Week_19-Training_Logistic_Regression_via_Stochastic_Gradient_Ascent.ipynb

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    "colab": {
      "name": "Training Logistic Regression via Stochastic Gradient Ascent_CLA10-NB01.ipynb",
      "provenance": []
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZDgAL2ySzRWZ"
      },
      "source": [
        "# Training Logistic Regression via Stochastic Gradient Ascent\n",
        "\n",
        "The goal of this notebook is to implement a logistic regression classifier using stochastic gradient ascent. You will:\n",
        "\n",
        " * Extract features from Amazon product reviews.\n",
        " * Convert an SFrame into a NumPy array.\n",
        " * Write a function to compute the derivative of log likelihood function with respect to a single coefficient.\n",
        " * Implement stochastic gradient ascent.\n",
        " * Compare convergence of stochastic gradient ascent with that of batch gradient ascent."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WuiXi0DwzRXL"
      },
      "source": [
        "# Fire up Turi Create\n",
        " \n",
        "Make sure you have the latest version of Turi Create."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
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        "id": "4wzyC3K6zvLd",
        "outputId": "b0b20c3f-0beb-4f38-a8b0-d37b6c677d3c"
      },
      "source": [
        "pip install turicreate"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
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            "Successfully installed coremltools-3.3 gast-0.2.2 h5py-2.10.0 keras-applications-1.0.8 llvmlite-0.33.0 numba-0.50.1 numpy-1.18.5 prettytable-0.7.2 resampy-0.2.1 tensorboard-2.0.2 tensorflow-2.0.4 tensorflow-estimator-2.0.1 turicreate-6.4.1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.colab-display-data+json": {
              "pip_warning": {
                "packages": [
                  "numpy"
                ]
              }
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K1tOHzcxzRXX"
      },
      "source": [
        "from __future__ import division\n",
        "import turicreate"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vrLdq071zRXl"
      },
      "source": [
        "## Load and process review dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HN1Y-joZzRXo"
      },
      "source": [
        "**1.** For this assignment, we will use the same subset of the Amazon product review dataset that we used in Module 3 assignment. The subset was chosen to contain similar numbers of positive and negative reviews, as the original dataset consisted of mostly positive reviews."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bkaoaP1D0lvy",
        "outputId": "e449c981-4610-4275-90b8-0d860cf39dd1"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount ('/content/gdrive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xVoGOwU2zRYl"
      },
      "source": [
        "#products = turicreate.SFrame('amazon_baby_subset.sframe/')\n",
        "\n",
        "products = turicreate.SFrame('/content/gdrive/My Drive/Turicreate/Week 19/amazon_baby_subset.sframe/')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5JQJ9Dq9zRYp"
      },
      "source": [
        "**2.** Just like we did previously, we will work with a hand-curated list of important words extracted from the review data. \n",
        "\n",
        "**3.** We will also perform 2 simple data transformations:\n",
        "\n",
        "* Remove punctuation using [Python's built-in](https://docs.python.org/2/library/string.html) string manipulation functionality.\n",
        "* Compute word counts (only for the important_words)\n",
        "\n",
        "Refer to Module 3 assignment for more details."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hTvZcClmzRY3"
      },
      "source": [
        "import json\n",
        "with open('/content/gdrive/My Drive/Turicreate/Week 19/important_words.json', 'r') as f: \n",
        "    important_words = json.load(f)\n",
        "important_words = [str(s) for s in important_words]\n",
        "\n",
        "# Remove punctuation\n",
        "import string \n",
        "def remove_punctuation(text):\n",
        "    try: # python 2.x\n",
        "        text = text.translate(None, string.punctuation) \n",
        "    except: # python 3.x\n",
        "        translator = text.maketrans('', '', string.punctuation)\n",
        "        text = text.translate(translator)\n",
        "    return text\n",
        "\n",
        "products['review_clean'] = products['review'].apply(remove_punctuation)\n",
        "\n",
        "# Split out the words into individual columns\n",
        "for word in important_words:\n",
        "    products[word] = products['review_clean'].apply(lambda s : s.split().count(word))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZHT6BZMfzRas"
      },
      "source": [
        "The SFrame **products** now contains one column for each of the 193 **important_words**. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "ffUhuc6uzRa6",
        "outputId": "cb83f103-8733-4027-dd08-918ea5d63143"
      },
      "source": [
        "products"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">review</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">rating</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">sentiment</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">review_clean</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">baby</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Stop Pacifier Sucking<br>without tears with ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">All of my kids have cried<br>non-stop when I tried to ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">All of my kids have cried<br>nonstop when I tried to ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Nature&#x27;s Lullabies Second<br>Year Sticker Calendar ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">We wanted to get<br>something to keep track ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">We wanted to get<br>something to keep track ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Nature&#x27;s Lullabies Second<br>Year Sticker Calendar ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">My daughter had her 1st<br>baby over a year ago. ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">My daughter had her 1st<br>baby over a year ago She ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Lamaze Peekaboo, I Love<br>You ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">One of baby&#x27;s first and<br>favorite books, and i ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">One of babys first and<br>favorite books and it is ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">SoftPlay Peek-A-Boo<br>Where&#x27;s Elmo A Childr ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Very cute interactive<br>book! My son loves this ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Very cute interactive<br>book My son loves this ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Our Baby Girl Memory Book</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Beautiful book, I love it<br>to record cherished t ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Beautiful book I love it<br>to record cherished t ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Hunnt&amp;reg; Falling<br>Flowers and Birds Kids ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Try this out for a spring<br>project !Easy ,fun and ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Try this out for a spring<br>project Easy fun and ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Blessed By Pope Benedict<br>XVI Divine Mercy Full ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">very nice Divine Mercy<br>Pendant of Jesus now on ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">very nice Divine Mercy<br>Pendant of Jesus now on ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cloth Diaper Pins<br>Stainless Steel ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">We bought the pins as my<br>6 year old Autistic son ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">We bought the pins as my<br>6 year old Autistic son ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cloth Diaper Pins<br>Stainless Steel ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">It has been many years<br>since we needed diaper ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">It has been many years<br>since we needed diaper ...</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "</table>\n",
              "<table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">one</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">great</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">love</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">use</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">would</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">like</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">easy</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">little</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">seat</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">old</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">well</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">get</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">also</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">really</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">son</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">time</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">bought</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "</table>\n",
              "<table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">product</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">good</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">daughter</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">much</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">loves</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stroller</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">put</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">months</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">car</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">still</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">back</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">used</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">recommend</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">first</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">even</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "    </tr>\n",
              "</table>\n",
              "<table frame=\"box\" rules=\"cols\">\n",
              "    <tr>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">perfect</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">nice</th>\n",
              "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">...</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
              "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
              "    </tr>\n",
              "</table>\n",
              "[53072 rows x 198 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
              "</div>"
            ],
            "text/plain": [
              "Columns:\n",
              "\tname\tstr\n",
              "\treview\tstr\n",
              "\trating\tfloat\n",
              "\tsentiment\tint\n",
              "\treview_clean\tstr\n",
              "\tbaby\tint\n",
              "\tone\tint\n",
              "\tgreat\tint\n",
              "\tlove\tint\n",
              "\tuse\tint\n",
              "\twould\tint\n",
              "\tlike\tint\n",
              "\teasy\tint\n",
              "\tlittle\tint\n",
              "\tseat\tint\n",
              "\told\tint\n",
              "\twell\tint\n",
              "\tget\tint\n",
              "\talso\tint\n",
              "\treally\tint\n",
              "\tson\tint\n",
              "\ttime\tint\n",
              "\tbought\tint\n",
              "\tproduct\tint\n",
              "\tgood\tint\n",
              "\tdaughter\tint\n",
              "\tmuch\tint\n",
              "\tloves\tint\n",
              "\tstroller\tint\n",
              "\tput\tint\n",
              "\tmonths\tint\n",
              "\tcar\tint\n",
              "\tstill\tint\n",
              "\tback\tint\n",
              "\tused\tint\n",
              "\trecommend\tint\n",
              "\tfirst\tint\n",
              "\teven\tint\n",
              "\tperfect\tint\n",
              "\tnice\tint\n",
              "\tbag\tint\n",
              "\ttwo\tint\n",
              "\tusing\tint\n",
              "\tgot\tint\n",
              "\tfit\tint\n",
              "\taround\tint\n",
              "\tdiaper\tint\n",
              "\tenough\tint\n",
              "\tmonth\tint\n",
              "\tprice\tint\n",
              "\tgo\tint\n",
              "\tcould\tint\n",
              "\tsoft\tint\n",
              "\tsince\tint\n",
              "\tbuy\tint\n",
              "\troom\tint\n",
              "\tworks\tint\n",
              "\tmade\tint\n",
              "\tchild\tint\n",
              "\tkeep\tint\n",
              "\tsize\tint\n",
              "\tsmall\tint\n",
              "\tneed\tint\n",
              "\tyear\tint\n",
              "\tbig\tint\n",
              "\tmake\tint\n",
              "\ttake\tint\n",
              "\teasily\tint\n",
              "\tthink\tint\n",
              "\tcrib\tint\n",
              "\tclean\tint\n",
              "\tway\tint\n",
              "\tquality\tint\n",
              "\tthing\tint\n",
              "\tbetter\tint\n",
              "\twithout\tint\n",
              "\tset\tint\n",
              "\tnew\tint\n",
              "\tevery\tint\n",
              "\tcute\tint\n",
              "\tbest\tint\n",
              "\tbottles\tint\n",
              "\twork\tint\n",
              "\tpurchased\tint\n",
              "\tright\tint\n",
              "\tlot\tint\n",
              "\tside\tint\n",
              "\thappy\tint\n",
              "\tcomfortable\tint\n",
              "\ttoy\tint\n",
              "\table\tint\n",
              "\tkids\tint\n",
              "\tbit\tint\n",
              "\tnight\tint\n",
              "\tlong\tint\n",
              "\tfits\tint\n",
              "\tsee\tint\n",
              "\tus\tint\n",
              "\tanother\tint\n",
              "\tplay\tint\n",
              "\tday\tint\n",
              "\tmoney\tint\n",
              "\tmonitor\tint\n",
              "\ttried\tint\n",
              "\tthought\tint\n",
              "\tnever\tint\n",
              "\titem\tint\n",
              "\thard\tint\n",
              "\tplastic\tint\n",
              "\thowever\tint\n",
              "\tdisappointed\tint\n",
              "\treviews\tint\n",
              "\tsomething\tint\n",
              "\tgoing\tint\n",
              "\tpump\tint\n",
              "\tbottle\tint\n",
              "\tcup\tint\n",
              "\twaste\tint\n",
              "\treturn\tint\n",
              "\tamazon\tint\n",
              "\tdifferent\tint\n",
              "\ttop\tint\n",
              "\twant\tint\n",
              "\tproblem\tint\n",
              "\tknow\tint\n",
              "\twater\tint\n",
              "\ttry\tint\n",
              "\treceived\tint\n",
              "\tsure\tint\n",
              "\ttimes\tint\n",
              "\tchair\tint\n",
              "\tfind\tint\n",
              "\thold\tint\n",
              "\tgate\tint\n",
              "\topen\tint\n",
              "\tbottom\tint\n",
              "\taway\tint\n",
              "\tactually\tint\n",
              "\tcheap\tint\n",
              "\tworked\tint\n",
              "\tgetting\tint\n",
              "\tordered\tint\n",
              "\tcame\tint\n",
              "\tmilk\tint\n",
              "\tbad\tint\n",
              "\tpart\tint\n",
              "\tworth\tint\n",
              "\tfound\tint\n",
              "\tcover\tint\n",
              "\tmany\tint\n",
              "\tdesign\tint\n",
              "\tlooking\tint\n",
              "\tweeks\tint\n",
              "\tsay\tint\n",
              "\twanted\tint\n",
              "\tlook\tint\n",
              "\tplace\tint\n",
              "\tpurchase\tint\n",
              "\tlooks\tint\n",
              "\tsecond\tint\n",
              "\tpiece\tint\n",
              "\tbox\tint\n",
              "\tpretty\tint\n",
              "\ttrying\tint\n",
              "\tdifficult\tint\n",
              "\ttogether\tint\n",
              "\tthough\tint\n",
              "\tgive\tint\n",
              "\tstarted\tint\n",
              "\tanything\tint\n",
              "\tlast\tint\n",
              "\tcompany\tint\n",
              "\tcome\tint\n",
              "\treturned\tint\n",
              "\tmaybe\tint\n",
              "\ttook\tint\n",
              "\tbroke\tint\n",
              "\tmakes\tint\n",
              "\tstay\tint\n",
              "\tinstead\tint\n",
              "\tidea\tint\n",
              "\thead\tint\n",
              "\tsaid\tint\n",
              "\tless\tint\n",
              "\twent\tint\n",
              "\tworking\tint\n",
              "\thigh\tint\n",
              "\tunit\tint\n",
              "\tseems\tint\n",
              "\tpicture\tint\n",
              "\tcompletely\tint\n",
              "\twish\tint\n",
              "\tbuying\tint\n",
              "\tbabies\tint\n",
              "\twon\tint\n",
              "\ttub\tint\n",
              "\talmost\tint\n",
              "\teither\tint\n",
              "\n",
              "Rows: 53072\n",
              "\n",
              "Data:\n",
              "+-------------------------------+-------------------------------+--------+-----------+\n",
              "|              name             |             review            | rating | sentiment |\n",
              "+-------------------------------+-------------------------------+--------+-----------+\n",
              "| Stop Pacifier Sucking with... | All of my kids have cried ... |  5.0   |     1     |\n",
              "| Nature's Lullabies Second ... | We wanted to get something... |  5.0   |     1     |\n",
              "| Nature's Lullabies Second ... | My daughter had her 1st ba... |  5.0   |     1     |\n",
              "|  Lamaze Peekaboo, I Love You  | One of baby's first and fa... |  4.0   |     1     |\n",
              "| SoftPlay Peek-A-Boo Where'... | Very cute interactive book... |  5.0   |     1     |\n",
              "|   Our Baby Girl Memory Book   | Beautiful book, I love it ... |  5.0   |     1     |\n",
              "| Hunnt&reg; Falling Flowers... | Try this out for a spring ... |  5.0   |     1     |\n",
              "| Blessed By Pope Benedict X... | very nice Divine Mercy Pen... |  5.0   |     1     |\n",
              "| Cloth Diaper Pins Stainles... | We bought the pins as my 6... |  4.0   |     1     |\n",
              "| Cloth Diaper Pins Stainles... | It has been many years sin... |  5.0   |     1     |\n",
              "+-------------------------------+-------------------------------+--------+-----------+\n",
              "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
              "|          review_clean         | baby | one | great | love | use | would | like |\n",
              "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
              "| All of my kids have cried ... |  0   |  0  |   1   |  0   |  0  |   0   |  0   |\n",
              "| We wanted to get something... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
              "| My daughter had her 1st ba... |  1   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
              "| One of babys first and fav... |  0   |  0  |   0   |  0   |  0  |   0   |  1   |\n",
              "| Very cute interactive book... |  0   |  0  |   1   |  0   |  0  |   0   |  0   |\n",
              "| Beautiful book I love it t... |  0   |  0  |   1   |  1   |  0  |   0   |  0   |\n",
              "| Try this out for a spring ... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
              "| very nice Divine Mercy Pen... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
              "| We bought the pins as my 6... |  0   |  1  |   0   |  0   |  1  |   0   |  0   |\n",
              "| It has been many years sin... |  0   |  1  |   0   |  0   |  0  |   0   |  1   |\n",
              "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
              "+------+--------+------+-----+------+-----+------+--------+-----+\n",
              "| easy | little | seat | old | well | get | also | really | ... |\n",
              "+------+--------+------+-----+------+-----+------+--------+-----+\n",
              "|  1   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  1  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  1  |  0   |  1  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   0    |  0   |  1  |  0   |  0  |  0   |   0    | ... |\n",
              "|  0   |   1    |  0   |  0  |  0   |  1  |  0   |   0    | ... |\n",
              "+------+--------+------+-----+------+-----+------+--------+-----+\n",
              "[53072 rows x 198 columns]\n",
              "Note: Only the head of the SFrame is printed.\n",
              "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DS1Sx11rzRbH"
      },
      "source": [
