2) collaborative.ipynb

{
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      "cell_type": "markdown",
      "metadata": {
        "id": "k9QYysgCeVsm"
      },
      "source": [
        "<center>\n",
        "    <h1>Collaborative LSA applied on movies</h1>\n",
        "    <h2>Project and Project Work in Text Mining</h2>\n",
        "    <h3>Enrico Pittini enrico.pittini@studio.unibo.it</h3>\n",
        "</center>\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n",
        "In this notebook, we follow the *collaborative* approach. We don't have anymore any information about the content of the movies. We have only a database of rates  in $[0..5]$ given to the movies by a community of users. By exploiting this information, still in the LSA space, we can capture the similarities and relations between movies in a very poweful way. We are also able to build a recommender system, to predict the rates given by an user to a certain movie. In this second part, three different [MovieLens](https://grouplens.org/datasets/movielens/) datasets are used: small, 100k, 1M. On each of these three datasets, the recommender system is evaluated and compared with SOTA results and with the results achieved by a paper.\n",
        "\n",
        "For more detailed informations about the used functions, look into the corresponding docstrings inside the python files, inside the `utils` folder."
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "EPEETosS3hHf"
      },
      "source": [
        "## Colab initialization for accessing the repository files on GitHub\n",
        "Run this section only if you are interested in achieving the repository files on GitHub. If you have already these files, you don't need to run this section."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ygUdhDDOOtcs",
        "outputId": "5308142a-11bd-481e-baad-b6d0713f9c11"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "8qPRRU6ZOprR"
      },
      "outputs": [],
      "source": [
        "! mkdir \"gdrive/My Drive/textmining\"\n",
        "! cd \"gdrive/My Drive/textmining\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JChVOh08Oyu4",
        "outputId": "d587ec5c-36c5-4546-a9e2-c6d0b50ba52c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Cloning into 'text-mining'...\n",
            "remote: Enumerating objects: 327, done.\u001b[K\n",
            "remote: Counting objects: 100% (225/225), done.\u001b[K\n",
            "remote: Compressing objects: 100% (161/161), done.\u001b[K\n",
            "remote: Total 327 (delta 116), reused 172 (delta 64), pack-reused 102\u001b[K\n",
            "Receiving objects: 100% (327/327), 48.47 MiB | 17.33 MiB/s, done.\n",
            "Resolving deltas: 100% (169/169), done.\n",
            "Checking out files: 100% (52/52), done.\n"
          ]
        }
      ],
      "source": [
        "! git clone \"https://github.com/EnricoPittini/LSA-on-movies\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W4kh_dSaSF3p",
        "outputId": "a967990a-477c-489d-f33e-e4fb3b5dacd5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "/content\n",
            "/content/text-mining\n"
          ]
        }
      ],
      "source": [
        "%cd -0\n",
        "%cd \"LSA-on-movies\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "70R8lqOzeVst"
      },
      "source": [
        "## Initialization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "Is2NSUqteVss"
      },
      "outputs": [],
      "source": [
        "# Settings for autoreloading\n",
        "%load_ext autoreload\n",
        "%autoreload 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "U8Mm5FlweVst"
      },
      "outputs": [],
      "source": [
        "import csv\n",
        "import numpy as np\n",
        "import pandas as pd "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "vsjxLqsDeVsu"
      },
      "outputs": [],
      "source": [
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U9jZlhrTeVsu"
      },
      "source": [
        "## MovieLens small \n",
        "The first dataset taken into account is the MovieLens small. It is a dataset for education and development.\n",
        "- Around $100$ k ratings\n",
        "- Around $10$ k movies\n",
        "- Around $600$ users"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "zJONsY5HeVsv"
      },
      "outputs": [],
      "source": [
        "movies_file = 'datasets/collaborative/movies_small.csv'\n",
        "ratings_file = 'datasets/collaborative/ratings_small.csv'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m4PEaadSeVsv"
      },
      "source": [
        "Movies dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "lWnBJaEGeVsv"
      },
      "outputs": [],
      "source": [
        "df_movies = pd.read_csv(movies_file)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "sjdXQ1AHeVsw",
        "outputId": "ffd1a0be-8adc-408b-fc70-dd95e3427cc7"
      },
      "outputs": [
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          "data": {
            "text/html": [
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>movieId</th>\n",
              "      <th>title</th>\n",
              "      <th>genres</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Toy Story (1995)</td>\n",
              "      <td>Adventure|Animation|Children|Comedy|Fantasy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>Jumanji (1995)</td>\n",
              "      <td>Adventure|Children|Fantasy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Grumpier Old Men (1995)</td>\n",
              "      <td>Comedy|Romance</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Waiting to Exhale (1995)</td>\n",
              "      <td>Comedy|Drama|Romance</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Father of the Bride Part II (1995)</td>\n",
              "      <td>Comedy</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   movieId                               title  \\\n",
              "0        1                    Toy Story (1995)   \n",
              "1        2                      Jumanji (1995)   \n",
              "2        3             Grumpier Old Men (1995)   \n",
              "3        4            Waiting to Exhale (1995)   \n",
              "4        5  Father of the Bride Part II (1995)   \n",
              "\n",
              "                                        genres  \n",
              "0  Adventure|Animation|Children|Comedy|Fantasy  \n",
              "1                   Adventure|Children|Fantasy  \n",
              "2                               Comedy|Romance  \n",
              "3                         Comedy|Drama|Romance  \n",
              "4                                       Comedy  "
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_movies.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-igDF1xVeVsw",
        "outputId": "1f6cf09b-396d-49bc-ae52-0c44f2018e91"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 9742 entries, 0 to 9741\n",
            "Data columns (total 3 columns):\n",
            " #   Column   Non-Null Count  Dtype \n",
            "---  ------   --------------  ----- \n",
            " 0   movieId  9742 non-null   int64 \n",
            " 1   title    9742 non-null   object\n",
            " 2   genres   9742 non-null   object\n",
            "dtypes: int64(1), object(2)\n",
            "memory usage: 228.5+ KB\n"
          ]
        }
      ],
      "source": [
        "df_movies.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YdP7PRA5eVsw"
      },
      "source": [
        "Ratings dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "vCRS3FDYeVsx"
      },
      "outputs": [],
      "source": [
        "df_ratings = pd.read_csv(ratings_file)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "gt8KFe8PeVsx",
        "outputId": "fba073d0-39c1-4b17-dc17-4544bda95d8f"
      },
      "outputs": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>userId</th>\n",
              "      <th>movieId</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>4.0</td>\n",
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              "      <td>4.0</td>\n",
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              "      <th>2</th>\n",
              "      <td>1</td>\n",
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              "      <td>4.0</td>\n",
              "      <td>964982224</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>47</td>\n",
              "      <td>5.0</td>\n",
              "      <td>964983815</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>50</td>\n",
              "      <td>5.0</td>\n",
              "      <td>964982931</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
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            "text/plain": [
              "   userId  movieId  rating  timestamp\n",
              "0       1        1     4.0  964982703\n",
              "1       1        3     4.0  964981247\n",
              "2       1        6     4.0  964982224\n",
              "3       1       47     5.0  964983815\n",
              "4       1       50     5.0  964982931"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_ratings.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Bjc_uZpMeVsx",
        "outputId": "50c1b569-d8b7-4956-8e08-613d4f5d1757"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 100836 entries, 0 to 100835\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count   Dtype  \n",
            "---  ------     --------------   -----  \n",
            " 0   userId     100836 non-null  int64  \n",
            " 1   movieId    100836 non-null  int64  \n",
            " 2   rating     100836 non-null  float64\n",
            " 3   timestamp  100836 non-null  int64  \n",
            "dtypes: float64(1), int64(3)\n",
            "memory usage: 3.1 MB\n"
          ]
        }
      ],
      "source": [
        "df_ratings.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7MjljDzEeVsy"
      },
      "source": [
        "### Preprocessing\n",
        "Some preprocessing must be performed. In particular, the users ids and the movies ids must be transformed and remapped in order to ease the futuer operations involving the rating matrix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "f0noYXa6eVsy"
      },
      "outputs": [],
      "source": [
        "from utils.preprocessing import preprocess_movies_ratings_coll\n",
        "df_movies, df_ratings = preprocess_movies_ratings_coll(df_movies, df_ratings)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "ARjcFOmPeVsy",
        "outputId": "52891b6f-1889-48a4-8b89-98a597dcee35"
      },
      "outputs": [
        {
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              "\n",
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              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>title</th>\n",
              "      <th>genres</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Toy Story (1995)</td>\n",
              "      <td>Adventure|Animation|Children|Comedy|Fantasy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Jumanji (1995)</td>\n",
              "      <td>Adventure|Children|Fantasy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Grumpier Old Men (1995)</td>\n",
              "      <td>Comedy|Romance</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Waiting to Exhale (1995)</td>\n",
              "      <td>Comedy|Drama|Romance</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Father of the Bride Part II (1995)</td>\n",
              "      <td>Comedy</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                title  \\\n",
              "0                    Toy Story (1995)   \n",
              "1                      Jumanji (1995)   \n",
              "2             Grumpier Old Men (1995)   \n",
              "3            Waiting to Exhale (1995)   \n",
              "4  Father of the Bride Part II (1995)   \n",
              "\n",
              "                                        genres  \n",
              "0  Adventure|Animation|Children|Comedy|Fantasy  \n",
              "1                   Adventure|Children|Fantasy  \n",
              "2                               Comedy|Romance  \n",
              "3                         Comedy|Drama|Romance  \n",
              "4                                       Comedy  "
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_movies.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bF19rGGIeVsz"
      },
      "source": [
        "Now the movies ids are simply the indices of the movies dataframe, in the range $[0..n_{movies}]$.\n",
        "\n",
        "The users ids are the integers in the range $[0..n_{users}]$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wKlmiLh1eVsz",
        "outputId": "915e8629-1a0a-4db4-cd86-2016c0a108d7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "610"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "users = df_ratings['userId'].unique()\n",
        "n_users = len(users)\n",
        "n_users"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3LrzeWNceVsz"
      },
      "source": [
        "### Rating matrix\n",
        "Let's now build the rating matrix. \n",
        "\n",
        "The rating matrix is a bidimensional matrix with shape $n_{users} \\times n_{movies}$: so, the rows correspond to the users, while the columns correspond to the movies. Each cell contains the rate given from that user to that movie. \n",
        "\n",
        "1. **'fill_na' strategy.** A very important point is the handling of the missing values: a missing value is a cell $(user_{id},movie_{id})$ s.t. that user\n",
        "has never rated that movie. These missing values must be replaced with something. The four following strategies can be specified.\n",
        "    - `'zero'`. The missing values are simply replaced with $0$.\n",
        "    - `'items_means'`. Each missing value is replaced with the mean of the column in which it belongs, i.e. the mean of the rates of that movie. If a movie has no rates, all its values are replaced with the global mean of all rates.\n",
        "    - `'users_means'`. Each missing value is replaced with the mean of the row in which it belongs, i.e. the mean of the rates given by that user. If a user has never given a rate, all its values are replaced with the global mean of all rates.\n",
        "    - `'items_users_means'`. Each missing value is replaced with the mean between the mean of the column (i.e. item mean) and the mean of the row (i.e. user mean). \n",
        "\n",
        "2) **'subtract_mean' strategy.** Another important point is that it is typically useful to subtract the values in the rating matrix by certain means. Basically, it is typically beneficial to do not work directly with the ratings, but working with the differences of the ratings from certain means. The four following strategies can be specified.\n",
        "    - `'zero'`. Zero values are subtracted from the rating matrix values. Basically, the matrix remains as it is.\n",
        "    - `'items_means'`. The items means (i.e. the means of the columns) are subtracted from the rating matrix values. Basically, each rate is subtracted with the average rate given to that movie. The purpose of this operation is to have a more balanced view of the ratings from an items point of view. Indeed, the less popular movies have lower ratings w.r.t. the popular movies, and so they will have much lower similarity scores even in cases in which they are more appropriate.\n",
        "    - `'users_means'`. The users means (i.e. the means of the rows) are subtracted from the rating matrix values.  Basically, each rate is subtracted with the average rate given by that user. The purpose of this operation is to have a more balanced view of the ratings from an users point of view. Indeed, there can be generous users which are more prone to give high rates, and greedy users which instead give often low rates. In simple terms, a 3 rating given by a generous user has not the same importance of a 3 rating given by a greedy one: the former is less important and significative. Therefore, we want to normalize with respect to the users average rating.\n",
        "    - `'items_users_means'`. The means between the items means and the user means are subtracted from the rating matrix values. Basically,  each rate is subtracted with the average between the average rate given to that movie and the average rate given by that user. The purpose of this operation is to normalize w.r.t. both items and users.\n",
        "\n",
        "Both the 'fill_na' and 'subtract_mean' strategies together compose what we call a **rating strategy**. Overall, there are $16$ possible different strategies.\n",
        "\n",
        "Let's now, for example, build the rating matrix by using `fill_na=users_means` and `subtract_mean=users_means`. \n",
        "\n",
        "For more details, consult the docstring of the function `build_rating_matrix`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "v89UCu4ueVs0"
      },
      "outputs": [],
      "source": [
        "from utils.preprocessing import build_rating_matrix\n",
        "\n",
        "rating_matrix, no_rating_mask, test_dict, means_dict = build_rating_matrix(df_movies, df_ratings, n_users, \n",
        "                                                                           fill_na='users_means', \n",
        "                                                                           subtract_mean='users_means')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EDmHpclMeVs1"
      },
      "source": [
        "It is always important to remind that this rating matrix does not contain the original ratings. But it contains the ratings after the subtraction with certain means values (the ones specified by the strategy)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "srdfQbYLeVs1",
        "outputId": "e92675a8-b890-41f9-8e72-4f902b3412e1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(610, 9742)"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rating_matrix.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nxE1RX28eVs2",
        "outputId": "3b41faad-c6da-4601-ae9f-cd1038d38422"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5841784"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Number of original missing values\n",
        "no_rating_mask.sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u-wbYU3PeVs2"
      },
      "source": [
        "The following is the proportion of the missing values w.r.t. all cells in the matrix. It's $0.98$, a very huge number."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gz1t0mZbeVs2",
        "outputId": "b85dfd9b-116d-4c64-bd12-388ad09a8c3d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.9830317267467884"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Sparsity factor\n",
        "no_rating_mask.sum()/(rating_matrix.shape[0]*rating_matrix.shape[1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d7mqt69heVs2"
      },
      "source": [
        "### LSA\n",
        "Now, the Latent Semantic Analysis (LSA) is applied on the rating matrix. Basically, we apply the SVD.\n",
        "\n",
        "Singual Values Decomposition (SVD): $$rm = u * D(s) * v^h$$\n",
        "\n",
        "Let $d = min\\{n_{users},n_{movies}\\}$.\n",
        "- $rm$ is the rating matrix.\n",
        "- $u$ is a matrix $n_{users} \\times d$. The rows correspond to the users: each row vector is the vectorial representation of the corresponding term.\n",
        "- $s$ is a vector with length $d$, containing the singular values, sorted in descending order.\n",
        "- $D(s)$ represents the diagonal matrix containing the singular values.\n",
        "- $v^h$ is a matrix $d \\times n_{movies}$. The columns correspond to the movies: each column vector is the vectorial representation of the corresponding movie."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "1k_v1lHNeVs3"
      },
      "outputs": [],
      "source": [
        "u, s, vh = np.linalg.svd(rating_matrix, full_matrices=False)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6lhZ2VtveVs3",
        "outputId": "450e7416-8834-47bc-aebc-609707d588bd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(610, 610)"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "u.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KSLEtpjSeVs3",
        "outputId": "86853c25-1dfc-4a41-879c-b1129649a382"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(610,)"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "s.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XjbP7PkveVs3",
        "outputId": "aa89f482-1719-40a1-cce4-b97f1c74ed51"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(610, 9742)"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "vh.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "Dvf1Ej9KeVs4",
        "outputId": "2904e6d4-1c7d-4a20-992b-8accc496e293"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt \n",
        "plt.plot(s)\n",
        "plt.grid()\n",
        "plt.title('Singular values');"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "hYIUvBH6eVs4",
        "outputId": "7a77aa89-04e0-465a-9dc3-285d08a744dc"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(s[:50])\n",
        "plt.grid()\n",
        "plt.title('First 50 singular values');"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "_88l6SijeVs4",
        "outputId": "da2eded8-55aa-4052-e411-1030af83a81e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(s[:5])\n",
        "plt.grid()\n",
        "plt.title('First 5 singular values');"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "gDDNVOZreVs5"
      },
      "outputs": [],
      "source": [
        "def diff_function(x):\n",
        "    return x[1:] - x[:-1]\n",
        "\n",
        "def curvature_function(s):\n",
        "    s_diff = diff_function(diff_function(s))\n",
        "    return s_diff/((1+np.square(s_diff))**1.5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "NkLI7A7ueVs5",
        "outputId": "f8c4f468-f807-4524-fb33-34f37ef61a31"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(curvature_function(s)[:50])\n",
        "plt.grid()\n",
        "plt.title('Curvature function of the first 50 singular values');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hvJzo1X-eVs5"
      },
      "source": [
        "### Similarity\n",
        "Now, we can exploit the truncated SVD for capturing the similarity between movies. \n",
        "\n",
        "We represent each movie as a $k$-dimensional vector in the compressed LSA space. Then, by computing some metric between these vectors (in our case, cosine similarity), we hope to be able to capture the semantic similarity between movies. \n",
        "\n",
        "Of course, $k$ has a big impact in the quality of the results. \n",
        "- The bigger $k$, the more our sparse is our model, becoming more and more similar to the full rating matrix.\n",
        "- The smaller $k$, the more compressed is our representation. We loose details and information, but hoping to gain some high-level meaning and semantic.\n",
        "\n",
        "It is important to point out the power and beauty of the collaborative approach, by underlying the differences with the content-based one.\n",
        "- In the content-based approach, we try to exploit the content (i.e. the overviews) of the movies for capturing the similarity between movies.\n",
        "- In the collaborative approach, we do not use any information about the movies, but we simply use the ratings given by a community of users. By exploiting this model, in an appropriate compressed space, we can capture the semantic similarities between the movies. \n",
        "\n",
        "For having more information in how this is achieved, look at the function `compute_most_similar_movies_lsa_coll`. The first most similar movie is always the film itself."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pc0zCYtherzZ",
        "outputId": "e8af81fe-2624-4af5-cf3c-6375caf8ca00"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://pypi.ngc.nvidia.com\n",
            "Requirement already satisfied: colorama in c:\\users\\pitti\\appdata\\local\\programs\\python\\python310\\lib\\site-packages (0.4.4)\n"
          ]
        }
      ],
      "source": [
        "!pip install colorama"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "qAGWQKqweVs5"
      },
      "outputs": [],
      "source": [
        "from utils.similarities import compute_most_similar_movies_lsa_coll"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H2Z4atT8eVs5"
      },
      "source": [
        "Let's see the most similar films to `Goodfellas`, `Star Wars: Episode IV`, `Pulp Fiction` and `Interstellar`... Quite impressive results!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "pQxGYAGveVs6",
        "outputId": "9e3f4b4e-d585-4749-fa4e-67e200e10a95"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>movie index</th>\n",
              "      <th>title</th>\n",
              "      <th>similarity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>914</td>\n",
              "      <td>Goodfellas (1990)</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>828</td>\n",
              "      <td>Reservoir Dogs (1992)</td>\n",
              "      <td>0.728015</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>922</td>\n",
              "      <td>Godfather: Part II, The (1974)</td>\n",
              "      <td>0.712027</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>659</td>\n",
              "      <td>Godfather, The (1972)</td>\n",
              "      <td>0.698767</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>909</td>\n",
              "      <td>Apocalypse Now (1979)</td>\n",
              "      <td>0.596851</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   movie index                           title  similarity\n",
              "0          914               Goodfellas (1990)    1.000000\n",
              "1          828           Reservoir Dogs (1992)    0.728015\n",
              "2          922  Godfather: Part II, The (1974)    0.712027\n",
              "3          659           Godfather, The (1972)    0.698767\n",
              "4          909           Apocalypse Now (1979)    0.596851"
            ]
          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Goodfellas (1990)', df_movies=df_movies, vh=vh, s=s, k=100)\n",
        "df_most_similar.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "U3S5-im5eVs6",
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              "      <th>title</th>\n",
              "      <th>similarity</th>\n",
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              "      <th>0</th>\n",
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              "      <td>Star Wars: Episode IV - A New Hope (1977)</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>898</td>\n",
              "      <td>Star Wars: Episode V - The Empire Strikes Back...</td>\n",
              "      <td>0.845900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>911</td>\n",
              "      <td>Star Wars: Episode VI - Return of the Jedi (1983)</td>\n",
              "      <td>0.779794</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>900</td>\n",
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              "      <th>4</th>\n",
              "      <td>990</td>\n",
              "      <td>Indiana Jones and the Last Crusade (1989)</td>\n",
              "      <td>0.524425</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   movie index                                              title  similarity\n",
              "0          224          Star Wars: Episode IV - A New Hope (1977)    1.000000\n",
              "1          898  Star Wars: Episode V - The Empire Strikes Back...    0.845900\n",
              "2          911  Star Wars: Episode VI - Return of the Jedi (1983)    0.779794\n",
              "3          900  Raiders of the Lost Ark (Indiana Jones and the...    0.624925\n",
              "4          990          Indiana Jones and the Last Crusade (1989)    0.524425"
            ]
          },
          "execution_count": 30,
          "metadata": {},
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      ],
      "source": [
        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Star Wars: Episode IV - A New Hope (1977)', df_movies=df_movies, vh=vh, s=s, k=100)\n",
        "df_most_similar.head() "
      ]
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              "  <tbody>\n",
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              "      <th>0</th>\n",
              "      <td>257</td>\n",
              "      <td>Pulp Fiction (1994)</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>46</td>\n",
              "      <td>Usual Suspects, The (1995)</td>\n",
              "      <td>0.813218</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2226</td>\n",
              "      <td>Fight Club (1999)</td>\n",
              "      <td>0.792085</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>828</td>\n",
              "      <td>Reservoir Dogs (1992)</td>\n",
              "      <td>0.790005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>43</td>\n",
              "      <td>Seven (a.k.a. Se7en) (1995)</td>\n",
              "      <td>0.743790</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
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              "   movie index                        title  similarity\n",
              "0          257          Pulp Fiction (1994)    1.000000\n",
              "1           46   Usual Suspects, The (1995)    0.813218\n",
              "2         2226            Fight Club (1999)    0.792085\n",
              "3          828        Reservoir Dogs (1992)    0.790005\n",
              "4           43  Seven (a.k.a. Se7en) (1995)    0.743790"
            ]
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        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Pulp Fiction (1994)', df_movies=df_movies, vh=vh, s=s, k=50)\n",
        "df_most_similar.head()"
      ]
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        "id": "PpxUSYXoeVs6",
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              "      <th>0</th>\n",
              "      <td>3141</td>\n",
              "      <td>Memento (2000)</td>\n",
              "      <td>1.000000</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4909</td>\n",
              "      <td>Eternal Sunshine of the Spotless Mind (2004)</td>\n",
              "      <td>0.741582</td>\n",
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              "      <th>2</th>\n",
              "      <td>2226</td>\n",
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              "      <td>0.702679</td>\n",
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              "      <th>3</th>\n",
              "      <td>3562</td>\n",
              "      <td>Donnie Darko (2001)</td>\n",
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              "</table>\n",
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            "text/plain": [
              "   movie index                                         title  similarity\n",
              "0         3141                                Memento (2000)    1.000000\n",
              "1         4909  Eternal Sunshine of the Spotless Mind (2004)    0.741582\n",
              "2         2226                             Fight Club (1999)    0.702679\n",
              "3         3562                           Donnie Darko (2001)    0.666969\n",
              "4         4615                      Kill Bill: Vol. 1 (2003)    0.665941"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Memento (2000)', df_movies=df_movies, vh=vh, s=s, k=50)\n",
        "df_most_similar.head() "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bZioZPtieVs7"
      },
      "source": [
        "The collaborative model is able to capture many semantic things.\n",
        "- Different films of the same serie. Like different films of the `Star Wars` saga.\n",
        "- The genre and the kind of film. Like `Goodfellas` and `Godfather: Part II, The` are both films about mob. Or like `Goodfellas` and `Reservoir Dogs` are both 'dark' films, with a lot of violence. \n",
        "- The directors and the actors. Like `Pulp Fiction` and `Reservoir Dogs`. Or like for `Interstellar`, in which the most similar films are with Leonardo DiCaprio.\n",
        "\n",
        "Others examples will be also shown later, with the others datasets.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eb8h4UN8eVs7"
      },
      "source": [
        "By using different rating strategies, the similarities results are different. \n",
        "\n",
        "In particular, we have noticed that using a 'subtract_mean' strategy involving the items means, it can end up in being more fair with non-popular films. Indeed, if we do not use the items means, most of the times the most similar films are very popular films, with a lot of ratings. Instead, using the items means, non-popular movies appear much more often among the most similar movies. However, this is not always beneficial. Like in the following examples about `Pulp Fiction` and `Goodfellas`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "WAPGPz2ZeVs7"
      },
      "outputs": [],
      "source": [
        "rating_matrix, no_rating_mask, test_dict, means_dict = build_rating_matrix(df_movies, df_ratings, n_users, \n",
        "                                                                           fill_na='items_means', \n",
        "                                                                           subtract_mean='items_means')\n",
        "u, s, vh = np.linalg.svd(rating_matrix, full_matrices=False)"
      ]
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      "execution_count": 39,
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        "id": "RRIDzQ8aeVs7",
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              "   movie index                       title  similarity\n",
              "0          257         Pulp Fiction (1994)    1.000000\n",
              "1          600         Stupids, The (1996)    0.397032\n",
              "2         2226           Fight Club (1999)    0.392891\n",
              "3          635               Alaska (1996)    0.383143\n",
              "4           46  Usual Suspects, The (1995)    0.376493"
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        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Pulp Fiction (1994)', df_movies=df_movies, vh=vh, s=s, k=100)\n",
        "df_most_similar.head()"
      ]
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              "      <td>914</td>\n",
              "      <td>Goodfellas (1990)</td>\n",
              "      <td>1.000000</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>828</td>\n",
              "      <td>Reservoir Dogs (1992)</td>\n",
              "      <td>0.459824</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5061</td>\n",
              "      <td>Zelig (1983)</td>\n",
              "      <td>0.448357</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>997</td>\n",
              "      <td>Killing Fields, The (1984)</td>\n",
              "      <td>0.443723</td>\n",
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              "      <th>4</th>\n",
              "      <td>4671</td>\n",
              "      <td>Slacker (1991)</td>\n",
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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-de799d8a-f96a-4365-830b-2aa9935d3bcb button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-de799d8a-f96a-4365-830b-2aa9935d3bcb');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   movie index                       title  similarity\n",
              "0          914           Goodfellas (1990)    1.000000\n",
              "1          828       Reservoir Dogs (1992)    0.459824\n",
              "2         5061                Zelig (1983)    0.448357\n",
              "3          997  Killing Fields, The (1984)    0.443723\n",
              "4         4671              Slacker (1991)    0.437832"
            ]
          },
          "execution_count": 40,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_most_similar = compute_most_similar_movies_lsa_coll(movie_title='Goodfellas (1990)', df_movies=df_movies, vh=vh, s=s, k=100)\n",
        "df_most_similar.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sog-hJMkeVs8"
      },
      "source": [
        "We have instead found that using users means in the 'subtract_mean' strategy is typically beneficial. Probably, normalizing the ratings by the users 'generosities' is effective in capturing the similarity between movies."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bm5ZSBBMeVs8"
      },
      "source": [
        "### Processing genres\n",
        "Let's process the genres column, in order to contain the set of genres of each movie."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "wiWhAohieVs8"
      },
      "outputs": [],
      "source": [
        "df_movies['genres'] = df_movies['genres'].map(lambda s: set(s.split('|')))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VDK6GLAueVs8",
        "outputId": "cb81a12d-c1c7-40f5-efb3-b99a292abf7b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "{'IMAX', 'Thriller', 'Musical', 'Mystery', 'Horror', '(no genres listed)', 'Sci-Fi', 'Comedy', 'Drama', 'Children', 'Western', 'Romance', 'Animation', 'War', 'Film-Noir', 'Crime', 'Adventure', 'Action', 'Documentary', 'Fantasy'}\n"
          ]
        }
      ],
      "source": [
        "genres = set([])\n",
        "df_movies['genres'].map(lambda genres_set: genres.update(genres_set))\n",
        "print(genres)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qCxYJPugeVs9"
      },
      "source": [
        "### Visualization\n",
        "Let's try to visualize the movies vectors among two of the first LSA dimensions. For the visualization, we have typically found more beneficial to use 'zero' or 'items' strategies."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "ZTr1SkvSeVs9"
