PandoraRiot · March 5, 2025 22:16
diff --git a/funcionesdeactivacion.ipynb b/funcionesdeactivacion.ipynb
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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyP4SBI4NiYqJ0purxKQlRh5",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/PandoraRiot/5fdcdccb8f2f7c7bbb2f4dd2a58b99e0/funcionesdeactivacion.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "xruwDtj6N1sA"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Función Sigmoide:\n",
        "\n",
        "La función sigmoide, también conocida como función logística, es una función matemática que tiene una forma de \"S\". Se utiliza ampliamente en diversos campos, especialmente en el aprendizaje automático y las redes neuronales. Aquí tienes un resumen completo de lo que debes saber sobre ella:\n",
        "\n",
        "Rango de Salida: La función sigmoide siempre produce valores entre 0 y 1. Esto la hace ideal para modelar probabilidades.\n",
        "\n",
        "No Lineal: Introduce no linealidad en los modelos, lo que les permite aprender relaciones complejas en los datos.\n",
        "\n",
        "##Aplicaciones:\n",
        "Clasificación Binaria: Se utiliza comúnmente en la capa de salida de los modelos de clasificación binaria. La salida de la función se puede interpretar como la probabilidad de que una entrada pertenezca a una clase determinada.\n",
        "\n",
        "Regresión Logística: Es la base de la regresión logística, un algoritmo utilizado para la clasificación binaria.\n"
      ],
      "metadata": {
        "id": "g9WGudhxO_LW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sigmoid(a):\n",
        "  return 1 / (1+np.exp(-a))"
      ],
      "metadata": {
        "id": "tT5C6ZCZOJ__"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x= np.linspace(10,-10,100) #Valores de 10 a - 10 y 100 posibles valores"
      ],
      "metadata": {
        "id": "HJBCXfMiOklP"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bnL4qy2XOwPO",
        "outputId": "34ae6712-9aa6-44ed-bda7-32a78cf6d67c"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 10.        ,   9.7979798 ,   9.5959596 ,   9.39393939,\n",
              "         9.19191919,   8.98989899,   8.78787879,   8.58585859,\n",
              "         8.38383838,   8.18181818,   7.97979798,   7.77777778,\n",
              "         7.57575758,   7.37373737,   7.17171717,   6.96969697,\n",
              "         6.76767677,   6.56565657,   6.36363636,   6.16161616,\n",
              "         5.95959596,   5.75757576,   5.55555556,   5.35353535,\n",
              "         5.15151515,   4.94949495,   4.74747475,   4.54545455,\n",
              "         4.34343434,   4.14141414,   3.93939394,   3.73737374,\n",
              "         3.53535354,   3.33333333,   3.13131313,   2.92929293,\n",
              "         2.72727273,   2.52525253,   2.32323232,   2.12121212,\n",
              "         1.91919192,   1.71717172,   1.51515152,   1.31313131,\n",
              "         1.11111111,   0.90909091,   0.70707071,   0.50505051,\n",
              "         0.3030303 ,   0.1010101 ,  -0.1010101 ,  -0.3030303 ,\n",
              "        -0.50505051,  -0.70707071,  -0.90909091,  -1.11111111,\n",
              "        -1.31313131,  -1.51515152,  -1.71717172,  -1.91919192,\n",
              "        -2.12121212,  -2.32323232,  -2.52525253,  -2.72727273,\n",
              "        -2.92929293,  -3.13131313,  -3.33333333,  -3.53535354,\n",
              "        -3.73737374,  -3.93939394,  -4.14141414,  -4.34343434,\n",
              "        -4.54545455,  -4.74747475,  -4.94949495,  -5.15151515,\n",
              "        -5.35353535,  -5.55555556,  -5.75757576,  -5.95959596,\n",
              "        -6.16161616,  -6.36363636,  -6.56565657,  -6.76767677,\n",
              "        -6.96969697,  -7.17171717,  -7.37373737,  -7.57575758,\n",
              "        -7.77777778,  -7.97979798,  -8.18181818,  -8.38383838,\n",
              "        -8.58585859,  -8.78787879,  -8.98989899,  -9.19191919,\n",
              "        -9.39393939,  -9.5959596 ,  -9.7979798 , -10.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x,sigmoid(x))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "OXuvEK1TOzS2",
        "outputId": "53556c00-eb4e-497c-f00f-f09f4d97b34c"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7a55efff5a90>]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Función Step\n",
        "\n",
        "La función \"step\" (o función escalón) es una función matemática que produce una salida binaria, cambiando abruptamente de un valor a otro en un punto específico. Aquí te presento una descripción completa de la función escalón:\n",
        "\n",
        "##Función Escalón Unitario (Heaviside):\n",
        " la función es 0 para valores de entrada negativos y 1 para valores de entrada no negativos.\n",
        "\n",
        "##Aplicaciones:\n",
        "\n",
