unidad1/Notebook_2_b.ipynb

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    "### Unidad 1: Taller de resolución de problemas de clasificación automática\n",
    "\n",
    "<h1> Notebook 2 - Logistic Regression from Scratch in Python</h1>\n",
    "\n",
    "Tutorial realizado por Jepp Bautista: https://www.kaggle.com/jeppbautista/logistic-regression-from-scratch-python/notebook"
   ]
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   "source": [
    "![Foo](https://imgur.com/10nqpqw.png)"
   ]
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    "_uuid": "5bfb1bf45a1dbe94fe3ea071abeb57f962b0f285"
   },
   "source": [
    "![](https://imgur.com/Bw5gMJX.jpg)\n"
   ]
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    "_uuid": "e0c1623d0db8166d7d7f526c13dd33b970859de3"
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   "source": [
    "In this notebook I will try to implement a Logistic Regression without relying to Python's easy-to-use [scikit-learn](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html) library. This notebook aims to create a Logistic Regression without the help of in-built Logistic Regression libraries to help us fully understand how Logistic Regression works in the background. <br>**Beware: Mathematical mumbo-jumbos are present in this notebook**"
   ]
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  {
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   "source": [
    "<h2>Introduction: What is Logistic Regression?<br></h2>\n",
    "Logistic regression is a regression analysis that predicts the probability of an outcome that can only have two values (i.e. a dichotomy). A logistic regression produces a logistic curve, which is limited to values between 0 and 1. Logistic regression models the probability that each input belongs to a particular category. For this particular notebook we will try to predict whether a customer will churn using a Logistic Regression.<br><br>\n",
    "**Prerequisites:**\n",
    "1. Python knowledge\n",
    "1. Atleast basic differential calculus \n",
    "1. Matrix algebra\n"
   ]
  },
  {
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   "execution_count": 4,
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    "_uuid": "5097943f58f3195124bba1c97ec8dbe124ecdc17"
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    {
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       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "import plotly as py\n",
    "import plotly.graph_objs as go\n",
    "import time\n",
    "\n",
    "init_notebook_mode(connected=True)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "c3c513a51d9ec462e235253a0ee7296962cad209"
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   "source": [
    "<h2>Objectives:<br></h2>\n",
    "* To learn the theory behind Logistic Regression (Mathematical part, ugh).\n",
    "* To be able to implement the Logistic Regression without using built-in Logistic Regression libraries.\n",
    "* To be able to predict whether a customer will churn or not.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "5c44a58af55b399e077e2898ad72a0bc1be0ead0"
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   "source": [
    "<h2>Logistic Regression behind the mask</h2>"
   ]
  },
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   "source": [
    "Before we start coding let us first understand or atleast try to understand the things happening at the back-end of Logistic Regression. The aim of this section, **Logistic Regression behind the mask** is to explain the math behind Logistic Regression and to accomplish the first objective of this kernel. To be able to do this we must answer the question, how does a Logistic Regression work? In theory, a Logistic regression takes input and returns an output of probability, a value between 0 and 1. How does a Logistic Regression do that? With the help of a function called a *logistic function* or most commonly known as a *sigmoid*. This sigmoid function is reponsible for *predicting* or classifying a given input.\n",
    "Logistic function or sigmoid is defined as:\n",
    "![](https://imgur.com/Bw5gMJX.jpg)\n",
    "Where:\n",
    "* *e* = Euler's number which is **2.71828**.\n",
    "* *x0* = the value of the sigmoid's midpoint on the x-axis.\n",
    "* *L* = the maximum value.\n",
    "* *k* = steepness of the curve."
   ]
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   "source": [
    "For Logistic Regression however here is the definition of the logistic function:<br>\n",
    "![](https://imgur.com/903IYoN.jpg)\n",
    "Where:\n",
    "* Θ = is the weight."
   ]
  },
  {
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   "metadata": {
    "_uuid": "a3d1a7e169b256ffbc800713aa5c97c197ec0ec9"
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   "source": [
    "In python code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "_uuid": "098959420fb8067564d2d19d50c4374ce9b38836"
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   "source": [
    "def sigmoid(X, weight):\n",
    "    z = np.dot(X, weight)\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
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    "_uuid": "1cd6e3357876ac3155aed874421dd53b2bef9b34"
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   "source": [
    "From here, there are two common ways to approach the optimization of the Logistic Regression. One is through loss minimizing with the use of **gradient descent** and the other is with the use of **Maximum Likelihood Estimation**. I will try to explain these two in the following sections."
   ]
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   "source": [
    "<h4>1. Loss minimizing</h4><br>\n",
    "Weights (represented by theta in our notation) is a vital part of Logistic Regression and other Machine Learning algorithms and we want to find the best values for them. To start we pick random values and we need a way to measure how well the algorithm performs using those random weights. That measure is computed using the loss function. [[1]](https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac) <br><br>\n",
    "The loss function is defined as:\n",
    "![](https://imgur.com/riDHhZS.jpg)\n",
    "Where:\n",
    "* m = the number of samples\n",
    "* y = the target class"
   ]
  },
  {
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   "metadata": {
    "_uuid": "5c7e9633a4ddb223a3aab559ea3f5668190a5488"
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   "source": [
    "In python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "_uuid": "b4143de23fd832463c63513fbbc2fa0ad6b8d02a"
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   "source": [
    "def loss(h, y):\n",
    "    return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The goal is to **minimize the loss**  by means of increasing or decreasing the weights, which is commonly called fitting. Which weights should be bigger and which should be smaller? This can be decided by a function called **Gradient descent**. The Gradient descent is just the derivative of the loss function with respect to its weights. Below links explains how Gradient descent is derived (I'm just too lazy to explain it): <br>\n",
    "* [https://ml-cheatsheet.readthedocs.io/en/latest/gradient_descent.html#step-by-step](https://ml-cheatsheet.readthedocs.io/en/latest/gradient_descent.html#step-by-step)\n",
    "* [http://mccormickml.com/2014/03/04/gradient-descent-derivation/](http://mccormickml.com/2014/03/04/gradient-descent-derivation/)"
   ]
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   "source": [
    "![](https://imgur.com/rBVzJbt.jpg)\n",
    "The weights are updated by substracting the derivative (gradient descent) times the learning rate, as defined below:\n",
    "![](https://imgur.com/TAIpnwI.jpg)\n",
    "Where:\n",
    "* α = learning rate (usually 0.1)"
   ]
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   "source": [
    "In python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    "_uuid": "ae89d7d2a0018f52d75a3e555fbeff4128518933"
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   "source": [
    "def gradient_descent(X, h, y):\n",
    "    return np.dot(X.T, (h - y)) / y.shape[0]\n",
    "def update_weight_loss(weight, learning_rate, gradient):\n",
    "    return weight - learning_rate * gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "9618558cc40298f400ddb84c3b0f550e043f2b16"
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   "source": [
    "So, we've finished covering one of the steps on LR optimization **Loss minimization** with the use of gradient descent. We will now jump to maximum likelihood estimation."
   ]
  },
  {
   "cell_type": "markdown",
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    "_uuid": "96a6b8095ac04176264ff3dee14c16748e21a0d7"
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   "source": [
    "<h4>2. Maximum likelihood estimation</h4><br>\n",
    "One step to optimize logistic regression is through likelihood estimation, the goal here is to **maximize the likelihood** we can achieve this through Gradient ascent, not to be mistaken from gradient descent. Gradient ascent is the same as gradient descent, except its goal is to maximize a function rather than minimizing it.<br>\n",
    "Maximum likelihood:\n",
    "![](https://imgur.com/VCU0TKj.jpg)\n",
    "z is defined above"
   ]
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   "cell_type": "markdown",
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    "_uuid": "f29173d95670aef1293178f8906a1ba4a2ad1213"
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   "source": [
    "In python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "_uuid": "ee1e02db124e850c9f8de411c67f503e41d342e4"
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   "source": [
    "def log_likelihood(x, y, weights):\n",
    "    z = np.dot(x, weights)\n",
    "    ll = np.sum( y*z - np.log(1 + np.exp(z)) )\n",
    "    return ll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "57d94c7eedeb26682fb77fc10b7cd93d5f74e285"
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   "source": [
    "Now, the gradient of the log likelihood is the derivative of the log likelihood function. The full derivation of the maximum likelihood estimator can be found [here](https://www.analyticsvidhya.com/blog/2015/10/basics-logistic-regression/) (too lazy to explain again).\n",
    "![](https://imgur.com/Uvo3rPv.jpg)\n",
    "The weights are now updated by adding the derivative (gradient ascent) times the learning rate, as defined below:\n",
    "![](https://imgur.com/hIB0LQ0.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "_uuid": "96882de87d77d132ef7a8af92d5f8a0fad66e6a3"
   },
   "outputs": [],
   "source": [
    "def gradient_ascent(X, h, y):\n",
    "    return np.dot(X.T, y - h)\n",
    "def update_weight_mle(weight, learning_rate, gradient):\n",
    "    return weight + learning_rate * gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "a513305cc64457e2c767a37b6cbec9309e3ba74d"
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   "source": [
    "Now I think we're done understanding the math behind Logistic Regression, just a recap:<br>\n",
    "1. We learned that Logistic Regression can be used for Classification because the output is a number between 0 and 1.\n",
    "1. We understood the two common ways of optimizing Logistic Regression, minimizing the loss and the other is maximizing the likelihood.\n",
    "1. We learned the difference between Gradient descent and gradient ascent.<br>\n",
    "\n",
    "If you want to add more, or if there's something wrong with the things I stated above or you want to share an improvement, please feel free to leave a comment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "f897ed8cf84f384c191467925e461d3a68f35a76"
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   "source": [
    "Looks like we've completed our first objective, let's get to coding now."
   ]
  },
  {
   "cell_type": "markdown",
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    "_uuid": "8e8153c1c9b4f6b1bd322706f7beaff15b0793aa"
   },
   "source": [
    "<h2>Python implementation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Let us now start implementing what we learned from the previous section into python codes. We will use the Telco Customer Churn data ofcourse, by the end of this section we will be able to make predictions using our \"home-made\" Logistic Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "6bad8a2a7bb329186fa9d53b0fbdca646ecb13ae"
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   "source": [
    "**Dataset initialization**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "_uuid": "d7723b475a93783962f05ffdb404eabd59c5a335"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset size\n",
      "Rows 7043 Columns 21\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"datos/WA_Fn-UseC_-Telco-Customer-Churn.csv\")\n",
    "print(\"Dataset size\")\n",
    "print(\"Rows {} Columns {}\".format(data.shape[0], data.shape[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "_uuid": "7605b4f1b5ec77fb1efc592295339da27f4fe01e",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns and data types\n"
     ]
    },
    {
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       "<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>dtype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>customerID</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gender</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SeniorCitizen</th>\n",
       "      <td>int64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partner</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dependents</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tenure</th>\n",
       "      <td>int64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PhoneService</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MultipleLines</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>InternetService</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OnlineSecurity</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OnlineBackup</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DeviceProtection</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TechSupport</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>StreamingTV</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>StreamingMovies</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Contract</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PaperlessBilling</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PaymentMethod</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MonthlyCharges</th>\n",
       "      <td>float64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalCharges</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Churn</th>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    dtype\n",
       "customerID         object\n",
       "gender             object\n",
       "SeniorCitizen       int64\n",
       "Partner            object\n",
       "Dependents         object\n",
       "tenure              int64\n",
       "PhoneService       object\n",
       "MultipleLines      object\n",
       "InternetService    object\n",
       "OnlineSecurity     object\n",
       "OnlineBackup       object\n",
       "DeviceProtection   object\n",
       "TechSupport        object\n",
       "StreamingTV        object\n",
       "StreamingMovies    object\n",
       "Contract           object\n",
       "PaperlessBilling   object\n",
       "PaymentMethod      object\n",
       "MonthlyCharges    float64\n",
       "TotalCharges       object\n",
       "Churn              object"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Columns and data types\")\n",
    "pd.DataFrame(data.dtypes).rename(columns = {0:'dtype'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "_uuid": "d267dec8e9e139dcbeb17d1b7f371e44d64f392b"
   },
   "outputs": [],
   "source": [
    "df = data.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "d8b971a323629fffe8e27aa09f2eae1b0f05e0a6"
   },
   "source": [
    "That's a lot of columns, to simplify our experiment we will only use 2 features **tenure** and **MonthlyCharges** and the target would be **Churn**  ofcourse. Let us do a simple EDA and visualization on our features and target."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "074b7104853ee4f2064798f58df4682a5fc9ab12"
   },
   "source": [
    "<h3>EDA: Independent variables</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "_uuid": "b224a46fdf2d9dc78c97245cccb0246441f7147b",
    "scrolled": false
   },
   "outputs": [
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          82.4,
          70.9,
          45.3,
          104.4,
          94.85,
          74.45,
          76.45,
          29.95,
          84.5,
          79.25,
          24.8,
          91,
          79.9,
          106.6,
          46,
          70.15,
          50.05,
          55.2,
          84.6,
          54.4,
          95,
          74.4,
          48.55,
          70.4,
          40.2,
          44.6,
          41.15,
          106.9,
          19.35,
          94.45,
          24.8,
          70.6,
          85.4,
          105.05,
          95.15,
          70,
          74.5,
          44.85,
          76.1,
          73.6,
          95.45,
          74.9,
          80.6,
          80.3,
          93.15,
          82.45,
          70.35,
          73.85,
          80.6,
          75.8,
          104.6,
          103.4,
          90.4,
          84.8,
          41.9,
          80.25,
          30.75,
          96.5,
          85.65,
          104.95,
          50.65,
          90.85,
          19.95,
          85.45,
          73.95,
          99.45,
          19.9,
          19.6,
          81.35,
          83.3,
          75.3,
          19.4,
          45.4,
          105.9,
          69.55,
          81.05,
          101.15,
          99.8,
          55.95,
          55,
          74.7,
          80.25,
          96.1,
          69,
          45.3,
          83.55,
          74.35,
          74.4,
          43.75,
          28.45,
          99.7,
          94.1,
          94.2,
          80.5,
          74.35,
          104.8,
          75.2,
          75.6,
          100.05,
          85,
          86.05,
          45.55,
          86.3,
          80.35,
          100.25,
          100.3,
          19,
          75.3,
          89.2,
          85.7,
          61.65,
          105.25,
          29.95,
          65,
          20,
          90.05,
          110.75,
          105.5,
          104.55,
          85.25,
          56.15,
          89.55,
          94.55,
          45.7,
          89.5,
          69.55,
          74.6,
          19.65,
          19.85,
          24.25,
          69.65,
          45.65,
          75.05,
          49.15,
          34.7,
          80,
          49.25,
          75.1,
          50.15,
          79.85,
          19.55,
          85.95,
          45.35,
          94.5,
          91.7,
          87.25,
          98.55,
          98.55,
          85.9,
          89.25,
          70.3,
          93.35,
          19.9,
          88.9,
          95.8,
          82,
          45.35,
          52.2,
          110,
          96.75,
          98.5,
          85.35,
          101.3,
          69.55,
          103.25,
          104,
          86.2,
          111.2,
          89.45,
          95.6,
          90.95,
          108.55,
          78.85,
          44.4,
          100,
          19.8,
          89.9,
          100.15,
          50.8,
          73.65,
          95.1,
          94.65,
          80.6,
          85.55,
          50.8,
          105.1,
          110.1,
          83.9,
          100.55,
          103.85,
          24.6,
          98.9,
          98.3,
          93.85,
          100.5,
          72.85,
          73.55,
          79.4,
          81.15,
          84.6,
          79.05,
          74.4,
          99.05,
          44.95,
          44.7,
          45.7,
          100.3,
          19.25,
          96,
          90.55,
          30.35,
          108.05,
          69.9,
          103.75,
          86.6,
          80.6,
          85.3,
          70,
          94.3,
          95.35,
          75.5,
          90.1,
          68.95,
          99.55,
          57.45,
          53.65,
          100.6,
          83.75,
          88.3,
          92.1,
          79.45,
          90.45,
          69.75,
          19.65,
          43.65,
          39.5,
          97.1,
          80,
          84.7,
          89.55,
          90.6,
          90.05,
          99.05,
          69.75,
          49.05,
          98.05,
          114.5,
          80.95,
          74.3,
          89.7,
          100.45,
          90.4,
          56.15,
          94.4,
          78.95,
          44.85,
          105.65,
          74.65,
          64.7,
          104.05,
          35.55,
          95.15,
          96.65,
          80.4,
          31.35,
          89.75,
          94.4,
          19.85,
          109.9,
          101.35,
          60.05,
          60.15,
          90.45,
          94.25,
          74.9,
          80.25,
          69,
          66.35,
          86,
          80.3,
          90.55,
          75.9,
          45.85,
          49.95,
          78.3,
          76.95,
          96.15,
          45.3,
          19.4,
          90.15,
          45.05,
          75.8,
          79.3,
          30.9,
          95.25,
          89.6,
          110.15,
          89.5,
          75,
          44.75,
          44.05,
          85.6,
          115.55,
          86.6,
          85.2,
          97.65,
          109.55,
          89.55,
          19.45,
          20.35,
          69.25,
          99.5,
          25.2,
          45,
          20.15,
          105,
          54.7,
          87.25,
          79.95,
          88.35,
          94.75,
          95.05,
          78.45,
          70.2,
          41.05,
          85.6,
          79.2,
          70,
          49.95,
          69.25,
          94.25,
          73,
          100.05,
          99.8,
          35,
          76,
          93.85,
          84.3,
          84.4,
          101.1,
          50.45,
          99.95,
          91.4,
          75.55,
          80.8,
          100,
          20.55,
          85.3,
          70.4,
          98.8,
          74.4,
          98.75,
          106,
          104.7,
          96.7,
          55.05,
          88.2,
          19.75,
          75.65,
          74.7,
          76.65,
          25.8,
          42.6,
          68.85,
          90,
          75.35,
          100.85,
          69.95,
          107.5,
          45.85,
          106.1,
          91.7,
          95.6,
          74.95,
          95.35,
          45,
          99.5,
          98.6,
          59.5,
          80.45,
          77.95,
          74.7,
          88.8,
          90.25,
          64.65,
          89.05,
          87.4,
          94.75,
          86.45,
          98.25,
          75.75,
          85.35,
          106.1,
          45.05,
          109.8,
          84.65,
          79.5,
          85.8,
          79.1,
          44.3,
          105.95,
          69.75,
          94.65,
          96.05,
          50.15,
          113.6,
          78.9,
          60.05,
          34.7,
          85.3,
          102.45,
          104.4,
          99.75,
          74.4,
          74.25,
          59.85,
          69.6,
          45.4,
          19.5,
          69.9,
          87.15,
          84.75,
          89.95,
          113.2,
          90.5,
          79,
          20.15,
          71.65,
          20.35,
          84.25,
          78.1,
          89.65,
          98.7,
          76.35,
          79.15,
          85,
          85.3,
          86.55,
          73.85,
          44.85,
          45.1,
          96,
          20.05,
          108.65,
          45.55,
          35.1,
          46.2,
          45.15,
          43.3,
          57.15,
          73.2,
          85.35,
          45.95,
          83.75,
          70.05,
          86,
          100.5,
          72.65,
          21,
          45.1,
          50.4,
          78.95,
          94.45,
          84.8,
          50.9,
          99.8,
          107.35,
          19.55,
          79.1,
          25.5,
          80.75,
          91.85,
          75.35,
          75.45,
          49.55,
          78.6,
          81.1,
          74.95,
          93.55,
          102.1,
          90.9,
          29.2,
          89.15,
          108.85,
          84.75,
          45.7,
          69.95,
          44.6,
          74.95,
          95.25,
          89.85,
          100.45,
          47.15,
          80.2,
          87.1,
          75.9,
          98.75,
          86.45,
          45.3,
          104.1,
          81,
          90.6,
          88.15,
          20.2,
          90.8,
          79.35,
          96.8,
          83.35,
          49.4,
          79.2,
          48.7,
          95.6,
          59.75,
          108.15,
          71.35,
          20.15,
          69.75,
          93.2,
          80.85,
          33.65,
          79.95,
          19.3,
          99.2,
          85.2,
          75.25,
          54.35,
          24.95,
          42.35,
          75.3,
          94.8,
          70.55,
          86.15,
          85,
          80.55,
          75.8,
          98.5,
          95.25,
          74.4,
          85.15,
          88.55,
          54.75,
          91.3,
          79.5,
          70.1,
          111.3,
          95.25,
          86.25,
          100.8,
          86.3,
          89.95,
          76.45,
          70,
          64.4,
          102.45,
          80.1,
          80.2,
          98.15,
          112.95,
          70.9,
          86.85,
          99.85,
          74.5,
          109.15,
          65.2,
          99.5,
          71.55,
          93.9,
          108.4,
          48.75,
          85.65,
          106.7,
          25.15,
          110.35,
          103.25,
          47.8,
          98.6,
          83.05,
          70.4,
          104.75,
          94.25,
          45.95,
          70.15,
          85.55,
          70.3,
          106.35,
          103.7,
          88.35,
          94.2,
          96.25,
          70.7,
          33.55,
          94.55,
          112.95,
          35.9,
          99.25,
          24.45,
          103.35,
          84.8,
          99.95,
          90,
          104.85,
          106.1,
          74.2,
          89.35,
          77.15,
          35.25,
          48.55,
          98.4,
          93.85,
          100.7,
          80.45,
          55.25,
          54.45,
          75.35,
          75.7,
          74.25,
          89.7,
          96.4,
          69.5,
          85.25,
          19.4,
          83.3,
          80.1,
          62.7,
          25.3,
          98.15,
          93.7,
          105.95,
          82,
          95.75,
          94.05,
          54.75,
          95.65,
          94.6,
          98.9,
          76.05,
          69.75,
          34.5,
          105.55,
          30.1,
          70.3,
          80.2,
          94.35,
          44.6,
          19.6,
          110.45,
          70.7,
          99.25,
          84.8,
          105,
          54.45,
          85.3,
          83.35,
          33.5,
          90.35,
          90.75,
          89.6,
          49.25,
          19.75,
          95.15,
          101.35,
          70.05,
          74.65,
          50.4,
          79.65,
          79.85,
          78.75,
          80.45,
          50.1,
          76.4,
          98.7,
          100.8,
          90.1,
          51.55,
          79.25,
          94.85,
          85.7,
          44.4,
          89.5,
          86.05,
          44.55,
          35.4,
          95.65,
          20.95,
          34.7,
          19.75,
          92.55,
          60.05,
