{ "cells": [ { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import display, Latex\n", "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read()) " ] }, { "cell_type": "code", "execution_count": 30, "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 4 - Étude de la convergence" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

\n", "
" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "IPython.notebook.set_autosave_interval(300000)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Autosaving every 300 seconds\n" ] } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "%autosave 300\n", "\n", "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "WyG-bTRQE3f6" }, "source": [ "## Exercice\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", "$$\n", "\\begin{cases}\n", "y'(t) = y(t), &\\forall t \\in I=[0,1],\\\\\n", "y(0) = 1\n", "\\end{cases}\n", "$$\n", "dont la solution est $y(t)=e^{t}$. \n", "\n", "Estimer l'ordre de convergence des méthodes:\n", "1. EE, AB$_2$, AB$_3$, AB$_4$, AB$_5$, N$_2$, N$_3$, N$_4$, EM, RK4$_1$, RK6$_5$, RK7$_6$ \n", "2. EI, CN, AM$_2$, AM$_3$, AM$_4$, AM$_5$, MA$_2$, BDF$_2$, BDF$_3$, RK1_M\n", "3. Heun, AM$_4$-AB$_1$, AM$_4$-AB$_2$, AM$_4$-AB$_3$\n", " \n", " \n", "Remarque: puisque la fonction $\\varphi(t,y)=y$ est linéaire, toute méthode implicite peut être rendue explicite par un calcul élémentaire en explicitant directement pour chaque schéma l'expression de $u_{n+1}$. Cependant, nous pouvons utiliser le le module `SciPy` sans modifier l'implémentation des schémas (mais on payera l'ordre de convergence de `fsolve`).\n", "\n", "**Attention: les schémas multistep ont besoin d'initialiser plusieurs pas de la suite définie pas récurrence pour pouvoir démarrer. \n", "Dans cette étude, au lieu d'utiliser un schéma d'ordre inférieur pour initialiser la suite, on utilisera la solution exacte (en effet, l'utilisation d'un schéma d'ordre inférieur dégrade l'ordre de précision).**" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "WyG-bTRQE3f6" }, "source": [ "
Rappels de la démarche pour le calcul de l'orde de convergence.\n", " \n", "+ On écrit les schémas numériques :\n", " + les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt` (qui change en fonction de `h`) \n", " + les valeurs $[u_0,u_1,\\dots,u_{N}]$ pour chaque méthode sont contenues dans le vecteur `uu`.\n", "+ Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$. On sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \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 $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$. \n", "+ 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 $\\ln(\\text{err})$.\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schémas explicites" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "y69SGZjfIDo9" }, "source": [ "### Schéma de Adam-Bashforth à 1 pas = 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": 32, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "_Bgo6mNyIQgu" }, "outputs": [], "source": [ "def EE(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " uu.append(uu[i]+h*phi(tt[i],uu[i]))\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "bJ2pbhejIQM2" }, "source": [ "### Schéma de Adam-Bashforth à 2 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(3\\varphi(t_n,u_n)-\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "g38fKrIgSiBQ" }, "outputs": [], "source": [ "def AB2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " uu.append( uu[i] + (3*k1-k2)*h/2 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "nI8swyc6RxIR" }, "source": [ "### Schéma de Adam-Bashforth à 3 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_n+\\frac{h}{12}\\Bigl(23\\varphi(t_n,u_n)-16\\varphi(t_{n-1},u_{n-1})+5\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "3ymFHJHrSkOh" }, "outputs": [], "source": [ "def AB3(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " uu.append( uu[i] + (23*k1-16*k2+5*k3)*h/12 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "awcWzBp7SXvQ" }, "source": [ "### Schéma de Adam-Bashforth à 4 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_n+\\frac{h}{24}\\Bigl(55\\varphi(t_n,u_n)-59\\varphi(t_{n-1},u_{n-1})+37\\varphi(t_{n-2},u_{n-2})-9\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "-r1BaNeLTrHq" }, "outputs": [], "source": [ "def AB4(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " uu.append( uu[i] + (55*k1-59*k2+37*k3-9*k4)*h/24 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "heLmvMe_S0y6" }, "source": [ "### Schéma de Adam-Bashforth à 5 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{4}=y_4,\\\\\n", "u_{n+1}=u_n+\\frac{h}{720}\\Bigl(1901\\varphi(t_n,u_n)-2774\\varphi(t_{n-1},u_{n-1})+2616\\varphi(t_{n-2},u_{n-2})-1274\\varphi(t_{n-3},u_{n-3})+251\\varphi(t_{n-4},u_{n-4})\\Bigr)& n=4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "yPXMx8CITt4C" }, "outputs": [], "source": [ "def AB5(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " uu.append(sol_exacte(tt[4]))\n", " for i in range(4,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " k5 = phi( tt[i-4], uu[i-4] )\n", " uu.append( uu[i] + (1901*k1-2774*k2+2616*k3-1274*k4+251*k5)*h/720 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "OldEmxFfTJfq" }, "source": [ "### Schéma de Nylström à 2 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{n+1}=u_{n-1}+2h\\varphi(t_{n},u_{n})& n=1,2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "BCR9Z7VzTxEN" }, "outputs": [], "source": [ "def N2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " k1 = phi( tt[i], uu[i] )\n", " uu.append( uu[i-1] + 2*h*k1 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "dADQEhyYTVQz" }, "source": [ "### Schéma de Nylström à 3 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(7\\varphi(t_{n},u_{n})-2\\varphi(t_{n-1},u_{n-1})+\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "bS1FABgRTzdC" }, "outputs": [], "source": [ "def N3(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " uu.append( uu[i-1] + (7*k1-2*k2+k3)*h/3 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "LsgdqQnfTf66" }, "source": [ "### Schéma de Nylström à 4 pas\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{1}=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(8\\varphi(t_{n},u_{n})-5\\varphi(t_{n-1},u_{n-1})+4\\varphi(t_{n-2},u_{n-2})-\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "dbDTaW5LUcss" }, "outputs": [], "source": [ "def N4(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " uu.append( uu[i-1] + (8*k1-5*k2+4*k3-k4)*h/3 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "p4f0txAsIwNG" }, "source": [ "### Schéma d'Euler modifié\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+\\frac{h}{2}\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2},\\tilde u\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "O5rOYvtPI7TO" }, "outputs": [], "source": [ "def EM(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\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": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK4-1\n", "$$\\begin{cases}\n", "u_0 = y_0 \\\\\n", "K_1 = \\varphi\\left(t_n,u_n\\right)\\\\\n", "K_2 = \\varphi\\left(t_n+\\frac{h}{2},u_n+\\frac{h}{2} K_1)\\right)\\\\\n", "K_3 = \\varphi\\left(t_n+\\frac{h}{2},u_n+\\frac{h}{2}K_2\\right)\\\\\n", "K_4 = \\varphi\\left(t_{n+1},u_n+h K_3\\right)\\\\\n", "u_{n+1} = u_n + \\frac{h}{6}\\left(K_1+2K_2+2K_3+K_4\\right) & n=0,1,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK4(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i]+h/2 , uu[i]+h*k1/2 )\n", " k3 = phi( tt[i]+h/2 , uu[i]+h*k2/2 )\n", " k4 = phi( tt[i+1] , uu[i]+h*k3 )\n", " uu.append( uu[i] + (k1+2*k2+2*k3+k4)*h/6 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK6_5 (Butcher à 6 étages d'ordre 5)\n", "$$\\begin{array}{c|cccccc} 0 & 0 & 0 & 0 & 0 &0&0 \\\\ \\frac{1}{4} & \\frac{1}{4} & 0&0&0&0&0\\\\ \\frac{1}{4} & \\frac{1}{8} &\\frac{1}{8}&0&0&0&0\\\\ \\frac{1}{2} & 0 &-\\frac{1}{2}&1&0&0&0\\\\ \\frac{3}{4} & \\frac{3}{16} &0&0&\\frac{9}{16}&0&0\\\\ 1 & \\frac{-3}{7} &\\frac{2}{7}&\\frac{12}{7}&\\frac{-12}{7}&\\frac{8}{7}&0\\\\ \\hline & \\frac{7}{90} & 0&\\frac{32}{90} & \\frac{12}{90} & \\frac{32}{90} & \\frac{7}{90} \\end{array}$$\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK6_5(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " k1 = phi( tt[i] , uu[i] )\n", " k2 = phi( tt[i]+h/4 , uu[i]+h*k1/4 )\n", " k3 = phi( tt[i]+h/4 , uu[i]+h*(k1+k2)/8 )\n", " k4 = phi( tt[i]+h/2 , uu[i]+h*(-k2+2*k3)/2 )\n", " k5 = phi( tt[i]+h*3/4, uu[i]+h*(3*k1+9*k4)/16 )\n", " k6 = phi( tt[i+1] , uu[i]+h*(-3*k1+2*k2+12*k3-12*k4+8*k5)/7 )\n", " uu.append( uu[i] + (7*k1+32*k3+12*k4+32*k5+7*k6)*h/90 )\n", " return uu\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_50Xo95mT9tC" }, "source": [ "### Schéma de Runge-Kutta RK7_6 (Butcher à 7 étages d'ordre 6)\n", "$$\n", "\\begin{array}{c|ccccccc} \n", "0 & 0 & 0 & 0 & 0 &0&0&0 \\\\ \n", "\\frac{1}{2} & \\frac{1}{2} & 0&0&0&0&0&0\\\\ \n", "\\frac{2}{3} & \\frac{2}{9} &\\frac{4}{9}&0&0&0&0&0\\\\ \n", "\\frac{1}{3} & \\frac{7}{36} &\\frac{2}{9}&-\\frac{1}{12}&0&0&0&0\\\\ \n", "\\frac{5}{6} & -\\frac{35}{144} &-\\frac{55}{36}&\\frac{35}{48}&\\frac{15}{8}&0&0&0\\\\ \n", "\\frac{1}{6} & -\\frac{1}{360} &-\\frac{11}{36}&-\\frac{1}{8}&\\frac{1}{2}&\\frac{1}{10}&0&0\\\\ \n", "1 & \\frac{-41}{260} &\\frac{22}{13}&\\frac{43}{156}&-\\frac{118}{39}&\\frac{32}{195}&\\frac{80}{39}&0\\\\ \n", "\\hline \n", " & \\frac{13}{200} & 0&\\frac{11}{40} & \\frac{11}{40} & \\frac{4}{25} & \\frac{4}{25} & \\frac{13}{200} \\end{array}$$\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "rbRn1INwGY-8" }, "outputs": [], "source": [ "def RK7_6(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " k1 = phi( tt[i] , uu[i] )\n", " k2 = phi( tt[i]+h/2 , uu[i]+h*( k1 )/2 )\n", " k3 = phi( tt[i]+h*2/3, uu[i]+h*( 2*k1 +4*k2 )/9 )\n", " k4 = phi( tt[i]+h/3 , uu[i]+h*( 7*k1 +8*k2 -3*k3 )/36 )\n", " k5 = phi( tt[i]+h*5/6, uu[i]+h*( -35*k1 -220*k2 +105*k3 +270*k4 )/144 )\n", " k6 = phi( tt[i]+h/6 , uu[i]+h*( -k1 -110*k2 -45*k3 +180*k4 +36*k5 )/360 )\n", " k7 = phi( tt[i+1] , uu[i]+h*(-41/260*k1 +22/13*k2 +43/156*k3 -118/39*k4 +32/195*k5 +80/39*k6) )\n", " uu.append( uu[i] + (13/200*k1+11/40*k3+11/40*k4+4/25*k5+4/25*k6+13/200*k7)*h )\n", " return uu " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schémas implicites" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "y69SGZjfIDo9" }, "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", "avec $u_{n+1}$ zéro de la fonction $$x\\mapsto -x+u_n+h\\varphi(t_{n+1},x).$$" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "_Bgo6mNyIQgu" }, "outputs": [], "source": [ "def EI(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*phi(tt[i+1],x), uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "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 $u_{n+1}$ un 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": 45, "metadata": {}, "outputs": [], "source": [ "def CN(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\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])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=u_n+\\frac{h}{12}\\Bigl(5\\varphi(t_{n+1},u_{n+1})+8\\varphi(t_n,u_n)-\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "def AM2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*( 5*phi(tt[i+1],x)+8*phi(tt[i],uu[i])-phi(tt[i-1],uu[i-1]) )/12, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-3\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=u_n+\\frac{h}{24}\\Bigl(9\\varphi(t_{n+1},u_{n+1})+19\\varphi(t_n,u_n)-5\\varphi(t_{n-1},u_{n-1})+\\varphi(t_{n-2},u_{n-2})\\Bigr)& n=2,3,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "def AM3(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*( 9*phi(tt[i+1],x)+19*phi(tt[i],uu[i])-5*phi(tt[i-1],uu[i-1])+phi(tt[i-2],uu[i-2]) )/24, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-4\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{n+1}=u_n+\\frac{h}{720}\\Bigl(251\\varphi(t_{n+1},u_{n+1})+646\\varphi(t_n,u_n)-264\\varphi(t_{n-1},u_{n-1})+106\\varphi(t_{n-2},u_{n-2})-19\\varphi(t_{n-3},u_{n-3})\\Bigr)& n=3,4,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "def AM4(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*( 251*phi(tt[i+1],x)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de AM-5\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{3}=y_3,\\\\\n", "u_{4}=y_4,\\\\\n", "u_{n+1}=u_n+\\frac{h}{1440}\\Bigl(475\\varphi(t_{n+1},u_{+1})+1427\\varphi(t_n,u_n)-798\\varphi(t_{n-1},u_{n-1})+482\\varphi(t_{n-2},u_{n-2})-173\\varphi(t_{n-3},u_{n-3})+27\\varphi(t_{n-4},u_{n-4})\\Bigr),& n=4,5,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def AM5(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " uu.append(sol_exacte(tt[4]))\n", " for i in range(4,N):\n", " temp = fsolve(lambda x: -x+uu[i]+h*( 475*phi(tt[i+1],x)+1427*phi(tt[i],uu[i])-798*phi(tt[i-1],uu[i-1])+482*phi(tt[i-2],uu[i-2])-173*phi(tt[i-3],uu[i-3])+27*phi(tt[i-4],uu[i-4]))/1440, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma MS-2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=u_{n-1}+\\frac{h}{3}\\Bigl(\\varphi(t_{n+1},u_{n+1})+4\\varphi(t_n,u_n)+\\varphi(t_{n-1},u_{n-1})\\Bigr)& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "def MS2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " temp = fsolve(lambda x: -x+uu[i-1]+h*(phi(tt[i+1],x)+4*phi(tt[i],uu[i])+phi(tt[i-1],uu[i-1]) )/3, uu[i])[0]\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma BDF2\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{n+1}=\\frac{4}{3}u_n-\\frac{1}{3}u_{n-1}+\\frac{2}{3}h\\varphi(t_{n+1},u_{n+1})& n=1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "def BDF2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " for i in range(1,N):\n", " temp = fsolve(lambda x: -x+4/3*uu[i]-1/3*uu[i-1] + 2/3*h*phi(tt[i+1],x) , uu[i])[0]\n", " uu.append(temp)\n", " return uu " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma BDF3\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_1=y_1,\\\\\n", "u_{2}=y_2,\\\\\n", "u_{n+1}=\\frac{18}{11}u_n-\\frac{9}{11}u_{n-1}+\\frac{2}{11}u_{n-2}+\\frac{6}{11}h\\varphi(t_{n+1},u_{n+1})& n=2,3,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "def BDF3(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " for i in range(2,N):\n", " temp = fsolve(lambda x: -x+18/11*uu[i]-9/11*uu[i-1] + 2/11*uu[i-2]+6/11*h*phi(tt[i+1],x) , uu[i])[0]\n", " uu.append(temp)\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": 53, "metadata": {}, "outputs": [], "source": [ "def RK1_M(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\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": [ "## Schémas predicteur-correcteur" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma de Heun\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+h\\varphi(t_n,u_n)\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},\\tilde u)\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "1ewZyxhHRYxg" }, "outputs": [], "source": [ "def heun(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " for i in range(N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i+1], uu[i] + k1*h )\n", " uu.append( uu[i] + (k1+k2)*h/2 )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "23PyYGzhQwuo" }, "source": [ "### Schéma AM-4 AB-2/3/4/5\n", "\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "def AM4AB2(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " pred = uu[i] + (3*k1-k2)*h/2\n", " uu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", " return uu\n", " \n", "def AM4AB3(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " pred = uu[i] + (23*k1-16*k2+5*k3)*h/12\n", " uu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", " return uu\n", " \n", "def AM4AB4(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " for i in range(3,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " pred = uu[i] + (55*k1-59*k2+37*k3-9*k4)*h/24\n", " uu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", " return uu\n", " \n", "def AM4AB5(phi,tt,sol_exacte):\n", " h = tt[1]-tt[0]\n", " uu = [sol_exacte(tt[0])]\n", " uu.append(sol_exacte(tt[1]))\n", " uu.append(sol_exacte(tt[2]))\n", " uu.append(sol_exacte(tt[3]))\n", " uu.append(sol_exacte(tt[4])) \n", " for i in range(4,N):\n", " k1 = phi( tt[i], uu[i] )\n", " k2 = phi( tt[i-1], uu[i-1] )\n", " k3 = phi( tt[i-2], uu[i-2] )\n", " k4 = phi( tt[i-3], uu[i-3] )\n", " k5 = phi( tt[i-4], uu[i-4] )\n", " pred = uu[i] + (1901*k1-2774*k2+2616*k3-1274*k4+251*k5)*h/720\n", " uu.append(uu[i]+h*( 251*phi(tt[i+1],pred)+646*phi(tt[i],uu[i])-264*phi(tt[i-1],uu[i-1])+106*phi(tt[i-2],uu[i-2])-19*phi(tt[i-3],uu[i-3]) )/720)\n", " return uu\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "cnwNf75iGe0F" }, "source": [ "On initialise le problème de Cauchy" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "OLLu4aFJFENg" }, "outputs": [], "source": [ "t0, y0, tfinal = 0, 1, 3" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ve4iOfOIGsYc" }, "source": [ "On définit la solution exacte:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "W3EcAN2eGz2j" }, "outputs": [], "source": [ "def sol_exacte(t):\n", " return exp(t)\n", " #return exp(-t)\n", " #return sqrt(2.*t+1.)\n", " #return sqrt(t**2+1.)\n", " #return 1./sqrt(1.-2.*t)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "xpjn_ogYGo20" }, "source": [ "On définit l'équation différentielle : `phi` est une fonction python qui contient la fonction mathématique $\\varphi(t, y)$ dépendant des variables $t$ et $y$." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "df9F-MXWGm2a" }, "outputs": [], "source": [ "def phi(t,y):\n", " return y\n", " #return -y\n", " #return 1./y \n", " #return t/y \n", " #return y**3 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$, à savoir $N_k=2$, $2^2$, $2^3$, ... $2^{10}$). 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 $e_k=\\max_{i=0,...,N_k}|y(t_i)-u_{i}|$ avec $N_k=2^{k+1}$.\n", "\n", "\n", "Nous pouvons utiliser deux méthodes différentes pour stocker ces informations. \n", "\n", "### Méthode 1\n", "\n", "La première méthode est celle utilisée lors des deux premiers TP: on crée autant de liste que de solutions approchée." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [], "source": [ "H = []\n", "\n", "err_ep = []\n", "err_AB2 = []\n", "err_AB3 = []\n", "err_AB4 = []\n", "err_AB5 = []\n", "err_N2 = []\n", "err_N3 = []\n", "err_N4 = []\n", "err_RK4 = []\n", "err_RK6_5 = []\n", "err_RK7_6 = []\n", "\n", "err_er = []\n", "err_CN = []\n", "err_AM2 = []\n", "err_AM3 = []\n", "err_AM4 = []\n", "err_AM5 = []\n", "err_BDF2 = []\n", "err_BDF3 = []\n", "err_MS2=[]\n", "\n", "err_em = []\n", "err_heun = []\n", "err_AM4AB2 = []\n", "err_AM4AB3 = []\n", "err_AM4AB4 = []\n", "err_AM4AB5 = []\n", "\n", "N=10\n", "for k in range(6):\n", " N += 50 #2**(k+3)\n", " tt = linspace(t0,tfinal,N+1)\n", " h = tt[1]-tt[0]\n", " H.append(h)\n", " yy = array([sol_exacte(t) for t in tt])\n", " \n", " # schemas explicites\n", " uu_ep = EE(phi,tt,sol_exacte)\n", " uu_AB2 = AB2(phi,tt,sol_exacte)\n", " uu_AB3 = AB3(phi,tt,sol_exacte)\n", " uu_AB4 = AB4(phi,tt,sol_exacte)\n", " uu_AB5 = AB5(phi,tt,sol_exacte)\n", " uu_N2 = N2(phi,tt,sol_exacte)\n", " uu_N3 = N3(phi,tt,sol_exacte)\n", " uu_N4 = N4(phi,tt,sol_exacte)\n", " uu_em = EM(phi,tt,sol_exacte)\n", " uu_RK4 = RK4(phi,tt,sol_exacte)\n", " uu_RK6_5 = RK6_5(phi,tt,sol_exacte)\n", " uu_RK7_6 = RK7_6(phi,tt,sol_exacte)\n", " # schemas implicites\n", " uu_er = EI(phi,tt,sol_exacte)\n", " uu_CN = CN(phi,tt,sol_exacte)\n", " uu_AM2 = AM2(phi,tt,sol_exacte)\n", " uu_AM3 = AM3(phi,tt,sol_exacte)\n", " uu_AM4 = AM4(phi,tt,sol_exacte)\n", " uu_AM5 = AM5(phi,tt,sol_exacte)\n", " uu_BDF2 = BDF2(phi,tt,sol_exacte)\n", " uu_BDF3 = BDF3(phi,tt,sol_exacte)\n", " uu_MS2 = MS2(phi,tt,sol_exacte)\n", " # schemas predictor-corrector\n", " uu_heun = heun(phi,tt,sol_exacte)\n", " uu_AM4AB2 = AM4AB2(phi,tt,sol_exacte)\n", " uu_AM4AB3 = AM4AB3(phi,tt,sol_exacte)\n", " uu_AM4AB4 = AM4AB4(phi,tt,sol_exacte)\n", " uu_AM4AB5 = AM4AB5(phi,tt,sol_exacte)\n", " \n", " # erreurs\n", " err_ep.append( norm(uu_ep-yy,inf))\n", " err_AB2.append(norm(uu_AB2-yy,inf))\n", " err_AB3.append(norm(uu_AB3-yy,inf))\n", " err_AB4.append(norm(uu_AB4-yy,inf))\n", " err_AB5.append(norm(uu_AB5-yy,inf))\n", " err_N2.append( norm(uu_N2-yy,inf))\n", " err_N3.append(norm(uu_N3-yy,inf))\n", " err_N4.append(norm(uu_N4-yy,inf))\n", " err_em.append(norm(uu_em-yy,inf))\n", " err_RK4.append(norm(uu_RK4-yy,inf))\n", " err_RK6_5.append(norm(uu_RK6_5-yy,inf))\n", " err_RK7_6.append(norm(uu_RK7_6-yy,inf))\n", " \n", " err_er.append(norm(uu_er-yy,inf))\n", " err_CN.append(norm(uu_CN-yy,inf))\n", " err_AM2.append(norm(uu_AM2-yy,inf))\n", " err_AM3.append(norm(uu_AM3-yy,inf))\n", " err_AM4.append(norm(uu_AM4-yy,inf))\n", " err_AM5.append(norm(uu_AM5-yy,inf))\n", " err_BDF2.append(norm(uu_BDF2-yy,inf))\n", " err_BDF3.append(norm(uu_BDF3-yy,inf))\n", " err_MS2.append(norm(uu_MS2-yy,inf))\n", " \n", " err_heun.append(norm(uu_heun-yy,inf))\n", " err_AM4AB2.append(norm(uu_AM4AB2-yy,inf))\n", " err_AM4AB3.append(norm(uu_AM4AB3-yy,inf))\n", " err_AM4AB4.append(norm(uu_AM4AB4-yy,inf))\n", " err_AM4AB5.append(norm(uu_AM4AB5-yy,inf))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "SnKKU27oGyQb" }, "source": [ "Pour estimer l'ordre de convergence on estime la pente de la droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$ en echelle logarithmique en utilisant la fonction `polyfit` basée sur la régression linéaire. " ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 } }, "colab_type": "code", "id": "ySox-VsNGt8p" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EE 0.97\n", "AB2 1.98\n", "AB3 2.96\n", "AB4 3.94\n", "AB5 4.92\n", "N2 1.99\n", "N3 2.97\n", "N4 3.95\n", "EM 1.98\n", "RK4 3.98\n", "RK6_5 4.95\n", "RK7_6 6.18\n", "\n", "\n", "EI 1.04\n", "CN 2.00\n", "AM2 2.98\n", "AM3 3.96\n", "AM4 4.95\n", "AM5 5.93\n", "BDF2 1.97\n", "BDF3 2.95\n", "MS2 4.00\n", "\n", "\n", "Heun 1.98\n", "AM4_AB2 2.95\n", "AM4_AB3 3.94\n", "AM4_AB4 4.93\n", "AM4_AB5 4.76\n" ] } ], "source": [ "print (f'EE {polyfit(log(H),log(err_ep), 1)[0]:1.2f}' )\n", "print (f'AB2 {polyfit(log(H),log(err_AB2), 1)[0]:1.2f}' )\n", "print (f'AB3 {polyfit(log(H),log(err_AB3), 1)[0]:1.2f}' )\n", "print (f'AB4 {polyfit(log(H),log(err_AB4), 1)[0]:1.2f}' )\n", "print (f'AB5 {polyfit(log(H),log(err_AB5), 1)[0]:1.2f}' )\n", "print (f'N2 {polyfit(log(H),log(err_N2), 1)[0]:1.2f}' )\n", "print (f'N3 {polyfit(log(H),log(err_N3), 1)[0]:1.2f}' )\n", "print (f'N4 {polyfit(log(H),log(err_N4), 1)[0]:1.2f}' )\n", "print (f'EM {polyfit(log(H),log(err_em), 1)[0]:1.2f}' )\n", "print (f'RK4 {polyfit(log(H),log(err_RK4), 1)[0]:1.2f}' )\n", "print (f'RK6_5 {polyfit(log(H),log(err_RK6_5), 1)[0]:1.2f}' )\n", "print (f'RK7_6 {polyfit(log(H),log(err_RK7_6), 1)[0]:1.2f}' )\n", "print('\\n')\n", "print (f'EI {polyfit(log(H),log(err_er), 1)[0]:1.2f}' )\n", "print (f'CN {polyfit(log(H),log(err_CN), 1)[0]:1.2f}' )\n", "print (f'AM2 {polyfit(log(H),log(err_AM2), 1)[0]:1.2f}' )\n", "print (f'AM3 {polyfit(log(H),log(err_AM3), 1)[0]:1.2f}' )\n", "print (f'AM4 {polyfit(log(H),log(err_AM4), 1)[0]:1.2f}' )\n", "print (f'AM5 {polyfit(log(H),log(err_AM5), 1)[0]:1.2f}' )\n", "print (f'BDF2 {polyfit(log(H),log(err_BDF2), 1)[0]:1.2f}' ) \n", "print (f'BDF3 {polyfit(log(H),log(err_BDF3), 1)[0]:1.2f}' )\n", "print (f'MS2 {polyfit(log(H),log(err_MS2), 1)[0]:1.2f}' )\n", "print('\\n')\n", "print (f'Heun {polyfit(log(H),log(err_heun), 1)[0]:1.2f}' )\n", "print (f'AM4_AB2 {polyfit(log(H),log(err_AM4AB2), 1)[0]:1.2f}' )\n", "print (f'AM4_AB3 {polyfit(log(H),log(err_AM4AB3), 1)[0]:1.2f}' )\n", "print (f'AM4_AB4 {polyfit(log(H),log(err_AM4AB4), 1)[0]:1.2f}' )\n", "print (f'AM4_AB5 {polyfit(log(H),log(err_AM4AB5), 1)[0]:1.2f}' )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour les schémas AM4-ABx, on remarque que l'ordre du schéma predictor corrector est égale à celui du predictor +1. Par conséquente, si le schéma corrector est d'ordre $p$ (ici $p=5$ pour le schéma AM4), pour ne pas perdre en ordre convergence il faut choisir un schéma predictor d'ordre $p-1$ (ici AB4).\n", "Est-ce outil de choisir un predictor d'ordre $p$?" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "4HPS2hE6G54k" }, "source": [ "Pour afficher l'ordre de convergence on utilise une échelle logarithmique : on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées. Le but de cette représentation est clair: si $\\text{err}=Ch^p$ alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$." ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "colab": { "autoexec": { "startup": false, "wait_interval": 0 }, "base_uri": "https://localhost:8080/", "height": 3818, "output_extras": [ { "item_id": 1 }, { "item_id": 2 }, { "item_id": 3 }, { "item_id": 4 }, { "item_id": 5 }, { "item_id": 6 }, { "item_id": 7 }, { "item_id": 8 }, { "item_id": 9 }, { "item_id": 10 }, { "item_id": 11 } ] }, "colab_type": "code", "executionInfo": { "elapsed": 2188, "status": "ok", "timestamp": 1520423878951, "user": { "displayName": "Gloria Faccanoni", "photoUrl": "//lh4.googleusercontent.com/-gY6sCpFtBJo/AAAAAAAAAAI/AAAAAAAABdo/a_W4-RMG5X0/s50-c-k-no/photo.jpg", "userId": "116371262733782746288" }, "user_tz": -60 }, "id": "oz1tVYNtG4-3", "outputId": "9b89f5ec-83c5-4797-e057-8d6c20560051" }, "outputs": [ { "data": { "image/png": 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RERERERERkSWlgJOIiIiIiIiIiCwpBZxERERERERERGRJKeAkIiIiIiIiIiJLSgEnERERERERERFZUgo4iYiIiIiIiIjIklLASURERERERERElpQCTiIiIiIiIiIisqQUcBIRERERERERkSWlgJOIiIiIiIiIiCwpBZxERERERERERGRJKeAkInI+u+8+6O4Gj8d5vO++ardIRERWC50jRESkgoce2s2TT76fVGp02b6jZtnWLCIiy+u+++DmmyGRcF4PDDivAW68sXrtEhGR6tM5QkRE5hGPP0IicZCxsXtpaflNurvvJBBoXdLvUMBJRKSaslmYmHCm8fHFPU4/f/RRZ/liiQR8/OP6MSEishbl88454OTJhafvfQ9SqdLldY4QEVn3stlxYrFHALA2jbUwOvoFxsb+mpaWm+juvm3JAk8KOImInI18HmKxxQWG5nucvvM8H68X6uqgvn7msa0NDhwoP//g4NJuq4iILK1cDk6fnj9gdOLE3PdOnXLOP5VEIrBxozPNDjZN0zlCRGTdSKfHmJw8QCx2gFjsYSYnD5BMHi47bz6fZHT0cyQSj7N79wNL8v0KOInI+mItTE2deWBo9nuTk866FhKNlgaKNm6Enh7n9ewgUqXHUAiMmbvu7m6ni8RsnZ3nvJtERGQRMhknCLRQoGj2dPr0/OvdsGEmcDR93ih+XW5qaAC/f2YdOkeIiKwb1lpSqUEmJx8mFjtQeEynRwrzBIO9RKN7aG19F5HIbh599PrCZ8b4McbL5s030dV125K1SwEnETl/ZDJnHhgq9zi7G1o5odDcwE9LS+XAULn3olGnUOtyufvu0vocALW1zvsiIrJ4yeTiuqnNniYnK6/T43GCQNMBoeZmuOiihQNHGzZAzRJcouscISKyJlmbI5F4mlhsOrjkZC9ls6fcOTzU1m6noeFlRCJ7iER2E4nswufbMGddswNNgcDmJW2rAk4i4hQW/fjHnTT7zk7nYnQp6zvkcs5F+ZnWKpodREomF/6umhon4FMc/OnsnD8wVC545PMt3fYvl+m/0XL+7UREzhfWOsGVswkczde9uaamNCDU3g47d84NFDU2lr6uq1vemw4L0TlCROS8l8+niccfL8laisUeIZ93zlvG+IlELqO5+Y1EInuIRncTDu/E661dcN3h8C7q669clkDTNAWcRNa7+UaxeetbnffPNasoFlu4HcbMDQht2gTbti0uQDT9PBgs3/1srbrxRv14EJG1xVrnJsVig0XFXdjS6crr9ftLg0I9PfD855cPFhVPkcj5e17ROUJE5LyRy8WJxX5ZElyKxx/D2gwAXm+ESGQ3ra3vIRLZTTS6h9ra7Xg8Z3ej/IorKtSDXUIKOImsVdOjn42PlwZ/Zr++5565d3YTCXj72+Ed73CykxYSDs8NBLW3n1lWUThc3TvBIiJS2dlkwubzznnmTIpiT0/znXtqa0uDRNu3L9xNbePGyvXwREREVlgmc7KoO5zTJS6ReBJwasT6fE1EIrvZsuV3iUZ3E4nsIRTaijHn1+8lBZxEVhtrnZFlygWH5ntv9uvFjH7m8zl1kcrJ5+FjH1s4qygaXZpaEyIisjr99V/D+97nDLgATibsu94F3/0u9PZWDhqdOjX/4Ap1daUBoY6OxRXGDgZXZrtFRETOkbWWdHq0qDuck72USs0M6hAIdBCJ7GbTpre49Zb2EAi0Y9bATRL9SpT1ablqFuXzTvexhYJBC72uFAQqVpxVND11dJS+nv357NeBgNOloNwoNl1dKiwqIrJWWAvx+EwgqDgotNDzcoWx02n42tecjKHZI6pt3Tp/0Kix0VnmfKiVJyIiskjWWpLJvkIR7+ngUiZzvDBPKHQhdXUvIhp9vxtc2o3f31TFVi8vBZxk/alUsyifh+uvP7dg0cTE/Hdzwek2NjtjqLUVLr544QBR8XJLlVWkUWxERM4f2SycPn1mAaPp1/PdzPD5KhfG/sxnyi9jjLNOr3d5tlVERGSVyuezJBKHCt3hprvG5XITABhTQ23tpTQ2Xl/IWopEnkdNTbTKLV9ZCjjJ2jC7C9p8AaK//dvKNYsW4vfPDQBt3br4jKK6utVXfFSj2IiIzLWco3cWj6ZWLjA03/OJifnXPd1NraHBedy5c+Z5cbe02c9rayufm/7xH8tnwnZ2KtgkIiJrXi6XJB5/tKRLXDz+K/J5ZwRtjydEOHwZLS03FhXzvhSvV13AFXCSM7eUF+HWOjUhKgWLKtUvmv15KrXwd4XDTtBnvtpGn/nMwl3Q1iKNYiMiMmO+0TuLj5XT2UZn2kXt1Kn5R1Pz+UqDQm1tsGPH/AGjjRudbmrLUVNPmbAiIrJOZLMT7khxDxe6xsXjBwFnMAuvt55odDdtbe8vBJdCoQvxeBRaKUd7Rc5MuYvw974Xhofh6qvPPGA0MeFcsM/HGKcwdXHgp6UFLrxwbkBo9lSuC1p3d+WaRR/4wJLuLhERWeXKZRt96EPlM2Hf8x741Kdm5hsfn3/d0WhpYOjSS+cPGE0/D4eVCSsiIrLM0ulnCxlL013jpqaeKXzu87UQje6hsfG1RKN7iER2Ewz2rIli3itFAafVajlT+cGpVzS79tB8WUTT089/PrcGxNQUfPSj5b/H45kbBOrocO7UlssgKhcwikad9SwV3akVEVl7MpmZQNCZPi5moAaAZNKpuXfJJYvLNlpLRbGVCSsiIucpay2p1JAbXJop6J1KDRfmCQa7iUT20NLyjkJwKRBorWKr1wYFnFajhVL5s1knQLTYIFG5qdyIM7P5fHMDQJUuyo2B+++fO/98NSGqRXdqRUSW19neNJm+GXI2gaNYbP5119fPBIQaGkprG81+vPFGGB2du46uLvj2t89un4iIiMiyszbP1NQzJVlLk5MHyGZPuHN4qK29iPr6a4hGp4t578Lna6hqu9cqBZwqWa4Mo2x24WDQn/1Z+VT+d7wD3vc+Z1jjhcwubj3dDW2+bKLZUzA4N1hUqTtaZye86lVnvVtWnO7Uiogsj/vuc7paT005rwcG4N3vhgcecEbjnC9wdPq0E3SqJBgsDQx1dcHu3ZUDR9OP9fVnVtvoz/5MmbAiIiKrXD6fIZE4WAguOcW8f0ku59yEMsZPOLyD5uZfc0eK200kchleb7jKLV8/FHAqp1KGUS4H118P4+NEnnrKqftwpplF8xWsXkgu51zELzZYtBzUHU1EZHVY7q7XmYwTAKoUIKoUNDp2bO66Uin4whec5x5PaUCosRG2bZs/YNTQ4Eyh0NJt33yUCSsiIrKq5HIJYrFflWQtxeOPYq0zCIfHEyYS2cXmze90s5Z2Ew5fgsfjr3LL1zcFnMr5+McrZxi5Lq+0bDA4N/izZUv5oNCGDeVrFl10UeWi1p/+9JJt5lnRRbiISPUtdhS16S5qCwWJyn22UBe1aLQ0ILR9u/P4xS+Wn98YZ91LXZdvuSgTVkREpCoymdNuYGmmoHcicQhwsqBrajYSje5hy5YPEInsIRrdTSi0DWO81W24zKGAUzmDg5U/+8xnoL6ex4aG2HHVVXMDRv4liKCu9iwiXYSLiCx/htG02aOonTo1/yhqn/nMzHwLdVELBEoLXnd2wq5dlTOMpp/PVxD7+9+v3PW6vv7s94OIiIisOanUsUIR7+ngUjJ5pPC5399ONLqH5uY3EonsJhrdQyDQoZHizhMKOJXT2Vk5w+gDHwDguf37Yd++5fl+ZRGJiKxui80wKpZKVc4oWqir2pmMotbUBBdeODdItFJd1Fb7TRMRERFZUg89tJu6ur10d99WcWQ3ay3JZH+hO9x017h0eqYrfii0jWj0clpbb3YLeu/G79+0Upshy0ABp3JWw8WysohERFavSl2vb70VfvADOHWKXUeOONlF00GkhWr41deXBoO2bKmcYfS2t1UeRe3++5duO8+GbpqIiIisK/H4IyQSBxkbu5eWlpvo6voYudxESdZSLHaAbPa0u4SXcPgSGhpeSTS6xy3m/TxqapQJvdYo4FSOLpZFRGQ+lbpeT046AaeNG52aRcXFsOfrplZfD94zqDuw2kdR000TERGRdSGfTwFgbRprYXT0fzE6+peFzz2eIOHwZTQ3/3ohuBQO78DrXaGBQKSqFHCqRBfLIiJSyXxdr/v7AXhk/372qeu1iIiIrBG5XNwdKe5hN3PpYeLxx2fNZd1HQySyhz17/hWPR2GH9Up/eRERkTOlrtciIiKyhs0dKe5hEoknmR4pzudrIhLZQ0fHqxkc/GRhOWP8GONl8+ab6Oq6TcGmdU5/fRERkTOlDCMRERFZI9LpMbeQ98NFI8X1FT4PBLYQieymufnNbre4PQQC7YWR4gYHPzkn0BQIbK7W5sgqooCTiIjI2VCGkYiIiJxHrLWkUkMlWUuTkw+TTo8U5gkGtxKNPp/W1vcueqS4cHgX9fVXKtAkc5yXASdjTC/wcaDeWvvGardHREREREREZLWwNs/U1OGSrKXJyYfJZk+4c3iorb2YhoaXEYnscTOXdp3VSHFXXHFgaRsva8aKB5yMMV8GbgCOW2t3FL3/auCzgBf4orX2kxVWgbW2D3i3MeZ/L3d7RURERERERFarfD5LIvFESeZSLPYIudwkAMb4CId30tz8a0Qiu4lE9hCJXIbXW1vllstaV40Mp78C/gL46vQbxhgvcA/wCmAYeMgY8y2c4NMnZi3/Lmvt8ZVpqoiIiIiIiMjqkMsliccfK8lcisd/RT6fBMDjqSUSeR4tLW93s5Z2Ew5fisfjr3LLZT1a8YCTtfZHxpjuWW+/AHjGzVzCGPN3wOuttZ/AyYY6Y8aYm4GbAVpaWti/f//ZNrmsWCy25OsUERERERERAchmY8Tjvyypt5RIHMTaLABebz3R6B7a2n7Lrbe0h9raC3HyOUSqb7XUcGoHhopeDwMvrDSzMaYRuBvYbYz5AzcwVcJa+3ng8wCXX3653bdv35I2eP/+/Sz1OkVERERERGT9yWROFnWJcx6npp4CLAA+3yai0T00Nt5QyFwKBnsKI8WJrEarJeBU7n+JrTSztfYEcMvyNUdERM5nGlxCREREVqtUanRWvaUDJJP9hc8DgU6i0T20tLy1UNDb729VcEnOO6sl4DQMdBS93gKMVJhXRERmuWP/Hdyx745qN2NJaHAJERERWc0eemg3dXV76e6+jUCgteJ81lqSyYFCUGk6wJROHyvMEwpdQDT6QtrabnULeu/G729aic0QWXarJeD0EHCBMaYHOAq8BXhrdZskInL+uPOBO9dMwAkNLiEiIiKrWDz+CInEQcbG7qWl5Sa6u2/D729haurponpLB4jFHiabPeUu5SUcvoSGhle6XeL2EIk8j5qauqpui8hyWvGAkzHmb4F9QJMxZhi43Vr7JWPMfwL+CefHw5ettY+vdNtERFarbD7L6OQog+ODpdPEIEPjQwuv4DyyUoNLiIiIiJwta9NYC6Ojn2N09HOAB3CKeRvjJxK5jObmNxGJ7CYa3UM4vBOvN1TVNoustGqMUvcbFd7/DvCdFW6OiEjVWWs5nTzN4PggQxNDc4NK44OMTI6Qs7mS5YLeIMlcsvDa3On067/9mtvXUrbTtCUfXEKjmYqIiMhCcrkk8fijhVHiYrGHZ82RLzyGQhdy6aXfoLZ2Ox6Pb6WbKrLqrJYudSIia1Y6l2Z4YrgQPBoaHypkJ02/F0vHSpbxe/1sqdtCZ30nL+15KZ11nXTWz0wd9R1E/JHC/OZOg7294lgLa8GSDy6h0UxFRESkWDY7SSz2y6Lg0gHi8ccB56ZfTU0DkcjukmWM8WOMl82bb6Kr6zYCgc1VaLnI6qSAk4jIObDW8lziuTkZScWZSsdix7CzYiObwpvorO/kosaLeEXvK0qCSZ31nWwKb8JjPFXaqlVJg0uIiIjIkslkThYV8nYep6aeYvp+ls/XQjS6h8bG1xZqLgWDXRhj2L/fKNAksggKOImIzGMqM1Wxm9t0YCmZTZYsE6oJFQJH119wPR11HSXBpC11Wwj5lrYP/+3X3L6k61uFNLiEiIiInJVU6tickeKSyf7C54FAJ9HoHlpabiwEl+YbfS4c3kV9/ZUKNIksQAEnEVm38jbPseheDHwAACAASURBVNix0m5us7q6PZd4rmQZg6E12kpnfSe7W3fz+oteX+jiNh1Qagw1Yky5HmDLZy3VbNLgEiIiInI2rLWkUkNFI8U5j+n0aGGeUOgCotEX0tZ2K5HIbiKR3fj9TWf0PVdccWCpmy6yJingJCJr1mRqsmI3t8HxQYYnhsnkMyXLRPwRuuq76Kzv5Iq2K2ZqJrlZSu117fi9/ipt0fqgwSVERERkIdbmmZo6XBJYmpx8mGz2pDuHh3D4EhoaXk4kssfNXNpFTU1dVdstsp4o4CQi56VsPsvI5Mi8tZNOJ0+XLOM1Xtrr2ums72Rvx96yhbjrA/Urnp10rlKpUQ4efAuXXPJ1pXWLiEgJnSNkLcjnsyQSh0qCS7HYI+Ryk4BTuDsc3kFz8xsKwaVweCdeb22VWy6yvingJCKrjrWWU8lTpd3cZnV1G5kcIW/zJcttDG2ks76Trvouru68ek4h7tZIK16Pt0pbtTzuGxvj9598mNH87bT+/Bf86UWXc2NLS7WbJSIiq0R//x8yPv5j+vtv56KLPlft5ojw0EO7qavbS3f3bWXrJOXzKeLxx0qKecfjvySfd2pmejwhIpFdtLS8vVBvKRy+BI9HGegiq40CTiKy4lLZFMMTw2W7uU1P8Uy8ZBm/11/o1vaynpeVzU6K+CNV2qKVZ22O2x54Df+ND5IiDMBIPsy7nzjAoSc+y1377q9yC0VEZKVks5Mkk0dIJo8wNdVHMnmEo0fvAWZuzIyOfp7R0c/j8QR5yUumqtdYWffi8UdIJA4yNnYvLS1vo7HxdaRSg4XMpXj8MazNAuD11hGN7qGt7f1ucGk3tbUXYczauoEoslYp4CQiS8pay7OJZ0u7uY0PlWQnHYsdm7PcpvAmOus72d68nVdtfVVJEe7O+k42hTfhMZ4qbFF15HJxkslBEslBBmNHOZI4wWAyxmAqw9GMh9FcLT/n98jiK1kuRZCv+j/OXVVqt4iILL18PkMqNVQSUJp+TCb7yGRKB7jweuuord1ONjtOOn0MyOLxhGhqegNbt/636myErHuZzGlisUcAsDaNtTA6+kVGR78IQE3NRqLRK+jouI5IZDfR6B6CwR7MOrr+E1lrFHASkYI79t+x4GhniUyibFe34vdSuVTJMqGaUCFw9JoLXjOnEPeWui2EfKFl3LLVxdo86fRxUqlBnosP0pcYoz8xzmByiuF0nqNZP8fsBo6ziWdpJkcv0FtYvs6kaPOlyWbKH8KH0tkV2hIREVkK1loymWdLgkhTU86j83oIyBXmN6aGYLCbYLCHpqb/SCjUQzDYSzDYQyjUS01NA8YYnnzy1kJWUz6fwuutUx0nWRHp9LNuvaUDhbpLyeTheZYwhMM7eN7zvrtibRSR5aeAk4gU3PnAnbx3z3srdnMbHB/kxNSJkmUMhtZoK531nexu3c3rL3r9nK5ujaHG864Q97nI5ZKkUkPEpgYYjB/lSLw0O2kkF2KMZo6ziRhNwMxQvDXkaPFO0e7L82J/DZ0hHz21jfSEN9EdCtMRCFBX4xy6ux98kIFUas73dwYCK7WpIiKySLlc3A0izQ0oTU0dIZ+f1ZXcv5lgsIe6uqtoaSkNKAUC7YvqUpTJjNHWdgttbTczMvL5kqHhRZaCtZZ0eqRklLhY7GFSqeHCPMFgL9HoHlpb3000uodf/erVhc+M8WOMl82bb6Kr67ZqbIKILCMFnETWkVg6VjGQNDA+AMCWT28pWSbqj9K1oYuOug5e0P6COYW426Jt+L3rp0ijcxf6BKnUAMfjg/TFj9OfOMVgMslwJs/RjJ9jtq6QnZSnC+gqLF9nkrT70mz1w0sDAbprQ/TUNtNTu5GuUIjNfj/eRQbn7u7t5eYnnySRn6nRUevxcHdv7zxLiYjIcsjns6RSwxUCSn1kMsdL5vd6IwSDPQSDW2loeHlJQCkY7F6S0bV27PiHwvMLL7znnNcn65u1lmSyvySwNDn5cNG/bUNt7UXU17+kUMw7EtmFz9cwZ12zA03KvBNZmxRwElkjcvkcx2LH5gaTJgYZOD3A4Pggp5KnSpbxGi9hf5iJ1MSc9d3y/Fv45Ms/SX2wfqU2YVXI59OkUsNMTg0yED/KkfhzTnZSMsNwxjCaCzFGE8fZRJwGYOYiqoYcm70J2mvyXB2ooSvopTu8kd5wC92hCB2BANGapTvsTo9G9/G+PgZTKToDAe7u7dUodSIiy2D6hkOlgFIqNVgodOzwEgx2Egz20tT0ulkBpR58vqZ1lf0r5xdrcyQST5cEl2KxA2SzpwGnW2dt7aU0Nr6GSGQP0egewuHLqKlZeACXcHgX9fVXKtAksg4o4CRynqiUnTQw7gSThieGyeZLa/fUB+oLmUhXdlxJZ30nXfVdhfdao63UeGYOA+ZOg73drvSmrRhrLdnsaZLJAcYSQ/TFxuifOl1UO8nHaN7JTjpBI3nagfbC8hvMFG2+NBf44dpADd2hAD3hTfSEm+gKBmk5g+ykpXJjS4sCTCIiSySXmyKZ7C8bUEomj5DLTZbM7/M1Ewz2Ulf3AoLBt5QElAKBDjweXWpLdTz00G7q6vbS3X0bgUDrvPPm8xkSiSdmdYt7pNDN05gAkchlNDf/eiFzKRzegdcbPKu2XXHFgbNaTkTOPzoLiqwClbKTpoNJlbKT2uvaZ4JJdZ10begqKci9/rKTsk4dgakB+mNOdtJAMsZQKs1wxsNINsQxGjnOJqaIAtHCsj6ytHoTtAdyXBqooTNk6AltoCfSQk+ojo5gkLBXQ/CKiJzPrM2RSh2dNcrbzPPZNY48nhDBYC+hUA8bNuwrCSgFgz2LyuYQqYZ4/BESiYOMjd1LS8tNhcBTLpckHn90VubSo1jr1IT0eMJEo7tpbX1XIXOptnY7Ho9vgW8UEZlLASeRFVAuO6k4mLSY7KTizKRy2UlL4fZrbl/S9S21bHaSZHKAY/FB+uJj9CdOM5BMFLKTjuWjjLnZSZbNwEya9kaToM2XYrvf8MqAoTvkoze8iZ5wM13BEJv8fjzq2iAicl5zMllPlQSRikd+SyYHsDZTtISHQKCDUKiHjRuvKwkohUK9+Hyb1O1NzlvWprEWRkc/z+jo56mpqXe7xDm1H2tqNhCJ7GHLlt8uBJdCoW2LKkgvIrIYCjiJnKNy2UnFwaTFZCfNDiZVKzvpjn13rPh3TrM2Tzp9jIlEP0fiI0520tQEQymndtJILsiY3cgYLSSpBXoKy/rJstkbpz2YY4ffS1cwT3ftBnojm+mp3cCWQIBaZSeJiKwJzkigA2UDSlNTR8jlxkvmr6lpJBTqIRLZQ1PTfywJKAUCncrckDUhkzlNLHagkLlUKgdANnuSQKCDbds+TSSyh2CwWwFVEVlWCjjJunbH/jsWDLIUZydNF98enBhcdHbSVR1XzRnZbTmyk1a7XC7B1NQAo4XaSScZmK6dlPExmo9wnGZOshFLE9BUWHajidNWk2K7D14VzNMV8tIbbqY3vJmuUC3NPp+yk0RE1gjnBsRoxYBSOn20ZH6PJ0gw2O3WUrqqJKDkdHurq9KWiCyPdPo4sdiBkppLyWRf4fNAoKNkfo0IJyLVsr5+8YrMcucDd/LePe+tmJm0UHZSuWDS+Vo7KZUa5eDBt3DJJV8/4wsRZ+Se45xODHAkdpQj8WcZmIoxmE5zNO1kJx2zDRxnEymCQIc7QYAMrd447cEsl/lr6Apm6a7dyNbIZnpqN7IlECCk7CQRkTUlkzk9a7S34uf9hXoyDkMgsIVgsIeNG19RqJ80HVDy+zdjjKdq2yLnH2PMduADOHe3/tla+5dVblJZ1lqnNmVJMe+HSaWGC/MEg1uJRp9Pa+t73YLeu/H7m9m/3yjQJCJVp4CTrGkL1U4C2PLpLSXLTGcndW3oWjfZSfeNjfH7Tz7MaP52Wn/+C/70ostLRj7L5ZIkk0McjQ/SFz9WqJ00lM4x4mYnjdHMKTYCDe7kaDIx2mpS7PRBRzBDdyhET3gTveFWukO1NPl8SucWETkPnMmNiXw+TTI5UHG0t2y29GZOTU0DwWAPkchOmppeVyjUHQz2Egx24vEElnPT5DxijPkycANw3Fq7o+j9VwOfBbzAF621n6y0DmvtE8AtxolUfmGZm7wo1lqSySOzgksHyGSOu3MYamsvpr7+msJIcZHILny+DWXXFw7vor7+SgWaRGTxRkfhrrvgwQfhwNKMJrm2fjXLupK3+ZLaSeW6u52cOlmyjNd4CfvDTKQm5qzv1stv5RPXfuK8zE46F7ftv44/4wOkCAMwkg/zzid+xeeeeJANNSG3dtIGjrOJNAGg3Z0gQJo2Nztptx+6gkm6azfSG26lJ9xIRzBIwKO7ziIia0F//12Mj/+E/v4/5MIL7yGdPlYxoORkYNjCssb4CQa7CYV6qat74ayAUk/FH80iZfwV8BfAV6ffME6V63uAVwDDwEPGmG/hBJ8+MWv5d1lrjxtjXgd81F3Xknvood3U1e0tjA5XzNocicTTwA945plvuyPFHXALeoMxNYTDO2hsvKEouHQZXm940d9/xRVL82NRRNaBkRH4vd+Db34T8nlIp5ds1Qo4yaoVT8cZmhiqGEwaGh8ik8+ULBP1R+na0EVXfRd7t+wtyUzqqu+ak51k7jTY2+3sr15T8vkMyeQwR+MDHI4dY2DqFP1TCYbSeY5ma/gJv0uW0oKpWXz8mKtpzsVoq0nyPB90BpN0BQP0hJvYGm2jOxRlY02NspNERNYoZ2TQI/ziF5eXjOw2OvqXjI7O7YHk97cRCvWyYcO+OQGlQKBN3d5W2O7d8Mgjc9/ftWvJblxXhbX2R8aY7llvvwB4xlrbB2CM+Tvg9dbaT+BkQ5Vbz7eAbxlj/h/wN+XmMcbcDNwM0NLSwv79+8+gpY8Qjz/G6OiXgCuBS4ER4GngGSAJwPCwD9gKvAS4ALgAa3uIxfzEYnDsGEAKeOgMvltEZH41sRjNP/whW77xDWqHhpj9i+7MjnfzfM+SrEXkDOVtnuPx46XBJDegNP36xNSJkmU8xkNbtI2u+i5e2P5C3nTJmwqBpOmg0nrLTgLIZsc5nRigb3KII4nn6E9MMJROMZyGkWyQUbuB4zS72Umb3QmCpGnzxshWOAwYDMevee3KbYiIiKwoa3OkUsNuVlJf0aOTsZTJPFthSS+h0AVs3vx2IpFdbk2lbrze4Iq2X+a3dy8cPFh6o9rvhyuvrF6bllE7MFT0ehh4YaWZjTH7gDcAAeA7leaz1n4e+DzA5Zdfbvft27foBjm/1aYHldnvTjVEo3uoq7uZaHQPhw7leMlLflMjJYrI8rMWfvlLuP9++M53nG5zuVzF2c/keDcfBZzkrM03wttUZoqhiaGKwaShiSHSudJUvYg/UggevaD9BXOCSW3RNnzepT0h337N7Uu6vqVmbY5kcoSR+CCHYyP0T51iYCrOUDrH0UwNI7laxmhyayeF3cnRZCZpq0lymc/SEZiiO1RDb7iJ3kg7PbX1heyk7gcfZCCVmvPdnQHVyxAROd9lMqfKBpOmpvpIpQawtniUVS/BYBehUC9NTf/BzVLqJRjsZWTkHo4d+yoej598Ps2GDS+lq+sPqrZdMlcsBkeOwOHD0NcHU1OQLR1EF68XbrutOu1bZuXSrSumsFtr9+NEgFZYHo8nyAUXfBaAQ4f2K9gkIstnfBy+/30nyPTd7zpd5wD27IGPfhRe8ALns698xQk+LWFXumkKOMkZs9ZyPH6cOx+4k52bdpYtxv1sovSuqMHQFm2js76Ty9su5w3b31ASTOqs72RDcMOKd8+qFDBbKblcnPHEAEdiQ/TFj9OfmGAwlWI4bRnJBRjN1xWN7NbsTk7tpFZPjC2BDLv8ObqCMbprG+gJb2ZbZDNbgqFF1066u7eXm598kkQ+X3iv1uPh7