DataMining_week09.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "DataMining-week09.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "TLUdfI95-XSR",
        "h4XIbL5FIClk",
        "6AloWTjQjV4E",
        "-TfecgGzmBqu"
      ],
      "authorship_tag": "ABX9TyORHIK1XPLbclcFvufIxV3u",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/MLRG-CEFET-RJ/ml-class/blob/master/DataMining_week09.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lkO4wLTtubIS",
        "colab_type": "text"
      },
      "source": [
        "# Classification task: an overview"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RFNgxXW42Cht",
        "colab_type": "text"
      },
      "source": [
        "As a recap, remember that Data Mining techniques can be categorized in two types: descriptive and predictive (see figure below).\n",
        "\n",
        "![alt text](https://www.researchgate.net/profile/Ali_Al-Haboobi/publication/317731072/figure/fig1/AS:507840017645568@1498089903893/Data-mining-techniques_W640.jpg)\n",
        "\n",
        "Classification is a predictive task in which the features of the dataset are divided into two groups. One of the groups contains only one feature, which is called the *target*, that is, the feature for which a value must be predicted. In the case of the classification task, the target is categorical (i.e. its domain is composed of categories/classes). The other group contains the features to be used in the prediction of the target, called *predictive features* (or simply *predictors*). Each row of the dataset is called an *example* (aka *instance* or *case*)\n",
        "\n",
        "The image below ([source](https://docs.oracle.com/cd/B28359_01/datamine.111/b28129/classify.htm#DMCON004)) shows a toy dataset suited for the classification task. In this example, notice that the target has only two possible values, which configures a *binary classification task*.\n",
        "\n",
        "![alt text](https://docs.oracle.com/cd/B28359_01/datamine.111/b28129/img/class_sampledata.gif)\n",
        "\n",
        "The classification task can be understood as the search for a *classification function* (aka *predictive model* or simply *model*) that allows each instance to be correctly associated with one or more categorical labels (or classes). The examples in the original dataset are initially split into two parts, the *training dataset* and the *test dataset*. The search for the classification function is done by a *learning algorithm* (aka *classificaion algorithm*), which process the training dataset. During this search, we say the algorithm is *learning a model* or *fitting a model*. Once the model is built, its predictive performance is evaluated using the examples in the test dataset. This evaluation will give us an estimate of how good the model is in predicting the class for unseen examples. After being evaluated, the model can be applied to new cases in order to predict their classes. The figure below ([source](https://www.researchgate.net/publication/317731072_Popular_Decision_Tree_Algorithms_of_Data_Mining_Techniques_A_Review)) provides an overview of this process.\n",
        "\n",
        "![alt text](https://www.researchgate.net/profile/Ali_Al-Haboobi/publication/317731072/figure/fig2/AS:507840016154625@1498089904007/Classification-task-steps_W640.jpg)\n",
        "\n",
        "As an example, consider a finance company that stores data about its customers and their behavior in relation to the payment of previously contracted loans. Also consider three types (classes) of customers: *risky*, *low*, and *safe*. These are the classes of the problem (i.e., the values ​​of the target feature). An application of the Classification task, in this case, consists of applying a learning algorithm to discover a function that correctly maps customers, based on their data (i.e., the values ​​of the predictive features), in one of these classes. \n",
        "\n",
        "The image below ([source](http://greatislamians.blogspot.com/p/data-mining-classification-prediction.html)) illustrates the example described above. This image presents a particular type of classification funtion, which is comprised of a set of classification rules. In general, each classification algorithm has its particular way of representing classification functions.\n",
        "\n",
        "![alt text](http://www.tutorialspoint.com/data_mining/images/dm_build_classifier.jpg)\n",
        "\n",
        "Continuing the example about customers, once discovered, the model can be used to predict the behavior of new customers who wish to borrow from the finance company. This model can be actually incorporated into a decision support system that assists in filtering and granting loans only to customers classified as good payers, as the image below ([source](http://greatislamians.blogspot.com/p/data-mining-classification-prediction.html)) illustrates. \n",
        "\n",
        "![alt text](http://www.tutorialspoint.com/data_mining/images/dm_using_classifier.jpg)\n",
        "\n",
        "In this notebook, we will study some of the many available classification algorithms. In particular, the following algorithms are described here for carrying out the classification task:\n",
        "\n",
        "- Logistic regression\n",
        "- $k$-nearest neighbors\n",
        "- Decision trees\n",
        "- Naive Bayes classifier\n",
        "\n",
        "In the following sections, consider the following notation:\n",
        "\n",
        "- $\\mathbf{x}$ is an instance whose class is to be determined.\n",
        "- $m$ is the size of the training set.\n",
        "- $n$ is the number of predictive features. \n",
        "- $k$ is the number of classes (values) of the target feature.\n",
        "- $\\mathbf{x}^{(i)} \\in \\Re^{n}$ is a vector that represents the $i$-th training example.\n",
        "- $y^{(i)}$ is the target feature value for the $i$-th training example.\n",
        "- $X = \\{\\mathbf{x}^{(i)}, y^{(i)}\\}_{i = 1}^{m}$ is the training dataset."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eheXoU_tR5tJ",
        "colab_type": "text"
      },
      "source": [
        "# Examples in a dataset: a geometric interpretation\n",
        "\n",
        "A common characteristic of many Data Mining algorithms (for classification and for other tasks) is that they interpret each example in a dataset as a *geometric point*. See the following figure (taken from [here](https://www.mathplanet.com/education/geometry/points,-lines,-planes-and-angles/an-introduction-to-geometry)). \n",
        "\n",
        "![three points in 2D](https://www.mathplanet.com/Oldsite/media/43053/picture04.png)\n",
        "\n",
        "To get a sense of this interpretation, consider a ficticious dataset for binary classification with 17 examples. Furthermore, for simplicity´s sake, consider that each example has only two features, which means that each example is of the form $\\mathbf{x} = [x_1, x_2]$. The code cell below presents this dataset as two separated numpy arrays, $X$ and $y$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mFksDhm3UBAS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[-0.1, 1.4],\n",
        "              [-0.5,-0.1],\n",
        "              [ 1.3, 0.9],\n",
        "              [-0.6, 0.4],\n",
        "              [-1.5, 0.4],\n",
        "              [ 0.2, 0.2],\n",
        "              [-0.3,-0.4],\n",
        "              [ 0.7,-0.8],\n",
        "              [ 1.1,-1.5],\n",
        "              [-1.0, 0.9],\n",
        "              [-0.5,-1.5],\n",
        "              [-1.3,-0.4],\n",
        "              [-1.4,-1.2],\n",
        "              [-0.9,-1.1],\n",
        "              [ 0.4,-1.3],\n",
        "              [-0.4, 0.6],\n",
        "              [ 0.3,-0.5]])\n",
        "\n",
        "y = np.array([0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RRXIv5AiUV-x",
        "colab_type": "text"
      },
      "source": [
        "Since each example is represented by a pair of numbers, we can plot these examples for visualization purposes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i4ljwlU7TNWg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 480
        },
        "outputId": "9a76b7a3-a260-4871-98bc-a3166ed26f66"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('classic')\n",
        "np.set_printoptions(precision=3, suppress=True)\n",
        "\n",
        "colormap = np.array(['r', 'b'])\n",
        "\n",
        "def plot_scatter(X, y, colormap):\n",
        "  plt.grid()\n",
        "  plt.xlim([-2.0, 2.0])\n",
        "  plt.ylim([-2.0, 2.0])\n",
        "  plt.xlabel('$x_1$', size=20)\n",
        "  plt.ylabel('$x_2$', size=20)\n",
        "  plt.title('Input 2D points', size=18)\n",
        "  plt.scatter(X[:,0], X[:, 1], s=50, c=colormap[y])\n",
        "\n",
        "plot_scatter(X, y, colormap)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAHPCAYAAABHgU5sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAMTQAADE0B0s6tTgAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdeVhUZfsH8C8Oy4AoqCmYlRtuRZKmuJSZaaGlUYmhaWoumUupU686lPWWuZAtktnruKSZmtiiiKZjlqbvm6gtoqaomKVlg4qCIAyDML8/Cn7CmUE8zszD4fl+rsvLi3POzNzfORd1e849z3ht377dDiIiIiIqo4boAoiIiIiqIjZJRERERA6wSSIiIiJygE0SERERkQNskoiIiIgcYJNERERE5ACbJCIiIiIH2CQREVVRFosFPXr0wJw5c0SXQiQlb9EFEJFr9OjRAwCwfft2wZVUzsCBAwEAa9asua7HHTx4EP/73/+wf/9+WCwW5OXloV69emjfvj2eeuopNGrUSPGYSZMmITU1tfTnGjVqICAgAHXq1EGzZs3QqVMn3H///fD397+xUFWY2vebSGZskohIU1577TVkZ2fjjjvuQK9evaDT6fDLL7/gq6++wrfffou3334bd9xxh8PHRkVFITQ0FHa7HXl5efjrr7/w008/4bvvvsOSJUvwr3/9C507d/ZwIuduuukmfPzxx6hZs6boUoikxCaJiDRlwIABePDBB3HTTTeV2b5y5UosXboU77zzDj766COHj+3duzfuuuuuMttsNhvWrl2LZcuW4dVXX8XcuXMRERHhtvqvh7e3N2677TbRZRBJi00SUTVmsVgwaNAgREVFYfjw4Vi0aBF+/PFH5Ofno2nTphg+fDi6dOlS5jFbtmxBfHw8pk6diqCgIKxatQonTpyAt7c32rdvj9GjR+OWW24p85iS21mObvVd/Xy9e/fG/v37MXny5NL9JbcJgb+v9EybNq3CTIMGDXK6feXKlTh58iSys7MRFBR0zfcHAHx9fTFkyBAUFhZixYoV+OCDD7B48eJrPu7q9/app57CokWLcODAARQWFiIsLAxDhw5Fx44dFY+z2Wz4/PPPsW3bNpw5cwY6nQ7NmzfH448/Xua9KP8aV78vc+bMgdlsxqeffoq9e/di/fr1+OOPPxAYGIiuXbviueeeQ2BgIABU+v0+cOAA1qxZg+PHjyM7OxuBgYEIDQ1Fp06dMGzYsEq9l0TVDZskIglkZGRg7NixaNiwIR566CFcunQJ27dvxyuvvIK3334b7dq1Uzxm165d2LNnD+69915ERETgxIkT2LlzJ/bv34/58+ervsIRGhqKYcOG4fPPPwcAxMTElO4LCwtTFxCAl5cXdDodAJT+fT1iY2ORmJiI9PR0nDx5Ek2bNq3U4/766y+MHz8ezZo1Q79+/ZCZmYnt27dj2rRpePnll/HAAw+UHltYWIgpU6YgNTUVt912Gx577DFYrVbs3LkTb7zxBtLT0zF69OhK17xw4UL88MMP6NKlCzp06ID9+/dj06ZNOHPmDN59910AlXu/9+7dC6PRiICAAHTt2hU33XQTcnJy8PvvvyMpKYlNEkmLTRKRBPbv34/hw4eX+Z9dz549MXXqVCQmJjpskr7//nvMmjWrzJWmzz//HAsWLMC8efNK/yd8vUJDQzF8+HBs2bIFADB8+HBVz1Pejh07kJeXh9tvv730Ksr1CAgIQMuWLXHw4EGkpaVVukk6cOAAYmNj8dxzz5Vue/zxxzF+/Hi899576NSpU+lM0dq1a5GamopOnTph5syZpc3csGHDMHbsWKxevRpdunRBeHh4pV77yJEjWLp0KUJCQgAARUVFMBgM+Pnnn3HkyBG0adOmUu/3xo0bUVxcjPfee0/RqGZnZ1eqFqLqiEsAEEkgJCQEQ4YMKbMtMjISISEhOHLkiMPHtGvXTnEr7vHHH8fNN9+Mn3/+GRaLxW31Xq+//voL8+fPh06nw7hx41Q/T8mcU1ZWVqUfU7NmTQwdOrTMtlatWqFXr17Izc3Frl27Srdv3rwZXl5eGDduXJmrXXXq1MHTTz8NANi0aVOlX3vo0KGlDRLw9xW03r17AwDS0tIq/Twl/Pz8FNsqe9uSqDpik0QkgbCwMIe3oOrXr4/c3FyHj3E0vKzT6XDnnXcCANLT011bpEoXL17E1KlTkZWVhQkTJjj9ZFtl2O12AH/fuqusli1bIiAgQLG9ZEC85H3Ky8vDn3/+iXr16jm8Vdm+ffsyx1dGq1atFNsaNGgAAMjJyan08/Tq1QsAMG7cOLz77rv49ttvce7cuUo/nqi64u02Igk4u/2k0+lQXFzscF+dOnUcbq9bty4AOG2uPOnixYswGAw4ffo0JkyYgMcee+yGni8zMxMAEBwcXOnHXOt9unz5cpm/69Wr5/D4ku3X8746Oq8lzbCz8+rIfffdh1mzZuGzzz7D5s2bkZycDODvBnD06NHo0KFDpZ+LqDphk0REDl28eNHh9gsXLgAo+z/oGjX+vihdVFSkuGLlrmYqMzMTL774Ik6dOoWJEyfecIOUl5eHY8eOAQDatGlT6cdd630qmUcq+btke3klDZqoNZG6dOmCLl26ID8/H0eOHMHu3buxYcMGxMXFYdGiRWjSpImQuohE4u02InLo6hWqSxQVFeHgwYMAyn4SraRhOnv2rOIxR48edfj8FV3FupZz585h0qRJOHXqFCZPnnzDDRLw90rUBQUFaNGiBRo3blzpxx07dgx5eXmK7fv37wfw/+9TQEAAbr75Zpw/fx5//PGH4viff/4ZANCiRQs15V9TZd9vf39/tG/fHuPHj8fgwYNRWFiIvXv3uqUmoqqOTRIROfTzzz9j9+7dZbatW7cOZ86cQbt27RAaGlq6veTKy8aNG8sc/+OPP+Lbb791+Py1a9dGVlYWCgoKrqsui8WCiRMn4syZM5gyZQr69et3XY8vz2azYeXKlVi1ahV8fHzw/PPPX9fjL1++jBUrVpTZdvToUWzbtg01a9ZEt27dSrf36dMHdrsdCxcuRFFRUen27OxsfPLJJwCAhx9++AbSOFfR+52amlqmnhIlV8kcDXQTyYC324jIoa5du2L69Om499570ahRI5w4cQJ79uxB7dq1MWnSpDLH9u7dG2vWrMHq1atx4sQJNGnSBKdPn8bevXtx7733YufOnYrnb9++PdLS0jBlyhRERETAx8cHzZs3R9euXSusa/LkybBYLGjZsiUsFguWL1+uOKZ3795lmrgSW7ZsKb3CU/K1JAcOHMClS5dQr149TJkypXQwvbLatm2LTZs24ciRIwgPDy9dJ8lut8NgMJS5fRYbG4u9e/fif//7H0aNGoVOnTqhoKAA3333HS5evIiBAwde9+tXVkXv9/z583H+/HmEh4cjNDQU3t7eOHbsGH7++WeEhISUWeuJSCZskojIoW7duqFv375YuXIl9uzZA51Oh27dumH06NG49dZbyxxbp04dzJs3DyaTCQcOHEBqaipatWqFuXPnwmKxOGyShgwZgtzcXHz//fc4dOgQiouLERUVdc0mqWTpgWPHjpXOEJV31113OWySzGYzgL9nqPz9/VG3bl20b98enTp1Qvfu3VV9wW3Dhg1hMBiwaNEibNiwAYWFhWjRogWGDh2KyMjIMsf6+Pjg7bffxtq1a/HNN99g3bp1pStujx8/Hj179rzu16+sit7vwYMH47///S+OHj2KH3/8ETVq1ECDBg0wePBgxMTEoFatWm6ri6gq89q+fbtddBFqLFq0CCkpKcjIyIBer8ddd92FMWPGlH781RGbzYYPP/wQ27dvR2FhISIiIjB58uQKH0Mkm/JfI0KOOfvKECKqPjQ7k+Tl5YWpU6di/fr1+PjjjwEAcXFxFT7mww8/xMGDB2EymfDZZ5+hVq1aePnll1UPjxIREVH1pdkmafTo0WjVqhV8fHwQGBiIQYMG4cSJE04XULPZbNiyZQueeeYZhIaGombNmhg/fjxOnjyJQ4cOebh6IiIiquo02ySVt2/fPoSEhDi9d37q1CkUFBSUWf8kKCgIDRs2xPHjxz1VJhEREWlEtRjc/vHHH7FixQq8/vrrTo8pWcek/Aq1gYGBDtc4KS4uRmZmJvz9/a/rKwqItK5bt26lH1svWSWalGrVqlW65AHfJ6Kqw263Iz8/H/Xq1Std6FYtzTdJu3fvxsyZMxEXF6f4JMnVSr5bKTc3t8yaH7m5uQ6/dykzMxNPPvmk6wsmIiIit1u7di3q169/Q8+h6Sbp66+/RkJCAl599dUKGyQAuO222+Dn54e0tDTcc889AP5ewM1isThc4bbko8CnT59G7dq1XV98FRYVFVX6UWmZMLdcmFsuzC2PS5cu4dZbb1W1pEd5mm2S1q1bh48++gizZs1C27Ztr3m8r68vevfujWXLliEsLAy1atXChx9+iMaNGyM8PFxxfMktttq1a0vXJLVq1Uq6zABzy4a55cLc8nHFqIxmB7fff/995OfnY+rUqejTp0/pnwMHDpQe06dPH3z99delP48bNw7h4eF49tln0b9/f2RnZ2PWrFk3fM+yuin59nLZMLdcmFsuzE1qaPZK0vbt2695zObNm8v87Ovri0mTJim+UoHKioqKEl2CEMwtF+aWC3OTGryEQgpBQUGiSxCCueXC3HJhblKDTRIppKamii5BCOaWC3PLhblJDc1+d5u7Xb58GX379kV2dra0Q29ERERac+nSJQQFBWHjxo2oWbPmDT0XryQREREROcAmiYiIiMgBNkmkYDQaRZcgBHPLhbnlwtykBmeSnJB5JslisSA0NFR0GR7H3HJhbrkwtzw4k0RuJdsvVAnmlgtzy4W5SQ02SUREREQOsEkiBdm+DLEEc8uFueXC3KQGmyRSyMrKEl2CEMwtF+aWC3OTGhzcdkLmwW0iIiKt4uA2ERERkZuxSSIFq9UqugQhmFsuzC0X5iY12CSRQlxcnOgShGBuuTC3XJib1OBMkhMyzyRZrVbo9XrRZXgcc8uFueXC3PLgTBK5lWy/UCWYWy7MLRfmJjXYJBERERE5wCaJFBITE0WXIARzy4W55cLcpAabJFIIDg4WXYIQzC0X5pYLc5MaHNx2QubBbSIiIq3i4DYRERGRm7FJIgWLxSK6BCGYWy7MLRfmJjXYJJFCQkKC6BKEYG65MLdcmJvU4EySE5xJIiIi0h7OJBERERG5GZskIiIiIgfYJJGCyWQSXYIQzC0X5pYLc5MabJJIISIiQnQJQjC3XJhbLsxNanBw2wkObhMREWkPB7eJiIiI3IxNEimkpaWJLkEI5pYLc8uFuUkNNkmkkJSUJLoEIZhbLswtF+YmNTiT5ARnkoiIiLSHM0lEREREbsYmiYiIiMgBNkmkEB8fL7oEIZhbLswtF+YmNdgkkUJ0dLToEoRgbrkwt1yYm9TwFl2AWt9++y3Wr1+PEydOIC8vD9u2bYNOp3N6/KRJk/DLL7/A2/v/I48ZMwaPPfaYJ8rVlNatW4suQQjmlgtzy4W5SQ3NNkmBgYGIjo5GQUEB5s6dW6nHDBw4ECNHjnRzZURERFQdaPZ2W2RkJHr27Imbb75ZdCnVTkpKiugShGBuuTC3XJib1NBsk6TGhg0b0K9fPwwdOhSLFi1Cfn6+6JKqpNTUVNElCMHccmFuuTA3qaH5xST379+PyZMnX3Mm6dChQ7jtttsQGBiIX3/9FfHx8bjlllvw2muvOTyei0kSERFpDxeTVCE8PBy1a9dGjRo1EBYWhvHjx2Pnzp0oKCio8HEDBgyAwWCAwWBAcnIyDAYDrFZr6f7ExESYzebSny0WC4xGY5nnMJlMZS55pqWlKT6WGR8fX+Y7dlJSUmAymcocYzQaYbFYSn82m81ITEws/dlqtbI+1sf6WB/rY33S1Wc2mzFmzBhERkYiLi4OriLNlaTyUlNTYTAYsGnTJuj1esV+XkkiIiLSHl5JAlBUVASbzYbCwkIAgM1mg81mQ3FxseLYCxcuYO/evcjPz4fdbsfJkyfx4Ycf4p577nHYIMmu/L8UZMHccmFuuTA3qaHZK0lbtmxxuJLoe++9h4YNG2L48OGIj49H27ZtYbFY8Prrr+P06dMoKipC3bp10a1bNwwdOhQBAQEOn1/mK0kWiwWhoaGiy/A45pYLc8uFueXhyitJmm2S3E3mJomIiEireLuNiKR3/vx5zHjjDbRt3hzNQkMxoF8/7Ny5U3RZRFSNsEkihas/zSAT5taOU6dOoUN4OLbPno1Xfv0VSzMy0Pyrr9C3Vy+89847lXoOLeZ2BeaWi6y5XUWzX0tC7pOVlSW6BCGYWzvGPfMMHsjMxNIrV+D1z7YexcUYUFyMe6dNQ59HHrnmd1ZpMbcrMLdcZM3tKpxJcoIzSURV0+nTp9G8SROcLC5GIwf7n/b1RYOxY/HOvHker42IxONMEhFJ69dff0Ujvd5hgwQAnWw2pP/yi0drIqLqiU0SKVy9oqlMmFsbGjRogAybDZec7D+u06FBJb74Wmu5XYW55SJrbldhk0QKrlzSXUuYWxvatGmD8Fat8IGDfX8BWKHTYdjo0dd8Hq3ldhXmlousuV2FM0lOyDyTZLVapVyJnLm1IyUlBQ/efz/G2GwYa7ejPoAtAF7R69H18cexbNUqeHl5VfgcWsztCswtFxlzcyaJ3Eq2X6gSzK0dnTt3xs7du3EiKgotvbwQBMDYsCHGzZqFj1auvGaDBGgztyswt1xkze0qXAKAiDSpXbt2WLd5M6xWK6xWK4KCgirVHBERVRavJJFCYmKi6BKEYG5t0uv1CA4Ovu4GSeu51WJuucia21XYJJFCcHCw6BKEYG65MLdcmJvU4OC2EzIPbhMREWkVB7eJiIiI3IxNEilYLBbRJQjB3HJhbrkwN6nBJokUEhISRJcgBHPLhbnlwtykBmeSnOBMEhERkfZwJomIiIjIzdgkERERETnAJokUTCaT6BKEYG65MLdcmJvUYJNEChEREaJLEIK55cLccmFuUoOD205wcJuIiEh7OLhNRERE5GZskkghLS1NdAlCMLdcmFsuzE1qsEkihaSkJNElCMHccmFuuTA3qcGZJCc4k0RERKQ9nEkiIiIicjM2SUREREQOsEkihfj4eNElCMHccmFuuTA3qcEmiRSio6NFlyAEc8uFueXC3KQGmyRSaN26tegShGBuuTC3XJib1GCTREREROQAmyRSSElJEV2CEMwtF+aWC3OTGmySSCE1NVV0CUIwt1yYWy7MTWpwMUknuJgkERGR9nAxSSIiIiI3Y5NERERE5ACbJFIwGo2iSxCCueXC3HJhblJDszNJ3377LdavX48TJ04gLy8P27Ztg06nc3p8Tk4OEhISSif9O3fujEmTJiEwMNDh8TLPJFksFoSGhoouw+OYWy7MLRfmlgdnkgAEBgYiOjoa48ePr9TxM2fOxMWLF7Fq1SqsWrUKFy9exOzZs91cpTbJ9gtVgrnlwtxyYW5SQ7NNUmRkJHr27Imbb775msdaLBbs2bMHY8eORVBQEIKCgjB27Fh8//33yMjI8EC1REREpDWabZKuR3p6Onx8fBAWFla6LSwsDD4+PkhPTxdYWdVkNptFlyAEc8uFueXC3KSGFE1SXl6ew9mjwMBA5OXlCaioasvKyhJdghDMLRfmlgtzkxpSNEkBAQHIzc1VbM/NzUVAQECFjx0wYAAMBgMMBgOSk5NhMBhgtVpL9ycmJpbp1C0Wi+LTBCaTqczS8GlpaYiPjy9zTHx8PNLS0kp/TklJgclkKnOM0WiExWIp/dlsNiMxMbH0Z6vV6pL6IiIiqnR97nr/oqOjq3R97nr/YmNjq3R9gHvev9jY2CpdH+Ce9y82NrZK1we45/2LjY2t0vUB7nn/YmNjq3R9JW60PrPZjDFjxiAyMhJxcXFwFc1+uq3E/v37MXny5Ao/3WaxWDBo0CAsWbIEzZs3BwCcOHECo0aNwpo1axASEqJ4jMyfbiMiItIqfroNQFFREWw2GwoLCwEANpsNNpsNxcXFimNDQ0PRqVMnLFy4ENnZ2cjOzsbChQvRtWtXhw2S7K7u1GXC3HJhbrkwN6mh2Sbp66+/RlRUFKZMmQIAePjhhxEVFYUDBw4gIyMDffr0wYEDB0qPj4uLQ+3atTF48GAMHjwYQUFBXGTLCVdeqtQS5pYLc8uFuUkNzd9ucxeZb7dZrVbo9XrRZXgcc8uFueXC3PLg7TZyK1l+oex2O9atW4eo++5D05AQ3Hf33Zg/f750n3iU5XyXx9xyqSq5d+/ejSeeGISGDZujadNwvPLKq25dr6+q5NYqNkkkJbvdjvGjR2PcoEG4f9cuLD97FmMPH8ZHU6agR5cuyMnJEV0iEVUzJtMidO/+IDZsuBkWy2L89tvrePvtfbjjjvZcs6+KYpNECld/7LK6Sk5OxpcrV2JvQQGMALoDCACQYrUi4OhRvPbKK4Ir9BwZzrcjzC0X0blPnTqFCRNeQGHhFhQVvQPgAQD9UVDwFbKy+uOpp0a65XVF59Y6NkmkEBwcLLoEt1uUkIAJNhtuvWpbMAA/AG8UFGDZkiWln5ys7mQ4344wt1xE5168eCl0uj4A7i23xwtFRa/hp5/2lllLyFVE59Y6NkmkEBUVJboEtzt+9Cgi7WU/s1CSuhOArLw8ZGZmerwuEWQ4344wt1xE5z58OB0FBZFO9taDXh+GEydOuPx1RefWOjZJJKWQkBA4mwBIB+Dr7Y2goCBPlkRE1VijRg3g4+PsvzpWFBb+gQYNGni0Jro2NkmkcPXS8NXV0LFj8YG/P67+HJsFgB3AW97eePKJJ+Dv7y+oOs+S4Xw7wtxyEZ37mWeGwm5fA+B3B3sX4+abG6JDhw4uf13RubWOTRIpJCQkiC7B7Z5++mk0aNsWD/j5YSuAXAAvAxjq7Q1zrVqYUe67h6ozGc63I8wtF9G527VrhxEjnoFe3x3AKgDZAH6Dl9fL8PWdho8+WgAvLy+Xv67o3FrHxSSdkHkxSVnk5eVh1ptvYvGHH+Jsdjb0Pj4YOGAAXps5E02aNBFdHhFVM3a7HQsXLsTs2fNw+vQxeHl5oUePhzFr1nR06tRJdHnVhisXk2ST5ASbJHkUFRUhOzsbgYGB8PX1FV0OEVVzdrsd2dnZ8PPzk+a2vie5sknydlFNRJql0+lQt25d0WUQkSS8vLz40XyN4EwSKZhMJtElCMHccmFuuTA3qcEmiRQiIiJElyAEc8uFueXC3KQGZ5Kc4EwSERGR9rhyJolXkoiIiIgcYJNECu74/iAtYG65MLdcmJvUYJNECklJSaJLEIK55cLccmFuUoMzSU5wJomIiEh7OJNERERE5GZskoiIiIgcYJNECvESfbnr1ZhbLswtF+YmNdgkkUJ0dLToEoRgbrkwt1yYm9Rgk0QKrVu3Fl2CEMwtF+aWC3OTGmySiIiIiBxgk0QKKSkpoksQgrnlwtxyYW5Sg00SKaSmpoouQQjmlgtzy4W5SQ0uJukEF5MkIiLSHi4mSURERORmbJKIqNJycnJw6dIl0WUQEXkEmyRSMBqNoksQgrmd27RpE+5p1w61a9dGUFAQIsPD8eWXX3qgOvfh+ZYLc5ManElyQuaZJIvFgtDQUNFleBxzO/bR0qWYNHYsXi8sxFMAdAASAbzi64vX33oLL0yc6KlSXYrnWy7MLQ9XziSxSXJC5iaJqERubi5url8fn1mtiCq373sAPX188Mdff6FevXoiyiMiUuDgNhF5xPr169GsRg085GBfVwB3+/jgs88+83RZREQewSaJFMxms+gShGBupbNnzyLMboeXk/1hhYU4e/asewpzM55vuTA3qcEmiRSysrJElyAEcyuFhYXhBwBFDvbZAez19kZYWJi7SnMrnm+5MDepwZkkJziTRARcuXIFTRs2xNTz5zGh3L6PAbxYqxb+OHsWer1eRHlERAqunEnydlFNRFQNeXt7Y/WXX+KRhx7C7uJiPGWzQQdgrY8P1np54cvPP2eDRETVFm+3kYLVahVdghDM7Vi3bt3w08GDuGnUKBgaNcILN98Mv6FD8UNqKh56yNFItzbwfMuFuUkNTTdJdrsdy5YtQ0xMDPr06YOJEyfi5MmTTo+fNGkSHnzwQfTp06f0z/r16z1YsTbExcWJLkEI5nYuLCwMCQsW4Ogff+DYn3/iP0uWoHXr1h6ozn14vuXC3KSGpmeS1qxZgy+//BJz5sxBo0aNsGLFCmzduhUrVqyAv7+/4vhJkybhzjvvxMiRI6/53DLPJFmtVilvoTC3XJhbLswtD66T9I+kpCQ8+eSTaNasGfz8/DBixAgUFhZi165dokvTNNl+oUowt1yYWy7MTWpotknKzc2FxWJBmzZtSrfpdDq0aNECx48fd/q4DRs2oF+/fhg6dCgWLVqE/Px8T5RLREREGqPZJikvLw8AEBgYWGZ7YGBg6b7yRo0ahU8++QRJSUl49dVXsW/fPrz11ltur1VrEhMTRZcgBHPLhbnlwtykhmabpICAAAB/X1G6Wm5ubum+8sLDw1G7dm3UqFEDYWFhGD9+PHbu3ImCggKnrzNgwAAYDAYYDAYkJyfDYDCU+bRAYmJimRVNLRaL4luXTSYTUlJSSn9OS0tDfHx8mWPi4+ORlpZW+nNKSgpMJlOZY4xGIywWS+nPZrO5zC+A1Wp1SX05OTlVuj53vX8BAQFVuj53vX/BwcFVuj7APe9fcHBwla4PcM/7FxwcXKXrA9zz/gUHB1fp+gD3vH/BwcFVur4SN1qf2WzGmDFjEBkZ6dJhdU0Pbg8aNAgxMTHo378/AKCoqAgxMTEYO3ZspT6anJqaCoPBgE2bNinu28o8uE1ERKRVHNz+R3R0NNauXYuTJ0+ioKAAy5Ytg7e3N7p166Y49sKFC9i7dy/y8/Nht9tx8uRJfPjhh7jnnns42EZEREQKml5xOzY2Fnl5eXjxxReRl5eHVq1aIT4+Hv7+/sjIyMDw4cMRHx+Ptm3bwmazYdmyZTh9+jSKiopQt25ddOvWDUOHDhUdo8qxWCwIDQ0VXYbHMbdcmFsuzE1qaPpKkpeXF0aMGIEvv/wSW/+6CbQAACAASURBVLZsQUJCApo1awYACAkJwebNm9G2bVsAQGhoKP7zn/9g48aN2Lx5M1atWoXnnnvO6fySzBISEkSXIARzy4W55cLcpIamZ5LcSaaZJLvdjvXr12Phe+/h2NGjqH/TTXj6uecwcuRINpEacP78efznww/x2ccfI/fyZdzdsSOe/9e/cN9994kujYjI4ziTRC5jt9sxfvRojBs0CPfv2oXlZ89i7OHD+GjKFPTo0gU5OTmiS6QKnDp1Ch3Cw7F99my88uuvWJqRgeZffYW+vXrhvXfeEV0eEZGmsUmSXHJyMr5cuRJ7CwpgBNAdwDMAUqxWBBw9itdeeUVwhVSRcc88gwcyM/GN1YonAfQAMKe4GNsLCxE3bVqZj90SEdH1YZMkuUUJCZhgs+HWq7aZAPgBeKOgAMuWLEFhYaGg6jyr/LodVd3p06exdccOzLhyBV7l9t0NIKZGDSxeuPCaz6O13K7C3HJhblKDTZLkjh89ikh72bG0iH/+7gQgKy8PmZmZHq9LhIiIiGsfVIX8+uuvaKTXo5GT/Z1sNqT/8ss1n0druV2FueXC3KQGmyTJhYSEIL3cts7//J0OwNfbG0FBQR6uSozOnTtf+6AqpEGDBsiw2XDJyf7jOh0a3HzzNZ9Ha7ldhbnlwtykBpskyQ0dOxYf+Puj/Lfd2QG85e2NJ594Av7+/iJKo2to06YNwlu1wgcO9v0FYIVOh2GjR3u6LCKiaoNNkuSefvppNGjbFg/4+WErgFwASQCGenvDXKsWZpT7Dp7qTItDzu8vWYLZfn54ycsLJwBcArAWQHe9HtH9++Oee+655nNoMbcrMLdcmJvUYJMkOT8/P3z17bfoZTDg6aAg1MLfA7/eTz6J3T/9hCZNmogu0WOSkpJEl3DdOnfujJ27d+NEVBRaenkhCICxYUOMmzULH61cCS+v8iPdSlrM7QrMLRfmJjW4mKQTMi0mWaKoqAjZ2dkIDAyEr6+v6HLoOlmtVlitVgQFBVWqOSIiqo5cuZikpr+7jVxLp9Ohbt26ossglfR6Pb+smYjIhXi7jYiIiMgBNkmkEC/RsPbVmFsuzC0X5iY12CSRQnR0tOgShGBuuTC3XJib1GCTRAqtW7cWXYIQzC0X5pYLc5MabJKIiIiIHGCTRAopKSmiSxCCueXC3HJhblKDTRIppKamii5BCOaWC3PLhblJDS4m6YSMi0kSERFpHReTJCKqon744QcsWbIcp09b0KZNczz77Ei0bNlSdFlEpAJvtxERuYDdbseYMRPQtWsPLF1aiK++6oL580/h9tvb4t1354kuj4hUYJNECkajUXQJQjC3XFyde9GiRVixIhmFhb/gyhUTgBdhs32KoqL/wWh8Ddu3b3fp66nF8y0XWXO7CmeSnJB5JslisSA0NFR0GR7H3HJxZW673Y6mTe/A779PAzBUsd/L62VERR3G5s3rXPJ6N4LnWy4y5nblTBKvJJGCbL9QJZhbLq7MnZeXh99/PwKgj8P9dvvD2LfvB5e93o3g+ZaLrLldhU0SEdEN8vX1RY0aOgCZTo7IhL9/gCdLIiIXYJNECmazWXQJQjC3XFyZ28fHB336PIYaNRY52GuHn58JQ4bEuOz1bgTPt1xkze0qbJJIISsrS3QJQjC3XFyde+bM6fDxWQxgDoDcf7aeg073AmrW/BkTJz7v0tdTi+dbLrLmdhUObjsh8+A2Eamze/dujBgxHunpx+Dn1whW6++IjLwHK1aYEBYWJro8IilwMUkioiqoS5cuOHz4Rxw6dAgZGRlo0qQJmyMiDWOTRApWqxV6vV50GR7H3HJxV24vLy/ceeeduPPOO13+3K7A8y0XWXO7CmeSSCEuLk50CUIwt1yYWy7MTWpwJskJmWeSZP2XB3PLhbnlwtzy4GKS5Fay/UKVYG65MLdcmJvUYJNERERE5ACbJFJITEwUXYIQzC0X5pYLc5Maqj/dtnr1aiQlJeHSpUuIiIjA+PHjceuttwIANm3ahPT0dOTn52PatGkuK5Y8Izg4WHQJQjC3XJhbLsxNaqga3F67di3WrFmDjh07IigoCMeOHcPRo0fx+uuvIzIyEgCwd+9eGI1GfPPNNy4v2hNkHtwmIiLSKuGLSe7duxcff/wxatWqVbrtyJEjeP/99+Hj44N27drdUFFEREREoqmaSWrZsmWZBgkA2rRpg/feew9btmzBTz/95JLirsVut2PZsmWIiYlBnz59MHHiRJw8edLp8Tk5OXjzzTfRt29f9O3bF2+++SZyc3OdHi8ri8UiugQhmFsuzC0X5iY1VDVJXl5esNlsSE9Px44dO0q36/V6GI1GHDp0CPv27XNVjU4lJiZi8+bNeOutt7B+/XqEh4djypQpyM/Pd3j8zJkzcfHiRaxatQqrVq3CxYsXMXv2bLfXqTUJCQmiSxCCueXC3HJhblJD1UzShQsXsGTJEhw5cgRZWVlYt26d4pgtW7bg3XffxdatW11SqCODBg1C//79ERMTAwAoKipC//79MW7cODz00ENljrVYLBg0aBAWL15c+l1K6enpGD16NNasWYOQkJAyx3MmiYiISHuEzyTVrVsXU6ZMwZ9//glvb8dP0bt3b4SHh99QcRXJzc2FxWJBmzZtSrfpdDq0aNECx48fVzRJ6enp8PHxKfNlk2FhYfDx8UF6erqiSSIiIiK5Xdfttt9//x3vv/8+Dh8+DABo1KhRhc3FLbfccmPVVSAvLw8AEBgYWGZ7YGBg6b7yx5c/tqLjiYiISG7X1SStXLkSycnJmDt3bpntmzZtwty5c3Hu3DmXFleRgIAAAFAMXufm5pbuK3+8oyFtZ8eXGDBgAAwGAwwGA5KTk2EwGGC1Wkv3JyYmwmw2l/5ssVhgNBrLPIfJZEJKSkrpz2lpaYiPjy9zTHx8PNLS0kp/TklJgclkKnOM0WgsM4RnNpvLLBRmtVpdUt/rr79epetz1/v3wQcfVOn63PX+mUymKl0f4J73z2QyVen6APe8fyXHV9X6APe8fyaTqUrXB7jn/Sv5u6rWV+JG6zObzRgzZgwiIyNd+qW+1zWT9P7776Nr164oLi4uXQ+pRHZ2Nt5//30MGTIETZs2dVmBFRk0aBBiYmLQv39/AH/PJMXExGDs2LFOZ5KWLFmC5s2bAwBOnDiBUaNGcSapnJSUFHTu3Fl0GR7H3HJhbrkwtzyEfsHtLbfcomiQACAoKAgvvfQSPv300xsq6HpER0dj7dq1OHnyJAoKCrBs2TJ4e3ujW7duimNDQ0PRqVMnLFy4ENnZ2cjOzsbChQvRtWtXziOVI9svVAnmlgtzy4W5SY3rapKee+45LFiwAAsWLMC+ffsUH7X39/eHj4+PSwusSGxsLKKiovDiiy8iOjoaBw8eRHx8PPz9/ZGRkYE+ffrgwIEDpcfHxcWhdu3aGDx4MAYPHoygoCDFpUMiIiIi4Do/3fbNN9/g+++/h91uxxdffAFvb2+0aNECd911F1q3bo38/HxkZGS4q1YFLy8vjBgxAiNGjFDsCwkJwebNm8tsq127NqZPn+6p8jQrLS0NrVu3Fl2GxzG3XJhbLsxNalzXlaQdO3Zg9erV+OKLLzBr1iw8/vjjKCwsxJo1a/Daa69hyZIlGDVqlLtqJQ9JSkoSXYIQsuS22+1Yt24dou67D01DQvBg9+6YP3++dJ/ylOV8l8fccpE1t6tc9+D2Cy+8oNiek5ODvXv3YseOHRg9ejRuu+02lxYpgsyD21R92e12jB89GutWrsQLBQXoCuBXAO/r9fBt2RLb/vtfxVcOERFpibDBbZ1OhwsXLii216pVCz179sT06dOxevXqGyqIiNwnOTkZX65cib0FBTAC6A7gGQApVisCjh7Fa6+8IrhCIqKq47qapGHDhmHBggU4ePCgYt9HH32ETz/9FP7+/i4rjohca1FCAibYbLi13HY/AG8UFGDZkiUoLCwUURoRUZVzXU1SYGAgjEYjjh8/jm+++abMvn379uHjjz/mf2CrgfILgclChtzHjx5FpL3sHfaS1J0AZOXlITMz0+N1iSDD+XaEueUia25Xue7vbvP29sYTTzyh2D5nzhzs37/f4RpKpC3R0dGiSxBChtwhISFI//NPXL3UaknqdAC+3t4ICgoSUJnnyXC+HWFuucia21WuezFJZ4KCgtC9e3febqsGZP24qAy5h44diw/8/XH159haA7ADeMvbG08+8YQ0v8MynG9HmFsusuZ2FZc1SURU9T399NNo0LYtHvDzw1YAuQAOABjq7Q1zrVqYwUvzRESl2CSRwtVfVigTGXL7+fnhq2+/RS+DAU8HBaEWgI46HbyffBK7f/oJTZo0EV2ix8hwvh1hbrnImttV2CSRQmpqqugShJAld0BAAN6cNQtnMjORmZmJdxMSsGzVKqkaJECe810ec8tF1tyucl2LScqEi0kSERFpj7DFJImIiIhkwSaJiIiIyAE2SaRgNBpFlyAEc8uFueXC3KQGZ5KckHkmyWKxIDQ0VHQZHsfccmFuuTC3PDiTRG4l2y9UCeaWC3PLhblJDTZJRERERA6wSSIFs9ksugQhmFsuzC0X5iY12CSRQlZWlugShGBuuTC3XJib1ODgthMyD24TERFpFQe3iYiIiNyMTRIpWK1W0SUIwdxyYW65MDepwSaJFOLi4kSXIARzy4W55cLcpAZnkpyQeSbJarVCr9eLLsPjmFsuzC0X5pYHZ5LIrWT7hSrB3HJhbrkwN6nBJomIiIjIATZJpJCYmCi6BCGYWy7MLRfmJjXYJJFCcHCw6BKEYG65MLdcmJvU4OC2EzIPbrtTYWEhcnJyEBQUBJ1OJ7occjOebyLyNA5uk+acOXMGzz7zDIIDA1GvXj00CA7GlBdfRE5OjujSyA3OnDmDZ555FoGBwahXrx6CgxvgxRen8HwTkaawSSIFi8Xi0uc7c+YMurRvj6xVq7DLZkMOgC9yc7FnwQL0vOceXL582aWvp5arc2uFO853+/ZdsGpVFmy2XQBykJv7BRYs2IN77unJ8y0Yc8tF1tyuwiaJFBISElz6fDNefRUdL1xAYmEh2gMIBHA/gK0FBSg6fhyLFy926eup5ercWuHq3K++OgMXLnREYWEicNUZLyjYiuPHi3i+BWNuucia21U4k+QEZ5Jco6ioCMGBgdhmtaKTg/2fAHi3RQv8fOyYp0sjNygqKkJgYDCs1m2AkzPeosW7OHbsZ0+XRkSS4EwSaUZ+fj5yrVaEOdkfBuBcZqYnSyI3ys/Ph9WaC1RwxjMzz3myJCIi1dgkkVvVrFkToXXqYK+T/XsANG/WzJMlkRvVrFkTdeqEAhWc8WbNmnuyJCIi1dgkkYLJZHLZc3l5eeHZ8ePxb70eeeX2ZQB4V6/HmMmTXfZ6N8KVubXE1ed7/Phnodf/G3BwxvX6dzF58hiXvd6N4PmWC3OTGmySSCEiIsKlzzctLg76tm3R0d8fiwB8B+BtAB30etwfHY2BAwe69PXUcnVurXB17ri4aWjbVg9//47AVWdcr++A6Oj7eb4FY265yJrbVTi47QQHt12roKAAy5cvx/IFC5Bx9iyaNWuGZydNQkxMDGrUYK9e3ZSc7wULluPs2Qw0a9YMkyY9y/NNRG7nysFtzTZJ3333HZYuXYqMjAyEhoZi5MiRuO+++5wev3z5cnzyySfw9fUt3da1a1dMnz7d4fFskojIE+x2O3bs2IG9e/fC398f0dHRaNy4seiyiDRL+k+3HT58GDNnzsTIkSOxadMmjBgxAjNnzsTRo0crfNztt9+OzZs3l/5x1iDJLi0tTXQJQjC3XKpC7pMnT6JNm/bo3XsA/v3vn2A0bkKzZi0wevR4XLlyxS2vWRVyi8DcpIYmm6Tk5GR06tQJ3bt3h7e3N7p3747IyEgkJSWJLq1akPV9ZG65iM5dUFCA++57CCdOdIHN9ges1kTk5ZlRXJyGlSu3w2h0zz/iROcWhblJDU3ebhs9ejTuv/9+DB48uHTbypUrsXPnTixatMjhY5YvX47ExET4+flBr9fjjjvuwKhRo9CwYUOHx/N2GxG506pVqzB69BvIzz8C5b9X98HP7wGcPfsn//tDdJ1cebvN20U1ucScOXNgNpud7o+IiMC8efOQl5eHwMDAMvtq1apV4XdCde/eHb1790ZISAjOnz8Pk8mEl156CUuWLIG/v7/LMhARVcamTV8jPz8Wji/od0SNGg2we/duREVFebo0IvpHlbrdNnHiRKxfv97pnzfffBMAEBAQgNzc3DKPzcnJqbBjbNq0KUJDQ+Hl5YX69etjypQpOHfuHA4dOlRhTQMGDIDBYIDBYEBycjIMBgOsVmvp/sTExDKNncVigdFoLPMcJpMJKSkppT+npaUhPj6+zDHx8fFl7h2npKQo1rcwGo1lvqzQbDYjMTGx9Ger1cr6WB/r00h9f/31J4BfrjrCCsDwz99/++677/j+sT7WV4n6zGYzxowZg8jISMTFxcFVNHm7LT4+HpcvX8Ybb7xRuu3VV19FYGAgpkyZUqnnKCwsRN++fTFjxgxERkYq9st8uy0+Ph5Tp04VXYbHMbdcROcWdbtNdG5RmFse0n+6rV+/fkhJScGuXbtw5coV7Nq1C3v27MGjjz7q9DHbt29HdnY2AODChQuYO3cu6tSpg/DwcE+VrRnR0dGiSxCCueUiOndMTAzq1SuGt/cEXH31CPgVev1QPP/8BLf8A010blGYm9TQ5JUkANixYwc++ugjWCyW0nWSunfvXrp/+PDh6NWrF4YMGQIAePnll/HLL7/AarWiVq1aaNu2LUaMGIFGjRo5fH6ZryQRkWf89ttv6N37cfz222l4efVEjRpZsFq3Y8SI0fjPfxLg7V2lxkaJNIGLSXoAmyQi8gS73Y7vvvsOe/bsQUBAAB599FEuJkl0A6S/3UbudfUQnkyYWy5VJbeXlxfuv/9+TJ06Fc8//7zbG6SqktvTmJvUYJNECqmpqaJLEIK55cLccmFuUoO325zg7TYiIiLt4e02IiIiIjdjk0RERETkAJskUii/oqosmFsuzC0X5iY1OJPkhMwzSSVrT8mGueXC3HJhbnlwJoncSrZfqBLMLRfmlgtzkxpskoiIiIgcYJNECld/67NMmFsuzC0X5iY12CSRQlZWlugShGBuuTC3XJib1ODgthMyD24TERFpFQe3iYiIiNyMTRIpWK1W0SUIwdxyYW65MDepwSaJFOLi4kSXIARzy4W55cLcpAZnkpyQeSbJarVCr9eLLsPjmFsuzC0X5pYHZ5LIrWT7hSrB3HJhbrkwN6nBJomIiIjIATZJpJCYmCi6BCGYWy7MLRfmJjW8RRdAVU9wcLDoEoRgbrkwt2v98MMPWLJkOU6ftqBNm+Z49tmRaNmypVteSw2eb1KDg9tOyDy4TURUWXa7Hc899zyWLfsYdvtTuHKlJXx9f0BR0Tq89dYcGAyTRJdIknHl4DavJBERkWqLFi3CihXJKCz8BcBtAACbDQB+hNH4ANq1i0CPHj1ElkikGmeSSMFisYguQQjmlgtz3zi73Y7ZsxNgtc5ASYP0/+5GYeEEvPXW+y57vRvB801qsEkihYSEBNElCMHccmHuG5eXl4fffz8CoI/D/Xb7w9i37weXvd6N4PkmNTiT5ARnkoiIKlZYWAi93h/FxYcAtHZwxAbccsu/cPr0UU+XRhLjYpJERCScj48P+vR5DDVqLHKw1w4/PxOGDInxeF1ErsImiYiIVJs5czp8fBYDmAMg95+t56DTvYCaNX/GxInPC6yO6MawSSIFk8kkugQhmFsuzO0aERER2L59K1q3Xgtv71DUrNkKOt2tiIw8jD17diI0NNSlr6cWzzepwSUASCEiIkJ0CUIwt1yY23W6dOmCw4d/xKFDh5CRkYEmTZogLCzM5a9zI3i+SQ0ObjvBwW0iIiLt4eA2ERERkZuxSSKFtLQ00SUIwdxyYW65MDepwSaJFJKSkkSXIARzy4W55cLcpAZnkpzgTBIREZH2cCaJiIiIyM3YJBERERE5wCaJFOLj40WXIARzy4W55cLcpAabJFKIjo4WXYIQzC0X5pYLc5MamlxxOz09HYsXL8bx48dx8eJFvP3227j77rsrfIzdbsfy5cuxadMmXL58GS1btsSkSZPQtGlTD1WtHa1bO/o27+qPueXC3HJhblJDk1eSfHx80K1bN8yePbvSj0lMTMTmzZvx1ltvYf369QgPD8eUKVOQn5/vxkqJiIhIqzTZJDVu3Bh9+/ZFq1atKv2YpKQkPPnkk2jWrBn8/PwwYsQIFBYWYteuXW6sVJtSUlJElyAEc8uFueXC3KSGJpuk65WbmwuLxYI2bdqUbtPpdGjRogWOHz8usLKqKTU1VXQJQjC3XJhbLsxNalSpmaQ5c+bAbDY73R8REYF58+Zd9/Pm5eUBAAIDA8tsDwwMLN1H/2/MmDGiSxCCueXC3HJhblKjSl1JmjhxItavX+/0z5tvvqnqeQMCAgD8fUXparm5uaX7nBkwYAAMBgMMBgOSk5NhMBhgtVpL9ycmJpZp7CwWC4xGY5nnMJlMZS55pqWlKT6WGR8fX+Y7dlJSUmAymcocYzQaYbFYSn82m81ITEws/dlqtbI+1sf6WB/rY33S1Wc2mzFmzBhERkYiLi4OrqL5ryXp0aNHpT7dNmjQIMTExKB///4AgKKiIsTExGDs2LF46KGHFMfza0mIiIi0R/qvJbHb7bDZbLDZbACAK1euwGazoaioyOljoqOjsXbtWpw8eRIFBQVYtmwZvL290a1bN0+VrRnl/6UgC+aWC3PLhblJDU1eSbJYLBg0aJBi+7BhwzB8+HAAwPDhw9GrVy8MGTIEwN+N1bJly7Bx40bk5eWhVatWmDhxIpo1a+bwNWS+kmSxWBAaGiq6DI9jbrkwt1yYWx6uvJKkySbJE2RukoiIiLRK+tttRKKkp6dj3LgXcMstrdCoUQuMGjUWR44cEV0WERG5AZskUqhoGYbq7Fq5d+3ahTvvbI+lSy/gzz/fw5kz87FiRQHuuqsjtm7d6qEqXY/nWy7MLRdZc7tKlVoniaqGrKws0SUIUVHuK1eu4IknnoLVOgvAhNLthYW9AXRHTMxTyMg4DX9/f/cX6mI833JhbrnImttVOJPkBGeS6GobNmzAwIEvID//BABdub12+PvfgSVLXsFTTz0lojwiIvoHZ5KIPCw9PR1ABygbJADwwpUrkf8cQ0RE1QWbJFK4ekVTmVSUu0GDBvDySgfg+MKrj086GjRo4KbK3IvnWy7MLRdZc7sKmyRScOWS7lpSUe7HHnsMxcW/AnA0oP09Cgt/xIABA9xWmzvxfMuFueUia25X4UySEzLPJFmtVuj1etFleNy1ci9d+hHGjp2EwsLXATyFv2+9JcLX9xW89dbrmDjxBU+V6lI833JhbrnImJszSeRWsv1ClbhW7pEjR2Dduk/Rrt0XAEIB1Mcdd3yMTz9dqtkGCeD5lg1zy0XW3K7CJQBItby8POzbtw/FxcXo2LEjAgMDRZfkdo888ggeeeQR5OTkwG63S3eVkYhIJrySRAqJiYkV7i8uLsaMf/8bjerXx5A+fTD8kUdwc/36eHnq1Aq/ZLiqu1buq9WqVavaNEjXk7s6YW65MDepwStJpBAcHFzh/qkGA740mbDBasW9/2zbC+CZ99/HhfPn8Z+lS91eoztcK3d1xdxyYW65yJrbVTi47YTMg9sVsVgsaHzLLfi5qAi3l9v3G4BWOh3Sjh9H06ZNBVRHRESy4+A2CbNhwwZ09vNTNEgA0ARAL19ffPnllx6uioiIyPXYJJGCxWJxuu/y5cuoZ3d+8bFeURHy8vLcUZbbVZS7OmNuuTC3XGTN7SpskkghISHB6b6OHTtiR1ERHLVBNgBfe3mhQ4cObqvNnSrKXZ0xt1yYWy6y5nYVziQ5wZkkx+x2OzrccQcijx/HgitXSrtsO4ApNWog+dZbcfjXX1GjBvtvIiLyPFfOJPHTbXRdvLy88MVXX+HBbt0QnpmJgfn50AFY6++PrNq1sdVsZoNERETVApskum5NmjTBwePHsXbtWmxJSoK9uBjPP/IIBg0adMNdOxERUVXBf/KTgslkuuYxer0eQ4cOxeovvsCn69Zh1KhRmm+QKpO7OmJubSkuLsZXX32FwYOfQd++AzB79hycPXu20o/Xau4bxdykBpskUoiIiBBdghDMLRct5r58+TK6dXsQTzwxEp9+2gCbNkVixoxv0Lhxc5jN5ko9hxZzuwJzkxoc3HaCg9tEVNUMH/4s1qw5hoKCTQCuvnK7Gn5+Y/Dbb8cRGhoqqjyiKoGLSRIRSebChQtYvfoTFBR8gLINEgA8BS+ve7B48RIRpRFVW2ySSCEtLU10CUIwt1y0lvvQoUPw9q4PINzhfqv1Yeza9cM1n0druV2FuUkNNkmkkJSUJLoEIZhbLlrLXbNmTVy5cglAoZMjMlGrVsA1n0druV2FuUkNziQ5wZkkIqpKiouL0ahRGCyWGQAGl9trhV7fGqtXv4fHH39cRHlEVQZnkoiIJFOjRg28994s+PiMA7AGwJV/9qTDz+9xtG7dEP369RNYIVH1wyaJiEgjBg4ciI8/XogGDabBzy8UAQEtoNPdgUcfvQk7dmyBtzfXByZyJTZJpBAfHy+6BCGYWy5azT1o0CCcOXMCO3ZsxIYNC/Hnn6ewdu0nCAoKqtTjtZr7RjE3qcF/dpBCdHS06BKEYG65aDm3TqdD586dVT1Wy7lvBHOTGrySRAqtW7cWXYIQzC0X5pYLc5MabJKIiIiIHGCTRAopKSmiSxCCueXC3HJhblKDTRIppKamii5BCOaWC3PLhblJDS4m6QQXkyQiItIeLiZJRERE5GZskoiIiIgcYJNECkajUXQJQjC3XJhbLsxNamhyJik9PR2LFy/GOZnJMQAAE5xJREFU8ePHcfHiRbz99tu4++67K3zM8uXL8cknn8DX17d0W9euXTF9+nSHx8s8k2SxWBAaGiq6DI+TKbfNZsPGjRtx9OhR+Pr6YsSIEahTp47osjxKpvN9Neau2MGDB7F161bY7Xb07NkT7dq180B17iPj+XblTJImV9z28fFBt27dMGLECDz33HOVftztt9+O+fPnu7Gy6kG2X6gSsuTetWsXHnssFvn5/igu7gSd7iSMxul4++14vPDC86LL8xhZznd5zO1YTk4OYmKG4JtvtsLXNwp2ew0Yja+ha9d7sX79Gs3+I0LW8+0qmmySGjdujMaNG4sug0hzfv31Vzz00COwWucAeA7/f8f9v/jXv/qhYcNQDBgwQGCFRGLExg7Dd9/loKjoD+Tn1/tnaxb27BmMfv2exH//+7XQ+kgMqWaS0tPT8dhjj2HgwIGYMWMG/vrrL9ElVUlms1l0CULIkHvevA9QXPwIgHH4/19/M4B7YbPNxvTps2G3a+4OvCoynG9HmFvpyJEj2Lr1KxQUrAFQ76o9wSgoWI09e3bjhx9+cHuN7iDr+XaVKnUlac6cORWe0IiICMybN0/Vc3fv3h29e/dGSEgIzp8/D5PJhJdeeglLliyBv7+/2pKrpaysLNElCCFD7o0bv4bN9ma5rSW5B+Lo0bG4cOEC6tWrV/6h1Y4M59sR5lbatm0b/Px6Ii+vgYO9QdDpHsHWrVvRoUMH9xXoJrKeb1epUleSJk6ciPXr1zv98+ab5f/jXnlNmzZFaGgovLy8UL9+fUyZMgXnzp3DoUOHKnzcgAEDYDAYYDAYkJycDIPBAKvVWro/MTGxTGNnsVgUnyYwmUxlloZPS0tDfHx8mWPi4+ORlpZW+nNKSgpMJlOZY4xGIywWS+nPZrMZiYmJpT9brVaX1BcREVGl63PX+xcdHV2l63PV+wf8AeDq+mL/+flYlajPU+9fbGxsla4PcM/7FxsbW6XrA9zz/sXGxjqt7+TJk1dtSUPZ3w/gypUjOHfunFvrA9zz/sXGxlbp+krcaH1msxljxoxBZGQk4uLi4Cqa/HTb1Xr06FGpT7eVV1hYiL59+2LGjBmIjIxU7Jf5021UfU2caMDChX/BZvvUwd6FaN16MQ4f/gFeXl4er41IlLS0NISH34WiolMAyl9Nyoa3dyOkpHx33f+fITGkX3HbbrfDZrPBZrMBAK5cuQKbzYaioiKnj9m+fTuys7MBABcuXMDcuXNRp04dhIeHe6RmLbm6U5eJDLknTpyAGjU2AVgAoPifrVYAu+Dra8Qbb0yTpkGS4Xw7wtxKrVu3xkMPPQw/v4EAMq/akwU/v6fQuXMXzTZIsp5vV9Fkk5SRkYGoqChERUUBAKZNm4aoqCh88sknpccMHz4cK1euLP1527ZtGDZsGHr37o0xY8agqKgI77zzDgICAjxef1XnykuVWiJD7mbNmmHr1k2oW3cm/P1bQK9/Ct7eTeHjE4W5c9+Q6pNtMpxvR5jbscTEj3H//bWh090Cf/9o6PVPwNu7ETp3LsKGDWs9VKXryXq+XUXzt9vcRebbbVarFXq9XnQZHidT7sLCQiQnJ+PYsWMIDg5GbGysZteBUUum83015q7YoUOHYDabq81ikjKeb+kXkyT3ku0XqoRMuX18fPDEE0+ILkMomc731Zi7YuHh4dVqDEPW8+0qmrzdRkRERORubJJI4eqPXcqEueXC3HJhblKDTRIpBAcHiy5BCOaWC3PLhblJDQ5uOyHz4DYREZFWSb9OEhEREZG7sUkihauXhpcJc8uFueXC3KQGmyRSSEhIEF2CEMwtF+aWC3OTGpxJcoIzSURERNrDmSQiIiIiN2OTREREROQAmyRSMJlMoksQgrnlwtxyYW5Sg00SKURERIguQQjmlgtzy4W5SQ0ObjvBwW0iIiLt4eA2ERERkZuxSSKFtLQ00SUIwdxyYW65MDepwSaJFJKSkkSXIARzy4W55cLcpAZnkpzgTBIREZH2cCaJiIiIyM3YJBERERE5wCaJFOLj40WXIARzy4W55cLcpAabJFKIjo4WXYIQzC0X5pYLc5MabJJIoXXr1qJLEIK55cLccmFuUoNNEhEREZEDbJJIISUlRXQJQjC3XJhbLsxNarBJIoXU1FTRJQjB3HJhbrkwN6nBxSSd4GKSRERE2sPFJImIiIjcjE0SERERkQNskkjBaDSKLkEI5pYLc8uFuUkNziQ5IfNMksViQWhoqOgyPI655cLccmFueXAmidxKtl+oEswtF+aWC3OTGmySiIiIiBxgk0QKZrNZdAlCMLdcmFsuzE1qsEkihaysLNElCMHccmFuuTA3qcHBbSdkHtwmIiLSKg5uExEREbkZmyRSsFqtoksQgrnlwtxyYW5SQ5NNktlsxoQJE/Doo48iOjoakyZNwsGDB6/5uHXr1mHgwIHo3bs3nn32WX7xnxNxcXGiSxCCueXC3HJhblJDk01SXl4ehg4dijVr1uCLL77Avffei6lTp+LcuXNOH7Njxw4sXboU06ZNQ3JyMvr06YNp06bh7NmzHqxcG3r06CG6BCGYWy7MLRfmJjU02SQ9/n/t3W1sU+X7B/BvWbux2boow3aKm2DnQGFbYuwMYw55SIYBCwkxbJI5NwkpM9mDOCJEDZqpUxSmyTJwOtDwAnzhBs7NYKhmTjeJ0WFHCrQuAQmtMZQ9ta5d198LXf/0v9PRdg9tz76fhITdvU97Xb1O22vndPfZsgUajQYJCQmQSqXYunUr5s2bB6PR6HeblpYWbNiwAVlZWZDJZNiyZQsWLVqE9vb2WYw8Ouj1+nCHEBbMe25h3nML86ZQRGWT9P9duHABDocDDz74oN85JpMJS5cu9RlLT0+HyWSa6fCIiIgoCknDHcCt3nnnnUkXvsrMzMShQ4d8xv766y+88cYbKCwsxL333ut3W7vdDrlc7jOmUChw/fp1wfkez78rIwwMDAQavmj09vYy7zmEec8tzHtumYt5j+c7/jk+FRHVJJWXl0On0/m9PSYmxufna9euYffu3Vi9ejVKS0snve+EhAQMDQ35jA0ODvpdQ8HhcAAA7r///kBCF53ExMRwhxAWzHtuYd5zC/OeWxwOx4SDI8GKqCYpPj4e8fHxAc01m82orq6GVqtFUVHRbeer1WoYjUasXbvWO3bp0iWsWrVKcP6CBQtw8uRJxMfHQyKRBJYAERERhZXH44HD4cCCBQumfF8R1SQFymAwYO/evSgqKsLWrVsD2kar1eLAgQPIzc3FsmXL8PXXX+Pq1avIz88XnD9v3jwsXLhwOsMmIiKiWTDVI0jjovKyJJWVlejp6UFcXJzP+LPPPovt27cDAPbs2QOlUomqqirv7V9++SVOnDgBm82G1NRU7Nq1C1lZWbMaOxEREUWHqGySiIiIiGaaKJYAICIiIppuUfmdpJnwzTff4PTp07hy5QokEgkWL16M0tJSrFixYtLtxk/h3bx5EykpKSgrK0NmZuYsRT11JpMJH3/8MS5fvgybzYYDBw7g0UcfnXSbo0eP4vPPP0dsbKx3bOXKlXj11VdnOtxpE0reHo8HR48eRWtrK4aHh/HQQw+hoqICixcvnqWop8f333+PTz75BFarFSqVCqWlpXjiiSf8zo/Gegdbq8HBQdTV1aGrqwsA8Pjjj6OiomLavtcwW4LNu6KiAr29vZBK/++jYOfOndi8efNshTxlZ8+eRXNzM8xmM+x2O7799tsJfwl9K7HUOti8xVBrADhy5Ai6urpgtVoxf/58ZGVlYefOnbjnnnv8buN0OlFfXw+9Xg+Xy4XMzExUVlZOus04Hkn6z1y91IlMJkNubi7efvvtoLZ7+OGH0dbW5v0XyR+YQkLJ+8SJE2hra8O7776L5uZmLF++HNXV1d7lIqLBhQsXUFNTg9LSUrS2tqKkpAQ1NTW4ePHipNtFW72DrVVNTQ1sNhuOHz+O48ePw2azBf2aiASh7KPbtm3zqW20fWjK5XJotVqUlZUFNF8stQ42byD6aw0AEokEe/bsQXNzM44dOwbg9tenq6+vx++//47Dhw/jiy++gEKhwL59+zA2Nnbbx2OT9J+5eqmT1NRUbNy4Eenp6eEOZVaFkndLSwueeeYZLFmyBHFxcSgpKYHL5UJHR8cMRjq9Tp8+jezsbOTl5UEqlSIvLw8ajQYtLS3hDm1aBVMri8WC7u5u6HQ6JCYmIjExETqdDj/++COsVmsYog+dGPbRYGk0Gqxdu3bSxYTHianWweQtJjt27EB6ejpkMhnkcjkKCgpgNpsxODgoON/pdKK9vR3PP/88VCoV7rjjDpSVlaGvrw8Gg+G2j8cmyQ9e6mRyJpMJmzdvxrZt2/Dmm2/6XblcLIaGhmCxWLBs2TLvWExMDNLS0nD58uUwRhacUPfZaKp3sLUymUyQyWRQq9XeMbVaDZlMFlWv5VD30VOnTmHTpk0oKirCkSNHourIaLDEUutQibHW586dg1KphEKhELz9ypUrGBkZ8XldJCYmIjk5OaD3btF/JymSLnUym0LJO1B5eXnIz8+HUqnE33//jcOHD2P37t1obGwMeDHQmTJTedvtdgAT196Qy+Xe28Ip0Lz97bPDw8N+t43kegsJtlZCz8lk8yNVKPvoCy+8gJSUFMjlcvzxxx+ora3F9evX8frrr894vOEgllqHQoy1/uWXX/DZZ59h//79fudM9b1b9E1SJF3qZDYFm3cwbv0S6MKFC1FdXY2NGzfCYDDgscceC/l+p8NM5Z2QkAAAE+o9NDSEpKSkkO5zOgWadyj7bCTXW0iwtRJ6Tsbnj99XNAhlH12+fLn3/2q1GmVlZXjppZcwMjIyYR06MRBLrUMhtlr/9NNPqKmpwd69e6HRaPzOu/V1cWuegdZc9E1SJF3qZDYFk/dUSSQSSCSSabmY4FTNVN5yuRwqlQpGoxGPPPIIAMDtdsNkMmH9+vXT/njBCjRvtVo94Uvaly5d8jn9cDuRVG8hwdZKrVbD5XLBbDZ7T6+bzWa4XK6gnpdwm459dPwSTJFa26kSS62nQzTX+syZM6irq8Nrr702aYMEACkpKYiLi4PRaEROTg4AoL+/HxaLBWlpabd9LH4n6T8GgwGVlZUoKCgIqEEC/r3USVtbG86fPw+Xy4WWlpZJL3USiTweD5xOJ5xOJwBgdHQUTqcTbrfb7zZ6vR79/f0AgBs3buC9997DXXfd5fObSqQLJW+tVouTJ0+ir68PIyMjaGpqglQqRW5u7myFPWWbNm1CV1cXOjo6MDo6io6ODnR3d+Ppp5/2u0001juYWqlUKmRnZ6OhoQH9/f3o7+9HQ0MDVq5cCaVSGYboQxdM3jdu3MDPP/8Mh8MBj8eDvr4+1NfXIycnB/Pnzw9D9KFxu91wOp1wuVwA4H1dC/3lkphqHUzeYqk18O+yOx9++CHeeuut2zZIABAbG4v8/Hw0NTXBarXCbrejvr4eqampAb2HccXt/8zVS51YLBYUFBRMGH/uuedQXFwMACguLsa6deu8z8O+ffvQ29uLf/75BwqFAhkZGSgpKcF99903m6FPSSh5ezweNDU14auvvoLdbkd6ejrKy8uxZMmS2Qx9yr777jt8+umnsFgs3nWS8vLyvLeLod6T1cpqtaK4uBi1tbXIyMgAAAwMDKCurg7d3d0AonftnGDytlgs2L9/P65evQq32427774bubm5KCoqiqpTT+3t7aitrZ0wfvDgQSQnJ4u21sHkLZZaA8CTTz6JmJgYyGQyn/Fba7xhwwZUVVV5j6Deuk6S0+lEZmYmqqqqAloniU0SERERkQCebiMiIiISwCaJiIiISACbJCIiIiIBbJKIiIiIBLBJIiIiIhLAJomIiIhIAJskIiIiIgFskoiIiIgEsEkiIiIiEsAmiYiIiEgAmyQiIiIiAWySiIiIiARIwx0AEdFMGBwcxLFjx+B2u3Ht2jWsXr0a69atQ0NDAzweDwYHB7F9+3Y88MAD4Q6ViCIUmyQiEh2Xy4VDhw5Bp9MhKSkJFosFhYWF6OzsxIsvvog///wTr7zyChQKBcrLy8MdLhFFKJ5uIyLROXXqFLRaLZKSkgAAsbGx8Hg8UKlUSE5OxtjYGBYtWoQ1a9Z4t/F4PDhz5gwOHjwYrrCJKMLwSBIRic6dd96JjIwM788XL14EAGg0GgBAdnY2srOzvbefPXsWRqMR58+f5+k3IvLikSQiEp3169f7/Pzbb78hJiYGK1asEJy/Zs0a7Nq1iw0SEflgk0REovfrr78iLS0NCQkJ4Q6FiKIImyQiErWBgQGYzWZkZWX5jLe2toYpIiKKFmySiEhUbt68CZ1Oh8bGRgDAuXPnMDY2hqVLl/rMMRgM4QqRiKIEmyQiEpWenh4YjUZIpVKMjIxAr9cjKSkJDocDAOBwOPDRRx+huLg4vIESUcTjX7cRkahoNBo89dRTsNlseP/997Fjxw4MDw+jsbERPT09GB0dRWFhIZRKZbhDJaIIxyaJiEQlPj4eL7/88oTxDz74IAzREFE04+k2IiIiIgE8kkREc94PP/yAzs5OdHZ2wuPxoLa2Fjk5OVi1alW4QyOiMJLo9XpPuIMgIiIiijQ83UZEREQkgE0SERERkQA2SUREREQC2CQRERERCWCTRERERCSATRIRERGRADZJRERERALYJBEREREJYJNEREREJOB/nT0WGPcv3SMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JvpNQqRXWNkS",
        "colab_type": "text"
      },
      "source": [
        "In this plot, each point represents a example in our toy dataset. Also, we use colors blue and red to represent the class of each example.\n",
        "\n",
        "The above example is for a 2-dimensional dataset so that we can visualize them. Nevertheless, this geometric interpretation can also be used for high dimensional datasets."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IPOf31zBjY7l",
        "colab_type": "text"
      },
      "source": [
        "The geometric interpretation is useful because we can view the distance between two points as a kind of similarity measure between the corresponding examples: the closer the two points are, the more similar they are. \n",
        "\n",
        "The image below (source) illustrates this concept in the simple case of 2-dimensional points. But you should convince yourself that this interpretation of *distances as similarities* can be extended to $n$-dimensional examples $\\mathbf{x} = [x_0, x_1, x_2, \\cdots, x_n]$, $n > 2$. \n",
        "\n",
        "![Source: Wikipedia](http://chrisjmccormick.files.wordpress.com/2013/08/2d_euclidean_distance_illustration.png)\n",
        "\n",
        "In the particular case of a binary classification task, consider that points $A$ and $B$ belong to the positive and negative classes, respectively. Then, if an unclassified point $C$ is closer to point $B$ than to point $A$, we would expect $C$ to belong to the negative class.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bzlmRPUUDaws",
        "colab_type": "text"
      },
      "source": [
        "The following code cell presents a heatmap, which is a graphical way to inspect distance matrix. In general, a distance matrix shows the pairwise distances between points in a dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m_GjdgiE2_4P",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "outputId": "a952ca4a-bc0e-4949-d3c6-bd93c492c0f6"
      },
      "source": [
        "from scipy.spatial import distance_matrix\n",
        "import seaborn as sns\n",
        "import matplotlib.pylab as plt\n",
        "\n",
        "dists = distance_matrix(X, X)\n",
        "\n",
        "ax = sns.heatmap(dists, linewidth=0.5)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WUKl4DdEAy5V",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        },
        "outputId": "9bb1e09d-959a-4e8d-ff9f-13e292a44498"
      },
      "source": [
        "print(dists)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.    1.552 1.487 1.118 1.72  1.237 1.811 2.341 3.138 1.03  2.927 2.163\n",
            "  2.907 2.625 2.746 0.854 1.942]\n",
            " [1.552 0.    2.059 0.51  1.118 0.762 0.361 1.389 2.126 1.118 1.4   0.854\n",
            "  1.421 1.077 1.5   0.707 0.894]\n",
            " [1.487 2.059 0.    1.965 2.844 1.304 2.062 1.803 2.408 2.3   3.    2.907\n",
            "  3.421 2.973 2.377 1.726 1.72 ]\n",
            " [1.118 0.51  1.965 0.    0.9   0.825 0.854 1.769 2.55  0.64  1.903 1.063\n",
            "  1.789 1.53  1.972 0.283 1.273]\n",
            " [1.72  1.118 2.844 0.9   0.    1.712 1.442 2.506 3.22  0.707 2.147 0.825\n",
            "  1.603 1.616 2.55  1.118 2.012]\n",
            " [1.237 0.762 1.304 0.825 1.712 0.    0.781 1.118 1.924 1.389 1.838 1.616\n",
            "  2.126 1.703 1.513 0.721 0.707]\n",
            " [1.811 0.361 2.062 0.854 1.442 0.781 0.    1.077 1.78  1.476 1.118 1.\n",
            "  1.36  0.922 1.14  1.005 0.608]\n",
            " [2.341 1.389 1.803 1.769 2.506 1.118 1.077 0.    0.806 2.404 1.389 2.04\n",
            "  2.138 1.628 0.583 1.78  0.5  ]\n",
            " [3.138 2.126 2.408 2.55  3.22  1.924 1.78  0.806 0.    3.189 1.6   2.64\n",
            "  2.518 2.04  0.728 2.581 1.281]\n",
            " [1.03  1.118 2.3   0.64  0.707 1.389 1.476 2.404 3.189 0.    2.452 1.334\n",
            "  2.138 2.002 2.608 0.671 1.91 ]\n",
            " [2.927 1.4   3.    1.903 2.147 1.838 1.118 1.389 1.6   2.452 0.    1.36\n",
            "  0.949 0.566 0.922 2.102 1.281]\n",
            " [2.163 0.854 2.907 1.063 0.825 1.616 1.    2.04  2.64  1.334 1.36  0.\n",
            "  0.806 0.806 1.924 1.345 1.603]\n",
            " [2.907 1.421 3.421 1.789 1.603 2.126 1.36  2.138 2.518 2.138 0.949 0.806\n",
            "  0.    0.51  1.803 2.059 1.838]\n",
            " [2.625 1.077 2.973 1.53  1.616 1.703 0.922 1.628 2.04  2.002 0.566 0.806\n",
            "  0.51  0.    1.315 1.772 1.342]\n",
            " [2.746 1.5   2.377 1.972 2.55  1.513 1.14  0.583 0.728 2.608 0.922 1.924\n",
            "  1.803 1.315 0.    2.062 0.806]\n",
            " [0.854 0.707 1.726 0.283 1.118 0.721 1.005 1.78  2.581 0.671 2.102 1.345\n",
            "  2.059 1.772 2.062 0.    1.304]\n",
            " [1.942 0.894 1.72  1.273 2.012 0.707 0.608 0.5   1.281 1.91  1.281 1.603\n",
            "  1.838 1.342 0.806 1.304 0.   ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sj5AiUauBJYs",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "a79000ce-111c-43ad-c51c-c3fa9996bc6c"
      },
      "source": [
        "print(X[3,:])\n",
        "print(X[15,:])\n",
        "print(np.sqrt(np.square(X[3,0]-X[15,0]) + np.square(X[3,1]-X[15,1])))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-0.6  0.4]\n",
            "[-0.4  0.6]\n",
            "0.28284271247461895\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jh3MKB2R3FVB",
        "colab_type": "text"
      },
      "source": [
        "# Logistic Regression\n",
        "\n",
        "The predictive model that the logistic regression algorithm learns corresponds to a vector of coefficients $\\Theta \\in \\Re^{n + 1}$, that is:\n",
        "\n",
        "$$\n",
        "\\Theta =  [\\theta_0, \\theta_1, \\theta_2, \\cdots, \\theta_n]\n",
        "$$\n",
        "\n",
        "Consider a binary classification task (i.e., the target can only assume two values, 0 or 1). A logistic regression model for this task would predict the most likely class for an instance $\\mathbf{x} = [x_0, x_1, x_2, \\cdots, x_n]$ by doing the following:\n",
        "\n",
        "1. Compute $z = \\Theta^T \\cdot \\mathbf{x}$, i.e., $z \\in \\Re$ is the dot product between the vectors $\\Theta$ and $\\mathbf{x}$. Notice that $z$ is just a weighted sum: $\\theta_0 + \\theta_1 \\times x_1 + \\theta_2 \\times x_2 + \\cdots  + \\theta_n \\times x_n$.\n",
        "2. Compute $\\sigma(z)$, the logistic function.\n",
        "3. If $\\sigma(z) < 0.5$, then predict class($\\mathbf{x}$) = 0; otherwise predict class($\\mathbf{x}$) = 1.\n",
        "\n",
        "## Probabilistic classifiers\n",
        "Logistic regression builds a probabilistic classifier, i.e., it is a classification algorithm that produces probabilistic models. This means that this algorithm produces a distribution of probabilities on the possible values ​​of the target feature. In the case of binary classification, the result of the function $\\sigma(\\Theta^T \\cdot \\mathbf{x})$ is interpreted as the probability that the example $\\mathbf{x}$ belongs to the positive class, which, by convention, corresponds to 1.\n",
        "\n",
        "$\\sigma$ is known as the *sigmoid function* (aka *logistic function*). Its mathematical expression is as follows:\n",
        "\n",
        "$$\n",
        "\\sigma(z) = \\frac{1}{e^{-z} + 1}\n",
        "$$\n",
        "\n",
        "The code cell below shows a part of the graph of the logistic function.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SCr01vHvO2_v",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "outputId": "d5e68ab0-8aa6-481c-c3ce-0717b2040f58"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "sigmoid = lambda x: 1/(1+np.exp(-x))\n",
        "\n",
        "def plot_sigmoid():\n",
        "  plt.grid()\n",
        "  plt.xlim([-10.0, 10.0])\n",
        "  plt.ylim([-0.1, 1.1])\n",
        "  xs = np.arange(-10, 10, 0.001)\n",
        "  plt.xlabel('$z$', size=10)\n",
        "  plt.ylabel('$\\sigma(z)$', size=10)\n",
        "  plt.title('Sigmoid function', size=10)\n",
        "  plt.plot(xs, sigmoid(xs), label=r'$\\sigma(z)= \\frac{1}{1+e^{-z}}$')\n",
        "  plt.legend(loc='lower right', fontsize=15)\n",
        "\n",
        "plot_sigmoid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEUCAYAAAAFnmACAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXxU9b3/8dcnGwn7vhhAQHZQ2QQq1oJii9alFlvBC3Vr+dXftbX1ut3be61Xvf2Jvff21qW1XrXaPnBBUIuUilXBHWWTfYuAkrDvJJCQTD6/P2aAISYkJDNzZpL38/GYx8yc851z3jk5mU++ZzV3R0RE5HSlBR1ARERSkwqIiIjUigqIiIjUigqIiIjUigqIiIjUigqIiIjUigqIpBwz+4WZrTKz5Wb2mZmNiAx/ysz6x3nec8ysZSXD7zOzOyoZ3s7MPjGzpWb29RjmuMHMzoh6H/efXaSijKADiJwOM/sacDkwxN1LzKwtkAXg7j+M9/zd/bLT/MjFwIo4ZLsBWAlsjeSK+88uUpF6IJJqOgG73b0EwN13u/tWADObb2bDIq9vNrP1Zvapmf2vmT0WGf6smf3ezBaY2UYzG21mz5jZGjN79thMzGyima0ws5VmNjVq+OZI0TrWE1pvZh8AfSoGNbNBwMPAVZGeUo6ZFUaNv+bYPCO5HjGzjyK5rolqd3ckyzIzeygybhgwLWq60T97VdkLzew/ItNZYGYd6vrLkIZNBURSzZtAl8gX9+/M7BsVG0Q27fwbMBIYBfSt0KQV8DXg58As4DfAAOBsMxsU+fxU4CJgEHCemX2nwjyGAhMi4y8DzquYw90/A+4FXnL3Qe5+pJqfrRNwAeEe1kOR+VwKXAWMcPdzgYfdfQawCPiHitOtJnsTYEFkOu8BP6omj8gpqYBISnH3QmAoMAXYBbxkZjdUaDYceNfd97p7KfByhfGve/gaPiuAHe6+wt3LgVVAN8LFYL6773L3MmAacGGFaXwdeNXdD7v7QcKFqK5ec/dyd18NHOsdjAX+6O6HAdx9bzXTOFX2o8DsyOvFhH9WkVrTPhBJOe4eAuYD881sBXA98OxpTKIk8lwe9frY+wygtO4pqxR98bnsKnIBWBzmXeonLn4XQn//UkfqgUhKMbM+ZtYratAg4IsKzRYC3zCzVmaWAYw/zdl8Gvl8WzNLByYC71Zo8x7wncj+h2bAFTWc9g4z62dmacDVNWj/d+BGM2sMYGatI8MPAc1qmV0kJvQfiKSapsCjkUNpy4A8wpuzjnP3AjP7FeEv073AWuBATWfg7tvM7B5gHuGewF/d/S8V2iwxs5eAZcBOwkWrJu4hvBlpF+H9GE2ryfJGZGf8IjM7CswB/oVwj+sJMztCeH9OjbOLxIrpcu5SH5lZU3cvjPRAXgWecfdXg84lUp9oE5bUV/eZ2WeEz5XYBLwWcB6Rekc9EBERqRX1QEREpFZUQEREpFZS+iisli1bes+ePYOOUa2ioiKaNGkSdIxqKWfspEJGUM5YS5Wcixcv3u3u7eo6nZQuIB06dGDRokVBx6jW/PnzGT16dNAxqqWcsZMKGUE5Yy1VcppZxXOnakWbsEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFZUQEREpFYSUkDM7Bkz22lmK6sYb2b2iJnlmdlyMxuSiFwiIlJ7ieqBPAuMO8X4S4FekccU4PcJyCQiInWQkPuBuPt7ZtbtFE2uAv7k4Ru0LzCzlmbWyd23JSKfiAiAuxMqd0LulJdDKPK+/Pgwjxp2Yjw47lBwqJx12w/heGR6kUdk/In5nDzMI/P2yLhjQ8PtTgyLbnNsHif/ADUaFDPmHs/JR80oXEBmu/vASsbNBh5y9w8i798G7nb3r9wtysymEO6l0K5du6HTp0+PZ+yYKCwspGnTpkHHqJZyxk4qZITUyOnu7DpQBFmNKSx1Dpc6xWVQEnKKQ1BSFn4uLjvxvrQcysqhtNwpK4cyP/E+VE5k/Ilx7lDu8f2yTSZfTL18sbsPq+t0Uu6OhO7+JPAkQJ8+fTwV7v6VKncpU87YSYWMEGzOULmzdf8Rth8sZtuBYnYciDwfLGbnoWL2Fh1l/+FS9h8pJVRuwJEqp2UGTbIyaJyVTuOsdLIz08nKSqNJehpZGWlkRp6zMtLISo88Iu8z0o10M9LTjLTI84nXVDIs3D4t7cT4NDMA1qxezYABAzADi8oGVmGYYZFxkY9ihBtYZHx4WKRN5PPHhlFh2EnLotLlc/LQEVOr+eXUULIUkAKgS9T7zpFhIpLiiktDrNt+iDXbDrJpdxEbdxexaXcRX+45zNFQ+UltG2el07FFNu2bNaJPx2a0bJxFq8aZ7Nm6hWHn9KNV40xa5GTSpFFGuGA0SqdJVgbZmWlf+ZIMQrN96xl9TqegYyRMshSQWcCtZvYiMAI4oP0fIqnH3dmws5BPNu5h6Zb9rN56kA07CyP7CSArI41ubRpzVrsmXNyvPd3bNOGMljl0bJFNxxbZNGuUUWkhmD9/O6OHdk70jyPVSEgBMbMXgNFAWzPLB34JZAK4+xPAHOAyIA84DNyYiFwiUnfbDxTz9todfLBhN59s2sveoqMAtG3aiIG5zRnbrwMDzmhO/zOa07lVY9LTgu8pSGwk6iisidWMd+AfE5FFROpu8+4iZi3byltrdrA8/wAAuS1zGNOnPSN6tGZk9zZ0aZ2TFJuVJH6SZROWiCS5g8WlzF62jZlL8ln8xT7MYHCXltw1rg+X9OtAz/ZNVTAaGBUQETmlLXsP88yHm5i+cAtFR0P0bN+Uu8f15erBuXRskR10PAmQCoiIVCpvZyG/eWs9f1uxjTQzrjj3DK4/vxvndm6hnoYAKiAiUkH+vsP89q0NzFyST05mOlMuPIsbzu+m3oZ8hQqIiABQUhbiqfc38eg7Gyh3uGlUd24ZfRZtmjYKOpokKRUQEeHTTXu555XlbNxVxKUDO/Kvl/cnt2VO0LEkyamAiDRgZeXO1DfW8sS7n9O5VQ5/vPE8xvRpH3QsSREqICIN1ObdRTywoJgvDn7OxOFd+Ndv96dJI30lSM1pbRFpgN5dv4ufPL+EUKicP0weyrcGdAw6kqQgFRCRBsTdeer9Tfy/v62hd4dm3Ny7TMVDak33RBdpIMrLnX9/fTX/MWcN4wZ2ZOYt59Ousb4CpPbUAxFpAEpD5dw9YzmvLC3gplHd+ddv9yNNFzWUOlIBEannSkPl3Pr8Euau2sEd3+zNP47pqTPJJSZUQETqsVC580/TlzF31Q5+eUV/bhzVPehIUo9oA6hIPVVe7vzLKyuYtWwrd4/rq+IhMacCIlJP/eat9by0aAs/vagnt4w+K+g4Ug+pgIjUQzMX5/PoO3lMOK8LP7+kd9BxpJ5SARGpZz7ZuId7XlnO+We14YHvDNQOc4kbFRCRemTbgSPcMm0JXVo35vf/MJTMdP2JS/xo7RKpJ0pD5fzk+aWUlIb43x8Mo0XjzKAjST2nw3hF6on/nLuORV/s49GJgzmrXdOg40gDoB6ISD3w9pod/OG9jUweeSZXnHtG0HGkgVABEUlxe4uOcvfMFfTr1JxffLtf0HGkAdEmLJEU929/WcmBI0f5883Dyc5MDzqONCDqgYiksFnLtvLX5dv42dje9OvUPOg40sCogIikqN2FJdz7l5UM6tKS/3Nhj6DjSAOkAiKSon41Zw1FJWX85/fOIUPne0gAtNaJpKCPP9/DK0sKmHJhD3q2bxZ0HGmgElZAzGycma0zszwzu6eS8V3NbJ6ZLTWz5WZ2WaKyiaSSo2Xl/NtfVtK5VQ63jukVdBxpwBJSQMwsHXgcuBToD0w0s/4Vmv0rMN3dBwMTgN8lIptIqnnqg43k7Szk/qsGkJOlo64kOInqgQwH8tx9o7sfBV4ErqrQxoFjh5G0ALYmKJtIyth5qJjH3snjkv4duKhvh6DjSANn7h7/mZhdA4xz9x9G3k8GRrj7rVFtOgFvAq2AJsBYd19cybSmAFMA2rVrN3T69Olxz19XhYWFNG2a/JeWUM7YiVfGP64s4YOCMv7jghw6Nqn7/3+psCxBOWNtzJgxi919WJ0n5O5xfwDXAE9FvZ8MPFahze3AP0Vefw1YDaSdarq9e/f2VDBv3rygI9SIcsZOPDKu3XbQu98z2++btTJm00yFZemunLEGLPIYfLcnahNWAdAl6n3nyLBoNwPTAdz9YyAbaJuQdCIp4P/9bQ1NG2Xw04u041ySQ6IKyEKgl5l1N7MswjvJZ1Vo8yVwMYCZ9SNcQHYlKJ9IUnt/wy7mr9vFTy7qRasmWUHHEQESVEDcvQy4FZgLrCF8tNUqM7vfzK6MNPsn4Edmtgx4Abgh0tUSadDcnf+cu47cljn84Pwzg44jclzCLqbo7nOAORWG3Rv1ejUwKlF5RFLFO2t3siz/AFPHn02jDB22K8lDZ6KLJDF35zdvradr68Z8d0jnoOOInEQFRCSJ/X31DlYWHOSnF/fS/c0l6WiNFElS5eXOb97aQPe2TfjOIN1lUJKPCohIknpz9Q7WbDvITy/uqavtSlLSWimShNyd38/Po1ubxlx5bm7QcUQqpQIikoQ+3riHZfkH+NGFPUhPs6DjiFRKBUQkCT3x7kbaNm3EeB15JUlMBUQkyazaeoD31u/ixlHdyM7UeR+SvFRARJLMH97dSNNGGUwaqbPOJbmpgIgkkS17DzN7+VauG9GVFjmZQccROSUVEJEk8syHm0hPM24a1T3oKCLVUgERSRKFJWW8vCify885g44tsoOOI1ItFRCRJDFzcT6FJWXccH63oKOI1IgKiEgSKC93nvtoM4O7tuTcLi2DjiNSIyogIkngvQ272Li7SL0PSSkqICJJ4NmPNtOuWSMuHdgp6CgiNaYCIhKwjbsKmb9uF5NGnElWhv4kJXVobRUJ2J8+/oLMdOO6EV2DjiJyWlRARAJ0+GgZMxaHD91t16xR0HFETosKiEiAXl+2lcKSMiaNVO9DUo8KiEiAnv90C707NGVI11ZBRxE5bSogIgFZtfUAy7bsZ+Lwrpjpnh+SelRARALywqdf0igjje8O1j0/JDWpgIgE4PDRMl5bupVvn9OJFo111V1JTSogIgE4tvP8uuHaeS6pSwVEJADPf7qFXu2bMvRM7TyX1KUCIpJgx3aeXzdCO88ltSWsgJjZODNbZ2Z5ZnZPFW2+b2arzWyVmT2fqGwiiXRs5/nVg3ODjiJSJxmJmImZpQOPA5cA+cBCM5vl7quj2vQC/hkY5e77zKx9IrKJJNKRoyH+snQrl53diZaNs4KOI1InieqBDAfy3H2jux8FXgSuqtDmR8Dj7r4PwN13JiibSMK8uXo7h0rK+N4wHborqc/cPf4zMbsGGOfuP4y8nwyMcPdbo9q8BqwHRgHpwH3u/kYl05oCTAFo167d0OnTp8c9f10VFhbStGnToGNUSzljp6qMv154hB2HnYcvzCEtCfZ/pMKyBOWMtTFjxix292F1nU5CNmHVUAbQCxgNdAbeM7Oz3X1/dCN3fxJ4EqBPnz4+evToBMc8ffPnz0c5YycVclaWcev+I6ye+w4/vagXF43pHUywClJhWYJyJqtEbcIqALpEve8cGRYtH5jl7qXuvolwb6RXgvKJxN2rSwtwh/FDtPlK6odEFZCFQC8z625mWcAEYFaFNq8R7n1gZm2B3sDGBOUTiSt3Z8bifEZ0b03XNo2DjiMSEwkpIO5eBtwKzAXWANPdfZWZ3W9mV0aazQX2mNlqYB5wp7vvSUQ+kXhb8uU+Nu0u4pqh6n1I/ZGwfSDuPgeYU2HYvVGvHbg98hCpV15elE/jrHQuO1v3PJf6Q2eii8TZkaMhZi/fxqUDO9GkUTIdtyJSNyogInE2d9V2CkvKtPlK6h0VEJE4m7E4n86tchjRvXXQUURiSgVEJI4K9h/hw893c83QzqSlBX/ioEgsnXYBMbMmkWtbiUg1Xl2Sr3M/pN6qtoCYWZqZXWdmfzWzncBaYFvkqrm/NrOe8Y8pknqOnfsxskdrurTWuR9S/9SkBzIPOIvwlXI7unsXd28PXAAsAKaa2aQ4ZhRJSYu+2MfmPYe5ZmiX6huLpKCaHFM41t1LIxdEXHFsoLvvBWYCM81MN3UWqWBG5NyPSwd2DDqKSFxU2wNx99LIyz8Dz0fv/zCzGyu0ERGgpMz564ptXHa2zv2Q+ut0dqKvBd7l5B7HT2IfSST1Ld4Z0rkfUu+dTgFxd38CeAWYZWY5gI5LFKnEBwWldG3dmOHddO6H1F+n07c+dqfAP5nZYeCvgA4tEakgf99h1uwp52djde6H1G81LiDufnHU6xlmVgw8G49QIqns1SUFOPDdIblBRxGJq5qcB1Lpv1DuPtvd256qjUhD4+7MWJJP39ZpOvdD6r0anQdiZj8xs67RA80sy8wuMrPngOvjE08ktSz6Yh9f7DnMBbk68krqv5qs5eOAm4AXzKwH4X0hOYSLz5vA/7j70vhFFEkdMxeHz/0Y1kEFROq/atdydy8Gfmdm7YFfAW2AI+6+P97hRFJJ9H0/sjP2BR1HJO5O59+kfyPc82gNLDGzF1RERE54c/WJ+36UbFEBkfrvdK/GW0z43uVdgI/NbFDsI4mkphmL88ltqft+SMNxOj2Qte7+y8jrGWb2LPAEcFHMU4mkmG0HjvBB3m5+clEvnfshDcbp9EB2m9nQY2/cfT3QLvaRRFLPK0sKIvf90Lkf0nCcTg/kp8CLZraY8FV5zwE2xSWVSApxd2Yuzmd4t9ac2aZJ0HFEEqbGPRB3XwYMAl6IDJoHTIxHKJFUsnTLfjbuLmL8UPU+pGE5rYPV3b2E8DWw/hqfOCKpZ8bifLIz07js7E5BRxFJqNO+J7qInFBcGuL1ZVu5dGAnmmXrvmrSsKiAiNTB31fv4FBxGeOH6L4f0vCogIjUwcwl+ZzRIpuvndUm6CgiCZewAmJm48xsnZnlmdk9p2g33szczIYlKptIbew4WMx763dx9ZBc0nXuhzRACSkgkfuoPw5cCvQHJppZ/0raNQNuAz5JRC6RupixOJ9yh2uGdgk6ikggEtUDGQ7kuftGdz8KvAhcVUm7B4CphC+ZIpK0ysudlxZuYWSP1nRvq3M/pGFK1DWnc4EtUe/zgRHRDcxsCNDF3f9qZndWNSEzmwJMAWjXrh3z58+PfdoYKywsVM4YSoacq/eE+HJvMeM6hyrNkgwZa0I5YytVcsZKUty0wMzSgP8Gbqiurbs/CTwJ0KdPHx89enRcs8XC/PnzUc7YSYacr764lObZO7n9e2PIzkz/yvhkyFgTyhlbqZIzVhK1CauA8BV8j+kcGXZMM2AgMN/MNgMjgVnakS7JaP/ho/xt5XauHpxbafEQaSgSVUAWAr3MrLuZZQETgFnHRrr7AXdv6+7d3L0bsAC40t0XJSifSI29trSAo2XlXHte1+obi9RjCSkg7l4G3Er4XiJrgOnuvsrM7jezKxORQSQW3J0XF27hnM4t6H9G86DjiAQqYftA3H0OMKfCsHuraDs6EZlETtfy/AOs3X6I/7h6YNBRRAKnM9FFTsOLC7eQk5nOleeeEXQUkcCpgIjUUFFJGa8v28q3z9GFE0VABUSkxv7y2VYKS8qYOFxnnouACohIjbg7f/p4M/07NWdI11ZBxxFJCiogIjWw+It9rN1+iMlfOxMzXThRBFRARGrkzwu+oFl2BlcN0s5zkWNUQESqsetQCXNWbOOaoZ1pnJUUV/8RSQoqICLVmL5oC6UhZ9LIM4OOIpJUVEBETqEsVM60BV9wQc+2nNWuadBxRJKKCojIKbyzdidbDxSr9yFSCRUQkVN45sNNnNEim7H92gcdRSTpqICIVGFlwQEWbNzLjaO6k5GuPxWRivRXIVKFpz/YRJOsdK7VmecilVIBEanE9gPFvL5sK9ee15Xmuu6VSKVUQEQq8dzHmyl358ZR3YKOIpK0VEBEKigqKWPagi8YN7AjXVo3DjqOSNJSARGp4OVFWzhYXMbNF/QIOopIUlMBEYlytKyc/31/E8PObMXQM3XVXZFTUQERifLa0gIK9h/hHy/qGXQUkaSnAiISESp3fjc/j4G5zRndu13QcUSSngqISMTs5VvZvOcwt47ppXt+iNSACogIUF7uPD4vj94dmvLN/h2CjiOSElRARIA3V+9g/Y5C/nFMT9LS1PsQqQkVEGnwQuXOf725jh7tmvDtszsFHUckZaiASIP32tICNuws5I5v9tFFE0VOg/5apEE7WlbOb95az8Dc5owb0DHoOCIpRQVEGrQXPv2S/H1HuPNbfbXvQ+Q0JayAmNk4M1tnZnlmdk8l4283s9VmttzM3jYz3QJO4qqopIxH38ljePfWXNirbdBxRFJOQgqImaUDjwOXAv2BiWbWv0KzpcAwdz8HmAE8nIhs0nA98e7n7C4s4e5xfXXeh0gtJKoHMhzIc/eN7n4UeBG4KrqBu89z98ORtwuAzgnKJg3Qlr2H+cN7G7lq0Bm65pVILZm7x38mZtcA49z9h5H3k4ER7n5rFe0fA7a7+4OVjJsCTAFo167d0OnTp8cveIwUFhbStGnToGNUqyHlfGxpMct3h3jo6zm0zo79/1ENaVkmgnLG1pgxYxa7+7A6T8jd4/4ArgGeino/GXisiraTCPdAGlU33d69e3sqmDdvXtARaqSh5Pwob7efefds/+1b62MTqBINZVkminLGFrDIY/DdnlHnClQzBUD0jaU7R4adxMzGAr8AvuHuJQnKJg1Iaaicf399Fbktc5hyoe73IVIXidoHshDoZWbdzSwLmADMim5gZoOBPwBXuvvOBOWSBubJ9zaydvshfnlFf7Iz04OOI5LSElJA3L0MuBWYC6wBprv7KjO738yujDT7NdAUeNnMPjOzWVVMTqRWNu0u4rdvb+DSgR35pk4aFKmzRG3Cwt3nAHMqDLs36vXYRGWRhsfd+ZdXVtAoI41/v3JA0HFE6gWdiS4NwgufbuHjjXu459K+tG+eHXQckXpBBUTqvU27i3hg9mpG9WzDxPO6Bh1HpN5QAZF6rTRUzs9eXEpWRhr/+b1zdb0rkRhK2D4QkSA88vYGluUf4PHrhtCpRU7Qcerk4MGD7Ny5k9LS0phNs0WLFqxZsyZm04sX5ayZzMxM2rdvT/PmzRMyPxUQqbfeXb+Lx+bl8d0huXz7nNS+UdTBgwfZsWMHubm55OTkxOzaXYcOHaJZs2YxmVY8KWf13J0jR45QUBA+xS4RRUSbsKRe2rL3MLe9uJQ+HZrx4HcGBh2nznbu3Elubi6NGzfWhR+lUmZG48aNyc3NZefOxJxKpwIi9U5xaYhbpi0mVO48MWkojbNSv6NdWlpKTk5qb4KTxMjJyYnpZs5TSf2/LJEo5eXOnTOWs7LgIE/9YBjd2jYJOlLMqOchNZHI9UQ9EKlXHp67jteXbeXucX0Z279D0HFE6jUVEKk3/rzgC55493MmjezKj7+hCyWKxJsKiNQLMxfnc+9fVnJx3/bcd8UAbe4RSQAVEEl5ry0t4I4Zy/hajzY8/g9DyEjXai2SCPpLk5T2ypJ8bp/+GSO6t+bp68/TJdolKd1yyy3k5ubWu56xCoikJHfnD+9+zu3TlzGiexuevv48crJUPCQ5TZw4kSVLlgQdI+Z0GK+knHJ37p+9mj9+uJlvn9OJ//7+uTTKUPGQ5HXhhRcGHSEu1AORlLK36Cj/taiYP364mZtGdefRCYNVPOohd2fQoEE899xzNf7Mrbfeys033xzHVFKRCoikjBX5B7ji0Q9Yt6+cqePP5t4r+uvquvXU9OnT2bt3L9ddd12NP3PHHXcwbdo08vLy4phMoqmASNIrC5Xz6NsbuPp3H+Lu/GJENtfqvh712iOPPMLkyZPJzMys8We6devGBRdcwO9///s4JpNoKiCS1NbvOMT4Jz7mv/6+nsvO7sSc275O9xbaZJXKtm/fzvXXX0+HDh1IS0vDzI4/hg4dSl5eHh999BHXXHPNSZ976aWXTmob/Th48CAA48ePZ9q0aZSXlwfxozU42okuSelgcSm/fWsDz320mabZGTx23WAuP+eMoGNJHRUXFzN27FiKiop4+OGHadu2LVOnTuX9999nypQpjBkzhrfffpsmTZpw7rnnnvTZCy+8kI8//vj4+7179zJ58mRGjhx5/NLl559/Pjt27GDFihVf+TyE962EQqFqc2ZkxPar8Yc//CFvvPEGAJ07d2bcuHE89dRTMZ1HEFRAJKmUlIWYvnALv307jz1FJUw4rwt3fLMPbZo2Cjpa0vn311exeuvBOk0jFAqRnn76Pbr+ZzTnl1cMOO3PPfjgg2zZsoXVq1eTm5sLQN++fenZsycXXHABEyZMYMqUKfTr14+0tJM3kHTq1IlOncL3dTl48CAXX3wxAwcO5OWXXz7eZsCAAaSnp/Ppp59WWkCee+45brzxxmpzuvtp/2ynUh+KRWVUQCQplJSFmLE4n8ffyWPrgWKGndmKZ24YxjmdWwYdTWJo2rRp/OhHPzpePAB69OiBmbF//34gvImrbdu2VU6jqKiIyy67jLS0NGbPnk3jxo2Pj8vIyKBly5Zs37690s9eccUVLFy4MEY/jaiASKC2Hyhm2idf8MKnX7K78CiDu7bkofHn8PVebevdWbuxVpseQEWJvIPe2rVr2bx5M2PHjj1p+K5du3D3472L4uLik4pCtOLiYq688kqKiop45513Ks3eqFEjiouLK/1869atadGiRR1/EjlGBUQSrrg0xDtrd/La0gLeWbuTkDsX923PDed3Z1TPNioc9VR+fj4A7du3P2n43LlzyczM5JJLLgHCX/KV9SBKS0sZP34827Zt491336VVq1aVzmf//v20bt260nG13YSVzOtkrDe3nQ4VEEmIQ8WlfJi3m7fW7GTuyu0cKimjXbNG3HRBdyaNOJOubSr/j1Pqj5Ytw5sj161bx5AhQ4Bwj+LBBx/k+9///vGeQZ8+fU7aWQ7hfTUTJ05k3bp1vPfee7Rr167SeezatYvDhzaaAucAAA2HSURBVA/Tu3fvSsfXdhNWTb+kU+Xe7bGiAiJxUVwaYkXBARZu3st763exaPM+ysqdZtkZfGtgR74zKJevndWGdJ0I2GAMGjSIHj16cPfdd5Oenk5aWhpTp06luLiYRx999Hi7UaNGcf/997Nr167jheLnP/85c+bM4dlnn+XLL7/kyy+/BKBJkyacffbZxz+7aNEizIzzzz+/0gxt2rShTZs2tcp/yy23MGvWLLZu3RrIf/3btm3j8ccfZ//+/cybN49Vq1YlPENFKiBSZyVlIT7fWcTa7QdZvfUgi7/cx8qCA5SGwn9kfTs240cX9mBMn/YM6dpSl1tvoDIyMpg1axY//vGP+cEPfkCzZs24/PLL+dWvfnXS5qjRo0fTunVr3njjDSZPnoy7M3PmTI4cOcK111570jSvuOIKZs2adfz9G2+8wTe+8Y1aF4lTmThxIvfddx8dO3asUftu3bqxefPm057P6tWrueuuu04a9vOf/5yLL76Y2267jdtuu40333zztKcbDyogUiOloXK27S9my77DfLn3xGPDjkNs3FVEWXm4WGSlp3F25xbcNKo7Q89sxdAzW+kQXDluwIABvP/++6dsk5WVxaRJk3jxxReZPHkyZkZBQUG1m4ZCoRAzZ87koYceimXk42J9QcTt27dz++23s3HjRg4ePMgDDzzA+PHj6d+/P7Nnz/5K+4KCAu666y4eeeSRUx6llkgJKyBmNg74LZAOPOXuD1UY3wj4EzAU2ANc6+6bE5WvIXF3jpSGOFRcxqHiUg4cCT8v2FbGpg83setQCbsOlbC7sIRdhcdeHyVUfqLbnpFm5LbKoWe7plzSvwN9OjanX8dmdGvbhEz1MKSO7rzzTnr37s369eur3J9R0csvv0xOTg4TJkyIc7q6C4VCTJo0iV//+tcMHjyYnTt3MmTIEMaPH1/lZ8aOHcvYsWP5n//5HyZNmkTfvn0TmLhyCSkgZpYOPA5cAuQDC81slruvjmp2M7DP3Xua2QRgKnDtV6d2Qshhd2EJxzZHOg7HX4N7ZNjx15Fx7kRvwqys3bFtnMemc3wOJ02nwueickRPf/OBEMvz939l+uUOoXKnrLw88uyUR55Dx5/LKQuF34c8Mjx0YnxpqJySshDFpeUUl4YoKavwXHpifLholHKouOx4j+Erlq0mI81o27QR7Zo1ol3TRvTv1JwOzbPp0qoxXVo3pkvrHDq1yNH+C4mbzp0788wzz7Bt27YaFxB35+mnn475WeSn49prr2Xr1q0AbN26lUGDBgEwcuRInnjiiePt5syZw7Jly046IqyqQ5ePWbNmTRwS102ilvRwIM/dNwKY2YvAVUB0AbkKuC/yegbwmJmZn2Jv1ZZD5Qx78K34JI61jz+M26TT04zsjDSyM9NpdOw5M53szDQaZaTRqkkW2Rnh982yM2mek0Gz7EyaZZ94bp6dydoVS7lszAW0yMnUVW4lcKfbk5g4cWKcktTcSy+9dHxTW7du3fjss88qbbd8+XLuuusu7rzzzkTGi7lEFZBcYEvU+3xgRFVt3L3MzA4AbYDd0Y3MbAowBaBF+1wm9cvCDKK/7ux425PfE9WuyjacOOb7pLZR7Sq+j55v9OHix94fOVJMTk52hXmEr2SZnmakGccf6cef7aT3x1+nWVSb8HNGpV/2ocijCg4ciTyAQ0ALDrNs4UdVfyZJFBYWMn/+/KBjnFKsM7Zo0YJDhw7FbHrHhEKhuEw31pItZ1VZonO6e5XtWrduzUsvvcTNN99MZmYm27dvJy0t7SvnyNRWcXFxQv5GUm4nurs/CTwJ0KdPH3/w+ksCTlS9+fPnM3r06KBjVEs5YyfWGdesWROX8wtS5byFZMgZfUHEfv36VXpBxOicZlZl5ptvvpkFCxYwfPhwmjZtSps2bXj++edj9jNmZ2czePDgmEzrVBJVQAqALlHvO0eGVdYm38wygBaEd6aLiATudC+IeKpDeLOysk7rbovJKlGHyywEeplZdzPLAiYAsyq0mQVcH3l9DfDOqfZ/iIhIsBLSA4ns07gVmEv4MN5n3H2Vmd0PLHL3WcDTwJ/NLA/YS7jIiIhIkkrYPhB3nwPMqTDs3qjXxcD3EpVHRETqRmd8iYhIraiAiKQI7RKUmkjkeqICIpICMjMzOXLkSNAxJAUcOXKEzMzMhMxLBUQkBbRv356CggIOHz6snohUyt05fPgwBQUFMTshsTopdyKhSEPUvHlzIHx9pdLS0phNt7i4mOzs7JhNL16Us2YyMzPp0KHD8fUl3lRARFJE8+bNY/7FMH/+/IScsVxXypmctAlLRERqRQVERERqRQVERERqRQVERERqRQVERERqRQVERERqxVL5pCQzOwSsCzpHDbSlwp0Vk5Ryxk4qZATljLVUydnH3et896pUPw9knbsPCzpEdcxskXLGTirkTIWMoJyxlko5YzEdbcISEZFaUQEREZFaSfUC8mTQAWpIOWMrFXKmQkZQzlhrUDlTeie6iIgEJ9V7ICIiEhAVEBERqZWkLyBm9j0zW2Vm5WY2rMK4fzazPDNbZ2bfquLz3c3sk0i7l8wsKwGZXzKzzyKPzWb2WRXtNpvZiki7mBxWd5o57zOzgqisl1XRblxkGeeZ2T0B5Py1ma01s+Vm9qqZtayiXcKXZ3XLxswaRdaHvMh62C0RuSpk6GJm88xsdeRv6bZK2ow2swNR68K9ic4ZyXHK36GFPRJZnsvNbEgAGftELafPzOygmf2sQptAlqeZPWNmO81sZdSw1mb2dzPbEHluVcVnr4+02WBm19dohu6e1A+gH9AHmA8MixreH1gGNAK6A58D6ZV8fjowIfL6CeCWBOf/L+DeKsZtBtoGuGzvA+6opk16ZNn2ALIiy7x/gnN+E8iIvJ4KTE2G5VmTZQP8X+CJyOsJwEsB/J47AUMir5sB6yvJORqYnehsp/s7BC4D/gYYMBL4JOC86cB24MxkWJ7AhcAQYGXUsIeBeyKv76ns7wdoDWyMPLeKvG5V3fySvgfi7mvcvbKzza8CXnT3EnffBOQBw6MbmJkBFwEzIoOeA74Tz7yVzP/7wAuJmmccDAfy3H2jux8FXiS87BPG3d9097LI2wVA50TO/xRqsmyuIrzeQXg9vDiyXiSMu29z9yWR14eANUBuIjPE0FXAnzxsAdDSzDoFmOdi4HN3/yLADMe5+3vA3gqDo9fBqr4DvwX83d33uvs+4O/AuOrml/QF5BRygS1R7/P56h9FG2B/1JdPZW3i6evADnffUMV4B940s8VmNiWBuaLdGtkU8EwVXduaLOdEuonwf6CVSfTyrMmyOd4msh4eILxeBiKyCW0w8Eklo79mZsvM7G9mNiChwU6o7neYbOvjBKr+BzEZlidAB3ffFnm9HehQSZtaLdekuJSJmb0FdKxk1C/c/S+JzlMTNcw8kVP3Pi5w9wIzaw/83czWRv6DSEhO4PfAA4T/aB8gvLntpljOv6ZqsjzN7BdAGTCtisnEfXmmMjNrCswEfubuByuMXkJ4M0xhZF/Ya0CvRGckhX6Hkf2pVwL/XMnoZFmeJ3F3N7OYnbuRFAXE3cfW4mMFQJeo950jw6LtIdzFzYj891dZm1qpLrOZZQDfBYaeYhoFkeedZvYq4U0iMf1jqemyNbP/BWZXMqomy7nOarA8bwAuBy72yEbbSqYR9+VZQU2WzbE2+ZF1ogXh9TKhzCyTcPGY5u6vVBwfXVDcfY6Z/c7M2rp7Qi8MWIPfYULWxxq6FFji7jsqjkiW5Rmxw8w6ufu2yOa+nZW0KSC83+aYzoT3O59SKm/CmgVMiBzl0p1wdf80ukHki2YecE1k0PVAono0Y4G17p5f2Ugza2JmzY69JryjeGVlbeOlwrbjq6uY/0Kgl4WPZssi3GWflYh8x5jZOOAu4Ep3P1xFmyCWZ02WzSzC6x2E18N3qiqA8RLZ5/I0sMbd/7uKNh2P7Zsxs+GEvxsSWuhq+DucBfwgcjTWSOBA1OaZRKtyC0MyLM8o0etgVd+Bc4FvmlmryKbsb0aGnVqijxKoxVEFVxPeHlcC7ADmRo37BeGjYNYBl0YNnwOcEXndg3BhyQNeBholKPezwI8rDDsDmBOVa1nksYrwpppEL9s/AyuA5ZGVrFPFnJH3lxE+cufzgHLmEd4++1nk8UTFnEEtz8qWDXA/4WIHkB1Z7/Ii62GPAJbfBYQ3Uy6PWoaXAT8+to4Ct0aW2zLCByqcH0DOSn+HFXIa8Hhkea8g6sjMBGdtQrggtIgaFvjyJFzQtgGlke/Nmwnvc3sb2AC8BbSOtB0GPBX12Zsi62kecGNN5qdLmYiISK2k8iYsEREJkAqIiIjUigqIiIjUigqIiIjUigqIiIjUigqIiIjUigqIiIjUigqISIyZ2TtR94EoNrPvB51JJB50IqFInJjZLcAYYKK7h4LOIxJrSXExRZH6xsx+QPhie+NVPKS+UgERiTEz+x7wD8BV7l4adB6ReFEBEYkhM7uc8G1sL3f34qDziMST9oGIxJCZ7SF8S9GiyKBH3f3pACOJxI0KiIiI1IoO4xURkVpRARERkVpRARERkVpRARERkVpRARERkVpRARERkVpRARERkVr5/8Y6A42CsbNuAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gwvtL7xC5Vmv",
        "colab_type": "text"
      },
      "source": [
        "Notice that\n",
        "\n",
        "- the range of values ​​that $\\sigma(z)$ produces is the open range $ (0,1) $;\n",
        "- $\\sigma(0.0)$ is equal to 0.5;\n",
        "- for ever-increasing $z$ values ​​(in magnitude), $\\sigma(z)$ returns values ​​ever closer to $0$ or $1$.\n",
        "- $\\sigma(z) \\geq 0.5$ when $z \\geq 0$\n",
        "- $\\sigma(z) < 0.5$ when $z < 0$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1hw6vD565_Kd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "f2cf6452-edf4-476c-a155-46e98a1c62af"
      },
      "source": [
        "print('sigma(0.0) = %.3f' % sigmoid(0.0))\n",
        "print('sigma(0.5) = %.3f' % sigmoid(0.5))\n",
        "print('sigma(-0.5) = %.3f' % sigmoid(-0.5))\n",
        "print('sigma(10.0) = %.3f' %  sigmoid(10.0))\n",
        "print('sigma(-10.0) = %.3f' % sigmoid(-10.0))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "sigma(0.0) = 0.500\n",
            "sigma(0.5) = 0.622\n",
            "sigma(-0.5) = 0.378\n",
            "sigma(10.0) = 1.000\n",
            "sigma(-10.0) = 0.000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vXLmXnqw6GI_",
        "colab_type": "text"
      },
      "source": [
        "To give you a more concrete view of what a logistic regression model does, consider a binary classification problem over a training set with 2 predictors, $x_1$ and $x_2$. Also, consider that the logistic regression algorithm produced a model represented by the vector $\\Theta = [-3, 1, 1]^T$. The code cell below is a toy implementation of a logistic regression classifier."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LF1WfLhA6Rhm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "def sigmoid(x):\n",
        "    # Sigmoid function\n",
        "    return 1 / (1 + np.exp(-x))\n",
        "\n",
        "def dot_product(theta, x):\n",
        "    # Compute the weighted sum.\n",
        "    return np.dot(x, theta)\n",
        "\n",
        "def predict(theta, x):\n",
        "  y_prob = proba(theta,x)\n",
        "  return np.round(y_prob).astype(np.int)\n",
        "\n",
        "def proba(theta, x):\n",
        "    # Returns the probability that x belongs to the positive class\n",
        "    return sigmoid(dot_product(theta, x))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XFc9c9YHLcxu",
        "colab_type": "text"
      },
      "source": [
        "Further, consider that we want to determine (predict) the class for the examples $[3,3]$ and $[0.4,1.3]$. The following code produces the probability value that $\\mathbf{x}$ belongs to the positive class."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dS50v_iU6XAW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        },
        "outputId": "04c010b3-5e25-43e7-8108-5444c3879b6c"
      },
      "source": [
        "theta = np.asarray([-3, -1, -1]).T\n",
        "\n",
        "X = np.asarray([[3, 3],[0.4, 1.3]])\n",
        "\n",
        "print('Example(s):\\n', X)\n",
        "\n",
        "col = np.ones((2,1))\n",
        "X = np.append(col, X, axis=1)\n",
        "\n",
        "print('Predicted class(es) for each example:', predict(theta, X))\n",
        "print('Probability of each example belonging to the positive class:', proba(theta, X))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Example(s):\n",
            " [[3.  3. ]\n",
            " [0.4 1.3]]\n",
            "Predicted class(es) for each example: [0 0]\n",
            "Probability of each example belonging to the positive class: [0.00012339 0.0090133 ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ShKvWs_BF3nN",
        "colab_type": "text"
      },
      "source": [
        "In the example above:\n",
        "\n",
        "1. How do you interpret the output when $\\Theta = [-3, 1, 1]^T$? \n",
        "2. What happens if you change $\\Theta$ to $[-3, -1, -1]^T$?\n",
        "3. What happens if you keep $\\Theta = [-3, 1, 1]^T$ and try to classify the example $\\mathbf{x}=[0.4,1.3]$?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SM3linNFpTfy",
        "colab_type": "text"
      },
      "source": [
        "## Decision boundaries\n",
        "\n",
        "We can have a graphical intuition of the example above. Again, suppose $\\Theta = [-3, 1, 1]^T$. Then to classify an example $\\mathbf{x} = (x_1, x_2)$:\n",
        "\n",
        "$$\n",
        "\\Theta^T \\cdot \\mathbf{x} = [-3, 1, 1]^T \\cdot [1,x_1,x_2] = -3 + x_1 + x_2\n",
        "$$\n",
        "\n",
        "Recall that, if $(\\Theta^T \\cdot \\mathbf{x}) \\geq 0$, then $\\mathbf{x}$ is classified as positive. That is:\n",