        "Procesamiento de Señales:\n",
        "Se utiliza para modelar señales que cambian abruptamente.\n",
        "Por ejemplo, para representar la activación de un circuito o la aparición de un evento.\n",
        "\n",
        "Sistemas de Control:\n",
        "Se utiliza para modelar la respuesta de sistemas de control a entradas escalón.\n",
        "Por ejemplo, para simular el comportamiento de un termostato.\n",
        "\n",
        "Matemáticas y Física:\n",
        "Se utiliza en diversas áreas de las matemáticas y la física para modelar fenómenos que implican cambios abruptos."
      ],
      "metadata": {
        "id": "-XoUuAbaP2hA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def step(x):\n",
        "    return np.piecewise (x, [x< 0.0 , x> 0.0], [0,1])"
      ],
      "metadata": {
        "id": "-GNlhI1NO9A2"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.linspace(10,-10,100)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OyricSNiRKFv",
        "outputId": "2dad8a24-95e1-4d8f-ab7d-9ce09bcf742b"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 10.        ,   9.7979798 ,   9.5959596 ,   9.39393939,\n",
              "         9.19191919,   8.98989899,   8.78787879,   8.58585859,\n",
              "         8.38383838,   8.18181818,   7.97979798,   7.77777778,\n",
              "         7.57575758,   7.37373737,   7.17171717,   6.96969697,\n",
              "         6.76767677,   6.56565657,   6.36363636,   6.16161616,\n",
              "         5.95959596,   5.75757576,   5.55555556,   5.35353535,\n",
              "         5.15151515,   4.94949495,   4.74747475,   4.54545455,\n",
              "         4.34343434,   4.14141414,   3.93939394,   3.73737374,\n",
              "         3.53535354,   3.33333333,   3.13131313,   2.92929293,\n",
              "         2.72727273,   2.52525253,   2.32323232,   2.12121212,\n",
              "         1.91919192,   1.71717172,   1.51515152,   1.31313131,\n",
              "         1.11111111,   0.90909091,   0.70707071,   0.50505051,\n",
              "         0.3030303 ,   0.1010101 ,  -0.1010101 ,  -0.3030303 ,\n",
              "        -0.50505051,  -0.70707071,  -0.90909091,  -1.11111111,\n",
              "        -1.31313131,  -1.51515152,  -1.71717172,  -1.91919192,\n",
              "        -2.12121212,  -2.32323232,  -2.52525253,  -2.72727273,\n",
              "        -2.92929293,  -3.13131313,  -3.33333333,  -3.53535354,\n",
              "        -3.73737374,  -3.93939394,  -4.14141414,  -4.34343434,\n",
              "        -4.54545455,  -4.74747475,  -4.94949495,  -5.15151515,\n",
              "        -5.35353535,  -5.55555556,  -5.75757576,  -5.95959596,\n",
              "        -6.16161616,  -6.36363636,  -6.56565657,  -6.76767677,\n",
              "        -6.96969697,  -7.17171717,  -7.37373737,  -7.57575758,\n",
              "        -7.77777778,  -7.97979798,  -8.18181818,  -8.38383838,\n",
              "        -8.58585859,  -8.78787879,  -8.98989899,  -9.19191919,\n",
              "        -9.39393939,  -9.5959596 ,  -9.7979798 , -10.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x, step(x))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "caHS84m-RQ2e",
        "outputId": "8ffe2dab-15e8-45a0-d649-c28ce997cc21"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7a55eff9ced0>]"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Función ReLU\n",
        "\n",
        "ReLU es una función de activación muy eficaz que ha revolucionado el entrenamiento de redes neuronales profundas.\n",
        "\n",
        "\n",
        "La función ReLU (Rectified Linear Unit o Unidad Lineal Rectificada) es una de las funciones de activación más utilizadas en redes neuronales profundas.\n",
        "\n",
        "Se define: si la entrada (x) es positiva, la salida es la misma entrada. Si la entrada es negativa o cero, la salida es cero\n",
        "\n",
        "##Características clave:\n",
        "\n",
        "No Lineal: Introduce no linealidad en la red neuronal, lo que le permite aprender patrones complejos.\n",
        "Simplicidad: Es una función muy simple y computacionalmente eficiente.\n",
        "Rango de Salida: Su rango de salida es [0, ∞).\n",
        "Mitigación del Gradiente Desvaneciente: Ayuda a mitigar el problema del gradiente desvaneciente, lo que permite entrenar redes neuronales más profundas.\n",
        "Esparsidad: Promueve la esparsidad en las activaciones, lo que puede mejorar el rendimiento.\n",
        "\n",
        "##Ventajas:\n",
        "\n",
        "Eficiencia Computacional: Es mucho más rápida de calcular que funciones como la sigmoide o la tangente hiperbólica.\n",
        "Aprendizaje Rápido: Ayuda a acelerar el proceso de aprendizaje en redes profundas.\n",
        "Reducción del Gradiente Desvaneciente: Disminuye la probabilidad de que los gradientes se desvanezcan durante el entrenamiento.\n",
        "\n",
        "##Aplicaciones:\n",
        "\n",
        "ReLU es la función de activación predeterminada para muchas redes neuronales convolucionales (CNN) y redes neuronales profundas en general.\n",
        "Se utiliza en una amplia variedad de aplicaciones de aprendizaje profundo, como reconocimiento de imágenes, procesamiento del lenguaje natural y reconocimiento de voz."
      ],
      "metadata": {
        "id": "1CXQgn9gRtIu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Usos más frecuentes:\n",
        "\n",
        ". Redes Neuronales Convolucionales (CNNs):\n",
        "\n",
        "Procesamiento de Imágenes:\n",
        "ReLU es la función de activación dominante en las CNNs para tareas como clasificación de imágenes, detección de objetos y segmentación semántica. Su capacidad para mitigar el gradiente desvaneciente permite entrenar redes profundas que capturan características visuales complejas.\n",
        "\n",
        "Visión por Computadora:\n",
        "En aplicaciones como reconocimiento facial, realidad aumentada y vehículos autónomos, ReLU ayuda a extraer información visual crucial de las imágenes.\n",
        "\n",
        "edes Neuronales Recurrentes (RNNs) y Transformers:\n",
        "\n",
        "Procesamiento del Lenguaje Natural (PLN):\n",
        "Aunque las RNNs tradicionales pueden sufrir del gradiente desvaneciente, las variantes como las LSTM y GRU, junto con los Transformers, utilizan mecanismos que pueden beneficiarse de ReLU en ciertas capas para mejorar el rendimiento.\n",
        "En tareas como traducción automática, generación de texto y análisis de sentimientos, ReLU contribuye a un aprendizaje más eficiente.\n",
        "\n",
        "prendizaje por Refuerzo:\n",
        "\n",
        "Agentes Inteligentes:\n",
        "ReLU se utiliza en redes neuronales que controlan el comportamiento de agentes en entornos simulados o reales. Ayuda a los agentes a aprender políticas óptimas para maximizar las recompensas.\n",
        "Robótica:\n",
        "En robótica, ReLU se utiliza para procesar información sensorial y controlar el movimiento de los robots.\n",
        " Redes Neuronales Generativas (GANs):\n",
        "\n",
        "Generación de Imágenes y Videos:\n",
        "ReLU se utiliza en las GANs para generar imágenes y videos realistas. Su capacidad para promover la esparsidad ayuda a generar imágenes nítidas y detalladas.\n",
        "Generación de Datos Sintéticos:\n",
        "ReLU se utiliza para generar datos sintéticos para entrenamiento de modelos en casos donde los datos reales son escasos o sensibles.\n",
        "\n",
        " Análisis de Datos y Predicción:\n",
        "\n",
        "Predicción de Series Temporales:\n",
        "ReLU se utiliza en redes neuronales para predecir valores futuros en series temporales, como precios de acciones, demanda de productos o datos climáticos.\n",
        "Análisis de Datos Médicos:\n",
        "ReLU se utiliza para analizar datos médicos, como imágenes de resonancia magnética o datos genómicos, para diagnosticar enfermedades o predecir la respuesta a tratamientos."
      ],
      "metadata": {
        "id": "H4RwNa4zV7t-"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "7oXZao6WRsrG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def ReLU(x):\n",
        "  return np.piecewise(x, [x < 0.0, x >= 0.0], [0, lambda x: x])\n"
      ],
      "metadata": {
        "id": "NEBtjZhVS1pk"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.linspace(10,-10,100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kH9xAzZzTNbe",
        "outputId": "96191b93-89f6-43c2-e2a0-39ba67052cb0"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 10.        ,   9.7979798 ,   9.5959596 ,   9.39393939,\n",
              "         9.19191919,   8.98989899,   8.78787879,   8.58585859,\n",
              "         8.38383838,   8.18181818,   7.97979798,   7.77777778,\n",
              "         7.57575758,   7.37373737,   7.17171717,   6.96969697,\n",
              "         6.76767677,   6.56565657,   6.36363636,   6.16161616,\n",
              "         5.95959596,   5.75757576,   5.55555556,   5.35353535,\n",
              "         5.15151515,   4.94949495,   4.74747475,   4.54545455,\n",
              "         4.34343434,   4.14141414,   3.93939394,   3.73737374,\n",
              "         3.53535354,   3.33333333,   3.13131313,   2.92929293,\n",
              "         2.72727273,   2.52525253,   2.32323232,   2.12121212,\n",
              "         1.91919192,   1.71717172,   1.51515152,   1.31313131,\n",
              "         1.11111111,   0.90909091,   0.70707071,   0.50505051,\n",
              "         0.3030303 ,   0.1010101 ,  -0.1010101 ,  -0.3030303 ,\n",
              "        -0.50505051,  -0.70707071,  -0.90909091,  -1.11111111,\n",
              "        -1.31313131,  -1.51515152,  -1.71717172,  -1.91919192,\n",
              "        -2.12121212,  -2.32323232,  -2.52525253,  -2.72727273,\n",
