\left(b-\\frac{a}{y_2(t)}\\right)y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1(t)(a-by_2(t))-\\left(b-\\frac{a}{y_2(t)}\\right)y_2(t)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(by_2(t)-a)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(a-by_2(t))(dy_1(t)- c)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.942278004158254e-07\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = 0.3*yy0[0]+yy0[1]-log(yy0[0])-2*log(yy0[1])\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = 0.3*sol_1+sol_2-log(sol_1)-2*log(sol_2)\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 2\n", "\n", "Considérons l'EDO $y''(t)=-\\sin(y(t))$ qui décrit le mouvement d'un pendule non amorti, équivalente au système différentiel\n", "$$\n", "\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=-\\sin(y_1(t))\n", "\\end{cases}\n", "$$\n", "avec $y(0)=0$ et $y'(0)=1$. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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DDIoJYEafCIseXwghrFFtUytLMkr4bkcRWw9VoSgwtFsgD42LZWJiKD7uUpSwRTonhdtHxHD7iBha9QbeSTvAKyuN81Z8sqmATzYVAPDujf2ZlBSmYVIhLpzWy4xe0prkVqNTNMxZDKufhk1vQnUhzP4MXKy7B+zZnzIprKrn67uGajbj8vWDurLtUBVvrM5jVM9g+sjM+8KeHFoPX10HHgFwx0oI733+bX4roh/csdpYpFj9tHFCzamvgpP1ti0YDCofZDTRqld498Z+eLhqc9fm0Ym92Haoir/+sI/+UZ2I7OSpSQ4hhNDansIT/G/LYRbvLaGhRU9MkBePTOzJzH6RMmeBnXHWOfHAuFgeGBdLbVMrT/6wj+9PLVt6z+c7AON8FW9d1w8/TylICeul9Soel7wmudXQOcPEZyEgBhY9DF9fD9d+BS7WudTS8v3H+Ca9kD+kdmdQTIBmORRF4ZkZSWw/VMWfvtnN4gdH4Olq/aNPhDivvFXG60BADNy0AHw7sKymqyfM+gg6RcHG10DfDJe/ZbVFio9+PkRWlYGXr0ohKtBLsxzOOifeuKYvk99Yz8Pz9vDVnUOklUwI4TAaW/T8uOcon285zN6iarxcdVzRN4JZ/SPp19Xf4iPbhOV5uznz6jV9ePWaPmSV1HDTh1upqG1mQ14FvZ9ZAcDHcwYyJi5E46RC/J58IjSVAbeBzhUW3g/f3grXfH5hw7kt6HhdM49/n0FShC9/HN9T6zj4ebjwyuw+XP/BFl5elsNTlydqHUmIjilKh3k3QXAvuHkheJqgCKgoMO7v4OwOaS+ARye47LmO79fE8stO8vKyHPqG6Lh6QKTWcega6MlTlyfy6Ld7+WxzAbcOj9E6khBCmFVBRR1fbD3MvPQiqhtaiA3x5pkZiczsGyEtHA4sPtyX9L9OwGBQeX11Hm+uzgPg1k+2A3DTkCieujxRCvnCakiBwpT63ggtDbDkEeOM/ZOe1zrRr7y4NJvqhha+uHOw1cxuP7R7IDcNieLTzQXM7BtBb2n1ELaqIh++uBq8Q+DG70xTnGijKDD6L8b5LDa/BX6RMORe0+2/g1RV5fEF+/Bw1XFroovV3J2b1T+Sn/aW8M/lOUxMDJPhzEIIu7TzyHHeW3eAFZml6BSFy5LCuGlIFINjAqzmeiy05+Sk8PCEnjw8oSf7j1Zzxds/06JX+d+Ww/xvy2ESwn354o7BsnKL0Jx1fEq1J4PuhMH3Glf52P6h1mlO23aoim/SC7l9ZAxxYb5ax/mVRy7rRbC3G48vyKBVb9A6jhAXr6nW2NahKHDj98YihakpCkx6EeKmwbLHIH+16Y9xib7bWcy2Q1U8NjkOXzfreTOsKArPXZGEqsKTP+zD2DUohBC2z2BQWZVZyux3N3Plfzax5WAV96X2YNPcsbx9fT+GdAuU4oRoV2JnP/Kem0LmM5cxplcwAJklNfR9diXRcxdzsLxW44TCkUmBwhwuew56TIClf4HinVqnobnVwOMLMojw9+AhK1wxw9fdhacuT2T/0ZrTsw0LYTNUFX56ECrzYNbHENjdfMdy0sGV/4WQePj+TqguNt+xLtDxumaeX5JF/6hOzB7Q5fwbWFiXAE/+PLEnq7PLWL6/VOs4QgjRIc2tBualFzLx9fXc8Vk6xSca+Pv0BDbNHcsjl/UixNc650AT1snT1ZmPbx3EoRem8MjEX9q/x76yjui5i9lTeELDdMJRSYHCHJx0cOX7xruo394GjTWaxvno50Pkl9Xy7BWJVjsR5eSkMMb0CubVlbmU1TRqHUeIC7f9A9j3HYz9K3Qbbf7juXoaVwtqbYL5c0DfYv5jnsPLy42tY8/NTMLJSvtX5wyLpmeoN88vyaKpVa91HCGEuGgtegNfbzvCmH+l8X/f7sVF58Qb1/Yh7dFUbh0eg5ebdb6/E7ZBURTuHxtLwYtTefv6fqcfn/H2z0TPXczWg5UaphOORgoU5uIZAFd9aFwacPGfNYtRWdvE22vyGRcXwti4UM1ynI+iKDw5PZHmVgOvrcrVOo4QF6YiD1b81ThiavifLHfcoFi4/E0o2gYbXrXccX8j+1gNX28v5Jah0VbXOnYmZ50Tf5uWwJGqej75uUDrOEIIccFa9AbmbS9k7CtpzP0+gyBvVz6eM5AlD45gRp8IXHTyVl6Y1tSUcApenMqXdww+/dg1728heu5i0guqNEwmHIVc1cwpaqhxYruMeZC1SJMIb67Oo75Fz2NT4jQ5/sWICfLipqFRfLO9kJxjJ7WOI8S56Vvhh3uNq2vM0GDpz6SrIPlqWP8ylOy17LFPeWFJNj5uzjw4rocmx78YI2ODGRcXwr/X5FN+sknrOEIIcU6tegPz0wsZ/+o6/u+7vfh7uPLRnAH8cN9wxsSFyPwSwuyG9Qii4MWpfHfv0NOPzXp3M9FzF5NVou3ocGHfpEBhbiMfhtBkWPwwNBy36KEPlNfyxdYjXDeoCz1CfCx67Ev14NhYvN2ceW5JltZRhDi3zf+Gou0w9RXwCdMmw+SXwTPQWChpbbbooTfklbMut5wHxsbi72kbM34/PjWexhY9r66UUVpCCOukqiqrs0qZ9MYGHv12L95uznxw8wB+vH84Y+NCpTAhLK5/VAAFL05l3t2/FComv7GB6LmLKalu0DCZsFdSoDA3nYvx7mpdBSx/wqKHfnFpNu4uOv44vuf5X2wlOnm58sDYWNbnlrM+t1zrOEKc3fECSHsR4qdD8iztcngGwPQ3oHSfcflRC9EbVJ5fkk1kJw9uHhZlseN2VPdgb24cEsW89EIKKuq0jiOEEL+SUVTNS9sbuf3TdPQGlXdv7MeiB0YwPkEKE0J7g2KMhYqP5gw4/djQF9bwl/X1NDTL/E7CdKRAYQmd+8DwB2H3F3Bki0UOubvwBCszS7l7VDeCvN0sckxTuXlYFBH+HryyIkeWBRTWaelcUHQw6SWtk0CvycalR9f/E04UWuSQi/YeJaukhkcv64Wbs84ixzSVP4zpjotO4Y3VeVpHEUIIAAqr6nno611Mf2sjxScNPDMjkRV/GsWkpHApTAirMzYulIIXp/KPK5IAKK1XiX9yGY/O3yPv24VJSIHCUkY9Cj6dYen/gcH8VcbXV+XSydOFW0fEmP1YpubmrOP+sT3YU1TN2pwyreMI8Ws5SyF3KaTOBb8IrdMYTXrBuNzp8sfNfii9QeXN1Xn0CvVhekpnsx/P1EJ83LllWDQ/7C4mr1TmuhFCaKe+uZV/Ls9m3KvrWLbvGPeN6c7Loz25eWi0TH4prN6NQ6I49MIUxnY1riAzf0cRMY8tYdHeoxonE7ZOrn6W4uoFE5+Fkj2w639mPdTOI8dJyynnzlHd8LbRZadm9Y+kS4AHr6/Kk2qssB4tDbD0LxAcB0Pu1TrNL/y7wqg/Q9aPkL/arIdatPcoB8rreGh8rNUuK3o+d4/qjqeLTlYMEkJoQlVVlu0rYfwr63h77QGmJoeT9mgqj14Wh4ezbV5XhWNSFIWbE9zIfnYS3YK9ALj/y11Ez11MYVW9xumErZIChSUlXQVdh8LqZ8w6YeYbq/II8HLllqHRZjuGubnonHhgTCx7i6pZnSWjKISV2PounDgMU/5pnF/Gmgx7EAK6wbLHjCuMmMGZoycmJWo0MagJBHi5cvuIGJZkHCPzqMxELoSwnIPltdzy8Xbu+Xwnvh4uzL9nKK9d04dwPw+towlxydxddKz5cyqr/zz69GMjX17Lde9vwWCQG43i4kiBwpIUxTjrfn0VbHjVLIfYeeQ463LLuWtUN7xsdPREm5n9Iuga4Mnrq3NlFIXQXn0VbHgNek6CmFFap/k9ZzcY/zRU5MCeL81yCHsYPdHm9pHGEWbvrDugdRQhhANoaNbzz+XZTHp9A7sOH+ep6QksemAEA6MDtI4mhMl0D/am4MWp/HNWCgCbD1bS7fElLNtXonEyYUukQGFp4SmQcg1sex9qTN+j9U7aATp5unDzUNuZWb89Ljon7h/Tg33FNWzIq9A6jnB0G16B5pMw7u9aJ2lf/HSIGABrXzC2o5iQqqq8vTbf5kdPtPHzcOGGIV1ZvPcohytlRQ8hhPlsOlDBpDfW8/baA0zv3Zk1j6QyZ3gMzjLPhLBTVw/owoHnp9Cvqz8A93y+k+i5iznZ2KJxMmEL5MqohTGPGSfKXPeySXd7oLyWVVml3DQ0Gk9X2x490WZG386E+rrx3nq5yyk0dOKIsajY+3oITdA6TfsUBSY8DSePwtb3TLrrtNxycktruXt0N5sfPdHm9uExODs58f76g1pHEULYoZrGFh77PoPr/7sVBfjqziG8Mrs3wT62tbqaEJdC56Tw/R+Gs+JPv4w6TX5qBe+kyXt6cW5SoNBCp2joP8c4WWal6X5JP9hwEFedE7fYweiJNm7OOm4bHsPP+ZVkFFVrHUc4qrUvgOIEY8y/SkaHRY+A2Imw8VVjW4qJvL/uIGG+7kzvbXsrd7QnxNedq/pHMn9HEWUnG7WOI4SwIyszS5nw6jq+2X6Eu0d1Y+lDoxjaPVDrWEJYXM9QHwpenMqdI40rC760LJvouYspP9mkcTJhraRAoZVRj4LOFdY+b5LdlZ9s4rudxczqH0mgt31V5q8b3BUfN2cZRSG0UXUQ9n4DA263nmVFz2fck9BYbZzU0wQyiqrZfLCS20bY39J3d4/qRqvewIcbD2kdRQhhB47XNfPAV7u487N0Onm68sN9w3lsSjwerjqtowmhqSemJrD9ifGnvx/43Cr+k5avYSJhrezrnaYt8QmFwXfDvu+gvONL3X26qYAWvYE7RnYzQTjr4uvuwvVDurIko4QjlbJkkbCwDa+CkzMMf1DrJBcuLBnipsGWd42Fig56f8NBfNycuW5QVxOEsy7RQV5MTg7nq61HqG82z+onQgjHsD63nMteX8+yfSX8aXxPfrx/BCmR/lrHEsJqBPu4UfDiVB69rBcALy/LIXruYqobZG4K8QspUGhp6P3g7A4bX+vQbuqaWvnflsNclhBGTJCXicJZl9uGx6BzUvh4k9zlFBZ0/DDs+crYkuVjYxNDjv4/aKqGre93aDeFVfUsySgxjmRyt7KlVU3ktuHR1DS28v3OYq2jCCFsUGOLnqd+3M/NH23D18OFBX8YzkPjY3F1lrfZQpzNfWN6sO2Jcae/7/30Cr7bUaRhImFN5MqpJa8gGHCrcfj48YJL3s33O4uobmjhzlH2N3qiTaivO1OSw/k2vYi6JrnLKSzk59eNc08Mf0jrJBcvvDf0nAxb3oamk5e8m49/LkABbh0ebbJo1qZf104kR/jxyaYCWdJYCHFR9hVXM/3fG/lkUwFzhkWz6IERJEX4aR1LCKsX4uNOwYtTuX2EcW6KP8/fw6DnVtGqN2icTGhNChRaG/YAOOng5zcuaXNVVfl082FSIv3oH9XJxOGsy81DoznZ1MqCXXKXU1hAdTHs+hz63mg7c0/81uhHoeE4bP/gkjavb25l/o5CJieHE+7nYeJw1kNRFOYMiya/rJaf8yu1jiOEsAEGg8r76w8w8z8/U93Qwqe3DeKpyxNxd5G5JoS4GH+blsCqh0cDUHayiR5PLCXn2KXfWBG2TwoUWvPtDH1uMH4Qqim56M23HKwiv6yWm4bYz8od7enX1Z/kCD8+2yx3OYUFbPo3qAYY8Setk1y6iP7QfRxs/g+0Xvxs2Qt3H+VkYys329HKQO2Z1jucIG9XPpE2MiHEeZyob+bOz9J5fkk2Y+NCWP7HUYzuGax1LCFsVo8Qbw69MIXEzr4AXPb6el5alq1xKqEVKVBYgxF/BIMetr5z0Zv+b0sB/p4udrX0X3sUReHmoVHkltay+aDc5RRm1HAcdn4GSbPA38Ynhhz2ANSVwd55F7WZqqp8tvkwcWE+DLDz0VlgXNL4+kFdWZ1dxuHKOq3jCCGs1K4jx5n65kbW55Xz1PQE3r2xP528XLWOJYTNUxSFxQ+O5I1r+wDwTtoBoucuprlVWj4cjRQorEGnaEi4HHZ8Ak21F7zZsepGlu8v5ZoBXRxmSOH03p3p5OnCp5sKtI4i7NmOT6GlDobdr3WSjuuWCqHJsPktuIiRRzuPHCerpIabhkahKIrZ4g51NMwAACAASURBVFmTG4ZEoVMUPt10WOsoQggro6oqH248xOz3NqMo8O09w5gzPMZhro9CWMqMPhHs/NuE09/3/OtSskpqNEwkLE0KFNZiyH3G5QB3f3nBm3y57QgGVeWGwfY//LqNu4uOawd1ZWVmKcUnGrSOI+xRazNsfQ9iRhuX67R1imIstJRnQ/6qC97ss82H8XFz5oo+Njr/xiUI9XVnUlIY3+0sorFFr3UcIYSVONnYwr2f7+TZRZmk9gph8QMj6d1Flg8VwlwCvFwpeHEqg2ICAJj8xgY+2HBQ41TCUqRAYS26DITIQbDlP8Z2j/NobjXw1bYjpPYMpmugpwUCWo8bBndFBb7ZdkTrKMIe7V8AJ48aWyPsReKV4BNunFfjAlTUNrEko4Sr+kfi5eZs5nDW5bpBXaluaGHZvmNaRxFCWIFDFXXM/M8mVmaV8tep8bx/U3/8PO1zyWUhrM28u4fy6uzeAPxjcRZT3tgg89A5AClQWJOhf4DjhyB32XlfuiqrlPKTTdzkAJPX/VZkJ09GxQYzf0cReoNcpIQJqaqxFSKol3FySXvh7AqD74FD66Bkz3lfPi+9kBa9yo0OMPnubw3tFkhUoCdfSQHULimKMklRlBxFUfIVRZl7lucfVRRl96k/+xRF0SuKEnDquQJFUTJOPZdu+fTC0tblljPjrY1U1jbx+e2DuWNkN2npEMLCruwXybpHUwHILKkh5rEl1Da1ahtKmJUUKKxJ3HTw6wqb3z7vS+elFxLu587oniEWCGZ9rh3YhZLqRtbnlWsdRdiTgg1wbC8MvQ+c7Ozy2H8OuHobV/Q4B1VVmbe9kEHRAfQI8bZMNivi5KRwzcAubD1UxYHyC58TSFg/RVF0wNvAZCABuE5RlIQzX6Oq6j9VVe2jqmof4DFgnaqqVWe8ZMyp5wdYLLiwOFVVeW/dAW79eBud/T348f4RDO0eqHUsIRxWVKAXec9NPv190t+Xk3lU5qWwV3b2DtzG6ZxhyD1w+Gc4uqvdl5VUN7A+t5xZ/SPROTlmJX9cfCiBXq58s61Q6yjCnmx9DzwDIWW21klMz8Mfel8L+7+Huop2X7btUBUFlfXMHtjFguGsy6z+kTg7KXyzXa4vdmYQkK+q6kFVVZuBr4EZ53j9dcBXFkkmrEZji54/frObF5ZmMzkpnO//MIwuAY7VSiuENXLROVHw4lSmJIcBMOXNDXy/s0jjVMIcHKu52Bb0vRHWPAfbP4QZb531Jd+mF2FQ4er+jvsBwtXZiav6R/LRxkOUn2wi2MdN60jC1lUXQ84SGPYguHhoncY8Bt4B2z8wLqE68uGzvmReehHebs6n3wA4ohAfd8bHh/LtjiL+PLEnbs6OsUqSA4gAzqw6FQGDz/ZCRVE8gUnAmUv5qMAKRVFU4D1VVd8/y3Z3AXcBhIaGkpaWZprkVqi2ttbufr6aZpU3dzZy4ISBq2JdmNa5mm2bNlo0gz2eV2sh59Y8LH1eZ0dAmOrKR/uaeXjeHn7avJ9bEu3zc4Cj/puVAoW1cfeD5Fmwdx5M/IfxrucZDAaVeTsKGdY90OEmx/yt2QO68P76g3y/s4i7R3fXOo6wdTs/Nc5BMeBWrZOYT0g8RI+E9I9h+EPg9OsP3icbW1iSUcIVfTvj6erY/z1cO6gLy/YfY2VmKdNSOmsdR5jG2YYctjeR0XTg59+0dwxXVfWooighwEpFUbJVVV3/q50ZixbvAwwYMEBNTU01QWzrlJaWhj39fAfLa7n1k+0cq4V3buzHpKRwTXLY23m1JnJuzUOL85oKXFF0gsvf+pm1ha0cqHNl3aOpdjdHjKP+m5UWD2s08HZobYA9X//uqS2HKimsamD2AMcdPdGmR4g3A6M78c32QpnRV3SIYmiFHZ9C7AToFK11HPMaeAdUH4G8Fb97avHeEhpa9Fwt1xdGxgYT4e/B/HQZPmpHioAz/3FHAkfbee21/Ka9Q1XVo6f+LgMWYGwZEXYgvaCKK9/ZxMnGVr66a4hmxQkhxIVLifRnx1/HA3Ckqp6Yx5bQojdonEqYghQorFF4b4gYAOkfGe/onmHe9kJ83J2ZlOS4w6/PdM3ArhysqCP98HGtowgbFlSxFWqPGT+827u4qcYlR7f993dPfZNeSGyIN327+J9lQ8eic1KY2TeCDXnllNY0ah1HmMZ2IFZRlBhFUVwxFiF+/O2LFEXxA0YDC894zEtRFJ+2r4GJwD6LpBZmtWjvUa7/YCudPF1Z8Idh9OvaSetIQogLFOjt9qvJM2OfWEp1Q4uGiYQpSIHCWg24DSpyoOCX3sfqhhaW7jvGFX0icHeRnmiAyUlheLjo+H5nsdZRhA3rfHSpcQWdHuO1jmJ+Ohfjih4HVkPlgdMP55WeZNeRE8we0MXuhkheqpn9IjCosHC3XF/sgaqqrRjnlFgOZAHzVFXdryjKPYqi3HPGS2cCK1RVrTvjsVBgo6Ioe4BtwGJVVc+/Jriwah9tPMT9X+4iJcKP7+8dRlSgl9aRhBAXyUXnxKEXphDhb5w/rPfTKyg+0aBxKtERUqCwVklXgrs/pH94+qGlGSU0tRqY1T9Sw2DWxcvNOJpk8d6jNLXqtY4jbFF5Dp1OZBjnnnBykMJf/zng5GwcpXXKdzuL0TkpXNE3QrtcVqZ7sDd9uvjz3Y5iaSOzE6qqLlFVtaeqqt1VVX3u1GPvqqr67hmv+URV1Wt/s91BVVV7n/qT2LatsE2qqvLqylyeWZTJpMQwPr9jMJ28XLWOJYS4RIqi8PPcsYyPDwFg+Itr2FdcrXEqcamkQGGtXDygzw2Q9ROcLAXgh93FdAvyIiXST+Nw1uWKvhHUNLayNrtM6yjCFqV/hEFxhr43aZ3EcnzCoOck4zw3rc0YDCo/7i5mVGyQrIjzG1f1iyCn9CSZJbLeuhD2wGBQefqnTN5cncfsAZG8dX1fGZUqhJ344JaB3DkyBoBp/97Ipvz2l1UX1ksKFNZswG1gaIVdn3H0RANbDlYxo0+EDL/+jeHdAwn2cWPBLhmGLS5SSyPs+Yry4KHgHax1GsvqdwvUV0DuMrYVVHG0ulFGT5zFtJTOuOgUaSMTwg606A08Mn8Pn2wq4M6RMbx0VQrOOnkrLIQ9eWJqAs/MSATg+g+2sjSjRONE4mLJVdmaBfUwLgm463N+3G2cSf6KvrLc3W8565y4vHdn1mSXcaK+Wes4wpZkL4LGakrCJ2idxPJ6jAOfzrDzMxbuLsbTVceEhFCtU1mdTl6ujI0LYeHuYlpldnAhbFZji557P9/J97uKeWRiTx6fEi83fISwUzcPjebN6/oCcO8XO/l2h6zIZUukQGHt+t4Exws4kL6Cvl39ZQKndszsG0GLXmWxVEnFxdj1Ofh15YR/stZJLM9JB31vQM1fRfreDC5LDMPT1VnrVFbpqn6RVNQ2sz6vXOsoQohL0Nii5+7/7WBVVinPzEjk/rGxUpwQws5d3rszn9w6EIBH5u/hi62HNU4kLpQUKKxd/HT0rj4MqV7KTBl+3a7Ezr7EhnizQIZhiwt14ggcTIM+14PioJfCPjegoDKpZQ0z+sjorPak9grB39OFH3cf1TqKEOIitRUn1uWW89JVydw8NFrrSEIIC0ntFcKXdw4G4IkF+/hw4yGNE4kL4aDvym2Iqyd7/ccx2Wkb03p6a53GaimKcfWB9MPHOVJZr3UcYQt2fwWoxgKFowqIIdujH9e6rGdE9wCt01gtV2cnJieFsTKzlIZmWS1ICFvx2+LENQO7ah1JCGFhw7oH8d29QwF4dlEmH0mRwupJgcLKGQwqbx8fgqfSREDBYq3jWLW2Cf5+2C2jKMR5GAyw+3OIGQ2dorROo5maxhbeqx1OBGU4H96gdRyrNj2lM3XNetbmyGpBQtgCKU4IIdr0jwpgwR+GAfDMokw+3VSgbSBxTlKgsHLbCqpYdbILNT7djf3yol0R/h4Mig5g8V6Zh0Kcx+GNxhYPR1pa9CyWZRxjSUt/Wl39YOdnWsexaoO7BRLk7cZPe6TNQwhr19Sq557PpTghhPhF366d+O5eY5Hi7z/uZ356ocaJRHukQGHlftpzFA8XZ9wH3gxF26A8V+tIVm1qSjg5pSfJKz2pdRRhzXZ9Dm5+ED9N6ySaWrinmPBAf3S9Z0P2Ymg4oXUkq6VzUpiaHMaa7DJqm1q1jiOEaIfeoPKnb3aTllPOi1dKcUII8Yv+UZ34+q4hADz67V6W7ZObmtZIChRWrFVvYNm+Y4yND8G13/Wg6IzD0kW7JieFoSjIah6ifY3VkLkQkq8CFw+t02imoraJzQcqmZbSGaXPdaBvgswftI5l1ab37kxTq4FVmaVaRxFCnIWqqjz+fQZLMo7xt2kJXDtIihNCiF8b0i2Qj+YMAOCez3eyQVbosjpSoLBi2w5VUVnXzLTkcPAOgZ6TYM/XoJe7d+0J8XWXNg9xbvu+g9ZG6Huj1kk0tXz/MQwqTEkOh879IDAW9nyjdSyr1q9rJzr7uUubhxBWSFVVnl+SxTfphTw4LpbbR8RoHUkIYaXGxoXy7+v6AnDTh9vYV1ytcSJxJilQWLHFGSV4uOhI7RVifKD3tVBbCofWaRvMyk1LCSevrJZcafMQZ7PnGwjqZfxQ7sCWZJQQE+RFfLgPKAr0vgaObILjsk54e5ycFKb17sz6vHKq61u0jiOEOMPba/P574ZDzBkWzZ/Gx2odRwhh5ab37sxT0xMAmPbvjRRWySqA1kIKFFbqzPYOD1ed8cHYieDuB3vnaRvOyl2WFIaTAotkFIX4reMFULgFUmYbP5Q7qMpT7R1TksNQ2s5D8mzj33J9OafpKZ1p0ass339M6yhCiFM+33KYf63I5cq+ETw5LeGX65oQQpzDnOEx3DO6OwAjX15LTaPcfLAGUqCwUm3tHVOTw3950MUdEq6A7EXQXKddOCsX4uPO4JhAFu89iqqqWscR1iRjvvHv5Ku1zaGx5ftLf2nvaNMpCqKGw96vQX5v2pUU4UtUoCc/7ZU2DyGswZrsUp5cuI+xcSG8NCsFJycpTgghLtzcyXGMjw8FIOWpFbToDRonElKgsFJt7R1j2to72qTMhuZayFmqTTAbMTUlnAPldeRIm4doo6qwdz50HWr8MO7AlmSUEB3oSUK476+f6H0tVOZD8U5tgtkARVGYmhzO5gOVnKhv1jqOEA4to6ia+7/cRWJnP966vi8uOnlbK4S4eB/cMoBQXzcAYp9YKjc4NSZXcit01vaONl2HgW8k7JXJ7M5l0qk2D5ksU5x2bC9U5Dj86ImqumY2H6xkSnL474dBJ8wAZ3fjKArRrklJYbQaVFZnlWkdRQiHVXyigds+3U4nT1c+vGUAnq7OWkcSQtiwLY+NO/116r/StAsipEBhjc7a3tHGyQlSrob81VAry+K0J8jbjaHdA1m0t0SqoMJo7zxwcobEmVon0dTy/cfQG9Rft3e0cfeDXpNPrXQiowPakxzhR2c/d5bJPBRCaKK6oYVbP95GY4uej28dSIivu9aRhBA2TlEU8p6bDMDhynrmfrdX40SOSwoUVqjd9o42KdeAqof9CywbzMZMSgrnUEUdeWW1WkcRWjPojR+6e0wAzwCt02hqSUYJUYGeJHb2PfsLUq6F+krIX2XZYDZEURQmJoaxPrecuiZZ9lkIS2rVG7jvi50cqqjjvRv70zPUR+tIQgg74aJzYuffJgDw9fZCFuwq0jiRY5IChZXRG4yzw4+NO0t7R5uQeAhNljaP85iYYJzwZoXc5RQFG+BkiXEOFwd2or6ZTQfaae9o02MceAZBhqzmcS6TksJoajWwLldGsglhSc8tyWJjfgXPz0xmWI8greMIIexMgJcrP94/HIA/fbOHnGMyn52lSYHCyuwuPE5FbTMTE0PP/cKU2VCcDpUHLBPMBoX6utOniz/L95dqHUVobe98cPUxti84sNVZZegNKpMSw9p/kc7FOBdF7nJZLegcBkYHEOjlyrJ9UgAVwlLmpxfy8c8F3DY8hqsHdNE6jhDCTqVE+vPczCQALnt9PbUyWtKipEBhZVbsL8VFpzAmrp32jjbJswDF2Fcv2nVZYhgZxdUcPdGgdRShlZZGyPoR4qeDi4fWaTS1MrOUUF83kiP8zv3CpKugpV5WCzoHnZPChIRQ1mSX0dSq1zqOEHZv15HjPLFgH8N7BPL4lDit4wgh7NwNg6OYnGS8oZP09+Uyp50FSYHCiqiqyorMUoZ0C8TX3eXcL/btDNEjjH318gvTrssSpc3D4eUug6Ya4+SyDqyxRc+63HImJITi5NROe0ebrkPBJxz2fW+ZcDbqsqQwapta2ZRfqXUUIexaaU0jd/9vB6F+brx1XT+cZTlRIYQFvHNj/9NfT39ro4ZJHItc4a3IgfJaDlXUnZ474bySroTKPCjdZ95gNqxbsDc9QrylzcORZcwH71CIGa11Ek1tzKugoUXPxIRztHe0cXKCxCshfyU0nDB/OBs1rHsgPm7O0uYhhBk1txq45/Md1Da18t+bB9DJy1XrSEIIB9K2sse+4ho+21ygaRZHIQUKK9L2IXr8hRYo4meAopO7nOdxWWIo2wqqOF4nyyY6nMYayFtpXFrUqZ1JZx3EysxSfNycGdIt8MI2SLoK9M2Qvdi8wWyYm7OOsfEhrMwqpVVv0DqOEHbphaVZ7Dpygleu7k1cWDurDwkhhJm46JxIeyQVgCcX7udAuawOaG5SoLAiKzJL6R3pR7jfBfbJewVCt9HG5UalzaNdExPC0BtUVmeXaR1FWFructA3GQsUDkxvUFmVVcqYuBBcnS/wsh/RD/yjYL8UQM9lUmIYVXXNbC84rnUUIezOsn0lfPxzAbcOj2ZycrjWcYQQDio6yIvnZyYDMO6VdbTITQmzkgKFlThW3ciewhNMPNfs+meTOBOOH4KS3eYJZgdSIv0I83VnucxD4Xj2LwCfzhA5SOskmtp55DiVdc1MuNDRWQCKYmwjO7AW6mSOhfaM7hWMm7OTXF+EMLEjlfU8+u1eenfx57HJ8VrHEUI4uOsHdyUl0jjJeNLfl2ucxr5JgcJKrMwytndc8PwTbeKmgZOztHmcg6IoTEwMZUNeOQ3NMtu+w2isMc6hkHiFcU4FB7Zi/zFcdAqpvYIvbsOkq0DVQ9ZC8wSzA56uzozoEcSqrFKZ4VsIE2lq1XPflztRgLeu63vhI7+EEMKMFt43HICmVgNvrs7TOI39kiu+lVix/xgxQV70CPG+uA09A6D7WNj/g7R5nMNliWE0thhYl1uudRRhKTlLjXMoOHh7R9vqQMO6B+FzvtWBfis0CYJ6SgH0PMbFh1J0vIHcUulLFcIUnlucRUZxNa/M7kOXAE+t4wghBGC86bnt8XEAvLoyl0MVdRonsk9SoLACNY0tbDlYycSEUBTlPMv/nU3iTKg+AkXppg9nJwbFBODn4cKKTBmG7TD2LwDfSIgYoHUSTeWV1XK4sp6JiRc5OgtOtXlcBQUboabE9OHsxNi4EABWZclqQUJ01OqsUj7bfJg7RsRcXFuaEEJYQIivOy9dZZyPYsy/0mT0pBlIgcIKpOWU06JXL+0DBEDcVNC5Gj+QibNy0TmR2iuYtJxy9Aa5kNi9hhNwYLW0d2AcnQUwIf4Sry+JVwIqZP5gulB2JszPnaQIX1ZLgUKIDqmobeIv3+0lPtyXRyf10jqOEEKc1TUDuxLq6wbA9Lc2apzG/jj2O3crsSqzlEAvV/p06XRpO3D3gx7jjQUKg8wq256xcSFU1TWzu/CE1lGEuUl7x2krs8ro08WfEF/3S9tBcE8ITZY2j/MYFxfKrsITVNQ2aR1FCJukqipzv8ugprGV16/pg5uzYy8NLYSwbpvmGls99hXXyA0KE5MChcZa9cZ5EVJ7haBzuoT2jjaJM+HkUSjcarpwdmZ0z2B0TgprsuUiYvf2LwC/LhDRX+skmio/2cSewhOMjw/p2I4SZ0DRNqg5appgdmh8fCiqCmtlOWMhLsnX2wtZlVXK/13Wi15hPlrHEUKIc9I5Kfx0/wgAbv80ncYWmYjfVKRAobFdhSeobmg53cN8yXpNBmd32C93Odvj7+lK/6hOrMmWiTLtWsNxOLDG2N5xKXO62JG0HOOH5TEdvb7EzzD+nfVTBxPZr6QIX0J93VidJQUKIS5WQUUdzy7KZHiPQG4bHqN1HCGEuCDJkX5MTQ4HIOWpFRqnsR9SoNDY6qwynJ0URvYM6tiO3HwgdgJkLpQ2j3MYFxdCVkkNR080aB1FmEv2EjC0SHsHsDanjDBfdxLCfTu2o+CeEBwPmT+aJpgdUhSFsXHG5YybWuUuihAXymBQeWT+HpydFP51dW+cOjKaVAghLOztG/oB0Kw38MOuYo3T2AcpUGhsbXYZA6MD8L3Y5f/OJn4G1JZC0faO78tOjTs11H2NDMO2X/sXgH9X6NxP6ySaatEb2JBbwZi44EtbHei3Ei6HI5ugVn532jM+PoS6Zj1bDlZpHUW0Q1GUSYqi5CiKkq8oytyzPJ+qKEq1oii7T/158kK3FZfmf1sOk374OH+fnki4n4fWcYQQ4qKt+fNoAP74zW4amuUmRUdJgUJDxScayCk92fH2jjY9J4KTC2TJXc72dA/2pmuApxQo7FV9FRxcaxw94eDtHdsLqjjZ1MqYXia6vsRfDqoBsheZZn92aHiPINxdnGSyLCulKIoOeBuYDCQA1ymKknCWl25QVbXPqT/PXOS24iIUHa/npWXZjOoZzJX9IrSOI4QQl6RbsPfpa1jvp6XVo6OkQKGhtg/JHe4Pb+PuB93HGAsUsibvWRmHYYfwc36FVDjtUc5SMLRCwgytk2hubXYZrjonhvfoYPtYm9BECOgubR7n4O6iY0SPIFZnlcm66NZpEJCvqupBVVWbga+BC71YdGRbcRaqqvL4gn0APD8zyTQjvYQQQiOvzu4DGFs9lu07pnEa2+asdQBHtja7jK4BnnQP9jLdTuOnQ94KOLYXwnubbr92ZFx8CJ9sKmDTgQrGxYdqHUeYUvYi8I10+PYOMBZAB3cLwMvNRJd5RTG2efz8pnGkimeAafZrZ8bFh7Iqq4zsYyeJ7+jcH8LUIoDCM74vAgaf5XVDFUXZAxwFHlFVdf+Fbqsoyl3AXQChoaGkpaWZJrkVqq2t7dDPt7G4hfW5zdwY70r+nm3kmy6aTevoeRXtk3NrHnJef/HscA/+9nMD93y+gw8nenZshUYc99xqWqBQFGUS8AagAz5QVfXF3zyfCiwEDp166Pu24Za2rqFZz8/5FVw3qKtp7xr0mgLKQ8a7nFKgOKtBMQF4uepYnV0mBQp70lQL+athwG0O395xpLKeA+V13DgkyrQ7TpgBG1+DnCXQ90bT7ttOtLXspeWUS4HC+pztwvDboS47gShVVWsVRZkC/ADEXuC2qKr6PvA+wIABA9TU1NQOBbZmaWlpXOrPV1HbxEPr1jEgqhPP3DRUJsY8Q0fOqzg3ObfmIef11xYd3czWQ1W8meXKwvuGd2hfjnpuNWvx6EgvqD3YfLCCplaD6eafaOMVBFHDZTnAc3Bz1jEyNpg1MgzbvuSvAn0TxE/TOonm1mQb50Aw+fUlvI9xAtLMhabdrx0J9XUnPtz39BKvwqoUAV3O+D4S4yiJ01RVrVFVtfbU10sAF0VRgi5kW3HhXlqaTV1TKy9cmSzFCSGEXfnqziEA7Ck8QV7pSY3T2CYt56Bw6H7ONdlleLrqGNzNDMOk4y+HihwozzH9vu3E2PgQjtU0kllSo3UUYSpZP4FnEHQdqnUSza3JKadbsBdRgSZsHwPjyJT4y+HAWmisNu2+7Uhqr2B2HD7OycYWraOIX9sOxCqKEqMoiitwLfCrSVUURQlTTg1rVBRlEMb3SZUXsq24MDsOH2f+jiJuHxlDbKiP1nGEEMKknJwU3jm19OiE19ZrnMY2adni0ZFe0N8xZ9+nqft/VFVl6e4Gevk7sXnjBpPtt41rUyDDgINL3uBI1GyT778jrKWXyq3JOHLio6Vbmd7dVeM0l8ZazqU1UAwtDM9aQnnwMHLWX/zvlD2dy6ZWlU359Yzr6myWn8m3sQv9DC1kLnyNstDU3z1vT+fyUvnX62k1qLz3wzoGhF36f7NyLk1LVdVWRVHuB5ZjbC39SFXV/Yqi3HPq+XeBWcC9iqK0Ag3AtapxqN1Zt9XkB7FheoPKkwv3EebrzoNjY7WOI4QQZjE5Ofz01++kHeDe1O4aprE9WhYoOtIL+vsNzdj3aer+n5xjJ6lcvp5HpiSQOqiryfb7K4Xv0K0hg26p/zHP/i+RNfVS/Td3A4UtzqSm2uYdd2s6l5rLWwn6esLH3k14z9SL3tyezuXKzFJaDencMr4/w0y1gseZDKMg/3US1DwSUp/63dP2dC4v1XC9gbf2rKTCJYTU1JRL3o+cS9M71bax5DePvXvG128Bb13otuLifLn1MPuP1vDv6/qabgJfIYSwQul/Hc+Af6zipWXZ3D4iBldnWTzzQml5pjrSC2rTTi8v2svE/eFnip9uXMnjeIH5jmHjRvcMZseR49TIMGzbl/UjuPpAt9FaJ9HcmuwyvN2cGRBtplU2nJyMbR75q4wTk4rfcTm1vGtaTrnMcyPEKZW1TfxzeQ7DugcyLSX8/BsIIYQNC/J2Y0pyGABXvP2zxmlsi5YFio70gtq0tTllJIT7Eubnbr6DxE83/i2TZbZrdM8Q9AaVTfkVWkcRHWHQQ/YS6DkRnN20TqMpVVVJyyljZGyQeSv1CZdDayPkrzTfMWxcaq9gjtU0kiMTZAkBwGurcqlv1vP05YmmXb1MCCGs1NvXG+eiyCypofhEg8ZpbIdmBQpVVVuBtn7OLGBeWy9oWz8oxl7QfafmoHiTX3pBbdbJxhZ2Hj7O6F7B5j1QQDcITZYCxTn07eqPj5sz63LLtY4iOuLIX+D0EAAAIABJREFUFqiv+KUo58ByS2spqW4k1dzXly5DwDMQsheb9zg2rO0an5Yj1xch8stq+WpbIdcP7ioTYwohHIaiKLxwZTIAw19co3Ea26FpM4yqqktUVe2pqmp3VVWfO/XYu239oKqqvqWqaqKqqr1VVR2iquomLfOawuYDlbQaVEbFmvkDBBjvchZuhZPHzH8sG9Q2DHudDMO2bdmLQOcGPSZonURz608V20b1NPP1RecMPSdD7grQS4vU2YT7eRAX5iPLjQoBvLQsGw8XHQ+Nk4kxhRCO5boz5hv8WUZtXxCZrcPC1ueV4+Wqo39UJ/MfTNo8zmt0r2COVjeSXya99DZJVY3/vruPBTdvrdNobn1eObEh3oT7eZj/YHFToKkaCjaa/1g2anSvYNILZLlR4di2HapiZWYp96Z2J9DbsdvwhBCOaeF9wwG44YOtGiexDVKgsCBVVVmXW87Q7oGWmck1OA4CY40TCIqzarvTLG0eNqpkD1QXQvw0rZNorqFZz9ZDVeYfPdGm2xhw9pA2j3NI7RlCq0Fl0wGbnzpJiEuiqirPLcki3M+d24bHaB1HCCE00buL/+mvv9x6RMMktkEKFBZUUFn//+zdeXhbV37f//cBuO8kuEiiVpIgJXmRLcu2SNmWvEleZkvTaTJpJmnSZjppJlvTNtO0nSTN0+eXNmmWJpPOTLYmTdJ2ksxkZjy2JXmRZUmUvO+SuGpfKIL7TgLn98cFZFqiZC0EzgXweT2PHlASCHwEUpe43/s938PJgUm2puoEwhhY+yQc2w+Tg6l5zjRTX1FIuLZEBYp0dfh7YILecoMsd6g3wsxcLHUFirwiaHoYjj7tdbLIZTatrqQkP0dzKCRrff/ds7x9cohf2t5CYV7QdRwREWfa//1DAPzKt991nMT/VKBIoZStD59v7ZNgo9CpaftXsq2lhkM9A0zMzLmOItfryFOwegsUh1wncW5vRz/5OQHuXZOk7UUXsvZJGDkNZ99K3XOmEW/OTYiXjvZpzo1knWjM8ru7O2iuK+EH7qx3HUdExKml5YVUx5e5/eELnY7T+JsKFCm0t+MCq0JFrAoVp+5J6zdBca3asK9ia3MtM9EYh3oGXEeR63GhAy4cgbXavQO8+RP3rKmiIDeFVynDO8AEdHy5im0ttZwZnqJTc24kyzz1zhm6L4zzC480EwxoW1ERkef+9QMA/PauDl24uAoVKFJkei7Kge5IanbvmC8QgJbHoOs5mJtO7XOniU2rKynMDWqZR7o5Eh/+uvZJtzl84PTQJF19Y6lbPpZQHIKVbSpQXMW2i9uNajcPyR5z0Ri//1wna5eU8tgtS1zHERHxhYqiPNYu8bZa/s1njjhO418qUKTI68cGmZyNpnZ5R0LLkzAzBsdeTv1zp4GC3CCtjSEVKNLNkadh2UYoV+uwk+VjCWufhL4PINKd+udOA0vLC2mqLeHlTm0tJtnju2+foad/nF94JExA3RMiIhf93U+3AfD1vT3qorgCFShS5KXOC+QEDK2NDtbKN2yF3CLvhE4WtLW5ht7+cY5Hxl1HkWsxeh5Ov+ZtdSns7bjAkrICwrUOtlpNfA2O6vhyJfc1VfNK7wBTs1HXUUSSbi4a438838m6pWVsX6/uCRGR+Urycy52UfzWzqOO0/iTChQpsrej/+JE95TLLYTGh+DoM5q2fwVbtd1oeul41rttUYFiLhpjX1c/DzRXY4yDK5WVq6HuVhVAr+KB5mqm52K8fly7KUnme+qdsxyLTKh7QkTkCv72i60A/NEedZ8uRAWKFOgbmeLw2RE37dcJa5+E0TNw5k13GXxsdXUxK6uK1IadLo4+AxUroXa96yTOvX1qiNGpOffHl5MHYUwFvoXcuyZEbtCwt1Ovj2Q2ay1fe6mbcG0Jj66rcx1HRMSXSgtyqS31dvT48/29jtP4jwoUKbA3ftKb8gGZ8yWm7asN+4q2NFVzsDvCXDTmOopczcwE9LzodU+46BjwmZc6+gkYbxmBM2ufBBv7sLNFPqI4P4c7V1ayTwVQyXAvd/Zz5NwoP/VAg7onRESu4qmfuw+AX//eB46T+I8KFCmwt+MC1SV5rF9a5i5EcQhWbFYb9lXcH65mdHqOt08NuY4iV9OzB+amoOVx10l8YW/HBTasqKCiKM9diCW3Q/kK7eZxFQ+Eq3n/zAj9Y9pNSTLX1/d2U1eWz6fvWOY6ioiIr9WWFlz8ePcH5x0m8R8VKJIsFrPs6+rn/nCN+6sJa5+Avvdh8JjbHD7V1hjCGLTMw++OPg355bBqi+skzg2Oz/D2qSG33VngdbK0PAE9LxKITrnN4lP3xb9G+7t0fJHM9N7pYfZ3RfiJLWvIzwm6jiMi4nu7fvEBAH7qL19znMRfVKBIsvfODDMwPsMDzQ7brxMSAwXVRbGgiqI8bq8v1wmEn8XiywjCj0Aw13Ua5/Z19WOto+1FL7X2SZibompAc24Wclt9OeWFuVrmIRnr63t7KMnP4UfuXek6iohIWmiuK734cfeFMYdJ/EUFiiTbFz/Zva/JBycQoUaoWas5FFexpamaN08MMTY95zqKLOT06zB+Qbt3xO3r7Ke0IIcNy8tdR4FVbVBQQXX/QddJfCkYMGxpCvFyZ7/2PZeMc35kiqffPcsP372CsgIVj0VErtVXf2QjAJ/5w/2Ok/iHChRJtr+rn7VLSqmJT2p1ruUJOH4AJgZcJ/Gl+8LVzMUsB7sjrqPIQo4+DYEcaHrYdRLnrPWWj7U1hsgJ+uBQHsyF8HZCkdchFnWdxpfua6rh3MiUrpJIxvmbQyeIWcvnW1e5jiIiklaevH0pAKPTc0zN6v0TqECRVFOzUV49NsgWl9P1L7X2SbBR6NztOokv3bWqkoLcwMXOF/GZo097V+oLK10nce7EwASnhybd7t5xqZbHyJ0bhZOvuE7iS/eHva/V3g4dXyRzzEZj/J9XTrC1uYZVoWLXcURE0s7n7lkBwC/97duOk/iDChRJ9PrxQWbmYmxpCrmO8qFlG6FkCRzVtP2F5OcEuWdNSAUKP4p0w4UjWt4Rl/gebfNTgaLpEWImCB3PuE7iSyuqilgdKtLxRTLK7g/O0zc6zec3q3tCRORG/OdP3wrA99856ziJP6hAkUT7uvrJCRjuWeOjAkUgAC2PQdfzMKft7hZyf1M1XX1jnB2edB1F5ut41rttfsxtDp/Y39XP0vICGqp9dMWyoJzh8lugY6frJL51X7iagz0RZuZirqOILIr/3X6c+opCtrXUuo4iIpKWcoMBivO83Y+05agKFEm1v6ufO1dWUJKf4zrKR7U8CTNj0LvXdRJfui/ehq1p+z5z9BmoXQ9Va1wncS4asxzojrClqRpjHG9ffIlI6G6v02Wg13UUX7o/XMPETJQ3Tgy6jiJy07r6RmnvifCjm1cRdL2VuohIGvvbL7YB2nIUVKBImqGJGd49Peyv+RMJax6A3GI4omUeC1m7pJTqkjy1YfvJxIA33LXlcddJfOGDMyMMTcz6a/5EXH/13d4HiY4X+YjWxhDBgFEBVDLC3752ipyA4bOblruOIiKS1tYvK7v48eRMdg/LVIEiSQ72RLAWX55AkFsAjQ9C5y7QdneXMcawpama/V3aDtA3up7zhrtq/gQwf/6Ej5aPxU0VLoXqZq/jRS5TVpDLhuXlvNx5wXUUkZsSjVm+/eZptrXUUF3ik53KRETS2I/cuxKA//AP7zpO4pYKFEmyr6uf4rwgG1ZUuI6ysJbHYeQ0nMvu/wBXcl9TNf1jMxw5N+o6ioC3e0dxrTfkVTjQ3U9LXSm1pQWuoyys+TE4vh+mhl0n8aX7wzW8c3qYoYkZ11FEbtj7kSh9o9P84EZ1T4iILIavfGI9AN9647TjJG6pQJEk+7si3NsQIjfo05c4vN271TC7Bd0frgE0h8IX5mag8zlvuGvAp/+fUmhqNsorvQO+7J64qOVxiM15w3jlMveHq7HW+zkhkq72n56jvDCXh9ZpOKaIyGIoyA1e/LirL3svkurdfhKcGpygt3/cn/MnEkpqof4urRO/giXlBTTVlvCy5lC4d3wfzIxqeUfcG8cHmZ6L+XP5WMLye6CwUseXK9iwooLivCAHunV8kfQ0MjXLG31RPrVhGfk5wY//BBERuSa//8N3APCFv3zdcRJ3VKBIggPxq2K+PoEArw379Osw1uc6iS/d11TNK70Rpueye1CNc0efgZxCWLPVdRJf2NfVTzBguLfBxx0UwRyvS6tzF0TnXKfxndxggHsbQhzoVgeFpKen3znLbAx+8C4t7xARWUyf2rAMgJ7+ccdJ3FGBIgn2d/dTXZJPc12J6yhX1/wYYL2TCLnMfU3VTM3GeP24tgN0xlqvQNH4IOQVuU7jC/u7+rlzhQ+3L75U82MwOQinXnGdxJfaGkP09o9zZmjSdRSR6/b9d89SW2TYsLzcdRQRkYxijKE4z+tMOzqQnRdJVaBYZNZa9nf1s6UphDE+3xN8yW1Qukxt2FewuTFEjrYDdOv8ezB8UtuLxg1PzPKOX7cvvlTTwxDI0fHlCtoava+huigk3QyOz3CgO8Kmuhz/v88REUlDX//8JgD+8M0px0ncUIFikR09P0r/2Ex6nEAYA807oPtFmJt2ncZ3SvJz2LCigvYenUA4kzi5De9wm8Mn2nv6ve2Lw2lwfCkoh1Vb4KgKFAtZu6SUquI8zaGQtLP78HmiMcvdSzR7QkQkGRLv80ZnHQdxRAWKRZa42p4WBQrw2rBnxrwtAeUybY0h3jk1zOhUlh4hXOvYBcvuhNI610l8YX9XhOK8IHf4dfviS7U8Dv1HYaDHdRLfCQQMrQ0hDnRFsNa6jiNyzZ559yzLKwtZXaa3kCIiyVJRlAvAK70DjpOknn66LLID3REaqoupryh0HeXaNGz1BhBqu9EFtTaGiMYsrx7LvoODc+MROPWquifm2d/Vzz1rqvy7ffGlmh/zbtVFsaDWxhDnRqbozeJBWKlmjHnMGHPUGNNljPnyAn//T40x78R/HTDGbJj3d8eMMe8aY94yxryW2uT+MDw5y76ufp64bamWd4iIJNHv/ZC3m8e//uZbjpOkXpq8y00Ps9EYB3si6dM9AZBb6BUpjj7jDSSUj9i4spK8nMDFnVkkhbqeAyw0b3edxBdOD03S4/ftiy9VtQZq1kLHM66T+FLia7lfcyhSwhgTBL4KPA6sBz5njFl/yd16ga3W2tuB3wC+ccnfP2itvcNauynpgX3oxSN9zEYtj926xHUUEZGMtq2lFoBTg9k3TFsFikX01skhJmaibGny8fZ/C2neAUPH4cJR10l8pyA3yKZVlRpk50LnTiiuhaV3uk7iC/u7vOVjaTF/Yr7mx+D4AZgadp3Ed1aHilhaXkC75lCkyj1Al7W2x1o7A/xf4NPz72CtPWCtTWzddBDQPprzvHi0j+qSPO5YnibLzEREMsCpwQnXEVLK5/vUpZd9nf0YA60NaXYCkWih73gWate6zeJDbY0hfntXB4PjM1QW57mOkx2ic14HxdpPQEB1VPAKFNUlebTUlbqOcn1aHof9v+d9PW/9QddpfMUYQ1tjNS8cOU8sZgkE1DKfZPXAyXm/PwXce5X7/3NgfvuPBXYZYyzwdWvtpd0VGGO+AHwBoK6ujj179txsZt+IWctz70+woSaHvXtfYmxsLKP+fX6h1zV59Nomh17X5PnMass/HDP83J/v5ec2FriOkzIqUCyi/V393F5fTnl8qEnaKK+HJbd7cyju+wXXaXyntbEa6OBgT4THb1vqOk52OPWqd8U9/KjrJL7gbV8coa2xOv3WfS+/G4pC3hwKFSgus6UpxN+/cYrD50a4ZVm56ziZbqH/PAuubTTGPIhXoLhv3h9vsdaeMcbUAruNMUestXs/8mBe0eIbAJs2bbLbtm1blOB+8MaJQcZ3HuCHt97Gtg3L2LNnD5n07/MLva7Jo9c2OfS6Js9c7EX+4dgEb/RFs+o11qXJRTI2PcdbJ4doS6f14fM1PwYnD8KEhkFe6vbl5RTnBbXMI5U6d0IgBxofcp3EF7r6xugfm6atMc2WjwEEghDeDp27vM4Y+Yi2Ru9nhubcpMQpYMW83y8Hzlx6J2PM7cCfAJ+21l78wlhrz8Rv+4Bv4y0ZyRp7jvQRMPBAui0zExFJUznzOiujseyZFagCxSJ59dgAczGbnicQ4BUobCw+mFDmyw0GuGdNFfu1Tjx1OnbBylYo0BVlgPYe7xypNW2PLztgaghOHnKdxHeWlBfQUFPMAR1fUuFVIGyMWWOMyQN+GPju/DsYY1YC3wI+b63tmPfnxcaY0sTHwHbgvZQl94E9HRe4Y0UFFUVa6igikiqtDd57v2+9ccpxktRRgWKRHOyOkBs0bFpV5TrKjVl2JxTXeHMo5DJtjdX0XBjn3PCU6yiZb+gk9L3vXXUXANq7I9RXFLKyqsh1lBvT+DAEcr3OGLlMW2OIV3oHmI3GXEfJaNbaOeBLwE7gMPBNa+37xpgvGmO+GL/bV4AQ8EeXbCdaB+wzxrwNvAJ831qbNT8wB8dneOfUMFuba11HERHJKr/8uDcf8Ld3Zc9mBipQLJL2ngh3rKigMC/oOsqNCQS8YZldz0F01nUa30lcuW7v0VXOpOvc5d0273CbwydiMcvBngibG0LpN38ioaAMVrV6nTFymS2N1YzPRHn75JDrKBnPWvu0tbbZWttorf0v8T/7mrX2a/GP/4W1tjK+lejF7UTjO39siP+6JfG52eKVY97yz7Tt4hIRSVN3rPB2TTo/Mu04SeqoQLEIRqZmee/08MUWnLTV8pg3mFBt2JdZv7SM8sJcrRNPhc5dULEKqptdJ/GFo+dHGZyYTf8Tg/B2uHAYhk64TuI7XvEJzbkR3zrUM0B+ToANK7TsTkTElcmZqOsIKaECxSJ4pWeAmIXN6X4C0bANgnla5rGAQMDQ2hDiQHcEa7NnSE3KzU5Cz0te90S6dgssssRJa/oXKOIdMZ3qorhUZXEe65eWsb9LHVriT4d6I9y5soL8nDTtEhURSWNPxncR/H+vZsdFHhUoFkF7T4S8nAAbV1a6jnJz8kth9X3edoBymbamEKeHJjk5MOk6SuY6th/mJj88mRXauyOsrCqivqLQdZSbUx2GytVa5nEFbY0h3jwxlDVXRyR9jEzN8sHZEe5dk+ZFUhGRNPWvHmwE4Kt7uh0nSQ0VKBZBe3eEjSsrKMjNgCsLzY9BpBMi2fEf4HokdmjRtP0k6twJOYWweovrJL4QjVkO9UbSd3eg+YzxCk+9e71OGfmItqZqZqIxXjuurZ7FX147NoC1cG9Dmg4BFxFJc7cs85bXXRjNjjkUKlDcpKGJGQ6fG6G1IUP2BU8MJuzQtP1LNdaUUFOar3XiyWKt933XsBVy07xbYJF8cGaE0am59F/ekdC83euQ6X3ZdRLfuWd1FTkBo+OL+M5rxwbJCZj07xIVEckA2bDUXAWKm3Swx7uykDEnEJWroWad5lAswBhDW6PmUCRNfwcMHdf2ovMkdo1J+wG8Cavug9wibTe6gOL8HO5YUcEBzaEQn3n39DAtS0ozo0tURCRNtdSVAnCoN/M7LVWguEkHeyIU5GbYZOvwo3D8AEyPuk7iO22NIfrHpunqG3MdJfMkunZUoLjoQHeEhppiassKXEdZHLkF3jDejl1ex4x8RFtTNe+eHmZ4Uls9iz9Ya3nn1DC3L8+g9zgiImnoJ+9bDcCf7et1GyQFVKC4Se3dETatqsqsydbNOyA2Cz17XCfxnbZGbymP2rCToHMX1N4CFStcJ/GF2WiMV3sHMqd7IiH8KAyfgAtHXCfxnbbGEDELr2TB1RFJDycGJhienOX25RWuo4iIZLVPbagHYNcH5x0nST4VKG5CZGyao+dHM2d5R8KKeyG/XHMoFrCiqojllYUalLnYpobhRLs3o0AAr616fCZ6sSiWMRIdMtpu9DLeNo4B2lUAFZ9459QwALfVq4NCRMSlwrwMuhj+MVSguAkHe7yrXJsz7QpnMBcaH4TO3WrDXkBbY4iDPQNEY3ptFk33CxCb0/ai8yROUjdn2uT88uVQd6u2G11Afk6Qu1ZV0t6jAoX4w7unh8nLCdCypNR1