        "### Split data into training and validation sets\n",
        "\n",
        "**6.** We will now split the data into a 90-10 split where 90% is in the training set and 10% is in the validation set. We use `seed=1` so that everyone gets the same result."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lacN7K4DzRbJ",
        "outputId": "e745f279-9dc6-4a1a-e641-2bff92555de1"
      },
      "source": [
        "train_data, validation_data = products.random_split(.9, seed=1)\n",
        "\n",
        "print('Training set  : %d data points' % len(train_data))\n",
        "print('Validation set: %d data points' % len(validation_data))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training set  : 47780 data points\n",
            "Validation set: 5292 data points\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r3BeDXoSzRbt"
      },
      "source": [
        "## Convert SFrame to NumPy array\n",
        "\n",
        "**7.** Just like in the earlier assignments, we provide you with a function that extracts columns from an SFrame and converts them into a NumPy array. Two arrays are returned: one representing features and another representing class labels. \n",
        "\n",
        "**Note:** The feature matrix includes an additional column 'intercept' filled with 1's to take account of the intercept term."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "cLfqTndNzRdR"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "def get_numpy_data(data_sframe, features, label):\n",
        "    data_sframe['intercept'] = 1\n",
        "    features = ['intercept'] + features\n",
        "    features_sframe = data_sframe[features]\n",
        "    feature_matrix = features_sframe.to_numpy()\n",
        "    label_sarray = data_sframe[label]\n",
        "    label_array = label_sarray.to_numpy()\n",
        "    return(feature_matrix, label_array)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mdrw3PTdzRdW"
      },
      "source": [
        "Note that we convert both the training and validation sets into NumPy arrays.\n",
        "\n",
        "**Warning**: This may take a few minutes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "22KQ28DXzRdY"
      },
      "source": [
        "feature_matrix_train, sentiment_train = get_numpy_data(train_data, important_words, 'sentiment')\n",
        "feature_matrix_valid, sentiment_valid = get_numpy_data(validation_data, important_words, 'sentiment') "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W8uqrtXYzRdb"
      },
      "source": [
        "**Are you running this notebook on an Amazon EC2 t2.micro instance?** (If you are using your own machine, please skip this section)\n",
        "\n",
        "It has been reported that t2.micro instances do not provide sufficient power to complete the conversion in acceptable amount of time. For interest of time, please refrain from running `get_numpy_data` function. Instead, download the [binary file](https://s3.amazonaws.com/static.dato.com/files/coursera/course-3/numpy-arrays/module-10-assignment-numpy-arrays.npz) containing the four NumPy arrays you'll need for the assignment. To load the arrays, run the following commands:\n",
        "```\n",
        "arrays = np.load('module-10-assignment-numpy-arrays.npz')\n",
        "feature_matrix_train, sentiment_train = arrays['feature_matrix_train'], arrays['sentiment_train']\n",
        "feature_matrix_valid, sentiment_valid = arrays['feature_matrix_valid'], arrays['sentiment_valid']\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9UNoLUTKzRdj"
      },
      "source": [
        "**Quiz Question**: In Module 3 assignment, there were 194 features (an intercept + one feature for each of the 193 important words). In this assignment, we will use stochastic gradient ascent to train the classifier using logistic regression. How does the changing the solver to stochastic gradient ascent affect the number of features?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "upQL73OOzRdm"
      },
      "source": [
        "## Building on logistic regression\n",
        "\n",
        "**8.** Let us now build on Module 3 assignment. Recall from lecture that the link function for logistic regression can be defined as:\n",
        "\n",
        "$$\n",
        "P(y_i = +1 | \\mathbf{x}_i,\\mathbf{w}) = \\frac{1}{1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))},\n",
        "$$\n",
        "\n",
        "where the feature vector $h(\\mathbf{x}_i)$ is given by the word counts of **important_words** in the review $\\mathbf{x}_i$. \n",
        "\n",
        "\n",
        "We will use the **same code** as in Module 3 assignment to make probability predictions, since this part is not affected by using stochastic gradient ascent as a solver. Only the way in which the coefficients are learned is affected by using stochastic gradient ascent as a solver."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "ao6yzIpHzRdo"
      },
      "source": [
        "'''\n",
        "produces probablistic estimate for P(y_i = +1 | x_i, w).\n",
        "estimate ranges between 0 and 1.\n",
        "'''\n",
        "def predict_probability(feature_matrix, coefficients):\n",
        "    # Take dot product of feature_matrix and coefficients  \n",
        "    score = np.dot(feature_matrix, coefficients)\n",
        "    \n",
        "    # Compute P(y_i = +1 | x_i, w) using the link function\n",
        "    predictions = 1. / (1.+np.exp(-score))    \n",
        "    return predictions"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "84ldae8pzRdq"
      },
      "source": [
        "## Derivative of log likelihood with respect to a single coefficient\n",
        "\n",
        "**9.** Let us now work on making minor changes to how the derivative computation is performed for logistic regression.\n",
        "\n",
        "Recall from the lectures and Module 3 assignment that for logistic regression, **the derivative of log likelihood with respect to a single coefficient** is as follows:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial\\ell}{\\partial w_j} = \\sum_{i=1}^N h_j(\\mathbf{x}_i)\\left(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})\\right)\n",
        "$$\n",
        "\n",
        "In Module 3 assignment, we wrote a function to compute the derivative of log likelihood with respect to a single coefficient $w_j$. The function accepts the following two parameters:\n",
        " * `errors` vector containing $(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w}))$ for all $i$\n",
        " * `feature` vector containing $h_j(\\mathbf{x}_i)$  for all $i$\n",
        " \n",
        "Complete the following code block:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "tFzxpoTqzReq"
      },
      "source": [
        "def feature_derivative(errors, feature): \n",
        "    \n",
        "    # Compute the dot product of errors and feature\n",
        "    ## YOUR CODE HERE\n",
        "    derivative = np.dot(errors, feature)\n",
        "\n",
        "    return derivative"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s8XkYpSUzRe1"
      },
      "source": [
        "**Note**. We are not using regularization in this assignment, but, as discussed in the optional video, stochastic gradient can also be used for regularized logistic regression."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BxEkuEG3zRe3"
      },
      "source": [
        "**10.** To verify the correctness of the gradient computation, we provide a function for computing average log likelihood (which we recall from the last assignment was a topic detailed in an advanced optional video, and used here for its numerical stability).\n",
        "\n",
        "To track the performance of stochastic gradient ascent, we provide a function for computing **average log likelihood**. \n",
        "\n",
        "$$\\ell\\ell_A(\\mathbf{w}) = \\color{red}{\\frac{1}{N}} \\sum_{i=1}^N \\Big( (\\mathbf{1}[y_i = +1] - 1)\\mathbf{w}^T h(\\mathbf{x}_i) - \\ln\\left(1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))\\right) \\Big) $$\n",
        "\n",
        "**Note** that we made one tiny modification to the log likelihood function (called **compute_log_likelihood**) in our earlier assignments. We added a $\\color{red}{1/N}$ term which averages the log likelihood accross all data points. The $\\color{red}{1/N}$ term makes it easier for us to compare stochastic gradient ascent with batch gradient ascent. We will use this function to generate plots that are similar to those you saw in the lecture."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_lONEa3QzRe6"
      },
      "source": [
        "def compute_avg_log_likelihood(feature_matrix, sentiment, coefficients):\n",
        "    \n",
        "    indicator = (sentiment==+1)\n",
        "    scores = np.dot(feature_matrix, coefficients)\n",
        "    logexp = np.log(1. + np.exp(-scores))\n",
        "    \n",
        "    # Simple check to prevent overflow\n",
        "    mask = np.isinf(logexp)\n",
        "    logexp[mask] = -scores[mask]\n",
        "    \n",
        "    lp = np.sum((indicator-1)*scores - logexp)/len(feature_matrix)\n",
        "    \n",
        "    return lp"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L0HxZUbBzRe8"
      },
      "source": [
        "**Quiz Question:** Recall from the lecture and the earlier assignment, the log likelihood (without the averaging term) is given by \n",
        "\n",
        "$$\\ell\\ell(\\mathbf{w}) = \\sum_{i=1}^N \\Big( (\\mathbf{1}[y_i = +1] - 1)\\mathbf{w}^T h(\\mathbf{x}_i) - \\ln\\left(1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))\\right) \\Big) $$\n",
        "\n",
        "How are the functions $\\ell\\ell(\\mathbf{w})$ and $\\ell\\ell_A(\\mathbf{w})$ related?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJf0f4fSzRfY"
      },
      "source": [
        "## Modifying the derivative for stochastic gradient ascent\n",
        "\n",
        "**11.** Recall from the lecture that the gradient for a single data point $\\color{red}{\\mathbf{x}_i}$ can be computed using the following formula:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})}{\\partial w_j} = h_j(\\color{red}{\\mathbf{x}_i})\\left(\\mathbf{1}[y_\\color{red}{i} = +1] - P(y_\\color{red}{i} = +1 | \\color{red}{\\mathbf{x}_i}, \\mathbf{w})\\right)\n",
        "$$\n",
        "\n",
        "\n",
        "**Computing the gradient for a single data point**\n",
        "\n",
        "Do we really need to re-write all our code to modify $\\partial\\ell(\\mathbf{w})/\\partial w_j$ to $\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})/{\\partial w_j}$? \n",
        "\n",
        "\n",
        "Thankfully **No!**. Using NumPy, we access $\\mathbf{x}_i$ in the training data using `feature_matrix_train[i:i+1,:]`\n",
        "and $y_i$ in the training data using `sentiment_train[i:i+1]`. We can compute $\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})/\\partial w_j$ by re-using **all the code** written in **feature_derivative** and **predict_probability**.\n",
        "\n",
        "\n",
        "We compute $\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})/\\partial w_j$ using the following steps:\n",
        "* First, compute $P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})$ using the **predict_probability** function with `feature_matrix_train[i:i+1,:]` as the first parameter.\n",
        "* Next, compute $\\mathbf{1}[y_i = +1]$ using `sentiment_train[i:i+1]`.\n",
        "* Finally, call the **feature_derivative** function with `feature_matrix_train[i:i+1, j]` as one of the parameters. \n",
        "\n",
        "Let us follow these steps for `j = 1` and `i = 10`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XnHBdaSCzRgb",
        "outputId": "0ebfbc71-969e-4319-cbae-baff20bdd5ff"
      },
      "source": [
        "j = 1                        # Feature number\n",
        "i = 10                       # Data point number\n",
        "coefficients = np.zeros(194) # A point w at which we are computing the gradient.\n",
        "\n",
        "predictions = predict_probability(feature_matrix_train[i:i+1,:], coefficients)\n",
        "indicator = (sentiment_train[i:i+1]==+1)\n",
        "\n",
        "errors = indicator - predictions        \n",
        "gradient_single_data_point = feature_derivative(errors, feature_matrix_train[i:i+1,j])\n",
        "print(\"Gradient single data point: %s\" % gradient_single_data_point)\n",
        "print(\"           --> Should print 0.0\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient single data point: 0.0\n",
            "           --> Should print 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CjNJJtXKzRgc"
      },
      "source": [
        "**Quiz Question:** The code block above computed $\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})/{\\partial w_j}$ for `j = 1` and `i = 10`.  Is $\\partial\\ell_{\\color{red}{i}}(\\mathbf{w})/{\\partial w_j}$ a scalar or a 194-dimensional vector?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JiaBa_wrzRgd"
      },
      "source": [
        "## Modifying the derivative for using a batch of data points\n",
        "\n",
        "**12.** Stochastic gradient estimates the ascent direction using 1 data point, while gradient uses $N$ data points to decide how to update the the parameters.  In an optional video, we discussed the details of a simple change that allows us to use a **mini-batch** of $B \\leq N$ data points to estimate the ascent direction. This simple approach is faster than regular gradient but less noisy than stochastic gradient that uses only 1 data point. Although we encorage you to watch the optional video on the topic to better understand why mini-batches help stochastic gradient, in this assignment, we will simply use this technique, since the approach is very simple and will improve your results.\n",
        "\n",
        "Given a mini-batch (or a set of data points) $\\mathbf{x}_{i}, \\mathbf{x}_{i+1} \\ldots \\mathbf{x}_{i+B}$, the gradient function for this mini-batch of data points is given by:\n",
        "$$\n",
        "\\color{red}{\\sum_{s = i}^{i+B}} \\frac{\\partial\\ell_{s}}{\\partial w_j} = \\color{red}{\\sum_{s = i}^{i + B}} h_j(\\mathbf{x}_s)\\left(\\mathbf{1}[y_s = +1] - P(y_s = +1 | \\mathbf{x}_s, \\mathbf{w})\\right)\n",
        "$$\n",
        "\n",
        "\n",
        "**Computing the gradient for a \"mini-batch\" of data points**\n",
        "\n",
        "Using NumPy, we access the points $\\mathbf{x}_i, \\mathbf{x}_{i+1} \\ldots \\mathbf{x}_{i+B}$ in the training data using `feature_matrix_train[i:i+B,:]`\n",
        "and $y_i$ in the training data using `sentiment_train[i:i+B]`. \n",
        "\n",
        "We can compute $\\color{red}{\\sum_{s = i}^{i+B}} \\partial\\ell_{s}/\\partial w_j$ easily as follows:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9znev7LRzRgh",
        "outputId": "8ff04191-ed1e-4a01-8bdc-3b98a7ece19c"
      },
      "source": [
        "j = 1                        # Feature number\n",
        "i = 10                       # Data point start\n",
        "B = 10                       # Mini-batch size\n",
        "coefficients = np.zeros(194) # A point w at which we are computing the gradient.\n",
        "\n",
        "predictions = predict_probability(feature_matrix_train[i:i+B,:], coefficients)\n",
        "indicator = (sentiment_train[i:i+B]==+1)\n",
        "\n",
        "errors = indicator - predictions        \n",
        "gradient_mini_batch = feature_derivative(errors, feature_matrix_train[i:i+B,j])\n",
        "print(\"Gradient mini-batch data points: %s\" % gradient_mini_batch)\n",
        "print(\"                --> Should print 1.0\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient mini-batch data points: 1.0\n",
            "                --> Should print 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Fgx4wL_zRgm"
      },
      "source": [
        "**Quiz Question:** The code block above computed \n",
        "$\\color{red}{\\sum_{s = i}^{i+B}}\\partial\\ell_{s}(\\mathbf{w})/{\\partial w_j}$ \n",
        "for `j = 10`, `i = 10`, and `B = 10`. Is this a scalar or a 194-dimensional vector?\n",
        "\n",
        "\n",
        "**Quiz Question:** For what value of `B` is the term\n",
        "$\\color{red}{\\sum_{s = 1}^{B}}\\partial\\ell_{s}(\\mathbf{w})/\\partial w_j$\n",
        "the same as the full gradient\n",
        "$\\partial\\ell(\\mathbf{w})/{\\partial w_j}$? Hint: consider the training set we are using now."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sVJia0Bt36lu",
        "outputId": "dbb74085-b9f2-4128-a0dc-b0a466032896"
      },
      "source": [
        "len(sentiment_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "47780"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fSsK1CAyzRgp"
      },
      "source": [
        "### Averaging the gradient across a batch\n",
        "\n",
        "**13.** It is a common practice to normalize the gradient update rule by the batch size B:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial\\ell_{\\color{red}{A}}(\\mathbf{w})}{\\partial w_j} \\approx \\color{red}{\\frac{1}{B}} {\\sum_{s = i}^{i + B}} h_j(\\mathbf{x}_s)\\left(\\mathbf{1}[y_s = +1] - P(y_s = +1 | \\mathbf{x}_s, \\mathbf{w})\\right)\n",
        "$$\n",
        "In other words, we update the coefficients using the **average gradient over data points** (instead of using a summation). By using the average gradient, we ensure that the magnitude of the gradient is approximately the same for all batch sizes. This way, we can more easily compare various batch sizes of stochastic gradient ascent (including a batch size of **all the data points**), and study the effect of batch size on the algorithm as well as the choice of step size.\n",
        "\n",
        "\n",
        "## Implementing stochastic gradient ascent\n",
        "\n",
        "**14.** Now we are ready to implement our own logistic regression with stochastic gradient ascent. Complete the following function to fit a logistic regression model using gradient ascent:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_z8jYapzRgs"
      },
      "source": [
        "from math import sqrt\n",
        "def logistic_regression_SG(feature_matrix, sentiment, initial_coefficients, step_size, batch_size, max_iter):\n",
        "    log_likelihood_all = []\n",
        "    \n",
        "    # make sure it's a numpy array\n",
        "    coefficients = np.array(initial_coefficients)\n",
        "    # set seed=1 to produce consistent results\n",
        "    np.random.seed(seed=1)\n",
        "    # Shuffle the data before starting\n",
        "    permutation = np.random.permutation(len(feature_matrix))\n",
        "    feature_matrix = feature_matrix[permutation,:]\n",
        "    sentiment = sentiment[permutation]\n",
        "    \n",
        "    i = 0 # index of current batch\n",
        "    # Do a linear scan over data\n",
        "    for itr in range(max_iter):\n",
        "        # Predict P(y_i = +1|x_i,w) using your predict_probability() function\n",
        "        # Make sure to slice the i-th row of feature_matrix with [i:i+batch_size,:]\n",
        "        ### YOUR CODE HERE\n",
        "        predictions = predict_probability(feature_matrix[i:i+batch_size,:], coefficients)\n",
        "        \n",
        "        # Compute indicator value for (y_i = +1)\n",
        "        # Make sure to slice the i-th entry with [i:i+batch_size]\n",
        "        ### YOUR CODE HERE\n",
        "        indicator = (sentiment[i:i+batch_size]==+1)\n",
        "        \n",
        "        # Compute the errors as indicator - predictions\n",
        "        errors = indicator - predictions\n",
        "        for j in range(len(coefficients)): # loop over each coefficient\n",
        "            # Recall that feature_matrix[:,j] is the feature column associated with coefficients[j]\n",
        "            # Compute the derivative for coefficients[j] and save it to derivative.\n",
        "            # Make sure to slice the i-th row of feature_matrix with [i:i+batch_size,j]\n",
        "            ### YOUR CODE HERE\n",
        "            derivative = feature_derivative(errors, feature_matrix[i:i+batch_size,j])\n",
        "            \n",
        "            # compute the product of the step size, the derivative, and the **normalization constant** (1./batch_size)\n",
        "            ### YOUR CODE HERE\n",
        "            coefficients[j] += (1./batch_size)*(step_size * derivative)\n",
        "        \n",
        "        # Checking whether log likelihood is increasing\n",
        "        # Print the log likelihood over the *current batch*\n",
        "        lp = compute_avg_log_likelihood(feature_matrix[i:i+batch_size,:], sentiment[i:i+batch_size],\n",
        "                                        coefficients)\n",
        "        log_likelihood_all.append(lp)\n",
        "        if itr <= 15 or (itr <= 1000 and itr % 100 == 0) or (itr <= 10000 and itr % 1000 == 0) \\\n",
        "         or itr % 10000 == 0 or itr == max_iter-1:\n",
        "            data_size = len(feature_matrix)\n",
        "            print('Iteration %*d: Average log likelihood (of data points in batch [%0*d:%0*d]) = %.8f' % \\\n",
        "                (int(np.ceil(np.log10(max_iter))), itr, \\\n",
        "                 int(np.ceil(np.log10(data_size))), i, \\\n",
        "                 int(np.ceil(np.log10(data_size))), i+batch_size, lp))\n",
        "        \n",
