lectures/04_kNNs-SVM-RBF.ipynb

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    "![](img/330-banner.png)"
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   "source": [
    "# Lecture 4: $k$-Nearest Neighbours and SVM RBFs  \n",
    "\n",
    "UBC 2021-22\n",
    "\n",
    "Instructor: Giulia Toti\n",
    "\n",
    "> If two things are similar, the thought of one will tend to trigger the thought of the other <br>\n",
    "-- Aristotle"
   ]
  },
  {
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   "source": [
    "## Imports"
   ]
  },
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   "execution_count": 1,
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   "source": [
    "import sys\n",
    "\n",
    "import IPython\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import HTML\n",
    "\n",
    "sys.path.append(\"code/.\")\n",
    "\n",
    "import ipywidgets as widgets\n",
    "import mglearn\n",
    "from IPython.display import display\n",
    "from ipywidgets import interact, interactive\n",
    "from plotting_functions import *\n",
    "from sklearn.dummy import DummyClassifier\n",
    "from sklearn.model_selection import cross_validate, train_test_split\n",
    "from utils import *\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "pd.set_option(\"display.max_colwidth\", 200)\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "source": [
    "## Learning outcomes\n",
    "\n",
    "From this lecture, you will be able to \n",
    "\n",
    "- explain the notion of similarity-based algorithms; \n",
    "- broadly describe how $k$-NNs use distances; \n",
    "- discuss the effect of using a small/large value of the hyperparameter $k$ when using the $k$-NN algorithm; \n",
    "- describe the problem of curse of dimensionality; \n",
    "- explain the general idea of SVMs with RBF kernel;\n",
    "- broadly describe the relation of `gamma` and `C` hyperparameters of SVMs with the fundamental tradeoff."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "```{important} \n",
    "If you want to run this notebook you will have to install `ipywidgets`. \n",
    "Follow the installation instructions [here](https://ipywidgets.readthedocs.io/en/latest/user_install.html).\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "## Motivation and distances [[video](https://youtu.be/hCa3EXEUmQk)]"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "### Analogy-based models\n",
    "\n",
    "- Suppose you are given the following training examples with corresponding labels and are asked to label a given test example.\n",
    "\n",
    "<img src='./img/knn-motivation.png' width=\"1000\">\n",
    "\n",
    "[source](https://vipl.ict.ac.cn/en/database.php)\n",
    "\n",
    "- An intuitive way to classify the test example is by finding the most \"similar\" example(s) from the training set and using that label for the test example.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "### Analogy-based algorithms in practice\n",
    "\n",
    "- [Herta's High-tech Facial Recognition](https://www.hertasecurity.com/en)\n",
    "    - Feature vectors for human faces \n",
    "    - $k$-NN to identify which face is on their watch list\n",
    "- Recommendation systems     \n",
    "\n",
    "<img src='./img/hetra.png' width=\"500\">\n",
    "\n",
    "[source](https://hertasecurity.com/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
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    }
   },
   "source": [
    "### General idea of $k$-nearest neighbours algorithm\n",
    "\n",
    "- Consider the following toy dataset with two classes.\n",
    "    - blue circles $\\rightarrow$ class 0\n",
    "    - red triangles $\\rightarrow$ class 1 \n",
    "    - green stars $\\rightarrow$ test examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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   "outputs": [],
   "source": [
    "X, y = mglearn.datasets.make_forge()\n",
    "X_test = np.array([[8.2, 3.66214339], [9.9, 3.2], [11.2, 0.5]])"
   ]
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   "execution_count": 3,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_train_test_points(X, y, X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Given a new data point, predict the class of the data point by finding the \"closest\" data point in the training set, i.e., by finding its \"nearest neighbour\" or majority vote of nearest neighbours. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def f(n_neighbors):\n",
    "    return plot_knn_clf(X, y, X_test, n_neighbors=n_neighbors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ce5ac59021654e53ad907534628baaab",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n_neighbors', max=7, min=1, step=2), Output()), _dom_cla…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactive(\n",
    "    f,\n",
    "    n_neighbors=widgets.IntSlider(min=1, max=7, step=2, value=1),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Geometric view of tabular data and dimensions \n",
    "\n",
    "- To understand analogy-based algorithms it's useful to think of data as points in a high dimensional space. \n",
    "- Our `X` represents the the problem in terms of relevant **features** ($d$) with one dimension for each **feature** (column).\n",
    "- Examples are **points in a $d$-dimensional space**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "How many dimensions (features) are there in the cities data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "cities_df = pd.read_csv(\"data/canada_usa_cities.csv\")\n",
    "X_cities = cities_df[[\"longitude\", \"latitude\"]]\n",
    "y_cities = cities_df[\"country\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(X_cities.iloc[:, 0], X_cities.iloc[:, 1], y_cities)\n",
    "plt.xlabel(\"longitude\")\n",
    "plt.ylabel(\"latitude\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Recall the [Spotify Song Attributes](https://www.kaggle.com/geomack/spotifyclassification/home) dataset from homework 1. \n",
    "- How many dimensions (features) we used in the homework? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of features in the Spotify dataset: 13\n"
     ]
    },
    {
     "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>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>duration_ms</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>key</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>mode</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>time_signature</th>\n",
       "      <th>valence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0102</td>\n",
       "      <td>0.833</td>\n",
       "      <td>204600</td>\n",
       "      <td>0.434</td>\n",
       "      <td>0.021900</td>\n",
       "      <td>2</td>\n",
       "      <td>0.1650</td>\n",
       "      <td>-8.795</td>\n",
       "      <td>1</td>\n",
       "      <td>0.4310</td>\n",
       "      <td>150.062</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1990</td>\n",
       "      <td>0.743</td>\n",
       "      <td>326933</td>\n",
       "      <td>0.359</td>\n",
       "      <td>0.006110</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1370</td>\n",
       "      <td>-10.401</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0794</td>\n",
       "      <td>160.083</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0344</td>\n",
       "      <td>0.838</td>\n",
       "      <td>185707</td>\n",
       "      <td>0.412</td>\n",
       "      <td>0.000234</td>\n",
       "      <td>2</td>\n",
       "      <td>0.1590</td>\n",
       "      <td>-7.148</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2890</td>\n",
       "      <td>75.044</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.6040</td>\n",
       "      <td>0.494</td>\n",
       "      <td>199413</td>\n",
       "      <td>0.338</td>\n",
       "      <td>0.510000</td>\n",
       "      <td>5</td>\n",
       "      <td>0.0922</td>\n",
       "      <td>-15.236</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0261</td>\n",
       "      <td>86.468</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.1800</td>\n",
       "      <td>0.678</td>\n",
       "      <td>392893</td>\n",
       "      <td>0.561</td>\n",
       "      <td>0.512000</td>\n",
       "      <td>5</td>\n",
       "      <td>0.4390</td>\n",
       "      <td>-11.648</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0694</td>\n",
       "      <td>174.004</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.904</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   acousticness  danceability  duration_ms  energy  instrumentalness  key  \\\n",
       "0        0.0102         0.833       204600   0.434          0.021900    2   \n",
       "1        0.1990         0.743       326933   0.359          0.006110    1   \n",
       "2        0.0344         0.838       185707   0.412          0.000234    2   \n",
       "3        0.6040         0.494       199413   0.338          0.510000    5   \n",
       "4        0.1800         0.678       392893   0.561          0.512000    5   \n",
       "\n",
       "   liveness  loudness  mode  speechiness    tempo  time_signature  valence  \n",
       "0    0.1650    -8.795     1       0.4310  150.062             4.0    0.286  \n",
       "1    0.1370   -10.401     1       0.0794  160.083             4.0    0.588  \n",
       "2    0.1590    -7.148     1       0.2890   75.044             4.0    0.173  \n",
       "3    0.0922   -15.236     1       0.0261   86.468             4.0    0.230  \n",
       "4    0.4390   -11.648     0       0.0694  174.004             4.0    0.904  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spotify_df = pd.read_csv(\"data/spotify.csv\", index_col=0)\n",
    "X_spotify = spotify_df.drop(columns=[\"target\", \"song_title\", \"artist\"])\n",
    "print(\"The number of features in the Spotify dataset: %d\" % X_spotify.shape[1])\n",
    "X_spotify.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Dimensions in ML problems \n",
    "\n",
    "In ML, usually we deal with high dimensional problems where examples are hard to visualize.  \n",
    "\n",
    "- $d \\approx 20$ is considered low dimensional\n",
    "- $d \\approx 1000$ is considered medium dimensional \n",
    "- $d \\approx 100,000$ is considered high dimensional "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Feature vectors \n",
    "\n",
    "**Feature vector**\n",
    ": is composed of feature values associated with an example.\n",
    "\n",
    "Some example feature vectors are shown below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An example feature vector from the cities dataset: [-130.0437   55.9773]\n",
      "An example feature vector from the Spotify dataset: \n",
      "[ 1.02000e-02  8.33000e-01  2.04600e+05  4.34000e-01  2.19000e-02\n",
      "  2.00000e+00  1.65000e-01 -8.79500e+00  1.00000e+00  4.31000e-01\n",
      "  1.50062e+02  4.00000e+00  2.86000e-01]\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    \"An example feature vector from the cities dataset: %s\"\n",
    "    % (X_cities.iloc[0].to_numpy())\n",
    ")\n",
    "print(\n",
    "    \"An example feature vector from the Spotify dataset: \\n%s\"\n",
    "    % (X_spotify.iloc[0].to_numpy())\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Similarity between examples\n",
    "\n",
    "Let's take 2 points (two feature vectors) from the cities dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "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>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>-104.8253</td>\n",
       "      <td>38.8340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-112.0741</td>\n",
       "      <td>33.4484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    longitude  latitude\n",
       "69  -104.8253   38.8340\n",
       "35  -112.0741   33.4484"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_cities = X_cities.sample(2, random_state=120)\n",
    "two_cities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The two sampled points are shown as big black circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    X_cities.iloc[:, 0], X_cities.iloc[:, 1], y_cities, s=8, alpha=0.3\n",
    ")\n",
    "mglearn.discrete_scatter(\n",
    "    two_cities.iloc[:, 0], two_cities.iloc[:, 1], markers=\"o\", c=\"k\", s=18\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Distance between feature vectors \n",
    "\n",
    "- For the cities at the two big circles, what is the _distance_ between them?\n",
    "- A common way to calculate the distance between vectors is calculating the **Euclidean distance**. \n",
    "- The euclidean distance between vectors $u = <u_1, u_2, \\dots, u_n>$ and $v = <v_1, v_2, \\dots, v_n>$ is defined as: \n",
    "\n",
    "$$distance(u, v) = \\sqrt{\\sum_{i =1}^{n} (u_i - v_i)^2}$$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Euclidean distance "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "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>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>-104.8253</td>\n",
       "      <td>38.8340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-112.0741</td>\n",
       "      <td>33.4484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    longitude  latitude\n",
       "69  -104.8253   38.8340\n",
       "35  -112.0741   33.4484"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_cities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "- Subtract the two cities\n",
    "- Square the difference\n",
    "- Sum them up \n",
    "- Take the square root "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subtract the cities: \n",
      "longitude   -7.2488\n",
      "latitude    -5.3856\n",
      "dtype: float64\n",
      "\n",
      "Sum of squares: 81.5498\n",
      "Euclidean distance between cities: 9.0305\n"
     ]
    }
   ],
   "source": [
    "# Subtract the two cities\n",
    "print(\"Subtract the cities: \\n%s\\n\" % (two_cities.iloc[1] - two_cities.iloc[0]))\n",
    "\n",
    "# Squared sum of the difference\n",
    "print(\n",
    "    \"Sum of squares: %0.4f\" % (np.sum((two_cities.iloc[1] - two_cities.iloc[0]) ** 2))\n",