          74.3,
          85.35,
          74.3,
          98.1,
          109.65,
          74.55,
          100.95,
          94.9,
          104.9,
          24.1,
          104.05,
          88.35,
          94.65,
          74.4,
          79.9,
          69.7,
          98.1,
          20.5,
          99.6,
          81.95,
          69.35,
          91.1,
          86.1,
          94.7,
          85.1,
          99.15,
          102.95,
          45.05,
          71,
          70.55,
          79.7,
          59,
          60.35,
          69.25,
          70.95,
          89,
          99.4,
          73.5,
          95.5,
          92.35,
          74.55,
          83.8,
          54.45,
          99.8,
          105.85,
          75.45,
          93.85,
          100.75,
          31,
          80,
          70.25,
          100.15,
          94.5,
          33.9,
          89.95,
          84.45,
          79.5,
          89.15,
          74.95,
          74.4,
          55.3,
          55.15,
          84.95,
          43.25,
          48.35,
          79.55,
          71.05,
          84.5,
          108.6,
          30.3,
          30.4,
          45.4,
          84.15,
          19.75,
          85.4,
          75.2,
          55.85,
          106.4,
          84.4,
          56.25,
          85.55,
          68.65,
          77.85,
          105.35,
          87.05,
          53.5,
          25.1,
          79.65,
          54.2,
          19.45,
          103.4,
          84.45,
          85.95,
          59.4,
          30.6,
          99.55,
          70,
          45.3,
          29.85,
          95.1,
          19.8,
          76.65,
          99.15,
          44.95,
          49.55,
          95.9,
          81.5,
          84.1,
          36.45,
          25.05,
          49.85,
          55.55,
          69.5,
          104.3,
          93.85,
          50.45,
          74.65,
          94.2,
          106.55,
          20.1,
          83.8,
          55.15,
          86.65,
          106.75,
          78.45,
          87.45,
          70.75,
          101.35,
          81.7,
          68.25,
          79.15,
          95.45,
          100.95,
          69.1,
          69.6,
          103.45,
          77.95,
          78.45,
          29.5,
          70.75,
          84.45,
          85.65,
          70.15,
          97.8,
          46.3,
          106.3,
          89.4,
          83.15,
          74.15,
          99.5,
          44.15,
          53.9,
          85.45,
          50.85,
          59.2,
          83.2,
          54.9,
          103.9,
          19.25,
          75.45,
          54.85,
          95.1,
          75.5,
          73.75,
          96.05,
          88.95,
          50.7,
          53.4,
          101.9,
          83,
          50.6,
          89.5,
          69.8,
          93.8,
          101.05,
          94.7,
          104.15,
          61.45,
          90.55,
          88.8,
          85.2,
          91.4,
          106.15,
          45.3,
          73.25,
          51.05,
          85.35,
          75.35,
          75.2,
          20.9,
          43.3,
          109.5,
          84.8,
          95.05,
          50.35,
          74.6,
          19.7,
          59.45,
          105.2,
          45.15,
          93.8,
          96.2,
          79.6,
          85.25,
          80.5,
          89.8,
          50.75,
          89.65,
          65.4,
          72.9,
          40,
          99.45,
          86.25,
          45.65,
          70.1,
          70.2,
          55.35,
          84.2,
          45.85,
          75.25,
          100.15,
          105.75,
          48.35,
          24.4,
          20.95,
          49.55,
          20.25,
          50.15,
          95.9,
          25.25,
          45.15,
          84.4,
          75.1,
          70.15,
          101.75,
          45.8,
          20.1,
          40.65,
          101,
          69.1,
          75,
          100,
          71.15,
          54.15,
          108.75,
          49.15,
          19.4,
          79.15,
          80.4,
          102,
          20.65,
          70.8,
          89.05,
          96.6,
          104.5,
          50.6,
          49.35,
          94.25,
          68.95,
          93.85,
          76.05,
          24.45,
          89.35,
          80.35,
          55.8,
          79.05,
          95,
          25.2,
          98.4,
          79.4,
          101.4,
          89.8,
          109.75,
          19.3,
          91.25,
          49.1,
          65.25,
          85.45,
          94.1,
          71.65,
          104.65,
          74.25,
          74.2,
          101,
          100.2,
          89.05,
          70.1,
          105.65,
          96.5,
          70.85,
          85.95,
          73.9,
          109.45,
          100.2,
          74.05,
          101.55,
          111.95,
          55.95,
          45.75,
          74.95,
          80.15,
          109.25,
          35.2,
          78.8,
          106.4,
          49.4,
          69.1,
          90.2,
          93.55,
          80.85,
          82.05,
          20.55,
          78.55,
          78.65,
          42.9,
          34.25,
          58.5,
          96.2,
          74.4,
          105.3,
          73.85,
          84.55,
          24.75,
          85.8,
          24.45,
          105.7,
          24.25,
          76.5,
          93.5,
          101.5,
          74.9,
          69.6,
          24.05,
          50.55,
          100.55,
          20.5,
          74.8,
          24.45,
          71,
          40.3,
          50.6,
          84.85,
          65.7,
          70.5,
          94.85,
          19.75,
          65.45,
          98.7,
          67.5,
          69.6,
          84.35,
          100.2,
          78.05,
          73.6,
          74.75,
          20.2,
          93.55,
          25.05,
          95.55,
          39.3,
          20.25,
          23.9,
          85.45,
          99.9,
          84.8,
          75.2,
          49.35,
          74.9,
          101.25,
          18.95,
          28.6,
          24.35,
          98.65,
          79.9,
          103.3,
          96.2,
          104.15,
          102.95,
          90.6,
          50.8,
          90.05,
          75.85,
          68.5,
          73.5,
          69.95,
          70.05,
          94,
          61.15,
          84.45,
          75.3,
          109.55,
          19.6,
          66.4,
          100.05,
          102,
          90.2,
          25.15,
          79.85,
          49.6,
          105.95,
          91.85,
          40.1,
          73.9,
          89.8,
          72.25,
          96.55,
          40.1,
          101.25,
          79.55,
          84.05,
          89.1,
          94.4,
          78.25,
          44.15,
          75.75,
          19.1,
          80.3,
          74.9,
          80.85,
          24.75,
          90.85,
          79.7,
          57.55,
          86.5,
          103.95,
          25.1,
          48.95,
          83.55,
          89.15,
          70.45,
          60.3,
          24.75,
          103.3,
          78.5,
          19.85,
          79.9,
          99.7,
          58.6,
          98.5,
          50.45,
          94.65,
          100.25,
          88.45,
          69.85,
          81.7,
          79.9,
          25.4,
          83.75,
          20.9,
          69.4,
          74.9,
          74.15,
          70.1,
          78.3,
          96.8,
          94.4,
          84.3,
          92.45,
          99.55,
          81.25,
          19.95,
          99.25,
          80.45,
          79.35,
          79.75,
          100.05,
          69.35,
          85.8,
          79.7,
          50.55,
          80.55,
          84.5,
          84.3,
          67.75,
          85.25,
          80.05,
          20,
          48.8,
          85.05,
          102.8,
          99.95,
          117.8,
          79.5,
          79.65,
          94.7,
          92.5,
          19.45,
          75.55,
          70,
          74.8,
          104.4,
          86.2,
          51.2,
          19.5,
          74.9,
          74.9,
          100.25,
          102.8,
          100,
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          108.5,
          84.5,
          100.15,
          88.6,
          52.55,
          104.8,
          59,
          64.05,
          20.4,
          60.9,
          19.8,
          116.25,
          80.7,
          65.2,
          84.05,
          79.45,
          78,
          19.85,
          94.3,
          106.45,
          105.45,
          95,
          54.3,
          70.05,
          20.05,
          105.4,
          51.6,
          85.5,
          91.25,
          115.75,
          94.7,
          19.6,
          99.9,
          21.1,
          20.05,
          79.95,
          107.15,
          89.55,
          81.55,
          58.45,
          95.65,
          80.6,
          113.1,
          58.95,
          19.55,
          78.95,
          105.05,
          101.9,
          19.75,
          110.3,
          115.6,
          19.35,
          25.6,
          68.75,
          19.9,
          70.6,
          70.2,
          49.3,
          107.25,
          23.6,
          69.7,
          99.5,
          64.3,
          70.85,
          101.9,
          73.5,
          40.4,
          19.25,
          59.6,
          64.9,
          110.85,
          81.05,
          98.05,
          70.5,
          94.55,
          19.65,
          19,
          20,
          63.25,
          20.1,
          99.15,
          90.4,
          111.9,
          24.9,
          83.5,
          84.3,
          45.6,
          54.85,
          65.55,
          90.35,
          20.4,
          74.55,
          19.95,
          74.25,
          108.65,
          109.55,
          86.65,
          81,
          47.85,
          114.55,
          20.55,
          109.8,
          69.5,
          48.85,
          25.25,
          102.85,
          87.55,
          78.55,
          34.55,
          92.05,
          85.05,
          19.7,
          95.15,
          84.25,
          104.6,
          111.65,
          55,
          89.85,
          20.35,
          54.55,
          99.45,
          70.9,
          25.4,
          89.85,
          25.25,
          69.65,
          70,
          20.1,
          24.8,
          95.1,
          88.85,
          78.8,
          20.35,
          45.25,
          20.05,
          69.55,
          19.5,
          74.75,
          30.2,
          57.8,
          19.85,
          25.55,
          24.85,
          110.35,
          24.55,
          107.95,
          81.4,
          73.8,
          64.4,
          103.75,
          71.1,
          49.9,
          24.6,
          30.1,
          83.4,
          20.45,
          75.25,
          20.55,
          20.05,
          20.65,
          85.15,
          84.95,
          66.5,
          63.3,
          83.15,
          84.9,
          20.55,
          49.25,
          59.6,
          104.65,
          75.3,
          80.1,
          81,
          24.7,
          86,
          25.4,
          89.15,
          58.25,
          85.65,
          50.35,
          80.35,
          20.2,
          20.55,
          21.25,
          26.25,
          80.85,
          74.2,
          20.35,
          75.5,
          79.05,
          90.15,
          50.6,
          110.45,
          101,
          79.35,
          89.85,
          65,
          80.45,
          24.1,
          44.05,
          110.8,
          114.95,
          75.05,
          19.25,
          90.05,
          56.7,
          80.15,
          71.35,
          20.25,
          90.35,
          19.7,
          19.85,
          90.35,
          20.8,
          66.85,
          19.9,
          35.8,
          78.85,
          20.4,
          74.25,
          64.8,
          20.45,
          110.65,
          40.3,
          107,
          73.35,
          44.8,
          54.75,
          40.6,
          55.3,
          60.85,
          78.4,
          69.65,
          59.85,
          76.9,
          19.85,
          67.65,
          45,
          64.2,
          81.7,
          25.55,
          20,
          75.65,
          23.8,
          64.2,
          76.8,
          55.2,
          108.55,
          25.25,
          30.4,
          20.05,
          84.6,
          103.7,
          88,
          106.35,
          79.15,
          103.1,
          63.95,
          25.8,
          25.55,
          44.85,
          25.05,
          74.1,
          88.8,
          93.25,
          71.4,
          79.2,
          20.4,
          105,
          30.85,
          20.55,
          84.85,
          33.15,
          92,
          89.8,
          115.8,
          85.15,
          24.85,
          64.35,
          20.5,
          86.05,
          89,
          64.8,
          19.8,
          93.4,
          39,
          20.5,
          26.4,
          98.2,
          97.55,
          19.95,
          99.7,
          34.8,
          60.15,
          64.75,
          54.65,
          19.3,
          111.25,
          35.8,
          20.05,
          84.35,
          110.5,
          91.2,
          89.3,
          81.1,
          81.2,
          94.3,
          116.1,
          105.55,
          94.4,
          19.5,
          105.6,
          81.35,
          56.4,
          65.35,
          19.95,
          111.25,
          89,
          106.1,
          20.05,
          25.2,
          75.4,
          65.55,
          80.7,
          104.55,
          24.15,
          20.45,
          75.4,
          79.7,
          81.7,
          76.3,
          103.75,
          86.45,
          75.1,
          80.6,
          19.3,
          33.6,
          83.25,
          80.85,
          108.05,
          19.9,
          21.05,
          30.15,
          79.85,
          65.5,
          104.1,
          20.5,
          91.35,
          20.5,
          75.6,
          55.1,
          58.95,
          95.1,
          25.45,
          56.75,
          81.75,
          86.1,
          29.8,
          20.5,
          60.9,
          73.25,
          20.85,
          77.35,
          93.85,
          70.1,
          75.95,
          75.25,
          54.95,
          19.5,
          19.6,
          47.85,
          23.75,
          43.8,
          19.75,
          19.15,
          19.6,
          80.3,
          24.35,
          25.25,
          26.1,
          20,
          20.7,
          70.3,
          69.55,
          19.85,
          20,
          95.85,
          20.75,
          50.15,
          58.65,
          95.9,
          49.5,
          80.1,
          24.4,
          40.05,
          19.5,
          51.05,
          54.35,
          84.7,
          86.1,
          70.35,
          110,
          94.9,
          69.75,
          71.6,
          23.65,
          81.85,
          25.1,
          114.7,
          49.15,
          80.9,
          19.3,
          70.2,
          54.25,
          99.3,
          74,
          50.25,
          19.8,
          35.5,
          80.75,
          19.55,
          20.05,
          112.4,
          50.2,
          62.25,
          55.7,
          19.65,
          89.25,
          54,
          56.75,
          21.1,
          96.65,
          24.5,
          79.2,
          69.55,
          20.05,
          98.85,
          25.75,
          19.6,
          87.65,
          74.75,
          107.45,
          75.35,
          64.95,
          100.45,
          68.5,
          80.55,
          81.25,
          89.55,
          55.7,
          24.8,
          20,
          105.2,
          19.55,
          79.75,
          97.45,
          24.25,
          24.6,
          50.15,
          39.6,
          89.85,
          98.85,
          53.85,
          24.25,
          89.45,
          105.25,
          59.5,
          70.55,
          82.5,
          61.6,
          49.05,
          66.25,
          19.4,
          86.05,
          19.15,
          19.25,
          81.95,
          114.65,
          20,
          19.8,
          65.15,
          19.65,
          88.95,
          20.2,
          75.2,
          56.8,
          75.5,
          35.6,
          60.25,
          40.35,
          18.85,
          54.85,
          64.3,
          24.65,
          76.1,
          18.7,
          97.95,
          94.1,
          95.1,
          72.35,
          82.7,
          19.9,
          53.8,
          51.55,
          19.65,
          44.05,
          114,
          100.4,
          54.25,
          80,
          79.2,
          94.3,
          49.8,
          53.75,
          93.45,
          87.9,
          61.05,
          104.05,
          99.25,
          85.7,
          104.85,
          69.15,
          74.45,
          50.45,
          60,
          85.25,
          19.45,
          20.75,
          78.9,
          104.5,
          49.4,
          25,
          25.55,
          70.15,
          69.4,
          93.15,
          69.55,
          20.2,
          20.4,
          23.75,
          70.45,
          65.75,
          24.6,
          69.25,
          24.65,
          90.4,
          100.85,
          75.35,
          87.2,
          64.4,
          24.7,
          105.85,
          98.3,
          19.45,
          58.7,
          20.15,
          64.5,
          28.5,
          90.45,
          105.15,
          83.15,
          103.2,
          19.45,
          88.8,
          85.9,
          34.2,
          20.15,
          50.3,
          80.15,
          51.25,
          95.2,
          94.8,
          80.25,
          76.1,
          115.55,
          24.65,
          53.6,
          19.45,
          88.2,
          101.15,
          56.8,
          99.4,
          20.1,
          60.7,
          20.95,
          114.85,
          19.25,
          62.8,
          105.5,
          19.85,
          74.1,
          107.5,
          19.55,
          68.8,
          84.45,
          84.5,
          111.2,
          80.6,
          80.7,
          75.6,
          57.6,
          110.6,
          58.2,
          81,
          19.7,
          59.55,
          75.55,
          45.1,
          70.95,
          20.9,
          19.95,
          24.6,
          66.7,
          94.8,
          65.85,
          19.95,
          24.65,
          51.25,
          54.25,
          19.4,
          56.25,
          25.15,
          23.95,
          35.4,
          75.35,
          20.4,
          56.05,
          20,
          73.05,
          20.5,
          100.75,
          19.95,
          49.65,
          65.65,
          20.45,
          60.95,
          20.35,
          19.5,
          75.2,
          111.45,
          70.15,
          92,
          85.5,
          82.15,
          84.4,
          60.9,
          20.25,
          95.3,
          19.85,
          84.35,
          19.85,
          82.3,
          66.8,
          44.6,
          98.45,
          70.7,
          24.95,
          102.5,
          86.55,
          24.3,
          58.35,
          68.75,
          85.8,
          20.1,
          20.35,
          110.8,
          82.85,
          84.35,
          19.55,
          19.95,
          66.25,
          23.3,
          25.3,
          44.55,
          104.1,
          92.55,
          101.45,
          94.55,
          95.5,
          100.3,
          55.5,
          49.85,
          89.55,
          19.15,
          99.8,
          113.05,
          19.95,
          74.15,
          92,
          73.85,
          24.45,
          24.8,
          64.85,
          20.75,
          68.95,
          109.4,
          49,
          50.25,
          19.9,
          97.8,
          100.3,
          55.8,
          111.15,
          98.55,
          50.05,
          20.85,
          19.5,
          19.35,
          69.5,
          48.8,
          94.5,
          20.65,
          106.05,
          108.3,
          99.65,
          95.9,
          20,
          64.95,
          74.6,
          49.2,
          73.75,
          92.3,
          19.2,
          88.65,
          95.95,
          105.4,
          20.25,
          49.05,
          35.55,
          65.1,
          96.85,
          69.75,
          99.2,
          106.8,
          51.25,
          57.75,
          70.85,
          19.55,
          79.5,
          98.15,
          20.25,
          79.15,
          94.25,
          40.2,
          19.95,
          55.35,
          102.15,
          71.1,
          54.1,
          19.65,
          88.45,
          80.4,
          19.25,
          84.8,
          19.5,
          68.6,
          92.6,
          100.55,
          20.55,
          19.6,
          67.45,
          43.55,
          109.85,
          20.65,
          95.4,
          21,
          56.2,
          18.4,
          25.75,
          19.6,
          19.8,
          64.2,
          75.75,
          78.95,
          50.3,
          80.3,
          19.85,
          21.1,
          50,
          104.75,
          19.85,
          85.9,
          80.8,
          25.25,
          80.55,
          81.5,
          20.9,
          67.25,
          20.35,
          45.05,
          34.65,
          69.35,
          81.55,
          75.4,
          67.8,
          111.4,
          46.3,
          20.4,
          20.05,
          96.1,
          19.65,
          60.65,
          71.7,
          36,
          65.2,
          48.95,
          53.5,
          80.45,
          109.05,
          26.3,
          106.8,
          64.95,
          19.35,
          21.1,
          18.85,
          26,
          70.35,
          96.9,
          19.55,
          80.4,
          94.65,
          95.75,
          19.55,
          104.1,
          20.1,
          111.55,
          60.5,
          90.95,
          19.7,
          50.95,
          20.05,
          19.4,
          59.45,
          81.5,
          29.05,
          70.6,
          97.2,
          59.2,
          75.9,
          90.05,
          70.95,
          102.6,
          43.8,
          59,
          69.95,
          24.35,
          29.45,
          84.4,
          20.65,
          87.1,
          19.85,
          90.35,
          65.5,
          80.95,
          56.15,
          34.4,
          20.75,
          18.8,
          90.8,
          25.6,
          70.8,
          25.4,
          108.8,
          76.85,
          20.25,
          24.8,
          115.65,
          74.6,
          103.15,
          72.1,
          25.1,
          80.15,
          25.4,
          105.4,
          45.75,
          24.45,
          25,
          85.25,
          19.6,
          50.15,
          70.55,
          26.4,
          20.15,
          58.85,
          97.55,
          19.65,
          25.25,
          114.45,
          70.7,
          75.55,
          84.8,
          20.65,
          20.45,
          35.65,
          90.45,
          97.65,
          73.85,
          69.1,
          82.75,
          24.4,
          55.25,
          61.35,
          76.75,
          19.4,
          54.75,
          19.7,
          19.9,
          107.95,
          83.8,
          56.4,
          20.1,
          94.9,
          94.2,
          49.9,
          71.05,
          81.65,
          89.45,
          99,
          19.05,
          114.45,
          44.25,
          90.55,
          20.4,
          71.4,
          24.85,
          104.45,
          19.8,
          116.45,
          20.05,
          110.75,
          89.7,
          48.7,
          96.6,
          74.3,
          54.3,
          74.85,
          79.95,
          20.05,
          19.4,
          54.9,
          24.45,
          89.65,
          45.4,
          75.7,
          110.65,
          20.55,
          115.15,
          58.55,
          93.25,
          19.35,
          48.75,
          109.05,
          25,
          54.9,
          24.75,
          91.15,
          104.35,
          66.05,
          92.2,
          105.2,
          19.6,
          30.4,
          61.5,
          69.4,
          24.75,
          91.05,
          73.65,
          19.4,
          26.2,
          43.85,
          69.7,
          38.55,
          53.1,
          20.65,
          64.45,
          25.1,
          95.15,
          79.35,
          96.65,
          75.5,
          19.7,
          20.5,
          19.2,
          98.35,
          74.35,
          51.35,
          45.65,
          20.3,
          54.2,
          90.65,
          50.9,
          25.05,
          74.85,
          20.5,
          63.55,
          47.95,
          45,
          90.05,
          25.3,
          24.3,
          75.95,
          19.7,
          66.4,
          35.75,
          18.8,
          19.4,
          19.3,
          67.45,
          20.1,
          58.9,
          19.45,
          50.5,
          25.1,
          60.7,
          99,
          104.4,
          44.05,
          24.1,
          45.55,
          93.8,
          19.7,
          70.65,
          86.45,
          114.1,
          95.2,
          88.55,
          20.75,
          44.65,
          60.2,
          55.45,
          70.3,
          60.4,
          55.8,
          31.1,
          50.95,
          69.1,
          43.95,
          86.5,
          69.95,
          90.95,
          19.9,
          20.15,
          90.6,
          92,
          24.85,
          36,
          78.5,
          19.95,
          20.65,
          30.5,
          106.1,
          20.5,
          95.5,
          64.6,
          51.1,
          89.1,
          54.95,
          20.45,
          85.95,
          60.35,
          19.8,
          85.35,
          72.1,
          81.05,
          20.5,
          111.8,
          20.2,
          19.7,
          19.85,
          60.5,
          19.55,
          20.9,
          21.05,
          71.5,
          54.65,
          19.2,
          49.8,
          20.5,
          90.4,
          90.25,
          104.6,
          50.2,
          95.5,
          95.4,
          101.3,
          53.1,
          84.85,
          34.25,
          88.6,
          60.15,
          99.95,
          70.7,
          54.8,
          54.8,
          100.3,
          53.6,
          19.35,
          85.6,
          80.8,
          19.6,
          90.7,
          69.75,
          20,
          95.25,
          19.95,
          80.85,
          93.3,
          46.35,
          78.75,
          83.55,
          19.6,
          67.85,
          105.65,
          75.5,
          20.15,
          45.2,
          79.25,
          85.7,
          20.1,
          61.8,
          49.9,
          20.4,
          75.4,
          108.15,
          86.25,
          95.7,
          116.85,
          105.75,
          20.15,
          19.6,
          60.95,
          25.05,
          60.3,
          63.95,
          74.3,
          70.6,
          90.55,
          19.45,
          64.45,
          69.65,
          19.5,
          110.5,
          24.7,
          77.4,
          85.4,
          47.6,
          19.4,
          103.85,
          108.45,
          81,
          86.65,
          92.95,
          90.35,
          25.15,
          76.4,
          19.55,
          85.35,
          24.8,
          103.15,
          100.75,
          94.1,
          19.35,
          19.9,
          101.05,
          59.1,
          55.85,
          106.05,
          84.1,
          75.3,
          24.7,
          55.8,
          39.7,
          29.5,
          20.15,
          79.55,
          24.8,
          19.65,
          94.05,
          90.75,
          78.85,
          99.5,
          80.55,
          70.2,
          59.45,
          93.35,
          44.95,
          26.1,
          20.2,
          21.25,
          59.4,
          95,
          61.9,
          118.65,
          64.45,
          80.15,
          20.2,
          21,
          20.45,
          75.85,
          80.45,
          75.5,
          44.45,
          74.55,
          48.15,
          19.65,
          20.15,
          106.6,
          91,
          25.4,
          69.95,
          66.85,
          20.15,
          64.85,
          74.85,
          50.5,
          72.9,
          115.05,
          19,
          19.55,
          101.1,
          84.1,
          24.15,
          50.1,
          74.6,
          19.75,
          106.8,
          84.5,
          25.05,
          83.7,
          96.6,
          101.1,
          20.2,
          94.05,
          81,
          60.25,
          60.85,
          43.95,
          86.05,
          20.25,
          19.4,
          102.65,
          19.9,
          19.55,
          95.5,
          84.15,
          103.2,
          50.2,
          19.95,
          116.25,
          31.2,
          24.45,
          84.2,
          85.65,
          21.2,
          25.55,
          20.2,
          63.85,
          61.95,
          25.75,
          58.2,
          85.85,
          104.9,
          99.85,
          19.55,
          104,
          104.4,
          19.5,
          25.25,
          49.85,
          108.95,
          89.9,
          82,
          89.95,
          79.35,
          64.05,
          101.15,
          39.1,
          34.6,
          19.55,
          104.45,
          70.5,
          20.35,
          19.45,
          69.9,
          59.7,
          78.35,
          71.45,
          45.85,
          95.85,
          35.7,
          89.55,
          24.95,
          24.85,
          100.8,
          105.35,
          19.65,
          54.45,
          70.5,
          20.1,
          69.35,
          19.8,
          74.4,
          93.05,
          51.2,
          65.6,
          80.55,
          52.7,
          20.85,
          52.15,
          114.95,
          104.45,
          113.65,
          20.6,
          91.55,
          49.85,
          19.8,
          104.15,
          48.2,
          25.1,
          100.15,
          55.9,
          64.4,
          85.3,
          107.45,
          91.3,
          85.95,
          45.2,
          79.2,
          55.5,
          90.25,
          91.25,
          100.9,
          97.7,
          69.85,
          65.6,
          104.65,
          90.45,
          63.7,
          104.5,
          20.1,
          104.3,
          93.25,
          73.45,
          20.7,
          25.25,
          100.5,
          90.6,
          89.4,
          95.45,
          20.45,
          19.95,
          109.15,
          85.7,
          102.05,
          94.7,
          64.4,
          26.8,
          66.05,
          65.2,
          85.05,
          55.8,
          19.95,
          45,
          114.9,
          106.4,
          46.1,
          39.7,
          20.05,
          95.75,
          24.4,
          33.6,
          90.45,
          84,
          67.4,
          19.7,
          80.35,
          19.6,
          54.2,
          45.2,
          75.1,
          19.7,
          72.75,
          20.05,
          39.2,
          44.75,
          82.65,
          93.9,
          117.15,
          99.25,
          112.55,
          25.7,
          90.3,
          49.4,
          19.4,
          109.7,
          61.25,
          55.3,
          103.75,
          19.5,
          39.5,
          26.05,
          91.05,
          29.65,
          50.2,
          105.3,
          55.45,
          85.45,
          19.8,
          59.25,
          90.7,
          79.05,
          90.7,
          95,
          30.25,
          49.85,
          93,
          54.55,
          19.7,
          84.8,
          94.45,
          20.85,
          60,
          80.45,
          84.95,
          49.65,
          20.2,
          100.5,
          35.75,
          86.45,
          53.8,
          38.55,
          39.9,
          70.05,
          20.1,
          20.3,
          35.65,
          82.95,
          55.65,
          25.2,
          50.8,
          19.65,
          59.8,
          73.55,
          61.4,
          19.9,
          19.45,
          81.5,
          109.55,
          74.4,
          74.9,
          59.65,
          110.45,
          74.45,
          24.55,
          24.55,
          90.65,
          105.05,
          20.45,
          19.55,
          19.7,
          70.45,
          85.65,
          20.55,
          97.95,
          20,
          25.25,
          70.9,
          19.85,
          106.35,
          99.5,
          84.7,
          86.05,
          44.55,
          75.85,
          25,
          45,
          20.5,
          90.45,
          60.45,
          78.45,
          100.55,
          20.35,
          90.75,
          20.25,
          20.05,
          19.6,
          53.8,
          70.2,
          75.5,
          20.35,
          26.05,
          20.6,
          20.1,
          24.3,
          24.5,
          110.5,
          25.25,
          90.1,
          68.75,
          19.2,
          115.1,
          99.65,
          91.45,
          84.75,
          78.75,
          20.25,
          19.9,
          97.75,
          100.4,
          24.45,
          101.1,
          50.9,
          107.2,
          92.2,
          113.4,
          40.55,
          26,
          111.95,
          53.8,
          72.1,
          78.85,
          70.75,
          76.15,
          39.1,
          69.95,
          20.05,
          20.05,
          19.45,
          26.9,
          19.2,
          50,
          60,
          84.55,
          45.45,
          20.05,
          115.55,
          99,
          50.55,
          25,
          91.55,
          19.35,
          24.85,
          100.4,
          25,
          19.25,
          108.25,
          20.15,
          101.3,
          20,
          105.3,
          69.85,
          65.25,
          19.8,
          19.6,
          20.05,
          49.4,
          88.4,
          100.6,
          19.45,
          20.3,
          107.65,
          80.45,
          58.85,
          109.6,
          75.15,
          73,
          70.1,
          98.65,
          111.45,
          114.9,
          100.55,
          20.4,
          104.35,
          80.45,
          91.35,
          19.9,
          68.35,
          79.1,
          51,
          80.55,
          66.7,
          86.4,
          50.05,
          25.7,
          83.4,
          84.65,
          64.75,
          100.15,
          25.25,
          113,
          40.65,
          94.95,
          59.9,
          19.8,
          81.8,
          20,
          59.6,
          25,
          84.35,
          55.55,
          75.35,
          59.3,
          66.1,
          18.8,
          86.45,
          52.1,
          47.4,
          109.15,
          94.95,
          93.55,
          79.5,
          115.05,
          95.15,
          105.4,
          20.1,
          20.05,
          20.7,
          20.35,
          19.7,
          85.45,
          40.4,
          105.2,
          100.65,
          91,
          116.75,
          59.1,
          49.8,
          19.3,
          19.65,
          81.4,
          38.9,
          87.95,
          19.85,
          96.35,
          24.15,
          19.1,
          44,
          60.6,
          25.65,
          53.95,
          20.4,
          29.35,
          20.45,
          95.1,
          25.25,
          44.9,
          92.65,
          43.7,
          72.6,
          18.95,
          20.5,
          19.95,
          24.5,
          20.6,
          61.05,
          106.65,
          108.25,
          20.4,
          55.3,
          20.25,
          72.95,
          89.45,
          104.65,
          75.2,
          101.15,
          68.75,
          111.05,
          99,
          21,
          19.4,
          77.2,
          19.45,
          24.85,
          41.35,
          19.6,
          84.45,
          20.25,
          19.65,
          20.65,
          99.3,
          81.05,
          67.6,
          70.15,
          115,
          84.8,
          19.7,
          63.15,
          74,
          29.1,
          50.05,
          20,
          74.65,
          44.4,
          85.4,
          94.1,
          108.9,
          56.2,
          26.1,
          85.45,
          88.95,
          74.35,
          48.85,
          80.1,
          56.05,
          89.8,
          19.1,
          20.35,
          106.05,
          19.65,
          59.85,
          86.1,
          19.45,
          97.1,
          36.65,
          103.9,
          19.75,
          24.55,
          48.7,
          109.55,
          20.65,
          55.2,
          24.05,
          20.45,
          19.25,
          26.35,
          43.8,
          50.15,
          20.45,
          61.4,
          70.75,
          61.15,
          20.25,
          63.85,
          98.7,
          20,
          19.3,
          84.4,
          25.1,
          48.25,
          19.85,
          94.2,
          62.15,
          79.3,
          56.25,
          20.3,
          99,
          90.6,
          85.9,
          79.2,
          70.35,
          19.35,
          50.15,
          63.8,
          20.55,
          88.55,
          101.4,
          44.6,
          63.75,
          109.25,
          84.6,
          20.45,
          85.75,
          107.95,
          22.95,
          19.45,
          19.7,
          87,
          79.95,
          64,
          64.9,
          25.75,
          90.15,
          116.1,
          104.95,
          50,
          20.45,
          19.85,
          19.95,
          26.45,
          63.4,
          53.95,
          95.1,
          74.1,
          35.5,
          79.2,
          48.8,
          55.45,
          25.4,
          93.5,
          63.9,
          64.85,
          63.8,
          44.45,
          19.95,
          43.35,
          49.65,
          85.1,
          89.8,
          103.05,
          116,
          69.9,
          95.1,
          40.25,
          25.75,
          105.35,
          113.6,
          24,
          19.4,
          86.1,
          102.65,
          92.85,
          97.75,
          97.95,
          19.95,
          24.6,
          50.95,
          75.6,
          80.75,
          90.4,
          60.25,
          20.2,
          64.15,
          20.25,
          99,
          80.3,
          19.55,
          100.75,
          53.75,
          25.6,
          58.35,
          46.35,
          113.75,
          90.4,
          109.3,
          90.3,
          65.25,
          60.65,
          24.1,
          19.5,
          85.95,
          53.5,
          25.45,
          20.5,
          20.85,
          89.9,
          26,
          113.2,
          69.05,
          20.1,
          109.65,
          19.2,
          90,
          34,
          20.4,
          38.6,
          25.25,
          60.6,
          74.75,
          20.6,
          20.4,
          81.7,
          20.3,
          20,
          25,
          80.45,
          19.75,
          65.65,
          71,
          89.2,
          86.75,
          61.5,
          25.1,
          34.05,
          19.95,
          19.95,
          89.7,
          20.4,
          26.3,
          20.7,
          19.45,
          110.8,
          69.3,
          49.35,
          20.35,
          105.6,
          64.45,
          49.9,
          65.65,
          103.3,
          44.45,
          89.9,
          55.05,
          104.1,
          106.6,
          70.5,
          19.6,
          24.05,
          38.1,
          34.25,
          100.05,
          68.65,
          45.8,
          75.75,
          96.4,
          20.55,
          50.95,
          90.5,
          79.4,
          58.75,
          59.45,
          105.7,
          53.3,
          24.3,
          59.9,
          23.95,
          20.15,
          95.65,
          81,
          82.45,
          20.5,
          54.4,
          58.6,
          84.8,
          61.4,
          20.4,
          20.15,
          94.45,
          79.8,
          74.05,
          49.15,
          19.4,
          113.65,
          106,
          25.95,
          19.1,
          100.55,
          95.4,
          75.15,
          89.15,
          107.9,
          19.5,
          24.95,
          19.5,
          69.95,
          82.85,
          19,
          38.85,
          20.35,
          95,
          74.4,
          78.45,
          74.3,
          51.05,
          19.2,
          109.1,
          76.45,
          72.8,
          18.95,
          101.75,
          75.45,
          64.1,
          25.65,
          75.1,
          95.85,
          54.4,
          72.75,
          19.85,
          19.05,
          94.85,
          46.25,
          19.35,
          69.6,
          90.7,
          101.4,
          20.25,
          48.8,
          74.35,
          19.35,
          68.75,
          100.2,
          20.85,
          19.35,
          45,
          25.5,
          48.9,
          19.6,
          20,
          81.3,
          95.2,
          83.3,
          20.3,
          89.85,
          19.8,
          54.65,
          29.35,
          19.15,
          19.1,
          80.55,
          20.25,
          106,
          25.5,
          79.6,
          55.25,
          88.05,
          20.4,
          117.6,
          20,
          19.65,
          70.55,
          65.8,
          20.05,
          80,
          35.4,
          79.6,
          80.25,
          20.45,
          79.6,
          24.7,
          77.3,
          29.75,
          44.9,
          29.8,
          71.95,
          20.75,
          56.3,
          105.25,
          19.55,
          84.45,
          53.65,
          29.9,
          19.7,
          43.7,
          55.3,
          19.85,
          19.65,
          49.45,
          20.45,
          39.7,
          54.5,
          111.6,
          55.55,
          20.55,
          62.1,
          104.5,
          101.8,
          110.6,
          84.9,
          93.2,
          24.4,
          70.55,
          85,
          85.8,
          91.1,
          20.1,
          20.05,
          74.8,
          24.8,
          100.85,
          105.1,
          20.4,
          20,
          79.4,
          57.2,
          58.6,
          94.8,
          102.5,
          20.35,
          84.9,
          69.2,
          20.85,
          88.5,
          35,
          55.15,
          50.95,
          64,
          80.2,
          49.3,
          84.35,
          20.05,
          117.2,
          20.1,
          109.95,
          94.75,
          80,
          79.65,
          25.2,
          19.9,
          44.8,
          20.3,
          19.2,
          80.05,
          107.35,
          47.85,
          70.8,
          59.1,
          25.55,
          20.25,
          75.55,
          95.3,
          70.25,
          50.3,
          19.85,
          19.35,
          25,
          20.3,
          75.35,
          88,
          43.8,
          62.05,
          20.1,
          101.35,
          84.05,
          20.9,
          105.9,
          85.05,
          44.1,
          90.2,
          53.45,
          19.95,
          74.65,
          57.5,
          19.65,
          93.8,
          89.25,
          94.15,
          55.6,
          48.7,
          104.9,
          19.9,
          19.4,
          25.05,
          84.45,
          19.3,
          79.85,
          25.55,
          68.4,
          20.65,
          55.15,
          70.6,
          19.95,
          19,
          44.1,
          107.6,
          61.55,
          90.7,
          99.25,
          91.7,
          100.7,
          78.45,
          84.3,
          19.55,
          20.45,
          55.6,
          86.8,
          20.95,
          20.05,
          113.65,
          59.5,
          87.8,
          41.9,
          69.85,
          56.3,
          109.55,
          92.15,
          69.5,
          97,
          58.35,
          70.4,
          94.3,
          19.55,
          95.95,
          94.8,
          107.75,
          54.6,
          71.3,
          19.5,
          56.3,
          90.55,
          60.8,
          98.8,
          98.15,
          35.35,
          103.15,
          107.75,
          81.4,
          95.7,
          104.8,
          70.95,
          44.95,
          97.65,
          35.65,
          85.25,
          19.5,
          25.1,
          100.05,
          55.7,
          91.15,
          83.85,
          45.9,
          25.1,
          19.7,
          91.5,
          51.3,
          21.1,
          104.75,
          85.75,
          20.3,
          100.75,
          74.15,
          78.55,
          19.85,
          50.7,
          45,
          77.8,
          83.45,
          94.8,
          20.1,
          59.9,
          90.1,
          70.95,
          29.2,
          46.6,
          74.3,
          69.3,
          94.3,
          76.45,
          54,
          104.25,
          19.95,
          24.95,
          84.75,
          19.75,
          113.65,
          44.9,
          75.25,
          24.6,
          25,
          20.95,
          110.6,
          55.5,
          19.45,
          84.85,
          19.6,
          53.45,
          19.8,
          112.1,
          74.2,
          69,
          19.35,
          19.8,
          109.2,
          79.15,
          53.65,
          100.2,
          108.65,
          40.65,
          55.35,
          105.6,
          95.7,
          83.2,
          90.05,
          97.65,
          68.05,
          102.1,
          23.4,
          71.05,
          19.45,
          59.45,
          92.2,
          19.85,
          43.9,
          90.5,
          90.45,
          84.6,
          99.15,
          19.95,
          20.5,
          62.1,
          79.5,
          19.55,
          20.35,
          51.7,
          23.3,
          65.1,
          81.2,
          74.5,
          80.5,
          60.3,
          75,
          90.15,
          69.05,
          59.7,
          19.85,
          40.75,
          95.7,
          46.3,
          81.3,
          20,
          66.15,
          19.6,
          49.8,
          101.75,
          55.15,
          103.95,
          99.65,
          73.7,
          50.05,
          60.25,
          87.3,
          54.25,
          85.3,
          50,
          90.95,
          72.25,
          96.1,
          19.85,
          55.3,
          20.1,
          69.5,
          25.15,
          79.65,
          71.25,
          113.8,
          24.55,
          19.7,
          100.5,
          74.45,
          104.1,
          19.05,
          25,
          19.05,
          81.9,
          69.7,
          90.15,
          25.35,
          24.65,
          19.55,
          60,
          89.9,
          19.4,
          49.8,
          24.1,
          54.25,
          109.9,
          35.5,
          87.55,
          88.4,
          50.8,
          99,
          96.55,
          59.75,
          111.5,
          24.25,
          20.5,
          70.4,
          30.55,
          84.9,
          54.5,
          75.35,
          44.45,
          98.05,
          63.9,
          69.15,
          64.65,
          98.85,
          89.6,
          83.25,
          70.25,
          24.5,
          20.1,
          73,
          61.4,
          84.3,
          19.9,
          20.4,
          50.75,
          20.45,
          75.75,
          65.4,
          59.75,
          78.5,
          48.95,
          99.65,
          18.25,
          54.55,
          40.65,
          20.45,
          24.8,
          88.8,
          20.05,
          69.8,
          77.15,
          35.05,
          108.1,
          84.05,
          20.2,
          49.2,
          24.6,
          71.65,
          104.9,
          106.5,
          75.5,
          58.5,
          78.9,
          79.2,
          109.45,
          59.2,
          29.15,
          20.05,
          66.5,
          49.55,
          73.6,
          82.65,
          49,
          25.2,
          25.45,
          110.9,
          77.75,
          26.2,
          19.9,
          80.85,
          56.35,
          19.3,
          50.4,
          55.25,
          19.1,
          84.05,
          105.2,
          75.75,
          95.3,
          19.85,
          69.1,
          20.25,
          54.75,
          81.45,
          80.2,
          100.3,
          90.95,
          20,
          79.85,
          73.55,
          19.3,
          20.15,
          44.55,
          54.45,
          19.65,
          105,
          88.7,
          75.15,
          20.25,
          109.1,
          30.75,
          112.9,
          94.05,
          78.85,
          55.3,
          19.35,
          25.35,
          20.45,
          19.35,
          78.65,
          74.75,
          19.9,
          58.35,
          100.5,
          20.05,
          25.65,
          95,
          45.45,
          20,
          49.2,
          83.25,
          19.25,
          19.65,
          72.8,
          109.65,
          65,
          114.1,
          20.65,
          86.95,
          94.75,
          25.35,
          105.45,
          25.4,
          102.55,
          24,
          25.6,
          73.5,
          98.25,
          54.4,
          103.1,
          34.2,
          43.75,
          100.65,
          116.05,
          82,
          65.15,
          44.8,
          79.8,
          88.85,
          74.95,
          106.85,
          19.3,
          56.1,
          19.7,
          51.3,
          118.6,
          24.15,
          20.3,
          115.5,
          25.05,
          109.1,
          19.65,
          111.3,
          29.9,
          80.6,
          20.8,
          89.95,
          116.05,
          19.55,
          115.25,
          24.8,
          19.9,
          81.25,
          69.95,
          86.4,
          66.3,
          94.65,
          72.1,
          34.7,
          95.95,
          44.8,
          109.4,
          71.05,
          19.7,
          40.25,
          19.85,
          68.25,
          20.15,
          50.95,
          25.15,
          20.25,
          44,
          20.25,
          55.8,
          88.9,
          57.65,
          79.15,
          108.05,
          94.8,
          45.9,
          102.6,
          61.35,
          57.55,
          29.25,
          19.6,
          111.75,
          106.5,
          107.7,
          19.3,
          20.05,
          69.95,
          63.7,
          50.9,
          60.4,
          79.25,
          110.1,
          90.7,
          25.3,
          85.2,
          24.35,
          25.1,
          54.55,
          96.6,
          81.15,
          38.5,
          92.9,
          84.7,
          66,
          20.75,
          61.45,
          54.5,
          99.75,
          109.75,
          80.85,
          20.3,
          67.8,
          19.8,
          25.7,
          56.15,
          86.7,
          20.4,
          19.65,
          54.35,
          108.1,
          54.45,
          45.35,
          59,
          69.45,
          64.95,
          18.85,
          19.8,
          25.05,
          114.3,
          109.2,
          45.05,
          51,
          110.45,
          84.65,
          60.05,
          44.65,
          93.25,
          20.25,
          25.45,
          20.6,
          94.1,
          34.8,
          60.75,
          51.35,
          64.05,
          84.8,
          50.15,
          94.6,
          59.75,
          100.25,
          98.9,
          97.7,
          60.25,
          56.25,
          46.2,
          24.9,
          63.35,
          50.1,
          50.15,
          64.65,
          79.6,
          19.5,
          99.55,
          74,
          38.9,
          79.55,
          46.3,
          99.35,
          95.8,
          78.15,
          26.1,
          40.35,
          79.2,
          20.9,
          49.9,
          68.9,
          20.25,
          76,
          74,
          82.3,
          89.4,
          99.15,
          29.45,
          19.8,
          59.15,
          44.75,
          90.8,
          49.55,
          106.7,
          94.45,
          19.45,
          67.95,
          65.25,
          99.45,
          20.35,
          19.95,
          77.4,
          19.7,
          99.7,
          74.8,
          19.15,
          78.95,
          62.85,
          71.55,
          94.95,
          86.1,
          19.55,
          24.8,
          84.05,
          36.25,
          98.6,
          103.65,
          92.9,
          19.9,
          20.1,
          80.5,
          39.85,
          60.5,
          103.85,
          67.8,
          24.85,
          19.35,
          89,
          55,
          76.15,
          20.3,
          117.35,
          19.75,
          45.2,
          25.2,
          89.75,
          75,
          49.95,
          65.7,
          67.05,
          110.9,
          87.95,
          19.8,
          75.7,
          62.15,
          115.15,
          19.5,
          86.55,
          20.4,
          19.8,
          45.65,
          56.4,
          73.3,
          101.35,
          33.6,
          20.7,
          104.05,
          20.25,
          73.7,
          108.75,
          20.15,
          19.75,
          25.95,
          70.05,
          24.05,
          84.75,
          23.05,
          59.95,
          19.55,
          19.6,
          20.05,
          85.55,
          78.6,
          116.8,
          43.55,
          60.8,
          54.9,
          65.2,
          108.2,
          92,
          75.1,
          25.05,
          75.15,
          19.5,
          19.3,
          112.2,
          70.3,
          19.6,
          20.25,
          80.65,
          115.75,
          80.6,
          59.55,
          19.05,
          95.65,
          19.95,
          19.4,
          36.1,
          19.75,
          64.1,
          19.75,
          19.7,
          110.2,
          106.35,
          90.55,
          65.9,
          104.5,
          52.5,
          56.1,
          88.75,
          26,
          99.4,
          73.15,
          54.65,
          115.55,
          104.45,
          91.15,
          89.7,
          92.4,
          19.9,
          18.85,
          25.75,
          20.95,
          97.05,
          25.4,
          19.7,
          35,
          101.25,
          70.2,
          90.95,
          73.85,
          88.05,
          20.1,
          110.3,
          85.15,
          60.95,
          73.55,
          46,
          58.55,
          24.6,
          19.75,
          86.35,
          25.5,
          19,
          19.55,
          110.1,
          69.75,
          50.6,
          65.6,
          82.1,
          79.1,
          90.65,
          20.55,
          75.75,
          110,
          20.85,
          80.35,
          70.15,
          67.45,
          20.75,
          69.9,
          51.1,
          25.55,
          60,
          90.55,
          76.4,
          84.95,
          110.1,
          99.65,
          45.4,
          69,
          48.65,
          59.85,
          80.65,
          20.55,
          66.4,
          100.2,
          44.55,
          20.35,
          91.8,
          20.2,
          50.35,
          18.8,
          20.45,
          64.75,
          98.7,
          89.45,
          58.75,
          20.7,
          85.6,
          80.3,
          79.8,
          79.85,
          54.1,
          80.9,
          24.5,
          20.15,
          20.05,
          19.6,
          114.3,
          100.3,
          80,
          20.85,
          89.95,
          20,
          48.75,
          80,
          20.35,
          20.25,
          19.4,
          100.4,
          57.95,
          59.5,
          19.2,
          59.55,
          103.95,
          68.95,
          103.1,
          24.7,
          110.2,
          62.45,
          89.55,
          78.9,
          20.35,
          71.45,
          46.35,
          94.65,
          49.9,
          25.45,
          20.75,
          66.1,
          75.4,
          21.05,
          69.35,
          88.85,
          97,
          66.4,
          69.2,
          79.5,
          100.65,
          79.7,
          61.4,
          69.8,
          40.55,
          75.65,
          90.7,
          80.5,
          60.6,
          101.15,
          24.95,
          20.3,
          60,
          20.25,
          44.75,
          98,
          107.7,
          104.7,
          93.9,
          86.45,
          19.4,
          24.95,
          75,
          78.2,
          94.2,
          50.05,
          69.55,
          90.1,
          44.65,
          80.35,
          98.1,
          53.35,
          19.55,
          48.95,
          54.2,
          24.45,
          40.15,
          25.6,
          70.35,
          91.7,
          89.2,
          24.1,
          53.85,
          115.6,
          19.75,
          24.05,
          25.3,
          84.3,
          89.75,
          97.95,
          20,
          103.9,
          20.7,
          20.15,
          26,
          77.35,
          66.05,
          19.9,
          68.15,
          80.85,
          75.5,
          80.6,
          83.2,
          87.55,
          109.4,
          45.55,
          20.7,
          75.3,
          93.4,
          73.75,
          88.15,
          49.2,
          19.65,
          105.15,
          49,
          49.8,
          20.95,
          79.3,
          19.5,
          44.15,
          105.5,
          92.7,
          26.25,
          96.95,
          20.45,
          115.8,
          108.2,
          20.2,
          54.9,
          20.15,
          90.35,
          55.75,
          114.6,
          66.8,
          100.3,
          105.35,
          85.2,
          18.95,
          69.8,
          106.15,
          20.55,
          105.75,
          25.25,
          19.75,
          104.85,
          60.95,
          81.15,
          19.1,
          20.8,
          90.15,
          90.1,
          74.1,
          118.75,
          85.9,
          95,
          20.15,
          101.3,
          21.2,
          24.2,
          20.3,
          85.3,
          89.6,
          56.25,
          50.95,
          115.85,
          103.65,
          26.1,
          35.1,
          99.1,
          67.25,
          25,
          59.55,
          77.8,
          55.1,
          24.15,
          45.25,
          20.25,
          64.75,
          54.6,
          20.7,
          94.75,
          115.8,
          49.45,
          83.8,
          95.35,
          74.05,
          89.6,
          116.6,
          54.2,
          19.3,
          65.05,
          24.05,
          18.75,
          20.15,
          20,
          71,
          93.6,
          24.4,
          65.25,
          50.55,
          70.7,
          45.25,
          70.3,
          108.95,
          26.45,
          19.65,
          19.05,
          74.75,
          75.8,
          25.1,
          44.45,
          104.3,
          89,
          20.15,
          36.15,
          19.2,
          19.25,
          61.2,
          20.45,
          35.05,
          44,
          50.35,
          20,
          86.4,
          58.4,
          94.1,
          108.9,
          107.4,
          90.85,
          19.9,
          66.4,
          100.7,
          25.6,
          19.85,
          20.75,
          95.8,
          94.65,
          106.65,
          45.85,
          104.35,
          55.45,
          61.15,
          78.95,
          109.2,
          61.3,
          96.85,
          40.55,
          19.8,
          108.25,
          105.05,
          90.45,
          86.4,
          66.9,
          110.7,
          20,
          102.1,
          70.15,
          80.05,
          49.2,
          20.5,
          38.25,
          54.95,
          96.6,
          19.9,
          19.9,
          84.6,
          85.25,
          81.25,
          115.5,
          79,
          94.65,
          20.8,
          59.5,
          20.05,
          100.45,
          20.6,
          20.3,
          39.55,
          20.45,
          25.25,
          91.25,
          72.45,
          19.7,
          75.1,
          25,
          69.15,
          91.55,
          35.8,
          113.15,
          19.85,
          19.8,
          19.9,
          19.7,
          59.1,
          91.15,
          68.95,
          51.55,
          24.4,
          96.8,
          70.05,
          19.5,
          78.75,
          69.2,
          19.55,
          103.65,
          54.7,
          54.15,
          84.85,
          20,
          99.25,
          19.35,
          94.75,
          114.05,
          74.9,
          19.8,
          80.85,
          54.65,
          91.7,
          118.6,
          24.55,
          19.45,
          116.15,
          80.6,
          20.3,
          99.8,
          75,
          19.9,
          80.3,
          84.3,
          54.05,
          104.9,
          97.25,
          83.05,
          41.1,
          45,
          74.55,
          40.2,
          70.5,
          19.75,
          24.65,
          104.25,
          78.35,
          109.7,
          33.45,
          94.6,
          20.2,
          20.3,
          39.4,
          69.15,
          51.35,
          100.05,
          20.3,
          94.45,
          46.4,
          104.05,
          24.9,
          59.6,
          108.5,
          40.55,
          58.95,
          20.75,
          113.15,
          48.8,
          63.05,
          100.85,
          80.55,
          64.4,
          75.2,
          84.9,
          19.3,
          74.65,
          59.05,
          69.1,
          20.55,
          76.55,
          62.5,
          94.9,
          111.65,
          19.9,
          20.45,
          106.05,
          113.45,
          92.55,
          65.6,
          84.35,
          71.1,
          85.15,
          49.7,
          30.2,
          56.35,
          107.55,
          19.85,
          95.9,
          23.85,
          83.85,
          84.8,
          76.1,
          74.55,
          39.2,
          79.55,
          19.6,
          19.55,
          39.15,
          20.1,
          99.95,
          59.8,
          49.75,
          108.5,
          60.15,
          19.05,
          84,
          44.55,
          103.45,
          80.65,
          57.2,
          110.75,
          24.7,
          97.05,
          76.35,
          18.9,
          74.45,
          84.4,
          24.4,
          20.05,
          55.5,
          84.3,
          100.2,
          19.4,
          20.4,
          94.75,
          44.35,
          74.55,
          73.6,
          50.1,
          53,
          19.85,
          24.35,
          19.55,
          25.05,
          93.8,
          103.75,
          56.75,
          20.8,
          24.45,
          25.6,
          59.65,
          83.3,
          79.55,
          24.45,
          19.2,
          29.8,
          45.5,
          30.05,
          65.65,
          74.05,
          110.75,
          19.7,
          49.5,
          43.95,
          111.15,
          20.6,
          19.65,
          115.8,
          88.65,
          94.5,
          20.1,
          34.65,
          52.3,
          65,
          35.45,
          19.7,
          95.6,
          19.85,
          81.85,
          109.3,
          25.4,
          69.8,
          20,
          109.9,
          50.3,
          101.5,
          89.15,
          19.4,
          29.9,
          78.8,
          19.3,
          96.8,
          20.65,
          19.8,
          104.6,
          80.05,
          45.15,
          73.15,
          99.1,
          105.35,
          45.65,
          79.95,
          54.45,
          25.1,
          84.7,
          75.85,
          48.8,
          35.2,
          76.25,
          24.9,
          54.3,
          66.3,
          20.9,
          75.35,
          104.45,
          49.45,
          19.45,
          92.15,
          19.85,
          100.25,
          95.7,
          93.15,
          69.7,
          19.8,
          71.35,
          20.75,
          40.6,
          20.35,
          19.75,
          54.4,
          20.45,
          66.15,
          89.85,
          45.05,
          86.85,
          96.75,
          106.65,
          110.15,
          82.85,
          20.1,
          59.45,
          58.6,
          49.7,
          65.85,
          73.5,
          113.65,
          83.4,
          65.65,
          61.35,
          85.9,
          75.65,
          70.9,
          49.85,
          20.1,
          103.05,
          99.7,
          81.9,
          66.2,
          19.75,
          72.6,
          116.5,
          106.8,
          24.95,
          89.25,
          19.25,
          104.55,
          87.2,
          30.75,
          25.7,
          86.2,
          30.1,
          99.35,
          19.2,
          20.1,
          20.35,
          25.65,
          94.55,
          94.4,
          56.1,
          68.25,
          24.75,
          76.25,
          74.35,
          54.15,
          19.45,
          34.95,
          53.65,
          104,
          70.35,
          64.85,
          19.65,
          45.9,
          20,
          44.8,
          20.35,
          45.8,
          108.95,
          64.35,
          90.8,
          24.95,
          84.7,
          70.8,
          104.4,
          101.5,
          54.3,
          103.95,
          91.1,
          19.95,
          26.45,
          75.1,
          108.1,
          110.15,
          111.5,
          106.5,
          19.9,
          111.1,
          70.7,
          24.85,
          91.2,
          65.6,
          59.45,
          109.95,
          38.5,
          92.55,
          24.5,
          19.7,
          20.6,
          58,
          107.45,
          65.5,
          25.45,
          100.15,
          104.45,
          21.15,
          96.2,
          44.4,
          94.35,
          20.3,
          105.75,
          81.15,
          89.55,
          54.75,
          53.75,
          105.75,
          105.85,
          64.2,
          87.7,
          89.3,
          20.15,
          20.05,
          67.2,
          94.55,
          107.5,
          73,
          114.75,
          76.05,
          77.9,
          90.65,
          110.45,
          68.7,
          44.85,
          29.8,
          88.9,
          58.75,
          19.85,
          86.9,
          59.65,
          66.4,
          20.15,
          108.1,
          56.9,
          109.6,
          25.15,
          79.15,
          66.75,
          48.8,
          80.7,
          20.55,
          115.1,
          59.7,
          86.45,
          33.7,
          80.1,
          104.05,
          108.75,
          41.1,
          20.35,
          105.9,
          65.5,
          40.45,
          70.45,
          78.8,
          90.1,
          82.45,
          20.25,
          66.25,
          89.7,
          64.55,
          93.65,
          73.6,
          109.75,
          61.45,
          106.4,
          81.9,
          105.2,
          54.6,
          20.55,
          19.7,
          66.05,
          54.05,
          58.9,
          96.9,
          19.1,
          50,
          45.4,
          85.45,
          84.1,
          66.25,
          76.9,
          74.6,
          116.95,
          40.65,
          114.35,
          69.7,
          98.65,
          61.65,
          89.35,
          95.4,
          35.4,
          19.95,
          19.25,
          20.4,
          24.75,
          25.35,
          20,
          59.75,
          82.5,
          20.35,
          90.8,
          104.95,
          105.25,
          23.75,
          61.3,
          75.8,
          98,
          52,
          64.4,
          45.8,
          30.5,
          69.15,
          49.25,
          39.35,
          105.1,
          20.1,
          19.75,
          19.75,
          70.4,
          20.45,
          20.35,
          86.2,
          95.65,
          103.8,
          97.2,
          63.55,
          24.95,
          99,
          85.55,
          94,
          50.3,
          95,
          61.4,
          80.55,
          78.5,
          114.3,
          20.05,
          62.65,
          92.7,
          100.45,
          75.2,
          84.75,
          79.5,
          19.8,
          100.9,
          95.3,
          90.95,
          54.5,
          49.6,
          25,
          45.45,
          107.75,
          89.1,
          44.75,
          101.6,
          103.15,
          95.65,
          75.1,
          61.35,
          19.7,
          51,
          88.85,
          20.05,
          65.1,
          70.15,
          20.75,
          56.05,
          19.95,
          98.6,
          79,
          89.45,
          74.2,
          81,
          49.6,
          84.6,
          84.2,
          106.3,
          69.05,
          45.4,
          99.35,
          50.75,
          87.1,
          20.15,
          98.7,
          25.2,
          55.7,
          65.35,
          25.3,
          24.25,
          60.5,
          25.1,
          20.05,
          30.25,
          20.2,
          59.9,
          25.15,
          101.3,
          76.95,
          55.3,
          92.45,
          48.45,
          19.35,
          86.7,
          55.7,
          84.25,
          64.65,
          69.2,
          54.65,
          24.75,
          23.95,
          105,
          59.85,
          20.05,
          92.15,
          44.8,
          20.9,
          95.4,
          80.35,
          85.1,
          115.05,
          19.95,
          86.15,
          78.85,
          86.55,
          42.4,
          24.25,
          20.5,
          19.6,
          20.25,
          20.6,
          19.8,
          80.2,
          116.4,
          31.65,
          94.15,
          20.65,
          76.85,
          20.15,
          55.25,
          82.15,
          103,
          95.1,
          95.15,
          79.8,
          74.8,
          20.45,
          78.35,
          19.1,
          20,
          19.95,
          24,
          19.15,
          91.3,
          19.15,
          19.75,
          75.5,
          83.75,
          19.4,
          26.5,
          19.15,
          40.9,
          80.25,
          70.8,
          60.2,
          55.2,
          54.15,
          100.4,
          62.55,
          70.45,
          85.5,
          54.5,
          20.75,
          20.35,
          91,
          104.8,
          51.1,
          89.8,
          20.55,
          64.05,
          74.85,
          25,
          20.3,
          26.35,
          54.7,
          90.25,
          20.65,
          25.45,
          19.5,
          66.15,
          69.1,
          39.1,
          20.05,
          59.8,
          48.6,
          105.35,
          25.1,
          49.75,
          94.75,
          93,
          71.9,
          77.55,
          19.85,
          95.25,
          25.05,
          53.15,
          20.15,
          101.25,
          100.55,
          25.3,
          71.8,
          19.7,
          49.85,
          69.6,
          19.75,
          80.8,
          64.2,
          35,
          19.2,
          90.65,
          20,
          74.65,
          61.2,
          19.95,
          54.8,
          73.45,
          51.45,
          80.45,
          85.3,
          79.3,
          76.5,
          25.4,
          86.85,
          19.65,
          45.55,
          78.1,
          19.3,
          110.5,
          20.3,
          81.35,
          55.3,
          56.55,
          19.7,
          104.05,
          52.85,
          80.65,
          24.65,
          21.3,
          110.2,
          51.05,
          19.8,
          19.9,
          87.3,
          19.85,
          89.4,
          20,
          20.05,
          83.25,
          102.9,
          39.1,
          114.5,
          20.2,
          55.8,
          24.2,
          72.8,
          99.85,
          99.5,
          20.25,
          26,
          19.9,
          19.05,
          96.5,
          19.85,
          25.7,
          20.3,
          91.55,
          39.4,
          105.7,
          70.25,
          93.75,
          60,
          59.8,
          90.65,
          109,
          68.1,
          20.4,
          81.95,
          60.55,
          65.6,
          82.5,
          82.3,
          68.15,
          20.3,
          20.2,
          89.2,
          74.8,
          20.2,
          84.4,
          25.15,
          19.8,
          50.85,
          102.4,
          55.5,
          109.75,
          106.4,
          60,
          88.8,
          80.05,
          75.55,
          49.55,
          23.9,
          66.4,
          18.8,
          108.4,
          85.95,
          80.9,
          111.8,
          20.6,
          44.6,
          105.1,
          115.15,
          59.8,
          26.3,
          70.55,
          20.05,
          79.85,
          90.05,
          24.45,
          59.95,
          25.35,
          34.3,
          105.05,
          19.3,
          19.15,
          51.4,
          71.85,
          75.4,
          49.7,
          78.75,
          81.6,
          70.4,
          76.1,
          94,
          103.95,
          19.95,
          110.8,
          96.1,
          48.8,
          50.55,
          44.65,
          19.45,
          89.3,
          19.25,
          70.5,
          19.65,
          20.85,
          19.65,
          19.35,
          44,
          94.4,
          75.4,
          71,
          21.2,
          61.05,
          79.95,
          19.7,
          20.3,
          24.35,
          19.75,
          50.3,
          50.25,
          85.35,
          51.65,
          24,
          59.85,
          25.45,
          23.9,
          24.15,
          75.7,
          50.85,
          91.6,
          98.9,
          85,
          44.3,
          80.2,
          60.9,
          34.2,
          87.15,
          54.3,
          19.1,
          112.75,
          19.95,
          19.5,
          65.55,
          78.8,
          78.2,
          105.25,
          89.25,
          20.65,
          68.7,
          78.65,
          24.75,
          19.75,
          89.1,
          84.7,
          59.9,
          19.95,
          108.9,
          33.6,
          85.85,
          34.85,
          95.3,
          84.6,
          44.95,
          24.7,
          100.3,
          25.45,
          50.7,
          55,
          68.4,
          55.05,
          19.8,
          84.45,
          35.9,
          80.75,
          78.65,
          61.75,
          63.7,
          87.6,
          89.15,
          20,
          104.4,
          20.05,
          34.3,
          20.65,
          84.25,
          19.65,
          79.85,
          20.2,
          19.8,
          50.35,
          74.6,
          79.15,
          20.35,
          21.05,
          94.7,
          74.95,
          111.95,
          19.85,
          89.75,
          20.05,
          108.95,
          19.65,
          24.9,
          93.2,
          84.8,
          71.75,
          30.35,
          54.85,
          19.5,
          24.2,
          19.35,
          100.65,
          94.1,
          74.55,
          56.15,
          20.35,
          80.55,
          61.25,
          20.45,
          18.9,
          19.6,
          45.2,
          19.45,
          25.45,
          94.9,
          29.3,
          20.25,
          110.5,
          109.4,
          19.95,
          19.6,
          76.6,
          19.6,
          85.3,
          65.85,
          20.05,
          99.4,
          20,
          78.45,
          25.1,
          55,
          71.1,
          61.55,
          45.9,
          40.3,
          87.1,
          49.5,
          73.8,
          19.2,
          25,
          35.3,
          76.75,
          81,
          105.55,
          18.8,
          24.9,
          64.9,
          61.35,
          113.95,
          90.15,
          54.1,
          49.8,
          24.4,
          95,
          69.9,
          39.95,
          103.25,
          94.25,
          47.05,
          20.55,
          19.65,
          70.2,
          81,
          75.9,
          24.7,
          110.25,
          85,
          19.75,
          23.9,
          19.95,
          25.15,
          54.15,
          59.8,
          83.85,
          104.9,
          75.3,
          66.65,
          109.5,
          73.85,
          19.3,
          118.2,
          51.45,
          59.45,
          19.5,
          19.55,
          93.55,
          59.3,
          109.8,
          78.1,
          39.9,
          64.9,
          53.4,
          24.9,
          44.7,
          114,
          20.25,
          83.85,
          20.2,
          19.95,
          20.35,
          90,
          54.2,
          99.1,
          66.9,
          25.85,
          91.05,
          20.95,
          109.2,
          85.8,
          19.65,
          20.5,
          89.65,
          74.35,
          49.45,
          89.1,
          75.15,
          70.65,
          90.05,
          19.4,
          88.75,
          91,
          90.8,
          18.95,
          102.4,
          99.9,
          88.7,
          54.3,
          55.7,
          103.95,
          20.15,
          20.05,
          91.95,
          55.65,
          74.7,
          104.15,
          83.65,
          110.05,
          25.5,
          19.5,
          80.7,
          105.1,
          25.15,
          95.65,
          80.8,
          24.85,
          54.75,
          50.75,
          20.15,
          20.05,
          71.6,
          81.45,
          58.4,
          53.7,
          19.6,
          89.4,
          84.2,
          106.1,
          25.75,
          64.95,
          85.45,
          20.05,
          20.7,
          25.3,
          100.6,
          74,
          99.4,
          107.45,
          83.6,
          99.05,
          80.1,
          65.3,
          89.55,
          60.8,
          74.5,
          99.15,
          19.25,
          39.45,
          44.85,
          97.2,
          110.55,
          19.9,
          76.95,
          35.4,
          20.45,
          96.75,
          54.2,
          100.1,
          45.25,
          20.85,
          33.45,
          20.2,
          85.9,
          61,
          86.9,
          69.4,
          20.35,
          104.3,
          44.95,
          49.45,
          20.6,
          19.55,
          93.5,
          54.55,
          20.05,
          79.45,
          79.85,
          100,
          19.6,
          20.2,
          50.4,
          113.35,
          80,
          80.95,
          24.9,
          54.9,
          109.25,
          116.3,
          19.9,
          70.35,
          25.6,
          44.45,
          100.15,
          73.85,
          70.1,
          25.25,
          21.05,
          24.95,
          64.5,
          105.95,
          75.85,
          43.6,
          91.25,
          89.75,
          104.4,
          90.15,
          40.3,
          105.25,
          104,
          69.65,
          74.3,
          100.9,
          20.25,
          96.9,
          104.1,
          20.1,
          56.55,
          68.6,
          69.05,
          19.7,
          20.05,
          94.4,
          54.95,
          93.7,
          110.25,
          98.9,
          80.45,
          79.4,
          62.8,
          74.9,
          74.85,
          25.85,
          68.3,
          48.4,
          105.05,
          25.15,
          19.5,
          92.95,
          20.7,
          19.35,
          104.35,
          19.55,
          74.05,
          40.1,
          20.1,
          83.55,
          56.85,
          19.55,
          106.15,
          78.95,
          49.75,
          92.4,
          58.2,
          91.95,
          65.25,
          73.1,
          59.75,
          59.8,
          116.6,
          109.3,
          101.4,
          50.65,
          56.15,
          19.2,
          83,
          70.1,
          108.3,
          25.25,
          45.35,
          43.9,
          79.3,
          84.9,
          79.25,
          71.05,
          53.75,
          24.25,
          44.25,
          50.05,
          20.15,
          69.35,
          19.35,
          19.15,
          61,
          20.5,
          50.2,
          79.6,
          24.9,
          106.9,
          101.35,
          55.35,
          50.55,
          19.5,
          90.65,
          89.85,
          79,
          19.55,
          19.9,
          116.25,
          87.75,
          81.3,
          44.3,
          70.35,
          44.45,
          49.15,
          29.45,
          85.3,
          69.1,
          70.35,
          20.6,
          74.15,
          75.05,
          44.6,
          21.45,
          43.45,
          20.05,
          94.15,
          19.55,
          75.9,
          64.15,
          109.55,
          110.8,
          53.45,
          69.95,
          97,
          90.6,
          73.55,
          94.35,
          19.4,
          19.75,
          54.6,
          29.8,
          103.05,
          20.3,
          35.1,
          105.7,
          56.25,
          60.35,
          59.8,
          99.65,
          50.65,
          60.9,
          59.65,
          64.7,
          54.85,
          91.35,
          25.1,
          34,
          45.9,
          20.5,
          20.35,
          36.1,
          65.8,
          20.35,
          105.8,
          96.75,
          24.4,
          73.05,
          64.35,
          20.5,
          54.75,
          51.15,
          41.95,
          54.35,
          96,
          61.45,
          19.65,
          19,
          100,
          98.7,
          19.8,
          73.8,
          20.05,
          106.2,
          116.55,
          99.7,
          19.7,
          19.5,
          29.15,
          55,
          90.8,
          51,
          90.1,
          59.05,
          20.3,
          72.95,
          73.55,
          84.3,
          78,
          72.1,
          106.75,
          19.25,
          20.55,
          20,
          24.65,
          103.5,
          23.85,
          25.8,
          59.45,
          20.05,
          82.55,
          81.25,
          74.3,
          109.7,
          96.35,
          66.6,
          44.5,
          80.1,
          69.05,
          20.4,
          19.7,
          50.1,
          83.45,
          86.65,
          20.15,
          19.4,
          60.05,
          20.35,
          94.05,
          84.1,
          78.75,
          55.55,
          20.1,
          70.3,
          53.65,
          20.75,
          103.4,
          50.8,
          79,
          74.6,
          96.5,
          20.1,
          19.4,
          77.55,
          20.05,
          19.85,
          20.2,
          67.45,
          18.55,
          29.75,
          24.2,
          23.55,
          20.45,
          92.3,
          53.65,
          39.65,
          54.65,
          104.8,
          29.3,
          83.85,
          103.65,
          99.05,
          73.35,
          100.05,
          20.35,
          43.95,
          23.5,
          70.7,
          94.3,
          29.15,
          20.85,
          37.7,
          92.45,
          44.15,
          36.05,
          50.25,
          109.75,
          20.3,
          112.35,
          94.3,
          41.15,
          74.65,
          48.25,
          76.15,
          71.1,
          96.55,
          79.3,
          89.6,
          20.5,
          106.3,
          100.35,
          85.6,
          106.15,
          51.1,
          19.9,
          25.7,
          99.4,
          69.7,
          98.35,
          85.45,
          95.9,
          100.75,
          89.2,
          25.75,
          84.1,
          79.3,
          107.05,
          20.05,
          19.5,
          45.3,
          115.15,
          72.95,
          19.65,
          19.55,
          89.55,
          50.35,
          87.25,
          20.8,
          109.25,
          20.35,
          55.9,
          79.2,
          24,
          101.35,
          35.45,
          79.4,
          35.2,
          19.65,
          49.85,
          68.75,
          61.9,
          79.9,
          89.75,
          19.4,
          93.65,
          19.9,
          72.9,
          25.6,
          19.75,
          55.7,
          117.5,