t7eZdhiERFZSuWKc08Hl5zi3KdL5vf5mggGe4lGL2fTpjcXBZV6CAQ68FQYFGNwcJy2tltoa7uZkZHPk06PrsTmSZF83qnnOh1Qmp6mXx8/Xjp/fT1s3AgnTzrL+nxw002weW3Wjx5mevhbxxac/murwuzR4kREloW18OijTgbT/ffDz37m3Hmor4dXvhKuvx5e/erSE8HrXge33+4UC7/33iUPPCngJHMks0mGJ4ZLs5NmBZRSOScj5o3feCMAtb7aQgDp+a3PnzOyW3tdO36vv5qbteKcoWzHGI0PcHhyhCNTJ9zspCxHM15GsrUco5GTNOJkdM9cJzWZSVq9U+wI5OkIJugOeuhxs5N6axtoXMKR3aZHo/t4Xx+DqRSdgQB39/aWjFInIiLVYa0lkzleKMZd2v3tCKnUEKXFuQNFxbmvLGQoOfWUeqipqTurduzY8Q+F5xdeeM+5bpZUEI87WUqzg0l9fc77xQnJHg90dsLWrfD610NvrzNt3eo8NjQ4AareXkgmoaZmzWY3gVPg6AJjTA9wFHgL8NbqNmluoEmjxYnIkpuYgB/8wAkyffe7cPSo8/6uXfCRjzhBphe9yDkJVLJ5M9xzj3OSuOsuJ1C1RBRwWmestZyYOlF2ZLfp52PxsTnLtUZa6azvxOfxFYJNxT6898Pc+dI7V2ITVo1cLsnk1GBRdtJpBlNJhtOWo9kAo/kox2kmSQhocCcnO2mzJ8aWQJqdviydwQm6QxvojbTQG2mjKxRe8ZHdbmxpUYBJRKRKcrkEyWT/nGDS9PN8PlEyv9/fSjDYy4YN15QU5w6FevH7W1WcexXL550i0LODSdOTUyB6Rl2dE0C69FJ47Wtngkm9vU6wybdAb6zWVier6XOfWzvZTcaYvwX2AU3GmGHgdmvtl4wx/wn4J5yR6b5srX28is0kHN5Fff2VCjSJyNKyFh57bKYW009/OpPF9IpXwHXXOVlMbW1nvu7pwNMSUsBplZuvTlI56Vya4Ynh0syk0wMlo7slMqUXrqGaUCET6bKWy0q6unVt6KI92k6gZm49n/N5hLf7xsb42OGnGUpn6PD7+OOtF5QEXJw7yicK2Un9UycYmJpkMJXlaMbDSC7EmG3gBI1YvECrO0GjmaTVm2B7IM8r/XG6QobecCNbI2301DbR7PdrZDcRkXXE2jyp1Mic7m7Tz9Pp0iiDxxN2M5O20tDwCoLBnkKmklOcO1SlLZHFSCRKs5SKs5WOHHGyjaZ5PNDR4QSQbrhhJpg0PW3cCOd6yXDbbfD442snu8la+xsV3v8O8xQAX2lXXHEeDwUoIqvL5KSTxXT//c40POy8f9ll8OEPO0GmvXsXvgtRBQo4rXJ3PnBnIeBkreV08vSc7m3Fz0cnR7GzaiS2hFvorO/k0uZLuW7bdXNqJzXVNq2rAMh9Y2NFNYsMg+ksNz3xOF/r+y5he5KRrJ/RfIQxmpmiFoi6E/jJsNkzQZsvzaX+HJ3BCbpC9fSGW9gabaMzGCXk9VZz80REZImkUqMcPPgWLrnk6wtmKGSzE2WDSc5jP9YW10PwEAh0EAr1snHja0oylILBXny+9XVePt9YO5OlVK7r2+is8laRiJOZtH07vOY1pV3fOjudkeOWU2srPPDA8n6HiIgsIWudYUanazH95CeQyUA06mQx3XGHk8XU3l7tli5IAadVJJvPcnTiaEkgCeD6+64vBJVi6VjJMgFvoBA4etXWV80Z2W1L3RZCvuW5E7qaR3jLZMYZi/fTFzvKkfhzHJmKMZROczRt+JfsdjKUXt1l8PDdVBcNppE2b5wLAzmu9cfoClq6axvZFm2jN9zCJmUnySr0w1OnuOnQIe69+GJe2tBQ7eaIrBn9/XcxPv4T+vv/kAsu+Cyp1FCZYJJTrDubPVGybE1NA8FgL5HI82hq+g9FtZR63eLc66uu4flmagr6+yt3fZuampnXmJkspeuum1tLqbHx3LOURERkjYvF4J//eSbINDTkvL9zJ3zoQ04tpiuvXJVZTPNRwGkFTaQmSusmzcpOOjp5lLzNz1nu/mfuB+CF7S/kzZe+uSSg1BxuxlOlWg3VGuHN2hyJ1ChHJgfpi43SP3Wawak4g+k8I1kfI7kIYzSRIAzUAp0A+NzspAzl/5Ma4OQ1N6zYdogshR+eOsUNjz5KIp/nhkcf5ds7dyroJHIWrLVksyeZmurjwIGrsDZT+Gx09C8ZHf3LkvmN8REMdhMM9rJp0+UlGUrBYA8+34aV3gQ5A9Y6o7qVCyYdPjwzcvS0cNgJIF1wAbzqVaW1lLq6IDC38oCIiEhl1sITT8zUYvrxj2eymF7+cqcf9HXXwZYt1W7pOVHAaQGLraGUy+cYjY2WLcY9/Xo8NV6yjM/jo6O+g876Tl7W87KSbm5d9V101HcQ/uPweVsn6WzlcgmedbOTDseeZSA5wWAyxXDGMJINcszW8yxN5PECje4E9cRo9cbZGsyyzx+jK5SnJ9RAb6SVrdE2WvxBPMbQ/eCDDKTmFj7v1NWinGeKg02Agk4iC8jnUySTAxW7vuVyExWW9BIOb2fz5ncTje4mGOwhEGjHGHWhXs2SyZkspXJd3xJFJS2NcXom9PY6AaXiOkpbt0JTk7KURETkHMVi8C//MlOLacDp0cSOHfDBDzoBpquuWv6+1itIAacFTNdQiqfjJRlJPz7yY7586suF18MTw2Tz2ZJlG4INdG3oontDNy/pfEmhCPd0UGlzZHPVspPOxUIFt+djrSWZPs7A5AB98VGOxE8ykIwzlM5xNFPDSC7MGI3EiAI+oA1ow0uWzWaCtpoke31ZuoKn6ApF6altZlt0Cz3hRsKLrJ10d28v73niVySLMp2CZLi7d/uZ7wyRFTaVy3EwkeDvjx/nU8PDZG1pQFpBJ1nPnAEfjpd0dSvu+pZKDUNRnUOPJ1jITKqvv7okS2l4+DMcO3YvHo+ffD5NXd3VdHR8sHobJ3NYC88+Wz6Y1NfnjAxdfIisrXWCR1u3OiUwiru9dXVBMFi9bRERkTXIWnjyyZlucj/6EaTTTnG/a6+Fj33MqcXU2Vntli4bBZzm8T9+/j8AaPzTRk5OnSz5zIOHjnEnO+mqjqvmjOzWUddBNBA95zastjpJ5Qpu3/zkkwDc2NJCPp/mZGKAZyaHORI/Tv/UOAPJFEczlqPZAMfydRynmRw1QL07QR1xWr0xOgMZrvLH6Arm6K5toDeyma2RdtqCYbxLdGvRCY5dxsf7+hhMpegMBLi7d/uig2YiKyFnLc9MTfFoLMZj8TiPutPhqSnmdrwtlcjnuenQIfr37l2RtoqspFxuqigz6cisWkp95POlI7H6/e2EQj1s2PDSkjpKwWAvfn8LpsKNn2z2JG1tt9DWdjMjI58nnR4tO58sr1TKuQFcrutbX59zs7jYdJbStdeWdnvr7YVNm5SlJCIiyywehx/+cCbI1N/vvH/JJfDbv+3UYnrxi9dUFtN8FHAq4479d3DnA3cWXk8Hm95w8Rv43b2/S2d9J089/BTXvvTa5W9LleoklWOt5Xef2E+C0sBMIp/n3U8c4A8PjXLMbmSCepyKSC1AC15yNJsJ2mumuCKYoyNwku5QlJ7aRrZGt9BT20z9Chc/u7GlRQEmWRWstYyk03MCS08kEiTdrnIG2BYKsTMc5jc2bWJnOEw8n+f9Tz1V6E5XrNbj4d6LL17hLRFZGtbmSadHCwGl2QW6Zwd+PJ6wG0DaSkPDK2bVUurC6z27gTN27PiHwvMLL7znnLZJKrMWnnuufB2lvj5n5OfiLKVQaCaA9LKXlQaUenqUpSQiIivMWnjqqZlaTD/6kXO3JBx27n785//sdJXr6qp2S6tCAacy7tg3U7fJ3GnK1lA6bA6vcKuWXz6fZTx5lMMTgxxJjNGfOM1AMslQ2jKS9TOar+M45YeFThFgs9/HC/wxOgJ5emrr6Qm3cEG0g/ZghBrP+dd1UGSpjWezTlApFuPReLwQYDqVnemO2+r3syMc5v1tbewMh9kZibC9tpbaMl1GOwOBkhpO4ASb1J1OVoNUapSDB9/CJZd8nUCg9NyRzcbKZidNd4OztrjOnodAYAuhUC8bN143J0vJ52vS6KGrXDrtZClV6vo2OVk6f2urk5300pfOHfGtpUVZSiIiUmWJhJPFNB1kOnLEef/ii+G3fssJMF19tUaUQAGndSWTmeRofIDDsaMciT/HwFSMoXSGobRhJBdizDZwiukfqU1AE4Y8zWaCNm+CXYEs48kcMTv3n01XIMgDe9+2otsjslql8nkOJRJzAktDRcXqo14vO8Jh3tTczM5wmB1ucKnxDLL9XtrQwLd37iwEnRRsktXC2hyHD/8+4+M/5uDB36C+/qqSoFIm82zJ/F5vHaHQVmprL6Wx8bWzspQ68XjWR9r5arV7NzzyyNz3d+2CAwecm7snT5YPJh0+7GQpFSdjBoMzgaRrrint+tbd7dRaEhERWVWefnqmm9z+/U4WU22tk277kY84Qabu7mq3ctVRwGkB1aqhdKaFua3NE0uOcTg2QF/sGP2JUwwkpxhK5xnJ+hjJRRijiTQBIAC0AxAkRatnnHZfml3+OJ2BHN219fSGN7Et2kFnaAO+ouyk+8bGVHBbxJW3liPJ5JzucE8lEuTceXzGcHFtLVfX15cEljoDgSXJypgOOt106BD3Xnyxgk2yYrLZ8TLZSX2cOvV9igtzj4/vZ3x8P2BoaLiWpqZfm5Wl1ENNTYOylFaxvXvh4EEnU2ma1wsTE04wqq/PeV5s8+aZgFJxt7feXuczJT6LiMiqNjXlBJamg0yH3R5OF10Et97q1GK6+mr15V6AAk4LqEYNpUqFuU8mRnle4ASHY88xMDXBUCrNcAaOZkMcs/WcpAGLB9jgTtBoxmnzxLk0mOPV/hN0hcL01G6kN9LGtmg7jb4z+9GrgtuyXo2VqbP0eDxe0p2tJxhkZzjMG5qaCoGlC0OhkqDtcnhpQ4NTIHx0FN7/fnjwQSftzoqxrwAAIABJREFUQOQc5PNZUqmhCt3e+shmSwfTqKlpdLu9vZZk8hmmpp7B2jQeT5Cmpl9j69ZPzelaJ6uHtXDqVPlub089VRpsAsjlnKBTe7tzvV3c9a272yldISIicl555pmZbnL790My6RQPfNnL4EMfcrKYenur3crzigJOq4C1lqn0CY5MDnA4Psr7j+RIuKO3TUvk8/zOwGnAy3Qxbj9pWj3jtNak2O5P0BXI0RWqozfczNbIFnoizQSW4YeuCm7LWhZz6ywVB5Yei8d5NpMpzNPs87EzHOY9ra2FOkuX1tYSqanSIXV0FO66C+691+m3MvuXoUgZ1lqy2VNlg0nJZB/J5CAUcvXAGB/BYDfBYC+bNl1R0u0tFOqhpmbmvPXkk7eSSBzC4wmSz6fxejco2LQKZDIwNFR+xLfDh2F8vHT+lpaZLKVDh5xudbmcM7DOu98N//N/Vmc7RERElsTUFDzwgBNkuv9+p9scwIUXwvve5wSYrrlGWUzn4LwMOBljtgMfwCk09M/W2r+scpPmlc9neS4xxNOTgxyJP0v/1DiDyZSbneRnNF/PCTaSxwtE5lmT5Stdht5IC9uiHbQEwuqCIHKWMvk8T01NzamzdCSZLMxT6/GwIxzmtY2NhcDSjnCYltUwjGk2Cz/7GfzRHzlFC41xfk3KujJfYW6AfD5NMjlYMUsplyuNMPh8zQSDvdTVvYhNm95a0vUtEGjHmLnF68vJZMZoa7uFtrabGRn5/JyR5WT5FGcpzc5UGhx0AkbT/H5nZLfeXrjyyrkjvkWKLklGR533pzOb/ut/XfltExEROWd9fTPd5H74QyfoFAw6I1X8zu84QaatW6vdyjVjxQNOxpgvAzcAx621O4refzXwWZwUni9aaz9ZaR3W2ieAW4wxHuALy9HOM6mhlMpM0D95hL7YKEcSJxhIxhlMZTia8TKSq+WY3Ui8EEhyinHXkKXFnKatJsmLg1N0Bp6lKxSlN9zErf0ZRjPZOd/TFQjy9p69y7G5ImuWtZbBVGpOYOlQIkHGHWvbC1xUW8sV0Sjv2ry5EFjqCQbxVDuoa63zS+/RR0ungwedYoWyrvX3/yHj4z/h6ad/i+bmNxYFlI4wNdVHKjUEzHT7NCZAKNRDMNhLff1VblHunqJaStEladeOHf9QeH7hhfcsyTrFkc3On6V0+nTp/M3NznXz3r1w442lI761tS2+llJrK9x0E3zuc87jZiWsiYjI+SCZhB/9aCbI9NRTzvvbtsF73uPUYrrmGqfrnCy5amQ4/RXwF8BXp98wzi3Te4BXAMPAQ8aYb+H8DvzErOXfZa09box5HfBRd11LqlwNpfcceoJ/HXuIds9zDCSnOEyS3/3RMxzLRzlOIzlqgCDTxbijxGn1TNLpS3NV4BSdgSQ9tRvojbSwNdJBe6i+4g/ZWI0Kc4ucjROZzJw6S4/F40wW3dLvDATYEQ5z/caNhcDSxbW1y9L99IxNTsJjj80NLp0sqpXT1gY7d8K110JHB/zkJ/DtbztpB+pK9//ZO+/wqM4z7f/OjOpUBAIVhEQxIIGEAYExIGxsXMElcUlwiAsuJPba6c2bENubZJ0t17fJbpqdBCfOZm3vtynrLxA7sWNsBNjGVNHBIKpoQm3URjNzvj8ezZyZkUSzRvX5Xde5ZJ1zZvSOmTlz3vu9n/sZkIRCrbS0VMY4k44e/QHRQtKZM7/nzBkReVJSsklLG8uQIfPiyt7GkpKSg6zVKH2Z2trOxaQDB+DQoViXUnKy5VKaNSu249uYMeDuHg0RgOXLYccO+akoiqIofZaDB60sprfegqYmcTHNnw9/93fiYho/vrdHOSjoccHJNM13DMMYHbf7CmC/aZoHAAzDeBm43TTNZxE3VGfP8yrwqmEYK4H/ij9uGMYyYBlAVlYWq1evvuAxfpmTNBHrZmox4UdnXYALG0EyzRqyQj4mU8M1VJOFjSzSGYGHLDw4cELICX5kawg/UzUfUs2H5/j7I4Evk8wvgFPACOBhkhm5axerd+264NehKAOVFuAQcBA40P7zIFAddY4bGAMsaP8Z3lytreIMahdxaoD1PTZywQgGST9yBOeBA7gOHsR54ADOgwdJr7LKjgLp6TSOGUPj7Nk0jh1L49ix+MaMIeCNzXdjyhRSFi+m4MUXyX7tNYxgEFsgcFHXPKV3MU2TtrZTXWYptbYeI7rrm82WRnr6OILBRvz+U0AAw0glI+M6xo//d9LTNcyyrxMIwNGjHUvewtvZ2Dx2MjNFQLriCrjnntjSt5EjpcStJ8jJkagLRVEURelTtLaKiyksMu3ZI/vHjoUHHxSBaf58cDh6dZiDkb6S4TQSOBL1+1FgVlcnG4YxH7gDSAVWdXaOaZrPA88DzJgxw5w/f/4FD+ZUFxM1A9g/o5h8x1DK33mH+fPvuuDnvFjmA99N2LMrSv8gEArxYUtLpBwu7Fja39wcmX6n2WxMcji4xemMdIYrcTrJSUnp/Ywz04Rjxzo6lnbtstxIdru0V73qKnEutW9JBQV4bba49gHn4I474MQJCQ9ft46LueYpl875MpTCBIPNtLRUdpmlFAo1xZyfkpJLevpYhgy5NsahlJY2lpSUbAzDYM+eR6mqej4SzJ2amq9iUx+iru7cLqVAVOV8UpJ0dhs3DmbOjO34NmYMeDy99jIURVEUpW9SWWmFff/tb9DYCKmpUh736KOWi6m35wODnL4iOHX2LjA72ScHTHM1sDpRg8lPTeVQJ9ko+ampjHVlJurPKsqgxTRNjvv9HXKWdjY20tqes2QDLktPZ4rTyadGjIgIS+PS07H3hS+S+vrOy+FqaqxzRo4UQemGGyxxqahIvhy7g+xs+LHm5fQklZXfoa6unMrKZxg9+tsxQhKsY/Pm5TQ3H8DvPx7zOJvN2S4gjSMj4/ooQWkMaWmjsdvPnyOgwdyJY9o06cgWz9SpsHmz/HcwaLmUOnMqVVfHPnbYMBGRZsyAT3witvQtL6/nXErKICbc0XT9euuNrCiK0l9obZUoiXAWU7jyZ8wYuP9+yWKaPx+czl4dphJLXxGcjgKjon7PA453cW7C+d7YsZqhpCgJoratLSIoRf+siVruz01JocTp5NqRIyPCUpHDQXpfmJG1tYlNN15YOnTIOsftFjHpE5+whKXiYhg6tPfGrXQr77yTTihkdTSsqvoZVVU/izrDAIYDRQwdemOHLKXk5OEf2YGnwdyJY/ZsyeWPjkWz2+Xjf9NNIi4dOhTbGDIpCQoKREC6++7YsrexYyG+GlZReoyw0PTCCxAKad6foij9h8OHrTK5N98UF1NKiriYHnlERKYJE9TF1IfpK4LTBmC8YRhjgGPAYuBTvTUY6UY3hW8eOMDh1lbyU1P53tiiLrvUKYrSkdZQiF1RolJYWDoS5R702O0UO518YvjwiLA02elkWHLyOZ65hzBNsS90Vg4XnmUmJUk53OzZsGyZCEtTpkB+vn7xDXBmzTrAhx9+hdOn/xvTDABJuFzTyMv7Ah7PDNLSCnjnnfVMmza/t4eqnINgUKpe48vedu/uOCcPO5rS02H6dLjrrtjSt7w8uSQoSp/ANGHDBvj2t2WSFgzKPkVRlL6M3y8upnCp3I4dsr+gAO67T8rkrr1WXUz9iB6/NTIM4yUkoijTMIyjwFOmaf7SMIzHgdeRznQrTNPc0dNji2ZJVpYKTMqg4q2aGpbu3s0LhYVck5FxwY8LmSYHmps7CEt7m5oIN1JKNgyKHA6u8nojneFKnE5Gpab2fs4SSNhKvLC0fXtsf/FRo0RQuvlmy7VUWCirLMqgIzU1B7vdg2mGIhlKbvcMsrN7ba1E6YKGBmlW01nZW2VlRxdT2KVUVCSdk4NB6QR3333wi1/02stQlK4JhWD/fti0KXaLLulWFEXpqxw5YglMb7wBPp988V51lRX4XVioi7n9lN7oUndPF/tX0UUAuKIoieWtmhpuqaigKRTilooK/lRS0kF0Mk2Tk35/B2FpR2MjTSGrPfvYtDRKnE7uHD48IiyNT08n2dYHWrH7/Z2Xwx0+bJ3j8YiYtHhxbDncRYhwyuBAM5T6BqFQR5dStLh0+nTs+V6vOJKmTIGPfzy27C0/33IpVVXJvmBQ9n1XO3kofYFAQCx40cLSli2irIIsgpSUiAVv3DhxOa1aJW9kLaVTFKUv0NYGa9daWUzbt8v+/HxYskTK5K69Flyu3h2n0i2o+VtRBjnRYhNAUyjEoooK/mXsWFJsthiB6UxUYMmI5GRKnE6W5eZGhKVJDgeuvlBTYpoiIsULS7t3W62hkpNltaSsLKY7HKNG6QqKckFohlLP4fNZLqV4p9LBg7HzaJtN7lnHjYOPfSy27G3s2AvXjnNyYOlSeO45+ZnddRNCRUkMfr+Uk0SLS1u3QnOzHE9PlyT7++6TOs/p02HSpI7O23AH0xdeUOFJUZSeIb5JwbFjVhbTG2+ISJ6cDPPmwb/8i4hMRUV6Dz4A6QMzQ0VReou/nj3Lbdu30xLlUAJoDoV4fP9+AJw2G8VOJx/LzIwIS8VOJyP6SilZbW3n5XB1ddY5+fkiJt1yiyUsTZyo5XADGMMwioDPA5nAm6Zp/rSXhzRouJAOb/GEQnJv2lnZ24cfwqlTsed7PCIgFRfDbbfFdnzLz5d72O5g+XKZ7y9f3j3Ppyhd0twM27bFiksVFVZmoMcjH67PftYSlyZOvLD2huEOpsuXywRw3brEvhZFUQYv0U0KAgHZpkyR6xnIwu4990iZ3IIF0mhHGdCo4KQogwDTNDnW2sq2sFvJ56OisZFtjY3nfFxuSgpHZs/G1hdWG1pbxaEULy4dPWqdM2SIiElLlsSWw2l7qH6FYRgrgFuAU6ZpFkftvwn4IZL19wvTNL/f1XOYprkL+KxhGDbg5wkeshJFZx3eUlJg5kzRgjsrezt4UD7iYWw2uScdO1YEpfiOb0OH9swiaE4OvP124v+OMshoaBBVNlpc2rVL3Ecgb/DSUvjSlyxxaexY+WB8FMLCk6IoSndTVQXf+Aa89JJcy6IXszMz4Z//WUSmyZPVxTTIUMFJUQYYdYGAlMG1i0rhrTZcSgbkpaZS4nRS5HDwhzNn8HfSucZhs/GfRUU9LzaZpvQbjxeW9uyJLYcrKpKWqGFhacoUGDlSv8QGBr8CfgS8GN5hGIYd+DFwPXAU2GAYxquI+PRs3OMfNE3zlGEYtwHfaH8uJcGEQlK5c8MNHcO1/X74+c9lC+N2izNp0iQxH0aXvuXnqwFRGSCcPSvWvmhxae9e63hOjghKH/+4JS5pabeiKP2BYBDee0/K5H7wA+hqIftvf+vZcSl9ChWcFKWf4g+F2NPUZIlK7QLT4SibgMdup8TpZPGIEZRElcNlRNWbxGc4gYhNnQWHdztnz3ZeDhcOPwUYPVoEpdtvt8SlCRO6r2ZG6XOYpvmOYRij43ZfAew3TfMAgGEYLwO3m6b5LOKG6ux5XgVeNQxjJfBfiRvx4KG5WdxI8WVv4a2lpeNjDEMqfz796djSt2HDdE6tDDBOnuzYKa6y0jpeUCCC0r33ys9p00RwUhRF6S+cOQOvvy4i02uvyb283Q4zZsjxLVtk8Viz4pR2VHBSlD6OaZocaW2NEZUqGhvZ3dREW7szKckwKHQ4mOv18lmnkykuFyVOJ6NSUzHOM6O7JiODP5WURESnhIhNra1SLhAvLh07Zp2TkSFi0n33xZbDeTzdNw6lPzMSOBL1+1FgVlcnG4YxH7gDSKWLDqiGYSwDlgFkZWWxevXqbhqq4PP5uv05E41pwtmzKRw/nkZVVTpVVWkcP57O8ePy39XVqTHnp6cHyMlpITe3meLiFnJymsnNbSE9PcBXvnI5fr+dlJQg3/veewwdKjefTU1WQxpF6ZeYJqmnT+Pauxf3vn249u3DvW8fqWfORE5pysvDN348DTfcgG/CBBouu4xAfHn3nj2yKYqi9FVCIXFprlol23vvyc3CiBFw660S9n399VZHDm1SoMShgpOi9CFq29piyuAqfD62NzZSF851APLby+EWDRsWcS1NdDhI+QjZDmHRaenu3bxQWHjpYlMoJKu58cLS3r1WNkVKitTQXHttbHe43Fy1OyjnorM3R8da0PAB01wNrD7XE5qm+TzwPMCMGTPM+fPnX/roOmH16tV093OGuZRg7jDNzfIx7azj24EDVgMskI9kXp44kmbOjO32NnYsZGYmYRguoGPr4l27pMPbQw/ZueOOOR/p9SpKr2Ga8sGIdy6FxSWbTUq8b77ZKombOhWHx4MDGNGrg1cURbkEamvhr38VgenPfxb3pmHIjcBTT8GiRXKt62zuoU0KlDhUcFKUXsAfCrE7XA4XFeB9NKoczmu3U+JysSQrS4Qll4tipxNvUmI+ttdkZFA5e/aFP6C6uvNyOJ/POmfMGBGT7rjDEpbGj9dyOOVSOAqMivo9DzjeS2PpdboK5p4zR+bHp0513fHteNz/NadTxKPx4+HGG2PDuUePhtRYU9MFox3elH5HMCgLJNHC0ubNVtfT5GRx3t5+uyUuTZkCDkfvjltRFOWjYJryhb1qFaxcCWvXyvUwI0NuDBYulJ8jLkJC1yYFSjsqOClKAjFNk0MtLR1cS3uamwm0l8MlGwZFDgdXe72UtJfClTid5F1AOVxCCLczXb9ebrRbWmRmGy8uVVVZjxk2TMSkpUstYWnyZG11qnQnG4DxhmGMAY4Bi4FP9e6Qeo+vfhVWrIjdFwjAm2+CyyVla9GEXUo33NDRpTR8eGLMhdrhTenTtLXJd1u0uLRli/XhSUuDyy+HT33KEpcmT750BVZRFKUv4fNJmHe4VO5Ie2rB1Knw9a+LyDRrFiRooVsZPOg7SFG6iZqocrht7a6l7Y2NNESVwxWkpjLF5eL2zMyIa2lCejrJH7XVcXdw7Bh87WvwP/8jqxrBIBQWwr59VmvT1FQph7v++tjucNnZWg6ndBuGYbwEzAcyDcM4CjxlmuYvDcN4HHgd6Uy3wjTNHb04zIRimnD6dNdlb8eOyTnRDBkiH9mFCzu6lNLSeuVlKErfoKVFFkqixaWKCskXBLH5TZsGDz8MpaUiLhUW6kRLUZSBxd69lsD09ttik3a55L7+qafgppuk47OidCP6TaoMWt6qqbmkzKLWUIhd0Y6ldtfSsajaloykJEqcTu7Lyoq4loqdTjx95eb1zBnLqfTee/DGG1KDE09REXziE5a4dNllegOuJBzTNO/pYv8quggA74+0tsKhQ113fIuuTgW5Bxw7FhYskJ9Dh8KXvyz3i+np4obPzu6d16IofQafD7ZujRWXduywcgSHDBFB6YknLOfS+PGdZ5EoiqL0Z1paRFgKi0z798v+oiK5Bi5cCGVlUpOvKAlCZ47KoOStmppIV7ZbKio67coWMk0qw+VwUd3h9jY1EfYspRgGk5xOrs3IiJTClbhc5Kak9E45XDwtLbHd4bZt61gOl5QktTid8Yc/9Mw4FaWfcSGh3fEupXin0tGjsS6l9HTLlXTttR1dSunpHf/ezp0SzL10qYpNyiCktlY+cNHi0p491gdr+HBxLN1yiyUujR6tjlxFUQYuhw5ZAtObb0onkPR0ubH44helwcGYMb09SmUQoYKTMuiIFpsAmkIhFlVU8L0xY0gyjIiwtL2xEV9UOdyYtDRKnE7uyMyMuJbG95VyuFBIvmDihaXo7nDR5XBTpliuJYDvflfblyrKRdBZaLfdLvPcO+4QQWnfvrIOWUo5OZKfdM01lpgUzlPKyrr4ebAGcyuDhtOnO3aKO3DAOp6XJ4LS4sWWuKTdTxVFGei0tUF5uSUy7dwp+8eMgYceEhfT/Pmdr1opSg+ggpMyqHi9upqP7dhBSziTqJ3mUIgvffghAMOSkihxuVianR1xLU12OnH3lVKymppYUSncHa6hwTon3B3uzjtju8N19Rqi25eq8NTvaG2tYufOxUya9AqpqWpz6QmWL5ePSjTBIOzeLfd+IiSd4Oqr82JcSt3dzEqDuZUBh2lKK8V4cenoUeucsWNFUHr4Yfk5bdrFdU9SFEXpzxw/Dq+9JgLTX/4ic4DkZLj6arkuLlwIEyao4K70CfrIDFpRupfOyuG2NTayO95uEEdeSgqHZ8/uG+Vwfr/MXqOFpW3bJC04TEaGiEn3328JS8XFl9YdLty+NCw8rVvXfa9FSSiVld+hrq6cysp/YOLEn/T2cAYFOTlSxvbzn0tFanKyNLNascKKglm9ej/z5+f17kAVpS9jmlBZaYlK4fK4kyfluGHAxIlw1VWWa2nqVPnuUxRFGSwEg5K5GnYxhWv38/LgnntEYLr2Wu0OrfRJVHBS+j1n27vDbYvKWYovhxvbXg43w+3mv0+dwh/f3glw2Gy8WFTU82KTaUor0nhhac8eK1spOVkC/q65JrY7XCLKBcLCk9LneeeddEKhlsjvVVU/parqp9hsaVx1VXMvjmxwEHY5BQJiHvz+9zV3WFG6JBSSwNqwuLRxo0yaamrkuN0OkydLvkhYXLr8cumgpCiKMtg4fRpef10Eptdfh7Nn5To5Zw48+6yITCUl6mJS+jwqOCn9hs66w23z+TgeVfo1NCmJKecph3swOzsmwwlEbOosOLzbqauzRKWwsLR9u+wPk58vYtJtt1nC0oQJIjopgxrTNGltPUxdXTl1dWtJTR1Dc/OuyHGbzUFm5scZN+5fe3GUg4ewy0lDuxUljkBAHLrRJXGbN1utF1NS5Lvt7rstcamkBNLSenfcA4wN0zbgme1h9PLRpOak9vZwFEU5F6GQXCdXrYKVK+H992VResQIuPVWEZiuv14dnkq/QwUnpc9hmiaHWlrYFhaW2p1LezrpDrcgI4Mp7Z3hSpxOci6gO9w1GRn8qaQkIjolRGxqaxOHUnzW0uHD1jkej9xwf+pTlrBUXAxeb/eNQ+nXhEIBGhsrIgJTXV05fr+UVNrtbjye2djtTny+jRhGKqFQC3a7R3OcehAN7VYGJVVVUnq9fj28+658CKLFpa1bpUsqSHDZ1KnwwAOWuDRpki6i9ACNWxpp2tnEyRdOkrU0S4UnRelr1NbCX/8qItOf/yzlxIYBM2fC00+LyDR9utqnlX6NCk5Kr1LTXg4XXRK3vbGRhk66w328vTvclPbucEkf4eIbFp2W7t7NC4WFly42maZkKsULS7t2iegEUmtTWAhz58JnP2t1iBs1Sm2wSgyBgI/6+nepr19LXd1a6uvXEwyKIyA1NY8hQ+bh9Zbh8czF5SrBMOxs334HHs8V5OYu4/jx5/H7q3r5VQwuNLRbGVR8+CF89avwpz9JpkgoJJkh4e87j0cmR489ZolLEyZIGYjSo4QC4uI2/SYmJlU/q+LEihNkP5itwpOi9BamKZUN4SymtWvlWpqRATfeKALTjTdqEwRlQKGCk3JJvFVTc1FijT8UYndTU0zO0jafj2NR5XAZSUmUOJ3cH1UOV5zA7nDXZGRQOXv2hT+goUG+JOKzlmprrXPy8kRMuukmS1gqLJTyAUWJo7X1WLtzSdxLPt9WIAgYOJ1TyMq6D6+3DK93Lmlp+Z0+R3Hx7yP/PWGCZm8pitJN+HywZYtkLZWXw5tvWnlL0Xz5y5a4NGaMrsT3AqFAiKadTTRsbMC3ySc/t/hiTzLBbDWpeq6Kph1NTHt7Wu8MVlEGGz4f/O1vlsh05IjsnzoVvv51EZlmzeq6k7Si9HP0na1cNG/V1ETK0W6pqIgpRzNNk8OtrVT4fDElcXuamwm0B3UnGwaTHA6uyciICEtTXC5yL6AcLiFElwZs3izZE3v3xopKFRXSSSeM2y3lb5/8pBXiXVKiddVKl5hmiMbGHe3OJRGYWloqAcle8nhmUVDw93i9c/F4riQpSUsrFUXpIerqLHEpHOi9Z4+sxoOUv4VdTPE8+2zPjVMh1GaJS+GtcWsjoRZxNNmcNtzT3OQsy+HYD62utkaKgWE3yF6aTcHygt4avqIMXKLnE6+8YglMb78tnaddLslgeuopWZgeObK3R6woPYIKTspFES02ATSFQty0bRs3Dh1KdVsb2xsbqY8qhytITaXE5eL2zEwRl1wuJqSnk9wXVkCPH4cnn4SXXxY7azAI06ZJOVxrq5xjt0s5wKxZ8PDDVtZSQYGWwynnJBhsoqFhQ8S9VF+/nkBA3HApKdl4PHMZOfLzeL1zcbmmYrN9tDyTp5+WTVEU5ZzU1MR2itu0Cfbts46PHAmlpbB4sfwM54d85zvSljEYlMmTknBC/hCNOxrFsbSx3bm0zYfZKkKg3W3HNc1F7qO5uEvduEpdOMY7MOxyf3Lsh8c6CE2p2VpKpyjdSlWViEi//rUsWodCMHGiHCsqgieeEBdTWZlWPCiDEhWclPPiD4XY09TEy6dO8c9HjkScSpHjpsn/q66mxOnk01lZTGkP8C52OvH0FXtoY6OUw1VUSMDpqlXyBRFPVhZcd53lWCoq0q45ygXh95+KiEt1dWvx+TZimgEAHI5JDB/+CbzeuXi9ZaSljel2N98zz6jgpChKHGfOxApLGzfCwYPW8YICEZTuv98qi8vK6vy5fvxjScdX4SkhhPwhGitEXGrYJAKTb5sP098uLnnsuKe7Gfn4SNylbtylbtIvS8ewdf1d4pzqxDvHq0KToiSCDRukpHjtWhGZovnxj+Hmm6XMWFEGOX1EDVD6AqZpcrS1tUOI9+6mJtriRKbOqA8E+PGECT0w0nMQDEqoaXQp3LZtcOCAVRpgs3X8Ygjz2ms9N1al32KaJk1NeyKlcXV1a2luFoeAYaTi8cxk1Kiv4PHMxeudQ3Ly0ISN5cwZuddRFGWQc/JkR3EpujPq2LEwYwYsWybOpWnTIDPz4v5Gdnas8LRuXfe+hkFCqDWEr8IXcS01bGygsaIRs61dXPLacZe6yft8Hq7pLhHI7wd2AAAgAElEQVSXxp1bXOqMmZtnJmL4ijI4aWuTa97KlbJwvWNH1+c+9ljPjUtR+jgqOA1S6gMBtscJSxWNjdQGApFzRqWmMsXpZNGwYZQ4nbQEgzyxf3+knC4ah83GC4WFPfkS4PTpWFGpokIu/s3Nctxmg8suk1C+++6zyuHS0+F739MVWuWCCYVaaWjYGBGX6urWEghUA5CUNAyvt4ycnEfwestwu6djsyVmJdk0RU8tL5ftj3+E6mrreNg09dRT6nZSlAGLaYpDN1pY2rRJOqaGmTAB5syRUo7p00Vc6s6MwbDwpJyXYEuQxm2NEWHJt8lH43ZLXErKSMI13UXeF/MizqW0sWm9k2mpKEosJ07IYvSqVfCXv0jeXXIyXHUV3HWXZL7+8Y86n1D6LdOmSYRjPFOnSrRxd6CC0wAnEAqxt7k5Et4dDvKubGmJnOO22ylxOlk8YkQkxLvE6WRIcsdMmTHp6TEZTiBiU3RweLfT0gI7d3YUl06etM4ZPlzEpM98xuoON2kSOBydP6eWBijnoK3tLHV169qzl9ZSX78B05Rcr/T0CWRm3hYpj0tPn5CwiUFbm3wJlJeLi6m83HrbZ2TA3LkSCTB3LsybZ5n4FEUZIJimdDSKdy6FLwSGIZ1Qr7lGhKXSUrlL9Hh6d9yDlGBzEN9WX6RTXMPGBpp2NGEG2sWloUm4S92M+vIoXKXiXEobreKSovQZQiH44APLxfTBB7I/J0cEpkWLYMGC2GvsiRM6n1D6LbNnyzQ7+m2bkiJrVt2FCk59mLdqali6ezcvFBaeV8wxTZMqv7+DsLSrsZHW9lmoHZjocHClx8MjOTmR7nD5qakXfLNzTUYGfyopiYhO3So2hULSCS5aVKqokNWDsMCVliZC0s03W46lkpKuMyfOhZYGKMhnp6XlQJR7qZympl0AGEYybncpI0c+jtdbhtc7h5SUEQkbS0ODRIyFHUzvvgtNTXJszBhpblJWJltRkXYfV5QBhWnKd2BYVAoLTGfOyHG7Xb7/brrJCvO+/HLpfKT0OMEmEZeiA70bdzZCe9+U5MxkXKUuhi0ahnu6BHqnFai4pCh9jpoacS+tWgV//rNUUBgGXHklfPe7Evg9dWrXzYJ0PqH0Y5YvF600Grtd9ncXKjj1UaK7wd1SUREj6vgCAXY0NcUISxU+H9VR5XC5KSmUOJ1cn5cXEZYKHQ5Su2GGGhadLlQM65SzZy1BKSwwbd8OPp91ztixIibdfbclLl12mXwKuhMtDRhUhEJt+HxbYgSmtjZxCyQlDcHjmUNW1qfby+NmYrenJ2wsx45ZzqXycti6VbRVm03mkQ89ZDmYztc996mnEjZMRVG6m1BIsgXjy+JqauR4UhIUF8Ptt1vOpZKSrl27SkIJNgbxbfHFlsXtbIT2tbDk4cm4S90Mu21YpCwuddSFL+YpitKDmKbMOcIupnXrxJk0dKgI+osWwQ03XHrGnaL0E1pa4O235a1+9KjsS06GpUvl7dxdqODUB4kWmwCaQiFu3LaNK9xuTvj9HGhpIVw547TZKHY6uWP4cKsczuViWCflcN3JNRkZVM6eLTkSjz0G69d3Xujp98Pu3R1DvKOzJjIyREx64AHLsTR5MrjdCX0NyuAgEKijrm59JOC7vv59QiGxDaWljWHo0OvxesvweObidE7CMBJjGwqFYNcuS1xau9ZqFuVwyELat74lAtOsWRdfEaOZTYrSRwmFxKkbLSxt2gT19XI8JUW+++6+2xKXiou1Q2ovEfAF8G2OK4vb3WSJS1kiLmV+PBN3qTiXUkequKQofZrGRnjzTRGYVq2SUmUQ59I3viEuplmzun9RW1H6GKYptyAvvAC//S3U1sqidlISBALyszvdTaCCU5/hlN/PNp+P3585w/PHj4cd2RHaTJN19fVc5fVyf3Z2xLU0Oi0NW2/c5FRVWfXKoZAIS0eOdMxZ2r1b3r0gkmlRkWRNRJfD5eZ2bVNVlIukpeVwjHupsbECMAE7LtdUcnIebi+Pm0tqam4CxyGl/2EH09q1lnkhK0uEpc99TtxLU6fKx0NRlH5OIAB79sQ6l7Zssdy7aWliX1yyxCqLmzxZRCelxwk0iLgUcS5t9NG0p4nwql5KTgruUjfD7x4uzqXpblJyU1RcUpT+wP79lotp9WqZq7hckk/w1FPiZjqffVxRBghnzojAtGKFTNPT0uDOO+HBB2H+fHj8cXjuue53N4EKTj1OczDIjnAZXFSHuFNtbed9rAlUtrSwfPTohI+zS6qqRPb8zW/EfhqMksby82P/u6QEbr3VEpcmTNBZtdKtmGYQn29bRFyqr19La6t4Qu12Fx7PbIYPvxOvdy5u9yySkhKXdXL2rLiyww6mDRusAL7CQrjjDit/adw41VgVpV8RXmSJdvO2tUnSZrRzacsWq1OqwyFq8tKllnOpqEiWD5UeJ1AfoGGTlbfUsKmB5r3Nlrg0UsSlEYtHRAK9U3MS03FUUZQE0NoK77wjAtPKlbBvn+yfOFFm0wsXSocVFfiVQUIwKPFkK1bA//6v3LbMnAk//SksXgxDhljnLl8uzd67290EKjidk4sJ7Y4nZJocbGmJCEphcWl/c3PYlU26zcZkp5Nbhg2LlMLVBQLcu2tXTBe4MA6bjRcKC7vhlV0ggYBcrKNdS3/5i1zQO+MnPxFxqbg49h2sKN1EIOCjoeG9KIHpXYLBBgBSU/PweOZG3EtOZwk2W2IuceFs37C4VF4u804QTbW0VNxLZWXS5WH