        "        # if we made a complete pass over data, shuffle and restart\n",
        "        i += batch_size\n",
        "        if i+batch_size > len(feature_matrix):\n",
        "            permutation = np.random.permutation(len(feature_matrix))\n",
        "            feature_matrix = feature_matrix[permutation,:]\n",
        "            sentiment = sentiment[permutation]\n",
        "            i = 0\n",
        "                \n",
        "    # We return the list of log likelihoods for plotting purposes.\n",
        "    return coefficients, log_likelihood_all"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_zLGjFUdzRjf"
      },
      "source": [
        "**Note**. In practice, the final set of coefficients is rarely used; it is better to use the average of the last K sets of coefficients instead, where K should be adjusted depending on how fast the log likelihood oscillates around the optimum."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jw95Z2oozRjh"
      },
      "source": [
        "### Checkpoint\n",
        "\n",
        "\n",
        "The following cell tests your stochastic gradient ascent function using a toy dataset consisting of two data points. If the test does not pass, make sure you are normalizing the gradient update rule correctly."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9gptk2vtzRjj",
        "outputId": "87cca86a-ebc7-4e65-b615-949a8805c169"
      },
      "source": [
        "sample_feature_matrix = np.array([[1.,2.,-1.], [1.,0.,1.]])\n",
        "sample_sentiment = np.array([+1, -1])\n",
        "\n",
        "coefficients, log_likelihood = logistic_regression_SG(sample_feature_matrix, sample_sentiment, np.zeros(3),\n",
        "                                                  step_size=1., batch_size=2, max_iter=2)\n",
        "print('-------------------------------------------------------------------------------------')\n",
        "print('Coefficients learned                 :', coefficients)\n",
        "\n",
        "print('Average log likelihood per-iteration :', log_likelihood)\n",
        "if np.allclose(coefficients, np.array([-0.09755757,  0.68242552, -0.7799831]), atol=1e-3)\\\n",
        "and np.allclose(log_likelihood, np.array([-0.33774513108142956, -0.2345530939410341])):\n",
        "\n",
        "    # pass if elements match within 1e-3\n",
        "    print('-------------------------------------------------------------------------------------')\n",
        "    print('Test passed!')\n",
        "else:\n",
        "    print('-------------------------------------------------------------------------------------')\n",
        "    print('Test failed')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0: Average log likelihood (of data points in batch [0:2]) = -0.33774513\n",
            "Iteration 1: Average log likelihood (of data points in batch [0:2]) = -0.23455309\n",
            "-------------------------------------------------------------------------------------\n",
            "Coefficients learned                 : [-0.09755757  0.68242552 -0.7799831 ]\n",
            "Average log likelihood per-iteration : [-0.33774513108142956, -0.2345530939410341]\n",
            "-------------------------------------------------------------------------------------\n",
            "Test passed!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WVSaKeSfzRjl"
      },
      "source": [
        "## Compare convergence behavior of stochastic gradient ascent\n",
        "\n",
        "**15.** For the remainder of the assignment, we will compare stochastic gradient ascent against batch gradient ascent. For this, we need a reference implementation of batch gradient ascent. But do we need to implement this from scratch?\n",
        "\n",
        "**Quiz Question:** For what value of batch size `B` above is the stochastic gradient ascent function **logistic_regression_SG** act as a standard gradient ascent algorithm? Hint: consider the training set we are using now."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0E0oBnJizRjm"
      },
      "source": [
        "## Running gradient ascent using the stochastic gradient ascent implementation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FF53yMptzRjn"
      },
      "source": [
        "**16.** Instead of implementing batch gradient ascent separately, we save time by re-using the stochastic gradient ascent function we just wrote &mdash; **to perform gradient ascent**, it suffices to set **`batch_size`** to the number of data points in the training data. Yes, we did answer above the quiz question for you, but that is an important point to remember in the future :)\n",
        "\n",
        "**Small Caveat**. The batch gradient ascent implementation here is slightly different than the one in the earlier assignments, as we now normalize the gradient update rule.\n",
        "\n",
        "We now **run stochastic gradient ascent** over the **feature_matrix_train** for 10 iterations using:\n",
        "* `initial_coefficients = np.zeros(194)`\n",
        "* `step_size = 5e-1`\n",
        "* `batch_size = 1`\n",
        "* `max_iter = 10`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cg223aPSzRjo",
        "outputId": "4eff9dea-e6de-470d-f3f5-0acdee954b61"
      },
      "source": [
        "coefficients, log_likelihood = logistic_regression_SG(feature_matrix_train, sentiment_train,\n",
        "                                        initial_coefficients=np.zeros(194),\n",
        "                                        step_size=5e-1, batch_size=1, max_iter=10)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0: Average log likelihood (of data points in batch [00000:00001]) = -0.25192908\n",
            "Iteration 1: Average log likelihood (of data points in batch [00001:00002]) = -0.00000001\n",
            "Iteration 2: Average log likelihood (of data points in batch [00002:00003]) = -0.12692771\n",
            "Iteration 3: Average log likelihood (of data points in batch [00003:00004]) = -0.02969101\n",
            "Iteration 4: Average log likelihood (of data points in batch [00004:00005]) = -0.02668819\n",
            "Iteration 5: Average log likelihood (of data points in batch [00005:00006]) = -0.04332901\n",
            "Iteration 6: Average log likelihood (of data points in batch [00006:00007]) = -0.02368802\n",
            "Iteration 7: Average log likelihood (of data points in batch [00007:00008]) = -0.12686897\n",
            "Iteration 8: Average log likelihood (of data points in batch [00008:00009]) = -0.04468879\n",
            "Iteration 9: Average log likelihood (of data points in batch [00009:00010]) = -0.00000124\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nbYPi3_2zRjw"
      },
      "source": [
        "**Quiz Question**. When you set `batch_size = 1`, as each iteration passes, how does the average log likelihood in the batch change?\n",
        "* Increases\n",
        "* Decreases\n",
        "* Fluctuates "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6cMV6W7NzRjx"
      },
      "source": [
        "**17.** Now run **batch gradient ascent** over the **feature_matrix_train** for 200 iterations using:\n",
        "* `initial_coefficients = np.zeros(194)`\n",
        "* `step_size = 5e-1`\n",
        "* `batch_size = len(feature_matrix_train)`\n",
        "* `max_iter = 200`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uAAqB1XAzRjy",
        "outputId": "040ede91-1d5a-47c6-9471-fc995eef1b22"
      },
      "source": [
        "# YOUR CODE HERE\n",
        "coefficients_batch, log_likelihood_batch = logistic_regression_SG(feature_matrix_train, sentiment_train,\n",
        "                                        initial_coefficients=np.zeros(194),\n",
        "                                        step_size=5e-1, batch_size = len(feature_matrix_train), max_iter=200)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration   0: Average log likelihood (of data points in batch [00000:47780]) = -0.68308119\n",
            "Iteration   1: Average log likelihood (of data points in batch [00000:47780]) = -0.67394599\n",
            "Iteration   2: Average log likelihood (of data points in batch [00000:47780]) = -0.66555129\n",
            "Iteration   3: Average log likelihood (of data points in batch [00000:47780]) = -0.65779626\n",
            "Iteration   4: Average log likelihood (of data points in batch [00000:47780]) = -0.65060701\n",
            "Iteration   5: Average log likelihood (of data points in batch [00000:47780]) = -0.64392241\n",
            "Iteration   6: Average log likelihood (of data points in batch [00000:47780]) = -0.63769009\n",
            "Iteration   7: Average log likelihood (of data points in batch [00000:47780]) = -0.63186462\n",
            "Iteration   8: Average log likelihood (of data points in batch [00000:47780]) = -0.62640636\n",
            "Iteration   9: Average log likelihood (of data points in batch [00000:47780]) = -0.62128063\n",
            "Iteration  10: Average log likelihood (of data points in batch [00000:47780]) = -0.61645691\n",
            "Iteration  11: Average log likelihood (of data points in batch [00000:47780]) = -0.61190832\n",
            "Iteration  12: Average log likelihood (of data points in batch [00000:47780]) = -0.60761103\n",
            "Iteration  13: Average log likelihood (of data points in batch [00000:47780]) = -0.60354390\n",
            "Iteration  14: Average log likelihood (of data points in batch [00000:47780]) = -0.59968811\n",
            "Iteration  15: Average log likelihood (of data points in batch [00000:47780]) = -0.59602682\n",
            "Iteration 100: Average log likelihood (of data points in batch [00000:47780]) = -0.49520194\n",
            "Iteration 199: Average log likelihood (of data points in batch [00000:47780]) = -0.47126953\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2K8TqlAFzRjz"
      },
      "source": [
        "**Quiz Question**. When you set `batch_size = len(feature_matrix_train)`, as each iteration passes, how does the average log likelihood in the batch change?\n",
        "* Increases \n",
        "* Decreases\n",
        "* Fluctuates "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rcqfbe5YzRj1"
      },
      "source": [
        "## Make \"passes\" over the dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i1e7miXWzRkA"
      },
      "source": [
        "**18.** To make a fair comparison betweeen stochastic gradient ascent and batch gradient ascent, we measure the average log likelihood as a function of the number of passes (defined as follows):\n",
        "$$\n",
        "[\\text{# of passes}] = \\frac{[\\text{# of data points touched so far}]}{[\\text{size of dataset}]}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9m3OWvwGzRkC"
      },
      "source": [
        "**Quiz Question** Suppose that we run stochastic gradient ascent with a batch size of 100. How many gradient updates are performed at the end of two passes over a dataset consisting of 50000 data points?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RRT7bfizzRkD",
        "outputId": "2ea0822f-784a-4b60-9c87-52ef31f24ef7"
      },
      "source": [
        "# number of passes is number to complete the whole dataset\n",
        "# For each batch size, we update 1 gradient, so\n",
        "\n",
        "2*(50000/100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1000.0"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_grMrbshzRkE"
      },
      "source": [
        "## Log likelihood plots for stochastic gradient ascent"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cy_HyjAyzRkF"
      },
      "source": [
        "**19.** With the terminology in mind, let us run stochastic gradient ascent for 10 passes. We will use\n",
        "* `step_size=1e-1`\n",
        "* `batch_size=100`\n",
        "* `initial_coefficients` to all zeros."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3LmI7TPYzRkG",
        "outputId": "0243cace-7e9d-4619-b21f-e50511e601c6"
      },
      "source": [
        "step_size = 1e-1\n",
        "batch_size = 100\n",
        "num_passes = 10\n",
        "num_iterations = num_passes * int(len(feature_matrix_train)/batch_size)\n",
        "\n",
        "coefficients_sgd, log_likelihood_sgd = logistic_regression_SG(feature_matrix_train, sentiment_train,\n",
        "                                       initial_coefficients=np.zeros(194),\n",
        "                                       step_size=1e-1, batch_size=100, max_iter=num_iterations)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.68251093\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.67845294\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.68207160\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.67411325\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.67804438\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.67712546\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.66377074\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.67321231\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.66923613\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.67479446\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.66501639\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.65591964\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.66240398\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.66440641\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.65782757\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.64571479\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.60976663\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.54566060\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.48245740\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.46629313\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.47223389\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.52216798\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.52336683\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.46963453\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.47883783\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.46988191\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.46365531\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.36466901\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.51096892\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.54670667\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "upLelm7_zRkH"
      },
      "source": [
        "**20.** We provide you with a utility function to plot the average log likelihood as a function of the number of passes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2tMc9DMFzRkJ"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "def make_plot(log_likelihood_all, len_data, batch_size, smoothing_window=1, label=''):\n",
        "    plt.rcParams.update({'figure.figsize': (9,5)})\n",
        "    log_likelihood_all_ma = np.convolve(np.array(log_likelihood_all), \\\n",
        "                                        np.ones((smoothing_window,))/smoothing_window, mode='valid')\n",
        "    plt.plot(np.array(range(smoothing_window-1, len(log_likelihood_all)))*float(batch_size)/len_data,\n",
        "             log_likelihood_all_ma, linewidth=4.0, label=label)\n",
        "    plt.rcParams.update({'font.size': 16})\n",
        "    plt.tight_layout()\n",
        "    plt.xlabel('# of passes over data')\n",
        "    plt.ylabel('Average log likelihood per data point')\n",
        "    plt.legend(loc='lower right', prop={'size':14})"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 370
        },
        "id": "Zer8nRWmzRkK",
        "outputId": "5c6195d6-587c-46af-cae2-5abc10828f1a"
      },
      "source": [
        "make_plot(log_likelihood_sgd, len_data=len(feature_matrix_train), batch_size=100,\n",
        "          label='stochastic gradient, step_size=1e-1')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-Zc7S3RzRkT"
      },
      "source": [
        "## Smoothing the stochastic gradient ascent curve\n",
        "\n",
        "The plotted line oscillates so much that it is hard to see whether the log likelihood is improving. In our plot, we apply a simple smoothing operation using the parameter `smoothing_window`. The smoothing is simply a [moving average](https://en.wikipedia.org/wiki/Moving_average) of log likelihood over the last `smoothing_window` \"iterations\" of  stochastic gradient ascent."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "id": "fiqPeE-HzRlW",
        "outputId": "cc4e8834-4a61-4d4b-eafc-95101bb074ab"
      },
      "source": [
        "make_plot(log_likelihood_sgd, len_data=len(feature_matrix_train), batch_size=100,\n",
        "          smoothing_window=30, label='stochastic gradient, step_size=1e-1')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xv7y1nXlzRlY"
      },
      "source": [
        "**Checkpoint**: The above plot should look smoother than the previous plot. Play around with `smoothing_window`. As you increase it, you should see a smoother plot."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TgByOXg2zRlZ"
      },
      "source": [
        "## Stochastic gradient ascent vs batch gradient ascent\n",
        "\n",
        "**21.** To compare convergence rates for stochastic gradient ascent with batch gradient ascent, we call `make_plot()` multiple times in the same cell.\n",
        "\n",
        "We are comparing:\n",
        "* **stochastic gradient ascent**: `step_size = 0.1`, `batch_size=100`\n",
        "* **batch gradient ascent**: `step_size = 0.5`, `batch_size=len(feature_matrix_train)`\n",
        "\n",
        "Write code to run stochastic gradient ascent for 200 passes using:\n",
        "* `step_size=1e-1`\n",
        "* `batch_size=100`\n",
        "* `initial_coefficients` to all zeros."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DnMx96WCzRla",
        "outputId": "bb9aa0dc-b38d-416c-fa7c-972395cf69a7"
      },
      "source": [
        "step_size = 1e-1\n",
        "batch_size = 100\n",
        "num_passes = 200\n",
        "num_iterations = num_passes * int(len(feature_matrix_train)/batch_size)\n",
        "\n",
        "## YOUR CODE HERE\n",
        "coefficients_sgd, log_likelihood_sgd = logistic_regression_SG(feature_matrix_train, sentiment_train,\n",
        "                                       initial_coefficients=np.zeros(194),\n",
        "                                       step_size=step_size, batch_size=batch_size, max_iter=num_iterations)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration     0: Average log likelihood (of data points in batch [00000:00100]) = -0.68251093\n",
            "Iteration     1: Average log likelihood (of data points in batch [00100:00200]) = -0.67845294\n",
            "Iteration     2: Average log likelihood (of data points in batch [00200:00300]) = -0.68207160\n",
            "Iteration     3: Average log likelihood (of data points in batch [00300:00400]) = -0.67411325\n",
            "Iteration     4: Average log likelihood (of data points in batch [00400:00500]) = -0.67804438\n",
            "Iteration     5: Average log likelihood (of data points in batch [00500:00600]) = -0.67712546\n",
            "Iteration     6: Average log likelihood (of data points in batch [00600:00700]) = -0.66377074\n",
            "Iteration     7: Average log likelihood (of data points in batch [00700:00800]) = -0.67321231\n",
            "Iteration     8: Average log likelihood (of data points in batch [00800:00900]) = -0.66923613\n",
            "Iteration     9: Average log likelihood (of data points in batch [00900:01000]) = -0.67479446\n",
            "Iteration    10: Average log likelihood (of data points in batch [01000:01100]) = -0.66501639\n",
            "Iteration    11: Average log likelihood (of data points in batch [01100:01200]) = -0.65591964\n",
            "Iteration    12: Average log likelihood (of data points in batch [01200:01300]) = -0.66240398\n",
            "Iteration    13: Average log likelihood (of data points in batch [01300:01400]) = -0.66440641\n",
            "Iteration    14: Average log likelihood (of data points in batch [01400:01500]) = -0.65782757\n",
            "Iteration    15: Average log likelihood (of data points in batch [01500:01600]) = -0.64571479\n",
            "Iteration   100: Average log likelihood (of data points in batch [10000:10100]) = -0.60976663\n",
            "Iteration   200: Average log likelihood (of data points in batch [20000:20100]) = -0.54566060\n",
            "Iteration   300: Average log likelihood (of data points in batch [30000:30100]) = -0.48245740\n",
            "Iteration   400: Average log likelihood (of data points in batch [40000:40100]) = -0.46629313\n",
            "Iteration   500: Average log likelihood (of data points in batch [02300:02400]) = -0.47223389\n",
            "Iteration   600: Average log likelihood (of data points in batch [12300:12400]) = -0.52216798\n",
            "Iteration   700: Average log likelihood (of data points in batch [22300:22400]) = -0.52336683\n",
            "Iteration   800: Average log likelihood (of data points in batch [32300:32400]) = -0.46963453\n",
            "Iteration   900: Average log likelihood (of data points in batch [42300:42400]) = -0.47883783\n",
            "Iteration  1000: Average log likelihood (of data points in batch [04600:04700]) = -0.46988191\n",
            "Iteration  2000: Average log likelihood (of data points in batch [09200:09300]) = -0.46365531\n",