      },
      "outputs": [],
      "source": [
        "rating_matrix, no_rating_mask, test_dict, means_dict = build_rating_matrix(df_movies, df_ratings, n_users, \n",
        "                                                                           fill_na='zero', \n",
        "                                                                           subtract_mean='zero')\n",
        "u, s, vh = np.linalg.svd(rating_matrix, full_matrices=False)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "nAPFu-opeVs9",
        "outputId": "b0cf49fb-48a3-4538-cfe8-3491580ce0e0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "from utils.visualization import plot_movies\n",
        "\n",
        "plot_movies(vh=vh, s=s)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O9g59sPfeVs9"
      },
      "source": [
        "Distribution similar to the ones seen in the content-based approach.\n",
        "\n",
        "Let's plot some known movies. Also here, some kind of polarization up-left / bottom-left can be noticed. We have made this plot along dimensions $0$ and $4$ because thse dimensions enlight more this polarization of dark-bright movies. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "eVsw-g7-eVs-"
      },
      "outputs": [],
      "source": [
        "movies_of_interest = ['Titanic (1997)', 'While You Were Sleeping (1995)', 'Grease (1978)', 'Pretty Woman (1990)', \n",
        "                      'Goodfellas (1990)', 'Casino (1995)', 'Psycho (1960)', 'Shining, The (1980)']\n",
        "movies_subset = []\n",
        "for movie_of_interest in movies_of_interest:\n",
        "    movies_subset += list(df_movies[df_movies['title'].map(lambda t: movie_of_interest==str(t))].index)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "kn9XNs-UeVs-",
        "outputId": "da56ff0c-fb53-4502-84ef-a262c9626f49"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_movies(vh, s, dimensions=(0,4), labels=df_movies['title'].to_numpy(), subset=movies_subset)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wtkbl__9eVs-"
      },
      "source": [
        "Let's briefly analyze also the genres.\n",
        "\n",
        "As expected, the `Comedy` genre is quite broad."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "t8EQuUiJeVs_"
      },
      "outputs": [],
      "source": [
        "from utils.visualization import plot_genres_analysis_coll"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "F2mr83ByeVs_",
        "outputId": "423c235b-5c8c-4173-e21c-0709085b576c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_genres_analysis_coll(vh=vh, s=s, df_movies=df_movies, genres=['Comedy'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Emj2cR2qeVs_"
      },
      "source": [
        "Polarization `Romance`/`Sci-Fi`. Still dimensions $0$ and $4$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "hEQfAukheVs_",
        "outputId": "ab17177f-1c2e-46e7-de6f-9ced9bf79394"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_genres_analysis_coll(vh=vh, s=s, df_movies=df_movies, genres=['Romance', 'Sci-Fi'], dimensions=(0,4))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eewtp3R8eVs_"
      },
      "source": [
        "Polarization `Romance` / `Horror`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "JMNweLMbeVtA",
        "outputId": "9f05ff83-5b9e-462a-e9c4-7743633efc27"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_genres_analysis_coll(vh=vh, s=s, df_movies=df_movies, genres=['Romance', 'Horror'], dimensions=(0,4))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "ExdOH7_NeVtA",
        "outputId": "9291c831-fd62-4dd3-aab0-fa0aaa5fb026"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_genres_analysis_coll(vh=vh, s=s, df_movies=df_movies, genres=['Musical', 'Horror'], dimensions=(0,4))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zM--HCwAeVtA"
      },
      "source": [
        "### Rates prediction\n",
        "In this section, we use the strategy 'items_users'."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "id": "czulrdt2eVtA"
      },
      "outputs": [],
      "source": [
        "rating_matrix, no_rating_mask, test_dict, means_dict = build_rating_matrix(df_movies, df_ratings, n_users, \n",
        "                                                                           fill_na='items_users_means', \n",
        "                                                                           subtract_mean='items_users_means')\n",
        "u, s, vh = np.linalg.svd(rating_matrix, full_matrices=False)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "HsSzqdfJeVtB"
      },
      "outputs": [],
      "source": [
        "# In this section, we need also information about the used means and about the nan mask\n",
        "test_mask, test_target = test_dict['test_mask'], test_dict['test_target']\n",
        "items_means, users_means, items_users_means = means_dict['items_means'], means_dict['users_means'], means_dict['items_users_means']\n",
        "\n",
        "nan_mask = np.logical_or(no_rating_mask, test_mask)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aqXg2yMseVtB"
      },
      "source": [
        "With our model, we can also predict which is the rate given by a certain user to a certain movie. \n",
        "\n",
        "If $uk$ is the user vector in the $k$-dimensional LSA space and $mk$ is the movie vector in the $k$-dimensional LSA space, their dot product gives us the predicted rate. Of course, the two vectors must be first scaled according to the singular values. Basically, yhe formula is the following. $$(\\sqrt{sk} * uk) * (\\sqrt{sk} * mk)$$, where $sk$ are the first $k$-th singual values.\n",
        "\n",
        "This is very similar to computing the similarity between an user and a movie. We can also notice that this value is exactly equal to the value in the cell related to that user and movie of the reconstructed rating matrix, obtained using the $k$-rank SVD approximation. Estimation/approximation of the original rating matrix (i.e. of the true ratings), by means of the compressed $k$-dimensional LSA space.\n",
        "\n",
        "Actually, an important precisation must be done. What we achieve by proceding in this way are not the actual ratings in the range $[0..5]$, but are the ratings after having subtracted certain means (specified by the strategy). Basically, since we are trying to reconstruct the rating matrix and since the rating matrix contains the ratings after having subtracted the means, we are predicting these normalized values, and not the rates in $[0..5]$. For obtaining the rates we have to simply sum the used means."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "f0S465ufeVtB"
      },
      "outputs": [],
      "source": [
        "from utils.rating import predict_ratings, evaluate, rebuild_rating_matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "amMtBzn_eVtC"
      },
      "source": [
        "Reconstruction/prediction of the rating matrix, with $k=100$. These are the normalized values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SyQUuKQteVtC",
        "outputId": "e82bc578-1967-4933-ffd5-de47bbfc2528"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[-4.28436974e-01 -2.43417660e-01  2.63600393e-01 ...  2.86279932e-04\n",
            "   2.86279932e-04 -2.70794988e-03]\n",
            " [-7.54749421e-03 -1.64402034e-02 -1.55341786e-02 ...  2.99113917e-05\n",
            "   2.99113917e-05 -1.39921653e-03]\n",
            " [ 1.40372133e-01  1.72804624e-01  1.81854978e-02 ... -9.44674328e-04\n",
            "  -9.44674328e-04 -8.95800493e-04]\n",
            " ...\n",
            " [-1.03531254e+00 -1.37664407e+00 -1.25818298e+00 ...  2.59039734e-04\n",
            "   2.59039734e-04 -5.51903823e-03]\n",
            " [-1.03310641e-01 -4.34966171e-02 -5.71694544e-02 ... -6.46901303e-06\n",
            "  -6.46901303e-06 -9.34053083e-05]\n",
            " [ 1.29222218e+00  5.96506955e-02 -4.33002306e-02 ... -5.76867522e-04\n",
            "  -5.76867522e-04  9.91651270e-03]]\n"
          ]
        }
      ],
      "source": [
        "rating_matrix_pred = predict_ratings(u, s, vh, k=100)\n",
        "print(rating_matrix_pred)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "msmTrnU7eVtC"
      },
      "source": [
        "True rating matrix, normalized values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jmvpYRgoeVtD",
        "outputId": "f16f5c6e-636d-4359-d683-7107ab3f57b6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[-0.14365477  0.          0.18700265 ...  0.          0.\n",
            "   0.        ]\n",
            " [ 0.          0.          0.         ...  0.          0.\n",
            "   0.        ]\n",
            " [ 0.          0.          0.         ...  0.          0.\n",
            "   0.        ]\n",
            " ...\n",
            " [-1.02755296 -1.28299694 -1.19689554 ...  0.          0.\n",
            "   0.        ]\n",
            " [-0.59560025  0.          0.         ...  0.          0.\n",
            "   0.        ]\n",
            " [ 1.19525685  0.          0.         ...  0.          0.\n",
            "   0.        ]]\n"
          ]
        }
      ],
      "source": [
        "print(rating_matrix)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TtocN45_eVtD"
      },
      "source": [
        "Let's now see the predicted rates in $[1..5]$ and the actual ones. We just sum the used means (items-users in our case). We also mask out the original missing values."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_0ERzuUteVtD",
        "outputId": "5eac7617-7514-41f2-b58a-9545b6658ef3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[3.7152178         nan 4.07659774 ...        nan        nan        nan]\n",
            " [       nan        nan        nan ...        nan        nan        nan]\n",
            " [       nan        nan        nan ...        nan        nan        nan]\n",
            " ...\n",
            " [2.49224042 1.90635287 1.93871255 ...        nan        nan        nan]\n",
            " [3.49228961        nan        nan ...        nan        nan        nan]\n",
            " [5.09696533        nan        nan ...        nan        nan        nan]]\n"
          ]
        }
      ],
      "source": [
        "# Predicted rates\n",
        "rating_matrix_pred_rebuilt = rebuild_rating_matrix(rating_matrix_pred, means=items_users_means, nan_mask=nan_mask)\n",
        "print(rating_matrix_pred_rebuilt)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "haZUwSlPeVtE",
        "outputId": "9a787e17-8275-4cc0-ed67-974e55d1b3ba"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[4.  nan 4.  ... nan nan nan]\n",
            " [nan nan nan ... nan nan nan]\n",
            " [nan nan nan ... nan nan nan]\n",
            " ...\n",
            " [2.5 2.  2.  ... nan nan nan]\n",
            " [3.  nan nan ... nan nan nan]\n",
            " [5.  nan nan ... nan nan nan]]\n"
          ]
        }
      ],
      "source": [
        "# True rates\n",
        "rating_matrix_rebuilt = rebuild_rating_matrix(rating_matrix, means=items_users_means, nan_mask=nan_mask)\n",
        "print(rating_matrix_rebuilt)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qC6P5xM7eVtE"
      },
      "source": [
        "### Evaluation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "399HSbL1eVtE"
      },
      "source": [
        "We can evaluate the goodness of our predictions, by using *Root Mean Squared Error (RMSE)* or *Absolute Mean Error (MAE)*. Of course, we mask out the original missing values. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XIxT9TXPeVtE",
        "outputId": "f871b059-b969-4e4c-f617-c3bd0534f74d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8472345365804169"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Dumb model: always predict 0\n",
        "rmse = evaluate(rating_matrix, np.zeros(shape=rating_matrix.shape), mask_no_evaluate=nan_mask)\n",
        "rmse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cIVodhSfeVtE",
        "outputId": "b566360c-95be-4027-9b34-549de6e8251e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.7861301019161094"
            ]
          },
          "execution_count": 60,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# k=5\n",
        "rating_matrix_pred = predict_ratings(u, s, vh, k=5)\n",
        "rmse = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask, metric='rmse')\n",
        "rmse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0wyYkttIeVtF",
        "outputId": "e32c89c0-a8fb-464d-e10b-e967baf324a4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.5777508946767753"
            ]
          },
          "execution_count": 61,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# k=50\n",
        "rating_matrix_pred = predict_ratings(u, s, vh, k=50)\n",
        "rmse = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask, metric='rmse')\n",
        "rmse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h6knGb9KeVtF",
        "outputId": "8e486c43-da5f-47ce-ea47-0e2a91175df2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.4435976834253355"
            ]
          },
          "execution_count": 62,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# k=100\n",
        "rating_matrix_pred = predict_ratings(u, s, vh, k=100)\n",
        "rmse = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask, metric='rmse')\n",
        "rmse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IYWFjndmeVtF",
        "outputId": "c89ec75c-26bd-47c1-bd06-b3ec144e38b7"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.17166414765226218"
            ]
          },
          "execution_count": 63,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# k=300\n",
        "rating_matrix_pred = predict_ratings(u, s, vh, k=300)\n",
        "rmse = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask, metric='rmse')\n",
        "rmse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-kGdfe1xeVtG",
        "outputId": "de9e219b-34b5-4fe9-9ff8-d49c7058535e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.04357868916928781"
            ]
          },
          "execution_count": 64,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# k=300\n",
        "rating_matrix_pred = predict_ratings(u, s, vh, k=500)\n",
        "rmse = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask, metric='rmse')\n",
        "rmse"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FeXN2q1feVtG"
      },
      "source": [
        "Of course, the bigger $k$, the better is our model in making the predictions. The error becomes smaller and smaller. \n",
        "\n",
        "This because we are using more and more dimensions, going toward using all the original dimensions. We are simply reconstructing back the matrix using the truncated SVD: if $k$ is equal to the original rank, we get back exactly the true rating matrix. So the error is $0$!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Oo1CwNMVeVtG",
        "outputId": "ed18c6e8-8e23-42c4-ee39-899b40b0aeb3"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[4. , nan, 4. , ..., nan, nan, nan],\n",
              "       [nan, nan, nan, ..., nan, nan, nan],\n",
              "       [nan, nan, nan, ..., nan, nan, nan],\n",
              "       ...,\n",
              "       [2.5, 2. , 2. , ..., nan, nan, nan],\n",
              "       [3. , nan, nan, ..., nan, nan, nan],\n",
              "       [5. , nan, nan, ..., nan, nan, nan]])"
            ]
          },
          "execution_count": 65,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rebuild_rating_matrix(rating_matrix, items_users_means, nan_mask)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ug_i60vjeVtG",
        "outputId": "b5933c29-bb77-4111-abaf-f2a598e9a0ff"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[4.00752581        nan 4.00217896 ...        nan        nan        nan]\n",
            " [       nan        nan        nan ...        nan        nan        nan]\n",
            " [       nan        nan        nan ...        nan        nan        nan]\n",
            " ...\n",
            " [2.49715054 2.00183543 2.00075256 ...        nan        nan        nan]\n",
            " [3.1994648         nan        nan ...        nan        nan        nan]\n",
            " [5.00288162        nan        nan ...        nan        nan        nan]]"
          ]
        }
      ],
      "source": [
        "# @title Reconstructed rating matrix with different k: tuning k { run: \"auto\" }\n",
        "\n",
        "k = 415 #@param {type:\"slider\", min:0, max:500, step:1}\n",
        "\n",
        "k = int(k)\n",
        "print(rebuild_rating_matrix(predict_ratings(u, s, vh, k=k), items_users_means, nan_mask), end='')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IsuT8xDieVtH"
      },
      "source": [
        "However, this is not a fair and interesting evaluation of our model. We are like cheating: we knew the true rates, we compressed them, and then we reconstruct them back. We would like to evaluate our model in predicting rates which we don't know at all!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Av5tl6GXeVtH"
      },
      "source": [
        "### Train - Test evaluation\n",
        "We would like to evaluate our model in a test set, like in classic ML. Several approaches can be followed for implementing that in our context. We use the following one.\n",
        "\n",
        "A random subset of the ratings is taken and considered as test set: the proportion of this test set is arbitrary, and we fix it has $0.2$. These test set rates are 'masked out', in the sense that they are treated as missing values (handled in the same way of all the others missing values, using the 'fill_na' strategy). Of course, the true test set rates are kept and returned to the user, because they will be necessary for the evaluation.\n",
        "\n",
        "This is implemented in the `build_rating_matrix` function."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "id": "ywUInmxueVtH"
      },
      "outputs": [],
      "source": [
        "rating_matrix, no_rating_mask, test_dict, means_dict = build_rating_matrix(df_movies, df_ratings, n_users, \n",
        "                                                                           fill_na='items_users_means', \n",
        "                                                                           subtract_mean='items_users_means', test_prop=0.2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "id": "pz4zLwGEeVtH"
      },
      "outputs": [],
      "source": [
        "# Let's extract the needed information\n",
        "\n",
        "# test_mask: boolean mask telling me where are the test set cells in the matrix\n",
        "# test_target: actual test set rates\n",
        "test_mask, test_target = test_dict['test_mask'], test_dict['test_target']\n",
        "\n",
        "# Information about the means\n",
        "items_means, users_means, items_users_means = means_dict['items_means'], means_dict['users_means'], means_dict['items_users_means']\n",
        "\n",
