{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "z_iVa-x-Cq3c"
   },
   "source": [
    "**Chapter 4 – Training Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MbUGgHOwCq3e"
   },
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wS11Ecy4Cq3f"
   },
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a href=\"https://colab.research.google.com/github/ageron/handson-ml3/blob/main/04_training_linear_models.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://kaggle.com/kernels/welcome?src=https://github.com/ageron/handson-ml3/blob/main/04_training_linear_models.ipynb\"><img src=\"https://kaggle.com/static/images/open-in-kaggle.svg\" /></a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EF5ZcE2jCq3g",
    "tags": []
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8F4rq_OhCq3h"
   },
   "source": [
    "This project requires Python 3.7 or above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "a8z1HHrCCq3h"
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "assert sys.version_info >= (3, 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "207hOiW8Cq3i"
   },
   "source": [
    "It also requires Scikit-Learn ≥ 1.0.1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "CKv0XGh5Cq3j"
   },
   "outputs": [],
   "source": [
    "from packaging import version\n",
    "import sklearn\n",
    "\n",
    "assert version.parse(sklearn.__version__) >= version.parse(\"1.0.1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BFdnXKZBCq3k"
   },
   "source": [
    "As we did in previous chapters, let's define the default font sizes to make the figures prettier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "JywecD8xCq3l"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rc('font', size=14)\n",
    "plt.rc('axes', labelsize=14, titlesize=14)\n",
    "plt.rc('legend', fontsize=14)\n",
    "plt.rc('xtick', labelsize=10)\n",
    "plt.rc('ytick', labelsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cXGM6SBeCq3m"
   },
   "source": [
    "And let's create the `images/training_linear_models` folder (if it doesn't already exist), and define the `save_fig()` function which is used through this notebook to save the figures in high-res for the book:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "B1xNG81jCq3n"
   },
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "\n",
    "IMAGES_PATH = Path() / \"images\" / \"training_linear_models\"\n",
    "IMAGES_PATH.mkdir(parents=True, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = IMAGES_PATH / f\"{fig_id}.{fig_extension}\"\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GHD8wOYoCq3o"
   },
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FE3dhiQhCq3o"
   },
   "source": [
    "## The Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "cwDhM9ofCq3p"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(42)  # to make this code example reproducible\n",
    "m = 100  # number of instances\n",
    "X = 2 * np.random.rand(m, 1)  # column vector\n",
    "y = 4 + 3 * X + np.random.randn(m, 1)  # column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "T4fFJSG5Cq3p",
    "outputId": "e88d342d-e8f9-453d-83e6-a54a6c67decd"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BoeUIQQCMxjfwloslTLakFy7Ww092BCd6E72NEATAeG7/Bl5eLpWW+nToUGunmxJWtGEy1l64WA8/2TVBI72J3hZ1CHrooYfk8/n0pz/9KeTvly5dKp/Pp9mzZ7e4cQBguvqd97BhrXTLLcO0eLHP6SaFFW2YjKUXLpbDT3afBUhvondFHYIGDRokSXr33Xcb/e7o0aOaMWOGevbsqcLCwpa3DgAMdvLO27J8mjIl1fFxMPEUbXByYvxRJNzem4jQog5BAwYMUGpqqt55551GvysqKtKBAwc0b948ZWRkRPR4tbW1uvfee5WXl6c2bdqoZ8+eeuCBB2SdfPEWADBM6J23z+hT+CM9/HTi+B/G7SCcqGeM/t73vqe+ffuqrKxM3377rdLT0yVJO3bs0OOPP65hw4bpiiuuiPjx5s6dq+LiYi1dulR9+vTRpk2bNGHCBHXo0EG33XZbtM0DgKQRenZlS716ufeQWCI0N6NzqFnAFy6sOwRWW8u4HRwX02UzBg8erLKyMr3//vu68MILJUnTp0+XZVmaP39+VI+1YcMGXXnllRo5cqQk6fTTT9fy5ctDHm4DgGR38qUnTtx5p6QE9OSTAWVnc8WjcJdkCDf+Z+/eun+JuhQGvCGms8MGDx4sScFDYi+99JLWrFmjadOm6Zxzzon6sdauXauPP/5YkvT+++/rzTff1IgRI2JpGgB4VqgzmOoH3ZaUfKeFC0s0YUJihwq4ZT6eSG3YEH78D+N2cLKYvk6cODi6pqZGhYWFOu200zRz5syoH2vGjBmqrKzU2WefrdTUVNXW1uqhhx7SddddF/Y+NTU1qqmpCd6urKyUJPn9fvn9/qjb4GX19ZpWt0TtJ/40hd11l5dLu3b51KuXlfAdZV0PRisFAnWHuup6MCz95CffKTtb6tjRr6qqbxK6zRcv9mny5FQFAj6lpFgqLq5NeAiTIt/u9e2VGh4uTE21lJv7nbz4cfHiZz1en6NE1OyzYhyB3K1bN3Xo0EHjx4/Xf/3Xf2nhwoW65ZZbon6cFStW6K677tJvf/tb9enTR2VlZZo+fbrmzZun8ePHh7zPrFmzVFRU1Gj5smXL1LZt26jbAAAlJT305JP9ZVk++XyWpkwpU0HBvoQ9/7ZtnXXvvRc1Wv7AA2+qb9/DCWtHvUOHWuuWW4bJso4HipSUgBYuLFHnzt8kvD3NCdVeSfL5Apoy5f2EbkuTxfNzVF1drbFjx6qiokKZmZlxbmmdmEPQVVddpdWrV6tNmzbq3bu3Nm3apJSTh99HICcnRzNmzNDUqVODyx588EE999xz+uijj0LeJ1RPUE5Ojvbv369OnTpFX4yH+f1+lZSUqKCgQGlpaU43J6Go3bza7aq7vFzq1et4L4xU13uwc+d3CesRaq4Nid7mpaU+DRvW+GBBScl3uuSSxPYGRVJ7uPYuW/adfvYz755t7KXPerw/R4cPH1ZWVpatISjm0XWDBw/WqlWrVF1drccffzymACTVJb2T75uamqrAyQd1T5CRkRHyFPy0tDTXv0nsQu3UbpJ41713b+hT0T/9NE15eXF7mibl5YU6g8mnvLyGdSZqm59zTqgz06Szz26lpp7+5IHd8dRU7eHa+6MfNd1er/DCZz3en6NE1BvzZTPy/r+ia6+9VhdffHHMDRg1apQeeugh/fWvf9XevXu1cuVKzZs3T1dddVXMjwkA0XDLPDJumnk4lstB2HVpikhkZ0vjxjVcdv31DIJOJLd8jqIRUwiyLEuPPvqo2rZtq4cffrhFDfj973+vn/3sZ5oyZYrOOecc3XnnnZo0aZIeeOCBFj0uAETKTdd/ctMZTNGEMrsvTdGc8nLpj39suOy557xzVlsycNPnKFIxHQ4rLi7Whg0bNHfuXGW3sLr27dtr/vz5Uc8vBADx1NwEfKYKNx/PyZq6NEUiXkunnx91vPY5ijgElZeX67nnntPHH3+sP/7xj7r44ov1y1/+0s62AUBCRbrDR2OhZ7dO3KEQp58fx3npcxTx4bDXXntN99xzj1avXq0xY8Zo9erVSq3v8wIQ5LXJ5YB4cPpQiNPPD2+KuCfopptu0k033WRnWwDPC3XNIicHtwKJ5PShEKefH94T89lhABpyemAo3M2UHkI3DOyObfY7mIgQBMRJUwMzYTYnTx03Ca8zokUIQkxM+VYbDS/OkQH70UOYGLzOiAUhCFHj21boEMjAzMiZFKLpIUwMXmfEghCEqPBtq+kQ6KYZf93KtBBND2Fi8DojFoQgRMX0b1uRhEA3DAx1KxNDND2EicHrjFjEfAFVmMn0CcmYlbZlTH39OHU7MXidES16glzCK2MkTP+2RZd7yyT69XPT58pNPYRuel3izU2vM9yPEOQCXhsjYfK4F9NDYEsl8vXz2ueqJaIJNSa9LkBzCEEO8+oYCZO/bZkcAuu1pCchEa+fVz9XsYgm1Jj0ugCRIAQ5zPSBxl5lSggMFXbi0ZNg9+tnyucq2lBjyusCRIoQ5DDGmMCtQoUdr/QkmPK5ijbUmPK6AJEiBDmMMSZwo3BhZ8MGb/QknPy5SkmR5sxx1+cqHoOTow01/L0BGiIEuQBjTOA24XoYfD7v9CRMnCjNnl3X5kBAuvtu9wwCjtfg5FhCDX9vgOMIQS5hyhiTZJcspx6H62EYNMg7PQnl5dKMGcevKO6WQ3fxPqQYS6jh7w1QhxAExEkynXrcVA+DV3oS3DoI2I52EWqA2DBjNBAH4b7dDx/u3R1TU7PvZme7v654z25eXl4XYM48s2W1mz7rOuAm9AQBceDWXoeW8nIPQzwHAcezl4/ByYB70BMExAHf7t0pHteSsqOXj2tcAe5ATxAQB3y7d6+W9mbZ1cvn5V42IFnQEwTESby+3cdr7Anig14+IHnREwTEUUu/3SfTGWbJgl4+IHkRgpA0vD5HT6Tzx5SXS6WlPh061DrxjTSUV6YFABAdDochKSxadDxApKTUfXP32o6qqbEn9b0Ox+tsJZ9vmGpra3XrrYlvq1vZeSjRC9MCAIgOPUHwPK9c1LM5zV0H6uQ6LcunKVNSPVenXTiUCCBahCB43q5dvqSYo6e5sSehe4p8CanT7YcakyUIA0gsQhA8r1cvyzMX9WxOU2NPQvcUWbbX6XQPSyQBLFknqwRgL1eEoM8//1zXX3+9OnXqpDZt2qhv377atGmT081CGG7rFUi2s3fCnWF2cp0pKQE9+WStrXU63cNycgBbvNgXcr3mDiUCQCiOh6Cvv/5aF110kdLS0vTKK6/oww8/1O9+9zudeuqpTjcNITjdKxCOKWfv1NdZUvKdFi4s0YQJlq3P52QPS6gANmVKasiz4rwWhN32RQIwleNnh82dO1c5OTlavHhxcFleXp6DLUI4br9IqCln72RnS127Wvrb376x/bmcnCgw3Bio/fvbhVzfK5eiSIYzGYFk4XhP0EsvvaQLLrhAP//5z9WlSxf94Ac/0NNPP+10sxAC4y6c4WSvgZM9LOHGQGVlVYW9j9svReH04UUADTneE/TJJ5+ouLhYhYWF+s///E+99957uu2225Senq7x48eHvE9NTY1qamqCtysrKyVJfr9ffr8/Ie12i/p6E1H36adLKSmtFAgcH5eRmmopN/c7OfGyt6T28vK6s8p69bIi2mFGu368LF7s0+TJqQoEfEpJsVRcXKsJE6yEbvcbbqg7/Ll7t089e9bVn4jt3bWrVFxcNw1Aba1PqamWfv/7b9W58zee/Zz/858+BQIN/+zW1kofffSdunZt+tBmIre521C72bXbyWdZlr2DCpqRnp6uCy64QBs2bAguu+222/Tee+9p48aNIe8za9YsFRUVNVq+bNkytW3b1ra2nujQodbav/97yso6ps6d7T8s4RYlJT1UXNxPgUCKUlICmjz5fRUU7HO6WVEpKemhJ5/sL8vyyeezNGVKWZM1RLt+vBw61Fq33DJMlnU8dKakBLRwYYlR77m6z1o7ZWVVeb5utikQuerqao0dO1YVFRXKzMy05TkcD0G5ubkqKCjQf//3fweXFRcX68EHH9Tnn38e8j6heoJycnK0f/9+derUyfY2h/t27gS/36+SkhIVFBQoLS0tIc9ZXt6wVyDa+8arRyWW2svLpV69Gvdm7dz5Xcj2RLt+PJWW+jRsWOPO2pKS7zR48LcJ3+5Oqn/fnH66Xx9++Jqn6168uGHv1pNPRvb3w4nPultQu5m1Hz58WFlZWbaGIMcPh1100UXasWNHg2Uff/yxcnNzw94nIyNDGRkZjZanpaXZ/iYpL5cmTz7xmL5PU6a00uWXOzsOIRG118vLq/sXLbsGhEZT+969oQfbfvppmvLyGl92obn17XTOOaEHJZ99diulpdXtNBO53Z3S8H2TqsmTe+jyy71b9623SpdfXj+A26fs7Oj+DJuwzcOhdrNqT0S9jg+MvuOOO/T222/rN7/5jXbt2qVly5Zp4cKFmjp1qtNNC4nBwbFxy4DQpuaTCXX6v5Pzz3jttG87NH7f+FRc3K/Z943bT0F3+wBuwBSOh6ALL7xQK1eu1PLly3XuuefqgQce0Pz583Xdddc53bSQmJStaeF2Pm4Jj+GChRQ6pEnOBhFT5j8KJ9T7JhBI0e7doSdNlNw7lxUA93H8cJgk/fSnP9VPf/pTp5sRkfqd6KRJdTtxE7+dh9PU4S4n55s5Waj5ZNatCx/SnJ5/xpT5j0IJ9b5JSQmoZ8/QY2jcPpdVPTuvdg8gco73BHmR09/O3djV39zhLrcd2jn5cERzPXxeOXzhxvdGSzR+31iaPPn9sNvBLT2OTaGnCnAPQlCMnNopRnotpUSLZOfjdHhsittCWiySded64vtm587vmpyewO2Hq90yNg5AHUKQi538rT6aayklWqQ7Hzf3qLg5pDUn2Xeukb5v3B5mvdBTBZjEFWOC0Fio8TVnnBHdtZQSKVnGSnl1/E1TO1cv1tMSTo/haoqbxsYBoCcoyE1jKcJ9q//e96K/llIiebknxevcfhgo0dza4+j2nirANIQguW8sRbhv9VVVjf+APvlkbczT7dsR/Ny483FTwLWL23auJrzmseLLAuAexocgN46laOpb/cl/QGO9XIfbgp9dTKlTcs/O1aTXPFZu/LIAmMj4EOTGgYrNfatv6R/QSIOf17/NuzHg2s3pnauJrzkA7zI+BLl1LIWd3+ojCX7hvs17KRi5MeAmO15zAF5ifAhy21iKE8WjxydUYGku+IX7Nv/b33rrMEc8A66Xwp+T3PqlAgBCMT4ESe4ZSxFPTY3LaC74hfs2f/fd3jrMEa+AyxiXyLn5SwUAnMyoeYKaul5PS+aHcdt1gCK5flJTc6mEvl6TN+ehaemcMV65FpWbuHmeHgA4kTE9QXZ9m3djL0Gk4zLCHW4L9W1+7lzvHuZoyWFFxrjExukB2gAQCSNCkF1nrLj1TJh4jMs4+RDhnXeaeZgj0WNcGHsEAIljRAiy69u8W3sJ4jUu4+Rv85GOnUqmHXmo13L27LptH+/63NirCADJzIgxQXZdr8fN1wGya1xGc2OnQl3zzOsDzU98LTdtOj5APJ71MfYIABLPiJ4gu85YcfuZMIkel+HWw4PxkJ1dFyajOUMumh4xt/YqAkAyMyIESfadBu/l0+vjfdgq2Xfk0dQX7aEt5tcBgMQzJgRJsfWMRBIUQj1uebn0wgt1/+zoCWlpgLFj/Emy78gjrS+WHjG39yoCQDIyKgRFK5qgcGIoWbRI6tFDuuaaun89esR3kOuJ7erVq5VKSnpEdX+7Dlsl+4480vpi7RHzcq8iAHiREQOjYxHNQNUTBwP7fHXLrBMu7m5Zdb+PxyDXxu3yqbi4n375y1rl5UX2GE3tpFvavmSfKC+S+loyYL4lk3YCAKKTdD1B8RrnEum3+ZNDiWU1DED1AoH4jI0J1a5AIEW7d/sifgy7D1sl+0R5zdWX7D1iAJAskioEPfecL27jXCINCqFCSSgpKfEJGaHalZISUM+eIZJXGOyk7cehLQBwv6QKQXfckRq305cjDQqhQonPd/ywWP3thQvjEzIat8vS5MnvR/3Y7KTtl+w9YgDgdUk1JsiyGh4SCjfOJdIJ/SIZ/1EfSiZNqnu++rA0fLi0cWPdOoMGxXdHeGK7cnO/0wcf7JN0btSPw/gTAIDJkioE+XxWg/E40Zy+HG7QciRBIVxY+vnPY6+lOfXt8vulDz6w73kAAEhWSXU47NFHa207fbk5HPrwvmS65hkAoHlJFYKuv95qdpxLsk/oh9hw8VIAME9ShSCJ05cRvWS+5hkAILykGhMUqWSf0A/RsXPySACAexkZgiTOjMJxLZnhGQDgXa47HDZnzhz5fD5Nnz7d6abAEBwiBQAzuaon6L333tMf/vAHnXfeeU43BYbhECkAmMc1PUHHjh3Tddddp6efflqnnnqq081xJU7hthfTHACAWVzTEzR16lSNHDlS+fn5evDBB5tct6amRjU1NcHblZWVkiS/3y+/329rO52yeLFPkyenKhDwKSXFUnFxrSZMsIL1JmvdTaF282o3tW6J2k/8aRJqt5fPskJd8zyxVqxYoYceekjvvfeeWrdurSFDhqh///6aP39+yPVnzZqloqKiRsuXLVumtm3b2tzaxDt0qLVuuWVYg8uCpKQEtHBhiTp3/sbBloV26FBr7d//PWVlHXNl+wAA7lddXa2xY8eqoqJCmZmZtjyH4z1Bn332mW6//XaVlJSodevWEd3nnnvuUWFhYfB2ZWWlcnJyNHToUHXq1MmupjqmtNTX6LpogUCKcnMv1eDB36qkpEQFBQVKS0tzqIXHheuxsoPf73dV7Ylkau2m1i1RO7WbV/vhw4dtfw7HQ9DmzZv15Zdf6vzzzw8uq62t1fr16/XEE0+opqZGqfWn7fy/jIwMZWRkNHqstLS0pHyTnHNO6FO4zz67ldLS6gKGG2ovL5cmTz5x0kGfpkxppcsvt3ecjRtqd4qptZtat0Tt1G6ORNTr+MDoSy+9VNu2bVNZWVnw3wUXXKDrrrtOZWVljQKQibxyCrdd12UDAMAOjvcEtW/fXueee26DZe3atVOnTp0aLTeZF07hZtJBAICXON4ThMi5/RRur/RYAQAguaAnKJTS0lKnm4AYeaHHCgAAyaUhCN7GddkAAF7A4TCHMPszAADOIgQ5YNEiKTdX+slP6n4uWuR0iwAAMA8hKMHKy6Vbbz1xLh1p0iR6hAAASDRCUDPifdiKuXQAAHAHQlAT7DhsVT+XzomYSwcAgMQjBIVh12GrRM+lwwBsAABCIwSFYedhq4kTpb1768LJ3r11t+3AAGwAAMIjBIVh92Eru2d/ZgA2AABNIwSF4fVLQDAAGwCApjFjdBO8fAkILmYKAEDT6AlqhtsvWhqO13uyAACwGz1BSczLPVkAANiNEJTkuJgpAAChcTgMAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABiJEAQAAIxECAIAAEYiBAEAACMRggAAgJEIQQAAwEiEIAAAYCRCEAAAMJIrQtDs2bN14YUXqn379urSpYtGjx6tHTt2ON0sAACQxFwRgt544w1NnTpVb7/9tkpKSuT3+zVs2DBVVVU53TQAAJCkWjndAElas2ZNg9tLlixRly5dtHnzZv34xz92qFUAACCZuSIEnayiokKS1LFjx5C/r6mpUU1NTfB2ZWWlJMnv98vv99vfQBepr9e0uiVqP/GnKUytW6L2E3+ahNrt5bMsy7L9WaIQCAR0xRVX6MiRI3rzzTdDrjNr1iwVFRU1Wr5s2TK1bdvW7iYCAACbVVdXa+zYsaqoqFBmZqYtz+G6EDR58mS98sorevPNN5WdnR1ynVA9QTk5Odq/f786deqUqKa6gt/vV0lJiQoKCpSWluZ0cxKK2s2r3dS6JWqndvNqP3z4sLKysmwNQa46HDZt2jS9/PLLWr9+fdgAJEkZGRnKyMhotDwtLc24N0k9aqd2k5hat0Tt1G6ORNTrihBkWZZ+8YtfaOXKlSotLVVeXp7TTQIAAEnOFSFo6tSpWrZsmVavXq327dvrwIEDkqQOHTqoTZs2DrcOAAAkI1fME1RcXKyKigoNGTJEWVlZwX/PP/+8000DAABJyhU9QS4bmw0AAAzgip4gAACARCMEAQAAIxGCAACAkQhBAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABiJEAQAAIxECAIAAEYiBAEAACMRggAAgJEIQQAAwEiEIAAAYCRCEAAAMBIhCAAAGIkQBAAAjEQIAgAARiIEAQAAIxGCAACAkQhBAADASIQgAABgJEIQAAAwkmtC0IIFC3T66aerdevWGjhwoN59912nmwQAAJKYK0LQ888/r8LCQs2cOVNbtmxRv379NHz4cH355ZdONw0AACQpV4SgefPm6ZZbbtGECRP0/e9/X0899ZTatm2rZ555xummAQCAJOV4CPr222+1efNm5efnB5elpKQoPz9fGzdudLBlAAAgmbVyugGHDh1SbW2tunbt2mB5165d9dFHH4W8T01NjWpqaoK3KyoqJElfffWVfQ11Kb/fr+rqah0+fFhpaWlONyehqN282k2tW6J2ajev9vp9umVZtj2H4yEoFrNnz1ZRUVGj5WeddZYDrQEAAHY5fPiwOnToYMtjOx6COnfurNTUVB08eLDB8oMHD6pbt24h73PPPfeosLAwePvIkSPKzc3Vvn37bHuh3KqyslI5OTn67LPPlJmZ6XRzEorazavd1Lolaqd282qvqKhQjx491LFjR9uew/EQlJ6erh/+8Idau3atRo8eLUkKBAJau3atpk2bFvI+GRkZysjIaLS8Q4cOxr1J6mVmZlK7gUyt3dS6JWqndvOkpNg3fNnxECRJhYWFGj9+vC644AINGDBA8+fPV1VVlSZMmOB00wAAQJJyRQi65ppr9L//+7+67777dODAAfXv319r1qxpNFgaAAAgXlwRgiRp2rRpYQ9/NScjI0MzZ84MeYgs2VE7tZvE1Lolaqd2areDz7Lz3DMAAACXcnyyRAAAACcQggAAgJEIQQAAwEiuDUELFizQ6aefrtatW2vgwIF69913m1z/z3/+s84++2y1bt1affv21d/+9rcGv7csS/fdd5+ysrLUpk0b5efna+fOnXaWEJNo6n766af1ox/9SKeeeqpOPfVU5efnN1r/xhtvlM/na/Dvsssus7uMmERT+5IlSxrV1bp16wbreGWbS9HVPmTIkEa1+3w+jRw5MriOV7b7+vXrNWrUKHXv3l0+n0+rVq1q9j6lpaU6//zzlZGRoV69emnJkiWN1on270eiRVv3iy++qIKCAp122mnKzMzUoEGD9OqrrzZYZ9asWY22+dlnn21jFbGJtvbS0tKQ7/cDBw40WM/t21yKvvZQn2Ofz6c+ffoE1/HCdp89e7YuvPBCtW/fXl26dNHo0aO1Y8eOZu+XiP26K0PQ888/r8LCQs2cOVNbtmxRv379NHz4cH355Zch19+wYYOuvfZaTZw4UVu3btXo0aM1evRobd++PbjOww8/rMcff1xPPfWU3nnnHbVr107Dhw/XN998k6iymhVt3aWlpbr22mu1bt06bdy4UTk5ORo2bJg+//zzButddtll2r9/f/Df8uXLE1FOVKKtXaqbPOzEuj799NMGv/fCNpeir/3FF19sUPf27duVmpqqn//85w3W88J2r6qqUr9+/bRgwYKI1t+zZ49GjhypoUOHqqysTNOnT9fNN9/cIBDE8l5KtGjrXr9+vQoKCvS3v/1Nmzdv1tChQzVq1Cht3bq1wXp9+vRpsM3ffPNNO5rfItHWXm/Hjh0NauvSpUvwd17Y5lL0tT/22GMNav7ss8/UsWPHRp91t2/3N954Q1OnTtXbb7+tkpIS+f1+DRs2TFVVVWHvk7D9uuVCAwYMsKZOnRq8XVtba3Xv3t2aPXt2yPWvvvpqa+TIkQ2WDRw40Jo0aZJlWZYVCASsbt26Wb/97W+Dvz9y5IiVkZFhLV++3IYKYhNt3Sf77rvvrPbt21tLly4NLhs/frx15ZVXxrupcRdt7YsXL7Y6dOgQ9vG8ss0tq+Xb/dFHH7Xat29vHTt2LLjMK9v9RJKslStXNrnOr371K6tPnz4Nll1zzTXW8OHDg7db+nomWiR1h/L973/fKioqCt6eOXOm1a9fv/g1LAEiqX3dunWWJOvrr78Ou47XtrllxbbdV65cafl8Pmvv3r3BZV7c7l9++aUlyXrjjTfCrpOo/brreoK+/fZbbd68Wfn5+cFlKSkpys/P18aNG0PeZ+PGjQ3Wl6Thw4cH19+zZ48OHDjQYJ0OHTpo4MCBYR8z0WKp+2TV1dXy+/2NrrNSWlqqLl26qHfv3po8ebIOHz4c17a3VKy1Hzt2TLm5ucrJydGVV16pf/zjH8HfeWGbS/HZ7osWLdKYMWPUrl27Bsvdvt1j0dxnPR6vpxcEAgEdPXq00Wd9586d6t69u8444wxdd9112rdvn0MtjL/+/fsrKytLBQUFeuutt4LLTdnmUt1nPT8/X7m5uQ2We227V1RUSFKT1wRL1H7ddSHo0KFDqq2tbTRbdNeuXRsdA6534MCBJtev/xnNYyZaLHWf7O6771b37t0bvCkuu+wyPfvss1q7dq3mzp2rN954QyNGjFBtbW1c298SsdTeu3dvPfPMM1q9erWee+45BQIBDR48WOXl5ZK8sc2llm/3d999V9u3b9fNN9/cYLkXtnsswn3WKysr9a9//SsunyMveOSRR3Ts2DFdffXVwWUDBw7UkiVLtGbNGhUXF2vPnj360Y9+pKNHjzrY0pbLysrSU089pb/85S/6y1/+opycHA0ZMkRbtmyRFJ+/nV7wxRdf6JVXXmn0Wffadg8EApo+fbouuuginXvuuWHXS9R+3TUzRqNl5syZoxUrVqi0tLTBAOExY8YE/9+3b1+dd9556tmzp0pLS3XppZc60dS4GDRokAYNGhS8PXjwYJ1zzjn6wx/+oAceeMDBliXWokWL1LdvXw0YMKDB8mTd7pCWLVumoqIirV69usG4mBEjRgT/f95552ngwIHKzc3VCy+8oIkTJzrR1Ljo3bu3evfuHbw9ePBg7d69W48++qj++Mc/OtiyxFq6dKlOOeWU4IXG63ltu0+dOlXbt293zbgl1/UEde7cWampqTp48GCD5QcPHlS3bt1C3qdbt25Nrl//M5rHTLRY6q73yCOPaM6cOXrttdd03nnnNbnuGWecoc6dO2vXrl0tbnO8tKT2emlpafrBD34QrMsL21xqWe1VVVVasWJFRH/o3LjdYxHus56Zmak2bdrE5b3kZitWrNDNN9+sF154odGhgpOdcsopOuusszy/zUMZMGBAsK5k3+ZS3VlQzzzzjMaNG6f09PQm13Xzdp82bZpefvllrVu3TtnZ2U2um6j9uutCUHp6un74wx9q7dq1wWWBQEBr165t8M3/RIMGDWqwviSVlJQE18/Ly1O3bt0arFNZWal33nkn7GMmWix1S3Wj4x944AGtWbNGF1xwQbPPU15ersOHDysrKysu7Y6HWGs/UW1trbZt2xasywvbXGpZ7X/+859VU1Oj66+/vtnnceN2j0Vzn/V4vJfcavny5ZowYYKWL1/eYDqEcI4dO6bdu3d7fpuHUlZWFqwrmbd5vTfeeEO7du2K6AuPG7e7ZVmaNm2aVq5cqddff115eXnN3idh+/WohnQnyIoVK6yMjAxryZIl1ocffmjdeuut1imnnGIdOHDAsizLGjdunDVjxozg+m+99ZbVqlUr65FHHrH++c9/WjNnzrTS0tKsbdu2BdeZM2eOdcopp1irV6+2PvjgA+vKK6+08vLyrH/9618Jry+caOueM2eOlZ6ebv3P//yPtX///uC/o0ePWpZlWUePHrXuvPNOa+PGjdaePXusv//979b5559vnXnmmdY333zjSI3hRFt7UVGR9eqrr1q7d++2Nm/ebI0ZM8Zq3bq19Y9//CO4jhe2uWVFX3u9iy++2LrmmmsaLffSdj969Ki1detWa+vWrZYka968edbWrVutTz/91LIsy5oxY4Y1bty44PqffPKJ1bZtW+uuu+6y/vnPf1oLFiywUlNTrTVr1gTXae71dINo6/7Tn/5ktWrVylqwYEGDz/qRI0eC6/zyl7+0SktLrT179lhvvfWWlZ+fb3Xu3Nn68ssvE15fU6Kt/dFHH7VWrVpl7dy509q2bZt1++23WykpKdbf//734Dpe2OaWFX3t9a6//npr4MCBIR/TC9t98uTJVocOHazS0tIG79/q6urgOk7t110ZgizLsn7/+99bPXr0sNLT060BAwZYb7/9dvB3l1xyiTV+/PgG67/wwgvWWWedZaWnp1t9+vSx/vrXvzb4fSAQsO69916ra9euVkZGhnXppZdaO3bsSEQpUYmm7tzcXEtSo38zZ860LMuyqqurrWHDhlmnnXaalZaWZuXm5lq33HKL6/4w1Ium9unTpwfX7dq1q3X55ZdbW7ZsafB4XtnmlhX9+/2jjz6yJFmvvfZao8fy0navP/355H/19Y4fP9665JJLGt2nf//+Vnp6unXGGWdYixcvbvS4Tb2ebhBt3ZdcckmT61tW3VQBWVlZVnp6uvVv//Zv1jXXXGPt2rUrsYVFINra586da/Xs2dNq3bq11bFjR2vIkCHW66+/3uhx3b7NLSu29/uRI0esNm3aWAsXLgz5mF7Y7qFqltTgs+vUfp2ryAMAACO5bkwQAABAIhCCAACAkQhBAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAXGfQoEHy+XzauHFjg+WVlZXq37+/MjIyVFJS4lDrACQLQhAA15k7d64k6de//nVw2bfffqurrrpKH3zwgZYuXaqCggKnmgcgSRCCALjOj3/8Y40cOVKvv/66SktLZVmWbrzxRr3++ut69NFHNWbMGKebCCAJcBV5AK60bds29e/fX4MHD9aAAQM0b9483XPPPfrNb37jdNMAJAlCEADXGj9+vJ599llJ0k033aRFixY1WufFF19UcXGxNm/erK+//lp79uzR6aefnuCWAvAiDocBcK3TTjtNktS+fXstWLAg5DpVVVX68Y9/rPvvvz+RTQOQBFo53QAACOWJJ57Q7373O3Xt2lUHDx7U0qVLNWnSpEbrjRs3TpK0ffv2RDcRgMfREwTAdV544QXdfvvtGjp0qLZu3aoOHTqoqKhI1dXVTjcNQBIhBAFwlbVr12rcuHHq27evVq1apaysLN1xxx3av3+/HnvsMaebByCJMDAagGts2bJFQ4YMUadOnbRhwwZlZWVJqpskMS8vT7W1tfrkk0/UsWPHRvfdvn27+vbty8BoABGjJwiAK+zevVuXX3650tPTtWbNmmAAkqTMzEzdfffdqqio0OzZsx1sJYBkQk8QgKRATxCAaHF2GABP++qrr7Rv3z7t3r1bkvThhx/qyJEj6tGjR8jDZgBQj54gAJ62ZMkSTZgwodHyxYsX68Ybb0x8gwB4BiEIAAAYiYHRAADASIQgAABgJEIQAAAwEiEIAAAYiRAEAACMRAgCAABGIgQBAAAjEYIAAICRCEEAAMBIhCAAAGAkQhAAADASIQgAABjp/wDZgfvVd3oOwwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–1\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "Y133SAC9Cq3p"
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import add_dummy_feature\n",
    "\n",
    "X_b = add_dummy_feature(X)  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "b0U5e985Cq3q",
    "outputId": "77fd5820-e912-4faf-97a8-0df37dd789a9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "hSZ3gf3iCq3q",
    "outputId": "e885eb58-ab26-4665-bfbd-b7043b03a74c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = add_dummy_feature(X_new)  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b @ theta_best\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "XOx0pYy2Cq3s",
    "outputId": "a833cb91-cea9-44b6-b0f4-0569bb1f8349"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "plt.plot(X_new, y_predict, \"r-\", label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "\n",
    "# extra code – beautifies and saves Figure 4–2\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "plt.legend(loc=\"upper left\")\n",
    "save_fig(\"linear_model_predictions_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "gSN9EqThCq3s",
    "outputId": "fef3dbf7-169b-433f-86ea-b39d16b6e69c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lflEhWQ7Cq3s",
    "outputId": "94e9da0d-cb66-426b-9851-169d02fc293b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ksmo43bQCq3t"
   },
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "nO8kvfGzCq3t",
    "outputId": "fe24a9da-5bfb-4145-9d7f-d59a14a54370"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5ICEvu5wCq3u"
   },
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "shY_P6eqCq3u",
    "outputId": "3d8d6c02-00e6-4fa8-95ba-db451ed9bad1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b) @ y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q6Mg_prnCq3u"
   },
   "source": [
    "# Gradient Descent\n",
    "## Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "gS2KLLZfCq3v"
   },
   "outputs": [],
   "source": [
    "eta = 0.1  # learning rate\n",
    "n_epochs = 1000\n",
    "m = len(X_b)  # number of instances\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # randomly initialized model parameters\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "z_R9epKvCq3v"
   },
   "source": [
    "The trained model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IXLr2LC0Cq3v",
    "outputId": "ebab84f5-4d89-41e7-c39d-d68851c7e079"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "SZkex8mLCq3v",
    "outputId": "2dcabd32-d7c3-44e0-e69f-aeccb0498199"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–8\n",
    "\n",
    "import matplotlib as mpl\n",
    "\n",
    "def plot_gradient_descent(theta, eta):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_epochs = 1000\n",
    "    n_shown = 20\n",
    "    theta_path = []\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch < n_shown:\n",
    "            y_predict = X_new_b @ theta\n",
    "            color = mpl.colors.rgb2hex(plt.cm.OrRd(epoch / n_shown + 0.15))\n",
    "            plt.plot(X_new, y_predict, linestyle=\"solid\", color=color)\n",
    "        gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\")\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.grid()\n",
    "    plt.title(fr\"$\\eta = {eta}$\")\n",
    "    return theta_path\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(131)\n",
    "plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.subplot(132)\n",
    "theta_path_bgd = plot_gradient_descent(theta, eta=0.1)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "plt.subplot(133)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "plot_gradient_descent(theta, eta=0.5)\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SZCBSDuhCq3w"
   },
   "source": [
    "## Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "T4aso62hCq3x"
   },
   "outputs": [],
   "source": [
    "theta_path_sgd = []  # extra code – we need to store the path of theta in the\n",
    "                     #              parameter space to plot the next figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "BVIYPVkyCq3x",
    "outputId": "196e571b-dc2b-463d-9630-2344726933c4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "n_shown = 20  # extra code – just needed to generate the figure below\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for iteration in range(m):\n",
    "\n",
    "        # extra code – these 4 lines are used to generate the figure\n",
    "        if epoch == 0 and iteration < n_shown:\n",
    "            y_predict = X_new_b @ theta\n",
    "            color = mpl.colors.rgb2hex(plt.cm.OrRd(iteration / n_shown + 0.15))\n",
    "            plt.plot(X_new, y_predict, color=color)\n",
    "\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index : random_index + 1]\n",
    "        yi = y[random_index : random_index + 1]\n",
    "        gradients = 2 * xi.T @ (xi @ theta - yi)  # for SGD, do not divide by m\n",
    "        eta = learning_schedule(epoch * m + iteration)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)  # extra code – to generate the figure\n",
    "\n",
    "# extra code – this section beautifies and saves Figure 4–10\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.grid()\n",
    "save_fig(\"sgd_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "s128mXPKCq3y",
    "outputId": "843fae01-a237-43bd-96d8-8aa0ad577fd0",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 80
    },
    "id": "NP9vjXB5Cq3y",
    "outputId": "461005a0-fd65-42e8-ecfb-a82b8264bae7"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>SGDRegressor</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.SGDRegressor.html\">?<span>Documentation for SGDRegressor</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-5, penalty=None, eta0=0.01,\n",
    "                       n_iter_no_change=100, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())  # y.ravel() because fit() expects 1D targets\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BNEGqCiwCq3z",
    "outputId": "93143224-cce6-4800-d40e-75afd0568cfd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21278812]), array([2.77270267]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "onZAjXYICq3z"
   },
   "source": [
    "## Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sGM1mQVOCq3z"
   },
   "source": [
    "The code in this section is used to generate the next figure, it is not in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "ocHvK7s2Cq30",
    "outputId": "3926c455-bbef-449b-8674-23b0f84621ad"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–11\n",
    "\n",
    "from math import ceil\n",
    "\n",
    "n_epochs = 50\n",
    "minibatch_size = 20\n",
    "n_batches_per_epoch = ceil(m / minibatch_size)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta_path_mgd = []\n",
    "for epoch in range(n_epochs):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for iteration in range(0, n_batches_per_epoch):\n",
    "        idx = iteration * minibatch_size\n",
    "        xi = X_b_shuffled[idx : idx + minibatch_size]\n",
    "        yi = y_shuffled[idx : idx + minibatch_size]\n",
    "        gradients = 2 / minibatch_size * xi.T @ (xi @ theta - yi)\n",
    "        eta = learning_schedule(epoch * n_batches_per_epoch + iteration)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)\n",
    "\n",
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)\n",
    "\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1,\n",
    "         label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2,\n",
    "         label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3,\n",
    "         label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(r\"$\\theta_0$\")\n",
    "plt.ylabel(r\"$\\theta_1$   \", rotation=0)\n",
    "plt.axis([2.6, 4.6, 2.3, 3.4])\n",
    "plt.grid()\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "83utPbytCq31"
   },
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "id": "jIxj2b92Cq31"
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "yZI82kpACq31",
    "outputId": "1ee89637-1166-45a8-d500-673eeb585338"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–12\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "CPLP4gS1Cq31",
    "outputId": "a156e650-cb31-417c-dda6-4f902e83c22e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2aXFb6TzCq32",
    "outputId": "6fef19e5-a06e-42b7-a095-9f9bf73124d2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zvuaNif_Cq32",
    "outputId": "1018c04d-5cf2-4b8e-f121-82890103d82b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "gD8LZ2nuCq33",
    "outputId": "fd4d1c53-409a-4b61-e2f7-230de92d3cba"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–13\n",
    "\n",
    "X_new = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "4bwIyIvICq33",
    "outputId": "d8ac7b3f-0c17-4769-bee8-996f6c338c7f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–14\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "\n",
    "for style, width, degree in ((\"r-+\", 2, 1), (\"b--\", 2, 2), (\"g-\", 1, 300)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = make_pipeline(polybig_features, std_scaler, lin_reg)\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    label = f\"{degree} degree{'s' if degree > 1 else ''}\"\n",
    "    plt.plot(X_new, y_newbig, style, label=label, linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$\", rotation=0)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "plt.grid()\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y2x9ktEZCq33"
   },
   "source": [
    "# Learning Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "suomJIUHCq34",
    "outputId": "ae69b9c5-c2d6-4ff4-9bc8-491cdaf01275"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import learning_curve\n",
    "\n",
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "    LinearRegression(), X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "    scoring=\"neg_root_mean_squared_error\")\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)\n",
    "\n",
    "plt.figure(figsize=(6, 4))  # extra code – not needed, just formatting\n",
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "\n",
    "# extra code – beautifies and saves Figure 4–15\n",
    "plt.xlabel(\"Training set size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.grid()\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.axis([0, 80, 0, 2.5])\n",
    "save_fig(\"underfitting_learning_curves_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "HU8CpRROCq35"
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "polynomial_regression = make_pipeline(\n",
    "    PolynomialFeatures(degree=10, include_bias=False),\n",
    "    LinearRegression())\n",
    "\n",
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "    polynomial_regression, X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "    scoring=\"neg_root_mean_squared_error\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "ZtOXQc5qCq35",
    "outputId": "ac56b8a6-5bc8-467f-9bb4-56d650537d86"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–16\n",
    "\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"Training set size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.grid()\n",
    "plt.axis([0, 80, 0, 2.5])\n",
    "save_fig(\"learning_curves_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GIDb8hDTCq35"
   },
   "source": [
    "# Regularized Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "G3GTzFkTCq35"
   },
   "source": [
    "## Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zXhD4p0RCq35"
   },
   "source": [
    "Let's generate a very small and noisy linear dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "id": "0YAHks8QCq35"
   },
   "outputs": [],
   "source": [
    "# extra code – we've done this type of generation several times before\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 398
    },
    "id": "pctWR3_qCq36",
    "outputId": "36f38de1-6b2e-46b3-9282-9dc73eae620d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – a quick peek at the dataset we just generated\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(X, y, \".\")\n",
    "plt.xlabel(\"$x_1$\")\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.axis([0, 3, 0, 3.5])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QnecTNfQCq36",
    "outputId": "0e1efc39-0ec6-461d-bf5e-aed329d04dc6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.55325833])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "ridge_reg = Ridge(alpha=0.1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 345
    },
    "id": "pom-tzl4Cq36",
    "outputId": "bb0a1bef-b6be-4ba3-e7bb-237cc7dbe40c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZWVlOFSPtyRW/l/NUpbrvu7zP/Dw4J9hi0sQ6mzfTKTUVgIQOHeCPPyr8+nZP3Dw9PYmKigKgQ4cO7Nixg/fff59PP/3U6tiwsDDOnTtnse3cuXOEhYUV+f6TJk1i4sSJ5tdpaWnUq1eP3r17U7NmzSLPy8rK4tSpU/j6+uLt7V3WajklTdO4fPkyfn5+VguYugJ71z8rK4tq1arRs2dPh3+GDAYDa9asoW/fvnh4eDi0LPYmdXfNuicnJzu6CEUqT1yqijEJXDsuuXrdk5OT8fb2dooYaU+u/L1cFet+cNtBiFPP7+p6FwNaDzDvcyuQy4Q88UTVSNyuZTKZLLqQFBQTE8PatWt58sknzdvWrFlT5Jg4AC8vL7y8vKy2e3h4FPuhMRqN6HQ69Ho9en3VWN4urytGXr1cjb3rr9fr0el0JX7W7MmZymJvUnfXqrsz17c8cakqxiRw7bgkdcfpYqQ9uWq9oWrVfVfiLvPzLvW65NcrMRF++009r18ftxtvtMn17Zq4TZo0iVtvvZX69etz+fJlFi9ezIYNG1i9ejUAI0eOJDw8nOnTpwMwYcIEbrzxRmbMmMFtt93Gt99+y86dO5k3b549iy2EEEIIIYRwcSPbjKSefz32nttL0+Cm+Tu+/hqMRvX8gQfARjdn7Jq4nT9/npEjR3L27FkCAgJo3bo1q1evpm/fvgCcPHnS4i5Ut27dWLx4MS+99BKTJ08mOjqaFStWyBpuQgghhBBCCLsa2HggAxsPtN5RcO22kSNtdn27Jm4LFiwodv+GDRustg0dOpShQ4faqERCCCGEEEIIUU5//w3//KOex8RA48Zgo3HXrtXJWgghhBBCCCEqSsEJFkePtumlJHETQgghhBBCiGJsS9jGydST5nUJAUhLg8WL1XM/Pxg+3KZlcPiskkIIIYQQQgjhzO5Zeg+n0k4RFRTFkfFH1LIeixdDRoY64P77wdfXpmWQFjchhBBCCCGEKMK59HOcSjsFQLhfuEraNM2ym+S4cTYvhyRuQgghhBBCCFGEnWd2mp93rNNRPdmxA/bsUc87d4a2bW1eDknchFP76quvGDduHB07dsTLywudTsfChQtLPG/Hjh3cdtttRERE4OfnR9euXfnuu+9sX2AhhBBVWnnjkrPZsWMHAwYMoEaNGvj4+BQbJxs0aIBOpyv00atXL/sWXAgHKJi4darTST2ZOzf/ADu0toGMcRNO7qWXXiI+Pp7g4GBq165NfHx8ieesX7+e/v374+3tzZAhQwgKCmL58uXce++9nDp1iqefftoOJRdCCFEVlScuOZuCcXLYsGH4+fmxbNmyYuNkQEAATz75pNX2Bg0a2L7AQjjYzrPXtLilpMC336oN/v5w7712KYckbsKpzZ8/n+joaCIiInjrrbeYNGlSscfn5uYyduxY9Ho9GzZsoFGjRvj7+/Pqq6/SuXNnJk+ezN13301ERISdaiCEEKIqKWtccjYF4+SmTZtoe7V71yuvvFJsnKxRowavvfaa/QsshIOZNBNbT20FINA7kEaBjeDjjyEzUx3wwAPg42OXskhXSWElIyODqVOn0qRJE7y9vYmKimLOnDkAbNmyBZ1Ox7Jly+xSlj59+pQpyVq3bh1xcXHcd9995mAE6k7h5MmTycnJYdGiRTYoqRBCCFupzHEpj9Fo5KuvvqJ3794EBATg7e1Nhw4dWL58uQ1KWTSJk0KUzeGkwyRnqgW1u9fvjg7sPilJHmlxExbOnDlDnz59OHLkCPfccw8DBw7k66+/5rHHHqN9+/a8/vrrtG3bliFDhji6qIXasGEDAP369bPa179/fwA2btxozyIJIYS4DpU9LgFkZWUxcOBA1q5dS7t27Rg9ejTZ2dl8//333HXXXXz11Vfcf//9dilLeeNkdnY2Cxcu5MyZM/j7+9OpUye6dOli07IK4Qz+OPmH+Xn3+t1hwwbYv19tiImBVq3sVhZJ3ISZyWRiyJAhHDx4kOXLl3PnnXcCcPvtt9O7d29mzZrFqlWrWLFihZoGtRCzZ88mJSWl1NccPHiwxR2/63X06FEAoqOjrfaFhYXh6+trPkYIIYRzqwpxCeChhx5i7dq1vP322zzzzDPo9arD0yuvvELr1q156aWX7Ja4lTdOJiYmMnr0aIttnTp14ptvviEyMtI2hRXCCWw+udn8vEf9HjD+rfydEybYtSySuJXBzK0zmbl1ZonHta/dnh+H/2ix7Y5v7mDX2V0lnjsxZiITYyaaX1/Ovkyzj5uV+bzy+PHHH9m+fTtDhw41B0eAjh3VtKdLliyhffv2DBo0qMj3mD17dpkGajdo0KBCA2RqaiqgunwUxt/f33yMEEJUZlU9JkHViEtr167lm2++4ZFHHuGRRx6x2Fe7dm0GDBjAF198wYULFwgJCamw6xalPHFy9OjR9OjRg5YtW+Lr68uRI0eYOXMmX375JTfffDP79u3Dz8/P5mUXwhHc9e74ePhg1Ix0uBIAP/2kdtStC3Zu6ZfErQzSstM4ffl0icfVC6hnte3ClQulOjctO83itYZWrvPKY/HixQBMuObugbe3t/n5lClTin2PEydOXHc5hBAiIQGOHoXoaBUbhbWqHpOgasSljz76CFBj3N566y3zEgJ5Dhw4AKjWxcI8/fTTZGdnl/p6EyZMKLQ17Xq8+uqrFq/btm3LF198AcCXX37JZ599xsSJ15+oC+EsrlyB2bPV86HtPueTZ+ax/Ugc5yd9TF1NUzvGjwcPD7uWSxK3MvD38ifcL7zE40KqW98xC6keUqpz/b38LV7r0JXrvPLYtGkTgYGBxMTEFLq/U6dODBw48LqvY0t5dxCLalVLS0sjMDDQnkUSQpTRggXwyCNgMoFeD/PmwZgxji6V86nqMQmqRlz6/fffAViwYEGRx3h5eRXZ2vbpp5+SkZFR6uvdfffdxSZuFRknx40bx5dffsmff/4piZuoUp5/Hq7ec8HXF2bOdOf5caGc1D4HINezGu5jx9q9XJK4lcH1dP24tptKafl5+ZEwMaFc55ZFamoq586do0uXLua+93lWrVoFUKrg6OixBHnB6ujRo7Rr185iX2JiIunp6XTu3LnCrieEqFgJCflJG6if48ZB//7S8natqhyToGrEpZSUFNLT0xk0aBDLly8nLS0Nf39/q/oUJz09vULKkqdgnOzQoYPFvrLGyeDgYIAyJZZCVAbTpkHDhvD009CsGTz6KEzQPscX9VmfbxjFwCtB1A2yb7kkcRMAXLlyBcBqcHd2drZ5IU5395I/Lo4eS3DjjTcyffp0fvvtN+655x6LfatXrzYfI4RwTkeP5idteYxGiI2VxM3VVIW4pF3tUpWUlFQh71cRCsbJYcOGWewra5zcvn07IItwi6qnRg21PFutWhrHj+vYtSOXJ/jAvH+2NoGmDohLso6bACAkJARvb2/27NljMR7g6aefNs8uVZo7lidOnEDTtFI/HnzwwQqtx80330yjRo1YvHgxe/bsMW9PTU3lzTffxNPTk5EjR1boNYUQFSc6WnWPLMjNDaKiHFMe4ThVIS4FBgYSHR3Ntm3bWLdundX+nJwctm7dWmHXK42yxslDhw6Zk+iCDh06xPPPPw/AfffdZ/NyC2Fv7r6XmHAmmA11bmNQg4k0QN0AWsmtxLo1dUhckhY3Aai7liNGjGD+/Pn06NGDO++8kwMHDrB27VpefvllPvjgA+bOnYuHhwfPPvssNWrUsEu55s+fz+bNahrWffv2mbflrUPTvXt3Hn74YYt6zJ8/n/79+9OrVy+GDBlCUFAQy5cvJz4+nvfee0/uDArhJAqbgKRuXTWmbdw41dLm5qbWOZXWNtdTVeLSO++8w1133UX//v3p27cvrVq1IjMzk4SEBDZv3swtt9xS5Bg+WygYJ3v27MmwYcPw8/Nj2bJlhcbJb7/9lpkzZ9KzZ08iIiLw8fHhyJEjrFy5EoPBwKRJk+jZs6fdyi+ErVwbk7ac2sLFzIusO7WSfVpt83GzedJxcUmr4lJTUzVAS0pKKva4zMxM7cCBA1pmZqadSmZ7RqNRu3TpkmY0Gkt1fHp6ujZ+/HgtLCxM8/Dw0MLDw7WZM2dqmqZpX375pRYSEqJ5e3trBoPBlsW2MGrUKA0o8jFq1KhCz9u+fbvWv39/zc/PT6tWrZrWuXNn7dtvv7VpWZ3pM5STk6OtWLFCy8nJcXRR7E7qXjnqPn++pun1mgbq5/z5lvtPndK09evVz9JISkrSAC01NbXCy1rRShOXnOn7pCK5alzauHGjNmDAAC0oKEhzd3fXatWqpXXo0EF79tlntX///dduZS9o+/bt2i233KL5+/sXGyc3bNig3XPPPVp0dLTm7++vubu7a2FhYdqgQYO01atXl+paRqNRO3funPbvv/9Wuc90SSrT93JFq0x1LxiTdDpN++ADTXthzQsar6H1eBC1A7T9NNdCgk2ayVT8+9kqJuk0LW9Oy6opLS2NgIAAkpKSqFmzZpHHZWVlcfz4cRo2bGgxzXBlZjKZyjUQuqqwd/2d6TNkMBhYuXIlAwYMwMPOU9U6mtTd+euekAAREZZj2dzc4MSJ8t/BTE5OJjg4mNTUVPz9K2ZGQ1spTVxypu+TiuTKccnV656UlERSUhKNGjWqUp/pklSW72VbqCx1LywmAXT8pDs7z//Jqi/hlji1baTuS/a3HcG6dWocXFFsFZOkq6QQQgi7kglIhBBCOIvCYhLuWey9sIP2Z/KTtty6Dfhk3zB8a9i7hPlc65aPEEIIh5MJSIQQQjiLwmKSru4ODFoOk/7I3+b+4vP41nBsm5ckbkIIIewqbwISNzf1WiYgEUII4SiFxaQ7n9hM0wsw5ODVg8LCoIJnQi8PSdyEEELY3Zgxakzb+vXq55gxji6REEIIV3VtTEqtuZbnNxdIlJ5+GpxgbKaMcRNCCOEQdetKK5sQQgjnkBeTMnIyOLl3EyP+Udu1wEB048YBsH8/fP89bN0Kr70GdlzJA5AWNyGEEEIIIYSLiouD0aPh66/h/HnYfno7T20y4H513n3dhAng5wfAjh0wZQr89hts3Gj/sto1cZs+fTqdOnXCz8+PWrVqMXjwYA4fPlzsOQsXLkSn01k8XGkaWVvJyYG0NPVTCCGEcCSJSUIIR1m9GhYuhBEj1M+btAY8ukd1SjT6VIfx483HFmxh+/df+5YT7NxVcuPGjTz++ON06tSJ3NxcJk+eTL9+/Thw4AA+Pj5Fnufv72+R4Ol0OnsUt8q6cAHi4/NfR0RASIjjyiOEEMJ1SUwSQjjS+vX5z/v0AaZMQZebC4Db089AgfU2GzeGb76Brl3Vd5W92TVx+/XXXy1eL1y4kFq1avH333/Ts2fPIs/T6XSEhYXZunguISfHMkCCeh0QAJ6ejimTEEII1yQxSQjhaF9+CY89pro+tvU6CF99pXYEBsLEiRbH6vUwbJgDCnmVQycnSU1NBSAoKKjY49LT04mIiMBkMtG+fXvefPNNWrRoUeix2dnZZGdnm1+npaUBavV2g8FQ5DUMBgOapmEymTBZrcJXOWmaZv6ZV6esLB1g3WKZlaXhnteZt4oorP62ZDKZ0DQNg8GAW96csg6S91kv7jNfVUndXbvuzqg8cakqxiSw/l6WmOQaCtbdGWKkPcn3svPX3c0NundXD4a9ZF6N2/jMM5iqV4dylN9WddZpeb9NdmYymbjjjjtISUlh8+bNRR63detWjh49SuvWrUlNTeW9995j06ZN/Pvvv9QtZDqy1157jSlTplhtX7x4MdWrVy/yOu7u7oSFhVGvXj08q/BtPoNBR3y8P5aBUiMiIg0Pj6oVJO0tJyeHU6dOkZiYSO7VJnYhhH1cuXKF++67j9TUVPz9/R1dHAvliUsSkyQmVTUSI4WzCzh2jF5XW9jSA3xZO/dTqFb0UK7i2ComOSxx+89//sOqVavYvHlzoQlYUQwGA82aNWP48OFMmzbNan9hdzbr1avH2bNnqVmgj+q1srKyOHXqFA0aNKgyk59omsbly5fx8/OzGBeYnKy72jVFhwqQULNm1QuQRdXfVrKysjhx4gT16tVz+GfIYDCwZs0a+vbti4eHh0PLYm9Sd9ese3JyMrVr13bKxK08cakqxiQo/HtZYlLVp2kaycnJXLhwgfr161epz3RJXPl7ubLVXX/H7bj9uhqASXdU59XvknHTF946vG8fbNum59w5eOkl6xZ0W8Ukh3SVHD9+PD///DObNm0qU9IG4OHhQbt27YiNjS10v5eXF15eXoWeV9yHxmg0otPp0Ov16PVVY5WEvK4YefXKExKixg9kZ4OXl+7qOIKqF0SKqr+t6PV6dDpdiZ81e3Kmstib1N216u7M9S1PXKqKMQkK/16WmFT1Fay7K34/gWt+L+dx1rpfuaKm9u/TB3q6/YnH1aTtpD+cGjYAb6+ibzDcdhskJkJ4OEyZYp3c2aq+dv3m0DSN8ePH88MPP7Bu3ToaNmxY5vcwGo3s27eP2rVr26CErsPTUy1J4ew9cL766ivGjRtHx44d8fLyQqfTsXDhwhLP27FjB7fddhsRERH4+fnRtWtXvvvuu2KPHzBgADVq1MDHx6fE44UQQlScyhKToPxxSQjhXDZvhnfegf79TJwe/rR5+9Qb4eamA4o9N2/OxPPnwZ59F+3a4vb444+zePFi/ve//+Hn50diYiIAAQEBVKtWDYCRI0cSHh7O9OnTAZg6dSpdu3YlKiqKlJQU3n33XeLj43n44YftWXThIC+99BLx8fEEBwdTu3Zt4q+dfqwQ69evp3///nh7ezNkyBCCgoJYvnw59957L6dOneLpp58u8vhhw4bh5+fHsmXLijxeCCGE6ypPXBJCOJ/ff1c/h/Etjc5vB2B/CCxsC1Mi+xV77jPPQEYGhIaquUzsNd+OXVvc5syZQ2pqKr169aJ27drmx5IlS8zHnDx5krNnz5pfX7p0ibFjx9KsWTMGDBhAWloaW7ZsoXnz5vYsunCQ+fPnc+LECS5cuMCjjz5a4vG5ubmMHTsWvV7Phg0bmD17Nu+99x579+6lcePGTJ482SLIFjx+06ZNzJs3jxkzZhR5vBBCCNdW1rgkhHBOzz4LSxdd4UOfF8zbnu4PzWq3JNw/vNhz778fHnkEBg2yX9IGDugqWdjjwQcfNB+zYcMGiy4Hs2bNIj4+nuzsbBITE/nll19o166dPYvtcjIyMpg6dSpNmjTB29ubqKgo5syZA8CWLVvQ6XQsW7bMLmXp06cPEWVY4XDdunXExcVx33330bZtW/P2gIAAJk+eTE5ODosWLSr38UIIIeyvMsclIYRzCgmBu0/OpGbGKQBWRsFvUdA/sr+DS1Y01xodK0p05swZOnXqxNSpU+nQoQOPP/446enpPPbYY2zfvp3XX3+dtm3bMmTIEEcXtVAbNmwAoF8/6ybu/v3VL+LGjRvLfbwQQgj7quxxSQjhpM6cgbfeAsCo1/H01Xzt1qhbHVio4jl0AW7hXEwmE0OGDOHgwYMsX76cO++8E4Dbb7+d3r17M2vWLFatWsWKFSuKnMp49uzZpKSklPqagwcPtmjpul5Hjx4FIDo62mpfWFgYvr6+5mPKc7wQQgj7qQpxSQjhpF56SQ1UA+Z3cuNQSC41q9WkZ0TPUp1uNMKFC+DuDsHBtixoPknchNmPP/7I9u3bGTp0qDk4AnTs2BGAJUuW0L59ewYNGlTke8yePbtMY8IaNGhQoQEyNTUVUF0dC+Pv728+pjzHCyGEsJ+qEJeEEM5n9Rs76bdwITrA4OfDiz1VAjeoySA83Eqeyn/TJujVS80o+fzz5oY7m5PErbQ6dlQLNjizsDDYubPcpy9evBiACRMmWGwvuFDmlClTin2PEydOlPv6QgghSskFYhJIXBJCVLzLKUaCXxqHDjWPv/6VV1l8Zxu+P/A9w1sOL9V7BAXlLwNw7pytSmpNErfSSkyE06cdXQqb2rRpE4GBgcTExBS6v1OnTgwcONDOpSqbvJazolrJ0tLSCAwMLPfxQgjhFFwgJkHViEtCCOeS8OIndGAXAKeDWhE+4Un6eXjQr4QlAAqqXRs6dVLLAdizgV4St9LKW2nPmV1HGVNTUzl37hxdunRBr7ecs2bVqlUApQqOjh5LkDdW7ejRo1azjyYmJpKenk7nzp0LPb5Dhw4lHi+EEE6hisckqDpxSQjhRM6cockXL5pfHntuLuEeJXeNvFbNmvDXXxVZsNKRxK20rrO7h7O7cuUKgNXg7uzsbPMC1O7uJX9cHD2W4MYbb2T69On89ttv3HPPPRb7Vq9ebT6msOOHDRtW4vFCCOEUqnhMgqoTl4QQTuTJJ9GnX1bPx46lx/PdHFueMpLlAAQAISEheHt7s2fPHovxAE8//bR5VsXS3LE8ceJEkev1lbSGX0W4+eabadSoEYsXL2bPnj3m7ampqbz55pt4enoycuTIch8vhBDCPqpKXBJCOIlVq2DpUvU8OBjDG9O4Z+k9/Hf3f0m+kuzYspWStLgJQN21HDFiBPPnz6dHjx7ceeedHDhwgLVr1/Lyyy/zwQcfMHfuXDw8PHj22WepUaOGXco1f/58Nm/eDMC+ffvM2/LWX+vevTsPP/ywRT3mz59P//796dWrF0OGDCEoKIjly5cTHx/Pe++9R4MGDQo9vmfPngwbNgw/Pz+WLVtW6PFCCCHso6rEJSGEE8jIgMcfz389Ywbr0/ay9MBSlh5YyrCWw/jmrm8cV77S0qq41NRUDdCSkpKKPS4zM1M7cOCAlpmZaaeS2Z7RaNQuXbqkGY3GUh2fnp6ujR8/XgsLC9M8PDy08PBwbebMmZqmadqXX36phYSEaN7e3prBYLBlsS2MGjVKA4p8jBo1qtDztm/frvXv31/z8/PTqlWrpnXu3Fn79ttvi7zO9u3btVtuuUXz9/cv1fGFcabPUE5OjrZixQotJyfH0UWxO6m7a9Y9KSlJA7TU1FRHF6VEpYlLzvR9UpFcOS6Vte5VidFo1M6dO6f9+++/Ve4zXRJX/l52qro//rimqYkgteyYGzXNZNLG/jhW4zU0XkP7/t/vy/yWn3+uaQMHalrHjpp2+LDlPlvFJGlxE2Y+Pj58+OGHfPjhh1b7RowYwYgRI+xepoULF7Jw4cIyn9e5c2dWrlxJWloa/v7+VgPbCzs+b7C7EEII51CV4pIQwkHWrYOPPwYgW1+Nlls/w9TYSOrDKwCo7lGdW6NvLfPbHj4MP/+snickQOPGFVXgoskYtyokJwfS0tRPIYQQwtEkLgkhHCotDR56yPzyFa+3iSWaC77rSc66AMCA6AFU96he5rcODVU/9Xq4eLFCSlsiaXGrIi5cgIKTZkVEqKlKhXNJSICjRyE6GurWdXRphBDCdiQuOb+cHMjKAm9v8PR0dGmEsIFnnjF/ERl79sK92+N03wzxnRZwdW5JhrUYVvT5xRg9Gu67D4KDwc2tgspbAkncqoCcHMvgCOq1v79jyiMKt2ABPPIImEzq7sy8eTBmjKNLJYQQFU/ikvMrLLEOCXFceYSocKtXw2efqee+vrgt/Jw3GupJupJE+MwfwAgh1UO4vcnt5Xp7O82HZEG6SlYBWVmFb8/O1hW+Q9hdQkJ+0gbq57hxarsQQlQ1EpecW1GJtXRpFVXGhQuqSSzPe+9Bw4YAfPXPV+QY1Yd9ZJuReLpVnuZmSdyqAG/vwrd7eWn2LYgo0tGj+UlbHqMRYmMdUx4hhLAliUvOrejE2r7lEMImTCYYNQrOnlWv+/VTd88BTdNYsHuB+dAx7SpX1yfpKlkFeHqqLg7Xdnnw8IDMTMeVS+SLjlbdIwsmb25uEBXluDIJIYStSFxybkUn1vYthxA2MXOmWmwboFYtWLSIzCzV2n/qylEOXDgAwA31bqBZSLPrutTPP8Pp0+r5uHHX9ValIolbFRESAgEB6m6Zl5cKmte28AjHqVtXjWkbN061tLm5waefygQlzkYmjxGi4khccl5FJdYyQYnzkbhURtu3w6RJ+a+/+grCwlj6BTz8MHTp0pjFk08S57uI5iHNr/ty48bBmTNQu7Ykbg6haZW3G4enp3zpOlJJn50xY6B/f9U9MipKvoCdjUweUzlpGuiq8LCpyhyTQOKSMysssRbOReJSGaWkwLBhkJurXr/wAvTtC8DGjWAwwObNMK1aOPf2mFwhlwwLU4nb+fP5/0+2JGPcrnK7Oo+nwWBwcElEZZX32XErZk7YunWhVy9J2pyNTB5TuSQlwYQJ0LkzjB/v6NLYhsQkYQ+enuDnZ5+kLffqH9PFxUiRT+JSGZlM8OCDcOKEeh0TA1OnmneHh6ub5p6e0KVLxV322WfVxJU//GCfHgXS4naVh4cHXl5epKam4ufnh64q38IVFU7TNFJTU/Hy8sLDw8PRxRFlVNzkMZJkO05mJvz9t+qCEhmZv71aNfj4Y/V/VFXHS0lMElWJpmlkZGRIjCwDiUtlNG0a/O9/6nmNGvDNN2pQ7VVTp8Irr+WSesmdatUq7rLDyrcEXLlJ4lZAcHAwp0+fJiEhgYCAADw8PCp1sDSZTOTk5JCVlYXe1m23Tsge9dc0DYPBQGpqKunp6YSHh9vkOsK2ZPIY5/Pbb3DbbarHy0svqZicx8cH2rSBXbvU/1lVncK8qsUkcO245Ip1z4uRKSkppKam0qhRI0cXqdKQuFQGK1bAa6+p53q9StoiIiwO2XlmJwMXD+TBtg8ytv1YIoMird6mMpDErQD/qyuDJiUlcTpviphKTNM0MjMzqVatWqUP9uVhz/p7eXkRHh5u/gyJykUmj3GMAwfUjFxbt6rErGXL/H1Nm+YPU9i2zfrcr76C0FAICrJPWR2hqsUkcO245Mp19/T0JCkpiTZt2ji6KJWGxKVSOnAAHngg//X06XDLLVaHvf3n25zLOMfbf75NwxoNJXGrKvz9/fH398dgMGA0Gh1dnOtiMBjYtGkTPXv2dMmuCfaqv5ubm0v++1Y1MnmM7WganDoF9etbbl+zBp5/Xj3v29cycatXT40HbdQIbrrJ+j2bXd8MzpVGVYpJ4NpxyVXrnjembf/+/Q4uSeUjcakEly7BoEGQnq5e33uvGnR2jcNJR1h2YBkAYb5hjGo7qkKLkZurJifx8FCT/tiSJG5F8PDwqPRfrG5ubuTm5uLt7V3p61Ierl5/UXZ160pgrGgvv6wGbp87p9ZCDQvL3xcTk/981y7L83Q6WL/ePmWsDKpCTALX/l525brLJDvlJ3GpCNnZMGSIympB9Z9fsMBqmuHERGj7xLtoLdQMvU91fQpv9yIWMiyHP/6AG29UNyiffRbeeafC3rpQdu1kPX36dDp16oSfnx+1atVi8ODBHD58uMTzli5dStOmTfH29qZVq1asXLnSDqUVQghRGseOwddfw7vvWu8zGFTSBqpLZEFt28L8+fDvv6pLkBBCCFGivBkkN2xQr4OD1Tg3Hx+rQ3/4/TRZTRcB4KUF8GjHRyu0KDVrqqQN8mOdLdk1cdu4cSOPP/4427ZtY82aNRgMBvr160dGRkaR52zZsoXhw4czZswYdu/ezeDBgxk8eLA0uQshhAMUtqzYLbfAiBFqEpHsbMt9MTFqgq/+/cHX13Kfp6fqCtS8ue3XvhFCCFFFTJoE336rnlerpgZLN2hQ6KHLz84GN9XiOzj8Mfy9KnYugtq11fICd9wBHTpU6FsXyq5dJX/99VeL1wsXLqRWrVr8/fff9OzZs9Bz3n//fW655Raevdpnddq0aaxZs4aPPvqIuXPn2rzMQgjh6tLT1Vi0bdvUOIslSyz3x8SoqatzclSXx4JdIG+7DZKTJTETQghHSUuDffvghhus9x07psYSVxoff5zfH1GvVwlcEQuzXcq8xLZclSt46r2YPnhChRcnMLDwCbRsxaFj3FJTUwEIKmZasK1btzJx4kSLbf3792fFihWFHp+dnU12gVu+aWlpgOpf7Wp9rPPq62r1zuPK9Ze6S93LIyMDdu7UUbOmZjFRiIcHfP21O6mpOs6c0cjJybUYRnDXXToiInR07arRrJnGtZc3GtXDlpz5/1viUj75/ZS6uxpH133MGDe++06HlxckJOTiXWB41/790L69B+3aaTzzjJGhQwvpUnEdKrruuu++w+2JJ8gLP8YPPsB0661YBZ2rPtj2Aek5auKS0W0fpG6NILv9P9jqOg5L3EwmE08++SQ33HADLQv+hXCNxMREQkNDLbaFhoaSmJhY6PHTp09nypQpVtvXr19P9erVr6/QldSaNWscXQSHcuX6S91dU3nqfvhwIJMmdcdk0nPrrccZN+4fi/0NG8awd28Inp6XWbp0M76+lkGpQwcVOzduvK6il9uVK1ccc+FSkLhkTX4/XZPU3f4SEtqRnV2f7GyYPn0XXbrk//385ZfNgMbs3q1jw4YD+Pgct0kZKqLutbdto+M776C7urDdkbvu4mDdulDEvBeXcy/z3sH3ANCjp11mO7vOkWGrmOSwxO3xxx9n//79bN68uULfd9KkSRYtdGlpadSrV4/evXtTs2bNCr2WszMYDKxZs4a+ffu63AxW4Nr1l7pL3Qur++HDsGKFnm3bdDzzjIkbbsi/u9q9O7zwgrqPefZsAwYMsJzGrFkzCArKJSCgGtDXpvUoj+TkZEcXoUgSl/LJ76fUXepuOyaTdbd0nU7HgQMaQ4aYuOee9rRokb8vKUnH8eMm9u7V8eqrzahVq2LXWamouutWrsRtxgxz0mYaM4aGn3xCw2LWQ8wx5pAYlsjrf7zO7Y1v56HbHyr39cvDVjGpzInbG2+8wUsvvcRXX33F/fffb7V/0aJFPPjgg7z55ptMmjSp0PcYP348P//8M5s2baJuCXOchoWFce6aaVrOnTtHWME5pQvw8vLCy8vLantVmUq5PFy57uDa9Ze6u2bd3d09iI/3oFEjyyC+e7eanh+ga1c9vXrl76tZE+66S/XX795dZ/Vv17ix7ct9PZz5/1rikjWpu9Td1di67rt2qXWolyyxXBPzttvg9Om89fTcLM4ZM0Y9Tp+G8HDLsq1dCxcvwtCh11+266r7mjVqfba8roejRqGfNw99CQOnPTw82DbrGe4MfZDuDUw2/bf/73/h++/V0gNffw1Nm9ouJpV5uHjM1VHnf/31l9W+y5cv88ILLxAZGWk1Lg1A0zTGjx/PDz/8wLp162jYsGGprrd27VqLbWvWrDGXQwghRL7vv48mPNyd6Gg4cMByX8Gvzb17rc9dulRNyz9ypG3LKIQQouJs2wa9eqnv/AcfVAtC53FzU4/ihIdbvr54UcWBe+5x8FItq1ap6RrzxggPG6bWaivFbFdnzsCyZbDwk2Dmzqhl02IePap6bO7aBadO2fRSZU/cOnfujJubG9u3b7faN2XKFBITE5k5c2ahdxcff/xxvvrqKxYvXoyfnx+JiYkkJiaSmZlpPmbkyJEWLXUTJkzg119/ZcaMGRw6dIjXXnuNnTt3Mn78+LIWXQghqoTYWPjii/zWs4L0eo2kJNV95NqZriIj1XmHDsF339mhoEIIIWyuUSM1LT2oJO3ixet7v6+/VokPwAcfWC/zYhdLl8KgQZCVpV7feacKYCVkodm5qrB796olZ0AtWWNLeZ0A3dwgJcW21ypzV0lfX19atWrFnj17yMnJwfPqv8rhw4f54IMP6NevH3fccUeh586ZMweAXgX75wD//e9/efDBBwE4efKkRfNnt27dWLx4MS+99BKTJ08mOjqaFStWFDuhiRBCVBVGo3WcGjkyfzHrCRPU2qN5mjS5SFCQRteuOq7tUa7Tqa40Qgghqo5ateD332HqVHj/fbjeOY/Gj1ctR7/8orpMFtIWY1v//S88/LAatAeqv+ZXX6kpjothMBro+FlHetTvwdTeU0lODmb9etV10ZZGjYLhw9WQA1svfVOuyUm6devGnj172Lt3L506dQLgySefRNM0Zs+eXeR5WmErt15jQ94q6AUMHTqUoRXRyVYIISoBgwH+7/9UclazJqxbZ7m/a9f8xG37djWGIU+zZhc5ezYXT0/XHEcihBCuqF49+OyzinkvnQ7eflv16vDzq5j3LLXZs+Gpp/JfP/SQ6q9ZUn9PYM7OOew/v5/95/dz7NIxfh3xK7ffbrui5gkIsP018pQrL+zWrRuAubvkjz/+yK+//sr48eNp1qxiZ6QRQoiqKi1N3c28dsiwhwesXg3//KO6O167HMyQIfD66+rcazowoNdDMRNtVVomzcTJ1JOsP76e+bvmM+n3SWTkZDi6WEIIYXfbt8Nbb0Ep2kPKTacrPGm7Zr7AimM0qi4kBZO2CRNUNlqKpO1w0mFe+P0F8+upvafaopQOV64Wt4ITlGRnZzNx4kRCQkJ49dVXK7RwQghRVR08CC1aqMB7zz1qJrCCunaFkyehSRMVKAtOwNu9u3oUlJAABw/qSErypjLLys1i7bG1xF2KI+5inPp5KY5jl46RY8yxOPa+VvfRKrSVg0oqhBD2Fx+v5us4f16NV/70U/t0ZTQYYOJE+PZb+PtvqF+/5HMSEmDfvmBat4Zi5yNMT4f77oOffsrf9sor8NprpboTmWPM4f7l95OZq+bMeLTDo3QO71xyASuhciVujRo1IjQ0lO3btzNjxgzi4uKYN28eNWrUqODiCSFE5RUbC998o7o1PvqoCrZ5oqPVOISMjPxujwXNmKFuNPr6lnydBQvgkUfAZHJHp+uH0WjkkUcqrh4VKTUr1SIpa1+7Pf0i+5n3Z+VmMfCbgaV6r7hLcZK4CSFcyrp1KmkDOHHCfj0sXnkFPvpIPb/zTtUbpLghZyouuWMy3cCrr2rMm6eWHrBy+jTcfrtarwbA3V1low+Vft21KRum8PfZvwFoUrMJqUtn8MpfMGCAuglqa0ajSmjT0yEoqGKWUChKuRfgjomJ4X//+x9vvPEG7dq1Y0yh/xtCCFH1mUxw5Ag0aADeBRq8jh5VwQ7UOmgFEzd3dxgxQnVtjImxXji1Tp3SXTshIS9pU681Tcdjj7kxYIBlK5297U3cy57EPeYWs9iLscRdjCM503JR0kc7PGqRuNXwrkFQtSAuZuZPi1bNvRqNAhsRGRRJZODVR1Aknep0slt9hBDCGYwerbowTpumprvPmznR1p59Vs1GnJAAjz1WfNKWH5dUVmky6Rg3Dvr3vyYu/fGH6nKSmKheBwSoSt18c6nL9Uf8H0zfPB0Ad707s3t8za3/p2ZnWbkSdu4sUzXLbcQI9bNrVydN3Lp168aKFSu4cuUKH3zwQYkL4QkhRFX0/vswZQpcugQbN0LPnvn7Ct7pO3jQ+ty5c6//+keP5idteYxGHbGxtkvcDEYDJ1NPmhOyi5kXeannSxbHvP3n23yz/5sS3yvuUhyapqErcNt4Wu9pVHOvRlRQFJFBkYT5hqHXSYwRQgiAu+9WrV6lGPpVYYKCYMUKyMyEziX0Qiw8LpEflzRNBc9nnlE7QN35/OUXaN681GVKzUrlgR8eQEMN9pvaayoZsR3M+wcMKPVbXRc3N9WD5soVuHzZttcqd+KWt3j28OHD6X7tYAshhKhCjhyBzZthzx4Vawp2TfHzU0kbqC6PBRO3wED44Qdo1Uqts2ML0dGqpa5gkHRz04iKuv7+M8lXktkUv8lqvFl8SjxGzZh/PZ0bz9/wPB5u+bdgIwMjrd6vrn9dixazyMBIWtRqYXXcY50eu+6yi4p16pTq9nv8OLRpo7r+CiHsQ9Osu0TaM2nL06qUPdMLj0sQFYXqTzh2rOpbmOfmm9UXTEhIqctiMBq45/t7iE+NB6BnRE+eu+E53PSq9+Wvv6reLPYye7bqSRMaatvrlCtx0zSNWbNmUb16dd55552KLpMQQjiMwWDdBWTiRHUjENQ0/dHR+ftiYlSsiYmx3J5n8GCbFRVQdy/nzYNx49SNS73exCefmKhbt/ivd03TSLqSZJGUDW46mNahrc3HHEw6yJDvhpRYBqNmJD41nqigKPO2gY0HElw92JygNQxsiLd75Z44xZUtXw7PP6+e33GHdeI2Z4763Rk3zgFrPglRhZ0/DwMHqnHPPXo4ujTWjh9XXfsL/t7nxyUNo1GHm5vGp5/qqHt2B/S+TzW95Zk0SfX7LGMmqqERUl0leoHegXwx+Avc9Oo96tQp0xC5CjF2rH2uU67Ebc6cOWzZsoW3336buo4cRCGEEBVA01Sf/T/+UHcJ//nHcn9MTH7itnWrZYLWtKma9dGRU/CPGaPGDhw6lEt8/FpGjrzJYv8f8X9wKOmQucUsL1FLy06zOK5mtZoWiVthrWb+Xv4WLWZ5z+v4WQ7K61K3C13qdqnAWgpHGj9e3RDfvl2NXynIaIQ331Tbv/kGfvyxTDfOhRBFMJlg5EjYsUMt/fLVV2qhZ2egaWqd7AkT1I2cd9+13D9mDNx0Uy5ff72d+4d1pOF3M6Hbq5Cbqw7w94dFi8p9d9PTzZMv7vyCiIAIbo2+lYgaEddXoUqi1IlbQkICX331FUeOHOHLL7+ke/fuPP3007YsmxBCVKjUVPWHp4cH9O6dv12nU2up/fuvep6aarmg5sCB6mZgTAx0umY+DEevmZaVm8XxS8eJuxLHkWpHiCWWkVgmbo+vfJx95/eV+F5xl+IsXof5hjGt9zQa1mhIZFAkUUFR1KxW02I8mqiaru2a5eYGX38NFy6ooSgF/fVXfjKn09l3MVohqrLLlyE7Wz0PCYGbbir+eHs6cQL+8x/IyVGtgbffbjlUAFTLW5fg/USMnqTGG+Tp0kV9oURa3xwsC71Ozxs3v3Fd71HZlDpx++2335g0aRJBQUEMGzaM999/HzdHdLAVQohyOHsWwsPVH6R9+lgmbqCSsr171fids2ct//hs00Y9HOlk6km2ntpqNd7sdNpp88BsgHre9Xif9y3OjQyKtEjc3HRuRNSIsGgxiwqKok2oZSV1Op3VpCOi6tu6FV54QQ1BqV07f3tkZOF/Z8XEqHOeegq+/95+s9wJUdUFBMDvv8Mbb0C3brYfP1UWDRuqlvZnnlGta+3bX3OA0Yh+1ix6v/wy+pyra3Dq9fDii/Dyy8VPS1mEuTvn0iy4GTc2uNFqX96aqD16wLBhUKtWOSp1HTQNsrLylwSwlVInbg899BAP2bvDqBBClMGJE7BggZ6ff44hKUlnsWZMWJj6I/TMGdXqZjRadql/9VV45x01M5S9mTQTZy+ftUjKJnSZQIhPfn+zlUdX8p9f/lPieyVmJ2LSLKfzeqjtQ/Rr1M/cvbF+QH2LiUSEyJOQoGarO3cOOnaETZtKd1O8a1fYssXxLdBCVDVubvnLyjibp56CDh1UN04L+/bBmDG47diRvy0iQvX1LMeEhibNxAu/v8C7W94l0DuQLWO20DS4qcUxf/2lbhx9/73qrv3772Wvz/W47778+VaOH1cTl9lCuWeVFEIIRzGZ4MABFQcKfjmePw+vv+4G1GLdOpNF4qbTwahRqutJTIx14maPMTm5plzWxK2xajU7dukYWblZFsf2bdSXG33y7yoWNt4suHqwxXizCP8Izh86j6ZpFsfd3uR221RIVDkpKfktZk2aQP36pT/32qQtN1dN5tO7t7oTLoSoWvT6a5K21FS1Ps6HH5rHsmk6HabHH8dt+nTw9S3zNbJysxi1YhTf/fsdAJeyLvHzkZ+tErd16/Kf562pZk8+PvnP09MlcRNCCADmz4enn4a0NDXT3Z135u9r2xa8vDSys3UcO2Z97ptv2rZsl7Mvc+zSMXNiFl0zmsFNB1scc8e3d5Bryi3xvWIvxlp0B2kd2prpN0+3SNQCvC0HExkMBlYmrDTPrCVEWbVsqSZCePpptfRFOXozAWpczl13qUl9Pv9ctXY744x4QjibLVtU18hPP7XdWpwVzmRSE4288IK6g3qV1qQJf4weTczEibiV48sk9mIsI38YydaErYAa0/bxgI95tKP1eiSTJsGgQapR7667yl+V8mreHG68USVstpxZVxI3IYTTOXxYddHavh0++gi8C8wiHxKikjZQ42oKJm6enrB8uZGEhHU8+GBvwDaLNh+4cIC/z/xtNUvj+YzzFsfd0+Iei8TNXe9OgxoNiL2YPxWyp5snjQIbWY0361C7g8V7hfqG8kL3F2xSHyEKCg1Vf/xcD0/P/PE4mqa6KAshipeRoXqGxMaqmyh//FH6tdMcZu1albDt3GnelOPmjecrk8idOJFLa9eW+S2NJiMfbP+AF9e9SGZuJgDVPaqz5O4lDGw8sMjzmje3/Q3aokycqB55kpNtcx1J3IQQDpWZCdWqWW6bPl3dvAM16LngIppdu6q79zExqm/9tfr21Vi5MrPcY21yTbmcSj1lTshOpZ1iWu9pFjMpfrLjEz7e8XGJ71UwQcszqfskTJqJyECVoIX7h6PX2SbBFMJRdDqYO1f9ITpunPVkQEIIa8ePw5Ur6nmzZioRcVq7dqmEbc0ai83fcxdPG2fwQZsIBngZyvy2+8/v55GfHjG3sgE0qNGApUOX0rFOx+sudmUniZsQwiGefBJ+/VW1np0+bTk+JiYmP3HbutUycQsNtT6+PNKy09hwYoO5tSz2Yixxl+I4kXLCqivjU12fomb1mubXhY03q+1b29xaltd61iS4idVxD7WTSZ6Ec3njDTUc5ZlnLMdpXC8Pj/zB+kKIkrVsCfv3q67Kzz9f5jWp7WPPHnj9dVi2zHJ7q1b8dusshr5zM126qDGy5fHoz4+akzYdOv6v8//xxs1v4OtZ9vFxVZEkbkIIm0lOhm3bVPf326+ZH+PgQdUlEiA+3nJtqL591WKeMTGFTDFM6ZK2i5kXiT8fb07M+jTqQ9e6Xc37E9ISGPTtoFLVI/ZirEXidnOjm5nRb4a5a2OjwEZU93DAdJRCXKdTp9TfYFlZsHAhHDpk2/EZALm5MvWks+vRQzWo6PVqQqeCTCY1+YK/v2PKVtUFBqpxodf66/Rf7E3cS4YhA4PRgMFkIMeYgw4d7np386N+QH2Gthhqce659HN4u3vj7+Vf/nU4t29XXxY//2y5vUEDmDYN7ruPvjo933WEIUNU0mkoocEtPScdN50b1Tzyu91M6j6Jgd8MJDooms8HfU73+sXPQvnZZ6pII0eqNVdt/f3laJK4CSFsIiNDtY4ZjdCunXXiFhMD69erxOziRcvErVEjdfe/NLYnbGf/+f3m8WaxybEcvnCYjD0ZFsdpmmaRuDWs0dDqvXw8fMwTfxQcb9YspJnFca1DW9M6tHXpCiiEE9u0yTz5G3fdZfs/er7/XseECX1o0QKaNi35eGE7GRnw3/9CixbWXVmzs1WXPZ3OejH2devUJBBDh6oxPa3lq7Dckq8k88+5fzh68ShHk49y9OJRjl06xuWcyxyfcNzi2K/++YoP//qwxPfsXr+7VeJ255I72ZqwFQ+9B7V8ahHmG2Z+1PGrQ7hfOOH+4bQObU39gAJTyRqN8NNPMGuW+rIoKDQUJk9WfaGvfnHoUJ+LomiaRtylOLae2sryQ8v5NfZX5g2cxwNtHjAfMyB6AAvuWMDwlsMtErqiLFigcsoff1RrsTrq87h7txrmcfmymtXylltscx1J3IQQ5ZaQoMaxbN0KAwao7h15fHxU//x9++Cff9QfCQW7YT31lOoeX3DikWtl52ZzIuWEebyZSTMxoesEi2Oe//15NsZvLLGssZcsx5tV86jGO33eIdQ31Ny9sZZPrfLfjRSiErr/fujUSd0wf/FF215r4UIYPdodcGfUKBObN5d/1kpxfY4eVTfPkpOhZ0/rxC06WrXCenqqv93dC/y1uGCBSuoWLVItHJK4lV7cxTgW7V3E7sTd7EncQ0JaQpHHXs6+jJ9X/pzyNbxrlOoahXUpTM5UM2UYTAZOXz7N6cunCz339d6v82LPF9W6IF98gWn2LPTHT1gckxFWk/hx95J+/z14+wfinR6Pd5Y3dfzq4K7P/6AcvHCQnad3su7cOlb9so7YtH/5++zfpGSlWLzfsoPLLBI3nU5X6iEFKSmq1wBAmzaO/SwmJ8PSpep5+/aSuAkhHCg3V/W7Dw+3XO8sK0uNjwF1w61g4gbwwANw9qyaUER/zfwbAQVmsj97+Sx/nvrTYm2zuItxnEw9iUb+mmRhvmFWiVtkYKRF4qbX6anpXpOWdVoSXTPa3ILWKtR6aq5nb3i2bP8QQlRBjRvDl1/a/jp33w1vvKERG6sjIkK16kji5hiRkeq7PDlZNaQcPKgmw8jz9ddFn1u7tvr+9vCAO+6w3Hdt65wru5h5EXe9O9X0+a1GZ9PPMm3TtGLP89B7EO4fTkpWikXidkeTO6gfUB8fDx883TzxdPPEw039AuWacjGajBhMBoKrB1u9Z6+IXtQPqM+FjAucyzjH+YzzmDST5UEatDmeCf8dDUuWQGamxbzMB4NhRgx80SYZg+4TWPyJxemnnjpFXf/89Qs+3/05721972rFC69rqE9oob1fSqtGDTh5UrUC55a8yo5NFVy3LT3ddteRxE0IUaxvv4WHH1YtZvPmwdix+fsiIyE4GJKS1IQh13r2WdU14lzGOXZdyE/IRrcbTYMaDczH/XHyD+79/t4Sy5KYnkh6TrrFHcXhrYbTrnY7c9fGcJ9wfl/9OwMGDMBD/ioUwmn4+sKiRUa+++4f3nmnFZ6eMpuqvRiNlhNd6PX5EwI++6xl0laSmTPVUKeDB/MXa88za5aaFX72bKhVq0KKXmlomsbfZ//mx8M/8mvsr/x99m8+vPVDxrbND5od63TE082THGMO/l7+NPRuy77f22A614zIwGh+XRxNw6C6ha7F2bFOx3LPqvjp7Z9avDaajCRnJnPm8hmSj/6D7/c/0uCnPwg9/obVub81glkxsDoStGJ+Zb3dLbvP1ParY3VMbd/adKzTkQ61O9C7YW9uqHfDda876uamxsU7Wps2cOKE+p7z87MeG1pRJHETQnD4sFqKZds2FZSDC9ywq1tXJW2g9hdM3HQ6+OEHNT4tPFzjt7g1xF2MMy9CHXsxlmOXjpFhsBxv1jasrUXiVtgsjYHegYWON/N0s/xLoU+jPvRp1Mf82lDSaGhR+eTmqubdYh668+dLfh9hdvIk1K9f8nEVrVMnjQsXTqHTOfviVFXH4sWqZ8TmzWriizyjRqlHeVSvbr0cy4ULMHUqpKaq8cu7d0NYWPnLXRnkmnLZcGIDyw4s46cjP1l1Qfwt7jeLxM3b3Zufh/9MVFAUDWo0QKfTsb+PGib20dsQZd1YZhNuKanU+nEltb7+WgV/TbM8ICAAHniA3LFjaNEghNfTExmfnsjFzIvmR0pWClm5WWQZs8jKzbKaoKt3g16MjXiHz2bUI8ijNu+/Gs2IQdbJXFXh7Q0REba/jiRuQriYtDTr2cDmzVMJG8A996hxC3k6dICGDaFtpwyiuh1jxSHValbHrw7DWw2nu3nCJx33LbvP3Je+ONeub9a4ZmPeuOkNc4IWGRhJYLXAIs4WdqVpkJNTYuJEdnb59pXmHKOxxGJKMCu9+Hg1AVD37mrK8QEDHF0iYSvvv6+WXgE1rnjhQttd6+DB/LFwffpU7aRt19ldfL77c5YeWMr5jMJvGrWq1Yq2YW2ttveNtGweatlSJdU272J64YKawWPpUpWsFda3sFs3eOQRNcNI9eq4A+FAuH94mS/XrnY7Pr6/JdX3/MPzz7emdu2K6wFz4oRqaatXr8LestKQWCeEi3juOVi+XI05S0mxHFvSNX+yRVZuO0paxA6L8WZZj8fxQ/pZfkgAlqjj+jTqw/BWwy2uERkUSfLp/MTNQ+9Bw8CGFq1mkYGRtK9tOce/n5cfk3tMruAaVxEmU6mTHF16OvV37EB/6pSah7mwpCkzs+SE6trtokqZO1d9rDZtUn9gOzJx27dPzSC7YIFq3RcV65Zb1DiglBR1/yM313KikYrUsyf8+y+89BLMmGGbaziLtcfW8vGOjy22ebl5cXOjmxnUZBADGw+kztWugqXpBWKTpE3T1H/ITz+px7Zt1i1roMY8jBihHlFRFV6M3r0TCA6u2FlDJkyA1avh//4PXnnFcnxZVSeJmxBVyIULaobHlBSdxeQfoGaAjDtmAv8EPl8Xh1uIajmb0nsKPXt6MmuWSuB+vPwl9y8vfvA0WLeaATzZ5Uku51w2J2n1/OtZ9F9PSFCzmWk+QGVYA0jT8rvpFZUA2bKlKSur5IVwCnAH2tnuX8O23N3VDDfVqqk+J97exb/28rJ4bTQa4a23HF2LSqFpU/WIi7Ps+mxvy5fDvfeqX7EJE6zX8xXXr0kT9e+8bx888YTtrxcaqtbVutbx4xAbW8P2BSijvJgUHV34jYPs3GyWHVxG9/rdLabJv6fFPTz3+3N4uXkxsPFA7m1xL7dG31qqRaKPHIG//4Zhw2yQsJ0/D7//rgYvrllT+OBzUP2k775bPbp2tfuMMrt3q2WCymPLFtVwCKob8NSpFVeu6/Xrr/k3xnv1ss017Jq4bdq0iXfffZe///6bs2fP8sMPPzB48OAij9+wYQO9r52jFjh79ixhVbkNXohyMBpVl8aMDAhvkM2DU3YQ91ccJ9LUdPo7m8XBi8fBPYdHt+Wf91C7h4gOjTZ3pzm8x3q8WahPqLm1LG/q/Oia0VbHXdsCV9CCBaoHhsmkBsbPmwdjxpRQKU1TiUwZEiB9RgaNdu1Cf+BAfqtTeZOmrCxVYFfg5VVyspT3Ou95WfcX9d5eXpYzJ5SDKTlZErdSGjVKLVb777+O7c7WqxcEBam/Nf/9Fy5dshyDJcouK8t6iZXeva2n+7en1FQYPNiduLgbqFtXJevOoLiYFHsxlnl/z+O/e/5L0pUkJnefzBs350/cEVEjgl/u+4Xu9bvj71X6u5AmEzz0EPz5J3zzjVpoO/h6xrUlJqqm840b1ePff4s+tnlzNQ7irrvUGiAOmP7TaIRJk+Ddd+GLL9TM02XVtKmaUOfDD+G111QIcRYPPKAma2vUCP76yzbXsGvilpGRQZs2bXjooYcYMmRIqc87fPgw/gUG5dRytamKhLjq/Hk1Fm3zzhSiu8Rx632q1axL3S7c1PAmOnWCDRvgdNJl3jj+Bhy/5g0K+Y2PvRhrkYR1q9eNd/q8oxI1/wZE+tTF1+RundDEZ8HhdaVKgC4nZWH8PIsFZONNFt6mLKo9nEX2/Cy8tBISqTJyAyrdtAc6nfprq7DWpGuTnsISrKvbjB4e7IuNpWWHDrj7+lomUMUlU56e1us1iCpNp1Nja+xl8b7FzNg6gyxDFhfTLuJ5zBN/b3+Cnwkm+EowPdrX4qsjTWlZqyU31L/BahIiUbJz51SC9vjj6uEs3noLDh7UAe68+qrGnXdaz0ZpbwkJ+UkbqJ+PjDPh2eI3von7gFWxqyyOX7B7Aa/2etXiczkguux9jH/7TSVtAAcOqEleSi0nRzWdbtumutZs2aKaMotSrZrqvzpggErYGjUqc3kr2i+/qKQN1IQsffuW/eZRUBC8845qQXa2NhxfX5W42WpGSbBz4nbrrbdy6623lvm8WrVqUaNGjYovkBBOymCAf/ZqXND+IilnF6fOHeX0hTgSzh0n7nw83o3SiD0Ln70N3rlQu+EAaHqaKfWySL4pm4a1M1ixyR13Qy7eueoYH5MbwW6+BOl8CNS88NM88TW54fe/yWB4zpwsRWdl8Wxe4lRBC6P4AY8UtmNbYRsdwMOj1K1JGVo1UrO88a/ljW/NYpKp0rQ25T13d6+Qu58mg4H4lStpMWCALJAl7CrHmMOm+E2sOrqKX+N+Zf2o9dTyyb/J6u3uza6zuwqcAKTlvzxQYFfK8ykWfyBnGjLxdvdGJwuEFSk9HW66SU0QMn68+qp5qHRrGNvca6/BqVMmfvwxlx9+0OHp6fjvpqNHC3Sm8MiAtgsxdfmQkasPWxzn6ebJ3c3v5tEOj+Khv/5y33KL6hL8n/+oFr8iE7fMTLV46t69sGuXWmNh716VvBXBpHcjt3UHPPv3hn791EQj1za/Otgdd6iEed48+Oij60u8nHFM7PPPq/86W/YcqBRj3Nq2bUt2djYtW7bktdde44YbbnB0kYQryOumd71d7YrYbsrMJDsjFUNGGrmZGeizsqmBNzmXs8hNz6It2bhR2m56K4GV9Cywpa3VMUYg9erDyRTXmlSahKhAspXr7s6eQ4do27Ur7j4+pWu5KmU3vXJ19xTCSaxeDZ07V+wfFYnpiXyy4xPm7pzLhSsX8q8Vu5oH2uT3g2pSswnuene83LzQm/RU965OSlYK2UbLVvV6/vUI8LYcoDtp7SSWHljKoCaDuLPpnfRq0Mu88LBQfHxg8GDVilO/vkrinIWXF3z+uZFFizYQFeXAPpsFREer73BT2A4YcQtUv2ixv35AfR7r+BgPtXuIEJ+QCr32kCHQv7/6PyM3F44dU10c//1XJWv79sGhQyV30/f2hk6d2Ot7Ay/82ovNpm5c+cePeeNhjBP9/1/rk0/UZ7Us7TgLFqi1Brt1s1mxKsSjj+Y/Ty55gu1ycerErXbt2sydO5eOHTuSnZ3N/Pnz6dWrF9u3b6d9+/aFnpOdnU12ge5VaWnqlp7BYHC59Z3y6ltp6200Fp4AZWejKyI5sth+5QrNDx+G1asxGgyW+wqMm9IVkVzpytFNryz0QLWrj4I8rz7sRdPr8xOZgkmNlxfatd3prr7WCh5fIJnSrk2ICuxbsboar7zpQ4apGrl6T16f6cmIMVfftwLvpBsMBk6vWUPzvn3RStPqZDKVahyb6lrjjsmkM582bpzGTTflOs2dv0r/O38dnLnOzhCXLl1S44x0Ohg3zsQ771zf2M0DFw4wY9sMlhxYQo7RshVAr9NzOOmwRd0aBzbmygtXMBgMrFmzhr59++Lu7s4VwxUuXLnAmctnOJh0kLSMXD77LJcHH8yf/W798fWcuXyGOTvnMGfnHGp41+COxncwouUIekb0RK+rHN18bf37+eqrEBCg5447TISHl2leI5vLzTVQq1amRd01Db78Use992p4edm3PKGhMGeOjv880RwT+fHnxvo38ninxxkYPRB3vfoT+Xr/vww5OXhduoRxwwZ08fHojh6l2pEjaIcPQ2wsulK8v6bTQePGaB06oHXsiNa1K1rr1iSc96R9lDsm7WodnCwuFfWZ79PH+vP5xBN6OnfWuOsuzWLc2rff6nj4YXd8fTX+9z8jPXoUMjOmE7LV77lO0wqbG9T2dDpdiZOTFObGG2+kfv36fPnll4Xuf+2115gyZYrV9sWLF1O9TJ2JXZymocvNxc1gQJ+To34WfF7gpz43F7ecHPQGQ5l/Wm0reK1SrN1UFeToIctdPapXCwJPLxKSAtG8PNACroB/BnovH9y9fXH38gNPL0yenhg9PDB5eOQ/v/bn1YfR07PYYzRbzQ1diKQkb86e9aF27QyCg7Psdt2KsG9fMC+/bN3aP23aZlq1stGtNVFqV65c4b777iM1NdViTLQzcIa49Pvv9fnoIzWN28CBcTz88P5yvU+mMZMl55bw0/mfMJL/Ha1HT9caXekW0I02fm3wcy/7/NybN9fhs89ak5rqxZQpW2jT5gJGzcj049PZe3kvBs36D6EQjxBuCrqJm4JuItQrtFx1Eo6xZEljvvmmGW3anGfy5L/w8rJtzI+9EkvclTj6B/c3b0tK8uab099zpdpxhta9jUbVyzEOTNPwyMig2vnzVL9wQT3OnTM/qp09h2dO6eOdyd2dtHr1SGvYkNQGDUht2JDUyEhyC/muqCpxKT7ejwkTVDNhs2bJTJ++2bzvr79CefPNrgAMHXqY++8/5JAylpWtYlKlS9yeffZZNm/ezNatWwvdX9idzXr16nH27Flq1qx5PUW2r2K66ekK215IK5QpM5OTR45QPzQUt4IL6BY436q1qeA+x3w07E4rbIa7QlqbLmjpXCKLS9oVkk0ZnDelcS43lVRdDtnukHk1+RrRcQy9Gvfj6+XV+XVDdU5cuUjWfUPNyVm2G+i9/Lh4LpLstChaN2jEo/c0olGNRnQJ70I1j+ufIqngXW0PFxvrZKu6JyRAVFR+ixuAm5vG0aPOcWcTXPv/PTk5mdq1aztl4uYMcWnvXvj8cz3LlulZvtxI587l+35/es3TfLjjQ/PrQO9AxrQbw2MdHqOuf8m/CMV9Rr/4Qt1ZB+jQwcSWLUZzY3x6Tjqr41az4vAKVsau5HKO5eh/HTqWDV3GwOiB5apXeSUkQGysjqgorcTvgYr+/Zw9W8/Qoap1zdldW/eEBGjVyp2MDPUfvGRJLnfeWfF/c2iaxqaTm3jrz7dYe2Itnm6eHHnsiHmNtRKZTGq2iTNn0J05o36ePq2eJySgO3VK/UxPL3vZvLwgOhqtcWO05s3Vo0ULtZZaKT8fzh6XSvuZf+MNPVOmqCELs2YZefzx/B4BKSkQFubOE0+YePttkyMmwywzgwEuXUqmbt2Kj0lO3VWyMHv27KF27dpF7vfy8sKrkDZ3Dw+Psn1RFtZNr7hxSwUXtS1urFNpjylmAGppuQHWE7s7mbxueoUlT9eMZYo97c0f2724QjWy8eamAV607VrNYnxTwe55uW5ubNu7l669eqkZ9gobJ+XpiU6nI9OQyfGU4+ZFp/08/RjT3nLwUo8PG3P04tESq1S7awh9+tzDzj/g23OAPpeRnafSv1P+ItRexposWqQjJgZat7bdPBJl/txXIRVd94YN1Zi2cePU14ObG3z6qY6GDZ3v39cV/9+dub4VFpeuQ8eO6vHhh6DXu5f7j5+XbnyJL/d9SaYhkxe6v8Cz3Z7Fx9OnzO9TWN1Hj1ZrgEVEwLvv6vH0zO8CGegRyLDWwxjWehiZhkz+d/h/LNq7iN/ifsOkmfDx9KFPZB+7fg7KO+a1Iv7fZ8+G556DDz5wY+VKaFVJptLNq3vDhmqZsVtvVZOX3HNPxf45qmkaq2JX8cYfb7Dl1Bbz9hxjDgv2zGdq26fUNM3nz6vpOM+fV1PrnzunfiYmwpkz6vV1TNJldPckNrcBx2jExaAo7n0xGvemUdCkCboGDcDNjevJQypLXCrpM//qq2qGyQULYNQoNzw88sedh4So+VnatHFD/WXrvF54AWbNUn/C//abbQa92DVxS09PJzY2f9He48ePs2fPHoKCgqhfvz6TJk3i9OnTfPHFFwDMnj2bhg0b0qJFC7Kyspg/fz7r1q3jt99+K/O13R59VLVilXaCiQqaTc/peXqWONlDkYveFnV8EYlUoZNMlLKbXkICNInAYqoOt9Vw4tOiZxbSDAaSc3PROnUyZ0bxKfFsS1hP3CU1jX7spVjiLsZx+rLlIpXtwtpZJW6RQZEWiZu73h3tUgTGC5G4p0fy5jORRNeMpG1YWwBiYtSXUKdO7jxQ/2X6XBNYx48vVdWFExkzRg0qj41VN0Wd4Y6mEGVR1uXyNE2zmM2xlk8tvh7yNY1rNiYqKKpCy6bXw7p1JU+RXs2jGsNaDmNYy2GcuXyGRXsWkWvKxc/LsnvmC7+/QI4xhwldJhBRI6JCy1rYdPLjxqnvB1t/L6Snqz8O88rx99+VJ3ErKCYGDh9W482uS1aWmgkiORlT0gV27P2VdTuXkHnmFPdegfFXICQD6uR4EpFdjeqvvwW5r1dIHahWDerVU4+ICPVo0ED9bNQIrVYdvpympsDf/KsJ904Vn1BVhbik08ENN6hHYdq0sW95ykuvz293KUcjbKnYNXHbuXOnxYLaEydOBGDUqFEsXLiQs2fPcvLkSfP+nJwcnn76aU6fPk316tVp3bo1v//+e6GLcpdE//33118BWyhuJr2S1l4qLJkqcGyuhwdbdu0ipndvPHx9ra/l7V1p1m6ymLr3KqNRfVHlfUmZNBNnLp8xt5odSTpCq1zLaPbDoR94avVTJV4v7lIcmqaRmqrjjTfUkinV2j/CnJGDzK1m9QPqM+wed5Ytg1zglqnQqmn+e9x1FwwdKrOyVzV161bOwChEWa06uopXNrzC6hGrCaoWZN5envWrSqusQ/7q+NVhUo9JVtuTryTzwfYPyMzN5IPtH3BPi3t4ofsLtA5tXSHlLE1MshVfX7W47913q3XbHnzQttezJYukzWiElBSObr9IqHsy/rkX4eJFc1Jm8Tw5WXVhTE6GjAzzW+iBLlcf1nKuPkpBp4NataB2bahTR/0MD7d81KunFhUrpvnaHXj1VQORkWtp2/bm0l27HCQuOYf69VWS6ednu4XB7Zq49erVi+KG1C1cuNDi9XPPPcdzzz1nuwK5u1snPSVNO17W5Kq49/bwsOnK9ZrBwKWMDGjbttJnD+ape02AWw40XIuuZhxfJcUx85s4Yi/GcjzlOFm5lgOA345+2+J1ZKB159Hg6sE0qhFJDS2S6JpRdI6KNB9XvbrqWpSdDZGJd/LoB5bn3nuvKltMjLrJVpC9Z8kSQohrJSXBnj3Qq1epOzgA8PFfH/N/q/4PDY37l9/Pz8N/xk1v/25KJpMa4xIUVOKhFraf3o6G+nvDqBn5Zv83fLP/GwZED+CFG16gR0SP6yqXRUy6ys1NtXjYQ2ioap2049xSpZebq5KsAg/d+fM0+vNP9H/9Bamp+fvyErKLF9V/NBBtq3J5eqp+d7Vq5f8MDc3/GRqqFhYLC4Pg4Ar9xw0Ksu0s1cI5PPpo/pIAycm2mSfCGX/lbcKwY4e6Y1Kwtckpv/HE5ezL5q6McZfiaB7SnIGNB+b349aZ4P7b0HQaC/4t/r0SsxMtXrev3Z63bn6LyKD88WZ7tvvTr59Kzlo/AyPvyj/e0xM6dIAtV7vIZ2RcXXvlqqFD1UMIIZzRkiWqW3atWmr82B13lHzOR399xP+t+j/za293b7KN2VTX23dm5u3bYcIEFa7Xry/bfc4B0QM4+eRJPtnxCR/+9SHJmWqGvZVHV7Ly6Ep61O/Biz1epF9kv3It7F23bmFji2zX6qFp1vW3+f1Yo1GtI1GwtevanwUTr7xHWprVW7kDFdmbU3NzQ6sZhL5mMNSsCcHB5AbWYO6JpWjBNenZYQitm/VGl5ekhYSoZhA7zGzx9deqJbROKec/EaIsXCdzadhQ/XILp7H//H52n91N7MVYlahdTdYKLuIK8EDrBxjYeGCBftze3L+zLmcyTpmP8XLzomFgQ6KColRCFhhJhH8El/69BKhuLb/8Alu3hvP888/Tvnn++zdpopI2UF0ir/XZZ+rmW61aFf5PIIQQNrVkifp5/rx1r4DCXJu0vXDDC7xx8xt2XyvNaISRI+HIEfV62TLVNbAsQnxCeLXXqzzT7Rk+3/057219j5OpajjGHyf/4Javb+GOJnfwv2H/K1cZ7Tm2aPJkNZTr3XfLec85bxxYXvfCvJ/XPi/4uNoCZlN6vVoRPigIgoJI9whk9c6a5AbUZNDoILzrBKm/3YLUz2x/H7468ytT98ymT6O+LBi0wPxW7sCdaa9Tx69OuZLxirB6tfrcBgXBokUwwHa9ioWLcp3ETdhVrimXk6knza1mZy+fZUpvy3WM3t/2PvN3zy/xveIuxZmf5/Xjfs3vZfQ6vbnlLNw/3PyHxZkzqnE1N9fAyiMrAdWl5KmrQ9u6dIGC67eHhsJNN6m7Y716WV+/eXPrbUJUBQkJ6qZGdLSMj6iqnnhC3XQ6frzkCSzyukfmeanHS0ztPdUhfwS7uakkZdAg9R0cElL+9/Lx9OH/uvwfj3Z8lG/2f8P0zdM5lHQIgBsjbryuctpjbNHy5fDWW+r5wYOw8icj+pSLKuFKSoILFyx/Fnyel5jZaqaEPG5u5uSLwECLZIvAQIw1arA7Pp62vXvjHhqaf2xAgMVYe1+gTay6WepdI//trxiu8Nnfn/HOL+9w5vIZAL745wtevvFlGtRoYD4u3N9xayNompodMW8FgV27JHErK4lJJZPETVyXlKwUNp7YaDVLY3xqPLkmy5k5n+n2jMWsX5FB1uPN6vjVITIwMr/lLCiSpsFNrY4b22Gs1bbp0+GTT9Qv/vHjWKxtExOT/3znTut6rF1bisoKUYWUdypzUbncfbd6mEzF9xL7cu+XjF+VP9Xtiz1edFjSluf22+H771X3zoroFujh5sHINiO5v9X9/HDoB+bunMu4DuMsjolPiWfDiQ3c1+o+PNzsNDbcZFJdEvOmp897XLgA58/TdvsFNnKeYC7QYPMF9N4XrWdGqUjXJl55j6Cgwn8GBqoErJjPislg4PTKlbTp37/E/8yC4wRTs1L5eMfHzNo6i6TMJIvj+jbqS3au84wd0+ng11/hnnvUBDKTJzu6RJVLVYhJ8fHwxhtw+TJ06WKb705J3ESRNE3jYuZFi/Fmt0TdQsc6Hc3HHL90nMFLBpfq/Y5dOkabsPw5XftF9sPLzcvcatYosFGJi08nJKjujPHx8Mwzlvuys9V+UMcU7FbTogXMmQNdu0LLlqUqrhBVliOnMheOUdwEwn+d/ouxP+XfDHuxx4tM6z3NoUkbqD+E77qr5OPKyk3vxt3N7+bu5tZ9L9/+823m7JzDaxtf47luzzG63Wi83b3LfpHsbLUGWN4aYefOoT9zhpZ//YXbt9+qJpmCCZrRWORbNbr6ACCjyMOs6fXm8V/mn3mPvGSs4PO8JKysa0bYwPmM87y/7X0+3vExqdmpFvsGNx3MSz1eokOdDg4qXdFq1ICVK9WU8JVk0m6nUFViUlqaGl4D4O5umw+AJG4CgK2ntnLgwgHiLsXljzm7GGf1henp5mmRuBXWaubr6WtuLcsbbxYZFGl1bPva7Wlfu73V+XkKG4w9YADs26fiyn/+YzlRSEyMet25sxqDXJCbW/5MP0K4OkdOZS6czzt/vkO2UbVcjOswzimSNke4kHGBBbvVmKkTKSd4bOVjTNs0jYkxExnXYRx+em+VZCUmwtmz+Qs15yVoBZ8XMj7MDbCOmGVQvXr+RBsFH8HBls/zkrHAwEqbPfT/qj97EvfkbzDp4d97qXt8EktfbOU0c8tpmppEs2Ajoru7zH1XVlUlJvn65j+vEuu4CcfIzs0mLjW/1Uyv0zO+s+XqzxN/m8i2hG0lvlfcxTiL1/5e/ky/eTrhfuFEBqkujiHVQ8od9DMzVfeCrVvVOLUffrDcHxOjEjejEXbssByTdvPNKlbmfWEaDOUqghBVnqOnMhe2d+CA+i5s3LjkY78e8jUBvwRw9OJRPrj1A6dN2i5cUPHhnnugb98KelNNU/2azp4lJDGRvTUmsXHbElJOHKL2ZQhLP0vYO8+SlfEcPlc09BU5w7enZ/509HmzH159neUXgne9AlPXh4SUfZG7Smx8p/E8/NPDeOg9uLfpSPZ+/DwH/4zmv6ucJynSNHjySTU0Y+lSWQLoelSVmBQeDnv35iVwRlasqPhrOMnHX1SE02mn2XJqS/54s4ux7D+zn+Q9yeb1bAAiAiKsErfIwEiLxE2v01M/oL5li1lgpEVXxzwvdH+hzGXNylIDd319oXWB9VC9veGrr1QvksDA/L7Oee66S8WvmBjLCUbAeb7MhXB29p7KXNjfa6+pPyajomDNmuJnlPRy92L+HfPJzM3E083TXkUskyNH1MRSKSmwebP648izuKJqmuq3dOZM/uPsWeufZ8/ClSvm05pefRTyhqUrqK9v/ppg1zxyg4LYeuwYXQcNwiM8HPz9Cx0X9tdfqnfJnDkwtGMh16giTJqJX478woytM5jZf6ZFD5wRrUdwIuUE4zqOo65/XS7fAn/8AX36OLDA15g0CT64urbr0KHwv//ZZbWBKqmqxCRPz/y/aZOTbXMN+VO3ktA0jcT0RIvxZo90eIS6/vmf6nXH1zFyxcgS3+tU2ilyjDkWAXpE6xHE1I0xJ2gRNSJsFsD37FHdGQ0GeOghNSA1j06nkrKfflI3Gi9cUDEvT79+6iGEuD72nMpc2JfBAL/9pp4nJ5fu/1an01Hdw3lbdKKioFkz1RsjOSGTw7+cplXNqwnZ6dOWCVreo0BCdj0MHnpO+5hI9IFzvpBR049hfZ5EX7tO/qLNeQlawf7719AMBi6uXKmaF4qYoCM5WSUBycmqZXHFCjWzZlWSmpXKwj0L+WjHR8RejAVgxtYZfD3ka/MxXu5eTLtpmvm1n1/hMzT+/jt0765u+tpb//4qccvKgiFDJGm7XhKTSkcSNydj0kz8fux3c3KWN+bs2KVjXDFYBqGudbtaJG6FjTfzc/OjSa0mRNWMsmg9u3ZNnluibqnQesTFqW6OW7fC44+r6fbzNGmiboZC4eumzZ4N//2vLLsnhK3ZYypzYX85OfDii2qShPr1rXsjxKfE8/BPD/PhrR8WOmuvw+TNo376tJqt4PRp80N/+jRrz5/G5Hkan/QUGFIB1wsIUH3yC3uEhZl/etSogVtaAku2zuSzXZ/x5s2vo+/yhMVbrTq6it5edbje/MHbG3r0UIs433BD1ZpO/mTmSZ5c/SRf7PuC9BzLAUD/nPvH6oZySf73P7jzTmjbVq1XGB1dwQUuQe/e6nfsxAl48EH7XruqkphUMknc7CwjJ8Oi1SwiIIKhLYaa9+vQcdd3d1l9qRUm705VnmbBzXjjpjfMyVmEXwRb1m1hwIABeFTEXMqF0DQ4eVL16y34x8Hu3fDss+p506aWiVu1aqrLY7Vq0K2b9SQkjRohhBCinHx81Pfvs8/m3yTLY9JMPPTjQ6w7vo52n7bjf8P+R79IO3RjyM2Fs2fRxcdTe8sW9LGxqptiXpKWkKBayXJyinyL4uccLiAgQAWlOnXUo3bt/J8FH2UYM1YvoB6zbpnFKze+gpe75WCmAxcOMGDxAIKrB/Nwu4cZ22EsjQLLF8h8fODLL9X47VtvrZhlEBwp05DJ9we+Z+7OuWxJ2GK1/+aGN/Nk1ycZED2gTIu8X76seuxomvp7Y80a2yduKSnWqx4UtvarcG07d+YtoSjLAVQqh5MOs/PMTnOrWV6ilpieaHHcbdG3WSZuOh2RgZHsPbfXvM1D70HDwIZW65tdOyNjYLVAJvfIXzjEYOPZOWbPhrffVhNp7dgBHQv0xe/aNf/5nj3W5377rU2LJoQQAuvuW5/s+IR1x9cBEFI9hC7hXa7/Irm5KulKSIBTpyx/5j1PTASTCXegc3mv4+WlErK8pKxgclbwuQ0n8QisFmi17aO/PgIg6UoSb/35Fm/9+RZ9GvVhbPuxDGoyyCrRK4lOBw8/XCHFdbidZ3ZaDeGo7lGdka1HMr7zeFrUalGu9/Xzg/XrVXfS5s3VLNO2lLfE0Esv2f5aonIbORIOHgQfH9ssqyGJWzkYTUYS0hLMCdmxS8d4/abXcdPn/yd9vvtz3tnyTonvdW2rGaiFqjMNmebxZnX961q8tz3Fx8OWLfDvv/D665b73NxULAb1pVYwcatbFxYtUhOINGtmv/IKIYQo3JHkIzy35jnz688HfU6Ad0DxJ5lM6ov+1KnCHwkJquXseheEDgpSgSM8PP/ntY+gIItMNDdXTeAx6jY1z4ejjGozipSsFJYeWEquKReA34/9zu/HfqdmtZrc2+JeRrQeQYfQwtcdO3NGzWniyDpUhNiLsVzIuEBMvRjztu71u9M8pDkHLhygvnd9nurxFA+2f5Aa3jWu+3qtW6vWDaPR+gbF+vWqq2mxE9iUUkaGGnt1+TJMmADt2lnenBaioLzlqDIypMXN7tJz0tlwYoN5hsa81rMTKSfIMVp25/hPp/9QP6C++XVh481CfUJVi1mB9c0a17Seq3lE6xEVX5lSuHYGR4DRo9UXIKi7TOHh+fu6dlWBpksXdZPzWiNLnidFCCFEBYqNVTPyXjtG2Ggy8uCKB8nMzQTg8U6P06fh1TVUTp5USdjJk5bP8xKz3NzyF0inU5N2hIdDvXoY69ThUHo6TXr3xr1hw/ykrFqpO0ICarmDESNUN7kjR+DDD8tfxOvVpW4XFtddzMz+M1m4ZyGf7fqMY5eOAZCcmcwnOz/hk52f8J8O/6E//S3OzcqCO+5Qaz4tX65ajyqTuItxLDu4jCX/LmHX2V20C2vHrnG7zPt1Oh2z+8/GU+fJpX8ucVun2yp06EbBdbPy/PuvWi4iKkp9Lq536QgfHzXb4XvvqcnTGja8vvcTVdvo0aqbs05n5LXXKv79XTpxS8lKMXdhjL0YS/f63ekZ0dO8P/lKMrd/c3up3iv2YqxF4tYzoifv9n3X3K2xUWAjfD0L+YZxMJMJnnoK/vxTDYrevNlyf0xMfuKW11UgT4cOcOlSpV3fUwghqpynn4aff1Y31H74zkBo7mk4eZI/Nn1Br/VbGZkKTTOr0/O7dTAsQDUjXI+wMNVCVq9e4T/r1LFo9jAZDMSuXEnjAQOuawBX9epw+LB6PneuGs9Xv37x59hamG8YL3R/gedueI71x9czf/d8VhxaQVZuFgB9G/WFo/nHp2WnMWryDv7e0x2MXtx/v1omx5lnJ8w15bItYRs/Hf6Jn478xMGkgxb7dyfu5mjyUaJr5g846xvZF4PBwMp9K+1SxqeeUq1whw+r+w6lpWlqaMdPP6lEreCM1pMnq3sLL79c+ccdCtt69FH1MznZJInb9Vi8bzHnTOcsxptdzLxocczzNzxvkbjV9a+Lh94Dgyl/rFg192rmFrPixps1DW7qVLN1XbmiuhR4elo28ev1atroQ4fUl1FWluW0unfcobbHxKhHQZKwCSGEA6Wmqpax+Hg4eZLc4ycZ8Us8z5lO0mD7SWpFnDF3Yex19aFcAQ4W9o6WAgNVNlSvXv6j4Ovw8Irpi1YODRrA1KmqS/5nnzk+aStIr9Nzc6ObubnRzaRlp/HDwR/43+H/0a9RP34/+rv5uJ8O/8SKgBHoJlVHF9+Lfnf2Z++5nrSq1cphwyOKcjrtNI/+8igbT2zkck7hyX6H2h24p8U9FdIN8npMn666N+7bp8bAFfTzz2p/q1bq81OrluV5L76onoeHq+np8wQGquOFcDSXSdyeWP0EJc3Te+14Mze9G+/0fYdA70BzshbmG4bOmW+HFeL4cWjRQvV2GTQIq5XcY2JU4hYdrSb4iizQy7NLF/UQQghhR5oG58+rucbzkrNrH6mpFqe4A+aprkoacubllZ+ERURYJmV5P4tZk8wZTJgATzzh3C0g/l7+jGo7ilFtR1lNGLb80HIANPcraJEreeeflbzzD/h5+tG1ble61etGu7B2tK/dnnoB9WxeVqPJyLFLx9h/fj+B1QLp1aCXeV/N6jVZE7eGbGO2eZtepyembgwDGw/k7uZ3ExUUZfMylkaHDqr3UFyc9Ud4xw41bn/LFtWlrWDidvPN+YnbTz9ZJm5COAuXSdwK0qGjXkA9i3XNIgMjaVmrpdWxT3Z9stD3SEiAo0dVsuMMa06cOKHWMdm6FR54QE23nyciQvUDT0lR+6+dfn/aNJg5E2rUsHOhhRDClSUkqMFa8fHqS7xgUnbypOoCUU5arVroIiLIrB3Cpxd+5YS/icQgD2Y+vJQ6LWMgJMS5++SVwrXr01U297e6Hz9PP1bHrbaYcfpyzmXWHFvDmmNrABjWchjf3PWNxbnf7PuGEJ8QQqqHEOITQnD14FKtgXYx8yInU09y9vJZ4lPjiU+JJz41nkNJhziYdNDcrfOOJndYJG7e7t7cUP8G9p/fz00Nb+LWqFsZEK2WQHBGOp0a43atM2fyn19z34NOneDee6FnTxg40LblE6K8KvnXXum9edObtI5oTWRQJA1qNMDbvfzLZC5YAI88kj+Zx7x59rszo2lw7JgaNlBwLPexY/DCC+p5WJhl4qbXw333QXa2al0zGi0DXsEJRwrjbEmqEEJUBR5t25bzRI/8lrL69SEigk0nI3h9UX1OaPU5ravHB29WY8wYtfZZ6+PrWPDrBO5seid1eg+qyCo4RHExaflytbZWUJBDilaizEx3PvpIz4QJMKTZEIY0G4Kmaew7v491x9fx56k/+fPkn5xNP2s+p01oG4v3yMjJ4L7l91m9t6ebJ15uXni7e+Pp5olRM7J1zFYa1GhgPmb+rvk8//vzJZZze8J2NE2z6GG0dOhSAr0DK12vo4I++0xNMrJ/v/UkI3q9LFUkrt+HH6oGkcuXbZNiuUzi9kj7R6h57TRb5ZCQkJ+0gfo5bpyaKtbWSc28eWpg7PnzsHo19CuwZmrnzupLx2RSX0jX+vjj8l3TkUmqEEK4JB8flZQV9QgLU+uxXJWQAL0jwJS32LZmGZduangTu8ftxmgyOqY+FaiomJSWBv/3f/DFFzB0qOqB4mz5hdEIM2Z0YOdON7ZuhYUL1SQrOp2O1qGtaR3amie7PommaZxIOcHOMzvZe24vNze82eJ9jqccL/T9c4w55BhzLMag5bWg5QmqVnhGq9fpiQqKokVIC1rWaknbsLZoaOjQlXhuZRMQoJYKEMIWcnPhwgUA23wBuUziVlGOHrVersZoVFMwV0Tidvy4muFxxw7VfbFAbMbXVyVtoLo8FkzcfH1h6VK1ZlqTJtdfDnBskiqEEFWd6ZZb1Bd2XkLWoIH6ec16ZSUpTVxy17vjrq/cIb+4mKTTqXFJoGLhf/4DvXs7rqyF+fNPHbt2qakK16xR3fYK686n0+loGNiQhoENGdpiqNX+kOohvH/L+ySmJ3Ih4wIXrlwg6UoSVwxXyMrNIis3ixxjTqETnLSq1YpH2j9CiE8I9QPq06BGAyICIoioEXFdPZGEEEqtWuqrvFo1jYOlmAOqrCr3t7gDREfnt2zlcXMr/Mu3JLm51n30n30Wli1Tzx9+WM18lCcmRs1s1LUrNLZe/o3OnVUA9/OrmMTK1kmqcCzpAiuEYxm/+sp6wbVyiI623qb3uUhUlONbSCrye6a4mNSrl2p9e+gh1cOkV6/ru5Yt9OypMXnydj7+uAvff68r198NAKG+oTzR5Ylyndulbhe61HXOGcckJomq4P771SM5OZdgGwwBlQndy6huXRUc8lrC3Nzg00/L9iXz9NPQrh20tJ4LxWLK/a1bLfc1aABJSbByJQwfbrlvwQJ1o/amm9TPBQtKX56i5CWpBZU3SRXOxRafFyGEY9Sti8UfCDo3I7Um3cCI33ux4cQGh5Wror9nSopJd9+txns/8IDzdZPM07HjOY4ezeWmmxxdEuciMUmI0pHErRzGjFETgK1fr34WNuYrPV3tX7fOet/27WqRx8OH87s+5rnlFrVWyJo11smZTlf42mlFdR8py8KThamIJFU4H1t9XoQQjpGVpbrO16oFbdvCB2u/IzH3EBvjN/Ly+pfRNK3E96hotvieKU1MssUd7utx6ZL1Nn9/+5fDmUlMEqL0pKtkOdWtW3QCc+mSmmnZaFQDYK+9s9a1q2pNa9kSEhMt1xFp0UI9yqKo7iNxcdd/y3HMGDV+IDZW3dWUpK3yky6wQlQt3t7w9ddq1uHki0Z6fjvNvO+1G19zyCyAtopLZY1JW7eqiUpmzbJ/K9wvv6gZnZcsUTdlReEkJglRepK4lVNCAixapILCoEEwdmz+vsBA1a0xLg527oScHPAssLzK88/Dq6+qsWgVoahxd5GRGv/8c/3vX1ySKiqfihynKYRwHjodrD37PQeT1Ij4G+rdwE0NHdMnz5ZxqbQxafFitchyTo5q5ZoyxX7J27//qq6bWVlwxx1q0rHyrv5Q1UlMElXJpUvw5puQlGSbTo127Sq5adMmbr/9durUqYNOp2PFihUlnrNhwwbat2+Pl5cXUVFRLFy40OblLEjTVJfGaxdqvHgRXnpJ3VH77Tfr84YPV039n35qfScpJKTikjaQLo2ibOTzIkTVZNJMTN001fz6tV6OaW0D5/ie8fZWSRuo1ht79hht1gyGDFHPhwyB9u3td+3Kxhk+K0JUlOxstVbgwoXWs7pWBLu2uGVkZNCmTRseeughhuR9oxXj+PHj3HbbbTz66KN8/fXXrF27locffpjatWvTv39/m5f366/hiSdUkrZ4seWYsxYtVPJ1+TIcOWJ97rRp1ttsqbDuIwaDfcsgKg/pAitE1WA0qtYKnQ6+P/A9By4cAKBbvW5W63/Zm6Pj0pAhMHs2bNigesgUNkbcVvR6+PxzNSTimWdUMnLtTVyRT2KSqCoqsmGmMHZN3G699VZuvfXWUh8/d+5cGjZsyIwZMwBo1qwZmzdvZtasWRWWuB07Bps2qS6PM2ao9dDyBAerpA3U/oKJm5sbfP89NGzoPM350qVRlIV8XoSo/ObNg+nTofdNGtvbvmne7qixbddy9PfMhAlqYW5bJ23p6RAfbzlG3csLJk2y7XWrEkd/VoSoCNWrq7zCYDBwsw3unTn1GLetW7fSp08fi239+/fnySefLPKc7OxssrOzza/T0tIA9Q94+bIB72vWl5w+Xc/8+ao58+67c+nVK78vRfv2UKuWOx07arRpY8JgsOxnkbe4Z25uWWtmH4artzYNLtr05sr1l7pL3V2NM9e5uLh0veX+/Xc3Tp3S88WGP6DhXgA61u7IjfVudMp/E0d9Ro3G/Ofx8TB+vBuzZhkr5Mbrpk06xo51w2iEXbtyi5w1Un4/pe6uxlXr3rUrJCfbps5OnbglJiYSGhpqsS00NJS0tDQyMzOpVq2a1TnTp09nypQpVts7dcolNdXEokW/Wtx5q1atHqA6ny9adIQrV45anPfpp/mDmVeuvL76OMqaNWscXQSHcuX6O1Pdk5K8OXvWl9q10wkOzrL59Zyp7vbminW/cuWKo4tQpKLi0vr166levfp1vff58x3w9KyNsdss8nKTHp49WLVq1XW9r6056jNqMsGrr3Zj374Q2rUz8eKL22ndOqnc76dp6v2OHw8BYMSIBB59tPjZV1zx9zOPM9VdYpL9uGLdbRWTnDpxK49JkyYxceJE8+u0tDTq1atHQoI/4EVU1ACaNs0/vmVLqFXLSNeuGh06ROPrG23/QtuIwWBgzZo19O3bFw8PD0cXx+5cuf7OVvf//lfHf/7jhsmkQ6/XmDPHyOjRtpkpwNnqbk+uXPfk5GRHF6FIRcWl3r17U7Nmzet67wEDIDvbxMLND/G/8+kcuHCAacOm4enmWfLJDuDoz+jp05CRof70CQ114z//6UxAwPW9Z4sW0L69Rps2GrNm1SUysvD+fo6uuyM5W90lJtmHK9fdVjHJqRO3sLAwzp07Z7Ht3Llz+Pv7F9raBuDl5YWXl5fVdr1eo00bSE/3oOBnJzJSzQ5ZlXl4eLjcL0xBrlx/Z6h7QgL85z8FF1fV8dhj7gwYYNvxDM5Qd0dxxbo7c32LiksV9f/k4QHjb7md8dxOSlYKPt4+1/2etuaoz2iDBrB3Lzz7LAwdqiM42LIMP/ygxq1HRFgulJ2VpWaRXr0abr0V7rwzf190NGzZAs2b63BzK3kwnSv+fuZxhrpLTLI/V6t7XBzExtrm5plTJ24xMTGsvKZ/4po1a4iJiSnzex0/nkv9+hVVMiFEacniqkLYTw3vGo4ugtPz9YU5c6y3JyXBsGFqCYERI+DLL/P3GY1qXTaA/fstEzeAVq1sV15RsSQmCVsbMwY2brRNimXXddzS09PZs2cPe/bsAdR0/3v27OHkyZOA6k4ycuRI8/GPPvoox44d47nnnuPQoUN88sknfPfddzz11FNlvraP89+AFKJKyltctSBZXFUI4Wy+/DJ/3bdr/4D38YFGjdTz/ftVq42onCQmCVuz5ZIAdk3cdu7cSbt27WjXrh0AEydOpF27drzyyisAnD171pzEATRs2JBffvmFNWvW0KZNG2bMmMH8+fPtsoabcG0JCbB+vQTniiCLqwpR8Q4dgi5dNVq/9DDv/fQTJk0WCbteQ4bAG2/AqFFqVrhrvf66WgYoIcH+318SkyqOxCRha7ffDuPGGUs+sBzs2lWyV69eaFrRgz8XLlxY6Dm7d++2YalcT0KC6ioQHS1fVIVZsAAeeUR1pdDr1Rf8mDGOLlXlJourClGxNm2Cv5LWgMcCnt21gF05w1l812JHF6tcnCUmRUTA5MlF7y+4lqs9SUyqeBKThC098ggkJ5v49NOKf2+7trgJx1uwQAWnm25SPxcscHSJnEtCQn6ABPVz3Di5y1kR6taFXr0kQApREY4eBTrONb8e0myI4wpzHSQmFU9iku1ITBKVkSRuLkQCQMmKG7QshBDO4tnXzuPe4icAwnzCGNx0sGMLVA4Sk0omMUkIUZAkbi5EAkDJZNCyEKIy+Pqfr8k15QIwss1I3PVOPUl0oSQmlUxikhCiIEncXIgEgJLJoGUhhLPTNI3/7vmv+fXodqMdWJryk5hUMolJQlQ+y5ZB585VYDkA4VgSAEpnzBg4cULN4HXihAwCF0I4l11nd7Hv/D4AYurG0DS4qYNLVD4Sk0pHYpIQlUtODiQm2ua9K1/fCnFdZCal0qlbV/5thBDOafSHn4P31edtK2drWx6JSaUjMUmIymP4cOjXL5fg4Ip/b0ncXJAEACGEqJzOXshin6am/dflVuPelvc6uETXT2KSEEKUjnSVFEIIISqJeWvWQbUUAJoY78Lfy9+xBRJCCGE30uImhBBCVBIvDxtAy617+HjLf7m3y92OLo4QQgg7ksRNCCGEqCT0erjrhjbcdcNsRxdFCCGEnUlXSSGEEEIIIYRwcpK4CSGEEEIIIYSTk8RNCCGEcHJxF+No8l4nhn/0Lpv3nUTTHF0iIYQQ9iaJmxBCCOHkvvv3O45k7OTb5Ofo8Z9vOXrU0SUSQghhb5K4CSGEEE7uuwPfmZ/XODOU6GgHFkYIIYRDyKySQgghhBM7knyEPYl7AAinE2MeaIhO59gyCSGEsD9J3IQQQggntvTfpebnT/a9h2e6ObAwQgghHEa6SgqnlZAA69ern0II4aoKdpMc2nyoA0vi2iQmCSEcTRI34ZQWLICICLjpJvVzwQJHl0gIIezvUNIh/jn3DwBdwrsQUSPCwSVyTRKThBDOQBI34XQSEuCRR8BkUq9NJhg3Tu5yCiFcT8FukoOi7nFgSVyXxCQhhLOQxE04naNH8wNkHqMRYmMdUx4hhHCUgt0kX7zzbqZPd2BhXJTEJCGEs5DETTid6GjQX/PJdHODqCjHlEcIIRwhPiWeAxcOqBenYtBS6tOggUOL5JIkJgkhnIUkbsLp1K0L8+apwAjq56efqu1CCOEqImpEcO6ZczwX/QW3+r5I69bQTWaUtDuJSUIIZyHLAQinNGYM9O+vuqJERUmAFEK4puDqwbx93wNwn6NL4tokJgkhnIEkbsJp1a0rwVEIIYRzkJgkhHA0h3SV/Pjjj2nQoAHe3t506dKFv/76q8hjFy5ciE6ns3h4e3vbsbRCCCGEEEII4Vh2b3FbsmQJEydOZO7cuXTp0oXZs2fTv39/Dh8+TK1atQo9x9/fn8OHD5tf63Q6exVXCCGEsLsJqyaQlZtFt5CBDO94K57u0kFGCCFcnd1b3GbOnMnYsWMZPXo0zZs3Z+7cuVSvXp3PP/+8yHN0Oh1hYWHmR2hoqB1LLIQQQtiPwWhg4d6FzNs1j4d+HEWtWjBkCGiao0smhBDCkex6Cy8nJ4e///6bSZMmmbfp9Xr69OnD1q1bizwvPT2diIgITCYT7du3580336RFixaFHpudnU12drb5dVpaGgAGgwGDwVBBNakc8urravXO48r1l7pL3V2NM9e5rHFp/Yn1pGWrY0yHbyX1kjvnzpnIzTXap8A2JJ9Rqburkbq7dt0rml0Tt6SkJIxGo1WLWWhoKIcOHSr0nCZNmvD555/TunVrUlNTee+99+jWrRv//vsvdQsZJTx9+nSmTJlitX39+vVUr169YipSyaxZs8bRRXAoV66/1N01uWLdr1y54ugiFKmscenz0/k9UCKN3UkKyKJWrVOsXHnApuW0J1f8jOaRursmqbtrsVVM0mma/TpfnDlzhvDwcLZs2UJMTIx5+3PPPcfGjRvZvn17ie9hMBho1qwZw4cPZ9q0aVb7C7uzWa9ePc6ePUvNmjUrpiKVhMFgYM2aNfTt2xcPDw9HF8fuXLn+Unepu6vVPTk5mdq1a5Oamoq/v7+ji2OhLHFJ0zRazG1B7KVY3HRunHnyDDW8A8nOhqowL5crf0al7lJ3qbvrsFVMsmuLW3BwMG5ubpw7d85i+7lz5wgLCyvVe3h4eNCuXTtiY2ML3e/l5YWXl1eh57nahyaPK9cdXLv+Unepu6tw5vqWJS4dTjpM7CUV33pE9KCWv5q0y9PT9uW0J1f8jOaRukvdXY0r1t1W9bXr5CSenp506NCBtWvXmreZTCbWrl1r0QJXHKPRyL59+6hdu7atiimEEEI4xE9HfjI/Hxg90IElEUII4WzsPr/wxIkTGTVqFB07dqRz587Mnj2bjIwMRo8eDcDIkSMJDw9n+vTpAEydOpWuXbsSFRVFSkoK7777LvHx8Tz88MP2LroQQghhUz8f+dn8/PYmtzuwJEIIIZyN3RO3e++9lwsXLvDKK6+QmJhI27Zt+fXXX80Tlpw8eRK9Pr8h8NKlS4wdO5bExEQCAwPp0KEDW7ZsoXnz5vYuuhBCCGEzKVkpbD65GYBabtHccUNjYmJg4kRo1crBhRNCCOFwDlnRc/z48YwfP77QfRs2bLB4PWvWLGbNmmWHUgkhhBCOs/74eoyamvI/KHkAhw7D4cPw6KMOLpgQQgin4JDETQghhBCWbmt8GxtGbeD3Y7+z5YtbiPMAvR7atXN0yYQQQjgDSdyEEEIIJ+Dp5smNDW7kxgY3wk2QNReOHKl6M0oKIYQoH7vOKimEEEKI0vH2htatHV0KIYQQzkISNyGEEEIIIYRwctJVUgghhHCw97a8h5ebF30j+9KkZhN0Op2jiySEEMLJSOImhBBCOJBJM/HW5rdIzkzG38ufrhuT6dDOnZtvhptvdnTphBBCOAtJ3IQQQggH2pO4h+TMZAA6BN3Eb7+689uvcPSoJG5CCCHyyRg3IYQQwoF+P/a7+Xnd7L7m5zExjiiNEEIIZ+XyLW4JCequZnQ01K3r6NIIIYRwNWuOrTE/f/imPtz+HVy6BH36OLBQQgghnI5LJ24LFsAjj4DJpBY5nTcPxoxxdKmEEEK4ikxDJn/E/wFAkFt9erWORisQkxo1cnABhRBCOA2X7SqZkJCftIH6OW6c2i6EEELYw5+n/iTbmA3AxZ190ExqNkmJSUIIIa7lsonb0aP5SVseoxFiYx1THiGEEK5nTVx+N0ni+lrsk5gkhBCiIJdN3KKjVVeUgtzcICrKMeURQgjhen4/nj8xCcctp5CUmCSEEKIgl03c6tZV4wfc3NRrNzf49FOZoEQIIYR9pGalsvvsbgDahLahab0Q8z69XmKSEEIISy49OcmYMdC/v+qKEhUlAVIIIYT96NAxq/8sNp3cRIvgVsw8pbbXqgV//y0xSQghhCWXTtxABUYJjkIIIezN39ufCV0nMKHrBEwmuPMP2LJFjb+WuCSEEOJaLp+4CSGEEI6m10O7duohhBBCFMZlx7gJIYQQQgghRGUhiZsQQgjhAFtPbSUrN8vRxRBCCFFJSOImhBBCOMDtS26nxls1WLr7V777ThbbFkIIUTxJ3IQQQggHyTZmkxrbnHvvhXr1YOpUR5dICCGEs5LETQghhHCQiIAIju6sb37dqpUDCyOEEMKpyaySQgghhIP0jOjJ4C7g4QFbt0JMjKNLJIQQwllJ4iaEEEI4SM+InsS0l4RNCCFEyaSrpBBCCOEgPer3cHQRhBBCVBIOSdw+/vhjGjRogLe3N126dOGvv/4q9vilS5fStGlTvL29adWqFStXrrRTSYUQQgjbCK4eTOOajR1dDCGEEJWE3RO3JUuWMHHiRF599VV27dpFmzZt6N+/P+fPny/0+C1btjB8+HDGjBnD7t27GTx4MIMHD2b//v12LrkQQghRcWLqxnDkiI7MTEeXRAghRGVg98Rt5syZjB07ltGjR9O8eXPmzp1L9erV+fzzzws9/v333+eWW27h2WefpVmzZkybNo327dvz0Ucf2bnkQgghRMXpVrcb/fqBvz/cdBNomqNLJIQQwpnZNXHLycnh77//pk+fPvkF0Ovp06cPW7duLfScrVu3WhwP0L9//yKPF0IIISqDRh5dOXkScnNV0qbTObpEQgghnJldZ5VMSkrCaDQSGhpqsT00NJRDhw4Vek5iYmKhxycmJhZ6fHZ2NtnZ2ebXqampAFy8ePF6il4pGQwGrly5QnJyMh4eHo4ujt25cv2l7lJ3V6t73ne85oTNVkXFpSBTbR54IIWtW3V06GAiOdnkqCLajSt/RqXuUnepu+uwVUyqcssBTJ8+nSlTplhtb9xYBoALIURVl5ycTEBAgKOLYaGouNT35qbm5zNmqIcQQoiqo6Jjkl0Tt+DgYNzc3Dh37pzF9nPnzhEWFlboOWFhYWU6ftKkSUycONH8OiUlhYiICE6ePOl0wdzW0tLSqFevHqdOncLf39/RxbE7V66/1F3q7mp1T01NpX79+gQFBTm6KFYkLuVz5c+o1F3qLnV3HbaKSXZN3Dw9PenQoQNr165l8ODBAJhMJtauXcv48eMLPScmJoa1a9fy5JNPmretWbOGmCJWK/Xy8sLLy8tqe0BAgMt9aPL4+/u7bN3BtesvdZe6uxq93vmWJ5W4ZM2VP6NSd6m7q3Hluld0TLJ7V8mJEycyatQoOnbsSOfOnZk9ezYZGRmMHj0agJEjRxIeHs706dMBmDBhAjfeeCMzZszgtttu49tvv2Xnzp3MmzfP3kUXQgghhBBCCIewe+J27733cuHCBV555RUSExNp27Ytv/76q3kCkpMnT1pkp926dWPx4sW89NJLTJ48mejoaFasWEHLli3tXXQhhBBCCCGEcAiHTE4yfvz4IrtGbtiwwWrb0KFDGTp0aLmu5eXlxauvvlpoN5WqzpXrDq5df6m71N3VVKa6V6ayVjSpu9Td1Ujdpe4VSac549zJQgghhBBCCCHMnG8UtxBCCCGEEEIIC5K4CSGEEEIIIYSTk8RNCCGEEEIIIZxclUjcPv74Yxo0aIC3tzddunThr7/+Kvb4pUuX0rRpU7y9vWnVqhUrV660U0krXlnqvnDhQnQ6ncXD29vbjqWtOJs2beL222+nTp066HQ6VqxYUeI5GzZsoH379nh5eREVFcXChQttXk5bKGvdN2zYYPX/rtPpSExMtE+BK9D06dPp1KkTfn5+1KpVi8GDB3P48OESz6sKv/PlqXtV+Z2fM2cOrVu3Nq8FFBMTw6pVq4o9x9H/5xKXXCsuSUySmCQxSWJScSrq/7zSJ25Llixh4sSJvPrqq+zatYs2bdrQv39/zp8/X+jxW7ZsYfjw4YwZM4bdu3czePBgBg8ezP79++1c8utX1rqDWgTx7Nmz5kd8fLwdS1xxMjIyaNOmDR9//HGpjj9+/Di33XYbvXv3Zs+ePTz55JM8/PDDrF69+v/bu7/Qqus/juOvOT1bki5nNk/4p6U4ykYLYbEFOv8l6IV4Y7sZUy9cscHsoloQiApOoRxSUkE1/3Qhkk3BQJ37B+m8cJt45iRqjiSYi8hmbaJxzvt38cPz8+jmbzvufL/f8z3PB+xi3/P5wvvNxw8v3ud7dkxwpRNvvL3f99NPP8Xs/XPPPZegChOnra1NlZWVunjxohobG/Xvv//qzTff1NDQ0Kj3+OXMx9O75I8zP2fOHO3Zs0cdHR26dOmSVqxYofXr1+vq1asjrnd7z8ml1MslMolMIpPIJEcyyZJcYWGhVVZWRn8Ph8P2/PPPW21t7YjrN27caOvWrYu59vrrr1tFRUVC60yE8fZeX19vWVlZDlXnHEnW0NDw2DXvv/++LV68OObaW2+9ZWvWrElgZYk3lt5bWlpMkt26dcuRmpz0+++/myRra2sbdY2fzvyDxtK7X8+8mdmMGTPsq6++GvE1t/ecXErtXCKTGh67hkzyz3l/EJnkTCYl9RO3e/fuqaOjQ6tWrYpemzRpklatWqX29vYR72lvb49ZL0lr1qwZdb1XxdO7JP3zzz+aP3++5s6d+9h3B/zGL/v+JAoKChQMBrV69WqdP3/e7XImxODgoCQpOzt71DV+3fux9C7578yHw2EdPXpUQ0NDKioqGnGNm3tOLpFLY+GXPX8SZNL/+GHvySRnMimpB7c//vhD4XBYOTk5MddzcnJG/az0zZs3x7Xeq+LpPS8vT998841Onjypb7/9VpFIRMXFxfrtt9+cKNlVo+377du3defOHZeqckYwGNQXX3yh48eP6/jx45o7d65KSkrU2dnpdmlPJBKJaNu2bXrjjTf0yiuvjLrOL2f+QWPt3U9nPhQK6emnn1ZGRobefvttNTQ06OWXXx5xrZt7Ti6RS2NBJpFJD0rG8/4gMsm5TJocV7VISkVFRTHvBhQXF+ull17Sl19+qV27drlYGRIpLy9PeXl50d+Li4vV29ururo6HTlyxMXKnkxlZaW6u7v1448/ul2K48bau5/OfF5eni5fvqzBwUF99913Ki8vV1tb26hBieTgp3+jGBsyyX/IJOcyKamfuD377LNKT0/XwMBAzPWBgQHNnj17xHtmz549rvVeFU/vD5syZYpee+01/fLLL4ko0VNG2/fp06frqaeecqkq9xQWFib1vldVVenUqVNqaWnRnDlzHrvWL2f+vvH0/rBkPvOBQEALFy7UkiVLVFtbq1dffVX79+8fca2be04ukUtjQSbFIpOS77zfRyY5m0lJPbgFAgEtWbJETU1N0WuRSERNTU2jfs60qKgoZr0kNTY2jrreq+Lp/WHhcFihUEjBYDBRZXqGX/Z9oly+fDkp993MVFVVpYaGBjU3Nys3N/f/3uOXvY+n94f56cxHIhHdvXt3xNfc3HNyiVwaC7/s+UQhk5Jv78mkWI5l0ri/zsRjjh49ahkZGXbw4EHr6emxrVu32jPPPGM3b940M7OysjKrqamJrj9//rxNnjzZPv74Y7t27Zpt377dpkyZYqFQyK0W4jbe3nfs2GFnzpyx3t5e6+josNLSUsvMzLSrV6+61ULc/v77b+vq6rKuri6TZPv27bOuri779ddfzcyspqbGysrKouuvX79uU6dOtffee8+uXbtmBw4csPT0dDt9+rRbLcRtvL3X1dXZiRMn7Oeff7ZQKGTV1dU2adIkO3funFstxO2dd96xrKwsa21ttf7+/ujP8PBwdI1fz3w8vfvlzNfU1FhbW5v19fXZlStXrKamxtLS0uzs2bNm5r09J5dSL5fIJDKJTCKTnMikpB/czMw+/fRTmzdvngUCASssLLSLFy9GX1u2bJmVl5fHrD927JgtWrTIAoGALV682H744QeHK5444+l927Zt0bU5OTm2du1a6+zsdKHqJ3f/64Qf/rnfb3l5uS1btuyRewoKCiwQCNiLL75o9fX1jtc9Ecbb+969e23BggWWmZlp2dnZVlJSYs3Nze4U/4RG6ltSzF769czH07tfzvyWLVts/vz5FggEbNasWbZy5cpoQJp5c8/JpdTKJTKJTCKTyKT7ErnnaWZm439OBwAAAABwSlL/jRsAAAAApAIGNwAAAADwOAY3AAAAAPA4BjcAAAAA8DgGNwAAAADwOAY3AAAAAPA4BjcAAAAA8DgGNwAAAADwOAY3AAAAAPA4BjcAAAAA8DgGNyBJFRUVKS0tTe3t7THXb9++rYKCAmVkZKixsdGl6gAAqYRMAhKPwQ1IUnv37pUkffTRR9Fr9+7d04YNG3TlyhUdOnRIq1evdqs8AEAKIZOAxGNwA5LU0qVLtW7dOjU3N6u1tVVmpk2bNqm5uVl1dXUqLS11u0QAQIogk4DESzMzc7sIAPEJhUIqKChQcXGxCgsLtW/fPn344YfavXu326UBAFIMmQQkFoMbkOTKy8t1+PBhSdKWLVv09ddfP7Lm+++/1+eff66Ojg7dunVLfX19euGFFxyuFADgd2QSkDh8VBJIcrNmzZIkTZs2TQcOHBhxzdDQkJYuXaqdO3c6WRoAIMWQSUDiTHa7AADx++yzz/TJJ58oJydHAwMDOnTokCoqKh5ZV1ZWJknq7u52ukQAQIogk4DE4okbkKSOHTum6upqLV++XF1dXcrKytKOHTs0PDzsdmkAgBRDJgGJx+AGJKGmpiaVlZUpPz9fJ06cUDAY1Lvvvqv+/n7t37/f7fIAACmETAKcwZeTAEmms7NTJSUlmjlzpi5cuKBgMCjpv//JaW5ursLhsK5fv67s7OxH7u3u7lZ+fj5/CA4AmBBkEuAcnrgBSaS3t1dr165VIBDQ6dOnowEpSdOnT9cHH3ygwcFB1dbWulglACAVkEmAs3jiBqQQ3t0EAHgFmQSMD98qCaSAP//8Uzdu3FBvb68kqaenR3/99ZfmzZs34sdXAABIFDIJiA9P3IAUcPDgQW3evPmR6/X19dq0aZPzBQEAUhaZBMSHwQ0AAAAAPI4vJwEAAAAAj2NwAwAAAACPY3ADAAAAAI9jcAMAAAAAj2NwAwAAAACPY3ADAAAAAI9jcAMAAAAAj2NwAwAAAACPY3ADAAAAAI9jcAMAAAAAj2NwAwAAAACPY3ADAAAAAI/7D9Htd7Got8mWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–17\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kwargs):\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    for alpha, style in zip(alphas, (\"b:\", \"g--\", \"r-\")):\n",
    "        if alpha > 0:\n",
    "            model = model_class(alpha, **model_kwargs)\n",
    "        else:\n",
    "            model = LinearRegression()\n",
    "        if polynomial:\n",
    "            model = make_pipeline(\n",
    "                PolynomialFeatures(degree=10, include_bias=False),\n",
    "                StandardScaler(),\n",
    "                model)\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=2,\n",
    "                 label=fr\"$\\alpha = {alpha}$\")\n",
    "    plt.legend(loc=\"upper left\")\n",
    "    plt.xlabel(\"$x_1$\")\n",
    "    plt.axis([0, 3, 0, 3.5])\n",
    "    plt.grid()\n",
    "\n",
    "plt.figure(figsize=(9, 3.5))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BGGBtMUkCq37",
    "outputId": "cd4492f7-595f-436a-96a9-3280742eb61a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.55302613])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", alpha=0.1 / m, tol=None,\n",
    "                       max_iter=1000, eta0=0.01, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())  # y.ravel() because fit() expects 1D targets\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Kyc_7hmgCq38",
    "outputId": "fc7777b6-a9ec-40c3-980f-1dd59ed9fe98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.55326019])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extra code – show that we get roughly the same solution as earlier when\n",
    "#              we use Stochastic Average GD (solver=\"sag\")\n",
    "ridge_reg = Ridge(alpha=0.1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "u021FqiqCq38",
    "outputId": "5d4df12c-544c-43d5-cc41-e9da0f4fbc09"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.97898394],\n",
       "       [0.3828496 ]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extra code – shows the closed form solution of Ridge regression,\n",
    "#              compare with the next Ridge model's learned parameters below\n",
    "alpha = 0.1\n",
    "A = np.array([[0., 0.], [0., 1.]])\n",
    "X_b = np.c_[np.ones(m), X]\n",
    "np.linalg.inv(X_b.T @ X_b + alpha * A) @ X_b.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "l_bbRMgzCq38",
    "outputId": "7551af33-3bcb-486e-dcfe-a160e7b7f1ff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.97896386]), array([0.38286422]))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg.intercept_, ridge_reg.coef_  # extra code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lVPCqFbtCq38"
   },
   "source": [
    "## Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8N1m7N0tCq38",
    "outputId": "bf3c0793-e6fb-4019-8e5d-289b1211d7d3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 345
    },
    "id": "lUez7cZdCq39",
    "outputId": "da04f8ee-fa3c-4622-92f5-44753c3318c7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this cell generates and saves Figure 4–18\n",
    "plt.figure(figsize=(9, 3.5))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$  \", rotation=0)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 1e-2, 1), random_state=42)\n",
    "plt.gca().axes.yaxis.set_ticklabels([])\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 795
    },
    "id": "QMisIPOWCq39",
    "outputId": "2da163b6-ab2f-4e1e-ca9e-50a98e81ea4d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1010x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – this BIG cell generates and saves Figure 4–19\n",
    "\n",
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[1, 1], [1, -1], [1, 0.5]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1 / len(Xr) * ((T @ Xr.T - yr.T) ** 2).sum(axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(J.argmin(), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])\n",
    "\n",
    "def bgd_path(theta, X, y, l1, l2, core=1, eta=0.05, n_iterations=200):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = (core * 2 / len(X) * X.T @ (X @ theta - y)\n",
    "                     + l1 * np.sign(theta) + l2 * theta)\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "\n",
    "for i, N, l1, l2, title in ((0, N1, 2.0, 0, \"Lasso\"), (1, N2, 0, 2.0, \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * N2 ** 2\n",
    "\n",
    "    tr_min_idx = np.unravel_index(JR.argmin(), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levels = np.exp(np.linspace(0, 1, 20)) - 1\n",
    "    levelsJ = levels * (J.max() - J.min()) + J.min()\n",
    "    levelsJR = levels * (JR.max() - JR.min()) + JR.min()\n",
    "    levelsN = np.linspace(0, N.max(), 10)\n",
    "\n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(theta=np.array([[2.0], [0.5]]), X=Xr, y=yr,\n",
    "                      l1=np.sign(l1) / 3, l2=np.sign(l2), core=0)\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid()\n",
    "    ax.axhline(y=0, color=\"k\")\n",
    "    ax.axvline(x=0, color=\"k\")\n",
    "    ax.contourf(t1, t2, N / 2.0, levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(fr\"$\\ell_{i + 1}$ penalty\")\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\")\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid()\n",
    "    ax.axhline(y=0, color=\"k\")\n",
    "    ax.axvline(x=0, color=\"k\")\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\")\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KxbPOIPsCq39"
   },
   "source": [
    "## Elastic Net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "sAKmR9nuCq3-",
    "outputId": "441a679d-d07d-47bb-c822-9b3776d1c0a2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Bn7T1RXbCq3-"
   },
   "source": [
    "## Early Stopping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rFNy8C_VCq3_"
   },
   "source": [
    "Let's go back to the quadratic dataset we used earlier:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cVxyC0owCq3_"
   },
   "source": [
    "**Warning**: In recent versions of Scikit-Learn, you must use `root_mean_squared_error()` to compute the RMSE, instead of `mean_squared_error(labels, predictions, squared=False)`. The following `try`/`except` block tries to import `root_mean_squared_error`, and if it fails it just defines it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "id": "H4OJQ3y0Cq3_"
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    from sklearn.metrics import root_mean_squared_error\n",
    "except ImportError:\n",
    "    from sklearn.metrics import mean_squared_error\n",
    "\n",
    "    def root_mean_squared_error(labels, predictions):\n",
    "        return mean_squared_error(labels, predictions, squared=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 395
    },
    "id": "ozu0tomXCq3_",
    "outputId": "4d59494f-0236-4d50-a846-bed8c499cf83"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from copy import deepcopy\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# extra code – creates the same quadratic dataset as earlier and splits it\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)\n",
    "X_train, y_train = X[: m // 2], y[: m // 2, 0]\n",
    "X_valid, y_valid = X[m // 2 :], y[m // 2 :, 0]\n",
    "\n",
    "preprocessing = make_pipeline(PolynomialFeatures(degree=90, include_bias=False),\n",
    "                              StandardScaler())\n",
    "X_train_prep = preprocessing.fit_transform(X_train)\n",
    "X_valid_prep = preprocessing.transform(X_valid)\n",
    "sgd_reg = SGDRegressor(penalty=None, eta0=0.002, random_state=42)\n",
    "n_epochs = 500\n",
    "best_valid_rmse = float('inf')\n",
    "train_errors, val_errors = [], []  # extra code – it's for the figure below\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.partial_fit(X_train_prep, y_train)\n",
    "    y_valid_predict = sgd_reg.predict(X_valid_prep)\n",
    "    val_error = root_mean_squared_error(y_valid, y_valid_predict)\n",
    "    if val_error < best_valid_rmse:\n",
    "        best_valid_rmse = val_error\n",
    "        best_model = deepcopy(sgd_reg)\n",
    "\n",
    "    # extra code – we evaluate the train error and save it for the figure\n",
    "    y_train_predict = sgd_reg.predict(X_train_prep)\n",
    "    train_error = root_mean_squared_error(y_train, y_train_predict)\n",
    "    val_errors.append(val_error)\n",
    "    train_errors.append(train_error)\n",
    "\n",
    "# extra code – this section generates and saves Figure 4–20\n",
    "best_epoch = np.argmin(val_errors)\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_valid_rmse),\n",
    "             xytext=(best_epoch, best_valid_rmse + 0.5),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05))\n",
    "plt.plot([0, n_epochs], [best_valid_rmse, best_valid_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(val_errors, \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(best_epoch, best_valid_rmse, \"bo\")\n",
    "plt.plot(train_errors, \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.axis([0, n_epochs, 0, 3.5])\n",
    "plt.grid()\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f259NNZNCq4A"
   },
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EDWlbkRhCq4A"
   },
   "source": [
    "## Estimating Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "id": "ryTx1lNYCq4A",
    "outputId": "a769a1e1-bdfb-4d58-966d-47f2ab57d7b4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extra code – generates and saves Figure 4–21\n",
    "\n",
    "lim = 6\n",
    "t = np.linspace(-lim, lim, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot([-lim, lim], [0, 0], \"k-\")\n",
    "plt.plot([-lim, lim], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-lim, lim], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\dfrac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.axis([-lim, lim, -0.1, 1.1])\n",
    "plt.gca().set_yticks([0, 0.25, 0.5, 0.75, 1])\n",
    "plt.grid()\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "toYFt3STCq4B"
   },
   "source": [
    "## Decision Boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SkWL7NA4Cq4B",
    "outputId": "a9689607-e783-490c-f246-c87f0188110e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'data_module']"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris(as_frame=True)\n",
    "list(iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Ja8UEeGwCq4B",
    "outputId": "ce38d9b8-850b-490c-b7bd-fe5628ef5fbf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      ":Number of Instances: 150 (50 in each of three classes)\n",
      ":Number of Attributes: 4 numeric, predictive attributes and the class\n",
      ":Attribute Information:\n",
      "    - sepal length in cm\n",
      "    - sepal width in cm\n",
      "    - petal length in cm\n",
      "    - petal width in cm\n",
      "    - class:\n",
      "            - Iris-Setosa\n",
      "            - Iris-Versicolour\n",
      "            - Iris-Virginica\n",
      "\n",
      ":Summary Statistics:\n",
      "\n",
      "============== ==== ==== ======= ===== ====================\n",
      "                Min  Max   Mean    SD   Class Correlation\n",
      "============== ==== ==== ======= ===== ====================\n",
      "sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "============== ==== ==== ======= ===== ====================\n",
      "\n",
      ":Missing Attribute Values: None\n",
      ":Class Distribution: 33.3% for each of 3 classes.\n",
      ":Creator: R.A. Fisher\n",
      ":Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      ":Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. dropdown:: References\n",
      "\n",
      "  - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "    Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "    Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "  - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "    (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "  - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "    Structure and Classification Rule for Recognition in Partially Exposed\n",
      "    Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "    Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "  - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "    on Information Theory, May 1972, 431-433.\n",
      "  - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "    conceptual clustering system finds 3 classes in the data.\n",
      "  - Many, many more ...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)  # extra code – it's a bit too long"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 143
    },
    "id": "S596tPeHCq4C",
    "outputId": "eebc98b8-1229-4407-a383-db1be10e98d0"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.google.colaboratory.intrinsic+json": {
       "summary": "{\n  \"name\": \"iris\",\n  \"rows\": 3,\n  \"fields\": [\n    {\n      \"column\": \"sepal length (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.19999999999999973,\n        \"min\": 4.7,\n        \"max\": 5.1,\n        \"num_unique_values\": 3,\n        \"samples\": [\n          5.1,\n          4.9,\n          4.7\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sepal width (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.2516611478423583,\n        \"min\": 3.0,\n        \"max\": 3.5,\n        \"num_unique_values\": 3,\n        \"samples\": [\n          3.5,\n          3.0,\n          3.2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal length (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.0577350269189625,\n        \"min\": 1.3,\n        \"max\": 1.4,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          1.3,\n          1.4\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"petal width (cm)\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 3.3993498887762956e-17,\n        \"min\": 0.2,\n        \"max\": 0.2,\n        \"num_unique_values\": 1,\n        \"samples\": [\n          0.2\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}",
       "type": "dataframe"
      },
      "text/html": [
       "\n",
       "  <div id=\"df-10df04af-42c1-4a8f-bc1a-6d8218832f3d\" class=\"colab-df-container\">\n",
       "    <div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</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",
       "    </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",
       "    </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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    <div class=\"colab-df-buttons\">\n",
       "\n",
       "  <div class=\"colab-df-container\">\n",
       "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-10df04af-42c1-4a8f-bc1a-6d8218832f3d')\"\n",
       "            title=\"Convert this dataframe to an interactive table.\"\n",
       "            style=\"display:none;\">\n",
       "\n",
       "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
       "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
       "  </svg>\n",
       "    </button>\n",
       "\n",
       "  <style>\n",
       "    .colab-df-container {\n",
       "      display:flex;\n",
       "      gap: 12px;\n",
       "    }\n",
       "\n",
       "    .colab-df-convert {\n",
       "      background-color: #E8F0FE;\n",
       "      border: none;\n",
       "      border-radius: 50%;\n",
       "      cursor: pointer;\n",
       "      display: none;\n",
       "      fill: #1967D2;\n",
       "      height: 32px;\n",
       "      padding: 0 0 0 0;\n",
       "      width: 32px;\n",
       "    }\n",
       "\n",
       "    .colab-df-convert:hover {\n",
       "      background-color: #E2EBFA;\n",
       "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
       "      fill: #174EA6;\n",
       "    }\n",
       "\n",
       "    .colab-df-buttons div {\n",
       "      margin-bottom: 4px;\n",
       "    }\n",
       "\n",
       "    [theme=dark] .colab-df-convert {\n",
       "      background-color: #3B4455;\n",
       "      fill: #D2E3FC;\n",
       "    }\n",
       "\n",
       "    [theme=dark] .colab-df-convert:hover {\n",
       "      background-color: #434B5C;\n",
       "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
       "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
       "      fill: #FFFFFF;\n",
       "    }\n",
       "  </style>\n",
       "\n",
       "    <script>\n",
       "      const buttonEl =\n",
       "        document.querySelector('#df-10df04af-42c1-4a8f-bc1a-6d8218832f3d button.colab-df-convert');\n",
       "      buttonEl.style.display =\n",
       "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
       "\n",
       "      async function convertToInteractive(key) {\n",
       "        const element = document.querySelector('#df-10df04af-42c1-4a8f-bc1a-6d8218832f3d');\n",
       "        const dataTable =\n",
       "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
       "                                                    [key], {});\n",
       "        if (!dataTable) return;\n",
       "\n",
       "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
       "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
       "          + ' to learn more about interactive tables.';\n",
       "        element.innerHTML = '';\n",
       "        dataTable['output_type'] = 'display_data';\n",
       "        await google.colab.output.renderOutput(dataTable, element);\n",
       "        const docLink = document.createElement('div');\n",
       "        docLink.innerHTML = docLinkHtml;\n",
       "        element.appendChild(docLink);\n",
       "      }\n",
       "    </script>\n",
       "  </div>\n",
       "\n",
       "\n",
       "    </div>\n",
       "  </div>\n"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 178
    },
    "id": "hDv_UHKDCq4C",
    "outputId": "f9205f65-9397-4c4a-ac47-b8d6a057fa7b"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><br><label><b>dtype:</b> int64</label>"
      ],
      "text/plain": [
       "0    0\n",
       "1    0\n",
       "2    0\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target.head(3)  # note that the instances are not shuffled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "y04MS8utCq4C",
    "outputId": "b6862603-2d29-4edd-80ca-bcc086b07ffc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 80
    },
    "id": "VCWvXwY_Cq4C",
    "outputId": "d3fd5c60-6b7e-49ee-ce2d-e2129fdffd2d"
   },
   "outputs": [
    {
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       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
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       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
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       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression(random_state=42)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = iris.data[[\"petal width (cm)\"]].values\n",
    "y = iris.target_names[iris.target] == 'virginica'\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "log_reg = LogisticRegression(random_state=42)\n",
    "log_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "id": "mmOY56cMCq4D",
    "outputId": "d3caa2ae-73c5-4f61-913e-6457686311ca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)  # reshape to get a column vector\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0, 0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))  # extra code – not needed, just formatting\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2,\n",
    "         label=\"Not Iris virginica proba\")\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica proba\")\n",
    "plt.plot([decision_boundary, decision_boundary], [0, 1], \"k:\", linewidth=2,\n",
    "         label=\"Decision boundary\")\n",
    "\n",
    "# extra code – this section beautifies and saves Figure 4–23\n",
    "plt.arrow(x=decision_boundary, y=0.08, dx=-0.3, dy=0,\n",
    "          head_width=0.05, head_length=0.1, fc=\"b\", ec=\"b\")\n",
    "plt.arrow(x=decision_boundary, y=0.92, dx=0.3, dy=0,\n",
    "          head_width=0.05, head_length=0.1, fc=\"g\", ec=\"g\")\n",
    "plt.plot(X_train[y_train == 0], y_train[y_train == 0], \"bs\")\n",
    "plt.plot(X_train[y_train == 1], y_train[y_train == 1], \"g^\")\n",
    "plt.xlabel(\"Petal width (cm)\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.legend(loc=\"center left\")\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "plt.grid()\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ynj1AvuOCq4E",
    "outputId": "673af67f-1caf-4000-a2f9-09b10694cdbe"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.6516516516516517)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ri1Ixg18Cq4E",
    "outputId": "8f58c470-9e3d-4141-a28f-94735897170d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  }
 ],
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  "kernelspec": {
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   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
   "version": "3.13.5"
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