{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import display, Latex\n", "from IPython.core.display import HTML\n", "css_file = './customNEW.css'\n", "HTML(open(css_file, \"r\").read()) " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python version 3.8.10 (default, Nov 26 2021, 20:14:08) \n", "[GCC 9.3.0]\n" ] } ], "source": [ "import sys #only needed to determine Python version number\n", "print('Python version ' + sys.version)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62 TP 2 - Implémentation des schémas \"classiques\" et étude de la convergence" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

\n", "
" ] }, { "cell_type": "markdown", "metadata": { "hide_input": false }, "source": [ "## Rappel de CM : implémentation des schémas d'Euler explicite et implicite\n", "\n", "Considérons le problème de Cauchy\n", "\n", ">trouver la fonction $y \\colon I\\subset \\mathbb{R} \\to \\mathbb{R}$ définie sur l'intervalle $I=[0,1]$ telle que\n", ">$$\n", "\\begin{cases}\n", "y'(t) = -4y(t)+t^2, &\\forall t \\in I=[0,1],\\\\\n", "y(0) = 1\n", "\\end{cases}\n", "$$\n", "\n", "1. Calculer la solution exacte en utilisant le module `sympy`.\n", "1. Calculer la solution approchée obtenue avec la méthode d'**Euler explicite** avec $h=1/N$ et $N=8$ (pour bien visualiser les erreurs);\n", "2. Même exercice pour la méthode d'**Euler implicite**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction 1** \n", "Calculons la solution exacte en utilisant le module `sympy`:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = t^{2} - 4 y{\\left(t \\right)}$" ], "text/plain": [ "d 2 \n", "──(y(t)) = t - 4⋅y(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\left(C_{1} + \\frac{\\left(8 t^{2} - 4 t + 1\\right) e^{4 t}}{32}\\right) e^{- 4 t}$" ], "text/plain": [ " ⎛ ⎛ 2 ⎞ 4⋅t⎞ \n", " ⎜ ⎝8⋅t - 4⋅t + 1⎠⋅ℯ ⎟ -4⋅t\n", "y(t) = ⎜C₁ + ─────────────────────⎟⋅ℯ \n", " ⎝ 32 ⎠ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : \\frac{31}{32}\\right\\}$" ], "text/plain": [ "⎧ 31⎫\n", "⎨C₁: ──⎬\n", "⎩ 32⎭" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\frac{t^{2}}{4} - \\frac{t}{8} + \\frac{1}{32} + \\frac{31 e^{- 4 t}}{32}$" ], "text/plain": [ " 2 -4⋅t\n", " t t 1 31⋅ℯ \n", "y(t) = ── - ─ + ── + ────────\n", " 4 8 32 32 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "edo= sym.Eq( sym.diff(y(t),t) , -4*y(t)+t**2 )\n", "display(edo)\n", "solgen = sym.dsolve(edo)\n", "display(solgen)\n", "\n", "t0=0\n", "y0=1\n", "consts = sym.solve( sym.Eq( y0, solgen.rhs.subs(t,t0)) , dict=True)[0]\n", "display(consts)\n", "solpar=solgen.subs(consts).simplify()\n", "display(solpar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On définit la solution exacte à utiliser pour estimer les erreurs:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "sol_exacte = sym.lambdify(t,solpar.rhs,'numpy')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction 2 et 3** \n", "On commence par importer le module `matplotlib`et la fonction `fsolve` du module `scipy.optimize` pour résoudre l'équation implicite présente dans le schéma implicite:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve # pour les schémas implicites" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On initialise le problème de Cauchy" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# variables globales\n", "t0 = 0\n", "tfinal = 1\n", "y0 = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On définit l'équation différentielle : `phi` est une lambda function qui contient la fonction mathématique $\\varphi(t, y)=-4y+t^2$ dépendant des variables $t$ et $y$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "phi = lambda t,y : -4*y+t**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On écrit les schémas numériques : les valeurs $[u_0,u_1,\\dots,u_{N}]$ pour chaque méthode sont contenues dans le vecteur `uu`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler progressif :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_n,u_n)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def EE(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " uu.append(uu[i] + h * phi(tt[i], uu[i]))\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler régressif :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_{n+1},u_{n+1})& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "\n", "Attention : $u_{n+1}$ est solution de l'équation $x=u_n+h\\varphi(t_{n+1},x)$, c'est-à-dire un zéro de la fonction (en générale non linéaire) $$x\\mapsto -x+u_n+h\\varphi(t_{n+1},x)$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def EI(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " temp = fsolve(lambda x: -x + uu[i] + h * phi(tt[i + 1], x), uu[i])\n", " uu.append(temp[0])\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On introduit la discrétisation: les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt`. \n", "On a $N+1$ points espacés de $h=\\frac{t_N-t_0}{N}$.\n", "\n", "On calcule les solutions exacte et approchées en ces points:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "N = 8 \n", "tt = linspace(t0,tfinal,N+1)\n", "# print(tt)\n", "\n", "yy = [sol_exacte(t) for t in tt]\n", "# yy = sol_exacte(tt) # si vectorisée\n", "uu_ep = EE(phi, tt, y0)\n", "uu_er = EI(phi, tt, y0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On compare les graphes des solutions exacte et approchées et on affiche le maximum de l'erreur:\n", "$$\n", "\\max_n \\left| y(t_n)-u_n \\right|\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(18, 7))\n", "\n", "subplot(1, 2, 1)\n", "plot(tt, yy, 'b-', tt, uu_ep, 'r-D')\n", "# err_ep = max( [abs(uu_ep[i] - yy[i]) for i in range(N)] )\n", "err_ep = norm(array(uu_ep)-array(yy),inf)\n", "title(f'Euler explicite - max(|erreur|)= {err_ep:1.10f}')\n", "grid()\n", "\n", "subplot(1, 2, 2)\n", "plot(tt, yy, 'b-', tt, uu_er, 'r-D')\n", "# err_er = max( [abs(uu_er[i] - yy[i]) for i in range(N)] )\n", "err_er = norm(array(uu_er)-array(yy),inf)\n", "title(f'Euler implicite - max(|erreur|)= {err_er:1.10f}')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rappel de CM : étude empirique de la convergence des schémas d'Euler explicite et implicite\n", "Considérons le même problème de Cauchy.\n", "\n", "1. On se propose d'estimer empiriquement l'ordre de convergence de la méthode d'**Euler explicite**. \n", "\t- On calcule d'abord la solution approchée avec différentes valeurs de $h_k=1/N_k$ \n", "\t- Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on la sauvegarde dans le vecteur `err_ep` de sort que `err_ep[k]` contient $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$. \n", "\t- Pour estimer l'ordre de convergence on affiche les points (`h[k]`,`err_ep[k]`) en echèlle logarithmique. On trouve ainsi une droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$. \n", " Pour estimer la pente globale de cette droite (par des moindres carrés) on utilisers la fonction `polyfit` avec une régression linéaire. \t\n", "\n", "2. Même exercice pour estimer l'ordre de convergence de la méthode d'**Euler implicite**.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$ et on sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \n", "\n", "Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on sauvegarde toutes ces erreurs dans le vecteur `err_schema` de sort que `err_schema[k]` contient $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "H = []\n", "err_ep = []\n", "err_er = []\n", "\n", "N = 10\n", "for k in range(7):\n", "# N = 2**(k + 3)\n", " N+=20\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu_ep = EE(phi, tt, y0)\n", " uu_er = EI(phi, tt, y0)\n", " H.append(h)\n", "# err_ep.append(max([abs(uu_ep[i] - yy[i]) for i in range(len(yy))]))\n", " err_ep.append(norm(array(uu_ep)-array(yy),inf))\n", "# err_er.append(max([abs(uu_er[i] - yy[i]) for i in range(len(yy))]))\n", " err_er.append(norm(array(uu_er)-array(yy),inf))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour afficher l'ordre de convergence on utilise une échelle logarithmique, i.e. on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées. \n", "En effet, si $\\text{err}=Ch^p$ alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. \n", "En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(log(H), log(err_ep), 'r-o', label='Euler Explicite')\n", "plot(log(H), log(err_er), 'g-+', label='Euler Implicite')\n", "# loglog(H, err_ep, 'r-o', label='Euler Explicite')\n", "# loglog(H, err_er, 'g-+', label='Euler Implicite')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "legend(bbox_to_anchor=(1.04, 1), loc='upper left')\n", "grid(True)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour estimer l'ordre de convergence on doit estimer la pente de la droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$ en echelle logarithmique.\n", "Pour estimer la pente globale de cette droite (par des moindres carrés) on peut utiliser la fonction `polyfit` (du module `numpy` que nous avons déjà importé avec `matplotlib.pylab`). " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler progressif : ordre = 1.03\n", "Euler regressif : ordre = 0.98\n" ] } ], "source": [ "order_ep = polyfit(log(H),log(err_ep), 1)[0]\n", "print (f'Euler progressif : ordre = {order_ep:1.2f}')\n", "order_er = polyfit(log(H),log(err_er), 1)[0]\n", "print (f'Euler regressif : ordre = {order_er:1.2f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : implémentation et étude empirique de la convergence des méthodes d'Euler modifié, RK1_m, de Crank-Nicolson et de Heun\n", "Ajouter l'implémentation et l'étude empirique de la convergence des méthodes d'**Euler modifié**, **RK1_M**, de **Crank-Nicolson** et de **Heun** . \n", "Pour cela **modifier directement le code ci-dessus** : les endroits où il faut écrire du code sont indiqués par les commentaire commençant par\n", "``# !!!!!! ``." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**\n", "\n", "On écrit les quatre schémas:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler modifié:**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+\\frac{h}{2}\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2},\\tilde u\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "qu'on peut réécrire sous la forme\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "k_1 = h\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2}, u_n+\\frac{k_1}{2}\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def EM(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " k1 = h * phi( tt[i], uu[i] )\n", " uu.append( uu[i]+h*phi( tt[i]+h/2 , uu[i]+k1/2 ) )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma RK1_M:**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(\\frac{t_n+t_{n+1}}{2},\\frac{u_n+u_{n+1}}{2}\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def RK1_M(phi,tt,y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " uu.append( fsolve(lambda x: -x+uu[i]+h*phi( (tt[i]+tt[i+1])/2,(uu[i]+x)/2 ), uu[i])[0] )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma de Crank-Nicolson :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},u_{n+1})\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "avec $u_{n+1}$ zéro de la fonction $x\\mapsto -x+u_n+\\frac{h}{2}(\\varphi(t_n,u_n)+\\varphi(t_{n+1},x))$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def CN(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " temp = fsolve(lambda x: -x+uu[i]+0.5*h*( phi(tt[i+1],x)+phi(tt[i],uu[i]) ), uu[i])\n", " uu.append(temp[0])\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma de Heun:**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+h\\varphi(t_n,u_n)\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},\\tilde u)\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "qu'on peut réécrire sous la forme\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "k_1 = h\\varphi(t_n,u_n),\\\\\n", "k_2 = h\\varphi(t_{n+1},u_n+k_1),\\\\\n", "u_{n+1}=u_n+\\frac{k_1+k_2}{2}& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def heun(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " k1 = h * phi( tt[i], uu[i] )\n", " k2 = h * phi( tt[i+1], uu[i] + k1 )\n", " uu.append( uu[i] + (k1+k2) /2 )\n", " return uu" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 8 \n", "tt=linspace(t0,tfinal,N+1)\n", "\n", "yy = [sol_exacte(t) for t in tt]\n", "uu_ep = EE(phi, tt, y0)\n", "uu_er = EI(phi, tt, y0)\n", "uu_em = EM(phi, tt, y0)\n", "uu_rk1m = RK1_M(phi, tt, y0)\n", "uu_cn = CN(phi, tt, y0)\n", "uu_heun = heun(phi, tt, y0)\n", "\n", "figure(1, figsize=(18, 10))\n", "\n", "subplot(2, 3, 1)\n", "plot(tt, yy, 'b-', tt, uu_ep, 'r-D')\n", "# err_ep = max( [abs(uu_ep[i] - yy[i]) for i in range(N)] )\n", "err_ep = norm(array(uu_ep)-array(yy),inf)\n", "title(f'Euler explicite - max(|erreur|)= {err_ep:1.10f}')\n", "grid()\n", "\n", "subplot(2, 3, 2)\n", "plot(tt, yy, 'b-', tt, uu_er, 'r-D')\n", "# err_er = max( [abs(uu_er[i] - yy[i]) for i in range(N)] )\n", "err_er = norm(array(uu_er)-array(yy),inf)\n", "title(f'Euler implicite - max(|erreur|)={err_er:1.2f}')\n", "grid();\n", "\n", "\n", "subplot(2, 3, 3)\n", "plot(tt, yy, 'b-', tt, uu_em, 'r-D')\n", "# err_em = max( [abs(uu_em[i] - yy[i]) for i in range(N)] )\n", "err_em = norm(array(uu_em)-array(yy),inf)\n", "title(f'Euler modifié - max(|erreur|)={err_em:1.5f}')\n", "grid()\n", "\n", "subplot(2, 3, 4)\n", "plot(tt, yy, 'b-', tt, uu_rk1m, 'r-D')\n", "# err_rk1m = max( [abs(uu_rk1m[i] - yy[i]) for i in range(N)] )\n", "err_rk1m = norm(array(uu_rk1m)-array(yy),inf)\n", "title(f'RK1_m - max(|erreur|)={err_rk1m:1.5f}')\n", "grid()\n", "\n", "subplot(2, 3, 5)\n", "plot(tt, yy, 'b-', tt, uu_cn, 'r-D')\n", "# err_cn = max( [abs(uu_cn[i] - yy[i]) for i in range(N)] )\n", "err_cn = norm(array(uu_cn)-array(yy),inf)\n", "title(f'Crank Nicolson - max(|erreur|)={err_cn:1.5f}')\n", "grid()\n", "\n", "subplot(2, 3, 6)\n", "plot(tt, yy, 'b-', tt, uu_heun, 'r-D')\n", "# err_heun = max( [abs(uu_heun[i] - yy[i]) for i in range(N)] )\n", "err_heun = norm(array(uu_heun)-array(yy),inf)\n", "title(f'Heun - max(|erreur|)={err_heun:1.5f}')\n", "grid();" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler progressif : ordre = 1.05\n", "Euler regressif : ordre = 0.96\n", "Euler modifié : ordre = 2.08\n", "RK1_M : ordre = 2.00\n", "Cranck Nicolson : ordre = 2.01\n", "Heun : ordre = 2.08\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "H = []\n", "err_ee = []\n", "err_ei = []\n", "err_em = []\n", "err_rk1m = []\n", "err_cn = []\n", "err_heun = []\n", "\n", "for k in range(7):\n", " N = 2**(k + 3)\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu_ee = EE(phi, tt, y0)\n", " uu_ei = EI(phi, tt, y0)\n", " uu_em = EM(phi, tt, y0)\n", " uu_rk1m = RK1_M(phi, tt, y0)\n", " uu_cn = CN(phi, tt, y0)\n", " uu_heun = heun(phi, tt, y0)\n", " H.append(h)\n", " err_ee.append(max([abs(uu_ee[i] - yy[i]) for i in range(len(yy))]))\n", " err_ei.append(max([abs(uu_ei[i] - yy[i]) for i in range(len(yy))]))\n", " err_em.append(max([abs(uu_em[i] - yy[i]) for i in range(len(yy))]))\n", " err_rk1m.append(max([abs(uu_rk1m[i] - yy[i]) for i in range(len(yy))]))\n", " err_cn.append(max([abs(uu_cn[i] - yy[i]) for i in range(len(yy))]))\n", " err_heun.append(max([abs(uu_heun[i] - yy[i]) for i in range(len(yy))]))\n", "\n", "figure(figsize=(10,7))\n", "loglog(H, err_ee, 'r-o', label='Euler Explicite')\n", "loglog(H, err_ei, 'g-+', label='Euler Implicite')\n", "loglog(H, err_em, 'm-x', label='Euler Modife')\n", "loglog(H, err_rk1m, 'b-^', label='RK1_m')\n", "loglog(H, err_cn, 'y-d', label='Crank Nicolson')\n", "loglog(H, err_heun, 'c-v', label='Heun')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "legend(bbox_to_anchor=(1.04, 1), loc='upper left')\n", "grid(True);\n", "\n", "order_ee = polyfit(log(H),log(err_ee), 1)[0]\n", "print (f'Euler progressif : ordre = {order_ee:1.2f}')\n", "order_ei = polyfit(log(H),log(err_ei), 1)[0]\n", "print (f'Euler regressif : ordre = {order_ei:1.2f}')\n", "order_em = polyfit(log(H),log(err_em), 1)[0]\n", "print (f'Euler modifié : ordre = {order_em:1.2f}')\n", "order_rk1m = polyfit(log(H),log(err_rk1m), 1)[0]\n", "print (f'RK1_M : ordre = {order_rk1m:1.2f}')\n", "order_cn = polyfit(log(H),log(err_cn), 1)[0]\n", "print (f'Cranck Nicolson : ordre = {order_cn:1.2f}')\n", "order_heun = polyfit(log(H),log(err_heun), 1)[0]\n", "print (f'Heun : ordre = {order_heun:1.2f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : Fonction intégrale\n", "\n", "Il existe des fonctions définies par des intégrales qu'on ne peut pas calculer explicitement.\n", "Il est pourtant possible de calculer des valeurs approchées de ces fonctions. \n", "\n", ">Pour $x\\in\\left[0;\\frac{\\pi}{2}\\right]$ calculer et afficher la table des valeurs et tracer le graphe de la fonction\n", "$$\n", "x \\mapsto f(x)=\\int_0^x \\sqrt{1-\\frac{1}{4}\\sin^2(t)}\\mathrm{d}t \n", "$$\n", "en approchant numériquement un problème de Cauchy (lequel?) avec la méthode d'**Euler explicite**. \n", ">\n", ">Vérifier que $f\\left(\\frac{\\pi}{6}\\right)\\simeq0.51788193$ et $f\\left(\\frac{\\pi}{2}\\right)\\simeq1.46746221$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction $f$ est solution du problème de Cauchy\n", "$$\n", "\\begin{cases}\n", "y'(t)= \\sqrt{1-\\frac{1}{4}\\sin^2(t)},\\\\\n", "y(0)=0.\n", "\\end{cases}\n", "$$\n", "En effet, $f(0)=0$ et si on intègre l'EDO entre $0$ et $x$ on a \n", "$$\n", "f(x)=\\int_0^x \\sqrt{1-\\frac{1}{4}\\sin^2(t)}\\mathrm{d}t=\\int_0^x y'(t)\\mathrm{d}t=y(x)-y(0)=y(x).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans le code ci-dessous:\n", "1. On définit l'équation différentielle : `phi` est une *lambda function* qui contient la fonction mathématique $\\varphi(t, y)$ dépendant des variables $t$ et $y$ (même si $y$ n'apparaît pas explicitement).\n", "1. On définit la condition initiale $t_0=0$ et $y_0=0$.\n", "1. On introduit la discrétisation: les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt`. \n", "\n", "Comme nous devons éstimer ensuite $f$ en $\\frac{\\pi}{6}$ et $\\frac{\\pi}{2}$, faisons en sort davoir ces deux valeurs dans nos noeuds de discrétisation. \n", "Étant donné que \n", "- $t_0=0$, \n", "- $t_N=\\frac{\\pi}{2}$ et \n", "- $t_i=t_0+ih$ avec $h=\\frac{t_N-t_0}{N}=\\frac{\\pi}{2N}$, \n", " \n", "on a $\\frac{\\pi}{6}=i\\frac{\\pi}{2N}$ ssi $i=\\frac{2N}{6}=\\frac{N}{3}$ et bien sûr $\\frac{\\pi}{2}=t_{N}$. Pour que $i\\in\\mathbb{N}$ on choisira $N$ multiple de $3$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On calcule enfin la solution approchée et on vérifie que $f(\\pi/6)\\simeq0.51788193$ et $f(\\pi/2)\\simeq1.46746221$ et on affiche le graphe de la fonction approchée." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(pi/6.0)=0.5179648116355586\n", "f(pi/2.0)=1.4678129540121247\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "\n", "# schéma\n", "def EE(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " uu.append(uu[i] + h * phi(tt[i], uu[i]))\n", " return uu\n", "\n", "# EDO\n", "phi = lambda t,y : sqrt(1-0.25*(sin(t))**2)\n", "\n", "# CI\n", "t0, y0 = 0, 0\n", "\n", "# DISCRETISATION\n", "tfinal = pi/2\n", "k = 100\n", "N = 3*k # ainsi t_N=pi/2=3pi/6 et t_k=pi/6\n", "tt=linspace(t0,tfinal,N+1)\n", "\n", "# CALCUL DE LA SOLUTION APPROCHÉE\n", "uu = EE(phi,tt, y0)\n", "\n", "print(f\"f(pi/{pi//tt[k]})={uu[k]}\") \n", "print(f\"f(pi/{pi//tt[-1]})={uu[-1]}\") \n", "\n", "# AFFICHAGE, NON DEMANDÉ\n", "plot(tt,uu)\n", "plot([tt[0],tt[k],tt[k]],[uu[k],uu[k],0],'m--');\n", "plot([tt[0],tt[-1],tt[-1]],[uu[-1],uu[-1],0],'c--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Et `sympy` ? " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = \\sqrt{1 - \\frac{\\sin^{2}{\\left(t \\right)}}{4}}$" ], "text/plain": [ " _____________\n", " ╱ 2 \n", "d ╱ sin (t) \n", "──(y(t)) = ╱ 1 - ─────── \n", "dt ╲╱ 4 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\int \\sqrt{1 - \\frac{\\sin^{2}{\\left(t \\right)}}{4}}\\, dt$" ], "text/plain": [ "⌠ \n", "⎮ _____________ \n", "⎮ ╱ 2 \n", "⎮ ╱ sin (t) \n", "⎮ ╱ 1 - ─────── dt\n", "⎮ ╲╱ 4 \n", "⌡ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle E\\left(t\\middle| \\frac{1}{4}\\right)$" ], "text/plain": [ "E(t│1/4)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "edo= sym.Eq( sym.diff(y(t),t) , sym.sqrt(1-sym.Rational(1,4)*(sym.sin(t))**2) )\n", "display(edo)\n", "# solgen = sym.dsolve(edo)\n", "# display(solgen)\n", "\n", "t = sym.Symbol('t')\n", "f=sym.Integral(sym.sqrt(1-sym.Rational(1,4)*(sym.sin(t))**2))\n", "display(f)\n", "f.doit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : Système de deux EDO avec invariant\n", "\n", ">Considérons le problème de Cauchy\n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t) ,\\\\\n", "y'(t)= x(t), & t\\in[0;4\\pi]\\\\\n", "x(0)=1,\\\\\n", "y(0)=0.\n", "\\end{cases}\n", "$$\n", ">1. **Invariant** \n", "Vérifier que $I(t)=x^2(t) + y^2(t)$ est un invariant pour le système. \n", ">1. **Approximations** \n", "Dans une simulation numérique on aimerait que l'invariant soit préservé aussi bien que possible. Nous allons regarder ce qui se passe avec certaines méthodes vues en cours. \n", "On notera $u_n\\approx x_n=x(t_n)$ et $w_n\\approx y_n=y(t_n)$. \n", "À chaque instant $t_n$, on calculera $J_n\\approx I_n=I(t_n)$. \n", "Choisissons $N=193$ points de discrétisation ainsi $h=t_{n+1}-t_n=\\pi/48$.\n", " 1. Dans un premier temps on se propose d'appliquer la méthode d'**Euler explicite** à la résolution du système. \n", " 1. Tracer $(t_n,u_n)$ et $(t_n,w_n)$ sur un même graphique; \n", " 2. sur un autre graphique tracer $(t_n,J_n)$; \n", " 3. tracer enfin $(u_n,w_n)$ sur un autre graphique et vérifier que la solution numérique tourne vers l’extérieur \n", " 4. Après avoir constaté que l'invariant $J_n$ n'est pas conservé mais augment au cours du temps, montrer analytiquement que $J_n=(1+h^2)^n$. \n", " 1. Même exercice pour le schéma d'**Euler implicite** (la linéarité du second membre permet de rendre ce schéma explicite). Que peut-on constater? Commenter les résultats et écrire l'expression analytique de $J_n$. \n", " 1. Même exercice pour le schéma de **Crank Nicolson** (la linéarité du second membre permet de rendre ce schéma explicite). Que peut-on constater? Commenter les résultats et écrire l'expression analytique de $J_n$. \n", " 1. Même exercice avec la fonction ``odeint`` du module ``scipy.optimize``.\n", ">1. **Solution exacte** \n", "Dans ce cas il est même possible de calculer analytiquement la solution exacte. Calculer donc la solution exacte avec le module `sympy`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Invariant**\n", "\n", "Pour tout $t$ on a\n", "$$\n", "I'(t)=\\left(x^2(t) + y^2(t)\\right)' = 2x'(t)x(t)+2y'(t)y(t)=-2x(t)y(t)+2x(t)y(t)=0\n", "$$\n", "donc $I(t)=I(0)=0^2+1^2=1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Approximations**\n", "\n", "On notera $u_n\\approx x_n=x(t_n)$ et $w_n\\approx y_n=y(t_n)$.\n", "\n", "À chaque instant $t_n$, on calculera $J_n=u_n^2+w_n^2\\approx I_n=I(t_n)$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "# from scipy.optimize import fsolve # non necessaire car on resout l'equation implicite a la main\n", "\n", "t0 = 0\n", "tfinal = 4*pi\n", "\n", "#h = pi/48\n", "N = 192 #*100\n", "tt = linspace(0,tfinal,N+1) #arange(t0,tfinal+h/2,h)\n", "\n", "x0 = 1\n", "y0 = 0\n", "\n", "phi1 = lambda t,x,y : -y\n", "phi2 = lambda t,x,y : x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler explicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_n,u_n,w_n)=u_n-hw_n,\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_n,u_n,w_n)=w_n+hu_n\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def EE(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append(uu[i]+h*phi1(tt[i],uu[i],ww[i]))\n", "\t\tww.append(ww[i]+h*phi2(tt[i],uu[i],ww[i]))\n", "\treturn [uu,ww]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a\n", "$$\n", "J_{n+1}\n", "=u_{n+1}^2+w_{n+1}^2\n", "=(u_n-hw_n)^2+(w_n+hu_n)^2\n", "=(1+h^2)(u_n^2+w_n^2)\n", "=(1+h^2)J_n\n", "$$\n", "soit encore\n", "$$\n", "J_n=(1+h^2)^nJ_0=(1+h^2)^n.\n", "$$\n", "On voit que \n", "- l'invariant n'est conservé que si $h=0$, ce qui est impossible,\n", "- pour $h$ fixé, $\\lim\\limits_{n\\to+\\infty}J_n=+\\infty$,\n", "- pour $n$ fixé, l'erreur $|J_n-I_n|$ diminue comme $h^2$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_ep, ww_ep] = EE(phi1,phi2,tt,x0,y0)\n", "JJ_ep = [(uu_ep[i])**2+(ww_ep[i])**2 for i in range(len(tt))]\n", "\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_ep,tt,ww_ep)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Euler progressif - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_ep)\n", "xlabel('t')\n", "title('Euler progressif - Invariant')\n", "\n", "subplot(1,3,3)\n", "Y1,Y2 = meshgrid(linspace(min(uu_ep),max(uu_ep),21),linspace(min(ww_ep),max(ww_ep),21))\n", "V1,V2 = phi1(tt,Y1,Y2),phi2(tt,Y1,Y2)\n", "r=sqrt(V1**2+V2**2)\n", "quiver(Y1, Y2, V1/r, V2/r) \n", "plot(uu_ep,ww_ep,'r')\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Euler progressif - y(x)'); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler implicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_{n+1},u_{n+1},w_{n+1})=u_n-hw_{n+1},\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_{n+1},u_{n+1},w_{n+1})=w_n+hu_{n+1}\n", "\\end{cases}\n", "$$\n", "En resolvant le système linéaire on obtient une écriture explicite\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=\\dfrac{u_n-hw_{n}}{1+h^2},\\\\\n", "w_{n+1}=\\dfrac{w_n+hu_{n}}{1+h^2}.\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "# Notons que ici il est inutile de passer phi1,phi2 car non utilisées explicitement dans le code\n", "def EI(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append((uu[i]-h*ww[i])/(1+h**2))\n", "\t\tww.append((ww[i]+h*uu[i])/(1+h**2))\n", "\treturn [uu,ww]" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# VERSION AVEC fsolve (non demandé)\n", "from scipy.optimize import fsolve\n", "\n", "def EI(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tsys = lambda z : [ -z[0]+uu[i]+h*phi1(tt[i+1],z[0],z[1]) , -z[1]+ww[i]+h*phi2(tt[i+1],z[0],z[1]) ]\n", "\t\tutemp,wtemp = fsolve( sys , (uu[i],ww[i]) ) \n", "\t\tuu.append(utemp)\n", "\t\tww.append(wtemp)\n", "\treturn [uu,ww]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a\n", "$$\n", "J_{n+1}\n", "=u_{n+1}^2+w_{n+1}^2\n", "=\\frac{(u_n-hw_n)^2+(w_n+hu_n)^2}{(1+h^2)^2}\n", "=(u_n^2+w_n^2)\\frac{1+h^2}{(1+h^2)^2}\n", "=\\frac{1+h^2}{(1+h^2)^2}J_n\n", "=\\frac{1}{1+h^2}J_n\n", "$$\n", "soit encore\n", "$$\n", "J_n=\\left(\\frac{1}{1+h^2}\\right)^nJ_0=\\left(\\frac{1}{1+h^2}\\right)^n.\n", "$$\n", "On voit que \n", "- l'invariant n'est conservé que si $h=0$, ce qui est impossible,\n", "- pour $h$ fixé, $\\lim\\limits_{n\\to+\\infty}J_n=0^+$,\n", "- pour $n$ fixé, l'erreur $|J_n-I_n|$ diminue comme $h^2$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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bUsoyUkprKaWnlPJnKeViKeViw3YppRwupawspawjpQzOFLtNSlnVsO3rwnsXystAq9WafDGr1WoJDQ1l9+7dBAUFGd1fSsnKlSvp378/vXr1ok+fPsTGxhqNK168OPv27aN27dqUK1eOwYMHmzRsoUmTJgwbNozly5czevRodu7cSXJystG4xo0bs337du7du8eOHTv45Zdf0Gq1RuP8/PxYs2YN1apVY/bs2ezevdtoDECbNm2YMGECvXr1on///oSFhRkPAkaPHs0333xDcnIyEyZMMOl7E0Lw/fffs3XrVj766COOHDliUlnu7u7s37+f999/n549e5KammpSnDmEqd0/jB5IiErAFill7Sy2LQH2Syl/NTy/DLQEKgFTpJTtDK9PAJBSTsuprAYNGsjg4OCcdnlMZFwKey5G0dW3LE52atZ6RSloFy9epEaNGoVdjaeMHTuWgIAAunbtyooVKwgODmb+/PmA/o9n/fr1OXToEA4ODk/FZvWehBDHpZQNCqTyZspNG23oFpwlc9thgJ3nIylXwp7a5YqbFacoimKO57ktzmu5aYuLotxOupebOFNjntxPp9NhYZHzvd+bN29SoUKFR3Hp6elYWWW/ZkBCQgKbNm2iYsWKtGjRAiklKSkpWFpakaKD+GQN8cnpJKRoiE1K4+ylq5y7eJkrV64Qff8+77zzDvYO9tjZ2VHM0REHewcQ4GBjSXF7a5ztrIm/H8nXU75g5+ZNIHV07NiRFi1aUK1aNapWrUq1atWwtLR8qm46nY5ly5bx2WefodPp8PT0JCAggJYtW9KqVStymr8kODiYt956i+bNmxMYGMhrr71Gv379aN68eY6f/blz51i3bh3p6els2LCBfv36MWzYsBzLAjh48CDe3t5Mnz6dwMBAvv76azp27JhjDOjndUhJSWHw4MFUrFiR77//npIlS+YYk56ejoWFBbt27eLjjz9m1qxZdOjQwWhZGbGjR4/mzp07rFq1Ksvz06xcu3aNrl27Mm/ePF577TWTYgC++eYbgoOD+e2333L8PcxKTu1wQSUgtgDfSikDDc/3AuPRJyDaSykHGV5/F2gspRyRxTEyz/jrf/PmTZPrtupIKBP/ex57a0tGvObDh69WxsJCjeFWlIJS2AmIv//+m4EDBxIUFIRWq6VRo0asW7eON954g4sXLyKEwMfHh+TkZMqVK8eECRPo06cPH3/8MU2bNqV3795PHbOIJSCybKMz35kzvJ7rdjhFo+W17/ZjZWnBlo8CcFbJYEVR8snz3BbnNXMTEAsXLsTW1paBAweaHHP+/HkmTpzI+vXrjV5AZ0hMTOTDDz9kyJAhNG/e3KQYnU7H0qVLOXXqFIsXLza6f8YF/p49e/jyyy/ZtGkTpUuXzjEmNjaWEiVKEBQUxPfff0/9+vUZP358jjGHDx+mdu3anDx5kl9//ZW///6boKCgLC+6M97HypUriYyMpEyZMuzfv5+jR4/y7bff0rVr1yxjzpw5w/Tp09m7dy89evTgypUr3Lp1Cz8/P9atW/fYvmnpOk5eDuXr2YsIPHURaV8S5zJeWDi7Ie1LgLU9wto+6yVUnpGFNg0nW0vsLHRYpMaRFnOHD/p0pUqZklRwdaB8SQccbR+/UI2JieHw4cO0aNGCwMBA9u/fT926dXnnnXdyLCshIQFra+tHF+vbt29n/vz5RpM/Gb8XiYmJLFu2jLp169KyZUuT3+OVK1f4448/mDBhgskxUkp++umnR4kZU4WHh7Njxw4GDRpkcgzAsmXL6NKli9HESma3bt0iODiYHj16mFXW8uXL6dOnj8nJjgzPQwJiKzDtiZPbcYA30O6JBEQjKeXInMoyt7GVUnI6PI5F+6+x83wUHeuUZm5fP6ws1RycilIQMl+s/2vzeS5EmDamz1Q1yzozuUutHPf58ssvSUlJITk5GU9PT/r27UuvXr0ezfT7ZA8IgNWrV3P06FHmzZv31PGKWAIiyzZaSpntNMi5uesWHBpDn6VHaVvTg4Vv11eTeSqKki+e57Y4r5nSFmdckM2YMYPdu3ezadMmHB0djR47OTmZv/76i9GjR7Nq1Sr8/f2Nxty6dYu4uDjeeecdBg8ezPDhw4229bt376ZixYoMGTKEqlWrMmPGDEqUKJFjzIEDBzh69Cj79+/HysqKb7/9llq1cj4P2Lx5M1999RW2trY4ODjw6aef0qZNm2zrp9VqmTZtGlOmTMHb2xt/f3/69etHu3btsLGxyTLm+PHjjBgxgqNHj1K2bFkGDx5My5Ytady4Mfb29lnG7Ny5kzlz5nDlyhXCwsJYsWIFzZo1w71MWa7fS+JCRDznI+K4GJnAregkohJSyHz5JpCUtIWq5VwpU9ze0HPBCmdDDwanJ362tbZAq9Vx5sxpfH39gH/We5VSIiUka7TEJWuIS9IQl6whPkX/b1yyhvhkDbFJGm7HJhMWk8TDtMeHLLg42lC+pD0VXR2pWdaZ2mWLU6usMyUds/7MlKIpp3bYvL4UuZfd0kI22byep4QQ+JYvweJ3/FlyMIRvt1/C3ekiU97IuaFSFKXomDRpEg0bNsTOzo65c+dy7Ngxo5ljd3d3IiLyvEl6Hpm8/NuzaFDJhXHtqjFt+yVWHrnJ+80q5XURiqIoyhNmz57NzZs3uXHjBps3b8bOzs5ozM6dO/nuu++IjY1l165deHp6Go05deoU3bt3p1ixYqxYscKkhMW5c+fo2bMnHh4eLFmyxKTu4YGBgXTq1AmtVsumTZto166d0ZgFCxbw0UcfodPpWLBgAcOGDctx/5iYGEaPHk1QUBC+vr706dOHsWPH5hij0Wh48OABY8aMITExkbS0NPr37290Ir927doR0LI1527HcSbsAcci4li56RbX7p5Ho9WnBhxtLKlexpmAKqXwLGmPZ0kHw7/2lHa2y9VNVc+WzcyOeZKUkgdJGsJikgh7kERYTDK3YpIIf5DE8ZsP+PP0P6cS5UrYU6usM7XLFad2OX1iwt3Z+O+iUvQUVALiT2CEEGIt0BjDkkNCiHsYlhwCbqNfcqhfflVCCMHQVysTnZjKj3/doF754nT3M96gKoqSd4z1VMgvMTExJCYmotFoSElJwd7e3uhsxxn7vQSybKPzo6DBzb0JuhHDV1sv4FehBHU9c77LpSiKouTe3bt3mTJlChqNhkOHDpmUfEhISGDIkCHcunWLZcuWmZR8SExMpE+fPoSGhjJ27Fj8/PyMxkRFRdG5c2ccHBxo06YNjRo1Mhpz9OhRPvnkE3r27EmjRo2M9noAuHr1KhYWFmzbtg0vLy8qVqxoNMbFxYWVK1ca3S8za2tr2rRpY9K+KRotJ2494Mj1aA5fj+Z0WCzpOn2yoVQxW2qVdaZVNTdqlnWmVtniVHRxeC6HjwshcHG0wcXRhnrln/57HpuUxvmIeM7djtP/GxHH7otRj3pwlC1uR9PKpXjFx5VXfErhoRISL4U8SUAYlhxqCZQSQoQDkwFrAMOsv9uAjuiXHEoCBhi2pQshMpYcsgSWFcSSQ591qMHxmw/41+YLNK/iRqlitvldpKIohWzIkCH8+9//5saNG4wfP57p06cTGhr6aLuTkxMJCQmPxVy5coXatZ8asfDCyW0bnR8sLATfvVmPTnP/YviaE2wZ2Zzi9mo+CEVRlPwwadIkKlasyJQpU6hXr55JMRMnTqR+/fqsXLmSFi1amBQzd+5c3n//fd5++22TLvBB32Ni/fr11K9f3+S5Jfz8/ExahSGzKlWqUKVKFbNi8ppGq+NMeCyHr+kTDsdvPSAtXYeFgLqeJRjSwpuGlVyoVc4Zd6eicxFewsGGV3xK8YpPqUevJaamc/GOPinxd2gM/7sUxR8nwgGo7ObIKz6laFa5FE29XSnuoM4PiqI8mwOiIOXFjL9XoxLoNDeQznXLMKuPbx7VTFGUrBT2JJQrV65k06ZNbNiwAa1WS7NmzZg2bRpff/01S5YswcfHh5iYGNq1a4dGo3k0CWXnzp2ZNm0aderUeeqYL9ocEHntWdvhE7ce0HvxEVrXcGfxO/5qPghFUfKMaov14uLi2Lt3L926dTP5Aj89PZ2wsDC8vLxMrkPGtYRqxx+XnKblwJW7bD8Xyd6Ld0lMTQegZhlnmlV2pWllVxp6ubz0kzLrdJILd+I5fP0+h65FE3QjhmSNFgsBdcoV5/WaHnSsUwZvt2KFXVXFDAUyCWVByqslh77dfoklB6+zY1QLqpV2yoOaZSE+Ao4tgYubIe0hlKoCvm9D3T5g4h8DRXnRFXYCIjsbN27k+PHjfPXVV09ti4qKol+/fuzduzfLWJWAePZ2+Ke/Qvhq60Umda7JBwGmn+wqiqLkRLXFSmFJTE3nf5fusuPcHfZdukeyRktJB2va1ixNy2puNPZ2xUVNxpijtHQdp8JiOXTtPgev3uPkrVgAqpd2omOdMnSsUwYfd5WMyA8ajQYLC4tsV3gxx/MwCeVzaeir3qw+epNZuy+z5N18+Dt1bQ/8MRhS4sCnNRRzh1tHYdNQOPs79FgKjqWMH0dRlHzRvXt3oqOjs9x269Ytvv/++wKu0ctlYIAXR0NimLb9IvUrlsQ3i/GjiqIoivI8S0pLZ+f5SLadjeTAlXukpetwc7Klp385OtQuQ2MvF7XynhlsrCxo5OVCIy8XPn69Knfiktl+NpLt5+7ww54rzNp9haoexR4lI6p65NNN5DyWkJCAnZ2d0UlJn3Tq1ClcXFyoUKGCWXFLly6lSZMm1K1b1+QYS0tLBgwYwNixY/N1CPJL/b+hhIMNg5p7s/N8FBfv5O2ygFzbA6t7g1MZGH4M3v4dui6AEcHQ+Qe4eQhWdYOUPC5XURSzZLf2csOGDfH1VcOz8pMQgu/frIe7kx3DV58gLklT2FVSFEVRFJOcux3HFxvP0ujrvXy87jTnbsfxduMK/PZ/TTk6oTVfdavDKz6lVPLhGZUpbs8HAV78PrQZRye05l9v1KKEgw1z9l6l7Q8H6TDnL1YdCSUhxfxziIsXLxqdkPxJOp2OGTNmsGXLFtLS0kyOs7GxoXPnzkydOpXIyEiT47y9vQkICGDYsGGEhYWZHBcQEIC/vz9Dhw7l3r17JsVYWFjQpEkT/Pz8mDRpktmfjale6iEYoJ+dtcm0vXStV47pvUzPEOUo6gL8/DqU9IIB28DO+el9ru6BX/tApebwzgY1HEMp0p7XIRjPQg3ByLt2+FRYLG8uPkzLau4sfVfNB6EoyrNRbbGSXxJT09l8OoJfg25xJjwOWysLOtUtw1uNKuBfoeRzuVLFiyQlJYW0tDScnJyMngvcjU9h+7lIfgsO43xEPJYynVrFkulRz4OuzX0pWbKk0fLOnDlD27ZtqVWrFq1bt2bYsGGUKGG8N+bVq1fx9/fHysqKzz//nE8//dSkc5fg4GCaNGmCra0tBw4coEED05qpZcuWMXDgQBo3bsyePXsoVsy0ISj9+vXj119/5YcffmD06NEmxTx8+JAKFSpgY2PDsWPHzO55kSGndvilv+ot4WBDj/qebDx1m+jE1Gc/oFYDG/8PrB3g7d+yTj4AVGkDHb+DkH0QtOTZy1UURXlB+ZYvwWcdarD7QhQ/B94o7OooiqIoymPOhscxYcNZGn+9hwkbzpKq0TGlS02CPm/DrN6+NKzk8lIkH3Q6HXFxcUb3k1KydetWFixYwOzZs5k5cyb37983GmdpacnUqVOxs7OjbNmyfPrpp2R3s9zd2Y73m1Viy8gANg1/hQbuFpyKtWbK4SQ6zTnImmO3eGiY+DM7devWZe3atQQGBrJw4UJu3DDtHKRKlSqsWLECKSVbtmwxuWdCgwYNGDduHDVq1GDhwoWkppp27dm/f38GDBiAVqvlv//9r0kxoF8FZ+rUqfz000+Eh4ebFOPo6Mgvv/zCe++9x/Tp07P9/J/FS5+AABjQrBJp6TrW/m16t5ZsHZoDkWeg8yxwLpvzvv79oWp72DMFoq8/e9mKoigvqA9eqUS7Wh58u/0SJ249KOzqKIqiKC85KSX7L9+l95IjdJkfyMaT4XSsU4YNw5qxY3Rz+r/i9VwsE5mUlMTNmzdN2ldKyfXr11mxYgUTJkxAq9UajQrqkpkAACAASURBVLlx4wZ9+/alSpUq2Nvb8+WXX3L58mXS07O/uBdCEBAQwIULF/jkk0+YMmUK//73v9m2bRsPHz7MNs7a2prvvvuO1atXk5CQwI4dO+jWrRubN2/OtjwhBL7lS7Du0y4seL04Ze8Eci86hs83nqXBv3cx6b/nCItJyrbMli1b8ssvv7BkyRL+7//+j48++sikJEuPHj3Yt28fn332Ge3ateOPP/4wGgMwefJkDhw4QOXKlXn99de5e/eu0RgLCwuWLl3Krl27WLRoEYsXLzaprOrVqzNx4kRmz55Np06dTCoLoEOHDkybNo2oqCjmzJljUow5VAICqOLhRGMvF34PDnu2LE9CJPz1PdR4A2p0Mb6/ENBlDlhYwe5JuS9XUZRcuXPnDp07dwb0k/xs27bt0bYtW7YwefLkwqraS0cIwYxe9Shd3I6Ra07y4KHp4yoVRVEU04SEhBAUFGRWjFarZc2aNWafI+/du5eQkBCzYu7evcvatWvNiklPT2fhwoXEx5s+r5qUkj179rB58+antml1kq1n7tB5XiD9l/9NWEwSX3SsRtAXbejno+O/P882evykpCROnz5Neno6R44c4V//+heBgYE5xgQFBTFo0CBOnz7N2rVrmTRpEpMmZX19oNVq2bNnD/3798fDw4OxY8fy0UcfMWDAAHr27Mnly5efitHpdPz000+8/vrrDBgwgAULFlCzZk1q1qxJkyZNmDZtWpZleXl5sXTpUgYOHIizszMpKSl88skn1K5dG19fX2JjY7OMK168OAsWLODQoUN8/vnntGrVis2bN9OgQQMWLlyY42fRq1cvgoKCOHr0KBMmTODPP/+kUaNGRhMmXdq34X9LJnN5zvt83sgWi4izrD4aSsvv9vPJb6e4djcxy7g333yTTp06ceTIEapWrUrfvn1N+n339fWlffv27N+/n59++okjR44YjbG1tcXR0ZEvvviCUaNGMX78eKMxAFZWVpQsWZIdO3awefNmk3trALRp04apU6cye7bx390MFhYWrFq1ir1792b7HefWSz8HRIb1x8MZ8/tpfh/alIaVXHJ3kK2fwvEVMDwIXCubHndgJuz7Cj7YCRWa5K5sRXmOPa9zQIwdO5aAgAC6du3KihUrCA4OZv78+YD+5KR+/focOnQIBweHp2LVHBD5M+74THgsPRcdJsCnFD+/3/Cl6NKqKEreUm1x1sLDw2nfvj2LFi2iefPmJsVoNBref/993N3dmTVrFhYmzlm2YMECli9fzoYNG4yOIU9LS8Pa2ppdu3YxevRopk6dyptvvpljjE6nIywsjPDwcD766CNeffVVpk6dmuPY+PT0dNatW4ebmxtTp07Fw8ODKVOmUKdOHX090nVsOnmbxQeuE3L/Id5ujrzXsAzrvxtPsyaN2LBhA25ubgwcOJDu3btnu1Thrl27+PDDD7GxsUGj0eDv70+7du3o3Lkz7u7uT+1/6NAhpk6dyq5duxBC0K1bN2rVqkXNmjWpW7cutWrVeirmzp07bN26lYMHD3LgwAHatWtHz549cXZ2xtnZGW9vb+zt7bOsn5SSw4cPc+TIEcaMGYNWqyU+Ph4pJS4uOV8DJSYmkpaW9mi/xMREHB0dzZq7SUpJWloatra2JseA/vuzsjJ/AcfwmIcsO3STNUE3SU3X0b5WaYa38qF2ueLZxuh0OpN/1zNIKXM1h1Vu4nJbVkHKqR1WCQiDpLR0Gn61h051yzCjVz3zD/DgJsyrD/Xf069yYY60hzC3Prj6wICt5petKM+5wk5ATJw4kVKlSjFq1CgAvvjiCzw8PJg9ezYXL15ECIGPjw/JycmUK1eOCRMm0KdPHz7++GOaNm1K7969nzqmSkDk38Rnq47eZOKmc3zyelU+al0lX8pQFKXoUm3x4+7cuUNKSgrdunVj5syZtG3b1uhx09PT2bdvH3PnzsXf35/JkycbveCRUvLDDz9w7do1IiMjWblypUmT5Y0aNYr4+HhCQkJYtWqV0YSFlJLRo0ezc+dO3N3dmT9/vtGlBlNTU+nXrx+bNm2iU6dOfPXVV49iUtO1rDl2i6UHQ7gTl0Ltcs4Ma+mDhyaS3m/2IiQkhDZt2rBs2TLKly+fbRlarZa5c+eyYsUK0tLScHd3Z/v27VnexMgsOTmZ0NBQbty4QUhICJ07d6ZSpUo5xjwpISEBJ6cXYznKwhKdmMqyQzdYefgmCanptKzmxohWPjTI7Y1nJUc5tsNSyhfu4e/vL/PDmN9OyZoTt8vktHTzg7d/JuW/XKSMDc9d4YfnSznZWcqwv3MXryjPsQsXLhRq+Tdu3JB+fn5SSim1Wq309vaWwcHBsn79+o/2Wb58uRw+fPhjcb/88oscMWJElsfM6j0BwfI5aCML4pFf7bCUUup0Ovnx2pOy0mdb5P7Ld/OtHEVRiibVFj9uxIgR0sXFRW7YsMHkz3DevHnS0tJSjhkzxuSYtWvXSkA2bdpUpqSkmBTz66+/SkCWKlVKhoWFmRTz7bffSkCWKFFCBgcHG90/MTFRdujQQVavXl327NlTbtq0SUqp/1vz56nbMmD6Xllx/BbZe/FheeDyXanT6WRCQoKcP3++XLZsmfzzzz/lsWPHpE6nM6l+yvMtLjlNzv/fVek3dZesOH6L7LvkiDwbHlvY1SpycmqHze/HUoS94VuW34+Hc+DKPdrVKm16YEocnFgJtXpA8XK5K7z+e3Bgun4Syz6rcncMRXkRbP8MIs/m7TFL14EO32a7uVKlSri6unLy5EmioqLw8/MjNTUVNze3HA/r7u5ORERE3tZVMUoIwdfd63DhTjyj1p5ky8gAPEvmfAdJURRFeVp4eDhLly7Fzc3N6J34DNHR0UyaNInKlSvj5+eHlMa7e9+9e5eRI0fStm1bRo4caVJX+QsXLjBjxgwmTpxInz598PT0NBpz6dIldDodR44coUGDBiaVo9Vq2bBhA3Z2do9eCw6N4autFzkVFkv10k6sGtiI5lX+OScoVqwYw4cPN3ps5cXjbGfN8FY+fPCKF2uCbrFw3zW6zA+ku185xrarRpniWQ9dUfKOSkBk0tTblZIO1mw9c8e8BMTJXyAtEZoOy33htk7QcLB+EssHoVCyUu6PpSjKUwYNGsSKFSuIjIzkgw8+wN7enpSUlBxjUlJSsh1DqeQvextLFr3jzxvzAhm++gS/DW2KrVXW420VRVGUrM2ePZvPP/+cMWPG4OjoaFLMmjVrmDdvHn379s12noMnnT17lr/++otq1aqZXDcPDw+OHz9u1lj26tWrM2HCBJP3B3B2dn70c+j9h0zfcYnt5yLxcLZlZq+69KjviaWab+ilY29jycAAL95s4MnCfddZFniDbWfvMKRFZf6vhTeOtuoyOb+oTzYTK0sL2tcuzX9PRZCi0WJnbUKjKyUEL4fyTaCs37NVoMEHEDhL35uitVoVQymicuipkJ+6d+/OpEmT0Gg0rFmzhpSUFEJDQx9td3JyIiEh4bGYK1euULt27QKuqZLBq5Qj3/Wux/+tOs6/Nl/gm+51CrtKiqIoLwwpJePGjcty4sOcjBgxwuwJ7lq3bm3W/gCurq5mx+RWbFIac/Ze5ZejN7G2tOCT16syqLkXDjbqUuhl52xnzWcdqvN24wpM33GJuXuvsjboFmPaVqOn/8uXnNJqtSYnHnNLLcP5hE51ypKUpuXAlXumBYQdg+irUP/dZy+8eDmo0k7fo0KrefbjKYryiI2NDa1ataJ3795YWlri6OhI5cqVuXbtGgCtWrXiwoUL+Pr6sm7dOgD27dtHp06dCrPaL712tUoz9NXKrDl2i/XHwwu7OoqiKC8MIYTZyYeMuKJCSsmWMxG0mXWA/xwOpZd/efaPbclHrauo5IPymPIuDszvV58/PmxGuZL2jPvjDJ3nBXIsJDpPjq/T6Xj48KHZcdHR0Vy6dMnsuEOHDpm95C7oe02dPHnS7DhzqATEExp7u+BkZ8WeC1GmBZxcBTbFoGa3vKmAf39IjILL2/LmeIqiAPqG/+jRowwcOPDRayNGjGDFihUAuLi48Pfff3Pq1Cn69OlDVFQUycnJj5bnUgrPmLZVaertyhcbz3IhwvR13hVFUZSX1524ZAavDGbEmpOUKW7P5pEBTOtRB3cnO+PBykshLCyM1NTUx17zr1iSDR82Y95bfsQna+iz9ChfbDxLQso/N4fXrVvHjh070Ol0JpdlYWHB559/zjfffEN8vOnnMi4uLgwbNoxRo0YRExNjcpyfnx9dunTh008/NSvx0axZMxo3bsysWbPMen/mUAmIJ1hbWtCqmjv/u3QXrc7IEqVpD+HcRqjVDWyNLzNkkiqvg1MZOL02b46nKAoXLlzAx8eH1q1bU6XKP8s6du/ePdulrm7dusX3339fQDVUcmJlacHct/wo4WDNh6uPE5eseogpiqIoWdPpJKuO3uT1WQcJvHafLzvVYOOwZtQqW7ywq6YYodPp0C+gYJ6oqCimTJnCpk2biIoy8SYyYGlpia+vL2+99Ra//fbbo6G4Qgi61CvLnk9eZVCAF78G3aLtDwf53yX9sdu2bcvAgQPx8fFhxowZaDSmnZeMGzeOb775hooVK7J+/XqTYoQQfPnll8ydO5fGjRsTFhZmUpyDgwODBg1i1qxZjBo1yuRkQpMmTfD29mbChAn89ddfJsWYSyUgstC6hjvRD9M4FRab845XdoLmIdTtk3eFW1hC7Z5wdTckmZ7lUhQlezVr1iQkJCTLhMKgQYOyjGnYsCG+vr75XTXFRG5Otix8uz63HyTz6W+n0RlLECuKoigvnWt3E+mz9AgTN53Dt3wJdo1+lUHNvbGyVJc8Be3EiRMcPHiQwMBAjhw5QnS08aEMOp2O8ePHU61aNdq2bcvkyZPRarVG4zw8PGjUqBG9e/emdOnS/PTTTybVsWzZsixfvpwNGzYwcODApy7u7W0s+bJzTf74sBlOdlZ8sCKY0WtPIm0cWbZsGbdu3WLHjh2kpaWZVF65cuX44osvsLa25syZMyYnW1q1asUbb7yBnZ0d169fNykGYNiwYfTq1YuTJ0+SmJhoUowQgvHjx/P222+rBERBalnVHSsLwd6LRjJo5zdAMQ+o+EreVqBOL9Bp4MJ/8/a4yiOJqekcuR7N/st3uRuf80oIiqI8H/wruvBFpxrsuRjF4oOm/wFWFEVRijadTrJo/3U6zvmLK1GJzOxVl1UDG1HB9eVewjldqyMuScPt2GQuRyZw/OYDDly5x+bjN5j16072XYzk0LX7HLkezbGQaIJDYzh3O47wB0k8TE1HSsmtW7eYOnUqQ4YMoVOnTo+GrhpTqlQp/v3vf9O8eXNatmzJ7t27SUpKyjHGysqKGTNmMHLkSPbu3cvq1av54YcfePDggdHyOnbsyG+//Ubt2rX57rvvmDlzptHVzkB/x3/x4sWMGTOGHj168Mcffzy1j1+FkmwZ2ZzRbaqw9ewd2sw6QGrpOvz555/06NGDV199lRs3bhgtC+CTTz4hKCiIa9eumdwzQQjB6tWr2bJlC8OHD+fYsWMmlVWuXDnWrl3L0KFDeeutt0hPTzcpbsCAASxatIgtW7awZ88ek2LMIXLTzaWwNWjQQAYHB+drGX2XHiEuOZ3to5pnvUNqAsz0gfrvQceZeVu4lDC/IRRzhwFqLoi8FJes4dvtF9l48jYpmn/+wzf2cmFSl5qqe14+uXjxItWrVy8yE1tJKbl06RI1atR47HUhxHEpZYNCqlaBKoh2OCtSSkb+epJtZ++wamBjXvEpVeB1UBTl+VaYbbEQoj0wB7AEfpJSfvvE9rHA24anVkANwE1KGSOECAUSAC2Qbsp7MLct1mq1pKWlmb3EdHx8/GPLWZoiMTEROzs7rKzMm+wxOjrarBUy7iWkMnxVEEG34ulQuzRTu9bGzcnWaJxGoyE6OprSpUubVb8rV65QtWpVo/vpdDosLPT3em/evImtrW2OZUkpCQwMJCAgACkloaGh3L17lyZNmmS5f1xSGpv3HWH9tr24VayKg5snEbHJ3HuYThJ2xKemP3aumxs2lhaUcLDGTmi5H3GTe+EhFLfUYJEUg7e7E/WrlGfC6A9xKpb1UHQpJUuWLGH79u1UrFiRXbt2Ua1aNUaNGsVrr72WY9k7duzAy8uLDRs28J///IfWrVszd+5coys0REVF4eDgwPTp09m4cSNLliwhICDA6HuVUhIZGcngwYNxc3Nj2bJlWZ63Xo5MYNwfZzgdFkubGh5M71mHs8FH+PDDD1mzZg1+fqatiqjT6Rg5ciRarZbFixebFAP637+uXbuydetWvL29TY4bO3YsVlZWTJs2zeSY0NBQ2rdvz+HDh3FxcTE5DnJuh1UCIhsL9l1j5s7LHP+yDa7FsmjEzq6HPwbCgB1QsWneV2D/t/rHmCv6RITyzC5ExDPwP39zNyGV3g3K066WB/bWlgTffMDPgTeIS9bwTffa9GlYobCrWuTcuHEDJycnXF1dX/gkhJSS6OhoEhIS8PLyemybSkAUjIep6XRbcIiYh2lsHhlA2RLmnUgrilK0FVZbLISwBK4ArwPhwN/AW1LKC9ns3wX4WEr5muF5KNBASnnf1DLNbYtHjRqFt7c3o0aNMjnmwIEDjBs3jsOHD5u8PN+9e/fo0qUL06dP59VXXzUpJj09nbFjxxIbG8vy5ctNivnr6j2GrjjCw1Qt49tWZujrdXI8z0hMTMTR0ZE///yTiRMnMmLECIYMGZJjGSdOnKBcuXLs3buXefPmUapUKTZu3JhtYkVKyc8//8yFCxdwcnJiy5Yt2NnZMWPGDF55Jete0wcPHmTixImcPn2a2rVrExkZiZeXF6+//jqffDqG0OiHXLyTwKXIeC7eSeB8+AOiEh+fd0BILfa6FJwsNfhV96KCe0kcbawoZmdFMVtLitla42hrSWRYKDu2b+Xq1eu81a8f8QmJxCcm4ubmTsNGjUnWaIlNSuNBkoYHSWnEPjT8m6Th1r1Y7idL0jMNg7SxsqCCiwOVXB2pXc6Zup7FqVOuxGNJoJSUFOzs7JBScurUKYQQZg1z1Wg0HDx40OzlXsPDw5FSUr58eZNjpJScOXOGevXqZbuPVidZfugGM3ZepqSDNXP7+lHG6iGurq44OjqaVVZISAiVK1c2OQb0CS1PT0+zlsvU6XRERETg6elpVlnh4eFmx4BKQOTKqbBYui04xLy3/OhSr+zTO/w+AEID4dPLYJEPI1mizsOiZtB5NjQYkPfHf8lcioznraVHsbO2ZPE7/tQrX+Kx7XFJGkauPcnBK/eY0qUm/V/xyuZISm5oNBrCw8NN6gr3IrCzs8PT0xNra+vHXlcJiIJz7W4i3RYcorKbI+v+ryl21vm7ZrWiKC+OQkxANAWmSCnbGZ5PAJBSZnnLUQixBtgnpfzR8DyUfEpASClZsGABe/bs4Y8//jDpwkWj0XDixAk++OADtm3bRsWKFY3G3Lt3j5SUFLp06cKkSZPo0aOH0ZjQ0FCSkpIYOXIkjRo14quvvjJav7DbEXz88x6CH7rgkB7PiiEtaFQt54ukq1evMmDAAKytrfHw8OCbb74xegd548aNvPPOO7i7u9OlSxdGjBiRY++HsLAwBg8ezM6dO3Fzc2PatGl07twZDw+PbGP27dvHihUrCAsL4/bt28xd9CNWZaoRdCOGYzdiuHgnntR0fU8GKwtBZbdiVC/jRPXSzpQpZkl02DU8nKzp1LqFWTd50tPTze6dAvqL74jYZG5GJ3Ez5qH+3+iHXL/3kOv3Esm4tCxb3I46nsWp61mCup7FaVDRBXubovW3+nxEHCPWnORm9EM+blOVYa18sLR4sW+05RWVgMgFrU7iO3UXneqU4duedR/fmJ4GMyvrV794Y17+VEBKmOsHLt7w7ob8KeMlEZuURqe5gaTrdKwb0pRKpbLOTKal6xi+5gR7L0axfEAjXq3qVsA1VV50KgFRsHadj2TIquP08vdkZq+6L3zvGkVR8kYhJiB6Ae2llIMMz98FGkspR2SxrwP6XhI+UsoYw2s3gAeABJZIKZcaK9OUtvj8+fP8/PPPBAYGsm/fPpPu0CYmJvLuu+9y+fJlNm3aZNKQA61WS/PmzYmLi2Pu3Lkm3a3W6XS0atWKc+fOsWjRInr37m00JiQylnb/WoumeHnqOCbw2/g3jV7Y3rhxgxYtWhAeHs7QoUNZtGhRjvtLKZk+fTpff/015cuXp0OHDsyYMSPHxIiUkm3bthEfH48QAgsLCzp27EixbIYnZIhP0RAUEsOxG9EcDYnhfEQcOgnWloJ6niXwLV+C6mWcqVHGCR/3YthaPb8X8Ymp6VyIiOdMeCxnb8dxJjyOG/f1S0DaWFrQoFJJAqqUokUVN2qWccaiCFysJ6am8/mGs/x5OoIAn1L80MfXpCFARV1O7bD5aa+XhKWFoFllV/66eh8p5eMntjcDITUeqnXMvwoIATW6wNFFkBwL9iWMxyhPkVIy5vcz3E1I4fehzbJNPoC+C9nsPr70XHSYkWtOsPuTV/FwLqC1oqXUf+eKopisba3SfNS6CnP3XqWuZ3Hea1qpsKukKMrLLas/5Nnd6esCHMpIPhi8IqWMEEK4A7uFEJeklAefKkSIIcAQgAoVjA8bnTNnDj/++CNTp041uXv4/Pnz2bRpE126dMl2ueonLV26lCNHjlC/fn3q1KljUszs2bM5ePAgzZs3f2pepaz872IUQ5YfJt3Bjca6C4zv1Npo8iExMZGFCxcyatQomjRpQv369Y2Wo9FoGDJkCOPHjzc5uS2EoFOnTibtezc+hV0Xoth5PpKjIdFotBIbSwt8K5RgxGtVaOLlgl+Fki9cj4FitlY08nKhkdc/8wXEJWs4FRZL4NV7/HX1PjN2XGbGjsu4ONrQrLIrLaq60bamByUcbAqx5rlXzNaKOX19aVbZlcl/nqfj3L+Y08eXZmqOqmzlSQKioCfcKSgBPqXYeT6KWzFJVHTN1GBf3g5W9uBl2pi2XKvRBQ7PhWt79CtjKGb783QEey5G8WWnGviWN57EcbS1YtE7/rSffZAvN51j6bv++XNXNfmBPrl07g+IvQWWNlCxGTQeCj7mjW9TlJfZ6NZVOH87jqmbL1C9tPNjJz2KoigFLBzIPNjcE4jIZt++wK+ZX5BSRhj+vSuE2Ag0Ap5KQBh6RiwFfQ+InCp0//59Vq9ezYcffmjyvA/x8fHMmzePCRMmMGHCBGxsjF8YRkdHs3z5cn766Sfeffddk2Ju375NZGQk586do1atWjnuK6Vk2aFQvt56gUqujvz8QTO83HLuWZChWLFizJxp3oTxNjY2Zk+6Z0zo/YfsPB/JzvORnAyLRUqo5OrAB6940bKaO34VShTJ4YTF7a15tarbo57FdxNSOHTtPn9dvU/g1ftsOXOHzy0EAVVK0bluWdrW8sDZztrIUZ8vQgj6NqqAb4USDF99grd/PsbI16owunWVItHLI6898xCMF2HCndwKuZfIa98f4OvutXm7caZxb3PqgVsN6Lc2fyug0+qHelTtAN1z7iqmPC0+RcNr3x2gXAk7Ngx7xawxWUsOXGfa9kssers+HeqUyduKXdsLm4ZBYhR4vwplfPU9aq7sgvhwqPEGdF8MNqZPYqM8H9QQjMIRn6Kh2/xDxKdo2DwygDLF1aSUivIyK8QhGFboz4lbA7fRnxP3k1Kef2K/4sANoLyU8qHhNUfAQkqZYPh5NzBVSrkjpzKNtcXr16/H3d2dFi1amPw+jh8/jouLy1MTLefk7t27uLi45GpOAWM0Wh2T/zzPmmO3aF+rNLP61MPB5sXoxJ2QouHP0xH89ncYp8PjAKhV1pl2tUrTrlZpqnoUe6mHD0opOR8Rz+YzEWw5fYfbscnYWFrQoqobXeqVoU0NDxxtX4zvOsPD1HQm/vccG07cpm1ND2b39X1hfl+Bp3v+51J+D8FoBFyTUoYYClsLdAWyTEAAb/FExvd55VXKkbLF7Qi8ev+fBETMDXgQCk2G538FLCyh8mtwfa/qop8LC/ZdI/phKsv6NzB7QpiBAV5sOHGbb3dconUND2ys8mii0fOb9KunuFaBfuugbKYZgNNT4ch8+N9XsLwDvLsJHNTdXEUxxtnOmqXv+dN1/iGGrjquJqVUFKVQSCnThRAjgJ3oewUvk1KeF0IMNWzPWGuvO7ArI/lg4AFsNJz4WwFrjCUfTNGzZ0+zLyb8/f3NLsfdPX9WbItL0jBszXEOXYtmWMvKjGlb7bm/oyyl5O/QB6z7O4ytZyNI0eio5uHEFx1r0L52acq7OBR2FZ8bQghqlytO7XLF+ax9dU6GxbLl9B22ntX3YHawsaS7XzneaVKRGmXMWwa2sDjaWvH9m/WoXbY4/956gd5LjvDz+w3xcLYjKSkJBwfzv/8zZ85Qt25d4ztmkpSUxO7du+natatZcYcPH+bhw4e0bdvWrDhz5MVVVTkgLNPzcMNrTzFMuNMe+CPTyxLYJYQ4bhjT9twQQvCKTykOX49Gm7HcTMh+/b/eLQumEpVb6++UR50rmPKKiLsJKfzncCjdfMtR19P8+TOsLC34rGN1bkYnsfrYzbyp1I2DsP4DKOcPA3c9nnwAsLKF5p9C31/h7kVY944+KaEoilE+7k7M6uPL6fA4Jm46x4s4wbKiKC8+KeU2KWVVKWVlKeXXhtcWZ0o+IKVcIaXs+0RciJSynuFRKyP2Wb3Id9dD7z+k+6JDBN2I4bs36zGuffXnOvkQl6xhyYHrtP7+AL2XHGHn+Ui6+3myafgr7BjdnMEtvFXyIQdCCOpXKMmkLjU58llr1g1pQsc6ZVh/PJwOc/6i16LD/PfUbVLTtXlWZkxMDHFxcWbHnTp1irVr16LVZl0XIQQfBHjx47sNCLn3kK7zD3E+Io7Nmzczbtw4V9CLBAAAIABJREFU4uPjzSpv48aNDBw4kNjYWJNjHBwcWLp0KcOGDTNrFTp/f3969+7NrFmz8u1cKi8SEHkx4U59oAMwXAiRZR8xIcQQIUSwECL43r17z1ZjMwRUKUVcsobzEYZfzpD94FQWSlUpmApkzAdwbU/BlFdELN4fgkYr+ah17r+nllXdaOrtyoJ910jRPGNjFx+hTz64Voa314NdDlncau2h60K4eQi2j3+2chXlJdKuVmk+es2H34+H88vRPEocKoqiKAXuaEg03RYeIuZhGr8MbEwv/5yX2CxMkXEpfL31As2m7WXa9ku4FrNhZq+6BH3Rmmk96uBbvsQLnQgqSFJKpJRYWAgae7vy3Zv1ODqhNV90rMG9xFRGrT1Fs2n/Y/qOS9yJS34Ul5qaysyZM9m1a5dZF9vOzs707NmT9957jwMHDph8wV2vXj0WLVpEjRo1WLbs/9k78/CYzi+Of272TUKCRBCCWCIaS4g99qraYleKamsptVTRai2laO1bq9SuqoTWEmvsaxBLIraECBKySWTf5/39MfgpSeaOJpngfp4nz8TMe+acGZk79573nO9ZQ0ZGRo7r2jjb4jWsEZIEPX87S4mazdixYwdOTk6sWrVKtr+hQ4eyceNGatasycmTJ2W/vgEDBrB8+XLatWsnO9FiYmJC27ZtGTduHEuWLJHtSxvyIwGRb4I7wDPBnVcQQqwUQrgJIdxKlSq88YiNK6sVTE/djgGVCu4eh8otC68dopgd2NZS6wYoyCI2OYM/z9/Ds05ZHPOYeqEJSZIY1dqJmKQMvPweaDbIDSFg5wjISIHef+SdfHjGez2h8Si4uBaCDry+bwWFd4wxbarSqnppfth9nQuhsZoNFBQUFBSKFAeuRfDx6nPYmBuxc0QT3CvZ6DqkHLkdlcjXXv40m3OE1afu0rqGLXtGNcVrWGN6upV/o/r+C4L79+/z4MED4uLiyMzMlG23cOFCmjRpwpAhQ1iyZAkmetl83rwSR8e1YP3gBtStUIIVx+/QfM5RJv1zlQexKRgbG9OyZUs8PT2xtrZm/vz5snwZGBjw+++/s2PHDlq1asWRI0dk2UmSxC+//EJISAizZ88mKSkp17U17a3YMaIJlUtZMGzTZdqOmElcXBw3btyQnZiys7Ojd+/eGBgYYGwsf8Rn586dadSoEWlpaVrZeXp60rZtW7KysmTbaEN+JCAuAE6SJDlKkmSEOsmw6+VFTwV3PICdL9xnLklSsWe/A+2AItVrUKqYMZVLmeMXGgcR/urpBZVaFG4QVVrD/bOQnli4ft9Q/jx3j7RMFUOaV/rPz9WwkjV1HIqz4kQIWdmq13uSgK1w5wi0mQalqsm3a/U9lK4Ju76ENO1KtRQU3lX09CQW9q5NeWszhv9x6V87JAoKCgoKRZvd/g/5YtMlatpb8ffwJv+eQldECAyP57P1frRZcALvgId81MCB4+NbsqRvHWraW+k6PNlkZ2fn2kLwIhEREXh7e7N27VrmzJnDzp07NdoApKWl0aVLF6ytrTExMeHEiVcGuryCJEl89dVX9OjRg99//50lS5Zw7tw5QP397lG1FL8PcOP4+Jb0ciuPl98DWs47xoRt/pSsWIO//voLS0tL1q1bx+HD8jZvHR0dWb58OT179uTrr7/mxo0bsuxcXFxYsWIFvXv3ZuDAgaSkpOS61tbShC1DG9Kmhi17HpkxcMlervj7s2LFClm+AH7++WcOHDjAoEGDCAsLk2VjamqKj48Pnp6ejBs3Trav3r17s2PHDtavX8/167nJOv4HnpW6/JcfoANq1d87wHdP7xsGDHthzSDgr5fsKgH+T3+uPbPV9FOvXj1RmEzw8hfvTTsgsk8sEGKqpRAJEYXqX4ScUPu94V24ft9A0jOzRf0ffUT/Vb759pwHAh+JChO9hbf/Q+2N0xKE+LmSECtbCZGdpb192EX1//2B77W3VSh0AD+RD8fUN+GnsI/D2hIUkSCcJ+8TnZedEmmZr/HZU1BQeGNRjsVvJlsv3BeO33iLnr+dEYlpmboO5xXuP04WX/55SVSY6C1cfzggFhy8JWIS0/LVR3Z2tlCpVLLXq1Qqce7cOXHx4sVX7s/pufft2ye+//570apVK+Hk5CROnDghrl+/LiIiIkR6enqOPrKyssTq1auFvb29AEStWrXE6NGjxaZNm8Tt27fzjDctLU189dVXolatWqJevXqidevWYvXq1SIuLk7ja1u7dq3w8vISnTt3Fs2bNxeHDh16xdfDJyli6s5A4fTdXuH4jbcY89dlcfCsv7h165Zo1aqVGDhwoIiJidHoSwgh0tPTha+vr6hRo4bYsmWLLJtnLF68WDRt2lTExsbmuS47WyV+9L4mKkz0FqM2XRCNmzQVGzdu1MrXwYMHRf369UVSUpJsm+zsbNG+fXutX9fp06eFu7u7yMzU/vOY13E4X6T9RRET3Mlv3CqWID41k9Rbh6G0MxSzLdwAyruDkYXShiGDfYGPiEpMZ3BT+aOjNNG6hi3lSpiy4Wyo9sZnlkFKDHSYo55qoi1l60Lt/uC7HB7f0d5eQeEdxcm2GPN7ueL/4AlTdlxD/V2ooKCg8G5z4sQJ1q1bp5VNSkoKw4YN07oce/HixRw/flzW2o2+9xi/LYD3bE2wvbkNCy1GLyYkJNC/f3/u3ZOv/ZOVlcX8+fOZM2eOxrWxSen8sCuQVvOPsS8gnOIPz3FkbFPGtq2KjUXOZe3p6elcunSJuLg4Vq9eTZs2bdi+fXuOa59x8OBBPvzwQ7Zt28aECRNo0aIFnp6eOa6NjIxkzpw51KxZE3d3dwYNGkStWrWoVq0a1apVIyAg4BUbPT09nJ2dMTIyIjQ0lMzMTNatW8e3335Lz549mTp1ao6+9PX1GTx4MMHBwcycOZPly5fTqlUrrl+/zrBhw/LUFjA2Nmb+/Pns3bsXPz8/lixZwt27d9m2bVue7wXAoEGD6NGjBzt37mTRokV4eXm98jdYxsqUaZ1rcmpCSwY3cWRf4COG7nzAhuvpbNmxhxYtWnDhwgWNvgCMjIxwd3fn+PHjXL9+XavzhlGjRjFixAju37+f5zo9PYlJHWowtk1VdgZEUmvIPB7Hxsn2A9C2bVvGjBlDbKz8NlM9PT02bNhAerp24vaNGzfmiy++yLPF5HWQ3sSTssKeP383Jpn28w5y3WwI+g0+h/azCs33czZ/BJFXYXSAMo4zD/qu9CXsSQrHv26Zr0rJvx2/w0/7bnJgTHOq2RWTZ5QUDUtqq1toem14feeJkernqd4Ruv/++s+jUODoava8Lijs4/DrMv/gLZYeuc20Ts4MapJ/iUkFBYWii3IszpmoqChatGjB7t27qVy5siwblUpFnz59aNy4MWPGjJEd18qVK9myZQve3t6YmprmuXbVyRB+3HOD2qUNuLVmPH9t2oirq6tGH48fP+bhw4f069ePL7/8ks8++0xjT/2hQ4ewsrLiiy++wMPDg2nTpmFhYZHj2rTMbNacusuC/dfIlvQxuO9HsxLxTJ0whgoVKuTq4+bNm/Tt25e4uDjMzMzo3r07ffv2xdnZOcf1ly5dYuLEiRw6pBacHzVqFM2bN6d+/fqUL18+x9eUlZVFQEAAZ86c4cyZMzRu3JjPP/9cdp+/SqXiypUr1K1bV9b6N4WYpHSWHA5m07n7mBnpM7q1EwMaVcTIIF/23POV5cfu8PP+m3zgYsfiPnWKZIz/hbyOw++2OopMKtqY0cosBH1VRuHrPzyjcku4tQfi7oL1f9c2eBsJjUnmbMhjvm5XNd/HNPV2K88CnyD+8L3HjK4u8ox8f4GMZGg1+b85L2YL9T+Ds8ug+XgoVfW/PZ+CwjvE2DZVuRmRyIw9N6hSuhhNnUrqOiQFBQWFQic8PJzBgwczffp02ckHf39/tm/fjrW1NaNHj5Zls2fPHiIjI9mwYQP79+/XmHxYdiSYeQeDsMt8xJ31v7Bn1w4qVdJ8nnv+/HmGDBlCVlYWGzZskHUhvXPnTnr37o2Liwu///47derUyXXtyeBoJv19lQdxqaTcvohl6DGO7vyTcuVyn8YhhODPP//k22+/RZIk7O3t2b17NyVL5v29U61aNVauXElUVBRRUVHUrFlT43tgYGBA3bp1qVu3LiNHjsz7heeAnp7eW5d8AChpYcz0Li70b1iBGd7X+XHPDf48d5/vO9agZbXSRWoayfAWlTE20GO693Uy/rjIL/3qYmL4GtXSbyBvV6qlgJAkiS6WQWShDxUa6yaIis3Ut6GndeP/DWCr3wP0JOhRr7zmxVpSwtyI9jXt2OX/UN5IzrQEuLAGnDvnz8jWxqPAwAROzP3vz6Wg8A7xTJSySikLvth0kbsxyboOSUFBQaFQCQwMpE6dOtjb29OjRw9ZNklJSbRt2xYvLy/mzp0r68ItKyuLsWPHMnLkSJYtW5ZrZcEzVp0MYd7BIAzDL3Nu4VAmfP2VrORDYmIiH330Ef7+/vTp00fWhfT58+fp27cv5cuXp3Pnzrz33ns5rnuclM7YLVf4ePV5EhPiaZDsy5SWpfl93g8aEwmSJNGvXz/u37/PvXv3OHv2rEYbAHNzcxwdHXF3d6dTp06y3gOFvKlqW4wNgxuwZpB6A37wOj8GrDlPaBE7Bxjc1JEfu7pw+GYUn2/wIzVDxjXGW4CSgJBJbXEDf1UlojJ0VDRSqhqY2cA9JQGREyqVYMflcDyqlsLOyqRAfPR0K0d8aiaHbkRqXnxxHaTHQxP55Yp5YlEK6n0C1/6G+PD8eU6FdwZJktpLknRLkqTbkiR9k8PjJSRJ+keSpABJks5LkiSzzOfNwMLYgFUD3dDXk/hs/QUS0uSPA1NQUFB409m4cSPR0dGYm5uTkZEhy2b9+vVER0fTrFkzVCp5U8D++OMPQkNDGT58OBUrVsxz7d+Xwvhxzw2cTJLIPLWaX5YtpWfPnrL8TJs2jQ8//JDLly/z/fffa1yvUqkICwsjMDCQ4OBgpkyZgr7+v3eahRBs9XtA6wXH8Q54yKhWVfCd1pmtS2cwcuRIWrZsiYlJwZxfKhQMkiTRqrot+8c0Z3JHZ648eEL7xSdYdTKEbFXRkSDo37ACc7q/x6nbMQxed4GUjIIZfVmUUFow5JCZRunEG+xUtSUqNI4PapUp/BgkSV19oSQgcuRCaCwP49OY+EH1AvPRuHJJyliZsO1iGB3fs899oSobzq9UV62UzcfyNvehcG65+rnb/pB/z6vwViNJkj7wC9AWCAMuSJK0Swjx4lylScAVIYSnJEnVn65vXfjRFhzlrc1Y3r8e/VedY9Tmy6weWB/9fG7VUlBQUChqZGdns3fvXv7+++9cBQ1fRqVS4e3tjY+PD23atJFlk5mZSUBAANeuXcPJKe/Kz6M3o5iwLYCGlazpUTKTLkFBGBoayo5t1qxZsrUOQN1u0K1bt1wfv/84hYnbAzgb8hi3CiWY3a0WTrYy9b4UijxGBnp82tSRD2uV4bt/rvLjnhvsC4xgTo/3qFwq7yqdwqJX/fIYGejx1dYrjNh0iZUD3DDUf3vrBN7eV5afPLqCnioDf6k6F0K1UyrNVyo0hSf34ckD3cVQRNnp/xBTQ33a1Ci4CSX6ehKedcpyIiiamKQ8VGSDfSD+gVq3IT8pUUEtRHlxnVpbQiFfyVYJTt+OYeae64z56zIrjr81U0caALefTh3KAP4Cury0xhk4DCCEuAlUlCSpkMf9FDwNK9nwQ5eaHLsVzc/7b+o6HAUFBYUCJzIyEm9vb9nJB4DU1FS8vLxkJx9ArUmwYMECjcmHi/fiGL7pItXsivH7ADd6dOsqO/kA6mSCNskHTey4HE6HJScJfBjPTE8Xtg5tpCQf3lLsrExYNdCNhb1duR2VRIfFJ1l54k6hVkOkpKTkOl2ja52y/Ni1FkdvRfPN9qv/WhcSEqL1FBqAw4cPk52tXVuHEII1a9Zo7UsblASEHO77ApBRpj4X78kfeZLvVGyivlWqIP5FZraKvVcf0a6mLeZajG16HTq+Z49KwMFrebRh+K0GCzuo/mH+B9BwOKQ9gcC/8/+532HOhTymw+KT9Ft1jg1n73HxfhyP4tN0HVZ+URZ4MWsZ9vS+F/EHugFIktQAqAC8orQlSdIQSZL8JEnyi46OLqBwC5Z+7hUY0KgCK0+EsO1imK7DUVBQUChQ7O3t85zYkBPm5uYa9RteRo5GRFBkIoPXXcDW0oR1nzSgmIn8xEN+k5SexVdbrjBmyxVqlCnG/jHN6edeId9FzBWKFpIk4VmnHD5jm9O8ailm7b1Jx0VHtNaGyMjIYNGiRVqPp8zMzKRv376Eh+fcTv2RuwNj2jix/VIYcw7cen5/eno6rVu35tGjR1r5CwkJwdPTU6s4JUli165dTJw4scBGmCsJCDk8OAfWlalW2ZHAhwm6680p7QwmVkoC4iXO3HnMk5TMvNsi8okaZYpR0caMvVdzOQA8ua+ugKg7APQL4IvVoRGUrAaX1uf/c7+DCCFYc+oufX73JSk9i8V9auM/tR0nJ7RiWueaug4vv8jpbOrlb5SfgBKSJF0BvgQuA68c6IQQK4UQbkIIt1KlSuV/pIXE5I7ONKpkw6S/r3Lxng6r2hQUFBTeEcKfpDJg9XmMDPTYONidUsXyr4pBWwLCntBxyUl2XAlndGsnNn/ekLLF857WoVB4vM5OP8C6dev4+++/SUvTvIFU2tKElR/XY3Gf2oREJdHq54Ms2HpE9gW3kZERaWlpVKtWjQ0bNsjWSbGysqJ48eK4uLiwYcOGHP2Nbu3ER+4OLD92hzWn7gJQo0YN4uPjqV27NkeOHJHlC6BDhw7s3r2bpk2b8uCB/Ap6Dw8P5syZw5AhQ7SuoJCDkoDQhBDqBIRDQ9wqWJOtElx58EQ3sejpg0NjZRLGS+wPjMDMSJ9mhTBeT5IkOtQqw9mQx8Qm5yDk5L8FEFCnf0EFAPUGQdgFiAgsGB/vEEuP3Ga693XaOdvi81VzutQu+zaOQAoDXhwNUw54+OICIUSCEOITIURtYABQCrhbeCEWLob6evzary5lipswdONFHj5J1XVICgoKCm8tyelZfLL2PMnpWaz/pAEONmY6iUMIwcoTd+j26xkyslT8NaQRY9tWxeAt7rXXJVFRUSQkJGi9i75//36aNWvG119/zT///EN8fLwsu06dOjF27Fjs7Oz4+uuvyczMW3BakiS61C7LvrEeiPhHLLmUSveZm8nIkpdMGDlyJBkZGQwbNowrV67IsgEYMWIET548YdWqVTlWJkiSxIwuLrSvacd07+vs8lefsn300UfEx8dz86b8FtKyZcvSvHlz4uLiMDIykm3n4eFBpUqVKF68eIGMLlU+cZp4fBtSHkN5d2qXLw6A/wN5H4QCoUJjiL0DiRG6i6EIka0S+FyPoGX10oV24dihVhmyVYKD1176PxAC/DertTpKaFfuqBWufUDfGC5vLDgf7wBbLtxngU8Q3eqW5dd+9TAzems1eS8ATpIkOUqSZAT0AXa9uECSpOJPHwP4DDghhEgo5DgLlRLmRqwa4EZaZjZDNr47o68UFBQUChMhBOO3+XM7Kolf+9fF2d5SJ3GkZWYz6q8rzNp7kzY1bNk7uhkNHK11EsubRlJSEnfu3OHy5cucOHGCc+fOybJLS0ujZcuWWFhYULlyZXx9fWXZdezYkSFDhrBgwQI+//xzIiLkXfPY2NiwdetWVCoVR48eJSQkRJZdJdvirOhVDfPw81xKssJz2QnC4lI02llYWDB16lQ+++wzFi9eLLsKolatWuzatQtJkvDx8clxjb6exKI+tWngaM24rVc4FRxDv379OHHiBL/88gtPnsjfDN+6dSuffvopS5culW3j6urKhQsX2Lt3L2Fh+d+uqiQgNPFU/wGHhpQwN6KCjRn+uqqAAEUH4iX8QmOJScrgAxe7QvNZ094SB2sz9ga+dEAMu6BODtXuW7ABmFlD1XZqHQiVctH0OgSGxzN5xzWaOZXk5+7vvdXTEIQQWcBI4ABwA9gqhLgmSdIwSZKGPV1WA7gmSdJN4ANgtG6iLVycbIuxpG9trj1MYPw2/wLrdVRQUFB4V1l+/A57r0YwsX11mjnppnUvMiGNXivO4h3wkAntq7G8f12Km8nfDS7qCCFITEyUtTY1NZWzZ8+yePFiRo8eLWssqyRJrF27loYNG+Lh4cH06dPZs2ePxsoEBwcHTp06Rbdu3UhJSWHQoEH88MMPueofvMjHH3/M8uXL+fLLL+nRoweTJk2S9Rrd3d3x8fFhyZIldOvWjXXr1sn6bm/XpjW+v37NIKdMrj14zAeLjnP4Rh56b08ZMWIEixcvxsLCgi+//FL2eUSnTp3w8vJi8uTJ+Pv757jGxFCf3we4UbmUBUM3+pGoX4wGDRrw9ddfM2TIENm+bG1t+eabb9i3b5/sSg19fX2sra2ZMWMG48ePl2WjDUoCQhP3fcHUGkpWBcC1XHECwnSYgLBzBSMLpQ3jKT7XIzHS16NFtdKF5lOSJD6oZceZ2zE8SXnhwB2wBQxMwfnlAQMFgEsPSI6CuycK3tdbRkpGFqP+ukwJc0MW96nzVo85eoYQYq8QoqoQorIQYubT+34TQvz29PezQggnIUR1IUQ3IcQ7I4zQqrotE9tXxzvgEUuP3NZ1OAoKCgoFSlxcHNeuXdPa7uTJk7J3eJ/xx+FLzN1/i47vlWFI80qybLKysjh8+LDW8R09epTk5FeFBAPCntB52SluRyWxon89vmhR5XlJeXh4OCdOaHcelZaWxpo1a2Rd/D1bk5GRwZYtW7h06ZLG9fv27QPgwYMHbNq0icWLF+e6Pi4ujmXLllG3bl2+++47Fi1axHfffcfQoUO5c+fVSV4qlYrt27czbtw4xowZw5o1a3BxccHFxYUWLVqwYMGCHP2Ym5vz448/cv36dTp37kyLFi3Yt28fHh4euLm5EReX+ymDqakpGzZsYNeuXZw7d45SpUrRsWNHli1blud7ATB06FAmT56Mn58fNjY2NG/eXFbCxN3dnSZNmnDq1Cm8vb3ZtGmTRhuAYsWKMe3Trsx/vxTpsRF8ut6PlSfu5Pl/LUkSkiSxdOlSkpOTtfrbLV26NH/++SczZ87MdY2VqSHrPmmAubEBQzdeJD41k0GDBmFqakpgoPxWbCMjI3777TdWrVol2wbA09MTIYTsKhTZCCHeuJ969eqJQmNJXSE29X7+z99P3BEVJnqLyITUwovhZTZ4CrGsge78FyFazz8m+q/yLXS//g/iRIWJ3mLLhfvqO7KzhJhTWYgtHxdOABkpQswsK8SOLwrH31vE7L03RIWJ3uJ0cHS+PzfgJ4rAMbIwfgr1OFzAqFQqMfavy6LCRG+x2z9c1+EoKCj8R5Rjce588sknYuXKlVrZHDx4UDRt2lRkZmbKtrkcHCYqfOUlms3aL5LT5dllZ2eLAQMGiAkTJmgV34oVK0SDBg1EZGTkv+7fdSVcVP1ur2g8+7C4/jBeCCFEVlaW+rFdu0T16tXFnj17ND7/48ePxcOHD8XmzZuFs7OzmDp1qsjIyMjT5tixY2L8+PFiwoQJwsnJSYwcOVLcvn071/X+/v7Cw8NDmJubi2rVqonmzZuL7777Thw5ciTH9eHh4WL48OGiRo0aAhCenp5i+fLlwsvLSxw9elQkJCTkGV9gYKBYtmyZEEKI9PR0ER4eLsLCwjS8E2pefO0xMTFCpVLJsnuGSqUSycnJWtkIoY5TW1QqlVZ/t89ITssQX2y6KCpM9Bbf/RMgMrOyZfl6HeTY+YU+FlUm7RGD1pwT2dmqAvWVX+R1HH5rm57zheQYtQbEC4KCz3QgAh7E08bZRDdxOTSEozMh9QmYFtdNDEWAB7Ep3I5Kok/98poX5zO1ylpRroQp+64+opdbeXVLTHI01OxWOAEYmqrHfF7fDR8uAAPdqUm/SQRFJrLqZAg965WjcZWCFy1VeDOQJInZ3WtxPzaFcVv9KVvclDoOJXQdloKCgkK+cvDgQe7fv8/q1atlrRdCEBUVxahRo9i/fz8GBpovG9LT00nNVNFriQ+mxUryx5BmGjWWhBCEhYUxe/ZsLCws+Omnn2TFt3//fk6fPo2fnx+HDh2iWLFizx9bcfwOs/fdpEFFa5b3r4uNhTFCCEaOHImBgQE3btzg8OHD2NvnPUEtPj6e999/n9jYWJo1a8bBgwcpW/blSdb/fi3Lli3jq6++Qk9Pj19++YUrV65gZpa78Ob58+dZsGABRkZGuLi4sGDBAho3bpxnXPb29vz666/PY4yKisLJySlPmxepWbMmNWuqp30ZGRlpfB9exNDw/1PebGxsZNs9Q5KkPN+P3NBGRPFFX3L+bl/GzNiQpX3qUL6EGb8dv0N4XCrLPqqLuXHuz/W6Yo1y7OpVsGZKR2cm77zG4sPBjG1btcB8FQZvf+3xf+HBefVt+YbP76ppb4W+noS/LtswytVX34Zf1F0MRYBjQdEAhdp+8QxJkmjrbMuZO4/V4nWBf4OhGTi1K7wgavWE9Hi4fajwfL7hzPC+joWJAd92qKHrUBSKGMYG+qz4uB62liZ8vuGiLAEqBQUFhTeFFStWMHbsWFauXCn7ImT+/Pl8/PHHzJgxgwoV5Ilr//XXFhqOWkqmWUlWDHSXNfHi6NGjNGjQgOTkZJYuXSorviNHjvDhhx/i6+vLrl27nicfhBDMO3CL2ftu0snVnj8+c8fGQr1Js3LlSn777Td8fHzYvn27xovupKQkOnTogJ+fH7a2tsydOzfP5APAgQMHuHPnDjNmzOC3336jffv2Gi+2GzRowF9//cXBgwfx9fXVmHx4GSsrK62SDwry0NOT+OaD6sz0dOFEcAy9VpwlMkHziM+Con/DCnSvW47Fh4Nl6VMUZZQERF6E+4GeAdjXfn6XqZE+VW1cYSfsAAAgAElEQVSL6W4UJ0DZeoCkFj18hzl+K4pyJUypXMpcJ/5bVitNepYK39tRcGM3VH0fjApxtFQlDzCzgavbCs/nG8zp2zGcDI5hZMsqWJu/PeJTCvmHjYUxawa5kZ6VzWfr/UhMy3uEl4KCgsKbQHR0NMOHDycrKwtjY3kVk9nZ2SxcuJBTp05RpkwZ2b7mbT9JWumatCyZTPOqmkUnhRBMmTKF6OhoHB0dZSUf0tPTGT58OPb29nTo0AF1tTeoVIIfdl9n2dHb9G1QnkW9a2NkoL7UuXjxInPmzOGrr75i06ZNWFpqnsZx9uxZvv32W6Kjozlz5gylSml+Pe3bt2fRokV88803fPLJJ5QrV06jjULRpp97BVYNdCM0Jpmuv5zmVoQ8wc/8RpIkZnq64FLWkjFbrnA35lXNkzcFJQGRF+GXoHQNdbn7C9Qub0VAWPzzA16hY2KpjusdTkCkZ2Vz5s5jWlYrrbNyogaO1pga6nPn8jFIiYHqHQs3AH1DcO4Kt/ZB+qtzhBX+jxCCn/ffpGxxU/o3LMARqQpvPFVKF2N5v3oERyUxavNlsrK1E11TUFBQKGrs27cPMzMz5s2bp3EH/xknT54kMTGRdevW0aRJE1k23kfPklDlfZys4Pevesmy8fHxwdzcHH9/f6ZNmybrnG7v3r189913hISEMHbsWIyMjMjKVjFhewDrzoTyeTNHZnnW+teEK2tra4KDg5k/fz716tWT5adt27Z07NiRkiWVls13nZbVSuM1rDEqIej7uy/XH+pmUrmJoT6/9a+HgZ7E0I1+JKdn6SSO/4qSgMgNIeDhZbCv+8pD75UrTnxqJvce67BEt5wbhPmBlorEbwsX7saRkpFNi2q6GekE6oNA48o2mNz1QegZQJU2hR9ErR6QlQpB+wvf9xvEsaBoAsLiGdW6CiaG+roOR6GI09SpJNO71OTorWh+3HND1+EoKCgo/CcCAgI4ffo0nTp1km0TGBiIn58fvXrJSyRkqwSLfGOxsLBg7bCWssdbV69enf379z/XI5CDp6cnAwYMeK5FkJGlYtRfl9l2MYyxbaoyqUONVxIMjo6O6Okplz0Kr4+zvSVbhjTC2ECPj1b5Ehie9xjS3EhJ0f76UQjBvXv3AChXwoylfetyOyqJSf9czdMuPDxc1tjTlzly5Aipqala28lF+STmRmwIpD2Bsq8mIFzLqYUfdasD0UAd3+N3c2zcsVtRGOnr0aiy9uI3+UmL6qWpn3GOtDINdCMIWr4hmJeCW3sL3/cbxPKjdyhjZYJnHaUUUkEe/dwr8GlTR9adCWXD2VBdh6OgoKDw2kybNg1XV1etbEaMGEHVqvKF7n4/GcLteJjexYVyJeS3ozo4OPynStZslWDslivsvRrB9x/WYHQbpyIjtKfwZhAUFCT7YrtiSXO2DGmEuZEBvX49yd/H/LT2N3/+fI4fP66VjSRJjBs3jvPn1fqETZ1KMqZNVXZeechu/4e52llbW9O2bVsePHiglb/Y2Fh69uxJZmbBtKIqCYjceHhZfZtDBURVWwtMDPXwf/B6ma984ZkQ5TvahnEsKBr3StYalZULmta2qVTTC8PfrJFuAtDTU2tPBB+CbKVfPSf8QmM5HxrL580qPe8FVVCQw6QONWhTozTTdl3j2K0oXYejoKCg8FpYWFhobaPNRfz1hwnMP3iLD1zs6FZXXotHfiCE4PsdV9lz9RHfdajBZ80qFZpvhYIjPj4e1WtUeD9r44mK0u772szMjNq1a7NlyxZZ7fUONmb8NaQhVmbGjNlxh3Ezl5CdnS3bX/PmzWndujWLFi3Sqp3f1dWVli1bsmfPHgC+aFEZ1/LF+X5HYK7imKamppiamuLh4UFoaKhsXy4uLuzZs4cBAwZo9drkopyN50b4JTAwUWstvISBvh4u9lYE6LIComRVMLZ6JxMQYXHq8Zu6mH7xMvaRxwDYluiiuyCqdVBPw7h3RncxFGFWn7qLlakhfRoU/rhWhTcbfT2JxX3qUN3OkpF/XtaZ8JSCgsKbgyRJ7SVJuiVJ0m1Jkr7J4fEWkiTFS5J05enPFLm2RZG0zGzGbrlCcTMjZnrWKtTqgzkHbrH5/ANGtKzM582V5ENRIzo6msjISK0189LS0mjSpAnDhg1j3759pKeny7JzdXXl7t27ODg48NlnnxERESHLrly5crz//vv06dOHfv36kZGRodGmvLUZXl80wURPhVeMHd8vXCXLF0DTpk2xsbFhxowZXL2adwvFi7Rp04aUlBRWrFhBamoqBvp6LOzlSnpWNhO2BeT6Pru7uxMWFsbFi/KnJ1apUgUbGxtCQkKIjMz/iRtKAiI3Hl4Cu/fUQn858F654gQ+jNedQJmeHpSr904mIE4FxwDgUbUIiAIF7SPGxIFdD0xJydCREEylFqBvrBajVPgXD5+kcvB6JH3ql9d5tYzCm4m5sQGrB7lhZqTP4HUXiE6UdyKkoKDw7iFJkj7wC/AB4Az0lSTJOYelJ4UQtZ/+TNfStkix0CeIW5GJzOnxXqFOmPrt+B2WH7tDP3cHvm5XrdD8votkZmaSkJBAXFwcjx8/JiYmRpadhYUFQ4cOxdramkaNGrFr1y5Zdra2tixfvpyNGzfSqVMnzp49KzvWBQsWYGlpyeHDh0lLkz8y85tvvsHFxYXg4GDZGg3lSpgxrXlxTPWy8Yosxe0oeZsU+vr6zJ8/n4YNGxIcHCw7xvr167Nt2zaCg4Oft0ZUKmXBpA41OB4UzaZz93O0GzVqFD///DN+fvLbRQwMDLh06RKpqalKBUShkZ0Fj/xz1H94hmt5K9IyVQRH6XD6QLkGEHUd0t+tXbmzIY8pVcyYyqW0LynMV9ISIPQ06Y7tyMhWceb2Y93EYWSuTkLc2qsWT1V4zh++9xBCKJMvFP4TZaxMWT2wPo+T0xmy0Y+0zPz/MlZQUHgraADcFkKECCEygL+ALoVgqxNuRSSy6tRd+tQvT8tCrEr96/x9ftp3k06u9kzv4qJoPmiJSqXi1q1bbNmyRVZ1QXp6OlOmTMHGxoaSJUvyySefEBsbq9HO1NSUbdu20a1bN65evcrs2bPZtWuXrPaK2rVrs2HDBj755BOGDx8uuz3CxsYGLy8v1q5dywcffMCFC/I2au3t7Tl+/DhjxoyhY8eOJCXJu77r0/l9Dk7qjISg26LDROXSCvEy/fv3Z/Xq1Xz//fc8evRIlo2BgQHdu3dn2LBhTJ069f/P5V6BZk4lmbnnBqE5jOasXr06I0aMYPfu3VppQTg4ODB+/Hh++ukn2TZyyZcExFtXbhYTBJkpYF8n1yU17a0AuKajMSyAWgdCqP6vV/EOIITAN+QxDSvZ6P4L585hUGVSyq0rZkb6HA+K1l0s1drDk3sQfVN3MRQxMrNVbPV7QKvqtpS3li+IpaCQE7XKWbGod20u33/COC9/VCol2aegoPAKZYEXz/DDnt73Mo0kSfKXJGmfJEnPxj/Itf1PCCFeq7/+5V1QIQSTdwZSzMSAie2r52iTlZX1WiPr8xK+OxUcw6R/ruJRtRTze7o+n7Yht0z/ZV5nIkFCgvbn/mlpabLsXnyfs7KyuHPnTp7rk5KSWLVqFSdPniQpKYnbt29z6tSpHH2pVCpWr16Nra0t1atXZ/jw4YwYMYLJkyfz66+/5lppYGFhwaJFizh9+jTOzs6ULFmS1q1b07RpU2bNmpXnxbqBgQGrVq3i77//ZvXq1Xh5eeHm5sbBgwc1vhfdu3dn+fLlHDt2jC1bttCzZ09ZVQ0eHh60aNGCf/75h8GDB3PgwAGNNqAWbOzXrx8DBgyga9eusnb+9fT0qGBjzp/DmpKYIei57ChJMkdj2tnZMWvWLIYMGSJr/TNGjBjB6dOn8ff3fxqDxJwe72GoL/HV1itk53B+YmRkxJQpU5g8ebJWvvr27cuJEydea5JGXvznBMRbWW728JL6NgcBymc4ljTH1FD/tUew5Avl6qlvH5zXXQyFzN2YZCIT0mlUSbfTLwAIOgAmxTGq2Ah3R2vO3JFXklYgVG2vvlXaMJ5z/FY0MUkZ9K6vaD8o5A/tXcowqUN19gQ84ucDSrJPQUHhFXLaGXn5auASUEEI4QosBXZoYateKElDJEnykyTJLzpau82P7du3/2v3VA6JiYk0btz4Xxf5O6885PzdWCa2r06JXFovxo8fz7Zt27TydebMGbp27ZrjY6ExyYz48xJOpYvxS7+6z4Wlnzx5QrNmzQgKCpLtJzs7m1GjRjFz5kzZNiqViiVLltCsWTNZF8L37t0jISGBOXPmULt2bU6fPp3nen9/f7p06cLatWvp1asXNWrUYNmyZTmuffToESNGjMDe3p7PP/+cjz76CA8PD0aPHs2aNWt4/PjVqlw9PT0+/fRTbt68ybx582jTpg0DBgzAxcWFjIwMHj7MfZoCQKNGjbh06RKLFi3i8uXLbN68mZIlS2JsbJynnSRJtGvXDmdnZzZu3Mi2bduwsZF3Hm9gYICtrS3bt2/nyy+/1OjrRapXr87hw4epXj3nBFluDBkyhIULF6KvL39se/3Ktsz1rE5Yoorhf1wkU2aLvqenJwsWLNAqPgMDA7Zv306NGv/XKSxjZcqMri5cuv+EFSdyTlr17NlT68++gYEB3t7elClTRis7jc+bD8/xvGQMQJKkZyVj1wvYtuAIvwTGlmBTJdcl+noSzvaWXNdlBYRpCbUYZZj2I2DeVM6GqA+ouh6/iRBw5whUbgX6BjSuXJKjt24QmZCGraVJ4cdjaQ9laqsTEM2+Knz/RZBtF8OwMTeiRbVSug5F4S3i82aVCItLZcXxEMoVN+XjRhV1HZKCgkLRIQx4MetdDvjXVZ0QIuGF3/dKkvSrJEkl5di+YLcSWAng5uYmu8QgIyODH374AW9vb7kmgHqMZ9++fZ9f/CWkZTJz7w1cyxent1vOSf5Dhw5x8eJF5s2bJ9tPeHg4n332GTt27HjlsaT0LD7f4Ickwe8D3LAwNiA7O5vU1FQ6duzIqFGjZI0NffjwIebm5vTr148aNWowY8YMjTZXr17lwoULbNiwAWdnZ06dOoWJSe7nekIIpkyZwrZt21CpVAwcOBBfX1+KF895XHtqairTp09n7ty5ZGdnU7FiRcaNG4ebm1uuF8FlypRhxowZeHp64ufnR5UqVejRo4fG1wLqNoVx48YhhNC6mtjY2Pj530H58uW13r0HqFRJe8FQSZLw8PDQ2q506ddrDapVq5bWNj2a1EBlbMGEbQFM3B7A/J6ust5fJycnrX2VL//q566zqz37AyNYfCiYTu/Zv1L9K0kSjo6OWvuqUCH/25jzIwGRU8mYew7rGkmS5I/6YPq1EOKaFraFy8NLUMZVLfSYBzXtLdl+MQyVSqCnp6N2APu6EHJMN751gG9ILLaWxlS00XFJffQtSIpUay/w/4TImTsxeNYpp5uYqnWAY7MhKRos3u2L7tjkDA7fjGRAo4oY6itSNwr5hyRJTO1Uk4dPUpm66xplrExp42yr67AUFBSKBhcAJ0mSHIFwoA/w0YsLJEmyAyKFEEKSpAaoq5EfA0802f4XEhISWLduHR06dJB9QREZGUlYWBgnTpz4V3n+Ip9gYpLSWT3Q7ZXz36ysLM6cOcOoUaPYs2eP7F3kTZs28csvvzB//vxXEgkqlWDsliuExCSzYXADHJ6eA06YMAF/f38GDBhA//79NfoQQjB8+HCuXbvG+PHjGTp0qEab6OhoOnfuzIMHD9i5cycffvhhnuuzsrIYPnw4q1atwsjICB8fH5o3b56nTVhYGC1atKBp06ZkZWVRuXJlXFw0T1eztramTZs2tGnTRuPanNB5K/NbSC+38jx6ksbCQ0E42pjzZWvtkwuviyRJTO7ozLFb0czwvs7KAW6F5ltb8uPMvMiXm2lFVjpEBOYpQPkMF3srkjOyuRerff9YvmFfB5IiIEGegMmbjBCCs3ce06go6D88S/pUagGAcxlLipsZ6k6IEsCpLSDeqYRUbuy6Ek5mtqBHPR0lgxTeavT1JJb0rYNLWSu+3HwZ/wc6HMmsoKBQZBBCZAEjgQPADWCrEOKaJEnDJEka9nRZDyDw6abcEqCPUJOjbX7FNmbMGObOncvgwYNl22zevJnWrVszdOhQDAzUe5Y3HiWw/mwofRs48F65V3f0T5w4QatWrahfvz7lysn7Dr5x4wb9+/cnMzOThg0bvvL4osPB+FyP5PsPa9CkinoCWmBgIAsXLuTmzZu0b99elp9t27axa9cuhBCydtMzMjLo3r07FhYWTJw4UdZO9c2bN+nSpQtBQUEkJydrTD6Aegf8/fff58MPP6RLly6ykg8KRZdRravQtbY9Cw4FFbo+nH1xU75sXYWD1yM5diuqUH1rQ34kIGSVmwkhkp7+vhcwfJ1yMyGEmxDCrVSpAtzdjbwGqsw8BSif4WxvCaBbHYhniZJ3QIjyTnQSMUnpNCwK+g8hx6CEI5RQ7yLo6Uk0qmTDmTuPX0twKV8o4wqm1urWkHecbZfCcClrSY0ylroOReEtxczIgNUD62NjYcSn6y/wQJeJaAUFhSKDEGKvEKKqEKKyEGLm0/t+E0L89vT3ZUKImkIIVyFEQyHEmbxs84vDhw+TmpqqlejioUOHyMjIwM7O7ll8TN15DUsTA8bnMvrSy8sLIyMj3n//fQwNcx5l/zIrVqygZMmSTJo0iRIlSvw77huRLDkcTM965RjUuOLz+3/44Qc8PDzw9vbGwcFBo4/Y2FjWrVvHH3/8wY0bN2TpAoSHh7N27VquXr3KzJkzZbV4uLi40LFjR5ycnJ4nbRTeLSRJYla3WlQtXYzRf10mLK5wzw8+beqIY0lzfth9nfSsojm1Kz8SEM/LzSRJMkJdMvavQa+SJNlJT7esXyo302hb6EQEqG/LuGpcWtW2GIb6EoEPdZiAsHUBSf+dSECcDVGP/NG5/kN2JoSeel798IzGlW0If5LKg9hUnYSFnr46pjtH3ulxnDceJRAYnkCPukr1g0LBUqqYMes+aUBmtmDg2vM8ScnQdUgKCgoKr/Do0SNSU1M5evQodepo3mAD9SSK69evc+zYMTp27AjA0VtRnA+NZVy7ajkKT2ZnZ+Pv74+vry8ffSSveyQlJYX4+HgCAwPx9PT812PRielM2BZAdbtizOj6/3Gbjx8/pn///hw5coTatWvL8mNiYoK3tzf9+vXDyChn0cyXcXR0pHLlyrLWKrx75LXhaGZkwG8f1yM7WzBi06V/JQJSU1Nfa7Py0aNHsuyMDfSZ2smZuzHJrD51l5s3tRfNFkJw8eJFre3k8p8TEEW53Oy1iLgKRsWgeEWNS40M9KhqW0y3QpRGZlC6xv8nd7zF+N55jL2VCQ66HqkYfgkyEl9JQDSqrC4L1Ok0jMqt1C05UTd0F4OO+ftSGIb6Ep1r5/v0MgWFV6hS2oLfB7gRFpvKkI0Xi+xug4KCwrvL/fv3OXbsmFbCeo8ePeLgwYM0aNAAUF+QzD8YhIO1Wa7TpRISEvD29ua9996T7cfAwIA1a9Zga/tvLR0hBBO2+ZOUnsWSvnUwMfy/loSNjQ1dunTRqh3XzMxM9+27CgWKEIKMDO03AoQQnDhxQms7lUrFrFmzch3X6VjSnHm9XPEPi+eH3f+fr5CRkcGwYcNkjfl8katXrzJ9+nRZa1tUK007Z1uWHr7NopXr2bNnj1a+JEliyJAhREREaGUnl3xRZyuq5WavxaMAsKulUYDyGS72VgSGx+uu7B7Avra6AuIt3vUWQuAb8piGRUb/QQLHf/f1VS5lTulixpy5o0MdiMot1bfvaBuGEIK9VyNo5lQK61zGgiko5DcNHK2Z38uV83dj+dorAFUOM7gVFBQUdIW7uzvOztpNuXdwcKBKlf9PgztwLYJrDxMY3dopV3HnEiVKYG1trZUfIyOjHM/rNvre4+itaCZ1qEFV22JaPafCm41KpeLKlStaX1tJksR3333Hjh07tLKVJIl//vmHzz77jKSkJNl2+vr6BAUF0alTJxISct6Mfr+mHUM9KvHnuftsuxgGgJWVFWfPnuXjjz8mMzNTtr9atWoxbdo02WM7J3d0RiUEIZau9O7dm0uXtNuszsrKonv37q+V1NGEIg//IqpstQZEGfmZW5eylsSlZPIoXvM84ALDvg6kPIb4B5rXvqHciU7icXIG7pW0+2IrEEKOqVt0zP4diyRJNK6sYx0Iq3Lq0awhR3XjX8dcDY8n/EkqH7jY6ToUhXeMTq72fPNBdXb7P2TOgVu6DkdBQUEh38hWCRb4BFGplDld6xR8dWFwZCIz99ygZbVSDGiU/yMAFQqH9PR0fHx8iI/XrlVdT0+PAwcO4Obmxpo1a7TSLenfvz+enp60adOGgIAA2Xaffvopq1evpk6dOty6Jf87vGPHjuzbt4+uXbuSnJyc45rx7arRsJI1k3cEEhqjXtOkSRM2b94sO5kAYGdnh42NDT/99JOs11be2ozhLSoTlFaMrBIVmT17tlYJjzJlyuDv74+Pj49sG7koCYgXiQ2BzGR1BYRMnO2tAB0LUT4TzHyLdSAu3osDwK2ijhMQ6UkQdv6V9otnNK5SkpikdG5Hyc+g5juVW0HoacjUYVJMR+wLjMBAT6KtMhZRQQcMbV6J/g0d+O34HTb63tN1OAoKCgr5gnfAQ4Iikxjbpir6BTx2PiNLxai/rmBhbMCcHq66r3pVID09nejoaK21C4yNjYmOjqZkyZLUrVuXRYsWybYfN24choaGfPrppyxcuFC2T1dXV7p3786JEyd49Ej+hEAXFxfatGmDnp4elpbyBczbtWtH27ZtEUJgamqa4xoDfT0W9q6Ngb7E+G3+ZKsE77//Pr1798bc3Fy2L0mSWLp0KTY2Ns+FYTUxzKMy1mYG1Bs0lWKWlrKFYQFmzZqFm5sbjo6Osm3koiQgXuSZAKWd/AqIGmWKoSfBNV3qQNi6gJ6hWpvgLcUvNI4SZoZUKin/g1og3DsDqqxcExCNnk7o0G0bRivISoUHvrqLQQcIIdh39RGNKttQ3Expv1AofCRJYlqnmrSuXpqpOwM5dD1S1yEpKCgo/CeyslUsOhRMdbtifFirTIH7W3niDjceJfBz9/coVcy4wP29y8TExJCWpnmzytDQkDVr1mBpaYmBgQHt2rWTrV/w0UcfsWjRIgIDA/Hy8uLKlSuy7AwMDFi/fj29e/fmjz/+4OhR+ZW906ZN4+DBg4wZM4agoCDZdps3b2bevHn06dNHdqWApaUle/fuxcnJiRUrVuS6royVKVM71eRCaBxrT9+la9eu/PbbbyxbtozY2FjZMfbt25fRo0czd+5cWetNDPUZ1boq4ZlmnL3zWCtNh7p16zJs2LA8X9froiQgXuRRgPpCvpTm0TzPMDMyoFIpC67pchKGgTHY1nzrKyDqVSih+0z43eOgbwQOr86pBnW5k72VCedD5R9M8p0KTdR/x++YDsTNiERCH6fwgUvBnyApKOSGgb4eSz+qQ62yVoz48xIX7+nwWKCgoKDwH/n7cjh3Y5IZ27YqegVc/XD/cQpLj9zmw1plaKNUMsomLS2NsLAwjetUKhVr166lbdu22NnZUbVqVXbv3o2fnx/R0dG5Vifo6ekxceJETp48iYODA+np6bi4uDBp0iQCAwM1+h0xYgQ7duxg3rx5DBs2jGHDhhETo1mwvVq1avzxxx/s27eP8ePH8+uvv8qqoHBxcaFly5asW7cOT09P7t2TV5FYsmRJOnXqRNOmTZk4caIsG1AnS+bOncvSpUvz9NW9blna1LBlzoFb3I5Konjx4owePVq2sOQzBg8ezJ49e4iMlLfJ0aeBA3aWJlg3/5ilS5dp5cvT05P9+/fn2l7yuigJiBeJCIDS1cFAu93TmvaWBIbrsAIC1G0YD6+8lUKUsckZhMQkU69CEdB/uHcGyrqBYc5lVgD1Ha25cDdWdzoQxhZQ3v2dS0Dsu/oIPQna1VROWhR0i5mRAWsG1aeMlQmfrvfjdlSirkNSUFBQACA0NJQ//vhD1lqVSrD82B1cylriv2ejVr34AEePHpW9cy2EYMquQPT1JMyD92vlB2D58uVa7XaDeqrA4sWLtbKJj49n6NChWl2QJScnM2XKFLZt26Zxrb+///PYJk2alOc40/DwcL7//nvKly/PV199xccff4yHhwfVqlXLsdJAT0+PQYMG8e233+Lu7o6dnR0XL15k/vz5dO3alfHjx+cZW8OGDbly5QpeXl74+vpStWpVxo0bx+PHmqt+O3ToQKNGjTh79iz169dn69atGm1AfXFfsWJFjh07RnBwMKmp8kfdu7u788svv2gtvjh9+nSKFy9OVlaWbBsrKyuWLFlCeHh4rmskSWJWNxfMjPQZ5+VPVraKzz//nLJly2p1zWBkZMTPP/8su3LCxFCfEa2qEJ5hQoaNdmNljY2NmT59utY6HppQEhDPEOLpBAz57RfPcC5jSURCGnHJOpwBb18H0uPVOhZvGf/Xfyih20DSE+GRP1RonOey+hWtiUpM536sdl/U+UqlFuqRssk6bAUpZPYFRtDA0ZqSFkrJpoLusbEwZsNgdwz09Biw+jyP4uWfNCkoKCgUFIsXL0alUslaeywoirsxybQpJ7F3755ce9xzIjMzk7Fjx1K2rDzRyv2BERy7FU21jCCsDLXbwPHx8WHDhg1UqCBfsDIoKIhevXrRokULWevT09O5desWHh4eNGrUSGPvfnZ2Nn///Td//vknbm5umJmZ0alTpzzXz549Gw8PD2rXrs3XX39N1apVWb58eY7rIyIiWLJkCefOnUOSJIyNjRk5ciSbN2/m+vXr1K5dO0c7SZJo1aoVO3fu5PDhw/z0009s3ryZ06dPM2/ePI3vg5WVFaVLl8bKyopBgwZx4MABbGxsNJyB0jkAACAASURBVNo9Q09Pj08//ZQvvvhCtg2AhYUFCxcuxMzMTCu7Fi1a4OnpqZWNvr4+U6ZMwcDAQCu7Nm3a0Lhx3tcIpYuZMKOLC/4PnrDyZAgGBgaMHz9e6wrvTp06UaNGDdnre7mVo2xxU4KMq2q9Qdq7d2/s7e21stGEdu/s20xiBKTEvFYConoZtVjJzYhEGlWW/yHMV14UotQyu1XU8bsXi6G+RK2yVroN5MF5ENkaExANHNWVGufvxlLBRkeaFY7N4Chw7zQ4d9ZNDIXI7ahEgqOS+LhRTV2HoqDwHAcbM9Z9Up8+K30ZtOYCW4c2wspMvgCUgoKCQn4SFxfHvn37+Pnnn2WtX3s6FFtLYw6tmcsPP/wg+yJJCMGKFSto1aoVVatW1bg+KT2LabuvUdHKgLAdm9h66pQsP1FRUaSkpDBq1CgOHDiAsbHmDYjIyEjOnj3LpEmTWLduHa6urhpt/P39mTx5MsHBwaxdu5aGDXNuw32GEIIhQ4awfv16evToweHDh/O8gAsPD2fgwIH4+vpibm7+vE0hL+zs7P71/5iYmEixYtqNKy1TRmlZ1QWdXO3ZHxjBIp9gOtayx8FGu6TK62BsoM/IVlX49u+rHL0VRavquq0WViognhFxVX2rxQSMZ9Qoo/7A33ikwzaM0jVA3/it1IG4GBqHS1krTAz1dRvI/bMg6UH5Bnkuq1LKguJmhlzQpQ6EfV0wNIPQk7qLoRA5cE3dB/d+TWX8pkLRwqWsFSs/rkdITBKfb/AjLVOecJeCgoJCfuLn58fs2bP55JNPMDLS3GocHJnIyeAY7BKDSE1JwsPDQ7avqVOnsmzZMqZMmSJr/eJDQUTGpxG9fymrVq6UrdS/dOlSGjZsyIIFC3BwcJBl8/PPP+Pp6cmIESNwd3fXuD4jI4OBAweye/duBg4cKCv5MG7cOLZt20a7du3o1auXxt3j0qVL4+PjQ1JSEpGRkRqTDzmhbfJBQbdM6eSMgb7Ej3uuF5rPHvXKUd7alAU+QbprE3+KkoB4RoS65+p1EhClLIyxMTfiZoQOExD6huokRIT8mbdvAulZ2QSEx+NWQcftF6DWfyjjCsZ5H+T19CTcKlhz/q4OExAGRmodiFB5uwhvOkdvRuFS1hJbSxNdh6Kg8AqNq5RkQa/anA+NZfRfl8lWvX1aPQoKCkWbkydPMnfuXCIjI2VdfKw7E4qhHngv/pa0tDQSE+Vp2SQnJzNr1iwSEhKIjo7WuD4sLoX1Z0LJun2aUL+jxMXFyfKTlZXF2rVrSU1Nla1N8fDhQ5YvX07jxo2pX7++LJsZM2ZgY2ODl5cX48aN07j+yZMnDBgwgNjYWPbu3Uu3bt002hgaGupeZF2hULG1NGFkqyocvB7JyWDNn5P8wFBfjy9bOREYnsDRW1GF4jM3lATEMyKuQglHMJE/+/UZkiRRo4wlNx7pWGiszHtqHYu3SIgyMDyBjCwV9XSdgMhKhzA/9YQJGbg7WhP6OIWoRM3jjQqMik0h6joka1YafpOJS87g0v04WlUrretQFBRypZOrPVM6OnPgWiRTdgbqfPdBQUHh3SIkJAQHBwdZ/ebxKZn8fSmcmhapFDOSWLZsmewd9vPnz2Nqasqff/6Jk5OTxvVLDgejEoLMS//g4+MjW5PhwIEDVKpUiYCAALp37y7LZvPmzaxbt45Tp07RoEHe1ayg1mUYOHAghw8fpkePHrIqM0qUKEHt2rX5H3vnHR5Vlf7xz5lJ76QXEnpCCaF3UFAWRbD+RIoCIgq2XaygLoig64pt14KLCioaERFBLFgABQFJaAESIARIII000nsmc39/TAYRSHJPSHITuJ/nyTNkct45J8Nk5p73vO/3azRqXLWr0yyo1VO5kLKyMmYO70A7LycWfXeEqmp1jyNj2WmltLSU/Px8AG7vE4Sfmz0f7zxVb1xSUpL0XGrRExBWzhxqUPWDla7+riRkFmFS+QJqEvwjoDwfClK0W0MjY7Ww09wBI20/VFfUq/9gZUCNDsSeJHWZ/CahwzWW2yu8CuL349mYFRjVVU9A6LRs7hvegQev7cTn0cm8veWE1svR0dG5ijh79iwbN25U1ff/5d5kyqqqCSxJYOPGjfTp00f1PEeOHGHz5s2qEgknsopZuy+VId5V7N76c70Cfufj5+fHb7/9JiU8+dhjjzFx4kTV1QZGo5HOnTurfnwd7cnLy5NyyrCSnp7Onj17pOP27t3Lpk2bpOMiIyOJPRDD/HHdOZFVzGe71FmFzp8/X5WF6fmYzWZmzZqFoijYGg3cM6gd24/ncCKruM6477//nnXr1knNpRY9AQEWd4O8pAYJUFrpGuBGhcnMqbMaOh8E1AjpWPUsrgD2nc6jnZcTPq4aOxuc3mm5DRmianiPQDccbY0a60D0AVvnKz4B8Wt8Fl7OdvRq66H1UnR06mXejWHc0TeI/2xO4IvdyVovR0dH5yrhxRdfpEeP+oWaq80KK/84zcAOnix67AGppADAzJkzVWkrAPxnUwKOtkb+88CNUokEgP79+0tXGehVCa2HhIQEfvzxR+k4Jycnxo4dS3x8vFScv78/EydO5Oeff5aKCw0N5bbbbuP333+XivP19eXmm28m1LmcEV28+c/mBM4WV9QbV1JSwpQpU6iuVq8n5eTkxFdffcWKFSsAmDwoBDujgU93naozzsbGhgcffJCsrMZv19ATEABZRy23fg1X0G8RQpR+PQBhqea4AlAUhX2n8+kb0kL0H3y6gZO6Sgxbo4G+7Ty01YEw2kLI4CtaiLLarLAtIZtrw3wwGPT+SZ2WjxCCJf8XwcgwH/65PpZfDmdovSQdHZ2rgE6d1DmkRSeeJS2/jHsGt8PHx0d6HgcHdVpMcWkF/BB7hpnDO+Dtqus3Xals2rSJZcuWqdb2sNKlSxdeeOEFbrrpJo4ePao6zt7enq5du9K/f38iIyNVxxkMBgYMGMD48eP5/PPPVcd5eHjg4+PDuHHjiI6OVh3XoUMHMjIyGD9+PE+OakdZZTVvbTleb5yPjw+bNm3ixRdfVD2XwWDAycmJp59+mvj4eLxd7BnfK4Cv96VSVF5Va5yNjQ3Z2dk88cQTjd42qicgADIPW279ujf4ITr7umBjENoKUdo5g3eXK0aIMr2gnJziCvqEaHyyXW2yWHCqbL+wMqC9J0czCims44+7yWk/HLLjobh5BG6amwMpeeSXVnGd3n6h04qwNRp47+6+9Axy5+9fxBCdeFbrJeno6OgAsOFAOs52Rv7WrWlt+l7/5RgeTrbcf03HJp1H5/JRFIWtW7dy8OBB1WKkVq677jrWrl2Lv78/U6ZMUZ2IEEKwePFifvzxR6ZMmXJOw0AN99xzD2VlZXz77bdUVNRfVXD+Wj09PSktLZXacI8bNw5fX1+pKp727dszZswY+vXrR892PkzoH8zq3SmcKai7faR///4MHz6csWPHqp4L4Nlnn6V79+6EhYUBcO/Q9pRUVrN2X2qtMd26dWPChAlMmDBBai416AkIsCQg7FzBXZ2Fz6WwtzHSycdFeyFK/4grpgLiQLLlzaZ3sMYJiMxYqCxqUAJCUSAmWf2bZqPTfoTl9gqtgvg1PgujQTCii/wpjY6OljjZ2fDRvQMIauPI/Sv3EpdWoPWSdHR0rnLKq6rZGHeGG8L9cbRrunaF+IxCth7L5v7hHXBzUGe5qaMdQgj8/Py47bbbcHNzo0+fPqoTEUajkc8++wx3d3f27dvHsWPHVM87ZswYHnvsMYxGI1u3blUdN3ToUDZt2kR8fLxU9cSECRPYunUr7777LlVV6g8P//Of/zBr1iyWL1+uOsbNzY2NGzeyd+9esrOzeXhkJ8yKwrKtJ+uMmzRpEk8//fS5dgq1zJ8/H4BTp04BENHWgz4hHqz84xTmWpy5hg8fzqxZs1i/fn2ju7ToCQiwOAX4dQfD5T0dXQNcideyBQMsThiFqVCqYel/I3EgJQ87GwNd/eWdSRqV5JqSKpX6D1Z6BXtgEBYdC80I7A12LlesDsSv8dn0a9cGd0f9AqYuhBA3CiGOCSFOCCGeucTP3YUQ3wkhDgohDgshZmixzqsNLxd7ImcOwtXBhukf7SYxu25BKB0dHZ2mZOuxLIrKTdzWO6hJ5/loRxIOtgbuGSyn+6BzeSiKwldffcXf//53xo4dS79+/VQ7HXTr1o2oqCj69++PEILRo0fz5ZdfYjKZ6o0NCAjgu+++Y8OGDTz88MO88cYbqioMhBC88cYbbNy4kYULF6oWezQYDFx33XWsXLmS6dOnU1ys7rPV09OTbt26MX78eN58801VMQB2dnY8+uijREZGSrWaGI1GHnroId577z2CPZ24s19bvtiTQkZB3Q56N910E9u2bVP9e1mZPHkyq1evPvf9vUPbc+psKdvqsAG99tpr2blzp6r/Zxn0BISiQGYc+Da8/cJKtwA30gvKKSjVsOTeKqR55qB2a2gkDqYU0CPQDTsbjV+mqbvBLQjc5T6QXextCPN3IyZZwwSE0RaCB/0ponkFcaagjKNnCvX2i3oQQhiBpcBYoDswWQhx4RveI8ARRVF6ASOBN4QQds260KuUQA9HPrt/EAowdcXuessvdXR0dC6HioqKc6egF/JNTDreLvYM7eR10c9OnDghJXwHkJOTc5Fif3ZRBd8cSOfOfm3xcLr0x4ysgCBYbEZLS+WE4E0mE4cPH5aea8+ePdL2i6dOneL48fp7/M8nKyuLr7/+us4xRUVFvPnmm/zwww/s37+f1atX8+KLL5KcfLHIsRCCm2++mZ49e5KQkEBGRgaTJ0+mc+fODBs2jHfeeafOufz8/Ni6dSvff/89kZGRbNu2jYiICLKz62/zHTRoEF27dmXHjh0cPXqUxYsX1xsDlmSCr68vP/zwA8888wwFBeqrBfv06cMDDzzAsmXLVMcAPPfcc/zwww9UVlaqjnF2duahhx7ihx9+kJrr3nvvJSoqCkVReGRUZ8xmhWXb6q6CsLGxYfLkyURFRUnNdddddxETE3Pu+7HhAfi42tfpwGFra8sNN9wgVbmiBj0BUZgO5QWXJUBppat/jRClljoQ55wwWncbhqnaTGxaQctwNkjZDcH1+0Vfir4hHhxIzq+1vKlZaDfEogNxBVTFnM/2BMtFzbWhevtFPQwETiiKkqgoSiWwGrj1gjEK4CosNXYuQC7QuOlunVrp5OPCp/cNpKCsiqkrdpNbov6iR0dHR0eGjRs38vrrr190f0FZFb/GZ3FzrwBsjH/dHlRVVTFu3DjKy+s+mb2QV199lQ0bNvzlvsio01SazMwY1uGSMYcOHeK+++6T6sE3mUzcddddnDghZ2/8wgsv8Nlnn0nFbNiwgYceekjV6bP1d/jmm28YO3YsGRl1iw4risL//vc/Dh8+zP3338+oUaNqdSDIyclhwYIFhISE8OSTTzJnzhyWLFnC4cOHadeuHc7OzpeMc3BwYNasWRw7dozPP/+cqKgojh8/zrp16xg/fny9v5OzszOBgYF06dKF9957j507d0qJlTo5ObF8+XLmzZunOgagbdu2REVF4e7uLhX3yCOP8MQTT0jFODs78/vvv2NnJ3cO849//IN77rlHeq6ff/4ZIQTBnk7c0TeIVbuTySys+2/thRdeYPTo0VJz+fr6smbNmnPf29kYuLNfW7YlZNfpwPHuu++qctCRwaZRH601ck6A8vKf2G4BllaB+DOFDO54cfa4WXDyBLe2rV4HIiGzmLKqau0FKAvPQEEKDH64QeF9Q9rweXQyx7OKCatJUDU71taRlGgIkxOtacnsOJGDj6v9ucSfTq0EASnnfZ8KXOiR9i7wLZAOuAITFUWRO97RuSzCg9xZPr0/0z/azb0f72bVA4Nxsdc/onV0dBqXVatW8fjjj190/09xZ6isNl+y/eL7779n1KhRtW5qL0VRUREbNmzg4ME/K3LLq6qJjDrN9V196eTjcsm4hQsXsnjxYqme86VLlzJixAgiIiJUjVcUhc2bN7N161Z+++03VTFZWVnExMSwcOFCfvnlF9zc6m4PVhSFhQsXUlhYSGxsLL/++isBAQG1jjeZTDz22GMsXbqUfv368c9//pP333+/VutQT09PZs2axciRI0lISMDb21tKLNDGxoaRI0cCf2o8NIQ2bRrmVKfWLeV8bG3l222FEA3SL2iumAvjHh3Vha/3p7Fs20kW3ty4m/5LcWvvQP639SQbY88wdUj7Jp/Pin51k1WTgGiEFgxfV3s8ne1agBBlz1ZfAXEgxSLcqHkFROpuy21DKyDaWd6Y9yfnaZeACOoHBltI3nXFJCDMZoWdJ3K4JtSn0YVxrkAu9QRdeLR0A3AAuA7oBGwSQmxXFOUv5VxCiFnALICQkIaL9upcmsEdvVg6pS+zI/cx69O9fHTvABxsdd96HR2dy8dsNpOfn09cXBxDhlysafXdwTN08HYmou1fT5hLS0v58MMPVZfMA5w9e5bIyEimTJnyl43mtwfSOVtSycwRF1c/ZGVlERcXR15eHtdff72qeaqrq1m7di3Lli1TbYGoKArz5s3ju+++46efflK1qS0pKWH06NEoisJPP/2Er2/9rZ/vvfceL774IkOHDuXXX3/F3t6+1rHFxcXMmTOHw4cPM2nSJK699lpuu+22Oq9vDAYDwcHBBAcHq36+dFo+IV5O3NorkC/3pPDE30JxbWKR1q7+boT5ufLtwfRmTUDoLRiZhy0VA46Xv9EVQtDV31VbK06wCFHmHIfKEm3XcRkcTMnHw8mWdl5O2i4kZTcY7f/U1pCkvZcTns522gpR2jpCYB9IlusVa8kczSjkbEklwzt7a72U1kAqEHze922xVDqczwxgnWLhBJAEdL3wgRRF+UBRlP6KovRviD+8Tv2M7u7H6xMi+OPkWf7xRQymar0QRUdH5/IpLi5myJAhhIaGcvbsX61/SypM7E7KZUx3v4s2vdOnT+fgwYM4Ojqqnuu///0vL7zwwjnLPyur9yQT6ufCkEtUCe/YsYOxY8fSs2dP1foKBw4cYNKkSYSEhNRaKXAh0dHRvPbaazg7O9dbxWBl6dKlxMbG4ufnh4vLpSs3zicmJobnn3+eadOmsWjRImxs6j7vdXZ2ZsWKFURFRfHFF1/w4IMP6ocrVzHTh7antLKadfvTmmW+W3oHsudUHql5choql4OegMg83CjtF1a6BbhxLLOIai17/v0jAOXP9pJWyIGUfHq19dD+DThlt2XzbtMwPT4hBH1DPNivpRAlQMhgSNsPVVeGwN2O4xb9h2F6AkINe4AuQogONcKSk7C0W5xPMnA9gBDCDwgDEpt1lTrnuL1PW164uTu/HMnkmXWx2mrI6OjoXBEUFxeTkJBAcXHxRWXzUYlnqaw2X1JTydpC4e2t/vM2MTGRiooKOnbseO6+pJwS9ifn8399217y2u7gwYOYzWbGjBmjOpmwZcsWHB0d+fvf/666PSQyMpLu3buzcuVKVe0DRUVFrFq1ipUrV/LLL7+o0iCorKwkOTmZlStXMnr06Hp/H82vdXUuC1lBUiu1iVz2CvagV1t3Pos6fZEWislkkhLHtFKXbeotvQIBSxXUheTn50vPpYarOwFhqoSchEZNQHT1d6W8ysypsxpWHwS0bieM4goTCVlF9A7WuP3CVAFnDkDwgMt6mD4hbUjMLiG/VENhuZAhYK6yJCGuAHacyKGLrwv+7vI9hFcbiqKYgEeBn4GjwBpFUQ4LIR4UQjxYM+xFYKgQIhbYAsxTFCXn0o+o0xzcO6wDj43uwtp9qby88aiUIJuOjo52qLA9vlsIcajm6w8hRK/zfnZKCBErhDgghNjbmOsqLi7G29ubzz777KIN8baEbJzsjPRrf/GGvKCggLVr10ppBJw+fZrPP/+cgQP/bF9dH5OGEHBrLRafcXFxfPHFF9x8882q5zl48CC//vqrKvFEsGz4nJ2d2b17t2pRvcLCQnbu3Mm0adMwGNRtmwYNGiSll6FzacrKGnZodvr06VrFO+ti3759DXJ7WL16NenpFxaW1s8rr7xSq73lPYPbcSKrmF2Jf61WKi4u5tVXX5We65NPPiEhIeGSPwv2dKJPiAffHrz4d3j22Wel51LD1Z2AyEkAs6nRKyAA4rXUgXAPBgePVqsDEZtagKKgfQLizCGoroS2DdN/sNI3xPKBHpPcNFlEVYQMttwm79JuDY1EeVU1u5NyGd5Fr35Qi6IoGxVFCVUUpZOiKP+quW+ZoijLav6drijKGEVReiqKEq4oSqS2K9YBmHN9F+4d2p7lO5JY+pucuruOjk7zo9L2OAm4VlGUCCzJ3w8u+PkoRVF6K4rSvzHXVlJSwieffEJgYOBFP9uWkM3QTl7Y2/w1MVFZWckLL7xwSc2Iunj44Ye5/fbbz32vKArrY1IZ3tm71oODOXPmcOedd0rN88orrzB48GDV421sbFiyZIlUciAoKEhPJlwmsvajVg4ePMjixYulKwzc3d0ZPXr0RRaw9eHq6sr48eMvalGqj/Lycu6++25pm9o9e/bw2muvXfJnN/cKxMPJlsiov1pkVlVV8eKLL0onSnJzc/nHP/5R62HGrb0COXqmkOOZf92/fv755/z0009Sc6mhURIQLTXbWy9ZRyy3jZiA6OzrgtEgOHpGQx0IISxVEBmx2q3hMjgnQKl1AiKlRtCogQKUVnoFu2M0CG3bMJw8wafrFaEDsfdUHhUmMyP0BITOFY4QgufHd+eOPkG8/ksCH+9M0npJOjo6dVOv7bGiKH8oimK9IIjCosvT5PTs2ZNx48ZddP+pnBJOny3lmku0X9jY2PDggw9edH99TJky5S/f7z2dR0puGbf3uXT1A8A111wjPU9wcHD9g85DbQWDTuOybds2brvtNmmb1IEDB/K///2Pu+66S5XtqRUPD49zwqEyyYTg4GBOnDjBnXfeKdXm4O7uztatW6WEWsHy97Vw4cK/OMVYcbA1MrF/MD8fziSj4E9LTmsLxqxZs6QSM8XFxfz8888X2eJaGRcRiEHAhgN/VkFUVVVRVFTEk08+WWulRkO57L/ElpztrZfMOIs7gFfnRntIB1sjHb2dtRei9I+AzCNQXaXtOhrAwZR8Qjwt4o2akrobPELA1f+yHsbJzoau/q4tQwciZTeY5TK0LY3tJ7KxNQoGddDI6lZHpxkxGASv3hnBDT38WPTdEb7ck6z1knR0dGrnUrbHte+6YSbw43nfK8AvQoh9Na5DjUZtQojbErIBLqn/YDAYGkWfYN3+VJzsjNzQ4/Kup3S049SpU9x999288847JCQkSLUFTp8+nUOHDtG9e3eWL1+uOs5gMHDrrbfy9ddf8+GHH0qtt1+/fhw7dox9+/apjnF0dDwn0pqWpl4A0sPDg5CQEAoLC6mqUr/v6tSpE56enrXG3D2oHWZFYfV5n/tVVVUMGjSI4OBgCgoKVM8VFBRE27Zt8fT0vOTPfVztGdzRi01HMs/dV1hYyJgxYwgPDyc3N1f1XGpojFRgi8321kvmEcupsLFxLU66Bbhpb8UZ0AuqKyxtJq2MuPQCeratX+SnyUnZc9ntF1b6tWvDgeR8bcVJQ4ZARQFkHdVuDY3AjuM59Alpg7O97iKsc3VgYzTw9uQ+XBvqwzPrYtlwoHmUsXV0dKRRY3tsGSjEKCwJiHnn3T1MUZS+WA71HhFCXLIsQAgxSwixVwixNzs7+7IWvC0hm/ZeTrTzapo2g2qzwo9xGYzp7qd/brdi2rdvz3333ccTTzxBWFgYv/zyi+pYW1tb5s+fj7+/P4mJcvrWkyZNYu7cuRw+LCesv3DhQh555BFOnjwpFbdjxw6EEHXapl7IsGHDWLVqFSkpKapsXa0sWbKEa665ptZqixAvJwZ38OLbA+nnEj7BwcGsWrWKtLQ0VSKqVubMmcPo0aPrrJq4NtSHY5lF5youvLy8eP/998nOzlZlPStDYyQgWmy2t16yjoJvt0Z/2K4BrqTll1FQpmH1gdU28kzr0oHIL60kNa+M8ECNExAFaVCUftntF1b6hrShpLKaYxkaJqZCano4W7EORH5pJUfOFOr2mzpXHfY2Rt6f2o9BHTx5Ys1Bfj6cofWSdHR0LkaN7TFCiAhgOXCroijnasQVRUmvuc0C1mM55LuIxrJENlWb2XXy7CXbLxqLmOQ88kurGN1dvYilTtOxYcMG/vGPfzB58mTGjx9PRob6z5Lrr7+e5cuXM3LkSB5//HG+/fZCQ63amTp1Knv27CE+Pp6XX35ZddzIkSP597//zenTp/nhhx9Ux/Xo0YNnnnmGt956i9JS9faSPj4+zJ49m//973+qYxwcHBg6dCjx8fFSlQJGo5E77riD9evX1zpmfK8AEnNKOFLT2i+EoGPHjmRnZ9fpbHEhQghGjRrFb7/9VusY6/vA78f/TGq2a9eO1NTUlteCQSvM9gJQXgiFqeB7kdX9ZdPN3yJEmZCp4WbTuwvYOLY6IcrD6ZY/sPAgdd7MTUZ6jVtEUL9GeTirEKWmbRgeIeAa2KoTEHtO5aEoMKjDpUvIdHSuZBxsjSyfPoCItu78fVXMudJpHR2dFkO9tsdCiBBgHTBVUZSE8+53FkK4Wv8NjAHimnKxCZnFlFVV06+d+pNUWX47loXRIBjRpemSHJdDQxyGGhojK1II6pwgqqurOX9vdObMmVrjxo8fT9++fdm+fTs7d+5k+PDhjBs3jsWLFxMVVb9O2PTp09mwYQM///wzy5cv584771S16ba1tcXPz48vvviC7du3s3Tp0npjrBgMBlasWMFTTz0ltcH39vZmypQpvP3226pjAKZNm8aXX35JeXl5/YNrEEJw1113sWbNGqm5brrpJjZu3Fjra2pseABGg+D7Q3+1yLz++uv59ddfpeYaOXIkW7durfXnXf1d8XG1Z/vxaG8aOwAAIABJREFUP8U7hRD06tWLQ4cadz/ZGAmIVpXtPUd2jXqoT+NXQIT5uwIQr6UQpcFoEddsZRUQcWmWfqYeWldApO0Hgw34hTfKwwV7OuLtYqdtAkIIiw7E6V3QSi399pzKxc5o0F6gVEdHI1zsbfhkxkA6+7ow69O9RCXKqXXr6Og0HSptj58HvID3LhBg9wN2CCEOAruBHxRFaXT5+ePHj/PYY48BcDC1RvS7bf2fqVOnTpV2Ffj222/5asdR+rVrg7ujutJ0k8nE2LFjpTf5ixcvlt6QxcfHM2PGDKkYk8nEmDFjpGweFUXhueeeY9myZapjysvLef7557nllltqfS4UReGHH36gd+/ezJkzh9tuu43Q0FAmTJjA6dOnLxljNBq59957SUhIYMWKFSQkJPDaa68RHBzMqVOnVK3Nzc2N4OBgNmzYwLRp03ByclL9e9nb2/P1119LO6uEhISwevVq3NzkDigff/xxJkyYIBXj4uLC+vXrpdopwOL+cuutt9Y/8Dzc3NzqTFp4OtsxtJMX3x9K/8vrYN68eYwYMUJqrpCQEN57771afy6EYEQXb3Ycz/5Ly/jrr79OaGio1Fz10RgJiFaV7T1Hdk0ffBNUQAS4O+DqYEO8luX2AP7hkBnbqjabcemFBHk4ai9Amb4ffLuD7aXtomQRQtAnpI22VpxgacMoSoeClPrHtkCik3LpHeyBg62x/sE6Olco7o62fDZzICGeTsz8ZA8xWgvc6ujonEOF7fH9iqK0qRFfPyfAXqOl1qvmq4c1trH59ddf8fe3iEEeTMnH3dGWdl51byCLi4vZt28fXl5y4s+frf2OrCo7ruuqvn988+bNBAQESIlflpWV8fnnn0tZcgLMnz+fu+66Syrm1VdfpVevXqp64q0bxn/9618cP36c2bNn1xvz2WefsXLlSgYOHIitrS3ff//9JZ+L/Px8HnroIaZOnUpcXBy5ubm89NJLHDlyhB07dtC1a937GycnJ+644w4MBgPdu3dnxowZTJo0qd71nY8QgltuuQUHB7lrZScnJ/r27SsVA9CrV69axVRrw9XVlU6dOknP1aNHD4xGuWtNb29vAgICGjRXXa/3myMCSckt41Dqn6KTgYGBtQpK1jdXXVwb6kNeadW5A2GwtGG4uLhIz1UXl52AaA3Z3kuSFW9pUfBo3+gPLYSgq7+rtv3+AP49obwAClK1XYcEh9MK6BGocfuFokB6DATJvznWRb92bUjKKeFscUWjPq4U7aw6EK3PjrOkwkRcWgED9fYLHR28XOyJvH8Q3q72TP9oN4fT1ath6+joXL1s3bqVkSNHAhbb817BHvVu9rdu3cqoUaOkkgKVlZXsP2MpYR8Vpj4BsXLlSqZNm6Z6vKIorFq1ittuu031SXxFRQV79uwhJyeHsWPHqopJSUkhOjqar776ipdeeklVzOrVq3n44YfZtWsXq1atqnfzvHnzZu677z6eeeYZvvrqKxYsWFCrGKKHhwfLli0jNzeXiooKPvnkE8LDw6U36Dotnxt6+GNrFHx/6KIGg0ZnWI3G2u9N3OLZKIa4LT3be0myj4JPKDSRJ3CYvyvHMosa1CfWaPj1tNxmxGq3BgmKyqtIzCkhPEjj9ovcREviJrBxExBWHQhNqyB8u4O9G5z+Q7s1NJD9yXlUmxU9AaGjU4OfmwOf3z8IF3sbpq7YzYksjZPeOjo6LZo//viDvXv30q9fP0orTRzPKqZ3Pa5je/fu5csvv+TGG29UfU2bl5fHokWL8Aq/hiAPR0L91J2eLl26lAMHDnDNNZeUg7skb7/9Nm+99RaPPPKI6phly5Yxffp0nnvuOdVJlU8//ZTrrruOxx57TNWJv8lk4oUXXmDZsmU8/PDD2NnVXdl76NAhZsyYwfjx41mwYAEy7eZ2dnbnqlp0rjzcnWwZ0cWHjbEZTb6v9HaxJzzI7S86EE1B0+y+WwNZ8U2i/2AlzN+NonIT6QXqBUwaHb/ugIDM5ulquVys1qXaC1DGWG4D+zTqw/YMcsdoEMSkaFgubTBanD1aoRDl7qRcDAL6NqFYlo5Oa6NtGyc+f2AwRoNgyofRnD5bovWSdHR0WihLliwhOTmZ1atXczi9kGqzQkQ9+g+xsbFERkayevVq1fOUlZXx8ssvk6W40DvIWfUm/4033iA5OZndu3ernmvTpk3Exsaybds21THR0dEcPXqUpKQk1THr1q3DycmJdu3aqRofGRlJQUEBH374ITfeeGO9411cXEhMTGT9+vU8/PDDDSqv17l8GrrBb2hcXbaY5zOqqy9p+WWcOlvaIDFTQHXcNV182J+cR3GFqdHdL6xcnQmIsnxLH3wT6D9Y6dYShCjtXcGzQ6txwrD2G2luwZkeAzYOjW7R6mhnpFuAKwdStNaBGAzZ8VDWuvrGdyflEh7kjovuI66j8xc6eDsTOXMQVdVmpnwYTUquessxHR2dqwcXFxfCw8OZMmUKB2uuRSKC677msrGxwcnJiZdeekl1IsFkMmF08wUHNwZ3UX8yn5+fz4IFC6S0HJKTk3nmmWeYOnWq6ph9+/axdOlSVZoMAKdPn0ZRFPbu3XuufaUuFEVBURSOHz/OzJkzVWkJdOzYUVr0sDVRWVnZoDiz2czhw4el46qrq9m8ebN03KFDhzh27Jh03KpVqxq0WV+xYoWqcSNqWiN2nMjhxx9/JDk5WXoutdaiA9p7YjIrxKUVsGPHDg4ePCg9V31cnQmIJnTAsBJqTUC0BB2IjNZRARGXXoCPqz2+bo0j/Nhg0vaDfwQYG/+DoHewBwdTCv6iLtvsBA+y3KburXtcC6LCVE1MSj4D2+snAjo6lyLM35XPZg6iqLyKyR9GkZZfv3Wbjo7O1YWrqyvvvvsuRqORuLQCAtwd8HWt+5rL1taWxYsX06FDB9XzVFVV8bfJswDoo9K1SlEUhg0bxty5c1XPA9C/f3/+9S/1HdyFhYXMmTOHhx9+WHVMeXk5O3bsUF39IIRgxowZuLq6qp6jNdDQk3ewbOxlXECsGAwGZs6cKWW/eX5cfr7coV9+fj6PPPKIdEXD9u3b+fDDD6ViTCYT8+bN4+zZ+t2s2nk5EeThyM7jOSQkJLBkyRKpucAihnrixIl6x0XUtGUdSs0nPj6e119/XXqu+rhKExBN54Bhxc3BliAPR+2FKP16Ql4SlGtYiaGSw2mFhGstQGmuhjMHG739wkqf4DYUV5g4mV3cJI+viqB+IIytSojyUGoBlSazrv+go1MH4UHuRN4/iIKyKiZ/EMWZAj0JoaOj8yezZ88+Z3+YdLaUTj71azNYLR5lcHd3p+/oO3CwNdDVX90m3GQy8fHHH2OQ0GYzm8288847UjGurq5SyQeAsLAwKavJK5WioiJmz55dq8VnXfTq1Ysnn3yyQZvZkpISJk2aJFVhIITgzJkz0q/dsrIytmzZUqc15qU4e/YsCxcupLBQ/X4rKyuLvLw8VckEIQTDO3vzx8kckk6dYvny5aSmqjcZKCgoICMjg9dee63esV4u9gR5OHIotYD4+HhWr15NSkrjuuddnQmIrHiwdQb3kCadJqylOGEAZB3Rdh31UFZZzfGsIu0FKHMSoKqk0R0wrPQOsZwEHNBSiNLO2fK6SInWbg2S7E6yZL4H6BUQOjp1EtHWg89mDiKvpJLJH0SRWaihDpGOjk6Lok+fPw9XTp8tqdd+E6Br167Szgre3t7EZZYS0dYDG6O6rYatrS3e3t5S8xgMBpydnaViZJw8dP6Kh4cHQUFBhIWFMX/+fIqL1R+m2draMnDgQObNm8dXX30lNW9AQAA7d+5k48aNUnEODg788ccfJCQkqI4pLS3FwcGBH3/8UbU+A1gSaIqisH37dtUxaWlpeHp6EhsbS1lZ/QcGw7p4U1huIqPSHicnJ3btUq/nduLECQICAkhMTKSkpH6tqIi27hxKLaCkpAQ3Nzeiohr30PLqTEBkHwWfsCZzwLAS5u/KyexiKk3qX8CNjn+45baFO2HEZxRiVqCH1voPafstt43sgGGlg5czbg422gpRgqUNI20fVDeNuExjE52US5ifK22c61aR1tHRsbR6rZw5kJxiSxIiS09C6OjonEd+aSX5pVW095LbvKulvKqaI+kF9AlR136h03yUlJQ0WI8BYM6cOTg5OfHxxx9LnfYD3HHHHQwdOhRfX/W2rAALFiygV69edOsm1zq/efNmnJ2dCQ0NVR0zYsQIXnzxRfr16ydVWfPJJ5/Qpk0bbrjhBtUxPXr04PXXX2fYsGE4OjrWO35oJy8Aht0xE19fX+644w7Vc/Xs2ZNFixbxt7/9TVXSLqKtB8m5pbz8+lt4eXkxYcIE1XOp4epMQGQdbXSBwUvR1d8Vk1khMUfDcnu3IHBs0+ITEHHpljcx7R0w9oOdK3h1bpKHNxgEvUPaaGvFCRYnjKpSyGzZrwsAU7WZ/afzGNBBd7/Q0VFL35A2fDJjABmF5Uz+MIrsogqtl6Sjo9NCOH3WIlSrpgKiIZzIKqaqWiEiSE9AtDQyMjIYNmwY9vb2eHt78/3330vFu7u7ExkZyWOPPcZDDz1EVVWV6thHH32U9957j6eeekpKT2LEiBHMnj2bDz74QGqtAwcOxNPTU6oCwsfHh9GjR7Nlyxapudzd3enZsyexseqvq52cnOjTpw8xMTGqxnu72NMtwI09yfl06tSJkydPqp7Lzs6O0NBQ1c+FVQfiaGYJbdq0kdbgqI+rLwFRmgvFmeDTdPoPVrr6WzbT8Wc0bMMQAvzCW3wC4nBaAR5OFt0MTUmPgcDeTVod0zvYg4TMIkoqNKw+CKlRmE5Rb3WlFUfPFFFcYWJgBy+tl6Kj06ro396Tj+8dQHp+OVM+jCKnWE9C6OjowKkau9723k1TAZGYY3n8Tr5N8/g6DadTp07s3LmTRx99FBsbG+bOncudd97JN998Q0WFus+Im266iaeffppevXoxbdo01ckEIQQ9e/ZkwIABfPLJJ1Lrvuuuu/j2228pL5er6LvjjjtYv369VExERARxcXHSoptDhgyRaosA6N69u5TLR98QDw6lFtAjPFzaHSQsLEy1w4e1JT42rYBOnTqRmJgoNVd9XH0JiOx4y20zVEB09HHG1ihagBNGhEUDogWX28elFxAe6K5tb56p0pKoaSIBSit9QjwwKxZhRc1wb2upjmkFOhDRSRZ1YN0BQ0dHnkEdvfjo3gGk5JVyz/JocksaXnqro6PT+ikqKuL7rZbP/hBP9RUQ69atU6XWD5CUXYIQQFF2g6wQV6xYIb35i46OlrYLrK6ulnYuAMtzkZ6eLhWTmJjIN998IxVTXl7OokWL6n0uysrKSEpKoqysjHXr1jFx4kQOHDhQ63g7OzveeOMNNm3axOHDh3niiSfYtGkTzz77rNT6Fi1aRGhoKKdOnZKOy8uTa0V2dHRk7ty5ZGdnS8Xdfvvt0i0fBoOBJ554QrrF5MYbb6Rt27ZSMXZ2dsyYMUP16z08yJ2ichODrx8n/Xv5+fkxfvx4VWPdHW3p4O3ModR8Jk6ciItL/YK1Mlx9CYisGgeMZqiAsDUa6OTjwrEMjR0o/MPBVA656kt1mpNKk5ljGUX00Lr9IuswVFc2eQKid9saIcqUFtCGkdzyExC7k3Jp5+WEv7vG9qw6Oq2UIZ28WDF9AEk5Jdy9PJr8Uj0JoaNztRIfH8+BE2n4uzngYGtUHffyyy9jNKobn5hTTKC7I9u3/srevXKW3xUVFbz22muq57LywQcfkJOTIxWzY8cOtm3bJhVTVVXFs88+K22x+dRTT0mJeVZWVjJhwgScnZ3rfC5iY2MZOHAgEydOpHfv3mzdupW///3vRERE1DtHz549EUIwdOhQli5dyptvvql6fWCpaFi0aBGdOnWSivPx8eGpp56SigGYOXMmwcHBUjFBQUHMmDFDeq6HH36YNm3kWn/Dw8O55ZZbpOeaN2+e6td7eI1WnmNgKMOGDZOaRwjBvHnzVI/vGeROXFoht956K127Nu6++epLQGTHW3r83eUyVA2lRTlhtNA2jITMIqqqlXN/VJqRXtOD1UQOGFbaONvR3suJmGSthSgHQ2EqFKi38WluzGaFPady9eoHHZ3LZFhnbz6c1p+T2cXcsyKaglL1fbs6OjpXDseOHUO4+khVP5jNZgoLC/HwUKfpkJRTQkcfZ2JiYv7ivKGGmJgY+vaVuw5TFIU//viDoUOHSsWtW7dOSsgP4JtvvuH666+XSkBs2bKFsrIyxo0bV+9YRVHYsmULkydPZtCgQbVu1M1mM2+99RYDBw48pwVw4MAB3n77bYYPHy4loKjTegj1d8HGIIhLa/oq6g7ezqQXlDWJmcLV9+rMqnHAaKZS/zB/V9ILyiko0/BizzsMDLYtNgFxON3yR6S5BWfafnD0BI92TT5Vn5A2xKTkoyhKk89VK8EDLbctWAfiRHYxeaVVDOigJyB0dC6Xa0J9+GBqPxIyirl7RZReCaGjc5VhNps5duwYip0T3q7qXKXMZjMnT56kQ4cOqsYrikJidgntPR2lExAVFRXs2rWLIUOGqI4xmUwcPnyYwMBAVU4CVs6cOcPPP/8s5Vpw8OBB3nvvPR566CHVMe+++y5PP/00b775pqo24y1btjBmzBiEEDz33HN1jp09ezalpaWUlpaye/duqd9fp3Vib2Mk1M/1nHh/U9LOywlFgdS80kZ/7KsvAZEdD75N335hpau/JUOakKlhFYSNnaXlpIUmIOLSCnGxt6GdRDa+SUiPsbRfNENyqnewB9lFFaQXaGiP598TbJ1atA7E7iSL6u4gPQGho9MojAzz5f1p/UjILGbKh7omhI7O1cSGDRuIjIykoMyEu4Ot6rjbb7+ds2fPcvTo0XrH5hRXUlxhInbXrxw7dkyqxeGnn37i1VdfJTY2VnVPfFVVFddccw3FxcWkpqqv6LzjjjsoLi6W0o2YN28ee/fuVT2PoigsWbKEEydOUFBQ/4m1oijMnz8fLy8vRo8ejdlc+8mzwWDAwcFBW+00HU0ID3LjcFpBkx9iWqukTufqCYjLo+QslGSDT9MLUFr50wlDax2InpAZp+0aaiEuvYDugW4YDBq+iVaWWqpjmrj9worVG/uAlnacRlsI6tfiExB+bvZSpaI6Ojp1MyrM91w7xpQPoziru2Po6FwVBAcHc+rUKaoMdrRxVlcBYTAYqKiooKSkhNDQ0HrHZxVZDlacDVXk5+cTFhamen2enp5kZGQQGhqquifewcGBvLw8AgMDpQQACwoK8PX1pX///qpj0tPTCQ8P57rrrlM1Pjk5mbS0NP7zn/8wePDgesdv2bKFUaNGceLECR588EEpzYjm5syZMw3aAFdWVnLkyBHpuPj4ePLz5a+Zd+7cKR1TWVlJVFSUdNzvv/8uHWMymaTXGB7kztmSSjIK5Q4xy8rKiI5Wf80fUmPTuyVKTtxVDVdXAiK7JnPbjBUQAe4OuDrYtAAnjHCL/WhxlrbruABTtZmjZwq113/IiAWluskFKK109XfDzsbAgRStdSAGwplDUFmi7TougaIo7E7KZWAHLz3Dr6PTyFwb6sOK6QM4dbaEyR9GkV2kJyF0dK50OnfujLO7FwoCDyf1FRDt27dnwYIFqpIC1qqqIC93Jk2apEoM0Yqnpyft27fn0UcfVR0jhMDLy4v//ve/qmMAjEYjn376KXZ26hIxYEnGrFu3Dnt7e1Xjo6OjWb16NTNnzlQ1/tprr+Xf//43bm4ai7KrYM+ePaxYsUI6LiMjg/nz50vH7du3j2XLlknHLVq0SKoyBiAuLo533nlHeq7//ve/0smV2NhY3n33XamYjt4WR4qo2BNScVFRUXz88ceqx/u42ONoa2T9pu3SAq/1cXUlIM45YDRfBYQQgq66EGWtJOaUUF5lJlxrB4z0/ZbbwOapgLCzMdAzyJ0YLSsgAIIHWRIvafu1XcclSMktI6OwnIF6+4WOTpMwvIu3xaIzt4zJH0adO7nU0bmSEUI4CCHuFEK8JYT4SgjxqRBirhCih9Zra2o8PDx49KlnLP92Ur/xvuGGG5g4caKqsdYERKe2fixatEhqfV5eXrzyyis4OMi5Xr3yyiu0ayen37Vw4ULCw8NVj6+urmb58uUEBASojhk3bhx33XWX6vG2tuqTQpfLli1bSEtLa3C8ra0tjz/+OImJiVJx6enprF+/nj179kjFxcfH89Zbb1FRoT5ZrigK+/bt4/3335eaa+/evaxdu1a17ax1rl27dvHRRx9JzbVz506++eYbVS06VgLdLQmwdb/IObj8/vvvrFmzhspKda2XQgiCPOzJKYO1a9dKzVUfV1cCIjse7N3ALbBZpw3zd+VYZpG2goN+NW+yLSwBYVVx1VyAMj0GXAPATf0Hy+XSO9iD2LQCqqobX11WNW0HWG5bYBtGdJLljV93wNDRaTqGdvLm4xkDSM8vY9IHUWRKlnTq6LQmhBAvADuBIUA08D6wBjABrwghNgkh1B/Zt0LuuudeANpIJCDmzJmjuiXCmoC4/aa/0aVLF6m1+fr6Sm3YraitMDifO++8U2q80WiUatcAcHZ2lhrfnHTq1Inw8HBefPFFysrKpONtbW0pLi7mvvvuU63XAZbWDUA6OXXs2DFycnL44osvVMekpqaSm5vLJ598IpW42Lt3L9XV1URGRqqOSU5OJiMjg9WrV1NVpd54YNeuXVRVVbFmzRrVMdmnE1AUM1GxJ6T2ltu3b6eoqIgff/xRdYyTuRSjhz9fffWV6hg1XF0JiKx4ixhjM5dzh/m7UVRu0lZw0MkT3Nq2OB2IuLRCHGwNdPTW+E06bX+ztV9Y6R3sQYXJTPwZDatjnDwtLikt0Aljz6lcPJxs6eLrovVSdHSuaAZ39GLlfQPJLChn0gdRnCmQvxjV0Wkl7FEUpZ+iKE8qirJKUZTNiqJ8ryjKm4qi3AzcDajfmbdCiistGxaZFgyZk/nckkoMArxc5R0ZDAZDg1ou9TZNedq3b8/EiRN5/vnnmTt3rvQhqbe3N5MnT+b222+XiuvcuTNTpkzhoYcekppz/vz5dOzYUXUlDoCdnR0LFy5k7ty5Umt85pln6Nixo1Riy9HRkQULFrBgwYI6xUMv5KWXXiI0NFTq92of0hZHpYKIoaMwmUyq415++WVGjBjByJEjVcf0CPHFwSuI559/vlEP0q+uBET20WbVf7BidcI4lqG1EGV4y6uASC+gW4AbNkYNX4rlBXD2eLO1X1g5J0TZEnQgUqJB4g2zOdidlMuA9p7aipPq6FwlDGjvyaczB5FdVMHE96NIy9eTEDpXHoqi/AAghJhw4c+EEBMURclSFGVv86+s+bDawrs7Nk25/9mSSjyc7DDqn90tnueee44777yTbdu2kZmZKRXbu3dvXnjhBTZs2KC6OgagZ8+eXHvttRw+fFgqcRQREYGtrS0Gg/r9gp+fHz169CAjI0O1bgdAx44dMRgMUramvr6+BAcHU1RUJDVXhw4dqK6ultL98PPzw81oIrdcLjnYtWtXioqKcHdXX3Ue1tYbs8GG0uqGJQdr4+pJQBRnQ+nZZtV/sBJWk4A4quVJN1h0IHKOQ1XLuLA0mxWOpLcAAcozNequQc1bARHk4Yi3iz0xKRrrQIQMhvJ8SxKmhZBZWM6ps6W6/aaOTjPSr10bPps5kLySSia+v4uUJrDe0tFpITyr8r4rjmqz5RTTpokSBIVlVU2W3NBpXEJCQvjiiy/497//zbhx46Q0DwBCQ0PJzc2VFijs27cv+/fLa4917NiRpKQkqZi2bds2SOvCy8uL3Nxc6ZjGFmusDU97hbOShfUuLi4UFxdLxVi1YrIKGles/upJQGjggGHFzcGWIA9H7YUo/cItgoNZ9fs4Nwenc0sprjDRU2v9B6sAY0DzJiCEEPQJ8dDWihMsQpTQonQgdidZ3vR1AUodnealT0gbIu8fRGFZFZM+iCL5rJ6E0LlyEEKMFUK8AwQJId4+7+sTLDoQVzzW8nDZ08zc3FxVve3VZuVccqOioqJB1onZ2dlSZewAxcXFlJTIb5KysuTd4fLy8qQ0BcBityi7wQfIzMyULn1PTU2lqEjdnsPGxoZx48bxzDPP8MADD0iv7/bbb+ePP/6QigkPD5euuABL9URGRoZUTHBwMOXl8i3woaGh0q9dPz+/BrUpBAcHS7+eAtzsKKo2SunIGQwGvL29peaxJhOLK9TrfKhaS6M+WksmK95yq0EFBNQIUWqdgLA6YbQQHQirAGWPluCA4dEOnL2aferewR4k5pSQX6pOkbZJ8OoMjp6Q3LISEM52RroHtHwrKh2dK41ewR6semAwJZUmJrz/Byey5E5MdHRaMOnAPqC85tb69S1wg4brajYKCi3XorL1D7Nnz+bo0foPsExm5Vz7RXR0NE8//bTsErn++uulhPwAPv/8c2m3A7PZzDXXXCMVA7BgwQK2bZNzIIiLi2P27NlSMYqicN1110k5JCQnJ3PjjTdy+PBhqbkmTJggJbpo5fnnn+eWW26RinFwcOC3336Tnutf//qXlH4BWCogVq9eLT3Xxx9/LC2iOmzYMJYsWSI91+bNm6XaNgCuG9IPBUF+qdzfyfbt26XGu9doxXTvM0Aqrj6ungRE9lFwcAdXf02mD/N35WR2MZUmDfvs23QAO5cWowMRl1aAndFAF19XbReSHgNBzav/YOVPHQgNqyCEsFRBtKAKiD2ncunbro222iA6Olcx4UHurJ41mGqzwsT3d3EkXWMNIx2dRkBRlIOKonwCdFYUZeV5X+sURdFYkKl5KCu3tOHKtnMXFBSo6lM3n5eAyMvLw8PDQ3qNlZWV0huyzMxM/Pz8pGKysrKkYwBOnDhBp06dpGL2799P375y15qHDh2iffv2qp7DzMxMkpOTuemmm3j77bcoILJzAAAgAElEQVQZPHiw1FwATk5O0jG6AKg2uDpYEgNF5XIJCFmsFRAFkomO+miUq3shxI1CiGNCiBNCiGcu8XNRU+J2QghxSAjRV21so5EVb6l+0OgPpau/KyazQmKOhidJBgP49YCMFlIBkV5AmL8rdjYabjJLciA/udkdMKxEtPVACI0TEGARojx7HErkywMbm/zSSuIzinT9Bx0djenq78aa2UOwszEw6YNdxCRfFfsznSsYIcR3Qoiba/lZRyHEYiHEfZc5R4u+JrZaLhokr4cLCwtVideZzmvByMvLo02bNlLzKIrSoDL2zMxMfH19pWJSU1MJCgqSnuv06dO0a9dOKkY2AaEoCmvXruX//u//VI295557uPHGG3n77be57rrrpNam0/pwdbABoKi8aTvHziUgylpYAkIIYQSWAmOB7sBkIUT3C4aNBbrUfM0C/icRe/koimYOGFbCzjlhtAAdiMw4y3OiIYqiEJdWSLjm7RcxlttmdsCw4mJvQ6ivawtIQNToQKRqb8e555RlkzOwQ/O3xOjo6PyVjj4urJk9BA8nO+5ZHk10ovZJSh2dy+ABYARwVAixRwixUQjxmxAiCXgf2KcoykcNffCWfk1sMpk4dMhSBSsjzPfHH3+Qk5OjSgCw2qxgMAjS09PZvXs3hYWFUr303333HTY2NsTHx6uO2bdvH/Hx8WRlZalOXhQXF7N69Wrs7e2l9Ai+/vprqqqqpMQQv/nmG7Zt2yblqvDmm28SGRlJ586d6x27adMmNm/eTFVVFcHBwarn0Gm9/FkBcZUmIICBwAlFURIVRakEVgO3XjDmVuBTxUIU4CGECFAZe/kUZ0FZnmb6DwAdvV2wNYqW4YRRUQj5pzVdRmpeGQVlVfTQ2gEjPQYQENBLsyX0CfHgQEp+o/rrShPUFww2LaINY3fSWexsDES01fi1oaOjA0CwpxNrZg/B392B6R/v5veEbK2XpKPTIBRFyVAUZS7wFpbN/4vA40APRVH+pijKhsucokVfE9vY2BAdbTloMErYGe7fv5+TJ0+yfv36esdWmxWMQuDu7s4HH3zAZ599hqur+lbbNWvWcOTIERITE1XH5Obm8uuvv/Ldd9+pbglwdnbmo48+4uuvv5ZqPdiwYQMnT54kISFBdczJkyeJi4tj586dqmOSkpI4deoU2dl1v9+azWaWLFnCa6+9xqFDh6R1CxoTWd0OGW0LK2fPnpW+XjabzQ1yp2iIQGlDxDWrq6vr/X++kD8rIOSe84yMDKnnz9ZowMnOSHpO4x6UNkYCIghIOe/71Jr71IxRE3v5aOiAYcXOxkAnHxeOZWjcR+sfYbnVWAficLrlTSe8JThgeHcBB+0qMXoHe5BfWsUpLdXmbR0tSZgU7Ssgdifl0jvYAwdb9b7SOnWjoiT4aSHEgZqvOCFEtRBC74HROYe/uwNfzh5CB28X7l+5l18OyymR6+i0MPyAr7AkH/yBxvInb/HXxKFhYQAEBAaojhkxYgQAU6dOrXesnY2Bqmozzs7O9O7dm6lTp2I0qv88Hzx4MIGBgYwZM0Z1TL9+/QCYNWuW6hghBL1792b69OlSCZKwsDB69OjB2LFjVccEBgbi5+fHnDlzVMdUVlYybdq0elswioqKWLt2LU899ZRUhUVjc/ToUb799lupmEWLFlFZKSfC/s4770jbam7evJlNmzZJxZSWlrJw4UKpGLAIlMo6Wvz222/89NNPUjEudpa/KdkKiGXLlklbmbrYGYiOadx9Y2MkIC6VarwwtVLbGDWxlgcQYpYQYq8QYq9slojCdBAGTSsgoIU4Yfh2szwXGutAxKUVYjQIuvprKECpKBYHDI3aL6z0CbH0R2reXx08CNL2gUk7R46SChNx6YUMbK/x3reycf2OtURNWa+iKK8pitJbUZTewLPANkVR5Aywda54vF3sWf3AYLoHuvHQ5/vZcEDeW11HpyWgKMp8LC0QK4B7geNCiJeFEHLKghfT4q+JI7qFAlBaqd5WLzw8nBtuuIHQ0NB6x7rY21BUYdkUDRs2jOnTp0utb8iQIUyfPh0bGxvVMZ6enowdO1baIaF379488sgjUjFhYWE89dRTGCQqSAICApg/fz7Ozs6qYwIDA3n77bfrHefu7i6ts6EWRVGIja1/41ldXc2MGTOkkgmpqam89957pKenq44pKytj6dKlqtxYzmfp0qXExMRIxaxdu5ZffvlFKqawsJDIyEj2798vFbdy5Up27NghFXNov+XAMK9EvcWooiisWrWKrVu3Ss1lLiviTJZ8BUldNEYCIhU4v+GoLRabIzVj1MQCoCjKB4qi9FcUpb+Pj4/cCntPgefOgIucOE1jE+bvSnpBeaP30Uhh52SxXdS4AiIuvYAuvi7annIXnYHiTM0cMKx09nXB2c7YMnQgTOWavjb2J+dRbVYYqLUA5ae3wZpp2q6h8ZAt650MfNEsK9Npdbg72RJ5/yD6tWvDY18eYM2elPqDdHRaIIqlDjmj5ssEtAHWCiFevYyHbfHXxAP7WCzZCyWuRY1Go6rNMFgSEMU1p7KPPPII3brJHf5FRETwwAMPSMUAvP3221JJAbCsr2tXueroIUOGMGXKFKmY8PBwqeoMgLlz56oS/WwqTp48ybhx49i9u/7K2DfffJPo6GgpR4x//etfVFRUkJqaqjrm008/JScnhyNHjqiOOX36NN9//710AmL58uUkJiZKtW6sWbOGsrIydu3a9Zf7f4rLYNDLm0m+RKVzUVER69atk05AfP3lKgBOnkpWHbN3716OHz8ubSFr/unfnPj0OYqKGu8QvTESEHuALkKIDkIIO2ASFj/l8/kWmFaj/DsYKFAU5YzK2MbB1kEzBwwr1tP+hMwWIESp4SbTIkBZoL3+Q1pNhlIjBwwrRoMgoq0HMcktIAEBmupA7E7KxWgQ9G3XNNl8VVQUWypjPC/3IKzFoLqsVwjhBNwIfN0M69JppbjY27ByxkCGd/Zm7teH+GSnXDmnjo7WCCH+IYTYB7wK7AR6KoryENAPqN92oHZa/DVxSIAlYVEo2TuupvoBwMXBhpKaCgi1Medja2tLhw4dpOPUiDVeiKyVJkBQUBB2dnZSMd7e3tIxDbHEbCxWrVpFjx49iI2Nrbftxmw2U1xcTMeOHVW32pjNZvz8/Ojfvz/l5epP8Nu1a0fbtm3x9vZWHVNQUED//v3p00f9tX5ZWRm9evXixhtvlNJ0aN++PUFBQRcJgRZXmMgsvHRbRmZmJqNGjWLw4MGqnwtFUejazVLIqpjNqtdXXV1NeHi41HNRUlLCoIEDGDt2LGfOnFEdVx+XnYBQFMUEPAr8DBwF1iiKclgI8aAQ4sGaYRuBROAE8CHwcF2xl7umlkqYv0VnIF7rNgz/nlCQDGXabHiziirIKa5sGQ4Ywmh5PjSmT4gHR88UUl6lviSy0XELAPcQSInSbAnRSbmEB7rhYq++9LLRSYkGswnaD9duDY2L6rJe4GZgZ23tF5fVCqdzReFoZ2T59P78rbsfL3x3hHe2HNdWSFdHRw5v4A5FUW5QFOUrRVGqABRFMQPjG/qgreGa2K1GvK6pqnFd7G0oqaym2qy/H7RWsrKy8Pf358knn6w3cWIwGKisrGTx4sXcdtttqh7fYDDg5eXF3XffzejRo1Wvq0uXLoSHh3P33XerjomIiEBRFP75z3+qjnF0dKR79+7ccMMN9OjRQ3XcNddcg4eHBxMmTPjL/dU1SQKj8eLLsc6dO+Pr68t9992Hg4ODqnmEEAwdOgyATp06ql7f4MGDsbe35/7771cd4+zszIABAxg+fHiDEoq10ShX+YqibMTyhnr+fcvO+7cCXLLJ6lKxVyqB7g64OtgQf0ZrIcqaDXdmnCabrLi0FiJAmb4ffLtbBBg1pnewByazwuH0Avq107D9IGQQnNph0cdo5oqhClM1B1LymT5Ezlu70Tm1w+IIYq0Iaf2oLuvFcuJWa/uFoigfAB8A9O/fX7+6vMqxtzHy3t19mbf2EG9sSiCvtIr547phMGhbbaijUx+Kojxfx8/kGswvjm/R18RWW73Csqax77Oq85dUmnCrsQrUaT188cUXrF+/nn379qneEG/cuJGnn34aW1v1/98HDx6USiQAJCYmNqg6Jj8/Hzc3uUPPrKwsaUeRvLw8PD0vvoavqrZcLtnW8tlYUFCAh4eH1Fz5hZa9pOzHbUlJiXR1TUlJiZR+iRoaowVDRyVCWEQXNReitCYgNBKijEsrRAjoFqBhBYSiWCoggrRtv7DSO8TyxtMi2jCKzkBB8/d1H0otoNJkZoDWApSndljacuxdtF1H46GqrFcI4Q5cC1yuDZ3OVYSt0cDrE3px79D2fLQziblfH8JUrb4kVEdHp3lxdbAmIJqmAsKagCgo1VDvTKdBFWmbNm3itdde45tvvsHLy0vVpvP48eN4eXldcuNdF4cOHaJXr15SMYmJiXTsqP7EHyxtB0ajUUqfAiA7OxtZfZXc3NxLPg/Wz0Qb46W33fn5+dIJiMJCy17SIPl7KYoirZVSXFysJyBaO2H+rhzLLNK2VNXFD5y8NdOBiEsvoIO3s7Zl9nmnoCxPcwcMK76uDgR5OBKjuRDlQMttcvPrQOxOslT9a5qAqCyxVMZcOe0XakuCAW4HflEU5cqxANFpFgwGwcKbu/PY6C6s/X/2zjwsqrL9458z7PsmguwgAqIIrrib5pa79Wpa7mmvmvZmpi0/zbJsUbPSTG0xyzT3Pa3XUnPLBRURcQeURXbZ95nz+2PE1xKYcxQ8aOdzXVwjw7nnfsBhmOd+7vv7PZXI5DWnlR0nU1FRqRJRW4ZGLJetAbFw4UKioqIMXtfATt9VmpxdRGxsLG+/XWWzSZW8+uqrssT/AI4cOcKKFStk5xo1apTs9+Rbtmxh69atsmK0Wq0kG9O/s3LlStkWjVqtll69enHt2jVZcfXr12fHjh2yXDXq16/PkiVLZOUB+Pzzz2UXLfr06cPw4cNlxYiiyOrVq2XFAEyZMoXWrVvLivHw8OD999+/5/7y2+NIxpWMYADMnz+f+vXlGSW0bqPv0pVbgPj+++9lXQ8wfPhwWbazUlALEA+ZQFdb8orLSc6RLrpS4wiCvgsiVZkCxPmkHJoqLUCZXDcEKO+muZc9kUp3QNRvAqbWighRHo/LItDFBgcreUJNNcrjp/8A6Nt6RVEMEEWxoSiK827ft/xvbcGrRFEcptwqVR5lBEHgle4BvNM/mP/GpDL2u5Pkl9ROi7eKisr9Y2Jigq64gGyZHQqJiYmSLBPdHfQFiKTsIjQaDcePy38/ERcXh1ydIa1Wy6lTp2TnunDhArm58kajdTodJ0+elBVjZGTEmTNnKCoqkhXn6enJhg0bZOeaM2cOAwcOJCEhQXKBJTQ0FA8PD1m57OzsZOkkVNCuXTvZMZ6enri7V6qhXSXGxsa0atVKdq6goCDZXQk2NjY0bdr0nvv/N4JR+ba7ZcuWssZXAJxuC3EayZzBCA+XP17s4+ODq6ur7LjqUAsQD5kKJ4xLKUrrQDSFtAugfbgtcpn5JSTnFCsvQJl0GozMwEX+i2ZtEeZpT1J2EWl5ChanjIzBveVDL0CUa3Wcis9S3n4z/rBemNSzrbLrUFF5RBnTwZdPnw3lRHwWz319jKwC6b7wKioqtY9Go0EoyuamzIMwW1tbSRt1d/vbBYhbRdjZ2ZGTkyN7jY6OjmRlVaqFXCXOzs6kpaXJzuXm5iapsHI3fn5+xMbGys4VEhJCdLS88ecuXbpw6NAhysvlFXQ7dOjAZ599Rr9+/ZgzZ47seJWaI6eoDBMjAXOTmtt2V4x1PKqaS2oB4iET4KIvQCjvhNEMtKWQceWhpj2frP/jpXwHRKS+C8So7ggkNb+tA6F4F4RnuF6gtOThPUdjbuZSUKqtGwUI9xaPk/6DispDZ3BzD1aMaMmllDyGLD9Kcra8Ez8VFZXaQ6vVIhRmcT0zX3KMTqfDxsaG7Oxsgyf45iZG1LM2JSm7CGtra3JycigokD7Zp9PpcHR0JCUlhZKSyq0LK6OiACGnm0EURdzd3bl69aqsXL6+vvfVpREaGsqRI0dkxZmamtK6dWsWL15Mfr70/zPQuzJ4eHjw3nvvsWbNGlmxKjVHZn4JTlZmsnUoqiP7toaLvUXd2cfIQS1APGTsLExwt7fg4k2FCxAut1uEHrIORHSyvhLeRMkChE4LNyPr1PgF6H8mJkaC8joQXuEg6iBJfivj/VKh/6BoAaK0QP89P2bjFyoqStA92IXvx7UhNbeEIcv/JDZd3htnFRWV2mHRokXk3YwjMatQslVmZmYmn3/+Oa+99pqkTbC7gyWJt4p4++23iYuL4+OPP5a8vtjYWFavXs2LL74oOQbg/fff59SpUyxbtkxyzOXLl9myZQujR4/GyMhIctynn37KmTNn+PzzzyXHFBQUsG7dOqZPny5L3yItLY2TJ08yffp0iovlda2Ympoyf/58evTowdy5cykrU4VBHwZ/H3nJLCjFydrweLEcLZJbt7sLHSzlFyB0OvlC0fcTUx1qAUIBAuuCE0a9RvoRhIesA3E+KRdPRwvs7uMXpsbIuAKl+fqT7jqEuYkRjRvYKt8B4d4KECDhxENLeSIuC28nS1xspVk+1QqPqf6DiopStPVzYt2LbSku0zJk+Z93LJhVVFSUo1+/fhRnJiEKGm7mSOtOcnZ2JiwsDA8PD0nOAB72FiRlF/HUU09RUlIiS8zP398ff39/AgICMDMzkxzXp08fSktLadmypeSYwMBAgoKC8Pf3x9hYujD60KFDKSsrIzAwUHKMlZUVw4YNQ6fTydJZqF+/Pm+88Qag716RS5MmTfj1119ZvHjxfelxPCzkFkcuX74sO8fBgwdlx+zcuVN2zKZNm/7yeWZ+CU7W1T+Xjx07Jks09FahvgARceQP2etbtWqV7JitW7dy69Yt2XFVoRYgFCDQ1YZr6fmUlitoVWZkAvWDFOmAUH784oz+to44YNxNc097ohKzJZ9K1AoW9lC/Mdw49lDS6XQiJ+OzaFMX7DdV/QcVlRqlqbsdGya2w8xYw7CvjnH0qjxlexUVlZqlcePGeDvpLfVuZBVKjhsxYgSdO3eWdK2fsxU3sgppFd4OPz8/2rdvL2uNY8eOlS1S2L17d3x9fWULDr700ks0by6vI7Zp06b06tWLxo0by4qbOnUqjRo1wsbGRlbcuHHj6NOnz30VIEAvEty3b186dnx4ByxyTsyXLVsmq6Bw9epV3nrrLVnrOXz4MF988YWsmKioKFndO6C31Hz55Zf/0s2QkV9KPQMdELNnzyYxMVFynqwCfcHm0rnTstZ37do15s2bJytGFEUWLFjAxYsXZcVVh1qAUIAgVxvKdSKxGQq3pLqGQEo0PCRL0JyiMq5nFtLUXekCxGkwsdJ3gdQxwrzsKSjVciVN4Q4Zz3BIPAk13HJVGVfT87lVWFY39B/cmqv6DyoqNUxDZ2s2TWpPAztzxnx3kl1R8gTfVFRUapaXxugNjxKzpOuzDBgwgL59+0q6tombLVqdyJW0Aj788EOcnJxkrW/o0KH06NFDVoxGo+Hjjz+W7VwwaNAgyd/X3cyYMYOgoCBZMVZWVrI3waAvIHz99deYmyvYJSqRrKwspk2bRlJSkqTrP/30U958803JxZz8/HwGDRqEqal0x7SCggLGjBkjS4NBFEVeeukl2Q4pH374ISkpKXfEV0VRJCO/BKdqHN4OHDjAb7/9JvlnBpCeo9dVSbl+Vdb6Fi5cSFxcnKxxniNHjnD8+HEuXLggK1d1qAUIBQi844RRB4QoCzMgL+WhpIu5LUDZxK0OOGC4hYFG+rzfwyLMU++9rPgYhmc4lORCes1VO6vi+G39h3BfeW9QapTSAv3zQh2/UFGpFdzsLdg4sR2hnnZM/ekMq47EKb0kFZV/LC8MfxojjSCrA8LS0pJ+/fpJurZC5+t8ci5DhgyRvT4bGxt69+4tO+5f//qX7BgTExP69+8vO+7JJ5/E2lr+gUXPnj1lx4DercPRUeGDmmrQarUsW7aMRo0akZubi6enp8GYH3/8kenTp9OmTRs0VVhU/p2vvvqK8+fP4+LiInltW7duJSkpSZbOx/Hjx4mLi5M1GpKTk8PBgwcxNze/o/ORkltMSbkOr9tdR5Xx22+/YWlpyc2bNyXnOnclDrGshJws6V2FeXl5REVFYW9vL2vc49ixY1haWnL9+nXJMYZQCxAK4FfPGmONoLwTRoUQZao8S6D75XxdEKDUlunHTuqYAGUFPk6W2FuacEbxAkQb/W1C7Y9hnIjLwsXWDE9Hi1rPVSUJJ0BXBj6dlFuDispjjr2lKatfCKd7Yxfe2RnDx79clCW6paKiUjOYGhvhZm/OdRkFCEDyCbKHgwU25sacT865b+X/+4l7mLn+aRhyCcnLy2Pp0qXk5ORIHo/w8vIiPDxcVgdKcHAwQ4cOZdCgQZJjOnXqRIsWLZg1a5bkmLZt22JnZ8f27dslx9jZ2dG+fXtWrVpF/fr1AbiWpu9UaFiv6gLEgAEDGDBgABMmTJCcy9bZDU154T16E9VhY2NDv379WLBgAX5+fpLjRo4cSfPmzXnzzTclxxhCLUAogKmxBv/61ly8Ka+tp8ZxrXDCiHoo6aKTcnC1NcfZRrqoUI2TFgPakjpbgBAEgTBPeyKVdsJw9AMr51oXohRFkZNxWbTxdVL2DUCF/oNXuHJrUFH5B2BuYsSy51swvI0Xyw5c47WNUZRpFdRDUlH5hxLoYktMcu0IwwqCQHAD2zvW6yqPHqmpqYSFheHs7Iyrqyt79uyp8lpRFJk3bx7h4eFs2LCBhg0bGnx8nU7HjBkzWLFiBVOnTpW8rhUrVvDyyy/TpUsXyTHbt29n0KBBBAcHS465ceMGTk5OBAQESI4BfbdAp06dsLXVd3tXjNs3rF91t0xkZCRhYWHY2Uk/oL2RUYBQmC27K+by5csEBgZiYSH90C82NpaGDRvW6AiQdMlXlRol0NWGk7dbzxXD3A7svfQ6EA+B6ORcmrrXgfELqHMOGHfT3NOBPy5fJq+4DBtzhdxCBEE/hlHLQpQJWUWk5BbXIf0HecJQKioq8jE20vDB4Ka42Jrx2W9XyCwo4cvnW2Bpqr4lUVF5WIS42/H7xVTyS8qxNqv5370mbnasPXEdrU7ESKN2GDwqXLx4kR9//JHNmzdTWlqKv78/69atw9vbu8qYDz/8kLi4ONavXy95zGHNmjU0a9aMZs2aSV5bcnIy8fHxskVNt23bxooVK2TF7N+/n27dusmKKS0tJSMjAzc3tzv3XUvLx8rUiPrVHL5GRkYycOBAWbmupeXiYCzfVrWiACGH2NhYWR0TUlA7IBQi0NWG5JxicooU9uR1bfZQnDAKS8u5lp6v7PgF6B0wzO3BwVfZdVRDmJc9ogjnEhW2rPNsA7fiID+t1lIcj8sEIFzJAkRpASSdUvUfVFQeIoIg8Er3AOYNbsrBy+kM//o4Wbd9zVVUVGoPrVbLpk2baOZhhyjCeYn2uEePHiUhIUFynhAPW4rLdHy7ueqT86rYs2ePbPG/5OTk+7JZXL9+vSzHBtC7MPz555+yYkRR5LvvvpM9dnbu3Dl++eUXWTEA06dP56uvviIzU/8+S4rDwubNm5k0aRJ+fn4cO3aMLVu2cPDgwWqLDzk5OVy+fJk1a9bI0liIjY3lvffek3w9QEJCAq+//rqsjlmdTkfr1q1p1Eie8LyFhYVsbZCcnBxefPHFv9wXm1FAw/rW1a7Z39+fFi2kH4zml5Rzq1hHq0AvWesDeOKJJ6hXr56sGGdnZ1kdJ1JQCxAKEXRbiPJyah3Qgci8qt+E1SIXbuYiitQNBwy35voT/jpKmIdewfmM0mMYFXaUtTiGcSIuCwdLE/ydFXSeUPUfVFQU4/lwb5aNaMmFm7n8a9lREmTOpKuoqMhDo9Hw5ptv3nk/dk5iAeL3339n3759kvO09dMLSy9a87PsNe7YsYNjx+R1YBYXF/Puu+/KzrVlyxbZuUpLS2XPwwuCwMGDB1m3bp2sOGdnZ2bOnMmBAwdkxU2YMIGbN2/StWtX+vbtS7t27VizZk21MU8//TT79+9n3Lhx2NnZERoaiolJ9Z24dnZ2rFq1CjMzeePVc+bMwdXVVVZMeHg4w4YNkxVT4Y4il6FDh9KyZUtZMc7OzkyfPv0v911JzcevGv0HgFdffRVnZ2fJeeIz9Hu2gU/K6wQBmDdvnuyR5549e/LEE0/IzlUdagFCIQJd9aMIigtRuoYAIqTVnLVKZUQn6SvZio5glBVBakydHr8AsLM0wc/ZSnkhygahYGRaq0KUJ+KzaOXjiEbJ9kxV/0FFRVF6NXFlzfhwMvJLeHrZ0TuOSSoqKjWPIAg4OTmhKc3H1dZccgGiSZMmxMTESM7TwM4Cv3pWlDn4yrL8A70AoNyigK+vL0lJSbJzDR48mK1bt8qKCQ4ORqfTcfGiPKewefPm8d5771FYKL3Q6urqys6dO3nppZc4duwYkZGRkuKCgoKYM2cOZ8+epVWrViQmJjJixAhGjhxZZXeJKsZZs9zM0Y8ZN/OQZw1riPhMfQHC10Bhoy6jFiAUws3OHBtzYy6l1BUhytodw4hOyqGetSmutgp6GKdEg6itswKUd1MhRKmoQryJOTQIq7UOiNTcYq5nFio7fgFw/Yiq/6CiojCtfRzZNKk9xhqBoSv+5ODldKWXpKLy2BIQEMDly5cJ8bCTVYA4f/68rPcl7f2dEJ39iYo+L2vMoaIAUV5eLjlGEATat2/P0aNHDTo23M1TTz3F7t27uXXrluQYgIkTJ7J8+XKuXr0qOcbNzY3nnnuOmTNn8vvvv0uO8/b2ZsOGDfTt25eXXnpJ1v+BIAi88847FBcXk5mZyYcffijr50HQVLMAACAASURBVKpy/5y+rj9IbOntUKOPW9EB4VONtWddRy1AKIQgCAS52nDxpsIdEPbeYGZb+wWI5FyauNkpW11Nvi1A6Va3OyAAmns5kJFfQuKtImUX4hWu180ol/7HXConbouwKipAWVoIiRHg00G5NaioqAAQ4GLDlsnt8XCwYNyqk2w4KX3eXEVFRRoJCQkkJyfz8ssv4+9oSlxGAXnFhvXIIiIiOH78OIsWLZKcK8hBg05jwqhXZpOdLb2r8/z58xw/fpx33nlHckxeXh63bt1i1KhRsooCFy5cIDc3l3/961+SY0A/8rF06VKWLVsmK87ExISlS5fy88/yR1OaNWvG0aNH2bt3r6w4QRAwMzPD0dERDw8P2c4JKvfH6Ru3MDPW0LhBzXZ/x2UU4mprjoWpdM2NuoZagFCQQFcbLqXmKXvKLQh6HYhaLEAUl2m5kppXNxwwrF3A1s3wtQrT3FPfrqW4HadnOGhLIVlay58cTsRlYWVqRHANvzDLIlHVf1BRqUs0sLNg48R2tGvoxMzNUSz67yVl/0aqqDxmeHh4kJaWRmxsLG0auUoWvba2tiYjIwNjY+mOGX1b+YMokmHkhIOD9FNgd3d3srKyZHVN2NjYUL9+fZKSkrC0tJQc16xZMywsLMjIyJAcA9CjRw8cHBxISUmRFTdlyhS6d+/OkSNHZMU1adKEffv2sWXLFr7//nv1dfEhUlYm3zAgLy+PU9dvEephj6mxtO12erq0zr+Ym7k0ctFrpxUVFd0RGpVDfHy87Bg5hT1DqAUIBQl0tSWvuJzkHHnzajWOawikngeZKsBSuZyaR7lOpGldcMCo4wKUFQS62mBuolFeB8Lzti5CwvEaf+gTcVm09HHE2EjBl6G4g3r9B09V/0FFpa5gY27CyjGtGdLSg8X7rjJ9w1lKy2vn75OKyj8NQRB44403aNSoEa28HTDSCBy+anjzPWDAAEJDQ/Hx8ZGcy8HKDG9bDdaNWsvqgA0PD+fZZ5+Vrdb/wQcf4OTkJKsAYWlpyapVq2TlAfD09GTTpk2yN39WVlbs3LkTDw8PWVoQoP+/Gzx4MCtXrlTHKNBv8uX+/FevXi3r+vLyctluHWVlZbw643XOJ+fQQuL4hSiKTJkyxeB1haXlXErJvXNQ+f7775OUlCRrfT///DM7duyQFZOens6sWbNkxVSHWoBQkAonjDqhA1FWoLdcrAX+J0CpYAGiJA8yLj8S4xcAJkYaQtztiEyQN5NY41jX11uW1nAB4lZBKZdS82jjU7NzcbKJ/QPcW4K5wt05Kioqf8HESMP8fzVjeo8AtpxJYvTKE8rbVquoPCYMHTqU3r17Y2NuQgsve0kFCEEQmD17Nr6+8mzMB4f7Qz0/0nLlHbZ9+OGHuLu7y4pxcnLi448/llWAAGjfvj3Tpk2TFQPQuXNnZs6cKTvO3NycdevWodVqZccCmJmZGXSneNTIy8uTZTcaGxtLr169sLaW7qK2cOFCNmzYIGtdr7zyChcuyBPqf/vttzlz4xZlWlGy/sMPP/zArl27DF53LjEHnQhhXvZER0czf/58WR0aJSUlvPLKK+TlyZMAeOedd4iLq7l9olqAUJAAF30Bom44YVBrYxjRyTnYmhvj4WBRK48vieRIQKzzDhh309zLgejkXOVP/jzD9QWIGmz3O35b/6HCpksRinP0uiB+NettrKKiUjMIgsDUJxuxaGgoEdezGLL8KEnZCuviqKg8BhgbG9/ZOHf0d+ZcUg63CkoNxg0ePJjAwEBZufqGNAAE9kTLG1Xw9fXl6aeflhUDMHbsWKys5IvzjR49WnYMQLdu3e4rzsTEBBubx1f8WqfTSRpr0el0fP/99wQEBEguHO3fv5/WrVvj6ekp2f5z8eLFzJgxgxYtpO8Dli5dytKlS/Hy8pIc8+uvv/LRRx8hugZjaqShXUPD73MTEhJ4+eWXMTIyrOlQMZod4mbLiy++SHl5uawCxKJFi7h69Sr5+fmSY2JiYvjqq6/IysqSHGMItQChIHYWJrjZmXNJ6QKEc2N9G3otFSDOJ+XQ1F1pAcoz+ttHwAGjgjBPe0rLdVy4qXCHjGcbKEiv0Q6Z43GZmJtoatyaSBbXj4KoA1+1AKGiUpd5uoUH349tw82cYgYtPUK0RNV+FRWVqqnY7HUKqIcowpFrhjeLGo1G8oavgkYuNgS4WPNz1E3Za7yfU36NRoNGI397o1pQPjiZmZmsXbuWkSNH0qJFC4qKDBeMP/vsM8aMGUNwcDCdO3c2eL1Op2Pbtm3cunWLgQMHSlqXTqcjJycHV1dXmjeXvg9wd3cnODiYRo0aSY4JDg6mYcOG6FyDCfdzxNrMsGaKvb09rVu3ZuzYsQavjUzIxsvREnsLY55++mmee+45WQW3IUOGEBoaSvv27SXHeHp60qlTJ6ZOnSo5xhBqAUJhghrYKu+EYWIO9QIgNbrGH7pMq+NCSp6y4xegP+m28wIrefOEShJWV4Qovdrqb2vQjvNYbBYtvR0kC/PUCrF/gLG5vsCioqJSp2nvX4/Nk9pjaqRh6Io/2X8xTeklqag8FjRzt8PG3JjDV+SJMMqhb4gbJ69nkSpzDENFOURRlCUCCnqRwnHjxrFlyxZWrlyJp6dntdcXFxeze/du+vTpw5w5cyTlyM/P57fffrsTJwVRFNmyZQsHDhyQ1bGybds2Pv74Y8aPHy855vDhw3Qb8Cy3dOZ0C6ovKUan05GSksJnn31m8NrIhGzCPO0xMTHh0KFDzJgxg5CQEMnri4yMpGfPnvTv319yjKWlJQkJCXWnACEIgqMgCHsFQbhy+/aeQRdBEDwFQdgvCMIFQRDOC4Lwn7u+9o4gCEmCIETe/pD2THqMCHS14Vp6vvJt9q4htdIBcSVV/701cVPaAePUIzV+AdDAzhwXWzPO3FBYB8I5CMzs9B0DNUB2YSkXU3IJ91Vw/AIg7g99ccVY3mmOioqKMgS42LB1cnv8nK0Y/0MEa45fV3pJKiqPPMZGGto3dOLQlYxac1bo20zvtrHnnPwuCBVlSElJoXnz5ri4uNCkSRPmzp1LSUnlluzl5eUsWLCAcePG8eqrr7Ju3TqDow5lZWU8++yz9OrVi23btknqfgCYMWMGkydPpnfv3tjbS+uiXbduHW3atCEwMBBbW2n7kbS0NCIiIujTp48s55fVq1fjGd4bQHIBoqKYYqgLJzW3mJs5xfoO6dJSLly4QLNmzSSvDeDAgQM88cQTsmKio6MJCQmp0S6hBz1+fAP4XRTFRsDvtz//O+XAdFEUGwNtgZcEQQi+6+ufiqIYdvtj9wOu55EjyNWGcp1IbIb0WZxawbUp5CZBYc3N9wB3WmUV7YDIT4fsG3qxwUcIQRAI87RXvgNCY6TfqF+XZxlVFSfishBFCPdV0Ic6Pw3SYtTxCxWVR4z6tuasf7EdnRvV4/+2RvPRnovodKodnYqKHAoKCv7yeadGziRlFxGXUVBFhH7DWNUGtDry8vLwr29DoIsNuySOYRQWFsp2eRBFkZwc+eNZt27JP+SRqm/wdxITE2XH5Ofn35f43549e4iIiKCkpARRFDl48KDBAlNERATDhg0jKCiIZ555BltbW+rVq8eCBQuYPXt2peM3JSUldOzYkdTUVE6cOMH7778v6XT9//7v/wgJCWHGjBmSR21Onz7N1atXmTRpkqTrQf+8WLJkCbNnz5YcA7B+/XpeeOEFWeM8OTk5pKWlcSnPFP/61ng7SRuN2Lt3L4MGDTJ43bFYveNHS28Hzp49S7t27WSPG50+fZqOHTvKiqnIVZM8aAFiIPD97X9/D9zz0xNF8aYoiqdv/zsPuADIk7V9jAm844TxeApRnkvKwdrMGF+Jv4S1QvJp/e0jVoAAaOHlQHxmIRn58v/o1yg+HSHzKuTJE5GqjONxWZgZawj1VFD/Ie6g/lYVoFRReeSwMjPm61GteD7ci+V/XGPymtMUlqqWdCrK8qh0Bet0Opo3b/6X9vouAc4A/HYhtcq4jz76iLVr18rKlZOTc2ezM7iFOxHXb3El1fD73ddee41ff/1VVq64uDj69esnKwZg4sSJ/Pbbb7Jizp07R79+/WQXSWbOnMnChQtlxcTHx9OvX787bgdSBQeTkpJYuHAhzZs3Jzw8nP79+9O9e3ciIiKqjHF1dWX69OlERUVx9OhRVq1axdmzZ6s9nTczM2Pjxo0sXLgQKysryRviN998U7a9ZfPmzdmxY4esTbcgCOzfvx8PDw9ZuaZMmSLJFvNu7Ozs2PXbHxyLzaR7YxfJcV9//TVt27Y1eN0fl9JxtDKlqbsdrVu35ttvv5W1PoBDhw5J7gKpYNSoUUyfPl12rup40AKEiyiKN0FfaACq7TURBMEHaA7c7ek3RRCEKEEQVlb2Yv2441fPGmONoLwThsvtAkQN60BEJeXQxM0WjUZBcZ/ECBA04Bam3Bruk1Y++i6BiHiFxzB8Ouhv4w8/8EMdj8ukuZc95iaG1X5rjdgDYG4HDR6954SKioq+bfz9QU2Z3S+Y/8akMHTFn6TkqPPlKorySHQFazQagoODOXfufwdOno6WNPOwq7ZDoUePHrKLAnZ2dtSrV4/Lly8zpKUHpkYafjxmeHRq2LBh/PDDD7Jy+fn5YWlpyalTp2TFzZo1i1mzZskaPwkNDaVz58589NFHsnKtXLmSX375heXLl1NYWCgppmnTppw4cYKMjAzatWvHyJEjiY42/F59/PjxrFu3jpiYGBYtWoS7uztarZYFCxZw6NChSmM8PDxo3bo1pqamADRs2FDS+IEhrYfKcHBwkN3SLwjCfTmcWFjId+ETBOG+RFB3R6dRrhN5uoX0s3YjIyODRRWdTuSPy+l0blQPo9t7KjmjIXfnuh/uR9i12sczdIEgCL8JghBdyYc06dH/PY41sBl4RRTFCln/ZUBDIAy4CXxSTfyLgiBECIIQkZ6eLid1ncbUWENDZ2vlOyCsncHatUY7IMq0egeHZh4KC1AmnYL6wWCqYBfGfRLiboeZsYaT8TU7GiMb11AwtXngMYycojLOJ+cqa78Jev0Hn0768RIVFZVHEkEQeKGjL9+MbkVcegEDlx5WHTJUlOSR6Qru0qULBw4c+Mt9/Zu5EZWYQ3wVYxitW7fm1KlTaLVaWbkGDx7M1q1bcbI2o0+IK1tOJ1FQUn3nQMeOHYmKiiInJ0eWEOLLL7/M4sWLZY2KhISE4O/vz9atW0lJkd7lOXfuXDZv3syaNWtITa26c+RuzM3N2bZtG2vWrOHJJ5/k/PnzkuKsrKyYP38+zz//POvXr6dPnz4kJydLXmvHjh2JiYnhwIEDrF+/nk6dOkmOVZHH5tOJhLjbEeBSsxar55JyyCwo5YlAaboSdR2DBQhRFLuLoti0ko/tQKogCA0Abt9WKkstCIIJ+uLDGlEUt9z12KmiKGpFUdQBXwNVytGLoviVKIqtRFFs5ezsLO+7rOMENbDhotJWi6DXgUipuQ6Iy6l5lJbrlNV/EMVHUoCyAlNjDWGe9kQoXYAwMtbrQMQ/WAEiIr5C/0HBAkRWnF4TRNV/UFF5LOgW5MKmSe0x1mgYsvxPfolWhe5UFOGhdQU/6KFcw4YN2bhxI7t3/6/Jom+zBgDsPFv5xjY7O5tGjRoxYcIEWbnCwsL44Ycf+PbbbxnR1pu8knJ2VJGjgsLCQtq3b0+fPn24eVP673NwcDD79u1j4sSJstbYu3dvxo0bxzfffCM5xtTUlM6dOzNixAh27NghOc7Kyorw8HCOHTvGu+++K2udY8eOZfPmzTz11FO89NJL5OUpfHip8hcupuRyPjmXZ2R0P0jlwKV0BAE6Bzwee+AH7afYAYy+/e/RwPa/XyDo+2u+BS6Iorjob19rcNeng4Ga94F8BAh0tSE5p5icImlzXbWGawikX4Ty0hp5uIqTqGYeCs76Z8VCcTa4t1JuDQ9Iax9HopNzDZ4Y1Do+HSDjkl7A8T45FpuJqbGG5l5K6j/8ob9V9R9UVB4bGjewZdtLHQhqYMPEH0/z5YGrtabor/LPpa50BT/oodyBAwc4cuTIX0QR3ewtaOPjyM6oyosDOp2OEydOsHHjRlm5zp07R0xMDFeuXKGltwNBrjb8eOx6tb+f5ubmXLlyhaNHj5KbK/2AThRFiouLqxwxqApvb2/Kyso4ffq05BiNRsO4cePw9vZm27ZtkuMEQWDBggWsXbuW48ePExUVJTnW3t6ep59+mhUrVrBly5ZKRSFVlGPL6SSMNQIDwmq+ALH/UhqhHvY4WpnW2GPez99IudasVfGgBYiPgB6CIFwBetz+HEEQ3ARBqCirdgBGAt0qEdaZLwjCOUEQooCuwLQHXM8jSdBtIcrLEoR5ahWXpqAr0xchaoCoxBxszIzxdrSskce7L5JuzwI+ggKUFbT2dUSrE5V3w/C53bL3AGMYx+OyCPNUWP8h7qB+3KhegHJrUFFRqXGcbcz4aUJb+oe6Mf+XS7y2MYqScnnt4ioq1VFXuoIflDlz5uDi4oK1tfVf7u8f2oDLqfmVjgU7OzvzySefyJ6LnzhxIj169KC8vBxBEBjR1pvzybmcvlH1expjY2PWrl2Lk5OTLGcLPz8/tmzZQmpqqqyNUqdOnfj555+5eFHe+9/Q0FBOnjxJeXm5rEKJIAgMHz6cCxcuUFx8f9o1giDc0WpQqX2ys6t/D16m1bH1TBJdg+rfKRLExMTIzrN///577ssqKOVsYjZPBFZebNy0aZPsPD/99BNFRUWyYiIjIzlypGYc8R6oACGKYqYoik+Kotjo9m3W7fuTRVHsc/vfh0VRFERRbPZ3YR1RFEeKohhy+2sDKlrX/mkEuurVSBUXoqwQ5Lt5tkYeLjoph6budsoKUCadAhNLcA5Sbg0PSAsvezQCyutANAgFE6v7FqLMKy4jOimHtkrab4qivgDh2xlq0M9YRUWlbmBuYsTiYWG80r0Rm08nMvKbE2QV1ExXn4qKAR6ZrmA7Ozvmz5+Pjc1f59SfCmmARoAdZ5MqjRs1ahRPPfWUrFyCIPDtt9/eKXYMbu6OvaUJX+6/Wm2ch4cHq1evlj1m0KlTJ5YsWUJamrxuzSeeeIIlS5bcY1FqCGdnZ3bt2iXbEQPA0tKSNm1qrc70j6CwsFDWc6SgoIDFixfLynHkyBGD7iW7opJJzyvhuTZeAKxZs4bvv/++2pi/s3bt2kpjfotJRRShW9C9U1379u3j008/lZUnLi6OyZMnyxLnLCkpYdSoUXWmA0KlBnCzM8fG3JhLKQrrQDj6gZktJJ954IcqLddx4WYeIXVBgLJBmF7D4BHFxtyEIFdb5QsQRiYPpAMREX8LnYiyApRpMVCQro5fqKg8xgiCwCvdA1g8vDmRidkMWnqEq2nqrLRKrfNIdQWPGDGC1q1b/+W+etZmdPCvx46zyeh097ZnC4LAZ599JjuXp6cn06bpvx0rM2PGd/Tl94tpBkVjn3rqqTs2nnIYM2YM9evLF+t78skn78tlwcTEBEdHBQ9XHhNKSkq4du2apGtFUWT9+vUMHjwYS0tpndYXLlygTZs2lJZKL0rv3LmT7t27ExZWtWuaKIp8fTAO//rWdAlwZuvWrYwePZqmTZtKznP48GHGjh2Lj4/PPV/beiYJ33pWhPxNUy8hIYFhw4bh4CDdRLKsrIznnnuOsrIyWS4k7777LufOnbtvF42/oxYg6gCCIBDkakNMssIFCI1Gf8p9M/KBH+pyah6lWt09vywPlfJSuBkFHo/u+EUFbXwdOXMjmzJtzVQe7xufDpB+AQoyZIcei8vExEiguZeCbruxt/UfVAFKFZXHngGhbqx7sS2FpeUM/vIoh648Pg5aKnWPR60rWKPR4Orqes/9z7TwICGriMNXK/87f79C8HZ2/3s/OKq9D7bmxizZd8Vg3P1YKELN2waq1A6iKBIREcGUKVMIDg6W9P8WHx9P586dGTZsGKNHj5a0Kb527Ro9e/bkwoULDB8+XNLakpOTmTFjBsXFxTzxxBNVXvfntUxibuYyvqMvhYUFfPnll2i1Wpo1ayYpjyiK7NixA51Od08BIjm7iGNxmQwKc7+nYBAVFUVRUVGlv8dVERsbS0FBAV5eXpJjSkpKSEpKwtXV9b6sPytD/e2sIzRxs+PCzTy0lVScHypuYXonjAcUojx3u6qtaAEiNRq0JY+0/kMFrXwcKCzVckFpt5QKHYj7GMM4FqvXf7AwVVD/IXa/vtPHXr5ntYqKyqNHCy8Htr3UAXd7C8Z8d5KVh+NUcUoVlWp4KsSVetam/PBnfK3lsDU3YWwHX349n6r8+xqVGqOsrIzly5fzyiuv0L9/f959912DoymZmZk888wzLF26lA8++ABfX1+DeTQaDSkpKTRp0oRnn31W0trKy8uxtbVl0qRJuLtLE4ms2Gx/+eWX1KtXr8rrvj4USz1rUwY1d8fS0pKMjAw2bNhA48aNJeURBIGCggJWrlxJt27d/vK17ZHJiCIMau5WaeyQIUOYN2+epDygF1yVK9RqZmaGTqdj7dq1kosqhlALEHWEJm62FJVpiavCf/mh4dZcv2lPv/BAD3MuKQcbc2O8nVQBypqglbe+te9EnMJjGG7NwdT6f04SEskvKSc6KUdZ+82yYn3hxL+7cmtQUVF56Hg4WLJpUnu6BdVn7q4YZm5SxSlVVKrCzNiI4W28+P1iGglZhbWWZ1wHX6zNjPliX/VaECrKsXHjRn799VeuXbtmsJAgiiKHDh1iyZIlfP755wQFBTF79uxqT8zT09N5/vnn6d+/P5MnT5ZUTEhJSaFfv3589dVXbN26VVL3Q3FxMSNGjOCrr77i888/N3h9BW+88QZvvfUWkyZNqvKaq2l57L+Uzsi2PpibGLFx40ZatmzJkCFDJIuEZmVlsW/fPoYPH/6XzgRRFNl6JpEWXvZ4O907GvTNN98wfvx4XFxcJH9Pu3fvplevXjg5SX8/XlZWxrFjx+jUqZPkcRdDqAWIOkITN32nwPlk6Wq/tYJbc/3tA+pARCflEOJuJ2u+qMZJOg1W9cHu0T/tdrUzx9PRom7oQPh0hNgDssJOxmeh1YnK6j/c+BPKCqHhk8qtQUVFRRGszYxZMaIlL3fzZ+OpRIZ9dYy03PtTn1dRedx5LtwLjSDw47HrtZbDztKE0e292R198x/TBXE/3VeiKN5X3N0OB6IocunSJYMxubm5HDx4kK+++opXX32V//u//6N3796EhYUxZ86cSgU6tVot69atIzw8nC+//JK5c+eyZMkSFixYUO04xeHDh+nSpQvjx4/niy++kCQMmZWVRd++fZk3bx5du3alUaNGBmMAZs6cyeDBg+nQoYPkEYKjR49y9epVRo4cWe11X+y7irmJhhFtvdBqtXzwwQfMmjVLUo4Kvv76a8aOHXvP2i7czONyaj6DW3jcE5OSkkJsbCzt2rWTleunn36SPIJSwR9//EHHjh1rbPwC1AJEnaGRizWmRhrldSAcfMHc7oEKEKXlOi7ezFN2/AIgKULf/fCYuB208XHiRFxWpcJQDxW/rpAVC7ekvzE5ciUDU2MNrXwU1H+49jsYmeoLKP8wBEHoLQjCJUEQrgqC8EYV1zxxWxDtvCAI8lpcVFQeATQagVd7BvLl8y24eDOPAV8c4azS9sYqKg8ZURSZMGFCtZvaBnYW9GriwrqTCRSV6ruFNmzYwO7du6uMqYzCwkImTpxY5dcndPLDzsKEuTtj/rKezz//nGPHjsnKlZKSwksvvSQrBuDNN9/k9OnTsmKuXLnC888/L9v5YsKECaxZs0ZWzJkzZ2jZsiXfffcdJSUlZGZmSipI/Pvf/yYgIID27dszZswYOnbsyMCBA/nzzz+rjDl16hQ//PADOTk5dO3alZEjRzJ37lxu3LjBvHnzKhXoFASBmJgY1q5dy6ZNm3jmmWeYMmWKwfVlZWWxbds2hgwZAiCpk0Gn0zF37lz69+9v8Nq76dKlC6+//rqsGEdHR1asWFHtQWpMci7bzyYztoMvTtZmaLVa5s+fX6mQZHV07NiRCRMm3HP/tsgkjDUC/UIa3PM1U1NTli9fLvug94UXXpBdtPD392fmzJmyYgyhFiDqCCZGGgJdbYhWugNCEPRdEA9QgLgjQKmkA0ZxDmRcfizGLypo19CJW4VlXEpVWM3d7wn9rYwxjMNXM2jt44C5iYL6D1d/17t4mFkbvvYxQhAEI2Ap8BQQDAwXBCH4b9fYA18CA0RRbAIMeegLVVF5SPQJacDmSe0x0ggMWfEnW88kKr0kFZWHhiAI3Lp1q9qNKMCodj7kFJWx82wyAA0bNmTp0qWycllaWhIfH8/Jkycr/bq9pSmv9gjgz9hMfj2feuf+1q1b8/bbb8vK5eLiQnx8PHv27JEVN2zYMMaMGSPLytHf3x9PT0/GjRsny5bw448/5qeffmLChAncunWLpKTK7U7vpkWLFmzbto3o6GiaNWvG0KFDefnll9Fqqx8j++GHH7h06RI7duxg0KBBlJSUcP36dRYtWsSvv/5aaUzXrl355ptvmDFjBv3792fWrFnMnj27WpcFjUbD3Llz8ff3N/i93M2AAQMICAiQFVOvXj369u0rKwbgmWeeke3eEBQUZFDDYeF/L2FjZszEzg0BfVGgV69estfXoUOHe37GxWVaNp9KpGtQfRys7h3lcHR0lF1IAOjdu7fsooWPj49kPQupqAWIOkQTN1vOJ+cqL5Dl1hxSY/Qz8/dBVGIdEKCsKKA8Bg4YFbRrqB9f+PNaprILcQ4Ea1fJYxjpeSVcTMmjg3/VAj61Tk6S3oLzn6n/0Aa4KopirCiKpcA6YODfrnkO2CKK4g0AURTlGairqDxiBLvZsmNKB1p42TNt/Vk+2H1BeRFoFZWHxHPPPcdPP/1U7TXhvo4Eutiw6mg8oijS3iXR4AAAIABJREFUokULUlNTSUhIkJVr2rRpfPrpp1WvpY0XAS7WfLD7AsVl+k11+/btMTIy4tChQ5LfEwuCwOLFi5k5cyb5+fmSuxNCQ0OZOHEikyZNIi4uTnKuDz/8EFtbW6ZMmcI333wjKc7JyYkdO3YQGBhIy5YtGTFihMFCAoCXlxeffPIJO3bs4Pjx43zxxRcMGjSI/Px8g+us2LTn5OQQGRnJxo0bJW+SFR2jruOciMti38U0Jnf1x87SpMYff0dkMpkFpYxt71Pjj10XUAsQdYgm7nZkF5aRnKPwXKpbc9CVQdr5+wo/l5SDrbkxXo4KClAmRuhvKzQtHgPc7S3wcrTkWKzCBQhB0HdBxB4ACZX/o9f0Vl4dlSxAXNunv/1nFiDcgbvfMSbevu9uAgAHQRAOCIJwShCEUQ9tdSoqCuFkbcbqF8IZ1c6brw7GMnbVSXIKy5RelopKrdOnTx9+/fVX9u7dW+U1giAwur0PMTdzOXw1A0EQGDt2LB988EGVHQ2V0bNnT2JiYnj//fcr/bqxkYa3+zXhRlYhK4/8rwAwd+5cXnvtNb788kvJuRo2bMgzzzxD+/btZY1VjBs3jri4OMLDw8nOljaWJQgCr7/+Otu3b2fq1KncvCnNNVWj0TBkyBCsra05cOBAlT+XyggICODGjRtEREQwatQoyWMqpqamajGhBhFFkfm/XMTF1ozR7Xxq5fFXHokjyNXmzuHj44ZagKhDNHGzBfQCjorygEKU55KyCfGoAwKUTv5goaDmQC3Q1s+R43VCB+IJKMzUW50a4MjVDOwsTO4IrSrC1d/ApgHUDzZ87eNHZb+If38CGQMtgb5AL2C2IAj39EYKgvCiIAgRgiBEpKen1/xKVVQeMiZGGuYObMqHT4fw57UMBn15hKtpCo+5qajUMkeOHCElJYU33qhUEugOz7R0x83OnE/3Xkan03HixAmWL19OVFSU5FxxcXGkp6fz9ttvU1paucV7x0b16BHswhf7rt4Rhz1//jwnTpyoclygMrRaLfHx8Zw7d459+/bJigsICCA9PZ1NmzZJjnN3d2fevHnY29vz0UcfSY7z9vbm7NmzHDp0iJSUFM6ePSspThAEHB0d77gsdO/+jzxUUZxfz6cScf0W/3kyoFas5f+8lsnFlDzGdfB9bAtHagGiDtHY1RaNAOeVFqK08wRLp/sqQJSUa7mUkkeIu30tLEwiovg/AcrHjHYNncgpKiNGacVovy76WwNjGKIocvhKBu38nDDSKPQiqi3Xr7Phk4+NIKlMEoG7rWA8gORKrvlFFMUCURQzgINA6N8fSBTFr0RRbCWKYitnZ+daW7CKysNmeBsv1k5oS15xGYOWHuX3C6mGg1RUHlG6detG3759K3U1uBszYyMmd/Xn9I1sDl/N5MMPP8TFxYWMjAzJufz8/O50MVQ3vjGrb2PKtSLv7NR3344ZM4Y5c+ZI3pyDXshw5cqVvPbaa7IKEFZWVnz33XesWrWKrVu3So7TaDSMGTOGK1eu4OzsTFaWdKcyQRDo2LEjy5Yto1mzZpLjVJQlv6Scd3eeJ8jVhiGt7nWnqAm+PRyHk5UpA8LcJMcUFsq3zJXze1zBjRs3ZMdUhlqAqENYmBrR0NmamLogRNkgDJIjZYdeSsmjTCsqq/+QfQPyU8GzjXJrqCXa+enHGBQfw7B1g3qBBgsQ8ZmFJOcU06GRguMXyaehOBv8uym3BmU5CTQSBMFXEARTYBiw42/XbAc6CYJgLAiCJRAOXHjI61RRUZTWPo5sn9IRn3qWjP8hgiW/X1G+20xFpRYQBIHly5dTv359g9cObeWp74L47TINGjRg/fr1kscUKhg4cCALFy4kPj6+ymu8naz4T/dG7D6Xwq4ofY18zpw5PPvss9y6dUtyLo1Gw4IFCxg8eHCVHRdVMXr0aD755BPZcdbW1syaNQtHR0dZcRU8rqfcdRm5ensV3TWf7b1MSm4x8waHYGJU/TY6Pj6e48ePy8qzZe9h9l1M4/m23pKF2//44w+Dmi5/58yZM3z22WeyYpKTk5kxY4asmKpQCxB1jAohSsVxaw5pF6BUXkXtXFIdEKBMuP3L7hmu3BpqCVc7c3zrWSkvRAnQsCtcPwrlJVVecuRqHdB/uPJfEDR6+9B/IKIolgNTgF/RFxU2iKJ4XhCEiYIgTLx9zQXgFyAKOAF8I4qi4fkaFZXHDHd7Czb+uz0DQ934ZO9lXlwdQW6xqguh8vhhZ2fHsmXLDF5naqzhpW7+nLmRzR+X0+nSpQv//ve/ZeebNm2awZP+f3f2I9TDjtnboknPK0EQBD7++GMsLCxk55s0aRImJvLFAYOCgjA1vdd1QKXuIuckXxRFtm/fzpYtWyTHJCYm0qNHD85ez+S7o/EMb+NFS+/qR7yPHj1K27Zt8fb2lpxn//79TPp0PUYagRFtvSTFnDx5kv79+9OwYUPJeRISEujbty9yOllLSkp45plnaswoQS1A1DGauNlxM6eYzPyqN3UPBfeWIGrhpvTWN4DIG9k4Wpni6Sj/j0WNkXAcTK0f23n/tn5OnIjLolwr3fqpVvDrCuVFcP1IlZccuZqBu70FPk4KCpJe2gOebcHy/k4mHgdEUdwtimKAKIoNRVGcd/u+5aIoLr/rmgWiKAaLothUFEV5ZXEVlccIC1MjPn02jHf6B3PgUjoDvzjCpRRVF0Ll8aNJkyaSrhvS0hN3ews+++0Koiji4+MjO5cgCAY3PMZGGhYOCaWgRMvsbdGIooggCJibm8vOV5FT5dHixo0bkjpQRFHkt99+Y9CgQWzYsEHSY0dHR9OjRw/Gjx8v2Qlk8+bNNGvWjLz8AlZGF+NgacLrvYKqjfnpp5/o1q0bXl5euLq6Sspz8OBBBjw7CvMmTzK4uTv1bQw/5xMSEhgyZAh5eXmEhIRIylNaWsq///1vbt68ia+vr6QYgC+++IJjx47RoEEDyTHVoRYg6hhN3PVClIp3QXi00t8mSlc6BohMyCZUaQHKhOP69WtqXhimLtCuoRN5JeXK60D4dgIjM7j830q/rNWJHL2WSfuGTso9H7Jv6IUyA59SJr+KisojiSAIjOngy08vtiW/pJxBS4+w8+zfpVNUVP4ZmBprmNLNn8iEbA5crl0B4kYuNkzrEcAv51PYGSXNWULl0UUURdatW8fo0aPx8fHhu+++M9iBotPpmDJlCj169CA7O5uJEycazKPT6Vi6dCm///47M2bMwNraWtLa4uLiKCoqIvRfUzmbkM2svsEGbTcbNGhAgwYN6Nevn8EcFTRq1AiXbqPRaIx4+clGkmLc3d1xcnJi8uTJODlJc8swNTUlODiYF198kYCAe7TGq6Rly5b069ePp56qmffTagGijtGkgX50IVppHQjr+mDvrRdzlEhecRlX0/MJ81TQeaIkD1LPP5bjFxW09dWf5Cs+hmFqpS9CXKlcoToy4RY5RWV0CVRQrPDSL/rbwD7KrUFFReWRpbWPIz9P7UgTN1um/nSG93fFKN99pqKiAM+08MDDwYKP91ys9d+BCZ18CfW05+3t0dzMKarVXCpVcz/t9vPnz6dVq1YEBgYycuRIg/odWVlZrF27lh9++IEBAwbw9ttvG8wRERHBvn37aNWqFStXrkSjMbydPX78OAcPHmTRokVMnjxZ0vcSGxvLt99+y7o9f3Ao14kuAc4MNCAMWVxczH/+8x927drFf/7zH0l5AF6d/QE6n7Y819YbT0dpXcPbtm0jJCSEL774QnKe3Nxcdu3axeLFiwkKqr6T426WL1/OtGnT6N27t+SY6lALEHUMO0sTvJ0sOZeocAECwKM1JEovQEQl5iCKEOaloANG0ikQdY+lAGUF9W3NaVTfmsNX5avX1jiNekFWLGRcvedLBy6lY6QR6OSvYAHi8h69HWs9f+XWoKKi8khT39actRPaMrqdN98cjmPEt8fJUHpMUkXlIWNqrOGtPo25mJLHTydqRgm/KoyNNCwaGkpZuY6X1pymtFwt+j0IOp2OkhLpr1k6nY7k5GSGDh1Kx44dmThxIl9++SV5eZWPopWVlbFnzx5GjBjBN998Q2RkJKNHj2bVqlU4OFR+KKnValm2bBkdOnRgwIABLFq0iM8++8xgx+zatWsZP348W7ZsYe/evfj5+Rn8fiIjI3nhhRfYvn0706ZNk9T9UFRUxLBhw1jy5XKWRRZjbWbMwiGhBtf37rvvMnToUJo0aYKdnTQ9vNOnTxOpdcPE2IiXn5TWlaDT6Zg3bx6zZs2S1WX8zTffMHLkSMzMzCTHpKWlcf78ebp2rTktNbUAUQdp5mHP2QR5CsO1gkdryE2CnCRJl0feXnOYh4IFiIQTgADurZRbw0OgS4Azx+OyKCrVKruQgJ7620q6IPZfSqOFl73BVrVaozgX4g6p4xcqKioPjKmxhncHNmXR0FDO3Mim3+LDnLkhXZlfRaWuIIoiO3b83QjJMDExMTQ0zaWdnxML/3uZrALDc/plZWXs3LlTdq4jR45gXprDx/9qxukb2Xy4x7ApU0FBAdu3b5eda+fOnaSlpcmKycrK4ocffpCda+XKlURHy9N3vnz5Mm+++SZRUVGIokhmZqakzoRXX32V8ePHM3fuXL7//ntatWrFnDlzuHmz6rGWX375hcaNG9O4cWOGDx9OfHw8Z8+exczMjJ49e2JjY3NPjFarJTw8nE2bNjFu3DgiIiI4ePAgb731FkZGVY9Cf/TRR1y4cIE///yT8ePHM23aNIOdDNevX2fNmjUcOHCAxo0bY28vbb/xxRdfsGHDBvz9pR9G/fHHHzz33HMcya/HxZQ8FgxphrNN9Zv20tJSEhMTmTlzpuQ8ANv3H6fYpRmj2/vgYitN7yQxMZFevXrJ+p4AkpKSJI2s3M3ly5eZNm1azY5Ti6L4yH20bNlSfJz5+uA10fv1XWJabrGyC0mIEMU5tqJ4fpuky19YdVLsumB/7a7JEKufFsWlbZVdw0Pgj0tpovfru8R9F1OVXoooLmktiqv6/+Wu1Nwi0fv1XeIX+64otChRFKO36p+/cYcfWkogQqwDr5EP4+Nxfx1WUamKc4nZYoePfhcbvbVb/PFYvKjT6ZReksrfUF+Lq6dHjx5iRESErJi9e/eKgwcPFi+l5Ip+b/4svrklymCMVqsV27ZtK545c0ZWri1btoj9+vUTdTqdOGd7tOj9+i5x19nkamOKiorE8PBwce/evbJybd26VWzVqpWYlZUlOSYvL08cPHiwOHHiRLGkpETya8CBAwfEFi1aiFOnThWzsrIk/Vzy8vLE77//Xuzdu7cYGhoqDhw4UBw4cKCYkZFRbdz169fFAwcOiKtXrxbnzp0rGhsbi8bGxmLz5s3FXbt2VRpTUlIilpeX3/n8zJkzYnZ2tsE13h0jlUfhdXP/xVTR+/Vd4pzt0bWaZ+LqCLHJ27+ImfkltZrnYVPd67DaAVEHaXa7gyAqUeEuCNemYGQqaQxDFEUiE7IJ81Sw+0Gng4STj/X4RQVtfB0xM9ZwsJbFoCQR0FNvx1nyv9a8Py7p1/WEovoPe8DC4bHWA1FRUXn4NHW3Y9fUjrRr6MT/bY1m5qYoissU7kZTUZHB9OnT+eSTT2TFPPnkk2RkZFB48xqj2nnz04kbRCdVPy6s0WhYuHAh06ZNQ78fkcbgwYOxsrJi7dq1vPlUEC287Jm56SzX0vOrjDE3N2f9+vVMnTqVhIQEiouLJeUaNGgQr7zyCv369SMmJobCQsP289bW1mzatAkXFxd69uzJrFmzKCoyrFXRpUsXjh8/TuPGjWnbti3dunXj1KlTBnONGjWKPXv2sHv3biIjI9m+fTuhoaEcOHCgyjgvLy+6dOnCiBEjmDx5MhEREeTn53P69Gn69u1baYypqelfuhbCwsIkjRFU1+lQFXXdoSQlp5jXNkYR6GLDG09J10qQy+kbt9gTncK4jr44Wv1z7F/VAkQdpKm7LRoBziqtA2FsBg1CJRUgkrKLyMgvUVb/IeMSlOT8Izac5iZGhPs58UddKEA06gW6Mri2/85dBy6lU9/GjOAGtsqsSVsOV/6rX5uRsTJrUFFReWyxtzRl5ZjWvNzNn42nEnlm2VGuZxYovSwVFUn07NmTixcvsn//fsrKyiTFCILAnDlzePfdd+lol4OjpSnv7DhvsLDQoUMHXFxc+Oijj7h48aLkNS5ZsoT33nuPue+8zdLnW2BmYsSkH0+RV1z1er29vfn8888ZNGgQb731luRczz//PMOGDaNt27YsW7ZMUoxGo2HOnDn4+PjwwQcfMHv2bElxxsbGTJgwge7du1NcXEzv3r0l/1xcXFw4efIksbGx/PLLL1hZWaHVGi5+Ojk5ERoaKmvu/59McZmWf6+OoKi0nCXPNcfcpHZc9bQ6kdnbonGxNePFzoa1LB4n1AJEHcTS1JgAFxvlOyBArwORfAa01f+BuqP/oGQHRMJx/e0/oAABeh2I2PQCErIMV+trFa+2YGZ3RweiXKvj4JV0ugbWV67CnXAMirIgsGbUelVUVFT+jpFG4NWegXw7uhWJt4rot+Qwv0SnKL0sFRWD5Obm4ujoSI8ePbhxQ7qgpCAI7N27l/fn/B+v9w4i4vottkVWrxOm0+lwcHDgrbfeqvbEvrI4jUbDBx98QGFGMkuGNyc2vYDJa05TVo0Lh4WFBZcuXeK7776T1JVQgYODA2ZmZnz88ccUFEgrJgqCwPTp05k4cSJff/01hw8flhRnbGzM0qVLyc7OZseOHZw+fRqdzrDQppGREc7Ozvj6+tK0aVNat259X90HKlUjiiJvbI7ibGIOnz4bRoDLvboXNcWPx65zPjmX2f2CsTb7Zx2WqQWIOkozD7vbrhLyLXBqFI9WUF6kt7ashsgb2ZgaawhyVejEG/QClJZO4PjPqCJ2CagHwMErCndBGJlAw65w+b+g03H6RjZ5xeXKjl+c3wrGFuDfQ7k1qKio/CN4srELu6Z2xK+eFRN/PMV7u2JU1X6VOo2dnR0DBw5Eq9USFxcnOa5jx4506tSJc+fO8UwLd0I97Xlv14VqXWE0Gg1vvPEG/v7+HDlyRHIuFxcXVq9ejZubG7t27aKDfz0+fDqEQ1cyeGPzuSrfH3fq1InDhw/ToEEDtm7dKjnfiBEjuHLlCqNGjeLrr7+WHBcSEsKyZctISEiQXLiowNTUlHbt2vHcc89JspJUqX1WHIxlW2Qyr/UMoGcT11rLk5ZXzMJfL9GpUT36hjSotTx1lQd6tguC4CgIwl5BEK7cvq3Ua0UQhHhBEM4JghApCEKE3Pj/Z++8w6K4vgb8Dl1UELABIlgQK6Bgj1hj77HEktiiBk00scQY8zMxMfYWE3s0osYWMWqUqFHsDVEsqCCCoCJNepG2e78/wHwWhFkFVnTe55ln2Z175pxd4O69Z055F3GsUo641EwexGu5/3GVxjmPDy7mO8zvfgINrE0x0NPiBBp2Bqo2hzc8r6ywqFGhDFamRm9GHYg6PSA1Gu6f53hgNHo6Ei3ty2vHFrUKbu6FWp3AsOBWSwoKCgqvi425MTs/bc7wFnasP32XD9ee42GClr+/FRTy4fPPP+eLL74gJCREtoyBgQGenp7UrVuX6OgoFvZzJCUjm292v9whADmpESdPniQxUbPUYhcXF3x8fIiMzIks6u9qwxcd7PG8/IClR4JeKufs7Iyvry8GBprl1JcrV45Fixbx0UcfaSQHYGJiQqdOnTSWU3hz8A6IYv7BALo7WjK+beG0b39SdPF55noFkJGtZlbPei9EC8fHx8tKrXmaoKAg2XVPnuDv7094uLxOh0/rOXfunEYyefG6u8WvgaNCCHvgaO7zl9FWCOEshHi6P6Im8u8UTrmFKK9qOw3D1AbKVILwlxfJyVKp8Q9P1G76RWI4xIeCbUvt2VDMSJJEa4cKnL0Tm284YrFQqxPoGsKNPXgHRONia4aJkZbab4adgdQYqNdHO/oVFBTeSQz1dPm+Zz1+HdyQ21EpdFt+iuOBmrX3U1AoThYtWkT9+vU1kjE2Nmb//v1kZ2dTq1JZpnSsxeGbUfzll/9GxtLSkg0bNpCdna2RPmtra3744Yf/nk9sb88A1yosPxrEjosvTx8xNjamX79+Gul6goWFxSvJKZQsnk57ufYggQnbrlDX0oSF/ZzyTCE+fvy47JopAI8ePWLGjBkvOCDOBcfyl184Y1tXp3qFZ2+U+fv78+mnn2qUWuPj48OIESMwMpLXwhPg6tWr9OjRg8qV5Ud53L9/nw4dOlChwutHOL+uA6IX4JH7swfQu5jl31ocKpfFQFeHa9ouRClJOVEQT+or5EFARDIZ2WrtOiDCcsP6bFtozwYt4GZfgeSMbPzuadlRZVgW7N8n+8ZeAiMT6VSEYWsF4r8b9I3BvqP2bFBQUHhn6e5oxb7PWlLJxIgRGy+y+HAgKrWW0ykVFPJAV1eXFi00XzeZmJhgY2MDwKj3qtPYzozv9t0oMOqnfPny6Olpnuuur///NzQkSeKnPg1wq1WBb/7y5/ANpe7Ku05sbCzx8fGyxqrVavbv38+YMWPIyMhJHQqKSmbYBh/KGeuzflhjShk8u/kPDAykW7dueHp6PvO3mB9eXl40aNAAMzOzZ9JrMrJVzNzrj415qReiLHbu3EnTpk1xcnKSpeOJnrZt22ok4+fnR7t27ahatapsR0dMTAzvv/8+MTExVKtWTbaul/G6DohKQogIgNzHii8ZJ4DDkiRdkiRpzCvIv3MY6OlQx8qEq/ffgEKUNk0hLgSSo/I8fSksDoBGtlrMoAk7k1MIsXID7dmgBVral0dfV+LIrbx/N8VK3V7opUbSSAqiU30tOSBU2XBrH9TqDAbG2rFBQUHhnad6hTLsGd+S/i5V+MX7DkN/u0B0smbhsQoKJQFdHYlF/Z1QqQXTPK8VS+0yfV0dVg5pRH1rU8Zvvaw4Id4SkpOTuXjxoqy0gNDQUJYtW0abNm0YMWIEJiYF16A7ceIEdevWpUePHgwcOJBSpUpxPy6NoesvoKerw5ZRTals+mwUwaVLl2jSpAlHjx5l+vTpst7H3bt3GT16NHFxcQwfPvyZc0sO3yYoOoUfetV/prtGQkICy5cvJy0tTXbkjkqlwsvLi8zMTNq3by9LBnI+u6ysLJo2lV+0PzU1lbS0NNzc3Aql8GmBDghJko5IkuSfx9FLAz0thRCNgC7AeEmS3DQ1VJKkMZIk+UqS5BsT8wbkvBcDTlVM8Q9P1P6dkydpDffO5nn6Ylg8VqZGWJcrVYxGPUfomZxuDDrvVjVgEyN9mlW34NCNSO0XLK3VmUz0+dj0ivb+FkJPQVos1O+rHf0KCgoKuRjp67KgnxML+znidz+ebstPcz4kVttmKRQR73JdNFuL0nzTtQ6ngh6x5YL8rhqvQxlDPTaPakI9K1PG/aE4Id4U7ty5w9WrV/H39+fmzZvExhY85+3atQsbGxtMTEzYuHGjrLQAb29vvvzySyIjI9m0aZOsTfHt27eJjIxk+PDhtG/fnuikdIauv0B6lprNo5pgV770CzIXLlygfv36uLu7Y2VlVaAOgCtXrmBvb8+cOXOeSVc4G/yItadCGNK0Km0dnr3nHhERQWJiIrt27aJWrVqy9GRlZXHy5EmOHDlC27ZtZclATtTEihUrmDBhgmyZ69ev895777F9+3bZMvlRoANCCNFBCFE/j2MvECVJkiVA7mOeyY5CiIe5j9HAX0CT3FOy5HNl1wohXIUQroWRe1IScKxSjtRMFSExKdo1xNIxJ6Q97MWiI0IIfEPjcLEz14JhuSRHQWzQO5d+8YRO9SoTFpvG7Sjt/p1EZhhwQuVIe/U5kNFOqki48RcYlIGaHbSjX0FBQeE5+rvasGd8S8oa6TF43Xl+9Q7S/o0FhaLgna6LNqRpVVrZl2fOgVsEF9O61cRIn02jmlDfOscJcUhxQhQq27dvZ8+ePdy7d0/WTa6wsDDmzp2Ls7MzTk5O/P7775Qq9fIbUunp6axatYqZM2fy+PFjvv/+e3799dd8nQmPHz9mypQprFu3jqlTp7Jv3z7Klcs/BVytVjN9+nR2797N+fPnWbRoEbEpGXy03oeY5Aw2jmicZxe/zZs3s337dg4fPsycOXMKfP8AN2/e5Ntvv2Xnzp1MmjTpv9cTH2cxZedVqlmUZka3Os/IZGZmMnz4cNasWcMHH3wgSw/A/Pnz+eCDD2jdujVmZvL8lTdu3ODKlSsMGTKEKlWqyJIRQjB79mz+97//FfhZy+V1UzD2AcNyfx4G7H1+gCRJpSVJKvvkZ6Aj4C9X/l3mSU0Fref36+qDTRMIezEC4kH8Y6KSMmhsp0VH/ZPIDLv3tGeDFulYtxKShNa/eA/fjOSAqillMqML7JpSJGRnwq2/waEL6GsxGkdBQUHhOWpXNmHfZ+/R3dGKRYdv8/EGJSXjLaTE1EVLS0vTWEalUvH48ctrPEiSxIJ+jpQy0OXTzZdIzcgpNpmcnKyxrtTUVNnF/p44IRpUMWX8H5c56K/ZWigmJuaZYoRyEEJw//59jWQgp4OAJkUMARITE/Hx8fnPRrmdDg4dOsTBgwe5cuUK4eHhjBs3Dm9v73wdCbdu3WL27NmMHz+evn37Mn36dPr06YO9vT2TJk0iKSnpBRm1Ws20adNwcnJi6NCh2NnZ4eTkxPnz51m4cCHGxnmnw+7atQtnZ2fCwsI4duwYhw4d4rvvvsuz+OMTHj58SPPmzTE3N+fUqVPMnz9fVrSAu7s78fHx/P3339SuXZtMPWMGrDlHaGwq6z52pWHVF/cwx48f59dff+Xvv/+mdOnS+TpSnpCdnc3QoUPx8PCgYsWKz7yXmXv9iU7OYOlAZ4wNnq2DsnTpUt5//32N6rFERETg6enJtGnTZMsAzJo1i3nz5mnU9vXYsWNUq1aiJN6tAAAgAElEQVSNOnXqFDxYLk/ag7zKAViQ46UNyn00z33dCvDK/bk6cDX3uAHMKEi+oMPFxUW8C6hUauE065D46s+r2jZFiGPzhPjOVIi0+Gde/uvyA2E7bb/wD0/QkmFCiP2ThZhtKUR2pvZs0DJ9VpwWXX8+qVUbBq09J3ouOiDED+WF+Ofr4jfgxh4hvjMR4vbh4tedC+ArXmNOLUnHuzIPKygUJmq1Wmz3CRMO33oJlx8Pi+OB0do26a1EG3MxkPDc8/iXjLsLXAYuAWM0lX/+0HQuVqvVokWLFiI4OFgjua1bt4rx48cXOO50UIyo9vV+Me6PSyIjI0M4OjqKu3fvaqTr559/Fp9//rlGMg+iYkW10StEta/3i60XwmTLzZkzR3zwwQciLS1NtszDhw9FvXr1xLJly4RKpRJqtVqW3IIFC0SdOnXEL7/8ItLS0sS1a9cKlAkODhb9+vUTNWvWFEOGDBHjx48Xw4YNE48ePcpXbu3ateLzzz8X/fv3F61atRJ6enoCELVq1RJ79+7NUyYwMFB4eHiIw4cPi+vXr4tff/1VzJ8/X0RH5z9PeXl5ibi4OCGEEJmZmSIjI6PA93X79u3/ZOSiUqlEYGCgRjJCCBEaGvrf7ygkJkW0mHtU1Jt5UJwPfvln+Pjx4wI/47yIiop64bU9fjl7peVHbucpk5CQIOsze57Y2FiNZTT9zIXI+dwTExM1lstvHtb6IvZVjndp4Tvydx/RbtExbZshRMiJnM1d4MFnXv5m9zVRb+ZBka2SN/kWCSuaCbGpt/b0vwGsPn5H2E7bL+7HpWpFf1xKhqg+/YBYcPCWEFsHCbHQXojsrOI1YnNfIRbXEUKVXbx6n0JxQCgoKMjhdmSS6LjkhLCdtl/M8bopMrNV2jbpraKo5mLgCDlRvM8fvTRwQFjlPlbMvTnnlvtctgMCGAP4Ar5Vq1bV+PPZs2ePGDhwoEYy2dnZomnTpuLixYsFjl15LGdNsu5ksDh48KBo3bq1yM6W/92cnZ0tunXrJn7//XeNbDzn6yeqDV8kbKftF3MP+MtyDKjVarFkyRLRokUL8eDBA3Hnzh1ZupKTk4W7u7twc3MT3333nWy56Oho8e2334patWoJc3Nz8ccff8iSy8zMFCdPnhTOzs4CEBUqVBDbtm2T9R4fPXokFi5cKLy9vUV8fHyB499Wbj5MFC4//isa/nBYXLtfPDdOH8SnifrfHRR9V54RWe/YPJ/fPPy6KRgKRUwjWzOCY1KJT83UriHWrqCj/0IaxqWweBpWLYeuzstDpoqU1FiIvvnO1n94QsfctpeHb2inG8aRW1Go1ILO9SzB6UNIiYKQY8VnQOIDuHMUnIe8c4VIFRQUSh72lcqy97OWDGlalTUnQui/+hz34zQPi1coXsRbUhetZ8+eREREcP78eeQWdtfV1WXFihWMHz+egICAfMd+2ro6nepVYu4/AZjau9KgQQMWLlzIqVOnZOvasmULS5cu5X//+x8RERGy5Jq5OLNl7HvohV1g9clQvtxxhczs/NMrJEniyy+/ZOrUqTRr1oxPPvnkiZMnX8qUKcPKlSsZPnw4s2bNokePHnmmKDxPhQoV+PHHHxk7dizZ2dkMGTKEn3/+uUA5fX19WrZsyerVq/Hx8eHgwYPUqVPnv1aS+WFhYcGUKVNo27ZtoeXwlzQuhcUzcM059HQkdo5tToMqpkWuMz1LxdjNvggBSwc4o6erbLufoHwSbziuua0tL9+T19+2yDAwBquGzzggEh9nERiVTGNtFqC8l1sY0/bdrP/whGrlS1OrUhmt1YHYd/UhVcxKUd/aBGp1glJmcHVb8RlwZSsgoOGQ4tOpoKCg8BoY6evyU58GrBjciOCYFLouP8WBa/I2WgpvJCWqLlr//v3p2rUrnp6esmXs7OzQ09OjcePG+W62JSmnNaethTGfbb1M2669mTlzJrNnz5aty9TUlNatWzN79mw2bNggW65endqYBR8k/oQHe648ZNgGHxIfF1x3oXbt2lhYWHD8+HGN9LVo0YI5c+ZgamrK0KFDUalUsuQmTZpEQkICDx8+xMnJifj4gtf5Ojo6NG3alMaNG9OoUSOcnJwwMjIqUO5d5y+/Bwxadx6z0gb8+WlzalYsU+Q6hRBM332dGw+TWDbQmaoWSmv4p1EcEG84jlXKoacjcSlMyw4IyIkyeOgHmTl3aS7fi0eI/3eSaIW7J0GvFFg30p4Nbwid6lXmYmgcsSkFe8MLk8jEdM7ceUSfhtY5BXf0DKFBfwg4AI+LoYCqWg1+m6F6GzCzK3p9CgoKCoVIN0dLvCa0okaFMozfeplv/rpOepa8TYzCG8U84H1JkoKA93OfI0mSlSRJXrljKgGnJUm6CvgAB4QQB/OTLwokScLa2pqUlBQuXLggW87MzIzGjRuTkpLCiRMn8h1b1kifNUNdSMtUsfGOPu937sLRo0dltWV8YuPXX39Nly5dWLduneyNvampKYcOHmRY48oY+m3HNyyOvivPEBSVfzHM2rVr4+fnx7///ou3tzdRUfIiSh0cHJg+fTrnzp1j7dq1JCTIX/dIkoSlpSVt2rSR3cVAQT4qtWDuP7f4csdVGtqU469xLbExLx5HwPrTd/nLL5xJHWrRoW6lYtFZklAcEG84pQx0qWdtiu+b4oBQZ0F4TtvqS6Hx6OpIOFfVYjhXyDGwa5mz6X3H6drAErUAr+vFewdt75Vw1AL6NnqqnU/DoZCdDtd2FL0Bd09Awj1o+FHR61JQUFAoAmzMjfnz0+Z82roGWy/co9evBW+YFN4shBCxQoj2Qgj73Me43NcfCiG65v4cIoRwyj3qCSF+Kki+qOjTpw+enp5cuXJFtoyOjg5Lly5l4cKFHD16tMDx9pXKsrCfE9fCk7EbOJMZM77l77//lq3PysqKAwcOMH36dE6fPi1bztzcnOXLl7Nn2TfM61yFxMdZ9Pz1DHuvhOcrJ0kSHTp04I8//sDCwkK2vidUrlz5leQUCp+k9Cw+8bjImhMhDG1WlS2fNMW8tEGx6D4d9Ig5XrfoXK8y49vWLBadr0p2drbGMnJSjQpCcUCUAFyqmnH1fkKBeWxFjk1TQIKwnLSHi6Fx1LMyeaGdTLGRcB8e3YYa7bSj/w2jduWy1KpUhr1XHhabTiEEnpcf0KhqOaqVL/3/JyydwNoFLq4HGbmUr8XlTTkpH7W7F60eBQUFhSJEX1eHr7vUxmNkEx6lZNDj19Ns97knKx9dQeFV6NGjB/PmzZPd2hFyNulTpkxh6NChssZ3c7Tk6y61OXA9El3XAXTq1EkjGyVJYuzYsbRq1UojOYA6derwQStH9n/eivrWJkzcfoX/7fEnI7vgaAo9PS2tbRVem5CYFPquPMupoEf82Ls+s3s3QL+Y6i/ci03js22XqVmxDIsGOKGjI2m8YU9OTubq1asayQQHB2vk3AO4du0aq1ev1kjm5s2bfP/99xrJ5IXigCgBuNqZkZGt5mbE63ucXotS5aByA7h7ksxsNVcfJOBqq8X6D0+KHFZvqz0b3iAkSaKXszW+YfHFVszsxsMkbkelPBv98ATXkfAo8IXCpYVK0kO4tQ+cBoO+kgepoKBQ8mldqwL/TGyFi60ZX+++jvuWy9ovRK3w1tKpU6dXqiPg6uoqe+xYt+qMaGnHhjN3+Tvo1dYnOjqvvmWpbGrE1tHNGONWnc3nw5Sir28pQgh2XrxP919OE5uSweZRTfmome1LxyYmJsq+tlqtZs+ePfj4+Lx0THJ6FmM2+6JWC9Z+5Ep0+D369etHSEiIbD3e3t44OztrVCx0z549uLi4ULt2bdkyXl5etGzZknr16smWuXjxIq1ataJ69eqyZV6G4oAoAbjk1ljwDS3SaDx51GgL9y9w/W446VlqmlTTYs5a8DEoUxkq1tGeDW8YPZ2sAAoMMywsdl8Ox0BXh+6Oli+erNcXjEzhgmbeVY3wWQtCDU3HFp0OBQUFhWKmookRm0c25ZuutTkaEEXnn09yOuiRts1SUHglJEnif93q0s3RkjleAezxK541ytPo6+rwTdc6rPnIhbsxqXRbfordlx8oEUYlnKysLHx8fDjre4XPtvnxlec1nKqU45+JbjSv8WI6TFhYGHPnzqVFixayuqtkZmayceNG6tWrx5w5c3BxcclzXHqWijGbLnEnOoWl/RuwZvFs6tSpg1qtxtnZuUA9Qgi+++472rdvT/369bG1zdtx8jw7duygb9++2NvbY29vL0vm6tWrfPTRR0iSxHvvySvin5CQwPjx44mLi6N169ayZPJDiS8qAVQyMaKKWSntd8KAnHSHMz/zwO8IklSRZtW1lOumVuVEQNTqApKWWoC+gdiYG9Okmjm7Lj1gfNuaOUUhi4gslZq9V8JpX6ci5YzzyKszMM6JgjjzM8SFgPnre0yfITMVfH+HOj3ATN5EraCgoFBS0NGRGONWgxY1yjNxux9D119gdKtqTOnkgKGe0m5YoWShoyOxZIATsSkZTN11FYsyBrSy17yF6OvSqV5lak8oy6SdV5m08ype1yOZ06c+FU2UKEptER4eTkBAABEREURGRtKuXTsaNcq/uHxgYCDu7u6cP38epw4fQLNhxKRkMq1zbca4VUdX58X174MHD3BxcSE2NpY//vhDVsRAWloa8+bNIygoiIsXL6Kr++Lcm61SM3G7H+dCYlk20Jm2dSqz9Pp19PT0ZKcrSJJEamoqdnZ2jBs3TpYMQHp6Oi1atKBfv36yZXR1dbGxsaF///7o6+vLkilVqhSPHz/m+++/1yhq4mUoERAlBBdbM3xD47XvqbVpBnpG6Iceo76Vad4bz+Ig4io8jlfqP+TBh41tCI1N48Ldoo2YOREYQ2xqZt7pF09oMhYkXTi/qvAN8N0A6QnQ/LPCv7aCgoLCG0J9a1P2f96Koc2qsu7UXXqvOKsUqFQokRjq6bL2Y1dqVCjDp5svcf2B/BD4wsTWojQ7xzbn2251OBUUw/tLT/KXnxIN8TxyWoM+z99//82QIUP49NNPmTZtGnfu3Ml3vEqlYv/+/XTo0IHhw4djZGREw4YN85WJjY1lxYoV+F2/QbXeXxBV70MM9XXxdG+Be5saeTofoqOjGTNmDK1bt2bs2LEMHjy4wPeSmprKkCFD+OCDD1i7dm2eThEhBDP+8ufQjSi+61GXXs5WjB8/nurVq3Pu3DkcHR0L1APg4eHBjRs3uHjxIu+//74smdu3bzN//nz27dvH+PHjZcmoVCrGjBnDqlWr+Oabb2TJACxbtozevXvz3XffvVY61BMUB0QJwdXWjOjkDO5pO2dN3whV1RY4pF6kRR6hTcXGf/Uf2mjPhjeULvUtKWuox46L94tUz5YLYVQsa0gbh3zuYJhYguMAuLwZUqILT3lmGpxZnvP7t2lSeNdVUFBQeAMpZaDL7N4N+O1jV6KT0un+y2k2nwtVNkwKJQ4TI308RjahnLEBQ347z9X7xdCuOw90dSQ+aVUdr4mtqFGhNF/uuMroTZeITJRfkFNTXuX/9XkZudd4um2pSqVi+/btpKXlv4fIzMzk3r17XLp0iYMHD/Lhhx9SpUoV+vbty6JFi/KsmSCE4NatW6xevZpBgwYxefJktm3bhp+fH/369aNmzby7QERERDB79mzq16+Pj48PPXv25MiRI3z22Wcvjd7Nysri559/pmXLlpSq7oL9BA9Sq7akv4sN+ye0wskm77oJ3t7etG7dmuHDh/Pnn3+ybNmyfD8HgJiYGDp06EC3bt346aefGDVqVJ7jFhwKZIfvfT5vV5PhLeyYNm0a6enpLFu2TLbz4fz58yxZsoRt27ZRvnx5WRv8zMxMPvroI9asWYO5ubnsSIZffvmFxo0b07x5c9lR0g8fPsTDw4Ovv/5a1ng5KA6IEsKTPKazwfL6JxclYeWaUUN6SJvKWiyKFXwspyBmmeIP33vTKWWgS6+GVnhdjyCuiAqXhT5K5XhgDIOaVC24snCryaDKhNNLC8+ASxshNRpaTyu8ayooKCi84XSoW4l/vmhFs+oW/G/vDUZ5+PIoJUPbZimUMCZOnKhRAT6AI0eOsH79eo1kVCoVI0aMICUl5ZnXK5kYsWNsM0yN9Rn62wUuPddq3sPDgy1btmikKzU1lX79+hEbq9k6eedvv9BG5cc3XWtzKiiGdouPs+LYHdKzXt4pIyoqitatW3Pu3DmNdE2cOJGRI0dy4cIFhBDcu3evQJlr167h4ODA0KFDWbt2LevWrWPevHlkZOT/fz906FAcHBxwcHCgRYsWjB49GktLS9zd3fH19c3TkeHt7c2oUaNYvHgx//zzDzo6Oujq6uLs7MzAgQMxNTXNU9ePP/5IYmIiEyZM4OLFi2zYsIFz587RuHHjl9p35MgRTExMOHfuHOvXr+fPP/+kTZs2+b6npKQkwqLicZvuwY7I8pQ1NmL7mGbM7+dIGcOXVxW4desWXl5eDBgwAB0dHVlFV6Oiovjqq6/yTYdYdzKEVceDGdK0KpPer4VaraZq1ar89ttvGkUJpKSksHPnTo0KTz5+/JhJkyZp3B3G0tKSn376qeCBT5GZmcnKlSspXbp0wYPlIoQocYeLi4t411Cr1aLx7H/FZ1sva9sUsd5zvxDfmYj0Cxu1Y0B6shCzLIQ4/D/t6C8BBEQkCdtp+8WKY0FFcv0f/74hakw/ICITH8sT+GucED9UECIx/PWVp8UJMc9OiI09Xv9ahQzgK96AObI4jndxHlZQeFNQq9Xi99Mhwn6Gl3D58bDwvhWlbZPeKJS5OH9WrFghxo4dq5FMYmKiqFevnvD399dIbtWqVaJ3795CpVK9cC48Pk20XuAt6v7vH+FzN/a/1+Pi4oSrq6vYvXu3Rrp27twpHB0dxd27d0VWVpYsmaSkJDFs2DDRq1cvceXOAzF09QlhO22/aDnvqPjn+kOhVqvzlLt06ZJo3bq1+PDDD8XatWuFn59fgbqys7PF33//Lbp37y5cXFyEra2tWL9+fYFy6enp4syZM2Lu3Lmibt26AhA1atQQe/fufal9T1Cr1SI4OFh07NhRfPXVV8LT01M8ePCgQJ1CCBEaGiqys7NljS1qMrNVYuOZu6L+zIPCfoaX+PnIbZGepT3bNp65K2yn7Rfj/rgkslX5/w7eVfKbh6Wc8yULV1dX4evrq20zip0vtvtx+s4jLs7oUKTFBQui16+n+T3uI8zrtIH+vxe/AYH/wLYP4aM9OV05FPJk8Lrz3H2Uyqmv2qJXiP2Pk9KzaDnXmza1K/LLoPzz9P4jPhR+bQz1P4A+r9kV49AMOLcCxp4ES3nhbcWFJEmXhBDye5OVYN7VeVhB4U0iMDKZidv9CIhM5uPmtkzvUodSBkqBSmUuzh+1Wk3btm2ZNWsWTZo0wdjYWJbchQsXcHd3Z+/evVhZWeVZkC8vxo0bh4WFBf369cPJyemZc5GJ6Qxed57IpHTWD2v8X8RvdHQ0HTt2ZOLEidjb28uu1n/ixAnc3d1xcnJi2bJlVKpUSZbcH3/8wU8//URmZiYrdh1hybF7BEYl07y6BTN71KWOpckLMkIIPD09GTJkCCYmJpw8eZI6deR1Zlu1atV/d9fHjRvH0qVLMTDIv66aEILt27eTmZmJiYkJJiYmNGnShLJly8rSWRIRQuB1PZJFhwO5+yiVFjUsmN27PtUrlNGaTSuP32HBwUA61q3EL4MbKkWBX0J+87CSglGCaFGzPI9SMrkdlVLw4CIiKT2L6+GJRFg0g5DjoFYXvxEBB8DQBGxbFr/uEsTwFnZEJKbj5R9ZqNfdcj6M5Ixsxrpp0NXCzA6aj4er2+D+y3soF0h0AFxYA85D3jjng4KCgkJx41C5LHvGt2Rky2psOhdGt+WnuKKlnHqFkoOOjg7r1q3D3d2dr776SrZc06ZN6dq1K66urhw/fly23Jw5c9i+fTudOnV6oQ5BZVMjto9thnW5UozY6PNfu9mKFSsye/ZsRo0axcyZM2XrcnNzw83Nje3btzN16lTZcj179sTOzo7g4GBWzJzA35+14Mde9bgVmUTX5af4bOtlbj9X/FWSJBo1asSMGTNo1KgRffv2LbDo4hPc3d1JT0/n3r17jBgxgqioqAJlJEli0KBBDBs2jD59+tC+ffu32vlwNvgRvVecYfzWy+jrSvz2sSt/fNJUa84HIQSLDgWy4GAgvZytWDGkkeJ8eEUUB0QJ4knRxzN3tNcL3CckDrUAg1od4HEcRF4tXgPUqpwICPuOoKelDhwlhPZ1KlGjQmlWHruDWl04kU7pWSo2nA6llX156lvnnQv4UlpNgbKWsP9LyH6FnGW1CvZ9BoZl4f1ZmssrKCgovIUY6esys0dd/vikKelZKj5YdZYlhwPJzNbCDQKFEsO9e/e4f/8+u3btQi3zZpJarUZXV5eYmBi2bt0qW5ckSbi5uREVFcX27dtfOF+xrBHbxjTDzqI0Iz0uctA/AoDGjRszevRoTpw4IdvhIUkSCxYsYOHChRw9epRjx47JkitbtixeXl74+/vj6OjI3/v28lFzO45PacOnrWtwLCCaTstOMv6PywREJv0nV716dWbOnMmhQ4fw9/d/aZ2EvDA0NMTGxgZXV1dsbGxky73t+N2LZ9gGHwavu0BMcgYL+znyz0Q3OtStpLUIcCEEP+6/xa/H7vBhYxuWDHAuuAaawktRPrkSRBUzY6qaG2u1EOXZ4FgM9XSwce2a80LQkeI14L4PpD2C2t2KV28JRFdHYnzbmgREJnM0oHA6UGw5H8ajlAzGtcm7qnG+GJaB7kshyh+OzdFc/vRSeHARuiyA0uU1l1dQUFB4i2lZszwHv3Sjt7M1y73v0GflmRfu2CooPKFDhw6cPn0aPT09Ll++LEtGR0eHWbNm4eXlxcmTJwsshPgEU1NT1q9fz4EDB9izZw95pX+XL2PI1tHNqGdlgvsfl1l7MpiKFSuyZs0aLl++zIkTJ/KUywsTExOmTJlCSEhIgWkNz1OvXj1mz57NBx98AEA5YwOmda7N6WntGNemBidux9B52Sk+3XwJ//BnC3nq6upSoYJSHP1VUKsFR29FMWD1OfqsPMuV+wnM6FoH7ylt6O9qk2drzeJCpRZM332dDWfuMqKlHXP7NtCqPW8DigOihNGypgUXQmLJVmnnzsbZ4Ee42JphZGYJ1i5w+5/iNSBgP+gaQM0Oxau3hNLTyYqq5sYs/ff2a0dBJKdnseLYHVrZl/8vR1NjHLpAo2Fw5uecSBa5hByHYz/l1JBo0O/VdCsoKCi85ZgY6bN4gBOrh7oQmZjTrnPdyRBUhRQFp/B24ezsjI+Pj6zw/6fp3Lkz3t7ePHz4UCO5rl274uHh8VLHhXlpA7aNbkbX+pbM8Qpgxh5/slVqnJycNErDeIKhoSEtWxZOuq5ZaQOmdqrN6Wlt+bxdTc7ceUT3X07Tf/VZ9l19qEQcvSIZ2Sp2XrxPx2UnGeXhS3jCY/7XvS5nvm7HaLfqGOlrN8UhPUvFhO1+bL+Y02pzZve6Wq3Dlx+PHz+WHc30hPDwcNLTNWs9GxgYqPH//vMoDogSRvMa5UnOyMb/YVLBgwuZ8ITHBEQm08Yh17vr0BXCL0FSRPEYIERO/YdqrcHoxWJACi+ip6vD5I61uBmRxG6/8Ne61poTIcSnZTG1k8PrGdV5Hlg5w65REC7jrstDP9jxMZSvBT2Wwxs68b/JSJLUWZKkQEmS7kiS9EIjZ0mS2kiSlChJ0pXcQ/OVnoKCwhtD5/qVOfSlG61rVeAnr1sMWnue+3FpBQsqvHNYWVnRrZvmUaU2NjZUq1ZNYzkzM7N82yAa6evyy6CGuLepwdYL9xjp4UtyehaSJL0RG79yxgZM7ujA6WntmNG1DlFJGUzY5kfL+d4s+fc2kYmabebeVUIfpbLwUACt5h/jK89r6OvqsGygM8entmHUe9XybatZXEQnpTNwzTm8rkfwTdfaTO6o+fpXrVZz4cIFjWTu37/PsmXLZEf8AJw+fZqJEydq1P7zwIEDjBw5UlZb0if8888/9O7dm8qVK8uWyQvFAVHCaF49587z2eDirwNxLDeMv13t3IrCDrlpGLcPFo8B0bcg/q6SfqEhPRytcKpiysJDAaRmZL/SNUJiUlh7MoRezlY4VpHfpzhPDIxh0HYwtgCPnhDsnY/i47CpN5QyhSG7ctI4FDRCkiRdYAXQBagLDJIkqW4eQ08JIZxzjx+K1UgFBYVCp3wZQ9Z+5MKi/k7cikii87KTbPe5p9GiVkFBG+joSEzrXJt5fRtw5s4j+q8+R3jCY22b9QymxvqMdqvO8Slt+H14Y+pbmfCLdxAt53szdrMvXtcjSM9SadvMN4q0zGx2XXrAgDXnaLPoOKuOB1PPyoTNo5rgNeE9eje0Lra6CgkJCfk6BvzDE+m14gxB0SmsHupCZzt9fvjhB5YvXy7r+tnZ2WzduhVHR0fZhUnT0tL4/vvvcXBwoFatWrIcbqmpqUycOBE3Nzc6deokS09mZiaTJ0+me/fudO3aVZaMEIKFCxfSvXt33NzcNHJ05IXigChhVChriEOlspy9U/x1ILwDorG1MKZGhdI5L1Ssk9PdINCreAwIOABI/+/4UJCFjo7EzB51iU7OYMHBAI3l1WrB//b6Y6ivw4xu8tpLFUjZyjDqEJSrCpv7woHJEHf3/88n3AOvqTnOh7KVYdjfUE4p0PSKNAHuCCFChBCZwHagl5ZtUlBQKAYkSaKfSxUOfumGk005vt59nVEevkQnK3dpFd58PmxSFY8RTQiPf0zvFWe4FBanbZNeQEdHom3tivw+ogknprRl1HvVuBSWwLg/LuPy4798ueMK3gFR72yKRka2imOB0Xy16yqNZx9hyp9XiUnO4KvODpyb3p7fRzShlX0FjaNbVCoVt2/f5q+//mL27AoJP6QAACAASURBVNl4enoWKJOWlsacOXNo1aoV1atXf+md/4P+kfRffQ4J2DG6KV5r52JnZ8euXbsYO3asLPvmzJnDkCFDsLCwYPDgwbJkDh06xKxZs3B0dKRLly6yZMLDw9myZQtVqlShVy95S7usrCx8fHwoU6YMgwYNkiUjhCA5OZly5crRu3dvWTL5of34FgWNaVmzPFsuhJGWmY2xQfH8Ch9nqjhz5xGDmlT9/0lCkqB2d/BZC+mJYKRhVwRNCdgPVRpDWXk9nRX+Hxdbc4Y1t2Pj2VA617fUqIbDhjN3OXMnlp/61KdiWflhWgViYpXjhPD+CXzWwMXfcrpkIEHyQ9DRA9eR0PFHMChdeHrfPayB+089fwA0zWNcc0mSrgIPgSlCiBvFYZyCgkLRY12uFFtGNcXjXCjz/gmg09KTzOpVnx6Olm9EWLuCwst4z748nuNa8ImHLwPWnOerTg6MblUdnTewCGBVC2O+6VqHaZ1rcz4klr+vPuQf/0j+8gunnLE+nepWpo1DBVrUKI+psb62zS0S7t69S2xSGgFJepwNS+HE7RhSM1WUNtClawNLBjS2wdXW7Jl5JygoiEmTJpGYmIhKpeLHH3+kXbt2+eoJCwujWbNmxMfHM2rUKKZPn16gbffu3WPz5s0EBQWxf/9+nJycnjkvhGDl8WAWHgrE2aYcaz92ISo0iGPHjmFtbc3WrVtlpSuEhobi6elJly5dmD9/vqw5Njk5mYULFzJr1iyaNGkiS0YIwbx58/jiiy9o1qwZenry9oS7d+/GwsKC8+fPU7FiRVkyYWFh7Nq1C19fX6ysrGTJ5IfigCiBtK1dgQ1n7nIuOJb2dYpnM342+BEZ2Wra13nuD7Vubzj3a05BQacPi86A+DCIuAIdvi86HW85X3V24MTtGD7f5se+z1piVa5UgTKXwuKYfzCATvUqMbhJ1cI3yrAsdJkHzcfBjT3wKBBU2VC5PtTtlRMhofC65PUt9nwM9mXAVgiRIklSV2APYP/ChSRpDDAGoGpV5XejoFCS0NGRGNGyGq3sKzD5z6tM2ObHgWsP+bF3ITuXFRQKmVqVyrJ/wntM23WNuf8EcOFuHIv7O2FW+s1sx66rI9GyZnla1izPD73qcyoohr+vPuTA9Qh2+N5HRwJnm3K0sq+AW60KOFUxRa8IUw+ys7NJSEigfHnNOoitXLmSuLg4mjdvTpMmTShbtmye4zKyVVy6+4h9525y9Pp9ojFF0tVDJzOFTvUsGfBebVrUsMBQ79mCktHR0ezcuZNt27Zx/fp1qlatyvbt26lfv/5LbYqNjWXp0qXs2rWLTp06UaVKFRYsWJDvhj0jI4N58+bh6enJqlWrCA0NpXPnzs+MSUrPYvru6xy4FkEvZyvmf+DIrh3bmDdvHh4eHpiZmVG9evUCPzN/f38GDBjAqlWraNasGYaGhgXKPH78mF69ejFixAhGjx5d4PgnLF68mPT0dL799lvZjuRbt24xb948Tp06hbm5uSwZtVrNyJEjWbZs2SvVfckLxQFRAmlSzRxjA128A6KLzQHhHRBNaQNdmlR77o+1iiuY2sCNv4rWAXH9z5zHen2LTsdbjrGBHms/cqHPyrN84uHLH580zffLOzAymZEbfbEqV4r5HzgW7V2yclWh5YSiu/67zQPg6fyVKuREOfyHECLpqZ+9JElaKUlSeSHEo+fGrQXWAri6uiqJ5AoKJZCaFcvg+Wlz1p++y+J/b9Nx6Um+71GPXs5WSjTEO8Lhw4fp0KGDRnnc9+7dIyEhAUdHR9kyQgj27dtHz549Nfrb8vPzo3Tp0tSqVeu/10yM9Fk5pBGbzoXx04FbdFt+il+HNKJRVTMgJyR/27ZtDB48WKP39e+//2JtbU3dunmVRsqb1NRU1q1bxyeffEKZMvnXpjLQ06F9nUq0r1OJ3z02ES+ZklXenrN341l+NIifjwZR1kgPZ5tyOFUph2MVU5xtylHRJMcpGBISwsqVK2ncuDGNGzcmNjaWpKQk2rdvn6/eb7/9lujoaMzNzTEzM2PZsmW0aNGC4cOH07lzZ/T1X4zAOHbsGLNmzSI2NpbMzEySkpKIjIzE0tKSkSNHMnXqVExNTUl8nIV/eCIX7sbhczeWC3eiEDo51zM3KI1+wEnG9XqPiUP6o/sSx8qvv/7Kb7/9xoABA9iyZQv+/v60b98eY2Pjl76n6Oho2rRpg7u7O35+fqjVaoyNjQv82xo3bhzW1tb4+PjkGcFw+V48E7b5EZGYzrTOtfm0dXVOnz7Ntm3bOHnypEYb9UmTJrF161acnZ1lyQD8/vvv9OjRQyPnQ1xcHN7e3nh6emr0v7V27VrWr18v+z0BXL16FScnJzp27ChbpiCkkliMyNXVVfj6+mrbDK0yepMvNx8mcXpa2yJfMAghaDHPG6cq5Vj9kcuLAw7NgAtrYOodKPWaBQrzNgBWNoNSZjCymApevsWcuB3D6E2+2Job89swV2wtXkxvOB30iPFbL2Oop4OnewtszF/+haDw/0iSdEkI4aptO55GkiQ94DbQHggHLgKDn06xkCSpMhAlhBCSJDUBdpETEfHSLwhlHlZQKPnciU5h6q6r+N1LoEOdSszpU/+/jU9J5k2ci4uKV5mL3d3dsbOzY9q0abJlrl+/zsCBAzl69CiWlpayZNRqNcOHD8fa2pq5c+fK1nXhwgWGDx/Oli1bcHF5cd157UEC47deJiIhZ8P4SatqZGVlMWHCBMLDw9m0aRPlypWTtT4+c+YM48ePp1evXkyfPp2kpKQCw9JTU1NZunQpmzdvZtiwYbRs2ZLy5ctTr169fOUuXryIh4cHhw8f5r333uNGUCidh08k06waV+4ncjsq+b+WuZVNjHCsYkp1c0NSIkKIDrlB0OWz3Pb34+HDh3Tq1In58+e/kEbwhMDAQCIjI4mLiyM6OpovvvgCOzs7WrRoQd++fenatesLn09ycjIpKSmYm5tjaGiI5559xGbqYlG9AUExaQREJhEYmUxEbqcPHQnqWpnQ0Los7zlUprGdOWX0c2rP5OXgeJr09HQMDQ013sNkZWUVeO3nUalU6Oq+2M5TrRasORnC4sOBVDIxYvmghrjY5ji0hBAIITQutiiE0Pg9vYrM68gVF/nNw6/lgJAkyRzYAdgBocAAIUT8c2Mccsc8oTowUwixTJKk74HRQEzuuW+EEAVWNFQWvrDN5x7Td1/n0BduOFTOOySqsLj5MImuy0+xoJ8jA1zzKAQYfgnWtctpkegyrPANiLgGa1pBtyXQeFThX/8d5GzwI8ZuukSWWs0n71Wnm6MlFcoaEhKTynafe/x1JZxaFcuy9mOXPB0UCnnzpi56c9MqlgG6wAYhxE+SJH0KIIRYLUnSZ4A7kA08BiYJIc7md01lHlZQeDtQqQW/n7nLwkOBGOrp8H3PevRpaP1GL2wL4k2di4uCV5mL09PTadWqFUuXLqV58+Z5bs7y4sCBA8yePZsjR44AULp0weuD7OxsBg4ciIuLC4MHD8bOzk6Wrlu3btGvXz+WLVuGjo7OC3f8Ex9nMW3XNQ7eiKR1rQrM7dsAq3Kl2LRpEwsWLKBz586MHj0aB4eCWyc+CdHfvXs3KpWKAwcOYGtrW6BccnIyK1euZOHChQgh8PLyomnTvEosPUtWVharV69mwoScyM9x48axaNEi0DXgxsNErj5I5Or9BK49SCAsLo2nt2qGkgqj7GTM9FWYlzagqVNdrCxMMCttgLmxAWalDTDS10VPR0JHR0JPRyIj/THZmZmUMzMjLTOb1AwVqZnZpOU+pqRnE5WcTkRCOhGJj4lITCciMZ241Mz/9OrrStSoUIbalcviUNmEOpZlaWRrholRyaxlEZ2czuSdVzkV9IhuDSyZ07cBpqVK5nt5UylKB8QCIE4IMS+3t7yZEOKl7tTcdnDhQFMhRFiuAyJFCLFIE73KwjenN23TuUeZ1KEWn7d/IVW7UPnVO4hFh2/jM6N93nmiQsCKJlDKPKeoYGFzcDr4rIMpt8FYfsiQQv5EJqbz/b4bHLoZ+cyXm5G+DsNa2DGhnT2l34A+zCUJZdGroKBQUgmJSeGrXdfwDYunXe2KzOnTgMqmJTMaQpmLCyYoKIhevXrRtm1bVqxYIVtuyZIlbNq0iVGjRvH555/LksnMzKRnz55cuXKFEydOyHIKQE76QdOmTSlVqhS3bt16weEhhGDz+TDmegWgqyPxTdc6DGpiw5o1a3B3d6dRo0acO3cOA4OCa0Wo1WqGDh3Ktm3bqFu3LmfOnKFcuYKjemNjY/n222+5du0aYWFh/P7777z//vsFysXExBAdHU1KSgqpqalYW1vn+blkZKu4H5dG6KM0QmNTc45HaTyITyMuNZOk9Fdrr54XpqX0sTQ1yjnKlcLK1Agbc2PqWJpQrXzpYmuRWdQcC4xm6p9XSU7P5rse9RjUxKZEO1zfVIrSAREItBFCREiSZAkcF0K8dFaRJKkj8J0QomXu8+9RHBCvzAerzpKepeLAhFZFqqfHL6fR0ZHYO77lywedXgpHvofPL4NFjcJTnpUOS2pD9TbQf2PhXVfhP6KS0jkb/IjEtCyqmBnT2M78ra3OXNQoi14FBYWSjEot2Hg2lIWHAtDX1WFm97r0c6lS4hbnylxcMPfv36dNmzaEhIRw+/Zt7O3l3czasWMHgwcPpkaNGgQEBMgKUc/MzGTChAmsWbOGIUOGsGXLFtk2zp49m40bNzJ58mTmzJmT57h7sWl8vfsaZ4NjaV7dgqmtrTi2/0/Wr19P9+7dWbBggSx9QgiuX7/OoUOHyM7OZtq0aRqF4AshiIuLw8JCfqex1yVLpSYhLYv4tEziUjOJT80kI1tNtlqgUj95FGSrcvZ7ZQz1MDbUpbShHqUN9DA20KWMoR4Vyhq+9TedYlMy+HH/TfZceYhDpbL8MrghtSoVbRT5u0xROiAShBDlnnoeL4Qwy2f8BuCyEOLX3OffA8OBJMAXmPx8CkdeKAvfHNadDOEnr1uc+qptkeXohz5Kpc2i48zoWofRbvlUf016CEvrwXuToP3/Cs+A67vAcxR8tAdqtC286yooFAHKoldBQeFtIPRRKl/tuoZPaBxtHCowp08DWZ2T3hSUuVgegYGBDBw4kJ49e/LDDz/Iljt//jwjR45k8eLFdOnSRbbcxYsXmTx5MmvWrKFOnTqy5cLDw1m+fDmff/45VapUyXOMEILtF+/z04FbqNSCqZ0c+Li5LZcv+VK/fv18ixsqvN0IIdh9OZzZB26SkpGNe5uajG9b44WuHAqFS37zcIFuPUmSjkiS5J/H0UtDIwyAnsCfT728CqgBOAMRwOJ85MdIkuQrSZJvTEzMy4a9U3SqVxmAQzcii0zHgesRAHR1LKDgkIkV1Hwf/DZDdmb+YzXh0kYoZwvVWhfeNRUUFBQUFBReil350mwf04zve9TlQkgc7y85waZzoajVJa9wucLLcXBw4Pz585iamqLJDclmzZpx+fJlWakNT9O4cWNOnDghK7XhaaytrZk/fz7W1tYvHSNJEoOaVOXfSW40q27OD/tvMmDNOcra1FacD+8w92LT+HiDD5P/vEq18qU5MKEVk96vpTgfXhO1Wv1a8gU6IIQQHYQQ9fM49gJRuakX5D5G53OpLuREP0Q9de0oIYRKCKEG1gFN8rFjrRDCVQjhWqFCBbnv762mqoUxdS1N2H8tosh0HLgWQaOq5bCWc+ejyRhIiYJb+wpHeeR1CD0FriNAwyq0CgoKCgoKCq+Ojo7E8JbVOPylG41szZi59wb915wjKCpZ26a9kUiSZC5J0r+SJAXlPr4QESxJkoMkSVeeOpIkSfoi99z3kiSFP3Wua3HYbWRkxOTJkzVOszEyMiqwFWReSJIku4tGXrIFYWlaig3DG7N0oBMhj1LptvwU03dfIyY545V0KpRMslRq1pwIpuOyE/jdS+CHXvXY9WmLEpNyoVarSUtL00gmIiKCe/fuaSRz8eJFLly4oJHMv//+y44dOwoemA+vu6vbBzxpezAM2JvP2EHAtqdfeOK8yKUP4P+a9rxz9HK24sr9BEIfpRb6tYOikrkZkUQ3Ryt5AjXagXl18FlbOAacWwH6pcFleOFcT0FBQUFBQUEjbMyN2TSyCYv7OxEck0K35af5+UgQmdmvdwfsLeRr4KgQwh44mvv8GYQQgUIIZyGEM+ACpAF/PTVk6ZPzcrrCKeSNJEn0aViFE1PaMrxFNf70fUDbRcdZefwO6VkqbZunUIQIITjoH0HHpSeZ+08A79WswL+T3Pi4uR06Oq9fyyYiIoKMDPnOrAcPHrBkyRJSUlJkjVer1Xh6etK7d2/ZOtLT05k7dy6dOnWicuXKsmTS0tKYMmUKPXr0eGkr1+fJzMxk6tSpdO/e/ZWcj0/zug6IecD7kiQFAe/nPkeSJCtJkv6bOCVJMs49v/s5+QWSJF2XJOka0Bb48jXteefo6WyFJMHeKw8L/dq7Lj1AT0eil7NMB4SOTk4UxP0LcN/n9ZQnReTUf2g4FEq9tKyIgoKCgoKCQhEjSRIfuFThyKTWdK5fmaVHbtP9l1NcCiuwbNe7RC/AI/dnD6CgHUR7IFgIEVakVr3DmBrrM7NHXQ5/6Uaz6hYsOBhIhyUnOHAtQqOUE4U3HyEEvqFx9Ft9jk+3XEZXR2L9MFfWfeyCpWmpZ8YFBwezZcsWfv75Z7KzC+4iEhwczKJFi2jRogXz58/H0NCwQJmzZ8/Sp08f7OzsMDU1pUyZMgXKBAQE0LBhQ/r168eQIUNkpQ7Fx8fTrl07vvnmGyZMmCArLUqlUjF+/HgWL17M6NGjMTKS1+1oy5YtLFq0iC5dulCxYkVZMi/jtcqdCiFiyZlAn3/9IdD1qedpwAslYYUQH72OfoWcULOm1czZeyWcCe1rFlql6myVmt1+4bRxqEj5MgX/o/1Ho4/h5EI4sQCG7np1A04vAQQ0c3/1aygoKCgoKCgUGuXLGLJ8UEN6N7Ti27/86bf6LMOa2zGlkwNl3vIK+jKoJISIAMjtDlfQCv1DnosMBj6TJOljNCjMrlAw1SuU4bdhrpy584gf999k/NbLuNqaMaWTA02rmZe4Li9vG3Fxcdy9exeVSoVKpcLY2LjAu/JpaWnMmDGDmzdvEhb3GJtu4wlKL0OFsobM7duA/i5V0HuubaharWbQoEHs3LkTW1tbTp48iZ5ewfPWqlWrWLx4MW3btmXhwoWy3lNISAh79+6la9eujBw5UpbMw4cPSUxMxM3NjQEDBsiSiY6OJj4+Hjc3N4YNG1awADmf3bVr1+jduzfu7vL2WUIITpw4wWeffUbnzp1lyeTHO/9t8TbQt2EVvvK8xuV78bjYmhfKNU8FPSImOYN+LnlXG34pBqWh+Xg4+gOEXwJrF82VJ9wD399zoh/Mq2kur6CgoKCgoFBktKtdicOTLFh4MACPc6EcvhHJT30a0Lb2690Ve9ORJOkIkFeM8wwNr/OkMPv0p15eBfwIiNzHxUCeOxdJksYAYwCqVq2qiep3mpY1y3NgQiv+9L3P4n9v8+Ha8zS2M+Ozdva42ZdXHBHPceHCBWxtbWWH9QMcO3aMJUuWYG1tjbW1Nb169cLR0fGl49PT0/H29mbIkCFkZmbSpk0bNmzYkK+O6OhoVq9ezfZ9h1DVak+ZDp0IV+vxZYcajHarhrHBi9vbqKgoZs6cSUhICPb29hw8eLDA/53k5GSmTJlCcHAw7u7u/PDDD+jr59+mXq1W88MPP3Ds2DH27duHi4uLrL+rvXv3MnPmTE6cOEFWVpYsmdDQUPr06YOHhwe1a9cu0DbIiX4YNGgQY8eOZeTIkbIcMADr168nNTWVjRs3yhpfEK/VhlNbKO3fniU1I5umc47SsV4llgxwLpRrfuJxkSv3Ezj7dXsM9DTM1ElPgp+doGJdGL4fNJ3Q/3IH/10wwQ9MNXSAKChoEaX1m4KCwrvGpbB4vva8RlB0Cj2drJjZo65mkZNFgDbmYkmSAoE2udEPlsBxIYTDS8b2AsYLITq+5LwdsF8IUb8gva8yFz9+/JhSpTRrq6pWq8nIyNBYLjk5mbJlNSv8l5qaioGBgawN1dPExsZiYfFCwHWepGep2HHxPiu8g4hO+b/27j0u6ir/4/jrgCiBCt5FQbxb4q00tDQrzfKWZG3ectOtXS2zVNLUUre27abumpva5mqXn7VbZJYmGmtKWni/YOKFVCQvgNwEL9xnzu+PGVxShvmOzjBcPs/HYx4MM9/DvOc7X8535sy5FNAl0I/J97flgdua2J0rQGvN6dOnCQ4OdijfyZMnCQgIuNq1Xmtt94PmxYsXOXbs2NWlRE+cOEG9evXsPs9t27ZRVFR0tfv/vHnzGDp0KMOHD7c5HCAhIYEtW7aQlZVFVlYW33//Pbt27aJNmzaEhYUxd+7c61Yw0VqzbNkyDhw4QGxsLJcvX+b48eN06dKFv/71rwwePLjU57ht2zaWLFlCbGws/fr14/Tp0wwaNIjnnnsODxsTz1+4cIHw8HB2Hf2VVoP+xLG8ugCMCm3B1Afa06hO6fXOkiVLWLp0KbNmzeL3v/89KSkpNGtW9vDyw4cPM2rUKCZOnMikSZMAbOYquS8ef/xxGjVqxOLFiw2vErNmzRrefvtt1q9fb3hoQ3Z2Nvfccw/vvfce995rfKXA2bNnU1hYyMKFCw2XOXLkCKNGjeKnn36ibt26hsuVVQ9LD4gqwLdWDR65vRkRe88yb2hH/H0cWxbpWmcyc9h8LJXJ97d1vPEBwLsu9JsDkeFw5BsIGW687K/b4eC/ofcUaXwQQgghKrjuwfVY/0If3v/hJEujT7D1lzRmDbqVkT2CnDLpWyVSPDH729zgxOzFQzhw8cTsI0eOZNKkSQ51pf7hhx948803Wb9+veEx42azmUGDBjF9+nSHJtVbv349//znP4mIiMDoynd5eXkMGDCAMWPGMG3aNDw9y15m0dvLk3F3t+TKz1Es2bmHJO/hTFi1j/aNfXm+f3sGdw7A08bxm5GRweOPP07Tpk2ZMmUKrVq1olatWmUuE1r8vJYtW0aHDh0ICwtj+/btPP/883TrZvvLw/T0dBYtWkRcnOVwqFevHrGxsUybNo1p06bZXNL04MGDHDlyhOzsbLKystiyZQsRERG0bNmSRYsWERYWdl3DwJUrV7hw4QL+/v4EBwdz/vx5AgICGDduHIMHDy71A7VSCm9vb8aOHcuCBQuoWbMmGzdu5NFHHy3zA7uPjw/h4eGEhobi4eFhqFHsRJaJzI6/I6cJJBR58uTdQfzxntZ2V+oLDQ3lD3/4A76+vgB2Gx8AAgMD+eqrr2jfvr3dbYsppZg3b16ZPT5K06tXLzZt2oSfn5/hMnXr1mX16tUO5QOYOHEiQUFBDpVp3749kZGRDjU+2CM9IKqII0kXGfyPH3ll8G38qW/rm/pbb244ysqfTvHTzPt/M3GLQ8wm+OBeyMmAZ2PAx8DQkMI8WH4fFFyB53ZahnMIUYlIDwghRHV2IvUSL38dx+5TmfQIrscbwzvToWn5L3vnph4QDYAIoAVwGnhca52plGoGrNBaD7Zu5wOcAVprrbNLlF8FdMMyBCMRmFiiQcKmG6mLz507x4ABA4iIiKBTJ7udLK5auHAhW7duZc2aNSilDHXfTk1NZejQoUyaNIlhw4ZRv76xocJr1qxh7ty5rFq1Cg8PjzI/pBe7cuUKs2fPJjY2lvHjx9OzZ09CQkLslouPj+elmbM47x1IRpM7KbylAc39b2F0aBAj7gyicZ3rG1y01uzYsYPFixezfft2zGbz1S73ZdFac+DAASIiInjnnXeoUaMGc+bM4eWXX7bb4yM3N5fnnnuOXbt2ERgYSOfOnXn55Zft7tPs7GxWr15Nnz59aN++veGhJoWFhQ73QnE2s1mz9XgaH2w9yc6ETPx9vBh3V0vG3d2S+r4394WrcK2y6mFpgKhCRn6wg9OZOWydcf+N9VwALuYV0vvtLdzTriHLnriB+RtKSjoAKwZAh4EwYpX9oRjfToV9H8GYL6F9qb0ShajQpAFCCFHdaa1Zve8sb244yqW8Ip6+pxVT+rcrdVy2q0hdbN+BAwcYO3YsI0aMYM6cOXZ7DBT785//TGxsLF27duUvf/mLoTIXL14kLCyM9PR0li5dSt++fQ2Vi4uLY9SoUaSnp7N//35D31wDfPvtt1dXINi9e7fhRo9nn32Wf36wnOC7H6b7qGnsO3uZGh6Kh0Ka8kSvFtzVusF1H95zc3MZP34827dvJysri08++YRHH33U7mP98ssv7Ny5E7PZjNlsplOnToSGhhrKWR0kZ+eyeu9Zvth7hrMXcgnw8+aP97Rm1J1B+MqEt5WCNEBUE9Hxqfzhoz0sfLyr45NHWr23+Th/2/QL65/vQ6fmxrsC2RTzD9g0F+6bDfddtyT2/+xZAZEvQu+pMOC1m39cIdxA3vQKIYRF5pUC3t54lIi9Z2nufwt/CQuh/21NyuWxpS62Lzc3l2HDhvH999/zzTffEBYWZqhcbGwsvXv3RinFqVOnDA2R0FqzYMECZs6cSZcuXdi3b5+h3hMXL15k0qRJfP755zz44INERkYa+vY+Pj6ejz/+mK+//poWLVqwYcMGQ4+XnZ3Nnj172LFjBxkZGTw97WXWHkrny31nyc4tpHUjX57oGcxjdzQvdbhzYWEhycnJBAYG2p0vQFyvyGRmy7FUvthzhuj4VMwaerdtwMg7WzAwpOkNf7kq3EMaIKoJrTWDFv9IgcnMf6f2vW75GXsu5xfR550tdG9Rj5Xj73ROKLMZ1j0PsZ9C35csjRAeJVrZtYYdS+C/c6DdQzDq3+ApLZuicpI3vUII8Vu7EjKY800cx1MvMzCkKX8e1vHGh3caJHWxMYcOHeLpp5/G19eX6OhoDAxjQAAAGOVJREFUw+ViYmKYMmUK/fr1Y/78+YbL7dmzh9dff52BAwdendjPiKSkJD788EN69Ojh8BKAR48excfHx+EJI0vKKzQR+XMyn+76lQOns/DyVPRt14ghXQJ4oGMT6nq7d5hCZaa1Jv78JdbFJrF631lSL+XTuE4tHu8RyMgeLWjRwMfdEcUNkgaIaiTqcAoTV+3jzeGdGdPTsaWZFkQdY2n0SdY+15uuQaVPanNDzCZYO9kyuWTgndDzGWjYDjJPwe5/wa8/wa1D4XcfQg33zpwtxM2QN71CCHG9giIz//oxgX9sPk4ND0X4gx0Yd1eww1+UGCV1sXEmk4nFixczdOhQhya0M5vNrFmzhmHDhhme7b9YYmIiLVu2dDBpxXA4KZtvDpwj8udkkrLzqOnpQd/2jRjaJYD+tzWmjjRG2GU2aw6ezeK7wylExaWQmJGDh4L7OzRmVGgL7u/QyGV1gyg/0gBRjWitGfHBDk6l5/DDjPuobXCc1OmMHB5YtJUhnQNYNNI5S3leEwwOfg5b/goXz/7vdp8G0H8e3P4kSHc1UcnJm14hhLDtdEYO89bF8UN8GiHN6vLG8M50c+YXHlZSFzvOyJKQ4n/MZk3s2Swif05mw6FkkrPzqFnDg3vbN6L/rY3p3bYhQfXl2/tiRSYzexIvEHU4he/iUki5mEcND8XdbRsyMKQpAzo2sbmMpnCtG1mWNyEhgVatWpVZZ0gDRDUTeyaL4ctiGB3agjeHd7a7vdmsGffRbvb9eoEtL95HUz9jyyvdELMJzu6BK+mWxofAO2XIhagy5E2vEEKUTWvNhkMpvPbtYdIu5zPqzha89FAH6jlxRnupi0V5Mps1B85cIPLnFDbGWRojAIIb+NCnbUP6tG3IXW0alDpvRFVlMmuOJl9kZ0IGO05msPtUJpfyi6hlbaQZ2Kkp/W9tgp9P9egx4uiKIsnJyWRmZhpaxQUs9WpkZCQmk8nwfC4FBQUsWbIEpRTTpk0zVCY3N5fXX3+d/Px8/va3v5W5bVn1sHzyq4K6Bfkz4Z7WfLAtgQG3NeH+WxuXuf2HMaf48Xg6rz/SybWND2CZ/6FFL9c+hhBCCCEqJKUUQ7oE0Ld9Q979/jgfb09kY1wyMwfeysgeQXh4yLfwonLx8FB0D65P9+D6zB16GydSL/PTiXRiTqSzNjaJz3adRino3NyPu9o0oFugP52a+xFY75Yq0+ukyGQm/vwldiZkWhscMriYVwRAq4a+DO3ajHvaNeS+Do3KdUUce8xms+EJQxMTE4mOjmbIkCE0blz2ZyuA8+fPExERQVRUFEuWLLE77Ehrzc6dO3nvvffYtWsX+/fvt/sYxQ0Pr776KikpKcTHxxt6LpGRkYSHh3P+/HkSExMNldm9ezdjx47lxIkTHD9+3FAZWyrOESCcatqA9mz9JY0X/nOALybeRcdmdUvdbsux87y98RgPdmzCWAfnjBBCCCGEuBF1vL2YO7Qjj/cIZN43h5m95hCf7znD62EhdAl0/rAMIcqDUop2TerQrkkd/tC7FYUmMz+fzeKn4xnEnEhn5Y+nKDJbep/X8/GiU3M/OjX3o7P1UhkaJS7mFXI06SJHky9yJPkiR5MvEX/+EgVFZsDS82NQpwDuatOAXq0buOTLTbPZzPnz50lPTyctLY3Lly8zePBgu6udrF69mp9++olDhw4RFBTEsmXL8PEpe6jM+vXrmTp1KidPnuTdd9811PgQFxdHz549ycnJYd26dYbmPMnIyGDMmDEkJiayceNG/Pzsr0ZoMplYuXIl+/bt49NPP8XX19duGYBTp06RkJDAnDlz8Pc3Vt96e3tz+fJlwsLCaNOmjaEytkgDRBXl7eXJyvF38rv3t/Pkh7tY9kR3Qlv9dh3kbw8m8eKXB7ktoC4LR3St8BWeEEIIIaqWW5vW5YuJvfgm9hxvRB4jbGkMY0JbMOOhDtWqy7qomrw8Pa72jpjyQDvyCk3Ep1zi0Lls4s5lc+hcNv/alnC1UaJOrRq0aOBDi/rWS4nrzfxvwascJmfUWpNxpYBzF3JIysrjXFYuZy/kcvZCDsdSLnH2Qu7Vbev71qRjQF3G3RVMSDM/6psyKcxOpWVLX4KCGhmaoDQtLY0JEyZQUFCAl5cXo0aNYuTIkWV+LsnOzmbAgAEcPnyYli1b8tVXX9ltfEhMTOTjjz8mMjKSxx57jOXLl9vNd/LkSZYuXUpmZiYzZsxgypQpdp9PcnIy4eHhdO/end69e/Pwww/bLZObm8vkyZPp168f9erVM7Tai9aaN954g4KCAlasWMGYMWPslgGIiopi5cqVbN68ma5duxoqk5KSwujRo4mMjDTcYFEWaYCowpr738Kqp3vyp//by6jlO3ikW3Pu7dCIQpMm8uckouPT6Bbkz0fj75QlhIQQQgjhFkopht8eSP/bmrBo0y98sj2RDYcswzJGyLAMUYV4e3nSNcj/N6vN5Rf9r1EiPuUSZzJziD9/ic1HUykwma9u5+mhaFS7Jv4+NfH38cL/FstPP+t1v1u88KnpiVKW/ykPBR5KYTab2LZ1K7169sTL24dLeUVczi/kUl7R1Uvx78nZuSRl5ZFfZP5tbk8IauBL1yB/Roe2oGNAXTo2q0vjOrXIzs7myJEjHN4bwzcxMXzyyScA3H333SxdupRu3a6f3D43N5cff/yR7777js2bN3PmzBl8fHxYsmQJjzzySKn7TmtNTEwMK1asYOfOnfTo0YPAwEA+++wzGjRoYHOfJyYm8uabb7J7925mz55NaGgoL7/8cpkNFnl5ecyfP58vv/ySBQsW0LBhQ+644w6b2xeLjIxk+vTpvPXWW/Tv39/Q5I5JSUk8+uijjBw5kqlTp2JkfkatNdOnT+fMmTN8/fXXhlei+fHHH5k+fTrfffcdzZs3N1QmJyeH4cOH884773D77bcbKmOPNEBUcW0b1+bb5/uwMCqer/adZc2BcwA0rlOLGQ91YGLf1rLUjRBCCCHcrq63F39+OIQRPYKYtzaOWWsO0bZxbXq0rG+/sDBs1qxZPPvsswQHBxsus2PHDrZt28bMmTMNl9FaM2HCBF555RWHlt2MiIjg1KlTzJgxw/D4/IKCAkaOHMncuXMNfVAs9ve//53U1FRefPFFGjVqZGg1kIyMDB5++GGefPJJRo8eTUFBAb6+vna78oeHh5OYmMiDDz7IQw89RFRUFCNGjKB+/fp0CfS/buiR2ayJ3rWfZ6fPpVGr26jbvA2XM2vwa2IOptbtyazlS1ZOIVk5hb9pqCidPxFf/3Z+AKWgdq0a1KlVgzreXhTkXOTM8cN4m3Kopwq4knaGEwd30bdHZ8aPHkFY2P2lPsfHHnuM5s2bExISwpAhQ0hMTOSVV17hgQcesLkvP/74Y/bv38/AgQOZN28e27dvp0+fPtStW/qQcYDMzEwWL17MU089xcqVK7ly5Qq+vr54enqW+cxXrVpFv379eP/99+1uW+zYsWOYTCZ2795teIUIrTXbtm1j06ZNBAYGGioDsG/fPubNm8fgwYMBDPVIv3LlCv7+/syfP9/wcwKIj49n7dq1hhsfAFJTU3nmmWcYOnSo4TL2yCoY1UhugYkzF3IAaNOoNp7yjYIQTiUzrwshhHNordmRkMHdbRo6XFbq4rJFR0czZcoUoqKiCAgIMFQmPz+f0aNH0759e9566y3A2AelrVu38swzz7B8+XJCQ0OpVcv+Uou5ubnMmDGDY8eO8cknn6C1NvSBbs+ePUyePJnQ0FDGjh1Lw4YN7Y5Vz8/PZ+XKlbz33nsMGzaM7OxsXn31VZo2bVpmuVOnTvHRRx8RERFBYGAgaWlprFmzpszHM5vNxMbGEhUVRVRUFDt27MDPz49FixYxZswYm/uzsLCQkydPcuTIEZYvX05UVBQ1a9bkiSeeYP78+TRo0IC8QjNZuQXkFpjQWP5/tLasRpGWlsYbb75Fx06d6Nn9dnp170YDP198vDzL7F20Z88eWrRoQZMmTcrcFyWZTCY8PDxkWLeQZTiFEKI8yJteIYRwP6mL7duwYQNz5sxh5syZhIWF4e1tf6LAoqIinnrqKWrXrk3btm0JDw839FgJCQk89thjBAcHM3HiRAYNGmSo3LfffstLL71EUVERUVFRtG7d2m4Zk8nEBx98wJw5c6hfvz4xMTGGPkDn5+czd+5cFixYQJs2bfj+++8N9drIz8+nT58+7N27Fz8/P1atWmVozP/x48dZuHAhNWvWxMvLiyFDhtC/f3+75Q4fPoy/vz8BAQGGe4cI4Q7SACGEEOVA3vQKIYT7SV1sn9aa8PBw3n33XRYvXswLL7xgqFxKSgqhoaEkJSVx8OBBQkJCDJX7/PPPGT16NM2bN+fw4cOGZvgvKipiwoQJfPTRR9xxxx3ExMQYaig5ffo0L730Eps3byY4OJjo6Gjq1Kljt9yBAwfYuXMncXFxZGdns2DBAkM9RLTWXL58mfT0dDIyMujatSteXjK3mqjepAFCCCHKgbzpFUII95O62Jjo6GimTp1KamoqCQkJhsa6a61Zu3Ytr732Go0aNSIqKspQd3uz2cymTZtYsmQJAQEBLF++3HDOY8eO8cUXX+Dn58fUqVMNlzObzcTFxWEymZw2eZ4QwhhpgBBCiHIgb3qFEML9pC42zmQysXLlSmrXrm14GT/4X0NESEgI7dq1c+gxExISaNasmaHeDNc+pswtIETlUFY9LKtgCCGEEEIIUQ15enoyYcIETCaTQ+WUUjaXS7THyFwOth5TCFH5yewlQgghhBBCVGOOLOUnhBA3QxoghBBCCCGEEEII4XLSACGEEEIIIYQQQgiXkwYIIYQQQgghhBBCuJw0QAghhBBCCCGEEMLlpAFCCCGEEEIIIYQQLqe01u7O4DClVBrwq4PFGgLpLojjCpLVNSpL1sqSEyTrtYK11o1c/BgVwg3WwyDHjCtUlpwgWV2lsmQtr5xSF7tHRToOJYttFSmPZLGtIuW5kSw26+FK2QBxI5RSe7XWPdydwwjJ6hqVJWtlyQmSVTiuMr0OlSVrZckJktVVKkvWypJT3JiK9PpKFtsqUh7JYltFyuPsLDIEQwghhBBCCCGEEC4nDRBCCCGEEEIIIYRwuerUALHc3QEcIFldo7JkrSw5QbIKx1Wm16GyZK0sOUGyukplyVpZcoobU5FeX8liW0XKI1lsq0h5nJql2swBIYQQQgghhBBCCPepTj0ghBBCCCGEEEII4SbVogFCKTVQKRWvlDqhlJrl7jy2KKWClFLRSqmjSqnDSqkp7s5UFqWUp1LqgFJqvbuzlEUp5a+UWq2UOmbdt3e5O5MtSqlp1tc+Tin1H6WUt7szFVNKfaiUSlVKxZW4rb5SapNS6rj1Zz13ZixmI+sC6zHws1Lqa6WUvzszVjdSD7uO1MXOJfWwc0g9XDUZOd6UUh2UUrElLheVUlOt972qlDpX4r7Brsxi3S5RKXXI+nh7HS3vrCxlnV+csV/snWeVxT+s9/+slLrDaFkXZHnCmuFnpdR2pVTXEveV+nq5OM99SqnsEvt/ntGyLsgyo0SOOKWUSSlV33qfU/dNafX0Nfe75pjRWlfpC+AJnARaAzWBg0BHd+eykTUAuMN6vQ7wS0XNas0YDvwbWO/uLHZyfgL80Xq9JuDv7kw2cjYHTgG3WH+PAMa7O1eJfH2BO4C4ErfNB2ZZr88C3nF3zjKyPgjUsF5/p6JkrQ4XqYddnlnqYudllHrYtVmlHq7kF0ePN2v9nwIEW39/FZhenlmARKDhzT6Xm81S1vnlZveLkfMsMBjYCCigF7DLaFkXZLkbqGe9Pqg4S1mvl4vz3FfaOdQd++aa7R8Gtrhw31xXT5fHMVMdekCEAie01gla6wLgcyDMzZlKpbVO1lrvt16/BBzF8maowlFKBQJDgBXuzlIWpVRdLP9cKwG01gVa6yz3pipTDeAWpVQNwAdIcnOeq7TW24DMa24Ow/KhAuvPR8o1lA2lZdVa/1drXWT9dScQWO7Bqi+ph11E6mKXkHrYCaQerrIcPd76Aye11r9WgCzOLu/Q33Lx+cXIeTYM+D9tsRPwV0oFGCzr1Cxa6+1a6wvWX11dF9zM8yv3fXON0cB/buLxymTjnFKSS46Z6tAA0Rw4U+L3s1TgN5PFlFItgduBXe5NYtO7wEuA2d1B7GgNpAEfKUsX5RVKKV93hyqN1vocsBA4DSQD2Vrr/7o3lV1NtNbJYDmxAo3dnMeop7C06IryIfWw60hd7ERSD5crqYcrJ0ePt1Fc/wFqsrU794c3M+zBgSwa+K9Sap9SasINlHdmFsDm+eVm9ouR86ytbZx9jnb07z3Nb+sCW6+Xq/PcpZQ6qJTaqJQKcbCss7OglPIBBgJflbjZ2fvGHpccM9WhAUKVcluFXvpDKVUby8E2VWt90d15rqWUGgqkaq33uTuLATWwdC16X2t9O3AFS9e4Csd6sgkDWgHNAF+l1Fj3pqp6lFKvAEXAZ+7OUo1IPewCUhc7n9TD5UPq4YpNKfW9dez5tReHvvlVStUEhgFflrj5faAN0A1LI9/fyiFLb631HVi6+j+nlOrryPNwchZb5xeH9ktpf7aU2649z9raxtnnaMN/Tyl1P5YGiJklbnbK6+Vgnv1Yhgl1Bd4DvnGgrLOzFHsYiNFal+yh4Ox9Y49LjpkaNxyn8jgLBJX4PZAK1J3yWkopLyyV0mda6zXuzmNDb2CYskyQ4w3UVUp9qrWuiG/SzgJntdbFLcyrqYBveq0eAE5prdMAlFJrsIyR+9Stqcp2XikVoLVOtnbJSnV3oLIopcYBQ4H+2jqITZQLqYddQ+pi55N62MWkHq74tNYP2LpPKeXI8TYI2K+1Pl/ib1+9rpT6F1Dm5LnOyKK1TrL+TFVKfY2l+/g2HPzfcUYWW+cXR/dLKYycZ21tU9NAWWdnQSnVBcvwwUFa64zi28t4vVyWp+QXDVrrDUqpZUqphkafizOzlHBd7yEX7Bt7XHLMVIceEHuAdkqpVtaW2FHAOjdnKpVSSmEZH3tUa/13d+exRWs9W2sdqLVuiWV/bqmgb3jRWqcAZ5RSHaw39QeOuDFSWU4DvZRSPtZjoT+W8YEV2TpgnPX6OGCtG7OUSSk1EEsL+zCtdY6781QzUg+7gNTFLiH1sAtJPVwlOHK8XTd+3frhvNhwoNTZ952VRSnlq5SqU3wdy0SocUbLOzmLzfOLE/aLkfPsOuBJZdELyxCzZINlnZpFKdUCWAP8Xmv9S4nby3q9XJmnqfX1QSkViuUzcoaRss7OYs3gB9xLiePIRfvGHtccM9pJs2hW5AuWGTx/wTJb5yvuzlNGzj5Yuq/8DMRaL4PdnctO5vuo+DOvdwP2WvfrN1hn3a2IF+A14BiWCmUVUMvdmUpk+w+WboGFWFpEnwYaAJuB49af9d2ds4ysJ7CMVyv+3/qnu3NWp4vUwy7PLXWx83JKPey6rFIPV/KLreMNy5ClDSW288HyAc7vmvKrgEPWemAdEODKLFjmnzlovRwuef5x5v+OwSw2zy/O2C+lnWeBZ4BnrNcVsNR6/yGgR1llb/I4sZdlBXChxH7Ya+/1cnGeydbHO4hlUsy73bVvrL+PBz6/ppzT9w2l19MuP2aU9Q8IIYQQQgghhBBCuEx1GIIhhBBCCCGEEEIIN5MGCCGEEEIIIYQQQricNEAIIYQQQgghhBDC5aQBQgghhBBCCCGEEC4nDRBCCCGEEEIIIYRwOWmAENWWUspfKTXJ3TmEEKK6knpYCCGEqF6kAUJUZ/6AvPEVQgj3kXpYCCHcSCkVoJRab73eTSk1uMR9Q5VSr7kvnaiKpAFCVGdvA22UUrFKqQXuDiOEENWQ1MNCCOFe4cC/rNe7AYNL3BcJDFNK+ZR7KlFlKa21uzMI4RZKqZbAeq11JzdHEUKIaknqYSGEKB9KqTuBlUAo4AnsBkYC64DbAA2cAG4BzgFvaa2/UEotAnZorSPcElxUOTXcHUAIIYQQQgghhOtorfcopdYBf8XSyPApcAW4oLXOB1BKzQN6aK0nlyi6F7gHkAYI4RTSACGEEEIIIYQQVd9fgD1AHvAC0BNIs1MmFWjm4lyiGpEGCFGdXQLquDuEEEJUY1IPCyFE+akP1Aa8AG8g1/qzLMXbCeEUMgmlqLa01hlAjFIqTiY/E0KI8if1sBBClKvlwFzgM+Ad4BegZYn7S2sUbg/ElUc4UT1IDwhRrWmtx7g7gxBCVGdSDwshhOsppZ4EirTW/1ZKeQLbsQzBOKmUaqu1PgFEA7OUUrFYJ6EE7gdmuy24qHJkFQwhhBBCCCGEqIaUUsOB7lrrOaXc1wT4t9a6f/knE1WV9IAQQgghhBBCiGpIa/21UqqBjbtbAC+WZx5R9UkPCCGEEEIIIYQQQricTEIphBBCCCGEEEIIl5MGCCGEEEIIIYQQQricNEAIIYQQQgghhBDC5aQBQgghhBBCCCGEEC4nDRBCCCGEEEIIIYRwuf8HDVXhKoEN1W4AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_er, ww_er] = EI(phi1,phi2,tt,x0,y0)\n", "JJ_er = [(uu_er[i])**2+(ww_er[i])**2 for i in range(len(tt))]\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_er,tt,ww_er)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Euler regressif - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_er)\n", "xlabel('t')\n", "title('Euler regressif - Invariant')\n", "\n", "subplot(1,3,3)\n", "Y1,Y2 = meshgrid(linspace(min(uu_er),max(uu_er),21),linspace(min(ww_er),max(ww_er),21))\n", "V1,V2 = phi1(tt,Y1,Y2),phi2(tt,Y1,Y2)\n", "r=sqrt(V1**2+V2**2)\n", "quiver(Y1, Y2, V1/r, V2/r) \n", "plot(uu_er,ww_er)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Euler regressif - y(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Crank Nicolson**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Big(\\varphi_1(t_{n},u_{n},w_{n})+\\varphi_1(t_{n+1},u_{n+1},w_{n+1})\\big)=u_n-\\frac{h}{2}w_{n}-\\frac{h}{2}w_{n+1},\\\\\n", "w_{n+1}=w_n+\\frac{h}{2}\\Big(\\varphi_2(t_{n},u_{n},w_{n})+\\varphi_2(t_{n+1},u_{n+1},w_{n+1})\\big)=w_n+\\frac{h}{2}u_{n}+\\frac{h}{2}u_{n+1}.\n", "\\end{cases}\n", "$$\n", "En resolvant le système linéaire on obtient une écriture explicite:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=\\dfrac{(4-h^2)u_n-4hw_{n}}{4+h^2},\\\\\n", "w_{n+1}=\\dfrac{(4-h^2)w_n+4hu_{n}}{4+h^2}.\n", "\\end{cases}\n", "$$\n", "De plus, on a\n", "\\begin{align*}\n", "J_{n+1}\n", "&=u_{n+1}^2+w_{n+1}^2\n", "\\\\\n", "&=\\frac{((4-h^2)u_n-4hw_n)^2+((4-h^2)w_n+4hu_n)^2}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{(4-h^2)^2u_n^2+16h^2w_n^2-8(4-h^2)hu_nw_n+(4-h^2)^2w_n^2+16h^2u_n^2+8(4-h^2)hu_nw_n}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{\\big((4-h^2)^2+16h^2\\big)(u_n^2+w_n^2)}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{(4+h^2)^2(u_n^2+w_n^2)}{(4+h^2)^2}\n", "\\\\\n", "&=(u_n^2+w_n^2)=J_n\n", "\\end{align*}\n", "\n", "\n", "On voit que l'invariant est conservé pour tout $h$\n", "\n", "Vérifions ces calculs avec `sympy`:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\left\\{ u_{np1} : \\frac{- dt^{2} u_{n} - 4 dt w_{n} + 4 u_{n}}{dt^{2} + 4}, \\ w_{np1} : \\frac{- dt^{2} w_{n} + 4 dt u_{n} + 4 w_{n}}{dt^{2} + 4}\\right\\}$" ], "text/plain": [ "⎧ 2 2 ⎫\n", "⎪ - dt ⋅uₙ - 4⋅dt⋅wₙ + 4⋅uₙ - dt ⋅wₙ + 4⋅dt⋅uₙ + 4⋅wₙ⎪\n", "⎨uₙₚ₁: ─────────────────────────, wₙₚ₁: ─────────────────────────⎬\n", "⎪ 2 2 ⎪\n", "⎩ dt + 4 dt + 4 ⎭" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle u_{n}^{2} + w_{n}^{2}$" ], "text/plain": [ " 2 2\n", "uₙ + wₙ " ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "\n", "sym.var('u_n, u_np1, w_n, w_np1, dt')\n", "eq1 = sym.Eq( u_np1 , u_n-dt/2*w_n-dt/2*w_np1 )\n", "eq2 = sym.Eq( w_np1 , w_n+dt/2*u_n+dt/2*u_np1 )\n", "sol=sym.solve([eq1,eq2],[u_np1,w_np1],dict=True)[0]\n", "display(sol)\n", "\n", "J_np1=u_np1**2+w_np1**2\n", "J_np1.subs(sol).simplify()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# Notons que ici il est inutile de passer phi1,phi2 car non utilisées explicitement dans le code\n", "def cn(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append(((4-h**2)*uu[i]-4*h*ww[i])/(4+h**2))\n", "\t\tww.append(((4-h**2)*ww[i]+4*h*uu[i])/(4+h**2))\n", "\treturn [uu,ww]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "# VERSION AVEC fsolve (non demandé)\n", "from scipy.optimize import fsolve\n", "\n", "def cn(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tsys = lambda z : [ -z[0]+uu[i]+h/2*(phi1(tt[i],uu[i],ww[i])+phi1(tt[i+1],z[0],z[1])) , \n", " -z[1]+ww[i]+h/2*(phi2(tt[i],uu[i],ww[i])+phi2(tt[i+1],z[0],z[1])) ]\n", "\t\tutemp,wtemp = fsolve( sys , (uu[i],ww[i]) ) \n", "\t\tuu.append(utemp)\n", "\t\tww.append(wtemp)\n", "\treturn [uu,ww]" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_cn, ww_cn] = cn(phi1,phi2,tt,x0,y0)\n", "JJ_cn = [(uu_cn[i])**2+(ww_cn[i])**2 for i in range(len(tt))]\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_cn,tt,ww_cn)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Crank Nicolson - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_cn)\n", "xlabel('t')\n", "title('Crank Nicolson - Invariant')\n", "\n", "subplot(1,3,3)\n", "Y1,Y2 = meshgrid(linspace(min(uu_cn),max(uu_cn),21),linspace(min(ww_cn),max(ww_cn),21))\n", "V1,V2 = phi1(tt,Y1,Y2),phi2(tt,Y1,Y2)\n", "r=sqrt(V1**2+V2**2)\n", "quiver(Y1, Y2, V1/r, V2/r) \n", "plot(uu_cn,ww_cn)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Crank Nicolson - y(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Avec ``odeint`` du module ``scipy.optimize``:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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klIhMXD9lJi6zx9Lr9eh0xp/9Pnz4EEtLy8f7T0pKwszMzGhMQEAA8fHx1KhheLslJiYihHgc9+BREpfD7xEW85B78QlcuRbKsdP+hEZE8UrjZtx/mMS9h4k8SJDYWFlgV8CcQtYWFLI2x87agvh7UezcspGrF89x48pFer3WhvYtm+Hk5ESpUqUoV65cmjmeOnWK0aNH4+Pjg52dHa1bt+aVV16hfv36NGjQgKJFi6b59SQmJjJ16lTGjRtHvXr1iIuLo1OnTnTp0oVGjRoZ/d4vXbqUTZs2kZiYyIULF+jbty99+vShWLFiRr+Hs2fPpkmTJowfP57IyEjGjh1L69atjcZIKTl37hwxMTEMGzaMpk2bMm7cOOzt7Y3GxcTEUKhQIZYsWcKUKVOYMWMGbdq0MRoDhvdPfHw8AwYMAGDevHnY2NhkGAdw8uRJ3n33XX777TdeffVVTTFSSkaPHk1QUBBLly7F3Ny0+yRj5+GcuuMqDVxP9fmN5NfSer1RWjsQQgzAUCmmXLlyJh18X0AE36w1VH2qlCjE2Neq0dTVwaR9ZFpMKGwdA2f/fvKa0EG9PtD6W7BJ+5dPyT6Hr97B+99z+N+MefyavY0Fn7WuRO8mLuhyokCV+BD2/wy+0yEh7snrLs2h42QoUT37c1CeEhr9gAkbz7PxzE0AXq3saHIBQlEURckam8/d4pt152hUoZjJBYg8LleviRcsWABA//79NcdcvnwZLy8vVq9eneENdIr4+HgGDx5M3759ad68uaYYKSXLli1j//79zJ07V3N+R44c4fPPP2fVqlU4ORl/wJeQkICFhQVXrlxhwoQJVKpUiVGjRhmNuXXrFra2toSFhTF//ny2b9+On5+f0Rsyf39/Ll++TLFixdiwYQObNm1i3LhxvP7662m2T0xMZOnSpcyZM4fevXtz7NgxTpw4QcWKFfnf//6XZvv1Gzbyy5K/ORWhx7F6UxILXkBaFDD6tTzhCDaOXDsdrq15kUbQuBElG8M2YNtRgOjkD38AdAKqlrSjTjl72rgVp2m1GmzcuJG9e/dy5swZ3N3dOXbsGOvWrSM8PJxevXqleShzc3O8vLzo2rUrLi4uxMbG4uPjw6JFi2jUKM1ficd69epFjx49sLS0JCwsjMWLF3P69GlatmxpNG7QoEEA/PPPP5w4cQIfH58MCxBCiMdFHz8/P+bMmUN4eHiGBQg7OzsA+vbti4eHB9u3bzfaPoVOp8PGxoalS5cyb9484uLiNBcg6tSpw8aNGzlx4oSm9mD4+iZOnMjChQtJSEgwuQBhdN851ANiI/CDlHJ/8uc7gC+BCkB7KeWHya/3AhpKKYcYO5ap1V69XnLtThxHgu4wY+dlQqIeMLl7Ld6qX1bzPjLl9iVY+jrE3YEmg6GqJ+iT4MxqOLoAilWEXmtVb4gctO5kCJ+vOkVJO2uGtq5I3XJFCIl+wO/7AvENiOSNeqWZ0r0W5mbZOD/ro1hY+T5c2QnVXof6H4BNMbi6F/ZNhYR4eOcvqOCRfTkoT7kcdo/3Fxzi7oMEBjSvQNtqJalUwhZrC+NPHZ6V20/dcpJ66qYoSnZ6d74fYTHxbP/cw+Snzbl9Ls6r18QLFixg8eLF+Pj4UKhQoQzbJyYmcvLkSXr16sXChQtp0qRJhjF37twhLi6Ot956i65du/LVV19l+PM7d+4cjo6ODBkyhKSkJObOnZvhE+tr165x8OBBdu7cyenTp5k5cyb16xv/kQcGBvLll19iZ2fHyZMnGT16NG+88YbRosrBgwfp3r07rq6uJCUl8dFHH/H2229TsGDBNNsnJiYyZcoUxo0bh42NDR06dKBLly506NAh3Sf+e/fuZeDAgfj7G27kx40bR4sWLahbty6FChUi4v5Ddl4IZ7t/GNvPh6E38dYtpTBQyt4aO2sLbK3NeRR7l9sh12j9alPsClhgZ21BQSszHiboiYlPICY+kXvxicQ8SOBefCL34hOIiU8g4t5DLoXf51686d3yX3EuQhu3ErRxK07F4raZ6kWi/HfkhR4QN4DUd/tlgFDAMp3Xs5ROJ3BxKIiLQ0E8aznx8dJjjPzfaawszHitdqmsPpxBTCgs9jT8/8PtUDLV36CyDcCtC/zVE5Z0ho92gnXh7MlDeWzLuVt8tvIkjcoX5fc+DbBNHnJRuUQhWlR2ZObOAKZtu4S5TjDlzdrZk4Q+yVB8CNwNXWdB3fefbCtZA2p0NxStlr8F/XygTL64l81VodEP6DnPD51OsHawO1VL2uV2SoqiKPla5P2H+AVGMqhFxZfxJiXHr4lXrVrF5cuX2bx5s+big7+/P97e3pw7d441a9bg5uaWYczt27fp2LEjsbGxTJs2jY4dO2YYEx0dTbdu3UhISMDb25vevXtn+DOPiIigXbt2BAQE8OuvvzJnzpwMe2b4+/vTtm1bQkNDGTVqFEePHs0wZt68eXz66ackJibi4eHBn3/+aTQ3vV7PggULCAoKok+fPhQsWJDvv/8+3WJFildffZUTJ04QHh5OcMhNzty1ZOLxu1zw2Ws0Dgw9u1u7Fce9ogNuTnYULWhKbyF3E9pmLD4hiUth9zgSFMWO82EcuPL0RJDHgqM4FhzF5M0XHr9mZ21O36YuvNfYmRJ21lmaj5J35VQB4l/gUyHECgzdye5KKW8KIW4DlYQQ5YEQoCfwbnYmYmNpzu996vPe/EN4/X2aak52VCxum7UHSUqA1X0NXes/3AHFqz7fpnxzeG81LO4M6wbD20vV2P9sFBwZy4hVp6hVujCL+zV87sm2EIKhrSuRkKRn5s4A6jsX5e0G2dBDZs9kQ8+HLtOfLj6kKFQC+m6EeS1gVR/4ZJ8appONHiXqGfzncR4m6lk72D3rzwWKoiiKybb6G57ydqxZMrdTyQ45ek386NEjRo8eTXBwMNu3b9dUfJBSMmjQIPbs2cP333+vqfggpWTAgAEcO3aMN998U/OY9t69exMQEED79u3p1KlThsWH+/fv4+npiU6n45NPPsHd3T3DQsKtW7eYMWMGH330ETVq1KBOnToZxsTFxdGoUSOuXbuGg4ODpu7nOp2Ojz/+OMN2qZ28Hs28vVfwOXMr3TaWZjo61ixJa7cSeFRypLBN9qxM8KKsLcyoVcaeWmXs6d+s/FPbEpL0HAm6w3b/cLb63+JGlGF5x5j4RGbsDGDGzoDHbWuVKUz/ZuXpUqtUzgyLVnJclhQghBB/YZhAx0EIcQMYC1gASCl/A3yATkAAEAf0S96WKIT4FNgCmAELpZTnsiInY6zMzfj13Xp4ztjHZytPsG5ws6ydmHL/L3D9EHRfkHbxIYVzU2jjDdu+gZPL074hVV6YXi/5fNUpdDrBr+/WM9qt/rM2lTlxLZpv/z1LE9dilC2qbWyVJtePwJ4pUOc9eKVv+u1sisLbS2BBO9j4Bby1KOtyUJ4ye3cAJ65FM+vdeqr4oCiKkkf8cyIE52I2VHP67/VIy2vXxPPnzycqKorJkydnOH4+xfLlywkJCWHevHn07t1bU0xK74DNmzfTtm1bTXNF7Nq1i3bt2vHbb79RqpS2HsmRkZGsW7eOkiW1F6dKlizJb7/9prk9gI2NDbVrZ31v2LsPEpi9K4C5ewPTbdOhekn6urvQqHzRl6YHkIWZjqauDjR1deDbLk8WdwmKiOWPg8EsPnD18dCS0zfuMmzFSYatOAlA66rFGdWpKhWLZ1w8U/4bsmwOiJyUVWOP/z0VytC/TjChWw3ea+ScBZlhWO1iVkOo3B7e/iPj9no9LGwPdwJhyDEoYHziEsV0/zt2gxGrT/Hjm9rm/QiNfkDrn/bwamUH5vbKoiEQ+iSY3wruh8GnR8BKw0l09yTY/QP0WQ/ltc1Yq2h3LTKONj/voX31ksx8p26W7DO3xx3nJDUHhKIo2eFYcBTd5xxgjKcbHzavkKl9qHOxQUJCArNnz6ZPnz4ZToyXQkrJ3r17adasWYarL6R27949Tb0r8hspJdv8w/huoz/X7zx4brtjISs+a1OJN+qWoYClafNOvYz0esm+gAjm7A7ALzDtJSq/6lCVfu4uJs/TpeSsvDAHRJ7UpZYTy/2C+XHLRTrXLJU1XZq2fWNY5aLdBG3tdTrwnApzPQzd8ztoW+9W0eb+w0QmbTpPvXL2dK9XRlNMKfsCfNqqIj9uuci+y7dpXsnxxRM5scywDGv3BdqKDwDuwww9Y3y+hIG+oFMn2qw0wccfc51gdCcjvZQURVGUHDV7VwBFbCx4t5Fpqzsoz7OwsGDYsGEmxQgh8PAwfRJsVXx4QkrJiiPXGbXmTJrb+zRxZmjrShSztcrhzPI+nU7gUdkRj8qGa++EJD0rDl/juw3neZSkB2Dy5guP55F4t1E5vu7kRkGrfH1Lm2W0LBWbFbL/CHmYEIJvu1QjOi6BRQeuvvgOb50F/3XQdAjYmzB/gFNtqPseHFkA99IfA6aYbplfMBH3H/FN52omjSP7sHl5StsX4Odtl3jhXkKJj2Dvj1C6vmGSSa0sCkCbcXD7PJz758VyUJ5yNuQuW86F8fGrrjgV1rpklaIoipJdkvSSH7dcYMeFcD5wL4+NpbqhUP5bNp+9iYvXRsqP8nmq+ODmZMefHzYiaJInQZM8Gde1hio+aGRhpqNXExcuTehI0CRP9n3Z8qkFBP48dI3qY7fg4rWRqVsu8ihRn4vZGqfXZy43f39/EhISTIqRUrJo0SKioqJMirt79y7Dhg0jIiLCpDhT5esCBED1UoVpW60EC/df5V68aT/c5+z9ESwLQeOBpsc2/wL0ieA748VyUB6Le5TI/L2BeFR2pG65IibFWpmb8UkLV45fi35uFl+TnV4Bd69DCy/TJxqt9jo4VoW9Uw3DdZQs8evOAApZm9PX3SW3U1EURcn39HrJF6tOMmvXFd5pWJYBHpkbeqEoOc0vMJJa3oYb4E+WHX/8ep2y9uwe0YKgSZ5sGtacphUdcjHLl0fZojbMeKcuQZM88R/fnl6Nnwyh/3VXAJXHbMLFayML9l9Fn8F6pVJKEhNNX040Li6O5cuXExYWZlJcYGAg77zzDv/++69Jx01ISMDNzY0ZM2YQGxurKUYIgZ2dHa6urkydOpX4+HhNcUWKFMHc3JwqVarw+++/Z7pokpF8X4AAGNqqEjHxiSz1C878Tm5fMvR+aPQxFDDtZheAohWgVg84uhBiX/CGVwFgxeHrRMY+YmjrSpmKf7t+GUraWTNz5+XMJ6FPgn3ToFRdqJjxjNDP0eng1ZGGXhAXN2Y+D+Wxy2H32HzuFv3cy1O4QN6cSVpRFCW/iE9IYuy/51h7MpQv2lbmhzdqYWWuhhwqeVd8QhLDVpzAxWsjPef5ERNvuJl0LmbDhiHNCJrkydrB7rg4GF9+U3kxNpbmfPd6DYImebKoiyN1iz25Wf5ugz8VRvvgPmkn1+/EpRkvhGDWrFm0aNECLy8v1q5dq+lG3cbGhqSkJJycnGjatCkrVqzQlG/FihVp0aIFXbt2pUqVKly+rO3+onbt2nTt2pVhw4bRs2dPHj16pCnujTfeoFKlSowcOZK///5bUwzA559/zr1795g0aRK3b9/WHGcKVYAAapYpTFPXYiw7GExiUiYrPUfmg5kFNPok84m4D4XEB3BCw+SVilF6vWTJwSDqOxfhFedMFIQw9ILo6+6CX+AdLtyKyVwil7dB1FVoOjTzy6xW7waFy8KhuZmLV56y5GAQluY6+jZ1ye1UFEVR8rVT16NpOXU3S/2C+cC9PJ+2qpjbKSlKus6F3qXy15uo+s1m1p0MBcDaQvd4eMWekS2pUbpwLmeZdzx48IAbN25w6tQpdu3apenp/e3bt/nwww/p3Lkz3bt3Z/78+ZqO1bR+bQqeWknw5M6E/vYBbsUMQ7hCoh/QfMouXLw2suro9efihg0bhoeHB5MnT+brr78mOjpa0/F69+7NyJEjOXLkCD4+Pty9e1dT3IABA3jttdcQQvDXX39p7mHg7e1Nhw4dCAwMZM+ePZpihBBMmTKFzz77jF9++YXISG0PuEuXLs0ff/yBu7s7c+bM0RRjKlWASNa7iTOhd+PZcSHc9OCH9+DkX4bu8rYvMGFhcTdwbgZHFihBfl4AACAASURBVBqenCuZtvfybYIj4+jV5MVWN+lRvyxW5jqWHsxk75gj88G2JLh1yXwSOjOo3w+C9kH4hczvR+FefAL/HA+hS61SFC1omdvpKIqi5Fsnr0fTa8EhzM0EKwY05tsu1V6aJQeVl4eUklm7AnDx2ojnjP2PJ0Ls2aAsl77vyIXvOuaJ4RVan4qnCA0NZcWKFZrmOQsKCmLx4sUMHz6cVq1asWjRogyHEOj1elavXk3jxo2pU6cOb731Fn/++Sdnz541etPt6OjITz/9RJEiRVizZg0//fQTI0aM4NChQ0ZztbKyYunSpYwdO5ZaFctydcEwOt/fxMhXSzxu8+X/TuPitZG+iw4/Neze29ubr776isGDB9OyZUu+++47TcWSiRMnsmHDBpo0aUKTJk3YsmVLhjFCCBYsWMDRo0cJCwujS5cu3LmT9mofqRUqVIh//vmHLVu24OXlxdKlSzOMAfDw8GDatGl8+eWXdOjQQXMRomfPnvz+++8cOnSIuXOz/gGoKkAka+NWAqfC1pm70Ty9Eh7dg4YDXjyRhh/B3WtweeuL7ysfW3owGAdbKzrWcHqh/RQpaMlrtUvxz4kQYkydIyTyCgRsNxQPzF6wq3+9PmBmCUd+f7H95HNrjocQ+yiJPk2zaNldRVEUxSQPHiUx4I+jvD7LF1src/78sDGNKxTL7bTyjaCgIA4fPmxSjF6vZ+XKlSZPyr13714CAwNNirlz5w4rV640KUav17NgwQLNT6FTHDx4kA0bNqS5LT4hiXfn+1F+lA8/brn4+PWJHcryoe0JJnargaW58duolO7rwcHBTJ06FV9fX6Pt4+PjmTt3Lg8fPsTPz4+ff/6Z8ePHp9s+KSmJf//9l7Zt2/Ltt98ya9YsRo0axfvvv8+lS5fSbD937lzq169P6dKlGTJkCJ06daJjx4507NiRKVOmpHkcJycnLCwsOHjwILt27WLBggXUrl2bypUr07hx4zS/7zqdjt69e3Pp0iXGjx9Py5YtuX37NqNGjaJy5crMmzcv3a+rcOHCLF26lBUrVrBnzx7q16/P5MmTadCggdHihRACb29vNmzYwJkzZ3B3d2fp+E/5udEj9n3ZkrJFDZOO7754m5reW3Hx2sjViFiEEPzwww8MHDiQY8eOodPpeOutt9I9TgozMzPat2/PwIED8fHx4ccff+TQoUMZxjk4OGBvb8+sWbPo2bMnI0aMyDAGwNramjJlyrBjxw6WL19OcLC2e1YhBG+99RZffvkl06ZN0xQDhlV0Vq9ezb///mvy71aGOb3wDP+5ILvWn5+x4zLTtl1i/1ctKVPERnvgvBaQlAif7Mt8N/sUSQnwc3Uo0wB6Ln+xfeVT4THxNP5hBwNbuDKy/YsvsXjqejRdZ/ky6Y2a9GxowrJgO76D/dNguD/YvVghBIC/P4LLW+CLS2Bh/eL7y4c8Z+xDJwTrhzTLlv2rtecVRVGMG7/en4W+VxnWuhJ9m7pQJBt6o6lzcdoiIiJo3bo106dPp0WLFppi9Ho9gwcPRkrJ7NmzNS/Rt2rVKiZOnMjatWtxcXEx2jblXuTkyZP06tULLy8v3n///QyPER0dTVRUFP3796dSpUpMnTo1w+VA/fz8cHR0ZNSoUdy+fZuffvqJevXqPd4e9yiR938/xPFrT7riO5nH8XF1WP+/FVy7do2hQ4fy7rvvYmaW9lwlMTExDBs2jKCgIB48eICZmRlvvvkm77zzDiVLlkzz61+xYgVeXl7cunWLChUqULduXZo0aUKzZs2oW7fuczG3bt3iq6++Yu3atcTExNC+fXs6duxImTJlKFu2LDVq1MDG5vl7Gb1ez9GjR1m/fj3+/v5MmTLlcc8jW1tbihcvbvT7d+TIEUqUKEG5cuWQUhIVFUWRIkUy7L306NEjLC0tH3+98fHxFChg2ipkqfehlZQSvV7/+GdlWG3nIr/tufJUu23DX6VSiSfvncwsR5nyPja1J5eUMkdiXiQuM4ydh9UaR6l0q1uaadsusfZECJ+20jhxYfgFCD0B7X948eIDGJ6U13zLMN4/NhIKqqcCplp3MhS9hO71ymTJ/mqVKYyrY0HWHA/RXoDQ6w09Yyq0zJriA0Cdd+DMKri0Gaq/njX7zEcu3IrhXGgM3l2q5XYqiqIo+dKuC+EsOnCV3k2cGd62cm6nk2/cv3+f+/fv0717d8aMGaO5+HDy5Enmzp1rUvFhzZo1BAcHs2bNGnbs2EGxYhlfxy5atIirV6+ybt06/vzzT2rVqpVhzOrVq5k+fTpRUVH88ssvtG3bNsOYBQsWMHz4cMqXL8/3339P586dH9+M3YtP4O25fpy/+WTOrx71y3B3x2/M/e03YmvWZMaMGXh4eBi9gfP19aVXr15cvXoVe3t7Dhw4gJubm9G8/Pz8uHDhAq+99hqRkZF4eXll+D0oWbIkS5YsQUpJUFAQd+/epU6dOhl+D3Q6HQ0bNqRhw4YZtk1LgwYNHv9fCEHRokU1xaUuHAghTC4+PLsPrYQQTxWKzHQCr45V8epYlfWnQhny1wkA2v68FwCfoc2pVsrO5OJDyrEyIzNxOXms7KAKEKmULWpDo/JFWXM8hMEtK2r7IZ1eAcIMar6ZdYnUfgcO/grn1hiGZCgm+fv4DeqUtaeCo22W7E8IwRv1yvDjlotci4yjXDENvWOCfQ1Lb7YemyU5AFDeAwo5wakVqgCRCf8cD8FcJ+iSav1oRVEUJfsl6SU/+Jzn9/1XqVzClq86vHjvREW7+fPn89NPP+Hl5aWpaznA9u3bee2113jjjTf4448/NN2QnTt3jp49e+Lq6srhw4cz7I0AcPnyZYYOHYper+fAgQOaig/Hjx+nT58+PHjwgNWrV2sqPvzxxx989NFHlClThg8//JAuXQxzc919kEC32b4E3n4y5r+fuwuj2lfi+++/505kJF9++SWVK1emWbNmRu8NpJQ4Ojqyfft2rK2tsba21vQ9SJlDIDOEEJQvXz5Tsfldl9ql6FK7FFvO3eLjpccA6DRjHwD/fupOrTL2uZneS00VIJ7RvV4Zvvz7NCevR1O3XAarJ+j1cHqVYXlFW+NdlkxSsgaUqAmn/lIFCBP5h8Zw4dY9vutaPUv3+3rd0kzdepF/ToQwrI2G3jGnV4ClLVT1zLokdGZQ6204OAvu336xCU/zmSS95J8TIbSoUpxitla5nY6iKEq+EfswkeErT7LVP4xejZ0Z3cmNApZqmc2c8vDhQ3766Sfu3LmDvb22Gyq9Xo+XlxdmZma4ublpmvtBSsnAgQMpXrw4H374oaaHeAkJCfTq1Qt3d3f69++fYU8B4PGwifHjx9OlSxeqVKmSYcz9+/cpXLgw169fp3Tp0oZjJ+npMffgU0MtPvFw5asOVR7nbmz+hbQIIahcWfXs+a9pX70kQZM82XUhnH6LjwDw2q+G+ToMc0eYMCxf0UQVIJ7RoWZJxqw9y8bTNzMuQNw4AjEh0GZc1idS803YPhaigqGImjBPq41nQjHTCTxrZe1T7tL2BWjgUpSNZ0IzLkAkPoLz66FqZ7DM4pNWzbfAdzpc2GCY3FLR5GjQHcLvPaRrHdX7QVEUJaccvxbFsBUnuBH1AO8u1ejrrp7U5rRly5ZRv359pk+fjrOztuvJdevW0bRpU3x8fDKcEyCFn58f/fr147333tPcVT40NJSVK1dqzgsME/gtX27aHGm2trZ07dr18efTt1/m5+1PJmkc1roSn7WplGe6pyu5o2XV4gRN8sQ3IIL3fjdMJtl8yi7cnOxYO7gpVuaqcJpV1CoYz7CztqBZJQc2nb2VccXXfx2YWUHl9lmfSLXkE+X5f7N+3y8pKSU+Z27RuELRbFlisVONklwKu09A+D3jDYP2Qvzd7BkmUaIGFK1geO8pmm06ewsrcx2tqmZhTyVFURQlXY8S9Qz58wRSwsoBTVTxIZc0bdqUtWvXmnST3759e2bMmKG5+ACGYQT9+vUzaZy+s7OzSXnBi41h9w2IwMVr4+PiQ7tqJQic2InhbSur4oPymHtFB4ImeTK5e00Azt+MocqYzUzZfCGXM8sZObFAhSpApKFjjZKERD/g9A0jS45IabgJdG0F1nZZn0TR8lCyFvirAoRWF8PucTUi9oWX3kxPh+T9bjpzy3hD/3VgWcgwAWVWE8JQnLq6F+IyXjdYAb1esunsTTwqO1LQSnX6UhRFyQlrT4QQEv2A716vQcPy2iaqU7KelmENz0pr9YT/srCYeFy8Nj5+qm1hJjjxTVvm9a6PTqcKD0raejQox9UfOj2eO2z27iu4eG1k18XwTO3P2BKixoSGhhIbG5txw2fs2rWLmzdvmhz3448/EhISYnKcKVQBIg1tq5XAXCfwOWvkhxZyHGJuPOmpkB2qdYUbh+Fu9r4JXhY+Z24hhGEsV3YoWdiaV5yL4HPWSAEiKRHOb4AqHbJvqcxqXUEmwYWN2bP/l8yJ61GExTykU83sKUwpiqIoT0tM0jNrdwA1SxemRWU1X5GSO6SU9FpwiEYTdzx+7Z9BTbk8oVO2LP+q/PckJSUZ3S6EYOY7dTk1th2Fkh9i9Vt0BBevjVwODjXpWI8ePeLjjz9m48aNJhUjChcuTPPmzfntt99ISEjQHFe+fHlq1KjBr7/+muHXmVq5cuWoWbMmK1eu1BxjKlWASIO9jSVNXIuxzT8s/UYXfQyrX1TpkH2JuL1m+PfSpuw7xktkm38YDZyL4lgo+yYZ7FC9JOdvxnD9TlzaDa4fggd3wK1LtuWAUx0oXM7wHlQytNU/DHOdoJWbGn6hKIqSE9afDiU4Mo5PW2lcUUxRstjxa1GUH+XDvssRAHh3qUbQJM+M53dT/pMCAgLYv38/0dHRGTdOxcfHB09PT3755Rf8/f3THX5QuIAFZ8a1Z8OQZo9fazvnBI37e/P3339rGrZgbW1Njx496Ny5MzVr1mTXrl2acixYsCADBgxg4MCBNG/enIiICE1xLi4udOjQgSFDhjBmzBjNQyu6deuGmZkZ/fv359ixY5piTKUKEOloXbU4gbdjuRqRTpeXgG1QthEUyMYTmUMlw3j/S1uy7xgvidDoB5y/GUPrbL7JTNl/ut2vLm0GnYVhaE52EcIw70jgbkh4kH3HeUnsPB9OowpFsbO2yO1UFEVRXnp6veTXnQFULVmItm4lcjsdJZ/R6yVdZ/nyxuwDADgXs+HyhI5qDpJcptfrNT2Fj4mJYdSoUXz++ed89913rFixQtONs4uLC/PmzaNIkSKULVuWffv2acqrS5cueHh4MHz4cFq3bs2tW8aHWdcoXZigSZ4MbW2YkP6WYwO+OGJN2F1t1+OtWrWiT58+XL9+neDgYE0xAP3796dRo0bcvXuX0FDtPS++/PJL2rVrh5+fHw8fPtQUY2VlxahRo2jbti2HDx/WfCxTqAJEOlon/9HceSGNG817YXDzFFRsnb1JCAGVO0DgHnhk+tif/CTl55TdBYgKjraUdyjIjvPpFSC2gEszsMp43ecXUrkDJMRB0P7sPc5/3LXIOC6H36dVVXURrCiKkhM2n7vFlduxDG5ZUY2vV3KUX2AkFUb7cOq64Sn40v4N2TOyJRZm6nYnLXfv3tW8xOqNGzfYsmUL06ZNY/fu3ZpiFi9ejLOzM7a2thQrVozz589nGGdnZ8fQoUM5fvw43377LTNmzGDDhg0ZDj0wNzdn8eLFDBo0CL1ez9ChQ1m1apWmoQ4jR45k0KBBdOnShY4dO7J3794MYz5vW5kjo588bGw8aRdj/9bWW2Dq1KkcPHiQZcuWMX78eE0/AwsLCzZs2MDKlSvp0aMHp0+f1nSs2rVrs379ejp27EifPn00D/0YPnw4S5cuZf78+ezfn/X3Guo3Mh1li9pQuYQtOy+kMQzjSvJYskptsz+Ryu0h6aFh0kElXTsvhONczAZXR9tsP1brqsU5eCWS2IeJT2+4EwgRFw3Fgezm0gwsChp6XCjpSvn9baOGXyiKouSI+fsCcSlmo+bdyaOSkpKIj483Oe7+/fsmx8TGxpKYmJhxw2dERUWZ1D5JL2kzdSc95/kB4OZkx5WJnWheyfj8I0lJSYSHmz6hYFBQkMkx4eHh3L59O8N2qYcQREdHc/z4caPtk5KSWLt2LX5+fsTHx3Pp0iW2bt2a7vfw8uXL/Pzzz7Rq1YqGDRuyfPlyli1bxrJly9K90QwICODbb7/ltdde44svvmDQoEF069aN4cOHM336dOLinh+WLISgb9++7NixAw8PD1xcXBgyZAhVq1alb9++Rm/ynZyc2L59O6NHj2bMmDGsX7+e6tWr88UXXxjtRaHT6fj111/ZuHEja9asYdu2bbzyyiscPHjQ6PdQCMGMGTOYPXs2f/31F9988w0DBw7MsDDgaFeAoEmeeHWsCsCSI7dw8drIzQx6Qzg4OFC9enV8fHy4cuUKw4YNM9o+dVytWrUeFyG0vg8tLS0ZOXIkxYsXZ+zYsZpihBDY2tqyatUqPvroI5N/JzOipoQ3olXVEvy+L5B78QkUSt19+/I2sC1hWKUiu5VralhR4eImqNIx+4/3H/TgURK+ARG826hcjow1beVWnN/3X2V/QMTTE15e2mr4t3K7bM8BC2twbWnocdFpqqG3jPKcHRfCcXUsiHOxgrmdiqIoykvv+LUoTlyLZtxr1TFTvR/ypDFjxuDg4MAXX3yhOebIkSMMGjSIgwcPYm6u7dbh3r17eHp64u3tTatW2oalSikZP348ly5dYvny5ZpizoXexXPGkxvnVR83Mbrqil6vR6fTcezYMQYNGkTv3r0ZPHiw0WPExMSg1+sJDAxk3Lhx3L9/n82bN2Nhkf7QzsDAQA4fPoyVlRWLFy8mKCiImTNn4uiYdlEkKSmJ+fPn88svv+Dp6cmePXtITEykW7du1KtX77n29+7dY9GiRUyfPp3AwEDKli2Lvb09zs7OuLi4UKVKFYoUKfLcMYKDgx9/JCYmPnUTa2ub9kO8SpUqsXDhQn744QfmzJnD66+/jqWlJUFBQQQFBRl9T1SsWJENGzZw9epVKlSoQHx8PIcOHUr3WCnMzc2ZMGECAJ06dSIuLo69e/diZmZmNE4IQZ06dQCYP38+V69ezTAGeNzGzc2NXbt2cfLkSc33FJ94uPJOg3LUHm+4D2jyw06+6lCVgS1cjcZZWlqyePFiAgICNB0nRa1atdi0aRNly5bVHCOE4JdffjFp+AYYfn5bt2597r30olQBwgiPyo78tucKhwLv0KZachdufRJc2QlVPXPmps/cEip4QKC2iUryoyNBd3iYqMcjh2babuBSFBtLM/ZffqYAcWUnFHU1zNuREyq2hgsbIPIKOFTMmWP+h8QnJHH46h3ea2TaGuOKoihK5izyDaKQlTndXymT26koaVi9ejWHDx9myxZtc4tJKbly5Qq9e/fmn3/+0VR8iIuLIykpCU9PT3r37q2p+BAXF0dUVNTjifIWLVqUYUxiYiKfzt3C5uuGz6uVsGHDsBZGh/08evSIIUOGYGNjg6+vL7Nnz6Z+/fpGjxMREUGHDh2wtLTE0tISb29vWrRoYTRm3bp19OnTh4SEBPr06cPXX39NgwYN0r2hPXr0KB9//PHj3g4fffQRmzdvxsHBId1j6HQ6mjRpgp2dHefOnaNmzZr07t3baF5mZma0adOGNm3a8PPPP3Pp0iUqV66s+Ua7RIkSeHt7P/68WrVqmuKEEFSoYLg2tra2xsPDQ1NcajY2NnToYHoP4/LlTZ/7Q6fTpVn0MaawjQVBkzxZ7HsV7/X+TN58gfn7AjnydRujxVghBJUqVTI5RxcXF5NjzMzMTCpapMhMTEaypAAhhOgATAfMgN+llJOe2T4SeC/VMd0ARynlHSFEEHAPSAISpZTGzwQ5qJ6zPdYWOnyvRDwpQIQcg/jo7J//IbXyHoYbzTtXoaiaROdZvlcisDATObbOuIWZjobli+J7JdUstEkJEOwLtd7OkRwAw/sC4OpuVYBIw/HgKB4m6nGvWCy3U1EURckT7j9M5MjVO5y8Hs2ZkLvYWZvTtKIDnjWdKGj1YpeEEfcfsunMTXo3ccH2Bff1X5YXr4kjIyOZP38+S5cuZffu3ZoKCVJKhg8fzo4dO/j999+pWrWqpmMNHjyYixcv8sEHH/Dhhx9qihk3bhzLly+nf//+eHt7Z3hDnJCkp8qYTeiTR5LP6Fmb1+oYL3pJKRkwYABLliyhffv2HDhwIMPvQ0hICO3atcPf35969eqxfft2bGxsjMasWbOGBQsW0LlzZ4oVK4aXlxdOTsaHI9WvX5+DBw8SGxvL/fv3sba2Nlp8AMPKCA0aNKBBgwZG26VHCEGVKlUyFaukr697edpVL0nTSTu5E/sI19E+7BrRgvIOqiduai/8F0IIYQbMAtoCN4AjQoh/pZT+KW2klD8CPya37wIMl1LeSbWbllJKbWuK5CArczMauBTlQEDkkxcvbwOhgwotcy6RCik3mntUASINBwIiqVu2CDaWOXfB4+7qwO6L57l1N56Sha0h5Dg8uv+kKJATilaAwmUNk5Q20PZHPj/xvRKBmS7nClOKoih5kZSSG1EP2HkhnBk7LhMZ+widgIrFbYmKS2DtyVDGr/enn7sLH3u4Zrp48M/xEBL1kncaZv3Tsv+KvHpNvGTJEkaNGsUnn3xCsWLaivJbtmxh+vTpNGjQgJo1a2qKOXHiBIsXL6ZEiRKan3KfPn2an376CXt7e1599dUMiw8Xb92j/S97SZnGbkyN2AyLDwATJkzgypUrjB8/nnbt2qHTGZ8GT0rJwYMHmTp1KjVq1KBMmTKaegq88cYbvPHGGxm2e1ZKD4us7uqu5LxS9gW4+kMn2kzbw5XbsbScuptvOlejfzN1D5ciK+7YGgIBUspAACHECqAr4J9O+3eAv7LguDmiqasDkzdfIPxePMULWRuW3yzTAGxy8KbGoTIUcjIsu/hK35w77n9AdNwjzobe5bPWlXP0uE2Tn6r7BkQYupoG7gYElH8155IQ4knvGH0S6DIe45af+AZEUrtM4afnb1EURfmPkFKSpJeYa5jB/2FiEqHR8YREPSD4TizXIuMIiowlODKO63fiiH1kmLitgUsRpvesS91y9hS0MkdKyfFr0Szcf5WZOwP46/A1hrWpzLsNy5k0h4OUkhVHrvGKcxEqlcjmVaDytjx3TSylZN68ebi7uzNy5MgMb7xTTJ48mTZt2jBr1izs7Ow0xYwZM4YPPvgAb29vTd22k5KSmDx5Mr/88gv9+vWjYEHjT4ln7rjMT9suAeBW3Bqf4a00FQVSVkUYM2aMpq8DDD0E3nzzTc3tFSU1IQQ7vmjBMr9gxqw9y3cb/FmwL5D9X7VSqwORNQWI0sD1VJ/fABql1VAIYQN0AD5N9bIEtgohJDBXSjkvC3LKMindtw9eiaRrJSsIPQEttZ/AskTKjWbANtDrQeMfj/zALzASKcnxbvZuJe0oWtAS3yvJBYire8CpVs4WpsDQO+bkMrh1GkrVzdlj52Ex8QmcvhHN4JZqaIqiKP9Nn/51gsth91gzyB1bK3M2nbnJr7sCcCpcgIrFbUlI0nPiWhTXox5w+97T67tbmusoW6QAzsUK0rhCMVwdC/KKc1HcnAo9dcMmhOAV5yK84lyEj65HM9HnPN+sPcvmszeZ+lZtnAoX0JSrb0AkV27HMuVN45Ou5QN57prYz8+Pfv36MWLECE2T8YFhlYcBAwbQs2dPzfMDREdHM2XKFKpXr645t6SkJJYsWZLhUAgpJY0m7iA8+X3+c4/adKurfZ4RnU6nuYiiKFnp/cbOeFR2pPmUXYTejafCaB+OjmmDg61VbqeWq7KiAJHWmSm9dUu6AL7PdDVzl1KGCiGKA9uEEBeklM+tzSKEGAAMAChXrtyL5qxZ9VKFKVzAAt+ACLpaBBpedM3B4RcpKnjA6RUQfg5KausKlx/sD4igoKUZtcva5+hxdTpBE9di+AZEIB/eR1w/DI0H5mgOwJMhH4F7VAEiFb8rkegluFc0PoZSURQlL9ruH8bG0zcB+GbtWfo0dWH4qpOUtLMmODKWPZfC0QlB7TL2tKziSGl7G0oXKUBp+wI4F7OhpJ21yU/Z6pS1Z+WAxqw6ep2x/57j1Sm7ePOVsozxdDM6P8T9h4mM+uc0zsVs6FKr1At93S+BPHdN3KBBA5o0aaIp+RQuLi4mT3Jnb2+Pvb1p12KWlpYZtolPSKLqN0+WHPcb1dow9FVR/iPKFrUhcGInmk7aya2YeOp/v50NQ5pRo3RhTfF6vZ7r16/j7GzapOphYWFcv349w4lWn7Vt2zYcHByoWzf77iuyogBxA0jdz6oMkN4aHz15pquZlDI0+d9wIcQ/GLqvPXeyTa4CzwOoX7++8YVZs5CZTtCkQjF8AyKRBXwRFgXBqXZOHf6J1DeaqgDx2IGASBqWL4qFhi6qWc3d1YGNp29y88xuSukTnszVkZMKlQBHN0MPjGaf5fzx86gDVyKxttBRt1zOFqYURVFe1KNEPd7rz1GpuC3tqpdg1q4r/HMiBAdbK1Z90oTihaxJTNIjIcv/9gkh6NGgHE1dHZi/L5BlfsGcuBbFuNeq07B80TSfhk/beokbUQ9Y/XETCljm+6GAee6aWOuymXnRrbvxNP5hx+PPr0zspJZ3VbJUQkKC0eVU03PgwAFKlCiBq6u2Xl86ncBvdGteG/8np+MK03nmfqb3rEPXOqU1xOr4/vvvKV++PCNGjNBUuAMoXrw4nTp14u233zapB1Tt2rVxdXVlzpw5vP/++5piTJUVf7mOAJWEEOWFEJYYTqj/PttICFEY8ADWpXqtoBCiUMr/gXbA2SzIKUu5VyxGSPQDEq7sg3KNwCwXxpQXLg3FKiXPNaAA3Lz7gMCI2Fx7yp0y7CPq7FYws4Rypj1hMpWLSAAAIABJREFUyDIVPCD4ICQ+zLhtPuEbEEEDl6JYmef7i2HNhBDWQojDQohTQohzQohxuZ2TouRHOy+EcyPqAV92qMoXbavwe+/6fNO5GisGNDbMRQWYm+mytfBetqgN47vWYHG/htyKiafHPD+6zznw3FCPxCQ9/5y4Qedapajvoib8JR9cE+eUY8F3Hhcf6pazJ2iSpyo+KOmKiIhgz549xMXFmRQXFBSEp6cns2bNIiwsTHNc1apVad68Od26dWPv3r1Iqe3Z+MJB7bi/ay4Aw1acZKLPeU1xgwYN4uuvv+aVV17h5MmTmmKEEPTu3RsvLy9ef/11zd+b4sWL06BBA3r16sXChQs1xZjqhf96SSkTMYxf2wKcB1ZJKc8JIT4RQnySqmk3YKuUMjbVayWA/UKIU8BhYKOUcjN5TNOKDhQhBss7F8C5ae4lUsEDgg9A4qPcyyEP8U1enSS3ChDlitpQ2r4AhUJ9oUxDsMylJXbKe0DiA7h+OHeOn8eEx8RzOfy+Gn5huodAKyllbaAO0EEI0TiXc1KUfOfv4zdwsLWiZRVHdDpBm2ol6N+sPBWL2+Z4Lq9WduSAVysmdquJ/80YXp/ly7qTISQm6QE4EhRFVFwCnWqUzPHc8qL8cE2cE1YeuUb3OQcB+PjVCvwzyD2XM1JyyqNHj/jxxx+ZPHkyf/31F76+vuj1+gzjHBwc2Lp1K4ULF6ZRo0b873//03S8SpUq8cEHH/Dpp5/i6urK+fPaCgJFixZl+vTprF27ls8//1zzzb2DgwOfdWnIrWUjAPg/e+cdV2X5/vH3w2EJCm6WuCVU3LhNXDjzZ7mVLE1zlZlaWlrOMvNrmaVFjhylaY5S1MyJe4ELxJEDRbYoU+bh+f1xgCyR8zyIPoz7/XrxEs65P9z3OT7Ac1/3dX2u5Udu0WfpMaO6Jk2a0LlzZ2JjY7G0VF6C9Prrr+Pm5kZSUpLizAmAgQMH0q5dO/R6vWKNGgokfC7L8m5Zll1kWa4ly/LnWY95y7Ls/diYNbIsD/6P7pYsy42yPupnawsbNSta41n6tuGLau20W0gND0hPglB/7dZQiDhx4z4VrM15SSPHbUmS8KxuSpW0m2S+yO4X/6V6W0Nr2NuHtVtDIeLEzazAVC0RgFCDbCAx60uzrI8XVu4mEAjgfmIqh65G0bepk6LuFy8CK3NThrasyqbRrbE0M2HixgtM+PU8siyzNygCc1MT2rtU0nqZhYbifk/8vJn+ewDTtgYA8N2QJnzcs67GKxJkk5qayuXLlwkKelpTl3+QZZlNmzbRoUMH2rVrR5cuXYiKijKqMzc3Z9iwYfzxxx8MHTqUDz74gPDwcEXr++yzzxg/fjyXLl1i9erVXLt2TZGuX79+TJkyhebNmzNx4kTCwp5WNfVv+vfvz6xZs3BxceH9998nPT1dkW7SpElsW/4VFY59DcDFe3FU/2gX+sy8b7mWL1/Oli1bGDBggKL3EqBChQocO3aM5s2bM2PGDEUagJEjR+Lj48M333zD33//rVinlMLx162QI0kSvWxukYI5spZGfzVeBiS4/UQ5YIlDlmVO3oqhda0Kmraz6WlzCxNkbpdRZ/BSoFjagmNTcV1kcfJmDLalzKjnKByv1SJJkk6SpAtAFLBPluXTWq9JIChJLD14g4xMmX5NlTv8vygaOZdl3yQPpni68GdgBP/76xp/BUbQvk7FPE0qBQKlvLXmLBtO3wVg54R29G5U4k1NFZGRkaGqfCAiIoJVq1YxZcoUMjMzkWU55yM3bt68Sc+ePbGyssLNzY158+axevVqjh07RkRERK46SZIYNGgQs2fPJioqisDAQNq3b8/YsWPZvn07CQkJT12fvb09hw4dwsvLi1deeYVevXoxZMgQTpw4kWepgyRJLF68mB07dvDee+8xePBgJk2axMOHD42+J1988QU+Pj688847dO7cmR07nqicynW+WbNmsX79ehwcHOjVqxdxcXFGddbW1vTs2ZN9OzZTyfeznMdrTd9Nuv7p2R41a9akZcuWfPbZZ6pKKmxtbfn888/x8/Nj27ZtijRmZmaULVuW77//njfffJOMjAxFOqWIAIRCGmQEcl5fm1uxBfsfoIpS5aByPQg5pd0aCgmhscmEx6XQooa2Naf10oNIkc049sh4v+vnSrXWhhax6SnarqMQcPbOA9yrlRO1ovlAlmW9LMuNMRintZAkye3x5yVJGi1Jkp8kSX7R0dHaLFIgKKasOHKLNSeCeaN1NV6y1yazzxgmJhLvdqpNZ9fKfO97k7C4FEUmaoLCw8mTJ1m9erUqTWpqKuPHj1d8wpuNt7c3hw4dUjTWa+UpDl41nOr2TDuquEMAQEpKCqNGjSI4OFixRpZlVq1axZdffqlYA3Do0CG6d+9OWprxcujY2FhkWebw4cP079+fzZs35zk+NTWVb7/9lsjISNauXcvgwYN57bXXnjr+0aNHLFu2DBcXFz744ANGjBhBu3btqFOnTq4+AXq9Hm9vbxo3bsyoUaNYvnw59evXp169etSrV4+pU6fmOk+tWrXYuXMnW7dupVWrVjRr1ozw8HBWrVrFgAED8tx0d+jQgYsXL7JhwwbOnz9Pnz59OHDgABs3bszzvbC0tOTnn39m2rRpnD9/nlGjRrFq1SqjJQEmJiZ4enrSrVs3zp49S506dTh1yvi+yczMjNKlS+esz8/PT5GvgyRJSJLE3LlzGTZsGHfu3DGqyaZ8+fL8tXsXkxxu5jxWZ8afpGXkXXLSp08fxo8fz4MHD/Ic9zimpqZs2LCBpKQk44Mfw8PDgzFjxpCYmGh8sBoej3oVlY9mzZrJL5TkWDlzlq28eMZwedOZuy927v/i874sf+4ky/oMbdehMX+cvydXm7ZTDgyN1XYhyzvK52e3ksev99d2HUE+sjzLRpbvnNR2HRoTk5gqV5u2U1526G9N5gf85ELwO7IgPoBZwAdPe/6F/x4WCIoxSanpsusnf8oj15yR9fpMrZdjlLQMvXz+7kM5Mi5Z66XkSnH6XWzsQ83v4vj4eNnNzU0OCgpSrJFlWR43bpw8d+5cVZrt27fLrVq1khMTE42O7ff9cbnatJ1ytWk75bqN3eUTJ04omiMtLU2Ojo6WX375ZXnBggVyZqbxn51bt27JMTExcr9+/eTBgwfLDx8+NKo5cuSI/Mcff8ivvvqq3LVrVzkwMDDP8ZmZmfKiRYtkDw8PuWnTpnK/fv3kw4cP57m+Y8eOya6urrJOp5ObNWsmf/LJJ/Lx48fl9PT0XMdHRkbKY8aMkevXry9bWFjI/fr1k48dOyZHREQYfR/0er188uRJ+ZtvvlH0nv33taWkpKjSCJRRZ/runJ+D5LSiv8/L6/ewyJlTwt1TSMhcNnMj7M4DBjbX8LTbuRX4/QRRQSW6Hadf8ENKW5jiaq9hmn3aIwi/SFS5gfgHP0SW5VxblL0QnFsa/r17CqqWXN9A/zuGNDv3asKNXS2SJFUC0mVZjpUkqRTQBVB3NCQQCPLF/itRJKfrefvlmpqWFSrFTGdCY2fR5rgoERcXx5QpUxgzZgx16yrzVbhz5w5Hjhzh7t27LF26VJEmICCA+/fvM336dA4cOIC1dd4G3b2/O0ZAqOEE3WrPLFb98B2tWxvvKpaQkMCIESO4fv06M2fOpH///kY19+/fp0uXLlhYWPDRRx8xbNgwo/dtZ8+epVevXpiZmbFu3Tp69uyZpyYtLY1x48bx008/odPp2L9/Px06dMhzjoCAADZu3IiHhwdt27Zl2LBheHjk3dq9cuXKeHsbbEX0ej0xMTFUrlw5T002JiYmtGrVilat1N8vSpKEhYWFap3AONc/70GD2X+RkJKB66d7uDqvO5ZmxbObmwhAKCH4GJiYYVqlBX53jNcRPVeqPrbRLMkBiDsPaVK1rLZp9mHnIDMDXbVWRJxMITQ2mSrlrLRZS+lKUL4WhJTskn2/Ow8w00k0rKI8dVOQgwOwVpIkHYbyvN9kWd6p8ZoEghKBz8Uw7GwsaC5aWQqeA/Hx8bRu3ZoqVaqwYsUKRRpZlhk4cCCRkZGcOXMGExNlVdvz589n69at7Ny5Ezs7uzzHen59mL+jDKnddxcP5JNpUxRvimfMmMHWrVvp27cvr776qtHxer0eLy8vbt26xSuvvELfvn2NBh8CAwPp27cvTZs2pW3btri7uxvV+Pv74+npyVtvvYWzszOOjsZ9LBo0aMB3331ndNzT0Ol0ioMPgsJNwOxuNP98P9EJqbh+uoegud2wMi9+23XhAaGEOyfAqRkNajpwKzqJB0katsEsWw1K25fojWZCSjrXIuJpVq2ctgu5a6gpc3TrAPxz+q4ZVVsZrgu55DYu8A9+iJuTbbGNGD9PZFm+JMtyE1mWG8qy7CbL8lyt1yQQlATiktM5fC2aVxo6FonsB0HRY+fOnVy5coXMzMw8zf8e59y5c5w5cwY7Ozvi4+MVaYKDg9m8eTPNmzc3uvFuv/BQTvAhYulQ+vfpxeuvv64ok/TkyZNs376dhQsXsnLlSkxNjW/QNm/eTJs2bbhy5Qo+Pj6ULm28ra21tTU3b97E19eXzz//3GhABaB169YMHjyYtm3bUrVqVUVrEwge5+yMLlQpVwqAejP/IjFVQ//B54QIQBgj7RGEX4BqrXPSujXdaEqSIQvibskNQJy/G0umXAjS7ENOQ8WXqFPdGWtzHX7BGgcgnFvCoxiIuaHtOjQiNUPPpdA43LUOTAkEAoEKfjp2mzR9Jq8KM0fBc2LLli18+OGH7NmzBxsbZaWra9as4ZNPPuHYsWPUrl1bsWbZsmUcPXoUNze3p44b9ONJ7j4wOPh/VDuSIwf38dtvv+Hi4qJonlKlSnHjxg0+/PBDypVT9jd/8ODBzJo1C1dXV0XjAWrUqIG5ubni8QJBQXFsWifqVDYEydxm/UVGHt0xiiIiAGGM8AuQmQHOLWlYxRYznYTfHeWuo88F51YQdxfilfWpLW743XmIiQSNq2pYf5qZaQhAVG2Jqc6EJlXLFYLynKy0xbsls0tKYGgcaRmZNNM6MCUQCAQKCXnwCO/DN+ndyJEGonRM8BzIyMhgxIgRLFy4UPFpvCzLjB49mnnz5mFmZqZ4rsmTJzNmzJg8yzVm77jM6duG++igud0YO+otWrRooXgOgMaNG6tal0BQWFDTznLfZA/KWhmu89oz/sw2CFfFkSNHVOsyMjJYv3696rnUIAIQxrh31vCvkzuWZjrcnGw5p/lGM8sHooSWYfjfeUBdBxtKa9l3/P51SIkzBIOAZtXKcS0inoQUdS2qCpQKdQytWkvodZGdgaJ5aY5AIBAoZMGeq5hIEh/3UH4qKxCowdTUlN69e6vSSJJEgwbqfcaMZVf8fOoOa04EA3B6eudiWdsuKFqkpqYqaqn6Xx48eMAff/yhenN/69YtpkyZorgd5vlPPXM+f+nDzYrLobI5efIkI0aMIDU1VbHG1NSU1atXM3/+/HwFPZQgAhDGuHcWylU3mPwB7tXKcfFeHKkZefehfa7YNwTTUiWyDCNDn8n5u7Hap9mHZGUZZGUduFcvR6ZsKA/RDBMTQxlGSQ1A3HlI9QpWVCoj3JkFAkHhJzA0jl2Xwhn1cg0cy5bSejkCwXPlyPVoPv0jEIBd77XDzsZS4xUJihN6vZ4dO3YQExOjSmdubs7IkSOZPXs24eHhinXly5fP8RU5evSoYp2LiwtXrlzBzc2NvXv3Gh0vSRJ/f94DgDRTaxq+sxQ/Pz/F8/3f//0fa9eupVOnTkRGRirWdejQgRkzZvD++++TmVnw5R8iAJEXsgwhZ6FK85yHmlUrR1pGJoGh6iJQBYrODJya/bMJLkFcjUjgUZqeploHIO6eBquKUL4mAI2dy2IioX0ZhnMLQ3bGI43LhF4wsixz7s5D7a8LgUAgUMjX+65jY2nKqJdrar0UgeC5cj0ygTd+OgPAyjfcqe8oyo0EuSPLMitWrGDRokXs2bOH0NBQRafwOp0OMzMzHBwc8PDw4Mcff1SkkySJefPmsWjRIqpVq8aOHTsUr3XevHn4+/vz6quvcuOGcv+1SZMmERwczDfffENKSorR8WY6Ey7O6mr4wqkRS31vK57L1dWVpk2bEh4ejk6n3KC9Y8eOVKtWTZFZa34QAYi8iA+FxIj/BCCyjSg13uBVbQnhlyBNWQpPccEv2PC+u2vdqizklCHbIMutuYylGS/Z22h/XWSVhJS0LIjb95OISUrT3phUIBAIFPB3ZAIHr0Yxun1NbEuJWnZB8eV+YipdFx8B4NNX6tGlnvFOEoLCTXq6snLjPXv2MHjwYN58803GjBlDcHCwUY0kSQwdOpS9e/fSo0cPPDw8iIuLUzRfjx49WLBgAUePHmXnzp08fKjsULB69ep8+eWX1KpVizVr1iguj6hZsyZTp06lS5curFixQnG5QpcuXVi9ejVRUVEcO3ZMkca2lBm/DDIEq33vW7Hp1E1FOkmS2LFjBwMHDsTb21uRBqBFixacPXuWbdu2qcoMUYoIQOTFvawUlyruOQ9VKmNBtQpWhaDjQSuQ9RDqr+06XjD+d2NxsLXESct01cRoeHDrHy+OLNyrleP83Vj0mRq2wXRqCiZmJc6IMrszjXt1kQEhEAgKP5v972FqIjG4RVWtlyIQPDf0mTLun+0HYHBzZ0a2q6HxigTZxMfHs2vXLkWb5tu3bzNixAhatmxJ5cqV+fjjj4mKijKq7d69O15eXvz555+sXbuWKVOmsHHjRhITE/PUWVtb4+Pjw2uvvUabNm1o3bo133//vSIfg0mTJrFp0yb69u1L27ZtFWc0jBs3jsOHD9O5c2c6dOhASEiIIt3cuXNZv349ISEhfPTRR4qzLoYPH87vv//Oe++9x+XLlxXN1a5JXbaOaw3AtD+ucjVcWTa+k5MTs2fPZsuWLVy6dEmRxszMjEqVKjFnzhw++OADRRo1iABEXtw7CzoLsPu3EU8T57JcuqcsGvfcyA6KhJ7Tdh0vmIshsTTRsvsFQFjWe/5YZgxAk6pleZSm50ZU3r9YnytmpcDe7Z81lhAu3oultIUptSs9n1QxgUAgKCjS9ZlsO3ePznUrU7G08KwRvFhiY2MVb3ge58SJE6prwRvN3gOAU9lSLOjXUJEmMzMTX19ftcvj2LFjRje2/+X+/fuKT6Cz0ev1bNiwQdV7Icsy+/bt4/z580bHZp/26/V6Dh8+bPTUOiUlhWXLlrFnzx7Onj3LmjVrmDp1KrdvP5mmr9frWb16NZ6enlSsWJFRo0bh5eXF0KFDGTp0KMuWLct1jho1arBgwQI8PDx49OgRISEhvPbaa7i4uBjNUOjduzcBAQGsWLGCDz/8kLNnz+Lu7s7y5cvzfF0WFhb89ttv/Pjjjxw5coS7d+/SunVro9kXkiQxYMAARowYwb59+/D29ubXX3/NUwNgYmJC5cqVeeedd5g/fz7Dhw9XFEwwMTHB1NSUdevWERISwqFDh4xqsnF2dubnn39mzpw5ijXNqpXnf/0NP0vdlxxV7EloaWnJ8uXLWbFiheK5AAYMGEBGRgYRERGqdMYQ9rN5cc8PHBuD6b97ADesUpY/LoQRGZ+inYmOVXmDOWYJyoB4kJTG3QePGNpS4xOjUH+QTMCh0b8ebljFEBi5GBLLS/ZltFiZAcemELDZ0Co0j1ZYxYmLIXE0cLLFxETSeikCgUCQJ7sDwrmfmMZAd2etlyIogcyaNQsXFxfq16+vWHPq1CkmTZrEsWPH8myx+Tif+wSQmGbYpB+b1lHxXNOnTycxMZEOHToo1uzZs4dp06axZ88exTXrly9fZtCgQcydO1fR+OyN98iRI2nWrBn9+vXDwuLpAcS0tDQOHTqEiYkJc+bMwd7ens8//zzPOfbv38+kSZPw8PBg7969NG/enCFDhuQ6Njk5meXLl/Pll18SHh5OjRo1aNmyJfXr16d169aUL/9kSapOp2Po0KE4OTnh6upKUFAQU6ZMQcoqJy5X7ulZpHZ2dixcuJCpU6eSmZlJ5cqVkWWZ8PBwo91P7OzsGDZsGACtWrVi0aJFisocTE1NMTU1pVSpUixYsIDZs2erar9apUoVdu3ahV6vrnGAp6cnnTp1ynlflGBqasovv/yi+Ocjm2bNmrFp0yZVmgHuzvx+PpQTN2N46ZM9BC/opUjXokULmjdvbnzgY0iSxObNm1VplCACEE8jIw3CL0DzUU881cjZYJ5zMSSWrvXtX/TK/sGx6T9tQksAl+4ZOkw01LpXeug5qOQK5tb/erhmRWvKWJhy8V4sA5treGPp1BT8VkHMDajkot06XhCpGXquRsTzlkjtFAgEhZxL92KZvi2Aug42eLhU0no5ghLGxYsXOXHiBF9//bViTUpKCmPHjuXnn39WvPnzC45hxfG7AJyZ0VnRRi4xMZFff/2VgIAAtm/frmie69evc+vWLaZNm8aff/6Jg4ODUc22bdvQ6/XMmjWLn3/+mWbNmhnVfP/99+zZs4fbt2+zbNky2rdvn+f4R48e0a9fP3x9fenZsyfff/89DRs+PQMkJSWF6dOns3jxYgBeeeUVLl68SKlSTy83zszMpEOHDlSvXp3bt29TqVIlvLy8jL4WCwsLunbtSteuXXNO+NVstCtWrJjzuSRJODo6KtY+rsuPuaGlpfpDX0mSMDVVv91VY9iYjdrgQzZq3v9sNrzdiuof7QJg8qYLfD2o8XOb63kgAhBPIzIQMlL+5f+QTX1HW3QmEpfuxWkbgHBqCpe3QWIUlK6s3TpeEJfuxSFJ0MBJwwCELBvKG1x6PPGUiYlEgyq22pfnOGX9MQ07VyICEFfCE0jXyzSuonFpjkAgEOSBLMtM+PU8Za3MWTOiOaa6kpGhJigc7N69mwULFrBkyRLFm6tt27axd+9e+vfvT4MGDYwLgFP+Fxi8ORSA5cOaUbmM8U3jw4cP6d69O3q9nkOHDinaMCYlJdGtWzesrKzYt2+foo1wdHQ0Y8aMIT09nbNnz1KnTh2jmgMHDvDee+8BcOTIEdq0aZPn+Li4OHr37s2NGzdo3749kyZNyjP4ABATE8OQIUMYMWIEFhYW2Nra5hl8AINPQqNGjWjUqFGe4/KisGxGBfkjYHZXGszey7bzofRq6EDnukXH4FX89Xsa2QaUTk8GICzNdLxkV4aLWSfympG90SwhPhAXQ2KpVak0ZSw1dAyPvQOPYgzBn1xoWKUsVyPiSUlXl+5VoFR0ATPrElOek5MZ4ywCEAKBoPByISSWOzGPmOzpol35pqBEIssyI0eO5Pr166pOntesWcOPP/5IrVq1FGuygw/O+nA8FXa8WLFiBWfOnMHR0VHxafU333xDcHAw1atXV5yZMWHCBExNTZk0aZLRsgGAmzdv8tVXXzFv3jwuXrxI69atjWoePXrE77//TlhYGH/99Rft2rUzqnFycqJ58+Y0aNAAFxcX7OyKzkZSoB1lLM3YMtZwTY5c68f9ROMmnYUFkQHxNO6dhdL2YFsl16cbOduyOyACWZa1iyA6NDJ4EYSdg5e6a7OGF4Qsy1y8F0d7l4rGBz9PsoM9TwlANKpiS7pe5kp4PE2qatSRwURn8C4pIYGpCyGxVCxtjqOtuKEXCASFF5+L4ZjrTPCsLzYXghfLtWvXiIiI4NNPP1WcyZCUlMS+ffsYP348/fv3V6R5feU/Hbj2zXtd0f1xeno6K1eu5Msvv2Ty5MmKAhD379/n8OHDHDp0SLFXxM2bN/m///s/1q1bh7m5uXEBUK1aNXbv3q1obDZKykAEgoLCvXp5xnjU5MfDt3D/bD+3v+hZJDJbRAbE0wj1N5RfPOU/sVGVssQlp3Mn5tELXthjmFsbvAhKwEYzPC6F+4mpNNI6zT7sHOjMoXLu5k2Nsk7htS/DaAoRAQYvk2LOpXtxNKpStkj8whUIBCWTzEyZXQFhdHipEjZaZvEJSiS+vr589913zJ07V/HfSl9fX77++muWLVumKMPg5M0Yjt2IAeDqvO6K6/Xv3r3L7t27mTp1quLsBzMzM/766y9VRpW1atVi6NChioMPQL68AwQCYyhpJ/pf9Ho9YWFhuT73cY+6WJoZtvTDV//bG/Du3btERUWpnu/gwYOkpKSo1ilFBCByIyUOHtw0nCI/hZyOB5qXYTQ1BEsUtIopylwMMbzPjbROsw89B/YNn+iMko2DrSUVS1tof104NgV9KkSpb7VVlEhMzeBmdGLOz6NAIBAURg5cjSIyPpVXGqk3bBMInpU+ffrw7rvvqtJ06tSJcePGKRqrz5QZssKQ/bB5bGsszZQb+NWqVYvatWurWputra04dBAUGKGhofnSbd26NV/tKbNLetSg0+kYO3Ysly5dyvX5S7O6AXD4enTOngkMnU06d+5MeHi4qvmio6MZOHCg0ban+UUEIHIjPOs/16HJU4e42JXG0syEiyEan3Q7NoXkBwZvgmLMxXtxmOkk6jpo2N4yUw9hF55afgEGQ5/GzoXIiLKYZ8cE3ItDlv/pTCMQCASFjUdpGczecZnalUvTXUvjakGJJT9lAcZMEB/H8+vDADSrVo7m1Z9s/ygQvAgOHjzIoUOHcrp7KOXq1at4enri76/OO61q1arUq1ePn3/+WdWczZo1o1WrVqxdu1bVfPXq1ePll1/mwIEDTzxnbmrC6uGGFpt9lh3PWU+ZMmWQJAkPDw/u3buneK4GDRrg4+PD8OHDyczMVLVOJRRIAEKSpO6SJF2TJOmGJEkf5fJ8B0mS4iRJupD1MVOpVhPCLxj+zSMDwlRngpujbY4BnmZkb4aL+Ubz0r1YXO1tsDBV3xanwLh/HdKTDEGfPGhYpSw3oxNJSHk+UUNFlK0KVhUMJSPFmIs5rVlFBoRAICicLD14g9DYZOa/1gBzU3HuU9wpdvfERjh0LYpb95N/1rTZAAAgAElEQVQAcgzxBIJn4dChQ0yYMIFt27YRExOjWNeqVSvGjRuHq6srX331FQkJCYp0nTt3xsTEBHd3d6ZMmYJer8xIvnnz5ri4uPDGG2/wyy+/KF5njx49MDMzY+rUqVy9elWxrmvXrsTHx7Ns2bJcyzg6ulamegUrAPp7n8x5vFWrVgQHB3P27NknNE+jTp06lC9fnhs3bhAZGalYp5Rn/ksoSZIOWAb0AOoBQyRJqpfL0KOyLDfO+pirUvtiCbsANlXAOm/Dw4ZVyhIYFkeGvuAjQ4qpXN/gSVCMOx5kZsoE3IujYRWNT7mz3+M8MiAAGlaxRZYhIFTDLAhJMgRKSkBgyrl8KcpbK6/pFAgEghfFg6Q01pwI5v8aOdKihjgZLu4Uy3viPEjXZzIiq+Z8+zttRVmE4F/4+fnh5eXFhAkTmDdv3lPLB/5Lx44dKVeuHP369aNWrVoEBwcr0llZWbFu3Tpu3rzJTz/9pOrkfsGCBTg7OxMYGEhamnL/tAkTJvDKK69w5swZxRpLS0sWL15MvXr1uH37tmJd27Zt2bBhA1evXn1qacT+yR4A+N95yJnbDwCYNGkS8+fPV5XhYWZmxrlz53j06BEZGRmKdUopiFB8C+CGLMu3ZFlOAzYCfV6A9vkRfiHP7IdsGjnbkpKeyfXIxBewqKdgam7wJAg7r90anjO37ieRkJpROPwfzMtAhbz7RmcbZRaKMozoq5CWpO06niMXQ+K0NyYVCASCp7Dq2C2S0/VM6KSuxl1QZCl+98R50PqLgwC8XKei9vdoAtWkpqYqKh0ICQlh1qxZvP322/Tu3ZvVq1cr+v7u7u6MHj2aTZs2MXPmzJzggBLmzJnDmDFjaNGiBf379+f48eOKdC1atOCXX35h8uTJeHh4KM4waNKkCadOnaJbt268+uqrJCcnK9INGjSI7du3c/fuXby9vRVpAEaOHMm6deuYPHmyYpNICwsLhgwZwltvvcXs2bNzHWOqM2HD2y0BGPjjSfSZMnXr1mXChAn8/vvvhISEKF5jtWrV+PDDD1mwYIFijVIKIgDhBDz+au5lPfZfWkuSdFGSpD8lScpuIaBU++JIiYOYG+CgIABRmIwowy4YPAqKIdllLppvNMPOGQJTJnn/2JSzNqdqeat/mcBoglNTkDMN10YxJCYxldDYZO2vC4FAIMiFxNQM1p24Qw83e+rYaehfJHiRFPp7YlmWVdfIA0+cJu8JjOB+oiENfN1bLXLV6PX6fM2VnxNXNafWj5Mfp/+kJPUHO+np6SQmqjuwlGVZkUFiSkpKTn2/Xq8nKCjoqXNFRUWxevVq+vbtS8uWLdm9eze7du1i165dnD+f+2Gms7Mzffv2JSwsjJ07d7JgwQIaN27MiBEjWLZsGY8ePb0joIeHB/7+/sybN4969erx+uuv4+npia+vb56vSZIkli1bxpYtW/jpp5+YPn06w4cPV9RBYvDgwYwcORJvb2/69u2bq2dCbjg6OjJ58mS6devGa6+9piiDwtTUFBMTE3755RdWrlzJ0aNHFc0Fhvd13rx5vP3224o1ABMnTsTX1/epGSVtalXEzckGgF7fGtZjYWHBzJkz+fTTT1XNNXToUA4fPpxvo86nURABiNzyrf772+YcUE2W5UbAd8AfKrSGgZI0WpIkP0mS/KKjo/O9WKNkG1AqyICoVsEKG0tTArVMtQdwbGLwJoi5oe06nhMBoXGUMtNRu3Jp7RaRkQaRlw3vtQIaVLElMKwQXBcA4eqcdosK2SUuDbQuzREIBIJc8LkYRkJqBiPb1dR6KYIXR6G/J969ezfTp09XpUlJSaFNmzY5p8KyLDP2F0M6958TX35q6cXs2bPZuHGjqrkCAwPp1auXKk1qaiqenp5cvqyu89eCBQuYMWOGKs2ePXto3bp1npvubLI3sIcOHaJFixbs37/fqMbHx4e4uDi+//573N3d89wwZmRksHr1alxcXBg3bhzt2rXD1dWVqVOn5tr1QK/Xc+zYMXx9fTly5AgxMTEcPHgw5yMoKOipczVq1Ihdu3Zx+PBh9u3bx5EjR3ICAjpd3v5szs7OfPLJJ7z11lucPHmSRYsWYWVlZfS90Ol02NjY0LBhQ3x9ffHy8lLVRrVVq1YcPHhQdZeVyZMn8+WXX2Ji5MDxccqUKcMff/xBo0aNVM3Vv39//ve//6nSmJmZsW3bNlxdXZ86Zsc77QC4GpHA35EGL4yBAwcya9YsVXOZmpqya9eufBnZ5vl9C+B73AOcH/u6CvCvRqWyLMc/9vluSZK+lySpohLtY7rlwHIAd3f359dzMtuAUkEGhCRJ1He0JTAs3ujY54pD1sUefhEqvaTtWp4Dl0PjqetQBp2JhrWF0VdBn/bPe20EN0dbdl0KJ+5ROrZWGvV8L10ZyjgU2wDE5ayfu3qONhqvRCAQCJ5k49kQXOxK07SqyNIqQRTqe2JZlpk3b57iFPpsli5diqenZ05njCmbDfcVNStaU9ch97/BQUFB+Pj48MknnyieJyUlhTfffFNVKrssy4wdO5auXbtSv359RePT09P5+uuvOXr0KNu2bTOqyczMzHk9Pj4+7N692+gGOioqik8++YSEhATu37/Pr7/+mueGMSMjg+nTp7N48WJq1arFkCFD+OOPP3B2ds51fGxsLDNmzODAgQPEx8cjyzK//fYbjo5Pb/Wr0+no27cvffv2Ra/Xc+7cOdzd3VV5d7Rv3z7ncw8PDzw8PBRrs1G7SQfDnsvT01O1zt4+f52H8rPGKlWq5GsuFxcX1ZqqVavm+byJiYT3680Y+4s/nouPELygF5IkUaNGDdVzVatWTbXGGAURgDgL1JEkqQYQCgwGhj4+QJIkeyBSlmVZkqQWGDIvYoBYY9oXTrYBZelKiobXd7Th51N3yNBnYqrTyN26ogvoLAwbzYYDtVnDcyIzUyYoPJ7XmmhbmUNEdmtWZb+Q6mdtii+Hx9GmVt5mps8V+4b/rL2YcTksLisLSaMAj0AgEDyFK+HxXAyJZeYr9YQxX8mi0N4Tp6WlsW/fPmrWrEndunUVaVJSUnjw4AErV67McdCPS05n2zlDOvbuiS/nqgsJCWHcuHF8++23WFhYKJrLz8+Pn3/+mf79+9O8eXNFmm3btnHp0iXS0tIUZ3Vs3bqVNWvWIMsy27ZtU7S+b7/9ljlz5tC3b18OHTpkVJOQkEDPnj3x9/fngw8+YMOGDXn+HoiJiWH06NFcunSJli1b8sYbbzB69Og85yhbtizLli3L+To1NVXxew2GYITS91lQNOnu9k/wZbNfCAPccw9macEzByBkWc6QJOld4C9AB/wky/JlSZLGZj3vDfQHxkmSlAEkA4NlQ1FYrtpnXdMzodCAMpv6TjakZmRyMzqJl+w1qvHUmYFd/WJ50n3nwSMSUzNyapk0I/wimJeG8rUUDc8JQITGaxuAcGgIN/ZDejKYKe/pXRQIDI3X/roQCASC/5CUmsGHWy5iZa7TPngueKEU5nviRYsWsWbNGlatWqVYc/r0aV5//XWGDRuWk/3Q5gtDPf24DrWwNHsy9T4+Pp4mTZrg5uZG48bK7qdlWWbQoEEkJSUpNhuUZZnPPvuMgIAA/vrrL0WBvvT0dGbMmMH169dZv369og17UFAQH330ETY2NnTo0MGoJjU1lbfffpuqVavy5ptv0rlzZ6NrK1euHFu3bjW6lrxQE3wQlByOTu3IywsP8eGWS/RvVqXQBMQLIgMCWZZ3A7v/85j3Y58vBZYq1WpGSrzBR6HhYMUSN0dD/fnlsDjtAhBg2Ghe/h1k2dCCsZhwOctHob6jxnX+4ZfAzs2oAWU2FUpb4GBrmbN+zXBoBLIeIoOgSjNt11KAxCWnc/fBIwY1LzzRXIFAIACYuvUSQWHxrHzTnXKiRXCJo7DeE/v7+3Pjxg1VZnKnTp3i3r17SJKETqfjQkgsSWkGw/Np3XMvJzh06BAxMTFUr14dS0tLRfOcPn2aW7duMWzYMMW15idOnODixYtMmzaNNm3aKNL89NNPmJubs3PnTnr27Gl0fEZGBmvWrGHdunW8+uqriv0HNmzYoMo/QM1YgUANzuWtaFjFlkv34hj3yzm8hxWOvYC44h8nQrkBZTY1K5XG0syEwNBC4AOREgexd7RdRwFzOSweM51EHTsNDSgzMyEiQHH5RTaFwh/EvqHh3/Di1QkjKOt9rS/8HwQCQSEiKj6F3QHhjPGoRSdXO62XIxDkEBgYiLe3N4MHKz9kO3XqFHPmzOGzzz5DkiReXWbITlg/quVTNXv37mXmzJmsXr1a8Yb9jz/+4IcffmDt2rWKzAnBEOg4ffo08+fPVxTokGWZGjVqcOHCBXr16qXoJFin07Fw4UIGDhyo+LVYWFiIgEIJIT8dXgCSk5PzpQ0LC8uX7vOO5QHYczmCB0nKu8WcPn1a9VxKET8hjxOm3IAyG52JRF0HG+1Puu2zjSiLV71/YGgcdSqXwcI0b4fd58qDm4YuIw4NVcnqO9pwKzqRR2nq20kVGGWrgmXZYucDUWgyYwQCgeAxdgWEI8vQr6kovRAUHpKTkxk7dqxRX4H/8uqrrzJz5kwkSWLl0Vs5j7et/fTS0oEDBzJnzhxVqd7jx49n7NixqjQff/wx7u7uisdLkkTXrl2Ndmz4r0ZQdMhvQCDbkFMt6enpfPXVV4radT5Oamoq48aNQ6/Xq9JdvXpVlalrNht++ZmeTukANJ23T7FuwoQJ3L17V/V8ShABiMcJvwhlHBUbUGZT39GGoLB4MjOfX3MOo9jVA0lXrHwgZFkmKCxe+1Pu7PfUXn0AIlOGK+EJz2FRCpEkQ+CkGF0XYMiMsbOxoFIZUfMoEAgKDzsvheNqX4balTUsyRQI/oOFhQWTJk1SrXvzzTdzPv9s1xUAzszonKcmP10RjDn654aaQIKgaJGcnKx6cw6GkpkPPviAK1euqNLpdDoWL17MjBkzSEtTniFgbm7O6dOnGThwIElJSYp1ZcuW5fjx47zxxhukp6cr1jVo0ID58+ezcOFCxRowdLFYPXVIztc3ohIV6UxMTOjbt29O+92CRAQgHicyEOwbqJbVd7QlITWDkIfGewI/N8xKGVpwFqOT7sj4VGKS0nBz0viUO+IS6Myh0tPbJ+VG9rqDNM+OaWjwgNAr/yVX2LkcFieyHwQCQaHiTkwS/nce0rvR09vgCQRa8KwlAUsP/g2AU9lSVC6jzNdBIMhvRoJOp2PAgAFMnTqVwMBAxTozMzPc3d1xc3Nj1KhR3Lt3T7F21KhRzJ8/n5YtW3L79m3Fuj59+rB161b69eunaqPerl07NmzYwOLFixVrKlWqhJ2dHYsWLeLCBeWl1TVq1CAlJYUaYQYD2S5fH1aks7Oz48qVK+zdu1fxXEoRAYhs0lMg+lq+AhD/GFEWgnr/YlSCERianWZfCDIgKtcFU3VmYg62lpSzMtP+unBoDPpUuH9d23UUEMlpem5EJeKm9XUhEAgEWciyzCd/BGJlrqOvKL8QFDMW7TXcP+yc0E7jlQiKEpGRkbz22msMGDCAOXPmcPToUUU6c3NzvvrqK5YvX06DBg3YsmWL4jkHDhxI48aNWbduHSEhIYp17du3p0WLFiQnJ2Njo/z+skePHnTs2JHMzEzFpqsA3bp1Y9CgQVhbWyvWACxZsoSKFSsqNmsFqFevHkuWLKGqFJPz2J0Y4xkbc+bMoW3btlSvXl3VGpUgAhDZRF81dAuwd1MtdbEvjamJlLNh1gyHRpAYAQmR2q6jgLgcFo8kQV0HDTeasmwI6qg0oARD7aCbky2BWmdAZHtXFJMyjKsR8WTKUE9kQAgEgkLCb34hHP37Ph/3cMXBtni1PBaUbFYcMXg/VCxtIbq6lFCioqJYtGgRM2fOZPLkyaxdu1aRzt7enuXLl3Pz5k1mz57Nxo0biYtTdk9co0YNVq5cycsvv8z8+fMJCgpSpDMxMeGrr77i119/ZfTo0YqDEJIksX37dmbNmsWQIUPIyFDm31a+fHn++usvnJycWLlypSINGPxVvL29+e6773j48KFi3aBBg3j//ff53//+p1jj7OzMu+++y/nz55ndrRoAHv/zNapr3Lgxo0ePZvny5YrnUooIQGQTEWD4V2WdP4CFqY7alUsXgpPurLUXkzKMy2Fx1KhojbVFgXSLzR/xoZD8IF/XBUA9RxuuRySSlqHOoKZAqVAbzKyKTXbMZdEBQyAQFCLS9Zks2f83zaqVw6tlNa2XIxAUKJ/vNtTT/znxZY1XIigoEhIS2Lp1KzNnzlRUJlG5cmU6duzI3r17Wbx4MfPmzWPMmDH8+uuvhIWF5amtVKkSBw8e5OOPP6ZGjRq0bNmSefPmKQpE9O/fn507d/LDDz8wYMAA1q1bp+j1dejQgX79+rF48WJ69uypOAhhb2/PkCFDaNiwIdOnT1ekAUPpx+LFi1m8eLEq08ayZcsyceJE5syZo1gDMHz4cHbv3k1kpPIDZxMTE8aPH8/f+3/NeSzkgXHrgD59+rB//35VHheK1lOg360oExkIZtZQrka+5G5OtlwOi8t3vVOBkF0+UkxaLl4Oi88pb9GM7KwBFZ1RHsfN0ZY0fSZ/R2loRGmiAzu3YpMBcTksDttSZlQpJ04ZBQKB9uy6FE5YXArvdKyFiYlwzRcUbkJCQhRv5NadDAagjKUp61f9oHoTcvz4cQ4cOKBKk56ezty5c1XfT69Zs0a1+eDt27dZsmSJKk16ejpTpkwhPl75oaMsy/z4449s3rxZ0VhZltHr9WzcuJHhw4cbHb9lyxb++usv9u7dy/Tp02nTpg3nz59/Yqxer8fb25vq1avTv39/vvnmG+rWrYurqyuurq588MEHT52nWbNmnDhxgtWrV/P777/Tr18/AgIC6N+/v9ET/LJly/L555/zwQcf4O/vT6lSpVi/fr3R9wLAxsaGli1bcuzYMc6cOaPKZ6FLly4sXrwYPz8/xRqABQsWYG1trTgLAgyv8dtvv1XlOwHw9ttv4+TkpOp6Nzc358svv+TBgweq5nrjjTdwdnbmf/0Nh6odFvka1ZiZmTF37lzFmStK0fBouZAREWjoJJFPo576jjZs8b9HVEIqdjYaGfRY2hoCKMXgpPthUhqhscm80Vrj06TwSyCZgF39fMmzT+kvh8Vra5ro0BAuboLMzHxf44WFy1mdUUR7LIFAoDWyLLP8yC3qVC5NB5fKWi9HIDDKqlWrsLOzUzR25vbLAKzsW40Joz5l4sSJiueRZZmPP/6Yb7/9VtX6fvzxR+Li4lT9jb927RqLFi3i9OnTijWPHj1i4MCBqlLZ09PTGTp0KK6urpQpY7zTzcOHD9HpdIwZM8bwu8JIKntmZibvv/8+rVq1YuHChbRs2TLP0/ErV64wYcIEDhw4QJUqVejVqxcdOnRgwoQJuXoE6HQ6xo4dy/Dhw/H19eXcuXN8/PHHit9rExOTnIBIgwYN6Nq1qyId/NPS1NraOs9Ax9MoV64cS5cuVa3r0qWLao2pqSmzZs16YXN9+OGHqnW9e/dWrbGysmLs2LEAfLjlEvpMmfC4ZKNlg4MGDVI9lzFEAAIMdf4RAdCgX76/RfbmMjA0TrsABBg2mmFFPwMiKDw7zb4QdMCoUAfMrfIlr17BGmtzHZdD48DduYAXpwL7hnB2JTy8DRVqabeOZyRDn8nViATe1DowJRAIBIDfnYcEhcezoG8Dkf0gKPRkZGSwceNGRRv17RdCATDXmbBh1Q9MnDhRVVDg4MGDVKxYkcaNlWWQyrLMw4cPWbp0KadOnVKsSU1NZeTIkSxbtkyxoV9ISAhTp05l2LBhdOjQQZFmw4YN/P7777i6ujJ37lyj70VcXBzdu3cnOTmZd955h9GjR+epycjIYNSoUaxduxY/Pz+2b99OtWpPv9dJTEzk6NGjeHp60qZNGypWrMiECRMU/R9ZWlrSvXt3unfvbnSsoHgy/7UGTP89gF7fHuPcp54vfH4RgACIC4HUOEOaej5xdTBEQq9GJNC5rrLI8nPBvgEEbYeUeLAsujXyV7ICEHUdNO6lHhkIVZrnW25iIuHqYMOVCA1LMOCf8pzIwCIdgLh9P4m0jExtjUkFAoEgi/Wn7lDG0pT/ayxabwoKN2FhYezYsYO2bdtia2v8cGfiRsNh1qS6j1jy2V+qMgU2bdrE0qVL+e677xRrtm3bxvr165k4cSJly5ZVpDl//jxjx46lVatWeHh4KNLcuHGD1q1b52QKKMHX1xcvLy/at2/Pzz//bHSTL8syo0eP5syZM3Tr1o3hw4fnqUlPT2fmzJnEx8fz6aef0qhRI6pUqZLnHKVLl2b06NGK1i8Q/JehLasy/fcAHiSlkaHPxFT3YrOji3YudkHxDAaU2dhYGmrSszfOmpEdRIlSVwdX2LgWkUDF0hZUKG2h3SJSEyD2LlSu90zfxtW+DFfD47X1B6nkaiglibys3RoKgKtZgZyX7DUOTAkEghLPg6Q0dgdG0LeJE1bm4jxHULi5fv0648aNIyoqitTU1DzHRsWn5Hw+8a0hpKSkqGppuHTpUvz8/FTVw+/fv5/ff/9dVa35jh07OHv2LI8ePUKv1yvSLF++nPv371OhQgWj7wMYggnTpk2jVq1ajB8/HnNz451AfvnlFyRJYteuXfj4+GBhkfe9rJmZGV988QXbtm1j7ty59OvXD51Op+j1CAT5xbOe4cB8/u6rL3xuEYAAg/8DksED4hlwtbfJ2SBpRrZXQWSgtut4Rq5FJuCq9SYzO4iTT/+HbFwdbIhPySA8LsX44OeFuRWUr1XkAxDXIhLQmUjUrlxa66UIBIISzpL910nLyGRIy6paL0UgMEpkZCQmJiZMmjTJ6IZ4xJqzALzb1oH09HTee+89atVSlj0pyzKBgYGMHDmSXr16KV7f8ePHGTFihKp6+B07dvDRRx+xfPlyRRv21NRU9uzZw65du/D29sbS0njJ9IkTJ3jzzTcJCgpi0KBBmCjw0RowYAAbN26kZ8+emJmZKXotgqKJ0sDXf0lMTMyXLjo6Ol+63AKIiwcZyqN+On47V82tW7fy/fqMIQIQAJEBUL4mmCurHXsa9RzKcCs6kZT05/OfpQhbZ7CwLdIBCH2mzPXIBO1PubM368+YAVEvq4xE8+wYe7d/sn2KKFcjEqhR0RoLU3EyIBAItGPD6busPXmHEW2r42ovSsIEhZ/IyEgWLlxIp06d8hwny3JOu+sWtomMGzeOSZMmKZ4nLCyM3r178+233yr2jIiNjaVTp06sXLlS8cl/dHQ0U6ZM4YsvvlAUFAC4f/8+Bw8epGfPnorGA7Rp00Zx5kM2SgIbgufDw4cPSU9PV62Liori+PHjqnXXrl1j06ZNqnV//vkne/bsUa1bsGABt27dUq0bPXr0E109Slv8k7nnf+fJTibnz5/Pl/GnEkQAAgybsuwa+WfA1cGGTBn+jsxfVKtAkCTDiX0RPum+++ARKemZ2gcgooLAvAyUfbbTLRe7f/xBNMWuPsTeMfiDFFGuRcZrf10IBIISTWqGngV/XqFNrQp80uvZAtQCwYvi5ZdfZvLkyUbHrTpmOA11c7LB2dlZVSABoFSpUvz000+KgwJg2LAvXrxYlaZSpUp4eXkpHg/g5ORExYoVVWlExy1tOH/+PLdv534ynxdmZmb06NFDtbZSpUoMHz4cHx8fVbratWvz1ltvsWvXLlU6BwcHBg0aRFBQkCqdJEkMGDCAlBR1WdV+fn4sWLDgicd/fbsVAP1+OJGr7uOPP+bmzZuq5lKCCECkxMPDYMPp8DOSXTJwJUJrH4j6EBlkaLlYBLmalSmgeQlG5GWoXNcQ1HkGylia4Vxe+IM8K4mpGYQ8SMbVTgQgBAKBdhy9fp/4lAzefrkmOtH5QlBEaNKkiaLN9Ge7DPcIPw1vTo0aNTA1VedvUr58edUaS0tLsdEvhsiyjK+vL7Gxsaq1tWvXxsPDg/fff19V2UHp0qVxdHSkSZMmbNmyRbFOkiRatmzJa6+9xurVqxXrzM3NqVmzJv379+fw4cOKdc7OzsTHx/N///d/3L9/X7GuXLlynDt3jo8++kixBgw/YwsWLMDf3/9fj7euVSHn89wy+JOTk3n//ffJLOA9pQhAZGcKPIMBZTbVKlhTykyn/UbT3g3SEgyn3UWQqxEJSBLUqazhRlOWDdfGM/qCZFPX3kb76yI7ABFZNMswrmVlkLiKDhgCgUBDfC6FUdbKjLa11Z2kCgSFndv3k3I+r1xGlBEIng1JkihVqhTOzs506dKF7777TnF5RJkyZZg6dSpLlixh0KBBJCcnK573jTfeID4+nm3btpGWlqZY17FjRypWrEhqaqoq4/iuXbvi5OSk2CcFwNHRkVdffZXGjRtTvnx5xbqGDRvStWtXVf4qAB999BG1a9emadOmTzw3NMvHaOqWS/96vHr16gwfPpyBAwcWeIBQBCCyvRKeoQVnNjoTCRf7MlwN1zrVPnujWTTLMK5FJFCjgjWlzDWs808Ih5TYArkuwLBpvn0/SWN/kCpgaVukrwsoBJkxAoGgxJKcpmdfUCQ93OwxNxW3UILixYRfzwHwv/7PfignKD4kJSUxa9Ys3nnnHaZMmcJ3332neIPesmVLvL29OXDgABs2bODhwye9Bp7G6NGjGTx4MJGRkfj5+SnWdezYkT///JOAgACuX7+uWNe3b18OHz7M999/rypwsWDBAiZMmIC3t7dijZmZGdu2bePmzZuEhoYq1vXu3ZupU6eydu1axRqAd955h0qVKnH16pMdL2b3Npjt77gY9q/HmzVrxujRo/Hx8REBiAInIgBKlQObgunhXc+hDFcjNG65WLkuIBXdjWahMKDMqsl6RgPKbOralykk/iBuRfe6iIjH2lyHU9lSWi9FIBCUUH7wvcGjND19GjtpvaG6To4AACAASURBVBSBoMAJDDVkavZvVkXjlQieN2lpaRw5ckTRfsXa2pqJEycSHR3N119/zbfffsuXX36p2BvAy8uLVatW8d5779G+fXs2bdqkaF5zc3PWrVuHj48PY8eO5ejRo4rm0+l0dOvWjdWrV/P6668r7jhRrlw5XnrpJfr06cPXX3+tSAOGYMLo0aPZvHkzMTExinWSJDFu3Dh++OEHxRowBFj8/f1VtawFQ3eWzZs3P/H448H0yPh/e0u0aNGC8+fPqwrIKEEEILINKAsosuNqb8PDR+lExhvvLfzcMLc2dPUogqn2yWl6gmOStA9ARGVt0guoBCO7bED7Mowsg9Ii6A9yNSIBF/symIiaa4FAoAFngx+w9NAN+jWtQquaFYwLBIJCSFpaGsHBwU88fiPqn01abqedN2/efMJF3xgPHjzIV9vAa9euqT7Iu3v3LklJScYHPkZmZiZXrqj3xQoICFDdnjA6Olq1mV96ejp79+5VNDa7RCE2Npa1a9cSFhb2xBi9Xs+GDRsYMGAAFStWZOjQobzzzjuMHz+e8ePH5+l9UL58eTZt2sTatWtZvnw5pUuXZsSIETRv3pwHDx4YXd9bb73FkCFDOHz4MJs2bcrVEDE3zMzMqFmzJj4+PkycOJH4eOX30e7u7owcOZIff/xRsQYMxou7d+8mNVX5Xq5UqVKMHz+e3bt3q5rLy8uLM2fOqLreTUxMGDp0KGfOnFE112uvvUZAQO57w2ndXQGY8fu/uyjqdDp69uzJtWvXVM1lDHUuMcUNfYah04H7yAL7lo8bUdrbalg/Z1e/SLbi/DsqAVkuBGn2kUFQxtGQHVMAVCtvZfAHKQwGpWmJBn+Q8jW0XYsKZFnmWmQCPdzstV6KQCAooXy+6woOtqWY06e+1ksRCPLNoUOH2LJlCytWrPjX4x9svgjkXn4hyzKvvPIKZ86coUwZ5fdn3t7e2NjY8O677yrWhISEMHjwYM6dO6dYAzBq1Cjmzp1Lq1atFGtWr17NmTNnVG1Qr127xqBBgzh27Jji2v3o6Gi6d+/O7NmzjfoEZGZmotfruXr1KqNGjaJTp054eno+NQU+KSmJKVOmkJGRQUREBMHBwfTp04euXbs+MVan09GrVy9MTU2xtLTk2rVr9O/fP+d5Ozu7PNcmSRJvvPEGYDiFf/fddwkPD6dcOeX3ynZ2dmzdulWVpwNAzZo1OX36NGZmZqp07777rupglpWVFUeOHFFddvDee++p1lhbW7Nv3z7Vuk8//VTVeDB0+sgtAwLg7Zdr8OWeq+y/EvnEc0uWLFE9lzFKdgDiwU3ISCmQFpzZZJ90Xw1PoONLlQvs+6rGvgFc8YHURLAord06VJLdqvIlrfuqRxWcASWAiYnES4XCHyTrWo+8XKQCEFEJqcQ+Sucl0QFDIBBowMWQWC6ExDK7d71/9U4XCIoaPj4+vPLKK088fiHE0Kkgt/ILPz8/XF1dVQUfZFnm119/xdfXV9X6fvjhB8aPH69qQ3b8+HF0Op2q4MODBw9YtGgRx44dUzRelmVSUlLw8vJixYoVioIPoaGhOZv+GTNm0Lt3b6Oa2bNnExoair+/Pz/++CMtW7Z86tizZ8/i5eXF33//Ta1atdiyZQuNGjXK872ztbVl4MCBDBw4kIyMDHQ63TPV9zs4OKjWSJKElZWVap3a4EP2XPl5fS9K8yy6gsRU909RRHRCKpXKWDzX+QqkBEOSpO6SJF2TJOmGJElP9AWRJMlLkqRLWR8nJElq9NhzwZIkBUiSdEGSJOUOIwVBRFYaSgG04MzGtpQZTmULQ8vF+oBc5FouXg1PwNLMhKrl1f9iKjD06RB9rcD8H7Kp61CGK5r7g7hi8AcpWtkx2T9PmgemBAJBiWTtyWCszXX0E7XxAiMU5nvizMxMDhw4QJcuXf71ePBj3S/+uxnKyMhg8+bNDBgwQPE8KSkpnDx5kpdeeokKFZSXK4WHh7Nlyxa8vLwUa4KDg5kzZw6zZs1SrDl69CgzZsxg0qRJite3YsUK3nrrLQYOHEjbtm0VaWbMmEHz5s2ZMWMGffv2NTp+06ZNzJs3j61bt7Jly5Y8gw8ZGRnExcXh7e3N8ePH+e2336hXr56qzaypqWmh2PwKCgeTPV0AmLXj+e8RnjkAIUmSDlgG9ADqAUMkSfrvzu024CHLckNgHrD8P893lGW5sSzL7s+6HlVEBoKJGVR8qUC/rau9wYhSU+yyUkSL2EbzWmQ8LnZltO2tHnMT9Gn/vIcFRF0HG2ILjT9IEbsuRAcMgUCgEfcTU9l5MZx+zapQxlL9CZyg5FDY74kHDx6MlZUVUVFR/3o8u/3eF32fzAj+4osvWL9+Pfb2yksgfX198fLyombNmop9I5KTk2nUqBFVq1ZVbBoIhrr2K1euYGOj/IBi5syZrFmzBhcXF8WaH374gd9++4369ZXdGwYEBLBu3TpkWVaUJeDv78/SpUuZM2cOvr6+Rks1TE1N6dKlC506daJNmzY0bdoUc3NzRWsTCHJjXAfDNbc7IOK5z1UQGRAtgBuyLN+SZTkN2Aj0eXyALMsnZFnO7rtyCigcRwgRAVDJFUwL9ge2roMNN6OTSM3QsOVi2WpgXqbIdTy4FpGg/SYzx4CyYAMQrlmn95r7QNgXvU4Y1yISsLOxoJy1+OP6vJAkyVmSpEOSJF2RJOmyJEkTtV6TQFAY2HjmLmn6TN5oXV3rpQgKP4X6nvj06dPcu3fvic36mWCDieDg5s5PaEJDQwkLCyNThXn1w4cPCQ4OxtraGlNTZSVL9+7dIzo6mrJly1KxYkVFmpSUFC5dukSdOnWoWbOmYs3Jkyfp1q1bnhkGj3Pp0iWCgoJYsmQJPXv2VKRZuHAhX3zxBdevX6d169ZGx9etW5ejR48yc+ZMGjduLDITNCC/Gcrp6en50qn1wcgmIUF9OXdsbKzR12f2WBnGwyRD1wslBqP5oSACEE5AyGNf38t67GmMBP587GsZ2CtJkr8kSaMLYD3Kibxc4JtMAFeHMugz5ULQcrFoGVHeT0zlfmKa9mn2kUEg6aCi8si4ErI7e2hfnuMGD24b/EGKCFcjErS/Loo/GcAUWZbrAq2Ad3I5uRMIShTp+kx+OXWXl+tUpHblouOnJNCMQn9P/P333/+r7CAp9Z8Mhdw2vSkpKUyaNOmJso28ePjwIZ6ennzyySeKNSEhITRt2pS1a9diYqJse3LlyhWaN2/O9u3bsbRUZvx+8uRJvLy82LJlC6VKKWvrffr0aU6dOsW7776rKDCQnp7OkiVLmDZtmmKvg/x4IhR31GTCPE5CQgL+/8/eeYdHVbR9+J5serJJgJAivYSE3gVBFFFEQFRULCjYeOH1BQQFVOyigGBFLIgKKjbAAtKioIINpYNACi3UNEJCNj3Zne+PzSKfQHImJDkbmPu69ko7v53JydnNmWee5/ds3qysy8zMZNGiRcq6v/76i59++klZ9/bbb5OaeqbpY3k8+eSTypqNGzfyzTfflHvcvT0aAzD31/2A0+yyoKCgDEXFqIwAxNleiWcNsQghrsL5ZvvYad/uKaXshDNdbbQQ4opzaEcKITYJITZVpKXPGeSdAFtypRoNunDtdLsMFU3D1XLRTM8BBdwmzT5tN4RGgWflGrC4/EHMN6KsWf4gJXYHe9NzzL8uLnCklMlSyi2ln9uAOMq+cdZoLniWbD1KSnYB9+jsB40x3Pqe+LbbbuOWW275f9/7ZP1BAG7pdPZEjKioKKZNm2Z4DHAupj/77DMsFothTUlJCUuXLiUgIMCwRkrJypUrlcwxmzZtygcffGA4MwPggQceoGPHjoaP9/LyMtwh40JHSsnx48crpD18+DDjx49Xbv8aGBjIsGHD2L17t5IuJCSEUaNGnbNV5bnw9vbmnnvuITMzs/yDTyM9PZ1x49STTb/44guWL1+upMnIyOCxxx6jqKiozOP+V1qG8e5aZ8vYv/76izlz5ijPsTwqIwBxBDg9Z6s+cEbzWSFEO+AD4EYpZYbr+1LKY6Uf04BvcaavnYGUcq6UsouUskvdunXPf9auxVclGw0CNAkNwMfTg3izd7oj2kBhNpw8XP6xbsA/HTDMbsG5q0quC3AaUZrvD1JqulpDsmOSMnIpKnHoDhjViBCiMdAR+MvcmWg05pGQYuPZ73bRqWEIV8WY2NVKU5Nw63viKVOmnPG911cnAjC2T/OzaiZNmmQ4u8DFsGHDUL1X79u3L/Xrq1WjdOrUSXmh36hRI+XyBqMZGZozEULw8ssv8/TTT5OdrXb/GxMTw4oVKxgwYIDS4l4IQUREBH379uXAgQOGdR4eHvj7+zN48GCl8Xx9fTly5AgPPvigUhmH3W5n4cKFLFu2zLAGnJkh48ePV8pMyMjIYN++fbz99ttlHhcW9P9f6ykpKUydOlX5b1celfGK2ghECSGaCCG8gTuA704/QAjREPgGGCalTDzt+wFCCKvrc+BaoHpWRWmlUbEqWGhaSlsuml7r71poptSMhWZCSjahgd6EBlZt65cyKbRB1sEqyYwBZ3bMvvRcCorN9AdpWOoPUjOuC7cJTF0kCCECga+B8VLK7H/9rHIz0TQaN+aRRdsI8PHk3bs7m2uMrKlJuPU98dlKDorsTm+HxqFnzzyoiLGhSuaDC+154N7ExcWRlZVVIe0jjzzC66+/TtOmTfn2228N64QQ3HDDDaxevVp5F75t27ZkZGSwceNGJV27du0oLi4mOTnZsMbX15fo6Gh8fHyUykbCw8OpV6+e4VIgcGYKXXbZZURHRyv5M4SEhBATE6MU5EvLLqBnz5507ty5wn/7c3HeAQgpZQkwBvgeZ8ruIinlLiHEf4UQ/y097BmgDvDOv1oLhQO/CSG2AxuAFVLK2POdkyFSd4FvMARdUiVPHxNhJS7ZZnLLxZbOjzXEcNBZ5292+YUrM6byvUHAaVBqd0j2prmDP0gNuS6SbVg8hK6/rgaEEF44gw+fSSnPKBas9Ew0jcZNSUy1setYNmOuak54kNrur+bipabdE2cXVMw8T3PxYbfbadWqFQ0aNODmm28+o5NKWYSHhzNx4kSEEEoLe4Bbb72Vp59+ml271O5ZH3roIZ577jn27NmjpFu4cCFNmjRR0jRt2pQVK1Zw4MABpXKgiRMnMnjwYHJzc8s/uBSLxcK3337L0aNHueQS42vYu+66i0GDBhkK9I260mnoOveX/cydO5e0tDQaNmxoeCwjVEpOkZRypZSyhZSymZRyaun35kgp55R+PkJKWau0rdCp1kKlLsHtSx+tXdpqIW23c5FZRRHXlpFBnMgtIj3HxJaLPlao1aRG7HTbHZLEVBvR4WYbULo6YFRRBkSk843JdH8QVyeMGuAPEp9io0loAL5e6jsqGuMI53+lD4E4KeVrZs9HozGT5duP4SFgQNvy2+dpNKdTk+6J5/3mTE+/89LKXVxoagYOh8PwRmmbNm349ddf8fT05Ndff+XFF1/k6NGjhseaMGECmzZtYvHixbzzzjuGdZdddhnPP/88mZmZLF261LCuWbNmjBkzhk8++USpfCAoKIiRI0cyd+6/u+OeG09PT5o1a0Z+fr5SgEUIwYABA1i1alX5B5+mCQ4OxtvbG9VM1Msuu4z169eXe9zIXs4AxAe/HSA4OJjCwsIKd+w4FxdnUZMsNeCrokUmnNZy0R0MB2tAAOLQiTwKih2nFuimkbbbWZ4QXDX/jBvXcfqDmN8Jo7XTHyTrkLnzMEBCarb5mTEXBz2BYUCf0l25bUIIY/3GNJoLCCkly3Ykc1mzOtS1mlgSqNFUMW+sce4Oj76qmckzufCRUlYoK1rVgBGcnUvOpcvJyWHJkiU88MAD9OrVi99///3UIyEhocznbdasGb/99hurV6+mY8eOXHvttTz00EOcPHmy3DlZrVYaNWrE8uXLWbx4Me+9957h30cIwdy5c3n88ceVyg4CAwO5//77mT17tmENwM0338zKlSuVF9233norX3/9tZKmd+/erFu3TvnauPLKK1m3bp2SxmgAos6/SuHbtWvHjh07lMYqj4szAHHyiHPx5SpRqAJaRrpRy8WMfVCUZ+48yiGh1C/D9E4Hqbud10UVGQ6d8gdxh+sC3D44lVNYwuET+cRoA8oqR0r5m5RSSCnbnbYzt9LseWk01c2ve45z4Hgu17ermhJNjcZMkpKSGDNmzP/7Xv1a5beAHDFihHL6/A8//MAbb7yhpJFSMnDgQBwOh5LujTfeUNpJBqfB3l133aWkAWc6+8GDB5U0n3/+OTNnzlTSbNmyhT59+hg6F1lZWRQUFDB79mw6dOhw1k4Odrudb7/9lvnz5/PFF1+QlJTE/PnzmTdvHvPmzTO0oK1Xrx4dOnTgvvvuY9u2bXTt2hUfH+OB2oCAAJYvX06XLl0Ma1zjfvnllwQFqWVKjx49mjvuuENJ4+vry5IlS/Dy8lLSjRgx4owuM+Xh5+fHV199paQBp69Gnz59lDQRERF88MEHSpq07AJeeuklWreu3NJ04z1oLiROGVBWTZ0/QIi/NxFBvqdaS5qGq+ViehzU62zuXMogPsWGEBAVZuJCU0pI2wWtbqzSYWIirPwYZ7x2rko45Q+yG2IGmjuXMkhM1QaUGo2m+kjLLuCRRdtpVjeAGzvoAITmwmPTpk0EBATgcBjfcXU4HKxdu5bw8HClsVavXk23bt2UNLt378bhcCh3nvj000+VWxPOmzePrl27Kmk2b97MsWPHaNSokWFNcnIyL7zwAr/++quh4+12O9u3b+euu+7iq6++KvdczJw5kx9++IEjR45wyy238Pvvv1OnTp0zjrNYLAwbNoxhw4aRn5/PH3/8QZ8+fSpsAOrl5cWwYcOUdQEBAXTurL4mad++vbImMDCQwEB1D7FWrdSz5M92zo1QkcV9ZGTFygON/l5DuzXk878OsWTbUUZeUfkZUhdnBoSrzr8KMyDAuWgyvdY/vPSiTlXrhVvdJKTYaFwnAD9vE+v8bSmQn1mlgSmA6IggMnKLSLeZ7A8S0sgZcHFjXAE8V0mTRqPRVCUvrIgjp7CYd+7qjL/3xblHo7mw2bx5M507d+avA85U9taXlP//NTExkaioKOWgwLp167jiiiuUNKtWraJ///5Kmr179xIYGEhERIRhjcPh4NNPP2X48OGGNSUlJTz//PM8++yzhjUHDx7kv//9Ly+++KKh1qQZGRncfffdp4IPZS1OpZQ8+eSTPPbYY6xbt4758+czdepUQwthPz8/rr76at19RHNWBnesB8C3W8/oIlwpXJwBiLTdEFQf/EKqdJiYCCv70nIotqulkVUqtRqDp98/WR9uSkKKjWiz0+zTqtaA0oWrzMQtsmNqQGDK39tC/VrGWxRpNBpNRUg+mc/Kv5MZ1r2RzrrSXJDs2rWLjRs30rlzZ5ZsdRoIuhYa5yI5OZlvv/2Wyy67TKlOPTY2lsLCQkOLbhfr1q1j2bJlSgGIbdu2MWPGDIYMGWJYk5OTw3333Ufnzp2pXbu2IY2UkhtuuIHMzEwuv/xyQ5q8vDy6detGSkoK1157rSHN9OnT+fLLL+natSsxMTFlHvvHH38QFBTEihUr2L9/P927dzc0hkZTHp0b1gKqzkrg4gxApO6u8kUmODMgiuwOko4bb69S6XhYICzGrVsu5hfZOZCRa/4N36nMmKq9Nly/Z3yKyT4QYa0gYy+UmJiJUQ5xyU4DSg8PHaHXaDRVy2d/HsIhJcMva2z2VDSaKuGbb77hxx9/5L333mPJNmcAYlD7skuNbDYbTzzxBAsXLlRqFzhx4kT27dtnuOwAYPny5fzyyy98+eWXhjWHDh3igw8+YPny5YYNG1NTU/nkk0/YuHGjYVPD5ORkVq1axbFjxwx3H1izZg2pqalERUUZ8hM4dOgQ8+fP5+mnn+att97CYik7K7hnz5489thjDBgwgAYNGuhshn9REdNPQNl/BJxlMxUZz263K2ugYuakKprT77uLiyu/Xe/FF4CwF8PxxCovv4DTF5om73SHtXbrDIg9aTakdBMDSmsk+BuLhleU0EAfQgO93SADohVIO6SX7XpsFlJKElJt5l8XGo3mgqeg2M4XGw5xdUw4DWqXb8in0dREIiMj8fHxYcyYMRSWOBdZ4UG+ZWpc6fzjx49XqqUPDAykX79+SiUYnp6eNG7cmEceecSwprCwkMDAQN566y08PY2VTaWmpuLn58eXX35pOANi586d1KtXjzVr1hiuv1+2bBnTpk1jwYIF+PmVn8l54MABdu7cyZQpU5TNFmsCx48fr5Du559/rtDiftGiRRUKJsyfP19Zk5iYqNyVAmDOnDnKc8zLy2PevHnKY82dO5fCQvVNxzlzjHcsMcrFF4DI2AuO4iqv8wdoHhaIxUO4wUKzNeSmQ47JxofnwBWgiYk0+c02bdc/nhlVTExEEAmpZl8XpZ0w3DQ4lWYrJCuv2PzSHI1Gc8GzfEcyGblF3NujsdlT0WiqjIiICEaPHk3DhsZbjYeEhNCuXTvuv/9+pbHq1q3La6+9pqSxWCzMmTOHgIAAw5qCggLefPNNmjUzbpSXmprKBx98QIcOHQxrUlJSWL16NU2aNDGseeCBB5g8ebLhzIQrr7yywuaCNYHRo0crtdF0sXbtWt555x1l3Q8//MCCBQuUdc8//zz79+9X0hw4cIApU6Yoj/Xdd9+xdOlSJU18fDyvvvqqcuDihx9+YNGiRYaPb1svGIBZX6yoUCCnLC6+AERq9dT5A/h4WmgaGmB+qr3rd3XTMoyEFBu+Xh40NHPXyV4C6YlVXn7hIjrCSkKKDbuCC3WlU7sZWHzcthWnKzAVrQ0oNRpNFSKl5OM/kmgeFkjP5hVzMddoagJRUVFMnjyZrLwiwxqLxcLcuXPLLQf4N88//7xSpwiAoUOH0q9fPyVNr169uPfee5U0V155JUOHDlXSDB06lJYt1bKnLzRPhr179zJjxgzy8vIq/Bz9+/fHZlPbgPP19WXixInExcUp6XJycnj00Uc5efKkYY3dbufo0aM888wzSmMlJSXx888/89tvvynpEhISmDFjhlKGx65du0hMTFRuO7tjxw5mz55t+PibSv1hMoOj+PHHH5XGKo+LLwCRthuEBUJbVMtwbtEJw5Xt4aY73QkpNlqEW7GYWed/Yh/YC6stAyI6wkphiYODGSb6g1g8oW4LtzWiTCgN3OkSDI1GU5VsPpjJ30dPck+PxrqGWnNBEx0dTWhoKLE7U4Dy/R9cqLbSBOjUqZOypiKtDxs3Vn/dGi27OB2j5R0XMs2bN2fLli1ERUXxwQcfKPsQtGnThg0bNjBlyhSlBbePjw+FhYV8+umnSuM5HA6KiopYu3atYU16ejrBwcHs3bvXsNcHQFpaGoGBgWzdutWwJj8/H4fDQWFhoVLGxdGjRwkKCiIhwXgJdXZ2NkIISkpKSEpKMqQZ1N6ZjRPY+ioSExMNj2WEiy8Akbob6jQHT59qGS4mwsqRzHxyCtXNQiqNwLoQUNdtF5rx7tABo5oMKF24TScMN/YHiU+xEWb1oVaAt9lT0Wg0Fyg5hSU8+tUOwqw+3FxONwCN5kLB1YKzV1SoyTPR1DRefPFF0tLSmDFjhlJmATizVR544AEiIiKUgkY33HADEyZMUM5AmTNnDvXq1ePqq682rAkJCWHhwoW0bdtWqYPL5MmT6d69OwMHDjSs8fLy4osvvqBdu3ZKJUQTJ06kc+fO3HbbbYY1AQEBvPvuu/To0YPGjRsb0oRZnf4wwtNbOcuoPC6+AERa9XTAcOFKHzd/odnqnzaTbsTxnEKO5xS6RwcMYYG60dUyXFSYFSHcwKA0vBXYkiFPvSavqolPtpnvC6LRaC5onvtuF0kZubx5Z0cCfPQOp+biYPvhLAA6NqjadvSaC4+oqCjmz59P//79mTRpkpI3QO/evXnllVeYO3euUkeV5s2bc/vtt7N48WKludapU4fLL7+c33//3bDG19eXrl27smXLFqWxfHx8aN26Nbt2GV9reXp60qJFC/bu3as0lsus1WgmAzhLqRo0aMDhw4eVxnKRnJxcId25uLgCEIU2yDpYLQaULtxmpzu8NaTFg6Ni7V6qCtd5iTG7zj+tejNj/LwtNK4TYP514ablOSV2B3vTc3T5hUajqTKy8opYsvUowy9rTPem2vtBc/Gwv7Q9fLO6xrtaaC4ciouL+emnn5S9B1zcfffdzJo1i8DAQEaMGKEUhAgJCWHo0KHMmTNHaczOnTuzZ88esrPVfPV69+6tVIIBzjnm5+crd4xo3bo1u3er3U+HhoYqlXq4UA1AANSvX58jR44ojwVw7NixCunOxcUVgEiLd36sxgyIeiF+BHhbTtWzm0ZYKyjJh8wkc+fxL/4xGnSDDIhqvC4AosOtbtAJw2VQ6l4BiKSMXIpKHOaX5mg0mguWH3alUuKQ3NxJl15oLh5O33n2UPDeWrp0qfJC6dChQ3z//fdKGoCPPvpI2V9gy5YtbN68WUkjpeT9999X0gDExsZy8OBBJU16ejpfffWV8lhz584lPz9fSfPll1+yadOmM75vt9t57733iIyM5Oqrr+bFF1+kZcuWxMTEEBMTw8SJEw2PIYRg1qxZREZGKi+Ex40bp9xVQQjB5MmTlbtoXHXVVTRv3lxJA862szk5OUqaXr16ER2tlkkthGDkyJHY7WobxNdcc42yyavValUq2zgdVzveyuIiC0BUb50/ON/coyOsxJm90+0yV3SzjgcJKdmEBnpT11o9mQdnxZUZU00GlC5iIq0kZeSSV2SiP4g1Evxqud114TaBKY1Gc8Gy/O9kGtb2P9VqTKO5GKhoCvabb75JQUGBkmbjxo3Ku88AU6dOVe668e2337Jnzx4lzaFDh/j888+VNAAzZ85UXkB//fXXyl0cdu7c5DNMZQAAIABJREFUyUcffYSvr69hzeeff87rr79+Vk8Bi8XCqFGj2LNnD59//jljx44lLi6O+Ph44uPjeeWVV5TmJ4Rg6tSpNG3aVEkXEhLCpEmTlDQAw4YNM+xf4CI8PJwHHnhAeayRI0cqL7pjYmK46aablMeaOHGi8vXeo0cPevXqpTzWY489pnS8v7dzXvWaRCmPVRYXVwAidTd4BUCIWsTofImOCCIhxVahNKdKo24MINxupzshxWb+ItOVGVONpTngLM+REvakqkVYKxUh3NKIMiHFhsVD0DxMp4dqNJrKJ91WyO97jzOwXaTufKG5qKhoKnVycjKRkZFKmqSkJJo0aaKkycrKIjg4WPl1uWvXLlq3VruP27x5M126dFHSFBQUcOzYMeWF8OLFixkyZIiSZsqUKTzzzDOGzsWqVav47LPPmDVrFrGxsdSqVeucx9aqVYs777yTadOm6fc/TZl0KPWJ2X5EzXC0PC6uAETabgiLAY/q/bVjIqyczC8mNVutlqhS8faH2k3dyojS4ZAkpuYQHW62/0PpOanuEgx3MSgNbwVpcaAYza9K4lNsNK7jj6+XWkRYo9FoysPukExYvB2LENyiyy80FxFSSo4dUzeTk1JSUlKi1IpSSklSUpLSQl1Kyd69e4mKUttttdvtJCQk0KJFC8Oa4uJiNm/eTOfOnQ1r8vPzWb9+Pd26dVNauG/bto0TJ04QExNj6PjCwkJee+01jhw5Qr9+/co9Pi8vjxEjRvDQQw/xxRdflBl80GhUcAUgth3KqtTnvXgCEFKWBiCqd5EJ/6SRx5vtAxHeyq0yIA6dyCO/2G6+0WDqbvAOhOCG1Tpsw9r++Hp5mN8JI6wVFOXAyUPmzuM0ElJ0BwyNRlM1vPfLPn5JTOfZG1rRPEyXeWkuHvbv38+Mtz8AINxqvMX1uHHjyM3NZcWKFYY1ixcvZvny5cTGxhrOAM7Pz+e+++4jKSlJqTPApEmTSE1NZdWqVYY1X375JfPnz2fTpk2G55ecnMyQIUM4duwYWVnGFmR2u53u3bsjpeTQIWP3WfHx8UyYMAEPDw9stvLvEWfPns3x48cZPnw4QUH63klTeZwKQBzOrNTnvXgCEDlpkJdR7XX+4EadMMJaw4n9UJRn7jxKcQVkTC/BSN0FYS2rPTPG4iFoEW4lIdXswJTLH8Q9glM5hSUcOpFHjDag1Gg0lUxRiYN5vx2gd3Rdhl5avUFnjcZsGjduzOEMZ9lno1DjJY7FxcUkJycb3sEHaNCgAUlJSdSqVctwtoC/vz/Z2dnYbDYlXwEppVKGATi7DyQnJ9O0aVPD8wsMDCQjI4OmTZsSEmKshWlhYSGFhYV06tSJhg2Nvefs3LkTX19fpk6dWm5AISsri6NHj5KQkMDrr79OaGiooTEqi4yMDLZv366s+/nnn5U1rkyS6hhr7dq1yj4fDoeDdevWKY9VkfllZGSwY8eOKh+rfi1/AI6cMN421QgXTwDCBANKFyH+3oQH+ZgfgAhvBUhIjzd3HqXEp9gQAlqYudCU0nltmHBdQGknDLOvi7CWzo9uUp6TmKoNKDUaTdXww+4UjucUcU+Pxrr2WXPRYbFYaNayLQAhfl6Gde3bt2fAgAFnNTY8F61atcLX15f//ve/SnOMjo7m0UcfxUNhU6hx48bcfvvtSgGIiIgImjVrxn/+8x/DmsDAQGrVqsXUqVMNawoLC2natCmzZs0yrElISODrr7/myiuvLPfY4OBg3nzzTWVPisoiNjaWJUuWKGnsdjtjxoxR7vywZMkSYmNjlTTp6ek89dRTShqA999/X7mrysaNG/nggw+Ux3riiSc4fvy4kmbVqlUVOu+jR49WOu8h/s73ibSsyvWru3gCEK7dXbMWmhFBbpBqX7rT7SaGgwkpNhrV9sfP28Q6f1sK5GeakhkDzkX28Zwi0m0m+oP4WCGkodtkQLgCMjEROo1Qo9FULp/9eYj6tfy4Iqqu2VPRmIQQwlcIcasQYpYQYrEQ4hMhxKNCCHNuBKqZ1h0vBf5ZWBihffv2jB07Vmmc4OBgnnjiCerWVXutXXPNNdx5551KmqZNmyovMiMiInjhhRfw8jJ+Hvz8/Jg+fbpSlkFxcTELFizAajW+qfKf//yHAQMGGDrW7EDqsmXLWLZsmZLmr7/+Yvfu3WzYsKHKx1q5ciXr168nNTXVsKakpIRVq1Ypj7Vs2TJWrlyptMBPTk7mzz//VCofco21fPlyJc369euJi4tj48aNhjWu9wlbYeX6xF08AYi0OAioC4Hm3HS0jLCyNy2HYruJRn+1m4Cnn7PkwA1ISLGZv8g8ZUBpzn1Hy0h3MaJs41bXhb+3hfq1/MyeikajuYDYefQk6/dncFe3Rlg8dPbDxYgQ4jngd+Ay4C/gPWARUAK8JIRYLYRoZ94Mq55uva4CnNm5RunUqRN9+/ZVHqsirRbHjRunFBQA6Nevn3IHjPDwcG6//XYljRBCKWMCICwsjB49eihpGjRooHS8WRQXF7N69Wq2bdum1F1lxYoVeHh4KHmKHD16lO3bt7N69WqKi4sN61atWoUQgpUrVxrW/P7775w8eVI5KLBq1SqysrJYv369YY3rXKiMVVRUxJo1a9i6dSvJycZNZSty3jNSnc/v8PCkpKTEsK48KiUAIYS4TgiRIITYK4R4/Cw/F0KIN0t/vkMI0cmottIwMc0enDvdRXYHSccrt4ZGCQ+LswuIGyw0C4rtJGXkmp9mb3pmjJsYlIa1goy9UGJiJkYp8SnZtAi34qEXCBqNphKZ/dMegnw9uau79n64iNkopewspZwgpfxcSrlGSrlcSvmalHIQcBdgfGV+Ftz9njin2Gm4GKxQguHj46NUEuHC19dXWePj46Os8fZW/5N5eHhU6HeqiKamkpuby6ZNm/j444+Ji4s74+fFxcW89NJLTJ48GX9/f8PPO378eKKiohg3bpxhTUBAAI8//jjTp09XCkBMmTKFSy+9lOuvv96wpnXr1txxxx1MmTLFsEGpw+HghRde4M4776Rly5aGx7rxxhvp0qULzz//vGFNSUkJ06dPZ/Lkyfj5Gd+se+SRR4iKiuKhhx4yrDk9c0flvJfHeb+KhBAW4G2gP9AKuFMI8e/VXH8gqvQxEnhXQXv+OOyQFm/aLjecvtB0gzIMNyjB2JOag0NifgeMtN1gjQT/2qYMHxroQ2igtxtkQLQCaYf0BFOnIaUszYzR/g8ajaby2H0sm+93pXJfzyYE+artrmouHKSUKwCEEEP+/TMhxBApZZqUclNFn78m3BNn5TkXESolGJqLj9jYWKxWK127dmXfvn1n9dfw9/cnICAALy8vw6acwKmyHJXynJCQELy8vAgMDFQKdlRkrNDQUIQQpz4awcPDg9DQUDw8PKhTp06Vzq+6z7sLlWBHeVRGGO9SYK+Ucr+Usgj4ErjxX8fcCHwinfwJhAghIg1qz5/MJCjJ/8dszwSahwVi8RDusdDMTYecdFOn4V4dMMzLjAHnOUhIdYPAFJgenEq3FZKZV6wDEBqNptIotjt4/JsdBPt5cV/PxmZPR+MeTDb4PVXc/p74ZH4RACF+55XooblAycrKYsqUKYwbN47WrVvz2muvMWXKFNO9JjQXFpURgKgHHD7t6yOl3zNyjBHt+eMqOQgzLwPCx9NCk9AAN8iAKF1sm9zxID7Fhq+XB43qBJg3CXuJc8c/3OQARHgQiak27A5jaV5VQp1mYPE2vTwnLsXVAcNkb5DPb4cVE8ydg0ajqRTe/HEPO46c5KWb2yrVvWsuPIQQ/YUQs4F6pWUQrsdHOH0gzhe3vyfOzHVmQKiUYABkZmZSVFSkpCkqKiIzM1NJA87OBaotEPPz87HZ1O+x09LSlDU2m428PLWW9g6Hg/R09c2/6jzv33//Pd27dycgIIAtW7YQGxvLww8/XKbGz8+PwEDjLV1dqJqTgrMLieouvCuTQRVXxoUKqhkJLlQyLVxU53mvCiojAHG2M/bvldS5jjGidT6BECOFEJuEEJuUX8B+tSDmeqf/gYk4d7pNrvV3laGY3PEgIcVGVJjVXCOwE/vAXmhqYAqcZSgFxQ4OnVD7Z1apWLwgNNr0DIiE0swYUzMgpIRD60GaaBir0WgqhcISOx/9nsTAdpH0bxtp9nQ05nMM2AwUlH50Pb4D+lXC87v/PbF0OvQ7DNa2uxg/fjxbt25V0vz999+MGTNGSQPOuvisrCwlzdKlS3n11VeVx7riiiuUNW+88QbffvutkiY7O5tBgwYpjzVu3Di2bdumpNm+fbtSnb+Lbt26sWXLFiZMmEBAQAD16pUf/xo8eDCPPPKI8li//vqrsmbChAncdNNNSpqQkBDlbhYAb731Fh06dFDSdOzYkTfffFN5rBUrVhAcHKykufnmm8sNDp2Nipz3qsCzEp7jCHC6XWt9nG/wRo7xNqAFQEo5F5gL0KVLF7V3zSa9nA+TaRlhZcWOZHIKSwj0qYxTXwECw5zdQEze6Y5PsdE72uQonOscmJwBERNZ6g+SnE2TUBMzQsJbw4F15o2P87oIs/pQK8DEXcrsY1Bw0vTSHI1Gc/78vvc4tsISbu1c3+ypaNwAKeV2YLsQ4jMpZeU5qv2D298TuzIfMvPUdtU1Fz4V2b3XaCpCZWRAbASihBBNhBDewB04I8mn8x0wvNT5tztwUkqZbFB7weBKKzfdByKslaklGBk5hRzPKTS/zj9tNwiLc+ffRKLCrAjhBgal4a3Algx5J0ybQkKKzXxfkLRSp2cdgNBoajyr/k7B6uNJz2bqKbiaCw8hxDIhxFm3oYUQTYUQU4QQ95/HEG5/Txzs69wAO5lfFfEXjUajKZ/zDkBIKUuAMcD3QBywSEq5SwjxXyHEf0sPWwnsB/YC7wP/K0t7vnNyV1wLbtMDEOGtnV1BHHZThnf9/jFm1/mn7oY6zcFLvU1UZeLnbaFxnQDzrwuTjShL7A72pOW4QWDK5RljnmmtRqM5f0rsDlbHpXJ1yzC8PS+e1nmaMvkP0AuIE0JsFEKsFEL8LIQ4ALwHbJZSzqvok9eEe+LcTKfnQfz+w+Uc+Q+JiYlkZmayceNGw94MUko2bNhAVlYWCQnGO2zt2LGD/Px8NmzYYFhjs9nYvXs3R48e5ejRo4Z1mzZtori4mE2bjDc+OXr0KEeOHCEuLo7sbONl1Rs2bKCgoIAdO3YY1lT0vG/cuJHMzEwSExMNj6XRVCeV8h9ZSrlSStlCStlMSjm19HtzpJRzSj+XUsrRpT9ve3qLo7NpL1TqhfgR4G05VeduGmGtnF1BMpNMGT7+lNGgGyw0TS6/cBEd7gadMFznwiR/kKSMPIpKHO4RmDKxNatGo6kc3vtlP1l5xQzQ3g+aUqSUKVLKR4FZOFtgvgA8DLSWUvaVUi6thDHc+p54z06nn8Dh1AzDmsLCQpYtW8aiRYvw8DC2dBBCsGjRIlauXEl+fr7hsfbu3cu2bdtYvHixYU1gYCDz58/no48+IiDAeCnrjz/+yP79+1mzZo3SWPPmzWP+/PlYrcbvYxctWsT27dvZs2ePYU1BQQHLly9XPu8LFy5kxYoVFBQUGB6rpmG3q2+iqlyHLlSCTC4qYgCakWH89egiNzdX2QwVUDJDdVSRQb7eEqhGPDwELSKs7pFqD6b5QCSk2KgT4E1dq48p4wNQmOMMwJhsQOkiOsJKUkYu+UXmZKUAzkW3b4hp5TkJbhOY2q3LLzSaGs5324/x8vcJ3NjhEq5pGW72dDTuRziwGGfwIQJQX5nUULp2cN73hIQbb7DRpk0bGjVqpGyiOGjQIBo0aED79u0Na6699lq8vb2VxhJCcP3119OrVy8lHwPXGCpjBQcHc+WVV3L99dcrdS4YNGgQ3t7eXHvttYY1bdu2pWHDhhU67w0bNqRt27ZKOrNQyXYBSEpKYulStVjhunXrWLt2rZJmx44dLFy4UEljs9mYNm2akgZg8mT1LsCffPIJu3erbRoeO3aMWbNmGT4+p8jZHMjiqNySLR2AqGZiIpw73VLRfbhSqdsSEKal2senZLvBIrO0zt9NMiBiIqxICXvSTAxOCeEszzEpAyI+JRuLh6B5mHpboUrDTVqzajSainMit4hnlu6kU8MQZt7aDg8zuy1p3BIp5VNAFPAhcC+wRwgxTQjRzNSJVQOXdXIGA/IU1hNCCAYNGlShhbDqQj0wMJD+/fvTt29f5bFU59eyZUv69u1Lq1Zq//MrMtY111xD//79lbImzue8Dxo0SLm1Y2VitCXq+vXreeKJJww/r91uZ9iwYRQWFhrWlJSUMGbMGOU2rU888QTHjp3VB/acvPPOO2zevFlJs2PHDt5//31ycnIMaxwOB2+88Qa7dqltGr733nts3LjR8PEnS98oCrMzSElJURqrLHQAopqJDreSlVdMms34C6fS8faH2k1MyYBwOCSJqTluEIBw1fm7x0LTdT5Mz44Ja+UMzij2364M4lNsNK7jj6+XpdrHPkXmgdLWrO5xXWg0GnVe/j4eW0EJ029uh4+nie8nGrdGOneCUkofJUAt4CshxExTJ1bFhNdyBvlVu2CMGTOG6Gg10+6oqCjGjRunpAGYMWOGUikFQJ8+fbj55puVNEIIZs+erbxQHzx4MH369FHSBAQEMGPGDCUNwNixY5XPe3R0NGPHjlUeqzKIi4vj5ptvZt++feUeu337dgYMGECTJk0MP//MmTP57bff8PU17t/2zjvvsHPnTqUF/q+//sqKFSuUFt25ubm88sorHDhwwLAG4OWXXwZQ8uxYtWoViYmJ7Ny507CmqKiI9957j+3btxvWZJUGIOwFOcpteMtCByCqmZhIZ317XLLJPhDhrU0JQBw6kUd+sd18o8HU3eAVACGNzJ1HKY3qBODr5UF8stnlOa2hyAYnD1X70AkpNjfwf3CvwJRGo1FjydajfLHhMPf3bGx+oFvjtgghHhJCbAZmAr8DbaWUDwKdgVtMnVwV07COPwD7j+cq6aKjoyu0o666eK6oxtfXl0aN1O/pKjJWw4YN8ff3r5axKqI5H11Fyc/PZ9SoUbRp0wZ/f386dOhQ5vFSSpYsWUJ2drbhUpGSkhLS09Np0KCBUgDCYrEQFRVl2EfDpYmMjFQKjqSmptKhQwc6duxo2KPCbrfTqFEjevToQW6u8ddkUFAQ9erVU/o7p6am0qNHD6644grD3hb70p1Bm0CZX6kZNToAUc24TSeMsNZwYj8UqZuXnA/x7tIBI223M81e4c2oKrF4CFqEW0lIdYPAFFR7GUZuYQmHTuSZv2BIiwPhAXXNbc2q0WjU+XN/Bo9+tYNuTWozsZ9+DWvKJBS4WUrZT0q5WEpZDCCldADXmzu1qiXM6ly4ZanUYGg05SClJC4ujlq1avHCCy+Ue7wQgmPHjvH+++8zYMAAQ2N4enqSk5PDnDlzuOqqqwzPzcfHh3vvvZd77rnHsKZx48Y0a9aMRx991LCmadOmFBQU8Pbbb2OxGMu+s1gsNGrUiJtuuolevXoZHuvSSy8lODiYESNGGNY0aNCAoKAgHn74YYKCjK3Dth3OAqBhoIPrrrvO8Fjl4R6rr4uIEH9vwoN8zA9AhLcCJKTHV+uwCSk2hIAW4SYuNKV07nS72S53dLjV/OvC1Xqymo0oE1PdxYByF9RuCl5+5s5Do9EosS89h1ELNtOgth9zh3XRpReaMpFSPiOlPHiOn8VV93w0GnfEqF9dXl4eN954I0OGDOGXX34xlDVw8OBB/vzzT+655x6aN29uaJzi4mJ+/vlnrrnmGqUMiJ9//pnevXsr7eBv3ryZzp07Gz4enOcrOTmZiIgIJd2ePXuIiopS0hw+fLhCGT+HDx+mfv36ho93BSCaBFWun4hnpT6bxhDREUFuUOtfutOdthvqdaq2YRNSs2lU2x8/bxNvDnNSIf/EP7v9bkJ0hJXFm49wPKeQ0ECTOoT4WCGkYbVnQLgCLy1Nz4yJ+ycIo9FoagQFxXZGfrIJTw/B/HsvJdjfy+wpaTQajalIKZVT5rOysjh69Oipr+fNm0daWhqDBg2iX79+BAcHn6HJz8/nxhtv5IYbblDynZg2bRqPP/644UwBgLVr19KzZ0+8vb0Na6SUbNy4kS5duhjWQMUCECkpKURERCif97179zJ8+HAlTVJSklJ5iIvk5GQiI423pnYFIFpHVu79uc6AMIGYCCt703MosVe/0d8pajcBT79qX2jGJ9vM3+VOLTVscbMMCFdZivlZEK2rvUNKfIoNf28L9WuZmHlQnO8sS3KT1qwajcYYb6zZw770XN64o8Op+naNRnN2SkpKKqSbNWsWmzZtUtIcOXKkQu0FH330UeXuA5s2beKNN95QHuvee++luFitHGXVqlV88sknShopJbfffjsORZPvhQsXKo/lcDjo168f8fFqWc47duzgmWeeOfVYs2YNn376Kc8++ywzZ84kMzPzDI2npyfjx49XNr0cPnw4t912m5Kmbdu2PP3000oaKSULFixQCloADB061HBpiIvg4GDeeecdJQ3AU089pZwB0aFDBx5++GHlsebNm4enp3r+we23DlbWlIUOQJhAdLiVohIHSRlqBkCViofFWedejan2BcV2kjJyiTZ7l9sVdHHDDAhwg04Y4a3g+B4oqb5OLfEp2bQIt5rbLi89HqRDZ0BoNDWIrzYf4f1f93N7lwb0iqpr9nQ0Grfn9MVHYYkxozxw7o4nJCQojRUcHMwPP/ygpKnoWEFBQRUaKzs7m9271TZdIiIiWLJkiZJGCIHdbmfDhg1KuiuuuIKZM2cqBUk8PDyYNm0agwcPJj4+3nDQ44orruDrr78+9Zg9ezZ79uwhLi6OqVOnUqtWrTM0Xl5eDBw40PDcXPTs2VMp+wGc571ZM7VOuR4eHnTr1k1JA9CiRQvq1KmjpPH396ddu3bKY3Xq1AkfH7XM59DQUMOlK6fTvXt3ZQ3AJZdcUiHdudABCBNwn4Vm62rNgNiTmoNDYn4HjLTdEBgB/rXNnce/qGv1oU6ANwkpJhtRhrUCaYfjxtsBnQ9SytIOGGZfF6Vlv24WmNJoNGfn3bX7mLh4O5c2rs2T1+vAoUZjFI+TzjR7lc5bDRo04PDhw0rjWK1WbDb1e93mzZuzd+9eJU2zZs0MtX78N507d2bz5s1Kmnbt2rFjxw7lbIYhQ4awaNEiJU1kZCTXXHMNn376qdJ4Xbp0YcGCBQwePJgHH3yQkydPKo0LzoBERRa5Gk156ACECTQPC8TiIdyj5WJuGuSkV8tw8aULa/NLMHaVmnC6HzGRVjcITLVxfqymNq3ptkIy84rd47qw+DhNKDUajVtzNCufN9Yk0q91OAseuJQgX+37oNEYQUpJYGEGAFsPnZlSfy5NvXr1OHz48FnT8MvSWa1WDhw4oKSJiooiMTGR9HTj96cWiwV/f3/lzInOnTuzYcMGkpKSlMZq1aoVCxcuNNxuEWDgwIGsXLmS2NhYpTk+9thjvPLKK4a6S5xOx44d6dq1K3PnzuWVV15R0mo0VYkOQJiAr5eFJqEB5i80XR4I1VSGkZBiw8fTg8Z1AqplvLNiL4H0BLfd5Y4ODyIx1YbdYcx5uEqo0wws3tUWgHC9DkwPQKTFOcuSPLR7vkbjzkgpmbbSmbH0zKDWeFr0rYxGY5Tvv/+elO0/A/BTgvEF/quvvsqHH37Ib7/9ZlizdOlS9u/fr9T+0OFw8PbbbzNr1iy2bNliWLdy5UqSkpKUzPyklHz88cfMnTtX6ffav38/mzdvZvjw4XgotHNfvXo1Bw8eVA4GbN26lcTERJYuXaqks1gsvPzyy4wZM4a33nqL5ORkJb3mwsVIh5N96TkAhFl9DGuMov9rm0R0hJWEVJNT7V2L8Goqw0hItdEi3IrFzDr/E/vBXui2RoMxEVYKih0cOpFn3iQsXhAaXW1GlC7TzRizvUHSdrttYEqj0TjJyivivo82smJHMg/2bka9EN0yV6NR4ZprrsHn+B4Afkk0FoAQQnDjjTdSWFhI+/btDY81YMAA/Pz8lAz2LBYLt912G8XFxbRo0cKwrl+/foSHhyu1GBRCMGrUKKSUSq0TmzZtypAhQwgMDFTqeHDTTTfRt29fCgoKDGvAeR4//PBD4uPjlU1Ew8PDmT17Nps2bWLnzp1K2guRipSiqGbVAPz555/KmtWrVytrvvvuO+XAgCuAVh5LtzpLtQZ3rIfdblcuHyoLHYAwiZhwK4dP5JNTWDE34kohMAz8Q6stAyI+xQ06YLh+VzctwXCdH9N9IMJbVVtgKj7FRpjVh9oBag7FlUreCbAlawNKjcbNmbJsN7/vPc7zN7Rm3NVqruEajcZpQjlyxP3KuuHDh9OoUSMaNGhgWOPt7c3o0aNp3VotuO8aq2HDhoY1FouFp556Srk1Ye/evenXr59SAALgueeeUzZEFELwwQcfEBISoqQD5zmZOXOmsjeGi2bNmtG3b98Kad2V2NhY0tLSDB9/5MgR5S4aa9euVe5ssXbtWt5++20lTUJCAs8++6ySJi8vjzFjxlBUVKSke/zxxw1lw3y7zRmAuKljPRYsWMBPP/2kNE5Z6ACESbgWmompZtf7V89CMyOnkHRboflGg6m7QFicO/xuSItwK0K4gUFpWCuwHYN847WeFSU+JdsNAlOlBpRumhmj0Whgy6FMvtl6lP/0aso9PRor91rXaDRORowYoayxWq289tpryq+7UaNG0bVrVyWNr68vb775pnKXhDvuuKNCi+zp06cTGRmppAkJCeHNN99UHissLIxXX31VWQcwZswY5QBLTSEpKYlZs2YZ2s2XUvL6668zadIkwsLCDD1/eno6ffv2JTAw0PCcDh8+zG233Ubt2sZN67Oyshg+fLhS20+Hw8HIkSPJzVXrjjh9+nQOHz5MTk6OYc0ff/y8W3tvAAAgAElEQVTB4sWLycjIKPfYwyfyAWhSy5tnn32WlJQUpfmVhQ5AmIQr3TzB9IVma2f7QYdxE52KkOAudf6pu50eB16+5s7jHPh5W2hU29/866KaynNK7A72pOWYH5hylZvoDAiNxi05mV/ME9/8TZjVh/9dpV3ZNZrzITIykogg533Q3jTj9xuDBw9WHis0NJTLL79cWXfDDTcoazw9PenXr5+yrmPHjsotFwF69OihrAGIjq74Jphqu0Z35/jx4zz88MNER0fTpk2bcgNcdrudBx98kEceecRw+8+SkhJGjRpFfHw8bdu2NaSRUjJ16lTS09MJDw83pAH48ssvOXr0KL6+xtcZv//+u3KZR1ZWFt9//z1eXl5KAYhly5bh4+NjKADhYt26dRQUFFSoo8250AEIk6hfy48AbwvxyWan2reG4jzITKrSYdzHaHDXP+abbkpMRJD5GRCnAhBVW56TlJFHUYmDaHfwf/ANhqDK7XOs0WjOn/wiO/fN38C+9BxeGdKeQB9Ps6ek0dR4buzo/H+3ZOsxw5qKZh3pbKWLg/z8fFavXs1rr73G/fffz+zZs8vNaIiNjeWNN96gd+/eXH311eWOYbFYCA0NpUWLFoaDVJ6enjRs2JD777/fsIeJEIJWrVoxfvx4Lr30UkMagK5duzJw4EBGjhxpWNOzZ0+sVisLFy40rAkJCaFTp058/vnnSiU9/fr1Y+jQoeWatRaV/NPytV+/fgQHByvNrzx0AMIkPDwELSLcoeVi6WK8iheaCSk2agd4UzfQxMhtYY4z0OLmRoPREVaSMnLJL6rarJQysUaCb0iV+4P8Y0DpBpkxYa1A3yRpNG6FlJLJ3+xg6+Es3ryjI1e0qGv2lDSaC4KbOtQD4NtSozmN5nw5fvw4Dz74IBMmTMDPz4/Ro0eXGXw6ePAgL730EjNnzuSll14yNMaWLVuIjY1lw4YNdOvWzZAmOTmZNWvWMGfOHFq1MrYJKaVk3rx5TJo0iU6dOhnSACxevJjbbrtNyax1y5YttG3blpiYGMMagN9++43rrruO4OBgw5r169dz2WWXUbdu2f9L15Ua1F7WtA6pqamEhoaWq1FBByBMJCbCSkKqrVLbmihTtyUgqrzjQXyqjZgIq7lR8PR450c3D0DERFiREvYopEVWOkI4z1MVl2AkpGTjIaB5mPGavEpHSqcHhJtnxmg0FyML/jzIkm3HeOSaFvRvq1ajrdFozk3LSGfm4dGsfJNnonFXli5dSmxsbLldO44cOcKYMWPo378/w4cP5/HHH+ett94qs0XpwYMHGThwIG+99RaTJk2iY8eO5c6nqKiI//znP7z//vsEBwcb9giZMWMGEyZMwMvLy9Dx4PRKaNq0KZdcYjwzVkrJd999p1w+tGrVKvr376+kSU5Oxmq1KnlawD8BiPJYcloHjM2bN9O5c2elccpDByBMJDrcSlZeMWm2QvMm4e0PtZtUaQaE3SFJdIcOGKml7YfcfKHpOk+mZ8eEtXIuzKswQBaXYqNJaAC+XmpGU5XKySNQeNJtO6NoNBcre9NsTF0Rx1XRdRmtfR80mkrB4XCwePFiZd369etJSkpS0thsNlasWKE8VmxsLJmZaibYKSkpFXLpX7hwIcXFxUqa/fv388svvyiP9eGHHyq30fz7778rdA6ffPJJ1q9fr6RZuXIlHTp0OPVwBRVCQ0MZO3bsWf8mxcXF3HXXXVx66aVs27aNJ598kunTp5e74fjpp5/y1ltv0bt3b8PzS0xM5K677jIUrHAhpUQIwd13321YA07TynHjxilpsrOzGTp0KEFBamXFwcHBygGIrKwsRo0apaQBaNu2raEskBV/O7tkDGgXia+vb4U8WcpCF1KaiKvuPT7FRniQiaaIYa2qNAPi0Ik88ovtp6LtppG6C7ytENLI3HmUQ6M6Afh6ebiBEWUrKLJB1iGoVTXnLD4lm/b11dtRVSqu4Fu4MWMijUZT9WTlFfHQF9vw97Yw49Z2eHjo8iiNpjLw8PDgySefZPDgwdS1+pBuK+TvIydpW7/sNO4///wTT09Pxo4da3gsLy8vJkyYwIABA5QyYH/66SeysrK44447DGuEEEycOJEtW7YY1gD8/PPPeHt7KxlsWiwWxo4dy5YtW5Q6dezcuZPXXnuNRx991LAmLCyM4cOH43A4GDRokGHdwIEDee655wB49tln+euvv3j44YfL1PTr148+ffqc+nr+/PmkpaUxaNAgOnbseNa/oZeXF+vWrTM8LxdPPvmksqZNmza0adNGSSOE4PXXX1ce66abblLWBAcH89RTTynrHnroIWVNy5YtadlS3Th96tSpSscH+nj+v2uistAZECbiqntPSHEDI8oT+6G4atLw4kqNNluabTSYstO5qC4jJcwdsHgIosKs5gcgXC0pqyg4ZSso5vCJfDcITP3t/HiRd8AQQswTQqQJIXaaPRfNxc3RrHwGv/MHe9NyePW29oRZ3bNrkUZTU2nZsiVxcXE80rcFAG+sSSxX0717d+UddV9fXy655BLlzIn+/fuzatUqJU14eDghISHK3QRGjhzJ3LlzlTSNGjXisssuY9GiRUq6qVOn8umnnxIXF4fD4ShfgPP3io2N5ZlnnmHZsmWGMy969OjB999/z3PPPcfYsWN55JFHeO6558os+7ZYLPj6+p56PPjggzz77LN06tRJG4leRBw47mwH6leF2cnntRITQtQWQqwWQuwp/VjrLMc0EEL8LISIE0LsEkKMO+1nzwkhjgohtpU+BpzPfGoatQK8CbP6uEeqvXT845FQycQnO+v8o8JNrvNP3eX2/g8uot3BoNS1IK+i8hz3MaDc5cyK8TU5EGI+HwHXmT0JjebZpbtIzS7gs/90o0+M8fZnGo2Z1KR74s6dO7N582ZuLu2E8WN8WrmaTp06sWXLFuUSgt69e7N27VoKC42XG/fs2ZP169crt/0bMmQIixcvVmox2KlTJzIyMvjll1+USjEmT57MSy+9xJo1awxr/P39effdd7nvvvuYNm2aYV14eDhLlizhgQce4J577lE6l5deein3338/w4YNY+nSpUyePNlw8ENzcfLmj3sATgUoq4Lz3Qp+HPhRShkF/Fj69b8pASZIKVsC3YHRQojTi09el1J2KH2sPM/51DhiIoOITzY71b40namKFppxKTaa1g10kzp/tdQts4iJsHI8p5DjOSb6g/gGQUjDKr0uADfIgNgFEbr8Qkr5C3DC7HloLm5+23OcNXGpjOnTnK6Na5s9HY1GhRpxT1xYWMi+ffuYNm0af/7xu2GdKyAwYsQIw5qSkhKOHj3K008/reTPsGPHDhwOBwMHDjSsATh58iQzZsxgwYIFhjWZmZn4+vpy9dVXk5ZWfiDmdF1aWhr33Xef0hyllPz999+8++67SoEADw8PBg4cyMGDB5kzZ45hncViYfTo0XzyySds3bqVF198UQcgNGXi6oxzd/eqK1k/3wDEjcDHpZ9/DJxRMCOlTJZSbin93AbEAfXOc9wLhpgIK3vTcyixm/hmULsJePpVWceDuORsN9jlLs0qrzEBCOei3C3KMKqoBCMuOZsgX08ig01Mry7Oh4y9NSYzRqO5kFmbkMbDi7bRoLYf9/dsYvZ0NBpVasQ9sY+PD1arlT179hAWFkb9Wn4AbD5YtuljdHQ0J0+eJCsry/BYnp6eNGjQgKNHjyq59bdu3RohhFImAzjLDnJzc8vt2nA6tWrVol+/fpSUlJCammpY1759e4YOHcqRI0eUDDMvv/xyvvjiC7Kzs5X8Kho0aMD8+fPZsWMH27dvJzu7YuXbnp6eeHpqC8DqoCJdDlUNUQFycnKUNSdOlL/f5Of9/zeOCwsLDemMcL4BiHApZTI431SBsLIOFkI0BjoCf5327TFCiB2l9cdnpKtd6ESHWykqcZCUkWveJDwsUDca0ip/pzu7oJgjme5Q5+8KQNSMTgdu0wkjvBUc3wMllZ+JEZ+cTUxkkLl1hWlxzvKjGhKYMhshxEghxCYhxKb09HSzp6O5gPhj73Hunb+RED8v3h/exdyMOY2mYtSYe+KnnnoKf39/IiMjDftAREZG8thjj1GnTh2lsSZOnEjTpk0JCAgwrPHz82Pu3LlKbRMBrrjiCh577DGlAAQ4yykGDx6sFIAQQvDKK68wYsQIdu5Us0664YYb+OOPP/j777+VdOA0Ypw3bx7+/v7KWo2T3NxcpeCAlJLffzeeLQSQl5fHJ598oqQ5efIkr732mpImPz9f2fhSSnlO40vXxmeQ75lBqhdffJHk5GSlsc5FuQEIIcQaIcTOszxuVBlICBEIfA2Ml1K6wnbvAs2ADkAy8GoZ+gvyxtd9FpqtqyQDIvFUmr3ZGRC7oFZj8DF5Hgapa/WhToC3+QalYa1A2uF4+QZVKjgckoQUG61MD0y5OmDoDAgjSCnnSim7SCm71K1b1+zpaC4Q7A7JlOW7qV/Lj+/GXH4qA0yjcTculHviiIgIJk+eTHBwMDe0d/pA/LrneLm6CRMm0K5dO6WxfH19mTVrllIGBMBVV11VoTaDzz//PK1bq/1P9/Dw4OOPP6Z2bbWyLyEEc+bMoX79+ko6cLZDvOeee5R1LnQWg5Pk5GQOHTpk+Pht27bxyCOPGN78cjgcTJgwQamEqKioiFtuuUUpW6CkpIQ77riDkydPGtYAjBs3Ttnkdc6cOef0Lnl9tfN+/9/+D1u3bmX69OlK45RFuQEIKeU1Uso2Z3ksBVKFEJEApR/PWjwlhPDC+Ub7mZTym9OeO1VKaZdSOoD3gUvLmMcFeePbPCwQi4dwg1T7VpCbBrnl/wNSwdUBw/QbypSdNW6XOzrCDTphuBbmlRycOpyZR26R3T1Kc7wCoJZO99ZozGLB+iTiU2w83j/mjJRPjcaduJDuiSdNmoQQAk/LP0uBgmJ7mRp/f3/+97//KY91/fXX07RpU2VdRQIQ3t7e3Hrrrco6q9VKt27dlHUWi4UmTSp2D+Hh5l3ZqhuHw8Hu3bsNZSdkZ2fz9NNPc9111xEREVHu8VJK3nnnHbp3727471xcXMw999zD66+/zlVXXWVIY7fbufvuu4mNjaVtW+P+YpMmTSI2NpaGDRsa1ixYsID333+fWrWMJ0vFx8czYcIEfH3PXv4cuysFgDu7/TOP4uJi7r//fuz2st8fVDjfK/87wBW+uwdY+u8DhDPE9CEQJ6V87V8/izzty8HARdf+zdfLQuM6/m6QAVFamlDJhoNxKTaC/bzMrfMvyoMT+2pkACIxNQe7Q72GrNKo0xw8vCq9PCeu1Hg1xh0yIGpAa9bqQAjxBbAeiBZCHBFCPGD2nDQXPgs3HuL55bu5okVdBraNLF+g0bgvNeqe2MfH59Tnt3Ry7uC73O/LQrUswkVFduwrukDXLSNrDsXFxSxbtowRI0ZQv359Dhw4UO7fLz09nV69evHiiy/yxBNP4O3tXe44hw8f5tVXX0UIYThAlZmZSVxcHHXr1uXSS88ZD/x/FBQU4OHhQcOGDQ0HIBwOB/Xr16djx45KAYh27doRExNDhw4dDGsiIyOJjo7m7rvvPuNnJ/P+8Z/w8fxnM8DhcDBgwACGDh16zsCFKuebv/MSsKj0RvUQMARACHEJ8IGUcgDQExgG/C2E2Faqe6LU3XemEKIDIIEkQD3UeQEQExHEjqPGTX2qhDDXTvcuaHplpT1tfKkBpan/DNLjS+v8a1aafUyElfxiO4dO5NEk1HjtZKVi8XL6g1RyYCo+JRshnB4opiGlMwOilVLm7AWLlPJOs+egubj4Y99xHv/mb3pF1WXusM560aCp6dTYe+Knr2/J11uO8M7afTx6XUx1Dau5AFm5ciX79++nsLAQu93OfffdR1lZOiUlJUyfPp3169fz8ssvG+p8smvXLux2OwMGDGDIkCGG5rVhwwaioqJ4+eWXCQoytvmVkJCA1Wrlr7/+MhTkAKf3w/bt29myZYthvxQPDw++/fZbPvvsM1q0MN768vvvv2fUqFHn9HM4GxkZGVitVl588cUzfvbCCme286gr/n+2ko+PDz/99BNfffUV9epVjmfueQUgpJQZwNVn+f4xYEDp578BZ72rkFIOO5/xLxRiIqys+DuZnMISAn1MqukKDAP/0Erd6XY4JPEpNm7r0qDSnrNCnDKgrGkBCFcnjGzzAhDgPG8Hfq3Up4xLzqZJnQBz062zj0F+Zo3LjNFoLgRO5Bbx8MJtNKkTwLt3ddKmk5oaT02+Jw7x/2dxVVTiwNtTZwVq4ODBg9SvXx+Lpfz356KiIlavXs3rr7/Ojz/+SIsWLfj000/LDD788ccfPPjgg9x5551cc801TJgwodxx1q5dy5gxY1ixYgV16tQxlCWzb98+nnnmGdauXUtYWJnesKcoKSlh/PjxfPzxx0olNq+++ipjx45VMmvdvHkzAQEBtGzZ0rBGSslnn33G6tWrlYL3ixcvPmfQ5qvNRwB4+F/+D6mpqZSUlFRa8AHOPwNCUwm4jCgTU210amhSIxAhnKnolVjrfzgzj7wiu3sYUNbAOv8W4VaEcBqUXtfGxNTksFawY6Fzse5XOddnfIqN1pe4QfkF6ACERlPNSCl59KvtZOYW8+E9XQkwK/Cu0Vyk5OTknGEKeUP7S/hu+zHe+nnvGQZ04EyVLykpwc/PT2ms7OxswzvOLnJzc/H29lYu98jMzFSqhwfnjnDt2rWVFnEOh4Pjx48bXsy6OHz4MA0aqG3K5ebmcvz4cRo1aqSkW7t2LW3btj21EHY4HOUu1nfv3s2KFStOff3jjz+yZcsWBgwYwKBBg+jXr98Z143D4WDEiBH8+uuv9OnTh7FjxxIVFcUrr7xSZueTt99+mwULFvD555/TunVrpJTl/g327t17Kvigcj7+97//MWfOHKW/15dffknv3r1p08b4PWL+/7F35vExXe8ff9/sEUlERCJILLHGEhL7FlVrq37Urg1KldZSSimKWlqUUpTytdNaahcUjX1vaIQIFXsihIjs+9zfH5OkWknmXsJN5Lxfr3klmTmfOU8mNzPnPOdZEhPZu3cvf/75p2INwJo1axg2bJgqTXBwMBUqVFB9De7fv5/169c/d39s0j/pF/89EDh69CgdOnRQNY8hhIszH/DPSbfWhSjd9ekKOl2ePF1Wnr/WBSgLaJ6/pZkxrsWLaH9d5HEhyvjkNO5EJlBN8+uiYLVmFQjeFFaevM0fwRGMa1+VGqVttTZHIChUyLKMl5cXKSkp/7p/ynv6z/qc6kDMnz+flStXqporLi6ORo0aoVO5rpw4cSLbtm0zPPAZ7t69y9tvv616rlGjRrFjxw5VmuDgYNq1a0dCQoIq3YQJE5gyZYoqzc2bN2nfvj1Lly5FlmXFv5+/vz8tW7akbdu2LF++nK5duxrslmBmZkbx4sWzbubm5hQrVgx7e3vs7e3/VTckEyMjI4YMGUJwcDBLly7lvffeY8mSJQbbrr7//vucOHEiq2OJEgdQxYoVOXbsmGpnzJYtW2jevLkqTe/evZkxY4YqjaWlJefOncv2dcqNuXPnqt7gV69enc2bN6vSgN4B4ezs/Nz93+69CsBHTZ4/rO3evTtff/216rlyo2DtyN5QythZUsTMOB9sNKtDagJE3cqTpwsOj8FI0p/ka4Ysw4NLBfaUO190wiiZsUGPyBsHRGbBVe0LUF6GYi5gITZAAsHrYtXJW0zzvcLb1Rzp36Sc1uYIBIUOSZJo3Lgxx44d+9f9xa3+ScNITX9+k9u5c2d+++03VXMVLVqUWrVqcfy4ujTOQYMGsXDhQlUaFxcXatSowc6dz9X+zJXp06czYcIE4uPjFWvc3d354IMPVOXeAyxfvpzAwECmTJlCVFSUom4PNWvW5PTp05w7d442bdowfPhwHjx4YFA3evRoAgMD+eGHHzh79izbt2+nVq1arFu3Lsd53dzcGDBgQNZtxYoV/P3338ydOxdvb+8cI1Lq1auXVWRUaSSJk5OT6sKkkiSpbpUK+g4najEyMnqhgosvojE1NX2hgqsvUhA2J82Gc/pWpmPaVsn28bxu+yocEPkAIyOJyo7WXH0QY3jwqySzEGWebTRjKFciH+T5Jz0tcPUfMqniZMPtyHiDrbFeKTbO+k16HhWizLzOtW/BGVRgHVMCQUHk8LUIvtl9hTbVHVnUu44oOikQaETHjh3ZvXv3c/d3qKlvZzj/j7+fe8zNzY24uDjCw8MVbZwz6devH6tXr1YVmVCtWjWsrKw4f/48ycnJinUTJ05k+vTpREZGKtaULVuWvn378u2333LlivL178iRI4mIiGDatGmKHSxmZmZs3LiRwMBAmjZtysGDBxXpbG1tWbFiBY0aNeKnn36ic+fOJCUlKdK6u7szZMgQNm3axKJFi0hMTOTWLWUHjSVKlFA0TlCwiYr/Jxrqde3ZhAMin1A146RbzZt6nlOyKiDlWah9cHhsPgqzL5gbzapO1uhkuP4wTjsjJEnvnMojx1RweAzW5iaUsVOXR5qnpCbB4+sF1jElEBQ0UtJ0TNt9hQolrFjUWxSdFAi0pGrVquzZs4clS5b86/7vutQC4KfDN57TJCQk0LhxYz788ENCQkIUz1W5cmX8/PwYN26cYo1Op6Nly5b06tWLffv2KdbZ2tpibm5O3bp1SU9XfnDj7e3NokWLGDVqlGKNJEm0b9+eSZMmqUpNMTMzo2nTply5coWxY8eqcsz4+Pgwd+5czM3N+fTTTxXvGerWrUv37t3x8fFh0KBBVKhQwbBIUGj4ZP15AEa3Ud6B42URDoh8QhUna6ISUomIVe7pzXPMrMCu3D+b9pcgLjmNu08S8kEByoKd559ZoDRY6+iYzAKleeAguxoeS9VS+aE1a3qBdUwJBAWJ1HQdM/Zc4ebjeL7uWF1U2BcINObSpUvcuHEDf3//f91va/lPePblsOh/PWZubs7Fixfx8/NTfPoOEB0dTUREhKo0DCMjI1JTU7l+/Tr37t1TrLO1tcXGxoa7d+9y8+ZNxTo3NzeqVavG8ePHn6uNkRt9+vShZ8+ebNmyRVUKx6hRozh79izFihVj48aNquwcNWoUR44c4fvvvycxMVGxViDIiXO3ngDwWUu31zanWAXkEzILNV7VOt/fMW9OujPrFuSLApQFOM+/nL0V5iZG2teBcHSHlFh4evelnkaW9a1Z88V1AcIBIRC8YlLSdPRYepo1p+/g08iVllXUVewWCAR5T7du3ejSpUu2j63qVw+A95ec+tf9xsbGrF27FhsbG1UOCA8PDxYuXEhUVJQqGydOnEjPnj1VOSDMzc3Ztm0bTZs25dKlS4p19vb2+Pn50aJFC1UdDGxsbPj111+ZN28eBw4cUKwDqF+/PocOHaJOnTqqdJnY29tTpEiRF9IKXh9paWmqNUpqfDyLLMtcvqzu8FiWZY4cOcKvZ/Xr+golrBQdDKot2JoTwgGRT8jMh7+m+Um3Ozy5Cakv51UNDs/I89c6AuLB5QK9yTTOqA+iuQMij+qDhEYlEpecRrX8UIDSxBKKF6zWrAJBQWPNqdtcuPuUOd1qM7VTwX0vFgjeJCRJYvHixVktGp+lZVW9kzA5TUdK2r/TA1xdXVm8eLEqBwTAwIED6dixo2obV65cSenSpVXpihQpgq+vr+pOBFZWVuzcuZNixYqp0kmSxMCBA3nnnXdU6TK11apVU60TvDxqr+HHjx9z9OhRVZotW7awf/9+xeNlWWbSpEmcP39elebLL78kICBAlW0zZ87kyJEjjN+ud9StG9jAoGbLli2sWrVK1Tw5IRwQ+QQ7KzNKWptrHwFRsjrIOn2I+ktw9UEM1hYmlC6mcZ5/5PUC7YAAfRqG9tdFxgfkSxaizDeOqYeXM1qzijx0geBV8Sg2mQV+1/Gu4kBXzzJamyMQCJ7B0dExx7oM/+ehb9M3edfzp6q9e/fGw8ND1VySJDFt2jTVNlpaWjJ06FDVOltb2xdyCJiamma1hVSLmZmZ4UGCV8Lt27dJTU1VNDYxMZFZs2bx888/K35+X19fatasSalSpRSNl2WZqVOn0qdPH5o1a6ZY88UXXzBt2jQaN26s2LYZM2YwZ84catasqVizefNmxo8fj12Ziln3GdqvBQUF0a9fP0qWzJsoRuGAyEfki5aLmUX5XrIQ5dWMApTa5/nrCnyhwapO1jyOSyYyTsP6IBY2YOvy0hEQVx/EIklQRfPWrJcL/HUhEORnbj2Op8fS0ySn6Zj4TsGswSMQvOnk1NJw5vv6YpQbzj2f/iBJ0gu1NXyR9oSgT/0QFB6Sk5OJjTW8F4qOjmb58uU0b96cn3/+WVFLyrVr11KpUiXmzp3LgAEDFNmzcOFCOnbsSLVq1ahcWVmRxo0bNzJ58mS8vb2xsVEW8Xvq1ClWrFiBu7s7dnZ2ijT37t1jw4YNmJiYULVqVUWalJQUtm3bhomJCRvC9RFQ33Ux7Lw4c+YMOp1OOCDeRKo6WXM9Io60bPovvzaKVwATi5faaOp0GXn++eGUG96ICAggHzinqr+0Yyo4PAbX4kWwMs/bfsKqiH0AiU8K/HUhEORX4pPT+HDFWaISUlg/sAFuJYtqbZJAIFDBs11qToY81tASQWFg165d9OjRA3d3d7p06YKRkeHt6Zw5c/j4449JSUlRHF1z584dHj9+zKRJkxQ70R4/foyHhweffPKJovEAT548oWvXrvTu3VuxJj09nXr16vHtt98q1lhbW5OWlsYff/yhOOXIzMyMp0+fsmv3bh7E6wvL96rvYlCXmprKmDFj+OyzzxTblxvCAZGPqOpkQ0qajpuPlVfSzXOMjMGhKjwIfOGnuBeVkD/y/B9cAtMiBT7PP7Ng45XwfFAf5PHf+tSWF+RKeIz2BSgfZBSmEg4IgeCV8P3+a4Q9TeR/Pl7UL5/9CaPlilgAACAASURBVKtAIMjfbP9UHwbeZ/lZjS0RFCS2bdtGmzZt6NKlCx9//DE3bjzf0vVZgoKCWLVqFb/99htVqlRh27ZtWFlZ5ThelmWWL1/Ojh076NWrFxs3blQU/bBw4UKOHTvG0aNHGTRokKLfZceOHRw9epSTJ0/SuXNnRZqbN2+yePFiVqxYgY+PjyJNeno6o0ePZt68ebz33nuKNADz589n0KBBtGjRQrEmKCiI+Ph4jifqa6s0qvB8HZj/kvmaDxgwAGdnZ8Vz5YaGx5CC/1KjtL5TQ9D9aCprGaJeqjZc2akPVX+BFIqg+/qNcg1njTtPhAeCU80Cn+fvYG2Oo4151uuqGaVq61tXRgRBaU/V8pikVO5EJtBN61zwBxf1X52U58sJBAJlnLkZyZrTt/mwoSte5YTzQSAoqNRx+ScMPODeUzzKqivOKHgeWZZVpybLGe3P1epSU1P/tTFXMndCQsK/upWsWrWKhw8f0rFjR1q0aJHtKbssy5w+fZojR45w5MgRbt++TUhICB06dGDs2LFUrFjxOQ1AcHAw33zzDbdv32bSpEl07tyZ3r17Y2KS89Y0Li6OwYMHk5KSwokTJ7Cyssp1fCYLFy5k165d7Ny5U3HnkODgYMaPH8/hw4cVa3Q6HQMGDODHH39UnHoBsGbNGjw9PVXVcXj69CkbNmzgwoULijWgd1qMHDmKURndL1ZmdL3JDX9/f5ycnHBxMRwpoRQRAZGPqOigb7kYFKb1RrMWJD2FaOWtj54l6H40JkYSlZ00DLvV6fQn3U61tLMhD3F3tiXofrThga+SzNcy/MWiY4IzHCju+cExVbyCvq6FQCDIMyLjkhm+4S/K21sxtp2yfFSBQPB6kWWZAQMGkJ6ebnDsrxmV8f/vp5Ns3bqVnTt3qporKSmJAQMGZG2ilZJ5Wq2GR48eMXDgQNVzTZgwgdOnT6vS3Lhxgx49epCSkqJKN2jQIH755RdVmgsXLtCwYUN8fX2RZVnxnH369KFevXqMHj0aX19f+vTpY7BV46lTp/Dx8cm6rVu3jkWLFtG3b1+++uqrHFup/vLLLzg4OPDTTz8REBDArl278PX1xc3NLce5rl69io+PD6dPn6ZDhw74+PgYdCakpqby1ltvsWnTJmxtbRU5HwAcHBxUOR9AX3tk3bp1ODo6Ktakp6fz+eef8/bbbyvWAFSpUoWpU6eq0gD873//yzVaJDu6dOlCoEklAGqXscXSzPAhraOjI999951q+3JDOCDyESbGRlQtZcNlrTeapTKqG4dffCH55bAY3EoWxdxEw8iDqFuQEqt3prwB1HC2ISQijsQUwwuGV4ZdOTC3ffHrItMBUVrjjX/4xTfGMSUQ5BfCoxP5cMU5niamsrB3HW3rvAgEghyRJAmdTsfvv/9ucGxjtxJZ31uUqsTMmTNVbfAtLCyIi4tT1YoQoEWLFowePVqRkyQTBwcHEhMTWbt2raq5fHx8GDBgAOHh4Yo1FStWpEaNGnTr1o2UlBTFr8msWbPYuHEjH3/8MVFRUYSFhRnUeHp6snr1ajZs2EDDhg356KOP2Lhxo0Hd5s2b2bt3L40aNWLHjh1s2LABDw8PRo4cSXR09vuMt99+Gz8/v6zbggULOHfuHGFhYfzwww/ZFkeUJImffvqJjz/+mEqVKlGkSBHeffddg/Z17tyZDh06qIrssLOz46OPPlIdDdKzZ09VzgeAypUr4+mpLtrX1NSUTp06qdIANGnSBAcHB1WaYsWK0bx5c9VztWvXjtWn7gDw68cNFWlcXFxURWcoQTgg8hnuzjZcuR+j2oObp5SsDpLRC510y7JM0P3orHQSzcjcJJeqra0deUR1Z1t0sr69qWZIkt6h84L1QYLuR+NgbU5J6xerhJ0nJEbB0ztvzHUhEOQHHsUm02XxKe4+SWDph57aRzkJBIJc+eSTT1i2bJmisav760O0P9t1jxIlSqiOFvj666+ZOnWqqnVtrVq1qFu3LmvXrlXcXhFgwYIFzJw5k3v37vH06VNFmipVqjBr1iy6d+/O2bNnFdv59ddf4+XlRbdu3RSfDhcvXpxdu3ZRtWpVPD096dOnjyInS7Vq1fjll1+YPXs2mzZtonfv3or+fg4ODrz//vuMHDmSNWvWsHnzZtq3b8/Dhw8V2du2bVvq1aunqCikoGAw6/drAFQrZaPpQYG4ovIZ7s42xCSlERqVqJ0RZkWgROUX2mhGxCbzOC4Fd+d8cMptZAoO1bS1I4/IfD0va10HwqkWPAyC9DTV0qCwGO2vi8wClG9IZIxAoDXpOpkRG/8iKiGFjYMa0rJK3rToEggEr44GDRpw7949Fi1aZHCs9zP/090GjmDq1Kls3bpV8Vw1atSgbNmydOvWjZgY5WuYadOmMWvWLEaPHq1YY29vz4QJE2jUqBGbN29WrGvbti1OTk40bdoUf39/xbohQ4YQHBzMhAkTFOskSaJr164ULVqUo0ePKu7gAODh4YGfnx+LFi0iICCAEydOKNK5u7vj4+NDly5daNOmjeJ2koI3C1mW+fmovijo5k+URT+8KoQDIp+RWbjxcpjWaRi1XyjUPrNOgeYnYA8CoWRVMDHT1o48ooydJbaWplzRPD2nNqQl6bthqCApNZ2QR3H5ozApgJOIgBAIXpaQiDh6LTvDqRuRTOtUQ/vIN4FAoIhbt27x8OFDPv/8c3Q6w63f/+fjBcCk08ns37+fP/74Q/FcsbGx3L59m61btxqsQfAs169fJywsjF9//VVV9ERsbCwPHjxg165dijUmJiY0a9YMExMTli5dqlhXokQJli5dSr169Rg7dqxiO11dXbl48SInTpwgIiKCgIAARTpbW1uaN2/Op59+yuLFi2natKliWwWC+X9cB6CCgxXWFoY7h7xKhAMin1HFyRpjI0n7jgdOtSA2HOIeqZJdziigWV3Lk25Z1jtP3qAwe0mScHe20f66yIwcUBkdc/VBLOk6WfsIiPCLYO0MRdXl2gkEgn/zJD6FnsvO8HdELLO71qKbV1mtTRIIBAqpUKEC06ZNIz09ncjISIPjW1f/pxBfy/f7cevWLcVzWVtbs2XLFlxcXFQ5IBo3bsz+/ftJTU3l77+VH3oMGTKEAwcO8NdffxEfr6ytvZGREcOHD+evv/4iJCQkxxoJ2dGyZUvOnj3LkCFDDLacfBZJkmjSpAmLFy+mdu03Z70qyJ/odDI/+ukdENs/bZJ1v5o6K5kkJCS8tD3CAZHPsDA1plLJotp3PMjcvD9QFwURdD+a8iWsKKplAbKY+5AQ+cadctcobcvV8FhS0w2fVrwy7CuBiaXq+iCZ17PmJ6QPAkX6hUDwksiyzMQdl4hOTOHXgQ3pLpwPAkGB46OPPmLIkCGK6wGsH6DviHHTrSvFiqlryVm2bFn++OMPHj1Sd6jVuHFjDh06xLVr11Tp3nrrLY4ePcrt27dV6apWrcrBgwdV1Z2Af9Iqcuv6YEgveDNJSkoiMVFdWv1ff/2lWrN58+Zc6558vFafIuTlaoetpT76YdmyZaqciQDr1q3j5MmTqjTZIRwQ+ZDqzjb5INc/o9qpyjSMoPv5Ic8/Y3P8BkVAgL4OREq6jpCIOO2MMDYBR/cXui5sLEwoY2f5igxTQEqCPnXkDbsuBILXSUhEHN1+Ps3eSw8Y2bqyttFuAoHgpZg/fz4lSpQwPBBoWumfcQ37TVA9V6VKlRg5cqRqXd26dRV1Vfgvbm5uuLu7q9aZmpoqfk0EBRdZllWd5KekpLBs2TLFxU0Bzp49S8+ePTE3N1esWbFiBV988QWWlsrWy7Is8/333zNz5swcHYOP45LxuxoBwMZB+toPixYtYvz48VSsWFGxbdu3b6d///4v9H/1X4QDIh9Sw9mWR7HJRMQkaWeEZTF920UVJ91PE1IIjUrUvv5D+EVA0m+U3yDc81N9kAeBoCBvNJOgsGjcnW219fI/DAJZJ1pwCgQvSHxyGgPX/MmNR3HM7FKTIS2UL1wEAkH+w8zMDCcnJ8Xjz01oBcD8I3dJe4FoTLWtEDMRXRgEuREZGcndu3cVjX369CkLFy6kXbt2JCUZ3mfpdDo2btxItWrVCAwMVBT9k5iYyJdffknjxo1p2bKlous3MTGRAQMGMHDgQMWtPHU6HSNGjODLL7+kdevWOY7zmq6v2TK+Q1VMjI1YsWIFw4YNo0GDBorX5RcuXKB///7Y2tpSqlQpRZrceKn/aEmSikuSdFCSpOsZX59vEKsfd1uSpEuSJAVIkuSvVl/YyIwg0Dzf36mWqpPuKxn2ah4BER4I9m5gXlRbO/KY8iWssDQ11v66KFULkmPg6W1Fw1PTdQQ/iNX+ushMJxIpGAKBanQ6mcm7grjzJIGfP/CkZ30XETYsEDxDYVgTl7S2oEVlfQ2l3v87q7E1gjeNxMRE7ty5o8iZEBQUxKhRo6hTpw7t2rVT5Bi4dOkSFSpUYPjw4YwaNYrixYsb1ISEhGSlKn399deKfo+EhAR27NiBtbU1/fr1U6QxMzPj0aNHlChRgm7duinSGBkZUbp0aapWrUqbNm2yHXMq5HHW94Oa6w8NMtvAtmrVStE8AJUrV8bR0ZERI0bkyWf/y7oUxwF+sixXAvwyfs6JlrIse8iy7PWC+kJD9SwHRD446Y66BUnK7Lic1QFDawfEm1WAMhNjI4nqzjb547oAxdExNx7FkZKm077+Q/hFsLQDW5GvLhCoITYplU/Wn2fL+VCGtnSjQQV7rU0SCPIjhWJNvKpfPQDO3X5CeLSGLeMF+ZKbN28SFBREZGSk4q4gx48fx9bWliJFitC3b18sLCxyHS/LMmfPnmXBggXExsbi6+uLjU3ue4+UlBQWL16Mi4sLQ4YMoW3btgbtSk9PZ/r06fTt25fp06fj6OhoUAPw/fff0759e/bu3YutrbK177Zt29DpdAQEBODs7KxIc/v2bdasWcPp06dz7IjSe7neUbjjM33hSVmWGTNmDP/73/8YMWKEonkAfvrpJ3x8fBQ7YQzxsg6ITsCajO/XAP/3mvVvJNYWppSzL5IPTrozC1Eqq1ocdD+GUrYW2BdVnuuU58RHQkzoG3vK7e5sw5X7Meh0yltS5Tklq4ORieJOGEFh+SgyxqkWiFNbgUAxyWnpDFp7nkNXI5jcsTqjWov+8QJBDhSKNbGRkcS0/6sBQKPvDmlsjeBV8vvvv3PmzBlFrVpjYmI4evQoP/74IzVq1KBEiRI0a9aMoKCgHDUXL17ks88+Y+DAgdjZ2TFixAgOHjxIyZIlc9QEBgbSokULjh8/zsqVKzlw4IBBx0B4eDitWrWiVKlSnDx5ku+//97g75Oenk7//v1xcHBg3rx5ijfra9euJSAggLlz59K4cWNFmrt37zJp0iRWrlxJ6dKlFWlkWeazzz5j9uzZFCtWLNs6E3P264u3Wpoa41FWHyGyefNmKleuTJ06dTA2NlY0V1xcHCtXrmTYsGF5Fvn4sg4IR1mWwwEyvuZ0xcjAAUmSzkuSNOgF9IUOd2dbLmmd65+ZKx+urD/x5bBo7TeZmWH2b2iev7uzDfEp6dyKVNZa6pVgYg4OVeG+wuvifjQWpkZUcNAwJSYtBSKuvLGOKYHgVaDTyYzafJHTNyP5vmst+jcpL9IuBIKcKRBrYlmW2blzp2pdcHAwwcHBAHzY0DXr/p0BYTlqUlNT2bFjh+q5Tp48qTinP5OEhAS2bt2qeq7du3fz4MEDVZonT56wevVqxSf8maxcuTLrNVTK9evXmTJlCvfu3QNQ3KFj3LhxTJ48mV27dhEWFsbkyZO5f/9+rpqDBw/i7e2ddRs+fDiNGjWiVKlSjBw5kqioqOc0sizTsGFDWrRowZo1a6hQoQLVq1fnt99+4/jx4zkWLJwzZw5jxoyhZcuWXLp0id9//5358+djamqao33h4eEMGjSImTNnsmrVKnx8fKhQoYLB1+Lrr79mzJgxTJo0CSsrK6ysrAxqjh49SsmSJZkzZw6SJCn67EtLS8PX15eNGzdiYqK8G6Cvry/z5s3L1fHyXx48eECFChVyLNAak5TKosMhAJwZ/0+qhb+/P9OnT1c8D+jTXYYOHWowykQVsiznegP+AC5nc+sEPP3P2KgcnsM542tJ4CLQPONnRfqMxwYB/oC/i4uL/Kaz5EiI7DrWV46MS9bWkDlVZXnLAIPDYhJT5HLjfOX5B/9+DUblwtHvZXmyjSwnPNHWjldEUFi07DrWV95+IVRbQ3Z8Ksszy8myTmdwaJfFJ+Uui0++BqNyIeyC/rq4tOWVTgP4ywbeU9+Um6enZ169bIJ8iE6nkyfvvCy7jvWVfz4SorU5AoEqXtV78ZuyJu7YsaN8+PBhVZrjx4/LrVq1knUZn/vXH8bIrmN9ZdexvnJCclq2mvT0dLl58+by0aNHVc21d+9e2dvbW05Ly/55syMpKUlu3ry5vGWLus/53bt3y7Vr15bDw8MVa2JjY+WuXbvK/fv3lxMTE7NeE0McPnxY9vDwkL/88ks5NjZWDg4ONqiJiYmRFy9eLNetW1d+99135U8//VSeM2eOwTmvXbsmr1u3Tv7888/lpk2bypIkyZaWlvK4cePkJ0+yXyMnJCTI4eHhWbdvv/1W/vzzz2U/Pz85JSUlx7mefSw5OVlOTU01+Hulp6cbHJMdSl/rl9UUdDL/N7/ZFaSZDbm9DxuMgJBl+W1Zlmtkc9sJPJQkqRRAxteIHJ7jfsbXCGA7UD/jIUX6DO0yWZa9ZFn2cnBwMGR2gad2GX2oTGCo8nYvr4TSdSHsgsFhl8KikWWoXVbjPP/7f0Hxivpc/zeQyo5FsTA14qLm14UnJD6Bp3dyHZaWriPofnTW9awZmddwaU9t7RAICgApaTrGbg1k9anbfNSkPIOaGz5hEggKA2/Kmnjy5MlMmTJFlaZp06bY2tqyb98+ANxKWtO5jj5c3H3y79lqjIyMWLJkCcOHDyc5OVnxXO3bt6dmzZrMnj2b9PR0RRpzc3O2bNnC5MmT+euvvxS3S3z33XeZPn067dq1488//+Thw4cGNUWLFs0KZW/ZsiVffPEFMTGG06a9vb05d+4cJUuWpF69erRs2ZK///47V421tTVDhgzB39+fCRMmsHnzZkaPHk3v3r2Jj885GrZy5cp88MEHzJs3j+XLlzNu3DhmzpxJnTp1sqIp/oulpSVOTk5Zt6+++op58+bx1ltv5RqZ8OxjZmZmik7/X7SzyYtE4RW2yL3lx29mfT+pY3UNLcmZl03B2AX0zfi+L/BcTJckSVaSJFlnfg+0Qe8tVqQvrNQsY4skwcV7GqdhlK4LT25A4vNhV88SGKq3s1Z+2GiWrqutDa8QE2MjajjbZr3emuGc8RqHnc912N8P40hK1eUDx9QFsCwOxVwNjxUICjGyLDNycwCb/UMZ9pYbE9+pVugWbwLBC1Jg1sSenp7Y2Niwbt06wsJyTqH4LzNnzmT8+PHs2rULgHk9PADQybDpz+xTJqpXr07Hjh0ZMWIEv/+evaMiO2bPns1vv/1Gjx49SEhIUKRxcHBg48aN9OnTR3H3AdA7Ib766iuaNWumODxdkiTGjh1LrVq1mDdvHp9//rkinampKcOHD6d+/fpERETQpk0bg6kRmfO5u7uzadMmfv31Vxo0aMDu3bszI2JypUqVKnz77bcMHz6c7t27U6uWSEd9U4mKT2H6Hn2az9nxyrtcvG5e1gExE2gtSdJ1oHXGz0iS5CxJ0t6MMY7ACUmSLgLngD2yLP+em14ARc1NqOhQVPsIiMyN5v2/ch128d5Tyha3pLiV2WswKgdiwiH2/j82v6HUKlOMy2HRpL5AD+48w9EdjM0NRsdkRmrkG8eU2EgJBLmy4sQt9gSG82W7KnzRpgpGRuJ/RiBQSIFZE6elpVGsWDF8fHzw9/c3LMggJSWFR48e0a9fv6yN77ExLQEYu/UScclp2eqKFy/O0qVLVdWDSE9Px87Ojq1bt7J3717DggyMjY2Ji4tj586dXL16VbGuePHiVKpUiZ9//pkbN24o0kiSxJdffsnYsWPZs2eP4toapqamrFmzhidPnrBo0SIOHjyoyJFgbW3NW2+9Ra9evfj888/p2bOncBAL/kWdaQcBGP6WG442uXcT0ZKXckDIshwpy3IrWZYrZXx9knH/fVmWO2R8f1OW5doZN3dZlmcY0gv01C5TjIuh0YrelF4ZznX0Xw1sNAND80GY/f3CEWZfu6wtyWk6/n4Yq50Rxqb6go4GHFOBoU+xsTChnH2R12RYNqTEw6Orb/x1IRC8DLFJqYzcFMD0PcG0qe7IkBYVtTZJIChQFKQ1sYmJCYMHD6ZIkSJcunRJsc7d3Z2hQ4cSFRXF9evXAXCxL4JPI310YY3J+7PVDRkyhO7du7N//37Fa1orKys2b95Mu3bt2LRpk2Ibq1WrRkBAAB9++CGLFi1SrGvdujUBAQEsX76cZcuWKdZVrFiRmTNncu/ePWxtbVWt2W1tbXn33Xfp27evcCQIXpr5f/yTzjOqTRUNLTHMy0ZACF4htcva8jgumfvRSdoZYVkM7N1ydUA8jksm7Gmi9g6IsAsgGYNTTW3teMX8Ux8kH6Rh3A8AXc75mRfvRVO7bDFtP1jDL4Kse+MjYwSCl2H89svsunif4W+5saBXHbEYFgjecBo3bszOnTuzHAlK+eqrr5g7dy5nzpzJum9qpxpZ368+ees5jYWFBRs2bKBr166KowsA7O3t2bNnD/Xr11echgH6aIa1a9fSrVs3RS0kMzE2NqZv375MnTpV9eGfmZkZ3t7e4r1ToAkRMUnM/0P/v3x+4tuKdWpSsDK5cMFwbUBDCAdEPiYzbD3wXj5Iw7if88UWmBVmnw/y/EtWBzMNT9tfA672RbC1NNU+Pad0XUiNh0fXsn04KTWdaw9jtb8usgpQCgeEQJAdW8+HsvvifUa1rsyoNlWwMFXWG1wgEBRs3n77bcaMGaNaN2rUKFq1+nd++alxbwEwZfcVQqOedxYYGRnx/fff4+zsrGouIyMjxowZg6WlpWo7W7Ro8ULFDs3NzYUjQZAnpKenq0oFArh27ZqqVrmyLFP/Wz8Axrarin1Rc0W6lStXqor2AVizZg0LFixQpckO4YDIx1QrZY2pscRFrU+6S3tCbDjEZF8kJ+BeNEYS1Cit4UZTlt/4ApSZSJJErTK2BGheoDQjpSEH51TQ/WjSdXI+iIw5D7ZloegraakuEBRYElPSGfrrBb747SKernZ8IrpdCASFjho1ahgelA2lS5f+18/OxSz5qn1VAJrOOky6LvsIgiJFXuyQSDgEBHmJLMs5dgPJjujoaH788Ue2bdum+Pl9fX2pU6cOsbHKUqZTUlKYMWMGnp6eeHh4KNIkJydTe6w+RclIgiHehtMn09LSGDVqFAMGDKBdu3aK5gGYM2cO/fr1o1mzZoo1OSEcEPkYcxNjqpWy4aLWERCZm/oc0jACQ59SqaQ1VuaG2+68Mp7chKSnhcIBAfo0jL8fxpKYoqw91SuheEUwt8mxE0ZmB5faZfNBbZDMWiYCgSCL7/YF4xsYzohWlVg/oAEmxmJJIBAIXpxPWlTMqvlU+5sDGlsjKAzExMRw6tQpjh07ZnBscnIy+/btY8iQIVSqVElR+kFSUhIjR46kTJkyrF+/nvfee8+gJj09naFDh9KxY0eqVatGvXr1FP0uc+fOZeLEibzzzju4uirr2jZh7R/EGFkD8Pf09oo0t27dYvPmzTg6OlK/fn3DAiA2NpZDhw5hampKy5YtFWlyQ6w28jm1ythyOSwaXQ6e5NeCU00wMsn2pFuWZQJDo7UPs88shlhI8vxrlbElXSdzJVzDKAgjI3D2yNUx5Whjrm0V3oQnEHW70DimBAKl7L0UztrTdxjQtDwjW1fG0kykXQgEgpfn8GhvAOKS05i5T13ouaBwEhoaysaNG1m9ejU///wzhw8fNqh59OgRdevWxdbWlqFDh1KtWjWDmri4OD777DN+/vlnJk+eTMOGDQ1qYmJiOHnyJACrVq3CxMTwYWtMTAznz5+nVq1aitu6pqam4ufnR69evRg1apQizfWHsWzJKKky0SNV8SFCQEAA9erV47fffsPYWNlnf3R0NLdv3+bUqVOUL19ekSY3hAMin1O7TDFik9O4+TheOyNMLfW1FbLZaIZGJfIkPkX7U+6wC2BiCSUNvwG9CXhkvN4X80MaxsMgSH2+UKrojCIQ5D9kWebHP67z2a8XqFXGljFt83elbIFAULCQJAn/jCJ4Px+9gf9t0eCuoPLo0SPVxThPnTrF+++/zxdffMGiRYsMdlkJDw9ny5YtfPjhh/Tv35+QkBAaNWqUq+bEiRP06tWLuLg4mjRpwqFDh3BwcMhVc/jwYVq0aMGQIUMYN24cH374ocHf5dKlS7z11luMGzeOgwcPKkpXioqKon379owYMYIjR45QqVIlgxpZlhkyZAhNmjRh/fr1NGjQwKAmOS2d1vP0UR+zutRgYM//M6gB/d/066+/ZsmSJapSKUaPHs0333yDl5dXnqRDaRgzL1BC7ayN5lPcShbVzpDSdSFou77WwjMX3sWMQoiabzTDzuvbQhqbamvHa6KkjQVONhZZr79mONcFXSo8vAxlvLLujk5M5ebjeN73LKOhcWQ4zSQopSyXTiB401lx4hbz/vibLnVL823nmqLgpEBQCImPj8fKykqVJj09neTkZEU1HEoUNWdFXy8GrPGn68+nuTSlDdYWytdn8fHxmJmZYWqqbk0XGRmJvb29Kk1ERAQlSpRQVaxSlmVCQ0MpW7asqrlCQkJwdXVV9XvFxMRw69YtatWqhSRJyLKsaAN4+PBhihUrRtWqVbGwsGDLli107tw51xP8kJCQf0Uf7N69m6CgIDp27EjHjh1p1qwZZmZmz+lmz57NxYsXuXLl6zsZqAAAIABJREFUCgkJCYSEhFCxYkUmTpyYY2TCvn37mDlzJvHx8XTt2pWPPvqI7t27P1fc9FkePXpEr169MDU1Zfr06ZQqVYoSJUoYvJa//vprjh49yvbt26lUqZIip8q5c+fo168fv/zyC3XqKEvj1el0dOzYkREjRtCrVy9FGoClS5eSmJjIlClTFG/uq0z8HYA6pa3pUV9ZugbA2LFjmTRpEk5OToo1Z86cITIykq5duyrWGEJEQORzKjoUpYiZsfYdD5zrQlK0vtbCMwSGRmNmbEQVJ2uNDAPS0/StFgtJ+kUmtcrYat+KM4f6IJcy7NI8NSfsApSoBBY22tohEOQD9l4KZ8beYNrXcGJO19rC+SAQFFLat2/PlStXVGm2b9/O0KFDFY9vVc2R//PQd7yoOeWAqpP0tWvXMmTIEFWa2NhYmjdvzrlz5xRrQB9W36VLF+Li4hRrHjx4QPv27Zk/fz46nU6xnVu2bKFOnTqsXr2atLQ0bt68aVDz6NEjxo8fT82aNZk4cSI//PADy5YtMzjn5cuXmTFjBvXq1aN69er079+fKlWqsGLFClJSUrLVpKamEhMTk3VLTU0lLi6O2NjYrJ+zw9XVlWHDhnH06FEuXLjA+vXrCQ4OxsfHJ0eHh4uLCytWrMDf359x48axZMmSXJ0PoG/LOmvWLPbt20fDhg1xdXVV5Ej78MMPOXz4cFY0gpJNfs2aNTl06JBi5wPoO7Zs2rRJlfMBoEePHqxYsUKx82HUpoCs77cPa65qru+//161ffXr12fz5s15WghWOCDyOcZG+o4Hf2ldiDLzdDv0z3/d/dfdKNxL22BmouGlFBEEaYn/OoEvDHi4FOPW43ii4rP/IHkt2JSGok7ZXheS9E8rWU2QZb1dpQvXdSEQZIdf8EOGb/gLTxc7fujugZGRqCgvEBRWpk6dyrBhw1Rt8N9//33u3bvHvn37FGvm9/xn86amKOXgwYNJTExk1qxZim20trZm27Zt9OvXj3Pnzil2KIwdO5Z27drh7e3NzZs3DaYMAJQqVYozZ84QEhJCy5YtmTJlCiEhIQZ148aNY//+/Vy4cAEPDw+aN29usN5BxYoV2bNnD8ePH8fNzY1FixbxySef0KlTJyIiInLUDRs2jC1btnD58mV27txJgwYNaN68OWFhYZw+fTpbTbVq1fjiiy+ybkuXLiU8PJwVK1bQuXPnHDf7PXr0oGHDhtjY2GBlZUWvXr0M1hZwd3fHzc0t62clEShGRkZ4eqpPqa1cubLiWgeZWFpaqooSyOS/3WGUYGdnh4WFsnppy4/fZNtf+uKZgVPaqJ7L3t5etSPByMgIOzs71XPl+px5+myCV4KXa3GC7seQkJKmnREO1fQdD+6eyborOS2di6HReLnm7UWpmrtn9V/LGs6ZepPwci0OwPk7UdoZIUng0gDunfnX3f53oqhc0hpbSw1TYp7chITHevsEgkLMxnN3GbTuPNWdbVjZv54oOCkQFHK8vb1xcnJi06ZNik7hQX9qvHz5cr744gv8/PwUOwZufNsBgJikNNp8u1vxXCtWrGDv3r0MHjwYf39/RboqVaqwfft2+vXrR4cOHRS3Pxw8eDCzZ8+mRYsWfPDBBzlGCDxL0aJFWbRoER999BFTp07lvffeIzracFRq6dKlWbBgAZ06deL+/fu0b9+e3bsNvy52dnb07t2bKVOm8NNPP+Ht7c3u3btJSzO8N6hcuTJ+fn6sWrWKSZMm0aJFC4Ma0EcpqElNEbxaDl55yPQ9wQAcGNkcGxVpTfkNcVUVADxd7UjXyQRoGQVhZARl6sG9s1l3XQ6LISVNh6fWDoh7Z/Qn8cXU5eIVdGqVscXUWMJfSwcE6B0/T+9CTDgAOp3MhbtR1NX6ush0lhUyx5RA8Cy7Lt5n3LZLNHUrwa8fNyzQCxaBQJB3dO/enQEDBvDjjz8q1pQsWZLKlSvTunVrLlzIvgPWfzE2ktjYTX8q/HeMEdN9laV+WFhY8M4777Bs2TLmzZun2EYXFxfKlSvH8ePH+eGHHxTrypcvT6VKlQgMDOS7775TrGvcuDEzZ87Ezs6OPn36kJ6urD36jBkziIuL4+TJk8TExChylpiZmdG3b18+/fRTRo0axYABAxR1ZRAUfC6HRfPxWr0jbt2A+lR21DD1PQ8QDogCQF0X/Ubu/G2NN5ouDSEiGBL1jpDzd/SVjT0zTuI14+7ZQrnJtDA1xt3ZNuvvoBllM9oYZURB/B0RS2xSmvaRMffOgIUtlBBV/gWFk+DwGMZtDcTL1Y7lfb0oai4WqgKBQE/FihUpVqyYopaHmVhaWtK1a1fMzMzYuXOnYp1X7Rp0NdO3S19+4hYbz91VpBs+fDjjxo1j27ZthIWFKbZxx44dLFy4kLVr1+aapvAs5cuX59ChQwQGBvLo0SNFKRUAlSpVYuzYsZw8eZIVK1bw9Knyw8IiRYrg6elJnz59sLYu2BtKwavjQXQS7y48AcCMzjVoVin3jh8FAeGAKADYFjGlsmPR/HHSjZyV7+9/OwpX+yI4WJtrZ1N0KMSE6p0jhRAvVzsuhkaTnKbM4/5KKFVL3wI1IxXGP8NR5lVO6wiIDMeUCB8UFEL+d+wmnX46SREzE37qUxdThf3BBQJB4aBGjRqcOnWK1NRUHj16pFj3wQcfcOTIEVXFHk1MTJgzdSKTGurXi+O2XeJkyGODOktLS7777jtOnz6dY92C7DAzM2Po0KEEBATw5Im6Q5qaNWuyaNEiKlasqEoH4OjoqLoLh0CQG/HJaTT8zg+A/k3K0aeB8o4XrxK17Vn/i1iRFBA8XYtz4W4UOt3L/cFfijJeIBnD3TPIssz5O1Hap18U8jB7r3J2pKTpuBwWo50RxqZQ2jMrAuL8nShKFDXHpbjhVl2vjIQn8Phaob0uBIWbPYH6bhctKjuwd3hTHG2UFbcSCASFC1dXV44dO0ZUlLoDroYNG7J8+XJFtRKe5aP/e5sF3WsA0Gf5WUIilNVo8PDweKEWgNbW1lStWlW1DpR1ShAIXhWyLJOckor75P0ANKxQnMkd3XPVhIaGkpiYqGqe48ePq3JAgr4jzuXLl1Vp/otwQBQQvFztiE1K42+Fb9avBDMrcKoJ985yOzKByPiUrEKImnHvLJhagWMNbe3QCM+sQpQap2G4NIDwQEiJx//OE7xc7bT98L6XcTJTSCNjBIWXS6HRfLUtkNpli7G4T11KCueDQCDIBQcHBypXrqxaV6ZMGczMzFTr3qvryvgOeqfA2z8c4++HGq5rBQKVpKamKq7zARAXF8eGDRtUaY4cOcKgwUOoMknfOaaImTEbBzXKcXx6ejoLFixg8ODBWFpaKpojNTWViRMnMmbMGBwclKV0pKenM2HCBIYNG4a7e+7OEEMIB0QBITOc3T8/1IEI9ef8zYdAfgizP6OPzDAunLnNDtbmuNoX0f66KNsQ5HSi/j7NvSeJ2l8X986AkQk419XWDoHgNTLr96t0XHQCU2MjfuzhIdIuBAJBvmRQ84p86q1PcWgz7xjB4RpGcQoKJXfv3mXPnj2KHANpaWn4+fnx8ccfM3bsWEWdQUJDQxk7dixly5YlJSVFURvQS5cu0aFDB1q2as1Bu45Z9wd90zZHzZ07d2jUqBEjRozgk08+MTgHQHx8PB07dmTGjBn069dPkUaWZb766iu+/fZbunTp8tLdUcTqpIDgUrwIJYqaa9tyEfQh7WmJPLj2JzYWJrg5FNXOluRYeHi50J9ye7racf5O1EvnY70UZesBEHHlWJZNmnL3LJSqDWYapoEIBK+RI9ciWHLkBl3qlubwGG/Klci+X7tAIBDkB75sV5URrSoB0P7H41wOM9zCUiDIJDExkb1797J06VImTpzIkiVL0Ol0uWrS09P58ssvKVu2LFWrVsXGxsagY0CWZcaMGcPbb7/N2bNnmT59uqII3507dzJ79mzq1auHj4+Pot8pPj6ew8eO4zpmBwAmRhK3Z76T63xmZmZER0dTt25d3nnnHUXzmJqaEhsbi5eXF7169VKkkSSJ+Ph4WrduTbdu3RRpckM4IAoIkiTh5WqHv+ah9vrNvlHoWTxd7TAy0jDMPtQfZF2hz/P3ci1OZHwKtyMTtDPC0g4cqmEcehZzEyPcnW21syUtBe5f+Kc7h0DwhnPvSQJfbbtEpZJF+bZzTdFqUyAQFAhGtq7MmLb6TlXvLjzBX3c1PmQTvDQ3btzg9OnTREZGKtY8fPiQxo0b4+npSaNGjdi0aZPBQ7Vr167x2WefMXjwYG7evEm/fv1yPZWXZZlt27axZ88eIiMj2bFjB82aNct1DlmWWbt2Lfv376dJkyZs3bqVIkUMH2z5+vqyePFipk6dytKlSxU5LIKCgug34GMch24EoKi5CSHfdshVExcXR6dOnZg3bx47duxQHJUwatQo2rZty+HDh7G1VbZe37dvH8HBwezdu5cmTZoo0uRG4YxbL6B4lbPj96AHRMQkaZfXa+OMzqYsrlGXkMt9qo0Nmdw7C5IRlKmnrR0a8096zhPKa3nq6dIApwu/4VHGBjMTDX2b4RchLUlfl0KgCkmS2gE/AsbAclmWZ2psksAAJ0Me89mvF0jXySz90BMLU8NhngKBQJBf+KylG2bGRszYG0znxafYMrgRXuU0ri/2ipBlWXV9rBfRAOh0uqwNqSzL3L17F1fX3DsopKWl/auw6KpVq3j48CEdO3bE09Mzxw1uaGgoISEhXL9+HX9/f5YtWwZAvXr1WLx4MV5eXs9pnjx5wv79+9m3bx+nT58mMTEROzs7Fi9eTIMG2a/f0tLSslqsmpiY8MEHH2BhYcH48eNzfY3Onz/PyJEjcXFx4ffff+fGjRt4e3vn+lo8ffqUwYMHk5aWxokTJzA1NVXUKnXhwoX88ssv/PHHHzg5OSl2PrzfoxdJHfVLrhJFzfCf2DpXTVpaGt27d2fgwIF06JC7o+JZ1q9fz61bt1iwYIFih8Xjx48ZNWoU+/fvx8Qkb1wHIgKiAJEZ1q51O86IYh54Gf2Np0sxTe3g7hko6Q4WNtraoTFuDkWxsTDRPD0nxbk+ReV42pbU+ATjXmZnFBEBoQZJkoyBn4D2QHWglyRJ1bW1SpAbfsEP6b/qT0pam7N7aFNqldH4PVkgEBQIhg8frro95aFDh/j5559VadLT0+nXrx9Pnz7NddzHzSswpaP+46brz6eZvPhXVq9erWqu+Ph4unTpQkREhCrdzJkzWbBggao01ocPH+Lt7c3Zs2dVzTV8+HCGDBnClStXAP3GzhAXL17E3d2d4cOHs2/fPvz8/Dhw4IBBXc+ePalatSpt27Zl2LBhNGzYkN69exMQEJCj5sCBAzRt2jTrNmvWLKZNm0arVq34/PPPc+yWMnToUH755ReioqJo0aIF9erVY+PGjZw6dSpb5wPArl27CAgI4KOPPiIoKIgNGzZw/vz5HJ0PALGxsRw6dIiffvoJPz8/pkyZwoQJEwxu8k+cOMHs2bNZv349ZcuWNeh8AAgLC6N169b89ttvFC9eXJHzQafTkZycjJ+fH6VKlVLsOLpx7z5J734HQOlilgadD6BPQenatSuDBg1SNEcmpqamrFu3TlUNh4SEBObNm4eLi4uquXJFluUCd/P09JQLI8mp6XKViXvlyTsva2rHvpXTZHmyjZwY/rd2RqSlyPIMZ1n2/UI7G/IR/Vedk1t+f1hTG/68cF6WJ9vI13bN1dQO+deesjy/tiZTA/5yPniPfJEb0AjY/8zPXwFf5TT+Rd6H9wTel3cFhMlHr0XIdyPjZZ1Op/o5BLKs0+nkZUdvyOXH+codFx6Xo+KTtTZJIMhXFOT3YrW3F3kvXr16tdytWzdV78GxsbGyh4eHfOrUKVVzrVmzRm7VqpWcnGz4fWr9mduy61hf2XWsr1y763B51apVqubavn277O7uLgcFBclJSUmKNLGxsfJHH30kt2/fXn7w4IF87do1Rbo///xTbtasmfzBBx/IK1eulC9dumRQk5qaKv/2229y8+bN5VatWsnVq1eXDxw4YFAXExMj79ixQ/7kk0/kUqVKyYDs4+MjP3782OB8N27ckDds2CCbmZnJbm5u8jvvvCPv27dP0e+4c+dO+cCBA4r+ds/OKT7blRMSEZt1zbecc1hrc/KU3N6HRQpGAcLMxIj65e05GWLYY/oq2R5dkXaARehxcKqkjRFh5yElDso312b+fEbjivYcuhpBeHQipWyVteDJaw49sMRRdqBCrL8m8wOQnga3T0CNLtrZUHApDdx75udQ4F9HEZIkDQIGAS/kCZ/me4Xw6KSsn+u4FOMzbzdaVSspeq4rJCEljS+3BOIbGE47dyfmdK9NUXPxUS4QCJTj4+ODr68v69ev55133qF4ccMpD0WLFmXjxo107tyZLVu24OzsTLFihqOufHx8uHPnDgMHDmTAgAG0aNEix7F9GrjiUNScQevO87RiG2Yfu8zjx3MoV64cXbt2NTjX//3f/1GmTBnef/99KlSowI8//oibm5vB32vFihVs2bIFb29vEhISOHfuHI6OjrnqvLy8OHr0KBs3bqRfv37Y2dlx/PhxKlXKeV1sYmJC165d6dq1K1OmTOGbb76hffv2LFiwgE8/zTmt2dramk6dOtGxY0dcXFyIiIjA2NiYVatWMXToUCwssk/LNjExoUKFCjg5OREbG6u6bep7772nanzmnAJlHL4aQf/VfwLQvoYTSz7w1Nii18dLpWBIklRckqSDkiRdz/j6XOl7SZKqSJIU8MwtRpKkzzMemyJJUtgzjylPYimkNKloz/WIOCJikgwPfgVExadw4KE1sWaOcPOoJjYAGXNLUD73AjKFhSZuJQA4GaK86E9ec/LmE65Z1sXk7gnQKe93nKeEB0ByDJTPeYEjyJHsPAD/ikmVZXmZLMtesix7Ke0b/SzbPm3MwZHN2TioIRPfqcaj2GQGrvWn3fzjrDt9m/jktBc0vXDwJD6F7ktPs/dSOF+2q8KSD+oK54NAkE8oSGtiSZJYsmQJ33zzDR9++KFiXZUqVfj0009p0KABGzZsUKwbNWoUV69epXXr1ty+fTvXsW3cnTg4Un+4lFCyBj/edmTsuHH/qk2QG56ennTq1Im9e/cyaNCgzIg+g7Rv357q1atz9+5devbsSVqa4c8jSZKoX78+X375JdWqVeO9997jzp07iuabOHEid+/e5dixY9jb2xMaGmpQY2RkxPjx45k/fz5z585l9OjROTofnqVIkSKqnQ+CV8tPh0OynA8TOlQrVM4HePkaEOMAP1mWKwF+GT//C1mWr8my7CHLsgfgCSQA258ZMi/zcVmW976kPW88mRvNUze02WievhmJLEskuzSFW8fAQMubV8bNI+Dsoe++IKCKozX2VmaaRcdEJ6ZyKfQpyS7NIClaXwhSC24e1n8VkTEvQihQ9pmfywD383KCUraWVHK0pmEFewY2q8Dh0d780L02RkYSX+8Motf/zpCQIpwQ2XH1QQw9l53m+sM4lvf14lNvNxE1IhDkLwrUmvjBgwfodDr27dvH/fvK3+rt7OwwMjJixYoVijVmZma8//77mJiYMH/+fIPjKzlac3FSGwCMixYnveuPLFm2XNFckiQxdepU1q9fT3R0NCtXrlSks7KyYuvWrdy+fZsOHTqwdetWRbqKFSsybdo0Dh8+TGBgIObm5op0JiYmlC1blsaNG9OjRw/KlCmjSCco+AxY/Sff778GwNqP6vNx8woaW/T6eVkHRCdgTcb3a4D/MzC+FXBDlmVl7kHBc1QvZUOxIqac0GijeTLkMVZmxhRzfxsSn8DDS6/fiJR4CP1TnHI/g5GRRKOK+vQcpd7+vOTMzUh0MjjVziicc/PIa7dBP+9RcKwJViW0mb9g8ydQSZKk8pIkmQE9gV2vckJTYyO61C3D3uFNWdKnLpfDohm5KecCWYWVlSdu8c6CEzyKTWZlv3q8VTX30GCBQKAJBWpNXKNGDfz9/Wnbti3btm1TrOvTpw8XL17EwsIi14KGz2JqasrYsWO5fPkyYWFhORYzfBbbIqbceKYN4bxQV+49jlE0n5mZGX369MHf35/69eurWhe5uroyZswYevTooViTiampKU5OTqp1gsKBLMtUmbgPv6v6QqlHRnvTvLL6aNI3gZd1QDjKshwOkPG1pIHxPYH/xmwNlSQpUJKkldmFqwn+jZGRRKMK9pzSaKN56kYkDSrYY1Kxpf4OLdIw7pwGXSpUEA6IZ2niVoKI2GRuPIp77XOfCnmMpakxNatUhpLV4ZYG10VqItw7J66LF0SW5TRgKLAfCAY2y7Ic9DrmliSJ9jVLMah5RfYHPSQmKTXbcclp6Zy68Zijfz8iNCrhdZimKbIss+rkLab6XqFV1ZIc+sI7KwpOIBDkOwrcmrh48eL4+voarJPwX8qVK8eRI0ewslLX+rtChQps3rxZcZSAsZHE7ZnvULuMLQDN5hzn4JWHiueTJImaNWuKaDGB5kTEJlH+q70kp+kjxy9/05ZyJdT9/7wqdC8QzR4Z+XKR+AYdEJIk/SFJ0uVsbp3UTJRxovYe8Nszdy8BKgIeQDgwNxf9IEmS/CVJ8n/06JGaqd84mriV4H50ErcjX+8CPOxpIrcex+sXwDaloERlbTaat46AsZlos/gfmmpYB+LkjUjqly+OmYkRVPDWt0hNfc11Su6egfRk/fyCF0KW5b2yLFeWZbmiLMszXvf81Urp21xlV+Pm8NUIvKb9Qe//naXvynM0n32Yob9eYNuFUG4/jtfEIfsqCYmIo8OCE3yzW+98WNS7LnZWIodXINCSN3FNbGxsTLt27VTrTExMci24mBOSJFGkSBFVmp1DmzK4RUUAPl7rz4CM3HmBoCCwMyCM+jP8ALA0Nebmtx0M1m9KTExUlRoF8Oeff/Lnn8r/N2RZZvXq1Wzfvt3w4AzS09P57rvv+OWXX1TZ9l8MVq+SZfntnB6TJOmhJEmlZFkOlySpFJBb8932wAVZlrNcl89+L0nS/wDfXOxYBiwD8PLyerNWmir5p+DgY8q/Ru9ZZn2BJm72+jvKt4CAXyAtBUxe48L45hEo2wDM1H2AvemULV6EssUtORHymL6Ny722eR9EJxESEUd3r4z8xfIt4MxiCD33emsx3DwCRibg0uj1zSnIUxxt9MW0HsYk41byn57bsiwz6/erlLA2Z14PD4oVMeXglYf8eu4uvoHhADjZWPCehzOd65SmWikbTezPKyLjkum/+hwJyenM7VabTh7OmBi/bMCiQCB4WcSaWDvGta9KW3dHOi8+hd/VCMqN28PFyW2wtTTV2jRBIUGWZa5evUrJkiWxt7dXNL7d9//f3n2HR1G1DRz+nRQIJaH3FnoCSA0dpNfQEVRALAgK+oriJ4QuyqsoCi8KSlFERAQUECQBDEjvoYeEGkINCSQQAimknO+PDUhJdifJbgo893XtxZY5M09mh7Mzz5yykVMRpoHZ32tXlVEdqpktc+PGDb777jtWr17Ntm3GbvKeOXOG8ePHc+DAAU6ePGmozIkTJxg+fDinTp2yODDsfefOnWPw4MH4+flx5coVQ2VSk9EzmrXAq8nPXwXWmFn2ZR5rapZcQd/XG/DPYDzPBNcieSldwInd5zJ3HIjdZ29QNH8uqpdIvjCo1Ario+FKJk67eDccrh2X8R9S0bxyUfYGhZOQmHmDg94/DptVTm4aXqEZKPvM755zfhuUbQi582fudoXV/JuAeLQFxP7zEZy8FsVbz1eifY0SeLgWZmxXd45M6siG91vyWe/nqFWmAAt3nqfLrB0MX3IwR7aI0Fqz8uBl+ny/m9Dbcfzwqgd9G5SV5IMQOYOcE9tYvfKFOPnpv6016kz5m62nzOV5xLPEyO/+tWvX2LRpEzNnzmTixIncuWO52/KWLVsYMmQI5cuX56uvvjI0be0/uw9QcazPg+SDz3stLSYfrly5goeHB5MnT2bixIm4uFi+mRIdHc2QIUP4/fff+fTTTw11b9Jas3DhQnbs2MHIkSPJkyePxTIAp06dYv/+/fTt25eiRTPWHTSjZzXTgA5KqTNAh+TXKKVKK6UejN6rlMqb/Pnjo9x8qZQ6rpQ6BrQBPshgPM8EpRTNqhRlz7lwkpIy5yRba82uc+E0rVz03750ri1A2WXuhWbwdtO/0s8/Rc2qFCUqNgH/q8YGarKGXWfDKZTXkRr37zo7uUCZBpnbPSfmJlw9IompHK6Ei+mH89pjCYhFu4MpkMeRnnXLPPK+vZ3CraQLAxqX54dXPdg3rh1vt6rMev9rrPC7lGlxW8s3m8/y4e9HyZfLgUWvNaReeRkWSYgcRM6JM4GToz3B0zwZ2Lg8AK/9dIB3lx7K4qhERkRGRvLHH3+wYcMGdu7cybFjxywmExITExk+fDjPPfccZcuWZcKECcTHpzx+1H1aaz788EM6dOjAN998w2uvvUb+/OZvWsXHx+Pr68vChQupWbMmc+fOtTimiPfRK7yx9t/E2KlPO1OjtPlkgtaapUuXUqZMGXr37k3v3r3NLn/fxo0buXv3LiNHjmTAgAGGypw8eRIfHx9mz57N8OHDDZWJiYlhypQprF69mo8++shQGXMyNIG41joc0yi+j79/Fej60Oto4Im2Klpr45MPi0e0qFKUPw5eJiDkNrXKFLD59s6G3eF6VBwtqjz0NeYpBKXqmpq+txlr8xgAU7IjlzOUrp8528thmlU2fT+7zt6gbrmCNt+e1prd527QrHJR7OweqpArtYYdX5um5HSy/fFJ8E5Ay/gPOVzeXA44OzkQdjvuwXtXb8Xwd0Aob7asSJ5c9mbLF8mfm9GdqnP44k2mrgtEKUWvumVMY5NkY2FRsXy/9Rw/7Qqmb/2yfNWvtgyaJkQOI+fEmeu/vZ+jV70y9Ju7h3XHQliK7sE8AAAgAElEQVR3zJu9Y9tRsoBTVoeW7dy/mE/r78rWrVspWbIk1atXN1Q2ISGB9evXM2XKFGrWrEnNmjXp0KED9erVS3H5xMREDh8+zJYtW5g6dSq3b9+mSZMmzJkzJ9XtxcfH4+Pjw6JFizh06BC3bt1i4cKF9O3bN9W4tNasXbuWqVOn4u7uTqtWrViyZInFqU/37NnDu+++S/v27VmwYAEvvvgijo6pd/lJTNJ0mbmF09djAHipThHGdnUnt6P5c5eEhARGjhzJ9evX2bx5MwkJCYb29+rVq5k6dSobNmygaNGihspcvXqVfv368csvv+Dh4WFxeTDtv7feeov+/fvTrVs3Q2UsyVACIjuJj4/n8uXLxMZm8sB3NuLk5ETZsmVTPdDvjwOx9VRYpiQgtiQ3cWtZ9bHpYqq0gx0zIDoC8lpukpQhWsMZX1PrB/un5tC1qqL5c1OrjAtbT4XxTpu0jWqdHqdCowiJjKVl1ceaYlVuC9u/hHNboKalmcis4MzfkNsFyhqrTEX2VcLFiWuR/9bjS/ZeQGvNK00qGCpvZ6f4ql8d3vrlIKP/OMbaI1dZ+FrDbJuEuBgeTa/vdnEr+h4vNSzHp71qSfJBCGFTGzdupH379tjbm78wetjFixeJiIigbt26hstorVmzZg09e/ZMU712+PBh8uTJg5ubm9nlGroWJuCTTtSYtBGAJp9v5s0WFZnQrYbhbfn6+lKmTBlq1DBe5u7duyxYsIChQ4emaSaQX375hSJFitCxY0ccHBy4d+8euXKZH0Pt/PnzLFiwgNatW9OsWTMuXLiAs7Mz5cuXN1tuypQpxMTE4OrqSoUKFZg+fToDBgxg0KBBODmlnKTZtm0bM2fOfPA6KCiI48ePU6VKFV544QVGjx5NoUJPtszz9PTk7Nmz2NnZUaZMGY4cOYJSik6dOlGrVq0UtzV//nymT59O3bp1ad26Nf3796d58+YMHjwYO7uUf69v3LhBs2bNaNu2LWPGjKFEiRIkJiZanMVlxIgR3L17l19//ZVq1aoRHR1tcSDUvXv38n//93/89NNP1K5d2+yyYLrxN/CHfQ9er323ObXLGrsR+NNPP5E3b16WLVuW6t/+uNu3b/PNN9+wYcMGihUzPpXnjBkzmD59uuHkA5jGi7Czs2PUqFGGy1iicmI/WQ8PD+3n9+i4A+fPn8fZ2ZkiRYrk+JM3rTXh4eFERUVRsWLFVJfrOWcXCvjzneY2j+nFeXu4HZvA+pEtH/3gsh/80A76/AC1+9k2iGvHYW4L6DEb6suNgtTM8D3N7H/OcHBCB5uPmj9ny1mmbzzF/nHtKO7y0A9aYgJ8VQWqdYbec20aA0lJMMMdKjSFfotsuy0LlFIHtdbPRBYkpXrYGgb9sI+79xJYPaI5sfGJNP18Mw1dCzN/cNp2q9aa3/ZfYtzq43SvU5ov+j5H3lzZK3F5Jy6BF77fTUhkLCveakr1ks6WCwkhLJK62LyRI0fi7OzM1KlTDZcJCAigb9++eHt7U6lSJUNlkpKSGDZsGLlz52b27NmGz88PHDjA4MGDmT9/Pi1btrRcAJi/9QyfbTj94PWOj1pTrojl5MDu3bsZMWIE3bp1Y/z48URGRlKyZEmzZe7evcuMGTNYsmQJQ4cOpWnTphQvXtzirCB79+5lwYIF7Ny5k549e3L8+HE++eQTGjZsmGqZyMhIfHx82Lp1K7t27eLevXtcvnyZ8ePH8+GHH6aaTPD39+f06dMEBwcTFBTE3LlzSUxMpFKlSnz77bd07dr1iTKRkZGPzLzw008/ERYWRvfu3enYsSPOzin/RoWGhlK0aFHs7e2Jiori6NGjNG/e3Oz3fffuXfLmzftgmaSkJEMX33FxcYancb0vPj7ebMuFlGit0VpbjCkhMYmOM7cTdOMuALXLFuDPEc0fbRVsYFvpuXZNT7n0bis9zNXD2fOWUDrExsY+FckHMDWRKlKkiMXWHO3cinP08i2uR8WZXS6jIqPj8btwk3ZuKUxpXbo+5C0KpzfYNAbg321U7Wj7beVg7dyKk6Rh22nbT1f7z8kwapct8GjyAUwtVKp0MLVMSEq0bRDXjsKda6Zkh8jxirvkftAFY+upMG5GxzO4qWua16OUYkDj8ozuXJ2/jl6l/dfbCMjEsVEsCYmMof/cPZwOjeLbl+tJ8kEIkWm++uordu3axapVq4iLM3YOWaNGDebPn0+vXr24fv064eGWp/y2s7Nj/vz5xMXF8e677+Lvb2xczYYNG+Lt7c27777L8uXLWbXq8eEynjSsdVWOTv73/LDl9K28tWCLxXLNmjVj//795MmTh0aNGtG2bVuCgoLMlsmXLx8TJ05k3759REdH06NHD1q2bMmxY8fMlmvSpAk//vgjhw4dIn/+/GzYsIEWLVowZ86cVMc8KFCgAC+//DLz5s3j+PHjdOrUifr167Njxw4+/vjjVAdRrFWrFn369GHUqFFMnDiRtWvXEhwczJkzZ1JMPtzflru7+4PHF198waJFi+jbt2+qyQeAEiVKPGhN4+zsTIsWLSxej+XLl++RZYze+U9r8gFIc/IBTOcQlmLaciqMKuPXP0g+rBzelLXvtkhT8uH+ttIjPeWyy3XyU5OAgOyzU63ByN/S1q04WmPzEYC3nblOYpKmrXsKCQg7O6jWCc76mu5629LpjaaEh3MJ224nh3uuTAGK5s/N5pO2PS4i7t7j0MWbtE0pMQWm4yI6HK4ctGkcnN4IKFPCQ+R4JVycCL0dS1KSZm9QBE6OdjSqmP7uXSNaV+GPt5uSkKR5f/lh4hJsnBAzwP9KJL3m7OJiRDQ/vtaQ56sZbz4phBAZ5ejoyPLly5k4cSJ9+vQhIcHY+VvLli2ZNGkSzZo147///a+hMveTELdv36Zp06Zs3rzZULlKlSqxYcMGPvjgA9544w1CQkIslimQx5HgaZ50L2m6KN94LhpXL2+Cky8QU5MrVy7Gjh1L/fr1CQwMpEuXLoYSLAULFmT48OH06NGDUqVK0alTJ/bu3WuxXL58+Rg0aBC+vr4sWbIER0dHQ9MnKqX49ttv2blzJxs2bGDatGkWB1EEU4Kga9euVKhQwfCF/v3tiSfdS0iiyWebef2nAwA0qVSY8593pUEFG3dFf4o8VQmI7CgkJOTBgB1HjhzBx+fBQMisW7eOyZMnp3vdNUu7UNLFiU2BoZYXzoBNAaEUyZeLOqn1ZarWyTTY4MU9tgviTpipu0e1TrbbxlPCzk7R1q0YW0+FcS/BdtNx/nMyDK1JPQFRpZ1pOs5TPil/bi2nfEzTb+azPCezyP5KujiRkKSJiL7HgeAI6pUrlOHxGzxcC/NF39qcDr3Dx2sDiL5n42SpGX+fuEa/uXtwsLPjj+FNaVM9lf8/QghhQ46OjuTPnx8fH59Hzk0tKVSoEGFhYcyfP5+IiAjD5apVq0ZSUhJjxowhKcnYuYmjoyPDhg3DwcGBkSNHGt7W1Nc7M6byv+fGrb/aSuf/bTebgLazs2PRokUEBgbyzjvvMH/+fENxFitWjJ9++onDhw9z6dIlypQpY7EMmBIs7du3p1+/fgwbNgx3d3dD5UTWmrXpDNUmrH8wW9df77Zg2bCmkqxJI0lA2NiMGTMYOnQo8GQCwtPTk7Vr1xIdHZ2udSul6FizBNtOX7fZCXVcQiL/nAyjQ40S2KfWpKhyO3BwgsC1NokBgMC/AA3u3W23jadIp5oliYpNYPe5Gzbbxgb/EEoXcOK51AZBzVMIKraEgLWmAURt4WYwhByV4+Ipcn8qzrNhdwgIuZ2h1g8Pa+NWnNebu/Lb/ou0mr6VM6FRVllvWqw6dJm3lhykWon8rH6nGW4lLc/xLYQQtlCoUCE2btzIK6+8wrx58wyXa9euHQEBAXTt2pXvvvvOUBk7OzsmTpzI2bNnadiwIWvWrDFUrmjRonz88cdcvHiR1q1bExAQYKhcgQIFGD70DYKneTKuTWkATl6LovqEDXyxIfWWBkop3NzceO+99xg7dmyaWgsAODg4UK5cuTSVETnDrrM3cPXyZuYm0zgjXZ8ryfnPu/Jc2UyY6e0pJAkIKzlw4AC1a9cmNjaWu3fvUrNmTfz9/Vm5ciWdO3fm3r17TJo0ieXLl1O3bl2WL1+OUorWrVuzbt26dG+3S61SxMYnsfWUbfr77zxzgztxCXR5rlTqC+XOD1Xam5IEBrPaaRa4FopUgeLGRyl+lrWoWpT8uR3Y4H/NJuuPio1n+5kbdK5VynzWt0ZPiDgHYcZOGtIsIDnpVaOHbdYvMt398UR8joegNVZLQABM7l6TlcObmqaUWnKQqFjzc4Zb04Xwu0z4059GroVZNqwpxZ1lqjghRNYqWLAgixcvZujQoURGRhouV6ZMGVasWJHqWAKpKVWqFN9//z0dOqSty2TevHkZMWJEmmaquG9Yp3qc/7wrveqaEhHfbz2Hq5c3W2zcTVU8Ha5FxuLq5f1ghovcDnYcmdSB7wY2kFYPGZC9hgS3kil/nbD6YGM1SrswuXvNVD9v2LAhPXr0YMKECcTExDBo0CDy5ctHoUKFHgyY8sknn+Dn58fs2bMflPPw8GDHjh30798/XXE1qliYIvly4XM8hK7mkgTp5HP8GgXyONKssoXm7TV6wcl1cPkAlG9s3SDuhsP5HdDifZD/7IbkdrCnnXtxNp64xtRetXCwt26u8Z+Tpu4dXZ8zP1I0bt3A+0MIWAMlUv//k24Ba6BUXSjkav11iyxRpmAeAH73u4yDnaJeeWPTWBnVoEJhZg+oz8Af9tH3+91M6VGLppbqtwzSWvPRH8ewt1PMfLEueXIZn/pOCCFsrVev9E2XXb9+/XSVMzJugTUppfjfS/X4pFctWn6xhciYeF5fZOq/v8ur7YPfHSHui09M4qX5ezl44eaD99IytWZWMTqbyMPOnz+Pq6ur4YSK1pr169fToUOHdA3wCdICwqomTZqEr68vfn5+jB49mpCQEItzsxYvXvyRKW/Syt5O0alWSf45GUbMPesOrnYvIQnfgGt0qFECR0sXsNU6gX0uCPjTqjEApsSGTjTdTReGdalVipvR8ewNMt5H0yif4yEUd85N/fJPzgf9iPzFoUJzOPGn9bth3LoEV/zkuHjKlHBx4ou+z1GqgBNt3YrbZOrMJpWK8MNgD2LiExn04z6OXLpl9W08bE9QOPvPRzC6U3VKy4muEEJkCRcnR45O7oj3ey0evNd82j94TN1k8xnlRM6QmKQZteIIVcevf5B8+LRnTYKneaY7+aC1NjSo6cPL+/n54evra7hMVFQUX3/9NXPmzDFc5uLFi7z++ussWrTIcPLhzJkzdOnShfXr16c7+QBPaQsIcy0VbCkiIoI7d+4QHx9PbGwsefLksTiV5v3lMqJb7VIs3XeRvwOu0bOuscFvjPjnZBi3YxPoVttAywonF9P0mMf/gA6fmqZhtJZjK6BwZShZ23rrfAa0rl4M59wOrD58hRZVi1ptvbei77Hl5HUGNilvbKqhmr3Be5RprIbSda0WB8dX/Lt+8VR5sWF5XmxY3qbbaONWnHUVWtLlf9v5YPkR1r7bHGen9P+YmjNvWxBF8+emn4f0DRZCiKxWs3QBgqd5suLAJUavPMaNO3E0/O8mnJ0c2DSqFSUen1pcPJW01sTHx5MrVy4SEpMYuewI3sf/nW2lvXsJ5r/SADs7xd27dzl48CB79+6lZ8+eVK9e3ey67927x/bt21m7di3btm1j+fLlFClivrVldHQ0P/zwAz/++CMREREWp3W9/zd8+eWXTJs2DRcXF8PjpKxcuZKBAweSP39+zp07Z6jMiRMnaN26Nbdu3UrTuDEpkRYQVjRs2DA+/fRTBg4cyJgxY6hWrRrBwcEPPnd2diYq6tGBz06fPk2tWrUytN0mFYtQuoATqw5dydB6Hrfq0GWKOeemRRWDF691XoK7YRC01XpB3LoIF3ZCnZel+0UaOTna0/W5Uqz3D7HqIKXrjoVwLzGJvvXLGitQs7epdczRZVaLAa3h6HIo3xQKV7TeesUzpUAeR2a8WJcL4Xdp89U21h1Lf2u01ARcvc2209d5vbkrTo7S9UIIIbKL/g3LETzNk4ndTGNLRMUm0PizzVQd78Plm+kbIF5kDq01W7duZd26daxcuZJly5Zx96756VYBli1bRrdu3ahZsybdu3fnZuRthiw6QJXx6x8kH1pXL8apqZ354VUP7OwU27Zto2DBgrRq1QpHR0eLyQeA4OBgXnjhBebMmcO0adNwc3OzWCYhIYGFCxfi7+/PkiVLKFTIQitjID4+nsOHDxMfH8/s2bPJly+fxTJaa44cOULp0qWZMGECBQoYG0gzMDCQypUr88Ybb1ChQgVDZVIjCQgrWbx4MQ4ODgwYMAAvLy8OHDjAvn37qFy5MmfPngWgTZs2BAQEPBiEEmDLli14enpmaNt2dore9cuw48x1wm6bb3FhVMTde2w5FUavuqWNjx9QtaNp5oOjv1klBgCOmfYTtdM3Rsazrk/9MkTfS2TjCesNRrnq0GWqlchPzdIGR/DPWxiqdYbjv0OilQb9u3oYbpwyJb2EyIAmlYqwcngzyhR04v1lRzh4wXpdlrTWfOYTSIE8jgxqnLEfayGEELYxpEVFgqd5MrWX6YZgfKKmxRdbcPXy5kK45Yvap9WdO3fSXObkyZMsXLgQPz8/YmJiDJUJDw/Hw8ODBg0a0LFjR+bNm2d2ClStNfv372fcuHF0796djz76iPLly5u9+E5MTGTlypV88803bNy4kfoejXDuMZ7GX+9jc/KApJ1qluDMf7uw6PVG5HawJykpiaVLlzJ8+HDc3d2ZNm0aH3zwgcW/Z/369fTq1YshQ4bw1Vdf0aVLF4tlAgICeP755xkxYgSLFy+mVatWFsvcvn0bT09Patasyc6dO+ne3fKMcFprJk2axMmTJ9m/fz/Dhw+3WAZg69atTJ06lXXr1jFr1ixDZcx5KrtgZIXBgwczePBgAOzt7dm3zzRaamRkJIsWLWLq1KkULlyYAwcOPCgTGhpKTEwMzz33XIa336d+WeZsOceqw1d4u1XlDK9vzZErxCdqetczeJcbwCE31OoLh5dAzE1TMiIjkpLgyG+mMQQKycl7ejR0LUzZQnn43e9y2r7LVJy7fodDF28xprNb2kb/rfOyaSaTM3+DW8YSbgAc+RXsc5sGPxUig+qVL8TiIY3p/u1O3vn1MN8Pqk89S+ObGPDPyTB2nr3Bx91rUCCvbbp3CCFEWkVHR5M3b940lUlKSiI2NjbN5aKionB2dk5Tmbt375IrV6409zEPDw+32Mz9cdevX6dQoUI4ODgwqEkFBjWpwAq/S4z+w9T8vdX0rQDMeqnug27OWmsuXbpE+fJp6yoYFBRE6dKlcXIy3sUjKiqKc+fOUatWLRwcHAgNDaVIkSI4OJi/hNuzZw+5c+emXLlyFC5cmOnTpzNgwACzMV+4cIH9+/c/eL1ixQqCgoLo3r073bp1o379+ikOcPjzzz8THBzM5cuXCQ4OZtOmTQA0atSIWbNm0aRJkyfK7N27l99++429e/dy584d4uLisLe3Z/LkyXTv3j3Fc8zIyEg+/fRTvL29cXd3p3Pnzri5uTFr1iyzx9jPP//Ml19+SYsWLZj01feMXHeJHUkKksdI61GnNDP613nkhuvp06cZPHgwNWrUeDAWQ5ky5ru5a615++23CQoKwsfHh3LlyhkaEHLDhg18+OGHLFq0iIYNG1pcHkzHRbt27Rg+fDhvvPGGoTIA06ZN4+TJkyxdutTw/6+zZ88yYsQIfHx8KFrUOl26pQWEjfXu3RtXV9cUP7t48SJff/21VbZTuVh+GrkW5td9F0hMythgf1prluy9QJ2yBahh9C73ffVfhYRYOLI0QzEAELTFNIVjg9cyvq5nlJ2d4qWG5dh9LpyzYWnPZD/ulz0XcLRXvNAgjcmMqh3AuRQc+CHDMRAXZep+UbMX5MneoxGLnKNAHke+H1SfRK3p/d1uvt9qrE+kOXO2nKVS0XwMbCIJVCFE9jFgwABWr16dpjLbt2+na9euaborrrXG09OTZcvS1gXT29ubdu3apWmQ9ri4ODp06MDnn39OQoLxbqerVq2iYcOGrF+/Hq010dHR9Pcwdc2Y9dK/41aNXHYEVy9vhi3243JIGH379qVv377s2rWL4OBgrl+/bnFba9asoXbt2gwcOJA1a9YwduxYLl++bLZMWFgYU6ZMwd3dnbZt2/LOO+9Qp04dfHx80GYG9969ezdffvklvXr1okaNGkyePJmKFSvSp08ftm3blmKZW7ducezYsQePiIgITp8+zfHjxzl+/Di3b6c8w+Dt27epUqUKgwYNYvr06bzyyivs3r2bvXv3pph8uK99+/asW7eOEydOsHTpUvz9/enRo0eqN7jy5s2Lh4cH+/fvZ9WqVYwbN46FCxdaTHBVrlyZYV8vY2OhHry99jJxSab1v+hRjnOfdeWbl+s90dq7WLFizJ07l4ULF1KmTBmLyQcwzbYyZMgQ/v77b1xdXbG3tzd0s65mzZps27bNcPIBTDPJLFq0KE3JB4D+/funKfkA4Orqire3d6rXs+mitc5xjwYNGujHBQQEPPFeTpfWv2ntkSu6wph1enPgtQxtd+eZ67rCmHX6d79L6VvBDx20nlVX68TEDMWhl76k9ReVtI6Pzdh6nnFht2N1lXHeevIa/wyt505svK41aYP+z9JD6VvBlmlaT3bR+vqZDMWh9803refi/oytxwYAP50N6sjMeKRUDz8NomLj9YglB7Wr1zq968z1dK8n7HasdvVap7/ZdNqK0QkhjJC62LzQ0FD93HPP6e3bt+ukpCTD5ebOnatbtWqlo6KidExMjKEy4eHh+vnnn9dff/21vnr1quHt/fXXX9rNzU1v3bpV79q1y1CZ6Oho/eGHH+omTZroOXPmaD8/P0PlTp06pXv16qXbt2+v27Rpo4OCgh75POj6He0x1VdXGLPukcePqzfpHj16aFdXV12pUiUdGBhocVsJCQl6y5YteujQoRrQBQsW1MuXL7dYLikpSZ8/f163a9dOK6V04cKF9TvvvKNv3bplsWxoaKh+55139Pfff693796tb9++bbGM1lqfPHlSx8bm3HPw8DtxutecnU98b+uPh2R1aM8Ec/WwMn2es3h4eGg/P79H3gsMDMTd3T2LIrKNtP5N9xKSaPHFP7iXcuHnNxqle7vDFvtxIDiCPWPbpW/QtON/wMohMPAP053v9Lh5Ab6pCy1GQbuJ6VuHeOD9ZYfZFBjG3nHtyJ87fT2vluy9wIQ//Vk5vCkNKhRO+wqiQmFmTWj4JnSZlq4Y0Bq+awIOTjBsa7YbmFQpdVBr7ZHVcWSGlOrhp8XduAR6zN7JjTv3GNvFjf4e5YzN+PKQ+6Or+7zXMu0tyYQQGSJ1sWVBQUF4enry/PPPM336dFxcjNVT8+bNY8mSJVSrVo0ff/zRUJnY2FgGDRrE4cOHmTp1Ki+//LLhGPv06cP58+fZu3ev4XPiv//+G09PT0qUKMGBAwcoVcrAbG7AiBEj+P7773F1dWXbtm1PdFdISExiqncgi3YHP/J+gVtnuLjqS4iPYfXq1bRu3drito4ePcrGjRuJjY0lNjaWPn364OFh+ZC9desWLi4uhpr2P4sSkzQ/7gziM5+Tj7xfo5QLi95oSHFnmeEks5irh+XofYrkcrDjlSYV2Hb6Ov5XItO1jjOhUfgGhjKwcYX0j9ju3gOcS8POmekrD7D7G1D24JG2pkUiZa83r8iduASW7L2QrvIJiUnM3x5E7bIFqJ/evvHOJaBWHzj0M9y9kb51nFoP109Ck+HZLvkgnh75cjvw46sNqVYiP16rjvPlxlNpXodvYCilCzjhXiptfZ+FECIzlC9fnrp16zJ//nzmzp1ruFz79u05c+YMCxcu5MiRI4bKODk50aVLFy5evMioUaO4deuWoXIlS5akRYsWJCUlMWDAAOLi4gyVq1KlCpMnT6Z06dL06dOH2FhjA7R//vnn+Pr6MmTIEGbMmPFEdxMHezs+7lGT4Gme/Ppm4wfvRxasSoE3FlDgrSWsPG9HdJzlLiB16tRh9OjRTJo0ic8++8xQ8gGgYMGCknx4jNaa3/0u4erlTeVxPo8kHz7qVJ3zn3fFZ2RLST5kI9ICIhtLz98UGRNPiy/+oXnlosx9pUGatzly2WF8A0LZOaYthfPlSnP5B/bNg/Wj4TVvcG2RtrK3r8KsOlB3IHT/X/pjEI8YvHA/J65EsmNMG/LmSlsriJUHL/Ph70dZMNiDDjVKpD+I66dgTmNo8QG0n5y2slrD/NYQewvePQj22W8MXbnr9nTRWjNutT+/7b/IdwPr0/U5Y3fRomLjafTfzfTzKMsnPTM2zbIQIu2kLjYmLCyM0aNH8/fffxMUFGR4cMTz588zadIkIiIi8Pb2Nry9ixcvMnPmTHLnzs20acZbQt65c4fff/+dggUL0rt3b8PlAK5evUp8fHyGpw1MTVxCIv/bdCbFcYPeb1+Vd9tUMT6bnEiTzYGhDF3sx+ND37WsWpTpL9ShZAFJOGQlc/WwJCCysfT+TTN8T/PN5jN4v9eCmqWNze0KcDYsio4ztzP0+UqM7ZLBfRkfY0oiFKkKr61L291q7/+Dgz/Bfw7J7BdWdPBCBH2/38PYLm68lYaZUuITk+g4cztOjvb4vNcibbNfpOT3102zYYw8CvnSMJruqfXw20vQYzbUfyVjMdiInPQ+fWLjE3lx3h6OXo5kQOPyfNy9JrkcUj+ZvJeQxOuL9rMvKII/hjejbjkZKFWIzCZ1cdrs2LEDpRQtWqTthtHRo0cpX748hQqlrWVkZGQkLi4uGT+fyGbuxCUwdV0Ayw5ceuIzz9ql8OrsRrnCaZtFRPwr+l4C86WgFYQAAB3CSURBVLYFMWvzmSc+q1XGhVkv1aNysfxZEJlIiXTByEIhISF069YNgCNHjuDj4/Pgs3Xr1jF5chrvAhswpHlFCuV1ZMraAIwmmLTWfLw2gHy5HRjWslLGg3DMA89/BBd2QsAa4+VCT4DfQtNsGpJ8sKoGFQrTpnoxvv3nLGG3jTVHBPhp13nO37jL/3WsZp2ThdZepplSNk8xXiYhDjaOgyJVoM5LGY9BCIOcHO1ZOrQJb7aoyNJ9F/n4rxNml/9+6zl2nQ3ni761JfkghMgRWrZsmebkA5i6EaQ1+QBQoECBpy75AJA/twPT+tYmeJonfhPa0/GhFqPex0Jo+eUWXL28qTLOh593BxOfmJSF0eYMO8/coNPM7bh6eVNj0sZHkg+lCjjx5zvNCZ7mybr/tJTkQyZLSkr/8SsJCBubMWMGQ4cOBZ5MQHh6erJ27Vqio6Otus0CeR0Z3dmN/cER/HnkiqEy6/2vsfPsDT7sUI0i+XNbJ5AGr0OJ52DjeIgzMG1TUhL4fAROBaDtBOvEIB4xqXtN7iUk8ZlPoKHlr0XGMmvTGdq6Faedewa6XjysWHVo/DYc+gUuG7xrs/sbiAiCLl+CfdrmBRcio/LldmBCtxq83aoyS/dd5H+bTqc63fF6/xAaVSxM37ROVSuEEOKpUTR/buYP9iB4micnP+2MVxe3B58lJGkmrz1B1fHrcfXyxvObHfxx8DKx8YlZGHHW01qz+9wN3vrFD1cvb1y9vBn04z5OhUY9WOaFBmXZM7YtwdM82TO23VOd6L8/Y0RaBAYGpmka2tjYWBYuXJjqFKspCQsL44MPPuDChfSNKweSgLCaiRMnMmvWrAevx48fzzfffMPKlSvp3Lkz9+7dY9KkSSxfvpy6deuyfPlylFK0bt2adevWWT2eFz3KUbdcQSavOcHFcPMJjiu3Yhi/+jg1S7swqIkVWx3YO4Dn13D7CniPMvXhN2f3LLiwCzpMgbzpmGVBWFSxaD7ealWJP49cZe1R8/NrJyQm8f7ywyRqzaRuNawbSGsvcC4Fq4ZCrIUBUy/7wdYvoEZPqNLOunEIkQYfdapOjzql+d+mMwxYsJeYe4+eLF69FcPJa1G0cyueRREKIYTIbpwc7Xm7VWWCp3kSPM2TTaNa0f6hmzonrt7m/34/itvEDQ8uvN9Zegi/4Ig0X4DmJJdvRvP5+kCqTzAlYiqO9WHAgn1sPBH6YJmKRfOx8DUPzn/eleBpnnzVrw6lCuTJwqjTduc/ISGBvXv34uvra2h5rTUHDx5k7NixhsdJiYmJYfHixTRv3pwlS5bg4GB5jLTbt2/zxRdf4OrqytmzZw3NghMVFcWUKVOoXLkyMTExVKxY0VB8KcnQKG5KqX7Ax4A70EhrneLtTKVUZ2AWYA/8oLWelvx+YWA54AoEA/211jczEhMA673g2vEMr+YRJZ8zO3XgkCFD6NOnDyNHjiQpKYlly5axYsUKfv75Z3LnNrUo+OSTT/Dz82P27NkPynl4eLBjxw769+9v1XDt7BTfvlwPz292MPzXgywb1gRnpyfvHN+NS2DEr4eIT9TMHlDf+gPllG8MrcfC1s+gTANo/FbKy53dDJs/gZq9oV727N//tHivXVX2nAvHa+UxqhTLn+IUgVprvthwkr1BEXzVrw6uRfNZN4jczvDCQljkCauHQ/+fU27ZcDsEfn8NXEpB91lPfi5EJrK3U8x6qS4tqhZlzMpjeK06xv9erPugKfGWU2EAtHOXBIQQz5pse04ssp0qxfPzw6umrvFaa3adDWfR7mA2Bf574e19LATvYyGPlGtUsTAd3EvQvkYJKlr7vMyGbt69x5ZTYWwKDGVTQBj3zHQ9cSvpzOvNXelRpwx5cqVzNj4zbty4wZUrVwgNDSU0NJTmzZtTqZL5rudnz55l2bJl+Pv7c+HCBb7++muaNWtmtkxkZCRvvfUW3t7elCpVil27dlmMLTExkSFDhvDzzz/ToEEDdu7caair0pw5c/joo4+oV6+e4a79/v7+TJw4kdKlSzNhgrFW54mJiSxZsgStdYaHEMjoMPL+QB9gXmoLKKXsgTlAB+AycEAptVZrHQB4AZu11tOUUl7Jr8dkMKYs4erqSpEiRTh8+DChoaHUq1ePuLg4ihUrZrZc8eLFuXrV/J3o9CpXOC//e6kuwxYfZMCCffz4mscjU9CE34njzcV++F+JZM6A+rarzJ7/CK4eNs2KkRALTf8DD08hFLAWVr4Jxdyhx7cyvaKNOdrbMXtAfXp/t4uX5u/hx9ca0tD13xYn8YlJfO5zkoW7zvNKkwq8YKum5BWaQufPTcfFilehz3zI/VD/vfBzsKQPxNyEV/+CPOmc/lMIK1JK0d+jHNej4pi+8RQXI6J5v301WlUrxj+BYZQrnEf6oQrxbJJzYpFmSilaVC1Ki6r/Dsp9Ny6BVYevsGjXec5dv/vg/f3nI9h/PoL/PtaNtkAeR1pUKYp7KWfcSrrgXtqF0gWcMm2cjcjoeAKv3eZkyG2OXgzn6JU7BN24a7FcHkd7XmvuSr+6JVm/8leKFi1KyZL5KekSg5Hcw7hx49i4cSMAjRo1Ytq0aRQokPrg+0lJScydO5eJEyfi4ODAjBkzLN7Fj4+PZ/PmzUyZMgUXFxc2btxoccrUhIQEFi9ezJ49e3B2dubvv/+2eD2oteaXX35h//791KpVi1WrVhmalWbz5s38+OOPvPjii0ycOJFcuSzPYHj+/HmGDx/Ol19+SaVKlcib1/LAqHFxcQwcOJA333yTunXrUqqUsVnBUpOhBITWOhCwdIA3As5qrYOSl10G9AQCkv9tnbzcz8BWrFHZmmmpYEtvvvkmixYt4tq1a7zxxhvkyZPH4tzDsbGx5Mlju6ZEbd1KMH9wA4YvOUTbr7YxsHF5qpVw5uz1OyzZe4G4+CTmDKhP51olbRYDdnbQf7Gpub3vJNOglM/1B4fcppkNzmyE0vVh0ErTnXFhcyULOPH7200Z9MM++s/bQ486pWleuSi3Yu6x/MAlzl2/yxvNKzLB08YzyzR+C5SdaeyPbxuAxxtQsBxcOQiHFkOufDB4LZSpb9s4hEijEa0r45LHkR92BPHqwv20rl6MraeuM+z5Sk/l4GpCCPOy7TmxyHHy5XbglSYVeOWhbtFxCYnsDYrA98Q1Np8MIyTy3+uLyJh4vI+H4H08JKXVPcHBTuHs5IBLHkecnRxwzu2ISx4H8uV2IC4+idux8dyOTeBK6A2iEyBBOXIvMf1dQXLZ29G+RnHau5egdfXiFM6Xi/j4ePz9/Tl4cCfT1xxkxYoVRERE4OHhweeff0716tWfWI/WmhMnTvDXX3+xbt06wsPDCQ4O5pNPPmHUqFGpdj0IDQ3lp59+4pdffqFevXo0btyYL7/8kueffz7VmOPj41m8eDEzZsygY8eOfP3117Rr146aNWua/Vt37drFe++9R8uWLdm5cye3bt3C1dXVbJnw8HCGDRuGg4MDO3fuJCEhgeLFzbek1Fozc+ZMli1bxoYNGyhdujSOjpbHSDt8+DADBw5k3rx5tGzZ0uLyYEo+9OnTh+eff54xY6xTJWW0BYQRZYCH56O5DDROfl5Cax0CoLUOUUqlureVUsOAYQDly5e3UagZ07t3byZNmkR8fDxLly4lNjaW4ODgB587OzsTFRX1SJnTp09Tq5Zt54lv61aC9SNb8vn6k/yw8zyJSRo7Ba2rF2dsFzeqlsiEi36HXPDCT3CsE2z5HDYkH8B5CkG7ydBkBDjKfL2ZqWyhvKz9TwvmbDnLkj0XWHPE1BKnWon8LBjsQXv34plzIdVoKJSqC74TTV11AOxzQa0XoN1EcClt+xiESCOlFK80qUC/BmUZ/ccx1h69yuCmFRjVoVpWhyaEyL6yxTmxl5cXQ4cOpXJl41Ny7927l82bNzNu3DjD5wZaa4YOHYqXlxdVqlQxvK3ff/+dM2fOMGbMGOztjTXDv3fvHv369WPChAk0bNjQ8LZmzpxJaGgoH374IcWKFUNrbfHvCw8Pp2fPnrzxxhu8+OKLxMXFkT9/fot3nz/44ANCQkLo3r07Xbp0wdfXl169ej3oqp2So0ePMmDAAOrWrUuDBg3IGxtLnYsXWTlpEqVLm86PQiJj2H8+gpPXojgZcpvAkCiumZntLCFJczM6npvR8Wbj/fcy0XzyQSXE4hQbTiEVQ6k8SWxa/gM9WjVgxPDhNGnSJMX9uWDBAjZv3oyHhwe9e/emWLFi1K5dm759+6a6/2/evMno0aPp1q0bv/32G0op7t69i5ubW4rL3zd37lxcXFzYvn07RYoUISoqCmdn89c+J06cwN/fn02bNhm+26+1ZuXKlSxcuJA6deoAUK5cOYvldu/eTe/evRk4cKDh/1sxMTFcv36dbdu2pelG9sGDpmRPWq49Q0ND8fT0ZMSIEYbLWHR/hM3UHsAmTM3KHn/0fGiZrYBHKuX7Yerjdv/1K8C3yc9vPbbsTUvxaK1p0KCBflxAQMAT72WFt956S48ZM+bB67Zt2+ozZ85orbUODw/XHh4euk6dOnrZsmVaa609PT31sWPHUlyXLf6mmHsJ+kzobR0dl2D1dRuWlKR15FWtI86bnossl5CYpIOu39Hhd+KyNpCYSK3DTmkdn8VxpBPgpw3UYU/DI6V6+FmVlJSkQ27FZHUYQohktqqLc8o5sSU7duzQNWrU0GfPnjVcJi4uTg8YMEAPHz5cJyQk6CSD5287duzQbm5uev369frOnTuGysXExOj3339ft2zZUgcFBelz584Z2taBAwd0kyZN9FtvvaV37dqlAwMDLZaJjY3Vc+bM0W5ubnrMmDH67bff1teuXbNY7ty5c9rLy0tXq1ZNd+vWTTdr1kxfvXrVbJmEhAS9c+dO7eXlpevUqaPz5s2ra9Soofft22e2XHR0tN6zZ4+ePXu2bty4sQZ0njx59JgxY3RERITZ7V29elX7+vrqChUq6K5du+oJEybojb6bdPidOB18444+fvmW3nXmul5//KpeceCi/uvoFb3tVJg+dCFCz1n8h/7h1xX62vVww993VFSUvn79uqFlxdPNXD1srQrZXGXbFNj40OuxwNjk56eAUsnPSwGnjGwvuyYgEhMTdZ06dfTp06cfvLdq1So9fvz4FJe/du2abtu2barryw5/kxDCOElACCFE1svKujg7nBMbcT8JMWfOHB0WFmaoTGJioh41apTu06eP9vLyMryty5cv66ZNm+oOHTroRYsWGS7n6+ur3d3dddmyZfXRo0cNx7hgwQJdqFAhXa5cOX3p0iVD5WJjY/WHH36oAV2tWjV94cIFQ+Xu3Lmja9SooQFdqlQpvWvXLkPl/P39dc+ePXWPHj1079699fbt2w2V8/X11f/8848OCAjQERERhhIDCQlZeNNRPLPM1cOZMQ3nAaCqUqqiUioX8BKwNvmztcCryc9fBdZkQjw2ERAQQJUqVWjXrh1Vq1Z98H7v3r1T7ftz8eJFvv7660yKUAghhBBCZKFsc07cokULXnzxRd555x0+++wzQ2Xs7OyYMGECJ06cYNq0aWzYsMFQuTJlyjBp0iR8fX35z3/+w4ULFwyVa9u2LR07duTKlSv06dOHmzctTwpiZ2dH586d6d69O1prOnXqREREhMVyuXPn5uWXX2b27Nm0adMGLy8vQkIsj6mQL18+Dh8+zKVLl1i3bh0xMTEkJCRYLFezZk3+/PNP1qxZw6pVqwz3x2/fvj1t2rTB3d2dQoUKGWqyb7QbixCZRZkSFOksrFRv4FugGHALOKK17qSUKo2piVnX5OW6Av/DNOXQQq31f5PfLwKsAMoDF4F+WmuLtYSHh4f283t0dqPAwEDc3W08YF4mexr/JiGeZkqpg1pr88MjPyVSqoeFECI7yIq6ODudExsVGBjIuHHj8PHx4eTJkxZnBLhv//79TJs2DX9/f44dO2ZotH4wDYA3b948QkJCWL16NXZ2xu6DXrt2jVWrVhETE8OoUaPSNAbFuXPnuHPnDnXr1jVURghhHebq4QwlILKKJCCEENmRJCCEECLrSV2cNrt378bf359hw4alqVxgYCD37t17MOCeUfcHZLc0EKAQIucyVw9nxiwYmUZryyPX5hQ5MTEkhBBCCCFylmbNmtGsWbM0l0vvTTJJPAjxbMuMMSAyhZOTE+Hh4U/FhbvWmvDwcMNN2oQQQgghhBBCiOzuqWkBUbZsWS5fvsz169ezOhSrcHJyomzZslkdhhBCCCGEEEIIYRVPTQLC0dHR8OA5QgghhBBCCCGEyFxPTRcMIYQQQgghhBBCZF+SgBBCCCGEEEIIIYTNSQJCCCGEEEIIIYQQNqdy4qwRSqnrwIU0FisK3LBBOLYgsdpGTok1p8QJEuvjKmiti9l4G9lCOuthkGPGFnJKnCCx2kpOiTWz4pS62LzscrxIHNkrBsgecWSHGCB7xJEdYoD0xZFqPZwjExDpoZTy01p7ZHUcRkistpFTYs0pcYLEKtIuJ30POSXWnBInSKy2klNizSlxPu2yy/cgcWSvGLJLHNkhhuwSR3aIwRZxSBcMIYQQQgghhBBC2JwkIIQQQgghhBBCCGFzz1ICYn5WB5AGEqtt5JRYc0qcILGKtMtJ30NOiTWnxAkSq63klFhzSpxPu+zyPUgc/8oOMUD2iCM7xADZI47sEANYOY5nZgwIIYQQQgghhBBCZJ1nqQWEEEIIIYQQQgghssgzkYBQSnVWSp1SSp1VSnlldTypUUqVU0ptUUoFKqVOKKVGZnVM5iil7JVSh5VS67I6FnOUUgWVUn8opU4m79umWR1TapRSHyR/9/5Kqd+UUk5ZHdN9SqmFSqkwpZT/Q+8VVkr5KqXOJP9bKCtjvC+VWKcnHwPHlFKrlVIFszLGZ43Uw7YjdbF1ST1sHVIPZy2lVL/k4zhJKZXq6PWp1c3WOq6MrEcpVV0pdeShx22l1PvJn32slLry0GddbRFD8nLBSqnjydvxS2t5a8Rh7jcoI/vC0m+wMvkm+fNjSqn6RsumhYE4BiZv/5hSardSqs5Dn6X4/dgghtZKqciH9vMko2WtHMdHD8Xgr5RKVEoVTv7MWvviiXr6sc9tc1xorZ/qB2APnAMqAbmAo0CNrI4rlVhLAfWTnzsDp7NrrMkxjgKWAuuyOhYLcf4MvJn8PBdQMKtjSiXOMsB5IE/y6xXAa1kd10PxPQ/UB/wfeu9LwCv5uRfwRVbHaSbWjoBD8vMvskusz8JD6mGbxyx1sfVilHrYtrFKPZx5+98dqA5sBTxSWSbVutlax1Va15Mc0zWgQvLrj4H/y+C+MBQDEAwUzejfkJE4zP0GpXdfGPkNBroC6wEFNAH2GS1r5TiaAYWSn3e5H4e578cGMbQmhd/TzN4Xjy3fHfjHmvsieT1P1NOZcVw8Cy0gGgFntdZBWut7wDKgZxbHlCKtdYjW+lDy8yggENPJULajlCoLeAI/ZHUs5iilXDD95/oRQGt9T2t9K2ujMssByKOUcgDyAlezOJ4HtNbbgYjH3u6J6aKC5H97ZWpQqUgpVq3131rrhOSXe4GymR7Ys0vqYRuRutgmpB62AqmHs5bWOlBrfcrCYubqZmsdV2ldTzvgnNb6Qjq3Z40YrF3e8Hps9Btk5De4J7BYm+wFCiqlShksa7U4tNa7tdY3k1/aoo7IyN+TqfviMS8Dv6VzW6lK5TflYTY5Lp6FBEQZ4NJDry+TjU8m71NKuQL1gH1ZG0mq/geMBpKyOhALKgHXgZ+UqYnyD0qpfFkdVEq01leAr4CLQAgQqbX+O2ujsqiE1joETD+aQPEsjseoNzBldEXmkHrYdqQutiKphzOV1MNZz1zdbK3jKq3reYknL7TeTW7+vTCd3R+MxqCBv5VSB5VSw9JR3lpxAKn+BqVnXxj5DU5tGWv+fqd1XUN4tI5I7fuxRQxNlVJHlVLrlVI101jWmnGglMoLdAZWPvS2NfaFETY5Lp6FBIRK4b1sPfWHUio/poPsfa317ayO53FKqW5AmNb6YFbHYoADpqZF32ut6wF3MTV7y3aSf0h6AhWB0kA+pdSgrI3q6aOUGg8kAL9mdSzPEKmHbUDqYuuTejhzSD1sHUqpTcl9wx9/GL0TaZW62Qpx3F9PLqAH8PtDb38PVAbqYkoKfm3DGJprretjavr/jlLq+bTEb8U4UvsNMrQvUlpdCu89/j2ntow1f78Nr0sp1QZTAmLMQ29n+PsxGMMhTF2A6gDfAn+moaw147ivO7BLa/1wSwVr7AsjbHJcOKQ7nJzjMlDuoddlyUbNKR+nlHLEVOH8qrVeldXxpKI50EOZBr9xAlyUUku01tnxJO0ycFlrfT97/AfZ8KQ3WXvgvNb6OoBSahWmvnBLsjQq80KVUqW01iHJTbLCsjogc5RSrwLdgHY6uRObyBRSD9uG1MXWJ/WwjUk9bD1a6/YZXIW5utnwcWUuDqVUWo7PLsAhrXXoQ+t+8FwptQBIcbBda8Sgtb6a/G+YUmo1pmbm28nkfZHab5DRfZECI7/BqS2Ty0BZowydCyilamPqVthFax1+/30z349VY3j4poPW2kcp9Z1SqqjR+K0Vx0OeaBVkpX2RkTgzdFw8Cy0gDgBVlVIVkzOrLwFrszimFCmlFKb+sYFa6xlZHU9qtNZjtdZltdaumPbnP9n0hBet9TXgklKqevJb7YCALAzJnItAE6VU3uRjoR2mvn/Z2Vrg1eTnrwJrsjAWs5RSnTFl0ntoraOzOp5njNTDNiB1sU1IPWxDUg9nO+bqZmsdV2lZzxP93JMv1O/rDaQ4Wn9GY1BK5VNKOd9/jmnAVH+j5a0YR6q/QRnYF0Z+g9cCg5VJE0zdz0IMljXK4rqUUuWBVcArWuvTD71v7vuxdgwlk78HlFKNMF0vhxspa804krdfAGjFQ8eKFfeFEbY5LnQGR8/MCQ9MI3iexjRa5/isjsdMnC0wNV85BhxJfnTN6rgsxNya7D/yel3AL3m//kny6LrZ8QFMAU5iqkh+AXJndUwPxfYbpiZ/8ZgyokOAIsBm4Ezyv4WzOk4zsZ7F1F/t/v+tuVkd57P0kHrY5nFLXWy9OKUetl2sUg9n3v7vnbzf44BQYGPy+6UBn4eWS7FuttZxldp6UogjL6aLvAKPlf8FOJ5cb6wFStkiBkzj1BxNfpzIqn1h7jcoI/sipe8ZeBt4O/m5AuYkf36ch2ZOSe0YSec+sBTHD8DNh/52P0vfjw1ieDd5G0cxDYTZLCv2RfLr14Blj5Wz5r5IqZ62+XGhklcghBBCCCGEEEIIYTPPQhcMIYQQQgghhBBCZDFJQAghhBBCCCGEEMLmJAEhhBBCCCGEEEIIm5MEhBBCCCGEEEIIIWxOEhBCCCGEEEIIIYSwOUlAiGeWUqqgUmpEVschhBDPKqmHhRBCiGeLJCDEs6wgICe+QgiRdaQeFkKILKSUKqWUWpf8vK5SqutDn3VTSk3JuujE00gSEOJZNg2orJQ6opSantXBCCHEM0jqYSGEyFqjgAXJz+sCXR/6zBvooZTKm+lRiaeW0lpndQxCZAmllCuwTmtdK4tDEUKIZ5LUw0IIkTmUUg2BH4FGgD2wH3gRWAu4Axo4C+QBrgCfa62XK6VmAnu01iuyJHDx1HHI6gCEEEIIIYQQQtiO1vqAUmotMBVTkmEJcBe4qbWOA1BKTQI8tNbvPlTUD2gJSAJCWIUkIIQQQgghhBDi6fcJcACIBd4DGgPXLZQJA0rbOC7xDJEEhHiWRQHOWR2EEEI8w6QeFkKIzFMYyA84Ak5ATPK/5txfTgirkEEoxTNLax0O7FJK+cvgZ0IIkfmkHhZCiEw1H5gI/Ap8AZwGXB/6PKWkcDXAPzOCE88GaQEhnmla6wFZHYMQQjzLpB4WQgjbU0oNBhK01kuVUvbAbkxdMM4ppaporc8CWwAvpdQRkgehBNoAY7MscPHUkVkwhBBCCCGEEOIZpJTqDTTQWk9I4bMSwFKtdbvMj0w8raQFhBBCCCGEEEI8g7TWq5VSRVL5uDzwYWbGI55+0gJCCCGEEEIIIYQQNieDUAohhBBCCCGEEMLmJAEhhBBCCCGEEEIIm5MEhBBCCCGEEEIIIWxOEhBCCCGEEEIIIYSwOUlACCGEEEIIIYQQwub+H36IGzTbf2+2AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "\n", "# Attention à l'ordre des paramètres dans pphi et dans odeint\n", "pphi_odeint = lambda yy,t : [ phi1(t,yy[0],yy[1]) , phi2(t,yy[0],yy[1]) ]\n", "uu_odeint, ww_odeint = odeint(pphi_odeint,[x0,y0],tt).T\n", "\n", "JJ_odeint = [uu_odeint[i]**2+ww_odeint[i]**2 for i in range(len(tt))]\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_odeint,tt,ww_odeint)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('ODEINT - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_odeint)\n", "xlabel('t')\n", "title('ODEINT - Invariant')\n", "\n", "subplot(1,3,3)\n", "Y1,Y2 = meshgrid(linspace(min(uu_odeint),max(uu_odeint),21),linspace(min(ww_odeint),max(ww_odeint),21))\n", "V1,V2 = phi1(tt,Y1,Y2),phi2(tt,Y1,Y2)\n", "r=sqrt(V1**2+V2**2)\n", "quiver(Y1, Y2, V1/r, V2/r) \n", "plot(uu_odeint,ww_odeint)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('ODEINT - y(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution exacte**\n", "\n", "La solution exacte est\n", "\\begin{align*}\n", "x(t)&=\\cos(t),\\\\\n", "y(t)&=\\sin(t).\n", "\\end{align*}\n", "Cette solution est périodique de période $2\\pi$ et on a bien\n", "$$\n", "I(t)=x^2(t) + y^2(t) = 1 \\quad \\forall t.\n", "$$\n", "Vérifions-le avec le module `sympy`:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} x{\\left(t \\right)} = - y{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(x(t)) = -y(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = x{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y(t)) = x(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ x{\\left(t \\right)} = - C_{1} \\cos{\\left(t \\right)} - C_{2} \\sin{\\left(t \\right)}, \\ y{\\left(t \\right)} = - C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}\\right]$" ], "text/plain": [ "[x(t) = -C₁⋅cos(t) - C₂⋅sin(t), y(t) = -C₁⋅sin(t) + C₂⋅cos(t)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : -1, \\ C_{2} : 0\\right\\}$" ], "text/plain": [ "{C₁: -1, C₂: 0}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\cos{\\left(t \\right)}$" ], "text/plain": [ "x(t) = cos(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\sin{\\left(t \\right)}$" ], "text/plain": [ "y(t) = sin(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "x = sym.Function('x')\n", "y = sym.Function('y')\n", "edo1 = sym.Eq( sym.diff(x(t),t) , -y(t) )\n", "edo2 = sym.Eq( sym.diff(y(t),t) , x(t) )\n", "display(edo1)\n", "display(edo2)\n", "solgen = sym.dsolve([edo1,edo2],[x(t),y(t)])\n", "display(solgen)\n", "\n", "t_0=0\n", "x_0=1\n", "y_0=0\n", "consts = sym.solve( [ sym.Eq( x_0, solgen[0].rhs.subs(t,t_0)) , sym.Eq( y_0, solgen[1].rhs.subs(t,t_0)) ] , dict=True)[0]\n", "display(consts)\n", "solpar_1=solgen[0].subs(consts)\n", "solpar_2=solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(17,7))\n", "tt=linspace(0,4*pi,193)\n", "xx=func_1(tt)\n", "yy=func_2(tt)\n", "subplot(1,2,1)\n", "plot(tt,xx,tt,yy)\n", "legend([r'$x(t)$',r'$y(t)$'])\n", "subplot(1,2,2)\n", "plot(xx,yy)\n", "xlabel(r'$x$')\n", "ylabel(r'$y$')\n", "axis('equal');" ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "308px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }