{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ML Reverse Lecture\n",
    "\n",
    "In this lab we will look at some examples on how to use ML for classification tasks over a music dataset.\n",
    "\n",
    "Specifically, we will use a Kaggle dataset with 218k songs [fetched from Spotify](https://github.com/tgel0/spotify-data). It has a schema that is almost identical to the one we used for lab 2, but with two additional columns: `genre`, and `popularity`. Schema columns are described in the [Spotify API docs](https://developer.spotify.com/documentation/web-api/reference/tracks/get-audio-features/).\n",
    "\n",
    "First, we will do some data exploration over the top 1k most popular songs in the dataset. Our goal in this phase is to understand some of the characteristics that these most popular songs have in common. We'll use visualization techniques and unsupervised ML (k-means clustering, PCA) to better understand the relationship between some of the features.\n",
    "\n",
    "Next, we'll try out a genre prediction task on the entire 218k songs dataset. We'll use supervised ML (classification) for this, and give you a chance to try out the same problem using regression.\n",
    "\n",
    "Finally, we'll see if we can use what we learned during the genre prediction task to try and predict song popularity.\n",
    "\n",
    "\n",
    "## Running this notebook\n",
    "\n",
    "To execute code from a cell, you can either click `Run` at the top, or type `shift+Enter` after clicking a cell.  You can either run the entire notebook (`Restart & Run All` from the `Kernel` drop-down), or run each cell individually.  If you choose the latter, note that it is important that you run cells in order, as later cells depend on earlier ones. And to be able to `Run All` successfully, you'll have to write code for answering some of the questions in the notebook.\n",
    "\n",
    "Once you open your notebook on the browser, and check that the cells are rendering correctly (e.g., try running the \"Python packages\" cell below), we're good to go from there."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python packages we'll need\n",
    "\n",
    "First, import the python packages we'll be using for the lab:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dataframes.\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Plotting.\n",
    "import matplotlib.pyplot as plt\n",
    "#%matplotlib notebook  # for interactive plots\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "\n",
    "# ML.\n",
    "from sklearn import tree\n",
    "from sklearn.cluster import DBSCAN, KMeans\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.metrics import classification_report, make_scorer, accuracy_score, roc_auc_score \n",
    "from sklearn.model_selection import cross_val_score, KFold, train_test_split\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC, LinearSVC\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from xgboost import XGBClassifier\n",
    "\n",
    "# Ignore warnings.\n",
    "import warnings\n",
    "warnings.simplefilter(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: data exploration\n",
    "\n",
    "First, we load our dataset into a pandas dataframe. Next, we store the top 1k most popular songs in a separate `top1k` dataframe.\n",
    "\n",
    "**Q1: Filter `df` for the top 1000 songs with largest `popularity` values, and store it on a `top1k` dataframe below.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/spotify_songs.csv')\n",
    "\n",
    "# Q1: YOUR CODE GOES HERE.\n",
    "# top1k = (...)\n",
    "\n",
    "# Q1: Sample answer.\n",
    "top1k = df.sort_values('popularity', ascending=False).head(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make sure that loading our data worked as we expect. A natural way to do that is to inspect the first few entries with [`head()`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.head.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>genre</th>\n",
       "      <th>artist_name</th>\n",
       "      <th>track_name</th>\n",
       "      <th>track_id</th>\n",
       "      <th>popularity</th>\n",
       "      <th>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>duration_ms</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>key</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>mode</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>time_signature</th>\n",
       "      <th>valence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Opera</td>\n",
       "      <td>Giuseppe Verdi</td>\n",
       "      <td>Stiffelio, Act III: Ei fugge! … Lina, pensai c...</td>\n",
       "      <td>7EsKYeHtTc4H4xWiTqSVZA</td>\n",
       "      <td>21</td>\n",
       "      <td>0.986</td>\n",
       "      <td>0.313</td>\n",
       "      <td>490867</td>\n",
       "      <td>0.23100</td>\n",
       "      <td>0.000431</td>\n",
       "      <td>C#</td>\n",
       "      <td>0.0964</td>\n",
       "      <td>-14.287</td>\n",
       "      <td>Major</td>\n",
       "      <td>0.0547</td>\n",
       "      <td>86.001</td>\n",
       "      <td>4/4</td>\n",
       "      <td>0.0886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Opera</td>\n",
       "      <td>Giacomo Puccini</td>\n",
       "      <td>Madama Butterfly / Act 1: ... E soffitto e pareti</td>\n",
       "      <td>7MfmRBvqaW0I6UTxXnad8p</td>\n",
       "      <td>18</td>\n",
       "      <td>0.972</td>\n",
       "      <td>0.360</td>\n",
       "      <td>176797</td>\n",
       "      <td>0.20100</td>\n",
       "      <td>0.028000</td>\n",
       "      <td>D#</td>\n",
       "      <td>0.1330</td>\n",
       "      <td>-19.794</td>\n",
       "      <td>Major</td>\n",
       "      <td>0.0581</td>\n",
       "      <td>131.798</td>\n",
       "      <td>4/4</td>\n",
       "      <td>0.3690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Opera</td>\n",
       "      <td>Giacomo Puccini</td>\n",
       "      <td>Turandot / Act 2: Gloria, gloria, o vincitore</td>\n",
       "      <td>7pBo1GDhIysyUMFXiDVoON</td>\n",
       "      <td>10</td>\n",
       "      <td>0.935</td>\n",
       "      <td>0.168</td>\n",
       "      <td>266184</td>\n",
       "      <td>0.47000</td>\n",
       "      <td>0.020400</td>\n",
       "      <td>C</td>\n",
       "      <td>0.3630</td>\n",
       "      <td>-8.415</td>\n",
       "      <td>Major</td>\n",
       "      <td>0.0383</td>\n",
       "      <td>75.126</td>\n",
       "      <td>3/4</td>\n",
       "      <td>0.0696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Opera</td>\n",
       "      <td>Giuseppe Verdi</td>\n",
       "      <td>Rigoletto, Act IV: Venti scudi hai tu detto?</td>\n",
       "      <td>02mvYZX5aKNzdqEo6jF20m</td>\n",
       "      <td>17</td>\n",
       "      <td>0.961</td>\n",
       "      <td>0.250</td>\n",
       "      <td>288573</td>\n",
       "      <td>0.00605</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>D</td>\n",
       "      <td>0.1200</td>\n",
       "      <td>-33.440</td>\n",
       "      <td>Major</td>\n",
       "      <td>0.0480</td>\n",
       "      <td>76.493</td>\n",
       "      <td>4/4</td>\n",
       "      <td>0.0380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Opera</td>\n",
       "      <td>Giuseppe Verdi</td>\n",
       "      <td>Don Carlo / Act 4: \"Ella giammai m'amò!\"</td>\n",
       "      <td>03TW0jwGMGhUabAjOpB1T9</td>\n",
       "      <td>19</td>\n",
       "      <td>0.985</td>\n",
       "      <td>0.142</td>\n",
       "      <td>629760</td>\n",
       "      <td>0.05800</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>D</td>\n",
       "      <td>0.0969</td>\n",
       "      <td>-23.625</td>\n",
       "      <td>Major</td>\n",
       "      <td>0.0493</td>\n",
       "      <td>172.935</td>\n",
       "      <td>4/4</td>\n",
       "      <td>0.0382</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   genre      artist_name                                         track_name  \\\n",
       "0  Opera   Giuseppe Verdi  Stiffelio, Act III: Ei fugge! … Lina, pensai c...   \n",
       "1  Opera  Giacomo Puccini  Madama Butterfly / Act 1: ... E soffitto e pareti   \n",
       "2  Opera  Giacomo Puccini      Turandot / Act 2: Gloria, gloria, o vincitore   \n",
       "3  Opera   Giuseppe Verdi       Rigoletto, Act IV: Venti scudi hai tu detto?   \n",
       "4  Opera   Giuseppe Verdi           Don Carlo / Act 4: \"Ella giammai m'amò!\"   \n",
       "\n",
       "                 track_id  popularity  acousticness  danceability  \\\n",
       "0  7EsKYeHtTc4H4xWiTqSVZA          21         0.986         0.313   \n",
       "1  7MfmRBvqaW0I6UTxXnad8p          18         0.972         0.360   \n",
       "2  7pBo1GDhIysyUMFXiDVoON          10         0.935         0.168   \n",
       "3  02mvYZX5aKNzdqEo6jF20m          17         0.961         0.250   \n",
       "4  03TW0jwGMGhUabAjOpB1T9          19         0.985         0.142   \n",
       "\n",
       "   duration_ms   energy  instrumentalness key  liveness  loudness   mode  \\\n",
       "0       490867  0.23100          0.000431  C#    0.0964   -14.287  Major   \n",
       "1       176797  0.20100          0.028000  D#    0.1330   -19.794  Major   \n",
       "2       266184  0.47000          0.020400   C    0.3630    -8.415  Major   \n",
       "3       288573  0.00605          0.000000   D    0.1200   -33.440  Major   \n",
       "4       629760  0.05800          0.146000   D    0.0969   -23.625  Major   \n",
       "\n",
       "   speechiness    tempo time_signature  valence  \n",
       "0       0.0547   86.001            4/4   0.0886  \n",
       "1       0.0581  131.798            4/4   0.3690  \n",
       "2       0.0383   75.126            3/4   0.0696  \n",
       "3       0.0480   76.493            4/4   0.0380  \n",
       "4       0.0493  172.935            4/4   0.0382  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that most of these columns are familiar to us, as they were present in our `top2018.csv` dataset from lab 2. The additional columns here are only `genre` and `popularity`.\n",
    "\n",
    "Let's examine the data types for each of the columns using [`info()`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.info.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 228159 entries, 0 to 228158\n",
      "Data columns (total 18 columns):\n",
      "genre               228159 non-null object\n",
      "artist_name         228159 non-null object\n",
      "track_name          228159 non-null object\n",
      "track_id            228159 non-null object\n",
      "popularity          228159 non-null int64\n",
      "acousticness        228159 non-null float64\n",
      "danceability        228159 non-null float64\n",
      "duration_ms         228159 non-null int64\n",
      "energy              228159 non-null float64\n",
      "instrumentalness    228159 non-null float64\n",
      "key                 228159 non-null object\n",
      "liveness            228159 non-null float64\n",
      "loudness            228159 non-null float64\n",
      "mode                228159 non-null object\n",
      "speechiness         228159 non-null float64\n",
      "tempo               228159 non-null float64\n",
      "time_signature      228159 non-null object\n",
      "valence             228159 non-null float64\n",
      "dtypes: float64(9), int64(2), object(7)\n",
      "memory usage: 31.3+ MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output of `df.info()` tells us that we have:\n",
    "- 7 `object` columns: (`genre`, `artist_name`, `track_name`, `track_id`, `key`, and `time_signature`)\n",
    "- 2 `int64` columns (`popularity` and `duration_ms`)\n",
    "- 9 `float64` (remaining columns)\n",
    "\n",
    "We can also take a look at aggregate stats for each of the numerical columns (both discrete `int64`, and continuous `float64`) the dataset has by running [`describe()`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.describe.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>popularity</th>\n",
       "      <th>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>duration_ms</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>valence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>2.281590e+05</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "      <td>228159.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>44.209130</td>\n",
       "      <td>0.351200</td>\n",
       "      <td>0.554198</td>\n",
       "      <td>2.366092e+05</td>\n",
       "      <td>0.580967</td>\n",
       "      <td>0.137310</td>\n",
       "      <td>0.214638</td>\n",
       "      <td>-9.354658</td>\n",
       "      <td>0.122442</td>\n",
       "      <td>117.423062</td>\n",
       "      <td>0.444795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>17.276599</td>\n",
       "      <td>0.351385</td>\n",
       "      <td>0.183949</td>\n",
       "      <td>1.166787e+05</td>\n",
       "      <td>0.260577</td>\n",
       "      <td>0.292447</td>\n",
       "      <td>0.196977</td>\n",
       "      <td>5.940994</td>\n",
       "      <td>0.186264</td>\n",
       "      <td>30.712458</td>\n",
       "      <td>0.255397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>0.056900</td>\n",
       "      <td>1.550900e+04</td>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.009670</td>\n",
       "      <td>-52.457000</td>\n",
       "      <td>0.022200</td>\n",
       "      <td>30.379000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>33.000000</td>\n",
       "      <td>0.030900</td>\n",
       "      <td>0.437000</td>\n",
       "      <td>1.862530e+05</td>\n",
       "      <td>0.405000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.097700</td>\n",
       "      <td>-11.287000</td>\n",
       "      <td>0.036800</td>\n",
       "      <td>92.734000</td>\n",
       "      <td>0.232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>47.000000</td>\n",
       "      <td>0.205000</td>\n",
       "      <td>0.570000</td>\n",
       "      <td>2.211730e+05</td>\n",
       "      <td>0.618000</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>0.128000</td>\n",
       "      <td>-7.515000</td>\n",
       "      <td>0.050600</td>\n",
       "      <td>115.347000</td>\n",
       "      <td>0.430000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>57.000000</td>\n",
       "      <td>0.689000</td>\n",
       "      <td>0.690000</td>\n",
       "      <td>2.648400e+05</td>\n",
       "      <td>0.793000</td>\n",
       "      <td>0.023400</td>\n",
       "      <td>0.263000</td>\n",
       "      <td>-5.415000</td>\n",
       "      <td>0.109000</td>\n",
       "      <td>138.887000</td>\n",
       "      <td>0.643000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.996000</td>\n",
       "      <td>0.987000</td>\n",
       "      <td>5.552917e+06</td>\n",
       "      <td>0.999000</td>\n",
       "      <td>0.999000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.585000</td>\n",
       "      <td>0.967000</td>\n",
       "      <td>239.848000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          popularity   acousticness   danceability   duration_ms  \\\n",
       "count  228159.000000  228159.000000  228159.000000  2.281590e+05   \n",
       "mean       44.209130       0.351200       0.554198  2.366092e+05   \n",
       "std        17.276599       0.351385       0.183949  1.166787e+05   \n",
       "min         0.000000       0.000001       0.056900  1.550900e+04   \n",
       "25%        33.000000       0.030900       0.437000  1.862530e+05   \n",
       "50%        47.000000       0.205000       0.570000  2.211730e+05   \n",
       "75%        57.000000       0.689000       0.690000  2.648400e+05   \n",
       "max       100.000000       0.996000       0.987000  5.552917e+06   \n",
       "\n",
       "              energy  instrumentalness       liveness       loudness  \\\n",
       "count  228159.000000     228159.000000  228159.000000  228159.000000   \n",
       "mean        0.580967          0.137310       0.214638      -9.354658   \n",
       "std         0.260577          0.292447       0.196977       5.940994   \n",
       "min         0.000020          0.000000       0.009670     -52.457000   \n",
       "25%         0.405000          0.000000       0.097700     -11.287000   \n",
       "50%         0.618000          0.000037       0.128000      -7.515000   \n",
       "75%         0.793000          0.023400       0.263000      -5.415000   \n",
       "max         0.999000          0.999000       1.000000       1.585000   \n",
       "\n",
       "         speechiness          tempo        valence  \n",
       "count  228159.000000  228159.000000  228159.000000  \n",
       "mean        0.122442     117.423062       0.444795  \n",
       "std         0.186264      30.712458       0.255397  \n",
       "min         0.022200      30.379000       0.000000  \n",
       "25%         0.036800      92.734000       0.232000  \n",
       "50%         0.050600     115.347000       0.430000  \n",
       "75%         0.109000     138.887000       0.643000  \n",
       "max         0.967000     239.848000       1.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Except for `popularity`, `duration_ms`, `loudness`, and `tempo`, most of the numerical features are already scaled between 0.0 and 1.0.\n",
    "\n",
    "**Q2: Looking at the documentation for [describe()](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.describe.html), what's a command to describe categorical features? Why is the output different for categorical vs numerical features?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "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>genre</th>\n",
       "      <th>artist_name</th>\n",
       "      <th>track_name</th>\n",
       "      <th>track_id</th>\n",
       "      <th>key</th>\n",
       "      <th>mode</th>\n",
       "      <th>time_signature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "      <td>228159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>26</td>\n",
       "      <td>13318</td>\n",
       "      <td>130254</td>\n",
       "      <td>153685</td>\n",
       "      <td>12</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>Comedy</td>\n",
       "      <td>Giuseppe Verdi</td>\n",
       "      <td>Home</td>\n",
       "      <td>6sVQNUvcVFTXvlk3ec0ngd</td>\n",
       "      <td>C</td>\n",
       "      <td>Major</td>\n",
       "      <td>4/4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>9681</td>\n",
       "      <td>1394</td>\n",
       "      <td>111</td>\n",
       "      <td>10</td>\n",
       "      <td>26538</td>\n",
       "      <td>147123</td>\n",
       "      <td>198092</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         genre     artist_name track_name                track_id     key  \\\n",
       "count   228159          228159     228159                  228159  228159   \n",
       "unique      26           13318     130254                  153685      12   \n",
       "top     Comedy  Giuseppe Verdi       Home  6sVQNUvcVFTXvlk3ec0ngd       C   \n",
       "freq      9681            1394        111                      10   26538   \n",
       "\n",
       "          mode time_signature  \n",
       "count   228159         228159  \n",
       "unique       2              5  \n",
       "top      Major            4/4  \n",
       "freq    147123         198092  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q2: YOUR CODE GOES HERE\n",
    "# df.describe(...)\n",
    "\n",
    "# Q2: Sample answer.\n",
    "df.describe(include=['O'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's check whether this dataset has missing data in the form of `null`s:\n",
    "\n",
    "**Q3: How would you check whether your data set has null values in any of its columns? Did you find any?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "genre               0\n",
       "artist_name         0\n",
       "track_name          0\n",
       "track_id            0\n",
       "popularity          0\n",
       "acousticness        0\n",
       "danceability        0\n",
       "duration_ms         0\n",
       "energy              0\n",
       "instrumentalness    0\n",
       "key                 0\n",
       "liveness            0\n",
       "loudness            0\n",
       "mode                0\n",
       "speechiness         0\n",
       "tempo               0\n",
       "time_signature      0\n",
       "valence             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q3: YOUR CODE GOES HERE.\n",
    "# df.(...)\n",
    "\n",
    "# Q3: Sample answer.\n",
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the dataset's [correlation matrix](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.corr.html) to see how column values co-occur with each other. This can help us spot features that may be predictive of other features in the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col7 {\n",
       "            background-color:  #8fb4d6;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col8 {\n",
       "            background-color:  #4295c3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col9 {\n",
       "            background-color:  #e7e3f0;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col10 {\n",
       "            background-color:  #cccfe5;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col0 {\n",
       "            background-color:  #4897c4;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col1 {\n",
       "            background-color:  #fdf5fa;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col2 {\n",
       "            background-color:  #4094c3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col3 {\n",
       "            background-color:  #f6eff7;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col4 {\n",
       "            background-color:  #045585;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col5 {\n",
       "            background-color:  #fff7fb;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col6 {\n",
       "            background-color:  #dcdaeb;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col7 {\n",
       "            background-color:  #023858;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col8 {\n",
       "            background-color:  #e6e2ef;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col9 {\n",
       "            background-color:  #a4bcda;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col10 {\n",
       "            background-color:  #589ec8;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col0 {\n",
       "            background-color:  #e5e1ef;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col1 {\n",
       "            background-color:  #6da6cd;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col2 {\n",
       "            background-color:  #a7bddb;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col3 {\n",
       "            background-color:  #f0eaf4;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col4 {\n",
       "            background-color:  #73a9cf;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col5 {\n",
       "            background-color:  #d6d6e9;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col6 {\n",
       "            background-color:  #4295c3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col7 {\n",
       "            background-color:  #9ab8d8;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col8 {\n",
       "            background-color:  #023858;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col9 {\n",
       "            background-color:  #ece7f2;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col10 {\n",
       "            background-color:  #c6cce3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col0 {\n",
       "            background-color:  #a5bddb;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col1 {\n",
       "            background-color:  #c6cce3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col2 {\n",
       "            background-color:  #c4cbe3;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col3 {\n",
       "            background-color:  #f1ebf4;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col4 {\n",
       "            background-color:  #5a9ec9;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col5 {\n",
       "            background-color:  #cacee5;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col6 {\n",
       "            background-color:  #ede7f2;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col7 {\n",
       "            background-color:  #5ea0ca;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col8 {\n",
       "            background-color:  #f1ebf5;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col9 {\n",
       "            background-color:  #023858;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col10 {\n",
       "            background-color:  #b1c2de;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col0 {\n",
       "            background-color:  #a4bcda;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col1 {\n",
       "            background-color:  #d6d6e9;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col2 {\n",
       "            background-color:  #2484ba;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col3 {\n",
       "            background-color:  #fff7fb;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col4 {\n",
       "            background-color:  #2081b9;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col5 {\n",
       "            background-color:  #e8e4f0;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col6 {\n",
       "            background-color:  #dfddec;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col7 {\n",
       "            background-color:  #2c89bd;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col8 {\n",
       "            background-color:  #dddbec;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col9 {\n",
       "            background-color:  #c2cbe2;\n",
       "            color:  #000000;\n",
       "        }    #T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col10 {\n",
       "            background-color:  #023858;\n",
       "            color:  #f1f1f1;\n",
       "        }</style><table id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >popularity</th>        <th class=\"col_heading level0 col1\" >acousticness</th>        <th class=\"col_heading level0 col2\" >danceability</th>        <th class=\"col_heading level0 col3\" >duration_ms</th>        <th class=\"col_heading level0 col4\" >energy</th>        <th class=\"col_heading level0 col5\" >instrumentalness</th>        <th class=\"col_heading level0 col6\" >liveness</th>        <th class=\"col_heading level0 col7\" >loudness</th>        <th class=\"col_heading level0 col8\" >speechiness</th>        <th class=\"col_heading level0 col9\" >tempo</th>        <th class=\"col_heading level0 col10\" >valence</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row0\" class=\"row_heading level0 row0\" >popularity</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col1\" class=\"data row0 col1\" >-0.42</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col2\" class=\"data row0 col2\" >0.29</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col3\" class=\"data row0 col3\" >-0.041</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col4\" class=\"data row0 col4\" >0.28</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col5\" class=\"data row0 col5\" >-0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col6\" class=\"data row0 col6\" >-0.2</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col7\" class=\"data row0 col7\" >0.41</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col8\" class=\"data row0 col8\" >-0.19</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col9\" class=\"data row0 col9\" >0.11</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row0_col10\" class=\"data row0 col10\" >0.12</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row1\" class=\"row_heading level0 row1\" >acousticness</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col0\" class=\"data row1 col0\" >-0.42</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col1\" class=\"data row1 col1\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col2\" class=\"data row1 col2\" >-0.38</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col3\" class=\"data row1 col3\" >0.035</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col4\" class=\"data row1 col4\" >-0.72</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col5\" class=\"data row1 col5\" >0.32</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col6\" class=\"data row1 col6\" >0.086</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col7\" class=\"data row1 col7\" >-0.7</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col8\" class=\"data row1 col8\" >0.17</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col9\" class=\"data row1 col9\" >-0.24</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row1_col10\" class=\"data row1 col10\" >-0.34</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row2\" class=\"row_heading level0 row2\" >danceability</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col0\" class=\"data row2 col0\" >0.29</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col1\" class=\"data row2 col1\" >-0.38</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col2\" class=\"data row2 col2\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col3\" class=\"data row2 col3\" >-0.12</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col4\" class=\"data row2 col4\" >0.34</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col5\" class=\"data row2 col5\" >-0.36</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col6\" class=\"data row2 col6\" >-0.034</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col7\" class=\"data row2 col7\" >0.45</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col8\" class=\"data row2 col8\" >0.14</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col9\" class=\"data row2 col9\" >0.019</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row2_col10\" class=\"data row2 col10\" >0.54</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row3\" class=\"row_heading level0 row3\" >duration_ms</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col0\" class=\"data row3 col0\" >-0.041</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col1\" class=\"data row3 col1\" >0.035</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col2\" class=\"data row3 col2\" >-0.12</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col3\" class=\"data row3 col3\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col4\" class=\"data row3 col4\" >-0.058</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col5\" class=\"data row3 col5\" >0.095</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col6\" class=\"data row3 col6\" >0.0068</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col7\" class=\"data row3 col7\" >-0.069</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col8\" class=\"data row3 col8\" >-0.018</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col9\" class=\"data row3 col9\" >-0.028</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row3_col10\" class=\"data row3 col10\" >-0.14</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row4\" class=\"row_heading level0 row4\" >energy</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col0\" class=\"data row4 col0\" >0.28</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col1\" class=\"data row4 col1\" >-0.72</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col2\" class=\"data row4 col2\" >0.34</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col3\" class=\"data row4 col3\" >-0.058</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col4\" class=\"data row4 col4\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col5\" class=\"data row4 col5\" >-0.39</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col6\" class=\"data row4 col6\" >0.18</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col7\" class=\"data row4 col7\" >0.82</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col8\" class=\"data row4 col8\" >0.14</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col9\" class=\"data row4 col9\" >0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row4_col10\" class=\"data row4 col10\" >0.45</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row5\" class=\"row_heading level0 row5\" >instrumentalness</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col0\" class=\"data row5 col0\" >-0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col1\" class=\"data row5 col1\" >0.32</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col2\" class=\"data row5 col2\" >-0.36</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col3\" class=\"data row5 col3\" >0.095</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col4\" class=\"data row5 col4\" >-0.39</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col5\" class=\"data row5 col5\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col6\" class=\"data row5 col6\" >-0.13</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col7\" class=\"data row5 col7\" >-0.52</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col8\" class=\"data row5 col8\" >-0.17</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col9\" class=\"data row5 col9\" >-0.11</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row5_col10\" class=\"data row5 col10\" >-0.3</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row6\" class=\"row_heading level0 row6\" >liveness</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col0\" class=\"data row6 col0\" >-0.2</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col1\" class=\"data row6 col1\" >0.086</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col2\" class=\"data row6 col2\" >-0.034</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col3\" class=\"data row6 col3\" >0.0068</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col4\" class=\"data row6 col4\" >0.18</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col5\" class=\"data row6 col5\" >-0.13</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col6\" class=\"data row6 col6\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col7\" class=\"data row6 col7\" >0.036</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col8\" class=\"data row6 col8\" >0.52</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col9\" class=\"data