{
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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lJQJoRBDSYnb"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy\n",
        "import sympy"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u1QfL9coSrh7",
        "outputId": "ed2ebe47-42f0-4917-e112-5d82c32896de"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Um básico sobre Python em estatística\n",
        "\n",
        "Atualmente a linguagem de programação mais usada no mundo, principalmente pela combinação entre desempenho, facilidade de aprendizado e seu caráter open-source, o Python é uma ferramenta importante em análises estatísticas e aplicações científicas. \n",
        "\n",
        "Atualmente, utilizamos o Wolfram Mathematica no curso para realizar algumas tarefas principais, como:\n",
        "\n",
        "1. Simular experimentos usando geradores de dados aleatórios, distribuídos conforme múltiplas funções densidade de probabilidade.\n",
        "2. Calcular estatísticas simples dos sistemas, como média, variância, desvio padrão, etc.\n",
        "3. Plotar histogramas. Plotar dados.\n",
        "4. Fazer ajustes lineares e não-lineares de curvas.\n",
        "\n",
        "Tentarei cobrir brevemente os tópicos listados acima."
      ],
      "metadata": {
        "id": "CAebNiUWTVNV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Geradores de números aleatórios via numpy\n",
        "\n",
        "O módulo random do numpy `numpy.random` possui uma série de distribuições das quais podemos amostrar números aleatórios. Vou mostrar aqui as principais, mas a documentação pode ser encontrada neste [link](https://numpy.org/doc/1.16/reference/routines.random.html)."
      ],
      "metadata": {
        "id": "jqPbQMJImp7j"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Distribuição gaussiana"
      ],
      "metadata": {
        "id": "YcaBxKrHpEnl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#para fixar os numeros aleatorios, podemos usar uma seed na célula da simulação\n",
        "np.random.seed(1)\n",
        "\n",
        "#gerar 10 numeros gaussianos de media 0, variancia unitaria:\n",
        "x_gaussian = np.random.normal(loc=0., scale=1., size=10)\n",
        "\n",
        "#gerar uma grade de 10x10 numeros gaussianos de mesmos parametros que acima\n",
        "x_gaussian_grid = np.random.normal(loc=0., scale=1., size=(5,10))\n",
        "\n",
        "#Vamos ver os numeros gerados e as dimensões dos vetores:\n",
        "print('Vetor unidimensional:\\n', x_gaussian)\n",
        "print()\n",
        "print('Array 5x10:\\n', x_gaussian_grid)\n",
        "print()\n",
        "print('Dimensão do vetor:',x_gaussian.shape)\n",
        "print('Dimensão do array:',x_gaussian_grid.shape)"
      ],
      "metadata": {
        "id": "t0dQIL4pSxPc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca345eee-168c-4de4-f197-1075e204f83f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vetor unidimensional:\n",
            " [ 1.62434536 -0.61175641 -0.52817175 -1.07296862  0.86540763 -2.3015387\n",
            "  1.74481176 -0.7612069   0.3190391  -0.24937038]\n",
            "\n",
            "Array 5x10:\n",
            " [[ 1.46210794 -2.06014071 -0.3224172  -0.38405435  1.13376944 -1.09989127\n",
            "  -0.17242821 -0.87785842  0.04221375  0.58281521]\n",
            " [-1.10061918  1.14472371  0.90159072  0.50249434  0.90085595 -0.68372786\n",
            "  -0.12289023 -0.93576943 -0.26788808  0.53035547]\n",
            " [-0.69166075 -0.39675353 -0.6871727  -0.84520564 -0.67124613 -0.0126646\n",
            "  -1.11731035  0.2344157   1.65980218  0.74204416]\n",
            " [-0.19183555 -0.88762896 -0.74715829  1.6924546   0.05080775 -0.63699565\n",
            "   0.19091548  2.10025514  0.12015895  0.61720311]\n",
            " [ 0.30017032 -0.35224985 -1.1425182  -0.34934272 -0.20889423  0.58662319\n",
            "   0.83898341  0.93110208  0.28558733  0.88514116]]\n",
            "\n",
            "Dimensão do vetor: (10,)\n",
            "Dimensão do array: (5, 10)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Distribuição exponencial"
      ],
      "metadata": {
        "id": "ldID5PvipIJf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(1)\n",
        "#gerar um vetor de 10 numeros aleatorios distribuidos conforme uma exponencial\n",
        "#de parametro 5\n",
        "x_exponential = np.random.exponential(scale=5., size=10)\n",
        "print('Vetor exponencial:\\n', x_exponential)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2z15NT0kodON",
        "outputId": "0a6bf116-06b2-4f33-bb2c-82caa375dbcf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vetor exponencial:\n",
            " [2.69802919e+00 6.37062627e+00 5.71906793e-04 1.80006377e+00\n",
            " 7.93547976e-01 4.84419358e-01 1.03057317e+00 2.11988241e+00\n",
            " 2.52726271e+00 3.86979887e+00]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Distribuição $\\chi^2$"
      ],
      "metadata": {
        "id": "NaXWZ8VUrTeK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(1)\n",
        "\n",
        "#vetor de 10 numeros aleatorios distribuidos como chi quadrado com 3 graus de \n",
        "#liberdade\n",
        "x_chisquared = np.random.chisquare(df=3, size=10)\n",
        "print('Vetor chi quadrado:\\n', x_chisquared)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "klyLvNDNpcBf",
        "outputId": "6be653c9-4232-4f48-b45a-f7a90eef3ec8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vetor chi quadrado:\n",
            " [7.89523814 1.24558467 1.36822429 0.69825022 8.49641899 1.04498082\n",
            " 7.13137433 0.11274373 5.73945707 0.67255189]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### $t$ de Student"
      ],
      "metadata": {
        "id": "9VDpXrobr4Br"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(1)\n",
        "\n",
        "#vetor de 10 numeros aleatorios distribuidos como t-Student com 3 graus de \n",
        "#liberdade\n",
        "x_student = np.random.standard_t(df=3, size=10)\n",
        "print('Vetor t-Student:\\n', x_chisquared)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "whnRy7Mtrp7z",
        "outputId": "4710b683-d007-4394-9b15-b6e07d1d8f86"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vetor t-Student:\n",
            " [7.89523814 1.24558467 1.36822429 0.69825022 8.49641899 1.04498082\n",
            " 7.13137433 0.11274373 5.73945707 0.67255189]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Estatísticas básicas dos dados"
      ],
      "metadata": {
        "id": "2LVc2WfUsIi0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Vamos usar a função `mean` do numpy para fazer médias e `var` para calcular o desvio padrão dos dados. Para isso, vamos usar nossos dados com distribuição gaussiana gerados anteriormente."
      ],
      "metadata": {
        "id": "24XNZoU8sQS7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Média\n",
        "\n",
        "A média é obtida usando a função `mean`, onde temos a liberdade de escolher dentro de qual eixo desejamos realizar a média, para o caso de arrays bidimensionais."
      ],
      "metadata": {
        "id": "naRAvZNNvKbB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#ao tirarmos a media dos valores no vetor unidimensional, obtemos um numero\n",
        "#como resposta:\n",
        "print('Média vetor unidimensional:', np.mean(x_gaussian) )\n",
        "print()\n",
        "#no entanto, no vetor 5x10, temos algumas opções:\n",
        "\n",
        "#tirar a média de todos os números no grid:\n",
        "print('Média de todos os valores no grid:', np.mean(x_gaussian_grid) )\n",
        "print()\n",
        "#tirar as médias variando as linhas no grid:\n",
        "print('Média variando linha no grid:\\n', np.mean(x_gaussian_grid, axis=0) )\n",
        "print()\n",
        "#tirar as médias variando as colunas no grid:\n",
        "print('Média variando coluna no grid:\\n', np.mean(x_gaussian_grid, axis=1) )"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fa45NclssEFf",
        "outputId": "bfff5125-51f4-45d6-cdbf-cfe543335462"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Média vetor unidimensional: -0.09714089080609985\n",
            "\n",
            "Média de todos os valores no grid: 0.029405380064324912\n",
            "\n",
            "Média variando linha no grid:\n",
            " [-0.04436744 -0.51040987 -0.39953514  0.12326924  0.24105856 -0.36933124\n",
            " -0.07654598  0.29042901  0.36797482  0.67151182]\n",
            "\n",
            "Média variando coluna no grid:\n",
            " [-0.16958838  0.08691254 -0.17857517  0.23081766  0.17746025]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Variância\n",
        "\n",
        "A variância usando `numpy.var` calcula a variância de máxima verossimilhança, ou seja, a estimativa tendenciosa desta. Escolhendo o parâmetro `ddof = 1` (delta degrees of freedom), que por default é 0, calcula-se a estimativa não tendenciosa. Para valores de `ddof` maiores que 1, calcula-se a variância como sendo `N - ddof`, onde `N` é o número de dados."
      ],
      "metadata": {
        "id": "ffh8CuX9vL8a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Estimativa tendenciosa da variância:',np.var(x_gaussian))\n",
        "print()\n",
        "print('Estimativa não tendenciosa da variância:',np.var(x_gaussian,ddof=1))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YMkqkZGuuPdj",
        "outputId": "290c0133-817d-4c3c-8b83-3b587fc964fd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimativa tendenciosa da variância: 1.4182393613078983\n",
            "\n",
            "Estimativa não tendenciosa da variância: 1.5758215125643313\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Também temos a liberdade de calcular a variância para diferentes eixos, assim como na média:"
      ],
      "metadata": {
        "id": "NSCUZiqg_lyk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Estimativa não tendenciosa da variância variando-se as linhas:\\n', \n",
        "      np.var(x_gaussian_grid, axis=0))\n",
        "print()\n",
        "print('Estimativa não tendenciosa da variância variando-se as colunas:\\n', \n",
        "      np.var(x_gaussian_grid, axis=1))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wWWon1nO_iYL",
        "outputId": "bea1cd2d-c539-48a3-8820-a3593fd888c5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimativa não tendenciosa da variância variando-se as linhas:\n",
            " [0.78891551 1.06427189 0.49089535 0.80496745 0.46064361 0.34905348\n",
            " 0.40085227 1.31150564 0.44949205 0.01627079]\n",
            "\n",
            "Estimativa não tendenciosa da variância variando-se as colunas:\n",
            " [0.99828042 0.6034416  0.65631337 0.89658093 0.41502918]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Desvio-padrão\n",
        "\n",
        "O desvio-padrão possui a mesma propriedade da variância, de modo que o desvio padrão como raíz quadrada da variância não tendenciosa exige que `ddof=1`."