        "# Boolean mask telling me where are missing values in the matrix: either original missing rates or test set cells\n",
        "nan_mask = np.logical_or(no_rating_mask, test_mask)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R3-vdZ91eVtI",
        "outputId": "d2a7f399-8303-4b87-bbc4-0cef85b40991"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sparsity factor of the original missing rates: 0.9830\n",
            "Sparsity factor after masking out the test set cells: 0.9864\n"
          ]
        }
      ],
      "source": [
        "# Sparsity factors\n",
        "print(f'Sparsity factor of the original missing rates: {no_rating_mask.sum()/(rating_matrix.shape[0]*rating_matrix.shape[1]):.4f}')\n",
        "print(f'Sparsity factor after masking out the test set cells: {nan_mask.sum()/(rating_matrix.shape[0]*rating_matrix.shape[1]):.4f}', )"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "id": "j_jRJn5EeVtI"
      },
      "outputs": [],
      "source": [
        "u, s, vh = np.linalg.svd(rating_matrix, full_matrices=False)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KjD_TmgzeVtI",
        "outputId": "5ae8818b-547a-41fe-f3e2-d32048d50ed3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Train error: 0.58\n",
            "Test error: 0.89\n"
          ]
        }
      ],
      "source": [
        "rating_matrix_pred = predict_ratings(u, s, vh, k=50)\n",
        "\n",
        "# Error on the train set cells, i.e. no missing rate and no test set cell\n",
        "train_err = evaluate(rating_matrix, rating_matrix_pred, mask_no_evaluate=nan_mask)\n",
        "print(f'Train error: {train_err:.2f}')\n",
        "\n",
        "# Error on the test set cells\n",
        "test_pred = (rating_matrix_pred+items_users_means)[test_mask]\n",
        "test_err = evaluate(test_target, test_pred)\n",
        "print(f'Test error: {test_err:.2f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3iD5ik0xeVtI"
      },
      "source": [
        "The test error is higher, as expected"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5bFvU4SyeVtJ"
      },
      "source": [
        "### Train - Test evaluation: different k\n",
        "This evaluation can be performed at different $k$, and visualizing the plots. The best $k$ is the one with lowest test error.\n",
        "\n",
        "We use this function `compute_train_test_errors`, to which we specify the particular rating strategy we want to use. Look at the docstring for more details."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "OU6gUNa0eVtJ",
        "outputId": "be88c4b7-aa1b-4de5-c8ff-237653ce9c85"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "min err: 0.8851680769313368; best k: 14\n"
          ]
        }
      ],
      "source": [
        "from utils.rating import compute_train_test_errors\n",
        "\n",
        "train_err_list, test_err_list = compute_train_test_errors(df_movies, df_ratings, n_users=n_users, fill_na='items_users_means',\n",
        "                                                          subtract_mean='items_users_means')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_DcRKEoAeVtJ"
      },
      "source": [
        "We can see that this is compliant with the classic plot of train-test errors in ML.\n",
        "\n",
        "Let's see only the test errors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "UTN-QMPmeVtJ",
        "outputId": "ce4d1165-4bb1-483e-aa65-69e29699a13d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "min err: 0.8750089237901935; best k: 17\n"
          ]
        }
      ],
      "source": [
        "train_err_list, test_err_list = compute_train_test_errors(df_movies, df_ratings, n_users=n_users, fill_na='items_users_means',\n",
        "                                                          subtract_mean='items_users_means', plot_train=False)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uFMCmH4BeVtJ"
      },
      "source": [
        "We can also specify to perform a cross-validation approach. `cv_splits` different training-test couples are generated and, for each $k$, their training-test scores are aggregated, in order to compute the single couple train_err-test_err for that $k$. Basically, not a single splitting training-test is considered, but `cv_splits` different ones."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "F39iL9soeVtK",
        "outputId": "4528b57e-ddfa-49fd-847e-9a2222a59acb"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "min err: 0.8828523399637399; best k: 14\n"
          ]
        }
      ],
      "source": [
        "train_err_list, test_err_list = compute_train_test_errors(df_movies, df_ratings, n_users=n_users, fill_na='items_users_means',\n",
        "                                                          subtract_mean='items_users_means', cv_splits=5, plot_train=False)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pftXF7HIeVtK"
      },
      "source": [
        "The plot is less noisy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xspgmKaieVtK"
      },
      "source": [
        "### Comparison of different rating strategies\n",
        "We can apply this same thing on different ratings strategies, for comparign them. A rating strategy name is encoded as '{fill_na_strategy}/{subtract_mean_strategy}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DVYUlGy2eVtK",
        "outputId": "512d37f9-e908-45eb-ed93-97f44d6c82fc"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Help on function compare_rating_strategies in module utils.rating:\n",
            "\n",
            "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies, k_range=(0, 200), test_prop=0.2, random_seed=44, metric='rmse', cv_splits=1)\n",
            "    Compare different rating strategies.\n",
            "    \n",
            "    A rating strategy is the combination of a `fill_na` (i.e. a strategy for silling the missing values) and a `subtract_mean`\n",
            "    (i.e. a strategy for subtracting the values in the rating matrix).\n",
            "    \n",
            "    The different strategies are compared by measuring the test errors among all the different 'k' values specified with `k_range`.\n",
            "    For each strategy and for each 'k', an error score is computed.\n",
            "    The test error plot of each rating strategy is made, for having a visualization of the comparison.\n",
            "    In the end, the best strategy with the best score and the best 'k' are printed in the console.\n",
            "    \n",
            "    This function is implemented using the `compute_train_test_errors` function. \n",
            "    As exaplained in the docstring of that function, a cross-validation approach is followed for computing the test score \n",
            "    for each strategy for each 'k'. Basically, not a single splitting training-test is c0nsidered, but `cv_splits` different\n",
            "    ones.\n",
            "    \n",
            "    Parameters\n",
            "    ----------\n",
            "    df_movies : pd.DataFrame\n",
            "        Movies dataframe\n",
            "    df_ratings : pd.DataFrame\n",
            "        Ratings dataframe\n",
            "    n_users : int\n",
            "        Number of users\n",
            "    rating_strategies : list of str\n",
            "        List of different rating strategies to take into account.\n",
            "        A rating strategy is represented as a string formatted as '{fill_na}/{subtract_mean}', containing both the 'fill_na'\n",
            "        and the 'subtract_mean' strategies.\n",
            "    k_range : tuple, optional\n",
            "        Tuple containing the lower and upper bounds for the range of the k values, by default (0,200)\n",
            "    test_prop : float, optional\n",
            "        Test set proportion, by default 0.2\n",
            "    random_seed : int, optional\n",
            "        Random seed for the test set random samples, by default 44\n",
            "    metric : str, optional\n",
            "        Metric for computing the error scores, by default 'rmse'\n",
            "    cv_splits : int, optional\n",
            "        Number of cross validation splits, by default 1\n",
            "\n"
          ]
        }
      ],
      "source": [
        "from utils.rating import compare_rating_strategies\n",
        "help(compare_rating_strategies)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WC2c1LJeeVtK"
      },
      "source": [
        "First of all, the strategies with 'zero' are much worse. We evaluate them separately."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "V4x7M28geVtL",
        "outputId": "311cc363-0aec-44a3-81c0-1c942b44830b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: zero/users\n",
            "Best k: 0\n",
            "Best error: 0.9405649272828601\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['zero/zero', 'zero/items', 'zero/users', 'zero/users', 'zero/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y9ngIOO9eVtL"
      },
      "source": [
        "Let's move to more interesting comparisons."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xU3DszPneVtL",
        "outputId": "3358b302-39e9-4756-eac5-b84be080f257"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 19\n",
            "Best error: 0.8925142809755361\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items/items', 'users/users', 'items_users/items_users', 'items/users', 'users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tG5oatU5eVtL"
      },
      "source": [
        "The best one is 'items_users_mean/items_users_mean'. Let's compare also with the remaining options."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bI3rnmkaeVtM",
        "outputId": "04dbefed-0993-43b6-9371-e3a09b206e17"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/users\n",
            "Best k: 15\n",
            "Best error: 0.8853423490702353\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items_users/items_users', 'items_users/users', 'items_users/items', 'items/items_users', 'users/items_users']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MkdQcLZ0eVtM"
      },
      "source": [
        "The best one is 'items_users_means/users_means'."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bru25VKFeVtM"
      },
      "source": [
        "## MovieLens 100k \n",
        "Let's move to a more ineteresting dataset, which is used in practice for evaluation purposes.\n",
        "- Around $100$ k ratings\n",
        "- Around $1700$ movies\n",
        "- Around $1000$ users"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2G0qRf_feVtM"
      },
      "outputs": [],
      "source": [
        "movies_file = 'datasets/collaborative/movies_100k.item'\n",
        "ratings_file = 'datasets/collaborative/ratings_100k.data'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JTDu-ooueVtM"
      },
      "outputs": [],
      "source": [
        "col_n = ['movie id' , 'movie title' , 'release date' , 'video release date' ,\n",
        "              'IMDb URL' , 'unknown' , 'Action' , 'Adventure' , 'Animation' ,\n",
        "              \"Children's\" , 'Comedy' , 'Crime' , 'Documentary' , 'Drama' , 'Fantasy' ,\n",
        "              'Film-Noir' , 'Horror' , 'Musical' , 'Mystery' , 'Romance' , 'Sci-Fi' ,\n",
        "              'Thriller' , 'War' , 'Western']\n",
        "\n",
        "\n",
        "df_movies = pd.read_csv(movies_file, \n",
        "                       sep = '|',encoding = 'latin-1',names=col_n )"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nyN0cW_reVtM",
        "outputId": "12b55be2-7bf6-4bf7-a171-d89bfab1b34f"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>movie id</th>\n",
              "      <th>movie title</th>\n",
              "      <th>release date</th>\n",
              "      <th>video release date</th>\n",
              "      <th>IMDb URL</th>\n",
              "      <th>unknown</th>\n",
              "      <th>Action</th>\n",
              "      <th>Adventure</th>\n",
              "      <th>Animation</th>\n",
              "      <th>Children's</th>\n",
              "      <th>...</th>\n",
              "      <th>Fantasy</th>\n",
              "      <th>Film-Noir</th>\n",
              "      <th>Horror</th>\n",
              "      <th>Musical</th>\n",
              "      <th>Mystery</th>\n",
              "      <th>Romance</th>\n",
              "      <th>Sci-Fi</th>\n",
              "      <th>Thriller</th>\n",
              "      <th>War</th>\n",
              "      <th>Western</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Toy Story (1995)</td>\n",
              "      <td>01-Jan-1995</td>\n",
              "      <td>NaN</td>\n",
              "      <td>http://us.imdb.com/M/title-exact?Toy%20Story%2...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>GoldenEye (1995)</td>\n",
              "      <td>01-Jan-1995</td>\n",
              "      <td>NaN</td>\n",
              "      <td>http://us.imdb.com/M/title-exact?GoldenEye%20(...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Four Rooms (1995)</td>\n",
              "      <td>01-Jan-1995</td>\n",
              "      <td>NaN</td>\n",
              "      <td>http://us.imdb.com/M/title-exact?Four%20Rooms%...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Get Shorty (1995)</td>\n",
              "      <td>01-Jan-1995</td>\n",
              "      <td>NaN</td>\n",
              "      <td>http://us.imdb.com/M/title-exact?Get%20Shorty%...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Copycat (1995)</td>\n",
              "      <td>01-Jan-1995</td>\n",
              "      <td>NaN</td>\n",
              "      <td>http://us.imdb.com/M/title-exact?Copycat%20(1995)</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 24 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "   movie id        movie title release date  video release date  \\\n",
              "0         1   Toy Story (1995)  01-Jan-1995                 NaN   \n",
              "1         2   GoldenEye (1995)  01-Jan-1995                 NaN   \n",
              "2         3  Four Rooms (1995)  01-Jan-1995                 NaN   \n",
              "3         4  Get Shorty (1995)  01-Jan-1995                 NaN   \n",
              "4         5     Copycat (1995)  01-Jan-1995                 NaN   \n",
              "\n",
              "                                            IMDb URL  unknown  Action  \\\n",
              "0  http://us.imdb.com/M/title-exact?Toy%20Story%2...        0       0   \n",
              "1  http://us.imdb.com/M/title-exact?GoldenEye%20(...        0       1   \n",
              "2  http://us.imdb.com/M/title-exact?Four%20Rooms%...        0       0   \n",
              "3  http://us.imdb.com/M/title-exact?Get%20Shorty%...        0       1   \n",
              "4  http://us.imdb.com/M/title-exact?Copycat%20(1995)        0       0   \n",
              "\n",
              "   Adventure  Animation  Children's  ...  Fantasy  Film-Noir  Horror  Musical  \\\n",
              "0          0          1           1  ...        0          0       0        0   \n",
              "1          1          0           0  ...        0          0       0        0   \n",
              "2          0          0           0  ...        0          0       0        0   \n",
              "3          0          0           0  ...        0          0       0        0   \n",
              "4          0          0           0  ...        0          0       0        0   \n",
              "\n",
              "   Mystery  Romance  Sci-Fi  Thriller  War  Western  \n",
              "0        0        0       0         0    0        0  \n",
              "1        0        0       0         1    0        0  \n",
              "2        0        0       0         1    0        0  \n",
              "3        0        0       0         0    0        0  \n",
              "4        0        0       0         1    0        0  \n",
              "\n",
              "[5 rows x 24 columns]"
            ]
          },
          "execution_count": 137,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_movies.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yMM53aa1eVtN",
        "outputId": "67ccd7b2-5baa-423b-bab5-bbe19a2e9158"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1682 entries, 0 to 1681\n",
            "Data columns (total 24 columns):\n",
            " #   Column              Non-Null Count  Dtype  \n",
            "---  ------              --------------  -----  \n",
            " 0   movie id            1682 non-null   int64  \n",
            " 1   movie title         1682 non-null   object \n",
            " 2   release date        1681 non-null   object \n",
            " 3   video release date  0 non-null      float64\n",
            " 4   IMDb URL            1679 non-null   object \n",
            " 5   unknown             1682 non-null   int64  \n",
            " 6   Action              1682 non-null   int64  \n",
            " 7   Adventure           1682 non-null   int64  \n",
            " 8   Animation           1682 non-null   int64  \n",
            " 9   Children's          1682 non-null   int64  \n",
            " 10  Comedy              1682 non-null   int64  \n",
            " 11  Crime               1682 non-null   int64  \n",
            " 12  Documentary         1682 non-null   int64  \n",
            " 13  Drama               1682 non-null   int64  \n",
            " 14  Fantasy             1682 non-null   int64  \n",
            " 15  Film-Noir           1682 non-null   int64  \n",
            " 16  Horror              1682 non-null   int64  \n",
            " 17  Musical             1682 non-null   int64  \n",
            " 18  Mystery             1682 non-null   int64  \n",
            " 19  Romance             1682 non-null   int64  \n",
            " 20  Sci-Fi              1682 non-null   int64  \n",
            " 21  Thriller            1682 non-null   int64  \n",
            " 22  War                 1682 non-null   int64  \n",
            " 23  Western             1682 non-null   int64  \n",
            "dtypes: float64(1), int64(20), object(3)\n",
            "memory usage: 315.5+ KB\n"
          ]
        }
      ],
      "source": [
        "df_movies.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "snIUbl0keVtN"
      },
      "source": [
        "We have the problem that the genres are not encoded as a single column, but they are one-hot encoded. Let's fix this."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yv2wo2zUeVtN",
        "outputId": "ba7a0ca7-e4ff-420f-9ff4-282fc5213043"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>movie id</th>\n",
              "      <th>movie title</th>\n",
              "      <th>genres</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Toy Story (1995)</td>\n",
              "      <td>{Animation, Children's, Comedy}</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>GoldenEye (1995)</td>\n",
              "      <td>{Thriller, Adventure, Action}</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Four Rooms (1995)</td>\n",
              "      <td>{Thriller}</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Get Shorty (1995)</td>\n",
              "      <td>{Drama, Comedy, Action}</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Copycat (1995)</td>\n",
              "      <td>{Thriller, Drama, Crime}</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   movie id        movie title                           genres\n",
              "0         1   Toy Story (1995)  {Animation, Children's, Comedy}\n",
              "1         2   GoldenEye (1995)    {Thriller, Adventure, Action}\n",
              "2         3  Four Rooms (1995)                       {Thriller}\n",
              "3         4  Get Shorty (1995)          {Drama, Comedy, Action}\n",
              "4         5     Copycat (1995)         {Thriller, Drama, Crime}"
            ]
          },
          "execution_count": 140,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from utils.preprocessing import preprocess_dfMovies_100k_coll\n",
        "\n",
        "df_movies = preprocess_dfMovies_100k_coll(df_movies)\n",
        "df_movies.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kk6KAxwLeVtN"
      },
      "source": [
        "Let's also rename the columns, in order to be compliant with the interface of before."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W_zjIihneVtO"
      },
      "outputs": [],
      "source": [
        "df_movies = df_movies.rename(columns={'movie id':'movieId', 'movie title':'title'})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fQCLG-mleVtO",
        "outputId": "d707ab08-9b07-4c75-e2a1-e311dfb328bd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1682 entries, 0 to 1681\n",
            "Data columns (total 3 columns):\n",
            " #   Column   Non-Null Count  Dtype \n",
            "---  ------   --------------  ----- \n",
            " 0   movieId  1682 non-null   int64 \n",
            " 1   title    1682 non-null   object\n",
            " 2   genres   1682 non-null   object\n",
            "dtypes: int64(1), object(2)\n",
            "memory usage: 39.5+ KB\n"
          ]
        }
      ],
      "source": [
        "df_movies.info()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zS325791eVtO"
      },
      "outputs": [],
      "source": [
        "df_ratings = pd.read_csv(ratings_file,\n",
        "                      sep = '\\t',names= ['UseID', 'ItemID', 'rating', 'Timestamp' ])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZJwgWJx3eVtO",
        "outputId": "5afabd6a-1e1f-4513-cf70-fc99c559ccd0"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>UseID</th>\n",
              "      <th>ItemID</th>\n",
              "      <th>rating</th>\n",
              "      <th>Timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>196</td>\n",
              "      <td>242</td>\n",
              "      <td>3</td>\n",
              "      <td>881250949</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>186</td>\n",
              "      <td>302</td>\n",
              "      <td>3</td>\n",
              "      <td>891717742</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>22</td>\n",
              "      <td>377</td>\n",
              "      <td>1</td>\n",
              "      <td>878887116</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>244</td>\n",
              "      <td>51</td>\n",
              "      <td>2</td>\n",
              "      <td>880606923</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>166</td>\n",
              "      <td>346</td>\n",
              "      <td>1</td>\n",
              "      <td>886397596</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   UseID  ItemID  rating  Timestamp\n",
              "0    196     242       3  881250949\n",
              "1    186     302       3  891717742\n",
              "2     22     377       1  878887116\n",
              "3    244      51       2  880606923\n",
              "4    166     346       1  886397596"
            ]
          },
          "execution_count": 151,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_ratings.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FQ4N-F4yeVtO",
        "outputId": "4547250b-92c3-4384-d8fd-37e116019d78"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 100000 entries, 0 to 99999\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count   Dtype\n",
            "---  ------     --------------   -----\n",
            " 0   UseID      100000 non-null  int64\n",
            " 1   ItemID     100000 non-null  int64\n",
            " 2   rating     100000 non-null  int64\n",
            " 3   Timestamp  100000 non-null  int64\n",
            "dtypes: int64(4)\n",
            "memory usage: 3.1 MB\n"
          ]
        }
      ],
      "source": [
        "df_ratings.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bbpTwBZSeVtP"
      },
      "source": [
        "Rename also its columns."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2t6IBIfAeVtP"
      },
      "outputs": [],
      "source": [
        "df_ratings = df_ratings.rename(columns={'ItemID':'movieId', 'UseID':'userId'})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XxTQo4MveVtP",
        "outputId": "4b8ae42c-c002-4f57-9913-137a50c30d04"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 100000 entries, 0 to 99999\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count   Dtype\n",
            "---  ------     --------------   -----\n",
            " 0   userId     100000 non-null  int64\n",
            " 1   movieId    100000 non-null  int64\n",
            " 2   rating     100000 non-null  int64\n",
            " 3   Timestamp  100000 non-null  int64\n",
            "dtypes: int64(4)\n",
            "memory usage: 3.1 MB\n"
          ]
        }
      ],
      "source": [
        "df_ratings.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NR-yhh3zeVtP"
      },
      "source": [
        "### Preprocessing\n",
        "Same preprocessing of before, for the users ids and movies ids."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yAdyffBOeVtP"
      },
      "outputs": [],
      "source": [
        "from utils.preprocessing import preprocess_movies_ratings_coll"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2DNW5qWpeVtP"
      },
      "outputs": [],
      "source": [
        "df_movies, df_ratings = preprocess_movies_ratings_coll(df_movies, df_ratings)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bCK8kXVmeVtP",
        "outputId": "a19eef01-c419-4ee6-cdf6-dcead4e2eea4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "943"
            ]
          },
          "execution_count": 162,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "users = df_ratings['userId'].unique()\n",
        "n_users = len(users)\n",
        "n_users"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hXRPFdFQeVtQ",
        "outputId": "12cbeabc-6991-4012-b081-7ba9b5ed42f6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sparsity factor: 0.9369533063577546\n"
          ]
        }
      ],
      "source": [
        "print(f'Sparsity factor: {1-df_ratings.shape[0]/(n_users*df_movies.shape[0])}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C9FSLU6BeVtQ"
      },
      "source": [
        "This dataset is more dense."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oJ3f8nESeVtQ"
      },
      "source": [
        "### Evaluation\n",
        "The evaluation on this dataset is more interesting. For two reasons.\n",
        "1. [Here](https://paperswithcode.com/sota/collaborative-filtering-on-movielens-100k) (paperswithcode) we can find the SOTA results on this dataset. (Even if the evaluation strategy is not exactly the same, but at least we can get a sense of the numbers). \n",
        "2. [In this paper](https://www.researchgate.net/publication/253996195_Evaluation_of_standard_SVD-based_techniques_for_Collaborative_Filtering) a very similar comparison has been carried out on this dataset. The paper makes the comparisons between three methods: the first two are basically mine 'items_means/users_means' and 'users_means/items_means' strategies. While the third one is a different strategy. However, we explote more different combinations. And we are able to reach a lowest score, using the strategy 'items_users_means/items_users_means'."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YsF16jzZeVtQ"
      },
      "source": [
        "**RMSE** (for comparison with paperswithcode)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rRCiUP4jeVtQ",
        "outputId": "37d41f03-813a-4845-ae36-7bc8e2ca38f1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 10\n",
            "Best error: 0.948645419762318\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items/items', 'users/users', 'items_users/items_users', 'items/users', 'users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, cv_splits=5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "phbTq-fMeVtQ"
      },
      "source": [
        "The strategy 'items_users_means/items_users_means' is much better than the others. It reaches scores which were the SOTA in 2015/2016."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "arqRAdTzeVtR",
        "outputId": "cf71512b-26cf-4f17-e528-462ae01f8901"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 11\n",
            "Best error: 0.9466428081233659\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items_users/items_users', 'items_users/users', 'items_users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, cv_splits=5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Geqb2ue0eVtR"
      },
      "source": [
        "These strategies are instead pretty much the same."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FCWieOs5eVtR"
      },
      "source": [
        "**MAE** (for comparison with the paper)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p55eOUeneVtR",
        "outputId": "0349b77b-e9b4-4ba1-d6d7-3bb3452b1767"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 18\n",
            "Best error: 0.757858228001773\n"
          ]
        },
        {
          "data": {
            "image/png": 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zO4Ka7OxsCgsLAZgzZw7Lli3jL3/5C16vFwCXy0VJSQkZGRldXnv16tVMnjyZKVOmsGfPno5rp6enk52djclkYsKECSxcuBCl1BHXPuOMM7jjjjt44oknaGhowGKR3ME3Ia+eEEKIYwo0Q9JbtNY8+eSTLF68+Ij7c3NzsdlsHbdNJlPHbZPJhMfjAeCZZ55h3bp1rFixgqlTp7Jp0ya2bt3KmWeeGdC1f/WrX3HLLbcccX9hYWFA177jjju4+OKLWblyJXPmzGHVqlWMHTv2FF4FAZJ5OSnOVndfN0EIIQaNiIiII2pDFi9ezNNPP43bbfwu3rdvHy0tLQGfLz8/n5kzZ3L//feTkJBAcXEx77//Puedd15A137uueew2+0AlJaWUlVVFfC1Dx48SHZ2Nr/85S+ZPn06e/bsCfi54uskeAmQvd7Bc7/4jPIDDX3dFCGEGBRycnIwm81MnDiRxx57jBtvvJHx48czZcoUsrKyuOWWWzoyG4G48847yc7OJisri9mzZzNx4sSOYt+jxcXFMWfOHLKysrjzzjs599xzufLKK5k1axbZ2dlceumlJ1V0+6c//YmsrCxycnKwWq3HDJhE4GTYKEBtzW58Pk1Lo6uvmyKEEANae3bDarXy8ccfH/HYQw89xEMPPXTEffPnz2f+/Pkdt3Nzc4/52L///e8jnldSUkJ8fDwhISEd97XXqABfm6Z92223cdttt32tvTt37uz4/vnnn+/4Pi0treOx5cuXD/i9jXqTZF4C5PNq41+fr49bIoQQojukpqby3nvv9XUzxCmQ4CVAPp8RvGh/ECOEEEKIviHBS4B8XiPjIokXIYQQom/1aPCilFqilNqrlDqglLrrGI8PV0p9opTaopTarpQ6v9NjOUqpL5VSu5RSO5RSfbqiT0fmxSeZFyGEEKIv9VjBrlLKDDwFLAJKgA1KqXe01rs7HXYP8KrW+mml1HhgJZCmlLIA/wSu0VpvU0rFAX06T1l31LxI8CKEEEL0pZ7MvMwADmitD2qtXcDLwEVHHaOBSP/3UUCZ//tzge1a620AWutarbW3B9vaJcm8CCGEEP2D0rpnPoyVUpcCS7TWN/pvXwPM1Fr/pNMxScBqIAYIA87RWm9SSv0MmAoMARKAl7XW/3eMa9wM3AyQmJg49eWXX+6RvtjtdnwNYRR/phk6WRE3RvXIdfqa3W7v2BBtoJI+DhyDoZ990ceoqChGjhzZa9fzer2YzeZeu97Rfv/735OSksL3vve9Hr1OX/ezN3zTPh44cIDGxsYj7luwYMEmrfW0o4/t63VergCe11r/Tik1C/iHUirL364zgelAK/CRUmqT1vqjzk/WWj8LPAswbdo03Xmef3fKzc1lWPJ4ij/bSUZGJpPnD++R6/S13Nxceuo17C+kjwPHYOhnX/QxLy+vV9cjaW5u7tHreTyeE+4jlJuby6uvvtojbej8Yd7T/ewPvmkfg4ODmTx5ckDH9uSwUSkwrNPtVP99nd0AvAqgtf4SCAbiMWpk1mita7TWrRi1MFN6sK1dkmEjIYToeYWFhWRlZXXcXr58Offddx9PPPEE48ePJycnh8svvxyAlpYWrr/+embMmMHkyZN5++23AWOhuAsvvJCzzz6bhQsXUl5ezrx585g0aRJZWVmsXbsWgKamJlwuFwkJCSxbtozXX3+947rtGa/jPXf16tXMmjWLKVOmcNlll3UsrJeWlsYvf/lLpkyZwmuvvdbR7lmzZnW0W3xzPZl52QCMUkqlYwQtlwNXHnXMIWAh8LxSahxG8FINrAL+SykVCriAs4DH6EM+KdgVQgw2790FFTu695xDs+G8h0/6aQ8//DAFBQXYbDYaGhoAePDBBzn77LN57rnnaGhoYMaMGZxzzjkAbN68me3btxMbG8vvfvc7Fi9ezN13343X66W1tRWADz/8kIULF57wui+99NLXnltTU8MDDzzAhx9+SFhYGI888gi///3vuffeewFja4HNmzcDkJycTEFBAS6Xq2Mna/HN9VjworX2KKV+ghGImIHntNa7lFL3Axu11u8APwf+opS6HaN4d5k2inDqlVK/xwiANLBSa72ip9oaCC2ZFyGE6DM5OTlcddVVLF26lKVLlwJG9uOdd95h+fLlADgcDg4dOgTAokWLiI2NBWD69Olcf/31uN1uli5dyqRJkwB4//33ue6660543WM999NPP2X37t3MmTMHAJfLxaxZszqe07l+pr3dixcv5oorruiW10L0cM2L1nolxpBP5/vu7fT9bmDOcZ77T4zp0v1Ce8bFJyvsCiEGi1PIkHxTFovliG1YHA4HACtWrGDNmjX85z//4cEHH2THjh1orXnjjTcYM2bMEedYt24dYWFhHbfnzZvHmjVrWLFiBcuWLeOOO+7g2muvZf369Tz99NNfu67P58Plch33uTExMSxatIh//etfx+xD52u3t/uNN97g97//PTt27DhhDY4IjKywGyAZNhJCiJ6XmJhIVVUVtbW1OJ1O3n33XXw+H8XFxSxYsIBHHnmExsZG7HY7ixcv5sknn6R91uyWLVuOec6ioiISExO56aabuPHGG9m8eTO7du1i7NixHQW1aWlpbNq0CYB33nkHt9t93OeeccYZfP755xw4cAAwam/27dv3tet2bvf999/f0W7xzUn4FyAZNhJCiJ5ntVq59957mTFjBikpKYwdOxav18vVV19NY2MjWmtuvfVWoqOj+c1vfsPPfvYzcnJy8Pl8pKen8+67737tnLm5uTz66KNYrVbCw8N54YUXeOONN1iyZEnHMTfddBMXXXQREydOZMmSJR3Zk2M9NyEhgeeff54rrrgCp9MJwAMPPMDo0aOPuG7ndnu93o52i2+ux9Z56W3Tpk3TGzdu7JFz5+bmEuPN5LPX9jPxnGGceemoHrlOX5OppwPDYOgjDI5+9tVU6XHjxvXa9fpqCvGiRYt44YUXSEpK6pXryVTprh3rvedfJqXfrfNy2pBdpYUQYuD44IMP+roJ4huQmpcAte8qLcNGQgghRN+S4CVA7UGLFOwKIYQQfUuClwDJbCMhhBCif5DgJUBS8yKEEEL0DxK8BKhj2GiAzM4SQgghTlcSvASofdhIMi9CCCFE35LgJUA+KdgVQoheMXv2bMDYYfqll17q49b0jvPOO4+SkhJuvPFGdu/eDcBDDz3Ux63qvyR4CVB7xkX2NhJCiJ71xRdfAAMrePF4PMd9rK2tjdraWlJTU/nrX//K+PHjgYETvJyo76dKFqkLUEfBrsQuQohB4pH1j7Cnbk+3nnNs7Fh+OeOXJzwmPDwcu93OXXfdRV5eHpMmTeL73/8+t956K3fddRe5ubk4nU5+/OMfc8stt5Cbm8t///d/Ex0dzY4dO/jud79LdnY2f/jDH2hra+Ott94iMzOT1157jf/5n//BbDYTFRXFmjVrjnn9559/no0bN/LHP/4RgAsuuIBf/OIXzJ07lxtuuIGNGzeilOL666/n9ttvJz8/nx//+MdUV1cTGhrKX/7yF8aOHcuyZcsIDg5my5YtTJ8+ncsuu4zbbrsNAKUUa9asISIi4oiVlOfPn8/y5ct5/fXXaWtrY9KkSUyYMIEXX3yRf/7znzzxxBO4XC5mzpzJn/70J8xmM+Hh4fzwhz9k5cqVJCUl8dBDD/Ff//VfHDp0iMcff5wLL7yQXbt2cd111+FyufD5fLzxxhuMGvX11eILCwu54IIL2LlzJwDLly/Hbrdz33338cQTT/DMM89gsVgYP348L7/8Mi0tLfz0pz9l586dOJ1O7r//fi666CKef/55/v3vf2O32/F6vbz88st873vfo6mpCY/Hw9NPP83cuXNP9W0kwUugZFdpIYToXQ8//DDLly/v2K/o2WefJSoqig0bNuB0OpkzZw7nnnsuANu2bSMvL4/Y2FgyMjK48cYbWb9+PX/4wx948sknefzxx7n//vtZtWoVKSkpNDQ0nHR7tm7dSmlpaccHe/s5br75Zp555hlGjRrFunXr+NGPfsTHH38MQElJCV988QWtra1ceeWVPPXUU8yZMwe73U5wcDAA7733HkuXLv1a3//4xz+ydetWwFg6/5VXXuHzzz/HarXyox/9iBdffJFrr72WlpYWzj77bB599FG+853vcM899/DBBx+we/duvv/973PhhRfyzDPPcNttt3HVVVfhcrnwer0n3f+HH36YgoICbDZbR98ffPBBzj77bJ577jmKi4tZuHAh55xzDgCbN29m+/btxMbG8rvf/Y7Fixdz99134/V6aW1tPenrdybBS4Dah410p63ahRBiIOsqQ9LbVq9ezfbt23n99dcBaGxsZP/+/QQFBTF9+vSOfYoyMzM7gprs7Gw++eQTAObMmcOyZcv47ne/y8UXX3zS18/IyODgwYP89Kc/5Vvf+hbnnnsudrudL774gssuu6zjuPbNGgEuu+yyjp2r58yZwx133MFVV13FxRdfTGpqKgCff/45y5cvP+G1P/roIzZt2sT06dMBY6hpyJAhAAQFBXVsMpmdnY3NZsNqtZKdnU1hYSEAs2bN4sEHH6SkpISLL774mFmXruTk5HDVVVexdOnSjmBr9erVvPPOOyxfvhyfz4fD4eDQoUOAsX9UbGwsANOnT+f666/H7XazdOlSJk2adNLX70xqXgJ0uGC3jxsihBCDlNaaJ598kq1bt7J161YKCgo6ghSbzdZxnMlk6rhtMpk6ai6eeeYZHnjgAYqLi5k6dSq1tbXHvI7FYsHX6Ze9w+EAICYmhm3btjF//nyeeeYZbrzxRnw+H9HR0R1t2rp1K3l5eR3Pbd+dGuCuu+7ir3/9K21tbcyZM4c9e/Zw8OBBhg0bRlBQUJd9//73v99xjb1793LfffcBxk7cSqkT9v3KK6/knXfeISQkhPPPP78jMxRo3wFWrFjBj3/8YzZv3sz06dPxeDxorXnjjTfYunUrn3/+OYcOHerYXLFz3+fNm8eaNWtISUlh2bJlvPDCCyfsb1ckeAlQR82LzDYSQoheERERQXNzc8ftxYsX8/TTT+N2uwHYt28fLS0tAZ8vPz+fmTNncv/995OQkEBxcfExj0tLS2Pr1q34fD6Ki4tZv349ADU1Nfh8Pi655BIeeOABNm/eTGRkJOnp6bz22muAEWRs27btuNfPzs7ml7/8JdOnT2fPnj289957HVmTo1mt1o6+Lly4kNdff52qqioA6urqKCoqCrjvBw8eJCMjg1tvvZWLLrqI7du3H/O4xMREqqqqqK2txel0dgzZtb8WCxYs4JFHHqGxsRG73c7ixYt58skn0f6C0C1bthzzvEVFRSQmJnLTTTdx4403snnz5oDbfiwybBQgmW0khBC9KycnB7PZzMSJE1m2bBm33XYbhYWFTJkyBa01CQkJvPXWWwGf784772T//v1orVm4cCETJ0485nFz5swhPT2d8ePHM27cOKZMmQJAaWkp1113XUdm4re//S0AL774Ij/84Q954IEHcLvdXH755cc89+OPP84nn3yCyWRiwoQJnHfeeVx66aU8+eSTx2zHzTffTE5ODlOmTOHFF1/kgQce4Nxzz8Xn82G1WnnqqacYMWJEQH1/9dVX+cc//oHVamXo0KH8+te/PuZxVquVe++9lxkzZpCSksLYsWMB8Hq9XH311TQ2NqK15tZbbyU6Oprf/OY3/OxnPyMnJwePx0NmZmZHwNNZbm4ujz76KFarlfDw8G+ceVF6gEyfmTZtmt64cWOPnDs3N5fWvFgKttUwJC2Sy+6a1iPX6WudK94HKunjwDEY+tkXfczLy+tI+/eG5uZmIiIieu16feVY/WwvOu6pz67e9k1/lsd67ymlNmmtv/ahK8NGAepYYVeGjYQQQnQDm802YAKX3ibDRgGSFXaFEGJgWbVqFb/85ZEzqtLT03nzzTf7qEW9p7a2loULF37t/o8++oi4uLg+aNHJkeAlQJJ5EUKIgWXx4sUsXry4r5vRJ+Li4jrWkDkdybBRgLQsUieEEEL0CxK8BEgyL0IIIUT/IMFLgKTmRQghhOgfJHgJkJZF6oQQolfMnj0b6N1dpadOnXrEsv6if5PgJUDtw0aSeRFCiJ71xRdfAL0XvBQUFJCSknLEFgPdpX15ftG9JHgJkGwPIIQQvSM8PBww9gJau3YtkyZN4rHHHsPr9XLnnXcyffp0cnJy+POf/wwYi/mdddZZXHTRRWRkZHDXXXfx4osvMmPGDLKzs8nPzwfgtddeIysri4kTJzJv3ryO673//vsdS/S3Xxvg9ddfZ9myZcd97onaM3fuXC688ELGjx9PS0sLl156KRMnTiQrK4tXXnmlZ1/AQUCmSgdIZhsJIQabiocewpm3p1vPaRs3lqHHWZr+aA8//DDLly/vWG7+2WefJSoqig0bNnSsTtu+MeO2bdvIy8sjNjaWjIwMbrzxRtavX88f/vAHnnzySR5//HHuv/9+Vq1aRUpKCg0NDR3Xef/993nsscdO2JZjPfdvf/vbcduzefNmdu7cSXp6Om+88QZJSUmsWrUKMHbDFt+MZF4C5PMae1nIsJEQQvSN1atX88ILLzBp0iRmzpxJbW0t+/fvB2D69OkkJSVhs9nIzMzsCCKys7MpLCwEjD2Lli1bxl/+8he8Xi8ALpeLkpISMjIyTnjtYz33RO2ZMWMG6enpHW345JNP+OUvf8natWuJiorq9tdmsJHMS4Bk2EgIMdgEmiHpLVprnnzyya8tLJebm3tEvYrJZOq4bTKZOupOnnnmGdatW8eKFSuYOnUqmzZtYuvWrZx55pkdz1VKdXzvcDg6vj/Wc0/UnrCwsI7bo0ePZs2aNaxdu5Z77rmHhQsXcu+993bDKzJ4SeYlQFoKdoUQoldFRETQ3NzccXvx4sU8/fTTuN1uAPbt20dLS0vA58vPz2fmzJncf//9JCQkUFxczPvvv895553XcUxiYiJ5eXn4fL4jtgk41nMDbU9ZWRmhoaFcffXV3HnnnWzevPmkXwtxJMm8BKgj8yI1L0II0StycnIwm81MnDiRZcuWcdttt1FYWMiUKVPQWpOQkMBbb70V8PnuvPNO9u/fj9aahQsXMnHiRG666Sbuv//+jmMefvhhLrjgAhISEpg2bRp2u/24z83JyQmoPTt27ODnP/85FosFq9XK008//U1fmkFPaT0wPoynTZume2p3ztzcXA68Y8LZaqQef/T0giNSiwNFbm4u8+fP7+tm9Cjp48AxGPrZF33My8tj3LhxvXa95uZmIiIieu16nZWUlHDTTTfx3nvv9fi1+rKfveWb9vFY7z2l1Cat9bSjj5VhowB1Hi6SuhchhDj9paam9krgIrqfBC8B6jxcJHUvQgghRN+R4CVAPp/GZDKGimStFyGEEKLvSPASIJ9PY7IaL9cAKRMSQgghTksSvARAaw0aLBZ/8CKZFyGEEKLPSPASAG0srovZn3mRmhchhBCi78g6L4HwxyodwYtkXoQQYkB4+OGHGTZsGM3NzYSGhnLttdfy/PPPc+6555KcnNzXzRPHIcFLANprXCwdNS8SvAghxOnA4/FgsRz/o27VqlW8+uqrJCQkdNz3/PPPk5WVJcFLPybDRgHoGDaySOZFCCF6UmFhIVlZWR23ly9fzn333ccTTzzB+PHjycnJ4fLLLwegpaWF66+/nhkzZjB58mTefvttwAg+LrzwQs4++2wWLlxIeXk58+bNY9KkSWRlZbF27VoAmpqacLlcJCQkcN9997F8+XJef/11Nm7cyFVXXcWkSZNoa2tj06ZNnHXWWUydOpXFixdTXl4OwPz587n99tuZNm0a48aNY8OGDVx88cWMGjWKe+65p6ON3/rWt5g9ezZZWVm88sorvflyDliSeQnE0ZkXqXkRQgwCa1/dR02xvVvPGT8snLnfHX3Sz3v44YcpKCjAZrPR0NAAwIMPPsjZZ5/Nc889R0NDAzNmzOCcc84BYPPmzWzfvp3Y2Fh+97vfsXjxYu6++268Xi+tra0AfPjhhyxcuPCI61x66aX88Y9/ZPny5UybNg23281Pf/pT3n77bRISEnjllVe4++67ee655wAICgpi48aN/OEPf+Ciiy5i06ZNxMbGkpmZye23305ubi7Jycm8/PLLRERE0NjY+A1ePdFOgpcAaKl5EUKIPpWTk8NVV13F0qVLWbp0KQCrV6/mnXfeYfny5YCxC/ShQ4cAWLRoEbGxsQBMnz6d66+/HrfbzdKlS5k0aRIA77//Ptddd90Jr7t371527tzJokWLAPB6vSQlJXU8fuGFFwKQnZ3NhAkTOh7LyMiguLiY7Oxsfv7zn3Pvvfdy8cUXM3fu3O55QQY5CV4CcPSwkdS8CCEGg1PJkHxTFosFn8/XcdvhcACwYsUK1qxZw3/+8x8efPBBduzYgdaaN954gzFjxhxxjnXr1hEWFtZxe968eaxZs4YVK1awbNky7rjjDq699lrWr1/f5SaJWmsmTJjAl19+eczHbTYbACaTqeP79tsej4fRo0ezefNm3njjDe655x4WLlzIvffee3IvivgaqXkJhGRehBCiVyQmJlJVVUVtbS1Op5N3330Xn89HcXExCxYs4JFHHqGxsRG73c7ixYt58sknO/6g3LJlyzHPWVRURGJiIjfddBM33ngjmzdvZteuXYwdOxaz2fy14yMiImhubgZgzJgxVFdXdwQvbrebXbt2BdyfsrIyQkNDufzyy7nzzjvZvHnzyb4k4hgk8xKArxXsSs2LEEL0CKvVyr333suMGTNISUlh7NixeL1err76ahobG9Fac+uttxIdHc1vfvMbfvazn5GTk4PP5yM9PZ133333a+fMzc3l0UcfxWq1Eh4ezgsvvMAbb7zBkiVLjtmGZcuW8YMf/ICQkBC+/PJLXn/9dW699VYaGxvxeDz87Gc/Y8KECQH1Z8eOHdx5552AkaXpKtMjAqMGyhDItGnT9MaNG3vk3O+//Qn572nGzk5izxflXPJfUxmaEdUj1+pLubm5zJ8/v6+b0aOkjwPHYOhnX/QxLy+PcePG9dr1mpubiYiI6LXrtVu0aBEvvPDCEfUrPamv+tmbvmkfj/XeU0pt0lpPO/pYybwEwp95sUjmRQghBoQPPvigr5sgvgGpeQnA0bONZG8jIYQQou9I8BKAr02VlsyLEGIAGyjlBOL0cbLvOQleAnH0VGkJXoQQA1RwcDC1tbUSwIheo7WmtraW4ODggJ8jNS8BOHpvI8m8CCEGqtTUVEpKSqiuru6V6zkcjpP60DpdDYZ+fpM+BgcHk5qaGvDxErwEQPY2EkIMFlarlfT09F67Xm5uLpMnT+616/WVwdDP3uyjDBsF4uiCXcm8CCGEEH1GgpcAyLCREEII0X9I8BKAjmEjybwIIYQQfa5Hgxel1BKl1F6l1AGl1F3HeHy4UuoTpdQWpdR2pdT5x3jcrpT6RU+2s0vtw0aySJ0QQgjR53oseFFKmYGngPOA8cAVSqnxRx12D/Cq1noycDnwp6Me/z3wXk+1MVBfW6ROghchhBCiz/Rk5mUGcEBrfVBr7QJeBi466hgNRPq/jwLK2h9QSi0FCoDAt+/sIfro7QFktpEQQgjRZ3psY0al1KXAEq31jf7b1wAztdY/6XRMErAaiAHCgHO01puUUuHAB8Ai4BeAXWu9/BjXuBm4GSAxMXHqyy+/3CN9qchro3abjfRzFAUfapKmKmJHqR65Vl+y2+2Eh4f3dTN6lPRx4BgM/ZQ+DhyDoZ890ccFCxb0y40ZrwCe11r/Tik1C/iHUioLuA94TGttV+r4QYLW+lngWTB2le6p3VffzP8E0EyfOY2CDzcwcuRIcuYP65Fr9SXZpXdgGAx9hMHRT+njwDEY+tmbfezJ4KUU6PwJn+q/r7MbgCUAWusvlVLBQDwwE7hUKfV/QDTgU0o5tNZ/7MH2Hpc+qmC3fRhJCCGEEL2vJ4OXDcAopVQ6RtByOXDlUcccAhYCzyulxgHBQLXWem77AUqp+zCGjfokcIFONS9WqXkRQggh+lqPFexqrT3AT4BVQB7GrKJdSqn7lVIX+g/7OXCTUmob8C9gme6Pu4F9bVdpSb0IIYQQfaVHa1601iuBlUfdd2+n73cDc7o4x3090riT8PVho/4XXwkhhBCDhayw2wXngQOYDxUDnRep68sWCSGEEIObBC9daP7wI2ybtgBgsiiUksyLEEII0ZckeOmK2YRWxstkMimUWUnBrhBCCNGHJHjpgjJb0MqEMoFSCpNSknkRQggh+pAEL11QZhNamTGZlP+2ko0ZhRBCiD4kwUtXOjIvRvBiMknwIoQQQvQlCV66oPw1Lyb/K6VMCi01L0IIIUSfkeClKyYzWpmPzLz0w3X0hBBCiMFCgpcuKIvZyLz494c0mSXzIoQQQvQlCV66YvIHL+0Fu1LzIoQQQvQpCV66YGRezCh/5kWZZJ0XIYQQoi9J8NIVU/tU6fabiv64d6QQQggxWEjw0gVlNoaNlNS8CCGEEP2CBC9daQ9eOk2VlpoXIYQQou9I8NIFI/NiPjzbyCTbAwghhBB9SYKXLihPq3/YyAhYJPMihBBC9C0JXrqS/4ExVRojYDHJbCMhhBCiT0nw0gVlCfIPG7VnXpBhIyGEEKIPSfDSFYvVP2zkA4zZRjJsJIQQQvQdCV66oNqDF3142EgyL0IIIUTfkeClKxarf9jIyLwok0lqXoQQQog+JMFLFw5nXvzDRiZk2EgIIYToQxK8dMUSZAQvtGdeFP44RgghhBB9QIKXLiirMWzUHrxIwa4QQgjRtyR46YrFZqzzor1Ae+ZFghchhBCir0jw0gVlDcKnzCiM4MUkK+wKIYQQfUqCly58vWBXdpUWQggh+pIEL13pKNj1DxtJzYsQQgjRpyR46YIKshnrvHSqeZHgRQghhOg7Erx0pT3zog/XvEjBrhBCCNF3JHjpgrLaJHgRQggh+hEJXrpiNYaNlPYA/poXKdgVQggh+oylrxvQ37VnXtprXkxKal6EEEIMHs42D9WHmqkpbqa2xE51iZ2GylYAzBYTWfOSmfWdkb3aJgleumL117z4Ds82kmEjIYQQA1Vrk4uqoiYqC5soyaunsrCp43MvNDKI+GHhpI6NwaQUXo+PhOGRvd5GCV66Yg4CZeoYNpJF6oQQQgwkXq+Pxso2Du2uZf+GSqqKmo0HFAwZEcnUJSNIyowiflgEoZFBfdtYPwleuuAz2wAOZ15MCjRonza+F0IIIfo5rTVupxd7nZO68hbjq6yF+ooWGipbO2o544eFc8bSjI5gJSi4f4YJ/bNV/YhuD146ZV4AfFpjRoIXIYQQfUP7NE21bbQ2uXG2unG2enC1eTq+d7S4aa5z0FTtoLXJhdfjO/xkBZHxIcQmhZGWHU9sUiiJ6VFEJ4b2XYdOggQvXdBmK3A482IyGwGL9mow91mzhBBCDAItjU4qDzbRXO/A0eLGYXfjaHHT0uCkpsSO2+E95vMsQSZsoVYiYm0MzYwiPNpGcISVsCgbsUlhRA8NxRp0+n6ISfDSBa3agxf/VOn2zIvUvQghhOgmWmvqylo4uLWayoImHC1uWptcNNc6Dh+kwBZqITjMSmhkEGNnDiV+eATh0TaCQi0Eh1oJCrFgC7VgtgzslVAkeOmCTxsvUedF6gBZ60UIIcQpc7Z5qC5qoqqouWNmj73OCQriUsIJjbASGRdJ9lmpJI2MImpICLZQa8dn0GAnwUsXfP51/I7OvGgtwYsQQoiuuZ1eWqo12z4qprKwiepDzR3rpABExgczND2KlCUxpE+MJyzK1oetPT1I8NKF9uGh9uClveZFMi9CCCHA+GO2rdmN2+lFKWizu6kuaqKyqJmqwibqy1vQGgrZT1i0jSEjIhgzcyhD0iIYMjyS4HBrX3fhtCPBSxf0UcGLUkfeL4QQYvDwuL2U5zdSebCR+spWGirbaKhsxdXm+dqxweFWhoyIJGNyAlVNRZx9wWzJqnQTCV660J5hMR2deZHgRQghBjSXw0PpvgZK99TTVNtGS4OT2rIWvG5jynF4jI3oxFBGz0gkekgotlALWkNQiJmE4RFExAaj/H/x5uYeksClG0nw0oWOIMV35DovknkRQoiBp66shcIdNRzaXUv5gUZ8Xo3FaiJqSAihUTYmzE1m2LhYkkdGExQyiD5CtQavC5x2aC6DpnLj3+YKSJoIY87r1eYMolf+1BweNjq8txFIzYsQQpyuGipbqT7UjM/rw+vVOOxuWhqdFO+uo77CKKSNSwln4sJhDB8fS1JmNGbrAJ567PMdDkja6qC1zvi3pRoqd0H5NrBXHv/5M38owUt/0x6kHK55kWEjIYQ4nXg9PmOTwT31HNxaTW2J/WvHWIJMJKZFkj0/lYxJCYRFn6ZDPD6fEXiYLMbefNoLXjc0l0NdAdQXGP82HDocqDSVGlmVoykzJIyBzIUQlQoWGwSFQ2QSRPi/whPB0vv7HUnw0oWO2UbeI2tetO+4TxFCCNEHfD6Nvd6Bw+7G4/Zhr3NQsK2Gop21uJ1eUDA0PZI5l45k2LhYLEEmTGYTwWFWrLbTdLVZtwPKtkDxV3DoKyheB231J35OcBREj4CwBIhJh/EXQkwaRKZCaCyExBj/2qLA1D8zThK8dEG3Z1601LwIIURf8/k0jVWt1Fe00ljdRlNNG03VbTTWtNFc6/jakH5IZBCjpicyfEIsKaNjCA47Taclaw2ttVC1G0o2QOlmqN4LdQeN7ApA3CgYewEkTjD+wva6jOyJ2WoEKrHpRrASGtu3fekGErx0oWN4yHvU9gBS8yKEED3G2eahobKVxqpWGipbaahqo7GqlbryFjyuw6lvW6iFyPgQEoZFkDl5CFEJIYREBmGxmrCFWogfFnH6rUrraoWCT+Hgp8YwT32RMczjbjl8TNxISBhrZE1SpsKwmRAW33dt7mUSvHShPXgx+Y7aHkAyL0II0S3s9U7yt1RRW2rvCFTamjrVYCiIiA0mekgIE85MIS41nLiUMCLjQ07fTAqAuw1aaqBmH1Tvgao849+KHeBxgDUUYjMhNgMyF0D0cCO7kjJlQGRPvgkJXrrQPmyEzw0cnm0kw0ZCCHFq2ppdlB9opKbUTuEGH7te+Rw0hERYiU4MJS07jughocZXYiiRCcFYrP20JsXnH57xuozCWK/T+N7jOny/u42Ukv/AK38zhnnaZ/N4HEeeKzQehoyDaTfAqEUwYrZRJCu+RoKXLviOmiotmRchhDh5LoeHgq3V7NtQSXFevfEHoAJbBEw7P40xM4YSnRja1808Nq2NgKMuHyq2Q8kmqNplrHHSUh3QDI5RAFHDjXqUpEkQEu0vjo01hoCGjBtUwz7flAQvXeiYKu31r/PSXrArNS9CCHFcHreXmmI7lYVNlB9ooHBHLV63j4jYYCafO5z0ifHEpYTz+RdrmTk/o+8a6rRDg7+mpLHE+LJXGsWxLTXGv6214Oo0vTo03liYbWiOMVU4KNSYlmy2GcWxFpv/dvuXlS8P1DFryWV9188BRoKXLhwOXo6cbeSTXaWFEIOco8VNdVEzIZFWgsOsVBU1U5JXR0VBE7Ul9o4MdVhUEOPnJDN6RiKJ6ZEd62X1Gp/PyJA0Fhv1JKUbjcXXGg4ZgUlnJitEDIXQOOMrbqTxb/Rwo/ZkyFhjmvFJ9sFZktt9/RESvHRFH709gFkyL0KIwcnr9lFX3kJNSTOF22sp3FmDz3Pk70JLkInE9CgmnTucxBGRDEmLJDymF+s2nHYo3QQFa4wgpeEQNJYatSjtQmKMzMm4bxuBSMwI49+oYcaU4n66tok4TIKXLhxd86Kk5kUIMYg42zyU7q3nwMZKCnbU4nEavwtDIoPIPiuVERPicLZ5aGt2EZcSRmJ6FGZLL3z4e1xw6Eso+twY6mkqhdp8I7sCxvomQ7ONIGXsBUZgEj0M4kcbGZTezv6IbtWjwYtSagnwB8AM/FVr/fBRjw8H/g5E+4+5S2u9Uim1CHgYCAJcwJ1a6497sq3Hc/T2ACZZ50UIMQB53T5qy+zUFNtprG6luc5JXZmd2rIW0BAcZmXMjERSxsSQMCyCqISQjj/mepyz2ViUrWQD1B4w1j2p3AnOJlCmw0vVD58FCd83alGGz4LgyN5pn+h1PRa8KKXMwFPAIqAE2KCUekdrvbvTYfcAr2qtn1ZKjQdWAmlADfBtrXWZUioLWAWk9FRbT0QfZ5E6LTUvQojTgMftpa6shbL9DVTkN2JvcOJoceP1+DqmH7fZXThbPeD/tWYyK8JjbEQPCSVzyhCSRkaTNDIKs7kXMio+nxGglKw3gpXiDVCdd3hGT2SKMcSTdYkxnTj9LLCF93y7RL/Sk5mXGcABrfVBAKXUy8BFQOfgRQPtoXEUUAagtd7S6ZhdQIhSyqa17jRo2TsOL1Jn/MeRzIsQoj/yuL00VLZSV9ZCXXkLdWUtxhL6Va20/60VGR9MZHwIkXHBmCwmvB6fkVUJtxISbiU2OZyE4eFExvVSVsXZTETTXthWaQQsZf7siqPReNwWBanTjNqU1OmQOtWoVxGDnuqpDIJS6lJgidb6Rv/ta4CZWuufdDomCVgNxABhwDla603HOM8PtNbnHOMaNwM3AyQmJk59+eWXu70ftfs0FZs1Z+/8OZUPPIbLrtn/riZlpiI6fWCNmdrtdsLDB/ZfMNLHgWMw9PNEfXS1aNpqoLVG01oDjgY6MicoCIowRk1sUWCLUoTGgzW0735nWdzNRDXuJqI5n7CWQsLtRYQ4Kjoe15hoCRtGU+SYjq/W0BRjWGgAGOzv11O1YMGCTVrraUff39cFu1cAz2utf6eUmgX8QymVpbWRH1RKTQAeAc491pO11s8CzwJMmzZNz58/v9sbuM1bTMXm/Zi0Zv78+TTXOdj/7heMHj2G8XOSu/16fSk3N5eeeA37E+njwDEY+tneR59PU1tqp/xAIxX5DZTnN2KvNxLRxuyeSIbOjCIuNZzYpDCiE0N7p2j2eBqKofAzKN8GTSVQV2BMTUYbwUjcSMicBYkT2FHlI/us76BiRhBusREODKzfrIbB9H7tDT0ZvJQCwzrdTvXf19kNwBIArfWXSqlgIB6oUkqlAm8C12qt83uwnSfUMTx01Aq7sj2AEKInOVvdNBRo3tu7g+K8OtwO43dQWLSNpJFRJGVGkZQZTVxKGKbeqEU5HnsVFK6Foi+NfXlq9oPdn1GxhkFUqjHLZ9yFkD4XkieDNaTj6bW5uZAwum/aLk5bPRm8bABGKaXSMYKWy4ErjzrmELAQeF4pNQ4IBqqVUtHACozZR5/3YBu75PPXuhy9wq7UvAghekJjdSvbPi4h74tyPE5NWFQjo6YlkjI6mqGZUUTEBvf+Im+dtdYZWZXCtVCw1iimBQgKN5a4zzwbknIgbS4MGS9rpoge0WPBi9bao5T6CcZMITPwnNZ6l1LqfmCj1vod4OfAX5RSt2OM1i7TWmv/80YC9yql7vWf8lytdVVPtfd44odFkNq64esr7ErmRQjRTRqr28jfUkX+piqqipoxmRWjpifiiqjkvO/M6b0pyceitbF+St7bsPttKN8OaGPH4+FnQM53IX2esV+Pua8rEcRg0aPvNK31Sozpz53vu7fT97uBOcd43gPAAz3ZtkCNmBCHo/U9lNbg88qu0kKIbtFQ1Ur+5iryN1dTfagZgCEjIpj1nUxGzxhKeIyN3Nyq3gtctDY2GqzOg6o9xr/Ve43vnf7ZP6nTYcHd/uGfKWAJ6p22CXEUCZMDYTKhtQKvG5PJCkjmRQhx8uorWsjfXE3+lipqio2N/hLTI5l9yUgyJycQGR/SxRm6gc9nLPBWlWesSttQdDhYaZ+iDMZux0PGQfalkDgeRi8x6leE6AckeAmEyWSsk+BzYzIZf2lI5kUIEYi68hZ/hqWK2tIWAIZmRDHn0pFkThlCRGxwzzagpRYqthkzf8q2GrUqnTcjDImFhLHGom8J44yNBxPGQVi8LKEv+i0JXgKgzWaUBrxulP8Vk4JdIURnWmvqylsoyauntcmJo9VD+YFG6stbQEFSZhRnfncUmZOH9OxGha5WyP8Y8v5jFNY2lRx+LHo4jDoXMuYbwz6RybI6rTgtSfASiPZhI5/n8PYAknkRQgAtDU52ri1l75cVNNc5ADBZFLZQK7FDQ8k+azQZkxIIi+6BgKV95k/ZFiOzUnvA2JhQ+yA42pj5k3yLsTnh0GwIje3+NgjRByR4CYA2dcq8KIUyKal5EWKQcju9FGyvpuJgE7UldiryG/FpzfDxsUw9bwTDJ8QRHmPruenMdQWwdyXsWWnsqqy9YLIY9Smp02Hi5cYsoLS5YLb2TBuE6GMSvHShutlJq89EmAa8LsBYIFIyL0IMHm6Xl5K8Og5uqebAlmo8Ti8Wm5n4lDAmnjOMCXOTiUoI7ZmLez1Qsf1wwFK1y7h/yHg483ZjGChpIlh7uHZGiH5EgpcuvLqxmJhGmOIzho3AWOtFal6EGJh8Pk1DRSvVxc1UHzK+qgqb8Lh9BAWbGTVtCGPPSCIpM6r7pzFrDVW7oegLKNnItPwvYU0Z+NzGX03DZ8G5D8LY8yE2o3uvLcRpRIKXLtgsJjzKbMw28roBI3hp351dCDEwVB9qZvdnZezbUImrzfhDxWI1EZcazvgzk0nLiSd5VHT37xnk80LFDsj/CLa/dnjF2vBEnLZhhE9aConZRv1KWFz3XluI05QEL10wghcTaGX89QMos9S8CHG68/k0NcXNFGyvIX9zNfXlLZitJjKnJDB8XCzxwyOISQzt/n2DWutg3yqjyLZqt7FibfsicMPOgG/9HkYtgqhh7Pj00wG/mZ8Qp0KCly7YLGYcygyAdrtQ+IeNJHgR4rTj9fo4tKuO/esrOJRXh7PFg1KQNDKa7MtHM2p6IsFhPVDk2lAMe1bAnneNISHtNfYCShgLWd+BEXOMr6iU7r+2EAOQBC9dsFmNYSMAPMYW9MqkpGBXiNOA1pqaEjule+upyG+kdF8DjhY3weFW0icmkDomhmHjYgmN7IFl7p3NsOtN2PqSMSsIjGDlzNth3AUwdKJsWijEKZLgpQs2iwlve+bF5TQyL2aF1yNFL0L0Ry6Hh5I99RTtqKFoZy0tjcYswcj4YIZnxTJqaiLDJsRi7u7hoHZtDbDuz/DVU8Zy+3GjYOG9MO4iiB/ZM9cUYpCR4KULNosZV/uyum4j82K1WfA4vX3YKiFEZ001bRTuqKVoRw0l++rxeTRBwWaGjY9lRFY8w8fH9swicQD2ajiYC0WfGQvFVe4yllUY8y2YcxsMmyHL7AvRzSR46YKReTH+QtP+4CUo2IxLghch+pTHoVn/bgH5m6uoKzP2DIpODCV7fipp2fEkjYzq/uyK1saaK3tWGIFK9V6oLzAeC46CpEkw8xbI/i4k5XTvtYUQHSR46YJR82K8TNptpJ+tNjNuhwQvQvQ2rTWVBU3sWlvKvnUa7SsgZXQ0cy4dSVp2PNGJPbBQXH2RMY25eAMUfW7swqxMRv1K8iSYcg1kLDAWijOZu//6QoivkeClCzaLGXd7wa73cPDS1uzqw1YJMbi4XV72flXB9k9KqC9vwWIzE50B5109k5ihYd13obYGY3+gmn3G14GPjEwLQGgcDJsJc38OY79l7LoshOgTErx0wVjnxZ95cfmDl2Azbhk2EqLH1ZW3sPercnZ/Vo6jxc2QEREsuGYsI6cO4YuvPvvmgUt9ERz4AA5+CsXrwF55+DGTxdh5edH/wpjzIS5TaleE6CckeOmCUbDbPlW6PfNiwSXDRkJ0K601deUtlO9voOpQM1WFzdSW2lEmRVp2HJPOGU7SyKhvvuFhSy1sfRF2/dtYKA4gMtUY+hkyDuJHG18xI2RjQyH6qYCDF6XUCGCU1vpDpVQIYNFaN/dc0/oHm9WEh/aaF3/Brk0yL0J0B621sSz/5+Uc3FJFW7OxinVwmJX4YeHMvmQkY2YO7Z51WEo2wYa/wM5/g9cJyZPhnP8xhoDiRkpWRYjTSEDBi1LqJuBmIBbIBFKBZ4CFPde0/sFmMeFunyrtOTxs5HX78Hl93b90uBADmLPNQ/7mKvI3V9HS4KSt2U1rkwuL1UT6xHhSx8WSMjqGyPjgb55hAfD5YPeb8MUfoWyzsartlGtg+o1GlkUIcVK0242ruBhXQQGuggKcBQWETp9O9NKlvdqOQDMvPwZmAOsAtNb7lVJDeqxV/YjNYsZl8mdePMZmbVabMYzkdnqxhUrwIsSJ+Lw+ivPq2ftVOQe31eB1+4gaEkJsUhhDRkQyZEQEo6YnYgvtxiEarWHvSvj4AWP/oLhRcN6jMPFyCI7svusIMUB5qquxr1mDt7HJCFgOFeHYuQtnfj74PwsBzPHxBKWm9nr7Ag1enFprV/tfQkopCzAo1scPspgOzzbqNFUa2oMXGRMX4niqDzXz4fO7qStrwRZmYfzsJMackcSQtIjuyawcS80BeO+/jOnNcaPgkr/BhO/INGYhjkP7fHjr63EeyKdt2zZavvyC1nXrjcylnzk6muDsbMLPOgtbZgZB6ekEpaVhjuybPwYCDV4+VUr9GghRSi0CfgT8p+ea1X+YTerwbCP/VOmgYOO2FO0K8XVaa+rKWti3vpKtHxwiOMLKuTdOIGNSAmZLD2QqXa1G8e2eFcbqtg1FYIuEJY8Yw0NmmZcghNYa5779uA7m42tz4G1sxLFzJ207duAuKzsimxKUkUHcLTcTueQ8rCnJKIsFZbP13B8cpyDQ/9V3ATcAO4BbgJXAX3uqUf2N9s840O6vDxsJIYz/CyV7D+8nZK83ittHTU9k3uWju3+n5qYyEity4e3XYPd/wNkIMWmQMsWoaZl8LUQkdu81hTgNaK1xHzpE2/YdOPbk4a2pxdNQj2PnLry1tUccaxk6lJCcHCKXLMGSkEDQ8GEE5+RgiYnpo9YHLqDgRWvtA/7i/xp8zO1TpY2ZENZgf/Di8BzvGUIMaD6fprbETtn+Bg7tqqV0XwNejw+LzcywsTFMOz+NEVnxhMd0435CPp8xFLT+L7B/NePQxpL8oxbBtOthxGyZMSQGHV9LC86CQlwFBbRu3Ih9zRo85eUAqKAgzPFxmKOiCZs9m7AzziA4awKmsDBMYWGnRZByPIHONhoF/BYYDwS336+1zuihdvUrynz0Oi+SeRGDU2N1GztyS9jzZTnOViN4j04MJeusFEZkxZE8MhqztZuHhuzVsP1l2PA3Yx+hsCEw7xdsbElm2re+L7UsYlBxV1bh2LXLqE356kscO3Z21KaYQkMJmzObsFtuIWTSRGwjR6IsA3PYNNBe/T/gv4HHgAXAdcCgmWZjMhl/zWl/5kVqXsRg4nF5KdhWw54vyzmUV4dJKTKmJJA+MZ7kkdGExwR3fZKT4WyGko1w6Cs48CGUbgI0DJ8FZ98D4y4ESxD23FwJXMSA4WttxedwgM+Ht6kJ5759uAoK8LU50C4XroIC2nbvwltdYzzBbCYkO5u4W24meNw4gtLSsKWloYK6YU2k00CgwUuI1vojpZTSWhcB9ymlNgH39mDb+o32tVyONVVaiIGqsrCJvM/L2L+xClebh/BYG9POTyNrbgph0d04HNRSA4VrofBzKP7KKLrVPkAZC8nN/xWMuwASJ3TfNYXoIdrrxdvQgLusHHd5GZ7yctxl5URt307BU3/CW1+Pr60N7XKhrFaU2Yy3uRntcBz7hBYLymLBmppC+OzZBE/IIjhrAsFjx2IK7YGNSE8TAU+VVkqZgP1KqZ8ApUB4zzWrf+kYNvIeXfMiwYsYeBoqW/ni3wco2FaDxWoic8oQxs4aSsroGJSpm2pK3G2w603Y+ByUbDDus4ZB6jSYdycMmwGp042aFiH6IW9jI60bNtC6cRPO/HxchYV4a2vxtbZ+7VgVEoIlKgpzZiZB6WmYQkJRViva40Z7PJjDIzDHxmIKC0WZTJhCQwkaORJbZiam4G7ObA4QgQYvtwGhwK3A/2IMHV3bU43qbw5nXvzBS1B75kUKdsXA4PP6OLSrjrwvyyncVoPZamLmRRnkzE8lKKQbx8xb64yC23XPQFudsYfQgnsgY76RZZFpzaKf0G43zoICnHv34TxwAG9DA77WVjxVVbiLi3GXl4PWKJuNoMwMQrKzsCQMwRQRgTkqCmtyEtakJCxJSZijo/n000/Jnj+/r7s1YAT6m0ID/wBGAO1zHv8C5PREo/qbji0APEamRZkUFpsZlwwbidOcz+tj3/pKNqwooKnGQUiElZyFw5i8aHj37CcEkP8x7FsFVXlGLYu7BUafB7N+BGlzZYaQ6FNaa7w1NTj27sO5dy/OfXuN7/PzwW38wYrFgjkqClNoKJbYWEKmTiUqPY2wGTMIzsnBNEjqTDpzuL3Ut7qob3ETEWxhWGzvDmEFGry8CNyJsc6Lr4tjB5yOzIt/2AiMuhepeRGnK0eLmz1flrPj01KaqtuIHxbOkluySMuJx9xd+3VV5cGqu43pzdYwSBgDOd+FGTdJ/YroEz6nE1d+fkeg4ti7B+fefXjr6jqOsSQmYhs9mvC5Z2IbPQbb6NHY0gdPISz4N0y1O8mvaqHJ4cbh9lJjd1HW0EZRbSt7K5sormvrOH7Z7DTuu7B3/08HGrxUa63f6dGW9GOm9lVBO69AaDNLzYs4rWifpnR/A3mfl5G/pRqv20dSZhRzLh5J+qT47ls9s6UWch+Cjf/P2Ahx8UMw/SawDJ5f/qL3+Vpa8FRX46mrx1tXi6e2ruNfT3U1zvwDuAoKwevPoNts2EaNIvzsBQSPHoNtzBhso0ed1mufnCy310dlk4OD1S3sr7JzoKqZ/ZV29lfZaWxzf+34EKuZYbEhTEyN5tIpw0iIsBETamXkkN4vgQ00ePlvpdRfgY8AZ/udWut/90ir+hmzv2BXew8HL9ZgybyI00NLo5O8z8vJ+6KMphoHQSEWxs1KYsK8ZOJTI7rvQvYqWP8srHsWXHZj4bj5v4KwuO67hhi0tM+H88ABnHl5OA8cwF1ahq+tDW9zE+6iQ3iqq4/5PFNkJJbYWIIyMohYtIjgMWOwjR5D0IjhhydjDEBaaw7VtVJa30Z5o4OKJgcVR/1bY3eiO+1SGBNqZVRiBBfkJDFqSDiZQ8KJCQ0iJMhMbGgQ0aHWfrNFQKDBy3XAWIx6l/ZhIw0MiuDlcM1Lp+DFZpYVdkW/5nF72frBITa9V4TH7SNldDQzvp1BxuSEjqLzb8zRCPs/gLz/GLs4e90w9ltw9m9gyNjuuYYYlFzFxbR88SWuwkKcB/Np27oNX2MjAMpqxZKchCk0DHNYGGFz5xI0YgTWpKGYY+OwxMZgjovDEhMzoIZ7HG4vdS0u2txeWpweKpucVDQ5aHa4aXV6aXF5aHV6qWhysLW44WvZk6gQK0MjgxkaFcz4pEiGRhnfp8WFMSoxnPjwblwCoYcFGrxM11qP6dGW9GPmjpqXzsGLBYfd1VdNEuKYPC4vzeWaz17dT/7WKux1TjImJzBraSbRid1QUOd1G4vG5X8CBz8xCnC111j1duoymPkDiMv85tcRA5rXbsdbUwMWK6a6Ohz79uFrbMRdXo6r6BAtn31G27ZtgLHEfdCIEUQsOofQadMIyc4maMSIAbtybH2Li8LaFioaHZQ2tLG/0s7eymZK6lupOcFnjklBmM1CWJCFmLAgzssayqRh0QyPCyUpKoShkcGEdNcfLf1AoD/9L5RS47XWu3u0Nf2U2dI+bHR4mMhqM9NUI8NGou9pn2bfhkr2raugdH8DXrem1FpKyqhozr56HMPGx576yX0+qNkLBWuNYKVgLbiaQZmMqc1n3g6jzjXWZDENmkW3xSlw7N5N3Qv/oHXTJtzFxR33JwAFnQ9UCtuYMQz5xc+JWLQI67BhqAHw3mpxa9bsq+ZAlZ2yhjbKGtsobXBQ2ejAbFKEBJmpa3FR13JkgBIXFsSoxHAWjU8kOSqE+AgbIVYzoUFmEv1ZlKgQKzaLqd8M6fSGQIOXM4CtSqkCjJoXBWit9aCYKm02t28PcDhYCZKaF9HHtNZU5Dfy+RsHqCxoIiohhKy5KTR4S1hyyVwsp/JXVmudkU0pWW8sHle6GZxNxmMxaZB9KWQugPR5EDJ4ChvFyfE2N9O2dRvOfXtxV1bi3LOX1vXrMYWFEXbmmURfcjGWoUPB62PPnjzGT52KKSICa1IS1pQUTLbTZ/jiaD6fUWuyraSBHSWNHKxp4WC1ncLaVmA9AMFWE8nRISRHhTByZDwaTZvLS1SIUfyaHh9GUlQISVHBxIQNnGGv7hRo8LKkR1vRz5ksxyjYlZoX0UeaatrY/nEJB7dW01znIDQyiIXfH8eYmUNRJkVubunJBS5eD3zxB9jyItTlG/cpszGdOfsyI6sy/AyITe+ZDonTmtYad3ExrZs307ZlK21btuDcv5/2SlAVGoo1OYmEn99BzOWXY444skjckZtL5Gm2eFuL08Ohulb2VDSxt8JOaUMbFY1tlDU4qGxy4PEZfbdZTGQkhDM+OZIpsW4uOWsKY4dGEBsWNKiyJD0hoODFv5/RoGXpWGG307CRP/OitZY3oegVbc0uNq4sZOeaUlAwfHwc076VxsipQzo2Cz1p9YXw71uMPYUy5sOUa4xgJXkyBIV1Z/PFaU5rjbuoiKb33qPxP+/iLinBFBEB/r18AEzh4YRMmkTEksWETp5M8IQJmCMj+7bhJ6F9hs6eimYK/BmTg9UtFNa24tOaILOJVpeHpk5/uAaZTSRFBzM0MpgZ6bEMjQpmeGwoE1OjGZ0Y3vH5kZuby5yR8X3VtQFnYFY8dTOz5VgFu2a0Bo/b130zN4Q4BpfDw7aPitnywSE8Lh/jZicx/VvphMecYmpda2M4aMNfYOcbYAmGi/8KOZd1b8PFaUtrjaeqGufePbRt30Hbju04tu/AW18PQOi0aYTPn4+vpQV8XoKzsgmZPAnbyJGnTX2Kz6cpqmtlR2kjO0sb2VHSyM6yRpo7BSbx4TYy4sM4e2wCVrMJl8dHSJCZpKgQUmJCGDc0gvT4sI4ARfQeCV4CcDh46VzzYrx0bodXghfRI7RPs+erCr56K5/WJhcZkxM446IMYoaeYkakqQw2v2AELDX7jAXkpnwf5twK0cO7t/HitONtbKRp1SqaVqzEsXOnEZiAUUA7MpPwBQsIyc4ibO48glJT+raxJ0FrTWWTkx2ljewoaSC/uoWS+lYO1rR0BCpBZhNjkyL49sRkslOiGJcUSUZCGJHB1i7OLvqKBC8BsHQsUnd4ZwSrrfPmjFJQJbpXxcFG1r6yj6qiZhLTIznvB9kMzTjFHZbbGuCzx4zNED1OSDsTzvghZF0KwadPSl90L29jI62bNtO6aSOtGzfi2LUbPB6C0tOJuugigjIzsI0cZQz9hPevIUS318eusiZ2ljZSVNtCdGgQQyJsKKVoc3upbnZSUNNCQY2dguoWWlzGH55mk2J4bCipMSEsnZRCVkokE5KjGJ0YQZBFsienEwleAmC1+t/UviNrXgCZcSS6VUNVKxtWFLBvXSVhUUGcc914Rk9PRJlOoa6qrR6+ega+etqYMZTzXVjwa2PWkBg0fK2ttHz1lbHp4P4DuCsq8FRW4i4rM3ZFtloJzskh7oYbjBVoJ4zvd3V8Xp+mrKGNgzUtfLi7khU7yjumFAdZjOGczkwKUmNCSY8PY9qIWDISwpiQHMn4pKgBtdbJYCbBSwA6CnaPkXlxyf5G4htytnk4tKuWvC/KKd5dh9liYup5I5iyeMQpFeJa3M3w8QOw7s9G0DL2Ajjrl5A0KFY2EICnvh5nXh7NH35E4zvv4LPbAbCmpGBNTSVkyhSiLrnYWPQtJwdTcHAft/iwGruTg9UtlDW0caDKzvrCOrYVN+D0Byg2i4lF4xNZkjWUianRpMaE4HD7qG52ohQEW81EhliwWSRIGcgkeAmAxf+fQB2r5kUyL+IU+Lw+CrbXsHttGSV76/F5NWHRNmZ8O53xc5IJiz7JYlxXCxz4CPau5Iydb4G3DcZdCGf9FwzN7pE+iL6ntcZbV4erqAjn/gO0bd5E68ZNuEtLAWN12ojFi4m+5GJCsrMxhfWP4Z9mh5vShjZK6tr4pMjNZ+/u5lBdK7vKmihtOLxbsdmkmJAcyVUzRzA6MZzhcaHkpEYTbjvyoyskyMzwuG5YQVqcNiR4CYClvWDXd4yaF8m8iAD5fJqK/AYObq3hwKYqWhqchMfYmHj2MNJy4hmaEXl4H61AlWyCzc/DzjeNlW+Do6iJn8XQix+ExPE90g/Rd7TPR9uWLTStWEHbjp24CgvxNTd3PG6OiyN06lRirryS4HFjCc7K6tWpyj6fZmtJA9uKG9hXaaei0QhENMbaKM0ODxVNDhpaj9xzJ9haRGpMKJOHR7NsdhqjEsNJjQkhJTpUhnnEMUnwEgCrRaEBdazgxSkL1Ymu1ZQ089Hf86gptmOyKIaPi+WsK0YzIjse08nWs2gNhZ/Bmv+DgjVgDYUJ34Gc78GI2exZ+zlDJXAZMJwFBbR8+SVtW7bSunEjnvJyVHAwoVMmE/XtCwhKS+v4sg4b1mv1Km0uL58fqGFLcT0Ot4+mNjdr9ldT2eQEIDrUyrCYUJQy3rJhNjPDYkOZlhZDaoxRNJsaE8qh3Vv49rnz+12djejfJHgJgNWk0EoZ+7xoDUp1FOxKzYs4Ea/Hx+ZVRWxcUYgt3MrC748jY3LCqS0qpzXkfwxrHoVDXxqbIZ77gDHdWWYNDQhaa9ylpbRt2ULr5s3EffgRB6urATAnxBM6eQoRt/+MiIULe20IyOH2sr2kkQ2FdWwuqqe2xYXD7aWgpgWnx2fsy2M1E2w1MW1ELEuyhjI7M44E/+yfrjTkKwlcxEmT4CUAVhNopdBaGTOOzBaCbFLzIk6soqCRT/6xh7qyFkZNT2Te90YTHH4K60bU5sOO1w6vzxKRDOf9H0y5Fqwh3d9w0Ws81dW0btiAY/du2nbtwrE7D19jIwCm0FC86Wmk3HIL4fPm9lpWpbHNzeZD9WwoqGNDYR3bSho7ZvOMHBJOUlQwQyJszM6MZ+G4IUxPi5VpxqLXSfASAKsJtEkZA7c+N5gtmCwKk0lJzYv4GrfTy7q3D7Ltk2LComyc/6Mc0nNOYVnwqj2wdrkRtGhtrM8y+6fG8JDl9N24bjBzV1bh2L0LR14eLWvW0rZtW8d0Zdvo0USeey7BE8YTMnEitlGj+PSzz5jUg/v+1Le42Hyonl1lTewua2JXeSPFdUaditmkyEqJ4vuzRjA9LZZpabHEyiaBop+Q4CUAVrPCp5Sxz5jXDdYQlH/oSDIvop2zzUP+5io2riykudZB1rwUZn0nk6CQk/hvVpsP2/4Fe9+Hyh1gDTMClpk/gMjknmu86HbuykpcRUV4Gxpw5efT9MEHOHfndTxuGz+O+J/+hPB5ZxE8ehQqqGcDA601eyub2V7cyK6yRjYU1pNX0dS+fyLp8WHkpERz+fThTEyNZvLwaMJs8hEh+id5ZwagfdgIrYzgpf1+m1kKdgWN1W1sXFHA/k1VeN0+YpPD+M4vppA8MjqwE2gNxevgiydhzwpQCobPgkX3w6SrISyuR9svTp2vrQ13WRnu0tKOL1dxCW07tuMpKz/i2JBJkxhy5y8ImTwZ2+jRmMPDe7RtdqeHPeVNFNe3srusifd3VXRkVcKCzOSkRnPHOaOZkR7LhJSor00/FqI/k3drACwmDmdefJ2Cl2CLDBsNYg2VrWz/uJhdn5VhMinGzU5izBlDSUyLDKw2weeFvP/Al3+Ekg0QEgNzfw4zboKIoT3fAREwb1MT9jVrafnyCzxV1Xjr6nBXVOCtrT3yQKsVa3ISITkTCV22DNvIkZhjYrAkJmKJje3xdh6stvPxnio+2VvF+oI63F4jrWI1K2ZnxvPj+SOZmRHHiNjQk5/lJkQ/IsFLAEyqfbYRx8i8SPAy2JTsrWfTe4WU7KnHZFKMnZPEjG+lB76wnLsNNv8DvnoK6guN5frPXw6TroSg/rGImADtctGcm0vjm29hX7sWPB7M0dFYU1Mxx8USPH68sWJtSgrWlGSsKSlYEhJ6dVflotoWPthdyc7SRrYUN1BU2wrAqCHhXH9mOmekxzE8LpSU6BCCrbJeihg4JHgJkDaZ/LONjgxeZKr04FFV1MRXbx+keHcdYdE2Zl6Yzrg5yYRFBRi0+Hyw/RVj6f6mEkidAYv+F8Z+C0zywdLXtNZ4qqpp274N+4cf0fzJJ/iamrAkJBB77bVELDqHkIkTezU4adfi9NDq8tLq8lDZ5KS0oZX/bCvnk71VaA1JUcFMSI7ihjPTWTBmCMNiZbVZMbBJ8BIgrUzGbCPv4RqXoGAzTXb38Z8kBoSGylbWvXOQA5uqCA6zMufSkWSdlYLlZP6Szf8EPvgNVOyApEnwnachfV6PtVkcn9YaT3k5rpISPOXlOPMP4sjLw7F7d8cwkCkykogFC4g8/zzC5sxBWXrvV6XD7WVnaSNbixtYtdXBr7/8iLJGx9eOiw+3cevZo7h8xjCSomTKvBhcevR/pFJqCfAHwAz8VWv98FGPDwf+DkT7j7lLa73S/9ivgBsAL3Cr1npVT7a1K9p0jJoXKdgd0DwuLxvfK2TL6kOYLCamnZ/GpEXDsZ3M7KHKXfDBvXDgQ4gaDhf/FbIugT74630wc5eX0/Te+9g//hjH3r1HLKmPxYJt5EjC580jePx4gsePIyQ7u8dn/3SmtWZLcQOvrC/mP9vLaHUZGd34EMUZo2K4OjmSiGArIVYzCRE2kqOCGREXJuuriEGrx4IXpZQZeApYBJQAG5RS72itd3c67B7gVa3100qp8cBKIM3//eXABCAZ+FApNVpr3WdjND5l8s82ctG2YweW+HiCgi242mTYaCCqLGjig+d20VjdxpiZQ5l1cWbgw0NaGxmW9X+GrS+BLcIYHppxM1j7z+69A5Wnvh7H7t049+zBsTsPx549uPLzAQgeP56ob1+AbfRogoYPx5KUhDU5GZOt99fNqW9xsfZADWv2VbNmXzVVzU5Cg8x8OyeZheOGMGl4NLs3fcX8+VN6vW1C9Hc9mXmZARzQWh8EUEq9DFwEdA5eNNC+rnkUUOb//iLgZa21EyhQSh3wn+/LHmzvCWmTCe0DvB5Kf3YnobPOIGjadbjaPGitZXnrAUJrzc5PS/nstf2ERdm48GeTGDY2gFkirXVQ9DmUbIT9H0DVLjAHwRk/MmYQhfb8TJPBSvt8OHbtwp77KfbcXBy7dnU8ZklOInjsOKK+/W0iz1tC0IgRvd6+ZoebvRXN1La4qGp2srusiR2lDewqM9ZYiQqxMndUPGeNTmBJ1lAigg+vwrz7BOcVYjBTun2Fou4+sVKXAku01jf6b18DzNRa/6TTMUnAaiAGCAPO0VpvUkr9EfhKa/1P/3F/A97TWr9+1DVuBm4GSExMnPryyy/3SF/sdjvRDz7EiNAyan56J0H3/RX36FEcWPBDKrdpxl2qMFlO/+DFbrcT3sNrT/S14/VRa429AmrzNC1VEJ4MKTMVFlsXP1etSaz8hFH7/4rF24JPWWiOGEVl4llUDTkTjzWih3pyfIPh56gcDnxbthC1/wBBO3dibmpCK4U7PR1XVhaujHQ8w4ahe2n/n86cHs2+ei95dT721HkpbPLh6/RrNtQC6VEmRsWYyY43kx5lwnScP34Gw89yMPQRBkc/e6KPCxYs2KS1nnb0/X1dsHsF8LzW+ndKqVnAP5RSWYE+WWv9LPAswLRp0/T8HlpGOzc3F2W2gFZMyp7AHpeLaGsQ47JGU7ltLzOmziI85vQfDsjNzaWnXsP+4lh9dLS4WfHUdioONhIWFcSZ3x1BzvxUVFfrYLTWwVs/hH3vw/DZsPBeTMmTibIGEwWM7rFenNhA/Tlqn4+2LVtoePU1mt5/H+10YoqIIHzumYTPn0/Y3LlYYmJ6vV0Ot5dNRfV8mV/Llwdr2VbcgMensZgUE4dFc/6UOKaMiGZIRDBx4UEMjQwOOFM7UH+WnQ2GPsLg6Gdv9rEng5dSYFin26n++zq7AVgCoLX+UikVDMQH+NzeZTKjNWhHK/h8eBsbsIUa6V1nq4fw3v+dKbqBs83Df57YSk2pnQVXj2XMGUMxB1IEWZUH/7ocmspg8W+N5fulCLfbeerqaFqxEvvaNbRt2YqvuRlTWBhRS5dyMCWZ2dddh7KewmaXp8Dn0xTUttDQ6qapzc22kga+zK9ly6EGXF4fJgXZqdHcODeDWZlxTBsRI8vrC9FDevJ/1gZglFIqHSPwuBy48qhjDgELgeeVUuOAYKAaeAd4SSn1e4yC3VHA+h5sa5e02QwafC3GIlC+xiaC/bNOnG0y4+h01NrkYuXT26kpsbPkluyuN090t0HBGmPa85Z/GAvKLVsJw6b3ToMHCVdJCfZPP8We+yktX3wBXi9BGRlEnnceodOnEXH22ZjCwtibm9vjgUtjq5vVuyv4eE8VXx2spb718GxDpWBCciTfnz2CWZlxTE+LPaJeRQjRc3oseNFae5RSPwFWYUyDfk5rvUspdT+wUWv9DvBz4C9KqdsxineXaaMIZ5dS6lWMejUP8OO+nGkEGJkXt8LXYgeM5cKDQv3BS6sEL6ebol21fPT3PFytHhbfmNV14FK1B16+EurywRIMGQvgW7+DqJTeafAA5a6swnlgP56qapx79mBfuxbXwYMAWIcPJ+66ZUReeCHBo3t+EM7r0xystrOrrIldZY3sLG1iY5GxxH5SVDALxyUyIz2WIRE2IoKtjEwIJypUghUh+kKP5jT9a7asPOq+ezt9vxuYc5znPgg82JPtOxk+sxVc4GuqA0A7nQRZfAC4WmWhutNFW53m/Wd3kr+5itjkMC66bRJxKScoMNPa2H/orR+BNQQufwkyF8qU52/A53DQtGIlje+8Q+v69bRva6yCggidPp2Yy79H+Lx5BKWl9VgbHG4veyuaOwKVXWVN7KlowuE2/k8HWUyMHRrBstlpXJCTTE5qlMwoFKIfkQHZAPksVrQ+HLwAWNzGEJIMG/V/9nonn/5rL4XbNUHBtUxdMoJp56dhCTrOKrk+H+R/BGuWQ/FXkDwZvveiZFq+AXdlFfX/eomGl1/B29BA0IgRxP/0J4TNmGFsXDhkSI+tt9Jer7LuYB0f5lXy2YEaXB4jUIkItjA+KZIrZ4xgQnIkE1IiyUwIx2qWGiYh+isJXgKkzUForfA1N3TcZ3EaQ0gybNR/aa3Zt66Cta/ux+v2MSRHcdF1cwg63iq5lbtgyz9h11vQXAaRqXDeozDlWsm2nAKtNW1bt1L/0r9oeu898HqJOGchMddcQ+j06T2azdBas6Gwnn+tP8THe6pobDMypKkxIVw5YzhnZMQyITmK1JgQyaoIcZqR4CVQFgtebcLX1Nhxl25pxmozS/DST1UXN/PZq/sp29/A0IxIFn5/PFvz1h87cCn8HNYuh/yPjcXlRi6CrP+FcReCpfeWiR8oPPX1NLzyKo1vvomrqAhTaCgxV15B7DXXEDRsWNcnOAU+n2ZrSQOf7q3uGAoqb3QQYbOwJGso09NimTIimsyEcAlWhDjNSfASIJPZjNdnxtfS1HGft7EJW2iQDBv1M26Xl3VvH2T7x8XYwqzMv2oM4+YkYzIpyDvqYI8LPv5f+OIJCE+EhffC1OtkRdxT5CospPbvf6fxzbfQDgeh06cTd/PNRCw+F3MPLNDV6vLw2f4aPsqr4qM9VdTYnZgUZCaEMz0tlrmj4vlWThKhQfKrToiBRP5HB0iZzXi1wmu3d9znbWokKCQJl2Re+o3y/EY+en43jdVtZM1LYeZFGQSHHWdGSPU+eOsHULoJpl0P5z4IQaG92+ABQPt8tK5bR92LL2L/6GOUxULkRRcSt2wZtpEju/VaTQ43GwvrWFdQx4db2yhavRqPTxNhszB/7BDOGTeE+aOHyCwgIQY4CV4CpMxmfNrUsc4LgK+pCVvoMJwy26jP+Xyaze8Xsf7dAsJjbFx0+2RSxxxn5UCvG754EnIfNmYQXfY8TPhOr7b3dKe1xrlvH82rVtP49tu4S0sxR0UR94NbiL3ySiwJCd/4Gk0ON/sr7RTWtLCzrJH1BXXsLjf2A7KaFWkRipvnZTA7M54Z6bGyw7IQg4gELwEyWfzBS6s/eFEKb0MjtlAr9npH3zZuENM+TdGuWjavKqL8QCOjpg1h/lVjj13X0lrH8KLXYNMPjWLccRfC+cshIrH3G36a8lRX0/DvN2n49xu4iw6ByUTYGTNJuP12Is5ZiCn4mxU1+3yaT/dV8+rGYj7Mq8TtNaZRB1tNTBkew20LRzEjPZbJw2JY98Va5s8f2x3dEkKcZiR4CZARvCh8Diem0DAwm/E2NWFLsVBbKsNGva2ppo196yvZ81U5jVVthEYFseCasYybnXTsYsyiL+DV75PRUmUsMHfhkzDqnN5v+GlI+3y0fPklDa+8SvPHH4PHQ+iMGcTdcAMRCxdiiYv7xtfw+TTv76rgiY/2s6eimbiwIK6dlcackXGkxYUxLDZUpi4LITpI8BIgk9mM9im0w4UKS8BkC8bb1IhtlEVmG/WihspWvvj3AQq21QCQNDKKGd9OJ3PykGPvSeTzwvq/wOq7IXoEG8f+imnfvr6XW336at28mYr/uR/n3r2Yo6OJveYaor97Gbb09G98bpfHx1cHa1m1q4LVuyupbnaSkRDGY9+byLeyk2UYSAhxXBK8BMhksRgbM7q9mEJCMYeH42s0tghwOTxon+56F2JxyloanGx6v4hda0oxW01M+1Ya42YlERkfcuwn+Hyw4zVY8yjU7ofRS+A7f8a+bmuvtvt05czPp/bZv9D49ttYkpJIfuRhIpYs+caLyLW6PHy6t5pVuyr4aE8VzQ4PIVYzC8YmcEFOMosnDMUs/4+EEF2Q4KUL/9j9D/5Y/EeespxpLFLnUZjCgjBFReJtbMQWYgENLoenY5dp0X08bi9fvX2QnZ+W4vNqxs1JYsYF6YRFneBDtKkM/n0zFK6FxCz47gsw9tuy6/MJ+Fpbadu2DUfeHlo+/5yWzz9HBQURd+MNxP/oR5hCT30WVmOb28iu7Kpg7f4anB4f0aFWFk8YyuIJQ5k7Kp5g63FWOhZCiGOQ4KULPu2j1dcKJoxdpd0mTDYr5sgonJVVHQGLs1WCl+7W2uTivWe2U1HQxNhZSUw7L42ohONkWgCcdiPb8tH/GOu3XPgkTLpagpYTcJeWUvfSSzS89jq+JmMNI2tKCgm33Ur0976HJfbU17vxeH28tP4Qv/9gHw2tbpKjgrlixnDOnZDIjLRYLFLDIoQ4RRK8dCHUavzFqc2gNPg8CrPNgjkqyijYlZ2le0RlYROr/rKTtiYXS27OInPykOMfbK8ypj1vfwVcdkiZCt95FuK7d42RgcJ58CDNH35E84cf4ti+HUwmIs49l+hLLiY4KwtLzHGmmHd1Xo+X1bsqWb27kspGB4fqWqlocjArI447l4xh8rBoWdlWCNEtJHjpQqilPXjRKK3xeRTWIDPmqEh8jY0EhRjpblllt3u4HB7WvX2QHbklhEbZ+M4vpjBkROSxD/Z6YN3TkPsIeNog53KY+n1InQ7yIdlBa41j506aP/iQ5g8/xHXwIADB2dkk3H47URd8C2vKqW042exw80V+LZ/uq+b9nRXUtbhIjLSRFhfG1LQYvp2TxOIJQyVoEUJ0KwleuhBmDQMgKNiE9gcvJqvCFBmJdrsJMhs708pCdd+M1+Nj19oyNq4soM3uJmteCmcszTRqio6loRjeuNHY8XnUYlj8IMSP6t1G91c+H80ffkjD62/gOnQIT0WFsT6R2Uzo9OnEXHklEQvPxpqUdAqn1uwub+LTfdV8uq+azUX1eHyasCAz88cM4bvThzF3ZLyxFYMQQvQQCV660J55UWaN0qA9JkxWjTkyCgCLx1i0ToaNTl3FwUY++H+7aapuI3lUNOdfnMnQ9KjjP2HfKvj3TcaMoov/CjmX9V5j+zGtNc3vvUfcbx+mpLoaS1ISIdnZhM2ZQ/D48YTPP+uUhoR8Ps2mQ/W8taWUVbsqqbE7AZiQHMnN8zKYNzqBKcNjZGqzEKLXSPDShfaaFzdegrXPyLxYfJijjKEMi8sIXlwybHTSfF4fG98rYuPKQsJjbFzw04kMHx974iGGDX+FlXf6ZxH9HWIzeq/B/Zhj3z6q/u9RWj77DD1sGCmPP07EOQtRllP7L97scLOhsI6P8qr4eE8V5Y0Ogq0mzhmXyIIxQ5g7Op4hEd9sNV0hhDhVErx0oT3z4lY+wnxeNApt8mCOMjIDZkcTSknm5WQ11bTxwXO7qTjYyJiZQ5l3+ehjL+nfrr4IPn8cNj5nrNlyyd/A1v27FJ9OnAUFNL//Pk0r38O5fz+msDAS776b7SnJ5Jx99kmfr6yhjbe2lvL+zgp2ljbi0xAaZGbuqHj+a8kYzh0/lDCb/MoQQvQ9+U3UhY7Miz4cnDg9TiIjjcyLr7mZoBCrBC8nYe+6Cj79116UUiy6YTyjpw89/sH1RbDq17BnBSgTzPyBsfuzefC+de1r1lD1+OM4d+cBEDJlCol3303k+ecZS/Xn5gZ8riaHm/d2lPPmllLWFdShNUwaFs1PFoxkZkYcU0fEyBosQoh+Z/B+AgQoxGKsK+JS3o77XL62jsyLsTnjUJxtUrDbFWerm0//tY/9GypJGhnFOdeNJzLuOOu2aA2b/w6r7jZuz70Dpt0AUac2K2Yg8NTVUfnbh2n6z38ISktjyF2/JHLJEqxDTxD8HUOby8tnB2p4a0spH+RV4vL4SI8P4/ZzRrN0UgrD4059QTohhOgNErx0oT3z4uqUefF62zD7My/GWi/DcEnm5YTKDjTw4XO7sTc4mXlhOlOWpB1/RoqzGd7+Mex+G9LnwUVPQfTw3m1wP6JdLupeeomap/6Ez+Eg/sc/Ju6WmzEFBQX0/IpGBxsK68grb2LLoQY2FdXj8vqIDQviyhnDWTo5hYmpUTKdWQhx2pDgpQtWkxULFpx0Ck50K6bwcFAKb1MjQSGyOePxuF1eNr1XyOb3i4iID+HiO6eceCZRzX54+SpjP6JF98Osnw7aFXLdlVU0vvkmDa+9hru0lLAzzyTx17/ClhFYkXJ1s5OnPjnAi+uKcHs1FpNidGIEy+akMXdUPGdkxMlOzUKI05IELwGwmWy4OgUvFtWGV4M5MhJfYxO2RAsNla192ML+x+XwkPd5OZtXFdHa5GLsrKHM/d5ogoJP8JbbswLe/AGYrXDNW5BxVq+1tz/Qbjct69djz/2U1vXrce7dC0DozJkk/uYews8664TZEa9P8/7OCv7fFgf/uymXotpWNHDZ1FSuPmMEoxLDsVmkfkUIcfqT4CUANmU7IvMSbmmlsLYFU/sWAemSeWlXtr+enWvKKNhWjcflI2V0NItvmkDyqBOsL+JxwqePwNrfQfJk+O4/IHpY7zW6DzkLCmhdt47WTZtpWbMGb2MjKjiYkMmTSLjtViLPO4+gtLRjPtfl8fHJ3ioKalqobnayencFxXVtxAYrpmWEsyRrKJdMSSUjYXDPyhJCDDwSvATAZrLh0ocLciMsbXxV2khO5OGdpQf7CrutTS4+f30/+9ZXEhxmZcwZSYyZOZSkzBMMEQHkfwIrfwG1B2Dy1XD+78A68NcPce7fT/WTf6R59WoAzAnxhM2bR+SSxYTNmYMp+PivQVWzg5fWHeKldYeoajYWjAu2mshOieLu88cRVL2HsxdM65V+CCFEX5DgJQA2ZcPB4eDEavVyoKSCyZGReJsasYVa8Lh8eD0+zINslVGtNfvWV7L2lX24XV6mfSuNqYtHYAk6wfCEowm2vQxb/wnl2yAmHa56A0ad03sN7wOe6mqaPviA5vdX0bphA6aQEOJ/9COill6EddiwEw4JVTc72XKonhU7ylm5oxy3VzN/TAKPzEpjenosYUHmjufn5u7trS4JIUSfkOAlADaTDafP3nHbZNHU1lRjiorEXVaGLdQKGKvshkQENgNkIHDY3Xzyzz0c3FpN0sgozr5mHNGJXUyzrdgJr1wF9YUwNAfOexSmXDsgsy2+1lYce/bg2LGD5o8+pnXjRvD5CMrIIP5HPyLm6quOu1y/x+tj7YEacvdUsWZ/DQU1LQBE2Cxcc0Ya18waQXp8WG92Rwgh+g0JXgJgZF7qO26bLJq25lqsQ4Zg/yQXi8lYA8bZOniCl7ryFlb8aTv2egezLx7JxHOGnXgzvtY62PUmrL4HbJGwbAWkndl7De4h2uPBkZdH64aNOPbk4co/iLusDF9LC9rl6jguKCOD+B/8gIgli7GNGnXcLEtjm5sXvijkpfWHKG90EGI1MyszjitmDGPK8BiyUqJk0TghxKAnwUsAbCYbDm18ECmrBWUCp72eiPOWUPf3FzDt2QxEUbC9hsmLBv56JAe3VvPR87sxB5n5zh1TGJpxgrqW+kJ460dw6EvQPhh2hrEnUcTJLazW37gKC6n/179o+Peb+JqbAbAkJmIbOZLg7CzM4eGYwiOwjR5N8IQJWBOHdHnO7SUN/PilzRTXtTF3VDz3XTiBs0YnSLAihBBHkeAlADZ1OHgxhRjDG77Wemw5EwkamYn68GXS5t/NurcPMmJCHLHJAzOd39bsYu2r+9m/oZL4YeGc/8McImJPMNxTVwDPXwAuO8y7E0YugpSpp+W6La5Dh2h8913aNm3GefAgnvJysFqJPPdcIs5ZSMjUqViHdB2gHM3n0+wqa2L17gr+/OlB4sODeOOHs5k64uR3fxZCiMFCgpcA2Ew22nzGrA5TqFHTEeZroaHNTcxll1H524eZfZeFfx808+Hzu7nkl1MxD7DFv+rKW3j78S047G5mfDudKYtHnLg4uSoP/nkJuFvh++9A0sTea2w30T4fzR99RN3/e562zZsBsI0bR+i0aQSPHUvUhd/GkpBw0udtcXr4MK+ST/dWs2Z/NTV2IzA+d3wij1ySQ0zY4Bh6FEKIUyXBSwCCVBB2/2wjU5iRVYlSLVQ0ORhz4YVULf8dzpVvsuCqm3nvzzvYtLKQGd8ObBXU00FtqZ23H9+CUorLfjWN+NSI4x/sccFnj8Ha5UZty/f/A0Oze6+x3cDnctH0zjvU/u05XAUFWFNTSfj5HURdcAHWpKRTPm9BTQvPf17AvzeX0uz0EBNqZd7oBOaPSWDuqATiw23d2AshhBi4JHgJgM1kw+dPMqgw44M7UrVQ1eRkQvIQIhYtovGddxj1i58zZuZQNr5XxIjseBLTIvuw1d2jOK+O1X/bhdmsuOj2ycQMPcGQWPU+eP16qNwB2ZfB4t9C+MlnJvqK1pqG11+n5sk/4qmqwjZ+HMm/W07k4sUoy6n/Vymua+XJj/fzxuZSzEpxfvZQrpw5gqkjYjCfqMhZCCHEMUnwEoBgFYzP/xljCgvFFxRBlMfIvABEXvAtmlauxLFzJ3O/N5HSffV89Pxuvvvr6Sde76Qfczk8fPX2QXZ8UkLM0FDO/2HOiadBb3sZ3r3DmPJ8xcsw5rzea2w3cFdWUn7Pb2hZu5aQqVNJ+u1DhM2efcqbFda1uHh9UzHv7axgy6EGgswmrp01gh/Oz2RIxMCbFi6EGFxcXhcHGw+yt24vqRGpTE2c2qvXl+AlADaT7XDwEhoG0cOY7NhPbmMbAEEjRgDgLi8ndNo0zr52HO/8YSvr3jnInEtH9VWzT0l9RQs7Pilh77oKXA4vOWenMmtp5omDsM8egw/vgxFz4JK/QmRyr7W3O9g//5yyn/8Cn9NJ4m/uIeaKK1AnUVSstWZnaROlDa043D42FdXz2qZiHG4f2SlR/OLc0Vw8JZXk6JAe7IUQQnQPn/ZR3VpNib2E/fX72Ve/j6KmIkqaS6hpq8GrvXi1t+P4S0ZdIsFLf2RTNrz+zzJTaCim6TcyacUdbCj/ChjTUQfhLisHYNi4WMbMHMrOtWXMuDAD62mSfWko0LzyxgbQkDk1gez5qSfeAVpr+PT/IPchyLoUvvNnMJ8+bynt8VD73P+j+vHHsWVmkvLEH7Clpwf8/H2Vzbz4VRGrdlV2ZOEAgswmlk5O5qa5GYxKPEF9kBBC9BGvz0tRcxF76/ZS3FxMmb2MUnspZfYyylvKcfsOryofGRRJRlQGUxKnkBCSgMVkwWq2kh6ZzujY0QyP6P0lQk6fT5o+FKSCOmpeTKGhMOkq6lbez6yyvwPfxxQaijk6Gnd5Wcdzxs4ayt51FRRur2HUtMS+aXiAWhqdbFxZSOk6TcroKBbdMIGwqC6KR9vqYeWdsOM1mHglXPRHMJ0eQZqvpYXG/7xL7V//irukhMjzzyPpf/+3oxi7KztLG3n4vT18dqAGm8XEgjFDWDQ+kXFJkQRbTcSF24gKsfZwL4QQInDNrma+KPuCjRUb2VO3h731e2nztHU8HhccR0p4CuPjxrNwxEJSwlJIDk9mZPRIhoYNPeUh9J4iwUsAbCYbXn9hpSk0FKzBfBR9KZfV/xXKtkDyZCzJSbjLyzuekzw6htCoIPZvqOy3wUttqZ117xykcEct2qeJGwMX3joJU1fTvPd/AO/8FFqqYf6vjTVc+vnaLe6KCuyffEL062+wb/9+tMtF8MQcEn/9K8IXLAjoP6bH6+NPufk88dF+okODuHPxGK6YMZxYmdoshOgntNZUt1WT35DPwcaDHGg4wIH6A+ys2YlHewi1hDI2diwXj7qYsbFjGRc7juGRwwmxnF7D2hK8BMCmOte8GEWru5Iv4bz6lwhf+zv43j+xJiXjPnSo4zkmk2LU1ER2rCnB2eru2P+oP9A+zdaPivnq7XyCbBYmnTOM8XOS2Zq3/sSBi7MZVt0Nm/8OCePgin9B8uTea/hJ0lpj/ySXmmeewbF9OwDmhARirriCiHMXETJlSkBBi8Pt5d+bS/nrZwc5WN3ChROTuf+iCUSHStAihOhere5WqtuqcXgctHnacHgdtLmNf4+4z9N2+Lb/38rWSg42HKTZ3dxxvihbFJlRmVwz4Rrmp84nJyEHi+n0/+g//XvQC4JNwV8LXqJj4nnWcz535L0O657FmpRE67p1Rzxv1PREtn1cTP6WasbP6fsiVq01h3bVsf7dAqoKm0ifGM+Cq8ce3o8p7wRPLvwM3vohNBTDnNuMjEs/3EzR/vnntH61Dl+Lnbadu3Bs3451xHCG/OLnhC9YwJeHDpG9YEFA56pqdvCPL4v451dF1Le6yUqJ5Jmrp7Ik6/Te2kAI0T+0edoobCzky/Iv+az0Mw7UH6DeWd/1E/2CzcGEWEIItgQTbAkmLjiO8zPOJzM6k8yoTDKjM4kNju13Qz7dQYKXANjU4XVeTGFG8JIYGczdnqX8cLSdkPd/idV2Mz67HW9zM+YIo0hzSFoEkQkh7N9Q2afBi9aaop21bFhRSFVhExGxwSxcNo4xMwMYx/Q4jZlEX/0JYtLh+vdh+Bm90u5Aaa1x7NxF9eOP0/L552C1Yg4PxxIfx9D/vZ/opUtRVn/mq7i4y/PllTfxt88KeGdrGW6fj3PGJXLjmenMSB+YvwSEED2n0dlISXMJm1o2sW/7Pg41HaK4uZiS5hKq2qo6jhsdM9qoNQlPITE0kVBLaEdQEmwJJsQcckSgYjPbMKn+PVzfkyR4CUCQ6aiCXSAx0oYPE3vn/J5JbVdi3fgvIAx3WRnmMWMAUEoxenoim94rpKXR2XURbDfzun0c2FzFto+KqT7UTERcMAuuHsuYM4aeeGn/di018PJVUPwVTL8JFv0PBPWffZtcxcXU//NFmj/6CHdJCaaoKBJ/dZcx1Tno5Id08sqbeHTVXj7eU0WI1cwVM4Zx3Zx00uL7T5+FEP2H1toYqmk8SFFTEUVNRRQ2FVLZUkmbp40mVxPNrsNDONTAkJAhpEakMjtlNsMihjE8YjiThkxiaJhkdE+GBC8BsCgL9ggrXuvhNV0SI40hk4o2E1z6HNadM2kPXoL9wQvAqGmJbFxZyIFNVUw8e1ivtLeppo1da0vJ+6KctmY3UUNCWHCNP2gJdM+lqj3w0nfBXgmXPgdZl/Rso0+Cq6SUmj/9ica330aZTITNnk3czTcRuXgx5qgTTO0+BqfHy5p9Nby5pYT3dlYQYbNw5+IxXD1zBFH9qE5JCNG37C47u2t3U9hUSHlLOQWNBWyr3kZNW03HMaGWUEZEjmB4xHDCrGGEWcNIjUhlWMQwKvZU8J2zv3PaFcb2VxK8BMgVG8Y7zyzm1xONDQbbg5fKJidkZWJJGwPUHTHjCCA2OYy41HD2b6js0eDF59Mc2lXLzjWlFO2sRQFpOfFkn5VK6tgY1MksQ1+yEV68FMxBcN1KYyfofsDb2EjNn5+l/h//AJOJmKuuJO6GG7Emntxuzm6vjy/ya3l3WxmrdlXQ5DD2GbplXiY/PCtTghYhBjmX18W++n3sqNnBzpqd7KzZSUFjARoN/7+9O4+Pqr73P/76JjPZZrJvZCF7Qti3ALLJjoK4IKL0utZqa12urdpb/dmqvV3V2treqq1aa7Uo4oaAKyhhk32TNSRkT8i+75OZ7++PCTFAggSSDJN8no8HD5MzZ2Y+X88s75zzXbD/QRtuDmdS2CRGBY0i0T+RaJ9ogj2Du7y0nJqZKsGlB0l4OU9eBi/q9bcTkQV4uWF0Ve2TkxnGXQsur9GanX7WfZMmhLLtwxNUlzbiG9xzL96q4gbSdhRRUVhPSU4NdZXNePm4kbIghmHTwvEOuIAOtRlfwju3gjkEblsF/jE9Vu/FaNi3j4IHf0JraSm+ixcT/OB/Ywzt3hD0fbmVvH6omZ9uWk9lgwWzu4F5w0K5ZnQ40xKDMPazlcCFEGez2CxUNlVS1lhGcX0xJQ0lFDcUt/8raSghrzaPVlsrAAEeAYwMGsmC2AWMCBpBgl8CwZ7BuDrJvFb9lYSX82Qymk6b0MfFRRHi7UFxW3hRw6/B6PkKluP7zrpvQkoI2z48QfruYlIWxFx0LVaLjb1f5LDn0xxsNo1vsCehMT5MvSGU2DFB539pqCObjcG578PG/9iHQd/6AXg7/hqstlqpXLGC4j88jXHQIGLefRfPEcO79RgZJbU881kaXxwpxt0V5o8IZ9GoMGYkBeNhlA8gIfqbZmszmVWZpFWmcbzyOBmVGZQ0lFDeVE5Vc9VZ+7sqV4I8gwg1hZLgl8DMwTMZETiCkUEjL8kJ2oSEl/PmZfCiwdJw2rZQH/f28ELwEIx+bljyc866r0+gJ2HxvqTvuvjwUlfZzCcvfUNpbi0JKSFMW5p48R2Bm6rhgx8Rn/kpDF8MV/8VPBy7IratsZHqVasof/11LDm5mC6fTsSzz3arT0tRdRPPrz/Oyt15eLkZeHheEok6nyvnXrpz0wghuqfV1srR8qPsLt7N0YqjHK84TnZNdvvaOx6uHsT7xRPjG8P40PEEegYS6BHYHlZCvEII9AiUMylORsLLefI0etLQemZ48SC9pM7+i1IYI6KoP3QCGirAK+C0fRMnhLJpxXHK8usIijRfUA2lebV8/MI3tDS2suCekcSNCb6gxzlNZQ68dROUp5OecDeJNzwLDvwrw1JcQtXKlVS+9RbWyko8Ro4k5Pk/4z1//nktlljTZGH9kWLWHy3my6Ml2LTm9ikx3D8rgUCzO6mpBX3QCiFET2hqbWLHyR1sP7mdOksdFpuFVlsrFquFeks9pY2lnKw/2X5WPNwUTlKAfchxkn8SQ/yHMNh7sASTfkjCy3nyMnhR1VR12rZwP082pJVgs2lcXBSGpDG07spCH1mLSrnttH0Txofw9fsZ7Pk0myvuHnFez6ltmuM7izi8pZDqkkYaalow+7tz/c/GX3AA+vbBNaR9AmseBGsL3PI+BbmQ6IDgYmtupvzVV6n9Yh3NaWkAmGfNIvDO7+OZkvKdp2xtNk1ORQNv7cjh7Z151DW3EuLtztKUSH50eTyDA7z6ohlCiIugtaassYycmhwOlh1kZ9FO9hTvobG1EU+DJ77uvhiUfUFAg4sBL4MXcb5xTAmfwuiQ0aSEphDkGeToZog+IuHlPHkZvc468zIk1Jsmi428ygaiA00Yk8aBXkXrgfUYzwgvnt5ujL0iml1rsxg5s5LwRP9zPt/JjCo2rjhOeX4dAeEmokcE4hviSfLksIu/TJS/G9Y9CTlbIDgZbnwTgpMgN/XiHvcCNGdmUfDQQzQfO4bXhAkEP/wQ3nPm4h537tWdC6oaeX9PPp8cPElmWT0trTZcXRSLRoVx+5QYxkT64dKdEVZCiF7XYGkgvSqd9Mp0KpsqcXd151j1Md798l32lew7bU6UWN9Yrom/hlmDZzFh0ATcXGU5DvEtCS/nycvgRb2l/rRtSYPsM+keK6q1h5dw+yy6luN76Wyw7dj5URzdWsjmleksfWxCl1+uhzcXsOnt45j83Zn3g2Ekjg/t3lDnrmRthk3PQNYm8AqEhX+E8XeAa98PDdYtLVS8+SalL7yIi5sbkS+9iPd5TNufV9HAM5+nsfabQrSGy+ICuGNKDDGBJi5PCiLSX86yCOForbZWcmpySK9M53jl8fbAUlDX+WXbGFsM86Pnk+SfRLRPNEn+SQR79cBlcdFvSXg5T14Gr9NGGwEkhtgv3RwvquWK4YMwhocBYCkug5pC8Dl9SQCjmytTliTwxauH2fZBBiNnReIT+O3Q6ZqyRvZ8lsORLYVEDQ9g/l0jcPfsgUPU2gLrnoAdL4F5EMz7NaR8H9y9L/6xu6EpLY3GAwdoLS6hZu1aWnJyMM+cyaBfPdXlsOfDhdUs35FLTaMFi9XGhrRSXBT86PJ4bp4UJZeEhHAQi9VCZnUm2TXZ1LTUUNVURWZ1JumV6WRWZ2KxWQD7SJ5on2hGBI1gccJiEv0TSfRPJMQrhGZrM1u2bGHh7IUObo1wNhJeztOpodJWm7W985fJ3UBUgBdpxfZTncZB9qHFlnpXyN0OI64/63ESxoeQsbuE/evz2L8+D99gT0x+9stAhRlVKGDM3MFMvj6hZy57VGTBe9+Hwn0w6R6Y+yuHLKhY+fbbFP3mt2C1jwBwT0pi8CsvY54+vdP99+dV8cKGDNYdKcbk5kqor73ma0eH89D8JMJ8ZbInIfqKTdsoaSghpyaH3cW7+brwa46UH2mfC+WUEK8QEv0TmRI+pT2kxPrG4u7a+aVud1d3vFzkDxDRfRJezpOX0f4Ga7I2YXL5dq2bpFBv0ors4cXFywu32BgaK9K7DC9KKRbcM5Kq4gayvimjOKuGhppmLM1WUhbGMHxaOGb/HgoXh1fB6gfso4duWg5DF/XM43aDraGBkuf+ROXy5ZhnzCD0l7/AGBr67UKJHWitST1eyj82nmB7ZgU+HgZ+OjeJO6bG4Osps94K0RcsVgtF9UUU1BdwrPwYWwu3sq9kH83WZgBclAsjg0Zy27DbSA5IJs43Dj93P3zcfWQGWdFnJLycp1NvygZLAybjt+FlyCAzqWklNLdacTe44jVhIjUf5aKzv+Zc5038Qr0YOy+q5wvVGrK3wI6/w7G1EJFiX5vIP7rnn+scbE1NVC5fTvk/X8NaUUHAHXcQ8rNHUK5nD1nUWrP2m5O8sCGDY0W1hPl68IurhrJsYhRmd3mJCtEbrDYrxyqPsb9kf/ulnoLaAkobS9unwQdI8EvghqQbiPONY7D3YIYHDcfHzbHzQAkh3wzn6dSZlzNHHCWFetNq02SV1ZM8yAevCROoWrmSprQ0PJtq+nayt6Zq+5wtudvA0x9mPArTHwZD3/bStxQVkX/vfTQdOYJp6lSC7rsPr3GdTwxXWd/CYx8c5LPDRSSGmPnj0tFcMzoct/NZ9VoI0SWL1cLRiqMcLDtIVnUWngZPPA2elDWWkVebx+Hyw+2je3zdfUnwS2By+GTCzeGEmcIIN4cT6xtLiFf31g4Toi9IeDlPXoa28HLGLLvJg+zhJK2o1h5eJk6w71dsxDN/FyTM6ZsCm+tg+VIo2AtXPQdjbgZj35/Crd+5k4KHH0Y3NBL54ot4z+58BJHFamPVvgKe++I45fXNPLYgmbunx8nwZiG6yWqzUtlsX6unvLGckoYStp3cxub8zdRZ7JNoert5Y7FaaLI24efuR6Q5knnR85g4aCLjQ8cT6hUqU+ALp9Kr4UUpdSXwF8AVeFVr/Yczbv8zcOrbzQsI0Vr7td32DHAV4AKsAx7UWmsc5NSZlzOHS8cGmTC4qPZ+L8bQUIyDI2kobSIwd3vvhpesTfZ+La5G+9wthftg6b9g2LW995yd0DYbdakbqXjtNRp278YYGcng117DPTHxrH1bWm28vzefFzZkkF/ZyPBwH169PYUREec/7b8QA4lN28irzaO2pZaalhryavLIrskmqyaL7OpsTtafxKZtp93H392fedHzmB45nVFBowg12UfzdRxwIIQz67XwopRyBV4A5gH5wC6l1Gqt9ZFT+2itf9ph/weAsW0/TwGmAqPabt4CzABSe6ve72Iy2Pu5nHnZyM3gQlywqT28AHhNnEjt2gJ05kbU7Md7vpi6UvjyKdj3H3Azg4srKFdY/I8+DS62lhZqVq+m/F+v03LiBIawMEIe/Tl+NyzF1Ww6bV+L1cbK3Xm88FUGhdVNjI705VfXDGd2coj8xSdEB1ablbzaPNKr0vmg/AN+9e6vKGssO20fT4MnMT4xjAoexVVxVxHsGUygp329nkCPQMLN4Rhczv54l+Ai+ovePPMyEcjQWmcCKKVWANcCR7rY/3vAk20/a8ADcAMUYASKe7HW79Te5+WMy0YAQwb5sC+38tt9J0yg+v0PaD64B4+TByBs9MUXUHocNj4NeTuhOtceVqb9FGb8vM8vD1lra6l8620q/vMm1tIy3JOTCX/2GXyuvPKsUURaa9YfLeEPnx7lRGk946L8+P2SUVyeGCShRQxoWmuKG4pJr0wnoyqDjKqM9o6zp0b2uCk3ZkTNYFrENAI9AjEZTUR6R8plHjHgqd66EqOUugG4Umt9V9vvtwKTtNb3d7JvNLAdiNTavhSoUuqPwF3Yw8vftNZnncJQSv0Q+CFAaGjo+BUrVvRKW+rq6rB4WHii4AmWBSxjqvfU025ffaKFD9ItvDTXC0+DwqW8nODHf0HQ+HpsU8dwdNhD3X5O96YSfGrSUNqKd20GEQWfYHNxpzxwPHXmWMoDJ9Bg6tnRSnV1dZjN51gzSWvc9+zFe+VKXGtqaB42lIZ582hJTu50McesaisrjrWQVmljkElx0xA3xgS7OvRD9zvb2A8MhDaC87VTa02ltZKDDQc52HiQ3OZcGvW3E1/6uvoSbgwnzC2MMGMY4cZwvFu88fc+91Iizs7ZjuOFGgjt7I02zpo1a4/WOuXM7ZdKh91lwHsdgksCMBSIbLt9nVJqutZ6c8c7aa1fBl4GSElJ0TNnzuyV4lJTU5kwdQJPvPUEkXGRzBx++vPoQSV8kL6LBv9EFoy3l5zxwos0tWgGl24hdMwL4Df4/J7M0ghb/gy7noe2v75AwbhbcZn9BKHmYEKB+J5qXAepqal09v9QWyzUbdxI5VtvU//113gMH86gp57Cc2TnC0zmVTTwxy/S+Gh/IYEmN359XRLLJgzG6Or4EURdtbE/GQhthEu3ndXN1eTX5VNUX0ReTR6Z1ZlkVWeRWZ1JTUsNYF+35+qoq9snckvwS8DX/ex+X5dqG3vSQGgjDIx29mUbezO8FAAdv7Ej27Z1ZhlwX4ffFwPbtdZ1AEqpT4HJwOZO7tsnPA2eKFR77/2OLk8KZmyUH7/5+AgzhgQTZHbHPHs2lStWYIl1wbj9Jbjyd+d+guZa2PsGbHsRavJhxA0w9b/tfVrcfcDc9+t8aK2p/uADSv78PNayMlyDgwh59OcE3HILynD2S6e60cKLqRn8a2s2Crh/VgI/mhGHt4dMMCf6v8K6Ql49+CofZnx42syzAR4BxPnGcWXMlcT5xTE5fDJxvnEOrFQI59eb4WUXkKiUisUeWpYB/3XmTkqpZMAf2NZhcy5wt1Lq99gvG80Anu/FWr+Ti3LBZDRR13J2eHF1UTyzZBRX/XULT60+zN/+axyB37+DyhUrKC8bxaA9r8PIJRAxvvMH/+Zd+OQRaKqC6Kmw+O8Q2/m0+X2lOTOLoiefpGHXLjzHjyfwN7/GPG1ap6GlpdXG8h05/PXLdKoaLVw/NpJHrpAp/EX/ZtM2dhXtYnP+Zg6UHuBQ2SGUUixJXMLk8MkMMg0i0hzZ6RkVIcTF6bXworVuVUrdD3yOfaj0a1rrw0qp/wV2a61Xt+26DFhxxjDo94DZwEHsnXc/01qv6a1az5fJaOr0zAtAYqg3989O4E/rjrNkXAmzkiPwXbSIqk8/JSgxAMO/FsI1f7OPDDr8gf1O0dOg6CDs/w8Mvgyu+C1EnnVpr0/ZWloof/kVyv/xD5SnJ4N+/b/4LVmCcjn7ko/Wms8OFfH0Z8fILm9gakIg/2/hUIaHy4e16D8aWxtJq0gjrzaPgroCWqwtNFmbSM1LJa82DzcXN4YHDef24bezLHkZg0yDHF2yEP1er/Z50Vp/AnxyxrYnzvj9qU7uZwV+1Ju1XQhvN++z5nnp6J4Z8byxLYdV+wuYlRxC4A/vpvqjj6hwuYWQ4A3wwV32Hc2D7LPeHl0DKLj8Z/bZcF37tguSbmmhOSODuo0bqd/6NUFZWRyvq0M3N+Nz1VWEPvYohqCgTu9b1dDC/7z3DV8cKSYp1My/vj+BmUnBMgJC9AulDaV8lv0Zm/I3sbd4Ly22lvbbXJUrrsqVUcGjuHfMvcyNmouHoe8XOxViILtUOuw6ha4uG53iZnBhcnwgX58oR2uNe1wc3vPnU/nO+xj/52H8rrwRFZIIMdPtZ2Cq8sDaAoG90f32dFprGnbtomH7dhr3H6D5xAlaS0rsayEphceIEbQkxBM8bDjm6dMwTZnS5WPtyq7gwbf3UVrXzOMLh/L9qTEYLoHOuEJcCKvNSm5tLscqjnGs4hgHyw6yp3gPNm0jwS+BZcnLSAlNIcY3hghzBG6ufbvchhDibBJeusFsNLevBdKVKfGBrDlQyInSehJCzIT87BEKTp6k6KlfUx4dxeC//Q33UxNFne8IpIvUsHcfpX/6Ew27d4OLC+5JSZgmT8YYEYFbTDSmyZMxBAWRk5rKuHP0FLfaNC9syOD59ccZHODF+z+ewqhIvz5pgxA9QWtNRlUGm/I3kV6VTk51DieqT9DYah+ybHAxkOiXyN0j7+aquKuI9Y11cMVCiM5IeOkGk9FEYX3hOfeZHBcIwLYTZSSEmHGLjCTmnRXUbdjAyV/8ksLH/h8x76zodHXlntS4fz/Vaz+mbvMmLDm5uAYFEfrEL/G95tqzZr/9Li2tNtYdKebVLZnsy63iujHh/Pq6ETKKSFzyShpK2Fm0k8Nlh8mvyye9Mp2COvugxzBTGDE+MVyfeD3JAckkByQT7xuP0VVe10Jc6iS8dIPZzUx9S9d9XgCiA70I9/VgW2Y5t06OAUAphffs2dgeb6Tw4UeoXL6cgNtu69HadEsLzZmZNB06RNW779F44ADK3R2vSRMJuO02/BYvxsXLq9uPu/abQn615giltc1E+Hny3NLRXD8uQvq2iEtWWWMZH2d+zJoTa0irTAPAw9WDSO9IkgOSuXPEncwcPFNWSxbCiUl46Qaz0dzlaKNTlFJcFh/IhmMl2Gz6tFWSfRYupHrVR5Q8/xe8587FGB5+0TVpral65x2Kn3kW3WBfusAYFUXo44/ju3hxt8+yAFQ3WMipqOfVzVmsPlDI6EhfnrlhFJcnBuMqqz6LS0hGZQY7inaQVW1fpDCrOouSxhIARgWN4qHxDzEpbBJD/IfIuj5C9CMSXrrBbDTT0NrwnSuzTokP4oO9BaQV1zI0zKd9u1KKQU8+QebV15D/wH8T+eILGENDu1WDrbmZ6g9XYSkowBAcRP32HdR99RWmKVPwu2EJ7snJuMXEdDq0+bscKmvl93/eRFqxvV+PwUXx0Lwk7p0ZLx1yxSVBa01jayN5tXn8q/Rf7F29F7C/N+N847gs/DLifOOYFTVLJoIToh+T8NINJuO3K0t7u3l3ud/keHu/l69PlJ8WXgDcIiOJeO45Ch95hKwlNxD517/iNW5sp4/TnJlF1bvv0rBzJ8bISIyDBlH9ycdYS8vA1RWsVpTRSOhjj+J/660XFFgA0opqefbzNNYfbSY60JXHFiQTE2RiWJgPgwO6f6lJiJ5ksVrYXLCZNSfWsLVwa3vnWjflxt0j7+bGITfKQoVCDDASXrrB7GZfcKqupe6c4SXCz5PoQC9S00r4wbSzRyt4z55FzDsryLvvfnJvv53wp/+Az8KFWAoKKPr972lJz8BaX4+1rAwMBrzGjqXp2FFqv/gCr4kTCXr2j3hNnIC1uhrl4oKrb/cnhbPZNPvyKvn31zms+aYQk5uBpUlGfnPb5bgb5PS6cCytNUfKj7D6xGo+zfqUyuZKAjwCuDruaiK8I/B398eQa+DqcVc7ulQhhANIeOkGs7EtvHxHvxeAJeMi+dO643y4L5/FYyPPut09MZHYle+Qd//9FDz0MPXbtlHz2edgs2GecTkuZm/coqPxvfaa9onitNV62iglg3/3V5stqGrk7R25fLivgIKqRjyNrtwzI54fTo/jwK6vJbgIh8qqzuLL3C9Ze2ItJ6pP4ObixqyoWVwTfw2TwydjdPl2JFBqQarjChVCOJSEl244FV7ONcvuKffOjGdLehmPf3iI0ZF+xAWfvUy4q58fUf/8J4WPPkrVu+/hOW4c4c88jVvk2WEH6Pbwaq01nxwsYvmOHFptGptNsze3ErAvJvnw/CTmDQuVIc/CIRosDRyvPM6ximMcrTjKnuI95NTkADA2ZCxPTn6S+THz8XHz+Y5HEkIMNBJeusHkZu/zcj5nXgyuLvzle2NY+JfN3PfWPlbfPxVjJ51eXdzdiXjuORpvuw3PkSM7XfjwQuzPq+IPnx5le2YFcUEmgr3dAfjRjHhunhRFpL/0ZRF9p7q5un0G2yPlRzhWcYzsmmxs2gaAn7sfI4JGcPPQm5kROYNw88WPxBNC9F8SXrqh/bLROZYI6CjM15PfXz+Ke/6zh5W787h5UnSn+ykXF7zGdt5p93xZbZqssjr25lbxzq489uRU4u9l5DfXjeB7E6NkiLPoM6UNpRytOMrR8qMcrTjKsYpj7RPDAQwyDSI5IJkrYq5gaMBQhgYOlQ63QohukfDSDadGG53PmZdTrhgeyvhof/7vywyWjIvEw9jzfUr25FRy9xu7qai3Lx4XFeDFk1cPY2nKYMzucohF7ymqL+Kb0m/sZ1QqjnCs/BjlTeXtt0f7RDMyaCRLk5YyNHAoQwOG4u/R/b5aQgjRkXyzdcOpEUbn0+flFKUUP7tiCMte3s5/tudw1/SenXsiraiWO1/fhb+XkccXDmVUpC/xwebTJscToqdYbBYOlBxgU8EmNudvJqMqAwCDMhDnF8e0iGntIWVIwJD2wC+EED1Jwks3eBo8UahunXkBuCwukOmJQbywIYOl4wfj69UzHWSPFNZwx7924m5w4c0fTJI5WUSvOVF1grePvc0nWZ9Q21KLQRkYHzqe61KuIyU0hQT/BNxd3R1dphBigJDw0g0uygWT0XTefV46emT+EBa/uJWpT3/F4rER3Dktltig7v9Vam0bMfTPzVl8drgIPy8jK354mQQX0aMaLA18lfcV+0v2c6jsEIfLD+Pm4sYVMVcwO2o2l4Vd1j7vkRBC9DUJL91kMpq6feYFYPRgPz64dypvbMvmnd15vLMrjx/PjOfeWfHfObdKSW0Tm46XkZpWwub0MqobLXi7G/jv2QncOS0WPy+3C22OEIB9WH1RfRFHKo6wvXA7azPXUmepw2Q0MSxwGA+Oe5DrE68nwCPA0aUKIYSEl+7ydvPuVp+XjsYM9mPM4DE8uiCZ36w9yl++TOeDffksmxDF3KGhbM0o49NDJ4nw8+TWydG4G1z521cZfH6kCK0hyOzO3KGhzBwSzIwhwfjI/CziAuXV5nG4/LB9RFDbqKCq5ioAjC5G5kXPY2nSUsaFjsNFybpWQohLi4SXbrrQy0YdhXh78NfvjWXJ+Ehe+CqDZz9P49nP0wBIHuTNl0dLWLW/EAAfDwP3zoxnwYgwhoX5SEdcccEqmypZfWI1azPXcqziGAAGFwOJfonMiZrTPmw50T8RT4Ong6sVQoiuSXjpJrPRTG1LbY881oykYGYkBZNZWsfWjDImxQWSFOpNfXMraw4U0mixcsP4SJkBV1yUqqYqlh9bzptH3qTeUs/IoJH8fMLPGR86ngS/BIyu8voSQjgXCS/dZDKaKKwv7NHHjAs2n7Z8gMndwLKJUT36HGLgaLQ18v7x9/ks+zPSK9Pb512ZFz2PH4/+MYn+iQ6uUAghLo6El24yu5mpb7mwPi9C9JbShlI25G1gc/5mthZsxZJnIcYnhumR04nxiWFqxFSSA5IdXaYQQvQICS/dZDaaL2i0kRA9rbyxnB0nd7A2cy1bC7di0zbCTeFMNk/mnun3MCJohEy5L4TolyS8dJPZaKahtQGrzYqrS89P9S9EV6qbq9l2chu7i3azq2gXmdWZAIR4hXDniDu5KvYq4v3i2bhxIyODRzq4WiGE6D0SXrrp1HTn9a31+Lj5OLga0d/ZtI1thdv4MONDNuRuoMXWgsloYmzIWK5NuJaU0BSGBw6XIC2EGFAkvHTTqVlF61skvIjeU1xfzPrc9aw4toLsmmz83P1YOmQpC2IXMDxwOAYXeesKIQYu+QTsJrPRHl6k34voSVablYNlB9mUv4lN+ZtIq7TP+zMyaCR/mP4H5kfPlyHNQgjRRsJLN50KLxc6y64QYD+zUlBXQF5tHttObmNrwVaqmqtwVa6MCRnDT8f/lOkR02VYsxBCdELCSzeZ3Ox9XuTMi+iumpYa1pxYw6qMVe0z3AL4u/szPWI6l0dezuTwyfi6+zqwSiGEuPRJeOmm9stGF7lEgBg4GiwN/Ofof3j90OvUWmoZGjCUn6X8jHi/eMJMYUT7REuHWyGE6AYJL910arSRnHkR36XZ2szKtJW8evBVKpoqmBk5k3vG3MPwwOGOLk0IIZyahJdu8nbzBqTPi7Cz2Cw0tTbRbG3mUNkhUvNSSatIw2KzUNpYSkVTBZPCJvHA2AcYHTza0eUKIUS/IOGlmzwNniiUnHkZoArqCliXvY7tRdvJrs6msK4QjW6/3WQ0MSpoFB4GD+L94lmSuISJYRMdWLEQQvQ/El66yUW5YDKapM/LAFHdXM2XuV+yt3gvB8sOts9qm+CXwKjgUSyKW4S3mzdurm7E+MSQEpoiQ5qFEKKXSXi5AEGeQewp3oPFZsHoIl9U/U2LtYXN+ZtZk7mGTfmbsNgsBHgEMDJoJNclXMfc6LkM9h7s6DKFEGLAkvByAR4Y+wAPb3yYV755hXvH3OvockQP0Fqzr2QfazPX8nn259S01BDoEchNQ25iUfwihgUMk0UOhRDiEiHh5QLMj5nP1XlX8/I3LzMtYhqjgkc5uiRxAU4FlnU56/gq9ysK6wvxNHgyO2o2i+IWcVnYZTINvxBCXILkk/kCPTbpMXYX7+YXW3/Bh9d8KPN0OBGbtvFV7le8cvAVjpQfwc3Fjcnhk7lv7H3MiZrTPhxeCCHEpUnCywXydvPmoZSH+NnGn5Gan8qcqDmOLkl8h+zqbD6u+pjfvf87TtafZLD3YJ6c/CQLYhdIYBFCCCci4eUizI2aS7gpnDcOvyHh5RJV1VTFqwdf5au8r8irzUOhmBI+hYdTHmZO1By5LCSEEE5IPrkvgsHFwM1Db+bZ3c9yqOwQI4JGOLok0cambazKWMWf9/yZupY6pkRM4dZht+KR78HiuYsdXZ4QQoiL4OLoApzd9YnXYzKaeOPIG44uRWDvhLs+Zz1LVi/hya+fJM43jpVXr+SFOS/wveTv4W/wd3SJQgghLpKceblIZjczSxKXsPzoch4e/zChplBHlzQgNbY2sjZzLW8dfYuMqgxifGJ4evrTLIhdIEOchRCin5Hw0gOWJC7hjSNvsDF/IzcOudHR5fR7FpuF45XHyazKJL0ynQOlBzhcfphmazNDA4byu2m/Y0HsAunPIoQQ/ZR8uveAWN9Ywk3hbCnYIuGlF31T+g0fZXzEFzlfUNVcBdj7HQ0LHMaNQ25kTtQcxoWMkzMtQgjRz0l46QFKKaZFTGNt5losVousbdODaltq2Va4jTePvMn+0v14GjyZGTmT2dGzSfJPYrD3YFmiQQghBhgJLz1kasRUVh5fyd6SvUwKm+TocpxWaUMpe0r2sLd4L3uL93K88jgaTYQ5gkcnPsp1CdfJnCxCCDHASXjpIZPCJmFwMbC1YKuEl27IrcllT/Ee9hTvYW/JXvJq8wDwNHgyKngUPx79Y8aFjmN86HjpwyKEEAKQ8NJjTEYT40PGs7lgMw+lPOToci55h8oO8bd9f2Nr4VYA/N39GRsylpuG3MT40PEMCRgil4OEEEJ0SsJLD5oWMY3n9jxHUX0Rg0yDHF3OJaXF2sK7x99ld9FuTlSfIKs6Cz93Px4c9yCzB88m1jdWOtoKIYQ4LxJeetCp8LKlYAs3JN3g6HIuGVsKtvD0zqfJrskmyjuKBL8Erk+4nqVDlkr/FSGEEN0m4aUHxfvFE2GOYEPeBgkvQHVzNb/f+Xs+zvyYGJ8YXpr7EtMipjm6LCGEEE5OwksPUkoxJ2oObx97m7qWOsxuZkeX5BAt1hbWnFjD/+37P6qbq/nx6B9z98i7ZQi5EEKIHiFrG/WwedHzsNgsbMrf5OhS+ly9pZ7XD73Ole9fyVPbniLMFMaKRSu4d8y9ElyEEEL0GDnz0sNGBY8iyDOI9bnrWRi30NHl9InyxnKWH13OirQV1LbUMilsEr+d9lsuC7tMOuEKIYTocRJeepiLcmFO1BxWn1hNY2sjngZPR5fUa/Jr8/n34X/zYcaHtFhbmBs9lztH3MmIoBGOLk0IIUQ/JuGlF8yJmsM7ae/wdeHXzIma4+hyetzR8qO8fvh1Ps/+HKUU18Rfwx3D7yDWN9bRpQkhhBgAejW8KKWuBP4CuAKvaq3/cMbtfwZmtf3qBYRorf3abosCXgUGAxpYqLXO7s16e0rKoBR83X35IvuLfhNeGlsb+Tz7c1amreRg2UE8DZ7cMvQWbh12K6GmUEeXJ4QQYgDptfCilHIFXgDmAfnALqXUaq31kVP7aK1/2mH/B4CxHR7iDeC3Wut1SikzYOutWnua0cXI1XFXs/zocm4cciPjQ8c7uqQLllWdxcq0lXx04iNqW2qJ9Y3l0YmPsihuEb7uvo4uTwghxADUm2deJgIZWutMAKXUCuBa4EgX+38PeLJt32GAQWu9DkBrXdeLdfaKB8Y+QGpeKo9veZz3rn7P6YZN7yraxd8P/J2dRTsxuBiYGzWXG4fcSEpoinTCFUII4VBKa907D6zUDcCVWuu72n6/FZiktb6/k32jge1ApNbaqpS6DrgLaAFigfXAo1pr6xn3+yHwQ4DQ0NDxK1as6JW21NXVYTZ3P3xkNmXyfPHzTDBN4JbAWy75L/26ujrwhFWVq9hRvwM/Vz+meU9jsnkyPq4+ji6vR1zosXQmA6GNMDDaKW3sPwZCO3ujjbNmzdqjtU45c/ul0mF3GfBeh3BiAKZjv4yUC7wD3AH8s+OdtNYvAy8DpKSk6JkzZ/ZKcampqVzIY89kJvX76nn5m5dx9XHlqSlPEW4O7/kCL5JN29hSsIV3t73L4arDWG1W7hp5Fz8a9SM8DB6OLq9HXeixdCYDoY0wMNopbew/BkI7+7KNvRleCrB3tj0lsm1bZ5YB93X4PR/Y3+GS0yrgMs4IL87gvjH3EeIZwp/2/InrPrqO52Y8x/TI6Y4uC7BPKrfmxBrePPImubW5mFxMLE5czLLkZcT7xTu6PCGEEKJTvRledgGJSqlY7KFlGfBfZ+6klEoG/IFtZ9zXTykVrLUuBWYDu3ux1l7joly4KfkmpkdO5ycbfsJDqQ/xyvxXGBMyxiH1aK3ZXbybVRmrWJezjsbWRkYGjeTZsc9izDYy57L+MTpKCCFE/9Vr4UVr3aqUuh/4HPtQ6de01oeVUv8L7NZar27bdRmwQnfofNPW7+UR4Etl7yiyB3ilt2rtC+HmcF6a+xK3fXob9315H69f+TqJ/ol99vzVzdWsObGGlcdXklWdhdloZmHsQq5LuI7RwaNRSpGak9pn9QghhBAXqlf7vGitPwE+OWPbE2f8/lQX910HjOq14hwg0DOQf8z7B7d9ehu3fHILv5z8SxbFLQLsZ0Sarc3UWerwdvPG3dX9gp4jszqT0oZSDC4GGlsbyavN42DpQb7I+YJmazOjgkbx66m/5oqYK/r17L9CCCH6r0ulw+6AEekdyfKFy3l086M8tvkx3j76NjUtNRTWFdJiawFAoQjxCiHEKwQvgxcmo4lBpkGEeIVQ21JLUUMRlU2V1FvqcVWujA4ZTZxvHB9nfsz2k9vPek5vozfXxl/L0iFLSQ5I7usmCyGEED1KwosDhJnD+OcV/+TVg6+SmpdKon8iMwfPxNfdFy+DF9Ut1eTX5lPWWEZjayPlteXsLNpJnaUOgzIQagol0CMQk9FEQ2sDbx55k1ZbKyFeIfxk3E8YFTyKVlsr7q7uRPlEEegReMkP0xZCCCHOl4QXBzG4GLhn9D3cM/qe875Pg6UBd1d3XF1cT9ve2NpIVnUWiX6JGF2NPV2qEEIIcUmR8OJEvIxenW73NHgyLHBYH1cjhBBCOIaLowsQQgghhOgOCS9CCCGEcCoSXoQQQgjhVCS8CCGEEMKpSHgRQgghhFOR8CKEEEIIpyLhRQghhBBORcKLEEIIIZyKhBchhBBCOBUJL0IIIYRwKhJehBBCCOFUJLwIIYQQwqlIeBFCCCGEU5HwIoQQQginIuFFCCGEEE5Faa0dXUOPUEqVAjm99PBBQFkvPfalZCC0U9rYfwyEdkob+4+B0M7eaGO01jr4zI39Jrz0JqXUbq11iqPr6G0DoZ3Sxv5jILRT2th/DIR29mUb5bKREEIIIZyKhBchhBBCOBUJL+fnZUcX0EcGQjuljf3HQGintLH/GAjt7LM2Sp8XIYQQQjgVOfMihBBCCKci4UUIIYQQTkXCy3dQSl2plEpTSmUopR51dD09QSk1WCm1QSl1RCl1WCn1YNv2p5RSBUqp/W3/Fjq61ouhlMpWSh1sa8vutm0BSql1Sqn0tv/6O7rOi6GUGtLheO1XStUopX7i7MdSKfWaUqpEKXWow7ZOj52y+2vbe/QbpdQ4x1XePV2081ml1LG2tnyolPJr2x6jlGrscEz/7rDCu6GLNnb5+lRKPdZ2LNOUUlc4puru6aKN73RoX7ZSan/bdmc9jl19bzjmfam1ln9d/ANcgRNAHOAGHACGObquHmhXGDCu7Wdv4DgwDHgKeMTR9fVgO7OBoDO2PQM82vbzo8DTjq6zB9vrChQB0c5+LIHLgXHAoe86dsBC4FNAAZcBOxxd/0W2cz5gaPv56Q7tjOm4n7P866KNnb4+2z6HDgDuQGzb56+ro9twIW084/bngCec/Dh29b3hkPelnHk5t4lAhtY6U2vdAqwArnVwTRdNa31Sa7237eda4CgQ4diq+sy1wL/bfv43cJ3jSulxc4ATWuvemmm6z2itNwEVZ2zu6thdC7yh7bYDfkqpsD4p9CJ11k6t9Rda69a2X7cDkX1eWA/q4lh25Vpghda6WWudBWRg/xy+pJ2rjUopBdwIvN2nRfWwc3xvOOR9KeHl3CKAvA6/59PPvuSVUjHAWGBH26b7207xvebsl1QADXyhlNqjlPph27ZQrfXJtp+LgFDHlNYrlnH6B2R/OpbQ9bHrz+/TO7H/9XpKrFJqn1Jqo1JquqOK6iGdvT7747GcDhRrrdM7bHPq43jG94ZD3pcSXgYwpZQZeB/4ida6BngJiAfGACexn+p0ZtO01uOABcB9SqnLO96o7ec2+8VcAUopN+Aa4N22Tf3tWJ6mPx27riilHgdageVtm04CUVrrscBDwFtKKR9H1XeR+vXr8wzf4/Q/Kpz6OHbyvdGuL9+XEl7OrQAY3OH3yLZtTk8pZcT+Alyutf4AQGtdrLW2aq1twCs4wenac9FaF7T9twT4EHt7ik+dumz7b4njKuxRC4C9Wuti6H/Hsk1Xx67fvU+VUncAi4Cb274QaLuUUt728x7s/UGSHFbkRTjH67NfHUullAG4Hnjn1DZnPo6dfW/goPelhJdz2wUkKqVi2/6yXQasdnBNF63tGuw/gaNa6z912N7xeuRi4NCZ93UWSimTUsr71M/YO0Eewn78bm/b7XbgI8dU2ONO++uuPx3LDro6dquB29pGN1wGVHc4je10lFJXAv8DXKO1buiwPVgp5dr2cxyQCGQ6psqLc47X52pgmVLKXSkVi72NO/u6vh40Fzimtc4/tcFZj2NX3xs46n3p6B7Ml/o/7D2mj2NPx487up4eatM07Kf2vgH2t/1bCLwJHGzbvhoIc3StF9HGOOyjFg4Ah08dOyAQ+BJIB9YDAY6utQfaagLKAd8O25z6WGIPYicBC/Zr5T/o6thhH83wQtt79CCQ4uj6L7KdGdj7Cpx6b/69bd8lba/l/cBe4GpH138Rbezy9Qk83nYs04AFjq7/QtvYtv114J4z9nXW49jV94ZD3peyPIAQQgghnIpcNhJCCCGEU5HwIoQQQginIuFFCCGEEE5FwosQQgghnIqEFyGEEEI4FQkvQgin0bYib3+Ys0YIcREkvAghhBDCqUh4EUI4JaVUXNvidhMcXYsQom8ZHF2AEEJ0l1JqCLACuENrfcDR9Qgh+paEFyGEswnGvn7K9VrrI44uRgjR9+SykRDC2VQDudjXWhFCDEBy5kUI4WxasK9E/LlSqk5r/ZajCxJC9C0JL0IIp6O1rldKLQLWtQWY1Y6uSQjRd2RVaSGEEEI4FenzIoQQQginIuFFCCGEEE5FwosQQgghnIqEFyGEEEI4FQkvQgghhHAqEl6EEEII4VQkvAghhBDCqfx/25SImOiiRMgAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items/items', 'users/users', 'items_users/items_users', 'items/users', 'users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, metric='mae', cv_splits=5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QcBvOLFgeVtR"
      },
      "source": [
        "The strategies 'items/users' and 'users/items' reach pretty similar results to the ones of the paper: the best results are around $0.78$. The strategy 'items_users/items_users' reaches quite better performances: around $0.76$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JdR8E8UceVtS",
        "outputId": "10460f4d-b5a7-4691-bb36-576c65a84ea8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/users\n",
            "Best k: 11\n",
            "Best error: 0.7557501144821936\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items_users/items_users', 'items_users/users', 'items_users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, metric='mae', cv_splits=5)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C10ovBlOeVtS"
      },
      "source": [
        "As before, pretty much same results."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6AaIFZDoeVtS"
      },
      "source": [
        "## MovieLens 1M\n",
        "Let's move to the final dataset, which is a biggest one.\n",
        "- Around $1$ M ratings\n",
        "- Around $4000$ movies\n",
        "- Around $6000$ users"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "P8bkULlHeVtS"
      },
      "outputs": [],
      "source": [
        "movies_file = 'datasets/collaborative/movies_1M.dat'\n",
        "ratings_file = 'datasets/collaborative/ratings_1M.dat'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x1dZBoIleVtS"
      },
      "outputs": [],
      "source": [
        "mnames = ['movie_id', 'title', 'genres']\n",
        "df_movies = pd.read_table(movies_file, sep='::', header=None, names=mnames, engine='python', encoding='latin-1')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IEugSKD-eVtS",
        "outputId": "9a88ddaf-9bac-4f0b-e4ac-2ec6a2b62a1d"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>movie_id</th>\n",
              "      <th>title</th>\n",
              "      <th>genres</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Toy Story (1995)</td>\n",
              "      <td>Animation|Children's|Comedy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>Jumanji (1995)</td>\n",
              "      <td>Adventure|Children's|Fantasy</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>Grumpier Old Men (1995)</td>\n",
              "      <td>Comedy|Romance</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>Waiting to Exhale (1995)</td>\n",
              "      <td>Comedy|Drama</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>Father of the Bride Part II (1995)</td>\n",
              "      <td>Comedy</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   movie_id                               title                        genres\n",
              "0         1                    Toy Story (1995)   Animation|Children's|Comedy\n",
              "1         2                      Jumanji (1995)  Adventure|Children's|Fantasy\n",
              "2         3             Grumpier Old Men (1995)                Comedy|Romance\n",
              "3         4            Waiting to Exhale (1995)                  Comedy|Drama\n",
              "4         5  Father of the Bride Part II (1995)                        Comedy"
            ]
          },
          "execution_count": 174,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_movies.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sh8n8XCKeVtT",
        "outputId": "c6fe6ec5-6a7e-4268-9a85-1e2f4edc4289"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 3883 entries, 0 to 3882\n",
            "Data columns (total 3 columns):\n",
            " #   Column    Non-Null Count  Dtype \n",
            "---  ------    --------------  ----- \n",
            " 0   movie_id  3883 non-null   int64 \n",
            " 1   title     3883 non-null   object\n",
            " 2   genres    3883 non-null   object\n",
            "dtypes: int64(1), object(2)\n",
            "memory usage: 91.1+ KB\n"
          ]
        }
      ],
      "source": [
        "df_movies.info()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JjDXcxXxeVtT"
      },
      "outputs": [],
      "source": [
        "df_movies = df_movies.rename(columns={'movie_id':'movieId'})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jLdg0r5UeVtT",
        "outputId": "372d9606-5be8-44ff-a46b-e5f966842c15"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 3883 entries, 0 to 3882\n",
            "Data columns (total 3 columns):\n",
            " #   Column   Non-Null Count  Dtype \n",
            "---  ------   --------------  ----- \n",
            " 0   movieId  3883 non-null   int64 \n",
            " 1   title    3883 non-null   object\n",
            " 2   genres   3883 non-null   object\n",
            "dtypes: int64(1), object(2)\n",
            "memory usage: 91.1+ KB\n"
          ]
        }
      ],
      "source": [
        "df_movies.info()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EoBC8vk4eVtT"
      },
      "outputs": [],
      "source": [
        "rnames = ['user_id', 'movie_id', 'rating', 'timestamp']\n",
        "df_ratings = pd.read_table(ratings_file, sep='::', header=None, names=rnames, engine='python')\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bS21a4V2eVtT",
        "outputId": "65346926-7832-4f35-ac72-2409fe48f59a"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1193</td>\n",
              "      <td>5</td>\n",
              "      <td>978300760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>661</td>\n",
              "      <td>3</td>\n",
              "      <td>978302109</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>914</td>\n",
              "      <td>3</td>\n",
              "      <td>978301968</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>3408</td>\n",
              "      <td>4</td>\n",
              "      <td>978300275</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>2355</td>\n",
              "      <td>5</td>\n",
              "      <td>978824291</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id  movie_id  rating  timestamp\n",
              "0        1      1193       5  978300760\n",
              "1        1       661       3  978302109\n",
              "2        1       914       3  978301968\n",
              "3        1      3408       4  978300275\n",
              "4        1      2355       5  978824291"
            ]
          },
          "execution_count": 179,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_ratings.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K75mExkYeVtU",
        "outputId": "a2304367-77f6-4efd-94d5-ee8bfe8333c8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1000209 entries, 0 to 1000208\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count    Dtype\n",
            "---  ------     --------------    -----\n",
            " 0   user_id    1000209 non-null  int64\n",
            " 1   movie_id   1000209 non-null  int64\n",
            " 2   rating     1000209 non-null  int64\n",
            " 3   timestamp  1000209 non-null  int64\n",
            "dtypes: int64(4)\n",
            "memory usage: 30.5 MB\n"
          ]
        }
      ],
      "source": [
        "df_ratings.info()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5Ewcz4EyeVtU"
      },
      "outputs": [],
      "source": [
        "df_ratings = df_ratings.rename(columns={'movie_id':'movieId', 'user_id':'userId'})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rCu8X3gdeVtU",
        "outputId": "85e26d45-7548-41cb-d61c-b23908c84526"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1000209 entries, 0 to 1000208\n",
            "Data columns (total 4 columns):\n",
            " #   Column     Non-Null Count    Dtype\n",
            "---  ------     --------------    -----\n",
            " 0   userId     1000209 non-null  int64\n",
            " 1   movieId    1000209 non-null  int64\n",
            " 2   rating     1000209 non-null  int64\n",
            " 3   timestamp  1000209 non-null  int64\n",
            "dtypes: int64(4)\n",
            "memory usage: 30.5 MB\n"
          ]
        }
      ],
      "source": [
        "df_ratings.info()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ElpqhrmaeVtU"
      },
      "source": [
        "### Preprocessing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WsxbmW5jeVtU"
      },
      "outputs": [],
      "source": [
        "df_movies, df_ratings = preprocess_movies_ratings_coll(df_movies, df_ratings)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "I5w_JBj3eVtU",
        "outputId": "db42f41a-8cc9-4f62-d02b-c6278c9f7261"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "6040"
            ]
          },
          "execution_count": 184,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "users = df_ratings['userId'].unique()\n",
        "n_users = len(users)\n",
        "n_users"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pd30m43AeVtV",
        "outputId": "dc827eb5-b967-441a-bbfb-fa4987fd158a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sparsity factor: 0.9573532020200125\n"
          ]
        }
      ],
      "source": [
        "print(f'Sparsity factor: {1-df_ratings.shape[0]/(n_users*df_movies.shape[0])}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UYCy1Co3eVtV"
      },
      "source": [
        "A little bit more sparse than 100k"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YgigHY9qeVtV"
      },
      "source": [
        "### Evaluation\n",
        "[Here](https://paperswithcode.com/sota/collaborative-filtering-on-movielens-1m) (paperswithcode) we can find the SOTA results on this dataset. (Even if the evaluation strategy is not exactly the same, but at least we can get a sense of the numbers). \n",
        "\n",
        "We use RMSE (for comparison with paperswithcode)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Aw02t0iUeVtV",
        "outputId": "a8929241-82d9-4176-ac01-91ff89f511df"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 25\n",
            "Best error: 0.9081147417808068\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items/items', 'users/users', 'items_users/items_users', 'items/users', 'users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, k_range=(0,50))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KkZLo5YTeVtV"
      },
      "source": [
        "The strategy 'items_users_means/items_users_means' is better than the others also in this case. It reaches scores which were the SOTA in 2015/2016."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WIbSobMneVtV",
        "outputId": "8bac67bc-cdbf-4e24-f5fe-103c0292925c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Best strategy: items_users/items_users\n",
            "Best k: 32\n",
            "Best error: 0.9089351645776419\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 648x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "rating_strategies = ['items_users/items_users', 'items_users/users', 'items_users/items']\n",
        "compare_rating_strategies(df_movies, df_ratings, n_users, rating_strategies=rating_strategies, k_range=(0,50))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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