        "\n",
        "$$\n",
        "-3 + x_1 + x_2 \\geq 0 \\rightarrow x_1 + x_2 \\geq 3\n",
        "$$\n",
        "\n",
        "The equation $x_1 + x_2 = 3$ actually defines what we call a *decision boundary*. According to the Wikipedia, the definition of a decision boundary is the following:\n",
        "\n",
        "> In a classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging to the other class.\n",
        "\n",
        "In the case of a 2-dimensional dataset, as the space of predictors is bidimentional, the decision boundary is a simple line in the cartesian plane. This line splits the space of features in two subregions, positive and negative. See the plot below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QC7KqyHSuYZ-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 440
        },
        "outputId": "4ececaa1-cb3f-49ef-c772-af21b5bb7012"
      },
      "source": [
        "from matplotlib import pyplot as plt\n",
        "\n",
        "point1 = [0, 3]\n",
        "point2 = [3, 0]\n",
        "\n",
        "x_values = [point1[0], point2[0]]\n",
        "y_values = [point1[1], point2[1]]\n",
        "\n",
        "plt.plot(x_values, y_values, c='black')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiQAAAGnCAYAAACHP0ybAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAMTQAADE0B0s6tTgAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3df0yb54EH8K8dDCmBwMooadmCVmhyaGkptue2RqD5Jg4y2NxBxbXEChttHfl64qDbYHNZ0cgSCjvGiq4ISqVQrIqVMugQqMOtiLkRKNS2NLadOBaWo9tYHImmTggBTOD+6JI1DSQGbB7/+H6kSq15/PrL0zfOF7/v8yA5ffr0GoiIiIgEkooOQERERMRCQkRERMKxkBAREZFwLCREREQkHAsJERERCcdCQkRERMKxkBAREZFwLCREREQkXIg7g15//XWYzWY4nU7s2rULBw4cwLFjx5CUlLThcy5fvoyXX34Z77//PgDg0UcfRWlpKSIiIjyTnIiIiAKGxJ2dWj/88EN87nOfQ2RkJFwuF3p6evCLX/wCb731Fnbt2rXuc37wgx/A5XLhxRdfBABUV1dj9+7dOHHihGe/AyIiIvJ7bl2y2b9/PyIjIwEAa2trkEqluHjxIi5fvrzu+PPnz2NsbAwGgwFRUVGIioqCwWDAyMgIHA6H59ITERFRQHDrkg0AjI6O4sSJE7hy5QokEgmeeOIJREdHrzv27NmzkMlkN13SSUpKgkwmw9mzZxEXF7f95ERERBQw3C4kjz32GPr6+nDp0iUMDAwgNjZ2w7ELCwvr3isSERGBhYWFWx5fXV3F3Nwc7rrrLkgkEncjERERkUBra2u4evUqYmJiIJVub52M24Xkur179yI/Px/f/OY38YUvfGHdG1vDw8MxPz9/y+Pz8/MIDw+/5fG5uTkUFBRsNgoRERH5gM7Oztt+UOGOTRcS4JNGtLKygr/+9a/rFpKkpCS4XC5MT08jMTERADA9PQ2Xy7Xu+LvuugsA8PTTT6OrqwvNzc34+te/vpVoQc9oNOLkyZOiYwQEzqXncC49g/PoOZxLz7h06RK++MUv3vh7fDvcKiRdXV3453/+Z9x99934+OOP8dprryEkJASHDh1ad/y+ffvwyCOPoLm5GZWVlQCA5uZmqNXqde8fuX6Z5mc/+xn+5V/+Bc888wz+/d//HdXV1QgJ2VJnClqhoaHYu3ev6BgBgXPpOZxLz+A8eg7n0rM8cbuFWxd8bDYbnnnmGRw+fBhPP/00Ll68iPr6esTExAAAHA4HDh8+jImJiRvPMRqN2Lt3L44cOYIjR44gKioKP/zhD+/4WgUFBRgbG0NPTw+ysrJw4cKFLX5rRERE5C/c+vihpqbmtl+Pi4vDO++8c9Nje/fuxY9+9KMthUpOTsb4+DieffZZyOVydHZ2Qq1Wb+lYwSYrK0t0hIDBufQczqVncB49h3Ppe3x26/jIyEh0dHSgvLwcmZmZaGxsxNraHfdwC3r8Q+Y5nEvP4Vx6BufRcziXvsdnCwnwyTWpkpISmM1m1NbWorCwcN3VO0REROTffLqQXJeWlga73Q6HwwGVSoXJyUnRkYiIiMiD/KKQAJ/cp2I2m6HVaqFSqdDZ2Sk6EhEREXmI3xQSAAgJCUFNTQ1MJhP0ej3KysrgcrlExyIiIqJt8qtCcp1Wq4XVasXg4CA0Gg1mZ2dFRyIiIqJt8MtCAnyyG+zo6CgSExORmpoKi8UiOhIRERFtkd8WEuCT35nT1taG48ePIycnB3V1dVwaTERE5If8upAAnywN1uv1GBoaQlNTE/Ly8uB0OkXHIiIiok3w+0JynVKphM1mw+LiIpRK5U3b2BMREZFvC5hCAgAxMTHo7++HTqeDWq2GyWQSHYmIiIjcEFCFBACkUimqqqrQ1dWF0tJSGAwGLC0tiY5FREREtxFwheS67Oxs2O12WK1WpKenY2ZmRnQkIiIi2kDAFhIASEhIwPDwMORyORQKBQYGBkRHIiIionUEdCEBgLCwMDQ3N6O+vh75+fmorq7G6uqq6FhERET0KQFfSK4rKirCmTNn0N7ejtzcXMzNzYmORERERH8XNIUEAFJSUmC1WhEaGgqFQgGbzSY6EhERESHICgkAREdHo7u7GwaDARkZGWhtbeXurkRERIIFXSEBPlkaXFFRgb6+PlRWVqK4uBgLCwuiYxEREQWtoCwk12k0GtjtdkxNTUGtVmN6elp0JCIioqAU1IUEAOLj42GxWKDRaKBUKtHb2ys6EhERUdAJ+kICADKZDA0NDWhpaYFOp4PRaMTKyoroWEREREGDheRTCgoKMDY2hp6eHmRlZeHChQuiIxEREQUFFpLPSE5Oxvj4OGJjYyGXyzEyMiI6EhERUcBjIVlHZGQkOjo6UF5ejszMTDQ2NnJpMBERkRexkGxAIpGgpKQEZrMZtbW1KCwsxPz8vOhYREREAYmF5A7S0tJgt9vhcDigUqkwOTkpOhIREVHAYSFxQ1xcHMxmM7RaLVQqFTo7O0VHIiIiCigsJG4KCQlBTU0NTCYT9Ho9ysrK4HK5RMciIiIKCCwkm6TVamG1WjE4OAiNRoPZ2VnRkYiIiPweC8kWJCUlYXR0FImJiUhNTYXFYhEdiYiIyK+xkGxReHg42tracPz4ceTk5KCuro5Lg4mIiLaIhWQbJBIJ9Ho9hoaG0NTUhLy8PDidTtGxiIiI/A4LiQcolUrYbDYsLi5CqVRiYmJCdCQiIiK/wkLiITExMejv74dOp4NarYbJZBIdiYiIyG+wkHiQVCpFVVUVurq6UFpaCoPBgKWlJdGxiIiIfB4LiRdkZ2fDbrfDarUiPT0dMzMzoiMRERH5NBYSL0lISMDw8DDkcjkUCgUGBgZERyIiIvJZLCReFBYWhubmZtTX1yM/Px/V1dVYXV0VHYuIiMjnsJDsgKKiIpw5cwbt7e3Izc3F3Nyc6EhEREQ+hYVkh6SkpMBqtSI0NBQKhQI2m010JCIiIp/BQrKDoqOj0d3dDYPBgIyMDLS2tnJ3VyIiIrCQ7DipVIqKigr09fWhsrISxcXFWFhYEB2LiIhIKBYSQTQaDex2O6ampqBWqzE9PS06EhERkTAsJALFx8fDYrFAo9FAqVSit7dXdCQiIiIhWEgEk8lkaGhoQEtLC3Q6HYxGI1ZWVkTHIiIi2lEsJD6ioKAAY2Nj6OnpQVZWFi5cuCA6EhER0Y5hIfEhycnJGB8fR2xsLORyOUZGRkRHIiIi2hEsJD4mMjISHR0dKC8vR2ZmJhobG7k0mIiIAh4LiQ+SSCQoKSmB2WxGbW0tCgsLMT8/LzoWERGR17CQ+LC0tDTY7XY4HA6oVCpMTk6KjkREROQVLCQ+Li4uDmazGVqtFiqVCp2dnaIjEREReRwLiR8ICQlBTU0NTCYT9Ho9ysrK4HK5RMciIiLyGBYSP6LVamG1WjE4OAiNRoPZ2VnRkYiIiDwixJ1Br776Kt5//304HA7s3r0bDz/8MI4dO4Z77rlnw+e89NJLeO+99yCTyW489vjjj+PYsWPbTx3EkpKSMDo6CoPBgNTUVLz55pv46le/KjoWERHRtrhVSCQSCSoqKnD//fdjaWkJDQ0NMBqNeO211277PI1GgxdeeMEjQekfwsPD0dbWhtbWVuTk5KCqqgrf//73IZFIREcjIiLaErcu2Tz77LM4ePAgZDIZIiIi8NRTT2F6ehqXL1/2dj7agEQigV6vx9DQEJqampCXlwen0yk6FhER0ZZs6R6SDz74AHFxcYiMjLztuNHRUWi1Whw5cgQ/+9nP8PHHH28pJG1MqVTCZrNhcXERSqUSExMToiMRERFt2qYLic1mQ3t7O55//vnbjvvWt76F9vZ2vP3226irq8Ps7CxeeOEF7jrqBTExMejv74dOp4NarYbJZBIdiYiIaFPcuofkutHRUZw4cQJGoxEqleq2Yw8ePHjj3+Pj4/G9730PTz31FP7yl7/gi1/84rrPMRqNCA0NBQBkZWUhKytrM/GCmlQqRVVVFR555BEcOXIEIyMj+PnPf46wsDDR0YiIKIAMDAxgYGAAALC8vOyx40pOnz7t1kcW7777Ll5++WW8+OKLdywj63E4HHjyySfx+uuvY//+/Td97cqVK8jNzYXT6cTevXs3fWy62czMDJ544glIJBK89dZbSEhIEB2JiIgC0KVLlxAVFYW+vj7s2bNnW8dy65JNT08PGhsbcfLkSbfKyPLyMoaGhm78/pXz58+jvr4eBw4cwBe+8IVtBaY7S0hIwPDwMORyORQKxY0mS0RE5KvcumTT2NiIXbt2oaKi4qbHa2tr8dBDDwEADh8+jOeffx6ZmZlYXV3FL3/5S9TX18PlciEqKgpf+cpX8IMf/ABSKfdi2wlhYWFobm7GY489hvz8fJSXl6OyspLzT0REPsntSzbexEs23vXb3/4W+fn5OHDgAEwmE2JiYkRHIiKiALDjl2zIv6WkpMBqtSI0NBQKhQI2m010JCIiopuwkASJ6OhodHd3w2AwICMjA62trVyCTUREPoOFJIhIpVJUVFSgr68PlZWVKC4uxsLCguhYRERELCTBSKPRwG63Y2pqCmq1GtPT06IjERFRkGMhCVLx8fGwWCzQaDRQKpXo7e0VHYmIiIIYC0kQk8lkaGhoQEtLC3Q6HYxGI1ZWVkTHIiKiIMRCQigoKMDY2Bh6enqQlZWFCxcuiI5ERERBhoWEAADJyckYHx9HbGws5HI5RkZGREciIqIgwkJCN0RGRqKjowPl5eXIzMxEY2MjlwYTEdGOYCGhm0gkEpSUlMBsNqO2thaFhYU3ficRERGRt7CQ0LrS0tJgt9vhcDigUqkwOTkpOhIREQUwFhLaUFxcHMxmM7RaLVQqFTo7O0VHIiKiAMVCQrcVEhKCmpoamEwm6PV6lJWVweVyiY5FREQBhoWE3KLVamG1WjE4OAiNRoPZ2VnRkYiIKICwkJDbkpKSMDo6isTERKSmpsJisYiOREREAYKFhDYlPDwcbW1tOH78OHJyclBXV8elwUREtG0sJLRpEokEer0eQ0NDaGpqQl5eHpxOp+hYRETkx1hIaMuUSiVsNhsWFxehVCoxMTEhOhIREfkpFhLalpiYGPT390On00GtVsNkMomOREREfoiFhLZNKpWiqqoKXV1dKC0thcFgwNLSkuhYRETkR1hIyGOys7Nht9thtVqRnp6OmZkZ0ZGIiMhPsJCQRyUkJGB4eBhyuRwKhQIDAwOiIxERkR9gISGPCwsLQ3NzM+rr65Gfn4/q6mqsrq6KjkVERD6MhYS8pqioCGfOnEF7eztyc3MxNzcnOhIREfkoFhLyqpSUFFitVoSGhkKhUMBms4mOREREPoiFhLwuOjoa3d3dMBgMyMjIQGtrK3d3JSKim7CQ0I6QSqWoqKhAX18fKisrUVxcjIWFBdGxiIjIR7CQ0I7SaDSw2+2YmpqCWq3G9PS06EhEROQDWEhox8XHx8NisUCj0UCpVKK3t1d0JCIiEoyFhISQyWRoaGhAS0sLdDodjEYjVlZWRMciIiJBWEhIqIKCAoyNjaGnpwdZWVm4cOGC6EhERCQACwkJl5ycjPHxccTGxkIul2NkZER0JCIi2mEsJOQTIiMj0dHRgfLycmRmZqKxsZFLg4mIgggLCfkMiUSCkpISmM1m1NbWorCwEPPz86JjERHRDmAhIZ+TlpYGu90Oh8MBlUqFyclJ0ZGIiMjLWEjIJ8XFxcFsNkOr1UKlUqGzs1N0JCIi8iIWEvJZISEhqKmpgclkgl6vR1lZGVwul+hYRETkBSwk5PO0Wi2sVisGBweh0WgwOzsrOhIREXkYCwn5haSkJIyOjiIxMRGpqamwWCyiIxERkQexkJDfCA8PR1tbG44fP46cnBzU1dVxaTARUYBgISG/IpFIoNfrMTQ0hKamJuTl5cHpdIqORURE28RCQn5JqVTCZrNhcXERSqUSExMToiMREdE2sJCQ34qJiUF/fz90Oh3UajVMJpPoSEREtEUsJOTXpFIpqqqq0NXVhdLSUhgMBiwtLYmORUREm8RCQgEhOzsbdrsdVqsV6enpmJmZER2JiIg2gYWEAkZCQgKGh4chl8uhUCgwMDAgOhIREbmJhYQCSlhYGJqbm1FfX4/8/HxUV1djdXVVdCwiIroDFhIKSEVFRThz5gza29uRm5uLubk50ZGIiOg2WEgoYKWkpMBqtSI0NBQKhQI2m010JCIi2gALCQW06OhodHd3w2AwICMjA62trdzdlYjIB7GQUMCTSqWoqKhAX18fKisrUVxcjIWFBdGxiIjoU1hIKGhoNBrY7XZMTU1BrVZjenpadCQiIvo7FhIKKvHx8bBYLNBoNFAqlejt7RUdiYiIwEJCQUgmk6GhoQEtLS3Q6XQwGo1YWVkRHYuIKKiFuDPo1Vdfxfvvvw+Hw4Hdu3fj4YcfxrFjx3DPPfds+Jzl5WU0NTXh9OnTcLlcSElJQVlZ2W2fQ7STCgoK8OCDDyIvLw9jY2Po6Ojg+UlEJIhbn5BIJBJUVFTg7bffxuuvvw4AMBqNt31OU1MTfve736GlpQVvvfUWIiMj8cILL3CTKvIpycnJGB8fR2xsLORyOUZGRkRHIiIKSm4VkmeffRYHDx6ETCZDREQEnnrqKUxPT+Py5cvrjl9eXsavf/1rfOc738G+ffuwZ88ePPfcczh37hx+//vfe/QbINquyMhIdHR0oLy8HJmZmWhsbOTSYCKiHbale0g++OADxMXFITIyct2vf/jhh1haWkJycvKNx6KionDvvffij3/849aSEnmRRCJBSUkJzGYzamtrUVhYiPn5edGxiIiCxqYLic1mQ3t7O55//vkNx1zf4yEiIuKmxyMiIrj/A/m0tLQ02O12OBwOqFQqTE5Oio5ERBQU3Lqp9brR0VGcOHECRqMRKpVqw3Hh4eEAgPn5eYSFhd14fH5+/sbX1mM0GhEaGgoAyMrKQlZW1mbiEXlEXFwczGYzfvSjH0GlUuG1115DQUGB6FhERD5hYGDgxm9TX15e9thx3S4k7777Ll5++WW8+OKLty0jALB//36EhYVhcnISaWlpAACn04nz58/jgQce2PB5J0+exN69e92NROQ1ISEhqKmpwaOPPoqioiKMjo6irq4OMplMdDQiIqE+/YHBpUuX8Morr3jkuG5dsunp6UFjYyNOnjx5xzICAKGhocjOzsapU6fgcDiwsLCApqYmJCQk4NChQ9sOTbRTtFotrFYrBgcHodFoMDs7KzoSEVFAcquQNDY24urVq6ioqMDhw4dv/DMxMXFjzOHDh/Huu+/e+O9/+7d/w6FDh6DX65Gfnw+n04mTJ09CKuVebORfkpKSMDo6isTERKSmpsJisYiOREQUcCSnT58Wvr7xypUryM3NhdPp5CUb8llra2tobW1FWVkZqqqq8P3vfx8SiUR0LCIiYS5duoSoqCj09fVhz5492zoWP64gcpNEIoFer8fQ0BCampqQl5cHp9MpOhYRUUBgISHaJKVSCZvNhsXFRSiVypsuXRIR0dawkBBtQUxMDPr7+6HT6aBWq2EymURHIiLyaywkRFsklUpRVVWFrq4ulJaWwmAwYGlpSXQsIiK/xEJCtE3Z2dmw2+2wWq1IT0/HzMyM6EhERH6HhYTIAxISEjA8PAy5XA6FQnFjF0MiInIPCwmRh4SFhaG5uRn19fXIz89HdXU1VldXRcciIvILLCREHlZUVIQzZ86gvb0dubm5mJubEx2JiMjnsZAQeUFKSgqsVitCQ0OhUChgs9lERyIi8mksJEReEh0dje7ubhgMBmRkZKC1tRVra8I3RiYi8kksJEReJJVKUVFRgb6+PlRWVqK4uBgLCwuiYxER+RwWEqIdoNFoYLfbMTU1BbVajenpadGRiIh8CgsJ0Q6Jj4+HxWKBRqOBUqlEb2+v6EhERD6DhYRoB8lkMjQ0NKClpQU6nQ5GoxErKyuiYxERCcdCQiRAQUEBxsbG0NPTg6ysLFy4cEF0JCIioVhIiARJTk7G+Pg4YmNjIZfLMTIyIjoSEZEwLCREAkVGRqKjowPl5eXIzMxEY2MjlwYTUVBiISESTCKRoKSkBGazGbW1tSgsLMT8/LzoWEREO4qFhMhHpKWlwW63w+FwQKVSYXJyUnQkIqIdw0JC5EPi4uJgNpuh1WqhUqnQ2dkpOhIR0Y5gISHyMSEhIaipqYHJZIJer0dZWRlcLpfoWEREXsVCQuSjtFotrFYrBgcHodFoMDs7KzoSEZHXsJAQ+bCkpCSMjo4iMTERqampsFgsoiMREXkFCwmRjwsPD0dbWxuOHz+OnJwc1NXVcWkwEQUcFhIiPyCRSKDX6zE0NISmpibk5eXB6XSKjkVE5DEsJER+RKlUwmazYXFxEUqlEhMTE6IjERF5BAsJkZ+JiYlBf38/dDod1Go1TCaT6EhERNvGQkLkh6RSKaqqqtDV1YXS0lIYDAYsLS2JjkVEtGUsJER+LDs7G3a7HVarFenp6ZiZmREdiYhoS1hIiPxcQkIChoeHIZfLoVAoMDAwIDoSEdGmsZAQBYCwsDA0Nzejvr4e+fn5qK6uxurqquhYRERuYyEhCiBFRUU4c+YM2tvbkZubi7m5OdGRiIjcwkJCFGBSUlJgtVoRGhoKhUIBm80mOhIR0R2xkBAFoOjoaHR3d8NgMCAjIwOtra3c3ZWIfBoLCVGAkkqlqKioQF9fHyorK1FcXIyFhQXRsYiI1sVCQhTgNBoN7HY7pqamoFarMT09LToSEdEtWEiIgkB8fDwsFgs0Gg2USiV6e3tFRyIiugkLCVGQkMlkaGhoQEtLC3Q6HYxGI1ZWVkTHIiICwEJCFHQKCgowNjaGnp4eZGVl4cKFC6IjERGxkBAFo+TkZIyPjyM2NhZyuRwjIyOiIxFRkGMhIQpSkZGR6OjoQHl5OTIzM9HY2MilwUQkDAsJURCTSCQoKSmB2WxGbW0tCgsLMT8/LzoWEQUhFhIiQlpaGux2OxwOB1QqFSYnJ0VHIqIgw0JCRACAuLg4mM1maLVaqFQqdHZ2io5EREGEhYSIbggJCUFNTQ1MJhP0ej3KysrgcrlExyKiIMBCQkS30Gq1sFqtGBwchEajwezsrOhIRBTgWEiIaF1JSUkYHR1FYmIiUlNTYbFYREciogDGQkJEGwoPD0dbWxuOHz+OnJwc1NXVcWkwEXkFCwkR3ZZEIoFer8fQ0BCampqQl5cHp9MpOhYRBRgWEiJyi1KphM1mw+LiIpRKJSYmJkRHIqIAwkJCRG6LiYlBf38/dDod1Go1TCaT6EhEFCBYSIhoU6RSKaqqqtDV1YXS0lIYDAYsLS2JjkVEfo6FhIi2JDs7G3a7HVarFenp6ZiZmREdiYj8GAsJEW1ZQkIChoeHIZfLoVAoMDAwIDoSEfmpEHcHDg4O4u2338b09DQWFhbw3nvvYdeuXRuOLy0txR/+8AeEhPzjJY4dO4bHH398e4mJyKeEhYWhubkZjz32GPLz81FeXo7KykpIpfx5h4jc53YhiYiIgFarxdLSEn7605+69Zwnn3wSTz/99JbDEZH/KCoqwsMPP4z8/Hy8//77MJlMiImJER2LiPyE2z/CqFQqfO1rX8N9993nzTxE5MdSUlJgtVoRGhoKhUIBm80mOhIR+Qmvfqba29uLb3zjGzh69CheffVVXL161ZsvR0Q+IDo6Gt3d3TAYDMjIyEBrayt3dyWiO3L7ks1mPfPMM9i/fz8iIiLwpz/9CbW1tfjb3/6Gqqoqb70kEfkIqVSKiooKqFQqPPnkkxgZGcErr7yC8PBw0dGIyEd5rZAcOnToxr8nJSXhueeew3e/+10sLS0hLCxs3ecYjUaEhoYCALKyspCVleWteES0AzQaDex2OwoKCqBWq/HLX/4SiYmJomMR0TYMDAzcWFG3vLzsseN6rZB8lkQiAYDbfnR78uRJ7N27d6ciEdEOiI+Ph8ViQXl5OZRKJV5//XV885vfFB2LiLbo0x8YXLp0Ca+88opHjuv2PSTXrl3D8vIyXC4XgE9a0fLyMlZXV28Z+9FHH2F8fBxXr17F2toazp07h6amJqSlpWH37t0eCU5E/kMmk6GhoQEtLS3Q6XQwGo1YWVkRHYuIfIjbn5C8++67qK2tvfHfX//61wEADQ0NuPfee/Htb38btbW1eOihh7C8vIxTp07hz3/+M65du4a7774b6enpOHr0qOe/AyLyGwUFBXjwwQeRl5eHsbExdHR04J577hEdi4h8gOT06dPCb3+/cuUKcnNz4XQ6ecmGKAhcvnwZzz77LIaHh9HZ2Qm1Wi06EhFtwaVLlxAVFYW+vj7s2bNnW8fiVopEtOMiIyPR0dGB8vJyZGZmorGxkUuDiYIcCwkRCSGRSFBSUgKz2Yza2loUFhZifn5edCwiEoSFhIiESktLg91uh8PhgEqlwuTkpOhIRCQACwkRCRcXFwez2QytVguVSoXOzk7RkYhoh7GQEJFPCAkJQU1NDUwmE/R6PcrKym5sM0BEgY+FhIh8ilarhdVqxeDgIDQaDWZnZ0VHIqIdwEJCRD4nKSkJo6OjSExMRGpqKiwWi+hIRORlLCRE5JPCw8PR1taG48ePIycnB3V1dVwaTBTAWEiIyGdJJBLo9XoMDQ2hqakJeXl5cDqdomMRkRewkBCRz1MqlbDZbFhcXIRSqcTExIToSETkYSwkROQXYmJi0N/fD51OB7VaDZPJJDoSEXkQCwkR+Q2pVIqqqip0dXWhtLQUBoMBS0tLomMRkQewkBCR38nOzobdbofVakV6ejpmZmZERyKibWIhISK/lJCQgOHhYcjlcigUCgwMDIiORETbwEJCRH4rLCwMzc3NqK+vR35+Pqqrq7G6uio6FhFtAQsJEfm9oqIinDlzBu3t7cjNzcXc3JzoSES0SSwkRBQQUlJSYLVaERoaCoVCAZvNJjoSEW0CCwkRBYzo6Gh0d3fDYDAgIyMDra2t3N2VyE+wkBBRQJFKpaioqEBfXx8qKytRXFyMhYUF0bGI6A5YSIgoIGk0GtjtdkxNTUGtVmN6elp0JCK6DRYSIgpY8fHxsFgs0Gg0UCqV6O3tFU9QHWEAAB2KSURBVB2JiDbAQkJEAU0mk6GhoQEtLS3Q6XQwGo1YWVkRHYuIPoOFhIiCQkFBAcbGxtDT04OsrCxcuHBBdCQi+hQWEiIKGsnJyRgfH0dsbCzkcjlGRkZERyKiv2MhIaKgEhkZiY6ODpSXlyMzMxONjY1cGkzkA1hIiCjoSCQSlJSUwGw2o7a2FoWFhZifnxcdiyiosZAQUdBKS0uD3W6Hw+GASqXC5OSk6EhEQYuFhIiCWlxcHMxmM7RaLVQqFTo7O0VHIgpKLCREFPRCQkJQU1MDk8kEvV6PsrIyuFwu0bGIggoLCRHR32m1WlitVgwODkKj0WB2dlZ0JKKgwUJCRPQpSUlJGB0dRWJiIlJTU2GxWERHIgoKLCRERJ8RHh6OtrY2HD9+HDk5Oairq+PSYCIvYyEhIlqHRCKBXq/H0NAQmpqakJeXB6fTKToWUcBiISEiug2lUgmbzYbFxUUolUpMTEyIjkQUkFhIiIjuICYmBv39/dDpdFCr1TCZTKIjEQUcFhIiIjdIpVJUVVWhq6sLpaWlMBgMWFpaEh2LKGCwkBARbUJ2djbsdjusVivS09MxMzMjOhJRQGAhISLapISEBAwPD0Mul0OhUGBgYEB0JCK/x0JCRLQFYWFhaG5uRn19PfLz81FdXY3V1VXRsYj8FgsJEdE2FBUV4cyZM2hvb0dubi7m5uZERyLySywkRETblJKSAqvVitDQUCgUCthsNtGRiPwOCwkRkQdER0eju7sbBoMBGRkZaG1t5e6uRJvAQkJE5CFSqRQVFRXo6+tDZWUliouLsbCwIDoWkV9gISEi8jCNRgO73Y6pqSmo1WpMT0+LjkTk81hIiIi8ID4+HhaLBRqNBkqlEr29vaIjEfk0FhIiIi+RyWRoaGhAS0sLdDodjEYjVlZWRMci8kksJEREXlZQUICxsTH09PQgKysLFy5cEB2JyOewkBAR7YDk5GSMj48jNjYWcrkcIyMjoiMR+RQWEiKiHRIZGYmOjg6Ul5cjMzMTjY2NXBpM9HcsJEREO0gikaCkpARmsxm1tbUoLCzE/Py86FhEwrGQEBEJkJaWBrvdDofDAZVKhcnJSdGRiIRiISEiEiQuLg5msxlarRYqlQqdnZ2iIxEJw0JCRCRQSEgIampqYDKZoNfrUVZWBpfLJToW0Y5jISEi8gFarRZWqxWDg4PQaDSYnZ0VHYloR7ldSAYHB1FSUoKcnBxoNBpcu3bttuMvX76Mn/zkJ8jNzUVubi5+8pOf8MYtIqLbSEpKwujoKBITE5GamgqLxSI6EtGOcbuQREREQKvV4rnnnnNr/IkTJ3Dx4kW88cYbeOONN3Dx4kXU1NRsOSgRUTAIDw9HW1sbjh8/jpycHNTV1XFpMAUFtwuJSqXC1772Ndx33313HHv+/HmMjY3BYDAgKioKUVFRMBgMGBkZgcPh2FZgIqJAJ5FIoNfrMTQ0hKamJuTl5cHpdIqOReRVXrmH5OzZs5DJZEhKSrrxWFJSEmQyGc6ePeuNlyQiCjhKpRI2mw2Li4tQKpWYmJgQHYnIa7xSSBYWFhAREXHL4xEREVhYWPDGSxIRBaSYmBj09/dDp9NBrVbDZDKJjkTkFSHeOGh4ePi6N7DOz88jPDx8w+cZjUaEhoYCALKyspCVleWNeEREfkUqlaKqqgqPPPIIjhw5gpGREfz85z9HWFiY6GgUhAYGBjAwMAAAWF5e9thxvVJIkpKS4HK5MD09jcTERADA9PQ0XC7XTZdxPuvkyZPYu3evNyIREfm97Oxs2O12PPHEE0hPT8dbb72FhIQE0bEoyHz6A4NLly7hlVde8chx3b5kc+3aNSwvL9/YsGd5eRnLy8tYXV29Zey+ffvwyCOPoLm5GU6nE06nE83NzVCr1YiLi/NIcCKiYJSQkIDh4WHI5XIoFIobP6kS+Tu3C8m7776LrKwslJeXAwC+/vWvIysrCxMTE3A4HDh8+PBNN1wZjUbs3bsXR44cwZEjRxAVFYUf/vCHnv8OiIiCTFhYGJqbm1FfX4/8/HxUV1ev+8MhkT+RnD59WvgC9ytXriA3NxdOp5OXbIiINuG3v/0t8vPzceDAAZhMJsTExIiOREHk0qVLiIqKQl9fH/bs2bOtY3HreCIiP5aSkgKr1YrQ0FAoFArYbDbRkYi2hIWEiMjPRUdHo7u7GwaDARkZGWhtbeXuruR3WEiIiAKAVCpFRUUF+vr6UFlZieLiYu77RH6FhYSIKIBoNBrY7XZMTU1BrVZjenpadCQit7CQEBEFmPj4eFgsFmg0GiiVSvT29oqORHRHLCRERAFIJpOhoaEBLS0t0Ol0MBqNWFlZER2LaEMsJEREAaygoABjY2Po6elBVlYWLly4IDoS0bpYSIiIAlxycjLGx8cRGxsLuVyOkZER0ZGIbsFCQkQUBCIjI9HR0YHy8nJkZmaisbGRS4PJp7CQEBEFCYlEgpKSEpjNZtTW1qKwsHDd38xOJAILCRFRkElLS4PdbofD4YBKpcLk5KToSEQsJEREwSguLg5msxlarRYqlQqdnZ2iI1GQYyEhIgpSISEhqKmpgclkgl6vR1lZGVwul+hYFKRYSIiIgpxWq4XVasXg4CA0Gg1mZ2dFR6IgxEJCRERISkrC6OgoEhMTkZqaCovFIjoSBRkWEiIiAgCEh4ejra0Nx48fR05ODurq6rg0mHYMCwkREd0gkUig1+sxNDSEpqYm5OXlwel0io5FQYCFhIiIbqFUKmGz2bC4uAilUomJiQnRkSjAsZAQEdG6YmJi0N/fD51OB7VaDZPJJDoSBTAWEiIi2pBUKkVVVRW6urpQWloKg8GApaUl0bEoALGQEBHRHWVnZ8Nut8NqtSI9PR0zMzOiI1GAYSEhIiK3JCQkYHh4GHK5HAqFAgMDA6IjUQBhISEiIreFhYWhubkZ9fX1yM/PR3V1NVZXV0XHogDAQkJERJtWVFSEM2fOoL29Hbm5uZibmxMdifwcCwkREW1JSkoKrFYrQkNDoVAoYLPZREciP8ZCQkREWxYdHY3u7m4YDAZkZGSgtbWVu7vSlrCQEBHRtkilUlRUVKCvrw+VlZUoLi7GwsKC6FjkZ1hIiIjIIzQaDex2O6ampqBWqzE9PS06EvkRFhIiIvKY+Ph4WCwWaDQaKJVK9Pb2io5EfoKFhIiIPEomk6GhoQEtLS3Q6XQwGo1YWVkRHYt8HAsJERF5RUFBAcbGxtDT04OsrCxcuHBBdCTyYSwkRETkNcnJyRgfH0dsbCzkcjlGRkZERyIfxUJCREReFRkZiY6ODpSXlyMzMxONjY1cGky3YCEhIiKvk0gkKCkpgdlsRm1tLQoLCzE/Py86FvkQFhIiItoxaWlpsNvtcDgcUKlUmJycFB2JfAQLCRER7ai4uDiYzWZotVqoVCp0dnaKjkQ+gIWEiIh2XEhICGpqamAymaDX61FWVgaXyyU6FgnEQkJERMJotVpYrVYMDg5Co9FgdnZWdCQShIWEiIiESkpKwujoKBITE5GamgqLxSI6EgnAQkJERMKFh4ejra0Nx48fR05ODurq6rg0OMiwkBARkU+QSCTQ6/UYGhpCU1MT8vLy4HQ6RceiHcJCQkREPkWpVMJms2FxcRFKpRITExOiI9EOYCEhIiKfExMTg/7+fuh0OqjVaphMJtGRyMtYSIiIyCdJpVJUVVWhq6sLpaWlMBgMWFpaEh2LvISFhIiIfFp2djbsdjusVivS09MxMzMjOhJ5AQsJERH5vISEBAwPD0Mul0OhUGBgYEB0JPIwFhIiIvILYWFhaG5uRn19PfLz81FdXY3V1VXRschDWEiIiMivFBUV4cyZM2hvb0dubi7m5uZERyIPYCEhIiK/k5KSAqvVitDQUCgUCthsNtGRaJtYSIiIyC9FR0eju7sbBoMBGRkZaG1t5e6ufoyFhIiI/JZUKkVFRQX6+vpQWVmJ4uJiLCwsiI5FW8BCQkREfk+j0cBut2NqagpqtRrT09OiI9EmsZAQEVFAiI+Ph8VigUajgVKpRG9vr+hItAksJEREFDBkMhkaGhrQ0tICnU4Ho9GIlZUV0bHIDSHuDlxbW0NbWxv6+/tx5coVHDhwAKWlpfjSl7607vjS0lL84Q9/QEjIP17i2LFjePzxx7efmoiI6DYKCgrw4IMPIi8vD2NjY+jo6MA999wjOhbdhtufkLz55pt45513UFdXh7fffhuHDh1CeXk5rl69uuFznnzySbzzzjs3/mEZISKinZKcnIzx8XHExsZCLpdjZGREdCS6DbcLya9+9SsUFBTg/vvvR1hYGIqLi+FyufCb3/zGm/mIiIi2LDIyEh0dHSgvL0dmZiYaGxu5NNhHuVVI5ufncf78eSQnJ994bNeuXXjggQfwxz/+ccPn9fb24hvf+AaOHj2KV1999bafphAREXmDRCJBSUkJzGYzamtrUVhYiPn5edGx6DPcKiTX13RHRETc9HhERMSG672feeYZmEwm/OpXv8KLL76IDz74AHV1dduMS0REtDVpaWmw2+1wOBxQqVSYnJwUHYk+xa2bWsPDwwHglkY5Pz+Pz3/+8+s+59ChQzf+PSkpCc899xy++93vYmlpCWFhYes+x2g0IjQ0FACQlZWFrKwsd+IRERG5JS4uDmazGT/60Y+gUqnw2muvoaCgQHQsvzIwMHDjty0vLy977LhuFZKIiAjs27cPk5OT+PKXvwwAuHbtGs6ePYvMzEy3XkgikQDAba/dnTx5Env37nXreERERFsREhKCmpoaPProoygqKsLo6Cjq6uogk8lER/MLn/7A4NKlS3jllVc8cly3b2rVarXo7OzEuXPnsLS0hFOnTiEkJATp6em3jP3oo48wPj6Oq1evYm1tDefOnUNTUxPS0tKwe/dujwQnIiLaDq1WC6vVisHBQWg0GszOzoqOFNTc3ofkX//1X7GwsIDvfve7WFhYwMGDB1FbW4u77roLDocD3/72t1FbW4uHHnoIy8vLOHXqFP785z/j2rVruPvuu5Geno6jR49683shIiLalKSkJIyOjsJgMCA1NRVvvvkmvvrVr4qOFZQkp0+fFr7+6cqVK8jNzYXT6eQlGyIi2nFra2tobW1FWVkZqqqq8P3vf//GrQa0sUuXLiEqKgp9fX3Ys2fPto7FreOJiCjoSSQS6PV6DA0NoampCXl5eXA6naJjBRUWEiIior9TKpWw2WxYXFyEUqnExMSE6EhBg4WEiIjoU2JiYtDf3w+dTge1Wg2TySQ6UlBgISEiIvoMqVSKqqoqdHV1obS0FAaDAUtLS6JjBTQWEiIiog1kZ2fDbrfDarUiPT0dMzMzoiMFLBYSIiKi20hISMDw8DDkcjkUCsWNXUrJs1hIiIiI7iAsLAzNzc2or69Hfn4+qqursbq6KjpWQGEhISIiclNRURHOnDmD9vZ25ObmYm5uTnSkgMFCQkREtAkpKSmwWq0IDQ2FQqGAzWYTHSkgsJAQERFtUnR0NLq7u2EwGJCRkYHW1tbb/vJYujMWEiIioi2QSqWoqKhAX18fKisrUVxcjIWFBdGx/BYLCRER0TZoNBrY7XZMTU1BrVZjenpadCS/xEJCRES0TfHx8bBYLNBoNFAqlejt7RUdye+wkBAREXmATCZDQ0MDWlpaoNPpYDQasbKyIjqW32AhISIi8qCCggKMjY2hp6cHWVlZuHDhguhIfoGFhIiIyMOSk5MxPj6O2NhYyOVyjIyMiI7k81hIiIiIvCAyMhIdHR0oLy9HZmYmGhsbuTT4NlhIiIiIvEQikaCkpARmsxm1tbUoLCzE/Py86Fg+iYWEiIjIy9LS0mC32+FwOKBSqTA5OSk6ks9hISEiItoBcXFxMJvN0Gq1UKlU6OzsFB3Jp7CQEBER7ZCQkBDU1NTAZDJBr9ejrKwMLpdLdCyfwEJCRES0w7RaLaxWKwYHB6HRaDA7Oys6knAsJERERAIkJSVhdHQUiYmJSE1NhcViER1JKBYSIiIiQcLDw9HW1objx48jJycHdXV1Qbs0mIWEiIhIIIlEAr1ej6GhITQ1NSEvLw9Op1N0rB3HQkJEROQDlEolbDYbFhcXoVQqMTExITrSjmIhISIi8hExMTHo7++HTqeDWq2GyWQSHWnHsJAQERH5EKlUiqqqKnR1daG0tBQGgwFLS0uiY3kdCwkREZEPys7Oht1uh9VqRXp6OmZmZkRH8ioWEiIiIh+VkJCA4eFhyOVyKBQKDAwMiI7kNSwkREREPiwsLAzNzc2or69Hfn4+qqursbq6KjqWx7GQEBER+YGioiKcOXMG7e3tyM3NxdzcnOhIHsVCQkRE5CdSUlJgtVoRGhoKhUIBm80mOpLHsJAQERH5kejoaHR3d8NgMCAjIwOtra0BsbsrCwkREZGfkUqlqKioQF9fHyorK1FcXIyFhQXRsbaFhYSIiMhPaTQa2O12TE1NQa1WY3p6WnSkLWMhISIi8mPx8fGwWCzQaDRQKpXo7e0VHWlLWEiIiIj8nEwmQ0NDA1paWqDT6WA0GrGysiI61qawkBAREQWIgoICjI2NoaenB1lZWbhw4YLoSG5jISEiIgogycnJGB8fR2xsLORyOUZGRkRHcgsLCRERUYCJjIxER0cHysvLkZmZicbGRp9fGsxCQkREFIAkEglKSkpgNptRW1uLwsJCzM/Pi461IRYSIiKiAJaWlga73Q6HwwGVSoXJyUnRkdbFQkJERBTg4uLiYDabodVqoVKp0NnZKTrSLVhIiIiIgkBISAhqampgMpmg1+tRVlYGl8slOtYNLCRERERBRKvVwmq1YnBwEBqNBrOzs6IjAWAhISIiCjpJSUkYHR1FYmIiUlNTYbFYREdiISEiIgpG4eHhaGtrw/Hjx5GTk4O6ujqhS4NZSIiIiIKURCKBXq/H0NAQmpqakJeXB6fTKSQLCwkREVGQUyqVsNlsWFxchFKpxMTExI5nYCEhIiIixMTEoL+/HzqdDmq1GiaTaUdfn4WEiIiIAABSqRRVVVXo6upCaWkpDAYDlpaWdua1d+RViIiIyG9kZ2fDbrfDarUiPT0dMzMzXn9NFhIiIiK6RUJCAoaHhyGXy6FQKDAwMODV1wtxd+Da2hra2trQ39+PK1eu4MCBAygtLcWXvvSldcdfvnwZL7/8Mt5//30AwKOPPorS0lJERER4JjkRERF5VVhYGJqbm/HYY48hPz8f5eXlqKyshFTq+c8z3D7im2++iXfeeQd1dXV4++23cejQIZSXl+Pq1avrjj9x4gQuXryIN954A2+88QYuXryImpoajwWn9Xm7wQYTzqXncC49g/PoOZzLzSkqKsKZM2fQ3t6O3NxczM3Nefw13C4kv/rVr1BQUID7778fYWFhKC4uhsvlwm9+85tbxp4/fx5jY2MwGAyIiopCVFQUDAYDRkZG4HA4PPoN0M34h8xzOJeew7n0DM6j53AuNy8lJQVWqxWhoaFQKBSw2WwePb5bhWR+fh7nz59HcnLyjcd27dqFBx54AH/84x9vGX/27FnIZDIkJSXdeCwpKQkymQxnz571QGwiIiLaadHR0eju7obBYEBGRgba2to8dmy37iFZWFgAgFvu/4iIiLjxtc+OX+9ekY3GX9+q9tKlS+7EodtYXl7mPHoI59JzOJeewXn0HM7l9hgMBnz5y19GUVERAHhky3m3Ckl4eDiATz4p+bT5+Xl8/vOfX3f8Z8deH3/9WJ92/T6UL37xi+7EoTt45ZVXREcIGJxLz+Fcegbn0XM4l55z9erVbS9acauQREREYN++fZicnMSXv/xlAMC1a9dw9uxZZGZm3jI+KSkJLpcL09PTSExMBABMT0/D5XLddBnnupiYGHR2duKuu+6CRCLZzvdDREREO2RtbQ1Xr15FTEzMto/l9rJfrVaLzs5OyOVy3HfffTCZTAgJCUF6evotY/ft24dHHnkEzc3NqKysBAA0NzdDrVYjLi7ulvFSqRSxsbHb+DaIiIhIBE9t5yE5ffq0Wxd+1tbWcOrUKfT19WFhYQEHDx7Ef/zHf+D++++Hw+HAt7/9bdTW1uKhhx4C8Mn9IC+//DLGxsYAcB8SIiIi2pjbhYSIiIjIW7h1PBEREQnn9j0k28Ft5z1ns3NZWlqKP/zhDwgJ+cf/6mPHjuHxxx/fqcg+aXBwEG+//Tamp6exsLCA9957D7t27dpwPM/JjW12LnlOru/VV1/F+++/D4fDgd27d+Phhx/GsWPHcM8992z4nOXlZTQ1NeH06dNwuVxISUlBWVnZbZ8T6LYyjy+99BLee+89yGSyG489/vjjOHbs2E5E9lmvv/46zGYznE4ndu3ahQMHDuDYsWPrLk65bjvvlTtyyeYXv/gFuru78dJLLyE+Ph7t7e0wm81ob2/HXXfddcv4H/zgB3C5XHjxxRcBANXV1di9ezdOnDjh7ag+b7NzWVpaigcffBBPP/20gLS+a3x8HJcvX8bS0hJ++tOf3vEvUZ6TG9vsXPKcXF9raysyMjJw//33Y2lpCQ0NDZiZmcFrr7224XN+/vOf43e/+x1OnDiByMhIvPzyyzh37hxaWlq88rtG/MFW5vGll17CtWvX8MILL+xgUt/34Ycf4nOf+xwiIyPhcrnQ09ODX/ziF3jrrbc2/DO+nffKHTljue2852xmLmljKpUKX/va13DffffdcSzPydvbzFzSxp599lkcPHgQMpkMEREReOqppzA9PY3Lly+vO355eRm//vWv8Z3vfAf79u3Dnj178Nxzz+HcuXP4/e9/v8Ppfcdm55E2tn//fkRGRgL45NN5qVSKixcvbjiX232v9Hoh4bbznrPZubyut7cX3/jGN3D06FG8+uqrG/5CRFofz0nP4zl5Zx988AHi4uJu/IXwWR9++CGWlpZuej+IiorCvffee9v3g2Bzp3m8bnR0FFqtFkeOHMHPfvYzfPzxxzuU0LeNjo4iNzcXWVlZaGpqwhNPPIHo6Oh1x273vdLr95B4e9v5YLLZuQSAZ555Bvv370dERAT+9Kc/oba2Fn/7299QVVXl9byBguekZ/GcvDObzYb29nb8+Mc/3nDMVt4Pgo078wgA3/rWt6DX6/G5z30Os7OzaGhowAsvvID/+q//CvrNOh977DH09fXh0qVLGBgYuO2eYdt9r/T6JyS323Z+vW3kN7vtfDDZ7FwCwKFDh7B3715IpVIkJSXhueeew3//939jaWnJ63kDBc9Jz+I5eXujo6OoqqqC0WiESqXacNxW3g+CibvzCAAHDx7E3XffDYlEgvj4eHzve9/D//zP/+Avf/nLDqX1fXv37kV+fj7+8z//c8NPO7b7Xun1QvLpbeevu77t/AMPPHDL+E9vO3/d7badDyabncv1XG/7nvhFSMGC56R38Zz8h3fffRcnTpzAiy++uO4u2J+2f/9+hIWF3fR+4HQ6cf78ebffDwLVZuZxPTwn17e2toaVlRX89a9/Xffr232v3JGbWq9vO3/u3DksLS3h1KlTbm0773Q64XQ6b7vtfLDZzFx+9NFHGB8fx9WrV7G2toZz586hqakJaWlp2L17t4D0vuPatWtYXl6Gy+UC8MkNgsvLy1hdXb1lLM/J29vMXPKc3FhPTw8aGxtx8uTJO/5EDwChoaHIzs7GqVOn4HA4sLCwgKamJiQkJODQoUM7kNg3bXYel5eXMTQ0dOMn+/Pnz6O+vh4HDhzAF77wBW/H9WldXV346KOPAAAff/wxGhoaEBISsuH5td33yh1Z9stt5z1nM3N5/vx5/PjHP8af//xnXLt2DXfffTfS09Nx9OjRoP9I99e//jVqa2tvebyhoQH33nsvz8lN2Mxc8pzcmEajwa5du27aCwPATefh4cOH8fzzz9/4paaf3odkeXkZKSkpeP7554N6H5LNzuPi4iLKy8vxf//3f3C5XIiKisJXvvIVfOc738Hdd98t4lvwGT/84Q/xv//7v7h69SrCw8PxT//0Tzh69CgOHjwIAB7/+5tbxxMREZFwwblzDhEREfkUFhIiIiISjoWEiIiIhGMhISIiIuFYSIiIiEg4FhIiIiISjoWEiIiIhGMhISIiIuFYSIiIiEi4/wdyPk7YALgWIQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7OnWmGJbOh_7",
        "colab_type": "text"
      },
      "source": [
        "In particular, all the examples that fall above this line are classified as being positive, while the examples predicted as negative are located below this line."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DEoPYF7H4rnl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "outputId": "6c4f2d2a-93da-4dc2-c656-bb86b7717840"
      },
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "data = np.array([\n",
        "    [0.4, 1.3],\n",
        "    [3, 3]\n",
        "])\n",
        "\n",
        "col = np.ones((2,1))\n",
        "x = np.append(col, data, axis=1)\n",
        "\n",
        "y_pred = predict(theta, x)\n",
        "print(y_pred)\n",
        "\n",
        "ax = plt.gca()\n",
        "ax.scatter(data[:,0], data[:, 1], c=np.array([0,1]), s=50,\n",
        "           cmap=\"RdBu\", vmin=-.2, vmax=1.2,\n",
        "           edgecolor=\"white\", linewidth=1)\n",
        "\n",
        "plt.plot(x_values, y_values, c='black')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0 1]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zUaevC9HoMkK",
        "colab_type": "text"
      },
      "source": [
        "Let us draw the decision boundary defined by the vector $\\Theta = [-3, 1, 1]^T$ along with the examples in the toy dataset presented above."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y0OARtsvKvyK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "f58fc22b-a548-47d4-ecc9-70aba18c4da2"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('classic')\n",
        "np.set_printoptions(precision=3, suppress=True)\n",
        "\n",
        "colormap = np.array(['r', 'b'])\n",
        "\n",
        "def plot_scatter(X, y, colormap):\n",
        "  plt.grid()\n",
        "  plt.xlim([-5.0, 5.0])\n",
        "  plt.ylim([-5.0, 5.0])\n",
        "  plt.xlabel('$x_1$', size=20)\n",
        "  plt.ylabel('$x_2$', size=20)\n",
        "  plt.title('Input 2D points', size=18)\n",
        "  plt.scatter(X[:,0], X[:, 1], s=50, c=colormap[y])\n",
        "\n",
        "plot_scatter(X, y, colormap)\n",
        "\n",
        "point1 = [-5, 8]\n",
        "point2 = [5, -2]\n",
        "\n",
        "x_values = [point1[0], point2[0]]\n",
        "y_values = [point1[1], point2[1]]\n",
        "\n",
        "plt.plot(x_values, y_values, c='black')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fa566272828>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V20itV5QlayV",
        "colab_type": "text"
      },
      "source": [
        "By analysing the image above, it should be clear that the decision boundary defined by the vector $\\Theta = [-3, 1, 1]^T$ is **not** the best one, in the sense that it does not correctly classify many of the examples in the training dataset. In particular, the *prediction error* of the corresponding classifier is $8/17 \\approx 47\\%$, which is worst than tossing a coin to determine the class of an new example!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f81qGdXd6Pz2",
        "colab_type": "text"
      },
      "source": [
        "## Optimization problems\n",
        "\n",
        "You now should understand that the goal in logistic regression is to find the components of the vector $\\Theta$, taking as input the training set $X$. You should also understand that, from the infinitely many vectors $\\Theta$, we want to find the one that minimizes the prediction error of the corresponding model.\n",
        "\n",
        "To determine the most appropriate parameter vector $\\Theta$, logistic regression must solve an optimization problem. An optimization problem is one in which, given a function, we want to find the point that corresponds to the optimal value (minimum or maximum) of the function.\n",
        "\n",
        "As an illustration, the following code computes the minimum value of the function $f(x) = x^3 - 3x^2 + 7$ within the range $[3,500]$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mQI8O4sW68HX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "7c9ecfde-7b7d-40a8-b507-b75896c785f8"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "f1 = lambda x: (x ** 3)-(3 *(x ** 2))+7\n",
        "\n",
        "# Get 1000 evenly spaced num bers between -1 and 3 (arbitratil chosen to ensure steep curve)\n",
        "x = np.linspace(-0.5,3,500)\n",
        "\n",
        "# Plot the curve\n",
        "plt.plot(x, f1(x))\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXxU1f3/8dcnkz1kIQsBkkAIO4QkQEQWC4oLLghaN7TWpbWIWm2//rTVanGrXWy/rVJblWKtVqu0CAKuVdwqSDBACAlrWEJIgGwkIYHs5/dHJn5jGmCAmdw7k8/z8ZhH7sw9mXnnAh9uzj33HDHGoJRSyvv5WR1AKaWUe2hBV0opH6EFXSmlfIQWdKWU8hFa0JVSykf4W/XBsbGxJjk52aqPV0opr7R+/fpyY0xcV/ssK+jJyclkZ2db9fFKKeWVRKTwePu0y0UppXyEFnSllPIRWtCVUspHaEFXSikfoQVdKaV8xEkLuogMF5GcDo8aEflxpzYiIgtEpEBEckVknOciK6WU6spJhy0aY7YDGQAi4gCKgWWdml0CDHU+zgaec35VSinVTU51HPr5wC5jTOdxkLOBV0zbXLxrRSRKRPoZYw64JaWXMMZQXHWMfRVH2X/4GNXHmmhobqHVQHiwPxHBAST2DmFwn17EhAUiIlZHVkp1s6c/2kHmwGjOGRrr9vc+1YI+B3i9i9cTgKIOz/c7X/tGQReRucBcgAEDBpziR9vToZp63s87yBcF5WwoPExFXaNL3xfbK5CzkqOZmBLD9BF9SIoO9XBSpZTV6hqaeWbVTn50/lBrC7qIBAKzgAdP98OMMQuBhQCZmZleu7JGU0sr7+Ud5NW1hXy1txJjYGBMKOcO78PYAVGkxIaRFB1KVGgAQf4O/ARqG5qpOtrEvsqjFJTWkldSTdbuSt7LO8gjK/JJT4xkVkYCV49LJDI0wOofUSnlAVsP1GAMjEmI9Mj7n8oZ+iXABmPMoS72FQNJHZ4nOl/zKY3NrbyWVcjCz3dzoLqe5JhQfnz+MC5L68uQPuEn/N6o0ECiQgNJjg1j6rD/m4ahsKKO9/IO8k7uAZ54ewu//WAbs9MTuH1aCilxvTz9IymlulFecTUAqTYo6NfTdXcLwArghyLyBm0XQ6t9qf/cGMO7mw/ym/e3sa/yKGcPiuYXV6Ry3vA++PmdWT/4wJgw5k0bzLxpg8kvqebVtYUs21jMkg37uXJsAvdMH8qAGO2OUcoXbC6uIbZXEH3Cgzzy/i4VdBEJAy4Ebu/w2jwAY8zzwLvApUABcBS41e1JLXKwup6Hlm1m1bZSRvQN5+XvTWDq0FiPXNAc3T+SX307jXsvHM5zn+7i1axC3tpYzK1TkvnxBcMIC7JsLjWllBtsLq4iPTHSYwMiXKoQxpg6IKbTa8932DbAXe6NZr0Vm0p4aNlmmlpaefiykdw6ZRCOMzwjd0VceBDzLx/F7dNS+P2/d/CX/+xh5aYDzL98FJek9tXRMUp5obqGZgpKa7l0TD+PfYbeKdqFxuZWHlmexz2vb2RYfDjv/2gqt30rpVuKeUfxEcH85uo03rxjMtFhgdz52gbmvbqeShdH0iil7GPLgRpaDaQleqb/HLSg/5eK2gbmLPySl78s5LZzBvHG3Ikkx4ZZmmn8wN6s+OEUHrxkBB9vK2XG05/z6fZSSzMppU5N7n7PXhAFLejfUFhRx1XPrSG/pIZnbxjLwzNHEeCwxyHyd/hx+7TBLL/rHHqHBnDLS1/xy3e30tzSanU0pZQLNu+vol9kMH3Cgz32GfaoVjaQX1LNVc+toepYE//4wdnMTOtvdaQujeofwYofnsONEwew8PPd3PTXdVTUNlgdSyl1ErnF1R49Owct6ABsKanhO4uyCHT48eYdkxk/MNrqSCcUHODgF1eM4bdXp5FdeJhZz67+enyrUsp+jtQ3sbusjjQt6J619UAN31m0ltAAB2/MncRgL7qZ55rMJN6cNxljDNe+8CWfaL+6UraUV1wDwBgPXhCFHl7Q91Uc5bsvZhHk7+D1uRO98gaeMYmRLLtrCoNiw7jt5WzeWLfP6khKqU42F1cBnrvlv12PLeiVdY3c/NI6mlsNr952NgNjrB3JcibiI4JZfPskzhkSywNLN7Ng1U7abg1QStlB7v5qEqJCiOnlmTtE2/XIgl7f1MJtL39FcdUxFt2UyZA+3tPNcjy9gvxZdHMm3x6XwO8/3MFTH2zXoq6UTWwurvbo+PN2Pe5ecmMMP1u2mY1FVfz5hnFkJtv7AuipCHD48bur0wkOcPDcp7uob2ph/sxRemepUhaqPtpEYcVRrjsr6eSNz1CPK+gvr9nL0g3F/M8Fw7jEg7fgWsXPT3jyilSC/P14afVeGppb+cXs1DOeREwpdXo2O0egpSVEefyzelRBz9pdwRPvbOWCkfHcPX2I1XE8RkSYP3MUIQEO/vzpLvz9hMdmjdYzdaUskNtNF0ShBxX0itoG7n59IwOjQ/n9dek+f8YqItw/YzjNrYaFn++mV5A/P7l4hNWxlOpxNu+vZmBMaLcsXNMjCroxhp++mUvV0Sb+dusEIoJ7xopAIsKDl4zgSH0zf/50F2FB/tx1nu/+ZqKUHeXur2bsAM93t0APKeivfFnIR1tLeeTyUYzqH2F1nG4lIvziilSONjbz2w+2Ex7sz02Tkq2OpVSPUFHbQHHVMW6ePLBbPs/nC/rOQ0d48t2tTB/Rh1smJ1sdxxIOP+F316RT19DCIyvy6RMexMWpvndBWCm7yXVeEB3TDRdEwcVx6CISJSJLRGSbiGwVkUmd9p8rItUikuN8zPdM3FPT0mq4f0kuYYEOnro6rUdfFAxw+PHH68eSkRTFj97IYX3hYasjKeXzNu6rwk88Owd6R67eWPQM8L4xZgSQDmztos1/jDEZzsfjbkt4Bl5avYecoioenTWaWA/foeUNQgIdLLopk76Rwdz28lfsKa+zOpJSPi2nqIph8eHdtnzkSQu6iEQCU4EXAYwxjcaYKk8HO1OFFXX87t/bOX9EH2al23MqXCvE9Arib7dOAODWl3TqXaU8xRjDpqIqMpK6p7sFXDtDHwSUAS+JyEYRWeRcNLqzSSKySUTeE5HRXb2RiMwVkWwRyS4rKzuT3CfU2to2qiXAz48nrxzTo7taujIoNoxFN5/Fgep67nh1A43NukiGUu62p7yO6mNNtivo/sA44DljzFigDnigU5sNwEBjTDrwR+Ctrt7IGLPQGJNpjMmMi4s7g9gntnRjMWt3V/Kzy0bSN9Jzq4N4s/EDe/PU1Wms21vJYyvzrY6jlM/JKWrryMjopiGL4FpB3w/sN8ZkOZ8voa3Af80YU2OMqXVuvwsEiEisW5O6qKa+iV+/t42xA6K4LtPzcyd4s9kZCdw+LYXXsvbx6tpCq+Mo5VNyiqoIC3QwtE94t33mSQu6MeYgUCQiw50vnQ9s6dhGRPqKs19DRCY437fCzVldsuCjnVTUNfDYrNE+fzeoO/xkxgjOGx7HoyvyydptyR+ZUj4pp6iKMYmROLqxDrk6yuVu4DURyQUygF+KyDwRmefcfzWQJyKbgAXAHGPB3K0FpUf425q9XJeZRFpi9/2a480cfsIz149lQEwod762gf2Hj1odSSmvV9/UwtYDNWQk9e7Wz3WpoBtjcpx932nGmCuMMYeNMc8bY5537n/WGDPaGJNujJlojFnj2dhdZuTRFVsIDXRw/4zhJ/8G9bWI4AD+clMmjS2t3P739dQ3tVgdSSmvll9SQ1OL6dYLouBDC1ys2lrKFwXl3HvhMI+vCuKLBsf14unrMsgvqeHxt7ec/BuUUsfVfkG0u+ZwaecTBb2l1fDUB9sYFBvGdyZ2z5wJvuj8kfHMmzaYf2Tt462NxVbHUcprbdx3mP6RwcRHdO8oO58o6Es37GfHoVruu2g4AQ6f+JEsc99Fw5iQHM2DSzez89ARq+Mo5ZVyiqq6dbhiO6+vfvVNLfzhwx2kJUZy6Zi+Vsfxev4OP/54w1jCghzc8doG6hqarY6klFcpr21g/+Fj3d5/Dj5Q0F9dW0hJdT0/vXiE3hHqJvERwTwzZyy7ymp5aNlmXWxaqVOQs895Q1E3j3ABLy/oNfVNPPtJAd8aGsuUIZbcx+SzpgyJ5X8uGMZbOSW8uUH705VyVU5RFQ4/6ZYl5zrz6oL+t9V7qTraxE91aTWPuOu8IZw9KJr5y/PYqzMzKuWSnKIqhseHExLo6PbP9tqCfqS+iRe/2MMFI/uQasH/hD2Bw0/4w3UZBDj8+NEbG2lq0Um8lDqRllbnDIsWXBAFLy7of19bSPWxJu6ePtTqKD6tf1QIv/72GDbtr+YPH+6wOo5Straz9AhHGprJHNj9/efgpQX9aGMzi/6zh2nD4ki34EpyT3PJmH7MOSuJ5z7bxZpd5VbHUcq2sve2rQQ2Xgu6615bu4/KukbuOV9XsO8u8y8fxaCYMO5dvInDdY1Wx1HKltYXHia2VxADokMt+XyvK+j1TS288PlupgyJYfzAaKvj9Bihgf4suH4sFXUNPLhUhzIq1ZX1hYfJHNjbsiHUXlfQ39pYTHltg/adWyA1IZL7Zwzn/fyDLNOpAZT6htIj9eyrPGpZdwu0rUbkVa4en0h8RDATU2KsjtIjff+cFD7ccohHVuQzaXAM/SJDrI6klC1sKHT2nydbV9C97gzd3+HHeSP6WB2jx3L4Cb+7Jp3mFsNPluRq14tSTtl7DxPo78fo/hGWZfC6gq6sNzAmjJ9dNpL/7CznH+v2WR1HKVtYv+8w6YmRBPl3/w1F7Vwq6CISJSJLRGSbiGwVkUmd9ouILBCRAhHJFZFxx3sv5RtuPHsA3xoay5PvbKWwQu8iVT1bfVMLecXVlg/UcPUM/RngfWPMCCAd2Npp/yXAUOdjLvCc2xIqWxIRfnNVGg4R7v9XLi2t2vWieq7NxdU0tRhLL4iCCwVdRCKBqcCLAMaYRmNMVadms4FXTJu1QJSI9HN7WmUr/aNCeGTWaNbtreSvX+yxOo5SlrH6hqJ2rpyhDwLKgJdEZKOILBKRsE5tEoCiDs/3O1/7BhGZKyLZIpJdVlZ22qGVfVw1LoELRsbzu39vZ49O4KV6qPWFh0mJDSM6LNDSHK4UdH9gHPCcMWYsUAc8cDofZoxZ6FxsOjMuLu503kLZjIjw5JWpBPr78dM3c2nVrhfVwxhj2LDvsOVn5+BaQd8P7DfGZDmfL6GtwHdUDCR1eJ7ofE31APERwTx82UjW7anUUS+qx9ldXkdlXSOZFo4/b3fSgm6MOQgUichw50vnA52XhV8B3OQc7TIRqDbGHHBvVGVn12YmMWVIDL9+bxslVcesjqNUt1lfaI/+c3B9lMvdwGsikgtkAL8UkXkiMs+5/11gN1AA/AW40+1Jla2JCL+6Mo2WVqPL1qkeJXtvJVGhAaTE9rI6imu3/htjcoDMTi8/32G/Ae5yYy7lhQbEhHLfjOE88fYWlueUcMXY/7ourpTPWbenkrOSo/Hzs35NY71TVLnVLZOTGTsgisdW5lNe22B1HKU86lBNPXsrjnL2IHvM/KoFXbmVw0946qo06hpaeHRFvtVxlPKorD2VAJw9yB6TBWpBV243ND6cu6cP4e3cA3y05ZDVcZTymKzdFfQK8mdkv3CrowBa0JWHzDt3MMPie/HIinzqGpqtjqOUR6zbU0lmcm/8HfYopfZIoXxOgMOPX145huKqYzz9kS4urXxPRW0DO0trmWCT/nPQgq48KDM5musnJPHX1XvJL6m2Oo5SbvXV3vb+cy3oqof46cUjiAoJ4GfL8nRGRuVTsvZUEhzgx5iEKKujfE0LuvKoqNBAfj5zFJuKqvhHVqHVcZRym6zdlYwb0JtAf/uUUfskUT5rdkZ/zhkSy1Pvb+dQTb3VcZQ6Y9XHmth6sMZW/eegBV11AxHhiStSaWhp5fG3O08DpJT3yd5biTH2GX/eTgu66haDYsP44XlDeCf3AJ9sL7U6jlJnZN2eSgIcwtgB9uk/By3oqhvdPi2FwXFh/PytPI41tlgdR6nTtnZPJemJUQQHWLcgdFe0oKtuE+Tv4Mkrx7D/8DGeWbXT6jhKnZa6hmbyiqs5O8Ve/eegBV11s4kpMVw9PpFF/9nNjkNHrI6j1CnLLjxMS6thgs36z0ELurLAg5eMICzIn/nL83TedOV11uwqJ8AhnGWDFYo6c6mgi8heEdksIjkikt3F/nNFpNq5P0dE5rs/qvIVMb2CuH/GcNburmTFphKr4yh1StYUVDA2qTehgS4tJ9GtTuUM/TxjTIYxpvNCF+3+49yfYYx53B3hlO+6fsIAxiRE8uQ7WzlS32R1HKVcUnW0kbySaiYPsV93C2iXi7KIw69tbHpZbQPPfKQXSJV3WLu7bfz55MGxVkfpkqsF3QD/FpH1IjL3OG0micgmEXlPREZ31UBE5opItohkl5WVnVZg5TsykqKYc1YSL63Zy/aDeoFU2d+aXeWEBDjISLLX+PN2rhb0c4wx44BLgLtEZGqn/RuAgcaYdOCPwFtdvYkxZqExJtMYkxkXF3faoZXvuH/GCMKD/fm5XiBVXmB1QTkTBkXbav6WjlxKZYwpdn4tBZYBEzrtrzHG1Dq33wUCRMSev5MoW4kOC+QnM0awbk8ly3P0Aqmyr0M19ewqq2PyYHv2n4MLBV1EwkQkvH0buAjI69Smr4iIc3uC830r3B9X+aLrzkoiPTGSJ9/dSo1eIFU2tWZXOQBThtj3XNWVM/R44AsR2QSsA94xxrwvIvNEZJ6zzdVAnrPNAmCO0d+flYvaL5CW1zbw9Id6gVTZ0+qCCiJDAhjVL8LqKMd10oGUxpjdQHoXrz/fYftZ4Fn3RlM9SVpiFDdMGMDLX+7lmsxERtr4H43qeYwxfLmrgkkpMfj5idVxjsuePfuqR7p/xnAigvUOUmU/hRVHKa46xhSbjj9vpwVd2UZUaCAPXDKCr/YeZtnGYqvjKPW1NbvaLglOtnH/OWhBVzZzzfgkMpKi+OW72/QCqbKN1bvKiY8IIiU2zOooJ6QFXdmKn5/wxOxUKuoaWKB3kCobaG1t6z+fMjgW52A+29KCrmxnTGIkc85K4m9r9lJQqneQKmvllVRTWdfI1GH2vxlSC7qypfsuGk5ooINHV2zRC6TKUp9tb5um5Jyh9u4/By3oyqZiegVx74XD+KKgnA/yD1kdR/Vgn+8sY0xCJLG9gqyOclJa0JVt3ThxIMPjw/nFO1uob9I1SFX3q6lvYsO+KqYOs//ZOWhBVzbm7/Dj0Vmj2X/4GC98ttvqOKoHWlNQTkurYdqwPlZHcYkWdGVrkwbHcFlaP/78aQH7Dx+1Oo7qYT7bUU6vIH/GDrDndLmdaUFXtvezS0ciAk++s9XqKKoHMcbw+Y4yJg+OIcDhHaXSO1KqHi0hKoS7zh3Ce3kHWV1QbnUc1UPsKqujuOoY04bbf7hiOy3oyiv8YGoKSdEhPLoin6aWVqvjqB7gsx1twxWnDtWCrpRbBQc4+Pllo9hZWssrXxZaHUf1AJ/vKCMlLoyk6FCro7hMC7ryGheOimfqsDie/nAH5bUNVsdRPqy+qYWsPRVedXYOWtCVFxER5s8cxbGmFp56f5vVcZQPW7enkvqmVq/qPwcXC7qI7BWRzSKSIyLZXewXEVkgIgUikisi49wfVSkY0qcX3ztnEP/M3k9OUZXVcZSP+mxHGYH+fkwcZO/5zzs7lTP084wxGcaYzC72XQIMdT7mAs+5I5xSXbl7+hDiwoN4ZEU+ra06z4tyL2MMq7YeYlJKDCGBDqvjnBJ3dbnMBl4xbdYCUSLSz03vrdQ3hAcH8MDFI9hUVMWSDfutjqN8zK6yOvZWHOWCkd5xd2hHrhZ0A/xbRNaLyNwu9icARR2e73e+9g0iMldEskUku6ys7NTTKuV05dgExg2I4qn3dSEM5V4fb2ubDG76yHiLk5w6Vwv6OcaYcbR1rdwlIlNP58OMMQuNMZnGmMy4OO+62KDsxc9PeGxWKhV1jTyjC2EoN/poaykj+oaTEBVidZRT5lJBN8YUO7+WAsuACZ2aFANJHZ4nOl9TymPaF8J4ec1edh7ShTDUmas62sj6wsNc4IVn5+BCQReRMBEJb98GLgLyOjVbAdzkHO0yEag2xhxwe1qlOvl6IYyV+boQhjpjn24vo6XVcL4X9p+Da2fo8cAXIrIJWAe8Y4x5X0Tmicg8Z5t3gd1AAfAX4E6PpFWqk/aFMFYXVPBB/kGr4ygvt2pbKbG9AklP9I7ZFTvzP1kDY8xuIL2L15/vsG2Au9wbTSnX3DhxIK+vK+KJt7cybVgfrxtqpuyhqaWVT7eXcvHovvj52Xsx6OPRO0WV12tfCKO46hgvfL7L6jjKS321t5Ij9c2c76X956AFXfmI9oUwnvt0F0WVuhCGOnWrtpYS6PDjW16wGPTxaEFXPuOhS0fiJ8Iv3tlidRTlZb6+O3RwDGFBJ+2Jti0t6Mpn9I8K4a7zBvNB/iE+36E3rinXtd8d6q2jW9ppQVc+5QdTU0iOCeXRlfk0NutCGMo17SOkvHX8eTst6MqnBPk7eOTy0ewuq+Ovq/dYHUd5iQ/yD5KeFEV/L7w7tCMt6MrnnDeiDxeMjGfBqp0cqD5mdRxlc8VVx8jdX80lqX2tjnLGtKArnzR/5iiaWw2/fFcXwlAn9n5eW3fLjNFa0JWypQExodwxbTArN5Xw5a4Kq+MoG/sg7yAj+oYzKDbM6ihnTAu68ll3nDuYxN4hPLIij6YWvUCq/lvZkQa+KqzkYh/obgEt6MqHBQc4mD9zFDsO1fLKl4VWx1E29OGWQxiDFnSlvMGFo+KZNiyOpz/cQemReqvjKJt5P/8gyTGhDI8PtzqKW2hBVz5NRHjk8lHUN7fw6/f0Aqn6P9VHm1hTUM6M1L6IeOdkXJ1pQVc+LyWuFz/4VgpLNxSTvbfS6jjKJj7ceojmVsMlqb6z/LEWdNUj/HD6EPpFBjN/eT4trboQhoKVm0pIig4hPTHS6ihuowVd9Qihgf48fNkothyo4R9ZeoG0p6usa+SLgnJmpvX3me4WOIWCLiIOEdkoIm93se8WESkTkRzn4zb3xlTqzF06pi+TB8fw2w+2U1HbYHUcZaH38g7Q0mq4PK2/1VHc6lTO0H8EbD3B/sXGmAznY9EZ5lLK7USEx2aN5mhjC7/9YLvVcZSFVm4qYXBcGCP7+cbolnYuFXQRSQQuA7RQK682ND6cW6ckszi7iJyiKqvjKAscqqkna08ll6f7VncLuH6G/jTwE+BEt9tdJSK5IrJERJK6aiAic0UkW0Syy8p0vmpljXvOH0pcryAeWZ6nF0h7oHdyD2AMzPSx7hZwoaCLyEyg1Biz/gTNVgLJxpg04EPg5a4aGWMWGmMyjTGZcXFxpxVYqTMVHhzAQ5eNZNP+av6xbp/VcVQ3W5lbwqh+EQzp08vqKG7nyhn6FGCWiOwF3gCmi8irHRsYYyqMMe1XmRYB492aUik3m5XenylDYnjq/W16B2kPUlR5lI37qrg83ffOzsGFgm6MedAYk2iMSQbmAB8bY27s2EZEOo7Mn8WJL54qZTkR4YnZqTQ0tfLkO/rXtadYnlMMwMw037mZqKPTHocuIo+LyCzn03tEJF9ENgH3ALe4I5xSnpQS14t55w5meU4JqwvKrY6jPMwYw9INxUwYFE1SdKjVcTzilAq6MeZTY8xM5/Z8Y8wK5/aDxpjRxph0Y8x5xhidNEN5hTvPHczAmFAefiuP+qYWq+MoD8opqmJ3eR1XjUuwOorH6J2iqkcLDnDwxOxU9pTX8cJnu62Oozxo6YZigvz9uGSMb3a3gBZ0pZg6LI6Zaf3406cF7CmvszqO8oCG5hZW5pYwY3RfIoIDrI7jMVrQlQJ+PnMUQQ4/5i/Pwxgdm+5rPtlWRtXRJr7tw90toAVdKQDiI4K5b8Zw/rOznLdzD1gdR7nZmxv2ExcexDlDYq2O4lFa0JVyunHiQMYkRPL421uoqW+yOo5yk8q6Rj7ZVsoVGf3xd/h2yfPtn06pU+DwE568MpXy2gb+Vyfv8hlvbSymudXw7XGJVkfxOC3oSnWQlhjFTRMH8sraQjbp5F1ezxjDG1/tIz0xkpH9IqyO43Fa0JXq5P/NGE6f8CB++mYuTS0nmo9O2d2GfVXsOFTLnAkDrI7SLbSgK9VJRHAAT8xOZdvBI7zw2S6r46gz8Ma6fYQGOnx27pbOtKAr1YWLRvflsjH9WLCqgILSWqvjqNNQU9/EytwSZqX3p1eQv9VxuoUWdKWO45FZowgJdPDg0lxadd50r7M8p4T6plau7yHdLaAFXanj6hMezEOXjeSrvYd5TedN9zpvrNvHyH4RpCVGWh2l22hBV+oErhmfyJQhMfzmvW0cqD5mdRzlos37q8kvqeH6CUk+t8zciWhBV+oERIRfXZlGc2srDy/TaQG8xStf7iUkwMHsDN++1b8zLehKncSAmFD+34XDWbWtVKcF8AKVdY0s31TCleMSiAzx3Ym4uuJyQRcRh4hsFJG3u9gXJCKLRaRARLJEJNmdIZWy2q1TkklLjOTRFfkcrmu0Oo46gTe+2kdjcys3T0q2Okq3O5Uz9B9x/KXlvg8cNsYMAf4A/OZMgyllJ/4OP3797TSqjzXx6Mp8q+Oo42huaeXVLwuZPDiG4X3DrY7T7Vwq6CKSCFxG2wLQXZkNvOzcXgKcLz3pSoTqEUb1j+CH04ewPKeE9/O068WOPtxyiJLqem6enGx1FEu4eob+NPAT4Hj3QScARQDGmGagGojp3EhE5opItohkl5WVnUZcpax113lDSE2I4KFleVTUNlgdR3XytzV7SYgK4YKR8VZHscRJC7qIzARKjTHrz/TDjDELjTGZxpjMuLi4M307pbpdgMOP/70mgyP1zTz8lo56sZOtB2rI2lPJTZMG4vDrmR0ErpyhTwFmiche4A1guoi82qlNMZAEICL+QCRQ4cacStnG8L7h/PjCobyXd5CVOurFNl78Yg/BAX5cd1aS1VEsc9KCbox50BiTaIxJBuYAHxtjbuzUbAVws3P7amcbPXVRPmvut1LISBF0wzQAAA+eSURBVIpi/vI8So/UWx2nxztQfYzlOcXMOWsAUaGBVsexzGmPQxeRx0VklvPpi0CMiBQA9wIPuCOcUnbl7/Djf69N51hjCz9bulm7Xiz21y/20Grg++cMsjqKpU6poBtjPjXGzHRuzzfGrHBu1xtjrjHGDDHGTDDG7PZEWKXsZHBcL+6fMZyPtpby5oZiq+P0WNVHm/hH1j5mpvUjKTrU6jiW0jtFlToD35syiAnJ0Ty2Ip+iyqNWx+mRXs0qpK6xhdunDrY6iuW0oCt1Bvz8hP+9Nh2A/1mcQ7OucNSt6ptaeGn1XqYOi2NUf99fYu5ktKArdYaSokP5xZWpZBce5k+f6ApH3enNDfspr21g3rQUq6PYghZ0pdxgdkYCV2T0Z8HHO1lfeNjqOD1CY3Mrf/5kF2MHRDEp5b/uY+yRtKAr5SaPX5FKv8hgfrx4I0fqm6yO4/P+mV1EcdUx/ueCYT1qzvMT0YKulJtEBAfwzJwMig8f45HlOoGXJzU0t/CnTwoYP7A33xoaa3Uc29CCrpQbjR8Yzd3Th7J0YzHLc3Qoo6cs/qqIA9X13Huhnp13pAVdKTe7e/oQxg/szUPL8thTXmd1HJ9T39R2dj4hOZrJg7XvvCMt6Eq5mb/Djz9ePxZ/h3Dnaxuob2qxOpJPeX3dPg7VNPDjC4fq2XknWtCV8oD+USH84doMth6o4TFdEMNtauqbWLBqJ5MHxzB5sPadd6YFXSkPOW9EH+48dzCvryti6Yb9VsfxCX/+ZBdVx5r42aUjrY5iS1rQlfKgey8cxoRB0Ty0LI+dh45YHcerFVcd46+r93Dl2ARSEyKtjmNLWtCV8qD2/vSwIAd3vLaB2oZmqyN5rd99sB0B7rtouNVRbEsLulIeFh8RzII5Y9lTXse9i3NobdWpdk/V5v3VLNtYzPfPGUT/qBCr49iWFnSlusHkIbH87NKR/HvLIRZ8vNPqOF6ltdXw2Mp8osMCmXeuzqh4IlrQleom35uSzFXjEnn6o518kH/Q6jheY8mG/WQXHuaBS0YQERxgdRxbc2WR6GARWScim0QkX0Qe66LNLSJSJiI5zsdtnomrlPcSEZ68MpX0xEjuXZzDDr1IelKH6xr51btbyRzYm6vHJVodx/ZcOUNvAKYbY9KBDOBiEZnYRbvFxpgM52ORW1Mq5SOCAxw8/93xhAT6M/eVbKqONlodydae+mA7NfXNPHFFKn5+ehPRybiySLQxxtQ6nwY4H3pVR6nT1C8yhBe+O46Sqnpu//t6Gpr1TtKubNh3mDe+2setk5MZ2U8Xr3CFS33oIuIQkRygFPjQGJPVRbOrRCRXRJaISNJx3meuiGSLSHZZWdkZxFbKu40fGM1vr0kja08lP12Sq4tMd9LQ3MKDb24mPjyYH184zOo4XsOlgm6MaTHGZACJwAQRSe3UZCWQbIxJAz4EXj7O+yw0xmQaYzLj4uLOJLdSXm92RgL3zxjOWzkl/OHDHVbHsZUFq3ay/dARfvntVHoF+Vsdx2uc0igXY0wV8AlwcafXK4wxDc6ni4Dx7omnlG+789zBXJeZxIKPC/hndpHVcWxhU1EVz326i2vGJzJ9RLzVcbyKK6Nc4kQkyrkdAlwIbOvUpl+Hp7OAre4MqZSvEhF+cWUq3xoay4NLN/PRlkNWR7JUfVML9/1rE/ERwTw8c5TVcbyOK2fo/YBPRCQX+Iq2PvS3ReRxEZnlbHOPc0jjJuAe4BbPxFXK9wQ4/HjuxvGk9o/gzn9sYM2ucqsjWeaJt7ews7SW31yVRmSIjjk/VWLVxZjMzEyTnZ1tyWcrZUeH6xq5buGXFB8+xms/mEhGUpTVkbrVu5sPcOdrG7h9agoP6myKxyUi640xmV3t0ztFlbKJ3mGB/P37ZxPTK4ib/7qObQdrrI7UbYoqj/LTN3PJSIrivhk6+dbp0oKulI3ERwTz6vfPJjjAjxv+ksWWEt8v6scaW5j36noA/nj9WAIcWpZOlx45pWxmQEwor/9gIoEOP25YtJa84mqrI3mMMYafvJnLlgM1LJgzlqToUKsjeTUt6ErZUEpcL/55+yTCAv254S9r2VRUZXUkj3j+s92s3FTC/TOGc96IPlbH8Xpa0JWyqQExoSy+fSJRoYHcuCiLtbsrrI7kVis3lfDUB9uYmdaPO6bptLjuoAVdKRtL7N1W1OMjg7npxXW8nVtidSS3WF1Qzr3/zOGsgdH87pp0RHTiLXfQgq6UzfWLDGHJvEmkJ0Vy9+sbefGLPVZHOiO5+6u4/e/rSYntxV9uziQ4wGF1JJ+hBV0pLxAV2jak8eLRfXni7S08tGwzjc2tVsc6ZZuKqvjOoiyiQgN4+XsT9OYhN9OCrpSXCA5w8OwN47h9WgqvZe3jhr+spfRIvdWxXLZx32FudBbzN+ZOpG9ksNWRfI4WdKW8iMNPePCSkfzx+rHklVQz64+ryd5baXWsk/p42yG+syiL6F6BLJ47icTeOjzRE7SgK+WFLk/vz9I7phDo78e1L3zJ7z/cQXOLPbtg/r62kNteziYlLox/3T6J/lEhVkfyWVrQlfJSo/pH8M4953DF2AQWrNrJtS98yZ7yOqtjfa2+qYUHl27m52/lce7wPiyeO4k+EdrN4kla0JXyYuHBAfz+2gwWXD+WnaW1zHj6c575aKfly9rtKqvlyj+v4fV1+5g3bTALvzueMF2owuP0CCvlA2al92fioGgef3sLf/hoB8s3FfPwZSM5b3ifbh3j3dTSysLPd7Ng1U5CAx28dMtZegdoN9Lpc5XyMZ/tKOOR5XnsrThK5sDe3D9jOGenxHj0M40x/GdnOb98dyvbDh7h4tF9eWz2aOK1i8XtTjR9rhZ0pXxQU0sri78qYsGqnZQeaeCs5N7cOmUQF42Kx9+NsxkaY/hydwULVu1k7e5KEqJC+PnMUVyc2tdtn6G+6YwKuogEA58DQbR10SwxxjzSqU0Q8Apta4lWANcZY/ae6H21oCvlefVNLbyWtY+XVu9h/+Fj9I0I5vL0fsxKTyA1IeK0u2MO1dTz3uYDvJa1j52ltcT2CuSu84Zww9kDCPLXOz896UwLugBhxphaEQkAvgB+ZIxZ26HNnUCaMWaeiMwBrjTGXHei99WCrlT3aWk1fLT1EP/KLuKzHWU0tRjiwoOYPDiGs5KjGdE3nKF9wokI8f+vIt/U0srB6nq2HKhhU1EVa3ZVkOOc/XFMQiTfnTSQWen99Rb+bnKign7Si6KmreLXOp8GOB+d/xeYDTzq3F4CPCsiYqzqz1FKfYPDT5gxui8zRvel6mgj/95yiC92lrO6oILlOf834Vegvx/RoYEEBfjR0mqob2qloq6B9n/J/n7C6IRI7rtoGBeN7svQPr10Yi0bcWmUi4g4gPXAEOBPxpisTk0SgCIAY0yziFQDMUB5p/eZC8wFGDBgwJklV0qdlqjQQK7NTOLazCSMMZRU17Pj4BEKSmspr22goq6RppZWHH5CkL8ffcKD6RcZzND4cEb3j9AzcRtzqaAbY1qADBGJApaJSKoxJu9UP8wYsxBYCG1dLqf6/Uop9xIREqJCSIgK0eGFPuCULncbY6qAT4CLO+0qBpIARMQfiKTt4qhSSqluctKCLiJxzjNzRCQEuBDY1qnZCuBm5/bVwMfaf66UUt3LlS6XfsDLzn50P+Cfxpi3ReRxINsYswJ4Efi7iBQAlcAcjyVWSinVJVdGueQCY7t4fX6H7XrgGvdGU0opdSp0ci6llPIRWtCVUspHaEFXSikfoQVdKaV8hGWzLYpIGVB4mt8eS6e7UG3Om/J6U1bwrrzelBW8K683ZYUzyzvQGBPX1Q7LCvqZEJHs401OY0felNebsoJ35fWmrOBdeb0pK3gur3a5KKWUj9CCrpRSPsJbC/pCqwOcIm/K601ZwbvyelNW8K683pQVPJTXK/vQlVJK/TdvPUNXSinViRZ0pZTyEV5R0EUkWkQ+FJGdzq+9j9OuRURynI8VFuS8WES2i0iBiDzQxf4gEVns3J8lIsndnbFDlpNlvUVEyjocz9usyOnM8lcRKRWRLhdVkTYLnD9LroiM6+6MHbKcLOu5IlLd4bjO76pddxGRJBH5RES2iEi+iPyoiza2OL4uZrXN8RWRYBFZJyKbnHkf66KNe2uCMcb2D+Ap4AHn9gPAb47TrtbCjA5gF5ACBAKbgFGd2twJPO/cngMstnHWW4Bnrf6zd2aZCowD8o6z/1LgPUCAiUCWjbOeC7xt9THtkKcfMM65HQ7s6OLvgi2Or4tZbXN8ncerl3M7AMgCJnZq49aa4BVn6LQtQv2yc/tl4AoLsxzPBKDAGLPbGNMIvEFb7o46/hxLgPPFmhV2XclqG8aYz2mbZ/94ZgOvmDZrgSgR6dc96b7Jhay2Yow5YIzZ4Nw+AmylbY3gjmxxfF3MahvO41XrfBrgfHQeheLWmuAtBT3eGHPAuX0QiD9Ou2ARyRaRtSLS3UX/64Wynfbz33/ZvrGYNtC+mHZ3cyUrwFXOX7GXiEhS90Q7La7+PHYxyflr+HsiMtrqMO2cv+6Ppe1MsiPbHd8TZAUbHV8RcYhIDlAKfGiMOe6xdUdNcGmR6O4gIh8BfbvY9VDHJ8YYIyLHG2s50BhTLCIpwMcistkYs8vdWXuIlcDrxpgGEbmdtrOI6RZn8gUbaPt7WisilwJvAUMtzoSI9ALeBH5sjKmxOs+JnCSrrY6vMaYFyHAu47lMRFKNMV1eX3EH25yhG2MuMMakdvFYDhxq/xXP+bX0OO9R7Py6G/iULlZa8qCvF8p2SnS+1mUbsXYx7ZNmNcZUGGManE8XAeO7KdvpcOXY24Ixpqb913BjzLtAgIjEWplJRAJoK5CvGWOWdtHENsf3ZFnteHydWaqAT4CLO+1ya02wTUE/iY6LUN8MLO/cQER6i0iQczsWmAJs6baE8BUwVEQGiUggbRc4Oo+0scti2ifN2qmPdBZt/ZV2tQK4yTkaYyJQ3aGLzlZEpG97H6mITKDt36AV/6m35xHa1gTeaoz5/XGa2eL4upLVTsdXROKcZ+aISAhwIbCtUzP31gSrrwS78qCtT2kVsBP4CIh2vp4JLHJuTwY20zZiYzPwfQtyXkrblfddwEPO1x4HZjm3g4F/AQXAOiDFwmN6sqy/AvKdx/MTYISFWV8HDgBNtPXffh+YB8xz7hfgT86fZTOQaeOsP+xwXNcCk63K6sxzDm0X6nKBHOfjUjseXxez2ub4AmnARmfePGC+83WP1QS99V8ppXyEt3S5KKWUOgkt6Eop5SO0oCullI/Qgq6UUj5CC7pSSvkILehKKeUjtKArpZSP+P9pAzg5Ke0tGAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iTHIXan16_Ye",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "26379c18-998f-4abd-b358-c6aba436fa37"
      },
      "source": [
        "from scipy import optimize\n",
        "\n",
        "result = optimize.minimize_scalar(f1)\n",
        "print(result.success) # check if solver was successful\n",
        "\n",
        "print('Minimum of function occurs at x = %.2f' % result.x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "True\n",
            "Minimum of function occurs at x = 2.00\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aGNrwqEV7Dtp",
        "colab_type": "text"
      },
      "source": [
        "The concept of optimization is also applicable to functions of more than one variable.\n",
        "\n",
        "In the following example, a function of two variables (a paraboloid in this case) is used to illustrate the optimization procedure."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "idBS3YI97S89",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "80948e8a-31e5-409f-fb61-e21c308d129b"
      },
      "source": [
        "from mpl_toolkits import mplot3d\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "def f_paraboloide(x, y):\n",
        "    return x ** 2 + y ** 2\n",
        "\n",
        "x = np.linspace(-6, 6, 30)\n",
        "y = np.linspace(-6, 6, 30)\n",
        "\n",
        "X, Y = np.meshgrid(x, y)\n",
        "Z = f_paraboloide(X, Y)\n",
        "fig = plt.figure()\n",
        "ax = plt.axes(projection='3d')\n",
        "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
        "ax.set_xlabel('x')\n",
        "ax.set_ylabel('y')\n",
        "ax.set_zlabel('z');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K6vuwnT17WdY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "31b6cb77-df69-4bb6-f418-db255be81da2"
      },
      "source": [
        "ax = plt.axes(projection='3d')\n",
        "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,\n",
        "                cmap='viridis', edgecolor='none')\n",
        "ax.set_title('surface');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HXM1BZDR7Z93",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "ac181564-5ef3-48e4-ea47-3c6727b31ac7"
      },
      "source": [
        "from scipy import optimize\n",
        "\n",
        "def f2(x):\n",
        "    return (x[0]**2 + x[1]**2)\n",
        "\n",
        "optimize.minimize(f2, [2, -1], method=\"CG\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     fun: 5.8281095370852615e-15\n",
              "     jac: array([-1.2166366e-07,  8.3183572e-08])\n",
              " message: 'Optimization terminated successfully.'\n",
              "    nfev: 12\n",
              "     nit: 1\n",
              "    njev: 3\n",
              "  status: 0\n",
              " success: True\n",
              "       x: array([-6.82824108e-08,  3.41412054e-08])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RwBUOrUh7g_K",
        "colab_type": "text"
      },
      "source": [
        "In general, optimization problems are difficult, because the function in question can be complex, as shown below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a84n2clz7kvr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "16984f04-3d2a-43cf-a494-1a398ca96231"
      },
      "source": [
        "from mpl_toolkits import mplot3d\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "def f(x, y):\n",
        "    return np.sin(np.sqrt(x ** 2 + y ** 2))\n",
        "\n",
        "x = np.linspace(-6, 6, 30)\n",
        "y = np.linspace(-6, 6, 30)\n",
        "\n",
        "X, Y = np.meshgrid(x, y)\n",
        "Z = f(X, Y)\n",
        "fig = plt.figure()\n",
        "ax = plt.axes(projection='3d')\n",
        "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
        "ax.set_xlabel('x')\n",
        "ax.set_ylabel('y')\n",
        "ax.set_zlabel('z');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wyJLEgfQ8MN8",
        "colab_type": "text"
      },
      "source": [
        "Logistic regression has to solve an optimization problem to find the best vector of parameters given the training dataset. In particular, the type of optimization problem to be solved in the logistic regression is minimization: given a function $J(\\Theta)$ that measures the error of the classification model on the training data, the objective is to find the combination of components of $\\Theta$ such that it produces the minimum value for $J(\\Theta)$.\n",
        "\n",
        "Consider a binary classification problem where there are $m$ examples in the training set. Also consider that $y^{(i)} \\in \\{0.1\\}$ is the class associated with the $i$-th training example, and that $g(z)$ is the value of the $g function$ corresponding to the $i$-th training example, $z_i = \\Theta^T \\cdot \\mathbf{x}^{(i)}$. The function that logistic regression must minimize is called cross entropy loss or logistic loss, and its definition is as follows:\n",
        "\n",
        "$$\n",
        "J(\\Theta) = -\\frac{1}{m} \\sum_{i = 1}^{m} [ y^{(i)} \\log (\\sigma(z_i)) + (1-y^{(i)}) \\log (1 - \\sigma(z_i))]\n",
        "$$\n",
        "To get an insight into the cost function above, let's just consider the cost corresponding to the $ i $ -th training example (for any $i$ any):\n",
        "\n",
        "$$\n",
        "y^{(i)} \\log(\\sigma(z_i)) + (1-y^{(i)}) \\log(1 - \\sigma(z_i))\n",
        "$$\n",
        "\n",
        "In the above expression, note that the cost is zero when the prediction and hypothesis are the same:\n",
        "\n",
        "- $(\\sigma(z_i) \\rightarrow 0)$ and $(y^{(i)} = 0)$ $\\Rightarrow$ (cost $\\rightarrow$ 0)\n",
        "- $(\\sigma(z_i) \\rightarrow  1)$ and $(y^{(i)} = 1)$ $\\Rightarrow$ (cost $\\rightarrow$ 0)\n",
        "\n",
        "However, if prediction and hypothesis are different, we have one of the following two cases:\n",
        "\n",
        "- $(\\sigma(z_i) \\rightarrow 0)$ and $(y^{(i)} = 1)$ $\\Rightarrow$ $($cost $\\rightarrow \\infty)$ \n",
        "- $(\\sigma(z_i) \\rightarrow 1)$ and $(y^{(i)} = 0)$ $\\Rightarrow$ $($cost $\\rightarrow \\infty)$\n",
        "\n",
        "The above analysis considers only the extreme values ​​that $\\sigma(z_i)$ can take. In any case, the general conclusion we should draw is that the minimization algorithm is penalized when it selects a $\\Theta$ vector that produces the wrong prediction for the $i$-th example.\n",
        "\n",
        "The above explanation was given in the context of a single example. What the function $J(\\Theta)$ does is to compute the *average error* over all $m$ training examples."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TLUdfI95-XSR",
        "colab_type": "text"
      },
      "source": [
        "### Gradient Descent (and its variants)\n",
        "\n",
        "One of the most used methods to perform numerically the minimization that the logistic regression needs is the descending gradient method. Using this method, the process of minimizing the cost function occurs in an iterative way. At each iteration, a small change is made to the components of the $\\Theta$ parameter array:\n",
        "\n",
        "Repeat until convergence: \n",
        "$$\n",
        "\\theta_j := \\theta_j - \\alpha \\sum_{i = 1}^{m}(\\sigma(\\Theta^T \\cdot \\mathbf{x}^{(i)}) - y^{(i)}) \\, x_j^{(i)}\n",
        "$$\n",
        "\n",
        "In the update expression presented above, $\\alpha$ is a numerical value called the *learning rate* of the optimization algorithm. This constant controls the amount of update on the components of the $\\Theta$ array.\n",
        "\n",
        "There are numerous gradient-based optimization methods. The study of these methods is outside the scope of this course. In any case, the following animations illustrate the behavior of some of these methods while minimizing a given function.\n",
        "\n",
        "([source]((https://www.datasciencecentral.com/profiles/blogs/an-overview-of-gradient-descent-optimization-algorithms)))\n",
        "![alt text](http://storage.ning.com/topology/rest/1.0/file/get/2808318953?profile=original)\n",
        "\n",
        "([source]((https://www.datasciencecentral.com/profiles/blogs/an-overview-of-gradient-descent-optimization-algorithms)))\n",
        "![alt text](http://storage.ning.com/topology/rest/1.0/file/get/2808327843?profile=original)\n",
        "\n",
        "The learning rate is a hyperparameter of logistic regression. The following animation illustrates the effect of different learning rate values ​​on the optimization process. When $\\alpha$ is defined as too large and the evaluation sequence starts to get out of control, the sequence of steps is said to diverge. On the other hand, if the value of $\\alpha$ is very small, the convergence of the process can take significantly.\n",
        "\n",
        "![alt text](https://github.com/jermwatt/machine_learning_refined/blob/gh-pages/html/gifs/steplength_1D.gif?raw=true)\n",
        "\n",
        "Source: [Machine Learning Refined](https://github.com/jermwatt/machine_learning_refined)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p70uCAmG_74A",
        "colab_type": "text"
      },
      "source": [
        "## Logistic Regression in Scikit-Learn\n",
        "\n",
        "The cells below * illustrate the use of the [LogisticRegression](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html) class.\n",
        "\n",
        "One of the parameters for instantiating the `LogisticRegression` class is called *solver*. This argument defines the optimization method to be used during training.\n",
        "\n",
        "*example adapted from the book [Hands-on Machine Learning with Scikit-Learn and Tensoflow](https://www.amazon.com/Hands-Machine-Learning-Scikit-Learn-TensorFlow/dp/1491962291)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mlQ1Gg8UA1sD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn import datasets\n",
        "import numpy as np\n",
        "iris = datasets.load_iris()\n",
        "X = iris[\"data\"][:, 3:] # petal width\n",
        "y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TmnfaIBnMr6C",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "70ef85f8-2088-4f66-8796-9eedb2e45d5e"
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.4],\n",
              "       [0.3],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.1],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.1],\n",
              "       [0.1],\n",
              "       [0.2],\n",
              "       [0.4],\n",
              "       [0.4],\n",
              "       [0.3],\n",
              "       [0.3],\n",
              "       [0.3],\n",
              "       [0.2],\n",
              "       [0.4],\n",
              "       [0.2],\n",
              "       [0.5],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.4],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.4],\n",
              "       [0.1],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.1],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.3],\n",
              "       [0.3],\n",
              "       [0.2],\n",
              "       [0.6],\n",
              "       [0.4],\n",
              "       [0.3],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [0.2],\n",
              "       [1.4],\n",
              "       [1.5],\n",
              "       [1.5],\n",
              "       [1.3],\n",
              "       [1.5],\n",
              "       [1.3],\n",
              "       [1.6],\n",
              "       [1. ],\n",
              "       [1.3],\n",
              "       [1.4],\n",
              "       [1. ],\n",
              "       [1.5],\n",
              "       [1. ],\n",
              "       [1.4],\n",
              "       [1.3],\n",
              "       [1.4],\n",
              "       [1.5],\n",
              "       [1. ],\n",
              "       [1.5],\n",
              "       [1.1],\n",
              "       [1.8],\n",
              "       [1.3],\n",
              "       [1.5],\n",
              "       [1.2],\n",
              "       [1.3],\n",
              "       [1.4],\n",
              "       [1.4],\n",
              "       [1.7],\n",
              "       [1.5],\n",
              "       [1. ],\n",
              "       [1.1],\n",
              "       [1. ],\n",
              "       [1.2],\n",
              "       [1.6],\n",
              "       [1.5],\n",
              "       [1.6],\n",
              "       [1.5],\n",
              "       [1.3],\n",
              "       [1.3],\n",
              "       [1.3],\n",
              "       [1.2],\n",
              "       [1.4],\n",
              "       [1.2],\n",
              "       [1. ],\n",
              "       [1.3],\n",
              "       [1.2],\n",
              "       [1.3],\n",
              "       [1.3],\n",
              "       [1.1],\n",
              "       [1.3],\n",
              "       [2.5],\n",
              "       [1.9],\n",
              "       [2.1],\n",
              "       [1.8],\n",
              "       [2.2],\n",
              "       [2.1],\n",
              "       [1.7],\n",
              "       [1.8],\n",
              "       [1.8],\n",
              "       [2.5],\n",
              "       [2. ],\n",
              "       [1.9],\n",
              "       [2.1],\n",
              "       [2. ],\n",
              "       [2.4],\n",
              "       [2.3],\n",
              "       [1.8],\n",
              "       [2.2],\n",
              "       [2.3],\n",
              "       [1.5],\n",
              "       [2.3],\n",
              "       [2. ],\n",
              "       [2. ],\n",
              "       [1.8],\n",
              "       [2.1],\n",
              "       [1.8],\n",
              "       [1.8],\n",
              "       [1.8],\n",
              "       [2.1],\n",
              "       [1.6],\n",
              "       [1.9],\n",
              "       [2. ],\n",
              "       [2.2],\n",
              "       [1.5],\n",
              "       [1.4],\n",
              "       [2.3],\n",
              "       [2.4],\n",
              "       [1.8],\n",
              "       [1.8],\n",
              "       [2.1],\n",
              "       [2.4],\n",
              "       [2.3],\n",
              "       [1.9],\n",
              "       [2.3],\n",
              "       [2.5],\n",
              "       [2.3],\n",
              "       [1.9],\n",
              "       [2. ],\n",
              "       [2.3],\n",
              "       [1.8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_sUfIEipB44u",
        "colab_type": "text"
      },
      "source": [
        "The next code cell fits a logistic regression model to the training set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o4x0KpWjB5Rw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "97f92a82-b690-4d9a-f7ee-e198c38b84c2"
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "log_reg = LogisticRegression(solver='lbfgs')\n",
        "log_reg.fit(X, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kRxUwOD8CL6p",
        "colab_type": "text"
      },
      "source": [
        "Once the model has been generated, it is possible to invoke the predict method, as shown in the following example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DjZRJB7UCMVj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "db50009a-dac7-41d9-c22f-dab1ae822aa3"
      },
      "source": [
        "log_reg.predict([[1.7], [1.5]])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 0])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fhAtNarYCeGp",
        "colab_type": "text"
      },
      "source": [
        "The following cell produces a graph that makes it easier to interpret the generated model. In this graph, the point where the solid and dashed curves meet corresponds to the decision boundary of the generated logistic regression model.\n",
        "\n",
        "What is the decision boundary in this example?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9ccJ1BNbChgA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "92d6472b-9041-4ffd-94f8-09cc7f184493"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
        "y_proba = log_reg.predict_proba(X_new)\n",
        "plt.plot(X_new, y_proba[:, 1], \"g-\", label=\"Iris-Virginica\")\n",
        "plt.plot(X_new, y_proba[:, 0], \"b--\", label=\"Not Iris-Virginica\")\n",
        "\n",
        "plt.xlabel('Petal length (cm)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jg65r9-UpFBw",
        "colab_type": "text"
      },
      "source": [
        "The vector of coefficients of the generated logistic regression model is stored in two different attributes of the LogisticRegression class: `coef_` and `intercept_`. See the code cell below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iBN9YDKCnB6O",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "16460b2a-aa1d-440a-d746-774faa7f602c"
      },
      "source": [
        "print(log_reg.coef_)\n",
        "print(log_reg.intercept_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[4.3330846]]\n",
            "[-7.1947083]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AHTwJOR_Ohpr",
        "colab_type": "text"
      },
      "source": [
        "$$\n",
        "\\Theta = [4.3, -7.19]\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LXztMJf6pbXL",
        "colab_type": "text"
      },
      "source": [
        "By inspecting the above output, we can conclude that the decision boundary is:\n",
        "\n",
        "$$\n",
        "\\theta_0 + \\theta_1 \\times x_1 = 0\n",
        "$$\n",
        "\n",
        "If we replace the values in the above equation, we get:\n",
        "\n",
        "$$\n",
        "4.33 - 7.19 \\times x_1 = 0\n",
        "$$\n",
        "\n",
        "By a simple manipulation of the above expression, we can find that the decision boundary here is a vertical line that crosses $x_1 \\approx 1.66$, which is consistent with the plot shown above.\n",
        "\n",
        "In this example, notice that $x_1$ represents the only predictor used to generate the model, *petal length*.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mjs5dquXoOUX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "48b08052-c37c-4656-a430-4fe089ffbad8"
      },
      "source": [
        "7.19/4.33"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.6605080831408776"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wygo_4LvljmC",
        "colab_type": "text"
      },
      "source": [
        "## Case study: Toy dataset\n",
        "\n",
        "Let us go back to our toy dataset and make build a decent classifier using Scikit-Learn. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7V76nVRml3Lk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[-0.1, 1.4],\n",
        "              [-0.5,-0.1],\n",
        "              [ 1.3, 0.9],\n",
        "              [-0.6, 0.4],\n",
        "              [-1.5, 0.4],\n",
        "              [ 0.2, 0.2],\n",
        "              [-0.3,-0.4],\n",
        "              [ 0.7,-0.8],\n",
        "              [ 1.1,-1.5],\n",
        "              [-1.0, 0.9],\n",
        "              [-0.5,-1.5],\n",
        "              [-1.3,-0.4],\n",
        "              [-1.4,-1.2],\n",
        "              [-0.9,-1.1],\n",
        "              [ 0.4,-1.3],\n",
        "              [-0.4, 0.6],\n",
        "              [ 0.3,-0.5]])\n",
        "\n",
        "y = np.array([0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mv4WnQ5ll4lx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "bc29de5e-136e-45fa-fdee-dcde84062c3e"
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "log_reg = LogisticRegression(solver='lbfgs')\n",
        "log_reg.fit(X, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QBNnQsV-mObt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "6062ba4a-acdf-4b68-b352-8b91cd4ab62b"
      },
      "source": [
        "print(log_reg.coef_)\n",
        "print(log_reg.intercept_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 1.52160613 -1.11119985]]\n",
            "[0.38532946]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d6LIw0EUmm6D",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "8eb8fa0a-85c4-413c-f88e-060483ba5605"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('classic')\n",
        "np.set_printoptions(precision=3, suppress=True)\n",
        "\n",
        "colormap = np.array(['r', 'b'])\n",
        "\n",
        "def plot_scatter(X, y, colormap):\n",
        "  plt.grid()\n",
        "  plt.xlim([-5.0, 5.0])\n",
        "  plt.ylim([-5.0, 5.0])\n",
        "  plt.xlabel('$x_1$', size=20)\n",
        "  plt.ylabel('$x_2$', size=20)\n",
        "  plt.title('Input 2D points', size=18)\n",
        "  plt.scatter(X[:,0], X[:, 1], s=50, c=colormap[y])\n",
        "\n",
        "plot_scatter(X, y, colormap)\n",
        "\n",
        "points_x = [x/10. for x in range(-50,+50)]\n",
        "\n",
        "bias = log_reg.intercept_\n",
        "w = log_reg.coef_.T\n",
        "points_y = [-(w[0] * x + bias)/(w[1]) for x in points_x]\n",
        "plt.plot(points_x, points_y, color = 'black')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fab5efc8198>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-IsYXNt2s0an",
        "colab_type": "text"
      },
      "source": [
        "## Case study: honor dataset\n",
        "\n",
        "Let us see a complete example of creating a logistic regression model with Scikit-Learn on the honor dataset. This is a dataset that contains 200 observations about students. The feature we will use a target is `hon` which indicates if a student is an honor class or not."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VO_aQdwpsfn_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 198
        },
        "outputId": "3bbd4dd6-b614-4428-9f96-5190ef1cb30e"
      },
      "source": [
        "import pandas as pd\n",
        "df_honor_data = pd.read_csv('https://raw.githubusercontent.com/OmaymaS/Logistic-Regression-Coefficients-Interpretation/master/honordata.csv')\n",
        "df_honor_data.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>female</th>\n",
              "      <th>read</th>\n",
              "      <th>write</th>\n",
              "      <th>math</th>\n",
              "      <th>hon</th>\n",
              "      <th>femalexmath</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>57</td>\n",
              "      <td>52</td>\n",
              "      <td>41</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>68</td>\n",
              "      <td>59</td>\n",
              "      <td>53</td>\n",
              "      <td>0</td>\n",
              "      <td>53</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>44</td>\n",
              "      <td>33</td>\n",
              "      <td>54</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>63</td>\n",
              "      <td>44</td>\n",
              "      <td>47</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>47</td>\n",