row6 col9\" >-0.056</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row6_col10\" class=\"data row6 col10\" >0.018</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row7\" class=\"row_heading level0 row7\" >loudness</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col0\" class=\"data row7 col0\" >0.41</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col1\" class=\"data row7 col1\" >-0.7</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col2\" class=\"data row7 col2\" >0.45</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col3\" class=\"data row7 col3\" >-0.069</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col4\" class=\"data row7 col4\" >0.82</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col5\" class=\"data row7 col5\" >-0.52</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col6\" class=\"data row7 col6\" >0.036</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col7\" class=\"data row7 col7\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col8\" class=\"data row7 col8\" >-0.0089</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col9\" class=\"data row7 col9\" >0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row7_col10\" class=\"data row7 col10\" >0.41</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row8\" class=\"row_heading level0 row8\" >speechiness</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col0\" class=\"data row8 col0\" >-0.19</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col1\" class=\"data row8 col1\" >0.17</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col2\" class=\"data row8 col2\" >0.14</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col3\" class=\"data row8 col3\" >-0.018</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col4\" class=\"data row8 col4\" >0.14</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col5\" class=\"data row8 col5\" >-0.17</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col6\" class=\"data row8 col6\" >0.52</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col7\" class=\"data row8 col7\" >-0.0089</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col8\" class=\"data row8 col8\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col9\" class=\"data row8 col9\" >-0.086</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row8_col10\" class=\"data row8 col10\" >0.035</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row9\" class=\"row_heading level0 row9\" >tempo</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col0\" class=\"data row9 col0\" >0.11</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col1\" class=\"data row9 col1\" >-0.24</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col2\" class=\"data row9 col2\" >0.019</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col3\" class=\"data row9 col3\" >-0.028</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col4\" class=\"data row9 col4\" >0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col5\" class=\"data row9 col5\" >-0.11</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col6\" class=\"data row9 col6\" >-0.056</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col7\" class=\"data row9 col7\" >0.23</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col8\" class=\"data row9 col8\" >-0.086</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col9\" class=\"data row9 col9\" >1</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row9_col10\" class=\"data row9 col10\" >0.12</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002level0_row10\" class=\"row_heading level0 row10\" >valence</th>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col0\" class=\"data row10 col0\" >0.12</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col1\" class=\"data row10 col1\" >-0.34</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col2\" class=\"data row10 col2\" >0.54</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col3\" class=\"data row10 col3\" >-0.14</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col4\" class=\"data row10 col4\" >0.45</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col5\" class=\"data row10 col5\" >-0.3</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col6\" class=\"data row10 col6\" >0.018</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col7\" class=\"data row10 col7\" >0.41</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col8\" class=\"data row10 col8\" >0.035</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col9\" class=\"data row10 col9\" >0.12</td>\n",
       "                        <td id=\"T_9e58dd2c_e61e_11e9_900f_0242ac110002row10_col10\" class=\"data row10 col10\" >1</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f8b40ef8860>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr = df.corr()\n",
    "corr.style.background_gradient().set_precision(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that `energy` and `loudness` is the pair of features with the strongest positive correlation, followed by `valence` and `danceability`. We also see strong negative correlation between `acousticness` and a few other features. Finally, some of these have a medium to strong correlation with popularity.\n",
    "\n",
    "**Q4: Why don't we see `genre`, `key`, and `time signature` on the correlation matrix? What could we do to address this?**\n",
    "\n",
    "**A:** This is because they're categorical features, and the correlation matrix can only correlate values for numerical (discrete or continuous) features. One way to include the categorical features in a correlation matrix is to map each unique string to an integer value. This preprocessing step is also known as [\"one-hot encoding\"](https://www.kaggle.com/dansbecker/using-categorical-data-with-one-hot-encoding). You can do this manually, as we do later in Part 3 of this notebook, or you can use `sklearn`'s [`OneHotEncoder`](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.OneHotEncoder.html#targetText=sklearn.preprocessing%20.OneHotEncoder)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at the [documentation for these features](https://developer.spotify.com/documentation/web-api/reference/tracks/get-audio-features/), we see that `energy` is defined as a \"perceptual measure of intensity and activity\".  The example they give for this is death metal (high energy) vs a Bach prelude (low energy). Similarly, `valence` is a score between `0.0` and `1.0` indicating how positive the song is. So it makes sense that the `energy` would be correlated with `loudness`, and `valence` with `danceability`.\n",
    "\n",
    "Now let's examine the distribution values for some of the features we mention above. In particular, let's look at the `top1k` subset, as we may have a better intuition for popular songs. For example, are the `top1k` songs more biased towards high `danceability`?\n",
    "\n",
    "We can use [`seaborn's distplot()`](http://seaborn.pydata.org/generated/seaborn.distplot.html) to plot a histogram for the `danceability` column:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Danceability distribution for top 1k songs')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(top1k['danceability']).set_title('Danceability distribution for top 1k songs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about `energy` and `acousticness`? From the API docs: acousticness is a score between 0.0 and 1.0 that indicates Spotify's confidence that the song is \"acoustic\", e.g., live performances would have a score close to or equal to 1.0. \n",
    "\n",
    "**Q5: Plot the distribution for energy and acousticness below.  What is the mean for each?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean energy:  0.6502619999999999\n",
      "Mean acousticness:  0.197825639\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8b3fed6c18>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Q5: YOUR CODE GOES HERE\n",
    "# (...)\n",
    "\n",
    "# Q5: Sample answer.\n",
    "print('Mean energy: ', top1k['energy'].mean())\n",
    "print('Mean acousticness: ', top1k['acousticness'].mean())\n",
    "\n",
    "# All 3 series in one plot, for easier comparison.\n",
    "p = sns.distplot(top1k['danceability'], label='danceability')\n",
    "sns.distplot(top1k['energy'], label='energy')\n",
    "sns.distplot(top1k['acousticness'], label='acousticness')\n",
    "p.set_title('Energy and Acousticness distribution for top 1k songs')\n",
    "p.set_xlabel('')  # remove x-axis label, o/w it uses the name from the last series that was added\n",
    "p.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q6: Discuss with the person next to you: what have we learned so far on the relationship between top1k songs and these 3 features above? How do you think this may affect our `popularity` prediction task?**\n",
    "\n",
    "**In other words, what kind of song would you write if you were trying to make it to the top as a musician, just based on these 3 features alone?**\n",
    "\n",
    "**A:** Low on acousticness, and high on both energy and danceability, i.e., make sure you write songs that are recorded in a studio, and that are both danceable and suitable for a gym workout ;)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: unsupervised ML with k-means clustering\n",
    "\n",
    "What if instead examining feature by feature we were to try and group songs by how similar they are in terms of these features?\n",
    "\n",
    "If you think of each song as a vector in a multidimensional space, where each dimension is a feature in the dataset, we can use co-sine similarity as a \"similarity\" metric to group together (or \"cluster\") songs that are similar.  And using the same idea, we can also \"profile\" each group, or \"cluster\".\n",
    "\n",
    "An unsupervised ML algorithm that can help us here is [K-means clustering](https://en.wikipedia.org/wiki/K-means_clustering). `K` stands for the number of clusters (or groups) you want to have. The term `mean` refers to the method you use to assign each element in the dataset to a target cluster: by choosing the nearest mean (also known as the \"centroid\" element, representing the cluster) to that element.\n",
    "\n",
    "Specifically, for our case, given a set of songs where each song is a `d-`dimensional real vector, `k-`means clustering aims to partition the set of songs into `k` clusters so as to minimize the within-cluster sum of squares (aka intra-cluster variance).\n",
    "\n",
    "At this point we don't know yet how many clusters we'll need, but let's give it a try using some of the features we've seen so far, plus other characteristics such as `speechiness` (i.e., amount of vocals in the song), and `instrumentalness`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We exclude non-numerical features, and those that are too fine-grained, such as \"key\", or too coarse-grained,\n",
    "# such as \"mode\".\n",
    "df_numerical = top1k.select_dtypes(exclude=[np.object])\n",
    "cluster_features = ['acousticness', 'danceability', 'energy', 'speechiness', 'instrumentalness']\n",
    "df_clusters = df_numerical[cluster_features]\n",
    "\n",
    "# numpy array with features\n",
    "X = np.array(df_clusters)\n",
    "\n",
    "# Q7: Do we need this scaling code?\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X)\n",
    "X = scaler.transform(X)\n",
    "\n",
    "# Hint: does this help you decide?\n",
    "#top1k[cluster_features].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many clusters should we use? If we pick too few, we get too many songs that don't quite \"fit in\" with that cluster (i.e., intra-cluster variance, or error, is too large). If we pick too many, error is minimized, but our clusters are too small.\n",
    "\n",
    "To figure out the \"sweet spot\", we can plot how the error decays as a function of the number of clusters we use.  This will give us a \"elbow\" shaped curve, and we can use the point at which the curve turns \"smooth\" as our number of clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist = []\n",
    "for k in range(1, 10):\n",
    "    km = KMeans(n_clusters=k, init='k-means++', random_state=1337)\n",
    "    km = km.fit(X)\n",
    "    dist.append(km.inertia_)\n",
    "    \n",
    "plt.plot(range(1, 10), dist, 'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Variance')\n",
    "plt.title('Elbow Method for choosing k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q7: We used co-sine distance between songs (represented as n-dimensional vectors) to cluster them a 5-D space (n=5 features).  A [`StandardScaler`](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html) standardizes features by removing the mean and scaling to unit variance.  Do we need to use that scaler in our features (see code 2 cells above)? Plot the elbow method above both with and without scaler to see the difference.**\n",
    "\n",
    "**A:** In general, it depends. When you have features with large values, and you don't want those to have larger weight on the distance calculation, then you want to scale. In our case, all 5 features have values ranging from 0.0 to 1.0. They're not scaled yet, however, as you can see from the output of `top1k[cluster_features].describe()`. You can also confirm that scaling is needed by looking at the elbow curve results: the breakpoint ends up being much earlier (at `k=2`) without scaling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the \"Elbow Method\" curve above that at `k=4` our curve starts turning smooth. We can use either `k=4` or `k=5` as our number of clusters for k-means below. We'll go with `k=5`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# k-means clustering\n",
    "kmeans = KMeans(n_clusters=5, random_state=1337)\n",
    "kmeans.fit(X)\n",
    "y = kmeans.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now try and visualize the clusters in a 2-D space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Features:\n",
      " ['acousticness', 'danceability', 'energy', 'speechiness', 'instrumentalness']\n",
      "Centroids:\n",
      " [[ 0.26738476  0.11318532 -0.18755981 -0.47252187  5.58850807]\n",
      " [-0.14284159  0.62984688  0.1625441  -0.31638741 -0.11293294]\n",
      " [-0.5010746  -0.79433895  0.56679914 -0.42829863 -0.13576529]\n",
      " [-0.40045451  0.66232282 -0.32472655  1.73669593 -0.15165669]\n",
      " [ 1.84854124 -0.64607645 -1.22526308 -0.19348971 -0.10663343]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the clusters\n",
    "centers = kmeans.cluster_centers_\n",
    "print('Features:\\n', cluster_features)\n",
    "print('Centroids:\\n', centers)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='viridis')\n",
    "plt.scatter(centers[:, 0], centers[:, 1], c='red', s=200, alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The centroid values for each dimension tells us some information on what the cluster profiles are, e.g., the last cluster is high on acousticness and low on both danceability and energy, so it's likely capturing live performances.\n",
    "\n",
    "But otherwise, as it turns out, directly visualizing the clusters in a 2-D space isn't so helpful for us at this point.\n",
    "\n",
    "First, we're using a 5-D dimensional space for clustering, so without doing something smart about how we reduce the number of dimensions when polotting, we're losing a lot of information on the visualization above.  Second, most songs in this dataset are highly biased towards one end of each of some features (e.g., we have a lot more danceable songs than we have non-danceable ones), so we'll have a lot of clusters fairly close to each other.\n",
    "\n",