    ")\n",
    "\n",
    "# Take the square root\n",
    "print(\n",
    "    \"Euclidean distance between cities: %0.4f\"\n",
    "    % (np.sqrt(np.sum((two_cities.iloc[1] - two_cities.iloc[0]) ** 2)))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>-104.8253</td>\n",
       "      <td>38.8340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-112.0741</td>\n",
       "      <td>33.4484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    longitude  latitude\n",
       "69  -104.8253   38.8340\n",
       "35  -112.0741   33.4484"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 9.03049217],\n",
       "       [9.03049217, 0.        ]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Euclidean distance using sklearn\n",
    "from sklearn.metrics.pairwise import euclidean_distances\n",
    "\n",
    "euclidean_distances(two_cities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Note: `scikit-learn` supports a number of other [distance metrics](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.DistanceMetric.html).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Finding the nearest neighbour\n",
    "\n",
    "- Let's look at distances from all cities to all other cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All distances: (209, 209)\n",
      "\n",
      "[[        inf  4.95511263  9.869531   ... 52.42640992 58.03345923\n",
      "  51.49856241]\n",
      " [ 4.95511263         inf 14.6775792  ... 57.25372435 62.77196948\n",
      "  56.25216034]\n",
      " [ 9.869531   14.6775792          inf ... 44.23515175 50.24972011\n",
      "  43.69922405]\n",
      " ...\n",
      " [52.42640992 57.25372435 44.23515175 ...         inf  6.83784786\n",
      "   3.32275537]\n",
      " [58.03345923 62.77196948 50.24972011 ...  6.83784786         inf\n",
      "   6.55573969]\n",
      " [51.49856241 56.25216034 43.69922405 ...  3.32275537  6.55573969\n",
      "          inf]]\n"
     ]
    }
   ],
   "source": [
    "dists = euclidean_distances(X_cities)\n",
    "np.fill_diagonal(dists, np.inf)\n",
    "print(\"All distances: %s\\n\\n%s\" % (dists.shape, dists))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's look at the distances between City 0 and some other cities. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature vector for city 0: \n",
      "longitude   -130.0437\n",
      "latitude      55.9773\n",
      "Name: 0, dtype: float64\n",
      "\n",
      "Distances from city 0 to the first 5 cities: [        inf  4.95511263  9.869531   10.10645223 10.44966612]\n",
      "The closest city from city 0 is: 81 \n",
      "\n",
      "with feature vector: \n",
      "longitude   -129.9912\n",
      "latitude      55.9383\n",
      "Name: 81, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"Feature vector for city 0: \\n%s\\n\" % (X_cities.iloc[0]))\n",
    "print(\"Distances from city 0 to the first 5 cities: %s\" % (dists[0][:5]))\n",
    "# We can find the closest city with `np.argmin`:\n",
    "print(\n",
    "    \"The closest city from city 0 is: %d \\n\\nwith feature vector: \\n%s\"\n",
    "    % (np.argmin(dists[0]), X_cities.iloc[np.argmin(dists[0])])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, so the closest city to City 0 is City 81. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Question\n",
    "\n",
    "- Why did we set the diagonal entries to infinity before finding the closest city?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Finding the distances to a query point\n",
    "\n",
    "We can also find the distances to a new \"test\" or \"query\" city:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[58.85545875],\n",
       "       [63.80062924],\n",
       "       [49.30530902],\n",
       "       [49.01473536],\n",
       "       [48.60495488],\n",
       "       [39.96834506],\n",
       "       [32.92852376],\n",
       "       [29.53520104],\n",
       "       [29.52881619],\n",
       "       [27.84679073]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's find a city that's closest to the a query city\n",
    "query_point = [[-80, 25]]\n",
    "\n",
    "dists = euclidean_distances(X_cities, query_point)\n",
    "dists[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The query point [[-80, 25]] is closest to the city with index 72 and the distance between them is: 0.7982\n"
     ]
    }
   ],
   "source": [
    "# The query point is closest to\n",
    "print(\n",
    "    \"The query point %s is closest to the city with index %d and the distance between them is: %0.4f\"\n",
    "    % (query_point, np.argmin(dists), dists[np.argmin(dists)])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## $k$-Nearest Neighbours ($k$-NNs) [[video](https://youtu.be/bENDqXKJLmg)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "small_cities = cities_df.sample(30, random_state=90)\n",
    "one_city = small_cities.sample(1, random_state=44)\n",
    "small_train_df = pd.concat([small_cities, one_city]).drop_duplicates(keep=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_small_cities = small_train_df.drop(columns=[\"country\"]).to_numpy()\n",
    "y_small_cities = small_train_df[\"country\"].to_numpy()\n",
    "test_point = one_city[[\"longitude\", \"latitude\"]].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gwYP55JNPOHDgQIP3ceONN1Y7iVeb2NhYBg4cSFJSEqmpqTz33HPs27evMtlGRUXx+uuv89lnn/HII48QFhZGREQEv/nNbwC49957SU1NJT4+3us4eHFxMSkpKZSVlVU2fFi0aBH33HMPzz33HHFxcfzhD3/w+/e6+eabefbZZ3G5XDz++OOMHj2ahx9+GGstxhgeeeQR9u/fj7WWIUOG0Lt3+T2RmzZtqjb9bYNZa5vtkZycbMX51qxZY6M6dbax3xpjr7x3if3qT962V967xMZ+a4yN6tTZrlmzJtghShP55JNPLll2/vx5O2fOHBsdHW0pnzqjXo/o6Gg7Z84ce/78+SD8Rv92zTXX2IKCgib/nAcffNCuX7++1vfPnz9vU1JS7IULF7y+7+3fANhpveRUDaHIJVJTU8nJzmJscjxnV87m0IK7OLtyNmOT48nJziI1NTXYIUozioyMpGfPnowc2bCuiaNGjaJnz56tZnbC2bNn+7zi5vPPP+fZZ5+lTZvGD4D41dAhUNTQQcTZamvoUFJSwksvvcTatWtZu3at3/sbPnw4w4cP11wo9dAUDR1EpJWwnvHbqtq2bcu0adOw1hITE+N1NsKqKmYjTElJYdq0aUrefqpvQa0ELiKV2rVrx/Hjx4mNjb0kiUdFRfHAAw+wevVqunfvXjkf+JEjRyguLiYyMpKuXbty0003cc0112g+8Hqy1nL8+HHatWvn9zZK4CJSqVu3bhw6dIiCgoJa1+nevTtf+9rXyM/P57rrrqt2k0/btm1JSkoiISGBiIgIzZlTT+3ataNbt25+r68xcBERh6ttDFxXoYiIhCglcBGREKUxcAkZ6oQuUp0SuDieOqGLeKcELo6mTugitVMCF8dSJ3QR35TAxbEa0wk9JiaGa665pnISfpGWSFehiCM1Zyd0kVClBC6O1Jyd0EVClRK4OFJzdkIXCVVK4OJIzdkJXSRU+XUS0xiTDxQCF4FSa20/Y8zlQDqQAOQDY6y1J5smTGmNgtUJXSRU1KcCv9la66oyocpPgY3W2uuAjZ7XIgHT2EsAG9oJXSRUNGYI5bvAUs/zpcDtjY5GxKM5O6GLhCp/E7gF1hljso0x93qWfcVa6wbw/OzibUNjzL3GmJ3GmJ2+5hhuDfLy8pg+YyYxsXGEhYcTExvH9BkzNWeyF4MHD+bGG29s1D787YQuEqr8TeADrbV9gVRgujHG7/8rrLWLrbX9rLX94uLiGhRkS5CRkYEruT/pu47S4e5nuPrhVXS4+xnSdx3FldyfjIyMYIfoKC6Xi4SEBKKjoxu0fXR0NAkJCfTu3TvAkYk4h18J3Fr7hefnMWAVMAA4aoyJB/D8PNZUQYa6vLw8xoybQNTo2UQNmkRE53hMWDgRneOJGjSJqNGzGTNuQkhU4s31LSIQndATExP57shhHDlyJKCxiThFnQncGNPBGBNd8RwYBuwF3gWmeFabArzTVEGGugULFxGZNIzIqy7t9g0QeVV3InsM5fkXftXMkdVPc3+LuO2220hJSWH48OH12m748OEMGDCA7B3bydy+jfnz5gY0LhGnqLOlmjHm/1FedUP5ZYfLrbX/bYyJBd4Evgp8DnzPWnvC175aa0u1mNg4Otz9DBGdaz8pd+Gkm7MrZ3PquDO/yOTl5eFK7k/U6Nle/xAVH95H0XvzyMnOIjExMWCfW9dshFVV7YT+ne98h/59erJxXBi3vlFG7t//QdeuXQMWl0hzqq2lWp3XgVtr/wFcMpBorT0ODAlMeC3bmVMn6NTJ6zneSm06xlF4yuffv6Dy51vEBc+3iBcXLQzY5za0E/pjDz/ElF7h9IkPY3JPw/x5c1mw6KWAxSXiBGpq3AxaQgXuhN+huLiY3bt3V3bksdZijKnsyNO7d28iIyNxu930uD6R3GnhxEeH4S4sI+mVi6rC5RJ5eXksWLiItOXLOXPqBB1jLmfC+PH8+KEHA/pNsrEaXIFL400YP570XRuIGDSp1nWK965n4oTxzRhV/TjhW0RkZCQDBgxgwIABPtebP28uU3qVJ2+A+OgwJvdEVbhUk5GRwZhxE4hMGkaHu5+hU6culJ4+RvquDSxL7s+bK9JITU0Ndpg+aS6UZvDjhx6keO86ig/v8/p+8eF9FOeuZ9bMGc0cmf86xlxO6WnflXXpmQKiYy5vpoi8c7vdLF36Ko+mVF/+aAosXfoHXZEiQMu5MkwJvBkkJiby5oo0it6bR9GWZVw46cZeLOXCSTdFW5ZR9N483lyR5qivbDVNGD+e4twNPtdxwreImtV3hfIqPFxXpAjQcq4M0xh4M8rLy+P5F37F62nLKTx1guiYy5k4YTyzZs5wdPKG4F2FUh81x74veV9j4eLhhHM69VHbGLgSuPitcsywx1Aik4bSpmMcpWcKKN67nuLc9UEfM5w140ew6zWev7X2L5azNpRh+k7WWHgrFxYeztUPr8KEhde6jr1YyqEFd3HxYmkzRuadTmJKo6WmppKTneX5FjG7+reIZcGrvCtk7djOtqwiFm7zvd7Akr80T0DiWBXndHxV4E44p1MXVeAi0upMnzGT9F1HifJxZVjRlmWMTY4P6H0NDVVbBa6TmCLS6rSEK8NAQygi0gpVXBk2ZtwELvg4pxPsYcG6qAIXkVap4pzO2OR4zq6czaEFd3F25WzGJseTk53l+Jt4QGPgIiKOpzFwEZEWRglcRCREKYGLiIQoJXARkRClBC4iEqKUwEVEQpQSuIhIiFICF5EWJy8vj+kzZhITG0dYeDgxsXFMnzHT8Q0a6ksJXERajLy8PEZ/93au+0YPfv3Sryg8V0JUn1FEDptF+q6juJL7k5GREewwA0YJXERChq/KOiMjg159+rH5SBjx97zIV3/yNl0n/RIT0Y5/vfM/hMd3J2r0bO4eM5aJU6a2iOpct9KLSEio2oQ4ssettPE0IS7O3cC5j9dSdrGUmDufqrVj1LG35hJz41RObnqFTn1Sad9rRLV9FO9dF7CmJIHudq+OPCISsvxp6Xf0j08RP+WFWps0HF/7Imc/2cxXxvy8SdsC+vpD09A/EpoLRURClj9NiKN6DcP96kOc2LiECyfdl6xjS0uJ6j28SRsZN3e3eyVwEXG8tOXLiexxq891ovuMwrRpg2nTliOvPcy5vOrf9s/9I4voPiN97iMyaSivpy1vcJxz//sZTHgb2nTy3jQ70N3u/U7gxphwY8wuY8xqz+s5xpjDxpgcz8P3kRERaaAzp07QplMXn+u06RhH2blCOt84hS53PcG/3l9QrRIvO3fGr30UnjrR4Dj/Nz2NsC+Pc27HG7Wu09g/ElXVpwKfCdTsP/S8tdbleawJSEQiIjVUNCH2pfRMAWHtOwKeIZXewyj8aHXl+6btZX7to6GNjN1uNxdKzrNp8mWcy93AxaKTXtdr7B+JqvxK4MaYbsAo4JWAfKqISD1MGD+e4twNPtcp+ngtHbrfWPk6qtdwzu77ECg/QWnLyijK8V1nFu9dz8QJ4xsU4/x5c/mBqy194sOZ2iu81io8kN3u/a3AFwKPAmU1lj9gjPnYGPN7Y0xnbxsaY+41xuw0xuwsKChoRKgi0lr504S4aPc6ovveVrmsTcc4yr48w4k/vcLR9J9x87cHUbpvU5M0Mna73Sxd+ipPDG4LwM8GhtVahTfmj0RNdSZwY8xtwDFrbXaNt34DJAIuwA380tv21trF1tp+1tp+cXFxjQxXRFqbimuqyy5e5OgbP+Pkn37HhZNu7MVSLpx0c/LDVzn21lyuGPXjapcQlp4pwLSJYPJ/XMP+fbn8aeN6VqYvp+i9eRRtWVZtH0VbllH03rwGNzKeP28uU3qFEx9dnlLjo8O8VuGB7nZf53XgxphngElAKdAO6Aj8r7V2YpV1EoDV1tokX/vSdeAiUh81r6m2ZRc5s+MtvvzbFmxpMWHtO9Gh+41E973tkuu/i7YsY2xyPC8uWlhteV5eHs+/8CteT1tO4akTRMdczsQJ45k1c0aDkrfb7abH9YnkTvt3AgdwF5bxtV+X0PkHv8VeLK3W7T5Q14HX60YeY8xNwE+stbcZY+KttW7P8llAirV2rK/tlcBFxF++bt65cNLNkWWz6HJ37XdeBuKmHH/MmvEj2PUaz9966YDGj94/z+93XaBdpysa9UeitgTepmEhAzDfGOMCLJAP/LAR+xIRqcbXzTsRneO54rafcPSPT9HJlUr73iNo0zGO0jMF1Srdpk7eFWPfudPCvb7/xOC2pH8aTm7ux3Tt6v3a8MbQrfQi4kgxsXF0uPuZWm+NBzh3cDen3n2Gy9pdFpDhkPryVX1XrrOhDNN3MgsWvdTgz2mKClxExKtATOZ05tQJOtVx4027bj0oPX+OU2cLAxF2vWXt2M62rCIWbvO93sCSvzTJ5+tWehEJqIyMDFzJ/UnfdZQOdz9D13t+TemVLl5e8ju+9rXriOrU2a/pW/29eSdQ11Q3xNbMXVhr63xszdzVJJ+vBC4iAVNzMqfzn+/hyLIf8+X+v1BW8mX5nZJf7UfaXz6jV59kBvTtyZEjR7zuy5+bdwJ5TXUoUgIXkYCpeuKxcPc6Tm74LdF9RhI/5YXyBgsTf0F4VGcK920lvGMcn36ylx/PfMDrvvy5eSeQ11SHIp3EFJGAqTjxCOB+dWatc29/uX8HRe/OZds9Hfj2q+f47OBhr1dpVF4H3mMokUlDvV5pEogGDE6n+cBFpMlVzBpY+NFqn3NvX8zbxlRXBH3iw5ncK5w5P3vc63qpqankZGcxNjmesytnc2jBXZxdOZuxyfHkZGe1iuTtiypwEQmYigr8yOuP0HXic14vASwtOsGJJT8g74HLiI8Ow11YxvW/Ps+nB/7ZJNdKtwSqwEWkyVWcePQ19/a5ra8ytVdYtXlDJiaZWqtwqZ0SuIj4xVdH+AoVJx7D2nXweglgadEJzu37kCcGR1Zb/sTgSJanvV7rFSninRK4iNSp5rXdVz+8ig53P0P6rqO4kvuTkZEBQGJiIm+uSCOcMopyPrhkPzWr7wqqwhtGY+Ai4pM/HeFrThz1pz/9iRG3fYfYu+ZUblNz7LsmjYXXTmPgItIg/nSEr9mo95ZbbuGdt/5I0XvzKNyylAsn3Zzb8gev1XcFVeH1pwpcRHzyZ1KpCyfdnF05m1PHq497V517+2JRAUUldX9ewpVXcOCwundVpQpcRBrE347w3hr1JiYm8uKihZw6fozevV1+fd5VV3VrSJitkmYjFBGfKiaV8lWB+zOpVFNN6NSaqQIXEZ80qZRzKYGLiE+aVMq5NIQiIj5VXNs9ZtwELviYVKo5OuBIdarARaROmlTKmXQZoYiIw+kyQhGRFkYJXEQkRCmBi4iEKCVwEZEQpQQuIhKilMBFREKU3wncGBNujNlljFnteX25MWa9MWa/52fnpgtTRERqqk8FPhOoei/tT4GN1trrgI2e1yIi0kz8SuDGmG7AKOCVKou/Cyz1PF8K3B7QyERExCd/K/CFwKNAWZVlX7HWugE8P71OGGyMudcYs9MYs7OgQJO0i0j9ud1uRgy5UU2Pa6gzgRtjbgOOWWuzG/IB1trF1tp+1tp+cXFxDdmFiLRy8+fNJXP7NubPmxvsUBzFnwp8IPAdY0w+8AZwizHmdeCoMSYewPPzWO27EGndVEE2nNvtZunSV9k4qR1Ll/5Bx7CKOhO4tfZxa203a20CMBb4k7V2IvAuMMWz2hTgnSaLUiTEqYJsuPnz5jKlVzh94sOZ3DNcx7CKxlwH/iww1BizHxjqeS0iNaiCbLiKY/doSvnrR1PQMayiXgncWvtna+1tnufHrbVDrLXXeX5e2tFURFRBNkLFsYuPLk9V8dFhOoZVaD5wkSbkdrvpcX0iudPKk5C7sIykVy6S+/d/0LVr12CH52g1j13l8lZ4DDUfuEgQqIJsuJrHroKO4b+pAhdpIqogG662Y1f5fis7hqrARZqZKsiGq+3YVdAxLKcKXKQJqIJsnEED+rAtK6fO9Qb2d7E1c1fTBxRkqsBFmpEqyMbZmrkLa22dj9aQvH1pE+wARFqirB3b2ZZVxMJtvtcbWPKX5glIWiQlcJEm0NorQ2keGkIREQlRSuAiIiFKCVxEJEQpgYuIhCglcBGREKUELiISopTARURClBK4iEiIUgJv5dSrUSR0KYG3curVKBK6lMBbMfVqFAltSuCtmHo1ihNoGK/hlMBbKXX7FqfQMF7DKYG3UurV2HCqGANHw3iNowTeCtWsviuoCvePKsbA0TBe4yiBt0Lq1dhwqhgDR8N4jacE3srUVn1X0P9EvqliDBwN4zWeEngro16NDaeKMXA0jBcYdbZUM8a0AzYDkZ71V1prnzLGzAGmAQWeVWdba9c0VaASGOrV2HDeK8by5QsWvRTk6EKL72E8HVN/GWut7xWMMUAHa22RMSYC2ArMBEYARdbaX/j7Yf369bM7d+5sTLwiQeF2u+lxfSK506onHXdhGUmvXCT37/+ga9euQYwwdNR2LCvf1zG9hDEm21rbr+byOodQbLkiz8sIz8N31hdpYXTiN3A0jBc4dVbgAMaYcCAb+BrwkrX2Mc8QylTgDLATeNhae9LXflSBSyhSxRhYgwb0YVtWTp3rDezvYmvmrqYPKAQ0uAIHsNZetNa6gG7AAGNMEvAbIBFwAW7gl7V88L3GmJ3GmJ0FBQXeVhFxNFWMgbU1cxfW2jofSt51q/MkZlXW2lPGmD8DI6qOfRtjlgCra9lmMbAYyivwhocqEhw68StO5c9VKHHABU/yvgy4FfgfY0y8tdbtWe0OYG8TxikSNKoExan8qcDjgaWecfAw4E1r7WpjzGvGGBflJzTzgR82WZQiInKJOhO4tfZjoI+X5ZOaJCIREfGL7sQUEQlRSuBSb5pOVcQZlMCl3jSdqogzKIFLvWg6VRHnUAKXetF0qiLOoQQuftN0qiLOogTeggX6ZKMm4K9OJ3Ml2JTAW7BAnmzUBPyX0slcCTYl8BYq0CcbNZ1qdTqZK06gBN5CBfJko/poXkonc8UJlMBboECfbNR0qtXpZK44Rb2mk5XQEOjejZpOtTr1xhSn8KsjT6CoI0/TU+/GpqXjK8HQqI48Ejp0srFp6fiKk6gCb0HUu7Fp6fhKsKgCbwV0srFp6fiK0+gkZguik41NS8dXnEYJvAVR78ampeMrTqMhFBGREKUELiISopTARURClBK4iEiIUgIXEQlRSuAi9aAmDuIkSuAi9aAmDuIkSuAiflITB3EaJXARP6mJgzhNnQncGNPOGJNpjNltjMk1xvzcs/xyY8x6Y8x+z8/OTR+uSHCoiYM4kT8VeDFwi7W2N+ACRhhj/gP4KbDRWnsdsNHzWqRF8t7EQVW4BFedCdyWK/K8jPA8LPBdYKln+VLg9qYIUCTYausJqipcgs2vMXBjTLgxJgc4Bqy31u4AvmKtdQN4fnapZdt7jTE7jTE7CwoKAhS2SPNREwdxqno1dDDGxACrgBnAVmttTJX3TlprfY6Dq6GDhBo1cRAnCEhDB2vtKeDPwAjgqDEm3rPzeMqrc5EWRU0cxMnqnA/cGBMHXLDWnjLGXAbcCvwP8C4wBXjW8/OdpgxUJBjUxEGczJ+GDvHAUmNMOOUV+5vW2tXGmO3Am8aY/w98DnyvCeMUCQo1cRAnqzOBW2s/Bvp4WX4cGNIUQYmISN10J6aISIhSAhcRCVH1uoyw0R9mTAFwsNk+sG5XAP8KdhD1oHibVqjFC6EXs+JtmGustXE1FzZrAncaY8xOb9dWOpXibVqhFi+EXsyKN7A0hCIiEqKUwEVEQlRrT+CLgx1APSnephVq8ULoxax4A6hVj4GLiISy1l6Bi4iELCVwEZEQ1SoSuDHme552cGXGmH5Vlg8wxuR4HruNMXdUeS/ZGLPHGPOZMWaRMcY4IN6hxphsT1zZxphbnBBvHTHHGmM2GWOKjDEv1tjGccfY897jnpj+bowZ7oR4a8TX2xiz3RPLe8aYjnXFHkzGGJcx5q+e/892GmMGVHnPifGmV8kL+Z5eCBXvOStea22LfwDdgespnwq3X5Xl7YE2nucVU+JWvM4EvgkYIANIdUC8fYArPc+TgMNV3gtavHXE3AEYBNwHvFhjGyce4xuA3UAkcC2QB4QHO94asWcBN3qe3wPMrSv2YD6AdRXHChgJ/NnJ8daI/ZfAk06Nt1VU4Nbafdbav3tZ/qW1ttTzsh3lreIq5jfvaK3dbsv/5ZbRjC3jfMS7y1r7hedlLtDOGBMZ7Hg9sdUW81lr7VbgfNXlwY65tngpbxX4hrW22Fp7APgMGBDseGu4Htjseb4euMvz3GvsQYivJgtUfEvoBFT8N+zUeAHwfMMaA6zwLHJcvK0igftijEkxxuQCe4D7PAn9KuBQldUOeZY5yV3ALmttMaERb01Ojfkq4J9VXlfE5aR49wLf8Tz/HnC153ltsQfbQ8Bzxph/Ar8AHvcsd2q8Fb4NHLXW7ve8dly8/swHHhKMMRsAbz2t/tNaW2uzCVve37OHMaY75fOeZ1D+FfmSVQMTabmGxuvZtgflTTWGVSzyslrArw9tTMzedudlmROOcW1xNcsxrgzCR+yUD5ssMsY8SXljlZKKzbys3yzXCdcR7xBglrX2LWPMGOB3lDeGcWS8Vf7bGMe/q28IYry1aTEJ3Fp7ayO332eMOUv52PIhoFuVt7vx7699AdHQeI0x3SjvSzrZWpvnWdzk8ULjj3ENTj3Gh/h3RQv/jqtZjnEFP2IfBmCM+TowyrOsttibnK94jTHLgJmel38EXvE8d2S8AMaYNsCdQHKVxUGLtzategjFGHOt5x8KY8w1lI8t5ltr3UChMeY/PONgk3FAyzhT3lT6feBxa21lky+nxuuLg2N+FxjrObdwLXAdkOmkeI0xXTw/w4CfAS973vIaezBirOEL4EbP81uAiiEJp8YL5d8Q/matrTps5rx4g32WtzkewB2U//UsBo4Caz3LJ1F+MjAH+Ai4vco2/Sgfa8wDXsRz12qQ4/0ZcNYTb8WjS7Dj9RWz57184ARQ5FnnhmDHXEe8/+mJ6e9UudIk2Me4ShwzgU89j2erxlFb7MF8UH4VUjblV3DsAJKdHK8nrlcpPydWc7mj4tWt9CIiIapVD6GIiIQyJXARkRClBC4iEqKUwEVEQpQSuIhIiFICFxEJUUrgIiIh6v8AEt9NDJJHSSMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_train_test_points(\n",
    "    X_small_cities,\n",
    "    y_small_cities,\n",
    "    test_point,\n",
    "    class_names=[\"Canada\", \"USA\"],\n",
    "    test_format=\"circle\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Given a new data point, predict the class of the data point by finding the \"closest\" data point in the training set, i.e., by finding its \"nearest neighbour\" or majority vote of nearest neighbours. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Suppose we want to predict the class of the black point.  \n",
    "- An intuitive way to do this is predict the same label as the \"closest\" point ($k = 1$) (1-nearest neighbour)\n",
    "- We would predict a target of **USA** in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_neighbors 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_knn_clf(\n",
    "    X_small_cities,\n",
    "    y_small_cities,\n",
    "    test_point,\n",
    "    n_neighbors=1,\n",
    "    class_names=[\"Canada\", \"USA\"],\n",
    "    test_format=\"circle\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How about using $k > 1$ to get a more robust estimate? \n",
    "- For example, we could also use the 3 closest points (*k* = 3) and let them **vote** on the correct class.  \n",
    "- The **Canada** class would win in this case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_neighbors 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_knn_clf(\n",
    "    X_small_cities,\n",
    "    y_small_cities,\n",
    "    test_point,\n",
    "    n_neighbors=3,\n",
    "    class_names=[\"Canada\", \"USA\"],\n",
    "    test_format=\"circle\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction of the black dot with 1 neighbours: ['USA']\n",
      "Prediction of the black dot with 3 neighbours: ['Canada']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "k_values = [1, 3]\n",
    "\n",
    "for k in k_values:\n",
    "    neigh = KNeighborsClassifier(n_neighbors=k)\n",
    "    neigh.fit(X_small_cities, y_small_cities)\n",
    "    print(\n",
    "        \"Prediction of the black dot with %d neighbours: %s\"\n",
    "        % (k, neigh.predict(test_point))\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Questions\n",
    "\n",
    "- Is it a good or a bad idea to consider an odd number for $k$? Why or why not? \n",
    "- Try different values of $k$ in the above code. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Choosing `n_neighbors`\n",
    "\n",
    "- The primary hyperparameter of the model is `n_neighbors` ($k$) which decides how many neighbours should vote during prediction? \n",
    "- What happens when we play around with `n_neighbors`?\n",
    "- Are we more likely to overfit with a low `n_neighbors` or a high `n_neighbors`?\n",
    "- Let's examine the effect of the hyperparameter on our cities data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "X = cities_df.drop(columns=[\"country\"])\n",
    "y = cities_df[\"country\"]\n",
    "\n",
    "# split into train and test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=0.1, random_state=123\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\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>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.002961</td>\n",
       "      <td>0.002204</td>\n",
       "      <td>0.710526</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001197</td>\n",
       "      <td>0.001730</td>\n",
       "      <td>0.684211</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001049</td>\n",
       "      <td>0.001605</td>\n",
       "      <td>0.842105</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001981</td>\n",
       "      <td>0.002834</td>\n",
       "      <td>0.702703</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000899</td>\n",
       "      <td>0.001616</td>\n",
       "      <td>0.837838</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.002961    0.002204    0.710526          1.0\n",
       "1  0.001197    0.001730    0.684211          1.0\n",
       "2  0.001049    0.001605    0.842105          1.0\n",
       "3  0.001981    0.002834    0.702703          1.0\n",
       "4  0.000899    0.001616    0.837838          1.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 1\n",
    "knn1 = KNeighborsClassifier(n_neighbors=k)\n",
    "scores = cross_validate(knn1, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "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>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.002871</td>\n",
       "      <td>0.007103</td>\n",
       "      <td>0.605263</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001770</td>\n",
       "      <td>0.003194</td>\n",
       "      <td>0.605263</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001701</td>\n",
       "      <td>0.002755</td>\n",
       "      <td>0.605263</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001362</td>\n",
       "      <td>0.002547</td>\n",
       "      <td>0.594595</td>\n",
       "      <td>0.602649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.001215</td>\n",
       "      <td>0.002341</td>\n",
       "      <td>0.594595</td>\n",
       "      <td>0.602649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.002871    0.007103    0.605263     0.600000\n",
       "1  0.001770    0.003194    0.605263     0.600000\n",
       "2  0.001701    0.002755    0.605263     0.600000\n",
       "3  0.001362    0.002547    0.594595     0.602649\n",
       "4  0.001215    0.002341    0.594595     0.602649"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 100\n",
    "knn100 = KNeighborsClassifier(n_neighbors=k)\n",
    "scores = cross_validate(knn100, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e10a7edc99924400926f03f69373a277",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n_neighbors', max=101, min=1, step=10), Output()), _dom_…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(n_neighbors=1):\n",
    "    results = {}\n",
    "    knn = KNeighborsClassifier(n_neighbors=n_neighbors)\n",
    "    scores = cross_validate(knn, X_train, y_train, return_train_score=True)\n",
    "    results[\"n_neighbours\"] = [n_neighbors]\n",
    "    results[\"mean_train_score\"] = [round(scores[\"train_score\"].mean(), 3)]\n",
    "    results[\"mean_valid_score\"] = [round(scores[\"test_score\"].mean(), 3)]\n",
    "    print(pd.DataFrame(results))\n",
    "\n",
    "\n",
    "interactive(\n",
    "    f,\n",
    "    n_neighbors=widgets.IntSlider(min=1, max=101, step=10, value=1),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_knn_decision_boundaries(X_train, y_train, k_values=[1, 11, 100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How to choose `n_neighbors`?\n",
    "\n",
    "- `n_neighbors` is a hyperparameter\n",
    "- We can use hyperparameter optimization to choose `n_neighbors`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "results_dict = {\n",
    "    \"n_neighbors\": [],\n",
    "    \"mean_train_score\": [],\n",
    "    \"mean_cv_score\": [],\n",
    "    \"std_cv_score\": [],\n",
    "    \"std_train_score\": [],\n",
    "}\n",
    "param_grid = {\"n_neighbors\": np.arange(1, 50, 5)}\n",
    "\n",
    "for k in param_grid[\"n_neighbors\"]:\n",
    "    knn = KNeighborsClassifier(n_neighbors=k)\n",
    "    scores = cross_validate(knn, X_train, y_train, return_train_score=True)\n",
    "    results_dict[\"n_neighbors\"].append(k)\n",
    "\n",
    "    results_dict[\"mean_cv_score\"].append(np.mean(scores[\"test_score\"]))\n",
    "    results_dict[\"mean_train_score\"].append(np.mean(scores[\"train_score\"]))\n",
    "    results_dict[\"std_cv_score\"].append(scores[\"test_score\"].std())\n",
    "    results_dict[\"std_train_score\"].append(scores[\"train_score\"].std())\n",
    "\n",
    "results_df = pd.DataFrame(results_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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>mean_train_score</th>\n",
       "      <th>mean_cv_score</th>\n",
       "      <th>std_cv_score</th>\n",
       "      <th>std_train_score</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n_neighbors</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.755477</td>\n",
       "      <td>0.069530</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.831135</td>\n",
       "      <td>0.792603</td>\n",
       "      <td>0.046020</td>\n",
       "      <td>0.013433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.819152</td>\n",
       "      <td>0.802987</td>\n",
       "      <td>0.041129</td>\n",
       "      <td>0.011336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.801863</td>\n",
       "      <td>0.782219</td>\n",
       "      <td>0.074141</td>\n",
       "      <td>0.008735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.777934</td>\n",
       "      <td>0.766430</td>\n",
       "      <td>0.062792</td>\n",
       "      <td>0.016944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.755364</td>\n",
       "      <td>0.723613</td>\n",
       "      <td>0.061937</td>\n",
       "      <td>0.025910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.743391</td>\n",
       "      <td>0.707681</td>\n",
       "      <td>0.057646</td>\n",
       "      <td>0.030408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.728777</td>\n",
       "      <td>0.707681</td>\n",
       "      <td>0.064452</td>\n",
       "      <td>0.021305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.706128</td>\n",
       "      <td>0.681223</td>\n",
       "      <td>0.061241</td>\n",
       "      <td>0.018310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.694155</td>\n",
       "      <td>0.660171</td>\n",
       "      <td>0.093390</td>\n",
       "      <td>0.018178</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean_train_score  mean_cv_score  std_cv_score  std_train_score\n",
       "n_neighbors                                                                \n",
       "1                    1.000000       0.755477      0.069530         0.000000\n",
       "6                    0.831135       0.792603      0.046020         0.013433\n",
       "11                   0.819152       0.802987      0.041129         0.011336\n",
       "16                   0.801863       0.782219      0.074141         0.008735\n",
       "21                   0.777934       0.766430      0.062792         0.016944\n",
       "26                   0.755364       0.723613      0.061937         0.025910\n",
       "31                   0.743391       0.707681      0.057646         0.030408\n",
       "36                   0.728777       0.707681      0.064452         0.021305\n",
       "41                   0.706128       0.681223      0.061241         0.018310\n",
       "46                   0.694155       0.660171      0.093390         0.018178"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_df = results_df.set_index(\"n_neighbors\")\n",
    "results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='n_neighbors'>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results_df[[\"mean_train_score\", \"mean_cv_score\"]].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_n_neighbours = results_df.idxmax()[\"mean_cv_score\"]\n",
    "best_n_neighbours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's try our best model on test data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test accuracy: 0.905\n"
     ]
    }
   ],
   "source": [
    "knn = KNeighborsClassifier(n_neighbors=best_n_neighbours)\n",
    "knn.fit(X_train, y_train)\n",
    "print(\"Test accuracy: %0.3f\" % (knn.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} Exercise 4.1: True or False\n",
    "1. Analogy-based models find examples from the test set that are most similar to the query example we are predicting.\n",
    "2. A dataset with 10 dimensions is considered low dimensional.\n",
    "3. Euclidean distance will always have a positive value.\n",
    "```    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions on distances and $k$-NNs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "#### Exercise 4.1\n",
    "\n",
    "What would be the Euclidean distance between the following two vectors `u` and `v`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.array([0, 0, 20, -2])\n",
    "v = np.array([-1, 0, 18, -4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Exercise 4.2 $k$-NN practice questions\n",
    "\n",
    "1. When we calculated Euclidean distances from all cities to all other cities, why did we set the diagonal entries to infinity before finding the closest city?\n",
    "2. Consider this toy dataset:\n",
    "\n",
    "$$ X = \\begin{bmatrix}5 & 2\\\\4 & 3\\\\  2 & 2\\\\ 10 & 10\\\\ 9 & -1\\\\ 9& 9\\end{bmatrix}, \\quad y = \\begin{bmatrix}0\\\\0\\\\1\\\\1\\\\1\\\\2\\end{bmatrix}.$$\n",
    "\n",
    "- If $k=1$, what would you predict for $x=\\begin{bmatrix} 0\\\\0\\end{bmatrix}$?\n",
    "- If $k=3$, what would you predict for $x=\\begin{bmatrix} 0\\\\0\\end{bmatrix}$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recap - $k$-NNs\n",
    "\n",
    "At home, you watched videos on analogy-based models, in particular $k$-nearest neighbors. \n",
    "\n",
    "Let's answer some questions about what you have learned (T/F):\n",
    "1. Unlike with decision trees, with $k$-NNs most of the work is done at the `predict` stage. \n",
    "2. With $k$-NN, setting the hyperparameter $k$ to larger values typically reduces training error. \n",
    "3. Similar to decision trees, $k$-NNs finds a small set of good features.\n",
    "4. In $k$-NN, the classification of the closest neighbour to the test example always contributes the most to the prediction.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Open questions (in break rooms)\n",
    "\n",
    "- Is it a good or a bad idea to consider an odd number for  𝑘 ? Why or why not?\n",
    "- In the video, diagonal entries of the Euclidian distance matrix were changed from 0 to infinity. Why?\n",
    "- Why is the training error always 0.0 when $k$ = 1?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More on $k$-NNs [[video](https://youtu.be/IRGbqi5S9gQ)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Other useful arguments of `KNeighborsClassifier`\n",
    "\n",
    "- `weights` $\\rightarrow$ When predicting label, you can assign higher weight to the examples which are closer to the query example.  \n",
    "- Exercise for you: Play around with this argument. Do you get a better validation score? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### (Optional) Regression with $k$-nearest neighbours ($k$-NNs)\n",
    "\n",
    "- Can we solve regression problems with $k$-nearest neighbours algorithm? \n",
    "- In $k$-NN regression we take the average of the $k$-nearest neighbours. \n",
    "- We can also have weighted regression. \n",
    "\n",
    "See an example of regression in the lecture notes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_knn_regression(n_neighbors=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_knn_regression(n_neighbors=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Pros of $k$-NNs for supervised learning\n",
    "\n",
    "- Easy to understand, interpret.\n",
    "- Simple hyperparameter $k$ (`n_neighbors`) controlling the fundamental tradeoff.\n",
    "- Can learn very complex functions given enough data.\n",
    "- Lazy learning: Takes no time to `fit`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Cons of $k$-NNs for supervised learning\n",
    "\n",
    "- Can be potentially be VERY slow during prediction time, especially when the training set is very large. \n",
    "- Often not that great test accuracy compared to the modern approaches.\n",
    "- It does not work well on datasets with many features or where most feature values are 0 most of the time (sparse datasets).    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "```{admonition} Attention\n",
    ":class: important\n",
    "\n",
    "For regular $k$-NN for supervised learning (not with sparse matrices), you should scale your features. We'll be looking into it soon. \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parametric vs non parametric \n",
    "\n",
    "- You might see a lot of definitions of these terms.\n",
    "- A simple way to think about this is: \n",
    "    - do you need to store at least $O(n)$ worth of stuff to make predictions? If so, it's non-parametric.\n",
    "- Non-parametric example: $k$-NN is a classic example of non-parametric models.     \n",
    "- Parametric example: decision stump\n",
    "- If you want to know more about this, find some reading material [here](https://www.cs.ubc.ca/~schmidtm/Courses/340-F16/L6.pdf), [here](http://mlss.tuebingen.mpg.de/2015/slides/ghahramani/gp-neural-nets15.pdf), and [here](https://machinelearningmastery.com/parametric-and-nonparametric-machine-learning-algorithms/). \n",
    "- By the way, the terms \"parametric\" and \"non-paramteric\" are often used differently by statisticians, see [here](https://help.xlstat.com/s/article/what-is-the-difference-between-a-parametric-and-a-nonparametric-test?language=en_US) for more..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{note}\n",
    "$\\mathcal{O}(n)$ is referred to as big $\\mathcal{O}$ notation. It tells you how fast an algorithm is or how much storage space it requires. For example, in simple terms, if you have $n$ examples and you need to store them all you can say that the algorithm requires $\\mathcal{O}(n)$ worth of stuff. \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Curse of dimensionality\n",
    "\n",
    "- Affects all learners but especially bad for nearest-neighbour. \n",
    "- $k$-NN usually works well when the number of dimensions $d$ is small but things fall apart quickly as $d$ goes up.\n",
    "- If there are many irrelevant attributes, $k$-NN is hopelessly confused because all of them contribute to finding similarity between examples. \n",
    "- With enough irrelevant attributes the accidental similarity swamps out meaningful similarity and $k$-NN is no better than random guessing.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "\n",
    "nfeats_accuracy = {\"nfeats\": [], \"dummy_valid_accuracy\": [], \"KNN_valid_accuracy\": []}\n",
    "for n_feats in range(4, 2000, 100):\n",
    "    X, y = make_classification(n_samples=2000, n_features=n_feats, n_classes=2)\n",
    "    X_train, X_test, y_train, y_test = train_test_split(\n",
    "        X, y, test_size=0.2, random_state=123\n",
    "    )\n",
    "    dummy = DummyClassifier(strategy=\"most_frequent\")\n",
    "    dummy_scores = cross_validate(dummy, X_train, y_train, return_train_score=True)\n",
    "\n",
    "    knn = KNeighborsClassifier()\n",
    "    scores = cross_validate(knn, X_train, y_train, return_train_score=True)\n",
    "    nfeats_accuracy[\"nfeats\"].append(n_feats)\n",
    "    nfeats_accuracy[\"KNN_valid_accuracy\"].append(np.mean(scores[\"test_score\"]))\n",
    "    nfeats_accuracy[\"dummy_valid_accuracy\"].append(np.mean(dummy_scores[\"test_score\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.DataFrame(nfeats_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Break (5 min)\n",
    "\n",
    "![](img/eva-coffee.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Support Vector Machines (SVMs) with RBF kernel [[video](https://youtu.be/ic_zqOhi020)]\n",
    "\n",
    "- Very high-level overview\n",
    "- Our goals here are\n",
    "    - Use `scikit-learn`'s SVM model. \n",
    "    - Broadly explain the notion of support vectors.  \n",
    "    - Broadly explain the similarities and differences between $k$-NNs and SVM RBFs.\n",
    "    - Explain how `C` and `gamma` hyperparameters control the fundamental tradeoff.\n",
    "    \n",
    "> (Optional) RBF stands for radial basis functions. We won't go into what it means in this class. Refer to [this video](https://www.youtube.com/watch?v=Qc5IyLW_hns) if you want to know more. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Overview\n",
    "\n",
    "- Another popular similarity-based algorithm is Support Vector Machines with RBF Kernel (SVM RBFs)\n",
    "- Superficially, SVM RBFs are more like weighted $k$-NNs.\n",
    "    - The decision boundary is defined by **a set of positive and negative examples** and **their weights** together with **their similarity measure**. \n",
    "    - A test example is labeled positive if on average it looks more like positive examples than the negative examples. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The primary difference between $k$-NNs and SVM RBFs is that \n",
    "    - Unlike $k$-NNs, SVM RBFs only remember the key examples (support vectors). So it's more efficient than $k$-NN. \n",
    "    - SVMs use a different similarity metric which is called a \"kernel\" in SVM land. A popular kernel is Radial Basis Functions (RBFs)\n",
    "    - They usually perform better than $k$-NNs! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Let's explore SVM RBFs\n",
    "\n",
    "Let's try SVMs on the cities dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(X_cities.iloc[:, 0], X_cities.iloc[:, 1], y_cities)\n",
    "plt.xlabel(\"longitude\")\n",
    "plt.ylabel(\"latitude\")\n",
    "plt.legend(loc=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_cities, y_cities, test_size=0.2, random_state=123\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean validation score 0.803\n"
     ]
    },
    {
     "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>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.001657</td>\n",
       "      <td>0.002129</td>\n",
       "      <td>0.794118</td>\n",
       "      <td>0.819549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001181</td>\n",
       "      <td>0.001677</td>\n",
       "      <td>0.764706</td>\n",
       "      <td>0.819549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001147</td>\n",
       "      <td>0.001611</td>\n",
       "      <td>0.727273</td>\n",
       "      <td>0.850746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.001485</td>\n",
       "      <td>0.787879</td>\n",
       "      <td>0.828358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000878</td>\n",
       "      <td>0.001389</td>\n",
       "      <td>0.939394</td>\n",
       "      <td>0.783582</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.001657    0.002129    0.794118     0.819549\n",
       "1  0.001181    0.001677    0.764706     0.819549\n",
       "2  0.001147    0.001611    0.727273     0.850746\n",
       "3  0.001167    0.001485    0.787879     0.828358\n",
       "4  0.000878    0.001389    0.939394     0.783582"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn = KNeighborsClassifier(n_neighbors=best_n_neighbours)\n",
    "scores = cross_validate(knn, X_train, y_train, return_train_score=True)\n",
    "print(\"Mean validation score %0.3f\" % (np.mean(scores[\"test_score\"])))\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean validation score 0.820\n"
     ]
    },
    {
     "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>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.034477</td>\n",
       "      <td>0.002362</td>\n",
       "      <td>0.823529</td>\n",
       "      <td>0.842105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.002432</td>\n",
       "      <td>0.001365</td>\n",
       "      <td>0.823529</td>\n",
       "      <td>0.842105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.002120</td>\n",
       "      <td>0.001338</td>\n",
       "      <td>0.727273</td>\n",
       "      <td>0.858209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001969</td>\n",
       "      <td>0.001192</td>\n",
       "      <td>0.787879</td>\n",
       "      <td>0.843284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.001811</td>\n",
       "      <td>0.001107</td>\n",
       "      <td>0.939394</td>\n",
       "      <td>0.805970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.034477    0.002362    0.823529     0.842105\n",
       "1  0.002432    0.001365    0.823529     0.842105\n",
       "2  0.002120    0.001338    0.727273     0.858209\n",
       "3  0.001969    0.001192    0.787879     0.843284\n",
       "4  0.001811    0.001107    0.939394     0.805970"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "svm = SVC(gamma=0.01)  # Ignore gamma for now\n",
    "scores = cross_validate(svm, X_train, y_train, return_train_score=True)\n",
    "print(\"Mean validation score %0.3f\" % (np.mean(scores[\"test_score\"])))\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Decision boundary of SVMs \n",
    "- We can think of SVM with RBF kernel as \"smooth KNN\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(16, 5))\n",
    "\n",
    "for clf, ax in zip([knn, svm], axes):\n",
    "    clf.fit(X_train, y_train)\n",
    "    mglearn.plots.plot_2d_separator(\n",
    "        clf, X_train.to_numpy(), fill=True, eps=0.5, ax=ax, alpha=0.4\n",
    "    )\n",
    "    mglearn.discrete_scatter(X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, ax=ax)\n",
    "    ax.set_title(clf)\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Support vectors \n",
    "\n",
    "- Each training example either is or isn't a \"support vector\".\n",
    "  - This gets decided during `fit`.\n",
    "\n",
    "- **Main insight: the decision boundary only depends on the support vectors.**\n",
    "\n",
    "- Let's look at the support vectors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "n = 20\n",
    "n_classes = 2\n",
    "X_toy, y_toy = make_blobs(\n",
    "    n_samples=n, centers=n_classes, random_state=300\n",
    ")  # Let's generate some fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(X_toy[:, 0], X_toy[:, 1], y_toy)\n",
    "plt.xlabel(\"Feature 0\")\n",
    "plt.ylabel(\"Feature 1\")\n",
    "svm = SVC(kernel=\"rbf\", C=10, gamma=0.1).fit(X_toy, y_toy)\n",
    "mglearn.plots.plot_2d_separator(svm, X_toy, fill=True, eps=0.5, alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  8,  9, 14, 19,  1,  4,  6, 17], dtype=int32)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm.support_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_support_vectors(svm, X_toy, y_toy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The support vectors are the bigger points in the plot above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hyperparameters of SVM \n",
    "\n",
    "- Key hyperparameters of `rbf` SVM are\n",
    "    - `gamma`\n",
    "    - `C`\n",
    "    \n",
    "- We are not equipped to understand the meaning of these parameters at this point but you are expected to describe their relation to the fundamental tradeoff. \n",
    "\n",
    "See [`scikit-learn`'s explanation of RBF SVM parameters](https://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relation of `gamma` and the fundamental trade-off\n",
    "\n",
    "- `gamma` controls the complexity (fundamental trade-off), just like other hyperparameters we've seen.\n",
    "  - larger `gamma` $\\rightarrow$ more complex\n",
    "  - smaller `gamma` $\\rightarrow$ less complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x288 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gamma = [0.001, 0.01, 0.1, 1.0, 10.0]\n",
    "plot_svc_gamma(\n",
    "    gamma,\n",
    "    X_train.to_numpy(),\n",
    "    y_train.to_numpy(),\n",
    "    x_label=\"longitude\",\n",
    "    y_label=\"latitude\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relation of `C` and the fundamental trade-off\n",
    "\n",
    "- `C` _also_ affects the fundamental tradeoff\n",
    "    - larger `C` $\\rightarrow$ more complex \n",
    "    - smaller `C` $\\rightarrow$ less complex "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g71NQDsLRA16OI+CrBC512XYlRxo35xNc8lgcFPh7FZSDgE44RlLYnZ/tBE+fL47b4/YDfYKpjzy8fk7ioMDeJ8Mc5LafxEGx5yBJHpv0QHwU6PtkZEzUDMftyppz+2rgqADrIT4K/DMzxUfyMPaBOCjQ9ylgBwEX4Uik5uNIlL4O1APXBXAchSP53df5963AbB/7r9HfJ7wkj50OqHOr/3N4Tx6PxMNIYBxTytQDuR5e818a39GR7TzmCS51udBl+zjgaQ+f+XlBfCZ9gF1uz91KAAMUgG/wkhzGQ27IzEcsznlcomlatf6HUipTKfW6c9Lpgzh+pFoopWxeXt8wF5qmaZXO/2a776Rp2mYco6eeBPYopT5wmTz8OBxD8N05BsftNa5sx9GDo7PT5f/tgZ5KqQP6A8f8J0d7qbs3ynEEFzrNgHLN+Y3ywVDA44TxSqlznfX4OIh6zAYylFI9nYsMdAOmOssL9nPSOQaX98x5Tju9787NwKnARqXUCqXUYOfz3j6zVkAqjT83X59Zaxw/LN+6fGbTnM8Hg/tnhvPvQ35eNxSHPLfqT2iaVq5p2kpN0+yapu0G7gYGKKXcyxeMQRzUlIAdpJTqB4zCEfCl4pgn7j9KqW5KqSzntnuCPL6OOChwAnaQcw626TjmA8xy1jkXx0gP1/1OAb4G/qJp2oIg6yMEjjioKYY4yG0/iYOOEBMOEqKC+KgpRvpoHI7bslvi+O5/iuN3NhDER4EjPopdxEFNCdhBmqZ9AzwBfOKs2zYc3/tf/B3EWd4HOEZUA1wPvKdvV0oNVUqtcTmXzjiuF1+0xjEgzvV9cX8PXXkHx/X4gVLqN+VYHDAFx2eyX9O0Ug+vafS5aJpWjmPaC1+fywNun8txznICJaTcj1LqOBy/C5O87NIkN2QmsZg8dv/SP4DjFoGemqY1wzF8Hhw9IeEdSNMma5p2Lo4vjMaRH4WdwMkeXvKbc19Xjscx1L6hWJf/7wTmaZrWwuWRrWnanQBKqUdU05UUGx4u5XyP4/YIna7O57yilOqN4wvvrVE0DPjUeTEFhKZp9ThuMbgOhzyKNE3TL4hQP6diHBenXm/l+reHOmzSNO06HPN5vQB87ExIefvM9uLoaXL93Hx9Zntx3I5xhstn1lxzTFaOUup4X5+ZUuoGZzmNPjNnHU/Gz+eGj4S/h/qGfQ0IHhEHheegbjhuDVqpaVq9pmkrgGU4evI74LgNbIFSaheOwDxPOVayPsFLeUdOTBxkloOOcp7zGE3TajRN24djepxLXF7fHpiFo2f+HW/vj2AI4iDzHOSKxEEuxbrtbzkHCVFDfGSuj7oCEzRN269pWg2O26t7KMcCbz4RH4mPEgRxUJi5IU3Txmqa1kHTtDY4ksjJOKZiCYT3gT842wE9na/X2wVv4hjU1lLTtBbOMv19DiU4RvS7euV4H3Wv0zTtKU3TTscxv/RgHPmSncBRSqkWHl7W6HNxXu8t8f25POv2uWRqmva+8/Vf+/hc9M6+n4BkpVQHl3L95uyc57JY07SffWz3lxsyDKsnj3cDJ/nZJwfHj8YBpdRROHpOwkYpdZpS6kKlVBpQ7TzGYefm/wBPK6U6KAf5SqmWwFfAqUqp65VSyUqpa4DTccyD4oki5/43KaVSnI+zlVKdADRNe05zWUnR/eFSziTgfqVUO+XoAXsAx+0zvhgGfOISRLieewaOOWqalKGUmquUetJHuZNx3HJxg/P/OqF+Tl8CZyilrlKO1S7/jI/eN6XUjUqp1s6A6YDz6cM4esH6KaWudn42LZVS3TRNO4wjsHpWKZXjFN39OCZeb4Kz3DeBV5RzJWTn+z7QuX2Hr89M0zS9N24q0FkpNUQplY5jXsV1mqZt9HFuvXD0iH3k9nxP5/c1yfk9/DeOWyDKvJUlBIw4yHgHrQD6KOeoGqVUAY5bedbhCCqOw9GY6gbcguMz6IazB1gcFHkHaZq2F8ciInc6694Cx2/IWv34OEY4jdU0bXxA76oQKOKgyDpIP3eJg2LIQc46pDnLAUhVSqUrpaQT3VjER5H30QpgqFKquXKMpvsT8JvzmhAfWdRHgmmIgwx2kPO3srOz3scDbwD/0pwjdpVSw5VS27y9L5qmrcaR8P0PjmkzDzg3ZeFIwJY4yxmBY+SxT5wO+BR4UjlGkZ+O4/ryiFLqAqVUF+UYWX4QR+fTYU3TinHcpfGaUirX+V7qHQmTgRHKcddrGo5pMZZpmubtPN8E7lCOnItSSmUppS5VSuU46zzIx+cyyLlPhfO8/uF8fW/gChwjp30xFO+fncfckKloEZgbI9QHjsnoi3H82FyNh/kvcYyenYtjKPhPOOZF0oBk5/a5eFktVjsyp8kpHo6dj2N1x0M45m8s4sjk3zYcK79udW5fgXMVTxwrx36LY6Lyb4FzXcpsqIvLc6fh+CEuwTFcfjbOBQOCeJ8Ujlue9jsfo3CZ0wZHj8YNLn+nO9/Ti7yUdx2Oofye5sXZAvT3Ux995cpUIz4n4GLnawJZ1fddHPMRlTvP+/cu2/rg6M0/iCMRNcz5fK7zdSXO5x+n8aq+7t+ZdByS+dlZ1gbgzyF8v/vhWK24ynn+J7hsewT42m3/14F3vHxeW3HM+VWM4wejyVxN8gj+gTgo0PcpWAfdjcMTh5zX0QNeyvX0fouDouAgHAn8uTgW+tiLI1Bp49z2hPO9LHd9RPv6jYcH4qBA3ydDHYTEQTHlIOf2bc730/VxQrB1kofPz0t8FNj7ZJiPcIyGew/HNX0AWAj0cNkuPrKgj+RhzgNxUKDvU8AOAlrg6KyqwDGFx/OAzWXfQuA9P8crdL5vf3R7/lnn8fcCL+PiCvf33vV9xzF1RZHzel4OPO3+Obm87joc8w9X4Ohc+LfLZ30UjlG5u53X6qdu36UtLp/lsb6+Azi8t8L53SvGcc3nBPm5HAV85qzrDpwLdjq3HY/jO3u8y3O/c+7r8Th4yQ2Z+dBXRhQEvyiljgU+0jTtd9GuiyAIiYc4SBCEaCIOEgTBKoiPBEEwG6XUDBxrmWyIdl2E6CPJY0EQBEEQBEEQBEEQBEEQBKEJVp/zWBAEQRAEQRAEQRAEQRAEQYgCkjwWBEEQBEEQBEEQBEEQBEEQmiDJY0EQBEEQBEEQBEEQBEEQBKEJyWYU2qpVK+2EE04wo2hBECLAt99+u1fTtNbRrkeoiIMEIXYR/wiCEE3EQYIgRBNxkCAI0cKXf0xJHp9wwgmsXLnSjKIFQYgASqnt0a5DOIiDBCF2Ef8IghBNxEGCIEQTcZAgCNHCl39k2gpBEARBEARBEARBEARBEAShCVFNHhcXF3PxReexa9euaFZDEIQERPwjCEI0EQcJghBNxEGCIEQL8Y8gxB6mTFsRCG+88TOfTHmc5UsWMuzGvzHk6qeiVRVBSChuu+2kaFfBEowaMZTlSxYyavhNvDx0RNjlzV+wl40Fgw2omSDEN+IgYPJkRk16OygHiWMEVzquLqJvn1bRrkbscf310a6BNQjBQYEgnhJ0xFFeEAcZ6p/5C/YCiHcES2FZ/4Xpn6glj8vK9rB0ySfMvSmDC979mH4D76Z585idF16wIMnJ9Zx0Ug2ZmfXRroql2LBhQ8P/09PTOfbYY0lJSYlijSJPcXExExfM55ubMuj37nwevPxKjm7RItrVEgQhQSguLRUHCYIQNcRBgmAeekITsGYCKcoY7R9JHAtCZIha8njWtDEM62qjIM/G0HyYNX2MjD4WDOWkk2o47rijyMnJRSkV7epYhtat0wDQNI19+/bxyy+/cOKJJ0a5VpFl1HNPMyw/2ekfjVGfTzWk11sQBCEQRn3xmaEOEhKT+Qv2SmJCCAlxkCAYj2t7oCGhuaCo4TnxtQPxjyDEJlGZ87i4uJilSz7h4V6OhN7DvRTLlnxMWVlJNKojxCmZmfWSOPaBUoqWLVtSXV0d7apElOLiYiZOnMCDvRz6e7BXEhMXzGfXgQNhlSu93oIgBIJ+54PRDhISC/nNEULFLAfJlBVCIuM6fYLrdeD6tww2kRhIEGKZqCSPRz33NMO62sjLcRw+LyeJofk2Zk0fE43qCHGMJI59k4jvj2PUsbt/khn1+dQo10wQhERAv/MhGAdJUkYQBKMIxUGCIHhH/4329Tvtb3uiIP4RhNgl4sljfdSfPupYR0YfC9Fk69YtPPTwA5x8ajvaHp3Jyae246GHH2Dr1i3RrppgIA2jjns2fl56vQVBiATudz7oiIMEQYgE4iBBMBbp3A0co/0j770gRJaIJ4/dR/3pyOhjIVp88810Lux/Lp9v2EvO1f/HcQ9MJefq/+PzDXu5sP+5fPPN9JDL3r17F7fddhNnn92Jc8/txnXXXcGWLZsMrH1jTjihpWllxwO+/RNar7cELoIgBIoZDhIEQQgUcZAgGIe0AYJD/CMIsU1Ek8feRv3pyOhjIdJs3bqFW24fTs7lj5Dd5yZScvNQSTZScvPI7nMTOZc/wi23Dw9pBLKmaQwffg29evVlxYoNLFy4hkce+QclJbtNOBPBH/78I6NuBEEwE3GQIAjRxEwHSRJN8EQ8z/Ebz+dmBhIDCULsE9HksbfeJh0ZfSxEmvFvvEZ65wGktevkcXtau06kde7P62+OC7rshQvnkpKSzPDhtzY816VLVzp37saQIRdz0UXncN55Z/L1118AsGPHNnr37sr9999Jnz4F/PGPl1JVVQXAO+/8lwEDenP++WczYsS1VFZWArB9+1YGDTqPAQN683//92TDccrLyz0eI5EJzD/S6y0IgjmE6iBJygiCYAQSBwmRJBF+txLhHI3CaP9I8l4QIk9yJA+2YtkSFq0oZ/Qi3/t1PGlVZCokJDwff/IBOVf/n8990jv35+OPHub/nnsxqLI3bvyBrl27Ny0vPZ0JEz4kJ6cZ+/btZdCgvlx8sSP4+PnnzYwfP4mXXx7HLbfcQFHRVP74x+u59NLfc9NNNwPw/PNPMHnyBG655U889thfGT78Vq655kb++9/xfo+RiAvk6QTqn96nBD6tiAQugiAEihkOEgRBCBRxkCAYg3TqBo8Z/pHPQBAiS0STxwuXr274/xtv/BzJQwuCR8oPlpLbvI3PfZKbtaa8rNSwY2qaxrPPPs6SJQtJSkpi167f2LPHMZXF8cefQJcuXQHIzy9g587tAGzc+D3PP/8kBw+WUVFRzvnn9wdg+fIlvPXWBwBcffX1PP30oz6P0bbt0YadR6zh6h8AJk82pFwJXARBCIRGDjLIP0Jis7FgMCwoom+fVtGuihADiIMEIXxk4EhoiH8EIfaJaPJYEKxGdrNc7GV7SMnN87qP/WAJ2c1zgy77tNM68cUXnzZ5/pNP3mffvr3MmrWElJQUzjzzVGpqqgFIS0tr2M9ms1Fd7Zi24s9/vpUJEz6ic+d8PvhgEosWzW/Yz9NoYl/HEARBEARBEAQjkFGYQqIh3/foIgl8QYgOEZ3zWBCsxh+GXEvN+lk+96leP5M/DLk26LL79LmA2tpa3nnnvw3PrV69kp07d9CqVWtSUlJYuHAuO3fu8FtWeXk5bdseTV1dHR9//EHD8z16/I6pUz8EaPT8wYMHgz6GIAiCYC0kKSMIgiAI1kCSltZBYiNBiDySPBYSmjtu+xPV62dQ8+sGj9trft1AzfqZ3H7rnUGXrZRiwoQpzJs3m7PP7kSfPgX885/P0K/fxaxZs4r+/XvxyScf0KHDaX7LeuihJxg0qA9//OMljfZ/5pkXeeut1xkwoDeHDpU1PD9kyLVBH0MIDknqCIIgCIIgCELiILG/IAiJSkxMW1FSsp2ZsyexbOlnUHsAUlvQ85zf0//CobRu3T7a1RNimBNPPJn/vD6BW24fTm3n/qR37k9ys9bYD5ZQvX4mNetn8p/XJ3DiiSeHVP7RRx/Df/7zXpPnv/56nsf9588/sljkXXfd1/D/ESNuY8SI25rs3779iY3K+vOf/wZAy5atvB5DCI4tu3fz8vQZvLNwEXU1h0hJy+Gmc3tz7lFnR7tqgiAkABIDCYIQTbbs3s3Tn3/OJ0sWUF5TT/OcZtzQ63fcP3AAv/5ki3b1BCEiyKjj6ODeDlPJ2QzscBZnHdtFYiDBknRcXRTtKpiG5Ucer18/l6efv4p1VZVknNyNtOQkMk7uxrqqSp5+/irWr58b7SoKMc5FFw1k9syF/P70NpR/9DC/vDyE8o8e5vent2H2zIVcdNHAaFdRiBJfr1lDt8InmXIwh+STziQtOYnkk85kysEcbv5stPhHEARTWbrjB4mBBEGIGnocNPWnndiURsszLybruheZcjCHboVPsnTHDzISU/BJPCVd5bseWTy1w9I7nMW87DYSAwmWJl4XMrZ08rikZDtvvPUAuVc+Smb3wdRsWsycoRnUbF5CVvfLyL3yUd546wFKSrZHu6pCjHPiiSfzf8+9yOYff2HXrgo2//gL//fciyGPOBZiny27d3P1a6+TfWUh6d0va+SfjO6X03zI4+IfQRBM4/2ijTw5Z7LEQIIgRAU9DsoY+Bfs+3cyZ2gGVT/MJiklney+w8i+spAn50wWBwleiZdkazwlwGMFX+0wiYEEITpYOnk8c/YkMvMHkNauE9XLPmB412QK8mwMz7dRtewD0tp1IqNLf2bNmRTtqgqCEGe8PH0GafkDxT+CIESFD9cvIL3bIHGQIAhRQY+D6nd828Q/AGntOpGeP0AcJCQE8ZIIjxWkHSYI1sPSyePlyz8no0t/7OX7qVo/i8d6O6r7WO8kqr6fxeHyUjLzB7Bs2RdRrqkgCPHGe4uXkNZlgPhHEISoMHPzKomBBL9sLBgso+IEU3hv8RKST+7h1T8AGV0vFgcJcY34NTpIO0wQrIelk8fVFQdIbt6mobcpL8dR3bycpIZep+RmramuPBDdigqCEHccLD8k/hEEIWpUVouDBEGIHgfLD2HfMNurfwBxkJAQyKjjyCPtMEGwHpZOHqdntaCm+KdGvU06eq9Tza7NpGe2iE4Fhbhj9+5irh3Sn927d0W7KkKUaZadI/4RBCFqZKaLgwQhEOYv2OvxIYRHdmYWlT78c7i8FPvBEnGQIAiGI+0wQbAelk4e9+hxOZWzxzfqbdLRe50qZ4+jZ8/LolRDId4YM/p5Vq9czNh/PW9IeTt2bKNv3+6Nnhs16mnGjn2FlSuXcfHFfbjggh707t2VUaOebrTfo48+QH7+SdTX1xtSFyE4buj1O6rEP4IgRIH5C/bS/5TuEgMJgh/0JPHGgsFNHpJEDo8OrVswPD/Jq3+qln1A5boZ4iAhbhF/RA9phwlCeJjRoW7p5PE5Z1+Kfc+WJr1NOo/1TsJe8jM9z5JbSYTw2b27mA+nvMM3N6Xz4ZRJpo8+vueeW3jxxbHMmbOc+fNXccUVf2jYVl9fz1df/Y927Y5lyZIFptZD8MyNvzuHOvGPIAhR4rRL7pIYSBB84Jo49oT+vCSAgqe4tJSfd++isE+Kx+2P9U6iav0MKtdOp98FQyNcO0GIHDJlRXSQdpgghIZrsljvTNefDxdLJ49Xr/iMkWdmNOlt0snLSWJk93RWr/wsshUT4pIxo59naL6NgjwbN3WxGTb62Bt795bQtu3RANhsNk47rVPDtoUL59Kx4xkMG3Yrn376oan1EDzz4ZKF3HpmuvhHEISoIDGQIHjHX+JYRxLIoTHqi88Y3jXFp3+GdVbkn3YmrVu3j3DthFgiVhf1jMU6xxPSDhOE4NCTxq53YOm4/x0qyWGXYCI7tq1mxs9VjF1W5XO/jietilCNhHhFH3X8/W02AB46Bzq/OYm7/vJwQ4LXaG6//R569cqnV6++XHhhf6655ibS09MBmDr1Q6688moGDbqM5557grq6OlJSPI/+EMxhxZZNLNpczb+XVfvcT/wjCIIZSAwkBMP8BXvp26dVtKsREQJNHOtsLBhMx9VFjvfoejNrFj84YqBKRi/1vV/Hk3ZHpkKCEAVk1HH0kHaYEIt0XF0UleMGGxeFiqWTx/c99EW0qyAkCPqoY9eVXG/qAmP/9Tz/eO5fIZerlPL6/F//+ihDhlzL3Lnf8OmnU5g69UM++2wmtbW1zJo1naef/ifZ2Tl07342c+fOon//QSHXQwiehU891+Q5vTdPEATBbCQGEgJFT44mAqE2kBLpPTICTzGQjsRCgiCYzcKnnotYQkwQjCTSHfmRvE4snTwWhEjgPupYx4jRx7m5LTlw4ECj5w4cKOX4408A4MQTT+bEE0/mpptG0qnTsezfv4/ly5dw6FAZ5513JgBVVVVkZGRI8lgQBCEBkFtlBcE3oTaQNhYMpq/BdUk0xE9CIiDfc+sgiWNB8E6kO1gsPeexIEQC91HHOo7Rx+HNfZydnU3btkczf/5sAEpL9zN79gx69uzFzJlfo2kaAD//vBmbzUbz5i2YOnUKL788jm+//Ylvv/2JFSs2Mm/eN1RWVoZ+kkLYSCApCEKkkMaSIDRFRrxaA/kMhERAvufRRdpdguCbaIzMl+SxkNDoo44fOsfz9ofOgQ+nTGL37l0hH2PMmP/yyiv/xwUX9OCqqy7mr399lBNPPJmPPprM737XhQsu6MFdd43ktdcmUFNTw5w5jaeoyMrKokePXsyY8WXIdRCMQQJJQRAEQYg8kkiIPvIZCImAfM+tg7S7BMEz0ZrSRaatEBIab6OOdYyY+/i00zoxdeqMJs+/8cY7Hvf/6afiJs9NmDAlpGMLgiAIgiDEA5JIiD7yGQihEkuLesr3PLpIAl8QvBPNucAleSwkNGtWLWPZ6nL+tdj3fj2r/Cw3LQiCIAiCECU2FgyGBUUxk5wJBkkkCEJsIwtWCsEiCXxB8E60rg9JHptAScl2Pi8aw6rV0zl8uA7NXkdyWiZndr+Yyy69i9at20e7ioKTL6Yvi3YVhBgg1hquGzcuZsonL1D82yY0ey0qOZW8YzpwzZCH6NixV7SrJwhCHCMxkGAk0RxhIxwhluablhhICJVYi/fjkVhyjSckBhLMJNrXhySPDWb9+rmMe+PPHEYjp+ASsvMHkty8DfayPfyw+itWPXsFd9wyms6dz492VRMCTdNQSkW7GpZFX7BP8E+sBDJFRa9SNG0cOd0Hk3fxXxr8U752GqPH3MLgi+9k8OB7ol1NQRDiEImBBDOIld/feCWWEmoSAwnhIr6JHrHkGk9IDCSYiRWuD0keG0hJyXZe/8+91CtF2z88SVq7Tg3bUnLzOOrCm6k5rRev//d+Hn9kqvQ8mUxlZRKHDpWSk5MrCWQPaJrGvn37SE9Pj3ZVBIPYuHExRdPG0faaZ5r4J/f8EWR2OIeiKY9xyilnyugbQbAg0R5REA4SAwlGY4WGkuAgFrwkMZAgxD6x4BpPSAwkdFxt3tRhVrkLS5LHBjJz9iRUbjuyj+/SSBiupLXrREbnfsyaM4nrri6McA0Ti59/TgP2k5kpjQ9X9u49ctmnp6dz7LHHRrE2gpFM+eQFcroP9umfnIJL+fCTF3j80f9FuHaCIMQzEgNFn3ic9zjaDaVEJ5YS+BIDWR8rL5oXy5238UAsucYTEgMJZmMFP0ny2ECWL/+cusN2Wg5+wOd+Wd0uZtnkv4s0TMZuT+KnnzKiXQ3LcdttJ0W7CjFFLAUzxb9tIu/iv/jcJ7vbIH5768sI1UgQhERBYiDBSGLptzfesUKDNRAkBrI2smie4I9YcY0nJAYSzMJK8ZAkjw2kuuIAGpDcvI3P/ZKbtaa68kBE6iQIQvjESjCj2WsD8o9mr41QjQRBSBQkBhKMJlZ+e+OVWBuJKTGQECpWSs4kIrHmGk9IDCSYiVWuj6RoVyCeSM9qQVJ6NvayPT73sx8sIT2zRWQqJQhCwqCSUwPyj0pOjVCNBEFIFCQGsgYbCwbHfCIk1usfD8TiZyAxkBAOVknOJBqx6BpPSAwkmIHVOlYkeWwgPXpcTkruMZSvm+Fzv4o10+jZ87II1UoQhEQh75gOlK+d5nOf8jVfc8wxHSJUI0EQEgWJgQQjsVJjKVGJtc9AYiBBiE1izTWekBhIMBordqxI8thA+l84lPp9Ozm0qoiaXzd43Kfm1w1UrZ9FvwuGRrh2giAEixWl7YtrhjzEoW99++fQ6i+5eshDEa6ZIAjxjsRA1iLWfr90YrXe8YTVRjoFisRA1seKd0ZYrT6JRDy99/0vHIpW+ivla76WGEgwDKv9Fsucxwaye/dWSEoi/dh89nz8D7K7DiS760CSm7XGfrCEQ6u/onr9LO64ZTStW7f3W15JyXZmzp7E8uWfU11xgPSsFvTocTn9Lxwa0OsFQQgfq0nbF3Z7LUlJSez+8AlyCgaR3fXiRv4pX/0VgwfdSceOvQIqTxwkCEKgGB0DgTgoVGJ9YapY+t2NN2I5mSMxkBAq4pzoES/vfevW7RnY72a++GqMFwd9SdW6mdx5278lBopDOq4uom+fVoaVZ9XfYkkeG0RJyXbeeOsBWg55nLR2nagrLebQqiJ2vfc36isPkpSejTps5893vR5Q0LJ+/VzeeOsBMvMHkHv9CyQ3b4O9bA/rvpvJ0uev4raRL9G58/nmn5ggCDGB7qDWV/+DpMwWjf2T2Yz04/NJTk6hZ8/LAypPHCQIkcWqgWIgGB0DgTgoXDYWDIYFxjZmzCaWr4F4QH//YzGZIzGQIMQWsXqHgzdKSrYzY/YEjr7uea8OSkpKom3bEwMqTxyUuFj5t1iSxwYxc/YkMvMHkNauEwApuXkcddGtHHXRrQ37lM2byOp13/htOOkBUO6VjzaUp5eZ0ncoaSefzRtvPUDhw59Kr5MgCEBTB7n7BxwOmjVnEtddXeizLHGQIEQHKwaKgWBkDATiICOZv2BvTCWQY/UaiBdi9f2XGCi2sIqX4i2BGSvEY0ehOEgwEqt6SeY8Nojlyz8no0t/n/tk5g9g2bIv/JblLh930tp1IqNLf2bNmRRSXQVB8E+sBTbiIEEQooWR/gFxkFHojY9Y+D2TJE50iYXviC8kBood5DoXNhYMjrvvgThIMAKr/xZL8tggqisOkNy8jc99kpu1prrygN+yjG6ECYIQGrEU2IiDBEGIFkb6B8RBRhJLCWQhOlj5FtlAkRhICBZxomAk4iDBKKz8WyzJY4NIz2qBvWyPz33sB0tIz2zhtyyjG2GCIMQ/4iBBEKKFkf4BcZDRuCaQrZgwkVHH0SfW33+JgWIPK7go1r/3gnUQBwnhYgUn+kOSxwbRo8flVH030+c+letm0LPnZX7LMroRJghC/CMOEgQhWhjpHxAHmYHrbcJWSiJbpR6JSrwk7iUGii3i4TsnCK6IgxKXjquLDCvL6m6UBfMMov+FQ1ny7BXUlO6iesc66qsOkpTRjKzTzyOn+2DqKw9Q9d1M+j38qd+yevS4nHXfzSSl71Cv+wTTCBMEIf4RBwmCEC36XziUpc9fha3NidT8upGKH+Y1clBau44B+wfEQWaiN0w6ri5qSNxGe+EqqzeW4pV4StxLDBSbRGvhvHjpNBGsgzgosQnXY7HiJEkeG8Tu3VvRAFtOS46+8Z8kN2+DvWwP5eumUzzxL9hQ3HnbvwNaEVNvhKWdfLbHidJrft0QVCNMEITgiBWBuyIOEgQhWrRu3Z4BFw6n6KvR5HQf3NhBa6ex76vRDL74zoBXBRcHmY8VksjxlLyMNeJhnmNXJAaKPTYWDDZ0xJ4gRBNxkBAqsRQLSfLYAEpKtvPGWw/QcsjjjS7wlNw8cs8bTuYpPdn/6TO0bXtiQOW1bt2e20a+xBtvPUBGl/5k5g8guVlr7AdLqFw3g6rvZnLbyJcCboQJghDfiIMEQYgmJSXbmTF7Am2veaapg84fQWaHc5gx9Vl69rw8IG+IgyJHtJPI8ZK8jEXi5b2XGCi2ifTo41hK1AixgThICJdY+T2W5LELJSXbmTl7EsuXf051xQHSs1rQo8fl9L9wqM+Lc+bsSWTmD/DYMwSQ1q4TmfkDmDVnEtddXRhQXTp3Pp/Chz9l1pxJLJv8d6orD5Ce2YKePS+j38OfiiwEIc4I1T8gDhIEIXzMdlBGl/7iIAvjnkQ2O5kTi3f4xBNWe+8lBkpMojX62GrffyH6iIOEaBBrnVmSPHayfv1c3njrATLzB5B7/QskN29D9c71LJ3/DvPnv492uJaMrFyPElm+/HNyr3/BZ/mZ+QNYNvnvAQsDHL1O111d2OQ1JSXbmTzl6ZDkJgiC9fDkH3vZHlavmMrCpy/DZrNRV1Xu9VqPpIPCCa4EQbAm4cRAIA6KJ/RkjpkJ5FhrLAnmEksxEEg7zAyiNfexIIDEQEJ0iaXOLEkec+RWg9wrH23oMaraspK9X75MdteBtBz8QEMgs+67mSx9/ipuG/kSnTufD0B1xQGSm7fxeYzkZq2prjwQdl29BVie6iUIQvBEulHryT8A9v2/Ur5xIdndBpHddaAlHCT+EYT4I9wYCMRB8UZDQ2aBY0SgGUmdWGosCeYRSzEQiIPMIJKjj+WOB8EdiYGEcAjHXbHoo6RoV8AKuN9qUFdazN4vX6bNkEJyzxtGSm4eKslGSm4ezfoOJffKR3njrQcoKdkOQHpWC+xle3wew36whPTMFmHV01VuzfoO9VsvQRBCI5Ii93SrUyMHnT/cEg4S/whCfBJuDATioHhF/y00slM1FhtLgnnESgwE4iCzkTsShGggMZAQLqF0sMeq7yR5jONWg4wu/Rv+PrSqiOyuAwOauw+gR4/Lqfpups9jVK6bQc+elwFHbne694GzueOODtz7wNlMnvK034s9mDkFBUGIDdz9A+Y6SPwjCIIr4cZAIA6KZ4xMIMdqY0kwj1iJgUAcZCZmdFS5I/4RPCExkBAtYrEjXZLHNL3VoHz9bA6Xl7Lz1RvZPupydr56I/u/eZO60uKGfTLzB7Bs2RcA9L9wKJXrZlDz6waP5df8uoGq72bS74KhrF8/l6efv4p1VZXkXv8Cx/11KrnXv8C6qkqefv4q1q+f67WengIsd1zrFSjhBFKCIISHp1udzHLQ8e1OE/8IgtCIcGMgEAfFOxsLBrOxYDDzF+wNOQGjvy4WG0uCecRKDATiILOJhBvEP4I7EgOJfyJNLHdkSfKYxrcaVG1ZCfZabNm5HH3jPzn+r1M5+sZ/opJT2fXOA47tNJ63pnXr9tw28iVKpz5L2byJ1JUWox22U1daTNm8iZROfZbbRr4EENbtBmbMpxNOMlsQhPBxv9XJLAddM+QhpnzygvhHEIRGhBsDgTgoUQh1dKAkjgVvxEoMBOKgSGFGYiWWkzWCuUgMJP6JBrEaD0nymCO3Guhz3LS99pkmc9zknjeMNkMK2fvly9SVFjeZt6Zz5/MpfPhTumVlUTr57+x8eQilk/9Ot6wsCh/+lM6dzw/7dgOj59ORuXMEoTHRCC5db3Uy00Hbf/lR/CMIQhOMiIFAHJQouCaQA/nNlMSx4ItYiYFAHBQJzJy+QhwkeEJiIPFPJIn1jqzkaFfACvS/cChLn7+KmtJdfue4ye46gEOrirAlpzbMYazTunV7rru6kOuuLvT4+uXLPyf3+hd81iUzfwDLJv/dYxk9elzOuu9mktJ3qNfXu86t7I9gktnezkkQ4o1IB5e6f9JOPpuKjQtNc5D4RxCsT8fVRVFzULgxEIiDEgX9O9pxdVFDQ8h9wRhJGguBECsxEATnoI6ri7zuo18T4iDPbCwY3OCWUBaicifWkzWCuUgMJP6JNLEcFyVU8rikZDvvTn6CH39aDmho9jpUcgoaiuPadWDnpqUcc/NYn2Vk5w9k1zsPkJKURL+HPw3q+OHebuAaYHm60BvmVg6wXkYEUoIgBM7SpVN5/8PnqKkpb+SfrIxm7PvoSexo5A37l88yQnWQ+EcQrE3fPq1MbeQmUgwUSOJGHBQ+npLI7tsEQaekZDtvTXyIn7euQ7k4KCkpmZIpj1GfZLNsDASBOahm7TRu+/29XpOe8xfsbfCTOMg7egLZyPIEwVc7rGLTEo65+TWfr49IDFRR2vDdd/3eSjss9pm/YG/Muyhhksfr189l7Lg7qdc0bBnNqK8+1LDNlp7Nzl9+BE2jbt9OUnLzvJaT3Kw19VWHuO2e/9C6dfug6qDfbuCrfF+3G+jz6bzx1gNkdOlPZv4Akpu1xn6whMp1M6j6bia3jXwp4HqZMXeOIAie+e9/72fFqmmkn3w2yft/wV76W0PgUlF1EOx1QH1A12QoDhL/CELi4oiB/kQ9zhio6mDDNlt6Njt3/ghoVG9fG7MxUM3aafzjgus555fvAkrciIOMI9YbQ4L5rF8/lzGv3Y6GatIOIzWDw5UHoa7GsjEQ+HZQ1dppVK+bwZMXXM91gzt6LUN30/wFe6muKBUH+WBjwWBYUBTW6GMZdSzo/Pe/97N85VfYspo3et6Wnk1FxQGsEgM1y85pGEzgmkSWdlhsEy8uSojkcUnJdsaMuxPtsB1lSyGjQ0+Sdm8EWzIZ591G1aYlHPq2CK2+jpL/vcAxI8d4vbDtB0tIz2pB587nB3X8mbMnUVtbxcGPHqbF9a9gy871uK+/2w30+XRmzZnEssl/p7ryAOmZLcjPPx+ty4W8+d8HoPYApLag5zm/p/+FQ71KxHXunEOriij/fg5pdQepSWlG9hkXkNPd0RgIdO4cQRA8s3TpVFasmkbW6edR8cM8srpcREZKUlMHHa6jbNkntPjd1V7LCtVBuUcdQ9nyT0kp20n2JQ95dFCo/unZ8zIKbnuVVWu/CdhB4h9BiAwlJdt57fW7qa8/jEqykXX6eaS2O53qGS+RPvCv1P7yvTMGOsz+WW+ASiKn6wCPZVkxBspKz6L/Kd3pe9FQNtVt4Zl3JlP3n0OkpOVw07m9uX/gAE5u2xZoPLVC5sRscZAgRICSku2Mee1OtPp63+0wLYn9cyfQ8sKbvZYVzRgIvDuo13Gn0/qsAp6ZN5knZrzu0T+u9O3TisyJOeKgAAh3+grp3BKWLp3K8hVfoGwpZJ1+HhkdzqF6/n+ot9ehte1ExXezTIuBIHAH1Xw3nRt79QLcpoJa4ByFXzBY2mEWouPq4Dq34sFFCbFg3kefvICmaShbCm2vfYY0G6j9W9F2/4R94xxyzx9B22ufQdlSQKunbPEUr2VVrpvBOedcEfCxXVexzD4xH1vlXspnj/O4b8PtBhd4n8sGjsynM/ql5Ywf9xO3jBjFmrXfsEklk3FyN9KSk8g4uZvflTJ79Licg/MnseudB9DqD5OVqkixKVqc0r1hVdGyeRMDnjtHEATPTP7wWdJPOouKH+b5dVDZovepKy32WlaoDipveTz2H2ahFf9A1bIPmuwXqn9Gv7ScLqf34bU37mFdVWXADhL/CEJk+OLLsZDRHJVkcywEc/4IahdPxFZXSe2iiUf8k2Qjtd1plM7+j1cHWS0Gmnvby3w59GluHXg2hXPeYcrBHJJPOpO05CSSTzqTKQdz6Fb4JF+vWdOknGF9e3Fo/kRxkCCYzEefvIBGYO2w8m+LLB0DQVMHFZ5/HYt/+YFp9rYB+wfEQYEQzgJ68TLSTwifdyc/2eCf3PNHYN84B/b8BHt/Js2GaTEQBOegmnUzuG9g/ybb+vZpRd8+rei4uog+v3wn7bAYI55clBDJ4+/Wz3P0Ip05GFvztlSun8WcoZkkJ0Hl+pkcLi8lrV0ncrpfCiqJyp8WeywnmMACGq9imdl9MHXbVzNnWBY1m5ewb+Z46kqL0Q7bqSstpmzeREqnPhvU7QaejlGzaTFzhmZQs3kJWd0v87lSZveuF1GxZTlthhSSergSW3UZV5xqo2bzEpqdeTlthhRSuWUFpfuL+ct9Z/KXu07mT/d05q4/53P77adw7wNnM3nK07IKpxAXmDkPUW1NBfbSXwNyUFJGMw4seMdjOeE4KKfXtSQpjTlDM6hcN43qXze6+GdCSP5xP0YwDgrFP3++t4Cnnr2CP9/XnTvu6CAOEuISI+d5BPh21TQOV5SSc+Zg0tp1omb3z9Tt3cGcYVnU7dtO7e6tDf6pLd5EdteBHFrVtA5Wi4H096ndqYe5+rXXyb6ykPTulzVyUEb3y8m+spCrX3udLbt3N3r9kDO7U75lhcRAgmAyQbXDkpJiIgbquLqIjquLaHfqYZ6e937Q/gFxUKCEkkCWBTsFV+oO1zXEQPby/U0clNz8aMNjIAjcQYfmvU351Kf58E+3e7xTQUcf5ar7x/0YZrfDEtE/vthYMNivl+LNRQmRPNa0ehQa2V0vpnrZBwzvoijIszGsayqnH1Xf0PuT3W0QCg3q7ZTNmxh2w8Z1FcvqZR8wvGsyBXk2hndPh9/Ws+u9v7HjpavYM+leumVlUfjwp0HfBuH1GPk2qpZ90GilTHdWrf2G5mdehq15W6o2zGPOsCy+2nyYqzsmNbw2u+ASNu7e3tCL1ey0nmQWDCIpI4eMc2/0O7pZEATQ7HXYS38LyEFadTlVm5aa4qAR3VIdfuiazIGPHmHHS1dRPPFesn7bGJJ/PB0jUAeF4p/MU7pTnncadfX1tLrqMXKvf0EcJMQVRqws7469prIhBgKonPYiIwtSKMizMbJbChXTXgScMZBWT07BJZR/N8vSMZDeaOrbpxUvT59BWv5Anw5Kyx/AK9NnNirjk29XkSsxkCCYTrDtMKvHQEb4B8RBwRBKAjlekjVC+LjGQN4cZHQMBIE5aNfEe2m3azVrnn6SQd26+S1TH4Wsj0ReOeUfZHXpF5F2WKL6J1ziyUWJkTy21zkWprIlU7l+FoV9UgB4sHcqP++3N/R6Jzdr3bBvt6wsSif/nZ0vD6F08t9DSu4uX/45GV36Yy/fT9X6WTzW2/F2F/a2UV9WzDHDX+WYW18nJTmd664uDHrEn69jPNY7iarvZ3G4vNSxUuayLzy+NjN/IFULJzA8P4mCPBtD81NIVfaG1+YUXEJt6W+NerGanXkFbYYUcmDeBDK69PfYo1VSsp3JU57m3gfOjtkRghs3LuapZ6/gjrtO5/bbT+GOu07nqWevYONGzyPTBcEbKjklCAfVmu+gPinYkhTH/mkiecNGs39/cUj+8XUMfw4K2T9n/Z42f3icfV+NBqBZ36Fx6SDxj2AUun+Sm7dpGHX8aJ80AB7tk9Yw+liPgZKbtUarqbRsDOSauAF4b/ES0roM8OmgtC4DeXdx42vnvcVLSJcYyCviIMEoLNcOCyMGMso/+mvFQZ4pKdnOWxMebBjleMddnbjo7Ud4ZvZk3i/a6PO1Zt5JKMQmegykjzr25CBlSzY0BoLAHHT0sNHs2LfP54hjb/Tt04o521aTnj/Qbzts5ZJPG0Ysd1xdxMoln0oeyAdGxEDxNF2FTkIkj1VyCio5hcqFExneRZGX4zjtvJykRj1O9oMlqORUVHJqk7lkQknu6qtY6r1ArsfVe4PCXcUynGNUVxxA2ZKp2jCPwr6OhuSDvVP5eIO9odcpuVlrUmoPeuzFyu46gEOripr0aLnOcZh7/Qsc99epMTdCsKjoVUaPuYXyvNPIGzmG4//2GXkjx1Cedxqjx9xCUdGr0a6iEENoKHGQ2zGM8g8Qdw4S/yQ2+mgSo7DZHDGQvWxPw6hj1+tUH32s+0f/14r+cU/cABwsPxTQcQ5VHGpU1sHyQxIDeUEcJBhJvLTDjPSP/lpxUFPWr5/LU89ewQ/2etoMG+30z1gyCwYxa/t3DP/kRUa9N79JYmb+gr2SOBY8osdA+qhjTw6qXDjR0BgIAneQJz8ESqAOqqwubzRqubK6XPzjBSNioHibrkInIZLHoCAlk+ofFzT0NOm49jgdXD4VlZZFmzahjcBzJz2rBTXFPzXqBdLRe4Nqdm0OaxXLcI6RntWCirlvMDw/qZFoXHudKn9eRZLCYy9Wdv5AKjbMA2gYWeg6706zvkNJyc1DJdlIyc3zOkLQamzcuJiiaeNoe41jUn3Xc8g9fwRtr3mGomnjZPSNEBAlJdtB09A0AnJQUkY2xxzTwZBjW9lBRvoH4sdB4h9Bx6gE8umdeqNpigOL3m806lhHH318YNEHJOceQ/marw1xkNH+8ZS4AWiWnRPQcXKycpq8TmKgpoiDBCMpKdmOFmQ7zGoxkD5ST0+6uBKqf/TXioMaU1Kyndf/ez8thzzOURfe3Ng/5w2n7R+fwp5ko3DOZH4t29uQMI7XRI0QPiUl29E0xcHlUxuNOtbRHVS1cT625m0Mi4EgcAd58kOgSAxkLKHEQJ46siA+fZQQyePc3DxS6g42ujh09B6nTrmHqVs/nfqqQ1x/TaEhx+3R43IqZ49v1Avketzh+TYqZ48LaxXLcI7RtWs/ajYvbeht0mnU6zRrNCMK0rz2YtVXHgRo6Ll3ndvHE77mYLYKUz55gZzug32eQ07BpXz4yQsRrpkQi8ycPYnszheQquwBOehw5UGuHvKQIce2soOM9A/Ej4PEPwIYO/dxRkYOacedgfbjnEajjnX00cfaj7PJ7tqfQ6u/NMRBRvrHW+IY4IZev6PKz3Gq5ozjxl69Gm37/ZkFEgN5QBwkGMnM2ZPIPuN8UuzlgbXDqg9ZJgZyXZTKm5ND9Q+Igzwxc/YkMpzzt3oirV0nsrtdjMo9hjf27GRjweBGD0FwZ+bsSaS370Ld+umNRh3rNIw+bgkZ2TmGxUAQmIO8+SFQJAYylmBjIPf52OM5cQwJkjyuKN+PLUk1uTh0HuydytbSwyjtMP0vGk7HjqFfwK6cc/al2PdsadILpPNY7yTsJT/T86zQv1zhHEOrOeBVNEPzU7Db66ivPNikh861FyspsxkA9oMlpGe2aJjbxxfe5mC2CsW/bWqYVN8b2d0G8dtvmyJUI8FszJyTaPnyz8nq0g+bLSkwB12YGA4y0j8QPw4S/wiuGDH6eN13c8jpfimgNRl1rON4XqN09tsM73ohv6/a32huPF8PbxjlH3/Jmxt/dw51fo5Tt+dnbvxdz0bP11SVSwzkAXGQYCQNMVASAcVA13Tu49U/wRKKg9yP52m0sSuh+gfEQZ5Yvvxzsvz5J38gdQd2WfYcBGuxfPnnNO91DUlKa3It6TzYO5WtB+qp++UH+p0/NKLtMG9+CBSJgYwllBhI77zSp82J18QxQHK0KxARag8yvHtak4tDR+9xmr/djqqvMuywq1d8xsgzM3wed2T3dFav/IyTTiqI6DHKyvawft03TL07w+PrHuydSsex5V5HKQ3PtzFp9jiyOp0HQOW6GfTseRnzZk8iuXkbn3UOd45Vs9HstQGdg2avjVCNQqekZDszZ09i+fLPqa44QHpWC9Z+dyP33/tnTj755GhXz1KYJfrqigNkbpjN8HybXwct2FmfEA4y2j8QPw6KJ/+AOCgc+vZpxfwFexuSGKE6qrriACmLJ3q8nnTycpIYWZDCnF9a8NZ9NwZctmv93OtohH/8JY4BPlyykFvPTPd5nFu7p/HhkoWc08FxK2pxaSlFq1fx092ZHl8jMVB8OEj8E32CiYEW7jzMMUcneb/eFwSXQP5m8Yfc3N23G24uSGPb16O5pNcfgeDv+gjFPyAO8oY+R6wvkpu1pr7qENVKRahWoSMOij4NDurmOwYyqx3mz0Ge/BAMEgMZSzgxkBWTxu4OevDho7jh+utDdlBCJI9Tkm2MW1HDuBU1PvfLTIHjt64y7Lg7tq1mxs9VjF3mW0IdTwr9mKEeY9a0MQzr6j2QA6jX8DpK6bHeSbz96s80u/BOan7dQNV3M+n38KcsW/Y59rI9pOTmeS1X752yKio51e851OzaRHoK/OW+M+l5zu/pf+HQkCbSN5P16+fyxlsPkJk/gNzrX3CsMlu2hymrZzHpzLP58P33GDRoULSrGfekZ7Xg8K/rGbcrQAelx7+DjPQPEFcOihf/gDjICPRERihJZH3/zPRsOLiLsSvqGLuizudr2mSXhVS/BlySO+H6J5DEMcCKLZtYtLmafy+r9rlf71OOjBIZ9cVnDPUw4sYViYFi20HiH2sQbAyUtsX7iPZgE7uPzPqFD9dVM2a5PzfsDHmqoFD8A+Igb6RntQio/iQlk6ZqxUGCX6LfDgvEQaHfyWOFGKhm7TT6Pfq/mPcPxE8MBOY4KCGSx2f2vol1VZU06zu04Tl7+X5K/3sLC4emcO47dpI7DaB7bkuuu9qY+Y4B7nvI/CH5oR7DIbNaXlvheeRIqg1u9jNKaXhBGu/OHkdt2T5uG/kSrVu3p0ePy1n33UxSXN5rd/TeKauSd0wHytdOI/f8EV73qfjmNdKSNOpqD7B0/gTmzZvMqaeezdAbnraEPFwnrHedsyclN4+Uc28i5cSzuPq6G1jz7Qrp+TaZHj0uZ11VJe2HjWv0vKuDek+opluPIQy/6XlDj21VBxnlnw/WFlGzeRlV382MGwcF5p9xpCVBVd0hls2fwNL5E6hLyuCs7oO4fPDd4qA4xFMSOdDXDdvaiykHc2jfd1ijbY3ioAnVXN3rPN6+9WbD6vn6gNuB0EZiBJo4Blj41HNBl+9obEkM5InAHaRRVVPGigUTmDf3XVq2Oo6hN/zDsNt9w0H8Yx0CiYGM8o87obghUscwzkGvYS8t4bZbRseFg3r0uJw1a6fRwod/ytd8TXp6Cmn2WmmHCX4J1EFdTWiH6XGQketYuBPNGOi9OeOoP1DCkxdczzm/fBfz/gFph/kjIZLH/S8cytLnryLt5LMb3rzqZR8wvGsyBXk2hnWpZ8La6fQrnBblmkYOfwmfV164jHErf2DcSt+jlNoeVcpDD3/acJF4eq9dce0dtyrXDHmI0WNuIbPDOR7PoXLTMuwlW5k/Moveb1WQBGSlJfHT5lUUPjGQKy77C4MG3Rn5irsQyIT1dWf055V/vcqYf4+ObOUSDG/XhKuDhufbWF/vuzc8njDKP9lpCznr3BvpF0cOCsw/PzN/ZBbnTqjClgT19ZCcrLH8269ZseILcVAcE0oD5P6BA5hU+CQpJ/fw6qBh+TZqDHSQESOmo9nYOveJRxi3crvEQH4c1PvtShSQnZZEzTGnM/rVW8jKbM6tN78U1SSy+Mc6BBIDGe2fWMAoB7U/ai/P//5e2tWVw+qimHdQ/wuHsuS5K8nw4p+aXzdw8NsiMmx25gyXdpjgn8AclGRaO8zMWCZUjPNPCd88/SQnt23L/AV7ub3tcdz82eiY9Q9IO8wfStM0g6p4hLPOOktbuXKlz33eeONnw4/rC33YdkaX/qSd0oODHz/Klj+lkpeTRPGhek57rZbCf8ynefPWEa1XPOL6XmfmDyC5WWvsB0uoXDejYYRg587nR7uaPikqepWiaePIKbiU7G6DGs7h0OqvqF1bxMhuNl4blMpfplXx1qo6bEnA8WdxaOdG6utqufC867nmGuNGsQfLvQ+cTe71L/i85aKutJiKjx/hwL49TbYppb7VNO0sM+toJoE4iMmTG/6rT3BvFu7XhEqysf/t29lyV1qDgzqNt/Pok3PFQQYQ6w7y5p/ytdOo+fYzRnZP4bVBqfzpyyoO1Wj870c7SYq4cVCi+ScSfL1mDVe/9jpp+QNI6zLQo4M6j6/l+3++wtEtWphSB9eFST351nVEtRUbW+54W1E71v0DwTlo4Q47O8o0kk7pQ1rB5ez+4DE0rZ7LLrmLwYPviUr9JQayVjvswP9G8eScyWR2Gxg1/yQCupOW7viBx+dNiVkHrV8/l/H/uZf0zv3IKbjkiH/WfM2hVV+SnXciNx6zg9cuTpZ2mEXx56Bo5oEi1Q6LREe4FRn13nyenDOZtK4Xx6R/QNphvvyTMMljcAzfnjVnEssXvc+wzvW8dumRxZr+PP0wP2ZdyZCrn4p4veIR/b1etuwLqisPkJ7Zgp49L6PfBdacE8adkpLtfPTJC3y3fh6aVo9mr0OlZpDcIo/ksh2NfmxO/nc5/7s2g99/WEtS50HUFm+itmQb993zn6iNvLnjjg4c99epqCSb1320w3Z+eXkIhw/bm2yL96AFiGjyGBpfE/VV+xlZkMJrl6Y3bBcHGUusO2jp0ql8+OkoKisOoNnrSMpsRlLWUaSUbWfL3ZkN/jnjtXJqDsPCEVmcO6E6LhyUaP6JFFt27+aV6TN5d/FiqivLGFmQ2shB9023o5r34uWh3m/VMwLXJLI7sdbI8pZAjnX/eIqBHKuqJ5FmL2vkoFP+Xc5n12ZwxZRqWt42iYMrplK5ZSWHD+7m3ruj4yCJgazVDuu4uoh2px62hH8ShfeLNvLR9wuYuXkVFdUVMeegjRsXM3nKM+zZsw3NXotKTiE59xhSWp0AWxez2WUAmLTDrIfVksfg3g7b18RBRrfDOq4uirmYxih0/0z7+bu4ioGkHZYg01botG7dnksG3s6qxR9Q2LfxBOAP91J0Gv8x/QbenbAj/9znUQwnmda6dXuuu7rQ0DmkI4XeO5l2ai8yTjuXqp9XoNnroN5OqlbTaIJ5x0rNKXy9+TDD8pN4v2I/lWW7ULZkPvzkBR5/9H9ROYdAF5zIaXFUBGuV2OjXxCUDb+eZJy6gsG9j/YqDjCXWHfTeB0+hctuhaqsd/gFsZTsZ3i2tkX9u6JLCsl8PN9x2Jw4SvHFy27aMGXojj152KWc8eD+FfVMbbX+wVxKdx8/nwcuvNHX0Xzw1phrOZUHjqTli3T8eYyAgufYgw7s3dtBIZww0vGsyH8x9g+zeQzm06ktyul8aNQeJf6yDawLFCv5JFK4b3JHrBnf0e8eHFVm/fi6v/+deRwyUkoZ22OEf+8E9ZB7VluulHSaEgGs77NnH+zZxkJHtsGDWpohH3P0TK+4B3zGQtMMSLHkMMGvaGIZ1tTWZADwvJ4mh+TZmTR+TUCP/vN0m6r4oTyQu+o0bFzPlkxco/m2Ts5c5lbxjOnDNkIci1mujTy6e2WMIZUs/IrvrQI6+8UWSm7ehpvgnDn74dwrPzWj0mkf6pNF5XAWzh2Yw8e1l1NfWg1L89lvoK6eGSyAT1tesn8mNN1wfwVoJIA6yMlZx0Lg3/ky9UmQf34WWgx9w80/jHuRH+qRxxmvl7Cqvp7BvGhPHiIME34z64jOG5TddZdvhoGRGfT5VRv8FSd8+rRripnDipWg7KLAYqKmD9BhowlsLyew7Es1eS3a3Qfz21pem19kT4h9r4CmBIv6JLMHMPx9t/4D3GMhetoeyZZ9S8/3XFP45u9FrpB0mBIOjHebNQca1w+KpozxUXGMj8J9PiraDQo2BEqkd5nkJxTilrGwPS5d8wsO9lMftD/dSLFvyMWVlJRGuWeTpuLqo0Vw87oLTn9OfN7sHrajoVUaPuYXyvNPIGzmG4//2GXkjx1Cedxqjx9xCUdGrph5fZ+bsSaSd2ouypR/RZkghuecNIyU3D5Vkw75xDsML0rz82KQwca2dYflJpKUlk5TRDM3ueQXTSND/wqFUrptBza8bPG6v+XUDNd/P5L6/RGc+wkRFHGRdrOKgz4vGcBiNNn94ool/Rnjxz7CuqYxaVOv4vzhI8EFxaSkTF8znwV6ew78HeyUxccF8dh04ENmKxQHhxktWcJC/GMibg/QYaHjXZMpnjUUlp5LcrHXUHCT+sQ6u7QvxT/Tw16azgn/AewyUkptHeopiRPd0aYcJIaO3w/7e2/Ot/Ea0wxJ91LE7geaTrOCgUGOgRGqHJdTIY28j/nQSZeRfsBO4GzWixhsbNy6maNo42l7zTKMVIVNy88g9fwSZHc6haMpjnHLKmU16nUpKtjNz9iSWL/+c6ooDpGe1oEePy+l/YfBz6pSUbGfRoo9I6/A7srsObFQXe/l+qtbPovBPqR5f+2Dv1CMjb9ZWkXZiPtWblwV1fCNp3bo9t418yeOiPTXrZ1Lz/Uw+fP89Tj755KjVMRERBwVGMIGXEU6ygoMayln5Jc3Ousyjfx7z458He6dS2DeNCWsrxEGCR7yN+tOR0X/hEWq8ZBUH+YuB/DnIMfr4W2y5J2A/WIJK9ry/2Yh/ok8wo451xD/m42mqHSv4Ry9r5bdfkXPm4Eb1AGmHCcYQqXaYjDpuirdpviB+YqBEaIclVPJ4x7bVzPi5gleX+t6v40mrIlOhCBPOqp9mJpCnfPICOd2bBgo6ae06kVPQdO48fU6azPwB5F7/QsNtTeu+m8nS568KajVPvSx7bSX1P6/g6BtfbLS9etkHHm9x0XEfeTNxy0aOOaZDYG+ASXTufD6FD3/qWBxg8t8bJqwfOeJG7pu0QgKWKJDoDvKHt2l0fOIhCAmWaDvItRyFRnb+wEbbq5d9wPAA/DNqUS0vD0wXBwleWbFlE4s2VzLaj4N6nxK9W+1inVDiJas4yFcMFIiD9BjonV2plK/5OqoOEv9EH/ffcfGPdXD11FNfvWmZdpim1TeJgUDaYYIxmN0Ok1HH/nFPIgNRd5BRMVAstMOatTiKG2+4PmQHKU3TDK+o1Vb5FcJLHLtixsTnd9x1Onkjx/ic0LuutJjit+5m/NgfAEfv0NPPX0XulY96FE3NrxsonfoshQ9/6rfXybWsPZ8+S31VGcf/9bNGq1MefO/PlP7i/zvb+zgbH/0xg5P/XU5tUgbnnntNSL3vZnLbbSf53SfeV/kFYPLkhv/OX7A3pibzjzdCShq7EY6boukg93K2v3AZx/8tdP8sHJnVsPp4q2O6cPtt/7KUf8C/gxLNP0L8EqiXrOIgI2OgqsM2unbrxx+HPGQpB0kM5MDsdpjrQnmCdZm/YC/n/+dv5I0ca4l22K53H2wSA4G0w2INfw6Kdh7Ik5+MaAuK94In2g4yOgayejssXP8k1JzHiYpRiWPXMozsWdPstSQ3b+NzH/e582bOnkRm/gCfPVQZXfoza84kr2WWlGxn8pSnefLpy6ipLGPPp8+S3KwVKiUDe9meRvs2u+Hf5B7ruNhSbXDnWSloTzRr8lg4Mou8nCSGd0slGTurS/fw9PNXsX793ADfDUFIHPzNvR4M4bgpmg567Y0/U2uvZdd7D7Hz1RtRKWke/dP+oSK/Dlo4MgugwUF7dm3gH89eIf4RhCgRqJei4aBgY6D2DxXRLDMtwBgohbSUJLZikxgoAZHRd7FD3z6t0Ox1lmmHeYqBQNphQmQIx13ivdCIloNCiYGkHSbJ47jHyMSxjtE9aio51WOg4Ir73HnLl39ORpf+Pl+TmT+AZcu+8Lht/fq5PP38VaytrKDNsNHk3TyOjJPOom7/b2i1VRRP/Av7v3mTutLihtfo4sjKO4lxK+tQTx30+hi3spbUzCw0Wwq5Vz7KG289QEnJ9iDeFUGIX4xMGrsSagI5mg461LYDra98lJzul4JWj1ZXQ/GEpv6BIw5Ky24eoIOyST6hQPwjCFEkEC9F2kGhxEAAufd8EmAMVCcxUIIjo+9iB5WcYpl2GMBvb9zGzldv9NoOCzwGEgcJgWPkIDshOCLtoFBjIN1B6TktErYdlrDJ47KyPYwdfV1Yq2laHTMSxzp9+7QyrIct75gOlK+d5nMf97nzqisOBNRDVV15oMnzJSXbeeOtB8i98lFST+jGno8eZ9eEv5CUkUPe8H85Vvcc9i+ULYVd7zxA1ZbGt92knX8nKiWNNtc+S/uHijjmtjfJOesKVEYz0pNBZTQj56wryLj4b1RsmBdQ77uQeCSCgzxhRtLYlVASyNFyUE6/26nds5WSj/8BSckcfdNLDv8M9+6fml83UF1bT1pmc4657U2v/jnmtjfJufqfVO9YJ/4RPFJcWsrFzz/NrgMHol2VuMeflyLpIImBBCsg/rEOZxx7rHXaYSNe5fi/fcbRN/4TlZzaxEHBxkDiIMEbU6dtMcxBMuo4PAJ10IlHHd3wd7RioJpfN1BTR8K2wxI2eTxr2hh2bFvJrOljol0VUzAzcezpOOFwzZCHOLSqiJpfN3jcXvPrBg6t/pKrhzzU8Fx6VouAeqjSM1sAsHTpVO5/8HfccVcnHnvsImrratk/5232fPgkhyvKaHvtMxx14c2k5OahkmzO1T2H02ZIIXuLXqJ2307qSospmzeB0qnPotXVkn5cZ6q2rGTXOw+gklNpcUp30pKTaHFKd1RyKnv/9wL1FWWA7953ITGJdwe54z7a2EyCTSBHx0E17P1yNDW//BCwfw7MeZv9nz7DHbeMprbqEHX7dnr1z653HqBu7w7qKw+KfwSPjPriM5Zv+YlRn0+NdlUSAl9eMttBJSXbeW38n7jz7jMofPJiairK2P3Rk+z56B/Yy0slBhIMI9A5P8U/1uFf119rzXbYecMcDvryZaq2r2X/7P+GFAOBOEhozMaCwXywdrqhDpJRx6ETqIPu6TG4oT0ZqoOMiIFuG/lSwrbDEjJ5XFa2h6VLPmH2TRksW/Jx3I38i3SCJlw6duzF4IvvZPeUxyid8xZ1pcVoh+3UlRZTOuctdk95jMEX30nHjr0aXtOjx+VUfTfTZ7mV62bQs+dl/Pe/9zPhnUexdexD3sixDSP70o45DZWcTPqJ3X3Ol5PVpR/Fb99D8Vt3c3z1QQof/pSM7Fyqd65n75cv02ZIITlnXkb1psXMGZpBzabFNDvzctoMKUSlpFJXWuy1911ITOLdQe6YPdrYE8EkkKPjoH+TU3AJypZMfXWFx9e7+6d97SEef2QqnTufT2pGDvu+fKXBPzVO/1RvnE9Wx760GVLIvq9Go9KzHP6pKA3i3RPineLSUiYumM83N2UwccF8Gf0XIbx5yUwHdTjlTJ74x6Ws+34B2WcOPuKgYaNpdualqKSkgB0UVgwkDhKciH+sxYVnnMGTlw+2bjus84Xs+fgfpG5fHVIMBN5HQQuJSVnZHqb/tLyJg0K5s1pGHYdPIA568vLB3Htdr4Y4auCJ+eE5KIwYyJODPMVA8dgOS8jk8axpYxjW1UZBno2h+ba4GvkXqcSxp2OGw+DB93Dv3f8hZ9dPFL91NztevJLit+4mZ9dP3Hv3fxg8+J5G+/e/cCiV62b47KGq+m4mLVsczYpV02h77TPknj+ClNw87GV7OLSqiIrv56DVVVO9ZTl7vxzdZF4bnZyCS0hKy6Lttc/w46blgCNoKpv/DtldB5LWrhPVyz5geBdFQZ6NYV0UVcs+IK1dJ3IKLuXQqiLsB0tITc8O+30S4oN4dpAreu9wJJPGrgRzzOg5qIqSz57z6qCcgktQyam0vPTeBv8AtGx1HNldBxzxT9dkCvJsDO9qo2Lai6S160R2fn+Smx+N/WAJ2FLiasEGITxGffEZw/KTnQ5KltF/EcRbAtkMB1Wum8EPPyxES7LR9uqnyD1vOAClc95i17t/4+AKx4riJZ+Pomr7Wo/lGBUDiYMEHfGP9Xj8qquY9bcHaL9njQXbYZeSlJzKwUP7Gp4LJgYCpB0mNMLRDjPOQTLqOHy8Oaj9njXM+tsDPH7VVQ379u3Tiqs796F6zddBOwiCj4ECaod5iIHisR2WcMljfcTfw70UAA/3UnEz8i9SiWPXecqMPFbHjr14/NH/MX7sD7z++mbGj/2Bxx/9X6Oebp3Wrdtz28iXKJ36LGXzJjbqoSqbN7HhloJps94i58zBDT3arrdYHn3jPzn+r5+RN3IstszmHue1AUdvdX3lQeqrK8jofBGz5kyi/4VDqd3zM9n5A7CX76fyu5kU9kkBoLBPCpVrvmTvtFdJP+lMKjbMo3ztNOyH7XEzWboQOvHsIB2zp6gIdq7EQDu4rOig5Gat0Wqr2T9jHMnHntEwZ9b+fb+Q3fVi7OX7qVo/i8d6O37OC/umUbd3O9v/dS2HKw9iP1BM+dppZHToGVcLNgiho4/6e7CX4zvzYK8kGf0XJOHO1+prBLKRDjq1w9kktTyW7G6DSGvXyYN/pnL0TS+TUzCIkk+fNS8GWjddHJQABPJbK/4JH7Pmi77wjDNY9+zT1E98i3l3jLZEDAROB1WXk3xsZz78+P+AAGKgV/7YEAMB0g4TGtDbYX/vbQM8OyjgdkOA0/TEG5FwkPbeu9RPfIt1zz7NhWec0WTf6wZ35MkLrg/KQaHGQJ7aYfv27mxwkK8Y6PDBPXEVAwWUPFZKnaqU+kYptd75d75S6jFzq2YO+oi/vBzHqeflJMXFyL9Ijjh2n6fMyMXzgqFz5/MpfPhTumVlUTr57+x8eQilk/9Ot6yshlsKKisOkN31YgDqSosbbrHMPW9Y43ltLhjRMK+We8+3/WAJSRk57P3yZVJP7M7Spf+jdev2aPY6kpu3oXzGvxnehUbfqeHdUlAlmxvm/CtfN5PMTn3jZrL0SCMOih0iMUVFMHMlhrKAXqBEwkH2gyUkZTajzZBCqravY/HiTwGoqTxIcvM2VC/7gGH5tib+yWnWDFt2LtjrOPhtES363BRXCzZEknjyDxwZ9dfYQTL6LxiMmK/VCD/6c9CWLauwH9hFdv4A3/45fwRtr37KvBho7QxxUBjEkoP8fa/FP+ETqfmi/cVNkW6H1excz7rv5lJSst1vDJSVVHckBlo+VdphYRJLDvKH53ZYcqO8RiAk8nQVVpmz/pzjT+fty+8JyEFhxUCe2mFVBwOLgSoPxlUMFOjI4zeBh4E6AE3T1gHXmlUps3Af8acT6yP/Ipk4tto8Za1bt+e6qwsZ/dJyxo/7idEvLee6qwtp3bo9QEPjBuDQqiKyuw7E1rwtZR/+ncPljeeeSWvXieyuAzi0qvGPQfm66WSdcQHZXQdQtWkZ1ZWOBWBUcioVPy2mZutKCvumNXpNYd806vftoOUlf3FMon7ecFLadWL+/Cnccdfp3H77Kdxx1+k89ewVbNy42Ky3J54w3UGRCALi1UEQuSkqQnGQmfUx20GHVn9FVqfznNsGUltbCTgWq6kp/snR232urVE5hX3TsO//jayOfWl77TPo37aklseJg0IjLmIgaDrqT0dG/wWOkXGQEZ3vvhxUXXHAMWKveZuox0D2g3uo2LKCefMmi3+CJy4cJP4Jn0i1wwKNmyLbDhsI1DNrziS/MVC93U5K65Npe+0zHFjwrrTDwicuHOStHebuIH+/zdGYJtQqWCkX1LdPK9o1bxWQg8Lyj4d2mLIlZgwUaPI4U9O05W7P2Y2ujNm49zTpxPLIv0jLy9s8ZdEafewPlZzSsBJnxQ/zyM4fQPWyD9CKf6Bq2QdN9s/OH0jFhnkNf9f8uoHytTPI6T64YZuyOW5L0LR6Kme/zohuqR6/U8O6QP32VWQXDKL8u1mUTh9LdsEl5I0c45iofeQYyvNOY/SYWygqetXEdyEuMNVBkbp+4tVBkb7zIdS5EqPhqHAc5PDPdHK6D3Zs6zoQpRzfnR49Lqfim9cYnp/k8fs0vFvKkXn/Cgax98tXxEGhExcxEDQd9acjo/8Cx4z5Ws1yU3pWC5LSsrCX7Yl6DFTy8T/IOOnMI4vViH+CIS4cJP4Jn1ibL9rQdljXgShlY9myL/zGQCMLUqie+VJDDCTtsLCJCwf5boc1vZ48/TYncuIYYtdB4foHGrfDNO1wQsZAyQHut1cpdTKgASil/gB4ntXeoug9TRPu9HzKD/dSdBr/Mf0G3k3z5q0jXLvQiLS89J6m7+9IBRy9dJ3Hz+fBy6/k6BYtIlIHd0pKtjNz9iSWL/+cqvJSktMyAbDXVpGR1YLklDQOrfmaoy4YSX3VQZQtmar1s1g4NINz35lFRs9rHbc1OdHn9qsrLebQ6q+o+G4WrQY/QEpuHtphO/VVhyDJ0cOdmpqOVnWAwr6eF2Ao7JvGxLEzyPnj85Sv/oq21z7baDVh/TaJzA7nUDTlMU455UyP84oJgDjIcrgGVLHgoL59WjF/wV5D6+Pqn+qKA6Rm5NCy1XHs3/cLNZUHSQ/DQaVz3+bQt0Xk9rudlNy8hm2avQ6Ac86+lGXzJ1B4nXf/TPj3dmp3byWn4FJxUHjEvH+g6fXjjhV+062OGXFQOG7y5yBbagaaUpSvmSYxUGxjeQf5m/tT/BM+kW6H9e3TChYUsbFgsNd9It0O0w7XUl15wG8M9GifNN5aXU75DwslBjIGyzvIH/7aYe7XU4PPFjROICdq0hislwvasns3ryz6nOnvPuW1HaaSbJSv+Tps/+jbNXsdHVcXkW5LTcgYKNCRx3cBrwMdlVK/AvcCd5pVKTPw1tOkE2sj/6LR6+VvnrJIjz5ev34uTz9/FeuqKsk490aSMnLILBhEm2GjOf6vU8m9/gXST+3NoW+LKPnfKEhKpmzyvVzdyeZYkTff1qTXyX6wBGVLpvitu7Ef2MXRQ18m4+SzXLalkJaWBUC71scwoluKz+/UsC5g3/AN2mF7I2G4oq9I/uEnLxj47sQdEXGQmd/feHGQ+0hjKznIH0Y6ytU/ude/QKurHqOuvp7yvNM46oZ/cpzTQantCzi06kt2/Osa0pM1yue8cWRVcK8OSuHQ6q/J7Xc7OV0HNN6W7AjYVq/4jJEFaT6/T/ro4+RmrcVB4RHzMRB4H/WnI6P//GPWfK2huCkQB7UZNpr047tycFURJNkkBopdYt5B4p/wsdp80dFohyWl55Ce2SKgGEgffSwxkCHEvIMCa4c1vZ70tk6k2zxWxEoO+nrNGroVPsn8rFY+22FpJ3Tn4Kovw46BGrYnp9K3TytOP6ZlQsZAAY081jTtZ6CfUioLSNI07ZC51TKeHdtWM+PnCl5d6nu/jietikyFwiAaiWNvIwai1eNUUrKdN956gNwrHyUpswW73nmANkMKm/ToZHQ4h/KNC7DltCSzRUts5cWkqhQghcd6JzFhXONep0OrvyK5VXtaX/5gQy+TzqHVX5HcvA2/63aR44n6GsatrGPcyjqfdW3W8luSMnJ87pPdbRC/vfVl8G9EghAJB5kxMtWVWHaQe1IjGsGTkQ7quNr3SBp/uPonrV0n6kqL2ffVaNr84fFGDrLv/5Wq7WtoduZgbJX7qN80j7otS3nsHkfyxbuDjvfooPI1X3PMMR0A/ftUw2sranzWNTt1BzW7NouDwiAeYiCAFVs2sWhzJaP9OKj3KZsiU6EYIxJxUKBuCsZBNTu/o9mZg7FvXiwxUIwSDw4S/4RHNNthnrwUjXZY+dpppOTm0bPT79j9wyxmFAcSA0H5hvnioDCJBwcF2g4TB3nGSrmgLbt3c/Vrr5N9ZWHEYiBwtMM6H9sOgPrDdQkZA/lMHiul7vfyPACapr1sQp1M4b6Hvoh2FQwhWvPsBDJP2ctDRzTUMZzETCDMnD2JzPwBJGW2YM/HT5HV+aImPTr6qppt//gktuZt2b/2f8wZnkW/dyp56oJ6x8i8fBtTln1A9kV3UvPrBiq+m8nRQ19pIgx9W7JS9LtgKAAdTu3NoLxilv9SxznH2nj1kowm9bz7qyomfFdK1hmDfJ6P4zaI2jDflfgjGg4y6/sbaw6yQsLYlWAc5AsjOgl0/6S160TV9rXs/eLFJg5yXdXX1rwtpf+9hYVDMzlvQgXOr2/QDjq0+ktuvvs/gOP79MmUx/l+xWSu7Jjs0T/3fFXF1B/tlH0zlqxO5/k8J3FQU+IpBgJY+NRz0a5CTGOUg7wRjJtCcdD+1VMlBoox4slB4p/wMNs/3vDmpWi0w8rXTidZKW5rcxztOvyNqVu/oG7/Apb5c9A3r4qDQiSeHOTeDvM31Y7QmGg5yBMvT59BWv5Aw2Og8tVf0fLSez0mjvV22Oi/PQDA+ad3pvfRpf79E2cxkL+Rx3qa/DTgbOBz59+XAfPNqpTgmWgljoOZp8zs0Zs6y5d/Tsa5N/Lbf+5AJdnIKbikyT76qppp7TpxaNrLDM+3OSd3T2HUolpeHpju6HV6bSY1do2K9d+g1R/m0OovySm4lORmrbEfLKF87TQOrfkaG4rbb/1Xw+qd+si/jGT4/LpMj/XU59xKbXW8z/NxvR1daEREHaR/fyPRAeILM6fPcD0vX8exUkBlxlyJ4XzGy5d/Tu71L1Dy5StUblyIQmviIFf/lH/zGsOcU1WMLDjiH8Cjg8rXfE12t0FHHLTmaw6t/pLBF9/ZaD6sn35czP4qjUf6NF7lV+eRPmn8d3UdWuVWmp13i89zEgd5RGIgAYjsfK2BuEl30O5Pn6V66yq/DpIYKGaJCQdJEsZcrDhf9PLln2PrdB6l/70LpYhIOyxF03i631CuG9wRgEdmbWLRZnGQycSEgwRzsZqD3lu8hKzrXgy4HRawf+w17PtyNLXFmzy2w568fDAXnnEGoN9Nk3j+8Zk81jTtKQCl1Aygu36LglLqSeAj02snANFf1TOYecoiNfq4qryUqmmvgi0FDUXxW3eh2etQqRlkntqL5r2uoeKHeRx94z+xl++nasM8Cu929Ag92DuVzuMqeLC3Y3XMYZ013lo3g3vveZuWLdvxxVdj+XbSvdirK1HJKdhsKfTofjGXXXp3Q6MJHD2Yo569mIvbbvM759aEJZOg28Vez8f1dnThCNFwUKQ6QHQ8JXBNvdZdFn6IlcZeKA7yRbifcXXFAQ4sep/KjQtJOaoddaW/NXFQ5eZl5A192eGf9bMo/JMjKHiod1qDf47OTnI6iAYHAXz4yQv89taXaPZaVHIqxxzTgZvv/k+ThRRstmRGFvieb2tkQQoT10H11lVktO/q9ZzEQU2RGEjQMdpB3gjUTdUVB9j7xUvU7vkZkpJA0/jtjdskBoozxEECRM4/wVBVvh9WfUlKbh51B3aZ2g5LTkqm34ldGNF9QEPiGByj2c9+9CF6tt4tDjIJcZAA1nPQwfJD1AXTDvPjn7fXTufli++g+7GnsuqXn3hr/desd2mHdT62HaP/9kBD4hgS1z8BzXkMHA+4jqWuBU4wvDZCE6KdOIbg5ymLSPItSQFJKFsyOd0vITt/IMnN22Av28Oh1V+xa9J91FdXkNy8DeUz/sXw/CS3yd2P9DoV9k3j3fW15OV1oHnz1owcNoqRw0YFVI3SfTsZu6OOsSt8z3eTk1pHza8bPE6W7n47uuCRiDpIX2EaMLQTJOKJYg/ESsLYFbPmSgy1kys5JZ3KDY4BF/ay3TQ767ImDsJeS92+ndRvX8mwru6LSzQefVzYN7WRgx5/9H8B1SNQ/+RmpnJgVRGZHc4RB4WGxEAJjtXma1VJNmp3b0Ylp0oMlBiIgxKYaPtHj4n1eGnp0qmQlAxaPfaDJR5jIKMc5K8dvGPvHlZuEwdFAHFQAhNtB7mTlpoacDvs8OaFfv3z/vfVXDvodI5u0YK+tOJeevk6fAOJ6J9Ak8fvAMuVUlMBDbgSmGRarQTAGoljsN48ZYsWfQgqmaSUVNr84YkmizMcdeHNZJ3Wi90fPEbFT4sb9TbpuPc6De+WwqzpYxhy9VNB1eX5l78PaL+iolcpmvIYOQWXBnQ7utCEiDvIdQoLCD6J7G1KiGhfz7GIGQ4KtZNr/fq51NXbwZZMki3Zt4M+epJ0aim8q/G0Eq7+0Ucfh+KgQP0D4qAwkRgowYlkHOSeqHFn0aIPqUeRlJomMVDiIA5KYKzUDlu/fi4T3nkksBgoDAcF2gbe/frbfus8f8FeXvx1qzgoPMRBCYyVHPT1mjVUH64PvB2mVVF4d+NpJZr4p2tqSKOmA/EPwD8+/ZQnP3iMnO6x75+Akseapj2rlPoa6ON8aoSmaavNq1ZiY5WkcTj4a/yESknJdt794B+ktjmR9Pb5jWRRs/tnyj9+mJw//B9p7TqRXXAJlXNeZ3i+zePk7teckUz70eXUHnY81/GkVYbW1ZXBg+/hlFPODPh2dKEx0XKQfg26JpFDeb1gXYIZfayvLp55yjnYy3b7dVDWUW246djfAvIPiIOsisRAglXwFQNBYweZGQMF26kq/gkPKzvIzDUaBGuhx0AZAcZAoTjI9ftkZAz913Yncsrd/xEHhYiVHSQkDlt27+bq114Prh3W7teA/GPmqOnHr7qKc087jVv/8x5bV8W2fwJKHiuljgf2AlNdn9M0bYdZFUtEzPrBtBJlZXt49+2/cOOIf9O8eeugX2e3ZaKhsB8oJvuyvzbap3Lai9jqKqiY9iKpw8aSeVovylZPpbBvtscyC/umMWGtnYf++hEnnVQQ1nkFQseOvQK+HV1oTLQdFK/XY6JRXFrKiPFjmHDnPY5bk4IYfVxWtod/v3w1qaf2puLHRaDV+3RQ0pCnObz/Fwqv87yYXWHfNCasqeO2217lzDObLjRjBuKg0Ii2f4T4wd1BvnDv2Cor28PoF4dQr+ExBoLGDsrsd7f/GCgAB3mbbslTp6qvZLL4J3Ss7iCJkWKDYPzjzr6KsqBioGDbYZeU/drwvNHfJ91Xv6/aT0dxUEhY3UFCbBCOg4pLS7no2adQp55L9Y+LDWuHffTnP/OHnj1DPaWAufCMM3j7qvsBY6fEjDSeZ3duypdAkfPxDfAz8LVZlUo0Oq4uajTaOJ6CMPeGxaxpY9ixbSWzpo8JqpxZ08awY+tKtmycj1ZXRX11OcnN2zRsr9n9M3V7dzBnWBZ1e7dTtXUt9g3fMKKbn8WkuqezeuVnQZ+XEHHEQULYjPriM5Zv+YlRn09t9HwgI6emTH6Emoq9JNsrqK866NdBlXPeYHgA/tm2ZVl4JyVEAvGPYAjeHOSOpzhwyuRHqKsqJbW+aQwETR1Us+qzgGIgTw7S41L32NQ1RvX0nIxCNQ1xkBA2gfrHE/9a+EFQMVCg7bCbC9LY9vVowNw2cDy1raNEXDlIfquiQzgOuuvt/3CgvIxke6Vh7bCbu6ex+McfQj6fYIkHDwU6bUUX17+VUt2B202pUQIR7yON3Uf1lZXtYemST5h7UwYXvPsx/QbeHdDo47KyPSxZ8jHzhmbQ+60KVHoOCoW9bA8puXmAo6dpZEEKBXk2hndL4Z2vnyc5K5dxu+oYt9L3JOZm3iouGIM4SAiX4tJSJi6Yzzc3ZdDv3fk8ePmVAY8+/vnnVfywfg6LRmZx7jtLUOnZKGjioBHdHA4a0S2Fd35YzrjKWsb5yQ2Lf6yP+EcwAm8OCgRXB/V+uxKVktnIP+DBQd8vZ1xV8DFQqFOnNexvwmKziY44SAiXcPyzZNMmlu/8wW8MFGo7rPcpOyPSDjZrSsVEIB4dFI+5FysTroOmrV1jSjssUov8uRLqgu1WINAF8xqhadoqpdTZRlcmUYj3pLE7+gUya9oYhnW1UZBnY2g+AS/OMmvaGIZ2UQ0ByaTtzalLzqJ83QxyzxvW0NP06PWO26IctyGUczivG6kqk9qSrZx/3vVcd3Wh2acqRAhxkBAso774jGH5yU7/aE0WRvD1Q/7h+48xvCCNgjwbw/LreWf7UdSq1CYOeszpoMf6pvH2mnIyzrgQ+56t2Et/ZfzYDRE5T8F8xD9CKPhzkCd0L7k6aHi3VCZsTG7wD+DVQckt22MvKw4oBjJqvQ3XKS1itXFkdcRBQrCE4h+duyf810MMlBZWOyya6/uIm8JHHCQEi/EOCqYd9hv1E98y8/QCJtQF261CQNNWKKXud3n8VSk1GSgxuW5xhbdbAOMd/Rz1UccP91IAPNxLsWzJx5SVef8abdy4mMf/cQnz57/Ho+c6+jkK+6ZRX1ZM7b6dlK/5mppfNzT0duu3JeTlJDGyIAW1dSEtzhuKApYt+yLkcygr28PY0df5rKtgLuIgIRz03u4Hezkc8WCvJCYumM+uAwcAz42XjRsX89SzV3D7Haex67cfKeyTAkBhbxv1B36jds/WRg5yvTUzLyeJEd1S4Ke52A/tRbP7HnXjC/FP9BH/COHiz0GesB+1m+GfvNTUQX1SoOoAh1Z/Sc2vjk4pbw7KoDqgGMhXIqe4tJSLn3/aZ13dkWksjMWqDuq4uigh2jKxTij+AZj9/fd0fOhhfvhlZ9MYKMR2mN4WDqYdHIqDvCHf19CwqoOE2CAUB83+/nu6PFqIunEoGzw5KKh2WG1YdTfKP67EanwU6JzHOS6PNBzz3lxhVqXiBV9zxiUa+qhj14t6aL7N69zHRUWvMnrMLVTU1zGiW2qj1w3PTyLn6PbU11az64NCR293n8aToT/aJw1NA63+MJq9jurKA2HVPZR5mgVDEQcJIaP3djf2T7LXuY91/5TnnUZ2VlqjObPycpIYlm8jlTq0+sPsmuJw0GN9Gzvosb5poNWjVR9CJaeEXHfxjyUQ/whhEaiDdP7x6af0++dL7DvpbI8OGt49nRR7Fbs/fIKSL1/26iB72W40e63PGMjfCMBQ5yiUBLKhiIOEkAnWP3DEQb8eTm7SDhuWb6P5CWeE3A4Lth0czjyp3hAvBY04SAiZUGOgHW0LyM5Kj2o7zAz/xHIuMNDk8Q+apj3lfDyradp7wGVmViwWcU0Wu/aqJmrCWGdfRRnLFn/YMOpYx9vo440bF1M0bRytLnuQw/t3Utg3tdH2wr5p2H/bAEqRlZrUqLdbR+/1rvrqBVRyKumZLUKquz5ievZNGX5HSgumIg4SQsK9t1vH2+hj3T9tr3mGtPbdOFxdQaFbQFJ4rg2bgqMG/YWsVJvHBWEaRv6lKKCx+wJF/GMZxD9CyATqIJ3Z33/Pk58X+XFQMjalkXbsGWg/zvHtoGTlNQbyNwLQdY7CQEYqupPIsa/BiIOEkAjWP3DEQV7bYefaqN22CpKSgmqHhTJSPVwHeUK8FBLiICEkzImBgmuHJalAU56e626kf1yJxU6sQN/JhwN8LuGQ0cX+mb9nPsO6Jnu8qD2NPp7yyQvkdB9M/Y5vGd5FeXzd8II0UtRh6msrm/R26zzaJ43D1RWQlkXPnqH9vjWep9n7SGnBdMRBQki493breOv1/uzdR8npPpi0dp2o+voFr42i4d1SqFz0DvU1FU16u3Ucvd4a7Y/vFFLdxT+WQfwjhEywDvrL5A8CdpA6+Btomm8HoXH66b2abAskkdN4jkLfIxW90bdPq5hsIFkMcZAQEsH6B444yGc7LN9GilYXcDvs4pO6eNwn0PqH4yBPiJeCRhwkhISZMVCg7bA+HU4Oq+5G+wditxPLZ/JYKTVIKfUq0E4p9W+XxwTAHpEaWgwZXRwceo/N33vbPG73NPq4+LdNZHQ4h8rvZjbp7dYp7JNCCvUehaKj93pn1u6n3wVDg657KPM0C8YiDhLCwVtvt46n0cfbSneR3fViKreu5nBVuddGUWHfNNSBXz32dus0zLlVcyDouot/oo/4RwiXYB0E8P0vvxjuoH2/ftfo+UCSJqHOk+oNSdQEj5UdJJ+n9QnFP+BwkN92WN9UUpQWcDvsj2f0CXnUsVEO8oR8j31jZQcJ1scqMVDpoX1h190M/0DsOSjZz/bfgJXA5cC3Ls8fAu4zq1JWw/1DlSRx4HjrbdJxHX085OqnANDstdg3zPbY2+36utZZirEr6hi7wvdiVDmpkJqaGXTdfc3TrNdVMB1xkBAygfknudGKv5q9juTmbTj4/n1+G0VHZSpeW1nHayt9Oyg3qzjouot/LIH4RwgLKzrI3xzH3uruqa6BEuuri0cRSztI2kPWJhT/gMNBRrfDLjj36LDrH46DPCFeCghLO0iwNlaJgVpnBZ88Nts/EJsO8pk81jRtLbBWKfWepmkJ1bskCWNjWLFlE4s2VzJ6qe/9Op60quH/KjmVuh2rGVdSy7iVvlfHzEpVDOuaythLPPdKAfx5+uGgEy76qL8Jdza+RB7upeg0/mP6Dbyb5s1bB1yeEBqJ7CAhfAL1T+9TNjX8XyWnULllJdSUM3YFPhtFqTa486xUXrs03es+f55+mB+zrgyq3uIfayD+EcLFag4KNHGsj7j5/o7Gow4f7JVE5/HzefDyKzm6RQvfJ+VG3z6tYEERGwsGB/W6REYcJIRDKP4Bh4MCbYe1yEzjxi42Xr3Ye0rhL9Pqgk64mOEgb3RcLV7yRjw6KNZGesYyVoiB7ptuRzVvOnWXLyLpH4gtB/lMHiulPtQ07WpgtVJKc9+uaVq+aTWLEq5CkYRx+Cx86jnAcRF2+ut9bPhTGnk5SRQfqqfTeDuPPjm3SRIk75gOlJXu4K6zUxhzSUaTMu/+qooJGzNokXs8Ocn1vLbiB15bUeOzHq7J6UBwH/XXUDcZ/RdREtFBgnHo/gGHg8548H6+vyO1wUGdx9fy/T9faRQAnHHssWyd+S+Gdw3MP+NW/uC3cSX+iU3EP0K4WMlBgSaOIbA5CkMdeRNLjaRoIw4SwiEU/4DTQfv2BtwOG7PsB8Ys810X9wS1P8x0kCuxOPIvksSrgyTHExmsEgNZ1T8Qew7yN23FX5z/xnWUJ6OMm1JcWsqI8WOYcOc9hvSsjPris0Zz0vhKglzQ51o+nfIYj/bJ9ljWo33SeGv1QS644jr69Lk27Lq5423Un46M/osoCeEgoSlmOCiQ24/uuegC7p34X/GPAOKfhMVo/4AFHBTAAnngfcSNTrijj2OpkWQBxEEJSrRiIDDWQYEszOmOmQ7yhnRqeUUclKDESjssFMf4Ihr+gdhxkM8F8zRN0ydJ+5OmadtdH8CfzK+eueiL3gGy6J0bo774jOVbfjJkVUlvk6V7WwBq6YKJAS3AsGTBxLDr5glvo/5cj68nvgVziXcHCd6JhIM8LX7w5jfTxT8CIP5JZIz0D0TfQcHcphvMHIWhIrcNB4ZVHSSfn/lEKwYC4xwUalInEg5yRdr+3rGqgwTziYV2mBm/RZH2D8SWg/yNPNbpDzzk9twgD8/FBDI1hW/0C/ybmzLo9274PSu+h/43HX1cum8nY3f4X4DhqKwdIdfJFzu2rWbGzxW8GsQ8zYLpxJWDBN9E1kGNe7137N3Dym3iH6ER4p8Ewmj/QHQdFMx0FRD6PKmBIqOPQ8JyDpL2k3lEMwaC6MdBZjvIG7Ey8i9KWM5BgnnEUjvM6N+iaPkHYsNB/uY8vhNHr9JJSql1LptygEVmVswMJGkcGPoFXpBnY2i+Fta8Lv6G/nu6Bfv5l78Pue5GcN9DX0T1+MIR4s1BQmBE0kHutx/tfv3tRtv1JEekfszFP9ZB/JOYGOkfCN9BrsxfsDckFwUT87rOUWgWsnheYIiDEpNoxkCAIQ4KZ0RgJBzkjnRqeUYclJhYpR3mqw1m9HQVOtHwD8SOg3xOWwFMBi4DPnf+qz/O1DTtRpPrZiju01MInnG/rcDbLU2BEtjQf7kFW/BK3DhICIzoOMj77Uf674XcppuQiH8SDKP9A9G5BVLH6t6yev0sgDgowbBaDORO3z6tAr5uY629Hcy5JRDioATDag7yljgWooPPkceappUBZcB1AEqpNkA6kK2UytY0zZz7VQwk2Nv1Ep1gFlQIhECH/sst2IIn4sFBQnBEy0G+bj+Kld5gwVjEP4mH0f4BY2+BDGbErtXjX/Gqf6zoIGm0m4sVYyAhcbGig8JB/OWfWHGQVWObcIiFu7ICmvNYKXUZ8DJwDLAHaA9sAM4wr2rhIVNUBI+32wrCWVXS29D/UG+9FBKTWHSQEDyRdFCwROIH3VtQK66MLuKfxMAM/0D0boGE2Ih/Y2GOv2hjNQfFwvcqFrFyDBQMsZygi4XkTTSwmoPCQfzlnVhwUCz7JR7wN22FzjPAOcBPmqadCFyEhee5kSkqQiOQycyNRC5+IQhiykFCaETaQcFi9C2NHVcXNXrov1nuD9d9hKgg/kkArO4fnUA8ZNZcgEYTC3W0COKgBCBWHBQIsX5tS7zVBHFQAmB1B1n9jiojsPr0OYEmj+s0TdsHJCmlkjRNmwN0M69aoZMIXyozcJ/fxh0j5v1zJZjPp6xsD2NHX0dZWYkhxzarTMFUYsZBQmhE2kHB1Ovi559uOK5rMjdUWi98j7efGcC+yoONksTecN1u5YAijhH/xDlW9Q80dZCONxcE4ghvZUYL8ZpfxEFxTiw6yGplGoXkEDwiDopzrOog95yNEdenlf1jdQJNHh9QSmUD84H3lFL/AuzmVSt43EduCcERrQVdAmkwzJo2hh3bVhq6qJ4ZZQqmYnkHCeERzUWl/NVr+ZafGh3XNZEbaNLDdfTwB2un8+PerSzYPS+ouriPRBYihvgnzrGqf8C/g1wJdACFpzKjhcTsASEOinNizUHeCDQ2sZKDvCFxViPEQXGOFR20sWBwQ87m23f/ali54p/QCTR5fAVQBdwHTAO24Fhp0xIk4mhjo3tMVmzZxOillainDnp9jF5ayfItxi2o0LdPK/ZVlPkcAVxWtoelSz5h9k0ZLFvysSEjhc0oUzAdSzso0TCjxzYaDgLf56L3wn9zU0aT3nb30cCuCV336Shcf6M6dLYxc/MKj2UGioxCjjjiH4sRDzGQTjgOgsa+CWQAha8yo4n4zCeWcFCsTIcSCeLFQf7OIxRfxKqDXJHveRMs4SDBQaK0w1ovfK8hZzP9p2Wc2iWg5dr8Hk/8EzoBfQKaplW4/DnRpLqERCImjqFxj0moK4C7Eq0FXT5YO71hBPCQq59qsn3WtDEM62qjIM/G0Hy87hcMZpQpmIuVHZSIGO0fiJ6DfJ2L3gvvcIXmcZ8mvz0LfP8mBVJmIPTt04r5C/YG/ToheMQ/1iNeYiAIz0GhxL5GOchIxGe+EQdZj3hxkL/z8OSL358YXs7Qig7yhizo6SAeHBRPnV+J0g77YO10hucrCvJsDO+WYsj5in/Cw+fIY6XUIaXUQQ+PQ0qpg5GqpDcSNXEcCz0mgVBcWsrMzSu8jgDWRwg/3EsB8HAvFfZIYTPKFMzD6g5KROLFP+D7XNzn/gp0ri9fI/9CLdPXsWS0nnmIf6yJOOiA58KCOJ6RZRqJ+Kwx4iBrEi8O8nce3nyxr9LzVy/Q+dat7CBXEi2/4AlxkPWIF/+A/xho5uYV/L23DUiMGMgVq/rHZ/JY07QcTdOaeXjkaJrWLFKV9ESiJo7Bvcck+itfhkrj87A1mX9YHyGsz73jmGun6X6BoE+2/uX//mlYmYL5WNlBiUq8+Ad8n4v73F/hzvVVXFpK36cK+UNHd/+E/x5KwsUcxD/WRBwU/Pnqt4U+8fEUQ71mJIkYz/vDSg6S35kjxIuD/J2HNwct2D3P6/fBV+e51R3kjUT+7lvJQYKDePEPSAwUCFbzT6BzHluSRAw0o9VjYvTcOu7n4T4C2H2EsE6oI4VnTRvDjq0r+Xbl/wwrUxASjXjxj16mt3PxtuJwOOf7xMdTKDlYinJbX8SI0cdgveBCEMxAHBTa+eq3hX6wZJGhXjMDcZl1ScR2lzvx4iB/5+HPQd5GH3sjlhzkinznBSsRL/7Ry5QYyDdW9E9MJo/jac6aYDF6NFwwxzVyVUrP53FkBLD7qGOdUEYK79z5AwsXvM/soRko7TCqce5YRh8LQoDEi3/0Mr2di7cVh0M53+LSUi74xxO8v3gRc4Zl8fEGO7vK68Mq051E/T0UEg9xUPDnu2bbNt6c/Q3f3JQBWr2XGMgaI2/EZYLViRcH+TsPfw6asmZ6o+d9dfrEkoO8IZ1asU28fH7x4h+9TImBAsNK39+YSx5b6c2LNGaMhgvmuEbNrePtPPQRwL/8ssHjqGP3/QIdKfz+pPsbFsgbWZDCqEW1YZcpCIlGvPjHtUxP5zJhwTzenj+vyTbXfYKpx6gvPuPbrZu5KV9fpLOpg4x4D2X+YyHeEQcd2SeYetz65jiGdk32GQNZaeSNuEywKvHiIH/nsXb7do/bXfeb/tOyJm0mb50/seYgd6RTKz6I9c8xXvzjWqbEQP6x2vc2ppLHZs5zbMZwfKMxshcmlOMaNbeO7/OwMXni/R5HHbvvF8hI4Z07f+C33zZR2DcNgId6pzFxbV2jkX/BlikIRiP+8X9cI+f28nUuN3RO4tRczY9/AqtHcWkpb8+fhwYNDnqwd2oTBxn5HkrSRQgFcZD/48aig9Zs28b3v/wSYAxk7ZE3QvQw+47PWPAPxI+D/J3HrW+85nF7o/26JgfUZoonB0l8Fb/EgoPixT+uZUoMFDhW8U9ytCsQLGYFL67D8V8eOsKUY4SD3kPz/R2pHrc/2CuJzuPn8+DlV3J0ixamHTfc4/g7j4d7Kf776iZe3aHx6lLfZXU8aZXf470/6X5GFqQ0uiXimjOSaT+6nNrDoZUpCEYj/gnsuEYcx9+5PHJuCif/uwb1lO/5/HqfssnvsUZ98RkdcjV6HBOYgwIp0xd9+7Ri/oK9YZUhJCbioMCOG2sOuvXNcdwcRAwUroOMom+fVrCgiI0Fg6NdFSECWN0/ED8OCuQ8Orz6Kyu2aYz20w7rmjcX8N25EKsOckfiq/jG6g6KF/94KtMdiYGaYiX/xEzy2Mxsu+tw/H7vGn/hGYG3Hhod1x4TI6Xnaz6aUI4TyHncfGYmP2ZdyZCrnwqr7vqo40f/kN3o+cK+aUz+wcYzT86lefPWYR1DEMJF/BP4cY04TiDncvtZmajmvcI6F33UsdLsfH5tUwdN+UHx/T9fMeWz7rhaki5C4IiDAj9uLDlIH3Hz+VWR9Y+RiMvin1jwD8SPgwI5j1vPzAjIP/MX7AU/cx3HuoNckU6t+CQWHBQv/vFUpjsSA3nHCjFRzCSPwdxRx0eG42uW7HVasWUTizZX+u0FNrLHxFvPUDi9ToGehxEjgN1HHeu4TlERboJaEMJF/OMZM/wDkTsXfdTxucel+rzFzOjP2kq900JsIA7yTKw7yH3EjY6Z/jEScZk1MPtW2VjwD8SPg8w4j0BHHevEioOE+MCfw2LBQfHiH5AYKFSsEhPFRPLYzLm2zBiObwYLn3oOgPsmvQ1li3ll4JGP7r7p9rB7ZzwRyNw6wR5TPw937pv0NhPnz2ZAh178qdcfw+5V8TbqWOfhXopO4z+m38C7ZfSxEDVizT8QOQeZ4R/w7CDdP8P7XmjIOfgadaxj9mdthd5pwfrEmoNiPQaCyDjI24gbHat+zp4Ql0WfRG+DQfw4yEj/+PpexJODXJHRx7GJt+9qrDhI2mHBEa/+gejHRDG1YJ4Z+BqObzUiucqmt2OZcUzX20Vmbl7Ovkrfc9wEgrdRxzqyQJ5gBWLJPxA5B0XLP0aVqY86Ht616ahjHTM/a6utzCtYl1hyUCLEQEaV6W3EjY6VP2dXxGXRJVKjjmPBPxCfDjLDPxA/DvKGVRavEsJDHBTcccw4nsRAgWOFmMjyyWMzRx3PXLeO17+ZFZEgwAgiucpmMHPrGHUsfRXPKWumh/WjXFa2hz27tzB2RR3qqYNeH68urWDHVlkgT4gOxaWlTJg/L2b8A5FzUDT9E26ZehCUpOoZvazWp4NGL61k+RbzFmeQxo3gizXbtvHm7G9ixkGJEgMZ4aCfin9ljJ8YyGz/GIm4LHqYOepYYqDgj2X0MY32D8Sng1yxQgJHCB9xUPDHMeN4EgMFTzRjopiYtsIsRr4+huHdYmMulEivshmp+Wg83y6ynGu6DQy5zFnTxjC8IIN/D7R53efP0w8bsiifIITKqC8+4/rOKib8A5F1UHT9E9456EHQKwPTve5j1i2urlhlbizButz65jiGdjX+lkQzSKwYKHwHjSzIaHRLqzuRcJBRiMviE4mBfBMJB5l1y368Ocgb0b59XPCPrySbOMg7EgNZl2jHRJZOHpuZVZ+5bh37yiso7Bsbc6FEepVNb3MTG42320WmrJnOnzKbhfSjvGPbamb8XMGrEViUTxBCQe/t/uHONI/breYfiKyDou2fcM4hGota+EIaN4InYm0+uESLgeLJQUYhLossZq83IzGQbyLhIDP8A/HrIFeincARAseTx8RBvpEYyPpEKyaydPIYzLs1ZOTrYwKYE9c6vU7xeCH4XsUz9NHH9z30hRHVEwTT8NbbrWM1/0D8OcisVYQjFXAFgjRuBG/c+uY4Rni480rHag6KN/9AYjjIKHSXSQI5MkRirmOJgaKLWf6B+HSQN8RJsYk4KPpIDBQ60WzfWT55bAZrtm3jQGUFY1fA2BV1Pve1ygUYjxeCv3l7whl9LAhWZv6G71m1o5bXVtT63M8q/oH4c5BZqwhbEWncCK7o88Gt3Kbx2kqJgaJFIjnICKQzLLKYOa+rxEDRR/wTPtKpFbuIg6KPOCh8ouEeyyaPzez1vvXNcQzvmsKrl2Q0PHf3V1Us3t2KVc+/aNpxhSMENm9PeHMfC4JVSUqycffZ4qBoEem5C6OJJFwEd0Z98RmntrRx7nFJvHLxkbm5//RlFfU5v2P8LbdHsXaJQSI5yGgkUWMukViIR2Kg6CL+MQ6JsayLL5eJg6KLOCh8ouUez2P1LYIZvd76PH+P9Gk8x82jfdLY+Fsx67ZvN/yYQlMCnbdnwe55hgayZWV7GDv6OsrKSgwrUxCCQRwUfSK5irArxaWlXPz805ZcwVlIDIpLS3l7/jw277fzYO/GQXth3zQmL14o388IIA4KDTNHwwpHki1mvs8SA0WfaPkHYt9B3ohEp4sQPJ5cJg6KPhIDGUek3WPp5LEZ3PrmOG72MNdxXk4SIwtSGD7+VSA+v1xWYsWWTYxeWol66qDXx+illSzf4rhdxKgLY9a0MezYtpJZ08cYUp4gBIs4KPoE6x+jGPXFZyzf8pMpDTJ/SMNGAMd3sEOuxvCuqR4ddGMXG09+PEX8YzKJ6CCj6NunlfjMANzfw0gkjkFiICsQLf9AfDjIHf2aES/FBuKg6CMxkDFEo0PdstNWmIG/1cUf7ZPGyf929Di9PW92w5dL5lsxnmDn7TFiWH5Z2R6WLvmEuTdlcMG7H9Nv4N00b9467HIFIVDEQdYgGvOG6bdofXNTBv3ejeytWHJbpQBHRh0rzc7n13p2UGHfNE4buxBN08Q/JpJoDjIDmb4ifFyTXZFohEoMZA2iNXdqvDnIFYmzrIW3RL44yBpIDGQcffu0ggWRi4csOfK44+oiU4IYbz1NOnqP0w1jRzd8uSYumC89ThYh3B7dWdPGMKyrjYI8G0PzbTL6WIg44qDERb9Fy+Efc24H9YeMiklsfI061snLSeLK05KYvHiR+CfOsIKDjCLUkX7iwCP07dOq0SMSSAyU2MSTg7whjrEOnrwmDkpc4t0/kXJPQo083rF3Dyu31TFmhe/VxXNSS7i5e4bzy6VJj5MFCLdHVx91POFOx1f+4V6KTuNl9LEQWcRBiYn7whDRWAhCRsUIK7Zs4ocSOyt/g9HLvK8wnmqDWwpSxD9xhBUcZDS60wIdgSxJnegjMVDiEo8OcidYJwmRRxyUmMS7fyLZxrPkyGOz2P362/w2Zgy5man8dn822hPNmjxW35aJvV7jwV6Ot+bBXkkB9zjF09w4Vj2XUIN/fdSx3tPomIhdRh8LkcVMB1n1mg2VeDof94UhzFyMRhC8sfCp56iY8J5PB/12fzaZKfBYX8dCMhIDHYh2VQwhXh0U6AjkSM3nK/hGYqDAibfziVcHuSPzH1sbcVBgxNO5QGL4J1LrQSRU8hj8r+44ca290e0MwXy54mkSbiueS6g/yPqo44d7qUbPP9xLsWzJx5SVlRhWR0Hwh1kOsuI1Gw7xcj56b7cehOoEk5QzClloSgDfDhq1qLbRtBYSA8X+uVjJQWbgGht6WgROEsfWQmKgwIin84l3B7kjCeTo4u99Fwf5J57OJdH8Y7Z3Ei557G91x/Hf1vJIn7RGrwnky+U6CXesfxGtfC6hBP/uo451ZPSxEA3McJCVr9lQiKfz8RakxmOvtxAb+HLQ+G9rebB3aqP9JQY6EO0qhUUiOMh13l49YeyaNJbEsXWQGMg/8XY+ieAgdySBHF18OV8c5Jt4OhdILP9EwjuWSx6btViezsKnnkN77z2Pj3sH9uOOszJD+nLF0yTcsXAugV4U3kYd68joYyHSmOGgWLhmgyFezsdbb7dOtHq9pTGT2HhzkMRADuLpXKzqILNwXwROksbWQ2Ig/8TT+SSag1zxdVeEED3EQb6Jp3NJRP+YnUC2XPI4WoTz5XJ/bSx+EfW5bdZu3275cwnmovA26lhHRh8LViFUB8WTf3YdOBAX56Pj79a4aPR6SzJF8ITEQLETAwWDFR0kCJ5I5BgIxEHx6iDXjixJIptPOO9vIjtI/BNf/jEzgZxseIkxSjBfLvfVNn1Nwh0rK3Pqc9vc+sZrMXEuga5ou2Pbamb8XMGrS32X1/GkVQbXUBCCI1QHxZN/Rn0+FQ1i/nx0VmzZxKLNlYz245/ep2yKTIUEwQsSA8VWDBQo4iAhVkjkGAjEQYngIOm8jwyhvs+J7CDxT/z5xzVXBvjMlwWDJI+dhPrl0nubvr+j6RyBncfP58HLr+ToFi0Mrq2xuM5tc+7bv/DmwMxG20M5l+LSUkaMH8OEO+8x7fw7dLZx1QuvcNVJPWnevLXHfe576AtTji0IRhOKg+LNPxe9O496DTbc2XSuMas5KJDyFz71nOHHNQp/HW9CYiExUOzFQLHuIEFwJVFjIIhNBwVavjhIiBUS1UGx6J9Aj5Ho/tE7UlyTyPDnsMqU5LGTUL9cgUzCHW5PjdkXoOvcNiO7pTBxrZ2Xjz7y1QjlXFxHEprVUzXqi8/4sWQr3777Vy68a6IpxxCESBGKgyLhHzDXQa7+uaFzEst+OWzI+ZjtoEg4ziz03mhB0LFyDASRc1CsxUCx6iBBcCdRYyCITQeJfwSrEe4t+onqoFj0T6SOES8YedeDzHkcBpGahNv14jAa93N4pE8aE9fWsau8vtF+wZxLJFbpbDjG0Aym/7SM1osmG34MQbAykVwEwCwHNfHPuSls3m9v4h+wloPibSViQQiFuHRQrMVA4iAhQYkH/0BsOkj8I1iVSE4NEg8OikX/ROoYgmckeRwGkZiE2+yLw/M8PSmMWlTbaL9gziUSq3S6HmN4txSmrJkuixAICUWkFgEw00Ge/DOsa2oT/+jbrOKgeFiJWF+8RRBCJV4dFGsxUKw6SBDCIR78A7HpIPGPIMSHg2LRP5E6huAZmbYiDCIxCXfji0MzdGi+13l6eqdy8r/LeWVp0wSOv3NxL9OMOX88H2M513QbKPN4CglDpBYBMMtBofgHou+gSDhOEGKBRHRQtP0TqWMIgtWJdf9AbDpI/CNYkY6riyK+IGGsOygW/ROpYwjekeRxGJg9CbfZF4eveXpuPysT1bxX0HKKxIqj3o6xYPc8fn/iZZJAFhKCSCwCYKaDzPCPp3KNdlA8rKrsivhSCBVxkP8yIxkDxaqDBCEUYt0/EJsOEv8IgoNYd1As+idSxxC8I9NWWBhfF0e4mDFPj7cyjZzzx98xTu3i6A+R27EFIXzMcpBZ84SZ7aBIOC6SRHqUhiAESyw5yAoxUKw5SBCsjLTDIlu+IIRCPLf5JQaK/DEE30jy2KKYfXGYMU9PICuOhksgx9ATIvH8YyIIZmOmg8yaJ8xsB0XCcYIgOIg1B1klBhIEIXykHRb58gUhVOJxMITEQNE5huAbSyWPozFfTaAUl5Zy8fNPR6xHw+yLY8WWTYxeWol66qDXx+illSzfEtg8PZFYcTSYY0gCWYg34slBRvsHzHdQJFdVjjTiScEfkfYPxJaDrBYDCUK8EU8xEMSeg8Q/QqITTw6KNf9E6hiCf2TO4wAZ9cVnLN/yU0TmU/E2gbmOEfPdGD1PTzA9WKG+f8Eeo2+fVsxfsFfm9BTignhykBnzhJntoEg4LhronhQEX0TSPxB7DrJiDCQI8UQ8xUAQew4S/whWJJIDD+PJQbHmn0gdQ/CPJI8DoLi0lLfnz6NzK8Xb8+eZvppjLF4cRq44WlxayojxY5hw5z2N3udQjiEJZCEeEAf5x2wHRWpVZUGwGnoj5oMhafzhw28Yft6F5Ldvb+oxY81BVo2BBCEekBjIPxIDCYJ5iIN8Y7QfxEHWRZLHATDqi8/okKvxQ8lhOhylTL9QY/HiMLIHy1vPXqjHkASyEOuIg/xjtoMisapyNBE/Ct7QGzFfb7JjS9K45Y3XWP7sC6YeM9YcZOUYSBBiHYmB/CMxkJBoRHLKNXGQb8wYySwOsiaSPPaD3tOkNDuzh2Zx0aQKNoXY47Rm2zYuHfUsXz/0mM9RO4l8cegjnL65KYN+74Z3S5grkkAWYhWjHFRcWsr1r45GKcXke+71+VpxkPEOsjIydYXgDf16mH1jMhdOqmX20CzOffsX1m3fHvToY3GQfxLRP4LgC2mHRRZxkBBLRGLKCmmHRRZxkLWx1IJ5VkTvaRreNZWCPBvDuqbSIVcLaZLyW98cR0V1Jbe88ZoJNY0P9BFOBXk2w1fNlEX0hFjEKAeN+uIzvt22mdXbNstqtD4w00GCEGvo18PEtXaGOR00sltKSHGMOMg/4h9BaIy0wyKLOEiIBaIx6ljaYZFBHGRtJHnsA72nafN+Ow/2dkxY/mDvVDbvt/P2/HlBrea4Zts2vv/lF+YMy+L7Xx2jdoTGuK+iacaqmZJAFmIJoxykl2MDZg/NZMKC4PyVKETCQValb59W4kWhEfr1MCwfJq6tbXDQI33Sgo5jxEH+SWT/CIInpB0WWcRBQiwRyVHH0g6LDOIg6yPJYx+49jTpE5bn5SSF1ON065vjuLkgJaxRO/GO++TwrpPBG4kkkIVYwSgHNZTTzdFrfkPnJOnJ9UCkHCQIsYD7qGPX6yLYOEYc5B/xjyA0RtphkUUcJMQC0Rp1LO0w8xEHWR9LJY83Fgy2zLyLnnqadILtcdJ7ux/pkwaENmrHbIpLS7n4+adZu307Fz//dMR7eNx7mnTM6nGSBLJgdYxykKdyHjk3xXK93sWlpVzwjye48Okno1KvSDvIqogTBfA+6lgnmDhGHBTYscU/gnAEaYcdiPjxxUFCrBCtUcc60g4z5/jiIOtjqeSxlfDU06RzpMepPqCeEL23O5xRO2ajr2rZ/9knG1a3jPTxXXuadMzscYrED48ghIpRDvLWa261Xm99LrBVWzfx5MdTonL8SDvIaogTBR1vo451goljYsVBT3w8hW+3Rmc+QvGPIDRG2mHiIEFwp+PqoojFqonWDotmDATioFhBksdeWPTjBtbvadrTpPNg71TW7znMwh83+izHvbdbx0q93npPzwdD0iivqeWbmzIi2sPjradJx+weJxlpJ1gRIxzkq9fcSr3ernOBzRmWxeTFCyNar2g7SBCsxootmxi9tJLx3zYddazzSJ80fvj1V5/XRSw56L1FC7GpyM9HKP4RhKZIOyxx2mGCEAiRbq8nWjssWjGQfnxxUGwgyWMv9D6tE3ecldmk90MnLyeJ4d1S6H7iST7Lce/tdn29VXq9R33xGUPzbXy96TAjnfOB3ZRvi1gPj7eeJp1IjD6WBLJgNYxwkL9ec6v0ejvqWd8wF9iNXWwRHX0cTQdZEfGhsPCp57h3YD+/DrrlzHSf10WsOOiJj6fQsaVqcND1EayX+EcQmiLtsMRohwlCMETyDrlEaodFMwYCcVAskRztCliVFVs2sWhzJaOX+t7vhKNWe92m93Z/flW2x+2P9EnjlFcdvd757duHU92Q0Xt6Zt+YzIWTavn+T466PtTLRufx83nw8is5ukULU+sQ6Hvd+5RNphy/b59WlplrWxB0wnWQ3tutNDufX+vFQeemcMb4eRG5zr1xpJ6H+fzaDAAK+6Zx2tiFPPmHayJSr2g7yEqIDwWdcK+LWHLQe4sWkmrTKLreMTLo0QjWS/wjCE2RdljitMMEwR+RnK5CJ5HaYdGMgUAcFEtI8tgLC596rslzxaWlnPHg/Xx/h6P3qPhQPZ3H17DrwAGPF5a33m6dvJwkRjh7vZc/+4LRpxAQem+3p9XU9V7vl4eOMLUOnt7raNBxdREbCwZHuxqCAITvIL23+9zjmvZ267j2ept9nXtDH3XsWs+8nKSG0cfjb7nd9DpYxUGCYCXcrwvP/qnl4/se9Pj6WHGQPuKmb/vGc6JeH6F6iX8EoSnSDku8dpggeCJad8MlSjss2jEQiINiCUkeB4H7kHrXIfSeLqwde/ewclsdY1bU+Sy3ddZuU+rrD2+93TqR7PWONjLaTogFgnHQii2b+KHEzsrfYPSyWp/lRqsn19OoY51Ijz4WjtC3TytYIJ1pQmOCjYFixUHuI250Ij3yRhAE30g7TBASCz1xbJUFneOxHSYxkBAMkjwOEP0H/vs7Gl9YD/ZK8vrDvvv1tz2Wdd+kt6FsMa8MTOa+6XZU815mVdsn3nq7dSLZ620VZPSxYFWCdZC3XlxP/rHSqGOdSI8+FgTBO6HEQLHgIE8jbnQiPfJGEATvSDtMHCQkFlZLHMdjO0xiICFYZMG8APE2kXewE3i7ryYZrdUj9XoMz1dMXOt9NfWHetkSZnVLq/w4CYInjHCQVfyj18WxAvFhr/4p7JvG5MULE8I/VkQWzhN04i0G0uvy3qKF/Hyg3quDHrXQauiCkMjEm4OkHSYInum4ushyiWOIz3aYxEBCsEjyOADcL3R3grnwfd3uEEn89XbruPZ6JwqSMBGshlEOsop/9Lp0yK33uAKxjuvoYyGyWClgF6JLPMZA4LK6uB8HRXrVcUEQGhOPDpJ2mJDouLe33ZPGVopD47EdJjGQEAoybUUAeOtp0vE355ZOKLdcmYVjVcsqMlOgss66c/FEGpn7WLAiRjjISv4BfS6ww6z87bBf//haTV0wF5nKR4jHGAhg5ro17DlUz6pdtRIDCYKFiUcHSTtMSGRuy17KfBonkK2ULHYnHtthEgMJoSDJ4wBw/MBXMnqp7/38XViB3O4QqTllFj71HOc+8QiLNm/3u2/vU9rLKpiCEEWMcJCV/APBOajdUUdFoEaCO9KZJkB8xkDg8Mq2/Yf87icxkCBEl3h0kLTDhETHyslid+KxHSYxkBAKkjwOACMuGG+9TTrR6HUSEXhHRtsJViLca9WK/gFxkCDEAhIDCYIQTcRBgiBEk3hsh4l/hFCw3JzHGwsGx+VIp2BudxCiSyz1hApCIIh/hFDp26eVzAMvhI04SBCEaCIOEgQhWoh/hHhBRh5HCKNuuRIEQQgW8Y8gCNFEHCQIQjQRBwmCEC3EP0K8IMnjCPH/7d1/iOT1fcfx1/v2YnJBSSgXqn8l1JBKNZceuUJY45E/SluKFfsDpLSa2JJSC/0jgWxKSEpbwZY1xCQotdA/YqFVyYGH5x8tJaHZ887LaaO99sJFY7RQuoZI1lQTMVW/+WNnzLm/zpvdnc93dh4PEHZn5mY+e7c8+fj5zPczLg0AWtEfNuPgVXuTo47yYXQaBLSkQUAr+sNO0btjK6AvXKoNAAAAwDSzeEwWl5bya399c5557rnWQ+kN5x7D+GhQ/zn7mJ1Kf4CWNAhoSYN4oywek/kjh3Pyyccd0g40oUGTwwIyO43+AC1pENCSBvFGWTyecotLS7nr6EK+cv2e3HV0wY4TMFYaNDlckcFOoz9ASxoEtKRBnI9eLh6f2X91Fo4+23oYU2H+yOF8eN/u7L9kJjfs271qx8llDMB22qhB+tNP3n3MTmEOBLRkDgS0pEGcj14uHjMew52mudnlX4O52V2rdpxcxgBsl3M1SH/6Z/juYwvITDpzIKAlcyCgJQ3ifFk8nmLDnaZLLlr+Nbjkol2v23FyGQOwnTZqkP70lwVkdgJzIKAlcyCgJQ3ifFk8nlKLS0v50sLXXttpGjp7x+lcl3MCjOpcDfqLQ/fqT49ZQGaSmQMBLZkDAS1pEKOweDyl5o8czu+/d9drO01Dwx2nP//yPee8nBNgVBs16Lcvm8k/HT+mPz1nAZlJZQ4EtGQOBLSkQYyi14vHPjRvewx3mj71wTetef/c7K7c+9Cx3LBvZt3LOQFGda4GJS/nev2ZCBaQmTTmQEBL5kBASxrEqHq7eHxm/9Wth7BjrbfTdLZXu1fzydmZ191m1wnYChs1aPH5V3Pom/+fzxx88+tu15/+OnjV3hy8am8ue/SB1/5by0b3wbiYAwEtmQMBLWkQo9rdegCM3/HHz+TkUy/l9pMvrXn/BTPJH+5/07qXc87ff18+d8ON4xgqsANt1CD9mVzDdyEvHH123UXi4WOgFXMgoCVzIKAlDWJUFo+n0Ox7Lsvsz34/t/3qT//5P/YvL6feNptP/Ma1uXzu4/nMwQvW/LNzs7tyxZ0LmbvmN3Px298+phEDO8l6DfrhW96fQye/rj8TzgIxfWYOBLRkDgS0pEGMqrfHVrA9FpeWXvchMEMrP1lzvcs5nXkDbMZGDVp5zuhK+gNshjkQ0JI5ENCSBrEZvX7n8Zn9VydHH/Aupi00f+Twmv9jNIzB4VOP5env/yifP7Hx81z57ie2cZTATrVRg35mT/KFEy/mCyde3PA59AcYhTkQ0JI5ENCSBrEZvV48ZmsNd5pO//H6lyL8w6mXsnjHHS5FALbcuRp0/A/emivu/HFO33qbBgFbyhwIaMkcCGhJg9gsx1ZMkfV2moZcigBsJw0CWtEfoCUNAlrSIDbLO4+nyMNPPpFj357MyzEXl5Zy452350s3/amdMJhQGgS0Msn9STQIJt0kN0h/YPJpEJvV+8Vj5x5vnQf/8pbWQxjZ/JHDOfnk45m//7587oYbWw8HGIEGAa1Mcn8SDYJJN8kN0h+YfBrEZjm2gt4bns/zlev35K6jC3nmuedaDwmYIhoEtKRBQCv6A7SkQf1h8ZjeG57Ps/+SmbGdw7Nw9Nltfw1gMrRoEMCQBgGt6A/Qkgb1x8QsHlvMm07Dnaa52eVf1bnZXWPbcTqz/+ptfw2g31o2CECDgFb0B2hJg/plIhaPLeJNr5WfCupTQIFx0iCgJQ0CWtEfoCUN6peJWDxmOq3caRqy4wSMgwYBLWkQ0Ir+AC1pUP9YPKa3Vu40DdlxAsZBg4CWNAhoRX+AljSof6rrui1/0gMHDnSPPPLIlj8v02NxcTGX//ylOf3RmVXBSJLF51/NFX//Sk5/6zu5+OKLG4xwZ6uqf++67kDrcYxKg9gsDWpHf0CDWtIgpp3+tKVBTDsNamej/njnMb00f8vN+fC+tWORDHac3juT+VtuHvPIgGmgQUBLGgS0oj9ASxrUT7tbDwDW8vDXH8qxh1/I549t/Lgrf3x8PAMCpooGAS1pENCK/gAtaVA/WTymlx48+WjrIQBTTIOAljQIaEV/gJY0qJ+25czjqvpekv/e8icGxuWdXde9o/UgRqVBMNH0B2hJg4CWNAhoZd3+bMviMQAAAAAAk80H5gEAAAAAsIrFYwAAAAAAVrF4DAAAAADAKhaPd7CqemEbnvOaqvqzwdfXVtUvjPAc/1ZVB7Z6bEB/6A/QkgYBLWkQ0Ir+sB0sHnNeuq67v+u6vxl8e22S844GwCj0B2hJg4CWNAhoRX+weDwFatmtVfVfVfWfVXXd4PYPDXZ/DlXVmar6x6qqwX2/Prjtwar6YlU9MLj9I1V1e1XNJrkmya1V9VhVXXr2TlJV7a2qpwdf76mqe6rqVFXdm2TPWWP7lap6qKq+UVVfrqoLx/u3A2wn/QFa0iCgJQ0CWtEfttLu1gNgLH4ryS8meV+SvUkerqqFwX37k1ye5H+THEtyZVU9kuTvkhzsuu6pqrp75RN2XXe8qu5P8kDXdYeSZNCbtdyU5Edd1+2rqn1JvjF4/N4kn07yy13X/bCqPpnk40n+agt+ZqAf9AdoSYOAljQIaEV/2DIWj6fDB5Pc3XXdK0m+W1VfS/JLSf4vycmu6/4nSarqsSTvSvJCku90XffU4M/fneSPNvH6B5N8MUm6rjtVVacGt38gy5c7HBsE54IkD23idYD+0R+gJQ0CWtIgoBX9YctYPJ4O624FJXnprK9fyfLvxEaP38jL+elRKG9ZcV+3zrj+teu63x3x9YD+0x+gJQ0CWtIgoBX9Ycs483g6LCS5rqpmquodWd4BOrnB488k+bmqetfg++vWedzzSS466/unk7x/8PXvrHj930uSqroiyb7B7SeyfHnEuwf3vbWq3vNGfiBgYugP0JIGAS1pENCK/rBlLB5Ph/uSnEryH0m+mmSu67pn1ntw13UvJvmTJP9cVQ8m+W6SH6zx0HuSfKKqHq2qS5N8NslNVXU8y2fqDP1tkgsHlynMZRCsruu+l+QjSe4e3HciyWWb+UGB3tEfoCUNAlrSIKAV/WHLVNet9S5ypl1VXdh13Qu1fAjNHUme6LruttbjAnY+/QFa0iCgJQ0CWtEf1uOdx6zno4OD008neVuWP3UTYBz0B2hJg4CWNAhoRX9Yk3ceAwAAAACwinceAwAAAACwisVjAAAAAABWsXgMAAAAAMAqFo8BAAAAAFjF4jEAAAAAAKv8BCp3g2FPo1F8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1800x288 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = [0.1, 1.0, 100.0, 1000.0, 100000.0]\n",
    "plot_svc_C(\n",
    "    C, X_train.to_numpy(), y_train.to_numpy(), x_label=\"longitude\", y_label=\"latitude\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Search over multiple hyperparameters\n",
    "\n",
    "- So far you have seen how to carry out search over a hyperparameter\n",
    "- In the above case the best training error is achieved by the most complex model (large `gamma`, large `C`).\n",
    "- Best validation error requires a hyperparameter search to balance the fundamental tradeoff.\n",
    "  - In general we can't search them one at a time.\n",
    "  - More on this next week. But if you cannot wait till then, you may look up the following:\n",
    "    - [sklearn.model_selection.GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)\n",
    "    - [sklearn.model_selection.RandomizedSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.RandomizedSearchCV.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### SVM Regressor\n",
    "\n",
    "- Similar to KNNs, you can use SVMs for regression problems as well.\n",
    "- See [`sklearn.svm.SVR`](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVR.html) for more details. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions on SVM RBFs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "#### Case study"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "A friend of yours shows you a SVM model they are working on, with very high accuracy on the training set (close to 100%).\n",
    "\n",
    "Upon closer inspection, you find out that almost all the original samples have been selected as support vectors.\n",
    "\n",
    "What can you guess about the values of `C` and `gamma` used to train this model?\n",
    "\n",
    "Do you think this model will generalize well?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "#### More practice questions \n",
    "\n",
    "- Check out some more practice questions [here](https://ml-learn.mds.ubc.ca/en/module4)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary\n",
    "\n",
    "- We have KNNs and SVMs as new supervised learning techniques in our toolbox.\n",
    "- These are analogy-based learners and the idea is to assign nearby points the same label.\n",
    "- Unlike decision trees, all features are equally important. \n",
    "- Both can be used for classification or regression (much like the other methods we've seen)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Coming up:\n",
    "\n",
    "Lingering questions: \n",
    "- Are we ready to do machine learning on real-world datasets?\n",
    "- What would happen if we use $k$-NNs or SVM RBFs on the spotify dataset from hw2?  \n",
    "- What happens if we have missing values in our data? \n",
    "- What do we do if we have features with categories or string values?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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