{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Estatística Descritiva com Pandas\n", "\n", "A estatística descritiva é usada para descrever as características básicas dos dados em um estudo. Elas fornecem resumos simples sobre a amostra e as medidas. Junto com a análise gráfica simples, elas formam a base de praticamente todas as análises quantitativas de dados.\n", "\n", "Para começar, precisamos coletar os dados para o nosso **DataFrame**. Para este exemplo, eu coletei os seguintes dados sobre estudantes:\n", "\n", "| Nome | Idade | Pontuação |\n", "|---|---|---|\n", "| Rafael | 20 | 70 |\n", "| Miguel | 22 | 80 |\n", "| Gabriel | 27 | 87 |\n", "| Emanuel | 19 | 92 |\n", "| Maria | 25 | 77 |\n", "| Sofia | 30 | 98 |\n", "| Luana | 18 | 100 |\n", "| Cassandra | 17 | |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Antes de iniciarmos, é necessário importar a biblioteca [pandas](https://pandas.pydata.org/):" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Criando um DataFrame\n", "\n", "Em seguida, precisamos criar o DataFrame com base nos dados coletados.\n", "\n", "Para nosso exemplo, o código para criar o DataFrame é:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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nomeidadepontuação
0Rafael2070.0
1Miguel2280.0
2Gabriel2787.0
3Emanuel1992.0
4Maria2580.0
5Sofia3098.0
6Luana18100.0
7Cassandra17NaN
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" ], "text/plain": [ " nome idade pontuação\n", "0 Rafael 20 70.0\n", "1 Miguel 22 80.0\n", "2 Gabriel 27 87.0\n", "3 Emanuel 19 92.0\n", "4 Maria 25 80.0\n", "5 Sofia 30 98.0\n", "6 Luana 18 100.0\n", "7 Cassandra 17 NaN" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dados = {\n", " 'nome': ['Rafael', 'Miguel', 'Gabriel', 'Emanuel','Maria', 'Sofia', 'Luana', 'Cassandra'], \n", " 'idade': [20, 22, 27, 19, 25, 30, 18, 17], \n", " 'pontuação': [70, 80, 87, 92, 80, 98, 100, None],\n", "}\n", "\n", "df = pd.DataFrame(dados)\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Digamos que você deseja obter as estatísticas descritivas para o campo '**Idade**', que contém dados numéricos. \n", "\n", "Nesse caso, a sintaxe que precisamos aplicar é:" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "count 8.000000\n", "mean 22.250000\n", "std 4.652188\n", "min 17.000000\n", "25% 18.750000\n", "50% 21.000000\n", "75% 25.500000\n", "max 30.000000\n", "Name: idade, dtype: float64" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['idade'].describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para saber as dimensões de nossos dados (quantas linhas e colunas existem), podemos acessar o atributo **shape**:" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8, 3)" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O atributo **columns** nos informa todas as colunas de nosso DataFrame:" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Index(['nome', 'idade', 'pontuação'], dtype='object')" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.columns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O atributo **dtypes** nos informa os tipos de dados de cada coluna:" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "nome object\n", "idade int64\n", "pontuação float64\n", "dtype: object" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.dtypes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O método **sum** nos permite obter a soma dos dados de uma coluna numérica:" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "178" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['idade'].sum() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos ainda dividir as estatísticas descritivas no seguinte:\n", "\n", "#### Count (Contagem)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].count() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Mean (Média)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "86.71428571428571" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].mean() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Mode (Moda)" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 80.0\n", "dtype: float64" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].mode()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Median (Mediana)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "87.0" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].median() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 0.25 Quantile:" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "80.0" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].quantile(q=0.25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 0.50 Quantile (Median):" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "87.0" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].quantile(q=0.50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 0.75 Quantile:" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "95.0" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].quantile(q=0.75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Standard Deviation (Desvio Padrão)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.812250547631695" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Var (Variância)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "116.90476190476188" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].var() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### CumSum (Soma Cumulativa)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 70.0\n", "1 150.0\n", "2 237.0\n", "3 329.0\n", "4 409.0\n", "5 507.0\n", "6 607.0\n", "7 NaN\n", "Name: pontuação, dtype: float64" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].cumsum() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Min (Menor Valor)" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "70.0" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].min() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Max (maior Valor)" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "100.0" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].max() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Podemos contar quantos valores nulos existem em nosso conjunto de dados usando o método **isna** combinado com **sum**:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].isna().sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Também podemos ordenar os valores de uma coluna com o método **sort_values**:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7 Cassandra\n", "3 Emanuel\n", "2 Gabriel\n", "6 Luana\n", "4 Maria\n", "1 Miguel\n", "0 Rafael\n", "5 Sofia\n", "Name: nome, dtype: object" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['nome'].sort_values()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Usando o operador de atribuição, podemos facilmente alterar a escala da pontuação dos estudantes, neste exemplo vamos dividir ela por 100:" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [], "source": [ "df[\"pontuação\"] /= 100" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### O método **head** nos permite controlar quantas linhas desejamos ver no topo do DataFrame:" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 0.70\n", "1 0.80\n", "2 0.87\n", "Name: pontuação, dtype: float64" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### O método **tail** nos permite controlar quantas linhas desejamos ver na cauda do DataFrame: " ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6 1.0\n", "7 NaN\n", "Name: pontuação, dtype: float64" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].tail(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### O método **skew** retorna a inclinação imparcial do eixo normalizada em **N-1**:" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.2482135835044105" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['pontuação'].skew() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### O método **corr** computa a correlação de colunas emparelhadas:" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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idadepontuação
idade1.0000000.124085
pontuação0.1240851.000000
\n", "
" ], "text/plain": [ " idade pontuação\n", "idade 1.000000 0.124085\n", "pontuação 0.124085 1.000000" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.corr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### O método **cov** computa a covariância entre as Series do DataFrame, o DataFrame retornado é a matriz de covariância das colunas do DataFrame:" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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idadepontuação
idade21.6428570.06000
pontuação0.0600000.01169
\n", "
" ], "text/plain": [ " idade pontuação\n", "idade 21.642857 0.06000\n", "pontuação 0.060000 0.01169" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.cov()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Pontuação Representada em um Gráfico de Barras" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "image/png": 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CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "df['pontuação'].plot.bar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Idade Representada em um Gráfico de Linha" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "image/png": 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NMTY4kL4JhW/sr/Hba0aii2ODt4bYkmJ/iIoSCianaRIlyLSBhwH3tMGRxQa9yZ+UyuSxibxSojf1jMSTm8qpPN/G926yf2zQG1eug+NnLlDfrIuOg0UbeBh4fvvJEccGvRERVuVlsfnYGWp1QuGw9MUGr5sznkVT7R8b9MblmYuyQ4/Cg0YbuM25Y4NHKHQ6RhQbHEhRXibGwKs6oXBYfhxmsUFv5mWlMCo2Si9kBpE2cJv7xTtHOdfq+7TB4ZiSkcyC7BTdlzkM+0438qedp/nK4lwmjw2f2GB/dNFx8GkDt7HyMxf49ZYKPnNpNnOzRh4bHMiqvCwOVDVxVOdd+MwYw/dfPUB6cvjFBr0pdDo4WNWkqaUg0QZuYw95YoN/t8I/scGB3LQgk+go0Vvrh2DNvmp2nHDHBkeHWWzQG1eug14Du06et7qUiKAN3KYCFRv0JmN0PIunpfNKSZWODfVBT6/h4XVHuGTCaP7aJkuK/WFhThrRUaJ58CDRBm5D3T29/OurB8lO839scCC35Ge6JxSe1AmFg3nzQA3H6y9w7zXTwzY22J+k+BjmZI7RC5lBog3chp7fforDtYGJDQ5kxewJJMRG87JezByQMYZfri9jSnoS188NTDIolOmi4+DRBm4zjW1dPLzuCIW5Dj4Z5OaQFB/DijnjWbNPJxQO5L0j9RyoauLrS6dG1NF3H5fTQWd3L/tO66LjQNMGbjOPvOuJDa4MXGxwIEV5WZxv7eK9I7oez5tH1x8jM2UURXlZVpdiCZczDdDBVsGgDdxGghkb9OaK6emMTYrT0yheFJc3UFzRwJ1XTiEuJjL/eo1NjmdqRpJeyAyCyPwTZlMPrvHEBv00bXA4PpxQWFpLk2Z9P+bRDWWMTYrjVpvvuRypwlwHO06co0cTSwGlDdwmNh09w9ultdxzzTTGjQ58bHAgOqGwf/srG9lwuJ6vXJFLQlzwLi6HIpfTQXN7N4dr9MavQNIGbgPdPb384LWDTHIk8JXFwYsNepP34YRCPY1ysV9tOMbo+Bhuv3yy1aVYrm+wld5WH1jawG3gw9jgJ4MbG/RGRCjKy2LLsbPUNOqEQoBj9S2s3V/NFxdNDrtlDcORnZbAxJRReiEzwLSBh7iLY4OhlCkuys/SCYUX+e8Nx4iPieLLIfAOKRSICC6ng+3luug4kLSBh7gPpw1aFBv0Jjc9iQWTUnVCIVB5vo2XdldymyuH9OR4q8sJGa5cB3XNHZxsaLW6lLA1aAMXkUkisl5ESkXkgIjc95Gv/52IGBEJ30n1Fjle38Kvt1Tw15dOsiw2OJCivEwOVjdxJMInFD6+8TgAd145xeJKQkuh5zx4scYJA8aXI/Bu4AFjzCzgMuAeEZkN7uYOXAucDFyJkeuhtaWMio22NDY4kJXzPRMKI/go/ExLB88Vn+RTC7PITE2wupyQMn1csnvRsZ4HD5hBG7gxptoYs8vzcTNQCvTdYvafwD8AepLLz94/Ws/bpXXcc/U0MkaH5tvyjNHxXBHhEwqf2lROZ08vX79qqtWlhJyoKMHlTGN7hQ4/C5QhnQMXESeQD2wTkZuBSmPMnkG+504R2SEiO+rr9fZrX/TFBnMciXzlCqfV5QzolvwsKs+3seNE5P0lbWzr4rcfnOCGeROZkpFsdTkhyeV0UH7mAnXNmlYKBJ8buIgkAy8A9+M+rfJd4HuDfZ8x5jFjTIExpiAjI2PYhUaS57af4khtC9+54RLiY6yPDQ7k2tnj3RMKIzAT/r9bT9Dc0c3dS/Xo2xtXbt+i48j7Bz4YfGrgIhKLu3k/a4x5EZgK5AJ7RKQCyAZ2iUjo5NxsqrGti4ffOswnch1cNyf0/3Mmxcdw3ZzxrNkbWRMK2zp7eHJTOVfPzGBOZuhdYA4VczM9i471QmZA+JJCEeBJoNQY8zCAMWafMWacMcZpjHECp4GFxhi9t3qE/uudo5xv6wrokmJ/W5WfRWNbFxsO11ldStA8v/0kDRc6uefqyNh1OVxxMVHkT0rTC5kB4ssR+GLgduAaESnx/LohwHVFpOP1LTyzpYJbCybZ6qhuyTTPhMIIOY3S2d3LYxuPU5jroMATlVPeuXIdlFbrouNAiBnsCcaYTcCAh4Keo3A1Qg+ucccGHwjCkmJ/iomO4qYFmfyu+CRN7V1hfyv5y7srqW5s598+Pd/qUmyh0OledLzzxDmWzhxndTlhRe/EDBEbj9TzzqE6vnFN6MYGB1KUn0Vndy9v7Avvs2g9vYZfvXeMuVljuHK63rvmi/ycVPeiYz2N4nfawENAd08vP1zjjg1+ebHT6nKGZUF2Cs6xiWF/GuX1/dWUn7nAPUun2eYahdWS4mOYmzmG7eWaRPE3beAh4Lnik57Y4KyQjw16IyIU5WfxwfHwnVDoXlZ8jKkZSbZICIUSl9NByWlddOxv2sAt1tjqnjZ42RQH180Zb3U5I1KU555QuHpPeB6FbzhcT2l1E3ctnUZUBC4rHglXrnvR8V5ddOxX2sAt9vO+2ODKObZ/S+5MTyJvUiov7Q6/EbPGGB5ZX0ZWagKr8jKtLsd2XDrYKiC0gVvoWH0Lv/mggttck5idOcbqcvyiKC+T0uqmsFulVVzewM4T5/jaVVOIjda/NkPlSIpj2rhkvZDpZ/on0UIPeWKD377WXrHBgaxc4JlQGGYXM3+54RjpyXH8dcEkq0uxLZfTwc4KXXTsT9rALdIXG7zXprFBb9KT41kyPZ3VYTShcN/pRjYeqedvrpgSEivt7KowN43mjm4O1TRZXUrY0AZugb5pg5PHJvIlm8YGB9I3oTBc3i4/uqGM0aNi+MJlOVaXYmsfLjrW8+B+ow3cAr8rPsnROnvHBgdy7ezxJMZF83KJ/S9mltU188aBGr60yMnoML/DNNCy0xLJTBml88H9SBt4kPXFBi+fMpYVs+0dG/QmMS6G6+ZMYM3eKtvnfn+14TijYqJ1WbGfuHIdFFfoomN/0QYeZD9/5yhNbV383xBbUuxvq/IyaWrvZsNh+y7xONXQyssllXy2MAdHUpzV5YQFl9NBfXMHJ87qomN/0AYeRGV17tjgra6csIkNenPFtHTSk+NsvS/z8fePEyXw1Sv16NtfCj0LHorD5PqI1bSBB9FDa0tJiI3mgRUzrC4l4GKio1g5P5N3DtXR2Ga/MaJ1ze08v/0Un16YzcQUXVbsL9MykklNjNULmX6iDTxI3jtSz7uH6rh32TTSk8MnNjiQW/omFO6vtrqUIXtqUwXdPb18TZcV+1VUlFAw2RE2CSWraQMPgotjg3csclpdTtDMz04hNz2Jl212a31jaxf/u/UEN87PJDc9yepywk5hbhoVZ1t10bEfaAMPgt8Vn6SsroXvhmls0BsRoSgvi63lZ6lubLO6HJ/95oMKWnRZccD8OQ+uccKR0gYeYOdbO3l43REWTR3LtWEaGxzIqrxM94RCm2TCWzu7eWpzOcsuGcesieF9odkqc7NSSIiN1tMofqANPMAiJTbojTM9ifycVF6ySRrlueJTnGvt4m5dVhwwsdFR5Oek6mRCP9AGHkBldS389oMT3FaYE9FHc0V5WRyqaQ75GRgd3T08vvE4l01xcOnkNKvLCWsup4PSmiaadNHxiGgDD6AH1xwkITaab18b/rHBgaycP9E9oTDEL2a+tKuSmqZ27tGj74ArzHVgPIuO1fBpAw+QDYfrWH+4nm8umx4xsUFvxibHc+X0dFaXVIbshMLunl5+9d4x5mencMU0XVYcaPk5qcREiebBR2jQBi4ik0RkvYiUisgBEbnP8/h/iMghEdkrIi+JSGrgy7WHrp5efrimFGeExQYHUpSfRVVje8jegbd2fw0nzrZyty4rDorEuBjmZKXohcwR8uUIvBt4wBgzC7gMuEdEZgPrgLnGmPnAEeCfAlemvfxumzs2+J0bZhEXo29y4M8TCl8JwUUPxhgeXV/GtHHJYTtgLBQVOtPYc6qR9i57Dzyz0qDdxRhTbYzZ5fm4GSgFsowxbxljuj1P2wpkB65M+ygub+DhdUdYPC0yY4PeJMbFcP2cCazZWx1yEwrfPVTHoZpm7l46VZcVB5HL6aCzRxcdj8SQDg9FxAnkA9s+8qWvAK97+Z47RWSHiOyor7fvZLrBdHb38u9vHOLWxz4gNTGWH6yaq2/FP2JVfhZN7d2sPxQ6fw76lhVnpyVw0wJdVhxMH97Qo6dRhs3nBi4iycALwP3GmKaLHv8u7tMsz/b3fcaYx4wxBcaYgoyMjJHWG5KO1jZzy6Ob+dWGY9xaMIm131zClIxkq8sKOYunjiU9OT6kJhRuPd7A7pPn+dpVU3VZcZClJcUxfVyy5sFHIMaXJ4lILO7m/awx5sWLHr8DWAksMxE4ob231/DMBxX82+uHSIqP4bHbL2XFnAlWlxWyYqKjuGnBRJ7depLGti5SEqzfcPPohjLSk+P5zKV6BtAKrlwHr5ZU0dNriNbTV0PmSwpFgCeBUmPMwxc9fj3wf4CbjTERN529prGdO54u5vuvHmTxtHTevP9Kbd4+uCU/i86eXl7fZ/2Ewj2nzvP+0TN8dUmuLiu2SKHTQXNHN6XVoX2TV6jy5T3jYuB24BoRKfH8ugF4BBgNrPM89t+BLDSUrNlbzXU/28iOinM8eMtcnryjIKw2ywfSvKwUpqQn8XIIpFEe3VDGmFExfP6yyVaXErFcuXoefCQGPYVijNkE9PfeZq3/ywltTe1d/L9XDvDi7koWZKfwn7fm6bnuIRIRivKzeHjdEarOt5GZas2yhKO1zbx5oJZvLptOcrxPZxJVAGSlJpCVmsD2igbdOzoMetXGR9uOn+WTP3ufV/ZU8c1l0/nTXYu0eQ/Tqjx32mP1HuturX90wzES46L5st5oZTmXM43i8nO66HgYtIEPoqO7hx+9Xsptj28lJlr449cv59vXztDEwghMHpvEwpxUy9IoJ8+2snpPFZ8rzCFNlxVbzpXr4ExLBxW66HjItAsN4EhtM0W/3ML/vHec21zueODCHJ1S5w9F+e4JhVZcvPqfjceIFuFvl0wJ+s9WH1f44YIHPQ8+VNrA+9Hba3hqUzkrf7GJuqZ2Hv9iAT/61HyS9Fyp39w4byIxURL0i5l1Te38ccdpPn1pNhNSRgX1Z6v+TRuXTFpibMjOyQll2sA/oqaxnS8+Vcy/vnaQJdPSeeP+K/WW+AAYmxzPlTMyWF1SFdQJhU9sKqe7t5evX6VH36FCRChw6qLj4dAGfpHX9lZx3c82svPEOR66ZR5PaDwwoIrys6hubGdbkN46n2/t5H+3nuCmBZlMHqvLikNJodPBibOt1DXpouOh0AaOOx74rd+X8I3f7SY3PYm19y3hc5/I0VkmAXbtrPEkBXFC4a+3VNDa2cNduqw45PTlwfU0ytBEfAPf6okHrt5Txf3Lp/Onr19ObroenQVDQlw0182dwJp91QEfKdrS0c3TmytYPms8l0yI3PV2oWpO5hj3omO9kDkkEdvAO7p7+NHaUj77+FZio4U/ff1y7l8+gxiNBwZVUV4Wze3dbDhcF9Cf89w29/yVu6/Wo+9QFBsdxcLJqRRX6Iq1oYjIbnW4xhMP3HiczxbmsPa+JeRrPNASi6aOJWN0fEC31rd39fD4+8dZNHWsxkBDmMvp4FBNE41tuujYVxHVwHt7DU+8f5ybHtlEfXM7T3yxgIdumUdinMYDrRITHcVN8zNZf6iextbA/MV9Yddp6po7dFlxiCt0uhcd79JFxz6LmAZe3djG7U9t44drSrlyujseuFzjgSGhb0Lh2v3+n1DY3dPLf793jAWTUlk0dazfX1/5T35OGjFRohcyhyAiGvjqPVVc958b2X3yPD/61Dwe/2JBxG+KDyVzs8YwJSMpILfWv7a3mlMNbdyzdKqmikJcQlw0c7NS9ELmEIR1A29s6+K+53fzzed2MyUjmbXfXMJnCzUeGGpEhFvysthW3kDl+Ta/vW5vr+HRDWXMGJ/M8ln6bssOCnMd7D2ti459FbYNfMuxM3zyZxt5bW8131o+gz99/XKcGg8MWavysgBYXeK/CYVvl9ZypLaFu5dO02XFNtG36HjPqfNWl2ILYdfAO7p7eHDNQT7/xDbiY9XHLqwAAA3XSURBVKN54a5F3Ld8usYDQ1zO2EQunZzmt9Moxhh+ueEYkxwJrJw/0S+vqQKvYLI7JaS31fsmrLraoZomVj2ymcffL+fzn8hhzTevIG9SqtVlKR8V5WVyuNY/Ewq3HDvLnlPn+fpVU/UfbxtJS4pjxvhkzYP7KCz+ZPf2Gh7feJybf7GZMy2dPP0lFz8s0nig3dw4P9M9odAPR+G/XF/GuNHxfHqhLiu2G5fTwa4T5+gJ4pAzu7J9A68638bnn9jGg2tLuWpmBm/ev4SrLxlndVlqGBxJcVw1I4NXRjihcNfJc2w5dpavLpmiy4ptqDDXQYsuOvaJrRv4KyWVXPezjew5fZ5///Q8Hrv9UsZqPNDWivKzqGlqZ2v52WG/xqPrj5GSEMvnPpHjx8pUsLg8Cx6KNU44KFs28MbWLu59bjf3PV/C9HHJvH7fEm51aTwwHCzvm1C4e3hplEM1TbxdWsuXFzt1AYdNZV606FgNbNAGLiKTRGS9iJSKyAERuc/zuENE1onIUc/vQRkysaXsDNf/fCOv76vmgWtn8IevXa6zncNIQlw018+dyNphTij8lWdZ8Zd0WbGtFea6FzzoouOB+XIE3g08YIyZBVwG3CMis4F/BN4xxkwH3vF8HjDtXT384LWDfO6JbSTERfPi3Yu4d5nGA8NRUX4mzR3drD80tAmFJ85e4NU9VXzhssmkJuqyYjtzOR2caemk/MwFq0sJaYN2P2NMtTFml+fjZqAUyAJWAc94nvYMUBSoIkur3fHAJzeVc/tlk1lz7xLmZ2s8MFwtmpo+rAmF//3ecWKiovjbK3IDVJkKlsJczYP7YkiHryLiBPKBbcB4Y0w1uJs80G/0Q0TuFJEdIrKjvr5+WEX+dusJGlo7efrLLn5QNJeEOE0WhLPoKOHmBZlsOFzP+dZOn76nprGdF3ae5jMF2Ywbo8uK7W5qRjKOpDiKyzUPPhCfG7iIJAMvAPcbY3zO9xhjHjPGFBhjCjIyMoZTI9+5YRZv3LeEq2dqPDBSfDihcF+NT89/4v3j9BjD167UhQ3hQEQomJymR+CD8KmBi0gs7ub9rDHmRc/DtSIy0fP1iUDAVqokx8doPDDCzMkcw9SMJF72YV/muQudPLvtJDcvyCRnbGIQqlPBUJjr4GRDK7W66NgrX1IoAjwJlBpjHr7oS6uBOzwf3wG84v/yVKQSEW7Jz6K4vIHT51oHfO7TWypo69JlxeFG8+CD8+UIfDFwO3CNiJR4ft0A/BtwrYgcBa71fK6U33w4oXCP90x4S0c3v95czorZ45kxfnSwSlNBMCdzDIlx0XoaZQCD3ulgjNkEeLtDZpl/y1HqzyY5EinwTCi866r+FzI8u/UETe3d3K3r0sJOTHQUC3PS9Ah8ABqiViFtVX4WR2pbKK1u/tjX3MuKy7liWrpOnQxTLqeDw7XNuujYC23gKqStnDfRPaGwn4uZf9x5mjMtHdx9tZ77Dleu3DSMgZ0n9Ci8P9rAVUhLS4pj6cwMVpdU/cV40a6eXv7nvWPk56Ry+RRdVhyu8ielERstmgf3Qhu4Cnl9Ewq3Hf/zhMJX91Rx+lwb9yydpkPMwtiHi471Qma/tIGrkLd81niS42M+PI3iXlZ8jEsmjOYanf0e9gqdDvaePq+LjvuhDVyFvFGx0Vw/dwKv76uhvauHtw7WUlbXwl1Lp+qy4gjgcjro6jGU6KLjj9EGrmyhKC+L5o5u3imt49ENZUwem8iN83RZcSQocHoGW2mc8GO0gStbuHzqWMaNjuehtaXsPd2oy4ojSGpiHDPHj6ZYz4N/jP4NULbQN6Gw8nwb48fE86mFWVaXpILIlZvGrhPn6O7ptbqUkKINXNnGpxZmIwJfu3Iq8TE6UjiSuJwOLnT29HtDVyTTpYHKNmZnjuHtb1/FlHRdoRdpCnM9g60qGpiXnWJxNaFDj8CVrUzNSNbcdwSamJJAdlqCXsj8CG3gSilbKHTqouOP0gaulLIFV66Dsxc6Oa6Ljj+kDVwpZQt9Cx70NMqfaQNXStnC1IwkxibFaR78ItrAlVK2ICIUOHXR8cW0gSulbMPldHCqoY2aRl10DNrAlVI2cnEeXGkDV0rZyOyJY0iKi9YLmR7awJVSthETHcXCyXoevI82cKWUrXy46LhVFx0P2sBF5CkRqROR/Rc9liciW0WkRER2iEhhYMtUSik3l9OBMbBDFx37dAT+a+D6jzz2Y+D7xpg84Huez5VSKuDyc1Ldi471NMrg0wiNMRtFxPnRh4Exno9TgCr/lqWUUv0bFRvN/OxUfrf1JK0dPazKy2RhTlpErtcTXwbDeBr4a8aYuZ7PZwFvAoL7KH6RMeaEl++9E7gTICcn59ITJ/p9mlJK+exIbTM/f+cobx+spaO7l6zUBG5akMnNCzKZNXF02E2sFJGdxpiCjz0+zAb+X8B7xpgXROSvgTuNMcsHe52CggKzY8eOodaulFL9aunoZt3BGl4pqeL9o2fo6TVMH5fMqrxMbl6QRc7YRKtL9At/N/BGINUYY8T9T12jMWbMAC8BaANXSgXO2ZYO1u6v4dWSqg/Pj+dNSuXmBZmsnD+RcWNGWVzh8Pm7gZcCdxljNojIMuDHxphLB3sdbeBKqWCoPN/Ga3uqeKWkioPVTUSJezH2qgVZXDd3AikJsVaXOCTDbuAi8hywFEgHaoF/AQ4DP8d9EbQduNsYs3OwIrSBK6WCrayumdUlVazeU0XF2VbioqNYOjODm/MyWXbJeBLiQn+/6oiOwP1FG7hSyirGGPaebmT1nipe3VNFXXMHSXHRrJgzgZvzMrliWjqx0aF5b6M2cKWU8ujpNWwrP8vqkirW7qumqb0bR1IcN8ybwM0LsiiYHFqxRG3gSinVj47uHjYeOcMrJZW8XVpLe1cvmSmjuCnPHUucPXGM5bFEbeBKKTWICx3drDtYy+o9VWw8Uk93r2HauGRu9mTMnelJltSlDVwppYag4UInr++v5pWSKoo942sXeGKJNwU5lqgNXCmlhqnqfBuv7XUnWfZXNiECl08Zy6q8TK6fM5GUxMDGErWBK6WUHxyrb/kwllh+5gKx0cLSmeO4eUEmy2cFJpaoDVwppfzIGMP+yiZeKank1b1V1DZ1kBgXzYrZ41mVl8UV0/0XS9QGrpRSAdLTaygub2D1nkrW7quhsa2LtMRYbpg3kZsXZOJyOkYUS9QGrpRSQdDZ3cvGI/Ws3lPFuoO1tHX1MDFlFD/9zAIWTUsf1mt6a+CDzgNXSinlu7iYKJbPHs/y2eNp7fTEEkuqmOTw/2REbeBKKRUgiXExrMrLYlVeVkBePzRv/FdKKTUobeBKKWVT2sCVUsqmtIErpZRNaQNXSimb0gaulFI2pQ1cKaVsShu4UkrZVFBvpReReuDEML89HTjjx3ICzU712qlWsFe9dqoV7FWvnWqFkdU72RiT8dEHg9rAR0JEdvQ3CyBU2aleO9UK9qrXTrWCveq1U60QmHr1FIpSStmUNnCllLIpOzXwx6wuYIjsVK+dagV71WunWsFe9dqpVghAvbY5B66UUuov2ekIXCml1EW0gSullE3ZooGLyPUiclhEykTkH62uZyAi8pSI1InIfqtrGYyITBKR9SJSKiIHROQ+q2vyRkRGiUixiOzx1Pp9q2sajIhEi8huEXnN6loGIyIVIrJPREpEJOT3HopIqoj8SUQOef78Xm51Tf0RkZme/6Z9v5pE5H6/vX6onwMXkWjgCHAtcBrYDnzWGHPQ0sK8EJErgRbgN8aYuVbXMxARmQhMNMbsEpHRwE6gKBT/24qIAEnGmBYRiQU2AfcZY7ZaXJpXIvJtoAAYY4xZaXU9AxGRCqDAGGOLG2NE5BngfWP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