{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import division" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapitres 1 à 4\n", "Quelques ajouts dans les sections déjà vues..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 Nombres rationels\n", "Une autre façon de créer un nombre rationnel" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.5" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "5 / 2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5/2" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import Rational\n", "Rational(5,2)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import S\n", "S?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.numbers.Integer" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(S(5))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5/2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S(5)/2" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "101/14" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S('13/2') + S(5)/7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 Nombres complexes" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import arg,re,im,I" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = 3 + 5*I" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "re(a)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "im(a)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.03037682652431" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "arg(a).n()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sqrt(34)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abs(a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2 Définir les variables symboliques x_1, x_2, ... x_n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import symbols" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x3,x4,x5,x6,x7 = symbols('x3:8')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "x3 + x4 + 6*x7" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x3 + x4+ 6 *x7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Initialisation" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Importer toutes les fonctions de Sympy:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *\n", "init_printing(pretty_print=True, use_latex='mathjax')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Importer quelques variables du module abc:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#from sympy.abc import * # à éviter\n", "from sympy.abc import a,b,c,n,t,u,v,w,x,y,z" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 5 Résolution d'équations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1 Définir une équation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Définir l'équation $x=3$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eq1 = Eq(x, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Définir l'équation $x^2+y^2=16$" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eq2 = Eq(x**2+y**2, 16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Résoudre une équation" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ 3\\right ]$$" ], "text/plain": [ "[3]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1, x)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ - \\sqrt{- x^{2} + 16}, \\quad \\sqrt{- x^{2} + 16}\\right ]$$" ], "text/plain": [ "⎡ ___________ ___________⎤\n", "⎢ ╱ 2 ╱ 2 ⎥\n", "⎣-╲╱ - x + 16 , ╲╱ - x + 16 ⎦" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq2, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Résoudre l'équation $x^2+2x=4$" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ -1 + \\sqrt{5}, \\quad - \\sqrt{5} - 1\\right ]$$" ], "text/plain": [ "⎡ ___ ___ ⎤\n", "⎣-1 + ╲╱ 5 , - ╲╱ 5 - 1⎦" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(Eq(x**2+2*x, 4))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.3 Résoudre un système d'équations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Résoudre le système $x+y=34$, $xy=34$" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ \\left \\{ x : - \\sqrt{255} + 17, \\quad y : \\sqrt{255} + 17\\right \\}, \\quad \\left \\{ x : \\sqrt{255} + 17, \\quad y : - \\sqrt{255} + 17\\right \\}\\right ]$$" ], "text/plain": [ "⎡⎧ _____ _____ ⎫ ⎧ _____ _____ ⎫⎤\n", "⎢⎨x: - ╲╱ 255 + 17, y: ╲╱ 255 + 17⎬, ⎨x: ╲╱ 255 + 17, y: - ╲╱ 255 + 17⎬⎥\n", "⎣⎩ ⎭ ⎩ ⎭⎦" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1 = Eq(x+y, 34)\n", "eq2 = Eq(x*y, 34)\n", "systeme = [eq1, eq2]\n", "solve(systeme)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Résoudre le système $x+y=34$, $xy^2=34$" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ \\left \\{ x : \\frac{17^{\\frac{2}{3}}}{\\left(1 - \\sqrt{3} i\\right) \\sqrt[3]{2285 + 3 \\sqrt{13791} i}} \\left(\\frac{136}{3} + \\frac{1}{102} \\left(1 - \\sqrt{3} i\\right) \\left(136 + \\left(1 - \\sqrt{3} i\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right), \\quad y : \\frac{17^{\\frac{2}{3}}}{\\left(1 - \\sqrt{3} i\\right) \\sqrt[3]{2285 + 3 \\sqrt{13791} i}} \\left(- \\frac{136}{3} + \\frac{1}{102} \\left(1 - \\sqrt{3} i\\right) \\left(68 + \\left(-1 + \\sqrt{3} i\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right)\\right \\}, \\quad \\left \\{ x : \\frac{17^{\\frac{2}{3}}}{\\left(1 + \\sqrt{3} i\\right) \\sqrt[3]{2285 + 3 \\sqrt{13791} i}} \\left(\\frac{136}{3} + \\frac{1}{102} \\left(1 + \\sqrt{3} i\\right) \\left(136 + \\left(1 + \\sqrt{3} i\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right), \\quad y : \\frac{17^{\\frac{2}{3}}}{\\left(1 + \\sqrt{3} i\\right) \\sqrt[3]{2285 + 3 \\sqrt{13791} i}} \\left(- \\frac{136}{3} + \\frac{1}{102} \\left(1 + \\sqrt{3} i\\right) \\left(68 + \\left(-1 - \\sqrt{3} i\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right) \\sqrt[3]{38845 + 51 \\sqrt{13791} i}\\right)\\right \\}, \\quad \\left \\{ x : \\frac{68}{3} - \\frac{\\sqrt[3]{17}}{3} \\sqrt[3]{2285 + 3 \\sqrt{13791} i} - \\frac{68 \\cdot 17^{\\frac{2}{3}}}{3 \\sqrt[3]{2285 + 3 \\sqrt{13791} i}}, \\quad y : \\frac{34}{3} + \\frac{68 \\cdot 17^{\\frac{2}{3}}}{3 \\sqrt[3]{2285 + 3 \\sqrt{13791} i}} + \\frac{\\sqrt[3]{17}}{3} \\sqrt[3]{2285 + 3 \\sqrt{13791} i}\\right \\}\\right ]$$" ], "text/plain": [ "⎡⎧ ⎛ ⎛ ______________________\n", "⎢⎪ ⎜ ⎛ ___ ⎞ ⎜ ⎛ ___ ⎞ 3 ╱ _______ \n", "⎢⎪ 2/3 ⎜136 ⎝1 - ╲╱ 3 ⋅ⅈ⎠⋅⎝136 + ⎝1 - ╲╱ 3 ⋅ⅈ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅\n", "⎢⎪ 17 ⋅⎜─── + ────────────────────────────────────────────────────────────\n", "⎢⎨ ⎝ 3 102 \n", "⎢⎪x: ─────────────────────────────────────────────────────────────────────────\n", "⎢⎪ ______________________ \n", "⎢⎪ ⎛ ___ ⎞ 3 ╱ _______ \n", "⎣⎩ ⎝1 - ╲╱ 3 ⋅ⅈ⎠⋅╲╱ 2285 + 3⋅╲╱ 13791 ⋅ⅈ \n", "\n", "__⎞ ________________________⎞ ⎛ ⎛ \n", " ⎟ 3 ╱ _______ ⎟ ⎜ ⎛ ___ ⎞ ⎜ ⎛ \n", "ⅈ ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎟ 2/3 ⎜ 136 ⎝1 - ╲╱ 3 ⋅ⅈ⎠⋅⎝68 + ⎝-1 + \n", "───────────────────────────────⎟ 17 ⋅⎜- ─── + ──────────────────────────\n", " ⎠ ⎝ 3 \n", "────────────────────────────────, y: ─────────────────────────────────────────\n", " \n", " ⎛ \n", " ⎝1 - ╲╱\n", "\n", " ________________________⎞ ________________________⎞⎫ ⎧ \n", " ___ ⎞ 3 ╱ _______ ⎟ 3 ╱ _______ ⎟⎪ ⎪ \n", "╲╱ 3 ⋅ⅈ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎟⎪ ⎪ 2/3\n", "─────────────────────────────────────────────────────────────────⎟⎪ ⎪ 17 \n", " 102 ⎠⎬ ⎨ \n", "──────────────────────────────────────────────────────────────────⎪, ⎪x: ─────\n", " ______________________ ⎪ ⎪ \n", "___ ⎞ 3 ╱ _______ ⎪ ⎪ \n", " 3 ⋅ⅈ⎠⋅╲╱ 2285 + 3⋅╲╱ 13791 ⋅ⅈ ⎭ ⎩ \n", "\n", " ⎛ ⎛ ________________________⎞ ___\n", " ⎜ ⎛ ___ ⎞ ⎜ ⎛ ___ ⎞ 3 ╱ _______ ⎟ 3 ╱ \n", " ⎜136 ⎝1 + ╲╱ 3 ⋅ⅈ⎠⋅⎝136 + ⎝1 + ╲╱ 3 ⋅ⅈ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎠⋅╲╱ 38\n", "⋅⎜─── + ──────────────────────────────────────────────────────────────────────\n", " ⎝ 3 102 \n", "──────────────────────────────────────────────────────────────────────────────\n", " ______________________ \n", " ⎛ ___ ⎞ 3 ╱ _______ \n", " ⎝1 + ╲╱ 3 ⋅ⅈ⎠⋅╲╱ 2285 + 3⋅╲╱ 13791 ⋅ⅈ \n", "\n", "_____________________⎞ ⎛ ⎛ \n", " _______ ⎟ ⎜ ⎛ ___ ⎞ ⎜ ⎛ ___ ⎞ 3\n", "845 + 51⋅╲╱ 13791 ⋅ⅈ ⎟ 2/3 ⎜ 136 ⎝1 + ╲╱ 3 ⋅ⅈ⎠⋅⎝68 + ⎝-1 - ╲╱ 3 ⋅ⅈ⎠⋅╲\n", "─────────────────────⎟ 17 ⋅⎜- ─── + ────────────────────────────────────\n", " ⎠ ⎝ 3 \n", "──────────────────────, y: ───────────────────────────────────────────────────\n", " \n", " ⎛ ___ ⎞ 3 ╱\n", " ⎝1 + ╲╱ 3 ⋅ⅈ⎠⋅╲╱ \n", "\n", " ________________________⎞ ________________________⎞⎫ \n", " ╱ _______ ⎟ 3 ╱ _______ ⎟⎪ \n", "╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎠⋅╲╱ 38845 + 51⋅╲╱ 13791 ⋅ⅈ ⎟⎪ ⎧ \n", "───────────────────────────────────────────────────────⎟⎪ ⎪ 3 ____ 3 ╱\n", " 102 ⎠⎬ ⎪ 68 ╲╱ 17 ⋅╲╱ \n", "────────────────────────────────────────────────────────⎪, ⎨x: ── - ──────────\n", "______________________ ⎪ ⎪ 3 \n", " _______ ⎪ ⎪ \n", " 2285 + 3⋅╲╱ 13791 ⋅ⅈ ⎭ ⎩ \n", "\n", " \n", " \n", "______________________ \n", " _______ 2/3 2\n", " 2285 + 3⋅╲╱ 13791 ⋅ⅈ 68⋅17 34 68⋅17 \n", "────────────────────── - ───────────────────────────, y: ── + ────────────────\n", " 3 ______________________ 3 ___________\n", " 3 ╱ _______ 3 ╱ \n", " 3⋅╲╱ 2285 + 3⋅╲╱ 13791 ⋅ⅈ 3⋅╲╱ 2285 + 3⋅╲\n", "\n", " ⎤\n", " ⎥\n", " ______________________⎫⎥\n", "/3 3 ____ 3 ╱ _______ ⎪⎥\n", " ╲╱ 17 ⋅╲╱ 2285 + 3⋅╲╱ 13791 ⋅ⅈ ⎪⎥\n", "─────────── + ────────────────────────────────⎬⎥\n", "___________ 3 ⎪⎥\n", " _______ ⎪⎥\n", "╱ 13791 ⋅ⅈ ⎭⎦" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1 = Eq(x+y, 34)\n", "eq2 = Eq(x*y**2, 34)\n", "systeme = [eq1, eq2]\n", "solve(systeme)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.4 Syntaxe abrégée" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Résoudre les systèmes ci-haut avec la syntaxe abrégée" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left [ \\left \\{ x : - \\sqrt{255} + 17, \\quad y : \\sqrt{255} + 17\\right \\}, \\quad \\left \\{ x : \\sqrt{255} + 17, \\quad y : - \\sqrt{255} + 17\\right \\}\\right ]$$" ], "text/plain": [ "⎡⎧ _____ _____ ⎫ ⎧ _____ _____ ⎫⎤\n", "⎢⎨x: - ╲╱ 255 + 17, y: ╲╱ 255 + 17⎬, ⎨x: ╲╱ 255 + 17, y: - ╲╱ 255 + 17⎬⎥\n", "⎣⎩ ⎭ ⎩ ⎭⎦" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([x+y-34, x*y-34])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.5 Trouver les racines d'une fonction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$3x^2 + 52x - 265$$" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ - \\frac{26}{3} + \\frac{\\sqrt{1471}}{3} : 1, \\quad - \\frac{\\sqrt{1471}}{3} - \\frac{26}{3} : 1\\right \\}$$" ], "text/plain": [ "⎧ ______ ______ ⎫\n", "⎪ 26 ╲╱ 1471 ╲╱ 1471 26 ⎪\n", "⎨- ── + ────────: 1, - ──────── - ──: 1⎬\n", "⎪ 3 3 3 3 ⎪\n", "⎩ ⎭" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roots(3*x**2+52*x-265)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$3x^3 + 52x - 265$$" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "r1,r2,r3 = roots(3*x**3+52*x-265)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left ( 3.20205243239924, \\quad -1.60102621619962 - 5.00231827937895 i, \\quad -1.60102621619962 + 5.00231827937895 i\\right )$$" ], "text/plain": [ "(3.20205243239924, -1.60102621619962 - -5.00231827937895⋅(-1)⋅ⅈ, -1.6010262161\n", "9962 + 5.00231827937895⋅ⅈ)" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r1.n(), r2.n(), r3.n()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6 Tracer une fonction" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.1 Tracer une fonction R -> R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$f(x) = x^2$$" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAETCAYAAAAWHuyQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = x**2\n", "plot(x**2, (x,-20,20))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "$$g(x) = {3x^2 + 52x - 265 \\over (x - 7)(x - 1)(x + 34)}$$" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD7CAYAAABKfn7LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wey0ofnqlqOfwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = (3*x**2+52*x-265) / ((x-7)*(x-1)*(x+34))\n", "plot(g, (x,-40,10), xlim=(-40, 10), ylim=(-2,2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Approximer les racines de $$x^3 + 2x^2 - 1$$ avec un dessin" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAD7CAYAAACc26SuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmJK4iIiPKYmLiPjY/wcjlf9EO+JP0wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(x**3+2*x**2-1, (x,-2,1), ylim=(-1,1))" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\left \\{ -1 : 1, \\quad - \\frac{1}{2} + \\frac{\\sqrt{5}}{2} : 1, \\quad - \\frac{\\sqrt{5}}{2} - \\frac{1}{2} : 1\\right \\}$$" ], "text/plain": [ "⎧ ___ ___ ⎫\n", "⎪ 1 ╲╱ 5 ╲╱ 5 1 ⎪\n", "⎨-1: 1, - ─ + ─────: 1, - ───── - ─: 1⎬\n", "⎪ 2 2 2 2 ⎪\n", "⎩ ⎭" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roots(x**3+2*x**2-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.2 Tracer plusieurs fonctions R -> R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer $f(x)$ en vert et $g(x)$ en jaune dans le même dessin" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD7CAYAAABKfn7LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f, g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.3 Tracer une fonction R^2 -> R" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy.plotting import plot3d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$x^2+y^2$$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXl4JHd57/up6n3vVrf2fR9ts9rGCwnGLAZDnJBwgJMT\nwmELgctNcsPNwsNNcnJOEoeTQ4CAHchygJsANmG3weAVA2Njj2eVNNJo33f1vlZ3VZ0/St0tydKM\nZqzRaDz1eZ55Rip1Vf2quupbb72/dxFUVUVHR0dHZ28Qr/UAdHR0dG4kdNHV0dHR2UN00dXR0dHZ\nQ3TR1dHR0dlDdNHV0dHR2UN00dXR0dHZQ4yX+LseT6ajo6Nz+Qjb/UG3dHV0dHT2EF10dXR0dPYQ\nXXR1dHR09hBddHV0dHT2EF10dXR0dPYQXXR1dHR09hBddHV0dHT2EF10dXR0dPYQXXR1dHR09hBd\ndHV0dHT2EF10dXR0dPYQXXR1dHR09hBddHVeNoqikMvl0Pvt6ehcmktVGdPR2RJVVVFVlWw2iyRJ\n5HI5BEErrGQwGDCZTBgMBkRRRBTFwt90dG50dNHVuSzWi20ikUAURYxGI4IgIIoimUyGXC6HLMsb\n1hNFEYPBUPini7HOjYpwiVdC/X1RB9gotoqiAJBMJlEUBVmWUVW1IKCCIGAymQrCunkb69HFWOcV\nyrYXsC66OhdFVdWCz1ZRFARBQFEUMpkM6XQag8GAzWYjl8uRiMcxWywFAVYUpfBzXkzzwrpeVNd/\nLo8uxjrXObro6lwe24ltOp1GkiTMZjOgiaPJZOL88eOc//rXecvf/R2CIBT+nt/O5n+qqhaEdP2/\nvKjmrWJdjHWuU7a9IHWfrs4GVFVFluVCNMJ6y1aSJCwWCx6PB1EUSaVShc+MP/IIc1/5Cv1veANd\nb3xjYXuCIBQEcvN+1otw3m2xlRgLgrBBjPOTd5vF2Gg0FoTYYDBsWE9HZ7+gW7o6wPZim0qlyGaz\nWCwWrFbrBh9tXnRNJhP/eOQI6sgIhqYmfuPHP8ZfXn7F49hNy3izVayLsc4eobsXdLbmUmJrtVqx\nWCwbxDZPXnRHnn2Wp9761sJVVvHe9/K2z35218f5csRYkqQNortejNf7mXUx1tkldPeCzkYuJra5\nXA6r1YrD4bikCKmqysjDD2+4wma/8hWe/aVf4va3v33Xxvty3RT5Y8yvv1XUBaCLsc5VRxfdGwxV\nVQtxtNuJrdPp3JHICIKAJEnMnDiBQjG9US4pIfhXf0X8rrtwlpRc1ePZqRjnrd28xbudzzgvxpvJ\n78NoNG65no7OTtFF9wYhL7a5XA7QxEqWZdLpNLIsX5bYrmfixz+m89Qp+js74fx5AOyVlXh7eznz\nZ3/Gq++/f9ePZSdsFmNVVQuiKctyQYzz0RlQjIzYLMh5AZdlGUmSNuxHF2Ody0UX3Vc4m8UWQJZl\nUqkUiqJcsdjmCT3yCCJQMT3NnM+HEAphCoUAyP3bvzH4+tdz4G1v241D2RUEQcBo3HjZ5/2+eSGW\nZbngplgfY7xTMc6vo4uxzlboE2mvUPJim0wmUVUVi8VCLpcjnU6jKAo2mw2z2fyyRGBlYYFfHDyI\nPRoF4EJbG4lolO6FBcxrn0nX1HDsySfxVVbuwlFdOflEDpPJtON1Novx+n+XEuOtsu90Mb6h0CfS\nbhQ2W7abLTGr1fqyxTbP6He+UxBcgNahIU52dGBeWCgss8zM8POPfYy3fvWr152w5MVwc+TGblvG\nsixjMpm2LBJ0vZ0znUuji+4rhPzNvN6NkMvlyGQyADgcDkwm067exJFHHiHrdmNbE14VaIhGSZSU\n4AgGAYhVVnLbI48w/s//TNPv/M6u7ftasttinE6nEUWx4Ftev5+tsu+2Ct/TuX7QRfc6Jz8ZtH7G\nPZvNkk6nAQqv0/m03N1iZXiYjmee4UxrK2o0igDE6+t57eQkJ1pakINBDIC5rAzz/DyW//E/WL39\ndvzd3bs6jv3ElYpx/u1kvbDm2fwgze9ns4siH3+ss//RRfc6ZTuxTaVSiKKIzWbDZDIhSRLZbHbX\n9x/+xjfw5nLcPDDA8+3tuC5cwOJ2IwKvGhnh511dOPr7sSwuAuCKRFj6vd/D+cMfYrFad308+5lL\niXEymSxEk1zKMs6zWYzzccnrxXir4kI61x59Iu06Y30CQB5JkgqvqDabrVDfFiCTyZDNZnE6nbs2\nBlVVOX/sGOVrIWLjJSXMyDKVqkrLmqthwWrlRG0tbxke3tCeZOT//ghH//pvd20sO+VKJtL2ing8\nviERJS/G60PbdlqxbXM69GYx1osE7Rn6RNr1zFa1bKEotgaDoeCz3Uz+xttN+h95mMCa4AI0BoOM\nHThA8+BgYVlFOk25zUJWFLGsjTktinieeJClO19N2RveuqtjeiVxMct4p0WCNovq5uxDoPA5XYz3\nFl109zHbiW2+lq3RaMTpdL4k7vRqU/KzHzB7sIv6c/2FZc1OganOA9Sf14Q3Iwi0SrPMHOmi+WQv\nAKutzdySGWblvo8Rae/CU9e4p+O+3tmNim3bifF69PKZVxdddPchm2vZ5lkvti6Xa8diu5uWbiIU\nwv3E9zFIOUIlJfiCQcJuF03BYVImO2GPB28kwkpbC7dIw4QzIYabm6kaHUX1WmEZAsF5xv/y98l9\n8dt7/sDYb+zGd3M1xDiXyxU+nw9p08V4d9BjT/YReT9evkZA3tJNp9NEIhFkWcbtdl+W4O72DRF5\n+Bv44yHqpBjRhgAKEG9ppJIcTdkooZZyFEDxaNESXgEcthiLHg+B4HhhO40nf8L4Z/77ro7tYuz3\nTsVXQ7jyYmwymbBYLNhsNhwOBw6HA4vFgsFgKLxJpVIpEokEqVSq0Ocuf84URSm4OvIJNolEglgs\nRiQSIRqNkkgkSKfTZLPZQl0Pna25sc2MfcJWFb/yYpvJZDCZTLjd7pdYMpez/d3C+INvFH6+dWmI\n410HsCjFBInbV4d4tLud7nUC25lc4pEDHRxZGtgwvZB74RGWfvYqyn7pLbs2vouhW2Qal2MZ56Nj\n8lExl7KM16Nbxluji+41JG9lZLPZDVlLebE1m80vS2xhd4Vm4dwJpOVitpkogtUYp1pJblhW7lMx\nJ10QKi6vDqj0urs4OKr5gWfdATpTI0j/9AdE6w/grmvetXHqXBlbiXE2myWXy2E2m6/YTbFVl48b\nWYx10b0GrLdsJUkik8ngdDpJJpOF/mP5ljj7CfWJryHbUyRMFhxZLdPNXOVjwWCnvD+IYe2eEZwy\nyy47vrABqyqzanVSkRpBFA3MllZTvTxLuLqa6vQKxBeZ+vSHkP7mYcw22zU8umvD5nq++431IWfb\nWcb50LbNFdsuVpdiu5ZLN4IY76+7+hVOPvMoHzubR5ZlIpEIgiDg8XhwOBy7Jri7FTKWikVx/vxb\nHMjOMdJ+AICEaMSeneBodoj+ti4AZl1+WqRRDsrjDLR3ArBc10ilKUe5IUOkRCVmtpKWgoVt1028\nwOwDf/qyx6izt+QtY7PZjNVqxW6343A4sNvtmM3mQmqzJEkkEokNft/1CSB5gd3sX17vM04mk68Y\nn7Fu6e4B2/lsk8lkQXz3o2W7ntDjD9GYWAKgKXqWieomMlYL7YYBAErlUeZLKgiWlVEtrwLQnOll\ntLqZlCEBa1FJncocj9a187rshQ2PfHnieeZ++EWq7vnQnh6XzsW5XEv8ahQJyheg36oz9PXYjFQX\n3avIVl0a1out1WrFarUSj8evmuDulqUr/eRbhZ9dBpi1plk1iLSvLas0pDldaiUnLcHaW6jbCAOW\nLDVrIpynttbCQKqLQ4uafzdksFMmDeP58Z+zVNVO6eE7X/Z4dfYXV1OM0+l0wbI+e/YsIyMjvP/9\n779GR3pp9q9pdR2Tf01Kp9MbSizG43Gi0SgGgwGv14vNZtv3T2WAxXPHySTHSAnFZ7TbnIXSjUV0\nHE6gamN7Hnulj7nKGuQ13ZdUULLzVFmHmfTUatsva6TaksWppnB9/cNE58a5UbgefLpXk7ywGo3G\nl7gp8vVD8nUpMpnMlm6K9X7n2dlZVldXL73ja4guurvIZrHN9x+Lx+PEYjGMRuNLxPZqpOmuZ1e2\nf/zLHDROcaGms7BotbyKw5bzDHmKWWUpr4M263lG3fUA5BSQ5TmO2S5wplxbd8rbSI9tmVKzRMYj\nETa5SItF/3ZpapbgV/6AdCL28sass2tci4fC5YgxaCFt99xzD1/84hd5+umn+fd//3dOnz79kvZK\nWzEzM8Ndd91FV1cXPT09/MM//AMAoVCIN77xjbS3t3P33XcTiUQK69x33320trbS0dHBY489dlnH\npovuLrCV2MqyTDweJx6PYzKZtrVsr7borh/jlRBdmsPT+x0A6pQ+Jj21JDFglidxmEB1RIkYHYQM\ndvzqKB4zZN1JIgYHEyWNHLQvI4rQYLvAhLuOhNNO/hS0WRY56y+nQhrdOFZpidVvffQl9WV1dNaL\nce9Pf4rFYgHAbrfzmc98hsOHD+N2u3n44Yd597vfTX9//yW2CEajkb//+7+nv7+f5557jvvvv5/B\nwUH+9m//lte//vVcuHCBu+66i/vuuw+A8+fP841vfIOBgQEeffRRPvKRj1zW/aWL7ssgH7O43o0g\nyzKxWIxEIoHJZMLj8WC1Wi9pLVwt4X25Vkroqf+NR4kDUGJWiLpUBktbabeHAWi3rDJc1sB8WRM1\nVq2G7wHbMkMV9cRddvIuPL9ZJuKSUHMLG7ZfWm1lquxA4fewYsGjjNK++B1mvvfn1/1M9fXOfnV/\nvPjgg4ROnCj8LooibW1t2O123ve+9/HQQw/R19fHkSNHLrmtiooKDh8+DIDT6aSjo4OZmRm+973v\n8Z73vAeA97znPXz3u98F4Pvf/z7vete7MBqNNDQ00NraygsvvLDjseuiewXkxTafLglaEHg8HieR\nSGCxWHYstvvxgs6TlSSW+79HjGL92x7TDNOujZfNIWM/I+rG17gWyxirxo0ZStZACdmqUnJrBqyq\nQoo4PYF+zrs04V3wNlHvSiMI0Dr8Oaaf/teCHy+forrel3e9s19FbT9z9vvf59Qf/iHtv/ZrLzl/\nsVgMr9d7xduemJjgzJkz3HrrrSwuLlJeXg5owry0pEXvzM7OUltbW1inurqa2dnZHe9DF93LIB9z\nuFlsY7EYqVSqILYWi+Wyw2z2m183l8sx9cyXucPWy5C3pbB8ylTNrVXnmbAUfblTllp66mdZEv2F\nZYueFjorp5g1VhWWpU0yN5cOcs7do61nqKDbPYHNAj7fJNPWWtLG4jjNoorY92US08cLfrz82PKx\nnPn4TUmSCsH5rwQx3i/st4fCwOOP8+Lv/i6uQ4eo7eh4yfii0Sgej+eKth2Px3n729/OZz/72S07\nZO/WedBFdwesF9u843692NpsNtxu92WLbZ698uvuhPxxxWIxbANfBeCApY9Rh5amG/EFKHdA2p4m\nrmr+tITbR6MnwazTh6QIqCrEhTiVzjRhl4GEamYJLzWWIQCafb2MWJuJucuxrJUArnSkWHQp2Jjf\nMJ6sMUfJ6Q8Rmj6F0WjcceGWZDJZsIp1F8Urg+HHH+enH/0ohnichl/91S0/E4lE8Pl8l73tXC7H\n29/+dt797nfzq2vbLi8vZ3Gt88nCwgJlZWWAZtlOT08X1p2ZmaG6unrH+9JFdxvysYP58JS82Gaz\n2ZeI7W51171a7ETU14utyWQiPPoCddHnAXBYQLbFmcaHxzAMwAHXPEOeNkKKDa9JW3bEP8J5Vxfj\nQgUHvRMAdHmnOe9qZclVh9+hjcFjBdyrhLIbQ3scZSWkqwIkZU2JV3NOKm0jlBiD2J/7r0QWx15y\nXFtV0cpnRK0PNVIUhXQ6vcFFoYvxpdkvlu7kT37Cs5/4BOb5ebJeL22/9mvAS8cXjUavyL3wvve9\nj87OTn7/93+/sOzee+/ly1/+MgBf+cpXCmJ877338uCDDyJJEuPj44yMjHDLLbfseF+66G4iL7Z5\nyza61n4mm80SjUbJZDK7LrbX0tLdLLZerxer1Upm8F8ZVcoLn2uzL9LnrqbOVSxi02Hr5WdiPXXu\nVGFZves8A6IX87q0m0PefkYzxc8AqA4f3hqRhFyM9U0JcQ5Vj9Jvb0FWYMnWQLlLc+OUiVPEn/oA\n8cjiJY9pq1AjURQxm82FUKP1JQqvpYtiv4jafmbypz9l5j3vQTSbkV0uXK95Df6KCuCl5y+bzV52\nS6bjx4/z1a9+laeeeoojR45w9OhRfvSjH/Enf/InPP7447S3t/Pkk0/yp3+qpap3dnbyjne8g87O\nTu655x4eeOCBy/oO9Yy0NbYrHA6ac14URRwOx4b+Y7vFtfDpyrJMKpUqZMat92GtTJ2jNfdDZisa\nSM4vYjdBRobyimVGhDZaVM1NYDaBJZAiKHspMWjRDCajAWtpjIjsxGPQoh4mhXpu6ZpiZrWGGsMM\nAEmLg0PVfZyY6OBYboBZuZT2Ui0p4ljDAKdGezCI6Q1jVlQJ6eRvk3rVQ9gcl2fNrA81Ws9OC33f\nqE0er/VD4fwPf0jowx8mHYkQNRopDQQ4/La3bfnZ/DV+ueO94447NjR4Xc8TTzyx5fKPf/zjfPzj\nH7+s/eS54S3drQqHg9Z/LG/l5i3bvJV0PZOPH75YZly2/wvYjTla7SMMrk16TZoPcLR2EdEWJKy4\nABgTmnlDzyTjxnLktefUtLGV13XNMmSoIf/sSlrdVPoyxB0ykZyDSNaK16K5Co7VDXCGbiK2Khxr\nRcZEEfyl00jW4uWpqpBRw9SbnyP+wnvJpIsW98vhYoW+1xdtWZ8NdaO4KK71cc0//hiz//OTWEMh\nJhobKXG7KZckGt5a7K+31UNhv9+jN6zobie2+S4N+Q66W5W02232wtLdidgCzE0N4px9qPB7q3eE\nwVw5cYv2mt/kX2HEVIeqQsJqQRThSPUF+tQubZlBs06P1Q/SSzfhrA2vTUt+OFA5z7CplmlDM/UB\nTTRFERoq+phJJTaMI2Gtp6VthBFJi5yYSpfTVTmljcH0JMvHP0h2B9lGV4ogCDvKhsq7KPK+/1di\nFMW1ELHZRx4m/f7/imlsHMlkwiKKtI2O4vqVX8FsLrqk1ovu9XK+bzjRXV9ecSuxzeVyuFyuQkuc\nvfC3Xs19yLKMLMskEglEUcTj8Vy05oM68yUmDQ2F312mFDGvm0bPSGHZ0Yp+nk50UOvTKoyJIlQF\nhvl5tIWeyrHisrJBnk8XBRbgpoZBRtIbX+VWaaD76DyzaW0GWFUhowTxu2VsFQvMZGuJmytYd69h\nygyw0v+75DZ1K7iabJWamreKrVbrtlEU68V48/d8rV/f9yPT//EQjg99gLnySiyJBAvNjTROTCAZ\nDJRs41oA7R62Wq3b/n2/cMOI7na1bFOp1EX7j+2ncK7LIR95EY1GEQShMKt/sWpmsdA8vsj/T3PZ\nJGPxQGG52Wdhwnaw8Lsogr3KgGIufqbUJSH5LeQES2FZwJlD9WcIZ1yFZTPxMm67bZALibbCsrTZ\nRU1ZgqQnRzDjZTxRzaEGLSSn2h8n40uymgptGGtSsNLm+SZLfR/Z1h+3V1yqF9lWdWXzLoq8e2I/\nXmPX4oHQ+0+fxfT//iGOVIqo0YTc3ETAbMWQy7Fwx+3U33rrtmOMRCJXHKO7l7ziRfdSYqsoCm63\nu+BK2G4bV5PdFPa82K4vip6vM3opYkNfwGcJ4bXFyflLkHIwnymjrrKftqpBzsdrAIhLZsorp5gX\n3GSy2nbDaRstbZOcTzeTP5TxWA2vv22YUaWS7Jouho2VlAfAUTXPXKqSWNqM261NoLXWLTJr9rGQ\n87F+vks1OyjrkFhNaZNn8YwJl2sCgHbPQ8yf+fBL+nPtB7Yr8r3eRZG/PteL8SvRRXEpVFVl9oFP\nIvzHV/HHYgybLZDJcPPQBRLRCPGuTm5+85tfch2vF92Xkxixl7xiRfdSYquq6iXFFvbGn7Uboqso\nCslkslAJyePxFCzbnWw/EVshOvmdwu+tJUP0qd2sWKrwuVQcFglXtchq0sCMeIDG6igHm0fpS2rV\nw2bVFuor4xzpOk9vVEvpjZk18TzWNURvooeUJGKwahZsTVmMiAv6Y9p6hf02TBA05JByxbGlDV4O\ntC4wb3UTSTuZy7TQWFVcxy4/w9zIh66qj3e32OyiMBqNmEymgovCaDRe0kWxV4WA9srSVRSFmb/5\nI9r+5a8xpwUSFgsr7S28fmKUk+XlqA4HR6YncL/9P110jOFw+GWlAO8VrzjRzV+w68U2Xzg8L7b5\nljg7mSDb7+6F9WK7/tgutyh6ZPzzuCpkYmvuV0EAn2uJpKGYIVbrmWLK2knWXExqaKk/z0i8sbDM\naIRAzQTnV2vweovVw1pbe3l6oYOOpmKbno7GeVYskMkWxzoVbuGtbx3kdLAbVYVkxoDJMQlAd8cU\nU8YyQtmN7oSYUkZ34zdZnX4/0qZ44Dz79TvMi8ZO26VLkkQymXzFRFFkkgnO/ekH6fjWPzFhdGKb\nnmW5u5bqVBpFhRWfl7sGzpO8+824y8svui3d0t1jtiocnhfbvF/zSgRpv06kbRZbt9u97bFdavvx\n6CJu6V9oKhtlRC36buOWSgJNbhLrwmVtrgyKszhZ4XGpLIgG6muKtUarStMs2VyU+IoWmcsBthqZ\n+XDxxpkNlvLLrzvP2eWOgksiuVYo/ebb+ji11M1Mspn2puK2q+uWiLllEinNdyzLIBu0ymWt1d8j\nNPMeotGN/t/rmc1ivJMC33kxfrkuiqtt6caW5kj8t9+g8sJpBAEuuGqQmkswpiOUj4xy8lAHx1ZW\nkEWQf+XeS45R9+nuEVvVslVVdcMk0vpX7ctlv4muoigv8Ufv1Grfjsj45/A7VwBoq7nAQKiScMqB\np2yM5qphhtKaEKsqpCwyVc1RpoPFyTFbmYGRWC35+SxZBldNlIFQYyFWdz4U4OAtg6yaTURTdgCC\nuSpcLjh2Wz9n5roJxp2UV2hREqIIHUf7GFzdmMwwH2vktrvHOS/Vk0iZmVitp6ermKVmN77IQuQ9\nxBPLLznOV0qUwMUKfOddFMAlXRTX0jIODvUi/MW9JMYuUDs7yorTh9uU5nB8grStkuGj3fhMOfyr\nq5y6/VXUvvVXttzOZtHV3QtXkUuJrcFgeFlim2e/uBdUVX1JpMWl/NGb19+KaHiG+aWnCuLosGWw\nltkYTjVRV6V1b2hrHOT8cg3jkQZ6ekYpLVkm7qoll4OpYDmtHRc4etMg5xa0jsAjyw30HJrl8G0D\nnJvXlq3kqvB44EDXDBeidSRSIqJdK4cnitDY08fzkw1Ulhf972nJSfltCwzMtBeWJdH8H52vGqE/\n3chqxsX6rzeYqqGp83ki8jsJR2+ctj9w6SiKy3VRXC1Ld+b491HueyeVK0Mo1mqCvnJOl3m5OTRB\nUoaRTJpXR/oQUwYGj3XT9ubXbnmdb76mdffCVSIvtuFwmFQqtaElzubA/91o9nitLd282IbD4SsS\n2/z2tyO+9CluPXyKM3NFYfM75lk0Fv2mDpuEq0pkLm0tRBUcaDrPmVAXQUpxuTThrG0dZGK1nrho\nRRTXYnU7BxmYbcDgmSls78itgzw53E5nx0phmdsNucocEwsNhWWz0SaaOyQM7UuMLrQwsxygtr3o\nJ246PMqcohKPW9bOFYRVzRVRXt1PxvRORseP7/g8XQv2YrJqOxeF3W6/qIsibxHvllWsqiqz3/0U\n0Qf/jIbYDDkFlqNppECKKrsbgwpPVLbzruQQw0YnyyaBQ5ELmN76ny95fKCJ7pVUGNtrrjvRzbcy\nz9dJuFj/sd3gWomuqqqk02nC4XAhYeNyxXbz9jYTXBkkYPsyBgPUNqwwvaq5DCYTbdzxumH6puuK\nYxRzSBXFGFxBgLLKeYJiuLDM75dZUsBTWRTYkhKZZasVf9nG/btazPSOdhV+H5up4eBrF1nxyCys\nVqCqEEFzJpeUZcnUheidq8LlLl6yc3MtHL13mdOrbUTjdibnq2g7Mlf4uyTFyfj/gOmlrfPnb2R2\n0oMsHz+8Gy6KZCzK/L/8Du3H/xKX6EQQ4GlzPe32aQJqBPvcPKfau2hzmTT/rreau8MDrN7+Rnz1\njVtuczdr6e4l153oiqJYEF5Jki7af2w32OseZuvFNpvNbsiOu1K2Oy8XBv8XLoc2219askrUWEco\nbsdaOY7dnsVeq7IS0vY7nw3QfesQJ0aKrXVCcgP+DjsLK8WJNYM3wHS8iXyUnqpCzmHiQrCaZFKr\n/rSw5CfQvoBav8rYrFanNySVYTSKVDYlmRCdnB5soOlIUbz9FWnCbpiZKT4IohnNN1x/0yJnw41M\nrgQwmYqXdCRcTVl1FKHyD5hY+rcrPn83EuvFOP/v5dYuDk2fZ+iBd9M+/BBBSSCwNMWZ8i7KKlxU\nGVOcFhpYrSilXBqjYmqUXzR10ZOLkTaZidy5tS8XXiq6uk/3KpHP6lkfdC4IAqdPn75q+9wrS3d9\n3YfdENv1bD6G+cWf0X7Ttzk11lpY1tHcz08nmqlr1Ar9VFdNM5XrZH61jEDnCCYzBDqjTC54iSct\nSL5FyusWGUt2oigQjVnJ+ZdovnWB00Naz6mp2WpqDs3TcGSJ06NaGNhitB5PiYqvTGHVmWN4opKc\nr9g7rbYzxJhcQSbtKCybHquj+84YiyYbs3O1RCI2zIHiOtU9S0xJZoLLJYXjjWY0n7TVnsV34FM8\n/uInkLKZXTmfu8V+mC/YjvVju5zaxetdFNPPfg3Xd++hPKHFZ4/IzUyU1VJl7acyPENSMJOyWLhJ\n7SdobWK4rhmjmKAitMgvOg/TcO87dzzeK62lu9dcd6Kbb/a4uWZmbW0tvefO7fr+rra/LW81yLJc\nKLKzm2ILLz0GVVVJ5f4KhzOHtzHF3LJW3iscc+PtTjIxXfSLtXac4+eT5XhLtBvQ6w+xaq1jeP4A\nta1agkLToRGevXCIyeUDVDZqoubtmuXCeDvLyQqsa9XC6m+b5rkzPSStRZdERWOKvkg13kDxeFNJ\nA7a6FAMyh98uAAAgAElEQVRjzSQSWsGFaLIEURTx10nMi3ZOnWunoraYQTE/Xkvn3TFGI2UszFYw\nPV5J06FiPPHiZDlNdz1JX/SjhKI772e1F+znqIpLjW07F4UoqEx//xO0vPhh5iMKdckxoqqNoFHg\nFncfs0IbFiXHc94ablamUBQYTMgcpQ9j1k5fWxt1r3vdRd1pmy3deDyOy+Xa9vP7hetOdPMZVptf\n+wOBALIsE1xdvcjal8/Vci+oqkomkylYtoIg7LrYbseJM/9MZa02wRQoX2I2p02ijYZbaTkUJqQ2\nF9wDwVAZ3oMq01PuwvpVjaOcXS5WnxEEgdKOBXrniyLodAssizIxQzFzTBRFsiV2BFNpYZmqqigu\nK0OT9aQSa+6H6Uaq2iUqD0fou3CA1WUrqqc46Raol1jCzcJUsf9aPOVGFEVKW9LM5JyMjmvuijyJ\npA9RFHE3nGPS/CH6x596WedQZ3tCM2dZ/M491Mx9E7OoIot1hMylnLIGeLVdS3SJxA1MV3gpsVpx\nyyl+YGnl7eZBhjI2VsnRrkxged1vXnQ/m0VXVdWrXhFwN7juRDfPVmJ4+MgRjj/zzFXfz8thvdhm\nMhkcDseWTfB2k/XHkEiGcdV/mTNnipNYzZ3nefxUB9bGtRTd9jFODx0FYCrYSO2BGMuJViRJiyub\nHO+k/e4U5/uKExyrS7UEjvpZnCtOtmWpImnyk4gVBTqSsxK2yyzNakkS85PllPZEKT8Uo+98G1JG\nIJwsvsVUHQ3x3IsH8FcWoylWZt1UvSrGosHC/EQtybgB2VEUZU9ljmWriZE+rSyklIH0ugk/SVlh\nzvdpTs7+6zUvlrOfudzICkVRmH3uc/ievwc5nqTcFEZRYGpVIhdI4vd4cRkkzqTL8NmX6bTOYI2l\neLGim0a/FVWAcWcdr2eIxa43YPIEdpx1t5/dNJu57kQ3fxFsJ4avvvNOHlzra7Rb+9uNKlD5+Mho\nNEo6ncbhcOByuTYUPtkLZkKfo6RyBn9jkqlp7VXMaIKkw4WU1QRTEATK2xc5fqIFU4PmN606MMW5\n3mNkJVjKKljtMoLfwty0HVVVWUqa8FRHmA93IkkKmbRIzJCivDvJ4GAzuZzK/EQAT0cUX7XKbMJJ\neNVJKFKKxaJdhhU3R/n5T9tx1m9MbDCUOxnsbSUrad99PFSB3WXAU62yZDNy6hctVDYXxTM4VUHT\nHSA1y5w90cH8RDX13UVfbmihDl+thNL+EM+u/gkr4WvnbriexOJiRFZGeO6rv0Hbwidwm+LYZCNZ\nGR6NtPPq+kGqHTGsiTgjlhZS3lIOuVd4IVxGyGal3jRIYHmKE6UddAgxFhwVLB/7lW1rF+ejKPKl\nMpPJZKEexX521eS57kQXijOsWxX+8JVovr8ffOtbu7avl8N6sV3fzHJ9F4q9atczOvUCklWbxfcE\nIoQSrSiKwtRkPRU3B1kOtxbOqcOdZiFbiWHtFV0QBPztSzz5RCc1B7UEBW9llPnoAUYG6ig/rBUh\nL+tc5NzZg8xNNFLVqfkoKm+OcOFcJ6FYZcG/G2iTOD9STUyMbBirpaKMuZHmwvlYmfbgao/jvSnF\nhXOtpJMQVaOFz3vKVSJWL7ODxaiGeEKbgDPbRBw3S/Re8JOKFV87RVvx4WJpPMtjc39O/8Lju3Gq\nr4j9KhQ7sXQVRWHu7P04z99FrXUFUYSpoA1zcpFztjYaqqx4bHButZSoYMXnH6VMiZJUTESsJdzu\nHWAy18qUvwaLkMYhS4xU1dP95ndsW7t4fRSFoijcf//91NbWMjY2xoc+9CE+//nP09vbu6NjfP/7\n3095eTkHDxbT3//yL/+Smpoajh49WuiXlue+++6jtbWVjo4OHnvssSs6r9el6MLFheodv/3bPPr9\n7xNcWdny77u5r+3YTmwv1szyagqvoiismu5ncbGlsKy2Y5RTZ3qYiXixOUQqu6bpW3M7LExX4L85\nzvR4Z+HzZkuWiNFDcLEoYJWd85zsL92QiBLoCXK6f+NEp1oZZ2Z14+Vm9gRIZOrIBxRkUhAzJLAe\nlRh+sR6AaDCA1aH5uT03pXju6SbK2orVxGJLVhwdaSLVCiNnGknGDEjuYu2FdFzE3C1yfrKR8IKX\nuQkDtsridTF1xkn5zWHmG/+Rnyz8LZH47lwzNwKri6fpf/RdtGU+jkEJ481pbwx9q7UoFQJN/iH8\nmWkyssC0HOBQzQBT8Rr8cpBT5lqO2BaQFIG5VI5bHP3EkzbCfiPlr/mNbe+R9VEU+f//6I/+iOPH\nj9Pa2kpPTw99fX08//zzOzqG9773vfz4xz9+yfI//MM/5NSpU5w6dYo3velNAAwMDPCNb3yDgYEB\nHn30UT7ykY9c0T37ihRdgE8+8AC/91u/tStCdjmieyViuxcZSaPLD+GuP0WgbYHhfq2TqigKSAYr\n+KTC57xNMSZGvUwvluL0iJR0LHD+lFZHd26kkeY3SiwvFi3i5Qk/Za8TGDtbLGQTmvYTeI2b2eHi\nTHIyWI+hw0R4Sit8rigqKykJz00ZRs/Woygq4akqSjvBaBQxdGcZfL6WuHljGx9zpZ+Rs7VIa0V4\n4itlOP1GbC4jarfM80/VUFI0eknMllLSZMTTDWOSj+mhOqyu4huS2VyOKAoYjCJq64t8d+KvOD33\n2Cvmtf/lsJ2lm0pGWBj4BCWRN1Jh7EMQYHixCb85yKlUD031OZpLV5gMt2ITJU4KLRyrWMFohFDS\nzYzXj8tmxa3G+LHUzlu8w5yJurEbQ/jsMu7bL56BttX4RFGkqqqKj370o3zhC1/gAx/4wI628epX\nv3rLLLatvv/vfe97vOtd78JoNNLQ0EBraysvvPDCjvaznutSdDfPWG6Fw+Hg3ne+k7943/t2ZX+X\nugnzoV+xWIxkMonVar2sNu1X08WwGplmPvtNBEHA5shhcLoJh0QSMQsJj4lEuq4wSebwpphfqcXS\nor32myzgqDEyM25jWdIul5KeJYZOaRbzcrAEZ4kRQ7WZ+TEtSSIYcWIPyKStFQTnDUhpWBUyOMsN\nLORMxJedrIyWUnJIi3Zw3pRm7GQ94WQxcsNsM5K0e0EuRjokgwZy5UmctwiM99WTSUIwVSzlaDSK\nGOpKGT1VRyahjTWRLlrl7joD6YpSxk/VI6UFpLSC6i5GVywNCzgOhphs/Ro/XL6PueDY7n0J23A9\ntetRFIWZ8S+zfO5uWt2fY3QyQINXS2AJRuwMGhqweuZptGk1L5bCZhY9Luw2qLIsMxwvw+tYpLtk\nCiWWpd/VQpPPTMzgJeGq5Sb7PBMNb8Xu2llW2dUsdnP//fdz+PBhPvCBDxRqVM/OzlJbW1v4THV1\nNbOzlz8fcF2KLrBl2Nhm3vHe9xJLpXj8X//1Ze/vYvvJi20ikcBiseDxeLBYLPviZlJVlcH0Z8Du\nIJXSjqGkfomZyS7Gx9opac7ia19mtFcLG8tlIWaysDDcVNiGsyzO1FQj3g7NvBQEAdeBBGd+Uo6x\nVbNEbYEMKbWGqT4X5nbN52urjbMUamVhsJKSTu1SczcJzCz5WFgwF1wSoigiBUSiqY39rRI5C5Fa\nkeV+zYpOLpThqdbcFvabFF58sgJPa9Fqjc+bEBqymG82MjZczfyAFWGtaA/AYr+AvT0DR0VGhuq4\ncLwEV21RtNVkBWaHiCgKyM3DPLz0jzy1+HViyY1+5xuF9aK2NP8kq1NvRAr9NQeqzgNgEQIoKhyf\nbqe5dYLDbWPIUjVmo8rxuRba68doq5zHppgYzbWwYPBztGyF4zMlZKwyVdZxjOFFhs1OmrKLPG/r\nJvCm372i8e1mWcePfOQjjI6OcubMGSoqKvjYxz62K9vNc12K7uVMQH36wQf5u099iokzV56xtt1+\nstks0Wh0V8T2alm652YexNp0mkDbKtODxb5kBmeSmVTxPLpbI0wOepgZrMN/VMXdHWOyzw9AJiWQ\nCViZPVcUYoszR0QpJZso+m6dzVFGxkqxOIqXlasjzLkLxTAyAKPfQERwkV1Xb1yK+8n2WFg5r7kf\n4rM2xBYJm8dEqEZgqb+MYGpjZwhHfRWzk5VkwtoYpKAfm0/72XbYyNRcFUKyaP2IShnGtUgJ20GR\noFDFYm8ZirJ23u1FAQ9OypjbUsy3PMf3hL/h6eHvkc3tv5ZAV5ul1RP89Nn/QrX712msfgGDWoHB\nALE4JKNhzqVbcJYaaCyPI0lgTCxzMtmNPWClPpBibMHBclyhpGqMSqNEMOdBdpRza+UYZ1eakEuM\nmAwuFmwV+NqaCNR1XNE4d1N0S0tLC/fwBz/4wYILobq6munp6cLnZmZmqK6uvuztX5eim2enQvUX\nDzzAx971LtKx2CU/u91+1pPL5QqWrdls3hXL9mqI7nxwmPOrPyqMy90aZnrIR1aC+UQAR62H8Fp0\nltUtk1QCzK/1PDPZwBBwEpw3EByvx90lYu5KMd2rpdlGZlyIxwwEV2oLron4ghXLbRamThT9u9ER\nD6W/7mX6RLGJZWrZh+vVNhb6ypFzCpmYQNiVweIyE6o0EB7ykwyVYHFp8b02j4lF1YZgKgqoFIOY\nJ4W5x8j0vJ/kgo2gtM5qVVVyPiuzNher5/zkcgqKsyiaseUs1m4z0W4XwyerGfmpCXN90X+shEsx\ne9YiN8pSDDtO8LXEfTw///QNEds7Pvkz5qMfxl71G1T7Z7CYVdJp8BgWSEsizwx0UN25xNHDI9hV\n7Xz8pLcGucTE0YN9uNUomazA+Ugdt3YPMhMsxarEGMZBm32BpWwJPnucA65ZhpdV2px9iIfee1lj\n3Nwf7UrdC5tDQhcWiunl3/72t+nu7gbg3nvv5cEHH0SSJMbHxxkZGeGWW2657P3dEKJ7x5130vNL\nv8yfv+G1V3TDrG8gGIvFiMfjhXTkfO2H/UZGSnNW/izu7iBzA9qEltWZJWf0M3KmAfehHLbqBMF1\nlcQk2YcsFn1Wtoo4ywt1LJk036vJBkKZk+C0kdWVADaPCXtPhrmz2kRbbNGPo9SCqUdgrlezOsIx\nO0aTAUOXyPxZN5moSMipuSmMNxuYO1lOYroUV4NmDVt9ZubNRuZWNlqVquwh2GgheE6b9JBmS3DW\na+tYOkwMDriw+ooTd+kJC5aDJixlFkKdDk5/x4GpvGgpZ2ZLMJdpoYeGm+2sZGqJDfmRc9oDRLUW\nb43QeAalIolcE6Wv9RH+afB/8uzCT8hI61pqXCH7yaerqiqTC08wsPIBYvx3atueQM7lKLFqfsvz\nAw1Iqp3eTB2NLUYqK1JcGPVR7Rymd6mTslo33W2TnBuuxmsK0ZttpqsmhtEIE0sBJH8Ws8kLBjOn\noiXc4p3hyZVm7qkaZMR6jPLuuy57vC9XdH/zN3+T22+/naGhIerq6vjSl77EH//xH3Pw4EEOHz7M\nM888w6c//WkAOjs7ecc73kFnZyf33HMPDzzwwJW91V5CtPblFG6+ylgsFsNisWA2my+9EvCfujq5\n+2A77//aty/rZMVisUJdUZvNdlX8tdFotBAMvhv88NynMN+spbrGxj24/VM43SKxRSfnTpfQ/ibN\nqpOzKok+CyWVKaYEN2avEeUCVB3Uepkt9dYQlYyUHyumV6+csJFryOAu1XywubRK4hcZxA4T9nLt\nu8itGMhcCCMedmJeC/nKBUViJ5L47i76brOSzPwjWep+vbgsPehiyStQk0hhbU4ghWExZsdea0NK\n5XAPpEmjYDtanHiLnXMTL5OpCGdwHIgR7/OR6y5evsleF7IQp8ofw1yZITRUjtCmxarlcgrJGTvG\nBgFOJzEkVnEds2K0acIbPePAcrj4EIhecGBqV2HGRO3CAW4ru5OAN3BF10Q8HsfhcFxT4Y0lQszG\nf8Rq9GGaDp8mGgKnrBAoi3HhRDW3N19gabWE585Xceudg0RCdsoSWXzuFE//rAunR6GyfgRHxIzP\nmeAHP+2itXmFeNLGEfsEZ5eb8RmWqfdHeerFAzRWLZOOVpDNgZBTMeRirHR8mCN3f3THY843LMif\nu09+8pPccccdvPnNb76KZ+qy2PYLva4t3e0SJLbjS8+/wMM/+wW/+NRf7OjzsiwTj8cLtRG8Xu9V\ns2x3071wbu4JQpXnCM1q43Q1RlgarieXU5mYKqH0l0SW+rUiNwaTgLlGYKDXhb3cjNEiIlRaCE0b\nSC1bWS6RUdth9XxRFDNGF9J00ZdltApkzAGyseJnjAGZcKqUbDE4AMGRI2TxEZ0sHmdu0oH6phoS\n57SEBlVVWU0qWCpszNhtpEcdyPNe7LXaeM02IxGPg3jCVvDFSmGI+HKYK2ws1thZes5O0Fh0FSSW\nM2TKc9DtZFz1MPW4kVxlsvD3+Dkw1K/9csROSKklPhQgG14LR3IUv+/wQBaxfq3GRE2WUcsIX3Z+\nka8v/hsnxl/YUObwWrfEuRiqqjI0+yzPTfwFF4zvYMHwAFVtfYiiQGSmikCZ5opTYmZeHD1Gb8bJ\noVvnsTtF4vMNeF0p+iZacVeFuOm2AVbmW/E6Ejw33MbBg5O0NS1iVZycDXWRNpio90d5Zqiahuo5\nZDXHalxGME6TTUbIlrjpfu3vXNFxrLd0r4daunCdiu6VZnI5nU5+8xN/zqc+84/8/P6/2fZzebHN\nd6LI953aL6+BF2M2OMyg79+w12RIB6sLDyVPR4QzPyrHebOIyQGi20VsWftbasWFUF1Dbq3vuak0\nSyJRw8KED3u1BaMTch4vsQWF5LiTTKcBpUsheEYTysyygXijmbS5jPiito3MnJHkESfxUC3pmGYl\nSuNOrHf6SKnVxOc1N08sbsFkN7PcYCU14CAzZkY8qNXJtVTamLFamZnZ9BqfcpK8o4zQiy7kjII6\n78RWq61jcprJlJSRi5ciJ9aujRkXxjLNKrZU2UmXNREe9JILad+n3eotfLeKoiBWOwgfcjMe8jP1\nYxGltCjQllwJBqsWhpaTcmTdOQwlAgut0zwlP84/p7/AY6EfMbI4smXx72vZtVdVVfrHfsGp5S/y\ndOS99CX+Dm/3YzgDCQyxAHan9t25bSrJpJEXftFO2p8kcPMcxmwp/oAmxJlwhmenDrFkVDnSoxWN\nV5IZTix0YfQbqC2PMzhuZTaUo+dwP36jxFC0FbfXQ1NplN6ZCo40DDIVqqGmIY29/T9j2uHb6vpj\n2VzA/Hoo6whw9UtaXUWuxDp854c/zFPf/Sb/8bn78VRV0PO2YhyvLMukUimy2Wwh7VAQBNLp9FWf\nPNkNSzeSCPLD2S9ia0xhQsTeGWb6ZAn1N4fJBO2kK/0kViM4/EYstSmSZ6uxmJdYtJixNEqET5cS\nOLqWzWVTWVlyE0B7BTdUZ4mfqyKdzWFq1C4bud5KeCSFEndjPWwFVJL91Zg9sySXS7AesiH7IXyy\ngtLDy6wmDYiA3ACJoRpywTlSLSZMgNltYTGnor6Qw95ctAXMKQdLPT48o0kMzRlyMZkVZw6LaCV5\niw/5pEhOzmChaGUnUyDdVEK6z0B5aQLsxegJRVGQ7EZyh/zExsz4h0IIjRmMa/ZH7JyM0KNZI+ZG\nJ3LCx/RcjOrZDKamKFmbQt4BlOwF89HijW+0m5DqJQYZ4NTJM7gcARqytdRK1bS7WzGbzYWOC/lU\ndtCuu/XV83aTcCzI8NIJJPcIq8Zz5JCpaprDDqjRksL+nHbtlWRs0EAuKLCgNqFaHHQc0kTVbZVQ\nFJWfPdNCoD5KU+cCSy82IAjwzHMVOEoyHDo2ytSJFsJxF9PROt7wmn7ODFQh5CwY3VM0CCrPTB/g\ntqYlelcC9FQtkciIuLt++7KPa6v+aLro7gH5/miXyxd//CS/1lrPyQf+DsFkoOPNv1WwRPI1Qden\ntV7rPmk7QcpKPBa9H/tNQZJnynH4lxENAvZ6I0sjIqspN55jIpmzFTj8WqqruSNG/6NufL+6Voug\nXSF43oynNcNyxIZwk5Von4K7W7NUZbOReMqJd02IRR/Ep71EzRJetNd/tQsWnvGQOSAUZFA+Ymby\ncTvmNxSLksttAgs/dGNrKp5ng2xipr6UphEVWjSrKx03YmxxMrVqoOYCiKqI5YC9sE6mxEk84iSw\nmkH0C8gLCvF6M2ZA7vZw4WcpypwKljVRTZyTyPZoEis2uVheNWKbkvEYkoh+FbvJR8ZQtHolGwjN\nJcwBie9L1DWaySWTGO0GbFY3iqA9jOPjKUxVYESzgh02N6m6DAOMcLL3NGbBSkWqjGq5AkfIQbOn\nkQpveaGOct4VIYqiNrlnMBR+3qkQy7LM1MowIWGOhcgImcA0ac88JosVT9MyNiArad91IiJjXysc\nP9VnpqZ0laHeThZWBHpeq02cxQe0iceZEStOIcqzZ4/gqjDT2DnH0qyRcs8oJ4cOYSyBg4fOMtBb\nhkdIMY6d5soIigLj827edNsAF4Z6GEoqON0KMclExhQAYYoh53/hdueVieX12DUCrlPR3Y1CMQ88\nfZz/57ZDCP90H4l0jJ573ofH49mymeVeVgG7ElRV5aG+z5NsHsaJEfOBOCvn7AQOJrGUprnwfAD/\nWzT7zNiRZuWsncChJJlJDxzzkpiK4agzYHAIKB4Py8/H4dV2DIBS6iY+vYg1ILIkW1B7bMT7sji7\ntYddNudAoBQ5FykUx8k5fChTAuQjxwRIeUpQTgvYj2nnUVlViB2pQBxQMBxMIBpFxAUb1h4fk4tx\n6kcSyM4skVojJsDotzEtqIjHV3CuE101biFz2MvCcIiqVBIxbMbcXfy721vNTIuZ8heWsHVLWE1+\nZEPxOza5nUTaLQSnIlSOR5BKsxjRXnXTZ9Ooh+yFGRFvcwNzXSYYDFESjqN4ktjRRMwedaKuVbpM\nhzNQYkBcE2CP4CZbpbJCiKm+aQzdTp4WXsS4IOCYM1BVXoVbcWGKinjsXsyKGSENFoMFZBWDYEAV\nFVQR0rk0BrtKRkyxHF1CcKZJWWKsJBaRWcF5QCYdzmJ3qFgrZDKzWRwVmntkqV+grkV74CbGvFQf\nmWZlysvSjJusx4m3R6JsRJOEuSEjLXXTxMI2xoaqaHzVEv7aIJaQ9v2NnakgXGrC1zZHaUR78IyN\nl3L4VRNkpkup9EzzeP8B7rx5GlmBkZkMv/qaIZ75eQv+phz2kShBbyXdv/wHV3zNrxfdTCaD1Wq9\nyBr7h+tSdPNcqRgqioLH5+O1H/y/ePx/fx7fD/4Zv8dOyxu2Txner5auqqo8PPYl0q8aQTrjh9II\nRquA4rcQW44hL5VhfJOd0Isy/lsyiGYBY4WF5YEkEZMdY40BZdBHTgpiNBtR7TkWEm58iqI9gMoV\n5IEy0isZhCMuBCBb7iU5tYzFYGa50YbJa0U8mcV1UxplSWWl1obRaUHoDWLrMcCEQPKon0xWQOhd\nxtYjIMxZMfY4iVeoqCcUbB0JlixmDICp3MkUAo7Tq5jeVBRQa8jEzGvasJ1cRTwKalRhyWPGBMit\nPiYmwLYcw4K2Ti4tkXa7MNgsrNxSi/EXs9isEoY1B0FqKIZSU4IAGOo8LK0akcMKZdkMQgvYTV6S\naw9hKZZG8qy5KQ74CJ2xknAJVJ6VsDqTqLbidLUwbkQ4UvT7Kk4Q1241F24yZu2TqWAM4SYrY4Yp\nsikJg8mAWKutZ7mgkmvXrF/TORWhW5vMVU7L2FrX3gJO5nCvZeSlTsv4jyiAgDJpxXpYcxeYVl3Y\nqrVgbKfqwWSJkoqIBBeNnDndgrE5h69DxVsrstAn0tY6DwjkVtzMZDxE7VmqDih4/TB1ys/RwwNc\n6OvAVZuh4eAcEycqqW3q58nnDnH0jmlKy1LM9jroE5ooKzNjNWd46uwB3v76QX54vIabusKcHfDS\nUq8gl9yF21csRH+51/3mN4DrYc4FbrCJNEVRSCQSRCIRBEHgd/6//4ajvoUnTs8y8q3/xQvfvO+i\n+7uaXIno5nI5vnHuSwzbnkcQBMydaYLnNGEwV2cIXwiw4DdpcbKtJqIj2vYNZVnmh9wIa7GxartC\nuk/rDBEdcyK+IUD6VDF0Ta5UmZovPp/lUoFctozgpBGzz44gCCR6HMRPiUjzNkzlDgSHkVRVCcnh\nLKmICaPZiOAwkKgJEDuZZsFRLBmZuMnN8s9UhJbi7LPBaWG21I9pqOhLl+NGTG4HM4eqyJ4Aw6QB\nU12xo4Uj62D+llaUkwqyJKOeV8jV24onzOpjtqIK4ayCkpVxpp0IjuJxGm1ukocqGa2tJvhzlViu\nOIFnGFFQa4q+YZPNhrHGw/KhUsZSbqaiFnL9duRpBbO1+KDI9WYQ6jUhVXIyGXuxu4bX4ERcs7rV\nQbkguKnJBJkKzaWjyiqKO1u4Bi3O4i1rtxcnn+zm4nHYLMV6E1ardv4ycZWVuQTj5xo4O1SC+1VG\nXEcgMWzGU6cJtBs3IDDdX0tQFTH3SEgRK2WNmmhnInDi5EGWFYWGA5qvNxnKcXqmE2eJidKyMH29\nAQwlqzQdHMaQDNMfaaSlUuH8fA1V5VbkXAy/R0aVVjDXfYjdYD+/hW7FdSm6sLPaC3kURSGZTBYK\nV3g8noLf9ovPvMB8XKR/MkbwZ1/j/Lf/+CV+4r1yL+x0H/kY5YdHvs7i0XMYUz4URcFgETEFLMQX\nZaSgkZUSF8qiJgAGnwCUkEnIpAfdqG+pJnNGu1EFQSDXLrD4hEq4y44gimTa7SQHtfMgTdnJ3VWN\ndK4ogDkRYqKvcK5Ei4GE08FssnjuFL+RdMLJ8rqQK9lnJCP7kdV1L1mySrSqDOVEcfv2KQHhWB3j\n/hKMAzLqSpaFtRhg0Wj8P+y9aZBk13mm99wlb+bNfc/K2veqruoV3Q2CAEhxl8hRkKK1UEvE0BqO\nrLBi5JDtmTHtscOUPZb4Q9KELJl2yDIlxciWxJDEfQiQAhewARCN7q7qrqVr37Mq9329eRf/uNWV\nDQ5JgCRACRP6/nTXufeek3c57/nOe77zfqSvDbK31YFmD8Q6dQvJo5K6OkJ7yYEl9MAPwHJ7EPr8\nHGZJOE4AACAASURBVFwaoX5XpK73rtX2a5SSdneQnA7anjB7wyPoizJCxsCpenvt7Neo9vXuyW95\n0K8Nsj+f5L4eZq8sYC27sLYt3A73GWBqy22s00VIXdPRfL3NGh5nj+/2VFSkgA2c2r0W0qhdXl9v\nYA7Yu+7qhy2sU9qgmW4jJW3grKU0pL6KvdHhuRb1Kuwt9LNwI4j6Lj/CRYGgI4wzdJrzzmXHnDdq\nBumjJiubY2Q0hYnH7QEn5HKhayJ3nx1EGu6SuF4nKHmRHRYvfnUQ10SLgQt5gs4qm5szNDoDXLqe\n5blnRrBCIMoNmp02RUMk5DphITVO3JtnS/wAofgEP6j9o6f792SvtJD2MNhalkUgELCT5n0bb/t/\nPb/M6maVk0qbwsJT3PjkL9Fq9EROflQLaa9kD4eyfSn9adatBSRZRDrXob5gA4zc36VzFCKdCuOc\n80K/i+bhqXTjpE5lwcuR14Uoy+gzCq21U6AzBYquGEbJ/lvwSZi+EM0FnZMxD4JLpjMQpLPTwTRM\nyhWZ+qMRrNs94DIbLrpj42j7vRArzXQjiANoObvManbJBvw0Xf3o+zaAuHZNtMuDFK4lMW52MQ2T\nXMeuV4x42OmPUL/ZQu7rebXunQ6Fn3qU5paMVNQR0x1yoz3gyoXcHApeXHun4WprJUpDPU+1LrrZ\nTQ4j39Wx2jqeqgqB3nHR7UMK+zi6PMh61kWxaCKl7Lr8VRUxYA8Apq7T9PbeXbjqRHvzMHvn+9iM\n9LFed1C954H7Kt2ciF6w34W13EEYtoG1nWvRifU2X0gPOecBVy+VU0DzIrvta1xFN46Q/R070iqC\n06S566C8pFJPJVlfiCCo02jXAnDFycBQDFE89ZZVu61qpguuPOmlfpa+Hif64wrB8xA+3fxTTpvU\na1VW18dQgkH6JkyqBQuX44SF2+fxRMMMTmhs3faTL3toRiqMDBxzcjxI34CD2YsHHO+FGL+QR694\n0SNxArJByZ3k3Jv+G34Yexh0NU171Ruk/iHYGxp0RVH8jmD47WDr9/u/I9g+sEg8znv/1W9y81sZ\nUkUd63CBzb95HzvrLwB//9ELD2iRarVKV+/y+cxfcjS/giOu0szoCIKAPA61XQujY1I2VFrGac+N\ngVgNYpomRtOk6ApiVk49XJ8Eqo92oUN7Q0V/MolUDGCeeoBazOTkQEFUT0PEIjKIEfSbXWoXowii\nSG0+TPduG+lIJzUeot3nQtdjaLkW0oFOeiZCZcKLkA2g1Tq49kQ6MwkaA27aQhztqEH5VBJDkETy\nV5M0n67Suth3dv+S4iA1MIDrdv3sGRkNO+SqcHGIbNGDud5GDvW8UX/DTfPyCOuBOI7FDp6WG0F9\naAquBiEZYuvSJKVNJ7VKz+vU98oUB3rnRk0fJ4/PsOkdQFsQqRZaWA8G+6U62uhDHvVDbfj2OgiP\nj5K9mGRtIExhfoI9YYDUokK94MJc8cB9hc4tHbEh0d3vUng2Q93fQG/rtEstOt46nVqHZrpFOV+i\nuydibDup53RaqyHKSyFOCjIbmTDZsQEc4wnq510ol304AvY9tUodxIidbaN0X0cdqdA4UkjfDpIW\norQvKAxM+BAEgUqmizueoZZR2b6dQDov4Z/r4PbYOeZ2X/STJ4xzrEwklqJWVimVggw/nqNz3Ee9\nEWZp383s9Daf//IMTz6+zfqGzOBIncO9NolhHXf4zQQjPTH9H9ZeS7GbH4W9YUH3O2nqWpZFq9Wi\nUqlgmuYZ2L6aDKE/86u/QWDuKl9/LkW2JdHINqm99N+SWvuLvzfQfZD/6QEt0hU1/qr178lIOTvO\ns99AzNgfmxSyENt+cnf8dB4NYw66aB/YoV3GnEXjlkxt1Yt2LYoVDtI5sb1MfUSkcVchPWdrGtTm\nVKy79vNyrDtovH8OabE3m2hGBdL5h1TD3DKdgTD55SZywAaf+oQX68RPI2UieWzwL82HYE3m2Hgo\noH3YS/vYTSnR81AFSaQV60N+qd3b2LHfRbs0ytaVSZSXmkipJqmBhwTS+4NsOiJ4V+1daHqrQzlg\nr2SLIS8bE/2kcwZK1p4yd1MVcn29le6WLrN15TzCbQ0l3SZQc4H3oQSbp9ypGPCQdjjZffMlivdE\nXKsWjm4v7ZK+VqQ61ANdRe25rN7tJnq/G0fER2soSP3SALvn+9k6N4wxMcXu6ChHI1NY6hT7Zj/r\nRz4OvimzVg+yWevn4DBK8S1z7I+Os9H1UH88SWYuQEYVcDzmwzMepLXewBiygbZzr408djpb2FNw\n9ZloNYvmroPU/SRHgSj+ySDecSe1ww6ufjs+u7asUEgl2bciJKYUXB6Z3IKCO1pj4/YYkTEPsekO\nrf0Q3Y6PxdUoc9fzWJbF3paFOVhjMKDy0tpVhhIqpbqLdncIvy+Nqnqot2pYgR+ey/12WUe/3/8K\nV/zDsTcs6EKP1zVNk1arRblcxjAM/H4/Xq/3+07H/PG//Rp108XGUp5qxyB/XKK89G+58fn/nGYj\n/yMj7B8MHuVy+Wzw2K5v8yf7f0x5tEB3Wqd1mgLKmu1QXxQxTYtqzUHDYauAWVERqeHH1O1A/Lbp\nIOu2gUbrl5DyfhvUSia5oX6U+73EfrVZH63nGuwF7c0h5fkQLNsgreyIlH/yAo47Pc9QqphUJ2Yx\nTnp7fjsehbLhfxn9Y3l80PS+rKwt+UFLYGTsa9W9OscXhjm8Po58q4Op65QaNuUhiiL7j05Rv9NE\ncvcALXLQpv34OVbGR3G9VMO5VKMx3PN8QtsNMu+5xr4WxLvUIJiX0EO9632KH9Hj4uDqJFtWlFK2\ng1Q6XURbzlIa7nmyIdyITge1y6OsxCJsqFHMRQv3uoanKp150939MqW+Hm/tcvXaCxx1MeL23/pu\nkfIpl2yaJmZIRk0G8UwmiE0N4JnrQ+0PElf9iLL9PUe6TkS3XXeo5UQ61bYIdl3Iqn1OSHYhigLd\nukEjo5FfirOZDiPNReCKipYykIfsKYa77EEQobiSxAiFMC+JaDkB/2gRy7KonsjsZhM0lS6xiSy6\nbpHa7VL1m0TcHhxOnW98YYQ3/3SWSk4iUxMIDKegm2enESfhP+bm9iRBb5my9OMkBi7ww9rrKWD+\netsbFnQf9gyr1eoPBbYP2ydv7rOTarG1WaFlCjTyGn18g/LWT7F4+49eN+B9MHg8SM+u67qdLVhx\n8Km1v+Kz0b9FHzNoHWhIThEx5qKV7iIpIlLcQerLAoVrcdozKtqaDZDarEB3UYIdmZOZfhxqiM4p\nmDTnFYzbFvUdJ92pKLXxINaWDXyWKlLp+DFP40wt1UEzEca4VWErYW+ZzZzvQ7zXxOoaFKsylakI\ncsWDXmvbHnoRso9Pot46rbPd5cSUSV0fw/2SPdV179VJnesnOx6BRgQjU8cqCYguJ4Iocnh9HP1r\nFXLnelSD2OiQOjeDtW3gLNptVeo2Rym6XGxen6NWEHEVHpJ5dNtesT4YY3luitxJB1fG5pj1TIVc\nvAeInmyL3bdfI1X341tq4mnKCE4bSPV6i3Kwxx1GUx30C8PsXx5naWKC3Y4L666Jb01HWW9g+U/F\nfw7LlPseig1We3WEyyCcSljK94q0x+3f0j2oUD+9baPRphWwvVbTNDHcvf/jtu/d1A0sTwfLsqhv\ntCllmxTuBllbcKE/Ead+wY2z5kAesQe8cFdFVkXaRYvcYYedfIwTLPzz9uwojBOt7Gbp7yJE3yIT\nmBKICC7aVQ+3nkow//4ODjfQLbO2NcrwuJNaReJoM8HFtx6xeSuGZ1qhm3XRTSRw6gKW38fE3L/6\nnv3g1drD/fAf6YUfkXU6HcrlMpZl4Xa7f2iwfWCKy8U/+52/4GA5TzGr0ZEUVrZCyC2ZhOP3WFr9\nJ+zsPvsa3EHPHshGGoZBp9M5S8++eLzIJ6p/yE50B72jQxSUmtvubH0Wci6A0TaopjwYA3ZkvuCT\nkJwBOqU2giCg+UR2j0XkkEprzIln3+7ggijStlwUvPa0zAgqCI4g3UIT9b5B5m2zKC0vesMG6U5U\noZJzYimn3ptLpjwUx/x6kcIVu+3cbBRlzcS9ViNzZQRBFDm6PIzzVpXgTofa+dOyq6OoN8uYJQHh\n1GPNjEewjhT2HgIkQRDQon14t8As2yAZOWjRmhzg+MIEpYIDz40Dshd7cpSO+8fsv+06mZpKaKuC\ntJ4jPdSbevqWjtl99+PsmRGCdyuEDjp0Yj0u2KP4EESR7lCCe6ND7Fh+AvcaKJkm/o0qrcFeXZa7\nR1F47x7TeHKO/UsTLM1OUUhOUljUUZZ0lKUmzpKBWW3bnm1/7zs1HxJ8Dyl25AhAqCRC6FS6cq2J\nOWS3JSyWMMdOQ9Du1dBCXawdi/JXGrSrXnYXXFQrUZrvGKF2KUhfIIzkO03sqdqpo3RNp9koU7kX\nZntRxfUeP+q4ShgXslOketIhe9ziwPDjj/lRQybVky6lXIODRpihMS+yA9a/5sWIKgjeNqaQYXt/\nkvkrZe58q4/JC3WKhQrRsTqHuyVmzhXp8HZUdz/dbvc10aB4LbR0/z5M+tjHPva9jn/Pg3+fZhgG\niqKc/ftaAO4DG56Y5qX7G2zeuIkQ9DM5KZOvdzENF4qjA+7PsJ+/RbsZIxQYeuUKv4s9ANt6vY6u\n2wtifr+f+ydrfLbxORb0BZrhGnJCQt50QMLCilkYdyykfgFd0Tl6RqD5zmG0mIRypwX9MkZIxLkO\nomyR7oaRgxE0q4WkOuiEJZSlOkpLYrM/iYpKV6shehS0oAPXvSYH0SAEPTQjKuGVOnpSxrfWZutN\n54ltNujEJXumoRtUcjKWZILfBs96zEP7G/sYp0AoSCINl0JzIU13NmmXiSJm26SV66KN9pICunNd\ndHccq1kBvwvfYYW9/n7KwwnCBy2MToVW1aLZZ2e0aEcCyIdtQm2dRszmhaOZLsWBCN2gj6zTQ+j2\nIZ2xCJbjdApesCgngpg+N9m+OOL9DAHDoBV2QbpMPeDDOAX+6Eqa7PVzZBJxSg0Rz24B1bLohJxI\nG1nKQ2E4rTdS0qnFbfB2Lh1SnemnOxijkAgjo3IwOUopa+JeqeA03Kh5C+12CqdPxVEz6KaqtBs1\nsCz0SgfjuAoSiBUDjuq4UHAUBPTjNs6Ol9aJSD2jk4tGqA0nCXTdlC/4EJI+AjUdM2rPnJz1FkJY\noJVq4vC14MRF5kWd7iU/xpibcENB7tNplTqoQo1Oyk9+WyH+HhlRFVDbLSzL4uiWm9g7LLS6QSSQ\nJb0xQCAiEZ+usf+8m9CEB7EuUK8r6F0XoWCB3OEQ0XgeueHnIOclFP1f8fnCZ1ufNU07czYebIN+\ntfoTmqbhcNh8+osvvojP5+ORRx75gfvi62C/+d0OvGFB90EkgqZpSJL0moIuwFt+4oN88XN/QWP/\ngNCAm0RC57AkokoZBEWhazSx/F9k5fAbVMoafvcoDofzlSs+NV3XaTQaaJqGqqpIksSN7Rt8Tfgq\nt82b5H0l5GEH0pqM0GdhBHT0+wZyQkJQBZpLbUrdCNa5PoxCEzHoxFRlrJMGYshBF4vMHYPuowNo\nQQfe+23MpIwgiVgVk5MMmDN9dAIKoa0OWlyErkGr4ESpC2j9No9Zi7jwvHDMcTCCHvFTTXiJL2TR\n+l14VuocPjZPMKuhCR0EVSG2XmbniWsk7uzTGbBBKLJVY/fyJSIbKbqni2au3Tq7j8zTt7BHZ8CH\nK1fnQA1QGY7jLelIlRKekkFh2AbqasSPfzlPJerDPI1ScOeqHIZjHCeSjN/do0GHui9E13PqgdYa\nlJMTyKk6wUadTr1BORLGUO335F3aJXX1IifhOMmFA9SjEtX5wbN35KlYVKI2NSHlyuRmJjlODOJZ\nPMGbqmDEvJhuBTNTpu1VMTw2WPdlu1T7bY/YtXxAZTyKIEtYPhWX4OR4bpBcPIy/rbB7fox8OIbj\nWCdzbY5KIEH7UKd6cYR6NEm5JtIaTZLvT5BBQoh7KYyFqThFXBEXYtKHnqshegzwyHR3yziSBoIi\nYS5WcJ0TMY8sWksGdclDfTZGyHQgDYt0ci1UTxPRDcWvtunKfrQLPsKmjhzRqd02UCwHJ4aLRATU\nqE75RZGOHqCt6AxNpln+epTRSw2UUJ3jZQfRC3WMbJuaESQgF0iloqguC3f4J5ka/+mztOmKopyl\nUX84SYCmaWee8MNADC9fPH8QJiYIAs8++yyDg4PMzc19Hz38dbfvCrpvWHrhgb2ekQV/+IVliobK\n3ksnrG4oDERBDvvJ7LkI+9ZpV7s4xCxW/+/x1O7P8NTyv+Ze+tMcpDe+628yDINarUatVqNYK7LW\nXOYv1v+Mf9f8HW5NvciheYAwIeA+sYHBmLZoL2tILglnRKGdaWMeOyh2IzTGfehRGXddwdR1zJCM\n0/SiH7cpFf3oVyYwD23+tHLej3i7Ck2dajeAnBjAOKUOshfCqHfqeNe6nDwyQXY2iWvVFi0XFJkW\nfoSudPa8U/P9KF89ZGvIBsT0ZILgoQmVJinJjaU4OJifwHc3i1Rrs+fy0vF7OBkew72SwX9YYXN6\nFNOpsHthBv/NFL5UEz1pZ/5NjyQwygqH2ssjVDqyh5ZrAP/KCQCRdBMjEUNQVe5dewTXizmsh3QV\n+lJNKokwqfMzrAaHcd/J0nX2oguCggcUB6Iss/bIBdKeQSILeTyZGvLGMamhnheerJnoPjvs8Ghu\ngtS5C+waUdTFKv5baczTZo1ak3yoN/jGLOWME/bePaQwbtdp1pqUQz0qxan2qIo+S0Y8HRjixS7G\n6aJf/KBON2EPhuH9JkbSLg+ndKyYfX6sJiJ4ZNjXMDKQvauyEx1AnIwinA+j7Vfp9tt8t3oAVkUh\nc8eLZzKJdNlDe6mOY6SJlpYp50Wa8wpCRcA70aC07EXsE/E9YuDpCOwsT+ENuXFHWix+MczMu6rs\nPO8iNOGifgJq0ovVslATMDbw6/9RXxAE4QyEnU4nbrcbj8dzJuYvCAK6rn9HicwH3wS88eiFN6z2\nwsOj3w+iNPZq7fc+v83/8sF+XHs50skYYdGNf0BheXOC/miLyOgGJ0cjhFUJZfSb3F/dxTus89SS\nC7+rH4cShpaKK+Cjkq9jBSVqjQYVVxU8BpploTwioy9KSFcV1LxKV9MQZ0T0exbyRQXZr9IuNFFU\nhdINidZ7+xBlGe9CjfYVB41ZJ+47NbSrMp2QSPEFkcZP2qsw4dUOTV1HVGTagwG63yiQfa89Detf\nOKF8xWXzu6qLfP009MnrohOJIhyWCLZEFh+9QCRfRzgqYQ2GMBWZqiOEu9imfpohff/CIPHP3yb7\n/icAMNwu0qPDRL+5TPV9bwGgFfCQ10cIvbgE75sCwHQppAf6URcO4XLvuStdB5nYKIGVQxrzg0T3\ncmzOTyO6XDRVheHnl9mNhs/ON3Wd4swVmhmD0VKW4/EoDXePf9U9bjLT1xDXaiQCNbJeiVRfD1Qj\n93Y5ujpHSpKQcwWmN06wfG1qHhVT16l4exEMyZVDUo/MIggCG4koA+4wh4aLsbtpPEfHiOeSGM8u\nEnjqRYq/9qFeGw6V5umMLLGVp3jFFoIXd9JkB22P2mi0qAV7szbL/VAImlvmwfKgS5V5sJ3C4Rbp\n5tq4ShLFTIeG6aUZDxK5qmPGXCiL2TNltUhFQugXsdZFMjkD5VIMc72OZ0QDJLwNi/r9EEftNiNv\nsWeUbs0kfSdO2zAYe7TOwa0WfmcY13gVx1adnbVZJi8WOFgNMzDeInXQYnTWYGNRYP5ilszerzF1\n7dUtdD2gF749pt6yrLPsLQ9kVvP5PO985ztJJBLk83lKpRKXLl1icnLyFSmKj3zkI3zhC18gkUhw\n7949AEqlEh/60IfY399ndHSUT33qU2cLdL/927/NJz/5SWRZ5vd///d5z3ve86ru5zvZG97T/W4b\nJF4r8/r9vO9f/3vW1mrs3SlRbViUTrL0DTQ5aQe5e3MUn7OOGjiitBonMVyh02wRVGVc83tUmodo\nlxbYzt2hfW2NbGUP43IOuSWgDImodRcI4ByG9n4Lc8pAWJYRnSLOmETnpIWeMKm/APvlCI2fmMK5\nfLr9c1qF1aodEjbtxnyhRKboofTOWdRl21MtnAvgWWza07S9Lu2pcxg1+/rjuSjeuwWcpQ7HzgjG\n8AhCyg6Crya8OAsCO5oTUVEo9YdxN12YtSZ994tsPXGNdrAPx4GtWuXL1Vm7dI34zYOzZyfoJnvx\nGQJrqbMyV7XNzuijLyuLZdusventJG7sAaAWq6wF4hTicXLBSUKLRzhKHcRTFam234vmjOLLiJin\nXk9yYZfDkSGKo2Pc8U0Q+ps7nPT3kmH2Le6SGh7kaHaOO/5JAjeOXpZPxe9wI5wCoqaqpGausKUn\nid3OEHlqgexYL9mm6untEvMtb3MwEseKR9m5dJ72xBxbLTdv+tBvcv3f/RWee8ckNkvIC3tkHtq5\n5lR73nCyDqbXvrfoep7m6cKfsnxMccSmUsSNDKVBxfb4X9ih3engXTMwnylwUDTZk/s4rjkovnMa\n7fIgiZwNuABxh4IoiRhljepxlfSam6OuE8c74oiyTMxyIDgE6je75CSR6iUffS4PDq9I4SWdoixg\nPiITCRpkln2InSTBCy0yz4Lh78fQm9SqIs2qA0uwEDoR8gU/0YjJ5uZVHrvyX33PPvZq7GGv+AGt\nEIlE+PSnP01/fz+qqvLnf/7n/OzP/uyrqu+Xf/mXefrpp19W9vGPf5x3vetdrK+v8453vIPf/m1b\ni2V1dZVPfepT3L9/ny996Uv82q/92g+FOW9Y0H0t5B1frb3txz9I3+O/wO5qieJ2HkfASWFPor8v\nQ3K2xmYqxupL/fhDaZplE6XmI3wuQ+mWin+qQGVFJDjdprlr4pls09zRkWdatFd1xHMa5h0RMWah\nViQbHCdMOlsaZtiks2iSXvdQevc0ck1EcEgYg17MgzqWR0bxeekWmjjzUCJic5CqAyMahGMbkEuz\nIfS/3WP92jyZyQjxrVN/yemgmgjQvFmgMjlEMRkkUJcxW3boUaOj4G4qZzOJ1HSS4EqFTTWIKIrk\nEyEU3Qv5Co6DJtpQPxvz5wjftoE3sNcgOzdHxTWAZ+sEy7IwMhrFwUGKrlF868e4C1WWPUksp5Ol\nc4+Q+OYusf0K7dPU1rVQgKIcpZx56B1rXbItF4vT14jeriKn8uDw97wbn4928hru2xVih7ZYi6z0\ngNJSVbKDj5A6DDBy5wjn9iH7iZ7XPLS+T3YgiREJc/fcFVqBedw3MgytpHGt7HDY3zs3YTnAadME\nrq1DUobGP/npX6UvncPT1pD/6mluTV3EtOLsakG0OyWUv9ulXtGJLVeIrRRp5evEN6rEN6uIhRbR\nzQbRjQbO4w7RbY3ASgvHbgdtSyB1t4vDMcLmxcssz04iJZK0H5tCDvkIq66z6AfJbT+vbqZKrVbB\nuidRuNml9uNTGBdixJCRFIl2tk6jUqG4pIISwHM9hFbqYLkqlO94kaUQwWseai81KVdclP0OIpNN\n0ktu/EMqzpEK1ZSBOqNhNrvUTAXT6FIpGjh8QebH/4vXfL3lQX+XJInJyUk0TeNjH/sYn/nMZ1hc\nXHxVC3FPPvkkoVDoZWWf/exn+fCHPwzAhz/8YT7zmc8A8LnPfY6f//mfR5ZlRkdHmZqaOkvL/oPY\nGxZ0H9iPSozm1//NHyImL3CymCdzz8AVcbCxEkGsOxmbqhK71GZjb5CjbR9ds8XhN90kJis0MwIB\nr4hhdXDrCoJbw2fIWJKB1yfTKWkokwat7Q7yBRPrjoHVhvaBzN49N/n3nEM0XIhOGRIqRqpON+rA\nXXdg6jqNfgnjRo3VYB/lN4+ROLB52nqfm0BJwjRNvFstilcuI+VsfvdoPklgIY1lWTgPOjSn56Bk\nB8ofziSJrlaILOW4f/0KW1dnGVg4Ak43bYgBgpme3kJqPIl3qcjSuC1eYqguDianCX91hcU+O5Ss\nEI/SEeMkvr7M6vQluywcpuwcwX/zgFbfqbyfw8H28CzF1drZVmSAQNlgZfwdDH1tF1PXGd1Jk5qy\n02LfH5/Dea9BpdETy/Fu7bMWHWF75AqbxST9f3ODvXj87Hj/4jp7A2PUEkM81/dm1NtN+o+r0LG9\nZtnZ2+3m2k+xnRxhY/o6z0evI28IxDdq9G2cQKFMOto7dyCV4z0f/q8ZWd85K5v/my8ReOYGolfF\nnB4n88hFpHiS1Tdd58758xx2nCy97UluT8+zpIRZe9M1Xpqa52ZsiNSFORZnp7k3NUp1doyTS1N0\n5kbpRGwu16g1qJ/qL1ipIuU+G9zk5TQdh4Fn1cC8o3FybZaji/1Eh+xMEd1MHS3RRdzR0W91KV0f\npH3ej+zr2jHWz9UoWQFKgzLOoTa1PROj7UK+LuEvSOT3fdSrEv7JOst/IzP9E022vyYw9JhBaUvE\nPVIiFIJSZojhxPeX4ffV2sPAWq/XX5M43Ww2SyJhz2j6+vrIZrMApFIphoZ6UUoDAwOkUqnvWMer\nsX8E3e+jnd/8P7/ORj1MaynF0o0S/YMCJzkP919QcNfdjMxX8U0aVDpxmiGF3XsxihsuurpB9bYD\n93QNfVnFOdVEWFEQhzRchypaU0fbFWktuimYKrtpD6V3jOOV/YiSiD6sYu3X0BIKgbLNYdfPqcjP\nlzEXTQ5+4jqhfXsLbPpcGP+i/bFk50JIn95heWaC8niCaK5rg5kiUx3tw/v0BvceucDxWJzkQf3M\noy1H/OSyNnUjSBK7s+NEllMMrGdZmL3M/Zl5+u7sAyA12xy7RhldKZxd3/a6qbb8RE5KZ88vHY3Q\nKHjxH2fPygzLYlecIbHWA6mRwxwr1z7IxIspqNYJ5IqsOIfAobA4+jgDzxWo7PXqBXA7Ipw4LzJx\nYx1T10nWRLpuO0pCC8UxvfMElkr079sdxSl44AFn2O1S7jvHTdeb8bxQZuCLz7MTi53VPVRuyf+V\njgAAIABJREFU0fLZ031T06gMTfKt/uvc8j6K58tHBI+7DG6eIO8cMPfR3yK5snF2rSaKNIaS/Mz/\n+DvsDdmgb+o6NW9v0SzodJ55pyPVFl2//btH9jLUk7Yn1rd8QGnY9q7jy4dURu1Fo+R2nvZphEgs\n1cBZ0gmsaugpi+3YKCuzwyiTUURZxtot0Bi0B07pVp72gYPdZAJ1KoSsyDjuVcAD1ZdkvDMxHLM+\nAimL6q5CPuvG+4hANd2iUjeRrgp4hC75rWGmLqjs344yMqOw+k0Xg+er5NeilCse5kf+5ffqUj+w\nfbvCmGEYyPJrvzz1eqmWvWFB90dJLzzczic+c8CNQwlzLcPRRhXVVSQ8aXF4ALs3Bby6E/9EBqeo\n4h10orxVJV9J0JjzsPDFAMddmbWnPZx0ZTaecrCuC6RPolTfNU5Jd9N5NEnI48dodGjMKjiWK+gR\nBV9HRtd0anNuPLeruFc1jkJJCm4fotNBcyiEvF+0ow0GA0h7RQK3S+y9/XGCpyB1eH6AvkU7RYs3\n3ybbP4tYsXeMbV0Ype/WPnK9Tb3u5PjyZSL3bZqg61FpODykjg1EWcZwOTnoHye8csjg/TxH4/Pc\nnbrMyHPbAIyu7rM6/26qzmFCmzY4T20csnrxvag1P94DW4s1flAkO3aBsjRGcmULd6XChpkAQWBp\n5CpDa02iS3tokb4HL4GG5MOwJgnt7QHg29tjIzBC2+3j7sDjDH95jVRP5Awlc8Kef4D9oWts1kYY\n/fwNDt29aeXo/VWOErZHfjB4BUuaxXOnxNTKLlK5TN7ZW4wb31jjKPlQXPbQNN+KPcodbZZf+sBv\n8FPfukNheBgAAzg6N8l717Z54lsLTP71fwAgubRJZsyO+pCPsxyfAqtpGNQe0seVH8rr5nM7e0pj\nqv1/q9GGXJnoWhPX3QYnHRdrYzMsxyI0rgwieVR8946ojdsgHsu1UI+heVuH6WFKV/vxrhXpTshY\n9S5aqs2R5UdziDABtZ0G5bpF62qQpFuhfSLSuOsi9BaJ9FdrSH1+dKNOqSQjCFApewj6BU4O+nA6\nBQbi72IwMfsqetb3bw+D7mvZ9xOJBJlMBoB0Ok38dHY0MDDA4eHh2XlHR0cMDAx8xzpejb1hQRe+\nP03d16Ity7KQJImPfeIuW7kupef2ONo2sSo6kZEuxCQKaZH8LTeRSBfTU0LacOKZbSCXnSSveRCG\nVQKzYcxpD8HZCK5xP+qgi26qjnFOQVyt0JxUCKxrCKqMI+zEyDSoT6sElluoexoF082OHKR5YQTZ\n48XMV2lFVHyajN5o0/E6EDaaLM1MoYf9mIEgYrqIIAicnBsg9Mw6S75+UhenSR5U7USJosjRuRHU\np9Y4nJ6h6ffS8URwHWawDAMhB1pkGmfa5kibfh9Gy8Vm2XX2fO5NXmbgqyucVH0gihQCUTSrj+DK\nJsdVu/MfRIZQqz6SC/dYVscBKPvC5JxTJL9xl3rfyNkzP/YmqFUCBFN7doFlIecq7EanMOsJxpfW\nGKnptD3+By8JhxzEsgaYvLsIwEwxTzVgL6hZ3iCSOol0aHF+fQ1B66A6/fBgAC8XSHlipIausuC8\nTvgLqwSLDYI52zt3qZ6zc6Oba2wkhhEaDX7113+Jty7b7V3aP6Tg9bE2PsMHTr1eEfjg//R7xBfW\ncRYqZzTGcLZCO2zTE333tsiO21Nbz9oex8MhzI6G9Pwy1XaL5GaR2HO7VIttrMUK5ZeKbD3+KAuz\nMxRNmcoT04iiyHCqjBa360w4JBzFDp6FKildZmNmgq4k0ZqwIzGCGDjvW+Rvtum+cwg56SOsQPO2\nQGtbRn7ST/ekSTnfoB6OEJuQKC8phKN+rGSLVtbCcb5Ns9ilalRwhpzolTZdZM73//Mfus99P/aD\neKWWZb0MO97//vfzp3/6pwD82Z/9GR/4wAfOyv/yL/8STdPY3d1la2uLRx999Af+rW9o0IUfbf6y\nB+0kB4d42y/8Pulil/H0LoWswP4iJN1e/KMStYBFat1J+baIbzpPZ9fC5xPoiE0CBRFjqItvX0Qf\nFfAfiBgJkXBJwnKLuH0O9FyD5qyCtFym0+8glDFxbrQp6k4Oqh4yb5rB7XRhlhqUhgMkUhqmaZKb\nChG5k0XYNFh7z48xsnUawdAfIpbTMXWdQLFFKjCCqNkc6PblGUZu79n3tVZkb+7t+PZsTzTbFyXU\nkBh+fp27o9fZjw0QyxlQqyN2NDpVFy73AJ4TO24W2YGhe/GVOmfPLBNOEDzS0cReyNVBdBh1r4u3\n0RPIEUyDI2WWmdWFs7LRTIqdsTehNN0Mbq4yfLLHZvwiACVvlON6iO5eEdqn4jT1GnlHmJw3zlbg\nEudeuE3pIVF1qZjj0BmjFB1n2XmJkadvoNVbcEqLnMsfUQz1dB5cyWmWfNcpH/uY+g/fQKs2kZq2\nG91nmWDBP/2ND/OTX3vq7JrBTptcNM7P7ayflWlA0+Hn+u9+muXYW8m9ZNF+OkN2p4PjG2nc38xg\n7Xdxv1BAeS6Pc71B7U6d9KqFxzHE8tyT3By5hOaNs/bEYxxdPs9oNIx5quAWdjrsXX6mieUREept\nvC+lyGVb7BKnbLnQHrdD9KIuCcu0kJ5Pc9wW2J8foi8eRHQ7qD27T7HrovRIH+FBJ1q2g7nUhbeE\nEHfq1EsK9baAEG9y9BUHoTfrpJ8RCF/R8FpujrabqCGDEc+v4HK+XED+tbRv93R/EMD9xV/8RR5/\n/HE2NjYYHh7mT/7kT/joRz/KV77yFWZmZnjmmWf46Ec/CsDc3Bw/93M/x9zcHO973/v4xCc+8UNR\nD8IrANY/6DwY3W4XXdcpl8uEw+FXvuCHME3TaLfbZwHbqqry+7/7L2jt/r8M9rlwv+caLcvmCl2x\nIHpU5rihY+y4UGQLK9lF7YawLlk07jgxzjtor4mYswrGmoV50Y11q033egDnokblggeeLyI4vOQU\nFclwkb8+TPC4TtlhQsxPcjHNyeU+LMMgvniMFfSw31ZRTZH0hVGEjsbg/T2yl0exLIvk03fYnb5I\ndXCAsc19UiN+BK8HudFi+Nk73Jx+O3h9jB8fUEqAHg3Rn8oh3iqw8qbrcMqbXdq6iywa3I6/GYCJ\nk00O4y5iukamEEByuBiorLFz/jKRUo5mCsKiSd3VpdI/yujJDntakv5OkY6rQ2F4nIsb97jnv4ik\ntZkpLpEaG6OT1Wif5tByt6oML3+Ztcd+5uydXNy7y73QJabLa5xEVPoredb7rp4dn965Tck1SMg4\nYmP+CnObd1lNXDk7fulwmbuBOcYLC5h9PgRTZDdh67yGD9ap+obQT1PvXDpc4m78Ar7sJkNCGl1r\n8Qv/z/+OeXLEm1fvAnZneW58mg/tbPD0wAjnU/uYwAszF/gv15coKE5+4m+f5eTCIwysL5I6Nw+i\niDt1gBD00PIHoFqh36pQ6OvD1DRGyikyw/2YmsZY7ojcWBIqVQbqJaoDYeSDDG6/hCWA+4VNvLEQ\neyE/I9UO6cu25zy+vkdxJoi1fMhAs0VJ8RKWRKoXPBipMmGthFz2IXTb6I96cdzL4dTbNBUP8WiT\njtBGWNVwv82L+EwGx1QEZyZLU1OIqDnqOZmAz8AolknGL/Heuf/59emEp9bpdOz0VIpCtVrlIx/5\nCE899dQrX/ijte+Kyv9JeLrw+uZJMgyDdruNruvIskwwGMTlcvHf/Zs/Rgs+wVG+Rf0bC4hmlWrX\nolapoad1opqHwJtkuqM+9G4/+5pI6ssS3a5I4yUd6jrtxTZmo0v3xQamIaB/vUHdclF8qsbeE4/Q\nVCOUL4/SnAqjbmUo93vpS7cwTZPjuSjhhRRyW6fTkdhuqBTnp6knY6j7GSynQnkoibpzQmInz3rf\neTxF21PbnRphYs32UBP5GvvuOYJlO0Z3p3+Ygb06aqlCdU9iZe7HuLC0cvY8ip4oze2eitd2corx\nwyLKehrdH6Wjekn7pxlZWyWxn6IVTJLyD+BryQSPdhHSZXCqHPsHkDU3o0vf4r5pA4ShuFiNPcLg\njedoe3pxtuFmkbX4uzh//yVoNZDKOVIO+5qN4CyOkgK7x72XZprogo+cO8GG5wpTd5Zo5atnh5XC\nCbtKH4giO7GrdLdrCEclpo/WQdcZNLQzwKVW4dhpD+q1+BTUZH7pD/6QX3nmi7z//hIHfpuXvTFz\nno/sbBABFFHCAG5Mz/Or67YOZ0Tr8C8+/t+DaRJRlbPFvMlW2QZcYOZkj0Kf7W1PbK2TPt31N3p/\ng+yoXT62k6Ia9hDZzhJdPsa53+ak6sYxPM7G1XnagwnaAXuA9CzvUYrKRFareLMWu49eoDgUoRU7\n1Wa4k6YlDZCKqhhTCt1CEyPdoTaXJGyYdIoGjQUB9495yX8pi3QpRHkjC6EAQq2O4Q8hmTrlTBVD\nknm0/7XJe/Zq7Y2mpQv/iYDu60UxPJyxQRRFRFFEVdWXTS1+63f+jpw5TqlcJ7p5F69QRw67SB11\nqNZLsA0BGczhJn7JjXItQinhhYEEJ+f7MX39pB6dRgsMcHBtks5wP4fjMYTHxnDul8heiJBYOKET\ndOETZaxKg5P5GIk7xyCLmC2d9ktlVh5/E95AEAplKtEAka6I1WhSi/hQd8qs1PxUxyepRwfw7dmr\n+PfPTTP8lVvsZYKcjM0TNBzIpSIAyyNTxD53l1RiDgSB5cHLzN67h7PVgMMm98fewvzy7bPn4NBF\n3G03nG5WaLr9KHWLWrW3o+ooMEjyKEtR7C1kZbx9eHJd+mqFs7JIM8+G7zHmt9eRqna5r1QET5Dl\n8HWmjw6Z2Vum4O1RAaHSMeuxH+f86j2UYobhvbvsBE6zE4giRlPjxHmZC+sLKMUMM40s1YdAPai6\n2YlcZ6M7zcDzL6CXKjhbdhjdbHGXXMBeOJHqVf75H/wPfOSFzwOQtEzyoX6eGz3PP1tf5sHy188c\n7vDVgRF+dWPlrJMVFCeTlX0++MmPsxU5DWHTdUru3lRc8vdkJt0eexOAWKniKhQZW08ztnhM67hF\nfs3iTuACxXOzbF46j2xanAzYwD14b4fSaBjPcRnPQYVySWUpHqc1bwP48EERPd/BuKNjXh6nNuxj\npNzGPNLp3NUx3tJHt92mmqlRGYgTHVFo3paIDYVpFrsE4m5yuQKhOSel+xUMRcPjFTgX/AUiwd47\neb3sYUrhjbYFGN7goPt6RTB8e8aGQCCA+lAWgG+3/+OPVlnLBjnJt4lu3aWwkGVw3IcjEiWX65Dd\nr+DZl3FNaZiFFgFDohHViO11aJxzErlbpjLrJryQpzruIblboxNxEdYtrFaH+mQQdTNLYTxA/47t\njXYtC/npfe4+9jjy4ABUahyPxJk4tEO39ieTDK+m6H9hl5sTb2eoqmOaJoVwiIDmQKhUiZWqnOhj\neE81GHb6RphKFzB1nfNLayzN/RTn1u/Yz8ShsBc9x8RXvs5h/DzIDtZDc0yv3SVWSLPdiLASv8L5\nrXug68jtJrWqTFUZYuhoFQBnu06+G0LVXMTSdqTDUGmfFfUyJXOAiT17O2Z//piuL8GK9wKj6Qqj\n689z3zVz9ry3hBiteoCRg2W7wDQR8IKssOy+SDSr40lnemFhgCD5aDsDLLmv4Es1MI6y0LBBNZTe\nYEMdPj1RIOj0sao+iWOjyIWde5ilMlgWSq3Ev/y37+dn73z9Ze8/IFpMtOo8/IV8bvwc/5lSJH/K\nbdYFkfvjSX6uss3v/uXvcPnuHc5vbjLzzJcJtHXmNraY/vo3kIstZu/uMvblFykfaCjPHGE9W2Bx\n6l284L/KTtXF+qNP0JqYYnJzlcyp9ztRqaEFPEj1JlKmhGcxz35V4eSxeRqTQ0wc5WglvEjLJ9Tq\nJqnJKZyiSWvIh7Z2QrXaJTM9SDyhoufbCM+W0N89hLVwQqvtQnOYtLs6+gmYkkgAlZMlHW9QRC9a\nBF3nefLCB1+5c70G9u0C5m8kLV14g4PuA3utQNeyLNrt9ssyNjzIrfZKbfzxn6a4cV9m76RFLHeX\n3FYG86RJpD+AZzzOcbFL4UYHR6VJM9QiuG3SOSfguVemM+vAtVqkec6HcyVHac5LYDFNacrPwEaZ\nbsCFx+FA3Mpiig7kL+xy9+pjtM/PIRXKHE0mmdixQ122Lo4xcnsDtVSj1nRT7ETA7WFp6jxTCzZF\nsDM8xOjiLtUNidTIFbquGP5jOyRmZWye+a98jXvqRZAVdsLTjO3a4DaePyQVe4K+9CYAulMl5Roi\n+MKLNAM297ocu8r8+h2mD+6TDs9TcYWp0cfQ0SozmW1yoWnSahJB95FIrdvREC4fdSXAoTjJ7OIz\nLBujZ8912zWGmm4zVNg9K5uvHrAbeoSUOcGFrVsM7dxkS506O25Wi2y4nuTCzhLe/CEDx/fY9vRy\nckU6JVbD72bgpMTszh0GzSZd5TRlkK5TFe3V/3pghELWZEN6M5Pf/DJ//b+9g986/AZ/N9IbAD47\nMc8vm6sEQ8aZLsLnJ87zYeM+Two1XpqcpAN8c2aGDzX3ABjr1Hj3//d/s2zNIYamWXZcYlm5hOIZ\nYjH6OAuBRxA9Sbam3kpu4hpDYRdd1f59/S4Ty2n7057AaaqgfIl2Okfidobuc2nW3vFWtq5cYkrr\n0gn7MXWdTraAZ6WDWRHJPjmDqciIqoF6u4I/A+UnRnAclqmWG9T1EJ6LEcyNBopbpXHRhXFQp9Hv\nQdK61GomuiXhMHQqpRbdrshbhn7le3eu19C+XcD8jebpvmGlHaEngqFpGrIs/8DbDS3LQtM06nU7\n8aHH48Hlcv1HohutVuu7eryiKPLkWz/Cpz7/BwRUjTElRaoTo2FaKKYTNeClO+MjW1cwNk0cbie1\n5QqiatJumXiCKk3dwK0otLUuoteBdu8Y2evBupWmpfgx8hZrj17CjIdxpksUR/sY3zqhEA9QjgUY\nWNigNhDDmyrSWmlx/8Jb6SougukUzVCYqtvPwOEOXt0gVwoTr1fJRfupu7wMVYqUBYvJQpodfYLp\n0g75UD+GrCBYEgMHSxx14tT9Sby6jqNRoO0JMpveJOW8SLS+T80bBUFA0XXknUMK0TEQBNqySrCc\np5WtUg3Zca4N2cNgfp+W7qLqsafahigTKeTo65TIuhMgiow1dtjkAh3Tx3TxLgXJiaWpNGQfpugg\nK/YxlLqPLgq03TbvOtopkFEGyEoJvM0OsfQqufA4iBKYJoFOk5IjQk0OUG0KOAs1Bjpp8pKL8cIa\n+/65s9Cw0W4BrdHmj/76V/jJ9CKCAGlBxFtt89XhEf6ptYlbgnNGlU9FzrMVivGLxgre009xqpPh\nz+Pj/Hp78+xb+XpkjLdai+QbTb556f2YsoKjeEIjGKDjdEO1hOlx0lR9CJUiuk+i5fbizJzQjqlo\nTifRG8/hdYioe20c6znW3/J20pEk00aVwmAUq1bDbbX4/9l772g5DuvM81fVOcfX/XLOARkEKIIi\nCZBiBJNEUbRFUlawJXt9bK9tBa9nbO3Ys+Jqx1ppLNkeexUsJtOSmMQAkQQBEgRI4CG+nHO/zjlW\nd1XNHw08UFSwmDQUz95zcA5OVXVVvequr27d+33f1c2GsQ4vsnrVDmINXpqKafJeM5YnhlFr61lt\n8eA2SpTyJUxTcVJ7OvDMR1BzFSrpCmK/ltLTYcz7a6i8GEJ/iQl9oEQxl0NjkNAWZK7p+T06Gwff\n0r33VqJcLqPVahFFkVOnTqHVat8WhetdivevtSO89Uz3AtimUqmfmtjwy9Qtv+w4NV4fv/fpZ5mP\nimSKEnsth6AQJbGWJxYLYVgsUes2UNlmJ6vokXe0E3A3UshaWVgsI50pEAyqSCMSU2E9FWc7I01d\nRHdsJuR0sXZZP22nZsm6bThVEJNp5oZaaT0xBToteZsF32NnOO67nEJrN+bQOmmbE73BgiESomSx\nok/L5M+kiNZ0Me3vp+N8Fjvr66B/fIxAwIDkqGXe0UPbSnWdJOrQBCtoKlWaWdDsx66ItM2fZKLQ\nQNrgoijU4A9OI0pFdKEU0zVXM7B0vErHUhQMqTxJfT+tgWpTSSflSOYsJNUmOoJVjmt7do4p7VZG\ntTsYCE2gycYR40nQ6ilprUxot9M/cYxY5aJwoCV+jjHbXuSCi761E3gjE0wIrRvrtdkYk7p9tC0t\n0bx6htbQaeYNHRvre+Uwi7atjClb8a4XsYQiWGOLANhjs6TiWf7h/tu5MXxm4zPXKhEebO3i48Ii\nptc95w3WAjs1K9gu2Dyq8MOmfnY05IiLVeHDSZufGnuUdl2R/+fsN6gLVqllPaUwaVu1xtyXWCTq\nrtZfe+JzFFRoX16gZ3yU2tk45sPLOPVNnKi9gnNNOxEaqw8t49oqKw0OxGiShudPIuXNzA7uQNvb\nhGo24h2ZIVmWsI3lMXa1E+700Ty9hhwuUV5RKe1qpLIWRyqUiW6pw6AUUdYsOHts5F/IYukyUDpW\nAJ0WIypSSKLBuI2tHZf/wnvi3Yg3lhfe6KHwXo/3RaZbLpcRRfFNSQHL5fLGxAaz2bxhJP6LQhAE\nisUiBoPhl3L06uqakCr1HHr1ALIo0FgJomn2knM3IUXKpGJpvKqJQoeRSqiCQ9AQb7FTk9USu6wN\n+0qeyOXdNKzlCWxupmUiQLCjjtpohrRRR8llxbocJtJVT9v4Col6L7Is4zk8xbRlAMFRR0GWSXr9\ndEbWiZospBwuugOruNYCzKhd+DUCSQRkix1V1GBNBPFUCkRTdlrzIcLOho0M15FYxhcMMe3cRVMx\nTk4pIxstlFUR78IiCWMNisFCQWPGUinTtHiMWeceEAQiujoGwifwyCmmlU1IGhNSxURTdpz6SpJ5\n7QCSaCSn2ulKnkHKq6T09dXPin56wicJCX5KxupNpcuFKYuNeMt5jFKYnMFFbSFNTOujJJqICvW0\nr59C0hsonv9MeylMUKwnKXpIld00RCYQhDI5cw3kU1DRktNUu9/2zCILuh1QNNCbmWdw4t/5zqk/\nZVU1sSVTFUgoKny3bogPuecpFC24lCon+RFXH/td0xzWd7I5E0EFHvZ3cbdlinZdjieMXSDJKDUS\nm3XVWnJFVTEEzjJVtx1NJoYPGX8yghgO4s8VsC0HKEeSRAzdJCputFYLczX9KLJCzuekZDTRMHuG\n9b4WVKD9+GtYJDuRohurx8hyVyu1oxMken0YFsI4AgkCg31oYnGyPS40M0G0qSLru3poTSSR0yVM\nyxnKVzUiPjmOdlsL6kwAvduFNpVCNVgwlItI0TTlQh5dzsLvX//ld00u+4vi9QbmL774Im1tbfT0\n9PzHH/z1xvsz030rjbRKpUI6nSaXy2E0GrHb7Rtf4K8Sv8pxbrnhXrbt+CKTSxDMytimD1G/dhpz\nkxOxs5Z0rEzxxTWsepmkRaJ+NkW834r79BqZQTeusTXivW48Yyus9tdSf2aOtU4/7TPrlBxmjEY9\nYiRO0mak7gfHWY3Xsda2C0EVWPI30JWMQKXCRFs3mxYmMRRyCEkJMagg273Mejvpjy2BopC0ePCk\nkpQmgiQdLYx6ttC3WhUoJExuvOsBApWqF8GcqY32bBIhl6R1ZYoJ55W0F+OI2arM2KhIpEvNuJPn\nvRREDSv6DoTpxY1rk9fZyRXtFJcushUkrRlBNmLLFuG80Y0gl8gWnRgKFlri1ey4TwkRE30s0UKm\nUEvf5JNM0b6xH29mhindHsopN0PhUzjDI0yWWzfWN2QnGdNdSTzVwlBglN7Qq4R0F+WcNXoRVWNA\n0trwTh7mXybvY6gS5DZhhGOGGsoqfLdhiE84RhgwF3nFV1XPPerq5AbHBA4d3GUe4yl7J9/xDXGX\nbWajl9duijDstbNNX6Wt5VSRA84u/lR3jM8995+ZtF7FeK6L1GqR0bq9jJgGqZRhse8qMFnoio2z\nVlM9Xk8lQtrpBkXBtb5E7+lVfC+tEmy/hNMtm3AnA6x0Vcs4rlAQ/9kUxZDKyqWDVCwmHLkUrpEk\nxnCJ6J4eNONL5LIVAl4PmlYLmpejWAbryC7F0LU6iAXDaPqcyOsJsqUislqikpD5gxu//DMluHc7\n3nj//f813V9zXMh0K5UKqqqi0+l+4bayLJPL5SgWixiNRiwWC1qt9k09pUulEgaD4Vf6oW3ftIfT\nI8uEcxN4/HBJ2wrjR8IY3V3gc5Bs9ZCdzKMLltE5jBSGl1CH/KihPHqXhWJOwmg1IGUl5Bo7uvUE\ncbcZ5/PnMBgccC7K2YZdZPzN2JMpAvWttMeCRPUmIjV1DE2PEK6pxZDL4Ts2wkTbVcRsPnoCI8Qc\ndYRtfgYXT2JRKoRjVnw6DVH0YDCT1dpoik3TlAowqt9Nk5IgV64g6y1EdR4Gp15kTLcTtDpiGi/d\nuTmyqoopnGLNNIBTzqMrRSkanbTHxpnQX8FA7gQRQy0IAo2JOWbV7fQVTxEx1WGuZChFyiyJgwxI\nY8QEPYPyIrPyIHksFMo2uqKHWdZ0ImmqDaUyOlySgL8UpaQUkAxOOsrrrNOIJBgJy3V0JkbRUyRl\nrHb4m9UYEaG2WgsuOTHnSzTLMcRCCG0lzbraiCLouG70b3l04fN4xWoWa9DAq3g4Z/Vxr3vyQrmX\nLiHEN+jjt5zTXPAaFwR4wljL7aY57GL1ATKFm5hbh99ZQsiLGBSJx22dfMxZLS1cUp7m5ZyVpfrL\naNYmCJ+vcTeKCSLW6v+9QoaYzQMrczjDqzSmJYxnJ1nq28Oas5X63CpLHdVmYZsaRrscwfvaPPPb\ndxBobKK/GCZWa8f12Cvke7pZ7GigVsmgWU9ji+WI7unCd3gEHF70ahm1UMEqqaiCgJUy+ek0Rhto\nMnkyizE+tvuzdDX2/cr3zjsZ5XIZw/lm4uOPP85VV1214Q72Hor334y0CyHL8sY8Jb1e/3PX5/N5\nCoUCer0eq9W6MQrkzUapVEKn0/3KT/cPXnojjz95hPVYkExJR19LmmJ4neWQHa/eitqRo5VZAAAg\nAElEQVTpJuFxIqR1JLd2kz0eRCiKCBnQBnKgGBCXk0gZDVJEYqXiJds+RDIvsrR5O0NT46w2tOKQ\nJSrZPOv1LWyaHSdUU0teFOk+dJhZ/WYKnmZ80UXSzlqKOjO+2CIZWw2udBxhNsC6fzNRvYeh5Dhh\ni5+K1kB9eIFo0kjO6iehddElrRJVdHSVVpnKdTNUmSWsq6l6LGhr6Jk/yLxxK2j1ZEU7TjlPY+w4\nk+qloNEQERsYKJzCrcaYKm5B1eiIyLUM5k/iVhIsMVAtK+CnozBJMpYja6xma7Kgo07JYi/lyCoK\nFb2NjsxpZqUBorIfi1ShJfEi0+IWlPO1U1d+lpDSQ1yqZUCewhA7y4J2E6pYRccu6SwLwmbCFR+5\nkoPOzFlslQSfWfkr/nPhmyTydmqEKh9hXTGyWONBazQyQLXMoKrwiLaHZm+IprKEXlRRVPhXQx+f\n65jgR1I/W8ohZgUny04z+1zrNBnzPCp1Mi7Y+e2a2Y39fE8Y5D/ZfsjL6UZGmj6AotXjCk+zZnbj\nWZmkYfokRq0daziDNxxgunsvIaOPFl2WQE0zVCpYDVlSskL7yy8h6eqY826h0Zgl2FyPY2kRTSKC\nPmHGWWMh0F1P86HXMOoshDU6hB4nhiNz0OMjZhYwB+IkvCZMyQyVdA6d1YqukKGczJJcCHLTtg+z\nd+v1b/r+eSfiwiy1C/f6I488wq233vpepI29P8sLF+LnlRfeKGy4wLV9W5rpt9Cw+9Z9j1MpbmFi\nWsOZaR1qMsT13YfIrQUpvrpAQ6lIol2HfSmCY6CRWE8DmC3MXbUdWdEye/Vl6AQNy3t20yMXSTls\nWM16DNEoMz1ddEyPsVbjp7WYgmKRqYYW+p95Ct2sxGrjldTkI+SMDmSTA1t0hZzJgWyw0Td8gKl8\nK4GarTRFJwAYcW5haP0kA9Fxxov9iHovzlTVJWzS1MNA9ByhNQHV6GJEt5XB1GlQFHrSI4wbbqC/\nNAulqsVkQTWQTzrwlpYuXDwWhW6E5RBI1ZomooaEWkclWEAsXbRrNKsCCh00F6oUN29umql8O2Ol\nIZx5hebUWRTZDkL155tQvWhppiu/hDNXLW006guURBto9IyV+rFKRgaLs1hz1bKKLFw0urGUgkSK\n9fzFyl/yFb5Lu1XitLE6cXgcL+M1Tu5snKHZFSCoGKko8G3tEL/VPsUNDQl+pNuErMKDYhv3NE0g\nivAx3zkerrSyYjNwtasqRlFUUOwSJkd10I6qwoPFFn6naZQaXZF/jv8Zl4w+xeDcNPXrqxjXVaK6\nbRi8nYxYBpk3tyH7qlm7Ib7GorsOFIXmY09ij5RxroqY6zuZa+zHFl1loclH7blpfPMBpnovI1sp\ns9juxf/SBJLPx9TmLhoiYawLJexuOxJQMx4mvr0R51KMuM+Eoc5GaTVELpMnORegzdjF1ZtuolQq\nUS6XN4ZH/q+K38TywvsOdFVVpVAo/JSwwWw2vyO1p7fKkvgf9z1NPt1BMidirtWRXExylf8J8Epk\n5nNYXpxH8esplgq0hJOs9NXQfmqa5aFGWobHWd7aTufIOFNDnQyOj7BSX0dXOoak1ZGp9+FeWSRi\nsTF0+CCW8TRLTVdjKUskzS6MBgOmxDpBWx2+SgFbdAXXWpiSthOtLJHTOygZPbgTCyAIyBUdlYUE\nGGysa2txImLKhnCWE8SzflrUVLXuKgiM6rYzsPoCi3EPaLSMi5vpK85AKYMvtsCybmeVj5urum21\n5meYFK+hVw2iL4RAKWNIhpmQ99BejmMrrFCrBhgLNxCu+AlmW+nLHqdGkJCEqm/sutyAMVnCkk9t\ngHdtaZSJXBcTuQHkjJve4LNMpy6alvuKE8yWt3EuPQQZBwPBHxPOXixFfYCX+G/xe/iE6cWNZbfX\nzPC9Sgd5X4l9vqod5i5nnOe1TXzfMMin2kc26rWX1YzzDbWPj3cubCwLKnay9SLttmq2rKjw7fwQ\n9/bPsrs9wEvlVh4o9HBn5xKiWF1/ouzjy4YvE4qlWPZsJmfx40rOMWWpCjdaomeZ93SAotCyPEzb\nWpCG8QUMdX2ccw8h5NNM+VurQLx4htrpPLGCm+XNm0Crwxecxz1ZQNAaiQy24njqKLH2VlZdZkqZ\nDJWYSslvwnp0DbnBgTuYozSfQqlUKATCuMsevvSJv/6FQyMvALEsy+8aEL/R4KZQKGA2v3vmOu9G\n/EaD7huHU14QNsiy/FPChnfyeG/1x/TA/3uQyHIzp09AvGgkvCrzgcyP8bqmSW/upHQ2iX4hhVSW\nqXniVSKDtdRNLpPp8uFZXCPR4aV2dpHF/hZapyaYbqyn94XnqQ+lqJmJkJxWGem4EX8pQ85op2xx\nYY8ts2xvoqWSgmIOKjJNU1NMiEPMmzroKa1DqUDY4MOu1dA/8wLjqS4WTFvoSFfVYYuaJppz6zgX\nJlnXdDPCVobyZ0BRsKkZYvkG2qWlDaeuCc0W+tYOMVOqjsOOKD6kspve8AHGUlWHsMlSDw1Knv7M\nYeblqkHNbLEDqyTiWBtGNlQbd5JgIZ/SISTL6KWq+EOU4qRLDYwmttNRCuMvTuPSalCEqsVkRnWi\nE5rwZwu05auZuM+gUDnvcpaV7RTpQ0k62Fwc5Y7I5/m25XOo+iKv/2qfkfoQWmT6nRed0MKSHtVb\npKMmtbEsU9Hwiq6L7s40xfPDK6aKTuYtZj69ZZ6XxfpqZpwf4pP9VaBudFQ4azKzo34Vraaa8T6U\n6OTewQn2Ocb57+pnKJ33mmq2FCnrLZjC81jTQTYtTlF7doSEfydnrYOIpSwzNVVhSC0J2hemaX/l\nCMs9H2Sito8OUxoxmab7qReY3Hw50/56FE2O+uEQrqY6YjYj/vFFVndtxrYWpOCoQSeUKQYyqFYr\nglwkvxomNRzjq3/09Q2WkF6vx2QyYbFYsFgsG81oWZYplUo/M733nQLin+cq9utu5r3d+M06218Q\nF56u5XIZm82G1Wp9x+cywdtXvj30tRcJLXs5e1ZhOagnnYWd0k/Yvvgg+XYbeb8XSWdndt+VaA8u\nkkmB7fgaxsU0NaeDWFYy1B2dpxQWsB5cYLzrZrIhmGi/km4hBwos+rpoDo4RstXiFyXEbIKI2UP/\nyeeZy7Qz7tvHULbKOR2zDDKUHIVyEVs8RKVSj6BWkLQWQpoWmrMTGOQcclrEjANKmarBONsYSB+n\nNjpLkH4m5F0M5ocBaJYXmcl9gF5lDqFUBSdZ1ZBK+GhVxzeuRbJiJRN2Ulee3FjmIMNK7oP0VM57\nOpRzCLKD8dRWfMUyDeVxBjRLBKUq42Au14EpkUTM5KBczXr95UkmYm0s51tZiG6iN/wckchFq8k2\n4QxzuQ5KFS03pL/OQ01fpcGY4862cZ7NdyAr8N3sZq7tn+CewUUeTVdJ/1NFN2eNHu7eskLOqJIt\nC8QkPc/JjdzTP8aNnWv8oLiFkaKfuF3D3qZqdnxX9yT/NdG/AbgAD0cH+Z1Lx5myeEmVtXwvPsCd\nA7OIIiSKOvT6BA+WP8TAxI8ox0s0z83hDMYZ9+7lnL4PjxkitqoC0Ooy4gzM0D/8DBHBz5R7K1af\ni4zNjXlimHKiiFSqR+xqoWQy0XnkEFFfHykU0moFz8kVQru7cT/1GpGrBjCdmyNa68Rs1SItrJJd\nDBE9tswj3/zhL7ynBEHYAGKj0bgxSt1gMKDRVOf+XQDiXC5HoVBAkiQqlcqbLk+8Wwbmv874jW6k\nqapKIpHYGMnscDje1ade5Tyd6ZexJP6juOumT/H//dsDGGtA1GrBZGSgPgKnR0jVtpA0u2leTxLe\n2oMiaZD8fhZsjZjRcc7bh1vRMOPtpsaiIyepFBxuPKEl5mv7GFo7w5qnDYOookvFyBqcdI6/SjDt\nIejZQW/yJFFLE2Gtl77UGaKmeoqCic7JFxjV7yMm1jCgzhJR7Eg6K6Zyjrq100xrLiOi1jAoThGW\n7SBq8aSW0ZVFImIDCCLhSi29+ZdIJ0xkxSaiFT89unmSskBLaZ5FaTv5so0O7TliQi3N+QkWCjsR\nJA2NugmKoplyJE9aaSBWqGFIfxavGmAmU82O02U72kwMsxQlKteBqAWlgkdTZCo5RIs2gF1Yw6UX\nCBXPz1wTRPyGMsuxLvoME8iVBBadEXN5hc9b7+WL9Y+iP48jGhEmUjpOST7u2TqJ7jzl26jL8mKw\nGb2/yBWtVQP3LneaB+c7CRts3Na7uPHdRksq8yUdN3RUs3JZgYcCrXzk0hnOBhpoMWX4UaiTa/sn\nsZmh15fiW+PtfLx/CpMRspLIc9F6PrxthX5HEFKr/ED3KaL6ZlqtScKmOihm0FmhmM/RPn0YdE6C\n2hZqLTIL/h4ssRXyGomu9XXsqsRYzwfwBacpimVqZiIUNrURMRppWphkdWCIutAi2pIeoxVMk0G0\nPjPmpSBqNI2cShI4eJZHv/lDzMY39wp/YYy6RqNBq9Wi0+nQ6XQbjCFVVTcSpQuZ8AUAfv0b7Bvj\nwjYXOPkPPPAAn/rUp97Uuf2a4v3ZSBMEYSOz/XUd7514uj79raMsnNKyGhRYDeg4PmLBbitxh+5B\nuseeImKC+pllDF49KRS6pQhT9XVsCU8y2djOUHiSRU8TXVKEjMaI4LRhi68y2riJ3pVTmIo5GgPz\nKGPrjNZcT7cSBFFkxrmF7uSZqqeCtZfepZ9gCCSYsF5HT6HKzR0TBxmqjGOuJLGk0iQ1m3EXq74H\no8om+iqj9OVfYzJzKWO5rQxWqlNRBSqU8xa8Snyj1DBV6Kc7e5bFeDUzlbAwmxmiL/440/FtAGQU\nF8vJPtpizxGrnPdHEHQsRr2UYyIO5aLnQqO5zETsKrrEZbzKHN36M8ylq59ZyrShJiWEZAmbXB0z\n1CCOMh5pR8bEeHQT9nSMvfK3Obbzcv7i0sM8E7/o1zCcqMPcIqJ6froLPi35WHdr2NUQ31g2mvDi\naM9R6ylvLHsp0oq3rUBjh0SkaKQiwwOrXfzWpYvUOUHnLvCdxR72DcxiP49fD80N8tnbZ3ks1kux\nDD8M9fCRnVUPjMOrzVw3dIpH2z9ET/IZJo2tWCLz9K0cwpkooI2bMPg7mLb3Y86HmXU1Y1+fozUw\nToValhUbC619WANL2BIR1m2DWJwaxFianqMnmdl3Ob7DR4kMDqJZWaZU40dbLlAIpagYNRSCARaf\nfpVH//sPsFlsvBNxAYh1Oh0GgwGTyYTZbMZsNv/COnGxWPypOvHrQblSqbwrb7TvdvxGm5jDxdJC\nIpHA5XK9q+qYQqHqY2uxWN7yPhRFIZ/PUy6X+cj/cQuejgq+BgNWi4IowL59JR440M2I6WosZg9q\nscRCWyvNyQJne7bRe3ackY4dDEyeY6x9B0OTJ1iz1NKwMAV6B4k0iIKJZdcgA+kxxrRVz4H+7Ajj\nzu1YpBSe1AxOQctSzI1ZyLNu7sUgZ2lQFpk3DuKWI9Qvv8qoeT8ADdo1MrJM2tDMQOUMJAqMKTur\n2aZapt94GlAZj+8CVWXQNsyovJVGQ4DwsoFaW56UKJLStODVBimuSbR6oowWukBro808x8Kij/7a\neaalRipaD4O6EUaDQzgNETyOZQqygVCyE5lq7dYmLNBommaifAVojaAodOlmmIn1YNMlaPEvUpQk\nZvO7qtuzwJea/4AvbH9m4zV/ZM2MPaXlRKaRzd3zdNUWmQ0ZkcJWeuxRvr+0idv3nMNqhKePtXNT\n0zyHgo24G1Nsasrw1LlmPmhY5Uisg+6OVTr81abZd17uB1Xkdy4b3fjeH5vtJKdRuKlmGYexwkNz\ng+zfPorVDOUy/Jcn+/nyh8YRBDgabMFdE6G3KU80o+epmRYeSnyJ59M3U+fOsGpsxZ8ZJ9LYjqLR\n0z//DGJNBytZFaWtlozZxUDgEKLRRS6dYn7nZRgXJuggyYynnRb9LMZYCbnPgfbcDOq2Ruwnxih7\njDgLKXInhkmPTPLDv32YWt+7b9X48+ICB/9CBnzhH1RruCMjI4TDYR5++GGeeOKJt3yc1tbWjTdk\nnU7H8ePHSSQS3HnnnSwtLdHa2sojjzzyVihpvxCI3hegqygK8Xgcp9P5rpYXisUisiy/JdC9wKq4\nILC4YKiz93NX4N+so75Tj79GIDBXor1VRrU6eFS4i8XiVjzpPMspaM5GKVhdmJMZcgYH+niSVX0d\nLarEeM1OBmNnGTUP4JWTkM8QtbcxFB9mxLoNg1ygNjWFWW+kEMyTk91ETO341BCynCdmbMOhJKlN\nnyGWbSaqtDBgPMWYuBOAZu0y5vwMk4ndIJoZtAwzWt4KopZecRgxV2a8sqtqp6iq9JuOkUhbWJeq\nI9drzeugSWCuFJk/n+V2uydYLxuwSHmC+WrttMW5gI4pZhN7QTjPu5az9FteZqp4CbKmSuUasJ5i\nbHUbbd5pCvoKFm2OufCODRpYm+UU+YIXtytKjfEk37rmLzgzU8NvdUxsiBuSBR3/9Gobf7JvGv3r\nKkb3H2tDFo3cffnEBkCfXHQyMlPH3p0zNHsujof/xjMtfGTXCvXuKiCkCloeX+3CWK7w0Z6qyc0D\nE33cdtUEZhN870AfJrnCDTtnsJqrRJD7Jwe450NjPPRYK4OeHIKjwKaOLMmcjheWG/nwvgVCCQN/\n9vjd3G/7h+o1Tz6PzugjF0+w3rKFgsHBZnWUMZOfjvlXiXZuJ2b00iosoM+k0VBiYtMeel/7AdnB\nrfgiE+BwYMwHUBUVg0ZCG14nv3iWzMgMD/7Fd2hpvDiv7r0QF2rDqqrygx/8gO9973ucOXMGv9/P\nli1b+PznP8+ePXve1D7b29s5efLkT/k3fOELX8Dj8fD5z3+e++67j0QiwVe+8pU3e7rv/8kRoii+\n64X1t1Je+Hl2ka+nsB38h8OsnawwNZxjalJA1huJSXaWp3J8sfPb7Ap8i6BFpM2qML35KgSNleXO\nXRT1LoKdu7BbTMz6B+hIjDLq3sRQ5jRRgxeLSYc5u86IcxsD8eN0SAGEmEQyILKo34HBbMReXCUs\n+LFotVjzKzSWl0glahFlGUQN48XN9FVOAGAvxymm67CoySpdLLeDfvEkXdoxJle6GE/tYtAwfL60\nUEYpGnFrNIiVKv82mK/DW0mgFi/6Y0zH+2hWFlHLF0Uta3E75VQtXZaRjWV9jknGg9dTJ+Rp1I3i\nFOZZDFXlvwvRbuIBF4Z0EgPV5hVKEaVsJ5utcE/bfRz87d9loC7KnZdO8OO5qkb/eKCOo4U6PnfX\nNK+tXZQCj4S8+HuyWGuEDcCtyDCSbqZSB03uKuAqCtx/tos7PrLE2UjVQCecMfBiuIl7rp3gsl1z\nHFtp4JGJLj58HnABbJ48WaOMxVQF3IdGe/jE9WOIGujfnucnUT99zVlyRZGn5jv48L4FZBkePdfN\n1//sfv6l+3J2zHydRXEHI2zC6vdQMDiwrw5TSeVwJBW09W3E7PW0Tx5AlxdIKlaWPI0MHHmGte2X\nUV6YIVnfRC6wQqq1GbGQoRBeJzN5BGl1hfu/9G0a6xrf1O/81xEX7nWtVsvdd9/NV7/6VT796U9z\n8OBB7rnnno3pvW8mLmTUr4/HH3+ce++9F4B7772Xxx577O2f/OviNz7TrVQqyLJMKpXakPa+WyFJ\nEqVSCZvtP65xqapKuVwmn88jiiJms/mXntveP7oRfX0Zp0eP1atl2x4t08cKDAxIrKU9PKXcipzu\nZa2mB3MgiGp1UUyWMOr0FFISGG2YExHW7W30R88x7txK3/KLaHUOwjEtTlFhSrcNvxqiXMoTN7bR\nISyyWjRj1OtoiJxkJjNIWV+LX7uOVCmQ0LWjUfJ0559iIncLiHpaLfOEJT15bSMdxnn08WUm8rur\nr/iqyqB7GFWVGVvdDUC3Z5aVopUGe47ZOS96nZZO3wTj6R10OWeYma3HbixT511gKreVIftZRpY3\nA2UGG0dZTmmgUk+6UHXg0ooFeuw/YSK9B0U4n/V6hxlb2oHXFsLnXaGsFOj1nOZP9n0Fl6SwpTm0\ncZ0PjXgJRazsvmSNFn+1JnvgRD17nEGenetl09Z5upqLnJm24ynKmHQSz6x1c/dNYygK/ODJPm7q\nnuThqUE+cXOVkTA86aS4qiNhtLB/zyJQBeWvPdHHDZvX6GtKo6rw/WODfPTGUfR6+PbDAxj1ZT6+\nv8phHl2uIWYU2LElyiOPdKCWdXxy/ziqCv96uJubPryEqgrcf2Azey5d5++euYtD87ei6PXU6nRI\nQpEJ304aUyPkLBrqUkliLc2E7PX0TTxFom07bnUJQdaguCqowTBylw3n2DiG3CTaSpj46QBP/9Uj\naEQNJpPpPUnFKhQKGw25Q4cO8dprr/E3f/M3b3l/7e3tuN1uBEHg937v9/j0pz+Ny+Uikbgo1nG7\n3cTj8V+yl58b7/9M99cxFfhXPUa5XCaTyWwQt+12+3/4MDj49acoruhJF0UKmDnynIq+3s7ZdT+J\ndYnPb32Ezcm/p/3MY7jyUdTVWVzJeVKRIO7MAvrQIs5CiL61YcRChZ5zzzJRuQKlYCCk62XJ0E1L\n6QwhwY/VpMNaWmOu0kBX7gzi4irjpatptaXQlOOEKnWY9UZc0gw96hgz2RvoPp95LubaqTWUaeME\n60tGJlJXMuCYgkoOBAFVNqHGNSBXKVzTsU4aNOvkAyEQHUiyhfHAFvpNh4kHJBAspEtOpgMDDGif\nYny56fwV0TG6soUmIYpViG5cpybrOGOLN1BLllbraWyaJVZCbQBEM37KqSD33fSHPP5nf8RV29YZ\nj9s2+LdjazVEtDZkj2kDcAF294f5b8OD7L9unK7m6hSNLd1pDszXcTzr4+6bqso4UYT61gDfHevi\nk7depICJeiOnZRv7dlTVdyUJvnN0iD/+gwlWZCuRtJHvHh3iY/tHMZqgXAHVX6LkNKGqMLrk2QDc\nYhFklx5bW4WxRRf/fHAzN314CRD4/rObueWGZURRZU/DQf75dz7LTtePyOeXmHENYIkuYMtFKChN\naB1mKoUifcNPMjFwPZrFsxRFN5VMFLFswJBZpnb6edzCSQyaKOGT6xz4P3+I3fbenjf2+vsvnU6/\nbfnvK6+8wvDwME8//TTf/OY3efnll3+mL/RO94l+40H3QrwXQFeWZTKZDLlcDoPBsOFg9qvGob//\nMdK0ntWxFHnVyFrYSDogUX+Jmxee0bPvmgSXdB6i13EYq9bOutpNs2JgQdyGVzAzoW6hqK1jttTM\nmu8ymuUZxrRDDIqjFDGTMLZQX5pgWa6npThJ2/qrjOY+hN8iQDnDTKmHbnsYKikKsh5/aZ2VsJ8K\nFuazfXSbqqN7BBXEBGjUKlVvLLqZfvsCHcYzTEw1MB7aSa8jgJ4IOiGPkhUpFzppslzk6cp5CzV6\nDRaxKpHVqSmSsc10mGM49YsAdDlPMzZ3BdFAE0PeM4jKKlLeB+gIxFtYXBqgRTMOcganaZH/dOen\n+KuP/gm37Tm7Ubf92HWz/OhkDw+eGELfkuWOmxe4Ys80w7NVWtmp+RqGkx4++ZlxRtcuvp4+MdzL\n7hvWKGgu3tSnZmvJOazU9RbJ5qsHeGm0CW19ms99dp5/H+4knRP59zNdfPKuKijv/WCAvz/axUeu\nG0FvgHxB4IFj3dx2d5Ab75rmfzzXRUKvbADuvx8a4kM3RbjkygQPjXSiuEVA4PvPbOLm6xfJZERe\nGm7i0iuyBGIuPnrti/xfv/tf+YzpM9xc809k7TlMq4cpZ7MUM1qSbb30jr+MUONAv/QCNuM4ndL3\nafZP4LbFKSRyrBwMcvi+x7CYq72KtzrW/NcVF84tmUy+bdCtq6v6FtfU1HDrrbdy/Phx/H4/oVD1\n7SgYDL6lssUvi99oni68PU/dt3KsUqmE0Wj8qeUXGAn5fH7DVOfNOphdiP27r+HZF48RLWcxuM04\nOz3MDWdoHjRx5pwBcznLlh0JWo1HUNfDnBZ3MaCsMq7rYrAyw7TYToc2QkgyoTGasOXXWTAMMFQ+\nyTp+GktzuCLTTBb24TeVSBQ0RNQWBixTREp2opVaBpQXSYd1rJZ24DcnUSsZioKXdNlBr3iA5bVW\nIsVuaq0ZUBKUVCcWfQF9MkmmZEfGSjTrpcUepIZTzKztIV+yUCkZ6PCOUWePMD61jWjKS40li820\nSpMtxexKF7GUB5Mg02Q/TirZTq5oQ1b0hKO1DHhOkC8ayJaqirVW7xgLSy3cs+8bPPDXn+G2K1+j\ntzPO80c66TxP8ToxWcd0Gm65dpGmuqpIwm5VeXnEx+SKm66dIbZuSmO3KZyetOM1FHhkuJebPzJJ\nfX2FilgkEbZxet6PuyfJzu0xenpSPPjjTcwGvAxdvkB7W3UYp8Nd5P4DzXz2nqqZTaEo8L3nhrjz\n91f58YFGGh0Zfnh6gFvuqlLazo43oGnQMLFYT0dtiCeP9HLdLSFUVeWxp9u55sNJGjsqfOubtezc\nmcVqqfDMK13svSbG6JgLraWMpwaOnfRz5U1JIoEcH7/jNM78ONt3ncYdfJ6trSfxGE/T4Zqioz+G\nUxunApTTBdbORsnOSLz6tR+g017sJL7er/a9FpIkbdDLjhw5Qn19PQMDA29pXxeky3q9nlwux1//\n9V/z0Y9+FL1ez9TUFHv27OGb3/wmLS0tXH311W929+9Pni78ry0v/Dyfh3fCVOdHf/NP1CZqWD4d\nY+5sBmx2xmetFApaXFtrOPFsHq9fpqt5jD/f/WVk5xwDuROMWocYks4xpe+gV79GTDFhVOP0pF5B\nlbS0rxxhLPNB0sYhnOoiU8UeemwBqGQYK26iT3OCfuU4Y8F91FklqORYybXgMqvYWaXbPMPs4k7a\nHasALCcbMev0dJlfIbYoMhXaTb29gENXBRWLkCQR3kSdvao6y0t2KgUzSjQHSvU1PhCtx1ZJUckW\nNvi9iaQLXcmO3xREr6lmHA2uCabnLiW23symhrOYNGe55vIHef7Hl3PNZc/SUmrJgzUAACAASURB\nVF8tZ+gNoFryzK1ZeOiVHup2Bfn0Hy3y49d6N67x6JyHkleD5DHQ3HixzNDcXuEbhwe45xMTGM83\nvvq6Mzx6zsnAniW6u6qS4HIZchaRklOmrraa7Y9M+zkVrmfvJ7M8e7SbeFLHw0cGufHuAKIosv26\nLPc9tYXrbqsa8rx2qpGcqKV3c5nLb4zxfz+0jcFLquOiHnu8kQ9cm0CjETnwVD1Xf85MROvlnx7s\npKs3x+SYBUUHnjqBI6/UcOneHC89Y2TrPpnjL1ro26thbUJl8AYrUhm0HicmN2STkAxLhGazLC9U\nkNcEjn31oZ+q3b7XVV6vz8LfbqYbCoXYs2cPW7duZffu3ezfv58PfehDfOELX+C5556jp6eHF154\ngS9+8Yvv1OkD74NG2oUsN5/PIwjCL53a+3bjggLO5XIhSRKFQgGNRoPZbH7HSNqvbwj+4d99mRdj\nI7g7PVhdOuo3e4ieCbPpg2amXynidcvotTKDHxT5yXc1ZAvdRIpXI4eDSMYWiK8xrVxGiyVBLCOS\nFzx0CiNMKztp0q2SSquktU30iq8hKBrW1j002iKMJ7aBqKXfdY7xRAdarUi35iirwXbSlTYESvTX\nn2MssZNW5xKVcBxVa2ItXQW2Otc6Lt05xqc+CIIJuzmJz7dIWqqjGC6SzrTQ1zHBUtyJxZCjlPKQ\nzjgY6BllNuynrWaVyfGtIIjU166hM6+hUWuYX2lDr4+y98p/5K++9C36B6tG6Mdf8bDJHcPnkSiX\n4fHDfSyG8/zh55Y2rmsiDuOHW1hLOum/eon2nhILM3p0a3oGuyM8+kIXvu1pHC6JzJiRS7ets7xq\n48C5Dq77eICD3/fx8VtGCYYNPHe6jX13xFma16Jbh0zeiOxT6N+cB+C1lx0EpnV85FPVB8baipnj\nk41cdk2Slx814/MUsfol2noUshmBw4cb2X1TnokTGlZGNNxyTxiNRuTxx5rZvT9DWdJw9AUb2/dr\nOfOSQCKgUt8skgkXuOxWePlpM4NXw6tHnPRdWmb4kJme3QqLYxpkgxm9WWJhTCafr1DUWclH0uhG\n07z8te/83N94Lpf7tQmO3kxcODeLxYIgCHzxi1/k3nvvfS/OR4P3M0/3wpyzd0K48KscK5FIoNFo\nNgD+7UiCf16kUqkNhQ7AV777j9y//ArWehsWrwm310AuXsJmUvF3W0jPR7CatbS2ZYkU/WhlmWee\n2YIYbWVU2cugMsxoaTttukUCWTOK1kGbMMV0ZQut6jlMUopo3IPXJDER66pycF0nGY1vqQKv5RCF\nlJmF6CU0uNYoSCXixXagTL/7AIsrW8iXG7GbktR4VpiLDdFbO0V4TofTnWc+VOXfWo1hmh2vMj5/\n08Zo9EbfOGbdOtPL+zb+/rb6VxFklfm1SzeWDba9htURZssHn+fOe5/FbEmRXzWwbXtwY5tHv91F\njU0iYdBy5W1hAssa1HXYPFT1vz1xqp7nj9byyc9NY7PJG5977LuNCMhc/dthtLrqg/O1gy7UiAah\nUWTrZdW3mHRK4ZV/8+HtlNi5N73x+fv/sYGh7Qk276wC7tSYi+WUFYNFoU6bQaOVWY7bGbq0WoI4\netDL4rLIzTeFEEWVQ0dauPzmJIqi8uMfNTO4N8HMSzaoFPng7WlKRQ1Hnnez82aVmTErMhVqOjQM\nP6fD0w7TR1V8zVrKmQJGj4FwXI/HL7O2qkenh1RRh6TRgN1BqVAmemqe5ryVH3/5az/396coCoVC\n4V29j95qvPGB8Pu///v85V/+5XtxVA+8n9kLF+Ld5ulWKhWy2errpcFgwGazveOACz/bKf3iJz7L\nf7n844TPhYiuSqwHVMqiHk2Dl8XTacyNbpI4ODvnJ3A8irelwg03HuXSO37MR3bfx5pOpE88xkK5\nlUZrFm0pjKooDOWeJrpqp1CoJ1dyMpHcwoB3DpQ8o4ntDLhO0m89zcJcFyatDVFNsZZoQKcx4zNN\nM+CbYnpqN+3+ICgS6YKTlWA7/e6nmR3xEE+3s7rWTn/jMKJYpMG6xvjofgZax9BpIqAoOHVllqd3\nMdAyDIoMpBAlL8tzW9jUeRbUKFde/S1u+sy/cOsnvsaX/uZh2ruS1NarTM25kOWqLPSVl+uIG0WK\njQJX3lYF2fpmmZEFP6trZh54bABNr4aPfT7GY48NAdUb+KknutH3mskafBuAWyzCSrSGMykXWz6Q\n3Nj2pYM9VNr02Pzaje0eeqCXSz+pMhNqJZXQ8NLBZqKqjYEPyHRuVnn5TBNnZzwbgHvwKR+eIdj3\nCYFDx2p58ulmLr85SaWi8uQPm9l9exarU09WMaE2Wjj8bC0HD9RWAXfUSkWVqOnQ8OpP7PTvt7G0\nUsPQ3W6yeg/2D7WzXKzDdUUTS7QjNNchdbchNHpR7XYSS0nWTqxymaHzFwLuez3e2OD7TRxKCe+j\nTPfNcGjfTLxetmsymcjn8++q8i2TyWAwGH6G9TAyOc5N//S32Le0YtErWH16LGYjuWgRp1VFkEp0\n3uRi/J9naN7sohTL0XO9nfB0nsCEldSSj6XJ7ZTTZpbzvWg1eup1c8znt9BmWyCcMJKjjkHXOVIF\nLdqMhEWrMLraB4KJ3oZpZsMeFNVCv+s4ibiLtVgVwAbazjG+1kJPY4iFUTvd7cuMzFVLFFBkoOlp\nxiauBaGaPbW2LGPSn2Pi3I1VBZmq0j80DgQYH7kaX/MZdlz9LDff+SS7r4kiCALLsyJGSaW7P7Hx\nvTz8zWbstQqX3JJBr9dw5Ekn1+ybw2yuguIzj/ezvp7n7j++SDlLRBXmj+pZT/i4/K4Yer2GWFAl\nN6vB4cxxZqaO3bcVUBSZkSe07Nkb5CdPt7H99uoxThyw0l0fZGLex85bqo05VVX5t79zctXtceqr\n7DUOPdWAp79IPqnBpeaZnTKz47Y8eqOW1Tk9CytmnH6ZylKWTNbMjo8oyBWF535Uy/aPVChmBE6+\n5MBiy6CJFbDWKbRs1XH0OSdbbxY587RC6149M0cN1O7UMH9YwrPbRWS8iKoxIdgE0oEcieUiGUkk\nvxblc+2X8qcfu+uX/v5kWaZYLL4nM903ZuH79+/nwIEDG6N73mPx/i0vABvmyYVCAbv9neEZ/iLZ\nbjKZxGazvWtGG9lsdsMQ5GfW5bIM/O+fQT/UjMmsx+LUYXQa0ahg88uwXqRhs0gyqKecKaKNxhm8\n0cjc4Qpd1xrJxcocfdiLptLEqeObKZe7adDPM5fbTItlDjUbwigYEEsKk4FeEGwMNJxlbKUdRBu9\n/teQs0Vmlq7AZk7hcy8xF6y6gA00HmBpvoVsvhdUlYHeESaWG+hvmmX01C56eqYJhM1kCo10tZ4h\nsl5Lbe0ak5NbAYVL9j6It2WOqz92is17Q2i1Asf+zcr1d65u/P0vPOzkhlsWOXSgh4SsxdORo8mV\np75F2tjmyCNOzJYKWa2OrddWWF9Q0aYVejcnqFRUnn+8jVBa4Jr9UVzeaplBUVQe+no9Ax9I0rfr\nojrp+AELgRkdt/5vyY1l5466ODescPvvZjAYBYp5lRcfr2HTHSrnfqjhmlvWePGJWnquq2CxaykV\nVV74vpmOvhJDe4rMnTWTkDS07dSTTcCJ5/SIWNhySYDRky62flgkE1GYPGWk61ozSydUZIceVSoy\n/1KJhm4L+ViW1qtMrJ3TULPLzPyLEu5L3QSOxSkZ7JSzErG4QtlsR65UyLw2xt/vv4eb9vzHo9Iv\n+OG+F43B33hu119/PS+99NJ7UsTB+x10JUmiXC6Ty+XeNm/vAi3sgvLljVMn3m3l2y8D3Qux6Y8/\nS7Ldjb29OnjS1muBtRzWWi3lPJTX0vRe66BSrBA+m8WoN2IoRRm8xcLCKwXcg3b0JpUj/wgGWxO5\ncYX1kW7kSieJtI5MpZke/ygzaw0ouOjxn0Wp5AjON+N2yaTykMy2oNfmaWsYQ6dRGR3eRFNTlKJU\nIJLoAlWmv+MnrC70kc60AlBbG8LuPMPq0m50tjU6LplkcMdBtt+wQPv2IqFFFTEj0rGpykSIBRXy\ny3qGLomyPGNk5IyTlUU9d/x5buNaHP5XC7fdXW2YnTjkYXLeTvegxMCuzMY2rz1hxG0rEc5a2Lq/\nCrSHvuvgw/fOMT9m5+yYh+13lDn17xquu6NaJz70mB/XFoHUuobu+ji1LQWefaiN+itKeBq1vPpt\nPbuvCjI24mDTzdXbpJBRefJrOm7/8wJGk0gypOG1l3xsuUMhtV5m9imV9ktLNAxoiK5qmB4x0n29\nkVxC4eQPstQ22WnszbE4Y6bzGiOzL4O+SYfRoWP+VYX6az3MPpml7kYPU99fQttoJT2RxdTqIJeU\nUK0udI1OiunK/2TvvcOkqs/+/9cp02dne+/ALktHYBcsQeUR1NgTWzQxRmMSnyTWKPokMfLNz2ie\naIomRh9j1JgoUWOJSUAUxUpHOgi7wLK9zLbZ6af8/hjPOCwLLGxf5nVde8FsmfnMzJn3uc/9ue/3\nTdgfwrOnFv+OGj6+ewkFuTl9Ov4URSEUCo1I0VUUJXrFqes6X/7yl3ttZhghjH3RVRQFj8dzwvOS\n+tq229XVNSgbaAZerxdJkg6rBe7JonsWs8UWIqkkByEQJCE3EVESkBtbyL92ErUvbCM9346uKmSd\nkULnvja6t3SRke8g2NLJpCtS8dQH6G4xkz1DpGp5FyEphVBLGjUbJFoap5EY9NPZ6MQUtiIqDuoa\nEwiEc8hMbQDRgyeQSUHSHmRNZ/vuSDohOclNYuJBnLYw2z+dQ1pGJekFmxCSkykp34YzvY6CiTVM\nXaQgSgKfviFw2pc7kE2RE9uHLzg57+p6RFHA0w7Ln0klIUNmwn/5Sco2sX+TSkGGn7S8iAdCOKyy\n8v8c2DJFpl8Ksiyx8Q0LX1pYh80ucHCPjQ1rstDVTs7/lj/6+vm8Km897mL6JSo5pZHH1jSNj/5k\nxpIY5pQrxOjJdsPSML5uB6feoES/t+09F5XrPHz17hCCINBQaWbP7gRKL7Sw9W8aZZOaqXOnMnFh\n5CO0/nUXKaeEca8NkT+umzavjeIzbXTWwd6tJorPT6Rlr8DBD5pxZaUhql1kzDEhylYObNHJPjuJ\nXa96KfxqOlX/9JC6KI26tztJOCWDjvowersfLdlB0BvEU+mmq6mDpLoOtj/y2+M6/mKFbaQRDodR\nFOUQ0f3oo4+Ge1lHYmyLrvFmnGhi3UhN6Lp+SOVAbxwp5zpQ9LX0Tdd1fvTYH3imoRL75GLsLguy\n10vGeaV0/nMLmbNy6WpSScxT8GxyM/E8B827VTIqEujc1UpoWwfOvFQEbysl5zkw2UR2vx6m5FIr\nmqZR/Zaf8edZ8NSF2PGygKsoC7wC9Z+GkBPzcciteOtaCelTEWWNlKRaPD6RpFyZ1Mxmuus6KJqv\nkV7ip3EHFJYFSUiPCNaa5yws+OYXve3r/2ZjwbWRDbD2Jp0Nr5kRnYmkTg+QN93CtpdDnHbFF9Mf\nVv9V5uxLW1j3dgadWHHmaBRneUkr/KIqYe3zIRTSyDo1RMYEE10tYbq3a8w8u4PtH9lo9CTgmiBj\n7VQomdONpul89I8MhPQwTk1j2oJINL19lQ2P5KC7BuZf0YYoCqx91UX6fBF7qsy+lwNk5IXw2c3k\nzI7kGis/0Kn9TKHiyzquLI0Nr1jJv8SK2WriwGqJms8ClJSqWJJEGpssFJ5to2ajhF9XyZiTxL43\nfaiuEMFaE5q3i8KFLpo3q2RflM6uN0JkL3TR+GE3tonJ+DqDdO/tQHPYaKvxEZBkQvXNTHGHeOPH\n9xxiJi6KYvTrSIx00VVVFas1coxecMEFcdEdLk7UU9cYz66qKjabrU9dOH25/O8PfRHd2LrkNdt2\ncMVfnsNUUUZCohPJ10VCTgqaAFLAjyNRIvX0FGredJPmCOFv7mbSNzNp3tCNM99K2Oun7a0mkvOT\nsFracSSLZJXbadrqw+6SSSqSqN/oJyHLTEKuROsuHxazSNJ4EyFfkLb1GoVnRj7EO18MMPNrkf/X\nbVFITlJILoy8npv/Cqd+PRJphgJhDqyyMPO8boJ+lY1vmFB8ZnDIZM0JE/TKJDo0MsdHRLRlfxiz\nL0zeFJXqbSYO7LTSUqdyzh1fvAcb/qKz6OutdDZJbF/tIpQCSZJI6Ze+aH5Y/7KGzy0x9RoRmyvy\nt5Xv+slI6Kb6gIuyr0by9vXbQlg6/RysdFHyFTX6u9v/0kVYcHLKN4zIWGfN8w4CXT7O/kHko7Lm\nrw6yzjNhT7ey700PwYNdzP5+JBDY9R8Zy2QLriIrB94J0Lrbz/Qvi3jqZdR0M4kldrYt1ci5PJGu\nvTpej4K9LIn9/2zBmSngrerAnpVER7uObIagION3e9DGl4KgE6xvwrd1LzcVlPDATRGXLGNumeFH\nq6pqr0IsCAKCIBwibCONUCiErutYLBZ8Ph9f//rXefvtt4d7WUdi7Iuu4anbF9E1dkFDoRBWqxWr\n1dpnoe7r5f+JEhtx96TnScJkMqFpGsFgiLJb76FzfC62gkwsgoopxUSCQ0BMtqB+5sZp8WKZVoSc\nodP6YhUZBVZCbi/jvpFHyB2gq0onZW4C+5/bi8spgZZIuLGBcadKJI2HquUCU66OtDbveDHE1KtE\nRFHgwLtBCk5RsSVL+DpDtG+RKJ4fEcuNz4mcel3k5ODrClH7kUBCqkZXi5m2mgCCw0rKVJ3sWYls\ne8HHvKvCiFJE0Ha87Kfi8jCCINDRqLP6byJJeRL559qwJVmo2xQkIzlIenFk48tdrbH5lQAF5zjI\nmhGJOA98HGJcoQeTVWP7KifWaVbatyqUXxZCkkWCPo0dyy001Oos/G8VSY489oG1IpVbFE45XyQp\nP7JhumuFjC/BRvdOlfk3ePE0wqZ3kphwbeTkuOdpD6IIE78V2QNo2SHQUqdjK7EQXOtDxEP6hSlY\nnBaql/sRJiXhKExgz58b0TQTRXNC1O+ykn9VCh0bfATsFkzJNhq2a7hmuehY34E8JRvvgQ4E0YLf\nZUOp6SSkmdA8Xfj2NaHuaeTlb1zK/PJZh3VOGsIKXwxyNcQ4VoiN3zc+EyMpXxoMBhEEAbPZTH19\nPT/+8Y955ZVXhntZR2Jsi65h79je3o7L5TpiZYHhbRsIBKLTTI9353OwO996M0o3Jh0bvg8WiyXq\nOWG0Jvv9fs77nwfZ5LRhnzUJU2crtgmZyO1eREXBfsEkwm+ux5aehjMzgOLMQE4O0fZ8FdmTXIS6\n2sj+r0ys6Wb2veBh3DUJaJpG7eteUmeF8O3sxLtLIa3YSshvJdziJn2cibBiIdzUSEqRnVBIxl0V\nICXPjMmsEQpqdNX5cBY6kRJCtNeHmXpxEraUyPuz/VkfFdd/8Rz3v+Zl5lcjt937FapWdGNKS8Ix\n3UpKiZOqv3cw86ov3tttL/jILwmxf3ciKadFGlasHh/ZMz6vue1S2fhnL+lzHOSf8UUp4b6/d+BM\n0+hUrBScG4lCdz/joeKybta97iLrQhv2NCvV/+pkQlkXe9ZYyf2KC7PdgqZpVD11gISpKWSdHtk/\naN2m0NxoQmnzM/EcgdatEEo1kTw9hYA7TNXybjTdwvhZGi1bgiRfkoFoljn4ejeui3MItak0rmrG\nZHcgd7ahZSbgyHXi7dSQc5LoOuBHSHMRDITxN0sIeRa8m+pQwwK+pm6CQYm0PbvZ8diS6HERm0ow\nxLPnZz1WVA0hNqJJiHxejGjY+Hc4hThWdHfv3s0TTzzB008/PSxr6QMnh+geqbIgtmutv227Pl+k\n82iwdndjRbdnJYUh9LGmy0a5nNlsxmKx8NCfl/KL9dsQSydgclmxWVTkc6agrtxK4sw81EYvZFgx\nba4kaX4hpgQNb5MZ+2SZ1ic3kViQh9PWiSTpZJ2bQtfeTrSgjaSpZtyferAlmkgYZ6JjZzcmUcRV\nZiHYFaBtDeQtiuTCK5/1MOX6SM67eUMXSWkCiUWR13v/i26mfC3y2oV8QdyfhBh/joTXrfDZsiBm\nXSFkd5Jyup2gW8AuKGRMjvxtV72f0AGVzDKFz1ZZCEkK4a4wM76REn09qpZ5KJoUoGajGTXHRMap\nGVQ9187cb0Zes7rNOpUbdRyJOtMuj6xD13X2/ttD444w8xZnR+9r/7saNRs9VHzbgTVZJuRT2fWq\nhmtRMq3/6mb2dRqV/9JgmovE8Qloisr2RxrJnmsj7ywHrVs1mmpFMr+cSrA1zL6lTThT7WRXaLRs\nDJB65Xi6tvvpcis4vpRLyysNyOflE97Siae2Bd1nQxK6kGQHQV0j7FUImax4QxKaPR3B0422Yxtf\nIsyy39wXXbcx9NH4MqLZvgixoihRYTOOtdioOFaIDTEeKiEOBAJIkoTJZGLNmjUsX76cRx55ZNAf\n9wQZ26KrqiqKovRaWdDTl6G/VQeD3W5siKiRtzLWLYriIWKrKAqBQABZlqM1xAZNzS3MuPMhPBOn\nYslMBFnFnpeG1tWBOdGGubMF+zUVeF9YjyXJgVxfQ9K5EzAVJND5Zh2uS4rpWrUbdb9GgstMqKaR\npMmpuArCtG4IMP6aJARRpPolN0WXJSCaJJo/6SSx2Io9WybY5adjjULBosgH98CLLZRdbUcQBIJd\nAVre7UB2uehuM+NvacKcLOMsT8U1Ppnqf7gpu0BEtkZOnHtf6mTGZaCrUPuJQs02H6kznOScFXEa\n66rtRqr1kTvPTEd1mKoPLbTVtjN3cU5UCIKdAdpW1OHxp5BybhKOTAfd+7uQGnxYXToHtkDuVZmE\nuhTC69vJnC2yb6WO6/w0LC4bdS83kJal0OK2kndp5HF9zWEOPFNJ8Y3F2NKseKuDHPhYIOuabHz7\n2vAsa8b1pUQSp6fQvdNHW72A45x8vDt9NH9QT1JqAqIcQpxgw1KUTNt/GjBfMZm211uR5iWh7uwm\nWJxIYHsIJjrRdnagWa0E/QJaqxttzwGEqir+ePVCvn7xomMeV7Ezx2K/YoXY+J7JZIp2eMZOZjHE\nNVbIDSHubbNuoIU41sB8xYoV7Nixg/vuu+/Yfzg8nByiG1tZoCgKPp8PTdMOmTbaX/ozJ62v9+/3\n+w85ScSOplZVNfpzq9V61Hrhs37wM9arNqSsbKQkO+q4fCzdbQiLJsE/NpBQnIoY8mG7Ygrdf1qL\nOcmO7PHiHG/B8aUcPP86gGNhHpLVRPuL1SRekYt/w378q+qwjyvAJoUIHGzCkpmN2awQbjyANScH\nJSyiuxsRXQkg2hEkP+GGekzFOYhJOmG/QM4MJ9bsSF58/7P1TPpmYvT92f+XZqZfZ8PXHKR5s0rb\njnbsczJI/1IkCm1YWknZVanRSG3Xn2sQBTOus9JIGJeMpmm0vFzHxKuctO8NU7teQcuUSE42kz4r\nEt36m4PsfKGTtCkmchdGplLous7e5xsI+zTKvlcEgBJQ2P+aF78/QOkFSVgzLbR86KVLlEk4PZ+u\n5QexBDtRclJxlWei+MLUv9aBfFE+obfqMIdDiNNTcUxNpWVZF0quDeu0NLr+cZDwpASEDU2E3BpJ\nZ6Tg2e3FcmUZvjfr0M4sQFl1AHV6McGdTQhuD36vDAdq0bpDZLr3s/uZBzGbTzyIMITY6Og0iI1i\n4YvW9J5a0ZsQG2I8GEJsWKfKsszLL7+Mx+Ph1ltvPeH7G2RODtHt7u5GkiRUVY2WvVgslgE94xqR\n6EC7MBl520AggCiKuFyuXvO2xs5yX08iT7+6nFv+/gHCxGlglRDHFyE11mPOthLOLgCbH9uuehyT\nkwnX+LBdU4Z3RSXmjjZk3YWpcx+u0/OR8u2E1nXhOCeLQG0nQn0Ie0UywUYP+r5unKdloClhvMvq\nSbooMl/L/WIVWVflIIgi3ZUd2AIhEqZGcqvNf99H4RUZCJ9H8PUvtZB7lkTXbpXWqjDBDj9pl+Xh\nHJdK0N2NsrWNrLMj+VdNVaj7y37sqQ48CCSfV0zjy3WUXRmJugGaPmyme3sbrvOKcRZHcq8tq5pI\nzQjj3gnhQhdJ5Vl0fVBNdiEEO1VqtuukXT0B/0EP8p52HKkadTUmUi8tAqDttUq05hDJV+ZhSXYQ\n9oSo+Uc3TLDgaA/jGC/TWeXHflEJqi9E+xutBGdnIK+rwaz5kS6aiIhM6z/dWL8xEWVtC51YkIqS\nCH1YTzjLjv7hXoTMNGjvIqQ4QAqjd4HkykBxN6JXbuMruWaef+jufh9zxh5HOByOHlPGsdgzIhYE\node8bs8NOyPdYHy/5zTfWEE/XiH2+XxYLBYkSeJPf/oTKSkp0VlmI5CxLbqRHfwgHo8nKkr99bU9\nEgPt8RCbtzWbzUiSRCAQiKYMBEGIRiJG3vZ4n1c4rDDpa3fTkJCFkF0IaclI6WkoFhWbvwu9wAmO\nNIS2WhwtbsxT0lAaujFdNAldU1HeaUB0+VF3dpCUJKBZklBbGkmeZ8U6MZXu9W0klDowZznw7m3H\nFNSxTU1E0zTaX6oh++rIGO/mN+vJmW8n7PbRXQveLc2Y0lKQzDrdQQ9yciLp50fMC7zr60jMELEV\nRk5ubWuacEpefI0iHV4bQr4Juy6SfsYXzTANz+wlZbxMU60Z26JclHofKaIH19QklO4QNcu78DR7\nyLtiPNb0SJTtr/Vx8IX9pC3IJGlOJgChVj+Nrx/AnGQl7fIJAHR80Eh7wIrgspJOF6og424B14Wl\nEfe5lytRWlrJuGwierdC+14vpgumE67uwrvejTIvH+lfuyAUxnHTDILLqgicWopeEyLQraO7ElAO\ndBC2ZyB4/cgtXsJOB6K7DWpr0VqbsdXu5Y37rue08mn9O+iIpKeMPY6e6ameHCk1MdBC3HPDride\nrzeaavvNb37D9OnTufTSS/v9WgwSY1t0Q6EQbW1t0dn1g9nCOJAeDz3zzaIooigKwWAweokGkcs4\ns9kcjW5P9GTyk9/+hd99sBctKx8hfzxSoAMtJQM9NxtzQyVqcS5MSESp8DdCDwAAIABJREFU1rCa\n22DzARJn5qK6Aoi2FMxzUvG/uQfr/DyERDue53ZgnWNFaPAS3lCLa1IamiIiNNUhJ7uQrDK+5gBC\nWMFa5ES3aPjX15B+x5cQrVaC1W6EWi+Jp0cu733v7cM1NQlzemTD0P3ybly5JjqqZUKyQNjjJfuq\nUmRHJFfsW3MQV4YMok7z6gBhWxiLJJN6UXH0Obvf3IvQHiScn0LC2ZGpvd7Xt5Mxy0H7Og+B0iwc\n03PwLdtN2mQrbeu8BHNdOE8rItTSSXj5PmQT6F8uw+RyonYHaP7LZwi6Ts7NUwg3+Gl5uw3z16cg\nSDJdj63DJIdI+OZMfB93Ek6SEMrHob65B9+4bEh0oT77HmpWGZK3ETlFRjfbCYQFVI+IYJbR97Uj\nO62oNXXo3gBip5tTXT5WPPmTEz7WDGKj2/7scfQmxMaeQ28bbL2VsMU6A8bmiI8kxLFeuvfffz8X\nX3wxZ555Zj9fkUFjbIuuUXcbDoePWOM6UCiK0m+PhyPV28bmbQOBALquRz8UxoENIEnSIV/HU/bW\n0dHF9K/9FHdSIWQVIaZlo9ONnJ6KZjGhB3zIATdKaR7a3DJM/9lC+NQJWFetwupIwpJqxldVj/Om\nU5AS7Hif2Y3jWxHzcmXpRixXzwDA+8wWkq8vQxAE/O9V4ShzIWe70MIh/K/vJ+WKiDAGPtqLvTgR\nc5YN7842/KuqsOa46AonoBfYUXd3kX3DF1Mf2p/eQv4NxYRbvHjWt9Nd2YT1nInYp0S8BYJ17Ui7\nmnEUm/Bs7sZblE64NkDmqYmYMhyEO/y4l7egtDSRfv0s5IRI44P3wxraP60n6fwybCUp6KpK66v1\nBHPtiHs9pF9dQPfaVnx+EfncyRGReGwlWm46jsunodZ10fFOPcLXZiMEVbQn30XKSEKcV4Dvw3b0\nK2agbWwj0ByEiUVYPthNcN4MeGsPTM3EvO0A4eRUpI6OSFVCMIjauA9z3XaW3ns1557df6NuI2Aw\nmUzHVZveV3RdP6xyIvaYPVrVBBCtFY4V4lgxNn7nqaeeoqqqihtuuIH58+f3e93Lly/ntttuQ9M0\nbrzxRhYvXtzv+2Ssi65REjbYm1zwxfDJE/F46NmU0Vu9bSAQQFGUI+Zte0YXRomPIcCyLEejjKPx\n41/+id+vrEQpOAVRCCGl5aK5XGgdboRTZ6J1BZHcB9EkK5JLQVkwA9O6zwhXTAKnFeHpNxBL87H5\nWzD5PQjpmUi6j7AviKkgDdmhoG6txTYnB0HXCa/bizylCM0PenMrJimMbk7EH5LR66uRy/OQTp8K\nokj4rxtJvi5ifq6FgvCfnbguGU9gZwvBvR6CldWIl8zFVJILQPjFT0i7ohRd0+l4pwHvATfW8ck4\nzp0Ufb6BpasxSRK+/Ews80oB8P9tI848mUCLgnLhTESrDXX1bsx1LQRFC9Jl5ZH61YYugn/9GNPC\nScgzi9AOthP4uAbv+acjVjdhX7+ZUHEO0tnT4NM62j8Lwn/NQlx3AGVXHdZEASnsxZedi2BKQXOH\nEdPsSPua0VzJqK0+zN5OQoIJufYAakc7YkMV83IlVjzT/915Y7/AOMkP5hzBnvRFiI82LihWpI3P\nxs9//nPef/996urqyMjIYOHChTz55JMntD5N0ygtLWXlypXk5ORQXl7O0qVLKSsrO/YfH52TQ3QH\ny1M3Fk3TjtvjoWfe1uhmiy0BO9G87dFKgXpGxD3vU1VVpl98FwfkQqSMYlSrgCkli3DYh8kSsYcU\nzj4FXRCRt29DsaUieyvRpk5Ay3Vi3t9CaMEc2F+L2BFCO2UcVNUgBYLo04vQ3G3Y91Wjz48MDjS/\n9j58bV7ksVfvxlaUiFCYGrn9lw9wfGN2JNLv8qC/dwBzvgW90YevtpNQdxDL9xYg2h2obR3YN1Zi\nXjgRXdMIrj2I773diPMmYF4QsZpUN+7FLmsIkoZveyfeskKEz5pIXZiDlOIkvKkW3x4PgXAQ5zll\nyNkuwtsb8G7qwF+YRUKXG8f5RXhe3oc/LxNhRin65r2Yt+xGqyiBaSVo1W3w0X58XzoTYdM2nC27\n6J51CuRlY3lrK4GpMxA8QfTNdXD6TOS3V6GYREytLYTDaUhCJ4Iqo/k8iAEFRZOhu4XErn2898fv\nMbG0mP5gmDgFAoFBi25PdF19jYiN3zcCDOOzceWVV7J06VJaW1upq6tjwYIFJ7SWNWvWsGTJEpYt\nWwbAQw89hCAIAxHtjm3RhcHx1O0NY2RPSkrKsX+ZiJjGOpcZnT8GR6u37c8aY4VYUZRoniw2GjYO\n7lf//SHf/cUb+JxZiFnjwZGCpHtRJs5AaNmHJMroQhitKB9t+hTEtz5Cm1MK27dh1nyEk7LQ25uR\nJ6ejpjgRWpsRSovQc9PRdh/AYVbRpuSjhYJY3t2IcOlsAMKvbcA6LRmxO0C4KYC2tx4tKRPBJhII\nBbAWZCCdHolK9V37sAkhxOmFaL4Agdc+Re70oBZkEZo/F0QR+e/vkHBDOboviG/lAZR99ZjKixBP\nnRJ9XfQ//gfVZCN8yelInx8n6t/fxRzoJrDgNMTszEjOccU6pN1VhG/6CoLdirC+ErXaR3Deadg+\nfAfJquDNGIc+cTLSlr1Q14Jafjq8tRKTt5nwhFngaYecTCTNhLCvBiV3IvKO7WjZxYi1NaDb0IPd\naO4mhI4maNnDt8+ZwG+W3NjvY8C4qtI0bcij2xOlt+DBSLnpus6GDRvIyMhg69at/OxnP6Oqqqrf\nnaH/+Mc/eOutt/i///s/AP7617+ybt06Hn300f4+nbEvugPpqXs0YodTHi1qMHaHVVWN2kT2lrcF\njllvO1Dr7nlAa5p2SCR88/88wUufuNFSJyAnJqKazAiyBbMYIjCtHAIdUF2LJTuFYEcbwqmT0VUN\nKaSglk5A2PQp+rgCQIH33kXIy0SwWdCa6rC4bJE5XZ1ehPYOKCtCt9uQD9SgXHoOmEzQ5oZtlYiL\nZgIg7vwMe6qGnpeCtL0G3yf7MLks+EtK0aZMg72VWDUv8txx6KqK8Ml2xC276Z4yE+ZE7kPfvAOn\nzQctXsI+kcDpZ2HesAHzJBdaGEKrm1AmT0LweZGDbQhOM8IBN8EzFoBsQv73P9GDIdSFiyDBhbBl\nD3pVK0wah7RjB2pQg1Nng2RC+ngT6pRpiB4fwq4qVIcTqmqRE0C0OsHTTUhPQgp2gE9BC4fQW+oh\n4GVamoePX72v3+b4xlWfMVp8oEsmhxJj/8QIFH70ox/x1ltv0dLSQnl5ORUVFdx33339GtkzHKI7\n8k9/x8FQjWE/GrF5W5vNFm3nNUpsINJZc7S87WCtW5blQ8Q9VogVReE3913PrxSFM698gH3uDEge\nh2Dxo6YXwJbtmMUwuiyiajLMOgfh/XfQ01Ogox52NmDOdhF89wOYOwsuuwLx449RTzkFZp9OcPU6\nKCyBtGT0mgNIwQDqpDKUSTMxvfYfwlcsBElGJIj85vuEQnY0v0ZXWwPiuFy0U8+Ci88ktGYduCJd\nYWRmoKx4H2XDPsgtQJl1NuTPR1ixDGbryDur0Pd24OkOIZfmo5w5BXQdRXYSemknZOXCwkg3l7R1\nJ+x2owsqoQvPhY4uTKu3EM6dDlYH8rIPkSQInnI6nD4ey+o1hK0ZUJCL9K93UMMm1DNPh/X70LIz\nkJKyMbV2oE6cjbK7DuQUZG8rJhW0kAvd0wRt+0gO1/D2c7cwqayo3++x0TgD4HA4Bm26yWATW2Fh\nBCz//ve/2bZtG8888wyzZ8/m008/ZePGjf3eNM/NzeXgwYPR27W1teTm5vb3KRyVMRPp9tdT93ho\nb28nMTHxsA2AwcrbDiXGJd7evQe46MYnaQy6EFMng1kAqx0ps4CwxYrcugfFWYBZqCc0bjqCHpnN\nRUER8sZ3UBwOQERq2YOaXAQmGdlTje5KQbRY0TpaEEwSij0d0JFrP0VZcBlk5MGBKgQ9hD71842w\n9eugtAASrJiq9qHt3IFqTYQJZVBUCvs+w2RVCE+fAnv3Ydp7kPBnu+DqayHh81TT/r1Y9m1HlZ0o\np8wHswVamjDvWE1ITYS5c8Fqh452WLYM0pJh4fnQ1g6rt0NOPgSD0Lgf2aSinHo+VFcj7duPOmU+\n8r7tqI31iJIZMdBFWE9GNgfQQzJiMIgaNiF1NaAoJvTWXdjx8tAtFVx+2Vm9VqMcz7ERG90aHZkj\n8djqC7H1wzabja6uLu6++25EUeS3v/3tgH+2VVVl4sSJrFy5kuzsbCoqKnjxxReZNGnSsf/46Iz9\n9MKJeuqeCLFz0mInThgHylDkbYeK9z/6lGt++CId8ngEs4yYUoyuehBdSWAxoeSVYardTTjRAZ3N\nWBJtBM1pyJ4q1LIZ6Jn5yNs+QZl9GlhsiBs+RJs2A5wuqNyJlGBFLRwHigIfrITzF4G7EWnnp2iS\nGXQLFl0l0FSDMKEUfepcAMRt6yA/Cy0zC7bugr2VoPpgwcWQEEkvSZ8sg7x01GoPJKdB/gSkzR+g\nnlYOn+5ADisok8/Asv19lIJMTPWtBJzZkFcGTdWYd32MkpyDNuMspNp9yAcOEBw/Dxr2ItdvQ7dn\noWYUIjfWo4ybg7RnC5rJhRwCze+FkAkh2I3u18Dfheo5iD1YxZ3fmsY9t18N9J7HhEitq5F7P5qp\njFF+KIriCbnmjRR61g/LssyqVau4//77+Z//+R8uvfTSQftML1++nFtvvTVaMnbPPfcMxN2eHKJ7\nPJ66/cFwMwMO83eITf4Pdd52sNB1nVdeXcmtS96hS0tBT5yIaA5DYgG6vx0pJQPF24Apu5iw4kW0\nJ6EVTkeu+gjFagJdg4Yq5OwsNMGM1taInJqAaLYQcrtBlpHT0lBUDQ5ug4XfAEci1FeC3weTIxUJ\n4t6NCElmVF8YU1c34cYGsFhh/iWRhXY0w/4dkJaG0NiCIMloYQ1xQiFabhFy1Q6E2kbCLY2IFaej\n5RZD5R7Emlo0RNBFKCvBsm8vQTkN8iYj7l2NVnsA8sZDwUTYtgNS0hFsSZgP7CaoCsjdDSjBMHJi\nDnQ1o9vS0VrqkEzJaO0H0bxubEozN11dxoNLrj/m630kIe4ZDRv7GEOZphoMjOjWOHH4/X5++tOf\n4na7efzxx0lPTx/uJZ4IY190Yz11e176DzSdnZ3R7jFj4sTx1tuOBnRdP+xy7+PVW7ju5hdo8ach\nOLLQXcUIuBETchDUNsIZc8BXBd2NmNIK0X01KCnjMCXaURp3oZedDq5MxMrVaNmlkJIBjXtADcG4\nKRD0Ytr2b8IFU6E7gNxVi6iH0UzJKJoZlBByZgZK0eetsI2ViJ4aBMGK2u4HWcSkegmfcjZY7FBT\nhVS1EdXfDWdcCyYL+D2w6R2EcDv6nEvAmYrUuA9T7X6CXe2YM/JQHAnIzQ0EU2eCKCHvX4fS3YHo\nSkdQg6j2cUi6itjeQthRgMldS1hxYAm3o4ZA8zWj++pwag3c/u0pLL7r6n69Fz2rUWKFuC8R8UjE\nSMkZdeuyLLN27Vruvfdebr31Vq655ppR81x64eQR3cEckW6IaeykYBh9edu+YETpRyo5qq6u5fzL\nHqGmLR3dnIjgyEB0FaEorZjlIIotHUlvR02fiqaGkQUdJXU61L4NKGBLR/DvR5AFcOWhedswKa2E\nC8+EhFzk/StRJpwKtiTwtsHBT2HOAoS2g1C7Cz3gAykRyWJCTSjG0rWb4JSzI1F19U6o3g4WC0w5\nH6xOCAcxbX8JwZJAyDkeMqZByI+w9WV0XYDJF4DNBZWbocsDkg6EQQ9AUimCJRVzwzaCYi5iWEVw\nb0RV7UhiCFHR0VURPRhAC7Qj+BpIdCj87hcL+epXzhqw96SnQY0sy8eMiI+3Y3Go6JkWCYVCPPDA\nA+zZs4cnnnhi0DezhoCxL7pGBNDZ2XnM4ZLHS8+8rdGeGytEozlvG0ts9NGXTRlN07jqml/y7sdu\nAuJ4BJOM4MxFkASkpCLC3bUIzlS0sBeJVgR7Frraimh3IlhchDrbkBIdiPYkwt3dSHorUlI2uqIR\nbqoGexKyNTL9VXXvhslXgTMdlBDmuncI5c8EdwN0eTAH9hGy58GEz/1lW7YheSpRNStIKZBVDu2V\n0P4ZZquJkJAJmadARzVizXtomgiTvoLYfgCtpQWc4yHQBq3bkMwSgi0T0d9MyDoeydOMqlkxBbtQ\ngmF0XwMmtZ7SwjAr/r2YpKSBrRU3atCPdnwdq+lgJAhxz+jWZDKxZcsW7rzzTr71rW/x7W9/e9R+\ndnpw8ojuQE/rNXx5dV2P+iR4vV5CoVD04DXyuEca2z4aiE0lnOiJ49XX3mfx/7xJo9uBbslGsqSg\nWnLR9RZMsgL2QtTwQUgqA0lH89ZB3iJAxdK+hmDGmSCYkJrfRs04BRwZ0LkTKdCAasuBgA+5ewdi\nQiKaZkcJm8HrRswpRUubCsFO5IYP0fGClIRqHgdJJYiNb4NJQAzpaJoVLel0pPaPkYV2NEUlnHAa\ngihi7thF2BPJxSIL6H4vimM2Zt9BQl4NUbBhUrpRwypawI0WDCEqNaQmerj2qnwe+P++NeDvi9HC\na6SyjjeY6CnExhVhbOv4UAlxbEmb3W5HVVUefvhh1qxZw5NPPsm4ceMG9fGHmLEvupqmEQ6HB2xa\nb8962555W+Py22i5Nb4fm1/riwfCSOBYqYQT4c4fPcnflu6gO1iIjgXRnI5gFhCtWaD7wZJA2DIV\nfO8hSjKaKQ9RrUIwWdDMOeihekyCh7CjAiw5iJ41aOnlYEmHzt3g3Y3oysSkhtAD7ajBVlTXHEia\nCWoQal9GTHAh61ZCWgbYpyK3/QPB6kBXzCjyeJCTENveB60bUXagWSZgCrkJhZ3IWCBYR7i7CQEd\nER9oSWiBWnQ1iF2uYfYpibz22o+x2QZnSOlgGdQcy6qxZ454IB6vZ0nb7t27uf3227nsssu45ZZb\nRm1N8VE4eUS3v9N6Y4dXWiyWqHgfK297NA+E2IN4MMaYnCixOcLBqu/UNI0f/OB3LFvWhrtNQRVy\nEEyZSKYcVG0PgtmFLiUiiq1I5kxULYhKEIs9DUXTQGlAtCSDmIQaakYLt4PrXLAWIXk/QrCoqIIT\nk+ZF6T6IpgfBPhmc8yBQhcX3MYpoBZJR5XJQmpC9H6KKZnQhFcGShynUhhIQ0MJ+zGIjqhZEIAs9\n3IyuONDVJlB9OG0NzJ6VwEsv3YXDMXhOdsPRwtsfD4+joWladK6g0bL7hz/8gWXLlvHEE08MRD3s\nSOXkEd0TndZ7PPW2hqgf6+x8rNbbWEewoRTiWCOUoc5BP/vsmzz22MfU1IgEAmmoahqiqRldygE0\nJIsdQUpEoAtdNqOoLiTRgyCHQHCg6wmowTpMZoUQU0CYhKj+C03KQJLNyIRQQo1IeAnJc5AECVHr\nRAnsi0TYchnoICphNEUDtRlR0hH1dnShGF2pRQ1JCHozFoufjIxOvvrVMv7f/7th0F+j2PdlJGzE\n9keIY5+LcULfv38/t9xyCwsWLGDx4sUDuu8yAhn7ohs78fd4PXV75m17+iQYkUfsz0+UY9Vg9tWa\n8UQx8moD8VwGYi2PPPICr766lYYGB52dQcKKE3QTkskJpILgQxfsyFIyqhZCw48kiOh6Lqq2B1FQ\n0ZiDLOmgf4ZocoLmRw2noYa6MFn86JIDET9KUAA9F1FsRqcOXdPQNStQgyg6sFobyc62U15u5dFH\nbxtUX+aexEa3/ZlWPdj0RYiNaSdANHj585//zNKlS/nDH/7AKaecMqhrvPHGG/nXv/5FZmYmW7du\nBSJdpFdddRXV1dUUFRXx0ksvDapHCyeT6B6Pp65x6WN0wQxHva2x0WFscPR2EMuy3O+0xFCkEgYC\nRVH4xS/+xMqVe2hqstDe7iEcTiQYDCEIIXQ9CbADHgShCEFIQ9f9CEIb4EAQNFRVAVoRhER0XUYQ\nOtD1MJJkQZbrEAQfTqeJrCyRefNy+clPbiQ1NXVYalzHQguv8ZlRFCXaGQrw85//nJaWFqqqqpg6\ndSqPPvroCflQHy8fffQRTqeT6667Liq6ixcvJjU1lbvvvptf/vKXtLe389BDDw3mMsa+6ELE3rEv\ngyN75m2tVmv0wDEw8rbD4UMaG00YYtzTEayv+eHhTCUMBm63m1deWcHu3dU0NHSgaU5CIYXu7i5U\nVUSSdEwmEZfLRFaWiylTCrnkkgVkZmYecj996foa7B392N18m802YqPbvtAzUgd48skneffddzGZ\nTNTW1rJr1y7ee+895s6dO+jrqa6u5qKLLoqKbllZGe+//z6ZmZk0NjZy1llnsXv37sFcwsnhMgYc\nloeNJTYFIUkSCQkJ0UoEA+ODIEnSsDk1xZbzGKVvsflhQ0Th6CLRs0RntJazwRelUyaTiRtuuLzf\n+UBjYoFxP7GlVbFz6gajIuV4a6FHOkaVhdlsxm6309LSwh133EFeXh6vvPJKVISN/ZDhoLm5OXri\nzcrKorm5eVjWAWNMdHvOWIolNm8b629rpBJi87YjUaBirRljKyoMIY4VCaOBQ1Ujk5FH84e65/QD\n40Q50BiphZ5CHPsaG5fO/dnRj/UZcDqdo/qqI3YMkJGH/uc//8mvf/1rHnroIRYsWHDI63KiFUWD\nwXB+HkaWsgwAPT11Y/O2RqfakfxtR1vU0TNa0zQtmh80fhYIBAiFQiO2bO1oDLc/bOwVh0Fs/lJV\nVUKhUJ9SPz1beEerH4dBbA2x0+mko6ODu+66C6vVyjvvvDPYm1THTWZmJk1NTdH0QkZGxrCtZUyJ\nbuwQu55528TExKjYGhgCNZgR1FBhlLMBOJ3OqFD07EYKBoNRkegpxCOFkXz5fSQhPtJrHLubL0nS\nqI9udV2PBilGdLty5Up+/vOfc99993HhhReOiPfK0ACDiy++mGeffZbFixfz3HPPcckllwzb2sbU\nRpphZN7R0RFtSjA2wWLzvEYHliiKfaq3HclomhbdPOxrBDXcZWtHoy8eA6MBoyIlNu0DI8cD4UQw\nUnSyLGOz2eju7ubHP/4xXq+Xxx57jLS0tOFeIgDXXHMNq1atwu12k5mZyZIlS7j00ku54oorqKmp\nobCwkJdeemmwKylOjuoFv9+Px+NBVVWcTudR620NgRqtxJYa9bfCYqjK1o5GbH5wtL830HsL70io\nmDgRejMY//jjj/nJT37CHXfcwVVXXTUiotsRxslRvWDU03q93mhVgnEwjIYa1b5ibMYIgjAguU4j\nLRNrEtSX3KUsy/2ube05SNEoph+t9Nxcit2QPVLFhPEaG1Fxf1tvB5JYP+WEhAQCgQD33Xcf1dXV\nvPHGG2RnZw/LukYzYyrSDYVC0QmiiqJEIzNVVaMmOKM9lTCc5ui9uVXBiUdqY6lOtWeVxYleeQyW\nB8KJrCM2ujWZTGzcuJG77rqL73znO1x//fUjLiIfYZwc6YUbbriBhoYGZs2ahdPpZNu2bTz44INR\nGzld1w+ruRwNB85AphIGmt4mGhxLIMbaTv5gG9Qcy8NjoKtSeo7PURSFX/7yl2zatIknn3ySoqKi\n/j+psc/JIbq6rvPJJ5/wwx/+kNraWubPn09dXR0lJSWUl5czb948xo8fD9CrQAx23vJEiE0ljIZo\nsGekpigKmqZFNzaBaAnbaB6kCIenRobSoKYvQny86Z/eDMZ37tzJ7bffzlVXXcX3v//9Uf1+DTEn\nh+gCvPXWW3z22WfcfPPN0UGRn332GatXr2bNmjXs3LkTi8XCrFmzKC8vp6KigqSkpKO6gA3HgTbc\nqYSBxMhbGp69RlnfSC5bOxYjMTXSn406VT10fI6maTz22GO88847PPHEE0ycOHGon85o5+QR3WOh\n6zrd3d1s2LCB1atXs3btWpqamigoKGDOnDnMnTuXKVOmRCdCxB64A23ufKT1DVf0NBgc6fkcTSCG\n4nU+UUabQU1fhNgwqjFO7pWVldx2222ce+65/OhHPxry7syioqLocFmTycS6deuG9PEHiLjoHg1N\n06iuro5Gw1u2bEHXdaZPn86cOXOYN28emZmZhxzAg2FOHptLG+31w3B8z6cvG0jDnf4xolsj1TOa\nInODnmZK4XAYiDhzLV26FLvdzpYtW3jqqaeGxJimN8aNG8fGjRtJTk4elscfIOKiezwYua1PP/2U\nNWvWsGbNGqqrq0lLS6O8vJy5c+cyc+ZMzGZztKwK6DWf1hd6zsE6nr8diQzURlnPsrWByFueCL3l\nOkf7+xMbrZtMJjZv3swjjzxCa2srfr+fnTt3cvPNN/PII48M+fqKi4vZsGEDqampQ/7YA0hcdPuL\nrus0NTVFRXjDhg34/X7KysqiaYni4uJD6i6PFaWNxVTCQJRNHesxYislBrvBoOdO/miMbmPpOT5H\nEAT+9re/8eyzz/Lb3/42Gt0Gg0E6OzuHxaNg3LhxpKSkIAgC3/nOd7jpppuGfA0DQFx0BwNFUdix\nY0c0LbFnzx4cDgezZ8+moqKCOXPmkJCQ0GuUBpGuJUnq2+ifkY7RWj2Uc70MTqRs7Vj0Vqc6mult\nfE5TUxO3334748aN4xe/+MVxj7gaLBoaGsjOzqalpYWFCxfy+9//njPOOGO4l3W8xEV3KNB1nc7O\nTtatWxfdpGtra6O4uDhaspacnMzOnTs57bTTgC8sG0dC99GJMBLNaY5UttbXutax4v9g0HPclCiK\nvPbaazz66KP87//+L2eeeeawv2dHYsmSJSQkJHDHHXcM91KOl7joDheaplFVVcX777/PU089xdat\nWzn77LMpLS2NpiXS0tIOEYnBKnofaEbTpXfPulZFUQ4rWzPcwIzc+liKbo30VXt7O3feeSeJiYk8\n/PDDuFyu4V7mIfh8PjRNw+l04vV6WbRoET/72c9YtGjRcC/teDk5vBdGIqIoUlJSwquvvkpOTg5L\nly4lIyODjRs3smbNGu69917q6urIysqK1g1Pnz4dQRCOOCFiuDccNGdYAAAM3ElEQVTaRuPGX6wJ\nvEHsic5IjQBRoyRFUUbdlYdBbJecw+FAFEXeeustHnzwQZYsWcL5558/Ip9XU1MTl112GYIgoCgK\n11577WgU3KMSj3SHCCOC7Q1d16mtrY1u0m3atIlQKMTUqVOjJWt5eXmHlaz1bOAY7A/RUGyUDTWx\n4mSkEo5UtjaUr3V/iB2fY7FY8Hg83HvvvYTDYR599FFSUlKGe4knA/H0wmgjFAqxdevWqBBXVVWR\nlJTE7NmzmTt3LrNnz8Zmsx22STdYHV4jsQOrP/R26d2bkA5Gu+1gEetwZrxHH374IT/96U+5++67\nufzyy4d9jScRcdEd7ei6jtvtZu3ataxevZr169fT1dUV9ZWYO3cuEyZMADiklKq/m3QjcaOsv/Sc\nXHu8J5C+lK0Ndcqlp3+v3+/n/vvvp76+nj/+8Y+HTUOOM+jERXcs0ldfCSM/ebwRmhEJjoaNsr4w\nWC28PScJD6UdY8/xObIss27dOhYvXsz3v/99vv71r4/6922UMnZE95VXXuH+++9n165drF+/nlmz\nZkV/9uCDD/LnP/8ZWZb53e9+N+YS8MfiSL4S+fn5URGeOnVqr74SsakJo0Z1rOziw9CnR3q22w6G\nHWPP8TmhUIgHH3yQ7du388QTT1BQUDDAzyrOcTB2RPezzz5DFEW++93v8vDDD0dFd9euXVxzzTWs\nX7+e2tpazjnnHPbu3TvqL4X7y9F8JWbPns28efPIyso6pN3WGEVuNpuH3e+gv4yk9MiRytaO1+O5\nt8aNrVu3cscdd3Dttddy8803x6Pb4WfslIwZFnM9TxZvvPEGV199NbIsU1RURElJCevWrRs2046R\ngiiKFBcXU1xczDXXXHOYr8T9999PdXU1ZrMZt9vN9OnT+fWvf43ZbD5sTM9os2GMrSMeCVN4j1W2\nZtQIH61hpuf4HEVR+NWvfsUHH3zAc889R0lJyZA+p+XLl3PbbbehaRo33ngjixcvHtLHH42MOtE9\nEnV1dZx66qnR27m5udTV1Q3jikYmgiBgtVo59dRTo6/XkiVLeOyxx/ja176G3W7nG9/4Bj6fj7Ky\nsugmneEr0RdhGG5G02SK3uamxQpxOByO5ochItJtbW3k5+ezZ88ebrvtNi688EJWrFgx5BUlmqbx\ngx/8gJUrV5KTk0N5eTmXXHIJZWVlQ7qO0caIFN2FCxfS1NQUvW1M833ggQe46KKLhnFlY5PTTjuN\n733ve4fscMf6Sjz66KOH+EqUl5dTXl6OxWJB07RBG1p5IsRGgiMhuj1eBEE4xJ8DvqhMME50t956\nK2vWrMFkMnHZZZdRXFyMx+MZ7JHih7Fu3TpKSkooLCwE4Oqrr+aNN96Ii+4xGJGi+/bbbx/33+Tm\n5lJTUxO9XVtbS25u7kAua8yycOHCw74nyzIzZsxgxowZfO973zvMV+Lpp58+xFdi7ty5lJWVIYpi\nr510sa22g8FYM6iB3i0lq6urAbj99ts57bTT2LRpE88//zylpaVDLrp1dXXk5+dHb+fl5Y1Ww/Eh\nZUSKbl+JzetefPHFXHvttdx+++3U1dVRWVlJRUXFMK5ubCEIAklJSSxatChaFWL4SqxevZq//e1v\nbNu2DUmSmDFjRlSI09PTo222g9XdFVujmpCQMGJTCcdD7Pgcp9MJwHPPPcdf//pXfve731FeXg7A\n+eefP5zLjHMCjDrRff311/nhD39Ia2srF154ITNnzmTZsmVMnjyZK6+8ksmTJ2MymXj88cfHxIdv\nJGP4SpSUlHDdddeh6zo+ny/qK3HPPfdQX19PVlYWc+bMoaKighkzZkRHxASDQTRNO+EJzbEdWEaN\n6mint+i2sbGRW2+9lUmTJvHuu+9itVqHe5lA5Ory4MGD0dvxq8u+MepKxuKMLo7lK1FRUUFhYeEh\nJWt9GeE+1jwg4NBaYrvdjiAIvPLKKzz++OM8/PDDnHHGGSPqeaqqysSJE1m5ciXZ2dlUVFTw4osv\nMmnSpOFe2khg7NTpjgaWLFnCU089FXXd/8UvfsF55503zKsaOYRCIbZs2cLatWujvhKJiYlREZ4z\nZ06vvhJGFBwOh6MtvGMluu3ZKed2u7njjjvIyMjgl7/8JQkJCcO9zF5Zvnw5t956a7Rk7J577hnu\nJY0U4qI7lIxi4+Vh4Wi+Eobn8Pjx49m4cSMTJ06MmtOM9MnBfaHn+BxRFPn3v//Nr371Kx544AEW\nLlw4Kp9XnDHUHDFaOMbJLE4MgiCQlpbGBRdcwAUXXAAc6ivxyCOPsHLlStLT07nwwgujLc3JycmH\n1bIO9ITmwaK38TldXV3R5oIVK1aM9mm4cY5APNIdBJYsWcJzzz2Hy+Vizpw5PPLIIyQmJg73skYl\nra2tTJkyhXvuuYfrr78+2km3du1aGhsbKSgoOMxXwsgPn0iL7VDQ2/icVatWcf/993PvvfdGTbzj\njGri6YWB5mgNHPPmzSMtLQ1BEPjJT35CQ0MDTz/99DCudnTT0dHRaw3qkXwlpk2bFk1L5OTkHHGT\nbqh9JXrz8PX5fPz0pz/F7Xbz+OOPk56ePiRriTPoxEV3uKiuruaiiy5i69atw72UMU9PX4k1a9ZQ\nXV1NWlpatItu1qxZWCyWXjfpYmuHB5qeHr6iKEbHNd16661cc8018eh2bBEX3aGksbGRrKwsAH7z\nm9+wfv16XnjhhWFe1cmJrus0NjZGUxIbNmw4xFeioqKCcePGHeIABgzoJl3P8TnBYJAHHniAPXv2\n8MQTT8RrW8cmcdEdSq677jo2b96MKIoUFRXx5JNPxp37RxCxvhJr1qxhz5492O12Zs+eTUVFBeXl\n5bhcrsPmpB3vJl3P8TmyLLN582buvPNOvvWtb/Htb397ROSY4wwKcdE92Ylb8B2Znr4Sa9euPcRX\noqKigkmTJkXN3xVFATisgSNWQHuOz1EUhYcffpg1a9bwxBNPMH78+OF6uvE68qEhLronM5qmUVpa\neogF39KlS+NuUEdB0zQqKyujIrx161YkSWLmzJmH+Er0tkln5IrNZjM2m41du3Zx22238ZWvfIVb\nbrll2Id6xuvIh4R4ne7JTNyC7/gRRZHS0lJKS0v55je/2auvRF1dHVlZWdFNOlVVaWpq4rzzzqOz\ns5M5c+ZQUlJCa2srd911F5dffvmwC65BvI58+IiL7klA3IKv/wiCgMPhYP78+cyfPx/4wldi1apV\nLF68mKqqKubPn8/q1aspLCykoqKCyZMnk56ezooVK3jwwQfZt28fNpttmJ8N/OEPf+D555+P15EP\nA3HRjRPnBBEEgfz8fCorK5k2bRrvvvsuDoeDLVu28Pzzz3P77bcfYrpv1HIPBUerI//v//5v7rvv\nvmgd+R133BGvIx9C4qJ7EhC34Btc7rvvvkPSBka6oSdDWYfb10EAN910U3wayxATr1c5CSgvL6ey\nspLq6mpCoRBLly7l4osvHu5ljRlGSp62rzQ2Nkb//+qrrzJ16tRhXM3JRzzSPQmQJInf//73LFq0\nKFoyFvc8PXm5++67D6sjjzN0xEvG4sSJE2fgiZeMxRnZFBUVkZiYGB1HHq+uiDNWiYtunBGBYW8Y\n95CNM9aJb6TFGRHouo6macO9jDhxBp246MYZEQiCwLnnnkt5eTlPPfXUcC8nTpxBI55eiDMi+Pjj\nj8nOzqalpYWFCxcyadIkzjjjjOFeVpw4A0480o0zIsjOzgYgPT2dyy67LL6RFmfMEhfdOMOOz+ej\nu7sbAK/Xy4oVK07agv1XXnmFqVOnIkkSmzZtOuRnDz74ICUlJUyaNIkVK1YM0wrj9Jd4eiHOsNPU\n1BQdxqgoCtdeey2LFi0a7mUNC9OmTeO1117ju9/97iHf37VrFy+99BK7du2itraWc845h71798ZH\n/IxC4qIbZ9gpLi5m8+bNw72MEcHEiROBw60X33jjDa6++mpkWaaoqIiSkhLWrVvH3Llzh2OZcfrB\nsTrS4sQ5KREE4WngQqBJ1/Xpn38vGfg7UAgcAK7Udb1zkB7/PeBOXdc3fX77MWC1rusvfH77T8B/\ndF1/dTAeP87gEc/pxonTO88A5/b43j3AO7quTwTeBe49kTsWBOFtQRC2xnxt+/zfuN3XSUA8vRAn\nTi/ouv6RIAiFPb59CXDm5/9/DlhFRIiP974XnsCS6oD8mNt5n38vzigjHunGidN3MnRdbwLQdb0R\nyBjkx4vdJfsncLUgCGbh/2/njlEQBqIgDP9zC9uAh7D0CN4g1h4tnSQkpbdYD2DlKSZNCkFSRIKw\nMF/1yq2WfW8eKzXAEcheXYVy6Ub8bvdARNJF0gs4AYOkCcB2ATqgACNwcwKZKiVIi1ixjBf6jyDt\nCZxtvyUdgIftfEwcm+SlG7FOfLf416Vugfu/DxT1mwGigIcGGxmKpAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "j" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$x^2-y^2$$" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5/8BDf6+LH4bfwQAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot3d(x**2-y**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$(x^2-y^2)\\sin(x)$$" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/09T/pNOSog2AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot3d((x**2-y**2)*sin(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.4 Dessiner une fonction R -> R^2" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy.plotting import plot_parametric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$x = \\sin(t)$$\n", "$$y = \\cos(t)$$" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAD3CAYAAADrGWTVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niEQwJXERkQimJC4iEsGUxEVEItj/AxxFDLJU53deAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_parametric(sin(t), cos(t))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Butterfly curve (transcendental)\n", "\n", "$$x = \\sin(t) \\left(e^{\\cos(t)} - 2\\cos(4t) - \\sin^5\\left({t \\over 12}\\right)\\right)$$\n", "$$y = \\cos(t) \\left(e^{\\cos(t)} - 2\\cos(4t) - \\sin^5\\left({t \\over 12}\\right)\\right)$$\n", "\n", "Voir: https://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAAD3CAYAAADBqZV6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUeKsUCgUOuT/AUg/L4WlKwXkAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sin(t)*(E**cos(t)-2*cos(4*t)-sin(t/12)**5)\n", "y = cos(t)*(E**cos(t)-2*cos(4*t)-sin(t/12)**5)\n", "plot_parametric(x, y)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "url = 'https://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Param_02.jpg/800px-Param_02.jpg'\n", "Image(url=url, width=500)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.5 Dessiner une fonction R -> R^3" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy.plotting import plot3d_parametric_line" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{align} x(u)&= \\cos(u)\\\\ y(u)&=\\sin(u)\\\\ z(u)&=u\\end{align}" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKxAIBG7k/wHqxCkQ3+ey3gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = cos(u)\n", "y = sin(u)\n", "z = u\n", "plot3d_parametric_line(x,y,z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{align} x(u)&= u \\cos(u)\\\\ y(u)&=\\sin(u)\\\\ z(u)&=u\\end{align}" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngajpEkKIA/0NNXc9VDGIaiYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = u*cos(u)\n", "y = u*sin(u)\n", "z = u\n", "plot3d_parametric_line(x,y,z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.6 Dessiner une fonction R^2 -> R^3" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy.plotting import plot3d_parametric_surface" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{align}\n", "X &= \\cos(u)(R+r\\cos(v))\\\\\n", "Y &= \\sin(u)(R+r\\cos(v))\\\\\n", "Z &= r\\sin(v)\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.abc import u,v\n", "R = 5\n", "r = 2\n", "X = cos(u)*(R+r*cos(v))\n", "Y = sin(u)*(R+r*cos(v))\n", "Z = r*sin(v)\n", "plot3d_parametric_surface(X, Y, Z, (u, -.5, 4), (v, -5, 5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\vec r(\\theta,\\phi) = (\\cos\\theta \\sin\\phi, \\sin\\theta \\sin \\phi, \\cos\\phi), \\quad 0 \\leq \\theta < 2\\pi, 0 \\leq \\phi \\leq \\pi.$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sympy.abc import theta,phi\n", "from sympy import pi,cos,sin\n", "x = cos(theta)*sin(phi)\n", "y = sin(theta)*sin(phi)\n", "z = cos(theta)\n", "plot3d_parametric_surface(x,y,z,(theta,0,pi), (phi,0,pi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.7 Dessiner les solutions d'une équation implicite" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer les solutions de l'équation $$x^2+y^2+xy-2x =5$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import plot_implicit\n", "eq = Eq(x**2+y**2+x*y-2*x, 5)\n", "plot_implicit(eq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.8 Tracer une région de R^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer la région délimitée par $$y>2x+1, y<5x, x+y<5$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.9 Dessiner une fonction complexe avec mpmath" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#from sympy import mpmath # Sympy (installation normale)\n", "import mpmath # SageMath" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer la fonction complexe identité $$f(z)=z$$" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from mpmath import cplot" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAAEKCAYAAAAM4tCNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nn8gAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cplot(lambda z:z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tracer la fonction complexe $$f(z)=z^5-1$$" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAAEKCAYAAAAM4tCNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvV2obkuX3/UbNZ/nWR9773NOdwIxJhHRCF4GkW66W/tV\nciMR9EoQDIJ4rQ3RkBCxwTaIGhKNUW/UmwgiKkIQRBSENglJ0JBIgkZUQj6wu0nI2zln773Wep45\na3hRNapGfcxnrX3exPOu112LuWbNMWvWrKpZ9a//GPXxiKry2X12n91n96kufNcJ+Ow+u8/udbrP\n4PHZfXaf3bdyn8Hjs/vsPrtv5T6Dx2f32X1238p9Bo/P7rP77L6V+wwen91n99l9K3f4rhPwEici\nn8eTP7vP7jtyqioz+asAD4D1lx6Sp8CIdOfqt7xaUAVsOouX/d7f/wv8K7/j53fD6Z5Mkkwn4QaZ\nS519ApUu+eJkMsrEXf/Bf/Nf4+d+z8/XcEFQ0fFZlIS5kTSXJ7oUxXLWiWwWzmTiciYowb02IPlc\n5QH4fb/wh/jdP/8v5nDtPf+c5AIsXYWCqFxJmt3T/FHaMKKCxv6jCCLpzdoUcJIJwi/8wd/Pz//c\n73QpHMO1svbQIqOcVaRJhtWDQdbdH2Tdsyb7fX/gF/iX/6Wfz9dS7qS0ONfVO38t+azkbAG//tfu\nQ8SrAY+2GUq+FifPfu1luKJ0T7royhPaxogLN5NNkzaRafOSMRvPPD7ezxlJadbhlsXd3moToBPZ\nLAWzUjc/9KWv07Kmuze+aXJvQO5ZS/KorrWgc5hmAqR7LsndGy1u8eXSpyijt8xkA3J38bXJmyV5\nyFqXvSauLlw5W/XPXULvSjYnWfP3X+peF3g0rXACHM059XLGQqYAMjzRNY6uYfdhnm31E7nHtj1Q\n2YvCugb1gVzF23PjvTlozOPoAScxDqueshOuL1er0OOXekGNLS3DXfctqsi1DaOTME3CpbsnXTnI\nGEYmskmchQH7oFqT1ciugMMuUORXTe/DLlyXLOy5F4LIKwIPczvAoWO1THfV/acUugA/+1PfqzFo\njQ133chcEqY9ZZ8qi1PaZ4dG2gNKf49aYX7yZ362aZWz1QUT8jW8SCeymfOQIO5ZYxq+ws6/APz0\n935iN/7rsOdue+Zh5x4oLFwf5hqImJPyj+/95E9TGUUfSNrM1Yddb9Ald5aEXuazco1kzYoB+Omf\n+l4bT99b2rV7vsme7JyvOHkNa1tERNdfep8udCfH/sN11xZmWteYdFaTTm4azoV9VuYP/4E825WX\nyBRCJw+zsPWNSnTX+zYNJQ6y/tzbPOz1wfmrjEE23pN6L0ct7rWynxSIMmal9ze2EFdAspM68aly\nBTzYNmaydFjp4F5frhsZL5Lh5BZnCTORAY6RSM0yLpnO73CzlQG//tccXr/BtDrfpSpTxuHg3Wix\nqg49oiKjTUOvMw0v203ansz3MsKUNfgHqi+/XbTpXUqc3fU0KVZUuRSG/DyTkja8B5B6Vcu3hqqy\nPobyZa692GXIfyhXkEOLs8NaY8m4S1H3Dt80GlVDmvCSZTqJQ3wyxQGFq659J/Qi2QxAdAIsLptN\nHXEGukSmrC65LNull72Aebwe8BhayB5wtOHUl2oTX0vYhXpxTQaMBtM+wCzJk3e2FzPQqJJGFTFp\nL5sBksyhovRKz7y39fk+tMp7sPD+KtPmflfKs1fmax1bz54RVbswBUSstbl3+dYysyQ6I6p5dCIr\nbMMNoTV4ZcmaNPhrMp/9PqtFPmErPn+Gs+33clDu2EaxBb8ANMy9HvBoKpsHDqq8WNF1J5zrRfoY\ntQmRgk1k1tlNk9bJrvbuXXauRNO38bnsGrg0ld3GNiZgvJNEu6r5qS21Zx50/ufdtHTGW5bpBii0\nvbZwszHQxrkW2yMhdCCSAw3sRKaZ9KykT0bf4Pdk/bN04ejC+aT3fktub98o36jDy08BkFcEHuZm\ngND794DDWr5Q/6cP0zd0zy508LjyfSZcn8Kh0lql6Bv+5OFdWZfN5l1D5erZ2jTJU6fuf8s2qv/b\ngIgfcRnKtWkV2sn7btuOsbNowg1A0Mv8474Au1Y4eU2TlAICdQTHs42XyOhkQ5a9zPLmGIVPajLR\n1PxOwWLy7J57ReBxBSymYLInG6MduInS14uhdelEJk7WN0bRUTYAwOQ5+udkIrN4ZmTMbvjENb7r\nLKSdMVDNfuque9DgBdet258DUh7u9QBgYB4eUNTfn7TuKZvgiurSxeGNpSrjq30SpEKsBxWGcK2M\nmWzn3H/B5qIRaJPHHkAKyLzAvR7wmCnzpd9L54Lve2CiZqbLzxUjajXeqcpQ6afd8jOykgI3IclS\n2nQVeRz3Ra/oGYp98L42NexDCo1qTcZt7L5x9x23p2b1Xo5TtRrhVEtbLViV0yJNnDkj0kYqzUty\nuag9puVaSiv135sOMLK8L5u+O+5ELTiYrAcRYSxrbxPpOivVUZNSrsrYk7kybWQuHzNsNKaRU+ry\n5/wdgMzqpHevBzyKc5W/a3Q6bV0VOObXFicvm03aB5hcF1xwklamtaeaDLnsvlL3r4csZqEOGagQ\nNrKMVqxt4TqP5nLJYKHVCtKzL9WuEmt6KoXrC053/PlSa2Nsu90JYDStq8+D5dPisxS6bngAkab1\n4VmHj6IpD7FykSkJ2pX1RKmX9ddSzwOZmoBI+UgljgQgM2y85l4ReHQVXp1/yuUnj9rzHZAIuB6u\nfU67ax9mOtTaNZYeSGbx7dXtXjYbvdE+oC+aJmifgh3gmCRE3f8aizWLGqY/eva7J5+8rPO7tzSg\nIJMXa3tt4Xx8s48xlfWtsgUMzzpK0mSSFM8UXiDz17i4fKOeFlN+ZpgAazIfvssSM/8z7hWBh7k9\n4OiuZ2zjCugMsw7cF5k1gh4kptg1AY2p7YNRNr32YOPb/rWsgqPR9nx7XV2Vz3HY5pS2oDMCgjb3\nxjDP1My+ZfTMopf7Z6xwGvDoUtgDBC7enn309wcQkWcBIzERaZI1WYozt3t4v7+vNRk1XTW8zGTX\nQMVj4guAA14VeMxaTg8cY/DkZuG8rA05jcqDifPPprHPnvcq0UtYyCyqXo0YgE5dWqV7rlz3ZZUb\nwA6gzEHE7vhB2xlY9E9Pc74f/d6z/iVN67ND2/uz+PaYBrStyOLwS5vL8yOj2QMRXipTBzzaxlnC\n+yT0eXJJ6pnFrqwDIY+Z19wrA4/J3MWrIOEaxEQmE7ZSbRC+sjojqm+gtB+wXa1Z0WCArEnbmTUn\n7f0zwCisQ9tiKfd93vqEyzQxz6XFS/eAY/6czm/sYYpvVQ4QmsWOqtke0h6SnxuX42WW6cqyGnx9\nmnwrEvd4BloHMB4wmvy4OFNytAmnk2ebOW35+and1/t7MOmT7GRN2hweNkZUmSzln7jXAx6lIsCk\nOXYy72YN5JqsU2DcaW9LIvvI0qfBP0t9pVyRdY+2si5AxYLaEnbtwn1NcixsJ1tO/hxEjE9aCJk+\nJX3w1q97N6XJbwWNkX2o1wtm+cqgUJmmtN2yAYcHiUmX3zR6e71OktWNuBiYD/M7fBzi3uFIUEnu\nBAhm4NAzjeHZkiedFdeu+6EAD0m7s/wvwF9V1X9iHqoDC3X+JlgHJs3t52S+1dW79np1/ga++nbU\nvaIjBfsyasUj+22jyAoUrb8BDXu3v+fJmM9vk/8mqiEzz8HEHrSMT+5RjGnE7nDsgx35HpAM76Yr\ndN+ysr+wMu9vn/UN2eHZdRBx1/gwnlloG96/ui85w7eWQdTrhiB5uS+HHlS6orrmfijAA/g54H8D\nvrgWKH23GXD4FtK3mK6Jahtbks2YTOqXlA4cXDTirk3qYwFGtqHjm2ZDxKXiaCfr09EBRemNO3+T\n/QFI+lo1b946XHngaEGkDdXG8ALoyMGfAwcvt3tdi22y5VqK69VTg/F0wrW4xoqYWqNR+pfYMHqA\nqOWRjKj+PpPwLfC7bHiC1BVZbxgtwCLtdSmRHlB62Y77zjdAFpHfCPw24D++HjIXe9NatJO7e7oX\nhuvP5WdLGar7Vtp8t+Hah7foGr8Dkl5WXt9nNY5+u1adXxc/7hpoVoOq9KWDLbKfNX7tJC1oaOPv\npSO07BzaJLa7Z17dOWAAkz4D1qqt9aj7cv6efSXt/DaTVEFVxiQxSSaTpPVhZ7I+K/6jeOez4VkE\nDJVToausXVhfDC9wPwzM498Bfifw5bVArSHTlWSTe+1kTj4r/GGUxsE9kvbUxBtR/bOjqBlRMb/O\nVZM512mzoJP8NPgHEEFDecBV7pKNki+V7o3Kiwxj9XXayTxU1DA9+LzcFb5WT8Pkh5ccRrsmefNk\ny6KVSQtrRl5aJqJtNWkavD0ygICRooZRdGxNx2f9O2clZc5/ag8oDck0BuIjmMnwdWXffafgISL/\nOPArqvpnReQf4QpZ+oU/8G8X//d+6mf43k/9jIPSHkxeKutcXyMsnX2y+me76x447O1W/5v628mm\nzgAi+wmg+Wzv9wSqZyT9C0b7x8hzx7R4UEiRSpN5Ha56nOtBpQfMASBM92oi6/h/00oH3cBnqb6r\nQe6u+/WjKx5ESAbTgks5KWV/5fxI2Y+5T6olrweQLpwHEJ8Mn7RGDdmTueKayly8XvYn/ugv8if+\n2C/yEved7iQmIv8G8NuBFbgD3gH/tar+s104vfyVX2kfLqVaQrlWcYWXDeHaL6T9F8v+2rN0dJV6\nNBVH3YZX2oVxstj5m3BZB1Kh3T3MbX5l9wZ/qP5yLUrZmktshzHbPcyOrZy1u27lESGWXcTsvORX\nLu71vWwBgrr72V+TIvV1/tW9vDlyQdmOYSop0xLalPjrqV86Wb6WqtL5IdZIO0nMb25WDpn4XdX0\n9xjO0qofkw3M+nkawwZndDIfjkkYJ/tN90f2dhL7Tm0eqvp7VPXvUtW/B/ingf+xBw4Xujto/VPb\nxaT/m4Vzfpl222NP6+0dJi6yHKVMwokL5+PBxzXJgrodAjVmkHLb8pl/ZvsYbCNWDAUwJxV+p9Rr\nVzN/yv/thWkOzWGbF04yUNB6drh708/qOozmnu+2Xdhpx5GZB7Jrzyidh7/HPKyFi3vhShJ136bR\nO8dA+n61B46h0hne0j17xf0w2Dxe6FyR9baKWWkO9oy9cM/5UzyiaUGZGJWmGs98WfvRFWsT0oVT\nKmj4OJrkTbKnUNSWxtZh7+oAZ8BA95K2L6kXOtSqWbHV6j3aPXR4rj+3zpXKLmLJpEX67l7b6/5l\nvuCtyzWe7r9zo7KQbCH+GUumvUonyZvds+s9P/W1Vh+mmrJP4o7fA0yj5tgtH+YK43gJgPzQgIeq\n/iLwi1dC5NMecPiW4Z/L8mm48Zmm8Zs4hxNsGX9dzt/mYZyJOpuW3gzXGnCoe7DEx+AaAFEaELlC\nmqqs1CAtaW5z7IDFdUMGFV3BOODIPSRaG4TLjY9Tm/fVwNo8kF+Xy77NT2qtpoGN93xuKhgUFcBa\nVrEqyhCuAIcflhXrMLRPyhwY7PqF4Vy/1Dhx9LTUm6wuNR2Sy2YBFV8MDgN7xiFONjCXHfdDAx7P\nuknjqpV7BiazZ3uZfbH+hkxf59/XzEPtAKdcu2d7JiJUEKmqjU7ngViUpWKF7Hcg8izr0Pr+Ers1\n9r67UW8w7QrP1Ixy1ykpOiorfRk18frPpq68nEGgzBQdWitVbTNbh0Wk/TelYQ6NkXTXYJr8xc4l\nNX9m1/A/Vmfk51MMpgUwaM/9UYChv4cDhJ6BMN732YdJPJ3sOfd6wGOoxPCtgOPatY/zarjSfe3+\nepwfafFDs+VsgFEARYc5JRNMqw3Rj7p0SfRtYQAQS36J00BwrDGz4qz31P1vQQSge+V+fEMg6367\nSDrgoAEOBzC5kFKZ5zz16see31pgBlbb1HhQSzpwKFqTBwYmIDIJ58tlinc+WdQGvgcaOnvWPedB\nqmchU2Zyxb1O8BiAw1W4nUeei7L6S1E/Ey69U8zv7zng8H5x1w2AUAFGOvkUx5zdo7CQfDR+AxZx\ncqAwC3tBo5q0edehAPqs9n9tY5iByDTKPuAMOIZhqQ44Zi1SZn5xH6EDjQIqYkXVNPaBYThgiDNg\nmYQr+NhVmxnjMHHPOOw56f2TcFOVRVz292TPuNcHHgNw0JW+drIxiqv+TwhXpq/7e1pTYg3fg4Nd\n+7Uto92DBmSKKFe8wWAaJ8nMDw/qjEhJzAgWs/kdHkDqMc4p7e+8wA0AMZEDbXdvRwccsQfwrgvt\nN/ax1uTrTgckKtKyhT4p0tlqe5Bhfq98R1oQ8a5hCuJAwiVzl4HQ4uKgsriiuSp7xr0+8Bia1JWg\nezLDF9/QTTwxotbW6MKqNb1qRLUIFbKhjzJLNcWad81Q+z2yumfqbBp8SXKPk4PBNNVGdTVTY4pI\nrWF59uFqYl2yLk0le644Te4h5LlB2uddBxI5jY3M5nEMk2c8Stb0SW4JRY0RaH+/uK5V8ezDG0zT\n65WY/WUuhwOWaLNFVfL9vHYlP9sAETVLPXD024aYrAEGyTAvOX250pTObAI6LRBpjUzMrw2A/Iip\nLdk1q8iaZr/vJsAxvX01nGtk3hxtDV0dE9F8o3wPLaCQUl3vNf4JgNgxQKdS1JeknqgDCAONnFyb\nUOABRMVaVpd/15j2i6yUxggcc6Mp3XVzbw9phi4bBxbml/nLakk7vyvRvMRepPuerkqpSNWUCkjk\nMwYc2snqaFMBlC4b0OBUc/jG3zTiKYB0X2fGQISRgQhpBMfiRT/J1mHu9YDHFCd0rDDXAKC75xti\nG6fsPjONTx2zKHzUJdsBgX+vTPwzABne6aanp7MUgGiSKySZvWQHQLSk1FfH/rpPhrr/PYjsg8YQ\nT1/2nv5YGgeVxfLjW+3eGzxgWKFU+QxQDEB7VaUHDm8oHQiRT7bf9MfltE/idGa8ZxAeGBzm7RlO\nJzbgEaRw1813eN69HvAw51vb8AWuZPoaCLwkXPdMeb0HfmulCsWU6kBk6p+B2ATk7PDhKoC4wVMH\nDprBYhdAoNS4/axeX+eyxzwsnlmDUVqP9oGbI7daPxVd+7P0ia4l1lQL19r6rt9t9rNr15gAR5yF\nc8k2PxO/Jan0i54l0CZvD0AG5rIXrovPirxlHC8DDXOvBzxKCc9am937NP8QxScAzO6zXp92rUWc\nbPB7gNiRNc5AITOPZpKYsQ/DMQOLWGWl0aoL57qlfthWJ1f2XzEA8UDyAuCYvWAXQLpjBhy73+s6\nYBTjqLEssWnoDkR2QKJXafaZR7Z2lXKu30ioyWpsGx17eI6B9HsaXWUtdGHdtzT/S9wrAo+dVi/2\nRfr7nX9WHi8OV4vVv7Z/ts7tkKGL8SAwW9syB43aNbfNOYtjbTslGR40oKguCUAc8HoAtF7Xslgi\nulIkDj6u2Tz2nh8i9+mZAcUAHL6Lz+dmy4HenmEtlIksN2yceuEAodow9oEjduEaG4fm8nLfytLZ\nNG4mAOKBwWVnGo5JOHQezsLmb1jNXL5buO5eD3iYExiAwgDEGoYAuzpwbdQFcvbGy/p72suEslZ+\nAiaSG6El0ZIupFWlRgauA8gINE3OtHt117MVlcWrLq4hluSXsvPMw/ohu64t/Rp07AFHn+4mD9b2\n94BjprJ4EPEtBsoAQrl4hnUoNhlMCjgYWNii3eeAYxiFsWR2r9ZJMnq2cQ1A+rj2mIr/jB40Uri+\nffRf7EcJPJqc4y6cvwCHf2hSCLk7GGZVNkDhAMI904+01FbZbjYqWm0FnnEABOR54FAQ0vjNdBi3\nYmBTElMgsYcjY0VW91yZbWplN8ZZZUoFjx5GmB6TSNqb14DDA0hpzbPIKyAIXWbFwN5koWmpHjh6\nu0dzjxZMZgAyy55LXnrvM2DRqxxMwvRAMTAVqKxCcqpMXnq52hpqq/hRBA8PEk5Uwsy6N3XXfiQF\nuMo6+jCzUZgSd22ZBhzShGsXzXkgCNpmq7INHUClf3fp6XxypT03vV3u5a1Wa19E+KFaa4iTInHn\n59SWF7k9xJkaSF2mVdqMQss0/OSwCeuwPTwalYUOozQNu8b8XQcW0gGIN5p6gKct1kGVmALIZP+O\nXfZBd+2rdR5VE1cpGwBx51a+714heGRXDQwmaGvrACT+OhVPE2TKOpjUABjKeyITn8SsE4iLxwOH\nmSJC80wFjZL9Lstq2Xa9THldfqhRWVxlaxbUWVzi/APzEHc15xvPMY8BUJ4LOGUcdijNHI+mZdrZ\nAwZtITgQqRO4pFVX7OyT0gOH3fMA4r7LDDgkf1gVeZZtXFNhBvbhsu0BpYJG/ZoNgJQZx34H2x8p\n8JhkRnfkPZBQ8bQVPiMrwGEy12OpmyOg/lzVFwOQdO0ms6sOwCFqM03dzAPtzs5v+Ss9nKsMBUhc\n0rx21Uwgs6x6+t6iCIN6597m/2LaV6tMfh3AYohAmuvCiDqVRaJLs4J40LCwjZM2T7usox4lvQLp\nN1bm8zwSYGgFFJt16sLZM64IS7JaUuQBxAybsq/C7IFGAR1tZbRMAxQV/zXrVxS6cD9S4OHdMPLi\nne+qncyAZha+NH4DiZkMX7aOsfTnYs3ArJFlxqlr1S1wpA8vWtmHZyHPAUma5k4dYaG8ptW0PIj4\nNhRwOOkblO/S+uJOvuhgIkyYB52/L3vV9M5qMLXuXEqXr36ux0ZuwerGRa14J10wLpMeLIo6087d\nGAiOyQWizSbFEZ9cVfpBob5f8cDRgsBkNGQHLGajJr77a9QXcO3EqSKqzng6VN4a7gXu9YCHLxTL\n267F2Lw6PjfM7hJ/kwocDkB8fAP/n/VkIYdvW2rbCdQ1LcGidtc6Oe8BSUlfBpC+4Vo2B/AI7jrb\nDhLYjMDRlnTtsUI+x9x8pIGTeVo0J6iqaL6Lt4ecrKgpuO7fQMYinAGH97egWNLgQMOiG9SWCbA0\n9g57tqsyvmr4xv8sMIQXhmMmS4Vq4NCCQf0avXwM97x7PeBhbsY6mlbZOXUecdfNuQcMO/t74mQT\nDGridDqBsQ8MAKQ8mIAi6dkeNISk0hiY7IKG1uw3y+/tVodrA3iU+R9CWkRX+7KarbEf8sWegMOz\nDh16YQ8gNZIs8YaBATBwrZdW1kTedLdXD3VH/gojaCBzM4sDk6KqdMnweRWXnL7xlwafN66WwPNg\n4WXMZK5iNG2igr0fop2pK638uns94OHacrr2IKJjuK5VSwk2aQoFMHIErhG1ymuV1R879i3Tnx37\nyExEfFodE9lTVwxAZoBiReA6uWbS2HPg0bAOIecpPeTXe2iJvS+5qqCEDCBkm8c10ND+YsY6mumc\ndADiWm9v7W2MAZbu/SMacDgwSEdaQTtlH+IMpl0+m/z2ycnHdQYizejKVQBhR5Yrmjd+NiDRDDS0\njKMFjQHuB/eKwKPLzAxEstwbhdqVFt3D6q+l80vTI5Z5A5rj3AUODxqCWCstci3xSrawGfsoAOJA\nQvy5+NM8kuLvs1LaleakCWaQ66erN0ZUNZhtgaOWnDRFZ+815pHOsRmd2AOS9Lzr3zTZPyRmdcYz\njKblkmbKeuDwn69EPgOMUFhHM0KCYxuio+1jD0DIECpSoNQnpHyXWeOfAUPQLNszomqNg+5ZOgDJ\nKSqgIbk+6DWDaSt7zr0e8DCXC2Hf6fB/dr/6c7FNZ6R6XK4rLlsrZH/2KovFbeH9clhbgSv52yYw\nMOAI1jaskhZAsZEarQZXsNX15XVlOvSWElc6562ee/Ulrc61JLUAYnnoSykBRgsgM9AYStdnqgAE\nlNXBudVK/zstZjBt4uq7efdjNeKuS54qgNRo1fmlBQ0XrthIxOetNur0gzSS1JDuJ2EawHDJG9mG\nOpmU3qMxiJaqswcGvtQdaNh8j+ZrqovhR3qSmHd9BvcyfA1EdhhN07fmLqrvyQZVpTuXvQLFxW21\nrjWghtyZWv0D6DcKKlPalQI0dm1JtVeYv7xSgAwYBUA8C7Fl/eqWpZe8wkwLNoNppFoOpJhOR9CY\nfp1cFqp1N/RhSMPOBUj6mPw36WdVtTNK1bGPEUB620cr80OylqQmK/k1PaMoDT+MyRsApB0UakGj\nkRkY1JId52l07AMflibsNUDZc68PPIbJYeZeAiQTmV6771ujtcg9oOjl3qjgdirW5E87kNlQbmos\nzaiKYyGefViYMrHM/K5Ycnus5GerMgMQIpV9uJ6+AAiUGjuudalXBhzGOszmUQFkf61LYTMGHMXu\nYaDBBDiy3KeitKK9Fme/aTcHDQ8YW87TlH30AEJNgh0zlWQYPelApAeQ9jlHL7F7Oe/iQaN8eSoY\ndOwDyoSw8TnacD+S4FHcs33alXtONl2tW3G43rCWOAGQwd9ZIxXq+nlKGNtFzFQmG32xJCiMdo8J\n6+hHX4DCMLS7NqbRsI88CUsLC7Daa+3bQMT8vlRa4NhTXXa/TQnUtdLSkqX9xcutlldJzsyAYD+A\n2XT17VT0AZfca1owqWDYzE/L1aJAa1cNBtWkV19mAGLP+ayY3CpJ/tgtQPTsw8taluHP/t7/Pwym\nTdt+IcPYk5XuumuBgw3E92zKFDiMZTjgKD+qpNTFco3M5olDsntomW0aVCvzcDjjh3bN7w2Ipdq4\nZCUgUZfU1Dq0sA7KLE4DDJuh6U08tYTspzkr+0gqi5/ncQVEPGiUTOJARAo7GmiCIx1zTh+SkbHI\nKoi0zEPzIQWXZjaQKLCVcq3G0bTGLs8bbkBDy/o7bwAtas2evWOyjkWDA42c53bItZb08yoLbjDB\nyWbhfrTAo/Pr9KJzLwARA4y+6x4e8R9G6nlQY5RSczzz0GwhUKWMvDTfOoWtwJFkM/Aw+0jM4YJq\n/eFouy8Qo4u+fQ3+N1DVtKqtS3rIIINviDlOrXzEmqOgGT58O2/VlqbYS3mRVSdBtpyxTRwFCM5v\nRd8xjc6ooFk3UKlMA4y81J/w3hxw9ARnUFksP6VsaMCg+B2zSAZTRb0RtWMeLWjUGafNqApazmAN\nvgcIS6FnJLQype2Ip2zjeeCA1woeVzP3iUzE4jXb5tX4c6v0E5x6AGlUm+DC21Ct1O+MoUK6L/n5\nQCCqFPsNOQDdAAAgAElEQVTGHnj4oV0DD6/GSGyrQ+noJ2RJrWI3ZhrJya6N1HbEsjjbaVeRbQAP\nC94NZXq2kVmPREEjyObYx0bq9osNxLUqDyBTo0I2kGb2FHNUBZegAY4BPLpjMG+FkUXQy8TJelCZ\nAMiogfVgMQLDddCYrVuhk1V/jeN59zrBQ/31WACj/4rM07+Bfej4yGxiUgMceyzE4vOTKnoGIkhm\nJ2bTSEDRMpA98DDG4tfN+GTbIEUDIMY6svpSRmDI93It9ovl/CyaCil1tkRjI6DLoi9QT4ncqIpG\nTQCyKWwhy7WLrGce3qiQgSMzj8QaxGtDDjC0sI8eTJqRFffpya8fGv+EjYixt0HGPoBAndOB7fJV\nVRMDhGuAsgsajbpTfZ86NR1eJXjodU1lcM+AiAcMa7FN16rdI77y98ABDe8vMmMjE7XFY5emSd5m\nSwgqGRzM9iG74GFG1MI+oDApW7ylkySra2+FgTjs8wbUskGwK8mqFFSbxww4tHuuRGSJaoylZBWG\nqsKUkRcqaPQzr2Z0wKDNMY4eILyh1B+WhzLAY3k29hHquTCLmWqS1ZZm76E9AJHckAtwtECwByA0\n933hwnX20X/RH8nRlnlmXi7dkUknKQDi3+kAq1mZq7WlQV0bMrTAVn3ROrSRw9s1ZSs+yeE0M48E\nFDqAR3TMo2EfaDWmeiLkQUNSfgtwLFQWIgCSQSc91M77ANQDR1VbSq/dHdPP0QAHWVVJrEONfXjm\nUX4ZzgGIZJVPWhqQ5rsKUWVkHA2YKBuw5iTY2YNH/jrjdHNvHC0AIhPVpNpK+vkercqSG7x4kPAG\n0ZcAxBVZM8PUfQjfiWIQct29IvCYCXXH/xKZYxtK5fTgWqWTl+ENHEOxqKyFdueiF2jr91sWeiCx\nawcookIg9foh0wd7ZHGPewAJqE10ZLOk5Pd5laUx/gXQlYpzmWqrZx5OSWnJW2pm0qktvd1DS/h8\nmLCwDbK6IqkFl3PoKEDXhUtAZSmgYa0ygYZk04mkqFBWlRr1zlEMpB1Ds6OfQTrYO1oNqiR1mOOR\nRz8KeZoAxlw96dkHk3C1nu+NqMjETxduz71i8NjL3EtBpHOmA5jaUoCiP+cww5qafD1Y1SbA4a2g\neVF7MR56v6aMiwqh2EfSXiBLDmKAseTOefHT1rWmpCSxAw5rGIV95BGXZPsQNHSgQZ7C7qodeAYS\n61wJXDZmn8S69mLNBN0kAwiwVhbSMo/KOCpgBDS3TjXmIZKHYeuIyqqwibJm2R6AlM8m9ezB4yUA\nMrAM59esX4q0DXtkGr6wZlyuD9PK5kDSqyVe7p+/7l4peGgjbiiWdfwvYR3DOX9sYxXeatkDR2El\nWko9aTRN174DHBkwClDYfRywpHRJbtnB5n/sMI+kvug48uKzXphHAg4buNDcitSBR6roko21KQ/G\nOHwf1tLimFUXzzx0B0TEPSbO8CAZQEjgsU7UGtMRyihLBo4MIDa8XLhQZhoNqSEBSA8eBny9cbQH\nhdkhucya9Szmd+pJ0S8L81CQnkl4dtGdpYJCPc9ZSHXzUZZqkK3V5Ed4tOVaxq4AhoFKM9vKP+Oe\n9erKFDjMn5+TFJ+WF1liHfto1BcHGMX2IW36SP5iA9E6dXxx+FLVFS3so7eBWBxpgms7cSt6tWXL\nQJJtHxrJakuq/XXNSwWQHjjaeR7tu3wpp6ITe7QCRm7huoIYeBg6lgQ75iG1VRtwaAaRKKGaUEig\nYWCR/JWB9AZTc8YYpAEIpuzD5nTgbR4GIpLvORApwDFlHHvqSy3zlwHH3Dg6B4megVx3rwY81Oem\nyd01hpFdbtyDy/YOb7uss6+odo0ZcIQMFn5hSXmPAw+FyjwcC/F2EvvZNyUBBOAZiK37sCX8xcYB\nBUjMpujBpCzbNxASUsuobTaxEAOPJYPHllnHItXmoXU2R6l2TZF6AKnAsWfzGFlHbuHO3pEMpoEK\n+HTMw46FMqcjG0mVdvKXsQ2zfdRDK3gI2GxTqMSmLFhbdMI4pGEZLKluNDLTsDLraEZV0AQiGgur\n2AMTK2fVFhyytNhMGpn/RDvso8z4+0T3nYKHiPxG4A8Dv470/f4jVf33ZmGbeppVhDLy0TAAH84q\nXd/v1UA6k7eTLKofWmCZbfPlQUd9mkxHsAQbYNhZM3AsVFVmaUFNkxoj2Xi6WKN24OGPJbORzQDF\n9PfNotNicigA0ts/CoBk9tEASM8+bMSlqitebek/qJitIwOHZoogW2YcF4Et1u9Xhr8XBxrpUFlQ\nCWxSjaQWxdr7Q8tAioFUSL9sn1UPlu4wNrGkT9PIl1ZVaZkI7UhKYQipZESvM44qo7vnAaKPuz+P\n7KP5GPmu58zPue+aeazA71DVPysib4E/LSL/var+hT5gaeQZOHQ3dxmBPViDU1vs0Mw4tJV7tmHX\nHkwAoqYhXZey4kp4Q3OhrEKrim4FksImIiNwqDuWkm4KgIRk+1DZAY9uFEarpqZL3fSmBw57PZtk\n1SVklWWc7l1LPRWgLYyroDGqLvY5CpMoFCG1bs2tXVbJw0X2sNMhiqF0KbaOBBoJQDYHEpd8mH+L\nFVBWgRhcFQikb7vIyDIcWIiVUaABkNbeoaVTSUO1mvM+B4vrwNGrLXbe6xh9aQ/QPXHaAcfz8PGd\ngoeq/jLwy9n/XkT+d+A3ADvgkZ3VPMVRtZ0n9tiHgUnswnu2gY6jLA0D2flgfpeewj46VcazDqMz\nBSRmgFFloupGX1K31gPHFusoTAERTAVKZWJTLGxaSgUOTYzjQBlC1ZCBw+weMjIPJRKIWT2oINKA\nhy+qsm8HBTjK2UBkM0bj9Aexrn5kHjHUUZRLBxKXQKeyVCMp9okkFbt4sOgYhh3iAGMAEskqSCCB\nxmAYHYEB4g5w4GR0specmV57gKi10/Z3ex5wvmvmUZyI/N3AbwH+1Oy+YbZZmNMzNYslw01paVtj\nPZBY0ODC9XM9THYNQPxOPZYGAwxx6SkZ8Q3Oqy8eIHrm4dUXigE0RCn+GevwzGOJ2dyRy0AjdTs9\nb/Ow4wCamYfNMk3VN49mqNQJtOW/5rUtOhyDyckZS1t7h1EGA5NYTUeSf7xamu49AUhYkr0iCptI\nAxjGPDyYbA5ILG3FtuFBYMI6husOSExNsTqQpppXGLV5Ma09owWTFlicfQQaWb2Hu78PIL2Txi8l\nLpmGbt0PBXhkleW/An5OVd/Pwmhj38A1yDrJBmrBjS9RGrEHl6KqeJm2Mv/OhnXkGwZSNvVTcy+T\nx/IRugaUu/6ivhiIeOBwthB32I5bUoyZpAlRPXjEHkTyljiu0ceog8oSF9LQ7VYBxO8uplABJMfk\n1ZYWQLqfYmiYBxAlG2kdRdgoOocUjU8ok8G8vSOkVhyjqS3CKlJUltWzjwAXtM73IIGM1YcWl9Sx\nDBltID3ANGBjLCMW1pGYhyly2dbhyk3QZ0ZfRkCoFXLHEOr84mQ9MCSMqxCT5gdO2lDnvnPwEJED\nCTj+U1X9I3vhfu8v/MFSFj/7vZ/kZ7/3k+Vei779CwxJXeieDXjQsErdy+hYh9JGor28PDiCWYRk\nGczgQZ4PXlpwzAASBuCow5bRgcmCxGpEjSoctKovUWFTTYZT/JEr45peF0PW/w2/DungomXWaUpi\nVlmc6mI5laK22ArbDCRWlAWAJZXDKtUYsQZYF2vZ2eaSWrQ4wFA5FDtHWjErrEG4iB1wBi6i6To4\n5hHyqIrAFpQYpGhABRgO+SgyhYO04GH3+0k1kj+wAYZ4y08FjZ55tP7KNBhkvrS1rdfOVQbhVZL+\nWouaYrI/+Yt/kj/1i3/qJSYPRAc++f+tE5E/DPx1Vf0dV8LoN5f/K11oW4i+IIrMN2zNYbS7xtVm\nf/Y/KNTLIqXx2ka9zb1icKjXuvl77uz3p4ikRtJRAC06hNMpYmrVWlr3QowLmwZWFVYNbBq4ROGs\n8KTwFDWdFZ5I50eUJ+AcIJ5gO9Wz3oLeKXpHPU4rGh7R5RENDxAe0fAR5T3wAeU9ynuOPHFPzMfG\nPZE3qrxVeAvprHB6At4LvHfnjws82nFI53gL8iYf94i8QeWOKDdouCFKOlZZOAfhLFLPprZkQLkI\nbLkIy3EAOQhyBDmQzuY/dP5FqpnlkM8CEpJqUs6ZQYjE7I9FZnYNx+Fav/T3PBB42Vj/84qCfO2B\nQprrViZzWY7oNx1/M1p2tGrddz1U+zPAPwP8ORH5M6Sm+ntU9b/rw6rzVYp2TWYvgTqOncfY1d5P\nyzbQausociczwMFdN/6eMuZDuvvq47R7I3jUmVrLwDY8C5HMPoIGlph2I1MVtgiHzDi2mDBt1cQ4\nykCA0RABFS177xjr0APokTKHoVT3ZvZp7R9NbamsY6sjLznJ5KwUW8cqbkhEkHWpNpBooyqBYhgN\neVhWAzGEoqpcyCABCTgmDMT/JIzXEo3YhB32MTAT8zu1BIn1TFVPagVrWUe9HudzzJkI7v4+2/ZM\ngmzHGIHCwlX20cuec9/1aMsfJ32CZ5217Z6mtaDRywwl6kmhGA3xz/Wg4SeLeVwotT9fi7aG1gE0\nsqw8p+2YaWFAUAyAzWFAYapMCxyWVlEI2bgpMQ3hbqpszu6xRMoUdqvvZcKbOCIUQM8OOC7YHLas\nuqR5H9qoLamSJ/BQIlv5i3lY3ONfHWGhqi6rwJrZms33yGoLwdSWxLpiWNKwrApbCMnOQWYZZOAI\nSVVJfuUShRjsu+XDDd6QyVyrstDO6+julY5BMoUshRrzvA4DkHbcaR9EcNeuDg8g4mW9k/K/HtIB\nRauyzGTPue/c5vFS19sNPECYv8hkUqi9elbYgIvRWEo/16N0me6RCYgU41iTyu7IE4LqkLB/prRm\nKpB44IhpPkhpiZqBQ5E8NEuUNFsxwkFpWMeWZWZITRPHlO3i3q5p4Zi3eWTtKE/9dqxD688Y2Jfw\nzGMrEBLTHqD+6GeUZqoglwUumoZqt2y9lZyYrD+oLERd2CSwhsCmcAnCRZOacgbOopxx9g5NDCTZ\najLrLCqIIgcIh/S6sJBsHBlI6oQwHed+OLAohwGJYxxpx3wDCOtcdJCJ+rqQ6/GsrvpqbDKnXRRQ\nkB449plGL3vOvSLwIFFrrRnzAOGHpHLQgtRe1g9zGWg0dpEMGn5ORAqsloA8TEtt/GW+iMXpu/fu\nsNVtjRzSpqOSbSqRskrP5oLYApRo6swhnWPMgBFT5YtK0IUQkwH1EPPy9JjUlksGkUPUMrhh2Y9b\nGo1ohmwNPMgAsiR7jE0H91q6oKzEfGxsrGwak6nHsw4DD9MtzgJPgp4VLiAXScZTzQYGrUYIDUc2\nPbCGJasqwhPKk0iy6QBPksBi1TzyEpK9I6GnFDuGHhNoYMbhA+hRcjgqG/HgUVYc2rdrlwJKDxxT\n1tGBRlcX7L8HjlHl6I8RIHpwmIWnk/EipeW1gYfr/HvWUeVa7jRgUoAnXzdnLeBU5U5mAGKgoQ4w\nCpBonUXYcsHqTH2SjggVI4zLgQrl1+XKXHEznMZ6xHydbR9mlBXVDB6BQwxoTPuirhGOCmtULpoq\nwGqvjppGXLTYZZPa4phHXASNeYs/lo55pNRvGUAydLDpVlfV52Q3KosZKYqeAboKsmXjcAGPZM2M\neiSGhVUDZw2cgwGG8kQCkEex+RyaZpwaeBSmUQEkGus4QjhCPGgClAwY2rCOTNlKozfQqADiR1Za\nW4cWmYo9T5HXbs6NoqhSrJeuGo1HCw42JL8HLvCDqSzw2sDD+XrWAZVtjP79yTXl2TKPxLVq26il\nMJDcE1i9MHuHZyJicXRMw511YB4uX8brBbqqQAWRyjiSMbWqMpLVmRCVJS7VzpDZxyXCUTWxj1hH\nG0UUXZO9Y4upQSXWoWhuYImJGHgsGUDmzGPLzGPN/MMGoirudczjSeApIGssw7a6ZrD0LTscUT2m\n0aUQuBhYKDwFEgNBeJLENhLJSUOyWsCjAkg4AMccvWMf8QBhSexD/WQZZxRN9WcEj5Z19P6eaVj9\n9XaOsdZbbR+BQnLt6FnHHgvp+7Z9NaZPTe9eDXhEyCzAJK064iUVONzsOm1l5ZyZhUKzT4K9S406\n5m+tqhVoOtWl7ANirmcg/tyrLWYLMfZQqHGOoNm5p9pAyjkDh2b7h8RkQF0UbCqpOuA4KhxjsgWE\nWAE5SgaPoxbmEY/GQCRPGgvEwjwMPHrmYebSlVW31LQMM3eZx4KuWuSyZgtlYR9H0BMxHNIELxXO\nKmkI2tgH8KjKU5D6WytCAuwgcEg2jWTjUOJRGrXFWAgH8giTEhdNQGIFS0SkLv1r1RUPIHPgKN/b\nrXXpO5GmDmWPlHNt8NatTAEjZ9neERqQGJnGnJHsu1cDHn3RirvzHIjIRJb8dXZqDVt7gzJurv7j\n0jZ+e0Fp8O1Rjaj92RKc2UipVHU4VqPSrguX+rLCPhY01mckVgYSorKoZvBIE66OGTiq3SNVAtv7\nI703g0bu8GNmH3oQ4jGgmzEPb/cIpSjWzD4ubFyMfWgiSMVcU4ZoM/N4FHg8IFvMhtSAbokWaDik\nI89vWXXholIA4zEfZut4EjiTlt+XFnYAMtsgz93gaABi6opjH4smxhEUQsyL3Awk/C+/VOAo6op2\ngCHWq8zYx6x2t26POYQMFHYew12X4WQeNHDna+51gYczFFwDEZO3TMOHH42rfkae3Rf3rN8rQdyD\npdcIQ4TjsZGAY/OViAo2TSWyiodbWSqVRhGBpDokfWMrh5pfNySeCDGiUQkxcojJgHrStA5kjcKZ\nxEgOWlV7TUL0CTZTW46gRyFuAY0GHvmQQMz9YJqyoZzZOHDhrGua3ammumidjn6WBBwPAg8xz/9I\nE00k3hA5sYVjYhshsAV4WuCDKh8VPqrwQZO6kkZaJJlODok9yTGDxRE4gZwUjkLIk+I4eTuH5nl4\nSghKlEjIaopnGdqBBrQspJ8dWmxk7vvWuRc0/pZJUNiDZw5ViZ0xkOeHYP1790DjRwo8vEbgtbEe\nMCpkzJnGDHRmBdcWvAMWBxiFtSjYkGm1g+wcxTbi5bjK5YHDsRTVvO+gpJ5NAqp578AYWuBQA46I\nREViZIkQ44ElBo4xsOVjjXDWxEZsGDeoEs+Vxm9LOvQo6Cmgm2Yzy6ECR7Z/IMJFlTORAxtnVs56\n4aI2XJyZzZZZx1Nw4LHlbAfgiOqJKDds4chlSWzjosKjpsmoHzWDCPAUhFVhFeUSJA3UmG3jKMgJ\n5EQGDYVTAhA9eeBQ9BDTvJeQ9D7NqorSsw5jGz1ozH6pd59ljI2/93t28XLAuCbrwcTX+bZtXHev\nBjwUsGEKDwbu7kD6evbRAo024bysZyIDiGQ2nHaA0hahItVGYl/YGG4DGt7ve6YdWQYoi6/0VSq5\np46o7SNYWEhVX3SDJSqHuHCMS7JrZOZh9o+DKrntIBfgnBpWDLAdFL0R4iroumQDbGUekbyPqCbm\ncSByZmNh5aKX1LCjVtVlI0/KCMhTgI8BPsaUJQJJr7hBw4k1HDnrgXMIPC3wkAHjgwofgY+kSWAb\nea/SoGwHQQ+JVchRCRlAyACip2Tv4EQFjhCJSyQsEZUtgYakj6cd6/DAUUGjqisN+/C2tKa+2dmD\nQesPkhq6GUUNROZ2j2uA0XeKPfsYgeU592rAIwJ1XUpyI1i0Eq/IlAbdfUD/3PhRW9Zhqouos4cI\n1YgKdUjYGIY6IPDrWgYAyWnr5xDYJDG3z2Czql8BlayqHBv1pdg/NtAoLFE4RGWLwikmw+ca4RTT\nnI9DzBPIIqxnzSMNWcM4gN4KegnETbPR1IGH1B+TvpCAaMngccaYR2YsRW0JyUj6GOAhwEPMLWFB\nwgHCiRhuWJcjF114XAKPZMYBfHQgcllyny9S1q2IG6TRoxJOCSwoIKLoSfKiwMQ0QtjQsGWVJf+i\ni1Qbh98frV8l61WWZl6HnyPQ1diqonSgkbuHoIKIOnkLAldZh8zD1Tr/g7GPVwMetoBvVDtcmInP\nwvYzVL2KMwUSpStop6MKGUCS/aMuca+DlmrLsvshXDu2/P49BtLMH48FRNRml9oSWdG8W3hGJT04\nG0hrQNUYWeKRQ5lnFli3ZEQ9xcw+NlhCnmUZ8uiLalID7kDPQrwIuipxc5vwyJI2DNLgVuxG0JUb\nvXAmzSvZSCNCGvMK2gvJwvkIPAoaFlgOaDjCcsNlOXHWAw9h4aOGZOdY4GPWdD4qPKCsecWvTerS\noyJZNeEE3AAnreBxJOtqwJJBQ/IRDDDs56DsXEGj7JWmNtfDfbdGXcGdu0au6Td5Asmu4ZYZFbmg\nCUBMLs8Axo6MTubr/Qw0xNkX99zrAY/d6/1M+g66DdYymBRWS+BRZalg0wKIybT5aBjiO0OZ7SpV\n35+AQ2zhnV/aHTQNWXZA0ozcYIa8rB+Jps0rYhooTevsV4grGtOZ7YLEG8K2cYgbuimneOAUhdMm\n3EThZpNkMzinqesobFsiCXoL8Tavtn1MvbsuQgwBXRYiB2I4JCaEsrFx4cKBC++IPIlyESUGTfty\ncFNpzfkWfbonLrdsyw1xuWGLR57igffxwIdD4APCB+BBlEeFRxEeF3g6wnZKYMGNwo3AHcitIrcQ\nb9OruAU5aZ67ouiSRlHUAYX5UefP6opoUmNa9lFVEslMUaRud+Bm6OQxKWMY4rYCyT+ZkdmCN4hW\nNSXL1LOKZ0DEdWwzlaWt1zLce869GvAYp1DsgYaWc8tV+uf78DsMxN3rAcTLq4rjpkw52kioBlWx\nL5sXyDUAIom11N9O6IAjr9isIwBZfk5GU7VfFNKlBY54gXiDbBth21iy6rBtyikGTlvgFAM3W0gD\nIDmJusG2JkOk3kK8A32AeE82qAp6CETSPhubJvvHBlw08sTKQc98JPJETOAhEZU8eSQKcjnC+Zb4\ndMd6uONyuGGNJy564kGPvNeF9wTeq/Bek4Zz1jT9/GkRLsc0ciInkJsEGtwK4Q7kFrgFbhVuQI6R\nqp9tab6GbKisDYjAhurW2Dw0D8Oq1KFZm8nsWWxp6M0hjllIBobxXj+S0hpP90dN9oZz6e73dfra\n+Tn3asCjZxojJDxPs7ybg08/rDsCiMn9VI0RSMhkQN3+DLkXMFkw0Mi9lbdnTIEj4lUZ7VWauKVh\nztWyYqMx6dDtAtuKbJElKrIJsgWOG5y2hVNcuNngJgpPpM2EQgTd0sK5VTJw3IM+KvExt31NZrwY\nFqIeED2wEbighOw7cOaByKNEVonEsOVZtrd5P8AjPN0Sz3es8ZZzvOV8uOGsRz7ogfe68A2Bb1T4\nBnjc8g82CayLsh4krVG5UcKNEG4raCQgqf54UAgbEjZ0WYkhb1cmdS91KapKMkKnCWFbZRrqy7+v\nV5SGWkFBOiDZk82Bo51B+jxg7NbJorL05737192rAY/xMyU3y+JLYKR9bnzCA4UHlVHue5yOfYiT\nZxCpW51mtpGX06NafoLQb3fut7EjeFXFzWbMi+LSZh3ZiKeS2cYFjReIZ4hrGn3Jy91DHjU5bcrN\nBudNuImBk8JhU8IKLKl9XyBtEPQR4pustpxSTqNkteVwRFlSxVNIBsSVI5l5yMZFNjaJmSFFJAq6\nHuF8R3y6z+Bxw6OeeNQTH/TIexW+Qfga4Wvg6QBRlS1k46izbyw3EG5gyaAhxjpuQW4UDhGRjShp\nP3WRS2IdRWWxX3JxWzgXAKkTwZKRPDbdSzV/2hCr2TSEBekAYwYe6p69Bhx7rONlQ7DXmMansI9X\nAx7z5t0vf3vJcz6GOfvwb+jDzgt6HMYtIKKajVxJZsO7Ipr1VyqAZBpcAKQ3npa1Ff7YCp1m2/K6\n+y3ZEmzYlhU4kuZ+ZFUpL4dftshhO2UAEe62hSdVTpK27kQghqz5P2TQeAR9ynNBQiAuCzEe0HhE\nwwnliJLngGjgpIH3KN+o8LXC30RJQ8wLsp6Qyy1yecPl8oYH7nnglgdOPHDgvSx8E+Abha8RvpGk\noZGNonqSwioORUWpoCE3CidFjppAZklzX9N0sguRM+JAQ9mIurKIA+dcvvaDTOl7x/wdDSToQEJY\nCN12p9IAxcg6eraxBxzPy6x+NpOZJ+fnZNfcqwGPkStkQ2E54/zt2Ira41ctyLWUZ5ZmcWGuFXz9\nkP21dhXCehp3ZIAooHbIMtG0xV23Jbr6jTlMrQkxT3AirU4NiaYrF9BLApNtBT2j8Yysdxy2O47b\nHbcbxHXhooH3pAGJkElEFIhZXYmPEJ8gnoW4BPRwIG5pUpdyS+QO1Tcob1EeeFDh+3HldluRbeW8\nrby93LNc3rKs71jWL1kuX7FevuRR3vAotzzKkcdFeFDlQYSPB3g4KQ+3wnav8EbgDchbhbdCeKNs\n98B9hDtNbOMUkWzfkJDnZ+gKcsnAkc+aVBfBGU67ORt1En76bos7GzAkv2YAMX8FjaU87+0fDjyk\nBQ0/76MBCTGlYs5IKHXMqyS+DrdKSQ8Ucq2ZOPeKwCO5yjSqnbuyhXYOqYeQT7OI2BMzFqL4SjU/\n1xSM05C1+EMGqmI5N1uI5VRMpoS8pl2WbFBd/GH2kDypKeRZkk9GMSSPuR5QWUEvaHyC7RFZ71m2\nldOq6JaYwBoP3JJGMm2btyiwPaYjPsH2RJ6FKuhxIcYjqjeo3hK5R3lDTGMsPGjgV+MFiReetgtf\nXy7cX+45ru84Xr7gcPmS4/pjxPVLnsJbznLLUzjwtKV9WM9BuRyE8w1c7pR4L8gbRd4K4S3IO0Xv\nFblT5C4itxG5ichpQw4bLCsiGyJplxHRC1FWByB1y+YKIH4UpTbyuomYB4jQgYg2gGKjJnusQybn\nfgJYrU97YDG/HuvvHBxewjR692rAw5syW1ZRmcfod2MvOj49NboOwpFteLenxoyjMhU0GgBxrCNN\nBtJmQ90Qk3oTl3QuC1DK7yrks8QypTqxkVjUnrR/hqbxVps6qid0e4DtiWWF47og6w2HdWPdlFtN\n4MuhOEAAACAASURBVGEbnm0GHhk4tnMGj2NANwOPmJnHPZE3RH0kck6Tx+KZp+3M1+uZv7aeuVvf\ncLq85Wb9gpv1S27Wr9D1S87hlku45bwdOW/CFjX9pILNcL0D3ijLm8Q2QgYQ7pXtNsLNhtxuCTyO\nK7JckHAhhgQWCTB6ANmQPLJSAaR+UVMnFqQ5DhiIqAOVETSqf846yllxKm5/tEOwSAsQLXj40ZUc\nWI1xjCwd/7MLDZO/7l4NePQA0U74rQNmXmXRTjKoMi9w9cm5LaRP3WhcrWBRAaWqKoV9QNqmU80W\nks6af8k65CX74n/R6WCHA478C0+aaXoaa42wbuk3WOWMkqdebkdkfWJZF+Ry4rDeEQ088qSxkH9P\nNqktlX2sWW3Rm4CuB+J2SpO/uGXTuwQenImsXAic9Ymv45lle2JZnzhe3nC3vuPu8gW365fcXb5C\n1i9Yw4FLOKbzknSmEJRwEMJJCXfC8gaWN8ryVljeKss7gTtFThG52dhu1sQ6lgsiZyScETkn+wYX\nBGMgazGWVtCwKejW/4f8PxQ7xqGAR3CqCg5gPFC0qovQgkjLNlq/Bw5TNfZkdOdSR3UHCvYawCdQ\n9FcDHjPm0TZpN+Kus3AjQ2khxSOy9/mi1+a/lBTkozNO9SqMnaU/ZwAJKEE0r2eg/O5QWj+be6+Y\n35XtG+J3trIRmSUDSfnlpnyOmkZgtgVdF7gssF4I2xHRI8t2QC8njmtkiUvaSDkubLqwLsJ6ljRs\nuyazSVxJy/PjkpfLK1GTzSOtbEm9etSFqGdUn4h6JuqZI/fcyZfcHb7g7viOu5u3hPWO7bSwnQLr\nTWA7CXILx1s43CuHN8LxnXJ4C/Et6JsIb4B7RW43tuOKnC7IcWU7XhJocEZ4SiDCE5o3DCg/kKsr\nIulnMoV0tvXBC0sGi8AB7c4hm4SrLWMOHJlpaB1+LSMrMgEMnYFH5gvigEP3gaOejXW4KpxZSS8r\nT04Y+p57NeDRFsto62ihpF73KxzNZuLtJdo860HD7pncF2gPPt45o2e59mdPRVtVph3rV/yWO2kW\nYgIJAw1Z8uiNVrkcFEnLY9P5GJFThJuI3kS4WeEk6DHAcUU/BDSu6PkBLu+J57esesdF7zlzx6Pe\n8RBPeVa85LWl5B0CBMRSqSinDB6XNMkKUDmBrGhYk/3hsKI3d2xvfw2XL78g/No75OFAeAjEo5RD\nT4q8gfilEL+C+CVsX4K8U+R+Y3uzJfvGKQPH4cwWMtvgQtRz9tcjOLDIc2JtXCitx5E0TnRQ4SiR\nA8KROn50yABxwMaTPEg4sEALgAQnS9+2X9DWqR0dgJT6olaHpMhqTezVEV/9rqgin8A0eveKwCPN\n7W7VFqiNHCdvlsTRA4k2MnK8s3B2D/ecv+7fX+/irqWTj3NDLIfd6IuBRncUQ+qi9YeFJBJCWhEq\nh0g4KHKIyDEZD7mNyO0GJ0VPWtZ26PKExg09P6C8R9fvE5/esclXXPiSJ77ikYXHaCtp80ClhPx7\nrAZ1h5ybmNnHSv1NtFtnj0mT2vTmhu3NF6xffYE83qGXA+ExwFHSzuV579TlPoFG/ALil0r8Qtju\nI3K3Ircr2+0lsY3DmW1JKsoWnhDObAU0LgQ9o3KGPIpixs68J1D5mRY7kqyCxtEApgBI3kRpAiAe\nLAxAxtmic5Zh9cIABEaQaMNVYGjhYc4mrk7++kQgeUXg0TMP7/fMw/s9CPRyDzSVYZjtyHORCkze\nfiLOn8P4pLknW6GPzdtFxkrUsBD14JHUlWBGVomEoCyLEo5pZGZZE3CEUyScM3DcbnDa4BjRw5am\naQP69Ih+eJ+ayOWUmIf8Oi6ycpYDj3LPY7xJE88S92m+gZYfMBHQ9JstBhyRBWVNk8JsPxKAmxPx\nzR2Xr+7R9Y6NA+FJ0sbEedtSOYDcQXynbO8E+QLkHcidEk8b2/GMnJ7YTk/I4QkJTwk45InII8KZ\nmCwu+XxJqVIQSXaLYz4O5lfhKMmecVTlIC14GIDU9cQVMBZGtiHUnb78cvqQf6V9AA5XZcQVs2cX\nrQIvLtyMYbQgUhV233Z61nKFqTj3isDDVpXtAQeDf9yUpQUMyp2qoqS/6O714CFNDA3INDud7QOH\nP7f2kXHY16sv5Sxpp6ug9byosuRtBxdNO4ctF4WLIpeIXiI8bXBa4XCBw4oeLmlm6gfSkKumFbPx\n6R1b2LiEwFO453H5ksd4Dxpy5Q55/olg2yMmPdp2U/fAcUrlmX/pjSX9WIreLGxvjuh6YOOAHA+E\nS2AJsCzCskgyIN/B9hbkLcR3EN8q201ElhWWM3J4RJYHtvCISDqiPLAZeOiF6OZ1WF0Kzp5xZOFI\n4ETgWI6qmvhjmRwtYIxso65J8SMmnWFdMwwUg12qk/4HqH3YuXriPVdAZPrMp7tXBB7S+XuUHAFi\nbvuY20OKLzcOpQWT1Gz7M4OMAjyG9kk28gzrMzz6+16gl3pVhsw4zBaSK3bQrMcrS0xqzHKILEcl\nrHnCFCvKBQ0XNJzRuLJ9jGwfN7YPkfhh42seeB/e8LB8yWP4yHm5cHmzIfeK3JEWoB0FDiB5LbmU\nfQkOxJxfzawkqTdl12FEDnBY0FthW7MVYBHCJqm48iJBWYR4EwlvIN4r8Y2yvVHkeGYLD0j4yBY+\nIOEDIg+o/QKvPBJ4JHBh4cKiKwdZOerKUYQTCycOnFi4YeGEZuBY0op9hYNItn0k9mG/vuCHZBdJ\nhtAKFBk4tF4Pe3BIZQuNeqJWM8RVRGFqr9CZ+qGV1XlZF27OJ17GNHr3isDDM48ZcHjW0Ssd7bU3\nkI7spD8i4zsMJOwcG5kHknFo2c62WkfSDzyV1GTVoIzLu6RTgaTYR7Q1qi4ZTBbqyE2yhWhaUXqj\naNS0tDwom0Qu28Z5WbncbpzfbfzqxzO/LGe+H858lAtrOMPdBf3xBX4c+DHgTUBuk1EzKf++8hkC\nHFzi7efZlgSoQeAoyI2kgQ+l7FFiv+0dQzL0xrstDcEeVwgbIo8g7xHeI3xg0/csPIKcWbhw5MyJ\nMydWTkRORI5snIjcqHArgVuN3IpwQ+Ckykm0GEbN3pHmcWgaFaeqjcWAHcftAUcjaGIPBhq4e6V6\nXvM/xwwGFvLtgODbuFcEHn78Yg84nrOBQAsM/fVMIdmLy79rBA6dXldKX8ZXNHZvTj1IOzuEIa2D\nYdXZRIqKk4HDAEZU0VNeSh4UPUTWQ+Rx2Xi83Xh8e+Hxx1Z+9fHMr3Dm+3LmI2dWuaCnC/IOeCfo\nO0k/dX+jcBK3/XrqNRXJ+3X4Ms4zISSkcCHZNzhl3b/gcureNaQ5LnrciKczcjojh2wQlY8I37DJ\ne9I62/dEnhBdCbJy0JWTrNxq5EaUG+BGlRuBGwK3xHRW5UaSYmV2DTsWnaknySZRJnmpM3KruO8h\nWS3ZW6Q2U0Oc2wOUvwVO6VjLD4Azrwo86rlvvDBC9Qwgql8b/zV24g8DiZ59qJNXJhIblcaqlvlp\nfsnSNrRTtbWbeX+qAiS4NPfGNKfW2AQz3EiMG5VR0poYPSp6o1xulQ+3Gx/ernz48ZUPH898fT7z\nNzjzfS581PQDCiwr3Ap6I8htQG+07s51EEcMpewponKo3yfvb1oAJEh67iarPksOGSg/sqRLJC5r\nMoYeHmB5hPCQWId8A2Wt7TeoPoHU4dcbIrcItyrciSQ/gVvgRgM3kgDkhpgMpiocG+NonRW6qK0z\n0WYSnwEE6hgGFLXCz8eAaqicttcZSEyBw5DW7u+wjudAoW8238K9IvAImFlzDhyfqsbs+QceUHzp\nz8Bgz2/nFjhiwxPyb7fm6lRgR2OequSPFlxGU27LRqiwUxfa2YrQ/PsjelQ0/xzDeYt8/Xbjm8vK\n12tad/J+e+J9vPBez3zUM2u8gFzQIEgIaDggQdFDAg45aJq9SkZD8jCuSq3omD8dkn+ASfIojBxz\nMAccaaevlRjOIA8QPoB8APkGkb+J8DUb6ZzWqCTichQ4qXIrgXsW7li4Z+FeF25ESD/oELhBOakW\n0OgNo5XR5Ule+bd6xH4jx84GEtYjOHVzyjSybLoArZF1LVzaGJ51k6DSAM8P5l4MHiLyDwL/MPB3\nAg/Anwf+B1X9/g+ejBelwPW514DDZHaeAUk66xAuf23tG2YXpmEbvd+rKWZsrUck/dK9/aWmHom6\nkfascsCh7W+QpWMytUx9zrr/flm/atohXA95HYrypJGvY+TrCF9H+JsRPsQTj7rwFANPMYFaWtrf\n7qWafmle0cUxj+KsXOZrO4uNJCQzSNLqDDi2xDpChHAh/ZzTA6SF/Yh8DRk0DnzNUb/mRi7cauBe\nhDcaeIvwloU7DtyrcqfCPYlxnPJoyonISUIFDKnAYZPyDECEWpS+WhQZmsumso+SV/Xt3tdTV72Y\ntXWtd/Y0jcZ40sXQRyik7/b/ldoiIv8c8C8AfxH408D/Qdo14R8CfpeI/HngX1XVv/ztk/ES5w2m\nHgz2wMT8I2iM537GxsuYyRxEPE8wf2RUa+o+mLaeov6Y0FYO+/FGnfrTmoxWvjr/hUTC8wgLazYd\nXrIZ8cKZlfesfJCVB1k5y8Yl3LHpj7HxFpUbkoHTsmdIlQHJdu4tQ7fum0hfmXsASfGo3ZJYNh+2\ntSboGeUBlY9EPhD4hqDfEOQ9N3zkXj9yLw+8040vWfhCQzpL4D4KNxq5VU32j5iAY5z85Re15cVp\navBsVUBd3vsq1AJF62ad2zNuFkxm/i7OCVg8e73HQK7dy+4lzOMe+BlVfZi+Q+S3AH8f8LcZPOoG\naXXEAnwBalOY+4xj/6y1onhZ4/cyb/8wEGoBxNhHPc9BpIJGOtcFWh5EWsCIjX/Nh/cf0byKNHIk\n/fR0+gHILfvPbHyUyEdVHiXyFCKr3rHGr4jhTV5mv7je1J1RN5PN9Y6zrrG0H1/ZtXwmNbYX8gZH\nsiKspJ+tfkT1I8J7Il9zlG9Y9AO38oG3PPCFPvIlkS858CULX6J8qQt3MXCMkVM+jjEPvapNR8cZ\nQ72xuU4lb+tD9mtfL3omkWXS3SvFMW/0jXQKFrmsTPRikKnXhXVIYkm7zz4DHPAC8FDV/wBARH6T\nqv6V5l0if4eq/tnnX/O3ws1KxYOIXff+vXMv8+xj79z7Pdtoj3Yy2mi5qPNH6j0toNGCSbstXgWO\nrQBI/iX6Agqr8x8dWNjv1q/l1+vPxPQ7r0KeVgUXbtnCV2y8JWpmHqUoOgCRyQEOJDrqrS5crr9m\nO1DbGU22DBwX0vTyRyIfET4gfEPUr1nkIzf6gbfywFc88mMoX2kCkK8UvkK42TYOW8i7pSnLlibS\n2aQ6b89odzv3E7jGMa/iZuBAx7hkJ/wzjfzq+aVx9X6d+D3Q+QlpLyBJn2Iw/Ysi8l8C/7yqfsyy\n/xb4Bz4hjh/ABff5fCnsXc/sH/3z43l8xzXw8P4eMPx9/xOE0T3T2kVmbKT/pTLPOAxAyq/Rl9+m\n9wCxdn8bl3Jny78pGzjLwtmmVckNm74j8hbVGwpINhWuK+fdxnCldxOwX4uv83YjSFK9JKcu7eWe\nbB7CNyjfsOgDN/LAG/3IV/LIjyt8pcpXwI+p8JWm3eDDFpFLTJPk1kjIv2FjiwlDMXoaUPSzfl1+\nvYVz2rAdcPhNNxo57f29shN23jE5X4ujkylajaaM94dmc8V9Cnj8OeCPAn9MRP4pVf2/GWrG3043\nZx463Evy0T+TfZv7cwAZAeM6I9kDkpl9xP9OiA4AEgvz2PLZQ8alg5JLOWK+p1zkwKoLq6TfeIuc\nUO5R7kHugBPCATf9M+fzOd58JZhnLszraiE6mltSfr/GwGGDmy3ydtv4crvwlcKXCF8QeEvgDZHT\nprApsmraHHqlAEcdJakA0YKGzhtrv22+B4Ni8+nvTcL18Q7v2fH3cVyLZ++e9veNArp7f4uZh6rq\nfygi/yvw34jI72L+zT/Jicg/Bvy7pBr5n6jqvzUP6Ydqy9N9Eju5uiqhXWL3wGLv3p7sJQzlJcAy\nYyRzMNmzk9SjXksj35rn0lgO+O170/mIyC2iN6QZEjekCRkHVNO8y3ZB+Q/i+pqeZ6aaXUFvIb5B\n9ZxGfKIg5yOHj4Gbjxv3Hx959xB5u0XuwsJN2DgETVsWoBDTjNr0SwnaklL/WiExIPND/X2dQTXT\nyXp6mTf62dHf5xn5t2EjO8ynIR09WMwI+xX3KeCRkqH6x0XktwL/BfD3f8LzY4QiAfj3gd8K/D/A\n/ywif0RV/8Ls9TOW4Rfnv4yB7N23KGb0/Fp8Lzm/BFiuMZS57WQOJi2w7KlDdRAYwP9IgCSWwRGR\nI6InJK3fR1kQST9gW7dzhm8PIn3tFVA3M7X8Bu8b2CK6CWwH5EPg8P2Nm1994v773/DF9yPvto27\nQ+S0RA6HtI6n/ORnaUBQdqI3nBLy7Fh/PTs/E8bYwN4mHS8AE5nIZtf9oNWngIoRjLboDS2Zg+uO\n+xTw+G3mUdVfEpF/FPjpT3h+5n4C+D9V9S8BiMh/DvyTwBQ85u5aTnXn/37YT5ddYyaz+9Uysgc0\n2vivgc1M7dkDmXmYujw7HfZDAsEWnMuCqB/IFFRCViFmPPnbOKu1ybaS2E1+hyq6belXp9YDut4g\nH4TD33ji9le+4f6XF979cuTdZeN02jidIsspIidNWzTaZtFpqmjNhu06X8ZnKdPiJdjrq7/OSe+u\nZ3sIPrev4DWA4YVyrvkd6+jve5BgIvsEAHnJPI/fDvxnqvpLXq6qK/A/icjfC/x6Vf1jz79ucL8B\n8CM4f5UEKBMXmjyXdOxG3ZfAC3jYEOy5Z64xm/Fau3sjnF0DHR9DCzw6+Ot96a5HAOrqqVgn6/5E\nsGG9siJY5PovWbzYuW+koJpbs8bEcKLAJuh6gMsNerlHPiiHv/ENN790x/1fOvDuL0fePq0stxuH\n243lNuafXtC8q4+m3Zxt1x/byedA3guWcclsAyxaZQ5oWkCRETx2Wcr8ukzIfQZY+om7u8xDcqE6\nlUr6MNqF6cHlinsJ8/g1wJ8RkT9NmiT210iTxH4z8D3grwO/+wXx/EDuD/3Cvw6kPP3Ez36Pn/je\n966EVsblyfJC/HCBhjieeUffmrT8G0FpwIlJuH5Sksm0v68OC8zfhWtk/y97bxdr25LV9/3/VXOt\ntfc593bfxiTguOWAQ8eRsCWDEhxEBAkWCSIKeYgiGVmJHB5jK5aMrdjGEnakKBESsWJHeYoViUQW\nD7EUzIMTGkW+xKabRiFEYGPHQhYG0m3opvuee87Ze6+15hx5qDGqRn3MtdY+fe89dze7tuaec9X8\nqlmz6jf/NepLar/2Jr6cD107QyFhjz6I0GGb6ws+Y0LXsJfAwhQ2a2B6F9KM1nc74Nkd8KW3gC++\nA/72x8DPPwP3e/D6Cri6Aq512W2B7QbYTGlt21MaEiCtdTvGeh0idHARIARgCcUvqCoKbpGQwmzb\nNmdw8Gsi9+sxSlhHwbMLyjni/Cry+Lg+J1na95K23/7MZ/D2Z37uoldGueDzQTIC+E4A3wbgdyPV\nm/0ygL/95bQsJfmvA/hLIvLd+vvPAZDWaEpS/tHNfkXkF+e/v0CTp9zv9tycZsWdW/mNfkv1O3Vi\nU8uEO2dp/FKfFml+p+NsW6doSfUqul3WyW/224vAKhTytq4PC3AUwVHXBwEOi+TtowgOTBNZH5lG\n+5gDsERgjrqeJJUg9EspKulPpMH2TfdeIzBqBMjsIuJugbw8Ai+PwIsj5OUR//znv4RP/Mbn8A3/\n3+fwid/4LL7hN/4ZPnY4YHu9xfZqi91VWofdBG4CsI3gNgKbAG4iOAVg0vUmgjEoOAIQAzgVSDBq\nZo+2rYvtDwoM6jpovx2DhG7TgMGRH/I+noOHDb7kfxs0qm2s7stVtR42Hk55G9j+/k9AZPwVvcjm\nISIzgE/q8l66nwPwDST/RQCfBfBHAXzfOBBrgTtx9fKxrGoGpdl/8nojOvnt+6wtDALrajIsTfg+\nFFzqfSdqdOvKl7VKmeZ4sUjxYIiAbAHZQKd0BGRK/nlUHKDuz3LBl2rV5TigVq0yhfcIyC3BFxF4\nBsi7BJ8FyG8/xfHZV+HuhnhxvMKz8Bam6YjrMEHChBgmbDghz6CVM4v7AtsXvylTMBs5LJONjztv\n2DjlP1IC9/Ebbbt1V6YZHNO9sNE5p919OsZ9PVIfl6/z54nI9156jdaJyEzyTwL4SZSq2l8eH1xD\nYO2Y1d+n9p069lJgrG17v3OLAwUbG2f1uwXEqLZWF67U4oqHT3TQCAqNHSBXktZzggkmpJ60QJ2u\n7TnvC5A2bhfo7FJAkkUEbwPwHJBnBL8YgC9FyBeB47vA3e0OL+eP4N3wz2GLBYgBMQRsQ4CEkPvL\nAIsSeWnyxlpmGywnjREX7D9bjDi1fR8YnF6vTzS5BpV1d5/alv8VwF8H8BModXxfthOR/w3A7z97\n4IIuvwOoa1bzRcf78/ZJOGhuuIeSGJeBmt+tghj5N2qinWv5LCyO/VpaP7eI3suabpiykC0gTwRy\nSOdLVklOcZxrK3apG8XHEal2ZQ/glsALgs8AfFGAzwvk2YTj8x3ubj6Kl/OMd8OMbRCECGwicEWo\nTWYGmKaaTC3EjihJt31RjiFwPYEr0AwUjO0bWjH99nkAcPWYU8etrH24WfaNBjDs637b7bG7Dzxu\nReSv3uP499bdR0V4v3Z9Zl8HmEugcaYYUikIKZn2omYbph5Stw9o9w+EWRWBzukUdZ2B4ZbgFjs3\n6DkHQRosKAASBUsQhCtA9pKmuQWASTJgECXnv2wbdYmzAHj0Mtacb91ZXycV4ViUlD7DEcAtiRcR\neGeTxhvlJgEkRsEUBMcwI/AA8gjyiACbs1byGLDkkoOfszlF4XNJRqNbXZqpK/mzsn0CNmcz+6X7\ncY/9vbsPPP5bkj+EVMS4M08R+fl7XOPV3ZI1QXGXFD3uAw+jxqmih99uFgNIBRJXDJERKHQfW1Xh\ngOGLH5b5oeAwP+qHNSoU5iMw6axu8yH9no/AcS4zvh2PyaB6S+AWOgAOBbwSYE4ZaNkK8FQ0Pbki\nCwSdxT8vgpwAuyJN8yII0F03jSrGNMAyBNylWePwBOBTgHfpUnMg7ph6u+wEoDDNoDml5RiIqyCI\nYcIUiBgCphAQmMbtsPFdo7YqDUCxZcI9FlbyauXY76+ajw8yZte/ZDS5whgI6bhTmX0dJF5d9e79\nUx5/EMB/hFTr4rXfd97jGq/uThQ1KqhcUtxYWQ9Vx7niyJkiyUhpGCxsMfsDnbqo7BYeEg1A8m+F\nxnJcWQ4KEgeT5Qjs0zQuiNrnY1kEy3XqrCZbwfJ0SbUgPrLzGqgNiOaIbtRvac7XiKRFPJL6YQw6\n3YC2dt0CvAL4BAh3AA9AEGImcEfiueg8UgswT8QxAseJOETgOgKbQGxDwIZRF0Ek0ojo1C75LM00\nBHRNNiTXxpdM52XqKT/vWrisZczLIbB+rUuh0vzOl79MdQD3g8d/COD3icj+Hue8d07q9CdAbe8w\n/zWFcZ9iyNr2qaUplmT10SgMcapiaMtooNDKdV9kgQNHnpLWpqW14suh+C8Ht+jvuwMQZtHijmA+\nLpifJHDMTxfwLQFnHbY5j0pmEc70oDRwGEgGysO/oGZ0M8BmvWMBCPT3DghXQHhCcK9FL0kN7O8E\neDEDciTmGTgGwKbgPQTgSYjYhYCrsGAXBDtO2NImpdNR0gkIgUAiquQgtMkGDG7NM1h1GVDion7Y\nwb5BRj3p7gOFS49LbWmyyQa4Fyxadx94/BKAtwD85ivf7ctx3kS7Bog1vzV4tKrjEpWxpjjOGD4r\n9dEUT7wtozVuZmgcy7aHi0Ek2zn8ti2HtJaDLvsEDtkneHAPyF4w7wX7veDwdMH8VBA/uoB3pjwG\nAMlDnvttQf5ci9v24MgAcbUgkFQriiTJc7OJLRM8Dmq3WVR5CHC7AMuR2B+Aw5E4MEFjT2IfgKeB\neBIE14x4QoULgS2JLRMgbL5dywg24nkAIPTqCKjq0H0Coduu1BUGSs1cVwg/4waZfHjNM+dc7Hfe\n3QcebwH4hyR/DrXN45Wrau/lWmVxCUDOwGMVGK8KjqZa1deW2HZYgGVhmu1egbEsSCl5FvCI1Hl0\nBpaZWI6CRYGwHAssvM3DIJPXbtu6o9taDgvkuOhasD/MmPYHbPYHbPZHbO4O2E0znh8EL5YFiwgO\nuXl2SCqDQdtD6EROgMtyGm0ufnIJxi305MwPAYARDBGBqV9N2ASEHRGORJxD6r6nBgmrmAGIeIBO\nG5lmqyeAJRBztCXVAh8DtVFcAchEYtL1zKRGbFjWkG0i9WQY7cx+IApYgQwNOz7rj6q40cJjABOu\n/jhx3LoneeY693D3gccPvSd3fFXnq2rPqQxbX7pd+Wl53T6Op6AxAIetxX9UFRqiRtOkRIgwC2RJ\n8BD1W0Qgkj72XetWpnXV1kkTQ6o90JJEUCVjtQnBpl5Io5ELD7o+4sA7XMcbvDG9xEeWG7yQGzzb\n7vHbW+C3t4JlC9xtBPtNBKcrIO7AsAN4BXILYKswUNkghCzMzwirsQlIERLSIlhAHiBySGsc9Auv\nTcOXgBAiOEWE3YSwTAiYEGNEjDot5UTECQgbIOyhcUkcF2C/pAEGbMaHhcnIuiewC8jrA4kNy/za\nk26bHSRSZ4IjEUiNU6QiVe7CX8BCB42EBylt1PQ9Wv6t+7JIfqfVb6D2L6venVUiKMWWexejencx\nPETk7Ve7xXvkTkFibX1iO6sYr0DcMvI7pziqokqGBGzA8dKuwsEijTfh/ISpmbuGVwxm9gj0aSkl\nR4NGag1NrUlAngw7cAHDDIYjhHtIuIPwDsI9juEl3ojv4HZ5htvNM9zwHbyzu8V2S8gGuNsQzzYA\npi0wvQnGN4HwBsg3QTzRhBeK8FfCyULQlBJQOpXZkwTVDdxD5BbkHdLwARFkAEMEJSBMG4RtSQYF\nUQAAIABJREFUmiAyRkHYEnHDVCW7IeIGiDuAdwTUIHw4AvujvUPmlu4HAHst1hwUHIcAbAOwUYgY\nPCYU9RGpI53QuqVQ12VgArIAI2+zFw4VQLrEfWq7XOPk71dy71OxhWl2ncFTaP4T+cgr3fm+rsnw\n5re6HqmLc78l3aADx4XAyEX4AUjMUGpG1PI7AcT7QQFSKWDd8N0dWmhEBUmuPWCaMS5yRuAM8qjg\nuElLuMEc3sUhfh57+QIO/AL2/Dy+tH0J2Qbcbolnm4BpQ3BzDcSvAuJXgeGYii1Mc8QDE5ibwKbw\n52LVUb2tJ2tum78gDTWY5pYVvAQxJ+WBVCyiRBBbhN2MEAVhGxCPE+I2JNWxVZjsgHALyIFY9sBx\nT9ztAczEsgDzDBwWYr8kxbEPSPYRJhvIQYGxYZrA7qhFmKhxWYEEZfJqK0INq3oJ2LzC9g5Ft7yN\n0g9X1Sfkdrv4cGXfOTe0j/Y0u8hdMgDym/e/7PvgWoPpPZWG/+3hsKowRvA4Aw4PixYc3i7YGU+F\nYNWbTv0kJ7cii2Fl8Vpp5ISuUju69gwxLAicEcJRFccNJLyA8DkkfBGz/Cbm6XOYw+ewhM/it7fv\n4nYb8Wwb8FvbiGkTgOkNML4E4wEMzEUWckIixKIZhLVR2CamB0rEEEmW4QhBmtCJeIFksEkjmlEB\nEsIOjJJsH5gQZYtwJYgbQdwlcMQrgqmxCpZb4HAL4A6QvbZlUSUyHYEdiSsm24cZUHeqOgwcVgsz\n2VptIhbHIccxdAglVKP4+cprq7Ux1aERofl1BIm1NQbH5ssVv/dEiVzmHs6McfeARaVQPCTQ+DXH\nWdoWD4ABCHwxRJxfhkMFFg7VjQ8zm/v7om6Rxa3SsFaSyKCIIY0OHrkghgUxHBB4QOQRIRzAcAvE\n55DNcwieJ3hMzyB8Bwve0fUzHN98F298LOLJmwFX1wHbbUijc4U3gHADaoML5nJJigACkCMhB2C5\ng3alR4qgKDqNZJoJjvEITrfg9Bxh8w44vYMQDogIiIyIjAgICLxCwBGBaXTVVIzYIcqEwIgYIuIU\nEbYB3CoBtsByS8x3iUfcM1VZHxS82sueUW0iAaknsa7nwGz/mBQsM5LqsL6Bk77iwNIupKxZgcM+\n7L4oU4qdRUUk+JSEPFIX1ATTIYWj49qDWqXz5bmHA49XUB6jJuO5phComhx0oBlsi1uGwaDz8IXb\ngR/9GqUo0hVN4IFh22Xu2cDFLXNSGbIgLEcE7hHCHRjSBNGMtxA8B+JzYHoBzs8BPoNsbsHtEdgQ\nYbNBfHOH6WsCNr+L2L1JXO2I6xjSHLSBOh6xDkrgxyRYEjhEBzuXG2C5QaomRgqzaO0Kt3eI188R\nr7+EeP0FTE8+jzDdgZxUeSQ4BDxBwK0ue0QeEMMVwrRF3G6TEuEGMU6Im5AUyjYg7oiwT4ZUHrSq\nd88c/zrGEI4u3s2wurDYPmZdzIhqCsRqZQwYpXamXtNvO3CE7l2nxEB3UGUYrzJD7eHbpuZ01rq6\nL8F74h4OPO6hPE4VU4YgWfHz0Mhru4T0QeqcwsI3h8h+KItBJCcst68tnqSEps3IOYMKDTLNEE/O\nCE5pMNwlxRF0ysbwApDnoLyA4AUQ3wWf3gBPjml6rycTwhs7TB8DNm8R2zeBqy1wFQIWsozT4+PB\n99bdp6IDXgKLTi2b1IfoeKRa77y7Q/jIC2w+8g42+Dw2288ixFsAG4BpAshU+foEkXeI2COmiSEQ\n+BQxXiFurxIwoyBMgrCJiJspVe0qOMK+hgjn9E0XKU1q7F0m/qUhoxM4mAFiQPFVuaYsoimTFiCo\nwVEVZ1CngVqJSPWLQFUssuxPTbhldLeVNOjOWlMkneS9wD04eLTKwfaNFMVa0cW376gAIgBc7UYL\nF3+9MTBYbgL3ohqA5K+NuLXzr4snVsYu/tTJq8EFDKn5KOWQliVVfZJ7LWLcpHW8AXgD8AXIFxC+\nTNu7F8BHb4GPHoGPAPzoBuFNQbwWbJ4Itk8Euy1wFQMWBMxk+mpDtFZIUqnFWrnumaZZeQngXQHe\nVZgcU/sS61zD6zvEwwtM+BK2m89j9/RzCJsbSNhgkQ0WbiDYgHgDIc0sk6CIGTEcEKenCg4gbEKq\nedmmRmXxEBw8FBz71ELVGuctCzAvwNGKnoI86NIsRW2YQrH1RGidkK4dOFIxpgeH9ytGVa6M9iHw\nxZkKGF2m5kCVlF3FlQRZaRQDyypRVj+LAB4SPFaKLeu9WRME2v0dfBrl0RVbmvvl6GzPdS5/Adx7\naYspWcYaQFhqM2vF0Vj6rbYid4SxbucHgHfa4OEulR2Wl0DQRRIwGF9C4ksg6vaTG/Cr9sBXH8Hf\nBchXbxDeJKa4YBMX7OKCq5hmnJ9JHJG+zAFpJLNkI5IEjgOw2BxNLwB5nrrS84WkXrp3C2Q/Q/ZH\n8MkdorzAZvMl7J78Fq6Pn0WQF5hli6NsMcsWc9iBfKnwUHBgTrVH05IUBwKiTKkB2QEIx4BwWFJf\nnz0R7lR93Jn6YGq+r50HYQ3yBIgLERQoE5jsHw1EZjiIUDsaKzhmuvGVV1SIKQ+vPmqIcACUkuTa\nCZs6VdIxQLKn+365LdbHdldfdw8GHv7rz3btFEUBh18DWS40aiU7f5zzau0hOTyDeE3Xc6MtaAA9\nQDrFQeRZ2HPbAQIUmzsVWgUrCpMFSX8fU0FetK0E7xI8mIooIrdAfAnwJSS8BOYbADfA5hbY3IHT\nHrI5AE9nLG8Jlo8C8lbE8tYGh6cBs1aZkAsmLNggTcFAbcdpdglZAmQOaiglwh0x3wj4AuC7wPIM\nwPPkH+6IeEeEPbHdA9fXM66eHnH9xh7XL27BcIvjZsFhWtI6CMCIgB0C0xTVkRNSvQsRAxGhxtWA\nVC0dtVv+TIQYEaaAMBFhw6Q+NOpKs32FiTV2tVa/SMZTG2GQzQBiosvilghdOxVSJs9mBQ1vw7LG\nYtaGxNu8vJ1Ek5H61ePeV4oC5eAODTylJxxeTnMDwAOCh3+mFiAA6qIISmQajdsRyE4LssbRrWS4\nK23bcU2xpSqWjMBhiUTMCGo2DTOIFgNpUhqaA3hIS9iDosBQ1cFwCwn6W3vHMSyQrYBbQLYB2EbI\n0wnzm8DxCXDYEsdIvGDALQR7pPnpAEHAFSKuAewAnQgqyBaybCDzhOUQIXeE3ADhJbG8AJbnguUd\nYHoOPNkTTw4B1/uIJ/sJV7LB7vkGu2cbbJ9usLuegGXC/mrC4WrCHhP2MaapqZjahCzcQ/ASQGq+\nHhEQmJqsR87JkBq1VoaCgCm1Ug1pvNIwxdSxTvvJ8MhsBwkm4gwilk4MEijqw+fkFiIeIFaF2xVl\nNAMvqGtjPAyqhb0fGj+sbPtJz+r02isOdv6n3YOBR1YebntosXTFjfalpAthnRyjfSdgTPT+9rIt\nzNXLF7et69KoSIGh7dcNFrVR1IoqWn0g+7JmMo4mgNyqCkkLuYdYn/0r0fxP8Cr1W5/fBPZPgLsd\ncReJF4y4heAAk9ai4LiCgYPYYcEWIhvIMWI5BMgdsdymUtLyApB3ieVd4Opd4q1DwMcOER87CD52\nEDyRCZt3N9g8nbB5MmFztcHCCXfzhDtE7GPE3S5gz4A9BAceccAd9ogQpkpT0qapSoosBAeOAISw\nRYhTamC22SgwUpTxwLTeKEhm1hBx6coyumNK8ndQiQ4kBgSDRNUuB/UygohffFU9BvtbWLRgKeky\n/UrN072E1r2mSC5nx8OBh7m2+LJWDPGq5F4qw+7TnFzFKeuXVq29GvLQ0N/WxaNSHVKUhrVpN1BQ\n7Rq04fSy4thDdJ3sHLdFcUhqJcW4h8Q9EA9plKDNAl4L5JrgdYBcB8j1hPkJsb8mbrfETSRecMEt\niAOAWZ8m4BqQKxBXmBUegi0WUx77BA+5JZYbQF4I5Dkg7wBPnhMfOwZ87SHgdx8jvvYIvCkbhOcT\n4rMN4tUGcTdh5oRbmXAbJ9zuIm4l4gbEDQU3OOIl9rghU5hYYt46rkVoS9QABElN2MOCVGxZIrgI\nwpEFHAe1g7ihDnIvZmf78gZVuPRnBtMMERQ/UyEGEdvOpWmnWEKznT8saIAyUiA47WdpNc/MgKRG\nfLG7/mZe3g7k4cCjURktOEb7O5NQoyxaIJwskjgPNkCpXhhL2PxLz9CAJhDxqsOub4bQBRA/RJgV\nU2zZA9yDqjqEd0jts1MDC8otBHepSeUmNa3k5gjZzWlUsCcAnhB8GoFrYN4Sh22Cx4sY8JKi8CAW\nEBQi4Apgggexg8gOiyg8THnsk/KILwF5Qci7gLwruH6XeOtIfO0c8Xtn4OuOxEdlAt/dgFcTuJvA\n7QaHOOFmirjZRdw8iXgpES9IvIsF7+KIyDsAC/b6MgRMbU9QhhVM7VMDUqGGCSISEJYlzSp5bMAx\nqZ+PbjdcgnUbWFwXBRGFktTFlQwFlCKLNBDJ7UJQK45WJedpXtAsXNluFn9uW4Rfc4TF62UC5MHA\no3uYUZHl5Dk1Hdh76Q5NjK3dwt2rozs8NKR/saJJXb+Qab/2xBS1cYikBlSuBgWYId62oZpbsId2\n8wJkn4olCpQ0oGlSKbKdwe0C2SzAFsCOkKeEPAlpeRpx3AGHidhPqchyS+KWwF4CZhXXyb7wBEGu\nIbjCgisItdiybLAsE5Y5Qg7JaIoD0hAAWjXxdAbeFOIjQrwlxMdAfFSbdXIfgZsN8HyDw26L7fUG\n27sJu8MGu+OEzRwRGLSWQSBccIcZC45YeMCCOyzasCwgIDJNlRkMHkgqhDEgSEQIrodsIEIkwlE0\nyplgokWYetwVVi2JU8tiZiWxWNLxCcMt3nZv5xggcnGHLOCB+9C0l+OgRmZwnFX6eoCY64ryr+Ae\nDDzC+UPu5U6pjkpRcEVpNC8rKw2648SDQpkuCg1KNpBaP33KrAApo/6QBy2eaGF9OagNQ+Gh7a4Z\nj5Dc8w4p1W0DsBVwGyBbAa4Ecp2GGVx2U1IcG2IfZ+wjcReIOxJ3AI6csCBN1hIxYYMnWPgEgmss\nGSI7iGywzFNSH8eQgilIGTcAYQLe2AquF2A3CzaLICw6l2wgIBE8TMDtFuFmh+lmwvZ2Au6m5D9N\nkBjThUIEOeEOAUcSRyw4YsYRqUt/qtKdkFqnBgWH1LaGMBWQ6LgkjEzAiALOToWYAVWHFqDrLU1t\nKddmSPtyL0xpYdG00hZXKpC4xdtJ6PzWFMY5JSKDbTS/h7bBC9yDgcfooe4HzFpiVK0+Kz9neW7A\nweq4urNa/9ERBYxU0EhjPyzFMGr2Da0jpByLAkFSHWQagyN90pOxlIsChHtAUpUBwwzhkgIQCe4I\n2SaIcKdzsOyA5Qo4XhHzFthvgH0g7sKc1iT2IGZssGADcoOIDSZ5igUJHkIFB7ZYZIIsExatruWR\nmBbtFxIFcQLe2AJPFmC3CKZFEGUBN6IGgwgcJvBmi/DygHg7YXsXwf2EuI/gZoKITgHJCQERtwzY\nA9hDsOeMPZIas6bt1vfVer0miKQvduCCEGN6LyGmid3mkEaUjw04ZgcOhQck+eVBq5uklWYNZFYj\nXWI9CY907nmAyFh9dEvCQQcTNmtBri72/ufcg4FHVh4tKtf8dT2ChB3uz2O77wQ4KqOoLWyOA7RX\nbFpKl3XtRMYZ8OBwNg5acQVWLXsAwwGyKDxg1bNpMJ1c9xgXMAokMOXenUFDtNgCyBaYd2bn0CIL\nZ+xJ3HFJ8GDAEVuIbEHsELHFxKcQPHGq4wqCHUQCliVC5ojlQISZ2IpgCx18eAO8cSSeJOGDjQjC\nIuCkymMJwHGjyuOI6SYi3EbEu4hlHxG2CgNGhDAhppE9cAfilslIShwwlxmqQevWjzK+WbCambAg\ncJPsIwKEKYCzOGBwvL0UxZFZ7ztQAtkeIkA2qKLsKsUVFAXSfgFfSYGcUiZw9g++N4rD3IOBR/tw\n93nY7lgHhrzfQ+QCcFh36q5GJe+zEaTct8UPky72KZsLOKTYOsgjBM7eAR1xK9hApKnYQjkk0Ewz\n0idfwAmQDYGdAkRnfoNOIblsgOOGOG6IwzTjAGKPZEu4A7U95xYLrwDsEOUKk6qOhddJfciVVtUG\nLAshMyHHgHgEdkvq9r4LwNUkeGMLXAuwE8EEQZA0ulnKRUl5QLbgzRG8jcBdhOwDcIiIx6DgiIgS\nFR4BL5lG+EoN5YEjU32LwEbbsFoYLULZYramAPWJCQgVNFqIQG0gdBBBPRldKX2mT4SoQRXJPxtG\nWWdaOD9v77gIICNorIDEUmKlQNwaK36n3MOBh7b0GoFgXPw47dcBI/uxt3GYzSL7SwUNWPGFDhxd\n/3yX2qwZowOH+IFIRWtVbJYz7b8CHpNdpJnyjUEgG6S3aaPabEJSGjsAWmSxeU2OE3GciH1Mk8/v\nJdWspGXBERGLpPE6Aq4QeY3JFIckO4dgSraOBWn4xDkZFONCbCHYEriKwNWGuF6IHYCNUMcD0jlh\ng44hyC0g18CSbA44BjAN+QXZR8wMye6xpOJI1EGIsiAncIBgwYKFMwRHLNgD2XCqf2YHAbMSCQwK\nFLV/UNJaJ6xOQ7ayDO3oVYezfXRjvAB1z2yXVAs0mG0iPhGa4bUApPSDsbR8ETQGfuAAEhwA41S1\njLoHA480oAqzTQIYK4oKEBcAwx/nIZIVCMq+5GcgMdtIURgJJEsGSPksuaKJh4cpDnjVYcZS3bZ5\nFdwEs3k+EWqoIsGJkE1II9noItsED9kmuMybNDXBMdoo48AeqZhywIKjCGYsWBAhTOUcyg4BV5iQ\nqmbDsoFIxLIEhJk6ax11HFZiktQXdktgG4HdlOaF2YCIopYI0cE0wgSELRiugHCdPtVgiqIjgTsg\n7NJkTZsp3dMGChLoYBxa8blH0L4n6RlmppGIgo7CEejsIIYdpoKNdf9PxtOYFMucJrou00GwKb6g\n+iaYIRUOGLaU0eT7dO3ViKD01DWDK1RB5bTo0ieR4NK5gV9b7bsmLe5ThHkw8Ej5sxQVhvaNtfMI\nmIHT7+gVRrlOtW3HQ9SvLpaYbaOCRrW2ThOW4hpw5JmdnNrADOKoto9jKfIgNTAgAbHedTFBg5sl\nFVfcmHqyIZZthGyBZWIaPTwQ+8A0RQGY6yqOTN/sWSakWU22CNwhapP0sGwhMmFZJoQ5pKLKrMpD\n20MkeCThs4nAdgK2or1hJGsAELGojnAF0OABcBbgKMAe4B0RY8B2k4YljHAjt1sdCgMmBI09wYEz\njjhCEEGkToN5dDL9S4ZU/aJTki0Ek+uoGMAlqOLQ4sqK+sgQEdR2kLwI6AAiGKgRlo5ylhbLx4ol\nfaKkz65rf6c02NnizHWqw5MJQ8517sHAY62qdk19eNVBt29k62gNoLbOEIE/z81dIg4Y7MFBLJCq\n7WFRDwUWHiQeHn4uBQ+ZJc0XGwQMhMQCjwSQZNeArtMimDfAPC15AJwDdX4TMjX/lpTxZggWThBs\nQdmBuEJEahwm2igszLF0htPgL9oOYiOl1LQ1eMB1pxP99jOmwPop4SKQ+8sfF/BOELbAtAngHBCW\ngI0CKMND1UeEgtBqs7QtCHlAsXwYOKwYYL/TzC0M1pjPF1NCqnJfmIZXdeoD1hJ1BJFOfbgFZa2l\n3txgTGOgMm562wcaGHiQdPmgca3h1O4/2r7EPRh4pIxeii0jaLTd41n5S+XXFVNGqqMCi+QbeJAU\na5lXG6PFqw8HA3EzOaHYNlJWtrbSi1tLgoeOhcdIiA17tQk9QCZgmSTZO6J1JqUzklI7l0rClQgW\npLE0wC0CdoBcIWCHBTsE2UAWhcfs4VGUxwTkYst2SpMspUrWRbOwZn5OAHYKj6Q8aH3kDzNwNyPs\nAB4C4hxSD161YpQiizZkQ8id0QDrSMfqGCAVQwwjpQhjI9Bb7Uyye4VABYcUSDj1wVBeb1Wc8aBY\nUJdLNNmMBvJenNL16sGSvh2ae+cqBCoFUqkPOa0+2PvZPS6ByMOCBwYPNYLGQHWc8mMDFl9z4osn\n8MUTs2W4AUuFPTTYwiN92xMk3ES01O9+mUtS24IE/wnToooN561DWnEKCosl2z1kAywxzd86TwuO\nIdk5DpKMogaQIwSpMajGAgGq6gjYpW3uILJVcExaNcsCDw2mwA0aHFLTjM2UpnYsbUBtjhOFB1Px\nCLxKk86a6lqO4JHaWpWQQ0hTvs0BSyS2TC1gZwYs1tjLmxWZYjy1nViSpuIxh8LsH1QjqmXCSu4L\ntN+RqhG1gcCqbA0k3pS16LEeNgMlUqkRNNuNs/fi1xkcVtxxgKiaNbSOBQ4c+N3HPTB4SPXAZ6Ex\nUBj5PK9Isp9rlq6F0tJwTMFRQUO3O5C0wKjhUdW2uIWcIX6qtdwZRh/Ojw6UARJSFe1GATIlgMik\n8IgLjgypqALiyAVHSbUTVjha1IBCzVIRmwQM7cOi9ScQSQ22whJS02xVG3kgaJSJkwwecbKJk7qW\nFwqPNNwguE2d94KaM80IMEuqfTlS6ZdqSGzW+60Nj+grZVVxzBndgoULFixIwxmZLaRoj/7Pvtyx\nZEwNm40zWo294Ysulgx8t9m26OIhAufvXVbMtUQwiMBu03xZDSzV0vjZsdL43QciDwYebSMx/4DD\nWhW39qBp9xXjqxQVosBg5dcWT/TTMiqycASQ0botuixpzI0OHChatZpMRMGRAULIFCCbBUsMOhI4\ncAyS5ilB6mZ/IHGUpD7SXUPq5i7WL2QL4ioBg1sEbCHYYEGCRxoASJWHCjKrBDOexahBU+VRzJVB\nE2sEzO6BrcJjLjlBwcHjArE5ErSKiAwIMWCKxIY2ZJIWh3Jxpox6NlNrYHQMtBocpSBF+CINYP2P\niiKRBBAJKd2oMaKthakUR6s+WoMqGiWCOi37bVnJ1ZXycIqkzgS1y9A4AZFz7sHAg/n/uvqo1MYJ\nyJgktWNrFSIZJqwq6t0nZFBkKYVdZxQdAmQAjzx7dUp5aZRxqYvrWXWgTCoSUcAxJbUhU6qWlShu\nhHAPD+0TogA5gqlqNhlQEGRCxDapjrwkeAQp8FiWpAy86jDl0QIkzbjWZlUrtpjy2KWGbvrCKKKD\njJrqYCq2HIgQkoF0YlJAiKZkEmXtLqkGKVmPmIuMAeQxhwZWfPHg0LY+pT2PK8bA1rFUz7J53e5b\nYkWbHEGhJJdWdbjSqcu9fU6+JGNnG4hfGsD46/lmHZeqjwcGjzKk3yoY2nMyGNT0ZEWTCiBOlmQV\n4kCRITJQGg4kuXaFHhg9PEpCboouQe8RROcTkaI2giT7RgRkCsk+MEGXADGAxAUyBSxxwYKgZljJ\nDcCy+oDgSGCWgCWPVD6laQykBYctBR65jYfBQ6PQiizRii2iY4PCrAxAzkWN8mA8qsTUC86LAqSA\nAweCkYgMqRm+BK0daSVaaQiW7qljomXA2ARTgz/xRkb3l/uTuH5NreJo1IcVX3JbkAwR1kWXTo2w\nfLykxFoWxi6dW5LtVEcmMYbOt/1o/S5xrw0eJH8YwL+HNDD/rwD4T0Tk2frxum6KH159FL9iu8j+\no6JLBQbd7vycznTQkFZ9KFhYVccuCogWJouGccnXFKBRGihKQ8Fh3TcyQKYlK5AMjJjWcwg4iqDU\n25TalDljLqi9w+CxQVD7QwHGRpepwEMCRCe0zukbKeFZzfEUFBwRiEFyJi72BIVHrnXZAGGrAE1G\nYy6xTJyiLU+hne9CIOIcElCRIJI6pGkxhkVLlISSYr/k0lSMAY+uSKXFGpz4cvu/0DwXqa1UWTK0\nQFtIl2TVFl8SRFwZwj54bVGmoUZWCeVfXbxpiy9NMeWc3yn3OpXHTwL4cyKykPyvAfx5XYYu2TwK\nc08WS7KH/S4xbuqjeDlIoHmb3ijq1/TQMIgM7B3WorRtBJDvhZxIkkFU0I1VF5FyY1zKb1McavuQ\nmJYlpBG/F4RUd8MFs4TS6hIBM0WnxtVJmxAAaisM2SAgNUsv0KjBgQYcVmQxdZ2nZAwluEHo9QDy\nqBW0+maFR9TewZyQbUF5ivuycA7gQoSFSFN1pgmpZgYsQiwsdTq+ipZqRE1v1f5SjZi1DfFtUL3p\ntGy1i147mGoxPynGCC1DeLtHTpuV8pBcU5PThtuuizN9+m9dPnR00KV+J9xrg4eI/JT7+WkA/8Gp\n40dKI/uP/MqdSo2Jrun2jYHR1HiIgwaa39U+D5FBscWOrz45LtAjcLQA8fMdxgBMkooqAVgYsFBy\nS9EjtNWoLDpxgeogBUjKPHaxDUKeK2UDkRFAtPOZBOUqc3GlVR7RBT9IMWmWxzXjplcem1RVDZ3/\nViKq4cmXpDowp967WBJEKIQI1fDbQANU42j6q2pgYDUwcweMVmHUqcontmJORQjl872gVx+WtPxv\nl8zapFiKMO6WXj03IGk3LcRrhtbqoHN+A/dhsXl8P4AfO3WAK/WVBOgKf52fAaM6r3kjJ2eHapRI\nZQVzEOm2FRai6wyMVpmI+3yZ8sBAdbglJFhkiKjqQAypKtIrfFUfRyyYGTCLWEuS1P6BFj2p4Uhq\n/5mKLamWRYEhSeYkeFDBkdSHyea8ZlEeGSBslQeQq2urYsuE1NdlKr8lKn+T2vDqI8wEl6SAgvZt\nXxCwwEZQ8Yqj1KcE0BUkRWOjrmepQeIUBjD4LaXmhkuqiREHjsWlycWBxJnUKP12BQuvPgbAyLY7\nl/TzO7Gs4E57L1QH8D7Dg+QnAXyN90J6jh8UkZ/QY34QwEFE/sbJa/l1UzwZ+ZUTDQ5ArS70d36r\nLUQaP19UqYovbXFEgWFJtIKKOzc3/sIFqqNd1N6hvyUAwgBtCuVsHEuBCEVbj7qma0QqijhwWJEF\npjjolIcSQsQWdKWvDA1pzDbd99tqSIrySX1djgqPVBZLX+u66MIjgQ21RysVZK6oYi1LrUdZiWQc\nFSNHfccp+HMO4Xq7jxV40EaGMzRZ0UNc8YQZIq36GCkPjvxyJJd1Zw9x26LX7wDij/3LuCpaAAAg\nAElEQVQyIfK+wkNEvuvUfpJ/HMD3APjOc9f6L//qX07nCPDtf/g78O1/+DsaaJRYYY61Vk30ftKp\njqVRJEuzbfsH4KhUSLoe208JS0arphAjqr5e/sPsFzFYhAAJWlwJbXOz1LZqhgFlUVgQi5Txz1Li\nL8ZSUQViXe6zgRQhZ9Jk41DVYbUALleZ6jAbb2Gkv6tGgBZb6IsvTMMNlmpclkhbFBgLGhsIIcEa\nj2k4m+JLzvKsCyWWIuwdWaGGnBtwJM1SzpzdVZvFEqZv3+GSXmpUxqHyQLN0xRe3rhSJ/abb5yRH\n3sX6sJweQZDApz/9Nj79s29fBBFKOxvSB+RIfjeAHwHw7SLyhTPHys2v7H3+yyDw29CVDfuXfmvs\nd2sgz/Kea038/sbPQKHHSzUa7jJetyrFgIWl5KqQ3nyqltUlNttukShYgkBCWi9BMAfRKljR6ljg\nIAvukCZuKov2a5H0BT4g4IjUv0R82w5xa7kCZAc5TpCbNKkTblG2X5ZFXgKbQxr451qAJ7aGLYKn\nur3BAWA6kbhJ27wBeFuvtzOgXV9wRZTpY1gt80TMkTiGgGPU3sOkPmdZjkzP7hdRMpf1BDKidOfz\nS6wXnUOmtC/RFi1CXbT4ZE3WxaDBAo38rWEHEg+edtvnhbRm87swYPS79NJ1SGfNja//lzYQGVtN\nXqfN468hDY73SZ1/89Mi8p+uHcxqW2odRhRYeEx7BWHHrNk6Kn9XIK2Mo26d/ZZ63X06XBj9p8l/\nFBUgZYJTrBdbAtQ4qoqDreoww2gpxlhtS7IHqKFSUkKP2Z7h1Aan1Pkt164EVy1balm8JhZ9nmzz\nKFz03/3mjfoWodbitKgOcnKpWVR92MJafWi/k8A0boiP4FLzUnSD/ytvzf7MDtKqDzbPQvc04q4u\nqqZSQw9rVZvUlmSAZAjQbbfgWFMgPmnxxNqOh4dF7xqhcpHyeJ21LZ+4z/GliGIiyyumJma7Lovj\nJQ2q00Akv9UWEt5PW4F6cHiDahgApFPQrJqel0Zh7MHRbmtmzaYArC9F/4QCDxsTVCJQ1aY4gGgD\nkgIOZuHla1iqF8RSRWvgaAHi3xizbaI2nCZoGEQ0SVudcKpnRjV1/ZyqSsOi87iEypxZgaN8Z0tt\nTKmBAQTJ8GyWoXopMMGw2GJ41IYFBHLVNFGUBx0MPBhEgKxM+v1rVbirawf3KuJbJ4409m4Gh7Xu\nw1LbctbVD+NBob9HhtALVEcFkLx2dg/04OjtIrat+jMXUTQ4GRrs1YazezCeAIg3jqJur1rURbNQ\nx+cQgY0sYlWzSXJPqadsA5BUu2JVslqzstSKQyze7eXoEh08vP23T4zaYdy+0Cb/PUg4Ic+Q5cmV\n6ptr5aHDBsaQighhkLVHqsOrjzSWCTSmRqojoQbV1XowVn75ax80HboiQk5iycC6Bg0PjhYkLVA6\n9YHmOLrjG+cPGTGmdQ8IHmO0SlYjDrXD6tf2uJLh6fxqJTIosjiYMMMinSM5NWCQbjkEhs4JUJS7\n+UWm7vcKDLVZwuyFVmuSG7lL070iK2NCaA3CCK3bRRphY9IJk4raSNBIneRyS1Id6ltEGtOQyzL6\nPFbbYvBoo6G8QaLUhvg2H6XhWFIg+j4tScuir6aWXhLNmJqqbkWIyKQXoikQ9ioE9ObPOox52gzo\nAEO04kwBiT8r+zfRQlDTWdA0FOq7BQ8OaWwjdZItqoVFIjhYDP3crSqIrBDiK055DNVGq9FWa1kG\nv9fWBo1OhTTFmOqNesS7xX5380tKXTVLzWmVzSMdI2rjyHObYlQk0TzUAsRhMWWAAHICte2GDdFj\nhkLqthVtBNaaFAoMJki6WK9qQ4MrtqAHCNw6nZsJqtAoRRhasSUApbHE4qLcIoQ5AqzqNlWNaod6\nIkPDg6NU6db2jLkKrYV0yefpBJzujHqrgMRfhfqsCoXKj+4Mp1YcOEZ2jwwRuP3+PIODJrlWVvj7\ntI97CTiAhwiPTkWgyfh2TAONEVDWjKf5ON+2o4GGbynq346pjOoDJz1Acs7qgeF/C5nziKDvbleB\nhMUkUIPDnNYGMNX5Bq1Z8KrDA8Rabnp7B0B0NXREtntm5YEaIm2WLKk3nVx62lrxZUKafdpyhS6Z\n7y5SFByS51RRgEhp8hVZNIRXHC08bMs0R3qzBSAeHu25qLbdYzq0pGdN6iNn+JxsnNqw8xuQ+CRc\nAaRRGzlJDmDjVUc3nMUJRdK6hwkPIGf49KyNAhgWT84ARdUGrfjRDsrT1bq0nwW9ddV3GwUODiBU\nRVFBxHeCa1SJkEWlY0V5wNkRhbDZxzSy9H9QQKg9ISsQA4ZVVWrnslxsgSoPXVepr+Rt0tk8LPj5\n7q1zQMgKRMFW1bxIgkgeeEJ6gFjTdadAZIHO/WrgSMWX8iku9x/Bo8BX/9TusgYP2C9TGO65W0WS\nIL4oLNTuYxBpVUbL6ZTIyj6i3/aqY3SN7lWwVhwXAuThwiNnar/tj1mBxSnjaDaiLgUg/vjWeGo2\nDp9HLR9kBeLURgUQpC7l/vOciy0FICmPCMqIFP2wQvU2te+KVUHmkSyREq0NBJIMpiJJdXiAUI2l\nSWWYzaOOylT1X4ZIsPyfRxFADxCLppKeCT+AT+5pm+0ec1FnOJYAZK734DA1QrPTIIU1WsamDwkH\noSsqIb1xwWLvHsjwqMHR/4e7mj0n8zUAq5ExiUB3Rqs26nWRKl1xBe64BiSVn50P5jxzH8Vh7uHA\nwzRX17QcKAI9/R5Wv17st6ii0bdhSqRTPrbU2pEmsxUWkg2ljQIJKLOmmRIJOlWkXtuUhiXd2ljq\nFqmaozmDaT0OFsXbNlIxxYoJxe6RDKUE3TplQKsRsHQIMnfLMQbY2MxttuzVh8usfjDjbDjV6Rky\noCNq+cPyBfayzNlBrLdryINUFPUhOQw1ULwp1GuMJYfbG1FTevFHeQtGueKiP3qApOO8ERUFCA5E\nBmkzqHqIeIBUfm10C3LRqPizO8+/nVPu4cAjP5VTG1WGlrHfJdAY2UDQbJurPisKDg+Rag0HjjFA\nvNKwtk3JQCo5maa8YJ3HxwBJ0EjjdJQQly96St41KDIs3HFSranQcA3Eqq8k4D/mdMpjpDrGAHEn\nO4Dk4ktYCjgYynuxDOQh0hhQEQA624fdsxRhgKo4A8uuRVksDgYlFRg8ih3EjoeeYdrFwFHuYEMS\n+OOKHYTuZtke4scCcfE+UhRDiLSq4szvHIYz7uHBowOG2x4WY84ojWrfUh/jLVfm2q68I+PoieJK\nhkYHkHS+OBuH8DQwRgCRvF0GBTYwlJqVVHSpFYcrsmSAFHBY1HqpmzOF5v0WHpmdcIkefqNBixVf\nfLVtHoLLrqoa4BQ0THksVF6nPj2Wbb36iFUYAIOLwcC2luxvzqxKPUA8HICk2Gzg7HIXDwy/1rtm\nYVHSm/kPa1csOkcQgffTtzjY317jnHuY8MiRcIHyOAeStX1rgAHcJ2GkOlDDYmAwLdBwgFFl4mtW\nLoXGGCIeHtb/ogdHbevwykPB0QAkRW9RIKY8bKkMpi5K0lne2Q778qriyLUuNsqXAsSuKiFngFp9\nACOYUOO/NBqz8KcYqQGWfluxxSPEkGAG1PKGgBoxRakUP7tygKmRokLs2eqiSwtZi6pKabQK4xRE\n2jXG2xcIjuweJjzyeg0UcNsXqI+R6mhh1KcxBw2/7WDhFcgFAClp3yuOdfWRVYaKgbZ9RwqYB8dI\nZZROXbYNK7KAXUnOYjtXaBo4THmgLFWl0+Btpi+p7S0AydCAKQ+1ffiM1kHDKw+UqlstupT4UMWR\ny/pjeHgkGBBKijCAFN8CDls7SNCUid2pQKQGiBSm5hAZtnTta0acCsnO/BqXOS2N6hgpjQvVx8OB\nx5rBtFIhUo69r8HUrlNVspeV1OkLQ7WRYVH2s7V3BGdEzXYObc8BW6cEupA9LKQ8QQ2Q8mkhLMAF\nDL4NhVRZPE0l4KcvECVZih52aSknRGqJ3QHEF1Oc7XcAkGZP19rUijAGkFAWf6U11SGobDVJvKQa\nl4D0XKLxVhqQoQqP1xBAKbpkW5TTeF7vFSNqAYvZOuoiTQ0OK7bkmhi9a0UUgVYHS1ES+Z2welGV\nesnfQMHoTbTuEgXycODRKg9fNVuBwY65FBoNeOx63uWU74Hh1+i3g9uf1Ua9T2hrOANpURpWqi6l\na2dErfZb6OmCbImwGhAw+/UQ0eTuDaT2DXVM9e3D8mOzAYiLMl+T3blCIY3bttbFbdMVYdr3MwQI\nYC1NsSDVYi36TFRM0rJ7QdsIJEWB1NDun6yM31KUBvNVSzGnVh41YIAEl1BduQMB82ei8md70qn4\nb57gEmB49/DgMVIaHSRwHhotMOza3Vozuf3OywggjX/7Gc5WRDhweCCIft2KKa41hko+pk7IvkVk\n+ap5aNTFFG9IzXaOXDXLKpqrkqB7G5mTDiDt+Ebenuyj1v8iq4hFUSFm73DqAzE9tQ+IrUfFGJvi\nwNe+ANqArLaF1K1P24RQ16XUKcfeTEpfBSBeZRRolDc3Lr4UgChQJcd24a0NFVYjpMSsUxtNbDe/\nB+eu+LfuAcED6JRFW23r1cil6qMzjmKc2kewQOMXBsd41eHtHUCuWRGKTplY4FBURlEdRZH04LDA\nMq8183X9+gOK6nAgyfXEpkDq6KTr05KjiO4Riapfi8eBP6d37rueW5o26iPXvmiGqy4k7vWxWJur\nNiAayEXvFNI62HvNMOi3verwlauLC4RUWx4c7e+x8bQ3nFo8AL7tSBVrlv5E7Ec5yoHjUkAUKK2c\nMHAPCB4nVEYHhdFxp9SH+6TadgsQryoyNJxfBxDUflWPWlMd+r1irTZ6YNTFkxocI4BY1vDFlhog\nvo1HXrum6JmtcAqkeRP5cYBKfTQ6ooNIFane1mHY8UWWChrW3sOncg1oW2RpoGHtPsyWY8WW9kXb\nEIu5Rs3t7xuMFQVWG1B9QzDvDBj2xnqDabmrQkS8/cNvKeLY3MWSaHOoR91Yq6BE7YXu4cCjKnRL\n7d8UY0aTOeVWolW/FLuGv4+LfW/0bPzqPiyt4mCubqhamLL45eIKkeFQ1j0cMlQcaPJ+sYcoGTG3\nlWiKJ2iX3MlGv6oeICgAAVhUiI8uNOBYUR+9Cmk+cSy1HBkm2TjaGFFzevAY8yFq1IeHitVWaC6x\nYovATJrlGl511PUldic6A7ct0hyDvIcYgaNAJzUoC8N4Ou+XKEEHvooDHUTqXZf4te7hwKNLbB4Q\nfvdAYVT6u7ls/vq4L9qpoonCgpcAhKjA0ds5antH7VfbP1qt1MeKQgNedfRL1XrUG0tb1TGKcn9P\nBYY3mHqzzpriYPuL/igDxQgi3niq798XOStY6PVaeLi1jSFq33qzd6Rna78q/doUSPteyvspwLBY\nY+NXm7ptbSoEVcjq+DP1UEOEFnaRSpF0cb7yK29Ld9jQPSB4qOuKLEAHi0E2Sx+ckZ5bAUeGBoZQ\nkQ4WKNuV7QM1OAwG7GtQisLo16cgkrbLV/oUPHqYMHeCK5muXDwLtibmzGUjqaoOLudVR75KBrcu\nXRGmAYeHh48xcdf0oMi/ix/9PiT/JBRdVhUftvaJ6yxtesLbQPzRluZqcJSzS83KomrRX71ApQ7N\nyA8ZHHXLsD7kFvej9iBt+E+5BwQPadbogdHVuABtkaYUP9yl24+fVxtYUxZrfij7fHWtASPbOgoQ\n+mJLX4wpIOkhUgLuwTGqom0XlrUzlFZR6aPF7qc/MhupxlJJ6zVwjL7fOdG3Z7Tqw4Mk2Ht0javM\n7mF3qNSG36YTLL5Wxde+jENb4qIUYWqIs3kn9Qeuf2u17ilKwte6DNRF9rPQ+4+kplkF4BoIWv9L\ngeHdA4KHc0P1YfvM2+UC6PB5vtHBOVicAUgqttR+RXWg8mttHHV1qwLClIjUwFhXHaWLWuodbw28\nWuWxDpG6COMznH2lZVV12Me5Uh726G5Bs929K5Tm3zU0XDi5oLbX+He5+It1oCgChdlgmpOFnlNm\nzx2hrkkshLMxFSTYrZOZs9a4JVG2rXJEL6mRLJJLTHVxpw1R69dCxKghzRFpq9nVhTQ/zBn3cODR\nGUy9khgokPb0ETS0GNH6DQEyUBts/FobiPhzHTjM6NkCxLcwTcCrbR6otnM2hrUHKDUnsQFIsm+w\nMY7WBQzkr3JRHC5Djl6Jg0agqo5lDJD+5N6jrq51VZZ+9C1YscVXaVpnOYsSzTBrIGn8zIJANuuC\nNPjaGeOQZVebXKEgoW2VaznVAyQF0BCUIZKjxgGmia7O2Gz72fop6fTj4u/RnevfNbtLDd3DgUfF\nd4uQU8AYpXiXuVGr3Boa5tfsP1lcqf1MlRTFIS7peKMo3PYAJjkpeXCUYFkS74FRVEXvZ9sue0iT\nXFph5z5qtnCwrBVbxjAZ7F0twmjxBKG5kFVpNuFsoTHy0+0MDAHCqrHUt/v0rTLqYX4slPbeCkRq\ngKR9rbqoz6r9vOuB0roaNg5lWttkB9AF6z7VtMBDhEdVFbCWwp3LSG7UhHkPoeH8TItb7K627yjn\niQNIXbU6AkjfgtT2W/Kq/fJDwZJF+QKPii0eIhcsPrOtRKmP2hwVLFE1BsU5N4KHqgobx8OybDZo\ne/BJAWALCIPLSH1Yy1NohzGH28sAUtedtON/1NHnAYK8pvqPiyr1FejOq/3Wf5snLZ6sKlfGB1/6\n3h4ePPK2qg3fv6U7Di2CdZ0yN3FCfeTC5wAW/hhvFHXHCYpfDQNpYDGqlvU2DlMf3q9ksLRnDRin\n/EbgWInukfPAEKzC4zRI/N4GCLk4YrDwPU8d7P1nNEPCkoPBZACN3O4DORGkYhOykrAY9mtfgPLA\nCG7ttUXrpInkuu+LhcKfXY5ndd7YrYOE8DLDJp9aO+8S94DgYc5D4wQ4+o9GnYq9vWOtyDICigdI\naPyaql1THSlka204+n0ZEmYrkdpg2mZLrgKDqIsu/mvdQkSv6z+X7bqJ005xNPAYRX/9y2cY1uHz\nAKmKLdbDVhp/5CKIBZkn7Bx+O0+HYCBRgBSmlafpG5P34FiaJy3p1AfOLt7WtLTYWS+2tHE6BECV\ntN1/LzscSO4DkYcDj8pgiupjlX9Xx9vaf9Xcdaj/2sZg/jgOjlsxjlpizraNQXFlvdHXuuLwqrt+\nOIOGB4G3ZdTVsQJqOwICNsgP3MUrm0d3w8H7cI++Ao/TAPFEMtlu76tZWqBQUFQIkYs1JT9W1bFr\n0Kj81ObhC/7WiY7C/Gz9+F8eHHVD80pdeoMCTYGYyiBqFeIPbd98gW4fr6N9atj3x4k/Vvc3r6Nr\n9j5wDwcent5Va9GG6ubaWpOBykgfGoNGc46Hg10iLydamOq9RooClV+9356kBYff7x4OBgZmhVGE\nNSq/pj0HGnCgJNuKaGvO54HCzLZN3EmAjC9q4G7P1iqcCiYGi1DOO3XtC9VH7qjq2khkTSTJmHoe\nHMWOlcNlaa0LpwcIuiPaOpvT4PBHtcqkvfvgOgbP/oKr7gHBw5xl6EEKp4vsLtV6GHhgtMeOgOC2\n9fhRC1PfctTCsW7DaBWHBUDgX27J4P6JCzhqldHUoHRFl3o7XZhVVHZZ8QRIchT5dXP+CCBtIqY/\nkv6sBhaVrGgUSOsqEDbPugKSDJAcumLnAHwRpVYg0vjB+ZePhH/mNqAWA/45LgNH68aw6K9XX1PX\npjbOqU51DwgeI1ic+J1B4M5tYLBu82gAMlIjFVzKtXr7RfEr1bI1ODDwG7citQerwdEDo62mHYGD\ngBTR3N3olAJx+byKCvQLmu3+Uk2iruSy3aiFiXvWCiRrEHGAPNnvBVl5SH4my461baMGR+9XqY9z\n4qgL90g9nFMc7b4RbLxfDY7q98mwFveA4KFu1CC/+qS1IGj8VttzONAMQaHH61gcVWMwpfaacdR/\nffpiSeu3YvdQV9e0+CLJqErWg6WpYbEM0kbnKWi00b4CjBFA0Pyu9zlftmcO4OGrayvl0YCoijgD\nhIMGGr8qrNSPcQrHKePomsHU66V+CgcZRnMHU3cWm6N618OibxQ29qsV72X0eDjwWEUuURVBzvmx\nbFvVnD/WV7HWtSvpuKyCc5WsnYcTtStw/ukEX1QRSNeaVKqX2CabYtNIzbe9zaO1dTiI2IA/5vIA\nQClgo2RzKinl7HxPiJx0lxhM4dWG+S3NjVxxyL+k/NwYqxIHT8lG1BQuu15p01rahng/1+Y1B8gb\nUc1/lI09COn8OiC4CO2h4iFie52fr0Tw8VQB5Lx7gPDQhzsHkFZhmN+acVS3CawYQt12znPpvFFR\nxNRGwYYllH6fVC8OebsVrh4O6OwYbXVtDRQX6Hxt2q3sjqfSzEqeNvaOQHLetUexwL26SgsQB5Jc\nQ9bYPkagaAGSvwTwEjCfUzJa+lVBQ329ncNn99pw2j5rh4KB699++r8GjnWIjP0MHDzjt+4eIDzs\nxwAM3s8Soc8RTXrM+9tju3TagKZSKn7xtSdtjYo/BijQGR3XAsgHui6u9IqD+RwOjgGYBzkuGcnF\no9ReOS83h7TR00bZKBpr1yZQR6TxS3CAcLUsvpp2eN32AdxzVy+weZkKMjbnWxa0okrZy8rP3LDa\nFj4dFCdNfLDZ2z7PGBz9ca1yKSrEttf8TrsHCg/zOAGL7O8SUwYB0KkJ3a6MqBwc19xnDIe+FsWr\nDjTHAZLSrrTQyIHOD+TVRgFJO01k8SsQ8YApcdg10D3jcrJiHUWt4hgBYz05tl8/lpt0AFmBivXI\n8/dq4Tga58NOaiFCgM5wasedVh9thl+LgfMZswVghQvX+7a9Wt1Mbs3P650Ci97vtHs48Ghh0fq1\nsGihcuq4wTm5IebKcTntlZt0ygEDsPjjLFwZJAoQc+WYWl2U33XxZKRCfCbr/LrMpavcUrPESU5W\nRgkLSQUQKl+luTPcf68ES6Kuqo/9Wayfu7ycMt6FFeNSeFcSfas2Kmiw5Je26MICEwuv3aJWHwUu\nvTE8+Q2HMczBE/3dh38EhDo+B3F71q8G9sjvnAtnj3ifHckfILmQ/KrTB6Iktiplsjxn68fm3FPH\nVQ0WmIe18PtSmmNZu+NEITWWpzkrNhDx8tVlDL1fZ6/QzG8TV7dg4WC7Pc4yuqUR6iBAxZhan2GR\nQBClqzrcb12bQZEGmLQwr0tcsnsXdI9Ot7Y4Kb/zPVHfo9tnLoMivyTkl9kWV9xxuW9MFq0KRnHP\n72K7mKfbt1aOqzsPjI4bna8vTG9sUVsXfPo6ufN+o3NrvzVrjLnXqjxIfhzAdwH41fMH+41GgZyz\nd/DEcWsKZGDbKGv/hfDG0hK+Aom2qtYXd9IWuteUP3Ww5OSrXGuD6djuYdt1coTzc3fz0dSmo5Gz\nPC0lmk4VW9r16jWHZziodtkqPX86fDSm+eAmjbLIx3mZ4BUGWbpRaRjprjfeHj0tT25ryuv21zpg\ndMToSdkd3/ulO7K688hv3b1u5fFXAPzZi46s0gxrP6BOvf64Lj2OjhucM9j2APHS1G7g1QYwPq5l\n+pjva9+jYsNov3uj79ZJ9eEy0lpUdNHu/NdOyl/GixdWNoXqIl4Ndv7NzconuX+CIg3dfqyqjsrP\n4keNzEkAjGK1fTujt9i+0baPc13BDgBk31ywh4V3fcocpcI6lZZjeuisu9emPEh+L4BfE5FfvKQT\nTh9jSscKDkTdXRs4qUo6oKhWGFXP6sleZQha1WHHjA2m3v5hx/mH614ZU2JOysML3VZ9lOrarmal\nTb6iyUYGUSr1Zrvf8lMVbY36sKeponuwxvB3k8GHxtFTJLJAjZ7AQaFVHgPVUX7rsayvY8Ard+CZ\n57k8FnzoxT1Gm0pGuaaESE74Ea1xdKRAzrn3FR4kPwnga7wXUqj+IoC/gFRk8ftW3X/xw/9NPuo7\nvu1b8R3f9q3lcjWqUeUMg8Wp4/Li/cp2leZg0JDykdI+ESL3M5jWCmSUXTWz6DSQSf2EBJSuh2yd\nkcZFFqBK8KJ+/YeqB0eTf/Kb9GugKimeAger3/7kAQy6q61BZe1u3g2gYfYaQRkAui2uqOKw9FRC\nWt9nVF07CldiUqntKvm7RLTIehGii7ucumr/Swym5R7Ep97+aXzq7f8T6/HnribSB+z9diT/AICf\nAvASKZQfB/AbAL5FRH5zcLwcf+vXAWgm6/LYIMV2AFk5rup6rx8kq4ZluU6rHIa/xeZfSb9te3HH\n9iOhtyOJ1UbXFLBQbafX7wRunuXe73O//dgdOqOUCMqsau0yl22Z+32i25Q0FlK+m27XM+SubfdT\nUOXprjgIFNuAtPs1Fv06dYVFd6PKj1Z5U+8rUZ390seCxuz0rli/u9FMfqNtdOf6j0v72zL9Cji7\njwcu8IM7F72f/vz49AZEqjJfdq+l2CIivwTga+03yX8C4JtF5IurJ1WfPan9vlyDaQeVUqQ43+Cr\nBgjQFlfKp8Wu6AWl+TUB1f++PUddXTkyipbvCN217TeK0gDHNZpOgbQhyn7uI5+jD6iMplVUDq6z\n7lo1Mdh3qthi7727o9vOL8vlXDvPv0iiqAA7Xp9XLP5YX7/Wjt0X7uyzu5R9j/NbxVGuVSuWNYNp\n2a6POf/GPiztPC4KrSXe/LBV+rgHQAaw6MbuQInmUetP2z8GSA0TD4zyqtsGY1UgMwzqWhTfp6WH\nSA2Ucm65byOy689ek9Tqw1o/y6tVK34fpXpi9ZuD65x0Z4DR+buAje7iQdE+qU+BrqFYBRA9vniX\n65TTR093DgTrv+tGfRYMj5j23LY16cjPF1fq0LsHbx+icx8KeIjI7zt7UPe+V2AxUhZrUDl1XM50\nbf+TtM/rh5EiQbPfrnXaL13bVIZXG+32CCK9ncOrD3eTJl0M4WD+7P19DA0rrxxQVk8860awWNmX\nIYLB2j1MSz/z96DweceDo3qYPkP3mXgQhnsfU6uRNlsz+45CNgKMND71lWpbyA1LBbcAAA2aSURB\nVPmX9KGAx2XOiO+VxBmAZP8Vv5ViTaVspS7C9HaPEr7OiJqv5lXI2K8EpIZBqyx61RFS7ZC0xlFL\nECVyqmSWi7G97O1gQrgGc25Z+zix/+mX9RME3cW7DF/eWw/RcoI1RBsFkXqrUpPBOr8YLBqAmMG0\nLQz0zzR4So4CcyqD1umiZOtRzUgKdH01DwQfWgzO1eMsn4xNHJ17OPCgrdpMr5m7Bcha0cT5SXct\nlAhEfb22EZgHQYYIy4ss77S2a/TAMN8xHFrl0VfDlkRdkgpLi1ErjgjANlGYtECbIVo1tPLNZA+G\napHmvPUfzq8tPBkwWmhajh4ZAcu6VMK46yocWP3Wc6qPrwHEXcieSX+Lf0Y2gPbhqB7ZNyof+ZU9\nbbHFgtseVV/Np7IGEJWfWLDh0zWHBrHePTh45B+tArnEOGrHtX5NZqnbaPgA9IbT9kWU/aiu4VuU\n9iWHPmOMiihr+8Z+vUg1z1qBaDRdWJTxQT4LjbWTL/qwtSDx5/q7ebViAZMSwPw0FwTGF19GAMnX\nRxNBPoMOrpsvfYlf33akDe9KzGDljcPrUH/cqDjTF47W3cOBhznW2+XjeSFAVqDSd0jysDhRTMn+\nbc2JHQOMbB39Y11Sm+L3we1H44fqGi0wRh8Wyf9ctPh95u8/+ihL8zB5tXrMSdfkzs4w6oBB/7sF\nSfswAyQOgWFr9vv9ZSzu2w9b9zgF5i0YRn7t1aTZX0On9MzO4akerr2uv6Pu15Gfy9mnYFvcw4EH\n2+3LwVCldPTH+eJIDYmWwPbyxqrDjmlVxwgi/nrpLuuGUPM7rTRGIHHJx5GvBYV/kvKraf/q8y1Q\nVcv63adAcRlEGnB0RBsApH7hJTefveFoZwsWDxB3jLuF6HHjrF+7cTGkNcBeaEdBH7T1RmHFjytn\nrsb7ins48DB3TzDk487ZNlCKI+V3XUSRVb/TwOj9/OP4atoeGGt+6+rDHSdtoqyjplUkzZHj5NpC\npFnaw85kz8GeJgFXwBglcPXPx7V3aFXJYJf5t6qj9XPQaEFS32F0nxro7XFr546KNv2TeSNqi6FB\neAZx0rY6vQTzDwceI2MkNWJHhtAVgEj+na5Zt9lIO+s+KHbCSDWs+5W0NfCrjk9rM3CeAoYeecIP\nzk9jyxlJi18fguxcBFXqvGGvZZj2/DW/S5ygl85VCX/YVH0Ah66O2B1T5a8GEGt+oyIL63gtk9GP\ncdmH6LTffQDjg1X29iDJ+1jH16iKdmT6bd0DgoffGIEB6Iyoo+MGGX6kNnyGb9VGHaixUunv4Y+y\nc0vmb3nvwVUDY+TnYQPUYAEgrp+Gu4e/0SipdFHm0lczLvRZYJwECIe6oDl7EJBh+w4PEX/RJoN0\neYsdgzpo5AhBF2HkqAZFj+9uN8revd9YT9R3OKVM6oDSBX8dHGPwjN3DgYe5NTBkiFwOkLo4UWf5\n8zUu94NK8wDdet1gigv80JwL51ffzT6+XeJH70a6qkrNvlSR7376miNXZxiPvUZKe2vtcG3HtKEf\ngCXfnIOAOg8PjU7R1yeuZvSKV5dm/job23EjjdCfc+IoSdAdXR2d32n3cODRxZG99JEKkfFvd4FR\ncaUFwxosxtlq7Hf6FdT0u0xNnAJGe675qbNoaQMl46RSmYXaPNyG3l3gXgA5ecAoAB5RlgZGcHAX\nHtVDrxQvusuUXO/ObyJgGOKx0bPHV+93ucG0R4A/Uqoj2uucUhxfccrDwUJ/XrK2BjDjosTpIsda\nMeQyI+oINGuNiFi+qjKASO4yvgaHkqFqP72DBqi790qGb3aV/YOPus9j5es2SHrN61tPm32c1Qla\nUJfZR8CwYwYPxcHvc0WW/EzMLMnn5zuXr76NT1M/arnYSDW0fjUy2cYAvAoZPWZ/ll4vv4TugQd+\np93Dgcfoc2Yp2iIk+zP/zu/3jHHUX3zs1+qIQU466Vd+lS9TAUHO8E1LSg8L0D6ilxhRi6u+hCtS\naAiLPtDpp8/DwLjdHRq/5sIjv9UbVn5uzQsS/+iDM76pXoYroGO+DVu/6qrMzd4LyNs73s9vgIAS\n3Ly/RYVer4qKkYob3+Ur0GA6+OStrl0C5BgWo6IJVv3s/PMQkZPH+d9EmyT6LNOCwcOhURju/iUw\nK82b60hYbzi28gRVjfgJWKy9nvNuAIVVxdGoj3wTGfituKFxVM8dqaVR/492fxMvo4rTNb+14I70\nxNjv1COPwDHef8o9HHiYW02h+bNcvXihz9SlKCEDv/LbLtL6uevqVXwRZQSM0bl9xi9g6NRG9bgt\nSFqIsLq+hb2KAIyTxeg7M/xQtwIPGNo7LofEuYNHwHCJm96vCegQGiMS1KesA8P8VgLsbCF1aAft\nbc74jTXVuPjSH+8ruAcQHoJjFMen3eseAPlyR6Cz1PntDJB2n2U4/7FNB7399qcqPx9d4o6r/bpA\njQK69gAVBPz/FiCtn13z02//3cF55+7aXGWQLsZ3qy+aXwFRdYqz3+0FzO9nPvN29btdn3f23lkC\nkZu4+gTA/pguZprfVVwQEOKnf+bT9f7umIHf4JrWdqe+u/2t+/mrraUKuDMI4Gfe/pTzb88dxcAp\nOJwHB/CQ4AGgSNdRIkINENbKXHwXbabfP/32p/J+u0AbbQkq9esoasOrjtaf7ty117kOC//n/X72\np/9ufkabp2T9PLurNUJrQiHjhNodN/C3jQoo5m35Vrf/3s+9XZ1z9ob+Ih4G+aYNOPyxTchtHpi8\n7QKa40nqGPs7f+9nUcYg0Ot1I7DDElabGKoHad9M/agjvypk+Tj3tNVZtv7U258C8rNalNXhZZUj\nvL9dp9Yq59zDKbb4xIJ2+77XOXfAORG/dsz747ogXxiU042HztzjVU5sL/Je7Lv03qPdXNlGm6nq\n7fW977d71Yi4/LT1Opr73+2BKY+RuzQTv9fHfYW7lZT0fmSlDzJ7frjdB5GW+9g+1xppzb2W0dPv\n63jp6CSP7tE9uvfcrY2e/iDg8ege3aP78LmvgGLLo3t0j+51uEd4PLpH9+heyT3CQx3JHyC5kPyq\n1x2Wc47kD5P8ZZK/QPJvkvzI6w7TyJH8bpL/kOT/S/I/f93hOedIfpzk/0Hy75P8RZL/2esO0yWO\nZCD58yT/1gd530d4ICUapHlzf/V1h+VC95MAvlFE/hCAfwzgz7/m8HSOaTLd/w7AvwPgGwF8H8l/\n5fWG6qw7AvjTIvKNAL4VwJ94AGEGgD8F4B980Dd9hEdyfwXAn33dgbjUichPiciiPz+NNNfvh819\nC4B/LCK/KiIHAD8G4N9/zWE66UTkcyLyC7r9HMAvA/g9rzdUp51++L4HwP/wQd/7dzw8SH4vgF8T\nkV983WF5Rff9AP726w7EwP0eAL/mfv86PuQZ0TuSXwfgDwH42dcbkrPOPnwfeLXpw2lh+mU4kp8E\n8DXeCymy/yKAv4BUZPH7Xrs7EeYfFJGf0GN+EMBBRP7GawjiV6wj+QaA/wXAn1IF8qF0JP9dAP9M\nRH6B5L+JDzjt/o6Ah4h818if5B8A8HUA/h+mjgAfB/B/kfwWEfnNDzCInVsLszmSfxxJrn7nBxKg\n+7vfAPB73e+Pq9+H2pGckMDxP4nIj7/u8Jxx3wbge0l+D4BrAG+S/FER+Y8/iJs/NhJzjuQ/AfDN\nIvLF1x2WU47kdwP4EQDfLiJfeN3hGTmSEcA/AvBHAHwWwGcAfJ+I/PJrDdgZR/JHAXxeRP706w7L\nfRzJ7wDwAyLyvR/UPX/H2zwad9koKK/f/TUAbwD4pFbR/fevO0CtE5EZwJ9Eqhn6+wB+7AGA49sA\n/DEA30ny/9a4/e7XHa4Pq3tUHo/u0T26V3KPyuPRPbpH90ruER6P7tE9uldyj/B4dI/u0b2Se4TH\no3t0j+6V3CM8Ht2je3Sv5B7h8ege3aN7JfcIj0f36B7dK7lHeDy6ezuSszag+kWSP37JeCIkr0j+\nHbbzAZT9G5Jva1f+R/cA3OOLenSv4l6IyDeLyB8E8EUAf+KCc74fwN+UlVaJ2m3/pwD80fcumI/u\n/XSP8Hh0X677FFxXe5J/huRndJSzH3LH/TEAP67H/GXX/PvXSf51PebH9bhH9wDcIzwe3au4NAVX\n6vz2RwD8Lf39XQA+ISLfAuCbAPyrJP8NkhsAXy8i/xQAROSHROSbAPxbAL6A1FcHAH4JwL/2gT7J\no3tl9zuiS/6je8/dNcmfR+pm/w8AfFL9/20A36X7COApgE8A+BUAXxpc538G8CNu9K6F5B3JpyLy\n4v1+iEf35blH5fHoXsW9FJFvRhqvgyg2DwL4r9Qe8k0i8i+LyP8I4AbAlb8Ayb8E4J+KyI82194B\nuH1fQ//o3hP3CI9H9yqOACAit0iD7/4ZrSX53wF8P8mnAEDyXyD51SLypf+/nbvHISiIwjD8nkh0\nNmAXeo1Eaw22QKW1G4WISkOhVCiE2hLs4ShM6BQTbkjep5pMZm6m+nLu3wFaEdEu8yNgWPa+Lvro\nXH8rv/PrxxkeqvF8Y1JuOc48Gv3sgAVwiIgLsAQ6ZekW6JfxFOgCx/LQdF7mB8Dm+8fXJ9jPQ42I\niB4wyczxmzUrYJaZ1+ZOplpWHmpEZp6A/buPxIC1wfE/rDwkVbHykFTF8JBUxfCQVMXwkFTF8JBU\n5Q4hJONfhknAKgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cplot(lambda z:z**5-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 7 Limites et séries" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.1 Limites" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sympy.abc import x" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\infty$$" ], "text/plain": [ "∞" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(1/x, x, 0, dir='+')" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$\\infty$$" ], "text/plain": [ "∞" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "oo" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(1/x, x, oo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.2 Sommes et séries" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.3 Produit" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.4 Développement en séries" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }