4. NN from Scratch.ipynb

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   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nxnfYcUL_Y3O"
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   "source": [
    "## Часть 1. Что такое нейронная сеть"
   ]
  },
  {
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   "source": [
    "\n",
    "\n",
    "$X = (x_1, x_2, \\ldots, x_n)$ — входные данные\n",
    "    \n",
    "$Y = (f(x_1), f(x_2), \\ldots, f(x_n))$ — ground truth, наблюдаемые ответы, где f — целевая зависимость, ее значения известны нам на множестве входных данных.\n",
    "    \n",
    "Мы хотим найти  аппроксимацию $f$, назовем ее $\\hat{f}$ используя обучащие данные $X' \\subset X$, такие что\n",
    "    \n",
    " $ \\hat{f}(X') \\sim f(X') \\text{ and } \\hat{f}(X'') \\sim f(X''),$\n",
    "где $X'' = X\\setminus X' $ - тестовые данные\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "id": "tBY6DjGab_9e"
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   "source": [
    "Допустим, мы задали функцию $\\hat{f}(x_i)$ (построили нейросеть). Как нам оценить, насколько наша функция близка к исходной?\n",
    "Для этого мы зададим функцию потерь = $ \\textbf{loss/ cost function}$ $\\mathcal{L}(f, \\hat{f}, x)$ .\n",
    "Будем усреднять значение функции потерь для множества семплов (в общем случае для всего обучающего множества):\n",
    "    $$\\mathcal{C} = \\frac{1}{t}\\sum_{i = 1}^{t} \\mathcal{L}(f, \\hat{f}, x_i), x_i \\in X'.$$"
   ]
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   "source": [
    "Примеры функции потерь:\n",
    "* **Кросс-энтропия** (записана для случая бинарной классификации):\n",
    "$ \\mathcal{L}(f,\\hat{f}, x) = -(f(x)\\cdot\\log \\hat{f}(x) + (1-f(x))\\cdot\\log(1-\\hat{f}(x)));$\n",
    "\n",
    "\n",
    "* **Квадратичное отклонение**:\n",
    "$\\mathcal{L}(f,\\hat{f}, x) = (f(x) - \\hat{f}(x))^2.$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Мы интерпретируем выход нейронной сети, как вероятность.  Допустим, мы предсказываем род существительных на данных русского языка. Наши классы _средний, мужской, женский_ . Допустим:\n",
    "$$f(x)  = [0.0, 1.0, 0.0], \\hat{f}(x) = [0.1, 0.56, 0.34];$$\n",
    "Тогда, используя кросс-энтропию(обобщенную на случай много классовой классификации), получаем значение ошибки:\n",
    "$$\\mathcal{L} = -(0.0\\cdot\\log(0.1)+1.0\\cdot\\log(0.56)+0.0\\cdot\\log(0.34)) \\approx 0.252$$"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "w_eGrG0hkZVf"
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   "source": [
    "После вычисления значения функции потерь $ \\mathcal{L}(f,\\hat{f)}$  мы оптимизируем параметры нашей сети $\\hat{f}(x_i)$ . Для этого нам понадобится понятие __градиентного спуска__.  \n",
    "\n",
    "**Градиент** в математическом анализе — это вектор, указывающий на направление максимального роста функции в заданной точке. Вектор-градиент состоит из частных производных функции от каждого из ее параметров. \n",
    "$ \\mathcal{L}(f,\\hat{f)}$ зависит от множества параметров  нейронной сети, каждый из возможных наборов значений параметров соответствует точке в пространстве параметров, принадлежащей функции потерь. Если, находясь в данной точке, мы знаем, в каком направлении надо двигаться, чтобы функция возрастала быстрее всего, то, двигаясь в противоположном направлении, мы добьемся минимализации ее значений."
   ]
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   "cell_type": "markdown",
   "metadata": {
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    "id": "t1pTxk4jrviR"
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   "source": [
    "Как может быть устроена функция $\\hat{f}(x_i)$? Нейросеть удобно изображать в виде  графа. Посмотрим, чему соответствуют его вершины и ребра"
   ]
  },
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    "colab_type": "code",
    "id": "WJcVbdPX2RQU",
    "outputId": "96a59c6c-0f63-46cb-f7b8-36264a9c025d"
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   "source": [
    "<img src='img/1_neuron.png' width='350' height='220' align='left'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "id": "YK2WYRAdsWnd"
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   "source": [
    "Вход в первый нейрон:\n",
    "$z_1^1 = \\theta^1_{11}\\cdot x_{i1}+\\theta^1_{12}\\cdot x_{i2}+\\theta^1_{13}\\cdot x_{i3}+\\theta^1_{14}\\cdot x_{i4}+b^1_1.$"
   ]
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   "source": [
    "<img src='img/sigmoid.png' width='350' height='220' align='left'>"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Сигмоида - одна из нелинейностей  (функций активации), применяющихся в нейронных сетях. Она принимает в себя выход с  одного из нейронов\n",
    "$\\sigma(x) = \\frac{1}{1+e^{-x}}.$"
   ]
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   "source": [
    "<img src='img/2_layer.png' width='350' height='220' align='left'>"
   ]
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   "source": [
    "$a_i = \\sigma(z^1_i)$\n",
    "\n",
    "Тогда вход в $\\hat{y}_1$:\n",
    "\n",
    "$z_1^2 = \\theta^2_{11}\\cdot a_1 + \\theta^2_{12}\\cdot a_2 + \\theta^2_{13}\\cdot a_3 + \\theta^2_{14}\\cdot a_4+ \\theta^2_{15}\\cdot a_5+b^2_1,$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "base_uri": "https://localhost:8080/",
     "height": 237
    },
    "colab_type": "code",
    "id": "Pf5Cln89-sNz",
    "outputId": "26bb6593-26ea-4e21-e72b-9f514199e485"
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   "source": [
    "<img src='img/full.png' width='350' height='220' align='left'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "Более формально нейронную сеть можно представить в виде графа вычислений:"
   ]
  },
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    "colab_type": "code",
    "id": "WOeJt6o1-7wc",
    "outputId": "5ec9dfcc-f2c8-40d7-811a-a43e7f115344"
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   "source": [
    "<img src='img/forward_backward.png' width='850' height='100' align='left'>"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Что еще почитать\n",
    "\n",
    "1. [Нейронные сети для начинающих. Часть 1](https://habr.com/ru/post/312450/)\n",
    "2. [Нейронные сети для начинающих. Часть 2](https://habr.com/ru/post/313216/)\n",
    "3. [Machine Learning for Beginners: An Introduction to Neural Networks](https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9)\n",
    "4. A Beginner’s Guide to Neural Networks: [часть 1](https://towardsdatascience.com/a-beginners-guide-to-neural-networks-b6be0d442fa4) и [часть 2](https://towardsdatascience.com/a-beginners-guide-to-neural-networks-part-two-bd503514c71a).\n",
    "5. [Tensorflow Playground](http://playground.tensorflow.org/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "deIpV-uR_JcE"
   },
   "source": [
    "## Часть 2. Пишем свою нейронную сеть"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7jWKINpbTT5N"
   },
   "source": [
    "Построим нейросеть с одним полносвязным скрытым слоем, которая будет брать на вход сэмпл, представленный в виде признаков, а на выходе отдавать вероятность класса. Мы рассмотрим случай бинарной классификации, поэтому в выходном слое нам будет достаточно одного нейрона"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jselA9EK8RR8"
   },
   "source": [
    "Загружаем данные. Классический датасет содержит информацию о длине и ширине лепестка и чашелистика для трех видов ирисов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZD-_3lS7ojHu"
   },
   "outputs": [],
   "source": [
    "iris = pd.read_csv('data/iris.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "id": "Lm5r6oBXojH3",
    "outputId": "cf062a82-9e71-4602-ad41-d994b0e3c46b",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width      species\n",
       "0           5.1          3.5           1.4          0.2  Iris-setosa\n",
       "1           4.9          3.0           1.4          0.2  Iris-setosa\n",
       "2           4.7          3.2           1.3          0.2  Iris-setosa\n",
       "3           4.6          3.1           1.5          0.2  Iris-setosa\n",
       "4           5.0          3.6           1.4          0.2  Iris-setosa"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4zREzoCM9XZ3"
   },
   "source": [
    "Для нашей тренировочной задачи упростим данные, оставив только два класса: __Virginica__ — 0 и __Versicolor__ — 1. Будем решать задачу бинарной классификации, классифицируя каждый семпл по двум признакам (длина и ширина лепестка)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bFnsUBMfojIJ",
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "iris.loc[iris['species']=='Iris-virginica','species_num']=0\n",
    "iris.loc[iris['species']=='Iris-versicolor','species_num']=1\n",
    "iris.loc[iris['species']=='Iris-setosa','species_num'] = 2\n",
    "iris = iris[iris['species_num']!=2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "y9IesQ5XojIQ"
   },
   "outputs": [],
   "source": [
    "X = iris[['petal_length', 'petal_width']].values.T #(2,100)\n",
    "Y = iris[['species_num']].values.T #(1,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LUYS3MVcAdCP"
   },
   "source": [
    "Визуализируем наши данные в двумерном пространстве признаков, разные цвета соответствуют разным классам"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 376
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    "colab_type": "code",
    "id": "rGwZrhscojIi",
    "outputId": "6b2b8ba9-a998-4b35-e3c0-005bca658626"
   },
   "outputs": [
    {
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HSExM5NixY0yfPp3CwkLGjRtX5fLLy8tJT08nLS3NcNK1V69eaDQaw9BWbGwsBw8e5MEHH6Rz585G/+bMmcOFCxdMrhCxZOPGjTg4OPDAAw+YLGvKlCls2rTJ6AqK2tJoNKSnp5Oens6VK1d477332Lt3L3fffbfFPtHR0ezcuZOvv/6ay5cv89prr/Hnn38apsvlcl5//XXefvttw0nbCxcu8PXXX/PYY4/VOebrpk6dilwuZ+bMmfTo0YNbb73VaPrLL7/MkSNHmDVrFseOHePq1avExMQwd+7cKq+yycrKYt68eezbt4+EhASOHj1KTEyMxSO2rl27MnbsWB588EE2b97M1atXOXLkCCtWrABg1KhRREZGMmnSJA4fPszp06eZOnUqtra2zJo1y+wyH3zwQZRKJVOmTOHkyZP88ccfTJo0iYiICMaMGVPLLVa9559/nuXLlxu2jzXb8Nlnn+Xjjz9m9erVXL58mTVr1rB169Z6jcvLy4vx48czf/58EhMTqz05bcno0aMJCQnh/vvv5/jx4xw/fpxp06ahVCrrdCRmziuvvMKWLVt48cUXOXv2LBcuXGDdunUkJCSgUCgIDQ1l48aNxMbGcuzYMSZOnFjtTlFd/KMTBMAzzzzDlStXjO47uNHQoUM5duwYkydPJiwsjBEjRpCWlsaPP/7I0KFDq1z2gQMH8PPzIzAw0LAHP2XKFM6ePWsYolmzZg3+/v5mx19DQkLo2bOn1Xv+a9euZdy4cWavyrrnnnsoLCyslz/CmJgY/Pz88PPzo2vXrqxbt47//e9/VQ6FzZ49m1mzZjFnzhx69epFTk6OyaW+Dz/8MJ9++inbt2+nR48e9OrVi9dff91wZU99cHFxYfLkyeTl5Zkdj7711ls5ePAg6enpDB48mKioKObOnYskSUZDUTezt7cnLS2N6dOn06lTJ0aOHEloaKjF7xXAl19+ybRp03juuecIDw/n3nvvNVzOqFAo+OGHHwgICGDYsGH06dOHkpISYmJiLF4Z5ezszM8//4xGo6Ffv34MGTKENm3a8MMPP1T7I3J92LM234/Jkyfj6enJq6++Cli3DadNm8aSJUtYsmQJXbt25dtvv+Xf//53jdddnTlz5pCXl0f//v2JiIio1TJsbGzYsWMHkiTRt29fxo8fz+TJk2nbti1KpbJe47377rv55ptv2LNnDz179qRv375s3rwZW1tbAD799FMKCgro0aMH9957L5MmTaqXYWNLZNLNA8PCP1afPn0YN24cL774YlOHIjSyHTt2MHXqVC5cuGB0MlYwLzc3l4CAAFauXMnMmTObOpwG8486SS0Ignnff/89ixYtEsnBgq1bt+Ls7ExYWBhpaWm8/PLLODk5VTvM3NKJBCEIQoNewNAaFBcXs2DBAq5du4aLiwu9evXi0KFDuLu7N3VoDUoMMQkG69evJzw8vNrr0QVB+GcQCUIQBEEwq8UPMd18bX1NeHl5GZXVbk5EbLXTXGNrrnGBiK22WnJs/v7+Vi3nH3+ZqyAIgmCeSBCCIAiCWSJBCIIgCGaJBCEIgiCYJRKEIAiCYJZIEIIgCIJZLf4yV0EQmoauTEPuH5ewdXbAtXuHeq1sKkkSBSfiKJclogj3ReFgXKZbr6kg749LyJW2uPUIRSYX+7oNQSQIQRBq7NqmPSSu+4nShHTkSjscO/hxy/uP4tyx7rWcii6ncOaJVZRcSUOvqUAV3IZ2Dw8n6IHKp++lbv+NuHe/oTQ+A7mtHFWIH1FvzcKtW4c6r1swJtKuIAg1UnI1nbh3tlManw4S6MvKKTqbyNknV5s8NbCmJEni7JOrKTqbiF5dDpJEaXzl+kri09FkFXDpzc2UxqWBXo9eo6X4fBLnnl2PXmv+mS5C7YkEIQhCjSSs/ZHyrAKT9pKraRTF1u3pZkXnEimJSzdpL88qIGHtThI/2oUmNdfMutPJPRRbp3ULpsQQkyAINaIr1Zht12u0FqfVZNk6C89X1pWokSnM79NKFVq0xZYfeSvUjjiCEAShRgLuG4DC0fRJaqpgH1y7htRp2a5dQ3AMbmPSrnBSEjBxAG2nDMLG3fTJfg5BPngN7FKndQumRIIQBKFGPPpF0uauniic/k4S9n4etH9yDHK7ug1KyO1taf/EGOx9/37OgsJJSZvhPfG4PRKXyCD8x/XFxkVlmG7n7Uq72cOxcXKo07oFU2KISRCEGpHJZHR+ZzZtJw8k+cv92LqqCJ49AqW/R70sP2DCHXj2jSRhzY8oynV43d0Ht9vCDJfRRrz2AH4T7iD5kz3IHewInn0XqiCfelm3YEwkCEEQakwmk+HeOxz33uENsnylvwfhS+63WLbarVsIbt3qNpwlVE8MMQmCIAhmiQQhCIIgmCUShCAIgmCWSBCCIAiCWeIktSA0IUmnJ/vXM5SlZuMTfSvKGy7vbGrlBSXEvbMdbXEZHZ4ahyrQu6lDEhpZoySI7OxsVqxYQX5+PjKZjOjoaEaMGGF23itXrrBgwQKefvpp+vTp0xjhCUKTKInP4NQjyym5nIq+XMvVNt/iO7oX4Yvvb+rQuLriO668vQ2porK+UepXB2kzoifdVj3RxJEJjalREoRCoWDatGmEhIRQVlbGiy++SJcuXWjbtq3RfHq9ns8++4xu3bo1RliC0KTOPr2GonN/1y7SZOSR/MWveAzojM/gpvsb0BarjZIDADo9GT/8ScGpq3W+W1poORrlHIS7uzshIZVfKgcHBwICAsjNNS24tXPnTnr37o2Li0tjhCUITUadlktpQoZJu65ETcrn+xo7HCPxK783Tg7X6SViF2xs/ICEJtPo5yAyMzOJj48nNDTUqD03N5c//viDRYsWsWrVKov9Y2JiiImJAWDp0qV4eXnVOhYbG5s69W9IIrbaaa6x3RxXcYkOmYXK2LYK20Z9DzfHds3W1uK8cj1NGltz8k+IrVEThFqtZtmyZcyYMQOVSmU07eOPP2bq1KnIq3kyVHR0NNHR0YbX5u6ytJaluzSbAxFb7TTX2G6OS1LJsQ/0QpNTaDSf3N4Wz7tubdT3cHNsvtMHceG97Ug3P19BJiPkpXubNLbmpCXH5u/vb9VyGi1BaLVali1bRv/+/endu7fJ9Li4ON577z0ACgsLOXHiBHK5nF69ejVWiILQaGQyGRGvPcCZp1YbHrxj46rCe1BXfMc27cUZdh4uBEweSPJne0EvXQ8Yt54d8e7fuUljExpXoyQISZJYvXo1AQEBjBo1yuw8K1asMPp/jx49RHIQWjW37h3o+9NrpHy5n7LkbPzG9cW1S/umDguAqDdn0u6h4ZxfsBFdqZpOCyfj3qtTU4clNLJGSRAXL15k//79BAUF8fzzzwMwefJkwyHQsGHDGiMMQWh2bFRK2j3YPL//Th38uO3LF5s6DKEJNUqCCA8PZ8uWLVbP/9hjjzVgNIIgCII1RKkNQRAEwSyRIARBEASzRIIQBEEQzBLF+gShCenU5aR98ztlydn4ju6Ncyfj8jPluUWkbN6PpNcTMHEA9l6uRtOL41JJ2/47Sj93/MffgcLBzjBNkiRyDp4j77fzuHTvgE90N2TV3GdUE2VJWaRsPYCdmzP+9/XHxlFZfae/6LU6MnYepfh8El6DuuDWs6PhkaLWUKflkrLlAAqVPQH39cfW1bE2b6HFKc8rJmXLfvTlWtpOHIC9j1uDrk8kCEFoIoVnEzn9xEpKrqaDTk/Sxhi8h3an87KHkclkJH22l6vLv0WdkgNA0sYYgh8dRbuZQ5EkidgXN5Cx8ygVuUUgl5Gw9idueWc2breGoisr5/j0tyk4FY+uRI1caYtzRBA9PnkeW7e6/5hefP0LUrcdojyrAICED3cR+e/peA24pdq+mox8jk1/m+JLKUjlWq5t2I3bbWF0/3Aectvqf5Li3vuGpE170GTkA3Dto92ELZyI70jT+6tak5RtB7ny1jbUyZVXfyZtjCH44eEEzzFf+LQ+iCEmQWgisS9toORyKuj0AFTkFZO+4zAZP/xJRX4JVz/YYUgOAOrUXBJWfU95TiFZv5wkdftvlckBQC9RGpdG7IKNSJLExX9/Se5v59GVqCsnqysoOBHHuRc31Dnu/JNXSf7iV0NyAChLyODiks+R/novVTn7/HqKziYilWsB0BaVkb3vNFeX76i2b0l8Otc2/GxIDlB5JHP5P1vRqctr8W5aBm1xGXH/225IDgCa9DwS1v2EOs20rl19EQlCEJpAWUo2pYmZJu16dQWp2w+R9u3vqJNMSyWoUyuHVlI2H0BfqjGdfi2L0vh0Ck7EmV1v8cWkOseetPFntAUlJu2l8ekUnLpaZV9Jr6fkSqrpBL1E7u/nrVh3DOXZhSbtpQkZZP96ptr+LVXGzmOUmfm+aNLzKu94byAiQQhCE5DJ5CA3P+Yuk8lAUcV4vEKGzEJfSQbI5FWM51s/zm+JTGbhZ0Mus+4cRw3ONZiuw8LyZZa3SWsgU8gsf3SKhvsZFwlCEJqA0t8DVTsfk3a5yh7/+wbgN6YvDkGm05VtvQi4tz9tpwxC4WR6UlgV3AZVsA9uPTua/UFx7tyuzrEHzRqGrbvpeQxVe19cugRX2Vcml+MUFmA6wUaO54Dq6zy1e3AYdj6uJu2OwW2sOv/RUvkM74GqXRuTdns/DwKnDmqw9YoEIQhNJOrth3Dq1BaZrQIAO28XAu65A5+h3bF1URH6/AQcgv5+zKdDoBcd5o3Dzt0ZrwGdaTtpIHbef/1Y2ihwDAsg6j8PIpPJCHvxPrwGdsHGpbJqskKlxK1XJ6L+PaPOcbtEtSNo+lDsrz8eVSFH1cGPyDemW3UE0fnth3DtFoL8ryuubNwc8Rl6KyGPja62r0NbL9o/MhJlgGdlgwwc2rch7OXJyO0tlylv6WxUSjq+dB8OwX/vNCjbehHyxJgGvZJJJkmShar0LUNqqpnxTCu15HK9TUnEVnOW4tJrdWTuPkZZcg6+d/XE4abnPmuLykjbcRhJ0uM3uo/J5ZxlqTlk/PAHyjYe+NzVw+QqoPyTceQdvohrl/a49w03O/RU222mycwn/bsj2Lo70WbEbSiUdtV3+oskSWT/eobiC8l4DeyMc0SQ2fksxVaeW0T6t4eRO9rjO6oXNirrL7GtL03xXdOWqEn/7gj68gp8R/fBzt2pVrFZW+5bJIhm+GMCIrbaaq6xNde4QMRWWy05NmsThBhiEgRBEMwSCUIQBEEwSyQIQRAEwSyRIARBEASzRC0mQRDMUqfmkvjhLnRlGgIfGIJzeKDVfSW9noydR8n+5RTOEUG0nXonCgf7Boy2ZdBXaEnb/ht5Ry7i2iOUgHv6I7drvj/DjRJZdnY2K1asID8/H5lMRnR0NCNGGBeYOnDgAN9++y0ASqWShx56iODg4MYITxCEmyR99gtx73yDJj0PgPTvjhBw3wA6vTy52r66snKOTXuLghNx6DUVIJeR9Pleun/0NI7Bpjd7/VOU5xVz7P7/UhR7DalCR8q2QyR/8gs9Pn0eO0+Xpg7PrEYZYlIoFEybNo133nmHN954g127dpGcnGw0j4+PD4sXL+btt99mwoQJrF27tjFCEwThJtoSNfErfzAkB6gsJJjy1QGKLyVX0bPSlWXbyDt8oTI5AOglSi6lcP7/Pm6giFuGC4s+ofBUPFKFrrJBq6PwTALnF25q2sCq0CgJwt3dnZCQEAAcHBwICAggN9e4AmGnTp1wcqq86aNjx47k5OSYLEcQhIaXve+U2cJwFblFJH3yS7X9849fMdteEp9hVbXX1qr4ovnkWnw5pZEjsV6jD35lZmYSHx9PaGioxXl++eUXunfvbnZaTEwMMTExACxduhQvL69ax2JjY1On/g1JxFY7zTW25hoXmMamaeONzFbx957uDZy9Pap9H/ZK83c129jZ4OXjXaMHA7Wk7VYdW3vz52Bs7e3r/T3W13Zr1AShVqtZtmwZM2bMQKVSmZ3n7Nmz7N27l1dffdXs9OjoaKKjow2v63InY0u+E7IpidhqrrnGBaax2XYNQhXsS8lNe7ZKfw+8J91R7ftwG3wLmYdjDc97uM4xIrDGIwMtabtVx7lnKLknr4D+huIVMnDq1r7e32OLu5Naq9XeNIxWAAAgAElEQVSybNky+vfvT+/e5p/8lJiYyJo1a3j++edxdnZurNAEQbiB3NaGqP/OxDEsoLKQ4F8F8UKfnWBVYbh2s/6F37i+2P01r42LCvfbI+j81kMNHXqzFvbSffgMuxVbz8rfNlsPJ7yjuxP+ypQmjsyyRjmCkCSJ1atXExAQwKhRo8zOk52dzdtvv83jjz9udXYTBKFhuN/Widt3v0HuoVh06nK8BnS2+jJVmUzGLf+bjTo1l7yjl3AM9cMlsu5lxls6ua0N3dfPo+RqOoVn43GOaodTh+b9W9coCeLixYvs37+foKAgnn/+eQAmT55sOAQaNmwYW7dupbi4mPXr1wOVVz4tXbq0McITBMEMuY0Cr4G1f8aC0t8DvzF96jGi1sExxBfHEN+mDsMqjZIgwsPD2bJlS5XzPPLIIzzyyCONEY4gCIJgBVFqQxAEQTBLJAhBEATBLJEgBEEQBLOab5UoQRDqRFem4drGGApPxePY0Z92Dw3H1uXv+480WQXEr/oB8kpw6t0R/wl3GD2ytOj8NRLX70KnqaDtpIF49Is03OQmSRJZe06Stv03bByVBD8yskYnXsvzikhY/SNl17Jw79WJtlPubBXPlJZ0etJ2HCbr5+PYeroQ8ugolP4eTR1WrYkEIQitUHluEUcnLaXo/DX4676s9B2H6f7xszgGtyH3yAXOzFuLOimrcuL2Q6R8dZCen81HobTj6srvSVj9IxW5RQBkxZzAd3RvOr/1EJIkcWruCrJiTqIv0wCQ+fMJQp8bT+DUwdXGVng2kZOPvE9ZQkZlXD/+Scq2g9z2xYvYODvU/8ZoJPoKLcenLyP38AXDTYKZu44R+fp0fIbd2sTR1Y4YYhKEVujCks8oiv07OQCUXEnjwqJPAbj0+pd/JwcArY78IxeJX/UDFQUlJH+yx5AcAHTFajJ+/JOCMwlk/3qarD0nDMkBoDyrgIS1O9Gpy62K7XpyqFy4nsKTV7n81tbav+FmIPnzfeQcMr6DXJOay5Vl25AkyXLHZkwcQQhCK1RyOdVse2lCBuV5xahTzZe8yP/jIo4d/ChLMi3ToC0oJeWLfWiLStGXmiaC0oRMCk/H496rk8W4JJ2eshsT0w0KzyZY7NcSZO89DWaKEZal5FB2LQtVO58miKpuRIIQhFbI0kNo5HY2KJS2yGwtTbfF1s0JuZ0N+ptqKQHYebmAhVp7Cgc7bJyqGSKSyyzHZiGmlkKuNH8ORWFvi8KxZT4sSQwxCUIr5B3dDdnNP8RyGe59wlE42OPS2bT0hY2zA23vH4Rnv0hUHfxMpjsEehE0cyjtHxmJfRvTmkyOof44RVT91DmZTIZr9w4m7XKVPb5j+1bzrpq3dg8Nx8bdyaTdMSwAey/XJoio7hSLFy9e3NRB1EVRUVH1M1mgUqkoLS2tx2jqj4itdpprbI0dl9ttYahTc6jILUJbqsHexw2vQV2IWjoTmUKO151dKDyTgLaoDKlCi0OgN4FTBhE4bQgyuQz3XmEUnIhDW6JGJpfh2MGPsIWTce0cjK2rI7YezpTEpaEtKkPhZI9LZDu6rpiLnZvpD+TNvO68haILSWiLytBpKlC29cJ//O2EPD7apBR4c/08wTQ2B39PZDIZZSnZaIvKsHF1xLVbCN1WP9Hoj1utbrtZWwxVJrXUsyd/SU01P9ZqjdZUSrgxidhqrqniKs8toiQuDVWQj9m9/tJrmSjVEnp/F5PhIUmSKD6fhE5TgcstwchtFEbT9eVaCs8kYOPsgGNH/xo95wGgLDUHdUoOTmEB2Lo6mp2nuX6eYDk2XZmGwnOJ2Hm64ti+aR6xWl/lvlv2oJ8gCFWy83DGzsPy3qIqyMfij4lMJsM5MshiX7mdDW49LD/4qzoO/p44+HvWun9zpXCwx71nWFOHUS/EOQhBEATBLJEgBEEQBLNEghAEQRDMEglCEARBMEucpBaEOtCpy7n20W7y/ryErasj7R8fjVPo31eIaLILuLp8B7qMAmz83Ql5YozRSeOiC8nEr/webVEp7n0jaDc92qhoXWbMCVI27wdJwn/CHfgM71Hjq4WEmik4m0Di6h/Rlqjx7N+ZwPsHW7y5r6bKc4u4+v4OShMycAj0JuTJMc36HolGSRDZ2dmsWLGC/Px8ZDIZ0dHRjBgxwmgeSZLYsGEDJ06cwN7enrlz5xISEtIY4QlCrejKNPw5cSkFJ64Yah5lHzhLxKv34zuyN8VXUjkx83+Uxv9ddyjrl1P0+OQ5VEE+pGw9yKU3vqQ8q6By2p6TZP50lNu+eBG5vS2xCzaS+tVBdKXqymX/eha/sX3o/PZDjf5e/ymSPvuFK//dRnlOIVD5eWX+dJQen82v853epdcyOXb/W5ReTTe0Ze89RfcNzxjtVDQnjTLEpFAomDZtGu+88w5vvPEGu3btIjk52WieEydOkJ6ezvLly5k9e7bh2dSC0FzFr/qBguNXjArilWfkc/X975AkiYuvfm6UHABK49K4uORzJJ2ehNU/GJIDAHqJ/KOXSfz4Z8qSssj44U9DcgDQl2nI3H2c4rja3/sjWKav0JK4fpchOQCg05N75GLlUVwdXVzymVFyACiNz+Dia1/UedkNpVEShLu7u+FowMHBgYCAAHJzc43mOXr0KAMGDEAmkxEWFkZJSQl5eXmNEZ4g1ErB8Tiz7eq0PDRpeZQlm79RqTQpk9JrWWjSzHy/9RJ5v58n/Yc/Kc8uMJlckVtE+jeH6xS3YF7JlTTUqbmmE3R6svedrvPySy0UKbRUvLA5sPqYqbS0lNTUVNRqtVF7586da7TCzMxM4uPjCQ01vsEmNzcXLy8vw2tPT09yc3Nxd3c3mi8mJoaYmBgAli5datSnpmxsbOrUvyGJ2GqnMWNzcDN/A5qto5I2wQHYO6koMTPd3smRNu3bYuPkQEWB6RyOXm54d2rHZRsFklZnPFEhx6tTu3p9j+LzrKQKAVsnB3QlapNpTj4eJnHUNDZ7J0eKzbU7q+r9PdbXdrMqQezbt48PP/wQpVKJnZ2doV0mk/HBBx9YvTK1Ws2yZcuYMWMGKpXKaJq5ih/mTsZFR0cTHR1teF2X2/Bb4m38zYGIrZLfjCGk7z9t9NwEAOeoIArKy3Ab2Jm8s/FGzweQ29viEd2VYipwimhLWYpxrHZeLvjNjEYVFoBjBz+KLxoPxTq298VlaJd6fY/i8/yLPTh2aos6w/jIzs7HDb+HhprEUdPYPAZ3Ie9UHHpNhaFNZmeD+8DO9f4eG7XUxhdffMEzzzxD9+7drYvODK1Wy7Jly+jfvz+9e/c2me7p6Wn0hnJyckyOHgShOXHv2ZHQ5yaQtPFn1Gl5KByVuHZpT+f35gAQ+szdVOQWkr3vDNr8EmzdnfCO7kb7R0cC0OX9uZx+fCWF5xLRlWpQ+nvQ7qHhuERVVlrtsmIu557/kNLETEDCIciHqKUPtopHczZXXVc+xqnHV1TWoCorR+nvSfu5I3EKMa1uW1PtHxuFJquA7D0n0eQWYufujPegLnR4+u56iLxhWJUg9Ho9Xbt2rfVKJEli9erVBAQEMGrUKLPz9OzZk59++ol+/fpx+fJlVCqVSBBCsxf0wBDaTh5IaWKmSd0jmUxG5Bsz0BaX4aCWKFPJsVEpDdNtnB24deOzlOcUUpFfgiq4DTLF36cFncMD6fPdYsqSs5H0elRBLe+BMy2NrZsjPT+djyarAG1hqclnUhcymYyIJfejfeEe1Ck5KP09sXFUVt+xCVmVIMaOHcu2bduYMGECcnnNN9bFixfZv38/QUFBPP/88wBMnjzZcMQwbNgwunfvzvHjx3nyySexs7Nj7ty5NV6PIDQFua1NlZcp2jg54BrsRYWFQ347TxfsPF0s9ndo2zzPD7Rm9t6u2Hs3zP0JNiolTh0DGmTZ9c1ignj00UeNXufn57Njxw6cnIzrva9ataralYSHh7Nly5Yq55HJZDz0kLi+WxAEobmwmCCeeOKJxoxDEARBaGYsJojIyEjD/3///Xf69jV9HODhw+J6bEEQhNbKqhMKq1evNtu+Zs2aeg1GEARBaD6qPEmdkVFZJkCv15OZmWl0r0JGRobRPRGCIJgqScwk7u1tSAVlyD0c6fDceFRtvQ3TE9b/RPyK79FXaFG196X7uqdQ+lp39Z62VM3V5TsoPBWPXGlLuweH4dm/ZjeutkR6rY7ED3eR8+sZZAo5fuP74Teuryhi2ACqTBBPPvmk4f83n5Nwc3Pj3nvvbZioBKEVKDwdz4nZy1HfUHIj74+LdP/oaZzDAzkxZzmZP/5pqOVUeCKOA/2fY8Dv/6u2wqdOXc7RSf+prAV1w7JDnhhL+0dGVNGzZZMkiRMPvkP2r2dApwcg9/BF8o9eJvKN6U0cXetTZYLYvHkzAIsWLWLJkiWNEpAgtBaX/rPFKDkAlF3L4tKbW+i66jGyfj5hVOgPQF9WzqnHVtJr80tVLvvaxz9TcNK4FpS2oJSUL/fRbubQVnszXc6vZ8g9fN6QHODvIoYdnhyLfRu3Joyu9bHqHIRIDoJQc2pzxfgAdVoO+X9eNirBcaOby2uYk3/0MuhNy9Oo0/IoiUurWaAtSMbOo+hLy03aNWm55P4W2wQRtW4WjyBeeeUVq8b0RPIQBPMUKnvz7Q5KVMFtQC4Hvd5kuo2FfjeydTdfKNDG2QE7n+b7AJq6UrVvY7Zd4ajEoZ2407y+WTyCGDx4MIMGDWLQoEFERkaSkZFBeHg4/fv3JyIigszMTKKiohozVkFoUXxH9kLuYHwhh1xlj//dt6Nq54O9uR9yuYzw16ZVu+wOT45B6edh0u7SpX2zfkJZXQVOG4IqxNek3alTAK7dOzRBRK2bxSOIO++80/D/BQsWsGDBAgIDAw1td9xxB6tWreK+++5r0AAFoaUKfmQE2qIyMnb+ia6wDIWrCt8xvQmaUVmN+Paf/83vwxeiychD0knIlbYEzRyGz5Dqi2I6BHoT8Z+ZxC3bjjotB4XSDteuIUQta93VCGwclXRd9TjnF26iLCkLmVyGY1gAt7w7R1zF1ACsqsWUnJxMmzbGh3Y+Pj6kpKQ0SFCC0BrIZDI6zr+HDk+Pw0WhpFCvQW6jMEy3c3di4JF3Kc8rpjy7AFUHvxrVOvMZ3A3vQV2pyCtG4WCHwqH6oanWwCWqHb23v0xFfgkyGzk2Tg5NHVKrZdW3MTIykpUrV5KWlkZ5eTmpqamsWrWK8PDwho5PEFo8ua0NSh83o+RwIzt3J5w6BtSqEKZMJsPOw/kfkxxuZOvmKJJDA7PqCOKxxx5j/fr1PPPMM+j1ehQKBb169RIVVwVBEFoxqxKEk5MT8+bNQ6/XU1hYiIuLS632dgRBEISWw2KCyMzMxMen8rKx6yU3rsvK+vsh2zefmxAEQRBaB4sJ4rnnnmPTpk2AccmNm12/21oQBEFoXSwmiOvJAeqeBFauXMnx48dxdXVl2bJlJtNLS0tZvnw5OTk56HQ6Ro8ezaBBg+q0TkGoD+r8Un4d8xq65EwAbMKCGLzj/7CxqyxlUXQhiRMPvUd5dgFyGwUBUwfR6aWJVi8/bcdhkr/Yh15dgWOoH2EvTTR6bGlDurJsG9c+jkHS6rB1d6LLmidwu6U9AJJeT+KHu8jcfQJJp8etRyihz45HobSuQGdpYgaX/7sVdUoONs4OtH90JB63R1bfkcp6S8mf7iX9u8MokOMQEUDH+ffW2+M5849f4eryb6nIL8HOx43Q5ybgHNYynvDW2GTSjSVab/Lbb78RGRmJm1vd6pvExsaiVCpZsWKF2QTx9ddfU1payv33309hYSFPPfUU69atw8am+lMkqamptY7Ly8vL8NjT5kbEVjv1GZtOp2NXp0eQq9Vcv8JeAvSuzow4t5KS+DQODfk/k5IZ3kO7c+uGZ6qNK275DhJWfY+2qMzQ5hQRSK9tC7F1UdXLe7Dk1NwPSN9xxKhNZqug767XcQ5ry5l5a0j79nekCp1husftEfT88kVk1Zx/LE3M4OiU/1KWmGlos/V0JuK1afiNMX2uzM3OL9xE8peVSfM611tD6bV1AXI7q06bWpS97zRnnl1HeUa+oU3Z1ovuH87DJapdjZbVkv8O/P0tPyL3RlV+0ps3b2bOnDk89dRTrF69mv379xudf7BWZGSkyaNKbySTyVCr1UiShFqtxsnJSZwEF5rcsVe/MkoOADJAXlDE5e1/cOqRD8zWU8r+9QxatWm9oBvpNRWkfX3QKDkAFJ9PIn7l9/UQfRXr1mrJ2HXcpF2q0HFq9nLKkrPJ/vWMUXKAyj3vzJ9PVLv8y//dapQcACpyikhY81O1fcvzisiMOWGUHAAKTseT8tWBavtXJ+79HUbJAUCdnM2V/26t87JboyrT8XvvvUd+fj7nz5/n/PnzfPfdd6xcuRIPDw8iIiKIjIxkyJAhdQ5i+PDh/Pe//2XOnDmUlZXx9NNPiwQhNLmcnUfN7kHJgGuf/QqpuWb7SRVais5fw717qMVll6Vko8ksMDut6HxSLaK1Xml8hsVCgZqsQvKOXKA8yzQ2vbqC7F9O0uZfPapcvjolx2x7eXYBkk6PTGH5b7v4fLJJBVwAtDpyf4slcGrdhp7NvS8ATVa+2fZ/umqP19zc3Ojbt6/hkaMlJSXExMTw/fffc/DgwXpJEKdOnaJdu3a88sorZGRk8NprrxEeHo5KZXqYHRMTQ0xMDABLly7Fy8ur1uu1sbGpU/+GJGKrnfqMzfmWEIpTM7i5gIME+A3sQm5aBtq8YpN+MoWCwO4RKG+oiXRzXC62Dti7O6EtLDXp7xrYpkG3r4tShcxGbnKEAGDrpCTgtiguuDpSUVBiPFEuw++2yGpjU3m6Ye7n1t7NGe82VRfUU97SEXsvVzTZpj/k3p071Hm7KN2dKSXdpN3B3aXGy/4n/B1UmyAkSSIhIYHz588TGxvLpUuXcHd3p2/fvkRERNQ5AIC9e/cybtw4ZDIZvr6++Pj4kJqaSmio6R5YdHQ00dHRhtd1GQNsyWOITemfElvPZTPYG/MHMp3xD6ne1pZOc6PJ6dyGE9P/Z1J226GdD8VUUHxDHObicrmtIyVJWUb9lQGeBDwyvMG3r2MHP4ov3FRWXC6j48uTkYLccYoIJO/wBaPJTh39cR3Vo9rY/GcNIevoBSpyiv5etNIOz6Hdqn9fzjY4dwlG88spo2ZViC/eU/rXebt4j7yN/PPX0JdqDG22bk74ThlY42W35L8Da89BVJkgli5dSnx8PP7+/nTq1Ino6Ggee+wxHBzq9/Z2Ly8vzpw5Q0REBPn5+aSmphruwRCEpqJ0UxG18XnOPvwucrUGCZAcVfT+eiEKhQKfQd3o+MK9XF2+A526HJlcjmOoH31/eNWq5Xd+6yEUDvbk/X4eXVk5ygBPOs6/B4e2Db9X2ven1zg8eknlsyd0+spCgQ8Px29UbwC6f/Q0555bT1HsNfQ6PY7t2xD55gyrrmLyvD2KiNemkbDmJ8qzC7BxdsBneE9Cnx1vVWzd1jzBufkfUXAyDpke7AM8CX/1fmxdHev0ngGCZ9+FvkJH2re/oy0owc7DmcBpg/Ed2avOy26NqryK6cknn0Sn0xEVFUVkZCTh4eH4+pqW2q3Ou+++S2xsLEVFRbi6unLfffeh1VaOgQ4bNozc3FxWrlxJXl7lA1bGjh3LgAEDrFq2uIqp8f0TY9OWV540vX5568305VqwkVs8d1ZVXJIkgV6qcmy+oej1ejzc3MgvLDQ7XZIkkKRqr1yypLpzDlX2lSQ8PTzIzTP/4KW6qkts0LL/Dqw9gqgyQQBGJ6nPnz9PUVERnTp1IiIigvDwcIKDg2sUeH0TCaLxidhqrrnGBSK22mrJsdXLEBNYPkm9bds2CgsLxZ3UgiAIrVSNT1JfvHiRkpISOnToIO52FgRBaMWqTBBvvvkmly5dQqvVEhoaSmRkJMOHDycsLAw7O+tuuRcEQRBapioTREREBOPHj6dDhw5Wlb0QBEEQWo8qf/XHjRvXWHEIQq0VXUji8tItqDPycXBzps29/fAf36+pwwLg8vkcft2dSEW5hJ29nEHDgwkJc2/qsATBKuKwQGjRShIyOD7zHdRJlTXCioDcU3FU5BXTbta/mjS2C2ez2fbpeYoL/67LlJFWzH3TowgN92jCyATBOqLgkdCiXXl7myE5XKctLCV5836quYK7we3fnWiUHACKCsrZtyuhaQIShBoSCUJo0TTp5m+iqsgrQndDOYWmUFJsvqJrSXGF2XZBaG4sDjHp9XqrFiCqrgpNydbd/MN1bF1UKBya9ko7B0fzd107OIiRXaFlsPhNnTx5slULEDfKCU2pwzPjKDh5BU3a30cScpU9bUb2qnV5iPrSu39bMtNKKCv9u7S2o5Mt/QYHNmFUgmA9iwnigw8+aMw4BKFWXCKCuGX5o8T9bzuazDyUbs54De9B8CMjmjo0uvfyRdLrOXIgBY1awt5BTr9BbYnqJgpRCi2DxQTh7e3dmHEIQq159o3A86vK0vPNrT7OrX38ubWPf7OLSxCsYfVg6NGjR4mNjaXwpqqPjz/+eL0HJQiCIDQ9qwZpv/rqK9auXYter+fw4cM4OTlx6tQps098EwRBEFoHq44g9u7dy8KFCwkKCmLfvn3MmDGDO+64g23btjV0fIIgCEITseoIoqSkhKCgIKDyWafXi/fFxsY2aHCCIAhC07HqCMLX15ekpCQCAwMJDAxk9+7dODk54eTk1NDxCYIgCE3EqgQxceJEiooqH0A+depU3nvvPdRqNbNmzbJqJStXruT48eO4urqybNkys/OcO3eOjz/+GJ1Oh7OzM0uWLLHyLQj/dAlx+fz83VWKCjU4OSmJ7OrJHUOCrOqr0+nZ9U0ccZdyqajQ4+nlwKh7w/D0bvjza3q9xJ4frnLhXA7ach1uHkruGt8RX/+Wv+OVc+gcce9+S3lW5TOp/e7pR7vpQ5s6LKGGrEoQt956q+H/oaGhvP/++zVayZ133snw4cNZsWKF2eklJSWsX7+eBQsW4OXlRUFBQY2WL/xzpacU8eVHZynIqyyrkUUpydfyKS/XMfiu9tX23/rJeU4fTed64YCs9FJysk/x6HM9cVCZvxO6vny35RJ//paCTltZMyozvZTszNM88mwPnF3tG3TdDang1FXOPLXGqAxK8eVUJI2W4Nl3NWFkQk1ZdQ5i5syZZtsfeughq1YSGRlZ5XDUwYMH6d27N15eXgC4urpatVxB2PNjvCE5XFdRruf00Qz0+qqL9RUXlRN/KY+bq8pkpZdycM+1+g7ViEat5VJsjiE5XJebXcaenfENuu6GFvfeNyY1snTFZaRuPdhEEQm1ZdURhE6nM2nTarVW12uqTlpaGlqtlsWLF1NWVsaIESMYOHCg2XljYmKIiYkBYOnSpYakUhs2NjZ16t+QRGzWKbdQj0+j0ePi4oZSafkooDAvx2LhvII8bb2+x5u3WXpqEeobSnDcqKxY36jbt74/T6nI/IeiK1Lj4e6OXKGwelnN6bt2s39CbFUmiFdeeQWZTEZFRQWLFi0ympaTk0NYWFidA4DKBBQfH8/LL79MeXk5CxcupGPHjvj7+5vMGx0dTXR0tOF1Xe5Obc53t4rYrKN0MH8QrHSQU1SUT3GxzGJfG7sKnFxsyc81/UHz8Lar1/d48zbTo8PB0YbSUtME5exq06jbt74/T7mb+fM3CjcVuXnmq+9a0py+azdrybGZ+201p8oEMXjwYACuXLnCoEGDDO0ymQxXV1c6d+5s1Uqq4+npibOzM0qlEqVSSUREBImJiVa/CeGfK3pUe5ISCsjLURvalA429Ojjj0xmOTkAqBxt6RjhyfEjaUZDPW38Hek3qGEL6tnZKYjq6s3v+5OpKP/7SNzLR8Wgu4IbdN0NLfTZ8RSejkedkmNos3F1JHDynU0XlFArVSaIO++8E4COHTsSEBDQYEH07NmTjz76CJ1Oh1ar5cqVK4wcObLB1ie0Ht5tHLl/Thd2fxtHYYEGRyclXW/zpmdf63Yuxk0Ox81dyYVz2Wgr9Hi1UTH6njDslQ1fknv43aE4u9px5ngWFRU6PLwcuGt8KI5OTVumvK6cwwPptu4pLv/3q8qrmJwcaHv/YPzvvr2pQxNqSCZZ8dgtSZLYs2cPhw4doqioiLfffpvY2Fjy8/O5/fbqP/R3332X2NhYioqKcHV15b777kOrrRx/HTZsGAA7duxg7969yOVyBg8ebHWCSE1NtWo+c1ryIWJTErHVXHONC0RstdWSY6uXIabrNm/ezJkzZxgxYgTr1q0DKoeFNm7caFWCmDdvXrXzjBkzhjFjxlgTjiAIgtAIrLrM9ddff+WFF16gX79+hnFdHx8fMjMzGzQ4QRAEoelYlSD0ej1KpdKoTa1Wm7QJgiAIrYdVCaJ79+5s2rSJiorKS/IkSWLz5s306NGjQYMTBEEQmo5VCeKBBx4gNzeXGTNmUFpaygMPPEBWVhZTp05t6PiEVsaKayJq7foOTG3WLUlSnWKr7qbR6pbdkNtFEGrLqpPUKpWK+fPnU1BQQFZWFl5eXri5uTV0bEIrIUkSu7+7yoXTWajVOlxc7Rj4r2Aiu9TPY22XLT5Edubf90HI5bD4nQHY2toiSRK/7k7k9NEMysoqcHKxp9+gQLrd5guAtkLPt5svkBhXgFarx93TgZETOuIf6GzVug/EJLLnx3jKNTrkChk+vo7MnX8bNjaV+16JG3aTsnk/+sIyFG4q2k4ZROD9lfcX6bU6Liz6lNzfYtGpy1H6exL24r2439apXraLINSVYvHixYstTdRoNGzZsoUff/yR1NRUunTpgre3d7M693C9ymxtqFQqSktL6zGa+tOaYtv1bRwH91yjqKAcdZmWgnwN8ZfyCA51w9Wtbt+lj1eeICne+DsgSfDr7kSGjAjh192J/LIznoJ8DZJ7NvAAACAASURBVOoyHYX5GuKv5OMX4Iint4rPPzzDqT8zKC2pQF2mJS9HTdzFXLre1gY7u6pLQlyKzWbrpvNo/7rJTtJDcWE5505k0ndgIEmf7+Py0i2ok7KpKChBk5FP3p+XUfq54xwRxNnn1pOyeT8V2YVoC0tRp+SQc/AcbUb0xNal8Z7W2Jq+a42pJcfm7GzdDlCVQ0wffvghx44dIyAggCNHjvDJJ5/ULErhH0+vlzh/JsukKF1RYTn7fkqo8/Ivns21sF4oK63gzPFMozuVAUqLKzgQk0RhgYakeNPKwTlZZezfnVjtur/54iLmRoayM0spLS4nZfOvaAuN/0i1BSUkffoL2qIycn+/ADrj2NQpOcS992216xaExlBlgjh58iQLFy7k/vvv56WXXuLYsWONFZfQSlSU61CXmRZ7BCgrM1+srr5kpJVQZqbWEVRWU83PVVss1pebU1bt8jVq8/Hr9ZCdWYa2yPwytMVlaLLy0RaUmF9uRn616xaExlBlgtBoNLi7uwOVd+Y118Mpofmys1fg5Gy+oqqbe8MOVQYEOVp8roKziz0+vo64uptOl8kgqH31JectDY8pbGT4tnXEzsvF7HR7L1ccAryw9zG/DufwttWuWxAaQ5UJQqfTcfbsWcM/vV5v9Prs2bONFafQQslkMvoMaIuDo/H1EJ7eDgwbE1Ln5f9rTLDZdpWjDba2tvQfEoTjTQnK3VPJsLEhKB1siOzija2t8Z+BX6AzfQZU/yM9+aHOKBSmBQE7hLljZ2dDh3njsPd1N5qm9POgwzPjkdvb4juuLwon4yTj1Kkt7R8bXe26BaExVFmL6bHHHqu6s0zGBx98UO9B1YSoxdT4ahPbhbPZ/LY3CY1ai5uHkn+NDcXDy6Fe4on57gp7dv59zqCNn4p5L/c1vL56KY9fdyeiLqvA2dWeoaNDaONX+QArSZL441Aqp49moNXq8fV3Yvi4DlY/TS4tuYhP1p6mpKgcuULOrX18GX3P31chFZyII+69b5CKNMhcHQh9+m5cbgk2TE/d/hspm39FV1aOYwc/wv5vIvZejfvArNb2XWssLTk2a2sxWVWsrzkTCaLxidhqrrnGBSK22mrJsVmbIKy6UU4QBEH45xEJQhAEQTBLJAhBEATBLJEgBEEQBLNEghCMlGt0Fm8Aa2r5uWqKi8tr1Ven01NSXIFeb/6ajNLScvKquDlOo9ZSrjF/w19rpivTWLzhT2j9Gv7Bu8DKlSs5fvw4rq6uLFu2zOJ8V65cYcGCBTz99NP06dOnMUIT/lJUoOGrTbFkZZSgl8DTy4G7p4Tj3caxqUPj+OE0dmy+SHm5DmSgcrTl0ed64uldfb0iSZLY+fVlLpzNQa3W4uhkx223+3P7oEAACvPVrPjPUYqLypEkCVs7OUNHd+COwUEAZGWUsP3zC+RklyGXVT4D+94HIi3egNdalOcUcubptRRfSkHS6VEFeRPxxnScwwObOjShETXKEcSdd97J//3f/1U5j16v57PPPqNbt26NEZJwA0mS2LT6FJfP55Kfq6Hw/9u79+ioynPx49+5ZCb3STIh3AIhhICEi2BQQTzIJQQvvVi0qb+qlWPxBtaV0/6syvoda2s9oqBSFAQLSlFRT7Vqq5VqUAREwBAQYiCEBEhC7pncMzPJzN6/P1JG4kzMQJKZSfJ81nIts999eebNkGfvd+/9vHV2ThXU89pLR3G0f38Z675Wb7HxzuvHsNudqGpHQbyWpnaeX3nAq+0/+aCIvZ+XUl3ZSlNDGxVnm8n6oIijOZUArP2fAzQ22FEUFVWFNrvCP/9WQFlJE+3tTl576SinCupprLNTb7FTcMzC1g1fD+jy3KqqknPnc9R8+jW20hrs5Rbq9ufz9b3P42i1db8DMWD4JEGkpKQQHh7+vet89NFHXHnllURGei5PIPpOYX4dFWXudYGqK1rI2V/uh4i+9deteShO9z/GdquTozkV3W5/7EiNW6FAq9XB/t1nKS5qoKXFvRaTqsDbr+aRs6+c6gr3fqksb6Eov+4CPkX/Up9zkubjpW7LWwrLKX19p+8DEn7jkyGm7lgsFg4cOMDvfvc7Xnzxxe9dNysri6ysLABWrlxJbGzsRR9Xr9f3aPu+5MvYclvrPV4pqCo0NyhucfgytsZ6e5dtDXXdx+Zo93ymrzg1WFs00MWFgLXVQUuj6rFaa3ubgrVVe0F90J++a02WozhbPFwpqOAstfj0c/SnfgskvRVbQCSILVu2cOutt6LVdn9Bk5aWRlpamuvnnrzJ2J/fhOxNIxOMhEcE0dzU+WzaGKwjcUK4Wxy+jG3i1Fh2ZxW7LddoYMJkU7exhUXoqaly3294pJ6RCcFotR3VV79r9JhIEseHY9yhw27rfHM6PCKIkQnGC+qD/vRdC5oSj3FoNPbKzldJ2lAjpnlTfPo5+lO/BZIB9SZ1YWEhf/rTn1i+fDn79u1j06ZNHDjg3Riz6LlocwgTJseiP69onVYLY5OjGZPk35kD03+UREiI+3nMsJHhXt1AX3B9IpFRnW8om4eEsOjGJMIjDSR4+HwGo46f3DaRMeOiGJsczfnnLfogLRMmxxJt7p06UoEoeFg0Q9Know0+rx6VVkP0FRMwXzPZf4EJnwuIK4h169Z1+v/U1FSuuOIKP0Y0+Nx020QSxpo4mlOFqqqMTzFz1bxRaDTu1Up9Sa/X8ts/zua1l45QVtKERgNTUody4y2XeLV98kQzS5ZdymfbT9Pa0k5UTDDpP0xyJY27/yuV7e+f5KsvylAUlaHDwrjt3qkEB3f807j17ins/ayEE3m1aDQaplwWx4yrvDv76s9S/mcJUZeNo/z9L1GdCuarJzHm7uv8/n0QvuWTYn1r1qwhLy+PpqYmTCYTGRkZOBwdz9qnp6d3WvdcgvD2MVcp1ud7EtuFC9S4QGK7WP05Nm+HmHxyBZGZmen1ut2VGBdCCOEbAXEPQgghROCRBCGEEMIjSRBCCCE8kgTRzyiKSk1VKy3N7m8A97W2NieHv6rgZH61x3ab1UHBsVoa6z2XY6i32Cg4Vktbm+digOWlTZw+WYfi4cUEVVWpq7XS1OD5xTmnU6GmqpXWVs/F/Ow2BzVVrX4vHSJEfxIQj7kK7+TsK2N3VgkN9TYMBh0jRkfwsyWTMAb3/a/x1Y1fk/f1uacivkGr1XDPb1IZndgxf/JLzx3kTFEDilNFq9UQHRtM5v+biV6vxWZz8Kc/7qOh3o6qgE6nIXliDHcs66i7VXK6gZefP4zd5kBVIShIS9oNY5iTngjAyeMWtr97kjqLFZ1Oy5ChoWQsmYQpOhiA3Vln+GpvGU2NbYSFGYkfE87Nt6eg12tRFJV3tx2nMN+C1eogPMLApTOGknbD2D7vMyH6O7mC6CfKzzbx0buFVJQ1Y2110FBv59iRGt565Zs+P/bRQxXnJYcOiqKy4ZlsAN55LY9TBfWumkmKolJbZWX9018B8MKTB6i3dCQHAKdT5XhuLVn/KERRFDatycFmdbjKWrS3K2z/exHVla20NLfxt9ePcbakidYWB02NbRQV1LNt01FUVeX40Wo+3X6a6opWbK0Oaqtb+PqrSt574zgA//xbATn7yqirtWFrdVBT2cqerGKyv7z4x6OFGCwkQfQTn//rDM1N7sMnZ0ua+ny46d3Xj3tcripwOLuC3EMealkAVRUttLU5upxn4ctdpXydXUlbm4chJQXeeTWPLz4toa7WfciqsqyFspImvtx1Flur+5DV6cJ6nE6Fk8ctbqU07HYnh/xchFCI/kASRD/x3XpA57S3ObG29m2CaPfwB/ycqvJmnB6qrQKoikqbTfFY8A46riSqK92rpZ7T2GCnoc7z/Qy73Uljg532tq76RcHpULts95SUhBCdSYLoJ8aMM3lcbooyEhPbt3WBRiZ0XYJ95px4wiMMHtsMRh3hkQaCgjx/zaKig7n8qpFouvgWps4aztTUoQQZ3FeINgczJimKocM912MyRRkxGHWu+xTfFevFZENCDHaSIPqJq+aNImFs5yQRHhHE7AWj0Wr7tj7OHcsuxVOh3bjhoUSagrn9nqno9J1j0GjhuhvHAXDNojF8t4SPXq/lF/dNJdocQkKie/ILiwhi3rVjGD/JzLgJMeh03+4gOETH9CuGERIaRPqPkhge33mukcgoo+sm9LU3JhFt7pwk4oaHcf3icV5/fiEGK5/UYupLg6kWU3u7k72flXD6ZD2GYD3XLBzNiFG+mWDJam3jz8/lUFneik6nYdY1o7juJ9/+kbXUtLJtUy71FhuhYUHcfHsKo89LaAXHanjvzRPYrQ5ih4by819OJjLq2z/cu3ecYU9WMU5FZUKKmZ/cOhG9viMrKYrKwS/LyDtSjU6nZdbceJLGx7i2tdscfP7JGcpLmogxRzBr3jBi4769sqi32Pj0n6doarQzZFgY864dQ0joeZVKfaC/fdcChcR2cXqrFpMkiH76C/Ynie3CBWpcILFdrP4cW7+aD0IIIUTgkQQhhBDCI0kQQgghPJIEIYQQwiOpxSRcVFWlsqwFRVEZNjLc7fFZh0OhvLQZZ7sR3UU8BNRQZ6Oh3s7Q4WEXXD/K6VSoONtMUJCOIcNCe33qy5qqVqytDobHh7uenhJisPNJgli/fj05OTmYTCaeeeYZt/bdu3fz/vvvAxAcHMzSpUsZM2aML0IT/3a2pIm/vZZHbbUVVVGJiQ3h+puSSZ5oBiB7bxm7ss5QV2PDGKwnNi6E//PLyV2+iHa+NruTNzYfpbS4CWtLO6boYKamxrHox969i3A0p4odHxZRW2NFr9cSGxfKz/5zErFxPX/ZraHOxhubc6mqbKHdrhAdG8yctIRBMe+0EN3xyanS3LlzWbFiRZftcXFxPPbYY6xevZqbbrqJl156yRdhiX9zOhX+uuUbykqasductLUpVJS18N4b+disDqorW/j474VUV7TicCi0NLdxpqiBN17O9Wr/f3vtGMdza2lubMPpVLHUWNm7s5QjByu73baxwc6H75ygsrwFR7uCzeqg9Ewjb2zOpTee0H7j5VzOFDVgbXHgcChUV7R2fNbvKQEixGDhkwSRkpJCeHh4l+0TJkxwtScnJ1NbW+uLsMS/5efWUl3Z6rbcUmPlqy/OsuuTMzQ1uhcKrKpooabKfbvzOZ0KJcWNbsvb7E6y93b/DsueHcU01LnPAVFd2ULxKff9XoiaqlaqKtwTQVNjG7uzinu0byEGgoC7B/Hpp58yffr0LtuzsrLIysoCYOXKlcTGxl70sfR6fY+270u+jE1DA4ri+Wzc0a4DReexrb1NwWgIIzbW3OW+7XaHq8y323E1um4/o9NR2OWxg/QhbttfSL81N1i6LESoOLW92v/yXbs4EtvF6a3YAipB5Obm8tlnn/GHP/yhy3XS0tJIS0tz/dyTNxn785uQvWnU2BBMUUYa6jufqYeG6Um5NIqqiiAOHyxzm40t2hxMaISz2zgjTQaPJb+HjgjpdttJ02I4uK/ErZptzJAQzHFat+0vpN+CwxSizcFUV3S+CtIHaZkwOapX+1++axdHYrs4A+5N6jNnzrBx40YefPBBIiIi/B3OoBIeYSB11nBCQr89XzAadUyZPpShI8KZNC2O5Ikx6M+ryhphMjBnYQI6XfdfoesXj+tUME+jgVGJkSy4PrHbbROTo7hkcmyniq5h4UHMmhPf45n09Hotc9ISiDB9W41WH6QleWIMk6bF9WjfQgwEAXEFUVNTw+rVq7n//vu9zmyidy38YRKXTInly52lKE6VGVePYNyEjoJ4Wq2G2+6eyjeHqziaU0VUdDhXXB1H7FDPpba/a/TYKO57cAa7PjlDQ52dMeOiuGL2yE4JpysajYaf/eck8r+p5dD+coKCdFy9YDTDRnZ9T+tCzLhqBGOSTOzKKsZmdTDlsjgmTYvr8wq5QvQHPinWt2bNGvLy8mhqasJkMpGRkYHD0TELWHp6Ohs2bGD//v2uMTOdTsfKlSu92rcU6/M9ie3CBWpcILFdrP4cm7cn4j65gsjMzPze9nvvvZd7773XF6EIIYTwUsDcgxBCCBFYJEEIIYTwSBKEEEIIjwLiKSZfUxSVM0UNnD1jJ3aorsePS/YXqqpytriJhjobY8ZFExbeueKe06lwqqAOp1MlaXyMV08ZCSEGrsHxl/E8FWXN/O+Wb1x1hWKGhDB77iiumjfK36H1qaZGO69tPEplWTN2u5OoaCNTZwxzzStddKKO99/Kp6aqFVVRMceFsvAHY5maOtTPkQsh/GVQnSKqqsrbW/MoL23G4eh4K9hSbeWz7aepGeDF2f73L3kUn2rAbu94I7m+zs7+3aUcO1qNo13hvTeOU1XeguJUUVWoqWzlo3dP0trS7ufIhRD+MqgSRHlpM9UeirM1N7Wxe8fALc7W2tJOVbn757bbnHy1p4xjR6uprXYvuldvsXFgz1lfhCiECECDKkG0tTlxODy/F9hmd3pcPhA4HAqK03NROqdTxW5zonRRUM9mdfRhZEKIQDaoEkR8QiTmuBC35cZgHZfPHumHiHwj0mQkyuz+ubVamDDJzKRpQ4iOcZ/4JzwiiMtnS+kTIQarQZUg9Hot869LxBRtdC0LDtExeXociclRfoys7/3gpmRihnybJIIMWsZNNHPlnJGEhAZx1fxRhEd+W7QuNExP6qwRmIf0fNY2IUT/NOieYpp2+TDGjo9mz45iVEXHlFQzoxNN/g6rzyUkRXH/Q5ez97MSLLU2plwWx4RJZtfczlfPH03K1CHs+bQYp1Nl1jXxDBvROwXxhBD906BLENAx5HL94uSALrbVF0JCg1hww9gu22NiQ/hRxgQfRiSECGSDaohJCCGE9yRBCCGE8EgShBBCCI8kQQghhPBoUN6k7kuKorBvdymFx+uYPD2O6VcMv6DtG+psfPxBIaEhIfzHwpFEmozdb3SektMNFBc1MCoxktGJvfvoblODnW8OVzF8pJX4RKPbfNTlZ5soyq9jeHwEiclRriekhBD9k08SxPr168nJycFkMvHMM8+4tauqyiuvvMKhQ4cwGo0sW7aMsWO7ftomUDXW23ju8X3YrB1vZed9XcOHbxfwf/9wFcFeVIx957U8Du4rR/33W817d57iyv+I50c/6/7JovZ2J69uPELJqQZsVifGYB3xCZH84r5LMRh0PfpcAB//vZCD+8porG9DpyvAHBfKT3+RQnxCJE6nwrZNuZwqqMPa6sBg1DI8PoI77ruUkNCg7ncuhAhIPhlimjt3LitWrOiy/dChQ1RUVLB27VruvvtuNm3a5Iuwet2GZw66ksM5Lc3t/HlNTrfb1la3cvDLb5MDgKLA/t2lNNbbut3+n+8UUJBncR3fbnNSmF/H39/Kv7AP4UHxqQb2fV5KY30b0FGeo6q8hXe3HUNVVXb88xTHjlRjbe0oy9FmVzhT2MC72473+NhCCP/xSYJISUkhPLzrl66ys7OZM2cOGo2G8ePH09LSQl1dnS9C61WN9XaPy2s8FAj8rg/+egLVQ5koRYGP3jvZ7fbFpxs9Lj9b3NTttt35cmcpVg81mWqrrVSWt1B0os5j7OVnm3t8bCGE/wTEPQiLxUJsbKzrZ7PZjMViITo62m3drKwssrKyAFi5cmWn7S6UXq/v0fZuuhpy12i6PY5O1/VQjF4X1O32ep3nYSSdTtfjzxhkMHTRoiEy0oRe5/lrpNVoe7d/vdDrv9NeEqhxgcR2sQZDbAGRIFQPp59d3eBMS0sjLS3N9XNP3oTu7Tepw8IMNDa4X0VExQR3e5wFPxhN3pEKtzNxjQbmXTeq2+3jhodQfKrebXlsXPfH7s7UGWaOZJ91zSVxTrQ5mOBQByNGh1F4otZtO/OQnh/7QgXq2/GBGhdIbBerP8c2YoR3RTgD4jFXs9nc6cPU1tZ6vHoIdEszLyPI0LlLg4N13PVfl3W77fCREUycGsv5eVGjgSmXxRET233BvB/cPJ6EJBNB/54mVB+kZXRiJD++peelM8ZNiGHalcMIPW+KUvOQEH5wczJarYaFPxxL0oRoDMaOY+t0GkaMiuAnt17S42MLIfwnIK4gZsyYwfbt25k9ezYFBQWEhob2ywQxZGgoj66+ho//XsipgjpSpg7hmkUJaLXe5eHb77mU8tImPni7AKPRwKIbxzB0uHcF84zBeu75dSr5ubWcKqgjIcnEJVOGoNX2zqOmN95yCbPnjSJnXznDRsRwyZRI11zeQUE6fvnAdArzLRTkWRgxOoIplw3ttWMLIfxDo3oa3+lla9asIS8vj6amJkwmExkZGTgcHTc909PTUVWVzZs38/XXX2MwGFi2bBlJSUle7busrOyi4+rPl4j+JLFduECNCyS2i9WfY/N2iMknVxCZmZnf267RaFi6dKkvQhFCCOGlgLgHIYQQIvBIghBCCOGRJAghhBAeSYIQQgjhkSQIIYQQHkmCEEII4ZFP3oMQQgjR/wzqK4iHH37Y3yF0SWK7OIEaW6DGBRLbxRoMsQ3qBCGEEKJrkiCEEEJ4pHvsscce83cQ/hTIU5tKbBcnUGML1LhAYrtYAz02uUkthBDCIxliEkII4ZEkCCGEEB4FxIRBfamtrY3f/e53OBwOnE4nM2fOJCMjo9M67e3tvPDCCxQVFREREUFmZiZxcXEBEdvOnTt59dVXiYmJAeDaa69lwYIFfR4bgKIoPPzww8TExLg9NuevPvMmNn/22fLlywkODkar1aLT6Vi5cmWndlVVeeWVVzh06BBGo5Fly5b5bBy7u9i++eYbnn76adfv8corr+Tmm2/2SWwtLS1s2LCBkpISNBoN9913H+PHj3e1+7PfuovNX/1WVlbGc8895/q5qqqKjIwMbrjhBteyHvebOsApiqJarVZVVVW1vb1dfeSRR9T8/PxO62zfvl3duHGjqqqqumfPHvXZZ58NmNg+++wzddOmTT6J57v+8Y9/qGvWrFGffPJJtzZ/9Zk3sfmzz5YtW6Y2NDR02X7w4EH1iSeeUBVFUfPz89VHHnkkYGLLzc312J++8Pzzz6tZWVmqqnb8W2hubu7U7s9+6y42f/bbOU6nU126dKlaVVXVaXlP+23ADzFpNBqCg4MBcDqdOJ1ONJrOU2FmZ2czd+5cAGbOnElubi6qD+7dexObv9TW1pKTk9Plmbe/+syb2AJZdnY2c+bMQaPRMH78eFpaWqirq/N3WH7V2trKsWPHmD9/PgB6vZ6wsLBO6/ir37yJLRAcPXqUYcOGMWTIkE7Le9pvA36ICTqGIx566CEqKipYtGgRycnJndotFgtmsxkAnU5HaGgoTU1NREZG+j02gP3793Ps2DGGDx/OHXfcQWxsbJ/HtWXLFm677TasVqvHdn/2WXexgX/67JwnnngCgIULF5KWltapzWKxdIrFbDZjsVh8Ngf798UGcOLECR588EGio6O5/fbbGTVqVJ/HVFVVRWRkJOvXr+fMmTOMHTuWJUuWuE6ewH/95k1s4J9+O98XX3zB7Nmz3Zb3tN8G/BUEgFarZdWqVWzYsIHCwkKKi4s7tXs68/XVmXx3saWmprJu3TpWr17NlClTWLduXZ/HdPDgQUwm0/eOVfqrz7yJzR99ds7jjz/OU089xYoVK/jXv/5FXl5ep3Z/fte6iy0xMZH169ezatUqrr32WlatWuWTuJxOJ6dOnSI9PZ2nn34ao9HIe++912kdf/WbN7H5q9/OcTgcHDx4kJkzZ7q19bTfBkWCOCcsLIyUlBQOHz7cabnZbKa2thbo+EK0trYSHh4eELFFREQQFBQEQFpaGkVFRX0eS35+PtnZ2Sxfvpw1a9aQm5vL2rVrO63jrz7zJjZ/9Nk5526Mm0wmLr/8ck6ePNmp3Ww2d5pMvra21mdXD93FFhoa6jozvuyyy3A6nTQ2NvZ5XGazGbPZ7Lp6njlzJqdOnXJbxx/95k1s/uq3cw4dOkRiYiJRUVFubT3ttwGfIBobG2lpaQE6nho6evQoI0eO7LROamoqO3fuBGDfvn1MmjTJJ2cn3sR2/nhhdnY28fHxfR7Xz3/+czZs2MC6devIzMxk8uTJPPDAA53W8VefeRObP/oMwGazuYa9bDYbR44cYfTo0Z3WmTFjBrt27UJVVU6cOEFoaKhP/tB5E1t9fb3rjPPkyZMoikJERESfxxYVFYXZbKasrAzoGE//7u/MX/3mTWz+6rdzuhpegp7324C/B1FXV8e6detQFAVVVZk1axapqam89dZbJCUlMWPGDObPn88LL7zAr371K8LDw8nMzAyY2D766COys7PR6XSEh4ezbNkyn8TmSSD0mTex+avPGhoaWL16NdBxVXX11Vczbdo0Pv74YwDS09OZPn06OTk5PPDAAxgMhoCKbd++fXz88cfodDoMBgOZmZk+G/668847Wbt2LQ6Hg7i4OJYtWxYQ/eZNbP7sN7vdzpEjR7j77rtdy3qz36TUhhBCCI8G/BCTEEKIiyMJQgghhEeSIIQQQngkCUIIIYRHkiCEEEJ4JAlCiAtwrmKm0+n0dyjfa/ny5Rw5csTfYYh+bsC/ByEGh+XLl1NfX49WqyU4OJjp06dz5513utXM+a6dO3eyY8cOHn/88V6L45577mHq1Km9sj9vrFu3DrPZzC233OKzY4rBQa4gxIDx0EMP8eqrr/LUU09RWFjIO++84++QhOjX5ApCDDgxMTFMmzaNkpISoKNk81/+8hcOHTqERqNh3rx5ZGRkUFZWxp///GccDge33347Op2OLVu2kJOTw5tvvkllZSWhoaGu9Xvq4MGDvPnmm1RXVxMfH89dd91FQkIC0HHlsWjRInbt2kV1dTXTpk1j+fLlGAwGAN5//30+/PBDNBoNGRkZbNy4kbVr15Kbm8uePXsA+PDDD5k0aZJrAqXTp0+zdetWj/sTwhuSIMSAU1NTw6FDe1LQngAAA0xJREFUh7jiiisAeOGFF4iKimLt2rXY7XZWrlyJ2Wxm4cKF3HXXXW5DTEajkfvvv5/4+HhKSkr44x//yJgxY1z7uxhFRUW8+OKLPPTQQyQlJbFr1y6efvpp1qxZ4yos+OWXX7JixQoMBgP//d//zc6dO0lPT+fw4cN88MEHPProo8TFxfHSSy+59puWlkZ+fr7HIaau9ieEt2SISQwYq1atYsmSJTz66KOkpKSwePFi6uvrOXz4sKuGv8lk4oYbbmDv3r1d7mfSpEmMHj0arVZLQkICs2fPdiuNfaF27NhBWloaycnJaLVa5s6di16vp6CgwLXOddddR0xMDOHh4aSmpnL69GkA9u7dy7x58xg1ahRGo5Gf/vSnXh2zq/0J4S25ghADxoMPPuh2c7i4uBin09mpmJmqqq7JjjwpKChg27ZtFBcX43A4cDgcHmvtX4iamho+//xztm/f7lrmcDiwWCyun88v12wwGFxtdXV1JCUludq+L/bzdbU/IbwlCUIMaGazGb1ez+bNm9HpdF5ts3btWhYtWsQjjzyCwWBgy5YtPa7vbzabWbx4MYsXL77gbaOjo11zbwCd/h98N+GQGHxkiEkMaNHR0Vx66aVs3bqV1tZWFEWhoqLCNWQUFRWFxWLB4XC4trFarYSHh2MwGDh58qTrJrC3nE4nbW1trv+cTicLFizgk08+oaCgAFVVsdls5OTkfO+0qefMmjWLnTt3Ulpait1u5+233+7UbjKZqKysvKAYhfCGXEGIAe/+++/n9ddf59e//jVWq5WhQ4fy4x//GIDJkye7nijSarVs3ryZpUuXsnXrVl5++WVSUlKYNWuWa2Inbzz55JOdfl68eDG33HIL99xzDy+//DLl5eUYDAYuueQSJk6c2O3+pk+fznXXXcfvf/97tFotN910E7t27UKv7/jnO3/+fJ599lmWLFlCSkoKv/3tby+gd4TomswHIUQ/U1paym9+8xu2bdvm9bCZEBdDhpiE6AcOHDiAw+GgubmZ119/ndTUVEkOos/JEJMQ/cAnn3zCunXr0Gq1pKSksHTpUn+HJAYBGWISQgjhkQwxCSGE8EgShBBCCI8kQQghhPBIEoQQQgiPJEEIIYTw6P8DvLpAXFOZulkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[0, :], X[1, :], c=Y[0,:], s=40, cmap=plt.cm.Spectral);\n",
    "plt.title(\"IRIS DATA | Blue - Versicolor, Red - Virginica \")\n",
    "plt.xlabel('Petal Length')\n",
    "plt.ylabel('Petal Width')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cwQYUNmiE35M"
   },
   "source": [
    "### Инициализация весов \n",
    "Напишем нейросеть прямого распространения с одним скрытым слоем.\n",
    "\n",
    "**Bias vector** — выход для нулевого входа (т.е. сеть должна уметь передавать на следующий слой не 0, даже если на вход поступил 0).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oxKBOIeyojIo"
   },
   "outputs": [],
   "source": [
    "# Функция для инициализации параметров\n",
    "\n",
    "def initialize_parameters(n_x, n_h, n_y):\n",
    "    \n",
    "    W1 = np.random.randn(n_h, n_x) * 0.01   # матрица весов размера (n_h, n_x)\n",
    "    b1 = np.zeros(shape=(n_h, 1))           # bias vector размера (n_h, 1)\n",
    "    W2 = np.random.randn(n_y, n_h) * 0.01   # матрица весов размера (n_y, n_h)\n",
    "    b2 = np.zeros(shape=(n_y, 1))           # bias vector размера (n_y, 1)\n",
    "       \n",
    "    #словарь параметров    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "SQ39IP2RojIt"
   },
   "outputs": [],
   "source": [
    "def layer_sizes(X, Y):\n",
    "    n_x = X.shape[0] \n",
    "    n_h = 6\n",
    "    n_y = Y.shape[0]\n",
    "    return (n_x, n_h, n_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Xj20A0ptGu49"
   },
   "source": [
    "### Прямой шаг\n",
    "\n",
    "Шаг вперед, пропускаем входную последовательность через нейроны сети, запоминая выходы с промежуточных шагов. A2 — полученное предсказание"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pklYZcfBojIz"
   },
   "outputs": [],
   "source": [
    "def forward_propagation(X, parameters):\n",
    "\n",
    "# достаем параметры из словаря \n",
    "    W1 = parameters['W1']\n",
    "    b1 = parameters['b1']\n",
    "    W2 = parameters['W2']\n",
    "    b2 = parameters['b2']\n",
    "    \n",
    "# Делаем прямой шаг и рассчитываем вероятность (А2)\n",
    "    Z1 = np.dot(W1, X) + b1\n",
    "    A1 = np.tanh(Z1)         # функция активации tanh\n",
    "    Z2 = np.dot(W2, A1) + b2\n",
    "    A2 = 1/(1+np.exp(-Z2))   # функция активации sigmoid\n",
    "    \n",
    "    cache = {\"Z1\": Z1,\n",
    "             \"A1\": A1,\n",
    "             \"Z2\": Z2,\n",
    "             \"A2\": A2}\n",
    "    \n",
    "    return A2, cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "61as9IaBH9lS"
   },
   "source": [
    "### Функция ошибки\n",
    "Насколько мы далеки от правильных ответов? Функция потерь сравнивает предсказания A2 c реальными результатами Y и возвращает оценку ошибки.\n",
    "\n",
    "В качестве функции ошибки, которую нужно будет минимизировать, возьмем кросс-энтропию."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "e3OVe-OGojI6"
   },
   "outputs": [],
   "source": [
    "def compute_cost(A2, Y, parameters):\n",
    "   \n",
    "    m = Y.shape[1] # количество примеров\n",
    "    \n",
    "    # W1 и W2 из словаря параметров\n",
    "    W1 = parameters['W1']\n",
    "    W2 = parameters['W2']\n",
    "    \n",
    "    # Считаем кросс-энтропию\n",
    "    logprobs = np.multiply(np.log(A2), Y) + np.multiply((1 - Y), np.log(1 - A2))\n",
    "    cost = - np.sum(logprobs) / m\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xO3bDThUIiQk"
   },
   "source": [
    "### Обратный шаг\n",
    "\n",
    "Шаг назад: обратное распространение ошибки. Хотим получить вектор градиента, состоящий из частных производных по всем из параметров. Вектор указывает направление, в котором функция потерь растет быстрее всего"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fHlUakxaojJA"
   },
   "outputs": [],
   "source": [
    "def backward_propagation(parameters, cache, X, Y):\n",
    "\n",
    "    # количество примеров\n",
    "    m = X.shape[1]\n",
    "\n",
    "    # параметры из словаря \n",
    "    W1 = parameters['W1']\n",
    "    W2 = parameters['W2']\n",
    "        \n",
    "    # достаем A1 и A2 из кэша\n",
    "    A1 = cache['A1']\n",
    "    A2 = cache['A2']\n",
    "    \n",
    "    # Обратный шаг: считаем dW1, db1, dW2, db2. \n",
    "    dZ2= A2 - Y\n",
    "    dW2 = (1 / m) * np.dot(dZ2, A1.T)\n",
    "    db2 = (1 / m) * np.sum(dZ2, axis=1)\n",
    "    dZ1 = np.multiply(np.dot(W2.T, dZ2), 1 - np.power(A1, 2))\n",
    "    dW1 = (1 / m) * np.dot(dZ1, X.T)\n",
    "    db1 = (1 / m) * np.sum(dZ1, axis=1)\n",
    "    \n",
    "    # градиенты\n",
    "    grads = {\"dW1\": dW1,\n",
    "             \"db1\": db1,\n",
    "             \"dW2\": dW2,\n",
    "             \"db2\": db2}\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "C07wrqqnJboU"
   },
   "source": [
    "Наша задача — минимизация функции потерь, поэтому мы идем в противоположном градиенту напривлении. Длина шага — **learning rate**. Сохраняем обновленные веса. С ними наша сеть будет предсказывать чуть лучше"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "nEYHh1egojJF"
   },
   "outputs": [],
   "source": [
    "def update_parameters(parameters, grads, learning_rate=1.2):\n",
    "   # Достаем параметры (=веса)\n",
    "    W1 = parameters['W1']\n",
    "    b1 = parameters['b1']\n",
    "    W2 = parameters['W2']\n",
    "    b2 = parameters['b2']\n",
    "    \n",
    "    # Достаем градиенты\n",
    "    dW1 = grads['dW1']\n",
    "    db1 = grads['db1']\n",
    "    dW2 = grads['dW2']\n",
    "    db2 = grads['db2']\n",
    "    \n",
    "    # Обновляем веса\n",
    "    W1 = W1 - learning_rate * dW1\n",
    "    b1 = b1 - learning_rate * db1\n",
    "    W2 = W2 - learning_rate * dW2\n",
    "    b2 = b2 - learning_rate * db2\n",
    "    \n",
    "    parameters = {\"W1\": W1,\n",
    "                  \"b1\": b1,\n",
    "                  \"W2\": W2,\n",
    "                  \"b2\": b2}\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "G4qEKujCJ-AH"
   },
   "source": [
    "### Собираем нейросеть\n",
    "\n",
    "Собираем все шаги в единую сеть, где процесс обучения выполняется циклом длиной в количество эпох:\n",
    "\n",
    "\n",
    "*  **Forward propagation**: делаем шаг вперед, пропуская входные данные через нейроны сети.\n",
    "*  Cчитаем значение **функции ошибки** *(cost/loss function)*.\n",
    "*  **Back propagation**: ищем градиент — направление максимального роста cost function при нынешних параметрах. \n",
    "*  **Обновляем веса**, перемещаясь по функции потерь в обратном градиенту направлении.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aqsuI-NBojJK"
   },
   "outputs": [],
   "source": [
    "def nn_model(X, Y, n_h, num_iterations=10000, print_cost=False):\n",
    "    np.random.seed(3)\n",
    "    n_x = layer_sizes(X, Y)[0]\n",
    "    n_y = layer_sizes(X, Y)[2]\n",
    "    \n",
    "    # Инициализируем параметры, достаем W1, b1, W2, b2\n",
    "    parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "    W1 = parameters['W1']\n",
    "    b1 = parameters['b1']\n",
    "    W2 = parameters['W2']\n",
    "    b2 = parameters['b2']\n",
    "    \n",
    "    # Градиентный спуск\n",
    "    for i in range(0, num_iterations):\n",
    "         \n",
    "        # Шаг вперед. Вход: \"X, parameters\". Выход: \"A2, cache\".\n",
    "        A2, cache = forward_propagation(X, parameters)\n",
    "        \n",
    "        # Функция потерь. Вход: \"A2, Y, parameters\". Выход: \"cost\".\n",
    "        cost = compute_cost(A2, Y, parameters)\n",
    " \n",
    "        # Обратный шаг. Вход: \"parameters, cache, X, Y\". Выход: \"grads\".\n",
    "        grads = backward_propagation(parameters, cache, X, Y)\n",
    " \n",
    "        # Обновляем веса. Вход: \"parameters, grads\". Выход: \"parameters\".\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "                \n",
    "        # Печатаем значение функции ошибок на каждой 1000 итерации\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" % (i, cost))\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iSGCsrqIL6s4"
   },
   "source": [
    "Обучим модель за 1000 итераций и за 50000 итераций, в обоих случаях сохраним параметры\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 906
    },
    "colab_type": "code",
    "id": "4LfYzQtXojJd",
    "outputId": "fd8b9ce9-1b60-4f18-fd22-9124083a37fe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693225\n",
      "Cost after iteration 1000: 0.402530\n",
      "Cost after iteration 2000: 0.149060\n",
      "Cost after iteration 3000: 0.132325\n",
      "Cost after iteration 4000: 0.132567\n",
      "Cost after iteration 5000: 0.115366\n",
      "Cost after iteration 6000: 0.099302\n",
      "Cost after iteration 7000: 0.097014\n",
      "Cost after iteration 8000: 0.095698\n",
      "Cost after iteration 9000: 0.094169\n",
      "Cost after iteration 10000: 0.092606\n",
      "Cost after iteration 11000: 0.102696\n",
      "Cost after iteration 12000: 0.084246\n",
      "Cost after iteration 13000: 0.086917\n",
      "Cost after iteration 14000: 0.101385\n",
      "Cost after iteration 15000: 0.089592\n",
      "Cost after iteration 16000: 0.153410\n",
      "Cost after iteration 17000: 0.078748\n",
      "Cost after iteration 18000: 0.100950\n",
      "Cost after iteration 19000: 0.074750\n",
      "Cost after iteration 20000: 0.085039\n",
      "Cost after iteration 21000: 0.074722\n",
      "Cost after iteration 22000: 0.077477\n",
      "Cost after iteration 23000: 0.080326\n",
      "Cost after iteration 24000: 0.064107\n",
      "Cost after iteration 25000: 0.082830\n",
      "Cost after iteration 26000: 0.079070\n",
      "Cost after iteration 27000: 0.073601\n",
      "Cost after iteration 28000: 0.066774\n",
      "Cost after iteration 29000: 0.080110\n",
      "Cost after iteration 30000: 0.079224\n",
      "Cost after iteration 31000: 0.077916\n",
      "Cost after iteration 32000: 0.079552\n",
      "Cost after iteration 33000: 0.063440\n",
      "Cost after iteration 34000: 0.063282\n",
      "Cost after iteration 35000: 0.073065\n",
      "Cost after iteration 36000: 0.079256\n",
      "Cost after iteration 37000: 0.069410\n",
      "Cost after iteration 38000: 0.056405\n",
      "Cost after iteration 39000: 0.047547\n",
      "Cost after iteration 40000: 0.036084\n",
      "Cost after iteration 41000: 0.033231\n",
      "Cost after iteration 42000: 0.031779\n",
      "Cost after iteration 43000: 0.030880\n",
      "Cost after iteration 44000: 0.030253\n",
      "Cost after iteration 45000: 0.029783\n",
      "Cost after iteration 46000: 0.029413\n",
      "Cost after iteration 47000: 0.029111\n",
      "Cost after iteration 48000: 0.028858\n",
      "Cost after iteration 49000: 0.028642\n"
     ]
    }
   ],
   "source": [
    "parameters_1000 = nn_model(X,Y , n_h = 6, num_iterations = 1000, print_cost=False)\n",
    "parameters_50000 = nn_model(X,Y , n_h = 6, num_iterations = 50000, print_cost=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "colab_type": "code",
    "id": "khMwdae7ojJm",
    "outputId": "e794eb4f-4f56-4617-fbde-9402ee77c291"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'W1': array([[-0.73141044, -2.89369836],\n",
       "        [ 0.56087706, -4.57804212],\n",
       "        [-0.61413975, -1.13668055],\n",
       "        [-0.21459578,  3.66758731],\n",
       "        [ 1.04207635, -8.36993525],\n",
       "        [-0.09082063,  6.15140858]]),\n",
       " 'W2': array([[ 0.18639226,  0.7308664 , -0.03472296, -0.27995301,  0.90962261,\n",
       "         -0.73329316]]),\n",
       " 'b1': array([[ 2.55350781],\n",
       "        [ 6.71412659],\n",
       "        [ 0.91551246],\n",
       "        [-5.33323044],\n",
       "        [10.35471932],\n",
       "        [-8.37471096]]),\n",
       " 'b2': array([[0.7122717]])}"
      ]
     },
     "execution_count": 37,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters_1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AoWMs4bcNUmE"
   },
   "source": [
    "Посмотрим на результаты для двух наборов параметров. Для этого просто сделаем forward_propagation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "k1CBOMF_ojJr"
   },
   "outputs": [],
   "source": [
    "preds_1000 = forward_propagation(X, parameters_1000)\n",
    "preds_1000 = preds_1000[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 376
    },
    "colab_type": "code",
    "id": "4bWElybsojJv",
    "outputId": "0bbfab45-2ba2-46ce-9183-654df1f3101d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[0, :], X[1, :], c=preds_1000[0,:], s=40, cmap=plt.cm.Spectral);\n",
    "plt.title(\"IRIS DATA | Blue - Versicolor, Red - Virginica \")\n",
    "plt.xlabel('Petal Length')\n",
    "plt.ylabel('Petal Width')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oW6ILVmOojJt"
   },
   "outputs": [],
   "source": [
    "preds_50000 = forward_propagation(X, parameters_50000)\n",
    "preds_50000 = preds_50000[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 376
    },
    "colab_type": "code",
    "id": "ElQRQoTuojJx",
    "outputId": "8fba08f1-1dac-4773-f0c4-670509ddb785"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[0, :], X[1, :], c=preds_50000[0,:], s=40, cmap=plt.cm.Spectral);\n",
    "plt.title(\"IRIS DATA | Blue - Versicolor, Red - Virginica \")\n",
    "plt.xlabel('Petal Length')\n",
    "plt.ylabel('Petal Width')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jmQ1tIkpwbjV"
   },
   "source": [
    "## Задание\n",
    "\n",
    "Попробуем с помощью той же самой сети решить задачу классификации для классического датасета 20 newsgroups. Классы в виде чисел лежат в атрибуте target, а имена классов – в target_names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 391
    },
    "colab_type": "code",
    "id": "GCZBThdkBv4V",
    "outputId": "d2649a6a-c33d-43dd-bb98-4dc8e8c97a10"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['alt.atheism',\n",
      " 'comp.graphics',\n",
      " 'comp.os.ms-windows.misc',\n",
      " 'comp.sys.ibm.pc.hardware',\n",
      " 'comp.sys.mac.hardware',\n",
      " 'comp.windows.x',\n",
      " 'misc.forsale',\n",
      " 'rec.autos',\n",
      " 'rec.motorcycles',\n",
      " 'rec.sport.baseball',\n",
      " 'rec.sport.hockey',\n",
      " 'sci.crypt',\n",
      " 'sci.electronics',\n",
      " 'sci.med',\n",
      " 'sci.space',\n",
      " 'soc.religion.christian',\n",
      " 'talk.politics.guns',\n",
      " 'talk.politics.mideast',\n",
      " 'talk.politics.misc',\n",
      " 'talk.religion.misc']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "from sklearn import metrics\n",
    "from pprint import pprint\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "newsgroups_train = fetch_20newsgroups(subset='train')\n",
    "newsgroups_test = fetch_20newsgroups(subset='test')\n",
    "pprint(newsgroups_train.target_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uoCGg6k2GZm1"
   },
   "source": [
    "Для упрощения задачи оставим любые два класса."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JNo8YQe7Gkoo"
   },
   "outputs": [],
   "source": [
    "categories = ['', '']\n",
    "newsgroups_train = fetch_20newsgroups(subset='train', categories=categories)\n",
    "newsgroups_test = fetch_20newsgroups(subset='test', categories=categories)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "QCQbwQMKHACK"
   },
   "outputs": [],
   "source": [
    "newsgroups_train.['target'][:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ra_7Nm7QCaBy"
   },
   "source": [
    "### Подготовка данных\n",
    "\n",
    "Обучающие данные *(X_train)* необходимо векторизовать, а после превратить получившуюся разреженную матрицу *(sparse matrix)* с множеством нулей в плотную матрицу *(dense matrix)*. Столбец с класcами *(Y_train)* нужно преобразовать в матрицу и затем транспонировать ее.  То же самое нужно проделать с тестовыми данными."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "w-hTpxrZC_8N"
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "vect = TfidfVectorizer()\n",
    "\n",
    "# YOUR CODE HERE "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UdAyTdPdDMoe"
   },
   "source": [
    "### Обучение\n",
    "\n",
    "Необходимо добавить значения параметров. При желании можно использовать `grid search` для подбора параметров (размер скрытого слоя, количество итераций)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sn5GE_PxDLw2"
   },
   "outputs": [],
   "source": [
    "parameters = nn_model(X, Y , n_h =, num_iterations=, print_cost=)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-okW9hEtEOcG"
   },
   "source": [
    "### Тестирование\n",
    "\n",
    "На данном шаге нужно посмотреть предсказания сети на тестовых данных. Не забудьте их векторизовать!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Jyy3hpopEZLt"
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "\n",
    "# здесь тестовые данные и сохраненные на предыдущем шаге параметры\n",
    "preds = forward_propagation() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vDtWFLsSE6v8"
   },
   "source": [
    "Оценим качетсво сети по основным метрикам (точность, полнота, f-мера, accuracy) и построим матрицу ошибок.  \n",
    "\n",
    "В нашем случае предсказания — это вероятность класса 1. Чтобы получить `classification_report`, нужно добавить в архитектуру сети функцию, которая по вероятности будет выдавать класс, или же обработать полученные предсказания соответствующим образом."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zhTavdnCF9nz"
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "\n",
    "print(metrics.classification_report()) # реальные классы и предсказания"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sQS4e-3HCO_0"
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "m = confusion_matrix() # реальные классы и предсказания\n",
    "\n",
    "plt.figure(figsize = (10,10))\n",
    "sns.heatmap(data=m, annot=True, fmt=\"d\", cbar=False, cmap=plt.cm.Spectral)\n",
    "plt.title(\"\")\n",
    "plt.xlabel('Predicted')\n",
    "plt.ylabel('True')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vL_PqUHsI6y5"
   },
   "source": [
    "Также оценим качество с помощью AUC-ROC — популярной метрики для бинарной классификации. \n",
    "\n",
    "**ROC-кривая** (англ. *receiver operating characteristic*, рабочая характеристика приёмника) — график, позволяющий оценить качество бинарной классификации. Он отображает соотношение  *true positive rate, (TPR)* и  *false positive rate (FPR)* при варьировании порога решающего правила. \n",
    "\n",
    "\n",
    "Количественную интерпретацию ROC даёт показатель **AUC** (англ. *area under ROC curve*, площадь под ROC-кривой) — площадь, ограниченная ROC-кривой и осью доли FP. Чем выше показатель AUC, тем качественнее классификатор, при этом значение 0,5 демонстрирует непригодность выбранного метода классификации (соответствует случайному гаданию). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "OkfXXkRhI-dS"
   },
   "outputs": [],
   "source": [
    "fpr, tpr, threshold = metrics.roc_curve() # реальные классы и предсказания\n",
    "roc_auc = metrics.auc(fpr, tpr)\n",
    "\n",
    "\n",
    "plt.title('Receiver Operating Characteristic')\n",
    "plt.plot(fpr, tpr, 'b', label = 'AUC = %0.2f' % roc_auc)\n",
    "plt.legend(loc = 'lower right')\n",
    "plt.plot([0, 1], [0, 1],'g--') # внешний вид можно изменить по своему вкусу\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([0, 1])\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.show()"
   ]
  }
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