    "We have a few options for dimensionality reduction that can help us here. The first one is Principal Component Analysis ([PCA](https://en.wikipedia.org/wiki/Principal_component_analysis)). Using PCA, we can tell what is the smallest set of features that contain the most information about our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEGCAYAAAB/+QKOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAbwElEQVR4nO3dfbQdVZ3m8W/6gjc4vjQi02pACRqfDihgJwYRB5QXOzYNOApDQGlU2lfwpRm1oXVAom1HXfY0PcbGFtJqi0YEtCMEAr3AdxmTCwjCXc8YMUAyzlIBQQ25JCHzR1Xsk0vdk7o3qXNOznk+a911qnbVrvrtg55fau+qXdO2bNlCRETEeH/Q7QAiIqI3JUFERESlJIiIiKiUBBEREZWSICIiotJu3Q5gZ7ntttu2DA8PdzuMtsbGxuj1GJsyyG2HwW7/ILcder/969ev/9WcOXP2rtrWNwlieHiY2bNndzuMtkZHR3s+xqYMctthsNs/yG2H3m//yMjIPRNtSxdTRERUavQKQtJ84CJgCLjE9qJx298GnAVsBn4LvMX2XeW284Azy23vsr2iyVgjImJbjV1BSBoCFgOvAg4ATpV0wLjdvmT7hbYPAT4O/H1Z9wBgAXAgMB/4dHm8iIjokCa7mOYBq23fbftRYClwYusOth9uWf1PwNZ5P04Eltoes/0zYHV5vIiI6JAmu5hmAPe1rK8FDh2/k6SzgHOAJwBHtdS9eVzdGe1ONjY2xujo6I7E27gNGzb0fIxNGeS2w2C3f5DbDrt2+7t+F5PtxcBiSacBHwTOmMpxchdTbxvktsNgt3+Q2w693/6RkZEJtzXZxbQO2LdlfZ+ybCJLgVdPsW5EROxkTSaIlcAsSTMlPYFi0HlZ6w6SZrWsHgf8pFxeBiyQNCxpJjAL+GGDsUZExDiNdTHZ3iTpbGAFxW2uS2zfKWkhsMr2MuBsSccAG4EHKbuXyv0uB+4CNgFn2d7cVKwREfF4jY5B2F4OLB9Xdn7L8rvb1P1b4G+bi25bGzZuZvruzd5J24l+yE60IyIGQ9cHqXvF9N2H2O/ca7odxg5bs+i4bocQEX0iU21ERESlJIiIiKiUBBEREZWSICIiolISREREVEqCiIiISkkQERFRKQkiIiIqJUFERESlJIiIiKiUBBEREZWSICIiolISREREVEqCiIiISkkQERFRKQkiIiIqJUFERESlJIiIiKiUBBEREZWSIIINGzc3fo7Zs2c3fg7oTFsiBsVu3Q4gum/67kPsd+413Q5jp1iz6LhuhxDRN3IFERERlZIgIiKiUhJERERUSoKIiIhKjQ5SS5oPXAQMAZfYXjRu+znAXwKbgF8Cb7J9T7ltM3BHueu9tk9oMtaIiNhWYwlC0hCwGDgWWAuslLTM9l0tu90KzLW9XtLbgY8Dp5TbHrF9SFPxRUREe01eQcwDVtu+G0DSUuBE4PcJwvZNLfvfDLy+wXgiImISmkwQM4D7WtbXAoe22f9M4NqW9emSVlF0Py2y/fV2JxsbG2N0dHSqsXbsQa5OmOz30E9th8m3vxM2bNjQk3F1wiC3HXbt9vfEg3KSXg/MBY5sKX6O7XWS9gdulHSH7Z9OdIzh4eG++6GbqkH/Hnqx/aOjoz0ZVycMctuh99s/MjIy4bYm72JaB+zbsr5PWbYNSccAHwBOsD22tdz2uvLzbuCbwIsajDUiIsZp8gpiJTBL0kyKxLAAOK11B0kvAj4DzLf9i5byPYH1tsckPR04nGIAOyIiOqSxKwjbm4CzgRXAKHC57TslLZS09ZbVTwBPAr4q6TZJy8ry2cAqST8CbqIYg7iLiIjomEbHIGwvB5aPKzu/ZfmYCep9H3hhk7FFRER7eZI6IiIqJUFERESlJIiIiKiUBBEREZWSICIiolISREREVEqCiIiISm2fg5C0D8UT0P8FeBbwCPBj4BrgWtuPNR5hRER0xYRXEJL+BVgCPAp8DDgVeAfw78B84LuSjuhEkBER0XntriA+afvHFeU/Bq6S9ATg2c2EFRER3TZhgqhKDpKeCzzR9h22HwVWNxlcRER0T+25mCT9DfA84DFJw7ZPby6siIjotgkThKR3AYttby6LDrZ9Srnt9k4EFxER3dPuNtf7getapua+XtJ1kq6nmMI7IiL62IQJwvZlwPHAQeV7GkaA1wAn235fh+KLiIgu2d6Dcs8FLgfeApwFXATs0XRQERHRfe3GID4HbASeCKyz/ebyFaGflbTS9sIOxRgREV3Q7i6mF9k+GEDSrQC2bwWOl3RiJ4KLiIjuaZcgrpO0Atgd+FLrBtv/1mhUERHRde0elPtrSU8BHrP92w7GFBERPaDdXEyvB347UXKQ9FxJL2sssoiI6Kp2XUx7AbdKGqG4xfWXwHSKp6mPBH4FnNt4hBER0RXtupgukvQp4CjgcOAgium+R4HTbd/bmRAjIqIb2s7FVE6zcUP5FxERAyRvlIuIiEpJEBERUan2dN9TIWk+xfQcQ8AltheN234O8JfAJopB8DfZvqfcdgbwwXLXj9j+fJOxRkTEtrZ7BSHpjyRdKunacv0ASWfWqDcELAZeBRwAnCrpgHG73QrMtX0QcAXw8bLu04ALgEOBecAFkvas36yIiNhRdbqYPkcxvfezyvX/A7ynRr15wGrbd5dvn1sKbDNFh+2bbK8vV28G9imX/xS4wfYDth+kGCSfX+OcERGxk9TpYnq67cslnQdge5OkzdurBMwA7mtZX0txRTCRM4Fr29Sd0e5kY2NjjI6O1gir2uzZs6dct9dM9nvop7bD5NvfCRs2bOjJuDphkNsOu3b76ySI30naC9gCIOklwEM7M4jyqe25FA/gTcnw8HDf/dBN1aB/D73Y/tHR0Z6MqxMGue3Q++0fGRmZcFudBHEOsAx4rqTvAXsDJ9Wotw7Yt2V9n7JsG5KOAT4AHGl7rKXuy8fV/WaNc0ZExE6y3QRh+xZJRwICphVF3ljj2CuBWZJmUvzgLwBOa92hfL/EZ4D5tn/RsmkF8NGWgelXAufVOGfEpGzYuJnpuw81fp5O/AuyU22JwbHdBCHpLOAy23eW63tKOtX2p9vVK8cqzqb4sR8Clti+U9JCYJXtZcAngCcBX5UEcK/tE2w/IOnDFEkGYKHtB6bayIiJTN99iP3OvabbYewUaxYd1+0Qos/U6WJ6s+3FW1dsPyjpzUDbBFHuuxxYPq7s/JblY9rUXQIsqRFfREQ0oM5trkOSpm1dKZ9veEJzIUVERC+ocwVxHfAVSZ8p199alkVERB+rkyD+miIpvL1cvwG4pLGIIiKiJ9S5i+kx4J/Kv4iIGBB17mI6HPgQ8Jxy/2nAFtv7NxtaRER0U50upkuBv6J47WidKTYiIqIP1EkQD9m+dvu7RUREP6mTIG6S9AngKmDrVBjYvqWxqCIiouvqJIitM7DObSnbAhy188OJiIheUecupld0IpCIiOgttV45Kuk44EBg+tYy2wubCioiIrqvzitHLwZOAd5JcYvryRS3vEZERB+rMxfTS23/BfCg7QuBw4DnNxtWRER0W50E8Uj5uV7Ss4CNwDObCykiInpBnTGIqyX9IcW7G26huIMpczFFRPS5OncxfbhcvFLS1cB02zv1ndQREdF7JkwQko6yfaOk11Rsw/ZVzYYWERHd1O4K4kjgRuD4im1bKJ6sjoiIPjVhgrB9gaQ/AK61fXkHY4qIiB7Q9i6m8l0Q7+9QLBER0UPq3MX075LeC3wF+N3WQtsPNBZVRER0XZ0EcUr5eVZL2RYgLwyKiOhjdW5zndmJQCIiorfUnazvBcABbDtZ3xeaCioiIrqvzjupLwBeTpEglgOvAr4LJEFERPSxOnMxnQQcDfw/228EDgae2mhUERHRdbUm6ytvd90k6SnAL4B9mw0rIiK6rc4YxKpysr7PAiPAb4Ef1Dm4pPnARcAQcIntReO2HwH8A3AQsMD2FS3bNgN3lKv32j6hzjkjImLnqHMX0zvKxYslXQc8xfbt26snaQhYDBwLrAVWSlpm+66W3e4F3gC8t+IQj9g+ZHvniYiIZtQZpF4GLAX+zfaaSRx7HrDa9t3lcZYCJwK/TxBbjyfpsUkcNyIiOqBOF9MnKR6W+ztJKymSxdW2N2yn3gzgvpb1tcChk4htuqRVwCZgke2vt9t5bGyM0dHRSRx+W7Nnz55y3V4z2e+hn9oOk2v/ILe9UzZs2NCTcXXKrtz+Ol1M3wK+VXYZHQW8GVgCPKXh2J5je52k/YEbJd1h+6cT7Tw8PNx3/2efqkH/Hga5/b3Y9tHR0Z6Mq1N6vf0jIyMTbqtzFxOS9gBeC7wNeDHw+RrV1rHt3U77lGW12F5Xft4NfBN4Ud26ERGx4+qMQVxOMZ5wHfAp4Fvlba/bsxKYJWkmRWJYAJxWJyhJewLrbY9JejpwOPDxOnUjImLnqDMGcSlwqu3Nkzmw7U2SzgZWUNzmusT2nZIWAqtsL5P0YuBrwJ7A8ZIutH0gMBv4TDl4/QcUYxB3TXCqiIhoQJ0xiBVTPbjt5RTTc7SWnd+yvJKi62l8ve8DL5zqeSOing0bNzN996FGz9Gp/vdOtGXQ1JqsLyL60/Tdh9jv3Gu6HcZOsWbRcd0Ooe/UGqSOiIjBM+EVhKQ/aVfR9i07P5yIiOgV7bqYPll+TgfmAj8CplHMm7QKOKzZ0CIiopsm7GKy/QrbrwB+DvyJ7bm251A8j1D7eYaIiNg11RmDkO2ts6pi+8cUt6FGREQfq3MX0+2SLgG+WK6/DtjubK4REbFrq5Mg3gi8HXh3uf5t4J8aiygiInpCnQflNki6GFhu2x2IKSIiesB2xyAknQDcRjEXE5IOKd8RERERfazOIPUFFJP1/RrA9m3AzCaDioiI7quTIDbafmhc2ZYmgomIiN5RZ5D6TkmnAUOSZgHvAr7fbFgREdFtda4g3gkcCIwBXwYeBt7TZFAREdF9de5iWg98oPyLiIgBUeeNcs8H3gvs17q/7aOaCysiIrqtzhjEV4GLgUuASb1VLiIidl11EsQm23lyOiJiwNRJEN+Q9A6Kd0ePbS20/UBjUUVERNfVSRBnlJ/vaynbAuy/88OJiIheUecupjw1HRExgNq9cvQo2zdKek3VdttXNRdWRER0W7sriCOBG4HjK7ZtAZIgIiL62IQJwvYF5ecbOxdORET0ijqD1Eg6jmK6jelby2wvbCqoiIjovjrvg7gYOIViTqZpwMnAcxqOKyIiuqzOZH0vtf0XwIO2LwQOA55f5+CS5kuypNWSzq3YfoSkWyRtknTSuG1nSPpJ+XfG+LoRETtiw8bOTAwxe/bsxs/RVFvqdDE9Un6ul/Qs4H7gmdurJGkIWAwcC6wFVkpaZvuult3uBd5AMddTa92nUbyoaC7FgPhIWffBGvFGRGzX9N2H2O/ca7odxk6xZtFxjRy3zhXE1ZL+EPgEcAuwhmLa7+2ZB6y2fbftR4GlwImtO9heY/t24LFxdf8UuMH2A2VSuAGYX+OcERGxk9R5UO7D5eKVkq4Gple8Ya7KDOC+lvW1wKE146qqO6NdhbGxMUZHR2se/vE6cRnYKZP9Hvqp7TC59g9y22Gw2z/Iba+r3YNylQ/Ildt67kG54eHhvvsPPlWD/j0McvsHue0w2O2fattHRkYm3NbuCqLqAbmt6jwotw7Yt2V9n7KsjnXAy8fV/WbNuhERsRO0e1BuRx+QWwnMkjST4gd/AXBazborgI9K2rNcfyVw3g7GExERk1DnjXJ7UdxR9DKKK4fvAgtt39+unu1Nks6m+LEfApbYvlPSQmCV7WWSXkwxjfiewPGSLrR9oO0HJH2YIslQni/Ti0dEdFCd21yXAt8GXluuvw74CnDM9iraXg4sH1d2fsvySoruo6q6S4AlNeKLiIgG1EkQz2y5kwngI5JOaSqgiIjoDXUSxPWSFgCXl+snUXQbRUREH6vzoNybgS9RvG50jKLL6a2SfiPp4SaDi4iI7qnzoNyTOxFIRET0ljqzuZ45bn1I0gXNhRQREb2gzhjE0ZJeC5wJ7AX8C/CtRqOKiIiuq9PFdFp519IdwO+A02x/r/HIIiKiq+p0Mc0C3g1cCdwDnC7piU0HFhER3VXnLqZvAP/D9luBI4Gf8B9POEdERJ+qMwYxz/bDALa3AJ+U9I1mw4qIiG6b8ApC0vsBbD8s6eRxm9/QZFAREdF97bqYFrQsj59JNW93i4joc+0SxLQJlqvWIyKiz7RLEFsmWK5aj4iIPtNukPrgcq6lacAeLfMuTQOmNx5ZRER0Vbs3yg11MpCIiOgtdZ6DiIiIAZQEERERlZIgIiKiUhJERERUSoKIiIhKSRAREVEpCSIiIiolQURERKUkiIiIqJQEERERleq8MGjKJM0HLgKGgEtsLxq3fRj4AjAHuB84xfYaSfsBo4DLXW+2/bYmY42IiG01liAkDQGLgWOBtcBKScts39Wy25nAg7afJ2kB8DHglHLbT20f0lR8ERHRXpNdTPOA1bbvtv0osBQ4cdw+JwKfL5evAI6WlHdNRET0gCa7mGYA97WsrwUOnWgf25skPQTsVW6bKelW4GHgg7a/0+5kY2NjjI6OTjnY2bNnT7lur5ns99BPbYfJtX+Q2w6D3f5BbntdjY5B7ICfA8+2fb+kOcDXJR1o++GJKgwPD/fdf/CpGvTvYZDbP8hth8Fu/1TbPjIyMuG2JruY1gH7tqzvU5ZV7iNpN+CpwP22x2zfD2B7BPgp8PwGY42IiHGavIJYCcySNJMiESwAThu3zzLgDOAHwEnAjba3SNobeMD2Zkn7A7OAuxuMNSIixmnsCsL2JuBsYAXFLauX275T0kJJJ5S7XQrsJWk1cA5wbll+BHC7pNsoBq/fZvuBpmKNiIjHa3QMwvZyYPm4svNbljcAJ1fUuxK4ssnYIiKivTxJHRERlZIgIiKiUhJERERUSoKIiIhKSRAREVEpCSIiIiolQURERKUkiIiIqJQEERERlZIgIiKiUhJERERUSoKIiIhKSRAREVEpCSIiIiolQURERKUkiIiIqJQEERERlZIgIiKiUhJERERUSoKIiIhKSRAREVEpCSIiIiolQURERKUkiIiIqJQEERERlZIgIiKiUhJERERU2q3Jg0uaD1wEDAGX2F40bvsw8AVgDnA/cIrtNeW284Azgc3Au2yvaDLWiIjYVmNXEJKGgMXAq4ADgFMlHTButzOBB20/D/ifwMfKugcAC4ADgfnAp8vjRUREhzTZxTQPWG37btuPAkuBE8ftcyLw+XL5CuBoSdPK8qW2x2z/DFhdHi8iIjqkyS6mGcB9LetrgUMn2sf2JkkPAXuV5TePqzuj3cnWr1//q5GRkXt2JOArT37GjlTvCSMjI1Oq1w9th6m1f5DbDoPd/kFue4vnTLSh0TGITpozZ87e3Y4hIqKfNNnFtA7Yt2V9n7Ksch9JuwFPpRisrlM3IiIa1GSCWAnMkjRT0hMoBp2XjdtnGXBGuXwScKPtLWX5AknDkmYCs4AfNhhrRESM01iCsL0JOBtYAYwCl9u+U9JCSSeUu10K7CVpNXAOcG5Z907gcuAu4DrgLNubm4o1IiIeb9qWLVu6HUNERPSgPEkdERGVkiAiIqJS39zm2uu2N+1Iv5K0BPhz4Be2X9DteDpJ0r4UU8n8EbAF+GfbF3U3qs6RNB34NjBM8Vtzhe0LuhtVZ5UzQKwC1tn+827HM1m5guiAmtOO9KvPUUyXMog2Af/d9gHAS4CzBui/O8AYcJTtg4FDgPmSXtLlmDrt3RQ36eySkiA6o860I33J9reBB7odRzfY/rntW8rl31D8ULSdEaCf2N5i+7fl6u7l38DcFSNpH+A44JJuxzJV6WLqjDrTjkQfk7Qf8CLgf3c5lI4qr55HgOcBi20PUvv/AXg/8ORuBzJVuYKIaJikJwFXAu+x/XC34+kk25ttH0IxG8I8SQMxDiVp67jbDk2S1G1JEJ2RqUMGlKTdKZLDZbav6nY83WL718BNDM541OHACZLWUHQpHyXpi12NaArSxdQZv592hCIxLABO625I0bRy6vpLgVHbf9/teDpN0t7ARtu/lrQHcCzlO1/6ne3zgPMAJL0ceK/t13c1qCnIFUQHTDTtSHej6gxJXwZ+UCxqraQzux1TBx0OnE7xr8fbyr8/63ZQHfRM4CZJt1P8I+kG21d3OaaYhEy1ERERlXIFERERlZIgIiKiUhJERERUSoKIiIhKSRAREVEpz0FEz5G0GbiD4n+fo8AZttdX7LccOK18CGsyx38W8I+2T5pifGuAubZ/NZX6uwpJbwCut/1/ux1LdEcSRPSiR8rpGZB0GfA24PcPmpUPoE2zPaVnCsofvCklhwHzBuDHQBLEgEqCiF73HeCgcrK7FRST3c0B/kzSt4C5wJOAa4HvAi+leFr9RNuPSHoecDGwN7AZOLn8vNr2C8p/Jf9X4KkUkyp+0faFAJK+TjFFynTgItv/3C7Q8p0fH6V458evbB8t6WnAEmB/YD3wFtu3S/oQMLMsfzbwVxRTgr+qjP942xvLq5XLy/JHKK6YVpffxxLg6cAvgTfavlfS54CHy+/lGcD7bV9Rxvc+4L9RvJ/ha7YvKI/zuO+OYhbSucBlkh4BDgMuAE6gmMb8etvvbfd9xK4vYxDRsyTtRvHDeEdZNAv4tO0Dbd8zbvdZFLOFHgj8GnhtWX5ZWX4wxQ/gzytONa/c/yDgZElzy/I32Z5D8UP5Lkl7tYl1b+CzwGvLc51cbroQuNX2QcDfULxAaKvnAkdR/Oh+EbjJ9gspEsFxLfs9VJZ/imKGUID/BXy+PO5lwD+27P9M4GUUL2paVMb3yvI7mkfxboY5ko6Y6Lsrk8oq4HXl1dwTKRLpgeU5PzLRdxH9IwkietEekm6j+IG6l2I+I4B7bN88QZ2f2b6tXB4B9pP0ZGCG7a8B2N5QNZZBMQXE/bYfAa6i+HGFIin8CLiZ4kpiVpuYXwJ82/bPynNtfQfGy4B/LctuBPaS9JRy27W2N1IkwCHgurL8DmC/lmN/ueXzsHL5MOBL5fK/tsQM8HXbj9m+i+JtdgCvLP9uBW4B/rilPY/77ira9xCwAbhU0msoroaiz6WLKXrR78cgtpIE8Ls2dcZaljcDe0zifOPnm9lSTrB2DHCY7fWSvknR1bQzjQHYfkzSRttb43iMbf+/uWWC5bbHLU1r+fw7259p3bHsYtrud2d7k6R5wNEU4zdnU1z9RB/LFUT0rfItbmslvRpA0rCkJ1bseqykp5Uzjr4a+B7FmMSDZXL4Y4orhHZuBo4oZ+ylHHuAYgzldWXZyynGJib7TohTWj5/UC5/n2JWYMrjf2c7x1gBvKl8NwWSZkj6z9up8xvKl92U9Z5qeznFeMnBk2pB7JKSIKLfnU7RVXQ7xY/qMyr2+SHFOxtuB660vYqiu2c3SaMU/fgTdW0BYPuXwFuAq8puqa+Umz5E0d9/e3mcM6bQhj3L+u+m+HEGeCfwxrL89HJbu/iup+iS+oGkO4Ar2P6bzj4HXFx29z0ZuLo833eBc6bQjtjFZDbXGGjlXUxzbZ/d7ViqDMozF9GbcgURERGVcgURERGVcgURERGVkiAiIqJSEkRERFRKgoiIiEpJEBERUen/A3BjBOptmlmtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(n_components=len(cluster_features))\n",
    "pca_components = pca.fit_transform(X)\n",
    "\n",
    "# plot the PCA variances\n",
    "pca_features = range(pca.n_components_)\n",
    "plt.bar(pca_features, pca.explained_variance_ratio_)\n",
    "plt.xlabel('Principal components')\n",
    "plt.ylabel('Explained variance (%)')\n",
    "plt.xticks(pca_features)\n",
    "\n",
    "# save pca components in a df\n",
    "pca_components = pd.DataFrame(pca_components, columns = ['PC0', 'PC1', 'PC2', 'PC3', 'PC4'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot above that after the second PC, the gain in information is reduced. That is, the first component contributes almost 30% of the information, and the second one contributes over 25%. So if we use just the first 2 PCs, we already have close to 60% of the data being preserved. If we kept the first 3 PCs, we get closer to 80%.\n",
    "\n",
    "Let's try and plot the k-means clusters using PCA instead, and see if that makes it easier to visualize the clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Principal Component 2')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# k-means clustering on first 2 PCA components\n",
    "X_pca = pca_components\n",
    "kmeans_pca = KMeans(n_clusters=5, random_state=31337)\n",
    "kmeans_pca.fit(X_pca)\n",
    "y_pca = kmeans_pca.predict(X_pca)\n",
    "\n",
    "# visualize the clusters\n",
    "centers_pca = kmeans_pca.cluster_centers_\n",
    "plt.scatter(X_pca['PC0'], X_pca['PC1'], c=y_pca, s=50, cmap='viridis')\n",
    "plt.scatter(centers_pca[:, 0], centers_pca[:, 1], c='red', s=200, alpha=0.5);\n",
    "plt.xlabel('Principal Component 1')\n",
    "plt.ylabel('Principal Component 2')\n",
    "\n",
    "# if you're curious, inspect the min and max values for the PC dimensions\n",
    "# X_pca[['PC0', 'PC1']].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see above, using k-means clustering after PCA, and plotting our clusters with the first 2 PCs as dimensions, helps a bit. Specifically, intra-cluster variance is smaller, and we can see that the centroids are not that far apart from each other (likely indicating that songs in the top1k are not that different from each other). But we can still improve this visualization.\n",
    "\n",
    "A more powerful technique for dimensionality reduction is t-Distributed Stochastic Neighbor Embedding ([t-SNE](https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding)). We'll leave for you to **try on your own** by following this [t-SNE vs PCA tutorial](https://www.datacamp.com/community/tutorials/introduction-t-sne), which has several example comparisons between the results you get with PCA vs t-SNE for visualization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: supervised ML for prediction tasks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this last part, we'll focus on two prediction tasks.\n",
    "\n",
    "In the first task, we'll try and predict genre for each song. We'll first try and see if we can do that on the `top1k` songs, and then with the entire dataset.\n",
    "\n",
    "In the second task, we'll try to predict song popularity, but using a larger dataset with features similar to those of the dataset above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) genre prediction\n",
    "\n",
    "As mentioned above, the dataset we've been using so far has been augmented with genre information (stored in the `genre` column). We'll use values in that column as labels for training a supervised ML algorithm to predict song genre.\n",
    "\n",
    "And unlike in k-means clustering, here we'll use all features as input. We start by scaling our dataset again, follow that by splitting into our data into training and test datasets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use our entire set of numerical features, instead of just the 5 we used for k-means clustering:\n",
    "df_numerical = top1k.select_dtypes(exclude=[np.object])\n",
    "X = np.array(df_numerical)\n",
    "\n",
    "# scaling won't make a difference for classifiers, but we leave it here in case you want to try other models\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X)\n",
    "X = scaler.transform(X)\n",
    "\n",
    "# the features and the label we'll use for training our supervised algo:\n",
    "features = X\n",
    "labels = top1k['genre']\n",
    "\n",
    "# split our data into training and test\n",
    "train_features, test_features, train_labels, test_labels = train_test_split(features, labels, random_state=31337)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then train our [decision tree classifier](https://scikit-learn.org/stable/modules/tree.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# train a decision tree on it\n",
    "genre_tree = DecisionTreeClassifier(random_state=31337)\n",
    "genre_tree.fit(train_features, train_labels)\n",
    "\n",
    "# predict labels on test data\n",
    "pred_labels_tree = genre_tree.predict(test_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how well the tree did on our genre prediction task:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decision Tree Results:\n",
      "                   precision    recall  f1-score   support\n",
      "\n",
      "     Alternative       0.00      0.00      0.00         3\n",
      "           Anime       0.00      0.00      0.00         5\n",
      "           Blues       0.00      0.00      0.00         8\n",
      "Children’s Music       0.00      0.00      0.00         2\n",
      "         Country       0.00      0.00      0.00         2\n",
      "           Dance       0.05      0.09      0.07        33\n",
      "      Electronic       0.00      0.00      0.00         0\n",
      "            Folk       0.00      0.00      0.00         1\n",
      "         Hip-Hop       0.04      0.06      0.05        31\n",
      "           Indie       0.00      0.00      0.00         3\n",
      "             Pop       0.17      0.15      0.16        89\n",
      "             R&B       0.00      0.00      0.00         6\n",
      "             Rap       0.00      0.00      0.00        44\n",
      "       Reggaeton       0.33      0.15      0.21        13\n",
      "            Rock       0.00      0.00      0.00        10\n",
      "\n",
      "        accuracy                           0.08       250\n",
      "       macro avg       0.04      0.03      0.03       250\n",
      "    weighted avg       0.09      0.08      0.08       250\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tree_results = classification_report(test_labels, pred_labels_tree)\n",
    "print('Decision Tree Results:\\n',  tree_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's pretty bad: our weighted average precision is as bad as random.  This is probably because this dataset doesn't have enough samples of each genre (there are only 1000 songs in total). As expected, we have a bias only towards genres in the top 1000.\n",
    "\n",
    "**Q8: Did we pick the wrong model? Try a [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) instead below, and see if we can get better results:**\n",
    "\n",
    "**A:** We didn't pick the wrong model. As you can see below, the RFC results are a little better, but not by much.  Another problem here is that not only do we have a small dataset, but we also have a large number of genres relative to the size of the dataset. So it's a multiclass prediction task, with several classes, and too little samples per class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RFC Results:\n",
      "                   precision    recall  f1-score   support\n",
      "\n",
      "     Alternative       0.00      0.00      0.00         3\n",
      "           Anime       0.00      0.00      0.00         5\n",
      "           Blues       0.00      0.00      0.00         8\n",
      "Children’s Music       0.00      0.00      0.00         2\n",
      "         Country       0.00      0.00      0.00         2\n",
      "           Dance       0.04      0.06      0.05        33\n",
      "            Folk       0.00      0.00      0.00         1\n",
      "         Hip-Hop       0.06      0.06      0.06        31\n",
      "           Indie       0.00      0.00      0.00         3\n",
      "           Movie       0.00      0.00      0.00         0\n",
      "             Pop       0.24      0.25      0.24        89\n",
      "             R&B       0.00      0.00      0.00         6\n",
      "             Rap       0.10      0.07      0.08        44\n",
      "       Reggaeton       0.33      0.15      0.21        13\n",
      "            Rock       0.10      0.10      0.10        10\n",
      "\n",
      "        accuracy                           0.13       250\n",
      "       macro avg       0.06      0.05      0.05       250\n",
      "    weighted avg       0.14      0.13      0.13       250\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Q8: YOUR CODE GOES HERE.\n",
    "# (...)\n",
    "\n",
    "# Q8: Sample answer.\n",
    "# train a random forest classifier\n",
    "genre_forest = RandomForestClassifier(random_state=31337)\n",
