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ArtStudies/L3/Méthodes Numériques/TP1_Equation_de_Poisson.ipynb
Arthur DANJOU d5a6bfd339 Refactor code for improved readability and consistency across multiple Jupyter notebooks
- Added missing commas in various print statements and function calls for better syntax.
- Reformatted code to enhance clarity, including breaking long lines and aligning parameters.
- Updated function signatures to use float type for sigma parameters instead of int for better precision.
- Cleaned up comments and documentation strings for clarity and consistency.
- Ensured consistent formatting in plotting functions and data handling.
2025-12-13 23:38:17 +01:00

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"$$\\newcommand{\\nr}[1]{\\|#1\\|}\n",
"\\newcommand{\\RR}{\\mathbb{R}}\n",
"\\newcommand{\\N}{\\mathbb{N}}\n",
"$$\n",
"### MEU357 - Méthodes numériques pour les équations différentielles. 2022/23.\n",
"\n",
"# TP1 - La méthode des différences finies pour l'équation de Poisson.\n",
"\n",
"**Remarques importantes** : Dorénavant vous allez programmer des méthodes numériques pour résoudre de manière approchée des EDP, et la complexité de vos programmes augmentera au fur et à mesure. Il faut veiller à respecter les points suivants:\n",
"\n",
"- Vos programmes doivent être ***souples***, ce qui veut dire qu'on devra pouvoir changer les données du problème sans avoir à tout refaire et même modifier facilement les programmes pour les adapter à un problème plus complexe (avec d'autre type de données, par exemple). Vous devrez donc utiliser des variables pour définir vos données, éventuellement des fonctions externes définies en dehors du programme principal, etc...\n",
"\n",
"- Vos programmes doivent être ***lisibles et compréhensibles*** par quelqu'un d'autre que vous et par vous mêmes si vous y revenez quelques jours plus tard. Il faut donc utiliser des noms cohérents pour les variables, des commentaires pour expliquer le programme, des titres et légendes pour vos graphiques, etc...\n",
"\n",
"Le principe de la **méthode des différences finies** est d'approcher la solution $u$ d'une équation différentielle en un ensemble discret de points du domaine de $u,$ en remplaçant les dérivés de $u$ en ces points par des *quotients de différences finies* qui les approchent. Par exemple, on a pour une fonction $u$ d'une seule variable que sa dérivé en un point $x$ de son domaine vérifie\n",
"\n",
"$$\n",
"u'(x)=\\lim_{h\\to0}\\frac{u(x+h)-u(x)}{h}=\\lim_{h\\to0}\\frac{u(x)-u(x-h)}{h}=\\lim_{h\\to0}\\frac{u(x+h)-u(x-h)}{2h}=\\dots,\n",
"$$\n",
"\n",
"et on peut donc approcher $u'(x)$ par les quotients\n",
"\n",
"$$\n",
"\\frac{u(x+h)-u(x)}{h},\\ \\frac{u(x)-u(x-h)}{h},\\ \\frac{u(x+h)-u(x-h)}{2h},\\dots,\n",
"$$\n",
"\n",
"avec $h\\,$ *petit*.\n",
"\n",
"On verra aussi que si $u$ est deux fois dérivable au point $x,$ alors\n",
"\n",
"$$\n",
"u''(x)=\\lim_{h\\to0}\\frac{u(x+h)-2u(x)+u(x-h)}{h^2}.\n",
"$$\n",
"\n",
"On peut donc aussi approcher $u''(x)$ par le quotient de différences finies\n",
"\n",
"$$\n",
"\\frac{u(x+h)-2u(x)+u(x-h)}{h^2},\n",
"$$\n",
"\n",
"avec $h$ *petit*.\n"
]
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"## Exercice 1. L'équation de Poisson en dimension 1 d'espace avec conditions aux limites de Dirichlet homogènes. \n",
"\n",
"On s'intéresse à la résolution approchée, par la méthode des différences finies, d'un problème aux limites pour l'équation de Poisson en dimension $1$ d'espace sur $\\Omega=]0,1[$, avec conditions aux limites de Dirichlet homogènes\n",
"\\begin{equation}\n",
"(P)\\ \\ \\ \\ \\ \\begin{cases}\n",
"-u''(x)=f(x),\\ \\,x\\in]0,1[,\\\\\n",
"u(0)=0,\\ \\,u(1)=0,\n",
"\\end{cases}\n",
"\\end{equation}\n",
"où $f\\in\\mathcal{C}^2(\\RR)$ est donnée.\n",
"\n",
"L'idée de la méthode des différences finies pour approcher le problème de Poisson (P) est alors la suivante :\n",
"- Discrétiser le domaine $\\overline{\\Omega}$ ($=[0,1])$ (*le remplacer par un ensemble discret de points*) ;\n",
"- Remplacer l'opérateur différentiel $u\\mapsto u''$ par l'opérateur aux différences discret\n",
" $$u\\mapsto \\frac{u(x+h)-2u(x)+u(x-h)}{h^2}$$\n",
" aux points de la discrétisation.\n",
"\n",
"--------------------------------------------------------------------------------------------------------------\n",
"\n",
"**Question 1.** \n",
" Supposons que $f$ est de classe $C^2$. On peut montrer que la solution $u$ de (P) est alors de classe $C^4$ sur $[0,1]$. Montrer qu'il existe une constante $C>0$, qui ne dépend que de $f$, tel que pour tout $x\\in]0,1[$ et pour tout $h>0$ tel que $x\\pm h\\in]0,1[$ on ait\n",
" \n",
" $$\n",
"\\Big|u''(x)-\\frac{u(x+h)-2u(x)+u(x-h)}{h^2}\\Big|\\leq Ch^2.\n",
" $$\n",
"\n",
"En particulier, la constante $C$ est indépendante de $h$. \n",
"\n",
"Ce résultat indique que l'opérateur discret est une approximation *d'ordre 2* de l'opérateur continu.\n",
"\n",
"---------------------------------------------------------------------------------------------------------\n",
"\n",
"En pratique on procède comme suit pour la discrétisation du problème (P) par la méthode des différences finies :\n",
"\n",
"- Discrétisation du domaine $[0,1].$\n",
"\n",
"Pour chaque entier $M\\ge1$ donné, on pose $h=\\frac{1}{M+1}.$ $h$ est le *pas de la discrétisation*.\n",
"\n",
"Associée à chaque $h$ ainsi défini, on construit une discrétisation uniforme de l'intervalle $[0,1],$ de pas $h,$ donnée par les $M+2$ points\n",
"\n",
"$$\n",
"x_j=jh,\\ j=0,\\dots,M+1.\n",
"$$\n",
"\n",
"- Calcul d'une solution approchée aux points de la discrétisation.\n",
"\n",
"Soit $u\\in\\mathcal{C}^2([0,1])$ la solution du problème (P). On cherche à calculer des valeurs approchées notées $u_j$ de la solution $u$ aux points $x_j,$ autrement dit on cherche $u_j\\in\\RR,$ pour $j=0,\\dots,M+1,$ tel que $u_j\\simeq u(x_j).$\n",
"\n",
"Comme la fonction $u$ est solution de (P), on a\n",
"\n",
"$$\n",
"-u''(x_j)=f(x_j),\\ \\textrm{pour }j=1,\\dots,M, \n",
"$$\n",
"\n",
"et, puisque $x_0=0$ et $x_{M+1}=1,$\n",
"\n",
"$$\n",
"u(x_0)=u(x_{M+1})=0.\n",
"$$\n",
"\n",
"La solution $u$ de (P) vérifie alors\n",
"\n",
"$$\n",
"-\\frac{u(x_j+h)-2u(x_j)+u(x_j-h)}{h^2}\\simeq f(x_j),\\ \\textrm{pour }j=1,\\dots,M,\n",
"$$\n",
"\n",
"ainsi que $u(x_0)=u(x_{M+1})=0.$ Remarquons que $x_j+h=x_{j+1}$ et $x_j-h=x_{j-1},$ si $j\\in\\{1,\\dots,M\\}.$\n",
"\n",
"La méthode des différences finies pour le problème (P) consiste alors à, pour $M>1$ entier positif donné, chercher des réels $u_0,\\dots,u_{M+1}$ vérifiant\n",
"\n",
"\\begin{equation}\n",
"(P_h)\\ \\ \\ \\ \\ \\begin{cases}\n",
" -\\frac{1}{h^2}\\big(u_{j+1}-2u_{j}+u_{j-1}\\big)=f(x_j),\\ \\ j=1,\\dots,M,\\\\\n",
" u_0=u_{M+1}=0,\n",
" \\end{cases}\n",
"\\end{equation}\n",
"\n",
"où $h=\\frac{1}{M+1}$ et $x_j=jh,\\ j=0,\\dots,M+1.$\n",
"\n",
"-----------------------------------------------------------------------------------------------------------\n",
"\n",
"**Question 2.** On introduit une inconnue discrète $(u_0,\\dots,u_{M+1})$, vecteur de $\\RR^{M+2}$ dont les composantes sont les valeurs approchées $u_j,\\ j=0,\\dots,M+1$. Vérifier que le problème discret (P_h) peut s'écrire de manière équivalente :\n",
"\n",
"Pour $M>1,\\ M\\in\\N,$ donné, trouver $(u_0,u_1,\\dots,u_M,u_{M+1})\\in\\RR^{M+2}$ tel que\n",
"\n",
"\\begin{equation}\n",
"(S)\\ \\ \\ \\ \\ \\begin{cases}\n",
" u_0=u_{M+1}=0,\\\\\n",
" (S_h)\\ \\ \\ A_h{U_h}=F,\n",
"\\end{cases}\n",
"\\end{equation}\n",
"\n",
"où\n",
"\n",
"\n",
"- $A_h\\in\\mathcal{M}_M(\\RR)$ est la matrice\n",
" \\begin{equation*}\n",
"A_h=-\\frac{1}{h^2}\\left[\\begin{array}{rrrrrr}\n",
" -2&1&0&&\\cdots&0\\\\\n",
" 1&-2&1&&\\cdots&0\\\\\n",
" 0&1&-2&&\\cdots&0\\\\\n",
" \\vdots&&\\ddots&\\ddots&\\ddots&\\vdots\\\\\n",
" 0&\\cdots&&1&-2&1\\\\\n",
" 0&\\cdots&&0&1&-2\n",
" \\end{array}\n",
" \\right]\\ \\, ;\n",
" \\end{equation*}\n",
"\n",
"- ${U_h}$ est le vecteur de $\\RR^M,$ ${U_h}=(u_1,\\dots,u_M)^T$ ;\n",
"\n",
"- $F\\in\\RR^M$ est le vecteur $\\big(f(x_1),\\dots,f(x_M)\\big)^T,$\n",
"\n",
"avec $x_j=jh,\\ j=1,\\dots,M,\\ h=\\frac{1}{M+1}.$\n",
"\n",
"-------------------------------------------------------------------------------------------------------------\n",
"\n",
"On a alors remplacé le problème continu (P) par le problème discret (P_h) ou le problème équivalent (S).\n",
"\n",
"Pour des questions pratiques on va résoudre le système $(S_h)$ sous la forme équivalente \n",
"\n",
"$$\n",
"A_M U_h=h^2 F,\n",
"$$\n",
"\n",
"où $A_M\\in\\mathcal{M}_M(\\RR)$ est la matrice $h^2 A_h$ (qui ne dépend plus explicitement de $h$ ; rappelons que le pas $h$ et $M$ sont liés par la relation $h=1/(M+1)$). \n",
"\n",
"On montrera en cours que le système ci-dessus admet une solution, i.e. que $A_M$ est une matrice inversible."
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"On considère $f(x) = (2\\pi)^2 \\sin(2\\pi x)$, de sorte que la solution du problème $(P)$ est donnée par $u(x) = \\sin(2\\pi x)$. \n",
"\n",
"**Question 3.** \n",
"Implementer en python une fonction `A(M)` qui retourne la matrice $A_M$, pour un nombre de points M donné. \n",
"\n",
"**Question 4.** Soit $M=49$. Obtenir la solution approchée $U_h$ en résolvant le système linéaire $A_M U_h =h^2 F$, en utilisant la fonction de numpy `np.linalg.solve`. Tracer sur la même figure la solution approchée obtenue et la solution exacte du problème $(P)$.\n",
"\n",
"---------------------------------------------------------------------------------------------------------------\n",
"\n",
"On cherche à illustrer numériquement la convergence du schéma aux différences finies $(P_h)$. On montrera en cours cette convergence : la solution $(u_0,\\dots,u_{M+1})$ du problème discret $(P_h)$ approche la solution $u$ du problème continu $(P)$ au sens suivant :\n",
"\n",
" $$\n",
" \\lim_{h\\to0}\\left(\\max_{j=0,\\dots,M+1}|u(x_j)-u_j|\\right)=0.\n",
" $$\n",
"\n",
"**Question 5.** Pour $M=2^{k}$, et donc pour $h=\\frac{1}{2^k +1}$, $2\\le k\\le 11$, calculer et représenter dans un même graphique la différence en valeur absolue entre la solution exacte aux points $x_j$ et la solution approchée. Observer que cette différence décroit avec $h$.\n",
"\n",
"------------------------------------------------------------------------------------------------------------------\n",
"\n",
"Pour $h>0$ fixé, on note\n",
"\n",
"$$\n",
"e_h:=\\max_{j=0,\\dots,M+1}|u(x_j)-u_j|\n",
"$$\n",
"\n",
"l'erreur global du schéma associée à une discrétisation de pas $h$. On montrera en cours que l'on a plus que la convergence\n",
"\n",
"$$\n",
"\\lim_{h\\to0} e_h=0,\n",
"$$\n",
"\n",
"on montrera que cette convergence a lieu *au moins à l'ordre 2*, dans le sens que la propriété suivante se vérifie : il existe une constante $C>0$, indépendante de $h$, tel que\n",
"\n",
"$$\n",
"e_h\\leq C h^2.\n",
"$$\n",
"\n",
"**Question 6.**\n",
"Calculer, pour chaque valeur de $h$ associée à $M=2^{k}$, $2\\le k\\le 11$, l'erreur globale en norme infinie entre la solution approchée et la solution exacte, définie par \n",
"\n",
"$$\n",
"e_h=\\max_{1\\le j\\le M}|u_{j}-u(x_{j})|.\n",
"$$\n",
"\n",
"Représenter dans une même figure $e/h$ et $e/h^2$ en fonction de $h$ et dans une autre figure $e$ en fonction de $h,$ ainsi qu'une droite de pente 1 et une droite de pente 2, en utilisant une échelle logarithmique. Commenter les résultats obtenus. Que peut-on déduire sur l'ordre du schéma ?\n"
]
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"import numpy as np\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"def A(M):\n",
" return 2 * np.eye(M) - np.eye(M, k=-1) - np.eye(M, k=1)\n",
"\n",
"\n",
"def solution_approchée(f, M, a=0, b=1, ua=0, ub=0):\n",
" X = np.linspace(a, b + 1 if b == 0 else b, M + 2)\n",
" U = np.zeros(M + 2)\n",
" U[0], U[-1] = ua, ub\n",
"\n",
" h = (b - a) / (M + 1)\n",
"\n",
" delta = np.zeros(M)\n",
" delta[0], delta[-1] = ua / np.power(h, 2), ub / np.power(h, 2)\n",
"\n",
" U[1:-1] = np.linalg.solve(A(M), h**2 * (f(X)[1:-1] + delta))\n",
" return X, U"
]
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z504eeeSRDD9jx44d1KtXz/YH+Z49e2jYsGG2cZUtWzZdr09OhYeH06NHD1uiZH2Pd955JwAPPvggycnJmb42LCyMXr16pZsYbn1vhZFDJUuXLl3in3/+sX1/5MgRwsPDKVu2LHfccQejR4/m33//5euvvwYs2fann37KiBEjCA4OJjQ0lFmzZqVb5TZs2DDuueceJk2aRI8ePVi2bBm//PILGzduzPf3J/krq2Gt6Lh4go7tZmLIp1S7aKmHtL2yH0v827KyditiinsAMOjuaszZdNS2+s3K+k/0ew/VB8jQI+T9X49QBz9vFmw/QVRMPAaQ6uTMT3XvYVXtlumSpqCvprLBbaatpynuv6RJ85qkqLH+IZMVA9INXee2l156iXPnzlGlShXbsdTU1Ay9NhEREfTq1YsDBw4A8Pbbb9OzZ0/CwsIAy1yhixcv2nqn0vrll1/SLUzas2cP8fHxBAUFcerUKVavXo2fn1+619zOMNyoUaPSHdu1axf33HNPtteytnvnnXdsiVVh51DJ0o4dO2jbtq3te+u8oSeeeIK5c+cSGRnJ8ePHbeerV6/OqlWreOmll/jss8+oVKkSH3/8cbru0hYtWrBgwQJef/113njjDWrWrMnChQtVY6mQy2pY6+17KhE05V16/PgtAJGlyvFmx6Gsvat5hmt08POmafWyWSZD1t6eDn7eWc41GtvNj6HzdqZLuFKdnFlZ9x5W127JJ66HuevzD9P1NH3e/BG+aPoQqf9NBM/Lm4NIQRIdl3WidCvtbsbatWvZtGkTu3btolixa7fO7du3M2jQIM6dO0e5cuUwDIOjR4/StWtXPvnkEw4ePMi///5LYGAg/v7+wLU9yq5cuZLhZ/zzzz/MmjXLdmzPnj106dKFCRMm8M4777BixYoMydKtDMPFxcVx5MgRGjdunO54eHg4L774YrbXOnz4MBcvXiQgICDbdoWJQyVLbdq0IbuyUHPnzs1w7N57771hrYpHHnkk0+5QKZwynfNgGARs/YWG735OhcsXAfim8QNMuvcJLrml3/TTWiPJmvRklwwBODuZskxkOvv7ML1fQJYJV0JyIJ0Sa6TraRr1+1e0PBrOi91f5XwJM5A3NweRgsbLI2e1mXLaLqeSk5MZNmwYr7zySobVa9Zl8uHh4bRr147Dhw9zxx13ULduXQ4dOsRbb73Fm2++ybx582w9NtWrV6dOnTqMHj0aV1dXKlSowNatWxkzZgz9+vWztbty5QqpqakMGjQIAFdXV8xmc4b4bmUYLjw8HCcnJ+rXr287duzYMS5cuJDhPV4vLCwMZ2fnGw4PFiYOlSyJ3K7M5jx4x57l7bXT6fDPVgCOVriDyPen8uZfLhleb02BxnbzsyVE2SVDOdHZ3yfLhCv00Ll0w3MP7V3H+LWf0+rYbn6aO4xne44mvFLtXL85iBRETauXxcfsbhu6vl7aP2Ry0yeffMK5c+d4/vnnM5zz9fWlRIkStmQpIiICf39/3NzciI2N5dy5c7Rs2ZLXXnuNZ5991hKnycTKlSsZOXIkjz32GElJSdx555288847PPXUU7ZrR0REpJsEHhERwdNPP50r72n37t3UqVMnXZHGXbt2Ubp0aapVq5bta3fu3Ent2rUpUaJEtu0KE4et4F2QqIK34wg9dI7HZ2yxfGMY9Nkdwuh1s/FIvEqiUzGmN3+Uz4J68dXQ1sRcTbT7CrSUVINWk35Ld3O468wxPl86kZrnT5LoVIypXYcyYvEUnJ2dVF5ACrTcqOBt7RmGzOcK2nvBw7vvvourqyuvvPIKCxcupH79+vj5+VGxYkVOnDiBq6trjq81c+ZMTp8+zZgxYwBo3Lgx69ato3Tp0nkUfeGkCt4iN8k6XGUyUhn3yxc8sXMlADsr1WZU5xc5WKGqrV2PRpVvOMSW15ydTBnmNR2sUJUeAz7kg1VTuP/vzbyy/BMYeIE1L45j7C9HVV5ACrUbDV3b+3d979699O/fH7BspwVw6tQpypcvf1OJEsCff/5Ju3btAMtQ4KVLl5Qo2Yl6lnKBepYcR+ihczwxfQOTV35It782kIqJ99oMZObdPUl1cra1mx/cvEBNmM50QrqnG3MubKDOR+9CSgp/VajGkJ6jOVr22kTOgvLXtgjk7t5w6kWVnMqNniUlS7lAyZLjSImJJaxJW5r+s5NEp2KM6DqCn+peWyabdoPbgvYPb5b71K1bz8XuD1Hu0gViXUvwctcR6VbvFeT3JEVLYdpIVxxHbiRLNy45LOKAUlINQg+dY1n4v4QeOkdKqgFnzuDcvh1N/9nJZRd3Bj8yNkOiBOknbxck1onkPRpVJqhmOVuM2+6oz/0DprC9sh+eiVeYsfgdXtowD/77OyhteQEREbl5mrMkhU5mQ1aNUy8y7/s3KXnsMJQvz+5PvuafI65QAOc83KzouHiiPcrx+OMTGL1+DoN3LGPY5gWYDIMP7+mfrp2IiNw8JUtSqGRWQ6n2maN8/v2blLx0nquVqlD8t19oUbs2GwvJnAdr2YBk52K83S6YY6W9eeuXL3gxdCHxLm5MC+qVrp2IiNwcJUtSaGRWQ6nJyb3M+vEtzAmX+at8VV7tP4kld9XCmduvj1RQXF975uvAbrgnJ/J/6+fw6h9fE1/MjdXte+d67RkRkaJCc5ak0Lh+36h2/2xl3sI3MCdcZntlP3r1ncQeShW6uTvW8gJwbd7Vl80e5qOWfQB487cZzIjf6ZC9ZiIiBYGSJSk00s7JaX58D9OXTMQ9OZFfat5N/95vEeteKkO7wsJae8bbfG2obWrLx5nX2jIE5//2KPjmGyCLye8iIpIlDcNJoWGdk1Pj3Ek+XzIB19RkVtZuyYvdXyUlTQ2lwjp3J9NtUyZ0gWEV4LPPYOBAdkVf5dnEmipcKSJyE9SzJIVG0+plqVMsgdk/jqd0/CV2VqrNiAdG2BIlE5bEoDDP3clQXsDZCT7+GAYNgtRU/F99lrphf6R7TVRMPEPn7SQkItJOUYuIFGxKlqTQcE5K5LvVk6h2MZLj5ooEP/QGCS5uQMGvoZSnnJxI+fwL1jRoi0tqCtOXTqTl0XDbaesg3PgV+zQkJ5KHxo0bR6NGjW77OnPnztW2J/lMyZIUDoYBgwZRduc2kjw8efXJCZwrWdp22tvsXqS3/Nh2PIZnOw7j57ua45aSxMxFb9Pk5F7beRWuFMledHQ0zzzzDHfccQdubm54e3vTqVMnQkND8/TnVqtWjSlTpqQ71rt3b/7+++88/bkFwdGjRzGZTISHh9s7FM1ZkkJi/Hj47jsoVgyXJYv5tu19haKGUm6Jjosn2bkYL3QfxZeL36HNkTC+XPwuXQdO4ZSnV7p2IpLRww8/TFJSEl999RU1atTg9OnT/Prrr5w/n/9/YBQvXpzixYvn+88tytSzJA7n+tVcqV9/Y0mWAD7/HNq1y3JrkKLKOqk9sZgLzzz4f/xZsSZlr8Yybel7uCYnZWgnItdcvHiRjRs3MmnSJNq2bUvVqlVp2rQpo0eP5oEHHrC1O378OD169KBUqVJ4enrSq1cvTp8+neV127Rpw/Dhw9Md69mzJwMHDrSdP3bsGC+99BImkwmTyfLvWGbDcNOnT6dmzZq4urpSu3Ztvvlv9auVyWRi5syZPPjgg5QoUYK77rqL5cuXZ/u+ExMTefXVV6lcuTIlS5akWbNmrF+/HrDst1avXj2efvppW/sjR45gNpuZMWMGAOfOnePxxx+nSpUqlChRgvr16zN//vx0PyM1NZVJkyZx55134ubmxh133MG7774LQPXq1QFo3LgxJpOJNm3a2F43Z84c6tati7u7O3Xq1GHatGnZvpfbpWRJHEpIRCStJv3G4zO2MGxBOB+9OZOUQYMsJ0eNgsGD7RtgAWUtXGkCElzcGNpzNBfdS9Eo8m9e/21mkZj8LgWUYcDly/Z55HAf+VKlSlGqVCmWLl1KQkJCFm/DoGfPnpw/f57ff/+dtWvXcujQIXr37n3LH83ixYupUqUKb731FpGRkURGZr4IY8mSJQwbNoyXX36ZiIgInnnmGZ588knWrVuXrt348ePp1asXe/bsoUuXLvTt2zfbnrEnn3ySTZs2sWDBAvbs2cOjjz5K586dOXjwIO7u7nz77bd89dVXLF26lJSUFPr370/btm0JDg4GLAlVYGAgP/30ExERETz99NP079+frVu32n7G6NGjmTRpEm+88Qb79u3ju+++o2LFigBs27YNgF9++YXIyEgWL14MwIwZMxgzZgzvvvsu+/fvZ8KECbzxxht89dVXt/xZ35Ahty0mJsYAjJiYGHuHUqit/vOUUW3UT0bV/x73Bn9hnHf3MAwwVtZuaazefdLeIRZo1s/P+hk+8chYIwWTYYAxvOvLxuo/T9k7RCnkrl69auzbt8+4evXqtYOXLhmGJW3J/8elSzmO/ccffzTKlCljuLu7Gy1atDBGjx5t7N6923Z+zZo1hrOzs3H8+HHbsb179xqAsW3bNsMwDGPs2LFGw4YNbefvvfdeY9iwYel+To8ePYwnnnjC9n3VqlWNjz76KF2bOXPmGGaz2fZ9ixYtjODg4HRtHn30UaNLly627wHj9ddft31/6dIlw2QyGatXr870/f7zzz+GyWQy/v3333TH27VrZ4wePdr2/fvvv2+UL1/eeOGFFwxvb2/jzJkzmV7PqkuXLsbLL79sGIZhxMbGGm5ubsaMGTMybXvkyBEDMHbt2pXuuK+vr/Hdd9+lO/b2228bQUFBmV4n09+7/+T0/q2eJXEI129lUvpqLHN+HEeZ+DjCfWox4oERjF/5l1ZzZeP6wpXra97NJy0eA+B/v3xGZ+OsPcMTKdAefvhhTp06xfLly+nUqRPr168nICCAuXPnArB//358fX3x9fW1vcbPz4/SpUuzf//+PI1t//79tGzZMt2xli1bZvi5DRo0sD0vWbIkHh4eREdHZ3rNnTt3YhgGtWrVsvWslSpVit9//51Dhw7Z2r388svUrl2bTz75hDlz5lC+fHnbuZSUFN59910aNGhAuXLlKFWqFGvWrOH48eO2uBMSEmjXrl2O3+uZM2c4ceIEgwcPThfXO++8ky6u3KYJ3uIQ0m5l4pSawrSl71H9QiQnPb146uE3iHdxs63mKgz7veWVDIUrB92N8fw5nNeugYcfhu3bwWy2d5hSlJQoAZcu2e9n3wR3d3c6dOhAhw4dePPNN3nqqacYO3YsAwcOxDAM25yitLI6DuDk5IRx3VBgUlJSpm1v5PqfkdnPdXFxyfCa1NTUTK+XmpqKs7MzYWFhODs7pztXqlQp2/Po6GgOHDiAs7MzBw8epHPnzrZzkydP5qOPPmLKlCnUr1+fkiVLMnz4cBITEwFuaZK6Nd4ZM2bQrFmzdOeujzM3KVkSh5B2ldYz2xbT4vgeLru4M+iRNzlbskym7SRzGTYQ/u5bCAyEgwfhySdh0SLI4h93kVxnMkHJkvaO4pb4+fmxdOlS2/Pjx49z4sQJW+/Svn37iImJoW7dupm+vkKFCunmIaWkpBAREUHbtm1tx1xdXUlJSck2jrp167Jx40YGDBhgO7Z58+Ysf25ONG7cmJSUFKKjo2ndunWW7QYNGoS/vz/BwcEMHjyYdu3a4edn2atyw4YN9OjRg379+gGWROfgwYO2uO666y6KFy/Or7/+ylNPPZXh2q6urgDp3n/FihWpXLkyhw8fpm/fvrf8/m6WkiVxCNZVWv5R/zBiwzwAxrV/hr8rVMu0ndyE8uXhxx+hVStYsgQmTyZlxMsqvSDyn3PnzvHoo48yaNAgGjRogIeHBzt27OD999+nR48eALRv354GDRrQt29fpkyZQnJyMs8++yz33nsvTZo0yfS69913HyNGjGDlypXUrFmTjz76iIsXL6ZrU61aNf744w8ee+wx3Nzc0g1zWb3yyiv06tWLgIAA2rVrx4oVK1i8eDG//PLLLb/nWrVq0bdvXwYMGMDkyZNp3LgxZ8+e5bfffqN+/fp06dKFzz77jNDQUPbs2YOvry+rV6+mb9++bN26FVdXV+68804WLVrE5s2bKVOmDB9++CFRUVG2ZMnd3Z1Ro0bx6quv4urqSsuWLTlz5gx79+5l8ODBeHl5Ubx4cUJCQqhSpQru7u6YzWbGjRvHiy++iKenJ/fffz8JCQns2LGDCxcuMGLEiFt+z9nKdkaT5IgmeOe95JRUo824FcahspUtE7prtTCqvrrCNtm72qifjOYTfjGSU1LtHarjmj7dMMBIcXY2hj412fbZVv3vs9UEcLld2U20Lcji4+ON1157zQgICDDMZrNRokQJo3bt2sbrr79uXLlyxdbu2LFjRvfu3Y2SJUsaHh4exqOPPmpERUXZzl8/wTsxMdEYOnSoUbZsWcPLy8uYOHFihgneoaGhRoMGDQw3NzfDesu+foK3YRjGtGnTjBo1ahguLi5GrVq1jK+//jrdecBYsmRJumNms9mYM2dOlu87MTHRePPNN41q1aoZLi4uhre3t/Hggw8ae/bsMfbv328UL1483UTrmJgYo1q1asarr75qGIZhnDt3zujRo4dRqlQpw8vLy3j99deNAQMGGD169LC9JiUlxXjnnXeMqlWrGi4uLsYdd9xhTJgwwXZ+xowZhq+vr+Hk5GTce++9tuPffvut0ahRI8PV1dUoU6aMcc899xiLFy/O9H3kxgRvk2HkcO2kZCk2Nhaz2UxMTAyenp72DqfQOvFof3x/nEdkqXJ0HvQpMcU9gGtbmRTlCt25wjD4t0cvKq/4kTMlS/PAE1OJ9rAM1+kzltwQHx/PkSNHqF69Ou7u6gWW/JHd711O799aDSeOYdkyfH+ch2Ey8W7v12yJEmgrk9ySYkDfwIHsr1CNCpcv8unySRRLSQa0f5yIFG2asyQFX2Skrdik6eWXmTrpZfpqPk2u23bkPEevwtCeo1n+1Us0PbmPlzfMY1KbgUD6/eO04lBEihL1LEnBlpoKAwfCuXPQqBG88462Mskj1pWER8tW5pUuwwF4ettiGkT+nWk7EZGiQsmSFCgZ9n37+GNYswbc3S0b5bq52TvEQivtSsKfa7dgqd+9OBupfLBqivaPE5EiTcNwUmCEREQyfsU+W/HJOtFHWP71q7gCTJ4Mt1EzRG7Mun9cVEw8BpbSDC2P7qb22eM8F7qQKa374a3940SkCFLPkhQIIRGRDJ2305YouSUnMmXF/3BNSeLXmncT0rqnfQMsApydTIztZikmZwIuFvfkzQ5DAHh2yw/UPX2Ysd38NOwpt02LsCU/5cbvm8MlS9OmTbMt/wsMDGTDhg1Zth04cCAmkynDo169erY2c+fOzbRNfLzmZeSX6/d9Axi1fi51zh7jTInSjLp/GON/2q9VWPng+v3jVtdpxapaLXBJTWHBli/oXDtjQTyRnLJut3HlyhU7RyJFifX37frtXm6GQw3DLVy4kOHDhzNt2jRatmzJF198wf3338++ffu44447MrSfOnUq7733nu375ORkGjZsyKOPPpqunaenJwcOHEh3TDVA8k/afd8A7jkcxqCw5QC80mUYZ0uWBq3CyjcZ9o97cCZGl1Z4/rUX3n8fxoyxd4jioJydnSldurRt89YSJUpkuW+ayO0yDIMrV64QHR1N6dKlb2vvOIdKlj788EMGDx5s20NmypQp/Pzzz0yfPp2JEydmaG82mzGn2RR06dKlXLhwgSeffDJdO5PJhLe3d94GL1lKu7qqROJVJoZ8CsDcgK6sr3l3pu0kb6XfP64yfPwx9OsHb70FPXtCmt5ZkZth/bc2q93uRXJb6dKlb/se7zDJUmJiImFhYbz22mvpjnfs2JHNmzfn6BqzZs2iffv2VK1aNd3xS5cuUbVqVVJSUmjUqBFvv/02jRs3zvI6CQkJJCQk2L6PjY29iXci10u7uurFTfOpHHeGE+aKvPdffZ/M2kk+69MHFiyAn36CQYNg0yYo5jD/fEgBYjKZ8PHxwcvLi6SkpBu/QOQ2uLi43FaPkpXD/Gt39uxZUlJSqFixYrrjFStWJCoq6oavj4yMZPXq1Xz33XfpjtepU4e5c+dSv359YmNjmTp1Ki1btmT37t3cddddmV5r4sSJjB8//tbfjKRjXYXl+c9fDN6xDICx7Z8h3sWSHJlAq7DszWSCzz8HPz/Yto3Ujz5i60ODVBhUbpmzs3Ou3MRE8oPDJEtW149vG4aRozHvuXPnUrp0aXr27JnuePPmzWnevLnt+5YtWxIQEMAnn3zCxx9/nOm1Ro8enW5n49jYWHx9fW/iXUhazk4mxj5Qh3IPvIhLago/39Wc3+5sClzbk0yrsAqAypXhww/hqadI+r/X+b+DZo6UrQyAj9mdsd38tOWMiBRKDrMarnz58jg7O2foRYqOjs7Q23Q9wzCYPXs2/fv3x9XVNdu2Tk5O3H333Rw8eDDLNm5ubnh6eqZ7yO3pvONn7j65jyuu7oxv/7TtuPZ9K1hCmt7PhmqNcUtOZNLqqZiMVACiYuIZOm8nIRGRdo5QRCT3OUyy5OrqSmBgIGvXrk13fO3atbRo0SLb1/7+++/8888/DP5vf7HsGIZBeHg4Pj66Oeebc+fg1VcBcH/nLSa/3J2pjzVifnBzNo66T4lSAZGSajD+p/281vkFLrkWp+nJfQzYuRLQRrsiUrg5TLIEMGLECGbOnMns2bPZv38/L730EsePH2fIEEvhvNGjRzNgwIAMr5s1axbNmjXD398/w7nx48fz888/c/jwYcLDwxk8eDDh4eG2a0o+GDXKkjD5++M0fLj2fSugrCUe/jV78d69AwEY9ftcqly09Pam3WhXRKQwcag5S7179+bcuXO89dZbREZG4u/vz6pVq2yr2yIjIzl+/Hi618TExLBo0SKmTp2a6TUvXrzI008/TVRUFGazmcaNG/PHH3/QtGnTPH8/gmVV1axZlueffw63UTRM8lba0g3fNr6frn9toPmJCMb+OoPgh9/ItJ2ISGFgMlR3/rbFxsZiNpuJiYnR/KWbkZQEAQEQEQGDB8PMmfaOSLIReugcj8/YYvu+5tkT/Dz7OYoZqfTv9RYbqgcAMD+4uYqHiohDyOn926GG4aSQmTrVkiiVKweTJtk7GrkBa4kH68DoofK+fB3QFYA3fp2JS0oyPirxICKFkJIlyTcpqQahh86xLPxfwjbsxhg71nLi/fctCZMUaNdvtAswpVUfzhf3pNa54/QNX60SDyJSKClZknwREhFJq0m/8fiMLQxbEM7ZwUMwXbnC+YCmMHCgvcOTHLp+o91Y91L8757+AIzZuoDO3ppzJiKFj0NN8BbHFBIRydB5O23Ly9v9s5VOB7eQ5OTM440G8NK+0yoP4EAybLQ76G6MRzfgsmcPjB0Ln31m7xBFRHKVepYkT6WkGoxfsc+WKBVPjGf82i8AmNWkB39XqKbaPA7IutFuj0aVCarlhcm62vTzz2HPHvsGJyKSy5QsSZ6y1uaxGrrlB6rERnPSswJTW/ZRbZ7Cok0beOQRSE2F4cNBi2xFpBBRsiR5Km3NnYpxZwnevhSAd+57iquu7pm2Ewf1wQfg7g7r1sGSJfaORkQk1yhZkjzl5XEtIRqx4VuKJyewvbIfIbVaZNlOHFS1avDKK5bnL78M8UqARaRwULIkecpam6fOmaM8EvErABPbPgkmy/JyE6g2T2EyahRUrgxHj8KHH9o7GhGRXKFkSfKUtTbPqPVzcDZSWVWrBTsr1wWu1epRbZ5CpGRJS90swJgwgbBNESwL/5fQQ+c0iV9EHJaSJclznU/vo+3hMJKdnHn/3idsx73N7kzvF6CyAYXN449zoVETTJcvc+yZFxm2IJzHZ2yh1aTfCImItHd0IiI3TXWWJG+lptrmsTgNHcLElx621ObxsAy9qUep8AnZG8VnDfuxLDyMh/auY17jLuysXJeomHiGztupBFlEHI56liRvzZ8Pu3aBpydOY8deq81Ts5wSpULIWlfrT+87+aF+ewDe/PVLTEaqrdaW6mqJiKNRsiR5Jz4e/u//LM9few0qVLBvPJLn0tbV+t89A4hzLU6jyIN03/c7gOpqiYhDUrIkeefTT+H4ccvqqGHD7B2N5IO09bLOlCrD9OaPAjBi47cUS0nOtJ2ISEGnZEnyxvnz8O67lufvvAMlStg3HskX19fLmhPYnTMlSlP1YhS9/lybZTsRkYJMyZLkjXffhYsXoX596N/f3tFIPrHW1bLORrvq6s6nLXoD8OKm+bgnJaiulog4HCVLkmtSUg1CD51j7cpQUj/51HLwgw/A2dm+gUm+sdbVgmt1tOY37MxJTy+8L52n/66VqqslIg5HyZLkipCISFpN+o3HZ2zhyiujcUpKZNudAYRUqm/v0CSfdfb3YXq/ALzNlqG2xGIuTGnVB4BXdi2h8x0l7RmeiMhNU50luW0hEZEMnbcTA6gfeZAe+38nFRPjWg1k/7e7mN7PpLo6RUxnfx86+Hmz7ch5S12tJ5tgHA7B9a+/LNugjBtn7xBFRHJMPUtyW6x1dQwAw2DMulkALPFvy76KNQDV1SmqnJ1M1+pq1a6I6e23LScmT4azZ+0bnIjITVCyJLclbV2dNod30PxEBAnOLkxu3Q9QXR1J46GHICAALl2C996zdzQiIjmmZElui61ejmHw0sbvAJgb2I1Tnl6Zt5Oiy8npWjmJTz+FkyftG4+ISA4pWZLbYq2X0+7QNhpGHeSyiztfNHs4y3ZSxHXqBK1bQ0KCpf6WiIgDULIkt6Vp9bL4eLox/L9epa8DunK+hNl23gSqqyPXmEwwYYLl+axZ8M8/9o1HRCQHlCzJbXF2MvFZqRPUP32IS67F+bLpg7Zz1ko6qqsj6bRqBV26QHIyqW+OJfTQOZaF/0vooXNaCCAiBZJKB8jtMQwC5nwMwKKgnlxI06vkbXZnbDc/lQ2QjN55B1atggXzGe8exF9e1QFLL6R+Z0SkoDEZhqE/5W5TbGwsZrOZmJgYPD097R1O/lq6FB58EDw8SDl0mG2xJktdHQ/L0Jt6lCQzIRGRJD/am65/bWDtnc0IfvgN4Fpv5PR+AUqYRCTP5fT+rWE4uXWpqdeKC774Is4Vyl+rq1OznBIlyZS1NteHrfqSbHKiwz9bafzvX4Cl1ASoNpeIFCxKluTWLV0Ku3eDhweMGGHvaMRBWGtzHS5XhR/rtwdg5IavbedVm0tEChqHS5amTZtG9erVcXd3JzAwkA0bNmTZdv369ZhMpgyPv/76K127RYsW4efnh5ubG35+fixZsiSv34bjS9urNGwYlNVqN8mZtDW3Pm75GAnOxWh5bA/Nj+/Jsp2IiD05VLK0cOFChg8fzpgxY9i1axetW7fm/vvv5/jx49m+7sCBA0RGRtoed911l+1caGgovXv3pn///uzevZv+/fvTq1cvtm7dmtdvx7EtWQJ//gmenupVkpuStubWKU8vFjboBMDzmxdm2U5ExJ4caoJ3s2bNCAgIYPr06bZjdevWpWfPnkycODFD+/Xr19O2bVsuXLhA6dKlM71m7969iY2NZfXq1bZjnTt3pkyZMsyfPz9HcRW5Cd6pqdCwIUREwJtvwvjx9o5IHEhKqkGrSb8RFROPAVSOiWb9l8G4pKbwUL8P2FW5Lt5mdzaOuk/z3kQkTxW6Cd6JiYmEhYXRsWPHdMc7duzI5s2bs31t48aN8fHxoV27dqxbty7dudDQ0AzX7NSp0w2vWaQtWmRJlMxmeOkle0cjDsbZycTYbn6AZfXbv2YvFvm3A+C50O8B1eYSkYLFYZKls2fPkpKSQsWKFdMdr1ixIlFRUZm+xsfHhy+//JJFixaxePFiateuTbt27fjjjz9sbaKiom7qmgAJCQnExsamexR2KamGpXjgzhNcGfOm5eBLL0EWPXYi2ens78P0fgF4my1DbdObP0KKyYl2h7bzbUAxlQ0QkQLF4YpSmkzp/9o0DCPDMavatWtTu3Zt2/dBQUGcOHGC//3vf9xzzz23dE2AiRMnMr4IDT2FREQyfsU+ImPi6br/D3oc/Is495Js7dCb9vYOThxWZ38fOvh5s+3IeaLj4jkf9RAVlv9Ii4VfQq9O9g5PRMTGYXqWypcvj7Ozc4Yen+jo6Aw9Q9lp3rw5Bw8etH3v7e1909ccPXo0MTExtseJEydy/PMdTUhEJEPn7SQyJh6n1BRe3LQAgBlNehK8/BAhEZF2jlAcmbOTyVabq8LE8Za94xYvhr177R2aiIiNwyRLrq6uBAYGsnbt2nTH165dS4sWLXJ8nV27duHjc62LPygoKMM116xZk+013dzc8PT0TPcojKzFA60rAB74ayO1zh0nxq0kc5p0B1Q8UHKRnx88/LDluXWzXRGRAsChhuFGjBhB//79adKkCUFBQXz55ZccP36cIUOGAJYen3///Zevv7YUuJsyZQrVqlWjXr16JCYmMm/ePBYtWsSiRYts1xw2bBj33HMPkyZNokePHixbtoxffvmFjRs32uU9FiTW4oEATqkpDNtkWR04o+mDxLmVBK4VDwyqWc5ucUohMmYM/PgjLFhgqeOVpsyHiIi9OFSy1Lt3b86dO8dbb71FZGQk/v7+rFq1iqpVqwIQGRmZruZSYmIiI0eO5N9//6V48eLUq1ePlStX0qVLF1ubFi1asGDBAl5//XXeeOMNatasycKFC2nWrFm+v7+CJm1RwPsPbObO8ye56F6KuYHds2wnclsaNYKuXeGnn2DiRJg9294RiYg4Vp2lgqqw1lkKPXSOx2dsAcPgp6+G43/6EB+17MPUVn3StZsf3Fw9S5J7tm6F5s2hWDE4eBCqVbN3RCJSSBW6OkuS/5pWL4uP2Z17j+zE//QhLru481VgV9t5E+BjdqdpdW11IrmoWTPo0AGSk2HSJHtHIyKiZEmyZi0eOHTLDwDMb9iJi8Utmbe1sIKKB0qeeP11y9fZs+Hff+0bi4gUeUqWJFud447S/EQESc7FmHn3g7bj3mZ3pvcLUPFAyRv33AOtW0NiIvzvf/aORkSKOIea4C128N57ADgP6M9HL3clOi4eLw/L0Jt6lCRPvf46dOqE8cUX7Hj8GU65euh3T0TsQhO8c0FhneDN3r3g728pFLh/P6Sphi6S5wyDiw0DKf3nLqY3e4RJbQYClnlyY7v5qVdTRG6bJnjL7bNOrn3oISVKku9C9kYxspZlQUH/XSsxX40DIComnqHzdqp6vIjkGyVLkrljx+C77yzPX3vNvrFIkWOtHv9Lzabs86pOqcSrPBm2HMBWUV7V40UkvyhZksz973+QkgLt20OTJvaORooYW/V4k4lPgnoD8OSO5ZRMuAJYEiZr9XgRkbymZEkyio6GmTMtz0ePtm8sUiSlrQofUrsFh8pWwZxwmcf2rMmynYhIXlGyJBl9/DHEx0PTptC2rb2jkSLIy8Pd9twwOTHj7p4ADNq+jGIpyZm2ExHJK0qWJL3YWPj0U8vz116zrIQTyWfW6vHW374l/vdxpmRpKsedoetfG1Q9XkTylZIlSe+LLyAmBurUgR497B2NFFHW6vFgqRafUMyVOf9t4PzM1kVgGKoeLyL5RsmSkJJqEHroHCu2HiLxg/+qJY8aBU769RD76ezvw/R+AXibLUNt8xp34bKLO3XPHOWHGnGqsyQi+UYVvIu4kIhIxq/YR2RMPI+Hh9DtTDRR5grsbtiWTvYOToq8zv4+dPDzZtuR80THxRMT8wQl535Bkx9mwTOP2zs8ESki1HVQhIVERDJ03k4iY+JxTk2xDG8AXzTpyZCFESr6JwWCs5OJoJrl6NGoMpXGjQZnZ/j1V9i5096hiUgRoWSpiLIW/bOW9Lv/wCaqXYzkfHFPFjSw9Cmp6J8UOFWrwmOPWZ5/8IF9YxGRIkPJUhFlK/oHYBgM3fIjAHMDu3HV1V1F/6TgeuUVy9fvv4cjR+wbi4gUCUqWiqi0xfxaHQ2nXvRhLru481VA1yzbiRQIDRtChw6QmgoffWTvaESkCFCyVESlLeYXvH0JAN836EBMcY8s24kUGK++avk6axacO2ffWESk0FOyVERZi/7VPnOUe4/sJMXkxKwm1+oqqeifFGjt2kGjRnDlCkybZu9oRKSQU7JURFmL/g3evhSAkFpBnCztDWCrmqyif1JgmUzXepc++QSuXrVvPCJSqClZKsI6lzfxyF9/ADDz7gdtx73N7kzvF6Cif1KwPfqoZXXcmTPw1Vf2jkZECjEVpSzKPv0Up6REjBYteHXcQKLj4vHysAy9qUdJCrxixWDECBg2DGPyZLbc9xDRV5L0Oywiuc5kGIYK6dym2NhYzGYzMTExeHp62jucnLl8Ge64A86fh0WL4KGH7B2RyM27dInEyr64xl5kSM/RhNRuCVjm243t5qfeURHJVk7v3xqGK6q+/tqSKNWooQ1zxWGFHI3ji3qWIqpD/ttgFyAqJp6h83aqCr2I5AolS0VR2vo0w4dbto8QcTDWKvRfBXYlwdmFRpF/0/TkXgBbZXpVoReR3KBkqShasQIOHoTSpeHJJ+0djcgtsVahP1uyDIv82wHw9H/7GwKqQi8iuUbJUlE0ebLl65AhUKqUfWMRuUVpq8vPaPogqZhof2g7Nc6dzLKdiMitULJU1GzfDhs2gIsLvPCCvaMRuWVpq8sfKVuZ32o2AeDJsOVZthMRuRVKlooaa6/S449DpUr2jUXkNlir0FsLBMy6uycAD0f8ivlqnKrQi0iuUbJUlBw7Bj/+aHk+YoR9YxG5TdYq9GCpOh96RwP2V6hGiaQE+uwOAVSFXkRyh8MlS9OmTaN69eq4u7sTGBjIhg0bsmy7ePFiOnToQIUKFfD09CQoKIiff/45XZu5c+diMpkyPOLjC+E8h6lTISUF2re37Nwu4uA6+/swvV8A3mZ3MJlsvUtP7lrJ573rq86SiOQKh0qWFi5cyPDhwxkzZgy7du2idevW3H///Rw/fjzT9n/88QcdOnRg1apVhIWF0bZtW7p168auXbvStfP09CQyMjLdw929cMxzSEk1CD10jpUb9pP85QzLwZdftm9QIrmos78PG0fdx/zg5tw79gUSy3vhFXuWTn9tsndoIlJIOFQF72bNmhEQEMD06dNtx+rWrUvPnj2ZOHFijq5Rr149evfuzZtvvglYepaGDx/OxYsXbzmuglrBOyQikvEr9hEZE0/w1sWMWT+bQ17VOPjLJjrX13wlKaTeegvGjoW774atWy2b7oqIZKLQVfBOTEwkLCyMjh07pjvesWNHNm/enKNrpKamEhcXR9my6Sd8Xrp0iapVq1KlShW6du2aoefJEYVERDJ03k4iY+IplpJsWyH0RWB3hn67S5WNpfAaMgTc3CwrP3P4b4OISHYcJlk6e/YsKSkpVKxYMd3xihUrEhUVlaNrTJ48mcuXL9OrVy/bsTp16jB37lyWL1/O/PnzcXd3p2XLlhw8eDDL6yQkJBAbG5vuUZBYKxtbuwy7HNhIpbiznClZmqV+bQFVNpZCzMsL+vWzPLdWqhcRuQ0OkyxZma7rUjcMI8OxzMyfP59x48axcOFCvLy8bMebN29Ov379aNiwIa1bt+b777+nVq1afPLJJ1lea+LEiZjNZtvD19f31t9QHrBWNgbAMHhq+1IAvgroSmIxF1U2lsJv+HDL1yVL4MgRu4YiIo7PYZKl8uXL4+zsnKEXKTo6OkNv0/UWLlzI4MGD+f7772nfvn22bZ2cnLj77ruz7VkaPXo0MTExtseJEydy/kbyQdqKxU3+3UeDqH+IL+bKt43uz7KdSKHi7w8dOlj2QczmDx8RkZxwmGTJ1dWVwMBA1q5dm+742rVradGiRZavmz9/PgMHDuS7777jgQceuOHPMQyD8PBwfHyyXnLs5uaGp6dnukdBkrZi8aDtywBYXK8tF0qYs2wnUui89JLl68yZUMCGykXEsThMsgQwYsQIZs6cyezZs9m/fz8vvfQSx48fZ8iQIYClx2fAgAG29vPnz2fAgAFMnjyZ5s2bExUVRVRUFDExMbY248eP5+eff+bw4cOEh4czePBgwsPDbdd0RNbKxlVioul0cAsAcwO72c6rsrEUCZ06QZ06EBcHs2fbOxoRcWAOlSz17t2bKVOm8NZbb9GoUSP++OMPVq1aRdWqVQGIjIxMV3Ppiy++IDk5meeeew4fHx/bY9iwYbY2Fy9e5Omnn6Zu3bp07NiRf//9lz/++IOmTZvm+/vLLdbKxv13/oSzkcqGqo34u0I1ANvWEKpsLIWek9O1uUsff2wpyCoicgscqs5SQVUg6yxdvkyST2Vc4mIY9PCb/HanJfnzMbsztpufKhtL0XDlCvj6wvnzsHgxPPigvSMSkQIkp/fvYvkYk+Snr7/GJS4G4847CZ74PD0uJ+LlYRl6U4+SFBklSljqLk2YgPHRR2xpcA/RcfH6f0FEbop6lnJBgetZSk0FPz84cMAy/PDCC/aOSMR+Tp0itWo1nJKT6PrEFCK87wTUyyoihbCCt9yENWssiZKnJwwcaO9oROwq5LyJZbVbATD4v5pjAFEx8Qydt1PV7EXkhpQsFUZTpli+Dh4MHh52DUXEnqzV7Gc26QFA1782UDHuLICtwr2q2YvIjShZKmz274eff7ZsHvr88/aORsSurNXs93rfyVZff1xSUxiwc6XtvKrZi0hOKFkqbD7+2PK1e3eoUcO+sYjYWdoq9bP+6116fPfPuCUlZNlOROR6SpYKkwsX4OuvLc+t9WVEirC0Vep/ubMpJ8wVKXs1lh77fs+ynYjI9ZQsFSYzZ1rqyjRoAPfea+9oROzOWs3eBKQ6OfNVgGXLoyfDloNhqJq9iOSIkqXCIjn52oahw4ZZ5iyJFHHWavZgqV7/fYOOXHFxo+6ZozQ/EQGomr2I3JiSpcJi6VI4cQLKl4c+fewdjUiB0dnfh+n9AvA2uxPrXorF9e4DYMjulUzvF6A6SyJyQ6rg7cBSUg22HTlPdFw8bd/7H55gqVbsrvkXIml19vehg583246c5+rdJeCR1dz712ZMpRJu/GIRKfKULDmokIhIxq/YR2RMPPUjD9IjbCtJzsXY2PYh2to7OJECyNnJRFDNclCzLXTogGntWpg2Dd5/396hiUgBp2E4BxQSEcnQeTuJjLEsd34ybDkAK2u3YtCaU6pILHIjL75o+TpjBly+bN9YRKTAU7LkYKwVia31hitcOk/X/RsAmN2kO6CKxCI31KUL1KwJFy/CvHn2jkZECjglSw7GWpHYqt+uVbimJrOjcl32+NRSRWKRnHByurbB9Mcfg/YTF5FsKFlyMGkrDbsmJ9EnPASAOYHds2wnIpkYOBBKlYJ9++DXX+0djYgUYEqWHEzaSsMP/LWBClcuElmqHD/XCsqynYhkwmyGJ5+0PLduEyQikgklSw7GVpHYMGwTu78JeIBkZ8vCRlUkFrkJ1s2mf/oJDh2ybywiUmApWXIw1orEjU/9RYOof0hwdmFBw06AJVECVSQWybFateD++y1zlj791N7RiEgBpWTJAXX29+GzcxsBWOZ3L+dLmAHwNrurIrHIzbKWEZg9G+Li7BuLiBRIJsPQMpDbFRsbi9lsJiYmBk9Pz7z/gadOQdWqkJzM7mW/cfSOWnh5WIbe1KMkcpNSU8HPDw4csOyvaB2aE5FCL6f3b/UsOaLPP7dsnNuqFQ27t6VHo8oE1SynREnkVqQpI3D1wyks23mC0EPnVKtMRGy03YmjSUiAL76wPLcOH4jIbVnbpCNBbiUodeQQi9+bw+81AvExuzO2m5+GtUVEPUsO5/vvIToaKleGnj3tHY2IwwuJiOTpJX+zoH4HAJ7cYVllGhUTz9B5O7V9kIgoWXIohgFTp1qeP/ssuLjYNx4RB5d2+6CvA7qSiok2R8Koce6kbUshbR8kIkqWHMmWLRAWBm5uEBxs72hEHF7a7YOOl/Hh1zvvBuCJnSsAtH2QiABKlhzLJ59YvvbpAxUq2DcWkULg+m2B5v63bdDDEb9RKuFKlu1EpGi56WTpwIEDjBs3jnbt2lGzZk18fHxo0KABTzzxBN999x0JCQl5EaecOgU//GB5bt0AVERuy/XbAm2q2pCD5XwplXiVR/78Jct2IlK05DhZ2rVrFx06dKBhw4b88ccf3H333QwfPpy3336bfv36YRgGY8aMoVKlSkyaNElJU25LUy6Axo3tHY1IoWDbPsh6wGTiq8BugGUozslI1fZBIpLzopRVq1bllVdeoU+fPpQtm/U/HKGhoXz00Uc0atSI//u//8u1QAuyPC9KmZAAd9xhWQX3/ffw6KO5/zNEiqiQiEiGztsJWOYolUi8ypZpA/FMuMzAR8bx2NinVT5ApJDK6f07x8lSYmIirq6uOQ7gZts7sjxPlr75BgYMsJQLOHJEq+BEcllIRCTjV+yzTfZ+/dcZPLVjGWdatqXCxt/sHJ2I5JVcr+Cd08TnypUrN9X+Zk2bNo3q1avj7u5OYGAgGzZsyLb977//TmBgIO7u7tSoUYPPP/88Q5tFixbh5+eHm5sbfn5+LFmyJE9ivxkpqQahh86xbNdJLn3woeWgygWI5InO/j5sHHUf84ObM/WxRgRMeh3DZKLCpnXw99/2Dk+kyLLdC8P/tWtl/VtaDdemTRtOnjyZ4fjWrVtp1KjR7caUpYULFzJ8+HDGjBnDrl27aN26Nffffz/Hjx/PtP2RI0fo0qULrVu3ZteuXfzf//0fL774IosWLbK1CQ0NpXfv3vTv35/du3fTv39/evXqxdatW/PsfdxISEQkrSb9xuMztjD3w4WU+jOchGIu/Nqqu91iEinsnJ1MBNUsR49GlQm4rwmmBx6wnPj0U/sGJlJEpb0XDlsQzuMzttBq0m92KRR7S8mSp6cnDRo0YMGCBQCkpqYybtw47rnnHrp3z7sb+ocffsjgwYN56qmnqFu3LlOmTMHX15fp06dn2v7zzz/njjvuYMqUKdStW5ennnqKQYMG8b///c/WZsqUKXTo0IHRo0dTp04dRo8eTbt27ZgyZUqevY/sWOdPWIcDBoZZ6r0sq3svT606pmrCIvnFup3QnDkQG2vfWESKmOvvhVb2qqx/S8nS8uXLmTBhAk899RR9+vShVatWzJw5k5UrV6ZLRHJTYmIiYWFhdOzYMd3xjh07snnz5kxfExoamqF9p06d2LFjB0lJSdm2yeqaeSltNWEAr7hzdDmwEcC2QkfVhEXySfv2UKcOXLoEX31l72hEiozr74WVY6Kpee4EgN0q699yUcohQ4bwwgsvsGDBAnbs2MH3339P+/btczO2dM6ePUtKSgoVK1ZMd7xixYpERUVl+pqoqKhM2ycnJ3P27Nls22R1TYCEhARiY2PTPXJD2mrCAH3DQ3BJTWFbFT/2VqypasIi+clkulbT7JNPIDXVvvGIFBHX3wufC/2eX2cO5fnNltEse9wLbylZunDhAg8//DDTp0/niy++oFevXnTs2JFp06bldnwZmEymdN8bhpHh2I3aX3/8Zq85ceJEzGaz7eHr65vj+LNzfZVgz4RLJDk526oKZ9VORPLIgAHg6QkHD8KaNfaORqRISHuPM1+N48G96wDY5uufZbu8dkvJkr+/P6dPn2bXrl0EBwczb948Zs2axRtvvMED1kmRuax8+fI4Oztn6PGJjo7O0DNk5e3tnWn7YsWKUa5cuWzbZHVNgNGjRxMTE2N7nDhx4lbeUgbXVwke3/4ZWg6ZzZq7mmfbTkTySKlSMGiQ5fnHH9s3FpEiIu09rveeNRRPTmCfV3W2VamXZbu8dkvJ0pAhQ/jjjz+oXr267Vjv3r3ZvXs3iYmJuRZcWq6urgQGBrJ27dp0x9euXUuLFi0yfU1QUFCG9mvWrKFJkya4/LcEP6s2WV0TwM3NDU9Pz3SP3JChmjAQ7VGOZOdiAJhA1YRF8ttzz1mG5FavtvQwiUiest4LnVNTGLBzJQBzA7pZ/j/EPvfCW0qW3njjDZycMr60SpUqGRKP3DRixAhmzpzJ7Nmz2b9/Py+99BLHjx9nyJAhgKXHZ8CAAbb2Q4YM4dixY4wYMYL9+/cze/ZsZs2axciRI21thg0bxpo1a5g0aRJ//fUXkyZN4pdffmH48OF59j6y4uxkYmw3PwCuHwS0fj+2mx/OTlkPEYpILrvzTujSxfJcZQRE8pz1Xtjun21UiY3mgrsHy/zuBex3L8xxspRVLaOs/PvvvzcdzI307t2bKVOm8NZbb9GoUSP++OMPVq1aRdWqVQGIjIxMF2f16tVZtWoV69evp1GjRrz99tt8/PHHPPzww7Y2LVq0YMGCBcyZM4cGDRowd+5cFi5cSLNmzXI9/pzo7O/D9H4BeJvTdy96m92Z3i9A2y6I2EPaMgJxcfaNRaQI6Ozvw8R/1wMwv1EnElzcAPvdC3O83UnFihXp3r07wcHBNG3aNNM2MTExfP/990ydOpVnnnmGF6wrSQq5vNjuJCXVYNuR80THxePlYeluVI+SiJ2kpoKfHxw4wJE332PPg/30/6VIXvrzT2jQAMPJiZ3rd3LSo3ye/D+X0/t3sZxecP/+/UyYMIHOnTvj4uJCkyZNqFSpEu7u7ly4cIF9+/axd+9emjRpwgcffMD999+fK2+kqLJWExaRAsDJiX0PD8BvwhhSP/2U4fF+GCYnfMzujO3mpx5fkdz235C36cEHCWzdkEA7h5PjYbiTJ08yadIkTp06xeeff06tWrU4e/YsB/+b8Ni3b1/CwsLYtGmTEiURKVRCIiLpdeUu4lyLU/P8SVof2QXYr5qwSKF2/rxlA3m4NgRuZznuWWrcuDFRUVFUqFCBl19+me3bt9uW34uIFFbWasKX3ErwQ/0ODApbzsCwFfxRIxADy4TT8Sv20cHPW0NyIrlh1iy4ehUaNoTWre0dDXATPUulS5fm8OHDABw9epRUVbMVkSIgbTXhrwMsdeTuO7yDaucti1hUWV8kF6WkwGefWZ6/8IKtXIC95bhn6eGHH+bee+/Fx8cHk8lEkyZNcHZ2zrStNakSEXF0aasEHy1bmd9qNOG+wzsYsHMlb7V/OtN2InKLVqyAY8egbFno08fe0djkOFn68ssveeihh/jnn3948cUXCQ4OxsPDIy9jExGxu+urBM8N7MZ9h3fw6J9rmdy6H5fdSmTaTkRugbVS/tNPQ/Hi9o0ljRwnSwCdO3cGICwsjGHDhilZEpFCz1pNOComHgPYUL0xh8pWoeb5kzwS8StfB3bDW5X1RW7fn3/CunXg7AxDh9o7mnRuqYL3nDlzlCiJSJFwfWV9w+TEnMBuAAwMW4HJSFVlfZHcYK2Q37Mn3HGHXUO53i0lSyIiRcn1lfUX+99HrFtJql84xffVYlVnSeR2FcByAWnd1DCciEhR1dnfhw5+3rbK+pdiBuA5ezpNln0DQ/vaOzwRx1YAywWkpZ4lEZEcslbW79GoMpXGjLQsa/75Z/jrL3uHJuKQUlINQv+O5spHlondqc89X2DKBaSlZElE5FbUqAHdLHOX+OQT+8Yi4oBCIiJpNek35rz2MSUiT3LB3YP7IisVyIr4SpZERG7VsGGWr199BRcv2jUUEUcSEhHJ0Hk7iYyJZ2DYCgDmN+rEsStGgdxCSMmSiMitatsW6tWDy5dhzhx7RyPiEKxbCBlA7TNHaXF8D8kmJ+Y17oLxX5vxK/aRkmpkd5l8pWRJRORWmUzXVu588ollqwYRyVbaLYSe+K9Xac1dzTnl6QUUzC2ElCyJiNyOfv2gTBk4cgRWrrR3NCIFnnVroDJXYnho7zoA5jTpnmW7gkDJkojI7ShRAoKDLc+tWzWISJasWwM9vvtn3JMTiahYk+1V6mXZriBQsiQicruefRacnODXXyEiwt7RiBRoTauXpUqpYvTfaemJnd2ke7pyASbAp4BtIaRkSUTkdlWtCg8+aHmuMgIi2XJ2MvGp22F8Lp3jTMnS/FTnHts5a8pU0LYQUrIkIpIbrBO9v/nGsnWDiGSp0eKvAVjWrBuJxVxsx73N7kzvF1DgthDSdiciIrmhdWvLVg27d3Ns0lTCH38aLw/LUEJB+gtZxO62boUtW8DVlSe/mUS9q65Ex8UX6P9flCyJiOQGk4k/H36C+rtH4Pz5dEYYgaQ4OeNjdmdsN78C95eyiN1MnWr5+thjOFfyIci+0eSIhuFERHJBSEQkj8RU41xxT6rEnqH9wa0ARMXEF8iKxCJ28e+/8MMPlufWCvgOQMmSiMhtslYkTijmyneN7gdgUNhygAJbkVjELqZNg+Rky7B1QIC9o8kxJUsiIrcpbUXieY3vJ9nkRLMTEdQ7fQgomBWJRfLd1avwxReW5w7UqwRKlkREblvaSsOnPcqzqk4rAAbtWJZlO5Ei57vv4Nw5S6mNHj3sHc1NUbIkInKbrq80PKuJ5UbQbd8fVLh0Pst2IkWGYcCUKZbnzz8PxRxrfZmSJRGR29S0ell8zO62gnq7K9VmR+W6uKYm02/XqgJZkVgkX61bZ6luX7IkDB5s72humpIlEZHb5OxkYmw3P+BaBeLZ//Uu9du1CrekhAJXkVgkX1l7lZ54wrLxtINRsiQikgs6+/swvV8A3mbLUNvPtYI46elFuaux/Oh5WHWWpOg6dAh++sny3Frp3sE41qChiEgB1tnfhw5+3mw7cp7ouHiSnZ+D98bi/8NcePPldJuFihR2KakG246cx+vNidQ0DIzO92OqXdveYd0Sh+lZunDhAv3798dsNmM2m+nfvz8XL17Msn1SUhKjRo2ifv36lCxZkkqVKjFgwABOnTqVrl2bNm0wmUzpHo899lgevxsRKaycnUwE1SxHj0aVqfbaMChVCvbuhbVr7R2aSL4JiYik1aTfCP70N7x+/A6Al7zvcdjirA6TLPXp04fw8HBCQkIICQkhPDyc/v37Z9n+ypUr7Ny5kzfeeIOdO3eyePFi/v77b7p3756hbXBwMJGRkbbHF9Y6ECIit8NshkGDLM8/+si+sYjkk5CISIbO20lkTDyP/rkWj8SrHCznyzIvf4etZu8Qw3D79+8nJCSELVu20KxZMwBmzJhBUFAQBw4coHYm3Xpms5m11/0l98knn9C0aVOOHz/OHXfcYTteokQJvL298/ZNiEjR9OKL8MknEBIC+/dD3br2jkgkz1ir2RuAU2oKA8NWADA3sBuGyYQJSzX7Dn7eDrXgwSF6lkJDQzGbzbZECaB58+aYzWY2b96c4+vExMRgMpkoXbp0uuPffvst5cuXp169eowcOZK4uLjcCl1EirqaNa8V4LOuCBIppNJWs7/v0A6qXowixq0ki+vdBzhuNXuH6FmKiorCy8srw3EvLy+ioqJydI34+Hhee+01+vTpg6enp+143759qV69Ot7e3kRERDB69Gh2796doVcqrYSEBBISEmzfx8bG3sS7EZEi56WXYOlS+PprePddKF/e3hGJ5Im0VeqDty8BYH6jzlx1dc+ynSOwa8/SuHHjMkyuvv6xY8cOAEyZrCIxDCPT49dLSkriscceIzU1lWnTpqU7FxwcTPv27fH39+exxx7jxx9/5JdffmHnzp1ZXm/ixIm2ieZmsxlfX9+bfOciUqRYNw2Nj7+2N5ZIIWStUl8/8iDNTkSQ5OTM3IBuWbZzFHZNlp5//nn279+f7cPf3x9vb29Onz6d4fVnzpyhYsWK2f6MpKQkevXqxZEjR1i7dm26XqXMBAQE4OLiwsGDB7NsM3r0aGJiYmyPEydO5OwNi0jRZDLB8OGW5599BomJdg1HJK9Yq9lbe5VW1L2HKM9rPamOWs3ersNw5cuXp3wOuqODgoKIiYlh27ZtNG3aFICtW7cSExNDixYtsnydNVE6ePAg69ato1y5cjf8WXv37iUpKQkfn6wLyLm5ueHm5nbDa4mI2PTuDaNGQWQkLFwI2azmFXFUzk4mJjbxpNWYjQDMvPtB2znrOJAjVrN3iAnedevWpXPnzgQHB7Nlyxa2bNlCcHAwXbt2TbcSrk6dOixZYslmk5OTeeSRR9ixYwfffvstKSkpREVFERUVReJ/f9UdOnSIt956ix07dnD06FFWrVrFo48+SuPGjWnZsqVd3quIFFKurvDcc5bnH31k2VhUpBBqE7KAYkYqO2o0Zl/FGrbj3mZ3pvcLcMhq9ibDcIz/Y8+fP8+LL77I8uXLAejevTuffvppupVtJpOJOXPmMHDgQI4ePUr16tUzvda6deto06YNJ06coF+/fkRERHDp0iV8fX154IEHGDt2LGXL5ryLMDY2FrPZTExMzA2H+USkCDt7Fnx9IT6evd8u4x+/QLw8LEMSjvaXtkimYmIsv+NxcaSs+IltdZsTHRdfYH/Pc3r/dphkqSBTsiQiOXXi0f74/jiPn+9qzjMPvQ5Y5nCM7ebnkH9xi6QzeTKMHGmpJxYRAU4FewArp/fvgv0uREQKkZCISJ40W4b4Oxzcyh0XLJWMo2LiHbaysYhNUhJMnWp5PmJEgU+UbkbheSciIgWYtbLxP+V9WV89ECcMngyzTCuwdu+PX7GPlFR19ouD+vFHOHECKlSAfv3sHU2uUrIkIpIP0lY2nnW3paL3o3/+gmf8JcBxKxuLAJYFCx9+aHn+3HPg7lh1lG5EyZKISD5IW7F4Q7XG/FW+KqUSr9I3fHWW7UQcxoYNsGOHJUl69ll7R5PrlCyJiOSDdBWLTSZmNH0IgCd3LMc1OSnzdiKOYvJky9cBAyzDcIWMkiURkXxgrWxsXTi93O8eIkuVw+vyBXruXeewlY1F+PtvWLHC8vyll+wbSx5RsiQikg+cnUyM7eYHWCoZJzm7MLuJZe7S09sWYzJSHbKysYityGrXrlCnjr2jyRNKlkRE8klnfx+m9wvA22wZapvfqDOxriW48/xJfqhyTnWWxPGcPQtz51qev/yyXUPJS3bdG05EpKjp7O9DBz9vth05T3RcPHFXBuP55ScEfj8LXhho7/BEciQl1WDbkfOUnjyJuvHxGAEBmO69195h5Rn1LImI5DNnJxNBNcvRo1FlKo99DVxcYONGCA21d2giNxQSEUmrSb8xcPoflP9qJgDj7uxEyN4oO0eWd5QsiYjYU6VK1wr4ffCBfWMRuYGQiEiGzttJZEw8Pfaup8KVi5zyKM93dzQr1FXolSyJiNjbyJGWr0uXWlYWiRRA1ir0BoBh8NT2pQDMCexOkrNlVk9hrUKvZElExN78/CwriQzjWr0akQImbRX6tod3UOvccS65FmdBo05A4a5Cr2RJRKQgePVVy9evvoLTp+0bi0gm0laXH7rlBwC+a9iZOLeSWbYrLJQsiYgUBK1aQbNmkJAAn35q72hEMrBWl29yci9NT+4jwbkYM+/umWW7wkTJkohIQWAyXetd+uwzuHTJvvGIXMdahX7olh8BWOTfjmiPcrbzhbkKvZIlEZGCokcPuPNOuHABZs+2dzQi6Tg7mfigFrQ7tJ0UkxNf/re/IWDbxqewVqFXsiQiUlA4O9tWxhkffkjogdMsC/+X0EPnCuUKI3E8rRZbkvh1/q05Wray7bi32Z3p/QIKbRV6k2EY+j/wNsXGxmI2m4mJicHT09Pe4YiII7t6lYQqvridP8eL3V5huZ+lKrKP2Z2x3fwK7c1IHMDhw3DXXZCaSsqOMLaVrkp0XDxeHpahN0fsUcrp/Vs9SyIiBUjIoYt8Wu9+wLLBLv/9PRsVE1+oi/6JA/jf/yA1FTp1wjkwwFaFPqhmOYdMlG6GkiURkQLCWvTvm8ZduOLihv/pQ7Q8thuw1LCBwlv0Twq4qKhr8+hee82+sdiBkiURkQLCWvTvYnFPFjboCMAzWxfZzhfmon9SwE2ZYilr0bw5FOINc7OiZElEpIBIW8xv1t09STY5cc/RXTSI/DvLdiJ5LiYGpk+3PH/tNUuZiyJGyZKISAGRtpjfSXNFltZrC8ALmxdm2U4kz02bBrGxlm15unWzdzR2oWRJRKSAsBb9s/7d/llQL1Ix0eGfrdSNPlyoi/5JAXX1qmUIDiy9Sk5FM20omu9aRKQAcnYyMbabH2Ap8nekbGV+qtsagOdCLXtxFdaif1JAzZkD0dFQtSo89pi9o7EbJUsiIgVIZ38fpvcLwNtsGWr7LKgXAF0ObOTrFh6qsyR5LiXVIPTQOZbvOEb8xEmWgyNHgouLfQOzo2L2DkBERNLr7O9DBz9vth05T3RcI86fWEXZtato/eNM6H6PvcOTQiwkIpLxK/YRGRNPj73r6H7yOOdLlmZHs/vpaO/g7Eg9SyIiBZCzk8lW9K/sxLcsB7/7Dg4dsm9gUmiFREQydN5OImPiMRmptg1zZwd045lFfxXpgqhKlkRECrrAQLj/fkhJgUmT7B2NFELWgqjWcqdtD+2gztljXHItztcBDwBFuyCqkiUREUfw+uuWr3PnwvHjdg1FCh9rQVQADINnt1gWFMxrdD+x7qWKfEFUh0mWLly4QP/+/TGbzZjNZvr378/Fixezfc3AgQMxmUzpHs2bN0/XJiEhgRdeeIHy5ctTsmRJunfvzsmTJ/PwnYiI3IIWLaBtW0hKgg8+sHc0UsikLXQadHwPTf7dT4JzMWY36ZFlu6LEYZKlPn36EB4eTkhICCEhIYSHh9O/f/8bvq5z585ERkbaHqtWrUp3fvjw4SxZsoQFCxawceNGLl26RNeuXUlJScmrtyIicmveeMPydcYMy15dIrnEVujUMHhp47cAzG/YmWiPcpm3K2IcYjXc/v37CQkJYcuWLTRr1gyAGTNmEBQUxIEDB6hdu3aWr3Vzc8Pb2zvTczExMcyaNYtvvvmG9u3bAzBv3jx8fX355Zdf6NSpU+6/GRGRW9WmjaWHafNmyw7w//ufvSOSQsJaELXm7i00PbmPBGcXpjd/xHbeBHgX4YKoDtGzFBoaitlstiVKAM2bN8dsNrN58+ZsX7t+/Xq8vLyoVasWwcHBREdH286FhYWRlJREx47XFkRWqlQJf3//G15XRCTfmUzX5i5Nnw5nz9o3Hik0nJ1MjO1al+H/9Sp916gzpz3KA9gqyhflgqgOkSxFRUXh5eWV4biXlxdR2XRF33///Xz77bf89ttvTJ48me3bt3PfffeRkJBgu66rqytlypRJ97qKFStme92EhARiY2PTPURE8kXnzpbVcVeukPrRR4QeOsey8H8JPXSuyK5UktzROTLCMlepmCvTm13rVfI2uzO9X0CRLohq12G4cePGMX78+GzbbN++HQBTJrscG4aR6XGr3r172577+/vTpEkTqlatysqVK3nooYeyfN2Nrjtx4sQbxi0ikiesvUsPPsiVyVN45nIDYt1LAZZ948Z28yvSNzW5RYYBY8cC4PLsEKa++ADRcfF4eViG3opqj5KVXZOl559/nsdusNdMtWrV2LNnD6dPn85w7syZM1SsWDHHP8/Hx4eqVaty8OBBALy9vUlMTOTChQvpepeio6Np0aJFltcZPXo0I0aMsH0fGxuLr69vjuMQEbkdITXuplr5qtQ5e4wnwlbwScvHAYiKiWfovJ1FvhdAbsGaNbBlC7i74/TaawT5lLvxa4oQuw7DlS9fnjp16mT7cHd3JygoiJiYGLZt22Z77datW4mJick2qbneuXPnOHHiBD4+ln9EAgMDcXFxYe3atbY2kZGRREREZHtdNzc3PD090z1ERPJDSqrB+JV/2faMG7RjOSUTrgDYCgoW5eKBcgvS9CoxdCj4KNG+nkPMWapbty6dO3cmODiYLVu2sGXLFoKDg+natWu6lXB16tRhyZIlAFy6dImRI0cSGhrK0aNHWb9+Pd26daN8+fI8+OCDAJjNZgYPHszLL7/Mr7/+yq5du+jXrx/169e3rY4TESlIrMUDV9ZpxaGylSkTH0e/8GslUYp68UC5BSEhsHUrFC8Or75q72gKJIdIlgC+/fZb6tevT8eOHenYsSMNGjTgm2++SdfmwIEDxMTEAODs7Myff/5Jjx49qFWrFk888QS1atUiNDQUDw8P22s++ugjevbsSa9evWjZsiUlSpRgxYoVODs75+v7ExHJCWtRwFQnZ6Y1t/QuPbN1MaX+6126vp1Itq7vVcqi1E5RZzIMQ321tyk2Nhaz2UxMTIyG5EQkT4UeOsfjM7YA4JyawppZz1Hz/Ek+bNWXj/+buwQwP7g5QTU170RuYOVK6NrV0qt05AjcxDzgwiCn92+H6VkSEZFrxQNNQIqTM5Nb9wMgeNtiylyJwYRlVVxRLR4oN8EwYNw4y/PnnityidLNULIkIuJAnJ1MjO3mB1iKBa6u3YKIijXxSLzK0K2LgKJdPFBuwsqVsGMHlCgBr7xi72gKNCVLIiIOprO/D9P7BeBtdscwOfG/1pZ9Mp/Y+ROzO/iobIBkKSXVsBQy3XWSS6P/qwb//POQSeFnucYh9oYTEZH0Ovv70MHPm21HzhMd25DYoyF47thC2x9nQLvp9g5PCqCQiEjGr9hHZEw87Q9upUfEbq64uhP6QH/a2Tu4Ak49SyIiDsrZyURQzXL0aFwFzw/ftxycORMOHbJvYFLghEREMnTeTiJj4sEwGL7pOwC+atyVp1YdIyQi0s4RFmxKlkRECoPWreH++yE5+dpScBH+K2S6Yp+taGnHg1vwP32IS67F+bKppe6gCplmT8mSiEhh8c47lq/ffQd//mnfWKTAsBYyBTAZqdd6lQK6cqGEWYVMc0DJkohIYREQAI8+alkS/sYb9o5GCoi0BUof3LsOv+gjxLqWYMZ/vUqZtZP0lCyJiBQmb70FTk6wbJllCwsp8rw83AFwS0rg5T/mATAtqBcXi3tm2k4yUrIkIlKY1KkDTzxheT5mjH1jkQLBWsj0ybAVVI47w78eFZgT2M12XoVMb0zJkohIYTN2LLi6wq+/krL2F0tdnfB/CT10TpN4iyBnJxPvtKrIs6HfAzD5nn4kuLgBlkQJVMj0RlRnSUSksKlaFYYMgY8/5q9BL/B4nw/AZLkR+pjdGdvNT4Uri5h2i2ZC4hX+9qnJUr82tuPe+n3IEW2kmwu0ka6IFDS/rd9D845NKZGUQPBDr7P2rubAtZ6E6f0CdIMsKg4dgrp1ISmJlJCf2XZnINFx8Xh5WIbeinKPkjbSFREpolJSDcaEnmF2kx4AvPzHNzilpgDYau2ork4R8n//B0lJ0LEjzp06WgqZNqpMUM1yRTpRuhlKlkREChlrXZ0vmz5EjFtJ6pw9Ro99v9vOq65OEbJ1K3z/vWUY9v337R2Nw1KyJCJSyFjr5cS6l+Lz5o8A8MofX1M8MT7TdlJIGQa88orl+YAB0LChfeNxYEqWREQKmbT1cmYHdueEuSKV4s4yZOuiLNtJIbRiBWzYAO7u8Pbb9o7GoSlZEhEpZKx1dUxAgosb77YdBMAz2xZROSZadXWKguRkGDXK8nz4cPD1tWs4jk7JkohIIePsZGJsNz/AsvotpFYLNt/RAPfkRP5v3WxAdXUKo5RUw1ZT69B7U+Gvv6B8eXjtNXuH5vCULImIFEKd/X2Y3i8Ab7M7mEy81S6YFJMTDxzYyILaCSobUMiERETSatJvPD5jC//31WY837NsqrzvqWFgNts5OsenopQiIoVUZ38fOvh5s+3IeaLjGnEmYSfe382h2dS3YEAPcHa2d4iSC0IiIhk6b6etLETw9iVUuHyRI2V86Jnsz8cRkUqOb5N6lkRECjFnJ5Otro731PehdGnYvRtmzbJ3aJILUlINxq/YZ0uUKlw6z9PbFgPw/j1PkOTsoppauUDJkohIUVG+PIwfb3k+ZgxcuGDfeOS2WWtqWb28YR4lkhLYWak2q2u3VE2tXKJkSUSkKBk6FPz84OxZeOste0cjtyltrayAf/fz2J41ALzbdrBtP8Dr28nNU7IkIlKUuLjAlCmW559+Cvv32zUcuT3WWlnOqSm8+/NnAPzg356wKn6ZtpNbo2RJRKSo6dABune31OJ56SVLpWdxSNaaWk/uWE7dM0e54O7BxLZP2s6rplbuULIkIlIUTZ5s6WX6+Wf2z5zPsvB/CT10ThOBHYyzk4kJd5dm+KbvAHivzUDOl7CUCrAOwqmm1u1TsiQiUhTdeSeH+wUD4D5qJCO/3c7jM7bQatJvhERE2jk4uRltP59IqcSr7LmjHt836GA77m12Z3q/AJUNyAWqsyQiUgSFRETyirkNv5X8juoXIhm4YwUzmj1EVEw8Q+ft1E3WUaxaBYsWgbMz9ZZ9y3ceVYiOi8fLwzL0ph6l3KGeJRGRIsZamyfOrQTv3/MEAC9unk+FSxds9XpUm8cBXLkCzz9veT58OM6NGtpqagXVLKdEKRcpWRIRKWLS1ub5sX47wn3uwiPxKmN//RJAtXkcxYQJcOQIVKkC48bZO5pCzWGSpQsXLtC/f3/MZjNms5n+/ftz8eLFbF9jMpkyfXzwwQe2Nm3atMlw/rHHHsvjdyMiYj9pa+4YJide7/gcySYnuv61gU4HNmfaTgqY/fvh/fctzz/+GEqVsm88hZzDJEt9+vQhPDyckJAQQkJCCA8Pp3///tm+JjIyMt1j9uzZmEwmHn744XTtgoOD07X74osv8vKtiIjY1fU1dyK87+SLZpZ/F99ZO43SV2MzbScFhGHAs89CUhI88AD07GnviAo9h5jgvX//fkJCQtiyZQvNmjUDYMaMGQQFBXHgwAFq166d6eu8vb3Tfb9s2TLatm1LjRo10h0vUaJEhrYiIoWVtTZPVEy8bY7Sxy0fp+PBLdx17gRv/jqDD/qOUW2eAiQl1fhvQ+R4/H5dzl3r10Px4vDJJ+kqdUvecIiepdDQUMxmsy1RAmjevDlms5nNmzdn88prTp8+zcqVKxk8eHCGc99++y3ly5enXr16jBw5kri4uFyLXUSkoHF2MjG2m6XCs/U2m1DMlVfvH0YqJh7au45Pzac0QbiACImIpNWk33h8xhbemLuRMm+OBuDvp4dD9er2Da6IcIhkKSoqCi8vrwzHvby8iIqKytE1vvrqKzw8PHjooYfSHe/bty/z589n/fr1vPHGGyxatChDm+slJCQQGxub7iEi4kg6+/swvV8A3uZrQ227KtdhQSvLcFzghNEQE2Ov8OQ/IRGRDJ230zYh/9Xfv6L8lRgOlvOlq0tT1cTKJ3Ydhhs3bhzjrTtgZ2H79u2AZbL29QzDyPR4ZmbPnk3fvn1xd08/Bh8cHGx77u/vz1133UWTJk3YuXMnAQEBmV5r4sSJN4xbRKSg6+zvQwc/b9vwjpeHO01fbwONw+Gff2DkSJgxw95hFlnWEg/WodJGpw7QJzwEgNc7PkuSswvjV+yjg5+3egHzmF2Tpeeff/6GK8+qVavGnj17OH36dIZzZ86coWLFijf8ORs2bODAgQMsXLjwhm0DAgJwcXHh4MGDWSZLo0ePZsSIEbbvY2Nj8fX1veG1RUQKGmcnE0E1y6U/OGsW3HsvzJwJvXpZ9pKTfJe2xIN7UjyTV36EEwaL/O9j6x31gWslHjL8N5RcZddkqXz58pQvX/6G7YKCgoiJiWHbtm00bdoUgK1btxITE0OLFi1u+PpZs2YRGBhIw4YNb9h27969JCUl4eOTdeVaNzc33NzcbngtERGHdM898Nxz8NlnEBwMf/4JHh72jqrISVu64fXfZlHz/EmiSpXl7fueyrKd5A2HmLNUt25dOnfuTHBwMFu2bGHLli0EBwfTtWvXdCvh6tSpw5IlS9K9NjY2lh9++IGnnnrq+sty6NAh3nrrLXbs2MHRo0dZtWoVjz76KI0bN6Zly5Z5/r5ERAqs996DqlXh2DFSX3uN0EPntNluPrOWbmh/cCv9wlcDMOKBEVws7plpO8k7DlE6ACwr1l588UU6duwIQPfu3fn000/TtTlw4AAx101IXLBgAYZh8Pjjj2e4pqurK7/++itTp07l0qVL+Pr68sADDzB27FicnZ3z7s2IiBR0pUpZhuE6dMBp2jQ+ungH23z9AfAxuzO2m5/2jstjTauXxd90mUmrpwLwRdOH2Fytke28CctmuSrxkPdMhmHoT4TbFBsbi9lsJiYmBk9Pzxu/QETEAYRERHKx70Ae27OGI2V8uP/JT4h3cbeVG9Bmu3ksNZUz97Sjwqb17PWqwYP9J5NYzAVA/w1ySU7v3w4xDCciIvnLuhLr3fsGE1mqHNUvRPLyhnkA2mw3v3z6KRU2rSfFzZ13Hh9jS5TA0qOkRCn/OMwwnIiI5B/bSiy3kvxf5+eZ8+N4Bm9fxm81mxJatUG6zXa1EisP/PknvPoqAM4fTmbekCfTl3ioXlblAvKRepZERCSDtCus1tW8m+/rt8cJg4+Xv49X3LlM20kuiY+HPn0gIcGy99vQobYSDz0aVSaoZjklSvlMyZKIiGRw/QqrNzsMYX+FalS4cpHPlk2iWEpypu3k1qSkGrYVh5FDh0NEBHh5WWpeae83u1OyJCIiGVg327XepuNd3BnaczSxriW4+999vLZ+Dj5aiZUr0u79tmjCLHzmfgHAjrGTIQeFlyXvKVkSEZEMMtts92jZyox84CUAntqxjOku/2g46Dal3fut7JUY/rdqCgBfBzzAo8fLaO+3AkLJkoiIZCqzzXbX1Ari63t6A9Bo/EjYv99e4Tm8dHu/GQaTVn+M1+ULHCzny7ttBgFacVhQaDWciIhkKdPNdt/qCJ1Ow/r18PDDsG2bpYil3JS0e78N3r6UDv9sJcG5GMO6vUKCi2VLLa04LBiULImISLYy3Wx3wQIICLD0LAUHkzLvW7YdvaCl7TfBupKww8EtjFk3G4CJbQaxr2KNTNuJ/ShZEhGRm1exInz/PbRpAwsWMPVSOT6ud7/ttLZEuTEvD3f8o/5h6ooPcMLg20admRvYLdN2Yl+asyQiIremZUv2v/wmAC+s+pyAk9fmL0XFxDN03k5NUM5G02KXmbP4bUokJfBHtcaMbT8kXZkAE2jFYQGhZElERG5JSqrBIM8gfqrTGpfUFKYtm0i5yxcBbYlyQ3FxOHfvRoW4cxwofwfP93yNZOdrgz3WlGlsNz8NZxYASpZEROSWbDtynsjYBEZ1foF/ylbB+9J5Pl0+CdfkJIB0W6JIGsnJ0Ls37NkDFSsS+e2PlPRKPydMe78VLJqzJCIit8Q68fiyWwmeeXAMy79+iaDjfzJ1xQc832MUKU7O6doVVSmpxrXVhKXcaPbRWJxWr4bixWH5cto0vZuN7Q3t/VaAKVkSEZFbknbi8aHyvjzz4BhmLRrP/X9vZvLKDxnxwAhSnZyL9ATlkIhIxq/YZysR8OSOZQT9OsNy8ptvoGlTIIsVh1JgaBhORERuyfVbomys3phne44mycmZnvt+Z8LPn1HJw7XITlBOW50boN0/W3nj15kATGzzJCG1W9gzPLkJSpZEROSWZLYlyq93NmNYt1dIMTnx2J41zN+3AOciOJqUrjo3UO/0IT5ebikR8F3DTnzZ9CFNfncgSpZEROSWZbYlyqo6rXj34ZEAVP1uNoweDUbRSgrSVueueuEUs34cT8mkeP6o1pg3OwzFMJk0+d2BaM6SiIjclky3RKneBWbUgCFDYNIkKFmSlDGvF5lJzNZJ7fWi/uGrH8ZS/koMf5e7g+d7jEpXIqCoT353FEqWRETktmU6QfmZZ+DKFRgxAt58k89C/+XDBtcqVBfmKt9eHu4EHdvNl4vfwSPxKhEVazLw0XHEupfK0E4KPg3DiYhI3nnpJf5+YRQAL67+gn47V9pOFeYq303DfuOrH8bhkXiVzXc04LHHJ3K2ZBnbeVXndixKlkREJM+kpBo84dOBz5o/CsA7a6fTa/caoHBU+U5JNQg9dI5l4f8Seuic5X1Mn47zY71xTUlida0WPPnoOC65lbC9RtW5HY+G4UREJM9YJzp/cM8AiiclMChsOe+HfEydM0eZ0HYQyc7FbBOdHa3O0PU1lDAMxoT9QPCvX1u+HzIE05AxlF114FobLNW5C+vwY2GlZElERPKMbQKzycRb7YK54urO86HfMyhsOfWj/uG5HqOI9ijncBOdrTWUrP1hTqkpjPvlSwbssgwz/jN0BHd+9j86m0x0qF+5yExsL6w0DCciInkm3QRmk4n/3TOA4IdeJ9a1BHf/u4+VXw2j2fE/HWqi8/U1lFyTk/h4+QcM2LWSVEy80WEo/X27kPJfA+vk9x6NKhNUs5wSJQekZElERPLM9VW+Adbe1ZxuA6ewv0I1Kly+yLcLx9Bs8WwwjMznABUwaWsoVYqN5qsf3qTrgY0kOhXjhe6v8k3AA6qhVMhoGE5ERPKMtcr30Hk7MXFtUvexMpV4qP//ePfnz3ho7zp49VWi1v5O36CnOZTgbHt9QSwvEB0Xj1NqCgN2ruSVP76mZFI8l1yL8/SDY9hcrVG6dlI4qGdJRETyVGZVvgFKly9NifnzYNo0Uou54L12JV9++ix3nTlma2PP8gJZ9XJVjTzConmvMu7XLymZFM+2Kn70GPBhukQJVEOpMDEZRhGrQZ8HYmNjMZvNxMTE4Onpae9wREQKpJRUI9OJzimpBk8//xlvzxtPpbizXHFxY0KbQSxs2JEkZxdMWFaQbRx1X77N98mw0g2oWsKJWafWUHPWp5iSk4l1LcF7bZ9kfsNOGKZrfQ/2iFduTU7v30qWcoGSJRGRWxd66ByPz9hC2SsxTF3+Aa2PhQNw0rMC04J68UP99iQ5uzA/uDlBNctlmXTllutXugHcfSKC90I+peb5kwCcbtuJHnUf57RH+XTtrFFM7xdQoIYOJXM5vX9rzpKIiNiVdW7P+RJmnug1nn67VvHclh+oEnuGCT9/xrOh3zMtqBdnzvsRcjUxQ4/Prcxryq6XK+1KN4+Ey4xaP5d+4astsZYsw0c9XuCdr8cybv/pDLGohlLh5DA9S++++y4rV64kPDwcV1dXLl68eMPXGIbB+PHj+fLLL7lw4QLNmjXjs88+o169erY2CQkJjBw5kvnz53P16lXatWvHtGnTqFKlSo5jU8+SiMits/YspeWWnMhju3/m2S0/UPGSZVVZrFcl3mv8oK2nyer63pwb9TxlNsRmTbjMxV3p98UmWhzbTc+96+j8dyglkyztvmvYiffaPEmse6l86+WSvFXohuHGjh1L6dKlOXnyJLNmzcpRsjRp0iTeffdd5s6dS61atXjnnXf4448/OHDgAB4eHgAMHTqUFStWMHfuXMqVK8fLL7/M+fPnCQsLw9nZ+QY/wULJkojIrUtJNWg16TeiYuK5/obklpzI47t/5rmtP1AhzpI0WYfnVtZuRUxxy7/l1nlCbzzgx9srs+55ymyIDcBkGPifPsSYC2HU/HUFFS5ftJ07WM6XNzoOZcsdDWzHpj7WiB6NKufipyD2UOiSJau5c+cyfPjwGyZLhmFQqVIlhg8fzqhRlk0cExISqFixIpMmTeKZZ54hJiaGChUq8M0339C7d28ATp06ha+vL6tWraJTp045iknJkojI7bEmMUCmc4BevucOznz0WbqeJoDDZSoRXqk2uyrVJtynNn95VUvX65T2Gp/1aczbK/enS6SqXIyi57719Ny7njv/m48EcL64Jz/Vac3Sem3YWakOmNL3Fll7lsSxFfk5S0eOHCEqKoqOHTvajrm5uXHvvfeyefNmnnnmGcLCwkhKSkrXplKlSvj7+7N58+YcJ0siInJ7rOUFspoDlJCcyv8Cu7GgYSce2/0zA3aupOb5k9S4cIoaF05ZajUBCc4uRFSsSXil2vxVoRpuyYmUuRpL6fhLpIZc4p1LsZS5Gos5/hJlrsZR9mqs7WfFF3Nl7Z3N+CWwA6t96pN4XdIF13qwmlYvm+efiRQchTZZioqKAqBixYrpjlesWJFjx47Z2ri6ulKmTJkMbayvz0xCQgIJCQm272NjY7NsKyIiOdPZ34cOft6ZzgEKPXQOgIRirnwV2I2vArthvhpHo8i/aXTqAI1PHaBh5N+UiY8j8NRfBJ76K0c/MxUTm6s2YGm9toTUasEltxIMalmNpE1H0xXRhGs9VGO7+WleUhFj12Rp3LhxjB8/Pts227dvp0mTJrf8M0zXdZ0ahpHh2PVu1GbixIk3jFtERG6edR+161m3TUk7rymmuAe/1wjk9xqBlgOGQbULp2wJVM1zJ7nkVoKL7qW4WNyTi8VLccHdk5jipbjo7sGF4h6cLlXONu/JqoOfN02rl9VKN7Gxa7L0/PPP89hjj2Xbplq1ard0bW9vb8DSe+Tjc+0XOzo62tbb5O3tTWJiIhcuXEjXuxQdHU2LFi2yvPbo0aMZMWKE7fvY2Fh8fX1vKU4REbmxrLZNAa59bzJxtGxljpatzNJ6bTO9TtmSrly4nJhhgrf1OtYhNmcnU5a9XFL02HW7k/Lly1OnTp1sH+7ut1Yuvnr16nh7e7N27VrbscTERH7//XdbIhQYGIiLi0u6NpGRkURERGSbLLm5ueHp6ZnuISIieSurbVO8ze5M69M4w4a9aZmwrIp7p4e/7fvrz0P6ITZrL1ePRpUJqllOiVIR5jBzlo4fP8758+c5fvw4KSkphIeHA3DnnXdSqlQpAOrUqcPEiRN58MEHMZlMDB8+nAkTJnDXXXdx1113MWHCBEqUKEGfPn0AMJvNDB48mJdffply5cpRtmxZRo4cSf369Wnfvr293qqIiGQhu3lNTk6mLHueANsQ2nSnrCeSa4hNMuMwydKbb77JV199Zfu+cePGAKxbt442bdoAcODAAWJiYmxtXn31Va5evcqzzz5rK0q5Zs0aW40lgI8++ohixYrRq1cvW1HKuXPn5rjGkoiI5K+s5jXdaEWdNRHKLuESyYzD1VkqiFRnSUSk4FBVbcmpIl9nSUREiqasep5EbpVdJ3iLiIiIFHRKlkRERESyoWRJREREJBtKlkRERESyoWRJREREJBtKlkRERESyoWRJREREJBtKlkRERESyoWRJREREJBuq4J0LrDvGxMbG2jkSERERySnrfftGO78pWcoFcXFxAPj6+to5EhEREblZcXFxmM3mLM9rI91ckJqayqlTp/Dw8MBkyr3NGmNjY/H19eXEiRPaoDeP6bPOH/qc84c+5/yhzzl/5OXnbBgGcXFxVKpUCSenrGcmqWcpFzg5OVGlSpU8u76np6f+R8wn+qzzhz7n/KHPOX/oc84fefU5Z9ejZKUJ3iIiIiLZULIkIiIikg0lSwWYm5sbY8eOxc3Nzd6hFHr6rPOHPuf8oc85f+hzzh8F4XPWBG8RERGRbKhnSURERCQbSpZEREREsqFkSURERCQbSpbsbNq0aVSvXh13d3cCAwPZsGFDtu1///13AgMDcXd3p0aNGnz++ef5FKlju5nPefHixXTo0IEKFSrg6elJUFAQP//8cz5G69hu9nfaatOmTRQrVoxGjRrlbYCFxM1+zgkJCYwZM4aqVavi5uZGzZo1mT17dj5F67hu9nP+9ttvadiwISVKlMDHx4cnn3ySc+fO5VO0jumPP/6gW7duVKpUCZPJxNKlS2/4mny/FxpiNwsWLDBcXFyMGTNmGPv27TOGDRtmlCxZ0jh27Fim7Q8fPmyUKFHCGDZsmLFv3z5jxowZhouLi/Hjjz/mc+SO5WY/52HDhhmTJk0ytm3bZvz999/G6NGjDRcXF2Pnzp35HLnjudnP2urixYtGjRo1jI4dOxoNGzbMn2Ad2K18zt27dzeaNWtmrF271jhy5IixdetWY9OmTfkYteO52c95w4YNhpOTkzF16lTj8OHDxoYNG4x69eoZPXv2zOfIHcuqVauMMWPGGIsWLTIAY8mSJdm2t8e9UMmSHTVt2tQYMmRIumN16tQxXnvttUzbv/rqq0adOnXSHXvmmWeM5s2b51mMhcHNfs6Z8fPzM8aPH5/boRU6t/pZ9+7d23j99deNsWPHKlnKgZv9nFevXm2YzWbj3Llz+RFeoXGzn/MHH3xg1KhRI92xjz/+2KhSpUqexVjY5CRZsse9UMNwdpKYmEhYWBgdO3ZMd7xjx45s3rw509eEhoZmaN+pUyd27NhBUlJSnsXqyG7lc75eamoqcXFxlC1bNi9CLDRu9bOeM2cOhw4dYuzYsXkdYqFwK5/z8uXLadKkCe+//z6VK1emVq1ajBw5kqtXr+ZHyA7pVj7nFi1acPLkSVatWoVhGJw+fZoff/yRBx54ID9CLjLscS/U3nB2cvbsWVJSUqhYsWK64xUrViQqKirT10RFRWXaPjk5mbNnz+Lj45Nn8TqqW/mcrzd58mQuX75Mr1698iLEQuNWPuuDBw/y2muvsWHDBooV0z9HOXErn/Phw4fZuHEj7u7uLFmyhLNnz/Lss89y/vx5zVvKwq18zi1atODbb7+ld+/exMfHk5ycTPfu3fnkk0/yI+Qiwx73QvUs2ZnJZEr3vWEYGY7dqH1mxyW9m/2crebPn8+4ceNYuHAhXl5eeRVeoZLTzzolJYU+ffowfvx4atWqlV/hFRo38zudmpqKyWTi22+/pWnTpnTp0oUPP/yQuXPnqnfpBm7mc963bx8vvvgib775JmFhYYSEhHDkyBGGDBmSH6EWKfl9L9SfcnZSvnx5nJ2dM/yFEh0dnSFjtvL29s60fbFixShXrlyexerIbuVztlq4cCGDBw/mhx9+oH379nkZZqFws591XFwcO3bsYNeuXTz//POA5aZuGAbFihVjzZo13HffffkSuyO5ld9pHx8fKleunG539bp162IYBidPnuSuu+7K05gd0a18zhMnTqRly5a88sorADRo0ICSJUvSunVr3nnnHfX+5xJ73AvVs2Qnrq6uBAYGsnbt2nTH165dS4sWLTJ9TVBQUIb2a9asoUmTJri4uORZrI7sVj5nsPQoDRw4kO+++07zDXLoZj9rT09P/vzzT8LDw22PIUOGULt2bcLDw2nWrFl+he5QbuV3umXLlpw6dYpLly7Zjv399984OTlRpUqVPI3XUd3K53zlyhWcnNLfVp2dnYFrPR9y++xyL8yzqeNyQ9ZlqbNmzTL27dtnDB8+3ChZsqRx9OhRwzAM47XXXjP69+9va29dLvnSSy8Z+/btM2bNmqXSATlws5/zd999ZxQrVsz47LPPjMjISNvj4sWL9noLDuNmP+vraTVcztzs5xwXF2dUqVLFeOSRR4y9e/cav//+u3HXXXcZTz31lL3egkO42c95zpw5RrFixYxp06YZhw4dMjZu3Gg0adLEaNq0qb3egkOIi4szdu3aZezatcsAjA8//NDYtWuXrURDQbgXKlmys88++8yoWrWq4erqagQEBBi///677dwTTzxh3Hvvvenar1+/3mjcuLHh6upqVKtWzZg+fXo+R+yYbuZzvvfeew0gw+OJJ57I/8Ad0M3+TqelZCnnbvZz3r9/v9G+fXujePHiRpUqVYwRI0YYV65cyeeoHc/Nfs4ff/yx4efnZxQvXtzw8fEx+vbta5w8eTKfo3Ys69aty/bf3IJwLzQZhvoGRURERLKiOUsiIiIi2VCyJCIiIpINJUsiIiIi2VCyJCIiIpINJUsiIiIi2VCyJCIiIpINJUsiIiIi2VCyJCIiIpINJUsiIiIi2VCyJCIiIpINJUsiIiIi2VCyJCJynTNnzuDt7c2ECRNsx7Zu3Yqrqytr1qyxY2QiYg/aSFdEJBOrVq2iZ8+ebN68mTp16tC4cWMeeOABpkyZYu/QRCSfKVkSEcnCc889xy+//MLdd9/N7t272b59O+7u7vYOS0TymZIlEZEsXL16FX9/f06cOMGOHTto0KCBvUMSETvQnCURkSwcPnyYU6dOkZqayrFjx+wdjojYiXqWREQykZiYSNOmTWnUqBF16tThww8/5M8//6RixYr2Dk1E8pmSJRGRTLzyyiv8+OOP7N69m1KlStG2bVs8PDz46aef7B2aiOQzDcOJiFxn/fr1TJkyhW+++QZPT0+cnJz45ptv2LhxI9OnT7d3eCKSz9SzJCIiIpIN9SyJiIiIZEPJkoiIiEg2lCyJiIiIZEPJkoiIiEg2lCyJiIiIZEPJkoiIiEg2lCyJiIiIZEPJkoiIiEg2lCyJiIiIZEPJkoiIiEg2lCyJiIiIZEPJkoiIiEg2/h/k1d0Ve4BI/AAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"M = 50\n",
"h = 1 / (M + 1)\n",
"\n",
"\n",
"def f1(x):\n",
" return (2 * np.pi) ** 2 * np.sin(2 * np.pi * x)\n",
"\n",
"\n",
"def u1(x):\n",
" return np.sin(2 * np.pi * x)\n",
"\n",
"\n",
"x, U_app = solution_approchée(f1, M)\n",
"plt.figure()\n",
"plt.scatter(x, U_app, label=\"$A_M U_h = h² F$\")\n",
"plt.plot(x, u1(x), label=\"Solution exacte\", color=\"red\")\n",
"plt.legend()\n",
"plt.ylabel(\"f(x)\")\n",
"plt.xlabel(\"x\")\n",
"plt.title(\"$-u''=f(x)$\")"
]
},
{
"cell_type": "code",
"execution_count": 307,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Différence en valeur absolue entre la solution exacte et la solution approchée')"
]
},
"execution_count": 307,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"H, E = [], []\n",
"for k in range(2, 12):\n",
" M = 2**k\n",
" h = 1 / (M + 1)\n",
"\n",
" x, U_app = solution_approchée(f1, M)\n",
"\n",
" e = np.abs(u1(x) - U_app)\n",
" plt.plot(x, e, label=f\"{h}\")\n",
" E.append(np.max(e))\n",
" H.append(h)\n",
"\n",
"H, E = np.array(H), np.array(E)\n",
"\n",
"plt.xlabel(\"$h$\")\n",
"plt.ylabel(r\"$\\max_{j=0,\\dots,M+1}|u(x_j)-u_j|$\")\n",
"plt.legend(fontsize=7)\n",
"plt.title(\n",
" \"Différence en valeur absolue entre la solution exacte et la solution approchée\",\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 308,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Erreur globale en fonction de $h$')"
]
},
"execution_count": 308,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(H, E / H, label=\"$E_h / h$\")\n",
"plt.plot(H, E / H**2, label=\"$E_h / h^2$\")\n",
"plt.legend()\n",
"plt.xlabel(\"$h$\")\n",
"plt.ylabel(\"Erreur globale\")\n",
"plt.title(\"Erreur globale en fonction de $h$\")"
]
},
{
"cell_type": "code",
"execution_count": 309,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)')"
]
},
"execution_count": 309,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(np.log(H), np.log(E), \"+-\", label=\"erreur\")\n",
"plt.plot(np.log(H), np.log(H), \"-\", label=\"droite pente 1\")\n",
"plt.plot(np.log(H), 2 * np.log(H), \"-\", label=\"droite pente 2\")\n",
"plt.legend()\n",
"plt.xlabel(\"$log(h)$\")\n",
"plt.ylabel(\"$log(E)$\")\n",
"plt.title(\n",
" \"Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)\",\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice 2. Conditions de Dirichlet non homogènes.\n",
"\n",
"On approche à présent le problème de Dirichlet $-u''=f$ dans un intervalle $]a,b[$, avec $a,\\ b\\in\\RR$, avec conditions de Dirichlet non-homogènes : \n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-u''(x) = f(x) \\hbox{ sur } ]a,b[ \\\\\n",
"&u(a) = u_a, u(b) = u_b,\n",
"\\end{aligned}\\right.$$\n",
"\n",
"où $u_a,\\ u_b\\in\\RR$ sont données. En suivant la même démarche que dans l'exercice 1, étant donnée une discrétisation de $]a,b[$ de pas $h=\\frac{(b-a)}{M+1}$, on cherche une solution approchée $(u_0,\\dots,u_{M+1})$ solution du système linéaire suivant : \n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-\\frac{1}{h^2}(u_{i-1} - 2 u_i + u_{i+1}) = f(x_i) \\hbox{ pour } 1\\leq i\\leq M \\\\\n",
"&u_{0} = u_a, u_{M+1} = u_b,\n",
"\\end{aligned}\\right.$$\n",
"\n",
"où la discrétisation considérée de l'intervalle $[a,b]$ est définie par les $M+2$ points $x_i=a+ih,\\ i=0,\\dots,M+1$.\n",
"\n",
"**Question 1.** Mettre ce système sous la forme $A_h U_h = F+\\Delta$, où $\\Delta \\in\\RR^M$ est un vecteur à déterminer.\n",
"\n",
"**Question 2.** \n",
"Donner la solution exacte du problème \n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-u''(x) = 1 \\hbox{ sur } ]1,2[, \\\\\n",
"&u(1) = 1, u(2) = 2.\n",
"\\end{aligned}\\right.$$\n",
"\n",
"**Question 3.** En suivant la démarche de l'exercice 1, calculer une solution approchée de ce problème par la méthode des différences finies, et représenter dans la même figure la solution exacte et la solution approchée. Refaire dans une autre figure les calculs de la question 5 de l'exercice 1. Refaire l'exercice pour le problème\n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-u''(x) = -\\frac{2}{(x+1)^3} \\hbox{ sur } ]1,2[ \\\\\n",
"&u(1) = 1/2, u(2) = 1/3,\n",
"\\end{aligned}\\right.$$\n",
"\n",
"dont la solution exacte est donnée par $u(x)=\\frac{1}{x+1}$. Chercher à comprendre les résultats obtenus."