              "        -2.92929293,  -3.13131313,  -3.33333333,  -3.53535354,\n",
              "        -3.73737374,  -3.93939394,  -4.14141414,  -4.34343434,\n",
              "        -4.54545455,  -4.74747475,  -4.94949495,  -5.15151515,\n",
              "        -5.35353535,  -5.55555556,  -5.75757576,  -5.95959596,\n",
              "        -6.16161616,  -6.36363636,  -6.56565657,  -6.76767677,\n",
              "        -6.96969697,  -7.17171717,  -7.37373737,  -7.57575758,\n",
              "        -7.77777778,  -7.97979798,  -8.18181818,  -8.38383838,\n",
              "        -8.58585859,  -8.78787879,  -8.98989899,  -9.19191919,\n",
              "        -9.39393939,  -9.5959596 ,  -9.7979798 , -10.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x, ReLU(x))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "5cpQ1BTMTPS4",
        "outputId": "9a149a4d-84cc-4f76-964d-3b842e9a6cdb"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7a55f41fe7d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Función Softmax\n",
        "\n",
        "La función Softmax toma un vector de números reales (llamados \"logits\") y los transforma en una distribución de probabilidad. Esto significa que:\n",
        "\n",
        "Cada elemento de la salida está en el rango de 0 a 1.\n",
        "La suma de todos los elementos de la salida es igual a 1.\n",
        "\n",
        "##Aplicaciones:\n",
        "\n",
        "La función Softmax se utiliza principalmente en la capa de salida de las redes neuronales para problemas de clasificación multiclase. Algunos ejemplos incluyen:\n",
        "\n",
        "Clasificación de imágenes: Determinar si una imagen contiene un gato, un perro, un pájaro, etc.\n",
        "\n",
        "Procesamiento del lenguaje natural: Identificar el sentimiento de un texto (positivo, negativo, neutral).\n",
        "\n",
        "Reconocimiento de voz: Transcribir un audio a texto.\n",
        "\n"
      ],
      "metadata": {
        "id": "wYSi2_P2UXYV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Usos más frecuentes:\n",
        "\n",
        "1. Sistemas de recomendación:\n",
        "\n",
        "En sistemas que recomiendan productos, películas o música, Softmax puede utilizarse para determinar la probabilidad de que un usuario interactúe con un elemento específico. Esto permite generar recomendaciones personalizadas basadas en las preferencias del usuario.\n",
        "\n",
        "Juegos y robótica:\n",
        "\n",
        "En el aprendizaje por refuerzo, Softmax se utiliza para seleccionar acciones en función de las probabilidades de recompensa. Esto permite a los agentes aprender a tomar decisiones óptimas en entornos complejos.\n",
        "\n",
        "En robótica, Softmax puede utilizarse para controlar el movimiento de un robot, permitiéndole elegir entre diferentes acciones en función de la probabilidad de éxito.\n",
        "\n",
        " Análisis de datos médicos:\n",
        "\n",
        "Softmax puede utilizarse para diagnosticar enfermedades a partir de datos médicos, como imágenes de resonancia magnética o resultados de análisis de sangre. La función permite determinar la probabilidad de que un paciente padezca una enfermedad específica.\n",
        "En el análisis de datos genómicos, Softmax ayuda a identificar patrones genéticos asociados con enfermedades.\n",
        "\n",
        ". Predicción de series temporales:\n",
        "\n",
        "Softmax puede utilizarse para predecir eventos futuros en series temporales, como la demanda de productos, el precio de las acciones o el clima. La función permite determinar la probabilidad de que ocurra un evento específico en un momento dado.\n",
        "\n",
        "Visión por computadora avanzada:\n",
        "\n",
        "Segmentación semántica: Softmax se utiliza para clasificar cada píxel de una imagen en una categoría específica, lo que permite identificar objetos y regiones de interés.\n",
        "Detección de objetos: Softmax puede utilizarse para determinar la probabilidad de que un objeto esté presente en una región específica de una imagen."
      ],
      "metadata": {
        "id": "3b4bbK2MVVen"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def softmax_numpy(x):\n",
        "    \"\"\"Función Softmax implementada con NumPy.\"\"\"\n",
        "    e_x = np.exp(x - np.max(x))  # Resta el máximo para estabilidad numérica\n",
        "    return e_x / e_x.sum(axis=0)"
      ],
      "metadata": {
        "id": "jE9XKWQsUR1n"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.linspace(10,-10,100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rlk34Sb7Us8I",
        "outputId": "cf3e635d-6935-413d-e636-cab5c51c70ad"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 10.        ,   9.7979798 ,   9.5959596 ,   9.39393939,\n",
              "         9.19191919,   8.98989899,   8.78787879,   8.58585859,\n",
              "         8.38383838,   8.18181818,   7.97979798,   7.77777778,\n",
              "         7.57575758,   7.37373737,   7.17171717,   6.96969697,\n",
              "         6.76767677,   6.56565657,   6.36363636,   6.16161616,\n",
              "         5.95959596,   5.75757576,   5.55555556,   5.35353535,\n",
              "         5.15151515,   4.94949495,   4.74747475,   4.54545455,\n",
              "         4.34343434,   4.14141414,   3.93939394,   3.73737374,\n",
              "         3.53535354,   3.33333333,   3.13131313,   2.92929293,\n",
              "         2.72727273,   2.52525253,   2.32323232,   2.12121212,\n",
              "         1.91919192,   1.71717172,   1.51515152,   1.31313131,\n",
              "         1.11111111,   0.90909091,   0.70707071,   0.50505051,\n",
              "         0.3030303 ,   0.1010101 ,  -0.1010101 ,  -0.3030303 ,\n",
              "        -0.50505051,  -0.70707071,  -0.90909091,  -1.11111111,\n",
              "        -1.31313131,  -1.51515152,  -1.71717172,  -1.91919192,\n",
              "        -2.12121212,  -2.32323232,  -2.52525253,  -2.72727273,\n",
              "        -2.92929293,  -3.13131313,  -3.33333333,  -3.53535354,\n",
              "        -3.73737374,  -3.93939394,  -4.14141414,  -4.34343434,\n",
              "        -4.54545455,  -4.74747475,  -4.94949495,  -5.15151515,\n",
              "        -5.35353535,  -5.55555556,  -5.75757576,  -5.95959596,\n",
              "        -6.16161616,  -6.36363636,  -6.56565657,  -6.76767677,\n",
              "        -6.96969697,  -7.17171717,  -7.37373737,  -7.57575758,\n",
              "        -7.77777778,  -7.97979798,  -8.18181818,  -8.38383838,\n",
              "        -8.58585859,  -8.78787879,  -8.98989899,  -9.19191919,\n",
              "        -9.39393939,  -9.5959596 ,  -9.7979798 , -10.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x, softmax_numpy(x))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "JpGFcpEiUtu1",
        "outputId": "b258ff19-0f3a-413f-84a1-54a42da6a012"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7a55f7ac6a10>]"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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EBLflCQkJ2rVrV5sU5HQ69fDDD+vb3/62BgwY4Fr+05/+VD169FBSUpK2bt2qxx57TLt379a7777b5HZyc3M1d+7cNqkJAID26mR1nWrqGm6R4Otjajw+/XS1zZgxQ9u2bdPnn3/utvy+++5zPR84cKC6du2q0aNHa9++ferdu/dF28nOzlZWVpbrtcPhUHJy8tUrHACAANQ4R02ELVgdQn33FgmSh6EmLi5OQUFBKi0tdVteWlraJmNdZs6cqVWrVumzzz7Tddddd8m2aWlpkqS9e/c2GWpsNptsNt9OlAAA+Dp/GSQseTimJjQ0VEOHDlVeXp5rmdPpVF5entLT01tdhDFGM2fO1F/+8hd9/PHH6tmz52XX2bJliySpa9eurf5cAABwaf4y8Z7UitNPWVlZmjJlioYNG6YRI0Zo0aJFqqysdF0NNXnyZHXr1k25ubmSGgYX79ixw/X8yJEj2rJliyIiItSnTx9JDaecli1bpvfee0+RkZGy2+2SpOjoaHXo0EH79u3TsmXLdOedd6pz587aunWrZs+erVtuuUWDBg1qk18EAAC4mL/MUSO1ItSMHz9eR48e1Zw5c2S325WamqrVq1e7Bg8XFRXJaj3XAVRcXKwhQ4a4Xi9YsEALFizQqFGjtG7dOknSyy+/LKlhgr3zLV26VPfee69CQ0O1du1aV4BKTk7WuHHj9OSTT3paPgAA8EDZySpJvj+bsCRZjDHG20VcCw6HQ9HR0aqoqFBUVJS3ywEAwC9kLd+idzcf0a/H9NN/3Nrnmn++J9/f3PsJAAA0q6SioacmKbqDlyu5PEINAABoVknFGUlSYnSYlyu5PEINAABokjGGnhoAAOD/yk/XqvrsbMIJ0b4/UJhQAwAAmlR89tRTXESobMG+PZuwRKgBAADNsJ899eQP42kkQg0AAGhGcWOoifL98TQSoQYAADTDfvb0U1IMPTUAAMCPlXD6CQAABIKScv+5nFsi1AAAgGbYHfTUAAAAP2eMUXH52TE19NQAAAB/df7Ee/FRvj/xnkSoAQAATWgcJNy5Y6jCQnx/4j2JUAMAAJrQeCPLrn5yObdEqAEAAE0o8bOJ9yRCDQAAaEKJn028JxFqAABAE/xt4j2JUAMAAJrgbxPvSYQaAADQBH+beE8i1AAAgAsYY85d/USoAQAA/qr8dK2qahsm3kuIItQAAAA/5Y8T70mEGgAAcAF/nHhPItQAAIAL+OPEexKhBgAAXMB+NtT40yBhiVADAAAuUMzpJwAAEAjoqQEAAAGhxBVqGFMDAAD8lL9OvCcRagAAwHkqzvjnxHsSoQYAAJynuNw/J96TCDUAAOA8dkfDqSd/upFlI0INAABwaeyp8bdBwhKhBgAAnMdfL+eWWhlqFi9erJSUFIWFhSktLU0bN25stu327ds1btw4paSkyGKxaNGiRa3aZlVVlWbMmKHOnTsrIiJC48aNU2lpaWvKBwAAzXBdzu1nE+9JrQg1y5cvV1ZWlnJyclRYWKjBgwcrMzNTZWVlTbY/ffq0evXqpXnz5ikxMbHV25w9e7bef/99rVixQp9++qmKi4t19913e1o+AAC4BH+9nFuSZDw0YsQIM2PGDNfr+vp6k5SUZHJzcy+7bo8ePczzzz/v8TbLy8tNSEiIWbFihavNzp07jSSTn5/fororKiqMJFNRUdGi9gAAtEe3zf/E9Hhslcnfd8zbpRhjPPv+9qinpqamRgUFBcrIyHAts1qtysjIUH5+fqtCVUu2WVBQoNraWrc2/fv3V/fu3Zv93OrqajkcDrcHAABonjHm3H2f/LCnxqNQc+zYMdXX1yshIcFteUJCgux2e6sKaMk27Xa7QkNDFRMT0+LPzc3NVXR0tOuRnJzcqvoAAGgvTlTWqKrWKYvF/ybekwL46qfs7GxVVFS4HocOHfJ2SQAA+LSDJ05LkhKjwvxu4j1JCvakcVxcnIKCgi666qi0tLTZQcBtsc3ExETV1NSovLzcrbfmUp9rs9lks9laVRMAAO1R0fGGUNM9NtzLlbSORz01oaGhGjp0qPLy8lzLnE6n8vLylJ6e3qoCWrLNoUOHKiQkxK3N7t27VVRU1OrPBQAA7orO9tT06OyfocajnhpJysrK0pQpUzRs2DCNGDFCixYtUmVlpaZOnSpJmjx5srp166bc3FxJDQOBd+zY4Xp+5MgRbdmyRREREerTp0+LthkdHa1p06YpKytLsbGxioqK0qxZs5Senq6bb765TX4RAAC0dwf9vKfG41Azfvx4HT16VHPmzJHdbldqaqpWr17tGuhbVFQkq/VcB1BxcbGGDBnier1gwQItWLBAo0aN0rp161q0TUl6/vnnZbVaNW7cOFVXVyszM1N/+MMfWrvfAADgAkUnKiVJ3Tt39HIlrWMxxhhvF3EtOBwORUdHq6KiQlFRUd4uBwAAnzPiP9eq7GS13pvxbQ1OjvF2OZI8+/4O2KufAABAy52pqVfZyWpJ/jumhlADAAB06JuG8TRRYcGKCQ/1cjWtQ6gBAADnBgn7aS+NRKgBAACSDh5vGCTcI9Y/BwlLhBoAAKBzc9TQUwMAAPyaa+I9P52jRiLUAAAA+f8tEiRCDQAA7V6907iufuL0EwAA8FslFWdUW28UEmRR1+gO3i6n1Qg1AAC0c42nnpI7hSvIavFyNa1HqAEAoJ0LhCufJEINAADt3sET/j9IWCLUAADQ7gXClU8SoQYAgHbv