    "genre_forest.fit(train_features, train_labels)\n",
    "\n",
    "# predict labels on test data\n",
    "pred_labels_forest = genre_forest.predict(test_features)\n",
    "\n",
    "forest_results = classification_report(test_labels, pred_labels_forest)\n",
    "print('RFC Results:\\n',  forest_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another problem here is that not only do we have a small dataset, but we also have a large number of genres relative to the size of the dataset.\n",
    "\n",
    "Let's try and see if we can do better with more samples by using the larger dataset, and also reducing it down to prediction of only 3 mainstream genres:\n",
    "\n",
    "**Q9: How many samples do we have per genre on the larger dataset (`df` pd dataframe)?** \n",
    "\n",
    "**A:** From the results below, we can see that aside from \"A Capella\" we have around 8k to under 10k samples per genre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A Capella            119\n",
       "Alternative         9353\n",
       "Anime               9353\n",
       "Blues               9353\n",
       "Children’s Music    9353\n",
       "Classical           9256\n",
       "Comedy              9681\n",
       "Country             8664\n",
       "Dance               8701\n",
       "Electronic          9377\n",
       "Folk                9299\n",
       "Hip-Hop             9295\n",
       "Indie               9543\n",
       "Jazz                9441\n",
       "Movie               7806\n",
       "Opera               8280\n",
       "Pop                 9386\n",
       "R&B                 8992\n",
       "Rap                 9232\n",
       "Reggae              8771\n",
       "Reggaeton           8927\n",
       "Rock                9272\n",
       "Ska                 8874\n",
       "Soul                9089\n",
       "Soundtrack          9646\n",
       "World               9096\n",
       "Name: genre, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q9: YOUR CODE GOES HERE.\n",
    "# df.(...)\n",
    "\n",
    "# Q9: Sample answer.\n",
    "df['genre'].value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This may be enough, but as we can see the number of samples is not exactly balanced for each genre, so we may still get some bias.  Also, it's a fair amount of genres, so let's pick 3 common ones and see how we can do at that task. We'll go with \"Hip-Hop\", \"Rock\", and \"Jazz\", which should be different enough from each other:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "hip_hop = df.loc[df['genre'] == 'Hip-Hop']\n",
    "rock = df.loc[df['genre'] == 'Rock']\n",
    "jazz = df.loc[df['genre'] == 'Jazz']\n",
    "\n",
    "# make it equal number of songs for each\n",
    "hip_hop = hip_hop.sample(n=len(rock), random_state=31337)\n",
    "jazz = jazz.sample(n=len(rock), random_state=31337)\n",
    "df = pd.concat([rock, hip_hop, jazz])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And train our forest on this larger dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# select only numerical features\n",
    "df_numerical = df.select_dtypes(exclude=[np.object])\n",
    "X = np.array(df_numerical)\n",
    "\n",
    "# scaling won't make a difference for classifiers, but we leave it here in case you want to try other models\n",
    "#scaler = StandardScaler()\n",
    "#scaler.fit(X)\n",
    "#X = scaler.transform(X)\n",
    "\n",
    "# features and label\n",
    "features = X\n",
    "labels = df['genre']\n",
    "\n",
    "# split our data into training and test\n",
    "train_features, test_features, train_labels, test_labels = train_test_split(features, labels, random_state=31337)\n",
    "\n",
    "# train a RFC on it\n",
    "genre_forest = RandomForestClassifier(random_state=31337)\n",
    "genre_forest.fit(train_features, train_labels)\n",
    "\n",
    "# predict labels on test data\n",
    "pred_labels_forest = genre_forest.predict(test_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how we did this time around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RFC Results:\n",
      "               precision    recall  f1-score   support\n",
      "\n",
      "     Hip-Hop       0.86      0.89      0.88      2345\n",
      "        Jazz       0.92      0.91      0.92      2264\n",
      "        Rock       0.87      0.85      0.86      2345\n",
      "\n",
      "    accuracy                           0.88      6954\n",
      "   macro avg       0.88      0.88      0.88      6954\n",
      "weighted avg       0.88      0.88      0.88      6954\n",
      "\n"
     ]
    }
   ],
   "source": [
    "genre_forest_results = classification_report(test_labels, pred_labels_forest)\n",
    "print('RFC Results:\\n',  genre_forest_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time around we did a lot better: 92% precision for Jazz, and an average precision of 88% for all 3 genres.\n",
    "\n",
    "**Q10: To try on your own: train a [`DecisionTreeClassifier`](https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html) with different values of `max_depth` and use `tree.plot()` to [`plot it`](https://scikit-learn.org/stable/modules/tree.html).**\n",
    "\n",
    "**What are some pros/cons of using a decision tree vs a random forest classifier?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r1rJ2zdo8623atIlNmzYB+R9WHBcXx+7duwEYMGBAYYYtIiIixaQVNSIiItkEBwfnXXbIVNawYUPzM09PT/M2k6CDQRbbxcfHc/LkSVPbRg0t1ilsvwAuri4AeSYCfv/9d+Li4vKMa0lWrPvc77OYpDEajXnOsyTYGGzM/dxIi5YtqFu3LteuXWPXrl3mlTXe3t7Y29sXaxxubm6MGDGCTZs3sWbtGoYMGYKrqyunTp1i3tx5dO7UmedGPcfWrVtJSUnJM05MbAzR0dFFepXmldVbt2wlNTUVW1tb+vfvf1P7MhqNHD9+HIBatWvd1L5ERERuBVpRIyIiks33W79nzJgx3HXXXTmeBwcHExYWBkCvXr3MzytUqECbNm04ePAgyz5ZRs9ePXMlOJYtW0ZKSgpOTk553pxT2H4B7rvvPnZs38GePXuYMHFCrpjLli4r4Kz/4eJiSv6cPXvWfEhydmvWrOHChQuFjltQWVeXx8fFF6j+o489ytvz3mbF8hX88ssvpmclcJBudk2bNqVp06ZMnjKZnTt34u/vz8GfDrJv3z727duHi4sLvXr3wtfXN9c5RXv27CnRseRl7ty5zJ07N89yHx8fgg8FM2DggHzrZVm/YT0AXl5eVKlSpVhjs/RzlN3qb1Zz8eJFALp07lKsvkRERG4HWlEjIiKSjZ2dHSOfHWlOjmRmZrJnzx7GjxsPQPsO7WneonmONuPGj8PGxoafT/7MSxNfMq9KSUxMZMmSJeaEyahRo8yJiJLot2fPnhgMBs6cOcPsWbPNq2euXLnCrFmz2LhxI2XLli3U/Nu1a4fBYODsmbPMmjXLHDMhIYFPP/mUmTNmUqFChULFLIz6DeoDEBoWar59KT8DBgzAzs6OY8eOkZaWRsOGDfH09LwpY3NwcMDb25vPPvuM3Xt2M378eO6++27i4+NZu2YtsbGxN6Xf/9qvv/7K0SNHgYJve/L19cXD3YNu3brlKps1axazZ80mNCSU5ORk8/NLly7x3rvvMXPmTADatGlDp86dSmAGIiIitzatqBEREcnmf5P+xwfvf8D/PfF/ODk5kZmZaf7lsk6dOhZXIzRv3pzpr09nxpsz2LZtG9u3b8fV1ZWEhATz9pV+/foxctTIEu23QYMGDB02lJUrVrJq1SpWrVqFq6sr8fHx2NjYMHPWTBYuXMj1i3nfzvRvdevWNcf88osv+fKLL81zyczMxMvLi8aNG7NkyZICxyyM1q1bc/fdd3PhwgV69+pNxYoVcSzrCMBXX31lvj0rS6VKlejWrRvbt28HYNAjg27KuP6tRo0aPD/meUY/P5rg4GDWr19frOurrcmGDaZDhMuXL0/3B7sXO15iYiIb1m9g1apV2NjY4OLiQkZGBgkJ/5yf1Kp1Kz5c8GGx+xIREbkdaEWNiIhINnfffTfrvl3HI488Yv6FslatWjz9zNOs+3YdVatWtdhuyJAhrF23Fm9vb6pUqUJSUhLOLs6079Ce+R/O551338n3JqSi9uvr68vrr7+Oh4cHDg4OGAwGvLy8WLFyBYMGFS1pMXnyZGbMnEHDhg2xt7cnIyMDT09PpkyZwsdLP8a2zM270cnOzo7lK5bz8MMPU61aNeLi4oi8GEnkxUjS09MttunxUA8A7O3t6dev300bmyUGg4HWrVszZ86cfK9Yv1VkZmby3UbTzVm9e/cu9lk/YPqz8cwzz9CsWTOqVq1KSkoKqamp1KhRgx49ejB//nxWrlx5U1dqiYiI3EoMBTmsT0REpBS4GTH+ATj+F51169aNyIuRrPx8JW3atPkvuizVfm8n06ZOY+3atfTp04f3P3i/tIcjt4ZMA4ZpwFulPRAREZF/04oaERERuWXFx8ezZcsWAAYPHlzKoxEREREpPiVqRERE5JaUmprK3DlzSUpKwt3dnbbt2pb2kERERESKTYcJi4iIyC1l27ZtvP3221yNvUpSUhIGg4FJvpNKe1giIiIiJUKJGhEREbmlJCUlEXkxEnt7exo2bMiYF8bQvn370h6WiIiISInQYcIiImKt/tPDhEXkjqLDhEVExGrpjBoRERERERERESuhRI2IiIiIiIiIiJVQokZERERERERExEooUSMiIiI35Ofnh4e7B76+viUa18fHBw93D/z9/Us0roiIiMitSrc+iYiIiBTQb7/9xrKlyzhw4ADR0dFUqFCBVq1a8cyIZ2jcuHGRYnq4exS47uerPqd169ZF6kdERERuDUrUiIiIyA1VrFiRe++9lypVqpRo3Jo1anLvvffi4uJSonFvhsDAQF584UWuX78OgIuLC9HR0WzdupUdO3bw1ltv0f/h/oWO6+bmlm95QkICycnJ2NnZ0aBBgyKNXURERG4dup5bRESsla7nFqsRFRVF7169SUhIoH2H9sycOZNatWpx5coV5s6Zy6ZNm7Czs8N/vX+JJ1MGPDyAU6dO0eOhHvj5+ZVo7DuYrucWERGrpTNqRERERG5g2dJlJCQkUKNGDfz8/KhVqxYAlStXZu68uTRq1Ii0tDQWLFhQov3+8ssvnDp1CoCBAwaWaGwRERGxTkrUiIiI3EEyMjJYuWIl/fv15/6m99OubTuee+45wkLDANN5KR7uHkRERORol99hwtnbREZGMm3qNDp36kyTxk3o3q078+bNIyEhweJ4boXDhDMzM9m6dSsAQ54YQrly5XKU29raMvzp4QDs/WFvnnMtig3rNwCmhFCnzp1KLK6IiIhYL51RIyIicodIS0vjhTEvsH//fgDKlClDRkYG+/buIzAgkPfef69Y8U+fOs2U16Zw7eo1ypUrh9Fo5OLFiyz/bDnBh4L5+puvsbOzK4mp/KfOnTtHdHQ0AF5eXhbreHUwPU9LSyM0NJTOnTsXu9/09HQ2b94MgLe3N2XK6J9tIiIidwKtqBEREblDLF68mP3792Nra8uUKVMICQ3hUPAhdu/ZjVdHL6ZNnVas+JMnT8bTw5PvNn1HaFgoYYfDmD17Nvb29pw4cYK1a9aW0Ez+W+HnwgEwGAzUr1/fYp2KlSpSuXJlwJTYKQn79+/nypUrAAwYOKBEYoqIiIj103/NiIiI3AESEhJYsXwFAGPHjWXosKHmslq1auHn58djjz5GXFxckfuoVq0aS5ctxd7eHgB7e3seefQRfv7lZ7784ku2b9/O/z35f8WaR5agoCCGDR1WpLatWrdi1apVBa4fFRUFgGt5VxwcHPKsV7VqVa5cuWKuX1zr168HwMPDA09PzxKJKSIiItZPiRoREZE7QGBgIElJSTg4OODj45Or3M7OjuFPD8d3Uu4zaApq+PDh5iRNdg8++CBffvElZ8+eLXLsf7Ozs7vhtdZ5qVC+QqHqJ11PAsDRIf8LyBwdTeVJSUlFGld2V69eZe8PewGtphEREbnTKFEjIiJyB/jl518A8PD0yHUYbpaWLVoWq4/GTRpbfF6tajWAYq3W+bfmzZsTEBhQYvGszZYtW0hLS6NMmTL069evtIcjIiIi/yGdUSMiInIHiI2NBaBqlap51qlaLe+ygsgrAWTvYFplk56eXqz4pcWprBMAySnJ+dZLTjaVOzk5FbvPrNueOnbsaD77RkRERO4MStSIiIiI5KNqVVMCK+5aHCkpKXnWu3z5MgBVqlQpVn/h4eEcP34c0LYnERGRO5G2PomIiNwBKlasCMDlqMt51slKNNwKwsLCGDd2XJHaNmvWDL+FfgWuX69+PQCMRiPnzp2jUaNGuerExsSab2jK62aoglrvbzpEuHyF8nTt2rVYsUREROTWo0SNiIjIHcCzoenWoFO/nCIxMdHiNqXQkND/elhFlpaWRnR0dJHaXr12tVD169Wrh5ubG9HR0RwIPGAxURN4IBAwHXLcokWLIo0LICMjg++++w6Avn37WjycWURERG5vStSIiIjcATp06ICTkxNJSUl89eVXjBw1Mkd5eno6K1euLKXRFV6bNm04dfrUf9KXjY0Nffr04fPPP+frr7/myaeezHEOTWZmJitXmN67rt264uzsXOS+Dhw4YF7ZNHDAwOINXERERG5JOqNGRETkDuDs7MywYcMA+PDDD1m1apX58NvIyEjGjxtPREREaQ7Rqo0cNRJnZ2ciIyMZO3YskZGRAMTExDDZdzLHjx/Hzs6OsWPH5mobERGBh7sHHu4e+Pv759vPhg2mQ4Tr169Pk6ZNSn4iIiIiYvW0okZEROQO8fyY5zl2/BiBAYHMnjWbeXPn4eTkRFxcHHZ2drz/wfuMfdGUaNCWm5yqVKnChws+5MUXXiQwIJBuXbvh4uJCQkICRqORMmXKMHv2bBo0aFDkPhISEti9azcAAwboEGEREZE7lVbUiIiI3CHs7e35+OOPmeQ7iQb3NcDGxgZbW1u6du3Kqi9W0aZNG3NdV1fXUhypderQoQPrN6xn0KBBVK9eneTkZNzc3OjduzffrP6G/g/3L1b877//nuTkZGxsbOjXv18JjVpERERuNQaj0VjaYxAREbHEzYjxD8CxtAdyp/jpp594evjT1KxVkz179pT2cERupkwDhmnAW6U9EBERkX/TihoREREB4NNPPgWgQ/sOpTwSERERkTuXEjUiIiJ3iIyMDMaNG8eP+38kPj7e/Pzs2bOMGzeOgIAA7OzseMrnqVIcpYiIiMidTYcJi4iI3CGMRiM7tu9gx/YdgOkmqIyMDK5fvw6YrqGeOm0q7u7upTlMERERkTuaEjUiIiJ3CFtbW15//XUCAgI4c+YMV65cISMjg5q1atKqZSuGDhtKo0aNSnuYIiIiInc0HSYsIiLWSocJi8jNosOERUTEaumMGhERERERERERK6FEjYiIiIiIiIiIlVCiRkRERERERETESihRIyIiIrl4uHvg4e5BREREaQ9FRERE5I6iW59ERERECiA2JpagoCBOnDjB8ePHOXnyJAkJCQAcPXYUBweHG8ZITU3l85Wfs3nzZi5cuICtrS1169Vl0KBBDB48GIPBkG/7AwcO8Pnnn3Ps6DESEhKoVq0aXbp04bnRz+Hm5las+R0/fpzlny0nODiYa9euUblyZTp06MDIUSOpU6eOxTYZGRksW7YM/2/9uXTpElWqVKFv376MHTcWe3t7i23Onj3LoIGD8PLyYvGSxcUas4iIyO1Itz6JiIi10q1PpcjD3QOAXbt3Ubt27VIejXVYuWIlc+bMsVhWkERNQkICw4YO4+TJkwCULVuW9PR00tLSAOjStQsLFy6kTBnL/4+2ZPES5s+fD4CNjQ1OTk7mRFGlSpVYsXIF9913X5Hmtn79eqZNnUZ6ejoGgwFnZ2fi4+MBcHJyYtGiRbRt1zZXu+nTp7Nm9RpzvaSkJAA6d+7Mx0s/ttjXU089xYnjJ9i8ZXNp/mzp1icREbFa2vokIiIiUgAGg4Hq1avTo0cPJkycwMSXJhaq/bSp0zh58iTlK5Rn8ZLFhB0O48jRI8yZOwcHBwf2/rAXPz8/i2337dtnTtI8/czTHAo+REhoCJs2b8LT05OYmBheGPMCqamphZ7X6VOnmT5tOunp6fTr14/AA4EEhwSze89u2ndoT1JSEuPGjSMmJiZHu/Pnz7N2zVpcXV35+puvCTscxqbNm6hevTr79u3jwIEDufrasGEDIcEhjB49WglAERGRPChRIyIiIlIATz71JHv37cVvoR+jR4/mgQceKHDbn3/+me+//x6AOW/NoWvXrhgMBmxtbRk4cCAvv/wyYFq1c+XKlVztP3j/AwB69OjBpEmTcHZ2BqBBgwYsXrIYJycn/vjjD1avXl3oeS1YsIC0tDQaN27M3HlzqVSpEgC1atXCz8+PGjVqEBcXx9KlS3O0CzoYhNFo5LHHHqNZs2bm8Yx4dgQAP/30U476cXFxvPP2O9xzzz08M+KZQo9TRETkTqFEjYiISDZZZ4gMGTKEVi1b0bhRYzq078DD/R9mxpszOHz4cK42wcHBzJ41m8GPDaajV0eaNG5C+3bteXbEs2zbti3Pvnx9ffFw98DPz4/U1FQWL1pMn959eOD+B+japSuzZs3i2rVr5vonTpxg7Itj8ergxf1N7+fRRx5l165dFmP7+/vj4e6Bj48PYNra8vjgx2nRvAUtW7Rk+LDh/Lj/xzwXF9gAACAASURBVCK/T4mJiSxZsoRHH3mUli1a0rRJU3o+1JNZs2Zx6dIli20yMzPx9/dnqM9Q2rRpQ+NGjWnXth3efb2ZMnlKscbzX7C1tS1y282bNgNw77330q17t1zlgx8fjIuLC8nJyezcsTNH2dmzZzl16hSAxQRH9erV6evdN0c/BRUXF8f+/fsBGP708FxzLFeuHI8PeRyALZu3kH3L/NWrVwG46667crSpc7fpPJursVdzPP/g/Q+4cuUK06ZPy/P8GhEREdFhwiIiImbp6emMGDGC4EPBgGmri4uLC1evXuXKlSucPn2aq1evmlcPgClh4fOUj/n7cuXK4eDgQExMDAEBAQQEBDD48cHMmDEjz37T0tJ45ulnCAkJMZ9zcunSJb5Y9QVHDh/hy6++JODHACZOnEhaWhrOzs6kpKSYEzfvv/8+vfv0zjP+nLfmsHLlSmxsbMxnjxw8eJCDBw/y6v9eZcSIEYV6n8LDwxk5ciSRFyMBKFOmDPb29vz+++/8vup3Nn23icWLF9O8RfMc7f736v/YvPmfRIKLiwsJCQnExsZy7tw5wsPD6dipY6HGcqsICgoCoINXB4vljo6OtGjZgr0/7OXgwYMMeWJIrrYuLi7cf//9Ftt7eXmxds1ajh07RmJiIuXKlSvQuEJDQ81n5HToYHlsXl5ezP9gPlFRUYSHh1O/fn0AKlSoAMAff/yRo/6FPy7kKAfTQcWrV6+md+/eefYjIiIiJlpRIyIi8rfNmzcTfCiYsmXL8vbbb3Pk6BEOBR/i2PFj7PlhD9OmT8Pdwz1HGxsbG3r27MnCjxZyMOggoWGhhISGcCj4ENOmT8PJyYk1q9ew7fu8V9Z8/dXX/P777yz5eAmHjxwm7HAYH330EeXKlePEiRMs9FuIr68v/fr1Y/+P+wkOCebATwfo3r07RqORt956i/T0dIuxf/n5F1auXMnIkSMJOhTEoeBD7Nu/j379+gHw7jvvEhoSWuD3KD4+nlEjRxF5MZJevXqxceNGjh47StjhMHbu2om3tzfXrl1j3LhxxMXFmdsFBwezefNmbG1tmTx5MiGhIQSHBHPs+DH2/7ifOXPn5Ers3C6MRiO//vorgDnJYUn9eqay8PDwHM/Dz5m+r1uvLjY2lv/plhXXaDRy/vz5Ao8tK3aVKlWoWLFivrEBzp07Z/66TZs2AKxdu5YjR46Yx/7pJ58CmA8fzszM5M033qRs2bL4TvYt8NhERETuVFpRIyIi8rejR44C8PDDD9P/4f7m57a2ttSsWZMnn3wyV5uyZcvy4YIPcz13dXXlySefxLmcM5MmTeKrr76iV+9eFvuNj4/no0Uf0bp1a/Oz7g92Z8SIESxYsIBly5bRpk0bZr8121xeqVIl3nn3HTp6dSQqKorDhw/TqlWrXLETEhJ47LHHePmVl83PqlatytvvvM3ly5cJCgpi4cKFLF+xvADvEHz6yadcvHiRvt59ee+993KU3XXXXbz73rtcu3aNH3/8kbVr15pX62S9t+3bt2fY8GHmNgaDgapVqzJw4MAC9Z9dUFAQw4YOu3FFC1q1bsWqVauK1LawEhISzLchVa1aNc96WWWXoy7neB4VFVXgttnrF0RW3SpVq+RZx9HREVdXV+Li4nLErluvLo8++ijr1q1jyONDctz61LFjR9q3bw/AN19/w4kTJ5jkO4lq1aoVeGwiIiJ3Kq2oERER+VvWAa2F+UX3Rrp26wrA0aNHycjIsFjngWYP5EjSZGnXvp3561HPjcpV7uTkxP0PmLbCnD1zNs8xPPfcc7meGQwGc8yDBw+azxu5kQ0bNgDw9NNP51nH29sbIMetP1nv7ZWYK2RmZhaorxuxs7PDzc2tSK8K5SvcuIMSkpW8AFPSIy+OZU1lSYlJOZ4nXTd97+iQT9tscbP3d8OxFSB29vj/jv3mjDcZP348tWvXJi0tjerVq/PMM8/gt9APg8HAlStXmD9/Pg3ua2A+L2nLli3079efpk2a0rVLVxZ8uCDPFWEiIiJ3Iq2oERER+VvHTh1ZtmwZu3fv5vnRzzNw0EBatWqV55aQLOnp6WxYv4Ft27aZz7HJOvcjS0pKCnHX4qhYKXes++67z2LcypUrm79u0KCBxTpuld0Acmwzyq5mzZrUvsvyNcgtWrTA1taWjIwMTv1yyrxVJS+XLl3izz//BOC5Uc9hMBgs1sua+5+X/jQ/a9uuLXZ2dvx88meG+gxl8ODBtGnbplgrLJo3b05AYECR20vx2dra8vyY53l+zPMWy9+e9zbx8fEsWryIMmXKsHHDRiZNmoSbmxu9+/Tm5ImTLFq0iMuXLzNr9qz/ePQiIiLWSYkaERGRv7Vu3Zpx48axaNEifvjhB3744QcA6tatS+cunXn88ce55557crRJTEzk2RHP5rgNytHRERcXF/N5ItHR0YBp9UJFcidqqlSxvO0k+3kkeW17sbE11UlLT7NYXrVa3ttlsra0xMbGEhMbk2e9LNlXGlm6QvrfridfN399zz338MYbbzBz5kxCQkIICQkBTFdAd+zYkcGPD6Zhw4Y3jHkrcnJyMn+dnJycZ73k66Yyp3JOOZ47lTV9n5yST9tscbP3d8OxFSB29viFiR0cHMzGjRsZMHAALVu2JC0tjXfeeQdHR0e+Wf0NtWvXJjk5mcGPDWbdunX4DPXB3d39xoFFRERuc0rUiIiIZDPmhTH079+frd9v5VDQIY4cOcL58+c5f/48qz5fxazZsxgwYIC5/uJFizl8+DAVK1Zkku8kOnbsmGMlTEZGBo0aNgLIcbXxrSj7lqVDwYdwdXUtVPtHHn2Ezl06s3XLVoKCgggNDeXixYt88803rF69mvETxjN69OiSHnapc3Z2Np/fcvny5TzrZZVVrZIzuWY+u6YAbSHvxJ8lWbGjLue93S85Odm8YqugsdPS0pjx5gxcXV159dVXAdP18tHR0fTq1YvatU2rvBwdHXls8GPMnjWbffv2KVEjIiKCEjUiIiK51L6rNqNGjWLUqFFkZGQQEhKCn58fIcEhzHhzRo5kzLZtptucpk6bSt++fXPFylpNU1ry++U+JSXF/At4pYqVbhgra5sVwKXIS4VO1AC4ubkxdNhQhg4bitFo5MTxEyxdupSdO3ey4MMFdO3SNdfNWnkJCwtj3NhxhR4DQLNmzfBb6FektoVlMBioW7cuJ06cyHFr0r+dCzeV1atXL8fzevVN358PP09mZqbFm5+y4hoMhlzt85MVOyoqitjYWIvb/LKPOb9bq7JbuWIlZ8+eZfr06eY/K5GRpuvcs5I0WercXcdU/vd17yIiInc6HSYsIiKSD1tbW9q0acOSJUuws7MjKSmJEydOmMv/+usvADw9PS22/+mnn/6TceYl8mIkERERFstCQ0PJyMjAYDDg4elxw1i176qNm5spWbN///5ij81gMNCkaRPmfzif6tWrk5mZSWhowa8KT0tLIzo6ukivq9cKdnhyScm6yvpA4AGL5SkpKeZr0v99VlBW2/j4eI4fP26xfWBgIABN729aqO1JLVq0wM7ODsj7ZzUrdtWqVQuUBLp06RKLFi2iUaNGDHliSK7ylJSUHN/faNuViIjInUaJGhERkb+lpqbmWWZvb29eyZC9XtZtRmfOnMnVJjExkSWLl5TwKAtv6dKluZ4ZjUaWLV0GQLt27ahQoWC3IGVdo/3ZZ5+Zk1SWGI3GHAcc5/fe2traUqaMaZFvalre9f6tTZs2nDp9qkiv/+pq7ix9vU2rrc6fP28++yi7NWvWEB8fj6OjIz169MhRVr9+fTw8TIm0Tz/9NFfbv/76iy2btwDQr1+/Qo3LxcWFTp06AbBi+YpcN3IlJSWx+pvV5jnkdYB0dm/Nfovk5GTeeOONHKt/atasCcDJkydz1M9KPtWqVatQYxcREbldKVEjIiLyN99JvkyePJkff/yRhIQE8/OIiAh8J/mSkpKCo6MjLVu0NJe179AegHlz53Ho0CHzOTTHjx3n6eFPF/ja65vF2dmZNavX8P777xMfHw+Ytrn4TvLlp59+wmAw8MILLxQ43shRI7nrrruIjY3liSFP8P3W73McZBsZGcnq1asZNHAQu3btMj//4IMPGDduHLt27crxnkRHRzNr1iwiIiIwGAy0b9++BGZ9c2RmZhIbE2t+JcT/8zNy9erVHGX/1rBhQ3r37g3AZN/J7Nu3DzCdYbRhwwbee/c9AIYNH5bjjKMsE1+aCMCO7Tt45+13zD+f586d4/nnnycxMZG77rqLwYMH52rr7++Ph7sHHu4eFldXjR03Fjs7O44dO8Zk38nm8UdGRjJ27FgiIyNxdXVl5MiRN3yP9u/bz86dO3nsscdo0rRJjrLGjRtTuXJlwsLC8Pf3x2g0cvz4cXMiqFPnTjeMLyIicifQGTUiIiJ/S0lJYevWraz3X4/BYMDFxYW0tDSuXzfdXmRra8ubb76Z44rtCRMmcCDwAJcuXWKoz1AcHBywtbUlKSkJR0dHFn60kGdHPFtaU8KzoScNPRuy9OOlfPrJpzg7OxMXF2dOKL3y6iu0aNmiwPFcXV355NNPGPP8GMLDw5k4cSK2tra4uLiQnJycI2mTffVFRnoGO7bvYMf2HYApgWQ0GklMTDTXGT9hfJ5XlVuDyMhIHuz+oMWyzp065/j+1OlTuerMnDWTCxcucPLkSZ4b9Rxly5YlIyPDvNqoS9cujB071nL8zp0ZP348H374IZ9++ikrVqygbNmy5oRNxYoV+WjRR9jb2xd6Xh4eHsyYOYNpU6exceNGvvvuO5ydnc2JPScnJxYsWEClSvmfY5SSksLMmTOpVKkSL738Uq5yOzs7Xnr5JV6b8hpTJk9hxpszzD8vjz76qA4SFhER+ZsSNSIiIn97+eWXad68OQcPHuT3338nKiqKjIwM7r77blq2bMmwYcNyHXR71113sXbtWhYsWEBgYCBxcXFUqFCB7t27M+q5UTRo0KCUZvOPyVMm4+7hzjdff0N4eDhOTk40btyYZ599lo6dOhY6Xp06dVi/YT3frvuWbdu2cebMGeLj43FwcMDd3Z37H7if7t274+XlZW4zbPgw7rr7Lg7+dJDw8HCioqJITU2lRo0aNGvWjP978v9o2bJlPr3e+pydnfn6m69ZuWIlW7Zs4cKFC9jb2+PZ0JNBgwYxePDgfLcWPT/mee5/4H5WrlzJsaPHzKtounTpwnOjnzOfH1QUAwcOpH79+nz26WeEhIRw9epVatSoQfv27Rn13Cjq1KlzwxgfL/mYP/74g9lvzaZ8+fIW6zzyyCPY29mzdNlSfvv1N6pXr86gQYMY88KYIo9dRETkdmO41a8KFRGR25abEeMfgGNpD+RW5O/vz5TJU2jVutV/fh6LyC0g04BhGvBWaQ9ERETk33RGjYiIiIiIiIiIlVCiRkRERERERETESihRIyIiIiIiIiJiJZSoERERERERERGxEjpMWERErJUOExaRm0WHCYuIiNXSihoRERERERERESuhRI2IiIiIiIiIiJVQokZERERERERExEooUSMiIiIiIiIiYiWUqBERESkCHx8fPNw98Pf3L+2hWJ2goCA83D1yvHx8fEp7WHKbatWyVa6fNxERkVtZmdIegIiIiNyebGxsqFSpEgAVylfIs15CQgKfLPuEHTt2EBkZiYOjA54engx5Ygi9evUqUt9//fUXmzdt5tixY5w7d44rV66QkJCAs7Mz9RvUp2fPnjz++OPY29sXKX5BHD9+nOWfLSc4OJhr165RuXJlOnTowMhRI6lTp06RYh48eJCAHwM4fvw4Fy9eJCYmhvT0dNyquPHAAw/w+OOP06ZNmxKeyT8yMzNZu3Yt/v7+nA8/T0ZGBnXq1MHb2xufoT5Fej9TU1Px/9afY8eOcerUKaKiorh69Sr29vbUqVOHDl4d8PHxoWrVqhbbV65cGQcHBzIyMoiNjS3uFEVEREqdrucWERFrZdXXc/v4+BB8KJi35rzFoEGDSns4ViUoKIhhQ4dRs1ZN9uzZk2/dP//8k6eefIqIiAgAnJycSE1NJT09HYAnnniC1994vdBj2LJlCy+/9LL5e3t7e+zt7UlISDA/q1evHp8t/4xq1aoVOv6NrF+/nmlTp5Geno7BYMDZ2Zn4+HjANMdFixbRtl3bQsd9dsSzBAQEmL93dnYmJSWFtLQ08zMfHx9em/pa8SfxL2lpabz4wovs27cPADs7O2xtbUlOTgagSZMmrFi5gnLlyhUqblRUFB29Opq/t7W1xdnZmbi4OLL+neri4oLfQj/ats37PYuIiODB7g8CcOr0qRt1q+u5RUTEamnrk4iIiJQKo9HI+HHjiYiIoFatWnz19VeEHQ4jNCyUV199FRsbG77++mvWrFlT6Ng1atTghRdfYMXKFRwMOsix48cICQ0hJDSEGTNn4OTkRHh4OJP+N6nE53X61GmmT5tOeno6/fr1I/BAIMEhwezes5v2HdqTlJTEuHHjiImJKXRsr45evPHGG2zavImjx44SEhrCsePH+H7b9wwYOACAVatWsXHDxpKeFh/O/5B9+/bh4ODAnLlzOHL0CIePHGbxksWUr1Ce48eP8/r0wifVHBwcGDZsGH4L/di3fx/HTxwn6FAQR48dZenSpdStW5f4+HgmjJ9AXFxcic9LRETE2ihRIyIiIqVi9+7dHD16FBsbGxZ+tJDmzZsDpl/cRzw7wnyujd8CP1JTUwsVu3nz5owdO5a2bdtSocI/266cnZ0ZPHgwU6ZMAUxbiS5dulRCMzJZsGABaWlpNG7cmLnz5pq3f9WqVQs/Pz9q1KhBXFwcS5cuLXTs4cOHM+SJITRo0AAHBwcADAYD9957L3PnzqVly5aAaUVPSYqKiuLzzz8H4OVXXmbgwIHY2tpiMBjo2rUrb802LUzZsmULp0+dLlRsV1dXJk+ZTI8ePahWrRo2NqZ/ntrb29OpcyeWfLwEgKtXr/LDnh9KcFYiIiLWSYkaERG5Zf355594enji4e7BmTNn8qyXkpJiPnB0967d5uepqals+34bk/43iYf7P0zbNm1p2qQp3bp245WXX+HEiROFHpO/v/8ND8/18/PDw90DX1/fPOvs2bOHMc+PwauDF00aN6F9u/aMHj2aH3/8sdBjslabvtsEQLv27fD09MxV/syIZzAYDERFRRF0MKhE+27SpIn568uXL5dY3Li4OPbv3w/A8KeHY2trm6O8XLlyPD7kcQC2bN5CSW9Bb9S4EVCycwLYsWMHqampuLi48Pjjj+cq7/5gd+655x6MRiObN28u0b7vvvtuypcvD5T8vERERKyREjUiInLLql69Oi1atgDI95fDffv2ER8fT/ny5enY6Z+zMAIDA5kwYQIbN27kzJkzGI1GDAYDkZGRbN68mSGPD7kpW0jyk5aWxquvvMqY58ewZ88eoqOjcXBwICYmhr0/7GXksyN59513/9Mx3SxBQabki5eXl8XyatWqUb9BfcC08qUkHT582Px1rVq1SixuaGio+byYDh06WKyTNd+oqCjCw8NLrG+j0cjRo0cBqF27donFhX8+q5YtW5pX8vxbBy/TfEv6szoffp5r164BJT8vERERa6REjYiI3NK8vb0B2Lpla551tmzeAsBDDz2U41YaJycnfHx8+OLLLwg7HGY+F2PPD3sYNmwY6enpTJ8+ncjIyJs7iWzefeddNm3aRJ06dZg/fz5hh8PMZ6u8/vrrlCtXjk8++aTEVy38165cucLVq1cBqF+/fp716tczlZ0LP1fsPlNTU4n4I4Lly5czb948AHr16oWbm1uxY2cJP2dKvFSpUoWKFStarJN9vufOFX9e8fHxHDt2jIkTJnLk8BEAnnzqyWLHzS5rXlmJM0uyPqvw8PBirxTKzMzk8uXLbN26ldGjRwNQs2ZNunbrWqy4IiIitwJdzy0iIre0Xr16MXvWbCIiIjh8+DDNmjXLUZ6QkGC+paavd98cZW3atLF4lXHNmjWZPGUyCQkJfPvtt/j7+/Piiy/evEn87bfffuPzzz+nUqVKrFi5gho1apjLnJ2deeL/nsC1vCsvv/QyHy/52JykKgh/f3+mTJ5SpHENGDiAuXPnFqltXqKiosxf53Xtcvay7PUL66EeD3HhwoUczwwGg+ln563ZRY5rSdY4q1StkmcdR0dHXF1diYuLK/K8QkNCefLJ3MkYZ2dnfH196dy5c5Hi5iVrnAX5rJKSkkhMTMTZ2bnQ/Ux9bSrr1q3L9dzT05MP5n+Ao6NVXgInIiJSorSiRkREbmkVKlQwb7nYsmVLrvLdu3aTnJxMtWrVaN26daFiZ/3vfVhYWPEHWgAbN2zEaDTSu0/vHEma7Hr27Im9vT1nz54t1Hkdjo6OuLm5Fenl4uxSUlM0S0pKyjG2PMdd1lSWlJiUZ50bqVipIm5ubjg5OZmf9e7dm4kvTSz0VdI3knTdNE5Hh/wTCllzzv4+FIadvZ3588k6B6ds2bJMmDghV0KyJFy/fh0o2GcFRZ+Xs4szbm5u5jNpwJSkmTp1Kvfcc0+RYoqIiNxqtKJGRERued7e3uz9YS/bvt/G5MmTcxzgmrVFqHef3ubbZLK7evUqX335Fft/3M+vv/5KQnwCGRkZOepEXS76ao7CyDo3ZcP6DWzftj3Peunp6YDpMOX8Vjhk16dPH/r06VP8Qd6CVq9ebf46OjqadevWsfTjpezevZt58+bRq3evUhxd0TRt2pSAwADA9PNw9uxZ/Bb4MWvmLNauWcvSZUupVq1aKY+y8Hx9fc2HbGethnvvvfd48sknefqZp5k0qeSvUxcREbE2WlEjIiK3vO7du+Pk5ER0dHSOg0xjY2L56aefACxuEzp37hzefb1ZsGABRw4f4drVazg6OlK5cuUc/6tf1NUBhZW1vSQxMZHo6Og8X5mZmcA/qxxuRdlXtyQnJ+dZL/m6qcypnFOedQrDzc2N0aNH8+5775KSksLkyZP566+/SiQ2gFNZ0ziTU/KeE/wz5+zvQ1GVKVMGT09PFi1exEM9H+L06dO8+cabxY6bXdmyZYGCfVZQMvNydnamb9++fP311zg7O7P8s+Xs3Lmz2HFFRESsnRI1IiJyyytbtizdunUDct7+tG3bNtLT07n33ntp3LhxrnZTJk8hOjqaho0asuyTZYSGhRIaFkrggUACAgOY/+F8AIyU7BXKeclKwEyePJlTp0/d8GXpfJ1bRfaVQPlt4coqq1Il7zNfiqJbt27UrFWT69evW9wyV1TmM3XyWYWVnJxMXFwcUPLzyjq3Zs+ePcTGxpZY3Kx5FeSzcnJyKtL5NHmpVq0aD/Z4EIBvv/22xOKKiIhYK219EhGR24J3P282b97Mrp27ePPNN7G3tzf/Am7pzI7IyEiOHTuGra0tixcvtrhNJDo6utDjKGNr+qs1NSU1zzoJ8QkWn1d2q8yvv/5K5KWSv2Vq69atvDX7rSK17d27N69Nfa1Ex1OpUiUqVqxIbGws586do2PHjhbrZd32lHWjUEmqVrUakRcj+ePCHyUWs179eoBpdVRsbKzFm5+y3/SU341XRZH95/iPP/7I8+apwqpXrx7nzp3j3Nm8b6nK+qzq1atXIn1mlzWvkvysRERErJVW1IiIyG2hQ4cOVKhQgfj4ePbu3culS5cIDQ0FLG97+vPPPwFTwiCvszx+OvBTocfh4uqSI74lx48ft/i82QOmG6sCfgwodL83kpycnO92qvxe8QnxJT4ewLwi6EDgAYvlf/31lzkx0LZd2xLv/+LFi0DJbNPJ0qJFC+zs7ADM2+7+LTAwEDCtUinppEZERIT565KcV9ZnFRoaSkpKisU6WZ/jzfissuZVknMSERGxVkrUiIjIbcHOzo5evUyHwm7ZvIWtW7ZiNBpp3LixxdtiXFxMCZXo6GiuXLmSq/z06dM5tlEV1H333QeYkgwnTpzIVR4SEpLnLVIPD3gYg8FAeHg433zzTb79XLt2rVDjGjRoUIG2U1l6lfTV3Fm8+5kSaIGBgZw6dSpX+fLlyzEajVSpUqXQ27yyDlzOy6bvNpm36rRo2aJQsfPj4uJCp06dAFixfIV5O1uWpKQkVn9jOty4r3dfDAZDgWPfaE6ZmZmsWL4CMCUg69atW4iR56/HQz2wt7cnLi6OtWvX5irfs2cPv/76KwaDAe++Bb82Hm48r99++43du3YDJftZiYiIWCslakRE5LaR9Yv/3r178ff3z/Hs3+rVq0f16tUxGo1MnDCR33//HYC0tDR27NjBiGdGFOl/72vVqkXTpk0B01kzp0+fNsfd9v02XnjhhRxXD2dXv359hg0fBsCMN2fw3nvv5ViZk5CQQEBAAK++8ioTxk8o9NisTffu3bn//vvJzMzkxRde5MiRIwCkpqby2Wef8fnKzwEYO24s9vb2udp369YND3cP8y1B2T311FMsXbqUc+fO5bjFKzIykoULFzJlyhQAGjVqRJcuXXK19/HxwcPdAx8fn0LPa+y4sdjZ2XHs2DEm+04mNibW3PfYsWOJjIzE1dWVkSNH5mobFBSEh7sHHu4eBAUF5SgLDQ1l2NBhbN26NUdyMT09nbCwMEaNHEVAgGk11ujnR+e65SwiIsIcO+vPR0FVqVKFoUOHAvDuO++yccNG8/u6b98+pkw2vZ99+/bF3cM9V3tfX1883D3MZ0llN3vWbGbNmkVYWFiO1TpxcXH4+/vj85QPycnJlCtXjuHDhxdq3CIiIrcinVEjIiK3jRYtWlCzZk0iIyMJDw/HxsYmzyupbWxseG3qa4wfN55Dhw7R86GelCtXjv9n787joqoXN45/DsOwg4q7llqau5WZWuaSmbnl1mKr2vLLbpvWvWXarexeLbtlZlpmmpZppVbuu5aamguuaW6ImguCuCA7DMz8/jg5SoACAoeB5/169SpnzjnzzEAyPPNdEpTO1wAAIABJREFU0tLScDgcVKtWjcGDBzN48OA85/j3m/+mf7/+hB8Ip2ePngQEBOBwOHA4HLRu3ZrGjRszYcKEbM997bXXSE1J5fvvv2fSxElMmjiJoKAgDMMgISEBl8tc2LhFixZ5zlXcGIbBJ2M/4fHHHuf48eM8/NDDBAQEkJaW5h5l8fDDD9OnT588X/vUqVOM/mg0oz8ajd1ud39tL93Bq0mTJoz/fHy227Zfjfr16/Pf4f/lrTffYt68ecyfP5+goCDi480pZAEBAYwdO5bQ0NA8X3vTpk3uAicgIABfX18SEhJwOByA+X39zIBn3KVKQRr08iDCw8NZs2YNr7/+Om+99RY2m829+1iTJk145z/v5Pm6ySnJzJ0zl+nTpuPl5UVwcDAul8u94DKYRdGYMWOoUqVKQT0dERGRYktFjYiIlBiGYdC1a1e+/PJLwCwzLt1d6O86duzI11O/ZsKECezcsZP09HSqVa9Gh7s6MODZAe7RMHl100038e133/LpuE/da3rUuq4WvXr14oknnmD8+PE5nmuz2Rj2zjC6d+/OjBkz2LJ1C6djzEWNq1arSv169bmj9R05FlCepkqVKsydN5dJkyaxYvkKTpw4QWBgIPXr1+eRRx6hc5fO+bruyJEjWbd2HWFbwog6GcXZs2fx8vKievXqNGzUkM6dO9O5c2dsNlu251/YtalJ4yb5evzevXtTp04dpkyewpYtW4iNjaVq1aq0atWKAc8OoGbNmnm+ZqNGjXj/f++zYcMG9uzZw+mY08THx+Pv70+dOnVodmszHnzgwWxHtMDF7d8Nw6BRo0Z5fny73c7nEz5n1qxZzJkzh4iDETidTho0aEC3bt3o179ftiOfrmTAMwOofX1tNm7ayNE/j3LmzBkcDgcVKlTghhtuoN2d7bj//vvd0xVFRERKOuPCJ3MiIiLFTAUXrmOAn9VBJG82bdpE/379qVa9Gr/88ovVcfIsJiaGNq3b4O/vz8qfV1K+fHmrIxWIiRMnMvqj0dzT6R7Gjh1rdZwCd/z4ce7uYG7jvW9/1jWP/sZpYLwF5G8rNBERkUKkNWpERERELhEWFgbAQw8/VGJKGoCwzWEYhsELz79gdRQRERG5DE19EhERkUIReSKS+vXqA9C8RXOmTZtmcaLc2RK2BT8/P55++mmroxSYjIwMtm/fTocOHXKcGuWpmt/a3L3+j4iISEmgokZEREQKlN1up0KFCpluK1umrEVp8u7tYW/z9rC3rY5RoGw2G1u2brE6RqEoX748vr6+VscQEREpMFqjRkREiiutUSMihUVr1IiISLGlNWpERERERERERIoJFTUiIiIiIiIiIsWEihoRERERERERkWJCRY2IiEgpMW7cOOrXq8+QIUOsjiIiIiIiOVBRIyIiIpIHffv2VeElIiIihUZFjYiIiIiIiIhIMaGiRkRERERERESkmFBRIyIiIiIiIiJSTHhbHUBERETyLyIigm+mfsPGTRuJjorGbrdTpWoVWrZsSa9evWjcuHGurhMVFcWiRYvY8NsGjh07RnR0NDabjRo1atD+rvY88cQThISEZHvu8WPH+fLLL9mwcQNRJ6MwDIPQ0FCqX1Od1q1b0+fBPpQLLec+3ul0MnfuXObOmcv+A/tJTEgkODiY8uXLc+ONN9KlSxfatG1TIK9PUTt39hxLlixh3bp1HD58mOjoaFwuF9WqVaN1m9Y89dRTVK5cOct59evVz9X1p34zlZYtWzJu3Dg++/SzKx7fvEVzpk2blufnISIiItZRUSMiIuKhpk2bxvsj3ycjIwOAgIAADMMg/EA44QfC2b9/f65/SX/vvfdYvmw5AHa7nYDAAOLj4tm7dy979+5l4YKFfDPtG6pUqZLpvD/++IN+ffuRmJjoPtff35/IyEgiIyMJ2xxGwwYNMxUvg18bzMKFC91/Dg4OJiEhgXPnznHw4EEiIiI8tqiZOGkiX035CgBvb28CgwJJiE8gIiKCiIgIFsxfwFdffUW9+vUynVehQoUcr+lId3A+9nym2wICAi57zvnz53E4HFfxTERERMQqKmpEREQ80NIlS3l3xLsAdOrUiYGDBlK7dm0AYmNjWfvrWv7Y80eur1f7+tr8+81/06ZNG2rUqIGXlxcOh4Pt27fz4QcfsmvXLoa9PYwvJn6R6bwP/vcBiYmJ3HTTTQx7ZxgNGzYEIDk5mYMHD7JwwUKCgoPcx4eFhbFw4UJsNhuDBw/m/gfuJygoCJfLRUxMDOvXr+fAgQNX+/JYpmrVqrzyz1e48847qV27Nt7e3mRkZLB3717GfDyGdevW8eqrrzJ/wXwMw3Cft279uhyv+c9//pPFixZTpUoV6t5QF4Cnn36ap59+Otvj9+zZw6OPPIrD4aBtm7YF+wRFRESk0KmoERER8TAOh4ORI0cC0O3ebnz00UeZ7i9btizde3Sne4/uub7moJcHZbnNbrfTokULJn05ia5duvLrr79y/PhxrrnmGvcxO3fuBOCNf7/hLmkA/P39adKkCU2aNMl0zZ07zONbtWpF/yf6u283DINKlSrRu3fvXGe+YNOmTfTv1//KB2ajoKcG9evXL8ttNpuNxo0bM/7z8dzX+z7Cw8MJCwujRYsWV7zexIkTWbxoMX5+fnz62aeZppBl58yZM7z4woukpKTQpUsXnhnwTL6fi4iIiFhDRY2IiIiH2bhho3sNmcGDBxf645UtW5amTZvy888/s3379kxFTVBQECkpKcTExOTqWkFB5uiaM2fP4HQ68fK6+n0N7Hb7ZacBXU7ZMmWv+vFzy8fHh1atWnHw4EG2bdt2xaJm9erVjPl4DAAj3h1xxfWGHA4HA18aSGRkJA0bNuS9ke8VWHYREREpOipqREREPMyOnTsAqFe/XrYL0+bX77//zozvZ7B9+3aio6NJSkrKcsypU6cy/blt27bMnj2b1we/zqOPPkqHuzvQqFEj7HZ7to9x2+23Ybfb2fPHHvr17UefPn1oeVvLq3oet9xyy2WnDhW1QxGHmP7tdLaEbeHEiRMkJSXhcrkyHfP31zG7a7z6r1dxOp08M+AZ7r333is+7vDhw9m6dSvly5fn088+xd/f/6qeh4iIiFhDRY2IiIiHOXP6DADVqlYrsGtOnjyZUR+OchcKNpuNMmXKuAuX+Ph4UlNTSU5OznTea4Nf4/Dhw2zfvp1JkyYxadIkfH19ufnmm+ncuTO97+uNn5+f+/hatWrxzjvvMHz4cLZs2cKWLVsAqF69Om3atKHPQ30yTaHyNIsWLWLI60PcC/l6eXkRHByMj48PAElJSSQlJWV5HS8VFxfH888/T0JCAne2v5NXXnnlio/73bffMWvmLOx2O2PHjqVatYL73hAREZGidfXjjUVERMSjhYeH89Goj3C5XDz2+GMsXLSQ33f9zqbNm1i3fh3r1q+jU6dOAFlGhpQrV47vvv+OKV9NoW/fvjRs2BCHw8GmTZv4z3/+Q/d7uxMVFZXpnPsfuJ+VP6/kjTfeoEOHDpQtW5YTJ04wY8YM7r/vfiZMmFBkz70gnT17lrfefAuHw0HXrl358acf2fn7TjaHbXa/jv37m2vp/P11vMDpdPKvf/6LI0eOULt2bUaNGnXF6WGbN292r1n09rC3aXZrs4J9YiIiIlKkNKJGRETEw5SvUB6AyMjIArne8mXLcTqdtG7dmrfeeivbY06fOZ3j+YZh0KpVK1q1agWYW0MvXbqU0aNHc+zYMUa+N5JPxn6S6ZwKFSrQr38/+vXvh8vlYveu3UycOJEVK1Yw9pOxtL+zfZYtrHOybds2Br40MJfPNrOmTZsy7tNx+Tr373799VeSkpKoU6cOoz7KvmC53OsIMOrDUaxdu5YyZcow/vPx7jV9cnLixAkGDRyEw+Hgsccf48EHH7yq5yAiIiLWU1EjIiLiYW6+6WYA9u/fT3R09FWvUxMVbY54adCwQbb3JyUluXdryo0yZcrw0EMP4XK5eGfYO4SFhV32eMMwaHJjE8Z8MoYOd3UgKiqKrVu35rqocTgcnD59+QIkJ7HnY/N1XnYujByqW69utiWNy+Vi08ZNOZ6/YP4CpkyZgs1m46PRH1GzZs3LPl5ycjIvPP8C586do2XLlgwdOvTqnoCIiIgUCypqREREPMxtt99G5cqViY6O5oMPPsiyPXdeBQcFA3DgwIFs758wYQKJiYlZbnc6nTidTry9s387cWFtmrS0NPdtaWlp7vVa/s5ms7mvleZIy/aY7LRs2ZJ9+/fl+vjCEhxsvo7h4eG4XC4Mw8h0/6xZszh69Gi25+7atYs333wTMNf9ad269RUfb+iQoezbt49rr72WMZ+MyfHrICIiIp5Fa9SIiIh4GLvdzutDXgdg0cJFvDzoZQ5FHHLfHxsby6xZsxgxYkSurtfqDnPK0prVa/jiiy/cC92ePXuWD/73ARO/mEjZslm3sU5ISOCee+5hwucT2L9/PxkZGYBZ4GzYsMG9tfSlpcPHH3/MwIEDWblyJbGxF0eznD59mhEjRnD8+HH3VCpPc/vtt2MYBuEHwhkxYgRxcXGA+TpN/nIyw/87PNvX8dzZc7z04kukpqbS+77ePPHEE1d8rIkTJ7J06VICAgL4bPxnlCtXrqCfjoiIiFhEH72IiIh4oK5duxIdHc2HH3zI0qVL3b+0e3t7uwuC5i2a5+parVu3puM9HVmxfAUfj/6YMR+PISQkhLi4OFwuFw888ADpGenMnTM3y7mRJyIZM2YMY8aMwW63ExAYQEJ8gru0ufbaaxkydIj7+Iz0DJYvW87yZcsBCAoKwuVyZRqxM+jlQdStWzffr01R+fuImeuvv55+/fsx9eupfDv9W76d/i0hISEkJCS41wBq3LhxlsWSD4QfcE+bWvXLKlrfkfNomrHjxnLLLbewdu1aANLT03nqyadyPL4g1+ARERGRoqGiRkRExEM9+eSTtLq9FVOnTmXTpk3ExMRgt9upV68eLVu2pFfvXrm+1scff8xXU75i7ty5HD16FJfLxS233MKDfR6kV69eDBkyJMs5QUFBTPhiAht+28D27duJiori3Llz+Pv7c91119Hh7g48/vjjmRbE7f9Ef66tcS0bN2wkIiKCmJgY0tLSqFq1Kk2bNuXRxx7l1ltvLZDXp7Bc2Hrbz9cvy31Dhw6ldu3azPh+BgcPHiQjI4MGDRrQs2dPHnv8McaPH3/Za186yuhyj31BWlraZdfnKcg1eERERKRoGDltDykiImKxCi5cx4Csvw2LWKjj3R05duwYzz//PAMH5W+3KbGc08B4C3jP6iAiIiJ/pzVqRERERHIpOjqa48ePA+R6VyoRERGRvFBRIyIiIpILJ06c4NVXX8XlchEUFESbNm2sjiQiIiIlkNaoEREREbmMxYsXM+ztYcTHxwPmIsJD3xhKQECAxcnkKmjuv4iIFFsqakREpLhKRj+npBhISUkhISGBMmXLcGOTG+n/RP9MW46LR0oHkqwOISIikh0tJiwiIsWV4cKVCtitDiIiJU6CgfEcMN3qICIiIn+nNWpERKS4cgHrrA4hIiWSHfjZ6hAiIiLZUVEjIiLFloExBYi3OoeIlDh7gZNWhxAREcmOihoRESnO5mOuJaF5uiJSUJKAj6wOISIikhMVNSIiUpzFGRitgfOorBGRq5cEjDQwtDaNiIgUWypqRESkuNtjYLQC1gOpQILFeUTEsziARCASeM3AGGFxHhERkcvSrk8iIuJJQoGeLlxNgMqUzO27vYDbAQP4DXBaG0dKsGuBpsCvQKzFWQrLWeCYgbEQ2IVG5omIiAdQUSMiIlJ8+AE/ASnAI0CatXGkFLgfGA90A7ZYnEVEREQomZ9EioiIeKIAYB5wGuiHOV1DpLD9hPm9thjoCWywNo6IiIhojRoRERHrBQGLMLcLfhyVNFK05mOWg/OAthZnERERKfVU1IiIiFgrBFgKRABPAhnWxpFSainmdLsfgbssziIiIlKqqagRERGxTllgOfA7MACVNGKtn4EHgRlAJ4uziIiIlFoqakRERKxRHvMX443AC2h3Jyke1gC9gGnAvRZnERERKZVU1IiIiBS9SsAvwErgFbRlsBQvv2GWNJOB3hZnERERKXW065OIiEjRqopZ0PwEDEMljRRPm4EumLtB+QAzrY0jIiJSeqioERERKTrVMUfSTAeGW5xF5Eq2AR2BZYAd8/tWRERECpmKGhERkaJRA7OkmQh8YHEWkdzaBdwNrMAcWTPF2jgiIiIln4oaERGRwnc95sLBnwBjLM4ikld7gPaYU/Z8gAnWxhERESnZVNSIiIgUrhswS5qRwOcWZxHJrwOYZc3PmGXNWGvjiIiIlFwqakRERApPA8wpI8Mwd9AR8WQRQDvMKXw+wChr44iIiJRMKmpEREQKR2NgOfA6MM3iLCIF5U8uljW+wLvWxhERESl5VNSIiIgUvKbAEuBlYIbFWUQK2nHMsubCNKh30DbzIiIiBUZFjYiISMFqDiwEngd+sjiLSGE5CdyJucCwLzAUlTUiIiIFwnC59DNVRESkgLQC5gJPAwssziJSFMpjrsO0BvgnKmtERESumooaERGRgtEW+BHoByy1OItIUSqH+T2/BXgJcFobR0RExLOpqBEREbl6HTDXonkYc90OkdKmDLAY2AM8i8oaERGRfPOyOoCIiIiH6wR8DzyAShopvc4DnYG6wBTAZm0cERERz6WiRkREJP+6Y2693QtzjQ6R0iwe6Apcg/n/hTatEBERyQcVNSIiIvlzH/Al0A34zeIsIsVFImaBWQ5zOqCPtXFEREQ8j4oaERGRvHsIGI851SPM4iwixU0y5igzO/AD5vbdIiIikksqakRERPKmL/Ax0BHYbnEWkeIqFXgQcABzAH9r44iIiHgOFTUiIiK59xQwErgb2GVxFpHiLg1zJ7TzwHwgwNo4IiIinkFFjYiISO48B7wD3IW5BbGIXFk68DgQibl9d5C1cURERIo/FTUiIiJXNggYDNwJHLA2iojHyQCeBMKBZUCItXFERESKNxU1IiIil/caMBCzpDlkbRQRj+UEngV2ACswd4USERGRbKioERERydmbwP8B7YA/Lc4i4umcwIuY29n/DJS3No6IiEjxpKJGREQkKwP4L/AI5kia45amESk5XMA/geXAKqCStXFERESKH2+rA4iIiBQzBvA+0AVoD5yyNo5IieMChmJu4b0a6ACctDKQiIhIcaKiRkRE5CIDGA20xSxpzlgbR6TEcgHDMLfwXoO5m5pGromIiKCiRkRE5AIvYBxwK+Yn/LHWxhEpFd7FLGtWY/5/p7WgRESk1FNRIyIiYpY0XwANgY5AnLVxREqVD8k8ska7q4mISKmmokZEREo7GzAFqAl0AhKsjSNSKn3CxTVr7gYOWJpGRETEQipqRESkNLMD3wAVgK5AkrVxREq1CZgja1ZhjmzbY20cERERa6ioERGR0soH+A4IALoDKdbGERHM0W1pwErMEW67rI0jIiJS9FTUiIhIaeQL/IC580xvzCkXIlI8TAccwAqgC7Dd2jgiIiJFS0WNiIiUNv7AbCAReBTz03sRKV5mYpY1SzFHvG22No6IiEjRUVEjIiKlSSAwDzgF9APSrY0jIpcxG7NIXQj0An6zNo6IiEjR8LI6gIiISBEJBhYDx4G+qKQR8QQLMf9/nQu0tTiLiIhIkVBRIyIipUEZzCkUB4CngAxr44hIHiwDHgZ+AjpYnEVERKTQqagREZGSrhzmoqQ7gGcBp7VxRCQffgHuB74HOlucRUREpFCpqBERkZKsAvAzsA54EZU0Ip7sV6An8A3mAsMiIiIlkooaEREpqSphfgq/DPgX5lbcIuLZNgDdgC8xR9iIiIiUONr1SURESqKqmCNpZgH/QSWNSEkSBnQClgB2YIa1cURERAqWihoRESlprsEcSTMVeNfiLCJSOHYAHYHlgA/mdCgREZESQUWNiIiUJDUxS5rPgVEWZxGRwrUbcxeoFZgjayZbG0dERKRgqKgREZGSojbmdKfRwFiLs4hI0dgLtMf8f98XGG9tHBERkaunokZEREqCusBKzKlOX1icRUSKVjjQDnM0nQ8wxto4IiIiV0dFjYiIeLqGmFMf3gKmWJxFRKxxmMxlzQfWxhEREck/FTUiIuLJbgSWAoOB6RZnERFrHeViWeMLDLc2joiISP6oqBEREU91C7AYGATMtDiLiBQPJzDLmp8xR9a8DbgsTSQiIpJHhsuln10iIuJxWgALgH8AcyzOIiLFT0XMdauWAa+jskZERDyIihoREfE0d2CWM08BCy3OIiLFV3lgObAWeAWVNSIi4iFU1IiIiCdpB/wA9MX8pFxE5HLKYq5jtQ14EXBaG0dEROTKVNSIiIinuBv4HngIc7FQEZHcCMFcz2of8CyQYW0cERGRy/OyOoCIiEgudAG+A+5DJY2I5E0c0BmoDXyFNtMQEZFiTkWNiIgUdz2AqUBPzLUmRETyKgHoBlQBpgN2a+OIiIjkTEWNiIgUZ/cDk4CuwAaLs4iIZ0vCLH6DgRmY23eLiIgUOypqRESkuHoE+BToBGyxOIuIlAwpmFMobcCPgK+1cURERLJSUSMiIsVRf+AjoCOww+IsIlKypAIP/vXveYC/tXFEREQyU1EjIiLFzf8B7wJ3AbstziIiJZMDc9TeGWAhEGhtHBERkYtU1IiISHHyPPAW0B5zK10RkcKSDvQDjgJLMNeuERERsZyKGhERKS5eBl4D7gTCrY0iIqVEBvA0ZjG8DChjbRwREREVNSIiUjy8DrwItAMOW5xFREoXJ/APYBuwAihnbRwRESntVNSIiIjV3gKexCxpjlqcRURKJyfwErAW+AWoYG0cEREpzVTUiIiIVQxgBPAw5nSnE5amEZHSzgW8irlezSqgsrVxRESktPK2OoCIiJRKBvA/4B7MkibG0jQiIiYX8G/MrbtXY+4+d9LKQCIiUvqoqBERkaJmAB8DrTF/CTprbRwRkUxcwH8wt/Beg/n31HFLE4mISKmiokZERIqSF/AZ0BS4G4i1No6ISI7ewxxZswboAByxNI2IiJQaKmpERKSo2ICJQF3MKU9x1sYREbmij4A0zGlQHYAIS9OIiEipoKJGRESKgjfwFVAd6AIkWBtHRCTXxnFxzZq7gf2WphERkRJPRY2IiBQ2OzANCAXuBZKsjSMikmcTMdes+QXoCOyxNo6IiJRkKmpERKQw+QAzAF+gB5BibRwRkXz7CrOs+RnoBPxubRwRESmpVNSIiEhh8QN+ADKA+zCnDoiIeLLpmGvWLAe6AtusjSMiIiWRihoRESkM/sBc4DzwGOan0CIiJcEszLJmCeZIwU3WxhERkZJGRY2IiBS0QGA+cBJ4Aki3NI2ISMGbi1lALwB6A+utjSMiIiWJl9UBRESkRAnG/JT5KNAflTQiUnItAh4H5gB3WhtFRERKEhU1IiJSUMoAy4C9wNOYa9OIiJRky4GHMdfjutviLCIiUkKoqBERkYIQCqwEtgL/AJzWxhERKTK/YC6Y/h3mAsMiIiJXRUWNiIhcrQqY29WuAQYCLmvjiIgUubWYCwt/DfS0NoqIiHg6LSYsIiJXozLmSJr5wJuopBGR0msj0AVz7Ro78KO1cURExFOpqBERkfyqhjmSZgbwX1TSiIhsBToBSwEfzOlQIiIieaKiRkRE8uNazHUZpgAjLc4iIlKc7AQ6Yi6ubgemWhtHREQ8jYoaERHJq1qYJc2nwGhro4iIFEu7gQ7ACsyRNZOsjSMiIp5ERY2IiORFbcyS5kPMokZERLK3D2iPOUXUB/jM2jgiIuIpVNSIiEhu1cNcOHg4MNHiLCIinuAgcCcXy5qPLU0jIiIeQUWNiIjkRiNgOebOTl9ZnEVExJMc5mJZ4wu8b2kaEREp9lTUiIjIldyEuYPJq8C3FmcREfFER4F2mFNHfTBHJmqnPBERyZaKGhERuZxmwCLgJeAHi7OIiHiySMyy5sLImjdRWSMiItkwXC79fBARkWy1BOYDA4B5FmcRESkpKmLuBrUCGIzKGhER+RsVNSIikp3WwGzgCWCxtVFEREqcUMx1v9YDL6OyRkRELqGiRkRE/u5OYBbwOOYvEiIiUvDKAkuAncDzgNPaOCIiUlyoqBERkUt1xFww+CFglcVZRERKumDMUYvhwDNAhrVxRESkOPCyOoCIiBQbXTFLmvtQSSMiUhTigc5ALWAq2uhDRERQUSMiIqaewNdAD2CdtVFEREqVROBezEWGvwXs1sYRERGrqagREZEHgS+ALsBGi7OIiJRGSZiFeSAwE/CxNo6IiFhJRY2ISOn2KDAW6ARstTiLiEhploI59dTA3HXPz9o4IiJiFRU1IiKl1xPAh8DdmLuOiIiItdKAPpjToeYBAdbGERERK6ioEREpnQYAw4G7gD8sziIiIhc5gMeAU8BCzOlQIiJSiqioEREpfV4A/g20B/ZbnEVERLJKxxz1eARYgrmNt4iIlBIqakRESpd/Av8C2gEHLc4iIiI5ywD+D9gDLAfKWhtHRESKiooaEZHSYyjwHGZJc8TaKCIikgtOzL+3w4CVQKi1cUREpCioqBERKfkMYBjQD7OkOWZtHBERyQMXMAhYBfwCVLQ2joiIFDYVNSIiJZsBjAAeAO4EIi1NIyIi+eECBmMuLrwKqGxtHBERKUzeVgcQEZFCY2Buv90Bc+Hg09bGERGRq+AC3sTcwns15t/tKt9FREogFTUiIp7NwHzznt3tnwC3Y76ZP1uUoUREpND8F7OsWQPcRc7TWXP6+SAiIsWcpj6JiHiudsD32dzuBUwAmgN3o5JGRKSkeR8Yj1nWXJfN/R2Bb4o0kYiIFBiNqBER8VxPABv/dpsN+BKoDdwDxBdxJhERKRofk3ka1MFL7tsC/AiEAHFFnkxERK6KRtSIiHgmP6AnMOtBmdU8AAAgAElEQVSS27wxP0GtCXRBJY2ISEn3GeaC8auB+pfcfg5ztE0vCzKJiMhVUlEjIuKZugA7uLiQpB34DqgA3AskWpRLRESK1iTMRYZ/ARpfcvv3wCOWJBIRkauiokZExDM9wsX1aXwxR9YEYI6ySbIqlIiIWOJr4FVgBXDTX7fNx1xQvqJFmUREJJ9U1IiIeJ5goBPwE+YUqNmYO3vcB6RYmEtERKzzHfASsBy4FXNk5RLgAStDiYhI3qmoERHxPD2BtZilzHzMtWgewlxU8oIgwKfoo4mISBEK/duffwQGAIuB29D0JxERj6SiRkTE8zyCOYpmIRANPA44gErA/2G+QY/EHHUjIiIlkzcQBuzBXFC4GWAA8zB3BbxQ5DcCrrUmooiI5IfhcrmsziAiIrlXHjgE7Ab2A//FHGFzH+a6BMswS5wlaEtWEZGSzgtojvkz4D7MkZRzMH8O+APTgc3AKmCURRlFRCSPVNSIiHiWl4HhmJ+g2oBamJ+azsFcRFJr1IiIlE4G5uiZC6VNVcwRN+2BE0Bd66KJiEheqKgREfEshzB38Pga8xPTtUC6lYFERKRYuh7oDfQHmgA1gGOWJhIRkVxRUSMi4lmCMLffdlodREREPEYw5no1IiLiAbytDiAlWghQ7a9/GxZnEZHiLQU4jbkIsj5BEBErBAHVgTLofYuIXF4yEAOctDqIlEwqaqSgBQEPxjuTn/Y17M3jnMmpya40p1O/d4lIDgwMfLAZIV7+PsBZb8M21cfw/gbYZ3U2ESnx/IH7XS7Xk8AdQBoasSgiV2ZgLt4dDUw1DOMbIMLaSFKSaOqTFKRySc7UdQccUTUXJ+8M3JQaQYrLYXUmEfEgdb2r0N6/QVoX/5vS/b18HsDcvUpEpDAEulyu1UADl5NAfaYkIvlheJGKQbphGF2BX63OIyWDihopKCFJztQNK5J31x4f/7Ov1WFExLPVt1fl/XIPJfl7+fQGlludR0RKHD+Xy7UWF41dTvysDiMiHs4Aw4tEwzA6AeutjiOez8vqAFJiPL7HceI6lTQiUhD2OU7y3vn5AQnOlPFWZxGREuk+zJE0KmlE5Oq5wOUk0OVyfWJ1FCkZVNRIgYh3Jj+1MGmHv9U5RKTk2JJ6GMwFyW+wOIqIlDAul+tJl5NAq3OISAliTlRpDFSxNoiUBCpqpCBU9DG8G29NPWJ1DhEpQZy4WJOyzyvdlfGA1VlEpEQJANpoTRoRKXAuMoCeVscQz6eiRgpCzZiM+JQ00q3OISIlTITjlG+Ky9HQ6hwiUqJUA7TbgYgUOJeLAJfLVdfqHOL5VNRIQSiT5Eq1OoOIlECJrlScuMpbnUNESpQyaAtuESk8Fa0OIJ5PRY0UBCNDu4cVmvglBzjSbjInBy0q8sd2nIznSLvJHGk3ucgfWwTAiRMXLv2sEpGCZIAmPhWlOXNm06BRffo90TfP5544cZwGjerToFH9QkgmUij0vkWumrfVAUTEMyVvP0nKjpP41AklsE0tq+OUCNH/XkHyuqMABHa+gYpD22Z73LGHZpIRlXDZa5V7rgVlHm6S5wwnBy0idUfUZY8J7t2A8i+3yvO1RURERC5wOp38+OMPzJ47m0OHDpGRkUHNGjXp1u1e+j7eFx8fn3xdd//+/WzfsZ1du3exe/cuIiIiyMjIoEuXroweNbqAn4VI4VBRIyI5Mry98K5RJtv7Unac5PzX2wnsfIOKmgKQuPaIu6TJLa9gH7Dbsr3P8Lu6v96NQDuGb/bX8ArI3xsnERGRvPL2tnPddddZHUMKmMPh4MWBL/Lrr2sAsNvt2Gw29u7by959e1m2bClfTfmawMC8b842ZOjr7Nu/r6AjixQpFTUikiPvioFcM00b7hQ2Z5KDs2M3YgTa8S4fgOPo+VydV3H43fg3rVoomUJfuo3gLloLT0RErFW5cmUWL1xidQwpYJ+M/YRff12Dr68v77z9Dt2798DLy4vVa1Yz9I0h7Nq9i3f+M4wPPxiV52t7e3vToH4DGjVqTJPGjVmxcgXr1q8rhGchUng0f05ESg1XhpOkDUfJiC9ei1/HTtlKxqlEyj3VDK9Qf6vjiIiISAnkcrnYHLaZyMhIS3PExMQwbfo3APzrn/+iV6/e2Gw2DMOg/Z3teXfEewAsWryI/fv35/n6M76fyeyf5jD8v8Pp0+chKlSoUKD5RYqCRtSIx7mwPkflMV2xVwsmdup2kjefION8Ct6h/gS0q0XZfk3xCsp5ekbqgdPEzdpNyo4oMmKT8Qqw41O3AsHd6xHYLvvhtVfzuBfW/Sg/pE2OoxQuvX5uR0lkxKaQuOoQyWEncBw7T0ZMErhceFcOwr9FdUIeboJ3haxDRh0n4znx8CwAaq15mpQ/ThE3cxepu6LJiE0h+L6GlH/ptizH/f1cgMSl4SQuDc90/eoz+pC6M4rTI3/FK9Sfa394GMM7+144eVsk0a8swfC1ce3sRy/7dcuvtCOxJCw9QOLyCDLOJFF9Rh9swb4F/jj5kXrgNHGz9+BTJ5Tg3g1IXHvE6kgiIpJPaWlpzJg5gyVLFxMREUFycjJlypShQvkK3HJLM7p3707Tm5u6j58zZzZvvPkGzZs355uvpzF37hy+nzmDiIiDGIZB40aNeerJp2nTps1lH3fVql/48acf+f333zl//jzBIcHc2ORGHnv0MVq3zvnctLQ0fvhhFkuWLuHgwYMkJSdRoUJFbr/tNp568mlq166d47nnYs8xffo0Vq9ZzbFjx3A4HFSuXJmGDRvRtUtX7u5w92Xzfj31a/bu20tGegZ1briBfo/3pVu3e7Mce+LEce6+x7zW3j8yT2cZ+sYQ5s6bywvPv8Bz/3ie6d9OZ86c2fx59E98fXy5uenNvPj8izRunPOabYmJiUz/dhorV67kyJ9HSEtLo0qVqrRt04annnyaqlWzvidzOp3MmzeXufPmsv/AfhITEwkODiY0tDw33XgjnTt1yfI1O378OF9O+ZKNGzcQFRWFYRiUKxfKNddUp/UdrXnwgT6UK1cux5xXIzIykrnz5jJ33hyOHTvG1K+mUq1atUJ5rNxYvmI5aWlpBAcH0+fBh7Lc3+GuDtSqVYsjR46wcNFC6tWrl6fr22zZTwsX8SQqasRjpZ+II+adX3DGpmD42zGA9KgE4mbuJmndUaqM64Z3+YAs58XP38eZj38Dp7nhg1eQD86ENFLCTpASdoKkjrWpMLQthi37YiG/j1sYzn+3k7iZu80/2Ay8An1wJqbh+DMWx5+xJKyIoMroLvjUDs3xGom/HCJmxGrIcGEE+YCXcdnHNGwGXqH+uJIduJLTMXxs5nl/Oyag/XUY4zbiPJtM8qbjBNxRI9vrJSw+AEBA21oFWtI4E9JI/OUQ8UsOkLYnxn27LdQfr6tcv6WguJwuzoxaD04Xoa+0yvF7TkREir/09HT+b8DThIWFAWAYBsHBwcTGxnLmzBn2H9hP7PnYTEXNpUa+P5Jvpk3Fy8uLoKAg4uPj2bhpIxs3beS1V1/jqSefznKOw+Hg32++wYKFC9y3BQUFcfbsWVavWc3qNat5+qn/49V/vZrl3FMxp3j22QHutTy8vLzw9/fn5MlIZs+ZzaLFi/jgfx9yT8d7spy7ZesWXhr4IrGxsYC5vkhAQADHjx/nzz//ZMmSxVlKlQvGfz6ecZ+OxcvLi8DAQJKSk/j99528Ongnp8+coX+//ld4pbNKT8/gH889y7r167B727H72Dkfd541a9awceNGvprydbave0REBAP+8Yx7hIm3tzc+dh+OHv2T6d/+yYIFCxj/2efccsstmc57fchgFi5a6P5zcHAwCQkJnDt3joiIgxyMiMhU1Pyx5w/6P9GPxMRE8/XytuMfYL7WJ09GEhYWRoP6Da9YyOVFSkoKK1auYM7cOWzcuAHXXzu0hoSEEBKS/fqDRWXz5k0A3NrsVnx9s//g7I5Wd3DkyBE2bdpYlNFEio3i8duKSD6c/XwztjJ+VBreAb8bq+Byukj+7SinP1hH+ok4Tr+3hiofdcl0TsruaHdJE9CuFqEv3oZ3pUCcSQ7ifvqD2MlbSVwRgb1GGcr2y/6NVH4et7B4Vwqi7DO3EnD7tdhrlsXw9sKV4STt4FnOfbmFlM0niBm+impf3YdhZF/AnP5gHQGta1LuuRbYqwbjSneSHpN42cesMedRzn21jfNfbyfgrutz3J0oqMP1xM/bR8KSA9kWNc7ENJLW/mke2/Xq10NxOV2kbIskYUk4SWuP4ErNMO/wsRFwRw2COt+Af/PqxaYQiZ+9h7T9pwnqVhe/xpXzfP65TzcSE5OEMzENrxBffG8oT2DHOgTedd1VP8e4mbuInbSVjPMpeAX64FO7HAHtriOoyw145bDIsIhIabZw0ULCwsLw9/fnnWH/odM9nfD19SUjI4Po6GhWrV5FYmL2O/bt3buXsLAw/u/pZxjwzACCg4M5FXOKUaM+ZMHCBYz6aBQ33XgzzZo1y3TeqI9GsWDhAmrUqMkrL79C2zZtCQgIIDExgfkLFvDR6FFMnvIlDerXzzRaxeFw8OKLL7Bv/z5uu+12Br40kMaNGmO32zkVc4rJkyfzzbSpDBn6OvXr1adGjYs/w48ePcpzz/+DhIQEGtRvwOuDX+fWW5tjs9lISUlh67atzJw5I9vnuW/fPrZt28bAlwbx2KOPERISwunTpxnx7nCWLV/Gx2NG07NHT8qWLZun1/77Gd9hGAajP/qYDnd1wMfHh/379/Pa668SHh7OyJHvMWvmD5nOiY+P59nnBhAZGUnnTp35x7PPUadOHWw2G8eOHWPsuE9YuGghg14eyKKFiwkJCQEgbEsYCxctxGaz8dqrg3ng/vsJDAzC5XIRczqG39av50D4gUyP9eGHH5CYmMiNN97EsLeH0bBBQwCSk5OJiDjIgoULCQoOytNzzsmOnTuYM2c2i5csJiHB/H6z2WzccUdrevXs5X59rBQREQFAnTp1cjymdm3zvohDEbhcrhzfx4qUVHq3LZ4rLYPKH3TCfo35g9PwMghoXZOKAXaiX1lCypZIUn6Pwu/GKu5TYidvBacL3yaVqTisvfuXWa8AO2X73owrOZ3z3+7k/He7CLm/EV6B2fwgy8fjFpaQBxpluc2weeFbrwKV3+1I5DNzcRyOJXVnFH43Zz+dyqdOKBXfuQvjr5E0hrcX9qrBBZIv6N56xM/bR9KGY2TEJmMrm3n9lcSfD+FKSce7ajB+V7EoruNEHAlLw0lYFk5G9MWSybdhRXNXqruuv+JUp9xseZ2T6jP65Pk1S49J5NzkrXiV8aXcs83z9bhpB89i+Hlj+NjcI5eSNx0nfuE+Ko24+6qmdzkOx4KPDS8/b5znU0jZdpKUbSeJn7eXyu/fg3flgnlDKSJSUuzcuROAHj160qN7D/ftNpuNatWq8dijj+V4bkJCAg/c/yD/+ue/3LdVqliJ/73/AadOnWLT5k18Ov5Tvpr8lfv+I38eYdr0bwgNDeXrKV9nmqITGBjEIw8/QkhICK++9i8mTPwiU1Ezd95cdu3eRbNmtzJxwkTsdnumxx06ZCipqSnMnDWTqd98zVtvvu2+/+Mxo0lISKBWrVpM+2YagYEXfx74+flxR6s7uKPVHdk+z/j4eAYNfJl/PPsP920VKlTg/ZH/I2xLmHskUK+evXJ8rbITFxfH9G++zVRk1atXj5HvjuSBPg+wa/cuIiMjM033mTxlMidOnKBb126M+vCjTNe79tpr+fCDUZw/f56169by408/uEc0Xfg6t7q9VabRP4ZhUKliJXr16p0l387fzXPeGPqGu6QB8Pf3p3HjJpedmpUbp05FM2/+fObOm8OhQ4fct9etW5dePXtxb7fuVKxY8bLX6PdEX/dosLya+tVUWrRomevjY06bI50rVaqU4zEX7ktKSiIpKTHT95lIaaCiRjxWQPvr3GXJpfxvqYZv40qk7j5F4poj7sIkIy6VlO0nASjz2I3Zjjgo8+iNxP2wG1eyg6SNxwjqkHVudl4f1yqGjw2/W6vjOBJLyq7oHIuakD6N3SVNQfOtWwGfuuVJO3CGhOURlOnTONP9CUvMT5yCOt+Q509KnEkOEtccJmFJOKk7o9y32yoFEnRPHYI634D92twP7bWV8cOVlpGnDBcYtry/fmfHbsSV5CD0tdbYyvjl6dyA1jXxu6kKfjdVcZ+bHp1A3Ow9xM3aTeqOKGLe+SVfI7v8bq5KcNe6+N1aHVuoP4ZhkHEumfhFB4iduh3HoXNEv76MapN6YeSwNbiISGkUFGT+Ink6JuYKR2bv2QHPZrnNMAyeeWYAmzZvYtOmjcTGxrpHm8ybNw+Xy0WXzl2yXUcFoNM9nXjj30M5eDCcUzGnqFSx0l/nzgWg3+N9M5U0l7r33u7MnDWT3zb85r4tMTGRlT+vBOClFwfm+ZdnX19f+vXtl+V2Pz8/7rijNQsWzCc8PDybMy+vWbNbs4w2AmjUqDFVqlQhKiqK8IPhmYqaefPN1+DJJ57M8brdut3L2nVr+e2339xFzYWv85mzZ3A6nXh5XXkEa1BgECkpKcTk83sjO2lpaaxa9Quz585h/fp1ZGSY72FCQ0Pp1rUbvXr1zlQKXUmZMmWpUD5/i+7m9D2Uk+SkZAB8fXN+/+Pnd/G+xKQkFTVS6qioEY+VU/EA4HdTVVJ3nyLtwGn3bWnhZ8AFGOb92fEK8sGnXgVSd0WTduAMZFPU5PVxC1van7HEz9lDys4o0qMScCU7zOd5iYwzSTme79so508zCkJQt3qcPfAbCUsOZCpq0o7EkronBrwMgrrckOfrRg6YR/oxcxtrw9+bgDa1COp8A35Nq+areKo2sWeez8mvpN+OkvTrEXwbViSoW96nfJV/6bYst3lXDiL0uRZ4Vwni7JgNpGyJJDnsOP7Nr8nTtcs9eUuW22zl/Cn7+E341C7HqSErcByOJWFJOME96uc5u4hISdWmTRu+nDyJn3/5medfeI5evXrTvHlzypW98gKxVatW45prsv/7utktzbDZbGRkZLBv3z5uu838GbBjx3bAHB2zbNmyHK+dnp4OQNTJKCpVrER6ejq/7/odgGH/GcbwEcOzPS/Daf7iHxV18cOQP/7YTXp6OoZh0OYyixTnpHbt2gQEZL+OX+VK5hTguLi4PF+3SePGOd5XqVJloqKiMl335MmT7uf17HPPYpD9+waHwwFkfg1uu+027HY7e/bsod8T/ejzYB9ua9mSSpVynsLctm1bZs+ZzZChr/PIw4/SoUMHGjVslOeC41LPv/Ac639bD5hFSfv2d9GrZy/atmmbr+uO+2RcvrOISMFTUSMey7tizgv22v66zxmb4r4tI9Zs770CffAKyPkHWHbnXs3jFqaEnyM4/d6vkO40b/AyFxTGxxzpcGHBX1dyeo7XsJXN22iOvAq6uzbnPt+M49A5Uvefxree+WnNhdE0fs2q5WsajctxcfSL301VCOxwPX43Vym00UEFxZns4MyY38BmmAsIF/Cc6+BeDYibsYv0qASS1h/Lc1FzOQG318D3piqk7owi6bejKmpERC7RonkLXnpxIJ9PGM+q1atYtXoVANdffz3t2rajT5+HqFWzVrbnVq6c84cmfn5+hISEcO7cOc6eO+u+/cLojMTERPcitZeTkmK+Dzp//ry7gLiwGPDlz7v4nub0mTOAuXhucHDep0kHBmbdifICX19zunl6uqNwruu4eN1LR7ac+es5XU7yX68dQK2atRj29juMeHc4W7duYevWLQBUr16d1q3b0OfBPllGsrz66mscPnyY7Tu28+XkSXw5eRK+vr7cfNPNdOrUmd69emcaQZIbaY409383adyErl260vqO1ldV/hQV/wB/HHEOUlNzfr986fddYA7lnkhJpqJGSp1Lf8H3ZBmxyZz5cD2kOwm46zrKPHwjPrVDM22DfW7yVs5/s+PvA2wyKeyFdb2CfAi48zoSl4aTsOQAvvUq4Ep3krD8IADB+VxEuPzLtxM/fz/Jm46RvPE4yRuP4xXqT9DdtQnqVAefOuUL8mkUmPPf7yIjOpGge+thv6YMzqS/vSHN+OurleF032f4e+e60DEMA5/6FUmPSiD9ZN4/lbwS3wYVSd0ZRfrJ+AK/toiIp3v+uefp0b0HS5YsZnPYZnbs3MGhQ4c4dOgQ06ZPY/h/R+R5/ZWcOF3mhzRDXh+ap52SnE6n+79n/ziHBg0aFEgeT3LhtQPYtGGze6Hg3Lr/vvtp17Ydi5csZvPmTWzdtpUTJ04wc+YMZs2ayaCBg3h2wMV1eMqVLce3079jw8YNrF69ii1bt7J//z5zStvmTXz19RS++XoaVarkftr8oJdeZsbM71n580q2bd/Gtu3bCAkJoXOnzvTs0SvLTlXFScWKlYiLi+PUqVM5HnPhvoCAAE17klJJRY14rPTTOU/nyfjrPq9LRotcWMjWlZqR7cK27nNjsp57NY8LF8uQy62B4kpIy/G+7CRvPI4r2YG9VlkqvtU+25EkGWeTszmz6AV3q0vi0nASV0YQ+nxLksOO4zybjFeILwGta+brmgG31yDg9hpknE0mYflBEpYewHE4lrhZu4mbtRt7nVBzrZqOdbCFZv+1vlTkgHmX3e3qcqp90QPvSrl7E5EebS5YnLBwPwkL9+d4XOKKCBJXmLsi5GexYhERscY111zDM88M4JlnBpCRkcHWrVsY99k4tmzZwvDh/6VN6zaUL5/5w4TL/cKamprqnrYTWi7UfXv58uU5fPgwJ09G5ilf2bJl3VOpTp48maeipsJfuePj44mPj8/XqJri4NK1WE6ePJnnogbMRZD79e1Hv779cLlc7N69m4lfTmTlyhWMHTeWO9u1p169eu7jDcOg1e2taHV7K8Ac2bRs2VJGjxnNsWPHeP9/Ixnz8Se5fvxmzZrRrFkz4uPjWbR4EXPmzOb3Xb8z64dZzPphFjVq1KRH9x707NEzx2l1l3pp0Evs2L49z68DwNhPxtK0ae6LoTq1a5vbmB88mOMxERHmfbWvz7oMgUhpUDz2qBXJh9QdUTnel/LX4rI+dS/+IPa5oTwXpiCnbDuZ7XnOhDTS9p/+69zsR2Tk9XHBHFUCkJFDEeA4Hoczj0XNhVLB5/rQbEsal8tFyva8vXnLC/cID9flxuuY/G6sgr1GGZzxaSSt+5OExeZCgYEdamP4XN2CtLZQf8o83ITqX99P1Qk9CO5RH68gHxwHz3Ju/GaOPfA90a8vI/GXQzhTc54ClnE+BefZ5Hz948q48mtQVFwuF2n7zCHd3oVQ7qTuLbxri4iUNDabjRYtWjJh/ATs3naSkpPY/cfuLMdFRkZy4sTxbK+xddtWMjIyMAyD+vUvTjm9+aamAKxbty5Pmex2O40amWu6/Lru1zyd26hRY7y9vXG5XPy6Nm/nFifXXHONu6wpiOdhGAZNmjRhzOgxVKlSBafTydZtWy97TpkyZejT5yFeefkVwNz2Oz+Cg4N5+KGHmTljFgvmLeSpJ5+iQoWKHD36J59+No57Onekb//H+fGnH93bdWfn/PlYTp85na9/HI68TVe7sEPU1m1bSU1NzfaYC4tYX1iTSaS00Yga8ViJqw5Rpv/N2Ktl/hQkZedJUndFAxB453Xu220hvvg1rUrKtpOc//53Au68LkvBcf6733GlZWD42wm47doCeVwAn+vLkbTmCEnrj1Lu/27Ncs3z3+3M5bO+6EL5k3b4HC6XK8vUmIQF+0k/UXjTU4xAcw50bgumoHvrcW78Zs7P2m0u7Az5Wkj3cnwbVMS3QUXKvdiSpLV/krDkACnbTrqnRhlBPgTeeR2hL7TMsk7RtTMfKtAsOak4tC0Vh7bN8f6TgxaRuiOKwM43ZHtcdl/rS8X/P3v3HR5F9TVw/DtbUza9QEKXXqQ3qQo2BBHEjgIW9GcD7IgFe280G6CIDbCAL1Up0nvvLSEg6WVTdrN95/1jYUNMAiEECHg+z5PnITP33rmzKJmcOffc/9uP+8Q244Fl/DdcljONXbjhuH+HrbMdWwghLndOpxODwVDqOb3egEarAbevXWm+nvw1r7/2RrFjqqoyecpkADp3vsq/4xPALf1vYeo3U0hITGDmrBncecddZc4tLy+PsLCinRAHDhjIzp07mDNnNnfdcVexANDp+gYHB3Nt72tZ9OciJk6awNU9e16yy1IGDBjIlKmT+XbaN/S/uT/VqpVeDFhVVQoKCvxZN6f7e9Zqteh0On878C0183q9/uP/dnLno7L+uzgbDRo04Llnn+epUU+zatVKfp8zmxXLl7N582Y2b97M2++8Re9evXn+uedLFD+ePu37c75+eV137XW8/8F75Ofn8+uvvzB48L3Fzv/99zKOHDmCoij0valfGaMIcXmTjBpx6dJrSX/+L+y7fcER1atSuOYYGa8uAyCgfTwBVxb/IRT+YDvQKDgPZpP5+t+4M3xZKd5CF7nfb/cHTMIGt/QV5a2k6wb1rAcKuBLNZI9fh6fA9/bAY7aRPW4dlr8OowScXdw0sF28b8wjZnLGrfeP6bU6yft5J9mfrUUTZjyrMc+Goa5vFwvHrnRcx/PO2N50QwPQa3DuywS3F0PDKIwNz08dGY1Rh+na+lT/uA81Z95B+INt0dUIQbU4scw7gCfvwhR7Ph9yxq0ne/w67DvTimUIuTMs5Hy1iZxx6wAIaBNXarDR/O1WknpOJann1BLn8n7cSdZ7K7FtSsZbWPTA6Mm1kffTTjJf8W3JqqsdVuHaQkIIcbkaPWY0Y156kdWrV2G1FmUuJCcfZ/SY0TgcDgICAmjfruQLG5PJxKxfZvHpZ59QUOB7yZKZmcnoMaNZv34diqLw+KOPF+vToEEDf22aN958g08+/bjY7kRWq4U1a1bz/AvPMerpUcX6Drp1EK1atcLhcDDsgaHM+mVWsec6uJkAACAASURBVGyLzMxM5s6by31D7+X7H6YX6ztq5FMEBweTlJTEfUPuY8OG9f66N3a7neUrlvPw/x6uyEd4QQ1/aDi1atXCbDZz9+C7WbhoYbECtikpKcyaNZNBt93K0hNbkgN8Nu5TRo4awZKlS4oVY87KyuLtd97i+PHjvmVOXXxLnCwWCzf0uZ4vv/qSgwcP+LfR9nq9rFu/jnHjPwOgW9dulXZvOp2Oa67pxYRxE1j+9wpGv/AijRs1xm63M3/BfJKSkirtWhURExPDfff6tmn/6JOP+OP//vB/LitWrmDMy2MA6HtT32LLx056ccxomjZvQu/repU6vs1mw2w2+79OBsFcLlex4+Upwi3ExSIZNeKSFfloR8yTN5P2+DyUQD14vagO3z/yuhqhRI/pWaJPQItqRD3VhexP11K4/AiFK46gMRl8RVtPLF8Jvq4+Yfe0rNTrGupFEHpbc/J/2UPBb3sp+G2v77pWJ2gUop7rRu60bXjSyk5J/Td97fCiMWfvpWD23qJ78aoEdKyBsXE0ed+ffbZOeQS0iUNXIwR3cgHJ9/6KJizAH2yKm9APXWzxHRi04YEEdalN4YokAEwX6Bd9XayJ8CFtCLuvNY4daVgWHkLRX7oxaq/NhXXRIQp+23tily89qldFtRalHRtbVyfmjd5nPbbq8mBZeAjLwkOggBJsQKF41pT+ighi37nunJesCSHE5cbpcLBw4QJmz5mNoiiEhITgcrmw2Xz14rRaLa+NfZ2IiJLbdTdt2pSmTZrx9eSvmfrNVEzBJvIL8lFPLC9+9plnadeuXYl+zz7zHHa7gxkzf2bylMlMnjIZk8mEoihYLBZ//44dOhbrp9frmTThc0aMfJKt27Yy9rVXef2N13xzdrootBXV4+vcqfjSkzp16jBpwiRGjBrBvv37GPbAMAwGA0FBQRQUFPh/4a7qQkNDmfzVFB5/4jESEhN4+pmn0Gq1hISEYLfbiwVtTs02dbs9/LX4L/5a/BfgC7Kpqlrsl/6RI0bSqGHRc05KSgrjxn/GuPGfodfpCQoOwmKx+D+rWrVq8cLzo8/LfUZGRjJ0yFCGDhnKnr17mD379zK3SL+QRo4YyaHDh1i5cgWjX3yBV8e+glar9f//cmWLK3lt7GsVGnvqN1OY9PmkEseXLFnMkiWL/d8PuGUA777zXoWuIcT5JoEaccnS1Qgl/utbyJ22Ddum43hy7eiqmwjqWZfwIW38S4P+LaR/EwxNosmfuRv79lQ8uXY0wQYMjaIIublJiWVLlXXdiMc7oasZRsHc/biP5YECgR1qEnZvSwJaxZE77ewLuEU+0Rl9nXAK/tiP82guqlfF0DAK0/X1CRnYjNzp2896zPJSdBqqf9IH89St2Lel4skphBPbkqseb6l9gnrU9QVqDFqCr7uwxeEURSGgdRwBreMu6HUrW0j/JmjDA3DsTsedbsWbb0dVQRsbjLFxNMG96xPUs26FtikPvroeeLw4dmfgSsnHm+/A6/aijQrC0CCSoJ71MF137nWFhBDicvT0U8/Qpk1bNmxYz9GjR8nMysTj8VC7Vm3at2/PkPuGlpodcNKLo1+kSePGzJg5g4TEBIKCgmjRvAUPPvAQ3bt3L7WPVqtl7KtjubnfzcyYNYMtWzaTleWrtRcXF0eTxk3o0qUrN910U4m+UVFRTP/uexYuXMDc+fPYu2cPeXl56PV6rrjiCq5scSVXX30Nva4pmbXQqVNnFsxbyLTvprFi5XKSjyfjdDipVasWzZs1p+9NfSv4KV5YderU4fffZvPb77/x55+LOHjoIAUFBRiNRho3akyrVq3o1at3sWyXoUOHUrt2LdavX09CYgKZmZk4nU7iqsfRuk0b7rn7nmJZUyaTiS8+/5J169axffs20tLTMOeYCQwMpF7devTu3Zt7B997QZaQNW/WnObNmp/365SHXq/ni0lf8Muvs5g9ZzYJCQl4PV6aNmnKTTf1Zch9Q8pcYibEf4GilqMQqBBncO0+Z8qvo3J+CDtz03P3z50z8aRZqPbZTQS2uXC/dF+s615Osj5YhWX+QYJ61SN2bOnpqkKcqkdAY54Ive7PME3QjRd7LkKIy0Z7VVWXqB4uyHPL6cye/TtjXh5Dhw4dLmiNECHEeaKAouFHRVHuPXNjIcp26eb/CyEuKV6LE+uyIwCE3Fx20UIhhBBCCCGE+C+TQI0Q4rxTXR5yJm1AtbnQ148ksG38xZ6SEEIIIYQQQlRJUqNGCHHeWJcfIeeLjXjz7Kg2NygQ+VjHM3cUQgghhBBCiP8oCdQIIc4br83l28nKoMXQMIqwoa0JbF/jYk9LCCGEEEIIIaosCdSIS06tmXf+p657KQvp04iQPhdmG24hhBDiUjNw4K0MHHjrxZ6GEEKIKkZq1AghhBBCCCGEEEJUERKoEUIIIYQQQgghhKgiJFAjhBBCCCGEEEIIUUVIoEaIy4z5260k9ZxK5rsrK3Xc1JHzSeo5lYKFByt1XCGEEEL8d02cNIGmzZvw4pjRlTrukGH30bR5E2bP/r1SxxVCiAtBigkLIS5LruN55P24E9vmZDxmG9rQAIytqhF2V0uMjaMrNKa30Il9WyqO/Vk492fhOJCJN88BQPz0QRjqhFfmLQghhBDiPyLpaBKTp0xm3dq1ZGVnER4eTvv2HXjw/gdo3rzFOY9/5EgiP/70I2vWriE9PR2tVktsbCytW7XmllsG0LFDx0q4CyFEZZFAjRCXGW1YALraYeiiAit1XF2sCU/tMDTBhkod93ywbUom4+UlqHY3AIrJgCenkMJlRyhckUT06B6Yrm9w9uNuSSHz5aWVPV0hhBDiPysiPIJ69eoRExNTqePGxcVTr149TCEhlTru+bBm7RqeHPEENpsNgJCQELKysli4cAGLF//F22+9Q/+b+1d4/O9/mM6HH32Iy+UCICgoCJfLRWJiIomJiSgajQRqhKhiJFAjxGUm9NZmhN7arNLHjXmpZ6WPeT64swvJGLsU1e4moH080c91Q1c9BI/ZRs6kDVgXJ5D1wSoMDaMw1Is46/E1EQEYG0djaBKDLjqI7I/WnIe7EEIIIf4bBg++l8GD7630cd9/9/1KH/N8yMzMZNRTI7HZbHTp0oU3Xn+TGvE1yM7O5v0P3mPuvLm8/MpLNG3alIYNGp71+DNnzeCdd99Bo9Hw0IPDufuuu4mPj/dfe+26tbjd7sq+LSHEOZJAjRDispL3005UqwttbDCxb16LJkgPgDYikOgXe+A6lofzQBa532wl9s3eZzV2UJfaBHev6//elVpQmVMXQgghxH/M5CmTsVgsxFWPY/xnEwgODgYgKiqKd995j8QjiezZs4cJE8YzftyEsxo7Ofk473/gC1iNffU17rj9jmLnY2JiuKX/LZVzI0KISiXFhIWoolSPl7xfdpN8/+8cvW4ax/r/SProv7DvSgcgqedUknpOLREsOF0x4VP7uNMtZH2win9u+5mka7/l+J0zyfl8A16rs9T5XArFhFWvinVZIgAhtzT1B2lOUrQaQm/3rfMuXHeszHsti6KVfzKFEEKI0ng8Hr6b/h23DOxP67at6NLtKv732CNs3boVgKbNm9C0eROSk48X63e6YsKn9klJSeGVV1/h6l49adn6Sq69vjcffPg+Foul1PlcCsWEvV4vCxcuAOCuu+7yB2lO0mq1DBsyDIDlK5aXea9lmf7999hsNlq2bFUiSCOEqNoko0aIKkh1e8kYsxjbhhMPM1oFxePFtu4fbBuPEzP2mnMa35WQQ9b7q/DmO1CC9OBVcadZyJ+5G/v2NOI+vxlFd+kFJVxJZrw5vvXdgR1rlNomsMOJ4y4v9l3pBHWudaGmJ4QQQlyWXC4Xjz/5OKtW+V4S6XQ6PB4PK1asYM2aNXz84cfnNP7+Awd46eUx5OXlERwcjKqqJCcn8+20b9m0aRM//fgzer3+zANVMYcTDpOVnQVA167dSm1z8rjL5WLL1i307FH+pejzF8wDoO9Nfc9xpkKIC+3S+01MiP+A3OnbfUEarULkk52ovXAIteffR82ZdxDYsSbZH6w+p/Gz3l2JoUEk8d8OpM7CIdRZNJSo57uDQYvzQBYFc/dX0p1cWK6kXN8fFNCXsQOTNjwATURA8fZCCCGEqLAvv/qCVatWotVqeXH0GDZt2MyGdRtZsngp3bp245Wxr5zT+GNeepGmTZryx5z/Y/PGLWzZtJW33nwbg8HA7j27+eXXXyrpTi6shIQEABRFoUH90jc5iIiIICoq6kT7w+Ue+9ixY2RnZwPQtGlTtu/YzqOP/Y/OXTrRum0rburXhw8/+sDfRghRtUhGjRBVjLfQSf6sXQCE39+W0NuKtmTUVQ8h9q1rSXnkD7yHcyp8DW1MENXevwHFoAVAMWgJ6dsI56FsCmbvpXBFEqEDK6cgsW1bKumjFlSor7F1deLGlf8tkCenEABNiBGNsex/3nRRQTjNdjzZhRWalxBCCCF8rFYL06ZNA+DJJ55kyH1D/OdqxNdg/LgJ3HHn7eTn51f4GrGx1fjqy68xGHw7TxoMBgbdOoh9+/by408/8tdff3LP3fec032ctHHjBobeP7RCfTt06MD0ad+Xu31mZiYAoaGhGI3GMtvFxsSSnZ3tb18eR48e9f9548aNfPHl53g8HoKDg1EUhSNHjnDkyBHmzpvL1CnfVKhQsRDi/JGMGiGqGNumZFSbG8WgJXRQ8xLnFZ2GsNtblNKz/EJvv9IfpDlVUPc6ADiPmM9p/FMpeg2ayMAKfWlDyn5oKY3XdmI7bmPJeys2pwDdifauit2UEEIIIQBYs2YNhbZCjEYj9w6+r8R5vV7P0KHDzukaw4YO8wdpTtW797UAHDp86JzGP5Veryc6KrpCX2FhpWfzlsVm870wCggIOG27k+cLC8v/gim/oCgw9vkXk6hbpy4zfp7pz0j66suviYqKIjMzk5GjRsjOT0JUMZJRI0QV4zzkS0E1NIgsUQz3JGOr6ud0DWOT6FKPa6ODAPAWOM5p/FMFtKhG7dmV85ZLCCGEEFXL3n37AGjSpEmJYrgntW/X/pyucWWL0l9QVYutBnBO2Tr/1qZNW1atPLcl5lWB6vX6/6woChPGT6BevSsA0Gg09Ojeg7fefJtHH/sfR44cYfGSxfS5sc/Fmq4Q4l8ko0aIKsaT5wuSaKOCymyjO8258lDKCAD5s2w86jmNf7FoAn2xZ9XhOW071e4+0f7SKzwohBBCVCW5ub4s3JiY2DLbxMaWfa48ygoAGY2+LJtLNRskMND3PGe320/b7uT5oKDyP/8FBRV9Zt26dfMHaU51dc+rqVu3LgDr168r99hCiPNPAjVCiMuGNsr3UOItcOB1lP3Q5j5Rm+Z0wTAhhBBCiPPpZAArPz8fh6PsbOaMzAwAYmJizmLsorb16tYrs93Jc6lpaeUeWwhx/snSJyGqGG2Yry7L6Qrdui+hIrj23elkvLK0Qn0DmscS+9a15W6vr3tibbgKrqO5GBuVXOLlybXjNduLtxdCCCFEhYSHRwCQeSKYUJrTnatqtm3byoiRIyrUt3WbNkwYN6Hc7evXrw+AqqocTjhM82YlaxOazWb/zkz1y9gZqvSxG6DRaPCesgTqdBRFKffYQojzTwI1QlQxhoa+LRidh3PwFrpKrVPj2HnpvPVQXV68ObYK9fWcZa0cfZ1wNJGBeHNs2DcnlxqosW1OPtFYQ8CV1So0LyGEEEL4NGvaFID9+/djtVpLXaa0ecuWCz2tCnO5XGRlZ1Wob15e7lm1r39FfaKjosnKzmLt2rWlBmrWrl0D+Ioct2vbrtxjBwYG0rpVa7Zu28qRpCNltjt5rkZ8jbOauxDi/JJAjRBVTGCHGiiBOlSbm4I5ewm7p1Wx86rbS/4vey7S7M5eYJs46q548IJcS9EoBPe6goJf95A/Zx8hA5sVq0OjelXyf9kNQFCX2miCS+4gIYQQQojy69q1K0GBQRTaCvnp558Y/tDwYufdbjffTf/uIs3u7HXs2Il9e/ZfkGtpNBr69LmJ73+Yzs8zfmbwPYOL1aHxer3+z+6aq6/BZDKd1fi39L+Frdu2snr1ao4cSSxRp2b5iuUkJSUB0KNHj3O7GSFEpZIaNUJUMZogA6Entt82T9lC/m97/PVW3OkWMsYuxZ1acDGnWKWF3dMSJViPJ91KxitLcadbAPDk2sh6dyXO/Vmg1xB+f9sSfV2pBST1nEpSz6kULDxY6vieXLv/69TdsbwWZ7FzqvfSLMgshBBCnI3gYBNDhgwFYPyEcfzw4/f+4rcpKSmMemokycnHL+YUq7ThDw3HZDKRmprCiJFPkpKSAkBOTg4vvvQiu3bvQq/X88QTT5bom5x8nKbNm9C0eRNmz/69xPlbbx1E/foN8Hg8PDlyBDt37gR8AaBVq1bxyisvA9CqVSt69uh5Hu9SCHG2JKNGiCoofEhrHPsysW9KJmf8enImbUATqMdrcYJOQ8zYa8g8UffFv1OTAHw7YsW+3puMl5dg35TM8TtmopgMqFYnqIBWIfr57hjqRVRo/H9u+bHU42mPzS32fY0Zd6CPC6nQNYQQQohLyaP/e5Rdu3ayZu0a3n7nbd7/4H2CgoLIz89Hr9Pz8cefMGKkL9CgN0g266liYmL47NNxPDniCdasXUPv63oREhKCxWJBVVV0Oh1vvfk2DRs0POuxdTodX0z6gqHDhpCQcJg7776D4OBgvF4vNptvWXr9+g0Y9+l4qVEjRBUjGTVCVEGKXku1964n4rGO6OtFgFYDWg2BXWpTfXxfAtrE+dtqTPLA82+BHWoQP3UApj4N0cYEozrcaCMCCbqmHnFf9Md0ffmL8QkhhBDi9AwGA19+8RUvPPcCDRs2RKPRoNVquebqa5g+/Xs6dezkbxsaEnoRZ1o1de3Sld9/m82tA2+levXq2O12oqKiufHGPsz4aQb9b+5f4bFr1arFH3P+j0ce/p8/u0ZBoVmzZjw96mlmzZhFtWpSs0+IqkZRVUnPF+fs2n3OlF9H5fwQdrEn8l9h25JC+tML0VY3UWvmnRd7OkKcNz0CGvNE6HV/hmmCbrzYcxFCXDbaq6q6RPUgzy0XyLr163jgwfuJj49n6eJlF3s6Qpw/CigaflQU5d6LPRVxaZOMGiEuQXkzfGuMA9vFX+SZCCGEEEKc3jffTAWgy1VdL/JMhBDi0iCBGiGqINXjJePVpRRuOO6rS3OC84iZjFeXYt+YDDoNoYNKbuMohBBCCHEheTweRo4awapVqygoKNrw4NDhQ4wcNYLVa1aj1+m5715JMhBCiPKQYsJCVEUqFK5IonBFEgBKsB48Kqrdt/sTGoWokVdhqB958eYohBBCCAGoqspfi//ir8V/AWAymfB4PP6CtRqNhpdfeplGjRpfzGkKIcQlQwI1QlRFWoXIp7pg23QcV6IZj9m33bO2uomAltUJvb05xkbRF3uWQgghhBBotVpefWUsa9as5uChg2RnZ+PxeIiPj6d9+w4MuW8IzZtJFrAQQpSXBGqEqIIURSF0QFNCBzS92FMRQgghhDgtRVG4+667ufuuuy/2VIQQ4rIgNWqEEEIIIYQQQgghqggJ1AghhBBCCCGEEEJUERKoEUIIIYQQQgghhKgiJFAjxGUuqedUknpOxZVacObGQgghhBAXSdPmTWjavAnJyccv9lSEEOKikmLCQoj/HOfRXApXJmHfnorrSC6ePDuKUYu+VhhB3eoQMqAp2hDjacewrkzCsuAgzgNZvv4GHboaIQR2rEnY7S3QRgae9bxUpwf79lQc+zNx7M/CuT8LT3YhALEf3EBQp5qn7W/fkYp56lac+zNBpyGgVRwRj7THUDei9OupKmlPzsd5OJsa0wehizWd9ZyFEEIIcX4kJx/n2uuvLXf7JYuXUiO+hv97p9PJxo0b2LV7N7t372LX7l1kZmYC8PWXk+nevfs5z3H7ju18N/07tm7dgtlsJiw0jCuvvJLBg++la5euZfY7ePAAH3/6CVu2bMbr9XJliysZOWIUbdu2LbPPs889w