          19.85,
          78.9,
          20.65,
          19.65,
          79.75,
          79.95,
          29.9,
          19.75,
          45,
          44.8,
          51.1,
          53.15,
          24.7,
          109.95,
          20.8,
          25.6,
          108.4,
          19.55,
          85.1,
          69.05,
          70.15,
          111.15,
          89.35,
          89.1,
          91.25,
          90.35,
          105.55,
          19.1,
          20.4,
          100.45,
          85.7,
          94,
          69.85,
          25.85,
          71.1,
          93.35,
          50.55,
          81.3,
          20.7,
          79.05,
          19.05,
          19.6,
          20.2,
          20.9,
          103.6,
          38.8,
          88.4,
          79.7,
          19.3,
          55.75,
          19.95,
          89.65,
          45.85,
          55.95,
          69,
          83.55,
          65.7,
          94.9,
          61.9,
          20,
          67.7,
          25.15,
          92.85,
          111.3,
          60.6,
          65.5,
          19.95,
          74.6,
          94.6,
          81.15,
          89.05,
          49.2,
          19.45,
          104.3,
          86.05,
          25.2,
          35.15,
          99.65,
          105.35,
          24.3,
          80.7,
          89.85,
          61.1,
          29.05,
          99.7,
          46,
          80.4,
          100.05,
          94,
          68.95,
          68.45,
          69,
          43.85,
          44.5,
          18.7,
          53.55,
          114.6,
          20.1,
          85.5,
          108.75,
          97.85,
          19.55,
          84.05,
          89.4,
          19.7,
          79.85,
          74.45,
          74.1,
          18.8,
          64.4,
          55.8,
          20.05,
          99.15,
          56.75,
          104.15,
          110.8,
          35.75,
          69.9,
          89.2,
          55.65,
          50.7,
          20,
          19.1,
          45.55,
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       "}\n",
       "});</script><script type=\"text/javascript\">window.addEventListener(\"resize\", function(){if (document.getElementById(\"041c2bfd-c2a8-4d13-925c-0d8c4b14f354\")) {window._Plotly.Plots.resize(document.getElementById(\"041c2bfd-c2a8-4d13-925c-0d8c4b14f354\"));};})</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "churns = [\"Yes\", \"No\"]\n",
    "fig = {\n",
    "    'data': [\n",
    "        {\n",
    "            'x': df.loc[(df['Churn']==churn), 'MonthlyCharges'] ,\n",
    "            'y': df.loc[(df['Churn']==churn),'tenure'],\n",
    "            'name': churn, 'mode': 'markers',\n",
    "        } for churn in churns\n",
    "    ],\n",
    "    'layout': {\n",
    "        'title': 'Tenure vs Monthly Charges',\n",
    "        'xaxis': {'title': 'Monthly Charges'},\n",
    "        'yaxis': {'title': \"Tenure\"}\n",
    "    }\n",
    "}\n",
    "\n",
    "py.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "_uuid": "b4c4553c27912a182331f3664aafd7aaf457d4ae"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
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       "}\n",
       "});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figs = []\n",
    "\n",
    "for churn in churns:\n",
    "    figs.append(\n",
    "        go.Box(\n",
    "            y = df.loc[(df['Churn']==churn),'tenure'],\n",
    "            name = churn\n",
    "        )\n",
    "    )\n",
    "layout = go.Layout(\n",
    "    title = \"Tenure\",\n",
    "    xaxis = {\"title\" : \"Churn?\"},\n",
    "    yaxis = {\"title\" : \"Tenure\"},\n",
    "    width=800,\n",
    "    height=500\n",
    ")\n",
    "\n",
    "fig = go.Figure(data=figs, layout=layout)\n",
    "py.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "_uuid": "e3c3edb17450b425470b2f87becafba3b58bce88"
   },
   "outputs": [
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     "data": {
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       "config": {
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        "plotlyServerURL": "https://plot.ly",
        "showLink": false
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       "data": [
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          34.7,
          85.3,
          102.45,
          104.4,
          99.75,
          74.4,
          74.25,
          59.85,
          69.6,
          45.4,
          19.5,
          69.9,
          87.15,
          84.75,
          89.95,
          113.2,
          90.5,
          79,
          20.15,
          71.65,
          20.35,
          84.25,
          78.1,
          89.65,
          98.7,
          76.35,
          79.15,
          85,
          85.3,
          86.55,
          73.85,
          44.85,
          45.1,
          96,
          20.05,
          108.65,
          45.55,
          35.1,
          46.2,
          45.15,
          43.3,
          57.15,
          73.2,
          85.35,
          45.95,
          83.75,
          70.05,
          86,
          100.5,
          72.65,
          21,
          45.1,
          50.4,
          78.95,
          94.45,
          84.8,
          50.9,
          99.8,
          107.35,
          19.55,
          79.1,
          25.5,
          80.75,
          91.85,
          75.35,
          75.45,
          49.55,
          78.6,
          81.1,
          74.95,
          93.55,
          102.1,
          90.9,
          29.2,
          89.15,
          108.85,
          84.75,
          45.7,
          69.95,
          44.6,
          74.95,
          95.25,
          89.85,
          100.45,
          47.15,
          80.2,
          87.1,
          75.9,
          98.75,
          86.45,
          45.3,
          104.1,
          81,
          90.6,
          88.15,
          20.2,
          90.8,
          79.35,
          96.8,
          83.35,
          49.4,
          79.2,
          48.7,
          95.6,
          59.75,
          108.15,
          71.35,
          20.15,
          69.75,
          93.2,
          80.85,
          33.65,
          79.95,
          19.3,
          99.2,
          85.2,
          75.25,
          54.35,
          24.95,
          42.35,
          75.3,
          94.8,
          70.55,
          86.15,
          85,
          80.55,
          75.8,
          98.5,
          95.25,
          74.4,
          85.15,
          88.55,
          54.75,
          91.3,
          79.5,
          70.1,
          111.3,
          95.25,
          86.25,
          100.8,
          86.3,
          89.95,
          76.45,
          70,
          64.4,
          102.45,
          80.1,
          80.2,
          98.15,
          112.95,
          70.9,
          86.85,
          99.85,
          74.5,
          109.15,
          65.2,
          99.5,
          71.55,
          93.9,
          108.4,
          48.75,
          85.65,
          106.7,
          25.15,
          110.35,
          103.25,
          47.8,
          98.6,
          83.05,
          70.4,
          104.75,
          94.25,
          45.95,
          70.15,
          85.55,
          70.3,
          106.35,
          103.7,
          88.35,
          94.2,
          96.25,
          70.7,
          33.55,
          94.55,
          112.95,
          35.9,
          99.25,
          24.45,
          103.35,
          84.8,
          99.95,
          90,
          104.85,
          106.1,
          74.2,
          89.35,
          77.15,
          35.25,
          48.55,
          98.4,
          93.85,
          100.7,
          80.45,
          55.25,
          54.45,
          75.35,
          75.7,
          74.25,
          89.7,
          96.4,
          69.5,
          85.25,
          19.4,
          83.3,
          80.1,
          62.7,
          25.3,
          98.15,
          93.7,
          105.95,
          82,
          95.75,
          94.05,
          54.75,
          95.65,
          94.6,
          98.9,
          76.05,
          69.75,
          34.5,
          105.55,
          30.1,
          70.3,
          80.2,
          94.35,
          44.6,
          19.6,
          110.45,
          70.7,
          99.25,
          84.8,
          105,
          54.45,
          85.3,
          83.35,
          33.5,
          90.35,
          90.75,
          89.6,
          49.25,
          19.75,
          95.15,
          101.35,
          70.05,
          74.65,
          50.4,
          79.65,
          79.85,
          78.75,
          80.45,
          50.1,
          76.4,
          98.7,
          100.8,
          90.1,
          51.55,
          79.25,
          94.85,
          85.7,
          44.4,
          89.5,
          86.05,
          44.55,
          35.4,
          95.65,
          20.95,
          34.7,
          19.75,
          92.55,
          60.05,
          74.3,
          85.35,
          74.3,
          98.1,
          109.65,
          74.55,
          100.95,
          94.9,
          104.9,
          24.1,
          104.05,
          88.35,
          94.65,
          74.4,
          79.9,
          69.7,
          98.1,
          20.5,
          99.6,
          81.95,
          69.35,
          91.1,
          86.1,
          94.7,
          85.1,
          99.15,
          102.95,
          45.05,
          71,
          70.55,
          79.7,
          59,
          60.35,
          69.25,
          70.95,
          89,
          99.4,
          73.5,
          95.5,
          92.35,
          74.55,
          83.8,
          54.45,
          99.8,
          105.85,
          75.45,
          93.85,
          100.75,
          31,
          80,
          70.25,
          100.15,
          94.5,
          33.9,
          89.95,
          84.45,
          79.5,
          89.15,
          74.95,
          74.4,
          55.3,
          55.15,
          84.95,
          43.25,
          48.35,
          79.55,
          71.05,
          84.5,
          108.6,
          30.3,
          30.4,
          45.4,
          84.15,
          19.75,
          85.4,
          75.2,
          55.85,
          106.4,
          84.4,
          56.25,
          85.55,
          68.65,
          77.85,
          105.35,
          87.05,
          53.5,
          25.1,
          79.65,
          54.2,
          19.45,
          103.4,
          84.45,
          85.95,
          59.4,
          30.6,
          99.55,
          70,
          45.3,
          29.85,
          95.1,
          19.8,
          76.65,
          99.15,
          44.95,
          49.55,
          95.9,
          81.5,
          84.1,
          36.45,
          25.05,
          49.85,
          55.55,
          69.5,
          104.3,
          93.85,
          50.45,
          74.65,
          94.2,
          106.55,
          20.1,
          83.8,
          55.15,
          86.65,
          106.75,
          78.45,
          87.45,
          70.75,
          101.35,
          81.7,
          68.25,
          79.15,
          95.45,
          100.95,
          69.1,
          69.6,
          103.45,
          77.95,
          78.45,
          29.5,
          70.75,
          84.45,
          85.65,
          70.15,
          97.8,
          46.3,
          106.3,
          89.4,
          83.15,
          74.15,
          99.5,
          44.15,
          53.9,
          85.45,
          50.85,
          59.2,
          83.2,
          54.9,
          103.9,
          19.25,
          75.45,
          54.85,
          95.1,
          75.5,
          73.75,
          96.05,
          88.95,
          50.7,
          53.4,
          101.9,
          83,
          50.6,
          89.5,
          69.8,
          93.8,
          101.05,
          94.7,
          104.15,
          61.45,
          90.55,
          88.8,
          85.2,
          91.4,
          106.15,
          45.3,
          73.25,
          51.05,
          85.35,
          75.35,
          75.2,
          20.9,
          43.3,
          109.5,
          84.8,
          95.05,
          50.35,
          74.6,
          19.7,
          59.45,
          105.2,
          45.15,
          93.8,
          96.2,
          79.6,
          85.25,
          80.5,
          89.8,
          50.75,
          89.65,
          65.4,
          72.9,
          40,
          99.45,
          86.25,
          45.65,
          70.1,
          70.2,
          55.35,
          84.2,
          45.85,
          75.25,
          100.15,
          105.75,
          48.35,
          24.4,
          20.95,
          49.55,
          20.25,
          50.15,
          95.9,
          25.25,
          45.15,
          84.4,
          75.1,
          70.15,
          101.75,
          45.8,
          20.1,
          40.65,
          101,
          69.1,
          75,
          100,
          71.15,
          54.15,
          108.75,
          49.15,
          19.4,
          79.15,
          80.4,
          102,
          20.65,
          70.8,
          89.05,
          96.6,
          104.5,
          50.6,
          49.35,
          94.25,
          68.95,
          93.85,
          76.05,
          24.45,
          89.35,
          80.35,
          55.8,
          79.05,
          95,
          25.2,
          98.4,
          79.4,
          101.4,
          89.8,
          109.75,
          19.3,
          91.25,
          49.1,
          65.25,
          85.45,
          94.1,
          71.65,
          104.65,
          74.25,
          74.2,
          101,
          100.2,
          89.05,
          70.1,
          105.65,
          96.5,
          70.85,
          85.95,
          73.9,
          109.45,
          100.2,
          74.05,
          101.55,
          111.95,
          55.95,
          45.75,
          74.95,
          80.15,
          109.25,
          35.2,
          78.8,
          106.4,
          49.4,
          69.1,
          90.2,
          93.55,
          80.85,
          82.05,
          20.55,
          78.55,
          78.65,
          42.9,
          34.25,
          58.5,
          96.2,
          74.4,
          105.3,
          73.85,
          84.55,
          24.75,
          85.8,
          24.45,
          105.7,
          24.25,
          76.5,
          93.5,
          101.5,
          74.9,
          69.6,
          24.05,
          50.55,
          100.55,
          20.5,
          74.8,
          24.45,
          71,
          40.3,
          50.6,
          84.85,
          65.7,
          70.5,
          94.85,
          19.75,
          65.45,
          98.7,
          67.5,
          69.6,
          84.35,
          100.2,
          78.05,
          73.6,
          74.75,
          20.2,
          93.55,
          25.05,
          95.55,
          39.3,
          20.25,
          23.9,
          85.45,
          99.9,
          84.8,
          75.2,
          49.35,
          74.9,
          101.25,
          18.95,
          28.6,
          24.35,
          98.65,
          79.9,
          103.3,
          96.2,
          104.15,
          102.95,
          90.6,
          50.8,
          90.05,
          75.85,
          68.5,
          73.5,
          69.95,
          70.05,
          94,
          61.15,
          84.45,
          75.3,
          109.55,
          19.6,
          66.4,
          100.05,
          102,
          90.2,
          25.15,
          79.85,
          49.6,
          105.95,
          91.85,
          40.1,
          73.9,
          89.8,
          72.25,
          96.55,
          40.1,
          101.25,
          79.55,
          84.05,
          89.1,
          94.4,
          78.25,
          44.15,
          75.75,
          19.1,
          80.3,
          74.9,
          80.85,
          24.75,
          90.85,
          79.7,
          57.55,
          86.5,
          103.95,
          25.1,
          48.95,
          83.55,
          89.15,
          70.45,
          60.3,
          24.75,
          103.3,
          78.5,
          19.85,
          79.9,
          99.7,
          58.6,
          98.5,
          50.45,
          94.65,
          100.25,
          88.45,
          69.85,
          81.7,
          79.9,
          25.4,
          83.75,
          20.9,
          69.4,
          74.9,
          74.15,
          70.1,
          78.3,
          96.8,
          94.4,
          84.3,
          92.45,
          99.55,
          81.25,
          19.95,
          99.25,
          80.45,
          79.35,
          79.75,
          100.05,
          69.35,
          85.8,
          79.7,
          50.55,
          80.55,
          84.5,
          84.3,
          67.75,
          85.25,
          80.05,
          20,
          48.8,
          85.05,
          102.8,
          99.95,
          117.8,
          79.5,
          79.65,
          94.7,
          92.5,
          19.45,
          75.55,
          70,
          74.8,
          104.4,
          86.2,
          51.2,
          19.5,
          74.9,
          74.9,
          100.25,
          102.8,
          100,
          99.85,
          94.2,
          83.85,
          88.3,
          104.05,
          94.7,
          100.65,
          80.55,
          78.85,
          44.45,
          84.9,
          20.25,
          74.35,
          62.05,
          80,
          104.1,
          39.1,
          76.5,
          49.2,
          23.15,
          80.85,
          60.1,
          78.95,
          45.15,
          79.4,
          53.95,
          99.3,
          80.65,
          71.1,
          106.25,
          20.8,
          94,
          89.85,
          46,
          66.25,
          90,
          70.45,
          19.75,
          53.95,
          105.5,
          81,
          69.8,
          73.75,
          54.55,
          76.25,
          93.9,
          70.4,
          91.15,
          70.95,
          99.5,
          83.9,
          117.45,
          104.4,
          29.4,
          44.65,
          25.25,
          84.05,
          85.7,
          74.7,
          90.8,
          106.15,
          85.35,
          90.85,
          35.75,
          46,
          89.4,
          19.8,
          50.9,
          81,
          98.35,
          51,
          91.65,
          90.85,
          69.4,
          94.45,
          20.15,
          95.7,
          74.95,
          47.95,
          63.6,
          36.85,
          44.1,
          50.75,
          104.4,
          39.3,
          106.45,
          96.05,
          75.1,
          44.7,
          55,
          74.35,
          104.7,
          55.7,
          19.85,
          70.3,
          85.55,
          94.5,
          85.35,
          79.65,
          79.6,
          90.6,
          20.2,
          106.05,
          99.15,
          55.9,
          82.35,
          40.4,
          75.35,
          85.15,
          93.8,
          20.4,
          94.7,
          30.5,
          77,
          20.1,
          75.3,
          99.2,
          85.5,
          20.05,
          70.4,
          49.75,
          75.3,
          94,
          118.35,
          30.45,
          96.1,
          104.25,
          80.2,
          104.2,
          69.65,
          80.8,
          80.3,
          84.1,
          69.35,
          79.6,
          36.45,
          89.4,
          80.35,
          40.65,
          60.45,
          84.9,
          73.55,
          20.15,
          34.7,
          107.55,
          98.75,
          101.15,
          88.7,
          79.75,
          94.55,
          69.05,
          96.25,
          101.1,
          104.7,
          55.25,
          90.1,
          53.75,
          89.3,
          95.2,
          45.7,
          74.5,
          79.65,
          101.3,
          80.05,
          89.2,
          83.65,
          19.5,
          51.25,
          45.6,
          49.65,
          20,
          34,
          92.5,
          88.35,
          107.95,
          74.45,
          64.75,
          89.8,
          95.5,
          29.65,
          84.5,
          90.7,
          70.3,
          103.95,
          74.75,
          50.8,
          80.25,
          78.9,
          84.75,
          85.45,
          19.9,
          99.45,
          70.6,
          81,
          84.85,
          89.15,
          24.8,
          105.65,
          80.85,
          89.45,
          72.15,
          76.4,
          61.6,
          79.9,
          96.15,
          65.3,
          19.65,
          84.65,
          69.55,
          31.05,
          51,
          44.35,
          79.7,
          55,
          84.85,
          73.65,
          73.9,
          77.75,
          84.35,
          84.95,
          73.85,
          51.8,
          46,
          79.4,
          71.8,
          88.4,
          46,
          51.75,
          94.4,
          70.15,
          34.7,
          81.1,
          20.55,
          106.6,
          106.75,
          89.45,
          97.9,
          55.7,
          79.8,
          39.05,
          83.9,
          69.85,
          53.55,
          93.9,
          113.15,
          84.95,
          80.5,
          19.3,
          49.65,
          54.35,
          88.45,
          90.5,
          94.85,
          69.95,
          48.6,
          55.8,
          80.15,
          75.5,
          20.2,
          74.75,
          104.05,
          96.65,
          20.05,
          103.45,
          19.9,
          46.35,
          19.95,
          79.6,
          75.9,
          76.2,
          19.25,
          84.3,
          79,
          70.25,
          84.6,
          24.1,
          60,
          86.55,
          20.85,
          50.75,
          105.5,
          85.15,
          54.2,
          109.5,
          104.4,
          105.1,
          75.7,
          90.8,
          97.95,
          108.15,
          80.5,
          104.3,
          71.35,
          89.4,
          20.6,
          99.95,
          81,
          70.15,
          70.15,
          96.55,
          95.55,
          69.65,
          89.3,
          87.55,
          96.3,
          85.2,
          35.1,
          81.3,
          19.6,
          85.45,
          71,
          85.05,
          44.4,
          70.3,
          79.35,
          90.8,
          70.45,
          45.25,
          75.8,
          71.3,
          69.1,
          88.25,
          70,
          97.35,
          25.9,
          55.65,
          69.65,
          100.6,
          86,
          106.95,
          29.6,
          59.9,
          95.6,
          41.6,
          100.85,
          40.2,
          84.5,
          78.95,
          20.2,
          85.2,
          98,
          94.45,
          105,
          93.85,
          84,
          48.75,
          84.85,
          56.65,
          73.9,
          24.5,
          89.9,
          78.55,
          99.45,
          25.2,
          74.05,
          55,
          89.75,
          85.15,
          94.6,
          94.25,
          72.45,
          105.2,
          82.85,
          103.85,
          83.6,
          108.45,
          91.5,
          80.85,
          49.05,
          105.3,
          88.95,
          110.85,
          114.2,
          36.5,
          70.75,
          40.15,
          94.45,
          97.35,
          45.3,
          94.95,
          44.55,
          23.45,
          29.7,
          101.1,
          50.65,
          55.4,
          90.6,
          86.85,
          99.05,
          111.25,
          55.1,
          102.25,
          95.9,
          95.05,
          53.85,
          104.2,
          50.25,
          99.5,
          71,
          93.2,
          19.35,
          19.85,
          104.2,
          79.25,
          44.9,
          70.1,
          29.65,
          77.85,
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          88.2,
          101.15,
          56.8,
          99.4,
          20.1,
          60.7,
          20.95,
          114.85,
          19.25,
          62.8,
          105.5,
          19.85,
          74.1,
          107.5,
          19.55,
          68.8,
          84.45,
          84.5,
          111.2,
          80.6,
          80.7,
          75.6,
          57.6,
          110.6,
          58.2,
          81,
          19.7,
          59.55,
          75.55,
          45.1,
          70.95,
          20.9,
          19.95,
          24.6,
          66.7,
          94.8,
          65.85,
          19.95,
          24.65,
          51.25,
          54.25,
          19.4,
          56.25,
          25.15,
          23.95,
          35.4,
          75.35,
          20.4,
          56.05,
          20,
          73.05,
          20.5,
          100.75,
          19.95,
          49.65,
          65.65,
          20.45,
          60.95,
          20.35,
          19.5,
          75.2,
          111.45,
          70.15,
          92,
          85.5,
          82.15,
          84.4,
          60.9,
          20.25,
          95.3,
          19.85,
          84.35,
          19.85,
          82.3,
          66.8,
          44.6,
          98.45,
          70.7,
          24.95,
          102.5,
          86.55,
          24.3,
          58.35,
          68.75,
          85.8,
          20.1,
          20.35,
          110.8,
          82.85,
          84.35,
          19.55,
          19.95,
          66.25,
          23.3,
          25.3,
          44.55,
          104.1,
          92.55,
          101.45,
          94.55,
          95.5,
          100.3,
          55.5,
          49.85,
          89.55,
          19.15,
          99.8,
          113.05,
          19.95,
          74.15,
          92,
          73.85,
          24.45,
          24.8,
          64.85,
          20.75,
          68.95,
          109.4,
          49,
          50.25,
          19.9,
          97.8,
          100.3,
          55.8,
          111.15,
          98.55,
          50.05,
          20.85,
          19.5,
          19.35,
          69.5,
          48.8,
          94.5,
          20.65,
          106.05,
          108.3,
          99.65,
          95.9,
          20,
          64.95,
          74.6,
          49.2,
          73.75,
          92.3,
          19.2,
          88.65,
          95.95,
          105.4,
          20.25,
          49.05,
          35.55,
          65.1,
          96.85,
          69.75,
          99.2,
          106.8,
          51.25,
          57.75,
          70.85,
          19.55,
          79.5,
          98.15,
          20.25,
          79.15,
          94.25,
          40.2,
          19.95,
          55.35,
          102.15,
          71.1,
          54.1,
          19.65,
          88.45,
          80.4,
          19.25,
          84.8,
          19.5,
          68.6,
          92.6,
          100.55,
          20.55,
          19.6,
          67.45,
          43.55,
          109.85,
          20.65,
          95.4,
          21,
          56.2,
          18.4,
          25.75,
          19.6,
          19.8,
          64.2,
          75.75,
          78.95,
          50.3,
          80.3,
          19.85,
          21.1,
          50,
          104.75,
          19.85,
          85.9,
          80.8,
          25.25,
          80.55,
          81.5,
          20.9,
          67.25,
          20.35,
          45.05,
          34.65,
          69.35,
          81.55,
          75.4,
          67.8,
          111.4,
          46.3,
          20.4,
          20.05,
          96.1,
          19.65,
          60.65,
          71.7,
          36,
          65.2,
          48.95,
          53.5,
          80.45,
          109.05,
          26.3,
          106.8,
          64.95,
          19.35,
          21.1,
          18.85,
          26,
          70.35,
          96.9,
          19.55,
          80.4,
          94.65,
          95.75,
          19.55,
          104.1,
          20.1,
          111.55,
          60.5,
          90.95,
          19.7,
          50.95,
          20.05,