              "      <td>52</td>\n",
              "      <td>57</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   female  read  write  math  hon  femalexmath\n",
              "0       0    57     52    41    0            0\n",
              "1       1    68     59    53    0           53\n",
              "2       0    44     33    54    0            0\n",
              "3       0    63     44    47    0            0\n",
              "4       0    47     52    57    0            0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ulQVfDttplz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = df_honor_data.drop(columns=['hon'])\n",
        "y = df_honor_data.hon"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U1SMcciePjzD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "outputId": "2a93aa71-0499-4c60-a968-e16208693aeb"
      },
      "source": [
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      0\n",
              "1      0\n",
              "2      0\n",
              "3      0\n",
              "4      0\n",
              "      ..\n",
              "195    0\n",
              "196    0\n",
              "197    0\n",
              "198    1\n",
              "199    1\n",
              "Name: hon, Length: 200, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuCoFedmuBjG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "db9099e7-6cfa-4507-a916-64799ff356d1"
      },
      "source": [
        "print(X.shape)\n",
        "print(y.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(200, 5)\n",
            "(200,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sRTZ5WPx25Nm",
        "colab_type": "text"
      },
      "source": [
        "In classification, it is very common to split the available observations in two datasets: training and test. In Scikit-Learn, we can do this by using the `train_test_split` function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wkfWHBBmuLGS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        },
        "outputId": "5a657934-0bc1-4041-d386-3db654c60b5a"
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
        "\n",
        "log_reg = LogisticRegression(solver='lbfgs')\n",
        "log_reg.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xpTA85LzSKEd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "ecddbaa6-308b-48c7-86ba-ad257299be85"
      },
      "source": [
        "print(X.shape)\n",
        "print(X_train.shape)\n",
        "print(X_test.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(200, 5)\n",
            "(160, 5)\n",
            "(40, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p_Wx4vawBl9n",
        "colab_type": "text"
      },
      "source": [
        "The following image illustrates the effect of applying the function `train_test_split` on the data matrix $X$ and response vector $y$. From these, two data matrices and two response vectors are created. \n",
        "\n",
        "![alt text](https://res.cloudinary.com/dyd911kmh/image/upload/f_auto,q_auto:best/v1543836883/image_6_cfpjpr.png)\n",
        "\n",
        "Please notice that, each time `train_test_split` is called, it randomly selects which examples to put in the training and test datasets."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mqn_JCdDu3_d",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_pred = log_reg.predict(X_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pv-9bu4pvf1y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "9d65f56a-8c20-4ec4-93fe-1e36cbc0f0b3"
      },
      "source": [
        "print(y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0\n",
            " 0 0 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K-wxSlgCvINK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "cb252eb9-2eef-4f3c-bf19-659a8d03bd44"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "accuracy_score(y_test, y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ACq9NUm6vdBo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "fe489296-c03e-4a44-e55a-2a003efc2bf7"
      },
      "source": [
        "print(y_test.values)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0\n",
            " 0 0 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7IDz3Iw2v74G",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "436f03f9-7757-4062-ee5c-faac924496a7"
      },
      "source": [
        "print(log_reg.coef_)\n",
        "print(log_reg.intercept_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-1.05519995e-02 -1.67596700e-03  2.32999559e+00 -3.62224213e-02\n",
            "  -1.02388613e-02]]\n",
            "[-138.314996]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Ft1zQ-UHYqz",
        "colab_type": "text"
      },
      "source": [
        "# $k$-Nearest Neighbors\n",
        "\n",
        "The $k$ nearest neighbors ($k$-NN) algorithm is one of the simplest Data Mining methods. Despite being simple, it often produces satisfactory results. It can be used for both classification and regression problems.\n",
        "\n",
        "$k$-NN is a *lazy learning* algorithm. This means the training phase consists only of storing the representations of the examples. That is, the algorithm does not explicitly produce a classification model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kvg1kn9YHkdH",
        "colab_type": "text"
      },
      "source": [
        "## Definition of neighbors\n",
        "\n",
        "To classify an example $\\mathbf{x}$, $k$-NN produces a total order on the $\\mathbf{x}$ “neighbors”, taken from the training set $X$.\n",
        "\n",
        "The meaning of neighbor here is in the context of *similarity*. The classes of the $k$ most similar neighbors are used to predict the class of $\\mathbf{x}$.\n",
        "\n",
        "The following figure ([source](https://www.datacamp.com/community/tutorials/k-nearest-neighbor-classification-scikit-learn)) illustrates the behavior of $k$-NN for $k = 1$ in the context of binary classification. Notice that there is only one example inside the ball of neighbors for $\\mathbf{x}$. Hence $1$-NN would predict that $\\mathbf{x}$ belongs to the *red* class.\n",
        "\n",
        "![alt text](http://res.cloudinary.com/dyd911kmh/image/upload/f_auto,q_auto:best/v1531424125/Knn_k1_z96jba.png)\n",
        "\n",
        "In the case where $k$ is chosen to greater than 1, then the [majority rule](https://en.wikipedia.org/wiki/Majority_rule) is applied to predict the class of $\\mathbf{x}$. See the image below for the case $k=3$.\n",
        "\n",
        "![alt text](http://res.cloudinary.com/dyd911kmh/image/upload/f_auto,q_auto:best/v1531424125/KNN_final1_ibdm8a.png)\n",
        "\n",
        "Usually, some distance measure is used to compute the similarity between examples. Some popular measures are listed below.\n",
        "\n",
        "Measures for continuous features:\n",
        "* Manhattan distance \n",
        "* Euclidean distance\n",
        "* Cosine similarity\n",
        "\n",
        "Measures for discrete features:\n",
        "* Hamming distance\n",
        "* Value distance measure"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Q-BIZzNRFn8",
        "colab_type": "text"
      },
      "source": [
        "Pr(pos) = 2/3\n",
        "Pr(neg) = 1/3\n",
        "\n",
        "![alt text](http://res.cloudinary.com/dyd911kmh/image/upload/f_auto,q_auto:best/v1531424125/KNN_final1_ibdm8a.png)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CgtFVJfD_THZ",
        "colab_type": "text"
      },
      "source": [
        "The animation below illustrates the behavior of $k$-NN in a toy dataset with two predictive features and two classes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_JuEazbKJGl1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "outputId": "9ace34b0-79ab-48b8-9108-91ee80447d37"
      },
      "source": [
        "from IPython.display import HTML\n",
        "\n",
        "HTML(\"\"\"\n",
        "<video width=\"640\" height=\"480\" controls>\n",
        "  <source src=\"https://assets.yihui.name/figures/animation/example/knn-ani/demo-a.mp4?dl=1\" type=\"video/mp4\">\n",
        "</video>\n",
        "\"\"\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "<video width=\"640\" height=\"480\" controls>\n",
              "  <source src=\"https://assets.yihui.name/figures/animation/example/knn-ani/demo-a.mp4?dl=1\" type=\"video/mp4\">\n",
              "</video>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h4XIbL5FIClk",
        "colab_type": "text"
      },
      "source": [
        "## Steps of the Algorithm\n",
        "\n",
        "* Compute the $k$ neighborhood for an example $\\mathbf{x}$. i.e., determine the $k$ “nearest” neighboring examples of $\\mathbf{x}$.\n",
        "\n",
        "* Count the amount $q(c_i)$ of examples in the $k$-neighborhood that belong to the class $c_i$.\n",
        "\n",
        "* Produce an estimate of $\\Pr(c_i \\mid \\mathbf{x})$:\n",
        "\n",
        "* Classify $\\mathbf{x}$ as belonging to the most likely class (called the *majority class*).\n",
        "\n",
        "No optimal number of neighbors suits all kind of datasets. The value of $k$ for a particular dataset can be determined using *model selection*, which is a concept we will cover later on in this course."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o892vfTYL2gg",
        "colab_type": "text"
      },
      "source": [
        "## $k$-NN in Scikit-Learn\n",
        "\n",
        "Scikit-Learn's [KNeighborsClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html) class implements the $k$-NN algorithm. In its simplest form of instantiation, it is only necessary to configure the hyperparameter $k$, which corresponds to the number of neighbors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gKZpaBFwMFPy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "76b91973-a6c5-430c-a7cb-d9bdc28917b1"
      },
      "source": [
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "from sklearn import datasets\n",
        "iris = datasets.load_iris()\n",
        "\n",
        "X = iris.data    # data matrix\n",
        "y = iris.target  # response vector\n",
        "\n",
        "train_X, test_X, train_y, test_y = train_test_split(\n",
        "    X, y, test_size=0.2, random_state=1, stratify=y)\n",
        "\n",
        "modelKNN = KNeighborsClassifier(n_neighbors=3) # k = 3\n",
        "\n",
        "modelKNN.fit(train_X, train_y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
              "                     metric_params=None, n_jobs=None, n_neighbors=3, p=2,\n",
              "                     weights='uniform')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DGGbhbSLAi3B",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "5051e99c-5ace-4825-a770-feeba5358ad1"
      },
      "source": [
        "# predict the class for example x = [1.1, 1.2, 3, 2] \n",
        "x = [1.1, 1.2, 3, 2]\n",
        "print(modelKNN.predict([x]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eGpxNUQ8Cg91",
        "colab_type": "text"
      },
      "source": [
        "Notice that we can predict the classes for a bunch of examples."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3MWWCd_BBanl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "e3f08441-a982-41c3-c848-20a407a1cb54"
      },
      "source": [
        "y_pred_prob_KNN = modelKNN.predict(test_X)\n",
        "\n",
        "# Imprime as estimativas de probabilidades para cada classe\n",
        "print(y_pred_prob_KNN)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2 0 1 0 0 0 2 2 2 1 0 1 2 1 2 0 2 1 1 2 1 1 0 0 2 1 0 0 1 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_sThq1NvNDE9",
        "colab_type": "text"
      },
      "source": [
        "Contrary to what one might think, \n",
        "$k$-NN can produce very complex decision boundaries. The following images illustrate this behavior of the algorithm.\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Coloured_Voronoi_2D.svg/220px-Coloured_Voronoi_2D.svg.png)\n",
        "\n",
        "[source](https://pt.wikipedia.org/wiki/Diagrama_de_Voronoy)\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Voronoi_growth_euclidean.gif/220px-Voronoi_growth_euclidean.gif)\n",
        "\n",
        "[source](https://en.wikipedia.org/wiki/Voronoi_diagram)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6LOq5VQ0U4jJ",
        "colab_type": "text"
      },
      "source": [
        "Voronoi cell"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Gd5SmUxiLdU",
        "colab_type": "text"
      },
      "source": [
        "# Decision Trees\n",
        "\n",
        "A decision tree is a predictive model that takes an example $\\mathbf{x}$ as described by a set of predictive features and their respective values, and returns a predicted value for the target feature.\n",
        "\n",
        "The following example ([source](https://en.wikipedia.org/wiki/Decision_tree_learning)) presents a decision tree that models the possibility of passengers surviving on the [Titanic disaster](https://www.kaggle.com/c/titanic). The feature \"sipsb\" corresponds to the number of spouses or brothers on board. The other predictive features are self-explanatory. The numbers under the leafs show the probability of survival and the percentage of examples on the corresponding leaf.\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/f/f3/CART_tree_titanic_survivors.png)\n",
        "\n",
        "A decision tree has several *nodes*, both internal and external. The latter type is also called a leaf. Each internal node is associated to a predicate involving one of the predictive features. Each leaf is associated to a single value of the target feature. In the tree given as example above, there are three internal nodes (for features `sex`, `age` and `sibsp`) and four external nodes. \n",
        "\n",
        "A decision tree is a classification model that determines the class for an new example by executing a test sequence.\n",
        "\n",
        "* Each internal node in the tree corresponds to a test on the value of one of the attributes.\n",
        "\n",
        "* Branches from each internal node are identified (labeled) with the possible values ​​of the test.\n",
        "\n",
        "* Each leaf node specifies the value to be returned if that leaf is reached.\n",
        "\n",
        "Decision trees are known for their ease of interpretation. In the example above, we can interpret that the chances of survival were greater for (i) a woman or (ii) a man under 9.5 years old and less than 2.5 siblings (or spouses)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S2R5bnhLir91",
        "colab_type": "text"
      },
      "source": [
        "## Steps of the algorithm\n",
        "\n",
        "The goal of a *decision tree learning algorithm* is to build a decision tree. The basic decision tree learning algorithm consists of the following steps:\n",
        "\n",
        "1. Start at the root node as the parent node\n",
        "2. Split the parent node using the $x_i$ attribute that minimize the sum of impurities in the child node (or maximize the *information gain*)\n",
        "3. Assign training samples to new child nodes\n",
        "4. Stop if the resulting nodes are pure or if any stopping criteria are met; repeat steps 1 and 2 for each new child node\n",
        "\n",
        "The following animation ([source](https://annalyzin.wordpress.com/2016/07/27/decision-trees-tutorial/)) illustrates the recursive procedure performed by the decision tree learning algorithm. Here, consider a dataset with fourteen examples, 6 positive and nine negative. Also consider that each example has two features (represented in the animation as X and Y) with range of values betweent 0 and 1. The animation shows that the building process starts with a tree with just one node (its root node) which is associated to the feature X. Notice that the predicate $X>0.5$ splits the original examples in two disjoint sets. Also notice that the examples associated to the the value Yes for the predicate are all negative. These examples are associated to a leaf node. On the other hand, the second set has 6 positive and 3 negative examples. As exists impurity in this set, the corresponding node has to be split. This process of node spliting continues until some *stopping criteria* is met. At the end of this process, a decision tree is built.\n",
        "\n",
        "![alt text](https://annalyzin.files.wordpress.com/2016/07/decision-tree-tutorial-animated3.gif?w=620)\n",
        "\n",
        "\n",
        "There are several possible stopping criteria:\n",
        "* Leaf nodes are pure\n",
        "* Maximum node depth is reached\n",
        "* Dividing a node does not lead to an *information gain*.\n",
        "\n",
        "From the above example, it should be clear that there should exist a way for the decision tree algorithm to select the best attribute when a node split is necessary. We call this the *feature selection criteria*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uAqVjDz_e9R4",
        "colab_type": "text"
      },
      "source": [
        "![alt text](https://miro.medium.com/max/661/0*DX1px-z340TgpXTN.png)\n",
        "\n",
        "\n",
        "Pr(Outlook = Rainy) = 5/14\n",
        "Pr(Outlook = Overcast) = 4/14\n",
        "Pr(Outlook = Sunny) = 5/14\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a7U81R28e8vR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "37afc098-bc79-41bf-f6d3-e2ffb90bfcf0"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "-((5/14) * np.log(5/14) + (4/14) * np.log(4/14) + (5/14) * np.log(5/14))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0933747175566468"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "54_CjS5yg5EC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "64241f26-e650-4c35-e55e-b6d3d8a0e4c1"
      },
      "source": [
        "-((12/14) * np.log(12/14) + (1/14) * np.log(1/14) + (1/14) * np.log(1/14))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.509137344082687"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ztHPmsoi_B5",
        "colab_type": "text"
      },
      "source": [
        "## Feature selection criteria\n",
        "\n",
        "The decision tree learning algorithm is recursive. During the construction of the model (i.e., the decision tree), the choice of features should be made in such a way as to minimize the depth of the decision tree. At each step, the algorithm chooses the feature that goes as far as possible in the exact classification of the examples.\n",
        "\n",
        "A perfect feature would divide the examples into subsets of the same class (i.e., all positive or all negative). To choose a suitable feature for a new internal node in the tree, the solution is to measure each feature according to the expected amount of information provided by it.\n",
        "\n",
        "There are two most commonly used criteria for feature selection when learning a decision tree:\n",
        "\n",
        "* information gain\n",
        "* gini index"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6AloWTjQjV4E",
        "colab_type": "text"
      },
      "source": [
        "### Information Gain\n",
        "\n",
        "The information gain is based on a measure from [Information Theory](en.wikipedia.org/wiki/Information_theory) called *entropy*.\n",
        "\n",
        "Given a probability distribution for a discrete random variable $V$ with $n$ values, if each possible value $v_i$ of $V$ has probability $p_i$, then the entropy $H$ of that distribution is given by:\n",
        "\n",
        "$$\n",
        "H = -\\sum_{v_i \\in V} p_i \\log_2 p_i\n",
        "$$\n",
        "\n",
        "The following figure illustrates the concept of entropy for a random variable that can assume only two values, with corresponding probabilities equal to $p$ and $q$. Note that entropy is maximum when the two values ​​are equally likely to occur (i.e., $p = q = 0.5$).\n",
        "\n",
        "![alt text](https://miro.medium.com/max/349/0*kt06lkLbs7-B7SmE.png)\n",
        "\n",
        "Entropy measures the homogeneity of a dataset with respect to the value of a given attribute. If this attribute has the same value for all examples in the data set, then entropy is minimal. On the other hand, if the values ​​of this attribute occur uniformly, then entropy of the dataset is maximal.\n",
        "\n",
        "You are encouraged to watch this nice and instructive [video](https://youtu.be/9r7FIXEAGvs) about the concept of entropy.\n",
        "\n",
        "Information gain is the difference in entropy measured before and after dividing a dataset by the values ​​of one of its predictive attributes.\n",
        "\n",
        "For example, consider the following toy dataset, where one of the predictive features is `outlook`.\n",
        "\n",
        "![alt text](https://miro.medium.com/max/661/0*DX1px-z340TgpXTN.png)\n",
        "\n",
        "If we divide the dataset by the values ​​of the Outlook feature, the result is 3 other datasets, as shown in the following figure.\n",
        "\n",
        "![alt text](https://miro.medium.com/max/446/0*N01l6jqQtVXvsEyk.png)\n",
        "\n",
        "We can measure the entropy $H_1$ of the original data set. We can also measure the entropy of each of the 3 sets resulting from the division by the Outlook attribute and compute the resulting weighted average entropy $H_2$. If we make $H_2 - H_1$, we get the value of the information gain for the Outlook attribute.\n",
        "\n",
        "The selection criterion based on information gain chooses the attribute that produces the highest information gain among the available attributes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Flo8JFPskHek",
        "colab_type": "text"
      },
      "source": [
        "In Scikit-Learn, the mutual_info_classif function can be used to compute the information gain for a set of attributes, as shown in the following example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4-DDSf_NkKT0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "outputId": "36d7df9a-46b3-441c-c331-074542506363"
      },
      "source": [
        "# fonte: https://stackoverflow.com/questions/46752650/information-gain-calculation-with-scikit-learn\n",
        "from sklearn.datasets import fetch_20newsgroups\n",
        "from sklearn.feature_selection import mutual_info_classif\n",
        "from sklearn.feature_extraction.text import CountVectorizer\n",
        "\n",
        "categories = ['talk.religion.misc',\n",
        "              'comp.graphics', 'sci.space']\n",
        "newsgroups_train = fetch_20newsgroups(subset='train',\n",
        "                                      categories=categories)\n",
        "\n",
        "X, Y = newsgroups_train.data, newsgroups_train.target\n",
        "cv = CountVectorizer(max_df=0.95, min_df=2,\n",
        "                                     max_features=10000,\n",
        "                                     stop_words='english')\n",
        "X_vec = cv.fit_transform(X)\n",
        "\n",
        "res = dict(zip(cv.get_feature_names(),\n",
        "               mutual_info_classif(X_vec, Y, discrete_features=True)\n",
        "               ))\n",
        "print(res)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading 20news dataset. This may take a few minutes.\n",
            "Downloading dataset from https://ndownloader.figshare.com/files/5975967 (14 MB)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "{'00': 0.0062217548845825985, '000': 0.01130246093292954, '00000': 0.0012412324256375618, '0005': 0.003108141579466518, '0010580b': 0.0018924586447506726, '001428': 0.0015319298587311032, '001718': 0.0018628591633699006, '002': 0.0012609485946591687, '01': 0.005063992737829265, '01wb': 0.003108141579466518, '02': 0.005670962638050225, '0200': 0.0018924586447506718, '02139': 0.0012499951251094144, '024423': 0.0018628591633699006, '03': 0.004760929256778008, '033': 0.0018628591633699006, '034101': 0.0012412324256375635, '0362': 0.0024851616866216134, '04': 0.012026433047572957, '040': 0.0012827028287951915, '0400': 0.003108141579466519, '04110': 0.0018628591633699006, '0423': 0.0012609485946591687, '05': 0.003530904851302254, '051746': 0.0024851616866216134, '06': 0.002860706403377422, '060': 0.0012412324256375635, '0608': 0.0013558269777203544, '0615': 0.0027400885069510696, '0674': 0.0018628591633699006, '07': 0.0025185031666803905, '08': 0.004287291177931728, '0891': 0.0018628591633699006, '09': 0.0023842979204709526, '091051': 0.0024851616866216064, '0988': 0.0018628591633699006, '0x100': 0.0018924586447506726, '10': 0.011263122832501294, '100': 0.006615927491390547, '1000': 0.0034011237993100307, '100lez': 0.0006417411980615632, '100m': 0.003108141579466518, '101': 0.002890209468168074, '101010': 0.0025246613755867744, '101044': 0.0024851616866216134, '102': 0.0013648307046852347, '102007': 0.0018924586447506726, '10206': 0.0019116724119796905, '1024': 0.0018924586447506718, '1024x768': 0.0037911514534976565, '103': 1.671875925648384e-05, '1030': 0.0006417411980615632, '103038': 0.0018628591633699006, '104': 0.00012627327507338994, '105': 0.0016997325156252636, '106': 0.0006703468019723805, '107': 0.0024851616866216134, '109': 0.0023041316498041723, '10_': 0.001825425726571352, '10m': 0.0012412324256375635, '10th': 0.0027400885069510696, '11': 0.004641632832754196, '110': 0.000995773562281057, '1100': 0.001304990985299034, '111': 0.0026020045737352856, '1113': 0.0012609485946591687, '112': 0.0019093075653275069, '11230': 0.0018924586447506726, '113': 0.0008961450543373099, '114': 8.088279674783698e-05, '114158': 0.0018924586447506726, '115': 0.001347039880397861, '1150': 0.0018628591633699006, '115397': 0.0018628591633699006, '115a': 0.0025246613755867744, '11632': 0.004425442103239911, '11670': 0.0018924586447506726, '1170': 0.0025246613755867744, '12': 0.004193038975187122, '120': 0.0010753398191192037, '1200': 0.002216599560448891, '120311': 0.0018628591633699006, '12091': 0.0025246613755867744, '121': 0.0009738105286627953, '122': 0.0009559019909431317, '123': 0.0013558269777203544, '125': 0.002436271697723395, '127': 0.0012609485946591687, '128': 0.006383495008360297, '129': 0.0033548231864259474, '13': 0.0026741423156522353, '130': 0.003929349355164791, '131': 0.0022994647346008977, '132': 0.0016958301188799586, '133': 0.0007163598861018444, '134': 0.0007671130286615313, '135': 0.0016089714328425542, '136': 0.0012717306823408032, '137': 0.002332493875067958, '138': 0.0009836938410219646, '139': 0.0018924586447506718, '13h': 0.003791151453497654, '14': 0.009988595121275111, '140': 0.0023967941675640553, '1400': 0.0010753398191192063, '141': 0.00232831174264492, '141824': 0.0024851616866216134, '142': 0.001347039880397861, '144': 0.0025838569364433238, '144339saundrsg': 0.0018628591633698963, '144843': 0.003157558429105277, '14496': 0.0024851616866216064, '145': 0.003417927223171884, '146': 0.0014174383459421144, '147': 0.0025799673166654906, '148': 0.0012801026179278053, '149': 0.001586166555485608, '15': 0.00888293723853991, '150': 0.002025101751074507, '1500': 0.0034673585379148266, '150493132018': 0.0027400885069510687, '151': 0.0010103293631748564, '152': 0.0019323989356155756, '152819': 0.0018628591633698963, '153': 0.0018924586447506718, '155': 0.0009559019909431317, '1550': 0.0015035858261545658, '158': 0.0018705330287465275, '159': 0.0018559239832745917, '15m': 0.0012412324256375635, '15mhz': 0.0012609485946591687, '16': 0.003039223390512498, '160': 0.0007473295087178644, '1600': 0.0010442927627179474, '160550': 0.0018628591633699006, '1607': 0.0024851616866216125, '160x2xx': 0.0025246613755867744, '161742': 0.0018628591633699006, '162501': 0.0018628591633699006, '163': 0.003791151453497659, '164': 0.000978451715284566, '164940': 0.004425442103239911, '165': 0.000978451715284566, '1653': 0.0018924586447506726, '167': 0.001347039880397861, '16712': 0.0012412324256375635, '168730': 0.003108141579466518, '169': 0.00010510953103124408, '17': 0.003866538557383308, '170493104859': 0.0027400885069510687, '171': 0.0015861665554856063, '172': 0.0012827028287951915, '174': 0.00035791381164745114, '1776': 0.0012412324256375635, '178': 0.0018924586447506718, '17804': 0.0036560569852768275, '17apr199316423628': 0.0018628591633698963, '18': 0.0055753610751617935, '180': 0.0025761699754157956, '1800': 0.0010442927627179474, '18084tm': 0.0074881014985187615, '183': 0.000978451715284566, '1838': 0.0012160848046758686, '184': 0.0006417411980615632, '185': 0.0018628591633699006, '1850': 0.0009236759316832519, '1865': 0.0018628591633699006, '187': 0.000978451715284566, '188': 0.0019965781299750842, '189': 0.00021074702514795735, '19': 0.006818744393343739, '1901': 0.0018628591633699006, '190493200420': 0.006411840182243063, '1915': 0.001520379122855315, '1919': 0.0012160848046758686, '192': 0.005101269883223629, '1920': 0.0015319298587311032, '1922': 0.00365605698527683, '192947': 0.0018924586447506726, '193758': 0.0025246613755867744, '194': 0.0010442927627179474, '195': 0.0018705330287465275, '1950': 0.0056068667373293845, '19549': 0.003157558429105277, '1958': 0.002276772298013972, '1959': 0.0012412324256375635, '1960': 0.0027493934435962623, '1960s': 0.003731800431935113, '1961': 0.003108141579466519, '1962': 0.0012412324256375635, '1963': 0.0006739571102848205, '1964': 0.002773679606040554, '1965': 0.003731800431935115, '1966': 0.0012603864489062547, '1967': 0.0015319298587311032, '1968': 0.002773679606040554, '1969': 0.0015448877753555896, '1970': 0.009224117658202843, '1971': 0.002485161686621608, '1972': 0.0015448877753555896, '1973': 0.005546277321773346, '1974': 0.0015319298587311032, '1975': 0.0024851616866216125, '1976': 0.0007008483508128818, '1977': 0.005606866737329385, '1977vii': 0.0018628591633699006, '1978': 0.0012603864489062547, '1979': 0.0025231056317136114, '1980': 0.004150284789101609, '1981': 0.00034465163587258686, '1982': 0.0024570044961898328, '1983': 0.006860335160339447, '1984': 0.002497187663458686, '1985': 0.0042144808865233994, '1986': 0.003777879447810153, '1987': 0.004038053680223708, '1988': 0.0024081994629620365, '1989': 0.001979624617771409, '1990': 0.005462209837128892, '1990s': 0.0018628591633699006, '1991': 0.002177142765337544, '1992': 0.004722913980597322, '1993': 0.021535363748277622, '1993apr10': 0.001226521686031947, '1993apr11': 0.0009433921007048016, '1993apr12': 0.0018628591633699006, '1993apr13': 0.002748269221361084, '1993apr14': 0.0027084589206508992, '1993apr15': 0.004057640106026542, '1993apr16': 0.0012588904301825748, '1993apr17': 0.0005982636427668865, '1993apr18': 0.0029139079579239696, '1993apr19': 0.0036882841201903525, '1993apr2': 0.002920544330616162, '1993apr20': 0.007531285132395171, '1993apr21': 0.009575399451715528, '1993apr22': 0.005906673577914566, '1993apr23': 0.00630025889426713, '1993apr25': 0.003108141579466519, '1993apr3': 0.0006417411980615632, '1993apr5': 0.003426922065493521, '1993apr6': 0.003582165403011002, '1993apr7': 0.0013262274963396362, '1993e': 0.003108141579466512, '1994': 0.005606866737329385, '1995': 0.002570679320947222, '1996': 0.003108141579466519, '1997': 0.0012412324256375635, '1999': 0.0033733168848706693, '19th': 0.0018134151655027544, '1b': 0.0031081415794665165, '1billion': 0.0018628591633699006, '1d': 0.0006516076727636853, '1d17': 0.0018628591633699006, '1d20': 0.0006516076727636853, '1g': 0.005606866737329392, '1m': 0.0009657853033023019, '1mb': 0.0018924586447506718, '1pr5u2': 0.0018628591633699006, '1pscti': 0.0018924586447506726, '1q77ku': 0.0012412324256375635, '1qevbh': 0.00365605698527683, '1qie61': 0.0027400885069510696, '1qjahh': 0.0027400885069510696, '1qjbn0': 0.0027400885069510696, '1qjd3o': 0.0027400885069510696, '1qk73q': 0.001825425726571352, '1qkgbuinns9n': 0.0025246613755867744, '1qn4bginn4s7': 0.0018628591633699006, '1qppef': 0.0027400885069510687, '1quvdoinn3e7': 0.005060432039124049, '1qv82l': 0.00365605698527683, '1qve4kinnpas': 0.0018628591633699006, '1r17j9': 0.0027400885069510696, '1r46j3inn14j': 0.0012412324256375635, '1r46o9inn14j': 0.0024851616866216134, '1r6aqr': 0.0024851616866216134, '1r6b7v': 0.0018628591633699006, '1r9de3innjkv': 0.0012412324256375635, '1scd1': 0.0027400885069510696, '1st': 0.0021681840274765983, '20': 0.0069827829324031355, '200': 0.0031613172636309585, '2000': 0.03156572212279566, '20006': 0.0012412324256375635, '2001': 0.0024851616866216125, '200231': 0.0027400885069510696, '20024': 0.0018628591633699006, '200493113800': 0.001825425726571352, '2005': 0.004356139840040938, '20084': 0.0018924586447506718, '201': 0.0012555613674905923, '2010': 0.004356139840040938, '20189': 0.0012609485946591687, '202': 0.004785805339046992, '203': 0.0009284200503372423, '2042': 0.0012609485946591687, '205': 0.004572425349743983, '206': 0.003791151453497659, '20771': 0.0010442927627179474, '209': 0.0010442927627179474, '20apr199301460499': 0.006411840182243063, '20th': 0.0013262274963396362, '21': 0.004518704154418488, '210': 0.0016997325156252636, '21000': 0.0015861665554856063, '2112': 0.000988318189986688, '211638': 0.003108141579466518, '212': 0.0025114946594801584, '212202': 0.0024851616866216134, '212441': 0.0018924586447506726, '213': 0.0031306480206918248, '213547': 0.0027400885069510696, '213917': 0.0012412324256375635, '214': 0.003672182344315246, '215': 0.0007163598861018444, '216': 0.0013578249502064956, '217': 0.002524661375586771, '2178': 0.004981161405813842, '218': 0.0012499951251094144, '21934': 0.0012412324256375635, '22': 0.0059742594539248794, '220': 0.0010442927627179474, '221': 0.0025005225130257675, '2213': 0.0025246613755867744, '2232': 0.00365605698527683, '2238': 0.0012412324256375635, '224': 0.00035791381164745114, '225': 0.0018925273642776512, '22534': 0.0018628591633699006, '225657': 0.0036560569852768275, '22647': 0.0018628591633699006, '227': 0.0025983775738100843, '2273': 0.00365605698527683, '2289': 0.0018628591633699006, '229': 0.0015332358208003521, '2291': 0.0024851616866216134, '22apr199323003578': 0.0018628591633699006, '23': 0.008846374447591815, '230': 0.00010510953103124408, '231': 0.0016738670852616978, '232': 0.0019965781299750842, '23536': 0.0024851616866216134, '238': 4.035731769314044e-05, '239': 0.0012499951251094144, '24': 0.012164516966970542, '240': 0.0018803995034486513, '2400': 0.0019270178337610988, '241': 0.0009218749734641136, '243': 0.0024851616866216134, '245': 0.0012691491483781065, '246': 0.0019784120197450395, '248': 0.0012609485946591687, '249': 0.007626005610329788, '2490747': 0.0012609485946591687, '2492930': 0.0012609485946591687, '24bit': 0.0031575584291052743, '24in': 0.00365605698527683, '24th': 0.0018628591633699006, '24x': 0.0031575584291052743, '25': 0.007347126268318042, '250': 0.004283001678691935, '250k': 0.0009433921007048016, '252': 0.001347039880397861, '253': 0.0009559019909431317, '254': 0.0016194133460181942, '255': 0.0021657174445653135, '256': 0.021288835018110498, '258': 0.0024851616866216134, '25k': 0.0024851616866216125, '25mhz': 0.0018924586447506718, '25x': 0.0025246613755867744, '26': 0.002501256984401977, '260': 0.0006417411980615632, '26022': 0.0018628591633699006, '26140': 0.0012412324256375635, '264': 0.003731800431935112, '265': 0.0006516076727636853, '267': 0.0006417411980615632, '2697': 0.003108141579466518, '27': 0.003937783185748935, '270': 0.0007163598861018444, '272': 0.0030847158139595578, '273': 0.0012717306823408032, '27467': 0.0018628591633699006, '275': 0.0017062962603481236, '277': 0.0009657853033023019, '28': 0.0034713416633355794, '280': 0.0027724937929534815, '2800': 0.0006516076727636853, '28186': 0.0018628591633698963, '282': 0.003108141579466518, '284': 0.0018452344383494239, '286': 0.0026572216870882825, '2888': 0.0018628591633698963, '29': 0.0013711025297248802, '290': 0.000978451715284566, '296': 0.000988318189986688, '297': 0.003731800431935113, '29848': 0.003108141579466518, '2ai': 0.0007163598861018444, '2d': 0.012091955633746555, '2mb': 0.0025246613755867744, '2nd': 0.0019551921910168765, '30': 0.01120496941769199, '300': 0.01025573654355808, '3000': 0.002560115984068111, '301': 0.004161235573188139, '303': 0.0016194133460181942, '304': 0.0018628591633698963, '30fps': 0.003791151453497654, '31': 0.004489571086684845, '310': 0.0019150563317796342, '312': 0.003487229486370913, '313': 0.0007671130286615313, '32': 0.0028557353898489065, '320': 0.0046705306586475905, '320x200': 0.005060432039124051, '320x200x256': 0.0063325164442827675, '325': 0.001562428115434343, '32768': 0.0025246613755867744, '3296': 0.0007163598861018444, '33': 0.0024107664448829056, '330': 0.001064042549779238, '336': 0.003579847425531215, '34': 0.0022139333921262416, '3426': 0.003157558429105277, '343': 0.0018628591633698963, '344': 0.0007163598861018444, '345': 0.0012609485946591687, '34deg': 0.003108141579466518, '35': 0.0032743375102650928, '350': 0.0022887445873255316, '35294': 0.0025246613755867744, '3539': 0.015712480324263707, '354': 0.002318128850905355, '355': 0.0033448506491764183, '3556': 0.003731800431935113, '35611': 0.003108141579466518, '3578': 0.0024851616866216134, '358': 0.0024917448724188695, '36': 0.005732289130204574, '360': 0.001914490397895912, '3618': 0.0012609485946591687, '364': 0.0007163598861018444, '3684': 0.010569929068483804, '37': 0.0025909420338976093, '370': 0.0018705330287465275, '373': 0.0012717306823408032, '378': 0.000988318189986688, '38': 0.0018707642764419436, '380': 0.0031361480610134374, '386': 0.007965509718145023, '387': 0.0015417795530505863, '39': 0.0020985724852642185, '390': 0.001306377566948104, '3d': 0.044128651499110605, '3d2': 0.0012609485946591687, '3do': 0.01337970361772855, '3ds': 0.006332516444282769, '3dstudio': 0.0012609485946591687, '3fj': 0.001825425726571352, '3g': 0.0024851616866216134, '3rd': 0.000323334060700212, '3xx': 0.0025246613755867744, '40': 0.006409412634736487, '400': 0.003660407855159837, '4000': 0.0011288666690330651, '404': 0.001914490397895912, '405': 0.0006516076727636853, '4060': 0.0018924586447506726, '407': 0.003143848162464603, '408': 0.005871700946922266, '40bps': 0.0012412324256375635, '41': 0.005609380199990404, '410': 0.0012499951251094144, '4100': 0.0018924586447506726, '412': 0.003685796326874803, '415': 0.004592564538770818, '416': 0.0019370569109456786, '42': 0.01219200894412501, '422': 0.0012259344989952962, '424346': 0.0018628591633699006, '427': 0.0018628591633699006, '42bis': 0.0012499951251094144, '43': 0.003285159999113156, '430': 0.0024851616866216125, '43011': 0.006233257448747934, '433': 0.0022171229967145236, '435': 0.000988318189986688, '436': 0.0009236759316832519, '4368': 0.004981161405813842, '44': 0.004128806216938716, '440': 0.0006417411980615632, '441': 0.0012609485946591687, '44135': 0.0006516076727636853, '442': 0.0018628591633699006, '444': 0.00039751840402391624, '45': 0.001084226581857699, '450': 0.0012412324256375618, '453': 0.0009236759316832519, '455': 0.0006604803272702029, '456': 0.0018362078142529865, '45g': 0.001862859163369898, '46': 0.0021813910775395923, '462': 0.003731800431935113, '464': 0.003731800431935113, '4650': 0.0024851616866216134, '4656': 0.003731800431935113, '47': 0.0010248096663689563, '471': 0.0009559019909431317, '47749': 0.0027400885069510696, '48': 0.003913980384007638, '480': 0.001304990985299034, '4800': 0.0012852074653554209, '483': 0.006860335160339446, '486': 0.004690718291751644, '488': 0.0012412324256375618, '48p': 0.0018628591633699006, '49': 0.0021468879943398024, '491': 0.0012499951251094144, '492': 0.0025120690482758456, '494': 0.001216655211329824, '495': 0.0007163598861018444, '497': 0.00218168103094784, '4d': 0.0018924586447506718, '4h9': 0.0018628591633699006, '4mb': 0.002524661375586772, '4th': 0.0019150563317796342, '50': 0.007718759827483174, '500': 0.005746474125564138, '5000': 0.005872522430745486, '5011': 0.0018628591633698963, '503': 0.0007974490228694411, '504': 0.0015319298587311032, '508': 0.0016870798481549085, '50m': 0.0018628591633699006, '51': 0.0009990755244300821, '510': 0.0032258908537603926, '512': 0.0016278394879277016, '513': 0.0018628591633699006, '515': 0.001347039880397861, '517': 0.004981161405813842, '52': 0.0015290550031731394, '525': 0.011172893020341775, '53': 0.00142952702286543, '530': 0.001064042549779238, '534': 0.00026602081583273606, '54': 0.002058864402262108, '543': 0.0012717306823408032, '5473': 0.0025246613755867744, '54909': 0.003731800431935113, '55': 0.005680256509447314, '550': 0.0024363865949890897, '553': 0.0012499951251094144, '5543': 0.0018924586447506718, '56': 0.0043499132562123954, '560': 0.000978451715284566, '565': 0.0018924586447506726, '57': 0.002602375988647953, '575': 0.012522643008530177, '5753': 0.0012609485946591687, '578': 0.0016958301188799586, '57th': 0.0021525282388884385, '58': 0.003224077268229085, '580': 0.0012717306823408032, '586': 0.0024851616866216134, '59': 0.0019985924145919463, '60': 0.006251961382991776, '600': 0.0010219278651325894, '6000': 0.0036915337036489545, '601': 0.000978451715284566, '602': 0.012534411974267676, '604': 0.0031491110450414476, '605': 0.0010442927627179474, '60637': 0.0025246613755867744, '61': 0.0031371545741315753, '615': 0.0027218795235153916, '617': 0.001936874273809796, '619': 0.0019096161933030145, '62': 0.0038205525267553404, '621': 0.01816764317527863, '624': 0.002454726329680262, '629': 0.0037427911267253564, '63': 0.0013084005919667407, '635': 0.0012412324256375618, '64': 0.0029547926879039685, '640': 0.0015332358208003521, '640x400': 0.002524661375586771, '640x480': 0.006332516444282769, '640x480x256': 0.0025246613755867744, '644': 0.0012412324256375618, '65': 0.004376995208167424, '650': 0.003103201131767868, '653': 0.0018705330287465292, '658': 0.0018628591633698963, '66': 0.003253042282480017, '663': 0.0018705330287465275, '666': 0.006110077022720121, '667': 0.0018559239832745917, '67': 0.002150237558546232, '6700': 0.0024851616866216134, '68': 0.0020672731084840903, '68000': 0.003157558429105275, '68010': 0.004425442103239916, '68040': 0.0025246613755867744, '68060': 0.003791151453497659, '68070': 0.005696122928293769, '680x0': 0.003791151453497659, '684': 0.000988318189986688, '69': 0.0010991151288512425, '6th': 0.0021484342404152522, '6v2': 0.0025246613755867744, '6zv82b2w165w': 0.003108141579466518, '70': 0.002390149391872623, '700': 0.0019701768565531744, '702': 0.0018250202487414676, '703': 0.002822349875197823, '705': 0.003157558429105275, '708': 0.001914490397895912, '70s': 0.0024851616866216125, '71': 0.0028758853321999593, '713': 0.00916575475788075, '72': 0.0008166188133887321, '72210': 0.00365605698527683, '724': 0.00035791381164745114, '725': 0.0018925273642776495, '727': 0.0012499951251094144, '73': 0.00012627327507338994, '734': 0.0024851616866216125, '7350': 0.001825425726571352, '74': 0.0013558269777203544, '7467': 0.003108141579466518, '747': 0.003731800431935113, '748': 0.003715395808255575, '75': 0.0028238828948431143, '750': 0.00037486756440209545, '76': 0.0015882723326083679, '768': 0.0018924586447506718, '77': 0.000790333061337781, '77058': 0.0024851616866216125, '78': 0.00034465163587258686, '786': 0.000988318189986688, '79': 5.819262377932885e-05, '7900': 0.0018803995034486513, '7951': 0.004356139840040938, '7968': 0.0013558269777203544, '7mhz': 0.0031575584291052778, '7th': 0.005795941940346829, '80': 0.0019384851869979867, '800': 0.004072172124619037, '8000': 0.0007163598861018444, '800x600': 0.0018924586447506718, '801': 0.0018924586447506726, '804': 0.003108141579466518, '805': 0.001386662615895041, '81': 0.00012179859452932009, '817': 0.002524661375586772, '818': 0.0030766609596601, '82': 0.0017254992060226218, '83': 0.001005728715167094, '84': 0.003203276717406286, '840': 0.0018628591633698963, '85': 0.002010883252134244, '8514': 0.002524661375586772, '86': 0.003172077923361049, '86deg': 0.003108141579466518, '87': 0.0019289692595422028, '88': 0.0009849752050109586, '89': 0.0019513823205328483, '890': 0.00035791381164745114, '8900c': 0.0025246613755867744, '895': 0.000988318189986688, '8bit': 0.002524661375586772, '8mm': 0.0012801026179278053, '90': 0.004209988851079983, '900': 0.0031669133684258883, '9000': 0.002569818270388373, '904': 0.0012412324256375618, '91': 0.00268442019573468, '91109': 0.00939658608064124, '92': 0.0034463887333665705, '92093': 0.0013558269777203544, '922': 0.0012499951251094144, '93': 0.01735799937795007, '93107': 0.0018628591633698963, '934': 0.0025246613755867744, '93apr19183833': 0.0027400885069510687, '93apr20145301': 0.0018628591633698963, '93apr20160116': 0.0018628591633698963, '94': 0.00034465163587258686, '95': 0.003893324487150453, '950': 0.002655022005264243, '9591': 0.004981161405813842, '96': 0.0012894538464725182, '9600': 0.0015035858261545658, '9615': 0.017555282105751656, '9630': 0.01195925481663676, '964': 0.0018924586447506718, '97': 0.0033978177019002498, '9760': 0.0004771206825240019, '978': 0.0018924586447506718, '98': 0.0013246579361134055, '980': 0.003157558429105277, '99': 0.0007262170680325539, '9w3': 0.0018628591633698963, '__': 0.013717282802296907, '___': 0.016563131178077617, '____': 0.0110999065660461, '_____': 0.01304200008604688, '______': 0.0013010267962684525, '_______': 0.0012827028287951915, '__________': 0.0012609485946591687, '_______________________________': 0.003157558429105275, '____________________________________': 0.0018924586447506718, '_______________________________________________________________________________': 0.0018628591633699006, '_me_': 0.0010442927627179474, '_perijoves_': 0.003108141579466518, '_the': 0.005496049080234763, '_when': 0.0015417795530505863, '_without_': 0.0024851616866216134, 'a2i': 0.003177257160071079, 'aa429': 0.0012412324256375618, 'aaa': 0.0045733355067311176, 'aamrl': 0.0012609485946591687, 'aas': 0.0024851616866216125, 'ab': 0.0055372198011372905, 'abad': 0.003157558429105277, 'abandon': 0.00039751840402391624, 'abandoned': 0.005089599210770964, 'abc': 0.0018803995034486513, 'abdkw': 0.0024851616866216134, 'abel': 0.0012609485946591687, 'ability': 0.0010041229459574223, 'able': 0.005679169471328818, 'abo': 0.0018705330287465275, 'aboard': 0.002570679320947222, 'abolish': 0.004573335506731118, 'abort': 0.002491744872418867, 'abortion': 0.011959254816636745, 'abraham': 0.0064118401822430655, 'abraxis': 0.0012609485946591687, 'absence': 0.002674481124809779, 'absolute': 0.005654222834072603, 'absolutely': 0.0032303027321876013, 'abstract': 0.0021863687208809766, 'abstracts': 0.003762574646668965, 'abuse': 0.0007018517160113221, 'abyss': 0.0024080850228676183, 'ac': 0.014232474254897274, 'acad3': 0.021476555284581453, 'academic': 0.0028014552835802778, 'academy': 0.0022072227891300807, 'acc': 0.00583474337634635, 'acceleration': 0.005606866737329388, 'accelerations': 0.002485161686621608, 'accelerator': 0.0069280907746618265, 'accelerators': 0.001304990985299034, 'accept': 0.01677317653104205, 'acceptable': 0.0028164576398575607, 'acceptance': 0.00065960320825413, 'accepted': 0.00460420556179393, 'accepting': 0.003817173033434862, 'accepts': 0.0013558269777203544, 'access': 0.03175891723295438, 'accessed': 0.0010442927627179474, 'accessible': 0.0013596855355406754, 'accident': 0.0015035858261545658, 'accidentally': 0.0015527953218988713, 'accompanied': 0.0015035858261545658, 'accomplish': 0.0003474108153178439, 'accomplished': 0.005874018745835265, 'according': 0.00970255758461052, 'account': 0.0031183919122810206, 'accounting': 0.003731800431935113, 'accounts': 0.00976527125822172, 'accredited': 0.0012412324256375635, 'accumulate': 0.0012827028287951915, 'accuracy': 0.0010484127952127007, 'accurate': 0.003810713034275207, 'accurately': 0.0017855205597762545, 'accusation': 0.004573335506731121, 'accusations': 0.0036560569852768275, 'accuse': 0.004573335506731121, 'accused': 0.004370099599025862, 'accusing': 0.0027400885069510687, 'ace': 0.0012827028287951915, 'achieve': 0.0013665824242313617, 'achieved': 0.0045458418556462085, 'achieving': 0.0033256832965099592, 'acid': 0.0024851616866216134, 'acknowledge': 0.0021084570578679554, 'acknowledged': 0.0007455261905868872, 'acknowledgement': 0.0021401823853150715, 'acm': 0.007306160784121247, 'acme': 0.0024851616866216064, 'acns': 0.006768614923881625, 'acpub': 0.002524661375586771, 'acquire': 0.0012801026179278053, 'acquiring': 0.0024851616866216134, 'acquisition': 0.0009657853033023019, 'acronym': 0.001884840403250123, 'acronyms': 0.0012412324256375635, 'acrv': 0.0012412324256375635, 'acs': 0.003488132483513426, 'acsc': 0.0018924586447506726, 'acsu': 0.005755680809886769, 'act': 0.011210725978332843, 'acting': 0.0033538046033891123, 'actinides': 0.0018628591633698963, 'action': 0.006909123755130653, 'actions': 0.016565677397681715, 'active': 0.005033462410433929, 'actively': 0.0006251111015571457, 'activist': 0.003108141579466518, 'activities': 0.021914655571954576, 'activity': 0.007135671577959659, 'actrix': 0.0006496982395886239, 'acts': 0.01387935819402963, 'actual': 0.005060239737749523, 'actually': 0.004374226462098226, 'acuity': 0.0012412324256375618, 'ad': 0.0054093188904824376, 'ad354': 0.0027400885069510687, 'ad994': 0.0018924586447506718, 'adam': 0.002856347522883539, 'adam4': 0.0018628591633698963, 'adams': 0.012246261601672529, 'adamski': 0.0037911514534976574, 'adapted': 0.000988318189986688, 'add': 0.0017860957973178746, 'added': 0.009246903310586169, 'adding': 0.0013761136283660328, 'addition': 0.002822955129222476, 'additional': 0.005424046099144744, 'additionally': 0.0016958301188799586, 'additions': 0.000995773562281057, 'address': 0.007968252948358009, 'addressed': 0.004641218920106217, 'addresses': 0.004046457011053882, 'addressing': 0.00437994929334529, 'adds': 0.004019707785561446, 'adelaide': 0.0024851616866216125, 'adequate': 0.0019965781299750842, 'adjusting': 0.001064042549779238, 'adjustment': 0.0025005225130257675, 'admin': 0.0006004597111942912, 'administration': 0.005751400532796909, 'administrative': 0.003731800431935113, 'administrator': 0.002715976736192463, 'admission': 0.003292686548050345, 'admit': 0.006112988976282878, 'admitted': 0.005491928440954983, 'adobe': 0.009525082451507575, 'adopted': 0.0024646783615664657, 'ads': 0.001907356230328468, 'adult': 0.0017855205597762545, 'adults': 0.00457333550673112, 'advance': 0.02868746340988773, 'advanced': 0.0028074161506412773, 'advancement': 0.00034465163587258686, 'advances': 0.0015035858261545658, 'advantage': 0.0028427207451996077, 'advantages': 0.0010753398191192037, 'adventists': 0.00365605698527683, 'advertisers': 0.0018628591633698963, 'advertising': 0.008745706591231313, 'advice': 0.001301692910380182, 'advised': 0.0018331313345243579, 'advisory': 0.004356139840040942, 'advocate': 0.004102384086440273, 'advocated': 0.0024851616866216134, 'aero': 0.004356139840040943, 'aerobraking': 0.003108141579466519, 'aeronautics': 0.006860335160339441, 'aerospace': 0.013925048699324694, 'af': 0.00419328905167315, 'af664': 0.00457333550673112, 'afb': 0.0018628591633698963, 'affairs': 0.001520379122855315, 'affect': 0.0027870607474464806, 'affected': 0.004356139840040938, 'affiliation': 0.0073330751497454084, 'afford': 0.008745706591231327, 'affordable': 0.0018628591633698963, 'afit': 0.0024851616866216064, 'afraid': 0.001635778999069186, 'africa': 0.0024851616866216134, 'african': 0.002750040538837272, 'afternoon': 0.000978451715284566, 'agate': 0.003113662722442605, 'agc': 0.0024851616866216125, 'age': 0.010071213020064897, 'agencies': 0.0028559707946024483, 'agency': 0.010036971236630884, 'agenda': 0.0024337964176860604, 'agent': 0.004579599811766369, 'agents': 0.008700208071738588, 'ages': 0.004033270862525228, 'aggravation': 0.003731800431935113, 'agian': 0.0024851616866216134, 'agnostics': 0.0027400885069510687, 'ago': 0.006127942456322585, 'agr00': 0.00365605698527683, 'agree': 0.024752449351710552, 'agreed': 0.003636285388138691, 'agreement': 0.002497828333128376, 'agrees': 0.0007117181907135006, 'agricultural': 0.0018803995034486513, 'ah': 0.00021074702514795735, 'ahead': 0.002096757418441583, 'ahithophel': 0.001825425726571352, 'ahura': 0.001825425726571352, 'ai': 0.006746795838933094, 'aiaa': 0.007488101498518761, 'aid': 0.0015500286817153337, 'aide': 0.0015319298587311032, 'aided': 0.004131903014840331, 'aiken': 0.002454726329680262, 'aim': 0.0016278394879277016, 'aimed': 0.0009559019909431317, 'aimla': 0.002524661375586771, 'ain': 0.0019116724119796905, 'aint': 0.0013262274963396362, 'aio': 0.006233257448747921, 'aips': 0.0012499951251094144, 'air': 0.017511468145990083, 'airborne': 0.00035791381164745114, 'aircraft': 0.010300249404484058, 'airliner': 0.0018628591633698963, 'airliners': 0.003108141579466518, 'airmail': 0.0018628591633698963, 'airplane': 0.001862859163369898, 'airport': 0.0016661801242341696, 'aix': 0.003157558429105275, 'ajackson': 0.0012609485946591687, 'ajjb': 0.001862859163369898, 'aka': 0.00011497600573342169, 'al': 0.004421692010932417, 'alabama': 0.0038767754584007694, 'alamut': 0.0027400885069510687, 'alan': 0.0026862203578136875, 'alas': 0.0016661801242341696, 'alaska': 0.03523665319492633, 'albany': 0.0012609485946591687, 'albedo': 0.000978451715284566, 'albeit': 0.0013371565680386924, 'albert': 0.004769285032991187, 'albrecht': 0.0027400885069510687, 'album': 0.0024851616866216134, 'albuquerque': 0.001027092726567722, 'alchemy': 0.0031179761169177313, 'alex': 0.0034756069173913105, 'alexander': 0.0003753054210443446, 'alexandria': 0.0012808370180140277, 'alexis': 0.0012412324256375635, 'alfred': 0.0007163598861018444, 'algo': 0.0025246613755867744, 'algorithm': 0.017316973066753973, 'algorithms': 0.017540999862071506, 'alias': 0.0012609485946591687, 'aliasing': 0.0037911514534976574, 'alice': 0.0031575584291052743, 'alicea': 0.016619192667934626, 'alien': 0.0009661235676352671, 'alike': 0.007626005610329788, 'alink': 0.026992776426506576, 'alive': 0.01179118906470562, 'alizard': 0.0036560569852768275, 'allah': 0.0036560569852768267, 'allegations': 0.0013262274963396362, 'alleged': 0.0030773288864334716, 'allegiance': 0.00365605698527683, 'allen': 0.011486275198720738, 'allow': 0.0018995898816949299, 'allowed': 0.00765508629861139, 'allowing': 0.002897278632376505, 'allows': 0.004037207106051669, 'almac': 0.0012609485946591687, 'almaden': 0.0020928628598154662, 'almanac': 0.0015319298587311032, 'alot': 0.004141346423062924, 'alpha': 0.005830647587400765, 'alphacdc': 0.003731800431935114, 'als': 0.0024851616866216134, 'alt': 0.004220804444140839, 'alter': 0.0018331313345243579, 'altered': 0.00029391542155923767, 'alternate': 0.0010753398191192063, 'alternative': 0.003127854998686824, 'alternatives': 0.00039751840402391624, 'altitude': 0.014439451979546165, 'altitudes': 0.0024851616866216134, 'altogether': 0.00010510953103124408, 'aluminum': 0.002485161686621608, 'alumni': 0.0012412324256375618, 'amail': 0.006411840182243066, 'amann': 0.0018924586447506718, 'amateur': 0.01152199271927813, 'amazing': 0.0009971867412477565, 'amber': 0.0018924586447506718, 'ambitious': 0.003731800431935113, 'amdahl': 0.011031336546395553, 'amendment': 0.00365605698527683, 'america': 0.006354294384755947, 'american': 0.006849891111916677, 'americans': 0.00580865035415028, 'americas': 0.0012808370180140277, 'amertume': 0.0012609485946591687, 'ames': 0.01333953047477449, 'amiga': 0.010401702983671957, 'amigas': 0.002524661375586772, 'amoral': 0.0027400885069510687, 'amorc': 0.007333075149745413, 'amounts': 0.0042657992359751385, 'amro': 0.0018803995034486513, 'amruth': 0.0018628591633698963, 'amsat': 0.003108141579466518, 'amsterdam': 0.0012499951251094144, 'amuse': 0.00365605698527683, 'amused': 0.001300553187035633, 'amusement': 0.0015417795530505863, 'amusing': 0.0018449705137248374, 'analog': 0.0019415370116521308, 'analogy': 0.0046282755193996885, 'analyses': 0.00012627327507338994, 'analysis': 0.006152372454782754, 'analyst': 0.0013356730305772568, 'analytical': 0.001300553187035633, 'analyze': 0.0020361452852944734, 'analyzed': 0.0024851616866216125, 'ancestors': 0.0024363865949890897, 'anchor': 0.0007163598861018444, 'ancient': 0.01560811607570475, 'anderson': 0.0067727652731370686, 'andre': 0.005060432039124053, 'andreas': 0.0030906791987805474, 'andreasa': 0.0025246613755867744, 'andrew': 0.004084033294569752, 'andy': 0.0023170086756430057, 'angel': 0.00039751840402391624, 'angeles': 0.0030515579824003875, 'angle': 0.005991262258194147, 'angles': 0.003170328842337095, 'angry': 0.0073330751497454084, 'angular': 0.0024851616866216134, 'angus': 0.0012412324256375635, 'animal': 0.008872178804771737, 'animals': 0.00938739766694436, 'animated': 0.0031575584291052743, 'animation': 0.02821329291765121, 'animations': 0.004425442103239916, 'animator': 0.0018924586447506718, 'animosity': 0.005491928440954983, 'ann': 0.002972292818235493, 'annihilation': 0.0012412324256375635, 'announce': 0.003414614675436892, 'announced': 0.0023894255310697287, 'announcement': 0.0028791503926915768, 'announcements': 0.0012691491483781056, 'annoyed': 0.0038079529923018395, 'annoying': 0.0018924586447506718, 'annual': 0.003198318740388898, 'anomaly': 0.0024851616866216134, 'anonymous': 0.0077749111998470085, 'ansi': 0.0029614890689189837, 'answer': 0.00807154131669988, 'answered': 0.001630049052250353, 'answers': 0.00833847513701565, 'antarctic': 0.0024851616866216125, 'antenna': 0.00748810149851876, 'antennae': 0.0018628591633698963, 'anthony': 0.005535148013104294, 'anthro': 0.0036560569852768275, 'anti': 0.017754587185370232, 'antiquity': 0.00365605698527683, 'antithesis': 0.0018331313345243579, 'antonio': 0.002524661375586771, 'ants': 0.0012603864489062547, 'anu': 0.0018924586447506718, 'anybody': 0.012509090076475712, 'anymore': 0.00038038517710336107, 'anyways': 0.0004771206825240019, 'ap': 0.014141307230098273, 'apart': 0.0027547680733187004, 'ape': 0.0012609485946591687, 'aperture': 0.0007163598861018427, 'api': 0.0012827028287951915, 'apogee': 0.0012412324256375635, 'apollo': 0.011629834639466253, 'apologies': 0.0032106847577353485, 'apologize': 0.003372550157593129, 'apology': 0.0027400885069510687, 'apostle': 0.006411840182243067, 'app': 0.0037911514534976574, 'apparent': 0.002029331777930245, 'apparently': 0.003933819263394933, 'appeal': 0.0026646314304903523, 'appear': 0.0030363785708950155, 'appearance': 0.0015445286413936655, 'appeared': 0.00247603593087636, 'appearing': 0.0007467754150442046, 'appears': 0.0025716071829513633, 'appelquist': 0.0012412324256375635, 'apple': 0.028817251438599804, 'applicable': 0.0018452344383494239, 'application': 0.006278202895996952, 'applications': 0.008069992931386667, 'applied': 0.0034007779370710967, 'applies': 0.0022069755013889953, 'apply': 0.004925075901000806, 'applying': 0.0007163598861018444, 'appointed': 0.00457333550673112, 'appreciate': 0.002965157335262191, 'appreciated': 0.01917466077115443, 'approach': 0.0042433613081931535, 'approaches': 0.0013598921843151496, 'approaching': 0.0024851616866216134, 'appropriate': 0.0026230126254209547, 'approval': 0.00010510953103124408, 'approved': 0.0019229696813196587, 'approximate': 0.001064042549779238, 'approximately': 0.008897096534022996, 'approximation': 0.0016738670852616978, 'apps': 0.0012609485946591687, 'apr': 0.006215734610614168, 'april': 0.017612920550042377, 'aqc': 0.00457333550673112, 'aqueous': 0.0012609485946591687, 'ar': 0.0026646314304903523, 'arabic': 0.00457333550673112, 'arbitrarily': 0.0009657853033023019, 'arbitrary': 0.004017601551070302, 'arbitron': 0.0012412324256375635, 'arbor': 0.004220752919707875, 'arc': 0.007317848584469546, 'archer': 0.004284527532590306, 'archie': 0.008885150472506754, 'archimedes': 0.002524661375586772, 'architecture': 0.004292400842054841, 'architectures': 0.001064042549779238, 'archive': 0.009918972353996146, 'archived': 0.0018705330287465292, 'archives': 0.0035790703070334284, 'archiving': 0.0018924586447506718, 'area': 0.007239011249287185, 'areas': 0.005793768473642038, 'aren': 0.006452364773029289, 'arff': 0.002524661375586772, 'argentinian': 0.0015319298587311032, 'argue': 0.004317195280345388, 'argued': 0.00457333550673112, 'arguing': 0.007333075149745413, 'argument': 0.024776813287830275, 'arguments': 0.014990377662470494, 'ari': 0.0012609485946591687, 'ariadne': 0.0016958301188799586, 'ariane': 0.004981161405813846, 'arianespace': 0.002485161686621608, 'arithmetic': 0.0031575584291052743, 'arizona': 0.011426459670433119, 'arlington': 0.003283923848578494, 'arlut': 0.0012412324256375635, 'arm': 0.004318779728668239, 'armed': 0.0024377731766381597, 'arms': 0.002132686638080832, 'army': 0.004491244457376839, 'arndt': 0.0027400885069510687, 'arno': 0.0018924586447506718, 'arnold': 0.0024851616866216134, 'aron': 0.0018924586447506726, 'arose': 0.0027400885069510687, 'arranged': 0.0022928590225269633, 'arrangement': 0.0012603864489062547, 'array': 0.0050175027283396135, 'arrays': 0.002939946605148594, 'arrested': 0.0027400885069510687, 'arrival': 0.0012603864489062547, 'arrive': 0.0027736796060405583, 'arrived': 0.005353593422480069, 'arriving': 0.0010172262518655445, 'arrogant': 0.00365605698527683, 'arromdee': 0.00549192844095498, 'arrow': 0.0031136322339350925, 'art': 0.0053967703549849715, 'arthur': 0.003344970223598127, 'article': 0.03898744236978316, 'articles': 0.0034404114648579516, 'artifacts': 0.003157558429105277, 'artificial': 0.001907356230328468, 'artist': 0.0033031972944793687, 'artists': 0.0013770281393766168, 'arts': 0.0038719766656407266, 'artwork': 0.0018924586447506718, 'asa': 0.0021524677623682162, 'ascension': 0.0012691491483781056, 'ascii': 0.0034843829634613743, 'asd': 0.0063965730773623474, 'asia': 0.00068051573464254, 'aside': 0.0021986328836594363, 'ask': 0.008737315307447448, 'asked': 0.004369658652028321, 'askew': 0.0018628591633699006, 'asking': 0.0006434656935352008, 'asks': 0.0007346838535750499, 'asm': 0.0031575584291052778, 'aspect': 0.0029499560858236764, 'aspects': 0.009090725426450404, 'ass': 0.001212678452377722, 'assassin': 0.003791151453497659, 'assembled': 0.0034212272345077862, 'assembler': 0.0025246613755867744, 'assembly': 0.0024854187680615546, 'assert': 0.010104763978199337, 'asserted': 0.0019116724119796905, 'assertion': 0.0073330751497454084, 'assertions': 0.0027400885069510687, 'assessing': 0.0018628591633698963, 'assets': 0.0012412324256375618, 'assigned': 0.0024448766353608346, 'assist': 0.004219311644540178, 'assistance': 0.002901299574849878, 'assistant': 0.0024851616866216134, 'assisted': 0.0018250202487414676, 'associate': 0.0013262274963396362, 'associated': 0.0006790947850922394, 'associates': 0.0019093075653275069, 'association': 0.0031388850161919767, 'associations': 0.0019116724119796905, 'assume': 0.007751277565832513, 'assumed': 0.003868824307338677, 'assumes': 0.0047028626136538035, 'assuming': 0.0029544219363055726, 'assumption': 0.0031427069941767434, 'assumptions': 0.0028376918700381793, 'assured': 0.0012563529269532898, 'asterix': 0.002524661375586772, 'asteroid': 0.0038683500554799206, 'asteroids': 0.009375548629619136, 'astor': 0.008116558095880515, 'astra': 0.003108141579466519, 'astro': 0.017001656351740186, 'astrology': 0.0021524677623682162, 'astronaut': 0.013169258181841663, 'astronautical': 0.0012412324256375635, 'astronautics': 0.005329523280080857, 'astronauts': 0.006233257448747924, 'astronomer': 0.003731800431935113, 'astronomers': 0.0056068667373293905, 'astronomical': 0.00647831738254493, 'astronomy': 0.0212277745557636, 'astrophysical': 0.004356139840040943, 'astrophysics': 0.0036683538927684226, 'atari': 0.0016194133460181942, 'ate': 0.0021524677623682162, 'atf': 0.005289595373482465, 'atheism': 0.007333075149745413, 'atheist': 0.0030538357627876035, 'atheists': 0.0036560569852768267, 'athena': 0.0032363811201593677, 'athens': 0.004191069260318682, 'ati': 0.004425442103239911, 'atlanta': 0.006967477326456206, 'atlantic': 0.004981161405813847, 'atlas': 0.007175844015547085, 'atleast': 0.0024851616866216125, 'atmosphere': 0.016520037011030414, 'atmospheric': 0.004725068562877295, 'atom': 0.003283923848578494, 'atomic': 0.004312151072359467, 'atoms': 0.004969526164972923, 'atone': 0.0027400885069510687, 'atonement': 0.004573335506731118, 'atop': 0.0010442927627179474, 'att': 0.00284924200595354, 'attached': 0.0028010455649708156, 'attack': 0.0045902649683736245, 'attacked': 0.006411840182243063, 'attacking': 0.0019116724119796905, 'attacks': 0.00365605698527683, 'attempt': 0.005130920466635203, 'attempted': 0.0012078054075533593, 'attempting': 0.001226521686031947, 'attempts': 0.0013125177987963273, 'attend': 0.001992851599602421, 'attended': 0.0012808370180140277, 'attendees': 0.003157558429105277, 'attention': 0.002772718837927135, 'attitude': 0.007145917911961773, 'attraction': 0.0019965781299750842, 'attractive': 0.0007561221414976588, 'attributed': 0.0038689170479104555, 'attributes': 0.0032392153061980324, 'au': 0.010941236463141334, 'auburn': 0.003731800431935115, 'aucun': 0.009179532565505875, 'audience': 0.0018496845972676042, 'audio': 0.0025582515566834555, 'aug': 0.0024851616866216134, 'august': 0.00289342766143985, 'aukland': 0.0012609485946591687, 'aurae': 0.00365605698527683, 'aurora': 0.032066179824246165, 'aus': 0.0016958301188799586, 'auspices': 0.003731800431935113, 'austin': 0.0009691147538363424, 'australia': 0.006237182174256796, 'australian': 0.0022737674281686797, 'author': 0.006183469349252007, 'authored': 0.0012808370180140277, 'authorities': 0.004200371242160982, 'authority': 0.016437352444300272, 'authors': 0.001933941329410451, 'auto': 0.000323334060700212, 'autocad': 0.0022512009151189147, 'automated': 0.0027218795235153916, 'automatic': 0.0031245408839466983, 'automatically': 0.0025261973877174345, 'autonomy': 0.001825425726571352, 'autotrace': 0.002524661375586771, 'autre': 0.009179532565505875, 'availability': 0.002426419523303175, 'available': 0.016356899889596956, 'avalon': 0.0012609485946591687, 'avatar': 0.0015417795530505863, 'ave': 0.0026154544465800053, 'avenue': 0.0022563576362111216, 'average': 0.0012878854715138322, 'aviation': 0.009375548629619139, 'avoid': 0.002273669094609112, 'avs': 0.0012609485946591687, 'aw': 0.008116558095880515, 'awaiting': 0.0010442927627179474, 'award': 0.0007661178213869187, 'aware': 0.004278060301123507, 'awareness': 0.0036560569852768267, 'away': 0.009829200905017068, 'awesome': 0.0015332358208003521, 'aweto': 0.008745706591231313, 'awful': 0.003656600893837685, 'awfully': 0.004284527532590309, 'aws': 0.014267526111911453, 'axed': 0.0027400885069510687, 'axes': 0.0012499951251094144, 'axiom': 0.0012801026179278053, 'axis': 0.0033237597708332253, 'az': 0.00898669497503797, 'b645zaw': 0.01381914678022806, 'ba': 0.0033924462191283443, 'baalke': 0.020933097040626788, 'baby': 0.0030470526777740398, 'babylon': 0.004573335506731118, 'bachelor': 0.0012412324256375635, 'backed': 0.0018031183160984914, 'backers': 0.0024851616866216134, 'background': 0.002545942832455128, 'backing': 0.010726756308362152, 'backup': 0.0017936949937184766, 'backwards': 0.00011497600573342169, 'bacteria': 0.003731800431935113, 'bad': 0.00471226892122487, 'badly': 0.0018496845972676042, 'bag': 0.0013558269777203544, 'bailey': 0.006411840182243065, 'balance': 0.0007008483508128818, 'bald': 0.0024851616866216134, 'ball': 0.002279515697097695, 'ballistic': 0.003108141579466519, 'balloon': 0.0044936388816965486, 'balloons': 0.002485161686621608, 'balls': 0.006661599656596525, 'balsa': 0.0018924586447506718, 'baltimore': 0.003153690623228918, 'band': 0.0035511893319027325, 'banding': 0.0012609485946591687, 'bands': 0.006295017573468683, 'bandwidth': 0.002901756017947163, 'bang': 0.0026646314304903523, 'bangkok': 0.00365605698527683, 'bank': 0.0017285247401475938, 'banks': 0.0024570044961898345, 'baptist': 0.007333075149745413, 'baptists': 0.0036560569852768267, 'baptized': 0.0027400885069510687, 'bar': 0.0024888185715904896, 'baraff': 0.0012609485946591687, 'barbara': 0.0025246613755867744, 'barn': 0.0073330751497454084, 'barney': 0.0027400885069510687, 'barnsley': 0.0018924586447506718, 'barrel': 0.0018628591633698963, 'barris': 0.0018924586447506718, 'barry': 0.0025005225130257675, 'bars': 0.0022691094528385783, 'bart': 0.0018924586447506718, 'basalts': 0.0012412324256375635, 'base': 0.014475856094203262, 'based': 0.008383749610119, 'baseline': 0.0024851616866216125, 'bases': 0.005650427112143868, 'basho': 0.00457333550673112, 'basic': 0.001711574233456207, 'basically': 0.006838973253978862, 'basis': 0.008575778060223246, 'bass': 0.0018134151655027544, 'batch': 0.0025246613755867744, 'bates': 0.0015417795530505863, 'batf': 0.01103133654639556, 'batse': 0.0018628591633698963, 'batteries': 0.0012412324256375635, 'battery': 0.0013262274963396362, 'battle': 0.0024363865949890897, 'batty': 0.0024851616866216125, 'baube': 0.003731800431935112, 'baud': 0.0018803995034486513, 'bauer': 0.0027400885069510687, 'bay': 0.0019062296053597707, 'bbn': 0.0012609485946591687, 'bbs': 0.00493213498177177, 'bbses': 0.0012609485946591687, 'bby': 0.0024851616866216064, 'bc': 0.00197115024547712, 'bce': 0.001825425726571352, 'bcstec': 0.00633251644428277, 'bd': 0.00489077602971169, 'bds': 0.0027400885069510687, 'beach': 0.0034448581851909887, 'beacons': 0.0018628591633698963, 'beam': 0.013884803683999199, 'bear': 0.006527242134641629, 'bearing': 0.005170042123874968, 'bears': 0.009179532565505872, 'beast': 0.008255637787672646, 'beasts': 0.0015035858261545658, 'beat': 0.001921522106299118, 'beaten': 0.0018628591633698963, 'beating': 0.0018362078142529865, 'beautiful': 0.0012225449270798988, 'beauty': 0.002791219946119309, 'beaver': 0.0031575584291052778, 'bed': 0.0027285530523395362, 'beer': 0.003974028634309299, 'beg': 0.0016084592037809847, 'began': 0.005874018745835265, 'begging': 0.00365605698527683, 'begin': 0.004409104187999177, 'beginning': 0.004540790347165889, 'begins': 0.0038332746998137324, 'begotten': 0.0027400885069510687, 'begun': 0.00021074702514795735, 'behaved': 0.00457333550673112, 'behavior': 0.008212330944950056, 'beings': 0.008564102403621265, 'belief': 0.015026042973746753, 'beliefs': 0.02691746950475967, 'believe': 0.03448226046029676, 'believed': 0.011288028122710236, 'believer': 0.004573335506731121, 'believers': 0.01010476397819933, 'believes': 0.004579461938140444, 'believing': 0.019431600557536545, 'bell': 0.002775749867654629, 'bellacera': 0.006411840182243066, 'belly': 0.0012603864489062547, 'belong': 0.0038332746998137324, 'belongs': 0.0022345089669202917, 'belt': 0.003754571461966229, 'ben': 0.001058781479937508, 'bend': 0.0015319298587311032, 'benefit': 0.004101280599512118, 'benefits': 0.004575577452606737, 'benign': 0.001825425726571352, 'berkeley': 0.004217471696622406, 'berkshire': 0.0018924586447506718, 'berlin': 0.0028387564496019342, 'bernard': 0.0012717306823408032, 'berne': 0.0021721839313897677, 'bernie': 0.0018705330287465275, 'best': 0.004031466687891883, 'bet': 0.0011846478535948142, 'beta': 0.0016491449891038934, 'bethesda': 0.0018924586447506718, 'bethlehem': 0.0027400885069510687, 'betrayal': 0.001825425726571352, 'betrothed': 0.001825425726571352, 'bettadpur': 0.0018628591633698963, 'better': 0.010162380068950528, 'bev': 0.0018628591633698963, 'beware': 0.0018250202487414676, 'bezier': 0.0069696142670419535, 'bga': 0.002524661375586772, 'bgi': 0.002524661375586771, 'bhagavad': 0.004573335506731118, 'bham': 0.0025246613755867744, 'bi': 0.000978451715284566, 'bias': 0.002540142959293225, 'biased': 0.0042623473629762884, 'bible': 0.07232747959557144, 'biblical': 0.04480893157826756, 'bibliography': 0.000988318189986688, 'bidder': 0.0018628591633698963, 'bielefeld': 0.001862859163369898, 'big': 0.00786717481169659, 'bigger': 0.0019156570680840378, 'biggest': 0.0005585608609487442, 'billboard': 0.01126925254787876, 'billboards': 0.008745706591231322, 'billion': 0.0358174050318502, 'billions': 0.0018496845972676042, 'binah': 0.0027400885069510687, 'binaries': 0.005677389561521958, 'binary': 0.006746756228222884, 'binding': 0.0015527953218988713, 'bingo': 0.0012808370180140277, 'bio': 0.0009393921967916297, 'biological': 0.0030614358371277364, 'bios': 0.004425442103239914, 'bird': 0.0016840886619538323, 'birds': 0.003043748562888326, 'birmingham': 0.005060432039124055, 'birth': 0.0010047383206371338, 'birthday': 0.0015417795530505863, 'bisector': 0.002524661375586772, 'bishop': 0.0024448766353608346, 'bison': 0.002513999296040385, 'bit': 0.010925061058132374, 'bitmap': 0.010807086540932364, 'bitmapped': 0.003157558429105277, 'bitmaps': 0.003157558429105277, 'bitnet': 0.005982435729739921, 'bits': 0.009584374492099002, 'biz': 0.0012499951251094144, 'bizarre': 0.0024496852878952745, 'black': 0.004977169528160241, 'blade': 0.005060432039124049, 'blame': 0.0043609395327504135, 'blank': 0.0007229880847217382, 'blatant': 0.0036560569852768275, 'blatent': 0.0013262274963396362, 'blaze': 0.004482007532535263, 'blessed': 0.0007974490228694411, 'blessings': 0.0027400885069510687, 'blew': 0.0019229696813196587, 'blind': 0.005191540929971686, 'blindly': 0.004573335506731121, 'blip': 0.003108141579466518, 'bliss': 0.005491928440954981, 'blkbox': 0.000988318189986688, 'block': 0.006837951185404297, 'blocks': 0.000988318189986688, 'blood': 0.016749530991725162, 'bloody': 0.0012808370180140277, 'blow': 0.0007262170680325539, 'blown': 0.0012516860117500169, 'blue': 0.0016347371359433736, 'blurb': 0.003731800431935113, 'blvd': 0.0010753398191192063, 'bmdhh286': 0.0024851616866216125, 'bmp': 0.008885150472506752, 'bnr': 0.004307268258637539, 'bnsc': 0.002485161686621608, 'board': 0.0032324721280154794, 'boards': 0.00322722105382976, 'boat': 0.001562428115434343, 'bob': 0.008436199776447318, 'bobbing': 0.0024851616866216134, 'bobc': 0.0015332358208003521, 'bobsarv': 0.007333075149745417, 'bode': 0.003108141579466518, 'bodies': 0.0035476347840805167, 'body': 0.008766930615335348, 'boebert': 0.0012609485946591687, 'boeing': 0.004122044193344127, 'boesel': 0.005060432039124052, 'bogus': 0.0015527953218988713, 'bohr': 0.0034519223629203167, 'boi': 0.010104763978199333, 'boise': 0.006411840182243063, 'boisvert': 0.0025246613755867744, 'boivert': 0.003157558429105277, 'bold': 0.005191692831752376, 'bolero': 0.003177257160071079, 'bolson': 0.005696122928293768, 'bolt': 0.003135992489550251, 'bomb': 0.0036797300056999136, 'bond': 0.0031136322339350925, 'bondage': 0.0027400885069510687, 'bones': 0.0012801026179278053, 'bongo': 0.0013262274963396362, 'bonn': 0.0012412324256375635, 'bonnie': 0.0012499951251094144, 'boo': 0.0027400885069510696, 'book': 0.009121488297965353, 'books': 0.008387380939269194, 'bookstore': 0.0018129847908006135, 'boom': 0.006899024652713957, 'booms': 0.0018628591633698963, 'boost': 0.0049811614058138465, 'booster': 0.012535219985229783, 'boosters': 0.003108141579466518, 'boot': 0.0007163598861018444, 'booth': 0.0020361452852944734, 'borden': 0.0031081415794665165, 'border': 0.0012499951251094144, 'boris': 0.0012499951251094144, 'borland': 0.003157558429105275, 'born': 0.019129537524416578, 'borrowed': 0.001355065105758356, 'bort': 0.0018924586447506718, 'boston': 0.001884840403250123, 'bother': 0.0019314476765712107, 'bothered': 0.00042856546042523147, 'bothering': 0.0018628591633699006, 'bothers': 0.00457333550673112, 'bottles': 0.0015319298587311032, 'bought': 0.002230912780753531, 'boulder': 0.0009738105286627953, 'bounce': 0.001599663558956902, 'bouncing': 0.00010510953103124408, 'bound': 0.0010794054476706777, 'boundaries': 0.0007229880847217382, 'boundary': 0.0007163598861018444, 'bounded': 0.0018924586447506718, 'bourke': 0.0018924586447506718, 'box': 0.005486538577276237, 'boxes': 0.008245929584991846, 'boy': 0.003045243424691374, 'boylan': 0.0015417795530505863, 'boys': 0.0025313802598213187, 'bps': 0.0017855205597762545, 'br': 0.002540142959293225, 'brader': 0.006233257448747934, 'bradford': 0.0012412324256375635, 'bradley': 0.0037539385145901353, 'brain': 0.0009784588912062553, 'brains': 0.0018496845972676042, 'branch': 0.006110500817918944, 'brand': 0.003521365703212571, 'brandeis': 0.0027697567078588774, 'brasil': 0.0012412324256375635, 'braun': 0.0016738670852616978, 'bread': 0.0024670432082186467, 'break': 0.004606453391529732, 'breaking': 0.004370099599025862, 'breaks': 0.0007117181907135006, 'breakup': 0.0024851616866216134, 'breath': 0.0009130487728999945, 'breathable': 0.0012603864489062547, 'breathing': 0.003108141579466514, 'brent': 0.002551096428842924, 'bresenhams': 0.0012609485946591687, 'bret': 0.001862859163369898, 'brewers': 0.001825425726571352, 'brewich': 0.0036560569852768267, 'brian': 0.017350836133389485, 'brick': 0.0012499951251094144, 'brief': 0.003920233612381479, 'briefing': 0.004356139840040942, 'briefly': 0.0018261194396886698, 'brigham': 0.006768271515653529, 'bright': 0.004981161405813846, 'brighter': 0.0012609485946591687, 'brightness': 0.0007561221414976588, 'bring': 0.0035109210566153974, 'bringing': 0.0009813417068165256, 'brings': 0.0013113511286082574, 'britain': 0.0018134151655027544, 'british': 0.002188673014139636, 'broad': 0.0024851616866216134, 'broadcast': 0.003996266628453278, 'broadcasting': 0.0012603864489062547, 'brochure': 0.0015035858261545658, 'brock': 0.0037911514534976565, 'brocku': 0.004425442103239916, 'broderick': 0.0018628591633698963, 'broke': 0.0027285530523395362, 'broken': 0.0019229696813196587, 'brookline': 0.00034465163587258686, 'brookpark': 0.0012827028287951915, 'brooks': 0.0012412324256375635, 'brother': 0.0077135954761821555, 'brothers': 0.0036686106438780647, 'brought': 0.009032948982928734, 'brown': 0.002087809530252392, 'browse': 0.0015332358208003521, 'bruce': 0.008457476843618928, 'brunel': 0.0022391211938598225, 'brush': 0.002454726329680262, 'brute': 0.0024851616866216125, 'bryan': 0.004981605524460879, 'bryanw': 0.005060432039124044, 'bskendig': 0.018492749815047314, 'btw': 0.004412956699525248, 'buchholz': 0.0012609485946591687, 'buchhorn': 0.0012609485946591687, 'buck': 0.0013649484181175245, 'buckeridge': 0.0024851616866216125, 'buddha': 0.00258352560392935, 'budget': 0.014031597672250281, 'budgets': 0.004356139840040938, 'buenneke': 0.001862859163369898, 'buffalo': 0.01528821367854881, 'buffer': 0.003791151453497654, 'bug': 0.004847556199674396, 'buggy': 0.0018924586447506718, 'bugs': 0.0026270903366118685, 'build': 0.008891629118214013, 'building': 0.0036386303564224453, 'buildings': 0.004573335506731121, 'builds': 0.0015332358208003521, 'built': 0.009629330093149764, 'bulf': 0.0018924586447506718, 'bull': 0.0080611410397898, 'bulletin': 0.0019928515996024227, 'bulletins': 0.0018628591633698963, 'bullinger': 0.001825425726571352, 'bumbling': 0.0027400885069510687, 'bump': 0.0012609485946591687, 'bunch': 0.0017771408094626167, 'bundled': 0.0018924586447506718, 'burden': 0.003372550157593129, 'burdensome': 0.00365605698527683, 'burdett': 0.0024851616866216125, 'bureau': 0.009389570772092173, 'burial': 0.0036560569852768267, 'buried': 0.0026646314304903523, 'burkhard': 0.0012609485946591687, 'burn': 0.006553461646813328, 'burned': 0.008583352420510362, 'burning': 0.006734033459694816, 'burns': 0.0024337964176860604, 'burnt': 0.0018134151655027544, 'burrill': 0.004573335506731118, 'burst': 0.003126050117186181, 'burstein': 0.0024851616866216134, 'bursters': 0.0062332574487479345, 'bursts': 0.001862859163369898, 'bury': 0.0015527953218988713, 'bus': 0.0031049598125434666, 'bush': 0.002238344217173881, 'business': 0.0044283157576002615, 'businesses': 0.0019481148578558583, 'busy': 0.00033144514648310135, 'butler': 0.004672115750695736, 'buttigieg': 0.0018628591633699006, 'buy': 0.0033943403355756385, 'buying': 0.002211052787148989, 'bx': 0.0018924586447506718, 'bye': 0.0018331313345243579, 'byte': 0.004928377582986543, 'bytes': 0.0067748738251235925, 'byu': 0.007696073912665542, 'byuvm': 0.006411840182243065, 'c5muiw': 0.00457333550673112, 'c5t05k': 0.006860335160339438, 'c5uhim': 0.0025246613755867744, 'c5y4t7': 0.0018628591633698963, 'ca': 0.00688758330387594, 'cable': 0.0014032577035624702, 'cables': 0.0010442927627179474, 'cacs': 0.008551982522370286, 'cad': 0.010807086540932362, 'cadlab': 0.007488101498518765, 'caesar': 0.0015525616407321653, 'cain': 0.0012412324256375618, 'cal': 0.003108141579466518, 'calculate': 0.0016084592037809847, 'calculated': 0.0012808370180140277, 'calculating': 0.005060432039124044, 'calculation': 0.0017062962603481236, 'calculations': 0.004163714266616541, 'calculator': 0.001064042549779238, 'caldwell': 0.004573335506731121, 'calendar': 0.0018628591633698963, 'caliber': 0.0009196424097302845, 'calif': 0.0017372288582959625, 'california': 0.005868159347478961, 'caligula': 0.0013558269777203544, 'callable': 0.0018924586447506718, 'called': 0.007380565972326499, 'callers': 0.000988318189986688, 'calling': 0.0025418022055825364, 'calls': 0.0020890093738950453, 'calpoly': 0.014439451979546138, 'caltech': 0.005588201262327517, 'cam': 0.0018924586447506718, 'cambridge': 0.0035971684109883323, 'came': 0.00831517437052243, 'camelot': 0.001825425726571352, 'camera': 0.003203071941700477, 'cameras': 0.0016886959513125145, 'camino': 0.0018705330287465275, 'camosun': 0.0012609485946591687, 'camp': 0.002229237881500654, 'campaign': 0.0015527953218988713, 'campbell': 0.004171895246043054, 'campus': 0.0012449186271783598, 'camtec': 0.00365605698527683, 'canada': 0.004217396285882988, 'canaveral': 0.0018628591633698963, 'canberra': 0.0031575584291052778, 'cancellation': 0.0024851616866216125, 'candidate': 0.0024570044961898345, 'candidates': 0.0022887445873255334, 'candy': 0.003108141579466519, 'canon': 0.008824562328781493, 'canrem': 0.0012609485946591687, 'canterbury': 0.0012499951251094144, 'canyon': 0.0021327447189448297, 'capabilities': 0.004856547491237157, 'capability': 0.005067284179130472, 'capable': 0.004867416727439167, 'capacity': 0.001935191723821708, 'cape': 0.0026198212843254187, 'capelli': 0.0018924586447506718, 'capital': 0.0019395955103878259, 'caps': 0.0013262274963396362, 'capsule': 0.0024851616866216125, 'captain': 0.0006739571102848205, 'capture': 0.0019353258300861091, 'captured': 0.0006395752914771244, 'car': 0.004506825638514517, 'carbon': 0.0009661235676352671, 'card': 0.026513728383732896, 'carderock': 0.0018924586447506718, 'cardhu': 0.0018924586447506718, 'cards': 0.009881946685611275, 'care': 0.00585337502577598, 'career': 0.0012691491483781056, 'careers': 0.0024851616866216064, 'careful': 0.0010603514829041856, 'carefully': 0.0019407607256267476, 'carel': 0.0012609485946591687, 'cares': 0.005255045040435697, 'cargo': 0.0024851616866216134, 'caring': 0.0027400885069510687, 'carl': 0.0018628591633698963, 'carleton': 0.004037604158481609, 'carlos': 0.0024851616866216064, 'carlosn': 0.0024851616866216064, 'carnegie': 0.006500569835195844, 'carolina': 0.005993220833086242, 'carpenter': 0.0069696142670419604, 'carriage': 0.000978451715284566, 'carried': 0.00549977438926778, 'carrier': 0.0011253818994855442, 'carries': 0.00414468656359209, 'carroll': 0.00039751840402391624, 'carry': 0.006553074074076589, 'carrying': 0.0014174383459421144, 'cars': 1.671875925648384e-05, 'carson': 0.005696122928293768, 'carter': 0.003671659554835985, 'cartography': 0.000978451715284566, 'cartridge': 0.0025246613755867744, 'cartwright': 0.002524661375586772, 'cary115': 0.0012609485946591687, 'case': 0.015795294502229412, 'cases': 0.004263454372601232, 'cash': 0.0018815982925785906, 'casper': 0.004573335506731118, 'caspian': 0.0063325164442827675, 'cassini': 0.003108141579466514, 'cast': 0.00365605698527683, 'caste': 0.001862859163369898, 'castle': 0.002161230461840069, 'cat': 0.0027367215398221706, 'catalog': 0.002603829285308345, 'catalogs': 0.0018705330287465292, 'catalogue': 0.0018628591633698963, 'catch': 0.004356139840040938, 'categories': 0.00113428437282334, 'category': 0.0034796469262504204, 'caterpillar': 0.008745706591231313, 'catharines': 0.003157558429105277, 'catholic': 0.008056038240496352, 'catholics': 0.006411840182243066, 'caught': 0.00279400378189759, 'cause': 0.0007916873918368331, 'caused': 0.004738126240510398, 'causes': 0.005344725923328038, 'causing': 0.0024695153745814113, 'caution': 0.0013690623068594856, 'cb': 0.0029208703184411015, 'cbis': 0.004356139840040947, 'cbl': 0.0012412324256375635, 'cbnewsj': 0.0036560569852768267, 'cboesel': 0.005060432039124052, 'cbw790s': 0.0012609485946591687, 'cc': 0.020003470031716725, 'cc_sysk': 0.003108141579466518, 'ccc': 0.010104763978199333, 'ccd': 0.00435943985137679, 'ccgwt': 0.0018924586447506726, 'cch': 0.0018924586447506726, 'cck': 0.003731800431935114, 'cco': 0.002036975282263315, 'ccr': 0.0012412324256375618, 'ccs': 0.00429584837941722, 'ccsua': 0.001825425726571352, 'ccu1': 0.0018924586447506718, 'ccwf': 0.0031179761169177313, 'cd': 0.014715912907367993, 'cdc': 0.003731800431935113, 'cdcolvin': 0.0027400885069510687, 'cdi': 0.0012609485946591687, 'cdrom': 0.0015332358208003521, 'cdx': 0.0012412324256375618, 'ce': 0.003685796326874803, 'cease': 0.004662266056376309, 'ceased': 0.0012691491483781065, 'cec': 0.0018924586447506718, 'ceccarelli': 0.017555282105751663, 'ced': 0.0018924586447506718, 'ceiling': 0.0012603864489062547, 'celestial': 0.004036506195587863, 'cell': 0.00011497600573342169, 'cellar': 0.003791151453497654, 'cells': 0.0018650454236717635, 'centaur': 0.009375548629619136, 'center': 0.011823720924179788, 'centers': 0.00539923915306303, 'central': 0.002200922958844387, 'centre': 0.004716004840570869, 'centris': 0.004425442103239911, 'cents': 0.0007163598861018444, 'centuries': 0.008395629338575464, 'century': 0.011444928322043007, 'ceo': 0.004356139840040942, 'ceremony': 0.00365605698527683, 'cern': 0.000988318189986688, 'certain': 0.004043363989854949, 'certainly': 0.007764924788853266, 'certification': 0.0018628591633698963, 'ces': 0.004070045905160602, 'ceux': 0.009179532565505875, 'cfa': 0.004981161405813848, 'cg': 0.000988318189986688, 'cgm': 0.0012609485946591687, 'cgro': 0.0018628591633698963, 'ch': 0.012716465335895558, 'ch981': 0.018492749815047303, 'chahine': 0.002485161686621608, 'chain': 0.00011497600573342169, 'chair': 8.226937839690696e-05, 'chairman': 0.0024851616866216134, 'challenge': 0.0020097007155879085, 'challenged': 0.0019116724119796905, 'challenger': 0.003731800431935112, 'challenges': 0.0018705330287465292, 'chalmers': 0.0012609485946591687, 'chamber': 0.0018628591633698963, 'champaign': 0.0024575018725063735, 'chance': 0.004783423757051527, 'chances': 0.001029871907008359, 'change': 0.005831597420031209, 'changed': 0.006047855675101508, 'changes': 0.002185142760328519, 'changing': 0.00066202945645701, 'channel': 0.001603659395087064, 'channels': 0.0021261502892459296, 'chaos': 0.0019191740400296845, 'chapel': 0.010648389958031423, 'chapter': 0.007451848741398307, 'chapters': 0.0022887445873255334, 'char': 0.003157558429105275, 'character': 0.0030173967078293475, 'characteristic': 0.0018667219248472162, 'characteristics': 0.004496030964233485, 'characterization': 0.0015311138319880398, 'characterize': 0.0012808370180140277, 'characters': 0.0014708651881893808, 'charge': 0.009174677636677267, 'charged': 0.0022345089669202917, 'charges': 0.006887180251920203, 'charity': 0.003581494522191157, 'charles': 0.0032947673490668255, 'charlie': 0.007340015087094005, 'charlottesville': 0.000978451715284566, 'charon': 0.0018848404032501213, 'chars': 0.0025246613755867744, 'charter': 0.0024363865949890897, 'charts': 0.001599663558956902, 'cheap': 0.003590601183718285, 'cheaper': 0.012087558686246214, 'cheaply': 0.0020928628598154662, 'check': 0.0040562274679599355, 'checked': 0.00325252063273116, 'checking': 0.0012691491483781056, 'checks': 0.00011497600573342169, 'cheek': 0.00457333550673112, 'cheers': 0.014718497232252707, 'cheinan': 0.0012609485946591687, 'chem': 0.0025246613755867744, 'chemical': 0.0031050964373476346, 'chemistry': 0.00254494301351073, 'chen': 0.0025246613755867744, 'chessboard': 0.0012609485946591687, 'chicago': 0.0041827810045299224, 'chief': 0.0059300712891108736, 'child': 0.008666391457147166, 'children': 0.03266692004127035, 'china': 0.0028150509947816194, 'chinalake': 0.0012609485946591687, 'chinese': 0.0018362078142529865, 'chip': 0.005498075799579989, 'chips': 0.00409132132463212, 'chlorine': 0.003108141579466514, 'chocolate': 0.0027736796060405583, 'choice': 0.008821022559886194, 'choices': 0.0028167539296515822, 'choose': 0.005502668175671896, 'chooses': 0.0028370754228893864, 'chorion': 0.001825425726571352, 'chorus': 0.0013262274963396362, 'chose': 0.006411840182243065, 'chosen': 0.00643990912742597, 'chris': 0.008931533000000795, 'chrisj': 0.0018628591633698963, 'christ': 0.05729373368021909, 'christian': 0.12862867565281702, 'christianity': 0.04336687928120413, 'christians': 0.06851132861181007, 'christmas': 0.0036560569852768275, 'christopher': 0.005095638931344164, 'chronicles': 0.0015626450162182998, 'chuck': 0.003135992489550251, 'chunk': 0.000988318189986688, 'church': 0.031763566421526196, 'churches': 0.0045733355067311176, 'churchill': 0.008745706591231313, 'cia': 0.002551096428842924, 'ciceran': 0.004425442103239911, 'cim': 0.0024851616866216125, 'circa': 0.0003979733363520454, 'circle': 0.004462826071710027, 'circles': 0.0030375849858686873, 'circular': 0.002929304697419195, 'circumference': 0.00358770551919327, 'cis': 0.00665937805944766, 'cite': 0.00365605698527683, 'cited': 0.0016816086674564185, 'cites': 0.011959254816636749, 'cities': 0.0015403097871164286, 'citizen': 0.003731800431935113, 'citizens': 0.0007032382976603913, 'city': 0.0064621417365893, 'civil': 0.0054687170463413, 'civilian': 0.002901756017947163, 'civilization': 0.0024851616866216134, 'cj195': 0.0036560569852768267, 'cjpeg': 0.002524661375586772, 'cl': 0.005123108675824984, 'claim': 0.010836998180929883, 'claimed': 0.00718197340209614, 'claiming': 0.0020607468774049807, 'claims': 0.00505698502338499, 'clanzen': 0.0018628591633699006, 'clarification': 0.008714844598090651, 'clarify': 0.000704321310029378, 'clark': 0.0012609485946591687, 'clarke': 0.002507404866341485, 'clarkson': 0.003143282228580878, 'class': 0.004096242986526069, 'classes': 0.0013651621567155724, 'classic': 0.003581494522191157, 'classical': 0.001520379122855315, 'classification': 0.002777177435087255, 'claudio': 0.0049811614058138465, 'claus': 0.001825425726571352, 'clean': 0.005201551388967981, 'cleaning': 0.0015035858261545658, 'clear': 0.0060513349576320295, 'clearance': 0.0010442927627179474, 'clearly': 0.01152805487900305, 'clearness': 0.00365605698527683, 'clementine': 0.005606866737329389, 'cleveland': 0.01557148179199495, 'click': 0.0025246613755867744, 'clicks': 0.0010442927627179474, 'client': 0.007607418082978782, 'clients': 0.003157558429105275, 'cliff': 0.0009284200503372423, 'clinton': 0.0036005432050575897, 'clip': 0.0031954450584297956, 'clipper': 0.004517481653799862, 'clippers': 0.0012412324256375635, 'clipping': 0.003157558429105277, 'clj': 0.0012412324256375618, 'clldomps': 0.003157558429105277, 'clock': 0.002599678349910775, 'clockwise': 0.0028387564496019342, 'close': 0.005263610641304003, 'closed': 0.002057314600819625, 'closely': 0.0034818660142473543, 'closer': 0.0041054899237834485, 'closest': 0.0009240396600638115, 'closeup': 0.003108141579466518, 'clothing': 0.0019111977739593115, 'cloud': 0.003731800431935114, 'clouds': 0.0031136322339350925, 'clp': 0.0018924586447506718, 'clrview': 0.0012609485946591687, 'club': 0.0020090940650232614, 'clue': 0.001333060559563835, 'clump': 0.0012691491483781056, 'clutter': 0.0024448766353608346, 'cm': 0.003731800431935115, 'cmu': 0.0304219515632988, 'co2': 0.0018628591633698963, 'coalition': 0.0018362078142529865, 'coast': 8.226937839690696e-05, 'cobb': 0.0033689742160000384, 'cobe': 0.0018628591633698963, 'cobra': 0.0012499951251094144, 'cochran': 0.00457333550673112, 'cocoa': 0.001825425726571352, 'code': 0.03001096705900719, 'codec': 0.0037911514534976565, 'coded': 0.001304990985299034, 'codes': 0.0056353901288690835, 'coding': 0.0012801026179278053, 'coe': 0.0024851616866216125, 'coercive': 0.0024448766353608346, 'coffee': 0.007287756008583687, 'coffman': 0.005606866737329388, 'cohen': 0.000978451715284566, 'coin': 0.0015417795530505863, 'coke': 0.0012603864489062547, 'col': 0.0036980400301083885, 'cold': 0.00411489321372603, 'collapse': 0.0026198212843254187, 'collect': 0.0014816125047449214, 'collected': 1.671875925648384e-05, 'collecting': 0.0036683538927684226, 'collection': 0.0015604536008801363, 'collections': 0.0007036071049306121, 'collectively': 0.001921522106299118, 'collectors': 0.0013262274963396362, 'college': 0.0025833107444930446, 'colliding': 0.003108141579466518, 'collins': 0.001924956539364077, 'collision': 0.005607968622531286, 'cologne': 0.0012609485946591687, 'colonies': 0.003417927223171884, 'colony': 0.004981161405813848, 'color': 0.028412607297956465, 'colorado': 0.007297258152829356, 'colored': 0.0018924586447506718, 'colormap': 0.0018924586447506718, 'colors': 0.01879004439723223, 'colorview': 0.0012609485946591687, 'colostate': 0.00437263999314957, 'colour': 0.006993916133548869, 'colours': 0.0031575584291052778, 'columbia': 0.0025684034569983874, 'columbiasc': 0.0018924586447506726, 'columbus': 0.0013371565680386924, 'column': 0.0028595024460431285, 'colvin': 0.0027400885069510687, 'com': 0.041183660387299474, 'combed': 0.0018628591633699006, 'combination': 0.000351228666426711, 'combinations': 0.0006604803272702029, 'combine': 0.0009657853033023019, 'combined': 0.0009221176897676745, 'combining': 0.0006417411980615632, 'combo': 0.003412582754313569, 'come': 0.018190391700934568, 'comes': 0.0043705408473688106, 'comet': 0.016006355273479198, 'cometary': 0.0018628591633698963, 'comets': 0.007488101498518759, 'comfortable': 0.004370099599025862, 'comic': 0.0015319298587311032, 'coming': 0.01078629458124927, 'comm': 0.0043954209234245735, 'command': 0.0055664697333849085, 'commanded': 0.0031155095932511624, 'commandment': 0.009179532565505867, 'commandments': 0.018492749815047293, 'commands': 0.0026009550790138634, 'comme': 0.009179532565505875, 'comment': 0.0021526387740479205, 'commentary': 0.002750040538837272, 'comments': 0.0025514339031324227, 'commerce': 0.0018815982925785924, 'commercial': 0.017624122765343055, 'commercialization': 0.0012412324256375618, 'commercially': 0.0018628591633699006, 'commercials': 0.0015332358208003521, 'commerical': 0.0021995226876789144, 'commericial': 0.0024851616866216134, 'commie': 0.001825425726571352, 'commission': 0.0033528339885715774, 'commit': 0.0033538046033891123, 'commitment': 0.003731800431935113, 'commits': 0.001921522106299118, 'committed': 0.008881221803391778, 'committee': 0.008753224390184484, 'committees': 0.001599663558956902, 'common': 0.007252910807897354, 'commonly': 9.215269075613097e-05, 'communication': 0.002231904146091531, 'communications': 0.017621330674384556, 'communities': 0.0012603864489062547, 'community': 0.00412167695770849, 'comp': 0.026346437008024127, 'compact': 0.0035264822214862834, 'companies': 0.007246728336502896, 'companion': 0.0036707932851855083, 'company': 0.00769363020826073, 'compaq': 0.0006398485452691399, 'comparable': 0.00013754316908168307, 'compare': 0.0009127359077657961, 'compared': 0.005692122850238999, 'compares': 4.035731769314044e-05, 'comparing': 4.035731769314044e-05, 'comparision': 0.0006417411980615632, 'comparison': 0.0010548109303811677, 'comparisons': 0.0020361452852944734, 'compass': 0.0012499951251094144, 'compassion': 0.011031336546395553, 'compassionate': 0.00457333550673112, 'compatibility': 0.001064042549779238, 'compatible': 0.00577087073426895, 'compelled': 0.002674481124809779, 'compelling': 0.0018331313345243579, 'compensate': 0.0018705330287465275, 'compensation': 0.0010442927627179474, 'compete': 0.0004771206825240019, 'competent': 0.0021524677623682162, 'competing': 0.0032866083804397065, 'competition': 0.003108141579466518, 'competitive': 0.0019965781299750842, 'compile': 0.0063325164442827675, 'compiled': 0.007250755472037719, 'compiler': 0.0037911514534976574, 'complain': 0.0021261502892459296, 'complaining': 1.671875925648384e-05, 'complains': 0.0010442927627179474, 'complaints': 0.0010293760086931428, 'complete': 0.002733243898169138, 'completed': 0.004520630070875184, 'completely': 0.0017992635609434728, 'completion': 0.0024851616866216125, 'complex': 0.005093463107631839, 'complexity': 0.0023269365271611185, 'complicated': 0.002483191394514202, 'component': 0.002276772298013972, 'components': 0.005172486279095695, 'composed': 0.004018131430648144, 'composite': 0.0009657853033023019, 'composites': 0.0037361966970264563, 'composition': 0.0021261502892459296, 'compound': 0.004955239387533913, 'comprehensive': 0.0010172262518655445, 'compress': 0.003143282228580879, 'compressed': 0.0029204260259767956, 'compressing': 0.0012609485946591687, 'compression': 0.004648025178708195, 'compressor': 0.0012609485946591687, 'compromise': 0.0015417795530505863, 'compton': 0.003731800431935114, 'compulink': 0.0012609485946591687, 'compuserve': 0.0008739689376770126, 'computation': 0.0023227915887476906, 'computational': 0.0031801493479349397, 'compute': 0.004854552676932347, 'compute1': 0.0025246613755867744, 'computed': 0.0009559019909431317, 'computer': 0.020590336460210003, 'computers': 0.004181287752752167, 'computes': 0.0007163598861018444, 'computing': 0.007281955124537647, 'concave': 0.0025469720216608743, 'conceivable': 0.0024851616866216134, 'concentrate': 8.088279674783698e-05, 'concentrated': 0.0024718333622407067, 'concentration': 0.0012412324256375618, 'concept': 0.010877132161071685, 'concepts': 0.0015495987653652218, 'concern': 0.008554019767615505, 'concerned': 0.004185671330991908, 'concerning': 0.0053021486522454, 'concerns': 0.0010375588680358871, 'conclude': 0.008638409843711049, 'concluded': 0.0034155122246012463, 'conclusion': 0.014002793857747975, 'conclusions': 0.007980649567500922, 'concrete': 0.0027400885069510687, 'concurance': 0.00457333550673112, 'concussion': 0.00365605698527683, 'condemn': 0.00365605698527683, 'condemned': 0.00457333550673112, 'condition': 0.00030106615376777543, 'conditional': 0.000952889200262875, 'conditions': 0.004572728895630101, 'condone': 0.0027400885069510696, 'condoned': 0.0027400885069510687, 'condor': 0.0012412324256375635, 'conduct': 0.005981776820415429, 'conducted': 0.003043748562888326, 'conducting': 0.0012499951251094144, 'cone': 0.0015035858261545658, 'cones': 0.0006417411980615632, 'conestoga': 0.0018628591633698963, 'conference': 0.008440761263079785, 'conferences': 0.0006251111015571457, 'confernce': 0.003731800431935113, 'confessor': 0.0018924586447506726, 'confidence': 0.0036560569852768275, 'confident': 0.0015448877753555896, 'configuration': 0.006828767221091464, 'configured': 0.0018924586447506726, 'confined': 0.0018628591633699006, 'confirm': 0.004571132049345648, 'confirmation': 0.0027400885069510696, 'confirmed': 0.004356139840040942, 'conflict': 0.0007117181907135006, 'conflicting': 0.0012160848046758686, 'conflicts': 0.00039751840402391624, 'conform': 0.004573335506731121, 'conformity': 0.0027400885069510687, 'conforms': 0.0018449705137248374, 'confuse': 0.0013113511286082574, 'confused': 0.0018200729433609855, 'confusing': 0.002930151045886476, 'confusion': 0.0007652759776482342, 'congress': 0.00614165356586544, 'connect': 0.0029204260259767956, 'connected': 0.00012157750024694054, 'connection': 0.002639412857655246, 'connections': 0.0018628591633699006, 'connor': 0.0025231056317136114, 'conrad': 0.00035791381164745114, 'conscience': 0.0027400885069510687, 'consciousness': 0.004299459616509723, 'consensus': 0.004573335506731121, 'consequence': 0.002161230461840069, 'consequences': 0.005491928440954982, 'conservative': 0.005828208567527146, 'conservatives': 0.0027400885069510687, 'consider': 0.014411226195127833, 'considerably': 0.0007376855490360884, 'consideration': 0.004957508371976524, 'considered': 0.013063814342710783, 'considering': 0.0006266416441856153, 'considers': 0.0019229696813196587, 'consist': 0.0021721839313897677, 'consisted': 0.0018628591633699006, 'consistent': 0.0020389298694387594, 'consistently': 0.0012259344989952962, 'consisting': 0.00011497600573342169, 'consists': 0.0015861665554856063, 'consortium': 0.0018705330287465275, 'conspiracy': 0.0036560569852768275, 'conspirator': 0.0027400885069510696, 'consrt': 0.0024851616866216134, 'constant': 0.0032627871314751325, 'constantly': 0.0007229880847217382, 'constants': 0.0022887445873255334, 'constellation': 0.002580777264774475, 'constitute': 0.0034519223629203167, 'constitution': 0.004579461938140444, 'constitutional': 0.0018496845972676042, 'constraint': 0.0012412324256375635, 'constraints': 0.0015773739227058674, 'construct': 0.0034519223629203167, 'constructed': 0.0004088156733638845, 'construction': 0.0031383243607757618, 'constructive': 0.0009433921007048016, 'constructs': 0.0018134151655027544, 'consult': 0.00039751840402391624, 'consultant': 0.0006417411980615632, 'consultants': 0.002674481124809779, 'consultation': 0.0009236759316832519, 'consulting': 0.0021327447189448297, 'consumables': 0.003108141579466519, 'consume': 0.0017855205597762545, 'consumer': 0.001347039880397861, 'contact': 0.006695345153599349, 'contacting': 0.0009661235676352671, 'contacts': 0.0008873373780814951, 'contain': 0.002089803425646688, 'contained': 0.0005914034791023991, 'containing': 0.0063669922338880644, 'contains': 0.004385892833182482, 'contend': 0.002130332690995644, 'content': 0.00317939183434299, 'contents': 0.0010323517896364829, 'contest': 0.006649369059341404, 'context': 0.022078898619665742, 'continent': 0.0009300965515126975, 'continental': 0.0020928628598154662, 'continous': 0.0024851616866216134, 'continue': 0.007945748715713317, 'continued': 0.0024564288294835184, 'continues': 0.003856275823403966, 'continuin': 0.003108141579466518, 'continuing': 0.006233257448747934, 'continuous': 0.002171944700968804, 'continuously': 0.004981161405813842, 'contour': 0.005060432039124051, 'contours': 0.001064042549779238, 'contract': 0.0054734187964165975, 'contractors': 0.0037318004319351165, 'contracts': 0.008745706591231316, 'contractual': 0.003731800431935113, 'contradict': 0.005959603311149807, 'contradicted': 0.00365605698527683, 'contradiction': 0.011959254816636747, 'contradictions': 0.013272836579596835, 'contradictory': 0.006411840182243067, 'contradicts': 0.0026646314304903523, 'contrary': 0.007434813902712173, 'contrast': 0.0025920344846817357, 'contrib': 0.0037757638523458394, 'contribute': 0.0027218795235153916, 'contributed': 0.0011884456798470933, 'contributing': 0.0010172262518655445, 'contribution': 0.0031155095932511624, 'contributions': 0.0016963960527636808, 'contributor': 0.0006417411980615632, 'contributors': 0.0012629530417339009, 'contridiction': 0.0018628591633699006, 'contrived': 0.001825425726571352, 'control': 0.008936657528224378, 'controlled': 0.002426914824401635, 'controller': 0.0019150563317796342, 'controllers': 0.001064042549779238, 'controlling': 0.0007163598861018444, 'controls': 0.0010442927627179474, 'controversial': 0.0019016336999508757, 'controversy': 0.0012412324256375635, 'convenience': 0.0051439256477059945, 'convenient': 0.00429945961650972, 'conveniently': 0.0015499786042360887, 'convening': 0.00365605698527683, 'convention': 0.006411840182243062, 'conventional': 0.003417927223171884, 'conversation': 0.0026646314304903523, 'conversion': 0.007255764998106885, 'convert': 0.011131046306344487, 'converted': 0.0024785640130935887, 'converter': 0.006581439092499914, 'converters': 0.0031575584291052778, 'converting': 0.0019566916420677826, 'converts': 0.0069850245783983494, 'convex': 0.0020930330758129317, 'convict': 0.001825425726571352, 'convictions': 0.00457333550673112, 'convince': 0.010310772039558283, 'convinced': 0.005562288269038132, 'convincing': 0.005289595373482465, 'convolution': 0.0012609485946591687, 'cook': 0.006233257448747928, 'cookamunga': 0.018492749815047317, 'cool': 0.002225138321039521, 'cooled': 0.0006417411980615632, 'cooper': 0.0012801026179278053, 'cooperating': 0.0009236759316832519, 'cooperation': 0.0033733168848706675, 'cooperative': 0.003108141579466518, 'coordinate': 0.0014348552136991552, 'coordinates': 0.0035557283578460845, 'coordination': 0.0016661801242341696, 'copied': 0.0015499786042360887, 'copier': 0.0012499951251094144, 'copies': 0.0008285804714812202, 'coplanar': 0.004425442103239916, 'copy': 0.003257280287330741, 'copying': 0.0018924586447506726, 'copyright': 0.002601892837037864, 'copyrighted': 0.003787470018340077, 'copyrights': 0.002524661375586772, 'cord': 4.035731769314044e-05, 'core': 0.0028712176950635403, 'corel': 0.0037911514534976574, 'coreldraw': 0.003157558429105277, 'corey': 0.0012609485946591687, 'cormack': 0.0012609485946591687, 'cornelius': 0.001825425726571352, 'cornell': 0.0025469720216608734, 'corner': 0.0018250202487414676, 'corners': 0.0012412324256375635, 'coronado': 0.003157558429105277, 'corp': 0.0025701357652110233, 'corporate': 0.0016661801242341696, 'corporation': 0.0015663935801165391, 'corporations': 0.0024363865949890897, 'corps': 0.0006739571102848205, 'correct': 0.004992503316244003, 'correctable': 0.0012412324256375618, 'corrected': 0.00023053054509156873, 'correcting': 0.0018331313345243579, 'correction': 0.0020195009821096666, 'corrections': 0.0023560671987039785, 'corrective': 0.0018628591633699006, 'correctly': 0.00037511401948891847, 'corresponding': 0.00010510953103124408, 'corruption': 0.003581494522191157, 'cos': 0.0009393921967916297, 'cosmic': 0.0066388020167906315, 'cosmological': 0.0012412324256375635, 'cosmos': 0.004981161405813847, 'cost': 0.03907149977206499, 'costa': 0.0018924586447506718, 'costar': 0.0024851616866216125, 'costing': 0.003412582754313562, 'costs': 0.014689961561613896, 'cotera': 0.005491928440954984, 'cotter': 0.0012412324256375635, 'couldn': 0.0023444927793361313, 'council': 0.0011253818994855442, 'counntries': 0.0018628591633699006, 'count': 0.0013735849746575731, 'counted': 0.0027285530523395362, 'counter': 0.000646833328958733, 'counterclockwise': 0.0009433921007048016, 'counting': 0.0018559545856247917, 'countries': 0.004018131430648145, 'country': 0.009021753135338224, 'counts': 0.0018924586447506726, 'county': 0.004356139840040942, 'couple': 0.0031192374979993063, 'coupled': 0.0024851616866216134, 'courage': 0.0019312331813316494, 'courant': 0.0015417795530505863, 'course': 0.009269722900151517, 'courses': 0.0010442927627179474, 'court': 0.0040605231180220105, 'courtesy': 0.0010442927627179474, 'cov': 0.0012852074653554209, 'covenant': 0.0027400885069510696, 'coventry': 0.0027381236550937, 'cover': 0.004432620404704367, 'coverage': 0.008019161874885598, 'covered': 0.0028454695233216575, 'covering': 0.003072932621342131, 'covers': 0.003821611224663515, 'coy': 0.0012609485946591687, 'coyote': 0.0009971908444932048, 'cpac': 0.006119567860396658, 'cps': 0.0012499951251094144, 'cptully': 0.0018924586447506718, 'cpu': 0.007607418082978782, 'cpuserver': 0.0018924586447506726, 'cpva': 0.0018628591633698963, 'cr': 0.0018628591633699006, 'crabtree': 0.007333075149745417, 'crack': 0.0019116724119796905, 'cradle': 0.0024851616866216125, 'craft': 0.007987559344243975, 'crafts': 0.003108141579466518, 'craig': 0.004784459952331774, 'crap': 0.0027400885069510696, 'crash': 0.0052448733031916365, 'crashed': 0.0006604803272702029, 'crashing': 0.0018628591633699006, 'crater': 0.003108141579466514, 'craters': 0.0012412324256375635, 'crawl': 0.001825425726571352, 'cray': 0.004425442103239914, 'crazy': 0.008217664786739612, 'create': 0.008382102490863, 'created': 0.010044003730724345, 'creates': 0.0024292841350173947, 'creating': 0.001983512154638725, 'creation': 0.007949881482746224, 'creationism': 0.005491928440954984, 'creationist': 0.005491928440954982, 'creative': 0.0034811180790796335, 'creator': 0.008136471404639807, 'creature': 0.0021891043107271193, 'creatures': 0.001825425726571352, 'credit': 0.0019701768565531744, 'credits': 0.0018628591633699006, 'creed': 0.0027400885069510687, 'crew': 0.009600437067301171, 'cri': 0.0028032790874212747, 'cried': 0.00365605698527683, 'crime': 0.0077135954761821555, 'criminals': 0.0027400885069510696, 'crimson': 0.004425442103239912, 'crisis': 0.0017855205597762545, 'cristy': 0.0012609485946591687, 'crit': 0.0019116724119796905, 'criteria': 0.0028272257285699588, 'critical': 0.0035005545150565056, 'criticism': 0.0006739571102848205, 'criticize': 0.0034519223629203167, 'criticized': 0.0015527953218988713, 'criticizing': 0.001921522106299118, 'critique': 0.0027367215398221706, 'crl': 0.0018924586447506726, 'croire': 0.009179532565505875, 'crop': 0.0016194133460181942, 'cross': 0.0011169457714232962, 'crossing': 0.0024851616866216125, 'crossposting': 0.0016958301188799586, 'crowd': 0.001921522106299118, 'crowe': 0.0037911514534976565, 'crowley': 0.0036560569852768275, 'crucial': 0.001058781479937508, 'crucified': 0.005491928440954984, 'crucifixion': 0.005491928440954984, 'crucis': 0.007333075149745415, 'cruel': 0.0027400885069510687, 'cruise': 0.003731800431935114, 'crystal': 0.007430395993023866, 'cs': 0.007291131362490715, 'csc': 0.0026980175548725355, 'csc3phx': 0.0012609485946591687, 'csd': 0.006312663945392873, 'cshow': 0.0012827028287951915, 'csiro': 0.0012827028287951915, 'csn': 0.0031213191949626155, 'cso': 0.007985085412321563, 'cspara': 0.0024851616866216064, 'csrv': 0.0027400885069510696, 'csugrad': 0.001825425726571352, 'ct': 0.0013027003049568232, 'ctron': 0.005491928440954983, 'cts': 0.0024917448724188695, 'ctstateu': 0.001825425726571352, 'cube': 0.004293975667654979, 'cubes': 0.002524661375586772, 'cubic': 0.0025032568485615645, 'cult': 0.023810770082206487, 'cultists': 0.0026646314304903523, 'cults': 0.00825563778767264, 'cultural': 0.004517119658459242, 'culture': 0.002824414541149587, 'cultures': 0.0028272257285699588, 'cunixb': 0.0012609485946591687, 'cunningham': 0.001347039880397861, 'cunyvm': 0.003972598793606089, 'cup': 0.0077387959730497915, 'curcio': 0.0012499951251094144, 'curiosity': 0.00039751840402391624, 'curious': 0.002814254267703221, 'currency': 0.0012412324256375635, 'current': 0.0032521835550305515, 'currently': 0.006487874094352249, 'cursor': 0.003157558429105275, 'curvature': 0.000978451715284566, 'curve': 0.0064061799569223, 'curved': 0.0018628591633698963, 'curves': 0.00692118715005538, 'cusp': 0.003791151453497659, 'custom': 0.001914490397895912, 'customer': 0.0036683538927684226, 'customers': 0.0013912815862016856, 'customization': 0.0012609485946591687, 'customs': 0.0013113511286082574, 'cut': 0.004281697067940164, 'cute': 0.0027400885069510687, 'cutoff': 0.0024851616866216134, 'cuts': 0.006449999517607799, 'cutter': 0.001825425726571352, 'cutting': 0.0024851616866216064, 'cv': 0.0016194133460181942, 'cv4': 0.0013558269777203544, 'cview': 0.014024661563466271, 'cw': 0.000978451715284566, 'cwis': 0.002542985343060032, 'cwru': 0.018606681225622927, 'cx5': 0.0018924586447506718, 'cyberspace': 0.002524661375586772, 'cycle': 0.0033256832965099592, 'cycles': 0.002161230461840069, 'cylinder': 0.003254754224239876, 'cylinders': 0.000978451715284566, 'cynical': 0.0014816125047449214, 'cyrus': 0.0027400885069510687, 'cz': 0.0012499951251094144, 'd012s658': 0.01943160055753653, 'd9hh': 0.0012609485946591687, 'da': 0.0012603864489062547, 'dactyl': 0.003157558429105277, 'daemon': 0.008245929584991853, 'daemons': 0.0027400885069510696, 'daily': 0.0024833148687912285, 'daimi': 0.0012609485946591687, 'dakota': 0.0036560569852768267, 'dale': 0.003083660745552869, 'dallas': 0.00013615658743255845, 'damage': 0.0019189330627768317, 'damaged': 4.035731769314044e-05, 'damaging': 0.0027400885069510687, 'damn': 0.00042184689183927954, 'damned': 0.0018496845972676042, 'damsel': 0.001825425726571352, 'dan': 0.002363870789179408, 'dance': 0.0007259062129681476, 'dancing': 0.0009433921007048016, 'dane': 0.0012609485946591687, 'danebury': 0.0018924586447506726, 'dang': 0.0006417411980615632, 'dangerous': 0.0018122573658307045, 'dangers': 0.0012449186271783616, 'dani': 0.00435943985137679, 'daniel': 0.004494668056306142, 'danny': 0.0018924586447506718, 'dannyb': 0.0024851616866216125, 'dante': 0.0024851616866216125, 'darcy': 0.0036560569852768275, 'dare': 0.0027400885069510696, 'darius_lecointe': 0.008255637787672639, 'dark': 0.002605178523829808, 'darker': 0.0012609485946591687, 'darkness': 0.004270595257845643, 'darling': 0.0012412324256375618, 'darmstadt': 0.0006417411980615632, 'darn': 0.0007226931651535132, 'darpa': 0.0006417411980615632, 'darren': 0.0012160848046758686, 'dartmouth': 0.0018924586447506718, 'dasa': 0.0027400885069510696, 'dat': 0.001586166555485608, 'data': 0.02073383239950813, 'database': 0.005108357766181041, 'databases': 0.0038127733064952244, 'datafiles': 0.0012609485946591687, 'datasets': 0.000988318189986688, 'date': 0.008333232865065869, 'dates': 0.0015401989175159942, 'daughter': 0.004245533677991849, 'dave': 0.004060938225615054, 'daveb': 0.0027400885069510687, 'david': 0.021787689712602462, 'davidian': 0.00365605698527683, 'davidians': 0.026992776426506604, 'davidr': 0.0018924586447506718, 'davinci': 0.0027400885069510696, 'davis': 0.003616802609469604, 'daviss': 0.0024851616866216064, 'dawn': 0.003043432067847251, 'day': 0.016001269207295412, 'daylight': 0.0024851616866216125, 'days': 0.022665077640485785, 'daytime': 0.0015035858261545658, 'dayton': 0.0016267651670370123, 'db': 0.001825425726571352, 'db6': 0.006860335160339438, 'dbf': 0.0018924586447506726, 'dbm0000': 0.004981161405813842, 'dc': 0.02835959571207814, 'dclxvi': 0.0027400885069510696, 'dcs': 0.004628813103086263, 'dcx': 0.011269252547878778, 'dds': 0.0012412324256375618, 'dead': 0.015846378265044342, 'deadhead': 0.0012609485946591687, 'deadline': 0.0012852074653554209, 'deadlines': 0.0018924586447506726, 'deal': 0.004085566079481163, 'dealing': 0.00380482951276673, 'deals': 0.0019314476765712107, 'dean': 0.004149953119111088, 'deane': 0.0027400885069510687, 'dear': 0.0010584451692119646, 'death': 0.02469979769084865, 'deaths': 0.006411840182243066, 'debate': 0.004265360369276912, 'debris': 0.007488101498518767, 'debt': 0.0012160848046758686, 'dec': 0.003669068113510851, 'decade': 0.007488101498518767, 'decades': 0.0022345089669202917, 'decay': 0.0019229696813196587, 'decayed': 0.0015527953218988713, 'deceit': 0.001825425726571352, 'deceive': 0.0027400885069510696, 'deceived': 0.0012160848046758686, 'deceiver': 0.00365605698527683, 'deceleration': 0.003108141579466518, 'december': 0.0019190199282519754, 'decenso': 0.01010476397819933, 'decent': 0.0015501930994756526, 'deception': 0.0027400885069510696, 'deceptive': 0.0027400885069510696, 'decide': 0.003304929216992037, 'decided': 0.002604550465110175, 'decides': 0.0018134151655027544, 'deciding': 0.0012259344989952962, 'decision': 0.004624072312923684, 'decisions': 0.005289595373482465, 'deck': 0.0007163598861018444, 'declare': 0.0024337964176860587, 'declared': 0.0021524677623682162, 'declination': 0.0018628591633698963, 'decnet': 0.004219311644540177, 'decode': 0.0018924586447506718, 'decoder': 0.0012609485946591687, 'decoding': 0.0025246613755867744, 'decompression': 0.003143282228580879, 'decreased': 0.0021525282388884385, 'decwrl': 0.0012499951251094144, 'dedicated': 0.0014404276965298314, 'dedication': 0.00365605698527683, 'deeds': 0.007333075149745417, 'deep': 0.0029690461101971677, 'deeper': 0.0018362078142529865, 'deeply': 0.0015527953218988713, 'default': 0.0037245538816913244, 'defects': 0.000988318189986688, 'defence': 0.0018250202487414676, 'defend': 0.00394158131478814, 'defending': 0.002130332690995644, 'defense': 0.01060176505837104, 'define': 0.003525516194039198, 'defined': 0.003607786478532741, 'defines': 0.002181350743583212, 'defining': 0.0016669917676286764, 'definite': 0.003591344216510528, 'definitely': 0.002319779538010933, 'definition': 0.013083220999557027, 'definitions': 0.003382596524808915, 'defray': 0.003108141579466519, 'deg': 0.0018628591633698963, 'degenerate': 4.035731769314044e-05, 'degradation': 0.0018705330287465275, 'degrade': 0.0012259344989952962, 'degree': 0.002382418396411284, 'degrees': 0.01117502642703485, 'degroff': 0.0018628591633699006, 'deimos': 0.0024917448724188695, 'deity': 0.009916857554918737, 'del': 0.000978451715284566, 'delaunay': 0.0037911514534976548, 'delay': 1.671875925648384e-05, 'deleted': 0.01679853016731883, 'deliberate': 0.0018449705137248374, 'deliberately': 0.0012160848046758686, 'deliberations': 0.0018628591633699006, 'delicate': 0.0018628591633699006, 'deliver': 0.0006417411980615632, 'delivered': 0.002410136813904725, 'delivering': 0.0012412324256375618, 'delivery': 0.0019189330627768317, 'delta': 0.013023731914993224, 'deluca': 0.0031081415794665165, 'deluxe': 0.0018924586447506726, 'delysid': 0.0027400885069510687, 'demand': 0.005147060473821017, 'demanded': 0.0017855205597762545, 'demands': 0.0028272257285699588, 'demo': 0.005306794120620091, 'demon': 0.004359439851376789, 'demons': 0.00365605698527683, 'demonstrate': 0.003708748692457995, 'demonstrated': 0.0027547680733187004, 'demonstrates': 0.001216655211329824, 'demonstrating': 0.0022321909792609963, 'demonstration': 0.0006780001494005429, 'demonstrations': 0.001064042549779238, 'demonstrator': 0.0018628591633698963, 'demos': 0.0018924586447506718, 'den': 0.005235630681754177, 'denial': 0.0034519223629203167, 'denials': 0.00365605698527683, 'denied': 0.0027400885069510696, 'denies': 0.00457333550673112, 'denman': 0.0012609485946591687, 'denmark': 0.0018924586447506726, 'dennis': 0.008532831292275419, 'dennisn': 0.003731800431935114, 'denominations': 0.0027400885069510696, 'denote': 0.001825425726571352, 'denotes': 0.0015319298587311032, 'dense': 0.004356139840040938, 'densities': 0.0012412324256375635, 'density': 0.003968742273122063, 'dent': 0.0018924586447506718, 'denton': 0.0018924586447506726, 'denver': 0.005303892451035952, 'deny': 0.010104763978199325, 'denying': 0.0012259344989952962, 'departed': 0.0028272257285699588, 'department': 0.0023333201962549965, 'depend': 0.002144107221564112, 'dependent': 0.0021969639431763084, 'depending': 0.0023161672867686557, 'depends': 0.001892387160074332, 'depletion': 0.0018628591633699006, 'deploy': 0.0018628591633699006, 'deployed': 0.003108141579466519, 'deployment': 0.0012412324256375635, 'depressed': 0.004981161405813843, 'dept': 0.006124250706863299, 'depth': 0.005901200453564606, 'depths': 4.035731769314044e-05, 'deputy': 0.004356139840040942, 'der': 0.0015332358208003521, 'derivative': 0.00010510953103124408, 'derive': 0.0021946697425983134, 'derived': 0.00217750243716405, 'derose': 0.002524661375586771, 'des': 0.0016238716719778907, 'descendant': 0.0012259344989952962, 'described': 0.006726908181325707, 'describes': 0.005461489160493545, 'describing': 0.003471160962920953, 'description': 0.0019787095382090905, 'descriptions': 0.0025067315957129008, 'desert': 0.0009236759316832519, 'deserts': 0.0017855205597762545, 'deserve': 0.0013440421785015002, 'deserves': 0.0012160848046758686, 'design': 0.0134726982146907, 'designate': 0.0021821359632759694, 'designated': 0.003108141579466518, 'designed': 0.009257901345946182, 'designers': 0.003143282228580879, 'designing': 0.0021995226876789127, 'designs': 0.003243744725599824, 'desirable': 0.0006563042909403238, 'desire': 0.008788489835370547, 'desired': 0.0013614980917216399, 'desires': 0.007775393704209693, 'desk': 0.0012629530417339009, 'desktop': 0.0018924586447506718, 'despite': 0.002295609842978918, 'destroy': 0.005419167532753305, 'destroyed': 0.004738485345841415, 'destruction': 0.0028272257285699588, 'destructive': 0.0024851616866216125, 'detailed': 0.0029745807322662447, 'details': 0.003897500668875741, 'detect': 0.00036440142293393384, 'detecting': 0.005646535283099122, 'detection': 0.003131202507321784, 'detector': 0.003108141579466512, 'detectors': 0.00248516168662161, 'determination': 0.0031260501171861818, 'determine': 0.004068855412638033, 'determined': 0.003231351191445849, 'determining': 0.003521365703212571, 'deuteronomy': 0.0036560569852768275, 'dev': 0.0009836938410219646, 'develop': 0.00456671055603701, 'developable': 0.0012609485946591687, 'developed': 0.013053345166219095, 'developer': 0.001987614546821075, 'developers': 0.001664525184717336, 'developing': 0.0046510302540447735, 'development': 0.016412063550133377, 'developments': 0.0012894538464725182, 'device': 0.003190516426634307, 'devices': 0.005321446213154204, 'devil': 0.004662266056376308, 'devine': 0.0015417795530505863, 'devising': 0.00457333550673112, 'devoted': 0.00011497600573342169, 'devotees': 0.001825425726571352, 'devotion': 0.0015319298587311032, 'deweese': 0.0012609485946591687, 'deweeset': 0.0012609485946591687, 'dfrf': 0.005606866737329394, 'dg': 0.0070390636348533165, 'dgf1': 0.003157558429105275, 'dgi': 0.0018628591633698963, 'dgp': 0.002524661375586771, 'dhhalden': 0.0025246613755867744, 'dia': 0.0018628591633699006, 'diablo': 0.005060432039124051, 'diagram': 0.0015861665554856063, 'diagrams': 0.0019024106766368197, 'dial': 0.001701658935340529, 'dialin': 0.00549192844095498, 'dialog': 0.001921522106299118, 'dialogue': 0.0027400885069510696, 'diameter': 0.007051824771941406, 'diameters': 0.0012412324256375635, 'diamond': 0.005133901820383011, 'diane': 0.002454726329680262, 'diaspar': 0.0012412324256375635, 'diccon': 0.00365605698527683, 'dick': 0.003346700100255955, 'dickeney': 0.0036560569852768275, 'dickens': 0.0009433921007048016, 'dictator': 0.0027400885069510696, 'dictionary': 0.004060697678301594, 'did': 0.03561324070689969, 'didn': 0.016575682998680747, 'didrectory': 0.0018924586447506726, 'die': 0.021791935179566378, 'died': 0.027230898300691368, 'diego': 0.003645504424189331, 'dies': 0.004306356182419327, 'diet': 0.0009236759316832519, 'dietz': 0.006860335160339445, 'diff': 0.0012499951251094144, 'differ': 0.0017018871514851899, 'difference': 0.0016963527580317285, 'differences': 0.0023689126839586353, 'different': 0.011431723370596777, 'differential': 0.001347039880397861, 'differently': 0.0036961433241503314, 'differing': 0.003045886007585912, 'difficult': 0.0023746283915965175, 'difficulties': 0.0016661801242341696, 'difficulty': 0.0037104463063565123, 'diffuse': 0.0006516076727636853, 'diffusion': 0.0003979733363520454, 'dig': 0.0012964773593636594, 'digest': 0.017968957812609945, 'digex': 0.041775058746329786, 'digibd': 0.001825425726571352, 'digital': 0.0075731316187886005, 'digitize': 0.0050604320391240505, 'digitized': 0.005060432039124055, 'digitizing': 0.003157558429105275, 'dignity': 0.0027400885069510687, 'dilemma': 0.00457333550673112, 'dillon': 0.005249184977328634, 'dime': 0.003108141579466518, 'dimension': 0.0012691491483781065, 'dimensional': 0.002949388144438729, 'dimensions': 0.003463434445380136, 'dinner': 0.0030737623444098035, 'dip': 0.0012412324256375635, 'dir': 0.0031801493479349397, 'direct': 0.00779630321396817, 'directed': 0.0018331313345243579, 'direction': 0.00273788917931346, 'directional': 0.0015035858261545658, 'directions': 0.0016838536312480043, 'directive': 0.0012160848046758686, 'directly': 0.00202275437374247, 'director': 0.007907900383152009, 'directories': 0.003737774831759086, 'directory': 0.015765983685881727, 'dirty': 0.00013754316908168307, 'dis': 0.0012717306823408032, 'disadvantages': 0.0018628591633699006, 'disagree': 0.010432989154398841, 'disagreeing': 0.0009236759316832519, 'disagreement': 0.0036560569852768275, 'disappear': 0.0024646783615664657, 'disappears': 0.0012160848046758686, 'disapproval': 0.0012160848046758686, 'disastrous': 0.0018628591633699006, 'discarded': 0.000978451715284566, 'disciples': 0.010104763978199323, 'disciplines': 0.000988318189986688, 'disclaimer': 0.004665494516859537, 'discount': 0.0030242362814067725, 'discounts': 0.0012499951251094144, 'discover': 0.002748269221361084, 'discovered': 0.0022837602226710016, 'discovery': 0.003732143721453348, 'discredit': 0.0027400885069510687, 'discrepancy': 0.0009236759316832519, 'discretionary': 0.003108141579466518, 'discrimination': 0.0019116724119796905, 'discuss': 0.007646019347635723, 'discussed': 0.002202878092805825, 'discusses': 0.0012449186271783616, 'discussing': 0.006080236221588833, 'discussion': 0.007702457986642845, 'discussions': 0.003080074816582794, 'disease': 0.00039751840402391624, 'dish': 0.0010442927627179474, 'dishonest': 0.0036560569852768275, 'disillusioned': 0.00365605698527683, 'disinterested': 0.00365605698527683, 'disk': 0.007319656735685251, 'diskette': 0.0007163598861018444, 'disks': 0.002674656736386347, 'dislike': 0.001226521686031947, 'disney': 0.0019312331813316494, 'disobey': 0.00457333550673112, 'display': 0.015026691245704306, 'displayed': 0.0024575018725063735, 'displaying': 0.006235498753197219, 'displays': 0.007860917731394867, 'disposal': 0.0024851616866216134, 'dispute': 0.0018496845972676042, 'dist': 0.0018924586447506718, 'distance': 0.005499251340630403, 'distances': 0.002844115383564493, 'distant': 0.0017062040508765046, 'distinct': 0.0012609485946591687, 'distinction': 0.0026646314304903523, 'distinguish': 0.00039751840402391624, 'distinguished': 0.0019116724119796905, 'distorted': 0.0021721839313897677, 'distorteddata': 0.0012609485946591687, 'distortion': 0.002803279087421274, 'distribute': 0.0008613659390572332, 'distributed': 0.0052928556092697795, 'distribution': 0.00717520502448615, 'dither': 0.0018924586447506718, 'dithering': 0.004425442103239914, 'diverse': 0.0012160848046758686, 'divided': 0.0018496845972676042, 'divine': 0.004844004454041068, 'divinity': 0.00365605698527683, 'division': 0.004553607642843949, 'dj': 0.0046165455504610115, 'djf': 0.0024851616866216134, 'djgpp': 0.0037911514534976548, 'djlewis': 0.0012609485946591687, 'dk': 0.0022062748258370284, 'dkbtrace': 0.0012609485946591687, 'dl': 0.0021721839313897677, 'dlecoint': 0.008255637787672639, 'dlphknob': 0.001825425726571352, 'dm': 0.0034518032100001447, 'dma': 0.0009433921007048016, 'dmcaloon': 0.004356139840040938, 'dmcgee': 0.001825425726571352, 'dmorf': 0.002524661375586771, 'dmorph': 0.0018924586447506718, 'dn': 0.0012412324256375635, 'dna': 0.0015527953218988713, 'dnv': 0.0024851616866216134, 'dobbs': 0.004913686425380573, 'dobson': 0.00365605698527683, 'doc': 0.003821993563448238, 'dock': 0.0012412324256375635, 'docking': 0.003731800431935115, 'docs': 0.005060432039124049, 'docterians': 0.0027400885069510696, 'doctor': 0.009179532565505875, 'doctrine': 0.012595661979579202, 'doctrines': 0.007333075149745417, 'document': 0.0009821113355156265, 'documentation': 0.00956418931355995, 'documented': 0.0020409970903436884, 'documents': 0.003722470469671578, 'dod': 0.003950288626390111, 'doe': 0.0024851616866216125, 'does': 0.019563819276137123, 'doesn': 0.013133866275128699, 'doesnt': 0.0018250202487414676, 'dog': 4.035731769314044e-05, 'dogfight': 0.003157558429105275, 'dogma': 0.0012160848046758686, 'doing': 0.00412249446264161, 'doink': 0.0012412324256375635, 'dokas': 0.002485161686621608, 'dollar': 0.004981161405813846, 'dollars': 0.005693658190488448, 'domain': 0.007739266041330638, 'domains': 0.001562428115434343, 'dominant': 0.0018705330287465275, 'dominik': 0.0018924586447506718, 'dompselaar': 0.003157558429105277, 'don': 0.023999948868581002, 'donald': 0.001586166555485608, 'donations': 0.0015035858261545658, 'dong': 0.003113632233935089, 'dont': 0.0009699455124686064, 'door': 0.004884774064075718, 'doors': 0.0010595219016541488, 'doppelganger': 0.0031081415794665165, 'doppler': 0.0018628591633698963, 'dos': 0.02354597714678633, 'dot': 0.0028462150971776193, 'doth': 0.00034465163587258686, 'double': 0.00294377064131504, 'doubt': 0.006347205327434612, 'doubting': 0.0027400885069510696, 'doubts': 0.0027400885069510696, 'doug': 0.012771547816977109, 'douginoz': 0.0018924586447506726, 'douglas': 0.003673735967616075, 'douses': 0.0027400885069510696, 'dover': 0.0012412324256375618, 'downey': 0.0024851616866216134, 'downlink': 0.0018628591633698963, 'downloaded': 0.0031575584291052778, 'dozen': 0.0010428158111027656, 'dozens': 0.0012160848046758686, 'dpg': 0.0012609485946591687, 'dps': 0.0012609485946591687, 'dr': 0.004681102796842908, 'draft': 0.0024917448724188695, 'drag': 0.006655557240663629, 'dragon': 0.002485161686621608, 'dramatic': 0.0027400885069510696, 'draper': 0.0018628591633698963, 'drastically': 0.00034465163587258686, 'draw': 0.006735274949737155, 'drawing': 0.010588271564927275, 'drawings': 0.00232831174264492, 'drawn': 0.001226521686031947, 'draws': 0.0015499786042360887, 'dream': 0.0013473781447308278, 'dreams': 0.003700625192925671, 'dresden': 0.0018924586447506718, 'drexel': 0.00435613984004094, 'drickel': 0.0012412324256375618, 'drift': 0.003108141579466518, 'drink': 0.0075926942760965845, 'drinking': 0.0018362078142529865, 'drive': 0.0012400560023378571, 'drivel': 0.0027400885069510687, 'driven': 0.0013418265164943256, 'driver': 0.00991433865275711, 'drivers': 0.009339245001283143, 'drives': 0.0007346838535750499, 'driving': 0.0031155095932511624, 'drop': 4.1274112522747194e-05, 'droplet': 0.0027400885069510687, 'dropped': 0.004849933577160703, 'dropping': 0.0018362078142529865, 'drops': 0.0019481148578558583, 'drube': 0.0018924586447506726, 'drug': 0.0027400885069510696, 'drwxr': 0.0015417795530505863, 'dry': 0.004356139840040942, 'dryden': 0.01380400161453519, 'ds': 0.0012609485946591687, 'ds0007': 0.0027400885069510696, 'dsav': 0.00457333550673112, 'dseg': 0.020833214811964443, 'dsi': 0.0012609485946591687, 'dsn': 0.0024851616866216125, 'dsnyder': 0.0012609485946591687, 'dsoconne': 0.0027400885069510687, 'dsp': 0.002315122536968045, 'dsto': 0.002524661375586771, 'dt': 0.002524661375586771, 'dtax': 0.0012609485946591687, 'dtek': 0.0012609485946591687, 'du': 0.002693439548552426, 'dual': 0.0021261502892459296, 'duane': 0.00039751840402391624, 'dublin': 0.002773679606040554, 'duc': 0.003108141579466518, 'duck': 0.01026579085493725, 'dues': 0.0015319298587311032, 'duff': 0.002524661375586772, 'duke': 0.003516859865157939, 'dumb': 0.001314222804558167, 'dump': 0.0009657853033023019, 'dumped': 0.002463395899066777, 'dundee': 0.0018924586447506718, 'dunn': 0.004981161405813843, 'duration': 0.004356139840040947, 'dust': 0.0020524960671726477, 'dutch': 0.0009657853033023019, 'duty': 0.0012412324256375635, 'dv': 0.0016194133460181942, 'dvpeg': 0.0012609485946591687, 'dwarf': 0.0012412324256375635, 'dwyer': 0.01943160055753655, 'dxb105': 0.0018628591633698963, 'dxf': 0.005060432039124051, 'dying': 0.001321817270076367, 'dynamic': 0.0009520174532068777, 'dynamics': 0.011967164461096629, 'dynamite': 0.003108141579466518, 'dzkriz': 0.006411840182243065, 'eager': 0.0019116724119796905, 'eagle': 0.0015448877753555896, 'eapu207': 0.0012609485946591687, 'earl': 0.001027092726567722, 'earlham': 0.00012627327507338994, 'earlier': 0.00222060790029552, 'earliest': 0.00010510953103124408, 'early': 0.004541467894869333, 'earn': 0.0024337964176860587, 'ears': 0.0013242262074587147, 'earth': 0.03940905843147546, 'ease': 0.00011497600573342169, 'easier': 0.001260862058756541, 'easiest': 0.001064042549779238, 'easily': 0.0022328351104158725, 'east': 0.00023623726339280521, 'eastern': 0.002144107221564112, 'easy': 0.004466545175029064, 'eat': 0.003855320467101282, 'eating': 0.004070799082890142, 'ebay': 0.0012412324256375635, 'ebu': 0.0012609485946591687, 'ec': 0.0018628591633698963, 'eccentric': 0.003731800431935113, 'ece': 0.006356904796360731, 'echo': 0.0031315407716547543, 'eclipse': 0.0012603864489062547, 'ecliptic': 0.0018628591633698963, 'ecn': 0.004474617237534675, 'eco': 0.004981161405813847, 'economic': 0.00453631115193302, 'economics': 0.0018628591633698963, 'economy': 0.006808265142538675, 'ecr': 0.0012609485946591687, 'ecs': 0.001776631115906653, 'ed': 0.004307649927202722, 'edb': 0.002524661375586772, 'eder': 0.003731800431935115, 'edgar': 0.0036560569852768275, 'edge': 0.006102027964795456, 'edges': 0.006301739687273127, 'edit': 0.0032606947822749503, 'edited': 0.00033144514648310135, 'editing': 0.002260600847370396, 'edition': 0.002188673014139636, 'editions': 0.00010510953103124408, 'editor': 0.003323620091559425, 'editors': 0.002491744872418865, 'edm': 0.0006398485452691399, 'edmonton': 0.0012609485946591687, 'ednobles': 0.003791151453497659, 'edu': 0.0236592039846268, 'education': 0.004566034211568611, 'educational': 0.005235631988790141, 'educators': 0.00010510953103124408, 'edward': 0.006791417309463365, 'edwards': 0.0062332574487479146, 'ee': 0.005696122928293771, 'eece': 0.0031575584291052778, 'eecs': 0.0018924586447506718, 'effect': 0.0021776919405402315, 'effective': 0.0037083658104250495, 'effectively': 0.0012827028287951915, 'effectiveness': 0.0024851616866216134, 'effects': 0.0016432195821698787, 'efficient': 0.0006671969666115956, 'efficiently': 0.0012852074653554209, 'effort': 0.002747115850271771, 'efforts': 0.0058748122007194065, 'ega': 0.0025246613755867744, 'egalon': 0.004981161405813845, 'egan': 0.000988318189986688, 'egerter': 0.0012609485946591687, 'ego': 0.007950032672143368, 'egs': 0.0012499951251094144, 'egypt': 0.0019116724119796905, 'egyptian': 0.0019116724119796905, 'eicn': 0.003791151453497654, 'einstein': 0.0025726896133709968, 'eisa': 0.0037911514534976556, 'eitech': 0.0045733355067311176, 'ekr': 0.0036560569852768267, 'el': 0.0013962324188771533, 'elaborate': 0.00034465163587258686, 'electric': 0.0016661801242341696, 'electrical': 0.0019558688405517007, 'electro': 0.000978451715284566, 'electromagnetic': 0.0012629530417339009, 'electron': 0.0007259062129681476, 'electronic': 0.0060444209410941835, 'electronically': 0.0010442927627179474, 'electronics': 0.0014024171455037666, 'electrons': 0.0012499951251094144, 'element': 0.005051516628863733, 'elements': 0.010147624848049938, 'elevation': 0.0012609485946591687, 'eliminated': 0.0019116724119796905, 'ellipse': 0.002524661375586771, 'elliptical': 0.0018803995034486513, 'elv': 0.0024851616866216125, 'elvis': 0.002141629960335612, 'em': 0.00082045014645962, 'email': 0.023868593621087376, 'emarsh': 0.0036560569852768275, 'embarassing': 0.0015311138319880398, 'embarrassment': 0.001825425726571352, 'embracing': 0.0036560569852768275, 'emergency': 0.003108141579466518, 'emmanuel': 0.003157558429105277, 'emory': 0.0010442927627179474, 'emotional': 0.00365605698527683, 'emotionally': 0.0027400885069510687, 'emphasis': 0.00253465847397498, 'empire': 0.0018134151655027544, 'employ': 0.0012225449270798988, 'employee': 0.004981161405813843, 'employees': 0.004919616655346288, 'employer': 0.002276772298013972, 'emr': 0.0018628591633698963, 'emx': 0.0023269365271611185, 'en': 0.0018991386326573465, 'enable': 0.0025246613755867744, 'enables': 0.001562428115434343, 'enblom': 0.0012412324256375635, 'enclosed': 0.007903863263687496, 'encode': 0.000988318189986688, 'encoders': 0.0012499951251094144, 'encoding': 0.0013558269777203544, 'encompass': 0.00039751840402391624, 'encounter': 0.0007174093917767946, 'encounters': 0.0010442927627179474, 'encourage': 0.001689372539872537, 'encouraged': 9.692610988414063e-05, 'encyclopedia': 0.0025313802598213187, 'end': 0.010620735029140327, 'endangered': 0.005491928440954982, 'endeavour': 0.003731800431935114, 'ended': 0.008052545238748786, 'ending': 0.0024414702830626916, 'endor': 0.0024851616866216125, 'ends': 0.010816449253018091, 'enemies': 0.004573335506731118, 'enemy': 0.0026646314304903523, 'energetic': 0.0024851616866216134, 'energia': 0.004981161405813846, 'energy': 0.011597544320709238, 'enet': 0.0027870607474464806, 'eney': 0.00365605698527683, 'enfant': 0.0024851616866216134, 'eng': 0.00903047912598676, 'engin': 0.013379703617728542, 'engine': 0.0068963647462546305, 'engineer': 0.005013480863825117, 'engineering': 0.010988401566011132, 'engineers': 0.007010472745985228, 'engines': 0.014439451979546153, 'england': 0.0016152319294256657, 'english': 0.003388546876043448, 'engr': 0.004443967393429537, 'engrg': 0.0024851616866216134, 'enhance': 0.0012691491483781056, 'enhanced': 0.00011497600573342169, 'enhancement': 0.002524661375586771, 'enhancing': 0.0018924586447506718, 'enjoy': 0.005376949304016038, 'enjoyed': 0.0018134151655027544, 'enjoyment': 0.0027400885069510687, 'enlighten': 0.0015035858261545658, 'enormous': 0.001974213813480285, 'enter': 0.0038570318518481384, 'entered': 0.0002992611575469784, 'entering': 0.0021756369937963533, 'enterprise': 0.0024851616866216125, 'entertainment': 0.00029391542155923767, 'entire': 0.003899227778735871, 'entirely': 0.00192293319818138, 'entities': 0.002456102764010641, 'entitled': 0.00010682631746858351, 'entity': 0.0021721839313897677, 'entries': 0.002443225671981978, 'entry': 0.0029069105594561797, 'envelope': 0.0021667751368718118, 'environment': 0.005421006716895076, 'environmental': 0.007079840883287663, 'environments': 0.002878645364615934, 'enzo': 0.008745706591231327, 'eos': 0.0068844492434083455, 'epfl': 0.0012609485946591687, 'ephemeris': 0.003108141579466518, 'episode': 0.00279400378189759, 'eps': 0.0025246613755867744, 'epsilon': 0.001300553187035633, 'epson': 0.0018924586447506718, 'eq': 0.001064042549779238, 'equal': 0.0023022831403158098, 'equality': 0.004573335506731121, 'equalization': 0.0012609485946591687, 'equally': 0.0024310293080461506, 'equation': 0.0017137386565996221, 'equations': 0.002918582143365115, 'equatorial': 0.0018628591633698963, 'equip': 0.0009559019909431317, 'equipment': 0.00184053110791555, 'equipped': 0.001058781479937508, 'equivalent': 0.003101033268550238, 'er': 0.0008320635873967719, 'era': 0.00318979845655927, 'erc': 0.0012609485946591687, 'erected': 0.0024851616866216134, 'eric': 0.004373251546652881, 'erich': 0.0018924586447506718, 'ericsson': 0.007090399309119852, 'erik': 0.0022512009151189147, 'erotica': 0.001825425726571352, 'erroneous': 0.001825425726571352, 'error': 0.00297666589278669, 'errors': 0.0030501234583700113, 'ers': 0.0031312025073217866, 'erwin': 0.0012609485946591687, 'es': 0.0026055542389956214, 'esa': 0.01063731994713023, 'escape': 0.004287327489920017, 'escapes': 0.0012808370180140277, 'esd': 0.002542985343060032, 'eso': 0.0015996635589569036, 'esoteric': 0.0024851616866216134, 'especially': 0.0036036846279378946, 'esperidon': 0.002524661375586772, 'esprit': 0.0010442927627179474, 'essence': 0.0036730266141353227, 'essential': 0.0008961450543373099, 'essentially': 0.003226051569361843, 'essex': 0.0018924586447506718, 'est': 0.0006739571102848205, 'establish': 0.0009196424097302845, 'established': 0.007014226383896778, 'establishment': 0.0024917448724188695, 'estimate': 0.004981161405813843, 'estimated': 0.0062332574487479345, 'estimates': 0.008116558095880515, 'et': 0.0014464096345025365, 'et4000': 0.002524661375586771, 'eternal': 0.01320837883382648, 'eternally': 0.003045886007585912, 'eternity': 0.0027400885069510687, 'ether': 0.006860335160339446, 'ethical': 0.00305573570190534, 'ethics': 0.0019229696813196587, 'ethz': 0.0018924586447506718, 'etna': 0.0037911514534976574, 'etrat': 0.0024851616866216125, 'etre': 0.009179532565505875, 'etry': 0.0018924586447506718, 'euclid': 0.0012412324256375635, 'eugene': 0.004672228926538125, 'europa': 0.0012412324256375635, 'europe': 0.0018907501666323235, 'european': 0.0061624740827733, 'euv': 0.001862859163369898, 'eva': 0.0013262274963396362, 'evaluation': 0.002544025914964133, 'evangelical': 0.0027400885069510687, 'evans': 0.0019150563317796342, 'evas': 0.0012412324256375635, 'eve': 0.006747895088237182, 'evening': 0.0020928628598154662, 'event': 0.0040658859952985805, 'events': 0.006079349437455259, 'eventually': 0.005423673713176803, 'everybody': 0.002194612039402936, 'evidence': 0.02746413734225542, 'evidences': 0.0027400885069510687, 'evil': 0.018860578633518716, 'evolution': 0.0015425388434893968, 'ex': 0.0034673478247941817, 'exact': 0.00024018765606540274, 'exactly': 0.0009304587249939801, 'examination': 0.00011497600573342169, 'examine': 0.0022321909792609963, 'examined': 0.0019546980436531153, 'example': 0.006694386287745745, 'examples': 0.0026311806609777095, 'exceed': 0.00010510953103124408, 'exceeds': 0.00034465163587258686, 'excellent': 0.0022421231397947924, 'exception': 0.0006004597111942912, 'excerpts': 0.0019965781299750842, 'excess': 0.0007163598861018444, 'exchange': 0.0013194421696253603, 'excited': 0.0009559019909431317, 'exciting': 0.0022345089669202917, 'exclude': 0.005491928440954982, 'excluding': 0.0018362078142529865, 'exclusive': 0.0017855205597762545, 'excuse': 0.0061302413142355315, 'exe': 0.0027988947708393764, 'executable': 0.0025246613755867744, 'execute': 0.0002992611575469784, 'executed': 0.00010510953103124408, 'executive': 0.0009130487728999928, 'exegisis': 0.0027400885069510687, 'exercise': 9.215269075613097e-05, 'exhaust': 0.001862859163369898, 'exhibits': 0.0018705330287465275, 'exist': 0.012751264939155502, 'existance': 0.003058413443451153, 'existed': 0.0036609367785014908, 'existence': 0.015735837388614633, 'existent': 0.009540040881607809, 'existing': 0.005114241915558349, 'exists': 0.004468917899460314, 'exit': 1.671875925648384e-05, 'exodus': 0.004573335506731118, 'exotic': 0.0012603864489062547, 'expand': 0.002436271697723395, 'expanded': 0.0010408805676875533, 'expansion': 0.0013371565680386924, 'expect': 0.0015255277902698205, 'expectations': 0.0012808370180140277, 'expected': 0.006861358394352799, 'expecting': 0.00011497600573342169, 'expending': 0.0024851616866216134, 'expenditures': 0.004356139840040938, 'expense': 0.0019772825845894414, 'expenses': 0.0012412324256375618, 'expensive': 0.008077599401775225, 'experience': 0.005895062809762258, 'experienced': 0.0007032382976603913, 'experiences': 0.0033683483211601525, 'experiment': 0.009622037506669408, 'experimental': 0.004028639117114583, 'experimentation': 0.0018803995034486513, 'experimenters': 0.003108141579466518, 'experiments': 0.009375548629619132, 'expert': 0.0056967643931079845, 'expertise': 0.0013550651057583542, 'experts': 0.002533981747863158, 'expiration': 0.003108141579466519, 'expires': 0.0075564564706580625, 'explain': 0.009329378786190074, 'explained': 0.0016171098597595277, 'explaining': 0.003283923848578494, 'explains': 0.0009284200503372423, 'explanation': 0.006705228415542357, 'explanations': 0.0019116724119796905, 'explicit': 0.0020072345244398155, 'explicitly': 0.008000365736522474, 'explode': 0.0015035858261545658, 'exploit': 0.0019965781299750842, 'exploiting': 0.0010442927627179474, 'exploration': 0.02304934212540359, 'explore': 0.0009221176897676745, 'explorer': 0.0031213191949626155, 'exploring': 0.001306377566948104, 'explosion': 0.0025231056317136114, 'explosions': 0.000978451715284566, 'explosive': 0.001932227409889329, 'export': 0.0036022670479505777, 'exports': 0.0009836938410219646, 'exposed': 0.0028376918700381793, 'exposure': 0.004408261865841435, 'express': 0.012869421361822909, 'expressed': 0.0019051232185768076, 'expressing': 0.002674481124809779, 'expression': 0.002822494175826525, 'expressly': 0.0038332746998137324, 'ext': 0.0010983486352568418, 'extend': 0.0019229696813196587, 'extended': 0.0028370027452311875, 'extension': 0.004380221644092401, 'extensions': 0.0031575584291052743, 'extensive': 0.0013267845861892604, 'extent': 0.0016175445195474878, 'external': 0.0028293627317099264, 'extinguished': 0.0024851616866216134, 'extn': 0.0018924586447506718, 'extra': 0.0048566282987270335, 'extract': 0.0031879727205346986, 'extracted': 0.000952889200262875, 'extraction': 0.000988318189986688, 'extreme': 0.004042532553052036, 'extremely': 0.0013638475496584, 'extremist': 0.008255637787672639, 'exu': 0.0015417795530505863, 'eye': 0.003469841399788529, 'eyes': 0.0022877355278844392, 'eyler': 0.0018924586447506718, 'eylerken': 0.0018924586447506718, 'ezekiel': 0.001825425726571352, 'f23': 0.0024851616866216134, 'f349': 0.004356139840040938, 'faa': 0.00435613984004094, 'fabrication': 0.001825425726571352, 'face': 0.009701537766115372, 'faces': 0.002528700130949014, 'facet': 0.0018924586447506718, 'facilities': 0.0072845597599939405, 'facility': 0.011606515441456123, 'facing': 0.0013371565680386924, 'facman': 0.004573335506731118, 'fact': 0.03529364986824487, 'factor': 0.00815196526462228, 'factors': 0.0006395752914771244, 'facts': 0.005306400253865663, 'factual': 0.00010510953103124408, 'faculty': 0.0009657853033023019, 'fag': 0.0027400885069510687, 'fail': 0.00435115528287489, 'failed': 0.002834818499367962, 'fails': 0.003303640017600043, 'failure': 0.005890286026154684, 'failures': 0.0037181677551411055, 'faint': 0.0031081415794665165, 'fair': 0.0028392013632979173, 'fairbanks': 0.018267095567843186, 'fairly': 0.003293724235576564, 'fait': 0.011029916709470509, 'faith': 0.04207016178087911, 'faiths': 0.004573335506731121, 'fake': 0.0010350509809422563, 'falcon': 0.002524661375586772, 'fall': 0.00580518567967243, 'fallacy': 0.001825425726571352, 'falling': 0.001027092726567722, 'falls': 0.0031155095932511624, 'false': 0.017555282105751656, 'falsify': 0.0027400885069510687, 'familiar': 0.0012389843481381583, 'families': 0.0012808370180140277, 'family': 0.004998740163288918, 'famous': 0.006494761002818329, 'fan': 0.0003474108153178439, 'fanatic': 0.00457333550673112, 'fanatical': 0.006411840182243067, 'fancy': 0.003180031128657364, 'fans': 0.0018803995034486513, 'fantasy': 0.0015725970481045033, 'faq': 0.01370975149051909, 'faqs': 0.0016738670852616978, 'far': 0.007360115364511719, 'farin': 0.003791151453497659, 'farley': 0.0031575584291052743, 'farming': 0.0013262274963396362, 'farside': 0.0024851616866216125, 'fascinating': 0.00010510953103124408, 'fashion': 0.0013447329508399731, 'fast': 0.01345124397922643, 'faster': 0.006399231588341046, 'fastest': 0.0020361452852944734, 'fat': 0.0021324977123564626, 'fatally': 0.00365605698527683, 'father': 0.020110381331942404, 'fathers': 0.0017855205597762545, 'fault': 0.0007560883876050022, 'favor': 0.003295311620948629, 'favorite': 0.000892850494205585, 'fax': 0.014409507510523117, 'fbi': 0.026042686594381106, 'fear': 0.01300055815745715, 'feasability': 0.0024851616866216125, 'feasibility': 0.002485161686621608, 'feasible': 0.005270942375426862, 'feast': 0.0036560569852768267, 'feature': 0.0038871481797709316, 'featured': 0.000988318189986688, 'features': 0.006938081107324902, 'feb': 0.004841471781548746, 'february': 0.002929304697419195, 'fed': 0.0006739571102848205, 'federal': 0.004433326455160005, 'fedex': 0.0024851616866216064, 'feds': 0.006411840182243067, 'fee': 0.004498391857905307, 'feed': 0.00354055505248974, 'feedback': 0.0007163598861018444, 'feel': 0.010085251481567775, 'feeling': 0.004689082216934307, 'feelings': 0.0034519223629203167, 'feels': 0.0029499560858236764, 'fees': 0.002848772955529746, 'feet': 0.00640985787376702, 'fell': 0.004060984582795472, 'fellow': 0.006020267636699933, 'fellowship': 0.00365605698527683, 'felt': 0.0007032382976603913, 'ferdinan': 0.003157558429105277, 'ferdinand': 0.004425442103239913, 'fermi': 0.008116558095880504, 'fermilab': 0.003731800431935114, 'fewer': 0.0006703468019723805, 'feynman': 0.0018705330287465292, 'ff': 0.0012499951251094144, 'fft': 0.000988318189986688, 'fi': 0.006512005458847743, 'fiber': 0.0024851616866216134, 'fiction': 0.008309423982006098, 'fido': 0.004378901872820053, 'fidonet': 0.006380125035288875, 'field': 0.008856692353610782, 'fields': 0.0033956076046081016, 'fifth': 0.002467372658018935, 'figaro': 0.0018924586447506718, 'fight': 0.00034465163587258686, 'fighter': 0.004356139840040938, 'fighters': 0.0012808370180140277, 'fighting': 0.0028272257285699588, 'figure': 0.003438166505215632, 'figured': 0.0042623473629762884, 'figures': 0.0030598981461642675, 'figuring': 0.0019965781299750842, 'file': 0.04805647804248116, 'filed': 0.00036440142293393384, 'filename': 0.0027988947708393764, 'files': 0.04136735186088755, 'filled': 0.0009280959011182428, 'filling': 0.0007163598861018444, 'film': 0.0038345245046140456, 'films': 0.0006739571102848205, 'filter': 0.004029559259700203, 'filtering': 0.002524661375586771, 'filters': 0.0012827028287951915, 'final': 0.0036336607968934544, 'finally': 0.0015773843301185664, 'financial': 0.004382482453913888, 'finding': 0.002695571946133611, 'finds': 0.0024496852878952745, 'fine': 0.007285855213284517, 'finger': 0.003303640017600043, 'fingers': 0.0019116724119796905, 'finish': 0.0004969380507820406, 'finished': 0.0011002014087067762, 'finite': 0.001306377566948104, 'finland': 0.0012780639613924746, 'fired': 0.003086751056060275, 'fires': 0.00457333550673112, 'firing': 0.0024337964176860604, 'firm': 0.0038095618319651543, 'firms': 0.002507404866341487, 'firsteps': 0.0024851616866216134, 'firstly': 0.001553067980998979, 'fiscal': 0.0024851616866216125, 'fischer': 0.002161230461840069, 'fish': 0.000976843714910633, 'fishes': 0.00365605698527683, 'fishing': 0.005201390624291056, 'fission': 0.0024851616866216064, 'fit': 0.00195119758131809, 'fits': 0.002582117324008192, 'fitting': 0.0034731620215266213, 'fix': 0.0029324437425031725, 'fixed': 0.001534583907707293, 'fixes': 0.0015861665554856063, 'fixing': 0.0025246613755867744, 'fl': 0.0037515837595050953, 'flag': 0.004443833699861959, 'flame': 0.00530787860062319, 'flames': 0.0010047383206371338, 'flaming': 0.00911042476729609, 'flammable': 0.0036560569852768267, 'flares': 0.0010442927627179474, 'flash': 0.0024448766353608346, 'flat': 0.0030181662428886242, 'flattening': 0.003157558429105277, 'flaw': 0.0004088156733638845, 'flawed': 0.004981161405813842, 'flb': 0.003731800431935114, 'fleet': 0.0024851616866216125, 'fleming': 0.0012609485946591687, 'flesh': 0.004499671758296702, 'flew': 0.008745706591231313, 'flex': 0.0012499951251094144, 'flexibility': 0.000988318189986688, 'flexible': 0.0022408043273308706, 'fli': 0.0037911514534976548, 'flight': 0.04779025670181753, 'flights': 0.008116558095880515, 'flip': 0.0016837503976208663, 'flipping': 0.000988318189986688, 'floating': 0.0004945813024330777, 'flood': 0.0012629530417339009, 'floor': 0.0019486061758606172, 'floors': 0.0021524677623682162, 'floppies': 0.0018924586447506718, 'floppy': 0.004479939105824773, 'florida': 0.0009096329652214415, 'flow': 0.001029871907008359, 'flowing': 0.0019116724119796905, 'flown': 0.002278512863596773, 'fluid': 0.002507404866341485, 'fluids': 0.0024851616866216134, 'flushed': 0.001064042549779238, 'fly': 0.008199150418350992, 'flyby': 0.006860335160339447, 'flybys': 0.003731800431935112, 'flying': 0.010058798703932743, 'fm': 0.0019116724119796905, 'fnal': 0.013520603616506845, 'fnalf': 0.011901885334985415, 'foci': 0.0024851616866216134, 'focus': 0.0022171229967145236, 'focused': 0.0010442927627179474, 'foil': 0.0018628591633698963, 'fold': 0.0022072227891300807, 'folks': 0.005342324308805427, 'follow': 0.023266934338021274, 'followed': 0.006735892467800935, 'followers': 0.019354135278405404, 'following': 0.0059969645606031945, 'follows': 0.0019285816094057624, 'followups': 0.0021946697425983134, 'folly': 0.0027400885069510687, 'fombaron': 0.0018924586447506718, 'fond': 0.002454726329680262, 'font': 0.0037911514534976565, 'fonts': 0.005696122928293768, 'foo': 0.0016194133460181942, 'food': 0.008774598532939678, 'fool': 0.0012647021471220267, 'foot': 0.0028906616381244488, 'football': 0.0015499786042360887, 'force': 0.012777030686094037, 'forced': 0.0050913269661304415, 'forces': 0.004914107069127355, 'forcing': 0.0033137400484304796, 'ford': 0.002182135963275971, 'foreign': 0.004404815646080222, 'foresight': 0.001588641835522998, 'forever': 0.0036376276663617636, 'forget': 0.0032308954285426633, 'forgive': 0.0004969380507820406, 'forgiven': 0.002130332690995644, 'forgiveness': 0.002130332690995644, 'forgiving': 0.0034617720572396897, 'forgot': 8.793789117982759e-07, 'forgotten': 0.0024851616866216134, 'fork': 0.0025114946594801584, 'form': 0.0020173964770212284, 'formal': 0.0024851616866216125, 'format': 0.03145866502278034, 'formation': 0.0028598161489366168, 'formats': 0.016164173302895282, 'formed': 0.002589919242580292, 'forming': 0.0025313802598213187, 'forms': 0.003090980679491851, 'formula': 0.0010620524702536945, 'formulae': 0.0012412324256375635, 'formulas': 0.000978451715284566, 'forth': 0.004336003197553282, 'fortran': 0.004251984873608397, 'fortunately': 0.0009221176897676745, 'fortune': 0.00036440142293393384, 'forum': 0.0051399364626545044, 'forward': 0.003343997774922493, 'forwarded': 0.022120623566036737, 'fossi': 0.0018924586447506718, 'foster': 0.0021401823853150715, 'fotis': 0.003157558429105275, 'foundation': 0.0035473523161648132, 'foundations': 0.0015626450162182998, 'founded': 0.01097471886743731, 'fourier': 0.0015861665554856063, 'fourth': 0.005099448905090447, 'foust': 0.0018628591633698963, 'fox': 0.006906470957412232, 'fp1': 0.00549192844095498, 'fps': 0.0037911514534976574, 'fpu': 0.0018924586447506718, 'fr': 0.0069696142670419535, 'fractal': 0.005209022119273202, 'fractals': 0.006969614267041949, 'fractint': 0.0025246613755867744, 'fraction': 0.003108141579466518, 'fraering': 0.010006085862371748, 'frame': 0.008040709950430752, 'frames': 0.004981605524460878, 'framework': 0.00012627327507338994, 'france': 0.0021243642772954003, 'francis': 0.000978451715284566, 'francisco': 0.005494480751453057, 'frank': 0.026013652492393402, 'frankborn': 0.00365605698527683, 'frankly': 0.0011253818994855442, 'franz': 0.0012801026179278053, 'fraser': 0.0018705330287465275, 'frater': 0.0027400885069510687, 'fraternity': 0.0027400885069510687, 'fraud': 0.002464678361566464, 'freaks': 0.004981161405813851, 'fred': 0.022069680872566742, 'frederick': 0.00011497600573342169, 'free': 0.00945032647940864, 'freebairn': 0.003731800431935113, 'freed': 0.003685796326874799, 'freedom': 0.005275693416015871, 'freely': 0.002610477945391684, 'freeman': 0.0023041316498041723, 'freemant': 0.0012609485946591687, 'freemason': 0.00365605698527683, 'freemasonry': 0.005491928440954979, 'freenet': 0.020122293492567327, 'freeware': 0.0031575584291052778, 'freeze': 0.001670031835008053, 'french': 0.003263446080399411, 'frequencies': 0.002152467762368218, 'frequency': 0.0041638221748979305, 'frequent': 0.0013262274963396362, 'frequently': 0.006957944861263577, 'fri': 0.0016716927856762131, 'friday': 0.0030289919897078126, 'friedman': 0.0018628591633698963, 'friend': 0.0007300059479042921, 'friendly': 0.0013558269777203544, 'friends': 0.008276453698041253, 'fringe': 0.0024851616866216134, 'frog': 0.0024646783615664657, 'frontier': 0.0039050360216904244, 'fruit': 0.003382596524808915, 'fs7': 0.0043561398400409415, 'fsu': 0.01051411793062421, 'ft': 0.003754571461966229, 'ftcollinsco': 0.0024851616866216064, 'ftp': 0.03130218269137808, 'ftpmail': 0.000988318189986688, 'fuel': 0.020568970727523894, 'fueled': 0.003108141579466519, 'fuels': 0.0018628591633698963, 'fuer': 0.0025246613755867744, 'fulfill': 0.003581494522191157, 'fulfilled': 0.0021946697425983134, 'fullmer': 0.0012609485946591687, 'fully': 0.00011708020564189965, 'fun': 0.0032616823967951116, 'function': 0.003602866201883495, 'functional': 0.0012801026179278053, 'functionality': 0.0035799498220573838, 'functions': 0.005835831512449789, 'fund': 0.012388701863953425, 'fundamental': 0.002595681415841611, 'fundamentalist': 0.008255637787672639, 'fundamentalists': 0.005491928440954982, 'fundamentals': 0.0012691491483781065, 'funded': 0.010006085862371748, 'fundies': 0.0027400885069510687, 'funding': 0.027956382612712664, 'funds': 0.012535219985229794, 'funet': 0.0022171229967145253, 'funny': 0.002978781262500725, 'furthermore': 0.0009453731425111455, 'fuselage': 0.003108141579466518, 'fusion': 0.004091281979189233, 'future': 0.006810020276802525, 'fuzzy': 0.0024089044989395727, 'fx': 0.0025246613755867744, 'g9134255': 0.003157558429105277, 'ga': 0.0016703102977515634, 'gabriel': 0.0013262274963396362, 'gain': 0.004138927900585776, 'gaining': 0.0017855205597762545, 'galactic': 0.005606866737329389, 'galatians': 0.0036560569852768275, 'galaxies': 0.004981161405813847, 'galaxy': 0.0067355794534795, 'galilean': 0.0018628591633698963, 'galileo': 0.011652082365662345, 'galki': 0.004425442103239913, 'game': 0.0020247423344911565, 'games': 0.001047414076534043, 'gamma': 0.010098541061016632, 'gang': 0.0024851616866216134, 'ganymede': 0.0012412324256375635, 'gao': 0.0012412324256375635, 'gap': 0.0026198212843254187, 'garbage': 0.0018134151655027544, 'garching': 0.001347039880397861, 'garden': 0.004573335506731118, 'garnet': 0.008255637787672639, 'gary': 0.004605022194297147, 'gas': 0.014271815513005982, 'gases': 0.0012808370180140277, 'gaskins': 0.0012609485946591687, 'gaspra': 0.0018705330287465292, 'gate': 0.0021484342404152522, 'gatech': 0.0038061449134529626, 'gates': 0.001907356230328468, 'gateway': 0.0010070869488322549, 'gather': 0.0019965781299750842, 'gathered': 0.0024851616866216134, 'gathering': 0.001932227409889329, 'gaul': 0.0012609485946591687, 'gauss': 0.000988318189986688, 'gaussian': 0.002524661375586772, 'gave': 0.005099436199141443, 'gavin': 0.0012499951251094144, 'gay': 0.006411840182243063, 'gays': 0.005491928440954979, 'gb': 0.004274677838270878, 'gboro': 0.001825425726571352, 'gd': 0.002570679320947222, 'ge': 0.000988318189986688, 'gee': 0.0031172114890410225, 'geese': 0.001825425726571352, 'gehrels': 0.007488101498518759, 'gehrels3': 0.004356139840040938, 'geller': 0.004573335506731121, 'gem': 0.0018705330287465275, 'gemini': 0.001566038423746783, 'gems': 0.006332516444282765, 'gen': 0.002169354523665773, 'gene': 0.00807475213969663, 'general': 0.009340011989013176, 'generalizations': 0.001825425726571352, 'generally': 0.005423009513030045, 'generate': 0.002002755702892384, 'generated': 0.005795341128311726, 'generates': 0.00012627327507338994, 'generating': 0.0016958301188799586, 'generation': 0.005601853103102799, 'generations': 0.002674481124809779, 'generator': 0.0007036071049306121, 'generators': 0.0018803995034486513, 'generic': 0.002364568441717449, 'generous': 0.0024851616866216134, 'genes': 0.0012609485946591687, 'genesis': 0.004052987031546835, 'genetics': 0.002524661375586772, 'geniuses': 0.007287756008583687, 'genoa': 0.0018924586447506718, 'gentile': 0.0073330751497454084, 'gentiles': 0.004573335506731121, 'genuine': 0.00365605698527683, 'geo': 0.002056171775947969, 'geochemical': 0.0024851616866216134, 'geod': 0.0018628591633698963, 'geoff': 0.000988318189986688, 'geographic': 0.0025005225130257675, 'geographical': 0.0021721839313897677, 'geological': 0.003643553676962851, 'geology': 0.004356139840040943, 'geomag': 0.0012412324256375618, 'geometric': 0.008885150472506759, 'geometrical': 0.0018924586447506718, 'geometry': 0.005307627763755102, 'geophysical': 0.0021261502892459296, 'george': 0.004011751085021472, 'georgia': 0.004289203141380266, 'geostationary': 0.003108141579466519, 'geosynchronous': 0.0024851616866216134, 'ger': 0.0018924586447506718, 'german': 0.0033716275150428568, 'germans': 0.0018628591633698963, 'germany': 0.0028211676248787237, 'gestures': 0.0024851616866216134, 'getaway': 0.001825425726571352, 'gets': 0.006954946999821894, 'getting': 0.0012247971022548527, 'gfk39017': 0.0024851616866216125, 'gfx': 0.003157558429105275, 'ghasting': 0.0012412324256375618, 'ghelf': 0.0018628591633698963, 'ghod': 0.0018628591633698963, 'ghost': 0.001595688418392572, 'giant': 0.00686033516033944, 'gibbons': 0.001862859163369898, 'gibson': 0.000988318189986688, 'gif': 0.028127595603747654, 'gif89a': 0.000988318189986688, 'gifs': 0.004247614121330846, 'gifts': 0.0027400885069510696, 'gilligan': 0.0015417795530505863, 'gingrich': 0.0027400885069510687, 'gis': 0.0016194133460181942, 'gist': 0.00365605698527683, 'gita': 0.004573335506731118, 'given': 0.0031330421122697178, 'gives': 0.0022649059058043, 'giving': 0.00240587869793532, 'gks': 0.002524661375586772, 'gl': 0.00824592958499185, 'glad': 0.002152550037368828, 'glasgow': 0.0012609485946591687, 'glass': 0.00011497600573342169, 'glen': 0.0018803995034486513, 'glenn': 0.0012499951251094144, 'glitch': 0.0010442927627179474, 'global': 0.004633703130386214, 'globe': 0.0012889215524966614, 'glory': 0.005189674796409438, 'gloster': 0.001825425726571352, 'gly': 0.0012412324256375618, 'gm': 0.0018628591633698963, 'gm2': 0.004981161405813846, 'gmi': 0.0012609485946591687, 'gmt': 0.012267059912888002, 'gnb': 0.0024851616866216134, 'gnp': 0.005606866737329393, 'gnu': 0.003791151453497659, 'gnuplot': 0.0037911514534976565, 'go32': 0.0037911514534976574, 'goal': 0.010178406916552703, 'goals': 0.003952490513227347, 'god': 0.12252523919766867, 'goddard': 0.006146595176250911, 'goddess': 0.0013262274963396362, 'gods': 0.0059672070085825864, 'godzilla': 0.0025114946594801584, 'goes': 0.0034377717048018498, 'going': 0.012325121172953372, 'gold': 0.0003921553221062149, 'golden': 0.005327936506023655, 'goldin': 0.005606866737329385, 'goltz': 0.0024851616866216125, 'gondwana': 0.0012609485946591687, 'gone': 0.0038688419061707873, 'gonna': 0.0012808370180140277, 'goo': 0.001825425726571352, 'good': 0.01618090446759075, 'goods': 0.001921522106299118, 'goose': 0.001825425726571352, 'gopher': 0.004425442103239913, 'gordon': 0.002559386741368291, 'gosh': 0.003731800431935113, 'gospel': 0.016619192667934636, 'gospels': 0.005491928440954981, 'got': 0.0019902144115766717, 'gothamcity': 0.007488101498518762, 'gotta': 0.0004515475724564313, 'gotten': 0.0009448142574399595, 'gov': 0.05354727448578558, 'government': 0.02511578862514973, 'governments': 0.0024377731766381597, 'gp': 0.0018705330287465275, 'gpc': 0.0012499951251094144, 'gpo': 0.0018628591633698963, 'gps': 0.006860335160339447, 'gr': 0.004429691192905085, 'grab': 0.0006469833237989584, 'grabber': 0.0018924586447506718, 'grace': 0.012087250378902705, 'grad': 0.0031403962761163686, 'grade': 0.0036545488809045404, 'grades': 0.0018628591633698963, 'gradient': 0.0022512009151189147, 'gradually': 0.0002992611575469784, 'graduate': 0.0023051158728379026, 'graeme': 0.0012609485946591687, 'grafsys': 0.0018924586447506718, 'grain': 0.0012160848046758686, 'grammar': 0.0015626450162182998, 'grand': 0.0016307803947861951, 'grant': 0.00496037476242825, 'granted': 0.0035359327571852983, 'graph': 0.004142027252334136, 'graphic': 0.010829593705349319, 'graphical': 0.0048567296606395775, 'graphics': 0.13044709565039875, 'graphs': 0.0020331065699866835, 'grapple': 0.0024851616866216064, 'grasp': 0.0032155982974811613, 'grass': 0.0021721839313897677, 'gravitational': 0.0049811614058138465, 'gravity': 0.01386281066696064, 'gray': 0.004758046239436719, 'graydon': 0.004356139840040946, 'grayscale': 0.004425442103239911, 'grbs': 0.0012412324256375635, 'great': 0.008107248709538942, 'greater': 0.004443372511560649, 'greatest': 0.002132686638080832, 'greatly': 0.009926825607752737, 'greece': 0.003143282228580879, 'greedy': 0.0006604803272702029, 'greek': 0.009785795606416271, 'greeks': 0.0027400885069510687, 'green': 0.006086843106507325, 'greenbelt': 0.003448682679121748, 'greetings': 0.002853354803460136, 'greg': 0.00559558505011376, 'gregory': 0.0031823759255185284, 'grenades': 0.005491928440954984, 'grew': 0.0007018517160113221, 'grey': 0.004129600369449204, 'grid': 0.0029614890689189837, 'grief': 0.0015035858261545658, 'griffin': 0.0037492932715365666, 'gripe': 0.0031575584291052778, 'grn': 0.0012609485946591687, 'gro': 0.0012412324256375618, 'gross': 0.0033538046033891123, 'ground': 0.013857263644426177, 'grounds': 0.002144107221564112, 'group': 0.009981052864777504, 'groups': 0.0038340283465033344, 'grove': 0.0007163598861018444, 'grow': 0.0027285530523395362, 'growing': 0.0006211034098319293, 'grows': 0.0044232811566846135, 'growth': 0.0024718333622407067, 'gs': 0.0019586284998014264, 'gsfc': 0.008546406808077188, 'gu': 0.0018924586447506718, 'guarantee': 0.0019501444979168892, 'guaranteed': 0.000774910454166714, 'guarantees': 0.0012691491483781056, 'guard': 0.0012603864489062547, 'guess': 0.005169562267110448, 'guest': 0.003442345468465534, 'gui': 0.0031575584291052743, 'guidance': 0.002852659462418008, 'guide': 0.0038591795362132022, 'guided': 0.00457333550673112, 'guidelines': 0.0010442927627179474, 'guides': 0.00365605698527683, 'guilt': 0.00457333550673112, 'guilty': 0.0051997796101179656, 'gum': 0.002524661375586772, 'gun': 0.006313859484773899, 'guns': 0.005198990562330337, 'guy': 0.008836651103319881, 'guys': 0.00046252417975243057, 'gvl': 0.0012609485946591687, 'gw': 0.0014348552136991544, 'gyros': 0.0024851616866216064, 'h7v': 0.00365605698527683, 'h8902939': 0.0012609485946591687, 'ha': 0.0015319298587311032, 'haavard': 0.0018924586447506718, 'hab': 0.0012827028287951915, 'habit': 0.0027713306741743637, 'habitat': 0.0024851616866216125, 'habits': 0.0027400885069510687, 'hac': 0.0012609485946591687, 'hadn': 0.0024851616866216125, 'hagoromo': 0.0018628591633698963, 'hahm': 0.0012609485946591687, 'haines': 0.005815919279463967, 'hair': 0.0024363865949890897, 'hal': 0.002538466458117771, 'halandri': 0.002524661375586772, 'halat': 0.007333075149745415, 'halcyon': 0.0018924586447506718, 'half': 0.006107477971353526, 'halftone': 0.0025246613755867744, 'hall': 0.0022673204549303033, 'halo': 0.0018628591633698963, 'ham': 0.0013371565680386924, 'hamilton': 0.0006496982395886239, 'hammer': 0.0012827028287951915, 'hanauma': 0.0012609485946591687, 'hand': 0.010550089832898507, 'handbook': 0.005201551388967976, 'handed': 0.0009300965515126975, 'handheld': 0.001825425726571352, 'handle': 0.00813779687607547, 'handled': 0.003163711809214067, 'handles': 0.002524661375586772, 'handling': 0.0017949076801095053, 'hands': 0.00038443288062902856, 'handy': 0.00010510953103124408, 'hang': 0.0019306435466962882, 'hanged': 0.001825425726571352, 'hanging': 0.003748353805784607, 'hannibal': 0.005606866737329394, 'happen': 0.0037388368367251377, 'happened': 0.018682188406238486, 'happening': 0.0009938843934603194, 'happenings': 0.0015319298587311032, 'happens': 0.0010203653539104752, 'happy': 0.004313183161056235, 'harbor': 0.001921522106299118, 'hard': 0.0031551897141380908, 'hardcopy': 0.002524661375586772, 'harder': 0.0018871483477936142, 'harding': 0.0036560569852768267, 'hardisk': 0.002524661375586772, 'hardly': 0.008416230285114488, 'hardware': 0.01695440070664947, 'hardy': 0.0012609485946591687, 'hare': 0.00549192844095498, 'harm': 0.006932564075008872, 'harmony': 0.003581494522191157, 'harmsen': 0.0012609485946591687, 'harold': 0.0015626450162182998, 'harper': 0.00010510953103124408, 'harris': 0.0032432393048343784, 'harsh': 0.0013262274963396362, 'hart': 0.000988318189986688, 'hartman': 0.0018705330287465275, 'hartmann': 0.0012691491483781056, 'harvard': 0.005416194382822989, 'harvey': 0.01724177338545085, 'hasn': 0.0013027003049568232, 'hast': 0.00457333550673112, 'hastings': 0.0012412324256375618, 'haston': 0.0018924586447506718, 'hat': 0.00019090439635994876, 'hate': 0.00815307902086218, 'hateful': 0.00365605698527683, 'hates': 0.0028370754228893864, 'hath': 0.0027400885069510687, 'hatred': 0.005491928440954982, 'hauke': 0.0012609485946591687, 'havardn': 0.0018924586447506718, 'haven': 0.0028614201682416324, 'having': 0.0033340938161347394, 'hawaii': 0.002515851779763151, 'hawking': 0.003731800431935108, 'hazardous': 0.0013262274963396362, 'hcf': 0.0012609485946591687, 'hcrlgw': 0.0018924586447506718, 'hdf': 0.0018924586447506718, 'hdsteven': 0.0012412324256375618, 'head': 0.009827342463249372, 'headed': 0.004223557231696154, 'header': 0.005645706734156318, 'headers': 0.00011497600573342169, 'heading': 0.0006739571102848205, 'headline': 0.0024851616866216125, 'headquartered': 0.0015448877753555896, 'headquarters': 0.005859128714882541, 'heads': 0.0009221176897676745, 'health': 0.007152616269399303, 'hear': 0.005348764610156, 'heard': 0.006472843125464223, 'hearing': 0.0030276081483345974, 'heart': 0.009711154395067107, 'hearts': 0.006411840182243063, 'heat': 0.009651945456408365, 'heating': 0.0012603864489062547, 'heaven': 0.014411100879651487, 'heavenly': 0.0012808370180140277, 'heavier': 0.0024080850228676183, 'heavily': 0.0010504470502403435, 'heavy': 0.0023878528772719497, 'hebrew': 0.0036560569852768267, 'heck': 0.0030563521490541345, 'heidelberg': 0.0030847158139595578, 'height': 0.0032383360080921516, 'heights': 0.0002992611575469784, 'heines': 0.001825425726571352, 'heinlein': 0.003108141579466518, 'hela': 0.00858756028014432, 'held': 0.005751868423230407, 'helios': 0.0006496982395886239, 'hell': 0.006670966791904577, 'hello': 0.007451572844490606, 'help': 0.02039732114555581, 'helped': 0.0028928863215904794, 'helpful': 0.003622844345859573, 'helping': 8.793789117982759e-07, 'helps': 0.0013841303006118409, 'helsinki': 0.0013371565680386924, 'hemel': 0.004425442103239911, 'hemisphere': 0.0012603864489062547, 'hendrix': 0.0015744872567363078, 'henrik': 0.0018803995034486513, 'henry': 0.045146286183235546, 'hep': 0.0024851616866216125, 'hepnet': 0.005606866737329394, 'herbert': 0.0012499951251094144, 'heresy': 0.0027400885069510687, 'heretical': 0.001825425726571352, 'hermes': 0.0028663993347338183, 'hermetic': 0.0027400885069510687, 'hernandez': 0.005696122928293773, 'hernes': 0.0036560569852768275, 'herring': 0.006010417942380506, 'herrings': 0.004573335506731118, 'herringshaw': 0.010807086540932341, 'het': 0.0012691491483781065, 'hewlett': 0.0030538357627876035, 'hex': 0.002524661375586772, 'hey': 0.004984797347275491, 'hga': 0.003108141579466514, 'hi': 0.03955943721735622, 'hicolor': 0.0018924586447506718, 'hidden': 0.006304866160052406, 'hide': 0.0018134151655027544, 'hideous': 0.005606866737329394, 'hierarchical': 0.0012691491483781065, 'higgins': 0.013731871458058022, 'high': 0.028877197471051688, 'higher': 0.0066057166319143466, 'highest': 0.0013085533219882404, 'highly': 0.002670398369663027, 'highway': 0.001562428115434343, 'hijaak': 0.0018924586447506718, 'hill': 0.008949985267687737, 'hillary': 0.00039751840402391624, 'hint': 0.001306377566948104, 'hints': 0.002327929713235535, 'hired': 0.0002992611575469784, 'histogram': 0.0012609485946591687, 'histograms': 0.0018924586447506718, 'historian': 0.0073330751497454084, 'historians': 0.004662266056376308, 'historical': 0.008252649844150077, 'histories': 0.002880736432187136, 'history': 0.015063657162867228, 'hit': 0.0017401743597438256, 'hitachi': 0.002524661375586771, 'hitchhikers': 0.0025246613755867744, 'hiten': 0.004356139840040943, 'hitler': 0.00825563778767264, 'hits': 0.0007117181907135006, 'hitting': 0.0018496845972676042, 'hj': 0.0012609485946591687, 'hk': 0.0025114946594801575, 'hku': 0.0012609485946591687, 'hkuxa': 0.0012609485946591687, 'hlv': 0.003108141579466518, 'hlvs': 0.0024851616866216064, 'hm': 0.0023913651981414584, 'hmm': 0.0009948550082779098, 'hmmm': 0.0016261937554672905, 'ho': 0.0013356730305772568, 'hobby': 0.0024851616866216064, 'hochschule': 0.0025246613755867744, 'hofstra': 0.0012609485946591687, 'hoi': 0.0012609485946591687, 'hold': 0.0034920972996137023, 'holding': 0.0012582804414488615, 'holds': 0.0018654019090710693, 'hole': 0.002996151513781583, 'holes': 0.00606365796607324, 'hollasch': 0.0012609485946591687, 'hollis': 0.0024851616866216134, 'holly': 0.004573335506731118, 'hollywood': 0.0018449705137248374, 'holonet': 0.003157558429105277, 'holy': 0.0213092749230199, 'home': 0.002766399510251558, 'homo': 0.0015319298587311032, 'homosexual': 0.009179532565505865, 'homosexuality': 0.013819146780228076, 'homosexuals': 0.008255637787672642, 'honest': 0.00544149756195332, 'honestly': 0.005347567868528998, 'honesty': 0.00365605698527683, 'hong': 0.0025005225130257693, 'honor': 0.006510834437234219, 'hood': 0.0024851616866216134, 'hook': 0.000961684845087009, 'hoover': 0.0015448877753555896, 'hop': 0.001216655211329824, 'hope': 0.0010048245102316517, 'hopefully': 0.0009773298502957486, 'hopes': 0.0006739571102848205, 'hoping': 0.0006299532136083384, 'hopkins': 0.008627511050547945, 'hopper': 0.0019116724119796905, 'horizon': 0.0016816086674564185, 'horizontal': 0.001296105875257923, 'horizontally': 0.001670031835008053, 'horrible': 0.003135225762272714, 'horse': 0.00421687548931048, 'horsepower': 0.0018924586447506718, 'horus': 0.01568447676757681, 'host': 0.011433006218069844, 'hostile': 0.0027400885069510687, 'hot': 0.00045039993935359207, 'hotel': 8.226937839690696e-05, 'hou': 0.00305573570190534, 'hour': 0.006218729894885562, 'hours': 0.008276317866146476, 'house': 0.006420677333848288, 'housekeeping': 0.0010442927627179474, 'houses': 0.004284527532590306, 'houston': 0.004275660889504831, 'hover': 0.0024851616866216064, 'howe': 0.0036560569852768275, 'hp': 0.010805314454702722, 'hparc0': 0.0016958301188799586, 'hpgl': 0.0018924586447506718, 'hq': 0.0023269365271611185, 'hqx': 0.0012609485946591687, 'hs': 0.0018579592253753089, 'hst': 0.005028308390166264, 'hsvaic': 0.003731800431935113, 'hubble': 0.005004465618062951, 'hudson': 0.015699719985528028, 'hue': 0.0018924586447506718, 'huffman': 0.0012609485946591687, 'huge': 0.0036657831922688646, 'hugh': 0.0018449705137248374, 'hughes': 0.0015773739227058674, 'huh': 0.0036391263827446818, 'hull': 0.002524661375586772, 'human': 0.004141594968873126, 'humanity': 0.003974028634309297, 'humankind': 0.0036560569852768267, 'humans': 0.008895463192002311, 'humor': 0.0007229880847217382, 'humour': 0.0012412324256375618, 'hundreds': 0.0025699306873833046, 'hung': 0.0044965301110362135, 'hunt': 0.00036440142293393384, 'hunter': 0.001599663558956902, 'huntington': 0.0012629530417339009, 'huntsville': 0.004395146651496549, 'hurry': 0.0017855205597762545, 'hurt': 0.005226758408730007, 'hurting': 0.0019116724119796905, 'hurts': 0.002674481124809779, 'husband': 0.007607450565371921, 'husc': 0.00035791381164745114, 'husc11': 0.0012609485946591687, 'hut': 0.0007117022779896962, 'huygens': 0.0012412324256375635, 'hydra': 0.0018705330287465275, 'hydrogen': 0.004356139840040947, 'hype': 0.001300553187035633, 'hyperspace': 0.0024851616866216134, 'hypocrisy': 0.005491928440954984, 'hypocrite': 0.009179532565505865, 'hypocritical': 0.006109718166077231, 'hypothesis': 0.0021946697425983134, 'i5b': 0.0027400885069510687, 'ia': 0.001300553187035633, 'ia522b1w165w': 0.003157558429105277, 'iam': 0.002824480249077538, 'ian': 0.002031245984652503, 'iapetus': 0.0018628591633698963, 'iastate': 0.0034846651097097748, 'iau': 0.004981161405813843, 'ibm': 0.01430995754043704, 'ibm3090': 0.0025246613755867744, 'ibp': 0.0012609485946591687, 'ic': 0.0019111977739593115, 'icbm': 0.003731800431935114, 'ice': 0.002491744872418865, 'icgeb': 0.0012609485946591687, 'icol': 0.0012609485946591687, 'ics': 0.0025005225130257693, 'id': 0.006177234751342289, 'ida': 0.0031081415794665165, 'idaho': 0.005939619263124774, 'idea': 0.020860572388543434, 'ideal': 0.003230950709826981, 'ideas': 0.0025221252317892294, 'identical': 0.0016463851446558084, 'identification': 0.0021401823853150715, 'identified': 0.0009284200503372414, 'identify': 0.0025939306276366843, 'identity': 0.0027730971122120907, 'idiot': 0.0021946697425983134, 'idl': 0.0018705330287465292, 'idr': 0.003157558429105277, 'ieee': 0.0016194133460181942, 'iff': 0.006969614267041952, 'iges': 0.0012609485946591687, 'ignite': 0.0024448766353608346, 'ignorance': 0.010477939442634693, 'ignorant': 0.00549958526301975, 'ignore': 0.0033423018425821458, 'ignored': 0.001216655211329824, 'ignores': 0.00010510953103124408, 'ignoring': 0.0015649231827278712, 'ii': 0.003956655125401989, 'iii': 0.0018034472229169832, 'il': 0.0031493247836394955, 'ilbm': 0.0018924586447506718, 'ileaf': 0.0018924586447506718, 'ill': 0.0028573361544391466, 'illegal': 0.004737623048579198, 'illinois': 0.004012309381130564, 'illumination': 0.0018803995034486513, 'illusion': 0.0009559019909431317, 'illustrator': 0.004425442103239913, 'ilmenau': 0.0012609485946591687, 'ils': 0.0018705330287465275, 'im': 0.0021401823853150715, 'imag': 0.0037911514534976548, 'image': 0.03882745625258918, 'imagemagick': 0.002524661375586771, 'imager': 0.0012499951251094144, 'imagery': 0.0019907290182996293, 'images': 0.023444465045779808, 'imaginary': 0.003799150718507647, 'imagination': 0.005266028641171278, 'imagine': 0.01210057038954708, 'imaging': 0.007960138467674488, 'imaginitive': 0.003731800431935113, 'imbalance': 0.0018628591633698963, 'img': 0.0018924586447506718, 'imho': 0.0004219068622879855, 'immediate': 0.0007288627777397782, 'immediately': 0.005922298132319887, 'immoral': 0.009179532565505868, 'immorality': 0.001825425726571352, 'immortal': 0.0017855205597762545, 'immortality': 0.0012691491483781065, 'impact': 0.0056917467588402096, 'impaired': 0.0018362078142529865, 'imperfect': 0.0027400885069510687, 'imperial': 0.003359124521680611, 'implement': 0.001654018501076624, 'implementation': 0.004521300086809368, 'implementations': 0.0015744872567363078, 'implemented': 0.0029138652012718133, 'implication': 0.0036560569852768275, 'implicit': 0.0022321909792609963, 'implied': 0.004438294231295022, 'implies': 0.00549192844095498, 'implodes': 0.0024851616866216134, 'imply': 0.006411840182243063, 'import': 0.003180149347934937, 'importance': 0.004984010161537017, 'important': 0.00896827870627, 'importantly': 1.671875925648384e-05, 'imported': 0.0016738670852616978, 'impossible': 0.001153763174405715, 'impressed': 0.002118873529427862, 'impression': 0.0024363865949890897, 'impressive': 0.0017949076801095053, 'improve': 0.0022408043273308706, 'improved': 0.00040176027498384833, 'improvement': 0.0007581834358946779, 'improvements': 0.0025246613755867744, 'impulse': 0.00463738713045095, 'impulses': 0.0012717306823408032, 'inability': 0.002454726329680262, 'inaccurate': 0.0015493889696007283, 'inadequate': 0.0012808370180140277, 'inappropriate': 0.0026646314304903523, 'inaudible': 0.0012412324256375635, 'inch': 0.0016963960527636808, 'inches': 0.0025074048663414894, 'incident': 0.002544025914964133, 'inclination': 0.005606866737329385, 'inclined': 0.0017855205597762545, 'include': 0.005196155778211043, 'included': 0.003816748081288037, 'includes': 0.005376606172013713, 'including': 0.005775520485971316, 'income': 0.00216677513687181, 'incoming': 0.003143282228580879, 'incompatible': 0.0027204633494797483, 'inconsistencies': 0.0006496982395886239, 'inconsistent': 0.0018331313345243579, 'inconstant': 0.003108141579466518, 'incorporate': 0.0013113511286082574, 'incorporated': 0.0009071547463395339, 'incorrect': 0.0031517615120046248, 'increase': 0.0034179640825193758, 'increased': 0.000564685991715567, 'increases': 0.004767320359424166, 'increasing': 0.007488101498518759, 'incredible': 0.0012691491483781065, 'incredibly': 0.0019279440725522672, 'incremental': 0.004987767079217312, 'independant': 0.0027400885069510687, 'independent': 0.003967458284968337, 'index': 0.004466301732965373, 'indexes': 0.0012499951251094144, 'indexing': 0.0012609485946591687, 'india': 0.002442551229109944, 'indian': 0.0018449705137248374, 'indiana': 0.001080424547029884, 'indicate': 0.0028621580563428645, 'indicated': 0.0008317159444114998, 'indicates': 0.002544122724936592, 'indicating': 0.00034465163587258686, 'indication': 0.0036961433241503314, 'indicative': 0.0026646314304903523, 'indigo': 0.003737774831759086, 'individual': 0.005619948567146728, 'individuals': 0.003935781367463654, 'indo': 0.0015319298587311032, 'induction': 0.001825425726571352, 'inductive': 0.003962749099286717, 'industrial': 0.004775624773499352, 'industries': 0.003108141579466519, 'industry': 0.010487030503796867, 'indyvax': 0.004356139840040946, 'inerrancy': 0.0027400885069510687, 'inerrant': 0.0036560569852768267, 'inerrantist': 0.0036560569852768275, 'inerrantists': 0.00365605698527683, 'inescn': 0.002524661375586771, 'inevitable': 0.0015035858261545658, 'inexpensive': 0.00358770551919327, 'inf': 0.0025337828159839983, 'infinite': 0.0019370569109456786, 'infinitely': 0.0018891842862327687, 'infinity': 0.001958628499801428, 'inflatable': 0.012535219985229804, 'inflated': 0.0043561398400409415, 'influence': 0.0029163611570287816, 'influenced': 0.0007032382976603913, 'info': 0.015045806219357694, 'infoline': 0.001825425726571352, 'informatik': 0.005696122928293772, 'information': 0.0174694613257267, 'informatique': 0.0018924586447506718, 'informed': 0.0016264403794319657, 'infrared': 0.002844115383564488, 'infrastructure': 0.004356139840040942, 'ingr': 0.001000446050815688, 'ingres': 0.0015417795530505863, 'inherent': 0.0007032382976603913, 'inherently': 0.003348518606404581, 'iniquity': 0.004573335506731118, 'initial': 0.00289342766143985, 'initially': 0.0006251111015571457, 'initiate': 0.0028272257285699588, 'initiated': 0.0024570044961898328, 'initiating': 0.00365605698527683, 'initiation': 0.0031155095932511624, 'initiative': 0.0024851616866216125, 'injected': 0.0013262274963396362, 'injury': 0.0024448766353608346, 'inland': 0.0024851616866216125, 'inline': 0.001064042549779238, 'inner': 0.0040146369270220245, 'innocence': 0.00365605698527683, 'innocent': 0.015760521850115596, 'innovation': 0.003108141579466518, 'innovative': 0.0024851616866216134, 'input': 0.006420335706407779, 'inputs': 0.0031575584291052778, 'inqmind': 0.002485161686621608, 'inquiring': 0.0018628591633698963, 'inquiry': 0.0012808370180140277, 'inquisition': 0.0027400885069510687, 'ins': 0.01601704782509033, 'insert': 0.003083660745552869, 'inserted': 0.00010510953103124408, 'insertion': 0.0012603864489062547, 'inside': 0.0019372084228691626, 'insight': 0.0004088156733638845, 'insist': 0.001921522106299118, 'insisting': 0.0072260767885087085, 'insists': 0.0015499786042360887, 'inspector': 0.0012412324256375618, 'inspired': 0.002730329824181926, 'inst': 0.003791151453497659, 'instability': 0.0024851616866216134, 'install': 0.002925187883448647, 'installation': 0.0021324977123564626, 'installed': 0.0026693226115685363, 'instance': 0.001996133200753353, 'instances': 0.00365605698527683, 'instead': 0.006743421066874941, 'institut': 0.0015332358208003521, 'institute': 0.008952489053138842, 'institution': 0.0022953390170244335, 'institutions': 0.0016377373134914552, 'instruction': 0.0021721839313897677, 'instructions': 0.0013418265164943256, 'instrument': 0.004092697010779709, 'instrumentation': 0.0012412324256375618, 'instruments': 0.014946040631592359, 'insult': 0.00335912452168061, 'insulting': 0.0024363865949890897, 'insults': 0.0018362078142529865, 'insurance': 0.004066483700723145, 'insure': 0.003108141579466518, 'int': 0.001386662615895041, 'intact': 0.0012717306823408032, 'integer': 0.0037911514534976565, 'integrate': 0.000988318189986688, 'integrated': 0.002215535753179989, 'integration': 0.008137896161126992, 'integrity': 0.0012808370180140277, 'intel': 0.0035171055630240818, 'intellect': 0.002238344217173881, 'intellectual': 0.003246269744490323, 'intelligence': 0.008695214665549383, 'intelligent': 0.00555286119411422, 'intend': 0.0010683284815711895, 'intended': 0.003043049293382509, 'intensities': 0.0025246613755867744, 'intensity': 0.001631189417626508, 'intensive': 0.0010753398191192063, 'intent': 0.007775393704209693, 'intention': 0.0026646314304903523, 'intentionality': 0.001825425726571352, 'intentionally': 0.00365605698527683, 'inter': 0.0019016336999508757, 'interaction': 0.0007036071049306121, 'interactive': 0.007312080444002397, 'interactively': 0.002524661375586771, 'interested': 0.0031130463119258796, 'interesting': 0.006400845101578975, 'interests': 0.000929986059247003, 'interface': 0.009653295869177255, 'interfere': 0.0018452344383494239, 'interference': 0.0019546980436531153, 'intergraph': 0.000988318189986688, 'interleaf': 0.0012609485946591687, 'internal': 0.0005325715277251465, 'internally': 0.001921522106299118, 'international': 0.02105813108603658, 'internet': 0.006281120701422496, 'interplanetary': 0.006233257448747928, 'interpolation': 0.0018924586447506718, 'interpret': 0.008682637649257894, 'interpretation': 0.012916384234053266, 'interpretations': 0.007589517655519603, 'interpreted': 0.005289595373482465, 'interpreter': 0.0031575584291052778, 'interpreting': 0.0031081415794665165, 'interprets': 0.00365605698527683, 'interrupt': 0.0010753398191192063, 'intersect': 0.0022512009151189156, 'intersecting': 0.0031954450584297956, 'intersection': 0.007607418082978779, 'intersections': 0.002524661375586772, 'interstellar': 0.003731800431935114, 'interval': 0.0015626450162182998, 'intervals': 0.0024851616866216134, 'intervention': 0.0012691491483781065, 'interviews': 0.0037515837595050944, 'intriguing': 0.0024851616866216134, 'intro': 0.0019249565393640788, 'introduce': 0.0007163598861018444, 'introduced': 0.002280237915053253, 'introduction': 0.0025082625690598243, 'inu530n': 0.0012609485946591687, 'invented': 1.671875925648384e-05, 'inventor': 0.0026253213246470314, 'invest': 0.005606866737329394, 'investigate': 0.0017855205597762545, 'investigates': 0.0024448766353608346, 'investigating': 0.0009300965515126975, 'investigation': 0.001321817270076367, 'investigations': 0.00013615658743255845, 'investigator': 0.0010442927627179474, 'investigators': 0.0024851616866216134, 'investment': 0.007730797663252694, 'investments': 0.0024851616866216134, 'investor': 0.0056068667373293845, 'investors': 0.0029218756862268887, 'invisible': 0.002674481124809779, 'invitation': 0.0017855205597762545, 'invited': 0.0016661801242341696, 'invoke': 0.002467372658018935, 'invokes': 0.0025246613755867744, 'involve': 0.00017108702810196205, 'involved': 0.008248696407476474, 'involvement': 0.0018134151655027544, 'involves': 0.0033485186064045793, 'involving': 0.006010274080105501, 'io': 0.0010442927627179474, 'ion': 0.0012412324256375635, 'iota': 0.0015319298587311032, 'iowa': 0.0009393921967916297, 'ip': 0.0009559019909431317, 'ipas': 0.0018924586447506718, 'ipmce': 0.0012609485946591687, 'ipx': 0.002524661375586772, 'ir': 0.001862859163369898, 'ira': 0.0012609485946591687, 'iraf': 0.0016194133460181942, 'iran': 0.0036560569852768267, 'iranian': 0.0027400885069510687, 'iras': 0.003108141579466518, 'ireland': 0.003402150153354033, 'irfan': 0.0027400885069510696, 'iris': 0.005009025956561702, 'irit': 0.002524661375586771, 'irix': 0.002524661375586771, 'iron': 0.0022495487598267684, 'ironic': 0.0013262274963396362, 'irony': 0.0034519223629203167, 'irrational': 0.004573335506731121, 'irregular': 0.0010753398191192063, 'irrelevant': 0.008628560149391621, 'irs': 0.002161230461840069, 'irvine': 0.0015332358208003521, 'irving': 0.002130332690995644, 'isa': 0.002961107039509709, 'isaac': 0.0015527953218988713, 'isas': 0.003108141579466514, 'isbn': 0.0032951249719746986, 'islam': 0.00825563778767264, 'islamic': 0.0036560569852768267, 'island': 0.002366505987355573, 'isn': 0.014581811801195858, 'isometric': 0.0018924586447506718, 'isp': 0.009566714137740798, 'israel': 0.0038690356243874157, 'israeli': 0.0027400885069510687, 'israelites': 0.007333075149745414, 'isscck': 0.004573335506731121, 'issue': 0.010356982879011885, 'issued': 0.002503485654094817, 'issues': 0.0017996059667021317, 'isu': 0.015125766591347761, 'isunet': 0.003108141579466519, 'isy': 0.0016194133460181942, 'italian': 0.0012629530417339009, 'italy': 0.0025227919288201258, 'itc': 0.00365605698527683, 'item': 0.005617822441349089, 'items': 0.0023006529366281035, 'iterated': 0.002524661375586772, 'iti': 0.012273515821294382, 'iupui': 0.004356139840040942, 'iv': 0.002347070196225649, 'ivan': 0.0018803995034486513, 'ivem': 0.0018924586447506718, 'jack': 0.0023729044329639784, 'jacked': 0.02083321481196443, 'jackson': 0.0012609485946591687, 'jacques': 0.0012609485946591687, 'jafoust': 0.0018628591633698963, 'jagged': 0.0015417795530505863, 'jah': 0.001825425726571352, 'jahn': 0.0012412324256375618, 'james': 0.00538361633561888, 'jamie': 0.0012609485946591687, 'jan': 0.0013204183084931731, 'jane': 0.0019116724119796905, 'january': 0.001355065105758356, 'japan': 0.007403549923064667, 'japanese': 0.011170309021904717, 'jaskew': 0.0018628591633699006, 'jason': 0.002772756994226599, 'jay': 0.001047442180395112, 'jbh55289': 0.01253521998522979, 'jbis': 0.0012412324256375635, 'jbreed': 0.0018628591633698963, 'jbulf': 0.0018924586447506718, 'jburrill': 0.004573335506731118, 'jdnicoll': 0.004981161405813843, 'je': 0.009179532565505875, 'jeff': 0.0038691531154225823, 'jehovah': 0.0027400885069510687, 'jemison': 0.0043561398400409415, 'jenks': 0.006860335160339446, 'jennise': 0.0018628591633698963, 'jeremy': 0.00034465163587258686, 'jerry': 0.0021327447189448297, 'jerusalem': 0.00365605698527683, 'jesus': 0.09245436105573257, 'jet': 0.01419396219594159, 'jets': 0.002485161686621608, 'jew': 0.011959254816636749, 'jewelry': 0.003108141579466518, 'jewish': 0.023200930076301883, 'jews': 0.032723463980702576, 'jfq': 0.0025246613755867744, 'jgarland': 0.0024851616866216064, 'jgreen': 0.007222180411934991, 'jhu': 0.003933488884024312, 'jhunix': 0.0012609485946591687, 'jhwitten': 0.0018705330287465292, 'jian': 0.0012609485946591687, 'jim': 0.017896354247743353, 'jk87377': 0.002524661375586772, 'jkatz': 0.0018628591633698963, 'jmcocker': 0.0031306480206918248, 'jmeritt': 0.009179532565505875, 'joachim': 0.0037911514534976556, 'job': 0.007080051585164485, 'jobs': 0.0035348768771874548, 'jockey': 0.011901885334985419, 'joe': 0.0036647500096297636, 'joel': 0.0013371565680386924, 'joerg': 0.0012609485946591687, 'john': 0.021404068019986573, 'johns': 0.0013010267962684525, 'johnson': 0.00738464804562038, 'johnston': 0.002803279087421274, 'join': 0.008848398614234558, 'joint': 0.006649369059341399, 'joke': 0.004314947843412291, 'jolla': 0.0018250202487414676, 'jon': 0.00477534101933906, 'jonas': 0.0018924586447506718, 'jonathan': 0.0021995226876789127, 'jones': 0.0032934471961592465, 'jordan': 0.0024917448724188695, 'jose': 0.006129793191741669, 'joseph': 0.0029196651979278036, 'josephus': 0.006411840182243062, 'josh': 0.006423197212475277, 'joshua': 0.005219412151416134, 'joshuaf': 0.0012609485946591687, 'joslin': 0.015684476767576803, 'journal': 0.005798362737964144, 'journey': 0.0027773506900804767, 'jovian': 0.0043561398400409415, 'joy': 0.0037680815842055723, 'jp': 0.003786960272433238, 'jpeg': 0.012683368596961089, 'jpegs': 0.002524661375586771, 'jpg': 0.006332516444282769, 'jpl': 0.029092937129891385, 'jpw': 0.0043561398400409415, 'jr': 0.010668010394380778, 'jr0930': 0.0012609485946591687, 'jrl': 0.0025246613755867744, 'jsc': 0.01922977726807094, 'judaism': 0.00365605698527683, 'judas': 0.006411840182243065, 'judeo': 0.0027400885069510687, 'judge': 0.005778260316031163, 'judged': 0.0038332746998137324, 'judgement': 0.0026646314304903523, 'judging': 0.0026646314304903523, 'judy': 0.003108141579466512, 'juhana': 0.002524661375586772, 'jules': 0.0024851616866216134, 'july': 0.002143693137843948, 'jump': 0.003448898213830679, 'jumping': 0.00365605698527683, 'jun': 0.0010442927627179474, 'june': 0.0034333754080542976, 'junior': 0.00010510953103124408, 'junk': 0.004981161405813843, 'jupiter': 0.018426250344796228, 'jurriaan': 0.000978451715284566, 'just': 0.022418659921599197, 'justice': 0.012888523361583604, 'justification': 0.007333075149745413, 'justified': 0.0077453427197134135, 'justify': 0.007930121220867222, 'juts': 0.010104763978199337, 'jyusenkyou': 0.0036560569852768275, 'kaflowitz': 0.0064118401822430655, 'kaiser': 0.0021721839313897677, 'kalki': 0.0027400885069510687, 'kalki33': 0.001825425726571352, 'karl': 0.0021929783002878093, 'karla': 0.003731800431935113, 'karlsruhe': 0.002524661375586771, 'kathy': 0.0024851616866216134, 'katkere': 0.0012609485946591687, 'kaufman': 0.0012609485946591687, 'kb': 0.0012412324256375618, 'kc': 0.0012412324256375635, 'kcochran': 0.005491928440954983, 'kd4nc': 0.0010442927627179474, 'ke4zv': 0.005606866737329387, 'kean': 0.0024851616866216064, 'keen': 0.0002992611575469784, 'keeping': 0.005057602364141396, 'keeps': 0.003296934828596834, 'keesler': 0.0012412324256375635, 'keeve': 0.0012609485946591687, 'keith': 0.008000632255829223, 'keithley': 0.003108141579466518, 'kelly': 0.001027092726567722, 'kelso': 0.0031081415794665165, 'kelvin': 0.020696836708992992, 'ken': 0.003736772675610139, 'kendig': 0.022256499021697507, 'kennedy': 0.004494929079031584, 'kenneth': 0.005506656647861461, 'kent': 0.04606472073959805, 'keplerian': 0.003108141579466518, 'kept': 0.0016988355750339988, 'kermit': 0.001212678452377722, 'kernel': 0.0019024106766368197, 'kevin': 0.007456027029800457, 'kevxu': 0.00365605698527683, 'key': 0.00682616647011835, 'keyboard': 0.004320243993087975, 'keys': 0.0012717306823408032, 'keyword': 0.000988318189986688, 'keywords': 0.021935549034687283, 'kfu': 0.019431600557536524, 'kg': 0.006233257448747929, 'kgb': 0.0019116724119796905, 'khan': 0.0018803995034486513, 'khan0095': 0.0012609485946591687, 'khoros': 0.003791151453497654, 'khz': 0.0018628591633698963, 'kick': 0.001921522106299118, 'kid': 0.0034617720572396897, 'kidding': 0.0013262274963396362, 'kids': 0.005236813766781592, 'kih': 0.004425442103239915, 'kill': 0.013573931656717227, 'killed': 0.019645009287790602, 'killing': 0.012016627481916634, 'kills': 0.011646626427650679, 'kilograms': 0.002485161686621608, 'kilometers': 0.003731800431935115, 'kilroy': 0.003064999644937951, 'kim': 0.0022062748258370284, 'kind': 0.003751756862730356, 'kinda': 0.0031470945968012946, 'kinds': 0.003443308556818331, 'king': 0.011156339415229932, 'kingdom': 0.008707078711674546, 'kings': 0.006411840182243067, 'kipling': 0.01762736761841005, 'kirk': 0.0015744872567363078, 'kit': 0.0025114946594801575, 'kits': 0.0018628591633698963, 'kitt': 0.0012629530417339009, 'kjenks': 0.008116558095880504, 'klaes': 0.0012412324256375635, 'kleros': 0.001825425726571352, 'km': 0.01635006172935829, 'kmembry': 0.0012609485946591687, 'kmr4': 0.005491928440954983, 'knell': 0.0012412324256375635, 'knew': 0.003688668018247897, 'knies': 0.004573335506731118, 'knight': 0.0007036071049306121, 'knives': 0.004573335506731118, 'knock': 0.009805506501867157, 'know': 0.0173011670238833, 'knowing': 0.0038839695555037924, 'knowledge': 0.015296477715502018, 'known': 0.0077095869003937605, 'knows': 0.0022767831291265785, 'knox': 0.0018628591633699006, 'koeln': 0.0012609485946591687, 'kong': 0.0018705330287465292, 'kongsberg': 0.002524661375586772, 'koran': 0.0027400885069510687, 'korea': 0.0025114946594801575, 'koresh': 0.04044622847727712, 'kotfr': 0.0024851616866216134, 'kouhia': 0.002524661375586772, 'kourou': 0.0024851616866216125, 'kpc': 0.003157558429105275, 'kr': 0.0018924586447506718, 'krasel': 0.001825425726571352, 'krishna': 0.0027400885069510687, 'kriz': 0.0073330751497454084, 'krumins': 0.0031081415794665165, 'ks': 0.0025631995326679882, 'ksand': 0.026992776426506576, 'ksc': 0.004981161405813842, 'ksr': 0.002485161686621608, 'kt': 0.002152467762368218, 'kth': 0.000988318189986688, 'ktj': 0.0012412324256375635, 'ku': 0.0007163598861018444, 'kubota': 0.004425442103239916, 'kuiper': 0.004356139840040942, 'kuo': 0.0006398485452691399, 'kw': 0.0012412324256375635, 'kyanko': 0.003157558429105275, 'kyle': 0.005191540929971685, 'kyoto': 0.0012499951251094144, 'la': 0.0016171098597595277, 'lab': 0.019787415757708135, 'laboratoire': 0.0012609485946591687, 'laboratories': 0.002332493875067958, 'laboratory': 0.015336841551248141, 'labs': 0.004414493526742409, 'labtam': 0.0012609485946591687, 'lack': 0.006585517564047593, 'lacking': 0.0027400885069510687, 'lacks': 0.0018250202487414676, 'lady': 0.006423094134181066, 'laid': 0.0024337964176860604, 'lake': 0.0026030612159438585, 'lakes': 0.003064999644937951, 'laking': 0.0018628591633698963, 'lamb': 0.005591611525152398, 'lamont': 0.0032151755627445704, 'lance': 0.0034338358417605273, 'land': 0.010100469688360491, 'landed': 0.0033256832965099592, 'lander': 0.0024851616866216125, 'landers': 0.0012412324256375635, 'landing': 0.024057213141819415, 'landings': 0.003868350055479919, 'landis': 0.0012412324256375618, 'landreneau': 0.001825425726571352, 'lands': 0.0015527953218988713, 'landsat': 0.0033777206714367854, 'landscape': 0.0012827028287951915, 'lane': 0.0013649484181175245, 'langley': 0.009375548629619139, 'language': 0.003848232965378208, 'languages': 0.002332493875067958, 'lanph872': 0.0036560569852768275, 'lanphier': 0.004573335506731121, 'laplacian': 0.0012609485946591687, 'larc': 0.006379914127526228, 'large': 0.023612708234890367, 'largely': 0.002804664754088184, 'larger': 0.009404090193608175, 'largest': 0.0018360024716489601, 'larrison': 0.004981161405813851, 'larry': 0.00426705981144742, 'lars': 0.0012609485946591687, 'larson': 0.0012412324256375635, 'laser': 0.002968905662021036, 'laserjet': 0.0018924586447506718, 'lasers': 0.0024851616866216125, 'late': 0.003226474501053905, 'later': 0.006274012052105399, 'latest': 0.00453237342065821, 'latin': 0.0012808370180140277, 'latitude': 0.0026253213246470314, 'laugh': 0.0033872766438555876, 'launch': 0.05988217938744486, 'launched': 0.0150605245269753, 'launcher': 0.01126925254787877, 'launchers': 0.004881962623000547, 'launches': 0.013169258181841666, 'launching': 0.005606866737329385, 'law': 0.01934207600523319, 'lawrence': 0.0006750392740673987, 'laws': 0.0135112755509555, 'lawson': 0.004356139840040942, 'laxman': 0.0018628591633698963, 'lay': 0.007417195184997675, 'layed': 0.00365605698527683, 'layer': 0.004666811736945867, 'layne': 0.0024851616866216125, 'layout': 0.00504281586153074, 'lb': 0.003108141579466518, 'lbh': 0.001825425726571352, 'lbl': 0.0018991386326573457, 'lbs': 0.0018628591633698963, 'lcii': 0.0025246613755867744, 'lcs': 0.0020551071491527262, 'lds': 0.012703414215628775, 'lead': 0.004115725166754556, 'leader': 0.00731222463935797, 'leaders': 0.008700208071738586, 'leadership': 0.0043739473277093184, 'leading': 0.003742888537508217, 'leads': 0.00026944467616753925, 'league': 0.0012603864489062547, 'leak': 0.0024851616866216134, 'leap': 0.0026573399917276495, 'learn': 0.0015065690152853495, 'learned': 0.00638819827107694, 'learning': 0.0026263410852709014, 'leasing': 0.003731800431935113, 'leave': 0.0009091075904455598, 'leaves': 0.0010052248362037485, 'leaving': 0.002142553112782955, 'lebanon': 0.001825425726571352, 'lectorium': 0.00365605698527683, 'led': 0.006467298755091803, 'ledges': 0.001825425726571352, 'lee': 0.013325840655469191, 'leech': 0.010637319947130214, 'left': 0.004086361249772403, 'legal': 0.0032965828173975335, 'legalize': 0.00365605698527683, 'legend': 0.0012895997174858778, 'legislation': 0.0033193706158301155, 'legislative': 0.0012412324256375635, 'legit': 0.0019116724119796905, 'legitimate': 0.0017855205597762545, 'leicester': 0.00365605698527683, 'leigh': 0.0037318004319351165, 'lem': 0.000978451715284566, 'length': 0.0036885539308582843, 'leo': 0.010688261989724508, 'lerc': 0.006312512205305228, 'leroy': 0.0027400885069510687, 'lesbian': 0.0027400885069510687, 'lesbians': 0.0027400885069510687, 'lesson': 0.0033528339885715774, 'lessons': 0.0018579592253753089, 'lest': 0.0012808370180140277, 'let': 0.014256282814482688, 'lets': 0.001610347310392059, 'letter': 0.006729858621625122, 'letters': 0.0025209183478641685, 'letting': 0.0003753054210443446, 'lev': 0.0021729183314759893, 'level': 0.0070426932842508425, 'levels': 0.006512521962844367, 'levine': 0.0007163598861018444, 'leviticus': 0.005491928440954984, 'levy': 0.003108141579466512, 'lewb': 0.001825425726571352, 'lewis': 0.004206365619569672, 'lewisville': 0.003731800431935113, 'lex': 0.0012609485946591687, 'lexicon': 0.0027400885069510687, 'lga': 0.0024851616866216064, 'lh': 0.0024851616866216125, 'lha': 0.0012609485946591687, 'liar': 0.0034519223629203167, 'lib': 0.003659118058841365, 'liberal': 0.0036560569852768275, 'libertarian': 0.0013558269777203544, 'liberty': 0.0018452344383494239, 'libraries': 0.0072508839678365605, 'library': 0.019004203517922383, 'librba': 0.001825425726571352, 'licence': 0.0015744872567363078, 'license': 0.002003702284851679, 'licensed': 0.0012827028287951915, 'licenses': 0.0013010267962684525, 'licensing': 0.0016958301188799586, 'lick': 0.004356139840040938, 'lid': 0.0012412324256375635, 'lie': 0.008763402840768174, 'lied': 0.002674481124809779, 'liek': 0.006233257448747934, 'lies': 0.008562706912841531, 'life': 0.028533651658663766, 'lifestyle': 0.006411840182243067, 'lifetime': 0.0018628591633698963, 'lift': 0.0031637118092140626, 'lifter': 0.0024851616866216134, 'liftoff': 0.006233257448747934, 'light': 0.015560843967474817, 'lighter': 0.0013224838249004927, 'lighting': 0.0012717306823408032, 'lightning': 0.0024851616866216134, 'lights': 0.003731800431935113, 'lightwave': 0.0012609485946591687, 'liguori': 0.008745706591231327, 'like': 0.0168788828367166, 'liked': 0.001520379122855315, 'likelihood': 0.0010983486352568418, 'likely': 0.008463184501117826, 'likes': 0.005038290998743198, 'lille': 0.0012609485946591687, 'limb': 0.002152467762368218, 'limit': 0.0030773055369859564, 'limited': 0.005099148121942783, 'limits': 0.0014816125047449214, 'lincoln': 0.00039751840402391624, 'lindbergh': 0.003731800431935108, 'lindblat': 0.0012609485946591687, 'line': 0.010227940358762002, 'linear': 0.0046705306586475905, 'lined': 0.0012691491483781056, 'lineup': 0.002561570375518963, 'link': 0.0011919118348989568, 'linked': 0.0012499951251094144, 'links': 0.0009948550082779098, 'linux': 0.005060432039124049, 'lipman': 0.0012609485946591687, 'lippard': 0.001825425726571352, 'liquid': 0.010006085862371745, 'lis': 0.0033689742160000384, 'lisa': 0.0012779397650279313, 'lisp': 0.000988318189986688, 'list': 0.009168492088911465, 'listed': 0.000867137964114301, 'listen': 0.002325046627523151, 'listened': 0.0012603864489062547, 'listening': 0.0024363865949890897, 'listing': 0.002585635864942218, 'listings': 0.0018803995034486513, 'lists': 0.0032382206606478307, 'listserv': 0.0019104359019973148, 'lit': 0.0018331313345243579, 'lite': 0.0025246613755867744, 'literal': 0.0027400885069510687, 'literalists': 0.00365605698527683, 'literally': 0.00370529825191548, 'literary': 0.0045733355067311176, 'literature': 0.003037119454345571, 'little': 0.006429767935448478, 'liu': 0.0018924586447506718, 'live': 0.020614285870924443, 'lived': 0.0058727526273997036, 'livermore': 0.006860335160339435, 'lives': 0.010310772039558283, 'livesey': 0.005491928440954983, 'living': 0.010703022529937854, 'lizard': 0.0036560569852768275, 'll': 0.00473590445713299, 'llnl': 0.0029174877819974805, 'llullaillaco': 0.002524661375586771, 'lm': 0.0024448766353608346, 'lo': 0.003108141579466518, 'load': 0.005446040103637866, 'loaded': 0.001027092726567722, 'loading': 0.003143282228580878, 'loads': 0.003770884744990515, 'loan': 0.0015448877753555896, 'local': 0.00613375597204978, 'locally': 0.0021525282388884385, 'locate': 0.0018875891446770519, 'located': 0.0017539362021883782, 'locating': 0.0010442927627179474, 'location': 0.0031446506134299324, 'locations': 0.003161685997468895, 'lock': 0.0027285530523395362, 'lockheed': 0.0035571857838797693, 'locus': 0.001909307565327506, 'lodge': 0.004573335506731118, 'lodges': 0.001825425726571352, 'loether': 0.001825425726571352, 'log': 0.010011528914982203, 'logic': 0.006170499420812147, 'logical': 0.003708807215912666, 'login': 0.0029082841412076416, 'logo': 0.0018628591633698963, 'logos': 0.0012499951251094144, 'london': 0.0033598436449106886, 'lonestar': 0.002899315837901778, 'long': 0.03238562425890639, 'longer': 0.0048963045310449664, 'longitude': 0.0016738670852616978, 'look': 0.005109193813425231, 'looked': 0.0027409893034521446, 'looking': 0.025285468704256145, 'looks': 0.0016578359062183945, 'lookup': 0.0012609485946591687, 'loop': 0.0023235169840191998, 'loops': 0.00034465163587258686, 'lord': 0.026149305337288313, 'lords': 0.00365605698527683, 'los': 0.003383564578074024, 'lose': 0.004063400667123651, 'losing': 0.00011497600573342169, 'loss': 0.011054248236803114, 'losses': 0.0018628591633698963, 'lossless': 0.000988318189986688, 'lost': 0.0034107125751665582, 'lot': 0.0026816398008007065, 'lots': 0.0036745034146758275, 'loud': 0.0024363865949890897, 'louis': 0.0001719679855335752, 'louisiana': 0.006233257448747934, 'lous': 0.003791151453497659, 'lousy': 0.0004088156733638845, 'love': 0.021880938888484358, 'loved': 0.00553311140705293, 'lovely': 0.001300553187035633, 'lover': 0.001825425726571352, 'lovers': 0.0019229696813196587, 'loves': 0.009636213018632074, 'loving': 0.025469206623518103, 'low': 0.014720351910383251, 'lowell': 0.003083923316132316, 'lower': 0.0029785909258575032, 'lowest': 0.0027694904740597267, 'lox': 0.006233257448747928, 'lpl': 0.016996509120754608, 'lpr': 0.0018924586447506718, 'lps': 0.0012412324256375618, 'lucas': 0.0037911514534976548, 'lucifer': 0.004573335506731121, 'luck': 0.0009567851509717897, 'lucky': 0.0007259062129681476, 'luis': 0.0031403962761163686, 'luke': 0.006911846434519768, 'luna': 0.003108141579466514, 'lunar': 0.04012432370765081, 'lunatics': 0.0024851616866216064, 'lunch': 0.0016963960527636808, 'lungs': 0.0012603864489062547, 'lusardi': 0.0012609485946591687, 'lust': 0.001825425726571352, 'luther': 0.0027400885069510687, 'lutz': 0.0012609485946591687, 'lyall': 0.003791151453497659, 'lying': 0.0031499522485351726, 'lynx': 0.0007229880847217382, 'm23364': 0.010104763978199333, 'ma': 0.003464248860138453, 'mac': 0.021176436211726466, 'mach': 0.0025669985123143698, 'machbanding': 0.0012609485946591687, 'machine': 0.007135828096930336, 'machines': 0.006306598134482609, 'macinteresteds': 0.0037318004319351165, 'macintosh': 0.005445841639035284, 'macs': 0.002524661375586772, 'mad': 0.0010442927627179474, 'madam': 0.008116558095880515, 'madison': 0.0006251111015571457, 'mae': 0.0024851616866216134, 'mag': 0.0013371565680386924, 'magazine': 0.0019069722095020809, 'magazines': 0.0010209765593575167, 'magellan': 0.01030024739338236, 'magi': 0.001825425726571352, 'magic': 0.004685795234141157, 'magical': 0.004573335506731121, 'magick': 0.009387839153151596, 'magnetic': 0.0044936388816965425, 'magnetometer': 0.002485161686621608, 'magnetosphere': 0.0012412324256375618, 'magnitude': 0.0010839471710155837, 'magnus': 0.0019111977739593115, 'mahler': 0.010637319947130235, 'mail': 0.013649764402800644, 'mailed': 9.215269075613097e-05, 'mailer': 0.004527204939744681, 'mailing': 0.003884042728689723, 'maimone': 0.0018628591633698963, 'main': 0.00381199664315788, 'mainly': 0.0024735408775392086, 'mainstream': 0.0029499560858236764, 'maintain': 0.0032946377033488622, 'maintained': 0.002169354523665773, 'maintaining': 0.0006407749850592991, 'maintains': 0.0010442927627179474, 'maintech': 0.0027400885069510687, 'maintenance': 0.0007346838535750499, 'major': 0.007144742771740515, 'majority': 0.01073141232736943, 'make': 0.017515913746444053, 'makela': 0.0012412324256375618, 'maker': 0.00036440142293393384, 'makes': 0.004257089733543895, 'making': 0.004697469647137658, 'malcolm': 0.01904332616542296, 'male': 0.004370099599025862, 'maliable': 0.00365605698527683, 'man': 0.0257904468300141, 'managed': 0.003078883822096058, 'management': 0.007393881567130455, 'manager': 0.006375851057087376, 'managers': 0.003731800431935113, 'manchester': 0.0031575584291052743, 'mancus': 0.002485161686621608, 'maneuver': 0.0024851616866216125, 'maneuvering': 0.004356139840040943, 'maneuvers': 0.004356139840040942, 'manifest': 0.004524529669456534, 'manifests': 0.0013262274963396362, 'manipulate': 0.002164572279005953, 'manipulating': 0.004425442103239911, 'manipulation': 0.004532517940014529, 'manipulator': 0.001862859163369898, 'mankato': 0.0012412324256375635, 'mankind': 0.004043668646930992, 'manned': 0.01698835691761831, 'manner': 0.0020839454560776186, 'mantis': 0.006411840182243065, 'manual': 0.006484418701604403, 'manually': 0.001064042549779238, 'manuals': 0.0025246613755867744, 'manufactured': 8.088279674783698e-05, 'manufacturers': 0.0019784120197450395, 'manufacturing': 0.0022282044564231416, 'manuscripts': 0.0027400885069510687, 'map': 0.007790642903392487, 'maple': 0.0025626053206787725, 'mapped': 0.0029680522607431906, 'mapping': 0.005775894158844779, 'maps': 0.004202181904062089, 'mar': 0.002393114620802937, 'marble': 0.0013558269777203544, 'marc': 0.003937770994470587, 'march': 0.003314854792735699, 'marching': 0.0019784120197450395, 'marco': 0.002533782815983999, 'marcus': 0.003108141579466519, 'margin': 0.004981161405813843, 'margoli': 0.001825425726571352, 'margolis': 0.001825425726571352, 'mariner': 0.001862859163369898, 'mark': 0.008506844261247051, 'markc': 0.002524661375586772, 'marked': 0.001586166555485608, 'market': 0.007160390814706468, 'marketed': 0.0007163598861018444, 'marketing': 0.004732165205358781, 'markets': 0.000978451715284566, 'marks': 0.0012852074653554209, 'markus': 0.0018924586447506718, 'married': 0.0009300965515126975, 'mars': 0.022616903889508884, 'marsh': 0.0028370754228893864, 'marshall': 0.0027381236550937, 'martian': 0.006860335160339441, 'martin': 0.0048774671255958, 'marvin': 0.0031136322339350916, 'mary': 0.013526043844085331, 'maryland': 0.007913555528625438, 'mask': 0.0015499786042360887, 'masking': 0.002524661375586772, 'mason': 0.0024448766353608346, 'masonic': 0.007333075149745416, 'masonry': 0.001825425726571352, 'masons': 0.0027400885069510687, 'mass': 0.01243181492818679, 'massachusetts': 0.002697700878012823, 'masses': 0.0015493889696007283, 'massive': 0.004981161405813843, 'master': 0.0037570193840903883, 'mastercard': 0.0018628591633698963, 'masters': 0.0027285530523395362, 'mat': 0.0045733355067311176, 'match': 0.004058674443072306, 'material': 0.005682535435148831, 'materials': 0.006494713954127577, 'math': 0.0035994684523501406, 'math9': 0.0018628591633698963, 'mathematical': 0.00293534657492018, 'mathematics': 0.0026032628090878443, 'mathematik': 0.002491744872418865, 'mathew': 0.007333075149745415, 'maths': 0.002689455576482807, 'matloff': 0.0024851616866216125, 'matrix': 0.003157558429105275, 'matrox': 0.0031575584291052778, 'matt': 0.002515398606515073, 'matter': 0.014089514963274642, 'matters': 0.0064883479674951545, 'matthew': 0.013402860996855306, 'maturity': 0.003108141579466519, 'maureen': 0.003157558429105275, 'max': 0.00148411885613319, 'maximize': 0.00010510953103124408, 'maximum': 0.00432411384506003, 'maximus': 0.003731800431935113, 'mayans': 0.006233257448747934, 'maybe': 0.00954910557109315, 'mazda': 0.001825425726571352, 'mb': 0.0032119602960755207, 'mbc': 0.0012609485946591687, 'mcaloon': 0.004356139840040938, 'mcc': 0.001914490397895912, 'mccall': 0.016988356917618304, 'mcconkie': 0.0036560569852768275, 'mccreary': 0.0006398485452691399, 'mcdonnell': 0.00623325744874793, 'mcdowell': 0.0024564372929426178, 'mcelwaine': 0.0030313281772180066, 'mcgill': 0.0018803995034486513, 'mcgwier': 0.0012412324256375618, 'mchp': 0.01568447676757681, 'mckissock': 0.004981161405813842, 'mclean': 0.0034519223629203167, 'mcluhan': 0.0012609485946591687, 'mcmains': 0.005696122928293773, 'mcs': 0.00506043203912405, 'mcsun': 0.0022062748258370284, 'mcwilliams': 0.004981161405813842, 'md': 0.0035349371691990794, 'mdata': 0.0012609485946591687, 'mdc': 0.003731800431935114, 'meal': 0.0036560569852768275, 'mean': 0.024879239086626634, 'meaning': 0.021180642514149993, 'meaningful': 0.003187567385637969, 'meaningless': 0.0018265222535953085, 'meanings': 0.0027400885069510687, 'means': 0.012065142535980802, 'meant': 0.004586464735611003, 'meantime': 0.001064042549779238, 'measure': 0.0029604218248104512, 'measured': 0.002825056729137315, 'measurement': 0.0016670629976400135, 'measurements': 0.002607330901113605, 'measures': 0.0016840886619538323, 'mechanical': 0.0013598921843151496, 'mechanics': 0.0024337964176860604, 'mechanism': 0.0047559369186626925, 'mechanisms': 0.0015525616407321653, 'med': 0.0022062748258370284, 'media': 0.0032480509959163318, 'median': 0.0021721839313897677, 'medical': 0.004455034524561654, 'medicine': 0.0016686368261328317, 'medium': 0.0015345839077072912, 'medtronic': 0.0027400885069510687, 'meet': 0.0017051692361448904, 'meeting': 0.0016557271862049942, 'meetings': 0.0012412324256375635, 'meets': 0.000978451715284566, 'meg': 0.0031575584291052778, 'mega': 0.0032258908537603926, 'megs': 0.0037911514534976565, 'melbourne': 0.0031597949289782316, 'mellon': 0.004985529823494779, 'member': 0.00594074870669145, 'members': 0.015147204694337382, 'membership': 0.004486663636334091, 'memorial': 0.00034465163587258686, 'memory': 0.006137953340489687, 'men': 0.01853864811899948, 'mental': 0.01288852336158361, 'mention': 0.003330517623631536, 'mentioned': 0.006462698756910209, 'mentions': 0.0036560569852768267, 'mentor': 0.002593063859137292, 'mentorg': 0.0018628591633698963, 'menu': 0.006419986606521075, 'menus': 0.0025246613755867744, 'merciful': 0.005491928440954982, 'mercury': 0.0043355688124445445, 'mercy': 0.003474863246163848, 'mere': 0.00365605698527683, 'merely': 0.008028717143161265, 'meridian': 0.003731800431935113, 'merit': 0.0009300965515126975, 'meritt': 0.013819146780228077, 'merlin': 0.009768545980219881, 'merlyn': 0.0036560569852768275, 'mesh': 0.0031575584291052743, 'mess': 0.001300553187035633, 'message': 0.012458234858275075, 'messages': 0.0015643688825842652, 'messenger': 0.007333075149745414, 'messiah': 0.007333075149745417, 'messianic': 0.0027400885069510687, 'met': 0.0034096431385651337, 'meta': 0.0015499786042360887, 'metal': 0.003108141579466519, 'metallic': 0.0012717306823408032, 'metaphysical': 0.001825425726571352, 'meteor': 0.003108141579466518, 'meter': 0.002216599560448892, 'meters': 0.005546277321773346, 'method': 0.00724098249508737, 'methodists': 0.0027400885069510687, 'methodology': 0.0019965781299750842, 'methods': 0.0009360369164278549, 'metric': 0.004356139840040942, 'mexico': 0.0007844713659154118, 'mfltd': 0.0018924586447506718, 'mfocus': 0.0018924586447506718, 'mhd': 0.0006398485452691399, 'mhz': 0.003861382716047486, 'mi': 0.002001010052587849, 'mice': 0.0015319298587311032, 'michael': 0.012998432286662101, 'michigan': 0.002460905220084235, 'micro': 0.004830283785764572, 'microgravity': 0.003108141579466518, 'microscopy': 0.001987614546821075, 'microsoft': 0.013682238919359315, 'microware': 0.0012609485946591687, 'microwave': 0.004356139840040946, 'mid': 0.01126925254787875, 'middle': 0.006680155960782995, 'midway': 0.003287870858766877, 'midwest': 0.0024851616866216134, 'mieux': 0.009179532565505875, 'mig': 0.003108141579466519, 'mighty': 0.0019546980436531153, 'mik': 0.002524661375586771, 'mike': 0.0022674530678029265, 'mikelson': 0.0012609485946591687, 'mil': 0.008371864034426978, 'mile': 0.010252086926532105, 'miles': 0.002307891321620647, 'military': 0.019240397660908123, 'millenia': 0.0027400885069510687, 'millennium': 0.0015417795530505863, 'million': 0.012539417224273403, 'millions': 0.001618471744492654, 'milliseconds': 0.0010442927627179474, 'milo': 0.001825425726571352, 'milton': 0.0018250202487414676, 'mimi': 0.0024851616866216134, 'min': 0.000976843714910633, 'mind': 0.00753194495194596, 'mindlink': 0.0010103293631748564, 'minds': 0.0023106613085256906, 'miner': 0.0056068667373293845, 'mineral': 0.0056068667373293845, 'minerals': 0.003731800431935115, 'miners': 0.003108141579466518, 'mines': 0.003135992489550251, 'mini': 0.0016958301188799586, 'minimal': 0.0010438413381664092, 'minimum': 0.0020369752822633064, 'mining': 0.01284046594433667, 'ministry': 0.008875518877860807, 'minnesota': 0.001064042549779238, 'minor': 0.0014337778254824842, 'minority': 0.00428074430412276, 'minute': 0.0012720682566177196, 'minutes': 0.007848818265958159, 'mips': 0.0037911514534976565, 'mir': 0.005119612818057788, 'miracles': 0.005427137065355771, 'miraculous': 0.0019116724119796905, 'mirage': 0.0018924586447506718, 'mirror': 0.0023907635432518035, 'mirrored': 0.0012609485946591687, 'mirrors': 0.0030025183455569078, 'misc': 0.004952204576085577, 'misconception': 0.0003091276322491551, 'miserable': 0.0027400885069510687, 'misrepresentation': 0.00365605698527683, 'miss': 0.00021074702514795735, 'missed': 0.003961044516461966, 'missile': 0.0039050360216904244, 'missiles': 0.004356139840040942, 'missing': 0.003438279208204236, 'mission': 0.02401706740247906, 'missions': 0.016942431734664795, 'missle': 0.0024851616866216134, 'missouri': 0.0018452344383494239, 'mistake': 0.008827112795453812, 'mistakes': 0.004370099599025862, 'misunderstand': 0.0015499786042360887, 'misunderstanding': 0.0019116724119796905, 'mit': 0.005494484004888826, 'mitch': 0.003754571461966229, 'mithraist': 0.00365605698527683, 'mithras': 0.010104763978199333, 'mitre': 0.01849274981504731, 'mits': 0.0012609485946591687, 'mitsubishi': 0.000988318189986688, 'mix': 0.0022377685504675632, 'mixed': 0.0009600453048841653, 'mixture': 0.0034818660142473543, 'miya': 0.0012629530417339009, 'mksol': 0.016988356917618297, 'ml': 0.0006604803272702029, 'mlee': 0.01803270896045355, 'mls': 0.0036560569852768267, 'mm': 0.0024917448724188695, 'mmc': 0.0027813534714171296, 'mn': 0.001921522106299118, 'mnemonics': 0.0018628591633698963, 'mnemosyne': 0.0030242362814067725, 'mo': 0.001321488617625875, 'mob': 0.0027400885069510687, 'mobile': 0.003731800431935114, 'mode': 0.011459768634633506, 'model': 0.007291164122346854, 'modeler': 0.0012609485946591687, 'modeling': 0.00457046666665073, 'modelling': 0.001347039880397861, 'models': 0.005211076930810104, 'modem': 0.003254754224239876, 'moderated': 0.0012412324256375635, 'modern': 0.009761368005089881, 'modes': 0.012996101131214629, 'modest': 0.0019965781299750842, 'modified': 0.0043373295224571505, 'modify': 0.0015231103901839687, 'modular': 0.002844115383564492, 'module': 0.007849198771564425, 'modules': 0.0032493109618079363, 'moffett': 0.0018628591633698963, 'mogal': 0.0012609485946591687, 'mohammad': 0.0018924586447506718, 'mohney': 0.008116558095880515, 'moins': 0.009179532565505875, 'mojo': 0.008116558095880508, 'molecular': 0.003203414591032262, 'molecules': 0.0019024106766368197, 'moment': 0.0013371251568549411, 'moments': 0.0029499560858236764, 'momentum': 0.0035256794592214554, 'mon': 0.00036440142293393384, 'monash': 0.002542985343060032, 'monday': 0.0022662066321295807, 'money': 0.01865372006048939, 'monitor': 0.005773212589020449, 'monitoring': 0.000978451715284566, 'monitors': 0.0031772710004690126, 'monkey': 0.0013558269777203544, 'mono': 0.0018924586447506718, 'montana': 0.0015525616407321653, 'month': 0.003914433435885266, 'monthly': 0.005606866737329385, 'months': 0.002707084587578068, 'montreal': 0.0016958301188799586, 'monty': 0.0012629530417339009, 'moon': 0.06497778107255724, 'moonbase': 0.014439451979546158, 'moons': 0.003108141579466519, 'moore': 0.0018705330287465292, 'moral': 0.027040721475013126, 'morality': 0.05023510439412315, 'morally': 0.004573335506731121, 'morals': 0.007333075149745417, 'moratorium': 0.0024851616866216134, 'morgan': 0.0024448766353608346, 'morgoth': 0.01010476397819933, 'morley': 0.0012609485946591687, 'mormon': 0.010104763978199326, 'mormons': 0.021313470328843204, 'morning': 0.008486173412915504, 'morphing': 0.005696122928293773, 'morphological': 0.0012609485946591687, 'morphology': 0.0021721839313897677, 'morris': 0.0013262274963396362, 'morrison': 0.0033689742160000384, 'moscom': 0.0025246613755867744, 'moscow': 0.002536280097565913, 'moses': 0.006411840182243063, 'moslem': 0.0027400885069510687, 'mot': 0.009999434632071197, 'mother': 0.00764201923856012, 'mothers': 0.005491928440954984, 'motif': 0.0072404251142656854, 'motifs': 0.0027400885069510687, 'motion': 0.0072654215351465636, 'motions': 0.0018628591633698963, 'motivated': 0.0007018517160113221, 'motive': 0.00365605698527683, 'motives': 0.0015527953218988713, 'motor': 0.005606866737329392, 'motorola': 0.004690278716467899, 'motors': 0.0036683538927684226, 'motto': 0.00365605698527683, 'mount': 0.003581494522191157, 'mountain': 0.0018228690019161421, 'mountains': 0.0003474108153178439, 'mounted': 0.0025074048663414894, 'mouse': 0.00614537234785446, 'mouth': 0.0018134151655027544, 'moved': 0.00032422826632379047, 'movement': 0.0027204633494797483, 'moves': 0.00023053054509156873, 'movie': 0.0030070125447859523, 'movies': 0.0034952528936401045, 'moving': 0.0019513823205328483, 'mp': 0.0037911514534976565, 'mpeg': 0.006969614267041958, 'mpeg_play': 0.0012609485946591687, 'mpg': 0.002561570375518963, 'mr': 0.024655492239614975, 'mrcnext': 0.0028370754228893864, 'mrs': 0.0026646314304903523, 'ms': 0.015370205089561504, 'msb': 0.005606866737329394, 'mscrap': 0.0012609485946591687, 'msdos': 0.007407693884057687, 'msfc': 0.005746273484484845, 'msk': 0.0018924586447506718, 'mss': 0.0012691491483781065, 'msstate': 0.002524661375586771, 'msu': 0.004205627565133461, 'msus': 0.0012603864489062547, 'mt': 0.0021693545236657723, 'mtechca': 0.0027400885069510696, 'mtv': 0.002524661375586772, 'mu': 0.002178132164272731, 'muchado': 0.005696122928293773, 'mudpuppy': 0.0010442927627179474, 'muenchen': 0.003791151453497654, 'muhammad': 0.004573335506731118, 'multi': 0.007096227141934902, 'multimedia': 0.00888515047250675, 'multiple': 0.004197474374765026, 'multiply': 0.0018924586447506718, 'multiprocessor': 0.002524661375586772, 'multiverse': 0.0031575584291052778, 'mun': 0.0018848404032501213, 'muniz': 0.0024851616866216134, 'munizb': 0.003731800431935112, 'murder': 0.008255637787672646, 'murdered': 0.00457333550673112, 'murdoch': 0.0015493889696007283, 'murmurs': 0.0024851616866216134, 'murphy': 0.0012801026179278053, 'murray': 0.0010683241754483406, 'museum': 0.003924872936382684, 'museums': 0.0018628591633698963, 'music': 0.0002245071894232762, 'muslim': 0.0036560569852768275, 'muslims': 0.008255637787672646, 'muttiah': 0.001825425726571352, 'mv': 0.0021721839313897677, 'mwm': 0.0018628591633698963, 'mwunix': 0.01010476397819933, 'mylar': 0.003731800431935113, 'mysteries': 0.003889340680750081, 'mystery': 0.0014541007597167173, 'mystical': 0.0036560569852768275, 'myth': 0.005491928440954982, 'mz': 0.0025246613755867744, 'n020ba': 0.0018924586447506718, 'n109': 0.004356139840040938, 'n2': 0.0012499951251094144, 'n4hy': 0.0012412324256375618, 'na': 0.0018858290260531044, 'nada': 0.000988318189986688, 'nagasiva': 0.01010476397819933, 'naive': 0.0034519223629203167, 'naked': 0.0036560569852768275, 'named': 0.0016557271862049942, 'names': 0.0013242023203587925, 'nanderso': 0.0024851616866216125, 'naplps': 0.0012609485946591687, 'narrow': 0.0031517615120046248, 'nas': 0.0027724937929534833, 'nasa': 0.11146392824624819, 'nasda': 0.004356139840040942, 'nashville': 0.0037318004319351165, 'nasm': 0.0024851616866216064, 'nasp': 0.003731800431935112, 'nasty': 0.0024377731766381597, 'nathan': 0.0018628591633699006, 'nation': 0.007491150178748031, 'national': 0.01736704255495801, 'nations': 0.005712038638915693, 'native': 0.0015035858261545658, 'natural': 0.00447667421260611, 'naturally': 0.0013528198191084034, 'nature': 0.007402979813964935, 'naval': 0.0031421342395136246, 'navigation': 0.006649369059341399, 'navstar': 0.003108141579466519, 'navy': 0.0056730339965237854, 'nazi': 0.0045733355067311176, 'nazis': 0.006411840182243062, 'nb': 0.003998548538543844, 'nc': 0.001987614546821075, 'ncar': 0.0018925273642776512, 'ncr': 0.0040752388134661, 'ncsa': 0.0031575584291052743, 'ncsu': 0.0026476614560085815, 'ne': 0.00890476931562081, 'neal': 0.0019093075653275069, 'near': 0.008257900398240352, 'nearby': 0.002844115383564493, 'nearest': 0.0013993173664014775, 'nearly': 0.0006536996592159368, 'neat': 0.0003169165451494156, 'neatly': 0.0002992611575469784, 'nebraska': 0.0003091276322491551, 'necessarily': 0.003355341198090411, 'necessary': 0.002844262007685985, 'need': 0.017919101249866926, 'needed': 0.003698694630882112, 'needle': 0.0024851616866216134, 'needs': 0.0017335914401212307, 'negative': 0.003352200140577627, 'negligible': 0.0024851616866216134, 'negotiators': 0.0015319298587311032, 'neidecker': 0.0012609485946591687, 'neighbor': 0.00429031142686725, 'neil': 0.003731800431935113, 'nelson': 0.0015493889696007283, 'neo': 0.004573335506731121, 'neosoft': 0.0012609485946591687, 'neptune': 0.0028906234517430424, 'nerdc': 0.0012609485946591687, 'nerone': 0.002524661375586771, 'nesse': 0.0018924586447506718, 'nestvx': 0.0012609485946591687, 'net': 0.018359149829460554, 'netcom': 0.014341675084144436, 'netd': 0.00457333550673112, 'netherlands': 0.004220752919707875, 'netland': 0.0017198570779606076, 'netnews': 0.0021261502892459296, 'nets': 0.0026646314304903523, 'netters': 0.010430903187581324, 'network': 0.004664428131080998, 'networks': 0.002630829945004615, 'neutron': 0.0049811614058138465, 'new': 0.012066192557455759, 'newbury': 0.0018924586447506718, 'newer': 0.0034000884517709383, 'newest': 0.0028836825388838796, 'newkirk': 0.003731800431935114, 'news': 0.012318027519980634, 'newsgroup': 0.00942964638268908, 'newsgroups': 0.0008672658117927085, 'newsletter': 0.0022110995201272783, 'newspaper': 0.001341653909414293, 'newsreader': 0.0115167614490514, 'newton': 0.03337159897436545, 'newtout': 0.004356139840040938, 'nff': 0.0012609485946591687, 'nfluence': 0.0018924586447506718, 'nfotis': 0.002524661375586771, 'ng': 0.0012629530417339009, 'ngis': 0.0018628591633698963, 'nic': 0.0017062962603481236, 'nice': 0.008098016891351667, 'nicely': 0.0023235169840192006, 'nicene': 0.0027400885069510687, 'niche': 0.0012827028287951915, 'nicho': 0.00560686673732939, 'nicholls': 0.004356139840040942, 'nick': 0.011710501298478782, 'nickh': 0.006233257448747934, 'nicoll': 0.004981161405813852, 'niederstrasser': 0.0024851616866216064, 'night': 0.01444398027484537, 'nih': 0.0012609485946591687, 'nikolaos': 0.002524661375586772, 'nineteenth': 0.0027400885069510687, 'nishantha': 0.0018924586447506726, 'nist': 0.000988318189986688, 'nj': 0.0022286832347011157, 'njit': 0.0015319298587311032, 'nl': 0.016467186164719035, 'nls': 0.003108141579466518, 'nm': 0.0018658918421247577, 'nntp': 0.00710411638743879, 'noaa': 0.0015035858261545658, 'noao': 0.0003979733363520454, 'noble': 0.0016463851446558084, 'nobles': 0.0037911514534976574, 'node': 0.0016084592037809847, 'nodes': 0.0016278394879277016, 'nodis': 0.00035791381164745114, 'nodomain': 0.00010510953103124408, 'noel': 0.003157558429105277, 'noise': 0.004807113627028934, 'nome': 0.0024851616866216134, 'nominal': 0.001586166555485608, 'non': 0.003171788705989405, 'noncommercial': 0.0012499951251094144, 'nonsense': 0.0007032382976603913, 'noon': 0.0024851616866216134, 'nope': 0.0035773163689901124, 'normal': 0.0019522274558929952, 'normally': 0.0012664460350769527, 'normals': 0.0037911514534976548, 'norman': 0.0009691436134594668, 'north': 0.006969608715689234, 'north13': 0.0012609485946591687, 'northern': 0.0027694904740597267, 'norway': 0.001304990985299034, 'nose': 0.0044232811566846135, 'nosubdomain': 0.00010510953103124408, 'note': 0.005796380050280985, 'noted': 0.0031226034349668046, 'notes': 0.0028544957320929916, 'notice': 0.002437886690709974, 'noticed': 0.0022763571667838364, 'noting': 1.671875925648384e-05, 'notion': 0.009494926937344772, 'notions': 0.0021401823853150715, 'nov': 1.671875925648384e-05, 'nova': 0.006496657295807389, 'novel': 0.0036560569852768275, 'november': 0.004042532553052036, 'npo': 0.003108141579466518, 'nps': 0.0018924586447506718, 'nrao': 0.002491744872418865, 'ns': 0.0013371565680386924, 'nsmca': 0.03384037679246742, 'nss': 0.003731800431935114, 'nssdc': 0.0012412324256375635, 'nssdca': 0.0031136322339350916, 'nsw': 0.0015861665554856063, 'nswc': 0.002524661375586771, 'nt': 0.0019229696813196587, 'nth': 0.000988318189986688, 'ntis': 0.0024851616866216125, 'ntsc': 0.005060432039124053, 'ntua': 0.002524661375586771, 'nuances': 0.00365605698527683, 'nuclear': 0.016006718178848814, 'nucleus': 0.0024851616866216064, 'nuetron': 0.0024851616866216134, 'null': 0.001027092726567722, 'number': 0.006071647183198918, 'numbered': 0.0015626450162182998, 'numbers': 0.0036880002993895933, 'numerical': 0.0010834761907074558, 'numerous': 0.0010063294500252734, 'nunnally': 0.0036560569852768267, 'nuntius': 0.0012964773593636594, 'nus': 0.0015319298587311032, 'nut': 0.006411840182243067, 'nuts': 0.0019229696813196587, 'nw': 0.0024851616866216125, 'nwu': 0.0012499951251094144, 'nx10': 0.002524661375586771, 'ny': 0.003236615603296713, 'nyc': 0.00488957081558654, 'nyikos': 0.0036560569852768267, 'nyjnlf': 0.001825425726571352, 'nyu': 0.003157558429105275, 'nyx': 0.005273678721493495, 'nz': 0.0048357024715551125, 'oac': 0.003157558429105275, 'oak': 0.004961199493802627, 'oakhill': 0.0012412324256375618, 'oakland': 0.001064042549779238, 'oaks': 0.0018705330287465275, 'oasis': 0.0012412324256375618, 'oasys': 0.0018924586447506718, 'obedience': 0.004573335506731121, 'obelix': 0.0012609485946591687, 'oberto': 0.0012609485946591687, 'obey': 0.005491928440954984, 'obfuscate': 0.00365605698527683, 'obispo': 0.0025120690482758456, 'object': 0.005287562672734765, 'objective': 0.02466598100338642, 'objectively': 0.006411840182243066, 'objectives': 0.0037318004319351165, 'objects': 0.007150795954515372, 'obliged': 0.0018891842862327687, 'obnoxious': 0.0006604803272702029, 'oboe': 0.004356139840040938, 'obscure': 0.002674481124809779, 'obscurity': 0.0018924586447506718, 'observable': 0.004597323577606557, 'observation': 0.006461700931127317, 'observational': 0.0021524677623682162, 'observations': 0.006807801868989556, 'observatory': 0.021224094609659967, 'observe': 0.003799966121618316, 'observed': 0.003246269744490323, 'observer': 0.006613822347964192, 'observers': 0.0055829162787621265, 'observing': 0.004664282585969842, 'obsolete': 0.002464678361566464, 'obtain': 0.0034962755327819965, 'obtained': 0.0033904579819518084, 'obtaining': 1.671875925648384e-05, 'obvious': 0.011335349154347987, 'obviously': 0.0038062800187400594, 'occasionally': 1.671875925648384e-05, 'occasions': 9.215269075613097e-05, 'occassion': 0.00365605698527683, 'occult': 0.004335059589182316, 'occur': 0.002416485351379391, 'occured': 0.0027400885069510687, 'occurred': 0.0024377731766381597, 'occurrence': 0.0027400885069510687, 'occurs': 0.0007922476542073899, 'ocean': 0.004659843304227393, 'ocf': 0.006411840182243065, 'oct': 0.003108141579466518, 'octavia': 0.0012609485946591687, 'october': 0.002056171775947969, 'odd': 0.0034359914392852434, 'oddly': 0.000978451715284566, 'odin': 0.0036560569852768275, 'oehler': 0.0012609485946591687, 'oeinck': 0.004425442103239914, 'ofa123': 0.0056068667373293845, 'offer': 0.00013948434103010741, 'offered': 0.0026179749488136395, 'offering': 0.0025313802598213187, 'offers': 0.0027219823464838637, 'office': 0.015305388022770322, 'officer': 0.0012603864489062547, 'officers': 0.004499671758296702, 'offices': 0.0023560671987039785, 'official': 0.009315338363654588, 'officially': 0.0007974490228694411, 'officials': 0.004643479835085382, 'offline': 0.001670031835008053, 'offs': 0.004573335506731118, 'offset': 0.0037911514534976548, 'offsetting': 0.0018628591633698963, 'ogi': 0.0012609485946591687, 'oh': 0.011295779535751178, 'ohio': 0.0028986599761363103, 'ohsu': 0.004573335506731121, 'oil': 0.0034458570805793644, 'oj2': 0.00365605698527683, 'ok': 0.0033327214795028943, 'okay': 0.000878092197791531, 'old': 0.009085247228552727, 'older': 0.002571020621605074, 'oldest': 0.0009559019909431317, 'oliveira': 0.0049811614058138465, 'olympics': 0.0024851616866216134, 'olympus': 0.004356139840040942, 'omaha': 0.0021721839313897677, 'omitted': 1.671875925648384e-05, 'omni': 0.0010442927627179474, 'onboard': 0.0056068667373293845, 'ones': 0.006609695997209722, 'oneself': 0.0027400885069510687, 'ongoing': 0.003280847197109191, 'online': 0.01353586614591857, 'ontario': 0.0033992915386289293, 'onyx': 0.002524661375586772, 'oops': 0.0006739571102848205, 'op': 0.0029327307778849584, 'open': 0.00328540203161057, 'opened': 0.00036440142293393384, 'opengl': 0.002524661375586772, 'opening': 0.002431022708017487, 'openly': 0.0019116724119796905, 'openwindows': 0.0025246613755867744, 'operate': 0.0017217890538766233, 'operated': 0.003260405362476882, 'operates': 0.0012717306823408032, 'operating': 0.0025358353052634787, 'operation': 0.005567033610468148, 'operational': 0.008265364016031708, 'operations': 0.009134505153946777, 'operator': 0.003293561067779593, 'operators': 0.0012964773593636594, 'opinion': 0.0027025471786415404, 'opinions': 0.0018677959416530379, 'opportunities': 0.0015035858261545658, 'opportunity': 0.002599220181731145, 'opposed': 0.0026492129405183895, 'opposite': 0.0021562716399695266, 'opposition': 0.006010417942380506, 'oppression': 0.0036560569852768275, 'ops': 0.003731800431935114, 'optical': 0.0037930027673624776, 'optics': 0.0010442927627179474, 'optimal': 0.0012629530417339009, 'optimistic': 0.002916366227908503, 'optimize': 0.000988318189986688, 'optimizing': 0.0010442927627179474, 'optimla': 0.002524661375586772, 'option': 0.004811257631176598, 'optional': 0.002524661375586772, 'options': 0.005787430562964883, 'optiplan': 0.0037318004319351165, 'opus': 0.0024917448724188695, 'oracle': 0.001921522106299118, 'orange': 0.0004088156733638845, 'orbit': 0.087254803670583, 'orbital': 0.033182895856503095, 'orbiter': 0.01316925818184167, 'orbiters': 0.003108141579466518, 'orbiting': 0.014439451979546158, 'orbits': 0.011901885334985419, 'order': 0.01886004164718516, 'ordered': 0.001690862476515842, 'ordering': 0.0024851616866216125, 'orders': 0.006218244166287217, 'ordinary': 0.0009300965515126975, 'ordo': 0.0073330751497454145, 'oregon': 0.003266004830693824, 'oren': 0.003791151453497659, 'org': 0.014289148935335817, 'organisation': 0.0009442341176501652, 'organizational': 0.00034465163587258686, 'organizations': 0.003667692018167453, 'organized': 0.0032143698337004185, 'organpipe': 0.00365605698527683, 'oriental': 0.0073330751497454145, 'orientation': 0.001585663121517377, 'orientations': 0.0016958301188799586, 'oriented': 0.003950112186900612, 'orienting': 0.0018924586447506718, 'orientis': 0.005491928440954983, 'origin': 0.00256816449699298, 'original': 0.007533024743133606, 'originally': 0.0004551053976298283, 'originate': 0.0007018517160113221, 'originator': 0.0034820656860078793, 'origins': 0.006411840182243065, 'orion': 0.007834303733177703, 'orlando': 0.0007163598861018444, 'orleans': 0.0024448766353608346, 'orourke': 0.003791151453497659, 'orphaic': 0.0027400885069510696, 'orphic': 0.001825425726571352, 'orteig': 0.0024851616866216064, 'orthodox': 0.006720289880989109, 'orthodoxy': 0.004573335506731121, 'ortn': 0.003791151453497659, 'orville': 0.004356139840040938, 'oryx': 0.0027400885069510687, 'os': 0.006560934449818638, 'osc': 0.0012412324256375635, 'oscar': 0.0024851616866216134, 'oscs': 0.0012603864489062547, 'ose': 0.007639288036092372, 'osf': 0.0018924586447506718, 'osi': 0.0012609485946591687, 'osiris': 0.0027400885069510687, 'osprey': 0.0037911514534976574, 'ot': 0.0036560569852768275, 'otago': 0.0018628591633698963, 'otis': 0.0012609485946591687, 'oto': 0.011031336546395556, 'ottawa': 0.00099301480816333, 'ottolini': 0.0031575584291052778, 'otv': 0.0018628591633698963, 'ought': 0.0006753080523944294, 'oulu': 0.0015417795530505863, 'outcome': 0.0021946697425983134, 'outer': 0.004402699635905067, 'outline': 0.0025005225130257675, 'outlines': 0.0025005225130257693, 'outlining': 0.0007163598861018444, 'outlook': 0.0018628591633698963, 'output': 0.00969836719660509, 'outputs': 0.006332516444282765, 'outright': 0.00457333550673112, 'outside': 0.002281811648984472, 'outward': 0.0007259062129681476, 'ove': 0.0012609485946591687, 'overall': 0.001618471744492654, 'overhead': 0.0031315407716547517, 'overkill': 0.0025246613755867744, 'overlays': 0.0012609485946591687, 'overlook': 0.00365605698527683, 'overlooked': 0.0012225449270798988, 'overly': 0.0019965781299750842, 'overruns': 0.0012412324256375618, 'overstress': 0.003108141579466518, 'overview': 0.0025120690482758456, 'overwhelming': 0.0036560569852768275, 'owe': 0.0021524677623682162, 'owens': 0.0027697567078588774, 'owl': 0.001921522106299118, 'owlnet': 0.0027400885069510687, 'owned': 0.0036794431012060324, 'owner': 0.0037642244295911535, 'owners': 0.00010510953103124408, 'oxford': 0.0018803995034486513, 'oxidizer': 0.0018628591633698963, 'oxygen': 0.0038068451768266736, 'oz': 0.009197847752324776, 'ozone': 0.01028136936569295, 'ozonehole': 0.001825425726571352, 'p1': 0.0018924586447506718, 'p2': 0.006239874442999969, 'p3': 0.0012609485946591687, 'p4': 0.0012609485946591687, 'p7': 0.0018924586447506718, 'p9000': 0.002524661375586772, 'pa': 0.0021389147225408284, 'pa881a': 0.0024851616866216125, 'pacbell': 0.0027400885069510696, 'pace': 0.002551096428842924, 'pacific': 0.003457915536755663, 'pack': 0.00017108702810196205, 'package': 0.028280973362988036, 'packages': 0.011627035981839413, 'packard': 0.0034617720572396897, 'packed': 0.001921522106299118, 'packing': 0.0012499951251094144, 'packmind': 0.0012412324256375635, 'packs': 0.0012499951251094144, 'pad': 0.016988356917618297, 'padi': 0.003731800431935113, 'pads': 0.009375548629619125, 'pagan': 0.005491928440954982, 'page': 0.002853502491826444, 'pager': 0.003157558429105277, 'pages': 0.0031330490550262142, 'paging': 0.0025246613755867744, 'paid': 0.0019130270242755923, 'pain': 0.009828389861614644, 'painful': 0.0015626450162182998, 'painless': 0.0015332358208003521, 'paint': 0.0028692970142323755, 'painted': 0.004356139840040938, 'painting': 0.0012717306823408032, 'pair': 0.002229223368296125, 'pairs': 0.001914490397895912, 'pal': 0.0018803995034486513, 'palette': 0.007607418082978782, 'palm': 0.002791219946119309, 'palmer': 0.007141166118730839, 'panel': 0.00354055505248974, 'panels': 0.0020928628598154662, 'panix': 0.004155287048693365, 'paper': 0.0029342893231298246, 'paperback': 0.0024851616866216134, 'papers': 0.0055809465760349175, 'parachute': 0.003108141579466518, 'paradise': 0.00420904956440052, 'paradyne': 0.0012609485946591687, 'paragraph': 0.0024337964176860604, 'parallax': 0.0018628591633698963, 'parallel': 0.004231286620295121, 'parameter': 0.0012717306823408032, 'parameters': 0.003254809916649769, 'parametric': 0.004425442103239911, 'paranoid': 0.0021401823853150715, 'paraphrase': 0.0019525691627003787, 'pardon': 0.0033336485356882115, 'parent': 0.0031517615120046248, 'parents': 0.0036391263827446818, 'pariah': 0.0018924586447506718, 'paris': 0.0019156570680840378, 'parity': 0.0027548934839178767, 'park': 0.003187259336580155, 'parking': 0.003108141579466518, 'parks': 0.0028370754228893864, 'parsec': 0.000988318189986688, 'parsons': 0.0025246613755867744, 'partial': 0.0027780381130627953, 'partially': 0.002144107221564112, 'participant': 0.0012609485946591687, 'participants': 0.0020928628598154662, 'participate': 0.0013242262074587147, 'participated': 0.0012808370180140277, 'participating': 0.001296105875257923, 'participation': 0.004359439851376789, 'particle': 0.0018850769431858509, 'particles': 0.003108141579466519, 'particular': 0.006112983752470223, 'particularly': 0.0028859924657961386, 'particulars': 0.001825425726571352, 'parties': 0.0003091276322491551, 'partly': 0.00010510953103124408, 'partners': 0.003243744725599822, 'parts': 0.0033132477776304063, 'party': 0.0031033849534333304, 'pas': 0.0069332138651698495, 'pasadena': 0.011207005776105564, 'pascal': 0.00960331226533902, 'pass': 0.007655803403704487, 'passage': 0.008582627633179428, 'passages': 0.008116755235618254, 'passed': 0.0022505879204074647, 'passenger': 0.003731800431935114, 'passing': 0.0028769129991096107, 'passover': 0.006411840182243067, 'password': 0.0030050280684344654, 'past': 0.00633988740455302, 'paste': 0.0018924586447506718, 'pat': 0.046365563132497886, 'patch': 0.0032432393048343784, 'patches': 0.0015332358208003521, 'patently': 0.0024448766353608346, 'path': 0.004065249539515275, 'pathology': 0.002853354803460136, 'paths': 0.0002992611575469784, 'patience': 0.001216655211329824, 'patient': 0.0024448766353608346, 'patrick': 0.0047115332825927595, 'pattern': 0.004539890495860691, 'patterns': 0.0015311138319880398, 'paul': 0.026272649157833363, 'pavement': 0.001825425726571352, 'pay': 0.004568653169568053, 'payable': 0.000978451715284566, 'paying': 0.004084412517350203, 'payload': 0.01727505264729066, 'payloads': 0.010006085862371748, 'pays': 0.0006604803272702029, 'pb93': 0.0012412324256375618, 'pbd': 0.0024851616866216125, 'pbm': 0.0018924586447506718, 'pbmplus': 0.0037911514534976548, 'pc': 0.024333030338343, 'pcs': 0.0025469720216608734, 'pcx': 0.010807086540932358, 'pd': 0.010807086540932343, 'pd1': 0.0025246613755867744, 'pdb': 0.0018924586447506718, 'pdbourke': 0.0018924586447506718, 'pds': 0.0012717306823408032, 'pdt': 0.0018628591633698963, 'pdx': 0.003157558429105277, 'pdxgate': 0.003157558429105277, 'peace': 0.004456144067961386, 'peaceful': 0.003581494522191157, 'peak': 0.0016661801242341696, 'pearson': 0.0012412324256375618, 'peculiar': 0.0012808370180140277, 'peek': 0.001064042549779238, 'pegasus': 0.00707503848271569, 'pekka': 0.0012609485946591687, 'pen': 0.003029348429260328, 'penalty': 0.0012629530417339009, 'pending': 0.002674481124809779, 'penn': 0.0026057505123544267, 'pennsylvania': 0.000978451715284566, 'peopel': 0.0024851616866216134, 'people': 0.06811837023435494, 'peoples': 0.0019116724119796905, 'pepsi': 0.001520379122855315, 'percent': 0.00247732401670928, 'percentage': 0.003135992489550251, 'perception': 0.000988318189986688, 'perceptions': 0.0027400885069510687, 'perfect': 0.005446116745150477, 'perfectly': 0.0019275260788990207, 'perform': 0.00015390186985808976, 'performance': 0.006911246376833772, 'performed': 0.003405974593774757, 'performing': 0.005606866737329384, 'performs': 0.0003671943352615125, 'peri': 0.003108141579466518, 'perigee': 0.0024851616866216134, 'perihelion': 0.0024851616866216125, 'perihelions': 0.0024851616866216134, 'perijove': 0.0024851616866216134, 'period': 0.004473347128193516, 'periodically': 0.0027163700651970076, 'periodicals': 0.003108141579466519, 'periods': 0.0015525616407321653, 'peripheral': 0.0007163598861018444, 'perl': 0.000978451715284566, 'permanent': 0.004280792231709427, 'permanently': 0.0027736796060405583, 'permanet': 0.004356139840040944, 'permission': 0.0030394846492825655, 'permit': 0.0031939224752976147, 'perot': 0.0018628591633698963, 'perpendicular': 0.002225894803455769, 'perpetual': 0.0024851616866216125, 'perret': 0.0018924586447506718, 'persecute': 0.001825425726571352, 'persecuted': 0.00365605698527683, 'persecution': 0.009179532565505865, 'persia': 0.0027400885069510687, 'persian': 0.001825425726571352, 'persians': 0.001825425726571352, 'person': 0.02656794927253884, 'personal': 0.01661707609352055, 'personality': 0.00457333550673112, 'personally': 0.004342418009720092, 'personnel': 0.0035256794592214554, 'persons': 0.00029391542155923767, 'perspective': 0.0038816072500294863, 'perspectives': 0.004284527532590309, 'persuade': 0.0039627490992867175, 'pertinent': 0.0021524677623682162, 'perturbations': 0.004356139840040947, 'pet': 0.0024851616866216134, 'pete': 0.004130345456935903, 'peter': 0.008729260034907683, 'peterborough': 0.003157558429105277, 'peters': 0.0019116724119796905, 'petition': 0.001825425726571352, 'petri': 0.001825425726571352, 'pex': 0.0031575584291052778, 'pexlib': 0.0012609485946591687, 'pgf': 0.009375548629619142, 'pgm': 0.0012609485946591687, 'ph': 0.0013987629874766963, 'phantom': 0.003108141579466519, 'pharisees': 0.006411840182243065, 'pharvey': 0.019431600557536545, 'phase': 0.006664274069701495, 'phased': 0.0018628591633698963, 'phases': 0.001520379122855315, 'phenomena': 0.0022345089669202917, 'phenomenon': 0.003581494522191157, 'phigs': 0.005060432039124049, 'phil': 0.007638818709193997, 'philadelphia': 0.0007032382976603913, 'philips': 0.0031575584291052743, 'phillips': 0.0022512009151189147, 'philosophical': 0.009068933229796135, 'philosophy': 0.0025123629884392746, 'phobos': 0.003108141579466514, 'phoenix': 0.003435767332073965, 'phone': 0.011442885327389695, 'phong': 0.0018924586447506718, 'photo': 0.004781697677448637, 'photographic': 0.001306377566948104, 'photographs': 0.0025566064981792994, 'photometer': 0.003108141579466518, 'photometry': 0.0012499951251094144, 'photos': 0.0022870703001714454, 'photoshop': 0.006969614267041957, 'phrase': 0.0034519223629203167, 'phy': 0.0012412324256375635, 'physical': 0.010665982367453038, 'physically': 0.0012225449270798988, 'physicist': 0.003108141579466519, 'physicists': 0.0015319298587311032, 'physics': 0.006558219225031961, 'physik': 0.0012609485946591687, 'pi': 0.0029056492725874185, 'pic': 0.0037911514534976548, 'picard': 0.000988318189986688, 'pick': 0.0013735916881133393, 'picked': 0.00020714522349830553, 'picking': 0.0034617720572396897, 'pics': 0.0018924586447506718, 'pict': 0.002524661375586771, 'picture': 0.00736878951424512, 'pictures': 0.005160053103774039, 'piece': 0.0014590633455948852, 'pieces': 0.003324861270298689, 'piggyback': 0.0012412324256375635, 'pigment': 0.0012412324256375618, 'pilot': 0.003340558889778243, 'pilots': 0.005606866737329394, 'pink': 0.0019116724119796905, 'pioneer': 0.004409729417750289, 'pipe': 0.0012808370180140277, 'pipeline': 0.003108141579466518, 'piper': 0.0012603864489062547, 'pit': 0.004590388518728338, 'pitch': 0.003108141579466519, 'pitt': 0.011281308908350945, 'pittsburgh': 0.0019342478884442366, 'pity': 0.0019116724119796905, 'pixar': 0.0018924586447506718, 'pixel': 0.00915973214356412, 'pixels': 0.008245929584991846, 'pixmap': 0.0025246613755867744, 'pizza': 0.0022321909792609963, 'pjs': 0.0018628591633698963, 'pl3': 0.002327929713235535, 'pl4': 0.0026057505123544267, 'pl5': 0.0013558269777203544, 'pl6': 0.002135540547690406, 'pl8': 0.0015624203136469124, 'pl9': 0.006548092890172009, 'place': 0.009678782108646528, 'placed': 0.004011990100495227, 'places': 0.005995013814819822, 'placing': 0.002278512863596773, 'plagued': 0.0025246613755867744, 'plain': 0.003316029356709428, 'plan': 0.006841885140394614, 'planar': 0.0018924586447506718, 'planck': 0.0012499951251094144, 'plane': 0.007041114187157471, 'planes': 0.004873159696752615, 'planet': 0.01847153435822746, 'planetarium': 0.0018628591633699006, 'planetary': 0.016340326994060007, 'planets': 0.017627367618410085, 'planned': 0.006590832720289995, 'planners': 0.0012412324256375635, 'planning': 0.002608119239833954, 'plans': 0.0065355355720615625, 'plant': 0.0024080850228676183, 'plants': 0.002278512863596773, 'plasma': 0.0022887445873255316, 'plastic': 0.003731800431935114, 'plate': 0.002221550920473124, 'platform': 0.005152685159523564, 'platforms': 0.006143759197217528, 'plausible': 0.003359124521680611, 'play': 0.003596365837135557, 'playback': 0.0021657174445653135, 'played': 0.003179274068395298, 'player': 0.0016377373134914552, 'players': 0.0016840886619538323, 'playing': 0.00372392893847161, 'plays': 0.0034673585379148266, 'plaza': 0.0021327447189448297, 'pleading': 0.001825425726571352, 'pleased': 0.0011253818994855442, 'pleases': 0.001216655211329824, 'pleasure': 0.00457333550673112, 'pleiades': 0.0018628591633699006, 'plenary': 0.0012412324256375635, 'plenty': 0.0027845339940066093, 'pliers': 0.003731800431935114, 'plk': 0.0021721839313897677, 'plot': 0.005352054820052473, 'plots': 0.0031954450584297956, 'plotter': 0.001914490397895912, 'plotters': 0.0018924586447506718, 'plotting': 0.0032360500317303318, 'plt': 0.0018628591633699006, 'plug': 0.0010753398191192063, 'plus': 0.0033826857696330447, 'pluto': 0.01126925254787877, 'plutonium': 0.0018628591633698963, 'pm': 0.0017823921772977674, 'pmy': 0.007333075149745415, 'po': 0.003147456840627059, 'poe': 0.00365605698527683, 'pogo': 0.013999610285133917, 'point': 0.017116076338016664, 'pointed': 0.0062127326762335625, 'pointer': 0.0019370569109456786, 'pointers': 0.007607418082978788, 'pointing': 0.000633232486315769, 'points': 0.015062842637847206, 'poison': 0.0061408710385161104, 'poker': 0.0018628591633698963, 'polar': 0.004981161405813846, 'pole': 0.004327848645535927, 'poles': 0.0021418510546180507, 'police': 0.001553067980998979, 'policies': 0.0012603864489062547, 'policy': 0.004369254487591607, 'political': 0.007796933658125666, 'politics': 0.0015445286413936655, 'poll': 0.0019116724119796905, 'pollution': 0.010006085862371741, 'poly': 0.0007163598861018444, 'polygon': 0.02051440872395608, 'polygons': 0.010807086540932351, 'polyhedra': 0.0012609485946591687, 'polymer': 0.0012499951251094144, 'polyray': 0.002524661375586771, 'polytechnic': 0.0017666414138195032, 'pond': 0.01258397680578259, 'pooh': 0.007333075149745417, 'pool': 0.0018628591633699006, 'poor': 0.0016195915502751294, 'poorer': 0.0015417795530505863, 'poorly': 0.0010927699423118938, 'pop': 0.001302386967591473, 'pope': 0.0037539385145901353, 'popec': 0.0036560569852768267, 'pops': 0.0012259344989952962, 'popular': 0.007092834300754545, 'popularity': 0.00457333550673112, 'population': 0.004613592807563708, 'pornography': 0.0036560569852768275, 'port': 0.005298111333951719, 'portable': 0.0035537494004474505, 'portal': 0.007938255711360465, 'ported': 0.0018924586447506718, 'portfolio': 0.0006516076727636853, 'portion': 0.001788226367799274, 'portions': 0.0013028475181700912, 'portland': 0.0022512009151189156, 'porto': 0.0012609485946591687, 'portray': 0.00365605698527683, 'portrayed': 0.00457333550673112, 'ports': 0.0016267651670370115, 'portugal': 0.0018803995034486513, 'portugese': 0.0015035858261545658, 'poseidon': 0.002485161686621608, 'position': 0.007809016203422629, 'positioning': 0.0024851616866216064, 'positions': 0.003070124404957214, 'positive': 0.002889358678871792, 'possess': 0.0027400885069510696, 'possibilities': 0.00042856546042523147, 'possibility': 0.00520171914331673, 'possible': 0.004311103600065183, 'possiblity': 0.003731800431935113, 'possibly': 0.0013560920373846663, 'possum': 0.0006417411980615632, 'post': 0.006242824139770861, 'posted': 0.0014371572701823059, 'poster': 0.0014422528716290222, 'posters': 0.0024695153745814113, 'posting': 0.007565947242918472, 'postings': 0.004809250533178167, 'postmaster': 0.0015417795530505863, 'postoffice': 0.0012609485946591687, 'posts': 0.0030990267017979196, 'postscript': 0.010528204461447154, 'potential': 0.00733981558652323, 'potentially': 0.0009236759316832519, 'potter': 0.002750040538837272, 'pound': 0.0028573361544391466, 'pounds': 0.006421250322249677, 'pour': 0.0012603864489062547, 'pov': 0.017909695893539447, 'povray': 0.006969614267041952, 'powder': 0.0018628591633699006, 'power': 0.01743217771103415, 'powered': 0.008116558095880515, 'powerful': 0.0020443327698129714, 'powerglove': 0.0018924586447506718, 'powers': 4.035731769314044e-05, 'pp': 0.0034245778045795643, 'ppm': 0.0028619847277388194, 'ppmquant': 0.0012609485946591687, 'pr': 0.0012412324256375635, 'practical': 0.007289667142867856, 'practically': 0.001027092726567722, 'practice': 0.00987167591242637, 'practiced': 0.0030242362814067725, 'practices': 0.002485919243235474, 'prado': 0.004981161405813846, 'prael': 0.0024851616866216125, 'praise': 0.003581494522191157, 'prakinf': 0.0012609485946591687, 'pratt': 0.0015319298587311032, 'pray': 0.009179532565505862, 'prayer': 0.004573335506731121, 'prayers': 0.0027400885069510687, 'prb': 0.04917699520440448, 'pre': 0.002200183727587671, 'preach': 0.00365605698527683, 'preached': 0.0027400885069510687, 'preachers': 0.0027400885069510696, 'preaching': 0.00457333550673112, 'preasure': 0.0012412324256375618, 'precedent': 0.0015417795530505863, 'preceding': 0.0018628591633699006, 'precious': 0.0019116724119796905, 'precise': 0.0013648307046852347, 'precisely': 0.003182286804136625, 'precision': 0.0014094782784925724, 'precognition': 0.0027400885069510687, 'predicated': 0.0018628591633699006, 'predict': 0.0009236759316832519, 'predicted': 0.002436271697723395, 'predicting': 0.0019481148578558583, 'prediction': 0.0017855205597762545, 'predictions': 0.003109807629435095, 'predicts': 0.004200371242160982, 'prefer': 0.000966723972832124, 'preferably': 0.002350951875989764, 'preferred': 0.0003716576742335345, 'prefix': 0.0018628591633698963, 'prejudice': 0.0026646314304903523, 'preliminary': 0.004356139840040943, 'premature': 0.0019116724119796905, 'premise': 0.010104763978199323, 'premises': 0.0027400885069510687, 'premium': 0.0024448766353608346, 'premiums': 0.001825425726571352, 'preparation': 0.000978451715284566, 'prepared': 0.0009454318272971649, 'presbyterians': 0.0027400885069510687, 'presence': 0.004037769104462169, 'present': 0.005179661211889525, 'presentation': 0.0038106634568270785, 'presentations': 0.006929875182282242, 'presented': 0.0019562892917980813, 'presenting': 0.003591344216510528, 'presents': 0.0047720704073991324, 'president': 0.013349458708869336, 'press': 0.0034501225002317682, 'pressure': 0.00915004568271267, 'pressures': 0.004356139840040942, 'pressurized': 0.003108141579466519, 'preston': 0.0031889516217291853, 'prestonm': 0.002524661375586772, 'presumably': 0.0006299532136083384, 'presume': 0.0011253818994855442, 'presumeably': 0.0024851616866216134, 'pretend': 0.0024337964176860604, 'pretense': 0.0012412324256375618, 'pretty': 0.0018296747439178057, 'prevent': 0.0003162291221670988, 'prevented': 0.00034465163587258686, 'preview': 0.001987614546821075, 'previewer': 0.0018924586447506718, 'previous': 0.008518219592420159, 'previously': 0.0012516860117500169, 'price': 0.002293437415627304, 'priced': 0.000978451715284566, 'prices': 0.006721016981688375, 'pride': 0.0024363865949890897, 'priest': 0.006112511563361862, 'priesthood': 0.003972383575805087, 'priests': 0.004880926335392262, 'primarily': 0.0020952825461521855, 'primary': 0.004689900626248745, 'prime': 0.003108141579466519, 'primitive': 0.0009407487786403362, 'prince': 0.0015720298448572857, 'princeton': 0.006309189474330523, 'principal': 0.002215535753179989, 'principle': 0.0067339692879736105, 'principles': 0.0067105380054825305, 'print': 0.005385118702425777, 'printed': 0.0013638088987355896, 'printer': 0.00696961426704196, 'printers': 0.0018924586447506718, 'printing': 0.00234866151017922, 'prints': 0.0007346838535750499, 'prior': 0.003012870177847726, 'priority': 0.003243744725599822, 'prism': 0.004191069138734335, 'private': 0.016754943781522716, 'privately': 0.008745706591231313, 'prize': 0.013377535592800895, 'prizes': 0.004981161405813843, 'prj': 0.0012609485946591687, 'prlhp1': 0.0012609485946591687, 'pro': 0.003872756701905065, 'probability': 0.0018496845972676042, 'probable': 0.0022264890154449837, 'probably': 0.006044505284058675, 'probe': 0.009115465390486091, 'probes': 0.005546277321773342, 'problem': 0.007080061835123065, 'problems': 0.004599378788960061, 'procedural': 0.000988318189986688, 'procedure': 0.0019312331813316494, 'procedures': 0.0015739228747028832, 'proceed': 0.0012808370180140277, 'proceeding': 0.0012412324256375635, 'proceedings': 0.0024925916919543633, 'process': 0.005788109160471281, 'processes': 0.005631543329654447, 'processing': 0.00898949813314651, 'processor': 0.008687434116057335, 'processors': 0.0044089411786199075, 'proclaim': 0.009179532565505865, 'proclaimed': 0.0042623473629762884, 'procurement': 0.0018628591633698963, 'produce': 0.0019715112406447164, 'produced': 0.003277875033024207, 'produces': 0.0030943523402957498, 'producing': 0.0006739571102848205, 'product': 0.010253609473861376, 'production': 0.003471160962920953, 'products': 0.004146222683271557, 'prof': 0.0029174877819974805, 'profess': 0.001825425726571352, 'professional': 0.0031812903747954558, 'professionals': 0.001586166555485608, 'professor': 0.00301525268720607, 'profile': 0.0022471464192203184, 'profit': 0.00463376164098832, 'profitable': 0.0018628591633698963, 'profits': 0.0024851616866216064, 'program': 0.03005894086431327, 'programme': 0.001064042549779238, 'programmer': 0.010340127255448906, 'programmers': 0.0028387564496019342, 'programming': 0.01868703066926819, 'programs': 0.015734435055461387, 'progress': 0.0007597303458520667, 'progressive': 0.000988318189986688, 'project': 0.024140340940470198, 'projected': 0.0013371565680386924, 'projectile': 0.0012412324256375635, 'projection': 0.002149158349233577, 'projections': 0.0023041316498041723, 'projector': 0.0012609485946591687, 'projects': 0.014819266813628834, 'prolegomena': 0.0027400885069510696, 'prominent': 0.0024570044961898345, 'promise': 0.020383425952355122, 'promised': 0.004293127920191015, 'promises': 0.0034818660142473543, 'promising': 0.0007346838535750499, 'promote': 0.0010428158111027656, 'promoted': 0.00010510953103124408, 'promotional': 0.0016958301188799586, 'prompt': 0.001731109994699536, 'prompted': 0.0006417411980615632, 'pronounced': 0.00011497600573342169, 'proof': 0.008181226213607624, 'proofs': 0.0027400885069510687, 'propaganda': 0.0026646314304903523, 'propagation': 0.0012412324256375635, 'propellant': 0.004356139840040943, 'propellants': 0.003108141579466518, 'propelled': 0.0009236759316832519, 'proper': 0.0013733053881231387, 'properly': 0.002495133028258029, 'properties': 0.002697700878012823, 'property': 0.001145131686546892, 'prophecies': 0.0019116724119796905, 'prophecy': 0.006411840182243065, 'prophesy': 0.007333075149745415, 'prophet': 0.006411840182243063, 'prophethood': 0.0027400885069510687, 'prophets': 0.011959254816636747, 'proponent': 0.0012412324256375635, 'proponents': 0.0012160848046758686, 'proposal': 0.005259829704366731, 'proposals': 0.004981161405813843, 'propose': 0.003950288626390111, 'proposed': 0.005429208021902198, 'proposition': 0.0021524677623682162, 'proprietary': 0.002883682538883877, 'propulsion': 0.02061263775522442, 'prospect': 0.0012160848046758686, 'prospecting': 0.0024851616866216134, 'prospector': 0.0018628591633698963, 'prospects': 0.0024851616866216134, 'protagonist': 0.001825425726571352, 'protect': 0.0012647021471220267, 'protected': 8.226937839690696e-05, 'protecting': 0.0012412324256375635, 'protection': 0.0033916432410878595, 'protective': 0.0024851616866216134, 'protest': 0.0009236759316832519, 'protestant': 0.006411840182243063, 'protestants': 0.0027400885069510687, 'protesting': 0.002278512863596773, 'proton': 0.006884449243408339, 'protons': 0.0024851616866216134, 'prototype': 0.005606866737329393, 'proud': 0.004971402022553719, 'prove': 0.011018869253152635, 'proved': 0.0018134151655027544, 'proven': 0.0055035257262512835, 'proverb': 0.0018628591633699006, 'proves': 0.0013113511286082574, 'provide': 0.00436031070173565, 'provided': 0.004203376102688388, 'provides': 0.0026580747236013592, 'providing': 0.002677213164470841, 'provo': 0.0018924586447506726, 'provoking': 0.0027400885069510696, 'proxima': 0.0012499951251094144, 'prussian': 0.0027400885069510687, 'ps': 0.0017230056235799304, 'psalm': 0.005491928440954983, 'psalms': 0.001825425726571352, 'pseudo': 0.002538466458117771, 'psi': 0.0012629530417339009, 'pss': 0.0012499951251094144, 'psu': 0.004064143009993481, 'psuvm': 0.0021681840274765983, 'psych': 0.0015417795530505863, 'psychic': 0.0015319298587311032, 'psychology': 0.0022512009151189156, 'psygnosis': 0.0012609485946591687, 'psyrobtw': 0.01755528210575166, 'pt': 0.0031829256144006203, 'ptolemy2': 0.0012609485946591687, 'pts': 0.0012609485946591687, 'pu': 0.0012691491483781056, 'pub': 0.011471486545150159, 'pubinfo': 0.0006417411980615632, 'public': 0.00982569054538094, 'publication': 0.0010275627439367187, 'publications': 0.00223881883979109, 'publicity': 0.0009971908444932048, 'publish': 0.001540698643374759, 'published': 0.004912281622403491, 'publishers': 0.0025034856540948128, 'publishes': 0.0016661801242341696, 'publishing': 0.0004088156733638845, 'puckey': 0.0024851616866216134, 'pull': 0.0006671969666115956, 'pulled': 0.0007032382976603913, 'pulling': 0.002436271697723395, 'pulsars': 0.001862859163369898, 'pulse': 0.0024851616866216125, 'pundurs': 0.001825425726571352, 'punishable': 0.007333075149745415, 'punished': 0.0027400885069510696, 'punishment': 0.009179532565505858, 'purchase': 0.0020894963117444824, 'purchased': 0.0031034105326142158, 'purchasing': 0.00036440142293393384, 'purdue': 0.008297570246329919, 'pure': 0.0030383957207663526, 'purely': 0.002917320589118175, 'purge': 0.0027400885069510696, 'purification': 0.0013262274963396362, 'purpose': 0.008977155161861702, 'purposefully': 0.0027400885069510696, 'purposes': 0.001694984177801567, 'purse': 0.001520379122855315, 'pursued': 0.003108141579466518, 'pursuing': 0.0024851616866216125, 'push': 0.0036683538927684226, 'pushed': 0.0016648102574299507, 'pusher': 0.0012412324256375635, 'pushes': 0.0006417411980615632, 'pushing': 0.0023051158728379043, 'puts': 0.0012638841051070202, 'putting': 0.002595856857785455, 'pvo': 0.0018628591633698963, 'pww': 0.001825425726571352, 'pyron': 0.005606866737329392, 'pythagorean': 0.001825425726571352, 'qb1': 0.0018628591633699006, 'qc': 0.004425442103239911, 'qed': 0.002161230461840069, 'qrt': 0.0012609485946591687, 'qt': 0.004425442103239913, 'qu': 0.001520379122855315, 'quack': 0.019431600557536524, 'quadra': 0.005696122928293768, 'quads': 0.0007036071049306121, 'quakertown': 0.0027400885069510696, 'qualified': 0.001416582374210198, 'qualify': 0.0012808370180140277, 'qualifying': 0.0015319298587311032, 'qualitative': 4.035731769314044e-05, 'quality': 0.0063968300366745385, 'quan': 0.0012609485946591687, 'quantitative': 0.0015417795530505863, 'quantities': 0.0004088156733638845, 'quantity': 0.004108256725665881, 'quantization': 0.0025337828159839983, 'quantized': 0.0012609485946591687, 'quantizers': 0.0012609485946591687, 'quantum': 0.0027658400197057348, 'quarks': 0.0013262274963396362, 'quarter': 0.0027872896418217096, 'quarterly': 0.0013794999981434353, 'quarters': 0.0006417411980615632, 'quasars': 0.0012412324256375635, 'qucdn': 0.0043561398400409415, 'que': 0.010730320869396043, 'queen': 0.006202489356038591, 'queensu': 0.004981161405813847, 'query': 0.0015332358208003521, 'quest': 0.0018628591633698963, 'question': 0.010322115081123032, 'questionable': 0.0012808370180140277, 'questioning': 0.00039751840402391624, 'questions': 0.007205764377826522, 'qui': 0.009179532565505875, 'quick': 0.0014558338651601303, 'quickdraw': 0.002524661375586772, 'quickly': 0.00147571545627822, 'quicktime': 0.006969614267041956, 'quiet': 0.0012808370180140277, 'quit': 0.0012647021471220267, 'quite': 0.004415959628691271, 'quotation': 0.0018628591633698963, 'quote': 0.010338475631446829, 'quoted': 0.007118400390180229, 'quotes': 0.01661722278776709, 'quoting': 0.010315339836964074, 'qur': 0.0027400885069510687, 'r3000': 0.0012609485946591687, 'r5': 0.0018924586447506726, 'ra': 0.00903369034150642, 'rabbit': 0.0028032790874212747, 'race': 0.01923351450290087, 'racial': 0.001825425726571352, 'radar': 0.006665788964392389, 'radial': 0.0009559019909431317, 'radiance': 0.0006703468019723805, 'radiation': 0.011269252547878757, 'radical': 0.0019229696813196587, 'radii': 0.004359439851376789, 'radio': 0.01908722879173935, 'radios': 0.003108141579466518, 'radiosity': 0.0044254421032399105, 'radiosity_code': 0.0025246613755867744, 'radious': 0.0025246613755867744, 'radius': 0.009128968845513313, 'rafia': 0.0024851616866216134, 'rahul': 0.008750040255253845, 'raider': 0.006038439941835297, 'rail': 0.0024851616866216134, 'railroad': 0.0012412324256375635, 'rain': 0.0010172262518655445, 'rainbow': 0.000988318189986688, 'raise': 0.004478115387642663, 'raised': 0.008555524319227677, 'raising': 0.0012160848046758686, 'raist': 0.0018924586447506726, 'raistlin': 0.0018628591633699006, 'raj': 0.0015417795530505863, 'ralph': 0.002814034533932281, 'ram': 0.010845214737995698, 'rama': 0.001825425726571352, 'rambling': 0.0015448877753555896, 'rambo': 0.006411840182243065, 'ran': 0.003104360599235192, 'rand': 0.0022215509204731258, 'random': 0.0013799359812177586, 'range': 0.007612956393568153, 'ranger': 0.0012412324256375635, 'ranges': 0.003731800431935113, 'ranging': 0.00012418828339355592, 'ranjan': 0.002454726329680262, 'ranking': 0.0019116724119796905, 'rape': 0.005491928440954982, 'rapid': 0.0025120690482758456, 'rapidly': 0.0012964773593636594, 'rare': 0.0017855205597762545, 'raster': 0.005060432039124051, 'rat': 0.001999735146975403, 'rate': 0.007343432989021971, 'rated': 0.0062332574487479345, 'rates': 0.0023560722344677654, 'rating': 0.002485161686621608, 'ratio': 0.005341176135285949, 'rattling': 0.0024851616866216134, 'raw': 0.0022592233498766887, 'rawlins': 0.006411840182243065, 'ray': 0.01110634904904052, 'rays': 0.003108141579466519, 'rayshade': 0.00569612292829377, 'raytrace': 0.003157558429105275, 'raytracer': 0.004425442103239916, 'raytracers': 0.0018924586447506718, 'raytracing': 0.0063325164442827675, 'raz': 0.0012609485946591687, 'rbarris': 0.0018924586447506718, 'rbdc': 0.007333075149745413, 'rborden': 0.0031081415794665165, 'rc': 0.004573335506731121, 'rchland': 0.004588872734862509, 'rcs': 0.001862859163369898, 'rd': 0.0006890098414027686, 'rdrc': 0.0012609485946591687, 'reach': 0.006366835084202892, 'reached': 0.009099472174277829, 'reaching': 0.0021051197101264072, 'reaction': 0.002228089108978819, 'reactions': 0.003382596524808915, 'reactor': 0.0024851616866216064, 'reactors': 0.003731800431935113, 'read': 0.009603952829704594, 'readable': 0.0012827028287951915, 'reader': 0.00139521481664002, 'readers': 0.0033287640105929862, 'readership': 0.0018628591633698963, 'readily': 0.0015332358208003521, 'reading': 0.00202982060344276, 'readings': 0.0015319298587311032, 'readme': 0.0035555654569057816, 'readouts': 0.0012412324256375635, 'reads': 0.003277206718229301, 'ready': 0.0007997999754534137, 'reagan': 0.0012808370180140277, 'real': 0.009814918480320213, 'realiser': 0.0018628591633699006, 'realistic': 0.0017062962603481236, 'realities': 0.00039751840402391624, 'reality': 0.006150257580700657, 'realize': 0.00448112661488505, 'realized': 0.0018129847908006135, 'really': 0.021187743126576675, 'realy': 0.0006516076727636853, 'reaped': 0.0009236759316832519, 'reason': 0.017094638325000074, 'reasonable': 0.0018908646904267556, 'reasonably': 8.793789117982759e-07, 'reasoned': 0.0015319298587311032, 'reasoning': 0.0022197760462525423, 'reasons': 0.004599269269794764, 'reassignment': 0.0018628591633699006, 'rebelled': 0.001825425726571352, 'reboost': 0.0012412324256375635, 'rebuilt': 0.0036560569852768267, 'rec': 0.0021261502892459296, 'recall': 0.0024611601267895637, 'recalled': 