48IQMQ1GURBPt5g0G5W7t0UdFXNq61fo+dLult/BnPmM5lyZO1PKMXqKtti3iXAoLTM37miPHU/NScZW6yFqSFclcSsnSSaii9DuOHpWg75Ur4Y03pHQuNVWqKZ54QkSmceN6e5SK0qPs2ye3LS++KCk2mZnycVi6VKbpnZGTI3lOiUAFpy44V2h3PNVtbR0CvLc3NtLYLhoZwLj0dEqcTu4ZMYISl4sSp5Nx6enYO7E5ZCQlxWQ4Ad3bDS4e05QWy/HlcDt3WjfTdrvcPN90k7T/3LxZHhftzHr00e4fmzKoaW09HhGX6urW4vNtQVoAGTidJWRl3YvXKyJTWlr++Z7ukgkE5GMRLo0rL4fjx+WYxyNlcUuWiMA0cyakJy5nXFGURNPSAm+9Bd//vnzgQyH5vgvz0ksiKD3xhOVcuuwybRvZS7TVtMXkLTVsbKDlw5bI8dT8VNylbrLvzxbn0nQ3KSNUXFKUfkkgIC18w1lMW7fK/vx8uO8+EZiuvVYbLCiDDp8P/ud/xM20Zo3ckixcCP/xH5KD35vGPhWcOqGz0O5bKir4fXExWcnJVDQ2shL4/tatbGtspCpcNwMMS0piisvFQzk5TGkXliY7nTgvYpUz3AUuPIZuFZuamsQvFx/iHW67DCJxTpkCCxZYOUtFRbJiEObEidhV36j/B4pyKZhmiMbGnZFw77q6tbS0SKq2zZaOxzOLgoIn211Ms0lK8iZsLD4fvPeeJS6tX29FsOTnS63z3LkiME2erCYGRem3NDfLd+DGjVZZ3PbtVvZgZ9TUaE1sL9F2ti2mU1zDxgZaDljiUtroNFylLnIezJFA7+kuUoaruKQo/ZrTp+H118XF9Prrcg222+Um7J/+SWbTkybpdVkZdJimzFFWrIBXXpG5yoQJsl52770Sk9wXUMEpjnixKUxTKMRN27ZFfk8GitvauD4jIxLgXeJ0kp3SPWGSYdHpUkv6Ii2X44Wl/futlVqHw2q7HBaWSkourA1ouPXn8uUiPK1bd/EvUhnUBIPNNDRsiIhL9fXrCARqAUhOzsLrLWPkyCfwestwuaZisyUu/+vECUtcKi8XA18wKPcuJSWyaFZWJiJTfuKMVIqiJJKmJlkND4tLGzeKkzecRZiZKW6lm2+GsWPFW/6733VcVNFJTY/gP+OPcS75NvpoqYwSl8ak4S51k/NITiTQO3mY5kQqSr8kOidv40a5EQu7mN57T+YuI0bInGXhQgn+1vgOZZBSVSXlci+8IH1KXC74xCckAHzOnL53m6KCUxxLd+/uND8pTGZyMu9MncrxDRtYMGNGQsdyTUYGlbNny7vqscdiw0qjqa62RKWwsLR9u9xcg7zrLrtMZs5Lllgh3mPHfvQSgLDwpCjnwe8/HRPu3dCwEdOUkkyHo4jhw++OKo8bm7AuQKYpF+fo/KUPP5RjaWnSFfcb3xCB6cor9X5GUfolPp8EeIcDvTduhF27ZDEGZOJSWiqTl3BZ3KhRsXdpDz8M//Iv6ubtAfyn/TF5Sw0bG2g9bOVFpo1Lw32Fm9xHcyPOpeQMFZcUpd8TnZMXCMg2cqSsBBqG5BQ89ZS4mKZP19JlZdDi94vJb8UKiS0LBiUD/xvfgLvuEtGpr6KCUxwvFBZ26nACyVH670mTKHI6OdkTg4m+CIdC8k7bsqWja6mqynpMZqaISY88YglLkyaB09kTI1YUAEzTpLl5b8S9VFdXTnOzdAsxjBQ8nivIy/tSe8D3bJKThyVsLH6/zDWj85eqq+VYZqYIS48+Kj+nTdPmJYrS72hokMWY6LK43bstN292tghKd94pP0tLxWd+IaK2unm7Hf9Jf4eyuNYjlriUPj4d7xwvrsddlrg0RMUlRRlQHD8OX/6yhM4Eg7E5eVdfLS6mm26SxQFFGcRs3y5SwG9+I9Wlubnwta/BAw9I+Vx/QAWnOOLzk8IkNLQ7nuPH4etfh//+b7kIh+3+IDNikFnx5MliKQ2Xw02ZAllZfc9Hpwx4QqFWGho2RZXHraWtTXLBkpKG4fXOJSfnYbzeMtzuUmy2xLWarq0VM2DYvfT++5IBDDB+PNx6q4hLZWVyodaPi6L0I+rqYsWljRulHUt4sjJypKyCf/KTlriUk/PR/666eS+J1qrWDoHe/mPtLjED0iek4y3zirBU6sI9zU2SV29NFWVA0twsDRlWrYJf/KLrrtcvv9yz41KUPkZdnXwMVqyQeUxyMtx2m5TM3XADJPWzr8l+NtyeIaGh3fHU18eWwm3bJt0XokWmaF5+WYSl8eP737tNGTC0tZ2lrm5dJOC7vn4Dpik3Dunp4xk27Ba83jI8nrk4HBMTVh4HcPhwbHnc9u0y90xKEn027F6aO1f0WEVR+gk1NeJWii6L27/fOj5qlAhKn/60JS7phzwhbJi2Ac9sD6OXjyY1p/MFg9bjrTF5Sw0bG/BXWeKSY6KDIfOHSN5SqRvXVBdJHr2PUZQBzaFDUge0ahX87W8iOjkccNVVYkF/7z2rikNRBjGhEKxeLSLT734ni+UlJfCDH0gizoVELPdV9Ju+Cz5yaHc8gQDs3duxHO7QIescr1feWffeK4Hf4ZC86IvwJz/50cahKF3Q2lrFzp2LmTTpFVJTsyP7TdOkpeVgTHlcU9NOAAwjCZerlJEj/669PG4OKSmJm/AFgyIohcWltWvhyBE55nJJUN7dd4vAdMUVWkmqKP2G6mpLWAr/PHDAOl5QIILS0qXiYJo+XUstepDGLY007Wzi5AsnyXogi5yHc/AfbS+N2yQCk/9E+72KDRyFDjKuy4g4l1yXu0hy6y2nogx42trk5mzVKhGadsr9ImPHSi7eokVSMpeWJvu167UyyDl0CH79a/kIVFZKduyDD8o2ffrAqMTol9/+hmHMB74D7ABeNk1zdSL+TiS0+2IwTbl4xgtLu3ZZ1lG7HQoLYfZs+MxnrJK4+MBSvQgrPUhl5XeoqyunsvJpcnIeign49vtPAGC3e/F655CVtQSvdy5u90zsdkfCxtTUJFbSsLi0bp2YAkFqmOfNs9xLJSVq+lOUPkl096HNmyWEINq1tHFj7OLLmDEiLj3yiPycNq1/L+31Y0zTpPWo3LuYfhMTk6qfVVH1s/bsSAOck51k3JAR41yyO+29OGpFUXqUkyclxXjVKvjLX6QeKDlZXEwPPSQiU1cZBpqTpwxCWlrgD3+QKf4bb8i+666Df/xH+NjHID29d8fX3fT49MwwjBXALcAp0zSLo/bfBPwQsAO/ME3z++d4GhPwAWnA0QQOV4i/WQ7T1AQ7dnQUl86csc7JzZWZ8PXXWzlLhYWQegEZNnoRVnqAt99Oi5TDAVRVPUdV1XMApKWNZsiQBe3upbk4nZMxjMR1CDl92gr2Li+XeWggIMeKi+Gee6z8pYKCgaH6K8qApaoKnnwSXnrJyiPMz7dsiQDjxklryMces8SloUN7b8yDGNM0aT3SsSyu7XRb5w8wwDPXw/Q103t2oIqi9C6hkNygrVwp2wcfyP6cHGmXtWgRLFgAHs+FP6fm5CkDHNOUtbYVK+C//ksyZ0ePhqefhvvvl3nNQKU3/AC/An4EvBjeYRiGHfgxcD0iIG0wDONVRHx6Nu7xDwJrTNN82zCMLOD/AEsSMtLoLnHBoNhEn3kGKiq44r334NgxK6jU4ZAZ8cc+ZglLJSUwrBu6b+lFWOlGWluPt5fHyWaa8c65JDyeKxk//t9xu6clbBymKXEs0flLe/fKsZQUKYn7yldEXJo9W+egitLnqaqSScjbb0vnocrKjufMnWvlLU2bJt5xpceJiEsfNMR0jIuIS3ZxLg27ZRjuUjf7Ht8XeayRYmDYDbKXZlOwfADfISuKYlFbK+6lVavEzXTqlKz6XXmlzJUWLYKpU3UlUFHiOHMGfvtbEZq2bZNq0jvvlJK5+fPBlrh1/D5DjwtOpmm+YxjG6LjdVwD7TdM8AGAYxsvA7aZpPou4obqiBujUKmQYxjJgGUBWVharV6++4DGmVFdT8OKL5KxciREMEn3pNJ95huaRI6kbNYqT111H45gxNI4bR3NOTsd3TEXFBf9NRUkMIeAwUNG+bQfaSyFIA4qAe4G9wHtAMtBGff1QNm6sA1Z320gCAYN9+1xUVHjZvl22mpoUADyeNoqL65g/v46SkjomTGggJcVqkbttW7cNQ1GU7uD48diSuI0bRXA6Hy+9lPixKTGYpknr4daYTnG+jT7azsSJS7cOi5TFOac4sadbZXH7Ht/XQWhKzU5ct1FFUXoZ05T8pXDgd3m5LL5nZMBNN8HChfJTy50VpQOBgOizK1bAq6+KZ2XmTPjpT2Hx4sG31tZXEk9GAlEee44Cs7o62TCMO4AbgSGIW6oDpmk+DzwPMGPGDHP+/PkXPpqrr5YLayjU8W83NOBwOnl/9Wou6jkVpQcIhVppaNjU7l5aQ13dWgKBswAkJ49oL42TzeWais2WDMD27XeQkvIoubnLOH78efz+KoqL53+ksdTXSxVquETu3XelOQlIduStt4rZoawMCguTsdkyAb1xUZQ+hWmKmzdaWNq0STIGQVazCwulfCLsXMrJgX/7N80f7AVM06TlUEukHC68BaqlNtlIMnBMdjDstq7Fpc5wTnXineNVoUlRBjJNTfDWW5bIFM7WmzIFvvY1cTHNmqWBmYrSBfv2ya3Pr38t63LDh8MTT0i/k+Li8z9+oNJXrhid+S/NTvbJAdP8PfD7hI3mlVe6DuvWtldKH6KtrZb6+vWR8riGhvcJhVoASE+fQGbmxyICU3r6ZRhdWJ2Li62P04QJl1a+efRobP7Stm2i2dpsUjnzyCNWwHdu7iX9CUVREolpSr5StLC0caOUToB8mIuK4IYbLHHp8sulRWQ80fmDKjwlBNM0aalsiclbatgUKy45i51kfiwzVlxKu/hA75mbZ3b38BVF6QscPGgJTG+9JWnGDockGP/934uTKS+vt0epKH0Wn09SBFasgDVr5FZp4UL40Y9Eo01J6e0R9j59RXA6CoyK+j0PON5LY+kY1q03y0ofoaXlSEz+UmNjBWBiGEm4XNPJzX0sEvCdkpK4luGhkDito/OXwgthTqeU9C9fLgLTrFngdidsKIqiXAqmCYcPdyyLCze9sNth0iS4+eZYceliFl208UW3YZomLQdbYgO9NzUQOBslLpU4Gf7x4bhKXSIulVyauKQoygClqkoSit98UzJnV62SLtoAl10mnbMXLpRKjwtpbqQogxTTlFuaF14Qn4rPJ40Yv/99uPdeXViPp68IThuA8YZhjAGOAYuBT/XukNCbZaVXMc0QjY07YgSm1tbDANjtLjyeOQwffhdebxkezxXY7R/dfff007LF09ICGzaIsLR2rWy1tXIsO1uEpS9+UX5efrm6rRWlT2GaEuAdXxZXXS3H7XaYPFnqXMPi0pQpssrdHWjji4siIi7FBXoHatrFpWRxLg2/czjuUjeuUheuEhe21EGQPKooysWzdavcpL39thUX8u//LsLSsmViwxg/vnfHqCj9gKoqePFFcTPt3SsG709+UgLAZ8/WzPyu6PFpoWEYLwHzgUzDMI4CT5mm+UvDMB4HXkc6060wTXNHT4+tS/RmWekBgsEWGho2RAlMawkG6wBIScnB652H1/sVvN4ynM4SbLbu//g+84wITtXVoq+G3UsffGAZ/IqK4O67rfylsWP1AqsovU64q+r69eLtji6J27QJzkqWG0lJVkfV0lKYPl3EpfT03h3/IMU0TVoOtMQGeseLSyVOht+l4pKiKBdIKCSrhK+8Ar/5jeVcjaa6Wu3ninIB+P1SdbpihTRoDAZh3jx48km4667OUwWUWHqjS909XexfBazq4eEoSq/R1lZNXd26qPylDzBNUXUcjkmMGPHJSP5SWtroLvOXPiqmKSX85eXy+6RJlsM6ORlmzIDPf17EpTlztCFJn6GlBd55RyzxJSXw0EO9PSKlpzFNEZieflqyN4JB2XfZZXI8OVneG3fcYTmXSkqkJ6/S45imSfOHzTGB3r5NPgK1UeLSFCfD7x5uZS4VO1VcUhTl/NTWSluslStlVnz69LnPV7FJUc7J9u0iMv3nf8rHKTdXsvMfeEDK55QLRwtfFKUHME2TlpbKmPK4pqadABhGMm73TPLyvtAuMM0hOXlYwsYSDEqgd9i9tGqV1B6HCYtNDzwAP/mJGh/6FIcPyz/YqlWSwdDUJOLB5z/f2yNTEk0oBPv3WyVx69fHWg+jee45EZeKizWHo5cwQyIuxQd6B+uCABgpBq4pLoZ/Mk5cSlFxSVF6CsMw5gPfAXYAL5umubpXB3QxmKaEaa5cKdvatXKDN3Qo3HSTZDFNmyYVGppFqygXRG0tvPyyCE0bNsi63e23S8nc9ddrZMilov/bFCUBmGYQn29bjMDk90sOvt3uxeudS1bWp/F6y3C7Z2C3J07VaW6G996zBKZ166ChQY7l5Ulsy7x54mCaMkXuYZQ+xLp18L//KzeUO9orjUePlh6rCxfCNdeoKjjQCIWkt2505tLmzVBfL8dTUmTravKwbFnPjXWAsmHaBjyzPYxePprUnHOLdmbIpHl/c4dA72B9rLg0YvEIFZcUpZswDGMFcAtwyjTN4qj9NwE/RCI6fmGa5vfP8TQm4APSkAZGfZumJnGzhrvKhbu1XH45fP3rck9w5ZWSyxdGmyApyjkJhWD1ahGZfvc7KSAoKYEf/ACWLNHKju5ABSdF6QaCwUbq69+PiEv19esJBkXVSU3NZ8iQ+ZHyOKdzMoaRuInGmTOiUaxZIwLTxo3Q1ibHiovl4hkWmPLzEzYM5VI5dUq++T7xCfn9hz+EP/xB/tEefFBuKCdO1OCsgUIoJMmT8eJSWBVOTZXJxJIlVlnc5MmSv6ETiITRuKWRpp1NnHzhJFlLsyLCkxkyad7XHJu5tNlniUupIi5lfSrL6hY3WcUlRUkAvwJ+BLwY3mEYhh34MXA9IiBtMAzjVUR8ejbu8Q8Ca0zTfNswjCzg/wBLemDcF0dlpeVieustmQ07nXDddfDNb0on0by8cz+HNkFSlA4cOgS/+pVslZUwZIjcZj/4oMRb6m1296GCk6JcAn7/Kerq1kYEJp9vE6YZAAyczhKysu5tF5jmkpaWOFUn3HyqvNwSmMIlcSkpMHMmfOlLolXMni1O63Px1FMJG6rSFcGg+HYLC+Xb7uWXpURuxgxJZP/Xf4Wf/xw8nk4f/tuK3/LNN7/J4brD5Hvz+d6C77GkpO/dMyvIv3Vn4lK4pjUtTcSle++1xKVJk8TTHU/8BEKFp27H9JuYmFT9vIqq56tIGZFCoD5AqFG6PBmpBq7LXWQtyYoEejsnO7Elq7ikKInGNM13DMMYHbf7CmC/aZoHAAzDeBm43TTNZxE3VFfUAJ1aGQ3DWAYsA8jKymL16tUfbeBx+Hy+mOc0AgG827cz9N13GfbuuzjbXUxNI0dydtEiqq+8ktopUzBTUuQB+/fLdqHcfbds3fw6FKU/0Npqo7w8kz//OZtNmzIAKC2t4d57T1BWdoaUlBANDdLQUek+VHBSlPNgmibNzftjyuOam/cCYBipeDyzGDXqa3i9ZXg8s0lOHpKwsQSDUFERKzAdl0o9vF7pHHfvveJemjnz4rOBn36624esdEZ1tRXu+dpr8vuLL8o/3uLFcNVVMGaMnDtqVJdP89uK37Ls/y2jqa0JgEN1h1j2/6ScSkWnHia6S9zmzRAM4jh4EI4ciRWXGhvl/PR0EZfuv98Sl4qKOheXzoWuXHcLZsikaW9TJG8pBsn0xl/lJyUnhTH/PgZ3qRvHJIeKS4rStxgJHIn6/Sgwq6uTDcO4A7gRGIK4pTpgmubzwPMAM2bMMOfPn99dYwVg9erVzC8qkqDvlSvl3qC+Xr4Lrr4avvAFWLgQx4QJOIDzeJkURYnDNKVZ74oV8F//JTlNo0fLnOf++6GgYChwnhV55SOhgpMyaGltrWLnzsVMmvQKqanZkf2hUBs+35YYgamt7RQASUlD8XrLyMl5uD1/aTo2W+JCeZub4f33Y/OXwjEueXlyL1JWJltxMdh07tM3MU3YssUK/H73XSmlyswUO/yiRXDjjXLuiBGynfPpTHaf2c3n/vy5iNgUpqmtiW+++U0VnHqKqip45hnxZLXn7eMAACAASURBVAcCogrPnQtbtnBFU/u/jcMBU6daPu2wuNSd6ZNh4Uk5L/HiUrhbXNAnZXG2tNgLqZFsYCQZZC/NpmB5AanZGsSuKH2UzopgukymNE3z98DvEzecOMILE+vWiXN55Uqmv/wy7Nkjx3NzpZx+0SJYsEA7ySnKR+D0afjtb0VoqqiQRfg775Rbsfnzdc7Uk6jgpAxaKiu/Q11dOQcPfosRIz4Zlb/0LqGQTBTT0sYwdOiNeL3z8HrLcDgmJjR/qbpaGo2EBaYPPojNX/rUpyyBqaAgYcNQuoNQSL7NWlth/HhxuoCUyn3rW5LFNGNGbLhnF7QF29hUtYnyw+WsObyG8sPlVDdXd3n+4brD3fUqlK4ITxyef15EpmgMAx5+mF0OB0Wf/rSUS17Av7PS/YTFpYYPrG5xvs2x4pLzcidZ92XhniGB3o4iB++kvIORYmDYVWhSlH7EUSDaFpwHHO+lsVhUVcn3/m9+I98XoRBccQUYBuakSfDd74rIdPnlGhyjKB+BQEBMgitWwKuvyhzqiivgpz+VAoIhiStCUc6BCk7KoOPtt9MwzdbI7ydO/JITJ34JgMs1jZychyL5S6mpIxM2juj8pfC2c6ccS0628pfKymDOnPPnLyl9iM98Bg4fFot8aqp4dseNEzdTVtZ5H97Q2sC7R9+NCEzvHn2X5kAzAOMyxnHrxFspG1XGt1d/m+MNHe+l872aBp/wdteLF8uHNhTqeKy8HICTq1dTNHlyt/5ZpWvMYLu4tLFrcck11UXW/VmRbnGOSQ5sSR0XEZxTnXjneFVoUgYEb9XUsHT3bl4oLOSajIzeHk4i2QCMNwxjDHAMWAx8qtdGE16YeO65jt8V//mfcOONbN6+ne4u01OUwca+fRJl+etfS9TI8OHwxBPS0Lm4+PyPVxKLCk7KgEbyl/ZSV1dObe0a6urKY8QmAMNIwuu9igkTfobDMT5hY4nOXwpvx47JMa9XRKVPf1oEphkztNN9vyDconjVKgnV+uADSWsvLo4ti/vOd875NCd9J2PcS1tObCFoBrEZNqZmT+WR6Y8wr2Aec0fNJcedE3lcWnJaTIYTgCPZwfcWfK/bX2pP0i/aXb/yioZ19yLR4lLEvbS5IRLo3UFcmiHOpc7Epc6YuXlmIoevKD3GWzU13FJRQVMoxC0VFfyppGRAiE6GYbwEzAcyDcM4CjxlmuYvDcN4HHgd+Z5YYZrmjl4b5LkWJpZo2buifBR8Pvi//1fcTOXlUlSwcCH86EdiGAzn6iu9jwpOyoBC8pc2x+UvnQYgOTkTr7eMkSMfpa5uHWfO/BGbLYVQyE96+sRuF5uam6X5WDjcOzp/aeRI6Rw3b54ITJMna8VNv+HAASuLKdyi2OGQFsXV1ZCTI8sqXWCaJvvP7o+IS+WHy9l3dh8AaUlpXJl3JU+WPcm8gnlcmXclntTOu9OBFQw+ALvU/Yq+3u5au8T1GGbQpGlPk5W3FC8upYu4lLM0B1epK1IWd6HikqIMVKLFJmBAiU6mad7Txf5VwKoeHk7n6MKEonQrpinzqRUr5OPV2AgTJ8I//ZP03cnJOf9zKD2PCk5KvyYQ8FFfv76L/KVxDB26EK+3jCFD5pGePgGjvTa+rm4tubmfJTd3GcePP4/fX/WRx1JdLRfBsMAUnb80eTLcc48lMOXna5l+v6KyEv7jP6SDTDjcc/x4KZ1btEj+YbtoCRgIBdh6YmuMwHSy8SQAQ9OHUpZfxrLSZZTllzE9Zzop9otbkllSsmQgCEwx9Lt213ffTcqCBRS8+CKeHTvY2P488e2ulQsgiPSY2hu17QNa2o+nApcBNwATZAsVhKi311NPu6JfDZT37LAVpa+xGXgSaI3b3xQKcfPWrTwLTOv5YQ0udGFCUbqF48clAm3FCti7F1wuMRA++CDMnq1zqr6OCk5Kv6K19USMe8nn24LMUGy4XFMj3eMkfym3y+cpLraakkyYcPGdnUwTDh0SYSksMMXnL33xiyIuzZ2r+Uv9jtZWePFFCXueN0/saj/6kbS1eOwxyWIa37kjrqmtifeOvhcRmNYfXY/P7wNg9JDRXD/ueublz6Msv4zCzEJsCQyhH2D0/XbXd9wBSI0HtLe7HoTZHBumbcAz28Po5aNJzek6/yjGufRBu3tpi6+Dc8n9sJTEuUpdOArVuaQo5+OU38/d779PayDQ6fFW4IepqVTOnt2zAxusxAtP69b19ogUpc/j98Of/iQi05//LJWp8+bBk0/CXXeJ6KT0D1RwUvoskr+0r11ckvyl5ub9ANhs6Xg8V1JQ8Pd4vWV4PFeSlNR16dFHJRiE7dtjBaZw/pLHI6LSkiUiMM2cqflL/Y5AAN59F2pq4NZbpV39k09atrTCQjh7FpzODg8903Qm4lxac3gNm6o2EQgFMDAoySrh/svvpyy/jLL8MvI8eb3w4gYMfbvdtRKhcUsjTTubOPnCSbKWZjF6+WhSRqTQtNsqi+sgLjnay+IezMFdquKSolwMvkCAd+rqeKOmhjdratjW2HjO8x02Gy8UFvbQ6JQIYeFJUZQu2b5dRKbf/AbOnIHcXPjGN+CBB7pc61X6OCo4KX0GyV/aEiMwhfOXkpKG4fWWkZv7WbzeMlyuadhsHz0N7umnZYsnnL8UDvdetw7q6uRYOH+prEy24mLNX+qXnD4Nr70mZXKvvw61tTBhgghOdjts22YVgxsGOJ2YpsnB2oMxAtPuM7sBSLGncMXIK/jqnK9Sll/GnFFzGJKm/Ve7kb7Z7lrpFNNvYmJS9VwVVc9ViVwozeI6iEvuGW4chQ4Mu3riFeVCaAuFeK++XgSm2lrera8nYJqkGgZlXi//OGYM12VkUBcIcPv27ZEMJxCxaSBkOCmKMnCorYWXXpKq0w0bpFrk9tulZO6GG3Se1d9RwUnpNSR/6d24/CVZlUtLG8vQoTfj9c7D6y3D4ZgYyV/qTp55RgSns2dh7VrLwRSdvzRpktQJhwWmggKtFe6XhEKwcaMV+L1hg9RGZmdLKdTChRL8HSY3l2AoSMXJipgOcscbROMYkjaEuaPmcv/l9zMvfx6luaWkJXWe46R0C32r3bUCtJfFRTuXPmiIPSGqOVP6xHSKf1es4pKiXCQh02R7Y2PEwfR2bS2NoRA2oNTt5qujRrEgI4M5Hg/pcTOzP5WURILDVWxSFKWvEApJ750VK+D3v5cePFOmwA9+IFUjmZm9PUKlu1DBSekx/P6TMflLDQ2bsfKXLicn58H2/KWyc+YvfVRMEw4fFmEJxKG0o71pbnIyzJhh5S/NmQPDhiVsKEqiqa2VIu+kJPjWt+DZZ0UtvPJK+Id/EJFp6lTppQo0tzWz4dA7EYFp3ZF11LdKEHGeJ4+rC66mLL+MefnzmDxisuYvJYh+0e56EBIjLkVnLjVFlcVNiw1VMFIMDLtB9tJsCpYXkJrddaaToigWlc3NEQfTmzU1nG5fBZuYns4D2dksyMhg/pAhZCQnn/N5rsnI4E8lJSzdvZsXCgtVbFIUpVc5dAh+9StxMx06BEOGwEMPiZtp2jRd1B+IqOCkJATJX9ofl78krd9ttrT2/KUn2/OXZic0fykUis1fWrkSGqIW4cNi0wMPwE9+ovlL/RrTFGtaSoosm1x/vfycN09sapMnw403RpZNzjafZd3+Vaw5tIbyI+V8cPwD/EHpHjN5+GTuKb4nEvBdMKSgN1/ZoKJftLse4FyouJTzcA7uGW7cpW4cE8W5tNpYrUKTolwkZ/x+/tYuLr1RU8OBFmnNmJOSwk1Dh7IgI4MFQ4aQ10VH1HNxTUaGBoQripJQpk2DLVs67p86VaJJ/vhHcTO9+absv+46+P734WMf67LRszJAUMFJuSRaW6vYuXMxkya9QmpqNqFQoJP8pVOAlb+Uk7MMr7cMt3t6t+QvdT02K39pzRq5yNXWyrHcXDG1lJWJBjF1qmgUSj/G55Nvr3Cp3OOPw9e/DtOnS8pgXntQ95QpHC4YQvnhv7DmXRGYtp/aDkCyLZkZuTP4/KzPMy9/HnNGzWGYQ61tyuAgIi59EBfoHS8uPdKeuRQlLnWGc6oT7xyvCk2Kcg4ag0HW1NbyZm0tb9TUsMUn3Uw9djvXDBnCF/LyuC4jg0KHIyGRAoqiKN3J7NnSsdvvt/YlJ8s6cG6uzMVGj5Yok/vvl4gSZXCggpNySVRWfpu6ujVUVNxKcvIQ6urWx+Uv3RQpj3M4ChN6s1RbK6JSWGDasEFEJ4CiIrj7bktgGj1arZr9HtOEffssgentt+Xbze2WZMGSEgBCHjc7P7eYNYdeo3xzOWsOreFI/REA3Clu5oyaw+LJiynLL2PmyJk4kh29+aoUpUe4EHHJPd19weJSZ8zcPDNRw1eUfktbKMSGhoaIg2l9fT1tpkmKYTDX6+W77UHfpS4XSTYt11YUpX+xfLmUyUXT1gb798tc7MEH4eqrIykWyiBCBSflgvD7T1FXt5YdO+4m0moI8Pk+aP8vO5MmvYLXO5fU1JEJHcvRo5a4VF4OFRWiQSQlQWmpGFzmzZP8peHDz/1cTz2V0KEq3c3y5dLG4sMP5fdJk+Bzn4NFi2i9opQPzmyTDnIv/ZS1h9dS01IDQLYrm3n58/hqvnSQm5I1BbtNW14o/ZcN0zbgme1h9PLRpOZ07iIKBUI07W7Ct9HXubjktOGe9tHEJUVROsc0TXY0NkYcTG/X1tIQDGIA010uvtjuYJrr9eLQFkyKovRjgkHYulWcTAcOyD7DgKuuklK6Idq0eVCjgpPSAdM0aWk5QG3tmkiJXHPzXgAMI5WkpGEEAmcxzQA2WzqZmXcwbty/kpqanYCxwK5dsQJTZaUcc7nEvnnXXeJguuIKcDov7vmffrq7R6x0KytXwquvwnPPye/Hjolt7ctfpm7BXNYZxyTg++C3eb/8fVqDYm2bOGwidxbdKQHfBfMYM2SMliQoA4rGLY007Wzi5AsnyVqaRf6T+QTrghcuLs1w45ig4pKidCeHW1oineTerKnhZHvQ9/j0dJZkZXFdRgbXDBnC0PMEfSuKovQHDh6UXKZf/UoMAUOHgt0uAlRaGrz8sopNigpOCmCaQXy+rTH5S37/CQCSkjLa85cebs9fKmXfvs9TVfU8NlsaoVArdrun28Qmvx82bbIEprVrobpajmVlibD0hS/Iz8svF1eTMkDw++UffNUq+OpXYcQIcTK98QbU1nLc3sSaL93Y3kHuOba99HeYmNgNO9NzpvN3M/+OsvwyyvLLGO48j7VNUfoxoYCISKbfxMSk6mdVVP20KnI8RlwKB3qruKQo3U51WxtvtXeSe6Omhv3NzQBkJSezICOD6zIyWJCRQb4m4iqKMkBoboY//AF++Uv429/EyXTjjfBv/wa33SbztOeeg6VLIbv7vQhKP0Sn64OQYLCJ+vr3I+JSff16gkFp25aaWkBGxnVR+UtFGHGt39vaTpKb+1lyc5dx/Pjz+P1Vnf2ZC6KhAdavt9xL770nFzKA8ePh9ttFXCorg8su0/ylAcfx4/Daa+Jk+utf5Q2RnIx53XXsnv7/2bvz+Kiq+//jrzvZ97lhyT4BAglEVpE9YZGgWCiKYEXTorggP7VI+1VrSylQvwGt1dpWv4pfEbGllDYuX0XEyp6wiSyyI2sWEgIkk8mezHJ+f5xkSCDsSSZkzvPxyIPkzsydMwHm3vncz3kfE5lDvMmIGUbm0ts5WXwSgACvAIbEDGHuiLkkmZIYHD2YAO/rbG1TlFvEJdPivpOdSw3ULXygQWD/QPpv66+KS4rSDCrsdjItFmcO0+6yMgQQ5OHBCKORZ6OiGG00cltAgOqqVRSlTdm1S3YzLVsm83M7d4aXX5YB4DExF+43Z45cAXzOHNeNVWldVMHJDVithbXdS/KrtHQnQlgBjYCAXoSF/cxZYPL1jbnq/nr2/MT5fXz829c1ljNnGk6P27MHHA4ZINevHzz11IUCU1jY9b5SpdWz22VVsS7we/duAKwxUeyaOpqMPkYy/c6R+X0qhdtka1sH/w4kxybz84E/Jzk2mT5hffDyUNMRlLanQXHpu3rT4iobTouLfCqS3DdznY/TvDU0D43waeHEzolVxSZFaSI2h4PvSkudHUxbLBZqhMBL0xgaHMz8Tp1I0XXuCArCSyXhKorSxpjNssC0eLH8zObjA5MmweOPw8iRjQeAR0TI9XwUpY4qOLUxMn/pVL0CUwYVFYcA0DRvgoMHEhPzX4SEJBMcPAQvL70ZxyIXE6tfYDp2TN7m7w+DB8NvfysDvgcNkouMKW3Q+fNw7pzMXrJYIDmZUh/YdlciGfffSaZeyrbi/VTaPoM86BralR8n/JhkUzJJpiS6hXZTV4qVNud6ikuB/QMvmRaX+2buJYUmn/DGw8MVRbk2QggOVVQ4O5g2FBdTYpcLpfQLDGRmbdB3UkgIASroW1GUNsjhgPXrZZHpk0/kyt+33w5vvw0PPQR68310VNooVXC6xQlhp7x8PxZLpjPku6bmNAAeHiGEhAyr7WBKJijoDjw8mi5HYN68hqHbNpusftcVlzIz4exZeVv79rJracYMWWDq1w9UZmYb5XBAVpbstQUYPZqCiGAy35hFRnYGma/GsafiBHaxH4PDQF+vvjx5+5MkxyYzLGYYEUERrh2/olyDa1klrk5dcan0u1Ln1LjrKS41JqBvACFDQ1ShSVFuUk5VlQz5Li5mrdlMfk0NAHG+vkzp2NEZ9N3e29vFI1UURWk+OTmwZIn8OnVKFpaefFJ2M/Xt6+rRKbcyVXBqxaqr8zl4cAqJiSucodx2exWlpTuc+UsWyxbsdgsA3t5RGI3JhIQkExKSREBAz0vyl5rS/PmyeFTXwbRtG5SXy9u6dIGxY+XtSUmQkKDyl9o0i0VmMK1ahfhqFce8ysj4+A0y87aR+XAhR6v2wr8z8fP0Y1D0IH5jmuLMXwr2CXb16BXlul28Slxd4clhc1BxqILSnaXwOez6za6bLi41ZsDuAc3xshSlzTNbrayvLS6tMZv5oTY4skP9oG+jkU5+fi4eqaIoSvOqrpaLQS9eDP/5j5ydMno0LFgAEyfKleYU5WapglMrdurUy1gsmRw58hgBAb2xWDIoLf0OIeTVN3//RDp2nFIvfym2WacenTt3oXMpI0NuS0mRhaQ+feCxx2RxadgwiIpqtmEorYEQcPAgrFqF7auV7Dm2mcwoO5lxXmQ+4UGBZxWseopQv1CSYpOYbppFkimJ2yNux9tDXSVW2gbnKnHv5ZP/Xj5e7b2wWWyIqtoUb1/Q7tBuurikKMqNq7Tb2WyxOHOYdpWW4gACDAZGGI3MiIxktK7TMyAAQxu8MlawrIATs09QnV2Nj8mHLmldCEtVIZmK4s727ZMB4H/7m1wNPCZGhnxPmwadOrl6dEpbowpOrUxVVTbbt3etDfWWioq+oqjoK0AjJub52gLTMLy82jXbOISAkycvFJcyMuDIkcvf9957G06vU9qu8q+/YPvcJ8j0PUuGCbYOM1A+QnZvdAqJ4q5Ymb2UZEqie/vuGJqxy05RWgUZ8YK1wIp3lDddXulCUP8gduTtoN/ofq4dm6K4GbsQ7CwtdXYwbbZYqBYCT01jcHAwv+vUidFGIwODg/Fu40HfBcsKODL9CI4KeYyuzqrmyHR5MqeKToriXiwW+Oc/ZTfTjh0y2uS+++SUuZQUULF0SnNRBScXEsJBeflBZ7i3xZJJdXV27a2egANwoGk+tG9/H127vumcWtfU7HZZ7a4f8J2XJ2/Tddm1VNfB1L+/XKVA02SxSbn1Ldu3jNlrZ5NtycYUYiJtdBqpvVIBOJd9iM2/epjMYTFk+BawK28XtntsaGj0Cu3Oo3F3OgtM0cHRLn4litLyNC8NzbOR8O4C145LUdyBEIIjFRXODqYNxcUU22wA9A4I4JmoKEbrOsNDQgj0dI/TXuEQlO0p4+izR53FpjqOCgcnZp9QBSdFcQNCyM91ixfDv/8NlZXQsyf86U/w05/KjF1FaW7uceRtJRyOGkpLd9YWlzKwWDZjs5kB8PYOr81ekivI5eW9S37++xgMvjgcNXh6hjZpsamqCr799kKBacsWKCmRt8XEyKUuk5JkBlNiYuPLXiptw7J9y5j+xXQqrBUAZFmyeOzjqbz/yRzOtPfh8PnD0B18ig4wMGYwLwx7gSRTEkNjhmL0Nbp49IriOmqVOEVxjbzqamcH01qzmdO1Qd+dfH2Z3KEDo41G7tR1OrpR0HflyUrMa8yYvzFjXmfGVmi77H2rs6tbcGSKorS0vDxYulROmzt2DIKDYepU2c10xx0qV1dpWarg1IxsthJKSrY6V48rLd2Ow1EFgJ9fPO3b309ISBJGYzK+vl0a5C9ZreeIjJxBZOR08vLeo6Ym/6bGYjbD5s0XCkzffQe152fcdhs8/PCFApPJdG37nDv3poaktAJ2h50Xvvqls9hUp0ZzsFGc5Ef6OB7p8wjJpmT6R/bH11OlByoKqFXiFKUlFVutbCgudnYxHa6Qx6z2Xl7caTTKoG9dp4sbBX1bC62Y19cWmNaYqTohzy+9o7xpN74doWNCOf6r49ScrrnksT4m9Z6lKG2N1Qpffim7mb76Ss5eGT5cZjNNngz+/q4eoeKuVMGpCVVX5zeYHldW9j1yWpwHQUH9iIycUdvFNAxv7yu3Mvfs+Ynz+/j4t697LDk5DafH7d8v2yq9vGRl+7nnZHFp6FBod4NRUCqz6dZTZatix+kdZGxbQebB1Wyxn8Ti5Wj8zprGyodXtuwAFeUWoVaJU5TmU2W3s6WkxNnF9F1t0Le/wcBwo5EnIiIYbTTSOzCwTQZ9N8ZeZadkcwnmNWaKvimibFcZCPAI8sA4ykj0rGj0MTr+Cf4NLmDWz3ACMPgb6JLWxRUvQVGUZnD4sOxk+ugjKCiAiAh48UUZAN6tm6tHp9wqqvOrOTjlIIkrEpv8QqoqOF1BdXU+Bw9OITFxRSPT2QQVFUewWDKdHUxVVccBMBj8CQ4eTGzsbwkJSSY4eDCenoHNNk6HAw4dalhgysqStwUGyqLST34iC0wDBqgKtzspripmS84WMn74howDX7Gj5iQ1dnm1M7EQHqwJ5+OoEgqpuOSxppBrbHVTFEVRlJtgF4LdpaXODqZMi4UqhwMPYFBwML+NjWW0rjPYDYK+69TlMJnXyA4mS4YFR5UDzVMjeEgwneZ1Qk/RCRoYhMGz8d9JXU6TWqVOUdqWsjL4179kN9OWLeDpCePHyylzY8fKnxXlepx6+RSWTAunfn+KhP9JaNJ9q3+OV3Dq1MtYLJmcOvV7unX7C2Vlu50dTLCeb78tBsDLqz0hIUlERf0/QkKSCQzsh8Hg1SRjmDfv0k6imhrYufNCgWnzZigqkreFhcnC0i9/KafI9e6t3nTcyemS02RkZ5CRtYnMo2vZZzmKQOCJB/1z7cwcOoXkoQ8x1Kcr7UMiQNcZflGGE4C/lz9po9Nc+EoURVGUtkoIwdHKSmcH0/riYsy1Qd89AwKYERnJaKOR4UYjwW50ElN5qtI5Rc689kIOU0DPACJnRKKn6IQMD8Ez6Np/J2GpYarApChtgBCwbZssMq1YIYtOCQnwhz/IfKYw9d9cuQGb/DbhqLrQBZv/Tj757+Rj8DUwvHJ4kzyH+xzFr8OmTX7OrCWA/Px3yM9/x/mzr29nYCDx8ZMJCUnG3z+hQftyU5o/XxaPtm69UGDavl2GfgPEx8slLZOTZYEpLk4FwbkLIQSHzx8mMzvTWWQ6ZZGtbYFWjSHZgsnxKSSl/oZBxtvwP3wcBg68ZN3TutXoLrdKnaIoiqLcrPzqatbVdjCtNZvJqZbB1SYfHya2b89oXedOo5FwH/fJF7IWWTGvMzu7mKqO1+YwRcocJj1FRx+t4xPhPr8TRVEaOntWTpf74AM5oyUgAB58UHYzDRmiPvcpN6f3f3pz+JHDVJ2Uxx+Dr4H2k9oT98e4JnuOqxacNE3rBvwaqBRCPNNkz9yKDRp0guPHn+fs2X8BNkDDz68bMTG/pF278fj4RLFhwwYiI0c2y/OfOXOhuASg63LanMEA/frBjBmyuJSUpKrZ7sRqt7L7zG4ysjLIyM4gMzuTwspCADpavUk+buO5U5B81pc+ve/Cc9yPYdw4OZkbYEjHy+47tVeqKjApN8wdjxOK4o7Wm81MO3yYJd27M0rXr3jfEpuNjfUKTAdqg75DPT25U9f5TW3Yd5yfX7NdtGtt7FV2SraUOLuYSneWXshhGmkk+rlo9BQd/+7+bf53oo4binJ5Nht8/bXsZvriC/nzkCHw/vsyJiUoyNUjVG51pXtKyV6Qzbn0c1A7K1vz0XDUOPAI9mjSHKdr6XD6GzAfeBVA07SewItCiKlNNopWxscnAg+PYMCBpvkghBWjcTSRkU81+XMJIZerzMi4kL907FjD+zhqu9xefBEWLmzyISitVFlNGdtytzk7mLblbnNOe4vT4/jxMQ+Sv4OkbOimx6CNGw+PjZNLUrjRFWKlVXC744SiuJv1ZjPj9+2jwuFg/L