          19.4,
          59.45,
          81.5,
          29.05,
          70.6,
          97.2,
          59.2,
          75.9,
          90.05,
          70.95,
          102.6,
          43.8,
          59,
          69.95,
          24.35,
          29.45,
          84.4,
          20.65,
          87.1,
          19.85,
          90.35,
          65.5,
          80.95,
          56.15,
          34.4,
          20.75,
          18.8,
          90.8,
          25.6,
          70.8,
          25.4,
          108.8,
          76.85,
          20.25,
          24.8,
          115.65,
          74.6,
          103.15,
          72.1,
          25.1,
          80.15,
          25.4,
          105.4,
          45.75,
          24.45,
          25,
          85.25,
          19.6,
          50.15,
          70.55,
          26.4,
          20.15,
          58.85,
          97.55,
          19.65,
          25.25,
          114.45,
          70.7,
          75.55,
          84.8,
          20.65,
          20.45,
          35.65,
          90.45,
          97.65,
          73.85,
          69.1,
          82.75,
          24.4,
          55.25,
          61.35,
          76.75,
          19.4,
          54.75,
          19.7,
          19.9,
          107.95,
          83.8,
          56.4,
          20.1,
          94.9,
          94.2,
          49.9,
          71.05,
          81.65,
          89.45,
          99,
          19.05,
          114.45,
          44.25,
          90.55,
          20.4,
          71.4,
          24.85,
          104.45,
          19.8,
          116.45,
          20.05,
          110.75,
          89.7,
          48.7,
          96.6,
          74.3,
          54.3,
          74.85,
          79.95,
          20.05,
          19.4,
          54.9,
          24.45,
          89.65,
          45.4,
          75.7,
          110.65,
          20.55,
          115.15,
          58.55,
          93.25,
          19.35,
          48.75,
          109.05,
          25,
          54.9,
          24.75,
          91.15,
          104.35,
          66.05,
          92.2,
          105.2,
          19.6,
          30.4,
          61.5,
          69.4,
          24.75,
          91.05,
          73.65,
          19.4,
          26.2,
          43.85,
          69.7,
          38.55,
          53.1,
          20.65,
          64.45,
          25.1,
          95.15,
          79.35,
          96.65,
          75.5,
          19.7,
          20.5,
          19.2,
          98.35,
          74.35,
          51.35,
          45.65,
          20.3,
          54.2,
          90.65,
          50.9,
          25.05,
          74.85,
          20.5,
          63.55,
          47.95,
          45,
          90.05,
          25.3,
          24.3,
          75.95,
          19.7,
          66.4,
          35.75,
          18.8,
          19.4,
          19.3,
          67.45,
          20.1,
          58.9,
          19.45,
          50.5,
          25.1,
          60.7,
          99,
          104.4,
          44.05,
          24.1,
          45.55,
          93.8,
          19.7,
          70.65,
          86.45,
          114.1,
          95.2,
          88.55,
          20.75,
          44.65,
          60.2,
          55.45,
          70.3,
          60.4,
          55.8,
          31.1,
          50.95,
          69.1,
          43.95,
          86.5,
          69.95,
          90.95,
          19.9,
          20.15,
          90.6,
          92,
          24.85,
          36,
          78.5,
          19.95,
          20.65,
          30.5,
          106.1,
          20.5,
          95.5,
          64.6,
          51.1,
          89.1,
          54.95,
          20.45,
          85.95,
          60.35,
          19.8,
          85.35,
          72.1,
          81.05,
          20.5,
          111.8,
          20.2,
          19.7,
          19.85,
          60.5,
          19.55,
          20.9,
          21.05,
          71.5,
          54.65,
          19.2,
          49.8,
          20.5,
          90.4,
          90.25,
          104.6,
          50.2,
          95.5,
          95.4,
          101.3,
          53.1,
          84.85,
          34.25,
          88.6,
          60.15,
          99.95,
          70.7,
          54.8,
          54.8,
          100.3,
          53.6,
          19.35,
          85.6,
          80.8,
          19.6,
          90.7,
          69.75,
          20,
          95.25,
          19.95,
          80.85,
          93.3,
          46.35,
          78.75,
          83.55,
          19.6,
          67.85,
          105.65,
          75.5,
          20.15,
          45.2,
          79.25,
          85.7,
          20.1,
          61.8,
          49.9,
          20.4,
          75.4,
          108.15,
          86.25,
          95.7,
          116.85,
          105.75,
          20.15,
          19.6,
          60.95,
          25.05,
          60.3,
          63.95,
          74.3,
          70.6,
          90.55,
          19.45,
          64.45,
          69.65,
          19.5,
          110.5,
          24.7,
          77.4,
          85.4,
          47.6,
          19.4,
          103.85,
          108.45,
          81,
          86.65,
          92.95,
          90.35,
          25.15,
          76.4,
          19.55,
          85.35,
          24.8,
          103.15,
          100.75,
          94.1,
          19.35,
          19.9,
          101.05,
          59.1,
          55.85,
          106.05,
          84.1,
          75.3,
          24.7,
          55.8,
          39.7,
          29.5,
          20.15,
          79.55,
          24.8,
          19.65,
          94.05,
          90.75,
          78.85,
          99.5,
          80.55,
          70.2,
          59.45,
          93.35,
          44.95,
          26.1,
          20.2,
          21.25,
          59.4,
          95,
          61.9,
          118.65,
          64.45,
          80.15,
          20.2,
          21,
          20.45,
          75.85,
          80.45,
          75.5,
          44.45,
          74.55,
          48.15,
          19.65,
          20.15,
          106.6,
          91,
          25.4,
          69.95,
          66.85,
          20.15,
          64.85,
          74.85,
          50.5,
          72.9,
          115.05,
          19,
          19.55,
          101.1,
          84.1,
          24.15,
          50.1,
          74.6,
          19.75,
          106.8,
          84.5,
          25.05,
          83.7,
          96.6,
          101.1,
          20.2,
          94.05,
          81,
          60.25,
          60.85,
          43.95,
          86.05,
          20.25,
          19.4,
          102.65,
          19.9,
          19.55,
          95.5,
          84.15,
          103.2,
          50.2,
          19.95,
          116.25,
          31.2,
          24.45,
          84.2,
          85.65,
          21.2,
          25.55,
          20.2,
          63.85,
          61.95,
          25.75,
          58.2,
          85.85,
          104.9,
          99.85,
          19.55,
          104,
          104.4,
          19.5,
          25.25,
          49.85,
          108.95,
          89.9,
          82,
          89.95,
          79.35,
          64.05,
          101.15,
          39.1,
          34.6,
          19.55,
          104.45,
          70.5,
          20.35,
          19.45,
          69.9,
          59.7,
          78.35,
          71.45,
          45.85,
          95.85,
          35.7,
          89.55,
          24.95,
          24.85,
          100.8,
          105.35,
          19.65,
          54.45,
          70.5,
          20.1,
          69.35,
          19.8,
          74.4,
          93.05,
          51.2,
          65.6,
          80.55,
          52.7,
          20.85,
          52.15,
          114.95,
          104.45,
          113.65,
          20.6,
          91.55,
          49.85,
          19.8,
          104.15,
          48.2,
          25.1,
          100.15,
          55.9,
          64.4,
          85.3,
          107.45,
          91.3,
          85.95,
          45.2,
          79.2,
          55.5,
          90.25,
          91.25,
          100.9,
          97.7,
          69.85,
          65.6,
          104.65,
          90.45,
          63.7,
          104.5,
          20.1,
          104.3,
          93.25,
          73.45,
          20.7,
          25.25,
          100.5,
          90.6,
          89.4,
          95.45,
          20.45,
          19.95,
          109.15,
          85.7,
          102.05,
          94.7,
          64.4,
          26.8,
          66.05,
          65.2,
          85.05,
          55.8,
          19.95,
          45,
          114.9,
          106.4,
          46.1,
          39.7,
          20.05,
          95.75,
          24.4,
          33.6,
          90.45,
          84,
          67.4,
          19.7,
          80.35,
          19.6,
          54.2,
          45.2,
          75.1,
          19.7,
          72.75,
          20.05,
          39.2,
          44.75,
          82.65,
          93.9,
          117.15,
          99.25,
          112.55,
          25.7,
          90.3,
          49.4,
          19.4,
          109.7,
          61.25,
          55.3,
          103.75,
          19.5,
          39.5,
          26.05,
          91.05,
          29.65,
          50.2,
          105.3,
          55.45,
          85.45,
          19.8,
          59.25,
          90.7,
          79.05,
          90.7,
          95,
          30.25,
          49.85,
          93,
          54.55,
          19.7,
          84.8,
          94.45,
          20.85,
          60,
          80.45,
          84.95,
          49.65,
          20.2,
          100.5,
          35.75,
          86.45,
          53.8,
          38.55,
          39.9,
          70.05,
          20.1,
          20.3,
          35.65,
          82.95,
          55.65,
          25.2,
          50.8,
          19.65,
          59.8,
          73.55,
          61.4,
          19.9,
          19.45,
          81.5,
          109.55,
          74.4,
          74.9,
          59.65,
          110.45,
          74.45,
          24.55,
          24.55,
          90.65,
          105.05,
          20.45,
          19.55,
          19.7,
          70.45,
          85.65,
          20.55,
          97.95,
          20,
          25.25,
          70.9,
          19.85,
          106.35,
          99.5,
          84.7,
          86.05,
          44.55,
          75.85,
          25,
          45,
          20.5,
          90.45,
          60.45,
          78.45,
          100.55,
          20.35,
          90.75,
          20.25,
          20.05,
          19.6,
          53.8,
          70.2,
          75.5,
          20.35,
          26.05,
          20.6,
          20.1,
          24.3,
          24.5,
          110.5,
          25.25,
          90.1,
          68.75,
          19.2,
          115.1,
          99.65,
          91.45,
          84.75,
          78.75,
          20.25,
          19.9,
          97.75,
          100.4,
          24.45,
          101.1,
          50.9,
          107.2,
          92.2,
          113.4,
          40.55,
          26,
          111.95,
          53.8,
          72.1,
          78.85,
          70.75,
          76.15,
          39.1,
          69.95,
          20.05,
          20.05,
          19.45,
          26.9,
          19.2,
          50,
          60,
          84.55,
          45.45,
          20.05,
          115.55,
          99,
          50.55,
          25,
          91.55,
          19.35,
          24.85,
          100.4,
          25,
          19.25,
          108.25,
          20.15,
          101.3,
          20,
          105.3,
          69.85,
          65.25,
          19.8,
          19.6,
          20.05,
          49.4,
          88.4,
          100.6,
          19.45,
          20.3,
          107.65,
          80.45,
          58.85,
          109.6,
          75.15,
          73,
          70.1,
          98.65,
          111.45,
          114.9,
          100.55,
          20.4,
          104.35,
          80.45,
          91.35,
          19.9,
          68.35,
          79.1,
          51,
          80.55,
          66.7,
          86.4,
          50.05,
          25.7,
          83.4,
          84.65,
          64.75,
          100.15,
          25.25,
          113,
          40.65,
          94.95,
          59.9,
          19.8,
          81.8,
          20,
          59.6,
          25,
          84.35,
          55.55,
          75.35,
          59.3,
          66.1,
          18.8,
          86.45,
          52.1,
          47.4,
          109.15,
          94.95,
          93.55,
          79.5,
          115.05,
          95.15,
          105.4,
          20.1,
          20.05,
          20.7,
          20.35,
          19.7,
          85.45,
          40.4,
          105.2,
          100.65,
          91,
          116.75,
          59.1,
          49.8,
          19.3,
          19.65,
          81.4,
          38.9,
          87.95,
          19.85,
          96.35,
          24.15,
          19.1,
          44,
          60.6,
          25.65,
          53.95,
          20.4,
          29.35,
          20.45,
          95.1,
          25.25,
          44.9,
          92.65,
          43.7,
          72.6,
          18.95,
          20.5,
          19.95,
          24.5,
          20.6,
          61.05,
          106.65,
          108.25,
          20.4,
          55.3,
          20.25,
          72.95,
          89.45,
          104.65,
          75.2,
          101.15,
          68.75,
          111.05,
          99,
          21,
          19.4,
          77.2,
          19.45,
          24.85,
          41.35,
          19.6,
          84.45,
          20.25,
          19.65,
          20.65,
          99.3,
          81.05,
          67.6,
          70.15,
          115,
          84.8,
          19.7,
          63.15,
          74,
          29.1,
          50.05,
          20,
          74.65,
          44.4,
          85.4,
          94.1,
          108.9,
          56.2,
          26.1,
          85.45,
          88.95,
          74.35,
          48.85,
          80.1,
          56.05,
          89.8,
          19.1,
          20.35,
          106.05,
          19.65,
          59.85,
          86.1,
          19.45,
          97.1,
          36.65,
          103.9,
          19.75,
          24.55,
          48.7,
          109.55,
          20.65,
          55.2,
          24.05,
          20.45,
          19.25,
          26.35,
          43.8,
          50.15,
          20.45,
          61.4,
          70.75,
          61.15,
          20.25,
          63.85,
          98.7,
          20,
          19.3,
          84.4,
          25.1,
          48.25,
          19.85,
          94.2,
          62.15,
          79.3,
          56.25,
          20.3,
          99,
          90.6,
          85.9,
          79.2,
          70.35,
          19.35,
          50.15,
          63.8,
          20.55,
          88.55,
          101.4,
          44.6,
          63.75,
          109.25,
          84.6,
          20.45,
          85.75,
          107.95,
          22.95,
          19.45,
          19.7,
          87,
          79.95,
          64,
          64.9,
          25.75,
          90.15,
          116.1,
          104.95,
          50,
          20.45,
          19.85,
          19.95,
          26.45,
          63.4,
          53.95,
          95.1,
          74.1,
          35.5,
          79.2,
          48.8,
          55.45,
          25.4,
          93.5,
          63.9,
          64.85,
          63.8,
          44.45,
          19.95,
          43.35,
          49.65,
          85.1,
          89.8,
          103.05,
          116,
          69.9,
          95.1,
          40.25,
          25.75,
          105.35,
          113.6,
          24,
          19.4,
          86.1,
          102.65,
          92.85,
          97.75,
          97.95,
          19.95,
          24.6,
          50.95,
          75.6,
          80.75,
          90.4,
          60.25,
          20.2,
          64.15,
          20.25,
          99,
          80.3,
          19.55,
          100.75,
          53.75,
          25.6,
          58.35,
          46.35,
          113.75,
          90.4,
          109.3,
          90.3,
          65.25,
          60.65,
          24.1,
          19.5,
          85.95,
          53.5,
          25.45,
          20.5,
          20.85,
          89.9,
          26,
          113.2,
          69.05,
          20.1,
          109.65,
          19.2,
          90,
          34,
          20.4,
          38.6,
          25.25,
          60.6,
          74.75,
          20.6,
          20.4,
          81.7,
          20.3,
          20,
          25,
          80.45,
          19.75,
          65.65,
          71,
          89.2,
          86.75,
          61.5,
          25.1,
          34.05,
          19.95,
          19.95,
          89.7,
          20.4,
          26.3,
          20.7,
          19.45,
          110.8,
          69.3,
          49.35,
          20.35,
          105.6,
          64.45,
          49.9,
          65.65,
          103.3,
          44.45,
          89.9,
          55.05,
          104.1,
          106.6,
          70.5,
          19.6,
          24.05,
          38.1,
          34.25,
          100.05,
          68.65,
          45.8,
          75.75,
          96.4,
          20.55,
          50.95,
          90.5,
          79.4,
          58.75,
          59.45,
          105.7,
          53.3,
          24.3,
          59.9,
          23.95,
          20.15,
          95.65,
          81,
          82.45,
          20.5,
          54.4,
          58.6,
          84.8,
          61.4,
          20.4,
          20.15,
          94.45,
          79.8,
          74.05,
          49.15,
          19.4,
          113.65,
          106,
          25.95,
          19.1,
          100.55,
          95.4,
          75.15,
          89.15,
          107.9,
          19.5,
          24.95,
          19.5,
          69.95,
          82.85,
          19,
          38.85,
          20.35,
          95,
          74.4,
          78.45,
          74.3,
          51.05,
          19.2,
          109.1,
          76.45,
          72.8,
          18.95,
          101.75,
          75.45,
          64.1,
          25.65,
          75.1,
          95.85,
          54.4,
          72.75,
          19.85,
          19.05,
          94.85,
          46.25,
          19.35,
          69.6,
          90.7,
          101.4,
          20.25,
          48.8,
          74.35,
          19.35,
          68.75,
          100.2,
          20.85,
          19.35,
          45,
          25.5,
          48.9,
          19.6,
          20,
          81.3,
          95.2,
          83.3,
          20.3,
          89.85,
          19.8,
          54.65,
          29.35,
          19.15,
          19.1,
          80.55,
          20.25,
          106,
          25.5,
          79.6,
          55.25,
          88.05,
          20.4,
          117.6,
          20,
          19.65,
          70.55,
          65.8,
          20.05,
          80,
          35.4,
          79.6,
          80.25,
          20.45,
          79.6,
          24.7,
          77.3,
          29.75,
          44.9,
          29.8,
          71.95,
          20.75,
          56.3,
          105.25,
          19.55,
          84.45,
          53.65,
          29.9,
          19.7,
          43.7,
          55.3,
          19.85,
          19.65,
          49.45,
          20.45,
          39.7,
          54.5,
          111.6,
          55.55,
          20.55,
          62.1,
          104.5,
          101.8,
          110.6,
          84.9,
          93.2,
          24.4,
          70.55,
          85,
          85.8,
          91.1,
          20.1,
          20.05,
          74.8,
          24.8,
          100.85,
          105.1,
          20.4,
          20,
          79.4,
          57.2,
          58.6,
          94.8,
          102.5,
          20.35,
          84.9,
          69.2,
          20.85,
          88.5,
          35,
          55.15,
          50.95,
          64,
          80.2,
          49.3,
          84.35,
          20.05,
          117.2,
          20.1,
          109.95,
          94.75,
          80,
          79.65,
          25.2,
          19.9,
          44.8,
          20.3,
          19.2,
          80.05,
          107.35,
          47.85,
          70.8,
          59.1,
          25.55,
          20.25,
          75.55,
          95.3,
          70.25,
          50.3,
          19.85,
          19.35,
          25,
          20.3,
          75.35,
          88,
          43.8,
          62.05,
          20.1,
          101.35,
          84.05,
          20.9,
          105.9,
          85.05,
          44.1,
          90.2,
          53.45,
          19.95,
          74.65,
          57.5,
          19.65,
          93.8,
          89.25,
          94.15,
          55.6,
          48.7,
          104.9,
          19.9,
          19.4,
          25.05,
          84.45,
          19.3,
          79.85,
          25.55,
          68.4,
          20.65,
          55.15,
          70.6,
          19.95,
          19,
          44.1,
          107.6,
          61.55,
          90.7,
          99.25,
          91.7,
          100.7,
          78.45,
          84.3,
          19.55,
          20.45,
          55.6,
          86.8,
          20.95,
          20.05,
          113.65,
          59.5,
          87.8,
          41.9,
          69.85,
          56.3,
          109.55,
          92.15,
          69.5,
          97,
          58.35,
          70.4,
          94.3,
          19.55,
          95.95,
          94.8,
          107.75,
          54.6,
          71.3,
          19.5,
          56.3,
          90.55,
          60.8,
          98.8,
          98.15,
          35.35,
          103.15,
          107.75,
          81.4,
          95.7,
          104.8,
          70.95,
          44.95,
          97.65,
          35.65,
          85.25,
          19.5,
          25.1,
          100.05,
          55.7,
          91.15,
          83.85,
          45.9,
          25.1,
          19.7,
          91.5,
          51.3,
          21.1,
          104.75,
          85.75,
          20.3,
          100.75,
          74.15,
          78.55,
          19.85,
          50.7,
          45,
          77.8,
          83.45,
          94.8,
          20.1,
          59.9,
          90.1,
          70.95,
          29.2,
          46.6,
          74.3,
          69.3,
          94.3,
          76.45,
          54,
          104.25,
          19.95,
          24.95,
          84.75,
          19.75,
          113.65,
          44.9,
          75.25,
          24.6,
          25,
          20.95,
          110.6,
          55.5,
          19.45,
          84.85,
          19.6,
          53.45,
          19.8,
          112.1,
          74.2,
          69,
          19.35,
          19.8,
          109.2,
          79.15,
          53.65,
          100.2,
          108.65,
          40.65,
          55.35,
          105.6,
          95.7,
          83.2,
          90.05,
          97.65,
          68.05,
          102.1,
          23.4,
          71.05,
          19.45,
          59.45,
          92.2,
          19.85,
          43.9,
          90.5,
          90.45,
          84.6,
          99.15,
          19.95,
          20.5,
          62.1,
          79.5,
          19.55,
          20.35,
          51.7,
          23.3,
          65.1,
          81.2,
          74.5,
          80.5,
          60.3,
          75,
          90.15,
          69.05,
          59.7,
          19.85,
          40.75,
          95.7,
          46.3,
          81.3,
          20,
          66.15,
          19.6,
          49.8,
          101.75,
          55.15,
          103.95,
          99.65,
          73.7,
          50.05,
          60.25,
          87.3,
          54.25,
          85.3,
          50,
          90.95,
          72.25,
          96.1,
          19.85,
          55.3,
          20.1,
          69.5,
          25.15,
          79.65,
          71.25,
          113.8,
          24.55,
          19.7,
          100.5,
          74.45,
          104.1,
          19.05,
          25,
          19.05,
          81.9,
          69.7,
          90.15,
          25.35,
          24.65,
          19.55,
          60,
          89.9,
          19.4,
          49.8,
          24.1,
          54.25,
          109.9,
          35.5,
          87.55,
          88.4,
          50.8,
          99,
          96.55,
          59.75,
          111.5,
          24.25,
          20.5,
          70.4,
          30.55,
          84.9,
          54.5,
          75.35,
          44.45,
          98.05,
          63.9,
          69.15,
          64.65,
          98.85,
          89.6,
          83.25,
          70.25,
          24.5,
          20.1,
          73,
          61.4,
          84.3,
          19.9,
          20.4,
          50.75,
          20.45,
          75.75,
          65.4,
          59.75,
          78.5,
          48.95,
          99.65,
          18.25,
          54.55,
          40.65,
          20.45,
          24.8,
          88.8,
          20.05,
          69.8,
          77.15,
          35.05,
          108.1,
          84.05,
          20.2,
          49.2,
          24.6,
          71.65,
          104.9,
          106.5,
          75.5,
          58.5,
          78.9,
          79.2,
          109.45,
          59.2,
          29.15,
          20.05,
          66.5,
          49.55,
          73.6,
          82.65,
          49,
          25.2,
          25.45,
          110.9,
          77.75,
          26.2,
          19.9,
          80.85,
          56.35,
          19.3,
          50.4,
          55.25,
          19.1,
          84.05,
          105.2,
          75.75,
          95.3,
          19.85,
          69.1,
          20.25,
          54.75,
          81.45,
          80.2,
          100.3,
          90.95,
          20,
          79.85,
          73.55,
          19.3,
          20.15,
          44.55,
          54.45,
          19.65,
          105,
          88.7,
          75.15,
          20.25,
          109.1,
          30.75,
          112.9,
          94.05,
          78.85,
          55.3,
          19.35,
          25.35,
          20.45,
          19.35,
          78.65,
          74.75,
          19.9,
          58.35,
          100.5,
          20.05,
          25.65,
          95,
          45.45,
          20,
          49.2,
          83.25,
          19.25,
          19.65,
          72.8,
          109.65,
          65,
          114.1,
          20.65,
          86.95,
          94.75,
          25.35,
          105.45,
          25.4,
          102.55,
          24,
          25.6,
          73.5,
          98.25,
          54.4,
          103.1,
          34.2,
          43.75,
          100.65,
          116.05,
          82,
          65.15,
          44.8,
          79.8,
          88.85,
          74.95,
          106.85,
          19.3,
          56.1,
          19.7,
          51.3,
          118.6,
          24.15,
          20.3,
          115.5,
          25.05,
          109.1,
          19.65,
          111.3,
          29.9,
          80.6,
          20.8,
          89.95,
          116.05,
          19.55,
          115.25,
          24.8,
          19.9,
          81.25,
          69.95,
          86.4,
          66.3,
          94.65,
          72.1,
          34.7,
          95.95,
          44.8,
          109.4,
          71.05,
          19.7,
          40.25,
          19.85,
          68.25,
          20.15,
          50.95,
          25.15,
          20.25,
          44,
          20.25,
          55.8,
          88.9,
          57.65,
          79.15,
          108.05,
          94.8,
          45.9,
          102.6,
          61.35,
          57.55,
          29.25,
          19.6,
          111.75,
          106.5,
          107.7,
          19.3,
          20.05,
          69.95,
          63.7,
          50.9,
          60.4,
          79.25,
          110.1,
          90.7,
          25.3,
          85.2,
          24.35,
          25.1,
          54.55,
          96.6,
          81.15,
          38.5,
          92.9,
          84.7,
          66,
          20.75,
          61.45,
          54.5,
          99.75,
          109.75,
          80.85,
          20.3,
          67.8,
          19.8,
          25.7,
          56.15,
          86.7,
          20.4,
          19.65,
          54.35,
          108.1,
          54.45,
          45.35,
          59,
          69.45,
          64.95,
          18.85,
          19.8,
          25.05,
          114.3,
          109.2,
          45.05,
          51,
          110.45,
          84.65,
          60.05,
          44.65,
          93.25,
          20.25,
          25.45,
          20.6,
          94.1,
          34.8,
          60.75,
          51.35,
          64.05,
          84.8,
          50.15,
          94.6,
          59.75,
          100.25,
          98.9,
          97.7,
          60.25,
          56.25,
          46.2,
          24.9,
          63.35,
          50.1,
          50.15,
          64.65,
          79.6,
          19.5,
          99.55,
          74,
          38.9,
          79.55,
          46.3,
          99.35,
          95.8,
          78.15,
          26.1,
          40.35,
          79.2,
          20.9,
          49.9,
          68.9,
          20.25,
          76,
          74,
          82.3,
          89.4,
          99.15,
          29.45,
          19.8,
          59.15,
          44.75,
          90.8,
          49.55,
          106.7,
          94.45,
          19.45,
          67.95,
          65.25,
          99.45,
          20.35,
          19.95,
          77.4,
          19.7,
          99.7,
          74.8,
          19.15,
          78.95,
          62.85,
          71.55,
          94.95,
          86.1,
          19.55,
          24.8,
          84.05,
          36.25,
          98.6,
          103.65,
          92.9,
          19.9,
          20.1,
          80.5,
          39.85,
          60.5,
          103.85,
          67.8,
          24.85,
          19.35,
          89,
          55,
          76.15,
          20.3,
          117.35,
          19.75,
          45.2,
          25.2,
          89.75,
          75,
          49.95,
          65.7,
          67.05,
          110.9,
          87.95,
          19.8,
          75.7,
          62.15,
          115.15,
          19.5,
          86.55,
          20.4,
          19.8,
          45.65,
          56.4,
          73.3,
          101.35,
          33.6,
          20.7,
          104.05,
          20.25,
          73.7,
          108.75,
          20.15,
          19.75,
          25.95,
          70.05,
          24.05,
          84.75,
          23.05,
          59.95,
          19.55,
          19.6,
          20.05,
          85.55,
          78.6,
          116.8,
          43.55,
          60.8,
          54.9,
          65.2,
          108.2,
          92,
          75.1,
          25.05,
          75.15,
          19.5,
          19.3,
          112.2,
          70.3,
          19.6,
          20.25,
          80.65,
          115.75,
          80.6,
          59.55,
          19.05,
          95.65,
          19.95,
          19.4,
          36.1,
          19.75,
          64.1,
          19.75,
          19.7,
          110.2,
          106.35,
          90.55,
          65.9,
          104.5,
          52.5,
          56.1,
          88.75,
          26,
          99.4,
          73.15,
          54.65,
          115.55,
          104.45,
          91.15,
          89.7,
          92.4,
          19.9,
          18.85,
          25.75,
          20.95,
          97.05,
          25.4,
          19.7,
          35,
          101.25,
          70.2,
          90.95,
          73.85,
          88.05,
          20.1,
          110.3,
          85.15,
          60.95,
          73.55,
          46,
          58.55,
          24.6,
          19.75,
          86.35,
          25.5,
          19,
          19.55,
          110.1,
          69.75,
          50.6,
          65.6,
          82.1,
          79.1,
          90.65,
          20.55,
          75.75,
          110,
          20.85,
          80.35,
          70.15,
          67.45,
          20.75,
          69.9,
          51.1,
          25.55,
          60,
          90.55,
          76.4,
          84.95,
          110.1,
          99.65,
          45.4,
          69,
          48.65,
          59.85,
          80.65,
          20.55,
          66.4,
          100.2,
          44.55,
          20.35,
          91.8,
          20.2,
          50.35,
          18.8,
          20.45,
          64.75,
          98.7,
          89.45,
          58.75,
          20.7,
          85.6,
          80.3,
          79.8,
          79.85,
          54.1,
          80.9,
          24.5,
          20.15,
          20.05,
          19.6,
          114.3,
          100.3,
          80,
          20.85,
          89.95,
          20,
          48.75,
          80,
          20.35,
          20.25,
          19.4,
          100.4,
          57.95,
          59.5,
          19.2,
          59.55,
          103.95,
          68.95,
          103.1,
          24.7,
          110.2,
          62.45,
          89.55,
          78.9,
          20.35,
          71.45,
          46.35,
          94.65,
          49.9,
          25.45,
          20.75,
          66.1,
          75.4,
          21.05,
          69.35,
          88.85,
          97,
          66.4,
          69.2,
          79.5,
          100.65,
          79.7,
          61.4,
          69.8,
          40.55,
          75.65,
          90.7,
          80.5,
          60.6,
          101.15,
          24.95,
          20.3,
          60,
          20.25,
          44.75,
          98,
          107.7,
          104.7,
          93.9,
          86.45,
          19.4,
          24.95,
          75,
          78.2,
          94.2,
          50.05,
          69.55,
          90.1,
          44.65,
          80.35,
          98.1,
          53.35,
          19.55,
          48.95,
          54.2,
          24.45,
          40.15,
          25.6,
          70.35,
          91.7,
          89.2,
          24.1,
          53.85,
          115.6,
          19.75,
          24.05,
          25.3,
          84.3,
          89.75,
          97.95,
          20,
          103.9,
          20.7,
          20.15,
          26,
          77.35,
          66.05,
          19.9,
          68.15,
          80.85,
          75.5,
          80.6,
          83.2,
          87.55,
          109.4,
          45.55,
          20.7,
          75.3,
          93.4,
          73.75,
          88.15,
          49.2,
          19.65,
          105.15,
          49,
          49.8,
          20.95,
          79.3,
          19.5,
          44.15,
          105.5,
          92.7,
          26.25,
          96.95,
          20.45,
          115.8,
          108.2,
          20.2,
          54.9,
          20.15,
          90.35,
          55.75,
          114.6,
          66.8,
          100.3,
          105.35,
          85.2,
          18.95,
          69.8,
          106.15,
          20.55,
          105.75,
          25.25,
          19.75,
          104.85,
          60.95,
          81.15,
          19.1,
          20.8,
          90.15,
          90.1,
          74.1,
          118.75,
          85.9,
          95,
          20.15,
          101.3,
          21.2,
          24.2,
          20.3,
          85.3,
          89.6,
          56.25,
          50.95,
          115.85,
          103.65,
          26.1,
          35.1,
          99.1,
          67.25,
          25,
          59.55,
          77.8,
          55.1,
          24.15,
          45.25,
          20.25,
          64.75,
          54.6,
          20.7,
          94.75,
          115.8,
          49.45,
          83.8,
          95.35,
          74.05,
          89.6,
          116.6,
          54.2,
          19.3,
          65.05,
          24.05,
          18.75,
          20.15,
          20,
          71,
          93.6,
          24.4,
          65.25,
          50.55,
          70.7,
          45.25,
          70.3,
          108.95,
          26.45,
          19.65,
          19.05,
          74.75,
          75.8,
          25.1,
          44.45,
          104.3,
          89,
          20.15,
          36.15,
          19.2,
          19.25,
          61.2,
          20.45,
          35.05,
          44,
          50.35,
          20,
          86.4,
          58.4,
          94.1,
          108.9,
          107.4,
          90.85,
          19.9,
          66.4,
          100.7,
          25.6,
          19.85,
          20.75,
          95.8,
          94.65,
          106.65,
          45.85,
          104.35,
          55.45,
          61.15,
          78.95,
          109.2,
          61.3,
          96.85,
          40.55,
          19.8,
          108.25,
          105.05,
          90.45,
          86.4,
          66.9,
          110.7,
          20,
          102.1,
          70.15,
          80.05,
          49.2,
          20.5,
          38.25,
          54.95,
          96.6,
          19.9,
          19.9,
          84.6,
          85.25,
          81.25,
          115.5,
          79,
          94.65,
          20.8,
          59.5,
          20.05,
          100.45,
          20.6,
          20.3,
          39.55,
          20.45,
          25.25,
          91.25,
          72.45,
          19.7,
          75.1,
          25,
          69.15,
          91.55,
          35.8,
          113.15,
          19.85,
          19.8,
          19.9,
          19.7,
          59.1,
          91.15,
          68.95,
          51.55,
          24.4,
          96.8,
          70.05,
          19.5,
          78.75,
          69.2,
          19.55,
          103.65,
          54.7,
          54.15,
          84.85,
          20,
          99.25,
          19.35,
          94.75,
          114.05,
          74.9,
          19.8,
          80.85,
          54.65,
          91.7,
          118.6,
          24.55,
          19.45,
          116.15,
          80.6,
          20.3,
          99.8,
          75,
          19.9,
          80.3,
          84.3,
          54.05,
          104.9,
          97.25,
          83.05,
          41.1,
          45,
          74.55,
          40.2,
          70.5,
          19.75,
          24.65,
          104.25,
          78.35,
          109.7,
          33.45,
          94.6,
          20.2,
          20.3,
          39.4,
          69.15,
          51.35,
          100.05,
          20.3,
          94.45,
          46.4,
          104.05,
          24.9,
          59.6,
          108.5,
          40.55,
          58.95,
          20.75,
          113.15,
          48.8,
          63.05,
          100.85,
          80.55,
          64.4,
          75.2,
          84.9,
          19.3,
          74.65,
          59.05,
          69.1,
          20.55,
          76.55,
          62.5,
          94.9,
          111.65,
          19.9,
          20.45,
          106.05,
          113.45,
          92.55,
          65.6,
          84.35,
          71.1,
          85.15,
          49.7,
          30.2,
          56.35,
          107.55,
          19.85,
          95.9,
          23.85,
          83.85,
          84.8,
          76.1,
          74.55,
          39.2,
          79.55,
          19.6,
          19.55,
          39.15,
          20.1,
          99.95,
          59.8,
          49.75,
          108.5,
          60.15,
          19.05,
          84,
          44.55,
          103.45,
          80.65,
          57.2,
          110.75,
          24.7,
          97.05,
          76.35,
          18.9,
          74.45,
          84.4,
          24.4,
          20.05,
          55.5,
          84.3,
          100.2,
          19.4,
          20.4,
          94.75,
          44.35,
          74.55,
          73.6,
          50.1,
          53,
          19.85,
          24.35,
          19.55,
          25.05,
          93.8,
          103.75,
          56.75,
          20.8,
          24.45,
          25.6,
          59.65,
          83.3,
          79.55,
          24.45,
          19.2,
          29.8,
          45.5,
          30.05,
          65.65,
          74.05,
          110.75,
          19.7,
          49.5,
          43.95,
          111.15,
          20.6,
          19.65,
          115.8,
          88.65,
          94.5,
          20.1,
          34.65,
          52.3,
          65,
          35.45,
          19.7,
          95.6,
          19.85,
          81.85,
          109.3,
          25.4,
          69.8,
          20,
          109.9,
          50.3,
          101.5,
          89.15,
          19.4,
          29.9,
          78.8,
          19.3,
          96.8,
          20.65,
          19.8,
          104.6,
          80.05,
          45.15,
          73.15,
          99.1,
          105.35,
          45.65,
          79.95,
          54.45,
          25.1,
          84.7,
          75.85,
          48.8,
          35.2,
          76.25,
          24.9,
          54.3,
          66.3,
          20.9,
          75.35,
          104.45,
          49.45,
          19.45,
          92.15,
          19.85,
          100.25,
          95.7,
          93.15,
          69.7,
          19.8,
          71.35,
          20.75,
          40.6,
          20.35,
          19.75,
          54.4,
          20.45,
          66.15,
          89.85,
          45.05,
          86.85,
          96.75,
          106.65,
          110.15,
          82.85,
          20.1,
          59.45,
          58.6,
          49.7,
          65.85,
          73.5,
          113.65,
          83.4,
          65.65,
          61.35,
          85.9,
          75.65,
          70.9,
          49.85,
          20.1,
          103.05,
          99.7,
          81.9,
          66.2,
          19.75,
          72.6,
          116.5,
          106.8,
          24.95,
          89.25,
          19.25,
          104.55,
          87.2,
          30.75,
          25.7,
          86.2,
          30.1,
          99.35,
          19.2,
          20.1,
          20.35,
          25.65,
          94.55,
          94.4,
          56.1,
          68.25,
          24.75,
          76.25,
          74.35,
          54.15,
          19.45,
          34.95,
          53.65,
          104,
          70.35,
          64.85,
          19.65,
          45.9,
          20,
          44.8,
          20.35,
          45.8,
          108.95,
          64.35,
          90.8,
          24.95,
          84.7,
          70.8,
          104.4,
          101.5,
          54.3,
          103.95,
          91.1,
          19.95,
          26.45,
          75.1,
          108.1,
          110.15,
          111.5,
          106.5,
          19.9,
          111.1,
          70.7,
          24.85,
          91.2,
          65.6,
          59.45,
          109.95,
          38.5,
          92.55,
          24.5,
          19.7,
          20.6,
          58,
          107.45,
          65.5,
          25.45,
          100.15,
          104.45,
          21.15,
          96.2,
          44.4,
          94.35,
          20.3,
          105.75,
          81.15,
          89.55,
          54.75,
          53.75,
          105.75,
          105.85,
          64.2,
          87.7,
          89.3,
          20.15,
          20.05,
          67.2,
          94.55,
          107.5,
          73,
          114.75,
          76.05,
          77.9,
          90.65,
          110.45,
          68.7,
          44.85,
          29.8,
          88.9,
          58.75,
          19.85,
          86.9,
          59.65,
          66.4,
          20.15,
          108.1,
          56.9,
          109.6,
          25.15,
          79.15,
          66.75,
          48.8,
          80.7,
          20.55,
          115.1,
          59.7,
          86.45,
          33.7,
          80.1,
          104.05,
          108.75,
          41.1,
          20.35,
          105.9,
          65.5,
          40.45,
          70.45,
          78.8,
          90.1,
          82.45,
          20.25,
          66.25,
          89.7,
          64.55,
          93.65,
          73.6,
          109.75,
          61.45,
          106.4,
          81.9,
          105.2,
          54.6,
          20.55,
          19.7,
          66.05,
          54.05,
          58.9,
          96.9,
          19.1,
          50,
          45.4,
          85.45,
          84.1,
          66.25,
          76.9,
          74.6,
          116.95,
          40.65,
          114.35,
          69.7,
          98.65,
          61.65,
          89.35,
          95.4,
          35.4,
          19.95,
          19.25,
          20.4,
          24.75,
          25.35,
          20,
          59.75,
          82.5,
          20.35,
          90.8,
          104.95,
          105.25,
          23.75,
          61.3,
          75.8,
          98,
          52,
          64.4,
          45.8,
          30.5,
          69.15,
          49.25,
          39.35,
          105.1,
          20.1,
          19.75,
          19.75,
          70.4,
          20.45,
          20.35,
          86.2,
          95.65,
          103.8,
          97.2,
          63.55,
          24.95,
          99,
          85.55,
          94,
          50.3,
          95,
          61.4,
          80.55,
          78.5,
          114.3,
          20.05,
          62.65,
          92.7,
          100.45,
          75.2,
          84.75,
          79.5,
          19.8,
          100.9,
          95.3,
          90.95,
          54.5,
          49.6,
          25,
          45.45,
          107.75,
          89.1,
          44.75,
          101.6,
          103.15,
          95.65,
          75.1,
          61.35,
          19.7,
          51,
          88.85,
          20.05,
          65.1,
          70.15,
          20.75,
          56.05,
          19.95,
          98.6,
          79,
          89.45,
          74.2,
          81,
          49.6,
          84.6,
          84.2,
          106.3,
          69.05,
          45.4,
          99.35,
          50.75,
          87.1,
          20.15,
          98.7,
          25.2,
          55.7,
          65.35,
          25.3,
          24.25,
          60.5,
          25.1,
          20.05,
          30.25,
          20.2,
          59.9,
          25.15,
          101.3,
          76.95,
          55.3,
          92.45,
          48.45,
          19.35,
          86.7,
          55.7,
          84.25,
          64.65,
          69.2,
          54.65,
          24.75,
          23.95,
          105,
          59.85,
          20.05,
          92.15,
          44.8,
          20.9,
          95.4,
          80.35,
          85.1,
          115.05,
          19.95,
          86.15,
          78.85,
          86.55,
          42.4,
          24.25,
          20.5,
          19.6,
          20.25,
          20.6,
          19.8,
          80.2,
          116.4,
          31.65,
          94.15,
          20.65,
          76.85,
          20.15,
          55.25,
          82.15,
          103,
          95.1,
          95.15,
          79.8,
          74.8,
          20.45,
          78.35,
          19.1,
          20,
          19.95,
          24,
          19.15,
          91.3,
          19.15,
          19.75,
          75.5,
          83.75,
          19.4,
          26.5,
          19.15,
          40.9,
          80.25,
          70.8,
          60.2,
          55.2,
          54.15,
          100.4,
          62.55,
          70.45,
          85.5,
          54.5,
          20.75,
          20.35,
          91,
          104.8,
          51.1,
          89.8,
          20.55,
          64.05,
          74.85,
          25,
          20.3,
          26.35,
          54.7,
          90.25,
          20.65,
          25.45,
          19.5,
          66.15,
          69.1,
          39.1,
          20.05,
          59.8,
          48.6,
          105.35,
          25.1,
          49.75,
          94.75,
          93,
          71.9,
          77.55,
          19.85,
          95.25,
          25.05,
          53.15,
          20.15,
          101.25,
          100.55,
          25.3,
          71.8,
          19.7,
          49.85,
          69.6,
          19.75,
          80.8,
          64.2,
          35,
          19.2,
          90.65,
          20,
          74.65,
          61.2,
          19.95,
          54.8,
          73.45,
          51.45,
          80.45,
          85.3,
          79.3,
          76.5,
          25.4,
          86.85,
          19.65,
          45.55,
          78.1,
          19.3,
          110.5,
          20.3,
          81.35,
          55.3,
          56.55,
          19.7,
          104.05,
          52.85,
          80.65,
          24.65,
          21.3,
          110.2,
          51.05,
          19.8,
          19.9,
          87.3,
          19.85,
          89.4,
          20,
          20.05,
          83.25,
          102.9,
          39.1,
          114.5,
          20.2,
          55.8,
          24.2,
          72.8,
          99.85,
          99.5,
          20.25,
          26,
          19.9,
          19.05,
          96.5,
          19.85,
          25.7,
          20.3,
          91.55,
          39.4,
          105.7,
          70.25,
          93.75,
          60,
          59.8,
          90.65,
          109,
          68.1,
          20.4,
          81.95,
          60.55,
          65.6,
          82.5,
          82.3,
          68.15,
          20.3,
          20.2,
          89.2,
          74.8,
          20.2,
          84.4,
          25.15,
          19.8,
          50.85,
          102.4,
          55.5,
          109.75,
          106.4,
          60,
          88.8,
          80.05,
          75.55,
          49.55,
          23.9,
          66.4,
          18.8,
          108.4,
          85.95,
          80.9,
          111.8,
          20.6,
          44.6,
          105.1,
          115.15,
          59.8,
          26.3,
          70.55,
          20.05,
          79.85,
          90.05,
          24.45,
          59.95,
          25.35,
          34.3,
          105.05,
          19.3,
          19.15,
          51.4,
          71.85,
          75.4,
          49.7,
          78.75,
          81.6,
          70.4,
          76.1,
          94,
          103.95,
          19.95,
          110.8,
          96.1,
          48.8,
          50.55,
          44.65,
          19.45,
          89.3,
          19.25,
          70.5,
          19.65,
          20.85,
          19.65,
          19.35,
          44,
          94.4,
          75.4,
          71,
          21.2,
          61.05,
          79.95,
          19.7,
          20.3,
          24.35,
          19.75,
          50.3,
          50.25,
          85.35,
          51.65,
          24,
          59.85,
          25.45,
          23.9,
          24.15,
          75.7,
          50.85,
          91.6,
          98.9,
          85,
          44.3,
          80.2,
          60.9,
          34.2,
          87.15,
          54.3,
          19.1,
          112.75,
          19.95,
          19.5,
          65.55,
          78.8,
          78.2,
          105.25,
          89.25,
          20.65,
          68.7,
          78.65,
          24.75,
          19.75,
          89.1,
          84.7,
          59.9,
          19.95,
          108.9,
          33.6,
          85.85,
          34.85,
          95.3,
          84.6,
          44.95,
          24.7,
          100.3,
          25.45,
          50.7,
          55,
          68.4,
          55.05,
          19.8,
          84.45,
          35.9,
          80.75,
          78.65,
          61.75,
          63.7,
          87.6,
          89.15,
          20,
          104.4,
          20.05,
          34.3,
          20.65,
          84.25,
          19.65,
          79.85,
          20.2,
          19.8,
          50.35,
          74.6,
          79.15,
          20.35,
          21.05,
          94.7,
          74.95,
          111.95,
          19.85,
          89.75,
          20.05,
          108.95,
          19.65,
          24.9,
          93.2,
          84.8,
          71.75,
          30.35,
          54.85,
          19.5,
          24.2,
          19.35,
          100.65,
          94.1,
          74.55,
          56.15,
          20.35,
          80.55,
          61.25,
          20.45,
          18.9,
          19.6,
          45.2,
          19.45,
          25.45,
          94.9,
          29.3,
          20.25,
          110.5,
          109.4,
          19.95,
          19.6,
          76.6,
          19.6,
          85.3,
          65.85,
          20.05,
          99.4,
          20,
          78.45,
          25.1,
          55,
          71.1,
          61.55,
          45.9,
          40.3,
          87.1,
          49.5,
          73.8,
          19.2,
          25,
          35.3,
          76.75,
          81,
          105.55,
          18.8,
          24.9,
          64.9,
          61.35,
          113.95,
          90.15,
          54.1,
          49.8,
          24.4,
          95,
          69.9,
          39.95,
          103.25,
          94.25,
          47.05,
          20.55,
          19.65,
          70.2,
          81,
          75.9,
          24.7,
          110.25,
          85,
          19.75,
          23.9,
          19.95,
          25.15,
          54.15,
          59.8,
          83.85,
          104.9,
          75.3,
          66.65,
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\"83aa3212-74ce-46d3-b634-5a6d3df6ff14\"}], {\"title\": {\"text\": \"MonthlyCharges\"}, \"width\": 800, \"height\": 500, \"yaxis\": {\"title\": {\"text\": \"MonthlyCharges\"}}, \"xaxis\": {\"title\": {\"text\": \"Churn?\"}}}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"}); \n",
       "}\n",
       "});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figs = []\n",
    "\n",
    "for churn in churns:\n",
    "    figs.append(\n",
    "        go.Box(\n",
    "            y = df.loc[(df['Churn']==churn),'MonthlyCharges'],\n",
    "            name = churn\n",
    "        )\n",
    "    )\n",
    "layout = go.Layout(\n",
    "    title = \"MonthlyCharges\",\n",
    "    xaxis = {\"title\" : \"Churn?\"},\n",
    "    yaxis = {\"title\" : \"MonthlyCharges\"},\n",
    "    width=800,\n",
    "    height=500\n",
    ")\n",
    "\n",
    "fig = go.Figure(data=figs, layout=layout)\n",
    "py.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "8be4e99448e9af78ae0de26401b57cc934427b3c"
   },
   "source": [
    "<h3>EDA: Target</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "_uuid": "4adc24837c701592fce5d9e763235376b9b8d218",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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        "plotlyServerURL": "https://plot.ly",
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         "type": "bar",
         "uid": "3f74dcd1-be07-4328-bf2b-1a0252463011",
         "x": [
          "No",
          "Yes"
         ],
         "y": [
          5174,
          1869
         ]
        }
       ],
       "layout": {
        "height": 500,
        "title": {
         "text": "Churn distribution"
        },
        "width": 800,
        "xaxis": {
         "title": {
          "text": "Churn?"
         }
        }
       }
      },
      "text/html": [
       "<div id=\"5372cbf1-1713-405e-8067-e264e6c0bc01\" style=\"height: 500px; width: 800px;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";\n",
       "if (document.getElementById(\"5372cbf1-1713-405e-8067-e264e6c0bc01\")) {\n",
       "    Plotly.newPlot(\"5372cbf1-1713-405e-8067-e264e6c0bc01\", [{\"y\": [5174, 1869], \"x\": [\"No\", \"Yes\"], \"uid\": \"3f74dcd1-be07-4328-bf2b-1a0252463011\", \"marker\": {\"color\": [\"rgba(255,190,134,1)\", \"rgba(142,186,217,1)\"]}, \"type\": \"bar\"}], {\"title\": {\"text\": \"Churn distribution\"}, \"width\": 800, \"height\": 500, \"xaxis\": {\"title\": {\"text\": \"Churn?\"}}}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"}); \n",
       "}\n",
       "});</script>"
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      "text/vnd.plotly.v1+html": [
       "<div id=\"5372cbf1-1713-405e-8067-e264e6c0bc01\" style=\"height: 500px; width: 800px;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";\n",
       "if (document.getElementById(\"5372cbf1-1713-405e-8067-e264e6c0bc01\")) {\n",
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       "}\n",
       "});</script>"
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     },
     "metadata": {},
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   ],
   "source": [
    "_ = df.groupby('Churn').size().reset_index()\n",
    "# .sort_values(by='tenure', ascending=True)\n",
    "\n",
    "data = [go.Bar(\n",
    "    x = _['Churn'].tolist(),\n",
    "    y = _[0].tolist(),\n",
    "    marker=dict(\n",
    "        color=['rgba(255,190,134,1)', 'rgba(142,186,217,1)'])\n",
    ")]\n",
    "layout = go.Layout(\n",
    "    title = \"Churn distribution\",\n",
    "    xaxis = {\"title\" : \"Churn?\"},\n",
    "    width=800,\n",
    "    height=500\n",
    ")\n",
    "fig = go.Figure(data=data, layout=layout)\n",
    "py.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "bdc113c2211cdaf6d2d09f58168e45844a8326bc"
   },
   "source": [
    "Insights from our simple EDA:<br>\n",
    "* We can see a difference between our target classes on tenure as you can see in the first boxplot, which is good because our model (Logistic Regression) may use this to separate the two classes.\n",
    "* There is also a slight difference between our target classes on monthly charges as shown in the second boxplot.\n",
    "* The barchart above shows a huge imbalance in our target classes, this may affect the prediction of our model. We may have to deal with this later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "c3b1ee516ef28f3839c01d2727bde08784558365"
   },
   "source": [
    "<h3>Logistic Regression in action</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "2ff6c9fd8f4daa714204d973fcb9212e502d0d39"
   },
   "source": [
    "Before we start predicting, an important step to do is to convert our **Churn** feature, which is a string, into integer. *Yes* will be converted to 1 and *No* will be converted to 0. We will name this new columns a \"class\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "_uuid": "217cbb254d2328060d46c8a0839afd3e18ad707b"
   },
   "outputs": [],
   "source": [
    "df['class'] = df['Churn'].apply(lambda x : 1 if x == \"Yes\" else 0)\n",
    "# features will be saved as X and our target will be saved as y\n",
    "X = df[['tenure','MonthlyCharges']].copy()\n",
    "X2 = df[['tenure','MonthlyCharges']].copy()\n",
    "y = df['class'].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "a56150b3fb46c156f5d265f6bf11b945ceb96267"
   },
   "source": [
    "Let us try first loss minimization with gradient descent and calculate the accuracy of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "_uuid": "671228c839e3e359f929784ff74fddf7fb2a64b4",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "[-1.51059421 -1.51059421 -1.51059421 -1.51059421 -1.51059421 -1.51059421\n",
      " -2.78199253  1.99663533]\n",
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      " -3.89308417 -1.04014423]\n",
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      " -3.41597215  0.93530444]\n",
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      " -3.13677165  0.81354292]\n",
      "[-1.5336147  -1.5336147  -1.5336147  -1.5336147  -1.5336147  -1.5336147\n",
      " -2.83524395  0.79310919]\n",
      "[-1.53791764 -1.53791764 -1.53791764 -1.53791764 -1.53791764 -1.53791764\n",
      " -2.55368882  0.68561981]\n",
      "[-1.54046642 -1.54046642 -1.54046642 -1.54046642 -1.54046642 -1.54046642\n",
      " -2.25172447  0.67565962]\n",
      "[-1.54487804 -1.54487804 -1.54487804 -1.54487804 -1.54487804 -1.54487804\n",
      " -1.98226958  0.52647302]\n",
      "[-1.54439805 -1.54439805 -1.54439805 -1.54439805 -1.54439805 -1.54439805\n",
      " -1.65787194  0.64898325]\n",
      "[-1.55426652 -1.55426652 -1.55426652 -1.55426652 -1.55426652 -1.55426652\n",
      " -1.50868043  0.07665018]\n",
      "[-1.52777055 -1.52777055 -1.52777055 -1.52777055 -1.52777055 -1.52777055\n",
      " -1.03161543  2.04874364]\n",
      "[-1.59175449 -1.59175449 -1.59175449 -1.59175449 -1.59175449 -1.59175449\n",
      " -3.26418377 -2.24482406]\n",
      "[-1.5652175  -1.5652175  -1.5652175  -1.5652175  -1.5652175  -1.5652175\n",
      " -2.78707175 -0.26937539]\n",
      "[-1.53868052 -1.53868052 -1.53868052 -1.53868052 -1.53868052 -1.53868052\n",
      " -2.30995972  1.70607328]\n",
      "[-1.58083886 -1.58083886 -1.58083886 -1.58083886 -1.58083886 -1.58083886\n",
      " -3.46061401 -1.38771931]\n",
      "[-1.55430188 -1.55430188 -1.55430188 -1.55430188 -1.55430188 -1.55430188\n",
      " -2.98350199  0.58772936]\n",
      "[-1.55015597 -1.55015597 -1.55015597 -1.55015597 -1.55015597 -1.55015597\n",
      " -2.60546132  1.00375611]\n",
      "[-1.56296692 -1.56296692 -1.56296692 -1.56296692 -1.56296692 -1.56296692\n",
      " -2.49541025  0.29310889]\n",
      "[-1.54804591 -1.54804591 -1.54804591 -1.54804591 -1.54804591 -1.54804591\n",
      " -2.04516445  1.40828801]\n",
      "[-1.58530654 -1.58530654 -1.58530654 -1.58530654 -1.58530654 -1.58530654\n",
      " -2.93599568 -1.28933046]\n",
      "[-1.55876955 -1.55876955 -1.55876955 -1.55876955 -1.55876955 -1.55876955\n",
      " -2.45888366  0.68611821]\n",
      "[-1.56188509 -1.56188509 -1.56188509 -1.56188509 -1.56188509 -1.56188509\n",
      " -2.16689601  0.63204641]\n",
      "[-1.56496928 -1.56496928 -1.56496928 -1.56496928 -1.56496928 -1.56496928\n",
      " -1.8817734   0.55523123]\n",
      "[-1.56676349 -1.56676349 -1.56676349 -1.56676349 -1.56676349 -1.56676349\n",
      " -1.58944143  0.5242499 ]\n",
      "[-1.56990431 -1.56990431 -1.56990431 -1.56990431 -1.56990431 -1.56990431\n",
      " -1.32820524  0.37100051]\n",
      "[-1.5664961  -1.5664961  -1.5664961  -1.5664961  -1.5664961  -1.5664961\n",
      " -0.98356185  0.62970699]\n",
      "[-1.59076579 -1.59076579 -1.59076579 -1.59076579 -1.59076579 -1.59076579\n",
      " -1.33421139 -1.11709789]\n",
      "[-1.5642288  -1.5642288  -1.5642288  -1.5642288  -1.5642288  -1.5642288\n",
      " -0.85709936  0.85835079]\n",
      "[-1.61302956 -1.61302956 -1.61302956 -1.61302956 -1.61302956 -1.61302956\n",
      " -2.44941563 -2.80548368]\n",
      "[-1.58649257 -1.58649257 -1.58649257 -1.58649257 -1.58649257 -1.58649257\n",
      " -1.97230361 -0.83003501]\n",
      "[-1.55995558 -1.55995558 -1.55995558 -1.55995558 -1.55995558 -1.55995558\n",
      " -1.49519158  1.14541366]\n",
      "[-1.60134501 -1.60134501 -1.60134501 -1.60134501 -1.60134501 -1.60134501\n",
      " -2.63971489 -1.93426718]\n",
      "[-1.57480803 -1.57480803 -1.57480803 -1.57480803 -1.57480803 -1.57480803\n",
      " -2.16260287  0.04118149]\n",
      "[-1.54827223 -1.54827223 -1.54827223 -1.54827223 -1.54827223 -1.54827223\n",
      " -1.685492    2.01654495]\n",
      "[-1.60608891 -1.60608891 -1.60608891 -1.60608891 -1.60608891 -1.60608891\n",
      " -3.65455274 -2.06769855]\n",
      "[-1.57955192 -1.57955192 -1.57955192 -1.57955192 -1.57955192 -1.57955192\n",
      " -3.17744071 -0.09224988]\n",
      "[-1.55301493 -1.55301493 -1.55301493 -1.55301493 -1.55301493 -1.55301493\n",
      " -2.70032869  1.88319874]\n",
      "[-1.59286365 -1.59286365 -1.59286365 -1.59286365 -1.59286365 -1.59286365\n",
      " -3.7176972  -1.01247829]\n",
      "[-1.56632666 -1.56632666 -1.56632666 -1.56632666 -1.56632666 -1.56632666\n",
      " -3.24058517  0.96297038]\n",
      "[-1.57280597 -1.57280597 -1.57280597 -1.57280597 -1.57280597 -1.57280597\n",
      " -2.99154018  0.71911891]\n",
      "[-1.57362215 -1.57362215 -1.57362215 -1.57362215 -1.57362215 -1.57362215\n",
      " -2.66198479  0.84019603]\n",
      "[-1.58052839 -1.58052839 -1.58052839 -1.58052839 -1.58052839 -1.58052839\n",
      " -2.42639256  0.54841795]\n",
      "[-1.57768074 -1.57768074 -1.57768074 -1.57768074 -1.57768074 -1.57768074\n",
      " -2.06856591  0.84787748]\n",
      "[-1.59097205 -1.59097205 -1.59097205 -1.59097205 -1.59097205 -1.59097205\n",
      " -1.98163437  0.07475065]\n",
      "[-1.56445205 -1.56445205 -1.56445205 -1.56445205 -1.56445205 -1.56445205\n",
      " -1.50454001  2.04882392]\n",
      "[-1.62443708 -1.62443708 -1.62443708 -1.62443708 -1.62443708 -1.62443708\n",
      " -3.57527136 -2.12556477]\n",
      "[-1.59790009 -1.59790009 -1.59790009 -1.59790009 -1.59790009 -1.59790009\n",
      " -3.09815933 -0.1501161 ]\n",
      "[-1.5713631  -1.5713631  -1.5713631  -1.5713631  -1.5713631  -1.5713631\n",
      " -2.6210473   1.82533256]\n",
      "[-1.61091087 -1.61091087 -1.61091087 -1.61091087 -1.61091087 -1.61091087\n",
      " -3.62397959 -1.04804204]\n",
      "[-1.58437388 -1.58437388 -1.58437388 -1.58437388 -1.58437388 -1.58437388\n",
      " -3.14686757  0.92740663]\n",
      "[-1.59042657 -1.59042657 -1.59042657 -1.59042657 -1.59042657 -1.59042657\n",
      " -2.89150599  0.70929846]\n",
      "[-1.59138079 -1.59138079 -1.59138079 -1.59138079 -1.59138079 -1.59138079\n",
      " -2.56530519  0.8149444 ]\n",
      "[-1.59815523 -1.59815523 -1.59815523 -1.59815523 -1.59815523 -1.59815523\n",
      " -2.32923186  0.52637702]\n",
      "[-1.59478088 -1.59478088 -1.59478088 -1.59478088 -1.59478088 -1.59478088\n",
      " -1.96799373  0.85014052]\n",
      "[-1.60943466 -1.60943466 -1.60943466 -1.60943466 -1.60943466 -1.60943466\n",
      " -1.92004743 -0.03075716]\n",
      "[-1.5828977  -1.5828977  -1.5828977  -1.5828977  -1.5828977  -1.5828977\n",
      " -1.44293543  1.94469059]\n",
      "[-1.64255687 -1.64255687 -1.64255687 -1.64255687 -1.64255687 -1.64255687\n",
      " -3.50088192 -2.21868058]\n",
      "[-1.61601988 -1.61601988 -1.61601988 -1.61601988 -1.61601988 -1.61601988\n",
      " -3.02376989 -0.2432319 ]\n",
      "[-1.58948289 -1.58948289 -1.58948289 -1.58948289 -1.58948289 -1.58948289\n",
      " -2.54665786  1.73221677]\n",
      "[-1.62705754 -1.62705754 -1.62705754 -1.62705754 -1.62705754 -1.62705754\n",
      " -3.43982668 -0.97105796]\n",
      "[-1.60052055 -1.60052055 -1.60052055 -1.60052055 -1.60052055 -1.60052055\n",
      " -2.96271465  1.00439071]\n",
      "[-1.60993717 -1.60993717 -1.60993717 -1.60993717 -1.60993717 -1.60993717\n",
      " -2.77383529  0.54360384]\n",
      "[-1.60467471 -1.60467471 -1.60467471 -1.60467471 -1.60467471 -1.60467471\n",
      " -2.38961996  1.00948369]\n",
      "[-1.61976435 -1.61976435 -1.61976435 -1.61976435 -1.61976435 -1.61976435\n",
      " -2.34338158  0.11936497]\n",
      "[-1.59356077 -1.59356077 -1.59356077 -1.59356077 -1.59356077 -1.59356077\n",
      " -1.86661982  2.066254  ]\n",
      "Training time (Log Reg using Gradient descent):1.3773541450500488 seconds\n",
      "Learning rate: 0.1\n",
      "Iteration: 1000\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "\n",
    "num_iter = 1000\n",
    "\n",
    "intercept = np.ones((X.shape[0], 1)) \n",
    "X = np.concatenate((intercept, X), axis=1)\n",
    "theta = np.zeros(X.shape[1])\n",
    "\n",
    "for i in range(num_iter):\n",
    "    h = sigmoid(X, theta)\n",
    "    gradient = gradient_descent(X, h, y)\n",
    "    theta = update_weight_loss(theta, 0.1, gradient)\n",
    "    print(theta)\n",
    "\n",
    "print(\"Training time (Log Reg using Gradient descent):\" + str(time.time() - start_time) + \" seconds\")\n",
    "print(\"Learning rate: {}\\nIteration: {}\".format(0.1, num_iter))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "_uuid": "b26d6770373e6ecd294a1866a39add5b55b9d8ec"
   },
   "outputs": [],
   "source": [
    "result = sigmoid(X, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "_uuid": "f2975af9d174631042ed4bdfe3bceac7edfdda5c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy (Loss minimization):\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "42.96464574755076"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = pd.DataFrame(np.around(result, decimals=6)).join(y)\n",
    "f['pred'] = f[0].apply(lambda x : 0 if x < 0.5 else 1)\n",
    "print(\"Accuracy (Loss minimization):\")\n",
    "f.loc[f['pred']==f['class']].shape[0] / f.shape[0] * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "91a71a8dedf39338d9e99f88feb5a7b1d66eaaca"
   },
   "source": [
    "Now let us try maximum likelihood estimation and compute the accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "_uuid": "e0f626b6b43949ff9eaf068bbc5bd38b2053eb77"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mvernier/.local/lib/python3.5/site-packages/ipykernel_launcher.py:3: RuntimeWarning:\n",
      "\n",
      "overflow encountered in exp\n",
      "\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-28-92adeea33aca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_iter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m     \u001b[0mh2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtheta2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m     \u001b[0mgradient2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgradient_ascent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#np.dot(X.T, (h - y)) / y.size\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0mtheta2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mupdate_weight_mle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgradient2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-2eeea9337b29>\u001b[0m in \u001b[0;36msigmoid\u001b[0;34m(X, weight)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweight\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweight\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "num_iter = 1000\n",
    "\n",
    "intercept2 = np.ones((X2.shape[0], 1))\n",
    "X2 = np.concatenate((intercept2, X2), axis=1)\n",
    "theta2 = np.zeros(X2.shape[1])\n",
    "\n",
    "for i in range(num_iter):\n",
    "    h2 = sigmoid(X2, theta2)\n",
    "    gradient2 = gradient_ascent(X2, h2, y) #np.dot(X.T, (h - y)) / y.size\n",
    "    theta2 = update_weight_mle(theta2, 0.1, gradient2)\n",
    "    \n",
    "print(\"Training time (Log Reg using MLE):\" + str(time.time() - start_time) + \"seconds\")\n",
    "print(\"Learning rate: {}\\nIteration: {}\".format(0.1, num_iter))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_uuid": "31e9123a64c79c2cf705e3aaee5b1a64862c5690"
   },
   "outputs": [],
   "source": [
    "result2 = sigmoid(X2, theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_uuid": "18da54b7cdcab18af2f3badd1ce057546836ce81"
   },
   "outputs": [],
   "source": [
    "print(\"Accuracy (Maximum Likelihood Estimation):\")\n",
    "f2 = pd.DataFrame(result2).join(y)\n",
    "f2.loc[f2[0]==f2['class']].shape[0] / f2.shape[0] * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "e49a72ab216bc7cce378731b7cffdd3bccd5aa83"
   },
   "source": [
    "Next, let us try using sklearn's LogisticRegression module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_uuid": "baa9151be6db67ebb0f5eba1f8e57deb385c5fd4"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "clf = LogisticRegression(fit_intercept=True, max_iter=100000)\n",
    "clf.fit(df[['tenure','MonthlyCharges']], y)\n",
    "print(\"Training time (sklearn's LogisticRegression module):\" + str(time.time() - start_time) + \" seconds\")\n",
    "print(\"Learning rate: {}\\nIteration: {}\".format(0.1, num_iter))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_uuid": "7733588210ee7cf06bc152c4b84d5c077a0b8ce6"
   },
   "outputs": [],
   "source": [
    "result3 = clf.predict(df[['tenure','MonthlyCharges']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "_uuid": "cd7c91a99c961ae2d26aeff19fcc2ec5e7b2e988"
   },
   "outputs": [],
   "source": [
    "print(\"Accuracy (sklearn's Logistic Regression):\")\n",
    "f3 = pd.DataFrame(result3).join(y)\n",
    "f3.loc[f3[0]==f3['class']].shape[0] / f3.shape[0] * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "d4b7789bd891c45d36af9319bf241d74a67807c4"
   },
   "source": [
    "Insights from the training, prediction and simple evaluation that we've done: <br>\n",
    "We've accomplished our second objective which is to implement a Logistic Regression without the help of built-in libraries (except numpy of course). <br>\n",
    "We've predicted and computed the accuracy of three different models\n",
    "1. Log Regression from scratch using loss minimization. \n",
    "1. Log Regression from scratch using maximum likelihood estimation.\n",
    "1. Log Regression class of sklearn.\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "ed3c7ccc808e235e9bd12578d1077d13d44c24c3"
   },
   "source": [
    "<h2>Summary and Conclusion</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "e70848dfe463280ba108bbff660343f3a59c4409"
   },
   "source": [
    "In this kernel, we've created a logistic regression from scratch. We've learned the computations happening at the back-end of a Logistic Regression. We've transormed these equations and mathematical functions into python codes. We've trained our logistic regression function in two ways: through loss minimizing using gradient descent and maximizing the likelihood using gradient ascent. The Telco Customer Churn dataset was used for training and also evaluation. Below is the result of the evaluation (not dynamic)\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <td>**LR model**</td>\n",
    "        <td>**training time (7043 records)**</td>\n",
    "        <td>**training accuracy**</td>\n",
    "    </tr>\n",
    "     <tr>\n",
    "        <td>Loss function + Gradient descent</td>\n",
    "        <td>56 seconds</td>\n",
    "        <td>68.5%</td>\n",
    "    </tr>\n",
    "     <tr>\n",
    "        <td>MLE + Gradient ascent</td>\n",
    "        <td>49 seconds</td>\n",
    "        <td>73.07%</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>sklearn</td>\n",
    "        <td>49 seconds</td>\n",
    "        <td>78%</td>\n",
    "    </tr>\n",
    "</table><br>\n",
    "While the table shows that MLE + Gradient ascent is better than the other method, we have to consider the number of training iterations we've set as well as other hyperparameters. I randomly chose 100,000 as the number of iteration for this exercise, increasing or decreasing it might change the result, that's yours to find out. Also we've only chosen **tenure** and **monthlyCharges** as our features to simplify things, there might be important features that we need to include in the future to make the algorithm perform better, again that's yours to find out. Despite all of these, our function performed quite well I would say, (LOL) it's not that far out from the accuracy of sklearn, however there are other metrics to consider in comparing these models, that's also yours to find out. <br>\n",
    "To wrap things up let us review our objectives and wether we've accomplished them. The first objective was to understand the theory behind Logistic Regression. We've discussed that in the section **Logistic Regression behind the mask**, and I do hope that we all understood the things I stated there. The second objective was to implement the Logistic Regression without using built-in Logistic Regression libraries, yes we've done that in the section **Logistic Regression in action**, it was trained, and evaluated. In the same section, we have also predicted the churn of the customers in the Telco Customer Churn dataset. <br><br>\n",
    "This logistic regression implementation would probably be never used in production and it is unlikely that it will defeat sklearn's own LogisticRegression module, however the goal of this kernel was to understand intrecately the structure of different algorithms, in this case, Logistic Regression. Stay tuned, for more of this kind of kernels. If you liked this kernel please leave an upvote, thank you."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_uuid": "5d66f79bc5bcce02909b48b56bdf4cc3c16fc76c"
   },
   "source": [
    "<h2>References:</h2><br>\n",
    "This kernel was heavily influenced by the following:\n",
    "* https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac\n",
    "* https://beckernick.github.io/logistic-regression-from-scratch/"
   ]
  }
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