bolt.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O jamaicano Usain Bolt é considerado por muitos o melhor velocista de todos os tempos. Mesmo tendo se aposentado das pistas em 2017, seu nome é ainda um dos primeiros a vir à mente do grande público quando o assunto é atletismo.\n",
    "\n",
    "Nesse artigo, veremos como podemos utilizar a linguagem Python para saber a velocidade e aceleração atingidas pelo jamaicano nas provas de 100 m da Olimpíada de Pequim de 2008, onde marcou o recorde mundial da prova, e no Mundial de Atletismo de 2009 em Berlin, onde quebrou seu próprio recorde. Aproveitaremos para discutir um pouco sobre modelos matemáticos e cuidados na seleção e interpretação de seus resultados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O código do artigo se encontra no formato Jupyter Notebook no [repositório do Ciência Programada no GitHub](https://github.com/Ciencia-Programada/bolt-vs-python). Dê uma olhada e pratique baixando o arquivo e alterando o código."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Obtendo os dados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O primeiro passo é, obviamente, obter os dados e passá-los para uma forma que pode ser tratada pelos pacotes que utilizaremos. O tempo total de cada prova é relativamente fácil de achar na internet mas, para que possamos ter uma noção melhor do desempenho do atleta na prova, quanto mais detalhes obtivermos, melhor.\n",
    "\n",
    "O site [Speed Endurance](https://speedendurance.com/2009/08/19/usain-bolt-10-meter-splits-fastest-top-speed-2008-vs-2009/) compilou os dados dos [relatórios](https://www.worldathletics.org/about-iaaf/documents/research-centre) da Associação Internacional de Federeções de Atletismo - IAAF (*International Association of Athletics Federations*) dos dois eventos. Segue uma tabela adaptada com os dados compilados:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![tabela_tempos](tabela_tempos.png)\n",
    "\n",
    "Na tabela, TR significa \"tempo de reação\", ou seja, o tempo que passou do disparo de início da prova até o atleta efetivamente se mover. Não estava ventando na prova de 2008 e havia um vento favorável 0,9 m/s na prova de 2009 de acordo com os dados dos relatórios."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O interessante é que temos os tempos de Bolt a cada 10 m, o que nos será útil mais adiante. Podemos pegar os tempos acumulados, colocar em uma planilha e exportar para o formato csv ([*comma separeted values*](https://en.wikipedia.org/wiki/Comma-separated_values), valores separados por vírgula), formato usualmente reconhecido por qualquer pacote matemático.\n",
    "\n",
    "Vamos dar uma olhada em nosso arquivo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Splits,\"2008 Beijing\",\"2009 Berlin\"\n",
      "0,0,0\n",
      "\"0 - 10\",1.85,1.89\n",
      "\"10 - 20\",2.87,2.88\n",
      "\"20 - 30\",3.78,3.78\n",
      "\"30 - 40\",4.65,4.64\n",
      "\"40 - 50\",5.50,5.47\n",
      "\"50 - 60\",6.32,6.29\n",
      "\"60 - 70\",7.14,7.10\n",
      "\"70 - 80\",7.96,7.92\n",
      "\"80 - 90\",8.79,8.75\n",
      "\"90 - 100\",9.69,9.58\n"
     ]
    }
   ],
   "source": [
    "!cat bolt.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split é o termo que se usa para cada divisão da prova, cada marcação de 10 metros. É tão comum que preferi manter o termo em inglês. Repare que coloquei uma linha com tempo 0 no início para facilitar a construção de gráficos futuramente. Como tudo em programação, o idioma padrão é inglês, então o formato dos números está no formato inglês, pontos para separar a parte decimal ao invés de vírgulas como estamos acostumados a usar. Recomendo fortemente que mude nas opções de seus programas para deixar ponto como padrão, nem todo pacote terá a opção de receber arquivos com vírgula. Na realidade, para se acostumar com o idioma, recomendo usar todos seus programadas e o sistema operacional em inglês, mas é apenas minha opinião."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos armazenar o caminho do arquivo em uma variável para ficar mais fácil de se referir durante o programa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "arquivo_dados = 'bolt.csv'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um dos pacotes mais utilizados para lidar com dados numéricos e computação científica em Python é o [NumPy](https://numpy.org/). Vamos importá-lo juntamente com o [Matplotlib](https://matplotlib.org/), para gráficos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para importar dados do arquivo csv, usaremos o método [genfromtxt](https://numpy.org/doc/stable/reference/generated/numpy.genfromtxt.html). Para entender o funcionamento deste método, vamos olhar o output passando apenas o arquivo e o delimitador (vírgula no caso de arquivos csv):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ nan,  nan,  nan],\n",
       "       [0.  , 0.  , 0.  ],\n",
       "       [ nan, 1.85, 1.89],\n",
       "       [ nan, 2.87, 2.88],\n",
       "       [ nan, 3.78, 3.78],\n",
       "       [ nan, 4.65, 4.64],\n",
       "       [ nan, 5.5 , 5.47],\n",
       "       [ nan, 6.32, 6.29],\n",
       "       [ nan, 7.14, 7.1 ],\n",
       "       [ nan, 7.96, 7.92],\n",
       "       [ nan, 8.79, 8.75],\n",
       "       [ nan, 9.69, 9.58]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.genfromtxt(arquivo_dados, delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repare que há `nan` em várias posições. Mais especificamente, nas posições onde havia texto. Isso porque o método, por padrão, espera tipo `float` em todas as posições. Quando encontra algo inesperado, de outro tipo, substitui por `nan` ([*not a number*](https://en.wikipedia.org/wiki/NaN)). Assim, precisamos informar que a primeira coluna é de texto (tipo `string`) e, além disso, que a primeira linha contém os nomes de cada coluna. Para isso, usamos os seguintes parâmetros do método:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:12.067054Z",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('', 0.  , 0.  ), ('', 1.85, 1.89), ('', 2.87, 2.88),\n",
       "       ('', 3.78, 3.78), ('', 4.65, 4.64), ('', 5.5 , 5.47),\n",
       "       ('', 6.32, 6.29), ('', 7.14, 7.1 ), ('', 7.96, 7.92),\n",
       "       ('', 8.79, 8.75), ('', 9.69, 9.58)],\n",
       "      dtype=[('Splits', '<U'), ('2008_Beijing', '<f8'), ('2009_Berlin', '<f8')])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.genfromtxt(arquivo_dados, delimiter=',', dtype=(str, float, float), names=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repare que a parte dos nomes funcionou, agora o output lista os nomes ao final. No entanto, os textos aparecem como strings vazias. [De acordo com a documentação](https://numpy.org/doc/stable/reference/arrays.dtypes.html#specifying-and-constructing-data-types) é necessário passar o tipo de codificação e a quantidade de caracteres esperada. No nosso caso, [unicode](https://en.wikipedia.org/wiki/Unicode) e 10 caracteres:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('0', 0.  , 0.  ), ('\"0 - 10\"', 1.85, 1.89),\n",
       "       ('\"10 - 20\"', 2.87, 2.88), ('\"20 - 30\"', 3.78, 3.78),\n",
       "       ('\"30 - 40\"', 4.65, 4.64), ('\"40 - 50\"', 5.5 , 5.47),\n",
       "       ('\"50 - 60\"', 6.32, 6.29), ('\"60 - 70\"', 7.14, 7.1 ),\n",
       "       ('\"70 - 80\"', 7.96, 7.92), ('\"80 - 90\"', 8.79, 8.75),\n",
       "       ('\"90 - 100\"', 9.69, 9.58)],\n",
       "      dtype=[('Splits', '<U10'), ('2008_Beijing', '<f8'), ('2009_Berlin', '<f8')])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.genfromtxt(arquivo_dados, delimiter=',', dtype=('U10', float, float), names=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora sim, mas repare que não armazenamos os dados em nenhuma variável. Podemos utilizar um pequeno macete do Notebook. Quando \"esquecemos\" de armazenar o resultado da última célula executada em uma variável, podemos criar a variável e atribuir a ela `_`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:12.825704Z",
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   },
   "outputs": [],
   "source": [
    "dados = _"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos verificar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
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     "iopub.status.idle": "2020-09-14T18:22:13.354138Z",
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     "shell.execute_reply.started": "2020-09-14T18:22:13.105867Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('0', 0.  , 0.  ), ('\"0 - 10\"', 1.85, 1.89),\n",
       "       ('\"10 - 20\"', 2.87, 2.88), ('\"20 - 30\"', 3.78, 3.78),\n",
       "       ('\"30 - 40\"', 4.65, 4.64), ('\"40 - 50\"', 5.5 , 5.47),\n",
       "       ('\"50 - 60\"', 6.32, 6.29), ('\"60 - 70\"', 7.14, 7.1 ),\n",
       "       ('\"70 - 80\"', 7.96, 7.92), ('\"80 - 90\"', 8.79, 8.75),\n",
       "       ('\"90 - 100\"', 9.69, 9.58)],\n",
       "      dtype=[('Splits', '<U10'), ('2008_Beijing', '<f8'), ('2009_Berlin', '<f8')])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos acessar cada coluna dos dados pelos seus nomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
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     "shell.execute_reply.started": "2020-09-14T18:22:13.355820Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['0', '\"0 - 10\"', '\"10 - 20\"', '\"20 - 30\"', '\"30 - 40\"',\n",
       "       '\"40 - 50\"', '\"50 - 60\"', '\"60 - 70\"', '\"70 - 80\"', '\"80 - 90\"',\n",
       "       '\"90 - 100\"'], dtype='<U10')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dados['Splits']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
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     "shell.execute_reply.started": "2020-09-14T18:22:13.584670Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 1.85, 2.87, 3.78, 4.65, 5.5 , 6.32, 7.14, 7.96, 8.79, 9.69])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dados['2008_Beijing']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:13.812403Z",
     "iopub.status.busy": "2020-09-14T18:22:13.811769Z",
     "iopub.status.idle": "2020-09-14T18:22:14.037575Z",
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     "shell.execute_reply.started": "2020-09-14T18:22:13.812323Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 1.89, 2.88, 3.78, 4.64, 5.47, 6.29, 7.1 , 7.92, 8.75, 9.58])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dados['2009_Berlin']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora já temos o que precisamos para começar a explorar esses dados. Vamos começar com alguns gráficos simples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Primeiros gráficos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos começar fazendo um simples gráfico de posição *versus* tempo. Para os dados do Mundial de Berlin, temos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f52a596d3d0>"
      ]
     },
     "execution_count": 12,
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    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dados['2009_Berlin'], dados['Splits'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por mais que na tabela a informação na forma de intervalo fique de mais fácil interpretação para o leitor, na minha opinião no gráfico o melhor seria o valor inteiro do final do intervalo. Ou seja, 0, 10, 20... Assim, vamos criar uma variável `marcas` que irá armazenar essas marcações a cada 10 metros para podemos utilizar como eixo vertical do gráfico. Para isso, usaremos o método [arange](https://numpy.org/doc/stable/reference/generated/numpy.arange.html) que, de acordo com a documentação, gera valores igualmente espaçados na forma `[início, fim)`. Repare, intervalo fechado no início e aberto no fim. Por isso, no código abaixo está 101, para que o valor 100 esteja incluso: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:14.387813Z",
     "iopub.status.busy": "2020-09-14T18:22:14.387676Z",
     "iopub.status.idle": "2020-09-14T18:22:14.456709Z",
     "shell.execute_reply": "2020-09-14T18:22:14.456153Z",
     "shell.execute_reply.started": "2020-09-14T18:22:14.387796Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,  10,  20,  30,  40,  50,  60,  70,  80,  90, 100])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marcas = np.arange(0, 101, 10)\n",