59rOzVq0HRqdrhYKvFwtriYtaazXxbUoId8DMYSA4JYWp4OCm6Tl83CvoWDkHZ97U5TN9clMM0uF4O04AgDF7ukU1VjzpuKMpFjh2DJUvgww8hLw86doRZs+Cxx6BHD1ePTmkLLFssZKVlUbSqCI9gD0wvmSj7vgzfTr5ETo8k7708avIvXd30ZlxLwckghPhK07QFAEKI/bUHhTbNai0gMnIGkZHTyct7j5qa/CbZr80G33/fMOC7oEDe1q6d7Fp66ik5Ra5fP1k3EKJJnlpp5c6Vn3MWlzKzM9mVvwu7sGPQDPQJ68MT9j4k7T5P0t82EhEUAQsWQA8/2cUUH+/q4bcIq9VKbm4uVVVVV7+zcglfX1+io6Px8mqajLl6WatjogAAIABJREFU3PI4oSjuon6xCXAWnd7o2pUSm401ZjMZFguVtUHfA4KD+XVsLKONRoaEhODjJkHfUJvDVDtFrnhtMdbzVgD8b/Mn4qkIQseEXncOUxuljhuKAlRUwMcfy26mjRvljJZ77oG33pJB4E1/yqa4GyEE5jVmstKysGy04NXei87/3ZnIZyLxMjb8Bxb/dtN/pryWo12epmmdAQGgyR5fvyYfyXXQNC0ZSEWOP1EIMbSpn6Nnz0+c38fHv33D+6mslJlLdcWlLVtkyBtAp04wZsyF/KXu3eWbjNL2CSE4WXySjKwMZ5HpSOERAHw8fBgUchsviWEkf3eWIe9+SXBUF1i6FE5tAu9QuZPf/MaFr8A1cnNzCQoKolOnTm1+ukFTE0JQWFhIbm4unTt3burdt7rjhKIoTePiYlOdCoeDGT/8AECivz9PRkQwWtcZYTQS4kZB39YiK8XrizGvMVP0TVGDHKbQH4VeyGGKVJ3HF1HHDcVtCSEXgFq8GP7xDygpkTm8aWnwyCMQFeXqESptgXAIzn9+nuwF2ZTuKMU70pu4P8UR+WQkHgEeV99BE7mWM4JZwPtAuKZp04CxwP4bfUJN0z4AxgNnhRA9620fC/wZ8ADeF0K8crl9CCEygAxN0+4DdtzoWJpDUZEsLNV1MO3cCVarDHTr2VOuIpCUJItM0dFX39/cuc0/ZqX52R129p/dL8O9azuY8krzADD6GkmKHMxjXgNJ2lNE/y924nN6l/xHM3AgFJZBFPII9Mgjrn0hLlZVVaWKTTdI0zTatWvHuXPnmmP3TXqcUBSldThbU8NPDhy4pNhUX5S3NwcGDmzBUbmWo9qBZbPF2cVU+l1tDlOgB8ZRRqJn1uYw9Wj7OUw3SR03FLdTWAh//7sMAN+7F/z8YPJkOWVu+HDVeKA0DYfNwbkV58hamEXFgQp8u/gS/1484VPDMfi0/D+yqxachBCnaotB9wF9gI3ABzfxnB8CbwEf1W3QNM0DeBsYA+QCOzRN+xxZfLo4tegxIcTZ2u8fBp64ibHctOzshvlLBw7I7d7eMGCAXGEuORmGDpXh39dr3rwmHa7SQqpsVew4vcNZXNqSswVLtQWA6OBoRsSOILlDf5K/LSBx9U4Mm9bKymRICNx9t5wmN3asnLytNKBO4G9cc/3umuE4oSiKC5Tb7WTUBn2vMZv5vrz8ivf3Nxj4WxsPFhEOQdneMmfQtyXDgqPSAR7IHKa5tTlMA90yh+mGqeOG4i4cDlizRnYzffYZ1NTAHXfAO+/AQw/JU39FaQqOagdnPjpD9qvZVB2vwv82f3os60GHn3TA4Om649M19TwLIWxAeu3XTRFCbNI0rdNFmwcCx4QQJwA0TfsncK8QYiGyG+oSmqaZAIsQouRmx3Ql8+ZdKPo4HHDwoCwuffxxD6ZOhZwceVtwsCwqPfywLDANGAC+vs05MqU1Ka4qZkvOFucKcjvydlBjl4FriR0SmdJzCsmmJJKyIDYoGkaOlO1wd3aEhASZCDhunPxHpCZrK7egpjxOKIrSMmwOBztKS50ryW0pKcEqBN6aRlJICAs6dyZF17HYbNy7f3+DTid/g+GS4PC2oiqryjlFrkEOU6I/EdMj0FN0jMONeAa7z9TB5qCOG0pblpUlA8CXLJENCqGhcqXxxx+H3r1dPTqlLbGX28n73zxy/phDzekagu4IIu7TONpPaI9mcP2F+tZypIwCcur9nAsMuspjHgeWXO5GTdOmA9MBwsLC2LBhw3UPymrVmD9/BPn5x9m3L4T9+0MoLZXFgNDQEHr3PsvEiRZ69bLQuXMZHrVTIe122Lbtup9OuYWcqz7HPss+9lr2ss+yj5PlJxEIPDQPEgITmBgxkV4hvbjdFknk6SLMgf2hCNrPnEZR+/bsfe01ALxXrKCmXTu5UyFg82YXvqrWLyQkhNLSUlcPgy+++ILU1FS+++474uPjycrKYsCAAXTr1g0hBP7+/rzzzjt069btksd++umnLFy4kCNHjrB+/Xpuv/32a37enj17EhgYiEftm83QoUN57bXXmDFjBps3byY4OBgAPz8/1qxZ0+g+qqqqbuj9UFGUW58QgsMVFc4Opg3FxZTY7WhAv8BAfhEdTYquMywkBH+PhvkOK3v1cmY5tbVik9V8IYfJ/I2ZymOVAHhHeBN6Tyj6GJXDpChKQ/36wZ49l26PjYVu3WDtWvnzmDHw2mtw771qEWmlaVmLreS9nUfum7lYz1sxjjTSfUl39BS9Vc0IaS0Fp8Z+I1dcm00IccV0IyHEe8B7AHfccYcYOXLkdQ9q+nT553vvxZGQAA8+eCF/KStrG6NGjQTUlKe2TgjB4fOHneHeGdkZnCo+BUCgdyBDY4byaMyjJMcmMzC8P/57DsCXX8KXH8Pu3RAUBOfPy3mWX31FQEwMIwMCXPuiblGHDh0iKCjo2h+wbBnMni0vLZlMMo0xNfWmx/HZZ5+RlJTEF198wbx58wgMDCQuLo69e/cCsGjRIv785z+zdOnSSx47YMAAPvvsM5566ikCAgKu6/VomsbGjRtp3759g+1eXl788Y9/ZPLkyVfdh6+vL/369bvm51QU5dZ2urqatbUFpjVmM/k1svs2zteXhzp2JEXXGaXrtLtKd+0oXWdlr15MO3yYJd2739LFJke1A8uWi3KYHLU5TCONRD0bhT5G5TApinJ5Q4bImS81F60gn5Ul/5w7Fx59VBagFKUp1ZytIffNXE6/fRp7iZ3QH4USOzuWkKGtc35mayk45QIx9X6OBvJcNBbmzYP58xtuO3IEpky5kNmcnd3iw1Ka0LJ9y5i9djbZlmxMISbSRqeR2ksWIqx2K7vP7HZOj8vMzqSwshCAjgEdSTYlM2vQLJJMSfQJ74NnSRl8/TUs/gC+ekAWlwwGOT1u4UI5Va7uRL57d1e9ZPezbJmsGldUyJ+zsi5UkW+i6FRWVsbmzZtZv349EyZMYF4jQWslJSXol/kw1qON550oiuJaFpuNjfVymA7Vvge29/JitNFIiq4zWtfp7Hf9C4KN0nVODRnS1ENuds4cptoCk2VTwxym2DmxhI4JVTlMiqJcs5kz4f33G27z8JCnnw88oALAlaZXlVtFzms55P9vPo4qBx0md8D0GxNBfa/jYrwLtJaC0w6gW+3yqKeBKchAcJeon9ukaXKmk9J2LNu3jOlfTKfCKk/CsyxZPP5/j/PJwU8ori5mW+42521dQ7syIWECSaYkkk3JdA3tKtvxHA55VFm+HH72MzmPMjQU7rlHFpjuvlv+rDSfWbMa72Wus20bVFc33FZRISfP/+//Nv6Yvn3hzTev+LSfffYZY8eOJT4+ntDQUHbt2kVoaCjHjx+nb9++lJaWUlFRwfbt26/r5Rw5coQHH3yw0ds2bNiA0WgEYNSoUc4pdY888gi/+MUvAHjhhRf47//+bwBuu+02li1bdl3PryjKrana4WBbSYmzwLSjpAQ7MmNpuNHI4xERpOg6vQICMLhRt05VdpUz6Nu81oz1XL0cpidrc5hGqBwmRVGunRCwaZMMAP/3v+V6P3W8veGJJ+SMGEVpShXHKsh5NYczS8+AgLCfhmF6yYR/gr+rh3ZNWvwoq2nacmAk0F7TtFxgrhBisaZpzwJfI1em+0AIcaClx6a4h5fWvOQsKNWptlfzyeFP6Bfejyf6PUFybDLDYoYRERTR8MFZWTBiBLzyimx5GzAAfvUrWWQaNAguyrxQXOjiYtPVtl+j5cuXM2vWLACmTJnC8uXLeeaZZ4iLi2NPbQFsxYoVTJ8+ndWrV1/zfhMSEpyPv5L169dfMqUO4LXXXrumKXWKotzaHEKwr7zcWWDaVFxMhcOBBzAgOJhfx8aSousMDg7Gx40usTfIYVpjpvJovRymsaHoKbU5TFEqREVRlOuTlwdLl8IHH8CxY3KxqEcfhfvuk19VVfIjwJw5rh6p0paU7Ssje2E2Z1ecRfPSiJgegekFE76xt9bKZC1ecBJCPHSZ7auAVS08nKuae8WkKKW1E0JwsvikzF+qnSKXW5Lb6H01NHY9tevChuxs+Ps7Mo/pttvg1VchOhqGDYOwMHmfrl1lLpDS8q7SiUSnThcm0tcXGws3GJpdWFjIunXr2L9/P5qmYbfb0TSNp59+usH9JkyYwLRp0wCYNm0au3fvJjIyklWrLv8Wd60dToqiuJ9TlZXOAtPa4mLO115W7+Hv7+xgGmE0EuLpPt06jmoHlq0WZxdTXQ6TIcAgc5ieiUJP0fFPVDlMiqJcP6sVVq2S3UyrVsnJDMOHw+9+B5MmgX9tc8m0abBokfwzPNy1Y1bahpLtJWQtyKLw80I8Aj2IeT6G6F9E4xN+a14wcZ8zkxvUSDyL0orZHXb2n93vzF7KyM4gr1TGgRl9jSSZkigoL6C4qviSx5qCY2Sf7Jdfyq8DtU12XbrIPCa4MDlbaf3S0hpmOIE8O7iJAmF6ejpTp05l0aJFzm0jRowgN7dhETMzM5O4uDgAliy57GKaDVxrh5OiKG1fodXK+npB38erqgCI9PbmntBQZw5TlBsteSQcgvJ95ZjXmCn6pqhhDtOgYGJ/G4s+Rid4YDAGb/fp7LpW8zbMY97Iea4ehqK0ej/8IDuZli6FM2dkEemFF+Cxx+TqcxebM0d+ZFDdTcrNEEJQvKGYrLQsitcW4xnqSaf5nYh6Ngqv0Csv6tHaqYKTckurtlWzI28HGVkZZOZksjl7M5ZqCwDRwdGMiB1BsimZ5NhkEjskYtAMl2Q4Afg7PEhbcQ5+OQI8PeVShNOmyalyCQkyzEu5tdQFgzfhKnXLly/npZdearBt0qRJLFiwwJnhJITA29ub9y9Okqz16aef8vOf/5xz584xbtw4+vbty9dff33NY6if4dS7d28++ugjoGGGE8C3336Lt7f39b5ERVFcoNJuJ9NicRaYdpeVIYAgDw9GGY08Fx1Niq7T3d+9unWqsqucU+TMa+rlMPXwJ+KJ2hymkSqH6VrM3zhfFZwU5TLKyyE9XXYzZWTI68vjxslMpnvukR8NLiciAjZubLmxKm2LEILCLwvJTsumZFsJ3uHedHmtC5FPReIZ1DaObW3jVShuw1JlYUvOFjKy5fS4Had3UG2XmTyJHRJ58LYHSY5NJtmUTKyx8XVIUwOHgmM8s4O3kV2Sg8keSNo6jdTESfDCOBgzRk7OVm59qak3VWC62IZGpuLNnDmTmTNnXvM+Jk6cyMSJE2/o+U+dOtXo9g8//PCG9qcoimvYhWBnaSlrawtMmy0WqoXAS9MYGhzM7zt1YrSuMyAoCE93ymEqviiH6YfaHKZwb0Lvrs1hSlE5TNfrTNkZQF6k8/FUvztFARkA/t13ssi0fDmUlMgOpldegalTZSFJUZqLsAvOpZ8ja0EW5XvL8e3kS7f/6Ub4tHA8fNtWJrAqOCmtWl5pXoP8pb0FexEIPA2e9I/oz7MDnyXZlMww0zDa+18apAzIyxZr10KfPjK/Z9cuUuf8i9TvvoP+/aGsDOb5q/VLFUVRlGYhhOBovRym9cXFFNtsAPQJCODZqChSdJ1ko5EAN1p8wpnDVFtgKt3RMIcp8v9FoqfoBNwW4FadXU3hdMlpnvj8CVYfv7B4hW+aDJqdO2Ku6nZS3FZhIfz977LQtG8f+PnBAw/IRYyTk9WkBqV5OWocFPy9gOxXsqk8Wol/d3+6L+1Ox4c6YvBqm59FVcFJaTWEEPxQ+EOD/KUT5hMABHgFMCRmCPNGziPJlMSgqEEEeAdcfmcnT17IYlq/Xq5M9uqr8OKL8KMfQX7+hWS/wMAWeHWKoiiKOzlTXc264mJnkSmndoXMWB8fJnfowGijkTt1nY5uNPVVOATl+8udQd/Fm4pxVNTmMA2szWFK0QkepHKYbkS2JZuPD35M+qF0tuRsAeC2DrfxQOIDzNs4D8fvHKpwp7glh0Nee168GD79FGpq4I474N135aLTISGuHqHS1tkr7eS/n0/OazlU51QT2C+Q29Jvo/3E9miGtv2+rApOisvYHDb2nNnj7F7KzM7kXMU5ADr4dyDJlMSzA54lyZRE3/C+eHlcITDNaoUtWy4UmQ4elNvj4+Hpp2H8eEhKktv8/OSXoiiKolzBerOZaYcPs6R7d0bp+hXvW2qzsaleDtP+8nIAQj09uVPXma3rpOg6XXx93epDf1VObQ7TN2bMa81Yz9bmMHX3J+Lx2hymEUY8Q9Qp6Y04aT5J+sF00g+l8+3pbwHoE9aHl0e9zKQek+jRoQcA8zbOc6t/d4oCkJMDS5bIr1OnQNdhxgzZzdS7t6tHp7gDW4mNvHfyyHkjB+tZKyFJIcS/F0/o3aFu856sju5Ki6mwVrA9d7szf2lrzlbKrfKEvLOxM/d0u0cGfJuSiW8Xf/X/hNXV4OMjJ2EnJMiuJi8vGDECnnxSpv01tpyEoiiKolzFerOZ8fv2UeFwMH7fPlb26tWg6GR1ONheUsIas5m1xcVsKynBJgS+BgPJISH8LCyMFF2nb2AgBjc5qYTaHKYNxc4uprocJq8wL/QxOqFjQjGONuIb7evikd66jhYe5eNDH5N+MJ2d+TsB6B/Rn4WjFzKpxyS6tbv03GfuiLktPUxFcYnqavj8c9nN9J//yI8JKSmwcCHcdx/4qrcepQXUnK/h9F9Oc/qvp7EV29Dv1omdHYsx2ejqobU4VXBSmk1hRSGZ2ZnO6XE783dic9jQ0Ogd1ptH+z5KsimZJFMSUcFRV9+hEBcmVv/iF/IocuCA3Pbii9Cxowz8Dgpq3hemKIqitGn1i02As+j0165dKbHbWWM2s9FiocxuRwPuCArihZgYUnSdocHB+LbBHKaCZQWcmH2C6uxqfEw+dEnrQlhqGI4aByVbSzCvMVP0TVHDHKYRRiJnRKKPUTlMN+vw+cOyk+lgOt8XfA/AoKhBvDbmNSb1mERnvfMVH68ym5S27sABWWT629/g/HmIjoY5c+Si0506uXp0iruozqsm5/Uc8t7Nw1HhoP397Yn9TSxB/d3386kqOCnXbdm+ZcxeO5tsSzamEBNpo9NI7ZVKVnGW7F7KyiAzJ5OD5+S0Nm8PbwZGDeT5Ic+THJvM0JihGH2vsbpbF/j95ZewerVcTqJDBxg6FIxGsNnkWqUzZjTjK1YURVHcxcXFpjoVDgeP//ADAPF+fkyt7WAaaTSie11hyncbULCsgCPTj8i8JaA6q5rD0w6T/YdsKo9VNsxhml2bwzRY5TDdDCEEB84dcBaZDpw7AMCwmGH86e4/cX+P+zGFmFw8SkVxrdJSWLFCFpq2bZMTHe69V06ZGzMG2mDtX2mlKk9Ukv2HbM4sOYOwC8IeDsP0komAxCtkDrsJVXBSrsuyfcuY/sV0KqwVAGRZsnjk00eYuWomRVVFAAT7BDMsZhg/7fVTkkxJDIgagK/ndfSvNhb4HRQEd90l1yzt0EEuJ6EoLvLpp59y//33c+jQIbp3786pU6fo0aMHCQkJCCEICAhgyZIlJCQkXPLYF154gS+++AJvb2/i4uJYsmQJRqP7tdcqSmtUbLXy4MGDlxSb6ovy9ubIoEEtOCrXO/6r485iUx1hFVQcrJAdTCk6xpEqh+lmCSH4vuB7Z5HpSOERNDSGxw7nr/f8lYndJ15bR7iitGFCyNjWxYvhX/+S16YTE+H11+FnP5MfExSlpZQfLCd7YTYFywvQPDQiHosg5oUY/LqovOA66sxAuSY19hp25u3k2VXPOotNdezCTpW9ir/e81eSTEn06tgLD8N1XlIoKJBHipUr4dAhua0u8HvcOLlOqRut5KM0rXkb5jXpdILly5eTlJTEP//5T+bNk/uNi4tjz549ACxatIgFCxawdOnSSx47ZswYFi5ciKenJ7/61a9YuHAhr776apONTVGUa1ftcLClXtD3d6WlXL7UBP4GA3/r0aPFxucqNotN5jDVTpOrOV3T6P2EXdDtryor8WYIIdiVv8sZ/H2s6BgGzcDITiN5btBzTOwxkfDAcFcPU1Fc7uxZ+OgjWWg6fFguMv3QQ7KbadCgC6kbitISSneWkrUgi/OfnMfgbyD6uWhi/isGn0gfVw+t1VEFJ6VRpdWlbM3d6lxBbvvp7VTZqi57/0prJc8OfPban0AI+PvfITRUFpS8vOCtt2DYMJg+XQV+K01q/sb5TVZwKisrY/Pmzaxfv54JEyY4C071lZSUoF9mRau77rrL+f3gwYNJT09vknEpinJ1DiH4vqzMWWDKsFiodDjwAAYFBzMnNpYUXafC4WDi/v0NOp38DYZLgsPbCkeNg5JtMofJvMZMybclYAeDv8xhsp61YjPbLnmcj0mdWN8IIQTfnv7WWWQ6VXwKD82D0V1G8+LQF7mv+310CFBtGopit8PXX8si0+efyySNoUPlzz/5iSw6KUpLKt5UTNaCLMxfm/E0ehI7J5aomVF4t1eNEZejCk4KAAVlBc5w74zsDPac2YNDODBoBvqF92NG/xkkxybz3FfPkVuae8njr5ojIAR8/z0cOwaTJ8vLEH/4g+xiGjdOFp4KC8FPtR8q12bW6lnsObPnmu8/8sORV71P3/C+vDn2zSve57PPPmPs2LHEx8cTGhrKrl27CA0N5fjx4/Tt25fS0lIqKirYvn37VZ/vgw8+4MEHH7zWl6Aoyg04WVnpLDCtKy7mvNUKQKK/P09GRJCi64wwGgn2bHhKtLJXL2eWU1srNgkhKD9Q7lxJrnhjMY5yBxhqc5h+XZvDNETmMF2c4QSyGNUlrYsLX8WtxSEcbM3ZSvrBdD4+9DE5JTl4GbwYEzeG3w3/HRMSJtDOv52rh6korcKJE/DBB/Dhh3D6tJwm99xzspvJDZpMlVZGCEHR6iKyF2RjybTg1dGLLq90IfL/ReIZrMopV6N+Q25ICMFx83FZYKrtYDpadBQAX09fBkcPZnbybJJNyQyOHkyQz4VU/UpbZYMMJwB/L3/SRqdd+kT1A7+//FIeMYKD5Zqknp5ylbmwsAv3V8UmpQmdKj5FliXL+fPGrI0AxIbE0snY6Yb3u3z5cmbNmgXAlClTWL58Oc8880yDKXUrVqxg+vTprF69+rL7SUtLw9PTk9TU1Bsei6Iolyq0WllXW2BaYzZzokp250Z6e/Oj0FBSdJ3Ruk6kz5W7c0bpOit79WLa4cMs6d79li82VeVWUby2mKJvijCvMWMtkIU3v3g/wh8Nd+YweRkvDUAPS5XH6sZWqVMuz+6wk5mdSfrBdD45/Al5pXl4e3gztutY0u5M48cJP772RVQUpQ3p1w/2NHLNMDYW4uJg3TowGODuu+Evf4Hx41WyhtLyhENw7pNzZC/Ipmx3GT4xPnT9a1ciHo/Aw08l0l8rVXByA3aHnb0Fe50dTJnZmeSX5QOg++okmZJ48vYnSY5N5vaI2/H2uPw7emov+eG4sVXqgMYDvwMDZeD3+PFwzz2y2AQQEdGsr1tp267WiVSfNl9DzBU3/ZyFhYWsW7eO/fv3o2kadrsdTdN4+umnG9xvwoQJTJs2DYBp06axe/duIiMjWbVqFQBLly5l5cqVrF27Vi0T3kw0TUsGUpHHuUQhxFAXD0lpJpV2O5n1cph2l5UhgCAPD0YZjcyKjiZF1+nu73/d/99G6TqnhgxpnoE3M1vJhRwm8zdmKg7LC0VeHbzQU3T0MTr6aB1f07Ut6hGWGqYKTNfA5rCxKWuTLDId+oSC8gJ8PX25p+s9TE6czPj48QT7BLt6mIriUkOGwMGDUHNRPFxWliw0vfwyPPooREe7ZHiKm3NYHZz9x1myX8mm4nAFft38SPgggbDUMLX66g1QBac2qMpWxY7TO5zT47bkbKGkugSAmOAYRnUeRbIpmSRTEokdEjFo1/cfJ7VX6oUCk9Uqp8sBvP8+PPmk/L5bNxX4rbQ56enpTJ06lUWLFjm3jRgxgtzchtNMMzMziYuLA2DJkiUNblu9ejWvvvoqGzduxN/fv/kHfQvSNO0DYDxwVgjRs972scCfAQ/gfSHEK5fbhxAiA8jQNO0+YEczD1lpQXYh2FVa6iwwbbZYqBYCL01jSHAw8zt1IkXXGRAUhKfBfU4MHVYHJdtLnNPkSrbX5jD5yRymiCci0MfoBPQMQDOoQndTstqtrD+1nvSD6Xx6+FPOV5zH38ufcd3GMTlxMj/q9iMCvVXYjKLUmTlTfmyoz8MDli+HSZNk0UlRWpq9ys6ZJWfI+UMOVaeqCOgTQOKKRDpM6oDmoY6bN0oVnNqA4qpituRscU6P25G3gxq7vGSQ2CGRh3o+5CwwxRpjb/4JhZAZTEePwoAB8O67MGUK3Hkn/OlPKvBbaXXmjpjbJPtZvnw5L730UoNtkyZNYsGCBc4MJyEE3t7evH/xmVStZ599lurqasaMGQPI4PB33323ScbXhnwIvAV8VLdB0zQP4G1gDJAL7NA07XNk8WnhRY9/TAhxtvb7h4EnmnvASvMRQnDsohymYpsMsO4dEMAzUVGk6DrJISEEerrPaY0QgoqDFc6V5CwbLdjL7GCAoDuCML1kQk/RCRkSgsFHfXprajX2GtacWEP6wXQ+O/wZ5iozgd6B/Dj+x0xOnMzYrmPx91IXFRSljhCwaZMsNKWny2vWdby94Ykn4IEHXDc+xX3ZSm3kLcoj9/Vcas7UEDw4mK5/7Uq7ce3UTIQm4D5nZreYZfuWXXba2umS0w0CvvcV7EMg8DR40j+iPzMHziQ5NpmhMUNp79/+5gcjBOzdK6fJrVwJAwfCm29Cly6QmionW4P8uTbbRlFak6ZaoW7Dhg2XbJs5cyYzZ8685n0cO3asScbSlgkhNmma1umizQOBY0KIEwCapv0TuFcIsRDZDXUJTdNMgEUIUXKZ26cD0wHCwsIa/fu9GWVlZU2+T3dhBnYBO2v/LKjd3hEYAvQH+gGh5eXEDEcqAAAgAElEQVQyLzA3l+9cMtIWdo6Gv5jC2u3RwJ3AHUBfKA0qpZRSssmGra4ZaltU46hhR9EONp7fyJbzWyi3lxPgEcDQdkMZETeCAaED8DZ4QwF8W/Ctq4erKK1Cfj4sXSpDwI8elXGujz4qI13vuw+qqmR305w5rh6p4m6sRVZO//U0uX/OxWa2oafo9PhHD4wjjarQ1IRUwakVWrZvWYNg7ixLFo/932O8u+NdTpee5mTxSQACvAIYEjOEeSPnkWxKZmDUQAK8A5pmEBUVDQO/66YM3XGHXFkO5NHh7beb5vkURVGuLArIqfdzLjDoKo95HFhyuRuFEO8B7wHccccdYuTIkTc5xIY2bNhAU++zrSq329lUXOzsYtpbXg6A0dOTO41GUnSdFF2nq5+fW50E2krr5TCtMVNxsDaHqb2XzGBKkV++sdeWw6Rcv0prJauPrebfB//NFz98QVlNGUZfIw/0eoDJPSaT0iUFH88rB9Arirux2WDVKli8WH6MsNth+HBZVJo0CeoSBaZNg0WL5J/h4a4ds+I+qs9Uk/tGLnnv5GEvs9NuQjtifxNL8CCVr9ccVMGplbE5bDz/n+cbrAIHsnV7S+4W7k24l58P/DlJpiT6hvfFy+PS1WRuyooV8jLE+vXykkNd4Pfvfy8Dv9XRQFEU12isynDFJHghRNPMpVRuyHqz+bIrvNkcDnbUy2HaWlKCVQi8NY2kkBAWdO5Miq5ze1AQHm5UYHJYHZR+W+qcJle6vRRhExj8DIQMDyF8mlxNLrB3oMphakblNeWsOrqK9EPpfPnDl5Rby2nn144pt01hcuJkRnUedcUFVhTFXR07JotMS5fKzqbwcHj+eXjssQvXq+ubMwcOHFDdTUrLqMqqIvsP2eQvzkdYBR0f7Ijp1yYCe6mMveakCk4uVmGtYHvuduf0uK05Wym3ljd6XyEEnzz4SdMO4PBhWLYM5s6Vq8dt3y77XWfMuBD4fZWloxVFUVpALhBT7+doIM9FY1GuYr3ZzPh9+6hwOBi/bx9f9OxJhI+Ps8C0obiYErsdDegXGMgvaleSGxYSgr+H+yw1LISg4lCFs4OpeEMx9lI7aDKHKeaFGPQxOsFDgvHwdZ/fiyuUVpey8oeVpB9K56ujX1Fpq6RjQEd+1vtnTE6czIhOI/A0qNNmRblYZSV8/LHMZtq4UQZ+jxsHjz8OP/oReF3h2nhEhHyMojSniiMVZC3M4uyys6BB+CPhxPwqBv+uKmevvnkb5jVZDEl96sjZwgorCtmcs9kZ8L0zfyc2hw0NjV5hvXi076Os2L+C85XnL3msKcR08wMoKoLVq+V6pJ07w/798MorMHky9Okjv3/jjZt/HkVRlKa1A+imaVpn4DQwBRkIrrQy9YtNABUOB6P37nXe3tnXlykdO5Ki64wyGmnvZquYVudXOwtM5jVmavLkIh9+Xf0ISw1DT9ExjjLiFdrEHczKJSxVFj4/8jnph9L5+tjXVNuriQiM4PF+jzM5cTJJpiQ8DKrQpyiN2b1bFpmWLQOLRUa6LlgAjzwCkZGuHp2iQOnuUrIXZnMu/RwGXwORz0QS83wMvtFqGnpj5m+crwpOt6JsS7azuJSRncHBcwcB8PbwZkDkAJ4f8rwz4NvoawRgSMyQBhlOAP5e/qSNTrv+AQghe1VXrpSTqLdsAYcD/vhH+K//gvHj4fx5CAmR93ezE39FUVofTdOWAyOB9pqm5QJzhRCLNU17FvgauTLdB0KIAy4cpnKRUpuNv+bmMjcrC5u4dLajt6bxQUICqW42NdtWasOyyULRN0Uyh+mAPLZ7tvN0ZjDpKTp+nfxcPFL3UFRZJItMB9P5z/H/YHVYiQ6OZsYdM5icOJmhMUMxaGpVP0VpTHEx/OMfstC0ezf4+spMpieekBlNBvVfR2kFLFssZKVlUbSqCI9gD0y/NhH9XDTeHdXn3MZ8f+Z7Xt/6OiCbY9r5t2vS/auCUxNyCAeHzh1yFpcysjLIKZEZt0HeQQwzDSO1VypJpiQGRg3E17Px6mrdanSXW6XuqiorZQZT3apy2dlye79+MHu27HMdMEBu8/WVX4qiKK2EEOKhy2xfBaxq4eEol2F1ONheUuKcJre9tLTRQlOdGiGYffJkmy84OWwXcpjMa8yUbC2ROUy+BkKSQwh/pDaHqY/KYWop5yvO89nhz0g/mM7ak2uxOWzEhsQyc9BMJidOZmDUQFVkUpTLEEJOe3v/fTl1rqpKfqR46y14+GG4KKJPUVxCCIF5jZmstCwsGy14tfei8393JvKZSLyMqmP4YkIIvj7+NU9/+bRzQTKA9q/JFe7njpjbZN1OquB0E2rsNezK3+XsYNqcs5miyiIAwgPDSTYl87zpeZJNyfQO631dbdmpvVKvvcAEclnogADZvdS1K+TlySUgUlLgt7+Vk6ijoq73JSrKLe9KwcU36tNPP+X+++/n0KFDdO/enVOnTtGjRw8SEhIQQhAQEMCSJUtISEi45LFz5szh//7v/zAYDHTs2JEPP/yQSNV7rtwChBAcKC93Fpg2WiyU1eYw3REUxAsxMbTz8uJ3J086p9PV528wsKR795YfeDMTQlBxpALzN7U5TOvr5TD1DyLm+Rj0FJ3gYSqHqSUVlBXw6eFPST+YzoZTG7ALO130LvzXkP9icuJk+kf0d6sVDxXleuXlyfDvxYvh+HE5GeKxx2Q20+23u3p0iiIJh+D85+fJXpBN6Y5SvKO8iftTHJFPRuIRoI65F6u2VbN8/3Je3/o6+8/uJzIokldGv8L0/tMJ/UMoYu4V1+O5IargdBnL9i27pMPo3oR72ZqzlYzsDFbuXcnhzYeptFUC0C20G/cl3EeSKYnk2GTi9LjmPZFxOC70rT79NKxbJwPADQZ4+WU5eXrkSNW9pLi1i4OLV/bq1SRFp+XLl5OUlMQ///lP5s2bB0BcXBx79uwBYNGiRSxYsIClS5de8tgXXniBl19+GYC//OUv/P73v+fdd9+96TEpSnPIrapibXGxs8h0pkbmDXXz8+NnYWGk6DojjUZC66XC3h4Y2CDDCWSxqan+/7WUgmUFnJh9gursanxMPnRJ60JYahggl1QuXlvsnCZXc1r+Xny7+NLx4Y5ymtwoHa926qpqS8orzeOTQ5+QfjCdTVmbEAji28XzUtJLTE6cTJ+wPqrIpChXYLPBqlWym2nVKrDb5ceJefPk1Dk/NfNXaSUcNgfnVpwja2EWFQcq8O3iS/x78YRPDcfgozpWL1ZUWcSi7xbxl2//wpmyM/Tq2Iul9y1lSs8pzb7qqio4NWLZvmUNMpSyLFlM/XQqQggEAoNmIC4gjidvf5Lk2GSSTEmEB7bAFIHiYvj6azlV7uuvZeB3hw4wZowMALfbwcNDXn5QFDfXWHBxUxSdysrK2Lx5M+vXr2fChAnOglN9JSUl6Jd5juDgYOf35eXl6sOP0qpYbDY21CswHa6Qx8EOXl6M1nVSar9ir3AxY5Sus7JXL+f/v1u12HRk+hEcFfL9ozqrmsOPH+bM389Qk1tD+X65mqxnqCf6aB19jI4+Wsevi/o01tJyLDmyyHQonc3ZmxEIEjskMmf4HCYnTqZnx57qfVZRruLoUdnJtHQpnDkD4eHw4ovyI0XXrq4enaJc4Kh2cGbpGbJfzabqRBX+t/nTY1kPOvykAwZPVWi62AnzCd7c9iaLdy+mwlrBXXF38dF9H5HSJeWSY+PcEXObZQyq4NSI2WtnNwjsBpnPFOwTzL8m/4shMUPYtXUXI0eObN6BCAFHjlwI/M7IkEWl0FC45x4oK5MFp4kTm3ccitIKzTp6lD1lZY3eZrbZ2F9ezsWTeiocDlK+/56eAQHonpe+/fUNDOTNbt2u+LyfffYZY8eOJT4+ntDQUHbt2kVoaCjHjx+nb9++lJaWUlFRwfbt2y+7j9mzZ/PRRx8REhLC+vXrr/paFaW51DgcbCsp4ZvaAtOOkhLsyI6k4UYjT0REkKLr9AoIwHAdH9rrik5NPZ21pZz4zQlnsamOqBaYV5vRU3TCfhqGPkYnsK/KYXKFU8Wn+Pjgx6QfSmdb7jYAeof1Zv7I+UxKnERih0QXj1BRWr+KCpnJ9P77sGmTvGY9bpwMAL/nHmjkNElRXMZebifvvTxy/phDTV4NQQOC6PpGV9r9uJ06DjdiW+42Xt/6Op8c+gQPzYOHez3ML4f8kt5hvS/7mOZYoQ5UwalR2ZbsRreXVpdyd9e7m38A+fnwyiuy0HTihNzWq5e81DBuHAweLI8KiqI06khFxSXFpjqO2tsH1+s0uh7Lly9n1qxZAEyZMoXly5fzzDPPNJhSt2LFCqZPn87q1asb3UdaWhppaWksXLiQt956i/nz59/QWBTlejmEYH/9HKbiYiocDgzAwOBgfh0bS4quMzg4GJ+bXG5olK5zasiQphl4MxNCUPlDJeY1Zoq+KaI6u7rxO2rQ55s+LTs4BYBjRcecRabv8r4D4PaI21lw5wImJU4ivl28i0eoKK1Lv35Qe1rSQHw8jB4tV5uzWGQH08KF8MgjEBHR8uNUlCuxFls5/dZpct/MxVZowzjSSPel3dFH66p79SJ2h53Pj3zO61tfZ3POZoy+Rl4c+iI/H/RzIoNclxerCk6NMIWYyLJkNbq9WQgBH3wAHTvCj38MPj7y5xEj4PnnZZHJ1EzPrSi3qCt1Il08na6+m5neU1hYyLp169i/fz+apmG329E0jaeffrrB/SZMmMC0adMAmDZtGrt37yYyMpJVqxousPbwww8zbty4my441dTI2nRcHHipyBi3ci2h+NlVVc4C01qzmbNWKwAJfn5MCw9nTGgoI0JCMLrZP56aghrMa83O1eSqc2SRybeTL4ZAA46yS98/fEw+LT1Mt3bk/BHSD6aTfiidPWfkJ+eBUQP5Q8ofmJQ4iS56FxePUFFaryFD4OBBeY5Q3w8/yAWsH3hABoAPHw7qc7vS2tScrSH3zVxOv30ae4md0HGhxP4mlpChIa4eWqtTYa1g6Z6lvLHtDY4VHaOTsRN/HvtnHuv3GIHega4enio4NSZtdFqDDCcAfy9/0kanNc0TOBywc6dc8mHKFPku/6c/QWKiLDiFhkJhIXg3b4CXorRVF2fI1LnZLJn09HSmTp3KokWLnNtGjBhBbm5ug/tlZmYSFxcHwJIlSxrcdvToUbrVFss+//xzujfBql35+XKGbV4exMbe9O6UW8TlQvHNVmuDHKYfKuXiFmFeXoypzWAarevEuNmiEvZyO8UZxc7V5Mr31uYw6bU5TLNlFpNfF79LMpwADP4GuqSpAkdzO3D2gLPItP/sfgCGRA/h9bteZ1KPScQa1ZucolyL2bNlLlN9mgYLFsCMGWA0umZcinIlVTlV5Pwxh/z/zcdR5aDDAx0w/dpEUN8gVw+t1SkoK+DtHW/zPzv+h8LKQgZGDeRfk//FxB4T8TS0njJP6xlJK5LaKxXgklXq6rbfkNJS+OYbOU1u1SooKJDri06eLCdJr1sn85jqqGKTotyU5gguXr58OS+99FKDbZMmTWLBggXODCchBN7e3rz//vuN7uOll17iyJEjGAwGYmNjb3iFOpsNvv9eNkjWOXdOfmka9O9/Q7tVbhGNheLftXcvXX19+aGyEgcQYDAw0mjk/0VGkqLr3BYQ4Fbt5w6bg7KdZc5pciVbShBWgeatEZIUQueFndFTdIL6BaF5NPy91K1Gd7lV6pSmI4Rg39l9ssh0MJ1D5w+hoZFkSuLPY//M/T3uJzo42tXDVJRbRl4efPihnCxRv7vJywuefBIuOo1RlFah4lgF2a9kU/BRAQgI+2kYppdM+Cf4u3porc6hc4d4Y+sb/G3v36ix1zAhYQLPD32eYTHDWuV5nio4XUZqr9SbKzABHDt2IfB740awWmWRaexYGD9e/lmXyNex480PWlGUBpo6uHjDhg2XbJs5cyYzZ8685n18/PHHN/TcQkBVlcxbsFhkR5MQsrhUV3QyGOQVy5iYG3oK5RaxtqiI8fv3U3XRlFGbEPxQWclPw8J4MiKCgcHBeN9kDtOtRAhB5dFK5xQ58zozdosdgMB+gUTPikYfoxMyLAQP/6vnIIalhqkCUzMRQrD7zG5nkelo0VEMmoERsSN4duCzTOw+kYggFSajKNfKapXXsxcvlh87HA4YNQpmzYIXXpDnD56eMGeOq0eqKA2V7Ssje0E2Z/91Fs1LI2J6BKYXTPjGulcX9tUIIdhwagOvb32dL49+ia+nL9P6TuMXQ37R6jMMVcGpKVmt8pOftze89x489ZTc3qMHPPecLDINHapCVhSlBd1KwcUXczhkc2Rdkam6NsfYzw/CwmT9uqjoQleTwyHXE1BvMW1PVlUV3xQVscZs5t/nzl0xFH9jcTFLe/RoyeG5TM3ZGszrzM5pcnVh3z6xPnR8oCN6io7xTiPeHVTXsKsJIdiRt8NZZDpZfBIPzYM7O9/J80Of577u99ExQF18U1qGpmnJQCrys1CiEGKoi4d0Q44elUWmpUvhzBkZ+v2rX8Fjj8kwcJA5TosWwbRpEB7u2vEqSp2S7SVkpWVR+EUhHoEexDwfQ/QvovEJV1mJ9VntVv598N+8vvV1duXvooP//2fvvMOjqrY+/J6Z9F5JJYQQQgiIVAEFAggaWlSaKH4IKijgxXijXL2ABBEUNYgoKkixYYBEQAkoV6V3EFEgdExCCqSQ3jNzvj82KUBCDZmU/T7PPMnsOWefNUOYc85vr/VbzszqPYuJnSfibOl88wnqAFJwulvKUgzOnIHOncU3+qhR0L8/fPyxMPy+4uUikUgkN6O4GDIzhcCUkyNEJI0GrK3FhaKt7dUVt5cuiWpcZ2chPF3xg5bUcy6XlLC1kg/T2Ss+TG4mJvSzt2dbZibFlespr2Ch0bCiBnzB6iq6fB1ZO7PKy+Ty/rriw2RnhF1fO7ze9MK+nz3mLczrZFp5Y0Ov6tmfsJ/ImEh+OPED8VnxGGmM6OfTj+m9pvNYq8dwtHA0dJiSeoaiKMuBwUCKqqptK40HAR8DWmCpqqrvVTeHqqo7gZ2KojwOHLzHIdco+fnwww+wdCns2CEWmgYPFgbgAwZUFE+UMWMGHD8us5skhkdVVTK3ZhI3N47M3zMxcjDCe5Y3Hv/ywNherpZWJrsom6WHl7Jg3wIuZF/A38mfJYOX8Ey7ZzA3Njd0eLeFFJxuF1WFv//G67vv4M03oWtXWLAAfHzg//6vQlxq3hxuo8xGIpE0TlRVlMeVZTFd0RUwNQUnJyEwWVsL0akqylYwQRqG12cKdTr2ZGfz6xWB6Y+cHFTAWqult50d//LwoJ+9Pa0tLFAUpcpOjDXhU1bXUHUqOX/klJfJZe3OQi2+4sP0kC3N5zTHvr891