FBERiYtl+DmIChQ3ob2nn6K8YGauzWzeAWPn4Nw7rpP4zpamaoYnZzl8dsR1lMzRuRsKKmD53a6T+MbBnggtdaWESvJdR1l84e1ex8zkkOskvtPaEOLw2REGx2dcRxHhgzMjrF1SSm5QbxdFRFxbGy8Wv35i0HGS5NJPnJvQ3h3h7tVVmfmDu+kR71Zt2JdJzATQMo9FEot532dND0Mwx3UaX5iZi/HqsYHMWz6W0LwDbNTrnJGPSHzND/Wqi0Lc6+wbJVyr7gkRET/4zJ3eHIp/ePO04yTJlYFn1qnRNzJF94XxzD2BKKmFZRvVhr2A2rICmmpL2N+lE4hFcfZNGL+g5R3zvHVyiKnZWOYtH0tYfjcUVqoAuoDbl1dQmBvUHApxbnhylvMj04TrSlxHERER4FMblgHwnbfOOE6SXCpQ3KDEGuGMm7A/X3g7nHoVxvVG+VKtDSFePTbAbDTmOkr669gFmA+7doT27gjGZOD8iYRA0Pt6d+72OmjkorycAJtWaw6FuJfYTjtcqwKFiIgfLKsoBGBses5xkuRSgeIGHeyJUJqfwy3LylxHSZ7m7YCF7uddJ/Gd1sYQEzPRixPO5SZ07vSuqBdncLHvOrX39LN+aRkVRXmuoyRPeDtM9MOZN1wn8Z3WxhAd58cYns7sIVjib119owA0qUAhIiIppALFDWrvjnDPmipyMnH+RMLSO6G4Rm3YC0i03rdrDsXNGT0PZ97U9qLzTM1GeePEUGZ3Z4HXQWECOr4sIPG1PzIQdZxEslnn+THycwIsryxyHUVERC5hM3inxQw+u06es8OTHItMZO78iYRAAJoeha7nIKY3yvNVFeexdkmp2rBvVtdu71bzJy5648QgM3OxzD++FFV5nTMdO10n8Z3b6sspyc/hsAoU4lBv/zhrqosJBozrKCIiEre80lvm0X1hzHGS5FGB4gYkhpdl7AC7+cKPwuQgnHrNdRLfaW0M8dqxQabndBJxwzp2QukyWHKb6yS+cbA7QsDA3WsydP7EfOHtcPYtGD3nOomv5AQD3LOmiiMRHVvEndNDkxffCIuIiD/cH64B4KWOzO3iVoHiBrR3RygvzGX90gyeP5HQ+BCYoDcnQD6irbGa6bkYb54Ych0lPUVnoftFrwhmdIUu4UB3hNuWV1BWkOs6SvI1xztnOne7zeFDrQ0hzk1Yzo9MuY4iWchay6nBSS3vEBHxma3N1QC83HnBcZLkUYHiBrT3RLh3TRWBbGh7LKyAlZu1TnwB96ypImDQdoA36kQ7zIx+eJIqTMzM8fapLJg/kVB3K5TVqwC6gEfX1/Fj6/MoyAm6jiJZaGRyjrHpOeor1EEhIuIn96zx3iO+0jvgOEnyqEBxnU4OTHBqcDLz14fPF94O596Fkczec/d6lRfmcmt9uQoUN6pjJwTzYM1W10l847Vjg8xGbfYcX4zxOmi698DcjOs0vrK6upiHVuZSXpQFnTTiOycHJwC0xENExGeqir0d3iZmMncZqAoU1ykxFDFrTiBgXhu2uigu1doQ4s2Tg0xm8EEiaTp3waotkK8t7BLaeyLkBAybVlW6jpI64R1eJ82JA66TiEjc6aFJAOpVoBARkRRTgeI6HeyOUFWcR3NtqesoqVOzFspXaJ34AjY3hpiNWl4/Pug6SnoZ6IX+Di3vuER7d4QNKyoozs9xHSV11jzgddJ0qAAq4hfnhr3ZJ0vKCxwnERGRbKMCxXWw1tLeE2FzQ5bMn0gwxlvm0f0izE27TuMrd6+uIidgONCduZN0kyLRjRPe7jaHj4xOzfLu6WHasqk7C7wOmtX3qUNLxEci496Sq6qiPMdJREQk26hAcR2ORyY4OzyVPQPs5gtvh9lxOK427PlK8nO4fXn5xaU/co06dkKoCUKNrpP4xqvHBojGbJYeX3ZApBMGelwnERFgYHyaiqJccoJ6mygi4lczczHXEZJCP3muQ1bOn0hY8wAE83WVcwFtjdW8c2qYsek511HSw8w4HNvnnZTKRe3dEfKCATZm0/yJhOZ4J42WeYj4wsD4DKFidU+IiPjRqpC3BXRioHGmUYHiOrR3R6gpzaexJguH+uUVwZr7VaBYQGtjiGjM8moGb/ezqHr3QnT6w5NSAbwC6J0rKyjIzcJtJasaIBTWdqMiPhEZmyFUnO86hoiILCBxLtpzYdxxkuRQgeIafTh/IoQxWTR/Yr7wDoh0QaTbdRJfuWtVJXnBgJZ5XKuOnZBXAivbXCfxjeGJWd4/M5Kd3VkJzTu8zprpMddJRLLewPjMxa3sRETEX1aHigHo7c/M90wqUFyj7gvjXBidzs714QnhR71b7ebxEQW5Qe5cWaFBmdfCWq8Lp2Eb5OjNb8Kh3gjWesuFslZ4O0RnoPcl10lEst7w5CwVRbmuY4iIyAKWVXg7LJ0ZmnKcJDlUoLhGWT1/IqFqDVQ3qw17Aa2NId4/M8LwxKzrKP52/n0YOa3tRS9xoDtCQW6ADSvKXUdxZ2Ur5JV6HTYi4tTkTJTCvCxcbiYikgaWVRQCcHZ40nGS5FCB4hod7I6wpKyA1fGhJFkrvN1rw57JzDVPN6q1IYS1cLBXyzyuKlHc0vaiH3GwJ8KmVVXk52TxCUFOHjRu8zq0rHWdRiRrWWuZmI1SpAKFiIgvLSn3OijODquDImtZaznYE6G1MYvnTyQk2rB71IY93x0rKyjIDdDerQLFVXXsgqUboHSJ6yS+MTA+w5Fzo2xuqHIdxb3wDhg9A+ffc51EJGvNRGNEY5aivBzXUUREZAHV8SHGA+MzjpMkhwoU1+D0mCUyPpPd8yehFfVyAAAgAElEQVQSEm3Y2s3jI/JzgmxaVcVBDcq8sokBOPWKthe9xCu9Wj52UaKzRss8RJyZnIkCUJiNOwqJiKSBimJvRtBQhi4tV4HiGhwe8H5Y6wSCeW3Yu9SGfYnWxhBHzo0SGZt2HcWful8AG9P8iUu0d0cozA1y+/IK11HcK62DpXeoACri0ES8QKElHiIi/lQc73Abm55znCQ5nBYojDGPGWOOGmO6jDFfXuDvjTHmf8T//h1jzEYXOY8MRKmvKGRFVZbPn0gI7/AGHZ5/33USX0kUsA72DDhO4lMdO6GoGpY5+W/sW+09ETatriQ3qHox4BWwTr3qddxIVjLGPGqM+WNjzB3x339hER/7ht93fNznZoqZuRgAeTk6JomI+FEwkNkjB5z99DHGBIGvAo8D64HPGWPWX3K3x4Fw/NcXgP+Z0pBALGY5MhBV98R8F7cb1VXO+W6rL6c4L0h7j7YbvUwsCl3Ped87Ab3pTegfm6bj/JiOL/OFd3idNl3PuU4i7vwr4N8CP2qMeQi4YzEe9Gbed1zj52aERG9kto/cEhERNz72TMEY8yVjTGUSnvseoMta22OtnQH+L/DpS+7zaeAvrecgUGGMWZqELFd0+NwI47No/sR8pUu8QYcqUHxEbjDAPWuqOKBBmZc79RpMDnxY3BIADsW7bTbr+PKhZXd6nTaaQ5HNLlhrh6y1/wbYDty9SI97M+87ruVzM4pBFQoREUm9a7mUuQR41RjzzXh742L9xKoHTs77/an4n13vfZIqsSuDrnBeIrwdTh6CyUHXSXyltTFEz4Vxzo9k5rY/N6xzJ5ggND7sOomvtPf0U5wX5Lb6ctdR/CMQ8ApZXc95nTeSjb6f+MBa+2XgLxfpcW/mfYfz9yOpYjVfSkREHPrYPaSstf/RGPOf8K5i/ATwh8aYbwJ/aq3tvonnXqjQcelPxWu5j3dHb43qFwDq6urYs2fPTUT7UPV0jH++1tLx1iE6FuURM0PZaA0bbYwPvvsH9NU9cM2fNzY2tmhfGz/KG/ZOqP70qX20LUvuFm3p9FpueuNbzJWt5a1Db7mOsiBXr+UL707QWBZg/8t7U/7cybIYr2XN7HJumRrije99g5HydYsTLA2l0//xxWCMeQ74JWvtd+b/ubX2DxbrKRb4s2t933FN70eS9V4klc6OeTMoDh8+TMVw5xXvl23fn6mi1zV59Nomh17X5LmW1zYTX/trOoOy1lpjzDngHDAHVAJ/Z4zZba39dzf43KeAFfN+vxw4cwP3SWT8BvANgE2bNtlt27bdYKzLVezZw2I+XkaI3Q9H/yvrc0+z/jpemz0Z/lpGY5bfeXMXw3m1bNt2e1KfK21ey+HTsKcXHvl1tt23zXWaBbl4LftGpzjz7PP82ANhtm1tTOlzJ9OivJaTd8Dh32FjcR9s++lFyZWO0ub/+OL5d8DvGmOOA79irT27yI9/M+878q7hc5P6XiRVui+Mwb6XWL9+HdvuuHKTSBZ+f6aEXtfk0WubHHpdk+eqr+2zXrNhJr721zKD4ueMMa8D/w3YD9xmrf1p4C7gB2/iuV8FwsaYNcaYPOCHge9ecp/vAj8Wn6q9GRhOwhsWuRGBIDQ9Al271YY9TzBguLchRHuP5lBclJhVou1FPyIxf0LzbRZQWAErWzXnJstYa9+w1j4EPAU8a4z5VWNM4SI+xc2877iWz80IwfhK3mhMSz1ERCT1rmUGRTXwj6y1O6y1f2utnQWw1saAT9zoE1tr54AvATuBw8A3rbXvG2O+aIz5YvxuTwM9QBfwx3iTvcUvwtthIgJn3nSdxFfaGkOcGJjg1OCE6yj+0LkbyldCzVrXSXylvSdCaX4Otywrcx3Fn5q3w/n3YPiU6ySSQvE5V0fxds/4WaDTGPP5xXjsm3nfcaXPXYxcflOQGwRgajbmOImIiCwkluEF5GuZQfGVq/zd4Zt5cmvt03hvBub/2dfmfWyBn7mZ55AkanwITMCbtr98k+s0vpEYqNreHeGzm4ocp3Fsbhp69sAdn9OedZc42B3h7jVV5AS17eqCwjtg91e8LopNP+k6jaSAMWYf0AC8DxwE/hlwBPh5Y8z91tov3Oxz3Mz7joU+NxMVxgsUk7PqjhQR8aPE8TlxvM40emcsN66oCpbfozbsSzTXlhIqztMyD4Bj+2B23DvZlIvOj0zR0z+u5R1XU9MCFSuhQ8eXLPJFoN5a+6i19j9Za5+y1nZZa38WuN91uGyRn+u9NZxSgUJExJcGJ2YAqCrOc5wkOVSgkJvTvB3OvgWj51wn8Y1AwLC5IUR7d0TbtXXugpwCWH2f6yS+cjBevNqsAsWVGeMtI+t9CWa1bW82sNa+Z6980HwypWGyWH5OAGNUoBAR8avImAoUIleWuDLe9ZzbHD6zuTHE2eEpjkeyeA6Ftd7ynzUPQF6WL3W5RHt3hLKCHNZr/sTVhXfA7AQc3+c6iThmre1xnSFbGGMoyAmqQCEi4lPnR7wLNzWl+Y6TJIcKFHJz6m6BsnrvRFQuaovPoTjQncXLPCJdMNjrXQWXjzjYE+GeNSGCAc3luKo190NOoZZ5iKRYcX4Oo1NzrmOIiMgCTg1OArCicjE3uvIPFSjk5hgD4Ueh+0WYm3GdxjcaqoupLc3P7jkUiaKVthf9iLPDkxyLTLC5ocp1FP/LLfQ6cDp3eh05IpISVcW5F9c4i4iIvyQKFMsrM7NDWQUKuXnh7TAzCifaXSfxDWMMrY1ZPoeicyfUrPMGHcpFifkTid1e5GM0b4fBY9Df6TqJSNaoLMpjcHzWdQwREVnAiQFvCflydVCIXMGarRDM024el2hrDNE/Nk1X35jrKKk3NQLH272TS/mI9u4I5YW5rFui+RPXJDHnplPLyERSpao4jwF1UIiI+FLPBe/corG2xHGS5FCBQm5efom3S4PmUHxEa0M1QHYu8+jZA7FZbS+6gPaeCPeuqSKg+RPXpmIF1K7X8UUkhSqK8hhSgUJExJd6+scBWB0qdpwkOVSgkMXR/BhEOmFAg9YTVlQVUl9RyIGuLCxQdO6E/HJYca/rJL5yanCCkwOTWt5xvcKPekvIpkZcJxHJCt4MillisSxdoigikgbycjLzVD4z/1WSeomdGjRt/6LEHIqDvZHsepMXi0Hnbmh6GII5rtP4ysGeAQA2N6hAcV3COyA2Bz0vuk4ikhVqSvKJxiyRcXVRiIhIaqlAIYujag1UN0PHs66T+EprQ4ihiVmOnBt1HSV1zr0NY+e1e8cC2rsjVBbl0lJX6jpKellxLxSUqwAqkiLLKrzBa2eHJx0nERGRbKMChSye8HY4vh+ms3Ao5BUkWvkPdPc7TpJCHTsBA02PuE7iOwd7ImxuCGn+xPUK5kDjw94g3ljMdRqRjJcoUJwZUoFCRERSSwUKWTzNOyA64w1IFMB7k7c6VHRxa8ms0LETlm+C4mrXSXzl5MAEp4cmtbzjRjXvgPE+OPuW6yQiGa8+XqA4PTTlOImIiMw3POFtAZ0XzNzT+Mz9l0nqrWyF/DJtB3iJ1sZqDvUMMBfNgiu/Y31w5g3t3rGAxG4uGpB5g5oeAYy2MxZJgYqiXApzg+qgEBHxmVePefPM7m2ocpwkeVSgkMUTzIXGh7wBiTaLhkJ+jNbGEKPTc7x/Jgt2IOjc7d02b3ebw4cOdkcIFecRztA9q5OuuNrrzNF2oyJJZ4xhWUUBpwdVoBAR8ZN9Xd6y8Uy+4KUChSyu5h0wehbOveM6iW9sjlc427NhmUfnTihdCktud53EV6y1tMfnTxij+RM3LLzd69AZ63OdRCTjrawq4sTAhOsYIiIyz0sdFwDY1lzrOEnyqEAhi6vpUcDoKuc8taUFhGtLONCd4QWK6Cx0v+idROok/CNODExwdniKzRlc7U6JxHbGXc+5zSGSBRprSujpH8uubbJFRHyut38cgHVLM3dHOBUoZHGV1ED9RhUoLtHaGOK1YwPMZvIcihPtMD2i7UUX0B4vTrVm8HrBlFi6AUqW6PgikgJNtSVMzcY4rTkUIiK+k8kduSpQyOIL74DTr8N4Fm2t+THaGkNMzER559SQ6yjJ07ETgnmwZqvrJL7T3hOhpjSfxhrNn7gpxkD4Ueh+wevYEZGkaYzPy+m6oK3DRUQkdVSgkMXXvB2wHw5MFO5dE8IYONCVwcs8OnbC6vsgXyfh81lrOaj5E4uneYfXqXPioOskIhktUVDt7lOBQkTEDy6MTgNQkJvZp/CZ/a8TN5bE27C13ehFlcV5rF1SlrmDMgd6INKp7UUX0Ns/zvmR6YvDUuUmNWyDQK6OLyJJVlWcR1VxHt3qoBAR8YXvv3MGgCdvW+Y4SXKpQCGLLxDw2rC7nlcb9jxtjSFePz7I1GzUdZTF17HLu9X2opc52OPtV93aoAGZiyK/FFZvUYeWSAo015XwwdlR1zFERAT41punAfjBjfWOkySXChSSHGrDvkxrQ4jpuRhvnsjAORSdOyEUhqoG10l8p70nQl1ZPmuqi11HyRzh7XDhCAwed51EJKPdVl/O4bMjmT3gWUQkTbxzahiAzRl+0UsFCkmOhm1qw77EPQ1VBAyZt8xjegyO7dPuHQuw1tLerfkTiy6xlKhzl9scIhnu1vpyZuZidJ7XMg8REb8IBDL7PaUKFJIciTbsDp1AJJQV5HJbfTnt3Rm2u0nvSxCdUYFiAd0Xxugfm874SnfKVTd53TrablQkqW6tLwfgvTPDjpOIiGS36bkMXCJ+BSpQSPI0Pwb9R2Gg13US39jcGOKtk0NMzmTQQabjWcgvg5WtrpP4zoFur1tmS2O14yQZKLwDjr0MMxOuk4hkrDWhYkryc3jvtAoUIiIuPfveOQC2Ntc4TpJ8KlBI8oTjAxPVhn1RW2M1s1HLa8cHXEdZHDa+nWzjgxDMdZ3Gdw50RaivKGRFVaHrKJmneTvMTUHvXtdJRDJWIGBYv6yMd1WgEBFx6s/3HwPgx1pXuQ2SAipQSPKEGiHUpDbseTatqiQnYC5eWU97596B0bPaXnQB0ZilvSfClibNn0iKVVsgt1hzbkSS7M4VFbx/eiQzd6ASEUkTb530huw/2FLrOEnyqUAhyRXe4Q1QnBl3ncQXivNz2LCigvZMKVAkZoyEH3Wbw4cOnx1heHKWNi3vSI6cfK9zp3O318kjIklx9+oqZqIx3j6ZgTtQiYikmUwfkAkqUEiyNW+H6DT0vOQ6iW+0NYZ49/Qwo1OzrqPcvM6dsGwjlGR+Nfd67e/yhqG2NWpAZtKEt8PwSeg77DqJSMa6e3UVxsArvRmyNFFEJM10X/B2UirOCzpOkhoqUEhyrWyDvFK1Yc/T2hAiGrO8eizN3+yN98Op17R7xxUc6I7QVFtCbVmB6yiZK9G5o+OLSNKUF+XSUlfKK+n+M0tEJE199cUuAL70UNhxktRQgUKSKyfPa8Pu2KU27LiNqyrJywmk/zKPrucA++EwVLloZi7GK70DbFH3RHKVLYMlt2k7Y5Eku3t1FW8cH2QuGnMdRUQk63zrjdMAfD4LBmSCChSSCs07YPQMnHvXdRJfKMgNsnFlRfoPyux4FoprYekdrpP4ztunhpicjdKq+RPJF94BJw/B5KDrJCIZ6541VYzPRHn/zIjrKCIiWaskP8d1hJRQgUKSr0lt2Jdqbajmg7MjDE3MuI5yY6Kz0PWCN2MkoMPIpfZ39WOMt5xHkqx5B9godD3vOolIxtocP5bti8/WERGR1Dh81isMlxVkR3ECVKCQVCitg2V3qg17nramENbCoXQdOnbyEEwPa3vRKzjQHeHWZeWUF+W6jpL56u+CohB06vgikiw1pfncWl/GSx0XXEcREckqv73zKAC//Phax0lSRwUKSY3wDjj1Krkzag8F2LC8gsLcYPrOoejYCYFcb76IfMTEzBxvnhikrUndEykRCELTI95MlFjUdRrxKWNMlTFmtzGmM35bucB9VhhjXjTGHDbGvG+M+fl5f/drxpjTxpi34r+eSO2/wL2tzTW8cXyQkUzYgUpEJE08f6QPgH+yaYXjJKmjAoWkRvN2wFI18IbrJL6QlxNg0+rK9C1QdO6CVW2QX+o6ie+8dmyQ2ailTfMnUie8HSYicFrHF7miLwPPW2vDwPPx319qDvgla+06YDPwM8aY9fP+/nettXfEfz2d/Mj+8kC4hrmY5UBXmv7cEhFJM7F5GwzkBrPntD17/qXi1tI7obiWUORV10l8o7UxxNHzo/SPTbuOcn0Gj8OFI9pe9Ar2d/eTGzTcvfqyC7SSLI0PgQlozo1czaeBv4h//BfAZy69g7X2rLX2jfjHo8BhoD5lCX1u46pKSvJztMxDRCRF9p6aA+D+cHZd9MqeaRviViAA4e1UvvdtiM5BUN96iQGKB3sifOL2ZY7TXIeOZ71bzZ9YUHt3hDtXVFKUp+/xlCmqghX3ekuPHvqPrtOIP9VZa8+CV4gwxtRe7c7GmNXAncCheX/8JWPMjwGv4XVaXLZ1jDHmC8AXAOrq6tizZ8+ihPeLlgrLzndOsr2yn/Hx8Yz79/nB2NiYXtck0WubHHpdk+d/ve8N03+sLruOt3oHLanTvJ3ct/7KG7C4eovrNM7dVl9OSX4O7d1pVqA4+gyEwlDd5DqJ7wxPzPLu6WF+/uGw6yjZJ7wdnv91GDkLZUtdpxEHjDHPAUsW+Kv/cJ2PUwL8PfAL1trE4KT/CfwGYOO3/x34yUs/11r7DeAbAJs2bbLbtm27nqf2vQslJ/m3f/cOofCdmK63yLR/nx/s2bNHr2uS6LVNDr2uSfTs9wH4p594yHGQ1NISD0mdhgeJmRy1YcflBAPcs6YqveZQTI3AsX3Q8pjrJL50sDeCtWj+hAvN8e9JHV+ylrX2EWvtrQv8+g5w3hizFCB+27fQYxhjcvGKE39trf3WvMc+b62NWmtjwB8D9yT/X+Q/j6yrIxgwPPPeOddRREQy2ivxnf6qS/IcJ0k9FSgkdQrKGC5f77VhC+At8+jpH+fc8JTrKNem+wWIzULz466T+NKBrn4Kc4PcsaLCdZTsU7sOKlZ6HT4il/su8OPxj38c+M6ldzDGGOBPgcPW2t+55O/mt+X8APBeknL6WmVxHq0NIZ597xx23vA2ERFZXP/6m28B8Fv/eIPjJKmnAoWkVCR0tzdgcaDXdRRfaG305lC09/Q7TnKNjj4DhZXeen+5zIHuCHevqSIvR4fWlDMGWp6Anj0wM+E6jfjPbwKPGmM6gUfjv8cYs8wYk9iRYwvweeChBbYT/W/GmHeNMe8ADwK/mOL8vvHYrUvo7R/n9JgKFCIiyXJqcBKAB9dedWRSRtK7aEmp/uq7vQ8Sgxaz3PqlZZQX5qbHMo9Y1NteNLxdQ04X0DcyRWffGFviRSdxoOVxmJvyihQi81hrI9bah6214fjtQPzPz1hrn4h/vM9aa6y1t1+6nai19vPW2tvif/epxMDNbLT9ljqMgdfOz7mOIiKSkd46OQRA0DgO4ogKFJJSU4VLoWYdHM26LeQXFAgYNjdU0d6TBgWKk6/A5MCHa/3lIxJfQ82fcGhlG+SX6fgikkS1pQVsWlXJq+fmtMxDRCQJ/uX/fg2An70z33ESN1SgkNRreQyO7YfJy3Zoy0qtDSFODkxycsDnbelHn4ZADjQ97DqJL+3v6qe8MJf1y8pcR8leOXnQ9Ig35yYWc51GJGN9+o56To9Z3j8z8vF3FhGR63J+ZBqAO2qzs2NZBQpJvZYnwEah63nXSXyhNX7F3fddFB3Pwur7oKDcdRLfsdZyoDvC5oYqgoEs7cfzi5YnYLwPzrzhOolIxvrE7UvJMfDtN0+7jiIiklFeOHIegLqy7OyeABUoxIX6u6C4Rm3Ycc11JYSK8zjo5zkUkW7o79DuHVdwPDLBqcFJtjRpeYdz4UfABLWbh0gSVRTlsaE2yHfeOsNcVN1KIiKL5Sf/l7e84xuf3+Q4iTsqUEjqBYLQvAM6n4O5GddpnDPGsLkxxIHuiH/X8yZO9lo0f2IhL3d5u7DcH65xnEQorIRVbSpQiCRZ27Ic+semLx7/RETk5swv+G7I4i3rVaAQN1qegOlhOHHAdRJfaGsMcW5kimMRn86h6HgWatdD5WrXSXxpX+cF6isKWR0qch1FwNvNo+99GDzuOolIxtpQE6SiKJdvvaFlHiIii+F3n+sA4OEs3Fp0PhUoxI2GbZBTAEe13Sh4gzIBDnT78ErU5CAcP6DdO65gLhrjQFeE+8PVGKP5E76Q+F7VdsYiSZMTMHxqwzJ2vn+OoQl1Q4qI3KyvvtgNwO/8kzscJ3FLBQpxI6/YK1IcfRr8uqwhhdZUF1NXlk+7H+dQdD7nDTVt0fyJhbx9apjR6Tkt7/CTUCNUt2jOjUiSfe6elczMxfi710+5jiIiktZ6Loxd/Li8KNdhEvdUoBB3Wh6HoePQd9h1EueMMbQ1VtPeHSEW81nBpuMZKKr2hpvKZfZ19mOMt0xHfCSxnfHUsOskIhlr3dIy7lpVyV8fOuG/n10iImnk83/6CgC/90PZ3T0BKlCIS4k2bF3lBOC+pmoi4zMcPuejfeWjs14HRfNj3nBTuczLnRe4rb6cyuI811FkvpYnIDar7YxFkuxHN6+kt3/c/1tli4j4VDRmOT00CcBn7qx3nMY9FSjEndIlsGyjpu3H3R/2tqjc2+GjORTHD3jDTLV7x4JGp2Z58+TQxa+d+Mjyu6EopOOLSJI9futSKoty+auDGkorInIjfmvnUQAeaNZyYVCBQlxreQJOvwaj510nca62rIC1S0p5ufOC6ygf6ngWgnnQ8KDrJL50sGeAaMxyX5N+oPhOIAjhHdC5C6JzrtOIZKyC3CCf3bSCXR+c5/zIlOs4IiJp52svecMx//BH7nScxB9UoBC3EoMXNW0f8Cqnrx0bZGLGBydU1npXn9c8APklrtP40sudFyjMDbJxVfbuVe1rLY/D1BCcPOg6iUhG+6f3riRmLX/Zfsx1FBGRtLLnaN/Fj8sKsns4ZoIKFOJW3S1QvlJt2HH3h6uZicY41DPgOgpcOAqDvdq94yr2dfZzb0MV+Tmaz+FLjQ95HUA6vogk1apQMTvWL+GvDp5gfNoHBXYRkTTxz/78VQCe+tn7HCfxDxUoxC1jvBPgnhdhZsJ1GufuXl1Ffk6AvX5Y5tERP6lr1vyJhZwemqSnf1zbi/pZfonXAaTtjEWS7qceaGB4cpa/fe2k6ygiImnh5MCH5z631pc7TOIvKlCIey2Pw9wU9L7kOolzBblB7m0I8XKnDwZlHvk+LN0A5ctdJ/GlffEikgZk+lzL4zDQA/2drpOIZLS7VlVy16pK/nR/L1FtOSoi8rGe+P2XAfjtz25wnMRfVKAQ91ZtgfwybTca90C4mq6+Mc7EtxtyYvQcnHoV1n7CXQaf29vZT11ZPuFazefwtUQHUIeWeYgk20/d38DJgUl2vn/OdRQREV8bnpxlNL4k7h/fpYuB86lAIe7l5EHTw3D0WYjFXKdxLrHFkNPdPBLFIhUoFhSLWQ509XNfUw3GGNdx5GrKl8OS2zWHQiQFHl1fx+pQEV9/qRurZVUiIlf0Q19vB+BLDzY5TuI/KlCIP7Q8AeN9cOYN10mcC9eWUFeWz16XyzyOfB8q10DtOncZfOz9MyMMTsxqeUe6WPsknDgIYz6Y7SKSwYIBwxe3NvL2qWFe6tD/NxGRhUzORDlybhSAX9re7DiN/6hAIf7Q9AiYoHdinOWMMdwfrmFfZ7+bdbxTw9DzkndSp+6ABSWGmG5pUoEiLax9ErBaRiaSAv9o43LqKwr5vec61UUhIrKAn/hfrwDeFs3qxL2cChTiD0VVsHoLHHnKdRJfuD9czfDkLO+eHk79k3fuhtislndcxb7OftYtLaOmNN91FLkWdbdCxSodX0RSIC8nwM882MRbJ4fURSEicomp2SgHewYA+I1P3+o4jT+pQCH+sfaT0N8BFzpcJ3Hu/nANxsDLLt7cHfk+FNfAintS/9xpYHx6jtePD2p5RzoxBtZ9Enr2wNSI6zQiGe8f3+V1Ufz+8+qiEBGZ7yf+/FUAPnvXcgIBdU8sRAUK8Y+1T3q3R77nNocPVBXnceuy8otLCVJmbtrroGh5HALB1D53mjjQHWEmGmNrfJippIm1n4DoDHTtdp1EJOPl5QT4Vw828uaJIbfzlEREfGRiZo72nggA//UHb3ecxr9UoBD/KK+HZRvhsNqwwVvm8caJIUanZlP3pL17YWZUyzuu4qWOPorygmxaXek6ilyPFfd4nUE6voikxGfvWkF9RSH/fddRYi7mKYmI+Mw/+qMDAPx46yp1T1yFChTiL+s+6e3kMXzKdRLnHmiuIRqztHdHUvekR56CvBJYszV1z5lGrLXsOXqBtsZq8nPUYZJWAkFvt6DO3V6nkIgkVV5OgF98tJl3Tg3z/XfPuo4jIuLUwPjMxZ07fu1TtzhO428qUIi/rPukd6vdPNi4spKivGDqlnnEYnDkaW9HldyC1Dxnmum+MM6pwUm2tWh5R1pa90mvQ6jnJddJRLLCD9xZz9olpfzWzqPMzMVcxxERcWbrb70IwC8/tlY7d3wMFSjEX6rDUN0ChzWHIi8nQGtDiL0d/akZMnb6NRjv0/KOq9hztA9ABYp0teYByCvVnBuRFAkGDF9+fC0nBib460PHXccREXGiq2+M0ak5AH56W6PjNP6nAoX4z7pPwvEDMJ7CpQ0+ta2lhhMDE/T0jyf/yQ5/DwI5EH40+c+Vpl7quEBTbQnLK4tcR5EbkZMPzdu9TqFY1HUakaywtbmGtsYQf/BCFyOpnKkkIuITj/yO17n5tR/d6DhJelCBQvxn3SfARqHjGddJnNvWUgvAi0f6kvtE1nrzJ1bfD4UVyX2uNDUxM8ehngG2afeO9Lb2EzDRDycPuU4ikhWMMfz7x45aO08AACAASURBVNcxMD7D1/Z0u44jIpJSz7537uLHj9261GGS9KEChfjP0jugfIWm7QMrqooI15aw52iS51BcOAoDPV5xSBbUHt9eNFE0kjQVfhSCeTq+iKTQbcvL+YE76/mTl3s5loqOQBERH7DW8sW/eh2A3b/4gOM06cNJgcIYU2WM2W2M6YzfLrhfnzHmmDHmXWPMW8aY11KdUxwxxrvK2f0CTI+5TuPcg2trOdQbYWx6LnlPciR+stbyRPKeI83tOXqBorwgd6/R9qJpLb8UGrZ5cyhSMdtFRAD48uNryQ0afuOpD1xHERFJia98530AlpUXEK4rdZwmfbjqoPgy8Ly1Ngw8H//9lTxorb3DWrspNdHEF9Z9AqLT0PWc6yTOPdhSy2zUsr+rP3lPcuQpqL8LypYl7znSmLWWPR19tDWGtL1oJlj7CRg6AefedZ1EJGvUlRXwcw+Hef5IHy8cOe86johIUo1OzfK/D3rDgZ/7pa2O06QXVwWKTwN/Ef/4L4DPOMohfrWyFYpC2s0D2LS6kpL8nIs7SCy6oRNw5k3t3nEVvf3jnByYZKvmT2SGlifABD7sHBKRlPiJLWtoqCnm17/3AVOzGlQrIpnrnv/yPABfeKCBorwcx2nSi6tXq85aexbAWnvWGHOlRd0W2GWMscDXrbXfuNIDGmO+AHwBoK6ujj179ixa2LGxsUV9vGx2Pa9lS9md1Bx+mv0v7MYGcpMbzOfWVlieffsU2ysjF/dOXqzvy+Unv0MTcGh0KZNZ+n3+ca/lrmPe5PmCwR727DmWmlBpKl2Ol3eUrSXntf/Ha6bNdZQrSpfXUuRa5eUE+LVP3sKP/dkr/Om+Xn7mwSbXkUREFl17d4TJeBH2V55Y5zhN+klagcIY8xywZIG/+g/X8TBbrLVn4gWM3caYI9bavQvdMV68+AbApk2b7LZt26438hXt2bOHxXy8bHZdr+Wyafib59i6wkD4Gj8nQ/WVnOTf/d071LXcxfplZcAifl/+yX+BJbdx7xOfu/nHSlMf91r+2Z+9QkPNBJ994sr3EU/aHC/zfxR2/grbbl8JVQ2u0ywobV7LNGCMqQL+H7AaOAb8E2vt4AL3OwaMAlFgLrG89Fo/Xz7eA801PHbLEv7ghU4+efsyVoa0bbOIZA5rLZ/744MA/P1PtzpOk56StsTDWvuItfbWBX59BzhvjFkKEL9dsHfdWnsmftsHfBu4J1l5xYfWbIW8Ejj8XddJnEtsbfniYi/zGD4Np16B9Z9e3MfNIJMzUQ72RNjWrN07Msq6T3q3H+j4kiVudvbV9Xy+fIxf/dR6cgIBfuXb72I1rFZEMsiX/s+bANRXFHLXqirHadKTqxkU3wV+PP7xjwPfufQOxphiY0xp4mNgO/BeyhKKe7kF3paAR5+GWHavVa0tK+DW+rLFn0ORmPGxXmNgrmR/Vz8zczEeXKv5ExmlYiUs2wgf/IPrJJIaNzv7SrOzFtHS8kJ++fG17Ovq5+/fOO06jojIojg5MMH33zkLwAv/RoMxb5SrGRS/CXzTGPPPgRPAZwGMMcuAP7HWPgHUAd+Or7fPAf7GWvuso7ziyvpPw/vfhuMHYM39rtM49WBLLV99sYuhiRkqivIW50E/+A7Urofq8OI8XgZ6/sh5SvJzuHdNyHUUWWy3fAZ2fwUGj0HlatdpJLludvbVNX1+Mudh+c3Nzkipt5bmygC/+g9vk9vfSXm+WbxwaUyzZ5JHr21y6HX90D97dty7vSWP9n0v3/TjZetr66RAYa2NAA8v8OdngCfiH/cAG1IcTfwmvB1yi7wiRbYXKNbW8gcvdLG3s59PbViE7UBHz8GJdtimTuUricUszx/u44HmavJyXDWcSdKs/7RXoPjgO7Dl512nkZuU6tlXC0nmPCy/WYwZKStvGeOJ33+Z3ZFy/vBHNi5OsDSn2TPJo9c2OfS6ev7bs0eAbgB+7fOPLspjZutrq3fc4m95xV6R4vB3s36Zx4blFVQW5bLnyCIt8zj8PcBqecdVvHdmmL7RaR5eW+c6iiRD5WpYdie8r2UemSDJs6+u6fPl+jTVlvCzDzXx1Dtn2fX+OddxRERuyLnhKf5oj1eceOsri1OcyGYqUIj/3fIDMH4Bju93ncSpYMCwtbmGPR0XiMYWYajYB9+B6haoXXvzj5WhnjvcR8B43SuSodZ/Bs68AYPHXSeR5LrZ2Vcf+/lyY/7l1kbWLy3jV779Lv1j067jiIhct83/3/MA/Mcn1y3eMuwspgKF+N/8ZR5Z7qF1dQyMz/DmiZvc3W4sXvDR7h1X9fzh82xcWUlVsX7YZKxb4h1EH+h8M8P9JvCoMaYTeDT+e4wxy4wxT8fvUwfsM8a8DbwCfH/e7KsFP19uXl5OgN/9oTsYmZzj339Lu3qISHr5z9/74OLH/+J+f25bnm5UoBD/yyuC5h3ekoTonOs0Tm1rqSE3aNh9+PzNPdCRp+D/b+++46uu7j+Ov042IYuRASQQwgibsBGULTJUELVuqYu6Wm3tz6J2aFstHbaOWlsnTnCiKIgDQRHZm7BHgEAgBAgkhOzz++NGRGQESHJy730/H488cu/3fu/3vnPyvcm9n3uGLVeB4hSyDh4hfdchBrfV8A6fVi8ZGqVpNQ8fZ63dZ60dbK1tVfF9f8X2XRUTc2Ot3WKt7Vzx1d5a++jp7i9VIzUhkvuHpfL5mj28syTTdRwRkUrZvDefl+ZuBWDlw0Mdp/EdKlCId9AwDwCiwoLpndKAz9ecY4FizQdQvwXEt6+aYD5o5lrPEPMhbTW8w+e1Hw07l0DudtdJRPzWzX2b0zulPo9MTWfH/gLXcURETslay+DHvwLg71d0Iios2HEi36EChXiHlhd6hnnoU06GtI1ny97DZOWXn90BDu+DrXM8vSeMlnU7mZlr99C0fjgt4yJcR5Hq1k7DPERcCwgw/OPKzgQYw31vr6iauZZERKrJ5c9+C0C98GCu7J7kOI1vUYFCvENIOLQeBmum+v0wjyHtPEMOlmWfZTusnwa2TMM7TqGguJS5m/cxuG0cRkUc31e/OTTqrHluRBxLrBfOI6PaszBjP0/O3Og6jojICc1YvZul23MBWPTQEMdpfI8KFOI92o+Gghy/H+bRJKYO7RtHsSz7LJddXf0e1Kt4QyYn9M3GHIpLyxmi+Sf8RzsN8xCpDcZ0TeTyrok8/eVG5m7KcR1HROQHDhWWcPvrSwD46O7zCQrU2+mqphYV79HyQgiuq0858Qzz2JRbfuZLsuXtga1fQ8crNLzjFGauzSYyNIgeyfVdR5GaotU8RGqNP41uT4vYCO6ZvJzsvELXcUREjur08GcAXN+7KR0Tox2n8U0qUIj3OLqah4Z5XNguHgt8WTGRY6Wt+cCzekeHy6slly8oK7fMXJdNv9RYQoL0J9Jv1E+BhE4qgIrUAuEhQTxzbVfyi0r45VvLNR+FiNQK415dfPTyn0d3dJjEt+nVt3iX9pdBwT7Y9o3rJE61bxxFg7CzWG509XsQ1x7i2lZPMB+wdPsBcvKLGNY+wXUUqWkdxniGeezf6jqJiN9LTYjkkUvbM3fTPv795SbXcUTEz32avpvPKlbRW/vHYY7T+DYVKMS7tLoQQiI8b7T9mDGGtLhA5mzcy5HiSs5FkbsddiyAjuo9cSozVu8mJDCAAamxrqNITfuuZ9Hqd93mEBEAftI9icu6NOGJmRuYvf4MewyKiFSR7EOF/Ow1z7wT793RhzohgY4T+TYVKMS7BNeBNhd7xomXnuH8Cz6mS1wQhSXlfFPZScS+K+poeMdJWWuZsXo357dqSKTWs/Y/MU2h6Xmw8h2w6lIu4poxhkcv60BqfCS/mLSMjJzDriOJiJ8pL7f0fGwmAD8f1JJuzeo5TuT7VKAQ79PxSig8CBs/d53EqTb1A4gMDeLzNbsrd4fV70GT7lAvuVpzebP0XYfYmXtEwzv8WccrIGc97FntOomI4JmP4vkbuxMQYBj32mLyi/x7DioRqVnd/ux5v1G/bgj3DU11nMY/qEAh3idlANSNhVVvu07iVFCAYWCbOL5Ym01pWfmpd967AXav8rz5kpP6NH03AQaGtNPyon6r3WUQEASr3nGdREQqJNUP59/XdGVTdj6/fnsFVj2cRKQGPDw1nQMFJQAsfmiI4zT+QwUK8T6BQdB+DKyf4elJ4cdGdExg/+FiFmzdf+odV78LJsAzyaic1IzVu+nVvAH164a4jiKu1G0ALQbDqveg/DSFPxGpMee3asiDI9oyI303z8zSpJkiUr0+Td/NxG8zAFjy2yEEBBi3gfyIChTinTr9BMqKYO1HrpM41b91HHWCA5m+KuvkO1nrGd6RfD5EaujCyWzKzmdjdj4XtVfvCb/X8Uo4lAk75rtOIiLHuOX85oxOa8zjn2/gk1P93xMROQdb9uYfnRRz8rjeNIgIdZzIv6hAId6pSTeo19zvu2HXCQlkUJs4Pk3fffJ14rNWwL5NmhzzND5N98zlMVTzT0jqcAgO9/u/LyK1jTGGCZd3Ii0phnvfWs6y7QdcRxIRH1NQXMqgx78C4KERbemd0sBxIv+jAoV4J2M8n3Ju/RryKjlJpI8a0bEROfnFLMo4yTCP1e9CQDC0vbRmg3mZT9N30zkphsYxdVxHEddCIyB1BKRPgdJi12lE5BhhwYE8f2N34qJCue3VxezYX+A6koj4CGst7X7/KQADUmO5rV+K40T+SQUK8V6dfgK2/PvlM/3UgNRYwoIDTtzdtazUs2RiqwshvH7Nh/MS+46UszLzoFbvkO91vBKOHIAts1wnEZHjNIwI5eWf9qS4tJybJi7iYMUkdiIi56LVQ58cvTzxpp4Ok/g3FSjEezVsBY3SYKV/r+ZRNzSIAa3j+GT1bsqPH+axdTbk74bO1zjJ5i2W7ikD0PwT8r0Wg6BOPQ3zEKmlWsZF8L8burNt32Fuf30JxaWa1FZEzt41z82ntOJ19JbHRjhO499UoBDv1vFKyFoOORtdJ3FqeMcEsvOKWHr8eNzlkyAsBlpf5CaYl1i4u5TU+EhSYiNcR5HaIigE2o2GddOgKM91GhE5gfNaNGDCmE7M27KPX7+z4sdFehGRSvjDh6uZt2UfAOmPXKQVOxxTgUK8W4fLAeP3n3IOahNHSFAA01cdMx9H4SFY97GnjYI0+/DJ7Mo9wsbcci7p3Mh1FKltOl8DJQWwZqrrJCJyEpd3S+T+YalMXbGLhz9Kx1oVKUSk8l6eu5VX5m0DYMGDg6kbGuQ4kahAId4tqhGk9IcVk6Dcf7t3RoYF069VLJ+szvr+E6Q1H0JpIaRd6zZcLTdtpWfujos7NXacRGqdpJ5QvwUsf9N1EhE5hTv6t+C2C5rz6rxt/OsL/+5RKSKVN31VFo98tAaAT+65gPioMMeJBFSgEF+Qdj3kbodt37hO4tSIjglkHSxkeWauZ8OKSdCgpWdJVjmpj1buIjkqgOSGdV1HkdrGGE+Bb9s3sH+r6zQichLGGB4c0ZYruyXy1MyNvDxXz1cRObVvN+dw5xtLAXjtlp60bRTlOJF8RwUK8X5tL4bQaFj2uuskTg1uG09woOHjFVlwIAO2zfV0UTcaR3cyGTmHWZl5kF6N1J1PTqLz1YDxFPxEpNYyxvCXMR0Z2i6eRz5aw5Rlma4jiUgttXxHLtc+vwCAp67pwgWtYh0nkmOpQCHeL7gOdBjjGSdeeNB1Gmei6wQzIDWOj1fuonz5ZM/GTle5DVXLTatYmrVnQqDjJFJrRSdCygDPhLN+PIxMxBsEBQbw1DVdOC+lAfe9vYKPV+5yHUlEapm1WYcY/cxcAB65tD2XdtYQ39pGBQrxDV2uh9IjkD7FdRKnRqc1ITuvkKIlb0DyBRCT5DpSrfbRil10a1aPBnX0p1BOIe06OKhhZCLeICw4kBfGdqdbs3rcM3k50ysK0SIim/fmM/zJOQDcPyyVsX2S3QaSE9KrcvENTbpBw1RY9obrJE4NbhvHBaGbqZO/XZNjnsbGPXms253HJZ20eoecRpuREBqlyTJFvETd0CBevqknXZJi+PmkZcxYrSKFiL/bvDefwY9/BcBdA1tw54CWjhPJyahAIb7BGOhyHWQuhL0bXKdxJiw4kJ/HzOOwDaOw5QjXcWq1j1ZmEWBghAoUcjoh4RXDyD6EojzXaUSkEiJCg5h4c086J0Zz95vL+DR99+nvJCI+6djixLh+KfzfRW0cJ5JTUYFCfEenq8EEwnI/7kVReJBu+bP4sOw8ZmcccZ2m1rLW8vGKXfRq3oC4SC0pJZWQdh2UFHiKFCLiFSJCg3jl5p50TIzmrjeWqkgh4ofWZh36QXHiwRFtHSeS01GBQnxHZDy0utAz235Zqes0bqx6h8CyQmaEDuPD5Zoc7GRWZB5kS85hRqVpYiSppMQenmV7l77mOomInIHIsOCjRYo731iq1T1E/MjyHblH55y4a2ALFSe8hAoU4lvSroP8PbDpC9dJ3FjyCsR3JKXT+cxcl82hwhLXiWql95dmEhoUoOEdUnnGQNexsGM+ZK91nUZEzkBUWDCv3dKLnsn1+eVbK3htXobrSCJSzb7dnHN0tY77h6VqWIcXUYFCfEvrYVA3DpZMdJ2k5u1aBrtXQrexjO6aSHFpOTNWqzvr8YpKy5i6YhdD2ycQFRbsOo54k7TrIDAEFr/sOomInKGI0CBevqkHQ9rG8bsP0/nP7E2uI4lINZm+Kotrn18AeJYS1YSY3kUFCvEtQSHQ9QbY+Cnk7nCdpmYteQWC6kDHK+mcGE2zBuF8sGyn61S1zqx1e8ktKGFM1yauo4i3qdsA2o2CFZOhuMB1GhE5Q2HBgTx7fTcu7dyYv81Yz19nrMNa6zqWiFShV77N4M43lgLw5NVpWkrUC6lAIb6n61iwFpa+4jpJzSnKh1XvQvvLoE4MxhjGdElk3pZ97NivN1LHen9pJrGRoVzQsqHrKOKNut0ERQch/X3XSUTkLAQHBvCvq9K4pmdTnp29mQfeX0VpWbnrWCJSBR6ems4fpqYD8OrNPRmVpg+jvJEKFOJ76jWDVkNh6atQ5idzMKRPgeI86Db26KbLu3n+KL+3VBOCfWf/4WJmrc9mdFpjggL150/OQrM+0DBVwzxEvFhggOGxyzpw98CWTF60g1tfXczhIj+dXFvER1z3wnwmfpsBwPRfXEC/1rFuA8lZ0yt08U09bvFMlrnuY9dJqp+1sPhFiG0DSb2Obk6sF875LRvyzuJMysvVhRXg45W7KCmzjOma6DqKeCtjoPtNsHMxZK10nUZEzpIxhl9flMpjl3VkzsYcrnpuHtl5ha5jicgZstaS+ttPmLtpHwDzHxhMu8ZRjlPJuVCBQnxTyyEQ3RQWveg6SfXbucQzQWaPWz1vno5xZfckduYeYd6WfY7C1S7vLcmkTUIkbRvpH5ecg85XQ1AYLFEvCm9hjKlvjPncGLOx4nu9E+yTaoxZfszXIWPMvRW3PWyM2XnMbSNq/qeQ6nBtr6a8cGN3tuw9zGXPfMum7DzXkUSkko4Ul9H8gekUlXqGaa1+5CISosMcp5JzpQKF+KaAQM9wh4w5sHeD6zTVa8H/ICTS86bpOEPbxRMVFsRbi/xswtATWLPrECsyD/KT7kmuo4i3q1MP2o+BlW9D4SHXaaRyxgMzrbWtgJkV13/AWrveWptmrU0DugEFwJRjdvnXd7dba6fXSGqpEQPbxPHWuPMoKi3n8mfnMW+zivoitd32fQW0/f2Mo9e3PDaCiNAgh4mkqqhAIb6r640QEOzbn3Lm7fHMP9HlOgiN/NHNYcGBjO7ShBnpuzlY4CfzcZzE5EXbCQkK0OodUjV63grF+bD8TddJpHJGAd/NnPwKMPo0+w8GNltrt1VrKqk1OiZGM+XOPsRGhnLDiwt4bb5+9SK11Zfr9tDv77MA6NuyARkTRhIQYE5zL/EWKjOJ74qI8ywJuOx1GPjgCd/Ae70lE6G8BHrcdtJdftI9iVfnbWPqip3ccF5yjUWrTY4UlzFl2U6Gd0ggJjzEdRzxBU26eeZ8WfBf6Hmbp9eW1Gbx1tosAGttljEm7jT7Xw1MOm7b3caYG4HFwH3W2gPH38kYMw4YBxAfH8/s2bPPOXhtlZ+f75M/332dLP9dEcDvPljNl0vWcV3bEIJq8I2Pr7ZrbaC2rR413a7vrC9m2lbPh25XtA7m4pRCn/29+us5qwKF+Lbed8Lqdz1Fit53uE5TpUx5CSx9yTPfRsOWJ92vfeMo2jaK4u3FmX5boJi+Kou8wlKu7tHUdRTxJb1uh3dvgo2fQepw12n8njHmCyDhBDc9dIbHCQEuBR44ZvOzwJ8AW/H9ceDm4+9rrX0OeA6ge/fudsCAAWfy0F5l9uzZ+OrPN3SQ5R+frefZ2Zs5HBTFs9d1pUFEaI08ti+3q2tq2+pRU+1qreX8v85iZ66nOPHGrb3o6+NLxvvrOashHuLbErtBUm+Y/yyUl7lOU6Vi986D/N3Q82en3M8Yw0+6J7Jq50FW7zxYQ+lql0kLt9O8YV16p9R3HUV8SdtLISoR5v/HdRIBrLVDrLUdTvD1IbDHGNMIoOJ79ikONRxYaq3dc8yx91hry6y15cDzQM/q/FnErcAAw2+GteHJq9NYsSOXS/89l/Rd/vn/U6Q22H+4mOYPTGdn7hEAFj442OeLE/5MBQrxfefdBbnbYN0010mqjrUkZk6F+imeHhSnMaZLImHBAbzuh2NqN+7JY/G2A1zdIwljND5RqlBgkGd4x9avYfdq12nk1KYCYysujwU+PMW+13Dc8I7vihsVLgP0C/cDo9Ka8M7t51FWbhnzn295WxNOi9S4rzfspeufPgcgJDCAzY+NIC5KK3X4MhUoxPe1GQkxzWDeM66TVJ2Mb4jK2wh9fg4Bp38aR4cHMzqtCR8s3+l3k2VOXrSD4EDD5d0SXUcRX9T1RggO98xFIbXZBOBCY8xG4MKK6xhjGhtjjq7IYYwJr7j9/ePu/zdjzCpjzEpgIPDLmoktrnVKjOHjX5xP9+R63P/eSn79zgqOFPtWj0yR2uqB91dy40sLAbi5b3M2PDqcQE2G6fNUoBDfFxDomX9ix3zYucR1mqox90mKg6Oh8zWVvsv1vZtRWFLOu0szqzFY7VJQXMo7i3cwtH0CDWto/LD4mfD6nufhyrchb7frNHIS1tp91trB1tpWFd/3V2zfZa0dccx+BdbaBtbag8fd/wZrbUdrbSdr7aXfTbgp/qFhRCiv3tyLXwxqyXtLM7nsP3PZsjffdSwRn3WkuIzk8dOYtNDTa+nN23rx+0vaOU4lNUUFCvEPXa6H0Cj49mnXSc7d7tWw6XMyEy+G4DqVvluHJtF0bRrD6/O3UV5uqzFg7TFl2U4OFZZyU59k11HEl/W527Oaji/10hKRHwgMMPxqaCov/7QHew4VcsnT3/Dxyl2uY4n4nAVb9tH29zOOXl/58FD6tNB8E/5EBQrxD6GR0ONWSP8Acja6TnNuvn0aguuyq/GZrxpw43nJbM05zDebcqohWO1irWXi3Aw6NImiW7N6ruOIL6ufAu3HwOKX4MiPVp4UER8yIDWOab+4gNSESO5+cxn3v7uCw0WlrmOJ+IS73ljKVc/NB+Ci9vFkTBhJVFiw41RS01SgEP9x3l0QFAZz/uk6ydnL3eFZNrXbWEqDI8/47sM7JtCgbgiv+cFkmd9u3sfG7Hx+2qe5JseU6nf+L6E4HxY+7zqJiFSzxjF1mDzuPO4c0IJ3lmQy4qk5LNuu4qTI2dqbV0Ty+GlMW+UZPffGrb343w3dHacSV1SgEP9RtyF0vxlWvgUHMlynOTvfPg3WeubUOAuhQYFc1SOJmWv3sH1fQRWHq11enptBw4gQLunc6PQ7i5yrhA7QerhnydEijU0X8XUhQQHcP6wNk2/rTWmZ5Yr/zuOpmRspLSt3HU3Eq7w8dys9Hv3i6PW1fxymJUT9nAoU4l/6/NwzaeY3T7hOcuYO7YIlEyHtWohpetaHGdsnmcAAw4vfbKm6bLXM9n0FzFy3h2t7NiU0KNB1HPEXF/zKM8Rj6Suuk4hIDemV0oDp91zAyI6N+OfnG7jqufk+/wGASFU4XFRK8vhpPPLRGgB+dWFrMiaMpE6IXrf5OxUoxL9ENYIuN8DyN+DgTtdpzsycf4Itg37/d06HiY8KY1RaE95enMmBw8VVFK52mfhtBoHGcF3vZq6jiD9J6gnJF8Dcp6BYb1BE/EV0nWCeuqYLT1yVxobdeVz0xNdMnLvVbyakFjlT7y/NpP0fPj16fe74QfxicCuHiaQ2UYFC/M/594Ith2+8aC6Kg5meT2XTroN65/6me1y/FI6UlPG6D85FceBwMZMXbeeSzo2JjwpzHUf8zcAHIX83LHrBdRIRqWGjuzRhxi/70aN5fR7+aA1XPTdPy5GKHKOguJRWD03nV2+vAOCq7klkTBhJk5jKr0onvk8FCvE/MU2h642e4RL7t7pOUzlzHvfMPdHv11VyuNbxkQxMjeWVeRkUlpRVyTFri1fnbaOguIzb+7dwHUX8UbM+0HKIpwBaeMh1GhGpYU1i6vDKTT34x5WdWb87j+FPzuF/X23W3BTi916fv412v/+UkjJPz6Iv7+vPX6/o5DiV1EYqUIh/6v8bCAiGWY+6TnJ6+zbD0teg6w3nNPfE8cb1a0FOfjHvL/WyoS6nUFBcysRvtzKkbRypCWe+yolIlRj0W89cFPOecZ1ERBwwxnBFt0S++FV/+rWO5S+frOPyZ79lzS4VLcX/ZB8qJHn8NH77wWoAru7h6TWREhvhOJnUVipQiH+KTPCshLHqHcha6TrNqc18BAJDPEWVKtQ7pT6dEqN5fs4WynxknOxbi3ZwoKCEOwao94Q41LgLtBsF8/4Nh3NcpxERR+Kiwnjuhm48fU0XMg8c4eKn5/DI1+YuRwAAHChJREFUR+nkFZa4jiZS7ay13Pf2Cno+NvPotrnjBzHhcvWakFNTgUL8V997ICzGUwCorbYvgDUferJGJlTpoY0x3DmgBVtzDvPRil1VemwXikvLef7rLfRMrk+3ZvVdxxF/N/C3UHIEZv/FdRIRccgYwyWdGzPzvv5c07MpE7/NYNDjX/Hh8p1Y6xsfDogc75uNOTR/YDrvLc0E4PcXt9NcE1JpKlCI/6oT45nTYdMXsPFz12l+zFr47CGISIA+d1fLQwxtl0CbhEiemrnR63tRvLNkB7sOFnLHQPWekFogtjX0uAUWvwR70l2nERHHYsJDePSyjnxwZ18aRYdxz+TlXPv8AjZl57mOJlJl9h8uJnn8NK5/cQEAsZGhrPvTMG4+v7njZOJNVKAQ/9bzZ9CgJXxyP5QWuU7zQ+nvQ+Yiz3j2kLrV8hABAYZ7h7RiS85hpq7w3rkoCkvK+PeXm+jaNIYBrWNdxxHxGPAAhEXDJ7/xFBxFxO91Tophyp19+fPoDqzJOsSwJ+bw8NR0n132W/xDebnllomL6Pqn7z/w+/Cuvix6aAhhwYEOk4k3UoFC/FtQCAz/G+zf4hkvXlsUHoJPH4KETpB2bbU+1He9KJ6euclrZxmftHA7WQcLuW9oKsYY13FEPMLrw8CHIGMOrP3IdRoRqSUCAwzX927Gl/f158ruSbw6L4P+f5/F819vocTLezOK//k8o4SUB6czc102AP93USoZE0bSOSnGcTLxVipQiLQcDG0uhq//AQczXafxmPUY5O2GS56AgOqtPB/bi+KD5d43F8WR4jKembWZ3in16dOiges4Ij/U7SaIaw+fPghF6sotIt9rEBHKX8Z0ZMa9/ejarB6PTl/Lg3OOMG1lluankFpvzsa9JI+fxhvrPL1/ujerx8ZHh3PXwJaOk4m3U4FCBOCixzxdsKf92n1X7F3LYeH/POPXm3SrkYcc2i6Bjk2iefyz9RSWlNXIY1aVV+ZlkJNfpN4TUjsFBsHF//IUP7+oxRPyiogzreMjmXhTT167pSehgXDXm0u5/Nlvmbd5n+toIj+SvusgyeOnccOLC49uW/jgYN69ow/BgXprKedOZ5EIQL1mnrkeNnwCK99yl6O0CD68C8IbwqDf1djDBgQYHhzRlqyDhbz4zdYae9xztS+/iGe+3MTA1Fh6JGvlDqmlmvaCXrfDouchY67rNCJSS13QKpY/9q3D3y7vxM7cI1zz/HyufX4+S7btdx1NhG37DpM8fhojn/rm6LaP7j6ficPqEhcV5jCZ+BoVKES+0/sOSOrtmTDzUJabDLP/AntWw6VPe1YZqUHntWjAkLbxPDt7M/vya9mEoSfxry82UFBSxkMj27qOInJqg38HMc1g6t1QXOA6jYjUUgHG8JMeSXz1fwP5/cXt2LAnn8ufncfYlxayYkeu63jih3bsLyB5/DT6/3320W2v3NyTjAkj6ZgY7S6Y+CwVKES+ExAIo57x9GL44A4or+EJI7fPh7lPQtcbIXVYzT52hfHD23CkpIwnvtjo5PHPxPrdeby5YDs39G5Gy7hI13FETi2krqfwuH8LfPqA6zQiUsuFBQdy8/nN+fr+ATwwvA0rM3MZ9cxcbn1lEctVqJAasCk7n+Tx07jgb7OObnvy6jQyJoykv1ZMk2qkAoXIsRq2hGETYMssmPN4zT3u4Rx49xaITvLMh+FIy7gIruvVlDcXbid910FnOU7HWsufp60hMiyYewa3ch1HpHJS+kPfe2HJRFj1rus0IuIFwkOC+Fn/Fsz5zSB+PbQ1izIOMPqZuVz93Dxmr8/WZJpS5VbsyCV5/DSG/POro9v+cWVnMiaMZFRaE4fJxF+oQCFyvG4/hY5XwuzHYOvX1f945WXw7s1weC/85FUIddsb4L4LU6kXHsyDU1ZTVkuXO/tk9W7mbMzhnsGtqFc3xHUckcob9FtI6gUf3QN7N7hOIyJeIiI0iLsHtWLu+EH8dmRbMnIK+OnLixjx1Dd8uHyn1y4TLrXHtJVZJI+fxqhnvp8r6b/XdyVjwkiu6JboMJn4GxUoRI5nDFz8BDRoCW+PhZxN1ft4X/wBtn4FIx+HxmnV+1iVEB0ezG9HtmPFjlzeXLDNdZwfOXikhD9MTadDkyhuPK+Z6zgiZyYwGK54CYJC4c2feHpPiYhUUkRoELdekMLX9w/k71d0oqSsnHsmL2fg47N56ZutHCoscR1RvEhZueWRj9JJHj+Nu95cenT7G7f2ImPCSIZ1aOQwnfgrFShETiQ0Aq59C0wAvHE55O+tnseZ9x/49mnofgt0vaF6HuMsjEprzPktG/K3GevJPlToOs4P/HXGOvblFzFhTCeCtJyVeKPoRLhmMhzaBZOvhZLa9RwTkdovJCiAK7sn8dm9/Xjuhm7ERYbxx4/X0PuxmTw0ZRXrd+e5jii1WPahQoY98TUtHpzOy3MzAAgJDGDmff3JmDCSvi0bug0ofk2v7kVOpn6K501E3m54fQwUVPEyXyve8kyW1/YSGPH3qj32OTLG8KfRHSgqK2f8+6tqzRjXbzfl8OaC7dzctzkdmmjmaPFiST1hzP9gxwJ463oVKUTkrAQEGIa2T+C9O/rw8c/P5+JOjXh3SSYXPfE1V/1vHtNXZVGi4R9SYeqKXSSPn0bPx2ayrqKI1a91LOmPXMSGR4fTIjbCcUIRCHIdQKRWS+oBV70Ok6+DiSPhxg8hIu7cj7tkInx0LyRfAGNe8KwgUss0b1iX8cPa8MeP1zBp4Q6u7dXUaZ6DBSX86u0VpMTW5VdDWzvNIlIl2l8GhQc9fwsmXQVXT4KQcNepRMRLdWgSzd+u6MwDw9vy9uIdvDZ/G3e+sZS4yFDGdE3kim6JtIzTG1B/szeviNtfX8KSbQd+sP13F7fj5r7JGGMcJRM5MRUoRE6n1YVw3dsw6Rp48UK4+k2Ib392xyovg1mPwZx/QKuhcOUrEBxWtXmr0E/7JDNz3R7+9PEazmvRgOYN6zrJYa3lwQ9WkZNfxJQb+xIeoj9d4iO6/RQCQ+DDu2DiCLjqDYjWLOkicvbq1Q3hZ/1bcOsFKcxal83kRdt5fs4W/vvVZro0jeGKbolc0rkxUWHBrqNKNSkrt/xn1iYe//yHkzE3jg7j1Vt6qVAltZpe5YtURsoAGPuRpyv2C0M8S4F2HQsBZzBKKncHTP25ZwnTLjfAxf/yTJhXiwUEGP5xZWeGPTGHO15fwpQ7+1InpOZ7e7y5cDvTVmbxfxel0jFRQzvEx6RdC2Ex8P5t8Fx/uORJaDPSdSoR8XKBAYYh7eIZ0i6evXlFfLBsJ+8s2cFDU1bzx4/WcFH7BM+cU60aEhpU+3pyypn7eOUu7n5z2Y+2PzC8DeP6pai3hHgFJwUKY8yVwMNAW6CntXbxSfYbBjwJBAIvWGsn1FhIkeMldodxX8H7t8LH98LKt2Hw76BZn1Pfr/AgLHwe5vwTsJ43H91+WhOJq0Sj6Do8eXUaN01cxPj3V/LEVWk1+g9uybb9PDw1nQGpsdzev0WNPa5IjWozAm6dCe/d4pk4s83FhEcOc51KRHxEbGQot/VL4dYLmrNq50HeWZzJ1BW7mLpiF5FhQQxtl8DITgmc3zKWkCBNUedNZq3L5ueTlpFfVPqD7Re0asgTV6XRICLUUTKRs+OqB8VqYAzwv5PtYIwJBJ4BLgQygUXGmKnW2jU1E1HkBCLj4capsOw1+OIReHk4NO4C7UZBUm+o39zTXftwDmSvgY2fw9qpUHQIWg+H4X+Fet63NOaA1Djuu7A1//hsA+0bRzGuX80UCrIOHuH215fSOKYOT17VhcAAVf7Fh8W1gXGzYe6T8M2/6FE8Hbp3PfshZSIixzHG0Ckxhk6JMfzu4nbM3ZTDxyuz+GzNbt5bmklUWBBD2ycwvEMCfVs2JCxYPStqG2st7yzJ5DfvreT4OcxbxNblP9d1IzUh0k04kSrgpEBhrV0LnO5T2J7AJmvtlop9JwOjABUoxC1joOuN0OEKT6FixST44uET7xsaDanDofed0DitRmNWtTsHtGRN1iEem76OuMgwRnep3nHyBw4Xc+OLCzlSXMZrt/QkOrx2D4cRqRKBwdDv19DtJjZNmUCruHauE4mIjwoJCmBgmzgGtomjqLTD0WLFp6t38+6STEKDAujTogGDKvZJrKdJfF05WFDCEzM3HF0S9FhJ9evwxFVd6NasXs0HE6kGtXkOiibAjmOuZwK9TrazMWYcMA4gPj6e2bNnV1mQ/Pz8Kj2eP/O9tkyF1g8T0mwfEfkZhBXuwdhySoPCKQhvQn5ECjYgGDbkwobZVfrILtpydIJly84A7nt7Ods2raVzbPX8CSkstfx9USHb8sq5r1sYu9ctZfe6ankowBfPS3fUllUnP6Y/O7/6ynUMEfEDoUGBDGoTz6A28RSVljF/y35mrcvmy3XZzFqfDh+m0zo+goFt4ujXKpauTes5mZPKX5SXWz5elcVfP1nHztwjP7q9R3I9Hr2sI63j1VNCfE+1FSiMMV8ACSe46SFr7YeVOcQJttkTbPPcYO1zwHMA3bt3twMGDKhMzEqZPXs2VXk8f6a2rDqu2rJ33xKueW4+/16ex5NXt2dEx0ZVevwDh4u5aeIith4q4Nnru3FR+xP9GalaOi+rjtqy6qgtRcSF0KBA+reOpX/rWP5wSTs27z18tFjx4pyt/O+rLYQEBpCWFEPvlPr0TmlA12b1NBzkHFhr+XJdNk/N3MiKzIMn3Ofmvs25Z3Ar9SgVn1dtBQpr7ZBzPEQmkHTM9URg1zkeU0TOUVRYMG/e1pubJy7i7jeX8sdRHbiuV9MqmThzZ+4Rxr60kO37a644ISIiIidmjKFlXAQt4yK4rV8KeYUlLN52gPmb9zF/yz7+PWsTT3256WjBokuzGNISY+iUFEPj6DCtGnESuQXFvLlwOy/M2cr+w8Un3Kdncn3uH5ZK9+T6NZxOxK3aPMRjEdDKGNMc2AlcDVzrNpKIAETXCea1W3py1xtL+e0Hq1m6/QB/Ht2B8JCz/5Mye302v3xrOaVllldu6sl5LRpUYWIRERE5V5FhwQxMjWNgahyAp2CRcYB5W/axYOt+Xv4mg+KycgAaRoSSlhRNp8QYOiZG0yYhkoQo/yta7DlUyAfLdvLe0kw27Mk/6X6dEqO5Z3ArBrWJ87s2EjmWq2VGLwOeBmKBacaY5dbai4wxjfEsJzrCWltqjLkb+BTPMqMvWWvTXeQVkR8LDwnihbE9ePrLjTw5cyPLt+fyx1EdOL9VwzM6zsGCEv7yyVomL9pBm4RInr2+G80b1q2m1CLij851eXNjTH3gLSAZyAB+Yq09UO3BRWq5yLDgoxNtAhSVlrEuK48Vmbks35HLih25fLE2+5j9g2gdH0nr+AhaxUWSmhBJi9gI4iJDCfDylbq27ytg1vpsvli7hzkbc067/1Xdk7jlguaaR0LkOK5W8ZgCTDnB9l3AiGOuTwem12A0ETkDgQGGe4e0pkdyfR6csorrX1xA/9ax3N6/Bb2a1z/li43svELemL+dl+du5XBxGT/rl8K9Q1pr0i0RqQ7nurz5eGCmtXaCMWZ8xfXfVH9sEe8SGhRI56QYOifFcON5nm2HCktYs+sQG/fksWFPPuv35DFj9W4mFXw/F35IUACJMXVIrB9OUr06JNUPJ6leOAnRYcRGhNIwMuScemmeK2st+w4Xk5VbyLIdB5i0cAdrsw5V6r5hwQGM6ZrI5V2b0LVpPfWOEDmN2jzEQ0S8RN+WDfn03n68PDeDF7/ZwjXPz6dRdBgDUuPo0CSK+MgwQoICyD1SwqY9eSzKOMCCrfsot3BR+3juHdKato2iXP8YIuKjqmB581HAgIr9XgFmowKFSKVEhQXTO6UBvVO+H7pprSUnv5iNe/LYnHOYzP0F7DhQwI79R1iZmUtuQcmPjhMeEkiDiBAaRoTSMCKU6DrB1A0JJDw0iIjQIMJDAqkbEkTd0CCCAg0BxhBg8HwPMKzOKSNoYw4l5eUUlZRTVFpGUWm556vEc/ngkRJyC4rJLSjxfB35/vJ3Q1dOJj4qlIGpcQxIjaN/61h94CJyllSgEJEqERYcyB0DWnBT32Smr8pi+qospq3cxaSF23+wX4CB1vGR3DWwJaO7NKFFbISjxCIiP3Cq5c3jrbVZANbaLGNMXE2HE/ElxhhiI0OJjQylT8sfDw3NKyxhx/4j7DlUSE5+ETn5xeTkF7Gv4vKO/QWsKSwlv6iUw0WllJafdKG/H1q84JQ3hwUHEFMnhJjwYGLCg0lpGEG9usFE1wmhUXQYCdFhxNQJJjQ4kPaNowgODDibH19ETkEFChGpUmHBgYzpmsiYrolYa9mZe4T9h4spLCmnXngwjWPqUDdUf3pEpGrV9PLmJ8kwDhgHEB8fz+zZs8/k7l4lPz/fp38+V9SuP2TwTFgXCxBR8XVUABAChFBabikshcIyz/cya7EWygFrPV+HjxwhLKwOQQEQHADBAYbgwIrvARy97FEOFFV8VSgG9sIRPF9zN1fvz+4tdM5WH39tW71LEJFqY4whsV44ifXCXUcRER9Xzcub7zHGNKroPdEIyP7RvT0ZngOeA+jevbsdMGDAOUaqvWbPno0v/3yuqF2rj9q2eqhdq4+/tq36JYmIiIgcs7y5MSYEz/LmUytumwqMrbg8FqhMjwwRERE5QypQiIiIiE8zxlxmjMkEzsOzvPmnFdsbG2OmA1hrS4HvljdfC7x9zPLmE4ALjTEb8azyMaGmfwYRERF/oCEeIiIi4tPOdXlza+0+YHB1ZhQRERH1oBARERERERGRWkAFChERERERERFxTgUKEREREREREXFOBQoRERERERERcU4FChERERERERFxTgUKEREREREREXFOBQoRERERERERcU4FChERERERERFxTgUKEREREREREXFOBQoRERERERERcU4FChERERERERFxTgUKEREREREREXHOWGtdZ6hyxpi9wLYqPGRDIKcKj+fP1JZVR21ZddSWVUdtWXWqoy2bWWtjq/iYcgLV8FqkttFzvXqoXauP2rZ6qF2rjy+37Ulfj/hkgaKqGWMWW2u7u87hC9SWVUdtWXXUllVHbVl11JZSm+n8rB5q1+qjtq0eatfq469tqyEeIiIiIiIiIuKcChQiIiIiIiIi4pwKFJXznOsAPkRtWXXUllVHbVl11JZVR20ptZnOz+qhdq0+atvqoXatPn7ZtpqDQkREREREREScUw8KEREREREREXFOBQoRERERERERcU4FitMwxgwzxqw3xmwyxox3ncdbGWOSjDGzjDFrjTHpxph7XGfydsaYQGPMMmPMx66zeDNjTIwx5l1jzLqK8/M815m8lTHmlxXP79XGmEnGmDDXmbyFMeYlY0y2MWb1MdvqG2M+N8ZsrPhez2VG8W/GmCsrnt/lxpiTLnun101nprLPc2NMhjFmlTFmuTFmcU3n9BanO/+Mx1MVt680xnR1kdMbVaJtBxhjDlaco8uNMb93kdPbnOj//3G3+905qwLFKRhjAoFngOFAO+AaY0w7t6m8Vilwn7W2LdAbuEttec7uAda6DuEDngRmWGvbAJ1Rm54VY0wT4BdAd2ttByAQuNptKq8yERh23LbxwExrbStgZsV1EVdWA2OAr0+2g143nZUzeZ4PtNamWWtPWiDyZ5U8/4YDrSq+xgHP1mhIL3UGz+05FedomrX2jzUa0ntN5Mf//4/ld+esChSn1hPYZK3dYq0tBiYDoxxn8krW2ixr7dKKy3l43gQ2cZvKexljEoGRwAuus3gzY0wU0A94EcBaW2ytzXWbyqsFAXWMMUFAOLDLcR6vYa39Gth/3OZRwCsVl18BRtdoKJFjWGvXWmvXn2Y3vW46c3qeV53KnH+jgFetx3wgxhjTqKaDeiE9t6vJSf7/H8vvzlkVKE6tCbDjmOuZ6E31OTPGJANdgAVuk3i1J4D7gXLXQbxcCrAXeLliuMwLxpi6rkN5I2vtTuAfwHYgCzhorf3MbSqvF2+tzQJPkReIc5xH5HT0uunMVfZ5boHPjDFLjDHjaiydd6nM+adz9OxUtt3OM8asMMZ8YoxpXzPRfJ7fnbMqUJyaOcE2rct6DowxEcB7wL3W2kOu83gjY8zFQLa1donrLD4gCOgKPGut7QIcRt3oz0rFuOlRQHOgMVDXGHO921QiciaMMV9UzCFz/FdlPynV66YTqIJ2Behrre2Kp7v3XcaYftUU15tV5vzTOXp2KtNuS4Fm1trOwNPAB9Weyj/43Tkb5DpALZcJJB1zPRF1WT5rxphgPMWJN6y177vO48X6ApcaY0YAYUCUMeZ1a63eDJ65TCDTWvtdb553UYHibA0Btlpr9wIYY94H+gCvO03l3fYYYxpZa7MqunNmuw4kvs1aO+QcD6HXTSdwqnY1xlTqeW6t3VXxPdsYMwVPl/uTzgfipypz/ukcPTunbbdjP3i01k43xvzHGNPQWptTQxl9ld+ds+pBcWqLgFbGmObGmBA8E75NdZzJKxljDJ5x/muttf90ncebWWsfsNYmWmuT8ZyTX6o4cXastbuBHcaY1IpNg4E1DiN5s+1Ab2NMeMXzfTCacPRcTQXGVlweC3zoMItIZeh105k77fPcGFPXGBP53WVgKJ5JS+WHKnP+TQVurFgZoTee4YhZNR3UC522bY0xCRX//zHG9MTzPnNfjSf1PX53zqoHxSlYa0uNMXcDn+KZkf4la22641jeqi9wA7DKGLO8YtuD1trpDjOJAPwceKPiH+4W4CbHebyStXaBMeZdPF08S4FlwHNuU3kPY8wkYADQ0BiTCfwBmAC8bYy5BU8B6Ep3CcXfGWMuw9NtOxaYZoxZbq29yBjTGHjBWjtCr5vOygmf58e2KxAPTKl47xcEvGmtneEob611svPPGHN7xe3/BaYDI4BNQAH6n18plWzbK4A7jDGlwBHgamutTw9FqAon+f8fDP57zhqdNyIiIiIiIiLimoZ4iIiIiIiIiIhzKlCIiIiIiIiIiHMqUIiIiIiIiIiIcypQiIiIiIiIiIhzKlCIiIiIiIiIiHMqUIhItTDGxBhj7nSdQ0REREREvIMKFCJSXWIAFShERERERKRSVKAQkeoyAWhhjFlujPm76zAiIiLiH4wxHY0xc4+53tUY86XLTCJSOcZa6zqDiPggY0wy8LG1toPjKCIiIuJHjDEBwC6gibW2zBgzC7jPWrvUcTQROY0g1wFERERERESqirW23BiTDrQ3xrQCtltrlxpjUoCHgGhr7RVuU4rIiWiIh4iIiIiI+Jr5QF/gYeBBAGvtFmvtLS5DicipqQeFiFSXPCDSdQgRERHxS/OBicAz1tqdjrOISCWpB4WIVAtr7T5grjFmtSbJFBERkRq2DigC/uo6iIhUnibJFBERERERn2KM+TewyFr7yjHbGgCPAhcCL1hr/+Iqn4icmAoUIiIiIiLiE4wxLYBpwFzNNyHifVSgEBERERERERHnNAeFiIiIiIiIiDinAoWIiIiIiIiIOKcChYiIiIiIiIg4pwKFiIiIiIiIiDinAoWIiIiIiIiIOKcChYiIiIiIiIg4pwKFiIiIiIiIiDj3/4F9UeIgovxsAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pphi = lambda yy,t : [ yy[1], -sin(yy[0]) ]\n", "\n", "t0 = 0\n", "yy0 = [0,1]\n", "tt = linspace(t0,10,1001)\n", "sol = odeint(pphi,yy0,tt)\n", "\n", "figure(figsize=(18,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,sol[:,0],tt,sol[:,1])\n", "xlabel('t')\n", "ylabel('y')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "plot(sol[:,0],sol[:,1])\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$')\n", "grid()\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons l'énergie suivante (somme de l'énergie potentielle et de l'énergie cinétique):\n", "$$\n", "E(t)=-\\cos(y_1(t))+\\frac{1}{2}(y_2(t))^2\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est conservée au cours du temps:\n", "\\begin{align}\n", "E'(t)\n", "&=\\sin(y_1(t))y_1'(t)+y_2(t)y_2'(t)\n", "\\\\\n", "&=-y_2'(t)y_1'(t)+y_1'(t)y_2'(t)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.448590565508397e-08\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "# valeur pour t=0\n", "E0 = -cos(yy0[0])+yy0[1]**2/2\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = -cos(sol[:,0])+sol[:,1]**2/2\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid(); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul analytique avec le module `sympy`\n", "--- \n", "https://docs.sympy.org/latest/modules/solvers/ode.html" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’une équation différentielle d'ordre 1\n", "\n", "Considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "u'(x)=-3x^2u(x)+6x^2,\\\\\n", "u(0)=4.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d x} u{\\left(x \\right)} = - 3 x^{2} u{\\left(x \\right)} + 6 x^{2}$" ], "text/plain": [ "d 2 2\n", "──(u(x)) = - 3⋅x ⋅u(x) + 6⋅x \n", "dx " ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.Symbol('x')\n", "u = sym.Function('u')\n", "phi = 6*x**2-3*x**2*u(x)\n", "edo = sym.Eq( sym.diff(u(x),x) , phi )\n", "edo" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle u{\\left(x \\right)} = C_{1} e^{- x^{3}} + 2$" ], "text/plain": [ " 3 \n", " -x \n", "u(x) = C₁⋅ℯ + 2" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solgen = sym.dsolve(edo,u(x))\n", "solgen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prise en compte des conditions initiales:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAVCAYAAAD7NJjdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADcklEQVRYCeWY7VEbMRBAbSYFACVAByFUENIBpINAB2HyC/55oANIBQl0ENIB0AGkAhI6IO/JkuYs644zjsmE7Mxaut29/dJqpfPw4eFhUMLh4eEytDfSmV+U/JfwTFxrxPEavGZ+W8a0VBIQ+gjte6RflvyX8hyTYUKOmH8DLYYMw2bFwNyGcwauML/PUi2TqGwX9juwKa+hU9BV2WPcb1GxEHK0m2xa+T/BfejXNYPQv0G/Z9xJ/FdpEsdNxlsEmkEWIuNHZKysT+AI3Gm+w3wbPIG+BR6BzwbYdTFOGF2sAMz14UoaWGsNJsyiyDC1lTKnZYLiZdAM74FvmR+DE4nk+Ty+rpM1RyJ7IYNJ0LcM+GP16KO7oRfMnBi02n8szw0MVkszWtYJy3OqsUX+ogar9Aa7y4UBF8hFdbEehZkSg1JXw07+gflElVQsua+/VuiLJpmArnZQJqzqT9ljqkISY6btKxpNW6VVXjnQPjM3YO8GJReME1ukphiZ3EALvgs6gN9V5fmVMjFms60SklO9gsUB9fRyIntTmaBHnyx/t++TAB0mRR3ppCr13EFYbRLzVuJlX3wPtgWeunafamnaCHMDBHfBqylmBwF5E+z1YaND7DGW/e4cHcctgsakfynGwfDg4MCE2DtCRmFWTxHov+LLQ8ZHAXkNhepjdMVsioL3mvXxdPG/2HKh1xjz8V2zCt/K/KwsOFqCYC8YgZeglyAFamAz7QXoMPMaCMCz125X61lPKGx6+Vxl7EzK2MtwJ0vFcb4kkRd1PPUQs1aDUEnI5YBrQpG2qc4O/sJZ2Hdx1hlzM9Z3sTQeZT1YvJeFOENiGoIGE7p3g5ambjch78Px4+QvipWzAv8a4IMxuDhls9X3WuV7479HPmx9HS9PJWlV4CWPabN/pgLwtCnIsz3Ekh3Jb/LmmaPLrW1/s6ofbcDIWBE2W4/38iDZgtbWgCcS1jsxGBqg1M6+wjR8kTKmBKjUhJUrBHk+QKeLYG+yB/YBP1dMjv2lBHdEL5gpMWrUUYbUj3oZmVcIm71PsVlku/wqe0yX7H/FKytm6gb4J7LBKlraVpl9yJPBBn3H2LbfYT8r2MdSWwiGyz+qDMDvEv9fedINN2j9h36I06T8AL3D5QNlIjHGA9Pk2ET9dvjC84tMUIzTKjbeqTh/A/R1SxpHaMtpAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : 2\\right\\}$" ], "text/plain": [ "{C₁: 2}" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0=0\n", "u0=4\n", "consts = sym.solve( sym.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n", "consts" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle u{\\left(x \\right)} = 2 + 2 e^{- x^{3}}$" ], "text/plain": [ " 3\n", " -x \n", "u(x) = 2 + 2⋅ℯ " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solpar=solgen.subs(consts)\n", "solpar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On transforme le résultat en une fonction:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "func = sym.lambdify(x,solpar.rhs,'numpy')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import *\n", "figure(figsize=(10,7))\n", "xx=linspace(0,3,101)\n", "yy=func(xx)\n", "plot(xx,yy)\n", "xlabel('x')\n", "ylabel('u')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’un système d'équations différentielles d'ordre 1\n", "\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(t, y_1(t),y_2(t))\\\\\n", " \\varphi_2(t, y_1(t),y_2(t))\n", " \\end{pmatrix}\n", " =\n", " \\begin{pmatrix}\n", " y_1(t)-y_2(t)\\\\\n", " y_2(t)-y_1(t)\n", " \\end{pmatrix}.\n", "$$\n", "avec $t\\in[0;10]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{1}}{\\left(t \\right)} = \\operatorname{y_{1}}{\\left(t \\right)} - \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₁(t)) = y₁(t) - y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{2}}{\\left(t \\right)} = - \\operatorname{y_{1}}{\\left(t \\right)} + \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₂(t)) = -y₁(t) + y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ \\operatorname{y_{1}}{\\left(t \\right)} = - C_{1} e^{2 t} - C_{2}, \\ \\operatorname{y_{2}}{\\left(t \\right)} = C_{1} e^{2 t} - C_{2}\\right]$" ], "text/plain": [ "⎡ 2⋅t 2⋅t ⎤\n", "⎣y₁(t) = - C₁⋅ℯ - C₂, y₂(t) = C₁⋅ℯ - C₂⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "\n", "y1 = sym.Function('y1')\n", "y2 = sym.Function('y2')\n", "\n", "phi1 = y1(t)-y2(t)\n", "phi2 = y2(t)-y1(t)\n", "\n", "edo1 = sym.Eq( sym.diff(y1(t),t) , phi1 )\n", "edo2 = sym.Eq( sym.diff(y2(t),t) , phi2 )\n", "display(edo1)\n", "display(edo2)\n", "\n", "solgen = sym.dsolve([edo1,edo2],[y1(t),y2(t)])\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left\\{ C_{1} : - \\frac{1}{2}, \\ C_{2} : - \\frac{3}{2}\\right\\}$" ], "text/plain": [ "{C₁: -1/2, C₂: -3/2}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{1}}{\\left(t \\right)} = \\frac{e^{2 t}}{2} + \\frac{3}{2}$" ], "text/plain": [ " 2⋅t \n", " ℯ 3\n", "y₁(t) = ──── + ─\n", " 2 2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{2}}{\\left(t \\right)} = \\frac{3}{2} - \\frac{e^{2 t}}{2}$" ], "text/plain": [ " 2⋅t\n", " 3 ℯ \n", "y₂(t) = ─ - ────\n", " 2 2 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t0 =0\n", "y1_0=2\n", "y2_0=1\n", "consts = sym.solve( [sym.Eq( y1_0, solgen[0].rhs.subs(t,t0)) , \n", " sym.Eq( y2_0, solgen[1].rhs.subs(t,t0)) ] , dict=True)[0]\n", "display(consts)\n", "\n", "solpar_1=solgen[0].subs(consts)\n", "solpar_2=solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(18,7))\n", "\n", "tt=linspace(0,3,101)\n", "yy_1=func_1(tt)\n", "yy_2=func_2(tt)\n", "\n", "subplot(1,2,1)\n", "plot(tt,yy_1,tt,yy_2)\n", "legend([r'$y_1$',r'$y_2$'])\n", "xlabel(r'$t$')\n", "ylabel(r'$y$')\n", "\n", "subplot(1,2,2)\n", "plot(yy_1,yy_2)\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy)\n", ">Calculer la solution **exacte** du problème de Cauchy \n", "$$\\begin{cases}\n", "y'(t)=\\dfrac{3}{2} y(t) \\left( 1-\\dfrac{y(t)}{6} \\right),& t>0\\\\\n", "y(0)=1.\n", "\\end{cases}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy)\n", ">Calculer la solution **approchée** du problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\sin\\left(t y(t)\\right), & t>0\\\\\n", "y(0)=a\n", "\\end{cases}$$\n", "pour $a=-2,-1,-\\frac{1}{2},-\\frac{1}{10},0,\\frac{1}{10},\\frac{1}{2},1,2$ et afficher le champ de vecteurs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy - système)\n", "> 1. Calculer la solution générale **exacte** du système \n", "$$\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}'\n", "=\n", "\\begin{pmatrix}\n", "0&1\\\\\n", "-1&0\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}\n", "$$\n", ">1. Pour $x(0)=-1$ et $y(0)=1$, afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe.\n", ">2. Afficher ensuite $x\\mapsto y$.\n", ">1. Calculer analytiquement $E'(t)$ avec\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système)\n", "> 1. Calculer la solution particulière **approchée** du système \n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t)+y^2(t)x(t)\\\\\n", "y'(t)= x(t)-x^2(t)y(t)\n", "\\end{cases}\n", "$$\n", "avec $x(0)=0$ et $y(0)=1$.\n", ">1. Afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe pour $t\\in[0,14]$. \n", "Afficher ensuite $x\\mapsto y$.\n", ">1. Afficher\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "Calculer analytiquement $E'(t)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système - stabilité)\n", "> Considérons le système \n", "$$\n", "\\begin{cases}\n", "x'(t)= x^2(t)+y^2(t)-25\\\\\n", "y'(t)= x(t)y(t)-12\n", "\\end{cases}\n", "$$\n", ">1. Afficher le champ des vecteurs et les solutions stationnaires.\n", ">1. Calculer les solutions particulières **approchées** pour des données initiales proches des points stationnaires." ] } ], "metadata": { "hide_input": false, "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": "3.8.5" }, "toc": { "base_numbering": 1, "nav_menu": { "height": "171px", "width": "166px" }, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "308px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }