{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# **SECITEC - 2019 - PARTE II**\n", "\n", "A Semana da Ciência e Tecnologia – SECITEC é o evento anual científico oficial do Campus Luzerna do Instituto Federal Catarinense, realizada a partir de 2012 como plataforma para divulgação da produção científica de seus alunos e professores.\n", "\n", "Carga Horária: 4h\n", "\n", "Prof João Marcello Pereira (joao.pereira@ifc.edu.br)\n", "\n", "Link para a parte I : https://share.cocalc.com/share/9110c074abc3ba6f36ef922980eaf978580ee422/SECITEC-2019-PARTE-1-EXE.ipynb?viewer=share\n", "\n", "Link para a parte III: https://share.cocalc.com/share/c36feb3553f76b64163a3d568ce5cd9c2081ed71/SECITEC-2019-PARTE-3-EXE.ipynb?viewer=share" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **PROGRAMAÇÃO BÁSICA**\n", "\n", "A estrutura de programação do CoCalc é baseada em Python, com algumas diferenças quanto à sintaxe de alguns comandos." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### **ESTRUTURA DE DECISÃO**\n", "\n", "#### **Condicional \"SE\" (IF)**" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "ename": "ImportError", "evalue": "No module named pygame", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# números aleatorios x e y\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mpygame\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mImportError\u001b[0m: No module named pygame" ] } ], "source": [ "# números aleatorios x e y\n", "\n", "import pygame" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# se x < y imprima \"x menor que y\", se x > y nada será feito\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# se x < y imprima \"x menor que y\", senão imprima \"x maior que y\"\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Codifique a função definida como: f(x) =\n", "$\\begin{cases} x^2 &; ~ x \\geq 0\\\\ x + 1 &; ~\\text{x < 0}. \\end{cases} $\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "![Drag Racing](graf1.png)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# se x < y imprima \"x menor que y\", senão se x > y imprima \"x maior que y\", senão imprima \"x igual a y\"\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### **ESTRURA DE REPETIÇÃO**" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### **Repetição \"PARA\" (FOR)**" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Aplicar um vetor à expressão (x^2 - 2) em um laço FOR\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "'Valor(y):' 0.0000676888000875620 ' . Raiz(x): ' 3.43681000001405" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'Valor(y):' 0.0000318979772357952 ' . Raiz(x): ' 3.43682000001405" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'Valor(y):' -3.89293696634319e-6 ' . Raiz(x): ' 3.43683000001405" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'Valor(y):' -0.0000396839425147455 ' . Raiz(x): ' 3.43684000001405" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'Valor(y):' -0.0000754750394051928 ' . Raiz(x): ' 3.43685000001405" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "fim\n", "CPU times: user 6.31 s, sys: 61.7 ms, total: 6.37 s\n", "Wall time: 7.04 s\n" ] } ], "source": [ "%%time\n", "# Método bruto de encontrar raízes de uma função sem otimização\n", "\n", "k = srange(0, 5, 0.00001)\n", "\n", "for x in k:\n", " if abs(sin(x)*x + 1 ) < 0.0001:\n", " show(\"Valor(y):\", sin(x)*x + 1 ,\" . Raiz(x): \", x)\n", "print('fim')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### **Repetição \"ENQUANTO\" (WHILE)**" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Enquanto a variável a for menor que 10 print a + 1\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **FUNÇÃO**\n", "\n", "Função, de acordo com a definição matemática, é uma correspondência unívoca entre dois conjuntos em que a cada elemento do primeiro conjunto corresponde a um e somente um elemento do segundo. Dessa forma, temos que uma função é uma relação entre das variáveis, sendo uma dependente e outra independente. Ex: $y(x) = x + 2, z = xy - 2x, f(x) = x^2 + y^2$.\n", "\n", "Para definir uma nova função no CoCalc de duas maneiras:\n", "\n", "- forma reduzida - utilizada de forma semelhante a definição matemática de função. **função_nome(argumento) = código**. \n", "\n", "- def - use o comando **def** e dois pontos após a lista de nomes das variáveis. Em Python, blocos de código não são indicados por colchetes ou blocos de início e fim, como em outras linguagens. Em vez disso, blocos de código são indicados por identação, que devem estar alinhadas exatamente." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Função cálculo área do circulo\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ ], "source": [ "# Calculo da área para r = 5\n", "\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Calculo da área para r = 5 numérico\n", "\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Função área do circulo simplificada\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Calculo da área para r = 5\n", "\n" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Calculo da área para r = 5 numérico\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **GRÁFICOS 2D E 3D**" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# resetar variáveis\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": { }, "output_type": "execute_result" } ], "source": [ "# dados\n", "\n", "x_dados = [0.0, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0]\n", "y_dados = [0.0, 0.5, 0.84, 1.0, 0.91, 0.6, 0.14, -0.35, -0.76, -0.98]\n", "\n", "len(x_dados) == len(y_dados)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# montar os pares ordenados\n", "\n" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico pontos discretos\n", "\n" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico espalhamento\n", "\n" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico melhorado com axes_labels = ['x','y'], gridlines = \"minor\", figsize = (5, 4)\n", "\n" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Funções f1(x) = sin(x)*x e f2(x) = cos(x)\n", "\n" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ ], "source": [ "# Gráfico funções f1 e f2\n", "\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico funções f1 e f2 com preenchimento\n", "\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico funções f1 e f2 com pontos em destaque\n", " \n" ] }, { "cell_type": "raw", "metadata": { "collapsed": false, "jupyter": { "source_hidden": true } }, "source": [ "# Gráficos múltiplos sobrepostos\n", "\n", "plot(y1, (x, -2, 2), legend_label = 'y1(x)', axes_labels = ['x','y'], color = 'red', gridlines = 'minor', figsize = (8, 6)) + plot(y2, (x, -2, 2), legend_label = 'y2(x)', thickness = 0.2, plot_points = 20, color = 'blue', marker = '*', markersize = 7) \n", "\n", "plot1 = plot(y1, (x, -2, 2), legend_label = 'y1(x)', axes_labels = ['x','y'], color = 'red') \n", "plot2 = plot(y2, (x, -2, 2), legend_label = 'y2(x)', axes_labels = ['x','y'], thickness = 0.2, plot_points = 20, color = 'blue', marker = '*', markersize = 7) \n", "\n", "# Gráfico matriz 2 linhas x 1 coluna\n", "\n", "show(graphics_array([plot1, plot2], 2, 1), gridlines = 'minor')\n", "\n", "\n", "# Gráfico matriz 1 linha x 2 colunas\n", "show(graphics_array([plot1, plot2], 1, 2), gridlines = 'minor')" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico 3d f(x, y) = cos(y^2 + x^2)*x^2 + sin(x^2) com color = 'green', mesh = True, aspect_ratio = 1, spin = 30\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **RAÍZES**\n", "\n", "De acordo com o dicionario matemático disponível em \"http://www.somatematica.com.br/dicionarioMatematico\" temos que:\n", "\n", "**Equação:** Expressão algébrica indicada por uma igualdade, onde há valores desconhecidos expressos por letras (incógnitas). Logo, todo conjunto de expressões no qual há uma igualdade cuja(s) incógita(s) satisfaçam a um conjunto limitado de soluções, então temos uma equação. Ex: $x + 2 =0, xy - 2x = 2, x^2 + y^2 = 2^2$." ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Função f4(x) x^2 - 2*x - 3\n", "\n" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico da função f4(x) com axes_labels = ['x','y'], color = \"red\", gridlines = \"minor\", figsize = (4, 3)\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# resolvendo f4(x) = 0\n", "\n" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# somente a segunda raiz\n", "\n" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico de f5(x) = x^2 - 3*x + cos(4*x) com axes_labels = ['x','y'], color = \"red\", gridlines = \"minor\", figsize = (4, 3)\n", "\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# raízes de f5(x)\n", "\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# método numérico para f5\n", "\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# mínimo local\n", "\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# máximo local\n", "\n" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# resetar variáveis\n", "\n" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Sistemas de Equações Lineares eq1(x) = 2*x+3*y-6 eq2(x) = 3*x-4*y-12\n", "\n" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico implícito de eq1 e eq2 com axes_labels = ['x','y'] e gridlines = 'minor'\n", "\n" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Solução do sistema\n", "\n" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "**Sistemas Equações Não Lineares**" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# definir eq3(x, y) = y^2 + 8*x e eq4(x, y) = -x^2 -8*y -2\n", "\n" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico implícito com color = 'red', axes_labels = ['x','y'] e gridlines = 'minor'\n", "\n" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Solução solnl\n", "\n" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# solução de y do primeiro conjunto solução\n", "\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# somente a parte numérica de y\n", "\n" ] }, { "attachments": { "sagemath_interpol.png": { "image/png": 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3k9XUZB9fEfx7/fo1nJycMNfaCp1aGVV4fOabt/C+fB0LFiyArq6uQvz+FME/Meupf+T8EwqVXklHRkaqtP7cuXNE48taX1rK5sju2hWIiwMCA9nkII0byye+ovinr68PDQ0NPEl7XunxT9MyoKGhUfZ4iPTvT1H8E6ue+kfWP6FQ6JW0t7c36tSpA3d3d5iamsLR0RExMTEYOXIkDh8+jDdv3mDIkCFISEhAdHQ0GIaBt7c3jI2N4eTkBAsLC9jb26Nr1644dOgQateujdu3b+Px48d49+4dLly4gF69esHZ2bnsWFNTU+zcuRONGjXCtWvXkJGRgYyMDFy9ehWNGjXCrl27yo7t1KkTfHx80LJlS5w7dw65ubl4+vQpbt26BW1tbRw6dAi9e/eGo6NjmaZjx47w9vaGRCLBP//8g8zMTJSWlsLHxwdffvkltm3bVnZs9+7d4e7uDh0dHURERODp06fIycnB+fPnYWRkhAMHDmD06NGwt7dHnz59sHPnThgYGODKlSvIzMxEeno6goOD0aBBA+zevRv9+/fHpk2b0L9/f2zevBm1atVCSkoK3r17h8ePH+POnTvQ1tbGkSNHYGJigi1btkhd6/HjxwGwSQQePHiAnJwchIeHo2PHjlLt7tGjBw4cOIC6desiPDwcSUlJePPmDQIDA2FoaAgXFxdYWFjA2dkZQ4cOhbOzM5o0aYKgoCBkZWUhNTUVISEhqF+/Ptzc3NCvXz9s3ry57Pxt2rSBv78/3r59i9zcXNy7dw/PntXB0KH5OHlSFyYm93DrliH8/e1hbGwMT09PqKur4/79+3j06BEKCwvh5+eHxo0bw9fXt+y8PXv2xL59+6Cnp4fQ0FAkJyfjzZs3uHjxIpo1a4YdO3aUHWtmZob9+/fDzMwMly5dwqtXr5CSkoLQ0FDo6+tj79696Nu3r1S727Zti1OnTqGwsBBxcXH4+++/0axZMxw7dgzdunXD1q1by47t3Lkzjh49Ck1NTdy7dw/x8fHIz8+Hv78/2rZti+3bt6Nz587w9PTEV199hb/+Oo+70Q8wZ+wIqH16ywDsM+lfNjtjwMDvkJqaiubNm+PixYvQ0tJCUlISwsLCoKurW3ZNDg4OZW1p3749fH19UVRUhIcPH5YlkTh16hQGDBgg9V3r0qULPDw8oKWlhbt37yIxMRF5eXk4c+YMWrduje3bt5cdW79+fdy9excNGjTA9evXkZ6ejpcvXyIoKAgGBgbYuXNn2bH9+vXD1q1bYWRkhPPnzyM7OxuJiYl49uzZZ2PEx+0+efIkSktLERsb+9kY4erqWvb9qWiMCAgIQKtWrcodI2rXro34+PhKxwhzc3Ns2bKl3DGipKQEly5dqnSMiImJQUxMTLljxK5duzBixIhKx4gP37Xyxoj09HRIJJJKx4jWrVvj7Nmz5Y4RrVq1wokTJyodI4qLi+Hr61vuGHH06FG0aNGi0jHC3t4eX331VbljRFhYGNq3b1/pGJGXl4eEhATcu3cPmpqa8PDwQM+ePbFlyxY0bdoUV65cqXCMaNq0qXCTXWWQfEmbD7JIZhIaGsqrDWLX79mzh2h8WegLCxnGzo5htLQY5ssvGSYsTLj4iuRfaGgoo6amxiyYOJopCQ9kJBEXyz4l4YHM/AmjGDU1NSbsI4NI//4UyT8x6ql/ZP0TCpW+3f3s2TOV1kdHRxONz1cfFJSLXr0Ae3v2/ee//wbMzYWLr0j+9e/fH66urtjtG4DuP86Bywl/BIRGwOWEP7pOmYPdvuewYIErzD8yiPTvT5H8E6Oe+kfWP8Eg/VcCV2Sxkv733395tUHs+rCaLDvlEL8yfWVpLXNzGWbRIoZRU5Mwpqblp8zkG786KKJ/YWFhzPjx1oyGhgYDgNHQ0GCsra2ZPn3CmEaNGObZM/nGrwmK6J+Y9NQ/sv4JhUqvpD88P1FV/YYNG4jGL09fVVrLy5eBbt3YrGHDhl1DRASb4lNW8WuCIvpnbm4OX18/5ObmIiMjA7m5ufDz88PFi+bQ12czlOXlyS9+TVBE/8Skp/6R9U8oVDqZSWlpKTQ0NDi3Qez6oqIi1KpVi1j8T/VVpbU0M3PFrVuzMXAgcOAA0Lo19a8m+uho4OuvgTFj2F3vEgn1T8x66h9Z/4RCpVfSDg4OKq3//vvvicb/WB8WVnVay1u35mLFinBcvQq0a0f9q6m+e3fg0CE2sYuzM/VP7HrqH1n/hEKlV9IUxWG8tTXioiIRfayStJbT5qBz7//SWlK4YWvLJnq5fBkYNIh0aygUSmWo9EqadIJ30npFSdCfn5+PM2fPwsaqirSWo6TTWlL/uOkdHNjJedSoPPz7r/DxPyBW/xRFT/1TjQIbKr27Ozk5mVcbxK6/desW0fgf9BkZGQwA5uxWO6n3ez/9nNm6jgHAZGRkyDQ+VxTFPy68esUwLVoUMz17Msz798LHZxhx+6cIeuofWf+EQqVX0levXlVp/YEDB4jG/6DnmtaS+sdd37AhYGPzF+Ljgf/9jy1IImR8QNz+KYKe+kfWP6FQ6Um6Y8eOKq3v06cP0fgf9Do6OhgzejTcz12ERCIp91iJRAL3cxcxduwY6OjoyDQ+VxTFP65YWhqUbSRzcRE+vtj9I62n/pH1TyhUepL+8GxTVfU5OTlE43+sX7xkCeKeJWPJjn2fTdQSiQSLXfYi7lkyFi9eIpf4XFAk/7jqJ00Cli9nP9euCRtfGfwjqaf+kfVPKDRJN4Akr169Uml9eno60fgf63V0+kNNzRW7fefi6r0o2FgNQ1vDZniallH2nrSrq3RaS+qfbPSbN7MpVSdOBO7dA1q3Fia+svhHSk/9I+ufUCh0FazKkEU9aU1NTTSuqI6hCugZhkGHDh2Ixf+gz80FBg8GWrUyhZeXJf5NTcbOo8fhffk6rtyLgsV332H//v0YN26cXOJzRVH846tXVwdGjACOHgXOnAGmTwe0tOQfX1n8I6Wn/pH1TyhU+nb3+fPnVVrv6upKNP4H/bx5QEYGcOIEMHDg52ktfX39pFbQso7PFUXxTxb6Ro0Af38gPh749dfqbSSj/tH+J2Y9X/+EQqFX0vKuJ52eno62bdtyric9b948bN++nXM9aU1NTcTFxXGuJx0WFoaBAwdyric9a9YsXL58mXM96a5du8Lf359zPelLly7h2TNzbNyoAXv7DLx/f76sVuzNmzdhaGiIAwcOVFgr9ssvv8TTp0/LrRX74djK6klbW1tL1SyuaT3px48fo2XLlpzrSQNArVq1ONeTXrhwIbZs2QITExO4ublBX18fN27cQGpqKrKysnD58mU0bdpUqt1ff/01tm3bhubNm+PFixfIzc0tqyfdrp0u0tNDcfx4J9y5cxlTp7artJ50fHw8unfvzrme9O+//47Dhw9zrif9oR4113rSwcHBZd8fLvWkBw0ahBs3bnCuJ923b18cPXqUcz3pmJgYmJqacq4nbWhoiMzMTM71pGfMmCH1+6xpPen79+9DX1+fcz3pd+/eoVGjRpzrSdvb22P79u20nrS8kMV70hs3buTVBrHrBw0aRDT+4sW7GV1dhpk2jUx8sfsnL/2yZQyjocEwV6/KN76y+ieUnvpH1j+hoGlBKUQoKgL69QOys4H79wE9PdItonygpAQYPhyIimI3krVqRbpFFIrqotLPpEmnpSOtJ5lWcOVKICqqFCdOcJ+gVdk/eeo1Ndn9Abq60qUtZR1fWf0TSk/9o2lBFRpZ3O7OzMzk1Qax6x8+fEgkfmAgwwAMs359LpH4stKT8k8ofVQUw+joMMzUqQwjkcg+vrL7J2899Y+sf0Kh0ivp06dPq7Se71+iXOI/fw789BN7O9XAwEvw+LLUk/BPSH2PHsDBg4CXF7Bjh+zjK7t/8tZT/8j6JxQKvbu7MmTxnrS6ujq++OILzm0Qu76goADdu3cXLL5EAowbB2RlAZcuAfr61D9Fv/5u3YB374ANG4ABA4A2bWQXXxX8k6ee+kfWP6FQ6ZX08+eVF3RQdn1iYqKg8bdsYVNPenoCTZqQv36x+UdK7+gIfPstm5EsKUl28VXFP3npqX9k/RMKlZ6kS0tLVVpfXFwsWPxbt4A1a4Dff2drGddUzze+PPRC+kdSr6kJ+Pj8t5HsQ8pk6h/tf2LW8/VPKFR6km5d3STFSqo3MTERJP7bt8DkyUCfPsD69TXX840vL71Q/imC/kNGskeP/stIRv0jq6f+8dPz9U8oVHqSDg0NVWn9yZMn5R6fYYBZs4DXrwFvb+mc0KSvXwz+KZK+Z092I5mnJ7uRjPpH+5+Y9Xz9EwzS28u5IotXsF69esWrDWLXP378WO7xDxxgX7fy8eGm5xtfnnoh/FNE/W+/sRnJzpzh/t1jGNX1T1Z66h9Z/4RCpVfSfBOsi10/a9YsucZ/+BBYuBCwsWE3HdVUzze+vPXy9k9R9R82kk2ZoiG1kaymqKp/stJT/8j6JxQ0LShFLuTnA2ZmbIrJe/eAOnVIt4giS7KyAFNT9ll1WBigo0O6RRSKcqLSK2nSaelI6+WZVnDZMiAhgd0VXNEETfr6Fdk/Rdc3bgyMGHEAcXHVL235Karsnyz01D+aFlShkcUzaT5aZdCnpKTIJf7p0+xz6D17uOn5xhdKLy//xKT38mJ/1y4uNddT/2j/I6nn659QKHTGMXnXk16xYgW+/fZbzvWkHzx4gOvXr3OuJ+3k5ITi4mLO9aSnT5+OqVOncq4nvWfPHkgkEs71pL29vfHo0SOpWrHLlu2EnV0fdOz4FEuWpOPmzYprxY4bNw7W1tbl1ooNCQlB/fr1K60Ve+LECWhpaXGuJx0WFoaQkBDO9aS/+eYbDB06lHM9aScnJ3z55Zec60nHxcUhKCiIcz1pW1tbNGrUqKyetK6uLvbv3w8zMzM4ODhI1WUur570woULsWLF9wgJ+RuHDhnh33+PoX9/o2rXkz5w4AAyMjI415PetWsXsrOzOdeTnjx5ctn3h0s96StXruDVq1ec60n7+/sjMjKScz3pr7/+GlOnTuVcT/rw4cOoV68e53rSkZGRuHbtGud60r/88gs6d+7MuZ70hg0b0Lt3b871pA8fPozExERaT1peyGIl/eDBA15tELv+7NmzMo1fXMwwAwYwTIsWDFOdjZekr1/R/BOrvriYYQYNYpjGjRkmKan6euof7X8k9Xz9EwqVfib96NEjldaHhYXJNL69PRAezhZkaNiw5nq+8YXWy9o/seo/lLasW1c6I1lVUP9o/yOp5+ufUKj0JF23bl2V1terV09m8UNCgI0bgXXr2EIMNdXzjU9CL0v/xK5v3JjNSBYXxyavqc5GMuof7X8k9Xz9EwqVnqQbVme5p8R6IyMjmcR/9QqYOhXo3x9Ytarmer7xSell5Z+y6E1MAHd34NgxYNeuqvXUP9r/SOr5+icUKj1JR0dHq7T++vXrvOMzDPDzz+wtTi8vQEOjZnq+8UnqZeGfsumnTAGWLmU/wcGV66l/tP+R1PP1TzBIPxTniiw2jqWlpfFqg9j1kZGRvOPv2sW+gnPmDDc93/gk9bLwTxn1xcUM8913VW8ko/7R/kdSz9c/oVDplfShQ4dUWm9ra8tLv2nTeSxbBsyfD4weXXM96esn7R/p9stL/6G0Zd26wLhxFW8ko/7R/kdSz9c/oaBpQSmceP8e6N0bqF2brRVduzbpFlEUjb//Bvr1Y/O2HzkCqKmRbhGFIj5UeiVNOi0daT2ftHiLFgFPnxbhxAnuEzTp6yedVpB0++Wt/7CR7OjR8jeSUf9o/yOpF0taUJVeSRcWFkJbW5tzG8Suz8nJ4eSdjw8waRKwd28xZs3SqlpQAaSvn5R/soovFv3SpcDOncDVq8A337D/lp+fj7S0NBgaGkKHY3UOsVy/vPS0/5H1TyhUeiW9Y8cOldZPmjSpxppnz9iCCpMmAW/fOvOKT/r6Sfgny/hi0W/dyk7OEyYAp06FYby1NfT09NChQwfo6elhvLU1wsPD5RZfWfW0/5H1TzDI7lvjjix2d/Mt+i12/dWrV2t0fFERw5iZMUybNgzz9i359pPW19Q/WccXkz4zk2EaNHBlADWmc5tWzPZFs5izW+2Y7YtmMZ1q32cTAAAgAElEQVTbtmLU1NQYNzc3ucVXRj3tf2T9EwqVXknfuXNHpfX+/v41On7NGiAyEvD2BurVI99+0vqa+ifr+GLSx8eH4e3beVgwcRSiPd2weNJYWA3oi8WTxiL6mBvmjbfC3Llza7SiFtP1y0NP+x9Z/4RCpSfpL774QqX17dq1q/axQUHAli1sfm4zM9nEF7u+Jv7JI76Y9C7OzjBu0xLOi2ZBXV162FFXV4fL4tkwbtMSLi7Vf4QipuuXh572P7L+CYVKT9IaNUmPpYR6TU3Nah334gXw44/A4MHA8uWyiy92fXX9k1d8sejz8/Nx5uxZ2FgN+2yC/oC6ujpsrIbB3/8M8qtZoUMs1y8vPe1/ZP0TCpWuJ71//37069ePcz1phmEQGBjIuZ60v78/3r17x7me9Nq1azFx4kTO9aSjoqLw7t27SutJ9+9vgV69niA/vx6mT/eCjk5JWa3Y+/fv459//im3VuyBAwdQt27dSmvF/vbbbxg1ahTnetKRkZGQSCSc60lnZWXh4sWLnOtJL126FAMHDuRcT/r06dNo27Yt53rSampqCAgI4FxPet++fdDX1+dcT9rFxQWDBw+W+q516dLls3rSGRkZ8PDwwFxrK3RqVXG+5Mw3b+F9+ToaN24MIyOjKutJX7x4EZmZmZzrSf/xxx9l3x8u9aRTUlKQlpbGuZ50XFwcwsPDOdeTnj9/PiZMmMC5nnRoaCh0dHQ415POy8vDX3/9xbmetL29PTp06MC5nrSXlxe6devGuZ70kydPEBUVRetJywtZbBx79uwZrzaIXR8aGlrlMU5ObNrPixdlH1/s+ur4J8/4YtHn5eUxGhoazPZFsxhJxMUKP9sXzWI0NDSYvLw8mcZXVj3tf/z0fP0TCpW+3X3ixAmV1leVDODuXWDlSmDZMmDoUNnHF7uebzIF0u0XSq+jo4Mxo0fD/dxFSCSSco+RSCRwP3cRY8eOqfZ702K5fnnpaf8j659QqHQyk5KSEl7PJcSuLygoQO0K0oXl5AC9egENGwJhYUCtWrKPL3Z9Zf4JEV9M+rCwMPYW7YRRn20ek0gkWOyyF3v8ziE0NBTm5uYyj6+Metr/yPonFCq9knZ0dFRp/ciRI8v9d4YB5s4FMjPZ163Km6BlEV/s+or8Eyq+mPT9+/eHq6srdvsGoPuPc+Bywh8BoRFwOeGPzpPnYI/fObi6ulZ7gq5pfGXU0/5H1j+hUOmVNKV8PDyAGTPY+tBTppBuDUWZCA8Ph4uLM/z9z6C0tPT/d+iOwY8/LsHhw9WfoCkUVUGlV9KkE7yT1peXYD4hAZg3j52kq5qgSbeftJ4WOKi53tzcHL6+fsjNzUX//v2Rm5uL337zg6+vOV68kH98ZdLT/qcaBTZUend3SkoKrzaIXX/nzh2p/y4oYBgTE4bp2JFhcnPlH1/s+k/9Ezq+2PUf/Hv9mmHq12eYefOEjS92Pe1/ZP0TCpVeSQcFBam03s3NTeq/V6wAHjwATpwAdHXlH1/s+k/9Ezq+2PUf/GvQgH2LYN8+4PFj4eKLXU/7H1n/hEKlJ2ljY2OV1vfr16/s/58/D+zYwVYsMjERJr7Y9R/7RyK+2PUf+7dgAdC0KZsfXqj4YtfT/kfWP6FQ6Uk6NzdXZfX5+fl49uwZ8vPzkZ7OPoMeORJYuFCY+Mqgz8rKIhpf7PqP/dPRAdavZ+/iREYKE1/setr/yPonFCo9Sb99+1bl9GFh/9Xz3bx5M/T09GDS0xpAOA4fBtTU5BtfmfSZmZlE44td/6l/P/0EGBsDv/8uTHyx62n/I+ufUMhsknZ1dUWbNm1Qu3Zt9O7dG6GhoRUee+TIEaipqX32KSgokFVzqkW3bt1USu/m5gYLCwvERUXCab4Nzm61g9N8G9SvHYnXrwfAz2+vXOMrm57v7lDS7Set/9Q/TU3AwQG4coWtuibv+GLX0/5H1j+hkMkk7ePjg8WLF2PVqlX4+++/MWDAAAwfPhzJyckVavT19fH8+XOpj9DZXy5cuKAy+rCwMMybNw/zJ4xC9DHper4PT3Cr5yum65eHfv/+/UTji11fnn+jRgH9+rGr6QoyiMosvtj1tP+R9U8oZJLMxMzMDL169ZLaLWdsbIwxY8bAwcHhs+OPHDmCxYsX87pdIYtkJu/evYNudbYxK4F+vLU14qIiEX3MrdxygRKJBN1/nIPOvUzh6+sn8/jKqM/IyECzZs2IxRe7viL/QkMBCws2292kSfKLL3Y97X9k/RMK3ivpoqIiREZGYsiQIVL/PmTIENy8ebNC3bt379CqVSsYGRlh5MiR+PvvvyuNU1hYiJycHKkPX1xcXFRCL696vmK5fnnpp02bRjS+2PUV+TdgAGBlBaxeDRQVyS++2PW0/5H1Tyh4T9JZWVkoLS39rPZm06ZNkZGRUa7myy+/xJEjRxAQEABvb2/Url0b5ubmSExMlDpuwYIFuHbtGr7//nusW7cO9erVK/u0aNECAHD8+HFs2rQJtra2CAgIgLW1NVJTU8ueN1haWuLJkyeYOHEi/Pz8sGrVKtjZ2cHLywtxcXGIi4uTOjYrKwtWVla4cOEClixZAicnJ+zbtw82Nja4ffu21LG2trYYOnQowsPDMXv2bLi6usLFxQULFy5EUFAQRowYgbdv30ppoqOjMX36dHh4eAAAVqxYAX9/f4wfPx7JyclSxyYlJWHChAk4deoUVq5cifXr18PT0xPTpk1DbGwsgoODy459/fo1rKysEBQUhEWLFuHPP/+Em5sbfv31V1y7dg2lpaVoZ/hFpb/LtobNUFpaitGjR+P169dSbYmNjcW0adPg6emJ9evXY+XKlTA2NsaECROQlJQkdWxycjLGjx8Pf39/rFixAvb29vDw8MD06dMRHR1ddmxwcDDevn2LESNGICgoCAsXLoSLiwtcXV0xe/ZshIeHY+jQoSgqKpI6/+3bt2FjYwMDAwM4OTlhyZIluHDhAqysrJCVlSV1bFxcHKZOnQovLy/Y2dlh1apV8PPzw8SJEzF58mSpY1NTU2FtbY2AgADY2tpi06ZN8PDwwIwZM3D//n2pY3NyclCrVi1cu3YNCxYsgIuLC3bv3o05c+YgLCwMw4YNQ0FBgZTm7t27+Pnnn+Hu7g5HR0e8fv0agYGBGDNmDDIyMqSOjY+Px5QpU+Dj44O1a9dizZo18PHxweTJk5GYmAhLS0usXr0alpaWSE9Px9ixYxEQEIDly5fDwcEBBw8exMyZMz9rd15eHoYPH47g4GCkp6dj165d2LVrF+bOnYvg4GAMHz4ceXl5Upr79+9j5syZOHjwIBwcHLB8+XIEBAQgMjIS6enpUscmJiZi8uTJ8PHxwZo1a7B27Vr4+PhgypQpiI+PlzrW09MTY8aMQWBgIJYuXQpHR0e4u7vj559/xpQpsXjyRIIDB9hjCwoKMGzYMISFhWHOnDnYvXs3dHV1pcaInJycz9o9Y8YMeHh4lDtGfPz9qWiMmDp1aoVjRO/evascI4qKiiocI8zMzKocI+zt7SscIwBUOUZ8fN5PxwgdHZ2yMSIiIgKDBw9GSUkJLC0tUVJSgsGDByMiIgK//vor3Nzc8Oeff2LRokUICgqClRX7eKyqMeLUqVMVjhFRUVFVjhGWlpYVjhGpqalVjhH79u2rcIy4cuVKpWOEwsA3G0paWhoDgLl586bUv9vb2zOdOnWq1jlKS0uZHj16MAsWLKjwmIKCAiY7O7vsk5KSwjvj2MaNGzlrxaSXVz1fsVy/vPSDBg0iGl/s+qr8mzGDYZo0YZicHPnEF7ue9j+y/gkF70m6sLCQ0dDQYE6fPi317wsXLmQsLCyqfR4bGxtm2LBh1T5eFmlBX758yVkrNr31uHHMl61aMSXhgeVO0CXhgUzntq2Y8eOt5RJfGfWPHj0iGl/s+qr8S0piGG1thrGzk098setp/yPrn1Dwvt1dq1Yt9O7d+7MUbUFBQdXO6MIwDKKiovDFF5XfjpU1fG9piEXPMACDJXiUlIwlO/ZB8sm22Q/1fOOeJWPx4iUyj6+s+vXr1xONL3Z9Vf61bAnMnw9s28aWTZV1fLHraf8j659QaNjZ2dnxPYm+vj7WrFkDQ0ND1K5dG5s3b8b169dx+PBh1K9fH9OnT8edO3fKnhmsX78ehYWFUFdXR1JSElatWoXLly/Dzc0NhoaG1YpZWFgIR0dHrFy5Etra2pzarampyWt3nxj0DAMsXgwcOdISU6Y0xSGf7fC7Hoai4hJkvnmLCxH38D/HHQi8eReurq4YN26cQrVfkfUlJSXo2rUrsfhi11fHv969gV27gOxsYPhw2cYXu572P7L+CYVM3pP+4Ycf4OLigg0bNqBnz564ceMGAgMD0apVKwBAcnIynj9/Xnb827dv8euvv8LY2BhDhgxBWloabty4ga+++koWzak2qampSq1nGGDJEmDnTmDvXsDLazZCQ0PRuZcplu92xxjb9Vi+2x2de5kiNDQUs2fPlml8Zdc/ePCAaHyx66vjX6NG7DvTe/cCT5/KNr7Y9bT/kfVPKDRldaK5c+di7ty55f7swy7KDzg7O8PZ2VlWoTnD8HxFXJH1DAMsW8YWzdizB5g1i/13c3NzmJubIz8/H3/88Qc2b94MHR0dmceneqqXlX7hQnY1vWYN4OUlfHyqp3qSqHTu7g+vcSmbnmEAW1tg+3Z2cCvvbycdHR307duX8wRdWXxV0fO9VUa6/aT11fWvTh3Azg44fhz4OJ0C6faT1tP+R9Y/oVDpSToiIkLp9AzD3h7cto1dRc+fX7H+zJkzMo+vSnrqn3D+zZwJdOokXXyDdPtJ62n/I+ufYAi2j1zGyOIVrKysLF5tUDS9RMIwv//OMADDODtXrU9ISJBpfFXTU/+E9e/UKbZvX7kim/hi19P+R9Y/oVDplfTHucbFrmcY9pmdoyN7m3vx4qr1c+bMkVl8VdRT/4T1b+xYwMwMWLGCLb5Buv2k9bT/kfVPKGRSYIMEsiiwoUysWwds2AA4ObEbxigUZSQkBPj2W8DHB5g4kXRrKBT5o9IraXt7e6XQr1/PTtBbttRsguZbT1VRrp+UnvonvH/ffAN8/z2wahWwfv1mXvFJXz/tf+L2TzBI32/niiyeSedUlBRYRPr169nndA4ONdenpaXxjq/KeuofGf/++Ydh1NQYZvv2fF7xSV8/7X/i9k8oVHolffDgQVHrJ02Kxrp1wKZN0rteq8u8efN4xSd9/aT11D8y/nXvDvz4I7BuXSneveMen/T10/4nbv+EQiZpQUkgi7Sg+vr6MDAw4NwGknoHB2Dv3pbYsIGtu8uFOnXqoFOnTtzEELd/stBT/8j516sX4OysCW1tNVhYcItP+vpp/xO3f0Kh0JO0t7c36tSpA3d3d5iamsLR0RExMTEYOXIkDh8+jDdv3mDIkCFISEhAdHQ0GIaBt7c3jI2N4eTkBAsLC9jb26Nr1644dOgQateujdu3b+Px48d49+4d9uzZg759+8LZ2bnsWFNTU+zcuRONGjXCtWvXkJGRgYyMDFy9ehWNGjXCrl27yo4tLS1FQEAAWrZsiXPnziE3NxdPnz7FrVu3oK2tjUOHDqF3795wdHQs03Ts2BHe3t6QSCTw8/NDdnY2SktL4ePjgy+//BLbtm0rO7Z79+5wd3eHjo4OIiIi8PTpU+Tk5GD+/BTs2WOErl39cOJEZ9jb26NPnz7YuXMnDAwMcOXKFWRmZiI9PR3BwcFo0KABdu/ejf79+2PTpk3o378/Nm/ejHv37uHNmzd49+4dHj9+jDt37kBbWxtHjhyBiYkJtmzZUtaWTp064fjx4wCAqKgoPHjwAHfv3kVkZCQ6duwo1e4ePXrgwIEDqFu3LsLDw5GUlIQ3b94gMDAQhoaGcHFxgYWFBRYuXIiRI0fC2dkZTZo0QVBQELKyspCamoqQkBDUr18fbm5u6NevHzZv3lx2/jZt2sDf3x937txBcXEx7t27B01NTXh4eKBnz55S7TY2NoanpyfU1dVx//59PHr0CIWFhfDz88PLly9x/vz5smN79uyJffv2QU9PD6GhoUhOTsabN29w8eJFNGvWDDt27Cg71szMDHPnzoWFhQUuXbqEV69eISUlBaGhodDX18fevXvRt29fqXa3bdsWp06dQmFhIeLi4uDr64tWrVrh2LFj6NatG7Zu3Vp2bOfOnXH06FFoamri3r17iI+PR35+Pvz9/dG2bVts374dAHD69GmYmJjAzc0N+vr6uHHjBlJTU5GVlYXLly+jadOmUu3++uuvsW3bNjRv3hx79uxB3bp1kZSUhLCwMOjq6mL//v0wMzODg4NDmaZ9+/bw9fVFUVERHj58iKioKACAk5MTBg0aJPVd69KlCzw8PKClpYW7d+8iMTEReXl5OHPmDFq3bo3t27eXHRsbG4tHjx6hQYMGuH79OtLT0/Hy5UsEBQXBwMAAO3fuLDu2X79+2Lp1K4yMjHD+/HmoqWXjwYPn8PNrhsGDk+HldaBsjPi43SdPnkRpaSliY2M/GyOWL1+O8ePHVzpGBAQEoFWrVuWOEUlJSUhKSqp0jDA3N8eWLVvKHSMePHiAkJCQSseImJgYxMTElDtG/PLLLxg3bly5Y8T58+dhZGRU9l0rb4wICQmBlpZWpWNE69atcfbs2XLHiPfv3+Ps2bOVjhHFxcXw9fUtd4yws7NDu3btKh0j7O3t8dVXX5U7Rnh4eKBz586VjhF5eXlISEgod4xISEjAnTt3KhwjmjZtSmbi+xTS99u5Iotn0pcuXeLVBhL6rVvZZ9Br1/KPv3nzZl56MfonSz31j6x/J09eY/T1GWbRIm560tdP2j/S7Set5+ufUKj0M+l69eqJSv/nn2y6z9Wr2TSJfOM3adKEl15s/slaT/0j61/LlnVgawu4ugLPntVcT/r6SftHuv2k9Xz9EwqVnqT5VkERUu/szL5etXIl+7qVmhr/+GFhYbz0YvJPHnrqH3n/Fi9mK2WtXctNzzc+ST3tf2T9EwzSS3muyOJ2N98t+ELpd+xgb3GvWMGm/pRV/MjISF56sfgnLz31TzH827uXfSUrKoqbnm98Unra/8j6JxQqvZI+dOiQwut37wYWLQKWL2d3dKupyS6+ra0tL70Y/JOnnvqnGP79/DPQvj17l4mLnm98Unra/8j6JxQ0LagCs2cPW8Xqt9/YdJ8fT9AUCuU//PyACROAa9eAgQNJt4ZCkR0qvZImnZauMv3evewEvWRJxRM06bR4iuyfEHrqn+L4Z20NfPUVm9SnussO0tevSP6pol4saUFVeiVdXFwMLS0tzm2Ql37/fmDWLPY2t7NzxStovvHz8vJQp04dznpF9U8oPfVPsfy7fh347jt2VW1tXXM93/hC62n/I+ufUKj0SvpDQghF0ru7sxP0/PmVT9CyiG9dnZGsEhTRPyH11D/F8m/gQGDYMOCPP4Di4prr+cYXWk/7H1n/BIPsvjXuyGJ395MnT3i1Qdb6gwfZXdxz50rv4pZX/OvXr/PSK5p/Quupf4rnX1QUu9N7715uer7xhdTT/kfWP6FQ6ZV0RESEwugPHwZsbIA5c9gd3dXZJMY3/smTJ3npFck/Enrqn+L516MHMHUqW771/fua6/nGF1JP+x9Z/4RCpSfpFi1aKITewwP45Rfgf/+r/gQti/jGxsa89IriHyk99U8x/duwAcjKAnbs4KbnG18oPe1/ZP0TCpWepBUBT09g5kx2knZzA9Tpb4RC4UWbNsDcucCWLcCrV6RbQ6HwQ6WnhJSUFKL6Eyc08NNP7CS9b1/NJ2i+8ePi4njpSftHWk/9U1z/Vq1iX8XavJmbnm98IfS0/5H1TygUulRlZciinrSuri4aNGjAuQ189N7ewKpVLTB9uhrc3bmtoPm2v27dumjdujVnPUn/FEFP/VNc/+rWBUpKgG3bgOnTgfr1a6bnG18IPe1/ZP0TCpVeSfv6+hLR+/gA06YBPXvGcp6g+cT/wJYtW3jpSfmnKHrqn2L7t2QJ0KBBxcU3SF+/ovun7Hq+/gmFQq+kvb29UadOHbi7u5cVdI+JicHIkSNx+PBhvHnzBkOGDEFCQsJnBd0/LkRfUUH3ly9fonXr1uUWdG/UqBGuXbtWaUH3pUuXwsnJqdyC7tra2jh06NBnBd3j47th5kxtDB36Cr/99gCPHj0ot6C7vb09unfvXmlB91u3buHbb78tt6B7ZmYm0tPTKy3ovnTpUgQGBpZb0N3ExARbtmyptKB7r169cOrUqXILuh84cAB169attKD71atX0bdv33ILuoeEhKB+/fqVFnTv3r07Hj9+XG5B9w/HVlTQ3c/PD1OmTJEqLt+zZ0/s27cPenp6CA0NRXJyMt68eYOLFy+iWbNm2LFjR9mxZmZmSElJgaGhIS5duoRXr14hJSUFoaGh0NfXx969e9G3b1+pdrdt2xanTp1CYWEh4uLioKWlBS0tLRw7dgzdunXD1q1by47t3Lkzjh49Ck1NTdy7dw/x8fHIz8+Hv78/2rZti+3bt2P58uVwcHCAiYkJ3NzcoK+vjxs3biA1NRVZWVm4fPkymjZtKtXur7/+Gtu2bUPz5s3x+vVr5OTkICkpCWFhYdDV1cX+/fthZmYGBweHMk379u3h6+uLoqIiPHz4EFFRUQCAp0+folu3blLftS5dusDDwwNaWlq4e/cuEhMTkZeXhzNnzqB169bYvn172bH29vbYv38/GjRogOvXryM9PR0vX75EUFAQDAwMsHPnzrJj+/Xrh61bt8LIyAjnz59HdnY2mjRpgtu3b382RvznYXs8eRINL68WaNr0JpKT70mNEWFhYWXfn4rGiICAALRq1arcMWL48OEIDg6udIwwNzfHli1byh0jLCwscOTIkc/GiI4dO8Lb2xsSiQQxMTGIiYkpd4xITEyEiYlJpWPEx/370zGiTZs2yMjIqHSMaN26Nc6ePVvuGDFr1iyp3315Y0RxcTF8fX3LHSNiYmKgq6tb6Rhhb2+Pr776qtwxorCwEA0bNqx0jMjLy0NCQkK5Y4SLiwu2bNlS4RjRtGlTYnOfFKTfAeOKLN6T3rhxI6821FTv58cwGhoMM2UKw5SUCB//UwYNGkQ0vtj11D/F96+oiGHat2eYESO46fnGl6ee9j+y/gmFSqcFFZLTp4EffmCLABw9Cmhqkm4RhaIanDzJfveCg4FvviHdGgqlZqj0M2mhEryfOcMOEtbW0hO02BPMk24/aT31Txz+jR8PmJoCK1ZIF98gff1i8U9Z9WIpsKHSt7uFKDp+9izDaGkxzIQJDFNcLHz8yqBF46l/JPVC+nflCpty9/Rpbnq+8eWhp/2PrH9CodIr6YsXL8pVf/48+1f8qFGAl9fnt7jlHb8qdu3aRTS+2PXUP/H4N2gQMGQIsHIl+2pWTfV848tDT/sfWf+EQqUn6S5dushN/9df7O3tkSPZd6LLq6gmz/jVoX///kTji11P/ROXf46OQHw8myefi55vfFnraf8j659QqPQknZ2dLRf9hQvAuHHA998DJ06UP0HLM351yczMJBpf7Hrqn7j8MzEBJk8G7OyAvDzy1y82/5RNz9c/oVDpSTo3N1fm+kuXgLFj2bq2Pj5ArVrCxq8Jr1+/Jhpf7Hrqn/j8s7cHXr4Edu4kf/1i9E+Z9Hz9EwqFTmZSGbJICwoABgYGvNrxsf7yZWD0aGDwYMDXF6hOs2QZv6YUFBSgU6dOxOKLXU/9E59/DRqwk/SePcDs2epo0aKxoPFlqaf9j7x/QqDSK+nLly/LTH/lCjtBDxoE+PlVb4KWZXwuHP7wcI5QfLHrqX/i9G/1aqC0FFi9+h2R+LLS0/5H1j+hUOlkJrm5udDT0+Pchg/6q1fZDWIDB7JJS2rXFjY+V9LT09G8eXNi8cWup/6J17/16wEHBwYJCWpo2VL4+LLQ0/5H1j+hUOmV9I6qqsJXQ3/9OmBlxWYyqskELav4fJg+fTrR+GLXU//E69/SpYCm5nusW0cmviz0tP+R9U8oVHolzZeQEHYHt7k5EBBQswmaQqGQZfduYNEi4J9/gK5dSbeGQikflV5J80krd+MGMHhwEfr1A86e5TZBiz0tHun2k9ZT/8TtX1bWZrRuDfzxB5n4YvdP7HqaFlTOyCItaFZWFiddaCjD1K3LMAMGFDHv33MOzzm+rPQJCQlE44tdT/0Tv3/e3my60NBQMvH5oAj+iVnP1z+hUOhXsORdT3rNmjWwsLCoUT3pZcv8sXJlTzRp8i9++skP4eFBNaon/XGtWBcXFxQWFnKuJ/3LL79g8uTJnOtJHzp0CMXFxZzrSZ8+fRoPHz7kXE960qRJGDt2LOd60qdPn4aGhgbnetJ3797FtWvXONeTHjJkCAYPHsy5nvSOHTvQsWNHzvWknz17hkuXLnGuJ7169Wo0bNiQcz3pZcuWYfjw4ZzrSXt5eSEtLY1zPel9+/bhzZs3FdaTbt++PU6ePInS0lLExsZ+Nkb89NNP2LhxMg4ceI5bt2qjsHBvjepJh4aGIjMzk3M96QsXLuDu3buc60kPHDgQkydP5lxP2svLC3p6epzrScfGxuLKlSuc60nPmjULxsbGnOtJOzo6lvV9LvWkT548iUePHtF60vJCFivpv//+u0bH37zJMLq6DPPNNwzz7l3N9Xzjy1p/4sQJovHFrqf+KYd/ly+zq+kzZ8jE54qi+CdWPV//hEKln0mnpKRU+9hbt4ChQ9nUgufPA3Xr1kzPN7489LGxsUTji11P/VMO/wYPBiwtpYtvCBmfK4rin1j1fP0TCpWepNXU1Kp13J077ATdowcQGAjo6tZMzzc+1VM91ctX7+gIxMWx9d4BID8/Hy9evEB+fr4g8alefHqhUOlJ2sjIqMpj7t5lS9x17So9QVdXzze+PPV8q8iQbj9pPfVPefzr3RdkOsMAACAASURBVBv44QdgxYowjB1rDT09PTRr1gx6enoYb22N8PBwucbngiL5J0Y9X/+EQqUn6Vu3blX688hIdoLu3JmtbPVpcpuq9Hzjy1t/9uxZovHFrqf+KZd/xsZuyMqywKOoSDjNt8HZrXZwmm+DuKhIDBgwAHv37pVr/JqiaP6JTc/XP8Eg/VCcK7LYOPby5csKfxYZyTANGjCMmRnDVBSiMj3f+ELoHz16RDS+2PXUP+XxLzQ0lFFTU2MWTBzNlIQHMpKIi2WfkvBAZv6EUYyamhoTFhYml/hcUCT/xKjn659QqPRK+tO/jD/w99/sRpIOHdjSkxUlNKtIzze+UPp58+YRjS92PfVPefxzcXaGcZuWcF40C+rq0sOiuro6XBbPhnGblnBxcZZLfC4okn9i1PP1TyhoWtBP+Ocf4LvvgLZtgaAgoH59mZ2aQqEoIPn5+dDT04PTfBssnjS2wuNcTvhj+W535ObmQkdHR8AWUlQZlV5Jf5pWLjqaLTXZpg1bG7qqCZp0WjvSafFIt5+0nvqnHP7l5OSgtLQU7Qy/qPT4tobNUFpaipycHJnG54qi+CdWvVjSgqr0Svrdu3fQ/f/t2rGxbKnJFi3Y2tANG9ZMzzc+CX1GRgaaNWtGLL7Y9dQ/5fCP60qa+iduPV//hEKlV9IHDhwAADx4wN7iNjKq/gT9sZ5vfFL62bNnE40vdj31Tzn809HRwZjRo+F+7iIkEkm5x0okErifu4ixY8eU3eqm/olbz9c/oVDo3N2VUVhYCEdHR6xcuRLa2tqcztGgQQNkZjbGd98BzZsDV68CjRrVTN+4cWNOsRVBr6+vjw4dOhCLL3Y99U95/GtuaAgnZxe8yX2HoWa9pRJdSCQSLHbZi8Cbd7F//360bNlS5vG5oEj+iVHP1z+hUOmV9IUL/+K774CmTdkVdE0maACIiYnhFZ+0/sqVK0Tji11P/VMe//r37w9XV1fs9g1A9x/nwOWEPwJCI+Bywh9dpszBHr9zcHV1hbm5uVzic0GR/BOjnq9/QqFJugGkiI8H7O0Hlq2gufxBVp/n1m/S+iZNmhCNL3Y99U+5/Js9eza6desGFxdnLN/tjtLSUqira0AiGYMDB7xgY2NeqZ5v/JqiaP6JTc/XP6FQyUk6IYHdJFavXimuXgUMDLidR+/TFGQi0/O5VSSL+GLXU/+Uzz9zc3OYm5sjPz8fOTk5qFtXH3366MDfH7CxkX/8mqCI/olJz9c/oVDoZ9LyqCft7x+LKVOaQ1e3GKamKzBiRJ8a1ZP+uFZsfn4+Ll26xLmetI+PD/Ly8jjXk/7jjz/www8/cK4nffPmTeTn53OuJx0REYGYmBjO9aQXLlyI0aNHc64nHRERAQCc60mnpaUhKCiIcz3pefPmYdCgQZzrSfv4+KBdu3ac60kXFhbir7/+4lxPeteuXahXrx7netJbt27F0KFDOdeTjoyMRFJSEud60gEBAcjKyuJcT3r58uVl359Pa84nJSWBYRhcvHgBX3/dEc7O2hg2DDhy5L8x4vHjx3j+/DnnetJRUVGIiIjgXE/axsYGP/zwA+d60teuXUOdOnU415P+8N3gWk963bp16NSpE+d60ocPH0aPHj0415OOjo5GTEwMrSctL7ikBU1MZBhDQ4b58kuGef6cYVJSUni1Qez6O3fuEI0vdj31TzX8KylhmC5dGGbIEDLxK0Is/imqnq9/QqEyG8eePGFvcevqAteuAc2aAUeOHOF1TrHrV65cSTS+2PXUP356sfinoQHY2bEJjsLChI9fEWLxT1H1fP0TCpVIZvL0KfDtt0Dt2kBwMPu6FYVCoVQXiQQwMWE3mF69Sro1FEXFxsYGBw8ehKWlJS5fvvxZzeq1a9di48aN6Nq1K+7du1et14eVfiX977/sClpbG7h+XXqCJp2WjrSephWk/pHUi8k/dXVg/Xr2LlxIiPDxy0NM/imiXh5pQV1cXNC2bVtcuXIFO3bskPrZ7du3sXnzZtSqVQuenp7Vzu+h1CvppCTgm28ATU12Bf1pjfCSkhJoanLf4C52fUFBAWrXrk0svtj11D/V8o9hgN692brywcFAaSn1T8x6vv5VxM2bN2FhYQEtLS3cu3cPXbp0QV5eHnr27InExERs2bIFtra21T6f0q6kk5PZW9waGuwK+tMJGgC2bdvGK4bY9WPGjCEaX+x66p9q+aemBmzYANy4wY4p1D9x6/n6VxH9+vWDra0tCgoKMG3aNBQVFWHp0qVITEyEhYUFli1bVrMTkt23xp3KdncnJzNMmzbsJymp4nM8e/aMVxvErg8NDSUaX+x66h8/vRj9k0gYpk8fhjE3Z5inT4WP/zFi9E+R9Hz9q4yioiLGxMSEAcAMHjyYAcDo6+sz//77b43PpXQr6dRU9hk0w7B/7f5/mt1yCft4qyYHxK738vIiGl/seuqf6vmnpsY+mw4PB/bufSJ4/I8Ro3+KpOfrX2VoaWnB09MTtWvXRlBQEABg586daNWqVY3PpVSTdFoaO0EXF7MTdFV+cDFMmfRdunQhGl/seuqfavo3bBjQty9w/nwf8NnRo6r+KYqer39V0b59+7JiLPXq1YO1tTWn84h2ks7Pz5f63/R0doIuLGQ3dbRuXfU5SktLebVB7PqSkhKi8cWup/6ppn8fnk0/fKiPCxeEj/8BsfqnKHq+/lXFqlWrkJCQAHV1dWRnZ2PJkiWcziO6STosLAzjra1haGgIADA0NMTIEdbo2zcc+fnsBN2mTfXO9fz5c15tEbv+yRN+t+tIt5+0nvqnuv5ZWgKdOmVi3TpwXk2rsn+KoOfrX2XcuHED27dvR506dRAUFIT69evD3d0d586dq/G5FDp396e4ublhwoQJQGEefv9xIuZaW8HUuCMu3wjFsxQXLFvWFGPGmFb7fHXq1EHDhg05t0fs+tq1a6NNdf+ikUN8seupf6rrn5oaUL/+W+zZo4/evYFOnYSND4jbP0XQ8/WvInJycjB06FC8efMGLi4umDhxIlq2bInTp0/j6tWrmDFjBurWrVvt84lmJR0WFoZ58+Zh/oRRiD7mhsWTxsJqQF8snjQWD73dMH+CFdatm4vw8PBqn/PUqVO82iR2Pd9XGEi3n7Se+qfa/qWne+Gbb4C1a7mtplXdP9J6vv5VxMKFC/Hvv/9iyJAhmDt3LgBgypQp+OGHH5CZmYlff/21RucTTTKT8dbWiIuKRPQxN6irf/63hUQiQfcf56BzL1P4+vpV65yFhYXVzvqijPqcnJwqU6rKM77Y9dQ/6t+tW9r49lvg9Glg7Fhh4yuDf2Luf+Xh7++PcePGoUGDBoiNjUXzj1JcvnnzBl27dkV6ejoOHTqEmTNnVuucCjtJMwyD3NxcAOzmMENDQzjNt8HiSRV/E1xO+GP5bnekpaVBR0enyhhbt26tUeYXZdOPGjUKAQEBxOKLXU/9o/7Z2tpi1Cjg5Uv2taxy1g9yi68s/pHSV8c/PT29z/JvV8SLFy/QtWtXZGVlwdvbG5MmTfrsmMuXL2PYsGHQ1dVFdHQ0Wldjh7PCTtIf0n5+zNmtdrAa0LdCTUBoBMbYrpd30ygUCoWiAlSngJO84Z74VM7o6ekhOzsbwH8r6Sdple/me5qWAQ0NjWqvpNu2bYunT59ybqOY9Tk5OWjRogVSUlI4d0IxXz9fPfWP+vexftw4NpFSRASbilje8ZXNP6H11fVPT0+Pa/NkhsJO0mpqamXm6evrY8zo0XA/dxELJ46u8Jm0+7mLGDt2DJo2bVqtGA0bNuT1V5LY9QDrLddzkG4/aT1A/aP+sfpNm9gEJ5cuAeXc5ZRLfEB5/COhB/j5JxSi2d29eMkSxD1LxpId+yCRSKR+JpFIsNhlL+KeJWPx4uq/MN6nTx9ebRK7ni+k209azxfS7Set5wvp9n+sNzMDRowA7OyA6ubYoP6Ju/8JhiyTissbNzc3Rk1NjencthWzfdEs5szWdcz2RbOYzm1bMWpqaoybm1uNznfnzh1e7RGzvrICJULEF7ue+kf9+1R/9y7DAAxz7Jj84yujf0LqZeGfUCjs7e7ymD17Nrp16wYXF2cs3+2O0tJSaGhoYOzYMdh/1Avm5uY1Ot/r1695tUfMem1tbQwcOJDXKwxivn6+euof9e9TvakpMGoUW4Bj0iS2jr284iujf0LqZeGfUIhqkgYAc3NzmJub48WLF2jWrBnS0tKq/Qz6U96/f8+rLWLWa2trw9TUlFcnFfP189VT/6h/5ent7IBevQBPT2DGDPnFV1b/hNLLwj+hEFVa0I+RSCRwdHTEmjVrOBvNMAwMDAw4t0Hs+vz8fHTiks9QRvHFrqf+Uf8+1X/xBRATA/j4AHPnVr7Tm/on7v4nFKLZOCYPrly5otJ6Dw8PovHFrqf+Uf/Kw84OePYMqOryqH/i7n9CobDJTKriQ7ITPi+b800LJ3Z9amoqjIyMiMUXu576R/2rSP/DD8Dt20BCAlCrlnziK7N/Quj5+icUKr2S3rlzp0rrZ1T10EzO8cWup/5R/ypi3TogORk4fFh+8ZXZPyH0fP0TDCG3kssSMW2hVyRCQkKYkSNHMl988QUDgPH39yfdJNGwefNmxtTUlNHV1WUMDAyY0aNHM48ePSLdLNHg6urKdOvWjdHT02P09PSYvn37MoGBgaSbJTcmT2YYIyOGKSiQz/k3b97MAGAWLVoknwBKyLp16xgAUp+mTZuSblalqPRK2t7eXuX079+/R48ePbB7925esbnGF7M+JCQE8+bNw61btxAUFISwsDAMGTKE8y5TsV0/X72R0f+1d+ZRUVzr194MioyKiKAiChFncEJRHJLfFedgYpxiTDQOSVCjQa9DTJaiucikQUSUMQqiooKCxBEiiIAThCCtEEFBBhGRQdAwCdT3B1/6hiu0UtVdh7LOXqvXSrSefk/vVf0eT1fV2UZwcXFBcnIykpOT8eTJE3z00Ue4d+8eL/X55rdvBwoLgYAA+ddPSkrCTz/9BAsLC9bv0d79UxQ/ZMgQPHnyBBMmTMCTJ08gkUg4jUPhIv2vBLaSx0q6tLSU0xiEzoPjSpr0+Enzt27dYgAwcXFxROoLnX/w4AGjq6vLBAQEEKnPB//FFwzTsyfDVFXJr/6LFy8YMzMzJjAwkHn//fdZr6SF4J+8eQcHB2bYsGEMwzSdf0KQqFfSISEhoua5ivT4SfN/P73YtWtXIvWFzDc0NGDx4sX466+/MG7cON7r88Vv2wY8fQr4+cmv/po1azBr1iycP3+eFc+1vtD5rKws9OzZE8OGDcOnn37KKeSDD4l6kp44caKoea4iPX6SPMMwKC4uxoQJEzB06FDe6wuVl0gk0NLSgpqaGiQSCcLDwzF48GDe6vPNm5kBS5YALi5AVRX3+idOnEBKSgqcnZ2xYMGCNvNc6wudt7KywpEjR3D58mVs2LABRUVFsLa2RmlpKaexKFLtejOTkJAQaGhoICAgAJaWlnBxcYFEIsGHH36Iw4cPo7y8HFOnTkVmZibS0tLAMAxCQkIwaNAg7N69G5MmTYKjoyOGDh2KQ4cOoVOnTrh16xYePHiAly9fws/PD2PGjMHevXulx1paWsLT0xN6enqIiYlBUVERioqKcOXKFejp6WH//v3SY1VVVREREQFjY2P8+uuvePHiBbKzs3Hz5k2oqanh0KFDGDVqFFxcXKRM//79ERISgsbGRkRGRqK8vBwNDQ04efIkBg4ciD179kiPtbCwQEBAANTV1XHjxg1kZ2ejsrIS586dg5GRERwcHPDJJ5/A0dERo0ePhqenJ/T19fHbb7+huLgYhYWFuHr1KnR1deHl5YUJEyZg165dmDBhApycnBATEwMDAwPo6OjgwYMHuH37NtTU1BAYGIgRI0bA1dVVOpYBAwbg+PHjAIDU1FTcu3cPd+7cQVJSEvr3799s3MOGDYO/vz80NTWRmJiI3NxclJeX48KFC+jVqxc8PDwwadIk/Pvf/8bMmTOxd+9edO/eHdHR0SgpKUFBQQHi4uLQpUsXeHt7w9raGk5OTtL3NzExQXh4OFJTU1FbW4vk5GSoqqoiKCgIw4cPbzbuQYMG4ejRo1BWVkZKSgr+/PNP1NbWIiwsDJWVlYiMjJQeO3z4cPj6+kJbWxvx8fHIy8tDeXk5Ll26BENDQ+zbt096bEhICKKjoxEUFITExESUlpYiPz8f8fHx0NHRgY+PD8aOHdts3Kampjh9+jRqa2uRkZGBs2fPonfv3ggODoa5uTnc3Nykxw4ePBhHjhyBqqoqkpOTcf/+fVRXVyM8PBympqZwd3eHmpoaQkNDMWLECHh7e0NHRwfXrl1DQUEBSkpKEBUVBQMDg2bjHjduHPbs2YOePXvCz88P6urqyM3NRUJCArS0tODn5wcrKys4OztLmX79+iE0NBR1dXVIT09HamoqAMDDwwP/93//1+y7NmTIEAQFBaFDhw5ISkpCVlYWqqqqEBERgb59++LIkSM4ePAgamtr0dDQgIMHD8LCwgJ37txBYWEhnj17hujoaOjr68PT01P6vtbW1nBzc4ORkRHOnTuHiooKREdH4/Hjx6/1iH+O+9SpU2hoaMDdu3df6xE//PCD9PvTWo+IjIxEnz59WuwRT548QU5OjsweMX78eFy/7ouYGEs8fPg7DAyypT0iKysLsbGxMnuERCKBRCJBQ0MDfHx8sGPHDsyaNQuzZ8/GqlWr0NDQgGfPnmHUqFEt9oi/v2st9YgbN25ARUVFZo/o27cvzp49i5cvX77WI+rr6xEeHi6zR7x69QqhoaEt9ohdu3bBxMREZo9wdHSU9uj/7RHHjx/HoEGDZPaIqqoqZGZmSntEYmIiFi1ahMDAQNTV1cHExARJSUm4e/cu+vXr16xHsN3JUu4i/HM7a8njmvS5c+c4jUHoPDhekyY9flL8t99+yxgZGTHr1q0jUv9d4R0cHJjJkyczX3/9NZH6fPJffcUw+voM8/Il+/rh4eEMAEZFRYVRUVFhlJSUGACMkpISo6KiwtTX17fp/YTknyJ4BwcHhmEYxsbGhrGzs+P0XoqUqH/u7tGjh6h5riI9fr55hmHw7bff4syZM4iJicGYMWN4rf+u8WZmZmAYBrW1tUTq88n/+CPw/Dlw4AD7+pMnT4ZEIkFqaipSU1Ph5OQES0tLLF68GKmpqVCRtQdpCxKSf4rgzczMpL9qke6lsiTqSTopKUl0/MuXL6VfcgDIyclBamoq8vLyeKkvZH7NmjU4evQojh8/Dm1tbZw+fRpFRUWorq7mpb7Q+R9++AHx8fF49OgRJBIJnJyccPXqVSxevJiX+iT5Pn2AFSsANzfgxQt29bW1tTF06FDpSyKRQFNTE3p6eqzuixCSf/LiN27ciLi4OOTk5CA4OBjz5s1DZWUlli5dymksChXppTxbyePn7uLiYk5jECIfGxv72sP8AJilS5fyUl/IfEu+AWAOHz7MS32h88uXL2f69OnDdOzYkdHX12esrKyYqKgo3uqT5vPyGKZjR4bZtUs+9dPT0zk9giU0/+TBL1y4kOnRowfToUMHpnv37swnn3zC3Lt3j9M4FC1Rr6R9fX1Fx3/wwQdgGAYMw2Dy5MnS/w4MDOSlvpD5v736X//Ybi8otM/Plf/ll1/w6NEj1NbWori4GFpaWpgyZQpv9UnzvXsDX38N7NkDVFRwr7927VpcvXoVHh4erHih+ScP/sSJEygsLERdXR3Mzc1x+vRp1k8X8CVRB2xQUVFR8anCQsDUtOka9bZtpEdDJQSJeiUt1G3t5MXb2NgQrS90nvpH/WurevYEVq0Cfv4Z+PHH3Zzqi9E/efJc/eNLol5JV1VVQUNDg/UYhM6XlJSgW7duxOoLnaf+Uf/Y8EVFTatpe/tXcHLqwLq+WP2TF8/VP74k6pW0t7e3qPlly5YRrS90nvpH/WMjQ0Ng9WrA3b0RZWXs64vVP3nxXP3jS+16xzFZqq2thYuLC7Zu3Qo1NTVW76Gnp8fpX1JC53V1dWFmZkasvtB56h/1jy0/fDiwb58yGEYJkyezqy9m/+TBc/WPL4l6JX3nzh1R81FRUUTrC52n/lH/2Kp7d2Dq1Pvw9ARKSti9h5j9kwfP1T++JOpJWk9PT9R8z549idYXOk/9o/5x0ZIlzwA0PZLFRmL3j/T5x5dEPUmrq6uLmuf66Brp8ZPmqX/UPy4yNFTFd98B+/cDxcVt58XuH+nzjy+JepLOzMwUNc91Wz7S4yfNU/+of1z5DRsAVdWm7ULbKuof2fOPL4n+xrHOnTuzHoPQeQMDAxgZGRGrL3Se+kf948obGnZGTQ3g4dG0t7e29tvz1D+y5x9fateTtKLzpLds2QIbGxvWedJ//PEHrl+/zjpP2sXFBQBY50kvWbIES5YsYZ0nfeDAAaiqqraYFfs2edLBwcHIzs5mnSc9d+5cLFiwgHWe9LFjx6ChocE6TzomJgY3btxglSdtZWUFGxsbzJo1C5cvX2aVJ+3q6oqhQ4eyzpO+c+cOrl27xjpPetOmTTA0NGSdJ71u3TrMnj27TXnS7u7u0mP9/PxQXl4OXV1dxMbGtjlP2sPDQ/qsLJs86c8++0z6/WGTJ33x4kW8ePHijXnSrq6uLfaIsLAwSCQSrFgxCvv21aOmRhXJya3nSf9vj3j//fexdOlSmT1CVp50QEAAunXrxjpP+saNG0hMTGSdJ718+XJYWFiwzpPeuXMnrKys2pQn/c8ecejQIeTl5bXaI9pLnrSoNzOhoqKiag/6z3+AXbuAhw+BXr1Ij4aqPUnU16RJb0tHmqfbClL/SPLUv//y330HaGgAzs5vz1P/6Lag7VryWEk3NDS0OSj9XeLr6urQsWNHYvWFzlP/qH/y5J2dgR07gAcPmhKz3iTqH9nzjy+JeiXtxuaWyneIt7W1JVpf6Dz1j/onT/7bbwEdHcDJ6e146h/Z84838ZxfLTdVVFQwAJiKigrW7/Ho0SNOYxA6n5CQQLS+0HnqH/VP3rybG8N06MAwOTlv5ql/ZM8/viTqlfS1a9dEzQcHBxOtL3Se+kf9kze/ejWgq9t0E9mbRP0je/7xJVFP0iYmJqLmLSwsiNYXOk/9o/7Jm9fUBLZsAQ4fbrrTW5aof2TPP74k6km6vr5e1HxdXR3R+kLnqX/UP0XwdnaAvj7wppuXqX9kzz++JOpJuqioSNR8dnY20fpC56l/1D9F8BoawNatQHAwkJXVOk/9I3v+8aV2veOYLMljW1A1NTVOSSpC51VVVfHee+8Rqy90nvpH/VMUP2wY8MsvQH4+MGdOyzz1j+z5x5dEvZKOiIgQNe/h4UG0vtB56h/1T1F8p07Ajz8Cx44Bf/7Z8jHUP7LnH18S9WYmNTU16NSpE+sxCJ1//vw5unTpQqy+0HnqH/VPkXxtLWBmBkyYAPz/LbGbifpH9vzjS6JeSe9hm7b+jvDz5s0jWl/oPPWP+qdIXk2taTV94gRw797rf0/9I3v+8SVRr6SpqKio2rPq6oD+/YExY4BTp0iPhoqERL2SJr3BO2mebtBP/SPJU//ezHfsCGzbBoSGAmlpzf+O+ieOgI12fXe3ovOkc3Nz0b9/f9Z50suWLcOBAwdY50kzDIMHDx6wzpOOi4vDlClTWOdJz58/H9evX2edJ21mZobz58+zzpM+f/48Jk6cyDpP2sTEBAUFBazzpGfNmgVfX1/WedISiQRmZmas86Tr6+uhqanJOk965cqV8PDwYJ0nXVBQgJqaGtZ50vfu3cPIkSNZ50mvXLkSoaGhrPOkNTU1kZqayjpP+rfffpN+f9jkSU+YMAE3b95knSc9fPhwnDhxQmaPkEgkUFK6ixs3THH5cg4WLVKRftdu374Na2tr1nnS3bt3R3l5Oes86YULF+LAgQOs86STkpLQtWtX1nnS5eXlMDQ0ZJ0nvW7dOvj7+7f7PGlR793t5+fHaQxC57/44gui9YXOU/+of3zxgYEMAzBMSsp//4z6R/b840ui/rl7+PDhouYnT55MtL7Qeeof9Y8vfvHipju9//m7J/WP7PnHl0Q9SZeWloqaz8/PJ1pf6Dz1j/rHF6+qCjg4AJGRQHIyUF1djYyMDFRXV/NS/13kuZ5/fEnUkzSXE/xd4F+8eEG0vtB56h/1j0/+008BY+MEzLadC21tbbi6ukJbWxvz5s5FYmKiwuu/azzX848viXqSNjMzEzU/duxYovWFzlP/qH988n5+3sjPnwTtDr9j97crcdZtB3Z/uxIZqb9j4sSJ8PHxUWj9d43nev7xJVFP0rGxsaLmjx07RrS+0HnqH/WPLz4hIQFr1qzBt/NnI/2EN+w/nQPbiWNh/+kcpAV7Y808W6xevbpNK2ohfX5F8FzPP74k6s1MKioq0LlzZ9ZjEDqfl5cHY2NjYvWFzlP/qH988fPmzkVG6u9IC/aGsvLra6vGxkZYfLEKg0daIjQ0TO7130We6/nHl0S9kt6/f7+o+eXLlxOtL3Se+kf944Ovrq5GxNmzWGk7vcUJGgCUlZWx0nY6wsMj3vparVA+v6J4rucfXxL1SpqKioqqvevp06cwNDTEWbcdsJ3Y+nXUyPgb+HjzThQVFbWfjTioOEvUK2nS29KR5um2gtQ/kjz17+14HR0dqKio4OHjJzKPy35cBBUVlbdetAjl8yuKF8q2oKJeSXONKhM6n5ubiz59+hCrL3Se+kf944tXxDVpIX1+RfBczz++JOqV9NGjR0XNb9y4kWh9ofPUP+ofX7z9+vXIyMnD+n2+aGxsbPZ3jY2NsPfwQUZOHuzt1yuk/rvIcz3/+FK7DtiQpdraWri4uGDr1q1QU1Nj9R7q6uqcrt0InVdRUcHgwYOJ1Rc6T/2j/vHFGxsbw8DAAA673REWm4C6V/UoLn+OizeSscxxHy7dSMJB74P45JNPFFL/XeS5nn981xcs8wAAIABJREFUSdQr6YcPH4qaT05OJlpf6Dz1j/rHJ29nZ4f4+HgMHmmJTV4B+HjzTmzyCkDXnpZgEI/eve0UWv9d47mef3xJ1JN0x44dRc136tSJaH2h89Q/6h/f/Pjx4xEaGoYXL15g48aNePHiBa5fD8OUKeOxdi3Qlp0yhfj55clzPf/4kqgnaa6PKQidf++994jWFzpP/aP+keLV1dUxbNgwqKurQ0kJ8PICCgoAFxd+6r8LPNfzjy+162vSISEhrwW6SyQSfPjhhzh8+DDKy8sxdepUZGZmvhbo/s8g+tYC3ffu3YuJEye2GOiup6eHmJgYmYHuz58/R3R0dIuB7mpqajh06JDMQPcjR46gpqYGDQ0NOHnyJAYOHNgsGN3CwkJmoPvGjRuxaNGiFgPdi4uLUVhYKDPQ/cqVK6irq2sx0H3EiBFwdXWVGegeFxeHe/futRjo7u/vD01NTZmB7qtWrcKcOXNaDHSPi4tDly5dZAa6x8XFQVlZucVA97+PbS3QPSwsDNnZ2bhy5Yr02OHDh8PX1xfa2tqIj49HXl4eysvLcenSJRgaGmLfvn3SY62srLBixQpMmTIFly9fRmlpKfLz8xEfHw8dHR34+Phg7NixzcZtamqK06dPo7a2FhkZGQgODoaZmRmCg4Nhbm4ONzc36bGDBw/GkSNHoKqqiuTkZNy/fx/V1dUIDw+Hqakp3N3dUVlZiYsXL2LEiBHw9vaGjo4Orl27hoKCApSUlCAqKgoGBgbNxj1u3Djs2bMHPXv2hLu7O3R1dZGbm4uEhARoaWnBz88PVlZWcHZ2ljL9+vVDaGgo6urqkJ6ejtTUVADArl27MH369GbftSFDhiAoKAgdOnRAUlISsrKyUFVVhYiICPTt2xfu7u7SY+Pj41FQUABdXV3ExsaisLAQz549Q3R0NPT19eHp6Sk91traGm5ubjAyMsK5c+dQUVGB0NBQlJWVvdYj/jnuU6dOoaGhAXfv3n2tR9jb20u/P631iMjISPTp06fFHnHv3j08ffpUZo8YP348XF1dW+wRt27dwu3bt2X2CIlEAolE0mKP+OKLL7Bo0SIEBATAyEgdRUXP8csvujA3T8e1axEwMjKSftda6hEXL16ElpaWzB7Rt29fnD17tsUe8eTJE0RFRcnsEa9evUJoaGiLPWLr1q0YOHCgzB7h6OiIMWPGtNgj/Pz8MHz4cJk9oqqqCpmZmS32iJs3byI9Pb3VHtFunjUnF2XNTRUVFQwApqKigvV7FBUVcRqD0HmJREK0vtB56h/1jyT/v/799RfD9OnDMDNmMExjo+LrC53nev7xJVH/3O3v7y9q3t7enmh9ofPUP+ofSf5//dPQAPbtAy5eBCIiFF9f6DzX848viXozEyoqKqp3SQwD2NoCaWlARgagqUl6RFRcJeqVNOlt6UjzdFtG6h9Jnvonf/+UlABPT+DZM+BNb096/KR5ui2ogiWPlXR1dTXU1dVZj0HofFlZGbp27UqsvtB56h/1r73699NPTZN0WhowcKBi6gud53r+8SVRr6QPHjwoan7p0qVE6wudp/5R/0jysvzbvBkwNgbWrGn6CVwR9YXOcz3/+FK7fgRLluSxLai+vj709PRYj+Fd4Lk8K9gexk+ap/5R/0jyrfmnqgqYmTWtpgcNAoYOVUx9ofNCeFZa1CvplJQUUfPnzp0jWl/oPPWP+keSf5N/M2YAc+YAGzYAL17Iv77Qea7nH18S9SStr68vat7Y2JhofaHz1D/qH0n+bfzz8ACePwda+r2U9PhJ81zPP74k6kma7c/k7wqvoaFBtL7Qeeof9Y8k/zb+GRsD27Y1PT8tkci3vtB5rucfX+I8STMMgx07dqBnz55QV1fHBx98gHv37slkduzYASUlpWYvQ0NDrkNps0insJDm//jjD6L1hc5T/6h/JPm39W/Dhqbr0/97Exnp8ZPmuZ5/vInrlmUuLi6MtrY2c/r0aUYikTALFy5kevTowVRWVrbKODg4MEOGDGGePHkifRUXF7eprjy2Bc3NzWXNvgv89evXidYXOk/9o/6R5Nvi35UrDAMwTFCQ/OoLned6/vElTitphmHg4eGBH3/8EZ988gmGDh2KoKAgVFVVSTdab02qqqowNDSUvrheX2Cj4OBgUfPbt28nWl/oPPWP+keSb4t///oX8OmnwKZNTdeo5VFf6DzX848vcdrMJDs7G++99x5SUlIwYsQI6Z9/9NFH6NKlC4KCglrkduzYgd27d6Nz585QU1ODlZUVnJycYGpq+ta15bGZSWNjI5SV2f87Reh8fX09VFVVidUXOk/9o/4Jyb/CQmDAAODLL4H9+8mPnzTP9fzjS5xW0kVFRQBez/U0MDCQ/l1LsrKywpEjR3D58mX4+/ujqKgI1tbWKC0tbZWpra1FZWVlsxdXOTk5iZqfPn060fpC56l/1D+SfFv969kT2LkTOHgQSEkhP37SPNfzjy+1aZI+duwYtLS0pK9Xr14BAJSUlJodxzDMa3/2T82YMQNz586Fubk5bGxscP78eQB4beW9du1axMTEYObMmXBwcEDnzp2lr969ewMAjh8/jl27dmHz5s2IjIzE3LlzUVBQIN2X1cbGBg8fPsSCBQsQFhaGH3/8ETt27MCxY8eQnp6OjIyMZseWlJTA1tYWFy9exPr167F79274+vpi5cqVuHXrVrNjN27ciGnTpiExMRF2dnY4ePAgPDw8sG7dOkRHR2PWrFl4/vx5MyYtLQ1LlixBUFAQGhsbsWXLFoSHh2PevHnIy8trdmxubi7mz5+P06dPY+vWrdi5cyeOHj2Kzz//HHfv3kVsbKz02LKyMtja2iI6Ohrfffcdfv75Z3h7e+Prr7/GjRs3MGXKFNTX18PGxgb19fWYMmUKduzYga+//hre3t74+eef8d133yE6Ohq2trYoKytrNpa7d+/i888/x9GjR7Fz505pFuz8+fORm5vb7Ni8vDzMmzcP4eHh2LJlCxwdHREUFIQlS5YgLS1NemxsbCyeP3+OWbNmITo6GuvWrYOHhwcOHjwIOzs7JCYmYtq0aairq2v2/rdu3cLKlSuhp6eH3bt3Y/369bh48SJsbW1RUlLS7NiMjAwsXrwYx44dw44dO/Djjz8iLCwMCxYswMKFC5sdW1BQgLlz5yIyMhKbN2/Grl27EBQUhC+//BIpKSnNjq2srESHDh0QExODtWvXwsPDA15eXli1ahUSEhIwffp01NTUNGOSkpKwfPlyBAQEwMXFBaWlpbhw4QI+/vhjFBUVNTv2/v37+Oyzz3Dy5Els374d27Ztw8mTJ7Fo0SJkZWXBxsYGP/zwA2xsbFBYWIg5c+YgMjISmzZtgrOzM3755RcsW7bstXFXVVVhxowZuHr1Kh4/foz9+/dj//79WL16Na5evYoZM2agqqqqGZOSkoJly5bhl19+gbOzMzZt2oTIyEgkJyejsLCw2bFZWVlYtGgRTp48iW3btmH79u04efIkPvvsM9y/f7/ZsYGBgfj4449x4cIFbNiwAS4uLggICMDy5cuRlJTU7NiamhpMnz4dCQkJWLVqFby8vKChodGsR1RWVr427i+//BJBQUEt9oh/fn9a6xGLFy9utUeMHDnyjT2irq6u1R4xevToN/YIR0fHVnsEwzBv7BH/fN+ysjJcufIxjI1fYObMR+jQQe2NPeLGjRut9gg7O7s39ojTp0+32iNSU1Pf2CNsbGxa7RF5eXlv7BG+vr6t9ohLly7J7BHtRm25gF1ZWclkZWVJX3fv3mUAMCkpKc2Omz17NrNkyZI2XRy3sbFh7OzsWv37mpoapqKiQvrKz8/nfOOYo6Mja/Zd4G1sbIjWFzpP/aP+keTZ+nftWtNNZB9/fI5TfdKfn/T5x5c43d3d2NjIGBoaMq6urtI/q62tZTp37sz4+Pi89fvU1NQwvXr1Ynbu3PnWDL27m/zdjaTHT5qn/lH/SPJc/FuyhGF0deuZkhL29Ul/ftLnH1/idE1aSUkJ9vb2cHJyQnh4OO7evYsvv/wSGhoa+Oyzz6THTZ48GV5eXtL/37hxI+Li4pCTk4Nbt25h3rx5qKys5H3D86tXr4qaP3z4MNH6Quepf9x46h83not/bm5AbW0Dtm5lX5/05yd9/vElzre2bd68GdXV1Vi9ejXKy8thZWWFqKgoaGtrS495+PAhSkpKpP9fUFCARYsWoaSkBPr6+hg7dixu3ryJPn36cB1Om8R1c3Wh8/+8I59EfaHz1D/qH0mei38GBsA33+TDw+M9rFgBWFm1/T1If37S5x9f4jxJKykpYceOHZAVpvXo0aNm/3/ixAmuZeWi2tpaUfNVVVVE6wudp/5R/0jyXP2bMSMXV6++h9Wrgdu3ARWVtvGkPz9p//iSqPfufvbsmaj5vLw8ovWFzlP/qH8kea7+lZU9kz6O5evbdp705yftH18SdZ60mpoapzxSofOqqqqcfjIiPX7SPPWP+id0/4YN08Pjx4CXF7B8OaCp2TZezP7xJVGvpCMjI0XNe3p6Eq0vdJ76R/0jycvLP2dnQFkZ2LyZHc+1Pimeq398idO2oCQlj21Bq6uroa6uznoMQufLysrQtWtXYvWFzlP/qH/vin/+/sDXXwPx8cCECW3nudYnwXP1jy+JeiX9888/i5pfsGAB0fpC56l/1D+SvDz9+/sO79Wrgfr6tvNc65PgufrHl0S9kqaioqKialJKCjB6NLBnD7B+PenRUP0tUa+kHR0dRc3/vdctqfpC56l/1D+SvLz9GzkSWLUKcHBoSsxqK8+1Pt88V/94E9kNz9hLHtuCFhUVcRqD0HmJREK0vtB56h/1jySvCP/KyhhGX59hFi1ix3OtzyfP1T++JOqV9NmzZ0XNu7i4EK0vdJ76R/0jySvCP11dYPduICQEiIlpO8+1Pp88V//4kqifkwaAnj17chqHkPmqqipYWFgQqy90nvpH/XsX/Rs2DLhyBQgLa7rjW9ZOZGL3jw+160k6JCQEGhoaCAgIgKWlJVxcXCCRSPDhhx/i8OHDKC8vx9SpU5GZmYm0tDQwDIOQkBAMGjQIu3fvxqRJk+Do6IihQ4fi0KFD6NSpE27duoUHDx7g5cuXCAwMxOjRo7F3717psZaWlvD09ISenh5iYmJQVFSEoqIiXLlyBXp6eti/f7/0WE1NTZw5cwbGxsb49ddf8eLFC2RnZ+PmzZtQU1PDoUOHMGrUKLi4uEiZ/v37IyQkBI2Njbhw4QLKysrQ0NCAkydPYuDAgdizZ4/0WAsLCwQEBEBdXR03btxAdnY2Kisrce7cORgZGeE///kP5syZA0dHR4wePRqenp7Q19fHb7/9huLiYhQWFuLq1avQ1dWFl5cXJkyYgF27dmHChAlwcnLCw4cPUVxcjJcvX+LBgwe4ffs21NTUEBgYiBEjRsDV1VU6lgEDBuD48eMAgNTUVNy7dw9//vknbt26hf79+zcb97Bhw+Dv7w9NTU0kJiYiNzcX5eXluHDhAnr16gUPDw9MmjQJ33//PWbMmIG9e/eie/fuiI6ORklJCQoKChAXF4cuXbrA29sb1tbWcHJykr6/iYkJwsPDkZ6ejurqaiQnJ0NVVRVBQUEYPnx4s3EPGjQIR48ehbKyMlJSUvDnn3+itrYWYWFhqKmpQUREhPTY4cOHw9fXF9ra2oiPj0deXh7Ky8tx6dIlGBoaYt++fdJjrayssGXLFowfPx6XL19GaWkp8vPzER8fDx0dHfj4+GDs2LHNxm1qaorTp0+jtrYWGRkZOH/+PIyMjBAcHAxzc3O4ublJjx08eDCOHDkCVVVVJCcn4/79+6iurkZ4eDhMTU3h7u4OHR0dnDx5EiNGjIC3tzd0dHRw7do1FBQUoKSkBFFRUTAwMGg27nHjxmHPnj3o2bMnAgMD0alTJ+Tm5iIhIQFaWlrw8/ODlZUVnJ2dpUy/fv0QGhqKuro6pKenIzU1FQBw4MABfPDBB82+a0OGDEFQUBA6dOiApKQkZGVloaqqChEREejbty/c3d2lxxYWFiItLQ26urqIjY1FYWEhnj17hujoaOjr68PT01N6rLW1Ndzc3GBkZIRz586hoqICV69eRX5+/ms94p/jPnXqFBoaGnD37t3XeoSDg4P0+9Naj4iMjESfPn1a7BGlpaV4+PChzB4xfvx4uLq6ttgjcnNzERMTI7NHSCQSSCSSFnuEvb09PvroI5k94u/vWks9Ijk5GcrKyq/1CCenXVi/fgKcnBi8evUchYWhLfYIZWVlnD59WmaPePXqFUJDQ1vsEa6urujbt6/MHuHo6IgxY8a02CPCwsIwYMAAmT2iqqoKmZmZLfaI0tJSJCQktNojDAwMiM19zUT693a2ksc16fDwcE5jEDr//fffE60vdJ76R/0jySvav/XrGUZDg2FaS4Qk/flJ+8eXRH1NmnQKC2ne0tKSaH2h89Q/6h9JXtH+7dgBdO7c+uNYpD8/af/4kqgn6bi4OFHzXNPISI+fNE/9o/6R5BXtn44O4O4OnDkDXLrUdp5rfUXz7SWN8U0S9WYmz58/R5cuXViPQeh8bm4upwxv0uMnzVP/qH/vun8MA9jYALm5wN27QKdObeO51lckz9U/viTqlbSXl5eo+RUrVhCtL3Se+kf9I8nz4Z+SUlNCVl5e06NZbeW51lckz9U/viTqlTQVFRUV1Zv1/ffAvn1AejpgYkJ6NOKSqFfSpLelI83TbRmpfyR56p9w/Nu2DdDXB9atY8dzra8IXijbgop6JV1RUYHOnTuzHoPQ+by8PBgbGxOrL3Se+kf9E5N/Z84Ac+cCZ88Cs2eT//yk/eNLol5JHzlyRNT8hg0biNYXOk/9o/6R5Pn2b84cYPr0ptV0VRX5z0/aP77UrncckyV5bAuqqamJ7t27sx6D0PkOHTpg0KBBxOoLnaf+Uf/E5J+SEjB2LODmBjQ0ALa24vaPL4l6JZ2VlSVq/ubNm0TrC52n/lH/SPIk/OvXD9iypelO77i4J7zXlyfP1T++JOpJWl1dXdS8trY20fpC56l/1D+SPCn/vv8e6NULOHRoBLjc0SR0//iSqCdpPT09UfO9e/cmWl/oPPWP+keSJ+Wfujrg6QmkpHTD6dP815cXz9U/viTqSfrvNB+x8leuXCFaX+g89Y/6R5In6d+HHwLDhj2CvT3w8iX/9eXBc/WPN5FM9+AieaRgPXnyhNMYhM7fuXOHaH2h89Q/6h9JnrR/t28XM+rqDLNpE5n6pP3jS+367m5F50lv3LgRNjY2rPOkk5OTcf36ddZ50k5OTgDAOk/6888/x5IlS1jnSe/btw+qqqqs86QDAwORnZ3NOk/6448/xoIFC1jnSR85cgQaGhqs86R/++033Lhxg3We9AcffIBZs2axzpN2dnbG0KFDWedJp6Sk4Nq1a6zzpDds2ABDQ0PWedJr1qzB7NmzWedJHzhwAOXl5azzpN3d3VFVVcU6T3rhwoXS7w+bPOnz58/jxYsXrPOkT548CYlEwjpP2traGkuXLmWdJ+3n54du3brJ7BF9+/bF2bNnW+wREkk8AODECRM8e+aDUaN6tylP+ssvv4SFhQXrPOnt27fDysqKdZ60r68v8vLy2n2etKg3M6GioqKiYq/aWsDCAujRA4iNbXpMi0q+EvU1adLb0pHm6baM1D+SPPVP+P6pqQH79wNxccD/X0TzWp+L6LagCpY8VtI1NTXo9M/sNZHxXKPeSI+fNE/9o/5R/5r4+fOB+Hjg/n3gbXfqFLp/fEnUK+n9+/eLml+8eDHR+kLnqX/UP5J8e/Jv796mu7wdHJr+v7q6Gk+fPkV1dTUv9dmIq3+8ieRda1wkj7u7MzMzOY1B6HxUVBTR+kLnqX/UP5J8e/PPzY1hlJTiGZvJnzAqKioMAEZFRYWZ+8knTEJCgsLrt1Vc/eNLol5J//7776Lmf/31V6L1hc5T/6h/JPn25p+6ujcYZhLys37H7m9X4qzbDuz+diUyUn/HxIkT4ePjo9D6bRVX//iSKukBkJShoaGoeVNTU6L1hc5T/6h/JPn25F9CQgLWrVuDtQtmY+9330BZ+b/rv3ULPoK9hw9Wr14Nc3NzjB8/Xu712Yirf3xJ1CtpVVVu/0YROt+xY0ei9YXOU/+ofyT59uSfx969GGRi/NoEDQDKysrwsLfDIBNjeHjsVUh9NuLqH18S9SSdk5Mjaj4tLY1ofaHz1D/qH0m+vfhXXV2NiLNnsdJ2+msT9N9SVlbGStvpCA+PkN5MJnT/+FK73nFMluSRJ92lSxdOt+ALndfV1YWxsTGx+kLnqX/UP+pfF5SVlWH37t1YPdcWA/oYtXp8cflzhETFYu3atdDS0hK8f3xJ1Cvp4219+v4d43/66Sei9YXOU/+ofyT59uKfjo4OVFRU8PCx7Hzp7MdFUFFRke5rIXT/+JKoNzNpaGiAiooK6zEIna+rq+N0XYb0+Enz1D/qH/WviZ83dy4yUn9HWrB3iz95NzY2wvzzVRgyyhKhoWFyr89GXP3jS6JeSTs7O4uanzlzJtH6Quepf9Q/knx78s9+/Xpk5ORh/T5fNDY2NjuusbER9h4+yMjJw/vvr1dIfTbi6h9fEvVKmoqKiopKPvLxaXrMapCJMVbaTodpL0NkPy5CwK+XkJGTh/79DyInxw7BwcCCBaRHKxyJeiVNeoN30nx72KBfyDz1j/pHkm9v/tnZ2SE+Ph6DR1pik1cAPt68E5u8AjB4pCXi4+ORlmaH+fOBhQubthEVun98qV3f3a3oPOns7GwMHDiQdZ70559/Dm9vb9Z50vX19cjOzmadJx0bG4upU6eyzpO2tbXF7du3WedJm5iY4OLFi6zzpH/99VdMmjSJdZ507969UVhYyDpPetq0afD392edJ52SkoIBAwawzpOuqamBtrY26zzppUuXYv/+/azzpHNzc1FbW8s6TzotLQ2Wlpas86QXL16MiIgI1nnSampqSEtLY50nHRUVJf3+sMmTHjt2LG7fvs06T3ro0KE4deoU6zzpxMRETJw4kXWedNeuXVFRUcE6T3ru3Lnw9vZu1iPi4+OxYMECTJs2DdOnT8fWrVuhqtoBNjY22Lt3D9zdJyE2NhH+/saoqemI0aOf4/p1dnnSJSUl6NGjB+s86a+++gqBgYHtPk9a1Ht3Hz58mNMYhM6vWLGCaH2h89Q/bjz1jxsvZP+8vBhGSamRWbCAYWpq+K/PMNz940ui/rm7f//+ouZHjx5NtL7Qeeof9Y8kL2T/1qwBdu26j8hIYNo0oLyc3/oAd//4kqgnaVkxamLgKysridYXOk/9o/6R5IXu35gxj/Hbb4BEAkycCOTn81ufq398SdSTdGlpqaj5wsJCovWFzlP/qH8k+XfBv/HjgcTEpizqceOaJmy+6nP1jy+16xvHZEke24KqqqqiW7durMcgdJ5hGJiZmRGrL3Se+kf9o/5x57t1a7rjOyIC+PlnYOxYwMRE8fW5+seXRL2SPnfunKj5gwcPEq0vdJ76R/0jyb9L/vXoAcTFAVZWTdeoT5xQfH2u/vElUW9mUlVVBQ0NDdZjEDpfUlLC6V+ipMdPmqf+Uf+of/Ll6+qAr74CjhwBdu8G/v1vQElJMfW5+seXRL2Sdnd3FzX/6aefEq0vdJ76R/0jyb+L/nXsCAQGAj/8AGzaBNjbAw0NiqnP1T++JOqVNBUVFRVV+5SPT9OjWnPmAEePAp06kR4RGYl6JU16WzrSfHvbVlBoPPWP+keSf9f9s7MDzpwBLlwApk4FysrkW18o24KKesex4uJiTmMQOp+enk60vtB56h/1jyQvFv+uX2cYPT2GGTSIYXJz5Vefq398SdQr6TNnzoia5/ovUdLjJ81T/6h/JHmx+DduHHD9OlBT0/R41p078qnP1T++JOrnpJWVldGjRw/WYxA6X1NTAwsLC2L1hc5T/6h/1D9+eD29pmepf/0V2LMHGDMGeO89sv7xJVGvpJ88eSJqPisri2h9ofPUP+ofSV5s/hkaAlevAuPHAzNmAMePt/Js1luKq398SdSTdENr9/aLhH/16hXR+kLnqX/UP5K8GP3T0gIiI4HPPwd+/nkEXF0Bts8ncfWPL7Xrn7sVnSd95coVmJubs86TtrS0RGBgIOs86fv376OgoIB1nvThw4cxc+ZM1nnSBgYGyMjIYJ0nXV9fj5iYGNZ50vv378e//vUv1nnStbW1KCkpYZ0n3bdvXwQHB7POkw4ODsawYcNY50mnp6eja9eurPOkrays4O/vzzpPOjY2FgzDsM6TjoyMxNixY1nnSffr1w8xMTGs86Tz8/Nx//591nnSfn5+0u8PmzxpPT093Llzh3WedMeOHREZGck6TzogIAA2Njas86TLyspQU1PDOk96yJAhOHz4sMwe8erVK4SGhrbYI0JCQmBoaCizR7SUJ11eXoKRIwuQk5OLgIA+uHz5dyxZYgBn57blSZubm+PMmTM0T1pRksfd3V5eXpzGIHR+/vz5ROsLnaf+Uf9I8tQ/L8bXl2GUlRlmzhyGqapqG8/VP74k6km6tLSU0xiEzj948IBofaHz1D/qH0me+tfER0YyjLo6w1hbM0xJydvzXP3jS6K+Js11g3Wh89988w3R+kLnqX/UP5I89a+Jt7UFYmOBzMymm8oePXo7nqt/fIluC0pFRUVFJXhlZTXd9f3XX027lI0YQXpE8pGoV9LtfVs8RfPv+raCiuapf9Q/kjz1rzlvZta06YmRETBpEhAVJZsXyragol5JV1ZWclqFC50vKCiAkZERsfpC56l/1D/qX/vjX75s2vgkKgr45RdgyZKWea7+8SVRr6QDAwNFzX/33XdE6wudp/5x46l/3HjqX8u8lhZw9iywdGnTy8np9Wepq6ur8c0336C6uprTGPhQu35OWpbksS2otrY29PX1WY/Nb4IEAAAG7UlEQVRB6Ly6ujoGDBhArL7Qeeof9Y/61z55ZeWmG8qUlIDt24GnT5uuV1+/noAN69dj6dKlyMzMhIuLC9Lu3EEvIyMYGxuzHosiJeqV9J9//ilqPiEhgWh9ofPUP+ofSZ76J5tXUgIcHICAAMDfHxg50huTJk1CRurv2P3tSpx124Hd365ERurvmDhxInx8fDiNR1FSJT0AktLU1BQ137lzZ6L1hc5T/6h/JHnq39vxK1YAZWUJ2Lx5DdYumI29330DZeX/rk/XLfgI9h4+WL16NczNzTF+/HhO45K3RL2S7tq1q6h5rjdNkB4/aZ76R/0jyVP/3p6/dXMvBpkYvzZBA01pXB72dhhkYgwPj72cxqQIEZmkz5w5g2nTpqFbt25QUlKS7gXMt9LS0kTNx8bGEq0vdJ76R/0jyVP/3o6vrq5GxNmz+Gr29Ncm6L+lrKyMlbbTER4e0e5uJiMySf/1118YP348XFxcSJSXasaMGaLm161bR7S+0HnqH/WPJE/9ezu+srISDQ0NeK+X7Oxp016GaGhoQGVlJadxyVtEJukvvvgC27dvJ/4w+aFDh0TNb968mWh9ofPUP+ofSZ7693a8jo4OVFRU8PCx7Pzq7MdFUFFRaXc7WBLdzOTRo0cwMTHBH3/8geHDh7eJpduCUlFRUVG9jebNnYuM1N+RFuzd4k/ejY2NsPhiFQaPtERoaBiBEbYuwdw4Vltbi8rKymYvrmpv29rxzdNtBal/JHnqH/WPL95+/Xpk5ORh/T5fNDY2Nvu7xsZG2Hv4ICMnD/b26zmNSRFS+GYmx44dg7W1NZycnODk5ISJEyeiT58+AIDnz59j3759sLOzg6Gh4WtsSEiINNA9OjoaM2fOhIuLC1xcXLB3b9NdeFOnTkVmZuZrge7/DKJvLdD92bNnMDExaTXQPSYmRmag+4YNG7Bnz54WA93V1NRw6NAhmYHuWlpaSE9PbzHQ3dHRERYWFjID3W/fvo0PPvigxUD34uJiFBYWygx0X79+PS5dutRioPuIESPg6uoqM9B91KhROHPmTIuB7v7+/tDU1JQZ6B4TE4OxY8c2C3QvKSlBQUEB4uLi0KVLF3h7e0vPn/8NdLewsMDDhw9bDHT/+9jWAt3DwsKwePFi7Nu3T3rs8OHD4evrC21tbcTHxyMvLw/l5eW4dOkSDA0Nmx1rZWUl3Vbw8uXLKC0tRX5+PuLj46GjowMfHx+MHTu22bhNTU1x+vRp1NbWIiMjA2pqaujQoQOCg4Nhbm4ONzc36bGDBw/GkSNHoKqqiuTkZNy/fx/V1dUIDw+Hqakp3N3dsWnTJri4uGDEiBHw9vaGjo4Orl27hoKCApSUlCAqKgoGBgbNxj1u3Djs2bMHPXv2RHl5OSorK5Gbm4uEhARoaWnBz88PVlZWcHZ2ljL9+vVDaGgo6urqkJ6eLr3RMycnB+bm5s2+a0OGDEFQUBA6dOiApKQkZGVloaqqChEREejbty/c3d2lx/70008ICAiArq4uYmNjUVhYiGfPniE6Ohr6+vrw9PSUHmttbQ03NzcYGRnh3LlzqKiogIGBAW7fvi3tEZaWls2+a/369cOpU6fQ0NCAu3fvvtYjEhMTpd+f1npEZGQk+vTp02KPmDVrFuLi4mT2iPHjx8PV1bXFHvH+++8jKChIZo+QSCSQSCQt9oisrCyMHDlSZo/4+7vWUo8wNTXF06dPZfaIvn374uzZsy32CDs7u2bf+5Z6xKtXrxAaGtpij7h37x60tbVl9ghHR0eMGTOmxR5RV1eHrl27yuwRVVVVyMzMRHFxMYYMGYLdB/0QFpOAulf1KC5/jos3kvGV8z5cuJ6E77//Ht27d5f2CAMDA0VOjW8vRWdhVlZWMllZWdJX1T+SuXNychgAzB9//PHG96mpqWEqKiqkr/z8fM550q6urqzZd4GfMWMG0fpC56l/1D+SPPWv7XxCQgIzb95cRkVFhQHAqKioMPPmzWUSEhI4jUWRUvgkLUttmaT/VxUVFZwnaa6h30Lnr1y5QrS+0HnqH/WPJE/9Y89XVVUxoaGhzRaN7VVEbhwrKytDXl4eCgsLMWvWLJw4cQIDBgyAoaFhiz97tyR64xgVFRUV1bsuIpN0YGAgli1b9tqfOzg44G0vkTMMgxcvXkBbWxtKSkpyHiEVFRUVFRV5CTZPmoqKioqK6l2XYB7BoqKioqKiEpvoJE1FRUVFRdVORSdpKioqKiqqdio6SVNRUVFRUbVT0UmaioqKioqqnYpO0lRUVFRUVO1UdJKmoqKioqJqp6KTNBUVFRUVVTsVnaSpqKioqKjaqegkTUVFRUVF1U5FJ2kqKioqKqp2KjpJU1FRUVFRtVP9PxTXn462q8hgAAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **INTERPOLAÇÃO**\n", "\n", "Os resultados de medições experimentais ou simulações numéricas fornecem, em geral,um conjunto de valores de uma função em pontos discretos de uma variável independente. Esses valores podem ser apresentados naforma de uma tabela para valores discretos de 𝑥. O processo de calcular a função para valores intermédios aos valores conhecidos de 𝑓(𝑥)é chamado interpolação [(MIRANDA, 2018)](https://fenix.ciencias.ulisboa.pt/downloadFile/2251937252639182/LabNum_2018_v4.pdf). Tipos de interpolação: \n", "- Interpolação linear (padrão da funçao `interp1d`)\n", "- Interpolação polinomial\n", "- Interpolação trigonométrica\n", "- Spline\n", "\n", "Gráfico interpolação linear: \n", "\n", "" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Dados \n", "\n", "x_dados = [0.0, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0]\n", "y_dados = [0.0, 0.5, 0.84, 1.0, 0.91, 0.6, 0.14, -0.35, -0.76, -0.98]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico com axes_labels = ['x','y'], gridlines = 'minor', figsize = (5, 4)\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Importar a função interp1d do scipy.interpolate\n", "\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# fint recebe interp1d(x_dados, y_dados)\n", "\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# testar a função\n", "\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# gráfico pontos + gráfico fint\n", "\n" ] }, { "attachments": { "sagemath_juste_curva.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## **AJUSTE DE CURVAS**\n", "\n", "Ajuste de Curvas é um método que consiste em encontrar uma curva que se ajuste a uma série de pontos e que possivelmente cumpra uma série de parâmetros adicionais. Ajuste de curvas pode envolver tanto interpolação, onde é necessário um ajuste exato aos dados, quanto suavização, na qual é construída uma função \"suave\" que se aproximadamente se ajusta aos dados. Outro assunto relacionado é análise de regressão, a qual se foca mais em questões da inferência estatística [(Wikipedia, 2019)](https://pt.wikipedia.org/wiki/Ajuste_de_curvas). \n", "\n", "" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Importar CSV e pandas\n", "\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# importar dados_reta.csv para variável dados\n", "\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# visualizar dados\n", "\n" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico dos dados com axes_labels = ['x','y'], gridlines = 'minor', figsize = (5, 4)\n", "\n" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Definir variáveis simbólicas a e b \n", "\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# função modelo_reta 'ax + b'\n", "\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# coeficientes coef recebe os dados da função find_fit(dados_pontos, modelo, [ai, bi], solution_dict = True)\n", "\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "#imprimir coef 'a'\n", "\n" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# substituir coef no modelo reta\n", "\n" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "# Gráfico pontos e modelo reta\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "FIM" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.8", "language": "sagemath", "metadata": { "cocalc": { "description": "Open-source mathematical software system", "priority": 1, "url": "https://www.sagemath.org/" } }, "name": "sage-8.8" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 4 }