h2v92GSGAadXseeC3uIionihxM/kJiTiInWhEdaPMLbvd8muFUw9uYN529UYhC+Aj4FvikbUBRFCywC+gMJwEFFUX5CiE/vXrP/c6qqplz5/WnghXsdcE1w+LAQmb7/Xlwv+PrCu+/Cs8+KzKbqcHMTzh4SiaFQVZX06HTi58aTvS8bE1cTWnzYArcX3TCyknJEZS5kXWDh/oUsObyE7KJsApsF8tmgzxjYciAapX7aJMh/4VshPx9+/10URW/cCAkJ+IDIaPK7UjOp1cKnnxoySolEUk8oKYHs7AqRSacTiZJWVuDpKUQmMzPZprgho1dVjuTmlmcw7czKolCvx0hR6GZjQ5i3N/3s7elibY1xFWrjvTDFrwuoqkrBuSs+TL9mkLklk9LMUgAs77fEc4on9v3sse15az5MktqhVF/KzridRMVEsfbkWi7mXsRUa8qAlgOY13oeg/0GY2t2b1pZl5SUkJCQQGFh4T2ZvzFhZmaGp6cnxnW8LltV1R2KonhfM/wAcFZV1fMAiqKsAh5TVfVdRDbUdSiK4gVkqaqaXd2xFEWZAEwAcHFxqdLL8W7Izc294Zw5OUb89lsTNm1y4+xZa0xMdAQGpjJwYDL335+FosCpU+IhkdQJ0oG3gZmALbAdWAmcB1yBV6E4qJhzJuc4d+ic4eKsY5zJOcOahDVsTd2Kqqr0du7NyKYjaWXdCpJgR9IOQ4d4x0jB6Uaoqugit2mTcNuzsoJHHoFZs9hjZ8eDQ4caOkKJRFIPUFWRuZSVJcrl8kQVEEZGwuTb1hZsbK5Pg5fUfbZmZNyyKf0/BQXlAtPvGRmklwohpa2lJS9d6STXy9YW61v8Q6hpU3xDUZxaTOaWzPIyuaK4Kz5MTU1xGuqEfX977PvaY9JE+jDVBcK2hRHWO4wSXQnbYrcRFRPFupPrSM1PxdzInEF+gxjeejgDWw7E2vTet7FOSEjA2toab29vWUZ5F6iqSnp6OgkJCTRv3tzQ4dwJHsCFSs8TgK432ed5YMWNNlBVdQmwBKBz585q79697yLE69m2bRvXzqmqIiNp6VJROldYCB06wKJF8PTTWuzsXBF37hJJ3ePUpFMkH0vG9hNbihOLKThTgIW/BV5fe9HkqSZojOtnls69QK/q+eXsL4TvDWfLP1uwMrFiStcpvNL1FZrZNZyyBXl7cyMURdS0vPiiKI7u2VPUuQDFNbzCIZFIGhY6nfBgKvNjKvNWsrQEd3chMllYyCym+kzlsrbBR49el2GUBUSmpJSLTOevZGB4mJgw2NGRfvb2PGxvj5vpnRtk1lVT/EsrL3F+2nmK4osw9TLFZ45Pecc3XUGFD1PGbxnk/pkLgNZWi31fe7ymemHf3x5zX+nDVNco1hUza/ssLmRdYP2p9VwuuIylsSWD/QYzPGA4A3wHYGliWasxFRYWSrGpBlAUBUdHR1JTUw0dyp1S1R/A9UZ3lV9U1Zn3KJY7IilJmH8vWwbnzonrhOeeE95MHTsaOjqJ5MbsMN+BvrCizD9rWxYAirFCl+NdUDTyO7qMwtJCVv69kvn75hOTGoOHtQfv93uf8Z3GY2dmZ+jwahwpON2MxYsNHYFEIqljrFu3jqFDh3LixAn8/f2JjY2ldevW+Pm1orRUxdTUkmnTVtCsWSu0WpG9ZGsrHmWVCh9++CGvv/46qampODk5GfYNSW6baz2U8vV6Bh09ytve3qSVlPBbRgaHATUmBhutlj52drzq6Uk/e3taXfFhaqhcWnmJUxNOoc8Xn01RXBEnXzhJ6k+plKaVCh+mIhXFWMHmQRuav9Mc+372WHWyQmMkVz7rGkWlRfx2/jciYyL58dSPAETGRBLcKpjhAcN5tMWjBjcwbcj/n2qTev45JgBNKz33BJIMFMsto9Mp/PSTyGbatEksVgUGQlgYDBsmutJKJHWd0pxSPF/z5MIHF1CLhM6rmCo4D3OmRXgLKTZdIT0/nc8Pfc6nBz7lUt4l2ru259snvmVkm5GYaBtuFne9FJwURQkAwhBVor+rqhpl2IgkEkldpagomZiYUQQErMbUtGZS0CMiIujRowcREasIDQ0jKQk8PVuwbNkRAH76aTEREXNZvvxrrKyuN/y+cOECv/76K15eXjUSj6R2qcqwG6BAr+f18+fRAg/Z2jIWGN+hA12srTGqzvW9AXJ+2vlysakMtVAlbU0alu0s8ZjsgX1/e+x62qG1lD5MdZHC0kJ+PfcrkTGR/HTqJ7KKsq56Pac4h5VHV+Lr4Mvj/o8bKEqJ5CoOAi0VRWkOJAKjEIbgBqNDBzhy5Prx9u1hzRpYvhyWLOnG5cuiC+3rr4uMppYtaz9WieROKMkoIfGTRBI+TqD0cikmHiYUJxWjMdWgL9ajtdVi6nrnWdwNhXOXz/HRvo9Y/udyCkoLCPIN4rXur9G3ed/6LvTfErV+BawoynJFUVIURTl2zXiQoiinFEU5qyjKGzeZZgDwiaqqE4Ex9yxYiURS74mNnU1W1i5iY9+ukfkuX85l587dvPXWMr7+ehWnT0N6uiiN8/KC++4Da+tsPD3tsbGpurvcq6++yvvvv98oTjINkXEnT14nNlXG3dSU7R06MAbobmvbKMSmkvQSUiJTODXhVLkH03Uo0OWvLviG++IY5CjFpjpGYWkhP578kWfWPkOTD5oQvCqYDac38ETrJ9j49EYKpxWizhQr1+pMFXWmSljvMMMGXYdYt24diqJw8uRJAGJjY1EUhRmVetGnpaVhbGzMyy+/XOUcf/zxB/fddx++vr5MmTIFVb1hRVg5sbGxmJub0759+/LHN998Q0wMeHp6k5SUdvdvsA6hKEoEsBdopShKgqIoz6uqWgq8DGwGTgBrVFU9bsg4u3cHk2uSFoyMICVF9Bz64APw98/hxx8hPl50nJNik6Q+UJxazPn/nmdfs33EzozFtoctHfd3xOYBG9wnutNxX0fcX3Kn5GKJoUM1KHsu7GHYmmG0/KQlXx7+klFtR3F04lF+Hv0zD/s83GjuAwyR4fQVd9nKFPgWmKkoSjDgWAsxSySSOsaZMyHk5laxdHiFrKydQIUokJz8OcnJnwMabG17VrmPlVV7WrZccNWYqgqT77KOclFR63nggSBcXPxwdHQgL+8wAQEOXLhwjkceaU9OTg75+fns37+/ymP89NNPeHh4cP/999/2e5bUDVb4+1eZ4QRgodHwtb+/AaKqXXSFOrJ2ZZV3k8v9MxdU0Npo0Zhr0Bdc/9mYeslVzrpGQUkBv5z9hciYSDac3kBucS4O5g6MCBjBiDYj6Nu8b8NL81+5EqZNE3f4Xl4wZw6MHn3X05Zlvq5atYqwsDAAfHx8iI6OZvbs2QBERkbSpk2baueYOHEiS5YsoVu3bgwcOJBffvmFAQMG3NLxW7RowZFr0mkOHQK9Hk6cEA2XvbyuF0DqI6qqPlXN+CZgUy2HUy0zZsCKayzJS0tFaf3cufDss3D69LHrTMMlkrpKUWIRFz68QNLiJPSFepxHOtPsv82wamcFQNu1bcu39VvkZ3hpC1oAACAASURBVKgwDYpOr2P9yfWE7w1nb8Je7M3sebPHm7z8wMu4WbsZOjyDUOuCU021MgUmXxGq1lb1oqHbmEokkprH1taWnJwcAEpKitHpdNVua2HRmeLifygtTUcITxqMjBwxMWle7X4lJcXk5OSg00FentGVhxadTgOomJvr2LZtJRMnTsLbO4cnn3yctWu/Zvz48TRv3pydO3cC8MMPP/Dcc8+xbt26q+bPz8/n7bffZv369eTk5KCqKrm5uZjehWn07VJYWCi/u+6Ssu5w14pOFhrNdcbhDQVVr5J7JJeMX4XRd9auLPSFeuHD1N0G71ne2Pezx7qLNamrU6/ycALQWGjwmeNjuDcgKSe/JJ+fz/xMZEwk0aejySvJw9HckVFtRjGizQj6ePfBWGtc7f4zA+uUz/LtsXIlTJgg1BeAuDjxHO5KdMrNzWX37t1s3bqV4ODgcsHJ3Nyc1q1bc+jQITp37szq1asZOXIkSUnXWwslJyeTnZ1N9ytNAMaMGcP69etvWXC6Eapa0cDCyQnc3BqG8FTXcXODsWPhiy/Ec40GhgyBtWsrsp9PnzZYeBLJLVPwTwHx8+K5uOIiqk7F5RkXmr3ZDItWFoYOrc6QV5zHiiMr+GjfR5zPOI+PvQ+fDPiEce3H1XozjbpGXfFwuq1WplcEq/8ClsAHVW1jiDamEonk3nLixAmsrUWb7YCAz266/alTE0lOXoJGY4ZeX4yz83Batbp+P1UVbYezsiAxEXJF0yyMjCrMvm1tFbKysti7dxvnzsXw+usKOp0ORVEICQlBo9GUx/bkk08yadIkrK2tGTduHH/++Sfu7u7MmzeP+Ph4evToAUBiYiK9evXiwIEDuLrWTotjMzMzOnToUCvHashcKzo1RLGp4J+C8k5yGb9nUJpeCoBlW0vcJ7pj388e2162GFldfSlR1o2uui51ktonrziPjWc2EhUTxcYzG8kvycfJwonR941mRJsR9PbujZHm1i4J63QZXUhI1aY5ZezbB0XXlHzm54s2YF9+WfU+7dvDggVVv3aF9evXExQUhJ+fHw4ODhw+fBgHBwcARo0axapVq3B1dUWr1eLu7l6l4JSYmIinp2f5c09PTxITEwFYuXIlH3xw/eWur68vUVHCxvTcuXO0b98eEMbT06Z9gq/v1dm8qgqpqVBQAI0gEbNO8NZbIsupqEg0uv7ii6pL7SWSukjeyTzi343n0spLKFoFt+fcaDq1KebNpZt9Gck5yXx64FM+P/Q5GYUZdPPsxvv93udx/8fRaqR1ANQdwem2WpmqqhrLlewliUQiqY6Skku4u7+Eu/sEkpKWUFycXP6aXg85ORWrvsXFYtzcXKxK2tqCpaXwZiojKiqKMWPGsLhS98rAwEASEhKuOu6uXbto0aIFACuuyadPSUkp/93b25tDhw7dfZe67GyIjQVvb9EST1IrlIlO406eZIW/f70Xm0oul5CxJaNcZCo8VwiAibsJjoMdse9nj/3D9pi63Twjz2W0ixSYDExucS4bT28kMiaSTWc2UVBaQBPLJoxpN4YRbUbQq1mvWxaZGgzXik03G79FIiIiCAkJAYTAFBERweTJkwEICgpixowZuLi48OSTT1Y7R1V+TWX+HqNHj2b0TTKwfHxasGnTEdLSxPnMyEiUb1XMJR6OjuDufrvvUHKnuLkJI/DFi2HcOGEOLpHUdXL/yiVubhypkalozDR4/suTpq81xdRDlsaXcTzlOPP3zue7o99Roivhcf/Hee3B13iw6YOGDq3OUVeuNOplK1OJRFK3adu2ouLWz28RRUXCrDMrS4hNer1YabSxqRCZblRmEBERwRtvXN3TYNiwYcydO7d8dVlVVUxMTFi6dOm9eltXk50NZ8+KN3P2LPj6StGpFuljb0/slRKY+oauUEf2nuxyH6acP3KED5O1Frvedni+4ol9P3ss/C0ajbFlfSenKIfo09FExkTy89mfKSwtxMXShXHtxzGizQh6evVs2CuuN8lEwttblNFdS7NmcIelxunp6WzZsoVjx46hKBWZr5MmTQLAxMSETp06ER4ezvHjx9mwYQMAOp2OTp06ARAcHMzEiROvWrxISEjA/YoyVF2GU4sWvixdGsU//4gs3aQk8fXv6Ql2dnD4sNhOUUQpnbu78A+S1C4zZsDx4+KnRFKXyT6QTdw7caRvSEdrrcXrDS88QzwxaSJrcEEsDGz5Zwvhe8P5+ezPmBuZ80KHF3i1+6v4OvgaOrw6S10RnOpcK1OJRFL/UVVRHldm+F1QIMZNTcXFt60tWFvfenp7Vd5HU6ZMYcqUKXcUX2xs7B3tV05lsQmk6CS5IapeJffvSj5MO7PQF+hRjBRsutngPdMb+/7Ch0ljLGs+6gvZRdlsOLWByJhIfjn7C0W6Itys3BjfcTzDA4bzUNOHGrbIdDvMmXO1hxOAhYUYv0NuJfM1NDSUwMBAHB0r+txotdrrTL6tra3Zt28fXbt25ZtvvuFf//oXcH2GU2EhpKWJDqnnzolzm7Gx6JJa2RLQwkKc3wICxKKKxDC4ucH27YaOQiKpnswdmcS9E0fGrxkYORjh/bY3Hi97YGwvFWqAEl0Jq4+vJnxvOEcuHsHF0oXZfWYzsfNEHC1k/7KbUeuC05VWpr0BJ0VREoCZqqouUxSlrJWpFlhu6FamEomkflJSInSYzEzxU6cTq7tWVhWrvqamV5fK1UuuFZvKkKKTpBKFcYVX+TCVpIoWxRYBFrhNcMO+nz12gXYYWdeV9SfJrZBZmMlPp34iKiaKzec2U6wrxsPag5c6v8TwgOE82PRBNIoUDa+jTLSpwS51N8p8LaNNmzY37E5Xxueff87YsWMpKChgwIABVxmG6/WQkSGEpiu9M7C1BWdnUSYXF3eOrl3bl2//3HPPMWXKFIyMZFaTRCK5HlVVyfhfBnHvxJG1KwtjF2N83vfB/SV3eU1whazCLJb8sYSFBxaSkJ1Aa6fWLB2ylNHtRmNmZGbo8OoNhuhSVy9amUokkvqBqorF6rIsprw8MW5sDPb24oLcxga0DWWBvyxtqyqxqQy9Xng6tWtXq6FJapdLKy9dZ8ztMNCBzK2Z5SJTwRmR1mfiZoJDkIPwYepnj6m79GGob2QUZPDjqR+Jionif+f+R4m+hKY2TZncZTLDA4bTzbObFJluhdGj70pgupbbzXwdO3YsY8eOrfK1zp07c+zYsavGCgqE0ffly8KTydQUPDyEyFRWAm5n501BWQrvNdx1Jq1EImlQqHqVtJ/SiHsnjtw/cjH1NMX3E1/cnndDa95QLpbvjrjMOD7e/zFLDy8lpziHvs37snjwYoJ8g+R59g6Q8qVEIql36HQiwadMZCoRSRtYWgqPCltbUUpQ77OYKpOfL+44Ll8WjrA3enMajfAqkTRYLq28xKkJp9DnC9GxKK6IE2NOwBUNUmOpwa63HR6TPYQPU4D0YaqPXC64zPqT64mKieK3879Roi/By9aLKV2nMDxgOA94PCAvfhsgOp3IZkpNFYsoiiKyc52dRRm4/K8skUhuF1WnkrImhfi58eQdy8OshRmtlrbC5f9c0JjI8wjAH0l/EL43nDXH1wDwZNsnCe0eSke3jgaOrH4jBSeJRFIvOH1aiEynT4tyAlUVWUs2NkJgsrVtgGUDRUUVIlPZ6rWtrVjetrMTdyLXZjppNLKcrgGj6lXyjuVx5uUz5WJTOXrQ2mq5L/o+bB6wkReQ9ZS0/LRyken3f36nVF+Kt503Id1CGB4wnC7uXaR42AApy9Yt82bS68HMTJSCOzo2wPObRCKpFfQlei59d4n4d+MpOFOARWsLWn/XGucnndEYyesEvapn05lNhO8NZ1vsNqxNrAnpFsKUrlPwsvUydHgNAik4SSSSOklREezYARs3isfZs/DzzyKLycVF6C6Wlrdu+F1vKC2tEJlyc8WYlZXwGrG3v/quw8ZGiEtlopMUmxokhRcKyzvJZfyeQUlKSbXb6rJ12PWwq8XoJDVBal4q606uIyomii3/bEGn6vCx9yG0eyjDA4bTya2TFJkaKGVf+WlpQnDSaMRXvZOT+OqX/+wSieRO0BXquLj8IvHz4imKL8KqgxVtfmiD0+NOKBr5xVJYWsi3f33L/H3zOZl2kqY2Tfmw/4e80PEFbM1sDR1eg0IKThKJpM6QlASbNgmB6bffhN5iZgZ9+kBIiEjsadvW0FHeA3Q6URuYni7SuFRVvHEPD3BwuLrt0LWUiU6xsaKMTopN9Z7SrFIytmZU+DCdEtltxi7G2PcXHkz/TP+H4sTi6/Y19ZLeTPWFlLwU1p5YS1RMFNtit6FTdfg6+DL1oamMCBhBe9f2UmRqoJRZ8aWlidI5vV6UgXt5ia98I3l1LpFI7pDS3FKSFydz4cMLFF8sxqa7DX6f++EwwEGeUxBZxJ8d/IxFBxeRkpdCR7eOrBy6khEBIzDWylTSe4E8pUkkEoOh08GBAxUi059/ivGmTeGZZ2DQIOjbV1yIA5w4YbhYK7Nu3TqGDh3KiRMn8Pf3JzY2ltatW9OqVStUVcXS0pIVK1bQqlWr6/YNCwvjyy+/xNnZGXQ65r76KgPbtxd3HMbG0KSJqJ8wN7/1pW0bG2kQXo/RF+vJ3pddnsWUfSAb9KCx0GAXaIf7i+7Y97PHsq1l+cWixlhzlYcTiO195vgY6m1IboGLuRdZe2ItkTGR7IjbgV7V4+foxxs93mBEwAjaubSTNwQNmJISsa6QlgaFhSKbydFRZDNZWho6OolEUp8pzSol8dNELnx0gdL0Uuz62tH6+9bY9baT5xXgdPppPtr7EV//9TUFpQUMajmI0O6h9PbuLT+fe4wUnCQSSa2SkQGbNwuB6ZdfxIW3VgsPPgjvvSdEpjZt6nYZQUREBD169GDVqlWEhYUB0KJFC44cOQLA4sWLmTt3Ll9//fXVO6oqFBfz6tixvDZypLj70GpF/YSDg3SDbSSoqkre8TxRIvdbBpnbM9Hn6UEDNg/Y0Oy/zbDvZ49N9+p9mFxGuwBc16WubFxSd0jOSeaHEz8QGRPJzridqKj4O/kzrec0RgSMoG2TtvJitwGjqsJ3MDUVMjPFcysrkZBqb9+AOqhKJBKDUJxWTMKCBBI/TUSXpcNhkAPNpjXDtrssC1NVld0XdhO+N5wfT/6IsdaYMe3G8Gr3VwlwDjB0eI0GKThJJJJ7iqrC8eMVXkx79ojMJkdHGDBACEyPPiouvOsDubm57N69m61btxIcHFwuOFUmOzsb+8pvqLBQLGuXGXVYWIg7DgcHYUbV4IyoJNdSlFhUXiKX8VsGxRdFOZy5nzmuz7pi398eu952GNvdejq3y2gXKTDVURKzE8tFpt3xu1FRCXAO4K3AtxgRMIIA5wApMjUwrs18PX06llatmjN+/HQmTJiNkREYGaXRubMbL774Ip9++ul1c0ybNo1vvvmGjIwMcss8/G6R06dPExISwunTpzE2Nua+++7jk08+4cSJE/Tp04effvqJIUOGADB48GBee+01evfuXRNvXSKRGICi5CIuhF8g6fMk9AV6nIc54/VfL6w7WBs6NINTqi9l3Yl1hO8NZ3/ifhzMHZjWcxqTH5iMq5WrocNrdEjBSSKR1Dj5+bBlS0WpXHy8GG/fHt54Q4hMDzxQAyu7t3KxPHgwvPZaxfZjx4pHWhoMH371ttu23XS69evXExQUhJ+fHw4ODhw+fBgHBwfOnTtH+/btycnJIT8/n/27dsGlS0Joys8XO1tbg50dn65ZwzdbttC5c2fCw8OvFqck9YZLKy9Vm2FUml0Ke+DM2jNk/JZB/gnxN2DsbIx9P/vyh5mXmSHfgqQGuZB1oVxk2nNhDwBtm7QlrHcYwwOGy9XUOkCHDnAlEfUq2revKOm+U8oyX7/6ahXPPx/GyZPg4eHDrl3RvPfebOzsYPHiSNq0aVPtHEOGDOHll1+mZcuWt3XswsJCBg0axPz588tFpa1bt5KamgqAp6cnc+bMKX9NIpHUXwrjCol/P57kZcmoJSouT7vg9aYXlgGyLje3OJflfy7no30fEZsZi6+DL4sGLuLZ+5/F0kR+PoZCCk4SiaRGiI2tyGLaulUk9VhaQv/+MGOGyGby8DB0lHdPREQEISEhAIwaNYqIiAgmT54sSur++AMyMlj93XdMeOYZfvnkE5HN5OkpsplMTJgYGsqMd99FURRmzJhBaGgoy5cvN/C7ktwul1ZeuspDqSiuiJPPnyRlbQoll0rI3pcNOkg2T8a2ly1uz7sJH6b7LGV3mAZEXGZcuci0L2EfAO1c2jG7z2yGBwzH38nfwBFKKtO9O8TEQHElv30TE1HSfTekp+eyY8dulizZypQpwTz1VBjOzmBra87997fm/PlDdO7cmdWrVzNy5EiSkpKqnKdbt253dPzvv/+e7t27XyUo9enTB4Bt27Zx//33U1JSwq+//kr//v3v6BgSicSw5J/JJ/7deC59ewkUcB3ritd/vDBvYW7o0AxOUk4Sn+z/hC/++ILMwkweavoQ8x+ZT3CrYLQaWbdsaKTgJJFI7oiSElEeVyYyxcSIcV9fePFFkcXUq9eNG6zdNbeQkVTt9k5Ot71/eno6W7Zs4dixYyiKgk6nQ1EUJj3zjLiDOXIEVJXghx5i3JtvQps2jJs0iT///BN3d3c2bdqEi0tFCdT48eMZPHjw7b0HSZ3g/LTzVxl2A6hFKulr07F+wBqv/3gR7xRPj0k90JjKksn6TNi2MMJ6h5U/j82MJSomisiYSA4kHgCgvWt75vSdw/CA4fg5+hkoUklISNUZTGUUFUFp6dVjpaUiu6m6hNn27WHBguvH9XrhyZSaCqtXr6dr1yBat/ajSRMHSkoO4+bmgKKIhYlVq1bh6uqKVqvF3d29WsGpOlauXMkHH3xw3bivry9RUVEcO3aMTp063XCO6dOnM336dCk4SST1jNxjucTPjSdldQoaEw3uE91p+npTzJrKDOmjl44Svjec749+j07VMbT1UEK7h9LN887Ee8m9QQpOEonklklJgZ9/FgLT//4HWVmisVpgIIwfDwMHgl8DvteKiopizJgxLP7iC9HTOj2dwGHDSDhwQNx9ODuDgwO79uyhha8vmJuzYsWKq+ZITk7Gzc0NEJ4fbdu2NcRbkdwlRfFFVb+gQKf94sYvflu8FJsaALO2z2LM/WPKRaZDSYcA6OjWkXcffpfhAcPxdfA1cJSSW8HUFFxc4OJF4S+oKODqKrKcbpWCAlGRnZ4uxCoTE9i+PYLQ0BBatoRnnhnF6tUi8xUgKCiIGTNm4OLiwpNPPnlHcY8ePZrRo0ff0b5l9OzZE4CdO3fe1TwSiaR2yD6UTfyceNLWp6G10tL0taY0/XdTTFxu4wurAaKqKr+d/43wveFsPrcZC2MLXur8EiHdQvCxl5166yJScJJIJAAkJ8OoUbB6tbgAB6Gh/PlnRRbTwYPiIt3NTdgfDRoE/foJa6LGQMTKlbwxfjwcPSoymjQahg0axNw1aziXmEj74GBUVcXExISlS5dWOcfUqVM5cuQIiqLg7e3N4sWLa/ldSGoCUy9TiuKuF51Mve5lSp+kNjl3+RyRMZEAtFjYAoAu7l2Y128ewwOGywvbOkhVmUjXkpwMPj6i7NvMDP74o+KcVx06neiwmpYm1hoUBezsRKJsSUk6e/Zs4ezZazJfJ00CwMTEhE6dOhEeHs7x48fZsGHDlTl15VlJwcHBvP3229Ue/2YZTm3atGH79u03fe/Tpk1jzpw5GBnJy3+JpK6SuSuTuHfiyNicgZGdEc1mNsNziifGDrfeVKQhUqwrZtWxVYTvDefvS3/jauXKnL5zeKnzSziYOxg6PMkNkGcciUQCwOzZsGsXTJ8u/JY2bRKPixfFxXXXrjBrlhCZOnQQY42CoiLRXe7yZbbNny/euLm5MKSys2NKx45MuY3pvv3223sWqqT28Jnjc5WHE4DGQoPPHClC1GfOpJ8hMiaShfsXcinv0nWvD2w5kKkPTTVAZJKaws0Nxo2DxYvFzxuJTXl5QmS6fFmITmZmwpLP0VFk9wIsXnwl87XS4kFgYCAJCQnlz0NDQwkMDMTR0bF8TKvVcuRG9X+VuFmG09NPP827777Lxo0bGTRoEAC//PILHtcYJz7yyCPMmDHjtkv6JBLJvUVVVTJ+zyDunTiytmdh7GyMz3s+uE90x8imcd+uZxZmsvjQYhYeWEhSThJtnNuwPHg5T9/3NKZGcpGvPtC4/4IlEgnm5mKlt4xly8QD4MknhcAUFCSqxRoNpaXlIhNlramtrMDLC+ztK+40JI2Wsm501XWpk9QfTqefJvJ4JJExkfx16S8Aunl2Y+pDUxnWehjeH3ujzlQNHKWkJpkxA44fFz+vpezrPy1NNBhVFPG17+wsTgPXLrZERETwxhtvXDU2bNgw5s6dW/68TZs2N+xOV8bUqVP5/vvvyc/Px9PTkxdeeIGwsLCb7mdubk50dDQhISGEhIRgbGxMu3bt+Pjjj0lPT79q22nTpvHYY4/ddE6JRHLvUVWV9Oh04t6JI+dADibuJvgu8MVtvBtai8Ztdh2bGcuCfQtY9ucycotz6efTj2XBy3i0xaMojWbVu2EgBSeJpBFSXAw7dogyOTc3+OefiteMjIR56ooVYiW30aDTCVOq9HTIzha1g2ZmIpPJweEeu59L6iMuo12kwFRPOZV2isgYITL9felvALp7dmf+I/MZFjAML1svA0couZe4uUHlCjRVFdlMqamidE6vF4sxXl7i6/9GFWjbqmg+MWXKFKZMqTr3dezYsYwdO7bK195//33ef//923gnFfj7+/PLL79cN+7i4kLvSo7owVdKvyUSieFQdSqpP6QSNzeOvL/yMPM2w+8LP1zHujZ678eDiQf5cO+HRMVEoVE0PNX2Kf7d/d+0d21v6NAkd4gUnCSSRsLFi8LwOzoafv0VcnKEhtK3r9BUdu8Wz4uLoWXLRiI2qaoQly5frrjLMDaGJk1EzYS5eSOqHZRIGjYnUk+Ui0zHUo4B8GDTB/no0Y8Y1noYTW2bVrnfzMCZtRmmpBYpKRFf/6mpItNXoxECk7MzWFjIr3+JRFKz6Ev0pESkEDc3joJTBZi3Msf/a3+aPNUEjXHjFZr0qp7o09GE7w1nR9wObExteK37a/yr67/wtGkMNyQNGyk4SSQNFL0eDh8WWUzR0XBINFbCwwOeflqUyvXtC5aWMHQoTJwIEybAkiXCVLXBUraUXVYyV1oKWq24y3B0rLpmQiKR1EtiUmPKy+WOpx5HQeEhr4f4OOhjhrUehoeNx03nCOsddu8DldQaqioWXFJTITNTPLe0hGbNxGlA27irWCQSyT1AX6Tn4lcXiX8vnsLYQizbWRKwJgDnoc4o2sZ7zVlQUsA3f33D/H3zOZ1+Gi9bL+Y/Mp/nOz6PjamNocOT1BBScJJIGhA5OSJ7aePGqw2/u3WDOXOEyNSu3fV6ytq1Fb8vWlS7MdcahYWiXO7yZWEEXtZmyMEBbG3F0rZEIqn3HE85Xp7JFJMag4JCD68eLAxayLCAYbhbuxs6RIkBKC4Wp4C0NHEK0GpFJpOTk8hmkkgkkppGl68jaUkSFz64QHFSMdZdrfH9xBfHQY6N2ocoJS+Fzw5+xqKDi0jLT6OTWycihkUwPGA4RhopTzQ05L+oRFLPOXtWZDBt3Cg8KUpKhH4SFNRIDb8rU1wsSuXS04X7K4C1tTDwsLO7sTGHRCKpF6iqyrGUY0TGRBIVE8WJtBMoKPRs1pNPBnzC0NZDpcjUSFFVYc2XliaymUCcAtzdhRG4XGeQSCT3gtLsUhI/SyRhfgIlqSXY9bbD/2t/7B+2b9RC06m0U8zfO59v/v6GwtJChvgNIbR7KL2a9WrUn0tDR95tSST1jOJi2LWrolTu9Gkx3ro1hIQIkenBBxtxIzWdTohMly8LfyYQy9eeniKbycTkrqZXFIV///vfhIeHA/Dhhx+Sm5t7XSeh/Px8RowYwblz59BqtQwZMoT33nvvro4tkUgEqqpyNOVoebncqfRTaBQNvZr14uUHXuYJ/ydws3YzdJgSA1FUJESmtDSxCGNsDK6uIpvJzMzQ0UkkkoZEUXIRMaNiCFgdgMZYQ8LCBBIXJlKaWYpDkANe07yw62Fn6DANhqqq7IzfyYd7PmTD6Q2Yak159v5nebX7q/g7+Rs6PEktIAUniaQecOmSMPzeuBE2bxalcyYm0KcP/OtfQmRq3tzQURoQvV6IS+npFaYcpqbg5kaRVREx58cRYL8a07sUmwBMTU1Zu3Ytb775Jk5OTjfc9rXXXqNPnz4UFxfz8MMP8/PPPzNgwIC7jkFyYxRFCQDCgHTgd1VVowwbkaQmUFWVvy/9XV4udzr9NBpFQ2CzQF7p+gpDWw/FxUp2DWys6PXi6z8trWKtwdZWiEyyaloikdwrYmfHkrUzi78H/E3h2UJ0uTqcHnfCa5oXNp0bpw9R2LYwpveazg8xP/Dh3g85lHQIJwsnZgbOZFKXSTSxbGLoECW1iBScJJI6iKrCn39WlModPCjG3N1h1CghMD38sPC3brSoKuTmCpEpI0NkNhkZifpBBwfhAqsoxJ6aRFbWLmJj36ZVq8/u+rBGRkZMmDCBjz76iDlz5lS7nYWFBX369AHAxMSEjh07kpCQcNfHb+goirIcGAykqKrattJ4EPAxoAWWqqp6o3SxAcAnqqruVBTlJ0AKTvUUVVU5cvFIebncmctn0Cgaenv35tVur/KE/xNSZGrklJTAhQviVFBaKhZj3N1FDwhT09qLY926dQwdOpQTJ07g7+9PbGwszZs3Z/r06cyePRuAtLQ03NzcePHFF/n000+v2l9mxUok9Ysd5jvQF+rLn+cdyQNAMVFou65tdbs1eHKKcpi1fRZfHfmKuKw4Wjq0TKJdMQAAIABJREFU5PNBnzPm/jFYGEvDvMaIFJwkkjpCbi789psQmDZuFJ3iFAUeeADefluITO3bywZq5OfD5cucufAGuSUnxAdiZATGRqAaiZyWdMjK2glUXAgkJ39OcvLngAZb255VTm1l1Z6WLRfcNITJkyfTrl07pk6dekshZ2ZmsmHDBl555ZVb2r6R8xXwKfBN2YCiKFpgEdAfSAAOXhGStMC71+z/HPAtMFNRlGDAsRZiltQgqqry58U/iTweSdSJKM5ePotG0dDHuw+h3UN5ovUTcnW0kZOfD1FRsHQp/Pe/Fd6Fzs5gY1P9efJgh4PYdLfBe4Y3pm41q0ZFRETQo0cPVq1aVV5i7ePjQ3R0dLngFBkZSZs2baqdQ2bFSiT1g4LzBTgNcyLl+xRQxZjGTIPTMCdafNjCsMEZiNS8VBbuX8inB4WY7mXrxcdBHzOk1RA0ikwxbcxIwUkiMSDnzlUITNu2CX8mGxt49FEhMA0YAE3kfRXExcH33wv1LS+vQmQyMrti/H393YW19QMUFp6npCQNITxpMDZ2wszs7i8EbGxsGDNmDAsXLsTc3PyG25aWlvLUU08xZcoUfHx87vrYDR1VVXcoiuJ9zfADwFlVVc8DKIqyCnhMVdV3EdlQVTH5ilC1tprXURRlAjABwMXFhW3btt1d8NeQm5tb43M2VFRV5XTuabanbmd76naSCpPQoKGjfUdC/ULp4dgDOxM7yIWYgzHEEGPokCUG4OxZKzZudOPXX13IyzPCwyMfK6sSfHxyMTISd325udXvn3ckj/yYfC6uuIjjaEfc/+OOsevdGx7m5uaya9cuoqOjGTVqFKGhoeTm5mJqaoqvry/bt2+nY8eOfP/99zz22GMkJyeTk5Nz3TydO3cuH2/bti1nz56tcrt7SWFhofzekkiqIe9kHvHvxnNp5SUUrYJFgAX5MfloTDXoi/VobbSYutZiamUdIDYzlvA94Xxx6AtK1dLy8Z3xO9kZv5OZgTMJ6x1muAAlBkcKThJJLVJSArt3V5TKnTwpxlu1qvBi6tGjERt+VyY9HSIjYeVK4ZIOsGULeHmBvT0tjb+66RSnTk0kOXkJGo0Zen0xTk7DaqSsDiAkJISOHTsybtw4AHQ6HZ06dQIgODiYt99+G4AJEybQsmVLQkJCauS4jRQP4EKl5wlA1+o2viJY/RewBD6objtVVZcASwA6d+6s9u7d++4jrcS2bduo6TkbEqqqcijpUHm53D+Z/6BVtDzs8zCzAmbxuP/jOFnc2CdN0vDJzoZVq+DLL+HQIVEmN2wYjB8PgYEWnDxpjL29qC8/E3KG3CM3UJwAtVgIU2nL00hbkYaJiwmmzUzRmFa9Am/V3oqWC1recM4ff/yRAQMG0LFjR5ycnDhz5gwODg5oNBr+7//+jw0bNtCiRQtMTExo3rw56enpWFtbVztfZmYmmzdv5vXXX7/hdvcCMzMzOnToUKvHlEjqOrl/5xI3J47UyFQ0Zho8p3jS9LWmnHn5DHaBdrhPcCdpSRLFycWGDrXWOHrpKO/veZ+IoxFoFA1j7h/D6w+9jr+TP8osBXWmaugQJXUEKThJJPeY1FRh+B0dDf/7n2jRbGICgYHw0ktCZPL1NXSUdYT8fPjpJyEy/fKLMOQICIA5c+Dpp6Gg4LZSvkpKLuHu/hLu7hNISlpCcXFyjYXq4ODAyJEjWbZsGc899xxarZYjR45ctc306dPJyspi6dKlNXbcRkpVBTLVXsmoqhrLlcwliWEJ2xZ21cqmqqocTDpYXi4XmxmLkcaIh5s/zLSe03jc/3EcLWQVZGNHVWH/fiEyrV4tElvbtoWPP4ZnnhE2fXd/EPEoTi5Gl6/Dqv2dmyJGRESULyqMGjWKiIgIJk+eDEBQUBAzZszAxcWFJ5988qZzyaxYiaTukH0wm7h34kj/KR2ttRavN7zwfNUTE2fRhKbt2gqvJr9FfoYKs1bZFb+L93a9x8YzG7E0tiSkWwgh3ULwtPE0dGiSOooUnCSSGkZV4ciRilK5/fvFmKsrDB8uBKZ+/aCWFy3rLqWl8PvvQmRat07UQ3h6wquvwujR0K5dhSHHiRO3NXXbthXVVH5+i2oyagBCQ0OvM34tIyEhgTlz5uDv70/Hjh0BePnll3nhhRdqPI5GQALQtNJzTyDJQLFIboNZ22cxM3AmBxIPlGcyxWXFYaQxor9Pf97q9RaP+T+Gg3lNKAiS+s7ly/Dtt8Kb6dgx0fth1Ch44QXo2vXmHoY3y0Tapmwr/10xUVC0Cq7jXGk2o9kdl8Gkp6ezZcsWjh07hqIo6HQ6FEVh0qRJgGga0alTJ8LDwzl+/DgbNmwAZFasRFKXydyVSdw7cWRszsDI3gjvWd54/MsDY/vGWYKgV/VsPL2RebvnsfvCbpwsnJjdZzaTukyq8vw9M3CmAaKU1FWk4CSR1AB5eUIziY6GTZsgMVGMd+kCYWFCZOrQQbZlLkdV4cABITKtXg0pKWBnB089JTKZevWqsx9WbiWDEBcXF/Lz86vcztPTE1WV6cQ1xEGgpaIozYFEYBTwtGFDktwIVVXZn7gfAO+PvYnPisdYY0z/Fv0J6x3GY60ew97c3sBRSuoCqio8DL/8EtauhaIice5cvFiITTY13FW8poSmMqKiohgzZgyLFy8uHwsMDLyqK2loaCiBgYE4OlZk78msWImkbqGqKplbMomdHUvW9iyMnY3xec8H94nuGNk0zlvmEl0Jq46tYt7ueRxPPU4z22Z8MuATnuvw3A07zknPJkllGuf/HomkBvjnH5HBFB0tLpaLikTW0iOPwODBwvDbRXbrvprTp4XI9P33cPasMOMYMkRkMg0YULs9rCV1EkVRIoDegJOiKAnATFVVlymK8jKwGdGZbrmqqscNGKakCvSqnv0J+/n35n+zL3Ff+Xh8VjwAr3Z7lXn95xkqPEkd4+JF+OorWLZMnA5sbUUm0/jxcP/99+aYlu0tsX3QtkaEpjIiIiJ44403rhobNmwYc+fOLX/epk2bG3anA5kVK5EYClVVubzpMnHvxJG9LxsTdxN8F/jiNt4NrYXW0OEZhLziPJb9uYzwveHEZ8XTtklbvnviO0a2GYmxtnFmeUnuHCk4SSS3SEkJ7NlTUSoXc6VJkp8fTJoksph69hT+TJJKJCcLx9fvvxeOrxoN9O0relkPHSruMiSSK6iq+lQ145uATbUcjuQm6FU9+xL2lXsyJWQnYKI1YbDfYEYEjODZ9c9K41BJOTodbN4sspk2bBDPe/WCt94SJec3afp513T5s0uNz1lVR7cpU6YwZcqUKrcfO3YsY8eOvW5cZsVKJLWLqldJW5dG3Dtx5B7JxczbDL8v/HAd61ptE4GGTnp+OosOLmLh/oWkF6TTw6sHnw38jIEtB6LcrKZZIqkGKThJJDcgLU14V0dHi4vkzEzRQa5XL7EKO2gQtLyxZUTjJDtb1EasXCk6y+n10KkTzJ8vaiTc3AwdoUQiuUP0qp69F/aWezIl5iRiojXh0RaPMrfvXIJbBWNrJoTkZ9c/a+BoJXWBuDhYvlw8EhLA2VnY9L3wgujSKpFIJLWFvlRP6upU4ubGkR+Tj3lLc1qtaIXLaBc0xo1TaLqQdYGP9n3Ekj+WkFeSxxC/Ifznof/wkNdDhg5N0gCQgpOk0ZKcLLSP1auFoTcIL4m//64oldu3T4y5uMATTwiBqX//mveUaBAUFYl2fCtXiqXroiJo0QKmTRMlc/KuQiKpt+hVPXsu7CHyeCQ/nPiBxJxETLWmPOr7KO8FvMcQvyHlIlNlpHFo46WkRDQdXbpULNiAOH9+9BEEB8tsYIlEUrvoi/Vc+u4S8e/GU3C2AIs2FrSOaE2TEU1QtI0ze+dE6gne3/M+3/39Haqq8vR9TzP1oam0bdL25jtLJLeIFJwkjZbZs2HXLpgxQ1z8lpXKlfl8duok0vwHDRK/11EPa8Oi18POnUJkioqCjAxo0gQmTBAi0wMP3LytkEQiqZPoVT2743cTGSNEpqScJEy1pgT5BjEvYB5DWg3BxvTG6rs0Dm18nD4tfJm++kr0g/DwgOnT4bnnwNvb0NFJJJLGhq5Qx8XlF4mfF09RfBFWHa1os7YNTo85oWga5zXqvoR9zNs9j/Un12NuZM7EzhMJ7R5KM7tmhg5N0gCRgpOk0WFuDoWFFc+XLhUPEFlMs2YJ/2pZ9VUNZWlgK1dCRIRQ6CwtxYc3ejT06wdG8qtFIqmP6PQ6dl/YXZ7JlJybjKnWlAEtBzAiYASD/QbfVGSSND4KCkQV9ZdfwvbtoNWK5hnjx8Ojj8pTgkQiqX10eTqSliRx4YMLFCcXY9PdBr8v/HAIcmiUfkSqqrL53Gbe2/Ue2+O2Y29mz1u93uLlB17G2dLZ0OFJGjDyEkDSKCgtFeVx0dHQrBmcOlXxmpGR8GRavly81mjZuhXGjYMVK6BPn+tfj4sTxt8rV8Lx4+KDCwqCDz4QKWIW1bdHbUgoisK///1vwsPDAfjwww/Jzc0lLCzsum2DgoJITk6mtLSUnj17smjRIrTaxtnxRFJ30el17IrfVZ7JdDH3ImZGZgzwrRCZrE2tDR2mxIB06ADdu4uM4MqLMUePCpHpu+9EgquPD8ydC88+C+7uhotXIpE0XkqzS0lclEjC/ARK0kqw62tH65Wtsett1yiFplJ9KVExUby36z3+uvQXHtYezH9kPuM7jcfKxMrQ4UkaAVJwkjRYLl8Wht8bNwproYwMoZH07AkODkKAMjWF4mJhL9ToxabBgyE/X/yMjhaiU3o6rFkjRKbdu8W2Dz0En30GI0aAk5Nh474dkpNFHeXevfDnn3c8jampKWvXruXNN9/E6Sbvf82aNdjY2KCqKsOHDycyMpJRo0bd8bElkpqiTGRac3wNa0+uLReZBrYcyIiAEQxqOUiKTJJyjhwRnVlXrBCJrP7+EBkJBw4IL6ahQ4UBeJ8+svxcIpEYhpLLJSR8nEDiwkRKM0txGOBAs+nNsH2wcXZDLigp4Ou/vuaDPR9wPuM8/k7+rHhsBU/f9zQmWmmiJ6k9pOAkaTCoqki8iY4WItOePcJiyNlZJOAMGgSPPAK2tuLieOJEYTW0ZInQIhotlcUmED+DgqBjRzh0SKSHtWkjlq2feqr+mXCUCU0rVog/iOLiu5rOyMiICRMm8NFHHzFnzpwbbmtzxV2+tLSU4uLiRrmyJqk76PQ6dsbvLC+Xu5R3CXMj8wqRyW+QXO2UVEvZV+eyZeKnnR2EhcHkyfVr7QFga0YG406eZIW/P33s7WtkznXr1jF06FBOnDiBv78/sbGxNG/enOnTpzN79mwA0tLScHNz48UXX+TTTz+9bg6ZFSuR3D7FKcVcmH+BpEVJ6HJ1OD3hRLNpzbDu1DgXTTILM/n84Ocs2L+AlLwUHvB4gPBHwgluFYxGkSsCktpHCk6Sek1BgdBLyrrKxceL8Q4d4L//FTpKly7Xr7iuXVvx+6JFtRdvneNasamM4mLYvx9GjoQ334R27eqe+XdIiFh2r46iIlEGeOmSUCNVteK13r2r3qd9e1iw4KaHnjx5Mu3atWPq1Kk33fbRRx/lwIEDDBgwgOHDh990e4mkJtHpdeyI20FkTCRrT6wtF5kG+Q1iRMAIBrYcKEUmSbVkZYkE16rIzoYtW2BmPWtEuDUjg8FHj5Kv1zP46FGi77uvRkSniIgIevTowapVq8pLrH18fIiOji4XnCIjI2nTpk21c8isWInk1ilKLCL+g3iSlySjL9LT5MkmeP3XC6u2jfOclpyTzIJ9C/j80OfkFOfwaItHeaPHGwQ2C5QLnhKDIgUnSb0jIaFCYPr9dyE6WVgIr+rp02HgQNEVR3ITVBWefvp6sany6/v2wf33125cNcWJE+Ju6R5gY2PDmDFjWLhwIebm5jfcdvPmzRQWFjJ69Gi2bNlC//7970lMksZL2Lawq7rBlepLhch0PJK1J9eSkpeChbEFg1pWiEyWJpaGC1hSp1FVUXn85ZewerU4x1bGxESYgo8bJzyd6hOVxSagxkSn3Nxcdu/ezdatWwkODi4XnMzNzWndujWHDh2ic+fOrF69mpEjR5KUlFTlPDIrViK5OQWxBVyYd4Hk5cmoOhXX/3PF600vLPwah5fotZxJP8MHez7g67++plRfysg2I5n64FQ6uHUwdGgSCSAFJ0k9QKcTPhFlpXJ//SXGvb3h+edFqVzv3mBmZsgo6xGnT4sl6++/h4sXq9/OwkKUodVVbpaJdPFiRSmdTnd1Kd22bXd9+JCQEDp27Mi4ceMA0Ol0dOrUCYDg4GDefvvt8m3NzMwIDg7mxx9/lIKTpMaZtX0W03tNZ3vs9vJMptT8VCyMLRjsN5gRASMY4DtAikySG3L5Mnz7rRCajh8HKyt45hlRet6ly/VCk6uroSO+npAzZziSm1vlaxmlpRzLy0N/zXi+Xk+/v/6iraUl9lW002tvZcWCli1veNz169cTFBSEn58fDg4OHD58GAcHBwBGjRrFqlWrcHV1RavV4u7uXq3gBDIrViKpjvzT+cS/G8/Fby+iaBXcnnOj6X+aYu5944W/hsofSX8wb/c8omKiMNGa8HyH5wntHkoLhxaGDk0iuYo6LzgpiuIDTANsVVUdXt2YpGGRmQmbN1cYfqeliQvdhx6C998XIlPr1nWvyqvOkpwMq1YJoemPP0SNYd++MG0aODrCqFFXZzpZWFQYh9dXXF1FveSMGdULT3eBg4MDI0eOZNmyZTz33HNotVqOVCrxy83NJScnBzc3N0pLS9m0aRM9e/askWNLJCAymbbFbgPAPdyd1PxULI0tK0SmlgOwMG6cK76SW0NVYccOITJFRYlK5C5dhLfhqFFgfcUCpX17ePDBuis03Qqn8vOvE5vK0F95vduVDKPbJSIigpCQEEAITBEREUyePBkQvkwzZszAxcWFJ5988qZzyaxYieRqco/mEj83npQ1KWhMNXi87IHX616YepgaOrRaR1VVtvyzhXm75/Hr+V+xMbXhjR5v8ErXV3CxcjF0eBJJldxTwUlRlOXAYCBFVdW2lcaDgI8BLbBUVdX3qptDVdXzwPOKokTdaExSv1FVOHmyolRu1y6hDTg4iBK5QYPg0Uehhrw9GwfZ2cKsauVKYbSh10OnTjB/vriTqNzbOjq6wsupIYhNlblWeNqzp8amDg0NrdL4FSAvL4/g4GCKiorQ6XT07duXl156qcaOLWmclIlM//n1Pxy+eLh8PDU/FYBXur7CnIdvbGYvkaSmwtdfw9KlcOoU2NiIjOHx44W4dC130dizVrlRJtK15XSVsdBo7risLj09nS1btnDs2DEURUGn06EoCpMmTQLAxMSETp06ER4ezvHjx9mwYQMgs2IlkpuR80cOce/EkbY+Da2VlqavN6Xpq00xcWl8HdZ0eh3rT67nvd3vcSjpEK5WrszrN48XO72IrVnj7MInqT/c6wynr4BPgW/KBhRF0QKLgP5AAnBQUZSfEOLTu9fs/5yqqin3OEaJgSgqgu3bK0rlzp8X4+3awdSpQv/o2lVkNklukaIikRK2ciVs2CCet2ghMplGj4ZWrarer08f8Q8xbpzIBGooYlNlyoSnuyS3UrmGi4sL+dV4YLm4uHDw4MG7Pp5EUqovZes/W4mMiWTdyXWk5adhaWzJqLajGBkwkqFrhqLOVG8+kaRRo9eLPhFLlsC6dVBSIrKWVqyAESPAsoFXXPaxtyf6vvuuE53uRmwCiIqKYsyYMSxevLh8LDAwkISEhPLnoaGhBAYG4ujoWD4ms2IlkqrJ2pNF3DtxXP75MkZ2RjSb2QzPKZ78P3t3HhdV9T5w/HPZURBF3HAB1FTEZE3TMPBnJZpSoSFp4VKZmZqmltbX0lzLJTMtxUrNFHBPrTRzQ1xKUzLcNxACVMgFhGGZub8/joyggAuDw3Ler5cvmDNz7zz40rnc5zznOeb25sYO7ZHLzsvmx6M/8vm+zzmddprm9s0J6xHGa+6vYWUme4lIFUOZJpxUVY1SFMX5juF2wNlbVUooihIBvKCq6nRENZRBKIoyGBgM4sZvlwF6thSUkZFh8HNWBampFvzxR20OHLDn0CF7NBpTLCy0eHld44UX0mjfPo169bIBsfJpzx4jB1wR6HTYHT1Kvd9/p05UFObp6eTUqsXl7t259MwzpOevPUxOFn+KoyiwdKn4vpz+27azsyM9Pd3YYVRoGo1GfnZVAPlJplXHVrH+5HrSstKwsbChZ4uevNz6ZQKaB2BtXjX7VkgPJiVFfLQvXiwmdmrVgqFDRTVTCRumVUp3Jp1Km2wCsZxu3LhxhcZ69erFtGnT9I/d3NxK3J0OZFWsVDVlJ2dzPOQ4rSNak3kik/gp8VzbeQ1zB3NcprnQ8J2GmNUo9x1gDC49O51Ffy3iiwNfkJSehFcDL1b1XkWQaxCmJnImXqpYjPE/uCGQUOBxItC+uBcrilIbmAp4KooyXlXV6UWN3XmcqqphQBiAj4+P6l/cNugPadeuXRj6nJWRTgeHDt1eKnf41gqQJk1EMc3zz0PnzqZUq1YbqF3iuaQCVBWOHhWNv8PDISFBTE+/9BL064fFM8/QyMyMRsaO08BOnDiBbX5TEemhWFlZ4ekpdy4pj3K1ueyM28nqY6sLJZkCWwbycuuX6dqsa5FJpk/8Kti+9FKZ02ph2zZRzbRpE+TlgZ8ffPop9OpVtTfZyE86DTx5kiWtWpUq2QQUmcAfMWIEI0aMKPL1AwYMYMCAAXeNy6pYqSqK+zSO63uuc8jzELmXcrFoYEGzOc1wHOyIafWql1i5fPMy8/6Yx4KDC7imuUYXly4se3EZXVy6yF0rpQrLGAmnov63FLsWQFXVNGDIvcak8uPGDfGL7ubN8MsvcPmy6FHdoQNMny6STG3ayIbfDyU+XiSZVqwQ2wiZmUFAgOikHhgo+i9JklRh5CeZ8iuZ/sv6776STAVN9J/4aIKVyr3ERLFE7ttv4eJFcHCAkSPhjTeKX1FdFXWuVYu4Dh2MHYYkVVlR1lHoNLeXtuZeyhVfr+bSeFRjY4VlNBeuXmDWvll8H/M92XnZBLkG8cFTH/BEwyeMHZoklZoxEk6JQMFPkkZA8fvDSuVScrLoOx0ZKVrjnDlzuxdTVJToDVGzJnTrJhJMAQFiMzTpIaSlwerVIskUHS3GnnoKvv5aNN5wcDBufJIkPZBcbS47LuzQ92T6L+s/bC1sbyeZmneVvRmk+5aXJ1r3hYWJSR6dDp55BmbOhBdeAMuqt5GTJEnllKpVubz6MpZOlmSdyhJlCCqYWJvgEORAs1nNjB3iI3X00lE+2/sZkbGRmCgm9Hfvz5iOY2jpIGcIykpubi6JiYloNBpjh1IhWVlZ0ahRI8zN77+nmjESTgeBxxRFcQH+BUKAvkaIQyqFiRNFf6WuXSErSyScQPSDGDVKNPzu0EEU4EgPITMTNm4USaYtW8QdRevWMHUq9O0Lzs7GjlCSpAeQq81l+4XtrD62mg2nNhRKMgW7BfNcs+dkkkl6IPHx8N134k9SEtSrBx98IHaba1a17tkkSSrndLk6Lq+8TPy0eLJOZ1HNtRo1/68m13Zdw8TSBF22DtMapljWr/wZclVV2XNxDzOiZ/Dr2V+xsbBh1JOjGPnkSBrWaGjs8Cq9xMREbG1tcXZ2lssUH5CqqqSlpZGYmIiLi8t9H1em6QBFUcIBf8BBUZRE4BNVVb9TFGUYsBWxM933qqoeK8s4JMO4dAkaNxbVS/mOHhVfzcxE0knmQUohLw+2bxdJpvXrISMDGjUSGbx+/cT2ffKDUZIqjDxdHlvObtH3ZLqquUoNyxr6SiaZZJIeVG6u6Mm0eDFs3SrGAgJg/nwx0fMAE46SJEllTpetI2VZChdnXERzQYONhw1ua9xweMmBY72P4TjEEcfBjiSFJZGTnGPscMuUTtWx+fRmZkTPYH/ifupUq8OUzlMY+sRQalmXrpecdP80Go1MNj0kRVGoXbs2V65ceaDjynqXuleKGf8F+KUs31sqPZ1ONPn++WfxJ7+XpbW12EFOqxXfBwXBrFliaZ30gFQV/vxTJJkiI0XDq5o1xXrFfv3g6adFAyyp3FAUhffee4/Zs2cDMGvWLDIyMpg4cWKxxwQGBnL+/HliY2MfUZTSozRx10R9H6UcbQ7bz29n9fHVrIldQ/qedH2SKbi1qGSyNKv8M7iSYZ07J/oyLVkiJn8aNoQJE2DQIHByMnZ0kiRJhWmztCR/m0zC5wlkJ2Zj286W5vOaU/v52vob/Tbr2uhf32JBC2OFWuZytbms/Gcln+/7nONXjuNc05kF3Rcw0GOg3G3WSGSy6eE9zN+dXPAkFZKeLhp+//yz6AWRkiKKap58EqZMEf2YFi4Us6tWVpCdDTVqyGTTAzt9WiSZVq6Es2dFk42ePUWSqVs32XTDwCZOFH8MwdLSknXr1jF+/Hgc7qN/1rp167CxsTHMm0vl0qTdk2jfsD2rjq/ip5M/6SuZnqz9JMM7D5dJJumhZGfDhg3iert9u5h7eP55GDxYVDXJJeuSJJU3eRl5JC1MImFWArmXcrHrZEfL71tS65laVe4m/2bOTb49/C2z988m4UYCj9d9nBVBKwh2C8bMRH6AS1WHLJ2QOHMG5s6FZ58Vjb179YK1a8UWyj/8IGZT9+2Djz4CDw9RhDNkCBw4IL6mpBj7J6ggkpPhiy/giSfEdkGTJ4up6e+/F3/Jq1fDiy/KZFMZmDTJcOcyMzNj8ODBfPHFF/d8bUZGBnPmzOF///uf4QKQypWPtn8EQPeV3Vl3Yh09WvRg0yubuDzmMh+2+pCeLXvKZJP0QE6dgjFjxIrqkBAxJzF5sth1buNGsXROJpvKn/Xr16MoCidPngQgLi4ORVGYMGGC/jWpqamYm5szbNiwEs+dCKKhAAAgAElEQVQVGBhImzZtSnyNJJUnedfziJsSxwGnA5wfex6btjZ47PbAM8oT+2ftK32yaeKuifrv0zLTmLRrEk3mNmHk1pG41HLh574/8/eQv+n7eF+ZbJLumoheunTpPa8LFZn8F18F5eSIht/5S+VOnxbjrVuL7ZOffx46diy+F8S6dbe/X7Cg7OOt0G7cEH9hK1bAjh1inaK3N8yeLe4kHB2NHWGFNXIkxMTc/+v9/e/9Gg8PkXy9l3feeYe2bdvy/vvvl/i6CRMmMHr0aKpVq3Z/QUoVxsRdE5m0u3Am80b2DZrWakqPFj2MFJVUUWVliYmexYvFTq9mZhAYKKqZnnkGTE2NHWHlU3AprCGEh4fj6+tLRESEfol106ZN2bx5M5MnTwZg9erVuLm5lXgeWRUrVSS5abkkzk0k8atEtNe11O5RmyYfNcHuSTtjh/ZITdo9iUGeg5izfw6LDy8mMzeTwJaBfPDUB3Rs3NHY4UkP6eBBT2rU6ICz8wQsLRsYO5wKSyacqohLl8QSuZ9/ht9+E0vnLC2hc2cYPlwkmR6g2bxUkuxssbPcihWiu6tGA02bihKxvn2hVStjR1glxMWJXZzy7d4tvjo5lb65fY0aNQgNDWXevHlYWxe9/j4mJoazZ8/yxRdfEBcXV7o3lMqdif63b1aVSQrqJ6pxA5IqpNhYkWRavhyuXhW7y82YAf37y6XqZW3S7kkGSzhlZGSwd+9edu7cSWBgoD7hZG1tjaurK4cOHcLHx4fIyEiCg4NJSkoq9jxz5swhLCyM4OBgg8QmSWUh51IOCbMT+Pfrf9Hd1OHQywGnj5yw9bQ1dmiP3PErxwFoNk9sD9rv8X6M7TgWt7olJ5el8u/mzRgyM49z6dIS6tUb+EgST1euXGHIkCFcvHgRgLlz5/LUU08xceJEbGxsGDNmDABt2rRh8+bNAHTr1g1fX1/27dtHw4YN+emnn4q9PzEGmXCqpAo2/N68GQ4dEuMNG8Irr4gEU5cuUL26ceOsNHQ6UTa2YgWsWSPuHOrUgTfeEH2Z2reXO8wZ2P1UIuVTFNGf3ZBGjhyJl5cXAwcOBECr1eLt7Q2I5RANGjTgr7/+wtnZmby8PC5fvoy/vz+7du0ybCCSJFUoN2/CqlUi0bR/v6gmDgoS1Uz+/nKfiNIYuWUkMSn3X/rqv9T/nq/xqO/B3ICSLzgbNmwgICCAFi1aYG9vz+HDh7G3twcgJCSEiIgI6tevj6mpKY6OjsUmnGRVrFTeaRI1JMxMIDksGV2OjrohdXH60InqblXvhuLNjW/y7ZFv9Y/zdHkAONd0lsmmCuLMmZFkZJR8zVDVHFQVkpMXkpy8CAuLelhaOmFiUnS7BBsbDx57rORrRlZWFh4eHvrH//33H4GBgQC8++67jBo1Cl9fXy5evEjXrl05ceLEPX6OM4SHh7N48WKCg4NZu3Ytr776aonHPEoy4VSJ3E/Db3d3mfcwqKNHRZIpPBwSEkQG76WXRJLpmWdko41KzN7enuDgYL777jsGDRqEqakpMXes8Xv77bcB0cujR48eMtlUSX3i94mxQ5AqgJgYCAsTl4wbN0Qrv1mzIDRUzE9IZS/uWhzx12+Xvu6OF6WvTnZOONd0fujzhoeHM3LkSEAkmMLDw3nnnXcACAgIYMKECdSrV48+ffoUew5ZFSuVZ1kXsrj42UVSlqSADuq9Vo8m45tQ7bGqlRxVVZWdcTuZtmca2y9sp6ZVTUa0G8GnUZ/KSudKTwVUcnKS0WozsbHxuOcRxbG2ti50z7B06VIO3aoO+f333zl+/Lj+uRs3bpCenl7i+VxcXPQJLG9v73J3DZF3wxXcmTO3q5iioiA3F+zsxA42zz8vvspfZA0sPl7sLrdypVgPYWYGXbvCZ5+JphuybKzc+aSM8gGjR49m/vz5ZXNyqcIwZB8YqXJJT4eICJFoOnRILGV/+WV4803o1ElOABnavSqRCjLUUti0tDR27NhBbGwsiqKg1WpRFIWhQ4cCYGFhgbe3N7Nnz+bYsWNs2rQJkFWxUsWQeTqTi9MvkrI8BcVUocGgBjT+oDHWzuVnuc6joFN1bDy1kenR0/nz3z+pb1Ofmc/O5C3vt7C1tOXTqE+NHaL0EO5VibRr1+2LtKJYoCim1K8/ECenCVhals26d51Ox/79++9aEmdmZoZOp9M/1mg0+u8tC2w4ZWpqSlZWVpnE9rBkwqkcS04WfaUjI2/3cijY8HvzZpFwgvtv+C09pLQ0sYvcihUQHS3GOnYUXdODg8HBwbjxSSW61U7DIDIyMvTf16tXj8zMzHse4+zsTGxsrOGCkCSp3FJVkVwKCxPFrzdvQps28OWX8OqrcGullVRJrFmzhtDQUBYtWqQf8/PzIzExUf949OjR+Pn5Ubt2bf2YrIqVyrOM2AwuTrvI5cjLmFia0Gh4IxqPaYxlw6q162quNpeI2Ahm7J3B8SvHcanpwsLnF9Lfoz9WZlb618lK58rrUSWa8j333HPMnz+fsWPHAqL61cPDA2dnZ33PpsOHD3PhwoUyjcOQZMKpHJs8WeQ2xo0DPz+RYNq2rXDD7xEjZMPvh7ZzJwwcCEuWiL/MO2Vmij2oV66EX3+FvDyR2Zs6VTTCkn/pkiRJ0i3Xr4s5ibAw+PtvqFYN+vQRvZlkG7/yx1A3iOHh4YwbN67QWK9evZg2bZr+sZub2z13p5Ok8iD9cDrxU+JJXZ+KqY0pjcc2pvGoxljUszB2aI9UVm4WS2KWMHPfTOKuxdGmbhtWBK0g2C0YM5O7b59lpXPlVL26B3Z2HR9JoinfvHnz9Lth5+Xl8fTTT7Nw4UJ69erFDz/8gIeHB0888QQtWrR4JPEYgqIaupNuOeTj46Pmr4s0lF27duF/P/usPwRra7GxWVEGD5YNvw1i507o0UMklapVE9m8zp1FUmn7dnHXsH49ZGTc7rTer59sgmVkJ06cwNXV1dhhVGhF/R0qivKXqqo+RgqpXKho1wmpfFBV0fh78WJRjZyVBR4e4lrdt69Y4i6VLXldMCx5jSheZb5OXD9wnfgp8fz383+Y2pnS6N1GNBrRCPPaVWvJxI3sG3xz8Bu+OPAFl25e4slGT/Kh74c83+J5TBS5o0NlIK8Zpfeg1wlZ4VROaDSwa5coqKlVSyyny2duDs8+C99+Cw3KdifGqqFgsgnE1+7doVs32LsXLl8WdwkhIeKO4emnwdTUuDFLkiRJ5cZ//8Hy5SLRdOwY2NjAa6+J3kze3nJeQpKk8k9VVa5HXSduchzXtl/DrLYZLlNdaPhOQ8zsqtYt4pWbV/jyjy+Z/+d8rmdf57lmzzHedzx+Tn4o8gNdkkqlan2alDNXroheTBs3wm+/iT4P1aqJ/tNXr4om4BYWom+Tk5NMNhnEncmmfBqNqGjq1AkWLhQJKMuqtU5dkiRJEjw9oUMHmDDh9rVXVcV1efFiWLMGsrOhXTvxOCREJJ0kSZLKO1VVubrtKvGT47kefR3zeuY0m9WMBm81wMymat0aXrx+kdn7ZrP48GI0eRqCXIMY7zseb0dvY4cmSZVG1fpUMTJVhRMnYNMmkWTav1+MNWwoZkYDA8WqLisrCAqCIUNEWX5YWOGKJ6kUXnvt7mRTQRcvwksvPbp4JEmSpHInJgaOHxct/kJCoHFjWLUKTp2CGjXgjTdENZO7u7EjlSRJKll2cjbHQ47TOqI16YdEj6b0P9OxbGRJ86+a0+D1BphaV61K/lOpp/hs72csP7ocgFfbvsoHT31AK4dWRo5MkiofmXAqY7m5Yle5TZvEn3PnxLiXl9iqvWdPMZN6Z7XmunW3v1+w4NHFWylduSJ2mAsPh3//Lf511aqJuwtJkiSpysvJEV+XLhVf69WDuXNFoqlaNaOFJUmS9EDiPo3j+p7rHHz8IHlpeVi5WNEirAX1+9fHxKJq9SU6nHyY6dHTWXt8LVZmVrzt8zZjOo6hiV0TY4cmSZWWTDiVgatXYcsWUcX0669i5xpLS9Hoe8wYsaKrUSNjR1nJ3bgBGzaIJNO2baDVih3mJk8GZ2d4663ClU4FG4dLUglMTU15/PHH9Y9DQkIYN24c/v7+nD9/nvj4eP16/xdffJHff/+djIwMY4UrSdIDuHTpdoLpTleuiMmgd999pCFJkiQ9lCjrKHQanf5xXloeADnJOTi+6WissB45VVWJio9iWvQ0fjv3G3aWdoz3Hc+7T75L3ep1jR2eJFV6MuFkIOfOiQTTpk2ix4NWC3XrQq9eoorp2WflrnJlLisLfvlFJJl+/ln0ZXJ2hrFjxS5zjz9+u5SsYcOid6mTKpUVly7x0fnzXMzOpomlJVObNqVfvXqlOqe1tTUxMTFFPlezZk327t2Lr68v165dI1muhZWkck+nE/MSixfDTz+JzUoLsrAQ+0YMHCh6OkmSVPEpitIamAikAdtVVV1j3IgMR5ej49LyS5jXMyc7PhsUQAUTaxMcghxoNquZsUN8JFRVZfPpzUyPns7+xP3UrV6XGV1mMMRnCHZWcgtRSXpUqlYdpQFptWJDs3HjROFM8+bw3ntiBvT990V/puRk+O47ePFFmWwqM3l5opysf3+x3qF3b4iOFmse9u2D8+dh+nRo27bwusXOnUWSyclJJpsqqRWXLjH41Cnis7NRgfjsbAafOsWKS5fK7D1DQkKIiIgAYN26dQQFBZXZe0mSVDpJSTB1KjRrBgEBYqfYd98VvRZBJJqsrUW/pvPnxfL2+vWNGrJUjq1fvx5FUTh58iQAcXFxKIrChAJZytTUVMzNzRk2bFiR5/D396dly5Z4eHjg4eHB5cuXH0nsFY2iKN8rinJZUZTYO8YDFEU5pSjKWUVRxt3jNN2Ar1RVfRsILbNgHyGtRsu/3/zLH4/9wak3TmHuYE6trrVAARMrE3TZOkxrmGJZv3JvipOny2PlPytxX+hOYEQgSelJLOi+gLh34/jA9wOZbJLKhdJcM9asWYOiKBw6dKjE93B3d+eVV14pNDZgwABcXFzw8PCgVatWTJo0Sf9cv379aNmyJW3atGHQoEHk5uaW9scEZIVTiZKTRbPQyEjxS2ZGhthNbuNG2LChI9evg5kZ+PmJBt89e4KLi7GjrgJ0OpFMCg8XXVxTU8HOTiSbXnlFJI/M7uOfdufOEBdX5uFKZWPkmTPElLBU7cCNG2SraqGxTJ2O10+eZHFSUpHHeNjYMPexx0p836ysLDw8PPSPx48fT58+fQDo0qULb775JlqtloiICMLCwpg8efL9/kiSJJUxrRa2bhWbcWzeLB7/3//BjBlicih/c1IPD+jYUVQ0ySRT5VHU7oOGEh4ejq+vLxEREUycOBGApk2bsnnzZv11YPXq1bi5uZV4nhUrVuDj42PY4CqfpcB84If8AUVRTIEFwLNAInBQUZSNgCkw/Y7jBwHLgU8URQkEaj+CmMuMNlNLUlgSCTMTyEnKoUaHGrRY2AL7AHuO9TqG4xBHHAc7khSWRE5yjrHDLTOaPA3LYpbx+b7POX/1PK4Orvzw4g+EtAnB3NTc2OFJlUFysmjPsn8/HDlSqlM97DUjPT2defPm0b59+xLPf+LECXQ6HVFRUdy8eZPqBapfZs6cSe/evdFoNLRu3ZrQ0FBcXFzo168fP/74IwB9+/bl22+/5e233y7Vzwky4VSiyZNFw+/gYLHqaudO0US0Vi144omrvPFGPQICRK5DKmOqKrYNCg+HiAhISBBTzz17iiRTt2637xQkCe5KNt1r/H6VtKTO1NQUX19fIiMjycrKwtnZuVTvJUmSYSQkwPffi6rjhASx5H3MGFG91Lz53a8v5e+RUjlVcPfB/CWShkg8ZWRksHfvXnbu3ElgYKD+5sHa2hpXV1cOHTqEj48PkZGRBAcHk1TMpId0f1RVjVIUxfmO4XbAWVVVzwMoihIBvKCq6nSgRzGneudWompdMc+jKMpgYDBAvXr12LVrV+mCv0NGRsbDnzMT+AlYBVwDPIDRcMPzBv8o/8BuYIR4adLVJHhZfG/on8HYMvMy2ZS8idWJq0nLSaOVbSsmu02mY+2OmFw1Ye+evcYOUSpH7OzsSE9Pf6BjlJQULD77DPMVK0CnQ8nJeeBzFJSRkUF0dDSbN28mJCSE0aNHk5GRgaWlJc2bN2f37t14eXmxcuVKXnjhBZKTk/Xv98EHHzBs2DC++uorbt68WWwcS5YsITg4mFOnThEZGcnLL4sPgNzcXLKyskhPT+fatWuoqoqqqqSnp9OpUyd939m2bdty/vz5Is+v0Wge6HNEJpyKYG0t2v/k27NHfDU1FSX3Tz0F0dEn8PcvXS8Y6T6cPi2STOHhYj9qMzPo2lUskwsMBFtbY0coGcm9KpGc9+8nPjv7rnEnS0t2eXqWVViEhITw0ksv6W84JEkyjrw8sXFHWJho76fTiX6Kc+aIy4eFhbEjlAxt5EiRVCpJ/u6DCxfCokViNb6TU/FzVh4eYnfCkmzYsIGAgABatGiBvb09hw8fxt7eHri91Lp+/fqYmpri6OhYYsJp4MCBmJqa0qtXL/73v//pN6GQ7qkhkFDgcSJQbAnArYTVh0B1YGZxr1NVNQwIA/Dx8VH9/f1LH2kBu3bt4kHPmXstl3/n/Uvi3ETyruZRq2stnP7nRE3fmgaNrbxLy0xj3h/z+Oqvr7iquUoXly6M9x3P/7n8n/x/IxXrxIkT2ObfP97ropGdDfHxYkcRVRV/brHt2bPoY+7jovHTTz/RrVs3vLy8cHBw4MyZM9jb22NiYsJrr73Gpk2baNasGRYWFri4uJCWloatrS1Hjhzh0qVLBAcH8/XXX1O9evXbP8sdNmzYwLZt2zh16hTz589n0KBBAJibm/Pxxx8ze/Zszp49y4gRI2jatGmhY3Nzc1m9ejVffvllkee3srLC8wHupWQPpyKcPw99+97+5cPKCvr1g8REsXzuflZrSaWQmAizZoG3N7RsCZMmiSnIRYsgJUWsg+jXTyabpBJNbdqUaiaFP+KqmZgw9Y4PVUPr1KkT48ePv2vNtCRJj0Z8PHz8sUgiBAbCoUOi3+K5c2JZfO/eMtkkifsGnU6skMjv2/WwwsPDCQkJAUSCKTw8XP9cQEAA27ZtIzw8XL/8ujgrVqzgn3/+Yc+ePezZs4fly5eXLrCqpagMQ7ElzaqqxqmqOlhV1X6qqkaXYVwGk5Oaw/mPznPA6QBxn8Rh18kOrz+9cN/iXqWSTf/e+Jf3tr5Hk7lN+DTqU/yc/fjjjT/4PfR3ujTtIpNNkuGcOCEuEjpdoWRTaT3MNUOn0zFq1Chmz559z/MfPHiQOnXq4OTkRJcuXTh8+DBXr17VPz9z5kxiYmJISUlh+/bt7Nu3r9DxQ4cO5emnn6ZTp06l/VEBWeFUpAYNoEYNyM0VyaacHPFY9nEoQ6mpsGaNqGTas0f8p/bxEVPRwcFiVzlJegD5u9EZepe6O3s4BQQEMGPGDP1jRVEYM2ZMqd5DkqQHk5sr5iIWLxb7SIBoBL5gATz/PJjL9h1Vwr0qkQreh965++DD/o6XlpbGjh07iI2NRVEUtFotiqIwdOjQW+9jgbe3N7Nnz+bYsWNs2rQJAK1Wi7e3NwCBgYF8+umnNLz1u46trS19+/blzz//JDS0UvSzfhQSgcYFHjcCKsXaxeyUbBJmJZD0TRK6LB11etfB6SMnbNxtjB3aI3Um7Qyf7/2cZX8vQ6fq6Pt4Xz546gPc6pbcF02SinWvi0ZKiuixs2SJaPqYU6AH2kMuTX3Ya0Z6ejqxsbH6isiUlBQCAwPZuHEj69ev5+effwYgJiaG8PBwTp48qW/tcePGDdauXcsbb7xRKBYbGxv8/f2Jjo6mY8eOAEyaNIkrV66waNGih/r5iiITTsW4dEk0Ah88WJTjy93Ny0B6OmzYIJJM27aJ9Q+urqKiKSQE7rFkSpLupV+9eqVOMN1Jq9UWOV7cWuaMEhqbS5JUOhcuwLffiv5MKSlibuJ//4PXXxcVTpJ0J0MlmvKtWbOG0NDQQr+c+/n5kZiYqH88evRo/Pz8qF37dm9qU1PTQv0A8/LyuHbtGg4ODuTm5rJ582aeeeaZ0gVXtRwEHlMUxQX4FwgB+ho3pNLRJGhImJlA8uJkdDk66vWtR5PxTajeumptfR2TEsP06OmsOb4GcxNz3vR6k7FPjcW5prOxQ5Mqu/r1xczVhAnFJ54e0MNeM+zs7EhNTdU/9vf3Z9asWfj4+ODj48PUqVMBUQm1evVqjh49qp/E2LlzJ1OmTLkr4ZSXl8cff/zB8OHDAfj222/ZunUr27dvx8TEcAvhZMKpGOsKtA9csMB4cVQ6Go1ophEeLqajNRpxVzB6tGj+3bZt4SlISZIkSSogJ0fsFhsWJuYqTEyge3cxQdStm1z2LhWvLHYfDA8PZ9y4cYXGevXqxbRp0/SP3dzc7rk7XXZ2Nl27diU3NxetVsszzzzDm2++aZggKxlFUcIBf8BBUZRE4BNVVb9TFGUYsBWxM933qqoeM2KYDy3rQhYXZ1wkZUkKqFAvVCSaqjWvZuzQHqk98XuYHj2dX8/+iq2FLWM7jmXkkyOpbyOXnEiP2J2JpzuWoD0IQ10zihMVFUXDhg31ySaAp59+muPHj5N8q4Jm7NixTJkyhZycHLp06UJQUBAAQ4YMwcnJiQ4dOgAQFBTExx9//FBxFKSoBlyPWF75+Piohw4dMug5H6bJX5WVlwc7dogk07p1cOOG2CIoOFgkmZ58UtwxSNI9nDhxAldXV2OHUaEV9XeoKMpfqqpW6X245XWi/Dt7ViyZW7oULl+Gxo3FLnODBkGjRsaOTjIWeV0wLHmNKF5ZXycyT2cSPy2eSz9eQjFVaPB6A5p80AQrJyuDvmd5pqoqW85uYVr0NKIvRuNQzYGR7UfyTrt3qGlVdfpUSWVHXjNK70GvE3IeUCobOh3s3y+STKtXi7uDGjUgKEgkmf7v/+Q0tCRJklSi7Gyx8josTMxbmJpCz57w5ptiw1JTU2NHKEmSVDoZsRlcnHqRy6suY2JpQqPhjWg8tjGWjsVsnVjJTNw1kQlPT2DN8TXM2DuDmJQYGtdozLyAebzu9TrVzKtWZZckVTbyjl96ODt3igYIS5ZA585iTFXh779FkikiAi5eFF3Xe/YUSaZu3cRjSZIkA1IUpSnwEWCnqmrv4sakiuPUKVHNtGyZ2FPCyQmmTBGXHUdHY0cnSZJUeumH0+FjOLTnEKY2pjQe25jG7zXGom7V2UYzOy+bSbsnsfKflZz57wwta7fk+8Dv6de2HxamVefvQZIqM5lwkh7czp3QowdkZoqvixaJzq0rV8LJk6Jy6bnnYOpUeOEFsLU1dsSSJJVTiqJ8D/QALquq2qbAeADwJaIXx7eqqs4o5hSoqnoeeF1RlDUljUnlm0YDa9eKaqaoKHEpeeEF0ZvpmWfkymtJkiqm7ORsjoccp3VkayzrW3L9wHXip8Tz38//QXVw+tiJRiMaYV676myneTPnJosPL2bWvlkA2FrasublNbzY6kVMTWTpqiRVJjLhJD2YgskmEF9fe018//TT8O670Ls3ODgYL0ZJkiqSpcB84If8AUVRTIEFwLOIra4PKoqyEZF8mn7H8YNUVb38aEKVysLx46Ka6Ycf4L//oFkzmDEDBgwAA28yKUmS9MjFTY7jevR1Tr91Gl2mjqu/X8WsthkuU1240PYCLj1cjB3iI3NNc40Ffy5g6p6pZOVl6ccPJx+m9+refOL3CRP9JxovQEmSDE4mnKT79+uv8OKLRW8FaW0NEyfeXl4nSZWUqakpjz/+OHl5ebi4uLB8+XJq1qxJXFwcPXr0IDY2FoDFixfzzTffsH37dmrVqgXArFmzGDt2LFeuXMHBwYG0tDR69+7NwYMHGTBgAPPnzzfmj2YUqqpGKYrifMdwO+DsrSolFEWJAF5QVXU6ohrKIBRFGQwMBqhXrx67du0y1KkByMjIMPg5KwuNxoTdu+uwebMjsbF2mJnp8PVNpUePJDw9r2FiAidOiD+SVBI7OzvS09ONHUalodFo5OeWgURZR6HT6PSP0zamAaCYKTwZ9yRmNmZc2HXBWOE9UpdvXuaL/V+w4OAC0nPS6f5Ydz70/ZCnmjyFMklB/aTyb2IlSVWVTDhJJdPpYM8eMfW8ZIno01SUrCzRXCMu7pGGJ0klWfHPCj7a/hEXr1+kiV0TpnaZSr/H+5XqnNbW1sTExADQv39/FixYwEcffVToNcuXL+err75ix44d+mRTQkIC27Zto0mTJvrXWVlZMXnyZGJjY/WJKgmAhkBCgceJQPviXqwoSm1gKuCpKMp4VVWnFzV253GqqoYBYSB2HzL0jnJVdZc6T0/o0EHsHtygQeHn/vlHLJlbvhyuX4fHHoOZM6F/fxPq1KkL1DVKzFLFdeLECWzl0n2DsbKywtPT09hhVArtz7fn3OhzXI64DCoo5goOQQ40n9scM5uqcQt28fpFZu2bxeLDi8nOy+Zlt5cZ7zsej/oexg5NkqRHRHZEkIp29ix8/LFY2+DvD6tWiS2BLIvZMaNaNZGQkqRyYsU/Kxi8aTDx1+NRUYm/Hs/gTYNZ8c8Kg71Hhw4d+PfffwuNrVq1ihkzZvDbb7/hUGBp6ahRo/j8889RFEU/Vr16dXx9fbGSzfTvpBQxVuz0p6qqaaqqDlFVtVl+YqmoMenRiImB776Dpk1h6FA4dw6+/14kodq2FQmn558XK7RPnYIxY6BOHWNHLUkPz9TUFA8PD9zd3fHy8mLfvn0AxMXFYW1tjaenJ66urrRr145ly5bpj1u6dCl16tTBw8MDDw8PQkND7zp3QkICnTt3xtXVFTc3N7788stH9nNJpWPZwBJTO9GPyMTKBFWrYmZvhmX9yr/73Om007z+0+s0m9eMbw59wyttXuHEOyeI7B15V7LpEzuqH/wAACAASURBVL9PjBSlJBnP+vXrURSFkydPAuJ6oSgKEyZM0L8mNTUVc3Nzhg0bVujYNWvWoCgKhw4dKvE93N3deeWVVwqNDRgwABcXFzw8PGjVqhWTJk3SP/f666/j7u5O27Zt6d27NxkZGaX9MQFZ4SQVdO2aSCz98APs3QuKIjq1TpkCL70kkkp39nACMb55s1xOJz1SI7eMJCYlptjnDyQeIFubXWgsMzeT1396ncV/LS7yGI/6HswNmHtf76/Vatm+fTuvv/66fiw+Pp5hw4Zx5MgR6tevrx/fuHEjDRs2xN3d/b7OLZEINC7wuBGQZKRYpIeQv/J60SL45hvxffPmMGcOhIZC7drGi02SsrOTOX48hNatI7G0rH/vA+6hYOXr1q1bGT9+PLt37wagWbNmHDlyBIDz588TFBSETqdj4MCBAPTp06fE5dRmZmbMnj0bLy8v0tPT8fb25tlnn6V169aljlsqe7mXcnF82xHHwY4khSWRk1xEW4pK5O+Uv5kWPY3Vx1ZjaWbJEO8hjH1qLE3smhR7jOzZJJVXnp5iEu1OHh5w62P9oYWHh+Pr60tERAQTJ04EoGnTpmzevJnJkycDsHr1atzc3Aodl56ezrx582jfvtjCf0BU/+p0OqKiorh58ybVq1fXPzdz5kx69+6NRqOhdevWhIaG4uLiwhdffEGNGjUAeO+995g/fz7jxo0r3Q+KrHCS8vLgl18gJATq14e33hJdW2fMgIQE+O036NdPJJVAJJU2b779WCabpHLqzmTTvcbvV1ZWFh4eHtSuXZv//vuPZ599Vv9cnTp1aNKkCatWrdKPZWZmMnXqVD799NNSvW8VcxB4TFEUF0VRLIAQYKORY5Luw52TYbpb7UsUBRwdYdQomWySjC8ubjLXr0cTF2f4z+UbN27ol1LfqWnTpsyZM4d58+bd9/kaNGiAl5cXALa2tri6ut5VWSuVX23WtaHFghbYuNvQYkEL2qxrc++DKqD9CfvpsbIHHos8+PXMr3zw1AfEvRvHV92/KjHZJEnlWYcOYGFReMzCAjp2LN15MzIy2Lt3L9999x0RERH6cWtra