            "Iteration  3000: Average log likelihood (of data points in batch [13800:13900]) = -0.36466901\n",
            "Iteration  4000: Average log likelihood (of data points in batch [18400:18500]) = -0.51096892\n",
            "Iteration  5000: Average log likelihood (of data points in batch [23000:23100]) = -0.43544394\n",
            "Iteration  6000: Average log likelihood (of data points in batch [27600:27700]) = -0.45656653\n",
            "Iteration  7000: Average log likelihood (of data points in batch [32200:32300]) = -0.42656766\n",
            "Iteration  8000: Average log likelihood (of data points in batch [36800:36900]) = -0.39989352\n",
            "Iteration  9000: Average log likelihood (of data points in batch [41400:41500]) = -0.45267388\n",
            "Iteration 10000: Average log likelihood (of data points in batch [46000:46100]) = -0.45394262\n",
            "Iteration 20000: Average log likelihood (of data points in batch [44300:44400]) = -0.48958438\n",
            "Iteration 30000: Average log likelihood (of data points in batch [42600:42700]) = -0.41913672\n",
            "Iteration 40000: Average log likelihood (of data points in batch [40900:41000]) = -0.45899229\n",
            "Iteration 50000: Average log likelihood (of data points in batch [39200:39300]) = -0.46859254\n",
            "Iteration 60000: Average log likelihood (of data points in batch [37500:37600]) = -0.41599369\n",
            "Iteration 70000: Average log likelihood (of data points in batch [35800:35900]) = -0.49905981\n",
            "Iteration 80000: Average log likelihood (of data points in batch [34100:34200]) = -0.45494095\n",
            "Iteration 90000: Average log likelihood (of data points in batch [32400:32500]) = -0.43220080\n",
            "Iteration 95399: Average log likelihood (of data points in batch [47600:47700]) = -0.50265709\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Le8vTCzBzRlb"
      },
      "source": [
        "**22.** We compare the convergence of stochastic gradient ascent and batch gradient ascent in the following cell. Note that we apply smoothing with `smoothing_window=30`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "d_IIQGtPzRlc",
        "outputId": "9a212176-5767-480f-cc9b-816e2a0147aa"
      },
      "source": [
        "make_plot(log_likelihood_sgd, len_data=len(feature_matrix_train), batch_size=100,\n",
        "          smoothing_window=30, label='stochastic, step_size=1e-1')\n",
        "make_plot(log_likelihood_batch, len_data=len(feature_matrix_train), batch_size=len(feature_matrix_train),\n",
        "          smoothing_window=1, label='batch, step_size=5e-1')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "avUDC5mAzRle"
      },
      "source": [
        "**Quiz Question**: In the figure above, how many passes does batch gradient ascent need to achieve a similar log likelihood as stochastic gradient ascent? \n",
        "\n",
        "1. It's always better\n",
        "2. 10 passes\n",
        "3. 20 passes\n",
        "4. 150 passes or more"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ENoY_UgmzRlo"
      },
      "source": [
        "## Explore the effects of step sizes on stochastic gradient ascent"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J-M4dLl0zRlq"
      },
      "source": [
        "**23.** In previous sections, we chose step sizes for you. In practice, it helps to know how to choose good step sizes yourself.\n",
        "\n",
        "To start, we explore a wide range of step sizes that are equally spaced in the log space. Run stochastic gradient ascent with `step_size` set to 1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e1, and 1e2. Use the following set of parameters:\n",
        "* `initial_coefficients=np.zeros(194)`\n",
        "* `batch_size=100`\n",
        "* `max_iter` initialized so as to run 10 passes over the data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ceqPtWA-zRlr",
        "outputId": "c080a75a-52b2-41b6-e3e5-82b9d9bc50dc"
      },
      "source": [
        "batch_size = 100\n",
        "num_passes = 10\n",
        "num_iterations = num_passes * int(len(feature_matrix_train)/batch_size)\n",
        "\n",
        "coefficients_sgd = {}\n",
        "log_likelihood_sgd = {}\n",
        "for step_size in np.logspace(-4, 2, num=7):\n",
        "    coefficients_sgd[step_size], log_likelihood_sgd[step_size] = logistic_regression_SG(feature_matrix_train, sentiment_train,\n",
        "                                       initial_coefficients=np.zeros(194),\n",
        "                                       step_size=step_size, batch_size=batch_size, max_iter=num_iterations)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.69313622\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.69313170\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.69313585\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.69312487\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.69313157\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.69313113\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.69311121\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.69312692\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.69312115\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.69312811\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.69311286\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.69310301\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.69310725\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.69311567\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.69310836\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.69308342\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.69298918\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.69277472\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.69228764\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.69222554\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.69186710\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.69230650\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.69174220\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.69139955\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.69123818\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.69088883\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.68976850\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.68569701\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.68597545\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.68736824\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.69303759\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.69299241\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.69303389\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.69292442\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.69299113\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.69298668\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.69278828\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.69294460\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.69288708\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.69295651\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.69280480\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.69270635\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.69274924\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.69283249\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.69275924\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.69251197\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.69158805\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.68946852\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.68492418\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.68415366\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.68114554\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.68489867\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.68027821\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.67693088\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.67561867\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.67367588\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.66156206\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.62798175\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.64157978\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.64571292\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.69205420\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.69160695\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.69201686\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.69095428\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.69159348\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.69154386\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.68964000\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.69112685\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.69056997\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.69124730\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.68980179\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.68882576\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.68929536\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.69003572\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.68929307\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.68702353\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.67916061\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.66049079\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.63235099\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.62183600\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.61150928\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.62979300\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.61553432\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.59156014\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.58842264\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.59076267\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.54480104\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.45761063\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.54362587\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.56306510\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.68251093\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.67845294\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.68207160\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.67411325\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.67804438\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.67712546\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.66377074\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.67321231\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.66923613\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.67479446\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.66501639\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.65591964\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.66240398\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.66440641\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.65782757\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.64571479\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.60976663\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.54566060\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.48245740\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.46629313\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.47223389\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.52216798\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.52336683\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.46963453\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.47883783\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.46988191\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.46365531\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.36466901\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.51096892\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.54670667\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.61201447\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -0.58843678\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -0.59771677\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -0.58770466\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -0.56939710\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -0.57554451\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -0.54068090\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -0.55212916\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -0.55311029\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.57672007\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.55455807\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.49771894\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -0.54708765\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -0.54286814\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -0.52361054\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.49731367\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -0.50102061\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.42406927\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.35064478\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.38344116\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.40170047\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -0.45117863\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.46493371\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.45343350\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.43128394\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.43169967\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.43029376\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.32703099\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -0.49162447\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -0.52452720\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -0.51319004\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -2.20035379\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -3.34199720\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -3.06285156\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -2.80822162\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -2.99629286\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -2.71489944\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -3.61713200\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -1.19526584\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -0.75357081\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -0.71310829\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -0.59361318\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -1.53764659\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -2.69588686\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -1.89731473\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -0.81254441\n",
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -1.19013437\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -0.48968363\n",
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -0.72860037\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -0.58719556\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -0.31220572\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -1.89468446\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -0.96096585\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -0.66616640\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -0.46114004\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -0.47236476\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -0.45227508\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -0.29378688\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -2.47834692\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -2.48776279\n",
            "Iteration    0: Average log likelihood (of data points in batch [00000:00100]) = -2.44471310\n",
            "Iteration    1: Average log likelihood (of data points in batch [00100:00200]) = -36.66862050\n",
            "Iteration    2: Average log likelihood (of data points in batch [00200:00300]) = -25.49870239\n",
            "Iteration    3: Average log likelihood (of data points in batch [00300:00400]) = -40.14565040\n",
            "Iteration    4: Average log likelihood (of data points in batch [00400:00500]) = -27.03748522\n",
            "Iteration    5: Average log likelihood (of data points in batch [00500:00600]) = -32.62294582\n",
            "Iteration    6: Average log likelihood (of data points in batch [00600:00700]) = -25.88017915\n",
            "Iteration    7: Average log likelihood (of data points in batch [00700:00800]) = -37.30720216\n",
            "Iteration    8: Average log likelihood (of data points in batch [00800:00900]) = -10.87360529\n",
            "Iteration    9: Average log likelihood (of data points in batch [00900:01000]) = -6.60878996\n",
            "Iteration   10: Average log likelihood (of data points in batch [01000:01100]) = -7.15375088\n",
            "Iteration   11: Average log likelihood (of data points in batch [01100:01200]) = -6.04741293\n",
            "Iteration   12: Average log likelihood (of data points in batch [01200:01300]) = -18.17389834\n",
            "Iteration   13: Average log likelihood (of data points in batch [01300:01400]) = -27.14619228\n",
            "Iteration   14: Average log likelihood (of data points in batch [01400:01500]) = -20.50685042\n",
            "Iteration   15: Average log likelihood (of data points in batch [01500:01600]) = -7.74332305\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: RuntimeWarning: overflow encountered in exp\n",
            "  \"\"\"\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration  100: Average log likelihood (of data points in batch [10000:10100]) = -10.64501703\n",
            "Iteration  200: Average log likelihood (of data points in batch [20000:20100]) = -4.03616365\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: overflow encountered in exp\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration  300: Average log likelihood (of data points in batch [30000:30100]) = -16.55449105\n",
            "Iteration  400: Average log likelihood (of data points in batch [40000:40100]) = -2.91342906\n",
            "Iteration  500: Average log likelihood (of data points in batch [02300:02400]) = -2.25758434\n",
            "Iteration  600: Average log likelihood (of data points in batch [12300:12400]) = -12.07111794\n",
            "Iteration  700: Average log likelihood (of data points in batch [22300:22400]) = -10.11151499\n",
            "Iteration  800: Average log likelihood (of data points in batch [32300:32400]) = -5.19312737\n",
            "Iteration  900: Average log likelihood (of data points in batch [42300:42400]) = -5.13644971\n",
            "Iteration 1000: Average log likelihood (of data points in batch [04600:04700]) = -4.46804044\n",
            "Iteration 2000: Average log likelihood (of data points in batch [09200:09300]) = -2.44065337\n",
            "Iteration 3000: Average log likelihood (of data points in batch [13800:13900]) = -1.78679483\n",
            "Iteration 4000: Average log likelihood (of data points in batch [18400:18500]) = -25.43670604\n",
            "Iteration 4769: Average log likelihood (of data points in batch [47600:47700]) = -22.28502317\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uDeWuK3qzRls"
      },
      "source": [
        "### Plotting the log likelihood as a function of passes for each step size\n",
        "\n",
        "**24.** Now, we will plot the change in log likelihood using the `make_plot` for each of the following values of `step_size`:\n",
        "\n",
        "* `step_size = 1e-4`\n",
        "* `step_size = 1e-3`\n",
        "* `step_size = 1e-2`\n",
        "* `step_size = 1e-1`\n",
        "* `step_size = 1e0`\n",
        "* `step_size = 1e1`\n",
        "* `step_size = 1e2`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ohYURDB8zRlt"
      },
      "source": [
        "For consistency, we again apply `smoothing_window=30`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        },
        "id": "ljNIcJbszRlu",
        "outputId": "de178147-5f45-467b-93f2-7f3cc22df051"
      },
      "source": [
        "for step_size in np.logspace(-4, 2, num=7):\n",
        "    make_plot(log_likelihood_sgd[step_size], len_data=len(train_data), batch_size=100,\n",
        "              smoothing_window=30, label='step_size=%.1e'%step_size)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TXTA5OdpzRl2"
      },
      "source": [
        "Now, let us remove the step size `step_size = 1e2` and plot the rest of the curves."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        },
        "id": "K9aQagTOzRl4",
        "outputId": "9230a2b6-be4d-42e1-e5d5-261a0401bb35"
      },
      "source": [
        "for step_size in np.logspace(-4, 2, num=7)[0:6]:\n",
        "    make_plot(log_likelihood_sgd[step_size], len_data=len(train_data), batch_size=100,\n",
        "              smoothing_window=30, label='step_size=%.1e'%step_size)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UvQAISZK+BRyJzP1CiK6Ojn85irmi3HKObEnHy8+Vtr1CFW+/xXlG5j2tPNGqGDS2LZ2HtpCtSzmcy68zlTeAqybG4unrpjodoMbDn8UpREZN3DwNjJnek4UvKt+0anLtQ51o2saPsiITfiEetpvGhsXHObj2TJ3jGHh7WzrFNWfjouOyaU+HYz93810955DCmlaFq7ueSR9Z3wY/e+gf2TbfIHfZjbcuIjoGcsN/u9iWSwsrMFdamP/MFtX24dH+3PxYd9Vjg1Vg1X7YXTWxHTod/P3tkTrH035AUw5vTnd6/FXU5yFY9QCcPXktFsuF5yEfOakj5SUmWncLxsPHsZVn71/JbPklEb2LjjHTexLU3Fv1e1Sj2/CWJB3MvmABWpPJs4Yya7K6+Hf3duGuV/ri5qkuVi0WwbFt6ZzYkyXzO6zNmOk92bcmmcRdmQ0y5voyZnpPQltVuz2kJeTJpqareOiTOHatSiL7TDHpifkYSytt23pcG4GHtyubfrIvuqssYRazhfTEAiS9pGold4SkkxD1OCerXnbtnUNVrgwmo5kv/6d8mXJ111NRbra7/9ue7slPb6o/exxtOx8enjWUirJK4tenKqz4NbF3j7tucmdada6elSnOK2fe0+r3MTUc+Vs6e41eLPrf0obctGKO1pgtqIm9l/SG4oLE3LkdeGKtBDEIq59aLrAe+FYI0XB3OOVxQ4AzwOtCiJdrrP8bCBVCdHLQNxar6KzJNVgDNu4CjgkhHF4Rl5uYO7otnTUqD+aYPmEMnRCL3qCTOeA74sFPhmBwsVqv7F0wOr2ExXzpi3+Mf7kvfiEe9bJ81ZdOQ8LpMDicRa8qpxlr8tCncZjKzcx5wjkrljM4+z3fOr0HOp3UoDfyi8mUz6+issLMF1MdWwrPh4c+s/4ux7adRQhBh0HhNktwfkap4gXi1qd68Ms7uxt8HA1FtxEt6X9LG9Vta749bPdhcrkx/uW+6AwSvoEefP3YBplQq6LLVS3Y/0/KeR8jtm8YQye2Y+GL2yjMUgZoNBYDxrRh88/2c88/PGuozP+zoYjtG3bZ/f7tBzbDzdNA+4HN2LUySeYaURd3vtCHJs2qg5yykovIO1tCYU4525fXbd27nPANcmfCa+qzXw3BBYu5S4kkSW8B04BngD3AWKzVIG4UQvxWo90aIEIIoX4HRGbRc6oCxOUk5tSmZGrz0GdxfO7AMlabu17th6evq+qb4+VGh0HNOLQx7VIPgyHjYlj//bG6G2oouGlaVzKSCp2afqkvbp4GhVCY8vlVdi0jVwI3P9bNFl1Zlbbi+M6z/DXHaRdgjUvI4Dui2bDoeN0NNZg8eyimcjNfPer8VPflSmNGdjeImDuXqLc3EI7VWrZDCHHCca8LR5IkPfA0MAl5Oa+fa7VbB0QKISId7OserlAx54y/Tn0JifQluleowymMKwG1KcZLzTUPdmTv6mQyTqk7+/8badraDyRU/RGrEJYijAVfAaB374WLx6DzPl6LdgGkHMk77/7/Jm6/LwzPmNaqvkBqDN74GBsGfdDIo2o4gjP3kBXiOICpJp3iv+RgxwcacUQa/x/x8HHhvnfP/55VF/bEnFMetpIkuUuSNBc4gjUVydvAQuCoJElfS5JU/4RG9UAIYRZCvCaEiBBCuAkhOtcWcufaxTkScufafCuEkK60uqw5qcXnLeSmfH4VfW6KUt2WmVR4QUIuotPFT7FRk8BwL+59ZyD3v1//i2fEfzrU2abvzVH0vC7yPEYGnr5uXDWxHa27B9OyfRNuf6bXee2noQlrdekirtJPFCiEnMEk99IwFi6y/W0u34nFnGtb7hKtjHR1RH2EXPvD3yAJ+z5Mjuhy4DO72+57qx9jn+vdaLnKatJt7/kVt2mWtpHsibeS3KcrcRv+R3Rnq59boGshfXa8Qtz6qTQ/8w9+lhxanVrB0HVTMJivrFJeMQmLZct+BfbtEDpzBcHZzvkJy/aZf/6Pla77Zp53X3voK8saZb+XCt/CJDocOv+CU2FnHftqny/hqRsJT91At+SF3PqU/ZRPjYmz8e/vYa328CLQBvA59/9LwATg3cYYnIaVivLKOv247NFvdGsAel4byYOfDLngsYyc1JEh42LoMKgZ1zzYkesnd3bY3jfYg4c+icPT175z+rUPdiKoRf0dRofd044x03va9u0ob1ptYvuF0apzkMOIQUkn0eOaSJkDd31wPbadJk29uOaBToya2pXglj5Mnj3U6f49r4vkhke61N2wHgQWJdLh+0lc1ymV25/tRUQH+2kae+98jcCcgwQZk2XrQyJ8GP2EuoVjxP0daNWl2hE6xlD3FFPXA5/SY8971StqBZgHpSwgKPsAEadXEfDVk3Q6+Hmd+zwfQjN3MXT9VLrum0mztE302vWm3bY3TetKq4x1RCf8SNz6/xGQp/45g7IPcGbUSLyLUpj4Rn88fdQTCnsVpzJgyzMXNP5eu94koCCRzgdm1aufwVRCdMKPtmWdpZLmMydw1bopdFn9NF6lGeiEmejEX+ix4QVanf6DS5ttDlom/12v9j12v4urqZieu96i+Zl1xB5bSNf99kVOz93vADBo05O2dd7FZ9BXOvbHczeenxW4Y/yXBOTbv1b6bn/JYf+YY9/Lltsm/MRV66YwZNMTNMk/Vmd/e2Pqv/W5everi7Cz2+i98/V69/MuPkOPPe8SmrUHndm5lzq92YhffiI6cwXNz6yj3dEF9Nn+ssM+/vkJdDg0hzbtPOkwqBld983kqnVT7LZvd3QBMQmLiElYTMDJLRhOOR9B3ZA4m2fuDuBlIcQbNdadBF4/F9L8KDC1gcemASQfymHFJ+pviHe92pfVXx+ymxsJkCVXNbjoeeiTOD5/ZJ3DYzZr6283rUJQc2/8Q+X5jkY/3p2l7ysjx2qG5t/5Yh/mPK4eMBDZJYiobsGsW3hU5hPnaIossLk3MX2bytbZE10TXu9HYXY5y8/ls3P1MDD4jhgMrnoiOwdxYo96pN9N06yBzlVh6/Why4HPyFx3mMzHIHr7NnS+vlQkJaH392fy7KHs/SuZ7ctOqkZ0Nmvrz82PdgMJJEniPx8Mspsy5P73BmEsM/Hd8869ccYenIuoMFL+6Zt4m/NwXX0aml+v2ta7JJ0u54RTy7lz8Oovd+qt7fzdLXURlRM20gro8+QTZH30MRaTiWNx9q1WAJ6lZ9GbK/AozaTMU5l4U1+ZS6f4L2zLQTkH6RmVx66TzicMdYYqgdIk/xhN8q0+kd5FyRT7yDMpxR5dQNHNU2hVq/+ALc+wuX/1LdKz5CwdDs+l0mLi1OhbAOgt6Vk3RCkieu55F73FRNO0zaQ3G1CvcQ9dN0UmrgLyj+NiKsbkonxB6htwFI+lnwBwJjwOi85A07Pb0AllegxniD36HUdj75Kta5q2mbCMHezt9qjDvnqzEbPe/qSOe1k25R5BivW9dr2FT3EKLqYiTrQe7fAY0Qk/Ep663vb9+Ban4JtYd6CFd6k1qtulslT2IC/2asaOXs+q9ukY/xUVrj5khNq3wLc/PJejMeOx1PrcTfKOIiFwqSjE5Cq/jw3e+BgGs5H2h7/hcPt7Fft0K88lPH0z4en2p8c9y7IYum4KRT4tcakoxuTqQ7FXM45Hj8Wik0dMh6Vvpf2x6uqZIRm7yAxVvijHrZ+qei7XJjhrL50OfV1nu7rouv9T2+84ZONjHIm9i7NhfWmb8CNNz25jc7/XMRvklTB67n4br9IMLJLOdo57lWUyYMszHIm9C/fyHLxK0hGSnrCMHbiaqnOLMlv+XYenbiQ1XD4DFJhziKa1rH1nn3+B1n/+ccGft744K+bcAHumoe1Ya6dqNBCF2WUseE49B1sVYVG++AV7ctvTvexGolYlkKyJ3kWHTic5TAsRHm1fzPmFKMvGNG3jp3A+bz+wmSyppruXi9UZvcLML2/vJifVetGM+E8HW7ue17Ui72wpuekldB7anF7Xt1L9bGFRvtw0Tb2gh1qaDN9AD3wDPWROqRUpKaS8/gb+Yf2wlw+7Kru42meuyfhX+rLk3d2UFZkY2PwUrt+9J9t+vE9f2XLAuHF0f+F5uo+wCu3iPCNnTxbg6edKYLg3LlIlZ6Y+QsnmLYiyMpq+9ip3PtyFH2bLH0L3PxXJqZ5Wy2i/Xtey1esG67jb+nJ1PxPz5yutCK4V5/z3hCB71mzCJR0JKmKubcJPsuXk++4HQOfrCxYLluJi3IAb3p+LrlUM4uNnKEmoFpyZ71q/A2csOFXTdV0OzuJ0i+GcUnzdkmLJd+5zXGUwcCD2PrKDnLdehvoZCQuF/cflD9PAHPUEwB0Of8P2Pi9Wj9VUorh5V+FWUcDQdVPI84+m1DOU4Oz96C1yP06dMDN44+NsGPQ+YBWLvXa/bfuEMQmL6yXm+m99TvEd6y0muu7/lOQWV+NaUUDk6T9wUbEotUhd5/Rx7NHs7FYqDe4kthkDgH/eMdodt1qJeux5lz1dH0Po1K2R3fd+wM6eT8vWDdr0BDpLJZKwoBNmiryby9q0SFmDT7H1Omieul5VzPXd/hKeZc7l0uuz4xW2935Bts6rxH6QlbeDbcHZ+zDr3TkefYfq9sikVYRl7iYgP1Em+n0LTtqugX7bXyahzRiKvZvRMvlvQrOqX5LtTft6lziXTkgCfIusVnYPYy6+RadxqyjgVOR1uJiKaXFmLQF5x5GQPxs6HvmG/LQN7On2GACdD84mMCceCYhb/wgnW40iueUIu8ftaEfIDdkwjfWDP3Jq7O0Pz8XVVG20kBC0P7qA9kcX2NZ1PfAppyKvx6JzISj7AOFpG9BbrM+k2i8rbhUFdHXgGqFGdMIihZjrcFg55WvKaJQsbXXibJ65pUCCEEJR0kuSpHeAaCHEzY0wvkvOpQiA+PrxDRhLlOH7NalZv89elKu9Gn85qcV2p23vf38QOr2kmjcsLMqPW5/qYXdMZ47lsXrOIWJ6h9J3dGuHCSWLcstxcdOrJn2tWWJHWIQiF1ddkULmSgt7/jyNwVVP12EtFAkxK3NySBhgLX0jkFgb96liHw99EockKsmeORNLWTn6m8bz4yylz2Jk0iqikn5D5+1N9M4dHG3X3uHYqmj6xhv4jb5ZtU5k7vffk/HKq4r1xaMeIiVkIAFhnrQr3kzex+/LtvvcOga/Cfdw5marqKtw8WbTgLdt21ud+p1Wp1cq9lviGcb23s/blt3Lsum742WnrTV+t95CwS9L7G6Pb38/mXYcz7vv/QD/Wr5LK7u0li2H5xbRJcV+nrRKvRvJLYbhe9tYDMu+pqhMT8I5cVGT9ke+JSzDmox5b5dHyAuoTlRqbxpFAIfb3WOztkQn/Ejz1MaNjN3c7zWMbnKro8FUQqWLvD5tt70fElBwebj+WiQ9Fp1B4UdXqXfD6OZPmXsQBzpPtq3vu+1FPMuzEUgU+bTEzZiPW4V6UIwA8gJi0VlM+BWckInXUo8QttUQ2wM3z5A99J1hR48ZFPtU593sv/VZ3I35BE2eTPYs5ZR1gU8ku3s8KVsXfXwRzdOsLzP/2LFE17Sgpof24UTUjbiYSmh/dD4+xXXnzrS376rv8lJS4eLDjp4zqHDzp03iEgyVpZj1bjQ9uw2D2X7uTbPORVXQDdw8nVLPUPL8ownMPWQToQBN7r+P3DlzG+Vz1IVAIiuoC0U+LYk8vdImFmviFh1Nq6VLkPSNU6P5QpMGDwIWAL8DPwEZQChwO3Ad1pxttlcWIcSVlRjGARdbzK3+Op6EOhJ8qpXJqV08Prp3KMPvs+/gn5tewg8vy0vjGFx1PDgzDlBP7lmzIsTFpCi3nPj1qXj6utJhULMLLmR+JLadbLncvQn7R75NSUEFsf3CiLsrFp1OUggz75/X8+un8kzkNW/QhqZNqUx3Puluk/vvw+fqq/Ho2hVJZxW+xlOnOHntdXb7hH/8Md5xQzjWxWGuaxsCKPBrjYupGM/SDLuWsgoXb5JbXI1F50rzM2sb9OGQGdSV+I6TVLepiajaYq5pfjHdTtf/bdciGch46gfKk1MI//l5XE0lsu1mnQEh6et05LdIOgp9W2GoLHNomWkoTAZPNg60uiG7VBTSZ+cbuJqKSJeAR50AACAASURBVGh9Cyktrgag3ZF5NM04Pz9ae7SY8zUp9/9HdZvO1xdLoTwqO2LBfE5PmNigY2hMgv77X7I/Vb64lXiGsqfrNEyuvnQ4NMdmDYuNP8jRjuppTOPb30tmiPV5GntsIc3SrQly3dq2IbnAj0Pt75O177XrTYVgEzhnua6JpdY0ffMza4lOVMQCXlFYJB3xHSaRHWSdZRiy4X+qIgkg/KOP8OzTm4R+jZfHrb549OyB34034taqFe7t26Pz8qq70wVwoWKu5it6zQ6SyjqEEI0jSS8BF1PMzX1qk62Woz3639qGbsPVq6EJIUg+nIt3gJtThb33/5PCph+rI1n/8+Fg3GrUNBVCcGRLOkkHsgmL8qPrsBYOa+hdCoTFQtZHH1OwYgX+t9xC8CP/VWyXdDqEyYTk4kLa9BkULF+u2E/o88/RZPx4W5+UBx+iZKPSTy3vjRXEr0/Fz8NIzMoX7FoTzgfvq66i+J86sp3r9WA+v4jLS4VF0rFuyCeK9YE5B20+eTWpLeaCC0voderiJEiNPXiAvEWLKd60kZL1zue7Cv7fVLI+brioQYtkoNQzBI+yLNlUbbmbPy6mUvQW9ftE07feJH3G06rbHBH4wAOEPGb1cRMWC2V79lCydRs+w4fhFhODKC0l9cmnKN29G59hV9P05ZcRRiPHelyayD2/MbdS8PMvTrePXPQDhuBgEq8e5lR777g4Wnw+G2NiIidvGOVUH9eICDz79yN30Y8kRVxLUqT1paz94bmEZdadnLr1339zYpj6+HxGjEAyGChcqbSsA0StWknqo49hPGotwdXq1+W4R0cDYDEaSX3scYrXrHHqc1TR4quv8OzerVF+Y/cOHSg/pO7aYI/gRx8l6EFrqpjjAwdhznbuhVPn54eloADXNq0JnjqV1Kn/q/d4HRG9bSt6/wuvE+0sFyrmnKq7WoUQYl592l/OXCwxl7Arg9Vf2z+5/YI96HdLa6K6BqtOzZ0vpYUVlJeYCAjzbND91peaU6vOYMrIIHFInOq2iO+/x611FMcHDgKT87nnon7/DdeoKIdTpSFPPYXPTTdxYkD9nNT/7ZR6BLOtz0uydVWO3bWpLeYArtvf6Oks8bnmGpp/VJ3aI3v2bKcEmu+Nowh/5x3Spk+nYPmvsm1egwZRmZ2N8Ujd5dRafvsNyfcoHdydpeW33+DVty+Fq1aR+uhjTvfzGjyIFl98cV7Xf20rdxVt/llD4lVX13t/ztBm/TpcQkNJGDSYyix137iQ6dPxu/km9P7+ss9VtHYtOZ9/gWtUFKHPPsPxnurBCjF796DzsDpvCiFACCSdjpOjRmFMUJ/abrNhPcYjR0h58CG7Y7cn2Npu2YyhSRPV79OjSxciFy+i4swZTgwbrrrfdkfrPr9Ktm2znV/6wEAMoSEYD6v3izmwH52r1RW+bP9+ksaq+wE6g2vr1lScqL5+wz+Zic+wYU67pFRR8zMKs5mzL79C/o8/Inl6EvHtN5gLCkiZJM8LGL1tK0IITKlpuMfGIBkMiIoK8hYtJuONN2Rtw156CY9uXXGLjqb8wAHZZ267dYuqNTBg4gTCnrmwKPT6ckVXgLiUXAwxZ69obxUT3+h/UXJUXWyEEGS++x65c6v9H3yGDyPsxRcxBCmj2ADKjx3n1E03Ncp4PHv3xpiQgDnPcXoB/zvGkr9oscM2AC2+/ILMd9+1e/O/VLT48gtSHniwznb+t40h/6f6T+G0/GYuyfdap5l8hg+n6K+/AKv5PqdJB0wuXoRk7bVZnAInTcJv9M2cvO56BLDKjphzi44m4vvvMefmcGLEyHqPqy7abt2CIUDuq6b2cNUHBtJ61Uryf/oZj+7d8OxWHYxTmZXF6Yl3I7m5EfLYo3gPHgxUW7vQ6Tg9brxin549exLx3QISrrqKyrT61cf1v/12wl54HslQbVU/M/V/FK1eDSgfpp49exL44IO4NA/HUlCAe5cu5/0ip/b9NH3jDfxvGU3+L0tIf1Y98tMZolatxHQmlZRJ1VP0gQ89SMi0aQBkffqZ6rSpztubmF07nTqGPTFqTxwJk4mjnZTpmAwhIbTdsB4hhF2REvXbCtzatMF48iQnr6sOOnJv355WS6xWRlFZydlXXqVs3z5cW0cROmMGLqGh5z1eZzAXl2DOzaH88GE8unfHJUQZUW48cYKT199gW/a/bQxNX7X69Vbm5pLQ3/7LbZUwrP3Cbi4oUASH2SPi++/x7K4e9FYbU1oaxoQEPHv3tgny80EIgTk/H72fH5JOR+Hq1QqrXtSKX3Fr2/a8j3E+aGLuPLkYYm7/mhTVxL13vdoXv+D6p8W4mJjOnqXi5Ek8+/VTfSBYSksxFxfLbhBCCFKnPUrRn3/a3W/Egvl4dO8ucyKtGbhwJdBm3VoQgoy338GYmEBFYv2tS23WryfloYccWnYkV1dEhXN5l3xGjqT5x9UOxzlz5tgiT2vT7ugRyuIPkTRGGUzQ4ssvyJ41m7J9+2Trm3/6CT41LA+WkhKH0zRZ3h4k9O+O3sWVzvmluG7Zzp+dlWLusUUrZOdXRXIyJVu3cfbFFxVtzxe1B6K5qIjjvXrblvVBQURvurCavLUffu4dOhC5eBGSwYApM5PEwc7lg3SLjSVq2VLVbUIIyuPj0Qc0wbV5OBUpKZRs3oJnr564tVZ+v+eL6exZEuOqcyf63nAD4e9Vpx0t2baNilOnOPvyK4q+ET98z+k7xynWxx4+ZPMhBes9pGTbdvR+vlb/0nP3hMqsLBIGDVb0r2lVqnP8Kt934KRJhDxu37KZ/vzzipecmufOsZ69sBQX1+4ma1P4xx9kvv8B+oAAmr31Fm5RtRPdqFO0di1nHq4OJLEA+nfewK9de5q2jXFqH41F2cGDlO7YibmwkLxFi/Do0J7QZ591eL6Z8/M53ref6jbfUaNwi2qF16DBeHSsO8H7xSB34UIyXn0NgJAnnyDw/vsv+hg0MXeeXAwx9/1L28g7K8+Cf82DHWndTfmGdDlR+y0xZvcumfNn6c6dCgdpr/79kVxcKF7vfESg5OaGPrBJvS0Wl5ra4kAIQdnefZwep3yA1Ubv70/0Nmt6muJNm0n5j7pjeuu/rNaXE8PlqQGa3Hsvud98o2jfdvMmDIHVVTsqs7NJGKisnlF7+qBozRpyvp5D8LRpePWxipvKrCzSnn2Wkg1WcdNy3jzbNoDKigp0ej0JffqqPtwEsLZdS8pdrRHNAU2bMWrAcOb/rPTSmLZwKXqDMvLZlJ5O4tDq6GY1R/2atFm/HlFhVHxfrf/8A9eICNU+hX/8SeZ776H386PpG6/jHtO4D838X34h/dnqZK3NZ82iPP4g2bNmy9rFHjl8SV0jalKZm4ve2xvJgYjKW7SYsy+9BECrpUtwb9cO48lTnLyuOuAnNv6gzMJYFzX3CfLpUWc5+8Yb5M2vTnFR1/dqMRpJuvNO2xRl7XOnYPly0qbPkPUJ/2QmvsPVp0jrS+b7H5DzlbXc3f7BvUgtsFZIuereB+l2jXP+fZcTwmTiWPceiHMuMQHjxuE3ejQenToq2ibmJWIWZtr4t0FvJ+XNxSK3PJchi60vAvd0uIfHez5+UY6ribnz5GKIuQXPbaEwWx6+PXn20MvmRl0bYbFwtL36m1K7o0ewVFRQunOn3ci4y4WYA/s51tlxjrK2W7eQO2cOOV/Xr4RM7KF4h6HpQghEWRlFf/2luPH7Xncdzd5/T/b7Z370ETmffyFr1/rvv3Btbs2RZykv58yU/1KyeTOBDz9E8NSplG7fLvPBcmvblqgVcp8ugOwvviTrQ3kZqNZ//41r83DnP3AtTu3dxarPPsBUXk4XXAndpcyRVamTWN1JXmbu/plfM2eq8rz57zc/4ubpnJU6d/4ChT8MQNtNG2XT92Xxhyjbtw//0Tc3egRafRBCkP/zz5Rs2IDXgIH4j70dSZIoP3aMrE8+QefuQdhzz15Up+vLGSEElpJS9N7n/xuWxR/CnJeHV/9+TqeUqAqqUqyvqCD9+RdsgVbeV19N85kfN3iqivyMs4pr5fHFvzXoMRwhhCBx51aMpaXE9h+MwUlr6PlgERZG/jKSsyXVgVA7xu/Aw+CBEIIlCUv49tC3jIkew90d6uXi7zQmswkXvfX3zinLIe7HOEWbn0f9TEyTxn3Z08TcedLYYq6irJKvHtsgiwce91IfAsIun4cLXLgT7KXEa9AgRWSq15DBtPziC5nZvDZVPi6OfDsMTZvSfOZMkm67DQDPfn2JULGIOYO5oABzUbGqiBJCcPrOcbZpzYiF3+HZw37OvyqKN28me+Yn6Js0IXjaNNxjolXbpT39DAVLrVN2XgMH0vLrr87rM1Qx74kpZKecBkCn03H1/hO4WOR56/Q9urGiUm5FG/f6+3z/rPIN9+GvFuLp6+f08Y0JCSTdNQFLgTXaOPjxxwiapJ4eRUOjMRAWC8JovCC/LUecPrCPn1+Xl9uq7Y7QmGxatIDtS62+wxGduzHmWWVuTDUS8hJYeGQhIyJG0D+87hQjZouZ/j/0p7SyVLFtyY1LuOXXW2TrvFy82DZOnti7wFhAqamUs6Vn6RTUCYNObv21CAs6ST1TQ3JhMtcvtfo4Dm4+mM+u/ow3t7/J90e/V22/f+J+u/tqCOyJOeft2RqNQsapQpmQC2jqddkJucq8vMtSyDV77z107m6YMjLwGTYMvbc3p++9j/IDB2xtQp95miYTJ1JxJtUWReY7ahTN3rEm0w0YO1ZVzLVZvx6XUOs0t97PvojwjhuCR6eOtDt6pN4RubXR+/nZPZYkSUT88D3GhAQMwcEKR3274xswAG8nIm+bvv4a3kMGYykpxfcG9fJezmIxm21CDsBisVDi5oJ/mTxyNfSVV+CZabJ1xhJ5Lria+6wPbm3bErN9W71/k8LsLAyurvUSjhoaQgi2pm3lZMFJhkcMJ9QrFEmnQ6pDyFmEhSfWP8Ffp/8i3DucRdcvwt9daXEtMBbg5eKFRVhw1VstYDX9CqswlpTg7u1NiamEN7a/QVJBEje3vZnbom+ztckoyeDv5L/xMHjg5+pH32Z98XJRPnOyy7KZsXEGMQExTOk6BU8XuWW8SsgBnD6wl4LMDPxCqoM1hBCkFqey6tQqWvq2ZETECK5dci2pxakA/JJgDfr4e8zfhHqFooYQgq4L7OfUrC3kAEpMJTyz8Rmi/KP4eM/HdvsGeQQR7BHMkVylr+z0XtO5q721TF2VkAPYcGYDo5ePJjHfflDbK1tf4aX+L9nd3lholrk6aGzL3M7fT7FjRXVlgfYDmjJ0gnrEUmMihKBg2XKyP5+N6bQ127Znz560XDC/3iHk9SX2UDzlh4+QNmOGLOrOEWEvvUjAHeoCU5hMmFJTMTRr5pQjdGVeHqn/m0bpjh2Ef/wxPiOGKwRAxenTnBh5jerYGyvT95VKSX4enz84QbZu/BsfUjb9GcrjrUmXm77+Orohg/hqijwVx81PPc+yd5Rv+JM+m4tvUOP6kG5evIBtSxajd3Hh2imPE9Pvygm2+TdxpugM0zdMZ3jEcO7ucHeDWqLMFjOPrnuUtSnWqjNdgrtwY+sbuaXtLQprTk06zZMnF+7TtA9fj5CXsdqcupmH/q5OW7L1zq18ffBr5sTLXThm9J7BuNhxSJJEQl6CQrDc1e4upveeztYtv7PlY7kf5bIRWeQblBasKrqHdGdPprKO9uY7N+NboyZsqamUPt/3kbUZGzOWZ/s8a/u+3x97g2y7bkIvBva8jl5hvbAIC13mO19mT82aJYTg5a0v20TflUKAWwBrbltjm5JtaC7YMidJkitwLRAD1M6TIYQQztlYNWScPSFPOhsadWksAskTJlJaS7SW7trFyVEN4FArSYR/8L5q7qvABx5A0uvx6NSRZq+/RvJ/JmEpLsazVy9azPka47FjJN12u629zs+Ptmv/QefAf0pyccE1MtLp4RkCAoiY7zg1omtEBDH793HyuusxpVrfLFvM+fpfKeSWv/c6iTutwRljX36b5rFy/8myImUAgrBYaPWztd5rlbUsP0OZCNhsJy+gpbJxEyWXFhawbcli2xg2/TDvXyfmLBYzGScS8QoIaHThfL4cyTnC7b9Z7wcHsg/w/u73OXj3QUU7o9lIZmkmFeYKZu+fzZ9J1sj5QeGD+CDuA9wN6qmentzwpE3IAezP2s/+rP38cPQHlt6kHjnc8ztltPb29O0UVRTh4+rDH0l/8OT6JxVt+v2gHsX51o63eGvHW/w06iduW3GbYvt3R75jfLvxvLz5JYYjt2hVmIwOn+pqQg5gwA8DuCHqBn47ad/nbvGxxSw+Vm2Nuwd5wNCvJ35lbo41yndszFj7g1Chy/wu7LlrDy56FwqMBQxcdOVee5IkcarwFNEB6i4tjYVTYk6SpGbAJiASeRWSmmY9TczVEyEEGaflD76mrS++mMtbtFgh5KqonU7DaNAjAPdKM25t29Bq+XIKfv3VbtZ5lxYtaP37b0iurugDmlB+KB7vIUPQBwba8vdU4dG1K63/Wk1lZhZubVqfE3mdaLN+PXnfLcA1IgLfUaPQubmpHqux0bm50Xr1n5QfPoxLeDiGJk0uyTguJRknE21CDmDxi9MVTtdlhcqqGDWnSave7NWEmz0xZzY7rlV8oWQmySsQ5mdcWZHTF4oQgiVvvsTpA3sxuLhy0xPPEtnVvk/m7H2zmbXfWrf03o738lgP55MU18W+zH1MWGW17I6IGMFNbW5iYPhAjucdtwm5mixPXM5NbapzT+48u5P7/rxP0Q5gY+pGei3sxfRe08k35vPFgS94uvfT3Bl7J1llWfx1+i/Vfon5iTLr2++jf6elb0u2pG7BaKcc3Kx9s7gh6gZVIecMakKuimuXXEsLoZzC1Ynzt1I6EnLOINVQAzVFn7N0/647H8V9xLR10+pufBkxqdMkTuSf4J+Uf3ig8wPc3/F+xZT0xcBZy9y7QBYwGEgG+pxbvg8YC4yw31XDHmVFJowl1Q8pg6sO/5CGPwnMBQUkDh+BpbCQoMmTCXrkv7YHaunevbLQfkek+XtzoEUwFp2OXnEjGPzwVAD8brpJIeZ0Pj5Eb9ksi/by6tsHr75y031tDAEBCn8wl9AQQh6/OGHfdVElMP+trJkzu842apY5i0VpWausUD4EK+2IOdHIJcwqStV99a4kFhxewJKEJTza41EGN1fmX7PH1rStvLfsefofsFqrKk0V/PnlJ9z50Uw8DZ5ISOh1eoQQHM87zqJji/j5eHWetW/ivyGvPI9p3afZIvyCPYJZfMNigj2DEUJQWFGIn5v9F1WLsLDq1Cr+SPqDdSnrbOtXn17N6tOriWsex7oz61T7Prf5OWKbxBLhG0GvheoVHWrz9s63bX+/ueNN9mXuY1XSKqf6gtWPas1ta3jwb/vJt7878h3fHfnO6X3WF0nFQ0pnUa67eFz4dHddQq5KRNee1ga4sfWN/HpCGa3f2EztPpX88nxe1b0qm6q+2Dgr5gYBTwBVVaYtQogk4AVJkvTATKBx0vL/PyY/Q/4A8Q/1RNI1jP9H7UoJFXodJZ5umGfPJnvWLEKefBLP3r1Vk3baY19EtUl/57rV9L13Eq7uHkiSRLujR8j+/HOyPvoY1zatiVy0WDVsX+PKpjg/t842atY1tQCGSpVEx/Ytc40s5srKFOsuNKDlYpFdls3QH6sT905ZMwWAn0b9RGyTWNU+paZSPAweDFk8hDxjHp3TfanpPVOck82AH5wvWbcscRnLEpfZlrPKsrjqp6sU7X64/gf8XP2YvGYySYVJgNWy90284whwe0KuikfXPUpKUYrT461NfYRcFVf/1DjlypxFZ1GemxdimbuYvDvk3XpbLPdN2GfLLbf5zs2y8/PFfi8yJnoM93S4RzUoAsDfzZ/XB77OrH2zOJSjLJ0ZHRDN8bzjdo9/a9tbFf57H8ZZUzqpBa1cbJwVc4FAmhDCIklSCVDTdPIP8F/1bhqOqJ0ouKGiWE2ZmTIhV+zmwrbW4VS46PE0VjDw+Bky333XwR6cozg3hybNmtuWgx56iKCH7Ncl1LjyCY9pz9FsecJni8WMrkYCT4tFaR5Qs6yVqAjDSpN6JQtLI0+zlpcokxrnluQQ6K1eVq4mW9O28sBf1pqQ866ZR/fQ7oo2ZouZtOI0Jv4xkUJjIfOvnU+HoGpfw/zyfA7nHKZTcCd8XH0U/S3CghBClih1d8Zu3tz+JsfyjqmOy9E0nWL/F0kD3Pn7nYp1dQk5Z7gQIWePBzo/wJcHvmzw/dpj0x2bHPqK6SU9ZlF9HakJNx+9N/f2uIfB4YNp6dsSV70reeV5zNg4gy1pW2ztpnabysQOE1X9/WoS7BHM24PftjttXRM1SyFYAzrGRI/hYNZBWvu3xtfVF71Oz9AWQ+s8fhVrb18rO/d9XX1VfSXbBrRl+7jtJBcl09q/NS46q0GhZuqRwc0HY7KYOJB1gGZezWjq3VSxn2/jv+X93e/blvdP3I/JYiI+O152vV3d8tIK+po4K+bOAFV3tRNYp1X/PrfcGyhX66ThGKWYa5gp1tqFnk8F+1HhYr0QSt1cORQeTJeUTNW+QZMn4z/mVkWRbLWbfVF2tkzMafz/5+hmZeWOX15/gduef922rDalqmZZ27FcGaVmKle/lTR2AESZStWI4YuuwuQi+Ozqz2TTllUWuzXJa3h5y8vkGatr+d79x922ZKbH847z28nfOJh1kF0Zcp/UO36/g0U3LKJDYAce+ushNqfJazOvvX0tge6BLD+xnOc3Py/b9p7rI+xdsYxij0rOds8C7wv//BZ7T+JLhYDY0z40y3YnsXkxyWFKy2l9aenTkuSiZKfaRgdE80i3R9iculnViqNGr7BejGk7hukbp6tu10t6dt61k0pLJb0XVldK8TR4svb2tXi6eLJz/E5WnVrFC1tekPVdd/s63A3u9P2+Ot+l2k82Z9hXNG0bg7BYyE1PxTsgkADPAL4Ybk04Xmoqxd3gbhM2O8bv4Iv9X9giaj+I+4BhLavL8VVZpnfdtYs7f7+ThDxl2ckqpnZ7hOdOy0sD3tzmZsa3s9Yi7hkmF25uejcOTDxA5/nKWrdgFWbzrpmn+nLjCE8XT4VFunakrIvOhR6h9n1C7+l4D7dG30qJqYQwrzDbeH++sf61qi8Wzoq5tcAQYBnwBfCZJEldARMw8tw6jXpSW8z5h164mDOePKmo45kSKPdVSW3iQ6usfHzL5VYQv9GjCZ76CABRK38n/fkXKNu9G0NoKK7DroL4HbL2P7/+HIPG3UPvm5S1OzX+PSTHy6s7CLPSMqcm8DJOKh8MFeXqD22LuZLyynLc9G4NPvX5T/I/LDgwh47I/V30FgkTgilrpvBoj0eJ8I1g2tq6nbNrPqgdccdvd7Di5hUKIQfIpk1r4lmmJ37lr7igI6DYlS4J/mzolu3U8RwhGi/H6XnR45g/nU5a71stMz1ZNjCNfF/1KXh7zOg9g64hXekQWG0BnRs/lw93f+igl5WfRlkjrxfdsIjfT/7Olwe+pENgB9JL0hXCvIo5I6yCSE3MtQ9sz+IbrEEBLjoXNt2xiT+T/sTH1YdhEcNsFiR3gzuj245mdNvRgDUq101fHfC1bdw2m6BTs8yZzZUIIVj23muc3L0DvYsLNz7+DFHdrL6EtR3zPQweTOsxjWk9HJ/Xbno3lty4hAJjAacKTtEhsAMzV46WtekR0oODcVZrWXZZNr6uvracePaQJImDdx9kbfJapq61+mAHeQTxzchviPSLdNi3sfFx9am3kLyUOCvmngOaAAghZkuSZMAa+OAJvAMoqyhr1Eltn7mGmGY9+9LLTrU70iyQPierI/a8hw6l2ZvVJZDcoqKIXFjtvJuXngrT5GIOYOsvP2hiTkOGmn+cswEM9ixz96+6n/Rd1m2B7oGsG7uOA1kHGL/S+tZf03omhEAgFG/jRrORJQlL2Je5j6d7P42/uz9LE5bywpYX6GNRJmE2mKsfls4IgPNh1LL6pf4Jz5ZHMEalezWImDsfy1xNYVGTEI8QMsvULf/OUiXkqhiyL4jlg633q7/G/EWQRxCrk1arCqcm7k1YP1a99vN9He/jvo7WKUOzxayakDaueZzs3Lk+6nquj6pOHLvwyELe2vGWbfm6Vtfx9uDqgIonez7Ju7vkbiyfXf2ZbNnPzY/bY5SRubWpKeTAWt3g4N0HqbRUsmXlz+w8KA+wsFSayU5O4uRu673abDKxedF3NjF3ofi5+dE1xH4S3yqCPOp2T6jJ0JZDVadNNZzHKTEnhMgGsmssfwJ80liD+jdQWWGmMKfGg0sC/5D6l33JmfsNme+8c66s1MeU7pALLp2fH5KkQwi5tSTHp/oNLWbPbod528B+Zv5Ko5FKkwmDFuxgl6Ob1/P317POJaN9jMguSp+qKwUv/wBK8vMctlHzmSs2Kn3S1Pjl8I+0UZk31NXQGjnlOYpotilrpiii2aZ0ncLdHe5macJS1iSvYcfZ6mtj5amV8v2r+BHoL5YjWQMR6RvJD9f/wIN/PciB7AN1dzjH0BZDuSdsBGsPfS5bP3/Et3QN626zhFaYK0gqTKK1X2ub/9JfY/5i+M/VBeS7BHdhwbULkCQJo9nIm9vfJKcsh6taXqWYOqyqq1lutt4He4f15vNhn+Oid+H9lfKEtAHFrkzuOplxseNsUbEjI0cqxFzvsN7MGelcHWW9Ts/ckXMV/mB1Ze8f3248YZ5hbE3fysDwgcS1iJNtvzP2TjalbmJrujWFz8rRK+stburCoDPgY1C+/FvMlaQnyp34M5OcS8ReH9SKDdR+xmhcXJzNM/cPMFkIcVRlWzTwuRBCGbqkYZf8zDJZlj7fQHcMrs4noC3duZPTEybalivT02XJdatotXgRQbM/IKtWHi2AmEPx6JxMgQAXDQAAIABJREFUeltZaX+KI+3YEVp2VPd7+LdjsZhZO+8rjOdSX/zz7Zfc9+HndfS6MHLOJJN86AAtO3QmsHnLevffdXYX+cZ88ox5FBgLuKvdXbYkqz5BwapizmSq4Lek3/nm0DcExJfQGfmLycubX+KBFmabhSO7LJuMgHJC8+TJW2taw2riTJRe7bQEn+37jM/2fWantRw14aY3X2Zzj4BQsaCNihrFc32fs02hLbx+IQBZpVn4ulmnjn8+/jO/nviVx3s8Tu+m1mngmk7hu39frthvO58Y2ZS2q95VkQg1zCuMg3cfxGQxYZAMsvZuejeZMGof2J4xK6xW/MldJ/Nwl4ed/tyhUW25q1Z7vU7Pvgn7WJK4hPLKcm5sfaPD9Cdq9Arrxdrb19qmteeOnEugR6CsTWF2FpsXzcdcWcmAOyYQENaMqyOu5uoIded3F70LX474stGjoS0q7gyFWZlwESKwhcoLm9p4NC4ezk6zxgH2Eqj4YPWn06gHfiEe3PJEd/IySsk7W4qLq/MPjsKVK0l9zLm8a66RkWCnZFt5cRGefs6FVDuaJjOWOmd1+TdSVlhIaUG+bTkv7UyjHi8nNYXvnn6UygojOr2BCW9/TFALa6Z2k9nEB7s/YG3KWp7q9RRDWwzFaDYiEHgYrOJr0upJbEuXF6n+eM/HPNbjMUI8Q8gsUlZtAOg7rycVLtbzzNPkC7XEnE7AjI0zaB/YnlZ+rRi7Yiy9LMpz3qVS/TpQs5w1JGr7f73vKzx8ZEadfUe3Gc0j3R7hje1v8Hfy34rtzb2bM7X7VEZGjkQn6bh71d2qmfhvbnMzbf3bKqbowGoBm394PjuTlFUIXhvwqiyauIpgz2Db3+Pbjbc5oldRcypRLYp49+9LGTB2gmK9GlU+X46IaRJz3lNpHj7qvks6ScdgQzdcfTzqLeSqCPIIcjiuP2d/SHK81dKZm57KxLdnOrXfxk5ro+aHum3JYvqNUUYMN/yxnfOL/TdgMZs5cyQed28fQiKjLtk4nC7nhbzaQ01aA9rTvJ64uOpp2safpm3ql5+mKpebMwSMt9681ZKzgv0ErWqoXbxV2MsNpqGOudKE3tAw09JZpVmsP7OeayKvwdvVm92/LbX93hZzJWvmzmbsi29xpugM1y651tbvf2v/J9vPc32eI8o/SiHkqvhg9wcA3FTSlACUTs2GSh0VLtabuU7lTiGds6zduOxG2zq9RZkSwL5lTnV1g6GWbLWFR7ginxXAlju3UF5Zzsy9MxkQPoBrIq01ez8cavWrq7RUkm/Mtzu1Nu/aedy+4nZZge/JXSbzcFer5Wloi6EcyT2Cu8GdLsFdbCLlqV5P8edhb+IPy6eIK41GXD0uLHhK7RretmQxvW++DRc39dJXFxU7wujvrz/jwN9/ADDsP1PoMvxa1XYXQpWQA8hKOkl5STHuXhcWQlyUk83KT94jJzWFbtfcQN9b7qi3+LNUKtP1FOVkNUTu3joRKsJNzVf238BvH71Nwg5r2per759M1xHXXZJx2BVzkiTdC1RVwRbAl5IkFdVq5gF0BNY0zvA0aiIqKpwWcmCtewpQYcepXM1UbvfYjsScyk1Fw4raDc5UbkTv7VjM5ZfncyzvGKm791GcmEyr7r0YOOgm2Q3/rpV3sT/LGkn68lZr4Mv9O+Qh+WcOx6tmS6/Na9tfq7MN2LeQeRj1lHpYP6uzmenVpjYNdqY2G9sy52fwAeSDrKyosJvPysfVh1cHqFcwNOgMdfpI/TjqR47kHGFtylpGRo6ktX9r27YWvi1o4dtCtV/8ypWKdRXl5Rcu5uy4UZxNPE6LDpfehULt1y8vLubgP6tty39//Rmdh11zQRaxlMMHyTx1gja9+uEXEqo+ndgA97udK37hzJF4ALb8uJCWHboQHtu+XvuwawlTuf5q54K8UFS/l3+hZa4kP88m5ADWzJl1+Yk5rHe2ql9HqrVcRQ4wG3gbjUYnbYb6lI9H166U7dunWO8Sai2WXZKnnrW/Phefo7YXYpkTQrBu/tccWPMHIRFRjHp0Bt5NAuvueAWQUZLBskM/KNZXlJfh7m3/zX7eoXm8t+s9wrLduWaHtepG1tb9PLfvVVY9vJFNqZt4fL36NHuWVEATFctZQ2HPdy00z40cf+tUnaTSRm2dmkBr6hpMBcrarjN6PEWXYdfapoMByivLcTe4k16czq8nfmVN8hoGNx+Mp4unIvrUIBn4fPjndA/tbpsSzCrNYm78XK5tdS3Hz/zE6dS9sj5qFSoaknaB7WgX2O6C91NRViZP434e2LuGS1Xy710SVARaSUGeQlSUFuTj5X9+X8aJ3TtY9o41McPWn3/gP5/MweCqvJbsJbZ2hpL8PA6tX8PeVStk6/f8saL+Ys6Oj5ray7W5woTOvQHFnFoARD2MA/9fUKtDXZiViW9wyEUfi10xJ4SYB8wDkCRpLfCwWgCExsWheOMmClcqS860WbcWl7AwLEYjpdu3U7JtO3pfHwLvs0ZoGUtLFX2qqI9Z3NGFeiE3t6T9e9iz0up8nfZ/7F13mBRF+n5remY278IuC0tYMkvOOQdBMOeAogie4TzDeZ7cmVHPS+rdmc506omYE3IiAkpGouSw5LAs7LI5z07o+v3R07Pd01XV3TOzC/70fR4edjpU1/R0V331ft/3fgf2YduSrzF2+syI27OLUwdycWL3DnTsPwhZXbrZOtcn+/DlwS/hIA5c1e0qEEJAKcVFX14UUqRPrXbiSrTVnXfhx+ejItk44HZO64wjFQ2JKiP26ielofuaY/gH4tq2gUb2R/JqP8b5FEbttr63oTMh2H9wif48RrckRluugATW0yT5oDPkAISSMlont8Yd/e/AHf0b6mTO7DUTx6uOI9mVjJaJ7IE1MzETfximZEPu839g2B+I4rluShQePYT0Nm3NDxSAx8zVMypjnA2w2DYfowRbdWlJxMbcklf/Ffq7vrYGO5Z9gwFTLzIcF+niVQ4E8P7Dv1NcoeH7BAlmPLBcnby28vbuQudBsZEnATgxcz9DNyvrPmxc8Amm3Nb0RbEsRd1TSif+YsidPfjLynDyHkXMN0AI8tJTUJiSiLb/fgWuLEWd2hEXh+Rx49BqzoNoceedIMEVpaeav7K2U7y8sWLmvvjLE7rPmxZ8GnFbdlF45BA+emIO1n38Hj545AEUnzhm+VyZyhj03iA8veFpPLn+SfSb1w8Hyg7gsXWPhQw5t9eBHseNgdtOTpC/1pADgGbVelYgo9KccWNlO4ajS1oX02PuGnAXNt6wETf3ulm3ncfMOWSCBZctwL2D7kWay5gr1dxtjA1lMXM8nTlvLVsahwfJIaFzWmeuIRcO1jPc2MycXfAWVLu+X8Lcbgd+L/sdXvbmy1G3bRdHtm22dBwrfCSakI+6Kv1YefrQfuYzIBoLRTi4aT3TkAMAV7x9WSqe8cSKhf5x0QLGkZGD9SzamU/+v4D1G5zcu/ss9MReAgQIIf0BdIe2InMQlNJ5serUL2iAv6QEB0c31Ovb2KUNypOU259YVQozrfmAoAySnUFJ9KL+FBMgvAEvvnjn+dCgRKmM5e+8jmuf+IvuuC8Pfonc0lzcM/AeJLsV16hMZfSf19/Q5lULrwr9TWTgknWtkVJnfMVcnCB/M1jRdTVT8Nh20zY4HQ198gV8GDRfr3uXlZSFO/rdAQdx4MGhD+LBoQ0FsV9eeR3qvUbD6paeM0NxX6yBflavWXjuwgsw+qPRkKmMd6e9ixXfPG44jmfMeTg6h7ECywiwkyCk4mTuHix9/SX4vfUYP2M2uo8cG4vuAeC/r3l7rGvK8cBj5gCg8OhhtOpkvgCIFbZ+s9C4kcHMsaqFxDJuS5KczPsSqdFSXnCKu88VF8fdxwOvXnE9Y+HjTrBvLIrAjpmTwz4HcGD9WoAQ5IwYHdOYvXMFrHGDVee5KWBVZ64ZgEUAVLlv9c3STi+NZswRQhwA/gDgDgBZAPYDeIpSaizuyD4/IXj+jQDaAygHsBnAlZTSc2v5HQatIVcZ7w4ZcgCw5oP/mlZfEBUotxPjIGTmInARiK8V22DdcCw+uhhzVs/BTYfaQ9KEVuft3YVqbzXK6stw8+KbUVzXoKz/Qa7ihnto2EOYt9f8Ue9YkMg05AA+M2cGFit2/+D7MbvPbORV5eHhNQ9DkozVAH7ffBZa9u2JKR2m6Aw5QNHE2jVzFwpqCrDk2BK4JTcu6nyRoXqCigDnedJOorwKEMnuZOy4WUnYqCopxgpGOzzhUbvMnF2wFiSRxACt+O8bIfmZJa++gM6Dh8Hltj9Rs8AzVHqPj77Yt2hBtm3xQky76/6or6EFpRSUysz3/PjObYwzjPDVGUNIYskOHdi4DmOm32zYHin7x4ozU+F02Y9z5cXMearD8xSBjHYdbLcvgpUEiKWvvYg9q5TcyOM7p2DqnfcZzvmpg+XS9tWz1SMaG1ZnlT8DyAAwDoohdwWASQDeB3AEMCWIosXTAOYCeBnABQA2APiUEGKaNkIIcQFYDCUz93kAUwDcBeAkgHN6qVC9Zq3uc53bFpEKQBzHELuYuciNubSWrQzbWEXPI0GZpwyzl8zGnd/ejg2bl6C46BSmfT4Nc1bPAcCOLxv54Uhc+MWFOkNOi79s+gvyq/NNr50ucIlaYeZemmQssOJ1NvwGXZt1xeYbN4dKE2WnZOO9C9/DoKyBhvPqv92FaR2nGQw5LbKSsjCz90xM7zEdqW6epCQ/k0/WMMBWBvq9q5dzr8FCPWPijiVYLA8vJokHn8eDM0cb1PZ99R6U5sdOV5BnqDhjYCyKFmQkxgurqtJizH/ot/jn9Muw6MVndc8Gi1UC2N+dyczFWLiWNbZ98OgD8NWzGeRIEYnrljd+e6qMxpzXE9v3h71ga/gOAb8/ZMgBwO4Vy2KeIBHw+7H5f1/gu7deRcFhY53npsC2JV8btrHmtKaAVetgKoAnoRhRAHCSUvojgJWEkFcB3AfAuISJAQghLQH8HsBfKaXPBTevIIR0BfBXAMZcfT0eADAIQG9KaZ5muyVW72yBUoq8226Luh1RGn34AOKpqcaZo0eQ0S7bEEQsMvyiYeZYE5GdWCVfwIfFxxbjkbWPAADaJrfFS5NewomqE/jtit/CEQAu/qE11lW9hBVOGZ7hRUBQW9RKfFmkEDV9fedrcP6lt+jkKwJyAJsLN8Mb8GJY1jDEO+PxI57Tndc8rjnWXPchUtwpoXJKxgsb12dVJUWoq6pEYmpkoqoqKKXc50DLALMYpPBJ1m6MUGPGr1FKdcLOKlgTrKemGq/Mvj70+a63PkRCshIX+dmfjW5jnmB3JLCTvWgXImZOctpfRIqw9ZuFIaM3d90q9J4wGR37KYsQ3vMVYBpzRoMq1vIYrPsiBwI4snULuo8cwzgjMthdOAD871pRVGjY5q3VG76+eg8O/7gJzVq1tpz4VXGmEMd3bkNW1xymW1j727HeJ7/XC1d8ZJqFO7/7Fms/moekZs1x4b0PIrN9R6z9aB62/O8LAMCeld/htlfejnqMs4uDG38wbGvKkAQtrL6lrQEcoZQGCCEeKFUfVHwB4KOY96wBUwG4AcwP2z4fwNuEkE6U0qOC8+8C8GmYIXdOg8oycnv1NmyXmqfbbks00GtXu9WlJfho7h9QUViA+KRkTP/Tc0hv007XJ+41omDmWG5gUXYspRTrTq3Dr79jlwLKr87HlQuvDH3ufTQV6VUKS+b2OzBofzMsG6YUAWfFl7l8BD5X9BPwJRlTcPToJua+7sldDTpkkkPCiNbGouU6yDKaxYtFpnnl2fwxoP5FLnutoWGFmYszqQUcjsY05nyeOstuVq0hBwD/vnU6Hvj4a5Tk5+HU/r2mbVBZRu4Pq1FeeBq9x51nS8KAN3lHYgiEQ/TOFecdi7p9LdQJWMWmLz8JGXM8VyQNBFBZfAaHt2xEs6w2iE9OZroTI2V/uEYkZ2zbu2a5fWNOYNhHkgkqc+KhC48cMmw7dbAhf1EOBJSEr7zjoW23vvgfNGuVxb1WdVkp5s25B966WjgkCZN/9RtjfzTPIbPkX70nImOutrICy995DQG/H3VVlZj34N347fsLkLtuVegYv7ceBzeuQ/8p0Wu8eWqqseTVF3D6YC56jB6P8Tfdaku7MNIEmWhh1ZgrAKDOIscBjASwMvi5a4z7FI7eAOoBhD+he4L/9wLANOYIIe0BZAM4Qgh5E8B1UAzDdQAeoJQaxdnOAZT8x1goOq5HD7R57CEgqINkFSLWTPvybV28EBWFSqkmT0019q5ejjHX36w5VmTMRc4MsBI0SqqKkIEG0dTiuuJQ7US7GHxAzzC2LW5ghFhDa/cTKdjdRe/mzYjPQImnhNn+F5d+gW7NuyG3NBdHyo9gQvYEJLoS8fx1FzOPB9juISsQxdyocDjYkRPRuMJV8CYPIIyZY0xM4dvsLgAa05jj3Rsr91tF5RkjGwIYGaWti/+HlfPeBABsX7IIt73yDpwua9VA+Kxo9Mac6PfIz92L56+7GFPvvA99Jk6J+loGaCZKnjFWU1GOeXPuQb1JIkyk94Ll3nXFJ3CN3KpidlZqpIjImLNhxJedOqkYU3Hx2L9+jc6QA4Dl77yGK/84l3v+5q8+gzcY6iAHAswsZ+134BlzkeDI1s0GUmLhP/6M6lL9mFxVwh6j7WL38qU4tHk9ACULuOuQEWjXq4/l88+W3p5VY24tlOSHrwG8B+AJQkhHAH4AMwEw0o9ihnQA5dQ4spZq9vPQJvj/H6AkPFwPIA6Ky3glIaQfpfRELDsbLajPh5I33zRsb/evf+JkqXEA2bViKfqMnwzCmcRFzJz25du+VO+tPrBhnc6YE63+o3Gz+nzGF/zOb29D0cbGz0vJSGqBWq9+0Bmyvzl6XTANl3W9DP0yG5TvZSpj2ufTcLrmdGjbW+e/hW7NFRdFj/Qe6JGur77AAy9j0wyWVnycFWQsNNNEz5LWaGH1M1y42q42YSQ6XJbb5kyk4YOyj1MWD+BnsIXLXaiGHKC4ok7u3YWO/QeFn2arn7Ex5swXZEteewHtevVFQkoKygsLkN62XUySO7SsB89AKc235lix62Y9sXsn6qoq0KJ9R8M+h+Tgjm1eRgynr96D3Su/gysuHr3GTTQkd1RzxNsB/m9YWXwGu5YvQ/Os1ug5dqLuXmmZKSs4sXsHugwejvxcI4N8dNsWw7aiE8dQXngaHfsPwrEd+lrCTGkSzTZWCclIxz2WAX/kR6PXIz4pKaL2w7Fq/tthn9/CjX/+p+E43jt/rjNzT6LBMHoWSjLEdQASoRhy91i9ICFkMoBlFg5dRSmdYLVdDlQLpxbAJZTS2mAftkBh+n4DxdAL7+PtAG4HgPbt20fZBXuoWLgQclgAa9bcJ+Du2BF1xw8bjl/62ouoKCzQGV5aiFbc2pdPkiRojyw7rQ/yF07kFliWSm8lDpUdQvf07iAgWHZ8GR5d9yiuq22HhLA8FIlT0imWWHHtCnyx6UHmvsdGPgYAKC8swNbFXyEprTkGX3wFll6tlA6q89chXoqPuGwQr7yaGXiZnlrwmbnojTlhZrRmMmIFq+euW4WL7m2433aZucYsGcdN6tC8H/W1Nfjo8TnM43gxdwCw9sN30XWIIvTMmsxEE7zhOjyR2Bi4Wa0uyFa99x8UHD6I6tISZLRrj+lPP4u4xCgnUS0zF2UCgx3DdsvXX2LVe4oXJDHNGL4g+wPc57SeIVi84Nk/4cQuxdlTeOQgzputDwXZsYwf3r1v7UoMnHYJWnfrHtrm9/nw/sO/Cz1btZUVGHLxFaH9dhmg8gJlIepwckIxfL4QS6y9Ny2yO1gae7T3nvW+Rjrurf3wXUvHNRZ7X19XB6+nDmeOHEZ6u+xQXJ6nmiNBci4bc5TSwwAOB//2QUkqYNcTMscPAKzUsFGXPmUAmhFCSBg7pzJyotFQ5V3XqYYcAFBK8wghuQCMqX/K/jcAvAEAQ4YMaeQS3w0IlJfj9COP6rYljhyB5tcrcTrrPg4PG1Sw8ctP+MacYJDWsikOkyBn7oMruEa1txrXL7oexyuPM/cDvJqdwq4Y0CKhBX7V91cYmjUUe4r34NnNz6LKV4VPL/kUi775ve7YhNS0UK1NnuEDKKvst+79Vejzlq+/xG/eUkpzhVcisAtfhG5Wpl84DFyGliMKawflQTc8s31dAoT5D2ibmWtEQVKe3Ip2sjy0eYPBNaU9jqeDV3KygfhnufLsJBfwmbnoJw+rxvWhzRtCf5ecPIHtS7/B8Muviera2kVRpCEIKuxIk6jGCsAO2A/4/VwXfLhUTk15WciQAxQXergxZ4aPnvgDZv/rNaS1VGLXDqxfo+vXqvfe0hlzdqF+F8nJdut7qiqRnJ4Bv9eruze85z4cOnkihjEXiZtV+Q2sjRUbv/oUI6663vxAm6itKMP8P/4WZafz4U5IxFUPP4k2OT2578y5zszFDEGjyk41iT1QXKNdoI+bUwvZGTnjBhwBIBodzqlicgfHjtN9JnFxaP1UQ4wcTz1cBNEgXVvR4GI0M+Z4kgEAsPb4ajz+bl9c2uVSjGozCh/lfoTtRdbCEVnaabwqA1psuGEDklxGRiCneQ6u6KYMeOHsIgC44+PhravFD59+gApOnBMAbF6oT3b2VFfBU10trKmqRbtefbhK4F7Gqt4KrAS682QkYsHM5TMC/FVoB28r7h+7cZY8gysclFLk79sDyeXSsRwi8Jg57f3e9q1RgiB0fiBgSQePxRzYeRZ4RpuIMbWKSJ+PHctiYMxpFiC561ZH1VYsJ1I54OdP2GFGYyyEYuWAH8d2bEP/KRcA0C8EYgH1+eMlSals2tqPIpOM1T6frIVHJPprdmITY5HkxUJ9TU3I1eutq8WGLz7GlX+cC3+NsS4rYM2D0hjgzuCEEEaePReUUvp0DPrDwrcAfFAEf5/UbJ8BYLcok5VS6iOELAIwjhCSRCmtAUKJET3QuLF+tlC3Ywdo2MDR4td3wp2dzTnDGkTuKa2em8R5wUPtCAb7NiUKU7Xw8EIsPGzvlrJKOiVLSSC0Du3OJMAvUVx+3ixc2/1apLnT4JKsBYsDwCdPPWzY5oqLx+r338GOZcY6t1oc2WqMITm+a1tMFP0jnXytBOTzzOBI4xp93np4qquQkt4CSQxXlArVGLA6qdmPmWMUD/f7sPWbhagoOoOB0y5GRttsLH/nNWxfsggAMPraGZZW6rx3RGsYJKbxJQ9kOSBc7KhgxRHZYaJ47tTGToAQIgZ+Cy0zZ7WUFw9WXc5W71nRsSPmBwGm98GqS3TX8qUhY87BYdBUJKY147r3WVCfP4fEnvbVexdp6S/td2SNN5Ewc7bPeaoFEJ8GXPYK0KIbaHJrHNy2FYGKQuR0SIJUmQec2Qv46pTs4vpKYL/i/qYUWFPUEYB4zj26bQswNw2lFZlQzAg96MmtxpOaACI6Zm7YZwr2XKE+xo1izFFKzxBC/gHgIUJIFYCtUOL1JgG4VHssIeR7AB0opdoM2ycAbAKwiBDyPJRSZE9AqQLR9IUHOTg1xxC6h/TZs3Wf3QmJzMBbEUSDtLYt3gsOAEW1RVh04H9oJ3hcmle6UJZqc0KggMRg4Z4a+SQOblqPAz+uAQAMaJ+GFgNaGI5TUVNehm3ffo2ElFQMmHpRyHUVnu0EKCyAmSEHAC3ad0DhEb0QJc+FyYLI9SUysD3V1di7ZgVTsoLK5jMnb9Lg1d4U4fSh/fj8mcdRX1uDPhPPR2aHjtxj1VV/hcAVq63sYTchg6UztuHzj7Dhi48BAPvXr8Gt/3ojZMgBwLpP5lsy5koE7lMVovdDDgR0Aqk8sBIoRDqQrOuwEJ5kYRW+eg/y9+1B8zbtIjb2Y8FCaI25jv0GWjegWP0JyCgK1ljOZCQ1qLC66Ni62Nri1Iw1Zz2/LGjHHLMSX3ZZSH9w4SCVHmDujzYLUz6TCxxdDbQfyWbmPrkNWBb0hqS0BqqCyWRdpwBtBwPDbgf8dcA/G2S5Tpe1ApBjoxM+oLYY+PA6lNQnYtnprsivUxZie5LKcHV7ft3U/LpUbC6xTp78WNqW04XYCkpbBXeEopSGZi5CSC8oLNYbUDTlCgG0AjAdwG0A+DoMscEjAKqhiBOr5byupZSG+z4khH0nSuleQsgkAH8D8DEUlm8FgMsppXw/WxOi/uBBeI/rJ5SWc+bA4Q4rtN42G6cP7bfVttWYOVbsztwf5iK/Oh8bTm/AOG8LiGz/4XvT8e0I/u2c1WcWrsm5BpXeSsRL8Sj1lCLVmYKvF//ecGxNWSkOrF8T+rz+sw8x6pobme1SSvHJkw+hNFhCqbKoEBNvuZ3bD6uB9CwWKsBwk5UVnIKnqgpZXXP0WXkC9q3oOJtMluUAPnj0AaZ7GLA2cfIG+EiyWZe98XKIcdq9Yin6nTeNe6x6b4TPm9cHR7xizNk1LllGj2rIAUq8z751K221qWItJxbV6uRmleVhuVntJHbw4sG0VSeswu/14r0/3Iey0/lwxsVF7KKyI9/Cg5bVTM2MTj1/3SfzQ2yViJkVxQBHgu/fetWwjVKqjAkBH+QjaxlncTBXMT6cpW2gRBc1QH4iDY7gMENrRgCw7qnwbXoHOPkwSHE7AJ0M++WXhgJxtQAi8z7I+xYBpQo/EmBcwytr5o+qBlUAHFqm/Fv1V0ObG0siS0DcVNIOa87or3+8pjkqfW6kuthj4eozxnsiQqEnxbCte2oRMrOaNmlShdWYuZcB/IdS+nfNthMA/hasm/oKgOgLBHJAKQ0A+FPwn+i4CZztmwBEJlTWBCj94APdZ0daGprPMBovopJGVJaZzJFIX0ydHM7UnsH+igPIgH4l+PnBhrgxJ8MdqkVWKVsMckbPGfjDMD3rWJx3HHE1iWiR3Y55ThWDUePhzNHDIUMOUFbS42++FQ7DZ5WqAAAgAElEQVSHhKRmzQ16R1aZECuF1/etW4XFLz8PKsvoPmocLr6vIdtRNMHXVpTDU1ON+CR9/N2hzRu4hpxV8Aw+u5lefq/XYHQWHjWKkYaO96nGHP/++n0NCvD1tfYm0/DfjcW6srbx3gstKhmK+YB15iMaY4537uEfN2LFf9+A0x2Hqb++D627do9pdYM9q74LPWvRxBrZZXNYxl9IKqO+CnKptWB7HrRux3WfzMfwTn6QuhKg9KjC2tRXA1l9EYi3JiMkRP5W4M2JkClwMtdoAPlX/gOuM9uAff/DqepmAPpaapZSxd2VV2N07e+vzETPNCWOjHKDKtgIBPkZ3nmyhVhlEajmfJlxjfqA/RD9Sp89keF9Fcr92VLCZs08ARfXmKvzWzeM6wPGsKQEyYuL2+YCQydYbieWsHp3h0Opz8rCZgCPcvb9AhPIHg8qF+lT1hOHDcPmRQuwe8UytOrcFVNuvxtxiUnCuBy/zwtXnPHBFxkvP5xch3vfVWqAXuNlPPwax7pkoZ7oxhs2QnJIcDvcXNmOnd8vUQQnBSt6phq/usoNQx1DBf6DR36PKx+ai9SWrQzGnFUmhHVc+MT1zYvPhv7e/8NqjLnuJjTLag0qy6Zsyc7vvsWwy67WbSs4xHZ/2AFvcrXrituvYUZViHSifF4LxpzGmLGbBBKeAKFl5VSwNM/8fl/EWmjaeylSoREZykRTXo0VM8csfSYHsPT1l0KGyYp338QNTz8X04zeaBMNQqgtAVY/q7jJvDXArk+BM7nAsNsA2Q/EpQIbXgUKdwFp7eG78St2O0E2ijLYqGgQWHA3nOE1mPcugFyXBKXKYxR4U+EHApS9WKhc+iwy4uogU+CLPOuis2XeBKw+0xGHq42hJSsKu4SMObvGl3p8gHNetCSr1oBjXYNl4AHA6boULD6VA2/AiQmtjqBH8PvV2DCuVKwo7IKuKSWoC7BrY4u+YoekcpSXW1MqWHraWAJt9I23A4OeA+KsJcnFGlaNuQooBeq/Y+w7P7j/F0SAqu++hxxWWN51z6+x9jFFk6u88DRaduqCoZdcibpK/m1mFj6mFNV1/En8ePmxUKxnksf4KDgDBH6n8vi7fRbixep8iEsVl2la9oaxgHw4WAZoxZlCZrkZlrxI4ZGD2PX9Em7QvBWwYmDMmJrivONoltUay//7hmn7WjZRRR2jQLZd8Iw5K4H2lFIUHj4Ip9uNHUvNSh7robpZRYsHbdKD3RJUVJZDLJvXU8fU7GJlvAZ8sTHmRBDFsVIqh2IFmcwc436VFxToGKbTB3KBunLIJYKqhbu/AFY8A5QcApJaAp4KIC4FaNUbkFzAIc3QTSR4jg2BUgwnOlBZBpYzHCbfGMMnUHECnheGQ+EG2IiWHQqHT5bgdBjvMc+wsANKFSPfzzHmVCPvVF2qLRat3BvPNOQAoC7QYODYZebUe0s591gGgVeOXONTx8wx7gl1B42c5CxgwHSgRXf41ryED9Y26P4vLeiKbqnFyK9NxZd5xpKWZqgLuHDmhjXAE39k93HGV0CfocGDywBXIuBUxof4j+YBX35i6ToHqjIN2zoMHg1ktbbd51jBqjH3NpQEhGQAn6IhZu5aKOK6PNbuF5ig4gt9ncL0mTOx7nN9qds1H/wXfSedL1yZa90XvoAPL217Ce/seQdD9jVDH7Az8VQJkMQ6diar2++A36lcMxNpAMSBnSUnTyCxlzVXgggsg4tnhPFcaGs/mscMgLbqZrVSkiockssFKsvYvoQvY6GCZYR6qu0HshcePQzZ70dWl24gDgfX4LTC6nz/9mvYsXQR/wABPeW3EDOnNWYi0UYLBAJwOhzYtvh/zP0s/b5o6gbTwj1A7jdAVh8hbeH7xpg1rYW86CE4SvfBvycfDdrrwX3l+cC6F4DDK4CaIoA4QMtqoZTD1uBvHSCLXHWfzWr4u0apPYzaeuAoQyaGBkADPvCMOYnIkCmxZCzYJXNq/WIDcn+lcZKMBj4qIQEMYy4GRmOAEjgJ5balGnPHqpsz9/NQ4hUviAOUQCLUNpMmO5R7L7fqB5QYs2ApJdgtD7HXqLb9QTOByX2A/K0IfLcFKNGHUsiDZwM33arblluWAax9MfTZJztRNnsrlr/4HPwRFmcqzuOfJ7s1cW4J+t8lWmHy+GRjDF1Twqox9ziU9/a3AO4MbiMAaqAYcnNj3rOfAXynTqFm/XrdtrQrr4Rn3uvGY01StFVj7lDZIVyxsEFYUhLEuqmCvZnlbOZi0WVfIy2zFVySC6+tvxk1JsbcJ08+hJnPvYIW2R2Ex5mBxWDwgr+JYMJhvZxWX1iWUaRlalixPw6HhGKL2lAsrScrcW1ad/PGBZ+G1NF7jpmAC+/5PZdNUo3YwqOHsXvFMuQMH4Xs3g3lynweD3Z9/63w2qKkDisxc9oEkkj0wORPZgF1BVi7jB1H46ssNl5z/3dAnF9x+R1bA5zZpzBVngogOQtyYgb/enmbgY+C8ax5PQGw2ZLqQ5sh0kEPbPoPnFIAfo9x1S7vWQiUNsQinuQwEpSK2SSVJdKizBuPal8c2iZWhILmVYjcxgmSD52TS7GzPPYsw74KY5a2Fqyg8mjgkyVQCpzxJEMiMlrEKyyqXVaLhQB1wIkA183qD7JcTpYyugClve8Ezizl7j9w/lfoOXo85OsvseUblTtNAB5eDXnem8Beo7tbnvUt1j/7Jyi5hvYhB2SgyySgyyTIh18H9octuhjxvEtfe9GwTYqLj0pjr6zgNHefcAwTlOuzgrhEsRHe2LBaAUIG8FhQ2qMvlGXjaQA7KaW/uFgjRPmCBaGXsdbtxIHunbD3i/dRyIi3MjNCrlt4LYpJBaq8elcdS8dNBQmuKLtn9EBDsQz9uaqum1WGY82H7+KKOWyJwvD6rzywkjZ4qf0iMVm2cKUHkstl+n1YxqM2vomlk/bZM9ZDR1mMopXMQDngDym4a/Wg9q1dibE33sI15gKBAAoOH8T7D98PANi+5GuMveGWUNxeXXWlKXsnm5SGC+z4FHLuNu4x/pXPA/uTgaRM0NO7AIi1DQ3Xz12MOgoAI5n7vTu+BKA3FgJf3Q24OYuQkkPwBSQAo5i7dRO+YO5fe6Yjfyca4od81Ph9tbFFlALf5HfXZ/0FIYMI2aRw3ajDVelYeLInZDiQnViOa9rv0hlwRMCpeWUJk7MOWTLmPAGTuKbsEUBeQ9WIAo8xnkgijSey6pu1HCvXr8XWbxTjZcLNt2HwRZdB3r0TeFrMqJoh8JutQMtsBM4UAvcZM+j9V/0XGD4Rrm++Aub9x3K7u1fwDTkAqC4pVsYKm9Sc+n77OYLdckCG0+1WKJoIoKsAwRiXw6WVeOEJ0UqkHN/JH4PEMb3RVcmxI13VGLCVXkIpLQdgjIz+BbZBZRkVXzZMxrvaZaLEIQPbf2Qeb2Z8nK4+BU+c8SUQMXPj24zFKzOfwt7Vy7H4u38Y9muLm1s15lgFkAElZuv7t/5tqQ2WjAaPmeO5TV3xCdwX18p3YTFHWmPHjj4YC6xx2MogFvAHjTmfxxBDWXNgPWQve4CUN/0H363+CEAD87Hmg/9iGFkN1Fei6FABzIaDQEU+AH78mf+zOxCoagGeLpQ/91vgpOLekb0DdH2xggAlyK/li/f6GPE+dQEXmgsYZZ/MNyipztDiv0flPnHQtGqE+Rn907JtVX43qvxs1lGmhBmHpN3vIMGHqnknLD7YBnKwNHVebTPk16WiXWKDGz90LANe2Qly1X+AZ8xrYroTEoC5Dc/hgY3rUFFYgF7jJiGpmd6NVVtRjlO3zzD2nTgb2rgutipXtTXVIUMOAFbOe1Mx5mKQGex3JgEOiTue+KUEgJCYl6KjlEZk8OTt2YXX7rjJkBQWaleW0bJTF1v1gsPPVxHws2O4Vfh9Psx/6LfMdqIdW4uDOoPMtgW/RTTMXM7w0RGfGys0eTmvX6CgdvMW+PLyQp9LUsQUbXH1GeF+3lQzse0E5OUbqxkAgJsoq2peZqHWGIq2HFTRMUHwdhiO7TAqaHOZOc6L7/PUwR1vL60daBCHZSaUaAaraMsG+XKXAW9/Bfg9AJVR4EnFCb6eZcN1XxwG+IqDwpT6AaTqk/uQn9+LeV59wMl0Yck/vgsHAVYfHgyz4UBkTACK24nncgKA3MpMdExWjDmRccS/PkGlj29MsgwzL0NCQLdfYMxpf2FeBqAVyANvAdp2hn9HBbBinX6f2q4rEXKb0cAhtuHpf/A4Als3Av9+gX2Nh08D8YpRWVtZgfof9NJGp0b/E+002dPkkd8Bouzpftcgs/2qkAAvDx36NZS3XvDsn3B4i8LCrX7/Hdw3/8tQ4XYAOMpZqFJZDoUPtO3RG/m5e4TXtAOmXA2ltmq48qCUcMvkjkFq2MTJfRZebBsI+HwRjT+UylxDDlCYtWh0A/WLXZYiQUOf965ejrLTp5jtsDLVYwWRmzWa+NoB0xpbatccZ5cX/BmDOAgSBg+2fPzL/2Fn54SgmWwcxIFb+9yK7TdtZ9YvVaG+fDzJEzWYXZYD+pWgKOCGg2gpaN5LKAq4Fw1couvIn9+BEz8aRT7lrfOBN88D/toB9BW2a46H9on6vtSVFAAn1gOntsGfvxMLN1lTDQ9UngZ8tfAypGIWcgw5gJ19BQBHq5VMslKToGvAPGjcTx3CY/ZUNGQjR5JNGKAOoUvORxjSPJQo2Z0dxgDdLwQG3Aj0vgJI7wJkD4evG38Qpr2uVBijx0oQaB/5yjsw+n5g5F3wx6cb9sk9LlWu8chpFPS+h9uGHAiEmDYWctetxru//w0+e+YxvPfH+wz7w0XBrbyPk2bfaXqMFqohp+L4Tv2i7Nt//5N7rjoW2S11N27GbOF+Vhyqp6Y6JjVca4MqBDwmSfb7UXLyBI5sja5EWTi8njrb2eBWIAcC8ESRUa815liLb62b9cTuHdx2WLJIsYLMYAwBReKqIKzijx207c4fe5sKvzBzZwmJQ4ei4/vzUX/0KCq++BLYtFx4fKeTYlfOvQPuQYtWbdEuuR2yU7KRFhfUbRIMWurLxytto644w1csTqfLNlNXWx4Zda9CXvI4sLpI0bJKSAf89YCnAoGTPgBdTc+3g6++2QmPzxgYT0uPA05F1JT6awBYT/QY3iIPJ040uJ1qNbFGxfVJXPdaOFRjqcKmmCYPq890QpeUUrRPKsOJGnHWnRk75Y9vgYArBygUTMgOFyD7ItK0Cty1Gdi9A3jHmCAEAL70HkCNXnRWvvZ9YPhobFvyNda8/18kpNbjkvsfQVYXRSfKt283sIQjY6C+O5ITARPRbBFCsUosaZLgfcjbsxOLNLqF4VDYGP4Erkr+FHNKkxGHnoFkZVOHo13PPhgw9WJhdrY6QbPYqfICfmm3cMhyABKctouxOxxi5lUtkK7FpgWfok1O9KLB6u/BY3TKTp8SGrCRwltXG3VcGQuVRYVCYXoz6GLmWDqd2gSIGFQOiQSsGOvTB/fj8788znxWrIKV0NbU+MWYO8uI69QJmb+7H7hebMyZ4dIulyC1Bauep8CY8/sBWUZ9FbtYc+DIWsC/D4FKvSEmET8j2b8Bp/48CicrXOiYWo2WrnLAWw1fSQpYRYmtQs7fBiQr7JZPPgYAcDlk+P3Rlf9h4Ug1O8NReyftShskOfUDvta957GhjK4G5YtivezA684AJjyMrM8/xwmTsUx2uAGBe6rmqo8RyN0L7HuPf705eXDHJ0C+/06AobUngt/rFQYwswwZGQrzvPzt1wAAviIP1n40D1c/opSSFgkha9kbltvIKtQ+iypAbPn6S5M2fFxWwQrCJxurTPmkW24XGnOHNq8HpRSn9u817ItPbkh2MGPCaCAAX0C2XDNVhd/EJijIN7rytvzvC3QaPs7WdVg4UVSF2lOVKCpk5wBu/LJx3IVH8gpQt4ufsRkpVnwwD47EyLOJTxRX47/rjiLeJaGk2Mjw7cmvwIEVSua2pyB6Tc1I8MH6o6jLTwMFIFMKr19G+ubPkBaFIed3JeDmtzchIMsIyBRDOqTj91O7x67TFmE6ixBC3FDqmn5AKY0tX/wzR7mnHN8e+xZfH1iIgeaHi7H5bSDRocRg+TxKwWJfHWgeP9ZOPr4BeDoD+/aNACuzUF7xNyClDAG/C8CI0HYp4IFIcPTDHYo7aQ1SALRGRlwNOiVFycwFjafcikwsOd0NFASTsw4JY7RiDa0BZ1faoLrPDcCRhrq63rgMHJ/2LmSHG/n7DwJ5yyy1c2rIH3G6/UDkFXiAea/Y6gMLdQEJy1reglNdEoEzS4THmgVyf/LkQ0gcKK6a9/qCtZCyOsFTbb8Y9esrDsBZeFKQgmHE55uPg/6Yrzvn+M5tePyr3XAQAueJg+Bx3rtPlmHVx9sBAC2LqyxL7FIQXbbo3C93oCq1CB1yTyOc+9xxvARfvLURA0xccffO34yU8uMR10b4x/eHkbdzJSilyKg4hlEHxXFcY/7WsLic6k5FopevgThn1h3Y27wfJoVtf+izbchd6gVkP4YVrxeOcQPmfotaEodby6phR+Dh6W/2C+s0HvlhBXP70Y3RV8B4YsFOHF1Wha7Vh3BB1K1ZR/X+7ZhTtx23xbhdWl+HkoALxqrU1nD4TBUW/k8x6i8tKDf4LXbmlWH5EmUMnHamCsYaCo2PzUeKsa9Iv4i859TOqNqsl4HVB4pCn5Pj7FeuiAVMjTlKqZcQcgcA8dLxF9jC4oML8NC6xxAgSqmsgYiuOC9d8w/AbXRR0Eq+PpYcCGBnaSb8DMkEoEH0MjwLz66UQEl9Ekrq+bF7VqAaUt+c6h4ypJaczsG4lkeiatcOvgkMx3zvlWhFylDkTUIO+HEf4bho2zDMQoMxV1jrwPgFLgAUPat8mGyxnWvXZqHaWYXfHDOvMmEFdZ563DZvC8aUnI5+QQGgdht78lQxf0MeSt3VuJOhCWeGJTtPop2nGMNsnLMitxABIuHCsO3z1iss3uSiLVyFuMKKOvxvm1K/dEZtnWVjzkeccNMGJm/b8RKcjnejWXWtwZhLKTmCNQeLMcCkzdxT5WjrqYnYmCus8eMoqUGXmiMYZWK0b2w2BCfLGpKivDKEBlZW3SkcjjeOX0OLN2JfQleMLv0BfauMzJ0WsiwDEiBxagtzz4sgfjdWcAS5+guKrC3EYgmC2LtZlXYjd39KtGGx56DGhZ/2lyJnyc3qsPl8WQENi2UNNIIL3Aqs0hrbYLVK8C+whD4t+kKNYbepKckEjykSMUgBECwrYMtIqPsBIL9OLwdR5Y/HhW1yI+hl5HjdfxGuqH/S8H1err+0yfpwimZgmTwE8wNTsEG2F/AaIPpXzUEDSPNVYHr+J5hcvNJyOw5QdK+OvoarCnUAdjTS5BAOB+SI+++kfjipvQB5B5XhYEwcXWoOA5SiZ/V+xlkK1IktPuBBc591OU2fQ79GVicQXt/jAuYspUQD0U1EwXswsmyD8LAz7hbYnaJ/tikxnybSfcZko0S5DlPPLDM15ICGeyTBuit5dfoow0TalHBQCncgOqHZSOGSo5PvYKGeuKMyslxywwImTjaGFOgNxbNkzDXCOBeezOWXz853sxqs8wCADwkhxwEsotHkL/8CAEB2s84Y4KnH9vi4UFktO2jmqtPpW+0sz8Lhqgw0d9dhSuuDoRgt0Q9lJg+xqbYrcpNycKTAyNy9k3g5SLNKtCxnp5fHGjvlzjgod8GYsPLATelm1U6mLANBhPBMRAdkDC7fihZeo3SCCIRSjCiLXbSDHJyoG2PFyoKDyuhQF5m6u0QDcNrM4nOAQmYM4OcXfY+3s9uJzw3ekxZeeyyin7gANDBbqsHMM+ZGmRhYABAn16Nf5S5b/dBCnUjNjNKP21xtyFa3knmc7mVnjneqYydkhCNB9sCDRB27I8LmFiNwsPkAdK2K3cLGLtqkupDQLB6IvFhBxJic7QLshZyawk1kON0O7aNrC5nxwIwR7VHvk5FeRIEwe657q2R0G9cFBIC0PAmw9mjEFJf1bYkZQ/qCEKV2kIMAx/4eXZupgWq8M2sonA4CyUHQPDH6mseRwKox9ymANABfAfARQoqgtxMopTS6Gk4/NxCC86u8KHc4cFFpvS3R7ZZpHlTU6iOHNpdkA1AkJvaf6YCqzCx44EaafBKJYMe7HJTbohn4g3tRmQuPN/s17pFfNez7JDARHeKO41I0jTE3rmQtCuKyDNtdNDrVbjtIdBG0TImD5CBoVu8G8q2f2z4zRTfou0DRu9o+u5nTMgkJp6PT/NOirlUOJvdsidY744AmiEm+pG9LuJZFNopf3b8lAvmV8JoTPSFc2L0Z6tctMGx30gAenNIFFW/xz8325OMvEzMRqHSg8DPr12yZnoL6Mw3v3P3ndUF6z4HY+8rXqGUkeI7vmo4Svmg9AOBa32Z4ApEHac+Z2h0dR47Hl3cb32Ut1j10HgIBGrLnKAWW/vkbVJwUy/y08op1MM3w2a0DkZ3TAy/MeM30WKfLjY9eUaqt7FuXhG9e/M7kjMbBg+fnoH2f/niTLZ/XqPjN2PZYsN78ODsgsh/JzohtOaRKATx4ueLAe3OVE5VhuSy9spJx0TQlCe7TLc6zYQOjX5sUDBvaEBLw5d+ejEm7E7uLy9Q1BazSGt8D+BzAPAAfAvguuE39F10q5s8UnXvOxUNtH0VOzlxb58k9LwHS2nL3OyuqccGsR3HlrDlo05ZvY7dOE8udAMDXv2HrqX33u/H46zWxiLKyhgS5HvfDqP12RS+jdldjYWJrBzY9MhnrHzoP82YNtXXu4vv1YdougQK/CC9PH4B4d+yS0Ef3zsZ/Zg7F6C5Ncx8nZUbuHhrZLhFd0u2kP4BpyKm4dlAb7j4Vp95+CgMy7QU0p6fpS1b1yUrG+JxMxDnYv/mgoebvkae0yPQYETJT3OicaSylFY62zRLQPiMR2enKv/YZiYh3N35At0MOWNaY02bimkmTNCbkgD/m1R2swuuJ1OQyaTcKaRJt5QjWb7n/hzUhUWKzWuONhfDfK9YagGcTVmuz3tLI/fhZYvRFtwAAygsLsO2jTy2f16lVGg7nOSGK1hjdVUl6OJXgBFt4RDEozIaE1Io85vauLZMRXxzbothmKD1pZHTCS1o1JvL27ITP44ErPt626KgUJg1hVxw1dJ4sg8Qw6PvkXsV1Z1b7N1bYvPDziM8tPXUS+9aujFlfrJYNWvIau+oCD644vQagKmzN0yMjFmLSokV4XUw7aAqDKeD3WX4GqcYp5JDOXsycHJAjfo+jhbc2cqNLhGjHgZL8PGS0zWZX0KEyjmzdjC6DhyG9TTucPtC0cddA5OPuTwG/VIA4B2B3dSc5XaYTeu4Pq1Fy8oRQKdzKg31sp7G0VvM2SqzR2S4sDABlp234OmMA1ZiwK9pJHI6Y3K9Yi4WWnT6Fwz9ujIkivhV4qq37ct0JeuZ4+5JFMe2L5YnLZnykK6yMnPp+s2oOK/ut9SM+JdVWP3SIIsyZNIEgasDns1xOSVuKqynFWsOraMgBf0R1RJOaNceY62+Oqi+NxcxFi2PblfmCN54sf+d1BPw+7Fl5dlzj6z/7MPT34leM9ch/yrA8uxBCBhJCviCEFBNC/ISQQcHtfyaETGu8Lv7/h93VguR0mhoGi174O/77wF04sZuvoWPFiGStysdcpxTLPhcGlEhKdkWDkpNKpEckJWckZ/TuqlP79wpLmKmITzJ3qan49tUXIpqU0tuIEwiiRXxyFMaLBVi5j5HAyMyxK6mE7zeDp4qv9WaG9Z99IBRIFqEp2K+Az2d4BlMyMpEzcqzwvKZcUDbL0rvlZb/f9iJo5NU34NYX38TwK67FVQ8/BafbXtiACl497bMNZ9AlzxtPKosK8fW/Iss4yOzYmbn9url/RedB1sNejm7bAk9NNfau/v8VHWbpTSCEjAGwHoqE/wdh58kA7BXx+wU62GbmXObMXKyuy3JjZrRT4vASkmPnZk1u3nSxb9FANQC2/O8Ly+dMvVOplRmLSXHV/LctMRjOOOuThKeqUlgqigd3oh15V/tISGlcN/7e1d/rPoczgZHCFXbv/V4lIMLPMR6bwsVdXVaKJa+/GNG5TeNm9cMf9lxLTicu+e0fhOc1ZcycgXGVZdtjd3qbtiFjv2P/QZj9wutIa2m/ik00sW2NCW9wwSAaTw5ttp+5ceG9D2LwhZcx9yWkpNoy6pe9+UpU4R7nKqzegb8CWAKgN4Dfhe3bCmBQLDv1c4NdVkRyOmMSZ2OlvurO5UaB0bjgJN6qSzekt82Ouh8A0LJTpHKoTYsdyxbbPqfPxCkAYsMiWJ08wg0KM9AIArntrIYjQXwMFwss/LjoK93njGxOspDNhZPk0ksTLH/ndXhqqhHwcow5i+7FaLH/h8iqHthZGESKgM9nYEolF5vJ1nqMm9LNGs64yn77CRDh7HxKegtccv9DtvsSK2auTQ5PMjsy+ILemmhKz4Wj73lT0XP0eIObW4UrPsHWfFhVUoRNC6zHqP9UYPUODALwalBfLjz4ohhAZkx79TODXVZEcrpAHNEzc34rRa0ZsTZxiUo1B0IIrn/ybxh88RVR9yUWLsimQvGJYxGd15QsgtNlT+vozPGjtq/BqgUcjsz2HW23q8KKQao+i7EAb7KwG2/GMkJ2LFusLzSuAS+W7lyBld85WvgZblYrY8LZZeYCtsduB+MZy+zQyXZf6mvt1bBlYfgV16HrsJFRt6OFLzinRML086D+xrznIT45GY5zIH77bMPqHfCAX9GlNSAQK/sFprC7ilGYubNXxka7Uk9IScWEm27FLc//O6o2eavwcxF5+8R1LbXoNa6hYmWs4nusuKTtsik1ZfZr5zocDoy69kbhMT3GTLDdbqh9C5N5Vld+BRPb15NiI/kSnrkMAFu/+YpxpIKqEnvC0U2NxNQ08xFRAzcAACAASURBVIOiRMDvM8TgWnmGmyI5Q4U7Xu+GlwMB24w2a8EQybhQF0X8pIox199k+E7RwuepU5K0YlhXQL0/rDnCFZ8Ad3xCo8ROuhOshZF0N4nrbCpYvQNrAfyWEKJ9c9Rf61b8ojMXFWwzcy5Xk8gZAEBimrHsMsuQzGjXHklRxL39lIw5O6vA8Tfd2nBejCaeaguGl103a0RwODDyqunCQ+KTrSdihIPLlGkQqzg3QAnOjgVYRmhtBU8gCNiz6uxk9oWjXc8+zO2xvMcqBl2gL8O3Z+V3qK/RiyLHJ/FYV400SRMyMuHvlBwIQA7YlChijHORLMxrymKT+OVwxtYY9no8OLrDvoqyyHBSx00WM5fcXKl2bNeYM1sodBs2Clc9/JSltoZfca2tazcWrN6Bx6C4WncE/6YAZhJCVgAYASA2Mso/U0SSAGGhwk5MoAZvqxgw9WLusdGwhXbdgrFC95FjMWl24+XvaFkNuwNOQhSMSKRZcnag/t6tOnfjHmMnqzYcVtxssWQWygtOWzpO5NrtMmS4JSP0XIMrLh4Tbv4Vd18s8buP/oej27fotpWcPGEI6rfCjDRpzJyBmfNHECITm2fDiiRTpwGDTY+JdXhLXWUFlr3+ku3zRN6GkDHnMt47lWwQja0Z7dobtpnFqfaecB7a5PTAba+8LXwO73z9vYjc5I0BS7MLpXQHgHEACgE8AsWUuDu4ezyllF+t+heYIpIBoamYOV9YXJ0kWMlFQ3WfLWbO4XRCsuleq49QsNMKi9C2Ry/c+Mw/8MDHX+OuN9+P6DpAbIw5s9/EysSUnJ5hegxvgSB61lSET7DRwKq7JDx2SovM9h2b1MCIFWY+9zJade7K3JfZMbaTFSEErbt2N2wPD+q3wgg2pTSJIQEiYD+bNRLjqUV2B/SZeL7t81zxCbjtlbdN+hPbhUdNRbklz4EW6W2zkdKCH3bvELhZE4Lai6KxtU1OD8M2UXn57N790GnAEABKvOjNf38JY6bPNBzXbfgoJDVrzm2nqWH5TaCUbqWUngcgBUA7AKmU0omUUpOqgr/ADLap+hglQLAw7LKrdZ/DRWqJIOA4GpakMVw5VuBwSLYn3/qayIKPrVynVeduMYkDi4bVA4CrHnkad7z6rnDVacUAj0sUM3MjrpqOUdfcwNzHChYPh1tgWNlFetvskIyMCCID0iE5f1LJPADQc+xEpLU01j1WIdpnF2oMac+wWEqny22ImeMxItqJuGmZuXBjzj4zZ+WZDsfM515B58H2M8dd8fFIbdESd/3ng5j2RwS/134yz+UPPio0ykVuVtWYE52fksEwFBnG3JBLrsStL7yJqx99WvdcpbVshUHTLmH069xi4G0vayilHgA+Sum5KXTzE0QkQbSNwcy17zsAKSaZa6KXJs6CSy2OEweTlHZ2VjgOp2R7QKuzWMVAGy8HWCvbFKuVstMdndu6eVZrU/0mK0aLGXOS1aUbd1C00n4sGV2Hw4Huo8aauhVFixaHJP3k3KyTZt0h3B/LjOE+EyYDgEHSKCE1zcjMWVgcNqUxF75wCPhjkwBh7dr2F7vqOQkpqWjeml2HONYxh+FhOVYQn5Iq7IdKILCeQyvGnEOS0O8887oGHfr0R7Os1swMaVaM3dlMQmTBTgWI8YSQVYSQOgAFhJA6QshKQsi4RuzfzwKRJUDE/kGSJIkZl6CFSAqAH7DcgLHTbzFsGzD1IvgiGARigdqKCtsTgpk0yZTb7sYNzzyPIWGSLVauE7OMSsGk0axVa9PzE1ODsSiC56zhGnyXhdlkIUkS1/A0m/iS0zNiujomkgRXXDwuvl8sVCtiAx2SFLOg8lhpOPLQedBQPPDx16ZxjbE0Tt3BCTmc5fJ56uD1hMfMsQ0YLTN3Nt2sVA5E4GZl38vs3v2Y29UFoFnYBIst1t5jni5drEmBSJg5SZKEHh91DGFlVcdbcLMSh8PSgr1Dv4H8NhjjYGNVkIkUVitAXAMlY7UlgGcB3AvgOQCtACwnhFwtOP0XmCCi2qyN4GZ1OJ1wmrAhosHTisgr64Vp3rptxKWGokVdZYXtyarg0EHh/k4DhzBjgqxMPLGaOEVGTr8pFwhFmhNS00ITgdiYEz8r5916l+l3djid3O9sZqidf/s9MV3UqBOCmXaZKGYuVm7WvpPOx0X3PsjdnzNiTNTXaKzAbRGTp/7W4caH1+OBt1ZvcKjHGBZBWjdrE+nMJaSkGgyCQATlvHjP9PgZs5GaafSKqAZti2xjEL8WSc2MqgNaNo9vzMV2HonEmCOSJDbGgr8/ix0LvWsCo9ThcJjG314+5zHbC4NY18mOFlZ7/xSARQB6U0ofp5S+Qil9DEpFiG8BPN1YHfw5IKLVXSO4WRVWQTwRiV46K5mLrInb6XaftVWOOyFB6Fa78J7fY8glV+q28cRfVfCMEyuDRfjExYz3sACRUUggli4Zfvk1DceKBkkTw7P/lAvMjTnBZGxm2Lbp3lMYyGwbwYnNzIgUyihE4LZnYeItt6Nlx85chf5YZJjGOktVRWIaP15TvbeS06l71uWAH3XVeu001ZBxC4zDpnKzXnL/Hw1jXyTlvOI4JfBade6KX730lmF7Qmpq8Dyx1yOREaaiZfN89ezFcqyNOV8E9bodDslSzByrr4mp5sycQ5JM32nVE/FThlWLoBOUChC6WSz4+d8AOsa4XzoQQhyEkIcIIccIIR5CyA5CyFUWz5UIIfcTQnYTQmoIIacJIV8SQti89lmAXQvf4WwcN6tDcprGIIkGTytxWkxjzuVGt6GxVSK3CsnlYmrpqUhMa4bR191kq03ewGHJzRp2f6bcfjfnSDEkpxP9z7+IuU9hE/jPT8nJE5oOCZg5wffJ7NAJhBBTN6vIJWn6LDokU8PaDo7t2Kq0a1JDV8jMOSThfbGCYZdfEzK0eCXTPDX8uM2xN9yCnOGjTa/TWIaQKGFCZUgIIYb7GK6dphpzooVHUxlzzVq3Mbybdst59R4/WbgQIIQYslYHaN7hK/74BPdcNXZMC+27NXHmbbp942bMDh509isnOBwOsTGnWfB1GTIi9DchjtBiR3Q+cThMjblIYm9juY6MBaz+kgfBL9mVCeBQbLrDxdMA5gJ4GcAFADYA+JQQcqHFc58DsADAJQDuA9AZwApCSLtG6a1N2I2ZczZizJzThFWINgGC9VI53e6YKvnbhSi9PJKAdt7q2xIzF3ZMR0Ech7AdyYmRV12PzoOHGfZRWUZ+7h7uufGaiYEIjD6VxWWxY+fN/rVyvkVmrmVHo9vXTHuQSFJMXR2q29GUmRMZc05zdtsMQy9pWKfy7p+oNmfrbt35dWY1aKxEDVEmtdYFHe5qrSnXS1qobkJR8L8d15iVIHgeJKfLwCLLcgDU4tgdl5SEqXfea3rc4IsuCxlmGe3ao9+UCxr6IPGfq4QUY4iLVnKp59iJodCKrK456HfeVABmjFbTJPIoxpYgZk6zuJp866/RqnM3uBMSMWb6zSHXtNiYM1csiDZh7FyA1TfhEQBPEkJ0y0RCyHAoRpb9SsEWQQhpCeD3AP5KKX2OUrqCUnoHgBUA/mqhiVsAfEwpfZRSupxS+gmA6wCkA2BTF00Mu9IkjijKebHiMlRILpfpCkX00PcaO9E0oJbFxKiFyS+6b47w3MYBCbkyWHA4JBBCbE0avGOtZI6F/65m1+UF7UpOJ5KaNccVcx437DMzgNSMQ+X6opg5/gDZtkev4PnmMXMAMO7GWYZ9yRktxOdKDltu1q4m7G+3YaOC7ZrFzPHZFUnixwBaQXavvrqqGbxnRiSy6o5PsBS2EK3RyUNiaio3oF+b1OCOM2PmlPs8bob+2dCKG9th5sKlT3hgxf5KTpdh7FIqQFgz5jr0G2RpDGmR3QG3/ONV3PDM87jpby/ApXGVihhjlstce28SUlJx4zP/wK/fmI/pTz+rq6/NbTO+8YXHB0xVpmAzN6mK5PQMzPjLP3H3Ox/rZLRE5xcdP2L6TkZmzJ1b1JzVGepBAPEANgRdnRsJIccA/AAgDsAcQsjq4L9VMe7jVABuAPPDts8H0JcQYhbF6wYQXshOra1z9jlmRFYBItIsruxefYXtmhlzojib5PQMXHD374Tn85g5IAZVICIwcAkRx22p99lqCr9qxLBQeOSw6fl2a6qmZrZEp4FDDNu1LqFmWfrs1ew+/YVtauNHhDFzFlbu5sycsr9DvwE6geG0VlnI6sKvLKH2jcrWB9TmbdoK9ycF3e1mBoKImSOSfd1CLcInFV5b8QwmRkVmh06mCvdAdMxc+74DBHsJcxEB6MeP8F8u3GWuGnMd+w9Cn4lT4IpPQKcBg9Fbs9iwE/dndcJmuUIlp9PIzPn9lhfidu51YmoaWnftbkikEb1L1aXG+r7hz45DkpCY1kz3PUTvt6sJqsi06W6+6GPts7PoLc0/ac7MnaUKRLGEVYsgACAXwGoARwHUBv9fDWB/cL/6L9YpHr0B1MPoylX9RPzZU8G/AcwghFxGCEklhHQObjsJ4JOY9jRCWKXqVSgJEJExc6J4H8nlNs3EMzM2eo6ZoCsub7gG46VSXyRnlJph8RHpYSn3kafDpA7CotR5LWQ//7e0osHUvLXY4AiH5HSi4NAB5nYVk3/1m9Dv1mnAYLTJ6SF2azi1g70VaRI+zGPmGtq4/ZV3MOX2ezBm+kxMf+pZ0/YJIbZi5iRJEtYPVr+3OTPHd/tJUerMhUtQsArJdx81Dtk92YsyV1w8HJIEvwVjLhqjM0GYuU6544x20k02Uc9XWTyHQ8LUO+/Dve9+iisfelKXaGXnXls15ljHKQkbYTFzcgAr571pqc1YZDiLxiBW9Q5Lv69IFaEJ4ulUg1G0oLaSsSwySgkhFmLm7BtzMU2+igEsvQmU0gmN3A8R0gGUU+OdK9Xs54JS+jghxAvgCzQYrwcATKCUGpczZwEiZq51t+44fVBfLU1yuiLSBxo/YzZqKyu4+50ud1TMnArhi8UYINRJVIoybiEuKQkem9UZVGOl9/jJWPvRPEbfVGPO2v0WGWxdhozA4S0buPszO3YWMnssSE4X6qrCiWe9kdSh7wDc+q83UFNRjpbBxITUzJbMWqRxiUn6yUxgzIUGSMGYZsrMaQZZ4nCEYnkAoL62hnWKDnakEBySUzihq7FepsycoFpJtNIk4feLZQznDB+FLkOHM8/v0E9hzOoqypn7tYjG6GyR3QH7168RHjN+xmysmt9QTioUdB/EmeNHhOdbFcptndMDpw/kmh4nWmhpwVpcK1pl+ueiJO+E4TgeYhGfKHKz5owcYxi/rGRVC5n3pjDmgvOJlWxWEYrzjnH3dR02ylTK62yVk4wlmtzNSAiZTAihFv6tjNH1fg0l5u9PACYCuAZAFYClhBAmHUMIuZ0QsoUQsqWoqCgW3RCCZ8ylt2mHPhOmGLY7JCmimLmBF1wiXKFYYcZEmWUqeC/mBXc/wNyurryiXb2alY5iIngbO3KKUqsDidWBTZTIMeTiy7n7Og4YjCv/OJe5CuXVzAT4g1A4A5qcnoFWnbqEfptJs+5knjf00qvC3DDRMXPmxpw9wz8c7ftYT0p3SBISU9jB+a27dm9gCUxW8WKduejcrDXl+rgxFhvjCAbjs7QCVdYw3LXOgh0Jlcm/+k3o755jJyJN0H73UYqOfO8Jk0Ou8tY5PQwJCAM42dYqrE6wwy+/1tIi0++zZvh3Hjwcgy64NPR5aDA2K/zdZC2ieIiJMSdgqFiCutYYLf77HYskO9WNyoMalyd0s1p4nw5v2cjd13nQUNP62xFloP8UmbkY4wcAbPEkPVQ58DIAzQghJIydUxk5blVfQkg6gH8CeJZS+oRm+3IAx6DEAt4ffh6l9A0AbwDAkCFDGv0XC89m7TJkBPpMmIwO/Qdi76rlhuOVgHz7L5rkdAknGsntFrqhAGvMHMvw6Tl2IroNH8U8Xn2Ro80oik/mlApr1hx9z5uGDZ9/yD23ZcfOzO3qIGBNI86JYZddw90vkmwYfc2N3KD2fpMvwLI3XmL3j2MAm8Vh8rJkh19xre6zcMVsodKBqZtVMMhauecd+7ONcBYkp1OXXKDFBI10g5k0iTuu8cp5seKcwqG2z2IIU4Pl+PpNnoZNX30mvJadybr/lAvQpntP1NdUo22P3ji4cR3zuF5jJyKri7KgSUhJxfSnn0N9XS3iEhMNxoXZWGK1f10GD8OvXn4Lr952o/A4q5qNgy+8DMnpGeg6bCSIw4G2QYMkmt81FsyP6H1gspgW7p9oHmFdr9/kadiz6ntLMZkAMOmW2zH/od9y96thBSJ9umiFocM1DcNBiFgahQeWHMzZRJMzc5TSWkpproV/Koe9B0qSRfgyVDX59woulxM8d3NYH0oBHIY1o7LRER5E27JjJ3QdOgIudxw389Cum7X7yLEAxJS15HSZxMKIWYlQ3xgDxIV3P8ANqFUHyWhXryxmbsrt9+DmZ19Gs1biYuGEELTqbAy4Vw0W0cveIrsDRl49HTf86TkhIyIa0EUsiei+8PaZGXPE4bDk0hVNqDFJgBDF7lmsmMHT0zO052TrKM589mW0yemhuW50btZoskTD2SO2Mae0zyrxpD5/aS2zcM1jfxZey27MT2b7jmjXsw83BklJgHpA98w4JAkJySnMexrLIu8sZkqLhJRUDLrwUt39PO/WuwzHtezYBSkZLUAIQXavvmjXo3fo+0RTOiw2zJw9FtvPEQrWnSeYR8oLCwwam+NunCWMiQ5HfHJyKEucBXU+ObJ1M/cYs8WVGRQxfP79t9q+KrekYqCGvT0XcE5kc5rgWwA+AOHLrhkAdlNKjwrOLQj+rxPbCjJ2XQHkx6qT0SB33UrdZ+3Ax9Wgs0mBj71hptK2YPJUJTq0wozhsJLhZMawtddkUyanZyC9TTvTvlkBS+cuZ/hoJKamceNvtDpqrIlenbREA2nHAYMx6pobhe5QIDKjTOmDfWHdQMAv7AtgMROQ85xJFuVxTKVqRCtmi5MnazBuz8jYdbrjmExmuCvTzMgQJQE5JPPSQQOmXow0zuIiPPaL9dyFSmIx3kWtoWnmgraTCRwOFisrkkthQeTaat3NWA7PDBdywjgAJSM2MTUN1839G/qeNxWTZt+J/pONunPFece5bUTFuMbAmOO5G3uOncjc7rVQIlH4DlOKoZdehTHX34ze48/DDc88j7jEJFvhME53nNDbo45BXYfy5xwryWeiscws9MGqnl7viZMx+KLL0CanJybNuoPrzTlbOBtuVluglJ4hhPwDwEOEkCoAW6HoxE0CoDONCSHfA+hAKe0aPPcYIeRrAA8SQmQAqwBkAJgDhbF7tem+CRuUUkMgelVpcehvHsNiN55BdfGJHmo1S0w0yFph5lp36wHgq9Dn8JJEk2bdie/ffhU+Tx3G3TgrNGlHGzPHcqGpA3ByRoZhHwDdpOp0GV+HUCmZKAN0zY4TrxwFRqDLhc6Dh+HIj5t02zsPZFcO0KLTwCGhqgeAkoARDt5zpjUi3YkCUVeT51QUyyIyBIdpSo4lMUoZxSUZXe6uuDim8WtMOhD/nqLnVGHmxMPquBmz0GPUOHz0hLmuImsiU78Da9EUrt3WtkdvrkB0NNUz2EybvfdXdHwkY0GPMRNAAax49014wuLZVAO8TU4PHQsbjvE33crdZzWjnYVYZLPyFpR9J53P3G4lpstswSQ5nYbQCzPJIC2cbrdwca8aYUMuuRK7li9lHmOFOUtITYWviG28qhnePFgdv13uOEy4+TbzA88SfgrMHNCQwHAfgCUARgO4llL6ddhxEowG6nXBc68GsBDACwAKAYyhlG5pzE5bQXimKgAUHG4o5B4rY06FlQQI0WRkJQGi08AhOomNQRfq6eiMdtm49vE/48Y//1MnLhotM8di31QGIatzNzRvoy/44ZCcurqrrAG3QZok+qwv0YAuMmqEJa+cToy7QS+q2m/yNGFVCxV9J50fEuYlDgdTuJf3nGkn4v5T9IVYhl9xnem1Q+0LY1n4Ys2DL7ws9HfOCH3pqhFXXc80Nng6ioY4NRNmTXJKyGjHLnyuxMzxf2dXfAJc7jiuizu8YgdrIgsZc4x30RWmkdZ95BhuX6KRVmCX5bPHDUS6uOGBEIJeYyfivFl3GPbx3ocr/zhX97nvJGPCmQozxlWEqpLoE+l490s1lrSlwIjDwY1R1iIS13H3kWN1JRBV4V9e30SJdep80jyLLQ0FWIuZG3UNP17STJe1qUrCNTa4bwwhhD1acaCJcYs5KKUBKAbZn0yOm8DYVgulpNfTjdK5KFFdZlRH0cot8GPmrBtzE29pGNxEA5KqtSOuv2puzLnjE3D9U3/HkR83Ib1ttnAlrEW0rgiHJKHbsFE4uOkHAIqmmjqxEocD1z7+Z2xf8jUOblqPNjk90W/yVF2sDXOid5q7Wa2u2MXJBAL2TcTMOV3IaJeNX730FgoOH0Cb7j2Rki6unKDCFRePmX9/GUe3b0FGu/ZMtwGvz9rJvMugYWjfdwBO7NqOrC7dMOTiKyxdHzDPInM4HAgw3gHt/Wreui0uuvdB7Fm9HC2yO2DYpVdjKSNhRHK6mIZW+G9rNnk4JCcm3nI7vv33Pw1irYQQuOMTILlczCBxs0D4C36jF91mvYshkW0WMxfGnIueTWcUbBGLVbPLPonclrKFMAEeWPeMV3+508AhuPe9z1FbXobk9BbCPlkZ+3jYvmSRIebKLni/pcpujbz6elQWn0FlUSGGX36tpQD9SEgBp9uNGX/5F/auXo5mWW2Q2aEjti9ZxDxWqffNZ+a0ng9CHEy22IqxlTNyDHJ/WI1j23/UbW+T0zNYIzp6Zu5ch2j2PAZ79Sr+f9yRJgZrshw7fWbob94kb2VFNfCCS5AzfDTa9eyjOU9kqKnGXGTxW1okpqahz0T+KpeFaIOEHZKEC+7+HbK+zQGlFAOnXazbn9w8HWOuvxljrr+Zc33GBGUhm9XqPREnE0Q22KjGQVrLVkhr2cpSP7SIT05GzzETuPu5blZdjc14XP3I0/DVe+Byx8Wk9JkKHnkU/qz0GD0ePUaPD31mMTESJwHC4GY1Zeac6NB3AO549V08f93Fhv1OtxuDLrgUmxd+btrvcMSHxX2yJqEGY47BzIWx0zwXlTshkVk5xCp8FoLrzSB6rk/u3R1Fu8Z7nMQx5gDFfSbKNFdhpns37PJrsGnBp8x9gzRMcqTg3S/VmEtt0RLXPCrkOwwQhTKwpG9UpGS0CLlfywsLuMcRQiyLwTucEgI+hjFnJWbOHYcr/zgX/vp6VBQVYs2H74IQB8YHS8GdCzVoGxuibzEbDcZcHIBHoZTF+gSKmzILwLUAUnCOsl4/BbCYt479B4X+btWJHVRvpfxI95Hj0La7Pl5NvPJ0B485O3Z5LJg5V1y8rmZftNdXJ3qRERyLlZ04Dst+AkTswE+A0B0VZKRiDR5DY8YCDb74cvy4aIFum0NywsVgs8KNOfOkjYbvntYqCxXBycwhSaEYzHE3zkLrnB5Y+Nwztvpt1jegwYiLY1Q8CWfmeBPhZb9/NCopoIy22YZtHgsiz1rEIsOT2S7jnbBT9osHs+o3Ldp35O7rpBnTIwXPILESx8yDSJpk5NU3WGrDLKbNqhi8Q3Iy2WwrOnOAMga54uPRIruDoZycqI1os2XPFXC/BaX0v5TSdyml70KRAdkKoC+l9ClK6euU0icB9AGwDeYltX4BB+ExcTkjxugG2ezefXVCtFN/rWj2WJnEWS+/aIXidJkzc40J1uA+4qrrLZ8fjXQAwL43KjMlXNnFQCldxAaJjLk4Rh3JWOL/2Hv3uCqrfPH/vTSuoqJxE1ABFREy5KIpOQqhEileCryRipWjNl44ZyzNK5pTHcGiQ+NozoTOnND5NmaWkzXYEbOjGWr+0jSnCG8UDo15vyCyfn8gO/bez97sDXuzEdf79dov2GutZ63P8+zn8nk+67M+H1M3e3s9iC2lvt9aa6r5PmcnzSTqhr9ffVNPdX+rxKkzaqbwhGBA6kQ9y5pPV+Np67rXrWWxC7XS392xxnr7GNU5GYRNMRUrzJpgy1q0vd/4+FZeu6bR0jTm7jNa+VEtRevctEmct3rOC62FOLVYm3NZc3xTlrlGTP+a2ydXjUVEWtRnObM076kplwtb3F9//uGsybp7wTJXlwlAhmFKLSmlFEKsBTagEXxXUT+GljnDm7cQgnHLXuH7Q1/g0dFL53924ZxxKiZDtG5g16+YTndV295RPgRaN4VuMQ/x+ZbNDd7eKsxFQ7ezA63ZsCVmHkRa1hlbYspK5egboCW+PkF9YnQ+NG5t2+Eb0p2fThuHnrD2JaDubxUcFcu03+cDxhlUtH63utua8gfUk01jP2sfjlq/veGDU+vcbEgqQEuwNJBsLeZeYBIyft1gObQXMtk/XZO5RUe2uF5M3d8aoyiaTedlg1X6YLkibUpZtcX99crPJnMLtBifOUuvag/AVPhsH8C+T5QWjKFlTust5D5nZ0L7D9RbSGDJw0zrInJxN/3Gq/OZc6DVxfDCsmRVpqltrcVsaptGppupJdpEoElziqi56Ut7/1amjkljraBQE6DVnsRPeoaAsHC8Onfl0d/8R80CCAt85urD8MF8n5OTpl+QpoXovrqWufrPG60Vp7XyOmsoc4a/l9a+NSR7jCVYG+qkdWvTD/mIwYkNlsNelrn6cHJxISo5RbPOFgqDqenAxqTdMncuWKqA1nf9WOozZ8oyZwurZriJWHxw7ylzRcBLQgi94FVCiH7A7+7UKxqAoWXO0pWRAWER9bbRehvt0ts4mGotOp85Eye3p2/9+R4by5Bpv6nJPduqFQkZv7bqQhaN9H0wu0DB7DSr5TeDwZOf1ltdDGhO/dXF0Km9oWM3CFOhSWzgZzLxdzn1ttHKduImwgAAIABJREFUtlA37I057g/szPjlq5iS83td3D3NFctWKnOWPjzrs8w1ViH269addnWmWrUCr9rTMmf4O3SOMH1v0cKcZa4xCorWC46tlDlz16Jo3crkSm5bKAxafn+Ntcw3jWXOQp85Ey+mloTDqg9z94ymUPSbAkuv6lnATeBzIcRJIcR+IcRJYB9w4069ogEYZniw9CEZOTS5nrRCrTWXpjs5m3CWrZOix9Qb2bAZcyySrTH0ThjG9LV/ZsbaPxOdPNLk9GNfjUUOjVVszN3YbDXN2qpVa6KTU3h47JNAzcMhacZcs9uY/Z3tvFjFtGWu4eO6tvFg7v9stWjqS0vRjZ/yTIPH1rTM2enNXHO6r67PXCMNZK3vc2L0c0sIHfAreg2MJ2GK8dSkpmXOBgnUAR4e96TeOANSLfdvBftN1Wsr0bZ5YD+iEcOullatWtPOy0czBqEt/L60aOxvaYv4mQ31mYsZrr/C11Q/1szOmMJ8Gst7yGdOSlkqhAgDMoD+QCfgKDXK3EYppXXOEgodxpY5yy4gF/c2NbF+9hRpJpDvkzRCc0rV1Aq2+5ycf3H2N3Hi1yactjd1Y7+ZuhGERPel2CCReKPffs3cF81OszbgRt3/ifFEDnuMVq1b1/t2bW4lnrkYdLbA1L41xjLX9cEoi6deBqRO5OM/5BqM3fB91oqtZq8HrbZV7JeTzJKYvYbhIToaBL727hpMSuZ80zJoPCBtNc0a2n8gj82p5sdvvyEsbjDtvIwXZJijvhiDtsRWv3Hn8AdM1tValrQsSfZ6YaCR+2V2NsJCJcfUvtXmCW7trH2t9xmmH9bH1P27KfwdWwIW3xXvKGzr73wUNsLIZ86Ki75DpwAeHptupMxFJ48kfrK29cKUSbnuw7Uxse1sjdbxyFi9hpsaK+ca7zPXsLfUho5rSVDP+vpv7NRyfZjMANEIy5w151HXB/s0eBwtbOEzZylax+5fp+qkkrZAm3Nt48GvJmbw2aY/4+zuRoIZy5CmDJqKm22UOSEEvR4eTK868f2swV7+nlo5Yt3bt9doaT1mA+DeuSa0Xjbs5ZfVWMuc2TSCFl7jpl7shjz9G0D7BSogLFyn7JmT5dFn7b+u0tqFO80Vq64mIcQDwGCgI/BvYLeUUjvxn8IiGmqZM4dnJ3/T02Mmyuta7Ey9MdtqesZaDKPpt/P24d9njBOONHqatYHWN3tZdnRjC0Gr1q01U7vZ3TJnxwUQluDRQSOnbj0rQM2hPe3YdC8pt+tmd7EwJnu/UalEJY1AtGpldWw4rZeeRs/v2gh7TW+5uLfB2c2dyus1++7Wtl2jQp3UxZx/Va1So+X6YC/f1sbekw2DVNfF8mDoxtdPQFi47kVMK85c2TfHLBqvKRYn3FPKnBDiPmrCj0xA/7VOCiEKqAlbop1EVGEW49WsjT95295vauGxaepecNYmzLY3jz77H3y8JpeqqlsMHD8ZJxdX7YdyIy98cw8Xe1jmrKFV6/s0lTm7Td/oBjC1AKJpLHNaD6tG7bPW6lArHogeHTWUSyvQ85GttjzBTkMDw2rFfpMm8j03NabOod6JSY3ue1b+Xzn1/x2CVq0IejCq0f3VYs49QOdzrHEPt5tlrrGxNVu3xj+0Fz/887hRncUhRTSun7C4X6y1lrpUaGXpaIp7a1VVw1PHNScsfTVaRk22h6XA/wDl1GSAePJO3fd3/iqspNoGlrlfTcxgT8EGoMZqFRJtPk1PjWKgfwLX9U1rbku1w+IG0fXBKOTt27/kWNS4gTR2hWVHjaj2tdyqY1ExxO4KFab3zd5+R6asVo15iDTWmtCYaP73d+6q992tneXTb/c5OTd62qeuJd5Sy1xjaOdl/GJXdcv0udyUmPKFakwQ3FqEEAT1iWl0P4aYtcy1qrXM3T3TrAAp/7GAdTOnGJU3JkNI3XNba2pa6zi6awRdbooZgHvKMkeN0rZSSlk3N80p4HdCiNbAVJQy1yCMggY34OTtO/IJPDrez+WfKnggYWi91r3Bk55i14Y39crqXlxaFirfkB5Wy2VL3AxWNWpnt2jcDbNbTD921kn2XDeH6+1K0xe83cODmBnD3sF7Td3QG+UzZ+W0Zo+H4vh2/16gxh/Kr3vDz0X3du2JGT6Kg3/fhmjVisFPPmXRdu28fXnylVyj89Ba9KyrlqyAaCRdNaxSzeXhZUrBaYqXo4Zi6rwXopVO8dBc+GI3v8zG9+vuqZ231tKQIvWhdQ95aPRYozK3dsY+xE1xb62uah7XQ2Ox9EngD+w1UbcXWGQbce49jEOTWH/yCiHMBkU0pEuEcSqfukm7tWR4aEya1XLZE6030sa+/bbx7MDjL2Rx5H//QceAzsQMH62ru23mgm8KS6Y9o6ObQ8uZHBrnJ2jtaspHps6g9X1O3Lh6hbi0iY2+wcdPnkbvxEdxcnGxeAVmh07+DVLkOkc8yJmvv9J9b+/jq/u/CXQ5zfOjyoyVuSkx6XxvZfDh5oCeJUrjBcvSqUZrscXKZFPXU6N8Guuc3Fr7fn9n4/At7naeZu0c3pszx44Yld9r06w/AA8DOzXq4u7UKxpA9W3bL4CoD62bqN5q1rsgV51WnDNbvMUFRUYTpJEU21TCd1uNWx8mrRh2Pl9M+Wo1xnpi7dSQR4eODJ/zXIPH00IrUbw5tDIxWELk0GQ9ZW7ItLohOZtAm9Ogqplb5k58/n/ET57WxNJYTnsfXy7+65x+YZ3zQ9OR305+yPZalObs5m6zvrUCv2uFnNJ6cbTl/e1XEzMoWPxbo/LmYqluLJYeqbeBRUKIJUKIECGEmxAiWAjxAjVWub/YT8SWjfE0a9M40xtS1xR+89pVo3o3D8vCaDQVWm+k9pyeuW3m7a1JFHAHrTA25Z/WqDfmZrKa0hrMpcEzR4+H4nh43CQ6h/cmYco0PWf8zgYWcv8miuN4u9n4zGm/NF75909NLIl1GPpdGqJ1bdjLt9VeK7H7aQRlbyiWPtO0lDlbPg879eipGfS5pUyzWnomZAF/A5YD3wJXgO+oSeX1N2CFPYS7FzCcZnWUYvDjd//U/f/zj2VG9Z1Ce9pVJmvRnma137Ezp8zZc9xfxjD+zRKfftbu45pKpdOYadbqquaxmtIchnEa41InNqifVq1a0//xcYxd9jLRj+lHvB+UPlV3vQvRioQpTWONaqiV0daYmgGwRcR/e6IVN60u5vLp2hp75dk1d7+zhPpOMa08vm00whA1ZhGGFn2SRhiVuWlM796NWJoBogqYKIR4CRgEdADOA5+qOHONw8gy1wT+V1pvxHWVo+A+MRz44F2DbZpXuBK3tsarEO1p1TRnim+S0CQa+2arQKjmMJWLsjHpvDoGBNbfyME8mPgo5384y7nvS4gY/AheXYJsPoZPUAjjl/8Xp746TJcHIvHr1jSLjKqbiY+Qqetm4ATjlZXNCS03lbpWpVs3bzaZLLayzHl06MiVn8/rvkcOTbZJv6a4z8n4JbGtlxfObm5UXr8O1DynvLsG2XRcIQSjn1/Ce6te1JUlPjXTpmM4Cquco6SUR6lJ46WwEYaxwxzlM1fXT6xzeG+92EOpi1faXSZrcWljnALLUDG2JWYtcw7ymWuKc8XkNKsVYw+f+zx/f31VTX+ubjyY+KhNZLMnTq6uDJ1m/5TT/qG98A/tZfdx6tLGxKKWpsaUi0DX3rbN+mFrtK7Fur/hj99+02Sy2CpJ/KRVeXz8h1wqTp9k4PjJNreOhg96hGOf/i9QE8Q5UCMtmpOzC3Fp6Xz69gaqb1cxIHWizYI91yU4KpYBqRMoPXyQoMhoQqLMh/K6W7BYmRNCuANP8UsGiPPALiBfSnndPuK1fBximdMYo65VQLRqxdhlL/Pjdydod7837byty7nYFAgh6OAfyM8/nNWVdfAPsNt45vwqmiTOnGYoliZQ5ly1p1mt2eewuEHc5+xCxanv6TlgEK4epqPOK2zPsOlz+Me6/9Z9f2h081qZbkhzT3yu+WJVp+zaxQtNJktjg1jX4t6uPWPm2zC6mME06uBJTyNateL6pYs8NGacyd84Zvhowh4ejKyuttm+GdKqVWvi0tKJS0u3S/+OwtIMEH5AERBKTXy5ciAEeAKYLYSIl1KeM92DwhQOscxp5g7UL2t9330EhkXYXZbGEJc6gY/WvEb17WoGTphcb8L6xmDeZ84xoUma4ly5z0QAV2sVye6xD9E99iFbiKSwkvBBj3Dl/L/58dtvCHt4sF2mjG2JNYGcHUF9GR4Gjp/MZ5v/rPvuG9LdZmMPnTaLwvVv6L4Pmphhs75tieHqXfd27Xl0ZqZF2zZ3n8nmiqWvQKuo8ZP7lZTy/2oLhRBxwBbgv4AMm0t3D+CQ1axauQM1ypo7YQ8PJigyhttVtxx6A2gaa6qGAt4EOUVNvUE3xaIPhW1ofd99DEid4GgxLMZROaAtRevFqu59+8Ehj/LVJx9xqeJfAEx4MdtmY0fED+HSTxX8+N0Jeg2MbzaKeczw0Rz8+3tAjR9faP+HHSzRvYelylwyML+uIgcgpdwrhFgMvGJzye4RHLKaVUNhbMpk47akOUzZOZtYJGBLtC1zjlks01RjK+5BmrkiB9ovMtcvX9T979a2HdPeeIuqW7dsHiy49X33MXD8JJv2aQv6jU7j2sUL/Fz+A9GPjcK9mVtXWyKWKnMemA4MfPZOvaIBGEZjd1he1GYSruBupKFJ0K1B6wHiqMUy0DT+eop7kLvgPqT1MqwViNleWR+aI+7t2vPY7HmOFuOextI78gnA1OvAk0DTLd9pYXzzf7v1vjd35997FXPTGY1J/G4pWpbTppjqNBWSptqOK4cV9xB3gSXOEK0XnJ4DBjpAEoXiFyzVHHKAPwshfIEC4EfADxgPDMG0oqewknPff0uvgfGOFkNhwOBJT7Pld0uMyls7OTWJAl43JVQtTZF2zdS+/XTmlN3HVrR8WrVqZbQIzBTV1dWcPXuWq1eNM9Q0JW1DIxj4m2C9MuHpyfHjxx0kkaKl4OTkhI+PD+3aWZ9xydKgwf9zJzTJCuCPdarOATOklAVWj6xQ3EUEPRhF974D+K54n155U0x1mqIplEhT06zNJfCs4u6mVavWFitzP/30E0IIevbs6dBp/ivn/60XYBego38gzm72951VtFyklFy/fp2yspoMTNYqdBZfEVLKNwF/IAL41Z2/AVLK9VaNqDBLn6QUR4ugMEG3mH5GZVVNGO3dEEdlCwG43ULyGSocizUvQxcuXMDX19fx/ppaU8N34XSxonkhhMDd3Z2AgAD+9a9/Wb29VVeFlLJaSnlcSvl/d/4qx5lGoJXDr52XtwMkgdY2zoHXEnGkFS4q2VjJb4ppVlOhcjoGdLb72IqWT2zK43rfDfPX1uX27ds4NdNFBUqXU9gKNzc3bplJH2kKazJAtAMeA7oAhh7fUkr5ovFWCnNU39afqmrVunWTrWYNCIug7Jtf0up2Du/dJOPezdgzXVh9tO3oZVTm5KId0Lcp6Dcy1WFjK1oOUY+O4Ju9n/LzD2dp5+1L7IgxZts3hxh02jI4Xi5Fy6Ch57ilGSAeBj4APE00kYBS5qykqlJf+27t1HTWsbi0ibz/6kvcvHaNAU+M10sUrdDGMIxMU6KVg9G1bVsHSFKDp18nh42taDm4tW3HpFdy+fnHH/D09bNLLk7bY/ywbQ5KpuLextJ5o1zgJNAXcJVStjL42NWcJIT4TyHEB0KIH4UQUgiRZeX2A4UQe4UQ14UQ5UKIV4UQDvdWvX1LXzloyrhEXR6IZPraP/ObP21qcTnq7EVVpbF/3OjnlzbJ2FohQpxMpNqyN64ejlMiFS0PJxdXfIJC7hJFzsSUagvS5YKCgsjJyXG0GAorsVSZ6wUsllIelFI6wjwxDfAB3rN2QyHEg0Ah8C9gBLAYmApssKF8DcLQ0mMqD6a9cHJ2wbWNivdsKVqWOa1FEU2Fw3z47oLArgqF3dDQ5kQDtLkNGzbg0Qwy2BhSXFzMs88+67Dx586dS2xsLK6urgQFBVm0jZSSrKws/P39cXNzIz4+nq+//rr+DS1gy5YthIeH4+LiQnh4OFu3bjXZdvr06QghHKIMW/o0OA04zkEHIqSUDwGzG7DtcmqyVKRJKT+RUv4RmAuMFUJE21JIazGMGt7aSQUMbs70MMg32C22f5ONrbVYxlFImo8sCkWzoAVNs3p7e+Pu7jgraXV1NVOmTGHy5MkWb7Nq1SpWr15NXl4excXF+Pj4MHToUC5fvtwoWfbt28e4ceNIT0/n8OHDpKenk5aWxv79+43a/u1vf+OLL77A39+/UWM2FEu1h+XAAiHEJ1LKS/YUSIuGrpoVQjgBjwKvSinrak7/D1gPjAIONV7ChmG4WyrfZfPm/oDO9H98HPvfewe3tu3o//i4Jhu7WS0cV7qcwsEELfi7Q8f/fFqofoEZXe7TTz/l+eef5+jRo7Ru3ZqePXsyefJkZs+usU3U+tstW7aMrKwsKisrWbJkCW+//Tbnz58nIiKClStXkpSUBEBRUREJCQl88MEHLF68mG+++YaIiAjefPNNYmJi6pX94sWLzJo1i48//phLly7h7+/PnDlzyMzMBGqmWWfNmsW8efPIyspi+fLlRn3UygqQn59PdnY233//PV26dGHmzJnMnTu3wSFk8vLyAMjJyeEf//hHve2llOTm5rJgwQKeeOIJADZu3IiPjw8FBQVMnz4dgLKyMn7729/y8ccfAxAXF0dubi49evQw2Xdubi4JCQksWrQIgEWLFrFr1y5yc3PZtGmTrt2pU6eYO3cuO3fuJDk5uUH73VhMKnNCiD8bFPkCpUKIfcB5gzoppZxia+FsQDdqVt4erVsopbwhhCgBwh0i1S+C6H1tOe92LZeHx02i36g07nNxaVqn52ZkmXNkiBaFojliapq1qqqKUaNG8fTTT/P2229z69YtDh06REREBLm5uSxcuJCSkhIA3ZTr1KlTKSkpoaCggMDAQD788ENSUlIoLi4mMjJS1/e8efN4/fXXCQgIYPny5YwYMYKSkpJ6rWqLFy/myJEjbN++HV9fX0pLS6moqNBsO2/ePGbMmKH7XlhYyFNPPcXAgTXpy9avX8/SpUvJy8sjJiaGo0ePMm3aNJycnJg1axYAycnJ7Nmzx6xMV65cMVtvjtLSUsrLyxk2bJiuzM3NjUGDBrF3716mT5/OtWvXSEhIIC4ujt27d+Ps7ExOTg5Dhgzh+PHjJo/Zvn37dEp3LUlJSbzxxhu671VVVUyYMIHFixfTq1evBu9HYzFnmRuE/ju4BC5REyzYkObzpNGndonmzxp15+vUOwTDqTP1kLw7cHK1fy5WQ7w6d9X73sE/sMllqKWNZweHja1QNEtMvNhdunSJCxcukJKSQrdu3QAICwsD4Msvv0QIgZ+fn659SUkJmzZt4uTJk3Tp0gWAWbNmsXPnTtatW8eaNWt0bZcsWaKz1uXn5xMYGEhBQQHPPPOMWVFPnTpFdHQ0/frV+Pt27drVZFsPDw+dknnixAnmzJlDdnY2Q4YMAeDFF19k1apVpKbWhCoKDg5mwYIFrFmzRqfM/fGPf+T69etmZWoM5eXlAPj6+uqV+/r66rIpbN68GSkl+fn5upfwdevW4ePjw/bt2xk7dqzJvrX6rR0TaqyUXl5ezJw502b71BBMKnNSyiB7DCiEGELNgoT62C2ljLeHDPUhhPg18GtAd0HZg+bkB6Vo3gSG9yYgLJyyb44B0GfYcIfJohUmRaG4lzFlpO/YsSMZGRkkJSWRmJhIYmIiqampJp8rhw4dQkpJeLj+pNHNmzd55JFH9MoGDBig+9/Dw4PevXtz7NixemWdOXMmqampHDx4kKFDh5KSksLgwYPNbnPhwgVGjhzJ2LFjddOxFRUVnDlzhunTp+spMlVVVXrPtoCAgHplsjcHDx6ktLSUtgbhnK5du0ZJSQmnT5/WO+YLFy5k4cKF9fZbVFTEhg0bOHz4sM1lthZHeNzvpWZ1bH1cs8FYtRY5LVNCR0Bzucud1GVvAsTGxtpP41KWOYWFCCFIXfw7viveRxvPDg4N8lx53RaXpkLRcE6+4riXmZvXrvLzjz8YlJp2ucjPzyczM5OPPvqI999/n0WLFvHee9qBGaqrqxFCUFxcbJTtws1GuV+Tk5M5deoUO3bs4JNPPmH48OGkpaWRn5+v2b6qqoq0tDQCAgL0pher7wRRX7t2LXFxcWbHs+c0a61l89y5c3pK8rlz53R11dXV9OnTh82bNxtt37FjR9q1a6enkHXs2FHX97lz5/Ta1+23qKiIH3/8kU6dfom7efv2bebPn09ubi5nz55t8H5ZizmfuS7Aj1LKW3f+N4uU8rQlA0oprwHfWC5ioygBbmIwNSyEcAVCgHeaSA5NjKZZHSSH4u7gPicnwuIGNfm4bm3bcf3yL+ueOjpwilehcDRaEyr1+c9GRkYSGRnJ/PnzSU5OZuPGjYwYMYLbt2/rtYuKikJKSXl5OQkJCWb7/PzzzwkJCQHg6tWrHD161OIVoF5eXkyaNIlJkyaRnJzMhAkTWLt2LS4aWWUyMzM5efIk+/fv11MwfX198ff3p6SkxOy49p5mDQ4Oxs/Pj8LCQvr27QvAjRs32LNnD9nZ2QBER0ezadMmvLy88PTUzn3QvXt3o7IBAwZQWFjIc889pysrLCzUKa/PPvusboq5lqSkJCZMmMC0adNssn+WYs4yVwoMAL6gJmBwfRaqZrcUU0pZKYT4iJowJFlSytr8WanUhFp533HSaUyzKsucohkybPoctuWs1H3v/8R4B0qjUDiWVq0sf+0uLS1l3bp1jBw5koCAAL7//nu++uorZs6cSVBQEDdu3KCwsJCoqCjc3d0JDQ0lPT2djIwMVq9eTXR0NOfPn6eoqIiQkBAef/yXXLYrV67E29sbf39/VqxYgbOzMxMnTqxXpqVLlxIdHU1ERARVVVW8++67hISEaCpy+fn5vPXWW+zYsYPKykqdr1itL93y5cuZPXs2np6ePPbYY7oFHmVlZbzwwguA9dOs3333HVeuXOGHH36gsrJSZzELDw/H2dmZsrIyEhMTefnllxkzZgxCCDIzM3nppZcICwsjNDSUlStX4uHhoTse6enp5OTkMGrUKFasWEGXLl04c+YM27ZtY8aMGSZXtM6dO5dBgwbxyiuvMHr0aLZu3cquXbv47LPPAPDx8cHHx0dvGycnJ/z8/OjZs6dV+91YzClzT1Fj2ar932EOXkKIWCCIX+LihQshatXhD+9Y+xBC/AmYIqWsu19ZwOfA/xNC/P5OP9nA36SUB+0vvRmMLHPKNqdofnSL6ceQZ57lzNdH6N63P526N+1NSqFoTji5uNKqdSuqb9dMM7q3a2+yrbu7O//85z9JS0vjp59+wtfXl/T0dObPn4+TkxMzZsxgwoQJ/Pvf/9aF+8jPz+d3v/sdzz//PGfPnqVjx47069fPyFL3yiuv8Nvf/pYTJ04QERHB9u3badOmTb3yu7i4sGjRIkpLS3F1daV///588MEHmm13797N9evXiY+P1yuvlfWZZ56hTZs2ZGdn88ILL+Dm5kZERIRu8UNDeOaZZ9i9e7fue1RUFFCjGAcFBXHr1i1OnDjBxYsXdW2ef/55rl+/zm9+8xt+/vlnHnroIf7xj3/ofOTc3d359NNPWbBgAWlpaVy8eBF/f38SEhLo0MH0gq64uDg2b97M4sWLWbp0Kd26deOvf/0rDz30UIP3z16Iu8EJXwixATAV+iRYSnmybjsppZ5WJIQYBPwXEAVcBDYBC2uVQHPExsbKAwcONFh2c5SXfMvbC/9D9903pDtPvpxrl7EUCoXibub48eMODf1Ql1s3b3L98kVa3+eEW7v2DY6p1hBq48xVVFTg5eXVZOMqmg5z57oQ4qCUMtaw/K5IOSClzAAyGtpOSvkpNVPGzQrjQLDKMqdQKBTNHScXF5xcfOpvqFA0EeYWQLxlRT9SSvm0DeS5tzAwigorfDEUCoVCoTDE3OpRS0NuKO4+zFnmHsFyP7nmP1fbDDFK56UscwqFQqEwQ3x8vNkYpeZWj9aG3FC0PJo8aLDiF4yuR2WZUygUCkUjaA5BehVNj4qF4UCUZU6hUCgUCkVjsViZE0K0EULMEUL8TQixSwjR4075eCFEmP1EbMEYZYBQypxCoVAoFArrsGg1qxCiM1AEBFKTveEBoDbJWQIwBDCf3VdhhLHfg1LmFAqFQqFQWIellrnV1KTFCgVi0Nc6dgO/srFc9wbKMqdQKBQKhaKRWBpnbijwaynlKSGEYdquMkB5XDYA49ysSplTKBQKhUJhHZZa5pyByybq2gNVJuoUZjBS5pRlTqFQKBQOJCgoiJycHEeLobASS5W5r4AnTNQlA47NcXqXonzmFAqF4t5kw4YNeHh4OFoMI4qLi3n22WcdNv7cuXOJjY3F1dWVoKAgi7aRUpKVlYW/vz9ubm7Ex8fz9ddf20SeLVu2EB4ejouLC+Hh4WzdulWvfsmSJYSFhdGmTRs6dOhAYmIie/futcnY1mCpMpcNPC2EWA8MulMWLoRYDjx9p15hLdUGoUmaML+fQqFQKBSGeHt74+7u7rDxq6urmTJlCpMnT7Z4m1WrVrF69Wry8vIoLi7Gx8eHoUOHcvmyqQlFy9i3bx/jxo0jPT2dw4cPk56eTlpaGvv379e16dmzJ7///e85cuQIn332GcHBwTz66KOcO3euUWNbjZTSog8wA7gA3Aaq73wuUuNLZ3E/d9snJiZG2ovvvzwgc8YO133eWbnYbmMpFArF3cyxY8ccLUKD2L17t3zooYdkmzZtZLt27WTfvn1lXl6epCZzku6zbNkyKaWUN2/elM8//7wMCAiQbm5uMjY2Vn700Ue6/nbt2iUB+cEHH8jIyEjp4uIio6Oj5YEDByyS58L4T4m6AAAgAElEQVSFC/LJJ5+U3t7e0sXFRQYHB8vXXntNV9+1a1eZnZ0tpZRy2bJlRnLWlVVKKd966y3Zq1cv6eLiInv06CFfffVVefv27UYft+zsbNm1a9d621VXV0s/Pz+5cuVKXdm1a9ekh4eHXLt2ra7s7Nmzcty4cdLT01N6enrKxx57TP7zn/802/fYsWPlkCFD9MoSExPl+PHjTW5z8eJFCej9ZtZi7lwHDkgNXcXSBRBIKdcKIf5CTcJ6H+DfwF4p5WUhhIeU8ootlMt7CaOgwcoyp1AoFPWT1d7B41+0qFlVVRWjRo3i6aef5u233+bWrVscOnSIiIgIcnNzWbhwISUlJQC6KdepU6dSUlJCQUEBgYGBfPjhh6SkpFBcXExkZKSu73nz5vH6668TEBDA8uXLGTFiBCUlJfVa1RYvXsyRI0fYvn07vr6+lJaWUlFRodl23rx5zJgxQ/e9sLCQp556ioEDBwKwfv16li5dSl5eHjExMRw9epRp06bh5OTErFmzAPO5Ymu5cqXh6kNpaSnl5eUMGzZMV+bm5sagQYPYu3cv06dP59q1ayQkJBAXF8fu3btxdnYmJyeHIUOGcPz4cZPHbN++fcyePVuvLCkpiTfeeEOzfWVlJW+++Sbt2rWjT58+Dd6nhmBpnLn/llLOkVJeBXYa1HkAHwMP20G+lo2By5zymFMoFIqWw6VLl7hw4QIpKSl069YNgLCwmhj7X375JUII/Pz8dO1LSkrYtGkTJ0+epEuXLgDMmjWLnTt3sm7dOtasWaNru2TJEpKSkgDIz88nMDCQgoICnnnGfMjXU6dOER0dTb9+/QDo2rWrybYeHh46JfPEiRPMmTOH7OxshgwZAsCLL77IqlWrSE1NBSA4OJgFCxawZs0anTJnLlesLSgvLwfA19dXr9zX15eysjIANm/ejJSS/Px8hKh50q5btw4fHx+2b9/O2LFjTfat1W/tmLVs376d8ePHc+3aNTp16kRhYaHRdvbGUsvcVCHEj1LKl+sWCiHaAB8BnW0u2T2AsswpFApFy6Vjx45kZGSQlJREYmIiiYmJpKam6hQ1Qw4dOoSUkvDwcL3ymzdv8sgjj+iVDRgwQPe/h4cHvXv35tixY/XKNHPmTFJTUzl48CBDhw4lJSWFwYMHm93mwoULjBw5krFjx5KZmQlARUUFZ86cYfr06cycOVPXtqqqSm9xX3PIFXvw4EFKS0tp27atXvm1a9coKSnh9OnTesd84cKFLFy40OL+ExISOHz4MD/99BPr169n7Nix7Nu3j06dOtlsH+rDUmUuDdgmhCiXUuaDTpHbAQTzy6IIhRUYLWZVKBQKRYsiPz+fzMxMPvroI95//30WLVrEe++9p9m2uroaIQTFxcU4OTnp1bm5udlEnuTkZE6dOsWOHTv45JNPGD58OGlpaeTn52u2r6qqIi0tjYCAAL3pxeo7C/jWrl1LXFyc2fHsOc1aa9k8d+6cnpJ87tw5XV11dTV9+vRh8+bNRtt37NiRdu3acfjwYb2y2r4NFzLU7beWNm3a0L17d7p3707//v3p0aMHf/zjH1myZEmD98taLFLmpJQfCSGmAeuFEBXAJ8CHQHdgsJSyxI4ytliUZU6hUCgagIU+a82FyMhIIiMjmT9/PsnJyWzcuJERI0Zw+/ZtvXZRUVFIKSkvLychIcFsn59//jkhISEAXL16laNHj1q8AtTLy4tJkyYxadIkkpOTmTBhAmvXrsXFxcWobWZmJidPnmT//v16Cqavry/+/v6UlJSYHdfe06zBwcH4+flRWFhI3759Abhx4wZ79uwhO7sm0EZ0dDSbNm3Cy8sLT09PzX66d+9uVDZgwAAKCwt57rnndGWFhYVmlVeoUR5v3rzZ0F1qENYsgPizEMIP+H/AEaArEC+l/NZewrV4DIMGC+U1p1AoFC2F0tJS1q1bx8iRIwkICOD777/nq6++YubMmQQFBXHjxg0KCwuJiorC3d2d0NBQ0tPTycjIYPXq1URHR3P+/HmKiooICQnh8ccf1/W9cuVKvL298ff3Z8WKFTg7OzNx4sR6ZVq6dCnR0dFERERQVVXFu+++S0hIiKYil5+fz1tvvcWOHTuorKzU+YrV+tItX76c2bNn4+npyWOPPaZb4FFWVsYLL7wAWD/N+t1333HlyhV++OEHKisrdRaz8PBwnJ2dKSsrIzExkZdffpkxY8YghCAzM5OXXnqJsLAwQkNDWblyJR4eHrrjkZ6eTk5ODqNGjWLFihV06dKFM2fOsG3bNmbMmEGPHj00ZZk7dy6DBg3ilVdeYfTo0WzdupVdu3bx2WefATU+katWrSIlJYVOnTpRUVHB73//e86ePWvSD89uaC1xvTPf3crE57+BfwG965ab6udu/9gzNMmJzz/TC03yXvbK+jdSKBSKe5C7MTRJeXm5HDNmjPT395fOzs6yc+fO8rnnnpOVlZVSSilnzJgh77//fr1wH5WVlXLZsmUyODhYOjk5SV9fX5mSkqILPVIbmmTbtm2yd+/e0tnZWUZFRckvvvjCIplWrlwpw8PDpZubm+zQoYNMTk7WO7Z1Q5NMmTKl3tAkBQUFMioqSrq4uEhPT0/58MMPy02bNjX4mA0ePFhzzNLSUimllKWlpRKQ+fn5um2qq6vlsmXLpJ+fn3RxcZGDBg2SR44c0eu3vLxcZmRkSG9vb+ns7CyDgoLk1KlTZUVFhVl53nnnHdmzZ0/p5OQkw8LC5JYtW3R1V69elaNHj5adOnWSzs7OslOnTnLkyJHy888/b/D+S9mw0CRCmnDcEkJUY7Te8pdqgzoppbTYync3ERsbKw8cOGCXvv/5+Wd88Noruu89Hopj5H9a7nSpUCgU9wrHjx+nV69ejhbD4RQVFZGQkEBFRQVeXl6OFkdhB8yd60KIg1LKWMNycwrYCkwrcwobYKhICxWcRKFQKBQKhZWYVOaklFlNKMc9iZFVVC2AUCgUCkUjMLd61NqQG4q7hxY5NXq3YGyZUygUCoXCNPHx8caGgDqYWz1aG3JD0fIwqcwJIZYCf5RS/nDnf3NIKeWLthXtHsBQmVOWOYVCoVA0guYQpFfR9JizzGVRk93hhzv/m0MCSpmzEnNvVwqFQqFQKBSWYM5nrpXW/woboixzCoVCoVAoGonSHhyI8plTKBQKhULRWJQy50CMlDllmVMoFAqFQmEl5hZAmAsabEiLDRpsTwxzsyrbnEKhUCgUCmtRQYMdicHRFa2UMqdQKBQKxxEUFMSsWbOYN2+eo0VRWIHJeT0pZZaUcrmln6YUuqWgLHMKhUJxb7JhwwY8PDwcLYYRxcXFPPvssw4bf+7cucTGxuLq6kpQUJBF20gpycrKwt/fHzc3N+Lj4/n6669tIs+WLVsIDw/HxcWF8PBwtm7dqqu7desW8+fP58EHH6RNmzZ06tSJiRMncvr0aZuMbQ13hZOWEOI/hRAfCCF+FEJIIUSWhdu1FkLME0L8rxDinBDishDikBDiaSGE4/ddWeYUCoVC0Yzw9vbG3d3dYeNXV1czZcoUJk+ebPE2q1atYvXq1eTl5VFcXIyPjw9Dhw7l8uXLjZJl3759jBs3jvT0dA4fPkx6ejppaWns378fgGvXrnHo0CEWLVrEoUOH2LZtG2fOnOHRRx+lqqqqUWNbi+MVGsuYBvgA71m5nRuwGDgK/BoYDewC1gP/ZUsBG4KhZU7lZlUoFIqWxaeffkr//v3x8PCgffv29OvXjzfeeIOpU6dy9epVhBAIIcjKygKgsrKS+fPnExgYiLu7O3379uXjjz/W9VdUVIQQgu3bt9OnTx9cXV2JiYnh4MGDFslz8eJFJk2ahI+PD66uroSEhJCbm6urDwoKIicnB4CsrCydfHU/tbIC5OfnEx4ejqurK6Ghobz22mtUVxvOOllOXl4es2fPJjQ01KL2Ukpyc3NZsGABTzzxBA888AAbN27k8uXLFBQU6NqVlZUxfvx4OnToQIcOHRg+fDjffvut2b5zc3NJSEhg0aJF9OrVi0WLFhEfH687Xu3bt6ewsJBx48bRs2dP+vXrx7p16zh+/DjHjx9v8DFoCHfLooUIKWW1EOI+YIYV210HQqSU5+uUfSKE6ADMFkIslVJq5z1pAgxjBivLnEKhUNRP7429HTr+kSlHLGpXVVXFqFGjePrpp3n77be5desWhw4dIiIigtzcXBYuXEhJSQmAbsp16tSplJSUUFBQQGBgIB9++CEpKSkUFxcTGRmp63vevHm8/vrrBAQEsHz5ckaMGEFJSUm9VrXFixdz5MgRtm/fjq+vL6WlpVRUVGi2nTdvHjNm/PLILSws5KmnnmLgwIEArF+/nqVLl5KXl0dMTAxHjx5l2rRpODk5MWvWLMB8rtharly5Us+RNE1paSnl5eUMGzZMV+bm5sagQYPYu3cv06dP59q1ayQkJBAXF8fu3btxdnYmJyeHIUOGcPz4cZPHbN++fcyePVuvLCkpiTfeeMOkPJcuXQKgQ4cODd6nhnBXKHPS2LnM0u1uA+c1qoqBqYAXcKYRojUK5TOnUCgULZdLly5x4cIFUlJS6NatGwBhYWEAfPnllwgh8PPz07UvKSlh06ZNnDx5ki5dugAwa9Ysdu7cybp161izZo2u7ZIlS0hKSgJqrGOBgYEUFBTwzDPPmJXp1KlTREdH069fPwC6du1qsq2Hh4dOyTxx4gRz5swhOzubIUOGAPDiiy+yatUqUlNTAQgODmbBggWsWbNGp8yZyxVrC8rLywHw9fXVK/f19aWsrAyAzZs3I6UkPz8fIWqes+vWrcPHx4ft27czduxYk31r9Vs7piGVlZX89re/JSUlhcDAwEbtl7XcFcqcHRgMXAB+dKgURnHmlDKnUCgULYWOHTuSkZFBUlISiYmJJCYmkpqaqlPUDDl06BBSSsLDw/XKb968ySOPPKJXNmDAAN3/Hh4e9O7dm2PHjtUr08yZM0lNTeXgwYMMHTqUlJQUBg8ebHabCxcuMHLkSMaOHUtmZiYAFRUVnDlzhunTpzNz5kxd26qqKr0Yqs0hV+zBgwcpLS2lbdu2euXXrl2jpKSE06dP6x3zhQsXsnDhQqvGqKqq4sknn+TChQu8//77NpHbGu45ZU4IkQSMBZZIKZvWQ9EA49ysSplTKBSKlkR+fj6ZmZl89NFHvP/++yxatIj33tN2/66urkYIQXFxMU5OTnp1bm5uNpEnOTmZU6dOsWPHDj755BOGDx9OWloa+fn5mu2rqqpIS0sjICBAb3qx1i9u7dq1xMXFmR3PntOstZbNc+fO6SnJ586d09VVV1fTp08fNm/ebLR9x44dadeuHYcPH9Yrq+373Llzeu3r9ltLVVUVEyZM4MiRIxQVFXH//fc3eH8aikXKnBDC3LKSauAi8KWU8qwFfQ0BCi0YdreUMt4S+SxFCBEObKJmEYTJBRBCiF9Ts2DC5BuUTVCWOYVCobAaS33WmguRkZFERkYyf/58kpOT2bhxIyNGjOD27dt67aKiopBSUl5eTkJCgtk+P//8c0JCQgC4evUqR48etXgFqJeXF5MmTWLSpEkkJyczYcIE1q5di4uLi1HbzMxMTp48yf79+/UUTF9fX/z9/SkpKTE7rr2nWYODg/Hz86OwsJC+ffsCcOPGDfbs2UN2djYA0dHRbNq0CS8vLzw9PTX76d69u1HZgAEDKCws5LnnntOVFRYW6imvt27dYvz48Rw9epSioiIjRa+psNQyt4FfAmnU1TjqllULIf4KTJVSVprpay/Qy4Ixr1kom0UIIUKoUSJLgTHmrHJSyjeBNwFiY2PtFjjZODerUuYUCoWipVBaWsq6desYOXIkAQEBfP/993z11VfMnDmToKAgbty4QWFhIVFRUbi7uxMaGkp6ejoZGRmsXr2a6Ohozp8/T1FRESEhITz++OO6vleuXIm3tzf+/v6sWLECZ2dnJk6cWK9MS5cuJTo6moiICKqqqnj33XcJCQnRVOTy8/N566232LFjB5WVlTpfsVpfuuXLlzN79mw8PT157LHHdAs8ysrKeOGFFwDrp1m/++47rly5wg8//EBlZaXOYhYeHo6zszNlZWUkJiby8ssvM2bMGIQQZGZm8tJLLxEWFkZoaCgrV67Ew8NDdzzS09PJyclh1KhRrFixgi5dunDmzBm2bdvGjBkz6NGjh6Ysc+fOZdCgQbzyyiuMHj2arVu3smvXLj777DPgF6tlcXExH3zwAUII3TFq3769zaypFiGlrPcDDAC+B14HfgWE3vmbR41ylAzMo0YBe8mSPhvyoUb5lECWldsF3pHzOOBlzbYxMTHSXhR/8K7MGTtc99m18U27jaVQKBR3M8eOHXO0CFZTXl4ux4wZI/39/aWzs7Ps3LmzfO6552RlZaWUUsoZM2bI+++/XwJy2bJlUkopKysr5bJly2RwcLB0cnKSvr6+MiUlRR44cEBKKeWuXbskILdt2yZ79+4tnZ2dZVRUlPziiy8skmnlypUyPDxcurm5yQ4dOsjk5GS9Y9u1a1eZnZ0tpZRyypQp8s4zV+9TK6uUUhYUFMioqCjp4uIiPT095cMPPyw3bdrU4GM2ePBgzTFLS0ullFKWlpZKQObn5+u2qa6ulsuWLZN+fn7SxcVFDho0SB45ckSv3/LycpmRkSG9vb2ls7OzDAoKklOnTpUVFRVm5XnnnXdkz549pZOTkwwLC5NbtmzR1dXKovWpK5+1mDvXgQNSQ1cR0shvyxghxBbghJTSyCNQCPES0EtKOUYI8SKQLqUMsVSZtIY7oUluAcullFkWbuMN7AFcgF9JC6aC6xIbGysPHDhgragWUfzBu3z6P2/pvscMH038ZPMrkRQKheJe5Pjx4/TqZcmkTsumqKiIhIQEKioq8PLycrQ4Cjtg7lwXQhyUUsYalls6zToMWGOi7n+BWXf+/xR43sI+LUYIEQsE8UuQ43AhROqd/z+UUl670+5PwBQp5X13vrsBH9/Z9ikgUAhRd73wMSnlJVvLazFGPnN3SwxnhUKhUCgUzQVLtYebQIyJuhig1keuFXC1sUJpMAt4B/jrne9pd76/Q01miFpa3/nU4gtEUWOVexvYZ/CJtoOsFmOJVVShUCgUCktJTk7W+bQZfl566SVHi6ewE5Za5t4BlgshbgN/A/5FjRKVBmQBtXOFfYATNpYRKWUGkGFtOynlSZpxvA9DZU5Z5hQKhUJhjvj4eLOGAHOrR2tDbihaHpYqc/8JtAVW3fnUpQD47Z3/j1Jj8VJYgtFqVoVCoVAoGk5zCNKraHosUuZkTf7SJ4UQK4D+gB812RO+kFKeqNPu73aRsoWiLHMKhUKhUCgai1UZIKSU/wT+aSdZ7jlUblaFQqFQKBSNxWJlTgjhTs2K0MFAR2oS2O8C8u9Y7hTWYuD2oDJAKBQKhUKhsBaL5vWEEH7AIeC/gVjA/c7fN4BDQghfu0nYglGWOYVCoVAoFI3FUietVUAHaoLuBkspB0gpg4GBgCdm8pwqTGO4IEkIpcwpFAqFQqGwDkuVuWTgBSnl/9UtlFLuBRYDw20t2D2BgWVOKXMKhUKhcCRBQUHk5OQ4WgyFlViqzHkAP5ioO3unXmElyjKnUCgU9yYbNmzAw6P5PTqLi4t59tlnHTb+3LlziY2NxdXVlaCgIIu2kVKSlZWFv78/bm5uxMfH8/XXX9tEni1bthAeHo6Liwvh4eFs3bpVr/7dd98lKSkJb29vhBAUFRXZZFxrsVSZOwFMMlH3JPCNbcS5tzDymVPKnEKhUCgciLe3N+7u7g4bv7q6milTpjB58mSLt1m1ahWrV68mLy+P4uJifHx8GDp0KJcvX26ULPv27WPcuHGkp6dz+PBh0tPTSUtLY//+/bo2V69eJS4ujldffbVRYzUWS5W5HGCCEGKnEOIpIUSyEGKqEOJjYCKQbT8RWy5GceaUMqdQKBQtik8//ZT+/fvj4eFB+/bt6devH2+88QZTp07l6tWrCCEQQpCVlQVAZWUl8+fPJzAwEHd3d/r27cvHH3+s66+oqAghBNu3b6dPnz64uroSExPDwYMHLZLn4sWLTJo0CR8fH1xdXQkJCSE3N1dXX3eaNSsrSydf3U+trAD5+fmEh4fj6upKaGgor732GtXVhov7LCcvL4/Zs2cTGhpqUXspJbm5uSxYsIAnnniCBx54gI0bN3L58mUKCgp07crKyhg/fjwdOnSgQ4cODB8+nG+//dZs37m5uSQkJLBo0SJ69erFokWLiI+P1ztekyZNYtmyZSQnJzdsh22EpUGD/+dOaJIVwB/rVJ0DZkgpC7S3VJjFeJ7VMXIoFArFXcTxsF4OHb/XN8ctaldVVcWoUaN4+umnefvtt7l16xaHDh0iIiKC3NxcFi5cSElJCYBuynXq1KmUlJRQUFBAYGAgH374ISkpKRQXFxMZGanre968ebz++usEBASwfPlyRowYQUlJSb1WtcWLF3PkyBG2b9+Or68vpaWlVFRUaLadN28eM2bM0H0vLCzkqaeeYuDAgQCsX7+epUuXkpeXR0xMDEePHmXatGk4OTkxa9YsoCZX7J49e8zKdOXKlXqOpGlKS0spLy9n2LBhujI3NzcGDRrE3r17mT59OteuXSMhIYG4uDh2796Ns7MzOTk5DBkyhOPHj5s8Zvv27WP27Nl6ZUlJSbzxxhsNltdeWBxnTkr5phDij0BPfokzd0Iax9dQWIiyzCkUCkXL5dKlS1y4cIGUlBS6desGQFhYGABffvklQgj8/Px07UtKSti0aRMnT56kS5cuAMyaNYudO3eybt061qxZo2u7ZMkSkpKSgBrrWGBgIAUFBTzzzDNmZTp16hTR0dH069cPgK5du5ps6+HhoVMyT5w4wZw5c8jOzmbIkCEAvPjii6xatYrU1FQAgoODWbBgAWvWrNEpc+ZyxdqC8vJyAHx99SOk+fr6UlZWBsDmzZuRUpKfn697zq5btw4fHx+2b9/O2LFjTfat1W/tmM0JazNAVAOWvZIo6kUpcwqFQtFy6dixIxkZGSQlJZGYmEhiYiKpqak6Rc2QQ4cOIaUkPDxcr/zmzZs88sgjemUDBgzQ/e/h4UHv3r05duxYvTLNnDmT1NRUDh48yNChQ0lJSWHw4MFmt7lw4QIjR45k7NixZGZmAlBRUcGZM2eYPn06M2fO1LWtqqrSe7Y1h1yxBw8epLS0lLZt2+qVX7t2jZKSEk6fPq13zBcuXMjChQubWsxGYVKZE0JY7n0ISCn/3Hhx7jFUaBKFQqFo0eTn55OZmclHH33E+++/z6JFi3jvvfc021ZXVyOEoLi4GCcnJ706Nzc3m8iTnJzMqVOn2LFjB5988gnDhw8nLS2N/Px8zfZVVVWkpaUREBCgN71Y6xe3du1a4uLizI5nz2nWWsvmuXPn9JTkc+fO6eqqq6vp06cPmzdvNtq+Y8eOtGvXjsOHD+uV1fZ97tw5vfZ1+21OmLPMbbCiHwkoZc5KjFzmWlm6HkWhUCjuXSz1WWsuREZGEhkZyfz580lOTmbjxo2MGDGC27dv67WLiopCSkl5eTkJCQlm+/z8888JCQkBalZUHj161OIVoF5eXkyaNIlJkyaRnJzMhAkTWLt2LS4uLkZtMzMzOXnyJPv379dTMH19ffH396ekpMTsuPaeZg0ODsbPz4/CwkL69u0LwI0bN9izZw/Z2TVrM6Ojo9m0aRNeXl54enpq9tO9e3ejsgEDBlBYWMhzzz2nKyssLDSrvDoKc8pccJNJcY+i0nkpFApFy6W0tJR169YxcuRIAgIC+P777/nqq6+YOXMmQUFB3Lhxg8LCQqKionB3dyc0NJT09HQyMjJYvXo10dHRnD9/nqKiIkJCQnj88cd1fa9cuRJvb2/8/f1ZsWIFzs7OTJw4sV6Zli5dSnR0NBEREVRVVfHuu+8SEhKiqcjl5+fz1ltvsWPHDiorK3W+YrW+dMuXL2f27Nl4enry2GOP6RZ4lJWV8cILLwDWT7N+9913XLlyhR9++IHKykqdxSw8PBxnZ2fKyspITEzk5ZdfZsyYMQghyMzM5KWXXiIsLIzQ0FBWrlyJh4eH7nikp6eTk5PDqFGjWLFiBV26dOHMmTNs27aNGTNm0KNHD01Z5s6dy6BBg3jllVcYPXo0W7duZdeuXXz22We6NufPn+f06dNcuHBBJ7+npyd+fn5Na8GTUqqPmU9MTIy0F5+8tVbmjB2u+xz8cJvdxlIoFIq7mWPHjjlaBKspLy+XY8aMkf7+/tLZ2Vl27txZPvfcc7KyslJKKeWMGTPk/fffLwG5bNkyKaWUlZWVctmyZTI4OFg6OTlJX19fmZKSIg8cOCCllHLXrl0SkNu2bZO9e/eWzs7OMioqSn7xxRcWybRy5UoZHh4u3dzcZIcOHWRycrLese3atavMzs6WUko5ZcoUSc3Mm96nVlYppSwoKJBRUVHSxcVFenp6yocfflhu2rSpwcds8ODBmmOWlpZKKaUsLS2VgMzPz9dtU11dLZctWyb9/Pyki4uLHDRokDxy5Ihev+Xl5TIjI0N6e3tLZ2dnGRQUJKdOnSorKirMyvPOO+/Inj17SicnJxkWFia3bNmiV5+fn1/vMbIWc+c6cEBq6CpCGs71KfSIjY2VBw4csEvfn7z1Bw5//Hfd94SM6UQnp9hlLIVCobibOX78OL16OTYkSXOgqKiIhIQEKioq8PLycrQ4Cjtg7lwXQhyUUsYalisnLQdi7DOnplkVCoVCoVBYh1LmHInhalblM6dQKBSKRpCcnKzzaTP8vPTSS44WT2EnrIozp7AthlPcyjKnUCgUCnPEx8cbPTvqYm71aG3IDUXLQylzDsT4glTKnEKhUCgaTnMI0qtoeqxS5oQQXkB/4H7gAynleSGEK1ApVVov61GWOYVCoVAoFI3EIp85UUM2cBZ4HzBUiR8AACAASURBVHgLCLpTvQ1YZBfpWjjKMqdQKBQKhaKxWLoA4gVgFrACeAh9reMDYISN5bonUD5zCoVCoVAoGoul06zPACuklC8LIVob1H0HdLOtWPcIhsqcsswpFAqFQqGwEkstcwHA5ybqKoE2thHn3sLYMqcixSgUCoVCobAOS7WHMuABE3WRQKltxLm3UNk3FAqFQtGcCAoKIicnx9FiKKzEUmXuHWCpEOLhOmVSCBEK/BbYbHPJ7gWUZU6hUCjuSTZs2ICHh4ejxTCiuLiYZ5991mHjz507l9jYWFxdXQkKCrJoGyklWVlZ+Pv74+bmRnx8PF9//bV9BQXWrFlDcHAwrq6uxMTEsGfPHr36mzdvMnv2bLy8vGjTpg0jR47k7NmzdpHFUu0hC/gG+BT49k7ZO8CRO99fsblk9wBG06wOkkOhUCgUCgBvb2/c3d0dNn51dTVTpkxh8uTJFm+zatUqVq9eTV5eHsXFxfj4+DB06FAuX77cYDk2bNhAfHy8yfq//vWvzJ07l4ULF/Lll18SFxdHcnIyp0+f1rXJzMxky5YtbNq0iT179nDp0iVGjBjB7du3GyyXKSxS5qSU14F4IAPYC+wEioFfA0OllJU2l+wewGiaVVnmFAqFokXx6aef0r9/fzw8PGjfvj39+vXjjTfeYOrUqVy9ehUhBEIIsrKyAKisrGT+/PkEBgbi7u5O3759+fjjj3X9FRUVIYRg+/bt9OnTR2cVOnjwoEXyXLx4kUmTJuHj44OrqyshISHk5ubq6utOs2ZlZenkq/uplRUgPz+f8PBwXF1dCQ0N5bXXXqO6uuFhZ/Py8pg9ezahoaEWtZdSkpuby4IFC3jiiSd44IEH2LhxI5cvX6agoEDXrqysjPHjx9OhQwc6dOjA8OHD+fbbb830bJ5XX32VjIwMpk2bRq9evcjLy6NTp0784Q9/AGqO85/+9Ceys7MZOnQo0dHR/OUvf+Grr75i586dDR7XFBYHDZZS3gb+cufTpAgh/hNIAGIBP2C5lDKrAf14Asfv9DFUSmn7I2oFyjKnUCgU1vP7Gf/r0PF/s/YRi9pVVVUxatQonn76ad5++21u3brFoUOHiIiIIDc3l4ULF1JSUgKgm3KdOnUqJSUlFBQUEBgYyIcffkhKSgrFxcVERkbq+p43bx6vv/46AQEBLF++nBEjRlBSUlKvVW3x4sUcOXKE7du34+vrS2lpKRUVFZpt582bx4wZM3TfCwsLeeqppxg4cCAA69evZ+nSpeTl5RETE8PRo0eZNm0aTk5OzJo1C6jJFWs4/WjIlStX6jmSpiktLaW8vJxhw4bpytzc3Bg0aBB79+5l+vTpXLt2jYSEBOLi4ti9ezfOzs7k5OQwZMgQjh8/brUlsrKykoMHDzJv3jy98mHDhrF3714ADh48yK1bt/Tk6ty5M7169WLv3r0kJSU1eJ+1uFvSeU0DLgHvATPqaWuO/7KNODZC+cwpFApFi+XSpUtcuHCBlJQUunWrieAVFhYGwJdffokQAj8/P137kpISNm3axMmTJ+nSpQsAs2bNYufOnaxbt441a9bo2i5ZskSnEOTn5xMYGEhBQQHPPPOMWZlOnTpFdHQ0/fr1A6Br164m23p4eOiUzBMnTjBnzhyys7MZMmQIAC+++CKrVq0iNTUVgODgYBYsWMCaNWt0ypy5XLG2oLy8HABfX1+9cl9fX8rKygDYvHkzUkry8/MRosZssm7dOv7/9u48vqrqWuD4bwEJBKMGCAkCIqSICFIgICpYASPSqIAowQGjoFjBOqRqmVQmEa2A0kIVtBqsBfS1UlEKarSC9DmUQaoIDysGZAoNIpQ5hKz3xz653NzcJDchyU3I+n4+55OcffY9Z917QljZw9lxcXEsWbKEwYMHl+qae/bs4cSJE0Gvmd/qlpWVRe3atYmNjS1UJz/m8hRSMicimUBRUy/zgP3AGuB3qrq+nGLz115V80SkDmVM5rzJG7cB9wMvl2dwZVV4BTRrmzPGmNNFw4YNGTp0KH379iUpKYmkpCQGDRrkS9QCrV27FlWlXbt2BcqPHTvGlVcWbA287LLLfN9HR0fToUMHNmzYUGJMI0eOZNCgQaxZs4Y+ffrQr18/evbsWexr9u3bR//+/Rk8eDBpaWkAZGdns23bNu655x5Gjhzpq5ubm1ug16kqrBW7Zs0aMjMzOfPMMwuUHz582NcyunLlSpKTk33HcnNzOX78eIFJKuPGjWPcuHGVE3QphdoytwLXzRmHGzO3G4gHegBZwFagH5AqIkmq+kl5Bnmq676KSAQwFzdR47tyCao8BKTHtgKEMcacXtLT00lLS+Pdd9/l7bff5tFHH+Wtt94KWjcvLw8RYdWqVURERBQ4FhUVVS7xJCcns3XrVpYtW8aHH37ItddeS0pKCunp6UHr5+bmkpKSQrNmzZg9e3aBWAHmzJlD9+7di71eRXaz5rds7t69u0CSvHv3bt+xvLw8OnXqxOuvF37wRsOGDQHo2rUr69at85UvWrSIN998k/nz5xeqGxsbS+3atdm9e3eBc/lfs0mTJpw4cYI9e/bQuHHjAnV+9rOflfn9FiXUZG4lkAhcoqq+9kEROQd4D1gGpAIfApOAPuUc56kaBUQCzwCXlVC30gTmqLYChDHGlCzUMWtVRceOHenYsSOjR48mOTmZV199Neisxs6dO6OqZGVl0bt372LP+dlnn5GQkADAoUOHWL9+fcgzQGNjY0lNTSU1NZXk5GRuueUW5syZQ926dQvVTUtLY8uWLXz++ecFEsz4+HiaNm3K5s2bi71uRXeztmrViiZNmpCRkcHFF18MwNGjR1m5ciXTpk0DIDExkYULFxIbG0tMTEzQ80RFRdG6dWvfflxcXKGyfJGRkXTp0oWMjAxSUlJ85RkZGdx4440AdOnShYiICDIyMrj11lsB2L59Oxs3biw2+S2rUJO50cA4/0QOQFV3icgUYKqqviQivwXmlHeQp0JEWgOPAf1U9Vh+f3lVUOiZwdYyZ4wxp43MzEzmzp1L//79adasGd999x1ffvklI0eOpGXLlhw9epSMjAw6d+5M/fr1adOmDUOGDGHo0KHMmDGDxMRE9u7dy/Lly0lISOCGG27wnXvKlCk0btyYpk2bMnnyZCIjI31JQ3HGjx9PYmIi7du3Jzc3l0WLFpGQkBA0kUtPT+eVV15h2bJl5OTk+MZ65Y+lmzRpEvfffz8xMTFcc801vgkeO3bsYOzYsUDpu1m//fZbDh48yM6dO8nJyfG1lrVr147IyEh27NhBUlISTz31FAMHDkRESEtLY+rUqbRt25Y2bdowZcoUoqOjfZ/HkCFDmD59OgMGDGDy5Mm0aNGCbdu2sXjxYkaMGMH5559fqhgBHnroIVJTU+nWrRs9evRgzpw57Ny50zdh5Oyzz+auu+5i1KhRxMXF0ahRIx566CF++tOf+sYclqdQk7lzgWNFHDuKW+4L3EoRkcWdSESuAjJCuOYKVe0VYnzFeQFYXJqZqyLyC9xjV4oc21AerGXOGGNOX/Xr1+ebb74hJSWFPXv2EB8fz5AhQxg9ejQRERGMGDGCW265hR9++IEJEyYwceJE0tPTefLJJxk1ahTbt2+nYcOGdOvWrVBL3dNPP83DDz/Mpk2baN++PUuWLOGMM0peWbNu3bo8+uijZGZmUq9ePS699FLeeeedoHVXrFjBkSNHCj1vLT/W4cOHc8YZZzBt2jTGjh1LVFQU7du3901+KIvhw4ezYsUK337nzp0Blxi3bNmS48ePs2nTJvbv3++rM2rUKI4cOcIvf/lLfvzxRy655BLef/993xi5+vXr8/HHHzNmzBhSUlLYv38/TZs2pXfv3jRo0KBMcd5000388MMPTJkyhV27dnHRRRexdOnSAhNKZs6cSZ06dbjppps4cuQISUlJ/PGPf6R27cAl7k+dhLKklIisxc0m7auqx/zK6wHvA9GqmigiNwNPq2rLYs5VHwglQzqsqt/7F3gTII4T4qNJRGQwkA5cDOz0ii8H3gGuB5ar6v4iXg5A165ddfXq1SGEW3p//c0kvlu7yrd//ajH+UmXSyrkWsYYU51t3LiRCy+8MNxhhN3y5cvp3bs32dnZhWZKmtNDcT/rIrJGVbsGlofaMjcKWAJ8LyJLgf/gJkNcA8R4XwG645K7IqnqYdxqEpWhHVAfCLaux1u4WbjBO9ArQeFE2lrmjDHGGFM6oa4A8QFuAsSHwBW4x3tcgVsJopOqfujVe0BVf1FBsZbFPNwsXP/tV96xR4DrwhOWp9Bz5iyZM8YYU3bJycm+MW2B29SpU8MdnqkgpVkBYgNQ8ujKCiAiXYGWnEw+24nIIO/7pV5rHyLyMnCHqtYBUNUtwJaAc+V/+y9V/UeFBl6CwitAWDJnjDGmaL169QrSq3NScbNH8x+tYU4/1WUFiPuAO/z2U7wNoBUnE7ba3lYtFErmqtBMW2OMMdVPVXhIr6l8ISdzIhIH3AJcANQLOKyqeld5BhZw8qHA0PKop6rLqSKD0wr9dWXJnDHGGGNKKdTlvC4APvXqnwHsARriWsF+xE0kMKVVqGXO1mY1xhhjTOmEmj1MA1bhlvASIBmIAoYDh4GBFRLdaa5wy1x44jDGGGNM9RVqN+vFuAXu858xV0tVc4FXRKQxMBM3U9SUhrXMGWOMMeYUhZo9RAN7vQXv9wP+TypchUv2TCkVngARpkCMMcYYU22FmsxtAZp432/i5ExScM9q21eOMdUYhZM5a5kzxhgTPi1btmT69OnhDsOUUqjZQwbQx/v+WWCYiGwSka+BB4FXKiK4052NmTPGmJpp3rx5REdHhzuMQlatWsW9994btus/+OCDdO3alXr16tGyZcuQXqOqTJw4kaZNmxIVFUWvXr34+utgCz+Vr+eff55WrVpRr149unTpwsqVKwscf/HFF+nduzcxMTGICFu2bKmwWEJN5sbiVkxAVf8HGIDrXt0EjAQmVEh0pztrmTPGGFOFNG7cmPr164ft+nl5edxxxx3cfvvtIb/mmWeeYcaMGcyaNYtVq1YRFxdHnz59OHDgQJnjmDdvHr169Sry+BtvvMGDDz7IuHHj+OKLL+jevTvJycl8//3JJeUPHz7M1VdfzcSJE8scR6hKzB5EpDbQFqibX6aq76jqbap6g6q+qMU9jtoUyQ1B9GOD5owx5rTy8ccfc+mllxIdHc3ZZ59Nt27dmD17NsOGDePQoUOICCLi+w8/JyeH0aNH07x5c+rXr8/FF1/Me++95zvf8uXLERGWLFlCp06dfK1Ca9asCSme/fv3k5qaSlxcHPXq1SMhIYGZM2f6jvt3s06cONEXn//mn5ykp6fTrl076tWrR5s2bXjuuefIy8sLvGzIZs2axf3330+bNm1Cqq+qzJw5kzFjxnDjjTdy0UUX8eqrr3LgwAEWLFjgq7djxw5uvvlmGjRoQIMGDbj22mv597//XeY4n332WYYOHcrdd9/NhRdeyKxZszjnnHN44YUXfHXS0tIYO3Ysl19+eZmvE6pQZrMqsBq4Fni/YsOpWWwChDHGlN6Mm8K7rPbDbywJqV5ubi4DBgzgrrvuYv78+Rw/fpy1a9fSvn17Zs6cybhx49i8eTOAr8t12LBhbN68mQULFtC8eXOWLl1Kv379WLVqFR07dvSd+5FHHuG3v/0tzZo1Y9KkSVx33XVs3ry5xFa1xx57jK+++oolS5YQHx9PZmYm2dnZQes+8sgjjBgxwrefkZHBnXfe6UtOXnrpJcaPH8+sWbPo0qUL69ev5+677yYiIoL77rsPcGvFBnY/Bjp48GAJn2TRMjMzycrK4uqrr/aVRUVFccUVV/DJJ59wzz33cPjwYXr37k337t1ZsWIFkZGRTJ8+nauuuoqNGzeWuiUyJyeHNWvW8MgjjxQov/rqq/nkk0/K/F5ORYnJnKrmicg23MOCTTnSvIBkrpZ1sxpjzOniv//9L/v27aNfv3785Cc/AaBt27YAfPHFF4gITZo08dXfvHkzCxcuZMuWLbRo0QKA++67jw8++IC5c+fy/PPP++o+/vjj9O3bF3CtY82bN2fBggUMHz682Ji2bt1KYmIi3bp1A+C8884rsm50dLQvydy0aRMPPPAA06ZN46qrrgLgiSee4JlnnmHQILdUeqtWrRgzZgzPP/+8L5krbq3Y8pCVlQVAfHx8gfL4+Hh27NgBwOuvv46qkp6e7ls2c+7cucTFxbFkyRIGDx5cqmvu2bOHEydOBL3mBx98UNa3ckpCfc7cXCBNRP6mqjkVGVBNogFN0bVqVZtlZY0xxpSgYcOGDB06lL59+5KUlERSUhKDBg3yJWqB1q5di6rSrl27AuXHjh3jyiuvLFB22WWX+b6Pjo6mQ4cObNiwocSYRo4cyaBBg1izZg19+vShX79+9OzZs9jX7Nu3j/79+zN48GDS0tIAyM7OZtu2bdxzzz2MHDnSVzc3N7dAr1NVWCt2zZo1ZGZmcuaZZxYoP3z4sK9ldOXKlSQnJ/uO5ebmcvz48QKTVMaNG8e4ceMqJ+hSCjWZOxP4CfCdiLwL7MJ1v+ZTVbVJEKWkeScK7FvLnDHGnF7S09NJS0vj3Xff5e233+bRRx/lrbfeClo3Ly8PEWHVqlVEREQUOBYVFVUu8SQnJ7N161aWLVvGhx9+yLXXXktKSgrp6elB6+fm5pKSkkKzZs2YPXt2gVgB5syZQ/fu3Yu9XkV2s+a3bO7evbtAkrx7927fsby8PDp16sTrr79e6PUNGzYEoGvXrqxbt85XvmjRIt58803mz59fqG5sbCy1a9dm9+7dBc7lf83KFmoy55+K3hnkuGIzWkvlRO5xsr/fUqDMkjljjClZqGPWqoqOHTvSsWNHRo8eTXJyMq+++irXXXcdJ04U/IO+c+fOqCpZWVn07l38okqfffYZCQkJABw6dIj169eHPAM0NjaW1NRUUlNTSU5O5pZbbmHOnDnUrVu3UN20tDS2bNnC559/XiDBjI+Pp2nTpmzevLnY61Z0N2urVq1o0qQJGRkZXHyxW7/g6NGjrFy5kmnTpgGQmJjIwoULiY2NJSYmJuh5oqKiaN26tW8/Li6uUFm+yMhIunTpQkZGBikpJx+7m5GRwY033lieby9kISVzqmpZRjkLlriJzYAwxpjTRmZmJnPnzqV///40a9aM7777ji+//JKRI0fSsmVLjh49SkZGBp07d6Z+/fq0adOGIUOGMHToUGbMmEFiYiJ79+5l+fLlJCQkcMMNN/jOPWXKFBo3bkzTpk2ZPHkykZGR3HrrrSXGNH78eBITE2nfvj25ubksWrSIhISEoIlceno6r7zyCsuWLSMnJ8c3Pi1/LN2kSZO4//77iYmJ4ZprrvFN8NixYwdjx44FSt/N+u2333Lw4EF27txJTk6Or7WsXbt2REZGsmPHDpKSknjqqacYOHAgIkJaWhpTp06lbdu2tGnThilTphAdHe37PIYMGcL06dMZMGAAkydPpkWLFmzbto3FixczYsQIzj///FLFCPDQQw+RmppKt27d6NGjB3PmzGHnzp0FJoxkZWWRlZXFN998A8CGDRvYt28fLVq08LXylRtVta2YrUuXLlpRpg++tsCW/f2WCruWMcZUZxs2bAh3CKWWlZWlAwcO1KZNm2pkZKSee+65+utf/1pzcnJUVXXEiBHaqFEjBXTChAmqqpqTk6MTJkzQVq1aaUREhMbHx2u/fv109erVqqr60UcfKaCLFy/WDh06aGRkpHbu3Fn/+c9/hhTTlClTtF27dhoVFaUNGjTQ5OTkAp/teeedp9OmTVNV1TvuuENxPW8FtvxYVVUXLFignTt31rp162pMTIz26NFDFy5cWObPrGfPnkGvmZmZqaqqmZmZCmh6errvNXl5eTphwgRt0qSJ1q1bV6+44gr96quvCpw3KytLhw4dqo0bN9bIyEht2bKlDhs2TLOzs4PGkZ6erj179iw21t///vd63nnnaWRkpCYmJuqKFSsKHJ8wYULQ9+IfezDF/awDqzVIriIa4iPixDUb9QOuABoBE1V1q4j0BP6tqjvLKb+sUrp27aqrV6+ukHMHTq9P/c3viGuZUCHXMsaY6mzjxo1ceOGF4Q4j7JYvX07v3r3Jzs4mNja25BeYaqe4n3URWaOqXQPLQ+pmFZEGwFLgEuAAEA3MArYCdwN7gQfKFrbJFzi71RhjjDGmJKGOhZsGnAv0wLXK+Q/u+gBIKue4aqS8gNmtxhhjTGkkJyf7xrQFblOnTg13eKaChDqbdQDwiKp+6i3v5e97XKJnTlF0g0bhDsEYY0wV1qtXr0KrB/krbvZouQ+6N1VGqMlcNLCjiGP1KNhSZ0LUM/UuVrz2MgDnd+vOmY1s/IMxxpiyqwoP6TWVL9RkbhNwNa5LNVBP4Ktyi6gG6XrdQM5pfQHHjhyiZcfEcIdjjDHGmGoo1GTueWC2iOwHFnhlMSIyDLgP+EVFBFcTNGvbruRKxhhj3CMY7Hmc5jQW6hNGAoX60OAXRSQBmARM9oozgDzgGVWdX+SLjTHGmFNUu3Ztjh8/TmRkZLhDMabCHDlypNBSbqEItWUOVR0jIi8AfYA44AcgQ1W/K/VVjTHGmFKIiYlh9+7dNGvWjFq29KE5zagqR44cYceOHcTHx5f69aE+Z662qp5Q1a3AH0p9FWOMMeYUxMbGsn37djZt2hTuUIypEBEREcTHx3PWWWeV+rWhtsztFJGFwGuquqbUVzHGGGNOQa1atWjRokW4wzCmSgq1rfpN4DbgnyKyQUTGiIg9W84YY4wxJsxCSuZU9V7gHOBGYCMwAcgUkY9EZKiInFmBMRpjjDHGmCKEPIpUVY+r6luqeiPQBLgXqI0bQ7erguIzxhhjjDHFCHk2qz9V3S8iy3DrtCbgWu2MMcYYY0wlK1Uy53WnpgCpwM+AY8DbwGvlH5oxxhhjjCmJhPK0YRG5DjcBoh9uLdaPcQncn1X1QIVGGGYikg1srYBTxwJ7KuC8pmzsflQ9dk+qHrsnVYvdj6qnou/JearaOLAw1GQuD7c+62vAn1T1+/KPr2YRkdWq2jXccRjH7kfVY/ek6rF7UrXY/ah6wnVPQu1m7aaqq4MdEJGewB2qemf5hWWMMcYYY0IR6qNJCiRyItJaRCaLSCbwETC4IoIzxhhjjDHFC/nRJCJytoj8QkT+F9fl+ijwIzASaFpB8Z3OXgx3AKYAux9Vj92TqsfuSdVi96PqCcs9KXbMnIjUAn4O3MHJyQ87gUXAL4HeqvpxJcRpjDHGGGOCKHLMnIjMAG4F4oCjwF+BV4EPgLOA+yojQGOMMcYYU7Tiull/hUvklgItVHWIqr6vqnlAyVNgTSEicq6I/EVE9ovIf0VkkYjYytFhIiKDRORNEdkqIkdEZJOIPGXL01UdIvKuiKiITAl3LDWZiFwjIh+LyEHvd9dqEbky3HHVRCLSQ0TeF5H/iMgBEVkrIjYBsRKISHMRmSUin4rIYe93U8sg9eqJyDQR2eX93/KpiFxRkbEVl8y9DBwArgU2ichsEelWkcGczkSkPvB3oC2u2zoVOB/4SETOCGdsNdgjwAlgHG44wQu4MaAZ3hADE0YicgvQMdxx1HQicg+wGFgDDMQ9OP7PQP1wxlUTichPcb1jEcDdwA3AKuBlERkZzthqiNa4CZ8/AiuLqfcy7v6MB67DLXn6noh0qqjAShozVw/3j/cOIAmX/H2D63IdjY2ZC5mIPAg8C1ygqt96Za2AfwOjVPXZcMZXE4lIY1XNDii7HTecIElV/x6eyIyINAA24noIFgBPqupj4Y2q5vFaHTYCY1V1ZnijMSIyFfdHaENVPehX/imAql4WrthqAhGp5fVOIiLDgZeAVqq6xa9OR2AdcKeqpntldYCvgU2q2r8iYiu29UFVj6rqQlX9OdACGItryRgDCPC0iNzmJX2meP2Bz/ITOQBVzQT+FxgQtqhqsMBEzrPK+9qsMmMxhfwGWK+qC8MdSA13J5AHzAl3IAaASOA4cCSgfD+leDqFKZv8RK4E/XH36A2/1+UCrwN9RaRuRcQW8s1X1V2q+oyqXgR0A36P6yb8I64J0RSvPbA+SPnXQLtKjsUUraf3dWNYo6jBRORy4HbcjHkTXpcD/wfcLCKbRSRXRL4VEbs34THP+/o7EWkqIjEicjeu5+y58IVl/LQHMlX1cED517hkvHVFXDTUFSAK8B4ivFpEHsL1B99erlGdnhri+tkD7QUaVHIsJggRaQZMBj4oasUTU7FEJBKYC0xX1U3hjsfQ1Num4caWbsaNmZstInVU9bfhDK6mUdX1ItILN9TpXq/4ODBCVV8PW2DGX3H/1+cfL3dlSubyqepx3A/VX8snHGPCQ0SicYO8c4FhYQ6nJhsFRAFPhjsQA7jemzOBoaq6yCv7uzeWbqyI/E5DWeDblAsROR94E9fKMwLX3ToAmCMiR1V1fjjjM+FzSsmcKZUfCd4CV1QWbyqJiEQB7wAJQE9V3R7mkGok7zE9jwLDgboBY0vqikgMcEBVT4QlwJrpB9xwmoyA8vdxM8DPwT1I3lSOqbiWuOu8xhSAD0WkEfBbEVkY4rguU3F+BM4LUp7fIrc3yLFTZgMmK8/XuL70QO2ADZUci/GISATwF6ArcI2qfhXmkGqyBNwqM3/C/ULM38DN4PsR6BCe0Gqsr0s4bolD5eoA/Msvkcv3T6AR7tmwJry+Blp5jyPz1w7IAb4t/JJTZ8lc5XkbuFREEvILvK6KHt4xU8m8Z8nNB64ErlfVz8IcUk23DugdZAOX4PWmgn4RmiLlD6HpG1D+c2C7qmZVcjw1XRbQyRtb6u8S3EpNFdLqY0rlHdxzAFPyC7xHk9wEvK+qxyriotbNWnlewi2BtlhEHsOtovEEsA034NtUvt/j/sE9CRwSkUv9jm23TPFR0wAACaFJREFU7tbKpar7gOWB5SICsFVVCx0zFW4p8BEwV0Rige9w/2auxsaWhsNs3AOb3xGR53Fj5voDtwDPqWpOOIOrCURkkPdtF+9rsohkA9mqukJVvxCRN4CZXs9PJu5h9K2AIRUWl41drTzemKDngD645/R9CKT5P3DQVB4R2ULwsQ0Ak1R1YuVFY4oiIoo9NDhsROQs4ClgEG7c7/8BT6vqgrAGVkOJSDLuof3tccMSNgMvAnNtPGnF834fBbNCVXt5dfIncd0KxAD/AkZX5B+klswZY4wxxlRjNmbOGGOMMaYas2TOGGOMMaYas2TOGGOMMaYas2TOGGOMMaYas2TOGGOMMaYas2TOGGOMMaYas2TOGBOUiKSKyPd++xtE5N5yvsZlIvK5iBwSERWRTuV5flP5RGSLiMwrw+uuF5GHKiAkY057lswZY4rSBVgDICLRwAX5++XoZdxKNP2Ay4Bvyvn8pvq4HrBkzpgysGTOGFMUXzIHJOIWVf9XeZ3cWxv3AuBvqvp3Vf1MVQ+X1/nNqRORuuGOwRhTMkvmjDGFeIlWJ04mc12BDap6NMTXnyUis0Vkp4gcE5FNIvIr8RZaFZGhwAnc76DHvS7WLcWcb6JXp4OIfCQih0Vkl4hM9mLNr1dPRJ4TkfUiclBEskTkHRFpG3C+JiLyql98u0RkiYjEecfriMgTIrJZRI6KyB4R+YeIXB5wnl+IyL/86rwsIg0D6jwoIhtF5IiI/Cgiq0VkYAif4W0B535NRM7xO/43EVkb5HXniEiuiPzKr6yViMwXkWzv/a4LjMHvM75IRN4TkYPA/5QQ44Net+pR7339LEidxiIyV0S+8e7bNhFZICLN/OrMA+4Amnkx+H4eQr2nxtRkdcIdgDGm6giyXu1SL//KP56//l+rotYU9pKrv+Fa88YDXwHXAs8CjYFx3vHLgX/gulr/ABwLIcS3gFdwa4X2BR7HtRhO9I7XBc4EpgC7gIbAvcCnInKhqmZ59V7z3uevgW1APJAE1PeOjwZ+BTwKrAPOwiW0vkRNRJ4GHgZ+552nmXfdi0Sku6qeEJEhwAxgMrASiAJ+6n+eYETkF8Bc4A1gLNAUmApcIiKJqnrQew8LRaSdqm7we/mt3tcF3rnOBT4H/uO9p2zgJuBNEbleVd8OuPxi3D35jffZFhXjXcBMYJ4XZ2tgIe7z99cQOOq9j2zvvTwM/K+ItPX+QHgC97NxMW7heDj58xDqPTWm5lJV22yzzTZUFaAdrkXuWeBr7/tOwH9xiUD+fmQx57gOUGBoQHl+whbr7dfx6k0MIa6JXt0xAeUvAQeAmCJeVxuXoB0AfuVXfhB4oJjrLQEWFXO8Ja5lcXxAeQ8vzuu9/dnA2lLeg9rAbuCjgPLLvXM/4O1HAfuBpwLqrQOW+u2/jEuiGgXUywDWBfmMHwwhxlq4JPjdgPKbvHPMK+H9nevVG+hXPg/YHuLnU+ie2mZbTd6sm9UY46OqG1R1He4/2+Xe94dwLSN/VtV13pZTzGmuwLXoLAgo/xMQiZvoUFaB3X6vA9HARfkFIjLYmyG7D8j14s+fwJFvFfBrr5uwg/g3P548fo2IPCkil4tIZMDxPriEZr7XJVtHROrgWsAO4D6D/PN0EpFZInKViNSnZBcAccB8/0JV/QewFejp7R8B/gIM8eu+7gB0xLXa5fs5sBTYHxDre0BHETkr4Pp/DSHG5t4WeD/exH3mBYjISK/L+KB3PH+W9AWBdYMJ8Z4aU2NZMmeMAUBEavv9R98D141VB/gZsAPI8o4HJj6BGgJ7gyR8WX7Hy2p3EfvNAESkH67LbyOuu/ESXNddNlDP73U3AW8Do4AvgR0iMl5Ojr+bCkzAdfmtBH4QkXQRifWOx3lfvwWOB2xnAo28438ERnpxvAfsFZFFItKymPeY//nsCnIsi4Kf32u4xLuXt5+KSybf8qsTB9weJM5p3vFGFBTsuoHyx+4VuB+qmgv84F8mIvcDzwMfADcA3YBLvcP+9ySoUtxTY2osGzNnjMn3IV6rj+c1CrbwHPe+9gaWF3OevUBDEYkMSOia+B0vq3jgu4B9cMkmwM3At6o6NL+CiEQQkECq6n+AXwK/FJELcIPvJ+EShBdU9ThuzNhvRKQJruv4WVz33k2cTFiuBn4MEucP3nUUN/Ztrog08OrPwCUnlxTxHvM/nyZBjjWh4ONhVuBauW4TkRW4ZOcvXqudfywrvfcTzM6AfQ1aq6D8hC/ev9BL/gOTw5uBD1X1Yb96rUK4hv/rS7ynxtRk1jJnjMl3D67FYzquxeliTraAPOa3X9Kz5lbgfrekBJQPAXKAT08hxsEB+zfjxr995e3Xp3A3XypunFVQqrpJVcfhkrKLghzPUtU/4FqW8o9n4LqSW6jq6iBbZpDz/Kiqb+C6Jgtdx88mXIvXzf6FItIdN2ljud85Fdd9PQi4BtdC6Z+AA7yLm3TxdRGxhjLxJNB23Ji5wPtxI4UbCepz8g+BfMOCnPMYbhxgoFLfU2NqGmuZM8YALqkBEJHHcc9+W+21WsUCL2voswaX4WapzhGRxriJFNcAw3GD9fecQph3e12hq3CzWYfjJlDs946/C1wvIs/hJjF0Be4H9uWfQETOxiVm84H/wyUaA4AGwPtencW4Z+qtxSV5nXFjz+YCqOpmEfkNMNv7jFbgZmyeixtP9wdV/UhEXsR1e36Km03aBpeIvF/UG1Q3C3Y8rjXvT7hkrRnwJPBv3Gxef6/hZgjPwbXSLQ84Ph74J/CxiMwGtnjv9SIgQVXvLCqWYmLME5FJwB9EJB03drE1MAY3Wcbfu8BoERnnxXElLvkMtAHXojsSWA0cVdWvCOGeGlPjhXsGhm222VZ1NtwEhYPAz739NGBNGc5zFm4m5y5ca9w3uNmw4lenLLNZLwI+Ao7gxo89AdTyq1cL9wiLncBhXJLVGZfAzPPq1MUlZV977/W/uOTwVr/zPAx8huuiPIJrLZsIRATElerVO+Sda6P3vpt7x+/AJVf/wbU8ZQLPAWeF8J5vwyWUx7w4XgPOKaLuKu/zmVrE8ea42cQ7vPuxC9e6eFuQz7hOKe7zg7hJGUdxCdjl/p+1VycKeAHXwnsAl5C1Crz3wBm4R5v86B3bEuo9tc22mr6JaijDI4wxJnxEZCJuQkKEukH2xhhjPDZmzhhjjDGmGrNkzhhjjDGmGrNuVmOMMcaYasxa5owxxhhjqjFL5owxxhhjqjFL5owxxhhjqjFL5owxxhhjqjFL5owxxhhjqjFL5owxxhhjqrH/B33dEnuSZ+uAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NmaYlJ-AzRl6"
      },
      "source": [
        "**Quiz Question**: Which of the following is the worst step size? Pick the step size that results in the lowest log likelihood in the end.\n",
        "1. 1e-2\n",
        "2. 1e-1\n",
        "3. 1e0\n",
        "4. 1e1\n",
        "5. 1e2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jq7MSdgjzRl7"
      },
      "source": [
        "**Quiz Question**: Which of the following is the best step size? Pick the step size that results in the highest log likelihood in the end.\n",
        "1. 1e-4\n",
        "2. 1e-2\n",
        "3. 1e0\n",
        "4. 1e1\n",
        "5. 1e2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "MOiAgl3QzRl8"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}