]
},
{
"cell_type": "code",
"execution_count": 316,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, \"$-u''=f(x)$\")"
]
},
"execution_count": 316,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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vvfce5cqVY8mSJeYaSal5rjU09/FkZteaFnWSZtRtj1dMJO13r6L66MFQozw0aWK1PoqIZLb7F7Yk5/6FLX7lCj3257/11ltERERQokQJ87n4+HiKFy9u0e7o0aN06NDBPJL0wQcf0KZNG/bv3w8k5AJdu3bNPBp1v40bN1qsuD58+DB37tzBz8+Pixcv8uuvv+Lt7W1xzaRJk5g0adJD+/7rr78mWYkXGBjIO++8Y3Hu4MGDNGzY8KH3Smw3ceJEc0CVG1h9g9vXX3+d119/PdnX5s2bZ/HziBEjGDFixCPv+corryQbraf2udbS3MeTpt4e7A2+Svj1OxTN50Ttic2hS2f46Sdo2xb++IO46jUs23gVzJDfoERErC21C1YyYmFLQEAAO3bs4ODBg9jZ3fu6/PPPP+nVqxcREREUKlQIwzA4c+YML774Il9++SWnTp3iwoUL+Pr64uPjA9zbQ+zWrVtJnvHPP/8wZ84c87nDhw/TsmVLJk2axMSJE1mzZk2SIGnAgAF06NDhof1/MJC7fv06wcHB1KhRw+J8YGAgb7755kPvdfr0aa5du5ZpZQqyCqsHSWLJ1saU9LehBQsgIgI2bSK66fN06fkp++zuDbOqKreI5FSpXbDyuBe2xMbGMnjwYIYPH55kNVpiTmpgYCCNGzfm9OnTlCpVisqVKxMUFMSECRN4//33WbhwoXmExsvLi0qVKjFq1CgcHBwoUqQIe/bsYfTo0XTt2tXc7tatW8THx9OrVy8gIY/Wzc0tSf/SM90WGBiIjY0NVatWNZ87e/Ys//77b5L3+KD9+/dja2v7yGnAnMbqJQAkFRwdYcUKoipVwfHqFT6ZM4LCN/81v5xZyYsiIpntwYUtDzJBhixs+fLLL4mIiGDgwIFJXitZsiR58+Y15yUdPXoUHx8fHB0diYqKIiIigvr165vPQ0LZmbVr11KuXDk6duxIw4YN+fbbb5k4caLFrMnRo0ctEq6PHj1KlSpVHst7OnToEJUqVbKoQH3w4EHy589PmTJlHnrtgQMHqFixInnz5n0sfckurLotSXb2uLcleZS4eIOXxvzMzBmDKBV5iSPu5ejYaTI3HRP+wpoADzcntr/znKbeRCRL+a/bkiSubgMsErizyrZNH374IQ4ODgwfPpwlS5ZQtWpVvL29cXd359y5czg4OKT6Xv/73/+4dOkSo0ePBhJ2mNi8eXOKW3FJ8rL9tiSSNnuDr3IsPi/dO0zgSl43ql4KYtaKiTjEJsxzqyq3iORUiQtbPNwsv+w83JysHiBBQp2jxBEjf39/vL29uXjxIoULF05TgARw5MgR83RYbGwsN27cUIBkRRpJSqfMHklaFXiBwYsDAagaeopFi9/FJeY26yrUY2Drd4i3sQVgesfqtK5e/CF3EhHJXI9rg9u4eEOLViRVNJKUy9yflHjEszz92o4m2taOln/vZOKGGebtS1SVW0RyqsSFLa2rF8evXCEFSJLhFCRlEw8mL+4sU503W40gzmRD50O/MXzrfFXlFhEReYwUJGUTiVW54V6y4m8V6/Hu828A8Mbun5h7dat+sxIREXlMFCRlI8klLy558nm+fr4PAJWmTYAHCnCKiIhI+qiYZDaTbFXuMi1gZH6YNg369IECBYhr9ZISHEVERP4DBUnZULJVuadOTajKPXcucR38GdR9EusKVTS/rKrcIiIiaaPptpzCZIJZs7j07PPYxkQzZf4YqlwKMr+sqtwiIiJpoyApB4mzsaVDo8HsLulDvpjbfL/0fbyuXgDuVakdv+Y4cfEqjSUiIvIoCpJykL3BVzl7K56+7d7jqHs5Ct+KZMGSMXhGXQZUlVtERCQtFCTlIOHX7wBw3dGZHu3HE1SwOCWiLrNwyXsUunktSTsREclY48aNo3r16v/5PvPmzdP2JFagICkHub/adoRzfrr5f8CFfEUod/U885e+j+udG0naiYhI8sLDw+nfvz+lSpXC0dERDw8Pnn/+eXbt2pWhzy1Tpgyff/65xTl/f3/+/vvvDH1uVnDmzBlMJhOBgYHW7gqgIClHebAq90XXonTtOJHLefNTJfw03/08Hq88hqpyi4ikQrt27Th06BDff/89f//9N6tXr6ZRo0ZcvZr5KQt58uShaNGimf7c3E5BUg6SXFXu4ILF6e4/gUhHZ2pdOMFPG6ZhezfGep0UEckGrl27xvbt25kyZQrPPvsspUuXpnbt2owaNYoXXnjB3C4kJITWrVvj4uKCq6srHTp04NKlSynet1GjRgwZMsTiXJs2bXj11VfNr589e5a33noLk8mEyZTwr3ly020zZ86kXLlyODg4ULFiRRYsWGDxuslk4n//+x9t27Ylb968lC9fntWrVz/0fcfExDBixAiKFy+Os7MzderUYcuWLUDCprFVqlShX79+5vbBwcG4ubkxe/ZsACIiIujUqRMlSpQgb968VK1alUWLFlk8Iz4+nilTpvDEE0/g6OhIqVKl+PDDDwHw8vICoEaNGphMJho1amS+bu7cuVSuXBknJycqVarEjBkzHvpeHgcFSTlMclW5TxQty7Cek4nNk5fCO/+Azp0hNpa4eINdQRGsCrzArqAIrXoTkcxhGHDzpnUOI3X/zrm4uODi4sLKlSuJjo5O4W0YtGnThqtXr/LHH38QEBBAUFAQ/v7+6f5oli9fTokSJZgwYQKhoaGEhiZftmXFihUMHjyYt99+m6NHj9K/f3969uzJ5s2bLdqNHz+eDh06cPjwYVq2bEmXLl0eOhLWs2dPduzYweLFizl8+DDt27enefPmnDp1CicnJ3744Qe+//57Vq5cSVxcHN26dePZZ5+lb9++QEIg5evryy+//MLRo0fp168f3bp1Y8+ePeZnjBo1iilTpvDee+9x/PhxfvzxR9zd3QHYu3cvABs3biQ0NJTly5cDMHv2bEaPHs2HH37IiRMnmDRpEu+99x7ff/99uj/rVDEkXSIjIw3AiIyMtHZXkhUbF2/s/OeKsfLgeWPnP1eM2Lh4wwgIMAwHB8MA4/xLHQy/iRuM0u/8Yj7qTtpo/HrkorW7LiI5zO3bt43jx48bt2/fTjhx44ZhJIQrmX/cuJHqfv/8889GgQIFDCcnJ6NevXrGqFGjjEOHDplf37Bhg2Fra2uEhISYzx07dswAjL179xqGYRhjx441nnzySfPrzzzzjDF48GCL57Ru3dro0aOH+efSpUsbn332mUWbuXPnGm5ubuaf69WrZ/Tt29eiTfv27Y2WLVuafwaMMWPGmH++ceOGYTKZjF9//TXZ9/vPP/8YJpPJuHDhgsX5xo0bG6NGjTL/PHXqVKNw4cLGoEGDDA8PD+Py5cvJ3i9Ry5YtjbffftswDMOIiooyHB0djdmzZyfbNjg42ACMgwcPWpwvWbKk8eOPP1qc++CDDww/P79k75Pk79x90vL9rZGkHCqxKnfr6sXxK1coYUuSJk1gyRLibW0pvnopfVd8afFblQpOiojc065dOy5evMjq1at5/vnn2bJlCzVr1mTe/++ReeLECUqWLEnJkiXN13h7e5M/f35OnDiRoX07ceIE9evXtzhXv379JM+tVq2a+c/Ozs7ky5eP8PDwZO954MABDMOgQoUK5pE0FxcX/vjjD4KC7hUnfvvtt6lYsSJffvklc+fOpXDhwubX4uLi+PDDD6lWrRqFChXCxcWFDRs2EBISYu53dHQ0jRs3TvV7vXz5MufOnaN3794W/Zo4caJFvzKCtiXJZeJeas3El4cx9qcp9Ny/hihHZz5r0BVIqKNkIqHgZFNvD+31JiIZI29euHHDes9OAycnJ5o2bUrTpk15//336dOnD2PHjuXVV1/FMAxzztD9UjoPYGNjg/HAlN/du3fT1KdEDz4juefa29snuSY+Pj7Z+8XHx2Nra8v+/fuxtbW1eM3FxcX85/DwcE6ePImtrS2nTp2iefPm5tc++eQTPvvsMz7//HOqVq2Ks7MzQ4YMISYmIRc2T548aX6fif2dPXs2derUsXjtwX4+bhpJymX2Bl9lbtkGvNd0AACDdy6m757l5tdVcFJEMpzJBM7O1jlSCF5Sy9vbm5s3b5r/HBISwrlz58yvHz9+nMjISCpXrpzs9UWKFLHIM4qLi+Po0aMWbRwcHIiLi3toPypXrsz27dstzu3cuTPF56ZGjRo1iIuLIzw8nCeeeMLi8PDwMLfr1asXPj4+zJ8/nxEjRnD8+HHza9u2baN169Z07dqVJ598krJly3Lq1Cnz6+XLlydPnjz8/vvvyfbBwcEBwOL9u7u7U7x4cU6fPp2kX4mJ3hlFI0m5TGIhyQU1XyRf9C1GbJ3P6C3fcdvBiYU1WiZpJyKSG0VERNC+fXt69epFtWrVyJcvH/v27WPq1Km0bt0agCZNmlCtWjW6dOnC559/TmxsLK+//jrPPPMMtWrVSva+zz33HEOHDmXt2rWUK1eOzz77jGvXrlm0KVOmDFu3bqVjx444OjpaTGclGj58OB06dKBmzZo0btyYNWvWsHz5cjZu3Jju91yhQgW6dOlC9+7d+eSTT6hRowZXrlxh06ZNVK1alZYtW/L111+za9cuDh8+TMmSJfn111/p0qULe/bswcHBgSeeeIJly5axc+dOChQowKeffkpYWJg5eHNycuKdd95hxIgRODg4UL9+fS5fvsyxY8fo3bs3RYsWJU+ePKxfv54SJUrg5OSEm5sb48aN480338TV1ZUWLVoQHR3Nvn37+Pfffxk6dGi63/MjPTJrSZKV1RO3U7Lznyv3krVHrDG+rvuKOaFxaMu3zK/t/OeKtbsqIjnEw5Jos6o7d+4YI0eONGrWrGm4ubkZefPmNSpWrGiMGTPGuHXrlrnd2bNnjZdeeslwdnY28uXLZ7Rv394ICwszv/5g4nZMTIzx2muvGQULFjSKFi1qTJ48OUni9q5du4xq1aoZjo6ORuLX9IOJ24ZhGDNmzDDKli1r2NvbGxUqVDDmz59v8TpgrFixwuKcm5ubMXfu3BTfd0xMjPH+++8bZcqUMezt7Q0PDw+jbdu2xuHDh40TJ04YefLksUigjoyMNMqUKWOMGDHCMAzDiIiIMFq3bm24uLgYRYsWNcaMGWN0797daN26tfmauLg4Y+LEiUbp0qUNe3t7o1SpUsakSZPMr8+ePdsoWbKkYWNjYzzzzDPm8z/88INRvXp1w8HBwShQoIDRsGFDY/ny5cm+j8eVuG0yjFSuhxQLUVFRuLm5ERkZiaurq7W7k2px8QZPT9lEWOSdhE1vDYOxv8+i5/41xJlsGNxqOPvrNmX7O88pJ0lEHos7d+4QHByMl5cXTk6q+C8Z72F/59Ly/a2cpFwmScFJk4kJjfuyqFozbI14PvtlGl/lO68ASUREcj0FSbnQgwUnDZMNo59/g9+efA77+Dh83+4HAQFW7qWIiIh1KXE7l2ru40lTbw/2Bl8l/PodiuZzovbEFtCpIyxfDq1bw2+/EVf/acs2XgU1yiQiIrmCgqRcLLHgpIVFi6BNG/j1V2JbtKR/94/43bWM+WVPNyfGtvKmuY9npvZVREQks2m6TSw5OMCyZUTUro/dzRt8+t07VA4/bX5ZVblFRCS3UJAkScQ5OtG+xUj2Fa+MW/RNFix5j3JXEoqlJS6FHL/muDbEFZE00WJqySyP6++agiRJYm/wVU7fMdGz/TgOezxB4VuR/LhkNGWuXgBUlVtE0iZx64jErSlEMtqtW7eApNuypJVykiSJxGrb1x2d6d5hAosWvUvly2f4cfFo/Dt/xLn8HhbtREQexs7Ojrx583L58mXs7e2xsdHv55IxDMPg1q1bhIeHkz9//v+8t5uCJEmiaL57hbeu5XGlq/9EFi8aRfmIcyxa9C7+nT/igltRi3YiIikxmUx4enoSHBzM2bNnrd0dyQXy589vsd9ceqnidjpl14rbqZGkKjdQ5MZVFi8aRbmrFzib34NB/T9jxSR/lQMQkVSLj4/XlJtkOHt7+4eOIKXl+1tBUjrl5CAJYP3RUF5beAC4l6ztfv0KS34cRZlrodwsXRbnXdvBU6UAREQk+9C2JPKfPViVG+BSvsIM6TeNW8VL4nz2NDz3HFy6RFy8wa6gCFYFXmBXUIRWvYmISI6gkaR0yukjSYni4o2kFbfPnoGGDeH8ea4/UYn2/h/yV6yj+RoVnBQRkaxK022ZILcESSn65x/u1Hsap8uXOFa0LJ07fkhknnzA/2+cC8zsWlOBkoiIZCnZarptxowZeHl54eTkhK+vL9u2bUvVdTt27MDOzo7q1atbnG/UqBEmkynJ8cILL5jbjBs3LsnrjyMLPjeJK1uOV7tM5rJzfqqEn2bB0vdwvXMDUMFJERHJGawaJC1ZsoQhQ4YwevRoDh48SIMGDWjRogUhISEPvS4yMpLu3bvTuHHjJK8tX76c0NBQ83H06FFsbW1p3769RbsqVapYtDty5MhjfW853d7gq+x2LEpn/w+JyONKtbB/mL/0ffJF3wRUcFJERLI/qwZJn376Kb1796ZPnz5UrlyZzz//nJIlSzJz5syHXte/f386d+6Mn59fktcKFiyIh4eH+QgICCBv3rxJgiQ7OzuLdkWKFHms7y2nSywkeapIabp0/JB/nfJRPfRv5i+5Fyjd305ERCS7sVqQFBMTw/79+2nWrJnF+WbNmrFz584Ur5s7dy5BQUGMHTs2Vc+ZM2cOHTt2xNnZ2eL8qVOnKFasGF5eXnTs2JHTp0+ncIcE0dHRREVFWRy52f2FJP8q6mUOlGqEnuT7pe/jEn0rSTsREZHsxGpB0pUrV4iLi8Pd3d3ivLu7O2FhYclec+rUKUaOHMkPP/yAnd2ji4Xv3buXo0eP0qdPH4vzderUYf78+fz222/Mnj2bsLAw6tWrR0RERIr3mjx5Mm5ubuajZMmSqXiXOVdtr4J4ujmZk7SPu5ela8eJXHNyoebFhECpnGMctb0KWrWfIiIi6WX1xG2TybJis2EYSc4BxMXF0blzZ8aPH0+FChVSde85c+bg4+ND7dq1Lc63aNGCdu3aUbVqVZo0acLatWsB+P7771O816hRo4iMjDQf586dS1UfcipbGxNjW3kD91azHXMvR5eOH3LNyQXfi3/x8+oPsL15w3qdFBER+Q+sFiQVLlwYW1vbJKNG4eHhSUaXAK5fv86+ffsYOHAgdnZ22NnZMWHCBA4dOoSdnR2bNm2yaH/r1i0WL16cZBQpOc7OzlStWpVTp06l2MbR0RFXV1eLI7dLruDkMfdyDO79MTGu+SkQuA+aN4fr11VwUkREsh2rbXDr4OCAr68vAQEBtG3b1nw+ICCA1q1bJ2nv6uqaZAXajBkz2LRpEz///DNeXl4Wry1dupTo6Gi6du36yL5ER0dz4sQJGjRokM53k3s19/GkqbfHAwUnW2LbqzY0bgw7d/LvM4155aX3CLpzLyZXwUkREcnqrBYkAQwdOpRu3bpRq1Yt/Pz8mDVrFiEhIQwYMABImOK6cOEC8+fPx8bGBh8fH4vrixYtipOTU5LzkDDV1qZNGwoVKpTktWHDhtGqVStKlSpFeHg4EydOJCoqih49emTMG83hbG1M+JV74HOuWRM2buTus40pcPBPJl8eSc9XxnHTMS8AYZF3eG3hARWcFBGRLMuqOUn+/v58/vnnTJgwgerVq7N161bWrVtH6dKlAQgNDX1kzaTk/P3332zfvp3evXsn+/r58+fp1KkTFStW5OWXX8bBwYHdu3ebnyuPR1yNmvTrNokoR2dqnz/O3J/HkTfmNqCCkyIikvVpW5J0yvXbkqTCrqAIOs3eTbXQv1m45D1co2+yp0QVer0y1jyiBLCob92kI1EiIiIZIFttSyI5V2IhycOeFejWYQJRjs7UOX+MeT+NM9dRur+diIhIVqIgSTLM/YUkDxWrSBf/iUQ6OvPUhePMX/qeuTK3Ck6KiEhWpCBJMsyDBSePeJan8//XUap58SQLl4yhvEOsCk6KiEiWpCBJMkyyBSc9nqBzx0lczePKk6Gn+HnZ+9he+9d6nRQREUmBgiTJUMkVnDzuXpY3+0wjpkBB3I4fTqinFBGhgpMiIpKlaHVbOml1W9rExRsPFJwsiO3xYwkBUng4URW88X9lAifi7gVTKjgpIiKPW1q+vxUkpZOCpMfkxAnuNGyE05Vw/ipcmi4dPyTCOT9wb4pOBSdFRORxUQkAyTbiKlaiR7cpXHIpSKUrZ1m06F2K3EjIUVLBSRERsSYFSWJVe4OvssehCP6dJhPqUogKESEsXjQK9+tXgIRAKTTyDnuDr1q3oyIikusoSBKrSiwkeaZgcfw7f8SFfEUod/U8S38cSfHI8CTtREREMouCJLGq+wtJhhTwxL/LR5zN70Hpa2Es+fEdSv0bmqSdiIhIZlCQJFb1YMHJ827u+Hf6iKCCxSkRdZmlP75D3ehwFZwUEZFMpyBJrCq5gpNhroXp2OkjThYuhceNq3w/f0RCuQAREZFMpCBJrC65gpOXXQowuP9nRFWqguPVK9CoERw4oIKTIiKSaVQnKZ1UJ+nxS7bgZOQ1eP55+PNP7uZzZUDXD/nd1ct8jQpOiohIWqiYZCZQkJSJoqL4t1ETChz8kxsOeej5ylj+LOkDqOCkiIikjYpJSo4S55KPdi+9z85S1XCJuc33P42l3plAQAUnRUQk4yhIkixvb/BVTt8x0fOVsWzx8iXv3Wjm/jye5/7ZC6jgpIiIZAwFSZLlJRaSjLZ3pN/LY/itfF0c4+7y7YoPeeHEtiTtREREHgcFSZLl3V9IMsbOnjdaj2Sl9zPYx8fxxZqPaX84IEk7ERGR/8rO2h0QeZTEgpNhkXcwgFhbO4a+MJRb9nnofGg9H/86HQ/bWGp7tbR2V0VEJAfRSJJkeckVnIy3seXd59/gf0+1AeDtX77G9qPJAKqlJCIij4VKAKSTSgBkvvVHQxm/5jihkfdyjzxdHVlw/leemPkpAKd7D6RL2daERkXfa6NaSiIi8v9UJykTKEiyjmQLTtqY4JNPYNgwAObVfJHxTfphmBIGSlVLSUREEqlOkuRYtjYm/MoVonX14viVK5QQIAFxbw1lSushxGPi1QO/MHXdF9jGxwGqpSQiIumjIElyhL3BV5lZqQlDXxxKrMmG9kc38sXqqTjE3gVUS0lERNJOQZLkCIk1klZWeZY32owk2taOF07u4H/LJpAn5k6SdiIiIo+iIElyhPtrJP1WoR69243lpr0TDc8cZMHS93C9cyNJOxERkYdRkCQ5QmItpcQk7e1eNejqP5FIR2dqXTjBkh9HUsXmFrW9Clq1nyIikn0oSJIcIblaSgeLV6JDlymEOxeg8uUzLP3hHWxDzlqvkyIikq0oSJIco7mPJzO71sTD7d6U2skiZXh9wHRuFS+Fc0gw1K8Px4+r4KSIiDyS6iSlk+okZV3J1lIKvQjNmsHx48TkL8CAzh+wKV8Z8zUqOCkikjuomGQmUJCUDUVEcK1RE/IfDeSGQx76vvweu0pXA1RwUkQkt1AxSZFkxBUoSLt2E9hRuhouMbeZ99NYmpzaA6jgpIiIJKUgSXKNvcFXCbpjQ69XxrGhfF0c4+7yzYoPeeXIRkAFJ0VExJKCJMk1EgtJRts58FqbUfzk0wQ7I55p6z6n355lSdqJiEjupiBJco37C0nG2dgyvOVgvq39MgDvbpnLqM3fgWGo4KSIiAAKkiQXebDgJCYTk5/txaRGPQHov3c5X238itollYgvIiIKkiQXSa7gJMCsOu0Y3mIwsSYbXjzwG7avtIPbt1VLSUQkl7N6kDRjxgy8vLxwcnLC19eXbdu2peq6HTt2YGdnR/Xq1S3Oz5s3D5PJlOS4c8cyzyS9z5XsLbmCkwDbG7Ti0PQ54OQEa9Zw9elGNB+3mk6zdzN4cSCdZu/m6SmbWH801Eo9FxGRzGZnzYcvWbKEIUOGMGPGDOrXr8+3335LixYtOH78OKVKlUrxusjISLp3707jxo25dOlSktddXV05efKkxTknp3tfiul9ruQMzX08aertkbTgpI0JnizL3RdbUfDAXr44N4TuHSZw2SVhv7ewyDu8tvCAaimJiOQSVi0mWadOHWrWrMnMmTPN5ypXrkybNm2YPHlyitd17NiR8uXLY2try8qVKwkMDDS/Nm/ePIYMGcK1a9ce+3Pvp2KSOVNcvMGrQ2bzyXcjKXrzX0Lc3Onm/wFnCxQDEqbpPNyc2P7OcwlBlYiIZCvZophkTEwM+/fvp1mzZhbnmzVrxs6dO1O8bu7cuQQFBTF27NgU29y4cYPSpUtTokQJXnzxRQ4ePPifnyu5w97gq2zLW5x2XT/mTH5PSkVe4ueFI/AJ+wdQLSURkdzEakHSlStXiIuLw93d3eK8u7s7YWFhyV5z6tQpRo4cyQ8//ICdXfIzhZUqVWLevHmsXr2aRYsW4eTkRP369Tl16lS6nwsQHR1NVFSUxSE5T2KNpHP5PXil61SOupejyK1rLF40iqeDDyZpJyIiOZfVE7dNJsspC8MwkpwDiIuLo3PnzowfP54KFSqkeL+6devStWtXnnzySRo0aMDSpUupUKECX375Zbqem2jy5Mm4ubmZj5IlS6bm7Uk2c3+NpCvOBejYaTLbSz+JS8xt5v48jtbHNidpJyIiOZPVgqTChQtja2ubZPQmPDw8ySgPwPXr19m3bx8DBw7Ezs4OOzs7JkyYwKFDh7Czs2PTpk3JPsfGxoannnrKPJKU1ucmGjVqFJGRkebj3LlzaX3Lkg08WEvphmNeerYfx6rKz2AfH8f0Xz5h6OE11PYqaNV+iohIxrNakOTg4ICvry8BAQEW5wMCAqhXr16S9q6urhw5coTAwEDzMWDAACpWrEhgYCB16tRJ9jmGYRAYGIinp2e6npvI0dERV1dXi0NynuRqKd21tWdIq7f5X63WALz567fYDh8G8fGqpSQikoNZtQTA0KFD6datG7Vq1cLPz49Zs2YREhLCgAEDgITRmwsXLjB//nxsbGzw8fGxuL5o0aI4OTlZnB8/fjx169alfPnyREVF8cUXXxAYGMjXX3+d6udK7pZYS2n8muOERibkHhkmG+a8PIinn6lGpU8+gE8/5eKJ0/j79efczTjztZ5uToxt5a0SASIiOYBVgyR/f38iIiKYMGECoaGh+Pj4sG7dOkqXLg1AaGgoISEhabrntWvX6NevH2FhYbi5uVGjRg22bt1K7dq1U/1ckZRrKTWG6hWI79mTYr+uZNLxM7zW9l1uOOYFVEtJRCQnsWqdpOxMdZJyr7h4g6F9pjJp4Tic797hqHs5Xm0/jivOBQDVUhIRycqyRZ0kkexqb/BVVhX1oWOnyVzJ64bPpSCWLxiG19ULgGopiYjkFAqSRNIosUbSEc/yFkUnly0cTs0LJ5K0ExGR7ElBkkga3V8j6WyBYrTr+jGBnuUpeDuKHxePptnfu5K0ExGR7EdBkkgaPVhLKcI5P506TmZjuadwio3hmxWTGHj8N9VSEhHJ5hQkiaRRcrWUbjs40f/lMfz4ZHNsMBi25ktsR41ULSURkWxMq9vSSavbZP3RUItaSgCero58f+l3KnzxEQAXW7Sho18/Qm7G32ujWkoiIlaTlu9vBUnppCBJIKEcQNJaSiaYP5/43r2xiY1lV6mq9G87mignF+De6JNqKYmIZD6VABDJJLY2JvzKFaJ19eL4lStkrosU17UbQ7p9yHWHPPiFHOGnH0bgGXUZSCgRADB+zXFNvYmIZGEKkkQywN7gq6wuWoUOXaYQ5lKQildCWLHgbbwvnQZUS0lEJDtQkCSSARJrJJ0oWpaXu03j70Kl8LhxlaU/vkOjoH1J2omISNajIEkkA9xfI+mia1Fe6TqVHaWr4RJzm/8tm0DnwF+TtBMRkaxFQZJIBniwllKUkwuvth/Pzz6NsTPimfTb13ywawG1S+e3ZjdFROQhFCSJZIDkaindtbVnWMshfPp0FwC6bV2CbedOcOeOaimJiGRBKgGQTioBIKmRbC0lNye+5TjVxr4Nd+/yb/VadHphFH/FOlq0US0lEZHHT3WSMoGCJEmtFGspbd7M3dZtsL8eRXABT3q+Mo4zBYsDqqUkIpJRVCdJJAtJsZbSM43o3uszzrsWxevfUJYvHI7v+eOAaimJiGQFCpJErGRv8FV2ObnTttsnHPIoT8HbUfy4eDStjv8BqJaSiIi1KUgSsZLEGkmXXQrQsdNkNpSvi2PcXb5c8zEDdy6G/58JVy0lERHrUJAkYiX310i67eDEgDajmPVUWwCGbVvIJ2s/xSH2rmopiYhYiZ21OyCSWyXWUgqLvIMBxNvYMum53pwpWIwJG2bS7thmyt68QrV3NgEPSQAXEZEModVt6aTVbfI4rD8aymsLDwD3krUBGgYf4KuVH+EacwueeIKtn83lnSPRSUoJqEyAiEjaaHWbSDbR3MeTmV1r4uFmOaV2qno9Di9ZC6VLwz//UK19C0od+dOiTVjkHV5beID1R0Mzs8siIrmGRpLSSSNJ8jilNJUWFxrG8TrPUfXcCWJs7Hi3+UB+rtrEfJ0J8HBzYvs7z2nqTUQkFTSSJJLNpFRLae8te15pP5FfKjXAIT6Waes+Z9jW+ZiMeEBlAkREMpKCJJEsLPz6HaLtHRn00nC+9PMHYOCupcxY+RF5Yu5YtBMRkcdLQZJIFpa4/N8w2fBJw2683fItYmzsaPH3Tpb++A7u169YtBMRkcdHQZJIFpZYJiAx22hZ1cZ07vQhEXlcqXopiNXzh/Ls9bPU9ipo1X6KiORECpJEsjBbGxNjW3kD9za93VeiCq27f8rJwqVwv3GV/815G9tlPwMJCeC7giJYFXiBXUER2vdNROQ/0Oq2dNLqNslM64+GMn7NcYs6SeUc41i0+QuKbvsdgFNvDKd7sWaERkWb26iWkoiIpbR8fytISicFSZLZki0TYMTD8OHw2WcArKr8DCNavEm0vSNwb/RpZteaCpRERFAJAJEcKdkyAba2xE37hMlt3+KujS2tT/zB4kXvUuTGv8C9Kt7j1xzX1JuISBopSBLJ5vYGX+XbCo3p3uEDrjm5UCP0JKvmv0WVS0GAaimJiKSXgiSRbC6xRtKu0tVo0+0TggqWoNj1K/y8cAQt/9qepJ2IiKSOgiSRbO7+GklnChanbbdpbPHyJU9sNDNWfcRb237AZMSrlpKISBopSBLJ5h6spRTl5EKvV95n9lNtABi8cxFz1n5M7aIJydwqEyAikjpa3ZZOWt0mWcn6o6G8tvAAcC9ZG6D94QAmbvgax7hYePJJtkydzaj9URalBFQmQERyE61uE8llmvt4MrNrTTzcLKfUtjdoxcF5y6BoUTh0CJ+2TSl+bL9Fm7DIO7y28ADrj4ZmZpdFRLI8jSSlk0aSJCtKtpaSjYm4M2cJqteYCqFBxNjYMabZ6yx9spn5OhPg4ebE9neeSygtICKSQ2kkSSSXSraWErA3zoXWHaewtmJ9HOJjmbr+C97fOAvb+DhAZQJERJKjIEkkFwi/fofbDk4MbP0On9XvDECv/av5fun75L8dZdFOREQSWD1ImjFjBl5eXjg5OeHr68u2bdtSdd2OHTuws7OjevXqFudnz55NgwYNKFCgAAUKFKBJkybs3bvXos24ceMwmUwWh4eHx+N6SyJZTuLyf8Nkw/SnO9O/zbvctHfi6bOHWP39W1S8fMainYiIWDlIWrJkCUOGDGH06NEcPHiQBg0a0KJFC0JCQh56XWRkJN27d6dx48ZJXtuyZQudOnVi8+bN7Nq1i1KlStGsWTMuXLhg0a5KlSqEhoaajyNHjjzW9yaSlTxYJuC3ivV4uds0zub3oFTkJZYvGEanc3up7VXQqv0UEclKrJq4XadOHWrWrMnMmTPN5ypXrkybNm2YPHlyitd17NiR8uXLY2try8qVKwkMDEyxbVxcHAUKFOCrr76ie/fuQMJI0qOuexQlbkt2k1yZALfb1/l61RSePhuYcGLMGBg/njhMySaAi4hkd9kicTsmJob9+/fTrFkzi/PNmjVj586dKV43d+5cgoKCGDt2bKqec+vWLe7evUvBgpa/IZ86dYpixYrh5eVFx44dOX369EPvEx0dTVRUlMUhkp0kVyYgMk8+RvaZwplu/RJOTJxIeOPmNBu/hk6zdzN4cSCdZu/m6SmbVCJARHIdO2s9+MqVK8TFxeHu7m5x3t3dnbCwsGSvOXXqFCNHjmTbtm3Y2aWu6yNHjqR48eI0adLEfK5OnTrMnz+fChUqcOnSJSZOnEi9evU4duwYhQoVSvY+kydPZvz48al8dyJZU3MfT5p6eyQzStQMmtQnrm8/im4J4Jsjf9Hv5TEEFywO3KulNLNrTRWdFJFcw+qJ2yaT5RC+YRhJzkHCtFnnzp0ZP348FSpUSNW9p06dyqJFi1i+fDlOTvd+e27RogXt2rWjatWqNGnShLVr1wLw/fffp3ivUaNGERkZaT7OnTuXqj6IZDUplQmI69qNvn0+IdSlEOUjzrFq/lAaBe0D7k3PjV9zXNuYiEiuYbUgqXDhwtja2iYZNQoPD08yugRw/fp19u3bx8CBA7Gzs8POzo4JEyZw6NAh7Ozs2LRpk0X7adOmMWnSJDZs2EC1atUe2hdnZ2eqVq3KqVOnUmzj6OiIq6urxSGSk+wNvsqmfGV4qcfn/FncG9fom3z383he37UUDEO1lEQk17FakOTg4ICvry8BAQEW5wMCAqhXr16S9q6urhw5coTAwEDzMWDAACpWrEhgYCB16tQxt/3444/54IMPWL9+PbVq1XpkX6Kjozlx4gSenppGkNwrsUbSZZcCdO70IT8+2RwbDEZsnc+MlZNxjr5l0U5EJKezWk4SwNChQ+nWrRu1atXCz8+PWbNmERISwoABA4CEKa4LFy4wf/58bGxs8PHxsbi+aNGiODk5WZyfOnUq7733Hj/++CNlypQxj1S5uLjg4uICwLBhw2jVqhWlSpUiPDyciRMnEhUVRY8ePTLpnYtkPffXSLpra8+7zQdy2OMJxm/8hpZ/7+SJiPP0e3k0RfPVtWIvRUQyj1WDJH9/fyIiIpgwYQKhoaH4+Piwbt06SpcuDUBoaOgjayY9aMaMGcTExPDKK69YnB87dizjxo0D4Pz583Tq1IkrV65QpEgR6taty+7du83PFcmNEmsphUXeMecgLa7enJNFyjBz5SQqRISwZsFQ8r7oCeVapbhPnIhITqENbtNJdZIkJ0qulhJAkRv/MmPVZJ46fxyAU68Po0exZly8HmNu4+nmxNhW3lr9JiJZWraokyQiWU9ytZQA7Ip7cnX1OnjjDQDKz5jG+HnvkS/6prlNYpkA1VMSkZwizSNJJ0+eZNGiRWzbto0zZ85w69YtihQpQo0aNXj++edp164djo6OGdXfLEMjSZKTpTSVFhdvMKnDO4xY+TmOcXcJKliCfi+PJqhQSQBMgIebE9vfeU5TbyKSJaXl+zvVQdLBgwcZMWIE27Zto169etSuXZvixYuTJ08erl69ytGjR9m2bRtRUVGMGDGCIUOG5OhgSUGS5Ea7giLoNHs3VUNP8c2KSRS/fpkbDnkY1nII6yvWN7db1LcufuWSL8wqImJNafn+TnXidps2bRg+fDhLlixJssXH/Xbt2sVnn33GJ598wrvvvpv6XotIlpe4/P+IZ3le6vEZX62egl/IEb5ZOZlv6rTj44bdibOxVZkAEckRUh0knTp1CgcHh0e28/Pzw8/Pj5iYmEe2FZHs5f4yARHO+enqP5ERf3xP/73LGbBnGdVCTzHopREW7UREsqtUJ26nJkCChA1l09JeRLKPxDIBidlGcTa2TH62F6+1HskNhzzUCznMugVvUTs8oXp9XLzBrqAIVgVeYFdQhLY0EZFsJV2r2xo1asT58+eTnN+zZw/Vq1f/r30SkSzK1sbE2FbeANyflv1rpadp0+1TggqWwD3yMrbPNOTY+1N4+qPf6TR7N4MXB9Jp9m6enrJJq99EJNtIV5Dk6upKtWrVWLx4MQDx8fGMGzeOhg0b8tJLLz3WDopI1pJSmYCb5cpzeu3v0K4d3L1LlQ9G8vaij3C8G21uozIBIpKdpLuY5DfffMOwYcN46aWXOHPmDCEhIcybN48mTZo87j5mSVrdJrldimUC4uKZ+eIAXvttDrZGPMeKlmVA23c5l98DUJkAEbGuDFnd9qABAwZw9uxZpkyZgp2dHVu2bEl2Y1oRyZlsbUzJLvPfe+Zfpj3Zmh35y/Dl6qlUCT/NL/MGM6TVMDaXewoDCI28w97gqyoTICJZWrqm2/7991/atWvHzJkz+fbbb+nQoQPNmjVjxowZj7t/IpLNJC7/31X6SVr1+JyDnhVxi77J3J/HM2zrfGzi4yzaiYhkVekKknx8fLh06RIHDx6kb9++LFy4kDlz5vDee+/xwgsvPO4+ikg2cv/y/1DXIvh3/ojvayb8uzBw11IWLH2PQjevqUyAiGR56QqSBgwYwNatW/Hy8jKf8/f359ChQ6qPJJLLPVgmIMbOnrFNX+PNVsO5Ze9I/bOHWT9/MLUvngBUJkBEsq50J27ndkrcFknZ+qOhvLbwAAD3/wNT/koIM1dM4omr58HOjhND36OXWz1Co+6tgPN0c2JsK2+a+3hmcq9FJDdIy/d3qkeSQkJC0tSJCxcupKm9iOQcKZUJuFGuAsHrNoG/P8TGUnnqWMbMH4dL9C1zG5UJEJGsItUjSe7u7rz00kv07duX2rVrJ9smMjKSpUuXMn36dPr378+gQYMea2ezEo0kiTzaw8oEfN52MIPWfoNDfCxBBYvzWptR/F2kDKAyASKScTKkBMCJEyeYNGkSzZs3x97enlq1alGsWDGcnJz4999/OX78OMeOHaNWrVp8/PHHtGjR4j+/ERHJ3h5WJuBL7+ZsdyvD16s+otzVC6ya/zZjmr3OsqqNVSZARLKEVE+3nT9/nilTpnDx4kW++eYbKlSowJUrVzh1KmGPpi5durB//3527NihAElEHipx+f/B4pV44dXpbC1Tgzyx0Xyy7jOmrJuO0907Fu1ERKwh1SNJNWrUICwsjCJFivD222/z559/UqiQfsMTkbS7f/n/v3ndeLX9ON7YtZQhOxbhfySAamGneKP1SIrmq2vFXopIbpfqkaT8+fNz+vRpAM6cOUN8fHyGdUpEcrYHywTE29jyZf1OdPX/gMvO+al8+Qxr5r9Fnb0BgMoEiIh1pDpxu1+/fsyfPx9PT09CQkIoUaIEtra2ybZNDKZyMiVui/w3KZUJKHrjKl+snkrdc0cBOOvfg25V/Am5ee8XM5UJEJH0Ssv3d5rqJK1fv55//vmHN998kwkTJpAvX75k2w0ePDhtPc6GFCSJ/Hfrj4Yyfs1xQiPv5R55ujkxrkUFnv/pG5g0CYDDHk/wRuuRFpvkAszsWlOBkoikSYYFSYl69uzJF198kWKQlBsoSBJ5PFIsExBvMKzXR7y/ZDIF7lwnytGZYS2HsKGCH6AyASKSPhkeJImCJJGMtisogk6zd+MZdZmvVk3B9+JfAHzn+xIfNepJjJ09AIv61lWZABFJtQypuC0ikpkSl/8nbpI766m2APTav5qffxhOyWthFu1ERB43BUkikiXdXyYg1taOSc/1pne79/jXKR/Vwv5h7dw3afHXdnM7rYATkcdN023ppOk2kYwVF2/w9JRNhEXesVj95hl1mS9Wf8xTF44DED9gABv7jGDshtNJEsC1Ak5EHqTpNhHJ9mxtTIxt5Q3cW80GCdNvnTtNYkbdVwCw+eYbSrRsjFNwkMX12ihXRP4rBUkikmU19/FkZteaeLg5WZwvXNCFsrO/IG7tOv7N64Z3eDBrvh/CS8e3mNskjj6NX3NcU28iki6abksnTbeJZJ6UygTsCopg8Kdr+WLNx+bik4uqNWN8k37csb8XWGkFnIgk0nSbiOQotjYm/MoVonX14viVK2SuixR+/Q7h+QrRpeOHTK/XiXhMdDq8gdXfD6Xi5TPm67UCTkTSQ0GSiGRb5pVtNrZ81qALXTpOJNy5ABUiQlg1fyidA38Fw7BYKScikloKkkQk23pwo9xdpZ+kRc8v2VzWF6fYGCb99jXfrZ1K7QIJ/9SpTICIpIVyktJJOUkiWUNyG+WajHj6/LmSEX98j318HJQuze6JX/LWubwqEyCSyyknSURyjeRWwBkmG35p2pk/f1gDZcvC2bPU6t6GtuvnYzLize1UJkBEHkYjSemkkSSRrCXFjXKvRfL7M21pdngzANtKV2foi29z2aUAoI1yRXIbjSSJSK6T0gq4vRGx9Gs+lOEtBnPL3pEGZwP5de5AGgX9CSRM0YVG3mFv8FUr9l5EsiIFSSKSo4VfvwMmEz9Va0qr7p9zokgZCt+KZN7P43l/4ywcYu/eaycich8FSSKSo92//D+ocEnadP+Uub6tAOi1fzUrFwyl3JVzKhMgIklYPUiaMWMGXl5eODk54evry7Zt21J13Y4dO7Czs6N69epJXlu2bBne3t44Ojri7e3NihUrHttzRSR7ebBMQLSdA+Ob9KfnK2OJyOOKd3gwa+cPoU7Az2AYKhMgImZWDZKWLFnCkCFDGD16NAcPHqRBgwa0aNGCkJCQh14XGRlJ9+7dady4cZLXdu3ahb+/P926dePQoUN069aNDh06sGfPnv/8XBHJflLaKHdzuado0esrtpWpgdPdaGxeG0BYsxdpOXYlnWbvZvDiQDrN3s3TUzZp9ZtILmXV1W116tShZs2azJw503yucuXKtGnThsmTJ6d4XceOHSlfvjy2trasXLmSwMBA82v+/v5ERUXx66+/ms81b96cAgUKsGjRov/03PtpdZtI9rL+aCjj1xxPWifphUo037CI+FHvYhN7l4v5CvPWi2+zp1RV4F5gNbNrTdVTEskBssXqtpiYGPbv30+zZs0szjdr1oydO3emeN3cuXMJCgpi7Nixyb6+a9euJPd8/vnnzfdM73NFJHtr7uPJ9neeY1HfukzvWJ1Ffeuy/Z3naF6tOHFD36ZX/+mcLlCMYtevsGjRuwzdugC7uFhzgcrxa45r6k0kl7FakHTlyhXi4uJwd3e3OO/u7k5YWFiy15w6dYqRI0fyww8/YGdnl2ybsLCwh94zPc8FiI6OJioqyuIQkewlxTIBwVfZ4lKKF1+dztKqTbDB4M1dS/jph3co/e9FlQkQyaWsnrhtMlkWbzMMI8k5gLi4ODp37sz48eOpUKHCf75nap+baPLkybi5uZmPkiVLPrQPIpJ9JC7/v+WQhxEthzDwpRFEOTpTI/Qk6+a+SfvDAWAYKhMgkstYLUgqXLgwtra2SUZvwsPDk4zyAFy/fp19+/YxcOBA7OzssLOzY8KECRw6dAg7Ozs2bdoEgIeHx0PvmdbnJho1ahSRkZHm49y5c+l63yKS9Ty4/P+Xyg1p3utLdpf0wfnuHT7+dTozVk6mWNxtQBvliuQWVguSHBwc8PX1JSAgwOJ8QEAA9erVS9Le1dWVI0eOEBgYaD4GDBhAxYoVCQwMpE6dOgD4+fklueeGDRvM90zrcxM5Ojri6upqcYhIzvBgmQCAi65F6dzxQ6Y804O7Nra0/HsntVo3Yu+cn3h6yiatgBPJBZJP7MkkQ4cOpVu3btSqVQs/Pz9mzZpFSEgIAwYMABJGby5cuMD8+fOxsbHBx8fH4vqiRYvi5ORkcX7w4ME0bNiQKVOm0Lp1a1atWsXGjRvZvn17qp8rIrlLYpmA1xYewATmZO14G1u+qdue7WVqsPiPL3A+c5paffzpUbstnzboRoydPXBvo1ytgBPJWayak+Tv78/nn3/OhAkTqF69Olu3bmXdunWULl0agNDQ0DTXLqpXrx6LFy9m7ty5VKtWjXnz5rFkyRLzSFNqnisiuU9zH09mdq2Jh5vl1JuHmxNvDOuA0+FDrKj9IjYYDNi7nBUL3qbclYRpd62AE8mZrFonKTtTnSSRnCku3mBv8FXCr9+haD4nansVxNbGxK6gCDrN3k3TU7uZ8usXFLwdxR07ByY16sn8mi/C/y/8WNS3Ln7lCln5XYhIStLy/W3V6TYRkawmsUzAgxJXtgWUr0ugZwWmrfucZ4IPMGHjtzQO+pPhLQYTnq+QVsCJ5CBWLwEgIpId3L8C7rJLQXq0H8/7Tfpzx86BZ4IP8Nt3A2l+coe5nVbAiWR/GkkSEUmFxBVwYZF3EnKQTCbm+7ZiR+nqfP7LNKpeCuKblZOJd71IwGvv8v7mc0m3QGnlrcRukWxEI0kiIqmQ0ka5QYVL0q7bNL7264BhY4PN/O+p/HwDShzdZ3F94go4lQoQyT4UJImIpFJKK+AKFcxHuVmfE7/lDy4U8KBEVDhLfhzFO1vmYR93F9AKOJHsSKvb0kmr20Ryr4etgOvz1Sbe/302/kcSCtYeK1qWt14cyt9Fypiv1wo4EetJy/e3RpJERNIopY1yw6/f4aZjXt5pOZj+bd8lIo8rVcJPs+b7IfTdsxyb+DhzOxHJ+hQkiYg8JvevgPutQj2a9/qajeWewjEultFbvmPRoncpcS1MK+BEsglNt6WTpttE5EFx8QZPT9l0bwUcgGHQ4XAA72+ajUvMbW465CHPl9PZ4PcC4385oRVwIplM020iIlaQ7Ao4k4mlTzajRc8v2VPSB+eY29j074d92zbEXrBc6aYVcCJZi4IkEZHHKKUVcLGly/DvL+uJ//hjYmztaRz0J7999wYt/rq3+bZWwIlkLZpuSydNt4nIwzxsBdzYSYv5dO1n+FwKAmCFdyPGNh1AlJOL+XqtgBPJGJpuExGxsoetgPu7SBnadpvGF37+xJpsaHt8CxvmvE6joHsFKLUCTsT6FCSJiGSixJVtd23t+bRhN17p+jFBBUvgceMq834ex+Rfv8Al+pbFSjkRsQ4FSSIimShxD7jExO7AYhVp+ep0/lerNfGY6HR4AwHzBlI7OBBQmQARa1JOUjopJ0lE0mv90VBeW3gAuJesDVDn3FE+XvsZpSIvAXC2U09erfgywbfv7RanMgEi/41ykkREsrCUVsCF+NTi5Ibt8NprAJReNJfvpvfD9/xxcxuVCRDJPBpJSieNJInIf5XSCri4eIO3+n7MOz9No/j1y8RjYnbttnz6dBei7R0xAR5uTmx/5zlzQriIpI5GkkREsoGUVsDtDb7K6iJVaN77K5ZWbYINBv33LmfdvMHUuPAXBhAaeYe9wVet+wZEcjgFSSIiWUzi8v/rjs6MaDmEXu3e55JLQcpdPc/PP4xg1ObvcLwbrTIBIhlMQZKISBbz4PL/TU/UpmnvGSzzeQ5bI948qlT2n6OAVsCJZBTlJKWTcpJEJKMku1Hu/3vun71M/u0r3G9cxbCx4Uz3fvT0asWZW/daagWcSMqUkyQiko0lu1Hu/9v8RG2a9Z7BhZfaY4qPx2veN8yZ3p+aF06Y22gFnMjjoSBJRCQLSqlMgIebE1P6NMRjxRKGdZ94L1dp4Qje3TQHx7vR2ihX5DHRdFs6abpNRDLDwzbK7TR7N653bjD291m0O7oJgNMFijGi5WD2lagCaKNckQel5fvbLpP6JCIi6ZBYJuBBiSvbopxcePuFoayt+DSTfvuKsv9eZOkPI5lf8wWmPtPD3C6lYEtEUqYgSUQkG0puBVyzEjN4d/N3dDy8gVcP/ELjoD+5Xn0G6+38GL/mOKGR90oGKLlb5NGUkyQikg09uFEuJIwqjWzxJl07fMB516KUjLyEd492XOvyKjfCIyyuV3K3yKMpSBIRyYYetgJuh1cNmvf6ijP+rwLQ8fAGNvzvdZ4N+tPcRsndIo+mIElEJJt62Aq4ab2fJvTDaXTo/BHBBTzxvBHB3J/H8+kvn1DgViSAtjcReQTlJImIZGPNfTxp6u2RbFL2qsAL7C3pQ4ueXzJ02w/03reKl49tpmHwAcY16c8vlRqAyaTtTURSoCBJRCSbS2kFXGJy9x17JyY915t1lZ5myq/TqXglhK9WT6X18S281/R1czutgBOxpCBJRCSHSkzuTtzeJLBYRV58dTqv7/qJN3Ytpek/e/E7d5S81e6w/uaLjF/7l1bAidxHOUkiIjlUcsndd23tmf50Z158dToHPSviEn0Lm9cGkP/F5jgGB1lcrxVwktspSBIRycFSSu6+/kRFLv26kfhPP+W2vRN1zx1l/dxB9N/zM7bxcYBWwIloW5J00rYkIpKdPGx7k+Efr2Ty+q9ocDYQgCPu5RjZ4k2OuZczX6/tTSSnSMv3t0aSRERygcTk7tbVi+NXrpA5ITv8+h3O5/egm/8HDGs5hEhHZ6peCmLV928xcvN3ON29Y24nktsoSBIRycXM25uYTPxctQlN+nzDL5UaYGfEM2Dvcn77biD1zwRarIDbFRTBqsAL7AqK0DSc5GiabksnTbeJSE4QF2/w9JRN5hVwiRr/s4cPNsyk2PUrAMR3687mfiMYsy1MK+AkW8tW020zZszAy8sLJycnfH192bZtW4ptt2/fTv369SlUqBB58uShUqVKfPbZZxZtGjVqhMlkSnK88MIL5jbjxo1L8rqHh0eGvUcRkawqpe1Nfn+iDs16z2CebysMkwmbBfOp3qwetXf+Cvf9bq0VcJKTWTVIWrJkCUOGDGH06NEcPHiQBg0a0KJFC0JCQpJt7+zszMCBA9m6dSsnTpxgzJgxjBkzhlmzZpnbLF++nNDQUPNx9OhRbG1tad++vcW9qlSpYtHuyJEjGfpeRUSyqpRWwOUrWhCPed8Sv30HQe5lKHQ7ium/fMK8n8ZRIvISoBVwkrNZdbqtTp061KxZk5kzZ5rPVa5cmTZt2jB58uRU3ePll1/G2dmZBQsWJPv6559/zvvvv09oaCjOzs5AwkjSypUrCQwMTHffNd0mIjnNw1bAdf9mG/32LOfNnYtxjLvLLXtHPn26C3NrtSbOxhbQCjjJHrLFdFtMTAz79++nWbNmFuebNWvGzp07U3WPgwcPsnPnTp555pkU28yZM4eOHTuaA6REp06dolixYnh5edGxY0dOnz6d9jchIpKDPGwF3F1be76u50/zXl+xu6QPee9GM2bzd6z+/i2qhf5tbieSk1gtSLpy5QpxcXG4u7tbnHd3dycsLOyh15YoUQJHR0dq1arFG2+8QZ8+fZJtt3fvXo4ePZrk9Tp16jB//nx+++03Zs+eTVhYGPXq1SMiIiLFZ0ZHRxMVFWVxiIjkBuYVcEBwweJ07DSZ4S3e5JqTC1XCT7NiwTDGbvwWD9NdQCvgJOew+t5tJpPl5omGYSQ596Bt27Zx48YNdu/ezciRI3niiSfo1KlTknZz5szBx8eH2rVrW5xv0aKF+c9Vq1bFz8+PcuXK8f333zN06NBknzl58mTGjx+f2rclIpJjPLgHHCYTP1VrxqZytRm9eQ4vH9tMz/1rMF44wIHhE3jjVmmtgJMcwWojSYULF8bW1jbJqFF4eHiS0aUHeXl5UbVqVfr27ctbb73FuHHjkrS5desWixcvTnGU6X7Ozs5UrVqVU6dOpdhm1KhRREZGmo9z58498r4iIjlBSivgIpzz8/aLb9OtwwfcLFkG04UL1BzSm/Fzx+AZddncTivgJLuyWpDk4OCAr68vAQEBFucDAgKoV69equ9jGAbR0dFJzi9dupTo6Gi6du36yHtER0dz4sQJPD1T/i3H0dERV1dXi0NEJLdIaQWch5sTXd7rjdOJY8xr1Jm7NrY0O7WbgDmv03PfKmzi47QCTrItq063DR06lG7dulGrVi38/PyYNWsWISEhDBgwAEgYvblw4QLz588H4Ouvv6ZUqVJUqlQJSKibNG3aNAYNGpTk3nPmzKFNmzYUKpR0pcWwYcNo1aoVpUqVIjw8nIkTJxIVFUWPHj0y8N2KiGRvzX08aertkeIKuHF1OvND2fpM/u0ral04wdjfZ9P22GZGN3uDI57lCY28w97gq1oBJ9mGVYMkf39/IiIimDBhAqGhofj4+LBu3TpKly4NQGhoqEXNpPj4eEaNGkVwcDB2dnaUK1eOjz76iP79+1vc9++//2b79u1s2LAh2eeeP3+eTp06ceXKFYoUKULdunXZvXu3+bkiIpK8xBVwD0pc2XaqSGnad5lCp0O/8c6WeVQL+4dV84cyv+YLfNKwm7ldSuUGRLISbUuSTqqTJCJyz66gCDrN3m1xrvDNfxm9aQ5tj28BINy5ANcmTeX0sy0Z/8sJJXeLVWSLOkkiIpJzJK6Au38s6IpzAd5qNYzO/hMJLlCMojf/pcLgvuRp3Qr7M8EW1yu5W7IiBUkiIvKfpbQCDmBXmeo07/UVf782jGg7e54JPkDAnNcZuHMxDrEJtZWU3C1ZkYIkERF5LB62Am76q3WJeHskz/f8im2lq+MYd5dh2xby69xB1DsTCCQESonJ3SJZgXKS0kk5SSIiyUspKXtV4AUGLw4Ew+ClE1t5b9Nsity8BsCqys8w8bneXHYpyPSO1WldvbhV34PkXGn5/rZ6xW0REclZUloBZ97exGRitfczbCnry9vbFtDtwDpan/iDZ4P+5NMGXSnasxagFXBifRpJSieNJImIpE1cvMHTUzbd297k//mE/cPEDV9TPTRh1wOjenV2D/uAoSF5tAJOHjutbhMRkSwnpeTuox5P0K7rNN59/g1iXPNjCgzEr2srBi35mPy3720mrhVwktkUJImISKZJKbm7aAFnGk4bje3Jv/il5vMAdD70G5tmD6DDoQ2YjHitgJNMp+m2dNJ0m4hI+qWUb5RYlLLW+WNM/G0Gla6cBeBAsYq81/Q1jnk8AcCivnW1vYmkixK3RUQkS3vU9ib7SlThxVen8+r+1QzZsYiaF0+yev5Qfqjegmna3kQyiYIkERHJMswr4IBYWzv+V/tlVld+htGbv6P1iT/ofnAtL/y1jX89J7Le5mXGr/1Lyd2SYZSTJCIiWUZy25uE5yvE4JeG06njJP4uVIpCt6N4YuSbFG3RmIInj1pcr+RueZwUJImISJbxsO1Ndpeuxgs9v+DE0Pe46ZDHPAU3YcNMXO/cALS9iTxeCpJERCRLedj2Jl/2qM211wfzbJ9vWFX5GWyNeLofXMvmWf0sVsFpexN5HLS6LZ20uk1EJGM9cnsToG7IYSZs+IYKESEABHqWZ2yTARwqVtG8vYmSu+V+afn+VpCUTgqSRESsI7FMQCK7uFh6HPiFIdt/IF/MbQCWVG1K2f99QUReN8avOa7kbjFTxW0REcmxHkzujrW1Y85TbXiu7yx+9mkMgP+RAKo3qcOeIWMJ//emxfVK7pbUUpAkIiLZSkrJ3ZddCjD8hbd4uevHRFauiv31KMb+Ppu1c9+kbshhczsld0tqKUgSEZFs52HJ3f3e6cLxlRsZ9fxAruZxpdKVsyxe9C5frZqCZ9RlACV3S6qomKSIiGRLzX08aertkWJy96LqzVlXsT5vb1tIl8BfefGvbTT+Zy8z677Ct7VfJtre0Vy5WyQ5CpJERCTbSml7k8TK3ZF58vF+s9dY/OTzjN34LXXOH2Po9h/ocDiAD5/tRVGXOoC2N5HkaXVbOml1m4hI1hUXb/D0lE2ERd4x5yBhGLz41zbe3fwdxa5fSTj17LPsGDiG4ScNrYDLJbS6TUREcrVkk7tNJn6p3JAmfb7hi3odiXN0wrR5M36vNGXAz5/hdvu6+XqtgBNQkCQiIjlUSsndbkXyU+HbT+H4cTZVaYCtEU+PA2vZMqsfXQ+sxTY+TivgBNB0W7ppuk1EJHtIKd8osSil39lDjN04i0pXzgLwV+HSTGjcl51lqgOwqG/dZPOeJHtKy/e3ErdFRCRHSym5O3Fl267ST/JCzy/ocnAdQ7f/QKUrZ/lxyRg2lK/Lh8/2MrdTcnfuoyBJRERypcQVcABxNrbM923FKu9GDNnxI90OrKXZqd08c3ofV4wBBPQaxPubzym5O5dRTpKIiORKD25vAgklA8Y36U/zXl+xtUwNHONiKT77K2o0rkPDrauwiY8zt1Vyd86nIElERHKllLY3AQgqXIoeHSaw74t5hBQqTuFb15iy/ktWzx9K7XNHAW1vkhsoSBIRkVzrYdubzOzmy92WL9K451d88Gxvohyd8bkUxNIfRzJjxSRKXgvT9iY5nHKSREQkV3vU9iZ3be2ZU7stK3ye4+1tC+h4aAMt/95J46C9zK3Vmq/9Oii5O4dSCYB0UgkAEZGcL7FMwP0qXj7DmN//R4OzgQBcyetG1MgxnGrlz7hf/1ZydxanitsiIiKPQXLJ3SeLlKGb/wf0avc+QQVLUPhWJGXfH07ppg14InCnxfVK7s7eNJKUThpJEhHJHdYfDeW1hQeAe8nakJDsbRcXy0rbI5T4Yqp5W5NNZWvx4XO9CSpU0tzOw82J7e88p6m3LEAjSSIiIo/Jw5K7v+xRm6i+r9Gw7yzm1GrNXRtbnju9j9/mvMH4gJkUvBWp5O5sTCNJ6aSRJBGR3CWlpOxVgRcYvDgQAK+rF3h383c0/WcPAFEOefm6Xgfm+b7E1K61aV29uJK7rSwt398KktJJQZKIiEDyyd1+Zw8xevN3+FwKAuCcmzu3x3/A6edeYPwvJ5TcbUWabhMREckkySV37yr9JK16fMbbLd8i1KUQJSMvUWFIP9yff45ixw5YXK/k7qxLI0nppJEkERFJ9LDkbqe7d1h1Zzcl/vcVeWMSRpDWVajHR416ElLA09xOyd2ZQyNJIiIimehhyd2f9axHxNCRPNN3Fj8++TxxJhta/r2Tjf97jfd+n03+21FK7s6irB4kzZgxAy8vL5ycnPD19WXbtm0ptt2+fTv169enUKFC5MmTh0qVKvHZZ59ZtJk3bx4mkynJcefOHYt2aXmuiIjIozT38WT7O8+xqG9dpneszqK+ddn+znM09/Ek/PodLrsU5N3mg2jZ8wv+8KqJQ3wsvfetYuu3fem3ZxmOsTEWlbt3BUWwKvACu4IitDeclVh1W5IlS5YwZMgQZsyYQf369fn2229p0aIFx48fp1SpUknaOzs7M3DgQKpVq4azszPbt2+nf//+ODs7069fP3M7V1dXTp48aXGtk9O96D6tzxUREUkNWxsTfuUKJTlfNN+976CTRcrQo8MEGgQf4N3N31H58hne3TKX7gfWcrvYeNbbtGL82r+U3J0FWDUnqU6dOtSsWZOZM2eaz1WuXJk2bdowefLkVN3j5ZdfxtnZmQULFgAJI0lDhgzh2rVrGfpc5SSJiEhqxcUbPD1lE2GRdyxylmzi43j52Gbe3roAzxsRABxxL8ekZ3uzq3Q1c7vELKWZXWsqUPqPskVOUkxMDPv376dZs2YW55s1a8bOnTtTuMrSwYMH2blzJ88884zF+Rs3blC6dGlKlCjBiy++yMGDB//zc6Ojo4mKirI4REREUsPWxsTYVt4AFqvg4m1sWVa1Cc/1+5aTg97hpmNeql4KYtHid5nz83jKXz4L3EsGH7/muKbeMpHVgqQrV64QFxeHu7u7xXl3d3fCwsIeem2JEiVwdHSkVq1avPHGG/Tp08f8WqVKlZg3bx6rV69m0aJFODk5Ub9+fU6dOvWfnjt58mTc3NzMR8mSJdP6lkVEJBd7VHL31cHDadh3Ft/XfIG7NrY0DvqT9XMH8dGvX+B+/YqSu63AqjlJACaT5VJHwzCSnHvQtm3buHHjBrt372bkyJE88cQTdOrUCYC6detSt25dc9v69etTs2ZNvvzyS7744ot0P3fUqFEMHTrU/HNUVJQCJRERSZPmPp409fZIsXJ3hHN+xjZ9jXm+LzHij+9p8fdOOh7eQOvjf/BdrZf4pu4rFsndqtydsawWJBUuXBhbW9skozfh4eFJRnke5OXlBUDVqlW5dOkS48aNMwdJD7KxseGpp54yjySl97mOjo44Ojo+8n2JiIg8TGqSu4MLFue1tu9S8/wJRm2Zy1MXjvPG7p/odOg3Ip1H8Ft8F8b9FqTk7gxmtek2BwcHfH19CQgIsDgfEBBAvXr1Un0fwzCIjo5+6OuBgYF4eno+1ueKiIg8TslV7j5QojLtu0yh78tj+KdgCQrejsLrwzFUfq4uT+1aj8mIN7dV5e7Hz6rTbUOHDqVbt27UqlULPz8/Zs2aRUhICAMGDAASprguXLjA/PnzAfj6668pVaoUlSpVAhLqJk2bNo1BgwaZ7zl+/Hjq1q1L+fLliYqK4osvviAwMJCvv/461c8VERHJbInJ3a8tPICJ+yp3m0xsLF+XzeWeYkWek3h8NoVSkZf4Ys00+u5dwUeNerKjTHUMEpLCx685TlNvD029PQZWDZL8/f2JiIhgwoQJhIaG4uPjw7p16yhdujQAoaGhhISEmNvHx8czatQogoODsbOzo1y5cnz00Uf079/f3ObatWv069ePsLAw3NzcqFGjBlu3bqV27dqpfq6IiIg1JCZ3j19z3GIqzeP/p9Ju5KlPw+tl6bVvFQP2/EzVS0H8sGQMW8vUYMozPTjm8YQ5uTu5KT1JG+3dlk6qkyQiIhklpaTsVYEXGLw4EICCtyIZtHMxXQ7+ikN8LABrKjVgWsNuDH2tJa2rF3/ovXKrtHx/K0hKJwVJIiKS2XYFRdBp9m6LcyWvhTF020JaH/8DGwzu2tgS0bE7Hp9MYv0VI8moVG5P8M4WxSRFREQkbZJL7j6X34O3Wg3jhZ7T2VzWF/v4ODx+nEts2bL80+8tboRHWNxDCd6ppyBJREQkm0ipcjfAX0XL0qv9ePZ8twyjTh3sbt9m4K4l/PFtX3rvXYFjbAyg6t1poSBJREQkG3lY5e6ZXWtSp+fL7F74C/3bvmsuG/De5jlsmtWfDoc2YBsfp+rdqWT1itsiIiKSNg+r3A0QfiOa3yrUY+MTdWh35Hfe2v4Dxa9fZur6L+i/dznTGnTl14r1Vb37EZS4nU5K3BYRkazqwQRvx9gYuh5Yyxu7f6Lg7YQN2g97PIHd5MmE+NZj/C8nck1ytxK3RUREcrEHE7yj7RyYU7stDfv/j+n1OnHDIQ/Vwv7Bu2d7XF9sgcfxQIvrldydQCNJ6aSRJBERycrWHw3ltYUHgPuqd5OQ8F3wViQ//7uZ4ou+xyHuLgAbytdlWoOu/F2kjLmdh5sT2995LkdNvWkkSUREJJd7WIL3h/2eJWzcRzTq9y1LqjYlzmRDs1O7Wf/dID5bM43S/15MktwdF2+wKyiCVYEX2BUUkStWxmkkKZ00kiQiItlBaqp3l7tyjqHbF/LCyR0AxJpsWFqtKV/W68jIfk1xtLPJMUUpVXE7EyhIEhGR7Cy56t1Vwv7h7W0Lee70PgCibe053roLfYs14Ypzfou2iRNwM7vWzFaBkoKkTKAgSUREsrO4eIOnp2wiLPIODwYCvuePM2LrfOqcOwrATXsn5tZ6iVm1XybKycXcLjvmLSknSURERB7qYdW7D5TwpmOnyayYPIdDHuVxvnuHgbuWsu2b3ryxcwnO0bcAcnxRSgVJIiIiudRDq3d388Wm+fO07v4p/dqO5mThUrhF32T4tgVs/bYPffYux+luQo7S/UUpc1Jyt6bb0knTbSIiklOklNx9f96STXwcL/61jSHbf6TsvxcBCHcuwFd+HWg5/X2uxZuyRXK3cpIygYIkERHJ6ZLLW7KNj+Plo5t4c+diSkZeAuC2RzEmPPkyP1VtQqztvR3PsmJyt4KkTKAgSUREcoOUilI6xN2l/eEAxgQuJ094GABn83swvX4nVno3It7GFsh6yd1K3BYREZHHIqW8pUIF89HgkzEc2ryP8Y37cjlvfkpfC+PTtZ8RMOcNXjr+Bzbxcdm6KKVGktJJI0kiIpKbPKooZZ6YO3Q/+AsDdi+jwJ3rAJwqVJLP63dmXaX6fN6pZpYoSqnptkygIElERCRpUUqX6Fv02L+GfnuX4xZ9E4C/Cpcm6PVhDLpTmniT5SRWZuctKUjKBAqSREREUi5KmS/6Jj33rabPnytx/f9g6XhRLz6v35kN5euC6V5+UmbmLSknSURERDJFSkUprzs682X9TjQYMIc9XV7nukMevMODmbXiQ9Z8P4TG/+yB/x+nyapFKRUkiYiIyH/ysKKUU/o0JGzYuzQYMIev/Dpw096JqpeCmLPsA1bPf4vn/tlrDpayWlFKTbelk6bbRERELKWmKGXBW5H027ucbgfW4vz/FbsPezzB5/U70/ejQUTeuZuhyd3KScoECpJERERSJ7m8pYK3Ium7dwXdD/xiDpYivasxtHIbfi/3VJKcJXg8yd0KkjKBgiQREZHUS6koZaFbkfTZu4K+h9dhdzth49zEkaVN9wVLjyu5W4nbIiIikqWklLfk4OmO1/++4OCWA8ys8wo37Z2oFvYP3y2bwPyl71s1udvu0U1ERERE/rvmPp409fZIoShlPFMavcrs2m3N03B7SvpYTLvBveTuzKAgSURERDKNrY0Jv3KFkpwvmi9hhOlqXjdzsBRta59iu8yg6TYRERGxutpeBfF0czInaV/N68ZNx7zm100krHKr7VUw0/qkIElERESsLqWilPf/PLaVd4ZX5L6fgiQRERHJEh5WlDKz9na7n3KSREREJMt4WHJ3ZlOQJCIiIllKSsndmU3TbSIiIiLJUJAkIiIikgwFSSIiIiLJUJAkIiIikgwFSSIiIiLJsHqQNGPGDLy8vHBycsLX15dt27al2Hb79u3Ur1+fQoUKkSdPHipVqsRnn31m0Wb27Nk0aNCAAgUKUKBAAZo0acLevXst2owbNw6TyWRxeHh4ZMj7ExERkezJqiUAlixZwpAhQ5gxYwb169fn22+/pUWLFhw/fpxSpUolae/s7MzAgQOpVq0azs7ObN++nf79++Ps7Ey/fv0A2LJlC506daJevXo4OTkxdepUmjVrxrFjxyhevLj5XlWqVGHjxo3mn21tbTP+DYuIiEi2YTIMw7DWw+vUqUPNmjWZOXOm+VzlypVp06YNkydPTtU9Xn75ZZydnVmwYEGyr8fFxVGgQAG++uorunfvDiSMJK1cuZLAwMB09z0qKgo3NzciIyNxdXVN931EREQk86Tl+9tq020xMTHs37+fZs2aWZxv1qwZO3fuTNU9Dh48yM6dO3nmmWdSbHPr1i3u3r1LwYKWG+KdOnWKYsWK4eXlRceOHTl9+nTa34SIiIjkWFabbrty5QpxcXG4u7tbnHd3dycsLOyh15YoUYLLly8TGxvLuHHj6NOnT4ptR44cSfHixWnSpIn5XJ06dZg/fz4VKlTg0qVLTJw4kXr16nHs2DEKFUq+wmd0dDTR0dHmnyMjI4GEiFRERESyh8Tv7VRNpBlWcuHCBQMwdu7caXF+4sSJRsWKFR967enTp43Dhw8bs2bNMgoWLGj8+OOPybabMmWKUaBAAePQoUMPvd+NGzcMd3d345NPPkmxzdixYw1Ahw4dOnTo0JEDjnPnzj00NjAMw7DaSFLhwoWxtbVNMmoUHh6eZHTpQV5eXgBUrVqVS5cuMW7cODp16mTRZtq0aUyaNImNGzdSrVq1h97P2dmZqlWrcurUqRTbjBo1iqFDh5p/jo+P5+rVqxQqVAiT6fFuuhcVFUXJkiU5d+6c8p0ykD7nzKHPOXPoc84c+pwzT0Z91oZhcP36dYoVK/bItlYLkhwcHPD19SUgIIC2bduazwcEBNC6detU38cwDItpMICPP/6YiRMn8ttvv1GrVq1H3iM6OpoTJ07QoEGDFNs4Ojri6OhocS5//vyp7md6uLq66n/CTKDPOXPoc84c+pwzhz7nzJMRn7Wbm1uq2lm1BMDQoUPp1q0btWrVws/Pj1mzZhESEsKAAQOAhNGbCxcuMH/+fAC+/vprSpUqRaVKlYCEuknTpk1j0KBB5ntOnTqV9957jx9//JEyZcqYR6pcXFxwcXEBYNiwYbRq1YpSpUoRHh7OxIkTiYqKokePHpn59kVERCQLs2qQ5O/vT0REBBMmTCA0NBQfHx/WrVtH6dKlAQgNDSUkJMTcPj4+nlGjRhEcHIydnR3lypXjo48+on///uY2M2bMICYmhldeecXiWWPHjmXcuHEAnD9/nk6dOnHlyhWKFClC3bp12b17t/m5IiIiIlYNkgBef/11Xn/99WRfmzdvnsXPgwYNshg1Ss6ZM2ce+czFixentntW4ejoyNixY5NM78njpc85c+hzzhz6nDOHPufMkxU+a6sWkxQRERHJqqy+d5uIiIhIVqQgSURERCQZCpJEREREkqEgKZNt3bqVVq1aUaxYMUwmEytXrnzkNX/88Qe+vr44OTlRtmxZvvnmm4zvaDaX1s95+fLlNG3alCJFiuDq6oqfnx+//fZb5nQ2m0vP3+lEO3bswM7OjurVq2dY/3KK9HzO0dHRjB49mtKlS+Po6Ei5cuX47rvvMr6z2Vh6PucffviBJ598krx58+Lp6UnPnj2JiIjI+M5mY5MnT+app54iX758FC1alDZt2nDy5MlHXpfZ34cKkjLZzZs3efLJJ/nqq69S1T44OJiWLVvSoEEDDh48yLvvvsubb77JsmXLMrin2VtaP+etW7fStGlT1q1bx/79+3n22Wdp1aoVBw8ezOCeZn9p/awTRUZG0r17dxo3bpxBPctZ0vM5d+jQgd9//505c+Zw8uRJFi1aZK4zJ8lL6+e8fft2unfvTu/evTl27Bg//fQTf/7550P3FJWEYOeNN95g9+7dBAQEEBsbS7Nmzbh582aK11jl+/CRG5dIhgGMFStWPLTNiBEjjEqVKlmc69+/v1G3bt0M7FnOkprPOTne3t7G+PHjH3+HcrC0fNb+/v7GmDFjjLFjxxpPPvlkhvYrp0nN5/zrr78abm5uRkREROZ0KgdKzef88ccfG2XLlrU498UXXxglSpTIwJ7lPOHh4QZg/PHHHym2scb3oUaSsrhdu3bRrFkzi3PPP/88+/bt4+7du1bqVc4XHx/P9evXKViwoLW7kiPNnTuXoKAgxo4da+2u5FirV6+mVq1aTJ06leLFi1OhQgWGDRvG7du3rd21HKVevXqcP3+edevWYRgGly5d4ueff+aFF16wdteylcjISICH/ptrje9DqxeTlIcLCwtLsuGvu7s7sbGxXLlyBU9PTyv1LGf75JNPuHnzJh06dLB2V3KcU6dOMXLkSLZt24adnf4JyiinT59m+/btODk5sWLFCq5cucLrr7/O1atXlZf0GNWrV48ffvgBf39/7ty5Q2xsLC+99BJffvmltbuWbRiGwdChQ3n66afx8fFJsZ01vg81kpQNmEwmi5+N/6//+eB5eTwWLVrEuHHjWLJkCUWLFrV2d3KUuLg4OnfuzPjx46lQoYK1u5OjxcfHYzKZ+OGHH6hduzYtW7bk008/Zd68eRpNeoyOHz/Om2++yfvvv8/+/ftZv349wcHB5j1I5dEGDhzI4cOHWbRo0SPbZvb3oX6Ny+I8PDzMm/QmCg8Px87OjkKFClmpVznXkiVL6N27Nz/99BNNmjSxdndynOvXr7Nv3z4OHjzIwIEDgYQvc8MwsLOzY8OGDTz33HNW7mXO4OnpSfHixS12O69cuTKGYXD+/HnKly9vxd7lHJMnT6Z+/foMHz4cgGrVquHs7EyDBg2YOHGiRvsfYdCgQaxevZqtW7dSokSJh7a1xvehgqQszs/PjzVr1lic27BhA7Vq1cLe3t5KvcqZFi1aRK9evVi0aJHyCTKIq6srR44csTg3Y8YMNm3axM8//4yXl5eVepbz1K9fn59++okbN27g4uICwN9//42Njc0jv4wk9W7dupVk2tjW1ha4N8ohSRmGwaBBg1ixYgVbtmxJ1f/71vg+1HRbJrtx4waBgYEEBgYCCUsaAwMDCQkJAWDUqFF0797d3H7AgAGcPXuWoUOHcuLECb777jvmzJnDsGHDrNH9bCOtn/OiRYvo3r07n3zyCXXr1iUsLIywsDBzMqGkLC2ftY2NDT4+PhZH0aJFcXJywsfHB2dnZ2u9jSwvrX+nO3fuTKFChejZsyfHjx9n69atDB8+nF69epEnTx5rvIVsIa2fc6tWrVi+fDkzZ87k9OnT7NixgzfffJPatWtTrFgxa7yFbOGNN95g4cKF/Pjjj+TLl8/8b+79U8FZ4vsww9bNSbI2b95sAEmOHj16GIZhGD169DCeeeYZi2u2bNli1KhRw3BwcDDKlCljzJw5M/M7ns2k9XN+5plnHtpeUpaev9P3UwmA1EnP53zixAmjSZMmRp48eYwSJUoYQ4cONW7dupX5nc9G0vM5f/HFF4a3t7eRJ08ew9PT0+jSpYtx/vz5zO98NpLcZwwYc+fONbfJCt+Hpv/vrIiIiIjcR9NtIiIiIslQkCQiIiKSDAVJIiIiIslQkCQiIiKSDAVJIiIiIslQkCQiIiKSDAVJIiIiIslQkCQiIiKSDAVJIiIiIslQkCQiIiKSDAVJIiIiIslQkCQiAly+fBkPDw8mTZpkPrdnzx4cHBzYsGGDFXsmItaiDW5FRP7funXraNOmDTt37qRSpUrUqFGDF154gc8//9zaXRMRK1CQJCJynzfeeIONGzfy1FNPcejQIf7880+cnJys3S0RsQIFSSIi97l9+zY+Pj6cO3eOffv2Ua1aNWt3SUSsRDlJIiL3OX36NBcvXiQ+Pp6zZ89auzsiYkUaSRIR+X8xMTHUrl2b6tWrU6lSJT799FOOHDmCu7u7tbsmIlagIElE5P8NHz6cn3/+mUOHDuHi4sKzzz5Lvnz5+OWXX6zdNRGxAk23iYgAW7Zs4fPPP2fBggW4urpiY2PDggUL2L59OzNnzrR290TECjSSJCIiIpIMjSSJiIiIJENBkoiIiEgyFCSJiIiIJENBkoiIiEgyFCSJiIiIJENBkoiIiEgyFCSJiIiIJENBkoiIiEgyFCSJiIiIJENBkoiIiEgyFCSJiIiIJENBkoiIiEgy/g9zu4bECiH06gAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"ua, ub = 1 / 2, 1 / 3\n",
"a, b = 1, 2\n",
"M = 49\n",
"\n",
"\n",
"def f2(x):\n",
" return -2 / np.power((x + 1), 3)\n",
"\n",
"\n",
"def u2(x):\n",
" return 1 / (x + 1)\n",
"\n",
"\n",
"x, U_app = solution_approchée(f2, M, a, b, ua, ub)\n",
"plt.figure()\n",
"plt.scatter(x, U_app, label=\"$A_M U_h = h² F$\")\n",
"plt.plot(x, u2(x), label=\"Solution exacte\", color=\"red\")\n",
"plt.legend()\n",
"plt.ylabel(\"f(x)\")\n",
"plt.xlabel(\"x\")\n",
"plt.title(\"$-u''=f(x)$\")"
]
},
{
"cell_type": "code",
"execution_count": 317,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Différence en valeur absolue entre la solution exacte et la solution approchée')"
]
},
"execution_count": 317,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"H, E = [], []\n",
"for k in range(2, 12):\n",
" M = 2**k\n",
" h = (b - a) / (M + 1)\n",
"\n",
" x, U_app = solution_approchée(f2, M, a, b, ua, ub)\n",
"\n",
" e = np.abs(u2(x) - U_app)\n",
" plt.plot(x, e, label=f\"{h}\")\n",
" E.append(np.max(e))\n",
" H.append(h)\n",
"\n",
"plt.xlabel(\"$h$\")\n",
"plt.ylabel(r\"$\\max_{j=0,\\dots,M+1}|u(x_j)-u_j|$\")\n",
"plt.legend(fontsize=7)\n",
"plt.title(\n",
" \"Différence en valeur absolue entre la solution exacte et la solution approchée\",\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 318,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Erreur globale en fonction de $h$')"
]
},
"execution_count": 318,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"H, E = np.array(H), np.array(E)\n",
"plt.figure()\n",
"plt.plot(H, E / H, label=\"$E_h / h$\")\n",
"plt.plot(H, E / H**2, label=\"$E_h / h^2$\")\n",
"plt.legend()\n",
"plt.xlabel(\"$h$\")\n",
"plt.ylabel(\"Erreur globale\")\n",
"plt.title(\"Erreur globale en fonction de $h$\")"
]
},
{
"cell_type": "code",
"execution_count": 319,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)')"
]
},
"execution_count": 319,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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9RkBZWVnpHdQlJSUqLCxMhYSE6MpGjRqltFqtSk1N1Vv+/vvvV9bW1urChQt6n7emyQSg1q5dW6NYK0smrlZWVqaKi4vVxo0bFaD27dtX7foqYr32bzB48GAFqA8++ECvvGXLlqp169a614sXLza4yCml1K5duxSgPvnkE11ZREREpX/Diu/l2hPbN998o7tgK6XU+fPnlZWVlUG91NRUpdVq1ZgxY5RS5Tcb3t7eqnXr1qqsrExXLyUlRZmbm+vtL7WJvzITJ040WL64uFi5ubkpQJcwKaVUZmamMjU1Vc8884yurKb7VE2/o5qIjIxUgwcPrrZOo0aNVKNGjVR+fn6VdSr2xXfffVev/PHHH1eWlpa6737btm0GSahSSqWlpSkrKyv1z3/+U1dWcTxcnXBVfG9WVlZ6icPevXuvezEvKSlRRUVFKjQ0VD399NPVfuYbiXPHjh16dcPDw1Xfvn3rZDsXL15U9vb2qmvXrnr78bUq9sFvvvlGr7x///6qSZMmute12ddrkkxMnTpV2draquPHj+vVmzt3rgL0fgyqzLXb+PTTTyv9HO+8844C1OrVq5VSSq1YsUIB6n//+59evbfeessgxmtVtT9UHF/dunUzWKay8/YTTzxR5XkYUB4eHionJ0dXlp6erkxMTNRbb72lK6s4fq7dD1q2bKkA9d133+nKKs4pQ4cO1ZVVlhB06NBBeXt76x23OTk5ytnZ+YaTib59+ypfX1+VnZ2tV2/atGnK0tLS4Hp/rZkzZypTU1O1YcOGauspZZhMvPDCC5UeZ4899pjSaDTq0KFDSimlPv74YwWoX3/9Va/e1KlTDT7nY489pqysrAyOqYrvpKp/mzdvNojXx8dHjRw5strPVF/nlYrlIyIi9MpqelwpVfN9995771WOjo665KAyy5YtqzKJvPa+bdWqVZVeS5YuXaoA9dlnn+nKAgIClKWlpd55Jz8/Xzk7O6upU6dWGY9SSv3vf/9TgPrxxx/1yidPnmywn4SFhalWrVoZJJIDBgxQXl5eqrS0tNptXXsc1fRa/9xzzymNRmNw/uzbt6/B93n//fersLAwg21X3Ndd/aOTUkq9++67ClCnT5/WKy8qKlIajUY9//zz1X6ma91QN6cFCxawa9cuvX+VPbx077334uTkVOk6HnroIb3Xv/32GyUlJUyYMIGSkhLdP0tLS7p3735TI0UNHDgQc3PzGtfv1asXHh4eutempqaMHDmSo0ePcuLECQDWrVtHr1698PPz01s2KiqKvLw8tm3bdkOxOjk53VS/y6SkJMaMGYOnpyempqaYm5vTvXt3gEq7/1RmwIABeq+bNm0KwAMPPGBQfvz4cd3rX375BUdHRx588EG9v2HLli3x9PSs1d9w4MCBeq+bN28OoNvetm3byM/PN3iA28/Pj3vvvZe1a9cCcOjQIU6dOsWYMWP0mvYDAgLo3Lmz3rJ1Eb9Go6F///6612ZmZoSEhODl5UWrVq105c7Ozri7u+t9f7Xdp673HdVE+/bt+fXXX3nhhRfYsGED+fn5eu8fPnyYY8eO8fDDD2NpaXnd9VUWU0FBARkZGUD5d6zRaBg3bpzed+zp6UmLFi0MvmMvLy/atGmje13xvbVs2RJvb29decU+evVnLykp4c033yQ8PBwLCwvMzMywsLDgyJEj1z0Wahunp6cn7du3N/js1/tb1HQ7W7duJScnh8cff/y6z5ZpNBoefPDBamOpy2O1Yn09e/bE29tbb333338/ABs3bqzV+tatW4eNjQ3Dhg3TK6843iuO74r1jhgxQq/e6NGjDdZZ2/3h2mvUjerZsyd2dna61x4eHgbHfoXKzr0ajUb3PcKVc0p1+9alS5fYtWsXQ4cO1Ttu7ezsDPaNmiooKGDt2rUMGTIEa2trvb9z//79KSgoYPv27dWu47XXXqOkpER3TaqNdevWER4ebnCcRUVFoZRi3bp1QPk+YWdnpzc6E1S+T5w6dQo3N7cqj6knn3zS4F5n165dtGzZ0qCuu7s7J0+erPYz1Nd5pSo1Pa4qXG/fzcvLY+PGjYwYMQI3N7cbiqmyGK+OqcLw4cOxsbExiLFly5b4+/vrXltaWtK4cePrfkfr16/Hzs7O4Jp17QP3R48e5eDBg7pnT67d70+fPl3r7sU1vdZv3LiRyMhIg8GNqtqX3d3dq9xmTe8XzM3NcXR0vO6+fK0begC7adOmNXoA28vLq8bvnTlzBoB27dpVWt/E5MYf76gujsp4enpWWZaZmYmvry+ZmZmVrrfiBiczM/MGIq19rFfLzc3lnnvuwdLSkjfeeIPGjRtjbW1NWloaQ4cONbhRrMq1oz5YWFhUWV5QUKB7febMGS5cuKCrf63aDBvq4uKi97rigfmKz1Dx/Vb1N/j999/16lX1N726b3NdxG9tbW1w021hYVHpSBrXfn+13aeu9x3VxH/+8x98fX1ZunQp77zzDpaWlvTt25f33nuP0NBQXf/5q0cvqc71Yjpz5gxKKb1k/WrBwcF6r6v63qraR6/+Pp955hk+/vhjnn/+ebp3746TkxMmJiY88sgj1/2OahvntZ8byj97XW2nNn+HyvZBrVZ7y47VivX9/PPPVf5oU9v1ZWZm4unpaXCT5+7ujpmZme5YyMzMxMzMzGB/qOz7rO3+cDPn4qvVZt+obL+u6pySk5NT5TbPnz9PWVlZtdey2srMzKSkpISPPvqIjz76qNI6t3Jo6MzMzEqHEL32/JiZmVnp37+ysorBX6ri6+tb48FmLC0tb5vzSlVqelzVdPvnz5+ntLS0xteHmsZoZmZmkJxoNBo8PT1rHWN126ns73Dt8VFxb/rss8/y7LPPVrquGzm/1eRan5mZWelomFXty1XtV1C7+4Wa7MvXuqFkoqaq+wXt2vcq5iFYvnw5AQEB1a7X0tLS4KFOqPoPWttRoip7AKeirOIP4uLiwunTpw3qVTzQUvF5Kk5U1z7cVFexXm3dunWcOnWKDRs26P3yc+1DS7dKxYM91z4IW+HqXzhuVsXfoaq/QcX3X1Gvur9phfqMvzI13afqko2NDTNnzmTmzJmcOXNG10rx4IMPcvDgQd0JvaJF7ma5urqi0WjYvHlzpSOq1eUoa1999RUTJkzgzTff1Cs/d+4cjo6Ot0WcNd3Orfg71OW+7urqSvPmzZkzZ06l71/dilQTLi4u7NixA6WU3jkxIyODkpISveO7pKSErKwsvRvxyo732u4Pt/McPtfj5OSERqOp0XmvqmvUtTdtTk5OmJqaMn78eJ544olKt1vZjU9dqen50cXFhZ07dxrUq+y7cHV15a+//qqT+LKysq47X0J9nv8qU9PjqqacnZ0xNTWts/NSRYwlJSWcPXtWL6FQSpGenl7lD843sp2a7CcV38mLL77I0KFDK11XbYdRrc2+XJHMVBdjxTJZWVm1iqMq58+fr/W+cNvMgN23b1/MzMw4duwYbdu2rfRfhcDAQA4fPqx38svMzGTr1q11EsvatWv1/oClpaUsXbqURo0a6TLwXr166W7er7ZgwQKsra11w8lVnFz279+vV++nn36qk1ivVnFyuPaENG/evDrfVmUGDBhAZmYmpaWllf79rj7gbubXFYBOnTphZWXFV199pVd+4sQJXRMilB/kXl5eLF68GKWUrt7x48cN9pfaxH8r1HSfulU8PDyIiopi9OjRHDp0iLy8PBo3bkyjRo2YP3++wc3GjRgwYABKKU6ePFnpd9ysWbM6+CTlNBqNwbGwYsWKGjXf1lecNd1O586dcXBw4NNPP9Xbj29mu3W5rw8YMEA3FGVl66ttMtGrVy9yc3P54Ycf9MorRmGrOL4rfjRZunSpXr3KRt+7mf2hOjfSInir2djY0L59e7777ju9FqmLFy/y888/69X18PDA0tLS4Br1448/6r22tramZ8+e7Nmzh+bNm1f6d67sV+K60qtXLxITEw1u/hcsWIBGo6Fnz55A+T5x8eJFfv31V716le0TYWFhZGZmVvrjZG2UlJSQlpZ23bm26vP8V5maHlc1ZWVlRffu3Vm2bFm1v87X5hipiOHaa/u3337LpUuXah1jVXr27MnFixcN7sW+/vprvddNmjQhNDSUffv2VXlvWtsfX2p6re/evTvx8fEkJibq1atqX65sBMDaOnXqFAUFBbWeN+6GWibi4+MrHe6vUaNGN9xvLjAwkFmzZvHyyy+TlJREv379cHJy4syZM+zcuVP3CyqUD101b948xo0bx+TJk8nMzOTdd9/F3t7+hrZ9LVdXV+69915effVVbGxs+OSTTzh48KDeH/D111/X9RN+7bXXcHZ2ZtGiRaxYsYJ3330XBwcHoLzbVpMmTXj22WcpKSnBycmJ77//ni1bttRJrFfr3LkzTk5OPProo7z++uuYm5uzaNEi9u3bV+fbqsyoUaNYtGgR/fv358knn6R9+/aYm5tz4sQJ1q9fz6BBgxgyZAgAzZo1Y8mSJSxdupTg4GAsLS1rdSJ1dHTk1Vdf5aWXXmLChAmMHj2azMxMZs6ciaWlJa+//jpQ3j1u9uzZPPLIIwwZMoTJkydz4cIFZsyYYdCcWZv4b4Wa7lN1qUOHDgwYMIDmzZvj5OTEgQMHWLhwIZ06ddLNb/Lxxx/z4IMP0rFjR55++mn8/f1JTU3lt99+Y9GiRbXaXpcuXZgyZQrR0dH8+eefdOvWDRsbG06fPs2WLVto1qwZjz32WJ18tgEDBhAbG0tYWBjNmzdn9+7dvPfeezVqkq+vOGu6HVtbW95//30eeeQRevfuzeTJk/Hw8ODo0aPs27eP//73v7Xabl3v67NmzeL333+nc+fO/N///R9NmjShoKCAlJQUVq5cyaefflqrrhATJkzg448/ZuLEiaSkpNCsWTO2bNnCm2++Sf/+/enduzcA/fr1o0uXLkyfPp2cnBzatGnDtm3bdDdHV3ePvZn9oToV56133nmH+++/H1NTU5o3b15lF7L6Mnv2bPr168d9993H9OnTKS0t5Z133sHGxkbvF8yKPvwVk5u1aNGCnTt3GtxUAfz73/+ma9eu3HPPPTz22GMEBgZy8eJFjh49ys8//6zr716VWbNmMWvWLNauXVvr5yaefvppFixYwAMPPMCsWbMICAhgxYoVfPLJJzz22GM0btwYgIkTJ/Lhhx8ybtw43njjDUJCQvj111/57bffAP19okePHiil2LFjB3369DHYZmpqaqXPgbi5uenNj7B//37y8vJ0CU1V6vP8V5maHle18cEHH9C1a1c6dOjACy+8QEhICGfOnOGnn35i3rx52NnZERkZCcBnn32GnZ0dlpaWBAUFVZp83nffffTt25fnn3+enJwcunTpwv79+3n99ddp1arVTQ/jW2HChAl8+OGHTJgwgTlz5hAaGsrKlSt1+8nV5s2bx/3330/fvn2JiorCx8eHrKwsDhw4wF9//cWyZctqte2aXuufeuop5s+fz/3338+sWbPw8PDg66+/5uDBg4Dhvjx//nwOHz6sOxZuRMX+fr192UBtntaubjQnQH3++ee6uoB64oknqlzHrl27Kt3GDz/8oHr27Kns7e2VVqtVAQEBatiwYWrNmjV69eLi4lTTpk2VpaWlCg8PV0uXLq1yNKf33nuvxp+xIu5PPvlENWrUSJmbm6uwsDC1aNEig7p///23evDBB5WDg4OysLBQLVq0qHREjMOHD6s+ffooe3t75ebmpv7xj3/oRiG5djSna0dfqE5lozlt3bpVderUSVlbWys3Nzf1yCOPqL/++qtGQ5hV9bep2M7Zs2f1yidOnKhsbGz0yoqLi9XcuXNVixYtlKWlpbK1tVVhYWFq6tSp6siRI7p6KSkpqk+fPsrOzk4Bur9bxWgpVw/Dq1TVI4588cUXqnnz5srCwkI5ODioQYMGVTpyzBdffKFCQ0OVhYWFaty4sZo/f77B/lKb+CtT2fehVNV/14CAAPXAAw/oldVkn6rtd1SdF154QbVt21Y5OTkprVargoOD1dNPP63OnTunV2/btm3q/vvvVw4ODkqr1apGjRrpjYBT1T5S1Whm8+fPVx06dFA2NjbKyspKNWrUSE2YMEFv5KbafG9KGZ5zzp8/rx5++GHl7u6urK2tVdeuXdXmzZurHA2uMjcTZ2X7181sRymlVq5cqbp3765sbGyUtbW1Cg8P1xtKsKp9sLJzRU339ZqM5qSUUmfPnlX/93//p4KCgpS5ublydnZWbdq0US+//LLKzc2t9vNXto3MzEz16KOPKi8vL2VmZqYCAgLUiy++qDc0pFJKZWVlqejoaOXo6Kisra3Vfffdp7Zv364A9e9//1tXr6b7Q1XH19XvXX3eLiwsVI888ohyc3NTGo1Gb3+v6jp47UhFtTnHVnxfV+9zVR37P/30k+786O/vr95+++1K94Xs7Gz1yCOPKA8PD2VjY6MefPBBlZKSUunfOTk5WU2aNEn5+Pgoc3Nz5ebmpjp37qzeeOMNgzivdTNDwyql1PHjx9WYMWOUi4uLMjc3V02aNFHvvfeewWg6qampaujQocrW1lbZ2dmphx56SK1cudJg9J7S0lIVGBhoMNLN9UZzGjt2rF79V199Vbm6uhrsm1Wpj/NKVcvX9Liq6b6rlFKJiYlq+PDhysXFRbevRUVF6a3zX//6lwoKClKmpqZ6+2plnyc/P189//zzKiAgQJmbmysvLy/12GOPqfPnzxvEUtm1oKbn+BMnTqiHHnpIbz/ZunVrpcfSvn371IgRI5S7u7syNzdXnp6e6t5771WffvrpdbdT2XFU0/vH+Ph41bt3b2VpaamcnZ3Vww8/rOLi4gxG6MzOzla2trYGo2BVdV9X2blMKaXGjx+vmjVrdt3PZPAZa71EA1fVASSEEOLOsGjRIgWoP/74w9ih3HauN6R4Q1Uxj1VaWppe+dy5c5WTk9N15xGqSklJiQoMDFQvvfRSXYQpxHVNnjxZ2draqsLCQr3yadOmqaZNm1Y7fHh1srOzlY2Njd7wuzV1Sx/AFkIIIW6lxYsXc/LkSZo1a4aJiQnbt2/nvffeo1u3bgbDP4u7Q0W3v7CwMIqLi1m3bh3/+c9/GDdunEG3tieeeIL//ve/fPzxx1WO1lOdr776itzcXJ577rk6iV2Iq82aNQtvb2+Cg4PJzc3ll19+4YsvvuCVV14x6Er5yiuvsGDBAr799luD4X9r4sMPP8Tf35/o6OhaLyvJhBANkFKK0tLSauuYmpre0SPWCAHlI08tWbKEN954g0uXLuHl5UVUVBRvvPGGsUMTRmJtbc2HH35ISkoKhYWF+Pv78/zzz/PKK68Y1LW0tGThwoXs2bPnhrZVVlbGokWLrjtCnBA3wtzcnPfee48TJ05QUlJCaGgoH3zwAU8++aRBXQ8PDxYtWsT58+dvaFv29vbExsZiZlb71ECjVB0MDSKEuK3ExsZe99eF9evX06NHj/oJSAghhBANkiQTQjRAmZmZJCcnV1unSZMmt3zuDCGEEEI0bJJMCCGEEEIIIW7IbTNpnRBCCCGEEOLOIg9gi5tWVlbGqVOnsLOzkwd6hRBCiDuEUoqLFy/i7e2tNwmaELUhyYS4aadOncLPz8/YYQghhBDiBqSlpd30bPDi7iXJhLhpFQ/xpqWlYW9vb+RohBBCCFETOTk5+Pn5yWAc4qZIMiFuWkXXJnt7e0kmhBBCiDuMdFEWN0M6yAkhhBBCCCFuiCQTQgghhBBCiBsiyYQQQgghhBDihsgzE6JelJWVUVRUZOwwxB3M3NwcU1NTY4chhBBCiKtIMiFuuaKiIpKTkykrKzN2KOIO5+joiKenpzwsKIQQQtwmJJkQt5RSitOnT2Nqaoqfn59MiiNuiFKKvLw8MjIyAPDy8jJyREIIIYQASSbELVZSUkJeXh7e3t5YW1sbOxxxB7OysgIgIyMDd3d36fIkhBBC3AbkZ2JxS5WWlgJgYWFh5EhEQ1CRkBYXFxs5EiGEEEKAJBOinkgfd1EXZD8SQgghbi+STAghhBBCCCFuiCQTQgghhBBCiBsiyYQQQgghhBDihkgyIe4YGTkFfPj7YTJyCowdigGlFCUlJQblt3KiPnkIWQgh7gKFuXDyL2NHIUSVJJkQd4yMi4X8e+0RMi4W1sv2lFK8++67BAcHY2VlRYsWLVi+fDkAGzZsQKPR8Ntvv9G2bVu0Wi2bN2+mR48eTJs2jWeeeQZXV1fuu+8+ABITE+nfvz+2trZ4eHgwfvx4zp07p9tWYGAg//rXv/S237JlS2bMmKF7rdFo+PTTTxk0aBA2Nja88cYbt/w7EEIIUc+yT8Dfy2Hlc/DpPfC2H8TcDyW37scpIW6GzDMh6pVSivzi0htatuDycgXFpeQVGbYCXI+VuWmtRgN65ZVX+O677/jf//5HaGgomzZtYty4cbi5uenq/POf/2Tu3LkEBwfj6OgIQFxcHI899hh//PGHbtK+7t27M3nyZD744APy8/N5/vnnGTFiBOvWravVZ3j99dd56623+PDDD2WeBSGEuNOVlkBGAqTugLTt5f/NOWFYz8YNstPApVH9xyjEdUgyIepVfnEp4a/9dlPrGPbpthtaLnFWX6wtarbLX7p0iQ8++IB169bRqVMnAIKDg9myZQvz5s1jypQpAMyaNUvX+lAhJCSEd999V/f6tddeo3Xr1rz55pu6svnz5+Pn58fhw4dp3LhxjT/DmDFjmDRpUo3rCyGEuI0U5MCJXZC2o/zfiT+hKFe/jsYUPCPBryP4dyj/r4OPceIVogYkmRCiEomJiRQUFBgkCkVFRbRq1Ur3um3btgbLXlu2e/du1q9fj62trUHdY8eO1SqZqGx7QgghbkNKlbcmXN3qkJEAqky/ntYefNuBf0fwaw8+bUFreL0Q4nYlyYSoV1bmpiTO6lvj+mcvFnL28jMSiadzeO3HBGYNiiDcyx4ANzstbnbaGm+7psrKyk/2K1aswMdH/xchrVbLsWPHALCxsTFY9tqysrIyHnzwQd555x2Dul5eXgCYmJiglNJ7r7IHrCvbnhBCiNtAaQmc+Vs/ebh4yrCeo79+q4N7UzCRbqviziXJhKhXGo2mxl2NAAJczAhwKb+BtrycDLT2dyLSx+GWxFchPDwcrVZLamoq3bt3N3i/IpmoidatW/Ptt98SGBiImVnln93NzY3Tp0/rXufk5JCcnFz7wIUQQtSPguzyLksVycOJ3VB8Sb+OxhS8musnD/ZexolXiFtEkgkhKmFnZ8ezzz7L008/TVlZGV27diUnJ4etW7dia2tLQEBAjdf1xBNP8PnnnzN69Giee+45XF1dOXr0KEuWLOHzzz/H1NSUe++9l9jYWB588EGcnJx49dVX5QFrIYS4XSgFF45f02UpEdBvUUbrUN5Vyb8D+HUAnzZgIS3KomGTZELcMdzttDzZKxT3GnZrulmzZ8/G3d2dt956i6SkJBwdHWndujUvvfSSrhtUTXh7e/PHH3/w/PPP07dvXwoLCwkICKBfv36YmJSPzvziiy+SlJTEgAEDcHBwYPbs2dIyIYQQxlJaDOn79ZOH3HTDek6B+q0ObmFgIqPui7uLRl3bUVuIWsrJycHBwYHs7Gzs7e313isoKCA5OZmgoCAsLS2NFKFoKGR/EkLcEvkXLndZ2l4+ytLJ3VCcp1/HxAy8WlyVPHQAO0+jhFtXqrt+C1FT0jIhhBBCiLuHUnA++XKrw+V/GQcw6LJk6VieMPi1Lx9pybs1WFgbI2IhbmuSTAghhBCi4SoputxlaXt5l6W0nZB7xrCec7B+lyXXxtJlSYgakGRCCCGEEA1HXpZhl6WSAv06Jubg3bK85cG/Y/l/bd2NEq4QdzpJJhqIlJQUZs+ezbp160hPT8fb25tx48bx8ssvY2FhUeVyUVFRxMXF6ZV16NCB7du33+qQhRBCiJujFGQlXWl1SN0B5w4Z1rNyvqbLUiswt6r/eIVogCSZaCAOHjxIWVkZ8+bNIyQkhPj4eCZPnsylS5eYO3dutcv269ePmJgY3evqkg8hhBDCaEoK4fS+K60OaTvg0lnDei4h13RZCgWNpv7jFeIuIMlEA9GvXz/69eunex0cHMyhQ4f43//+d91kQqvV4ul5Z49IIYQQogG6lHk5abj8rMPJv6C0UL+OqUV5S8PVXZZsXI0TrxB3IUkmGrDs7GycnZ2vW2/Dhg24u7vj6OhI9+7dmTNnDu7uVfcdLSwspLDwysk8JyenTuIVQghxF1MKMo/qd1nKPGJYz9pFv9XBuyWY1c/8Q0IIQ5JMNFDHjh3jo48+4v3336+23v3338/w4cMJCAggOTmZV199lXvvvZfdu3ej1VZ+cn7rrbeYOXPmrQhbCCHE3aK4AE7tudJdKW0H5GUa1nNtfFWrQ0dwaSRdloS4jcikdbe5GTNmXPfGfdeuXbRt21b3+tSpU3Tv3p3u3bvzxRdf1Gp7p0+fJiAggCVLljB06NBK61TWMuHn5yeT1olbTvYnIe5gl87ptzqc3gulRfp1zCzL53OomBTOrwNYX7+FXdwYmbRO1AVpmbjNTZs2jVGjRlVbJzAwUPf/p06domfPnnTq1InPPvus1tvz8vIiICCAI0cqaVq+TKvVVtlq0ZD16NGDli1b8q9//eum1hMYGMhTTz3FU089VSdxCSHEbaesrLyLUsWD0qnbIeuYYT0bN/1WB68WYCaDgAhxJ5Fk4jbn6uqKq2vNHiQ7efIkPXv2pE2bNsTExGByA5PtZGZmkpaWhpeXV62XFTWza9cubGxsdK81Gg3ff/89gwcPNl5QtTBjxgx++OEH9u7de9PrmjNnDitWrGDv3r1YWFhw4cKFm16nEMIIivPLH46uaHU4sRPyzxvWc2t6ZXhWvw7lE8VJlyUh7miSTDQQp06dokePHvj7+zN37lzOnr0yVN7VIzWFhYXx1ltvMWTIEHJzc5kxYwYPPfQQXl5epKSk8NJLL+Hq6sqQIUOM8THuaEVFRTUaVtfNza0eorkzFBUVMXz4cDp16sSXX35p7HCEEDWVm6Hf6nB6H5QV69cxswKfNlcelPZrB1ZOxolXCHHLyDzxDcTq1as5evQo69atw9fXFy8vL92/qx06dIjs7GwATE1N+fvvvxk0aBCNGzdm4sSJNG7cmG3btmFnZ2eMj3HbuHTpEhMmTMDW1hYvL69KH2QPDAzkjTfeICoqCgcHByZPngzAt99+S0REBFqtlsDAQINlAwMDdV2lKrqoDRkyBI1Go9dl7eeff6ZNmzZYWloSHBzMzJkzKSkpqTLmqKgoBg8ezMyZM3F3d8fe3p6pU6dSVHSlT7JSinfffZfg4GCsrKxo0aIFy5cv172/YcMGNBoNa9eupW3btlhbW9O5c2cOHSqfBCo2NpaZM2eyb98+NBoNGo2G2NhYoHz0sClTpui2fe+997Jv375qv+eZM2fy9NNP06xZs2rrCSGMqKwMziTCnzHw/aPw75YwNxS+GQ/b/gsn/yxPJGw9oOlA6PsmPLIOXkiF6BXQ6zVo3EcSCSEaKGmZaCCioqKIioq6br2rn7e3srLit99+u4VRVRoAFOfV7zYrmFvXuDn9ueeeY/369Xz//fd4enry0ksvsXv3blq2bKlX77333uPVV1/llVdeAWD37t2MGDGCGTNmMHLkSLZu3crjjz+Oi4tLpX+fXbt24e7uTkxMDP369cPU1BSA3377jXHjxvGf//yHe+65h2PHjjFlyhQAXn/99SrjXrt2LZaWlqxfv56UlBSio6NxdXVlzpw5ALzyyit89913/O9//yM0NJRNmzYxbtw43Nzc6N69u249L7/8Mu+//z5ubm48+uijTJo0iT/++IORI0cSHx/PqlWrWLNmDQAODg4opXjggQdwdnZm5cqVODg4MG/ePHr16sXhw4drNESxEOI2UZQHJ3frd1kqyL6mkgbcw/UflHYKlC5LQtyFJJkQ9as4D970Ns62XzoFFjbXrZabm8uXX37JggULuO+++wCIi4vD19fXoO69997Ls88+q3s9duxYevXqxauvvgpA48aNSUxM5L333qs0majo8uTo6KjXHW3OnDm88MILTJw4ESifhHD27Nn885//rDaZsLCwYP78+VhbWxMREcGsWbN47rnnmD17Nvn5+XzwwQesW7eOTp066da7ZcsW5s2bp5dMzJkzR/f6hRde4IEHHqCgoAArKytsbW0xMzPTi3fdunX8/fffZGRk6B7Onzt3Lj/88APLly/XJUJCiNvQxXT9Lkvp+6HsmlZQc+vLXZYuPyjt2xasHI0SrhDi9iLJhBDXOHbsGEVFRbobbgBnZ2eaNGliUPfqIXkBDhw4wKBBg/TKunTpwr/+9S9KS0t1LQ/Xs3v3bnbt2qVrUQAoLS2loKCAvLw8rK2tK12uRYsWeu916tSJ3Nxc0tLSyMjIoKCgQJcgVSgqKqJVq1Z6Zc2bN9f9f0VXuYyMDPz9/auMNzc3FxcXF73y/Px8jh2rZAQXIYRxlJXB2QP6ycOF44b17Lz0Z5T2bAam5vUfrxDitifJhKhf5tblLQTG2nYN1GbqlatHZapYVnNNM/+NTOVSVlbGzJkzK53r40bmV9BoNJSVlQGwYsUKfHx89N6/dqhfc3NzvWUrYqouXi8vLzZs2GDwnqOjY63jFULUkaJLcOLPK4nDiT+hsJIuSx6RVx6U9u8ADn7SZUkIUSOSTIj6pdHUqKuRMYWEhGBubs727dt1v8SfP3+ew4cP63UFqkx4eDhbtmzRK9u6dSuNGzeuslXC3Nyc0tJSvbLWrVtz6NAhQkJCahX7vn37yM/Px8rKCoDt27dja2uLr68vTk5OaLVaUlNTr/s5qmNhYVFpvOnp6ZiZmek9RC6EqGc5p67psvQ3KP3jFXOb8m5KFa0Ovu3AUiYsE0LcGEkmhLiGra0tDz/8MM899xwuLi54eHjw8ssv12jejunTp9OuXTtmz57NyJEj2bZtG//973/55JNPqlwmMDCQtWvX0qVLF7RaLU5OTrz22msMGDAAPz8/hg8fjomJCfv37+fvv//mjTfeqHJdRUVFPPzww7zyyiscP36c119/nWnTpmFiYoKdnR3PPvssTz/9NGVlZXTt2pWcnBy2bt2Kra2t7vmM6wkMDCQ5OZm9e/fi6+uLnZ0dvXv3plOnTgwePJh33nmHJk2acOrUKVauXMngwYMNuoNVSE1NJSsri9TUVEpLS3VzV4SEhGBra1ujeIS4a5WVQkbiVcnDDshONaxn76v/oLRHJJjK5f9OsTdjLweyDjA6bLSxQxGiUnI2EaIS7733Hrm5uQwcOBA7OzumT5+uG1K3Oq1bt+abb77htddeY/bs2Xh5eTFr1qxqR9p6//33eeaZZ/j888/x8fEhJSWFvn378ssvvzBr1izeffddzM3NCQsL45FHHql2+7169SI0NJRu3bpRWFjIqFGjmDFjhu792bNn4+7uzltvvUVSUhKOjo60bt2al156qaZfDQ899BDfffcdPXv25MKFC8TExBAVFcXKlSt5+eWXmTRpEmfPnsXT05Nu3brh4eFR5bpee+014uLidK8rnt1Yv349PXr0qHFMQtwVCi8adlkquqhfR2NyuctSxyvPPDgYDh4hbm9lqoyNaRuJSYhhT8YezEzMuNfvXjxsqj6fCmEsGnUjHbqFuEpOTg4ODg5kZ2djb6/fVF5QUEBycjJBQUE31Ndf1FxUVBQXLlzghx9+MHYot4zsT+Kukn1Cv8vSmXhQ1zy7ZGF3TZeltqC9u+cJupMVlRbxS9IvxCbEkpydDIC5iTkDGw3ksRaP1XkyUd31W4iakpYJIYQQwthKSyAjobyrUsX8DjknDOs5+F/psuTfsXyuB5OajRInbl85RTksO7SMRQcWcTb/LAB25naMaDKCsU3H4mbtZuQIhaiaJBNCCCFEfSvIgRO7ylsd0nZc7rKUq19HY1o+JOvVXZbsjTRPj7gl0i+ls+jAIpYdXsal4ksAuFu7MyF8Ag+FPoSthTw7Jm5/kkwI0UDExsYaOwQhRGWUguw0/VaHjATDLktaB/Brd+VBaZ82oJWbyYbo6PmjxCbEsiJ5BSWXJwgMcQwhOjKa+wPvx1zm9BB3EEkmhBBCiLpUWgJn/tZPHi5WMr+OY4B+q4NbmHRZasCUUuw+s5uYhBg2ndikK2/r0ZboyGju8bnHYJ4iIe4EkkwIIYQQN6MgG9J2XU4ctsPJ3VCcp1/HxAw8m+snD3aexolX1KvSslLWp60nJj6G/ef2A6BBQ++A3kRHRNPMrZmRIxTi5kgyIYQQQtSUUnDh+DVdlhKBawZGtHS40l2posuShbVRQhbGUVBSwE/HfmJB4gKO5xwHwMLEgsEhg5kQMYEA+wAjRyhE3ZBkQgghhKhKaTGk79dPHnLTDes5Bem3Org2gRpMdCkanuzCbJYeWsqiA4vIKsgCwN7CnlFhoxgdNhpXK1cjRyhE3ZJkQgghhKiQf/6qLks7yrssleTr1zExB68WV5IHvw5gJ5OJ3e1O555mQeICvj3yLfmX9xkvGy8mhE9gaOhQrM2lZUo0TJJMCCGEuDspBeeT9Vsdzh4wrGfldE2XpdZgblX/8Yrb0qGsQ8QkxLAqeRWlqhSAJk5NiI6Mpk9gH8xNZGQm0bBJMiFEDfXo0YOWLVvyr3/966bWExgYyFNPPcVTTz1VJ3EJIWqopAhO7ytPHNJ2lCcPlzIM6zk30u+y5BIqXZaEHqUUO9N3EhMfwx+n/tCVd/TqSHRENJ28O8nITOKuIcmEEPVs165d2NjY6F5rNBq+//57Bg8ebLygamHGjBn88MMP7N2796bWk5KSwuzZs1m3bh3p6el4e3szbtw4Xn75ZSwsLOomWHF3y8uCtJ1XWh1O/QUlBfp1TC3Aq+XlWaUvJxC2MtuwqFxJWQlrUtcQEx9DYmYiACYaE/oG9CUqMopwl3AjRyhE/ZNkQog6UlRUVKObYDc3uVEBOHjwIGVlZcybN4+QkBDi4+OZPHkyly5dYu7cucYOT9xplILMY5dnlL6cPJw7ZFjPyvlyq0P78uTBuxWYW9Z/vOKOkl+Szw9Hf2BBwgJO5J4AwNLUkiGhQ5gQPgFfO18jRyiE8Ui7rRCVuHTpEhMmTMDW1hYvLy/ef/99gzqBgYG88cYbREVF4eDgwOTJkwH49ttviYiIQKvVEhgYaLBsYGCgrqtUYGAgAEOGDEGj0eheA/z888+0adMGS0tLgoODmTlzJiUlJVXGHBUVxeDBg5k5cybu7u7Y29szdepUioqKdHWUUrz77rsEBwdjZWVFixYtWL58ue79DRs2oNFoWLt2LW3btsXa2prOnTtz6FD5TVlsbCwzZ85k3759aDQaNBqNbubt7OxspkyZotv2vffey759+6qMt1+/fsTExNCnTx+Cg4MZOHAgzz77LN99912VywihU1JYnjD88W9YPAbeC4H/toEfH4e/FlxJJFxCodU4GPhfmPYn/DMJRi+Grk9DQCdJJES1zhec5397/0ef5X14c8ebnMg9gaPWkcdbPM7qYat5qcNLkkiIu560TIh6pZTSjXJR36zMrGrch/W5555j/fr1fP/993h6evLSSy+xe/duWrZsqVfvvffe49VXX+WVV14BYPfu3YwYMYIZM2YwcuRItm7dyuOPP46LiwtRUVEG29m1axfu7u7ExMTQr18/TE3LZ7/97bffGDduHP/5z3+45557OHbsGFOmTAHg9ddfrzLutWvXYmlpyfr160lJSSE6OhpXV1fmzJkDwCuvvMJ3333H//73P0JDQ9m0aRPjxo3Dzc2N7t2769bz8ssv8/777+Pm5sajjz7KpEmT+OOPPxg5ciTx8fGsWrWKNWvWAODg4IBSigceeABnZ2dWrlyJg4MD8+bNo1evXhw+fBhnZ+cafe/Z2dk1rivuMpcy9VsdTu2B0kL9Oqba8paGq7ss2bgYJ15xRztx8QQLEhfw/ZHvKSgt7xrnY+tDVEQUg0IGYWUmD+ALUUGSCVGv8kvy6fB1B6Nse8eYHTUami83N5cvv/ySBQsWcN999wEQFxeHr6/hr0/33nsvzz77rO712LFj6dWrF6+++ioAjRs3JjExkffee6/SZKKiy5OjoyOenldmw50zZw4vvPACEydOBCA4OJjZs2fzz3/+s9pkwsLCgvnz52NtbU1ERASzZs3iueeeY/bs2eTn5/PBBx+wbt06OnXqpFvvli1bmDdvnl4yMWfOHN3rF154gQceeICCggKsrKywtbXFzMxML95169bx999/k5GRgVarBWDu3Ln88MMPLF++XJcIVefYsWN89NFHlbYCibuMUnDuiP6D0plHDOtZu+oPz+rdEsy09R6uaDgSMhOIjY9l9fHVlKkyAMJdwomOjKa3f2/MTOS2SYhryVEhxDWOHTtGUVGR7oYbwNnZmSZNmhjUbdu2rd7rAwcOMGjQIL2yLl268K9//YvS0lJdy8P17N69m127dulaFABKS0spKCggLy8Pa+vKk6IWLVrovdepUydyc3NJS0sjIyODgoICXYJUoaioiFatWumVNW/eXPf/Xl5eAGRkZODv719lvLm5ubi46P8KnJ+fz7Fjx677eU+dOkW/fv0YPnw4jzzyyHXriwamuKC8paGi1SFtB+RnGdZzbXKl1cG/IzgHg4yYI26SUoptp7YxP2E+O07v0JV38enCpIhJtPNsJyMzCVENSSZEvbIys2LHmB3Xr3iLtl0TSqkar/PqUZkqlr32olOb9VUoKytj5syZDB061OA9S8va9/HWaDSUlZX/yrZixQp8fHz03q9oTahgbm6ut2xFTNXF6+XlxYYNGwzec3R0rDa2U6dO0bNnTzp16sRnn31WbV3RQOSe1e+ydHovlBbp1zGzBO/WV3VZag/W0gVO1J3ismJWp6wmJj6GQ+fLn7Ex1Zhyf9D9REVE0cTZ8AckIYQhSSZEvdJoNLf9LKAhISGYm5uzfft23S/x58+f5/Dhw3pdgSoTHh7Oli1b9Mq2bt1K48aNq2yVMDc3p7S0VK+sdevWHDp0iJCQkFrFvm/fPvLz87GyKk+ctm/fjq2tLb6+vjg5OaHVaklNTb3u56iOhYVFpfGmp6djZmam9xD59Zw8eZKePXvSpk0bYmJiMJGx/BuesjI4d/iqVoftkJVkWM/GXb/VwbM5mMkQwaLu5RXn8d2R71iQuIDTl04D5T82PRT6EOPDx+Nt623kCIW4s0gyIcQ1bG1tefjhh3nuuedwcXHBw8ODl19+uUY3utOnT6ddu3bMnj2bkSNHsm3bNv773//yySefVLlMYGAga9eupUuXLmi1WpycnHjttdcYMGAAfn5+DB8+HBMTE/bv38/ff//NG2+8UeW6ioqKePjhh3nllVc4fvw4r7/+OtOmTcPExAQ7OzueffZZnn76acrKyujatSs5OTls3boVW1tb3fMZ1xMYGEhycjJ79+7F19cXOzs7evfuTadOnRg8eDDvvPMOTZo04dSpU6xcuZLBgwcbdAeD8haJHj164O/vz9y5czl79qzuvaufxxB3mOJ8OPmXfpelgguG9dyaXpU8dACnIOmyJG6pzPxMvj74NUsOLiGnKAcAZ0tnxjYdy8gmI3HQOhg5QiHuTJJMCFGJ9957j9zcXAYOHIidnR3Tp08nOzv7usu1bt2ab775htdee43Zs2fj5eXFrFmzKn34usL777/PM888w+eff46Pjw8pKSn07duXX375hVmzZvHuu+9ibm5OWFjYdZ8n6NWrF6GhoXTr1o3CwkJGjRrFjBkzdO/Pnj0bd3d33nrrLZKSknB0dKR169a89NJLNf1qeOihh/juu+/o2bMnFy5cICYmhqioKFauXMnLL7/MpEmTOHv2LJ6ennTr1g0PD49K17N69WqOHj3K0aNHDR5uv5GuYcJILp653GVpB6RuL59huqxYv46ZFfi0uarLUjuwcjJOvOKuczznOHEJcfx49EeKysq70/nb+RMVGcXARgPRmspD+0LcDI2Sq7a4STk5OTg4OJCdnY29vb3eewUFBSQnJxMUFHRDff1FzUVFRXHhwgV++OEHY4dyy8j+ZGRlZXD2oH6XpfMphvVsPfWHZ/VqDqbmhvWEuIX+Pvs3MQkxrDm+BkX5rU5z1+ZER0bT068npiY1GxCjIavu+i1ETUnLhBBCiMoV5cHJ3VeShxM7oeDaFjoNuIfrd1lyDJAuS8IolFJsPrmZmPgY/jzzp668u293oiOjae3eWkZmEqKOSTIhhBCiXM7py3M77CzvspS+H8qumXXd3Ppyl6WO5cmDb1uwcjRKuEJUKC4tZmXySmITYjl64SgAZiZmPBD0AFERUYQ41W4wCyFEzUkyIUQDERsba+wQxJ2krBQyDuh3WbqQaljPzlu/1cEjUrosidtGblEu3x75lgWJC8jIywDAxtyG4Y2HM7bpWDxtZDAHIW41SSaEEOJuUHQJTvx55UHpE7ugMEe/jsYE3CP0kwcHP+myJG47Z/POsujAIr459A0Xiy8C4GblxrjwcQxvPBw7CzsjRyjE3UOSiQYkMDCQ48eP65U9//zzvP3221Uuo5Ri5syZfPbZZ5w/f54OHTrw8ccfExERUaexyXP+oi7IflQL2Sf1h2dN/xuU/vwgmNuUd1Pyv/ygtG87sJSHMMXtKyk7ibiEOH4+9jPFl0cNC3IIIjoimgeCH8DCVOYmEaK+STLRwMyaNYvJkyfrXtva2lZb/9133+WDDz4gNjaWxo0b88Ybb3Dfffdx6NAh7Oxu/pedionaioqKdBOpCXGj8vLyAP0ZugXlXZbOJFxpdUjbAdlphvXsffVbHdwjwFQuA+L2tydjDzHxMaxPW68ra+3emujIaLr5dsNEIxNeCmEschVpYOzs7Go84ZdSin/961+8/PLLDB06FIC4uDg8PDz4+uuvmTp16k3HY2ZmhrW1NWfPnsXc3FxmOBY3RClFXl4eGRkZODo6Vjmb+F2j8OI1XZb+hKKL+nU0JuXPN1S0Ovh3BAffytcnxG2oTJWxIW0DMfEx7D27FwANGnr69SQ6MpqW7i2NGZ4Q4jKZZ6IBCQwMpLCwkKKiIt3Myc899xwWFpU3+yYlJdGoUSP++usvWrVqpSsfNGgQjo6OxMXFVbpcYWEhhYWFutc5OTn4+flVOU51UVERycnJlJWV3eQnFHc7R0dHPD09776hHS+kXdXqsL28FUJdczxZ2F3TZaktaKXfuLjzFJUW8UvSL8TEx5CSkwKAuYk5AxsNZELEBIIdgo0bYAMi80yIuiAtEw3Ik08+SevWrXFycmLnzp28+OKLJCcn88UXX1RaPz09HcBghmIPDw+DZy+u9tZbbzFz5swax2VhYUFoaChFRUU1XkaIa5mbm98dLRKlJXAmXr/LUs5Jw3oO/pe7LF1udXAPB5mES9zBcopyWHZoGV8d+Ipz+ecAsDO3Y2TYSMaEjcHN2s3IEQohKiPJxG1uxowZ171x37VrF23btuXpp5/WlTVv3hwnJyeGDRvGO++8g4uLS5XLX/srr1Kq2l9+X3zxRZ555hnd64qWieqYmJjIjMVCVKYgp3xkpau7LBVf0q+jMQXPZvpdluy9jROvEHUs/VI6XyV+xfIjy7l0ed/3sPZgfPh4hjUeho25jZEjFEJUR5KJ29y0adMYNWpUtXUCAwMrLe/YsSMAR48erTSZqHi2Ij09HS8vL115RkaGQWvF1bRaLVqt9nqhCyGupVT5XA5XtzqcSQCu6W2qdQC/duWJg1+H8knitNUPpiDEnebI+SPEJsSyMmklJap8csQQxxAmRU6iX2A/zGU+EyHuCJJM3OZcXV1xdXW9oWX37NkDoJcoXC0oKAhPT09+//133TMTRUVFbNy4kXfeeefGAhZCXFFaXD4k69XJw8XThvUcA/RbHdzCpMuSaJCUUvx55k9i4mPYfHKzrrydZzuiI6Lp6tP17nsmSog7nCQTDcS2bdvYvn07PXv2xMHBgV27dvH0008zcOBA/P39dfXCwsJ46623GDJkCBqNhqeeeoo333yT0NBQQkNDefPNN7G2tmbMmDFG/DRC3KHyL+h3WTq5G4rz9OuYmIFnc/3kwU5m6RUNW2lZKevS1hETH8Pf5/4Gykdm6h3Qm+iIaJq5NTNyhEKIGyXJRAOh1WpZunQpM2fOpLCwkICAACZPnsw///lPvXqHDh0iOztb9/qf//wn+fn5PP7447pJ61avXl0nc0wI0aApBedT9FsdMg5g0GXJ0uFKd6WKLksW1saIWIh6V1BSwE/HfiIuIY7Ui6kAaE21DA4ZzITwCfjb+19nDUKI250MDStumgwtJ+4KpcVwev/lWaUvJw+5ZwzrOQXptzq4NgGZX0XcZbILs1l6aCmLDiwiqyALAHsLe0aHjWZ02GhcrKoeFETUH7l+i7ogLRNCCFGZ/POQtvNK4nDyLyjJ169jYg5eLa4kD34dwK7qwQuEaOhO5Z5iYeJCvj3yLfmXjxdvG28mRExgSMgQrM2lVU6IhkaSCSGEUAqykvS7LJ09aFjPyulK0uDfEbxbgblV/ccrxG3mUNYhYhJiWJW8ilJVCkCYcxjREdH0CeyDmYncbgjRUMnRLYS4+5QUwel9V3VZ2gmXMgzrOTfS77LkEipdloS4TCnFjvQdxMTHsPXUVl15R6+OREdG08mrk4zMJMRdQJIJIUTDl5el3+pw8i8oLdSvY2oBXi0vzyp9OYGwlRl3hbhWSVkJa46vYX78fA5kHQDARGNC34C+REVGEe4SbuQIhRD1SZIJIUTDohRkHtN/UPrcYcN6Vs76zzp4twJzmaVdiKrkl+Tzw9EfiEuI42TuSQAsTS0ZGjqU8eHj8bXzNXKEQghjkGRCCHFnKymEU3sutzzsKP9v3jnDei6hV1od/DuCSwhIFwwhriurIIslB5ew+OBiLhReAMBJ68TopqMZ1WQUTpZOxg1QCGFUkkwIIe4sl87pd1k6tQdKi/TrmGrBpzX4tb/SZclGhqIUojbSLqaxIGEBPxz9gYLSAgB8bX2JiohiYMhArMxk8AEhhCQTQojbmVJw7sjlLks7yv+bedSwnrWr/oPSXi3ATFv/8QrRACRkJhATH8Pvx3+nTJUBEO4SzqTISfT2742piamRIxRC3E4kmRBC3D6KC+DUX1daHdJ2lM/3cC3XJvpdlpyDpcuSEDdBKcXWU1uJiY9hR/oOXXkXny5MiphEO892MjKTEKJSkkwIIYwn96z+g9Kn9kJZsX4dM0vwaXOl1cG3HVg7GyVcIRqa4rJiViWvIjYhlsPnywcqMNOYcX/Q/UyMmEgT5yZGjlAIcbuTZEIIUT/KyuDcoaselN5ePlHctWzc9VsdPJuDmUX9xytEA5ZXnMe3R75lQeIC0i+lA2BlZsWwxsMY33Q8XrZeRo5QCHGnkGRCCHFrFOVd02VpJxRcMKzn1vSq5KEDOAVJlyUhbpFz+ef4+sDXLD20lJyiHABcLF0Y23QsI5qMwEHrYOQIhRB3GkkmhBB14+IZ/QelT++DshL9OmZW4Nv2qi5LbcFKhpUU4lZLyU4hLjGOn47+RFFZ+ehnAfYBREVE8WCjB9GayoAFQogbI8mEEKL2ysrg7IErrQ6p2+HCccN6tp76rQ6ezcHUvP7jFeIutf/sfmLiY1ibuhaFAqC5a3MmRU6ih18PGZlJCHHTJJkQQlxf0SU4uftKq0PaLijMvqaSBjwirrQ6+LUHxwDpsiREPStTZWw+sZmYhBh2n9mtK+/u253oyGhau7eWkZmEEHVGkgkhhKGc09d0WdoPqlS/jrkN+La50urg2w4spb+1EMZSXFrMiuQVxMbHciz7GABmJmYMCB5AVEQUjRwbGTlCIURDJMmEEHe7slLISLyqy9IOyE41rGfnrd9lyaMZmMopRAhjyy3KZfnh5Sw8sJCMvAwAbMxtGNF4BGObjsXDxsPIEQohGjK5ExDiblOYCyf/vNLqcOJPKMzRr6MxudxlqeOVmaUd/YwTrxCiUhl5GSw6sIhvDn1DbnEuAG5WbowLH8fwxsOxs7AzcoRCiLuBJBNCNHTZJ/W7LKXHG3ZZsrC9PMrS5VYHn7ZgaW+ceIUQ1Uq6kERsQiw/J/1MyeUR04IdgomKiOKB4AewMJV5WYQQ9UeSCSEakrJSOBN/1YPSOyE7zbCeva9+lyX3COmyJMRtbk/GHubHz2dD2gZdWWv31kRHRtPNtxsmGhOjxSaEuHvJ3YMQd7LCi3Bil36XpaJc/ToaE/BsdiVx8OsADr7GiVcIUStlqoz1aeuJiY9h39l9AGjQ0NOvJ9GR0bR0b2ncAIUQdz1JJoS4k1xIuzKvQ9p2OJMAqky/joUd+LXT77KktTVOvEKIG1JYWsgvx34hNiGWlJwUAMxNzBnYaCATIyYS5BBk3ACFEOIySSaEuF2VlsCZv/W7LOWcNKzn4H+lxcG/I7iHg0xEJcQdKbswm2WHl7HowCLO5Z8DwM7cjpFhIxkTNgY3azcjRyiEEPokmRDidlGQfU2Xpd1QfEm/jsYUvJrrd1my9zZOvEKIOpN+KZ2FiQtZfng5eSV5AHhYezA+fDzDGg/DxtzGyBEKIUTlJJkQwhiUggvHy1sbKuZ3OJMAKP16Wodruiy1AQu5qRCioTh8/jBxCXGsTFpJiSofmSnEMYRJkZPoF9gPc1NzI0cohBDVk2RCiPpQWgzp+/W7LF08bVjPKbC8taGiy5JbUzCREVqEaEiUUvx55k/mx89ny8ktuvJ2nu2Ijoimq09XNBqNESMUQoiak2RCiFsh/8LlLkuXWx1O7obiPP06Jmbg1UK/y5Kdp1HCFULceqVlpaxNXUtMfAzxmfEAmGhM6O3fm+jIaCJdI40coRBC1J4kE0LcLKXgfPLlVofL/zIOYNBlydJBv9XBuzVYWBslZCFE/SkoKeDHoz8SlxhH2sXyeV+0ploGhwxmQvgE/O39jRyhEELcOEkmhKitkqLLXZa2X+mylHvGsJ5zsH6rg2sT6bIkxF3kQsEFlhxawuKDi8kqyALA3sKeUWGjGBM2BhcrFyNHKIQQN0+SCSGuJy/LsMtSSYF+HRNz8G55pdXBrwPYuhslXCGEcZ3MPcnCxIV8d+Q78kvyAfC28WZCxASGhAzB2lxaJIUQDYckE0JcTSnISrpqYrgdcPagYT0rp2u6LLUCc6v6j1cIcds4mHWQmPgYfkv5jVJVCkCYcxjREdH0CeyDmYlccoUQDY+c2cTdraQQTu+7kjik7YBLZw3ruYRc1WWpY/lr6bIkxF1PKcX209uJiY9h2+ltuvKOXh2Jjoymk1cnGZlJCNGgSTLRQGzYsIGePXtW+t7OnTtp165dpe9FRUURFxenV9ahQwe2b99e5zHeFvKy9FsdTv4FpYX6dUwtylsaru6yZONqnHiFELelkrISfj/+OzHxMRzIOgCUj8zUN7Av0RHRNHVpauQIhRCifkgy0UB07tyZ06f15y149dVXWbNmDW3btq122X79+hETE6N7bWFhcUtirHdKQeax8oekK5KHc4cN61m76Lc6eLUAc8v6j1cIcdvLK87j+6PfszBxISdzTwJgaWrJ0NChjA8fj6+dr5EjFEKI+iXJRANhYWGBp+eVOQqKi4v56aefmDZt2nWb2LVard6yd6ySQji1R7/LUl6mYT3Xxle1OnQEl0Yg3RCEENXIKshi8cHFLD64mOzCbACctE6MbjqaUU1G4WTpZOQIhRDCOCSZaKB++uknzp07R1RU1HXrbtiwAXd3dxwdHenevTtz5szB3f0OGIno0jn9Lkun9kBpkX4dUy34tNbvsmTtbJx4hRB3nLScNOIS4/jh6A8UXu4S6WvrS1REFANDBmJlJgMvCCHubhqllLp+NXGn6d+/PwArV66stt7SpUuxtbUlICCA5ORkXn31VUpKSti9ezdarbbSZQoLCyksvPKcQU5ODn5+fmRnZ2Nvb193H+JqSpV3UUrbcXlyuO2QedSwno2bfquDVwswayDdtoQQ9SbhXALz4+ezJnUNZaoMgHCXcCZFTqK3f29MTUyNHKEQNy8nJwcHB4dbe/0WDZ4kE7e5GTNmMHPmzGrr7Nq1S++5iBMnThAQEMA333zDQw89VKvtnT59moCAAJYsWcLQoUNrFVOdnoxKS+DETv0uS/nnDeu5NQW/9ldaHZyDpcuSEOKGKKX449QfxMTHsDN9p668i08XJkVMop1nOxmZSTQokkyIuiDJxG3u3LlznDt3rto6gYGBWFpeeWB49uzZfPTRR5w8eRJzc/NabzM0NJRHHnmE559/vtL366Vlojgf3vKDsuIrZWZW4NPmyoPSfu3K53sQQoibUFxWzKrkVcQkxHDk/BEAzDRm3B90PxMjJtLEuYmRIxTi1pBkQtQFeWbiNufq6oqra82HJVVKERMTw4QJE24okcjMzCQtLQ0vL68q62i12iq7QNUZcyto3Bc0Jle6LHk2ky5LQog6c6n4Et8e/paFBxaSfikdACszK4Y1Hsb4puPxsq36PCiEEKKcJBMNzLp160hOTubhhx+u9P2wsDDeeusthgwZQm5uLjNmzOChhx7Cy8uLlJQUXnrpJVxdXRkyZEg9R16JUYuMHYEQogE6l3+Orw98zZJDS7hYdBEAF0sXxjYdy4gmI3DQOhg5QiGEuHNIMtHAfPnll3Tu3JmmTSufMOnQoUNkZ5cPa2hqasrff//NggULuHDhAl5eXvTs2ZOlS5diZ2dXn2ELIcQtl5KdQlxiHD8d/YmisvKR3wLsA4iKiOLBRg+iNb3FLa5CCNEAyTMT4qZJn0shxO1s39l9xMTHsC51HYryS15z1+ZMipxED78eMjKTuGvJ9VvUBWmZEEII0eCUqTI2n9jM/Pj5/JXxl668h28PoiKjaO3eWkZmEkKIOiDJhBBCiAajuLSYFckriI2P5Vj2MQDMTMwYEDyAqIgoGjk2MnKEQgjRsEgyIYQQ4o53segiyw8v56vEr8jIzwDAxtyGEY1HMLbpWDxsPIwcoRBCNEySTAghhLhjZeRl8NWBr1h2aBm5xbkAuFm5MT58PMMaD8POQgaTEEKIW0mSCSGEEHecYxeOEZsQyy9Jv1BSVgJAsEMwURFRPBD8ABamMieNEELUB0kmhBBC3BGUUuzJ2ENMfAwbTmzQlbd2b010ZDTdfLthojExXoBCCHEXkmRCCCHEba1MlbE+bT0x8THsO7sPAA0a7vW/l6iIKFq6tzRugEIIcReTZEIIIcRtqbC0kJ+P/UxcQhwpOSkAmJuYM7DRQCZGTCTIIci4AQohhJBkQgghxO0luzCbZYeX8VXiV2QWZAJgZ2HHyCYjGdt0LK5WrkaOUAghRAVJJoQQQtwW0i+lszBxIcsPLyevJA8AD2sPJoRP4KHGD2FjbmPkCIUQQlxLkgkhhBBGdfj8YWLjY/k1+VdKVPnITCGOIUyKnES/oH6Ym5gbOUIhhBBVkWRCCCFEvVNK8eeZP5kfP58tJ7foytt7tic6Mpou3l3QaDRGjFAIIURNSDIhhBCi3pSWlbI2dS0x8THEZ8YDYKIxobd/b6Ijo4l0jTRyhEIIIWpDkgkhhBC3XEFJAT8e/ZG4xDjSLqYBoDXVMjhkMBPCJ+Bv72/kCIUQQtwISSaEEELcMhcKLrDk0BIWH1xMVkEWAA5aB0aHjWZUk1G4WLkYOUIhhBA3Q5IJIYQQde5k7kkWJCzg+6Pfk1+SD4C3jTcTIiYwJGQI1ubWRo5QCCFEXZBkQgghRJ05kHmAmIQYVqesplSVAtDUuSnRkdHcF3AfZiZy2RFCiIZEzupCCCFuilKK7ae3ExMfw7bT23Tlnbw6ER0ZTUevjjIykxA3KCOngEU7UhnbwR93e0tjhyOEAUkmhBBC3JCSshJWp6wmJiGGg1kHATDVmNInsA/REdE0dWlq5AiFuPNlXCzk32uPcF+4hyQT4rYkyYQQQohaySvO4/uj37MwcSEnc08CYGVmxdDQoYwPH4+PrY+RIxSiYSgtU/xx9JyxwxCiWpJMCCGEqJGsgiwWH1zM4oOLyS7MBsBJ68SYpmMY1WQUjpaOxg1QiAYiNesSS3am8f2ek5zOLgBg4+EM3fvudlpppRC3DY1SShk7CHFny8nJwcHBgezsbOzt7Y0djhCijqXlpBGXGMcPR3+gsLQQAD87P6IiohjYaCCWZnJTI0RdOH+piAXbjvPpxqPkF5dVWe/JXqE8fV/jm96eXL9FXZCWCSGEEJWKPxdPTHwMa1LXUKbKb2wiXSKJjoyml38vTE1MjRyhEA1DWlYeX2xOYumfaRRcTiLcbLUMaeWNr7M1r/2YwNtDmxHp4wCUt0wIcbuQZEIIIYSOUootJ7cQmxDLzvSduvJ7fO4hOjKath5tZWQmIerI/hMXmLcpiV//Pk3Z5X4iEd72TO3eiP6RnpiZmhB/srxLYaSPgy6ZEOJ2IsmEEEIIisuKWZW8ipiEGI6cPwKAmcaM/sH9mRgxkcZON9+lQghRnrBvOHyWzzYmsS0pU1ferbEbU7sF07mRiyTs4o4iyYQQQtzFLhVf4tvD37LwwELSL6UDYG1mzbDGwxgfPh5PG08jRyhEw1BUUsbP+07x2aYkDp25CICZiYaBLbyZ3C2Ypl6VP7PgbqflyV6h0rVJ3LYkmRBCiLvQufxzLDqwiKWHlnKxqPzGxsXShXHh4xjRZAT2FvIwphB14WJBMYt3pjJ/SwrpOeUjM9lYmDK6vT+Tugbh7WhV7fLu9pZ18rC1ELeKJBNCCHEXSc5OJi4hjp+O/URxWTEAgfaBREVEMaDRALSm8uunEHXhTE4B8/9I5uvtqVwsLAHAzU5LdJdAxnYIwMHK3MgRClE3JJkQQoi7wL6z+4iJj2Fd6joU5U96tnBrQXRkND39emKiMTFyhEI0DIfPXOSzTUn8uPckxaXlx1ojNxumdmvEoFbeaM1kFDTRsEgyIYQQDVSZKmPTiU3ExMfwV8ZfuvIefj2YFDmJVu6tjBidEA2HUoodyVl8timJdQevTC7XPtCZKd2CuTfMHRMTeahaNEySTAghRANTVFrEiqQVxCbEkpSdBICZiRkPBj9IVEQUwY7BRo5QiIahtEzxW0I68zYlsS/tAgAaDfQN92RK92Ba+zsZN0Ah6oEkE0II0UBcLLrIssPLWJS4iIz88l9Hbc1tGdFkBGObjsXd2t3IEQrRMOQXlbJ8dxpfbEnmeGYeAFozE4a18eWRe4IJcrUxcoRC1B9JJu4Qc+bMYcWKFezduxcLCwsuXLhgUCc1NZUnnniCdevWYWVlxZgxY5g7dy4WFhZVrrewsJBnn32WxYsXk5+fT69evfjkk0/w9fW9hZ9GCFGXzlw6w6IDi/jm8DdcKr4EgLuVO+PDxzOs8TBsLWyNHKEQDUPWpSIWbEthwbbjZF0qAsDR2pwJHQOY0DkQV1sZwEDcfSSZuEMUFRUxfPhwOnXqxJdffmnwfmlpKQ888ABubm5s2bKFzMxMJk6ciFKKjz76qMr1PvXUU/z8888sWbIEFxcXpk+fzoABA9i9ezempvKQmBC3s2MXjhGbEMsvSb9QUlY+Wkwjh0ZER0bTP6g/5qYyWowQdSE1M48vtiTxzZ9pFBSXAeDrZMXke4IZ3tYXawu5nRJ3L41SShk7CFFzsbGxPPXUUwYtE7/++isDBgwgLS0Nb29vAJYsWUJUVBQZGRnY2xuOGZ+dnY2bmxsLFy5k5MiRAJw6dQo/Pz9WrlxJ3759axRTTk4ODg4OZGdnV7odIUTdUUqxJ2MPMfExbDixQVfexqMNkyIn0dWnq4zMJEQd2Zd2gc82JfFr/GnKLt8tNfNxYEq3YO6P9MTM9M4+1uT6LeqCpNINxLZt24iMjNQlEgB9+/alsLCQ3bt307NnT4Nldu/eTXFxMX369NGVeXt7ExkZydatW2ucTAghbr3SslI2pG1gfsJ89p/dD4AGDb38exEVGUULtxbGDVCIBkIpxYZDZ5m36Rjbk7J05d0buzG1ezCdgl3QaGRkJiEqSDLRQKSnp+Ph4aFX5uTkhIWFBenp6VUuY2FhgZOT/mgTHh4eVS4D5c9ZFBYW6l7n5OTcRORCiOoUlhby87GfiUuIIyUnBQALEwsGhQxiQvgEAh0CjRqfEA1FUUkZP+07xWebjnH4TC4AZiYaBrb0Zkq3YMI85Zd7ISojyYQRzZgxg5kzZ1ZbZ9euXbRt27ZG66vslxKlVK1/QbneMm+99dZ14xZC3Jzswmy+OfQNiw4sIrMgEwA7CztGNRnFmKZjcLVyNXKEQtyZMnIKWLQjlbEd/HG3tySnoJjFO1KJ+SOF9JwCAGy1Zoxu70d0lyC8Ha2MHLEQtzdJJoxo2rRpjBo1qto6gYGBNVqXp6cnO3bs0Cs7f/48xcXFBi0WVy9TVFTE+fPn9VonMjIy6Ny5c5XbevHFF3nmmWd0r3NycvDz86tRnEKI6p3OPc3CAwtZfng5+SX5AHjZeDE+fDxDQ4diYy5DTgpxMzIuFvLvtUdo5e/Il1uS+XpHKhcLywcwcLfTMqlrEKPb++NgJQMYCFETkkwYkaurK66udfPrYqdOnZgzZw6nT5/Gy8sLgNWrV6PVamnTpk2ly7Rp0wZzc3N+//13RowYAcDp06eJj4/n3XffrXJbWq0WrVaGvxOiLh0+f5jY+Fh+Tf6VElV+Y9PYqTHRkdH0DeyLuYnc2AhRF45nlg+f/EjcLkrKB2Yi1N2Wyd2CGdTSG62ZjGQoRG1IMnGHSE1NJSsri9TUVEpLS9m7dy8AISEh2Nra0qdPH8LDwxk/fjzvvfceWVlZPPvss0yePFk3QsPJkyfp1asXCxYsoH379jg4OPDwww8zffp0XFxccHZ25tlnn6VZs2b07t3biJ9WiLuDUopd6buISYhhy8ktuvIOnh2Ijoyms3dnedBTiDpwJjuftQfP8t1fafx5/AIAJWUQ4W3PsDY+3B/hhad0ZxLihkgyUQvFxcWkp6eTl5eHm5sbzs7O9bbt1157jbi4ON3rVq1aAbB+/Xp69OiBqakpK1as4PHHH6dLly56k9ZdHf+hQ4fIy8vTlX344YeYmZkxYsQI3aR1sbGxMseEELdQaVkpa1LXEBMfQ0JmAgAmGhPuC7iP6IhoIlwjjByhEA1DaZliVXw6s35O4MzFQoP3E07lkHAqhwt5JTx9X2MjRCjEnU/mmbiO3NxcFi1axOLFi9m5c6feKEa+vr706dOHKVOm0K5dOyNGaVwyTrUQNZNfks+PR38kLiGOE7knALA0tWRwyGAmREzAz06ePRKiLuQXlbJ8dxqfb04mNav8BzRzUw29wz2I8LJn7urDvD20GZE+DkD5sxLu9pbGDNko5Pot6oK0TFTjww8/ZM6cOQQGBjJw4EBeeOEFfHx8sLKyIisri/j4eDZv3sx9991Hx44d+eijjwgNDTV22EKI28yFggssPrSYxQcWc77wPACOWkdGh41mVNgonC3rr5VTiIYsM7eQBduOs3D7cbIuFQHgZG3O+E6BTOwUgIutlviT2cxdfZhIHwddMiGEuHGSTFRj69atrF+/nmbNmlX6fvv27Zk0aRKffvopX375JRs3bpRkQgihczL3JAsSFvD90e91IzP52PowIXwCg0MGY21ubeQIhWgYjmde4ovNySzbnUZBcflT1X7OVky+J5jhbfywspCuu0LcKtLNSdw0aSYVQt+BzAPEJMSwOmU1paoUgKbOTZkUOYneAb0xM5HfcYSoC/vSLvDZpiR+jT9N2eW7mea+DkzpFky/CE/MTE0Mlrl2nom7mVy/RV2QK9p1jB8/nnnz5mFtLb8gCiGqppRi2+ltxMTHsP30dl15Z+/OREdG08Gzg4zMJEQdKCtTbDicwbyNSexIztKV92jixtRujegY7FztseZubykPWwtRh6Rl4jpMTU05ffo07u7uAEydOpW3335bb5K34uJizM3v3jHg5ZcNcTcrKSthdcpqYhJiOJh1EABTjSn9gvoRFRFFmHOYkSMUomEoKinjx70n+XxzEofP5AJgZqJhYEtvpnQLJsxTrj+1JddvURekZeI6rs21Fi9ezPPPP69LJs6cOUNAQAAFBQXGCE8IYSR5xXl8f/R7FiYu5GTuSQCszKx4KPQhxoePx9vW28gRCtEw5BQUs3hHKjF/pJCeU36ttdWaMaaDP9FdAvFykPkhhDAmSSZqqbKGnKKiIiNEIoQwhsz8TBYfXMySQ0vILswGwNnSmTFhYxjZZCSOlo7GDVCIBiI9u4CYP5JZtCOV3MLyWeE97LVEdwliTAd/7C3v3h4BQtxOJJmoA9IPWoiGLzUnlQWJC/jh6A8UlpbPN+Nv58/EiIkMbDQQS7O7+0FOIerKofSLfLYpiZ/2naS4tPwHvFB3WyZ3C2ZQS2+0ZjIykxC3E0kmauDrr7+mW7duuiFiJXkQ4u4Rfy6emPgY1qSuoUyVDzkZ6RLJpGaTuNfvXkxN5MZGiJullGJ7UhafbTrG+kNndeXtg5x5tHswPRq7Y2Ii114hbkeSTFxH165def3117l48SLm5uaUlJTw0ksv0bVrV1q3bo2bm5uxQxRC1DGlFFtObiEmIYZd6bt05ff43EN0ZDRtPdrKjwpC1IHSMsWq+HTmbTrG/hPl3QY1Grg/0pMp3RrR0s/RuAEKIa5LRnOqoSNHjrB7927++usvdu/ezZ49e7hw4YLuhqK0tNTIERqPjAYhGorismJWJa8iJiGGI+ePAGCmMaN/cH+iIqIIdZJJKYWoC/lFpSzbncYXm5NJzcoDQGtmwvC2vjzSNZhAVxsjR3h3kOu3qAvSMlFDoaGhhIaGMmrUKF1ZcnIyf/75J3v27DFiZEKIm3Wp+BLLDy/nqwNfkX4pHQBrM2uGNx7OuPBxeNp4GjlCIRqGzNxCFmw7zoJtKZzPKwbAydqc8Z0CmdgpABdbrZEjFELUlrRMVCM1NRV/f/8a1z958iQ+Pj63MKLbk/yyIe5U5/LPsejAIpYeXMrF4osAuFq5MrbpWEY0GYG9hezPQtSF45mX+GJzMst2p1FQXP7skZ+zFY90DWZ4W1+sLeS3TWOQ67eoC3L0VqNdu3YMHDiQyZMn0759+0rrZGdn88033/Dvf/+bqVOn8o9//KOeoxRC1FZydjJxCXH8dOwnisvKfx0NtA8kKiKKAY0GoDWVX0eFqAt70y7w2aZjrIpPp+zyT5fNfByY2j2YfhGemJmaGDdAIcRNk2SiGgcOHODNN9+kX79+mJub07ZtW7y9vbG0tOT8+fMkJiaSkJBA27Ztee+997j//vuNHbIQohp7M/YSEx/D+rT1KMrvbFq4tWBS5CR6+PXARCM3NkLcrLIyxYbDGczbmMSO5CxdeY8mbkzpFkynYBcZwECIBkS6OdVAQUEBK1euZPPmzaSkpJCfn4+rqyutWrWib9++REZGGjtEo5JmUnE7K1NlbDqxiZj4GP7K+EtX3sOvB5MiJ9HKvZURoxOi4SgqKePHvSf5fHMSh8/kAmBmomFgS2+mdAsmzFOuD7cbuX6LuiDJhLhpcjISt6Oi0iJWJK0gJiGG5OxkAMxNzHmw0YNMDJ9IsGOwkSMU4s6UkVPAoh2pjO3gj7u9JTkFxSzekcr8P5I5k1M+oaOt1ozR7f2I7hKEt6OVkSMWVZHrt6gL0s2phv7++2+aNm2KmZl8ZULczi4WXWTZ4WV8lfgVZ/PLJ7+yNbdlRJMRjG06FndrdyNHKMSdLeNiIf9ee4RW/o58sSWZr3ekkltYAoC7nZZJXYMY3d4fBytzI0cqhKgPcmdcQy1atMDCwoLw8HBatGhBy5Ytdf91dHQ0dnhC3PXOXDrDogOL+ObwN1wqvgSAu7U745uOZ1jjYdha2Bo5QiEahuOZ5cfXI3G7KCkfmIlQd1smdwtmUEtvtGYyK7wQdxNJJmpoy5YtDBs2jKCgIAoLC4mNjWXfvn1oNBpCQkIYMWIE06dPl8RCiHp29PxRYhNiWZG8gpKy8l9HGzk0Ijoymv5B/TE3lV9HhbhZZ7LzWXfoLN/uTuPP4xcAKCmDCG97HmrtQ/9ILzylO5MQdyVJJmpo2rRpfPLJJwwePFhXtnHjRh555BEmTpzI6tWr+eqrr9i5cydubm7GC1SIu4BSir8y/iImPoaNJzbqytt4tGFS5CS6+nSVkZmEqAOlZYrVCenM+DlB9zzE1RJO5ZBwKofs/BKevq+xESIUQhibPIBdQ9bW1uzdu5fGjfVPlr/88guxsbEsW7aMESNG4OjoyOeff26kKI1DHuAS9aW0rJT1aeuJSYhh/9n9AGjQ0DugN1ERUTR3a27kCIVoGAqKS1m++wRfbE4iJTMPADNTDfc19SDC2565qw/z9tBmRPo4AOXPSrjbWxozZHED5Pot6oK0TNRQu3bt+Oqrr5g1a5ZeeUREBKtXr0aj0fDcc88xcuRII0UoRMNVWFrIT8d+Ii4hjuM5xwGwMLFgUMggJkZMJMA+wMgRCtEwXMgrYuG248RuTSHzUhEADlbmTOgUwIROgbjZaYk/mc3c1YeJ9HHQJRNCiLuXJBM19Mknn9CpUyeOHj3Ka6+9RlhYGEVFRXz44Yc4OzsD4ObmxpkzZ4wcqRANR3ZhNt8c+oZFBxaRWZAJgJ2FHaOajGJM0zG4WrkaOUIhGoa0rDy+3JLMN3+mkVdUCoCPoxWP3BPEiLZ+2GjldkEIUTk5O9RQREQE27ZtY9q0aYSHh6PVaikpKcHMzIyYmBgA9uzZg7e3t5EjFeLOdzr3NAsSF/DtkW/JL8kHwMvGiwnhExgaOhRrc2sjRyhEw5BwKpvPNiXxy/7TlJaV93oO97Jnavdg+jfzwtzU8NkjdzstT/YKxd1OW9/hCiFuQ/LMxA1ISUlh//79mJqa0qZNGzw9PQHYvHkzZ86cYdiwYUaOsH5Jn0tRVw5lHSI2IZZfk3+lVJX/OtrYqTHRkdH0DeyLuYmMzCTEzVJKsfVYJp9uPMbmI+d05V1DXJnaPZiuIa5oNBojRijqi1y/RV2QZELcNDkZiZuhlGJX+i7mJ8znj5N/6Mo7eHYgOjKazt6d5cZGiDpQUlrGyvh05m08RsKpHABMNPBAc2+mdguW5x/uQnL9FnVBujnVUElJCe+88w6//PILhYWFNGvWjLFjx9KnTx9jhybEHamkrIQ1qWuIiY8hMTMRABONCX0C+hAVGUWES4SRIxSiYcgrKmHZnyf4fHMSJ86Xdxu0NDdhVDt/Hu4ahJ+zdBsUQtw4SSZq6IUXXmDx4sVMnjwZCwsLEhMTGThwICNHjiQ2NlZ+ORWihvJL8vnx6I/EJcRxIvcEAJamlgwOGcyEiAn42fkZOUIhGobM3ELith1nwbYULuQVA+BsY8HEToGM7xSAs42FkSMUQjQE0s2phry9vVm6dCn33HOPriw1NZX+/fszceJEnnvuOSNGZ1zSTCpq4nzBeZYcXMLig4s5X3geAEetI6PDRjMqbBTOls5GjlCIhuF45iW+2Fw+MlNhSRkA/s7WTO4WzLDWvlhZmBo5QnG7kOu3qAvSMlFDly5dwsfHR6/M39+f//znP0ydOvWuTiaEqM6JiydYkLiA7498T0FpAQA+tj5MjJjI4JDBWJlZGTlCIRqG/ScuMG9jEr/Gn+bywEw093VgardG9Iv0xNREWtCFEHVPkoka6tq1K3FxccycOVOvPCgoiNOnTxspKiFuX4mZicTGx/Lb8d8oU+W/jjZ1bsqkyEn0DuiNmYmcfoS4WUopNh4+y7yNSWxLytSV92jixtRujegY7CzdcIUQt5RczWvonXfeoUuXLpw/f55//OMfhIaGUlxczEcffURExK1/UHTOnDmsWLGCvXv3YmFhwYULF/Te37dvH2+//TZbtmzh3LlzBAYG8uijj/Lkk09Wu94ePXqwceNGvbKRI0eyZMmSuv4I4i6glGLbqW3MT5jPjtM7dOWdvTsTHRlNB88OcmMjRB0oLi3j532n+GxTEgfTLwJgZqJhYEtvpnQLJsxTuqwIIeqHJBM1FBkZyYYNG5g8eTL//e9/sbCwoLS0FGdnZ3788cdbvv2ioiKGDx9Op06d+PLLLw3e3717N25ubnz11Vf4+fmxdetWpkyZgqmpKdOmTat23ZMnT2bWrFm611ZW0u1E1E5xWTGrU1YTEx/DofOHADDVmNIvqB9REVGEOYcZOUIhGobcwhKW7Exl/pZkTmWXdxu0sTBldHt/JnUNwttRzt9CiPolyUQ1Bg0aRMuWLXX/WrVqxZ9//smhQ4dISEjAzs6ODh061MtDSxXdq2JjYyt9f9KkSXqvg4OD2bZtG9999911kwlra2vdxHtC1EZecR7fHfmOhYkLOXXpFABWZlY8FPoQ48PH420rM8ILURcyLhYQtzWFhduOk1NQAoCrrZboLoGM6xCAg7VM6CiEMA5JJqoRGhrKH3/8wSeffEJmZib29va0aNFCl1wEBQXd1r/iZ2dn4+x8/RFyFi1axFdffYWHhwf3338/r7/+OnZ2dvUQobhTZeZn8vXBr1lycAk5ReWTXzlbOjO26VhGNhmJg1YmvxKiLhw7m8sXm5P4dvdJikrLnz0KdrVhSrdgBrfywdJcRmYSQhiXJBPVmDt3ru7/T5w4wd69e3X/VqxYQXJyMmZmZoSFhbFv3z4jRmpo27ZtfPPNN6xYsaLaemPHjiUoKAhPT0/i4+N58cUX2bdvH7///nuVyxQWFlJYWKh7nZOTU2dxi9tbak4qcQlx/HjsRwpLy/cBfzt/JkZMZGCjgViaWRo5QiEaht3Hz/PZpmOsTjxDxQDurf0dmdq9Efc19cBERmYSQtwmJJmoIV9fX3x9fRkwYICuLDc3lz179rB///4bWueMGTMMRoe61q5du2jbtm2t1puQkMCgQYN47bXXuO+++6qtO3nyZN3/R0ZGEhoaStu2bfnrr79o3bp1pcu89dZb141bNCx/n/2bmIQY1hxfg6L8zibSJZLoyGh6+ffC1ER+HRXiZpWVKdYdzGDepmPsSjmvK+/d1INHuwfTNlDmYhFC3H5k0jojOnfuHOfOnau2TmBgIJaWV37tjY2N5amnnjIYzalCYmIiPXv25JFHHmHOnDm1jkkphVarZeHChYwcObLSOpW1TPj5+cmkNw2MUorNJzcTEx/Dn2f+1JXf43MP0ZHRtPVoKyMzCVFLGTkFLNqRytgO/rjbl5/bC0tK+XFv+chMRzNyAbAwNWFIKx8mdwsixF26nYpbQyatE3VBWiaMyNXVFVdX1zpbX0JCAvfeey8TJ068oUSiYh3FxcV4eXlVWUer1aLVam80THGbKy4t5teUX4mJj+HohaMAmGnM6B/cn6iIKEKdQo0coRB3royLhfx77RHuC/fA0sKUr3eUj8yUcbH8Bxo7rRljOwYQ3SUQD3vpNiiEuP1JMnGHSE1NJSsri9TUVEpLS9m7dy8AISEh2NrakpCQQM+ePenTpw/PPPMM6enpAJiamuLm5gbAyZMn6dWrFwsWLKB9+/YcO3aMRYsW0b9/f1xdXUlMTGT69Om0atWKLl26GOujCiPJLcrl2yPfsiBxARl5GQDYmNswLHQY48LH4WkjI34JUVfmb0lmdeIZcgvLR2bytLfk4a5BjGrvh52ljMwkhLhzSDJxh3jttdeIi4vTvW7VqhUA69evp0ePHixbtoyzZ8+yaNEiFi1apKsXEBBASkoKAMXFxRw6dIi8vDwALCwsWLt2Lf/+97/Jzc3Fz8+PBx54gNdffx1TU+kDf7c4m3eWRQcW8c2hb7hYXD75lauVK+OajmN4k+HYW0jTtxA3IyOngIyLhaRmXuLLP1IA+G7PSQD8na2I6hzEuI4BWJiZGDFKIYS4MfLMhLhp0ufyzpScnUxcQhw/HfuJ4rJiAALtA4mOjGZA8AAsTC2MHKEQdz6lFM8t38/y3SeqrPNkr1Cevq9xPUYlRDm5fou6IC0TQtxl9mbsZX78fDakbdCNzNTSrSXRkdH08OuBiUZ+HRXiZpWWKX5PTGfepiT2pF7QlUd62xN/Koe3hzYj0qd8PhZ3O3kGTQhx55JkQoi7QJkqY2PaRmISYtiTsUdX3tOvJ9GR0bRyb2XE6IRoOAqKS/nur5N8vjmJ5HOXALAwM2FYG18m3xPMpcISBny0hUgfB10yIYQQdzJJJoRowIpKi/gl6RdiE2JJzk4GwNzEnAcbPcjEiIkEOwQbOUIhGoYLeUV8tf04sVtTOJdbBICDlTkTOgUwoVMgbpdbH+JPZhszTCGEqHOSTAjRAOUU5bDs0DIWHVjE2fyzANiZ2zGiyQjGNh2Lm7WbkSMUomE4eSGfLzcns2RXKnlFpQD4OFrxcNcgRrbzw0arf5l1t9PyZK9Q6dokhGgwJJkQogFJv5TOogOLWHZ4GZeKy7tYuFu7MyF8Ag+FPoStha2RIxSiYThwOofPNiXx075TlJaVP3vU1MueR7sH07+ZF+amlT975G5vKQ9bCyEaFEkmhGgAjp4/SmxCLCuSV1BSVj5ufYhjCFERUfQP6o+5qYxbL8TNUkqx7Vgmn25KYtPhs7ryLiEuTO3WiHtCXWVWeCHEXUeSCSHuUEopdp/ZTUxCDJtObNKVt/VoS3RkNPf43CM3NkLUgZLSMn6NT+ezTUn8ffmZBxMNPNDcm6ndguVBaiHEXU2SCSHuMKVlpaxPW09MfAz7z+0HQIOG3gG9iYqIorlbcyNHKETDkF9UyrLdaXy+OYm0rHwALM1NGNnWj0fuCcbP2drIEQohhPFJMiHEHaKgpICfjv3EgsQFHM85DoCFiQWDQgYxMWIiAfYBRo5QiIYh61IRC7alELc1hfN55RM6OlmbM7FzIBM6BeJsIxM6CiFEBUkmhLjNZRdms/TQUhYdWERWQRYA9hb2jAobxeiw0bhauRo5QiEahtTMPL7YksQ3f6ZRUFwGgL+zNZPvCWJYGz+sLEyNHKEQQtx+JJkQ4jZ1Ovc0CxIX8O2Rb8kvKe9i4WXjxYTwCQwNHYq1uXSxEKIu/H0im3mbjrHy79NcHpiJZj4OTO0eTL8IT8yqGJlJCCGEJBNC3HYOZR0iJiGGVcmrKFXl49Y3cWpCdGQ0fQL7YG4iIzMJcbOUUmw6co55G4+x9Vimrrx7Yzemdg+mU7CLDGAghBA1IMmEELcBpRQ703cSEx/DH6f+0JV38OrApIhJdPLuJDc2QtSB4tIyVuw/zacbj3Ew/SIApiYaBrbwZvI9wYR72xs5QiGEuLNIMiGEEZWUlbAmdQ0x8TEkZiYCYKIxoU9AH6Iio4hwiTByhEI0DJcKS1iyK435W5I5eaG826C1hSmj2vkzqWsgvk7SbVAIIW6EJBNCGEF+ST4/Hv2RuIQ4TuSeAMDS1JIhoUMYHz4ePzs/I0coRMNw9mIhcVtTWLj9ONn55SMzudpaEN0liHEdAnCwlm6DQghxMySZEKIenS84z5KDS1h8cDHnC88D4Kh1ZEzYGEaFjcLJ0snIEQrRMCSdzeXzzcl8+9cJikrKR2YKcrVh8j3BDG3tg6W5jMwkhBB1QZIJIerBiYsnWJC4gO+PfE9BaQEAPrY+REVEMShkEFZmVkaOUIiGYU/qeeZtTOK3xHTU5ZGZWvo58mj3YO4L98TURJ49EkKIuiTJhBC3UEJmArHxsaw+vpoyVf7raLhLONGR0fT2742ZiRyCQtyssjLF+kMZzNuUxM7kLF15rzB3pnZvRLtAJxnAQAghbhG5kxGijiml2HZqG/MT5rPj9A5deRfvLkRFRtHBs4Pc2AhRB4pKyvhx70k+25TEkYxcAMxNNQxu6cOUbsGEetgZOUIhhGj4JJkQoo4UlxWzOmU1MfExHDp/CABTjSn3B91PVEQUTZybGDlCIe5MGTkFLNqRytgO/rjbW3KxoJjFO1OZvyWF9JzyboO2WjPGdvAnuksQng6WRo5YCCHuHpJMCHGT8orz+O7IdyxMXMipS6cAsDKz4qHQhxgfPh5vW28jRyjEnS3jYiH/XnuE1gGOfPlHMl9vT+ViYQkA7nZaJnUNYkwHf+wtZWQmIYSob5JMCHGDMvMz+frg1yw5uIScohwAnC2dGdt0LCObjMRB62DkCIVoGNKyLgHwcOwuLg/MRIi7LVPuCWZQK2+0ZjIykxBCGIskE0LUUmpOKnEJcfx47EcKSwsBCLAPYGLERAY2GojWVGvkCIW4853JzmfD4bN8u/sEO1PKh1EuKYNwLzseau3LA8288HSUUdCEEMLYJJkQoob+Pvs3MQkxrDm+BkX5mJPNXJsxKXISPf16Ymoiv44KcbPKyhS/HzjD6z/Gk55TaPB+4umLJK44QE5BCU/f19gIEQohhLiaJBNCVEMpxeaTm4mJj+HPM3/qyrv7dicqIoo2Hm1kZCYh6kBBcSk/7CkfmSnpXHm3JjMTDb2auhPh7cAHvx/m7aHNiPQp7z7obictgEIIcTuQZEKIShSXFvNryq/ExMdw9MJRAMxMzHgg6AGiIqIIcQoxcoRCNAzZecV8teM4MX+kcC63vCXC3tKMcR0DiOoSiLudJfEns/ng98NE+jjokgkhhBC3B0kmhLhKblEu3x75lgWJC8jIywDAxtyG4Y2HM7bpWDxtPI0coRANw6kL+czfkszinalcKioFwMvBkoe7BjGqvT+2Wrk8CSHEnUDO1kIAZ/POsujAIr459A0Xiy8C4GblxrjwcQxvPBw7C5n8Soi6cDA9h882JvHTvlOUlJU/e9TEw46p3YN5sIU35qYmBsu422l5sleodG0SQojbkCQT4q6WlJ1EXEIcPx/7meKyYgCCHIKIjojmgeAHsDC1MHKEQtz5lFJsT8pi3qZjbDh0VlfeKdiFKd2D6dHYrdpnj9ztLeVhayGEuE1JMiHuSnsz9jI/fj7r09brylq5tyI6Ipruft0x0Rj+OiqEqJ3SMsVvCenM23iMfSeyATDRwP2RXkzpFkwLP0fjBiiEEOKmSTIh7hplqoyNaRuJSYhhT8YeADRo6OnXk+jIaFq6tzRugEI0EAXFpSzbfYIvNidxPDMPAK2ZCcPb+vJI12ACXW2MHKEQQoi6IsmEaPCKSov4JekXYhNiSc5OBsDcxJyBjQYyIWICwQ7BRo5QiIbh/KUiFm4/TtzWFDIvFQHgaG3OhE6BTOgUgKutPPMghBANjSQTosHKKcph2aFlLDqwiLP55f207cztGBk2kjFhY3CzdjNyhEI0DGlZeXy5JZmlu9LILy4fmcnH0YrJ9wQxop0f1hZyqRFCiIZKzvB3iDlz5rBixQr27t2LhYUFFy5cMKhT2QOM//vf/3j00UerXG9hYSHPPvssixcvJj8/n169evHJJ5/g6+tbl+HXq/RL6Sw6sIhlh5dxqbh88isPaw/Gh49nWONh2JhLFwsh6kL8yWw+25TEir9PU3p5ZKYIb3umdm9E/0hPzCoZmUkIIUTDIsnEHaKoqIjhw4fTqVMnvvzyyyrrxcTE0K9fP91rB4fqJ3h66qmn+Pnnn1myZAkuLi5Mnz6dAQMGsHv3bkxNTess/vpw5PwRYhNiWZm0khJVAkCIYwjRkdHcH3g/5qbmRo5QiDufUoo/jmYyb9MxNh85pyu/J9SVqd0a0SXERWaFF0KIu4gkE3eImTNnAhAbG1ttPUdHRzw9azaxWnZ2Nl9++SULFy6kd+/eAHz11Vf4+fmxZs0a+vbte1Mx1welFLvP7CYmIYZNJzbpytt6tCU6Mpp7fO6RGxsh6kBJaRkr/j7NZ5uSSDiVA4CpiYYHmpWPzCQzUwshxN1JkokGZtq0aTzyyCMEBQXx8MMPM2XKFExMKu9qsHv3boqLi+nTp4+uzNvbm8jISLZu3VplMlFYWEhhYaHudU5OTt1+iBooLStlXdo6YuNj2X9uP1A+MlPvgN5ER0TTzK1ZvcckREOUV1TCN7vS+GJLMifO5wNgZW7KyHZ+PNw1CD9nayNHKIQQwpgkmWhAZs+eTa9evbCysmLt2rVMnz6dc+fO8corr1RaPz09HQsLC5ycnPTKPTw8SE9Pr3I7b731lq6lpL4VlBTw07GfiEuII/ViKgBaUy2DGg1iYsRE/O39jRKXEA1NZm4hcduOs2BbChfyyid0dLaxIKpzIOM7BuBkIxM6CiGEkGTCqGbMmHHdm/Jdu3bRtm3bGq3v6qShZcuWAMyaNavKZKIqSqlquwa9+OKLPPPMM7rXOTk5+Pn51WobtZVdmM3SQ0tZdGARWQVZANhb2DM6bDSjw0bjYuVyS7cvxN3ieOYlPt+cxLI/T1BYUgZAgIs1j9wTzPA2vlia31nPUgkhhLi1JJkwomnTpjFq1Khq6wQGBt7w+jt27EhOTg5nzpzBw8PD4H1PT0+Kioo4f/68XutERkYGnTt3rnK9Wq0WrbZ+xos/lXuKhYkL+fbIt+SXlHex8LLxYmLERIaEDMHaXLpYCFEX9qVd4LNNSfwaf5rLAzPRwteBqd0b0TfCE1MTefZICCGEIUkmjMjV1RVXV9dbtv49e/ZgaWmJo6Njpe+3adMGc3Nzfv/9d0aMGAHA6dOniY+P5913371lcdXE+YLzvLPrHVYlr6JUlY9b38SpCdGR0fQJ7IO5iYzMJMTNUkqx8fBZ5m1MYltSpq68ZxM3pnRrRMdgZxnAQAghRLUkmbhDpKamkpWVRWpqKqWlpezduxeAkJAQbG1t+fnnn0lPT6dTp05YWVmxfv16Xn75ZaZMmaJrRTh58iS9evViwYIFtG/fHgcHBx5++GGmT5+Oi4sLzs7OPPvsszRr1kw3upOx2Jrbsuv0LkpVKR29OhIdEU0n705yYyNEHSguLePnfaf4bFMSB9MvAmBmouH/27v3uKrqfP/j781tgwqIIjcBuaipoaGYBCpoZl66/hytTp4cSwmnY6frzKkzM1rNmM2xM03HxzmTltd00q7HsjpjaYn3CwET3lI2iIKIiAKKbG779we5JwYt3AJrA6/n48Hj0V57rbU/az12e/ve3/X9rLtjQ/RoUpQGBPkYXCEAoL0gTLQT8+bN06pVq+yPhw4dKkn66quvNGbMGLm7u+t//ud/9PTTT6u+vl5RUVF66aWX9C//8i/2bWpqanTkyBFVVlbal7322mtyc3PTfffdZ79p3cqVKw2/x4S7q7vmJcxTry69NKjnIENrATqKC9Zardubr+Xbc1VYViVJ6urhqn8aEa5HRkUqpLuXwRUCANobk81msxldBNq38vJy+fr6qqysTD4+/KIJGK24vEpr9+Rreny4Anw8VVxRpZU78rRm93GVVzXc0NG/m1mPjIrQ9Pg+8vXiskGgM+L7Gy2BkQkA6GCKK6x6ffNRDQj2Vtp3Z/RBeoGq6xo6M0X5d9WjSVG6d2hvOjMBAK4bYQIAOphDRQ03kvzFmm/sy4aFd1dqcrTGDwyUC52ZAAAthDABAB1A0flL+vTbU/rwmwIdOPX3u9KPiOihqXG9NeaGAAX4eBpYIQCgIyJMAEA7Zq2t04bMQi387JDOfX+n6h/am1eqvXmlemJcPz01vr8BFQIAOjLCBAC0Q+VVNfrLnnyt2JGr0+VWSVIXd1dNGhysG4K66eXPDuuVKYMV09tXkhTg3TY3mgQAdC6ECQBoR4rKqrRiR67W7snXBWtDZ6ZAH7NmjYrUP40Il7enu7ILyiRJMb197WECAIDWQJgAgHbg6OkKLU2z6H8zC1RT19DRu19ANz2aFKV7YnvLw83F4AoBAJ0RYQIAnJTNZtO+vHNasjVHmw8X25ePiOyh1KQojb0h4IqdmQK8zXpiXD8ubQIAtDrCBAA4mbp6m744eFpL0nKUkX9ekmQySRMGBenR5CgNC/f70e0DfDyZbA0AaBOECQBwElU1dfooo0BvpllkKbkoSfJwc9HUuFDNHhWpqF7dDK4QAIDGCBMAYLCyyhqt2XNcK3bkqeRCQ2cmH083zUiI0M8TI9SLy5UAAE6KMAEABik4f0nLt+fqnb35qqyukySF+Hpq1ugo3X9zmLqZ+YgGADg3vqkAoI0dOlWupWkWfZJVqNr6hs5MA4K8lZocpTuHhMjdlc5MAID2gTABAG3AZrNpl+Wslmy1aOt3Z+zLE6N7KjU5Wkn9/GUyNe3MBACAMyNMAEArqqu36f+yi7QkLUd/O9lwMzkXkzRpcLBSk6I0JLS7sQUCAHAdCBMA0AouVdfp/fQTenNbrvJLKyVJnu4uum94mGaPilJ4zy4GVwgAwPUjTABACzp3sVqrdx3Xql15Kr1YLUny6+KuGQkRmpHQRz270ZkJANBxECYAoAWcKK3UW9ssenf/SV2qaejMFOrnpZTRUZo2PFRdPPi4BQB0PHy7AcB1yC4o05I0iz79W6G+b8ykG0N8lJocrckxQXKjMxMAoAMjTADANbLZbNp2tERL0yzafqzEvnx0P3/NSY5WYnRPOjMBADoFwgQANFNtXb0+/faU3thq0aFT5ZIkVxeT7hwSrEeTonRjiK/BFQIA0LYIEwDwEyqra7V+3wm9tS1XBecvSZK83F31wIgwzRoVqVA/OjMBADonwgQASCour9LaPfmaHh+uAB9PSVLJBatW78zT6t3Hdb6yRpLUs6uHZiZG6J9v6SO/rh5GlgwAgOEIEwAgqbjCqtc3H9X4QYGqrK7Tm9ssej/9pKy19ZKkiJ5dNHt0lKbGhcrT3dXgagEAcA6ECQD4gYWfH9LOnLOyfd+Z6aZQX81JjtbtNwbJ1YVJ1QAA/BBhAkCnVVxepdPlVdp//Jze3pUnSdpx7KwkaXif7po1OkoTbwyiMxMAAFdBmADQKVXX1us3/5utTQdPX/H5/cfPa2TfCk2KCW7jygAAaD8IEwA6lQvWWq3bm69l23N1qqxKkuTp5qKbI3to29ESvTJlsGJ6N7R4DfA2G1kqAABOjzABoFMoLq/Sip15WrP7uCqqaiVJvbzNenhkhKbH99GJ0kptO7pdMb197WECAAD8OMIEgA4t58wFvZlm0YffFKi6rqEzU1SvrkpNitK9Q3vL7NbQmemEkUUCANBOESYAdEjpx0v1xlaLvjx02t6ZaVh4d81JjtZtAwPl8g+dmQK8zXpiXD8ubQIA4BoQJgB0GPX1Nm0+XKwlW3O0//g5+/LbBgZqTnKUhkf0uOq2AT6eemp8/7YoEwCADsPF6ALQPAsWLFBiYqK6dOmi7t27N3l+5cqVMplMV/wrLi6+6n7HjBnTZP0HHnigFY8EaHnW2jq9u++Exr+2VSmr92v/8XNydzXpvuGh+vLpJL318+E/GiQAAIBjGJloJ6qrqzVt2jQlJCRo2bJlTZ6///77NXHixEbLZs6cqaqqKgUEBPzovlNSUvTSSy/ZH3t5ebVM0UArK6+q0V/25Gv59lwVV1glSd5mN02/pY8eHhmhQB9PgysEAKBjI0y0Ey+++KKkhhGIK/Hy8moUAs6cOaMtW7ZcMXj8oy5duigoKKhF6gTaQlFZlZbvyNVf9uTrgrWhM1OQj6ceGRWhfxoRLm9Pd4MrBACgcyBMdFCrV69Wly5dNHXq1J9cd+3atVqzZo0CAwM1adIkzZ8/X97e3ldd32q1ymq12h+Xl5e3SM3AT/nudIWWplm0IbNANXUNs6r7BXRTanK07r4pRB5uXLkJAEBbIkx0UMuXL9eDDz74k5csTZ8+XZGRkQoKClJ2draef/55ZWVl6YsvvrjqNgsXLrSPlACtzWazaW9uqZakWbTl8N/n/4yI7KE5yVEa0z+gSWcmAADQNkw22+WmiWhrL7zwwk/+o3zfvn0aPny4/fHKlSv15JNP6vz581fdZteuXUpMTNT+/fsVFxd3TTWlp6dr+PDhSk9P17Bhw664zpVGJsLCwlRWViYfH59rej3gaurqbfriYJHe2GpR5onzkiSTSZowKEiPJkdpWLifsQUCQDtXXl4uX19fvr9xXRiZMNDcuXN/snNSRETENe/3rbfeUmxs7DUHCUkaNmyY3N3ddfTo0auGCbPZLLOZXvxoHVU1dfrwmwK9uc2i3JKLkiQPNxdNjQvV7FGRiurVzeAKAQDAZYQJA/n7+8vf379F93nhwgW9++67WrhwoUPbHzhwQDU1NQoODm7RuoCfcr6yWmt2H9fKnXkquVAtSfLxdNOMhAj9PDFCvbiZHAAATocw0U7k5+ertLRU+fn5qqurU2ZmpiSpb9++6tbt77/Url+/XrW1tZo+fXqTfRQUFGjcuHFavXq1RowYoZycHK1du1aTJ0+Wv7+/Dh48qGeeeUZDhw7VyJEj2+rQ0MkVnL+kZdtytW5fviqr6yRJvbt76ZFRkbr/5jB1M/MxBQCAs+Jbup2YN2+eVq1aZX88dOhQSdJXX32lMWPG2JcvW7ZMU6ZMkZ9f0+vJa2pqdOTIEVVWVkqSPDw8tHnzZr3++uu6cOGCwsLCdMcdd2j+/PlydXVt3QNCp3foVLmWpln0cVah6uobpm4NCPLWnORo3TEkWO6udGYCAMDZMQEb140JXGgum82mXTln9UaaRWnfnbEvT4zuqdTkaCX185fJRGcmAGgLfH+jJTAyAaDV1dbV6/8OFGnJVou+LSiTJLmYpEmDg5WaFKUhod2NLRAAADiEMAGg1VyqrtP76Sf05rZc5Zc2XF7n6e6i+4aHafaoKIX37GJwhQAA4HoQJgC0uNKL1Vq9K0+rdx1X6cWGzkx+Xdw1IyFCMxL6qGc3OjMBANARECYAOKS4vEpr9+Rreny4Anw8JUknSiv11jaL1u8/oaqaeklSWA8vzR4VpWnDQ9XFg48cAAA6Er7ZATikuMKq1zcf1fhBgSqusGpJmkWf/q1Q3zdmUkxvH6UmRWtSTJDc6MwEAECHRJgA4JDLjeB+/dG3yjpZZl8+up+/5iRHKzG6J52ZAADo4AgTAJqtuLxKhecvafuxEq3Zky9JyjpZJheTlNTPX7NGR2l0v14GVwkAANoKYQJAs1y01urZ97KUdrSkyXP1Nunr70p0U5gfYQIAgE6EMAHgR5VcsGrVzobOTGWXaiRJvp5uGhHZU18cOq1XpgxWTG9fSVKAN12aAADoTAgTAK4or+Si3txm0fvpJ2WtbejMFNGzi2aPjtLUuFAdK76gLw6dVkxvX3uYAAAAnQthAkAjmSfOa2lajj7PLtL3c6x1U6iv5iRH6/Ybg+TqwqRqAADQgDABQDabTV8fOaM3tuZoT26pffnYG3opNTla8ZE9mnRmCvA264lx/bi0CQCATowwAXRi1bX1+iSrUEvTLDpyukKS5OZi0j2xvfVoUpRuCPK+6rYBPp56anz/tioVAAA4IcIE0AlVVNVo3d4TWr4jV6fKqiRJXT1c9WB8uB4eGamQ7l4GVwgAANoDwgTQiRSXV2nFzjyt2X1cFVW1kqRe3mY9MjJSD8aHy9fL3eAKAQBAe0KYADqBnDMX9GaaRR9+U6DquobOTFG9uio1KUr3Du0ts5urwRUCAID2iDABdGDpx0v1xlaLvjx02t6ZKa6Pn1KTonTbwEC50JkJAABcB8IE0MHU19u0+XCxlmzN0f7j5+zLxw8KVGpSlIZH9DCwOgAA0JEQJoAOwlpbpw0ZhVqSlqOcMxclSR6uLvp/Q3srJSlSfQOu3pkJAADAEYQJoJ0rr6rRX/bka/n2XBVXWCVJ3p5u+udb+ujhxAgF+HgaXCEAAOioCBNAO3Wq7JJW7MjTX/bk64K1oTNTkI+nZo2K1AMjwuTtSWcmAADQuggTQDvz3ekKLU2zaENmgWrqGmZV9w/spkeTonX3TSHycHMxuEIAANBZECaAdsBms2lvbqmWpFm05XCxfXl8ZA+lJkdpTP8AOjMBAIA2R5gAnFhdvU1fHCzSG1styjxxXpJkMkkTbwzSo0lRGhruZ2yBAACgUyNMAE6oqqZOH35ToDe3WZRb8n1nJjcXTY0LVcroKEX6dzW4QgAAAMIE4FTOV1Zrze7jWrkzTyUXqiVJvl7umpHQRzMSItTL22xwhQAAAH9HmACcQMH5S1q2LVfr9uWrsrpOktS7u5dmjYrU/TeHqauZ/1UBAIDz4V8oQBspLq/S2j35mh4fbr/3w6FT5VqaZtHHWYWqq2/ozDQw2EepSVG6Y0iw3F3pzAQAAJwXYQJoI8UVVr2++ahuGxigY8UX9EaaRWnfnbE/P7JvT6UmRWt0P3+ZTHRmAgAAzo8wAbSR2rp6SdJT67N07MwFSZKLSZo8OFipSdEaHOprZHkAAADXjDABtKLi8irll1Zq86HTWr/vpCTp2JkL8nAz6faBgXpkVJSG9aG9KwAAaJ8IE0ArKb1YrcffydCe3NImz1XX2rTx2yJFB3gTJgAAQLvF7M52IC8vT7NmzVJkZKS8vLwUHR2t+fPnq7q6utF6+fn5uuuuu9S1a1f5+/vrX//1X5us84+sVqsef/xx+fv7q2vXrrr77rt18uTJ1jycDu9EaaXmb8hW4iub7UEi0Mese2JDJEmvTBmsjY+P0sbHR2l6fLiRpQIAAFwXRibagcOHD6u+vl5LlixR3759lZ2drZSUFF28eFGvvvqqJKmurk533HGHevXqpe3bt+vs2bP6+c9/LpvNpsWLF191308++aQ++eQTrVu3Tj179tQzzzyjO++8U+np6XJ1dW2rQ+wQvj1ZpiVpOfrs21P6vjGTBvf2VWpylCbeGKTDRRXakFmomN6+iunN/AgAAND+mWw2m83oInDtFi1apD//+c+yWCySpM8//1x33nmnTpw4oZCQhl/A161bp5kzZ6q4uFg+Pj5N9lFWVqZevXrp7bff1v333y9JKiwsVFhYmD777DNNmDChWbWUl5fL19dXZWVlV3ydjsxms2nb0RItScvRjmNn7cuT+vfSnKQoJUT3tHdmyi4o052Lt2vj46MIEwAAw3Xm72+0HEYm2qmysjL16NHD/njXrl2KiYmxBwlJmjBhgqxWq9LT0zV27Ngm+0hPT1dNTY1uv/12+7KQkBDFxMRo586dVw0TVqtVVqvV/ri8vLwlDqldqamr16d/O6UlaRYdOtVw/K4uJt19U4hSRkdpUEjTD+UAb7OeGNdPAdzFGgAAdBCEiXYoJydHixcv1n/+53/alxUVFSkwMLDRen5+fvLw8FBRUdEV91NUVCQPDw/5+TWeABwYGHjVbSRp4cKFevHFF6/jCNqvi9Zard93Qsu256rg/CVJUhcPVz1wc7geGRWhUL8uV902wMdTT43v31alAgAAtDomYBvohRdekMlk+tG//fv3N9qmsLBQEydO1LRp0zR79uxGz13pRmc2m+2ab4D2U9s8//zzKisrs/+dOHHimvbfHp2psOrVvx5R4itb9NLGgyo4f0n+3Tz07O39tfO5WzXvrkE/GiQAAAA6IkYmDDR37lw98MADP7pORESE/b8LCws1duxYJSQkaOnSpY3WCwoK0p49exotO3funGpqapqMWPxwm+rqap07d67R6ERxcbESExOvWpPZbJbZ3Dku1cktuag3t1n0fvpJVdc23HQu0r+rUkZHacqw3vJ0Z5I6AADovAgTBvL395e/v3+z1i0oKNDYsWMVFxenFStWyMWl8aBSQkKCFixYoFOnTik4OFiStGnTJpnNZsXFxV1xn3FxcXJ3d9cXX3yh++67T5J06tQpZWdn6z/+4z+u48jav4z8c1qaZtH/HSjS5RYFsWHdNSc5SuMHBcnV5dpGewAAADoiujm1A4WFhUpOTlZ4eLhWr17dqGVrUFCQpIbWsLGxsQoMDNSiRYtUWlqqmTNn6t5777W3hi0oKNC4ceO0evVqjRgxQpL0i1/8Qhs3btTKlSvVo0cPPfvsszp79uw1tYbtKN0g6utt+vq7Yr2x1aK9P7jR3LgBAUpNjtbNEX7XfMkYAADOqqN8f8NYjEy0A5s2bdKxY8d07NgxhYaGNnruchZ0dXXVp59+qscee0wjR46Ul5eXHnzwQft9KCSppqZGR44cUWVlpX3Za6+9Jjc3N9133326dOmSxo0bp5UrV3aqe0xU19br46xCLU3L0XenL0iS3F1Nuie2tx5NilL/QG+DKwQAAHBOjEzgurXXXzYqqmr0zt58Ld+ep6LyKklSN7ObpseH6+GRkQry9TS4QgAAWk97/f6Gc2FkAp3O6fIqrdiRp7W7j6vCWiup4R4Qj4yK1IPx4fLxdDe4QgAAgPaBMIFO41hxhZamWfRRRoFq6hoG5KJ7dVVqUrTuGRois1vnubQLAACgJRAm0OHtzyvVG1st+vLQafuymyP8lJoUrVsHBMiFzkwAAAAOIUygQ6qvt+mLQ6e1NM2i9OPnJEkmkzR+YKBSk6MU16eHwRUCAAC0f4QJdChVNXX634wCLd1mkeXMRUmSh6uLfhbXW7NHRym6VzeDKwQAAOg4CBPoEMoqa7Rmz3Gt3JmnMxVWSZK3p5seuqWPZiZGKMCHzkwAAAAtjTCBdq3w/CUt356rd/bm62J1nSQp2NdTs0ZF6oER4epm5i0OAADQWviXFtqlw0XlWppm0ceZhaqtb+jMdEOgt1KTo3TnkBB5uLkYXCEAAEDHR5iA0your9LaPfmaHh+uAB9P2Ww27baUaklajr4+csa+3i1RPZSaHK0x/XvJZKIzEwAAQFshTMBpFVdY9frmo7p1QID2Hz+nJVtzlHWyTJLkYpImxQTr0aQo3RTW3dhCAQAAOinCBJyWtbZhDkTqmnQVlVVJksxuLpo2PFSzR0Upwr+rkeUBAAB0eoQJOJXi8ioVV1h19qJVj635RpJUVFalbp5uunNwkGYmRmpAsI/BVQIAAEAiTMDJrN2Tr9c3H22y/EJVrdbtO6lAHy/CBAAAgJMgTMCpTI8P1/hBgZKkHcdKtPDzw3plymDF9PaVJAV4m40sDwAAAD9AmIBTCfDxbHKDuZjevvYwAQAAAOdBM34AAAAADiFMwGkFeJv1xLh+XNoEAADgpLjMCU4rwMdTT43vb3QZAAAAuApGJgAAAAA4hDABAAAAwCGECQAAAAAOIUwAAAAAcAhhAgAAAIBDCBMAAAAAHEKYAAAAAOAQwgQAAAAAhxAmAAAAADiEMAEAAADAIW5GF4D2z2azSZLKy8sNrgQAADTX5e/ty9/jgCMIE7huFRUVkqSwsDCDKwEAANeqoqJCvr6+RpeBdspkI47iOtXX16uwsFDe3t4ymUxGl+MUysvLFRYWphMnTsjHx8focpwa56r5OFfNx7lqPs5V83W0c2Wz2VRRUaGQkBC5uHDlOxzDyASum4uLi0JDQ40uwyn5+Ph0iC+ctsC5aj7OVfNxrpqPc9V8HelcMSKB60UMBQAAAOAQwgQAAAAAhxAmgFZgNps1f/58mc1mo0txepyr5uNcNR/nqvk4V83HuQKaYgI2AAAAAIcwMgEAAADAIYQJAAAAAA4hTAAAAABwCGECAAAAgEMIE0Ar+vrrr2Uyma74t2/fPqPLc0qffvqp4uPj5eXlJX9/f02ZMsXokpxSREREk/fUc889Z3RZTs1qtSo2NlYmk0mZmZlGl+OU7r77boWHh8vT01PBwcF66KGHVFhYaHRZTicvL0+zZs1SZGSkvLy8FB0drfnz56u6utro0oA2xx2wgVaUmJioU6dONVr229/+Vl9++aWGDx9uUFXO64MPPlBKSopefvll3XrrrbLZbPr222+NLstpvfTSS0pJSbE/7tatm4HVOL9f/epXCgkJUVZWltGlOK2xY8fq3//93xUcHKyCggI9++yzmjp1qnbu3Gl0aU7l8OHDqq+v15IlS9S3b19lZ2crJSVFFy9e1Kuvvmp0eUCbojUs0IZqamoUGhqquXPn6re//a3R5TiV2tpaRURE6MUXX9SsWbOMLsfpRURE6Mknn9STTz5pdCntwueff66nn35aH3zwgW688UZlZGQoNjbW6LKc3scff6x7771XVqtV7u7uRpfj1BYtWqQ///nPslgsRpcCtCkucwLa0Mcff6ySkhLNnDnT6FKczjfffKOCggK5uLho6NChCg4O1qRJk3TgwAGjS3Naf/jDH9SzZ0/FxsZqwYIFXGJxFadPn1ZKSorefvttdenSxehy2o3S0lKtXbtWiYmJBIlmKCsrU48ePYwuA2hzhAmgDS1btkwTJkxQWFiY0aU4ncu/5r3wwgv6zW9+o40bN8rPz0/JyckqLS01uDrn88QTT2jdunX66quvNHfuXP3pT3/SY489ZnRZTsdms2nmzJmaM2cOlxY207/927+pa9eu6tmzp/Lz87VhwwajS3J6OTk5Wrx4sebMmWN0KUCbI0wADnjhhReuOrH68t/+/fsbbXPy5En99a9/7XSX8DT3XNXX10uSfv3rX+tnP/uZ4uLitGLFCplMJr333nsGH0XbuJb31VNPPaXk5GQNGTJEs2fP1htvvKFly5bp7NmzBh9F22juuVq8eLHKy8v1/PPPG12yYa718+qXv/ylMjIytGnTJrm6umrGjBnqLFdEO/LZXlhYqIkTJ2ratGmaPXu2QZUDxmHOBOCAkpISlZSU/Og6ERER8vT0tD/+3e9+p8WLF6ugoKBTXTLQ3HO1a9cu3Xrrrdq2bZtGjRplfy4+Pl633XabFixY0NqlGs6R99VlBQUFCg0N1e7duxUfH99aJTqN5p6rBx54QJ988olMJpN9eV1dnVxdXTV9+nStWrWqtUs13PW8r06ePKmwsDDt3LlTCQkJrVWi07jWc1VYWKixY8cqPj5eK1eulIsLv9Gi86GbE+AAf39/+fv7N3t9m82mFStWaMaMGZ0qSEjNP1dxcXEym806cuSIPUzU1NQoLy9Pffr0ae0yncK1vq9+KCMjQ5IUHBzckiU5reaeq//6r//S73//e/vjwsJCTZgwQevXr+8UoUu6vvfV5d8brVZrS5bktK7lXBUUFGjs2LH2UVSCBDorwgTQBrZs2aLc3NxOd4nTtfDx8dGcOXM0f/58hYWFqU+fPlq0aJEkadq0aQZX51x27dql3bt3a+zYsfL19dW+ffv01FNP2e8RgL/7x/NxuX1udHS0QkNDjSjJae3du1d79+7VqFGj5OfnJ4vFonnz5ik6OrpTjEpci8LCQo0ZM0bh4eF69dVXdebMGftzQUFBBlYGtD3CBNAGli1bpsTERA0cONDoUpzaokWL5ObmpoceekiXLl1SfHy8tmzZIj8/P6NLcypms1nr16/Xiy++KKvVqj59+iglJUW/+tWvjC4N7ZiXl5c+/PBDzZ8/XxcvXlRwcLAmTpyodevWyWw2G12eU9m0aZOOHTumY8eONQmlXD2OzoY5EwAAAAAcwgV+AAAAABxCmAAAAADgEMIEAAAAAIcQJgAAAAA4hDABAAAAwCGECQAAAAAOIUwAAAAAcAhhAgAAAIBDCBMAAAAAHEKYAIAO6plnntFdd93Vovs8e/asAgIClJeX1+zXmTp1qv74xz+2aB0AAOdAmACADiozM1OxsbEtus+FCxfqrrvuUkRERKPXuemmm666zbx587RgwQKVl5e3aC0AAOMRJgCgg8rKymrRMHHp0iUtW7ZMs2fPbvI6PxYmhgwZooiICK1du7bFagEAOAfCBAB0QCdOnNDZs2ftYSI7O1uTJ0+Wj4+PgoKC9Mwzz6i6urrRNgcOHFBSUpK8vLwUGxurHTt2yGQyKSsrS5L0+eefy83NTQkJCU1ex8XFRePHj1eXLl10ww03aM+ePY32fffdd+udd95p3YMGALQ5wgQAdECZmZny9vZWVFSUMjIylJiYqGHDhumbb77R+vXr9c477+gPf/iDff0DBw7olltu0ejRo5WRkaF58+Zp6tSpcnd318CBAyVJaWlpGj58eJPXkaTFixfr+eefV1ZWlsLDw/Xcc881Wm/EiBHau3evrFZr6x44AKBNESYAoAO6PI/BZDIpJSVFDz30kH7/+9+rb9++Sk5OVkpKijZu3Ghff+7cuZo8ebIWLFigAQMGaMqUKUpISNCgQYPk4eEhScrLy1NISEiT1/Hz89O7776rW2+9Vf369dO9996rM2fONFqvd+/eslqtKioqav2DBwC0GTejCwAAtLzLk68PHz6s9PR0rVmzptHzHh4e9lGCvLw8ff3118rOzm60jtlsbjQX4tKlS/L09GzyOvfcc48CAgLsyywWi/r27dtoPS8vL0lSZWXl9R8cAMBpMDIBAB3Q5TBx4MABubu7q3///o2eP3jwoAYPHiypYQK1h4eHbrzxxkbrHDp0qNEEbn9/f507d67J6/xwDoUkZWRkNJn4XVpaKknq1avX9RwWAMDJECYAoIOpqKhQbm6uYmNj5e3trbq6OtXU1Nifz8/P1/vvv68HH3xQkuTq6qra2lpVVVXZ19m6dWuTLk1Dhw7VwYMHm7zO0KFDG73+lVrSZmdnKzQ0VP7+/i15qAAAgxEmAKCDyczMlKurq2JiYhQfH68ePXroueeek8Vi0ZYtWzRp0iRNmzZNkyZNkiTFxcXJ3d1dv/zlL2WxWLRx40bNmjVLkhqFggkTJujAgQP20YnMzEy5uLjYRzgk6fjx4zp37lyTMLFt2zbdfvvtrXvgAIA2R5gAgA4mKytLAwYMkNlslq+vrzZs2KDt27crJibGPhl71apV9vWDg4O1fPlybdiwQUOGDNHy5cv18MMPq2/fvurRo4d9vcGDB2v48OF69913G73OD+dRZGRkqHv37o1ualdVVaWPPvpIKSkprX/wAIA2ZbLZbDajiwAAOI/6+nqNHTtWI0eO1Msvv9zouc8++0zPPvussrOz5eLSvN+j/vu//1sbNmzQpk2bWqNcAICB6OYEAJ1cWlqazpw5o6FDh6qkpESLFi1SXl6ePvrooybrTp48WUePHlVBQYHCwsKatX93d3ctXry4pcsGADgBRiYAoJN777339Nxzz6mgoECBgYG67bbb9PLLLyswMNDo0gAATo4wAQAAAMAhTMAGAAAA4BDCBAAAAACHECYAAAAAOIQwAQAAAMAhhAkAAAAADiFMAAAAAHAIYQIAAACAQwgTAAAAABxCmAAAAADgEMIEAAAAAIcQJgAAAAA45P8D4WdseYbn0dUAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(np.log(H), np.log(E), \"+-\", label=\"erreur\")\n",
"plt.plot(np.log(H), np.log(H), \"-\", label=\"droite pente 1\")\n",
"plt.plot(np.log(H), 2 * np.log(H), \"-\", label=\"droite pente 2\")\n",
"plt.legend()\n",
"plt.xlabel(\"$log(h)$\")\n",
"plt.ylabel(\"$log(E)$\")\n",
"plt.title(\n",
" \"Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)\",\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice 3. Conditions aux limites de Neumann.\n",
"\n",
"On approche dans cet exercice le problème $-u'' + u=f$ dans $]0,1[$, avec conditions aux limites dites de Neumann (homogènes) : \n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-u''(x) + u(x) = f(x) \\hbox{ sur } ]0,1[ \\\\\n",
"&u'(0) = u'(1) = 0.\n",
"\\end{aligned}\\right.$$\n",
"\n",
"On considère la même discrétisation que dans l'exercice 1 de l'intervalle $[0,1]$ et on effectue les approximations suivantes des dérivées de la solution $u$ aux points 0 et 1 :\n",
"\n",
"$$\n",
"u'(0)\\simeq \\frac{u(h)-u(0)}{h},\\ \\ \\ \\ \\ u'(1)\\simeq \\frac{u(1)-u(1-h)}{h}\n",
"$$\n",
"\n",
"On cherche alors, pour $M>0$ donné et $h=\\frac{1}{M+1}$, des valeurs $u_0,\\dots,u_{M+1}$ solutions du système linéaire \n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&\\frac{u_{1} - u_0}{h} = 0,\\ \\ \\ \\ \\ \\frac{u_{M+1} - u_M}{h} = 0 \\\\[4pt]\n",
"&-\\frac{1}{h^2}(u_{i-1} - 2 u_i + u_{i+1})+u_i = f(x_i) \\hbox{ pour } 1\\leq i\\leq M\n",
"\\end{aligned}\\right.,$$\n",
"\n",
"où $x_j = h j$ pour $0\\leq j\\leq M+1$, approchant les valeurs $u(x_0),\\dots,u(x_{M+1})$ de la solution exacte aux points $x_0,\\dots,x_{M+1}$.\n",
"\n",
"Le problème discret peut être écrit à nouveau sous la forme $({A_N}_h + I_M)U = F$ où ${A_N}_h$ est une matrice de taille $M\\times M$, $I_M$ la matrice l'identité de taille $M$, $U = (u_1,\\dots,u_{M}) \\in\\R^M$, et où $F = (f(x_1),\\dots,f(x_M))$.\n",
"\n",
"**Question 1.** Donner l'expression de la matrice ${A_N}_h$. On peut écrire le système $({A_N}_h + I_M)U = F$ sous la forme équivalente $h^2({A_N}_h + I_M)U = h^2F$. Implémenter la matrice $A_N:=h^2{A_N}_h$ dans une fonction python.\n",
"\n",
"**Question 2.** En prenant $f(x) = ((2\\pi)^2 + 1) \\cos(2\\pi x)$ (et on a donc $u(x) = \\cos(2\\pi x)$), refaire les mêmes figures que dans l'exercice 1. Montrer que la convergence dans ce cas est d'ordre $1$ mais pas d'ordre $2$."
]
},
{
"cell_type": "code",
"execution_count": 326,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, \"$-u''(x) + u(x)=f(x)$\")"
]
},
"execution_count": 326,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def An(M, h):\n",
" mat = 2 * np.eye(M) - np.eye(M, k=1) - np.eye(M, k=-1)\n",
" mat[0, 0] = 1\n",
" mat[-1, -1] = 1\n",
" return mat + h**2 * np.eye(M)\n",
"\n",
"\n",
"def f3(x):\n",
" return (np.power(2 * np.pi, 2) + 1) * np.cos(2 * np.pi * x)\n",
"\n",
"\n",
"def u3(x):\n",
" return np.cos(2 * np.pi * x)\n",
"\n",
"\n",
"def solution_neumann(f, M, a, b):\n",
" X = np.linspace(a, b, M + 2)\n",
" U = np.zeros(M + 2)\n",
" h = 1 / (M + 1)\n",
"\n",
" U[1:-1] = np.linalg.solve(An(M, h), h**2 * f3(X[1:-1]))\n",
" U[0], U[-1] = U[1], U[-2]\n",
" return X, U\n",
"\n",
"\n",
"a, b = 0, 1\n",
"\n",
"plt.figure()\n",
"for M in [49, 99, 499]:\n",
" x, U_app = solution_neumann(f3, M, a, b)\n",
"\n",
" plt.scatter(\n",
" x,\n",
" U_app,\n",
" marker=\"+\",\n",
" s=3,\n",
" label=\"$h^2({A_N}_h + I_M)U = h^2F$ pour M={M}\",\n",
" )\n",
"plt.plot(x, u3(x), label=\"Solution exacte\", color=\"red\")\n",
"plt.legend(fontsize=8)\n",
"plt.ylabel(\"f(x)\")\n",
"plt.xlabel(\"x\")\n",
"plt.title(\"$-u''(x) + u(x)=f(x)$\")"
]
},
{
"cell_type": "code",
"execution_count": 321,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Différence en valeur absolue entre la solution exacte et la solution approchée')"
]
},
"execution_count": 321,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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hwyp/x9RRd35UJJfLqaSkhJycnGjy5MnV5ldWnvINJRXNmDFD7TVj/PjxJBKJVK6hzxt4EhG5ubmp/FaVUVfn1q1bU8OGDSk3N1dIk8vl5O7uTtbW1sI5WbafCRMmqOS5ePFiAkB3796tst7qVPW7ULafd999V2X9c+fOEQD6+uuvhbSya/D+/ftV1v3www9JQ0NDOGfK6u3g4EAlJSXCes/y3e3cuTM1aNCAHjx4UGWdanqMnuU74eLiQi1atKgUE/Ts2ZMsLS1Vyv00L3w4JarBbddnERERgQYNGqBXr16Qy+XCy9vbG40bN650m8nT0xPNmjWrlEdgYCCsrKxU8ujevTsA4NSpUyrr9+jRA2KxWCVPAEJT/PXr1/HPP/9g9OjR0NHRUVvuoqIiHDt2DO+++y709PRU9hscHIyioiK1t+/Ll1kkEuH9999X2bZx48bw8vKqVO/GjRvDz8+v0rF42m1FMzMz9OrVCz/99JNwi+XRo0fYv38/hg8fDonk38eAjx8/jrfeegvGxsYQi8XQ1NTE7NmzkZmZqXZEg/J1eZbP8Fn069evxuvu3r0b7dq1g4GBASQSCTQ1NbFx40ZcvXq10rpdunQRnlMGALFYjPfeew83b95EamoqAMDPzw+//fYbZsyYgZMnT6KwsFAlj7///hvp6ekYNmwYNDT+/aoZGBigX79+iImJQUFBwbNWuZKIiAi4u7vD29tb5fgGBQU9tdfz77//jqysLISEhKhsq1Qq0a1bN5w/f77S7c7evXurvPf09ERRUVG150BFFT+3qKgoyOVyDB8+XKUcOjo6CAgIeK5zJC8vD5999hkcHR0hkUggkUhgYGCA/Px8tZ95eX5+fnj8+DEGDx6M/fv3qx267fjx4+jSpQuaNGmikj5ixAgUFBTU6HGKF+l5zrfn+Syf9Zz53//+Bzc3NwQGBuLkyZPYunUrLC0tVfK8desWhgwZgsaNGwu/LQEBAQAgfFY1+d2tzn89x571OvJfyOVyLFiwAK6urtDS0oJEIoGWlhZu3Ljx1HO3VatWAICBAwdi165dSEtLq7TO8ePH4erqWumaMWLECBARjh8//sLqUhP5+fn4448/0L9/fxgYGAjpYrEYw4YNQ2pqKv7++2+VbdSduwCees171t+Fin1O2rZti6ZNmwq3x8sYGhpWKtOQIUOgVCpx+vTpSmXX1NQU3tf0u1tQUIBTp05h4MCBwiMd1XnaMarpd+LmzZu4du2acCwqxjN3796t9PlU57k6F1UlPz8fmZmZ8PDweGF53r9/H48fP4aWlpba5RUvCBV/0MryCA8PV/mgq8vDzMxM5X3ZQ79lgUXZc4kVO02Vl5mZCblcjlWrVmHVqlU12m/FMhORSvBTnr29fbVlLit3xWBInVGjRuHXX3/FkSNHEBQUhO3bt6O4uFjluaTY2Fh07doVnTp1woYNG4RnnPbt24dvvvmm2v0862f4LNR93uqEhYVh4MCBGDBgAKZPn47GjRtDIpHg+++/x48//lhp/caNG1eZlpmZCWtra6xcuRLW1tbYuXMnFi1aBB0dHQQFBWHJkiVwcnJCZmZmlWW0srKCUqnEo0ePoKen9yxVruT+/fu4efNmjc/vitsCQP/+/atcJysrC/r6+sL7p30/aqLiMSkrR9lFs6LyP8Y1NWTIEBw7dgxffvklWrVqBSMjI4hEIgQHBz+1rMOGDYNcLseGDRvQr18/KJVKtGrVCl9//TXefvttAKXnQVWfbdny2vQ859vzfJbPes5oa2tjyJAhmD59Onx8fITjVyYvLw8dOnSAjo4Ovv76azRr1gx6enpISUlB3759n+l3tzr/9Rx71uvIfzFlyhSsWbMGn332GQICAmBiYgINDQ188MEHTz13O3bsiH379mHlypXCc39ubm74/PPPMXjwYACl54q6Z4zr6tx99OgRiOiZvk/P+zv0rL8LVV0LKpZH3bW6/DWjvIr1rOl3Fyjtf1HT78DTjlFNvxNl602bNg3Tpk1Tu+6znP8vNPA8ePAgFArFCx3Dseyh2EOHDqldbmhoqPJe3UPP5ubm8PT0xDfffKM2j7ITu6bK/qdR1vKljomJifC/tY8++kjtOtUNCWVubg6RSIQzZ86o7e32InvABQUFwcrKCps2bUJQUBA2bdoEf39/uLq6Cuvs2LEDmpqaiIiIUGltqMmQOc/yGWpra6vtIFTVD2FNe0Jv3boVdnZ22Llzp8o2VXVGunfvXpVpZV9mfX19zJs3D/PmzcP9+/eF1s9evXrh2rVrwnp3796tlFd6ejo0NDRgYmJSZZl1dHTUli8jI0NlDFtzc3Po6uqqDaDLllelbNmqVauq7GVa1X9+/ouKn1tZOfbs2YOmTZv+5/yzs7MRERGBOXPmYMaMGUJ6cXExsrKyapTHyJEjMXLkSOTn5+P06dOYM2cOevbsievXr6Np06YwMzOr8rMtXyd1qvtsn9d/Pd9q6lnPmYSEBMyePRutWrXC+fPnsXz5ckyZMkVYfvz4caSnp+PkyZNCKyeASsMh1eR3tyblft5z7EVfR6qzdetWDB8+HAsWLFBJz8jIQIMGDZ66/TvvvIN33nkHxcXFiImJwcKFCzFkyBDY2tqiTZs2//ncBUq/S+WvQ//l3C0LrJ+3TDX1PL8LVV0LHB0dVdLKgjN121YMACv+/tX0uysSiSAWi5/7O1BRTb8TZevNnDlTpcNxec7OzjXe7wsLPO/cuYNp06bB2NgYY8eOfVHZomfPntixYwcUCsVzD2jas2dPREZGwsHB4YX88DZr1gwODg748ccfMWXKFLVBoJ6eHgIDA/HXX3/B09Ozyta+6sr87bffIi0tDQMHDvzPZa5OWYD83Xff4cyZM7hw4YLKyARA6RdFIpGoPIJQWFgojMFanWf5DG1tbXH58mWVtOPHjyMvL+8ZalSZSCSClpaWyhf+3r17VfZqP3bsGO7fvy9cQBUKBXbu3AkHBwe1/9ts1KgRRowYgbi4OHz33XcoKCiAs7MzpFIptm3bhmnTpgn7zs/Px6+//ir0XqyKumNx/fp1/P333yo/wj179sSCBQtgZmb2zOPbtmvXDg0aNEBiYuILHTS/pq3tZYKCgiCRSPDPP/880+MTVRGJRCCiSt/N0NBQlV6mNaGvr4/u3bujpKQEffr0wZUrV9C0aVN06dIFe/fuRXp6ukrQsWXLFujp6VU7XIytrS0ePHigco6VlJQgKiqq0ro1PZb/9XyrqWc5Z/Lz8zFgwADY2trixIkTmDFjBmbMmIF27doJvwVl5az4WVX8DarJ7275fCoes/96jtX0OvI8dwAqEolElep38OBBpKWlVQp4qqOtrY2AgAA0aNAAUVFR+Ouvv9CmTRt06dIFCxcuxMWLF1XGgd2yZQtEIhECAwOrzLOspfTy5csqLWXh4eFq91+T46Cvrw9/f3+EhYVh6dKlwhCISqUSW7duhbW1daVH6J7H8/wu/PLLLyrny++//47bt2/jgw8+UFkvNzcXBw4cULm9vW3bNmhoaKBjx47VlutZvrsBAQHYvXs3vvnmm/8cjNf0O+Hs7AwnJyfExcVV+s/Q83iuwDMhIUG4v//gwQOcOXMGmzZtglgsxt69e2v07EFNDRo0CL/88guCg4Pxf//3f/Dz84OmpiZSU1Nx4sQJvPPOO3j33XerzWP+/Pk4cuQI2rZti4kTJ8LZ2RlFRUVITk5GZGQk1q1b98y3b9asWYNevXqhdevWmDx5MmxsbHDnzh1ERUXhl19+AQCsWLEC7du3R4cOHTB+/HjY2toiNzcXN2/eRHh4eLXP0bRr1w5jxozByJEjceHCBXTs2BH6+vq4e/cuzp49Cw8PD4wfP/6ZylydUaNGYdGiRRgyZAh0dXXx3nvvqSzv0aMHli9fjiFDhmDMmDHIzMzE0qVLa9Ty+iyf4bBhw/Dll19i9uzZCAgIQGJiIlavXg1jY+P/VL+yYbYmTJiA/v37IyUlBV999RUsLS3Vjl1mbm6Ozp0748svv4S+vj7Wrl2La9euqQyp5O/vj549e8LT0xMmJia4evUqfv75Z5UficWLF2Po0KHo2bMnxo4di+LiYixZsgSPHz/Gt99+W22Zhw0bhvfffx8TJkxAv379cPv2bSxevLjS92vSpEn49ddf0bFjR0yePBmenp5QKpW4c+cODh8+jKlTp1YZ8BsYGGDVqlUICQlBVlYW+vfvj4YNG+Lhw4eIi4vDw4cP8f333z/r4YaHhwdOnjyJ8PBwWFpawtDQsNr/Edva2mL+/Pn4/PPPcevWLXTr1g0mJia4f/8+YmNjhdblmjIyMkLHjh2xZMkSmJubw9bWFqdOncLGjRtr1GL04YcfQldXF+3atYOlpSXu3buHhQsXwtjYWLjYzpkzR3jub/bs2TA1NcUvv/yCgwcPYvHixdWes++99x5mz56NQYMGYfr06SgqKsLKlSvVXvxqeiw1NDT+0/lWU89yzowbNw537twRPsNly5YhOjoagwYNwl9//YUGDRqgbdu2MDExwbhx4zBnzhxoamril19+QVxcXKV91+R3t+xRrxUrViAkJASamppwdnb+z+dYTa8jhoaGaNq0Kfbv348uXbrA1NRUOAdrqmfPnti8eTNcXFzg6emJP//8E0uWLKnRdWr27NlITU1Fly5dYG1tjcePH2PFihUqz81OnjwZW7ZsQY8ePTB//nw0bdoUBw8exNq1azF+/Phqg7zg4GCYmppi9OjRmD9/PiQSCTZv3oyUlJRK63p4eGDHjh3YuXMn7O3toaOjU+WjeAsXLsTbb7+NwMBATJs2DVpaWli7di0SEhKwffv2FzLO7/P8Lly4cAEffPABBgwYgJSUFHz++eeQSqWYMGGCynpmZmYYP3487ty5g2bNmiEyMhIbNmzA+PHjYWNjU225nuW7u3z5crRv3x7+/v6YMWMGHB0dcf/+fRw4cADr16+vdBe4Os/ynVi/fj26d++OoKAgjBgxAlKpFFlZWbh69SouXryI3bt313i/z9WrveylpaVFDRs2pICAAFqwYIHaXlb/tVc7EZFMJqOlS5eSl5cX6ejokIGBAbm4uNDYsWPpxo0bwnpNmzalHj16qC37w4cPaeLEiWRnZ0eamppkampKLVu2pM8//5zy8vKI6N8eZ0uWLKm0PdT0UoyOjqbu3buTsbExaWtrk4ODQ6Ueh0lJSTRq1CiSSqWkqalJFhYW1LZtW5UecdX58ccfyd/fn/T19UlXV5ccHBxo+PDhdOHChacet6p6zlalbdu2BICGDh1aZVmcnZ1JW1ub7O3taeHChbRx48ZKPRkr9romqvlnWFxcTJ9++ik1adKEdHV1KSAggC5dulRlr/bqRlio6NtvvyVbW1vS1tam5s2b04YNG9Sen3gyBMbatWvJwcGBNDU1ycXFhX755ReV9WbMmEG+vr5kYmIiHJPJkydTRkaGynr79u0jf39/0tHRIX19ferSpQudO3dOZR11PUKVSiUtXryY7O3tSUdHh3x9fen48eNqj29eXh598cUX5OzsTFpaWsIwXpMnT1bpnV+VU6dOUY8ePcjU1JQ0NTVJKpVSjx49VIaPKjtWFYciUlf2S5cuUbt27UhPT48ACOV92ue2b98+CgwMJCMjI9LW1qamTZtS//79VYboUUddr/bU1FTq168fmZiYkKGhIXXr1o0SEhKqHC2gvJ9++okCAwOpUaNGpKWlRVZWVjRw4EC6fPmyynrx8fHUq1cvMjY2Ji0tLfLy8qrUO7mqXsuRkZHk7e1Nurq6ZG9vT6tXr1Z7PlZ1LKvqyV+T8+1ZPsuqPO2c2bBhg9p637x5k4yMjFRGhPj999+pTZs2pKenRxYWFvTBBx/QxYsX1W5fk9/dmTNnkpWVFWloaFQ6Rs97jhHV7DpCRHT06FFq0aIFaWtrE4Bqzzd158ejR49o9OjR1LBhQ9LT06P27dvTmTNn1H73K4qIiKDu3buTVCoVrtHBwcEqQ/IQEd2+fZuGDBlCZmZmpKmpSc7OzrRkyZJKvZPVXftiY2Opbdu2pK+vT1KplObMmUOhoaGVzp3k5GTq2rUrGRoaEgDhelTVd+LMmTPUuXNn4XrXunVrCg8PV1mnqt+QmoxsQVTz34Wy/Rw+fJiGDRtGDRo0EIY2K3/NIvr3Gnzy5Eny9fUlbW1tsrS0pFmzZqn0Aq8uxiCq2XeXiCgxMZEGDBhAZmZmpKWlRTY2NjRixAgqKip6rmNU0+9EXFwcDRw4kBo2bEiamprUuHFj6ty5M61bt67aY16RiOgFd0NnjDHGGHuFbd68GSNHjsT58+dVZmpUp1OnTsjIyEBCQkItle7V9sKHU2KMMcYYY0wdDjwZY4wxxlit4FvtjDHGGGOsVnCLJ2OMMcYYqxUceDLGGGOMsVrBgSdjjDHGGKsVL3TKTPYvpVKJ9PR0GBoavpCBbxljjDH28hERcnNzYWVlJcxXzl4cDjxfkvT0dDRp0qSui8EYY4yx55CSkvLMsxqyp+PA8yUpm7YqJSUFRkZGdVwaxhhjjNVETk4OmjRp8kzTT7Ka48DzJSm7vW5kZMSBJ2OMMfaK4cfkXg5+eIExxhhjjNUKbvFkjDFW5xQKBWQyWV0Xg71hNDU1IRaL67oYbxQOPBljjNWpvLw8pKamgifSY7VNJBLB2toaBgYGdV2UNwYHnowxxuqMQqFAamoq9PT0YGFhwc/VsVpDRHj48CFSU1Ph5OTELZ+1hANPxhhjdUYmk4GIYGFhAV1d3bouDnvDWFhYIDk5GTKZjAPPWsKdixhjjNU5bulkdYHPu9rHgSdjjLE3WkREBJydneHk5ITQ0FCVZQUFBQgODoaLiwvc3d2xatWqOiolY68HvtXOGGPsjSWXyzFlyhScOHECRkZG8PHxQd++fWFqaiqs89lnnyEgIAD5+fnw9fVF9+7d4ejoWIelZuzVxYEnY4yxeoGIUChTvPB8dTXFVd5SjY2NhZubG6RSKQAgODgYUVFRGDx4MABAT08PAQEBAAB9fX04OTnh7t27HHgy9pw48GSMMVYvFMoUcJ0d9cLzTZwfBD0t9Ze79PR0IegEAGtra6SlpaldNyUlBZcvX4aPj88LLyNjbwp+xpMxxtgbS93YoepaR4uKivDee+9h6dKl0NfXr42iMfZa4hZPxhhj9YKuphiJ84NeSr5VkUqlKi2cqamp8Pf3V1mHiBASEoLg4GD079//hZePsTcJB56vmOwCGdKzC+HcyBAaGjwMBGPs9SESiaq8Jf6y+Pn5ISEhAWlpaTAyMkJkZCRmz56tss7MmTOhp6eHL774olbLxqpGRCiRK6GhIYKmmG/evko48HzFHLt2H1N2xcFYVxOtbE3gZ2cKPzszuFkZ8ZePMcaekUQiwbJlyxAYGAilUolPP/0UZmZmCA4ORmhoKJRKJRYtWgRXV1d4e3sDABYtWoSgoBffMsuqRkQokimRXyJHfrEc+cUKyJVKNDLSQSMjnbouHnsGHHi+YrLyS6CnJUZ2oQxHrz7A0asPAAB6WmL42JQFoqbwbtIAOtXcXmKMMVaqd+/e6N27t0paZGSk8DfPIV/7lEQoKlE8CTRL/1UoVT8HkUhUKY3Vfxx4vmI+6GCPkLa2SEzPQWxSFv5IysL55CxkF8pw9mYGzt7MAABoiTXg1cRYaBFt2dQEBtr8cTPGGKt/lEpCgRBoylFQooCyQsCvIRJBT0sMA20J9LUl0NUU8yNnryCORF5BmmINeDVpAK8mDfBhR3solYTrD3KFQDQ2KQsPc4txPvkRzic/wpoT/0BDBLhZGQstoq1sTWGqr1XXVWGMMfYGUiiVyC9RoODJbfMCmaJSy7JYQwR9rdIgU19bXO14rOzVwYHna0BDQwSXxkZwaWyE4W1sQUS4nVnwbyCanImUrELEp2UjPi0bG88mAQCaNTJAK9vSQNTfzgyNjfk5GcYYYy+eXFEaaJY+nylHkUyBijfJNcUaTwJNMfS1JdCWaHCg+RriwPM1JBKJYGuuD1tzfQxs1QQAcDe7ELFPWkNjk7Jw40Eert8vff3yxx0AgI2pntAi6m9nChtTPf7SM8YYe2YlciUKSuTIe9KiWSyvPCOVlkRDpUVTS8yB5puAA883hKWxLt7xluId79IZOjLzSm/Fxz55RvRKejbuZBXgTlYB9vyZCgBoaKgtBKF+dmZwamjAz9MwxhhTUTa0kdCiWSJHiVxZaT0dTTH0tUpbM/W1JNCU8EgsbyIOPN9QZgba6ObeGN3cGwMAcotk+PP2I6FFNC71MR7kFiPi8l1EXL4LAGigp1l6a/7J7Xk3KyNIeAgnxhh7oxARiuRK4bZ5fokCcoVqoCkCoKMl/rdFU0vM1wsGgKfMZE8Y6miik3NDfNrNBXvGt0X83CDsGNMaU95uhvaO5tDVFONxgQxHEu/jm8ireGfNOXjNO4xhG//A6uM3EJuUhSJZ5VspjDFW30VERMDZ2RlOTk4IDQ2ttPyjjz5Cw4YN4evrq5L+9ddfw8bGBubm5irpoaGhcHJygkgkQl5ensp+3N3doaGhgYSEBCE9NjYWvr6+0NTUREREhJCenJyMdu3aQUdHB6tXrxbS8/Ly0KVLFxgYGGDatGkq+3733XdhYmJSaYal/1KHnNxcFJTI8TC3CBu37UGz5m7Q19bEqZg/kV0og1yhRMKlixjaszNa2lngWuxJuFoZwamhIUoe30fwW51goK/3n+vAXg8ceDK1dDTFaG1vholdnLD1A39cntsVeye0xczuLnireUMY6UiQX6LAmRsZWHr4Ogauj4bnvMMYuC4aS6P+xunrD5FXLK/rajDGWLXkcjmmTJmC48eP4+LFi1i0aBGysrJU1hkyZAh+++23StsGBQXhjz/+qJTu7++Pw4cPo2nTpirpzs7O2LNnDzp27KiSbmVlhdDQUAwePFgl3cjICMuXL8fUqVNV0jU1NTFnzhwsWbKk0r4nTpyILVu2VEp/ljoolQSPFi3xy6/hkDaxwbW7Obj5IA93s4vQsIkdlq7bjJb+baGnJUEjIx3YWxigvacTft78IwYPHgw9LQnEGhovvA7s9cC32lmNaIo10MLGBC1sTDA2wAFKJeHv+7nCrfk/krKQkVeM2OQsxCZnASdKh8JwtzIShm9qZWsKEx7CiTFWFSJAVvDi89XUA6rotBIbGws3NzdIpaXPvwcHByMqKkolCGzXrh2Sk5MrbduqVSu1eXp4eKhNd3JyUptubW0Na2traGiotgWZmprC39+/UsCora2Njh074tatW5XyCgwMxMmTJyulV1cHhZJAAO5lFwpDG+k2sgNQeltdSSQMbdTa2w362hL8T1uCJqZ6wqxBBjZNYGPT5KXWgb0eOPBkz0VDQ4TmlkZobmmEkLalQzglZeTjfPK/Y4mmPipEXGo24lKzseFM6RBOzo0MhZ7zfnamPNUZY+xfsgJggdWLz3dWOqClr3ZRenq6EHQCpUFgWlraiy9DPaIytFGJHEUlCiiVhAe5xcI6ErEG9LXEEGuI4NDQEOYNjLjHOXshOPBkL4RIJIK9hQHsLQzwXisbAEDa40KcTyptAY1NysLNB3n4+34u/r6fi59jbgMAbM30VMYSbWKqyz9ujLFao246zNftN0gmL53j/F52IYpkSiTezVG7nomeltARSOvJGJoaIhEP3M5eKA482UsjbaALaQsp+rQobU3IyCvGhXItolfv5iA5swDJmQXY/WQIp8ZGOiotoo4WPIQTY28MTb3S1smXkW8VpFKpSgtnamoq/P39X3wZagkRoUShQIlciZSsApWhjR4VyIRAW0ciFgZqL30mU4QmplUfJ8ZeFA48Wa0xN9BGN3dLdHO3BADkVBjC6XLqY9zLKcKBuHQciCu9+JiUDeH0pEW0uaUhD8nB2OtKJKrylvjL4ufnh4SEBKSlpcHIyAiRkZGYPXt2rZbhvyAiFMnKZgQqnes8JasQhTIFHhWUAHgytJGmGKb6WtCSaMDVkofCY3WI2EuRnZ1NACg7O7uui/LKKCiW07mbD+m7I9dpyIZocv4ikpp+FqHycpt9iIZv/INWH79BsUmZVCST13WxGWP/QWFhISUmJlJhYWGdlWH//v3k5OREDg4OtH79eiIi6t69O6WlpRER0ejRo6lx48akqalJUqmUwsLCiIhozpw5JJVKSUNDg6RSKa1YsYKIiEJDQ0kqlZJYLCYrKyuaPn06EREdOnSIpFIpaWlpUaNGjWjQoEFERHTlyhWSSqWkp6dHZmZm1L59eyIqvY5IpVIyNDSkBg0aUNOmTUmpVFJ+sYycXZqTcQMT0tM3oIaNrejYn9coLuURtenYmUxMzUhHV5csrazoxJnfSa5Q1Ks6lHF1dSUTExMyMDAgqVRKd+/eJSKirl27krm5Oenq6pJUKqXY2NiX8KmXUnf+8fX75RIRqXnAhf1nOTk5MDY2RnZ2NoyMjOq6OK+kErkSCenZQovo+eQs5BapDtGkJdFAiyYNhNmVWtg0gL42N+Qz9qooKipCUlIS7OzsoKPDnQ0rUioJhU9aNPOK5SgoUUBZ4bKtIRJBr2xGIG0J9DTF/IhSDak7//j6/XLxFZrVW1oSDfjYmMDHxgTjAhygUBL+vpeL2KRMocNSRl4J/ngynBNws3QIJ6lxaSD6ZAgnYz3Nuq4KY4zViEJJKCj597Z5QYmiUgeosqGN9LVLZwbS0RJDgzv/sFfEGxl4nj59GkuWLMGff/6Ju3fvYu/evejTp4+wnIgwb948/PDDD3j06BH8/f2xZs0auLm51V2hGcQaIrhaGcHVyggj2tmBiHArI7+0NfRJ8Jn2uBBxKY8Rl/IYP5y+BZGodAgnfztTtHoSjDbkIZwYY/WEXKFEQbmhjQpLlCgdVfNfEg0NoSOQvpYEOpoa3MucvbLeyMAzPz8fXl5eGDlyJPr161dp+eLFi7F8+XJs3rwZzZo1w9dff423334bf//9NwwNDeugxEwdkUgEBwsDOFgYYLBf6RBOqY8KcP5Ja2hsUhb+eZiPa/dyce1eLn6KLh3Cyc5cX5hv3s/OFNYmPIQTY6x2yBRKlY5A6qYa1hJrPLltXtqiWTa0EWOvgzf+GU+RSKTS4klEsLKywqRJk/DZZ58BAIqLi9GoUSMsWrQIY8eOrVG+/IxI/fAwt8IQTvdyUPGMtzT+dwgnfztTOFgY8I88Y7XkdX7Gk4ggUyiRV6xAwZMWzeInQxuVp11uaKOyQJPVDn7Gs/a9kS2e1UlKSsK9e/fQtWtXIU1bWxsBAQH4/fffqww8i4uLUVz876wPOTnqB+hltcvCUBvdPSzR3aN0CKfsQhku3n70JBDNxOXUbNzNLsL+S+nYf6l0CCczfa3SKT7tTGFvoQ8zfS2YPnnpafFXhjGmSqkkyJUEhVIJuZJQIlcKLZoyhWqgWTa0UVmLpp6WBJo8tBF7g/BVtIJ79+4BABo1aqSS3qhRI9y+fbvK7RYuXIh58+a91LKx/85YVxOBLg0R6NIQAFBYosBfd0oD0fPJWbh45xEy80tw6Mo9HLpyr9L2OpoaMNPXhom+Jkz1tWGmrwUTPS2YGZQGpmV/m+hpwUxfC8a6mty7lLFXCBFBQQSFoiyYJMifBJRlaUKQ+eR9xV7m5YmezPzzb4umGGINDjTZm4sDzypUvNVKRNXefp05cyamTJkivM/JyUGTJk1eWvnYi6GrJUZbR3O0dTQHUDqEU3xa6RBOF5KzcDe7CFn5JcjKL0GJQokimRJpjwuR9riwRvlriEqnoTPVV32Z6WvBRPi7NJAt+1dbIn6ZVWbsjaKksuCRoFAoywWO9CRwVOLIoUh8M2cWlEolRo6fhL6Dh6nkEf/Xn5g97WPIiovRs/8gjJv0KQBg9ICeyHj4ANra2gCAvUfPQawhws2rV/Dl9ImQlRTD0MAAP//8Mywb2iMlJQW9hw3D48ePIRaLsW7dOrRq1Qpbt27FokWLIBKJ0LBhQ2zevBnW1tY4e/YsPvroI4hEImhqamLFihVo27YtkpOT4erqimbNmgEAevfujfnz5yMlJQXDhg3DgwcPIJFI8OWXX2LAgAEAgF9++QULFy4EEWHEiBGYPn26Sh379++P5ORkXLhwAQAQGhqKRYsW4ebNm8jNzYWBgQEAICIiAjNmzEBiYiIuX74Md3d3AMCSJUvwyy+/AAAKCwtx//59PH78GABw5MgRTJ06FUqlEm5ubti5c6ew37t378LZ2RkLFizAxx9/jL///hvvvfeesPzvv//G9u3b0adPH8TGxmLkyJEoLi7G8OHDhYH+O3XqhHv37gm3yi9duvQfzhj2snHgWUHjxo0BlLZ8WlpaCukPHjyo1Apanra2tvDjw15dWhINtGxqgpZNTQA4COlEhPwSBbLySpBVUIKs/GJk5pXgUUEJMvNLkFX+7yev3CI5lARk5pem15SBtqS09fRJgFoxaDXV04Kpwb/Bq6G2hJ9JZW8EIoKSINzSlitUb3FXapF8EmBWRy6X46svZyJ05wEYGBpiUPdO6NKtJ0xMTSERiyDR0MCi2Z/i+9DNaO7qit5vd8LQgQPg4eEOHU0xft29G55eHhCLRML3cOoH32DB118hKCgI33//PRYtWoT169dj8eLFGDx4MMaOHYvffvsNX3zxBaKiouDg4ICzZ8/C2NgYoaGhmDVrFrZs2QIfHx9cvHgRYrEYiYmJGDx4MOLi4gAArq6uQpBYRiKR4LvvvoO3tzcePHgAHx8fBAcHo7CwEF9++SX+/PNPGBsbo3fv3ujduzecnZ0BlAaGYrHqf3j9/f1x+PBhBAYGqqQ7Oztjz549GDdunEr69OnThWA2NDQUZ8+eBQA8evQIkydPxpEjR2BpaYkHDx6obDdjxgy8/fbbKvmXBY55eXmwtbUVln/00UfYvn07XF1d0aZNG/Tt21cIfPfs2SP8zeo3DjwrsLOzQ+PGjXHkyBG0aNECAFBSUoJTp05h0aJFdVw6VldEIhEMtCUw0JbAxqxm8xmXyJV4XCEYzXoShD4S/i7Go3xZaVpBCRRKQt6TgaLvZBXUaD9aYg2Y6GtWus1vqq8N0yePBJQPXE30NHm6PFYvKJSER/klpT29S+QoUhYjr6Sw9Pb1kwBSrlAKLZZyokpjWtaEjoYOJGIxxBqiJ8GkqPRvDQ1cPB8DD3c3tPZwgkRDhF49e+DO5Wh0GDoEAJCeng4xlOjaoXT+9uHD3sfpY4fQzq8FxBoiaGmKIalw61wkEiE3NxcAkJubKzRiVJXepk0bYVsfHx9s374dAKCn9+9vTW5u7lP/g2lpaSnk2bBhQ5iamiIrKwt3796Fq6srTExMAAABAQHYu3cvZsyYAZlMhgULFmDlypUYOXKkkJeHh4fafTg5OVVbBgDYtWsXJk+eDADYtm0bBg0apFKuMqdPn4aRkRHs7OzU5nPgwAF06dIF+vr6SE9Ph1wuh6enJwBgyJAhCA8P52DzFfRGBp55eXm4efOm8D4pKQmXLl2CqakpbGxsMGnSJCxYsABOTk5wcnLCggULoKenhyFDhtRhqdmrRkuigYZGOjUeN1SpJOQWyUuD0YISZOY9CVYLSltUhb/LBbEFJQqUKJS4n1OM+znFT9/JE8a6mhVu96u2sFZsbeVOVawmimQKlfOz2v9wFcjwqKAEVgZizA1sCMoqQLFIgdEnuz59R88oZnAM9KuYA77gcQZsbZrAUKd0oommNk1w9266sDw9PR1SqVR4b21tjVOnTgnvhwwZAolEgg8++AATJkwAUDokX1BQECZNmgQDAwPExsYCAGbNmoW3334b3333HZRKJaKjoyuVZ/PmzSqdW48ePYpPPvkE9+/fR2RkpJD+999/o0WLFjA3N8eyZcuEgKzMhQsXoFQq0aRJE+jr6yM+Ph5paWkwNzdHZGSkELAtX74cISEhL2yowIyMDMTFxeGtt94CANy4cQMKhQIdOnRAcXEx5syZgx49ekAul2P27NkICwvDypUr1ea1a9cuDB8+HMDzfQ6sfnojryYXLlxQuX1Q9mxmSEgINm/ejE8//RSFhYWYMGGCMID84cOHeQxP9lJpaIhgrKf5TDMtlb/Ql13YS1tYi5GVL0OW0KJajKz8EjwulIGotHd/dqEMyMiv0X4qdqoy1XvSuepJC6upPneqet0QEXIK5cKjJWXnk+p5pvp3QUnlMSlrQkMEaInFEItfzjlTXUuhuhbU8utXt3zbtm2wsrJCVlYWunXrBjc3NwQEBGDt2rX4/vvvERwcjDVr1mDKlCkIDQ3Ftm3bMH78eEyYMAEHDx7E6NGjcfToUSHfvXv3IiYmBmfOnBHS3nrrLVy9ehUxMTGYPXs2Dh8+DEtLS9y+fRumpqY4ceIE+vfvj+vXrwvbZGZmYvjw4QgNDQUAmJqaYsWKFejTpw+0tLTg5eUFiUSCtLQ0HD58GEePHq228+yzCAsLQ+/evaGpWfo7JpPJEB8fjyNHjiAzMxPt2rVD27ZtsWXLFgwYMACmpqZq88nJycG5c+ewY8cOAM/3ObD66Y0MPDt16lTt7RqRSIS5c+di7ty5tVcoxp6DjqYYVg10YdVAt0brK5SExwXqW6KEQOJJa2vZM6sl8hfXqUrdy0xfG7qa4tJxZthLVSxTCC3omeU+a3Ut64/ySyB/yvOR6miKRZU+e9UWddXOdLoaSqTeuQ07C31oa2vjjyF/vPB660qq/n5IpVKkpaUJ71NTU+Hv71/t8rLbxlZWVgBKA7t+/frh/PnzCAgIwPbt24VWvIEDB2LNmjUAgI0bN+LkyZMAgB49eiAkJETI9/z585g5cyaOHz+utr9A69atkZKSgocPH8LCwkJYJzAwEGKxGBkZGTA3N0dxcTHeffddzJw5E23bthW279OnjzBe9ddffw0TExNcunQJiYmJsLOzg1wux8OHDxEcHKzSsvqsdu7ciZkzZwrvra2t0aRJE+jo6EAqlcLNzQ03b95EbGwszp49iyVLlgidrfT09DBq1CgAwP79+xEUFCR0GHqez4HVT29k4MnYm0qsIYKZgTbMDGrWEa6sU5W6ltTyt07LB7HP26mK1U8G2pIqhw8zLQswDf7t9Pasnd2KioqEv0UiEfQ0a/YM9Yvi5+eHhIQEpKWlwcjICJGRkUJvaaA0qBGLxbh8+TJcXV2xfft2bNy4EXK5HI8fP4a5uTmKiooQFRUldK4xMzNDTEwMWrdujWPHjgmdeJo0aYJjx45h0KBBiImJEUY+SU5OxtChQ7Fnzx4hiAJKHwOzsbGBWCxGQkIC8vLyYGZmhocPH8LU1FQoV2FhIczMzIQe6507d8awYao98x88eICGDRvi3r172LlzJ06dOgVTU1PcvXtXKEP//v3/U9D54MEDXL16VeWOYu/evTF9+nR8+umnyMnJwdWrV2FnZyf0gAeAuXPnwtzcXAg6gdLb7GPGjPlPnwOrnzjwZIxVqXynqiamz96pqnxLqvB6QS1r7NmVb4muctSEci3RDfQ0oaP5eg/vJZFIsGzZMgQGBkKpVOLTTz+FmZkZgoODERoaCisrK6xevRqDBw9GUVERhg0bBg8PD+Tn5yMoKAgymQwKhQIDBw5E9+7dAQDr16/H+PHjoVQqYWxsjB9//BEAsHTpUnz44YdYuHAhtLS08MMPPwAobYEsuz0OlHZy3bt3L44dO4b//e9/0NTUhI6ODrZu3QoNDQ2cPn0as2fPhkQiEdJFIhHOnj2LnTt3wtPTE/v27QMA/Pzzz/Dw8MBHH32EK1euQCwWY+nSpVXe4i6zceNGzJkzB/fu3YOzszOGDh2KxYsXIyoqCqNHj8bDhw/x1ltvITAwUOgM9euvv+Kdd95R6SHv5uaG9u3bw93dHWKxGF999RXMzc2r3Xd2djZiY2Px66+/qqQ/6+fA6qc3fsrMl4Wn3GKsZoiIA89aIhaJ6t2zt6/zlJms/uMpM2sft3gyxuqUSCSC5kvqVMIYY6x+4cH8GGOMMcZYreDAkzHGGGOM1QoOPBljjDHGWK3gwJMxxhhjjNUKDjwZY4wxxlit4MCTMcbYGy0iIgLOzs5wcnISppksLzY2Fm5ubnB0dMT8+fOF9Pfffx9eXl7w8PAQxu0ESucrDwwMhJOTE/r27SsMkr9ixQp4enrC29sbQUFBuH//PoDSIcXGjRsHR0dH+Pr64p9//gEAnD17Fl5eXvD29karVq3w+++/C/sODQ2Fk5MTmjVrhoiICABAbm4uWrVqBW9vb3h4eGDDhg1vRB3K9O/fH76+vtV91Kw+IPZSZGdnEwDKzs6u66Iwxli9VVhYSImJiVRYWFgn+5fJZOTk5ESpqamUk5NDjo6OlJmZqbKOr68vxcXFkUwmI19fX4qPjyciUvl9HzhwIIWFhRER0ZQpU2jVqlVERDRp0iTh7/Lrr1mzhiZOnEhERAcOHKB+/foREdG+ffuEv/Pz80kulxMR0ZUrV8jT05OIiDIyMqhZs2aUk5NDKSkp5OjoSDKZjORyOeXn5wvb2tnZUUZGxmtfByKiw4cP08CBA6lly5aVP+RqqDv/+Pr9cnGLJ2OMsXqBiKAsKHjhL6pmnpSyVjSpVApDQ0MEBwcjKipKWJ6eng65XA5PT09IJBIMGTIE4eHhACAMLi6Xy1FYWChMFRoeHi5MWTl8+PBK6wOlLXvq1u/VqxfOnTsHIoKenp4wC1D59aOiohAcHAxDQ0NYW1vD1dUV58+fF+Y7B0oHRlcoFCCi174OMpkMCxYswBdffFHl58zqDx5AnjHGWL1AhYX426flC8/X+eKfEOmpn/I1PT0dUqlUeG9tbY20tLRql586dUp4379/f5w4cQJBQUHo3bs3gNIpH42NjdXm9+233+L777+HgYGBkE/5fWhoaMDU1BSZmZkwNzfH0aNH8cknn+D+/fvCPOrVlfnx48cICAjAjRs3sGTJEpibm+PChQuvdR2WL1+OkJAQGBoagtV/3OLJGGPsjaWuNbSsVa4my/fs2YO7d++CiHDs2LFKyyu+nzFjBm7fvo3Ro0dj1apVT93HW2+9hatXryIyMhKzZ89+6voNGjRAXFwckpKSsG3bNty/f/+1rkNaWhoOHz6MkJCQSstZ/cQtnowxxuoFka4unC/++VLyrYpUKlVpzUtNTYW/v3+1yy0tLVXy0NLSQp8+fbBv3z68/fbbMDIyEloM1a0PAEOHDkXnzp0xb948YR++vr5QKpXIysqCqampyvqtW7dGSkoKHj58CKlUivPnz1dbpkaNGsHT0xOnT59Gu3btXts6XLp0CYmJibCzs4NcLsfDhw8RHBwstKyy+odbPBljjNULIpEIGnp6L/xVsfWuPD8/PyQkJCAtLQ25ubmIjIxEUFCQsNzKygpisRiXL1+GXC7H9u3b0atXL8jlciQnJwMAFAoFDh48CBcXFwBAz5498fPPPwMAtmzZgl69egEAbty4IeR74MABteuHh4ejbdu2EIlESEpKgkKhAAAkJCQgLy8PZmZm6Nq1KyIjI5Gbm4vU1FRcuXIFfn5+uH//PnJycgAAOTk5OH36NJydnV/rOvTo0QN3795FcnIyzp49Cw8PDw4667va78/0ZuBecYwx9nR13audiGj//v3k5OREDg4OtH79eiIi6t69O6WlpRERUXR0NLm6upK9vT3NmTOHiIiKioqodevW5O7uTm5ubjR+/HgqKSkhIqIHDx5Qx44dycHBgd555x0qKCggIqKxY8eSq6sreXl5Uffu3enOnTtERKRQKOjDDz8ke3t78vHxoevXrxMR0YYNG4T1/f396eTJk0KZ169fTw4ODuTk5ET79+8nIqILFy6Ql5cXeXp6koeHB61du1ZY/3WtQ3lJSUncq/0VICKqprsfe245OTkwNjZGdna2Si9Axhhj/yoqKkJSUhLs7Oygo6NT18Vhbxh15x9fv18uvtXOGGOMMcZqBQeejDHGGGOsVnDgyRhjjDHGagUHnowxxhhjrFZw4MkYY4wxxmoFB56MMcYYY6xWcODJGGPsjRYREQFnZ2c4OTkhNDS00vLY2Fi4ubnB0dER8+fPF9K//vpr2NjYwNzcXGX9ESNGwN7eHt7e3vD29kZ6ejoAYMWKFfD09IS3tzeCgoJw//59AKXD9/To0QPe3t7w9PTEb7/9ppJfXFwcJBIJIiIihLSLFy/Cz88Pbm5uaN++vZD+7rvvwsTEBP3791fJw9bWVth3cHCwkP7+++/Dy8sLHh4eGD9+PJRKpbDP1q1bw9vbG+3atcOtW7dU8lu1ahVEIhHy8vKEtK1bt6J58+Zwc3PD1KlTAQDJyclo164ddHR0sHr1amHd5ORk6OnpCceobCrN3NxctGrVCt7e3vDw8MCGDRuEbXbs2AEPDw+4u7tj0KBBKC4uBgB06tQJLi4uQl6snqvrgURfVzwALWOMPV1dDyAvk8nIycmJUlNTKScnhxwdHSkzM1NlHV9fX4qLiyOZTEa+vr4UHx9PRESxsbGUnp5OZmZmKuuHhIRQeHh4pX2Vvx6sWbOGJk6cSERES5cupRkzZhARUWJiIjVr1kxYT6lUUvfu3albt25CnjKZjDw9PSkxMZGIiO7fvy+sf/z4cTpw4AD169dPZd9Nmzal3Nzcass0cOBACgsLIyKinj170qFDh4iIaO3atTRmzBhhvQcPHlC3bt3IxsZGyPPatWvUqlUrysnJUSlTZmYmxcTE0KxZs2jVqlVCHlUN9i6Xyyk/P5+IiPLz88nOzo4yMjJIqVSSpaUlZWRkEBHRe++9R9u2bSMiooCAAOEzeVY8gHzt4xZPxhhj9QIRQVaseOEvqmaelLLWTKlUCkNDQwQHByMqKkpYnp6eDrlcDk9PT0gkEgwZMgTh4eEAgFatWqmdw7wq5Qcjz83NFabyFIlEyM3NFdLL5/nzzz+jc+fOaNSokZAWFRWFVq1aoXnz5gCAhg0bCssCAwNhaGj4zGWSy+UoLCysUZlmzpyJefPmqUxFGhoaiokTJwr7LiuTqakp/P39oampWaPyiMVi6OnpASgd3F2h+PfzIyIUFBRAoVCgoKDgmY49qz8kdV0AxhhjDADkJUr88H+nXni+Y1YEQFNbrHZZeno6pFKp8N7a2hppaWnVLj916ullnDZtGj7//HP06dMHc+fOFYK0b7/9Ft9//z0MDAyEfMaMGYNevXrBysoKhYWFOHr0KIDSW/ChoaE4evQoxowZI+R948YNyOVyvPXWW3j06BE++ugjjBo1qtryiEQidOzYERKJBJ999hn69esnLOvfvz9OnDiBoKAg9O7dGwCwePFiBAUFYdKkSTAwMEBsbCwAICYmBkqlEn5+fir537hxAxoaGmjTpg0kEgmWLl0Kf3//asv0999/o0WLFjA3N8eyZcvg6ekJAHj8+DECAgJw48YNLFmyRHiUYfXq1XB3d4e2tjbeeustdOrUSchryJAhkEgk+OCDDzBhwoRq98vqFrd4MsYYe2Opaw0t35L3tOXqLFy4EFevXkV0dDT++usvbNmyRVg2Y8YM3L59G6NHj8aqVasAAIcOHULr1q2Rnp6O48ePIyQkBEqlEnPmzMFnn30GLS0tlfxlMhmio6Oxe/duHDt2DMuXL8e1a9eqLdO5c+dw8eJFhIWFYebMmbh586awbM+ePbh79y6ICMeOHQMArF27Ft9//z1SU1PxySefYMqUKVAqlZg5cya++eabSvnLZDLcuXMHZ8+exdq1azFkyJBqW5otLS1x+/Zt/PXXX5g1a5bKM6kNGjRAXFwckpKSsG3bNty/fx8ymQw//PAD4uPjhbJu3boVALBt2zZcvnwZR48exebNm2v0HwNWd7jFkzHGWL0g0dLAmBUBLyXfqkilUpUWztTUVJWWOnXLn3aLt2y5np4ehg4dijNnziAkJERlnaFDh6Jz586YN28eNm3ahLlz5wIAWrRoASJCRkYG/vzzT+zduxcfffQRMjIy8Ntvv+Hnn3+GtbU1AgMDYWJiAgAICAhAfHw8XFxcqiyTlZUVgNIW2y5duuDSpUtwdHQUlmtpaaFPnz7Yt28f3n77bWzfvh0rV64EAAwcOBBr1qxBbm4uEhIS0KZNG+FYuLm5IT4+XiiTWCyGh4cHdHR0kJGRAQsLC7Xl0dbWhra2NgAI22VkZKh01GrUqBE8PT1x+vRp2NraQiKRwMbGBgDQt29fnDhxAu+//75QN1NTU/Tr1w/nz59HQMCLP4/Yi8EtnowxxuoFkUgETW3xC39V10Lp5+eHhIQEpKWlITc3F5GRkQgKChKWW1lZQSwW4/Lly5DL5di+fTt69epVbT3u3r0LAFAoFIiIiICbmxuA0tvRZQ4cOCAEik2aNBFaGpOSkpCTkwNzc3OcPn0aycnJSE5ORv/+/bFx40Z07doVQUFBuHjxIoqKilBcXIyYmJhqg878/Hzhec3Hjx/j9OnTaN68OeRyOZKTk4WyHjx4UMjHzMwMMTExAIBjx47B2dkZxsbGePjwoVAma2trXLlyBUZGRujduzdOnDgBALh9+zby8vJgZmZWZZkePnwIhUIBALh8+TIKCwthZmaG+/fvIycnB0DpowanT5+Gs7MzpFIpLl++jEePHqmUSS6XIyMjA0DpM6FRUVHC8Wb1E7d4MsYYe2NJJBIsW7YMgYGBUCqV+PTTT2FmZobg4GCEhobCysoKq1evxuDBg1FUVIRhw4bBw8MDADB37lyEhobi0aNHsLa2xqeffoqJEydi6NChyMjIgEKhQKdOnfDhhx8CAJYtW4YzZ85AU1MTVlZWWL9+PQDgyy+/xPDhw7Ft2zaIRCL88MMP0NCoul3I1NQUEyZMgI+PDzQ0NDBixAihTGVBaX5+PqytrbF3716YmZnh3XffBQAolUpMnDgRbm5uKC4uxuDBg5GXlwciQseOHTFu3DgAwPr164XhlYyNjfHjjz9WexyDg4Nx6NAhuLm5QUtLC6GhodDQ0EBOTg5cXV2Rk5MDsViMpUuXIjk5GadPn8bs2bMhkUigo6ODrVu3QiQSITU1FaNHjwYRgYjw8ccfC89+zpgxA23btoVEIoG7uzvGjh2L4uJiBAUFQSaTQaFQYODAgejevft/OCPYyyai6h7CYM8tJycHxsbGyM7OVunJyBhj7F9FRUVISkqCnZ0ddHR06ro47A2j7vzj6/fLxbfaGWOMMcZYreDAkzHGGGOM1QoOPBljjDHGWK3gwJMxxhhjjNUKDjwZY4wxxlit4MCTMcbYGy0iIgLOzs5wcnJCaGhopeVl87k7Ojpi/vz5Qvo///wDX19fODo6Yty4ccJMPe+99x68vb3h7e0NqVSKPn36AAAmT54spNvZ2cHb2xsAsHnzZjRs2FBYduDAAQBAcnIy2rVrBx0dHaxevVqlTFOmTIG7uzs8PT2FKTZzc3PRqlUreHt7w8PDAxs2bBDSy/L29vaGsbExvvvuOwDAkSNH4O3tDTc3N0yePFnIPy4uDq1bt4a3tzfatWuHW7duqex/1apVEIlEyMvLq3QsRSIREhISAADFxcXCEFS+vr64dOmSsO7Fixfh5+cHNzc3tG/fXkh/9913YWJiojKbUUFBAYKDg+Hi4gJ3d3dh1qfy+vfvD19f30rprJ4h9lJkZ2cTAMrOzq7rojDGWL1VWFhIiYmJVFhYWCf7l8lk5OTkRKmpqZSTk0OOjo6UmZmpso6vry/FxcWRTCYjX19fio+PJyKivn37Unh4OBER9enTR/i7vKFDh9KmTZsqpX/++ec0Z84cIiLatGkTTZ06tdI6mZmZFBMTQ7NmzaJVq1YJ6QcOHKAePXqQQqGgrKwsatWqFcnlcpLL5ZSfn09ERPn5+WRnZ0cZGRkqeSqVSrKxsaFbt26RQqEgGxsbSkpKIiKicePGUVRUFBER9ezZkw4dOkRERGvXrqUxY8YIeTx48IC6detGNjY2lJubK6QXFhZS586dyc/PTzhGK1eupHHjxhER0a1bt6hz587Ccff09KTExEQiIrp//76Qz/Hjx+nAgQPUr18/IS0/P59OnjxJRER5eXnk4uJCN27cEJYfPnyYBg4cSC1btqx0HKuj7vzj6/fLxS2ejDHG3lhlrZlSqRSGhoYIDg5GVFSUsDw9PR1yuRyenp6QSCQYMmQIwsPDQUSIjo5Gjx49AADDhw9HeHi4St7FxcWIiooSWjzL2717N957771qy2Zqagp/f39oamqqpF+9ehWdOnWChoYGTExMYGFhgfPnz0MsFkNPTw9A6fiUCoWi0nzp0dHRaNy4Mezs7JCRkQFDQ0PY2toCADp37oywsDAApbNIlc12lJubqzJN6MyZMzFv3rxKM0ItXrwY48ePh66urkpZu3TpAgCws7PDvXv3cO/ePURFRaFVq1Zo3rw5AKBhw4bCNoGBgTA0NFTJW09PT5gGU19fH05OTsIMUTKZDAsWLMAXX3xR7fFk9QMHnowxxuoFIoKsqOiFvyoGX+Wlp6dDKpUK762trVXmZq9qeWZmJkxNTYXgq+J2APDbb7+hTZs2aNCggUr6pUuXoK2tLQRdALB9+3Z4enpi+PDhyMrKqvY4eXp64uDBgyguLkZaWhpiY2OFfT9+/BheXl7CTErl5z4HgF27dgkBr4WFBfLy8hAfHw+lUon9+/cL+SxevBhTp06FtbU1fvzxR0yZMgUAEBMTA6VSCT8/P5V8k5OTERMTo3J7vKys+/btg1KpRHx8PG7evIm0tDTcuHEDcrkcb731Flq2bPnUmZHKS0lJweXLl+Hj4wMAWL58OUJCQioFq6x+4ikzGWOM1Qvy4mKsDOn/9BWf0cSf9kCzilmR1AWl5Vvyqlr+tO0A1SCvuvRevXph8ODB0NLSwoIFCzB16lRs2rSpyvp069YNf/zxB/z9/SGVStGmTRtIJKWX8wYNGiAuLg73799H37590b9/fzRq1EioS1hYGM6dOyeUd+vWrRg3bhwUCgXat2+P/Px8AMDatWvx/fffIzg4GGvWrMGUKVPwww8/YObMmdi2bVulMk2bNg0LFy6slD569GhcuXIFPj4+cHFxga+vLyQSCWQyGaKjoxETEwORSIT27dujbdu21c45D5S25L733ntYunQp9PX1kZaWhsOHD+Po0aO4fft2tduy+oFbPBljjL2xpFKpSktlamqqym3lqpabm5sjKytLCEArbldYWIijR4+id+/elfa5a9cuDBw4UHhvZmYGbW1tiEQifPDBBzh//vxTyz1nzhxcunQJBw8eREFBARwdHVWWN2rUCJ6enjh9+rSQdvbsWdjY2KBJkyZCWvv27XHu3DnExMTA29tbyGf79u0IDg4GAAwcOBC///47cnNzkZCQgDZt2sDW1hapqalwc3NDTk4OLl68iHfeeQe2traIiYlBUFAQEhMToampiVWrVuHSpUvYsWMHMjMzYWtrC2trawQGBsLExAQNGjRAQEAA4uPjq60zESEkJATBwcFCy+qlS5eQmJgIOzs7tG/fHvHx8UK5Wf3ELZ6MMcbqBYm2Nib+tOel5FsVPz8/JCQkIC0tDUZGRoiMjMTs2bOF5VZWVhCLxbh8+TJcXV2xfft2bNy4ESKRCK1bt8bBgwfRs2dPbNmyBaNGjRK2i4yMRIcOHSrd/v3zzz9hbGwMJycnIe3evXto3LgxAGDfvn1wc3Ortj5yuRy5ubkwMTHBuXPnUFxcDDc3N9y/fx+6urowMjJCTk4OTp8+jfHjxwvbqWuBffDgARo2bIi8vDysWrUKP/30E4DSYDgmJgatW7fGsWPH4OzsDGNjYzx8+FDY1tbWFgkJCTAwMFDp9d6pUyesXr0arq6uyM/Ph0gkgp6eHnbs2IGWLVvC2NgYQUFB+N///oeioiKIRCLExMRg3Lhx1dZ75syZ0NPTU3mWs0ePHsKznsnJyejfvz8iIyOrzYfVLQ48GWOM1QsikajKW+Ivi0QiwbJlyxAYGAilUolPP/0UZmZmCA4ORmhoKKysrLB69WoMHjwYRUVFwtBAALBo0SIMGjQI//d//4cuXboIHY2Ayq2a1aV/9913iIiIgFgshlQqFYZBysnJgaurK3JyciAWi7F06VIkJyejuLgY7dq1A1DaKacsWExNTcXo0aNBRCAifPzxx/D09AQAKJVK7N27t1Jr6sKFC3Ho0CEAwKxZs4Rb3evXr8f48eOhVCphbGz8TM9glnfv3j0EBwdDJBLByclJeITA1NQUEyZMgI+PDzQ0NDBixAjhuAYFBeHixYvIz8+HtbU19u7dC0tLSyxatAiurq7CMFSLFi1CUFDQc5WL1R0RVffUNXtuOTk5MDY2RnZ2NoyMjOq6OIwxVi8VFRUhKSkJdnZ20KnloJMxdecfX79fLn7GkzHGGGOM1QoOPBljjDHGWK3gwJMxxhhjjNUKDjwZY4wxxlit4MCTMcYYY4zVCg481ZDL5fjiiy9gZ2cHXV1d2NvbY/78+VAqlXVdNMYYY4yxVxYHnmosWrQI69atw+rVq3H16lUsXrwYS5YswapVq+q6aIwxxl6wiIgIODs7w8nJCaGhoZWWx8bGws3NDY6Ojpg/f76Q/s8//8DX1xeOjo4YN26cMIvRp59+Ck9PT3h5eWHAgAEoKCgAUDrHeKdOneDt7Y2WLVsKY2pmZWWhV69e8PT0RIcOHXDnzh0ApQOit2vXDjo6Oli9erVKmUJDQ+Hk5IRmzZohIiJCSJdIJPD29oa3tzc++OCDp9ahU6dOcHFxEbYpExcXh9atW8Pb2xvt2rUTBohfsWIFPD094e3tjaCgINy/f1/YZuvWrWjevDnc3NwwdepUAMDJkyfRoEEDIf9169YBAE6cOCGkeXt7QywW49KlS9XWYceOHfDw8IC7uzsGDRqE4uJiAECHDh2E9S0sLDBp0iQApTMdTZ8+Hc2aNUPz5s2xa9cu9ScAq13EKunRoweNGjVKJa1v3770/vvv1ziP7OxsAkDZ2dkvuniMMfbaKCwspMTERCosLKyT/ctkMnJycqLU1FTKyckhR0dHyszMVFnH19eX4uLiSCaTka+vL8XHxxNR6XUhPDyciIj69Okj/F3+d3/69Om0fPlyIiL6+OOPad26dUREFBkZSV27diUioilTptC3335LREQxMTE0ePBgIiLKzMykmJgYmjVrFq1atUrIMyMjg5o1a0Y5OTmUkpJCjo6OJJPJiIjIzMxMbT2rqkNAQIDwd3k9e/akQ4cOERHR2rVracyYMZXqtmbNGpo4cSIREV27do1atWpFOTk5RER0//59IiI6ceIE9evXT22Zyty8eZNsbW2F9+rqoFQqydLSkjIyMoiI6L333qNt27ZVWq9du3Z04sQJIiLasGGDUG6lUkkPHz6stL6684+v3y8Xt3iq0b59exw7dgzXr18HUPo/v7Nnz1Y7/2txcTFycnJUXowxxuq3spZAqVQKQ0NDBAcHIyoqSlienp4OuVwOT09PSCQSDBkyBOHh4SAiREdHC7MVDR8+HOHh4QAgDDpORMjLy4NIJAJQOjNTbm4uACA3N1eY2/3q1avo0qULAMDf3x+HDx8GEcHU1BT+/v7Q1NRUKXNUVBSCg4NhaGgIa2truLq6Vju/e1V1qE5VZS0/oHpubq5Qt9DQUEycOFGYIrRhw4bV5l/ezp071c7yVBERoaCgAAqFAgUFBUKZyqSlpSEpKQkdO3YEUDr70pdffinUx9zcvMZlYi8PB55qfPbZZxg8eDBcXFygqamJFi1aYNKkSRg8eHCV2yxcuBDGxsbCq0mTJrVYYsYYe/UREZQlihf+omom6EtPT4dUKhXeW1tbIy0t7anLMzMzYWpqKgReFbebOHEirKyskJiYiLFjxwIonZLyp59+grW1NSZNmoR58+YBADw9PREWFgagNKjMzMxEVlbWc5U5JycHLVu2RPv27XHq1Kka1XHIkCHw8fHB2rVrhbTFixdj6tSpsLa2xo8//ogpU6YIy7799ls0bdoUW7ZsEeZNv3HjBuLj49GmTRt06NABf/zxh7D+yZMn4eXlhXfffRe3b9+uVJ+Kc8irq4NIJMLq1avh7u4OS0tLGBgYoFOnTir57N69G/369YOGRmlok5KSgtDQUPj6+qJv3764d+9elceU1R6eq12NnTt3YuvWrdi2bRvc3Nxw6dIlTJo0CVZWVggJCVG7zcyZM1W+mDk5ORx8MsbYMyCZEumzf3/h+VrNbwuRllj9PtUEpWXBZHXLn7bdypUr8d1332Hq1KnYsWMHRo4ciW3btmH8+PGYMGECDh48iNGjR+Po0aOYOXMmPv74Y7Ro0QKtW7eGvb09JJKqL89EpLKv8vtOTk6GlZUVEhIS0KNHD8THx1db1m3btsHKygpZWVno1q0b3NzcEBAQgLVr1+L7779HcHAw1qxZgylTpgjPv86YMQMzZszA8uXLsWrVKsybNw8ymQx37tzB2bNnkZiYiD59+uDmzZvw8fFBcnIyDAwMsHXrVowYMQInTpwQynH9+nXk5+fDx8dHSFNXB11dXfzwww+Ij4+HVCrF+++/j61bt+L9998Xttu1axeWLFkivM/Ly4OFhQUuXLiA9evXY+rUqfjll1+qPK6sdnCLpxrTp0/HjBkzMGjQIHh4eGDYsGGYPHkyFi5cWOU22traMDIyUnkxxhir36RSqUrrX2pqqsot3KqWm5ubIysrSwjqKm4HABoaGhg0aBD27NkDANi4cSMGDBgAAOjRo4fQmcbY2Bg///wz/vrrL3z33XdQKBQwNjZ+rjJbWVkBANzd3eHq6orr16/XaH1TU1P069dPuGW/fft24fGygQMH4vffK/+HYOjQoULdrK2t8c4770AsFsPDwwM6OjrIyMiAkZERDAwMAADvv/8+EhISVPLYuXOnSmtnVXW4dOkSJBIJbGxsIBaL0bdvX5UypaSkIDU1FW3btlU5Tv369QMA9O3bVzjerG5xi6caBQUFQlN9GbFYzMMpMcbYSyTS1IDV/LZPX/E58q2Kn58fEhISkJaWBiMjI0RGRmL27NnCcisrK4jFYly+fBmurq7Yvn07Nm7cCJFIhNatW+PgwYPo2bMntmzZglGjRgEove3s5OQEAAgPD4eLiwsAoEmTJjh27BgGDRqEmJgY4a7Y48ePoa+vD01NTfzvf//D0KFDq61P165dMW/ePMyfPx/Z2dm4cuUK/Pz88OjRI+jp6UFbWxupqalITEyEvb09TE1N1dZBLpfj8ePHMDc3R1FREaKiojB9+nQAgJmZGWJiYtC6dWscO3YMzs7Olep24MABoW69e/fGgQMHMGjQINy+fRt5eXkwMzPD/fv30ahRIwCljxHY29ur1GXXrl3Ytm2b8L6qOhQVFeHy5ct49OgRTExMcOzYMTRv3lwlnwEDBqi0BPfu3RsnTpzA4MGDcfLkSZX1WR2qmz5N9VtISAhJpVKKiIigpKQkCgsLI3Nzc/r0009rnAf3imOMsaer617tRET79+8nJycncnBwoPXr1xMRUffu3SktLY2IiKKjo8nV1ZXs7e1pzpw5wnbXr18nHx8fsre3pw8//JAUCgURlfYId3NzIw8PDxo0aBA9fvyYiIji4+OpdevW5OnpSb6+vhQbG0tERKdPnyYnJydq1qwZDR8+nAoKCoio9DoilUrJ0NCQGjRoQE2bNhX2vX79enJwcCAnJyfav38/ERGdO3eO3N3dydPTk7y8vGjv3r3C+urqkJeXRz4+PuTh4UGurq40d+5cYf2TJ0+St7c3eXp6UocOHejGjRtERDR27FhydXUlLy8v6t69O925c4eISnuNf/zxx+Tq6kre3t50+PBhIiJauXKlsH7Hjh3pypUrwj6uXr1KLi4uKp9FdXVYvXo1ubi4kLu7Ow0aNEjlnPHz86OYmBiVvDIzM6lr167k4eFBAQEBlJSUVOmz517ttU9EVM1T12+o3NxcfPnll9i7dy8ePHgAKysrDB48GLNnz4aWllaN8sjJyYGxsTGys7P5tjtjjFWhqKgISUlJsLOzg46OTl0Xh71h1J1/fP1+ufhWuxqGhob47rvv8N1339V1URhjjDHGXhvcuYgxxhhjjNUKDjwZY4wxxlit4MCTMcYYY4zVCg48GWOMMcZYreDAkzHGGGOM1QoOPBljjL3RIiIi4OzsDCcnJ2FayPJiY2Ph5uYGR0dHzJ8/X0j/559/4OvrC0dHR4wbN06YxSg0NBROTk4QiUTIy8sT1k9OTkanTp3g4eGB4OBgZGdnVyqHSCQSZvcpLi7GsGHD4OHhAV9fX2HmnZs3b6JFixbw9vaGt7c3Dhw4IOTx7rvvwsTEBP379xfScnNzhXW9vb1hbGwsjNrSoUMHId3CwgKTJk0CAHz66afw9PSEl5cXBgwYgIKCAgClMwR16tQJ3t7eaNmypTDT0ZIlS4R8nJ2d0aBBg2rrkJeXhy5dusDAwADTpk2rdMwLCgrQtGlTYVlBQQGCg4Ph4uICd3d3rFq1Slj3/fffh5eXFzw8PDB+/Hie7KW+q+NxRF9bPAAtY4w9XV0PIC+TycjJyYlSU1MpJyeHHB0dKTMzU2UdX19fiouLI5lMRr6+vhQfH09ERH379qXw8HAiIurTp4/w9+XLl+nWrVvUtGlTys3NFfLp27cv7dixg4iIduzYQTNnzhSWFRYWUufOncnPz0/If+XKlTRu3DgiIrp16xZ17tyZiIiKioqouLiYiIgePHhAUqmUlEolEREdP36cDhw4QP369VNbX6VSSTY2NnTr1q1Ky9q1a0cnTpwgIlK5dk2fPp2WL19OREQff/wxrVu3joiIIiMjqWvXrpXy2bBhA4WEhDy1DqdOnaK1a9fS1KlTK+Uxa9YsGjBggLAsPz+fTp48SUSlA9+7uLgIg9qXL+vAgQMpLCxMbd3V4QHkax+3eDLGGKsXiAglJSUv/EXVzJNS1poplUphaGiI4OBgREVFCcvT09Mhl8vh6ekJiUSCIUOGIDw8HESE6Oho9OjRAwAwfPhwhIeHAwA8PDxgZ2dXaV9Xr15Fly5dAACdO3dGWFiYsGzx4sUYP348dHV11a5vZ2eHe/fu4d69e9DW1hYmM8nPz1dp4QsMDIShoWGV9Y2Ojkbjxo0rlS8tLQ1JSUno2LEjAAgDpxMR8vLyhKkoRSIRcnNzAZS2pFacnx4onb6ybP716urQsWNHlfqWuXHjBq5duybMFQ8Aenp6CAgIAADo6+vDyckJd+/eVSmrXC5HYWGhyrSZrP6p1QHk7ezsnuuEmDRpEiZOnPgSSsQYY6y+kMlkWLBgwQvPd9asWVXOOpeeng6pVCq8t7a2RlpaWrXLT506hczMTJiamgrXtIrbqePp6Ylff/0VY8eORVhYmLB+cnIyYmJiMHv2bKxevVpl/X379qFv3764cuUKbt68ibS0NDRu3BiJiYl47733kJSUhK1bt9b42lo+KCxv9+7d6NevHzQ0/m2PmjhxInbv3g1nZ2csW7YMQOmxfPvtt/Hdd99BqVQiOjpaJZ+MjAzExcXhrbfeemodqjJt2jQsWbIEv//+u9rlKSkpuHz5Mnx8fIS0/v3748SJEwgKCkLv3r1rdCxY3ajVwHPz5s3PtZ2tre0LLQdjjDEGQG1raPkgrqrlT9tOnWXLlmHChAlYv349evToAX19fQClgdbChQsrrT969GhcuXIFPj4+cHFxga+vLySS0su2q6sr4uPjcfPmTQwfPhzdunV76pSjRISwsDCcO3eu0rJdu3ZhyZIlKmkrV67Ed999h6lTp2LHjh0YOXIktm3bhvHjx2PChAk4ePAgRo8ejaNHjwrbhIWFoXfv3tDU1HxqHdTZv38/mjVrhmbNmqkNPIuKivDee+9h6dKlwvEDgD179qCkpAQhISE4duwY3n777WqPBas7tRp4ljWTM8YYYxVpampi1qxZLyXfqkilUpWWytTUVPj7+1e73NLSEubm5sjKygIRQSQSCenVkUql2L9/v5DPoUOHAAAXL17EO++8AwC4d+8egoKCcOTIEbi6uqp0onFxcanUEOPo6AhjY2PEx8ejVatW1e7/7NmzsLGxQZMmTVTSU1JSkJqairZt21baRkNDA4MGDcL8+fMxcuRIbNy4ESdPngQA9OjRAyEhISrr79y5EzNnzhTea2pqPrUO5cXExGDHjh3YvXs38vLyIJPJYGRkhNmzZ4OIEBISguDgYJXOU2W0tLTQp08f7Nu3jwPPeqzOn/FctGgRAODy5cuQyWR1XBrGGGN1RSQSQUtL64W/qmuJ9PPzQ0JCAtLS0pCbm4vIyEgEBQUJy62srCAWi3H58mXI5XJs374dvXr1gkgkQuvWrXHw4EEAwJYtW9CrV69q65eRkSG0lH7zzTcYM2YMAODWrVtITk5GcnIyWrdujaioKLi6uiI/P1/oTb5jxw60bNkSxsbGSElJQXFxMYDSRwESEhLUPlNaUVW32Xft2oUBAwaoHKcbN24If4eHh8PFxQUA0KRJExw7dgxAaZBYPoh98OABrl69isDAQCGtqjpUZeHChUhJSUFycjKWLl2KDz/8ELNnzwYAzJw5E3p6evjiiy+E9eVyOZKTkwEACoUCBw8eFMrK6qk66tQkOHv2LBERvfvuu+Ti4kIeHh40ePBgWrBgAYWHh9O9e/fquITPh3vFMcbY09V1r3Yiov3795OTkxM5ODjQ+vXriYioe/fulJaWRkRE0dHR5OrqSvb29jRnzhxhu+vXr5OPjw/Z29vThx9+SAqFgoiIQkNDSSqVklgsJisrK5o+fToRlfZkd3JyIicnJ5oyZYqwfnkBAQFCr/abN29Ss2bNyNnZmXr27EkPHz4kIqKIiAhyd3cnLy8v8vb2pj179gjbd+3alczNzUlXV5ekUinFxsYSEZFCoSCpVErp6emV9unn50cxMTEqaT179iQ3Nzfy8PCgQYMG0ePHj4mIKD4+nlq3bk2enp7k6+sr5E9EtHbtWqEHe5mq6kBE5OrqSiYmJmRgYEBSqZTu3r2rsu2mTZuEXu0pKSkEgFxdXcnLy4u8vLzo0KFDVFRURK1btyZ3d3dyc3Oj8ePHU0lJSaU6VoV7tdc+EVE13f3qQEFBARISEhAfH4/4+HicOXMGwcHB+Oqrr+q6aM8kJycHxsbGyM7OFnrcMcYYU1VUVISkpCTY2dk99RlFxl40decfX79frlp9xrO8rKwsmJqaVkrX09ODn58f/Pz8hLSWLVu+coEnY4wxxhhTVWeBp7m5OaytreHl5aXyKpvtobyYmJg6KiVjjDHGGHtR6izwTExMxKVLl/DXX3/h/PnzWL9+PbKysqCrqws3Nzf88ccfwrrV9UhkjDHGGGOvhjoLPF1cXODi4oJBgwYBKB1f7NChQ/jkk0+EWQ4YY4wxxtjro86HUyojEonQvXt3bN26Fenp6XVdHMYYY4wx9oLVWeBZfm7Z8lq3bi0MTssYY4wxxl4fdRZ4GhgYwM/PD2PGjMGaNWtw7tw5ZGRkIDIyEnl5eXVVLMYYY2+YiIgIODs7w8nJCaGhoZWWx8bGws3NDY6Ojpg/f76Q/s8//8DX1xeOjo4YN26cMDh8RkYGAgMD4eTkhL59+6KoqAhA6ZzsnTp1goeHB4KDg5GdnQ0AWLJkCby9veHt7Q1nZ2c0aNAAAHDy5Ek0aNBAWLZu3Tph3xcvXoSfnx/c3NzQvn37p9bll19+gbu7O9zc3FSmxuzQoYOQv4WFBSZNmgQAGDFiBOzt7YVl5e9ELl26FM7OznB1dcX//vc/AKWPy40bNw6Ojo7w9fXFP//8AwAoLi7GsGHD4OHhAV9fX1y6dAkAcOLECSFvb29viMViYZlEIhHSP/jgA2G/mZmZeOedd+Di4gJXV1dhH19//TVsbGxgbm7+tI+a1Qd1NYDob7/9Rt9++y0NHjyYmjdvThKJhDQ0NEgsFtOCBQvqqlgvDA9AyxhjT1fXA8jLZDJycnKi1NRUysnJIUdHR8rMzFRZx9fXl+Li4kgmk5Gvr68wwHvfvn0pPDyciIj69Okj/D1lyhRatWoVERFNmjRJ+Ltv3760Y8cOIiodTH7mzJmVyrNhwwYKCQkhIqITJ05Qv3791JbZ09OTEhMTiYjo/v371dbl4cOHZGdnR1lZWaRQKKhHjx507dq1Svm2a9eOTpw4QUREISEhQn3KO3LkCAUHBwuDtJft+8CBA0JZ9+3bJ/y9cuVKYVD5W7duUefOnSvlefPmTbK1tRXem5mZVVqHiGjo0KH0yy+/EBFRfn4+5eXlERFRbGwspaenV7lddXgA+dpXZy2e3bp1w2effYZt27YhMTERubm5uHz5MlJTU1XmeWWMMfZmICIoFAUv/EXVzJNS1poplUphaGiI4OBgREVFCcvT09Mhl8vh6ekJiUSCIUOGIDw8HESE6Oho9OjRAwAwfPhwhIeHAyidYnLYsGGV0q9evSp0nu3cuTPCwsIqlaeqaS3Li4qKQqtWrdC8eXMAQMOGDauty61bt+Dq6goTExNoaGggICAAe/fuVckzLS0NSUlJ6NixY7X7Xr9+PWbOnCmMNlO27/J17tWrF86dOwciUqmznZ0d7t27h3v37qnkuXPnTgwcOLDa/WZnZ+PChQsYMmQIgNIxv/X19QEArVq1gqWlZbXbs/qjznq1V6SjowM3N7e6LgZjjLE6olQW4uQpjxeeb6eAeIjFemqXpaenQyqVCu+tra2RlpZW7fJTp04hMzMTpqamwrjT5bfLzs4W5iMvn+7p6Ylff/0VY8eORVhYmMp+gNJb9HFxcXjrrbeEtJMnT8LLywv29vb47rvv0LRpU9y4cQNyuRxvvfUWHj16hI8++gijRo2qsi5BQUGIj49HWloazM3NERkZCXd3d5V97969G/369YOGxr/tUdOmTcPnn3+OPn36YO7cuRCJRLhx4waOHj2KKVOmoEGDBli9ejWaNWumsm8NDQ2YmpoiMzMTnp6e2LdvH/r27YsrV67g5s2bSEtLQ+PGjYX97Nq1Cz/++KPwPicnBy1btoSuri6++eYbBAQEICkpCebm5hg6dCgSExMRGBiIxYsXQyKpN2EMq6F606udMcYYq23qWkPLT2JS1fLqtqs4CUrZ+2XLliEyMhI+Pj5ITU0VWuzKhIWFoXfv3kJroo+PD5KTkxEXF4d+/fphxIgRAACZTIbo6Gjs3r0bx44dw/Lly3Ht2rUqy2RqaooVK1agT58+6Ny5M5o3b14pYKvY0rpw4UJcvXoV0dHR+Ouvv7BlyxZh3wUFBYiNjcXUqVMxcuTIao/T6NGjYWJiAh8fH3zzzTfw9fVV2ff169eRn58PHx8fIS05ORl//vkn1q1bh+HDhyMnJwcymQyxsbGYPn06/vzzTzx48ACbNm2qtE9W//F/FRhjjNULGhq66BQQ/1LyrYpUKlVpeUxNTYW/v3+1yy0tLWFubo6srCwQEUQikZAOAEZGRkKrZ/l0qVSK/fv3C/kcOnRIpSw7d+5UedSs/Dzh77//PiZPngygtCUzMDAQJiYmAICAgADEx8dXW5c+ffqgT58+AEo745RtCwApKSlITU1F27ZthbSyMuvp6WHo0KE4c+YMQkJCYG1tjb59+wIAgoKChNvrZfv29fWFUqkUpsUWiURYtWqVkK+LiwtsbW1V6lzx0QIrKysAgLu7O1xdXXH9+nVYW1sLnZ0A4J133uERcF5R9aLF8+LFiygpKanrYjDGGKtDIpEIYrHeC39VbIEsz8/PDwkJCUhLS0Nubi4iIyMRFBQkLLeysoJYLMbly5chl8uxfft29OrVCyKRCK1bt8bBgwcBAFu2bEGvXr0AAD179sTPP/9cKT0jI0NoGfzmm28wZswYYT8PHjzA1atXERgYKKTdv39f+DsqKgr29vYASgO+ixcvoqioCMXFxYiJiYGLi0u1dXnw4AEA4N69e9i5cycGDx4s5L1r1y4MGDBA5TjdvXsXAKBQKBARESE8Cte7d2+cOHECAHD+/HnY2NhUqnN4eDjatm0LkUiE/Px8FBQUAAB27NiBli1bCo8hlO27fOD56NEjFBcXAygNnBMTE2Fvbw9LS0tYWFggKSkJQOkjCGXPuLJXTB11alKhoaFBf//9d10X44XiXnGMMfZ0dd2rnYho//795OTkRA4ODrR+/XoiIurevTulpaUREVF0dDS5urqSvb09zZkzR9ju+vXr5OPjQ/b29vThhx+SQqEgIqIHDx5Qx44dycHBgd555x0qKCggotKe7E5OTuTk5ERTpkwR1iciWrt2rdD7u8zKlSvJ1dWVvLy8qGPHjnTlyhVh2aZNm6h58+bk5uZGS5YsqbYuRET9+/en5s2bk7u7Ox06dEhlP35+fhQTE6OSFhgYSB4eHuTq6koTJkwgmUxGRERFRUU0cOBAcnNzIz8/P7p48SIRESkUCvrwww/J3t6efHx86Pr160RU2mO9WbNm5OzsTD179qSHDx8K+7h69Sq5uLio7PfcuXPk7u5Onp6e5OXlRXv37hWWnT9/nlq0aEHu7u70/vvvU1FRERERzZkzh6RSKWloaJBUKqUVK1ZQTXGv9tonIqqmu18t0dDQwLVr19CsWbO6LsoLk5OTA2NjY2RnZ6vcLmGMMfavoqIiJCUlwc7ODjo6OnVdHPaGUXf+8fX75aoXt9oZY4wxxtjrjwNPxhhjjDFWKzjwZIwxxhhjtYIDT8YYY4wxVis48GSMMcYYY7WCA0/GGGOMMVYr6kXgOWfOHJibm9d1MRhjjL2BIiIi4OzsDCcnJ4SGhlZaHhsbCzc3Nzg6OmL+/PlC+j///ANfX184Ojpi3LhxwuDwGRkZCAwMhJOTE/r27YuioiKV/FatWgWRSIS8vDwApcP39OjRA97e3vD09MRvv/0GAJDL5Rg+fDg8PDzg5uaGzZs3C3mEhobCyckJzZo1Q0REhEr+BQUFaNq0KaZNmya8Dw4OhouLC9zd3VVmEjpy5Ai8vb3h5uYmzIxU3rRp01Suz5MnT4a3tze8vb1hZ2cnzCS0ZMkSId3Z2RkNGjQAAPzyyy9CuoeHB8RiMbKysgAAU6ZMgbu7Ozw9PXH06NFq61Dd51Cmf//+8PX1Fd4TEaZPn45mzZqhefPm2LVrV6VtWB2o22FEX188AC1jjD1dXQ8gL5PJyMnJiVJTUyknJ4ccHR0pMzNTZR1fX1+Ki4sjmUxGvr6+FB8fT0REffv2pfDwcCIi6tOnj/D3lClTaNWqVURENGnSJOFvotLB5bt160Y2NjaUm5tLRERLly6lGTNmEBFRYmIiNWvWjIiI9uzZQ4MGDSIioocPH5K5uTkpFArKyMigZs2aUU5ODqWkpJCjo6MwwDsR0axZs2jAgAE0depUIiLKz8+nkydPEhFRXl4eubi40I0bN0ihUJCNjQ0lJSUREdG4ceMoKipKyOfKlSs0dOhQMjMzU3vsPv/8c5UB9cts2LCBQkJCKqUfOXKEAgICiIjowIED1KNHD1IoFJSVlUWtWrUiuVxeZR2q+xyIiA4fPkwDBw6kli1bqpRjzJgxRESkVCpVBq8vwwPI17560eLJGGOMERHyFYoX/qJq5kkpa0WTSqUwNDREcHAwoqKihOXp6emQy+Xw9PSERCLBkCFDEB4eDiJCdHQ0evToAQAYPnw4wsPDAZROGVk2h3n5dACYOXMm5s2bpzI9pUgkQm5uLgAgNzdXmCddJBKhoKAACoUC+fn5MDc3h4aGBqKiohAcHAxDQ0NYW1vD1dUV58+fBwDcuHED165dQ3BwsJC/np4eAgICAAD6+vpwcnLC3bt3kZGRAUNDQ2Hu9M6dOyMsLEzY7tNPP8WCBQuqPHa7d++uNM86UHkaTHXpV69eRadOnaChoQETExNYWFhUW4eqPgcAkMlkWLBgAb744guV/a1fvx5ffvmlcCz5zmr9IKnrAjDGGGMAUKBUwuF0/AvP95+OHtAXi9UuS09Ph1QqFd5bW1sjLS2t2uWnTp1CZmYmTE1NhQCy/HbZ2dnCfOTl02NiYqBUKuHn56dShjFjxqBXr16wsrJCYWGhcNu5d+/e2L17N6ysrFBQUIDt27c/tczTpk3DkiVL8Pvvv6utb0pKCi5fvgwfHx/o6ekhLy8P8fHxcHNzw/79+5GdnQ0A2LlzJ3x9fYW52Cu6dOkStLW1K82XnpGRgbi4OLz11lsq6XK5HAcOHMDXX38NAPD09MSiRYvwySefICMjA7GxsdXWoarPAQCWL1+OkJAQGBoaVqpraGgoIiIiYGNjg7Vr16Jx48Zq68NqD7d4MsYYe2Opaw0t3xpZ1fLqtiu/fdl7pVKJmTNn4ptvvqm03aFDh9C6dWukp6fj+PHjCAkJgVKpxB9//AFdXV2kp6fjypUrmDJlCnJycqrc9/79+9GsWbMqp58uKirCe++9h6VLl0JfXx8ikQhbt27FuHHj0LZtWzRu3BgSiQT5+flYuXIlPvvsM7X5AFW3aoaFhaF3797Q1NRUST9+/Dg8PDzQsGFDAEC3bt3QqVMn+Pv7Y8yYMWjTpg0kEkmVdaiqzmlpaTh8+DBCQkIqLc/Ly4OFhQUuXLiAoKAgTJ06tcr6sNpTpy2eMpkM9+7dQ0FBASwsLGBqalqXxWGMMVaH9DQ08E9Hj5eSb1WkUqlKC2dqair8/f2rXW5paQlzc3NkZWWBiCASiYR0ADAyMhJaPcvSc3NzkZCQgDZt2gj5uLm5IT4+Hps2bcLcuXMBAC1atAARISMjA9u2bUP37t0hFothY2MDJycnXLt2DVKpVLgtXb5M4eHh2LFjB3bv3o28vDzIZDIYGRlh9uzZICKEhIQgODgY/fv3F7Zt3749zp07BwDYunUrRCIRbt26hZs3bwqtmY8ePYKnpycuX74sbLdr1y6hE1R5O3fuxMyZM9WmVwxU58yZgzlz5gAA3nrrLTg6OmLr1q1q6/DBBx+o/RwuXbqExMRE2NnZQS6X4+HDhwgODkZkZCSkUin69esHAOjbty9WrlxZ+QRgta+2HyrNzc2ldevWUUBAAOnq6pKGhobwsrGxoQ8++IBiY2Nru1gvHD+czBhjT1cfOhc5OjqqdC7KyMhQWadly5ZCp5ZWrVrR5cuXiYjo3XffVelcdODAASIimjx5skrnopUrV1bab9OmTYXORWPHjqWFCxcSEdGtW7fI2tqaFAoFLVy4kMaOHUtERJmZmdS0aVN68OABPXz4UKVzkYODg0rnIiKiTZs2qXTM+eyzz2jEiBGVynH//n0iKr02+/n50dWrVyutU7Fz0YULF8jHx0dtXpaWliqdhIiISkpKqFGjRirHVSaTUVZWFhERnT17ltq3b18pv4p1qOpzKJOUlKTSuWjatGm0bds2IiLatWsX9evXr9I+uHNR7avVW+3/+9//YGtriw0bNggPMV+6dAl///03oqOjMWfOHMjlcrz99tvo1q0bbty4UZvFY4wx9oaRSCRYtmwZAgMD0aJFC0yfPh1mZmYIDg5Geno6AGD16tUYPHgwnJ2dERwcDA+P0lbZRYsWYc6cOXBwcICFhYXQ0WjmzJnYvXs3HB0dkZSUhA8++KDaMnz55Zc4cuQIPD090adPH/zwww/Q0NDARx99hAcPHsDd3R0dOnTA3LlzYWFhAXNzc0ydOhUtWrRA586dsXz5ckgkVd/ATE1NxaJFixAbGysMbVTWgWrhwoVo3rw5WrVqhY8//hguLi5PPWa7du3CwIEDK6X/+uuveOeddyCu8Dzt0aNH0aJFC5iZmQlpxcXFaNeuHVxdXfH555/jp59+eup+q/ocqjJz5kxs3rwZnp6eWLNmDZYuXfrUfbCXT0RUTXe/F2zAgAGYPXv2U0+W4uJibNy4EVpaWk/9wtZXOTk5MDY2RnZ2NoyMjOq6OIwxVi8VFRUhKSkJdnZ20NHRqevisDeMuvOPr98vV60+47l79+4araetrY0JEya85NIwxhhjjLHaxL3aGWOMMcZYreDAkzHGGGOM1Yo6DzwXLVoEALh8+TJkMlkdl4YxxlhdqMXuBowJ+LyrfXU+c1H79u0BAHPnzsXVq1ehqakJd3d3eHh4wMPDA61atUKjRo3quJSMMcZeBk1NTYhEIjx8+BAWFhaVBl9n7GUhIjx8+BAikajSgPfs5anVXu01UVBQgISEBMTHxyM+Ph5nzpxBcHAwvvrqq7ou2jPhXnGMMVYzeXl5SE1N5dYnVutEIhGsra1hYGAgpPH1++Wqs8AzNze30ryqVWnZsiX+/PPPl1yiF4tPXMYYqzmFQsGPW7Fap6mpWWncUb5+v1x1dqu9Q4cOOHToEBo3bvzUdWNiYmqhRIwxxuqKWCyuFAAwxl4/dda5yNfXF/7+/rh27ZpK+l9//YXg4GCVtLp49iItLQ3vv/8+zMzMoKenB29v71eu1ZUxxhhjrD6ps8AzNDQUo0aNQvv27XH27Flcv34dAwcOhK+vL7S1teuqWACAR48eoV27dtDU1MRvv/2GxMRELFu2DA0aNKjTcjHGGGOMvcrqtFf7nDlzoKWlhbfffhsKhQJBQUE4f/48fHx86rJYWLRoEZo0aYJNmzYJaba2tnVXIMYYY4yx10CdtXjevXsXEydOxFdffQVXV1doampi0KBBdR50AsCBAwfg6+uLAQMGoGHDhmjRogU2bNhQ7TbFxcXIyclReTHGGGOMsX/VWeBpb2+PM2fOYPfu3fjzzz8RFhaGCRMmCAPK16Vbt27h+++/h5OTE6KiojBu3DhMnDgRW7ZsqXKbhQsXwtjYWHg1adKkFkvMGGOMMVb/1dlwSjt27MCgQYNU0i5evIiePXuiT58+WLt2bV0UCwCgpaUFX19f/P7770LaxIkTcf78eURHR6vdpri4GMXFxcL7nJwcNGnShIdjYIwxxl4hPJzSy1VnLZ4Vg04A8PHxwe+//46TJ0/WfoHKsbS0hKurq0pa8+bNcefOnSq30dbWhpGRkcqLMcYYY4z9q1YDz+oCtzK2trY4d+4cgNIhjepCu3bt8Pfff6ukXb9+HU2bNq2T8jDGGGOMvQ5qNfBs1aoVPvzwQ8TGxla5TnZ2Nvbs2QN3d3eEhYXVYun+NXnyZMTExGDBggW4efMmtm3bhh9++AEfffRRnZSHMcYYY+x1UKvPeGZlZWHBggX48ccfoampCV9fX1hZWUFHRwePHj1CYmIirly5Al9fX3zxxRfo3r17bRWtkoiICMycORM3btyAnZ0dpkyZgg8//LDG2/MzIowxxtirh6/fL1eddC4qKipCZGQkzpw5g+TkZBQWFsLc3BwtWrRAUFAQ3N3da7tILxyfuIwxxtirh6/fL1ed9Wp/3fGJyxhjjL16+Pr9ctVZr/asrKy62jVjjDHGGKsDdTZlprm5OaytreHl5aXycnJygkgkqqtiMcYYY4yxl6TOAs/ExERcunQJf/31F86fP4/169cjKysLurq6cHNzwx9//FFXRWOMMcYYYy9BnQWeLi4ucHFxEQaSJyIcOnQIn3zyCbp06VJXxWKMMcYYYy9JnT3jWZFIJEL37t2xdetWpKen13VxGGOMMcbYC1ZngadSqVSb3rp16zqfMpMxxhhjjL14dXar3cDAAO7u7vD29oaXlxe8vb3h7OyM2NhY5OXl1VWxGGOMMcbYS1JngWdYWBji4uIQFxeHNWvW4MaNG1AqlRCJRPjqq6/qqliMMcYYY+wlqTcDyBcVFeGff/6BmZkZGjduXNfF+c94AFrGGGPs1cPX75erzlo8K9LR0YGbm1tdF4MxxhhjjL0k9aZXO2OMMcYYe73VaounnZ3dc81KNGnSJEycOPEllOgVJC8BNMSlL8YYY+xNRQQoSgCJdl2XhD2DWg08N2/e/Fzb2dravtByvNKu7AUOfAyY2gNmjv/+a+YImDkABo0AnnKUMcbY64AIKMgCMm8CWf+U/pt5E8i8Vfq+wxSg4/S6LiV7BrUaeAYEBNTm7l5PWf+U/g/v4bXSV0VaBqUBqJkjYOpQLii1B3RNar+8jDHG2NMU5wKZTwLLrFvlAsx/gKLHVW+X+U+tFZG9GPWmV/vz+PPPP9GyZcu6LoZaL61XnFIBZKf8+4XMLPc/wOwUgNQPzA8A0DMrF5A6/NtKamoPaOm/uDIyxhhjFcmLgaykCq2XT65jefeq39bIurQBRWhMeXItM2kKiDVfaDG5V/vL9UoHnjY2Nrhz505dF0OtOjlx5cXAo+RyX+Yn/2b9A+TerX5bI2mF2/ZPgtIGTQGJVq0UnzHG2CtOqQAe3ynXelm+cST1KY0j5v9ee8rfuTO1B7T0aq0KHHi+XPVmOKWqDBw4UG06ESErK6uWS1PPSbQBC+fSV0XFueVuX5S/jXGz9DZGTlrpK/mM6nYicen/KE0dKv8gGFkDGjwwAmOMvVGIgNx7/15DssrdfctKApSyqrfVMlS94ybceXMAdBvUWhVY3an3LZ6mpqb4+eefYWBgoJJORHjvvfdw//79OipZ9V6p/zGVPbhd/rZ92Q+JrKDq7SQ6gImdmh8RR0Dfgjs5McbYq6wgS8114UnjhSy/6u3E2k/uoDmoXhdMHQCDhvX+2vBKXb9fQfW+xbNTp04wMDBQ2zGpRYsWdVCi15CeKaDnBzTxU00nKr1FX/6Hp+zWfVYSIC8CHl4tfVWkbVS5xz3/r5YxxuqX4rxyd8P+Ub01Xvio6u1EGqWPYlX8jTdzLH10i4f8Y1Wo9y2er6rX/n9MCjmQfUf1tn3ZD9bjFADVnFbln+Mxti4dAsqwMWDQGDBsVPr+BT8szhhjbxyF/P/bu/couen77uMfaa7rtXcxN9tgx0BCMGCudgBzKTl5wDSEUHiSwjnNcUlCn1O3EKCkSU2TUyDhHDdAOJSckAYK9GkfaGiSQmlKA+YkmEsgEGMTg7kkmHAJNmAbe9fe3bnp9/yhkUaa0c7OrHc0q/X7dRgk/fST9JO8M/rq+9NopF3vu1/cGXy3Nhz4fS3YHOv+/xkHRPdqTeH7/6f8+bvLCDw7ZI/+wy2NBL7k5AWl1Q+5nS3eGjFt32owOitiOKcaoM6WMvmO7goATDrlovtZuvNdN3Ac3Fwdrxvuer/5l3k80/aJvo9/D33iyR59/o7BpO9qRwJl8tL+C9xXvZGBWhC6baM08E74g3Lnu5JTloa2uK93X2i+rXx/IFNaHc6Y05hFzc3ozL4CwEQpDjVmJwc3NQaVw218sday3Xvug5+HM+aEf4Rk2t6d2yegTuICT2PMuH52E5NEvk864Fj3FcVxpKGtdR++gQ/cwc21eZWCNLLDfW15pfl2M70RQWnEsGfmpL/xHUCCGOM+VST42RX5ufauVBhofb12pvrZNcbnWu9+3G+JSSVxgeeiRYv03HPPdbsZ6BTblqbv575mHzV6PWPcx0AFMwPeh3l9d1Nxp/sNzG0b3VczqVw4exoaBrr4p+3Do6SAPZkx7pdv/IAy4rPHGzZ7Oki9dE/EZ8/suqBytnuRzGcQEihxgSe3pEKSm5Xsmem+orr0gwo7A5mFiG4rbziy3c2ibn/TfTVjp6Xe/QOB6N7uN/nzfW63vj/eFx7P90mZaWRVgcnAGKk07GYkCwPurUCFHe70yECgbNAtH94evi2oUmx9W7m+0bOSoduC+vh8wJSWiMDzX/7lXyS5QecHH3zgT0vSn/7pn3arWUiK3HT3tc+Hm9crjTTeXxV1v9XQFvc+1MF33Fe7rJQbnOb7pFx/YLwvPB4VuAbn032GPZnjSMVAgBgKFnfUBZNNAkunvHvt6Jk59i08M2bvkV/SAaIkIvAMZjm9cTKfmHCZvDTzIPfVTKUk7XwvHJQObx/lJDcQHjeOZCpudnVk++61Nzs9IrsaDFz7R5nfXytL53avDcB4lIu1LGJk4Bjx3qmfXxycwAZZo7+P6t9T9Y9+4z0EtCVxj1M6/vjjE3GPJ49jQANjpOKuFrv1vKxN3Qm3MOg+uH+ipLLhWwQyve4zVNM5d14qGzGece+FTVfLQuN19RuWr9b3x6vT3KsWD8dxu4e9V7lQN15ybzepFN3gsGG8FLHMWMuX3Hscg3/HE/k3bGea9xI03P7S39izkOnlbxA+zt+dlYiMZ1DC4mSgxrJq3f6aM/71lAvVk3h9d2IwSN0xSvZ1MJwtqhRrj67qJjs9dqAbCly94Dg47gXEOfcRMlPhPjnHcYO3YFBX9gLH4HhUIFgfOBab/4Z2N2R6x3ebSTCbz7N8gURJXOC5Zs2abjcB6K50Nbjq3Xf863Aq1aC0LjAtDUdnsCKDnbEyYKMESOVCYwDklN1XO9/+xe6zM43Z56bZ6/qMdTDwj8qKe/PzjVnI7AwplbhTEIDdlLh3vU13CLD77JTUs5f76gZjmmTm6rJ0kV26xebLO5Xu7NdEs+xaUDeeWxiaBZGpLN3LAGI36QPP4eFh9fT0dLsZACaSZdUyt3w3AwD2GJM+8Jw+fbo+/OEP68gjj9TChQv912GHHaZ0etI3HwAAAFWTvp/l4osv1owZM7Ro0SIdcMABWr16tf7iL/5Cc+fO1VFHNfllGwAAAEwqXQs8H3nkkVHnff/73/fHb7vtNv34xz/W66+/rgceeEDLli3TY489ps2bN+vhhx+Oo6kAAACYAF17jmcul9Oll16qlStXKpvNSpLef/99ffGLX9STTz6pbdu2NSzz29/+Vt/85je1bds23XDDDVqwYIyfSuwingMGAEDycP7urK7dJPnYY49p2bJleuSRR3TPPffod7/7nb74xS/qiCOO0PPPP+/X+81vfqNXXnlFr7zyil566SW9+eabGhgY0Pr16yd14AkAAICwrv5y0a5du7R8+XL98Ic/lOM4uu666/SVr3xFVuDBz7Zt6+ijj9YFF1ygc845R4cffrgymUy3mtwyrpgAAEgezt+d1dWvhb/yyit69tlnNXfuXL3zzjt6+eWXNTQ0pN7eXr/ODTfcoBdffFH333+/br75Zs2fPz/07fazzjqri3sAAACAVnXty0V///d/ryVLlujMM8/UCy+8oGeffVZr167V0Ucfraeeesqv9+Uvf1l33nmnnnnmGb333nu69957df7556tQKOhf//Vfu9V8AAAAtKlrXe1z5szRnXfeqU9+8pN+WalU0t/+7d/qlltuUaFQ6EazJgypegAAkofzd2d1rat9/fr12nff8G9NZzIZ3XDDDTrnnHO61CoAAAB0Ste62uuDzqDTTz99zOU3bdqU+KwoAADAnqTrvzm5YcMGvfnmmyoWi6Hyc889t+lyy5Yt02uvvabPfOYzuvHGGzvZRAAAAEyArgWeGzdu1Pnnn6/169fLsix5t5p6j1KqVCpNl/d++ejll1/ubEMBAAAwIbrW1X755Zfr4IMP1rvvvqtp06bpxRdf1GOPPabFixfr0UcfbXk9PEQeAAAgGbqW8Xzqqaf0s5/9TPvtt59s25Zt2zr11FO1cuVKXXbZZVq7dm23mgYAAIAO6FrGs1KpaPr06ZLcLxq98847kqT58+frlVde6VazAAAA0CFdCzwXLlyoX//615KkE088Uddff72efPJJfeMb39AhhxzS0jquueaaDrYQAAAAE6lrXe1f//rXtWvXLknSddddp3POOUennXaa9tlnH917770trWPRokWdbCIAAAAmUNd+uSjKtm3bNHPmTP+b7UnGLx8AAJA8nL87q2td7ZI0MjKiZ555Rj/5yU/0wAMP6IknntB//dd/6YEHHmhp+Z/85CcdbqFr5cqVsixLV1xxRSzbAwAAmIq61tX+05/+VMuWLdPWrVsb5lmWNeZzPCXp2Wef7fjPaz777LO67bbbdPTRR3d0OwAAAFNd1zKel156qS644AJt2rRJjuOEXq0EnZJ07bXXdrSNO3fu1Oc+9zndfvvtmjlzZke3BQAAMNV1LfB87733dOWVV2rWrFnjXsfmzZsnsEWNLrnkEn3qU5/SGWecMWbdQqGggYGB0AsAAAA1XQs8P/vZz7b1C0VRLr744olpTIQf/OAHeu6557Ry5cqW6q9cuVL9/f3+a968eR1rGwAAQBJ17VvtQ0ND+uM//mPtt99+Ouqoo5TJZELzL7vssm40S5L01ltvafHixXr44Yd1zDHHSJI+/vGP69hjj9XNN98cuUyhUFChUPCnBwYGNG/ePL4VBwBAgvCt9s7qWuD5T//0T1q+fLl6enq0zz77hB6hZFmWNm7c2I1mSZLuv/9+nX/++UqlUn5ZpVKRZVmybVuFQiE0Lwp/uAAAJA/n787qWuA5e/ZsXXbZZVqxYoVsu6tPdWowODioN954I1T2hS98QQsWLNDf/M3faOHChWOugz9cAACSh/N3Z3XtcUrFYlEXXnjhpAs6JWnGjBkNwWVvb6/22WefloJOAAAANOpa1HfRRRe1/NOYAAAASL6uZTwrlYquv/56PfTQQzr66KMbvlx00003NV1+06ZN2nvvvZXL5TrZTN/ufgMfAABgT9e1wHP9+vU67rjjJEkvvPBCaF4rv9W+bNkyvfbaa/rMZz6jG2+8sSNtBAAAwMTpWuD585//fLeWf+SRRyRJL7/88kQ0BwAAAB3WtcCzHdu3b9dDDz2k3//+97IsS3PmzNFZZ52lmTNnasGCBd1uHgAAAFow+b5SXueOO+7QCSecoKefftr/Hfenn35aJ510ku64445uNw8AAAAt6tpzPFt12GGHac2aNZo+fXqofHBwUIsWLdKrr77apZY1x3PAAABIHs7fnTXpM56WZWnnzp0N5Tt37mzpS0gAAACYHCb9PZ433nijTj/9dC1cuFAHHnigJOntt9/Wiy++qG9/+9tdbh0AAABaNem72iX3mZ/PPPOM3nnnHRljdOCBB+qEE04Y8/fSu4lUPQAAycP5u7MmfcZTklKplJYsWdLtZgAAAGA3TPp7PAEAADA1JCrw3Lx5c2gIAACA5EhU4Hn22WeHhgAAAEiORAWengR8HwoAAAB1Ehl4AgAAIHkIPAEAABCLRAae/GIRAABA8iQq8Mxms6EhAAAAkiNRgefTTz8dGgIAACA5EhV4AgAAILkmfeD5rW99S5L061//WqVSqcutAQAAwHhN+t9qP/XUUyVJ11xzjV566SVlMhktXLhQRx11lI466ih97GMf06xZs7rcSgAAAIzFMgl7GvvQ0JBeeOEFrV+/XuvXr9fjjz+us88+W9/85je73bSQgYEB9ff3a8eOHerr6+t2cwAAQAs4f3dW4gLPKIsWLdKaNWu63YwQ/nABAEgezt+dNenv8WwF33IHAACY/KZE4JnJZLrdBAAAAIxhSgSeAAAAmPwIPAEAABALAk8AAADEgsATAAAAsSDwBAAAQCwIPAEAABALAk8AAADEgsATAAAAsSDwBAAAQCzS3W4A2vOzN3+m//fS/9Neub20d35v7ZXbSzPzMzUzN9MdBsazqWy3mwsAQNtKTknbR7brg8IH+mDkA3+4fWS7to1s0/bCdn0w8oGWHrRUFxx2QbebizYQeCbMGwNv6NnNz7ZUtzfTGwpIg8FqMGjdO7+39srvpRmZGbIsq8N7AADYkxhjNFQe0raRbW7wWKgGjyPbta3gDoPB5QeFDzRYHGxp3Qf3H9zh1mOiEXgmzCc+9AnN7p0dfpPWjW8vbFfFVLSrtEu7Srv09s63W1p32kprr3w4g7pXbi/1ZfvUn+tXX7ZPfbm+8HS2Tz3pHgJWANgDjJRHNFAc0EBhQDuKOzRQGNBAcUA7Cjv84Y7CjoZMZckptb0t27K1V26vcJKkrpfvI3t9pAN7iU4i8EyY+X3zNb9vftM6xhgNFAf8rgivW8K7wowKWIfKQyqbsrYMb9GW4S1ttSljZxqC0/5sf2hYH6x68zKpzO4cDgBAm8pOuSF4jAoivelgWaFSGPd286l8wy1hfg9cfi/tndvbLauOz8jOUMpOTeCeYzIg8JyCLMtSf65f/bn+MYNUT6FSaAhGvcC1/oPH/zAqDKhsyio5JW0d2aqtI1vbbmtPuscPRGdkZmh6drp6M72akZmh3myvpmemu68m5Vk7S8YVwB6hVClpsDSoXcVd2lna6b6KO/3xXaVd4eniLg2WBrWzuNP/LN9V2rVbbbAt208i1PeG9WX7alnJuiCzJ90zQUcBSUbgCUlSLpXT7N7Zmt07u+VlvPt2Gq6S67pdorplBouDMjIaLg9ruDysd4feHXfb03baDUgzvZqene4HpVGB6/SMO5yWmaaedI+mpavD6nQ+lSeIBTBhjDEqOkUNlYY0XB6uDcvuMBgo7irt0mBx0C0LBJX+dHGnik5xwto2PTM9MnAcq/eqN9Mr2+KhOBgfAk+Mm2VZ6s30qjfTqzma09ayjnE0WBysBa3FHQ0fsJEfxIHyXaVdMjIqO2U3S1v4YPf3SVYoEK0PTFuaztTK8+m8cqmc/yKoBSYfY4xKTkkjlREVygWNVEYaAkRv2i8r1eZFBZTBacc4E97maelp/kW1d0EdHJ+RneFfbHvlwWByena60jYhAOLHXx26wrZs/3aA8XKMo6HS0JgBan35rtKu0AnDe0mSkZvFHSoPTdSuhngBaD6VVy5dG8+msn6Q2sq8fCoQ0Fan03Za2VRWGTujjJ3xx7OprNJ2mgwFJjVj3IvIolNUqVJyh05JxYo7LDklFcoFFSruywsSC5WCRsojfnlwOlSnMqJipRgKLguVgj/fyHR8H/OpfOhCtSfdE+qJCQaLvdneUXtyetO93PuIxCLwRGLZlu1+IGen7/a6HONopDzSkMloN7NRP10oF1Q2ZX873olxQAO73eZ2pe10ZFDqlWVS1Xl2NnLcq5+yU0pbaaXttFJWKjxtp5SyUuF5dlppa+y6Xlnaqs2zLVu2ZcuSVRu3LNkKjFu2bNXGLVlTKrNsjJFjHDlyZIxRxVQayhzjyDGOjGrjjnFUdsoqm7IqTkUVU1HFqahsyio7ZX/cmxdVt+SU/HGvjl83MO4Fhn6QWCk1BI3BcX9+IMgsO+WxD0YMbMtWLpXTtPS0cfd0RNXLp/IEi4AIPAFJ7slmWsY90WiC738vO+WxszB184LZGH+8frpunncy907swYDXa0fZKWtYwxO7g5OQJUspK1ULTAPB62jBahy8wNAYI0dObbwuaAzO31OlrFTogihjZ0IZ/oZxrzfB6x0I3OZSf8vLaL0LuXROGZsnbQCdROAJdFjadjN8vZneWLfrZbSCWSiv+zIYpHrzIzNSdRmrolOMzH7VZ88qTkUlUxo10xZcvuIEsm2B7FrJKUlG4wrAjIwbeHe+93RS8QJqWQpljv2sc3C6LmMdykB7ZfVZ61Gy1MHseNbOhgPGujJvPDLbHigjOwhMTQSewBSVslNKKaVcKtftpkyIYPdyKDM4RpdzMHsYtVzcWUUvOBwt+xp8tXOLAffwAkgCAk8AiWBZbvd5SmTCACCpuEQGAABALAg8AQAAEAsCTwAAAMSCwBMAAACxIPAEAABALAg8I6xcuVIf+9jHNGPGDO2///4677zz9Morr3S7WQAAAIlG4Blh9erVuuSSS/T0009r1apVKpfLWrp0qXbt2tXtpgEAACSWZYzZw37bo33vv/++9t9/f61evVp/8Ad/0NIyAwMD6u/v144dO9TX19fhFgIAgInA+buzeIB8C3bs2CFJ2nvvvUetUygUVCgU/OmBgYGOtwsAACBJ6GofgzFGV155pU499VQtXLhw1HorV65Uf3+//5o3b16MrQQAAJj86GofwyWXXKL//u//1hNPPKG5c+eOWi8q4zlv3jxS9QAAJAhd7Z1FV3sTX/rSl/TAAw/oscceaxp0SlIul1Mul4upZQAAAMlD4BnBGKMvfelLuu+++/Too4/q4IMP7naTAAAAEo/AM8Ill1yie+65R//5n/+pGTNmaPPmzZKk/v5+9fT0dLl1AAAAycQ9nhEsy4osv+uuu/T5z3++pXVwjwgAAMnD+buzyHhGIBYHAACYeDxOCQAAALEg8AQAAEAsCDwBAAAQCwJPAAAAxILAEwAAALEg8AQAAEAsCDwBAAAQCwJPAAAAxILAEwAAALEg8AQAAEAsCDwBAAAQCwJPAAAAxILAEwAAALFId7sBaM/OJ57Ujgf+U3a+R3ZPj6xpPf64Pa1HVt4d2j09svJ52dOmhcfzeVlp/tkBAN1nKhU5wyMyI8NyhoflDA2POu6MDMvUjfeeepr6P31Ot3cDbSACSZjCb3+jgQf+a/dWksnIzufdILSnxx3603k3kA2MW/mcO53Ly87n3GFPYDqfl5XL1dYZrEuQCwCJYioVmZEROYWCOxwpuAHgSEGmMCJnZESmUHCHI9XpkYKcQnU4MiwzXC0fHnbXMzwsZ2SkYZ4plXarrXZ/P4FnwhAVJMy0xR/T/l/9qpzhIfeNPDziXg0OD7lv5mH36tBUh8FxGeOupFSSUyrJGRzsfINTKTcozeVCw9B4Pi87l5WVy8vKZWVls+68bE5WNisr501nm5dlM7Kz2ep44JVKdX4/AWACmEpFplh0X6WSP+4UizLFkkyx4JYVCm5AVyzJFAp+uVMo+vNNseAuVyi6AWKxIDNScJcNjhfcoVunKJXLXdl3q6fae9fT4yY+eqY1jNs91YRJzzTZPXnlFx7VlbZi/Ag8E6Zn4ZHqWXhk28sZY2ofLCNugGpGRtwujsJIoKujekU6EijzrmD9q91C3dXwSGjaFAq1DVcqMkNDqgwNTeBRaFMqJSuTCQSjGdmZQGCaydTme+NRZdmMrExWViYtK5OR0u7QSnv1vekm89PuS+mMrHQqPO3NJ1AGJoxxHJlyWSqVZMrl2qtUlsql0LQpl6Ry2Q34vGEpOF0Mr6tUcgO/UuDlBYzNyrzAsliUU/ICSndalUq3D1mIlc1WkwPVJEE+597SVZ228jnZueAwXwsQ896w1htm+71sjfMsy+r27iIGBJ57CMuyZOXzUj6vToc1xnHcD9GRkerVd6E2XhgJX2EXCtXum2o3TeBq3fGv7OvLvCt8r6wY+iA3xWItuyu5wW+16ygRLMsNRr0gNpWS0ik3gE2lqtMtlKfSslK2lErLsm2/TCk7PC+V8suUsmXZqebDVEqyvWHKXY9lu0O7bty23W2PNt+y3JNNtVx2eNqyLcmftqrrsmovWe4gWC7L/S+wnAInNCs4HTm0QkVq92RY/dur/QmaWrkxoToyRib4t+rVMUbGcaqLmrpyE1Hm1KYdx61jnNq8+mm/niNVX8YxklOpK4uYX3Gqw4pbXqlIFUfGaT6UU5EpV5ereMu7ZZHzvPdtpSyVytXxihsYNiuvBpJecBj6LEighh6cXFa23/OTG6UsU9drlHMDxmyuGiDW9zy5vU129bYpv9cpn3ffc8AEIvDEhLNsO7YgN4oxxj0JBbunSo3BqSm62YvIbERo2lveKytWsyPhTIi7zVJdeXBYck+UgaxLZJeWMe59T6WSkn3KBCapdK33we1xSPs9FcFeC7/3IlPXe+HXTbfeY9LQgxLocakPLjNZ2dmMe/FJFhBTDIEnphzLstwP7ExGdm9vt5vTlDHGzeyUa4Gs6rsDK14mp+KOl8u18UrFDYIr5ep6Km6AG8oaOdXlKtXsU2BeVLYpmKlqyHIFhpVqdqxSkTHVrFql4u6TE1y+PnPm1OYbueXG1NbhTxt/GX+6UnHH3YMXzvrVTYcyjEkTzOpWX5YUzuB6ZZYlpVLh7LFtV7O+XubZkqW6eXY1c21bkjfurcu23GVTqegyuzqsZrvHzpSnQpl1K13NlnvDVCqizK5m8Kv1g+OpaqY/7a037QaBwfF0unabTX2QSTAHdA2BJ9BFlmX52RZ0hgkGoKN0d0uqBbNRw3aN0pVvjTYvME5QBGAq42wHYEoL3dPZrF4MbQGAPR13DQMAACAWBJ4AAACIBYEnAAAAYkHgCQAAgFgQeAIAACAWBJ4AAACIBYEnAAAAYkHgCQAAgFgQeAIAACAWBJ4AAACIBYEnAAAAYkHgCQAAgFiku90AtOf3r3yg3655T3bKkp22ZacspVKW7FR1vFpmB8qalqeC5YF5duO0ZVvd3n0AwCRkjJFTMXKc6rDiVIdjT1dC8xxVyqPMLzeWzT1spj58/P7d3n20gcAzYba8vVMvPPb7rmzbshQKWmsBqi2rGgBbttUQuPplXnl12gpMWyk7MB6oYzcfD26vVia/PFQvqo5tybJqdWvjcsery/j1LQJwADXGGBnHyDiSUx13KqZaLnfaMRHD6HneuLsOyVTCdbx1O5XwtpxgPW+8Uht3p53AeCBIrJ/2AsPg+oLrCgaKTq0t3ZBK2QSeCUPgmTCzDu7Txz51UPWKr/oBELg69Msqpu6qMTi//uqz8UrURHyGGCNVyo4q5fj3e7LxglEvEPWnq8GrZSlQ7k77QaxVC2z9elZteUWUh+sG5gXLqtMKzvPKAuPeOmVZsqr7Ep6vWhssN8j2l6mOB+t7x8OdV5vvTUvh9frllmSpti7/2NbNC5e7ba6t3xsJDWrLB6Yj64VWPsq8UL1Rypucc0Oz6t5YJqqS8Qb+SEM9Y+rmVaf91Zvq8ia8SePXq5tn3K0Zp7rl4HqC6zbVYMgE11Gd7wS3aZrW9+c51WlJcmrzgkM5jWX+cv4wPE+mGkyZ2riM/DK3fuPyweAvWC8YKAbnOSb4j4MGlvwERKouWVHfy5ZKB8uDvXnB3j07NG2nLM0+pL/be4k2EXgmzOxD+mN5o3lXuV53RvAquiFQ9a94HVUqgats/0rbibiaDlyl11+pVxw3ezDqVXpjpsBbprE8OtNQn10wdeWtHB/jSA5nHQBNhC5SU7VeFitlybZUK6vrxfF7XwK9MO784O1Pauz5qfYeefNCPU8RvUfedMrvhbLDvVLBYDHYexXo4UrV92ylavWBegSeiGTZllK2pVRmz/z+mZfN8AJMP0CN6D7zyuqnTX2mpSGTUltPLRtj6rI24YyMIrI+3vINWaa6TJEaskamljEL1q3uf2iewtkkN8sWyGKptj33AIYzaMHMnJ+sq8u6hbJ41Q2Es3XhkfqsvAkUBDN23khUFr9hPaNV2l31Gd1Rq9RlcEMZXyuifm3Cqs8Oq5btDi5fKwtkrK3gOqpZ9sBGorLnfkLay8orYn5D5j1QxwvApFoGPriMHV7GW6cXuNXGA3Xqewn83gKr2pug0DDUg1DX8xBeT+AWHSuibkTPBvfFA9EIPIEIlm0pJUtKdbslAABMHXtmOgsAAACxI/AEAABALAg8AQAAEAsCTwAAAMSCLxclTLlYVLlUlG3bstxndPjj7rcsuZYAAEwd7tM4nOqTQZzquCNjjOxUSplcvttNRBsIPBPm14/8j37+f29vWsey7OrjPcIBqfu4j+B0YNzynvNmS9U6dnW+bNsfHy3YDa8rvE53OPr8hm3almQFthlcf8Q2ZXkPTLdC0/Lru8dEdcPo+q2vx5Ik23YfI2O7z4ixbMt9cHl1WF/uXRgEh/4jaUJt87bV2J7RxmVZtYemhx7KHnyMTnU8+HD20HLBx/JYtXUEH8huBcqxxzPVJ8QHHx7vP77KL/ceqeU/OyvwyKzAvOrjxGp1TJNtuMs322b9Nmrjxn+8l7/+4HaqQU3t5VQfOeZUHzvmVB9uX62nwKPU3OecBR6D5tTWG1q3U2270/ayCrTLfzSa6trtONWyQF2/3tjL1oaBccdxn8scnOeEA8LQ/Ki6xn22s5qtyxgZp1Kr2+QxZ4s+9Uf6+J/+nwn5W0Y8CDwTxjR5A9bqODIVSZVK5xsERASzVuABko0Bb/2vDdXKgs+yDP0CUmi5wG8S1QXBVlSdUTR9JzV5n7XyHmx7uWbba77Sca6zWcAWHK8Fb/4+BIJEoNu69VOdGD/LjPdTFE0NDAyov79fO3bsUF9f34St173irIS7HIz3CzwV/0rYq6PqFWNDN8WoV6ThOt6VqfHX4105e1emdetooY63HgXaOdrVdUPbQuuqXhVLgQxAIKMRzChUhwrNr69fy6qEMgMy1YeoR5U71QelO/6/j9sep27dCrWn6fZHLfd+yjSwfd6+2BN4WXmrdlHjPzjeuyixahcotQfoh8v9C5KoCxb/YfapcE+F3xsR6BFp6G2xw70dfs9MoOcj0Mvi3xZV15vi9TC57ajvlbHr2hPo3arvyRmlfd4xCfZ+qW6fwvtoh3vL7FrPVKgnrK6ubY0x305JgV4175h79ezqsbG9nq269bjbr8237Yl94HKnzt9wkfFMGMu2leI+TgQEu+286VqGSn5wGgpUI7s9q7VGrdP4M0LhXwsyddtqbE99N2lt1ER2w9bWG9U+Eyg2jW3x2tnktoDx3jLQdLlm22u+0vFtr9lamzYzOoCrD9qiArjaryDVMsz+9JhBYvPt1W8DwNRC4AkknJuh4CeWAACTH4Fnwgyte0+Dj//enQh9OUR+JiE8z/1f6HsmDXWC8xvnedOR22iYP/rykmq/XTza/NGWt2sbqd0GaCm8n7X6VkM7w/WtyOUtv66/L/Xzg9uSQtPWGPPHWt5ve8Nyba4neG/lbrSjvry2ePT8UbcTUccarS0N64ox6xXHbQvtbqLtJrW/D+Pa7UAGumGTwelQVrpuo6Hp6PWZ+oUblokuD2bCR91O5HLtbaeW4dcox6H5+kyz7dQfr6hJU7d+/x7cwPq8ddXVDfUk1M9zItbrt8uE97d+PcHtR7Rv1LY7wWMSXGe4rqnb5rRj99OM0+YKyUHgmTCVnSWVfr+z280AAKDrKgdxD2bSEHg2ceutt+qGG27Qpk2bdOSRR+rmm2/Waaed1tU2mYOnyfnfsyVTTQ4FLoQt78rWql01WiaYMQpPGxM131+bTHA6cAXubtfIyHLbYSl0deq1yyuy6q68LctvoH8hG2x76ErXG1ru8n57q1e8lreOwHKWf3Vs+cu7+xo+lrV9M9VNhNdd29fGREntkNUVjDU/qqjVddRXa5a9aaUtJmJ0nG2pP0CN+zj+toYWHWcCdNx507jvM4z7tsbxH5hwQtuKLo/MoofmW5EJ8tHr10asNrcTtepW6od2yWptGS9zatWXBz+EquWBj1z/796yLJnI/Q6Pe3Ws4IewZbljXk9PoEfMBN9DoV6h2rKBhlfXb2RZcj/v/Q94q7o+4/cuGa/9Xl3/BFUbN/42avUsf7zWLv/c4Y1XFzFWXR1LMvvPEJKFwHMU9957r6644grdeuutOuWUU/T9739fn/zkJ7VhwwZ96EMf6lq7XnzzZT300ENd2z5c9V98aHc6rnXEqePbHmX1U3qfY9h21INNRnvYyWQqn0xtQfecdNJJ+sOD/rDbzUAbeJzSKE488UQdf/zx+t73vueXHX744TrvvPO0cuXKMZfv1OMYHnzyFv1u4GeNM0ZJJAU1O02Z0Fz/erO9DUS0p34B07QVNZG1IrYd1ZzRtxAxxzRORO9is7UGU4fR9UY7bOMOHSJX2MramvwDRrQ9WNtq96+rS58szdvZmXVHlrf1j9t+m8faz7Y2b43vfdqKVtblZ75a1WSVrbc9ql79cWjNWNu0Rt1efUXT0jajt1db0qofs6Lr1U81rNWKrtdQzYo6Z0RVjN5SXe531G1GLb5v9ihd8L++2Xy7beJxSp1FxjNCsVjUmjVrtGLFilD50qVL9Ytf/KJLrXK90HeIbir+QVfbAADAZPDH0zfqgm43Am0h8IywZcsWVSoVzZo1K1Q+a9Ysbd68OXKZQqGgQqHgTw8MDHSkbbP6j9SsHdvHtezu5IGi8+KtrXG3trsby+728ruxcDz7HJUhGDuLM+raJv3+TrzdyexN/Pup89ttR8t5wxYr7k4ecnfqtWqi96OduhO+z5Pu36T+lqCJ2+4B/Ue2tjJMGgSeTdTfQ+XeSB39Vli5cqWuvfbajrfpog8drIu6d4spAADAuPETOBH23XdfpVKphuzme++915AF9Vx11VXasWOH/3rrrbfiaCoAAEBiEHhGyGazWrRokVatWhUqX7VqlU4++eTIZXK5nPr6+kIvAAAA1NDVPoorr7xSy5Yt0+LFi7VkyRLddtttevPNN7V8+fJuNw0AACCRCDxHceGFF2rr1q36xje+oU2bNmnhwoV68MEHNX/+/G43DQAAIJF4jmeH8BwwAACSh/N3Z3GPJwAAAGJB4AkAAIBYEHgCAAAgFgSeAAAAiAWBJwAAAGJB4AkAAIBYEHgCAAAgFgSeAAAAiAWBJwAAAGLBT2Z2iPeDUAMDA11uCQAAaJV33uaHHTuDwLNDBgcHJUnz5s3rcksAAEC7BgcH1d/f3+1mTDn8VnuHOI6jd955RzNmzJBlWRO67oGBAc2bN09vvfUWvyPbQRzneHCc48FxjgfHOT6dOtbGGA0ODuqAAw6QbXNH4kQj49khtm1r7ty5Hd1GX18fH2wx4DjHg+McD45zPDjO8enEsSbT2TmE8gAAAIgFgScAAABiQeCZQLlcTldffbVyuVy3mzKlcZzjwXGOB8c5Hhzn+HCsk4kvFwEAACAWZDwBAAAQCwJPAAAAxILAEwAAALEg8AQAAEAsCDwnoVtvvVUHH3yw8vm8Fi1apMcff7xp/dWrV2vRokXK5/M65JBD9I//+I8xtTT52jnW//Ef/6EzzzxT++23n/r6+rRkyRI99NBDMbY2udr9m/Y8+eSTSqfTOvbYYzvbwCmi3eNcKBT0ta99TfPnz1cul9OHP/xh3XnnnTG1NrnaPc533323jjnmGE2bNk1z5szRF77wBW3dujWm1ibTY489pk9/+tM64IADZFmW7r///jGX4VyYEAaTyg9+8AOTyWTM7bffbjZs2GAuv/xy09vba954443I+hs3bjTTpk0zl19+udmwYYO5/fbbTSaTMT/60Y9ibnnytHusL7/8cvOtb33LPPPMM+bVV181V111lclkMua5556LueXJ0u5x9mzfvt0ccsghZunSpeaYY46Jp7EJNp7jfO6555oTTzzRrFq1yrz++uvml7/8pXnyySdjbHXytHucH3/8cWPbtvmHf/gHs3HjRvP444+bI4880px33nkxtzxZHnzwQfO1r33N/PjHPzaSzH333de0PufC5CDwnGROOOEEs3z58lDZggULzIoVKyLrf/WrXzULFiwIlf35n/+5OemkkzrWxqmi3WMd5YgjjjDXXnvtRDdtShnvcb7wwgvN17/+dXP11VcTeLag3eP8P//zP6a/v99s3bo1juZNGe0e5xtuuMEccsghobJbbrnFzJ07t2NtnGpaCTw5FyYHXe2TSLFY1Jo1a7R06dJQ+dKlS/WLX/wicpmnnnqqof5ZZ52lX/3qVyqVSh1ra9KN51jXcxxHg4OD2nvvvTvRxClhvMf5rrvu0muvvaarr766002cEsZznB944AEtXrxY119/vQ488EB99KMf1V//9V9reHg4jiYn0niO88knn6y3335bDz74oIwxevfdd/WjH/1In/rUp+Jo8h6Dc2FypLvdANRs2bJFlUpFs2bNCpXPmjVLmzdvjlxm8+bNkfXL5bK2bNmiOXPmdKy9STaeY13v29/+tnbt2qULLrigE02cEsZznH/zm99oxYoVevzxx5VO8xHVivEc540bN+qJJ55QPp/Xfffdpy1btugv//IvtW3bNu7zHMV4jvPJJ5+su+++WxdeeKFGRkZULpd17rnn6jvf+U4cTd5jcC5MDjKek5BlWaFpY0xD2Vj1o8rRqN1j7fm3f/s3XXPNNbr33nu1//77d6p5U0arx7lSqehP/uRPdO211+qjH/1oXM2bMtr5e3YcR5Zl6e6779YJJ5ygs88+WzfddJP++Z//maznGNo5zhs2bNBll12mv/u7v9OaNWv005/+VK+//rqWL18eR1P3KJwLk4F0wiSy7777KpVKNVw5v/feew1Xcp7Zs2dH1k+n09pnn3061takG8+x9tx77726+OKL9cMf/lBnnHFGJ5uZeO0e58HBQf3qV7/S2rVrdemll0pyAyRjjNLptB5++GF94hOfiKXtSTKev+c5c+bowAMPVH9/v192+OGHyxijt99+W4ceemhH25xE4znOK1eu1CmnnKKvfOUrkqSjjz5avb29Ou2003TdddeRiZsgnAuTg4znJJLNZrVo0SKtWrUqVL5q1SqdfPLJkcssWbKkof7DDz+sxYsXK5PJdKytSTeeYy25mc7Pf/7zuueee7hHqwXtHue+vj6tX79e69at81/Lly/XYYcdpnXr1unEE0+Mq+mJMp6/51NOOUXvvPOOdu7c6Ze9+uqrsm1bc+fO7Wh7k2o8x3loaEi2HT7VplIpSbWMHHYf58IE6dKXmjAK71Edd9xxh9mwYYO54oorTG9vr/nd735njDFmxYoVZtmyZX597xESf/VXf2U2bNhg7rjjDh4h0aJ2j/U999xj0um0+e53v2s2bdrkv7Zv396tXUiEdo9zPb7V3pp2j/Pg4KCZO3eu+exnP2tefPFFs3r1anPooYeaP/uzP+vWLiRCu8f5rrvuMul02tx6663mtddeM0888YRZvHixOeGEE7q1C4kwODho1q5da9auXWskmZtuusmsXbvWf2wV58LkIvCchL773e+a+fPnm2w2a44//nizevVqf95FF11kTj/99FD9Rx991Bx33HEmm82agw46yHzve9+LucXJ1c6xPv30042khtdFF10Uf8MTpt2/6SACz9a1e5xfeuklc8YZZ5ienh4zd+5cc+WVV5qhoaGYW5087R7nW265xRxxxBGmp6fHzJkzx3zuc58zb7/9dsytTpaf//znTT9vORcml2UMuX4AAAB0Hvd4AgAAIBYEngAAAIgFgScAAABiQeAJAACAWBB4AgAAIBYEngAAAIgFgScAAABiQeAJAACAWBB4AkAbvvzlL+vTn/50t5sBAIlE4AkAbVi3bp2OOeaYbjcDABKJwBMA2vD8888TeALAOBF4AkCL3nrrLW3dulW2bevMM8/UtGnTdNhhh+mXv/xlt5sGAIlA4AkALVq3bp0k6Tvf+Y6uuuoqPf/88/rQhz6kFStWdLdhAJAQBJ4A0KJ169Zp5syZ+vd//3d94hOf0KGHHqrzzjtP77//frebBgCJQOAJAC1at26d/uiP/kj777+/X7Zx40Z95CMf6WKrACA5CDwBoEXr1q3TkiVLQmVr167Vscce250GAUDCEHgCQAsGBwf1+uuv67jjjguVr1u3jsATAFpE4AkALVi3bp1s29ZRRx3ll73xxhv64IMPCDwBoEUEngDQgueff14LFixQPp/3y9auXau99tpLBx10UPcaBgAJYhljTLcbAQAAgKmPjCcAAABiQeAJAACAWBB4AgAAIBYEngAAAIgFgScAAABiQeAJAACAWBB4AgAAIBYEngAAAIgFgScAAABiQeAJAACAWBB4AgAAIBYEngAAAIjF/wd7h7rKiSWfuAAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"H, E = [], []\n",
"for k in range(2, 12):\n",
" M = 2**k\n",
" h = (b - a) / (M + 1)\n",
"\n",
" x, U_app = solution_neumann(f3, M, a, b)\n",
"\n",
" e = np.abs(u3(x) - U_app)\n",
" plt.plot(x, e, label=f\"{h}\")\n",
" E.append(np.max(e))\n",
" H.append(h)\n",
"\n",
"plt.xlabel(\"$h$\")\n",
"plt.ylabel(r\"$\\max_{j=0,\\dots,M+1}|u(x_j)-u_j|$\")\n",
"plt.legend(fontsize=7)\n",
"plt.title(\n",
" \"Différence en valeur absolue entre la solution exacte et la solution approchée\",\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 323,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)')"
]
},
"execution_count": 323,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(np.log(H), np.log(E), \"+-\", label=\"erreur\")\n",
"plt.plot(np.log(H), np.log(H), \"-\", label=\"droite pente 1\")\n",
"plt.plot(np.log(H), 2 * np.log(H), \"-\", label=\"droite pente 2\")\n",
"plt.legend()\n",
"plt.xlabel(\"$log(h)$\")\n",
"plt.ylabel(\"$log(E)$\")\n",
"plt.title(\n",
" \"Erreur pour la méthode mon_schema en echelle logarithmique : log(E) en fonction de log(h)\",\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice 4. Méthode d'ordre 2 pour les conditions de Neumann\n",
"\n",
"On considère à nouveau le problème $-u'' + u=f$ avec conditions de Neumann : \n",
"\n",
"$$\n",
"\\left\\{\\begin{aligned}\n",
"&-u''(x) + u(x) = f(x) \\hbox{ sur } ]0,1[ \\\\\n",
"&u'(0) = u'(1) = 0\n",
"\\end{aligned}\\right.$$\n",
"\n",
"**Question 1 :** En partant de l'égalité\n",
"$ u(h) = u(0) + hu'(0) + \\frac{h^2}{2} u''(0) + O(h^3), $\n",
"\n",
"réécrite sous la forme\n",
"$\n",
"\\begin{align}\n",
"u'(0) &= \\frac{1}{h} (u(h) - u(0)) - \\frac{h}{2} u''(0) + O(h^2) \\\\\n",
"&= \\frac{1}{h} (u(h) - u(0)) + \\frac{h}{2} (f(0) - u(0)) + O(h^2) \n",
"\\end{align}\n",
"$\n",
"\n",
"proposer une discrétisation d'ordre deux pour la condition $u'(0) = 0$. Mettre le schéma sous la forme $AU = F + \\Delta$ où $A$ (taille $M\\times M$) et $\\Delta\\in\\RR^M$ sont à déterminer.\n",
"\n",
"**Question 2 :** Vérifier numériquement qu'on obtient effectivement une méthode d'ordre $2$."
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"## Exercice 5. Pour aller plus loin.\n",
"\n",
"Vous pourrez tester un problème de Neumann dans un intervalle $]a,b[$ autre que $]0,1[$, avec des conditions aux limites de Neumann non homogènes, c'est-à-dire du type $u'(a)=\\alpha,\\ u'(b)=\\beta$, avec $\\alpha,\\ \\beta\\in\\RR$ pas forcément égaux à 0.\n",
"\n",
"*Pour considérer un tel problème, vous pouvez partir d'une fonction $u$ que vous choisirez (cette fonction sera la solution de votre problème), prendre comme second membre $f$ la fonction correspondante à $-u''+u$, prendre un intrevalle $[a,b]$ de votre choix et $\\alpha,\\ \\beta$ égaux respectivement aux valeurs $u'(a),\\ u'(b)$.* "
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"## Exercice 6. Une application au traitement de signal.\n",
"\n",
"On s'intéresse à un problème de *débruitage*. Étant donné un signal 1D, $v:[0,1]\\to\\mathbb{R}$, continu, et un paramètre $\\alpha > 0$, on cherche à construire un signal régularisé en résolvant l'équation différentielle\n",
"\n",
"$$\n",
"(D)\\hspace{3cm} \\left\\{\\begin{aligned}\n",
"&-u''(x) + \\alpha (u(x) - v(x)) = 0 \\hbox{ sur } ]0,1[ \\\\\n",
"&u'(0) = u'(1) = 0\n",
"\\end{aligned}\\right.$$\n",
"\n",
"On remarque que si $\\alpha\\to\\infty$, on obtient formellement comme solution de l'équation $(D)$ $u=v$. D'autre part, on peut montrer comme on l'a fait pour le problème de Poisson avec conditions aux limites de Dirichlet, que la solution de $(D)$ est une fonction de classe $C^2$. L'idée alors pour obtenir une *régularisation* du signal $v$ est de résoudre $(D)$ pour une valeur de $\\alpha$ grande.\n",
"\n",
"On discrétise $(D)$ de la manière suivante. Étant donnée une discrétisation de $]0,1[$ de pas $h=\\frac{1}{M+1}$, avec $M>0$ donné, définie par les points $x_i=ih,\\ i=0,\\dots,M+1$, on cherche une solution approchée $(u_0,\\dots,u_{M+1})$ vérifiant :\n",
"\n",
"$$\n",
"(D_h)\\hspace{3cm} \\left\\{\\begin{aligned}\n",
"&u_{0} = u_1, u_{M+1} = u_M\\\\\n",
"&-\\frac{1}{h^2\\alpha}(u_{i-1} - 2 u_i + u_{i+1}) + u_i = v_i, \\hbox{ pour } 1\\leq i\\leq M,\n",
"\\end{aligned}\\right.$$\n",
"\n",
"où $v_i = v(x_i)$. \n",
"\n",
"**Question 1** Mettre le système $(D_h)$ sous la forme $A_M U = F$ où la matrice $A_M$ et le vecteur $F$ sont à construire. Écrire une fonction python $A(M,alpha)$ construisant la matrice $A_M$.\n",
"\n",
"**Question 2** Considérer le signal $v$ défini ci-dessous, auquel on a rajouté un bruit uniforme, à travers la fonction random.random de numpy. Pour $M=99$ et pour les valeurs de $\\alpha=50,100,1000,10000$, résoudre numériquement le système $D_h$. Représenter le signal $v$ ainsi que les solutions approchées obtenues pour les différentes valeurs de $\\alpha$. \n"
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"def v(x):\n",
" return (\n",
" 4 * np.exp(-500 * np.square(x - 0.8))\n",
" + np.exp(-50 * np.square(x - 0.2))\n",
" + 0.5 * np.random.random(x.shape)\n",
" )"
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