4Imzswl39t/ZhCVCDQAA7V5jT42/3p27EaEGAIB2rPx0jRxVdZIarn7yZ4QaAADasca7c8dH2tQhNMjL1VwZQg0AAO1Y45VP/n7qSSLUAADQrhUdbxgk3D3WvwcJS4QaAADatSJ6agAAQCA4GCBz1EiEGgAA2rVAuUWCRKgBAKDdqqqtl91RJUnqQU8NAADwV4e/OSNjpAhbsGI7hnq7nCtGqAEAoJ0qOtF45VO4LBaLl6u5coQaAADaqUAaJCwRagAAaLcOBsg9nxoRagAAaKf2lp2SJPXuEuHlStoGoQYAgHZqT9lJSVKfBEINAADwUxVnalXqqJYk9Y0n1AAAAD+192wvTdfoMEWGhXi5mrZBqAEAoB36urRhPE3fhEgvV9J2CDUAALRDX5c29NRcHyCnniRCDQAA7VLjlU99A2SQsESoAQCgXWrsqWn3p58WL16slJQUhYWFKS0tTRs3brxk+xUrVqh///4KCwvTwIED9eGHH7q9b7FYmnzMnz/f1SYlJeWi9+fNm9ea8gEAaNfOv/KpT3s+/bR8+XJlZWUpJydHhYWFGjx4sDIzM1VWVtZk+/Xr12vixImaNm2aNm/erLFjx2rs2LHatm2bq01JSYnb47XXXpPFYtG4cePctvXMM8+4tZs1a5an5QMA0O6df+VTVIBc+SS1ItQsXLhQ06dP19SpU3XjjTdqyZIlCg8P12uvvdZk+9///vcaM2aMHn30Ud1www36zW9+o5tuukkvvfSSq01iYqLb47333tNtt92mXr16uW0rMjLSrV3Hjh09LR8AgHav8cqnQOqlkTwMNTU1NSooKFBGRsa5DVitysjIUH5+fpPr5Ofnu7WXpMzMzGbbl5aW6oMPPtC0adMuem/evHnq3LmzhgwZovnz56uurq7ZWqurq+VwONweAABA2nM21FwfQONpJCnYk8bHjh1TfX29EhIS3JYnJCRo165dTa5jt9ubbG+325ts/8YbbygyMlJ333232/Jf/vKXuummmxQbG6v169crOztbJSUlWrhwYZPbyc3N1dy5c1u6awAAtBuNt0cIlJmEG3kUaq6F1157TZMmTVJYWJjb8qysLNfzQYMGKTQ0VPfff79yc3Nls9ku2k52drbbOg6HQ8nJyVevcAAA/MSeAJx4T/Iw1MTFxSkoKEilpaVuy0tLS5WYmNjkOomJiS1u//e//127d+/W8uXLL1tLWlqa6urqdODAAfXr1++i9202W5NhBwCA9qziTK3sjipJgTVHjeThmJrQ0FANHTpUeXl5rmVOp1N5eXlKT09vcp309HS39pK0Zs2aJtu/+uqrGjp0qAYPHnzZWrZs2SKr1ar4+HhPdgEAgHatcdK9xKjAuvJJasXpp6ysLE2ZMkXDhg3TiBEjtGjRIlVWVmrq1KmSpMmTJ6tbt27Kzc2VJD300EMaNWqUnnvuOd111116++23tWnTJr3yyitu23U4HFqxYoWee+65iz4zPz9fGzZs0G233abIyEjl5+dr9uzZ+tnPfqZOnTq1Zr8BAGiX9rgm3QusXhqpFaFm/PjxOnr0qObMmSO73a7U1FStXr3aNRi4qKhIVuu5DqCRI0dq2bJlevLJJ/XEE0+ob9++WrlypQYMGOC23bffflvGGE2cOPGiz7TZbHr77bf19NNPq7q6Wj179tTs2bPdxswAAIDLc93IMj6wxtNIksUYY7xdxLXgcDgUHR2tiooKRUVFebscAAC84uevbtDf9xzTvLsHasKI7t4u57I8+f7m3k8AALQj5658CrzTT4QaAADaCUfVuSuf+gTg6SdCDQAA7URjL01ClE3RHQLryieJUAMAQLvReOVToN0eoRGhBgCAdmJPWWDeyLIRoQYAgHbia3pqAABAIGicTfj6ALzySSLUAADQLpysqlVJReBe+SQRagAAaBd2FDskSV2jwwLyyieJUAMAQLvwzyMVkqSB3aK9XMnVQ6gBAKAd2Hq4IdQMuo5QAwAA/Jirp+a6GO8WchURagAACHAVZ2q1/1ilJE4/AQAAP7b9bC/NdZ06KLZjqJeruXoINQAABLitZ0PN4AA+9SQRagAACHj/PNw4niZwTz1JhBoAAALe1iPlkqRBATyeRiLUAAAQ0E5U1ujQiTOSpG8RagAAgL9qvJS7Z1zHgJ1JuBGhBgCAAPbPw+WSAvtS7kaEGgAAAlh7mEm4EaEGAIAA1h7u+dSIUAMAQIAqO1mlkooqWSzSAEINAADwV9vO9tL06RKhjrZgL1dz9RFqAAAIUFvbyaR7jQg1AAAEqMaZhAN90r1GhBoAAAKQMcZ1z6eBAX7Pp0aEGgAAAlCpo1pHT1YryGrRjV2jvF3ONUGoAQAgAP3j7KR7feMj1CE0yLvFXCOEGgAAAtA/29Gke40INQAABKAth8olSYPayXgaiVADAEDAqalzquDgN5KkET1jvVzNtUOoAQAgwPzzSLnO1NYrtmOo+sZHeLuca4ZQAwBAgPnyXyckSWk9Y2WxWLxczbXTqlCzePFipaSkKCwsTGlpadq4ceMl269YsUL9+/dXWFiYBg4cqA8//NDt/XvvvVcWi8XtMWbMGLc2J06c0KRJkxQVFaWYmBhNmzZNp06dak35AAAEtC//dVySdHOvzl6u5NryONQsX75cWVlZysnJUWFhoQYPHqzMzEyVlZU12X79+vWaOHGipk2bps2bN2vs2LEaO3astm3b5tZuzJgxKikpcT3+/Oc/u70/adIkbd++XWvWrNGqVav02Wef6b777vO0fAAAAlptvVObDjSMp2lvocZijDGerJCWlqbhw4frpZdekiQ5nU4lJydr1qxZevzxxy9qP378eFVWVmrVqlWuZTfffLNSU1O1ZMkSSQ09NeXl5Vq5cmWTn7lz507deOON+uqrrzRs2DBJ0urVq3XnnXfq8OHDSkpKumzdDodD0dHRqqioUFRU+5iECADQ/hQc/EbjXl6vTuEhKnjyf8lq9e/TT558f3vUU1NTU6OCggJlZGSc24DVqoyMDOXn5ze5Tn5+vlt7ScrMzLyo/bp16xQfH69+/frpwQcf1PHjx922ERMT4wo0kpSRkSGr1aoNGzZ4sgsAAAS0xlNPaT07+32g8ZRH9yE/duyY6uvrlZCQ4LY8ISFBu3btanIdu93eZHu73e56PWbMGN19993q2bOn9u3bpyeeeEJ33HGH8vPzFRQUJLvdrvj4ePfCg4MVGxvrtp3zVVdXq7q62vXa4XB4sqsAAPilc+Np2s+l3I08CjVXy4QJE1zPBw4cqEGDBql3795at26dRo8e3apt5ubmau7cuW1VIgAAPq+2/tz8NDf3bl/jaSQPTz/FxcUpKChIpaWlbstLS0uVmJjY5DqJiYketZekXr16KS4uTnv37nVt48KByHV1dTpx4kSz28nOzlZFRYXrcejQocvuHwAA/uyfRyp0uqZeMeEhuj4+0tvlXHMehZrQ0FANHTpUeXl5rmVOp1N5eXlKT09vcp309HS39pK0Zs2aZttL0uHDh3X8+HF17drVtY3y8nIVFBS42nz88cdyOp1KS0trchs2m01RUVFuDwAAAtm58TSx7W48jdSKS7qzsrL0pz/9SW+88YZ27typBx98UJWVlZo6daokafLkycrOzna1f+ihh7R69Wo999xz2rVrl55++mlt2rRJM2fOlCSdOnVKjz76qL788ksdOHBAeXl5+tGPfqQ+ffooMzNTknTDDTdozJgxmj59ujZu3KgvvvhCM2fO1IQJE1p05RMAAO1B46R77e1S7kYej6kZP368jh49qjlz5shutys1NVWrV692DQYuKiqS1XouK40cOVLLli3Tk08+qSeeeEJ9+/bVypUrNWDAAElSUFCQtm7dqjfeeEPl5eVKSkrS7bffrt/85jey2Wyu7bz11luaOXOmRo8eLavVqnHjxumFF1640v0HACAg1NY7VXCgfYcaj+ep8VfMUwMACGSbi77Rj/+wXjHhISoMgPlpGl21eWoAAIBvajz1NCKlfY6nkQg1AAAEhPZ6v6fzEWoAAPBzdfVObWrn42kkQg0AAH5v65EKVdbUK7pDiPontr/5aRoRagAA8HMf72yYoPY7feLa7XgaiVADAIDfW7uzYeb+/3VjwmVaBjZCDQAAfuzQidPaZT+pIKtFt/br4u1yvIpQAwCAH2vspRme0kkx4aFersa7CDUAAPixxlCTcUP7PvUkEWoAAPBbFWdqteHspHvtfTyNRKgBAMBvffr1UdU5jfrGR6hH547eLsfrCDUAAPiptTvOnnqil0YSoQYAAL9UW+/UJ7sb5qdhPE0DQg0AAH7oq/0ndLKqTnERoUpNjvF2OT6BUAMAgB9ac/aqp+/1j1dQO55F+HyEGgAA/Iwxhku5m0CoAQDAz3xdekqHTpyRLdiq7/SN83Y5PoNQAwCAn2nspflOnziFhwZ7uRrfQagBAMDPfLTdLolLuS9EqAEAwI/sKT2prYcrFGy1MIvwBQg1AAD4kf8uPCxJuq1/vOIibF6uxrcQagAA8BP1TqOVm49IksbddJ2Xq/E9hBoAAPzE3/ccVamjWp3CQ/S9/vHeLsfnEGoAAPAT/1PY0Evzo9RuCg3mK/xC/EYAAPADFWdqXVc9ceqpaYQaAAD8wAdbS1RT51S/hEgN6Bbl7XJ8EqEGAAA/8N8FhyRJ44Z2k8XCvZ6aQqgBAMDH/evoKRUWlSvIatHY1G7eLsdnEWoAAPBx/3N2bppb+sYpPirMy9X4LkINAAA+rN5p9O7Zq57+bWiyl6vxbYQaAAB82Bd7j6mkokpRYcEafQNz01wKoQYAAB/2vz/fL0m6+6brFBYS5OVqfBuhBgAAH7WzxKHPvj4qq0Wa9p2e3i7H5xFqAADwUX/67F+SpDsGdlVybLiXq/F9hBoAAHxQcfkZ/fUfxZKk+2/p5eVq/EOrQs3ixYuVkpKisLAwpaWlaePGjZdsv2LFCvXv319hYWEaOHCgPvzwQ9d7tbW1euyxxzRw4EB17NhRSUlJmjx5soqLi922kZKSIovF4vaYN29ea8oHAMDnLf1iv+qcRjf3itWg62K8XY5f8DjULF++XFlZWcrJyVFhYaEGDx6szMxMlZWVNdl+/fr1mjhxoqZNm6bNmzdr7NixGjt2rLZt2yZJOn36tAoLC/XUU0+psLBQ7777rnbv3q0f/vCHF23rmWeeUUlJiesxa9YsT8sHAMDnOapq9eeNDTMI339Lby9X4z8sxhjjyQppaWkaPny4XnrpJUmS0+lUcnKyZs2apccff/yi9uPHj1dlZaVWrVrlWnbzzTcrNTVVS5YsafIzvvrqK40YMUIHDx5U9+7dJTX01Dz88MN6+OGHPSnXxeFwKDo6WhUVFYqK4p4ZAADfteTTfZr3t126PiFCHz18S7u+LYIn398e9dTU1NSooKBAGRkZ5zZgtSojI0P5+flNrpOfn+/WXpIyMzObbS9JFRUVslgsiomJcVs+b948de7cWUOGDNH8+fNVV1fnSfkAAPi8mjqnln7RcBn39O/2ateBxlPBnjQ+duyY6uvrlZCQ4LY8ISFBu3btanIdu93eZHu73d5k+6qqKj322GOaOHGiWyL75S9/qZtuukmxsbFav369srOzVVJSooULFza5nerqalVXV7teOxyOFu0jAADe9Nd/FKvUUa34SJt+mJrk7XL8ikeh5mqrra3VT37yExlj9PLLL7u9l5WV5Xo+aNAghYaG6v7771dubq5sNttF28rNzdXcuXOves0AALSVeqfRHz/dJ0ma+u2esgUz2Z4nPDr9FBcXp6CgIJWWlrotLy0tVWJiYpPrJCYmtqh9Y6A5ePCg1qxZc9nzZmlpaaqrq9OBAweafD87O1sVFRWux6FDhy6zdwAAeNc7mw5pT9kpRXcI0U/Tunu7HL/jUagJDQ3V0KFDlZeX51rmdDqVl5en9PT0JtdJT093ay9Ja9ascWvfGGj27NmjtWvXqnPnzpetZcuWLbJarYqPb/o+GDabTVFRUW4PAAB81anqOj33f7+WJP1ydF9FdwjxckX+x+PTT1lZWZoyZYqGDRumESNGaNGiRaqsrNTUqVMlSZMnT1a3bt2Um5srSXrooYc0atQoPffcc7rrrrv09ttva9OmTXrllVckNQSaf/u3f1NhYaFWrVql+vp613ib2NhYhYaGKj8/Xxs2bNBtt92myMhI5efna/bs2frZz36mTp06tdXvAgAAr/njp/t07FS1UjqH6+c39/B2OX7J41Azfvx4HT16VHPmzJHdbldqaqpWr17tGgxcVFQkq/VcB9DIkSO1bNkyPfnkk3riiSfUt29frVy5UgMGDJAkHTlyRH/9618lSampqW6f9cknn+jWW2+VzWbT22+/raefflrV1dXq2bOnZs+e7TbOBgAAf1VScUZ/+nvDLREev6O/QoOZ8L81PJ6nxl8xTw0AwFdlvbNF7xYe0YiUWC2//2Yu4z7PVZunBgAAtK1/Hq7Qu4VHJEn/3103EGiuAKEGAAAvMcbotx/skCT9KDVJg5NjvFuQnyPUAADgJR9tt2vD/hMKDbbq0cx+3i7H7xFqAADwguOnqvXkyoabO0//bk9d1yncyxX5P0INAADXmDFGT67cpmOnanR9QoRmfa+vt0sKCIQaAACusfe2FOtv2+wKtlq08CepCgvhdghtgVADAMA1ZK+o0pz3Gk47zfpeXw3oFu3ligIHoQYAgGvEGKNf/89WOarqNOi6aP3Hbb29XVJAIdQAAHCNLNtYpM++PqrQYKsW/mSwQoL4Gm5L/DYBALgGth2p0G9X7ZQk/Tqzn/rER3q5osBDqAEA4Corc1Tp39/YpDO19brl+i76xbd7erukgESoAQDgKqqqrdf0/7NJdkeV+sRH6KWfDpHVyq0QrgZCDQAAV4kxRr9a8Q/943CFOoWH6NUpwxQVFuLtsgIWoQYAgKvk93l7tGpriUKCLFrys6Hq0bmjt0sKaIQaAACugncLD2vR2j2SpN+OHaC0Xp29XFHgI9QAANDGVmw6pEdW/ENSw32dxg/v7uWK2odgbxcAAEAgWbahSE/85Z+SpElp3ZV9xw1erqj9INQAANBG3lh/QDl/3S5JundkinJ+cKMsFq50ulYINQAAtIH//fd/6bcfNEyud98tvZR9R38CzTVGqAEA4ApU19Vr7vs7tGxDkSRpxm299avb+xFovIBQAwBAK5U6qvTgmwUqLCqXxSL9OrO/HhjVi0DjJYQaAABaoeDgCT3wZqGOnqxWVFiwfj9xiG7rF+/tsto1Qg0AAB6odxot/WK/frd6l2rrja5PiNArPx+mlDgm1vM2Qg0AAC20p/Skfv0/W7W5qFySdOfARM3/t8HqaOPr1BdwFAAAuIzaeqeWrNunFz/eq5p6pyJtwcq+8wZNHJHM+BkfQqgBAKAZxhj9fc8x/deHO7XLflKSNLp/vH774wHqGt3By9XhQoQaAACasOVQuX73t13K/9dxSVKn8BA9/cNv6YeDk+id8VGEGgAAzrPL7tCiNXu0ertdkhQaZNXP03toxm19FNsx1MvV4VIINQCAds/pNPp4V5le+2K/1u9r6JmxWqS7b7pOD2f01XWdwr1cIVqCUAMAaLdOVNZo5eYj+j/5B3Tg+GlJDWHmjgFd9VBGX12fEOnlCuEJQg0AoF05XVOnNTtK9d6WYn329VHVOY0kKSosWBNHdNfP03vQM+OnCDUAgIB37FS1Pt19VJ/sLtPHu8p0uqbe9d7AbtH6yfBkjbupm8JD+Vr0Zxw9AEDAqaqt1+aicn35r+Nat7tMW49UyJhz73ePDdfY1CT9MLWb+sRHeK9QtClCDQDArxljdKT8jLYXO1R48BttPHBC245UqLbeuLUb0C1Kt/WL1/f6xys1OYbLsgMQoQYA4DdOVtVq39FK7S07pT2lJ7W92KFtxRUqP117UduEKJuGp8Tqlr5dNKpfFyVEhXmhYlxLrQo1ixcv1vz582W32zV48GC9+OKLGjFiRLPtV6xYoaeeekoHDhxQ37599bvf/U533nmn631jjHJycvSnP/1J5eXl+va3v62XX35Zffv2dbU5ceKEZs2apffff19Wq1Xjxo3T73//e0VE0G0IAIGitt6pspPVKik/o0PfnNahE2d06MRpHfrmtPYfq1Spo7rJ9YKtFvVNiNSgbtEa3jNWI1JilRzbgd6YdsbjULN8+XJlZWVpyZIlSktL06JFi5SZmandu3crPv7iW66vX79eEydOVG5urr7//e9r2bJlGjt2rAoLCzVgwABJ0rPPPqsXXnhBb7zxhnr27KmnnnpKmZmZ2rFjh8LCGpL1pEmTVFJSojVr1qi2tlZTp07Vfffdp2XLll3hrwAAcLU4nUYnq+tUcbpW5WdqVH66Vt+crtGxUzU6fqpax0/V6HhltUod1SqpqNLxymq3sS9NiY+0qXeXCPWJj9CNSVEakBSt6xMjZAsOujY7BZ9lMeZy/3zcpaWlafjw4XrppZckSU6nU8nJyZo1a5Yef/zxi9qPHz9elZWVWrVqlWvZzTffrNTUVC1ZskTGGCUlJemRRx7Rr371K0lSRUWFEhIS9Prrr2vChAnauXOnbrzxRn311VcaNmyYJGn16tW68847dfjwYSUlJV22bofDoejoaFVUVCgqKsqTXQaAgGKMUZ3TqK7eqNbpVG2dU7X1RrX1TlXXOVVT53Q9r66rV3Vtw/Oq2nqdqa1v+FnT8Px0Tb0qq+saftbU6VRVnU5W1elUdZ0cVbU6VV132ZByoWCrRQlRYUqO7aDkTuFKjg1XcmwH9ejcUb27RCi6Q8jV+cXAJ3ny/e1RT01NTY0KCgqUnZ3tWma1WpWRkaH8/Pwm18nPz1dWVpbbsszMTK1cuVKStH//ftntdmVkZLjej46OVlpamvLz8zVhwgTl5+crJibGFWgkKSMjQ1arVRs2bNCPf/zjiz63urpa1dXnuikdDocnu9pie8tO6a0NB6/KtgFPvwz8WUv+/+rCFk2tYi5qdXG7pj7pXBvj9vr8dY3MueXnt5FxbbRhuXG9f/7rhmYN2zBnnztN43YanjtNw/vOsxt3GiOn8+xPc66N09nwvN7ZsLzeaVR/dnm9MaqvbwguTmNUW9/wfm29U/VO45qX5VrqEBKkmPAQRXcIUUx4iOIibIqLsKlzx1B1jrApPtKmxOgwJUSFqXPHUFmtnDaC5zwKNceOHVN9fb0SEhLclickJGjXrl1NrmO325tsb7fbXe83LrtUmwtPbQUHBys2NtbV5kK5ubmaO3duC/es9YrLz2jpFweu+ucAwNUUbLUoJMiq0OCzjyCrbMFW2UKCGn6efd4hxKoOIUHqEBokW3CQImzBCrcFqWNosMJDg9TRFqzIsGBFhoU0/LQFK6pDiMJCODWEqy9gr37Kzs526yFyOBxKTk5u889Jjg3XjNt6t/l2AW+w6Or933Frxms2uUoLNtRUiwtXa9zX85dbLmjb1CBTi8V9XUszyxvXt5zXzmKxnFvHYpH17DqNy6xn32/qp/Vse6v1vOcWi6xWi4IsFlmtUpDFoiDrxY9gq0XBVquCzgaX4CCLQqwNPxuf0zOCQOBRqImLi1NQUJBKS0vdlpeWlioxMbHJdRITEy/ZvvFnaWmpunbt6tYmNTXV1aasrMxtG3V1dTpx4kSzn2uz2WSz2Vq+c63UM66jHs3sf9U/BwAAXJrVk8ahoaEaOnSo8vLyXMucTqfy8vKUnp7e5Drp6elu7SVpzZo1rvY9e/ZUYmKiWxuHw6ENGza42qSnp6u8vFwFBQWuNh9//LGcTqfS0tI82QUAABCgPD79lJWVpSlTpmjYsGEaMWKEFi1apMrKSk2dOlWSNHnyZHXr1k25ubmSpIceekijRo3Sc889p7vuuktvv/22Nm3apFdeeUVSQ3