1xdXfWVS5GRkQQHBxc6dsKECbz//vv3XB2xcuVKXnvtNZ577jk2biz6V2iNRgOgT0blJ5tUVSUrK6vQqozSkBVOVdXRo7BsGaxYAZcuiTuAN9+E/v3B21vcHRQnP+k0cKBYRieTTZIR3KsSyXmuM/HX4+8ad7JzYteAXQ/9vvkz2devX6dHjx4sWLCAESNGAFCtWjV+/fVXfH19qVu3Lv369ePcuXNcuHBBX92UmJiIl5cXf/75Z6EqqKpKUZRwwB9wUBQlEfhEVdXvFEUZBmxF7Ez3vaqqx4wYpnQPhw+LpXIr7lixamEBpqbiclGgSlySysSZMyPJyCi+8vX69T3A7SbOycnfkJz8DWCCnV2nIo+xsfHgscdKvt7kT0RoNBqSk5PZsWNHsa/18vLSL6EAcUMRHR0NwLvvvquvfCpKXFwcR44cuefMtiQ9Cqqq8vv535kWPY1dcbuobV2byZ0n884T71DLuuikqySVJyNHFl3BlC87W9RmFJSXJ6qbimvR6eEBc++xWGLDhg0EBATQokUL7O3tOXz4MPb29gCEhIQQERFB/fr1MTU1xdHRkaQkUeR/5MgREhIS6NGjB7NmzSrxPSIjI9m2bRunTp1i/vz5hZbWjR07lilTpnD27FlGjBhB3bq3+2cOHDiQX375hdatWzN79uySf5D7JBNOVcmlS7BypVgyFxMD5uaikUb//tC9+90p3JJ07iwbhEvl2tQuUxm8aTCZubeXf1Yzr8bULlMNcn47OzvmzZvHCy+8wNtvv60fr1OnDlu2bMHf3x8HBwe6du3K5cuX9c87Oztz6NChQv2dqjJVVV8pZvwX4JdHHI70ANLTISJCLJv76y+wsoI+fcRcxp2JJplblcoDW9t2aDTnyc1NRSSeTDA3d8DKqlmpzltwSd3+/fsJDQ0tdiMI9Y7NV+61pC5fRkYGvXr1Yu7cufpZaEkyBp2qY+OpjUzbM42DSQdxtHVkznNzeNP7TWwsbIwdniQZjKUl1KsHKSli3yxFEb/PPMgtc1HCw8MZOXIkIBJM4eHhvPPOOwAEBAQwYcIE6tWrR58+ffTH6HQ6Ro0axdKlS+95/oMHD1KnTh2cnJxo1KgRgwYN4urVq/rq2/wldRkZGXTp0oV9+/bR8VbZ1pIlS9BqtQwfPpzIyMgSJ0Hul0w4VXYaDWzaJO4AtmwBrRaeeAK++koso5M3vVIllb8bnaF3qSvI09MTd3d3IiIi6NTp9uy4i4sLGzdupHv37qxbt67E2WhnZ2du3LhBTk4OGzZs4LfffpO9OaRy7a+/RDXTypViCV2bNuKS0q8f1KoFf/8tys1lokl61O5ViQRw6tTbJCeHYWJihU6Xg4NDL1q2/NpgMXTo0IHU1FSuXLlS5PNHjhzB1dW12OMTEhLo2bMnAEOGDGHIkCHk5ubSq1cv+vXrR1BQkMFilaQHkafLIzI2kunR0zl25RhNazVlUY9F9Hfvj6VZ5W+ELlU+96pEAkhOFpugaDRiYu2vv0r3u01aWho7duwgNjYWRVHQarUoisLQoUMBsLCwwNvbm9mzZ3Ps2DE2bdoEiN5NsbGx+t2PU1JSCAwMZOPGjaxfv56ff/4ZgJiYGMLDwzl58iTOzs6AWOq9du1a3njjjUKx2NjY4O/vT3R0tD7hBGIjjD59+jBz5kyZcJKKoapw4IBIMkVGimbgDRuKrYBCQ0HezEpVRL/H+xk0wQTctWND/oUAKDSj7e7uXmSfjbg7KgPvfCxJ5dGNGxAeLhJNhw+DtbWYsxg8GNq3L7wKu7SNNCWpLOXmXsLRcQiOjoNJSgojJyfZoOc/efIkWq2W2rVrk1lwgxXE5/2YMWMYPnx4scc3btxYXy0FoiLq9ddfx9XVlffee8+gsUrS/dDkaVgWs4zP9n7GhWsXcKvjxoqgFQS7BWNmIm8lpcqtQQNRrb1okfha2om0NWvWEBoayqJFi/Rjfn5+JCYm6h+PHj0aPz8/ahdoemlnZ0dqaqr+sb+/P7NmzcLHxwcfHx+mThUrOHQ6HatXr+bo0aM0bNgQgJ07dzJlypS7Ek55eXn88ccfDB8+HFVVOXfuHM2bN0dVVTZt2kSrVq1K98PeIj8lKpP4eFi+XCyZO3NG3BH06iWSTP/3f2J9gyRJkiTdB1WFQ4dEkik8HG7ehLZtYcEC6NsXatY0doSS9ODatFmn/75FiwUGOWd+DycQCaJly5Zheut3rnPnzuHp6YlGo8HW1pbhw4c/0Izx3r17Wb58OY8//rj+PaZNm0b37t0NErskFScjJ4Owv8KYtW8WyRnJPOH4BF90/YKeLXtiosh9p6SqY8IEOHbMML0ow8PD79r5rVevXkybNk3/2M3N7a7d6e5XVFQUDRs21CebAJ5++mmOHz9OcrKYYMnv4ZSTk0OXLl0ICgpCVVX69+/PjRs3UFUVd3d3vsnfZriUZMKpoktPh7VrRTXTrl1izN8fxo+H3r3B1taY0UmSJEkVzI0bYrncokWi3V+1arermdq1K3lPCUmqirRabZHjzs7OZGVlFXvcgAEDGDBgQInn9vX1vavvkySVpatZV5n/53y+/ONL0rLS6OzcmR9e+oEuLl0MtmuVJFUkDRrA7t2GOdeu/Pv1AkaMGKHfgOhOxV0nijoPiMqnAwcOFBozNTXVJ5uK6wGlKAp79+4tNu7SKPcJJ0VRmgIfAXaqqva+NeYKvAs4ANtVVTVM+q282bmz6J3gtFrx3LJlsG4dZGZC8+bw6afw2mtwa72mJEmSJN0PVYWDB29XM2Vmgrs7fP21qGayszN2hJIkSVJZupRxiTn75/D1oa/JyMmgR4sefOj7IR0adzB2aJIkVWBlmnBSFOV7oAdwWVXVNgXGA4AvEdtdf6uq6ozizqGq6nngdUVR1hQYOwEMURTFBFhcVvEb1c6d0KOH+K2/Rw/YvFmkV5ctgx9/hMREcQfw2mtiyVyHDnLaWZIkSXog16/DihUi0fT331C9ukgwDR4MPj7ysiJJklTZxV+LZ+a+mXx35Duy87IJdgtmvO943Ou7Gzs0SZIqgbKucFoKzAd+yB9QFMUUWAA8CyQCBxVF2YhIPk2/4/hBqqpepgiKogQC426dv3IpmGwC8fWZZ0CnE32YAgJgzhzo2VO0y5ckSZKk+6Sq8McfIskUGSkuMR4e8M03Itkkd1yXJEmq/E6mnuSzvZ/x49EfUVAIdQ/l/afep0XtFsYOTZKkSqRME06qqkYpiuJ8x3A74OytyiUURYkAXlBVdTqiGup+z70R2Kgoys/AyjufVxRlMDAYoF69esWuc3xYGRkZBj8nQM0jR3h8/HhMs7MLP6HToTMz4/j//keqn58Yu2N9piRVdnZ2dqSnpxs7jApNo9GUyWeXVP5du3a7munoUVHN1K+fqGby9pbVTJIkSZXVxF0Tmeg/EYAjyUeYFj2NtcfXYmVmxVCfoYzpOIbGdo2NG6QkSZWSMXo4NQQSCjxOBNoX92JFUWoDUwFPRVHGq6o6XVEUfyAIsAR+Keo4VVXDgDAAHx8f1d/f3yDB59u1axeGPicglsfdmWy6xSQvjzZLlsAnnxj+fSWpAjhx4gS2shF+qVhZWeHp6WnsMKRHRFXF3ER+NVNWFnh5iYbgr7wi95WQJEmqCibtnsQzTZ9h2p5p/Hr2V2pY1mCc7zhGPjmSutXrGjs8SZIqMWPsaVnUHGqx22+oqpqmquoQVVWb3aqCQlXVXaqqjlBV9S1VVQ2zp62xabXw7beQkVH8a6pVEw3EJUm6b8nJ4OcHKSmGOZ+pqSkeHh60adOGnj17cu3aNQDi4uJo00bfqo7Fixfj5eXF1atXAfjqq69o2bIlbm5uvP/++8WePy4uDmtrazw8PPDw8GDIkCGGCVyqUq5eha++grZtoWNHWLNGtPw7dAj++ktUNclkkyRJUuWmqipbz24FoNOSThxMOsjU/5tK/Mh4pnWZJpNNkiSVOWMknBKBgjWbjYAkI8RRfvz2G3h6wptvQqtW4i6hWrXCr6lWTTQOL7hbnSRJ9zR5MkRHi00cDcHa2pqYmBhiY2Oxt7dnwYK7c97Lly/nq6++4rfffqNWrVrs3LmTn376iaNHj3Ls2DHGjBlT4ns0a9aMmJgYYmJiWLhwoWEClyoVT08YOlQkVPOpKuzbBwMGgKMjjBgh2vyFhUFSkqhq8vY2WsiSVGnlT0S4u7vj5eXFvn37gNsTCJ6enri6utKuXTuWLVumP27p0qXUqVNHP8EQGhp617k1Gg3t2rXD3d0dNzc3PpFV7tJ90Kk6+qzug8mnJgSsCNCPp2amkqPNoaZVTSNGJ0nS+vXrURSFkydPAuJ6oSgKEyZM0L8mNTUVc3Nzhg0bVujYNWvWoCgKhw4dKvE93N3deeWVVwqNDRgwABcXFzw8PGjVqhWTJk2667jhw4djY2PzsD/aXYyxpO4g8JiiKC7Av0AI0NcIcRhfbCyMHQtbtoCLC6xaBb17i0Yabm63G4fLZJMk3WXkSIiJKf75PXtEn/1833wj/piYQKdORR/j4QFz595/DB06dODo0aOFxlatWsWMGTPYvn07Dg4Ot977G8aNG4elpSUAdevKGUWpdGJi4PhxUfTaty84O4slc8eOicqlAQPEHIaXl7EjlaRyLDlZzErs3w9Hjjz0afInIgC2bt3K+PHj2b17NyAmEI7cOvf58+cJCgpCp9MxcOBAAPr06cP8+cXvf2NpacmOHTuwsbEhNzcXX19funXrxpNPPvnQ8UqVV54uj8jYSKZHT+fYlWM0rdWUcU+NY/DmwaifFLugRJKkEmQnZ3M85DitI1tjWd/SIOcMDw/H19eXiIgIJk6cCEDTpk3ZvHkzkydPBmD16tW4ubkVOi49PZ158+bRvn2xHYkA0YZEp9MRFRXFzZs3qV69uv65mTNn0rt3bzQaDa1btyY0NBQXFxcADh06pF+9YShlWuGkKEo4sB9oqShKoqIor6uqmgcMA7YCJ4BVqqoeK8s4yp2UFLGewd1dNNeYNQtOnICXX77dtbVzZ5FkcnKSySZJegjt2kHduiLBBOJr3bpwj8/n+6bVatm+fTuBgYH6sfj4eIYNG8Zvv/1G/fr19eOnT59mz549tG/fHj8/Pw4ePFjiuS9cuICnpyd+fn7s2bPHMAFLlU5ODmg08P338PHHcPmyuJwkJYnkqkw2SVIxkpNFiWDTpvDddyXPXjygGzduUKtWrSKfa9q0KXPmzGHevHn3fT5FUfQzzbm5ueTm5qLIDv/SHbLzsgn7K4yW81vy6vpXAVgRtIJTw07xpvebRo5Okiq2uMlxXI++TtyncQY5X0ZGBnv37uW7774jIiJCP25tbY2rq6u+cikyMpLg4OBCx06YMIH3338fq3vsVL9y5Upee+01nnvuOTZu3FjkazQaDYA+GaXVahk7diyff/75Q/9sRSnrXepeKWb8F4pp9l2pZWbCnDnw2WfiLmH4cJgwAWrXLvr1nTtDXNwjDVGSKor7qUR6+22xnMjKStyc9+oFX39duvfNysrCw8ODuLg4vL29efbZZ/XP1alTB3t7e1atWsWoUaP043l5eVy9epUDBw5w8OBBgoODOX/+fJE3DQ0aNODixYvUrl2bv/76ixdffJFjx45RQ+5VLwH//Qc//FD0c2lpsHEjjB79aGOSpHLjXqWv2dkQHw+XLok1qGqBio/iNoK5j9LX/OuCRqMhOTmZHTt2FPtaLy8v/RIKEDcU0dHRALz77rv6yqeCtFot3t7enD17lnfeeeeeM9tS1XEz5yaLDy9m1r5Z/Jv+Lz6OPsx+bjaBLQMxUW7XFXziJ5diStKdzow8Q0ZM8f2Tr++5DgVWSyR/k0zyN8lgAnad7Io8xsbDhsfmPlbi+27YsIGAgABatGiBvb09hw8fxt7eHoCQkBAiIiKoX78+pqamODo6kpQkug8dOXKEhIQEevTowaxZs0p8j8jISLZt28apU6eYP39+oaV1Y8eOZcqUKZw9e5YRI0boV17Mnz+fwMBAGjRoUOK5H5QxejhVPTodLFsGLVqIBNNzz4m1EHPnFp9skiSp1C5dgiFDRCHhkCGGaRyev3QiPj6enJycQj2cqlWrxq+//srChQtZsWKFfrxRo0YEBQWhKArt2rXDxMSE1NTUIs9vaWlJ7VufC97e3jRr1ozTp0+XPnCpwlJViIqCV18VvZkK5DIBsLAAa2vxbzwy0jgxSlKFcOKEqG7S6Qonm0op/7pw8uRJtmzZQmhoKGox579zvE+fPvqefUUlm0D0iIqJiSExMZE///yT2NhYg8UuVUzXNdeZtmcazl86M2rrKJrZN2Prq1v5840/ebHVi4WSTQAT/ScaJ1BJqsBs29liXtf8dsbEBMzrmmPbvnS7roSHhxMSEgKIBFN4eLj+uYCAALZt20Z4eDh9+vTRj+t0OkaNGsXs2bPvef6DBw9Sp04dnJyc6NKlC4cPH9ZvYgRiSV1MTAwpKSls376dffv2kZSUxOrVqxk+fHipfraiGKOHU9Wyc6eYbj5yBJ54AsLDi28gI0mSQa1bd/v7Inp7l4qdnR3z5s3jhRde4O2339aP16lThy1btuDv74+DgwNdu3blxRdfZMeOHfj7+3P69GlycnL0/Z3udOXKFezt7TE1NeX8+fOcOXOGpk2bGjZ4qUJITRXVTIsXw8mTUKMGvPGG6M3k4SESTaamMHCgmMsosIpTkqqme5W+pqSInk1LlojdgXNybj+3a5dBQujQoQOpqalcuXKlyOePHDmCq6trsccnJCTQs2dPAIYMGVJop9KaNWvi7+/Pli1bCu2KKlUdqZmpzD0wl/l/zud69nW6Ne/Gh50+xLeJr7FDk6QK516VSACn3j5FclgyJlYm6HJ0OPRyoOXXLR/6PdPS0tixYwexsbEoioJWq0VRFIYOHQqAhYUF3t7ezJ49m2PHjrFp0yZA9G6KjY3F/1Y1bkpKCoGBgWzcuJH169fz888/AxATE0N4eDgnT57E2dkZEEu9165dyxtvvFEoFhsbG/z9/YmOjubq1aucPXuW5s2bA5CZmUnz5s05e/bsQ/+s+WTCqaycPAnvvw+bNkGTJrBiBYSE3G4oI0lShefp6Ym7uzsRERF0KpBIdnFxYePGjXTv3p1169YxaNAgBg0aRJs2bbCwsGDZsmXF9uCIiori448/xszMDFNTUxYuXKgvs5UqP1WF3bvFUtC1a8X9cIcO4v745Zchv+ejhwd07CgTTZL0QOrXF7MPEyYUn3gqpZMnT6LVaqlduzaZmZmFnouLi2PMmDElziA3btxY34AcxCSEubk5NWvWJCsri99//50PPvjAYPFKFcO/N/5l1r5ZhB0OIys3iyDXID7s9CFeDWSzPkkqS7mXcnEc4ojjYEeSwpLISS7d9WLNmjWEhoayaNEi/Zifnx+JiYn6x6NHj8bPz0+/4gHERHfB1RH+/v7MmjULHx8ffHx8mDp1KiAqoVavXs3Ro0dp2LAhADt37mTKlCl3JZzy8vL4448/GD58OM8//zwpBZaC2NjYGCTZBDLhZHhXrsDEiWL/6erVYcYMePdd0URGkqQKLyOj8Frv/JkHoNAyB3d3d/7991/94x9//PG+zt+rVy969epVyiiliiY1Vay8DguD06fBzg7eektUMz3++N2vL8WGWpIk3Zl42revVKfL7+EEYsncsmXLMDU1BeDcuXN4enqi0WiwtbVl+PDhxS6dK0pycjL9+/dHq9Wi0+kIDg6mR48epYpXqjjOXz3PZ9GfsfTvpWh1Wvo+3pfxvuNxrVN8lZwkSYbTZt3tatIWC1qU+nzh4eGMGzeu0FivXr2YNm2a/rGbm9tdu9Pdr6ioKBo2bKhPNgE8/fTTHD9+nOTkZOB2D6ecnBy6dOlCUFDQQ73X/ZIJJ0PRaEQp97Rpojn4W2+JxFOdOsaOTJIkSSqHVFWs4gkLE8s/c3Lgqafgo4+gd2+oVs3YEUpSJZefeColrVZb5LizszNZWVnFHjdgwAAGDBhQ4rnbtm3LEZlhrnKOXznO9OjphP8TjqmJKYM8BjH2qbE0rSWX2EtSRbariOXbI0aMYMSIEUW+vrjrRFHnAVH5dODAgUJjpv/f3r2HR1Wdexz/LSK3YEWi4RpLgkUQSDIBrMChCg0YxEirYEEuKojWoxzAC7Qq90cQW/SxFJ5j5VBpvYSLGo14uKgQCJZSbiENAoqaVKQicFSgIBqyzh+TTJMQJpPMTmb25Pt5nnlg9t6z5l07k3nh3WutHRXlKzYtW7YsoDgrXmAPBgWnYBUXS8uXS48+Kv3jH9LNN0u/+Y3UuXOoIwMQxtatW3fetIiEhARlZmaGKCLUlS+//PdopoMHpUsv9d5R8Z57pBpe0AIARICdh3dq3pZ5en3f64puGK1J107Sw30eVtsftA11aABQIxScgpGT410QfPt2KSVFWrZM6t8/1FEBcIG0tDSlpaWFOgzUkeJi7z0knn9eysyUvv9e6ttXmjlTGjrUe5c5AED9lFOYo3lb5mntwbVq3ri5pv1kmib1mqTLoyu/wQgAuAUFp5r46CN1nTHDW3Bq1857qXr0aBYEBwCUc+SI91rEkiXSxx9LMTHShAneu8116RLq6AAAoWKt1d/+72+a8cIM5fwjR7HRsZr303m6/5r71bxJ81CHBwCOoODkz8aN3vtNv/CCd+TS8ePexSUXL1bMRRd5//7QQyy0AQDwKS6W3ntPmju3i95/Xyoqkq67TpozR7r1Vu4hAQD1WbEt1pv739S8LfO04/AOxV0Sp98N+p3Gdx+v6Ib8nwJAZKHgdCEbN0rp6d4FwNPTpTvu8K7VdOKENH68tqWlqU8tr+gOAAhPKSlS797em1y1aePd9sUX3usTS5ZIn34qXXJJC02c6F2biWX9AKD+mpU9S9Oum6YV+Sv05JYntffoXl3Z4ko9ctUjeuK2J9T4osahDhEAagVzwCpTttgkef987jmpY0dpzx7pD3/QdzExoY0RQGA2bpTi471/Ag7JzZWWLpU6dPCmi8GDpSuukB57TGrfXnrlFWnVqq16+mmKTQBQn50tOqvZm2ar06JOGp05WpL08q0va/+E/bqpzU0UmwBENApOFVUsNpW1d6909GjdxwSgZkp/nwsLvX86UHSKioqSx+NRt27ddPPNN+vrr7+WJBUUFKhbt26+45YsWaLu3bvrq6++0vDhw+XxeOTxeBQfHy+Px+P3PfLy8tS7d2917dpViYmJ+vbbb4OOG8777jvp22+lt9+W1qzx3mEuJ8f7Mbv9dqlRo+JQhwigDhhjNGbMGN/zoqIixcbGKj09XZJ05MgRpaenKzk5WV26dNHgwYMrbeeZZ55Rly5dlJSUpNTUVBUWFtZJ/Kg91lr9+H9+LEmKaRqjzOGZyvvPPI1MHKmLGjDRBKivMjMzZYzR/v37JXn/H2GM0fTp033HHDt2TA0bNtSECRPKvfbVV1+VMUY7duzw+x7Jycm6/fbby2276667lJCQII/Ho86dO2v27NmV7vN4PMrNzQ22m5IoOJ1v7NjKi02Sd/vYsXUbD4CaqWykogNFp6ZNmyo3N1f5+fmKiYnR4sWLzzvmxRdf1O9//3utX79eLVq00IoVK5Sbm6vc3FwNHTpUt/qZjltUVKTRo0frueee0969e5Wdna2GDRsGFTPqxt//Lj3+eKijAODPkZePaGv8VmU3yNbW+K068vKRoNts1qyZ8vPzdebMGUnSO++8o3bt2vn2z5gxQwMHDtSePXv0wQcfaP78+ZW2k5KSoh07digvL0/Dhg3T1KlTg44NoTMre5YazGmgvCN5kqQdh3folhW3aM6mOSGODEB1zcqe5Wh7RPL4YgAAEERJREFUGRkZ6tu3r5YvX+7b1qFDB61evdr3fNWqVeratWu51508eVILFy7Utdde67f9ffv2qbi4WJs3b9a//vWvcvt++9vf+v5f8qc//UmffvpppfuqukAeKApOFb3wwoUXAY+O9u4HEHqTJ0v9+lX+SE6WBgw4v3h8+rR3e3Jy5a+bPLlaIfTu3Vuff/55uW0rV67U/PnztX79el1+efnbGVtrtXLlyvOuNpS1fv16JSUlKTk5WZJ02WWXKSoqqlpxoW41aiQ1bSrdd5+0YkWoowFwIUdePqID9x7Q2cKzkpXOFp7VgXsPOFJ0uvHGG/X2229L8v5Houz3/D//+U/FxcX5niclJVXaRv/+/RVd8m/QXr166dChQ0HHhdCZ1W+W7EwrO9NKku/vs/rNCm1gAKpt9qbZVR8UoFOnTun999/X0qVLyxWcmjZtqquvvto3cmnFihX6xS9+Ue6106dP19SpU9WkijvQvPLKKxozZoxuuOEGZWVlVXpM6QyKZs2aBdOdKjGWs6L+/aXVq8+fVhcd7d3ev3/oYgMQmAMHvLcKq0xxsXd/r15BvcW5c+f03nvv6e677/ZtKyws1IQJE7R79261bt36vNfk5OSoVatW6tix4wXb/fDDD2WMUVpamo4ePaoRI0ZwlTtMNWokRUV5B75Ony5V8iMHUIc+mvyRTuWeuuD+E389IXvWlttWfLpY++/er8NLDlf6mos9F6vjsxf+zi41YsQIzZkzR+np6crLy9O4ceOUk5MjSXrggQc0fPhwLVq0SAMGDNDYsWPVtm1bv+0tXbpUN954Y5XvCwComclrJyv3i8CnjfVb1q/KYzytPXp20LN+j3njjTc0aNAgXXXVVYqJidGuXbsUU7I+9IgRI7R8+XK1bt1aUVFRatu2rQ4f9uan3bt367PPPlN6eroWLFjg9z1WrFihd955RwcOHNCiRYvKXQSZMmWKnnjiCR08eFATJ05Uy5Ytffsef/xxzZkzR6mpqZo/f74aNw5+jTkKTpWpWHSi2ASEn2f9fJn7W4styN/nM2fOyOPxqKCgQD169NDAgQN9+2JjYxUTE6OVK1fqwQcfPO+1Fa96V6aoqEhbtmzR9u3bFR0drdTUVPXo0UOpqak1ihe1w+OR+vSh0AS4ScViU1XbqyMpKUkFBQXKyMg4b42mtLQ0ffLJJ1q7dq3WrFmjlJQU5efnKzY2ttK2XnrpJe3YsUObNm0KOi6Eh5nXzwx1CACqqeDrAhV+8++19DYVer+T2zdvr/hL42vcbkZGhiaXzKoYMWKEMjIy9MADD0iSBg0apOnTp6tVq1YaPny47zXFxcV68MEHtWzZsirb3759u2JjY9W+fXvFxcVp3Lhx+uqrr9SiRQtJ3mlzw4YN06lTp5Samqq//OUv6tOnj5588km1bt1a3333ne6991499dRTmjFjRo37WYqC04WUFp3GjvVOo6PYBLhHLY5ULF3D6ZtvvlF6eroWL16siRMnljQfrTVr1qhv375q2bKlRo0a5XtdUVGRXn/9de3cudNv+3Fxcbr++ut90/EGDx6sXbt2UXAKM7t3hzoCABVVNRJpa/xW73S6Chq3b6yU7JSg33/IkCF65JFHlJ2drePHj5fbFxMTo5EjR2rkyJFKT0/X5s2btWvXLt80vNLFWd99913NnTtXmzZtcuTKMsID0+iA8FPVSKSyzGzjmx4bjOPHj2vDhg3Kz8+XMUbnzp2TMUb333+/JKlRo0bq0aOHnn76ae3du1dvvfWWJO/aTfn5+erXr58k6YsvvtCQIUOUlZWlzMzMcrkkIyND+/fvV3x8vCTpxIkTeu211zR+/PhysVx88cXq16+ftmzZoj59+qhNmzaSpMaNG2vs2LFVjqIKFGs4+dO/v1RQQLEJcKPSolPpmmwOj1Rs3ry5Fi5cqAULFuj777/3bY+NjdXatWv12GOPad26db7t7777rjp37lxuHY/KpKWlKS8vT6dPn1ZRUZE2bdqkLl26OBIzANRnHeZ2UIPo8v/0bRDdQB3mdnCk/XHjxmnGjBlKTEwst33Dhg06XXLx4+TJk/r444/1wx/+UHPnzvUtzip5p0v88pe/VFZWVrkpDgCAyPDqq6/qjjvuUGFhoQoKCvTZZ58pISGh3Jp9Dz/8sJ566ilddtllvm3NmzfXsWPHVFBQoIKCAvXq1UtZWVnq2bNnuVxSXFysVatWKS8vz3fsm2++qYyMjPNiKSoq0rZt23TllVdK8q43KHnXnH3jjTfK3X07GBScAESu0qJT+/a1Mi02JSVFycnJ5Rb8k6SEhARlZWVp3Lhx2rZtmyRp+fLlVU6nk6QWLVrooYce0jXXXCOPx6Pu3bvrpptucjRuAKiPWo1qpU7Pd1Lj9o0l4x3Z1On5Tmo1qpUj7cfFxWnSpEnnbd+5c6d69uyppKQk9e7dW+PHj9c111xz3nFTpkzRqVOndNttt8nj8WjIkCGOxAUACI5T02IzMjJ0yy23lNs2dOhQzZs3z/e8a9euuvPOO2vU/ubNm9WuXbtyd0q97rrr9MEHH/gKSlOmTJHH41FSUpISExN9d88eNWqUEhMTlZiYqGPHjmnatGk1iqEiY23wQ8PCXc+ePW3pau9Oyc7O9g1pA1A39u3bp6uvvjrUYbhaZefQGLPTWtszRCGFBfIE4E7kBWeRIy6MPAG4HzkjeNXNE4xwAgAAAAAAgKNYNBwAQmDdunX61a9+VW5bQkKCMjMzQxQRAAAAADiHghMAV7HWyhgT6jCClpaWprS0tDp9z/owhRpA/RMpeSHUyBEA6gNyRs3VJE8wpQ6AazRp0kTHjx/nH8U1YK3V8ePH1aRJk1CHAgCOIS84gxwBoD4gZ9RcTfMEI5wAuEZcXJwOHTqko0ePhjoUV2rSpIni4uJCHQYAOIa84BxyBIBIR84ITk3yBAUnAK7RsGFDJSQkhDoMAECYIC8AAAJFzqh7TKkDAAAAAACAoyg4AQAAAAAAwFEUnAAAAAAAAOAoUx9WaDfGHJVUKKm5pG8cavZyScccagvu4eRnKJJF2nlyQ3+CibG9tTbWyWDchjwBB7nh+yIcRNp5Cvf+kCOCRJ6Ag8L9+yJcRNp5Cvf+1EqeqBcFp1LGmOettfc61NYOa21PJ9qCezj5GYpkkXae3NAfN8ToBuQJBIvfxcBE2nkK9/6Ee3xuQp5AsPh9DEyknadw709txVffptS9FeoA4Hp8hgITaefJDf1xQ4xuwHlEsPgMBSbSzlO49yfc43MTziWCxWcoMJF2nsK9P7USX70a4eQkrkgAAPwhTwAA/CFPAIh09W2Ek5OeD3UAAICwRp4AAPhDngAQ0RjhBAAAAAAAAEcxwgkAAAAAAACOouAEAAAAAAAAR1FwAuqYMebnxpglxpg3jTE3hDqecBSJ5ygS+wTAeXxXBCbSzlOk9QdA7eH7IjCRdp7c2h8KTohoxpgrjDEbjTH7jDF7jTGTgmjrj8aYL40x+ZXsG2SMOWCMOWiM+bW/dqy1b1hr75F0l6ThNY3HKcaYJsaYvxlj9pSco9lBtBVW58gYE2WM2W2MWR1EG2HVJwDOIUcEJlLzBDkCQFXIE4EhT/htI2z6EwosGl4LjDE/l3STpJaSFltr14c4pHrLGNNGUhtr7S5jzA8k7ZT0c2vtB2WOaSnpjLX2ZJltP7LWHqzQ1nWSTkn6s7W2W5ntUZI+lDRQ0iFJ2yXdLilK0pMVQhpnrf2y5HVPS3rZWrvLsQ7XgDHGSGpmrT1ljGkoaYukSdbav5Y5xpXnyBjzkKSeki6x1qZX2OfKPiEykCfCAzkiMJGaJ8gRCGfkifBAnggMecId/QkJay2PMg9Jf5T0paT8CtsHSTog6aCkXwfYVgtJS0PdJx7lfiZvShpYYdttkjZIalLy/B5J/3uB18dX8tnoLWldmeePSnrUTwxG0lOSBoT6fFQSW7SkXZKudfs5khQn6T1JP5W0upL9rusTj/B4kCci90GOCOgcRUSeIEfwqM0HeSJyH+SJgM4ReSIM+xOqx0VCRcskLZL059INJdXHxSpTfTTGZKmK6qOkaSWvQxgwxsRLSpG0rex2a+0qY0yCpOXGmFWSxsn7sw5UO0mflXl+SNK1fo7/L0kDJDUvqYI/V433qhUln/Gdkn4k71W0SDhHz0qaKukHle10aZ8QHpaJPBFxyBH+RWCeIEegNi0TeSLikCf8I0+EfX9CgoJTBdbazSVfJmX9WNJBa+0nkmSMWS7pZ9baJyWlVzi2dEjhfElrrFuGukU4Y8zFkl6TNNlae6Lifmvtb0p+rv8t6Upr7anqNF/JtgvOVbXWLpS0sBrt1zpr7TlJHmPMpZIyjTHdrLX5FY5xzTkyxqRL+tJau9MY08/P+7imTwgf5InIQ46oWiTlCXIEaht5IvKQJ6pGngjf/oQSi4YHprLqYzs/x5dWH4cZY+6rzcBQtZJ5xK/JO9f19Qsc8xNJ3SRlSppZzbc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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(20,7))\n", "\n", "subplot(1,3,1)\n", "loglog(H,err_ep, 'r-o',label='AB-1=EE')\n", "loglog(H,err_AB2, 'g-+',label='AB-2')\n", "loglog(H,err_AB3, 'c-D',label='AB-3')\n", "loglog(H,err_AB4, 'y-*',label='AB-4')\n", "loglog(H,err_AB5, 'r-.',label='AB-5')\n", "loglog(H,err_N2, 'y-*',label='N-2')\n", "loglog(H,err_N3, 'r-<',label='N-3')\n", "loglog(H,err_N4, 'b-+',label='N-4')\n", "loglog(H,err_em, 'c-o',label='EM')\n", "loglog(H,err_RK4, 'g-o',label='RK41')\n", "loglog(H,err_RK6_5, 'b-*',label='RK6_5')\n", "loglog(H,err_RK7_6, 'r-D',label='RK7_6')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas explicites\")\n", "legend() \n", "grid(True)\n", "\n", "subplot(1,3,2)\n", "loglog(H,err_er, 'r-o',label='AM-0=EI')\n", "loglog(H,err_CN, 'b-v',label='AM-1=CN')\n", "loglog(H,err_AM2, 'm->',label='AM-2')\n", "loglog(H,err_AM3, 'c-D',label='AM-3')\n", "loglog(H,err_AM4, 'g-+',label='AM-4')\n", "loglog(H,err_AM5, 'b->',label='AM-5')\n", "loglog(H,err_BDF2,'y-*',label='BDF-2')\n", "loglog(H,err_BDF3,'r-<',label='BDF-3')\n", "loglog(H,err_MS2, 'm-o',label='MS-2')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas implicites\")\n", "legend() \n", "grid(True)\n", "\n", "subplot(1,3,3)\n", "loglog(H,err_heun, 'y->',label='Heun')\n", "loglog(H,err_AM4AB2, 'r-<',label='AM4-AB2')\n", "loglog(H,err_AM4AB3, 'b-v',label='AM4-AB3')\n", "loglog(H,err_AM4AB4, 'm-*',label='AM4-AB4')\n", "loglog(H,err_AM4AB5, 'g-+',label='AM4-AB5')\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas predicteur-correcteur\")\n", "legend() \n", "grid(True)\n", "\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version compacte\n", "\n", "De manière compacte en utilisant une liste des noms des schémas et des dictionnaires:" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EE\t 0.97\n", "AB2\t 1.98\n", "AB3\t 2.96\n", "AB4\t 3.94\n", "AB5\t 4.92\n", "N2\t 1.99\n", "N3\t 2.97\n", "N4\t 3.95\n", "EM\t 1.98\n", "RK4\t 3.98\n", "RK6_5\t 4.95\n", "RK7_6\t 6.18\n", "EI\t 1.04\n", "CN\t 2.00\n", "AM2\t 2.98\n", "AM3\t 3.96\n", "AM4\t 4.95\n", "AM5\t 5.93\n", "BDF2\t 1.97\n", "BDF3\t 2.95\n", "MS2\t 4.00\n", "RK1_M\t 2.00\n", "heun\t 1.98\n", "AM4AB2\t 2.95\n", "AM4AB3\t 3.94\n", "AM4AB4\t 4.93\n", "AM4AB5\t 4.76\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "schemasEXPL = ['EE','AB2','AB3','AB4','AB5','N2','N3','N4', 'EM', 'RK4', 'RK6_5', 'RK7_6']\n", "schemasIMPL = ['EI', 'CN', 'AM2', 'AM3', 'AM4', 'AM5', 'BDF2', 'BDF3', 'MS2', 'RK1_M']\n", "schemasPRCO = ['heun', 'AM4AB2', 'AM4AB3', 'AM4AB4', 'AM4AB5']\n", "\n", "schemas = schemasEXPL+schemasIMPL+schemasPRCO\n", "\n", "H = []\n", "err= { schemas[s] : [] for s in range(len(schemas)) }\n", "\n", "N=10\n", "for k in range(6):\n", " N += 50\n", " tt = linspace(t0,tfinal,N+1)\n", " h = tt[1]-tt[0]\n", " H.append(h)\n", " yy = array([sol_exacte(t) for t in tt])\n", " uu = { schemas[s] : eval(schemas[s])(phi,tt,sol_exacte) for s in range(len(schemas)) }\n", " for key in uu:\n", " err[key].append(norm(uu[key]-yy,inf))\n", "\n", " \n", "for key in err:\n", " print (f'{key}\\t {polyfit(log(H),log(err[key]), 1)[0]:1.2f}')\n", "\n", "\n", " \n", "figure(figsize=(20,5))\n", "markers=['^', 's', 'p', 'h', '8', 'D', '>', '<', '*','+','o', 'x']\n", "\n", "subplot(1,3,1)\n", "for s in range(len(schemasEXPL)):\n", " loglog(H,err[schemasEXPL[s]], label=f'{schemasEXPL[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas explicites\")\n", "legend()\n", "grid(True)\n", "\n", "subplot(1,3,2)\n", "for s in range(len(schemasIMPL)):\n", " loglog(H,err[schemasIMPL[s]], label=f'{schemasIMPL[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas implicites\")\n", "legend()\n", "grid(True)\n", "\n", "subplot(1,3,3)\n", "for s in range(len(schemasPRCO)):\n", " loglog(H,err[schemasPRCO[s]], label=f'{schemasPRCO[s]}',marker=markers[s])\n", "xlabel('$h$')\n", "ylabel('$e$')\n", "title(\"Schemas predicteur-correcteur\")\n", "legend()\n", "grid(True);\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "default_view": {}, "name": "EdoExplicites.ipynb", "provenance": [], "version": "0.3.2", "views": {} }, "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": true }, "toc": { "base_numbering": 1, "nav_menu": { "height": "190.994px", "width": "160px" }, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }