simple-neural-network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network From Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook can help you to understand how to build neural network from scratch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our neural network would have three layers:\n",
    "1. Input layer\n",
    "2. Hidden layer with 3 neurons\n",
    "3. output layer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/nn.png\" alt=\"Neural Network Architecture\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the layers and their parameters are hardcoded, which can be viewed as limitation, but for illustration purposes it's the ideal set up. The limitations for the network are following: \n",
    "1. We have predetermined input size. In our case it's two features, so input size is 2\n",
    "2. We have one hidden layer has 3 neurons, we cannot add more layers to the network\n",
    "3. We have predetermined output size, because we a working on regression problem\n",
    "\n",
    "It is possible to change every hardcoded parameters manually, so I encourage you to play with the code, change parts, optimize it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sean/anaconda3/lib/python3.7/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.datasets.california_housing module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "#from tensorflow import keras\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import california_housing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "California housing dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "housing_data = california_housing.fetch_california_housing()\n",
    "Features = pd.DataFrame(housing_data.data, columns=housing_data.feature_names)\n",
    "Target = pd.DataFrame(housing_data.target, columns=['Target'])\n",
    "df = Features.join(Target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = MinMaxScaler()\n",
    "df_scaled = scaler.fit_transform(df[['MedInc','AveRooms','Target']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "                            \n",
    "    df_scaled[:10000, :2], # Features\n",
    "    df_scaled[:10000, 2:], # Target\n",
    "    test_size=0.33, \n",
    "    random_state=42\n",
    "\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dense:\n",
    "    \n",
    "    def __init__(self):\n",
    "        pass\n",
    "    \n",
    "    def add(self):\n",
    "        pass\n",
    "    \n",
    "    def fit(self):\n",
    "        pass\n",
    "    \n",
    "    def predict(self):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = np.array(\n",
    "    [\n",
    "        [1],\n",
    "        [2],\n",
    "        [3]\n",
    "    ]\n",
    ")\n",
    "W = np.array(\n",
    "    [\n",
    "        [0.1,0.2,0.3],\n",
    "        [0.1,0.2,0.3],\n",
    "        [0.1,0.2,0.3],\n",
    "        [0.1,0.2,0.3],\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.4],\n",
       "       [1.4],\n",
       "       [1.4],\n",
       "       [1.4]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(W, I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Simple Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SimpleNeuralNetwork:\n",
    "    \n",
    "    def __init__(self): \n",
    "        \n",
    "        '''        \n",
    "        Initial weights and biases assigned random values ranging '0' to '1'. \n",
    "        We have a total of 9 weights and 4 biases.\n",
    "        6 weights are coming in the hidden layer, two for each neuron, hence 3 x 2 = 6.\n",
    "        The rest of the weights are coming into the output layer.\n",
    "        Same story for the biases. Each bias is attached to the neuron in the hidden layer\n",
    "        and output layer.\n",
    "        '''\n",
    "        # Weights\n",
    "        self.w1, \\\n",
    "        self.w2, \\\n",
    "        self.w3, \\\n",
    "        self.w4, \\\n",
    "        self.w5, \\\n",
    "        self.w6, \\\n",
    "        self.w7, \\\n",
    "        self.w8, \\\n",
    "        self.w9 = np.random.rand(9)\n",
    "\n",
    "        # Biases\n",
    "        self.b_n1, \\\n",
    "        self.b_n2, \\\n",
    "        self.b_n3, \\\n",
    "        self.b_y_hat = np.random.rand(4) \n",
    "\n",
    "    # Activation function for the neurons\n",
    "    # Each neuron IS an actually activation function itself\n",
    "    # sigmoid is for forward propagation, sigmoid derivative is for back propagation\n",
    "    def sigmoid(self, x): return 1 / (1 + np.e**-x)\n",
    "    def sigmoid_der(self, x): return self.sigmoid(x) * (1 - self.sigmoid(x))\n",
    "\n",
    "    \n",
    "    '''\n",
    "    Feedforward function produces result of the network prediction for each sample.\n",
    "    First we find neurons' values for hidden layer, then for output layer.\n",
    "    '''\n",
    "    def feedforward(self, x):\n",
    "\n",
    "        # x[0], x[1] - features\n",
    "        # n* - neurons in the hidden layer, y_hat - predicted value\n",
    "        self.n1    = self.sigmoid(x[0]*self.w1 + x[1]*self.w2 + self.b_n1)\n",
    "        self.n2    = self.sigmoid(x[0]*self.w3 + x[1]*self.w4 + self.b_n2)\n",
    "        self.n3    = self.sigmoid(x[0]*self.w5 + x[1]*self.w6 + self.b_n3)\n",
    "        self.y_hat = self.sigmoid(self.n1*self.w7 + self.n2*self.w8 + self.n3*self.w9 + self.b_y_hat)\n",
    "\n",
    "    \n",
    "    '''\n",
    "    Backpropagation updates all the weights and biases of the network.\n",
    "    By using Gradient Descent technique, each trainable parameter (weight or bias)\n",
    "    is changing a little bit towards minimum of MSE.\n",
    "    Unlike forward propagation, we tweak our parameters starting\n",
    "    from the right end of the network, meaning first we update\n",
    "    weights and biases for output layer, then for the hidden.\n",
    "    If we had more than one hidden layer, we would go over them \n",
    "    is similar fashion, \n",
    "    like this: \"output layer\" => \"hidden layer 2\" => \"hidden layer 1\"\n",
    "    '''\n",
    "    def backpropagation(self, x, y):\n",
    "\n",
    "        # We calculate some values here to use them later\n",
    "        y_hat_der = (-2 * (y-self.y_hat) * self.sigmoid_der(self.n1*self.w7 + self.n2*self.w8 + self.n3*self.w9 + self.b_y_hat))\n",
    "        n1_der = self.w7 * self.sigmoid_der(x[0]*self.w1 + x[1]*self.w2 + self.b_n1)\n",
    "        n2_der = self.w8 * self.sigmoid_der(x[0]*self.w3 + x[1]*self.w4 + self.b_n2)\n",
    "        n3_der = self.w9 * self.sigmoid_der(x[0]*self.w5 + x[1]*self.w6 + self.b_n3)\n",
    "\n",
    "        # Biases\n",
    "        self.b_n1    -= self.lr * y_hat_der * n1_der\n",
    "        self.b_n2    -= self.lr * y_hat_der * n2_der\n",
    "        self.b_n3    -= self.lr * y_hat_der * n3_der\n",
    "        self.b_y_hat -= self.lr * y_hat_der\n",
    "\n",
    "        # Weights\n",
    "        self.w7 -= self.lr * y_hat_der * self.n1\n",
    "        self.w8 -= self.lr * y_hat_der * self.n2\n",
    "        self.w9 -= self.lr * y_hat_der * self.n3\n",
    "        \n",
    "        self.w1 -= self.lr * y_hat_der * n1_der * x[0]\n",
    "        self.w2 -= self.lr * y_hat_der * n1_der * x[1]\n",
    "        self.w3 -= self.lr * y_hat_der * n2_der * x[0]\n",
    "        self.w4 -= self.lr * y_hat_der * n2_der * x[1]\n",
    "        self.w5 -= self.lr * y_hat_der * n3_der * x[0]\n",
    "        self.w6 -= self.lr * y_hat_der * n3_der * x[1]\n",
    "        \n",
    "    \n",
    "    '''\n",
    "    Training process is the combination of forward and back propagations.\n",
    "    '''\n",
    "    def fit(self, X, y, epoch=10, lr=0.01):\n",
    "\n",
    "        mse_list = []\n",
    "        self.lr = lr\n",
    "\n",
    "        # Loop to go over epochs. Each epoch train network on all available data.\n",
    "        # We also check MSE and store it to visualize training process\n",
    "        for i in range(epoch):\n",
    "            mse = mean_squared_error(y, self.predict(X))\n",
    "            mse_list.append(mse)\n",
    "            print(f'Epoch: {i+1} / {epoch}, MSE: {round(mse, 4)}', end='\\r')\n",
    "\n",
    "            # Loop to go over each training example for current epoch\n",
    "            for j in range(len(X)):\n",
    "                self.feedforward(X[j])\n",
    "                self.backpropagation(X[j], y[j][0]) \n",
    "\n",
    "        return mse_list\n",
    "\n",
    "    '''\n",
    "    This function is very similar to feed forward,\n",
    "    it's in fact uses 'feedforward' function to make predictions.\n",
    "    The only difference is that we predict outcome for all samples.\n",
    "    '''\n",
    "    def predict(self, X):\n",
    "\n",
    "        result = []\n",
    "\n",
    "        for x in X:\n",
    "            self.feedforward(x)\n",
    "            result.append(self.y_hat)\n",
    "\n",
    "        return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SimpleNeuralNetwork()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 100 / 100, MSE: 0.0286\r"
     ]
    }
   ],
   "source": [
    "history = model2.fit(X_train, y_train, epoch=100, lr=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAAAAAAAAAAFBOjAwAAAAAAAAAAAABQTIwOAAAAAAAAAAAAAEAxMToAAAAAAAAAAAAAAMXE6AAAAAAAAAAAAAAAFPsLkJOZDqmMDsQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 3632x1362 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.dpi'] = 227\n",
    "plt.rcParams['figure.figsize'] = (16, 6)\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "plt.plot(history)\n",
    "plt.title('Neural Network Training Process', fontSize=15)\n",
    "plt.xlabel('Epoch', fontSize=12)\n",
    "plt.ylabel('MSE', fontSize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.028523506310791816"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse = mean_squared_error(y_test, y_pred)\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Keras Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "keras.backend.clear_session()\n",
    "\n",
    "keras_model = keras.Sequential()\n",
    "keras_model.add(keras.layers.Input((2,)))\n",
    "keras_model.add(keras.layers.Dense(3, activation='sigmoid', use_bias=True))\n",
    "keras_model.add(keras.layers.Dense(1, activation='sigmoid', use_bias=True))\n",
    "\n",
    "keras_model.compile(loss='mse')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 3)                 9         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 4         \n",
      "=================================================================\n",
      "Total params: 13\n",
      "Trainable params: 13\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "keras_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "history_keras = keras_model.fit(X_train, y_train, epochs=100, verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gQQONxw8PD8f69esREhKi9t8JAKBOnTro2rUr+vfvj1KlSmn1HoiIiIiIiIjow6b5fwkhIiIiIiIiIqLPQkZGBiZOnCgJs1eoUAGbNm0qlDD78+fP4erqiqFDh+Ls2bO5BleePXuGgIAAdOrUCXv37s3X8V69egUXFxdJmB3IClAFBwfDyMhI6E9OTsa4cePwww8/YOfOnXmG2QHg7du3OHz4MH788UfMmzdPZehM2erVq9GrVy/s27cv1zA7AERFRSEgIACOjo7YuXNnnmMXJhsbG7i6ugp9sbGxmDt3bpEeNy0tDbNnz0b37t0RFBSkNswOZIWSDx48iB49esDb2xsZGRlFOreC2rJlC+bOnavy7x4dHa0y8Pb333+jc+fOmDlzJs6fP59nmB3IqgTr6+sLJycn3L59u1DmXtgMDAzg4+MjqfLs5eWF+Pj4Ij129me6ePFitWF24P+rQY8bNw7ff/89oqKiCm0OBgYGaNeundAXEhKi0b6nT5+W9IWGhua5X3p6Ov755x9FW19fHx06dFC5bXx8PH799VcMGDAAJ0+ezPW8e/fuHU6dOoWffvoJv/76q9pwb17mzZuH1atXq/x9uH37Np4/f56vcYGsRQAzZ84UrtHW1tbYvHnzRxlmV+fx48dwcXGRhNkB4M2bNzh79qwk7B0bG4tBgwZh0KBBOHDgQJ5hdgBISkrCrl270L17d2zZsqXQ5q9KZGQkevbsiWXLluX6u/zkyRMsXLgQ33zzTaF+V1U5ePAgnJycsHv37lzP9xs3bmDMmDFwc3PDu3fvNBo7OTkZ//vf//DLL7/gwoULau8rXr16hc2bN6Nbt264cOFCvt6Hrj19+lTSp+lTMXx8fODv76/yenHr1i2V5/Hr16/h6emJ7777DkFBQWrD7EDWvci5c+fg5uaGAQMGKJ4IoKkDBw6gc+fOWLRoUa5hdiDrHJ86dSr69OmD2NjYPMeWy+VYtmwZunTpgh07dqgNswNZ1+e///4bzs7OmDhxIt6+favR/ENCQtC5c2cEBATkGmYHgJcvX2Lfvn344YcfMHv2bKSnp+e6fUZGBmbMmIEBAwbgxIkTuf47AQDcuXNHseArODhYo/kTERERERER0ceBgXYiIiIiIiIiIlLIzMzExIkThcqXAFC5cmVs3rw5z8qrmrh79y5+/PFHhIWFqXzdzMxMZTXVpKQkTJw4EX/88YfWx5w+fXquASInJyeUKFFC0X79+jUGDhwo+RyymZiYoHTp0mqrvsrlcvj7+2Pr1q25zmvNmjVYsGCBUPU8W4kSJVC6dGkYGBhIXnvz5g2mTp0qWXRQ1EaPHo3q1asLfYGBgUUWKEpKSsLQoUOxadMmleF0Y2NjmJqaSvozMjKwfv16DBs2LNeAmi7dunUL3t7eal/X09PDDz/8IPTt378fw4cPVxkm09fXh7m5OczMzNRWdI2OjsawYcPyXDihK9bW1nBzcxP6Xrx4gZkzZxbZMTdu3IgRI0ao/UxLlSql8vO8fv06fvzxR1y9erXQ5uLg4CC0VQXVlaWmpuLcuXOSfnXX15zOnz8vVIS3tbWFubm5ZLuYmBj06tVLbcVqExMTlVWUAeDYsWNwdnbWOlAcEhKCgIAAta+bmZnB0dFRqzGzbdy4UVLRvmnTptiwYQMsLCzyNeaHKDMzE+7u7khISFC7jbOzs9COjY1Fnz59VC6IkMlkKFGiBMzNzVX+LgFZod+ZM2dqvBhDW1FRURg8eLDKavPqzsGoqCi4uLgU2XXv+PHjGDdunPBdArLOUXWfU3BwMCZMmJDn2MnJyXB1dcWRI0dUvm5qaio5xrNnzzB06FBcvHhRw3fw4QgPDxfalStX1ug7+ffff2PDhg1qXzc3NxeeXgAACQkJ6N27N3bs2KFyH0NDQ5X3F9nz/P7773Hjxo085wYAfn5+GDt2rMqguZ6entrv1JUrV9C3b99cQ+2pqakYO3Ysli5dqnKhkaGhodqn6OzduxcDBw7Mc9FYeHg4hg8frnJBoZGREUqXLq3y+yeXy7Fp0ybMmTMn1/FnzJiBbdu2SfplMhlMTU1hbm4uWewGZAXnR44c+VGe60RERERERESkmvS/ABARERERERER0WdJXZjd0tISmzdvRqVKlQp8jISEBAwdOlRSVbV169YYOHAgbG1tFaGY2NhYHD9+HKtXrxaqdi5fvhyVKlWShH3ViYiIEAJ9zZs3R/369ZGSkoJr167h5s2bkrGWLVuG69evC31t2rTBgAED0LRpU5QqVUrRHxsbi7CwMGzYsEESblq0aBF++OEHlcH3Bw8eYMmSJUKfra0tfv75Z9jY2CgCSHK5HPfu3UNgYCA2btwoVK709fWFvb09jI2NNfosCsrQ0BDe3t7o16+fEML39PREUFAQSpYsWWjHksvlGD9+vCSYW6NGDfz8889o3749LC0tAWSF/s6cOYN169YJVfhDQkIwY8YM+Pr6Ftq8CsvChQsVf0tzc3N07NgRFhYWiIqKwunTp9G8eXNUqFBBsX1cXBymT58uVOctVaoUhgwZAgcHB1SvXh3FihUDkBVwi4yMxP79+7Ft2zbhnImJicGmTZvwyy+/vKd3qp0RI0bgxIkTuHXrlqLv0KFDcHR0zHeAWZ0jR45IgnbGxsbo27cvevToASsrK8hkMmRkZOD69evYu3cvtm/frqg2Gx8fj+HDh2PPnj0oV66cME7Pnj3RuHFjAFmhwX///VfxWocOHYRK6Nn7tmvXDsWLF1eEEp8+fYrbt2+jbt26at/DpUuXVAZ1z549m+f7//vvv4V2p06dJNvEx8dj8ODBksrJtWvXVnwPswOn8fHxCA4OxqpVq/DgwQPFtg8ePMCwYcOwY8cOYeFQbubNm6f454oVK6J169YwMzPDgwcPcObMGXTv3l3yVA1NrF+/XrKQpGXLlvDz81MbiP5YHTp0SPHbp6enhzZt2qB27dpISEjApUuXFAsVcvLy8pL8Pnfv3h3Ozs5o0KCB8PeLiopCSEgI1q1bJ1mw4OvrK3niQGGYOnUqXr9+DQCoWrUqhgwZgo4dOyqq6sfHx+PgwYPw8/MTKvjHxMQgICAAv/76a6HO5927d3B3d1csuLK1tYWLiwtatmwJU1NTyOVyPHr0CDt37sSGDRuEa/Hhw4cRHh4OW1tbteNPnjwZ165dE/qqVKmCkSNHwt7eHiVLloRcLsfdu3cRGBiITZs2IS0tDSkpKUVeKb+wXbhwQeV9lyZyXi8qVaqE1q1bw9TUFPfv30doaCi6d+8u3IelpKTgl19+wZ07d4RxKlWqhKFDh8Le3l5xTiUlJeGff/6Bv78/IiIiFNvGxcXBzc0Ne/bsUdyLqLJ//34sXrxY6NPX18f333+PXr16oVGjRihWrBjS09Px77//Ys2aNTh16pRi25iYGEyYMAHr16+HTCaTjD979mwcPHhQ6KtYsSKGDBkCe3t7xb3727dvcfbsWWzevFl4MseVK1fg7u4Of39/lYu30tPT4eHhIVRZr1q1KkaMGIHWrVsLv32xsbE4cuQI/Pz8hJD8n3/+id69e8PKykoy/pkzZySLCrp06YL+/fujYcOGivvb9PR03Lx5E9u2bUNgYKDiXigtLQ1z587Frl27VH4+RERERERERPRxYaCdiIiIiIiIiIgUYfZ9+/ZJXnv58iWePn1aKIH2SZMmCWE5AwMDzJgxQ2U4vXz58ujXrx++++47jB07FidPnlS8NmvWLHz11VcaVYzPDvSZmJhg2bJlaN26tfD6tWvX0LBhQ0X78ePH2LRpk7DN4MGDMXHiRJXjly9fHj179kT37t0xdepUBAYGKl5LSkpCSEiIyqDo9u3bhXBbp06d8Mcff0gCRTKZDLVr18aECRNgZ2cHNzc3RXguLi4Ohw4dwnfffZfn51BYbGxs4OrqKlRPjo2Nhbe3d64Vx7W1YcMGSeC2T58+mDJlCooXLy70m5qaokuXLujcuTNWrVqFRYsWKV7bu3cv7Ozs8O233xba3ApD9nnZpUsXzJ07V6gEm5SUJKmYumjRIkWQEwDKli2Lbdu2oWrVqpKxixcvjkaNGqFRo0bo1asXBgwYIFRWPXDgwAcbaDcwMICPjw+cnZ2FAJ2XlxdsbW0LrYJ2dHQ0Jk+eLPTVrFkTK1askFxXihUrpvg8v//+ewwdOhQvXrwAADx//lwRNsypZcuWaNmyJYCswGDOQHuDBg3Qt29fyZxKlCiBVq1aCU88+Oeff3INtKur4v7s2TPcuXMHderUUbtvzu+XTCaDvb29ZJs5c+bg4cOHQt+AAQPg4eEhqZhrYWGBXr16wcnJCbNnz8aff/6peO3u3buYPn065s+fr3Y+OWV/PwYMGIAJEyYI3/lnz56pfGJDXlSF2Tt27IglS5aofdrGxyz7M7S0tMTatWuFMKlcLseNGzdQpkwZRV9YWBhOnDghjDFjxgyV5yqQFazO/o0ePny4sPjo7t27uHXrFurVq1eYb0lxDezRowdmzZolWdRgYWGB/v37w97eHn379sWTJ08Ur+3Zs6fQA+0ZGRnIyMiATCbDlClTMGDAAOF1mUyG6tWrY/z48WjTpg2GDBkinLt79uxRG2g/evSopDK7g4MDFixYILxvmUyGOnXqYOLEiejRoweGDh2q8okTH7L4+Hh4eHgIfTKZTPJ5qpN9rru4uGDcuHHC9SIuLk5YCAZkLYzMeU0GgG7dusHb21tyTpmZmaFbt27o2rUrli9fjqVLlypee/bsGcaOHSu5Z8w5L+UnjFhYWGDVqlVo1KiR0K+vr49mzZqhWbNmWLJkCVasWKF47ezZszhx4oTkKR6HDh3C9u3bhb4uXbrA29tbsnjIyMhIsZhq586dmD59uuJcDA0Nxdq1ayVPSAGyfidiYmIU7WrVqmHnzp3Cws5s5cuXx8CBA2Fvb4/evXsrzsPMzEy1ldo3b94stAcNGiQ5F7I/n4YNG6Jhw4Zo3Lgxpk2bpngtIiICFy9eRLNmzST7EREREREREdHHRfWzZ4mIiIiIiIiI6LORmZkJDw8PlWF2IKsq4rhx45CYmFig4/z7779CKB0Apk+fnmeldWNjYyxduhTNmzdX9L19+xZr1qzR6vhz5syRhNkBCGF2IKuaZs6ged26dTFu3Lg8xy9WrBimTJkiqfJ78+ZNldsrh6l++eUXldUxc2rTpo0kvH7mzJk851bYRo8ejerVqwt9gYGBQhC3IN68eQM/Pz+hr0ePHvDy8pKE2XOSyWQYNmwYhg0bJvQvX75cqCj/oahbty4WLFgghNmBrABdtWrVFO13797h8OHDwjZTpkxRGWZXZm1tjYEDBwp9d+7cEcLiHxpra2tJsC4+Pl4SDCyI1atXCyF/S0tLrFu3Ls9FMvXr18e6deuE8zAsLAwXLlwolHkpBxZDQkJy3T5noF35PAoNDVW73927d/H48WNFu0mTJoqKxNkiIyMllX9//PFHTJ06VRJmz8nAwABeXl6S6t9BQUG4ffu2+jejpF27dpg6darkO29paSk8vUATAQEBkjB7165dsXTp0k8yzJ6Tn5+fpDKyTCZD/fr1hb69e/cK7Y4dO6oNs+dkbGwshEuzqfvtK6imTZuqDB7nVLFiRUyYMEHoi46OlizOKCxDhgzJM3zdqlUrODs7C33qFqQAEILTQNZ3dMmSJbm+7y+//BIBAQEfzTmdkZGBo0ePolevXpIq/7169cp1QY6yjh07YvLkyZLrRbly5YRrW1xcnCRE3aFDByxcuDDXz1Ymk+HXX3+V3F+Eh4cLFc9zWrduHV69eqVo6+vrqwyzK/vtt9/QqlUroU85NJ+ZmSmp/G5nZ4eFCxfm+SQMZ2dnTJ06Vehbu3atyqd9KN+r/vTTTyrD7DlVrlwZ7u7uQp/y03ayXblyRWgPHz4817EBoHfv3pKFILn93hERERERERHRx4OBdiIiIiIiIiKiz9ykSZPw119/CX3KoZ6YmBhJ+EVbOSt6A4Ctra0k3KWOvr4+pkyZIvTt27cPz58/12j/6tWro2vXrhptqxxMHThwIIoVK6bRvqampmjQoIHQl105VJnyAoGcIfrcfPvtt+jQoQMGDBiAyZMn48cff9Rov8JkaGgIbwKfqZkAACAASURBVG9vSQDf09NTCG/l1+7du4XPzdzcXKvzb+TIkShbtqyi/ejRI8liig/Bzz//DAMDgzy3u3z5snB+VKpUCY6OjhofRzkYl5mZWSh/p6I0YsQISXXnQ4cOSYL9+REfHy8J77q7u2sckq5Xrx769Okj9Clf3/LL3t5e+F5dvHhRZcgQyKoOHxkZqWj3799feF1dgBCA5Pug6ikSGzZsEBaClC9fXlLVPjeenp6wtLRUtOVyOfz9/TXev7CeIrB27Vr4+voKfd9//z0WLlyo0ffvY9amTRvJoi1V5HI5Ll68KPQNHjxY4+PUrFlT8v1R99tXUMOHD891QUU2BwcHyXY5nxBTWIyMjPDzzz9rtK3ydTsuLk7lb/+lS5ckiz/mzJmj0fuuW7euTp7AkZycjG3btuX5P39/fyxatAgjR45Eu3btMGrUKDx9+lQYq2bNmlrfcyoHzdXZtm0b3r59q2ibmJhg7ty5kMlkGu0/atQoyVMz1q5dK9kuMzMTe/bsEfr69euXZ5g928iRI4X2xYsXhUVYJ0+eFBZoGBgYYObMmRqdI0BWMD3n+0hMTBSeMJSzPydN71UdHBxgZ2eH3r17w93dHRMmTFC5sFD5XkTTxXa9e/eGg4MDBg8ejGnTpuHrr7/WaD8iIiIiIiIi+rBp9l82iIiIiIiIiIjok6Uc7GzatCnmz5+Pn376CbGxsYr+o0ePYsuWLejXr5/Wx0hNTZVU71YOX+blyy+/RN26dRUhr7S0NISFhaF79+557tuiRQuNw0rr1q3D69evERUVhejoaLRo0UKreeYMUgNZ1bVVqVSpEu7fv69oL1q0CGvWrMm1QigANG/eXKhWrys2NjZwdXUVgryxsbHw9vaWVELW1rFjx4S2k5NTnhVBcypevDi6du0qVDQNDg6WVL/WNTs7O422a9myJa5evYqnT58iOjoaxYoVy7Oaf05lypSR9KWmpmq8vy4YGBjAx8cHzs7OQsDNy8sLtra2sLCwyPfYISEhwvfS3NwcTk5OWo3Rs2dPbNy4UdEODQ1Fenq6xmFCdcqUKYPGjRvj8uXLALKuc2fPnlUZ1jt9+jTkcrmi7eTkhMOHDytCjufPn1c7J00C7cpPf+jduzeMjY01fi8lSpRAnz59hErTwcHBkMvleV6PTUxM0KRJE42Ppc7q1auxYMECoW/AgAGYMmWKxr8JHzNNrzEymQzHjx9HYmIioqKiEBMTg2bNmml1rDJlygjB5KK4xhgZGaFNmzYabVu8eHFUrlwZjx49UvQlJSUV+pyaNWuG0qVLa7RtzZo1JX3JycmS/ZV/A1u0aIHatWtrPKe+ffvCz89P4/BxYYiPj8eMGTMKPE6tWrWwZs2aPKuM51SiRAmNg+LKVfG7d++u8jdSHX19fbi4uAiLLC9cuIDk5GThKRk3btwQ7qEBaPTEg2zNmjXDDz/8gHLlyqF69eqoXr26UH1e+Rxp3749qlSpovH4QNaTb+bPn69oBwcHS+7NK1asKLQ3bdqErl274osvvsh1bDMzM6xbty7POVSoUEGozu/r6wsfH58873GcnJy0/t0mIiIiIiIiog8fK7QTEREREREREZFC8+bN4e/vjy+++AI+Pj6SwJ+vry9u3bql9bgRERFCRUwAaN26tdbjfPXVV0JbuaKsOk2bNtXqOCVKlICVlRUcHBxgZmam8X4pKSmSwJyqipQAJKG88PBwdOvWDevXrxcCeB+y0aNHo3r16kJfYGCgZPGCNtLT03HlyhWhT9NQZk42NjZCW9Nz5X2pXLmyUL06L3p6eqhUqRJsbW0l34O8xMXFSfoyMjK0GkMXrK2t4ebmJvTFx8dj5syZBRpX+Vxo3ry51pW6ra2tYWJiomi/efMGN27cKNC8sikvvPjnn39Ubpez39LSEnXq1BHO++TkZFy7dk2yX3x8vPAdq1evHqpWrSpsc+/ePUkYMz8LQpSD8i9fvpRUnlalQYMGBV4csGrVKkmY3c3NDVOnTv0swuwAtF4UUKpUKTRo0ABdunTRatFMYmKiZPFWUVxjvvzyS42fmAIAJUuWFNpFEfCuX7++xtsqzwdQPafw8HChrWmIP5uFhYVGlfk/JObm5hg1ahQCAwNRuXJlrfZt3LixRufrq1evcP36daHP3t5eq2MB0mthenq65Hfl0qVLQrty5cqoUaOGxseQyWSYM2cOfvvtN3z77bdo3LixEGhXfppQfu6TlO8lLl++LLlnbdu2rdCOjY3Ft99+i/nz5+Pq1atq73E1pXxu//XXX+jZsyd27Ngh+Q0iIiIiIiIiok8fK7QTERERERERERGArCrQK1euVFTgtbOzw4ABA4QqxO/evcOYMWOwe/durSr1RkRECG1jY2Ps379f6zk+f/5caGsSjASyqqEXtsTERDx69Aj37t3D7du3cfXqVVy9elVSlTZnBeWcnJ2dsXbtWuE9xcTEKCqcf/HFF7Czs4OdnR1atmypcQXY98nQ0BDe3t7o16+fEGry9PREUFCQyvBeXu7evYs3b94IfdeuXVMZys5NTEyM0L5//36hVNAuLNoG9jSRnp6OJ0+e4P79+7h79y6uX7+Of//9V/JZAOrPyw/NiBEjcOLECWEhzaFDh+Do6AhHR8d8jal8PUpOTsa2bdu0HqdEiRJISUlRtG/duqVxleDcdOrUCb///ruiHRISItlGLpcjNDRU0c4OM3711VcIDAxU9IeGhkoW9Jw6dUr4vnbu3Fky/oMHD4S2sbGxVhWis9WpUwcmJibC53T//n3Uq1cv1/0K+v0ICAjAqVOnJP2GhoYFGvdjUxTXmRcvXuDRo0e4e/cuIiMjcfXqVdy4cUMSYC+Ka4zyE1DyorxQpaDhW1W0mZOqhTOqPqecT28BshbQaKtBgwaSUPWHwMDAAMbGxrCwsECVKlVQr149tGjRAq1atdJ6YVE2Te/xHj16JDlP8xP8Nzc3R7Vq1YTFhw8ePED79u0VbeW/oTYLH/KSkJCA6Ohooe/evXta/44pL8BMSkrCkydPhOtGo0aNYGdnJ/zeJCcnY82aNVizZg3Mzc3RsmVLtG7dGnZ2dnlWblfm6uqKPXv2CIteb926BU9PTwBZvyGtWrWCnZ0dbG1ttarcT0REREREREQfnw/j/70hIiIiIiIiIiKdatOmDZYvXw4jIyOhf9y4cQgLC8OdO3cUfffu3cOsWbMwd+5cjcd/+fKl0H7z5g1mzJhRoDkDWaEeTZQqVSrfx0hNTUVYWBiuXLmCu3fv4vHjx4iOjpYEgbRlamqKlStXwsXFBa9fv5a8Hh0djR07dmDHjh3Q09NDgwYN0L59e3Tq1CnPMOj7ZGNjA1dXVwQEBCj6YmNjFcF8bSmfKwDg5+dXoDkCWaHBxMRElClTpsBjFYaCnJNAVjAvNDQUN2/exMOHDxEdHY2nT59+FJXXtWFgYAAfHx84OzsjPT1d0e/l5QVbW1tYWFhoPabyORYWFoawsLACz1XT61FeqlWrhtq1a+Pu3bsAsq4FDx48EKr7Xr9+HfHx8Yp2dqC9VatWwlhnz57FyJEjhb6TJ08KbVWV15U/o/Lly2tVGTubnp4eLC0theCnqu+4soJ+P1SF2YGsa0mHDh3QoEGDAo3/sSjI55icnIwzZ87g2rVruHfvHqKiohAdHS1ZcPQ+mZqaFmj/ogjZF/acXr58KSwAAZCv3y1tngBSGKpWrYpjx46912Nm0/Q8V75GGxkZ5es3BMi6JuZ2XVOuLl6Yfw9V19AtW7YUytgJCQmShTALFy7ETz/9JAnpZ29/+PBhHD58GABQvXp1tGvXDg4ODmjWrFmevxvVq1fHggUL8Ntvvwm/8dnu3LmDO3fuYOPGjTAwMEDTpk3RsWNHdOrUCVWqVCnAOyUiIiIiIiKiD5Hmz4wkIiIiIiIiIqJPUocOHeDn5ycJswNZ1Wznz58vqZq5e/duHDhwQONjJCYmFnieBRk3PxUdX758CW9vb7Ru3Rpubm5Yvnw5jhw5gps3b+YaZi9evLjGx2jYsCH279+PDh065LpdZmYmrl69iqVLl6JHjx7o3r17vircF5XRo0ejevXqQl9gYCCCg4O1HquozhWg8ALHhSG/VUaDg4PRu3dvdO7cGTNmzMD27dtx7tw5xMTEqA2za3NOfoisra3h5uYm9MXHx8PLyytf4+n6eqQJ5ZD5P//8I7RPnz4ttLMD7ZUrVxa+i5cvXxYCyKmpqThz5oyiXbVqVVhZWUmOr/xdKUhoV/lJDa9evcpzn8KqwiuTyYS5p6enY+LEiXj37l2hjP8hK1asmFZPUskWExODSZMmoXXr1vjf//6HNWvW4OTJk7hz547aMLtMJst3dW1t5GdRRVEr7Dkph9mB/H0fzMzMCmM6HwVNPx/l61pBPiPlEL3y9V/571jQhQ+5HaswqRq7dOnS2LVrFwYOHJjn9/zhw4fYuHEjBg4ciPbt28PPzy/P662DgwN2796Nxo0b57pdWloawsPD4evrCwcHB/Tp00f4PSMiIiIiIiKijx8D7UREREREREREn7mlS5fmGni1srLCb7/9JumfNm0aoqKiNDpGWlpavueXG01DiTKZTKtxL1y4AEdHR6xfvz7P8GXFihXRqVMnTJo0CYcPH0aXLl20OlblypWxatUqHDhwAMOGDUOdOnXy3Of27dsYN24cBg0apNNqudkMDQ3h7e0NPT3xPzd6enpqFF7NqajOFSArzPuh0PacTE1Nxfjx4+Hm5oZ///03122NjIzQqFEjDBw4EH5+fti9e3dBpvpBGDFihOTJBDmrwmpD19cjTdjb2wvt3ALtdevWRbly5RTt1q1bK/45LS0NFy5cULTDwsKEoGWnTp1UHr8wK1krL7RQvk6oou33Q5VixYphzpw58PX1Ffrv3r2LRYsWFXj8T9HBgwfRtWtXBAYG4u3bt2q3k8lkqFatGpycnDBz5kycOnUK1tbW73Gmny5VgeHc/hbqfEi/d0VN0+tFZmZmoR1TuZr4+1xsUZT3Sep+x0qUKIEpU6bg1KlTmDRpkkbV1589e4bFixejW7duef77gpWVleKpRAMHDsQXX3yR51wvX76MwYMHY9KkSYX6tyUiIiIiIiIi3dHX9QSIiIiIiIiIiEi3NKnePGTIEISEhCA8PFzRl5ycjDFjxmDbtm15VmxUrtDbunVrBAQE5G/CRSwyMhKDBg2ShMFMTExgY2ODL7/8ErVq1UKNGjVQo0YNSZXO/AZBa9eujTFjxmDMmDH477//cObMGZw9exbnzp3Ds2fPVO4TGhqKsWPHws/PL1/HLEw2NjZwdXUV/q6xsbHw9vaGt7e3xuMonysGBga4du1aoQRcC5tyoK0oeXh4qHwqQq1atdC4cWPUrl0bNWvWRI0aNVClShUhaPbgwYP3Ns+iYmBgAB8fHzg7Owufu5eXF2xtbWFhYaHxWCVLlsSLFy8U7fnz56N79+6FOt+CatSoESpUqICnT58CAMLDw/Hu3TsYGhoiOTlZWNSQXZ09Z3vLli2KdmhoKNq2bQsA+Pvvv4Vt1QXala9rycnJ+X4vyk+0MDExyfdYmjIwMMCCBQsUC4ycnJwQFBSkeH3Dhg2wt7dH8+bNi3wuH4u///4bY8eOlfyGmZubw8bGBlZWVoprTI0aNSRVsRkoLRzm5uaSvvx8/3J7ksznSvmzLchnpPw3UX4aQmFeQ5Up3ycBWdf5MmXKFNox1ClbtixcXV3h6uqKV69eISwsDGFhYTh37hzu37+vcp/o6Gi4uLhg3759eVaqb9y4MRo3bowpU6bg3r17CA0Nxblz5xAeHq62Mn1gYCBKlSoFDw+PAr8/IiIiIiIiItItBtqJiIiIiIiIiChPenp68PX1RY8ePYQA0LVr17Bw4UJMnDgx1/2VQ0QxMTFFMs/CMHHiRCHMbmRkhAkTJsDZ2Vmj8H9hVEyvVKkSnJ2d4ezsDCCronBwcDAOHDiA69evC9uePHkSFy5cQLNmzQp83IIaPXo0Tp48iYcPHyr6AgMD4ejoCCMjI43GKF26tNBOS0tDXFwcypcvX5hTVUubUOb7qo5/7NgxSZjd1tYW06dPR+3atfPcPz/VfT9E1tbWcHNzw4oVKxR98fHx8PLywpIlSzQex9zcXAi0f6jXo6+//hpbt24FkPU3DA8PR9u2bXH+/HmhQq9yoL1ly5bQ19dXBP/DwsIUr+UMtJcrVw5NmjRReWzla3ZsbCwyMjK0rkKcnp6OuLg4oe99fJdnzZolPC1j6tSpCAsLU/zdMzMz4eHhgX379kmC2Z+jN2/eYMqUKUKYvXTp0vD09ISjo6NGf/dP5Tqja8WLF0eZMmWEa9TDhw9hY2Oj1Tg5f4cpi/J17e3bt4iPj9dqQVS2//77T2grX9eUA+3Pnz/X+hjqqFr0EBMT814C7TmVLFkSXbp0UVxrY2NjERISgqNHj+L06dPC/VRMTAy2bNmCX375RePxa9WqhVq1amHAgAHIzMzE9evXcerUKQQFBUnO782bN2PgwIGoVKlSobw3IiIiIiIiItKNvJ/tSUREREREREREhKyQtaenp6R/3bp1CA4OznXfWrVqCe1Hjx4hPj6+UOdXGM6fP4/IyEihb86cOejXr59GYXYAiorK2fJbsT2n2rVrY8iQIQgMDMSCBQsk4cLDhw8X+BiFwdDQEN7e3tDTE/+zo6enp8aVUGvUqCHZP2c16sKmXPlduTJ/bmJjYwt7Oipt2rRJaNerVw9r167VKMwOAE+ePJH0FcZ5qQsjRoxAvXr1hL7Dhw9r9R1Qvh4V5flVEA4ODkL7n3/+AQCcPXtW0WdgYCCpMm5qaopGjRop2pGRkYiPj0dERIRwfXJwcFD75IM6deoI7Tdv3uDOnTtav4fbt2/j3bt3Ql+VKlW0HkdbyqHG0qVLY9q0aUJfdHQ0fHx8inwuH4MDBw4IAWqZTIZVq1bhm2++0XgRQ1H89n2ulBeaXLt2Tesx8rPPp65WrVqS8zk/n1N8fLxkIVTVqlUlx8rp5s2bWh/Hz88PQ4cOhZeXFwICAhQLGi0tLSWB+cuXL2s9fmErX748nJ2dsWbNGuzevVsSsC/Ivaqenh4aNmyIUaNG4dChQ3B3dxdeT0tLw/Hjx/M9PhERERERERF9GBhoJyIiIiIiIiIijX377bfo1q2b0CeXy+Hh4SGpwptTs2bNhJCyXC7HyZMntT7+kiVLMHz4cMyePRvr168XKg8XhvDwcKFdvnx5fPPNNxrv//r1a9y+fVvoU1Xx++HDh9i9ezfmz5+PkSNH4o8//tD4GE5OTnB0dBT6oqKiNN6/qNnY2MDV1VXoi42NxYIFCzTa38zMDFZWVkLfiRMntJ7HsWPHMGTIEEybNg2rVq1CUFCQyr+F8kKFV69eaXyM/ATUtJWZmYlLly4Jff3794ehoaHGY6gKbH+sYVMDAwP4+PhAX198+KiXlxdev36t0RjKAfBz584hOTlZq3mkpKTAxcUF7u7uWLRoEXbs2IHo6GitxsiLra0tSpYsqWhnB9pzXveaNm0KExMTyb6tW7dW/LNcLsfZs2cl36NOnTqpPXbNmjVRtmxZoS8/YcFjx44JbVNTU0lY/n1xdHQUqrYDwI4dO/JckPU5OH/+vNBu1qwZGjdurPH+d+/elSxa+livMR+Cli1bCu2jR48qnrigiYiICFZoV8HU1FRyf1EY1zU9PT1hEREASUX9qKgorX8jjh8/jpCQEGzduhW+vr6KQLuenp5k/PzcJ128eBGurq6YMmUKli9fjr179wpPnnn58iUOHDiAZcuWwd3dHaNGjdJ4bGtra4wcOVLoU75XvXnzJrZv3w4fHx/88ssv2LFjh0Zj6+npwc3NDQ0aNMh1fCIiIiIiIiL6+DDQTkREREREREREWpkxYwbKly8v9MXHx2PChAkqA8MAULJkSUk4zt/fHxkZGRofNzY2FgEBATh58iQ2bdoEb2/vQg8iKlfcrlixotoKxqps3boVaWlpQp+qEFp4eDgmT56MNWvW4Pjx49i3b59W4b+KFSvmeQxdGj16NKpXry703b9/X+P927VrJ7QPHjyoVRAsMzMTK1aswOnTp7F9+3YsXLgQAQEBksrvACRVTh8/fqzxcZRDbUXhxYsXknNK+e+fm1evXmHPnj2SfuUxPybW1tZwc3MT+uLj45GQkKDR/m3bthW+1ykpKdi8ebNWc9ixYwfOnj2LoKAgrFy5Ep6enmoD9dpcQ3IyMDAQvgv3799HRESEsGjGzs5O5b5t2rQR2mFhYcIiInNzc9ja2uZ6/LZt2wrtHTt2CGHHvKSkpGDXrl1CX+vWrTWu+F0Upk+fDnNzc6FvypQpGp87nypVv33a2LBhg6TvY77G6FqPHj1gZGSkaD9//hy7d+/WeH8/P7+imNYnQfm6FhQUJDydIC8ZGRnYsmWL0NewYUOULl1a6LO2toaFhYWiLZfLtfobPn78GBEREUJfzmu28n3SuXPncOXKFY3HB4DVq1cjLCwMu3btwh9//IH58+cLi+Xi4+MxduxYLF26FEFBQTh27JjKJ76oo3wdUb7nDwoKwrRp07Bu3TqcOnUKhw4d0mr+yk/i0ObfKYiIiIiIiIjow8RAOxERERERERERaaVUqVLw9fWVhDTDwsKwatUqtfsNHjxYaN+/fx+LFi3S+Lhz5szB27dvFW2ZTIZevXppvL8mSpQoIbQfPHiA1NRUjfa9efMmlixZIul/9+6dpK9Vq1bC5xcVFaVVkOfixYtCu1atWhrv+z4YGhrC29tbZYBcE/369RMqp6elpWHChAkaB/e3bt2KGzduCH3fffedym2rVKkitP/66y+NFhfs3LlTUS21KCmfkwBw69YtjfefNm2ayqcnaHpef6hGjBiBevXq5WvfGjVqoEOHDkKfn5+fxhX3nzx5ghUrVgh99evXVzsfAwMDoa3NAhQHBwehvWDBAuH8zFmJPaeGDRsK1d2PHj2KyMhIRbtjx46SKvfKVD1pYe7cuZpOHd7e3pJzr2/fvhrvXxTKlCkDT09Poe/Zs2fw8vLS0Yw+DMpV/rW5xpw4cUJlZeWP/RqjS+bm5ujZs6fQ5+vrq9E1asOGDfmqOv65UL6/SElJweTJkzVeVOjn5yf5fqi6runr6+Onn34S+gICAjSunK98f/zVV18JCwV79eolCdF7eHho/KSS48eP49SpU0Jfz549hfu2WrVqoUKFCoq2XC7H2rVrNRofkN6r1qxZU2gr/36FhYXh2rVrGo2dlpYmCfB/aPfCRERERERERKQ9BtqJiIiIiIiIiEhrrVq1wsCBAyX9y5YtkwRYsjk4OMDa2lroW7NmDRYvXpxrkEgul2PevHk4cuSI0N+tW7d8B1rV+fLLL4V2YmIili1blud+R48excCBA1VWpFVV0bhKlSqSII+Xl5ekGqcqGzZswOXLl4W+bt265bnf+2ZjYyMJxGqqXLly6NOnj9B38eJFDB8+HMnJybnue/ToUfj4+Ah9lStXxo8//qhye+VK1o8ePVK5MCGnoKAgzJkzJ9dtCouJiQmqVasm9AUEBORZJTUxMREjRoxQu1AiJSWl0OaoCwYGBvDx8ckzlK3OyJEjhX3fvn2LIUOGqL1+ZYuLi4ObmxsSExOF/jFjxqjdR3lRgjbVgNu1ayeEL0NDQxX/XKpUKTRo0EDlfsWKFUPLli0VbeUK5MpBeVWsrKzQuXNnoW/Hjh2YM2dOrqH89PR0zJkzRxJybtOmDVq1apXncYuak5MT7O3thb6DBw/i4MGDOpqR7in/Nt+6dUtSXV+VTZs2YfTo0Spf+9ivMbo2ZswYlClTRtF+/fo1BgwYgH379qnc/vXr1/D29tZq0cnnqFy5cujdu7fQd+rUKbi7u6tcgJhNLpdj9erVWLp0qdBvZWWF7t27q9ynX79+wlNgsn9nHj16lOscV65cKbkeKT+VxNjYGEOHDhX67t+/j0GDBuHZs2e5jn/+/HlMnDhR6DMzM8PPP/8s2Vb5s9q6davKp74ou3jxIjZu3Cj0Kd+rtmrVSgjpy+VyjBkzBjExMXmO7+PjIzxZwsDAAJ06dcpzPyIiIiIiIiL6sDHQTkRERERERERE+eLu7o66desKfenp6Rg3bpwk7AkAenp6WLJkCczMzIR+Pz8/9OzZE3/99Rfi4+MV/cnJyTh27Bj69OkDf39/YZ9y5cph0qRJhfhusnTs2FGoagwAq1atgru7O65evaoIcWZkZCA2NhZ79+6Fi4sLRo0ahVevXqkc8+XLlyr7R48eLQRqExIS0KdPH8ydOxcRERFCOP7t27cIDw/H6NGjJWG1jh07okmTJvl6v0Vt9OjRQlhJG+PHj0f9+vWFvpCQEHTu3Bn+/v54/Pixoj8tLQ0XL16Eu7s7/ve//wmfXbFixTB37lwhFJyTvb09zM3NhT4/Pz/89ttvuHr1qqLKcHJyMoKDgzFs2DC4u7vjzZs3kMlkKFu2bL7enzZ69OghtF+8eAFnZ2fs3LlT8p2JiIiAj48PHB0dceLECbVjqjsvPybW1taSkJ+mGjZsiLFjxwp9L168QP/+/eHh4YHz588L51F0dDRWr16N7t274/bt28J+3333Hdq2bav2WOXKlRPahw8fxqVLlxTt3MLhJUqUUBsCb9myZa5PQbCzs1PZb2JiIlnIoc7s2bPxxRdfCH0bN25Ez549sXfvXuE8evnyJfbu3YuePXtKgoyWlpbvbRGIJry8vISgaXafqqcZfA6++eYbFCtWTOjz9PTE7NmzcefOHcWis7S0NERHR2PLli347rvvMHv2bLWV2D+Fa4wumZubY86cOcJ9QlJSEsaPH48uXbpg7ty5WL9+PVavXo2JEyeiY8eOWL9+vWJb5b+n8lN1PmcTJkyQ3F8cOHAAXbt2xbZt24SgdHJyMo4cOYI+ffpgwYIFwj6mpqb4/fffbBQd5QAAIABJREFU1S6ssrCwgLe3t9AXHR2Nb7/9FosWLcK9e/cU363U1FSEhYVhyJAhkursTk5OkqeKAFlPPmrXrp3Qd+XKFXTt2hVLly4VvrsZGRmIiIjAjBkz4OLiIlkcOH36dMm9EAD0798f5cuXV7QzMzPh4eGBUaNGITQ0VKgIn56ejsjISMybNw+urq7CtaFixYqSSvYymUyyGCwqKgo9evTAsmXLcPfuXWRmZipey74Pc3FxwebNm4X9+vXrJ/mtJSIiIiIiIqKPT/7K1xARERERERER0WfP0NAQv//+O3744Qch+Pnff/9h6tSpkiqWAFC1alUsX74co0aNEkLvkZGRmDBhAoCssKWBgQFevXqlsnK7ubk5li9fDktLy0J/T2ZmZnB3d8f06dOF/qCgIAQFBcHAwAAlSpRAcnKyyhBq5cqVMXLkSEyePFnR9+DBA6SmpkoC1Q0bNsSYMWPw+++/K/rS0tKwYcMGbNiwAcWKFYOZmRkyMjKQnJys8rOoVq3aB12N1dDQEN7e3ujXr58QStJE8eLFsWLFCgwdOlQIEL948QLz5s3DvHnz8vx76OnpwcvLS6hUrczU1BRjxoyR/M0PHz6Mw4cPQ09PDyYmJiorw3t4eCA8PDzX4HhhGDx4MP766y8hxP/s2TNMnToVU6dOhampKQCorV7v6uqKhw8f4tSpU4q+W7duaVSl+0M3YsQInDhxArdu3dJ63yFDhiAuLk4IgWZmZmLPnj3Ys2cPZDIZSpUqhXfv3ql80gKQVXV8xowZuR5HOTiZlJSEvn37wtTUFDKZDOXKlcu1OriDgwOCg4Ml/eoC6znnpkrbtm1hZGSU677ZSpUqhZUrV8LNzQ3//fefov/OnTuKCr8mJiYA1FfkLl++PNasWYMKFSpodMz3wdLSEpMnTxaqFCckJGDq1KlYvXq1DmemGzVq1ICLiwsCAgIUfZmZmdi0aRM2bdqE4sWLw8TEBK9evVJ5La9fvz6cnJzg6+ur6MvPd5JEHTt2xLx58zB+/HhkZGQo+h8+fIiHDx+q3c/FxQU3b95EeHi4os/AwKAop/pRUXd/ERMTgxkzZmDGjBkwMjKCvr6+2t/VkiVLYsWKFZKFncrs7e0xceJEzJs3T3Ef9+bNG6xcuRIrV65U3MckJSUJf+NszZs3x+zZs1WOLZPJMH/+fIwYMQIXLlxQ9CclJWHZsmVYtmwZ9PX1YWpqitevX6t8ihAAjBo1Sm2V+ZIlS2LevHlwc3MTKtgfPXoUR48ehUwmg6mpKYoVK6b2XszExASLFy9W/Fbk5OjoiN69e2P79u2KvuTkZCxduhRLly5VfD5paWlCeD4nGxsbuLu7q3yNiIiIiIiIiD4urNBORERERERERET5ZmVlhdGjR0v6jx49ii1btqjcp0WLFtixYwesra1Vvp6SkoLExESVAe769etj27ZtaNSoUcEmnos+ffrg119/VVnNNC0tDQkJCZLAjp6eHpydnfHXX3+hR48eQlg0u7q6Kj///DOmTJkCQ0NDyWsZGRlISEhAUlKSys+iVatW2Lp1KywsLLR9i++VjY0NXF1d87VvhQoV8Oeff6Jbt24qX1f39wCyAqsrVqyAs7Nznsfp06cPxo0bJ6loC2SFOpUDbUZGRvD09Mz3+9KWiYkJ/P39UbVqVZWvJycnqwzdVa5cGWvWrMGkSZPQuHFj4bV//vmnSOb6vhkYGMDHx0dthdy8TJo0CbNnz1YsCshJLpcjISFBZZhdT08PAwYMwMqVK1V+f3Nq3ry5yirrycnJSEpKwoMHD9SGwYGsQKSqSuytW7fO9bhVqlRBlSpVJP2dOnXKdT9lderUwe7du9UeLyUlRe38v/76a+zatQv16tXT6pjvQ8+ePdG+fXuhLzg4GDt37tTRjHRr/Pjx6NWrl8rXUlNTkZCQIAmzGxgYYNiwYfjzzz/RuXNn4bWHDx8iKiqqyOb7ufjmm2+wbds2tfdMOZUsWRJeXl6YPHmy5G+V13Xqc5N9f/HNN9+ofP3t27dqw+zNmjXDzp070bx5c42ONXjwYCxZskRlBfTs+xhVYfbvvvsOq1evhrGxsdqxS5UqhXXr1uGnn35S+TuRnp6OhIQElWF2MzMz+Pj44Ndff811/i1btsSqVatULiSVy+VISkpSey9WrVo1bNy4MdcnCXl5eWHw4MEq55/9+agLszs5OcHf31/tU3iIiIiIiIiI6OPCQDsRERERERERERXI4MGDYWtrK+n39fVFZGSkyn2qV6+OwMBA/PHHH2jWrFmeYdQmTZrA29sbu3btQs2aNQtl3rkZNWoU1q9fjxYtWuS6nbm5OXr16oU9e/Zg9uzZMDMzg8H/sXfvcVbXdf7A32fuMMMd5DZoIArIZTDW0uRX0aqkgmkYopV7sd2y7GLb/rbdUql9ZNpF+6mV1W6LupkJ3gIVL2ulFhQmDJfiaioyMCDDbRhgbuf3hz/mx/HAMMAM3xnm+fzre97ne76fF6jj54/X+Ux+flZh9L777jvkM66++up4/PHH48orrzxo2elARUVFMWnSpPj+978fs2bNir59+7b8D5WgL3zhCzF06NCj+mxxcXHcfvvt8dBDD8XkyZOjuLi42ftLS0vj85//fMyfPz8mTZrU4nX+4R/+IR577LG44IILDln8KywsjAsvvDAeeeSR+NjHPnZEf45jdfLJJ8ejjz4an/zkJ6NXr16HvC8nJyfGjBkTN954Y8yfPz/e+973RkRkfSlg8eLFsWzZsjbNfLycccYZ8clPfvKoP/+Rj3wknnvuufj0pz8dpaWlzd7bpUuX+NCHPhQPPfRQfPWrX23RqcepVCruvPPOuPDCCw/6fmNj4yF/VkZE9OnTJ6sMWFpaetCy+tu9vYSen59/RP9d7Ne7d+/46U9/GrNmzYqJEyc2Wx4sLCyM8847L+6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      "text/plain": [
       "<Figure size 3632x1362 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.dpi'] = 227\n",
    "plt.rcParams['figure.figsize'] = (16, 6)\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "plt.plot(history_keras.history['loss'])\n",
    "plt.title('Keras Neural Network Training Process', fontSize=15)\n",
    "plt.xlabel('Epoch', fontSize=12)\n",
    "plt.ylabel('MSE', fontSize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_keras = keras_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.028092162461256922"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_keras = mean_squared_error(y_test, keras_model.predict(X_test))\n",
    "mse_keras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Comparing Our Neural Network with Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE Simple: 0.028\n",
      "MSE Keras:  0.028\n"
     ]
    }
   ],
   "source": [
    "print(\"MSE Simple:\", round(mse, 3))\n",
    "print(\"MSE Keras: \", round(mse_keras, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared Simple: 0.497\n",
      "R-squared Keras:  0.502\n"
     ]
    }
   ],
   "source": [
    "print(\"R-squared Simple:\", round(r2_score(y_test, y_pred), 3))\n",
    "print(\"R-squared Keras: \", round(r2_score(y_test, y_pred_keras), 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple neural network has the same capabilities as the Keras analog, and was able to produce identical accuracy. That means it's working correctly and is efficient enough."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Next Steps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are plenty of things we can do with our neural network, such as:\n",
    "- Rewrite feedforward and backpropagation to the matrix form\n",
    "- Make adding more than one layers and as many neurons as we want possible\n",
    "- Add different activation functions, like Tanh or ReLu\n",
    "- Add different cost function, like a binary cross-entropy for classification problems"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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