    "marcas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fazendo o gráfico novamente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:14.457455Z",
     "iopub.status.busy": "2020-09-14T18:22:14.457307Z",
     "iopub.status.idle": "2020-09-14T18:22:14.794785Z",
     "shell.execute_reply": "2020-09-14T18:22:14.794348Z",
     "shell.execute_reply.started": "2020-09-14T18:22:14.457437Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dados['2009_Berlin'], marcas)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fica bem mais fácil de entender, na minha opinião. Mas apenas números não significam coisa alguma. Seria melhor colocar título no gráfico e informar do que se trata cada eixo. Além disso, linhas de grade (*grid*) facilitariam a interpretação do gráfico por parte do leitor. Vamos resolver cada caso.\n",
    "\n",
    "O Matplotlib possui alguns estilos de gráfico pré-definidos que podem ser [vistos aqui](https://matplotlib.org/3.1.0/gallery/style_sheets/style_sheets_reference.html). Vamos escolher um que apresente linhas de grade:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:14.795530Z",
     "iopub.status.busy": "2020-09-14T18:22:14.795398Z",
     "iopub.status.idle": "2020-09-14T18:22:14.936937Z",
     "shell.execute_reply": "2020-09-14T18:22:14.936520Z",
     "shell.execute_reply.started": "2020-09-14T18:22:14.795513Z"
    }
   },
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esse estilo irá valer para todo o Notebook a partir do momento da execução da célula."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, um pouco de Matplotlib básico para identificar o gráfico e os eixos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:14.937891Z",
     "iopub.status.busy": "2020-09-14T18:22:14.937641Z",
     "iopub.status.idle": "2020-09-14T18:22:15.326987Z",
     "shell.execute_reply": "2020-09-14T18:22:15.326323Z",
     "shell.execute_reply.started": "2020-09-14T18:22:14.937873Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dados['2009_Berlin'], marcas)\n",
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Posição / m')\n",
    "plt.title('Usain Bolt - Mundial de Berlin - 2009')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos comparar os dados das duas competições no mesmo gráfico:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:15.328035Z",
     "iopub.status.busy": "2020-09-14T18:22:15.327803Z",
     "iopub.status.idle": "2020-09-14T18:22:15.608331Z",
     "shell.execute_reply": "2020-09-14T18:22:15.607755Z",
     "shell.execute_reply.started": "2020-09-14T18:22:15.328005Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dados['2008_Beijing'], marcas, label='2008 - Beijing')\n",
    "plt.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin')\n",
    "plt.legend()\n",
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Posição / m')\n",
    "plt.title('Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repare que no gráfico fica mais fácil de perceber que Bolt começou pior na competição de 2009 (trecho entre 0 e 3 segundos), mas recuperou na metade final para quebrar seu próprio recorde."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos também apresentar os gráficos lado a lado. Caso tenha dificuldade de entender o código a seguir, [leia esse artigo](https://cienciaprogramada.com.br/2020/09/graficos-python-pint-matplotlib/) onde também apresento um pouco de Matplotlib e explico um pouco como trabalhar com eixos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:15.609651Z",
     "iopub.status.busy": "2020-09-14T18:22:15.609406Z",
     "iopub.status.idle": "2020-09-14T18:22:16.309241Z",
     "shell.execute_reply": "2020-09-14T18:22:16.308566Z",
     "shell.execute_reply.started": "2020-09-14T18:22:15.609620Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# útil para mudar a frequência dos ticks (marcações, traços) nos eixos\n",
    "import matplotlib.ticker as plticker\n",
    "\n",
    "# criando o grid\n",
    "fig1, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "# associando eixos a cada posição do grid\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "# marcações no eixo de posição de 10 em 10 e no de tempo de 1 em 1\n",
    "ticks_posicao = plticker.MultipleLocator(base=10)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "# os gráficos em si\n",
    "ax1.scatter(dados['2008_Beijing'], marcas, label='2008 - Beijing', color='red')\n",
    "ax2.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin', color='blue')\n",
    "\n",
    "# nomeando os eixos e colocando as marcações no intervalo desejado\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Posição / m')\n",
    "    ax.yaxis.set_major_locator(ticks_posicao)\n",
    "    ax.legend()\n",
    "\n",
    "# título principal\n",
    "fig1.suptitle('Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como eixo de posição é igual nos dois gráficos, poderiam ser unificados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:16.310345Z",
     "iopub.status.busy": "2020-09-14T18:22:16.310125Z",
     "iopub.status.idle": "2020-09-14T18:22:16.649147Z",
     "shell.execute_reply": "2020-09-14T18:22:16.648604Z",
     "shell.execute_reply.started": "2020-09-14T18:22:16.310317Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), sharey=True, facecolor=(1,1,1))\n",
    "\n",
    "# removendo espaço horizontal entre os plots\n",
    "fig2.subplots_adjust(wspace=0)\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_posicao = plticker.MultipleLocator(base=10)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.scatter(dados['2008_Beijing'], marcas, label='2008 - Beijing', color='red')\n",
    "ax2.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin', color='blue')\n",
    "\n",
    "ax1.set_ylabel('Posição / m')\n",
    "ax1.yaxis.set_major_locator(ticks_posicao)\n",
    "\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')    \n",
    "    ax.xaxis.set_major_locator(ticks_tempo)    \n",
    "    ax.legend()\n",
    "\n",
    "fig2.suptitle('Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Não gosto muito dessa forma, mas deixo aí para conhecimento. Se for colocar gráfico em páginas web, lembre-se que muitos veem pelo celular, então é melhor deixar os eixos separados para facilitar aqueles que usam zoom para conseguir enxergar os gráficos separadamente. Unificar eixos costuma ser uma opção melhor em trabalhos feitos para ler em computador ou em papel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Como \"ligar os pontos\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repare que, por enquanto, apenas plotamos os pontos referentes a cada posição de Bolt no tempo em cada prova. Mas, como ligar esses pontos? Ou, aqueles mais conhecedores de Matplotlib devem estar se perguntando por que não usei o método `plot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:16.650061Z",
     "iopub.status.busy": "2020-09-14T18:22:16.649897Z",
     "iopub.status.idle": "2020-09-14T18:22:16.909858Z",
     "shell.execute_reply": "2020-09-14T18:22:16.909305Z",
     "shell.execute_reply.started": "2020-09-14T18:22:16.650043Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ERRADO!!\n",
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Posição / m')\n",
    "plt.title('Usain Bolt - Mundial de Berlin - 2009')\n",
    "\n",
    "plt.plot(dados['2009_Berlin'], marcas, marker='o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora, é simples saber o problema com o gráfico acima. Reparou no que o método fez? Ele simplesmente ligou os pontos, bem parecido com o que você fazia bem criancinha naqueles livros de desenho com pontos para ligar e formar desenhos. Mas, depois, quando ficou uma criancinha um pouco mais esperta, você começou a perceber que, para o desenho ficar esteticamente mais aceitável, nem sempre era para ligar com retas, né?\n",
    "\n",
    "Então, aqui não é um desenho de ligar pontos mas a ideia é mesma. Será que é para ligar com retas? E aqui o parâmetro obviamente não é estético e, sim, uma análise lógica e física da situação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logicamente que Bolt não correu com velocidade constante durante toda a prova. Especialmente na arrancada inicial, onde ele saiu do repouso (velocidade zero), certamente acelerou utilizando toda a explosão muscular possível até atingir um máximo de velocidade e tentou manter esse máximo até o final da prova, mas pode não ter conseguido. Aliás vamos ver as provas.\n",
    "\n",
    "No vídeo da prova de 2008, fica perceptível que ele já comemorava nos metros finais:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:16.910705Z",
     "iopub.status.busy": "2020-09-14T18:22:16.910555Z",
     "iopub.status.idle": "2020-09-14T18:22:17.319468Z",
     "shell.execute_reply": "2020-09-14T18:22:17.318711Z",
     "shell.execute_reply.started": "2020-09-14T18:22:16.910686Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/93dC0o2aHto\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f52a38173a0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "\n",
    "YouTubeVideo('93dC0o2aHto', width=600, height=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Em 2009 não comemorou com antecedência, apenas olhou para o cronômetro nas passadas finais:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:17.320805Z",
     "iopub.status.busy": "2020-09-14T18:22:17.320580Z",
     "iopub.status.idle": "2020-09-14T18:22:17.621508Z",
     "shell.execute_reply": "2020-09-14T18:22:17.620718Z",
     "shell.execute_reply.started": "2020-09-14T18:22:17.320782Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/3nbjhpcZ9_g\"\n",
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       "        "
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      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f52a351b9d0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('3nbjhpcZ9_g', width=600, height=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É de se esperar que a comemoração em 2008 tenha diminuído um pouco a velocidade.\n",
    "\n",
    "E o que velocidade tem a ver com nosso gráfico de posição? Ora, velocidade é a variação da posição no tempo. Logo, mais pontos de posição seriam úteis para um melhor estudo da velocidade. Aqui entra o conceito de interpolação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Precisamos estimar pontos intermediários aos pontos experimentais que temos. O nome formal disso é interpolação. Não confunda com regressão. Em uma regressão, tentamos verificar qual função matemática melhor descreve um determinado conjunto de dados, não necessariamente passando por pontos desses dados. Na interpolação você passa pelos pontos.\n",
    "\n",
    "Para os fins desse artigo, essa definição de interpolação basta. Caso queira mais rigor, veja [esse artigo sobre interpolação](https://en.wikipedia.org/wiki/Interpolation), [esse sobre regressão](https://en.wikipedia.org/wiki/Regression_analysis) e [essa discussão](https://stats.stackexchange.com/questions/33659/how-is-interpolation-related-to-the-concept-of-regression/) sobre a diferença entre os dois conceitos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para fazer a interpolação utilizaremos a biblioteca [SciPy](https://www.scipy.org/scipylib/index.html) que possui rotinas numéricas para estatística, álgebra linear, problemas de otimização, regressão e interpolação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O assunto é tão extenso que uma [olhada na documentação](https://docs.scipy.org/doc/scipy/reference/interpolate.html) mostra a existência de diversos métodos de interpolação. Mas vamos por partes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiro vamos mostrar que realmente o método `plot` do Matplotlib realiza uma interpolação linear entre cada par de pontos. Vamos utilizar o pacote [interp1d](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html#scipy.interpolate.interp1d) do SciPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:17.622888Z",
     "iopub.status.busy": "2020-09-14T18:22:17.622606Z",
     "iopub.status.idle": "2020-09-14T18:22:17.870982Z",
     "shell.execute_reply": "2020-09-14T18:22:17.870291Z",
     "shell.execute_reply.started": "2020-09-14T18:22:17.622852Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos então interpolar linearmente nossos pontos. Para tornar o artigo menos longo, farei apenas para os dados de 2009:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:17.872349Z",
     "iopub.status.busy": "2020-09-14T18:22:17.871905Z",
     "iopub.status.idle": "2020-09-14T18:22:18.301842Z",
     "shell.execute_reply": "2020-09-14T18:22:18.301283Z",
     "shell.execute_reply.started": "2020-09-14T18:22:17.872317Z"
    }
   },
   "outputs": [],
   "source": [
    "linear_2009_berlin = interp1d(dados['2009_Berlin'], marcas, kind='linear', fill_value='extrapolate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O `kind='linear'` é auto-explicativo. O parâmetro `fill_value` resolve o que fazer caso sejam passados valores para a função resultante que estejam fora do intervalo de interpolação. No caso, solicitei que faça extrapolação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora que temos nossa função interpoladora, precisamos passar valores de x, nosso caso tempo, para ela. Vamos criar um array (vetor) de tempos espaçados de 0,1 s:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:18.302697Z",
     "iopub.status.busy": "2020-09-14T18:22:18.302550Z",
     "iopub.status.idle": "2020-09-14T18:22:18.542361Z",
     "shell.execute_reply": "2020-09-14T18:22:18.541706Z",
     "shell.execute_reply.started": "2020-09-14T18:22:18.302679Z"
    }
   },
   "outputs": [],
   "source": [
    "tempo = np.arange(0, 9.7, 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fazendo o gráfico:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:18.543504Z",
     "iopub.status.busy": "2020-09-14T18:22:18.543164Z",
     "iopub.status.idle": "2020-09-14T18:22:18.879920Z",
     "shell.execute_reply": "2020-09-14T18:22:18.879277Z",
     "shell.execute_reply.started": "2020-09-14T18:22:18.543475Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Posição / m')\n",
    "plt.title('Usain Bolt - Mundial de Berlin - 2009')\n",
    "\n",
    "plt.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin')\n",
    "plt.plot(tempo, linear_2009_berlin(tempo), label='Linear')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É o mesmo gráfico gerado pelo método `plot`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tudo bem, mostramos que foi feito realmente uma interpolação linear entre cada par de pontos. Mas o que devemos fazer então?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aqui cabe destacar que há várias formas de abordagem quando se trata de interpolação. Uma forma de abordagem é procurar um [polinômio](https://en.wikipedia.org/wiki/Polynomial_interpolation) que passe por todos os pontos. Dados *n* pontos, há um polinômio de grau *n-1* que interpola tais pontos. Essa abordagem é computacionalmente cara e pode exibir alguns artefatos oscilatórios nos pontos extremos, o que é conhecido como [fenômeno de Runge](https://en.wikipedia.org/wiki/Runge%27s_phenomenon).\n",
    "\n",
    "[Essa animação interativa](https://www.geogebra.org/m/ddxsk6k8) ilustra bem tal fenômeno para aqueles que tiveram dificuldade de visualizar o escrito acima.\n",
    "\n",
    "Uma outra abordagem é fazer um interpolação por partes (também chamada de interpolação por polinômios seccionados), ou seja, ao invés de buscar uma função única que passe por todos os pontos, divide-se os pontos em intervalos. Cada intervalo é interpolado e anexado ao intervalo seguinte de manera a obter uma curva contínua."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dentre as formas de interpolação por partes, destaca-se a chamada de [spline](https://en.wikipedia.org/wiki/Spline_interpolation). A vantagem é que boas interpolações são conseguidas com polinômios de baixa ordem, evitando o fenômeno de Runge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um bom ponto de partida é começar com splines cúbicos, ou seja, utilizando polinômios de grau 3 em cada intervalo. É um grau baixo e garante continuidade da função até sua derivada de segunda ordem, algo que será importante para gente mais adiante. Cabe destacar que é um ponto de partida comum quando se tem pouco conhecimento do comportamento dos dados, mas não é uma bala de prata, sempre busque conhecer ao máximo o contexto de seus dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mesmo dentre os splines cúbicos há [diferentes tipos](https://en.wikipedia.org/wiki/Natural_cubic_spline), a depender das condições de contorno, mas que não entrarei no mérito aqui nesse artigo. Vamos utilizar um método específico do SciPy para spline cúbicos o [CubicSpline](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.CubicSpline.html). Como é possível ver na documentação linkada, há como alterar o tipo (condições de contorno), mas irei manter o padrão aqui nesse artigo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:18.882479Z",
     "iopub.status.busy": "2020-09-14T18:22:18.882319Z",
     "iopub.status.idle": "2020-09-14T18:22:19.257016Z",
     "shell.execute_reply": "2020-09-14T18:22:19.254923Z",
     "shell.execute_reply.started": "2020-09-14T18:22:18.882460Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import CubicSpline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos então obter os splines para nossos dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:19.260909Z",
     "iopub.status.busy": "2020-09-14T18:22:19.260459Z",
     "iopub.status.idle": "2020-09-14T18:22:19.929376Z",
     "shell.execute_reply": "2020-09-14T18:22:19.928481Z",
     "shell.execute_reply.started": "2020-09-14T18:22:19.260854Z"
    }
   },
   "outputs": [],
   "source": [
    "cs_2009_berlin = CubicSpline(dados['2009_Berlin'], marcas)\n",
    "cs_2008_beijing = CubicSpline(dados['2008_Beijing'], marcas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:19.930553Z",
     "iopub.status.busy": "2020-09-14T18:22:19.930319Z",
     "iopub.status.idle": "2020-09-14T18:22:20.569424Z",
     "shell.execute_reply": "2020-09-14T18:22:20.568919Z",
     "shell.execute_reply.started": "2020-09-14T18:22:19.930524Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_posicao = plticker.MultipleLocator(base=10)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.scatter(dados['2008_Beijing'], marcas, label='2008 - Beijing', color='red')\n",
    "ax1.plot(tempo, cs_2008_beijing(tempo), label='Spline Cúbico', color='red')\n",
    "ax2.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin', color='blue')\n",
    "ax2.plot(tempo, cs_2009_berlin(tempo), label='Spline Cúbico', color='blue')\n",
    "\n",
    "# nomeando os eixos e colocando as marcações no intervalo desejado\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Posição / m')\n",
    "    ax.yaxis.set_major_locator(ticks_posicao)\n",
    "    ax.legend()\n",
    "\n",
    "# título principal\n",
    "fig3.suptitle('Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente, parece que agora temos um gráfico que nos permite continuar nossas explorações"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Obtendo a velocidade e a aceleração de Bolt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Velocidade média"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora que temos o que parece um modelo mais aceitável de como varia a posição de Bolt no tempo podemos calcular sua velocidade. Mas precisamos esclarecer que tipo de velocidade estamos querendo determinar. Afinal, se for apenas a velocidade média, isso já poderia ter sido calculado posto que sabemos o total de deslocamento, 100 metros, e o tempo que durou o deslocamento, o tempo final da prova, que é a última posição de cada array de tempos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:20.570212Z",
     "iopub.status.busy": "2020-09-14T18:22:20.570061Z",
     "iopub.status.idle": "2020-09-14T18:22:20.602754Z",
     "shell.execute_reply": "2020-09-14T18:22:20.601665Z",
     "shell.execute_reply.started": "2020-09-14T18:22:20.570194Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Velocidade média em Beijing (2008): 10.32 m/s\n",
      "Velocidade média em Berlin (2009): 10.44 m/s\n"
     ]
    }
   ],
   "source": [
    "velocidade_media_beijing = 100 / dados['2008_Beijing'][-1]\n",
    "print(f'Velocidade média em Beijing (2008): {velocidade_media_beijing:.2f} m/s')\n",
    "\n",
    "velocidade_media_berlin = 100 / dados['2009_Berlin'][-1]\n",
    "print(f'Velocidade média em Berlin (2009): {velocidade_media_berlin:.2f} m/s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Já escrevi [aqui sobre o pacote pint](https://cienciaprogramada.com.br/2020/09/python-unidades-cerveja-pint/) que permite lidar com unidades e fazer conversões. Vamos usar esse pacote para converter os valores para quilômetros por hora, unidade que estamos mais acostumados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:20.604276Z",
     "iopub.status.busy": "2020-09-14T18:22:20.603974Z",
     "iopub.status.idle": "2020-09-14T18:22:21.330429Z",
     "shell.execute_reply": "2020-09-14T18:22:21.329741Z",
     "shell.execute_reply.started": "2020-09-14T18:22:20.604244Z"
    }
   },
   "outputs": [],
   "source": [
    "import pint\n",
    "\n",
    "ureg = pint.UnitRegistry(fmt_locale='pt_BR')\n",
    "Q_ = ureg.Quantity\n",
    "\n",
    "velocidade_media_beijing = Q_(velocidade_media_beijing, 'm/s')\n",
    "velocidade_media_berlin = Q_(velocidade_media_berlin, 'm/s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:21.331553Z",
     "iopub.status.busy": "2020-09-14T18:22:21.331331Z",
     "iopub.status.idle": "2020-09-14T18:22:21.754675Z",
     "shell.execute_reply": "2020-09-14T18:22:21.754027Z",
     "shell.execute_reply.started": "2020-09-14T18:22:21.331523Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Velocidade média em Beijing (2008): 37.15 quilômetros por horas\n",
      "Velocidade média em Berlin (2009): 37.58 quilômetros por horas\n"
     ]
    }
   ],
   "source": [
    "print(f\"Velocidade média em Beijing (2008): {velocidade_media_beijing.to('km/hour'):.2f}\")\n",
    "print(f\"Velocidade média em Berlin (2009): {velocidade_media_berlin.to('km/hour'):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Impressionante, não?\n",
    "\n",
    "## Velocidade instantânea\n",
    "\n",
    "Mas o que seria mais interessante é estimar a velocidade em cada momento da prova, a chamada velocidade instantânea. Afinal, como já discutimos, a velocidade de Bolt durante as provas não é constante. Para obter tais médias, certamente em alguns momentos Bolt correu *acima* desses valores. Como podemos obter velocidades instantâneas?\n",
    "\n",
    "Utilizaremos um pouco de cálculo aqui e o fato de que agora temos uma curva unindo os pontos experimentais. Para a velocidade média, pegamos dois pontos distantes, o início e o fim da prova. Agora, imagine pegar pontos cada vez mais próximos, ou seja, diminuindo cada vez mais o intervalo de tempo entre os pontos. No limite em que esse intervalo tender a zero, teremos a velocidade instantânea.\n",
    "\n",
    "Fica mais fácil visualizar com uma imagem. Observe a animação abaixo. Nela temos uma curva de uma função qualquer, a marcação de dois pontos, **A** e **B**, e a visualização do triângulo formado para obter a variação da quantidade do eixo *y* e a do eixo *x* com auxílio de um terceiro ponto **C**. No caso de nossos gráficos, variação da distância e do tempo, respectivamente. Na animação, os pontos vão se aproximando cada vez mais. Observe que, no limite em que os pontos se tornam mais próximos, a hipotenusa do triângulo, inicialmente uma [reta secante](https://en.wikipedia.org/wiki/Secant_line) da curva, torna-se uma reta tangente no ponto de virtual encontro **A**. A reta azul é a tangente no ponto **A**, apresentada justamente para mostrar como a secante se aproxima cada vez mais de uma tangente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![animacao_tangente](animacao_tangente.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assim, matematicamente, a velocidade instantânea em um dado momento é a inclinação da reta tangente à curva do gráfico posição vs tempo no momento desejado. Em [cálculo](https://en.wikipedia.org/wiki/Calculus), isso é o mesmo que dizer que a velocidade instantânea é a [derivada](https://en.wikipedia.org/wiki/Derivative) da posição com relação ao tempo em um dado dado ponto do gráfico.\n",
    "\n",
    "Eu havia citado anteriormente que o fato dos splines cúbicos garantirem que a curva obtida possui derivadas primeira e segunda era importante. Agora sabemos o porquê."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O bom do `CubicSpline` do SciPy é que é muito simples solicitar a primeira derivada, bastando passar o parâmetro `1` para o spline obtido. Veja o código abaixo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:21.755539Z",
     "iopub.status.busy": "2020-09-14T18:22:21.755382Z",
     "iopub.status.idle": "2020-09-14T18:22:22.266700Z",
     "shell.execute_reply": "2020-09-14T18:22:22.266202Z",
     "shell.execute_reply.started": "2020-09-14T18:22:21.755520Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig4, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_velocidade = plticker.MultipleLocator(base=2)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.plot(tempo, cs_2008_beijing(tempo, 1), label='Spline Cúbico - 1ª derivada', color='red')\n",
    "ax2.plot(tempo, cs_2009_berlin(tempo, 1), label='Spline Cúbico - 1ª derivada', color='blue')\n",
    "\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Velocidade / m/s')\n",
    "    ax.yaxis.set_major_locator(ticks_velocidade)\n",
    "    ax.legend()\n",
    "\n",
    "fig4.suptitle('Velocidade - Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perceba que obtivemos perfis condizentes com o que esperávamos. Na prova de 2008, a velocidade cai próximo ao segundo final de prova, quando Bolt já visivelmente comemorava. Na de 2009, o jamaicano é mais consistente na velocidade.\n",
    "\n",
    "Podemos verificar as velocidades máximas que nosso modelo fornece para cada caso:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:22.267378Z",
     "iopub.status.busy": "2020-09-14T18:22:22.267197Z",
     "iopub.status.idle": "2020-09-14T18:22:22.355037Z",
     "shell.execute_reply": "2020-09-14T18:22:22.354371Z",
     "shell.execute_reply.started": "2020-09-14T18:22:22.267357Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.26 metros por segundos\n",
      "12.37 metros por segundos\n"
     ]
    }
   ],
   "source": [
    "velocidade_max_2008_cs = Q_(max(cs_2008_beijing(tempo, 1)), 'm/s')\n",
    "velocidade_max_2009_cs = Q_(max(cs_2009_berlin(tempo, 1)), 'm/s')\n",
    "\n",
    "print(f'{velocidade_max_2008_cs:.2f}')\n",
    "print(f'{velocidade_max_2009_cs:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Em quilômetros por hora:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:22.356103Z",
     "iopub.status.busy": "2020-09-14T18:22:22.355919Z",
     "iopub.status.idle": "2020-09-14T18:22:22.567670Z",
     "shell.execute_reply": "2020-09-14T18:22:22.565749Z",
     "shell.execute_reply.started": "2020-09-14T18:22:22.356080Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44.14 quilômetros por horas\n",
      "44.53 quilômetros por horas\n"
     ]
    }
   ],
   "source": [
    "print(f\"{velocidade_max_2008_cs.to('km/hour'):.2f}\")\n",
    "print(f\"{velocidade_max_2009_cs.to('km/hour'):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Já dá para multá-lo em perimêtros urbanos. Anotaram a placa?\n",
    "\n",
    "Seguindo a lógica de tudo que mostramos até agora, podemos obter uma curva para aceleração. A aceleração é a variação da velocidade no tempo, o que é o mesmo que dizer que a aceleração é a derivada primeira da velocidade em relação ao tempo. Ou, a derivada segunda da posição em relação ao tempo. Daí:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:22.570775Z",
     "iopub.status.busy": "2020-09-14T18:22:22.570197Z",
     "iopub.status.idle": "2020-09-14T18:22:23.147344Z",
     "shell.execute_reply": "2020-09-14T18:22:23.146824Z",
     "shell.execute_reply.started": "2020-09-14T18:22:22.570707Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig5, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_velocidade = plticker.MultipleLocator(base=1)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.plot(tempo, cs_2008_beijing(tempo, 2), label='Spline Cúbico - 2ª derivada', color='red')\n",
    "ax2.plot(tempo, cs_2009_berlin(tempo, 2), label='Spline Cúbico - 2ª derivada', color='blue')\n",
    "\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Aceleração / m/s²')\n",
    "    ax.yaxis.set_major_locator(ticks_velocidade)\n",
    "    ax.legend()\n",
    "\n",
    "fig5.suptitle('Aceleração - Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Os gráficos também estão relativamente bem coerentes, uma grande aceleração inicial e depois mantendo uma aceleração positiva buscando aumentar a velocidade. Em 2008, uma aceleração negativa bem próximo ao final, indicando desaceleração perto da linha de chegada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Embora estejam coerentes, precisamos ter cuidado com nossos modelos. Nos gráficos de aceleração observamos alterações bruscas nos perfis. Isso é um pouco estranho, lembre-se que é um humano, não há um pedal de acelerador ou freio! Talvez fosse de se esperar variações menos bruscas.\n",
    "\n",
    "# Melhorando nosso modelo\n",
    "\n",
    "Obviamente que diversas pessoas e empresas fazem estudos sobre o desempenho dos atletas. Inclusive há todo um ramo de estudos chamado [biomecânica esportiva](https://en.wikipedia.org/wiki/Sports_biomechanics) voltado para isso. Analisando estudos da área, vemos que usualmente se utilizam splines, mas só que de grau 5 e não 3. Em inglês, o termo é *quintic splines*, sendo *quintic* relativo ao grau 5. Não por outro motivo que há uma [empresa chamada Quintic](https://www.quinticsports.com/about/) que justamente trabalha com softwares de biomecânica esportiva. Alguns livros de biomecânica, [como esse](https://www.amazon.com/Introduction-Sports-Biomechanics-Analysing-Movement-ebook-dp-B001ROAJR2/dp/B001ROAJR2/ref=mt_other?_encoding=UTF8&me=&qid=), possuem trechos dedicados ao estudo de splines de grau 5 dada a importância na área."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logo, podemos verificar como ficaria uma interpolação com splines de quinto grau. O SciPy possui o `UnivariateSpline` onde podemos passar um parâmetro para indicar o grau do spline desejado:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:23.148127Z",
     "iopub.status.busy": "2020-09-14T18:22:23.147983Z",
     "iopub.status.idle": "2020-09-14T18:22:23.150814Z",
     "shell.execute_reply": "2020-09-14T18:22:23.150075Z",
     "shell.execute_reply.started": "2020-09-14T18:22:23.148109Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import UnivariateSpline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:23.151981Z",
     "iopub.status.busy": "2020-09-14T18:22:23.151747Z",
     "iopub.status.idle": "2020-09-14T18:22:23.373037Z",
     "shell.execute_reply": "2020-09-14T18:22:23.372411Z",
     "shell.execute_reply.started": "2020-09-14T18:22:23.151952Z"
    }
   },
   "outputs": [],
   "source": [
    "s_grau5_2008_beijing = UnivariateSpline(dados['2008_Beijing'], marcas, k=5)\n",
    "s_grau5_2009_berlin = UnivariateSpline(dados['2009_Berlin'], marcas, k=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos fazer os gráficos de posição, velocidade e aceleração *versus* tempo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:23.374177Z",
     "iopub.status.busy": "2020-09-14T18:22:23.373929Z",
     "iopub.status.idle": "2020-09-14T18:22:23.975596Z",
     "shell.execute_reply": "2020-09-14T18:22:23.974999Z",
     "shell.execute_reply.started": "2020-09-14T18:22:23.374146Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig6, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_posicao = plticker.MultipleLocator(base=10)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.scatter(dados['2008_Beijing'], marcas, label='2008 - Beijing', color='red')\n",
    "ax1.plot(tempo, s_grau5_2008_beijing(tempo), label='Spline grau 5', color='red')\n",
    "ax2.scatter(dados['2009_Berlin'], marcas, label='2009 - Berlin', color='blue')\n",
    "ax2.plot(tempo, s_grau5_2009_berlin(tempo), label='Spline grau 5', color='blue')\n",
    "\n",
    "# nomeando os eixos e colocando as marcações no intervalo desejado\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Posição / m')\n",
    "    ax.yaxis.set_major_locator(ticks_posicao)\n",
    "    ax.legend()\n",
    "\n",
    "# título principal\n",
    "fig6.suptitle('Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:23.976551Z",
     "iopub.status.busy": "2020-09-14T18:22:23.976363Z",
     "iopub.status.idle": "2020-09-14T18:22:24.338108Z",
     "shell.execute_reply": "2020-09-14T18:22:24.337506Z",
     "shell.execute_reply.started": "2020-09-14T18:22:23.976532Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig7, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_velocidade = plticker.MultipleLocator(base=2)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.plot(tempo, s_grau5_2008_beijing(tempo, 1), label='Spline grau 5 - 1ª derivada', color='red')\n",
    "ax2.plot(tempo, s_grau5_2009_berlin(tempo, 1), label='Spline grau 5 - 1ª derivada', color='blue')\n",
    "\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Velocidade / m/s')\n",
    "    ax.yaxis.set_major_locator(ticks_velocidade)\n",
    "    ax.legend()\n",
    "\n",
    "fig7.suptitle('Velocidade - Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:24.339365Z",
     "iopub.status.busy": "2020-09-14T18:22:24.339134Z",
     "iopub.status.idle": "2020-09-14T18:22:24.668225Z",
     "shell.execute_reply": "2020-09-14T18:22:24.667638Z",
     "shell.execute_reply.started": "2020-09-14T18:22:24.339336Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7d+zatQtA2meofv366T5DSUlJ+O6777LwKl8vf/78ePjwYbr398GDBxk+v1y5crh+/fpL90+ZMgV79+7FL7/8km4UtEyZMrh06VK6/V+6dMk6WlymTJl0o7MXL160Pvbnn3+iePHiaNq0KaRSKUqUKIGWLVumWwru6tWrCAkJeWnk9blOnTrhyJEj+Oeff7Bt2zZrgw1k/Pl7k5CQEDRv3jzdz2nSpEnpfk7JycnppoRl5vPyNl718zAYDGjXrh0KFChg/SPguRff79u3b8NgMKB48eIoXrw4TCZTuikf//15PD+SdvfuXfzzzz8oU6YMgoKC0v3/uHr1aropKESUhg020X9s374dMpkMf/31Fy5cuIALFy7g6tWrqFu3LtasWYNq1aohf/78+OSTT6DT6aDX63HixAkAaYfKv/rqK+v8xfj4+Fce2pdKpRg4cCBGjx6NyMhIAMDDhw+xf//+DPNKTEyEh4cH/Pz8EBMTgy+++ML6WP78+dG8eXMMGzYMsbGxSE1NtTbSr9suODgYtWrVwoQJE6DX63Hp0iUsX778rdd9btasGf7++2+sXbsWqampiImJwcSJE9GhQwfI5XI8ffoUO3bsgE6ng7u7O7y8vCCVSq15enl5wdfXFw8fPsTs2bPfKoc3MZvNWLlyJTw8PFC4cOEsvQcBAQGQSqW4ffu2zfJJSkrChg0brA1Nq1atcP36det7mJqaijNnzmQ4H/dt1KxZEzKZDN9++y1MJhN27NiB06dPZ/j8atWqIS4uLt2o/ldffYX169cjIiIC/v7+6Z7foEEDyGQyLFy4EAaDAd9++y0AoFGjRgCA3r174+uvv8bDhw/x6NEjzJ07F3379gUAVKxYETdu3MChQ4cgCAJu3bqF3bt3o1y5ctb9Hz16FM2bN88w34CAADRo0AD9+vXDO++8g1KlSgHAaz9/b/LPP/9g37591p/TwIEDER4ejlOnTkEQBOh0OuzZsyfDkX5batGiRbrpU6mpqejYsSM8PDywevXql15Tjx49sGvXLvz666/Q6XSYPHky3nvvPXh7e0OlUuG9997D5MmTodPpcOLECezYsQO9evUCkHbS6a1btyAIAv766y+MGTMGkydPThfjTT8PIpclEJFV06ZNhTFjxrx0/8aNG4W8efMKqampwr1794S2bdsKGo1G8Pf3Fz788EPr89asWSOULVtW8Pb2FgoUKCD069fP+hgA4caNG4IgCEJKSoowYcIE4Z133hG8vb2FkiVLCgsWLBAEQRAOHz4sBAUFpYv/8OFDoX79+oJKpRKKFSsmhIeHCwCE1NRUQRAEITo6Wujdu7egUqkEAEL79u0ztd2DBw+Eli1bCmq1WihcuLDw3XffZev9O3HihFC7dm3Bz89PyJ8/v/D+++8LMTExgiAIwqNHj4R69eoJPj4+gq+vr1C/fn3hypUrgiAIwp9//ilUqlRJUKlUQvny5YU5c+akew8KFSokHDhwQBAEQZgyZYrQo0cP62N37txJ95peBEDw9PQUVCqV4O3tLVSpUkXYt2+f9fHXvQcvxvrss88ErVYr+Pr6Cr/99luW35/Dhw8LEolEUKlUgkqlEjQajdCiRQvr50IQBOHvv/8WWrRoIWi1WkGj0QgNGzYUzp8/LwiCIPTp00eYNGmSdV9v+x6dOXNGKF++vKBSqYSOHTsK7du3F6ZOnZph3h999JEQFhZmvQ1AUCgU1tehUqmEGTNmWB8/d+6cUKlSJUGpVAoVK1YUzp07Z33MYrEI48aNE9RqtaBWq4Vx48YJFovF+vjGjRuFMmXKCF5eXkJQUJDw8ccfC2az2fp42bJlhQsXLrz2fV6zZo0AQJg1a5b1vtd9/l40ZcoUQS6XW19bvnz5hMGDBws6nc76nL179wpVqlQRfH19hXz58gkdO3YUEhISBEFI/7N4LqOfz6s+v/Xr1xe+//77DF9flSpVhN9//10QBEE4cuSIAEDw8PBI9/M4duyY9fnr1q0TgoODBU9PT6FNmzZCdHS09bHo6Gihbdu2gqenpxAcHCysW7fO+ti1a9eE4sWLCx4eHkLBggWFuXPnpsvj9OnTQsWKFTPMk8iVSQTBDsdhiUgUOp0OnTt35rJZLuDQoUMYMGCATUbUq1evjiFDhqBfv36vfPz5qjjnz5/P9El79rBr1y6sXbs23dKFruiXX37B4sWLRV8/vUOHDnj//ffRokULUfMgckZssIlyCZ1OB4VCgbJly+Ly5ctQKBRip0R2tHDhQuzYsQMHDx7M8rZHjx5FiRIloNVqsW7dOgwZMgS3b99G/vz57ZApEZHrefPinESUI0RERKBbt25o3Lgxm+tcbuTIkdi5c+dLF0HKrGvXrqFz587Q6XQoXLgwfvrpJzbXREQ2xBFsIiIiIiIb4ioiREREREQ2xAabiIiIiMiG2GATEREREdkQG2wiIiIiIhtig01EREREZENssImIiIiIbIgNNhERERGRDbHBJiIiIiKyITbYREREREQ2xAabiIiIiMiG2GATEREREdkQG2wiIiIiIhuSi51Adjx69CjL22i1WkRFRdkhG8Z0lZhixWXM3BszMDDQobHFwHrNmIyZu2KKFVfMmFmp1RzBJiIiIiKyITbYREREREQ2xAabiIiIiMiGcvQcbKLnBEGAXq+HxWKBRCKxe7ynT5/CYDDYPQ5j5p6YgiBAKpVCqVQ65DNK5KwcWa9zaz1xhphixbV3TFvVajbYlCvo9Xq4ublBLnfMR1oul0MmkzkkFmPmnpgmkwl6vR4eHh52j0XkrBxZr3NzPRE7plhxHRHTFrWaU0QoV7BYLA5rronellwuh8ViETsNIlGxXpOzs0Wt5ieccgUecqecIqd/Vh89eoR58+ZZb0dGRqJz585o2bKliFlRTpLT/w+Qa8ju59QpGmwWbMoNFixYgO3bt0Mmk0EikWDmzJmoVKlShs+fO3cuVCoVhgwZgtmzZ6N69eqoV6+eAzPOnurVq8PLywtSqRRyuRx79+7N0vYffPABLl68CDc3N1SoUAEzZ86Em5sbVqxYgTNnzuDx48eYNGkSKlasmOE+Hjx4gD59+uDQoUNZit2mTRvs3LkzS9u8yqhRoxAaGopWrVple185RWBgIGbPng0gbSRy8ODBqFatmshZEWUN6zXrtb05RYPNgk053R9//IGIiAjs27cP7u7uiImJgdFozPT248aNs2N2LzObzTaZw7Z582ZoNJq32rZ9+/b45ptvAADDhw/H+vXr0adPH/Ts2RO9e/fGmTNnsGnTptcW7KwymUyQy+U2KdYEXL58Gfny5UNAQIDYqRBlGut11rFeZ51TNNj/xYJNOVFkZCQ0Gg3c3d0BIF0Rq169Olq3bo3Dhw9DqVTi22+/xTvvvJNu+//+ZV29enV06tQJBw4cgMlkwpIlS1C0aFHodDpMmDAB165dQ2pqKsaOHYumTZum24/FYsGkSZNw4sQJBAYGws3NDV26dLHut02bNjh27BiGDRuGpKQkrFu3DkajEe+88w4WLlwIDw+Pl/7KL1asGG7cuGHz96xx48bW7ytUqIDHjx8DADZs2IBLly4hMTERbm5uL2136dIljBkzBgBQv3596/1msxlffvklfvvtNxiNRvTp0we9evXCyZMnMXv2bPj6+uLmzZs4fvy49TUNHToUHTp0QLNmzQD8/8+hfPnyGDFiBJKTkwEA06dPR9WqVSEIAj799FMcO3YMgYGBUCgU1vjz5s3DgQMHoNfrUaVKFcycOTPXHwo/ceIEateuLXYaRFli73pdsmRJJCcn49NPP3VYvW7Xrh0A1mvAeeq10zXYryvYERERiIiIAACEhYVBq9Vmad/Sb76B1N8f2u7ds51nVsjl8iznyphZi/n06VPrSTNen34K+ZUrNo1jKlMGSdOnvxT7ucaNG2P+/PmoW7cu6tWrh7Zt26JWrVoA0uZx+fr64ujRo9i0aRM+//xzrFu3DlKp1Hq4TiqVQiaTQS6XQyKRQKvV4uDBg1i5ciWWLFmCefPmYebMmahXrx4WLlyI+Ph4NGvWDA0aNIBKpbLmsWvXLjx8+BDHjx9HVFQU6tSpg+7du1v36+/vj4MHDwIAYmJi0KdPHwDAV199hY0bN2LAgAHpcnnVa31OIpGge/fukEgk6NWrF3r37v1W721qaiq2bt2K6dOnQy6X4+zZszAajShUqBB0Ot1LsceMGYOvvvoKNWvWxBdffGHNb/369fD19cUvv/wCg8GA1q1bo1GjRpDJZLh8+TKOHj2KQoUKpXtN7du3x549e9CsWTNYLBacOHECs2fPhiAI2Lx5M5RKJW7fvo0hQ4bgl19+wZ49e3D79m0cP34cz549Q926da3v74ABA6wjW8OHD8ehQ4de+oUKAO7u7tBqtaL8f7Elk8mEs2fPonsG9TQ79fr2bWDxYhnGjpUgf37XqWOuEvO/9frTT71w5YptW5EyZUyYPj0pXdz/ckS9/uabbxxar//7OlmvbVOvn9fq5/Gz+v/FqRrsNxXs0NBQhIaGWm9n9Vr0/hs3Qmo2I+rdd7OVZ1Y9v4Y9Y9ovpsFgsBYZi8UCQRBsGsdiscBkMllvy+XydLfd3d2xd+9enDp1CidPnsSgQYMwYcIEdOnSBYIgoE2bNjCZTGjdujU+++wzmEwmWCwW634tFgvMZjNMJhMEQUDTpk1hMplQpkwZ7N69GyaTCUePHsX+/fuxaNEiAGlLXd2/fx/FihWz5vHbb7+hZcuWsFgs0Gg0qFWrVrr9tmrVypr3lStXMGvWLCQkJECn06F+/fov5fK8WP73tT63bds25M+fH1FRUejatSsKFy6MGjVqZPm9/fjjj1GtWjVUqVIFJpMJCxYsSBfvv9/Hx8cjPj4eVatWhclkQvv27XHw4EGYTCYcPnwYV69exa5duwAAiYmJuHnzpnXOYFBQ0Ev7rVevHiZNmgSDwYCIiAhUr14dbm5uSEhIwKRJk/DXX39BKpXi9u3bMJlMOHHiBNq2bQtBEKDValG7dm3re3Xs2DF89913SElJQVxcHIoVK5Zu1Oc5g8GAqKiodP9fAgMDs/y+ie38+fN455134Ofn98rHs1OvnzyR45tv8qB0aRPatHGdOuYqMR1Zr1+s1YD96zUAHDlyxKH1Gvj/Wsl6bZt6/bxWA///2c1KrXaqBvtNBTu7DI0awX3mTEgjI2HJk8cuMUh8CVOnihJXJpOhVq1aqFWrFkqWLInNmzejS5cuANKfjZyZw1DPD13KZDJr8RQEAUuXLkXRokXfOkdPT0/r96NHj8by5ctRpkwZbNy4Eb/99huA9MsTWSwWpKamvnJf+fPnB5BWeJo3b44LFy6kK9hms9l6KO/dd9995bzFr7/+GtHR0Vi2bJn1vrlz5+Lvv/8GkHa4tm/fvpl+fdOnT0eDBg3S3Xfy5Ml0r/u/lEolatasicOHD2Pnzp1o27YtAOD7779HQEAADhw4AIvFgsKFC782rl6vx8SJE/Hzzz8jKCgIc+fOFeWiD45kz+khxYqZkC+fGRERErRpY5cQ5CSmTk0QJS7rNeu1veu1U62Dbe/5fPpGjQAA7ocP2y0GuaabN2/i9u3b1ttXrlxBgQIFrLefn6Sxc+dOVK5c+a1iNGjQACtXrrSO9vz5558vPadq1arYs2cPLBYLnj17Zi3Cr5KUlIS8efMiNTUV27Zts95foEABXL58GQCwb9++Vxbs5ORkJCUlWb8/evQoSpQoke45MpkMBw4cwIEDB15ZrNevX48jR45g0aJFkEr/vxSNHTsW3333Hb777ruXirWvry98fX1x+vRpAEiXd/369bFmzRprvrdu3bLOyXudNm3aYMOGDTh16pS12CckJCBPnjyQSqXYsmWL9ZdmjRo1sHPnTpjNZjx9+hQnT54EAGtx1mg00Ol02LNnzxvj5mR6vR6XLl1C9erV7bJ/iQSoV8+AQ4ek+PetJ7IZR9Tr+vXrO7xe//LLL6zXTlSvnWYE+3nBHjRokN1imMqUgRAYCOWhQ0j59y9VIlt4fkJLQkIC5HI5QkJCMGvWLOvj8fHxCA0NhUKhsB4yzKoxY8Zg0qRJCA0NhcViQXBwMNasWZPuOS1btsTx48fRoEEDBAYGomzZsvDx8Xnl/saNG4dWrVrB398fFStWtBbgHj16oF+/fggNDUXjxo1fOZrw7NkzvP/++wDSRj7atWuHhg0bZun1fPLJJyhQoADa/DtE2aJFC4wePfqN23399dcYM2YMJBJJupNmunfvjgcPHqBZs2YQBAEajQYrVqx44/7q16+PkSNH4t1337WeBNOnTx8MGjQIP/30Exo2bGh9D5o3b44TJ06gQYMGCAoKsv7y9fX1Rffu3dG4cWMEBASgfPnyWXovchqlUpmp9zY76tc3YNMmT1y65IaKFV89Kkf0NhxRr0eNGoUpU6Y4rF43bNgQDRo0YL12onotEWw9+cmBHj16lOVt8n72GSQ//YQnly4Brzjj1R5cbX6dGDGTk5MzPKxkD6+a15eR6tWrY+/evW+9PFJWY+p0OqhUKsTExKBVq1bYvn078rzllKisvE5bye0xn39Wc/oc7KzKar2OjpaiXLl8GDcuAaNGJb15AxtxtdopRkxH1uus/t+2Rb3OSkxb1Wsx6qZYcR0V87+f0xw/B9sRLM2awW3FCijOnoXxLSb4Ezm7Pn36ID4+HqmpqRg5cuRbN9dEYvL3t6BiRQuOHXN3aINN5Eis17mXyzXYQsOGENzc4H7wIBtscohTp045NN5PP/3k0HhE9hIaKmDePAWSkiTw8sqxB1spB2G9JltxqpMcHcLHB8Zq1aDM4qU6iYjIsUJDLTCZJDh5UvHmJxMRORHXa7CRtpqI299/Q/bwodipkI3k4FMJyMXws5p5NWsK8PBImyZCuQf/D1BOkN3PqUs22IZ/FxN35yh2riGVSkU5wYMoK0wmU7olruj13N2BmjWNOHpUKXYqZEOs1+TsbFGrXW4ONgCYihaFqWBBKCMikNyrl9jpkA0olUro9XoYDIZMXRggu9zd3R1+IRHGzNkxBUGAVCqFUslmMSvq1zfg0CElHjyQITiYi2LnBo6s17m1njhDTLHi2jumrWq1SzbYkEigDw2Fav16SFJSIHh4iJ0RZZNEIoGHA3+OrrasFmOSWBo0SPtFeuSIO3r1evOFKMj5ObJeu0o9EauGudJrzSqXPVZpaNIEEr0eiuPHxU6FiIgyUKSICQUKmHDkCOdhE1HO4boNdo0asKhUUB44IHYqRESUAYkkbRT7+HF3GI1iZ0NElDku22BDoYChfn0oDx4EeEYzEZHTatjQgKQkKc6e5XJ9RJQzuG6DDUDfpAlkT57A7fJlsVMhIqIM1K5tgFwucJoIEeUYLt1gGxo3hiCRcJoIEZET8/YWULWqEYcPcwUWIsoZXLrBtvj7I7VyZbizwSYicmoNGhhw5Yobnj516V9bRJRDuHyl0oeGQnH5MqSPH4udChERZaBhQz0AcJoIEeUIbLCbNAEAKCMiRM6EiIgyUrq0CXnymHHkCKeJEJHzc/kG21SiRNpVHX/5RexUiIgoA8+X6zt2zB1mXtCRiJycyzfYkEigb9oU7sePQ5KUJHY2RESUgQYN9IiLk+LcOTexUyEiei022AD0TZtCYjTC/cgRsVMhIqIM1K9vgEwm4NAhThMhIufGBhuAsWpVmNVqKPfvFzsVIiLKgJ+fgCpVjDh4kA02ETk3NtgAIJfD0KRJ2lUdU1PFzoaIiDLQuHHacn2PH/PXFxE5L6epUDqdDnPnzsWoUaMwevRoXL9+3aHx9U2bQhofD8Xvvzs0LhERZV6jRmnL9fGiM0TkzORiJ/DcypUrUaFCBYwdOxYmkwkGg8Gh8Q3168OiVEK5fz+Mdes6NDYREWVOyZImBAaacPCgO7p3TxY7HSKiV3KKEezk5GRcvXoVjRo1AgDI5XKoVCqH5iB4eMBQr17aPGxBcGhsIiLKHIkEaNTIgF9/dYeDx2GIiDLNKRrsyMhI+Pj4YPHixfj4448RHh4OvV7v8Dz0zZpB/ugR3P780+GxiYgocxo31kOnk+LUKYXYqRARvZJTTBExm824c+cO+vfvj2LFimHlypXYvn07unbtmu55ERERiPj3iothYWHQarVZjiWXyzPernNnCB99BM3RozA3bJjlfb9VTDthzNwXlzEZ01nodDqEh4fjwYMHkEgkGDp0KIoXL+6w+HXqGOHunrZcX716RofFJSLKLKdosP39/eHv749ixYoBAGrUqIHt27e/9LzQ0FCEhoZab0dFRWU5llarzXg7iQT+1atDumULoj74IMv7fquYdsKYuS8uY+bemIGBgQ6NnV1inzPj6SmgZk0DDh5U4vPPExwam4goM5xiioifnx/8/f3x6NEjAMDly5dRoEABUXJJadkSbtevQ37zpijxiYicmTOcMwOkLdd3+7Yct2/LHB6biOhNnKLBBoD+/ftj4cKF+Oijj3D37l20b99elDz0zZoBAJQ//yxKfCIiZ+Ys58yEhqbFPHCAy/URkfNxiikiABASEoKwsDCx04Alf34YK1WC8uefkTRihNjpEBE5FWc5Z0arBUqXtuDoUW9MmuSR9RfyFjHthTEZMyfGFCtuTonpNA22M0lp0QK+06dD9uABzMHBYqdDROQ0nOacGQCNGnnju++8cPNmNPz8bLO8qtjz8RmTMXNKTLHiihkzK+fLOM0UEWeib94cAKeJEBG9yJnOmWnSRA+zWYIjRzhNhIicCxvsVzCHhCC1dGko9+4VOxUiIqfjLOfMVKyYCn9/Mw4ccBclPhFRRjhFJAMpLVrAe+5cSJ8+hSVvXrHTISJyGs5yzoxMlraayP79SqSmAm5uYmdERJSGI9gZ0LdoAYkgcBSbiMiJNWmiR3y8FGfO8KqOROQ82GBnwFSiBFKLF4fH7t1ip0JERBmoX98AhULgcn1E5FTYYL9GSuvWUPz+O6RPn4qdChERvYJKJaBWLQMOHFBCsM1CIkRE2cYG+zX0rVpxmggRkZNr0kSPO3fkuHmTpxURkXNgg/0apuLFkVqiBDx27RI7FSIiysC776Zd1XH/fk4TISLnwAb7DVJat4bi1ClInzwROxUiInqFwEALKlQwYt8+NthE5BzYYL/B82kiHrzoDBGR03r3XT3On1fgyRP+WiMi8bESvYGpWDGkliwJJVcTISJyWs2apU0T4WoiROQM2GBnQkqrVlCcPg3p48dip0JERK9QvLgJISEmzsMmIqfABjsTUlq3TpsmwlFsIiKnJJEATZvqceKEOxITJWKnQ0Qujg12JpiLFoWxbFl47NghdipERJSBZs30MBolOHzYXexUiMjFscHOpJR27aA4fx6yu3fFToWIiF6hcmUj/P3NnCZCRKJjg51J+jZtAICj2ERETkomS7vozMGDShgMYmdDRK6MDXYmmYOCYKhWjQ02EZETa95cj8REKU6c4DQRIhIPG+wsSGnbFm7XrkF+9arYqRAR0SvUrWuAl5cFe/dymggRiYcNdhboW7eGIJPBY/t2sVMhIqJXcHcHQkP12LdPCZNJ7GyIyFWxwc4Ci78/DHXrwmPnTkAQxE6HiIheoUULPWJiZDh9WiF2KkTkouRiJ/Dc8OHDoVQqIZVKIZPJEBYWJnZKr5TSti3Uo0fD7Y8/kFq1qtjpEBHRCxo2NECptODnn5WoVcsodjpE5IKcpsEGgClTpsDHx0fsNF5L37w5LBMmwHPrVsSzwSYicjqengIaNjRg714PTJ2aACmP1RKRg7HsZJHg7Q1906Zp00SMHBkhInJGzZvr8eSJDBcuuImdChG5IKdqsGfMmIHx48cjIiJC7FReK6VDB0jj4qA8fFjsVIiI6BVCQ/VwcxPw888eYqdCRC7IaaaITJs2DRqNBvHx8Zg+fToCAwNRunTpdM+JiIiwNt9hYWHQarVZjiOXy99qu3Q6dIAwdiz8du+GqUcPx8TMIsbMfXEZkzEp83x9BdSpY8CePUpMmpQAiUTsjIjIlThNg63RaAAAvr6+qFq1Km7evPlSgx0aGorQ0FDr7aioqCzH0Wq1b7Xdi3zatIHqhx8QfesWBF9fh8TMCsbMfXEZM/fGDAwMdGhsV9GqVQrGjlXj8mU3lCuXKnY6RORCnGKKiF6vR0pKivX7S5cuoWDBgiJn9XopHTpAYjDAY88esVMhIqJXaNpUD7lcwO7dvOgMETmWU4xgx8fHY86cOQAAs9mMOnXqoEKFCuIm9Qap5cohtUgReGzZguTu3cVOh4iIXqBWC6hb14BduzwwYUIip4kQkcM4RYOdN29ezJ49W+w0skYiQUqHDvCZNQuyBw9gDg4WOyMiIofIKdctADhNhIjE4RRTRHKqlI4dIUgk8PjpJ7FTISJyqClTpmD27NlO3VwDnCZCROJgg50N5qAgGOvUgeemTYDFInY6RET0ArU6bTWRXbs8IAhiZ0NEroINdjYld+4M+f37UJw6JXYqREQOk1OuWwAArVun4P59OS5f5kVniMgxnGIOdk6mb94cFm9veG7aBGPNmmKnQ0RkdznqugUAuncHxo8XEBGhQaNGZofEzArGZMycGFOsuDklJhvsbBI8PJDSpg08tm2DZPp0CCqV2CkREdlVTrtuAQDUravBpk1yjB4d9drVRMReE50xGTOnxBQrrpgxs3LNAk4RsYHkTp0gTU6GcvdusVMhIrKrnHjdAgBo0yYFDx7Ice4cp4kQkf1xBNsGUqtUgalwYXhu3oyULl3EToeIyG5y4nULAKBZMz0++UTAjh0eqFyZy/URkX2xwbYFiQTJnTvDJywMsjt3YH7nHbEzIiKyixx53QIAPj4CGjXSY9cuD0yZkgCZTOyMiCg34xQRG0nu1AmCTAbPDRvEToWIiF6hbdsUREbK8PvvCrFTIaJcjg22jVjy5YO+ceO0NbFTefiRiMjZhIYa4OlpwY4dHmKnQkS5HBtsG0ru1g2yyEgoDx0SOxUiInqBh4eApk312LPHA0aj2NkQUW7GBtuGDI0awZwvHzzXrxc7FSIieoW2bVMQFyfFr7+6i50KEeVibLBtSS5HcufOcD90CNJHj8TOhoiIXlC/vgF+fhZs385pIkRkP2ywbSy5a1dILJa0udhERORUFAqgZcsU7NunRHLya644Q0SUDWywbcxcqBAMderA88cfAfPrL8lLRESO9957KUhOlmL/fqXYqRBRLsUG2w50PXtC/s8/cD96VOxUiIjoBdWqGREUZMLWrZwmQkT2wQbbDvRNm8IcEADVmjVip0JERC+QSoH27VNw9Kg7oqL4a5CIbI+VxR4UCiR36wb3gwche/hQ7GyIiOgF772XArNZgp07OYpNRLbHBttOknv0AAQBnuvWiZ0KERG9oEQJE0qXTuU0ESKyi9c22CaTCQ8ePLDevnv3rr3zyTXMBQrA0KhR2smOvLIjEdkZ63XWdeiQjPPnFbh9WyZ2KkSUy7y2wZ4/fz7WrVuHhQsXwmQyYePGjY7KK1fQ9e4NWWQkJLt2iZ0KEeVyrNdZ17ZtCiQSAVu3eoqdChHlMm8cwf7kk09Qt25dLF68GIIg2DUZi8WCjz/+GGFhYXaN4yiGhg1hKlAAsiVLxE6FiHI5R9fr3CB/fgvq1DFiyxYPWCxiZ0NEuclrG2yFQgEAqFixImrUqIHLly/bNZmff/4ZQUFBdo3hUDIZknv2hPTIEcivXxc7GyLKxRxdr3OLTp2Scf++HKdPK8ROhYhykdc22H369LF+X61aNcyePdtuiURHR+PcuXNo3Lix3WKIIblHDwju7lCtXCl2KkSUizmyXucmzZvroVJZsHkzT3YkItuRv+5Bf39/AMA///wDLy8vBAYGQq/XY+fOnZBIJGjTpg3c3d1tksiqVavQs2dPpKSkZPiciIgIREREAADCwsKg1WqzHEcul7/Vdm9NqwW6doXnTz/Bbc4cwNfXIWEd/jpdKKZYcRmTMV/HkfU6N/H0FNCqlR67d3tg+vQEsdMholzitQ32cwsWLMDo0aPh5+eHNWvW4PHjx3Bzc8PSpUvx4YcfZjuJs2fPwtfXF4ULF8aVK1cyfF5oaChCQ0Ott6OiorIcS6vVvtV22REwdCjcVq9GyuLF0A0c6JCYYrxOV4kpVlzGzL0xAwMDbbZfe9fr3KhTp2Rs3OiJvXuVGDRI7GyIKDfIVIMdGRmJwMBACIKA06dP4+uvv4ZCocAHH3xgkySuXbuGP/74A+fPn4fRaERKSgoWLlyIESNG2GT/YhMqVoSxShWoVq2C7v330y4jRkRkB/au17lR9epGBAebsHmzBxtsIrKJTDXYCoUCKSkp+Oeff6DVauHj4wOz2YxUG63v3L17d3Tv3h0AcOXKFezatSvXNNfPJfXvD82wYXA/fBiGXDbPnIich73rdW4klQIdO6Zg/nwv/PNPKpRKsTMiopwuU0OptWvXxtSpU7Fo0SI0aNAAAHDnzh3kyZPHnrnlKvoWLWDOmxeqFSvEToWIcjHW67fTsWMyBEGCdet4hJGIsi9TI9h9+/bFxYsXIZPJULZsWQCARCJJd9a6rZQpUwZlypSx+X5F5+YGXe/e8Jk9G/Lr12EqXlzsjIgoF3Jkvc5NQkLMqFnTgNWrFejfH5BIxM6IiHKy1/6p/tlnn2Hr1q24e/cuypcvby3WAFCkSJF0t+nNknv3hqBUQrVsmdipEFEuw3qdfV26JOPWLQlOneKa2ESUPa9tsHv16gWj0YjvvvsOQ4cORXh4OE6fPg29Xu+o/HIVi0aD5I4d4fnTT5BGR4udDhHlIqzX2deqlR7e3gJ+/JGXTiei7HntFJHixYujePHi6Nq1K+Li4nDu3Dn8+uuvWLJkCUJCQlCxYkVUrFgxd1190c50AwdC9cMP8FyzBkmjR4udDhHlEqzX2efhIaBzZwvWrVNi+nQJvL15uXkiejuZPpvDz88PjRo1wtixY7F06VK89957iI2Nxdy5c7Fjxw575pirmIoWhb5RI6hWrwYMBrHTIaJcyBH12mKx4OOPP0ZYWJhN9ucs+vWzQK+XYscOXtmRiN5epk5yfJFMJrOejNirVy+YTCZb55WrJQ0aBG3XrvDYvh0pXbqInQ4R5WL2qtc///wzgoKCXnv13ZyoShUBJUumYsMGT/TsmSx2OkSUQ2WqwY6KisLmzZtx9+7dl+bzLViwAHL5W/XpLstYpw5SS5WC15IlSOnUiReeISKbcUS9jo6Oxrlz5/Dee+9h9+7d2d6fM5FI0k52/OILX/z9txwlS3IAiYiyLlOV9uuvv0ZgYCA6d+4MhYJnV2ebRIKkYcOg/vBDuB88CEOTJmJnRES5hCPq9apVq9CzZ89cN3r9XMeOKfjqKx+sX++JqVMTxE6HiHKgTDXYDx8+xPTp0yHlSKvNpLRuDe+wMHgtXswGm4hsxt71+uzZs/D19UXhwoVx5cqVDJ8XERGBiIgIAEBYWBi0Wm2WY8nl8rfaLjvkcjmKF9egXTsLtm5VYe5cBTzsPB1brNfJmIyZE+PmlJiZarArV66Mv/76i+uo2pKbG3SDB8N38mS4nTmD1KpVxc6IiHIBe9fra9eu4Y8//sD58+dhNBqRkpKChQsXYsSIEemeFxoaitDQUOvtqKioLMfSarVvtV12PI/ZsaMCmzZpsXq1Dh072nekXszXyZiMmdPiihkzMDAw09tkqsHu378/Pv30U+TNmxe+vr7pHhs2bFjWsiSr5G7d4P311/BavBixK1eKnQ4R5QL2rtfdu3dH9+7dAQBXrlzBrl27Xmquc4NatYx45x0T1q3ztHuDTUS5T6aOIS5evBhSqRRBQUHQaDTpvujtCZ6e0PXrB49ffoH8xg2x0yGiXID12jYkEqBnTx1On3bHtWs8kZ+IsiZTVePPP//EkiVL4GHviWguSNe/P1TffQevRYsQN3++2OkQUQ7nyHr9fPm/3KpTpxSEhflg3Tqe7EhEWZOpEexChQohMTHR3rm4JItGg+QePeCxdStk9++LnQ4R5XCs17bj729B8+Z6bNniiVy6YAoR2UmmRrDLlCmDGTNmoEGDBi/N6WvUqJFdEnMlSUOHQrV2LbwWLUL8zJlip0NEORjrtW316KHDzp0e2LXLA507s8smoszJVIN97do1aDQaXLp06aXHWLCzz5I/P5K7dIHnxo1IHDkSliycpUpE9F+s17ZVu7YRRYumYs0aFRtsIsq0TDXYU6ZMsXceLi9p+HB4rl8Pr/BwJEydKnY6RJRDsV7blkQC9OmTjM8+88XFi24oXz5V7JSIKAfglWOchDk4GCkdOsBz3TpInz0TOx0iIvpXx47J8PCwYPVqldipEFEOwQbbiSR+8AEkRiO8wsPFToWIiP7l4yPgvfdSsGOHB2JjJWKnQ0Q5ABtsJ2IuUgQp7drBc9UqjmITETmRPn100Osl2LjRU+xUiCgHeG2D/eTJE0flQf9KHD0aktRUeC1eLHYqRJSDsF7bV5kyJlStasDatSpYLGJnQ0TO7rUnOYaFhUEQBFSsWBGVKlVC6dKlIZfb/opWRqMRU6ZMgclkgtlsRo0aNdC5c2ebx8kJzIULI6VDB6jWrEHSkCGw5M0rdkpElAM4ql67sr59kzF8uBqHD7ujcWOD2OkQkRN7bfWdP38+nj59inPnzmH37t1YsGABSpQoYS3g/v7+NknCzc0NU6ZMgVKphMlkwuTJk1GhQgUUL17cJvvPaRJHjYLHli3wWrSIK4oQUaY4ql67shYtUpA3rw9WrFCxwSai13rj8EbevHnRvHlzNG/eHEajEZcvX8b58+exfft2eHh4oGLFimjYsCECs7F2s0QigVKpBACYzWaYzWZIJK57Iom5UCEkd+kC1Q8/pI1ic11sIsoER9RrV6ZQAL166TBnjg9u3pSjaFGT2CkRkZPK0vFDhUKBypUro3LlygCABw8e4Pz587h//362C7bFYsH48ePx5MkTNG3aFMWKFcvW/nK6pJEj4bl5M7znz0f8rFlip0NEOYw967Ur69UrGQsXemPFChW+/DJe7HSIyElla4JecHAwgoODbZKIVCrF7NmzodPpMGfOHNy/fx8FCxZM95yIiAhEREQASJtvqNVqsxxHLpe/1XbZ8VYxtVpYBg6E55IlcPvkEyCL02VyzOvMgTHFisuYjJkdtqzXrkyrtaBduxRs3uyB8eMT4OsriJ0SETkhpzsDRqVSoUyZMrhw4cJLDXZoaChCQ0Ott6OiorK8f61W+1bbZcfbxpQOHow8q1bBPGECYpcscUjM7HCVmGLFZczcG5MjyjnL++8nYdMmT2zY4InBg3Vip0NETsgp1sFOSEiATpdWpIxGIy5duoSgoCCRsxKfRauFbvBgeOzeDbeLF8VOh4iIAJQta0L16gasXKmC2Sx2NkTkjJxiBDs2NhaLFi2CxWKBIAioWbOmdd6gq0saPBieq1bB56uvEL1hg9jpEBERgAEDdBg4UIN9+5Ro2VIvdjpE5GQy3WBfuXIFR48eRWxsLNRqNerVq4eyZcvaJIlChQphFk/keyXB2xtJI0bA94sv4H7sGAz16omdEhE5OXvWa0rTtKkehQqZsGSJFxtsInpJpqaIHDx4EPPmzYOfnx+qVasGtVqNBQsWWE84JPvS9e4NU3AwfKZOBY9HEtHrsF47hkyWNop99qwCf/zhJnY6RORkMjWCvXPnTnz66acICQmx3lerVi3MnTs33UmHZCdKJRImTIBm2DB4/PQTUrp0ETsjInJSrNeO06VLMubM8caSJV6oUiVW7HSIyIlkagQ7MTERBQoUSHdfYGAgkpKS7JIUvUzfpg2MFSvCZ+ZMSJKTxU6HiJwU67XjqFQCevXSYd8+Je7dk4mdDhE5kUw12CVLlsSaNWtgMKRdGlav12Pt2rUueylzUUgkiJ8yBbKnT6EKDxc7GyJyUqzXjtWvnw4yGbBsmUrsVIjIiWRqisjAgQMxf/589O3bF15eXkhKSkLx4sUxcuRIe+dH/5FatSpSWraE1+LFSO7eHZZ8+cROiYicDOu1Y+XLl3bhmR9/9MTo0YnQaHjhGSLKZIOtVqvxxRdfICoqCnFxcVCr1fD397d3bvQKCZMmIc+BA/D58kvELVwodjpE5GRYrx1vyJAkbN7sidWrVRg9mlNxiCiLF5rRarUoUqQI1Go1LBYLLBaLvfKiDJgLFUpbG3vLFridOSN2OkTkpFivHadkSROaNNFj+XIVkpMlYqdDRE4gwxHslJQUeHh4AABiYmKwfPlyXL161XrFxec2btxo3wzpJUkffgjPzZvhO3kyonbvTlsviohcFuu1+IYPT0S7dgH48UdPvP8+L59O5OoyHMH+9ttvsXTpUgDA0qVLIZfLMXnyZCiVSsycORNVqlTBwIEDHZYo/T9BpULCZ59BcekSPPkLk8jlObJeG41GTJgwAePGjcOYMWOwadMmm+w3p6taNRXVqxsQHq5CaqrY2RCR2DJssJs3b46EhAQAwLVr1zB06FCEhIRAIpEgJCQEQ4cOxe7dux2WKKWX0rYtDNWrw/urryCJixM7HSISkSPrtZubG6ZMmYLZs2dj1qxZuHDhAq5fv26Tfed0w4cn4dEjObZv9xA7FSISWYYN9oIFC9C7d28AgEwmg+zfaQgqlQoJCQlwd3dHTEyMY7Kkl0kkiJ82DdL4ePh89ZXY2RCRiBxZryUSCZRKJQDAbDbDbDZDIuG8YwBo1MiAUqVSsWiRFzjlnci1Zdhg9+jRAz/99BMAoGjRojh//jwAoHz58pg3bx7mzJmDIkWKOCZLeiVTmTLQ9e8P1Q8/wO2PP8ROh4hE4uh6bbFYMG7cOAwYMAD/+9//UKxYMZvtOyeTSIAPPkjCjRtu+PlnpdjpEJGIJIIgvHHRTp1OB0EQ4OXlBaPRiF27diElJQUtW7aEWq12RJ6v9OjRoyxvo9VqERUVZYdsxIkpSUpCnvr1YdFo8GzvXkAut3vMjLhKTLHiMmbujRkYGGiz/TqyXut0OsyZMwf9+vVDwYIF0z0WERGBiIgIAEBYWBiMRmOW9y+Xy2EymWySq6Nims1A+fJu8PAQcPq0CZkZ3M+Jr5MxGVOsuGLGVCgUmd8mM09Sqf7/ClUKhQIdOnTIenZkF4KXF+KnTYNm4ECoVqyAbtAgsVMiIhE5sl6rVCqUKVMGFy5ceKnBDg0NRWhoqPX22/wBI/YfPm9r2DAPjB6txo8/JuLddw0OiZlVjMmYOTWumDGzMhiSqXWw58yZg6tXr6a77+rVq5g7dy6AtHl4JB598+bQN24M79mzIfvnH7HTISIR2bteJyQkWJf/MxqNuHTpEoKCgrK1z9ymffsUFCxowvz53njzMWIiyo0y1WD/9ddfKFGiRLr7ihcvjtOnTyMsLAxjx47FrFmz7JIgZYJEgvgZMwAAvp98AlZ0Itdl73odGxuLL774Ah999BEmTJiAcuXKoXLlytlNO1dxcwM+/DAJFy8qcOSIu9jpEJEIMjVFxM3NDXq9Hp6entb79Ho93N3dMWbMGEilUvTr189uSdKbmYODkThhAnw/+wweW7YAQ4aInRIRicDe9bpQoUIcUMmEjh2TMX++F+bN80aDBoZMzcUmotwjUyPY5cuXx9KlS5GcnAwASE5OxvLly1G9enUoFAqYzWaMHDnSronSm+n69IGxShX4TpkCPH0qdjpEJALWa+egUKStKHL2LEexiVxRphrs3r17IyUlBf3798eAAQPQv39/JCcno2/fvgAAd3d3VKlSxZ55UmbIZIibMweS5GTIRo8WOxsiEgHrtfPo2jUZBQqYMGcO52ITuZpMTRHx8vLChAkTEBsbi+joaGi1Wvj5+dk5NXobpmLFkDh6NHxmzoQyNBT6Nm3ETomIHIj12nkoFMCoUUn46CM/HDjgnqkVRYgod8jUCPZzarUaRYoUgY+PDywWCyy8VJVTSho2DJaqVeE3YQKknCpC5JJYr51Dx47JCAkxYc4cH17dkciFZGoEOyYmBsuXL8fVq1etyzM9t3HjxmwnERUVhUWLFiEuLg4SiQShoaFo0aJFtvfrsuRymJYtg1v16vAbNw4xq1eDZ9gQuQZ712vKGjc3YNSoRIwapca+fUq0aKEXOyUicoBMjWAvXboUcrkckydPhlKpxMyZM1GlShUMHDjQJknIZDL06tUL8+bNw4wZM7B//378w/Wcs6dkSSRMmADlwYPw3LBB7GyIyEHsXa8p69q3T0GRIqmYPdsbvGwEkWvIVIN9/fp1DB06FCEhIZBIJAgJCcHQoUOxe/dumyShVqtRuHBhAICHhweCgoIQExNjk327Ml3//jDUqgWfKVMgu3NH7HSIyAHsXa8p6+RyYNy4RFy/7oYtWzzEToeIHCBTDbZUKoVMJgOQdmnchIQEuLu726UJjoyMxJ07d1C0aFGb79vlSKWInT8fcHODevhwwGgUOyMisjNH1mvKvJYt9ShXzog5c7xh4LmORLlepuZgFy1aFOfPn0e1atVQvnx5zJs3DwqFAkWKFLFpMnq9HnPnzkXfvn3TXSThuYiICERERAAAwsLCoNVqsxxDLpe/1XbZIWpMrRbmJUug6NIFeRctgvnfKz7aNaYDiRFTrLiMyZiZ4ah6TVkjlQITJiSiWzd/rF2rwoABujdvREQ5lkQQ3rw6p06ngyAI8PLygtFoxK5du5CSkoKWLVtCrVbbJBGTyYSZM2eifPnyaNWqVaa2efToUZbjaLVaREVFZXm77HCGmL4ffwzP9esR/eOPMNat65CYjiBGTLHiMmbujRkYGGiz/TqiXr8N1us0Xbr446+/5Dh5MhLe3oJDYr4KYzJmTo0rZsys1Oo3ThGxWCxYuXIl3N3TrkSlUCjQoUMH9OzZ02bFWhAEhIeHIygoKNPNNWVNwhdfwFS0KNQffghpZKTY6RCRHTiiXlP2TJiQgJgYGZYs8RI7FSKyozc22FKpFJcuXYLEjsu8Xbt2DceOHcOff/6JcePGYdy4cTh37pzd4rkiwcMDseHhkCQmQj1sGGAyiZ0SEdmYI+o1ZU+FCqlo2TIF4eEqPHmSpUtREFEOkqn/3S1btsSmTZtgslNTVrJkSWzatAlz5szB7NmzMXv2bFSqVMkusVyZqWRJxIeFwf233+A9Z47Y6RCRHdi7XlP2TZyYAJNJgjlzvMVOhYjsJFMnOe7btw9xcXHYs2cPfHx80j323Xff2SUxso+UTp2gOH0a3t98A2OVKjCEhoqdEhHZEOu18wsJMaNvXx2WLVOhf38d6tUTOyMisrVMNdgffvihvfMgB4qfOhWKixeh/vBDPNuzB+Z/1yAnopyP9TpnGDkyEZs3e2L6dB/88ovY2RCRrWWqwS5durS98yBH8vBAzPLl0DZvDk3//ojavRuCF0+4IcoNWK9zBrVawMiRifjiC1/s35+KypXFzoiIbClTc7BTU1Px448/4oMPPkCfPn0AABcvXsS+ffvsmhzZjzk4GLFLlkB++zb8RowALBaxUyIiG2C9zjn69tUhJMSEjz+WIzVV7GyIyJYy1WCvXr0aDx48wIgRI6xnpwcHB+MXHtfK0Yy1ayNhyhR47N8P77lzxU6HiGyA9TrnUCiAKVPi8fffEqxapRI7HSKyoUxNETl9+jQWLlwIpVJpLdgajYaX3s0FdP37Q371Krznz4cpJAQpnTqJnRIRZQPrdc7SpIkBoaEWfP21N957LwX+/jyaSJQbZGoEWy6Xw/LCFIKEhAR4e3OJoRxPIkH8l1/CULs2/MaNg+K338TOiIiygfU6Z5FIgDlzTEhOlmDmTP6MiHKLTDXYNWrUwLfffovIf68AGBsbi+XLl6NWrVp2TY4cRKFAzNKlMBUqBM2AAZDdvCl2RkT0llivc55SpdLmY69f74nLl93EToeIbCBTDXb37t2RJ08ejB07FsnJyRgxYgTUajU6cTpBriH4+SFmzRoIMhn8e/SA9MkTsVMiorfAep0zjRmTCI3GgokTfXnOOVEukKk52HK5HH379kXfvn2thxp5Kd7cx1yoEGLWroV/x47w79kTUVu2QPD1FTstIsoC1uucyddXwGefJWDUKDV+/NETPXoki50SEWVDhg3206dPM9woJSXF+n3evHltmxGJKrV8ecQuXw5N797Q9OuH6HXrAA8PsdMiotdgvc4dOnZMwYYNnvjySx80a6bnCY9EOViGDfaIESMytYONGzfaLBlyDoZ69RC7YAHUw4dDM2gQYpYvT1tPioicEut17iCRAF9+GY933w3Al196Y+7ceLFTIqK3lGGDzULs2vRt2yI+MRF+48dDPWwYYr/7DnDjyTdEzsiR9ToqKgqLFi1CXFwcJBIJQkND0aJFC4fFz+1KlDBh0KAkLF7sjS5dUlCtmlHslIjoLWTqJMfnoqKicP36dXvlQk4muWdPxE+dCo+9e6EeMQIwm8VOiYgyyV71WiaToVevXpg3bx5mzJiB/fv3459//rF5HFc2alQSChQwYdw4XxgMYmdDRG8jUyc5RkVFYcGCBbh79y4AYO3atfj9999x4cIFDBkyxJ75kch0778PGI3wnT4dgkSCuAULOJJN5MTsXa/VajXUajUAwMPDA0FBQYiJiUGBAgWyvW9Ko1IJ+OqrePTq5Y9vv/XG2LGJYqdERFmUqRHspUuXomLFili9ejXk8rSevFy5crh06ZJdkyPnoBs6FAmTJsFzxw6ohw0DjDxkSeSsHFmvIyMjcefOHRQtWtTm+3Z1jRoZ0L59Mr75xgvXrmVqLIyInEim/tfevHkTn3zyCaTS/+/HPT09kZzMZYRcRdKwYRAUCvhOmQLJgAGIWboUUCrFTouIXuCoeq3X6zF37lz07dsXnp6eLz0eERGBiIgIAEBYWBi0Wm2WY8jl8rfaLjucKeY33wDHjgETJ2px+LAJ0ixN6ny7mPbEmLkrplhxc0rMTDXYvr6+ePLkCQIDA633/fPPP6L8MEk8ugEDICgU8JswAf49eiBmxQquk03kZBxRr00mE+bOnYu6deuievXqr3xOaGgoQkNDrbejoqKyHEer1b7VdtnhTDElEmDyZA+MHKnGrFkpGDBAZ/eY9sSYuSumWHHFjPnfuvommfp7uHXr1pg5cyYOHz4Mi8WC48ePY968eWjbtu1bJ0s5U3Lv3ohdtAiKs2eh7dCBV3wkcjL2rteCICA8PBxBQUFo1aqVTfZJGevQIQWNGunx1VfeuH1bJnY6RJRJmRrBbtSoEby9vREREQF/f38cO3YMXbp0QbVq1eydHzmhlHbtYFGroR4wANp27RCzdi1MxYqJnRYRwf71+tq1azh27BgKFiyIcePGAQC6deuGSpUq2WT/lJ5EAsyaFYfGjfNgzBg/bNkSDRn7bCKnl+kzJ6pWrYqqVavaMxfKQQz16yN682Zo+vSBtk0bxC5ZArz3nthpERHsW69LliyJTZs22WXf9Gr581swdWo8Ro5UY9kyFQYPtt1UESKyj0xNEVmxYgWuXbuW7r5r165h1apVNktk8eLFGDBgAMaOHWuzfZJ9pVaogKg9e2AODISmZ09Ily4VOyUil+eIek2O16FDCt59NwUzZ/rgxg2uKkLk7DLVYJ84cQJFihRJd1/hwoVx/PhxmyXSoEEDTJw40Wb7I8cwFyiAqO3bYahfH/IPP4Tv+PHglRGIxOOIek2OJ5EAM2fGQ6Wy4IMP/LhaKpGTy1SDLZFIYLFY0t1nsVggCILNEildujS8vLxstj9yHMHbGzGrVsH80UdQ/fADtB07Qvr4sdhpEbkkR9RrEkeePBbMmROPP/9UYM4cb7HTIaLXyNRxppIlS2LDhg3o2bMnpFIpLBYLNm/ejJIlS9o7v3S4rqpzx5TMnInUypXhNmAA8rZoAdOKFRCaNLFrTK79yZiMmZ6z1Guyj6ZN9ejRQ4fFi73QoIEBtWpxKJvIGWWqwe7Xrx/CwsIwePBg61qAarUaH3/8sb3zS4frquaAmPXqQb57N9RDhsCtVSskDh+OxHHj7HZ5da79yZi5IWZW1lZ9E2ep12Q/U6Yk4MQJd4wc6YdffnkGtZpHJ4icTaYabH9/f8ycORM3b95EdHQ0/P39eWlcypCpeHFE7dkDnylT4L1oEdxPnkTs/Pkw8zNDZHes17mfSiVg0aJYtG2rxUcf+WHZslhIJGJnRUT/lekLr0qlUhQvXhw1a9aEUqnEunXrMHToUHvmRjmY4OGB+FmzEBMeDvmdOwho2hSq5cuBF+aGEpHtsV7nfhUqpGLixATs2+eBlStVYqdDRC/I9Fo/CQkJOH78OI4ePYq7d++iZMmS6Nu3r80SmT9/Pv766y8kJiZiyJAh6Ny5Mxo1amSz/ZM49K1bI7JqVfiNGwffyZOh3LsXcTNnwvzCKgdEZDv2rtfkHAYN0uHkSXdMm+aDKlWMKFcuVeyUiOhfr22wTSYT/vjjDxw5cgQXL15Evnz5ULt2bTx79gxjxoyBr6+vzRIZNWqUzfZFzsWSLx9i1qyB54YN8Jk6FXmaNEHihx8iafhwQKEQOz2iXMGR9Zqcg0QCzJsXi3ffzYOhQ9X4+edn8PXlfGwiZ/DaBnvgwIGQSqWoX78+OnfujMKFCwMAfvnlF4ckR7mIRILkbt2gb9QIvlOmwGfOHHhs24aEzz+HgUcqiLKN9do1aTQCvvsuFh07+mPkSDVWrIiBNNOTP4nIXl7737BQoULQ6XS4efMmbt26haSkJEflRbmUJW9exIaHI3rNGkgsFvj36gVN796Q3boldmpEORrrteuqWtWIyZMTcOCAEt9+y+tJEDmD145gf/7553j27BmOHj2KXbt2YeXKlShXrhwMBgPMZrOjcqRcyNC4MSLr1IFqxQp4z5+PPA0bIrlrVySOGQNLvnxip0eU47Beu7b+/XU4d84Ns2Z5o3z5VNSvzyvqEonpjQeSAgIC0LFjRyxcuBCTJ0+GWq2GRCLBuHHj8MMPPzgiR8qt3N2hGzoUkcePQ9e7Nzw3bUKe2rXhM20apM+eiZ0dUY7Deu26JBJg9ux4lChhwrBhaty9KxM7JSKXlqWZWiVLlsTgwYOxdOlS9OvXD/fv37dXXuRCLAEBSJg+HZFHj0LfogVUS5ciT40a8Jk8GdJHj8ROjyhHYr12PZ6eApYtiwEA9OunQWIiF8cmEstbnQqhUChQp04dTJw40db5kAszFyqEuG++QeSRI9C3aQPVqlXIW7Mm/D74AG6XL4udHlGOxHrtWt55x4wlS2Jw65YcH3ygBmcHEYmD5xqT0zEXKYK4efMQeeIEdP36QXngAAKaNYO2bVt4/PQToNeLnSIRkdOqU8eIqVPjERGhRFiYt9jpELkkNtjktMzBwUj4/HM8PXMG8VOmQBoTA/XIkchXuTJ8Pv0UbhcvAgLXfCUielHfvsno3VuHxYu98cMPnmKnQ+Ry2GCT0xN8fKAbNAiRx44hauNGGOrWhWr9egS0aAG3ChXg9fXXkF+/LnaaREROZdq0eDRqpMfEib44dMhd7HSIXAobbMo5JBIY69RBbHg4npw/j7hZsyBotfD++mvkadgQAQ0bwvurr+B25gw48ZCIXJ1cDoSHx6JUqVQMHqzG5ctuYqdE5DLYYFOOJPj6IrlHD5gOHsTTs2cRN306LFotvMLDEdCuHfKWLw/1kCHwXLcOsvv3OZWEiFySSiVg9eoYqNUW9Oql4fJ9RA7y2gvNEOUElrx5kdyvH5L79YMkPh7uR45AeegQ3I8fh8euXQAAc758MFSvDmPVqkitWBGppUoB7jxkSkS5X758FqxbF4P27f3RrZs/tm+PglYrdlZEuRsbbMpVBF9f6Nu2hb5tW0AQIL95E4oTJ+B+6hTcT52C544dac9TKJBasiRSS5eGqUwZpJYsCVOxYrBotWlXbCAiykWKFTPhhx9i0KmTP3r08MfhwzyqR2RPbLAp95JIYCpWDKZixZDcty8gCJA+egTFhQtQnD8Ptz//hPKXXyDbsMG6icXPD6bChWEKCYGpcGGYg4NhLlAg7StvXsCNcxiJKGeqUCEVy5fHoE8ff7RtK2D1agm8vdloE9kDG2xyHRIJLEFB0AcFQd+yZdp9ggDpkydwu34d8hs30r5u34bi99/huXVrus0FiQSWgACY8+WDPCgIvn5+sGi1sPj7w6LRpH35+aV9+fpC8PFJO8uIiMhJ1KtnxHffxWLwYDV699bghx9ioFKxySayNf72J9cmkcCSPz8M+fPDUL9++sf0esgePoT8n38g++cfyB4/hvTJE8iePAEeP4by3DlIo6Igec2KJRZPTwg+PrB4eUHw9obg5ZX2/fN/Vaq0Ly8vWP79N91zvL0h+PhAUKns/EYQkato1kyPNWtM6NVLgT59NFi7NgYeHmyyiWyJDTZRRpRKmIsUgblIkZce0mq1iIqKAiwWSOLjIY2JSfuKj4c0Lg7S+HhIEhIgTUhI+zcxEZKkJEgTEyGPjEz7XqeDJCkJEpPpjakIUing64s8Pj6w+PqmjZKr1RDUapifj6JrtTDnyQNL3rww58nDkzjJLhYvXoxz587B19cXc+fOFTsdeksdOgiIiYnDiBF+6NVLg9WrOZJNZEtssImyQypNa3LV6lc24pliMPx/s/288U5MhCQxEdKkpLR/ExLgaTTC+PRpWgMfGwv5/ftp38fFvXK3Zq0W5qCgtK+CBWEqWBDmkBCYihSBOTAQkHKVTsq6Bg0aoFmzZli0aJHYqVA2tW+fAgAYOdIP3bv7Y+3aaPj4sMkmsgU22ERic3eHxd0d0Ghe/zStFnFRUS8/kJqaNnr+7BlkkZGQPX2aNpXl0SPIHj2C/Pp1KA8ehMRgsG5i+Xd0PrVkSZj+XU0ltVw5WN6QA1Hp0qURGRkpdhpkI+3bp0ChEDB8uBpduvhj3bpoaDRssomyiw02UU7n5gZL3ryw5M2LDCebWCyQPn0K+d27kN+6BfnNm5DfuAH3EyfguWWL9WmmoCCkVqgAY5UqMFauDDRs6JCXQLlPREQEIiIiAABhYWHQvsXCy3K5/K22yw5XjNmnDxAQYELXrm7o3Dkvdu0yITjYvjEdhTFzX9ycEtNpGuwLFy5g5cqVsFgsaNy4Mdq1ayd2SkS5h1QKS/78MObPD2PNmukeksTGwu3KFbj9+ScUFy/C7fx5eOzZAwAQPD2hqVoVxlq1YKhXD6lly3JqCWVKaGgoQkNDrbejXnX05Q2s5zo4kKvGrFYN+OEHBfr316BuXRnWr49G8eJvPj8kOzEdgTFzX1wxYwYGBmZ6G6dosC0WC5YvX45PP/0U/v7+mDBhAqpUqYICBQqInRpRrieo1TDWqQNjnTrQ/Xuf9MkTKP74A74XLkB26BB8vvoK+OormAMCYKhfH/p334WhYUMInp6i5k5EtlOrlhFbtkShZ09/tG+vxcqVMahWzSh2WkQ5klMMRd28eRP58uVD3rx5IZfLUatWLZw5c0bstIhcliVfPuhbtYJ5/nw8O3QITy5cQOyCBTDUrg1lRAQ0gwYh3//+B3X//vDYvh2S5GSxUyYiGyhTxoQdO6Kg0VjQpYs/tmzxEDslohzJKUawY2Ji4O/vb73t7++PGzduiJgREf2XJSAAKR07IqVjR8BkguLUKSj37YPHzz/DY/9+WDw9oW/WDMldusBYqxankeRi8+fPx19//YXExEQMGTIEnTt3RqNGjcROi2yoYEEzdu58hoEDNRgxQo1bt+T46KNE/rcmygKnaLAziyfNMKYzxBQrrlPFbNsWaNsWZosFluPHIf3xR3hs3QrPrVshFC4Mc79+sPTtC+TJY7uYduQqMW1h1KhRYqdADqBWC1i/PhqffOKHBQu8cf26HPPnx8HLiyuMEGWGUzTYGo0G0dHR1tvR0dHQvGK5MJ40w5jOEFOsuE4bs3RpYNo0YOJEeOzdC8/16+H+2WcQpk1DStu20L3/PlL/9z/bxrQxsWNm5cQZIkdRKIC5c+NQsmQqpk/3QatWWixbFoOiRTO+ei0RpXGKAz5FihTB48ePERkZCZPJhJMnT6JKlSpip0VEWeHhgZT33kP0Tz8h8uhRJHfvDuWePQho1gz+XbtC8euvgMDRL6KcRCIBBg3S4ccfoxEdLUWrVgHYs0cpdlpETs8pGmyZTIb+/ftjxowZGD16NGrWrIlgeyzCSUQOYSpaFPEzZuDp2bOI//RTyK9dg7ZrV2hbt4b7kSNstIlymNq1jdi3LwpFi5owaJAGkyb5Qq8XOysi5+UUU0QAoFKlSqhUqZLYaRCRDQk+PtANHQpdv37w3LwZXt9+C/8ePWCoVg2J48fDWKOG2CkSUSYFBZmxdWsUwsJ8sGSJF86cUWDRolgUK2bb9bKJcgOnGMEmolxOqURyr16I/PVXxH35JeT370PboQPU/ftDduuW2NkRUSYpFMDkyQlYuTIajx9L0axZAJYvV8FiETszIufCBpuIHEehQHKfPnh6/DgSPvkE7sePI0+jRvCZMgWSxESxsyOiTHr3XQMOHnyG2rUNmDzZF926+ePBA5nYaRE5DTbYROR4Hh5I+vBDRJ44geQuXaBavhx56teHcscOzs8myiHy5LFg9eoYzJwZh/Pn3dCwYQC+/14FMxcZIWKDTUTisQQEIH7WLETt2QNzvnzQDBsGecuWkD14IHZqRJQJEgnQs2cyDh9+hpo1jfj8c1+0bavF5ctuYqdGJCo22EQkutTy5RG1axfiZsyA5NQpBDRuDM9Vq8CJnUQ5Q1CQGWvWxODbb2Px4IEMzZtrMXGiL+LiJGKnRiQKNthE5BxkMiT37YvUc+dgrFwZfpMmwb9rV0gfPRI7MyLKBIkEaN8+BceORaJ/fx3WrvVEnTp5sHy5Ckaj2NkRORYbbCJyLoUKIWb9esTNng238+eRp0kTKPfsETsrIsokX18BU6cmYP/+ZyhTxoTJk33RsGEebN0q4UEpchlssInI+UgkSO7eHc/274epUCFoBg2C78cfg1e2IMo5Spc2YcOGaKxdGw13dwHdurmhWbMA/PKLO89lplyPDTYROS1z4cKI2rEDicOHQ7VuHbRt20J2757YaRFRJkkkQKNGBhw48AwrVpig00nQr58/mjfXYvduJVccoVyLDTYROTc3NyROnIjoVasgf/AAAc2awf3AAbGzIqIskMmAHj0sOHIkEnPnxiIpSYrBgzVo0CAPfvjBEykpPBmSchc22ESUIxiaNMGzffvSpoz06wevRYu4ZjZRDuPmBnTtmoKjRyMRHh4DlcqC8eP9UKVKXsyY4c2L1VCuwQabiHIMc8GCiN62DfrWreHz5ZfwGzECSEkROy0iyiKZDGjdWo+9e6OwdWsUatUyIDzcCzVr5kG3bhrs2qWEwSB2lkRvTy52AkREWSF4eCB28WKkliwJn1mzIHvwADErVkDQaMROjYiySCIBqlc3onp1Ix4+lGLjRk/8+KMnhgzRwM/PglatUtChQwqqVDFCyiFBykH4cSWinEciQdLIkYgJD4fi0iVo27WD7P59sbMiomwICrJgzJgk/P57JH74IRqNGumxZYsH2rfXomrVvPj0Ux+cPKmAySR2pkRvxhFsIsqx9K1bIzpPHmj694e2TRtE//ADTGXLip0WEWWDTAY0bGhAw4YG6HQS7N+vxJ49Svz4oworV3rBz8+C+vX1aNzYgHr1DAgI4OLa5HzYYBNRjmasXh1R27dD06MHtJ06IWbNGhirVhU7LSKyAZVKwHvvpeC991Kg00lw+LA7Dh5U4tAhd+zY4QkAKFkyFbVrG1CjhhFVqxrZcJNTYINNRDmeqVgxRG/bBv8uXaDp1g2xy5fDUL++2GkRkQ2pVAJatdKjVSs9LBbg8mU3HD/ujl9/dce6dSosX+4FAAgJMaFiRSMqVEhF/foS5M8vgZcXVxwix2KDTUS5gjkoCFHbtsG/Wzdo+vZFzNKlMDRpInZaRGQHUilQvnwqypdPxfDhSTAa0xruM2cUOHNGgd9+c8e2bZ7/Pjs/QkJMKF06FcWKmVCsmAlFi5oQEmKCtzcbb7IPNthElGtYAgIQ9dNP8O/eHZpBgxDz/fcwhIaKnRYR2ZlCAVSunIrKlVMxZIgOAPD4sRR37/rj999T8Ndfbvj7bzfs26eExfL/F7XRas0oVMiMAgVMCA42I39+MwIDzcif34KAADO0Wgvk7JToLfBjQ0S5iuDnh+j169NGsgcORMyyZTA0bix2WkTkYPnzW/C//wmoWTPJep/BANy+Lcft23LcvSvHnTsy3L8vx4ULCuzZI4PJlP6KkhKJALXaAn9/CzSatC8/Pwt8fQX4+lrg42OBt7cAb28LVCoB3t4CChQADAYpPD0FeHoKcHNz9CsnZ8AGm4hyHcHPD9E//gj/rl2hGTAA0atXw1ivnthpEZHI3N2BUqVMKFXq5bX+zGbg2TMpnjyR4ckTGSIjpXj2TIZnz6SIiUn7un1bjvh4KeLipNDrX3d593zW79zcBHh4/P+XUpn+3xe/njfmKlVa065SCfDyet7I/39j7+5uhzeIbEb0Bvu3337D5s2b8fDhQ3z55ZcoUqSI2CkRUS7wvMnWduoEzfvvI3rDBqRWrix2WrnChQsXsHLlSlgsFjRu3Bjt2rUTOyWibJPJgHz5LMiXzwIg9Y3P1+uBxEQpEhIkSEqSIilJAp1OAqnUF0+fJkGnkyA5WYKUlP//0uvT/k1OTvs+Kkqa7r6052fuEiVKpQA/PwvUagvy5pXB19cPWq0FWq0FefOa/30tZgQFmXmSpwhEb7CDg4Px0UcfYenSpWKnQkS5jKBWI3rdOmjfew/+vXsj6qefYCpVSuy0cjSLxYLly5fj008/hb+/PyZMmIAqVaqgQIECYqdG5FBKJaBUWhAQAABm6/1arQVRUclvvV+LBdDr05rtpCTJv427FImJEiQmShEfL0FCghTx8VLExkoRGytBYqIMFy8qEB0tRWLiyw26n58FQUFmFCqUdnLnO++YUbRo2smeGg2XNbQH0RtsFmUisidL3rxpI9nt28O/e3dE7dwJc3Cw2GnlWDdv3kS+fPmQN29eAECtWrVw5swZ1nIiG5FKYZ0motVmbhutVouoqCgAQEoKEBmZNs3l8WMZHj2S4Z9/ZHjwQIZr1+Q4cECJ1NT/n96i0Zj/nTaTijJl0lZmKVrUBJnMHq/OdYjeYGdFREQEIiIiAABhYWHQZvaT9x9yufyttssOxsxdMcWKy5jZoNXCsncv5A0bIk+fPkg9ehRQq+0b8w3E+uxmV0xMDPz9/a23/f39cePGjZeex3rNmIwpXsyMxxAEmM2puHcPuH5dgr//Tvu6fNkN69YpkJKS1nh7egqoUkVAjRoCata0oFYtAX5+b47rCDklpkMa7GnTpiEuLu6l+7t27YqqWbjiWmhoKEL/s+TW87/WsuK/f+U5CmPmrphixWXMbMqTB4ply+DfvTuEdu0QvX49np8lJPbrDAwMdGhsR2C9ZkzGdN6YPj5AlSppX8+ZzcCtW3JcvOiGS5fccPasAnPnusFslkEqFfC//6WiVi0j6tXTo3p1I9zdc8ZrtWXMrNRqhzTYn332mSPCEBG9lrFmTcTOnw/NsGFQjxqF2EWL0o7HUqZpNBpER0dbb0dHR0Oj0YiYERHZgkwGFC9uQvHiJnTqlAIASE6W4MIFN/z2mztOnlRg2TIVvvvOCx4eFtSubUSHDlLUqiWFVst53C/KUVNEiIiyS9+2LRIePoTPjBlILVYMSWPGiJ1SjlKkSBE8fvwYkZGR0Gg0OHnyJEaMGCF2WkRkB56eAmrVMqJWLSPGjk1ruE+cUODIESUOHnTH0KFySKV5UbWqEW3apKBVKz2b7X+J3mCfPn0aK1asQEJCAsLCwhASEoJJkyaJnRYR5WJJQ4dCfuMGfObOhalYMaBfP7FTyjFkMhn69++PGTNmwGKxoGHDhgjmSaNELsHTU0CTJgY0aWLA9OnA48cB+PFHPX7+WYlJk/wwebKAunUN6Nw5GU2b6qFUip2xeERvsKtVq4Zq1aqJnQYRuRKJBHFhYZDfvg2/UaNgrlDhdWcF0QsqVaqESpUqiZ0GEYlIIgHKlRMQGJiIsWMTcfWqHNu3e2DbNg8MG6aBn58F7dsno3fvZBQv/vKFfXI7Tj4kItfk7o6YZctg8feHvGNHSEU4WZaIKLcoVcqECRMS8fvvkfjxxyg0aKDHunUqNGyYB506+WPvXiXM5jfvJ7dgg01ELssSEICYFSuAqCiohw4FTK43ykJEZEtSKVCvnhGLFsXhjz+eYsKEBNy7J8OAARrUq5cHa9Z4IiVF7Cztjw02Ebk0U9myMH/zDdxPnoT3rFlip0NElGv4+1vwwQdJOHkyEuHhMfD1tWDCBD/UrJkXS5aorOtu50ZssInI5Vl694auZ094L1oE5d69YqdDRJSryOVA69Z67NkThc2bo1CihAlTp/qiRo08WLpUBYNB7Axtjw02ERGA+KlTYaxYEX6jR0N2757Y6RAR5ToSCVCrlhEbN0Zj27YolCxpwhdf+KJevTzYssUDlly0wh8bbCIiAHB3R+x33wFSKdTDhgFGo9gZERHlWtWqpTXaGzZEQa22YMQINVq00OLMGYXYqdkEG2wion+Zg4MRN2cOFBcuwCcsTOx0iIhyvbp1jfj55yh8+20soqJkaNdOiw8/9MOTJzm7Rc3Z2RMR2Zi+RQvo+vSB15IlcI+IEDsdIqJcTyoF2rdPwbFjkRg5MhF79nigfv08WLXKM8cu7ccGm4joBfGTJyO1dGn4jRkD6bNnYqdDROQSPD0FfPxxIg4dikSlSkZMmuSHdu20uHZN9OsiZhkbbCKiFymViP32W0iTkuA3diwgCGJnRETkMkJCzFi/PgYLF8bi7l0ZmjULwOLFXjlqNJsNNhHRK5hKlEDCxIlQHjwIzx9+EDsdIiKXIpEAHTqk4MiRZwgN1WPGDB+0b6/FzZtiZ5Y5bLCJiDKg698fhrp14fPFF5DduiV2OkRELsff34KlS2Px7bexuHlTjurV3bBli4fYab0RG2wiooxIpYidNw9wd4d61CjkqOOTRES5hESSdhLkgQPPUKGCgBEj1Bg50g86nfNeCZINNhHRa1jy50f8tGlQnDsH1bJlYqdDROSygoLM2L/fhLFjE7B1qwdattTi5k3nPAGSDTYR0RuktG+PlHffhc+sWZwqQkQkIrkcGDMmCT/+GI2YGClatNBizx6l2Gm9hA02EdGbSCSIDwuD4O6etqoIp4oQEYmqTh0j9u17huLFTRg0SIOwMG+nutQ6G2wiokyw5M2L+KlT4X7mDFQrV4qdDhGRywsMtGDLlih0767DN994Y9AgNZKTnWNeNhtsIqJMSunQAfpGjeA9cyZkDx+KnQ4RkctzdwdmzYrH55/HY/9+Jdq10+LxY/HbW/EzICLKKSQSxH/5JSAI8J04kRegISJyAhIJMHCgDqtXx+DuXRnatBH/6o9ssImIssAcHIzEjz6CMiICyj17xE6HiIj+1aiRAVu3RsFkkqB9ey1+/10hWi6iN9hr167FqFGj8NFHH2H27NnQ6XRip0RE9Fq6AQNgLFsWvpMnQ5KQIHY6RET0r7JlTdi5MwparRndu/tj/35xVhgRvcEuV64c5s6dizlz5iB//vzYtm2b2CkREb2eXI74WbMgffYMPjNnip0NERH9R3CwGdu3R6F06VQMHKjGtm2Ov/Kj6A12+fLlIZPJAADFixdHTEyMyBkREb1ZavnySO7dG55r1kD+559ip0NERP+h0QjYsCEa1aoZ8eGHfli71tOh8UVvsP/r0KFDqFChgthpEBFlSsK4cbCo1fCbNAlOtQArERHBy0vA2rXRaNTIgE8+8cOqVY5rsh1yiuW0adMQFxf30v1du3ZF1apVAQBbt26FTCZD3bp1M9xPREQEIiIiAABhYWHQarVZzkUul7/VdtnBmLkrplhxGdMJY2q1EL76CopBg5Bn/35YevWyf0wiIso0Dw9g2bIYDB6sxqRJfpBIgD59ku0e1yEN9mefffbax48cOYKzZ89i8uTJkEgyXiA8NDQUoaGh1ttRUVFZzkWr1b7VdtnBmLkrplhxGdNJYzZvDm2lSpCNH4/oWrUg+PpmOWZgYODbxXaw3377DZs3b8bDhw/x5ZdfokiRImKnRET0RgoFsGRJLAYNkmDixLQmu3dv+zbZok8RuXDhAnbs2IHx48fD3d1d7HSIiLJGKkX8l19CGhMDz82bxc7GroKDg/HRRx+hVKlSYqdCRJQlaU12DEJD9ZgxwwdRUfZtgcVdhRvA8uXLYTKZMG3aNABAsWLFMGjQIJGzIiLKvNT//Q9RP/+M1P/9T+xU7KpAgQJip0BE9Nbc3YGlS2Nw65YcWq19z5sRvcH+5ptvxE6BiCjbUsuVEzsFp8JzZhiTMXN3TLHi2iJmUJD9Y4reYBMRkfPIzEnpmcFzZhiTMXN3TLHiihkzK+fLsMEmIiKrN52UTkREbyb6SY5ERERERLkJG2wiIsqU06dPY8iQIbh+/TrCwsIwY8YMsVMiInJKnCJCRESZUq1aNVSrVk3sNIiInB5HsImIiIiIbIgNNhERERGRDbHBJiIiIiKyITbYREREREQ2xAabiIiIiMiG2GATEREREdmQRBAEQewkiIiIiIhyC5cbwf7kk08YkzFzZFzGZExX4yo/F8ZkzJwYU6y4OSWmyzXYRERERET2xAabiIiIiMiGXK7BDg0NZUzGzJFxGZMxXY2r/FwYkzFzYkyx4uaUmDzJkYiIiIjIhlxuBJuIiIiIyJ7kYifgKBcuXMDKlSthsVjQuHFjtGvXzu4xFy9ejHPnzsHX1xdz5861ezwAiIqKwqJFixAXFweJRILQ0FC0aNHCrjGNRiOmTJkCk8kEs9mMGjVqoHPnznaN+ZzFYsEnn3wCjUbjkDOLhw8fDqVSCalUCplMhrCwMLvH1Ol0CA8Px4MHDyCRSDB06FAUL17crjEfPXqEefPmWW9HRkaic+fOaNmypV3j7t69G4cOHYJEIkFwcDCGDRsGhUJh15g///wzDh48CEEQ0LhxY7u8xlfVgqSkJMybNw/Pnj1DQEAARo8eDS8vL5vHzolcoV6LUasB8eq1o2s14Br1mrXa9mxWrwUXYDabhQ8++EB48uSJkJqaKnz00UfCgwcP7B73ypUrwq1bt4QxY8bYPdZzMTExwq1btwRBEITk5GRhxIgRdn+tFotFSElJEQRBEFJTU4UJEyYI165ds2vM53bt2iXMnz9f+OqrrxwSb9iwYUJ8fLxDYj33zTffCBEREYIgpL2/SUlJDo1vNpuFAQMGCJGRkXaNEx0dLQwbNkwwGAyCIAjC3LlzhcOHD9s15r1794QxY8YIer1eMJlMwtSpU4XHjx/bPM6rasHatWuFbdu2CYIgCNu2bRPWrl1r87g5kavUazFqtSCIV68dXasFwfXqNWu1bdiqXrvEFJGbN28iX758yJs3L+RyOWrVqoUzZ87YPW7p0qUdPiKlVqtRuHBhAICHhweCgoIQExNj15gSiQRKpRIAYDabYTabIZFI7BoTAKKjo3Hu3Dk0btzY7rHEkpycjKtXr6JRo0YAALlcDpVK5dAcLl++jHz58iEgIMDusSwWC4xGI8xmM4xGI9RqtV3jPXz4EEWLFoW7uztkMhlKlSqFU6dO2TzOq2rBmTNnUL9+fQBA/fr1HVKTcgJXqddi1GpAnHrtCrUaEL9es1bbhq3qtUtMEYmJiYG/v7/1tr+/P27cuCFiRo4RGRmJO3fuoGjRonaPZbFYMH78eDx58gRNmzZFsWLF7B5z1apV6NmzJ1JSUuwe679mzJgBAGjSpIndz2aOjIyEj48PFi9ejHv37qFw4cLo27ev9RekI5w4cQK1a9e2exyNRoPWrVtj6NChUCgUKF++PMqXL2/XmMHBwdiwYQMSExOhUChw/vx5FClSxK4xn4uPj7f+UvLz80N8fLxD4jo7V6zXjqzVgOPrtVi1GnCtes1abT9vU69dYgTbFen1esydOxd9+/aFp6en3eNJpVLMnj0b4eHhuHXrFu7fv2/XeGfPnoWvr691BMhRpk2bhpkzZ2LixInYv38//vrrL7vGM5vNuHPnDt59913MmjUL7u7u2L59u11j/pfJZMLZs2dRo0YNu8dKSkrCmTNnsGjRIixZsgR6vR7Hjh2za8wCBQqgbdu2mD59Or788kuEhIRAKnV8WZRIJA456kPOx9G1GnBsvRarVgOuVa9Zqx0ns/XaJUawNRoNoqOjrbejo6Oh0WhEzMi+TCYT5s6di7p166J69eoOja1SqVCmTBlcuHABBQsWtFuca9eu4Y8//sD58+dhNBqRkpKChQsXYsSIEXaLCcD6ufH19UXVqlVx8+ZNlC5d2m7x/P394e/vbx1hqlGjhkMb7PPnz+Odd96Bn5+f3WNdvnwZefLkgY+PDwCgevXquH79OurVq2fXuI0aNbIe0l2/fn260VN78vX1RWxsLNRqNWJjY62v29W5Ur0Ws1YDjqnXYtVqwLXqNWu1fb1NvXaJEewiRYrg8ePHiIyMhMlkwsmTJ1GlShWx07ILQRAQHh6OoKAgtGrVyiExExISoNPpAKSdoX7p0iUEBQXZNWb37t0RHh6ORYsWYdSoUShbtqzdC7Zer7ce4tTr9bh06ZJd/4gA0g5F+fv749GjRwDSCluBAgXsGvO/HHXIEQC0Wi1u3LgBg8EAQRBw+fJlu3+OAFgP9UVFReH06dOoU6eO3WMCQJUqVXD06FEAwNGjR1G1alWHxHV2rlKvxajVgOPrtRi1GnC9es1abV9vU69dYgRbJpOhf//+mDFjBiwWCxo2bIjg4GC7x50/fz7++usvJCYmYsiQIejcubP1ry97uXbtGo4dO4aCBQti3LhxAIBu3bqhUqVKdosZGxuLRYsWwWKxQBAE1KxZE5UrV7ZbPLHEx8djzpw5ANIOBdapUwcVKlSwe9z+/ftj4cKFMJlMyJMnD4YNG2b3mMD//1IaNGiQQ+IVK1YMNWrUwPjx4yGTyRASEuKQK3bNnTsXiYmJkMvleP/99+1yUtKrakG7du0wb948HDp0yLrsE7lOvRajVgOs1/YmRr1mrbYtW9VrXsmRiIiIiMiGXGKKCBERERGRo7DBJiIiIiKyITbYREREREQ2xAabiIiIiMiG2GATEREREdkQG2wiIiIiIhtyiXWwKXfo1auX9Xuj0Qi5XG69VOqgQYNQt25dsVJ7rZEjR2L8+PEIDAwUOxUiIodgvSZXxwabcoy1a9davx8+fDgGDx6McuXKiZjRmz158gQWi4XFmohcCus1uTo22JTjWSwW7Ny5EwcPHoROp0PZsmUxaNAgeHl5ITIyEh988AGGDh2KTZs2Qa/Xo1u3bihcuDDCw8MRFRWFunXr4v333wcAHDlyBAcPHkRISAiOHTsGtVqN999/H//73/8AADExMfj+++/x999/w8vLC23btn3tFazOnTuHihUrvvKxI0eO4KeffkJCQgK8vb3RtWtXpx3VISKyBdZrchVssCnH27dvH86cOYPPP/8cPj4+WLlyJZYtW4ZRo0ZZn3Pjxg0sWLAAV69exaxZs1C+fHl89tlnMJvN+Pjjj1GzZk2ULl3a+tzq1atj+fLlOH36NObMmYNFixbBy8sLCxYsQHBwMJYsWYJHjx5h2rRpyJcvH8qWLfvK3M6fP4+WLVu+dL9er8fKlSvx1VdfITAwELGxsUhKSrLL+0NE5CxYr8lV8CRHyvEOHDiArl27wt/fH25ubujUqRNOnToFs9lsfU7Hjh2hUChQvnx5uLu7o06dOvD19YVGo0HJkiVx584d63N9fX3RsmVLyOVy1KpVC4GBgTh37hyioqLw999/o0ePHlAoFAgJCUHjxo1x9OjRV+ZlMBhw69YtlClT5pWPSyQS3L9/H0ajEWq1GsHBwbZ9Y4iInAzrNbkKjmBTjvfs2TPMmTMHEonEep9UKkV8fLz1tq+vr/V7hULx0m29Xm+9rdFo0u0rICAAMTExiI2NhZeXFzw8PKyPabVa3Lp165V5Xb58GcWLF4ebm9tLjymVSowaNQq7du1CeHg4SpQogd69eyMoKCiLr56IKOdgvSZXwQabcjx/f38MHToUJUuWfOmxyMjILO8vJiYGgiBYi3ZUVBSqVKkCtVqNpKQkpKSkWIt2VFQUNBrNK/dz/vx5VKpUKcM4FSpUQIUKFWA0GrFhwwYsWbIEU6dOzXK+REQ5Bes1uQpOEaEcr0mTJtiwYQOePXsGAEhISMCZM2feen/x8fHYu3cvTCYTfvvtNzx8+BAVK1aEVqtFiRIlsH79ehiNRty7dw+HDx/O8ESXCxcuZFiw4+LicObMGej1esjlciiVynSjMEREuRHrNbkKjmBTjteiRQsAwPTp0xEbGwtfX1/UrFkTVatWfav9FStWDI8fP8b7778PPz8/jBkzBt7e3gDS1kj9/vvvMXjwYHh5eaFTp06vXHrq/v37UCqV0Gq1r4whCAJ2796Nb7/9FhKJBCEhIRg4cOBb5UtElFOwXpOrkAiCIIidBJGzeL7s07Rp07K1nx07diAxMRE9e/a0UWZERPRfrNfkzDiCTWQHAQEBqFy5sthpEBHRG7Bekz2wwSayg1q1aomdAhERZQLrNdkDp4gQEREREdkQVxEhIiIiIrIhNthERERERDbEBpuIiIiIyIbYYBMRERER2RAbbCIiIiIiG2KDTURERERkQ/8Hy9niRehrk0IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig8, axarr = plt.subplots(nrows=1, ncols=2, figsize=(10,5), constrained_layout=True, facecolor=(1,1,1))\n",
    "\n",
    "ax1 = axarr[0]\n",
    "ax2 = axarr[1]\n",
    "\n",
    "ticks_velocidade = plticker.MultipleLocator(base=1)\n",
    "ticks_tempo = plticker.MultipleLocator(base=1)\n",
    "\n",
    "ax1.plot(tempo, s_grau5_2008_beijing(tempo, 2), label='Spline grau 5 - 2ª derivada', color='red')\n",
    "ax2.plot(tempo, s_grau5_2009_berlin(tempo, 2), label='Spline grau 5 - 2ª derivada', color='blue')\n",
    "\n",
    "for ax in axarr:\n",
    "    ax.set_xlabel('Tempo / s')\n",
    "    ax.xaxis.set_major_locator(ticks_tempo)\n",
    "    ax.set_ylabel('Aceleração / m/s²')\n",
    "    ax.yaxis.set_major_locator(ticks_velocidade)\n",
    "    ax.legend()\n",
    "\n",
    "fig8.suptitle('Aceleração - Usain Bolt - Beijing (2008) vs Berlin (2009)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repare que agora as curvas de aceleração são mais suaves. Mais coerente com uma variação gradual do atleta. Inclusive, contrariamente ao spline cúbico anterior, o gráfico de 2009 agora mostra uma leve desaceleração ao final.\n",
    "\n",
    "Vamos ver como a mudança de interpolação mudou a estimativa de velocidade máxima:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:24.669069Z",
     "iopub.status.busy": "2020-09-14T18:22:24.668858Z",
     "iopub.status.idle": "2020-09-14T18:22:24.673050Z",
     "shell.execute_reply": "2020-09-14T18:22:24.672583Z",
     "shell.execute_reply.started": "2020-09-14T18:22:24.669051Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.28 metros por segundos\n",
      "12.27 metros por segundos\n"
     ]
    }
   ],
   "source": [
    "velocidade_max_2008_s5grau = Q_(max(s_grau5_2008_beijing(tempo, 1)), 'm/s')\n",
    "velocidade_max_2009_s5grau = Q_(max(s_grau5_2009_berlin(tempo, 1)), 'm/s')\n",
    "\n",
    "print(f'{velocidade_max_2008_s5grau:.2f}')\n",
    "print(f'{velocidade_max_2009_s5grau:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como as curvas foram \"suavizadas\", não mais tantos máximos e mínimos no gráfico. Será mesmo que Bolt atingiu uma menor velocidade máxima em 2009 quando comparado a 2008?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Será que nossos modelos estão certos?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Não. Modelos tentam descrever a realidade, não são a realidade. Não faz muito sentido dizer \"certo\" ou \"errado\", podemos avaliar com base nos dados que temos se estão coerentes, se fazem predições que tenham sentido. Ou seja, as discussões que estamos fazendo a cada etapa aqui nesse artigo. Eles podem ser, no máximo, tão bons quanto os dados de entrada o famoso [GIGO - *garbage in, garbage out*](https://en.wikipedia.org/wiki/Garbage_in,_garbage_out), em português menos agressivo, dados de entradas ruins, saídas ruins. Como só temos dados de posição a cada 10 metros, tudo que vier dessa análise será limitado por esses dados de entrada. \n",
    "\n",
    "No caso da velocidade máxima, por exemplo, se ela foi atingida em algum ponto intermediário, obviamente que a forma de interpolação para obter esses pontos terá grande efeito no resultado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Obtendo dados experimentais de velocidade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O desempenho de Bolt nas Olimpíadas de 2008, quando quebrou o recorde mundial dos 100 m pela primeira vez, chamou tanta a atenção que mudou a forma de preparo da comunidade científica para o Mundial de 2009. Muitos [pensavam qual seria o tempo](https://aapt.scitation.org/doi/pdf/10.1119/1.3033168) se ele não tivesse desacelerado para comemorar nos metros finais e havia muito interesse em entender o desempenho do jamaicano."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assim, foram utilizadas câmeras especiais, medidores de velocidade e muitos outros equipamentos para estudar a biomecânica dos atletas da competição. O [artigo gerado](http://www.meathathletics.ie/devathletes/pdf/Biomechanics%20of%20Sprints.pdf) vale muito a leitura. Os detalhes são sensacionais.\n",
    "\n",
    "Um ponto interessante do artigo é que, com os medidores de velocidade utilizados, puderam estimar as velocidades médias dos atletas a cada 10 metros. Vamos importar esses dados e comparar com nossos modelos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:24.673985Z",
     "iopub.status.busy": "2020-09-14T18:22:24.673825Z",
     "iopub.status.idle": "2020-09-14T18:22:25.014121Z",
     "shell.execute_reply": "2020-09-14T18:22:25.011913Z",
     "shell.execute_reply.started": "2020-09-14T18:22:24.673967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Splits,\"2009 Berlin\"\n",
      "0,0\n",
      "\"0 - 10\",5.77\n",
      "\"10 - 20\",9.99\n",
      "\"20 - 30\",11.11\n",
      "\"30 - 40\",11.63\n",
      "\"40 - 50\",12.08\n",
      "\"50 - 60\",12.20\n",
      "\"60 - 70\",12.29\n",
      "\"70 - 80\",12.17\n",
      "\"80 - 90\",12.17\n",
      "\"90 - 100\",11.96\n"
     ]
    }
   ],
   "source": [
    "!cat bolt_berlin_vel.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:25.017682Z",
     "iopub.status.busy": "2020-09-14T18:22:25.017102Z",
     "iopub.status.idle": "2020-09-14T18:22:25.126926Z",
     "shell.execute_reply": "2020-09-14T18:22:25.126396Z",
     "shell.execute_reply.started": "2020-09-14T18:22:25.017615Z"
    }
   },
   "outputs": [],
   "source": [
    "arquivo_berlin_velocidade = 'bolt_berlin_vel.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:25.127865Z",
     "iopub.status.busy": "2020-09-14T18:22:25.127610Z",
     "iopub.status.idle": "2020-09-14T18:22:25.345591Z",
     "shell.execute_reply": "2020-09-14T18:22:25.345059Z",
     "shell.execute_reply.started": "2020-09-14T18:22:25.127847Z"
    }
   },
   "outputs": [],
   "source": [
    "dados_berlin_velocidade = np.genfromtxt(arquivo_berlin_velocidade, delimiter=',', dtype=['U10', float], names=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:25.346462Z",
     "iopub.status.busy": "2020-09-14T18:22:25.346189Z",
     "iopub.status.idle": "2020-09-14T18:22:25.550536Z",
     "shell.execute_reply": "2020-09-14T18:22:25.548169Z",
     "shell.execute_reply.started": "2020-09-14T18:22:25.346434Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('0',  0.  ), ('\"0 - 10\"',  5.77), ('\"10 - 20\"',  9.99),\n",
       "       ('\"20 - 30\"', 11.11), ('\"30 - 40\"', 11.63), ('\"40 - 50\"', 12.08),\n",
       "       ('\"50 - 60\"', 12.2 ), ('\"60 - 70\"', 12.29), ('\"70 - 80\"', 12.17),\n",
       "       ('\"80 - 90\"', 12.17), ('\"90 - 100\"', 11.96)],\n",
       "      dtype=[('Splits', '<U10'), ('2009_Berlin', '<f8')])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dados_berlin_velocidade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A velocidade máxima obtida foi de:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:25.554398Z",
     "iopub.status.busy": "2020-09-14T18:22:25.553580Z",
     "iopub.status.idle": "2020-09-14T18:22:25.716799Z",
     "shell.execute_reply": "2020-09-14T18:22:25.716138Z",
     "shell.execute_reply.started": "2020-09-14T18:22:25.554297Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "12.29 metros por segundos"
      ],
      "text/latex": [
       "$12.29 \\frac{\\mathrm{meter}}{\\mathrm{second}}$"
      ],
      "text/plain": [
       "12.29 <Unit('meter / second')>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_(max(dados_berlin_velocidade['2009_Berlin']), 'm/s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mas lembre-se, essa velocidade é resultado de uma média feita a cada 10 metros. Já vou explicar mais sobre isso adiante. A real velocidade máxima de Bolt na prova, de acordo com o artigo citado, foi de 12,34 m/s quando já havia percorrido 67,90 m."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos comparar esses dados com nosso modelo feito com spline cúbico:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:25.717923Z",
     "iopub.status.busy": "2020-09-14T18:22:25.717693Z",
     "iopub.status.idle": "2020-09-14T18:22:26.054663Z",
     "shell.execute_reply": "2020-09-14T18:22:26.054137Z",
     "shell.execute_reply.started": "2020-09-14T18:22:25.717894Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f527f8cc4c0>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Velocidade / m/s')\n",
    "plt.title('Usain Bolt - Mundial de Berlin - 2009')\n",
    "\n",
    "plt.scatter(dados['2009_Berlin'], dados_berlin_velocidade['2009_Berlin'], label='Vel. média experimental')\n",
    "plt.plot(tempo, cs_2009_berlin(tempo, 1), label='Spline cúbico')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E agora com o spline de quinto grau:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-09-14T18:22:26.055469Z",
     "iopub.status.busy": "2020-09-14T18:22:26.055321Z",
     "iopub.status.idle": "2020-09-14T18:22:26.255477Z",
     "shell.execute_reply": "2020-09-14T18:22:26.254998Z",
     "shell.execute_reply.started": "2020-09-14T18:22:26.055451Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f52ca1a3bb0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Tempo / s')\n",
    "plt.ylabel('Velocidade / m/s')\n",
    "plt.title('Usain Bolt - Mundial de Berlin - 2009')\n",
    "\n",
    "plt.scatter(dados['2009_Berlin'], dados_berlin_velocidade['2009_Berlin'], label='Vel. média experimental')\n",
    "plt.plot(tempo, s_grau5_2009_berlin(tempo, 1), label='spline grau 5')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E aí? Alguma conclusão? Difícil dizer. Ambos falham nos tempos iniciais. O modelo de quinto grau apresenta melhor a queda de velocidade no trecho final. Mas devemos ficar atentos se a comparação faz sentido.\n",
    "\n",
    "O modelo de interpolação gera pontos intermediários nos dados de posição, cria o spline de posição, que é então derivado para obter a curva de velocidade. A velocidade tabelada no artigo é, como já dito, uma média a cada intervalo de 10 metros feita com base nas medições de velocidade. Vamos ver um dos gráficos do artigo para entender:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![artigo2009](artigo_2009.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infelizmente a resolução da figura disponível não é das melhores. Mas temos a velocidade no eixo vertical e a posição no horizontal. A linha azul é resultado dos dados experimentais dos medidores e, a vermelha, uma linha média desses dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consegue entender por que utilizaram uma média? A velocidade oscila muito, afinal, ao correr ocorre o impacto rítmico de cada pé, em cada passada. Inclusive o próprio artigo e outras referências [como esta](http://www.johk.pl/files/15mackala.pdf) e [essa](https://hrcak.srce.hr/ojs/index.php/kinesiology/article/view/5579#:~:text=THE%20KINEMATICS%20OF%20USAIN%20BOLT'S%20MAXIMAL%20SPRINT%20VELOCITY,-Milan%20%C4%8Coh%20University&text=Despite%20a%20relatively%20slow%20reaction,and%204.36%20strides%2Fs%20frequency) mostram que o grande diferencial do Bolt é na sua passada. A leitura dos artigos também deixa clara as dificuldades experimentais de medir velocidade, afinal se trata de corpos e não de pontos, precisando se determinar a posição do corpo que vai ser monitorada, a influência do tempo de reação do atleta nos resultados, especialmente nos primeiros metros, dentre outros fatores."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## O que poderia ser melhorado?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Espero que você tenha entendido que há muitos fatores envolvidos e que isso aqui é apenas um exercício para demonstrar a linguagem Python, ferramentas matemáticas disponíveis e um pouco de cálculo e física. Mas vamos terminar o artigo pensando em como poderíamos melhorar nossa análise. \n",
    "\n",
    "Analise novamente os gráficos de velocidade obtidos. Há algo estranho? Bom, não sei se reparou, mas os gráficos não começam em zero. Isso pode ser resolvido forçando uma condição de contorno onde a primeira derivada deve ter valor zero no ponto inicial. Isso é possível de ser feito e já havia citado que há diferentes tipos de spline a depender das condições de contorno. Uma leitura na documentação dos métodos de spline mostra como isso poderia ser feito. Escreva na seção de comentários caso queira um artigo onde isso é feito ou caso você tenha feito e queira mostrar.\n",
    "\n",
    "Mas não é tão simples assim, afinal há o tempo de reação do atleta. A velocidade é nula até que o atleta comece a se movimentar. Cabe a você considerar se isso irá afetar muito a análise ou não. E como seria implementar isso. Ah, vai tentar descontar a influência do vento ou não?\n",
    "\n",
    "Outra abordagem é partir de modelos matemáticos previamente definidos na literatura. Recomendo a leitura [deste artigo](https://jeb.biologists.org/content/jexbio/208/14/2809.full.pdf) e também [desse aqui](https://staff.fnwi.uva.nl/a.j.p.heck/Research/art/ModelingSprinting.pdf). Assim, as condições de contorno poderiam ser as equações propostas nesses artigos e caberia verificar se representam bem as situações ou não.\n",
    "\n",
    "Por fim, lembra mais acima que escrevi sobre o método de interpolação polinomial? Quando se busca um polinômio que passa por todos os pontos? Outras pessoas já fizeram estudos nesse sentido: como [aqui](https://web.archive.org/web/20141006173930/http://rcuksportscience.wikispaces.com/file/view/Analysing+men+100m+Nspire.pdf) e [aqui](https://education.ti.com/sites/UK/downloads/pdf/TI-Nspire_STEM_MathsMotion.pdf). Veja os resultados e compare com a abordagem que utilizamos. Busque também reproduzir os estudos e tire suas conclusões."
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    "# Conclusão\n",
    "\n",
    "Ufa, não foi fácil fazer esse artigo. Muita leitura, matemática, esporte, física e Python. Mas o objetivo era mostrar ferramentas matemáticas disponíveis para a linguagem utilizando um problema real. Acredito ser muito mais produtivo que mostrar exemplos batidos que todo livro e site tem. \n",
    "\n",
    "E usar um problema real permite também discutir as limitações de métodos e modelos e como analisá-los criticamente. Infelizmente, enxergo que há alguns problemas na forma que são ensinados e utilizados hoje. A saber:\n",
    "\n",
    "- muitos confundem modelo com realidade;\n",
    "- há aplicação de ferramentas em contextos onde não se aplicam;\n",
    "- relacionado ao item anterior, há muitos usuários de métodos e modelos, mas poucos analistas e entendedores dos mesmos;\n",
    "- são pouco utilizados casos reais no ensino, de forma que não se exercita análise crítica. Dados de livros são sempre bonitinhos, né?\n",
    "- a divulgação/interpretação da mídia de estudos científicos e dos resultados de modelos é lastimável.\n",
    "\n",
    "A consequência disso tudo se relaciona ao que vivemos nesse ano de 2020, quando escrevo esse artigo. Afinal, boa parte do que vivemos esse ano foi consequência de predições feitas a partir de modelos lá no início do ano. [Lembra](https://g1.globo.com/bemestar/coronavirus/noticia/2020/03/27/sem-isolamento-e-acoes-contra-a-covid-19-brasil-pode-ter-ate-1-milhao-de-mortes-na-pandemia-diz-estudo.ghtml)? Obviamente que a doença é séria e não deve ser negligenciada, não é esse o ponto. Mas será que todos os cuidados foram tomados no modelo e no software do mesmo? [Parece que não](https://www.akitaonrails.com/2020/05/07/o-modelo-do-imperial-college-sobre-a-covid-19-pode-estar-errado). Será que pensaram nas consequências políticas e na vida e liberdade das pessoas? As previsões se confirmaram? Fica a reflexão.\n",
    "\n",
    "Caso queira receber notificação quando novos artigos e vídeos sobre ciência e programação forem lançados, nos acompanhe nas redes sociais linkadas no cabeçalho e no rodapé da página. Comente o que achou abaixo e compartilhe com mais gente interessada em ciência.\n",
    "\n",
    "Até a próxima."
   ]
  }
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