fsww8/rN/+9rfq27ev65LupKQkjR07VpJ0ww03aMyYMZo+fbqWLFmi2tpazZw5UxMmTGjRlU8AACDweRxqxo8fr6NHj2rOnDmy2+1KTU3V6tWrXQN9i4qKZLWe6wAaOXKkli1bpieffFJPPPGE+vbtq5UrV7rmqJGkX//616qsrNR9992n8vJyfec739Hq1atdc9RI0ltvvaWZM2dq9OjRrsn3XnjhhSvZdwAAEEA8nqfGXzFPDQAA/seT72+PxtQAAAD4KkINAAAICIQaAAAQEAg1AAAgIBBqAABAQCDUAACAgECoAQAAAYFQAwAAAgKhBgAABASPb5PgrxonTnY4HF6uBAAAtFTj93ZLboDQbkLNyZMnJUnJyclergQAAHjq5MmTio6OvmSbdnPvJ6fTqeLiYkVGRspisbTpth0Oh5KTk3Xo0KGAvK8U++f/An0fA33/pMDfR/bP/12tfTTG6OTJk0pKSnK7YXZT2k1PjdVq1XXXXXdVPyMqKipg/7FK7F8gCPR9DPT9kwJ/H9k//3c19vFyPTSNGCgMAAACAqEGAAAEBEJNG7DZbMrJyZHNZvN2KVcF++f/An0fA33/pMDfR/bP//nCPrabgcIAACCw0VMDAAACAqEGAAAEBEINAAAICIQaAAAQEAg1LfCf//mfGjlypMLDwxUTE9Nkm6KiIt11110KDw9XfHy8Hn30UdXV1V1yuydOnNCkSZMUFRWlmJgYTZs2TadOnboKe+CZdevWyWKxNPn46quvml3v1ltvvaj9Aw88cA0rb7mUlJSLap03b94l16mqqtKMGTPUuXNnRUREaNy4cSotLb1GFXvmwIEDmjZtmnr27KkOHTqod+/eysnJUU1NzSXX8+VjuHjxYqWkpCgsLExpaWnauHHjJduvWLFC/fv3V1hYmAYOHKgPP/zwGlXqudzcXA0fPlyRkZGKj4/X2LFjtXv37kuu8/rrr190rMLCwq5RxZ55+umnL6q1f//+l1zHn46f1PR/UywWi2bMmNFke18/fp999pl+8IMfKCkpSRaLRStXrnR73xijOXPmqGvXrurQoYMyMjK0Z8+ey27X079jTxFqWqCmpkb33HOPHnzwwSbfr6+v11133aWamhqtX79eb7zxhl5//XXNmTPnktudNGmStm/frjVr1mjVqlX67LPPdN99912NXfDIyJEjVVJS4vb493//d/Xs2VPDhg275LrTp093W+/ZZ5+9RlV77plnnnGrddasWZdsP3v2bL3//vtasWKFPv30UxUXF+vuu+++RtV6ZteuXXI6nfrjH/+o7du36/nnn9eSJUv0xBNPXHZdXzyGy5cvV1ZWlnJyclRYWKjBgwcrMzNTZWVlTbZfv369Jk6cqGnTpmnz5s0aO3asxo4dq23btl3jylvm008/1YwZM/Tll19qzZo1qq2t1e23367KyspLrhcVFeV2rA4ePHiNKvbct771LbdaP//882bb+tvxk6SvvvrKbf/WrFkjSbrnnnuaXceXj19lZaUGDx6sxYsXN/n+s88+qxdeeEFLlizRhg0b1LFjR2VmZqqqqqrZbXr6d9wqBi22dOlSEx0dfdHyDz/80FitVmO3213LXn75ZRMVFWWqq6ub3NaOHTuMJPPVV1+5lv3tb38zFovFHDlypM1rvxI1NTWmS5cu5plnnrlku1GjRpmHHnro2hR1hXr06GGef/75FrcvLy83ISEhZsWKFa5lO3fuNJJMfn7+Vaiw7T377LOmZ8+el2zjq8dwxIgRZsaMGa7X9fX1JikpyeTm5jbZ/ic/+Ym566673JalpaWZ+++//6rW2VbKysqMJPPpp58226a5/x75opycHDN48OAWt/f342eMMQ899JDp3bu3cTqdTb7vT8dPkvnLX/7ieu10Ok1iYqKZP3++a1l5ebmx2Wzmz3/+c7Pb8fTvuDXoqWkD+fn5GjhwoBISElzLMjMz5XA4tH379mbXiYmJcev5yMjIkNVq1YYNG656zZ7461//quPHj2vq1KmXbfvWW28pLi5OAwYMUHZ2tk6fPn0NKmydefPmqXPnzhoyZIjmz59/ydOFBQUFqq2tVUZGhmtZ//791b17d+Xn51+Lcq9YRUWFYmNjL9vO145hTU2NCgoK3H73VqtVGRkZzf7u8/Pz3dpLDX+T/nSsJF32eJ06dUo9evRQcnKyfvSjHzX73xtfsGfPHiUlJalXr16aNGmSioqKmm3r78evpqZGb775pn7xi19c8gbK/nT8zrd//37Z7Xa3YxQdHa20tLRmj1Fr/o5bo93c0PJqstvtboFGkuu13W5vdp34+Hi3ZcHBwYqNjW12HW959dVXlZmZedkbgv70pz9Vjx49lJSUpK1bt+qxxx7T7t279e67716jSlvul7/8pW666SbFxsZq/fr1ys7OVklJiRYuXNhke7vdrtDQ0IvGVCUkJPjc8WrK3r179eKLL2rBggWXbOeLx/DYsWOqr69v8m9s165dTa7T3N+kPxwrp9Ophx9+WN/+9rc1YMCAZtv169dPr732mgYNGqSKigotWLBAI0eO1Pbt26/6zXs9lZaWptdff139+vVTSUmJ5s6dq+9+97vatm2bIiMjL2rvz8dPklauXKny8nLde++9zbbxp+N3ocbj4Mkxas3fcWu021Dz+OOP63e/+90l2+zcufOyg9n8SWv2+fDhw/roo4/0zjvvXHb7548HGjhwoLp27arRo0dr37596t27d+sLbyFP9i8rK8u1bNCgQQoNDdX999+v3Nxcn57GvDXH8MiRIxozZozuueceTZ8+/ZLrevsYQpoxY4a2bdt2yTEnkpSenq709HTX65EjR+qGG27QH//4R/3mN7+52mV65I477nA9HzRokNLS0tSjRw+98847mjZtmhcruzpeffVV3XHHHUpKSmq2jT8dP3/SbkPNI488cskULUm9evVq0bYSExMvGsHdeFVMYmJis+tcODiqrq5OJ06caHadK9WafV66dKk6d+6sH/7whx5/XlpamqSGXoJr8YV4Jcc0LS1NdXV1OnDggPr163fR+4mJiaqpqVF5eblbb01paelVO15N8XQfi4uLddttt2nkyJF65ZVXPP68a30MmxIXF6egoKCLrjS71O8+MTHRo/a+YubMma6LBjz9v/WQkBANGTJEe/fuvUrVtZ2YmBhdf/31zdbqr8dPkg4ePKi1a9d63LvpT8ev8TiUlpaqa9euruWlpaVKTU1tcp3W/B23SpuNzmkHLjdQuLS01LXsj3/8o4mKijJVVVVNbqtxoPCmTZtcyz766COfGijsdDpNz549zSOPPNKq9T///HMjyfzjH/9o48ra3ptvvmmsVqs5ceJEk+83DhT+7//+b9eyXbt2+fRA4cOHD5u+ffuaCRMmmLq6ulZtw1eO4YgRI8zMmTNdr+vr6023bt0uOVD4+9//vtuy9PR0nx1o6nQ6zYwZM0xSUpL5+uuvW7WNuro6069fPzN79uw2rq7tnTx50nTq1Mn8/ve/b/J9fzt+58vJyTGJiYmmtrbWo/V8+fipmYHCCxYscC2rqKho0UBhT/6OW1Vrm20pgB08eNBs3rzZzJ0710RERJjNmzebzZs3m5MnTxpjGv4xDhgwwNx+++1my5YtZvXq1aZLly4mOzvbtY0NGzaYfv36mcOHD7uWjRkzxgwZMsRs2LDBfP7556Zv375m4sSJ13z/mrN27VojyezcufOi9w4fPmz69etnNmzYYIwxZu/eveaZZ54xmzZtMvv37zfvvfee6dWrl7nllluuddmXtX79evP888+bLVu2mH379pk333zTdOnSxUyePNnV5sL9M8aYBx54wHTv3t18/PHHZtOmTSY9Pd2kp6d7Yxcu6/Dhw6ZPnz5m9OjR5vDhw6akpMT1OL+NvxzDt99+29hsNvP666+bHTt2mPvuu8/ExMS4rjj8+c9/bh5//HFX+y+++MIEBwebBQsWmJ07d5qcnBwTEhJi/vnPf3prFy7pwQcfNNHR0WbdunVux+r06dOuNhfu49y5c81HH31k9u3bZwoKCsyECRNMWFiY2b59uzd24ZIeeeQRs27dOrN//37zxRdfmIyMDBMXF2fKysqMMf5//BrV19eb7t27m8cee+yi9/zt+J08edL1XSfJLFy40GzevNkcPHjQGGPMvHnzTExMjHnvvffM1q1bzY9+9CPTs2dPc+bMGdc2vve975kXX3zR9fpyf8dtgVDTAlOmTDGSLnp88sknrjYHDhwwd9xxh+nQoYOJi4szjzzyiFtS/+STT4wks3//ftey48ePm4kTJ5qIiAgTFRVlpk6d6gpKvmDixIlm5MiRTb63f/9+t99BUVGRueWWW0xsbKyx2WymT58+5tFHHzUVFRXXsOKWKSgoMGlpaSY6OtqEhYWZG264wfzXf/2XW6/ahftnjDFnzpwx//Ef/2E6depkwsPDzY9//GO3kOBLli5d2uS/2fM7Z/3tGL744oume/fuJjQ01IwYMcJ8+eWXrvdGjRplpkyZ4tb+nXfeMddff70JDQ013/rWt8wHH3xwjStuueaO1dKlS11tLtzHhx9+2PX7SEhIMHfeeacpLCy89sW3wPjx403Xrl1NaGio6datmxk/frzZu3ev631/P36NPvroIyPJ7N69+6L3/O34NX5nXfho3Aen02meeuopk5CQYGw2mxk9evRF+92jRw+Tk5PjtuxSf8dtwWKMMW13MgsAAMA7mKcGAAAEBEINAAAICIQaAAAQEAg1AAAgIBBqAABAQCDUAACAgECoAQAAAYFQAwAAAgKhBgAABARCDQAACAiEGgAAEBAINQAAICD8P4YL2Wa2vkSaAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
 }
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