0.0006417411980615632, 'receive': 0.002596968258412915, 'received': 0.0020896344793826698, 'receiver': 0.004356139840040942, 'receivers': 0.0018628591633698963, 'receiving': 0.0020467256091089518, 'recent': 0.005463354736664109, 'recently': 0.0032867291387838407, 'recherche': 0.0012609485946591687, 'recieved': 0.0002992611575469784, 'reckon': 0.004573335506731121, 'recognition': 0.0019323989356155756, 'recognize': 0.0022113292191522534, 'recognized': 0.0033485186064045793, 'recognizing': 0.0009236759316832519, 'recommend': 0.005800978469390024, 'recommendations': 0.008222707964233848, 'recommended': 0.0012717306823408032, 'reconcile': 0.0036560569852768275, 'reconciled': 0.004573335506731118, 'reconnaissance': 0.0018628591633698963, 'reconstruction': 0.0015417795530505863, 'record': 0.001780321344114169, 'recorded': 0.0011253818994855442, 'recorder': 0.0012499951251094144, 'recording': 0.0012691491483781056, 'records': 0.0013028475181700912, 'recover': 0.0012412324256375635, 'recovered': 0.003417927223171884, 'recovery': 0.003731800431935113, 'rectangle': 0.0012609485946591687, 'rectangular': 0.005060432039124044, 'rectification': 0.0012609485946591687, 'red': 0.014065036260117389, 'redeemed': 0.0027400885069510696, 'redelfs': 0.004573335506731118, 'redemption': 0.0027400885069510687, 'redesign': 0.01190188533498543, 'redhill': 0.0012609485946591687, 'reduce': 0.00030106615376777543, 'reduced': 0.0024691398402267037, 'reduces': 0.0003091276322491551, 'reducing': 0.0019965781299750842, 'reduction': 0.002545596806177072, 'reductions': 0.0018628591633699006, 'redwood': 0.0012499951251094144, 'reed': 0.00010510953103124408, 'reef': 0.0012499951251094144, 'reentry': 0.003108141579466519, 'ref': 0.00010510953103124408, 'refer': 0.00377590959947026, 'reference': 0.004289408276604315, 'referenced': 0.0018924586447506726, 'references': 0.005528225586863239, 'referred': 0.003536080786370685, 'referring': 0.0022703644172842197, 'refers': 0.0019546980436531153, 'refinement': 0.001347039880397861, 'reflect': 0.00039751840402391624, 'reflecting': 0.0011727949367685234, 'reflections': 0.0016194133460181942, 'reflective': 0.0015035858261545658, 'reflector': 0.0012412324256375635, 'reflects': 0.001921522106299118, 'reform': 0.0012160848046758686, 'refs': 0.0018803995034486513, 'refuge': 0.0012160848046758686, 'refuse': 0.0012808370180140277, 'refused': 0.0031155095932511624, 'refuses': 4.035731769314044e-05, 'regard': 0.007510428261863593, 'regarded': 0.0009813417068165256, 'regarding': 0.0032059522970806316, 'regardless': 0.00516609214888155, 'regards': 0.0051001473173499555, 'region': 0.0025132603265296694, 'regional': 0.0019249565393640788, 'regions': 0.0006395752914771244, 'register': 0.002558627520305585, 'registered': 0.0012609485946591687, 'registers': 0.0015499786042360887, 'registration': 0.002066088936621512, 'regolith': 0.0012412324256375635, 'regret': 0.0027400885069510696, 'regular': 0.0029808468000555154, 'regularly': 0.00012418828339355592, 'regulars': 0.00010510953103124408, 'regulations': 0.0015448877753555896, 'regulatory': 0.0018628591633699006, 'rehashing': 0.0012499951251094144, 'reid': 0.0018705330287465292, 'reiken': 0.003731800431935113, 'reilly': 0.0018803995034486513, 'reinhard': 0.0018924586447506718, 'reinterpret': 0.00457333550673112, 'reinventing': 0.0018924586447506726, 'reiterated': 0.0009236759316832519, 'reject': 0.009626363324312649, 'rejected': 0.0032926865480503442, 'rejecting': 0.0036560569852768275, 'rejection': 0.0019116724119796905, 'rejects': 0.0012160848046758686, 'rejuvenated': 0.0018628591633699006, 'relate': 0.0012259344989952962, 'related': 0.006542800575881132, 'relates': 0.0027400885069510687, 'relating': 0.0011727949367685234, 'relation': 0.0015319298587311032, 'relations': 0.001884840403250123, 'relationship': 0.010681095242165385, 'relationships': 0.0012160848046758686, 'relative': 0.004420689921300467, 'relatively': 0.0038306978172011775, 'relativism': 0.0036560569852768275, 'relativistic': 0.0012412324256375618, 'relativity': 0.003718167755141101, 'relay': 0.0015915545650855133, 'relays': 0.0012412324256375635, 'release': 0.004251810575829442, 'released': 0.0025595540670109657, 'releases': 0.0031136322339350916, 'releasing': 0.0006417411980615632, 'relevance': 0.0017855205597762545, 'relevant': 0.00348085033198562, 'reliability': 0.0010442927627179474, 'reliabity': 0.0018628591633699006, 'reliable': 0.0013125177987963273, 'relief': 0.0012412324256375635, 'relies': 4.035731769314044e-05, 'religion': 0.06769561709612532, 'religions': 0.019437160685438073, 'religious': 0.03753908484573401, 'religous': 0.0018924586447506726, 'rely': 0.0053859786121099535, 'remain': 0.0031353094902888687, 'remained': 0.0028376918700381793, 'remaining': 0.004084412517350203, 'remains': 0.0023909485556506994, 'remark': 0.0026646314304903523, 'remarkable': 0.00011497600573342169, 'rember': 0.001520379122855315, 'remeber': 0.0018496845972676042, 'remember': 0.01284028697173466, 'remembrance': 0.001825425726571352, 'remind': 0.004954450339746287, 'reminded': 0.0009236759316832519, 'reminder': 0.0012808370180140277, 'reminds': 0.0030242362814067725, 'remorse': 0.0027400885069510696, 'remote': 0.005694348431922069, 'remotely': 0.0010442927627179474, 'removal': 0.006894635397161904, 'remove': 0.0015716272411609427, 'removed': 0.0020595016555052933, 'removing': 0.0024866039775706082, 'rend386': 0.0012609485946591687, 'render': 0.004793429695304837, 'rendered': 0.002542985343060033, 'renderer': 0.0037911514534976548, 'renderers': 0.0012609485946591687, 'rendering': 0.008885150472506754, 'renderman': 0.0031575584291052743, 'renders': 0.000995773562281057, 'rendezvous': 0.0018628591633698963, 'rene': 0.005148514088580695, 'renew': 0.004029559259700203, 'renner': 0.0012609485946591687, 'reno': 0.0012160848046758686, 'rensselaer': 0.0024575018725063735, 'rent': 0.0021095234966925806, 'rep': 0.002538709114058773, 'repair': 0.0024851616866216134, 'repairstation': 0.0018628591633699006, 'repeat': 0.00024468772484026804, 'repeated': 0.0009738105286627953, 'repeatedly': 0.0034617720572396897, 'repeating': 0.0013262274963396362, 'repent': 0.00365605698527683, 'repentance': 0.01195925481663676, 'repenting': 0.0027400885069510696, 'repertoire': 0.0027400885069510696, 'replace': 0.002082241417067727, 'replaced': 0.0016261937554672905, 'replacement': 0.0018848404032501213, 'replacing': 0.0012691491483781056, 'replied': 0.004077421088867908, 'replies': 0.002176210339652637, 'reply': 0.006034803587452688, 'repo': 0.006233257448747934, 'report': 0.007725580582390026, 'reported': 0.005662871084368295, 'reportedly': 0.0006417411980615632, 'reporting': 0.0017855205597762545, 'reports': 0.006975539425864263, 'repository': 0.000988318189986688, 'reppert': 0.00035791381164745114, 'represent': 0.002112332723708087, 'representation': 0.0018250202487414676, 'representative': 0.0009130487728999945, 'represented': 0.001914490397895912, 'representing': 0.002183606910529332, 'represents': 0.0020662477151468855, 'reprints': 0.0012499951251094144, 'reproduced': 0.0013558269777203544, 'reproduction': 0.00065960320825413, 'republic': 0.0019150563317796342, 'reputable': 0.003685796326874803, 'request': 0.004955626120590262, 'requested': 0.0019156570680840378, 'requests': 0.0019980789705594127, 'require': 0.007458439137760398, 'required': 0.004449710183618756, 'requirement': 0.00011761931230783867, 'requirements': 0.0019046975015823116, 'requires': 0.004094166316249868, 'requiring': 0.00042856546042523147, 'res': 0.0012609485946591687, 'rescorla': 0.0036560569852768275, 'rescue': 0.0012412324256375635, 'research': 0.021681365928656365, 'researchers': 0.00021074702514795735, 'resembles': 0.003108141579466518, 'resembling': 0.0010442927627179474, 'reserve': 0.007348374214674434, 'reserved': 0.0016307803947861951, 'reserves': 0.0024851616866216125, 'reset': 0.004356139840040947, 'residents': 0.010637319947130214, 'resides': 0.0020361452852944734, 'residual': 0.003731800431935113, 'resigned': 0.0012808370180140277, 'resistance': 0.0007473295087178644, 'resized': 0.002524661375586772, 'resolution': 0.0073410568907191455, 'resolutions': 0.0025246613755867744, 'resolve': 0.0006739571102848205, 'resolved': 0.0012808370180140277, 'resort': 0.0019116724119796905, 'resource': 0.0042971130887007915, 'resources': 0.008130694919976153, 'respect': 0.010766266237198082, 'respective': 0.0010442927627179474, 'respectively': 0.0024041199385484865, 'respects': 0.0027400885069510687, 'respond': 0.002074946649063117, 'responded': 0.0022264890154449837, 'responding': 0.0038332746998137324, 'responds': 0.000952889200262875, 'response': 0.004433723881362266, 'responses': 0.001598081512357975, 'responsibilities': 0.0024851616866216134, 'responsibility': 0.010232844672217745, 'responsible': 0.004106012707415825, 'rest': 0.010177480698648485, 'reston': 0.0038683500554799206, 'restore': 0.0024448766353608346, 'restored': 0.0019481148578558583, 'restoring': 0.003108141579466518, 'restrict': 0.00039751840402391624, 'restricted': 0.00247732401670928, 'restriction': 0.0015493889696007283, 'restrictions': 0.001064042549779238, 'restricts': 0.0012160848046758686, 'result': 0.002427224653412643, 'resulting': 0.0023200895038188525, 'results': 0.0037530696384279706, 'resumes': 0.0012499951251094144, 'resupply': 0.0031081415794665165, 'resurrected': 0.00457333550673112, 'resurrection': 0.004573335506731118, 'retain': 0.0018628591633698963, 'retired': 0.0024851616866216134, 'retirement': 0.0018628591633699006, 'retrieval': 0.0012412324256375635, 'retrieve': 0.004399120673022062, 'retro': 0.0012412324256375635, 'return': 0.007392582307877736, 'returned': 0.0024479590039273116, 'returning': 0.001670031835008053, 'returns': 0.0016044324068992056, 'reusable': 0.005465628948198191, 'reuss': 0.004573335506731121, 'reveal': 0.0012808370180140277, 'revealed': 0.0028561370557908267, 'revealing': 0.003359124521680611, 'revel': 0.0027400885069510696, 'revelation': 0.0073330751497454145, 'revenues': 0.0012603864489062547, 'reverse': 0.0015861665554856063, 'review': 0.001658654151580949, 'reviewed': 0.0010442927627179474, 'reviews': 0.0012852074653554209, 'revised': 0.0036765854494721605, 'revision': 0.0012629530417339009, 'revolt': 0.0015527953218988713, 'revolting': 0.004356139840040938, 'revolution': 0.0030839233161323214, 'revolutionary': 0.0018628591633699006, 'reward': 0.009122354577945725, 'rewarded': 0.0015319298587311032, 'rewrite': 0.00011497600573342169, 'rf': 0.0012827028287951915, 'rfd': 0.001921522106299118, 'rfox': 0.004573335506731118, 'rgb': 0.010807086540932365, 'rgc3679': 0.0056961229282937636, 'rhea': 0.0018628591633698963, 'rhoemer': 0.001825425726571352, 'ricardo': 0.00569612292829377, 'rice': 0.0037539385145901353, 'rich': 0.009272962018010322, 'richard': 0.002664937381236964, 'richardson': 0.0006417411980615632, 'richmond': 0.0028377632635275185, 'rick': 0.005475821970543135, 'rickel': 0.0018628591633698963, 'ricky': 0.003157558429105277, 'rid': 0.0013315655255009143, 'riddle': 0.0015319298587311032, 'ride': 0.004068613808573207, 'rides': 0.0012603864489062547, 'ridge': 0.0018924586447506726, 'ridicule': 0.0027400885069510696, 'ridiculous': 0.00033144514648310135, 'ridout': 0.0012609485946591687, 'rigel': 0.005353617008090851, 'right': 0.01096431396935536, 'righteous': 0.011288028122710236, 'righteousness': 0.0036560569852768267, 'rightly': 0.0007117181907135006, 'rights': 0.0060264576157264774, 'rincon': 0.0012609485946591687, 'ring': 0.0025301834178473783, 'rings': 0.003108141579466514, 'rins': 0.003731800431935113, 'rintintin': 0.0012691491483781056, 'rios': 0.0012412324256375618, 'rip': 0.0013262274963396362, 'risale': 0.0027400885069510696, 'risalesi': 0.0027400885069510696, 'risc': 0.004425442103239916, 'rise': 0.006236609206626363, 'risen': 0.0027400885069510687, 'rising': 0.0010442927627179474, 'risk': 0.0019375778089176987, 'risks': 0.004981161405813843, 'risky': 0.0018628591633699006, 'rite': 0.0036560569852768275, 'ritter': 0.0012609485946591687, 'ritual': 0.0048809263353922615, 'rituals': 0.0027400885069510696, 'river': 0.0006251111015571457, 'rivers': 0.0018705330287465275, 'rix': 0.002524661375586772, 'rjck': 0.0031575584291052743, 'rjl': 0.001825425726571352, 'rjs002c': 0.0012609485946591687, 'rjungcla': 0.0012412324256375635, 'rknight': 0.0012609485946591687, 'rl': 0.002221550920473124, 'rle': 0.0031575584291052778, 'rls': 0.0024851616866216125, 'rm': 0.002524661375586772, 'rmit': 0.0018924586447506718, 'road': 0.0025063846837866492, 'roads': 0.009355553028283954, 'rob': 0.0035197890024430455, 'robert': 0.007943193348495671, 'roberts': 0.0012609485946591687, 'robertson': 0.003181360993385343, 'robin': 0.0028573361544391466, 'robinson': 0.001825425726571352, 'robot': 0.0015035858261545658, 'robotics': 0.0027218795235153916, 'robots': 0.0012717306823408032, 'robust': 0.0018924586447506718, 'rochester': 0.008873889855164695, 'rock': 0.002756524925716284, 'rocker': 0.001825425726571352, 'rocket': 0.02613941970225676, 'rocketdyne': 0.002485161686621608, 'rocketeer': 0.0024851616866216134, 'rocketry': 0.00560686673732939, 'rockets': 0.02276542144064513, 'rocks': 0.0031517615120046248, 'rockwell': 0.0065020889945605585, 'rocky': 0.0015527953218988713, 'rod': 0.0018924586447506718, 'rodney': 0.0012499951251094144, 'rodrigues': 0.0012412324256375635, 'rods': 0.0015319298587311032, 'roehm': 0.0036560569852768267, 'roger': 0.0012717306823408032, 'rogers': 0.0009836938410219646, 'roi': 0.0012499951251094144, 'rokne': 0.0012609485946591687, 'roland': 0.000978451715284566, 'role': 0.0046170428020167464, 'roll': 0.002408254005395841, 'rolled': 0.0018628591633699006, 'rolling': 0.0013262274963396362, 'rollout': 0.0024851616866216125, 'rolls': 0.0006417411980615632, 'rom': 0.003227172826608583, 'roman': 0.004973853600981847, 'romance': 0.0006398485452691399, 'romanick': 0.003157558429105275, 'romans': 0.008255637787672635, 'romantic': 0.0024851616866216125, 'rome': 0.0015626450162182998, 'roms': 0.0021657174445653135, 'ron': 0.014611573504751953, 'roof': 0.001520379122855315, 'room': 0.0017639685451044836, 'root': 0.005590019104670484, 'roots': 0.000952889200262875, 'rope': 0.0015319298587311032, 'rosa': 0.0018924586447506718, 'rosae': 0.006411840182243065, 'rose': 0.011235068704328149, 'roseae': 0.00365605698527683, 'rosicrucian': 0.0156844767675768, 'rosicrucianum': 0.0027400885069510696, 'ross': 0.0052937953156299055, 'rostamian': 0.0018628591633698963, 'rot': 0.004067548280286904, 'rotag': 0.0036560569852768275, 'rotate': 0.0007680836434790653, 'rotated': 0.0006516076727636853, 'rotating': 0.001304990985299034, 'rotation': 0.002274298567388134, 'rotational': 0.0018628591633698963, 'rotations': 0.0012499951251094144, 'rotfl': 0.0012609485946591687, 'rouben': 0.0018628591633698963, 'rough': 0.0030470526777740398, 'roughly': 0.0015893362630325786, 'round': 0.001790400007907384, 'rourke': 0.003791151453497659, 'rousseau': 0.009179532565505875, 'route': 0.0013558269777203544, 'routine': 0.007046228026662233, 'routinely': 0.0009236759316832519, 'routines': 0.011407795739921647, 'rover': 0.003108141579466512, 'row': 0.0013649484181175245, 'rowan': 0.002454726329680262, 'rowlands': 0.0012609485946591687, 'roy': 0.004288333772413589, 'royal': 0.009426616262932045, 'royalroads': 0.019431600557536538, 'royalty': 0.0006516076727636853, 'royc': 0.007333075149745416, 'rpi': 0.008342035783580764, 'rpm': 0.0012412324256375635, 'rrz': 0.0012609485946591687, 'rs': 0.002332493875067958, 'rs43873': 0.0018924586447506726, 'rs6000': 0.0037911514534976548, 'rsg': 0.0012609485946591687, 'rsiatl': 0.0018628591633699006, 'rt': 0.0026253213246470314, 'rtfm': 0.0012609485946591687, 'rtg': 0.0024851616866216125, 'rtgs': 0.0012412324256375635, 'rtrace': 0.002524661375586771, 'rubber': 0.0012603864489062547, 'rubeae': 0.00365605698527683, 'ruca': 0.0012412324256375635, 'rudimentry': 0.004425442103239911, 'rued': 0.0012609485946591687, 'ruff': 0.0018924586447506718, 'rui': 0.0012412324256375635, 'ruin': 0.0012808370180140277, 'rule': 0.0035599421150790227, 'ruled': 0.0024851616866216134, 'ruler': 0.001825425726571352, 'rules': 0.008135481500024409, 'ruling': 0.0024851616866216125, 'rum': 0.0018924586447506718, 'rumor': 0.0026573399917276495, 'rumors': 0.0019027489409697857, 'rumours': 0.013379703617728549, 'run': 0.008303073942953383, 'running': 0.010119682097231675, 'runs': 0.003511681481220473, 'runyon': 0.0024851616866216125, 'rusnews': 0.007333075149745417, 'russell': 0.0018650454236717635, 'russia': 0.00511989925861302, 'russian': 0.016958061920745525, 'russians': 0.00686033516033944, 'rutgers': 0.001954133783715657, 'rutherford': 0.0019306435466962882, 'ruu': 0.004237073704067396, 'rw': 0.0030847158139595578, 'rwd4f': 0.00365605698527683, 'rws2v': 0.0012609485946591687, 'rwtms2': 0.003731800431935112, 'ryan': 0.002225142193562536, 'ryde': 0.0018705330287465275, 'ryukoku': 0.003731800431935113, 'rz': 0.0013558269777203544, 's3': 0.0012609485946591687, 's_braun': 0.0012609485946591687, 'sa': 0.004274677838270878, 'sabbath': 0.007333075149745414, 'saber': 0.0012412324256375635, 'sabin': 0.008255637787672635, 'sacam': 0.003791151453497659, 'sacco': 0.00457333550673112, 'sacred': 0.0024363865949890897, 'sacrifice': 0.010104763978199323, 'sad': 0.005499864164451124, 'saddam': 0.0036560569852768267, 'safe': 0.004591397082138003, 'safety': 0.016576158772451766, 'sagan': 0.0018628591633698963, 'saic': 0.0019677348354746535, 'said': 0.029727826087116868, 'sail': 0.0034628723206869957, 'sailing': 0.0018628591633698963, 'sails': 0.006233257448747928, 'saint': 0.00430726825863754, 'saints': 0.008255637787672646, 'sake': 0.0033834040847699432, 'sal': 0.0024851616866216134, 'sale': 0.006233257448747921, 'salem': 0.0006496982395886239, 'sales': 0.004173398321553421, 'salt': 0.002182135963275971, 'salvation': 0.0213134703288432, 'salyut': 0.0018628591633698963, 'sam': 0.0015861665554856063, 'sample': 0.0023624285434110243, 'samples': 0.001599663558956902, 'sampling': 0.0018803995034486513, 'samson': 0.002524661375586772, 'samuel': 0.00365605698527683, 'san': 0.005951074373799566, 'sandman': 0.0010442927627179474, 'sands': 0.0030586826493494415, 'sandvik': 0.04434345690825281, 'santa': 0.0012077905511578323, 'sao': 0.0012603864489062547, 'sarah': 0.0012609485946591687, 'sarver': 0.007333075149745417, 'sat': 0.0022662066321295807, 'satan': 0.010104763978199326, 'satellite': 0.02338989759924945, 'satellites': 0.020250848240356202, 'satisfactory': 0.0003671943352615125, 'satisfied': 8.793789117982759e-07, 'satisfy': 0.0003091276322491551, 'saturation': 0.0012609485946591687, 'saturday': 0.003050031671462089, 'saturn': 0.00859924987999338, 'saturnian': 0.0018628591633698963, 'saucers': 0.0024851616866216134, 'saul': 0.00365605698527683, 'saundrsg': 0.004356139840040942, 'save': 0.005048090563717456, 'saved': 0.007059622299767098, 'saves': 0.002283925816559054, 'saving': 0.006490479844330896, 'savings': 0.0018803995034486513, 'saviour': 0.005491928440954983, 'saw': 0.0044244767814958985, 'sawyer': 0.0024851616866216125, 'say': 0.04177454569631092, 'saying': 0.016444013879271586, 'says': 0.02971485876690703, 'sbc': 0.00549192844095498, 'sbctri': 0.0027400885069510687, 'sc': 0.0037033366669536093, 'scaffolding': 0.0027400885069510696, 'scalar': 0.0015319298587311032, 'scale': 0.0053134916511120385, 'scaled': 0.0027218795235153916, 'scales': 0.0031136322339350925, 'scaling': 0.003775763852345842, 'scan': 0.003963966096004946, 'scandals': 0.001825425726571352, 'scanned': 0.004448597730836989, 'scanner': 0.0032269421523983856, 'scanners': 0.0016958301188799586, 'scanning': 0.0016958301188799586, 'scares': 0.0007018517160113221, 'scarolina': 0.0036848945946956037, 'scary': 0.0019677348354746535, 'scene': 0.006159248682041933, 'scenes': 0.0032606947822749503, 'scf': 0.002524661375586771, 'schaefer': 0.0022072227891300807, 'schaumburg': 0.003108141579466518, 'schedule': 0.004524634624964533, 'scheduled': 0.009375548629619129, 'schedules': 0.0033733168848706693, 'scheme': 0.003731800431935114, 'schemes': 0.0007163598861018444, 'schiewer': 0.0024851616866216125, 'schmidt': 0.0022391211938598225, 'scholar': 0.005491928440954982, 'scholarly': 0.005591611525152398, 'scholars': 0.012888523361583592, 'scholarship': 0.0026646314304903523, 'school': 0.0049154762684760905, 'schools': 0.003753723296789132, 'schuerkamp': 0.0018628591633698963, 'schumach': 0.0018628591633698963, 'schumacher': 0.0018628591633699006, 'schwartz': 0.0012609485946591687, 'schwarzenegger': 0.004981161405813842, 'sci': 0.04336381710767926, 'scic': 0.001825425726571352, 'scicom': 0.003731800431935114, 'science': 0.020388954129590173, 'sciences': 0.003902822236612805, 'scientific': 0.015361286828955469, 'scientist': 0.002295609842978918, 'scientists': 0.0033361690736612255, 'scintillation': 0.0018628591633699006, 'sciviguy': 0.0013558269777203544, 'scn': 0.0012609485946591687, 'sco': 0.0013558269777203544, 'scodal': 0.0031575584291052743, 'scope': 0.0008317159444114998, 'scotched': 0.00365605698527683, 'scott': 0.002070436037964898, 'scotti': 0.0012412324256375635, 'scout': 0.003126050117186181, 'scratching': 0.0012160848046758686, 'screen': 0.025546627931455304, 'screens': 0.0021891043107271193, 'screw': 4.035731769314044e-05, 'scri': 0.00010510953103124408, 'script': 0.0006703468019723805, 'scripting': 0.0012609485946591687, 'scripture': 0.013819146780228081, 'scriptures': 0.013819146780228083, 'scroll': 0.0018924586447506726, 'scrolling': 0.004425442103239913, 'scrowe': 0.004425442103239911, 'scsi': 0.0012609485946591687, 'sctc': 0.0012609485946591687, 'sdcc12': 0.0027400885069510696, 'sdi': 0.0049811614058138465, 'sdio': 0.009375548629619139, 'sdsc': 0.0012499951251094144, 'sdsu': 0.004425442103239914, 'se': 0.002469361246499778, 'se92psh': 0.0012609485946591687, 'sea': 0.00467936932423363, 'seal': 0.00216277133786857, 'seale': 0.0012412324256375618, 'sealed': 0.0002992611575469784, 'seals': 0.0036560569852768267, 'sean': 0.00957291497180817, 'seanmac': 0.0018924586447506718, 'search': 0.008145888243554219, 'searched': 0.0018924586447506726, 'searches': 0.0018705330287465275, 'searching': 0.0009746168316737665, 'searcy': 0.00365605698527683, 'seas': 0.0031136322339350925, 'seat': 0.00365605698527683, 'seattle': 0.0013261027446605563, 'sec': 0.003457915536755659, 'second': 0.006618116734909674, 'secondary': 0.0002992611575469784, 'secondly': 0.00039751840402391624, 'seconds': 0.005155657758904601, 'secret': 0.007397479015976069, 'secrets': 0.001825425726571352, 'sect': 0.005491928440954982, 'section': 0.006383761578817272, 'sectional': 0.0018628591633698963, 'sections': 0.0021327447189448297, 'sector': 0.0081165580958805, 'secular': 0.007333075149745415, 'secure': 4.035731769314044e-05, 'security': 0.003412582754313569, 'seder': 0.001825425726571352, 'seds': 0.0018628591633698963, 'seed': 0.004096479038702244, 'seeing': 0.0019263242567578824, 'seek': 0.004033231128531583, 'seeking': 0.0028443456125091925, 'seeks': 0.005491928440954984, 'seemingly': 4.035731769314044e-05, 'seen': 0.007684204992027789, 'sees': 0.0009082785328602561, 'segment': 0.0012912531670693506, 'segmentation': 0.0018924586447506726, 'segments': 0.0019111977739593115, 'sei': 0.003108141579466519, 'seirio': 0.002524661375586772, 'seldom': 0.0018924586447506726, 'select': 0.004922895177811775, 'selected': 0.0018656673615770596, 'selection': 0.0022919027082398792, 'selective': 0.0010442927627179474, 'self': 0.017727578137229853, 'selfish': 0.005491928440954983, 'sell': 0.0025562036134266237, 'selling': 0.0007939361763243617, 'sells': 0.0013356730305772568, 'selway': 0.0027400885069510696, 'semi': 0.0008309688672377153, 'seminar': 0.003131202507321784, 'semitism': 0.0036560569852768275, 'send': 0.011214961170832606, 'sender': 0.025965288292502775, 'sending': 0.0006750392740673987, 'sends': 4.035731769314044e-05, 'senior': 0.0008089055265102047, 'sense': 0.01637934460832872, 'sensed': 0.0012499951251094144, 'senses': 0.0018667219248472162, 'sensible': 0.0018134151655027544, 'sensing': 0.004081074272103518, 'sensitive': 0.0009236759316832519, 'sensitivity': 0.0013371565680386924, 'sensor': 0.003731800431935113, 'sensors': 0.0062332574487479345, 'sent': 0.0030521889064098707, 'sentence': 0.004579599811766367, 'sentient': 0.001825425726571352, 'sep': 0.001355065105758356, 'separate': 0.0016278312473784456, 'separated': 0.0009284200503372414, 'separately': 0.0012412324256375635, 'separates': 0.0018628591633699006, 'separating': 0.0021524677623682162, 'separation': 0.0018830022181066785, 'seperate': 0.003043748562888326, 'sept': 0.0012808370180140277, 'september': 0.003108141579466518, 'septuagint': 0.0027400885069510687, 'sequence': 0.0025740536802989072, 'sequences': 0.002961107039509709, 'sequent': 0.0012499951251094144, 'seri': 0.0012609485946591687, 'serial': 0.0016958301188799586, 'series': 0.00948582489880792, 'seriously': 0.007515786273798033, 'sermon': 0.00825563778767264, 'seront': 0.0018628591633699006, 'serpent': 0.0012160848046758686, 'servant': 0.005491928440954984, 'serve': 0.005800173460912416, 'served': 0.001940510021398465, 'server': 0.004421286719744849, 'servers': 0.005402936260006723, 'serves': 0.004060118891597639, 'service': 0.003892729151453816, 'services': 0.005813226790760745, 'servicing': 0.003731800431935114, 'session': 0.003153690623228918, 'sessions': 0.0018815982925785906, 'set': 0.007422566617326402, 'seth': 0.004346767947602697, 'seti': 0.0024851616866216125, 'sets': 0.003968719654569768, 'setting': 0.0009800134385635371, 'settings': 0.0012717306823408032, 'settle': 0.0003091276322491551, 'settled': 0.002436271697723395, 'setup': 0.0007163598861018444, 'setups': 0.0018803995034486513, 'seven': 0.003246269744490323, 'seventh': 0.0012259344989952962, 'severe': 0.00010510953103124408, 'severely': 0.0018628591633699006, 'sex': 0.008195460094086619, 'sexist': 0.0012412324256375635, 'sexual': 0.008255637787672646, 'sexuality': 0.0027400885069510687, 'sexually': 0.0027400885069510696, 'sez': 0.003108141579466519, 'sf': 0.004033138557964387, 'sfsu': 0.0018628591633699006, 'sfsuvax1': 0.0018628591633699006, 'sfu': 0.0037605978194303457, 'sg': 0.003435066656521998, 'sgi': 0.016067175110820956, 'sgis': 0.0025246613755867744, 'shade': 0.001300553187035633, 'shaders': 0.0012609485946591687, 'shades': 0.002674481124809779, 'shading': 0.008885150472506749, 'shadow': 0.0029350303442129645, 'shadows': 0.0013356730305772568, 'shafer': 0.013804001614535159, 'shag': 0.0012412324256375635, 'shakala': 0.0024851616866216125, 'shake': 0.0018496845972676042, 'shakespeare': 4.035731769314044e-05, 'shall': 0.013613964274034508, 'shalt': 0.008255637787672635, 'shame': 0.0026646314304903523, 'shannon': 0.0018628591633699006, 'shape': 0.002762045852294007, 'shaped': 0.003731800431935113, 'shapes': 0.0024432256719819773, 'share': 0.003594157106186883, 'shared': 0.00036440142293393384, 'shareware': 0.009694205823037021, 'sharing': 0.00012627327507338994, 'sharp': 0.001347039880397861, 'sharply': 0.0009236759316832519, 'shea': 0.0021667751368718118, 'shed': 0.0007018517160113221, 'sheep': 0.0031965114464401123, 'sheet': 0.002229333024755002, 'sheets': 0.0018628591633698963, 'shelf': 0.0035184432127872067, 'shell': 0.0013649484181175245, 'shelley': 0.005728118948639728, 'sherwood': 0.0018924586447506718, 'sherzer': 0.018907542508795887, 'shielded': 0.0017855205597762545, 'shielding': 0.003108141579466518, 'shin': 0.0018924586447506718, 'shine': 0.001825425726571352, 'shines': 0.001825425726571352, 'ship': 0.0029482530894099314, 'shipped': 0.0012412324256375635, 'shipping': 0.003845521124814356, 'shirlene': 0.0012412324256375618, 'shit': 0.00256625082338921, 'shock': 0.0012412324256375635, 'shoemaker': 0.003731800431935112, 'shoot': 0.0020879936223278618, 'shooting': 0.0011727949367685234, 'shop': 0.0016958301188799586, 'shopper': 0.0018331313345243579, 'short': 0.0024574596904589916, 'shorter': 0.0012629530417339009, 'shortly': 0.00033144514648310135, 'shot': 0.0032728767361999865, 'shots': 0.003382596524808916, 'shoulders': 0.0027400885069510696, 'shouldn': 0.0029595989910271014, 'shouted': 4.035731769314044e-05, 'showcase': 0.000988318189986688, 'showed': 0.004224674840391082, 'showing': 0.002634559771954051, 'shown': 0.0026892771228665515, 'shows': 0.004741986478782406, 'shrewd': 0.001825425726571352, 'shroud': 0.0018628591633699006, 'shround': 0.0018628591633699006, 'shuffle': 0.0018628591633699006, 'shut': 0.001714315136659394, 'shutdown': 0.0018628591633699006, 'shuttle': 0.05344097661835926, 'shuttles': 0.0024851616866216134, 'si': 0.008737557245493592, 'sic': 0.001520379122855315, 'sick': 0.006000296511006597, 'sides': 0.0017456059304056214, 'sieferman': 0.004573335506731118, 'sieferme': 0.0027400885069510696, 'siemon': 0.0036560569852768275, 'sig': 0.0003903364187397918, 'siggraph': 0.008885150472506754, 'sigh': 0.002791494288202423, 'sight': 0.002144107221564112, 'sighted': 0.003108141579466518, 'sightings': 0.002485161686621608, 'sigma': 0.0020361452852944734, 'sign': 0.004011990100495227, 'signal': 0.006377442207887095, 'signals': 0.0021995226876789144, 'signature': 0.0013770281393766168, 'signatures': 0.0006516076727636853, 'signed': 0.0015035858261545658, 'significance': 0.009423893276521704, 'significant': 0.004906510406218669, 'significantly': 0.0012685919551770498, 'signing': 0.00011497600573342169, 'signs': 0.0015448877753555896, 'sigurdsson': 0.007488101498518765, 'silence': 0.004438294231295022, 'silent': 0.0033949855597089846, 'silicon': 0.005523985375379084, 'silly': 0.0014294663767678868, 'siltanen': 0.0012609485946591687, 'silver': 0.002288022904467858, 'sim': 0.0022953390170244335, 'similar': 0.0030630127025403284, 'similarly': 0.0018362047985634447, 'simon': 0.004998838893841578, 'simple': 0.004693449630102368, 'simpler': 0.0016958301188799586, 'simplicity': 0.0022056355455956, 'simply': 0.008165681617751903, 'simtel20': 0.002524661375586771, 'simulated': 0.0024851616866216125, 'simulation': 0.0037962528390088224, 'simulations': 0.0034728585782364393, 'simulator': 0.00010510953103124408, 'simultaneous': 0.0018924586447506718, 'simultaneously': 0.0016661801242341696, 'sin': 0.028855692287660325, 'sincerely': 0.0021274006410962427, 'sinful': 0.00549192844095498, 'sing': 0.00039751840402391624, 'singapore': 0.0028032790874212747, 'single': 0.008900533155463445, 'sink': 0.0021484342404152522, 'sinners': 0.00365605698527683, 'sins': 0.013056411348755981, 'sipp': 0.0012609485946591687, 'sir': 0.009057062429398695, 'sirtf': 0.0012412324256375635, 'sister': 0.0012603864489062547, 'sit': 0.0018452344383494239, 'site': 0.008891060792723369, 'sites': 0.006870341476453304, 'sits': 0.0012629530417339009, 'sitting': 0.0025107468547136344, 'situation': 0.004712066166527839, 'situations': 0.0012761027140146368, 'situnaya': 0.0025246613755867744, 'sixteen': 4.035731769314044e-05, 'sixth': 0.0018650454236717635, 'size': 0.006037318656535546, 'sized': 0.001907356230328468, 'sizes': 0.0021327447189448297, 'sjc': 0.0018628591633699006, 'skates': 0.0018628591633699006, 'skeptic': 0.0018924586447506726, 'skewed': 0.0012499951251094144, 'skiba': 0.0027400885069510687, 'skies': 0.004641374584998533, 'skills': 0.001907356230328468, 'skin': 0.00011497600573342169, 'skinner': 0.001825425726571352, 'skip': 0.0009433921007048016, 'skndiv': 0.005606866737329392, 'sky': 0.02449483218359259, 'skylab': 0.003731800431935114, 'slac': 0.0012609485946591687, 'slander': 0.00365605698527683, 'slc': 0.0012412324256375635, 'sleep': 0.0027588032383091786, 'slice': 0.0016194133460181942, 'slices': 0.002524661375586772, 'slick': 0.0019229696813196587, 'slide': 0.0033843263835107214, 'slides': 0.0012499951251094144, 'slight': 0.0018891842862327687, 'slightest': 0.004370099599025862, 'slightly': 0.00040640211783123537, 'slimy': 0.0012259344989952962, 'sloan': 0.003791151453497654, 'slope': 0.0012609485946591687, 'slots': 0.0012499951251094144, 'slow': 0.004157146365564233, 'slower': 0.002525274210515814, 'slowly': 0.0003091276322491551, 'sls': 0.0025114946594801584, 'sluice': 0.0018628591633698963, 'sm': 0.0028032790874212747, 'small': 0.010842474860194466, 'smaller': 0.0026687255736107876, 'smallest': 0.002456102764010641, 'smart': 0.0012717306823408032, 'smell': 0.0019116724119796905, 'smi': 0.0012412324256375635, 'smile': 0.0012259344989952962, 'smiley': 0.0031939224752976104, 'smith': 0.004278182733641778, 'smithsonian': 0.004356139840040938, 'smoke': 0.0051896747964094376, 'smoking': 0.0012808370180140277, 'smooth': 0.0022685703799729144, 'smoothing': 0.00312131919496262, 'smsu': 0.0012609485946591687, 'snail': 0.0008613659390572332, 'snake': 0.0015417795530505863, 'snap': 0.0012412324256375635, 'sni': 0.01568447676757681, 'snide': 0.00365605698527683, 'snip': 0.0012609485946591687, 'snow': 0.003731800431935113, 'snr': 0.0012412324256375635, 'snydefj': 0.003731800431935114, 'snyder': 0.0031081415794665165, 'soc': 0.0022361234919634635, 'social': 0.004713805861049243, 'societies': 0.005089599210770964, 'society': 0.011070472699801586, 'socs': 0.0006417411980615632, 'soest': 0.0015626450162182998, 'soft': 0.0025688945788112294, 'softlab': 0.0012609485946591687, 'softquad': 0.0024851616866216064, 'software': 0.02044773427580651, 'soil': 0.0022953390170244335, 'sol': 0.0026253213246470314, 'solar': 0.03367160232174896, 'sold': 0.002037460398852411, 'soldiers': 0.0015527953218988713, 'solely': 0.002278512863596773, 'solid': 0.008203992504460723, 'solntze': 0.00549192844095498, 'solomon': 0.0028370754228893864, 'solution': 0.007918711740197669, 'solutions': 0.0028644073180025794, 'solve': 0.0025681335673431735, 'solved': 0.0007036071049306121, 'solving': 0.001304990985299034, 'somalia': 0.0018628591633699006, 'somebody': 0.00230290912068859, 'someday': 0.0018496845972676042, 'somenone': 0.0018924586447506726, 'somewhat': 0.001928785092858959, 'somwhere': 0.0010442927627179474, 'son': 0.014012531749160957, 'sonderen': 0.0012609485946591687, 'song': 0.0021418510546180507, 'songs': 0.0018134151655027544, 'sonic': 0.0012412324256375635, 'sons': 0.004486663636334091, 'sony': 0.000988318189986688, 'soon': 0.0011028667660178777, 'sooner': 4.035731769314044e-05, 'sophia': 0.0037911514534976556, 'sophisticated': 0.0013371565680386907, 'sorrow': 0.0009433921007048016, 'sorry': 0.0017895376824758153, 'sort': 0.0050278277264269615, 'sorts': 0.0028056740801960228, 'sought': 0.0028032790874212747, 'soul': 0.005675216410945488, 'souls': 0.006109718166077233, 'sound': 0.005604520538500296, 'sounded': 0.0026573399917276495, 'sounder': 0.0018628591633698963, 'sounding': 0.004193371194327906, 'sounds': 0.00388852511356212, 'source': 0.006133792529102277, 'sources': 0.004814286065902566, 'south': 0.004944239449164895, 'southern': 0.004889774820182214, 'southwest': 0.000988318189986688, 'southwestern': 0.004984797347275491, 'soviet': 0.008969342631002367, 'soviets': 0.0018628591633698963, 'soyuz': 0.004356139840040938, 'sp': 0.003398079117558732, 'sp1marse': 0.002524661375586772, 'space': 0.20115901737978983, 'spacecraft': 0.04312610680155269, 'spaced': 0.0015332358208003521, 'spaceflight': 0.00874570659123132, 'spacehab': 0.003731800431935113, 'spacelab': 0.001599663558956902, 'spacelifter': 0.0024851616866216064, 'spacelink': 0.0037361966970264554, 'spacenews': 0.0018628591633699006, 'spaceship': 0.0018628591633699006, 'spacewalk': 0.002485161686621608, 'spacewalks': 0.0012412324256375635, 'spacewatch': 0.003108141579466519, 'spam': 0.0034021501533540374, 'span': 0.008116558095880515, 'spanish': 0.0012160848046758686, 'sparc': 0.002524661375586772, 'sparcstation': 0.005060432039124044, 'spare': 0.0018031183160984914, 'spark': 0.0003091276322491551, 'spartan': 0.004425442103239916, 'spatial': 0.0036168424934634336, 'spd': 0.0012609485946591687, 'speak': 0.01267916483244641, 'speakers': 0.0016459550803904766, 'speaketh': 0.001825425726571352, 'speaking': 0.003364994260850936, 'spec': 0.006969614267041954, 'special': 0.006264678344778512, 'specialist': 0.0024851616866216125, 'specialists': 0.0018628591633698963, 'specialized': 0.0022928590225269633, 'specializes': 0.0006417411980615632, 'specialty': 4.035731769314044e-05, 'species': 0.007775393704209693, 'specific': 0.0034672098984988835, 'specifically': 0.005607477187129936, 'specification': 0.0056961229282937636, 'specifics': 0.0018331313345243579, 'specified': 0.0016571985107683958, 'specifies': 0.00036440142293393384, 'specify': 0.0024575018725063735, 'specs': 0.00437263999314957, 'spectra': 0.0007163598861018444, 'spectral': 0.0016738670852616978, 'spectrograph': 0.0018628591633698963, 'spectrometer': 0.002844115383564492, 'spectroscopy': 0.0012412324256375635, 'spectrum': 0.003204581618239592, 'speculate': 0.0018496845972676042, 'speculation': 0.005029955221654784, 'speculative': 0.0024363865949890897, 'speech': 0.0033902916313473174, 'speed': 0.009322420674577829, 'speeds': 0.0027163700651970076, 'speedstar': 0.007607418082978784, 'spell': 0.001321817270076367, 'spelling': 0.0019116724119796905, 'spencer': 0.03291133454117677, 'spend': 0.0045609905967906525, 'spending': 0.009375548629619132, 'spent': 0.0047514109458345315, 'sphere': 0.009440970111605993, 'spheres': 0.001064042549779238, 'spherical': 0.003340558889778243, 'spin': 0.008724006222202428, 'spinning': 0.00435943985137679, 'spinoffs': 0.004356139840040938, 'spirit': 0.010351935349017394, 'spiritual': 0.009179532565505862, 'spite': 0.002697221850857013, 'spl': 0.002225894803455769, 'splat': 0.0018924586447506718, 'splendid': 0.0015527953218988713, 'spline': 0.003157558429105275, 'splines': 0.003157558429105275, 'split': 0.008927842769132237, 'splitting': 0.0013010267962684525, 'spock': 8.226937839690696e-05, 'spoiled': 0.0025246613755867744, 'spoke': 0.004079561782361937, 'spoken': 0.0019116724119796905, 'sponsor': 0.002916366227908503, 'sponsored': 0.0024377731766381597, 'sponsoring': 0.001064042549779238, 'sport': 0.0021524677623682162, 'spot': 0.0032715375549426553, 'spotted': 0.0021524677623682162, 'spotting': 0.0015319298587311032, 'spouting': 0.0018134151655027544, 'spraying': 0.0019116724119796905, 'spread': 0.0019141810522399936, 'spreading': 0.005191692831752376, 'spring': 0.003837718822518367, 'springs': 0.0016648102574299507, 'sprites': 0.006969614267041952, 'sps': 0.0018628591633698963, 'sputter': 0.0012412324256375618, 'spworley': 0.0012609485946591687, 'spy': 0.0006604803272702029, 'spyglass': 0.0018924586447506718, 'sq': 0.006257100220851242, 'sqrt': 0.0018803995034486513, 'square': 0.0035098342503132917, 'squick': 0.001825425726571352, 'sr': 0.0012717306823408032, 'srb': 0.008745706591231327, 'srbs': 0.004356139840040938, 'srinivas': 0.0018628591633698963, 'srl02': 0.006860335160339442, 'srl03': 0.006860335160339436, 'srp': 0.0025246613755867744, 'srvr1': 0.0063325164442827675, 'ssd': 0.0012852074653554209, 'ssf': 0.008745706591231323, 'ssi': 0.001862859163369898, 'ssme': 0.003108141579466518, 'ssrbs': 0.0024851616866216134, 'ssrt': 0.005606866737329389, 'ssto': 0.0163500617293583, 'st': 0.004222749118959974, 'stability': 0.0024851616866216125, 'stabilized': 0.0012412324256375618, 'stable': 0.006092977970755283, 'stack': 0.002982401929814333, 'staff': 0.0006395752914771244, 'stage': 0.013162248275540824, 'staged': 0.00279400378189759, 'stages': 0.0040425325530520344, 'stake': 0.002278512863596773, 'stand': 0.00175133817311586, 'standard': 0.00642531915016136, 'standards': 0.005427197667987379, 'standdown': 0.001862859163369898, 'standing': 0.0034519223629203167, 'stands': 0.0083749150102344, 'stanford': 0.006573687409819602, 'stanley': 0.0012412324256375635, 'star': 0.012767134339569384, 'starbase': 0.002524661375586772, 'starcat': 0.001599663558956902, 'starfleet': 0.005562288269038132, 'starflight': 0.0024851616866216134, 'starowl': 0.001825425726571352, 'stars': 0.010048209504995248, 'start': 0.004135635209741684, 'started': 0.006187548944200043, 'starting': 0.002817936697739899, 'startled': 0.004356139840040942, 'starts': 0.002252617530935923, 'startup': 0.0012717306823408032, 'stastny': 0.0012609485946591687, 'state': 0.0028083069143604892, 'stated': 0.006839132572462532, 'statement': 0.009787784912157243, 'statements': 0.004738485345841415, 'states': 0.007766440086990046, 'static': 0.0016958301188799586, 'stating': 0.002215296735425124, 'station': 0.03023038226731784, 'stationary': 0.0012812770092071055, 'stations': 0.0007117022779896962, 'statistical': 0.0015773739227058674, 'statistics': 0.002840760520354757, 'stats': 0.000978451715284566, 'status': 0.008388415130281612, 'stay': 0.0012585105691053098, 'staying': 0.003731800431935113, 'std': 0.0006883898093058465, 'stdvax': 0.0024851616866216125, 'steel': 0.0015996635589569036, 'stefan': 0.0018924586447506718, 'stein': 0.003044610441776843, 'stein2': 0.00035791381164745114, 'steinly': 0.0074881014985187675, 'steinn': 0.007488101498518765, 'stellar': 0.003108141579466519, 'step': 0.001224949387507471, 'stephan': 0.002843684528578072, 'stephen': 0.010792746742924006, 'stephens': 0.0018628591633698963, 'stephenson': 0.0018628591633698963, 'steps': 0.0013151414756681174, 'stereo': 0.001347039880397861, 'sterling': 0.0018803995034486513, 'sternberg': 0.0015319298587311032, 'stesis': 0.00035791381164745114, 'steve': 0.005831236753698749, 'steven': 0.004300259713237105, 'stevens': 0.0012412324256375618, 'stewart': 0.0013598921843151496, 'stgprao': 0.0031575584291052778, 'stick': 0.0022332067160148942, 'sticks': 0.004036506195587863, 'stiff': 0.0024448766353608346, 'stoakley': 0.0012609485946591687, 'stock': 0.0018925273642776512, 'stockel': 0.0012609485946591687, 'stockholm': 0.0010442927627179474, 'stole': 0.0012603864489062547, 'stone': 0.0013745494237725423, 'stones': 0.0036560569852768267, 'stood': 0.00365605698527683, 'stooke': 0.0012412324256375618, 'stop': 0.015238717041633827, 'stopped': 0.004981161405813843, 'stops': 0.00318979845655927, 'storage': 0.004355402843705817, 'store': 0.001394832982560613, 'stored': 0.004496525096192449, 'stores': 0.00036440142293393384, 'stories': 0.010714744876041554, 'storing': 0.0018924586447506718, 'storm': 0.002456102764010641, 'story': 0.007707911609936648, 'straight': 0.0026946875025441455, 'straightforward': 0.005969173989463066, 'strange': 0.002012773090467694, 'strangers': 0.0019744478307144615, 'strap': 0.0018628591633698963, 'strategic': 0.0018628591633698963, 'strategies': 0.0007163598861018444, 'strategy': 0.0024851616866216125, 'stratosphere': 0.0024851616866216125, 'stratospheric': 0.0018628591633698963, 'stratus': 0.0015319298587311032, 'straw': 0.0036560569852768267, 'strawberry': 0.0018628591633699006, 'stream': 0.0009603124800421498, 'streams': 0.0018705330287465275, 'street': 0.00299432047560893, 'strength': 0.007950032672143375, 'stress': 0.003108141579466518, 'stretched': 0.0024851616866216134, 'stretching': 9.215269075613097e-05, 'strict': 0.0012808370180140277, 'strictly': 0.0003671943352615125, 'string': 0.0031056512445498032, 'strings': 0.0017855205597762545, 'strip': 0.0018982996883828178, 'strive': 0.0026646314304903523, 'stroke': 0.0034617720572396897, 'strong': 0.0037180359506708213, 'strongly': 0.003910217509326141, 'struck': 0.0036560569852768275, 'structural': 0.003243744725599822, 'structure': 0.006607221562846738, 'structured': 0.003157558429105277, 'structures': 0.0017533327292326506, 'sts': 0.010357183070602884, 'stsci': 0.0038919247626030768, 'stuart': 0.0019111977739593115, 'stuck': 0.0025597218965381823, 'student': 0.001519347206832584, 'students': 0.0038974316007252038, 'studied': 0.0021418510546180507, 'studies': 0.006446229250588497, 'studio': 0.010165727234577163, 'studserv': 0.001825425726571352, 'study': 0.01378906725939243, 'studying': 0.0010837266885755205, 'stuff': 0.004142393411183859, 'stupid': 0.003170196661821988, 'stupidity': 0.0032106847577353485, 'stusoft': 0.0012609485946591687, 'style': 0.0032227080347523316, 'styles': 0.0015417795530505863, 'su': 0.004584606683832497, 'sub': 0.005119583874059922, 'subcontractors': 0.0012412324256375618, 'subdirectory': 0.0016997325156252636, 'subjected': 0.004272197057295717, 'subjective': 0.012888523361583592, 'subjects': 0.000988318189986688, 'submission': 0.001987614546821075, 'submissions': 0.000988318189986688, 'submit': 0.0015390833645905584, 'submitted': 0.0003091276322491551, 'suborbital': 0.0024851616866216125, 'subroutines': 0.0018924586447506718, 'subsampling': 0.0012609485946591687, 'subscribe': 0.0018190340165897692, 'subscription': 0.0012499951251094144, 'subset': 0.00010510953103124408, 'substance': 0.0059685992049193295, 'substantial': 0.001296105875257923, 'substantially': 0.0031081415794665165, 'substitute': 0.0004088156733638845, 'substituted': 0.00039751840402391624, 'subsystem': 0.0009559019909431317, 'subsystems': 0.0010442927627179474, 'subtly': 0.001921522106299118, 'succeed': 0.0012808370180140277, 'success': 0.0026275289178987185, 'successes': 0.0024448766353608346, 'successful': 0.010445194711989056, 'successfully': 0.004839299230551304, 'successive': 0.001064042549779238, 'successor': 0.00034465163587258686, 'sucked': 0.002278512863596773, 'suddenly': 0.0003091276322491551, 'sue': 0.0025681335673431735, 'suffer': 0.003868824307338677, 'suffered': 0.006137132627071873, 'suffering': 0.005929769568805347, 'sufficient': 0.00011171793155750204, 'sufficiently': 0.0026573399917276495, 'suggest': 0.006022110279069243, 'suggested': 0.0016647236795765009, 'suggesting': 0.0012808370180140277, 'suggestion': 0.0010310489646127123, 'suggestions': 0.00798366694024668, 'suggests': 0.0003753054210443446, 'suicide': 0.007333075149745413, 'suis': 0.009179532565505875, 'suit': 0.001606967953415207, 'suitable': 0.002029331777930245, 'suite': 0.003036998907942683, 'suits': 0.0006604803272702029, 'sum': 0.0003671943352615125, 'sumex': 0.003157558429105275, 'summaries': 0.0018628591633698963, 'summarize': 0.0003474108153178439, 'summarizes': 0.0013262274963396362, 'summary': 0.010153148798724466, 'summer': 0.003965430940937572, 'sun': 0.013855146476642616, 'sun121': 0.0024851616866216134, 'sun4': 0.002524661375586772, 'suncad': 0.0012609485946591687, 'sunday': 0.011456382658907555, 'sunee': 0.0018924586447506718, 'sunfish': 0.00365605698527683, 'sunlight': 0.004608121329177177, 'sunnyvale': 0.0030012838003982975, 'sunos': 0.0016459550803904766, 'sunrise': 0.008116558095880508, 'suns': 0.0012827028287951915, 'sunset': 0.00874570659123132, 'sunsite': 0.002524661375586771, 'sunvax': 0.0012609485946591687, 'sunview': 0.0018924586447506718, 'sunysb': 0.0012609485946591687, 'super': 0.004455357820281984, 'supercomputers': 0.0012609485946591687, 'supercomputing': 0.0030847158139595578, 'superior': 0.0034926346423121866, 'supermac': 0.003157558429105277, 'supernatural': 0.0036560569852768275, 'supernova': 0.0031081415794665165, 'supersedes': 0.0093708729023382, 'supersonic': 0.003108141579466518, 'supplied': 0.002630829945004615, 'supplies': 0.0012717306823408032, 'supply': 0.004688392987772459, 'support': 0.00993067326359057, 'supported': 0.0038814867196750383, 'supporting': 0.0043378226270364, 'supports': 0.004863063334865505, 'suppose': 0.004732955862318835, 'supposed': 0.007607387248515513, 'supposedly': 0.005018053094609341, 'supreme': 0.007333075149745417, 'suprise': 0.0021524677623682162, 'sure': 0.004462800725492571, 'surely': 0.005181315757914063, 'surface': 0.011886094261614678, 'surfaces': 0.005274886473881489, 'surprise': 0.0009715652420128435, 'surprised': 0.004973843532917272, 'surprises': 0.0010442927627179474, 'surprising': 0.0006739571102848205, 'surrender': 0.00549192844095498, 'surrounding': 0.0017764102635305238, 'surroundings': 0.0021946697425983134, 'surveillance': 0.0024917448724188695, 'survey': 0.006727961226783299, 'surveyor': 0.0012412324256375635, 'surveys': 0.0012629530417339009, 'survival': 0.0017855205597762545, 'survive': 0.001228643094538167, 'survives': 0.0013262274963396362, 'surviving': 0.0007032382976603913, 'susan': 0.0027400885069510687, 'susie': 0.004573335506731118, 'suspect': 0.0007421564424255388, 'sustained': 0.002278512863596773, 'sutherland': 0.003131202507321784, 'svga': 0.015316754161408402, 'svr3': 0.003108141579466518, 'svr4': 0.0016459550803904766, 'sw': 0.001355065105758356, 'swaim': 0.0027400885069510687, 'swam': 0.00365605698527683, 'swartz': 0.0018628591633698963, 'swastika': 0.0036560569852768275, 'swear': 0.002750040538837272, 'sweden': 0.0019150563317796342, 'swedish': 0.0007561221414976588, 'sweep': 0.000978451715284566, 'sweet': 0.00011497600573342169, 'sweetpea': 0.004981161405813852, 'swept': 0.0019016336999508757, 'swiss': 0.0025835256039293516, 'switch': 0.0032014569418138284, 'switching': 0.0025246613755867744, 'switzerland': 0.0063325164442827675, 'sword': 0.007333075149745417, 'syd': 0.0012499951251094144, 'sydney': 0.001599663558956902, 'sylvester': 0.0025246613755867744, 'symbol': 0.0027400885069510687, 'symbolic': 0.0037440888202707632, 'symposium': 0.001862859163369898, 'synonymous': 0.0009236759316832519, 'syntax': 0.0015744872567363078, 'synthesis': 0.0007163598861018444, 'sys': 0.005696122928293773, 'sysmgr': 0.011269252547878765, 'systems': 0.013074890337353665, 'sz': 0.0012609485946591687, 'szabo': 0.002491744872418865, 'szechuan': 0.0013558269777203544, 't4': 0.0012412324256375635, 'ta': 0.0003474108153178439, 'table': 0.0012950364740119368, 'tables': 0.001586166555485608, 'tact': 0.0015499786042360887, 'tactic': 0.0027400885069510687, 'tad': 0.0013558269777203544, 'tag': 0.0012801026179278053, 'tahiti': 0.003731800431935113, 'tahko': 0.0012609485946591687, 'tail': 0.0019481148578558583, 'tainted': 0.0036560569852768275, 'taiwan': 0.0018803995034486513, 'taken': 0.010528455854442127, 'takers': 0.0019229696813196587, 'takes': 0.00309984647568097, 'taking': 0.009667329626432561, 'talent': 0.0015525616407321653, 'talk': 0.00899663239037234, 'talked': 0.0006395752914771244, 'talking': 0.005834608645412864, 'talks': 0.0021780845319029204, 'tall': 0.0033528339885715774, 'tamsun': 0.002524661375586771, 'tamu': 0.005420582631930906, 'tamvm1': 0.0016194133460181942, 'tan': 0.003359124521680611, 'tandem': 0.0012412324256375635, 'tang': 0.001967421132581167, 'tangent': 0.00039751840402391624, 'tank': 0.008455096294956105, 'tanks': 0.006147491657059367, 'tao': 0.000952889200262875, 'taoism': 0.001825425726571352, 'tape': 0.006598649524938153, 'tapes': 0.0021721839313897677, 'tar': 0.00949960490974269, 'tares': 0.00365605698527683, 'targa': 0.005060432039124049, 'target': 0.005063685317423764, 'targeted': 0.001586166555485608, 'tarot': 0.0027400885069510687, 'task': 1.7300406278118394e-05, 'tasks': 0.004256311680462348, 'tasmania': 0.002524661375586772, 'taste': 0.0033868270071100064, 'taught': 0.004370099599025862, 'taurus': 0.0025114946594801584, 'tax': 0.0022443123353151516, 'taxed': 0.0025246613755867744, 'taxes': 0.004370554294552052, 'taxpayers': 0.003731800431935114, 'taylor': 0.0009402340405303159, 'tc': 0.0018924586447506718, 'tcd': 0.001974318021271856, 'tcl': 0.0012609485946591687, 'tdawson': 0.011449162096457681, 'tea': 0.0018559239832745917, 'teach': 0.005566617657216946, 'teacher': 0.0013118303758140105, 'teachers': 0.0025637740991381747, 'teaches': 0.010116884682326716, 'teaching': 0.005880453496492892, 'teachings': 0.018492749815047296, 'teal': 0.0018705330287465275, 'team': 0.012230728804035447, 'teams': 0.0024851616866216125, 'teapot': 0.0012609485946591687, 'tear': 0.009179532565505865, 'tearing': 0.001825425726571352, 'tech': 0.0024457483439892617, 'techbook': 0.0012412324256375635, 'technical': 0.012107274501689403, 'technically': 0.0010758071351369362, 'technik': 0.00035791381164745114, 'technique': 0.00397661988382793, 'techniques': 0.002222191054314344, 'technische': 0.002561570375518963, 'techno': 0.003157558429105277, 'technological': 0.004433088527631561, 'technologies': 0.008217044044655189, 'technology': 0.0162182632182724, 'ted': 0.003108141579466519, 'teh': 0.006233257448747923, 'tek': 0.0024980674354368945, 'tektronix': 0.001145131686546892, 'tel': 0.006752357230280665, 'tele': 0.0012412324256375635, 'telecom': 0.003108141579466519, 'telecommunications': 0.002485161686621608, 'telemetry': 0.003731800431935114, 'telepathy': 0.005289595373482465, 'telephone': 0.0021028972547882116, 'telescope': 0.01871841680214667, 'telescopes': 0.001884840403250123, 'telesoft': 0.0024851616866216134, 'television': 0.002855970794602451, 'televison': 0.006233257448747934, 'tell': 0.008931022000750416, 'telling': 0.0017788830519170871, 'tells': 0.0035454892782826692, 'telnet': 0.002784594164535083, 'telos': 0.010569929068483804, 'temp': 0.006969614267041957, 'temperature': 0.003525679459221457, 'temperatures': 0.0018628591633698963, 'templars': 0.0064118401822430655, 'temple': 0.0021818111756709236, 'templi': 0.005491928440954983, 'temporarily': 0.0024851616866216134, 'temporary': 0.010874577810802151, 'temptation': 0.00039751840402391624, 'tend': 0.0009448773470485073, 'tended': 0.0015448877753555896, 'tender': 0.0018362078142529865, 'tends': 0.00034465163587258686, 'tennessee': 0.0018924586447506718, 'tens': 0.004981161405813843, 'term': 0.008021721259483403, 'terminal': 0.002921408262213314, 'terminals': 0.0019249565393640788, 'terminus': 0.004573335506731118, 'terms': 0.003479912898435791, 'terrain': 0.0019111977739593115, 'terrestrial': 0.004356139840040942, 'terrorism': 0.0033955669675567813, 'terrorist': 0.0027400885069510687, 'terry': 0.0035557283578460854, 'tesla': 0.002221550920473124, 'test': 0.007833742848291874, 'testament': 0.01755528210575165, 'testbed': 0.0012412324256375635, 'testbeds': 0.0024851616866216125, 'tested': 0.0031294004199932616, 'testify': 0.005491928440954982, 'testimony': 0.007775393704209693, 'testing': 0.001645719436296397, 'tests': 0.00489604714086937, 'tex': 0.000988318189986688, 'texans': 0.0024851616866216134, 'texas': 0.0033553544344056014, 'text': 0.007520122097580065, 'texts': 0.005089599210770964, 'texture': 0.006693240150457217, 'textures': 0.0037911514534976574, 'tffreeba': 0.004356139840040938, 'tga': 0.008245929584991842, 'th': 0.0025626053206787725, 'tha': 0.001300553187035633, 'thank': 0.0038793640470155483, 'thanks': 0.060202010019767334, 'thanx': 0.004533898111499477, 'the_doge': 0.0027400885069510696, 'thee': 0.003382596524808915, 'theism': 0.0027400885069510687, 'thelema': 0.0027400885069510687, 'theme': 8.088279674783698e-05, 'themes': 0.004573335506731118, 'theologians': 0.004573335506731121, 'theological': 0.005491928440954982, 'theology': 0.004573335506731121, 'theoretical': 0.0047850067731189955, 'theoretically': 0.0013262274963396362, 'theories': 0.006695720830118065, 'theory': 0.006572642663904422, 'theporch': 0.00686033516033945, 'therapy': 0.0027400885069510687, 'thereof': 0.001300553187035633, 'thermal': 0.009375548629619127, 'theseas': 0.002524661375586771, 'thesis': 0.0007456560000294937, 'thief': 0.004573335506731121, 'thier': 0.0033844189921217096, 'thing': 0.00932083078925897, 'things': 0.016962970228628853, 'think': 0.020363135668536817, 'thinking': 0.006442587710211214, 'thinks': 0.006206393773766193, 'thinman': 0.0012609485946591687, 'thinning': 0.000988318189986688, 'thiokol': 0.003108141579466512, 'thirty': 0.0027658400197057348, 'tholen': 0.0018628591633699006, 'thomas': 0.007953408834221493, 'thor': 0.0016661801242341696, 'thoroughly': 0.0010172262518655445, 'thou': 0.012557456603401667, 'thought': 0.01428980429275653, 'thoughts': 0.004404085874525873, 'thousand': 0.002414496711372037, 'thousands': 0.003500796776259917, 'thread': 0.0057671613201356, 'threat': 0.007024808001670799, 'threshold': 0.000978451715284566, 'threw': 0.0033193706158301155, 'throw': 0.0028864361583316738, 'throwing': 0.0006739571102848205, 'thrust': 0.003193922475297612, 'thruster': 0.004356139840040946, 'thrusters': 0.0019965781299750842, 'thu': 0.0019420334121340024, 'thumb': 0.0006703468019723805, 'thursday': 0.001058781479937508, 'thyagi': 0.010104763978199323, 'ti': 0.01912858363237869, 'tiang': 0.0012609485946591687, 'tides': 0.0012412324256375635, 'tie': 0.0019965781299750842, 'tied': 0.0034818660142473543, 'ties': 0.0019116724119796905, 'tiff': 0.02510133172259103, 'tight': 0.002715976736192463, 'tih': 0.0018924586447506726, 'tikal': 0.0018924586447506718, 'tile': 0.0018924586447506718, 'till': 0.0014096828568242745, 'tilt': 0.0031081415794665165, 'tim': 0.003341088893440014, 'time': 0.016619313429501265, 'timer': 0.005606866737329381, 'times': 0.007155225011550325, 'timing': 0.0016997325156252636, 'timothy': 0.001216655211329824, 'tin': 0.011114961423042954, 'tiny': 0.003135992489550251, 'tio2': 0.003108141579466518, 'tips': 0.00036440142293393384, 'tired': 9.215269075613097e-05, 'tiros': 0.0018628591633698963, 'titan': 0.016988356917618304, 'titanium': 0.0012412324256375635, 'title': 0.0014692699937626239, 'titles': 0.0016911718604693694, 'tkelso': 0.0018628591633698963, 'tlc': 0.0018924586447506718, 'tm': 0.004740318521831598, 'tm0006': 0.004981161405813843, 'tmc': 0.005060432039124044, 'tmp': 0.0031432822285808815, 'tn': 0.0015861665554856063, 'tnt': 0.0012603864489062547, 'toaster': 0.0006703468019723805, 'toby': 0.0012609485946591687, 'today': 0.01634399680564592, 'todd': 0.003731800431935113, 'tog': 0.0018924586447506718, 'token': 0.00457333550673112, 'tokyo': 0.0017062962603481236, 'told': 0.011287137370664415, 'tolerable': 0.0024851616866216134, 'tolerance': 0.00256625082338921, 'tolerances': 0.0012609485946591687, 'toleration': 0.0027400885069510687, 'tom': 0.005883234126600206, 'tommy': 0.00858665101633221, 'tomorrow': 0.0049875519744539696, 'tonga': 0.0012603864489062547, 'tonight': 0.0027773506900804767, 'tonnes': 0.0012412324256375635, 'tons': 0.002614563958568212, 'tony': 0.013226847848052135, 'took': 0.004265935012091129, 'tool': 0.0032348861904746406, 'toolkit': 0.005696122928293772, 'tools': 0.007093342962974309, 'toontown': 0.0018924586447506726, 'topaz': 0.0074881014985187675, 'topex': 0.001862859163369898, 'topic': 0.001663236873354043, 'topics': 0.0014615223916101703, 'toppoint': 0.004425442103239913, 'tops': 0.0024917448724188695, 'torah': 0.007333075149745417, 'toronto': 0.03404913728178305, 'torture': 0.0021401823853150715, 'toss': 0.005289595373482465, 'total': 0.008376426096682705, 'totally': 0.0026407605971026293, 'totten': 0.0018924586447506726, 'touch': 0.0007590516117853951, 'touched': 0.00010510953103124408, 'tough': 0.0030242362814067725, 'tour': 0.0024080850228676183, 'tourist': 0.016517609203981886, 'tours': 0.0016816086674564185, 'tower': 0.0013690623068594874, 'town': 0.0035948341258382087, 'toxic': 0.005491928440954983, 'tr': 0.001884840403250123, 'trace': 0.0019096161933030145, 'traced': 0.0057123670598720165, 'tracer': 0.002916687176001748, 'tracers': 0.0012609485946591687, 'traces': 0.0025246613755867744, 'tracing': 0.009525082451507582, 'track': 0.004399227186279235, 'tracking': 0.00749557668495301, 'trade': 0.0018740969633760079, 'tradition': 0.011411066773134587, 'traditional': 0.002117643616973648, 'traditionally': 0.001921522106299118, 'traditions': 0.003045886007585912, 'traffic': 0.0013280734100246695, 'tragedy': 0.0019116724119796905, 'train': 0.002152467762368218, 'training': 0.004567521630165189, 'trajectories': 0.002844115383564493, 'trajectory': 0.010006085862371748, 'transactions': 0.0025114946594801584, 'transcendental': 0.0015417795530505863, 'transfer': 0.004685985611093387, 'transferring': 0.0010442927627179474, 'transform': 0.002337946219163344, 'transformation': 0.001914490397895912, 'transformations': 0.0022062748258370284, 'transit': 0.002485161686621608, 'transition': 0.0037768419510085995, 'translate': 0.0018924586447506718, 'translated': 0.004200371242160982, 'translating': 0.000995773562281057, 'translation': 0.0046247171824471515, 'translations': 0.005491928440954982, 'translator': 0.0018924586447506718, 'transmission': 0.0016238716719778907, 'transmit': 0.0010442927627179474, 'transmitted': 0.0039050360216904244, 'transmitter': 0.0024851616866216125, 'transmitting': 0.0007259062129681476, 'transparent': 0.0007163598861018444, 'transponder': 0.003108141579466519, 'transponders': 0.0018628591633698963, 'transport': 0.006010489508133578, 'transportation': 0.005393981025851218, 'transported': 0.0024851616866216134, 'transporter': 0.003731800431935114, 'trapped': 0.0004088156733638845, 'trash': 0.005145451226773765, 'trashing': 0.0015319298587311032, 'travel': 0.0025926393803433695, 'travelled': 0.0019116724119796905, 'travelling': 0.0018628591633699006, 'travis': 0.0018924586447506718, 'trb3': 0.0018924586447506718, 'treason': 0.0009236759316832519, 'treat': 0.0006739571102848205, 'treated': 0.0042623473629762884, 'treating': 0.001300553187035633, 'treatise': 0.0027400885069510687, 'treatment': 8.088279674783698e-05, 'treats': 0.0012259344989952962, 'treaty': 0.0018628591633699006, 'tree': 0.006102661869042433, 'trees': 0.00335912452168061, 'trek': 0.003997922214750769, 'tremendous': 0.000978451715284566, 'trend': 0.0012412324256375635, 'trent': 0.003157558429105275, 'trenton': 0.001825425726571352, 'trentu': 0.003157558429105275, 'tri': 0.0015319298587311032, 'trial': 0.0015744872567363078, 'triangle': 0.003471933775876109, 'triangles': 0.0037911514534976548, 'triangulation': 0.0037911514534976574, 'tribe': 0.0015527953218988713, 'tribes': 0.0024337964176860587, 'tricks': 0.003157558429105277, 'tricky': 0.0006371000114397899, 'trident': 0.00322722105382976, 'tried': 0.002148632701131214, 'tries': 0.0019093075653275069, 'trieste': 0.0012609485946591687, 'trignometry': 0.0012412324256375635, 'trillion': 0.00039751840402391624, 'trimming': 0.0012609485946591687, 'trinity': 0.0031517615120046248, 'trip': 0.004332786382830693, 'tripoli': 0.002278512863596773, 'trips': 0.0019481148578558583, 'triton': 0.0006417411980615632, 'trivial': 0.0020432186981276853, 'trondheim': 0.0018924586447506718, 'troop': 0.0013262274963396362, 'trouble': 0.0020652236935895544, 'troy': 0.002327929713235535, 'truck': 0.0019744478307144615, 'true': 0.026493029662623478, 'truecolor': 0.002524661375586771, 'truly': 0.0013267321800180558, 'trumpet': 0.010637319947130235, 'trust': 0.004200371242160982, 'trustworthy': 0.0027400885069510696, 'truth': 0.045082445263345, 'truthfully': 0.0009236759316832519, 'truths': 0.005581761830832915, 'trw': 0.0015319298587311032, 'try': 0.003773016025245376, 'trying': 0.013096872185246886, 'ts': 0.0018628591633698963, 'tsa': 0.0037911514534976574, 'tsd': 0.0012412324256375635, 'tseng': 0.0037911514534976565, 'tsr': 0.004425442103239913, 'ttacs1': 0.0024851616866216134, 'ttu': 0.0024851616866216125, 'ttyl': 0.0006516076727636853, 'tu': 0.00618005137484293, 'tuba': 0.004356139840040938, 'tube': 0.0039072379085277175, 'tucson': 0.009134458799709554, 'tue': 0.003083067597018533, 'tuebingen': 0.001825425726571352, 'tuesday': 0.0004515475724564313, 'tug': 0.0018628591633699006, 'tully': 0.0018924586447506718, 'tune': 0.002674481124809779, 'tuned': 4.035731769314044e-05, 'tuning': 0.003157558429105277, 'turbo': 0.004234967125591898, 'turf': 0.0006417411980615632, 'turing': 0.0012609485946591687, 'turkey': 0.0015319298587311032, 'turn': 0.006652855888670903, 'turnaround': 0.0024851616866216134, 'turned': 0.0030114653210515374, 'turner': 0.003791151453497659, 'turning': 0.002181703454841561, 'turns': 0.0009140435251862545, 'turpin': 0.001825425726571352, 'tut': 0.0025246613755867744, 'tutorial': 0.0006417411980615632, 'tv': 0.003742636766259335, 'tw': 0.002524661375586771, 'tweek': 0.0027400885069510696, 'tweekco': 0.0036560569852768275, 'twice': 5.513140760338327e-05, 'twilight': 0.0024851616866216125, 'twist': 0.0033916432410878595, 'twisto': 0.0006398485452691399, 'twosies': 0.0018924586447506726, 'tx': 0.003783074205052613, 'txt': 0.0018924586447506726, 'type': 0.004336048746387207, 'typed': 4.035731769314044e-05, 'types': 0.002631804249248063, 'typical': 0.0051648614945725, 'typically': 0.0039050360216904244, 'typing': 0.0021324977123564626, 'tyre': 0.01010476397819933, 'uab': 0.003157558429105275, 'uaccess': 0.0025246613755867744, 'ualberta': 0.0012609485946591687, 'ualr': 0.0012609485946591687, 'uars': 0.001862859163369898, 'ubc': 0.0018924586447506726, 'ubvms': 0.0073330751497454084, 'ubvmsb': 0.01475112969811668, 'ubvmsd': 0.005491928440954983, 'uc': 0.00036440142293393384, 'ucar': 0.0012499951251094144, 'ucf': 0.0007163598861018444, 'uchicago': 0.0034626547494137636, 'uci': 0.004792444500306352, 'uco': 0.004356139840040938, 'ucr': 0.0018628591633699006, 'ucs': 0.002804529445789721, 'ucsc': 0.00752263991968579, 'ucsd': 0.0037893555531265527, 'udev': 0.0018628591633699006, 'ufl': 0.0047687790653142565, 'ufo': 0.0031081415794665165, 'ufr': 0.0012609485946591687, 'ufrima': 0.0018924586447506718, 'uga': 0.006887180251920203, 'ugly': 0.0022345089669202917, 'uh': 0.002850709813263388, 'uidaho': 0.0036560569852768275, 'uihepa': 0.0024851616866216125, 'uiuc': 0.00862855774766823, 'uk': 0.013102981175199417, 'uk02183': 0.0025246613755867744, 'uk03': 0.0018924586447506726, 'uka': 0.0012609485946591687, 'ukc': 0.002152467762368218, 'uky': 0.003157558429105275, 'ulowell': 0.005491928440954983, 'ulrich': 0.004425442103239911, 'ultimate': 0.002760597630028492, 'ultimately': 0.0028272257285699588, 'ultra': 0.0015390833645905584, 'ultraviolet': 0.004356139840040943, 'ultrix': 0.0015744872567363078, 'uluhe': 0.001825425726571352, 'ulysses': 0.0033882509713317795, 'um': 0.0012499951251094144, 'umanitoba': 0.0012609485946591687, 'umbc': 0.0018628591633698963, 'umd': 0.010562864646183206, 'umich': 0.01596389235389883, 'umn': 0.002524661375586771, 'umr': 0.0015626450162182998, 'unable': 0.0010350509809422563, 'unauthorized': 0.0018362078142529865, 'unaware': 0.00039751840402391624, 'unb': 0.0012499951251094144, 'unbelievable': 0.0018628591633699006, 'unbelievers': 0.00365605698527683, 'unc': 0.014222578751735989, 'uncertain': 0.002901756017947163, 'uncertainty': 0.0018134151655027544, 'uncle': 0.0024414702830626916, 'unclear': 0.0018628591633699006, 'uncompressed': 0.0018924586447506726, 'unconditional': 0.0027400885069510687, 'uncorrected': 0.0012412324256375618, 'uncountably': 0.0027400885069510687, 'uncovered': 0.00457333550673112, 'undecidable': 0.0021721839313897677, 'undefined': 0.003064999644937951, 'undergo': 0.0021524677623682162, 'undergone': 0.0027400885069510696, 'underground': 0.0007018517160113221, 'underlying': 0.001553067980998979, 'underneath': 0.002551096428842924, 'understand': 0.007763736034521406, 'understandable': 0.0018924586447506726, 'understanding': 0.007590633613805415, 'understands': 0.00457333550673112, 'understood': 0.00621124648822348, 'underwater': 0.0018628591633698963, 'undesirable': 0.0007018517160113221, 'undocumented': 0.001347039880397861, 'unequivocally': 0.00365605698527683, 'unexpected': 0.0024080850228676183, 'unfortunately': 0.0013483411278449476, 'uni': 0.001957035569578022, 'unibe': 0.003791151453497654, 'unified': 0.0015319298587311032, 'uniform': 0.00042856546042523147, 'uniformly': 0.0018803995034486513, 'unimi': 0.0012609485946591687, 'union': 0.001935191723821708, 'unique': 0.0005655494586295799, 'unit': 0.005192221647129124, 'united': 0.0030771793705684216, 'units': 0.004732131440647581, 'unity': 0.0019116724119796905, 'univ': 0.0012167965358313238, 'universal': 0.0032926865480503442, 'universe': 0.003504437183116757, 'universitaet': 0.0025246613755867744, 'universite': 0.002524661375586772, 'universities': 0.00222820445642314, 'university': 0.014500452069739232, 'univesa': 0.0031575584291052743, 'unix': 0.01430890703568635, 'unizh': 0.0012609485946591687, 'unknowable': 0.001825425726571352, 'unknown': 0.0024038418505573293, 'unknowns': 0.0007163598861018444, 'unl': 0.002454726329680262, 'unless': 0.008122026315437047, 'unlike': 0.0008317159444114998, 'unlikely': 0.0013370286469754824, 'unlimited': 0.0007032382976603913, 'unm': 0.0032227345497274117, 'unmanned': 0.005606866737329392, 'unnecessary': 0.00010510953103124408, 'unobservable': 0.0012412324256375618, 'unocal': 0.005060432039124052, 'unomaha': 0.0018991386326573457, 'unstable': 0.0015035858261545658, 'unt': 0.005696122928293773, 'unto': 0.006411840182243066, 'unusual': 0.003669726602799476, 'unverzagt': 0.0012412324256375635, 'unwilling': 0.0027400885069510687, 'uokmax': 0.0012609485946591687, 'uoknor': 0.002524661375586771, 'uoregon': 0.005491928440954979, 'uow': 0.003157558429105277, 'upcoming': 0.003243744725599822, 'update': 0.009945354597797046, 'updated': 0.0030274570425361845, 'updates': 0.0025566064981792994, 'upenn': 0.0018705330287465275, 'upgrade': 0.0029702913427132275, 'upgrades': 0.002524661375586772, 'upgrading': 0.003157558429105277, 'uphrrmk': 0.0012603864489062547, 'uplink': 0.0012412324256375635, 'upload': 0.0018924586447506718, 'upper': 0.006564456246825909, 'ups': 0.002130332690995644, 'upset': 0.0024363865949890897, 'uranium': 0.0024851616866216125, 'uranus': 0.006233257448747934, 'urban': 0.0018815982925785906, 'urbana': 0.004528880284918888, 'urc': 0.005060432039124049, 'ureply': 0.003135992489550251, 'urge': 0.0036560569852768275, 'urz': 0.002454726329680262, 'usa': 0.010065674580375383, 'usaf': 0.003340558889778243, 'usage': 0.0009546028802023708, 'usc': 0.008171134633925176, 'usd': 0.0040459711920391335, 'use': 0.012064360916048306, 'used': 0.007216699610670371, 'useful': 0.005279604196291252, 'usefulness': 0.0027285530523395362, 'useless': 0.0016558722410640186, 'usenet': 0.011059995404280494, 'user': 0.008836759092503824, 'useragent': 0.0012964773593636594, 'username': 0.0019784120197450395, 'users': 0.006869267074811081, 'uses': 0.0037868208860801222, 'usgs': 0.003230027532625305, 'using': 0.010591993817841951, 'usingthe': 0.0018628591633698963, 'usl': 0.008414867928917363, 'usno': 0.0018628591633698963, 'usouthdakota': 0.0036560569852768275, 'usr': 0.0016238716719778907, 'ussr': 0.009057062429398695, 'usu': 0.0015417795530505863, 'usual': 0.00024784733589163985, 'usually': 0.0054990119506447424, 'ut': 0.0020068866468152275, 'uta': 0.013819146780228067, 'utah': 0.002628366843554982, 'utarlg': 0.013819146780228067, 'utas': 0.003157558429105275, 'utc': 0.0012629530417339009, 'utexas': 0.006892374491454607, 'utilities': 0.008885150472506749, 'utility': 0.006449841366778347, 'utilization': 0.004981161405813842, 'utk': 0.002524661375586771, 'utkvx': 0.002524661375586771, 'utoronto': 0.001347039880397861, 'utrecht': 0.002784594164535083, 'uts': 0.0016997325156252636, 'utsa': 0.0012609485946591687, 'utzoo': 0.02405721314181944, 'uu': 0.0050966817649088746, 'uucp': 0.004579238315953589, 'uuencode': 0.0007163598861018444, 'uug': 0.00365605698527683, 'uunet': 0.0022934326157266396, 'uv': 0.0019965781299750842, 'uva': 0.002454726329680262, 'uvacs': 0.002524661375586772, 'uvic': 0.003108141579466512, 'uw': 0.0012499951251094144, 'uwa': 0.002524661375586772, 'uwaterloo': 0.0018924586447506718, 'uwe': 0.0024851616866216064, 'uwo': 0.006884449243408318, 'ux': 0.0018924586447506718, 'ux1': 0.001300553187035633, 'ux4': 0.004425442103239913, 'uxa': 0.014110044077555787, 'v1': 0.0022728444928677392, 'v2': 0.006969614267041954, 'v3': 0.0025246613755867744, 'v4': 0.00232831174264492, 'va': 0.005700971513133267, 'vacation': 0.015136831594217161, 'vacuum': 0.012185878186721913, 'vague': 0.0018658918421247577, 'vain': 0.003581494522191157, 'vak12ed': 0.0012412324256375618, 'valiant': 0.00365605698527683, 'valid': 0.001238682228150662, 'valley': 0.002088227094760223, 'valuable': 0.002544025914964133, 'value': 0.010414014328799815, 'values': 0.011315393246009487, 'van': 0.0036077461398789814, 'vancouver': 0.0015940299686368394, 'vandalism': 0.0031081415794665165, 'vandalize': 0.004356139840040942, 'vandalizing': 0.016350061729358267, 'vandenberg': 0.003731800431935114, 'vanderveen': 0.0012609485946591687, 'vanishing': 0.0012717306823408032, 'vanity': 0.0036560569852768275, 'variable': 0.0022980988614725167, 'variant': 0.000988318189986688, 'variation': 0.0033949855597089846, 'variations': 0.0015035858261545658, 'varied': 1.671875925648384e-05, 'varies': 0.0019965781299750842, 'variety': 0.002540448652562974, 'various': 0.007146799900518861, 'varmit': 0.0024851616866216125, 'vary': 0.002456102764010641, 'varying': 0.0018452344383494239, 'vast': 0.0018674835876189228, 'vastly': 0.001226521686031947, 'vaux': 0.007639288036092372, 'vax': 0.008941407588476672, 'vax1': 0.003108141579466518, 'vcr': 0.0018924586447506718, 'vdoe386': 0.0012412324256375618, 've': 0.010771079539335728, 'vector': 0.004981605524460878, 'vedas': 0.0027400885069510687, 'vedic': 0.0036560569852768267, 'vegetable': 0.008745706591231313, 'vehicle': 0.02883928058016956, 'vehicles': 0.0064555610779521285, 'veikko': 0.0018628591633699006, 'velocities': 0.0024851616866216134, 'velocity': 0.007631682353070341, 'venari': 0.016350061729358267, 'vendor': 0.0037911514534976565, 'vendors': 0.0022408043273308706, 'venera': 0.0018705330287465292, 'ventura': 0.0012412324256375618, 'venture': 0.006133526194189831, 'ventures': 0.0019481148578558583, 'venus': 0.017145480488019817, 'verification': 0.002540142959293225, 'verify': 0.0022928590225269633, 'verlag': 0.0025246613755867744, 'verne': 0.0024851616866216134, 'versa': 0.0010442927627179474, 'verse': 0.008441943831777465, 'verses': 0.013819146780228077, 'version': 0.023403824299696327, 'versions': 0.004375762179897205, 'versus': 0.0016424345826056446, 'vertex': 0.0018924586447506718, 'vertical': 0.003243744725599824, 'vertices': 0.006969614267041961, 'vertigo': 0.0012499951251094144, 'vesa': 0.01531675416140841, 'vest': 0.0012412324256375635, 'vga': 0.03171850194258613, 'vgalib': 0.0018924586447506718, 'vhf': 0.0031081415794665165, 'vhs': 0.0007163598861018444, 'vi': 0.001027092726567722, 'viamar': 0.0012609485946591687, 'vicar': 0.0016837503976208663, 'vice': 0.003135992489550251, 'vicinity': 0.0024851616866216134, 'victims': 0.00365605698527683, 'victor': 0.0018628591633698963, 'victoria': 0.009505105097621537, 'video': 0.028832692180787434, 'videos': 0.0015527953218988713, 'videotape': 0.0018924586447506718, 'view': 0.005758783592579828, 'viewed': 0.00013615658743255845, 'viewer': 0.013574836876276801, 'viewers': 0.005133901820383008, 'viewing': 0.006506341288185669, 'viewpoint': 0.0010595219016541488, 'views': 0.006145394898744418, 'viking': 0.0032613482059591315, 'village': 0.0036560569852768267, 'vincent': 0.0010442927627179474, 'violates': 0.0024448766353608346, 'violation': 0.005518924866080454, 'violence': 0.004499671758296702, 'violent': 0.0019229696813196587, 'violet': 0.0024851616866216125, 'virgin': 0.0053859786121099535, 'virginia': 0.014124640475167555, 'virtual': 0.011798791235922049, 'virtually': 0.0009256483073534954, 'virtue': 0.0018134151655027544, 'virus': 0.0034617720572396897, 'vis': 0.0025469720216608734, 'visa': 0.0024851616866216125, 'visible': 0.005028604473923693, 'vision': 0.00534005480873213, 'visit': 0.0044744768492190334, 'visited': 0.0026573399917276495, 'visiting': 0.0009559019909431317, 'visix': 0.0012412324256375635, 'visser': 0.0018559239832745917, 'vista': 0.0012609485946591687, 'visual': 0.004465564778903867, 'visualisation': 0.0031575584291052778, 'visualization': 0.008118855656302134, 'visualizer': 0.0012609485946591687, 'visuals': 0.0025246613755867744, 'vivaldi': 0.0073330751497454084, 'vivid': 0.002524661375586771, 'vlbi': 0.0024851616866216125, 'vm': 0.0022197760462525423, 'vma': 0.0012609485946591687, 'vmode': 0.0012609485946591687, 'vms': 0.008090334460485625, 'vnet': 0.006235210287746655, 'vnews': 0.008290990882765144, 'vogl': 0.0012609485946591687, 'voice': 0.0011950355506473867, 'void': 0.0015525616407321653, 'vol': 0.005842577917578366, 'volts': 0.0012412324256375635, 'volume': 0.0066140063344462385, 'volumes': 0.0020409970903436884, 'volunteer': 0.001304990985299034, 'von': 0.0017855205597762545, 'vote': 0.0017855205597762545, 'voyager': 0.006233257448747934, 'voyages': 0.0024851616866216134, 'vr': 0.0043730492156299995, 'vs': 0.003347093531212532, 'vt': 0.00218168103094784, 'vulcan': 0.005155464964046538, 'vulih': 0.0012609485946591687, 'vus': 0.009179532565505875, 'vuw': 0.001608441199563806, 'w165w': 0.0027400885069510687, 'wa': 0.002266218647312913, 'waco': 0.011031336546395553, 'waddles': 0.001825425726571352, 'wageningen': 0.0012609485946591687, 'wages': 0.0015417795530505863, 'wait': 0.0018898200343583742, 'waited': 0.001921522106299118, 'waiting': 0.0011229164191361518, 'waiver': 0.0018628591633698963, 'wake': 0.00457333550673112, 'waldron': 0.0012412324256375618, 'wales': 0.004160516512830372, 'walk': 0.0028122564335253918, 'walked': 0.0008613659390572332, 'walking': 0.00039751840402391624, 'wall': 0.005709385496036415, 'wallace': 0.0024917448724188695, 'wallacen': 0.0018628591633699006, 'wallops': 0.0031081415794665165, 'walls': 0.0025833670033896354, 'walter': 0.005316119809044223, 'wam': 0.002476892902538075, 'wampyr': 0.003157558429105277, 'wandersman': 0.002524661375586772, 'wang': 0.0037911514534976574, 'wanna': 0.0016738670852616978, 'want': 0.011458541602727006, 'wanted': 0.00598083171454564, 'wanting': 0.0003753054210443446, 'wants': 0.00798765552078658, 'war': 0.0048423468482910416, 'ward': 0.0039072379085277175, 'warfare': 0.0016573572911101966, 'warned': 0.006411840182243067, 'warning': 0.003272349852575542, 'warping': 0.0025246613755867744, 'warrant': 0.0030538357627876035, 'warranty': 0.0025246613755867744, 'warren': 0.0015417795530505863, 'warrent': 0.004356139840040938, 'warrior': 0.0010442927627179474, 'wars': 0.00012157750024694054, 'warwick': 0.0006496982395886239, 'washed': 0.00429945961650972, 'washington': 0.0077136620251249425, 'wasn': 0.006556783750432083, 'waste': 0.008472998309465546, 'wasted': 0.0025120690482758456, 'wasting': 0.0006299532136083384, 'watch': 0.003426922065493521, 'watched': 0.0024377731766381597, 'watching': 0.004084412517350203, 'wate': 0.007607418082978788, 'water': 0.008151165948121784, 'waterland': 0.004425442103239915, 'waterloo': 0.0012499951251094144, 'wats': 0.003731800431935115, 'watson': 0.0033005645319088292, 'watts': 0.0017855205597762545, 'wau': 0.0012609485946591687, 'wave': 0.003170328842337101, 'wavefront': 0.0012609485946591687, 'waves': 0.0025706793209472204, 'way': 0.015073354809944501, 'wayne': 0.004138082315148346, 'ways': 0.0031115406037523063, 'wd': 0.0014348552136991544, 'wdm': 0.0012609485946591687, 'wdwells': 0.003731800431935114, 'weak': 0.0018559239832745917, 'wealth': 0.0010474421803951112, 'wealthy': 0.0019116724119796905, 'weapon': 0.001520379122855315, 'weapons': 0.008788489835370547, 'wearing': 0.0019116724119796905, 'weather': 0.004573547634736214, 'webb': 0.0018924586447506718, 'weber': 0.0012499951251094144, 'wed': 0.0015861665554856063, 'week': 0.005727312935670743, 'weekend': 0.003108141579466519, 'weekly': 0.0026115425721869277, 'weeks': 0.003800997032620372, 'weigh': 0.002278512863596773, 'weighs': 0.0007163598861018444, 'weight': 0.008194010897153117, 'weilej': 0.0012609485946591687, 'weiler': 0.0012609485946591687, 'weimar': 0.0018924586447506718, 'weird': 0.001306377566948104, 'weiss': 0.024146768396433465, 'weitek': 0.002524661375586771, 'welcome': 0.0010812656301393102, 'welfare': 0.0027736796060405583, 'wells': 0.001935191723821708, 'went': 0.009000201133412173, 'weren': 0.0010428158111027656, 'west': 0.003415875164469128, 'western': 0.009794345749266527, 'wetstein': 0.004356139840040947, 'whatsoever': 0.005499864164451124, 'wheat': 0.003359124521680611, 'wheel': 0.0018250202487414676, 'whichever': 0.002456102764010641, 'white': 0.009482561479534014, 'whiting': 0.002524661375586772, 'whitten': 0.001825425726571352, 'whoosh': 0.005606866737329394, 'whosoever': 0.001825425726571352, 'wicked': 0.0024670432082186467, 'wide': 0.0029641852107510757, 'widely': 0.002229526336041999, 'widespread': 0.0003979733363520454, 'widget': 0.002524661375586771, 'widgets': 0.0012499951251094144, 'width': 0.0009988442940766775, 'wierd': 0.0024851616866216134, 'wife': 0.008953979937685562, 'wilbur': 0.003731800431935113, 'wild': 0.000929986059247003, 'wiley': 0.003762574646668968, 'william': 0.002676888271189651, 'williams': 0.003435584079079364, 'williamson': 0.0018924586447506718, 'willing': 0.007669285182979617, 'willmann': 0.001862859163369898, 'willner': 0.0012412324256375635, 'wilson': 0.0031262811829464087, 'wilsonville': 0.0027400885069510696, 'wilt': 0.00365605698527683, 'win': 0.0034214100590218674, 'win3': 0.0018924586447506718, 'wind': 0.006949225138900311, 'window': 0.0075960884247848045, 'windows': 0.0387991556755202, 'wine': 0.0036560569852768267, 'wing': 0.0028506517323993973, 'wingert': 0.0018628591633698963, 'wingless': 0.003108141579466519, 'winglets': 0.0012412324256375635, 'wingo': 0.003731800431935113, 'wings': 0.007175844015547083, 'winjpeg': 0.0012609485946591687, 'winner': 0.0043561398400409415, 'winning': 0.003704873408028552, 'wins': 0.003417927223171884, 'winter': 0.00034465163587258686, 'wiped': 0.0018628591633699006, 'wire': 0.0024858380179126893, 'wired': 0.0006516076727636853, 'wireframe': 0.006332516444282774, 'wisc': 0.0028304466279165247, 'wisconsin': 0.0012389843481381583, 'wisdom': 0.003701665020672002, 'wise': 0.004773687720824861, 'wish': 0.008816109190218174, 'wished': 0.0012808370180140277, 'wishful': 0.001520379122855315, 'wit': 0.0009284200503372423, 'witch': 0.004573335506731118, 'witht': 0.0018924586447506726, 'witness': 0.018285605039795566, 'witnesses': 0.0027400885069510696, 'wittenberg': 0.000978451715284566, 'wives': 0.0027400885069510687, 'wixer': 0.002524661375586772, 'wizard': 0.0025114946594801584, 'wk': 0.004356139840040938, 'wlink': 0.004425442103239915, 'wmf': 0.0012609485946591687, 'wn': 0.004981161405813851, 'wolf': 0.002454726329680262, 'wolfram': 0.002454726329680262, 'wollman': 0.0012412324256375618, 'woman': 0.0030384654188648345, 'women': 0.014436246612622971, 'won': 0.0019081718829304034, 'wonder': 0.007863061266909055, 'wondered': 0.0021058905530445603, 'wonderful': 0.001670862552863116, 'wondering': 0.0029355537042340795, 'wonders': 0.0026646314304903523, 'wood': 0.0010442927627179474, 'woods': 0.00427114963677048, 'woodworth': 0.004425442103239911, 'word': 0.03578550128685093, 'worden': 0.003731800431935112, 'wording': 0.0012808370180140277, 'wordperfect': 0.0033689742160000376, 'words': 0.010393724620992806, 'work': 0.015282990727874883, 'workable': 0.00021074702514795735, 'worked': 0.0017433790867199322, 'workers': 0.0017855205597762545, 'working': 0.008864333174866979, 'works': 0.00795397074653301, 'workshop': 0.006332516444282765, 'workstation': 0.008245929584991853, 'workstations': 0.008245929584991842, 'world': 0.013891376920749026, 'worlds': 0.0015499786042360887, 'worldwide': 0.0019024106766368197, 'worley': 0.0031575584291052778, 'worm': 0.0018705330287465275, 'worried': 8.226937839690696e-05, 'worry': 0.0021739611575522207, 'worse': 0.0032848995177626045, 'worship': 0.018492749815047303, 'worshipers': 0.0027400885069510696, 'worshipped': 0.001825425726571352, 'worshipper': 0.0027400885069510696, 'worshippers': 0.0027400885069510696, 'worst': 0.0031526985217935426, 'worth': 0.004707293024288253, 'worthless': 0.0036609367785014908, 'worthwhile': 0.0033528339885715774, 'worthy': 0.0021946697425983134, 'wouldn': 0.00297873756485749, 'wound': 0.0013262274963396362, 'wounded': 0.0015527953218988713, 'wow': 0.00297859233677636, 'wp': 0.002485161686621608, 'wpafb': 0.0012609485946591687, 'wpd': 0.00549192844095498, 'wpi': 0.0018705330287465292, 'wpr': 0.006411840182243067, 'wrap': 0.0027893395999631755, 'wrapped': 0.00010510953103124408, 'wraps': 0.003108141579466519, 'wrench': 0.003731800431935112, 'wri': 0.001825425726571352, 'wright': 0.011901885334985412, 'write': 0.01296307528204449, 'writer': 0.004258943340010519, 'writers': 0.0031238080985761018, 'writes': 0.04379628125977583, 'writing': 0.0047469870245386995, 'writings': 0.01564663354720179, 'written': 0.007719298219234093, 'wrong': 0.017644505933898096, 'wrote': 0.02206003889765376, 'wrt': 0.0006417411980615632, 'wsf': 0.0012412324256375635, 'wsmr': 0.0007163598861018444, 'wsnc': 0.007333075149745413, 'wu': 0.0012609485946591687, 'wuarchive': 0.0067044331083628995, 'wustl': 0.005060432039124055, 'wv': 0.0028370754228893864, 'wwii': 0.0012603864489062547, 'wyatt': 0.0012499951251094144, 'x11': 0.004465293142291927, 'x11r4': 0.0037911514534976565, 'x3252': 0.0012609485946591687, 'x4': 0.0012609485946591687, 'x5543': 0.0018924586447506718, 'xa': 0.0018803995034486513, 'xarchie': 0.0018924586447506718, 'xbm': 0.0012609485946591687, 'xcpslf': 0.0027400885069510696, 'xenon': 0.0018803995034486513, 'xerox': 0.003157558429105275, 'xfig': 0.0018924586447506718, 'xga': 0.0012609485946591687, 'xia': 0.0025246613755867744, 'xli': 0.0012609485946591687, 'xlib': 0.002524661375586772, 'xloadimage': 0.0018924586447506718, 'xpm': 0.0012609485946591687, 'xpresso': 0.0012412324256375635, 'xr': 0.0015417795530505863, 'xrcjd': 0.003043748562888326, 'xssr': 0.0024851616866216134, 'xv': 0.011607791902633153, 'xv221': 0.0018924586447506718, 'xview': 0.002524661375586772, 'xwindows': 0.0025246613755867744, 'xx': 0.0012609485946591687, 'xxdate': 0.0012852074653554209, 'xxmessage': 0.0009559019909431317, 'xxx': 0.0015417795530505863, 'xxxxx': 0.0012609485946591687, 'xyz': 0.0012609485946591687, 'xz775327': 0.0018924586447506726, 'ya': 0.0010375588680358871, 'yadlowsky': 0.007333075149745415, 'yah': 0.001825425726571352, 'yale': 0.0004629837922963927, 'yamada': 0.0018628591633699006, 'yamauchi': 0.005606866737329394, 'yang': 0.0025838569364433238, 'ye': 0.0073330751497454145, 'yeah': 0.0016537427046808264, 'year': 0.036737476785562294, 'years': 0.030345830584152175, 'yee': 0.0018925273642776512, 'yeh': 0.00633251644428277, 'yellow': 0.000323334060700212, 'yep': 0.002467372658018935, 'yes': 0.006689356504768383, 'yesterday': 0.0009876343859988729, 'yf': 0.0018628591633699006, 'yfn': 0.0037440888202707632, 'yhwh': 0.001825425726571352, 'yield': 0.0006739571102848205, 'yo': 0.0024851616866216125, 'yong': 0.0012609485946591687, 'yoo': 0.0012609485946591687, 'york': 0.0034320440654052094, 'yoshiro': 0.0018628591633699006, 'young': 0.007703878903106989, 'youngstown': 0.001825425726571352, 'youth': 0.0021524677623682162, 'yr': 0.0012499951251094144, 'ysc': 0.0018628591633699006, 'yscvax': 0.0018628591633699006, 'ysu': 0.0039627490992867175, 'yuggoth': 0.0024851616866216134, 'yuma': 0.0006516076727636853, 'yup': 0.0015527953218988713, 'yuv': 0.002524661375586772, 'z1': 0.005049255093045841, 'z3': 0.0018628591633699006, 'za': 0.0022062748258370284, 'zdv': 0.001825425726571352, 'zealand': 0.010200706553509726, 'zen': 0.0012259344989952962, 'zenit': 0.0018628591633698963, 'zenith': 0.0012499951251094144, 'zenkar': 0.0025246613755867744, 'zeno': 0.0012609485946591687, 'zero': 0.0033881969492359594, 'zeta': 0.0024851616866216134, 'zeus': 0.007799423172833942, 'zhao': 0.001064042549779238, 'zhenghao': 0.0063325164442827805, 'zip': 0.008194777109154918, 'zippy': 0.0015417795530505863, 'zola': 0.0018924586447506726, 'zone': 0.003064999644937951, 'zoo': 0.03704873463209645, 'zoology': 0.024057213141819467, 'zoom': 0.002524661375586772, 'zooming': 0.0018924586447506718, 'zoroaster': 0.001825425726571352, 'zoroastrian': 0.001825425726571352, 'zoroastrianism': 0.001825425726571352, 'zoroastrians': 0.001825425726571352, 'zxmkr08': 0.001825425726571352, 'zyeh': 0.0063325164442827805}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yyoIWLTqkgQn",
        "colab_type": "text"
      },
      "source": [
        "## Decision Tree Classifier in Scikit-Learn \n",
        "\n",
        "In Scikit-Learn, the class [`DecisionTreeClassifier`](https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html) implements a customizable algorithm for learning decision trees. The following code example illustrates the use of this class. The example is given in the context of the Iris data set. Here, the third and fourth attributes represent the petal length and petal width of each flower. The classes have already been converted to integer labels, where 0 = Iris-Setosa, 1 = Iris-Versicolor, 2 = Iris-Virginica."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iIiqgKQVlR1Z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        },
        "outputId": "765af4fb-4597-4b5f-dc25-7ddce7945370"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn import datasets\n",
        "import numpy as np\n",
        "\n",
        "iris = datasets.load_iris()\n",
        "\n",
        "# petal length and petal width\n",
        "X = iris.data[:, [2, 3]]\n",
        "\n",
        "# response vector\n",
        "y = iris.target\n",
        "\n",
        "print('Class labels:', np.unique(y))\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(\n",
        "    X, y, test_size=0.3, random_state=1, stratify=y)\n",
        "\n",
        "print('Labels counts in y:', np.bincount(y))\n",
        "print('Labels counts in y_train:', np.bincount(y_train))\n",
        "print('Labels counts in y_test:', np.bincount(y_test))\n",
        "\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "\n",
        "tree = DecisionTreeClassifier(criterion='gini', \n",
        "                              max_depth=4, \n",
        "                              random_state=1)\n",
        "tree.fit(X_train, y_train)\n",
        "\n",
        "y_pred = tree.predict(X_test)\n",
        "\n",
        "print('Accuracy on test set: %.2f' % accuracy_score(y_test, y_pred))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Class labels: [0 1 2]\n",
            "Labels counts in y: [50 50 50]\n",
            "Labels counts in y_train: [35 35 35]\n",
            "Labels counts in y_test: [15 15 15]\n",
            "Accuracy on test set: 0.98\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ph23zFQS7nXi",
        "colab_type": "text"
      },
      "source": [
        "We can also visualize the decicions boundary of this model. See below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JrC6KIU86dhX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "outputId": "b13ee63a-7e0a-47f7-b8f3-8b787fe13f8d"
      },
      "source": [
        "from matplotlib.colors import ListedColormap\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02):\n",
        "\n",
        "    # setup marker generator and color map\n",
        "    markers = ('s', 'x', 'o', '^', 'v')\n",
        "    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n",
        "    cmap = ListedColormap(colors[:len(np.unique(y))])\n",
        "\n",
        "    # plot the decision surface\n",
        "    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
        "    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
        "    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n",
        "                           np.arange(x2_min, x2_max, resolution))\n",
        "    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n",
        "    Z = Z.reshape(xx1.shape)\n",
        "    plt.contourf(xx1, xx2, Z, alpha=0.3, cmap=cmap)\n",
        "    plt.xlim(xx1.min(), xx1.max())\n",
        "    plt.ylim(xx2.min(), xx2.max())\n",
        "\n",
        "    for idx, cl in enumerate(np.unique(y)):\n",
        "        plt.scatter(x=X[y == cl, 0], \n",
        "                    y=X[y == cl, 1],\n",
        "                    alpha=0.8, \n",
        "                    c=colors[idx],\n",
        "                    marker=markers[idx], \n",
        "                    label=cl, \n",
        "                    edgecolor='black')\n",
        "\n",
        "    # highlight test samples\n",
        "    if test_idx:\n",
        "        # plot all samples\n",
        "        X_test, y_test = X[test_idx, :], y[test_idx]\n",
        "\n",
        "        plt.scatter(X_test[:, 0],\n",
        "                    X_test[:, 1],\n",
        "                    c='',\n",
        "                    edgecolor='black',\n",
        "                    alpha=1.0,\n",
        "                    linewidth=1,\n",
        "                    marker='o',\n",
        "                    s=100, \n",
        "                    label='test set')\n",
        "\n",
        "X_combined = np.vstack((X_train, X_test))\n",
        "y_combined = np.hstack((y_train, y_test))\n",
        "plot_decision_regions(X_combined, y_combined, \n",
        "                      classifier=tree, test_idx=range(105, 150))\n",
        "\n",
        "plt.xlabel('petal length [cm]')\n",
        "plt.ylabel('petal width [cm]')\n",
        "plt.legend(loc='upper left')\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:44: MatplotlibDeprecationWarning: Using a string of single character colors as a color sequence is deprecated. Use an explicit list instead.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nSUSO2nwl4lD",
        "colab_type": "text"
      },
      "source": [
        "For curiosity's sake, notive that tt is possible to export the image above to a file. See below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J2sZpYsglzdG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from pydotplus import graph_from_dot_data\n",
        "from sklearn.tree import export_graphviz\n",
        "\n",
        "dot_data = export_graphviz(tree,\n",
        "                           filled=True, \n",
        "                           rounded=True,\n",
        "                           class_names=['Setosa', \n",
        "                                        'Versicolor',\n",
        "                                        'Virginica'],\n",
        "                           feature_names=['petal length', \n",
        "                                          'petal width'],\n",
        "                           out_file=None) \n",
        "graph = graph_from_dot_data(dot_data) \n",
        "graph.write_png('tree.png')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-TfecgGzmBqu",
        "colab_type": "text"
      },
      "source": [
        "## Advantages\n",
        "\n",
        "Some advantages of decision trees are:\n",
        "\n",
        "* Simple to understand and interpret. Trees can be viewed.\n",
        "* Requires little data preparation. Other techniques usually require data normalization, dummy variables need to be created and blank values ​​to be removed. However, note that this module does not support missing values.\n",
        "* The cost of using the tree (ie, predicting data) is logarithmic in the number of data points used to train the tree.\n",
        "* Able to handle numerical and categorical data. Other techniques are generally specialized in the analysis of data sets that have only one type of variable. See algorithms for more information."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GBmQS9s945nl",
        "colab_type": "text"
      },
      "source": [
        "# Naive Bayes Classifier\n",
        "\n",
        "The Naive Bayes Classifier (like a logistic regression model) is a  probabilistic classification model. The model generated by the Naive Bayes algorithm is a set of *conditional probabilities*. See a nice explanation about conditional probabilities [here](https://setosa.io/conditional/)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nYilH2au98cY",
        "colab_type": "text"
      },
      "source": [
        "0 --> 0.95\n",
        "\n",
        "1 --> 0.05"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EZPpo1nB-8-Y",
        "colab_type": "text"
      },
      "source": [
        "## Estimating probabilities from data\n",
        "\n",
        "Let us see an example of how probability estimates can be computed in a dataset. For this, consider the [Play Tenis dataset](https://www.kaggle.com/fredericobreno/play-tennis), which is another toy dataset with four predictors (`outlook`, `temp`, `humidity`, and `wind`) and fourteen examples. The target (`play`) is binary. Each example provides data about the weather condition in a particular day. Therefore, the classification task if to predict whether a given day is appropriate to play tenis or not."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3I5IkDcb68a6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 468
        },
        "outputId": "032ded88-d686-48cb-dac8-5da96297a871"
      },
      "source": [
        "import pandas as pd\n",
        "df_play_tennis = pd.read_csv('play_tennis.csv')\n",
        "df_play_tennis"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>day</th>\n",
              "      <th>outlook</th>\n",
              "      <th>temp</th>\n",
              "      <th>humidity</th>\n",
              "      <th>wind</th>\n",
              "      <th>play</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>D1</td>\n",
              "      <td>Sunny</td>\n",
              "      <td>Hot</td>\n",
              "      <td>High</td>\n",
              "      <td>Weak</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>D2</td>\n",
              "      <td>Sunny</td>\n",
              "      <td>Hot</td>\n",
              "      <td>High</td>\n",
              "      <td>Strong</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>D3</td>\n",
              "      <td>Overcast</td>\n",
              "      <td>Hot</td>\n",
              "      <td>High</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>D4</td>\n",
              "      <td>Rain</td>\n",
              "      <td>Mild</td>\n",
              "      <td>High</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>D5</td>\n",
              "      <td>Rain</td>\n",
              "      <td>Cool</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>D6</td>\n",
              "      <td>Rain</td>\n",
              "      <td>Cool</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Strong</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>D7</td>\n",
              "      <td>Overcast</td>\n",
              "      <td>Cool</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Strong</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>D8</td>\n",
              "      <td>Sunny</td>\n",
              "      <td>Mild</td>\n",
              "      <td>High</td>\n",
              "      <td>Weak</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>D9</td>\n",
              "      <td>Sunny</td>\n",
              "      <td>Cool</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>D10</td>\n",
              "      <td>Rain</td>\n",
              "      <td>Mild</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>D11</td>\n",
              "      <td>Sunny</td>\n",
              "      <td>Mild</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Strong</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>D12</td>\n",
              "      <td>Overcast</td>\n",
              "      <td>Mild</td>\n",
              "      <td>High</td>\n",
              "      <td>Strong</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>D13</td>\n",
              "      <td>Overcast</td>\n",
              "      <td>Hot</td>\n",
              "      <td>Normal</td>\n",
              "      <td>Weak</td>\n",
              "      <td>Yes</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>D14</td>\n",
              "      <td>Rain</td>\n",
              "      <td>Mild</td>\n",
              "      <td>High</td>\n",
              "      <td>Strong</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    day   outlook  temp humidity    wind play\n",
              "0    D1     Sunny   Hot     High    Weak   No\n",
              "1    D2     Sunny   Hot     High  Strong   No\n",
              "2    D3  Overcast   Hot     High    Weak  Yes\n",
              "3    D4      Rain  Mild     High    Weak  Yes\n",
              "4    D5      Rain  Cool   Normal    Weak  Yes\n",
              "5    D6      Rain  Cool   Normal  Strong   No\n",
              "6    D7  Overcast  Cool   Normal  Strong  Yes\n",
              "7    D8     Sunny  Mild     High    Weak   No\n",
              "8    D9     Sunny  Cool   Normal    Weak  Yes\n",
              "9   D10      Rain  Mild   Normal    Weak  Yes\n",
              "10  D11     Sunny  Mild   Normal  Strong  Yes\n",
              "11  D12  Overcast  Mild     High  Strong  Yes\n",
              "12  D13  Overcast   Hot   Normal    Weak  Yes\n",
              "13  D14      Rain  Mild     High  Strong   No"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZZsnGcSjEy75",
        "colab_type": "text"
      },
      "source": [
        "As an exercise, compute estimates for the following probatilities (likelihoods):\n",
        "\n",
        "- $\\Pr(\\operatorname{outlook} = \\text{Sunny} \\mid \\operatorname{play} = \\text{Yes}) \\approx \\text{_____}$\n",
        "- $\\Pr(\\operatorname{outlook} = \\text{Sunny} \\mid \\operatorname{play} = \\text{No}) \\approx \\text{_____}$\n",
        "\n",
        "- $\\Pr(\\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{Yes}) \\approx \\text{_____}$\n",
        "- $\\Pr(\\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{No}) \\approx \\text{_____}$\n",
        "\n",
        "- $\\Pr(\\operatorname{humidity} = \\text{High} \\mid \\operatorname{play} = \\text{Yes}) \\approx \\text{_____}$\n",
        "- $\\Pr(\\operatorname{humidity} = \\text{High} \\mid \\operatorname{play} = \\text{No}) \\approx \\text{_____}$\n",
        "\n",
        "- $\\Pr(\\operatorname{wind} = \\text{Weak} \\mid \\operatorname{play} = \\text{Yes}) \\approx \\text{_____}$\n",
        "- $\\Pr(\\operatorname{wind} = \\text{Weak} \\mid \\operatorname{play} = \\text{No}) \\approx \\text{_____}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RSp-vWKy_27t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "f83b0a99-fc04-40e0-b1bf-5fa2ace9c820"
      },
      "source": [
        "5/14"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.35714285714285715"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I-Au2EO4AD7q",
        "colab_type": "text"
      },
      "source": [
        "prior probability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ckwkHH0fAtJy",
        "colab_type": "text"
      },
      "source": [
        "Let us see some examples of probability estimates that can be computed from the above dataset. First, let us compute the estimates for the prior probabilites.\n",
        "\n",
        "$$\n",
        "\\Pr(\\operatorname{play} = \\text{'Yes'}) \\approx \\frac{5}{14} \\approx 36\\%\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\Pr(\\operatorname{play} = \\text{'No'}) \\approx \\frac{9}{14} \\approx 64\\%\n",
        "$$\n",
        "\n",
        "The way to interpret these prior probabilities is the following: if you do not know anything about the weather conditions in a given day, then there is approximately 64% chance that this day is appropriate to play tenis.\n",
        "\n",
        "We can also compute an estimate for the conditional probability $\\Pr(\\operatorname{outlook} = \\text{Sunny}  \\mid \\operatorname{play} = \\text{'No'})$:\n",
        "\n",
        "$$\n",
        "\\Pr(\\operatorname{outlook} = \\text{Sunny}  \\mid \\operatorname{play} = \\text{No}) \\approx \\frac{3}{5}.\n",
        "$$\n",
        "\n",
        "It is also easy to compute estimate for probabilities like $\\Pr(\\operatorname{outlook} = \\text{Sunny} \\text{ and } \\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{No})$:\n",
        "\n",
        "$$\n",
        "\\Pr(\\operatorname{outlook} = \\text{Sunny} \\text{ and } \\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{No}) \\approx \\frac{2}{5} = 40\\%\n",
        "$$\n",
        "\n",
        "As a final example of computing probability estimates, let us consider $\\Pr(\\operatorname{play} = \\text{No}  \\mid \\operatorname{outlook} = \\text{Sunny})$:\n",
        "\n",
        "$$\n",
        "\\Pr(\\operatorname{play} = \\text{No}  \\mid \\operatorname{outlook} = \\text{Sunny}) \\approx \\frac{3}{5} = 60\\%\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UU0R25fD2rFT",
        "colab_type": "text"
      },
      "source": [
        "## Bayes' theorem\n",
        "\n",
        "The term \"bayesian\" comes from Thomas Bayes, the name of a British Presbyterian minister who lived in the 18th century and who formulated the famous [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem).\n",
        "\n",
        "$$\n",
        "\\Pr(y \\mid x_1, x_2, \\dots, x_n) = \\frac{\\Pr (y) \\Pr (x_1, x_2, \\dots x_n \\mid y)} {\\Pr(x_1, x_2, \\dots, x_n)}\n",
        "$$\n",
        "\n",
        "The following is a description of each term in the above expression.\n",
        "\n",
        "* $\\Pr(y \\mid x_1, \\dots, x_n)$ represents the probability of the class $y$, given the values ​​of the attributes of the example $\\mathbf{x}$. This term, called **posterior probability**, is what must be determined (learned) by the algorithm.\n",
        "\n",
        "* $\\Pr(x_1, \\dots x_n \\mid y)$ represents the probability that a specific combination of values ​​$x_1, \\dots, x_n$ will occur in examples associated with a specific value of the target attribute $y$. This term is called **likelihood**.\n",
        "\n",
        "* $\\Pr(y)$ represents the probability that an example selected at random belongs to a given class (i.e., belongs to a given value of the target attribute $y$). This term is called **prior probability**\n",
        "\n",
        "* $\\Pr (x_1, x_2, \\dots, x_n) $ represents the probability that a given combination of values ​​$ x_1, x_2, \\dots, x_n$ will occur in an example selected at random.\n",
        "\n",
        "These probabilities are actually estimated from the training dataset by the Naive Bayes algorithm. These estimates are computed by counting the occurrences of values in a given feature, either separately  or in conjunction with values of other features."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kFFnKkPitdlR",
        "colab_type": "text"
      },
      "source": [
        "## Independence and conditional independence\n",
        "\n",
        "Recall the estimate $\\Pr(\\operatorname{play} = \\text{No}  \\mid \\operatorname{outlook} = \\text{Sunny}) \\approx 60\\%$. This estimate tells us that, if you are in a sunny day, then the chance is $60$% that this is not a good day to play tennis. Now, compare this value with the estimate for $\\Pr(\\operatorname{play} = \\text{'No'}) \\approx 36\\%$. We can conclude that, knowing that we are in a sunny day changes our bets that this day is appropriate to play tenis. In other words, it seems to exist a **dependence** between variables `play` and `outlook`. \n",
        "\n",
        "In general, two variables (events) $A$ and $B$ are said to be independent if and only if both identities below are true:\n",
        "\n",
        "1. $\\Pr(A \\mid B) = \\Pr(A)$\n",
        "\n",
        "2. $\\Pr(B \\mid A) = \\Pr(B)$\n",
        "\n",
        "Another related concept is *conditional independence*. Given three variables A, B, and C. We say that variables A and B are conditionally independet given the variable C if and only if knowing the value of C makes A and B independent of each other."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ssZtdQAdM119",
        "colab_type": "text"
      },
      "source": [
        "## Steps of algorithm\n",
        "\n",
        "Naive Bayes is an algorithm consisting of two steps, which are described below. Formally, let $X$ be a dataset. Also consider that $c_1, c_2, \\ldots, c_k$ are the classes of the problem (i.e., the possible values ​​of the target feature) and that $\\mathbf{x} = [x_1, x_2, ..., x_n]$ is a new example that should be classified. Let $a_1, a_2, ..., a_n$ be the values for the predictive features $x_1, x_2, ..., x_n$, respectively.\n",
        "\n",
        "### Steps:\n",
        "\n",
        "1. Calculate the posterior probabilities $\\Pr(y = c_j \\mid \\mathbf{x})$, $j = 1,2, \\ldots, k $\n",
        "2. Classify $\\mathbf{x}$ as being of class $c$ such that $\\Pr(y = c \\mid \\mathbf{x})$ is maximum.\n",
        "\n",
        "\n",
        "The term *naive* stems from the fact that Naive Bayes considers as a hypothesis that, given a value of the target $y$, the predictive features are statistically independent from each other. When considering this hypothesis, the computation of the conditional probabilities can be simplified like this:\n",
        "\n",
        "$$\n",
        "\\Pr(x_1, x_2, \\dots x_n \\mid y) = \\Pr(x_1 \\mid y) \\times \\Pr(x_2 \\mid y) \\times \\ldots \\times \\Pr(x_n \\mid y)\n",
        "$$\n",
        "\n",
        "In many practical cases, this statistical independence between predictors considered does not exist. For example, consider a dataset with information about customers of a company. Also consider that each customer is represented by the following features: *weight*, *education*, *salary*, *age*, etc. In this dataset, the values ​​of the first three feature are correlated with values ​​of the age. In this case, at least in theory, the use of Naive Bayes would overestimate the effect of the age feature. However, practice shows that Naive Bayes is quite effective even in cases where the predictive features are not statistically independent.\n",
        "\n",
        "Anyway, assuming the naive hypothesis is true, we can simplify the Bayes formula:\n",
        "\n",
        "$$\n",
        "\\Pr(y \\mid x_1, x_2, \\dots, x_n) \\propto \\Pr(y) \\times \\Pr(x_1 \\mid y) \\times \\Pr(x_2 \\mid y) \\times \\ldots \\Pr(x_n \\mid y)\n",
        "$$\n",
        "\n",
        "Therefore, to compute the probability that an example $\\mathbf{x}$ belongs to a given class, we just need the estimates for $\\Pr(y)$ and for $\\Pr(x_i \\mid y)$, which you already know how to compute (see the above examples for the Play Tenis dataset). Together, these probability values represent the model generated by the Naive Bayes algorithm. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DT__Dg-YTZ_L",
        "colab_type": "text"
      },
      "source": [
        "Consider the following question is: is it appropriate or not to play tennis on a sunny, hot, high humidity and light wind day? This question is equivalent to classifying an example $\\mathbf{x}$ corresponding to $[\\operatorname{outlook} = \\text{Sunny}, \\operatorname{temp} = \\text{Hot}, \\operatorname{humidity} = \\text{High}, \\operatorname{wind} = \\text{Weak}]$. To answer this question, we can apply the Naive Bayes classifier. \n",
        "\n",
        "For the propabilities $\\Pr(y)$, we find that $\\Pr(\\operatorname{play} = \\text{Yes}) \\approx 9/14$ and $\\Pr(\\operatorname{play} = \\text{No}) \\approx 5/14$. \n",
        "\n",
        "Similarly, estimates for conditional probabilities $\\Pr(x_i \\mid y)$ are calculated:\n",
        "\n",
        "- $\\Pr(\\operatorname{outlook} = \\text{Sunny} \\mid \\operatorname{play} = \\text{Yes}) \\approx 5/9$\n",
        "- $\\Pr(\\operatorname{outlook} = \\text{Sunny} \\mid \\operatorname{play} = \\text{No}) \\approx 2/5$\n",
        "\n",
        "- $\\Pr(\\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{Yes}) \\approx 2/9$\n",
        "- $\\Pr(\\operatorname{temp} = \\text{Hot} \\mid \\operatorname{play} = \\text{No}) \\approx 2/5$\n",
        "\n",
        "- $\\Pr(\\operatorname{humidity} = \\text{High} \\mid \\operatorname{play} = \\text{Yes}) \\approx 3/9$\n",
        "- $\\Pr(\\operatorname{humidity} = \\text{High} \\mid \\operatorname{play} = \\text{No}) \\approx 4/5$\n",
        "\n",
        "- $\\Pr(\\operatorname{wind} = \\text{Weak} \\mid \\operatorname{play} = \\text{Yes}) \\approx 6/9$\n",
        "- $\\Pr(\\operatorname{wind} = \\text{Weak} \\mid \\operatorname{play} = \\text{No}) \\approx 2/5$\n",
        "\n",
        "The posterior probabilitis $\\Pr(\\operatorname{play} = \\text{Yes} \\mid \\mathbf{x})$ and $\\Pr(\\operatorname{play} = \\text{No} \\mid \\mathbf{x})$ can now be computed. In the following, we ommit the feature names, for simplicity's sake.\n",
        "\n",
        "For $\\Pr(\\operatorname{play} = \\text{Yes} \\mid \\mathbf{x})$:\n",
        "\n",
        "\\begin{align*}\n",
        "\\Pr(\\operatorname{play} = \\text{Yes} \\mid \\mathbf{x}) & \\propto \\Pr(\\text{Sunny} \\mid \\text{Yes}) \\times \\Pr(\\text{Warm} \\mid \\text{Yes}) \\times \\Pr(\\text{High} \\mid \\text{Yes}) \\times \\Pr(\\text{Wind} \\mid \\text{Yes}) \\times \\Pr(\\text{Yes}) = \\\\\n",
        "&= 0.0071 \\times 9/14 = \\\\\n",
        "&= 0.004564286.\n",
        "\\end{align*}\n",
        "\n",
        "For $\\Pr(\\operatorname{play} = \\text{No} \\mid \\mathbf{x})$:\n",
        "\n",
        "\\begin{align*}\n",
        "\\Pr(\\operatorname{play} = \\text{No} \\mid \\mathbf{x}) & \\propto \\Pr(\\text{Sunny} \\mid \\text{No}) \\times \\Pr(\\text{Warm} \\mid \\text{No}) \\times \\Pr(\\text{High} \\mid \\text{No}) \\times \\Pr(\\text{Wind} \\mid \\text{No}) \\times \\Pr(\\text{No}) = \\\\\n",
        "&= 0.0274 \\times 5/14 = \\\\\n",
        "&= 0.009785714.\n",
        "\\end{align*}\n",
        "\n",
        "Now, since $\\Pr(\\operatorname{play} = \\text{Yes} \\mid \\mathbf{x}) + \\Pr(\\operatorname{play} = \\text{No} \\mid \\mathbf{x})$ = 1$, the numbers aborve can be mapped back to probabilities:\n",
        "\n",
        "\\begin{align*}\n",
        "\\Pr(\\operatorname{play} &= \\text{Yes} \\mid \\mathbf{x}) = \\frac{0.004564286}{0.004564286+0.009785714} \\approx 32\\%\\\\\n",
        "\\\\\n",
        "\\Pr(\\operatorname{play} &= \\text{No} \\mid \\mathbf{x}) = \\frac{0.009785714}{0.004564286+0.009785714} \\approx 68\\%\\end{align*}\n",
        "\n",
        "\n",
        "Since the highest obtained value corresponds to $\\operatorname{play} = \\text{No}$, then the class Naive Bayes predicts for $\\mathbf{x}$ is $\\text{No}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iQePXIuZ_VJD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "768620ea-e369-41eb-9c7a-8d5a61eb4495"
      },
      "source": [
        "print(0.004564286/(0.004564286+0.009785714))\n",
        "print(0.009785714/(0.004564286+0.009785714))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.31806871080139376\n",
            "0.6819312891986063\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qL9GxHM6EqGO",
        "colab_type": "text"
      },
      "source": [
        "## Dealing with continuous features\n",
        "\n",
        "The above description of the Naive Bayes algorithm was given in the context of discrete predictive features. However Naive Bayes can also be applied when the dataset contains continuous features. In this case, there are two possible alternatives.\n",
        "\n",
        "The first alternative is to discretize each continuous feature. One possibility for this is to use quartile ranges, such that values less than the 25th percentile are assigned a 1, 25th to 50th a 2, 50th to 75th a 3 and greater than the 75th percentile a 4. Thus, a single example will deposit one count in bin Q1, Q2, Q3, or Q4. After this discretization, the likelihood estimates can be computed on these categorical bins, as we saw earlier. Bin counts (probabilities) are then based on the number of samples whose variable values fall within a given bin.\n",
        "\n",
        "As a second alternative, the likelihood estimates are not computed by counting. Instead, the likelihood of each continuous predictive feature $x_i$ is computed considering that its values ​​follow a Gaussian distribution:\n",
        "\n",
        "$$\n",
        "\\Pr(x_i \\mid y = c_j) \\propto \\frac{1}{\\sqrt{2\\pi\\sigma^2_y}} \\exp\\left(-\\frac{(x_i - \\mu_y)^2}{2\\sigma^2_y}\\right)\n",
        "$$\n",
        "\n",
        "In the above expression, $\\mu_y$ and $\\sigma_y$ are the mean and standard deviation of the values ​​of $x_j$, but only for examples related to the class $c_j$. Both $\\mu_y$ and $\\sigma_y$ are estimated from the training dataset.\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/1280px-Normal_Distribution_PDF.svg.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NWGi7m6vq02U",
        "colab_type": "text"
      },
      "source": [
        "To give concrete examples of the first and second alternatives described above, consider again the Iris dataset. Remember that all the predictive features in the Iris dataset are continuous. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vY7ybidvkohW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 198
        },
        "outputId": "6494db3b-74c3-41fa-c8ac-aa99157a7572"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.datasets import load_iris\n",
        "\n",
        "iris = load_iris()\n",
        "\n",
        "# if you'd like to check dataset type use: type(load_iris())\n",
        "# if you'd like to view list of attributes use: dir(load_iris())\n",
        "\n",
        "# np.c_ is the numpy concatenate function\n",
        "# which is used to concat iris['data'] and iris['target'] arrays \n",
        "# for pandas column argument: concat iris['feature_names'] list\n",
        "# and string list (in this case one string); you can make this anything you'd like..  \n",
        "# the original dataset would probably call this ['Species']\n",
        "df_iris = pd.DataFrame(data= np.c_[iris['data'], iris['target']],\n",
        "                     columns= iris['feature_names'] + ['target'])\n",
        "\n",
        "df_iris.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  ...  petal width (cm)  target\n",
              "0                5.1               3.5  ...               0.2     0.0\n",
              "1                4.9               3.0  ...               0.2     0.0\n",
              "2                4.7               3.2  ...               0.2     0.0\n",
              "3                4.6               3.1  ...               0.2     0.0\n",
              "4                5.0               3.6  ...               0.2     0.0\n",
              "\n",
              "[5 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jtYIkwGFdXjN",
        "colab_type": "text"
      },
      "source": [
        "Concerning the first alternative, several discretization strategies are provided by Scikit-Learn class [KbinsDiscretizer](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.KBinsDiscretizer.html#sklearn.preprocessing.KBinsDiscretizer). See an example below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BIy1kFCEdMr_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 407
        },
        "outputId": "39bd215e-756b-4348-d114-4df5178fb324"
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.preprocessing import KBinsDiscretizer\n",
        "\n",
        "# let us discretize the continuous features 'sepal length'\n",
        "sepal_length = df_iris['sepal length (cm)']\n",
        "\n",
        "discretizer = KBinsDiscretizer(n_bins=4, encode='ordinal', strategy='quantile')\n",
        "\n",
        "df_iris['sepal length (cm) - discretized'] = discretizer.fit_transform(sepal_length.values.reshape(-1,1))\n",
        "\n",
        "# for visualization purposes, print the original and discretized features.\n",
        "df_iris[['sepal length (cm) - discretized', 'sepal length (cm)']]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>sepal length (cm) - discretized</th>\n",
              "      <th>sepal length (cm)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.0</td>\n",
              "      <td>5.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.0</td>\n",
              "      <td>4.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.0</td>\n",
              "      <td>4.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.0</td>\n",
              "      <td>4.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.0</td>\n",
              "      <td>5.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>3.0</td>\n",
              "      <td>6.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>2.0</td>\n",
              "      <td>6.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>3.0</td>\n",
              "      <td>6.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>2.0</td>\n",
              "      <td>6.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>2.0</td>\n",
              "      <td>5.9</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "     sepal length (cm) - discretized  sepal length (cm)\n",
              "0                                1.0                5.1\n",
              "1                                0.0                4.9\n",
              "2                                0.0                4.7\n",
              "3                                0.0                4.6\n",
              "4                                0.0                5.0\n",
              "..                               ...                ...\n",
              "145                              3.0                6.7\n",
              "146                              2.0                6.3\n",
              "147                              3.0                6.5\n",
              "148                              2.0                6.2\n",
              "149                              2.0                5.9\n",
              "\n",
              "[150 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gwJoSn9ukfwu",
        "colab_type": "text"
      },
      "source": [
        "For the second alternative, let us compute an estimate for the likelihood of a specific value of the continuous feature $\\text{sepal_length}$, that is, $\\Pr(\\text{sepal_length} = 5.1 \\mid \\text{species} = \\text{setosa})$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1n9p6LSKyn7g",
        "colab_type": "text"
      },
      "source": [
        "Now, let us compute the mean and standard deviation for this features, but only considering the value $0.0$ for the target (which is the numeric code for setosa species)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D_A-0YkKnaR4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "12c602d2-a600-49e9-d6d3-bb5f49f90024"
      },
      "source": [
        "df_iris_setosa = df_iris[df_iris.target == 0.0]\n",
        "\n",
        "mean_sepal_length = df_iris_setosa['sepal length (cm)'].mean()\n",
        "print(mean_sepal_length)\n",
        "\n",
        "std_sepal_length = df_iris_setosa['sepal length (cm)'].std()\n",
        "print(std_sepal_length)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5.005999999999999\n",
            "0.3524896872134512\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dh9G5Ki0mqdX",
        "colab_type": "text"
      },
      "source": [
        "We can finally compute the estimate for $\\Pr(\\text{sepal_length} = 5.1 \\mid \\text{species} = \\text{setosa})$. See the cell below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FJnOkiyWoKAc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "4a774a08-1ca1-4267-ac36-992557a1c899"
      },
      "source": [
        "from scipy.stats import norm\n",
        "x  = 5.1\n",
        "norm.pdf(x, loc=mean_sepal_length, scale=std_sepal_length)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0922477665179735"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fRzrTuiO3wL9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9549f1b4-aabd-4b97-f1a1-c60cb555ef88"
      },
      "source": [
        "from scipy.stats import norm\n",
        "x  = 4.6\n",
        "norm.pdf(x, loc=mean_sepal_length, scale=std_sepal_length)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5830198698153818"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TLm9wydf93sS",
        "colab_type": "text"
      },
      "source": [
        "## Naive Bayes in Scikit-Learn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uqypBmvttKUO",
        "colab_type": "text"
      },
      "source": [
        "### GaussianNB\n",
        "\n",
        "In Scikit-Learn, the class [GaussianNB](https://scikit-learn.org/stable/modules/naive_bayes.html#gaussian-naive-bayes) implements the Gaussian Naive Bayes algorithm. This variant of the algorithm is useful when the predictive features are continuous numbers known to approximately follow the Gaussian distribution. \n",
        "\n",
        "The code cell below (adapted from [here](https://www.geeksforgeeks.org/naive-bayes-classifiers/)) shows an example of using the Gaussian Naive Bayes for classification on the Iris dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RdO9vQ7xE0bt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "9640c5b5-6e00-44ed-9316-762d89e8ded9"
      },
      "source": [
        "# load the iris dataset \n",
        "from sklearn.datasets import load_iris \n",
        "iris = load_iris() \n",
        "\n",
        "# store the feature matrix (X) and response vector (y) \n",
        "X = iris.data \n",
        "y = iris.target \n",
        "\n",
        "# splitting X and y into training and testing sets \n",
        "from sklearn.model_selection import train_test_split \n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=1) \n",
        "\n",
        "# training the model on training set \n",
        "from sklearn.naive_bayes import GaussianNB \n",
        "gnb = GaussianNB() \n",
        "gnb.fit(X_train, y_train) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "GaussianNB(priors=None, var_smoothing=1e-09)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFywsNm-NlZK",
        "colab_type": "text"
      },
      "source": [
        "The `predict` method returns the inferred class for the provided examples.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zlscsNs8Khpr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "fedd5447-bb49-48bc-8467-651bf0f0bc0f"
      },
      "source": [
        "# making predictions on the testing set \n",
        "y_pred = gnb.predict(X_test) \n",
        "\n",
        "# comparing actual response values (y_test) with predicted response values (y_pred) \n",
        "from sklearn import metrics \n",
        "print(\"Gaussian Naive Bayes model accuracy(in %):\", metrics.accuracy_score(y_test, y_pred)*100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Gaussian Naive Bayes model accuracy(in %): 95.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6lgvg9O409Cn",
        "colab_type": "text"
      },
      "source": [
        "The `predict_proba` method produces the probability estimates for each example provided as argument. See the example below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LGHRwOM_000e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "c8e51159-8329-412f-b578-af09630bd2cb"
      },
      "source": [
        "gnb.predict_proba(X_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.00000000e+000, 4.85960219e-016, 2.24347925e-028],\n",
              "       [4.81032927e-029, 9.99999988e-001, 1.16657116e-008],\n",
              "       [8.55082235e-094, 9.69653014e-001, 3.03469859e-002],\n",
              "       [1.00000000e+000, 1.43672766e-014, 4.85229968e-027],\n",
              "       [1.81141042e-252, 4.01430066e-008, 9.99999960e-001],\n",
              "       [1.81704672e-113, 3.73062892e-001, 6.26937108e-001],\n",
              "       [3.00349394e-179, 6.53670270e-007, 9.99999346e-001],\n",
              "       [1.00000000e+000, 4.26226391e-011, 9.54068350e-022],\n",
              "       [1.00000000e+000, 4.42208196e-015, 7.70527673e-027],\n",
              "       [4.98375044e-215, 2.81534320e-008, 9.99999972e-001],\n",
              "       [5.82754537e-077, 9.99634071e-001, 3.65929013e-004],\n",
              "       [1.00000000e+000, 1.78045720e-012, 1.26705504e-023],\n",
              "       [3.19645958e-217, 5.66697917e-007, 9.99999433e-001],\n",
              "       [1.82392237e-100, 8.48782093e-001, 1.51217907e-001],\n",
              "       [6.88483197e-099, 9.55195818e-001, 4.48041816e-002],\n",
              "       [1.00000000e+000, 1.31188378e-016, 1.57589125e-029],\n",
              "       [1.72939933e-066, 9.99953970e-001, 4.60303620e-005],\n",
              "       [6.00311248e-097, 9.65219353e-001, 3.47806472e-002],\n",
              "       [1.00000000e+000, 2.56487548e-012, 3.73853769e-024],\n",
              "       [1.00000000e+000, 3.33019296e-016, 3.94536401e-029],\n",
              "       [5.69949366e-082, 9.99699116e-001, 3.00883644e-004],\n",
              "       [2.89510646e-096, 9.73284502e-001, 2.67154983e-002],\n",
              "       [3.44670432e-137, 3.60064094e-002, 9.63993591e-001],\n",
              "       [1.00000000e+000, 1.07144739e-015, 2.82710261e-028],\n",
              "       [1.83856418e-207, 2.28913424e-005, 9.99977109e-001],\n",
              "       [4.61419501e-073, 9.99657351e-001, 3.42649313e-004],\n",
              "       [1.00000000e+000, 2.21980438e-017, 2.30755160e-029],\n",
              "       [1.00000000e+000, 1.33859859e-015, 1.96204273e-027],\n",
              "       [4.47375288e-098, 9.92181642e-001, 7.81835798e-003],\n",
              "       [4.42105287e-145, 2.48728037e-002, 9.75127196e-001],\n",
              "       [6.03272053e-100, 9.56323001e-001, 4.36769985e-002],\n",
              "       [1.79267544e-249, 2.11779486e-009, 9.99999998e-001],\n",
              "       [7.33747663e-059, 9.99993649e-001, 6.35058362e-006],\n",
              "       [1.49702625e-192, 1.21254518e-005, 9.99987875e-001],\n",
              "       [4.36893203e-179, 9.96566789e-007, 9.99999003e-001],\n",
              "       [1.00000000e+000, 6.75030947e-016, 1.93782572e-027],\n",
              "       [3.29296702e-069, 9.99984843e-001, 1.51571083e-005],\n",
              "       [1.00000000e+000, 9.10365944e-016, 9.02238243e-028],\n",
              "       [1.39529648e-106, 8.93263555e-001, 1.06736445e-001],\n",
              "       [2.29089890e-190, 1.24216754e-003, 9.98757832e-001],\n",
              "       [3.65466238e-189, 5.79043639e-006, 9.99994210e-001],\n",
              "       [1.00000000e+000, 3.59222037e-015, 2.34019345e-027],\n",
              "       [1.45947185e-124, 9.72205301e-001, 2.77946988e-002],\n",
              "       [1.01669273e-174, 1.18289219e-003, 9.98817108e-001],\n",
              "       [1.68088179e-099, 9.72029753e-001, 2.79702465e-002],\n",
              "       [3.92919052e-309, 3.23293012e-010, 1.00000000e+000],\n",
              "       [1.00000000e+000, 1.99805458e-012, 2.98009258e-023],\n",
              "       [1.00000000e+000, 9.23545140e-017, 8.16523458e-029],\n",
              "       [1.00000000e+000, 1.89984128e-014, 3.50664019e-027],\n",
              "       [1.74777712e-067, 9.99909341e-001, 9.06586975e-005],\n",
              "       [1.00000000e+000, 1.51671980e-015, 2.83118999e-027],\n",
              "       [1.00000000e+000, 1.77722580e-015, 1.33863294e-027],\n",
              "       [5.12729719e-285, 4.78037292e-010, 1.00000000e+000],\n",
              "       [8.31346855e-184, 6.27973062e-006, 9.99993720e-001],\n",
              "       [1.14235929e-229, 1.13481293e-005, 9.99988652e-001],\n",
              "       [8.11621380e-199, 1.96110507e-006, 9.99998039e-001],\n",
              "       [2.12632207e-128, 9.61075946e-002, 9.03892405e-001],\n",
              "       [6.29573691e-102, 7.03622909e-001, 2.96377091e-001],\n",
              "       [1.21122614e-274, 7.60729859e-008, 9.99999924e-001],\n",
              "       [2.47437268e-073, 9.99476252e-001, 5.23747761e-004]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OXUkMFYnJkfV",
        "colab_type": "text"
      },
      "source": [
        "### MultinomialNB\n",
        "\n",
        "The [MultinomialNB](https://scikit-learn.org/stable/modules/generated/sklearn.naive_bayes.MultinomialNB.html) is the NB implementation to be used when the predictive features are discrete (as was the case in the Play Tenis dataset). From the Scikit-Learn documentation:\n",
        "\n",
        "> The multinomial Naive Bayes classifier is suitable for classification with discrete features (e.g., word counts for text classification). The multinomial distribution normally requires integer feature counts. However, in practice, fractional counts such as tf-idf may also work."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TosZiwppqFeB",
        "colab_type": "text"
      },
      "source": [
        "### BernoulliNB\n",
        "\n",
        "The class [BernoulliNB](https://scikit-learn.org/stable/modules/generated/sklearn.naive_bayes.BernoulliNB.html) implements the Naive Bayes algorithm for Bernoulli's multivariate models. A Bernoulli multivariate model considers that the predictive features are all binary (i.e., they assume values either 0 or 1). Hence Bernoulli Naive Bayes is a special case of Multinomial Naive Bayes."
      ]
    }
  ]
}