      ],
      "metadata": {
        "id": "M_1HL9NMARDl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('Estimativa tendenciosa:',np.std(x_gaussian))\n",
        "print()\n",
        "print('Estimativa não tendenciosa:',np.std(x_gaussian,ddof=1))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1mhxm4Iy_-fr",
        "outputId": "b5501160-f4a5-4d4d-a396-c6080631abe7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimativa tendenciosa: 1.190898552063902\n",
            "\n",
            "Estimativa não tendenciosa: 1.2553172955728489\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plotando\n",
        "\n",
        "A principal biblioteca para plots em python é o matplotlib, então focarei minha atenção nesta biblioteca."
      ],
      "metadata": {
        "id": "jPbox55yBABV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Scatter plot\n",
        "\n",
        "O scatter plot é como o ListPlot do Wolfram Mathematica, usado para plotar pontos. Ele usa dois argumentos: um para x, outro para y, formando as coordenadas cartesianas de cada ponto."
      ],
      "metadata": {
        "id": "wTYGBmxUBMEK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Plot dos dados exponenciais\n",
        "\n",
        "#antes, precisamos criar um array de índices:\n",
        "index = np.arange(0, len(x_exponential), 1)\n",
        "\n",
        "plt.scatter(index, x_gaussian)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "da8v6ucGA1_o",
        "outputId": "58e888cf-505f-49b5-bada-6c7705e206c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f2acc16b0a0>"
            ]
          },
          "metadata": {},
          "execution_count": 48
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Para maior controle do plot, podemos mexer na estética dele:\n",
        "\n",
        "#criamos uma imagem e um eixo:\n",
        "fig = plt.figure(figsize=(6,4))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "#assim, podemos plotar os pontos sobre a variável ax, usando o método scatter:\n",
        "ax.scatter(index, x_exponential)\n",
        "\n",
        "#adicionamos os nomes dos eixos com o tamanho da fonte:\n",
        "ax.set_xlabel('index', fontsize=14)\n",
        "ax.set_ylabel('x exponencial', fontsize=14)\n",
        "\n",
        "#podemos adicionar um grid para facilitar a visualizacao:\n",
        "ax.grid()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "id": "7pggctIHBazx",
        "outputId": "6ba8d992-4fbf-4527-a353-dad6a901600a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Histogramas\n",
        "\n",
        "O matplotlib também possibilita fazer histogramas dos dados, usando a função `hist`."
      ],
      "metadata": {
        "id": "W8ThzGS6DjgZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#gerando um vetor com 1000 numeros aleatorios para histogramar:\n",
        "x_hist = np.random.normal(loc=0, scale=1, size=1000)\n",
        "\n",
        "plt.hist(x_hist)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 523
        },
        "id": "8EHdibXeCt7G",
        "outputId": "1486512f-c7cb-4c6b-d1e7-34095350e0a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  2.,   6.,  43., 130., 230., 287., 195.,  80.,  23.,   4.]),\n",
              " array([-3.92751407, -3.1955684 , -2.46362274, -1.73167707, -0.99973141,\n",
              "        -0.26778575,  0.46415992,  1.19610558,  1.92805125,  2.65999691,\n",
              "         3.39194257]),\n",
              " <BarContainer object of 10 artists>)"
            ]
          },
          "metadata": {},
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#assim como no scatter plot, podemos mudar características do plot,\n",
        "#inclusive transformá-lo numa densidade de probabilidade normalizando\n",
        "#os bins:\n",
        "\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "#para 15 bins (canais), e normalizando-os\n",
        "ax.hist(x_hist, bins=15, density=True)\n",
        "\n",
        "#labels dos eixos\n",
        "ax.set_xlabel('x', fontsize=14)\n",
        "ax.set_ylabel('Densidade', fontsize=14)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 385
        },
        "id": "3z2tIUqdEUf1",
        "outputId": "f5655c39-fca9-4746-8624-4b0a375258ea"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Plots\n",
        "\n",
        "A função `plot` do matplotlib é semelhante ao scatter, porém ela conecta os pontos plotados. Assim, se tivermos muitos pontos formando uma curva, ela se assemelha a uma curva suave. O python não possui uma ferramenta que traduz uma expressão analítica num plot, como no Wolfram."
      ],
      "metadata": {
        "id": "_eZ77g8UFL4Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Exemplo de plot de uma função seno:\n",
        "\n",
        "#array de 1000 pontos de x, divididos igualmente entre 0 e 2pi:\n",
        "x = np.linspace(0, 2*np.pi, 1000)\n",
        "\n",
        "#array dos valores de seno calculados:\n",
        "y = np.sin(x)\n",
        "\n",
        "#plot:\n",
        "fig = plt.figure(figsize=(4,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "#plot com um label para usar na legenda:\n",
        "ax.plot(x,y, label='sin(x)')\n",
        "\n",
        "#ajustando os limites do plot\n",
        "ax.set_xlim(0,2*np.pi)\n",
        "ax.set_ylim(-1.1, 1.1)\n",
        "\n",
        "#usando o label acima para dar a legenda:\n",
        "ax.legend(fontsize=14)\n",
        "ax.grid()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 360
        },
        "id": "Qc_h0ctQEoeD",
        "outputId": "6a4ef759-06d0-447b-eeef-f93baae13f29"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x300 with 1 Axes>"
            ],
            "image/png": 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DefPmcffddzNt2jR27Nhx3eewZW317du31uKsLimwVipPD4+uiTU9c/38sTDcGjX8nus/adQq3nywC33bNOGqvoRHPj7AsYtV31BZiIZq+PDhBAQE8OCDD/LMM88wY8YM0wYr//rXvwgICKi1z1KpVAwbNoz4+PgKt30zMjIYN24cTk5OrF271vQMd/HixXTo0IF58+ZVWpijo6Nxc3OjT58+tRZndUmBtUJXi0r44LiGMxn5+LrYs+bR7rhbYXEtY2ejZsXDIYQGuJFTUMzYVTGcz8xXOiwhFLVo0SK6du1KTEwM7777Lp999hmNGzdm+fLlrF27ttY/b/LkyRiNxgptjx8/npSUFN577z2CgoJMx+3t7fniiy+wsbFh9OjR5OTkmN5LSkpi9+7djBs3rlZ72tWlMlrhnl46nQ4XFxcyMjKqPJ+roSguMfD4p7+z9fglnO1t+HpKD9p4OykdlsXo9Xp++uknhg4dWmF+X/ZVPaM+2Ed8io7WXo35ZmqPOrneck3cKH9rUJ38CwoKSExMJCgoSNF/pGuLwWBAp9Ph7OxcYbWkuqJ3795cunSJY8eO1SjGOXPm8NprrxEfH0/Lli2Bm+df1e93Wf3Izs6+6ZSluvmnLMxm4Q/H2Hr8ErYqI+8/3NWqiuvNuDjYsuqRULydtZxKz2Xa5wfRl1Q+gEIIUftef/11Tpw4UaNdcK5cucLSpUuZMmWKqbgqRQqsFfls31k+2XsWlQr+3dpAaICb0iHVOb4uDnw07nYcbDX8eiqDud8dlY3bhbCQO+64g/fff79GU4ASExP573//y9y5c2sxslsjKzlZiX1nLjN/41EAoga2onnecYUjqrs6NHXhnYe6MunT3/ki5hwtmzTisd4tlA5LCKtQ03WDu3XrRrdu3WopmpqRHqwVOJ+Zz5TPYik2GLm3sx+P9wm6+UVWblB7b+bc1R6Al3+KZ0+CrFsshKgeKbANXF5hMRM/+Z0r+Xo6NnXhtX91qtHyadbk0Z6BPNCtGQYjTP/iDy5mXVU6JCFEPSIFtgEzGo08t/4wx1NzaOKk5YOxIdjXYPFva6NSqXjpvg7c5udMZl4RUz6LpaAe7AEqhKgbpMA2YF/EnOe7uIto1CreG9MNXxcHpUOqd+xtNax4OARXR1v+vJBteo4trIcMcrMO5vg+S4FtoI4kZzP/+9JiMDOyLbcHyubit8rf3ZF3RnVFpYJ1B87z1e/nlQ5JWIBGU3q3R6/XKxyJsISy73PZ9702SIFtgHQFeqZ+fpCiYgMR7byYKCNga6xPmyZERbQBYO53Rzl9KVfhiIS52draotVqyc7Oll5sA2c0GsnOzkar1dbqAiwWmaazbNkyXn/9dVJTU+ncuTNLly6le/fulZ7br18/du7cWeH40KFD+fHHHwF45JFHWLNmTbn3IyMj2bRpU+0HX88YjUae/foQ5zLzaebmwBsjuqBWy6Cm2jC1fyv2nrnMntOXmb72D9ZP7SHPtBs4T09PkpOTuXDhAi4uLtja2tbbQYIGg4GioiIKCgrq7EpO5lRZ/kajEb1eT3Z2Nrm5uTRt2rRWP9PsBfbLL78kKiqKFStWEBYWxltvvUVkZCQnTpzAy8urwvnffvstRUVFpteXL1+mc+fOjBgxotx5Q4YM4eOPPza91mq15kuiHvnf7+f5+UgqthoVy0Z3s6rdccxNo1bx5sgu3Pn2r8Sn6Hjl5+PMv/c2pcMSZlS2FF5GRgbJyckKR1MzRqORq1ev4uDgUG9/SaiJG+Wv1Wpp2rTpTZc+rC6zF9glS5YwceJExo8fD8CKFSv48ccfWbVqFbNmzapwvrt7+WeF69atw9HRsUKB1Wq1+Pj4mC/weigxI48F3x8D4KnBbens76psQA2Qt7M9b4zozPjVB1i9J4keLT0YfJv8HDZkzs7OODs7o9fra3WTcUvT6/Xs2rWLPn36WO061JXlr9FozPbnYdYCW1RURGxsLLNnzzYdU6vVREREsHfv3iq18dFHHzFq1CgaNWpU7viOHTvw8vLCzc2NAQMG8OKLL1534f7CwkIKCwtNr3W60u3I9Hp9gxnAoC8x8OS6g+QXlRAW5MYjd/hfN7ey4w0l9+qojdx7tXRjQs8APtp9lplfH6KDb2OaONWPOyjW/L2HmudfmwNgLM1gMFBcXIxGo6nXedyqG+VfnZ+H6pxr1t10Ll68SNOmTdmzZw/h4eGm4zNnzmTnzp3X3Vy3TExMDGFhYezfv7/cM9uyXm1QUBCnT5/mueeeo3Hjxuzdu7fSH5z58+ezYMGCCsfXrl2Lo6NjDTKsO346p2ZzshoHjZFnO5fgVj/+va+3ig3w5hENF/JU3OZmYGJbA1Z4100Iq5Ofn8/o0aOrtJtOnV6L+KOPPqJjx44VBkSNGjXK9P8dO3akU6dOtGzZkh07djBw4MAK7cyePZuoqCjTa51Oh7+/P/37928Q29XFnr1C9L4DACx6oDN3dbzxLUu9Xk90dDSDBg2yultFtZl78O05DF++j6NX1OT7dGBESLNaitJ8rPl7D9advzXnDrWXf9kd0Kowa4H19PREo9GQlpZW7nhaWtpNn5/m5eWxbt06Fi5ceNPPadGiBZ6eniQkJFRaYLVabaWDoGxtbev9D1p+UTEzvz2KwQj3d23K8G7+Vb62IeR/q2oj99uaufP04LYs+vk4L/10gt5tvPF3rx93RKz5ew/Wnb815w41z78615p1rLadnR0hISFs3brVdMxgMLB169Zyt4wr89VXX1FYWMjDDz9808+5cOECly9fxtfXt8Yx1zevbTrBucx8mro6sGCYjGi1tMd6t+D2QDfyikp4+qs/MRhkvqQQopTZJ0NFRUXx4YcfsmbNGuLj45kyZQp5eXmmUcVjx44tNwiqzEcffcTw4cMr3MLNzc3lmWeeYd++fSQlJbF161aGDRtGq1atiIyMNHc6dUpMYiar9yQBsOj+jjjZW+9vpUrRqFW8MaILjnYa9idmsmp3otIhCSHqCLM/gx05ciSXLl1i7ty5pKam0qVLFzZt2oS3tzcA586dqzDp+cSJE/z2229s2bKlQnsajYZDhw6xZs0asrKy8PPzY/DgwbzwwgtWNRf2alEJM7/+E4CRof70adNE4YisV3MPR+bc1Z7n1h/m9c0niGjnTaBno5tfKIRo0CwyyGn69OlMnz690vd27NhR4Vjbtm2vuzSZg4MDmzdvrs3w6qU3tpwg6XI+Ps72/N/d7ZQOx+o91N2fnw6n8FtCBrO/PczaiWFWOZlfCPEX61svqwGIPXuFj67dilx0f0ec5daw4lQqFS/f1xF7WzV7z1zmf7IhgBBWTwpsPVNYXMKz3xzCaIT7uzWlf3DF5SaFMpp7OPLUoLYAvPRjPOm6AoUjEkIoSQpsPfPBzjMkpOfi2diOuXe3Vzoc8Q/jewbSqZkLuoJi5snesUJYNSmw9UhSRh5LtycA8Pzd7XF1tFM4IvFPNho1r9zfCRu1ip+PpLLpSKrSIQkhFCIFtp4wGo08/90RiooN9Grlyb2d/ZQOSVxHez9nHu9bugfvvI1HyC0sVjgiIYQSpMDWExv/vMivpzKws1Hz4vAOMkK1jvvPgNYEejiSpivkreiTSocjhFCAFNh6IDtfzws/lG5DN71/K5ljWQ/Y22pMe8V+vCeJ46lVX79UCNEwSIGtB17dfJyM3CJaNGlkuvUo6r5+bb24s4MPJQYjz284ct253UKIhkkKbB33x7krrN1/DoCXhndEa2N9+zjWZ8/f3R5HOw0Hkq7wzcFkpcMRQliQFNg6zGAwMv/aVI/7uzUlvGX931rP2vi5OvDEwNYALPopnux869zoXAhrJAW2Dvv64AX+vJBNY60Ns+4MVjoccYse7RlEK6/GXM4rYvGWE0qHI4SwECmwdZSuQM9rm44D8OTA1ng52SsckbhVdjZqXhjWAYDP9p/lSHK2whEJISxBCmwd9c4vp0wDm8b1CFQ6HFFD4S09GNbFD6MRFnx/VAY8CWEFpMDWQQnpOaZ9Xufe3R47G/k2NQTPDgnG3lbNgaQr/Hg4RelwhBBmJv9y1zFGo5EF3x+j2GAkop0X/drKYv4NhZ+rA5P7tgRg0U/HKdCXKByREMKcpMDWMb/Ep5eu2KRRM+cuWcy/oXm8T0v8XOxJzrrKyl/PKB2OEMKMpMDWIYXFJaYVmx7rHSQrNjVADnYanr02Ivy9HadJky3thGiwpMDWIZ/sOcu5zHy8nbVM699K6XCEmdzb2Y+QADfyi0p49dpIcSFEwyMFto64klfE0m2nAHhqcFsaaW0UjkiYi0qlMu3l++3BZOLOZykbkBDCLKTA1hFLtyWgKygm2MeJB7o1UzocYWad/V1N3+eFMm1HiAZJCmwdkJSRx6f7kgD4v7vaoVHLVnTWYOaQtjjaaTh4LoufZWN2IRocKbB1wGubj6MvMdK3TRN6t26idDjCQryd7ZnUp3R3pNc2HUdfYlA4IiFEbZICq7DYs5n8dDgVtQqeG9pO6XCEhU3s3QLPxlqSLufzRcw5pcMRQtQiixTYZcuWERgYiL29PWFhYcTExFz33NWrV6NSqcp92duXX4fXaDQyd+5cfH19cXBwICIiglOnTpk7jVpnNBp58cd4AB4M9aetj5PCEQlLa6S14cmI0t123v7lFDkFstuOEA2F2Qvsl19+SVRUFPPmzePgwYN07tyZyMhI0tPTr3uNs7MzKSkppq+zZ8+We/+1117jnXfeYcWKFezfv59GjRoRGRlJQUH9mlP40+FU/jiXhYOthqhBbZQORyhk1O3+tPBsxOW8Ij7cJYtPCNFQmL3ALlmyhIkTJzJ+/Hjat2/PihUrcHR0ZNWqVde9RqVS4ePjY/ry9vY2vWc0GnnrrbeYM2cOw4YNo1OnTnzyySdcvHiRDRs2mDudWlNUbDDNgXy8bwu8nGW3HGtlq1Ezc0hbAD78NZF0WXxCiAbBrJMti4qKiI2NZfbs2aZjarWaiIgI9u7de93rcnNzCQgIwGAw0K1bN15++WVuu+02ABITE0lNTSUiIsJ0vouLC2FhYezdu5dRo0ZVaK+wsJDCwkLTa51OB4Ber0evV+aW3Cd7SxeV8HLSMj7c36JxlH2WUrkrqa7mPqCNB139XfjjfDZvbDnBi8PMs0xmXc3fUqw5f2vOHWov/+pcb9YCm5GRQUlJSbkeKIC3tzfHj1e+gk3btm1ZtWoVnTp1Ijs7m8WLF9OjRw+OHj1Ks2bNSE1NNbXxzzbL3vunRYsWsWDBggrHt2/fjqOj462kViOFJfDWQQ2gol+TfHb8ssXiMQBER0cr8rl1QV3MvY8z/IENX/1+nhb6JHzM+KNZF/O3JGvO35pzh5rnn5+fX+Vz69xyQeHh4YSHh5te9+jRg3bt2vH+++/zwgsv3FKbs2fPJioqyvRap9Ph7+9P//798fDwqHHM1bVsxxlyixMIcHdk/tge2GosO5hbr9cTHR3NoEGDsLW1tehnK62u535sbRzR8ekcKPRl+b+61nr7dT1/c7Pm/K05d6i9/MvugFaFWQusp6cnGo2GtLS0csfT0tLw8fGpUhu2trZ07dqVhIQEANN1aWlp+Pr6lmuzS5culbah1WrRarWVtm3pH7QreUV89FsSAFGD2+BoXzEuS1Ei/7qirub+7J3t2HbiEr8cv8SfyTmEBrqb5XPqav6WYs35W3PuUPP8q3OtWbtOdnZ2hISEsHXrVtMxg8HA1q1by/VSb6SkpITDhw+bimlQUBA+Pj7l2tTpdOzfv7/KbSppxc7T5BQW087XmXs6+SkdjqhjWnk15sHQ0iUUX998QpZQFKIeM/u9yaioKD788EPWrFlDfHw8U6ZMIS8vj/HjxwMwduzYcoOgFi5cyJYtWzhz5gwHDx7k4Ycf5uzZszz22GNA6QjjGTNm8OKLL7Jx40YOHz7M2LFj8fPzY/jw4eZOp0ZSswtYvScJgGci26CWJRFFJZ4Y2Bo7GzX7EzP5LSFD6XCEELfI7M9gR44cyaVLl5g7dy6pqal06dKFTZs2mQYpnTt3DrX6rzp/5coVJk6cSGpqKm5uboSEhLBnzx7at/9rVOXMmTPJy8tj0qRJZGVl0atXLzZt2lRhQYq65u2tpygsNhAa4Eb/tl5KhyPqKF8XBx4OC2DV7kRe33yCXq08UanklzEh6huLDHKaPn0606dPr/S9HTt2lHv95ptv8uabb96wPZVKxcKFC1m4cGFthWh2iRl5/O/38wA8e2ew/IMpbmhq/5asO3COQxey2XIsjcjbqjZmQQhRd8haxBayJPokJQYj/ds24XYzDVwRDYdnYy3jewYCsGRL6c+OEKJ+kQJrAUcvZvP9nxcBeDqyrcLRiPpiUu+WONnbcCIthx8OXVQ6HCFENUmBtYDFm08AcE9nP27zc1E4GlFfuDja8vi17ezejD4p29kJUc9IgTWzg+eusP3EJTRqlSzoL6ptfM8gPBrZkXQ5n69jLygdjhCiGqTAmtmb0ScBuL9rU4I8GykcjahvGmltmNq/FQDvbD1Fgb5E4YiEEFUlBdaMYs9m8uupDGzUKv4zoLXS4Yh6akxYc3xd7EnJLmDtftmUXYj6QgqsGb0ZXboJ/L9CmtHcw/KbCoiGwd5WY/oF7b0dCVwtkl6sEPWBFFgzibm2Co+NWsW0a7f4hLhVI0Kb4e/uQEZuEZ/vP6t0OEKIKpACayZlz15HhPrj7y69V1Eztho106/9orZi52npxQpRD0iBNYN9Zy6z98xlbDUqpg+Q3quoHfd3a0YzN+nFClFfSIE1g7Le68jb/Wnq6qBwNKKhsNWo+c8A6cUKUV9Iga1le05nsD8xEzuNWp69ilonvVgh6g8psLXIaDSaeq+juvvj6yK9V1G7yvdiz0gvVog6TApsLdqdcJkDSVews1EztZ/0XoV5/NWLLZRerBB1mBTYWmI0Gnnzl9Le6+juzfFxqdt704r6S3qxQtQPUmBrya+nMog9ewWtjZqp/VoqHY5o4P7ei10bI6s7CVEXSYGtJe9uSwBgdFhzvJyl9yrM65/zYmWNYiHqHimwtWDfmcvEJJWOHH68j/RehWWU9WIv5RTyuaxRLESdIwW2FpT1Xh+8vZk8exUWY2cjvVgh6jIpsDV08NwV05rD0nsVlvZAyF+92C/kWawQdYoU2Boq673e17WprDksLM5Wo2bKtUF1H+w6Q2Gx9GKFqCukwNbAkeRsth1PR63CtCm2EJb2r5BmeDtrScku4NuDyUqHI4S4RgpsDZT1Xu/p7EeQZyOFoxHWSmujYdK1xxPLd5ymuMSgcERCCLBQgV22bBmBgYHY29sTFhZGTEzMdc/98MMP6d27N25ubri5uREREVHh/EceeQSVSlXua8iQIeZOo5yTaTlsOpoKYBpoIoRSHuruj0cjO85l5vP9oYtKhyOEwAIF9ssvvyQqKop58+Zx8OBBOnfuTGRkJOnp6ZWev2PHDh566CG2b9/O3r178ff3Z/DgwSQnl7/1NWTIEFJSUkxfX3zxhblTKaes93pnBx9aeztZ9LOF+CdHOxse7RUEwLLtpzEYjApHJIQwe4FdsmQJEydOZPz48bRv354VK1bg6OjIqlWrKj3/888/Z+rUqXTp0oXg4GBWrlyJwWBg69at5c7TarX4+PiYvtzc3MydismZS7n8cK2XIPu9irpibHgAzvY2JKTnsvna3RUhhHJszNl4UVERsbGxzJ4923RMrVYTERHB3r17q9RGfn4+er0ed3f3csd37NiBl5cXbm5uDBgwgBdffBEPD49K2ygsLKSwsND0WqfTAaDX69Hr9dVNi2XbT2EwQv+2nrRp4nhLbSipLN76FndtaMi522vg33c0Z9mOMyzddoqBbT1QqVTlzmnI+VeFNedvzblD7eVfnetVRqPRbPeSLl68SNOmTdmzZw/h4eGm4zNnzmTnzp3s37//pm1MnTqVzZs3c/ToUeztSxdxWLduHY6OjgQFBXH69Gmee+45GjduzN69e9FoNBXamD9/PgsWLKhwfO3atTg6Vm9qzeUCeDFOg8Go4r8digmUu8OiDsnTw/yDGooMKh4PLqG9m9wqFqI25efnM3r0aLKzs3F2dr7huWbtwdbUK6+8wrp169ixY4epuAKMGjXK9P8dO3akU6dOtGzZkh07djBw4MAK7cyePZuoqCjTa51Oh7+/P/37979ur/d65m48hsF4gZ4tPZg6MuQWslKeXq8nOjqaQYMGYWtrq3Q4FmUNuZ/WnuCj3Wc5kO/BU6NvL9eLtYb8b8Sa87fm3KH28i+7A1oVZi2wnp6eaDQa0tLSyh1PS0vDx8fnhtcuXryYV155hV9++YVOnTrd8NwWLVrg6elJQkJCpQVWq9Wi1WorHLe1ta3WH3RqdgHfHCx99vrEwNb1/oe0uvk3JA0598f7tuLT/ec5eC6L2PM5hLes+EtkQ86/Kqw5f2vOHWqef3WuNesgJzs7O0JCQsoNUCobsPT3W8b/9Nprr/HCCy+wadMmQkNDb/o5Fy5c4PLly/j6+tZK3Nfz/q7TFJUY6B7kTliL6vV8hbAUL2d7Rt3uD8C7208pHI0Q1svso4ijoqL48MMPWbNmDfHx8UyZMoW8vDzGjx8PwNixY8sNgnr11Vd5/vnnWbVqFYGBgaSmppKamkpubi4Aubm5PPPMM+zbt4+kpCS2bt3KsGHDaNWqFZGRkWbL43LuX2u9/kdGDos67vG+LbFRq9idcJmD564oHY4QVsnsBXbkyJEsXryYuXPn0qVLF+Li4ti0aRPe3t4AnDt3jpSUFNP5y5cvp6ioiH/961/4+vqavhYvXgyARqPh0KFD3HvvvbRp04YJEyYQEhLCr7/+Wult4Nqyek8SBXoDnZu50KuVp9k+R4ja0NTVgfu7NQVg2bU520IIy7LIIKfp06czffr0St/bsWNHuddJSUk3bMvBwYHNmzfXUmRVk1OgZ82eJACm9GtZYeqDEHXRlH6t+Dr2AluPp3P0Yja3+bkoHZIQVkXWIq6CL2LOoSsopkWTRgxuf+PBWULUFUGejbi7kx8A720/rXA0QlgfKbA3UVhcwspfEwGY3LclarX0XkX9Me3aOtk/HUnhzKVchaMRwrpIgb2Jbw8mk55TiK+LPcO7NFU6HCGqpa2PExHtvDAaS/eLFUJYjhTYGygxGHl/Z+mttcd6t8DORv64RP0zpV9pL/abgxdI1RUoHI0Q1kMqxg38fCSFpMv5uDramuYVClHfhAS40T3IHX2JkdV7ziodjhBWQwrsdRiNRtPAkEd6BNJIW6dXlRTihqb0K92Qfd2BC+RZ51rvQlicFNjr2HUqg2MpOhztNIwLD1Q6HCFqpF+bJrTzdSavqITf0mSgnhCWIAX2Ot7bXjo5/6HuzXFrZKdwNELUjEqlMvVid6aoyS8qVjgiIRo+KbCViD17hf2JmdhqVDzWO0jpcISoFUM7+ODv5kBesYqvr21aIYQwHymwlVi+o/TZ631dm+Lr4qBwNELUDhuNmom9AwH46Lck9CUGZQMSooGTAvsPJ9Ny+CU+DZWqdMF0IRqS+7v44Wxr5GJ2ARvjpBcrhDlJgf2HFdd6r0Nu86Flk8YKRyNE7dLaaujnW9pzXb7zNAaDUeGIhGi4pMD+zYUr+Xz3Z+lv9WUDQoRoaHp6G3GytyEhPZdf4tOUDkeIBksK7N98uOsMJQYjvVp50qmZq9LhCGEW9jYwpnvpwinv7TiN0Si9WCHMQQrsNRm5haw7cB6Q3qto+MaFN0droybufBb7zmQqHY4QDZIU2GvW7EmisNhAp2Yu9GjpoXQ4QpiVZ2MtD4aW9mKX75St7IQwBymwlN9QfapsqC6sxKQ+LdCoVew6eYkjydlKhyNEgyMFFtlQXVgnf3dH7unkC0gvVghzsPoCKxuqC2s2+dp4g58Pp5CYkadwNEI0LFZfYGVDdWHNgn2cGRDshUE2ZBei1ll1gZUN1YUoHXcA8E3sBdJkQ3Yhao1VV5St8emyobqweqGB7twe6EZRiYFVvyUqHY4QDYZVF9hVe84CsqG6EGVzvz/bd5bsfNmRXYjaYNUF9kRarmyoLgTQv60XwT5O5BWV8Om+JKXDEaJBsEiBXbZsGYGBgdjb2xMWFkZMTMwNz//qq68IDg7G3t6ejh078tNPP5V732g0MnfuXHx9fXFwcCAiIoJTp07dUmyyoboQ5Tdk/3h3EleLShSOSIj6z+wF9ssvvyQqKop58+Zx8OBBOnfuTGRkJOnp6ZWev2fPHh566CEmTJjAH3/8wfDhwxk+fDhHjhwxnfPaa6/xzjvvsGLFCvbv30+jRo2IjIykoKB6AzRkQ3Uh/nJXR1/83R24nFfE/34/r3Q4QtRJxdXYR9nsDx6XLFnCxIkTGT9+PAArVqzgxx9/ZNWqVcyaNavC+W+//TZDhgzhmWeeAeCFF14gOjqad999lxUrVmA0GnnrrbeYM2cOw4YNA+CTTz7B29ubDRs2MGrUqAptFhYWUlhYaHqt0+kAGNLeC09HG/R663rmVJavteUN1p073Dz/CT0Dmf99PB/sOs2Ibr7YahrWUyRr/v5bc+5Qe/nPWHewyueatcAWFRURGxvL7NmzTcfUajURERHs3bu30mv27t1LVFRUuWORkZFs2LABgMTERFJTU4mIiDC97+LiQlhYGHv37q20wC5atIgFCxZUON6G5Aq3n61JdHS00iEoxppzh+vn36gEGttqSM4q4OXPNnN7k4a50441f/+tOXeoWf4p+bDjZFGVzzdrgc3IyKCkpARvb+9yx729vTl+/Hil16SmplZ6fmpqqun9smPXO+efZs+eXa5o63Q6/P39GTm0Px4e1rewv16vJzo6mkGDBmFra6t0OBZlzblD1fJPc0lkcfQp9uucef7fPRrU6mbW/P235tyhdvKf+e0RIKHK51vF3BStVotWq61w3NbW1ip/0MpYc/7WnDvcOP+xPYN4f1cip9Lz+PX0FSLae1d6Xn1mzd9/a84dbj3/i1lX+f7PlGpdY9YHLJ6enmg0GtLS0sodT0tLw8en8kX1fXx8bnh+2X+r06YQouqc7W0Zc0cAAO/tSJAN2YUAPvz1DMUGI90D3at8jVkLrJ2dHSEhIWzdutV0zGAwsHXrVsLDwyu9Jjw8vNz5UHrPvOz8oKAgfHx8yp2j0+nYv3//ddsUQlTPo70CsbNRc/BcFjGJsiG7sG6ZeUWsiykdWf9Yn6rPPDH7EMGoqCg+/PBD1qxZQ3x8PFOmTCEvL880qnjs2LHlBkE9+eSTbNq0iTfeeIPjx48zf/58fv/9d6ZPnw6UztebMWMGL774Ihs3buTw4cOMHTsWPz8/hg8fbu50hLAKXk72jAhpBsB7O2QrO2Hd1uxJ4qq+hA5NnQlvUfVxO2Z/Bjty5EguXbrE3LlzSU1NpUuXLmzatMk0SOncuXOo1X/V+R49erB27VrmzJnDc889R+vWrdmwYQMdOnQwnTNz5kzy8vKYNGkSWVlZ9OrVi02bNmFvb2/udISwGo/3ackXMefYefISRy9mc5ufi9IhCWFxeYXFrN6TBMCUvq1Qqao+6M8ig5ymT59u6oH+044dOyocGzFiBCNGjLhueyqVioULF7Jw4cLaClEI8Q/NPRy5u5MfG/+8yIqdZ1j6UFelQxLC4r6IOUf2VT1Bno0Y0sGHvNycKl/bsGaRCyFq1eS+pcsn/njoIkmyIbuwMkXFBlb+WrrD1ON9WqCp5pQ1KbBCiOtq7+dM/7ZNSjdk/1U2ZBfWZcMfyaTqCvBy0nJft6bVvl4KrBDihqb0awXA179fIF02ZBdWosRgZMWu0gF+j/UOQmujqXYbUmCFEDfUPcid0IDSDdk/2i0bsgvrEH0slTOX8nC2t2F0WMAttSEFVghxU2Vb2X2+r3TAhxANmdFoNE1PG9cjkMbaWxsPLAVWCHFTA4K9aOvtRG5hMZ/tO6t0OEKY1Z7Tlzl0IRt7WzWP9Ai85XakwAohburvG7Kv+i2RAr1syC4aruXXeq+jbm+OR+OK69hXlRRYIUSV3N3Jl2ZusiG7aNgOXcjit4QMNGoVj/Wu+rKIlZECK4SoEhuNmsf7tADg/Z1n0JcYFI5IiNpX1nsd1tmPZm6ONWpLCqwQospGhPrj2diO5Kyr/HDootLhCFGrTl/KZdPR0n3FJ197JFITUmCFEFVmb6thfM/S22bLd5zGYJCt7ETD8f7O0xiNENHOmzbeTjVuTwqsEKJaHr4jgMZaG06m5bL9RLrS4QhRK1Kyr7L+j2Tgr2lpNSUFVghRLS4Otoy5ozlQupWdbMguGoKPfk1EX2Kke5A7IQFutdKmFFghRLVN6BmEnY2a2LNXOJB0RelwhKiRK3lFrI05B8DUWuq9ghRYIcQt8HK251+mDdkTFI5GiJr5ZO9Z8otKaOfrTN82TWqtXSmwQohb8nifFqhVsOPEJY5d1CkdjhC3JL+omNV7StfYntKvZbU2VL8ZKbBCiFsS4NGIuzr5AbB852mFoxHi1qyLOc+VfD0BHo4M7eBTq21LgRVC3LLJfUsXnvjx0EXOXpYN2UX9Urqheuk+x5P6tMBGU7slUQqsEOKW3ebnQr+yDdl3yYbson5Z/8cFLmYX0MRJywPdmtV6+1JghRA1MqVv6ajLr2IvkJ4jG7KL+qG4xGBaFnFS7xbY21Z/Q/WbkQIrhKiRsnmDRcUGVv2WpHQ4QlTJj4dTSLqcj5ujLaPDmpvlM6TACiFqRKVSmXqxn+07KxuyizrPYDCybHvp9LJHewbR6BY3VL8ZKbBCiBr7+4bsn+xJUjocIW4oOj6Nk2m5OGltGFuDDdVvxqwFNjMzkzFjxuDs7IyrqysTJkwgNzf3huf/5z//oW3btjg4ONC8eXOeeOIJsrOzy52nUqkqfK1bt86cqQghbkCtVjG1/7UN2XcnkldYrHBEQlTOaPyr9zq2RwAuDrZm+yyzFtgxY8Zw9OhRoqOj+eGHH9i1axeTJk267vkXL17k4sWLLF68mCNHjrB69Wo2bdrEhAkTKpz78ccfk5KSYvoaPny4GTMRQtzM3Z38CPJsxJV8PZ/vP6t0OEJU6reEyxy6kI2DrYZHe9ZsQ/WbMc+NZyA+Pp5NmzZx4MABQkNDAVi6dClDhw5l8eLF+Pn5VbimQ4cOfPPNN6bXLVu25KWXXuLhhx+muLgYG5u/wnV1dcXHp2qTggsLCyksLDS91ulKV53R6/Xo9db3vKgsZ8nd+pg7/0m9A5m9/igf7DrDQ6FNzTIysyas+ftvzbnDX3kvuzZyeGRoU5y16mr/eVTnfJXRTFthrFq1iqeeeoorV/5aCLy4uBh7e3u++uor7rvvviq1s3LlSmbPns2lS5dMx1QqFX5+fhQWFtKiRQsmT57M+PHjr7vE1fz581mwYEGF42vXrsXRsWY71gsh/lJigBfjNGQWqnggsIQ+vrLTjqg7EnSw9KgNGpWRuV1LcNVWv438/HxGjx5NdnY2zs7ONzzXbD3Y1NRUvLy8yn+YjQ3u7u6kpqZWqY2MjAxeeOGFCreVFy5cyIABA3B0dGTLli1MnTqV3NxcnnjiiUrbmT17NlFRUabXOp0Of39/+vfvj4eHRzUzq//0ej3R0dEMGjQIW1vzPX+oi6w5d7BM/jle55n3fTy/ZTqyYFxvtDZ1ZyylNX//rTl3KM1/+dtbARgR6s/oe9vfUjtld0CrotoFdtasWbz66qs3PCc+Pr66zVag0+m46667aN++PfPnzy/33vPPP2/6/65du5KXl8frr79+3QKr1WrRaiv+qmJra2uVP2hlrDl/a84dzJv/qLAA3tt5hjRdIRsPpZltjmFNWPP331pzP3Qhm+PZajRqFdP6t77lP4PqXFftXy2feuop4uPjb/jVokULfHx8SE9PL3dtcXExmZmZN312mpOTw5AhQ3BycmL9+vU3TSgsLIwLFy6Ue84qhFCG1kbD431KRxS/tyMBfYlB4YiEgBW7SnfMubeTD/7ulnk0WO0ebJMmTWjS5Ob75YWHh5OVlUVsbCwhISEAbNu2DYPBQFhY2HWv0+l0REZGotVq2bhxI/b29jf9rLi4ONzc3CrtpQohLO+h7s15b0cCF65c5bu4i6a9Y4VQwvFUHdHx6agw8nifFhb7XLM9HGnXrh1Dhgxh4sSJxMTEsHv3bqZPn86oUaNMI4iTk5MJDg4mJiYGKC2ugwcPJi8vj48++gidTkdqaiqpqamUlJQA8P3337Ny5UqOHDlCQkICy5cv5+WXX+Y///mPuVIRQlSTg52Gx3qX/kP23vYESgwy2Eko573tpSOHO3sYadmkkcU+12yDnAA+//xzpk+fzsCBA1Gr1TzwwAO88847pvf1ej0nTpwgPz8fgIMHD7J//34AWrVqVa6txMREAgMDsbW1ZdmyZfz3v//FaDTSqlUrlixZwsSJE82ZihCimh6+I4AVO09zJiOPHw5dZFiXpkqHJKxQ4rWfP4BBTS37uMKsBdbd3Z21a9de9/3AwED+PkuoX79+3GzW0JAhQxgyZEitxSiEMI/GWhse7RnEkuiTLNuewD2d/FCrK59KJ4S5vLc9AYMR+rXxpFmjqs1gqS11Z/y8EKLBGdcjECetDSfTctlyzLL/uAlx9nIe3/6RDMC0fpZ79lpGCqwQwmxcHGwZd20x9aXbEm56h0qI2rTs2vP/vm2a0MXf1eKfLwVWCGFWj/YKwtFOw9GLOrafSL/5BULUgnOX8/nmYGnv9cmI1orEIAVWCGFW7o3sePiOAADe2Sq9WGEZ724/Zeq9dmvupkgMUmCFEGb3WO8g7G3VxJ3PYufJSze/QIgaOHc5n28V7r2CFFghhAV4OdnzcFhpL/bNX05JL1aY1bLtCRQbjPRRsPcKUmCFEBbyeN+WONhq+PN8ljyLFWZT+uz1AgBPDlSu9wpSYIUQFtLEScvY8Gu92GjpxQrz+HvvNSRAud4rSIEVQljQpD4tcLTTcDg5m1/ipRcratf5zLrTewUpsEIIC/JorDXNi30z+qT0YkWtKuu99m7tqXjvFaTACiEsbFLvFjSy03AsRcfmo2lKhyMaiPOZ+XwdW9p7naHgyOG/kwIrhLAot0Z2jO8ZBMBbv5zEIDvtiFrw3o6/917dlQ4HkAIrhFDAY72DcNLacDw1h01HZY1iUTPnLufz1e9159lrGSmwQgiLc3W0Y3wv6cWK2vHWLydNI4dDA+tG7xWkwAohFDKhVxBO9qU77fx4OEXpcEQ9dSoth/Vxpas2PT24jcLRlCcFVgihCBcHWx7rVbqF2NtbS9eNFaK6lkSfxGiEyNu86dTMVelwypECK4RQzPhegTjb25CQnsv3f15UOhxRzxxJzubnI6moVPDU4LZKh1OBFFghhGKc7W15vG9LoLQnUlRsUDgiUZ8s3nICgGGd/Wjj7aRwNBVJgRVCKGp8z0A8G2s5l5nPl7+fVzocUU/8npTJjhOX0KhVzIioW89ey0iBFUIoytHOhicGtgLgna2nyC8qVjgiUdcZjUZe31zae30wtBmBno0UjqhyUmCFEIobdXtz/N0duJRTyOo9SUqHI+q43xIy2J+YiZ1GzX8G1J15r/8kBVYIoTg7GzX/vXabb8WO02Tn6xWOSNRVRqORxdd6r6PDmuPn6qBwRNcnBVYIUScM69KUtt5O6AqKWbHrtNLhiDoq+lgaf17IxsFWw7T+rZQO54bMWmAzMzMZM2YMzs7OuLq6MmHCBHJzc294Tb9+/VCpVOW+Jk+eXO6cc+fOcdddd+Ho6IiXlxfPPPMMxcXy3EaI+kyjVvF0ZOlUi493J5KuK1A4IlHXFJcYTM9eH+kZSBMnrcIR3ZhZC+yYMWM4evQo0dHR/PDDD+zatYtJkybd9LqJEyeSkpJi+nrttddM75WUlHDXXXdRVFTEnj17WLNmDatXr2bu3LnmTEUIYQER7bzo1tyVAr2BpdsSlA5H1DHfHLzAqfRcXB1tmXxtelddZmOuhuPj49m0aRMHDhwgNDQUgKVLlzJ06FAWL16Mn5/fda91dHTEx8en0ve2bNnCsWPH+OWXX/D29qZLly688MILPPvss8yfPx87O7sK1xQWFlJYWGh6rdPpANDr9ej11vespyxnyd361If8oyJa8fCq3/ki5hzjwv0JcHestbbrQ/7mUt9zv1pUwpItJwGY0icIR5vq5VJb+VfnepXRTDser1q1iqeeeoorV66YjhUXF2Nvb89XX33FfffdV+l1/fr14+jRoxiNRnx8fLjnnnt4/vnncXQs/Us2d+5cNm7cSFxcnOmaxMREWrRowcGDB+natWuFNufPn8+CBQsqHF+7dq2pXSFE3bH8mJrj2WpCPA2MbS2LTwiITlbxwzkN7loj/9elBBuFRhDl5+czevRosrOzcXZ2vuG5ZuvBpqam4uXlVf7DbGxwd3cnNfX621ONHj2agIAA/Pz8OHToEM8++ywnTpzg22+/NbXr7e1d7pqy19drd/bs2URFRZle63Q6/P396d+/Px4eHreUX32m1+uJjo5m0KBB2NraKh2ORVlz7lB/8g/oomP48n0cvKzm+RE9uM3vxv+QVVV9yd8c6nPumXlF/N+bvwHFPHd3R+7tcv07oNdTW/mX3QGtimoX2FmzZvHqq6/e8Jz4+PjqNmvy92e0HTt2xNfXl4EDB3L69Glatry1e+5arRattuLDcFtb23r3g1abrDl/a84d6n7+XQI8GNbFj+/iLvLq5lOsnRiGSqWqtfbrev7mVB9zX/HrSXILi2nv68z9Ic1Rq2/9Z6Gm+Vfn2moX2KeeeopHHnnkhue0aNECHx8f0tPTyx0vLi4mMzPzus9XKxMWFgZAQkICLVu2xMfHh5iYmHLnpKWlAVSrXSFE3fb04Lb8fCSVvWcus+14OgPbed/8ItHgnLucz2f7zgIwe2hwjYqrpVW7wDZp0oQmTZrc9Lzw8HCysrKIjY0lJCQEgG3btmEwGExFsyrKnrX6+vqa2n3ppZdIT0833YKOjo7G2dmZ9u3bVzMbIURd5e/uyPiegby/8wwv/xRP3zZNsNHI1H1rs3jLCfQlRnq39qR365vXnrrEbD+t7dq1Y8iQIUycOJGYmBh2797N9OnTGTVqlGkEcXJyMsHBwaYe6enTp3nhhReIjY0lKSmJjRs3MnbsWPr06UOnTp0AGDx4MO3bt+ff//43f/75J5s3b2bOnDlMmzat0tvAQoj6a1r/Vrg52nL6Uh7rDshGANbm8IVsNl7bxvDZIcEKR1N9Zv118PPPPyc4OJiBAwcydOhQevXqxQcffGB6X6/Xc+LECfLz8wGws7Pjl19+YfDgwQQHB/PUU0/xwAMP8P3335uu0Wg0/PDDD2g0GsLDw3n44YcZO3YsCxcuNGcqQggFONvbmnZKeeuXk+QU1M8pJqL6jEYjL/9UOp5neBc/OjR1UTii6jPbKGIAd3d31q5de933AwMD+fssIX9/f3bu3HnTdgMCAvjpp59qJUYhRN02Oqw5q/ckkZiRx/s7z5hWexIN25Zjaew9cxk7G3Wd3Ey9KuSBhhCiTrPVqJl1Z+ntwQ9/PUNK9lWFIxLmVlhcYuq9TuwdhH8tLjZiSVJghRB13uD23nQPdKew+K+1aEXDtXp3Emcv5+PlpGVqv7q9oP+NSIEVQtR5KpWK/7urHQDr/0jm0IUsZQMSZnMpp9C0DvXMIcE00pr1SaZZSYEVQtQLnf1dua9rU4xGmL/xKAaDWVZ5FQpbEn2C3MJiOjVz4f6uTZUOp0akwAoh6o1ZdwbjaKfh4Lks1v+RrHQ4opYdvZhtmo419+729WpRicpIgRVC1Bvezvb8Z0BrAF7ZdFym7TQgRqORhd8fw2iEuzv5EhrornRINSYFVghRrzzaK5Agz0ZcyinkXdkztsHYfDSV/YmZaG3UzB7aTulwaoUUWCFEvaK10TD37tJlUVftTuT0pVyFIxI1lV9UzAs/lE7LmdSnBU1dHRSOqHZIgRVC1Dv9g70YEOyFvqTstqIMeKrP3t2WQHLWVZq6OtTraTn/JAVWCFEvzb27PXYaNTtPXmJrfPrNLxB10ulLuXz46xkA5t3THgc7jcIR1R4psEKIeinQsxETegcBsPCHYxToSxSOSFSX0Whk3ndH0ZcYGRDsxaD2DWtLQimwQoh6a3r/Vvg423MuM18GPNVDPx5O4beEDOxs1My7pz0qVf2elvNPUmCFEPVWI60N8++9DYD3d53mVFqOwhGJqsotLOaFH44BMLVfSwI8GikcUe2TAiuEqNcib/Mmol3pgKf/W39EVniqJ97+5SRpukICPByZ3Lel0uGYhRRYIUS9plKpWDCsA452GmKSMvk69oLSIYmbOHoxm1W7kwCYf+9t2Ns2nIFNfycFVghR7zV1deC/1zZmf/nneC7nFiockbie4hIDs745TInByNCOPvRv66V0SGYjBVYI0SCM7xlIO19nsvL1vHRtL1FR93y8O4nDydk42//1/LyhkgIrhGgQbDRqFt3fEZUKvj2YzG+nMpQOSfzDucv5vBFdup/vnLva4+Vkr3BE5iUFVgjRYHTxd+XfdwQA8Ow3h8gtLFY4IlHGaDTy3PrDFOgN9GjpwYjQZkqHZHZSYIUQDcqzQ4Jp5uZActZVXv35uNLhiGu+OZjMbwkZaG3K7jQ0rDmvlZECK4RoUBppbXj1gU4AfLrvLHtPX1Y4IpGmKzDNeY0a1KZBznmtjBRYIUSD07OVJ6PDmgMw85s/yS+SW8VKMRqNPPvNIbKv6unY1IUJvYKUDslipMAKIRqk2XcG09TVgfOZV3lt0wmlw7FaXx44z44Tl7CzUbPkwc7YaKyn7Jg108zMTMaMGYOzszOurq5MmDCB3Nzr792YlJSESqWq9Ourr74ynVfZ++vWrTNnKkKIesbJ3pZXHugIwOo9Sew7I7eKLe18Zr7p1vAzg9vS2ttJ4Ygsy6wFdsyYMRw9epTo6Gh++OEHdu3axaRJk657vr+/PykpKeW+FixYQOPGjbnzzjvLnfvxxx+XO2/48OHmTEUIUQ/1bt2Eh7r7AxD1ZRy6q3qFI7IeBoORp7/6k7yiEroHuvOoFd0aLmNjrobj4+PZtGkTBw4cIDQ0FIClS5cydOhQFi9ejJ+fX4VrNBoNPj4+5Y6tX7+eBx98kMaNG5c77urqWuFcIYT4pzl3tWfv6cskXc5n7sZ4BjW++TWi5lbtTmR/YiaOdhoWj+iMRt3wRw3/k9kK7N69e3F1dTUVV4CIiAjUajX79+/nvvvuu2kbsbGxxMXFsWzZsgrvTZs2jccee4wWLVowefJkxo8ff91h34WFhRQW/rV0mk6nA0Cv16PXW99vtGU5S+7Wxxrzt1PD4n91ZOSHMfx4JBW3VioGW1H+ZSz5vT+emsNrm0ufe88e0hZfZ1vFf+ZqK//qXG+2ApuamoqXV/k1Jm1sbHB3dyc1NbVKbXz00Ue0a9eOHj16lDu+cOFCBgwYgKOjI1u2bGHq1Knk5ubyxBNPVNrOokWLWLBgQYXj27dvx9HRsYoZNTzR0dFKh6AYa84drDP/IU1V/Hhew1eJalp8H41Hw15E6LrM/b0vLIE3DmsoKlbR3tWAU/ohfvrpkFk/szpqmn9+fn6Vz612gZ01axavvvrqDc+Jj6/5OqBXr15l7dq1PP/88xXe+/uxrl27kpeXx+uvv37dAjt79myioqJMr3U6Hf7+/vTv3x8PD48ax1rf6PV6oqOjGTRoELa2tkqHY1HWnDtYd/6RBiMpK2M4eD6b7y+5s/ax7lY1otVS3/vnNhwl7WoyXk5aVk0Ox6ORndk+qzpqK/+yO6BVUe0C+9RTT/HII4/c8JwWLVrg4+NDenp6uePFxcVkZmZW6dnp119/TX5+PmPHjr3puWFhYbzwwgsUFhai1WorvK/Vais9bmtra3X/yPydNedvzbmDdeZvC7wxohN3vr2LPy7oWLYziacj2yodlsWZ83v//Z8X+So2GZUK3hrVBR/XuregRE3zr8611S6wTZo0oUmTJjc9Lzw8nKysLGJjYwkJCQFg27ZtGAwGwsLCbnr9Rx99xL333lulz4qLi8PNza3SIiqEEGWauTkwsoWBNac0vLs9gZBAtwa9XZolnc/M57lvDwMwrV8rerT0VDgi5Znt/ki7du0YMmQIEydOJCYmht27dzN9+nRGjRplGkGcnJxMcHAwMTEx5a5NSEhg165dPPbYYxXa/f7771m5ciVHjhwhISGB5cuX8/LLL/Of//zHXKkIIRqQbp5GxlybuvPfL+NIzrqqcET1X4G+hKmfHySnsJjQADdmRLRWOqQ6wawPID7//HOCg4MZOHAgQ4cOpVevXnzwwQem9/V6PSdOnKjw0HjVqlU0a9aMwYMHV2jT1taWZcuWER4eTpcuXXj//fdZsmQJ8+bNM2cqQogGZPadbenUzIWsfD3TPj9IUbFB6ZDqLaPRyNzvjnA4ORv3Rna8/VBXq3q2fSNmG0UM4O7uztq1a6/7fmBgIEajscLxl19+mZdffrnSa4YMGcKQIUNqLUYhhPXR2qhZNrobd73zK3Hns3j5p/gGv/m3uXwRc57//X4BtQqWPtSVpq4OSodUZ8ivGUIIq+Tv7siSB7sApUspfh17QdmA6qG481nM33gUgGcig+nZSp67/p0UWCGE1Ypo780TA1oB8Ny3h4k9m6lwRPVHek4BUz6LpajEwJDbfJjct4XSIdU5UmCFEFZtRkQbIm/zpqjEwOOfxsqgpyq4WlTCxE9iSckuoEWTRrw+opNVbKBeXVJghRBWTa1WseTBLgT7OJGRW8TENb/L/rE3YDAYeeqrOP48n4Wroy2rxt2Ok711zamuKimwQgir10hrw8pxoXg0suNYio4nvoijuERGFldm8ZYT/HQ4FVuNig/+HUqgZ91bTKKukAIrhBBAMzdHVvw7BDsbNb/Ep/H8d0crneVgzf534Dzv7TgNwKsPdKJ7kLvCEdVtUmCFEOKa2wPdeWdUF9Qq+CLmHG9vPaV0SHXGlqOpzF5fulLTEwNacX+3ZgpHVPdJgRVCiL8Z0sGXhcM6APDWL6f4fP9ZhSNS3p7TGUz/4g9KDEb+FdKMGRFtlA6pXpACK4QQ//DwHQGm6TvPbzjCd3HJCkeknEMXspi45neKig0Mbu/NK/d3RG2Fm6ffCimwQghRif8OasPosOYYjKVrFn//50WlQ7K4I8nZjF0VQ15RCeEtPHhHlkGsFvmTEkKISqhUKl4c1oEHQ5thMMKML+P46XCK0mFZzOEL2YxZuZ+sfD2d/V35cFwo9rYapcOqV6TACiHEdajVKl65vxMPdGtGicHIE1/8wUYr6MnGnc9i9Mp9ZF/V0625K59O6E5jrVmXrm+QpMAKIcQNqNUqXvtXJ+7r2pRig5En1/3Bmj1JSodlNntOZ/DvlfvJKSjm9kA3PpkQhrMsJHFLpMAKIcRNaNQqFo/ozNjwAIxGmLfxKEuiTza4ebLfxSUzblUMOYXF3NHCndXjpedaE1JghRCiCjRqFQvuvY3/Xpui8s7WU8z8+hCFxSUKR1ZzRqORFTtP8+S6OPQlRu7q5Mvq8d1pJMW1RqTACiFEFalUKp6MaM0LwzugVsFXsRcY/eF+0nMKlA7tlhXoS5j59SFe+fk4ABN6BbF0VFcZ0FQLpMAKIUQ1/fuOAD4e3x1nextiz15h2Lu7OXQhS+mwqi056yojVuzlq9jSDdOfv7s9z9/dXua51hIpsEIIcQv6tmnChmk9adGkESnZBTywfA8f7jqDwVA/nstGH0vjnqW/cTg5G1dHWz55NIwJvYKUDqtBkQIrhBC3qEWTxmyY1pPI27zRlxh56ad4xn0cQ7qu7t4yzi8qZva3h5n4ye9k5hVxm58z30/vRa/WnkqH1uBIgRVCiBpwtrdlxcMhvHRfB7Q2an49lcHAJTtZu/9cnevNHs9Scc+yvXwRcw6ASX1a8O3UHvi7OyocWcMkBVYIIWpIpVIxJiyA7//Ti07NXMgpKOa59YcZ9cE+jiRnKx0eqdkFPPnlnyyP13Au8yq+LvasfSyM54a2Q2sjg5nMRcZgCyFELWnj7cT6qT1ZvSeJN7acICYpk7uX/sbwLn48NbitxXuKV/KKWLHzNKv3JFFYbECFkXHhATwVGYyTLB5hdlJghRCiFmnUKib0CiLyNm9e33yC7+IusiHuIj8cSuGezn481juI2/xczBpDctZVPt17ls/3nSWnsBiAkOauDHDNYNLQYGxtpbhagtluEb/00kv06NEDR0dHXF1dq3SN0Whk7ty5+Pr64uDgQEREBKdOld/wODMzkzFjxuDs7IyrqysTJkwgNzfXDBkIIcSta+bmyNujupYOIGrlSbHByPo/krnrnd8Y+f5e/nfgPLoCfa19XoG+hC1HU5n8aSy9X93Gip2nySkspr2vMx8/cjtfPHY7zRrV2seJKjBbD7aoqIgRI0YQHh7ORx99VKVrXnvtNd555x3WrFlDUFAQzz//PJGRkRw7dgx7e3sAxowZQ0pKCtHR0ej1esaPH8+kSZNYu3atuVIRQohb1rGZC589Fsaf57P48Ncz/Hwklf2JmexPzGTOd0fo1cqTHi096NXak9ZeTmiqOAfVaDSSdDmfmMTL7Dl9mW3x6abeKkDPVh480iOIgcFeqNUq9PraK+aiasxWYBcsWADA6tWrq3S+0WjkrbfeYs6cOQwbNgyATz75BG9vbzZs2MCoUaOIj49n06ZNHDhwgNDQUACWLl3K0KFDWbx4MX5+fmbJRQghaqqzvyvvju5GctZVNvyRzIY/kjmVnsu24+lsO54OgNZGTSuvxrT2akwTJy0ejbVobdSogKISA1fy9WTkFJKYkUfCpVyy8ssXTV8Xe4Z29OXBUH/a+jgpkKX4uzrzDDYxMZHU1FQiIiJMx1xcXAgLC2Pv3r2MGjWKvXv34urqaiquABEREajVavbv3899991XaduFhYUUFhaaXut0OgD0er1V/lZXlrPkbn0kf+Xz92pkw6ReAUzs2ZyTabn8drq0B3og6QpX9QaOXtRx9KKuSm3ZalR0bubC7YFu9G3tSVd/V9MqTP/MsS7krqTayr8619eZApuamgqAt7d3uePe3t6m91JTU/Hy8ir3vo2NDe7u7qZzKrNo0SJTj/rvtm/fjqOj9c7/io6OVjoExVhz7iD516X8fYEHPOE+D7hcAClXVaRfhRy9ijw9FF+bSqtWQWMbaGRrpIk9eDkY8bIHO00GFGWQdvQUm47e/PPqUu5KqGn++fn5VT63WgV21qxZvPrqqzc8Jz4+nuDg4Oo0a3azZ88mKirK9Fqn0+Hv70///v3x8PBQMDJl6PV6oqOjGTRokNWNJrTm3EHyt+b8rTl3qL38y+6AVkW1CuxTTz3FI488csNzWrRoUZ0mTXx8fABIS0vD19fXdDwtLY0uXbqYzklPTy93XXFxMZmZmabrK6PVatFqtRWO29raWuUPWhlrzt+acwfJ35rzt+bcoeb5V+faahXYJk2a0KRJk2oHVBVBQUH4+PiwdetWU0HV6XTs37+fKVOmABAeHk5WVhaxsbGEhIQAsG3bNgwGA2FhYWaJSwghhLgVZpsHe+7cOeLi4jh37hwlJSXExcURFxdXbs5qcHAw69evB0qXGpsxYwYvvvgiGzdu5PDhw4wdOxY/Pz+GDx8OQLt27RgyZAgTJ04kJiaG3bt3M336dEaNGiUjiIUQQtQpZhvkNHfuXNasWWN63bVrV6B0YFG/fv0AOHHiBNnZf63TOXPmTPLy8pg0aRJZWVn06tWLTZs2mebAAnz++edMnz6dgQMHolareeCBB3jnnXfMlYYQQghxS8xWYFevXn3TObBGY/mdJlQqFQsXLmThwoXXvcbd3V0WlRBCCFHnyW46QgghhBlIgRVCCCHMQAqsEEIIYQZSYIUQQggzkAIrhBBCmEGdWYvYkspGL+fk5FjliiZ6vZ78/Hx0Op3V5W/NuYPkb835W3PuUHv5ly2V+M9ZMJWxygJ7+fJloHT1KCGEEKK6cnJycHFxueE5Vllg3d3dgdLVpm72B9QQlW12cP78eZydnZUOx6KsOXeQ/K05f2vOHWovf6PRSE5OTpVWD7TKAqtWlz56dnFxscoftDLOzs5Wm7815w6SvzXnb825Q+3kX9WOmQxyEkIIIcxACqwQQghhBlZZYLVaLfPmzat0j1hrYM35W3PuIPlbc/7WnDsok7/KWJWxxkIIIYSoFqvswQohhBDmJgVWCCGEMAMpsEIIIYQZSIEVQgghzEAKrBBCCGEGVllgly1bRmBgIPb29oSFhRETE6N0SBaxa9cu7rnnHvz8/FCpVGzYsEHpkCxm0aJF3H777Tg5OeHl5cXw4cM5ceKE0mFZzPLly+nUqZNpFZvw8HB+/vlnpcNSxCuvvIJKpWLGjBlKh2IR8+fPR6VSlfsKDg5WOiyLSk5O5uGHH8bDwwMHBwc6duzI77//bvbPtboC++WXXxIVFcW8efM4ePAgnTt3JjIykvT0dKVDM7u8vDw6d+7MsmXLlA7F4nbu3Mm0adPYt28f0dHR6PV6Bg8eTF5entKhWUSzZs145ZVXiI2N5ffff2fAgAEMGzaMo0ePKh2aRR04cID333+fTp06KR2KRd12222kpKSYvn777TelQ7KYK1eu0LNnT2xtbfn55585duwYb7zxBm5ubub/cKOV6d69u3HatGmm1yUlJUY/Pz/jokWLFIzK8gDj+vXrlQ5DMenp6UbAuHPnTqVDUYybm5tx5cqVSodhMTk5OcbWrVsbo6OjjX379jU++eSTSodkEfPmzTN27txZ6TAU8+yzzxp79eqlyGdbVQ+2qKiI2NhYIiIiTMfUajURERHs3btXwciEpWVnZwN/7axkTUpKSli3bh15eXmEh4crHY7FTJs2jbvuuqvc339rcerUKfz8/GjRogVjxozh3LlzSodkMRs3biQ0NJQRI0bg5eVF165d+fDDDy3y2VZVYDMyMigpKcHb27vccW9vb1JTUxWKSliawWBgxowZ9OzZkw4dOigdjsUcPnyYxo0bo9VqmTx5MuvXr6d9+/ZKh2UR69at4+DBgyxatEjpUCwuLCyM1atXs2nTJpYvX05iYiK9e/cmJydH6dAs4syZMyxfvpzWrVuzefNmpkyZwhNPPMGaNWvM/tlWuV2dsG7Tpk3jyJEjVvUcCqBt27bExcWRnZ3N119/zbhx49i5c2eDL7Lnz5/nySefJDo6Gnt7e6XDsbg777zT9P+dOnUiLCyMgIAA/ve//zFhwgQFI7MMg8FAaGgoL7/8MgBdu3blyJEjrFixgnHjxpn1s62qB+vp6YlGoyEtLa3c8bS0NHx8fBSKSljS9OnT+eGHH9i+fTvNmjVTOhyLsrOzo1WrVoSEhLBo0SI6d+7M22+/rXRYZhcbG0t6ejrdunXDxsYGGxsbdu7cyTvvvIONjQ0lJSVKh2hRrq6utGnThoSEBKVDsQhfX98Kv0S2a9fOIrfJrarA2tnZERISwtatW03HDAYDW7dutapnUdbIaDQyffp01q9fz7Zt2wgKClI6JMUZDAYKCwuVDsPsBg4cyOHDh4mLizN9hYaGMmbMGOLi4tBoNEqHaFG5ubmcPn0aX19fpUOxiJ49e1aYknfy5EkCAgLM/tlWd4s4KiqKcePGERoaSvfu3XnrrbfIy8tj/PjxSodmdrm5ueV+a01MTCQuLg53d3eaN2+uYGTmN23aNNauXct3332Hk5OT6Zm7i4sLDg4OCkdnfrNnz+bOO++kefPm5OTksHbtWnbs2MHmzZuVDs3snJycKjxrb9SoER4eHlbxDP7pp5/mnnvuISAggIsXLzJv3jw0Gg0PPfSQ0qFZxH//+1969OjByy+/zIMPPkhMTAwffPABH3zwgfk/XJGxywpbunSpsXnz5kY7Oztj9+7djfv27VM6JIvYvn27EajwNW7cOKVDM7vK8gaMH3/8sdKhWcSjjz5qDAgIMNrZ2RmbNGliHDhwoHHLli1Kh6UYa5qmM3LkSKOvr6/Rzs7O2LRpU+PIkSONCQkJSodlUd9//72xQ4cORq1WawwODjZ+8MEHFvlc2Q9WCCGEMAOregYrhBBCWIoUWCGEEMIMpMAKIYQQZiAFVgghhDADKbBCCCGEGUiBFUIIIcxACqwQQghhBlJghRBCCDOQAiuEEEKYgRRYIYQQwgykwAohhBBm8P/p3GGsI2V5NAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Funções de probabilidade via scipy\n",
        "\n",
        "O scipy é outra biblioteca riquíssima em estatística, e o básico dela será apresentado aqui, começando com as distribuições de probabilidade. A lista de funções de probabilidade é imensa, ainda maior que o numpy, e pode ser encontrada neste [link](https://docs.scipy.org/doc/scipy/reference/stats.html).\n",
        "\n",
        "No scipy, podemos usar a distribuição como um objeto, e chamar sobre o objeto métodos para retirar diferentes propriedades dele. Os exemplos deixarão mais claro:"
      ],
      "metadata": {
        "id": "ElS3rN2NGuKj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Um exemplo com a f.d.p. Normal\n",
        "\n",
        "Vamos criar uma função normal de média zero e desvio padrão unitário e utilizar os métodos para obter as propriedades. Veremos aqui os seguintes métodos:\n",
        "\n",
        "1. `rvs`: gera números aleatórios da distribuição, assim como fizemos com o numpy.\n",
        "\n",
        "2. `pdf`: nos dá a função densidade de probabilidade.\n",
        "\n",
        "3. `cdf`: nos dá a função cumulativa.\n",
        "\n",
        "4. `stats`: nos dá as estatísticas básicas da função.\n",
        "\n",
        "5. `fit`: esse método ajusta a distribuição em questão a um conjunto de dados fornecidos, usando como default o método da máxima verossimilhança.\n",
        "\n",
        "Uma lista com todos os métodos para a função normal pode ser encontrada neste [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm)."
      ],
      "metadata": {
        "id": "ndTJLg3vIGni"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#criando um objeto que representa a distribuição normal padrão:\n",
        "normal = scipy.stats.norm(loc=0, scale=1)\n",
        "\n",
        "#gerando 10 números aleatórios a partir desta distribuição:\n",
        "x_sp = normal.rvs(size=10)\n",
        "print('Numeros aleatorios gerados:\\n', x_sp)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6d-67KtCIGRZ",
        "outputId": "0f7054ff-bd88-4277-a796-36af3614ac4c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Numeros aleatorios gerados:\n",
            " [-0.13622086 -1.40935205  1.04291118 -0.10519759 -1.16748238 -0.70737032\n",
            " -0.06632832 -1.13749575 -1.87719891  0.38016198]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#vamos obter a pdf e plotar:\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x = np.linspace(-3, 3, 100)\n",
        "ax.plot(x, normal.pdf(x))\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 360
        },
        "id": "XJNKc-09GXc2",
        "outputId": "9405119b-14a8-46cc-8237-09cdf938f817"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#podemos inclusive sobrepor o histograma que fizemos anteriormente:\n",
        "\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x = np.linspace(-3, 3, 100)\n",
        "ax.plot(x, normal.pdf(x))\n",
        "ax.hist(x_hist, bins=20, density=True)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 360
        },
        "id": "BbrBDDq5JK9P",
        "outputId": "0af0a7a8-ee84-46e0-ab06-13e10a12207f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# vamos plotar a função cumulativa:\n",
        "\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x = np.linspace(-3, 3, 100)\n",
        "ax.plot(x, normal.cdf(x))\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 360
        },
        "id": "rpsw83DNKl4Z",
        "outputId": "a3c72d68-799f-453c-b02f-b6da9ca2231d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# vamos agora gerar um conjunto de dados usando a normal do numpy\n",
        "x_numpy = np.random.normal(loc=0, scale=1, size=1000)\n",
        "\n",
        "# vamos agora ajustar uma normal a esses dados\n",
        "media, std = scipy.stats.norm.fit(x_numpy)\n",
        "\n",
        "print('media estimada:', media)\n",
        "print('std estimado:', std)\n",
        "\n",
        "# agora plotamos a distribuição e o histograma normalizado\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x = np.linspace(-3, 3, 100)\n",
        "ax.plot(x, scipy.stats.norm.pdf(x, loc=media,scale=std))\n",
        "ax.hist(x_numpy, bins=10, density=True)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 396
        },
        "id": "b88Ng9wxMCp9",
        "outputId": "477056a4-0a8c-4b87-cfb7-acc5b5813d0f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "media estimada: -0.02461928423934475\n",
            "std estimado: 0.9910538332248929\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ajuste de curvas\n",
        "\n",
        "O scipy também fornece diversos recursos para ajuste de curvas, sejam elas lineares ou não. O sub-módulo `optimize`, cuja documentação completa pode ser encontrada neste [link](https://docs.scipy.org/doc/scipy/reference/optimize.html) mostra alguns métodos de ajuste de funções."
      ],
      "metadata": {
        "id": "E6O8vB7mPdhM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### curve_fit\n",
        "\n",
        "Talvez a função mais usada seja a curve_fit. Sua documentação pode ser encontrada neste [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html). Os principais parâmetros da função são:\n",
        "1. `f`: a função a ser ajustada.\n",
        "2. `xdata` e `ydata`: dados a serem ajustados.\n",
        "3. `p0`: um chute inicial.\n",
        "4. `sigma`: incerteza nos dados.\n",
        "\n",
        "Vamos simular uma medida e ajustar um seno aos dados:"
      ],
      "metadata": {
        "id": "bgq0H5rAStCc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(1)\n",
        "\n",
        "#vetor com 40 pontos de x\n",
        "x = np.linspace(0,5,40)\n",
        "\n",
        "#vetor com 40 pontos-resposta em y, mais um ruido gaussiano\n",
        "y = 1.5*np.exp(-2.33*x) + 0.2*np.random.normal(loc=0, scale=0.5, size=len(x))\n",
        "\n",
        "#agora vamos definir a função a ser ajustada pelo curve_fit:\n",
        "def teste(x, a, b):\n",
        "  return a*np.exp(b*x)\n",
        "\n",
        "#agora vamos usar o curve fit, retornando os parametros ajustados\n",
        "#e matriz de covariancia dos parametros:\n",
        "\n",
        "param, param_cov = scipy.optimize.curve_fit(f=teste,\n",
        "                                            xdata=x,\n",
        "                                            ydata=y)\n",
        "\n",
        "print('Parametros ajustados:', param)\n",
        "print()\n",
        "print('Matriz covariancia:\\n', param_cov)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3IUhPTQvNSfo",
        "outputId": "fd485620-cae1-4705-db4e-c4ed821b82f2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Parametros ajustados: [ 1.59686457 -2.67452687]\n",
            "\n",
            "Matriz covariancia:\n",
            " [[ 0.00693159 -0.01117485]\n",
            " [-0.01117485  0.05378234]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#plotando o grafico da curva e sobrepondo aos dados:\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x_ajustado = np.linspace(0,5,100)\n",
        "y_ajustado = teste(x_ajustado, param[0], param[1])\n",
        "\n",
        "ax.plot(x_ajustado, y_ajustado, color='black', label='Ajuste')\n",
        "ax.scatter(x, y, color='red', label='Dados')\n",
        "ax.set_xlabel('x', fontsize=16)\n",
        "ax.set_ylabel('y', fontsize=16)\n",
        "ax.legend()\n",
        "ax.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "zmxmNkB6VCqq",
        "outputId": "8e903341-0075-4006-fcd6-79390fd0fc5a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Ajuste com dados que contêm incerteza\n",
        "\n",
        "Para plotar os dados com barras de incerteza, podemos usar o `errorbar`, também do matplotlib."
      ],
      "metadata": {
        "id": "nGRAuo6XbmqM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Agora com incertezas nos dados:\n",
        "\n",
        "np.random.seed(1)\n",
        "\n",
        "#vetor com 40 pontos de x\n",
        "x = np.linspace(0,5,40)\n",
        "\n",
        "#vetor com 40 pontos-resposta em y, mais um ruido gaussiano\n",
        "y = 1.5*np.exp(-2.33*x) + 0.2*np.random.normal(loc=0, scale=0.5, size=len(x))\n",
        "\n",
        "#vetor de incertezas\n",
        "y_err = np.repeat(0.1, len(x))\n",
        "\n",
        "#agora vamos definir a função a ser ajustada pelo curve_fit:\n",
        "def teste(x, a, b):\n",
        "  return a*np.exp(b*x)\n",
        "\n",
        "#agora vamos usar o curve fit, retornando os parametros ajustados\n",
        "#e matriz de covariancia dos parametros:\n",
        "\n",
        "param, param_cov = scipy.optimize.curve_fit(f=teste,\n",
        "                                            xdata=x,\n",
        "                                            ydata=y,\n",
        "                                            sigma=y_err)\n",
        "\n",
        "print('Parametros ajustados:', param)\n",
        "print()\n",
        "print('Matriz covariancia:\\n', param_cov)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4Ag8j1ioVZXG",
        "outputId": "fc073835-20da-4d9e-c742-2a78902ac432"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Parametros ajustados: [ 1.59686457 -2.67452687]\n",
            "\n",
            "Matriz covariancia:\n",
            " [[ 0.00693159 -0.01117485]\n",
            " [-0.01117485  0.05378234]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#plotando o grafico da curva e sobrepondo aos dados:\n",
        "fig = plt.figure(figsize=(5,3))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "\n",
        "x_ajustado = np.linspace(0,5,100)\n",
        "y_ajustado = teste(x_ajustado, param[0], param[1])\n",
        "\n",
        "ax.plot(x_ajustado, y_ajustado, color='black', label='Ajuste')\n",
        "ax.errorbar(x, y, yerr=y_err, color='red', label='Dados', marker='.',\n",
        "            linestyle='')\n",
        "ax.set_xlabel('x', fontsize=16)\n",
        "ax.set_ylabel('y', fontsize=16)\n",
        "ax.legend()\n",
        "ax.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 386
        },
        "id": "RONxusW-af2J",
        "outputId": "2a4c57cb-f0b8-42af-c056-f4d74ce67f9f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}