8JFC5n580xatLjynOcuRFUmgRohxH+KfVc6aU/MKzqggCbYgLfQhfNEcKTgj/1U++B6DFdEluivelWy3lmBdXFC0RBBelSHG9fhHFyHc7DMO0C1D27A2DTmrObmPJpL+nN/Vuy+dqSS9vQicHvBoAW7G9vaY9h3phH/VX/0NcNK9LEsOIRjVzoRj3SQII0QQghRxWg0WqKjok/bJi8/D5fLRXRUNNViqxU7l5CQwPBHhp+3+U2eMplPP/sEVVV9O5aGhGLONfP38r/5e/nfPPLwI4wa+VSJfkeSjnDPvfdgtVrR6XRoNBo2btrIsAeG8u3UabRr165En/Xr1zN/wXzuuvNuCdKI/wQJ1Agh/lNUtxd0GoJ71CX4hgYEtKyOJkiP1+GmcOVRciaux5NpJf3FxdSYPgiNsfg/k5Z5B/xBmtDbmxM2uBXaiEBUtxf71hSyPlqNJ91K5pt/U+OH21E0ylnNT2MyYGgcjbFJNIYmMWS+srRc/cxfbQa3l7D7WhE+rC2q20v2R6uxLk4gd9o2Yl6+ulh7T74D81eb0NcJJ/SOFmc1RyGEEEKcf3FxcaxaubrM8y6Xi57X9MBsNtOvXz90upK/2oWGhtKsWXOubNGCFi2uZOSoEZUyt2XLlvHJpx8DMGjQbTw18imioqKwWi18N306EydN4Kuvv6Jhg4b07duvWN9JkyZitVoZOGAgr74yFq1Wy7jx45j6zRQ++fRjfvzhp2LtnU4nb779BpGRkYwaOapS5i9EVSeBGiHEf4q+Zig1vh+EPj602HGNUYfpuvpoo4NIH7UAT5qFwr+PYLqxYbF2liW+IE1A2zgin+jsP67oNAR2rEn0iz1JH7UAd3IBzoQcjA2jyj03Q/1Ias27F0UpCu5klqOf1+bCsS8TbWQg4fe3RdFqUHQaokZ1wbo0EfuWlBJ9zF9twptnJ+b1Xig6KVcmhBBCXGpWrFyB2WwGYMAtA0ucb9y4MevXbij2XFFZJk6aAEDr1q156423/MeDg0089uhjJCcf5/fZv/Pxp59www03Fgsird+wHq1Wy5gXXyIgIACAUSNH8ccfc9i+Yzs2m43AwKIl5N9O+4bExETeeesdwsJKZggLcTmSQI24bKkuDwV/7MO67AjOo7moNheaUCPayCACrqxG8HX1CWhRPEXUviMV64okHHsz8WRY8eTZfRkOjaII6duY4KvrlXqtzHdXYl10iLBhbQi/txV5P+/EujgBd7oFTVgAQd3qEP5AW3/dE8eBLPK+3459TwaqxYm+XgRh97UiuHvdEmMXLDxI9nurMLauTty4vlgWHSL/j324knJBAWPjaELvannG+iVl8Ra6yP9tD4WrjuI6nofq8qKLCSawU03C7r6y1CUxqlfF8uchrIsO40zMwWt1ojEZ0UYEYGwaQ9A1V1R4PuebLib4tOcD28Shq27CnWbBcSCrRKDGY7YBYCgjAGNsXHRctbvPam5nm31zkrfACV4VbXUTirYo6KIxGdCEGfHk2Yu1d+zNwDL/AMHX1SewTVyFrimEEKLyOJ1OZsycwcJFC0hISMBmsxEWFkZ0VDRt27bj5ptvpk3rNsX6bNq8icWL/2LHjh2kpqWSa84lJDSEZk2bcdug27jhhhtLvdaLY0Yz5485PP7Y4zw8/BGmfjOVefPnkpKSQkR4BL179+aJx5/0/0K8Z89uvvz6K7Zv20aBpYCGDRryyCP/49reJWunzJ79O2NeHkOHDh2YPu175syZzc8zZ5CQcBhFUWjRvAUP3P9ghWujWK1Wfvjxe5YsWULS0SScTifVq8fRo3t3Hrj/QeLiSv5M83q9/PHHHOb8MYcDBw9gtVoJCQkhMjKKVi1bcuMNfSqlVsvFMOePOQA0bdqMxo0blziv0ZyfFzEZmRns278PgCH3DS21zdChw/h99u+kpqawafMmrup8lf9cbm4uEeERmExFz5g6nY74+HiysrPIz8/3B2qSk4/z1ddf0a5tOwYMKBmMEuJyJYEacVlS3V7Snl2EY3ua78DJOiT5DrxmO66EHDz59mKBGm+hi7QRC/zfK0F6FKMWb64d+8Zk7BuTsd3cmOhnu5V9YZeXtKcX4tiZjmLQAuDJsFLw+14cezKoPqEv9k3JZLz+N7g8KMEGVKcH54Es3xKXV68huNcVZQ6fM3E9+b/sAY3iW65jdWLfmop9ayoRj3Yk7K6zW7PrTMol/YU/8aRZfAe0CopBizs5n4Lf92JdfJjYd68n4MriAa2st1dgXXJKjRaTAW+hE2+eHVdSLs6juVU2UFMemrAASLOAVy1xTlfdhPtYHs5D2aX2dRw4cdygRV83/HxO008TYgCNgifNgurx+oM1XosTb54DTXiAv63q8ZL9yVqUID0Rj3a8IPMTQghRNrfbzUMPP8imTZsAUBSFkJAQcnNzyc7O5sDBA+Tm5RYL1FitVoYMvc//fXBwMMYAIzk5Oaxes5rVa1Zzx+138Pprb5R5XZfLxQMPPcCWLZsxGn0vklLTUvnhxx/Yvn07P3z/I6vXrObpZ57C5XJhMplwOBzs3rObESOf5OOPPqHPjX3KHP/d995l+vffodFoMJlMFBQUsH7DetZvWM9zzz7HA/c/eFafU0JCAg//bzgpKb4sUZ1Oh0Fv4Nixo/zw41Hmzp3L55O+KFGM9oXRzzNvflFtupCQECwWC2azmYSEwxxOSLgkAzVms5mVK1YAMOCWARf02qmpqf4/16tb+kvMunXqotFo8Hq9rF27tligJjw8HHOuGYvF4g/WeDweUlJS0Gg0hIYWZT2//c7buFwuXn3l1fOSGSREVSWBGnFZsi5JwLE9DSVAR9QzXQnqWReNUYfq8eLJKqRw7TG8VlfxThqFoJ51fZk2reLQhvoefFOnXAAAIABJREFUWjwFDqxLEjB/tRnL3AMEtqtB8DWl/1DK/2MfGoOW2PeuI7BTLVBVbOv+IfPtFTgPZJE7bRsF/7cf07X1CX+oHbqoIDy5NrI+XI1t9TFyJm4gqEfdUpeiOA9l49ieRug9LQkf3AqNyYA7uxDzFxuxLk7A/OVGjM1iCGhZvVyfkdfiJONEkCbo6nqED2mNvm44ilaDKyWf3KlbsS5JIOPVpdSYPsifDWTfkeoL0mgVIh7tSEjfRmiCDKiqiifHhn1TMs7EnLP426paPPkOnEd8acT6eiV3Swrp19gXuNuaSs7E9aXWqAEIH9L6jDtHVRZNoB5jk2gcezPJnbaN8KFtfAGZcevAqxLYNt7ftmD2PpyHsol8sjO6qKALMj8hhBBlmzd/Hps2bSIwMJDXxr7ODdffgNFoxOPxkJ6ezt/L/8ZqtRTro9FouOH6G+jX72bat2tPeLjvxUB+fj5z583lk08/ZtYvs7jqqi7cWEZmzc8zfsZoDOCLz7+kR/ceqKrK8hXLeWH08+zes5uJkyYyc9YM+vW7mVEjRhETE0NOTg6vjn2FpcuW8u5773DdtdeVWhdl3759bNq0iYceHM7Dwx8mJCSEjMwMPvroQ+bOm8tHH39Eq5atSy0aW5qCggIeefRhUlJSuPGGG/nfI4/SoEEDtFot//zzD+MnjGPe/HmMHDWC+fMW+H/R37R5E/Pmz0Or1fLcs89z26BBBAebUFWVzKxM1q5Zw8FDB8/mr6vKmL9gHi63C71OT79/1YA53xSKAiYer6fUNl6vF1X1vfA6fPhQsXOdOnZiwcIFvPPu24x99TW0Wi3jJ4wjKzuLNq3b+LNpli1bxt/L/2bokKE0alQyY0iIy5kEasRlybE3AwDT9Q0wXd/Af1zRatBVMxE6sFmJPpoAHbFv9C5xXBtiJHRgMzRBerLeWUnBnH1lBmpUi5OYcTcR0Ppk6q1CULc6hN11JbnfbCX/p50EtIkj+oWiNzfa8EBiXr6af279GU92IY496QS0Kpm6q1pdmPo2IvKRDv5juqggol/qiSerEPu2VHKnbaP6J2W/3TpV3oyduNMsBPe+gphXryl2Th8fSswrV+PNd2DbeBzL/IP+bB3HHl/VlMB2NQi7vagIraIo6KKCSiwVKg/btlTSRy04c8NSnFwSVlnypm8DpwclSE/w1XVLnA/uWQ/XQ+3I/XYr+b/sIf+XPf5dn/Co6OuFEz66OyF9GlXanMojfHh70p9dRN707eTN2AUeL3hUlCA94cN8b2Hd2YWYv9mCoUEkIQObXtD5CSGEKN2OHTsA6N//Fvrf3N9/XKvVEh8fz+B7BpfoExgYyGefjitxPDQ0lMH3DMZkMjH6xRf4+eefygzUFBQUMHHCJDp2KMqu7N2rNw/c/yATJo5nytTJdOrYibfffNt/PjIykg/e/5AeV3cnMzOTbdu30aF9hxJjWywWbht0O888/Yz/WGxMLO+/9wEZGRls2LiBiZ9P5Nup35bjE4Kp30wlOTmZvjf15aMPPy52rlatWnz4wUfk5eWxavUqfv3tF3+2zsnPtstVXRg6pGiJjqIoxMbEVmgpzcaNGxh6f+nLfc7k5JKwyjB7zmwAevToQWRkyV0qz6dTl5glJCTQvFnzEm0SEhP8gZrMrOIV9x579HGWr1jO7DmzmTtvLhqNBqfTiV6n56mnngbAbrfzzntvExsby5NPPHke70aIqkkqSIrLkhJsAMCdU1hpYwZ2qQ34gkCqx1tqG2Pz2FOCNEUC2hVlNIQNblXivCZQj7GZbytnZ6K5zDmE3de6xDFFUfxj2rem4Ml3nOYuilgWHQYg9M6yl0sFX+tbhmXbnFx0vWA9AJ5cG2opS4MqQtFr0EQGVuirMrNWbBuPk//bXgDC72+LNjyw1HZh97YienQPlEBfrFstdIHH91moNjfePEelfTblFdg2nmof3YjxymooCihGHYGdaxI3sR/6Wr46A+ZJG1ALXUQ+1cWXOZWcT8ZLSzjaZzpHb5xO+pjFuJLzL+i8hRDiv+7k0o+szPKUjy+fa672vYDZsXMHHk/pGQ+tW7cuFqQ56aqripaoDB/+cInzQUFBtGrle+44dOhQifMnPfLwIyWOKYriH3PDhvXk5uae5i6K/PF/vlos9w+7v8w2J3cWWrt2rf/Yyc82Oycbr7f0Z7ezpdfriY6KrtBXWFjlLIk+eOgge/f6nlduucDLngBiYmJofCLDZdq0b0v9bKdMneL/s9VqLXaufv36/DD9R7p3647BYECj0dC+fXumTv3GH/j74svPSU5O5oXnRxMcbCI7O5vRL75A5y6daNOuNcPuH8qePbvP410KcXFJRo24LAV1qkn+TzuxrT5G+ouLMfVpSECr6mjDAk7bT3V7fUVylx/BdTgHT4EDXMV/+KhOD94CJ9rwkmPpryi5VAZAGxFY7jZei7P089WC0ceFlHrO2LIaaBXwqDgPZxdb6lIad4YFT6bvh2b6C39CWWt+Xb6HO09G0Q/YwHbxoNfgPJhN2sj5hNzchIC2ceiiT1+k93QCWlSj9ux7Kty/MjiTzGS+udy3VOiqWoTeXvLtEIC30EnmG8uxrfuHwKtqET60Dfo6YSeyj5IxT96M+YuNOA9kETP2mlLHOF8C28aX+Xdv25qCdWkipr6NCGhRDY/ZRtoT8/CYbb4gpAK2NcdI25dJ/LcDywxSCSGEqFzdu3dnytTJLF22lMcef5QBAwbSoUMHIsJLf144ye12M+ePOfz55yL2HzhAXl4uLlfxZd0Oh4P8/HwiIkqO1ahh6ZmfUZFFRfEbNiw9SzYqKhrwLbUqTVxcPDVrll6rrl3bdmi1WjweD/v376dz586ltjspNTWVtDRfzcFHHn2k2LKbU52895NtATp37oxer2fv3r0MGTaEO26/g86dOhEbW63UMcqjTZu2p90y+0L440QR4fDwcHr26HlR5vDo/x5l1NOj2Ld/HyNGjWDkiJHUrVOXjMwMpk37lkWLFqLX6XG5XaUWNW7atClffzW51LETExP5dtq3XHVVF27qcxMOh4NhDwzj8OFDdO58FRERESxZspghw4Ywa8Yv1K9f/3zfrhAXnARqxGUpoHUc4Q+0Jfe7bdjWHsO29hgA+tphBF5Vi5D+TdDXLL69n7fQRfpzi3DszvAfU4xalPAAOLEbjzfHt+OPancBJQM12rJqfpyym0+ZdUFOFIBV3aW/8TldIERj1KExGfHm2fHm2stsd5In2+b/s9d85vZeR9HuRfqaYUQ91ZWccWtx7EzHsTPdN7/qJgI71sR0c2OMjaLPOGZV4kotIP3ZRXjzHRibxxIz9poyC9blTNyAbd0/BLSLp9p71/uPa4IMvv+uaoeRNmoB1mWJBN/QgKDOtS7UbZRJdXnI+XQtmjAjESeWzuX9tBNPjo2IRzoQdk9LAHKnbyN36lbyftxJ5OOdLuaUhRDiP6Njh448+cQIvvjyc/5e/jd/L/8bgCuuuIKePXpyxx13UrdO3WJ9rFYrwx9+iG3bt/mPBQQEEBISgkbxPU9kZWcBUGgrLDVQExMTU+p8tKfsHhgbE1t6mxO/eLvdrlLPV6tWer+T8wwNDcVsNpNjPnNNu8xTMo2ys0sv5H8qm73oGadunbqMffU13nr7TbZs2cyWLZsBqFGjBt26deeO2++gWdOSy+GrMo/Hw9x5cwHo17cfBoPhoszjhhtu5InHn2DipIksXbqEpUuXFDvfvVt3DEYjS5cuISSk9BeNZXnzLV8R7FdeehmAX36dxeHDh7jrzrsZ++pYAP5v7v/xwujnGTf+M8aPm1AJdyRE1SKBGnHZCh/ahuDrG2Bdloh9eyqOPRm4juXhOpZH/q97iH6+e7F6KrnTt+HYnYEmLIDIxzoS2KlmsUwY1ePlaC/fWmr1wq5qqXSnLsupNe/es14+FNK3EUFX1cK6LAHbtlQcu9Jxp1ko+L/9FMzdT/iD7QgvZZlWVeTOsJL+1EI8mYUYGkQS+/71aAL1pbb1Wp1YFvnSvMvKuAloHYehUTTOA1kUrjlWJQI1eTN24TqWR9SzXf1ZZYXr/gGNQsiAolo1oYOak/vNVgrX/yOBGiGEuIAee/Qx+t/cn4ULF7Bx00a279hOYmIiiYmJfP/D97z5xlvFdvb54ssv2LZ9GxERETz/3At079adqKiiTBiPx0OLlid+Tl3iDy1etegF1oZ1G4vtCFQeg24dRM8ePVmwcAEbN25gy9YtJCcnM3PmDGbNmsnIESN55OH/Vfa0z5s1a9f4g1cXerenf3v8sSfo0qUrM2fOYPeePRQWFlKjRjz9+vbj9tvuYNgDvlo+df4VaDydefPmsn7Deh55+BHq1fMtwV++fDlAsXpN/fr24/0P3mPNmjV4PB60Wm2l3ZcQVYEEasRlTR8XQvjgVjC4FarHi31nOrnfbsWxI43sz9YWC8YULk8CIHJkZ0y9S6ZQesy2EscuJHd22fV2vA43XouvNo2mlCVZ/6aNLApAeTKsFarzoo0MJPS2FoTe1gJVVXHuzyLvxx0UrjpK7jdbCepSG0P98hW3s+9OJ+OVpWc9B4CA5rHEvnVthfq6swtJe3oh7tQC9LXDqPbxjaf9LFzH8/21aHRlLEM7ec55IAt3WkGF5lWZXKkF5P2wA0OzGEz9inZMcKdb0IQZ0QQVBaU0wQY04QFF27ULIYS4YGrWrMnw4Q8zfPjDeDwetmzZzIRJE9i8eTNvvvlGsWDMn38tAuClMS/T96aSBfWzT2TTXCwZGRllnju5HAsgMuLMzwnRUUVZuqmpqWcdqAGIjo5myH1DGHLfEFRVZffu3Xw95WuWLFnM+AnjubrnNTRuXL5dhbZt28qIkSPOeg4Ardu0YcI5Zn+cLCLcsGFDmjdvcYbW51+b1m2KbR1/ksfj4eAB345arVuV7+WdxWLh/Q8/oEaNGsWCZympvi3ZT11Op9FoqFmjJjt37cRsNhMdfWllcwtxJlJMWPxnKFoNgW3iqPbedaDToNrcOA4UPci4T9RsMTaMKrW/fXPKBZlnWTxpFlyppf/i79iV7gsgKGBoUPr8T6WPC0FzIlhj2/DPOc9NURSMTWOIeb0X2phg8KrYd6adueMJqsuLN8dWoS9PQfmKJ/+bJ9dO+jMLcf+Thy4+hGqf9jlzXZZTVkO5061lNnOn+wIdZWXmXEg549ejujxEPdWlxHIu1VmywKTqKL3opBBCiAtHq9XSsWMnvvz8S/Q6PYW2QnafUjg1Pc237LhZ09J38Fu7bt0FmWdZUlJSSE4+Xuq5LVu34PF4UBSFJk2anHGsmjVr+oM1K1etPOe5KYrClVdeyWeffEb16tXxer1s2bql3P1dLhdZ2VkV+srLK1/x5LLk5+fz99/LgIufTXMmq1avIi8/D71ezw3X31CuPuPGf0ZWViZjRr/k36L7VA5H8Wc+u+PMy/eFuFRJRo24LKkuD4q+9BRIRadF0SioFP9FVRNswJtnx5loRl+7eFV+b6GL3B92nM8pl0vejzuIfrZbsWOqqpL3004AAtrGow0tX3aM6caG5P+0k7wZuwm+rgG6mNJr4Kiqitfi9GeanPaz1WpQdCdq7bjKv7tCYJs46q54sNztz5XX4iT9uUW4juSijQ2m+qd9ylUMWV87HAxacHqwzDtAUKeShRIdB7NwHvQFAI3Nyl6jfyEUrjmKbe0xQgY2K1E3SFfNhPufPFzH89HX9L2ddB3LRS10oa8dVtpwQgghzgOn01lmnRG93oBGqwG3r91JphATZrOZgwcP+peHnGS1Wvnq6y/P65zL4+vJX/P6a28UO6aqKpOn+ArIdu58FeHh5dsFacCAgUyZOplvp31D/5v7U61a6cWAVVWloKDAn3Vzus9Wq9Wi0+n87cqrY8dO7Nuzv9ztK9PCRQtwOBxotVr69bv5osyhPAoKCvjoow8BGHTrbeXaPnzvvr38PONnru55Nb169Sp2Lj4uniNHjrBn7x66XNUF8AWtjh07RlBgUKk1mIS41ElGjbgsZb6zgqx3V2LbeBxvYdEPX1dqAZnvrkB1elCMWgJaVvefC2zv2y0nZ9IG7NtTUU+s6XbsyyTt6YV48y9u1F4J1mOZewDz15v9O0O5swvJemcl9i0poED4sJKpp2UJu6cluvgQvHl2Uh+fi3VZYrGiwe50X82Z1IfmULj6qP+4efJmMl5dinVVUrGtwD05NrLHrcOdWgBK0edZ1XhtLtJH/4XzYDbaqCCqf3oTuurlK3KnCdBhuqEBAIUrk8j6YBXuDF/2jNfhpnD1UTJeWgIeFSVYX6wG0klJPaeS1HMq5m+3lnoNT4EDT67d/3WSanUWO15W0Wn/fTrc5IxfjyYykIiH2pU4H9TZF2TKmbAOb6ETb6GLnAkbAAisAnV1hBDiv2L0mNGMeelFVq9ehdVatPQ0Ofk4o8eMxuFwEBAQQPt27f3nTv6y+v4H77Nx00b/M8uuXbt44MH7y73t9fliMpmY9cssPv3sEwoKfNnAmZmZjB4zmvXr16EoCo8/+ni5xxv+0HBq1aqF2Wzm7sF3s3DRQuz2op+RKSkpzJo1k0G33VqsqO1n4z5l5KgRLFm6pNhnkpWVxdvvvMXx48dRFIUuXbpUwl2ff3NO7PbUpUvXMgs9/1teXh5ms9n/dZLFail2/N87hgH0vq4XTZs34cUxo0ucy8rK4qOPP2LPnt3+TBeXy8WKlSu45957SEhMoHbtOjzz9DNnnKOqqrz+xuvo9XpeGvNyifM9Tuxs9emnn5CdnY3T6eSDjz7AbrfTtWtXqU8jLkuSUSMuS6rTg2XZEV/hV8WXLaO6vaj2E4EIrULUM12LbbEd/lA7bJtT8GRYSRu5AMWgBa2CanOjGLXEvn0t6c/+eZHuCAwNozA2jCLvxx3kzdiJJkjvC9icqBEY8b+OxQJPZ6INMVLtwxvJGLMY19FcMl//G7QKGpMB1e4utgTm1CUzqkelcEUShSuSfOeC9aCCWlj0Az78wXYYrihffZoLrXBFkm+pGL6ttlOfnFdm29Lq30Q+1glXUi6OXelY5h/EMv8gSqDO93mdKNKsBOmJfb1XqVu4n0nKQ3NKrRGT+frfxb6v9tlNBLaJK3OcvO+2406zEP1STzSmkm8Tw+5phWVJArb1xznW7wffQY+KNiqIsMEtz3reQgghKsbpcLBw4QJmz5mNoiiEhITgcrmw2Xy18bRaLa+Nfb1Y1sDIEaNYu24tqWmpDB02BKPRiFajpdBWSEBAABPHT+Shhx+6WLdE06ZNadqkGV9P/pqp30zFFGwivyDfH1B69plnadeu5EuEsoSGhjL5qyk8/sRjJCQm8PQzT6HVagkJCcFutxcL2pz6zOJ2e/hr8V/8tfgvwBdAUlUVq7Vo+fLIESPL3Kq8KjmSdITt27cDMHDAwHL3u/W2gaSklFy+//QzTxX7/rtvv6Njx/JvJOBw2Jn6zRSmfjMFRVEIDQnFWmjF7fY9azdp3IQvv/gKk8l0xrF++WUWO3fuYMSTI0vd1v2O2+9g5qwZ7N6zm+49u6HX63E6nQQFBTFyxKhyz1mIS4kEasRlKeLhDgS0qIZ9ayqu5Dw82TZUr4quRggBLasTenuLEoVu9fGhxH3Vn9ypW7BtTsZb4EQbZiSgWx3CBrfCUO/ip1VGPtEZff1ICv7Yj+toLkqgHmPjaELvblnqMpwz0dcMJX7KAAoWHKRw+RGciWa8FgeKUYe+fhjGZjEEdatDYIca/j5htzdHHx+CbWsKrqN5eLILUV0etLHBGFvEEjqgGQGtyh8wutDUU3a/UG1uVJu7zLal1b/RBOmpPu4mLH8exrosEeehbLwFDhSjFl31EALbxxN6W/NyZ+mcD86jueTN2oWxdXVM1zcotY02MpC4if3ImbQR+7ZUAALaxhH5eKcz1+oRQghRaZ5+6hnatGnLhg3rOXr0KJlZmXg8HmrXqk379u0Zct/QEoVua9WqxawZvzB+4njWrl1Dfl4+4eHh9O7dm+HDH6Zhg5IZnRfai6NfpEnjxsyYOYOExASCgoJo0bwFDz7wEN27dz/r8erUqcPvv83mt99/488/F3Hw0EEKCgowGo00btSYVq1a0atXb7p1LVoiPnToUGrXrsX69etJSEwgMzMTp9NJXPU4Wrdpwz1331MsU6kq++OPPwBf0KrXNb3O0Pr8i4iI5InHn2TDxvUkJSWRa84lNDSURg0b0efGPtx66yD/0rLTMZvNfPLZJ9SpU4cHHyh9GXxAQADTvvmODz/+kJUrVuBwOujUsRPPPfsc9euX3ABEiMuBol7iW/aJKuHafc6UX0fl/CCFLc6DgoUHyX5vFcbW1YkbV3JnByEuZz0CGvNE6HV/hmmCbrzYcxFCXDbaq6q6RPUgzy2VbPbs3xnz8hg6dOjA9GnfX+zpCHHhKaBo+FFRlHsv9lTEpU1q1AghhBBCCCGEEEJUERKoEUIIIYQQQgghhKgiJFAjhBBCCCGEEEIIUUVIoEYIIYQQQgghhBCiipBdn4So4kL6NCKkT9XfNlIIIYQQ/20DB97KwIG3XuxpCCHEJU8yaoQQQgghhBBCCCGqCAnUCCGEEEIIIYQQQlQREqgRQgghhBBCCCGEqCIkUCOEEEIIIYQQQghRRUgxYXFZSx05H8f2NKJGd5eCvP9i25ZK+qgFxY4ZW1cnblzfizQjcTnLnrCegl/3FDsm/18KIURJQ4bdx6ZNm3jnrXekMO+/bNy4gaH3Dy12rEOHDkyf9v1FmpG4nD3x5OMsXba02LHvvv2Ojh07XaQZif8SCdQI8V+nUdCEBwCgDTGW2cxrdZL3804KVyThTregGHUYGkQScktTgq+ud05TUF0e8n/Zg2VpAu7kfNBqMNQOw9SnEaabG6MoyjmNfzqu43nk/bgT2+ZkPGYb2tAAjK2qEXZXS4yNoys8rqqqWJcmYllwEOehbLw2F9qoIALbxRN2d0v0tcIq8S5Ksm1OJv/XPTj2ZeItdKGLDiLwqlqE39sabWTgOY3t2J9J3sxdOHak4ylwoA0PILBDDcLuaYW+ZmipfTRBejQnruvNd4Dbe05zEEII8d+l0WiIjIgEICwsvMx2FouFKVOnsHjJX6SkpGA0GmnapCl33XkXN9xwY6XO6dRf6gfcMoB333mvUsc/1e7du/hm2rds3ryJvLw8oiKj6NK1K8MfHE6dOnUqNKbZbGbDxg3s3r2b3bt3sWfvHiwWCwDbt+7AaCz7GbGyLPpzETNm/Mz+A/txOBzEx8dz3bXXM/yhhwgONlVozJOBz9O55+57eOXlV0scDw0NJTrK9yyYY87B65VnF3HhSKBGiP84bWwwtWbeedo27gwraSPm404tAEAJ1OO1OrFvTfV93dKEqKe7Vuj6XquTtKcW4jyQ5Rs7QIfqcOPYm4ljbyaFa48R+9a1KLrKX6lp25RMxstLUO1u37VNBjw5hRQuO0LhiiSiR/fAdH2Dsx5XdXnIfO1vClcf9R3QKmiC9HjSLFjmH8S6JIGYsdcQ1LViD1Nnkvv9dnKnbPF9o1FQAnW4Uwoo+G0v1qWJVP+0D4YrIis0tmXRIbI+WAUeFRRQgg14Mqy++1qWSOw71xHYNr5Ev4gH2xHxYDugKNNNCCGEqIjq1auzdPGy07ZJS0vjvqH3cvz4cQCCgoKwWq2s37Ce9RvWc9eddzP21bGVMp8lS5eUyLw4X+bMmc0rY1/B7XajKAomk4nUtFR+++1XFi5YwKSJn9O5c+ezHvf/5v4f773/7nmYcfm8OvYVfvn1FwB0Oh0Gg4HExES++vpLFiyczw/TfyA2tlqFxzeZTAQYA8o8V5p33i76PHpf14uUlJQKX1+IsyWBGiHEaamqSsbYpbhTC9BVNxH9ytUEtKiG1+Gm4Pe9mL/eTMEf+zE0jCLk5iZnPX7Wh6txHshCE2ok+sUeBF5VC7wq1sUJZH+8Btu6f8j9disRw9tX6n25swvJGLsU1e4moH080c91Q1c9BI/ZRs6kDVgXJ5D1wSoMDaMw1Is4q7HNX23yBWm0CpGPdcJ0c2M0Rh3uDCs5E9dTuCKJzNf/Jv7bW9HXKD0DpaIK1//jD9KE3tmC8GFt0AQZcB4xk/XWcpyHc8h4aQk1vhuEYtCe1djOhByyPlwNHpXg6+oT+UQntOGBuNMKyPpwNfbNKWT+P3v3HR9FuTVw/De72U2yqSQk9I60UETpIkhRQPCKV8FKUa+vDcWuqIAdvTYQ7DTFAuoVlSLSpPfepdcU0sumbJv3j0k2hGxCNiSZJJzv/fgRdmaePbPJNSdnnuc841dQ7/s7MIZe3qwdIYQQorRUVWXs02M5e/Ys9erV4/333qdjx2vIycnhu++/46OPP2TuvB9p3bo1w4cNv6z3slqtvPPO2wQGBhIZGcnx48fL6C4K++eff5gwcQIOh4NbhtzCSy+OIywsjHPR55gwcTwbNmxg7NNP8ueiJYSFefdARlEUateuTdu27WgbFYWiKHw8+eNyupOCfpz7Iz//8jMGg4Fnn3mW++4dgdlsZufOHTz3wnOcOXOGp595mu+/+6HU7/HySy/LUkJRpUgzYSFEsTLXncJ2IB4MChFv9cevrfY0w+DrQ8jd7Qm+vQ0AKTN3oNqdXo2dcziBzL9PAFDzpeux9GiIoigoRgOBA6+ixsNacSbt5304k7PK8K4g9Yc9qFY7xsgAIt/sj0/tIACMNfypOa4X5pY1we4iZeYOr8Z1JmeR9ttBAELuak/wHVEYfLWauE9kABET+uDTIAQ1x+n12CWR/PU2ACzXNyLssa4YLGYAzE1qEDnpJhR/kza7ZsEh78eeuR0cLswta1JzXC93McandhCRb/bHGBmAK8NG6vd7yu6GhBBCCC+tWLmCPXt2YzAYmDplGh07XgOAr68vDz7wIPfdOwKAqdOmYrPZLuu9PpkAAuBtAAAgAElEQVT6CTGxMTz5xJOEh4dfduzFmTrtE+wOO22j2jLpnXfdxZh6devxyeSp1Kldh7S0NL6e/pXXY997z738vWIVU6dM5eH/e4SrO1xd1uF7ZLPZ+PSzaQCMuG8ED9z/IGazlrt07HgNUz+ZhqIo7Ni5g7//Ln4WlRDViRRqRLlznLdy8oYZnOw9A9vxpCLPc+U4ODV4Did7z8hfMgKoNifWv08Q//Zqzj0wn9P/+o6TN87mzPC5xL+5ipzcJTPeSP/zMCd7zyBm7KIiz0metYOTvWcQP2lNkedkrj9N3MvLOH3bD5zsN4vTt35P3EtLydpy1uuYKivrsmMA+F1bF9+rCicgwXe2AwWcSVlk7YjxbuwV2lMnn4YhHpcBBd7SCiXQjJrjxLrmpPfBF0F1qVhXau8ddGtrDBZTgeOK0UDwsLYAZG48jcta8iQua0c02LU1zMHDogodV3wMBP9bK25lrjmJK9NeqnvwxHYiGftR7f9jwXe1K3TcJzKAgH5NAchYfsyrsZ3pOWRt0r6vg4e3RTEW/PFhsJgI+pc2o8q64jiqqnodvxBCVBaxsbG0adua1lGtOHzkcJHn5eTk0KVbZ1pHtSqw9MVms7HkryW8OO5Fht52K92v60aHju3p278vz7/wHPv37/M6pvnzf6V1VCtGjh5R5DnTPp1K66hWjHv5pSLP+fvvlTw+5jGu79WT9h3acd31PXj0sUdYt26t1zFVVgsXLgCge7futG7dutDxB+5/AEVRSEiIZ/PmzaV+n/0H9vP9D9/RulVr7rn73lKPUxJpaWmsWaPlpKNHjcZoLDgrNiAggDvv1JayL1q8yOufwxePV1E2bNxAYmIiiqJw/+gHCh1v07oN3bt3B2DBooUVHZ4QupFCjSh3PpEB+LavDYB1edHTQbM2n0XNsGEIMuPftX7+69vOEf/aSqxLj2I/ngQuFQVwxlmxLj9GzKN/kPHXkfK+jQJUh4v4t1Zx/uVlZK0/jSspC8XXiCslm6yNZ4h7/i+SvthSoTGVl+xdWvHFv3M9j8d9IgIwNdaWBmXv8G7tbvbO3LE7eR7b4OuDX7tauWN7VwQqjv1kMq4kbYaOfxfP7+2+X7uL7L1xJR7bGac13jMEmjHW8Lz8x9RQaySs2pxejX0peZ+nEmjGt02kx3Py7teW22S4pHL2xrkbABf1veDfRfv/rTMxE/uplBKPLYQQlU3t2rW59lqtr9aiYn45XL1mNenp6YQEh3B9z+vdr6/fsJ6nn3mKP/74ncNHDqO6VBRFISYmmoWLFnLXPXfx+x+/l/t9XMhut/PCi8/z2JjHWPn3ShISE/D18yUpKYlVq1fx0MMP8cGHH1RoTOVl8xat+NLzup4ej9eqVYvmzbUedJs2byrVe7hcLl57bSIul4vx4yeUe6Fj+47t2B3az+0e13nuC5h3v/Hx8Rw75t0DGb1syf1aXXXVVdSq5bkHTd59bS7l10qIqkgKNaJCBPZvBuCexeCJNfcJv6VXYxRT/g87xd9E0O1tqP3JYBouGUXDhSNotGw09X+6U5ux4FRJ/GA9jtxfkCtC8hdbsC47hk+9YCJe60vDJSNptHgkDf8cQdjTPVAsJtJ+3Ov1rIXKxpmchSs1B6DYPi2mxtqOC978cq6qKvbTKV6MnVzisS/FfjI3TgVMjTzvFmEM9cNQw6/g+SWi7VCluop+kqU684/ZT5blfWljmRuGoBg875RlapT7Wau4P/+Sja2dawzzxxjiuRlf3tfqwvOFEKKqGjJ4CACL/1xc5DmLF2szc2+88Sb3cg2AAIuFEfeNYM6337F96w42bdzMrh27WbFsJSNHjMLhcDDxtQkV2pz0gw8/YMHCBTRs2IiPP5rM9q072Lp5G9u2bGPC+IkEBAQwY+b0YgtTVUFiYiIpKdrPoLxijCfNmmnHjh0/Wqr3+f6H79i3fx///vftdLy6Y6nG8EZe4aVmzQhqhHrOm/LuSTu/dPdV0Y7m3lfzZpf+WiUlJZGcXLq8aebsWfS64Xrad2hHj57duf+B0fw490dycnJKNZ4Q5U2aCYsKYbmhCYlTNuKISSd7X5y7z0keV6aNrE1nAAjILerk8e9YB/+OdQqN6VMrkLAx3XBZ7WQsPkzGn4cJHX1N+d1ELvvZVNJ+2Y8h1I/akwfhE5nfKd5gMRM8tDWGIDMJb6wi9btd7iJVSaT/eZjEd0s39Thg4FVEjOtVqmuL4kzMdP/ZGG4p8jyfmpZC51+KarWjZjm8GLvsetQ4k7Q4DUG+7v4xHt873IItOdur+/KprX0/qJl2HOet+EQGFDrnwuKMN2NfSt5nZKxZ+D3d8dXM/6y9+UzzPjNjzaK/VgZfHwyBZlwZtjK9LyGE0MOAmwby9ttvc/bsWXbu2lnol3GrNYPVa1YDMGTw4ALHunTpSpcuXQuNWbduXca9NI4Mawa//vo/5v/2K48/Nqb8biLXyVMnmfPdt4SFhTF75mzq1MnPqwICArn7rrsJDg7mueef5YuvvmRwbpGqJObP/5WXX325VHGVxzbW8fHx7j9HRnqeXQoQGRFZ6PySiouLY8onUwgNDeXZZ571PshSyIszMjKiyHP8/PwIDg4mLS2N+ATv70sPCe77uvTXCiA+/jw1ani3yQPA0aNHMJvN+Fv8SU5Odu/+NXfej3z+6RfUrVt4x0oh9CQzakSFMAb7updL5PUluVDm2lOoOU6MERb8ri5clCmOf48GAGW6hKQ4GX8dBRUC+jQtUKS5UEDvJmA2Yj+RgsOLX1gNvj4YwvxL90+A6dJv4CVX7rbVAEoxBY28Y64sR5HnFB47f9mN4lv0dOH8scuul0tenMW9L2hbhXv73n5X14HcrcRT5xZuquvKcZD264H8v5dhj5q8z7TYz9Mv/+vozX3lf2bF1/fzP7OSfy8IIURlFBoaynW5S0zyZs5caPmKFWRnZ1OrVi06d+7i1dh9bugDwI6dZd9U3pPff/8dVVUZNHBQgSLNhQbcNACz2czRo0c4H3++xGP7+vlRM7xmqf4JCgoqq1t0y8rKz7t8i9iOGcDfXzuWmen9g4W333kLq9XKM08/W+TslrKWd19FbTGdx8+v9Pelh8zc+yrua+Xnn3/M6uV9denchXcnvceaVWvZtWM3mzduYd2a9Tz91NOYzWYOHz7Mw48+fNlNpYUoazKjRlSYgP7NyNp4BuuqE4SN6VqgGWle75qAPk09LtlwpuWQPv8AWZvPYj+TqjV3dRZcWlJRT/Bz9mkFoYy/jmBdfaLoE3P7eTjPW/EpZsbIhQL6NiWgb9PLjlHoxxjmT9AtrUiff4D0Xw9gCDAT9K9WGGv4YzueRPLnW3DGZoBRAafWs0AIIUTlNGTwEFatXsWSJUt46cVxBfqQ5C0RGjRwEAZD4WefKSkp/PDjD6xdt4YTJ06QkZGB01lwd8Tz5ytm1sOuXTsB+O333/jrr7+KPM/h0IrssTGxBWYxFOfmQTdz86CbLz/IKuLvVX+zbPkyOnTowB2336F3OOISxjz+RKHXwsPD+b+HHqZFi5Y8+tgjHD16hN9+m8/w4XfqEKEQnkmhRlQYS89GKP4+uJKyyN4R455h40zJJmv7OaDwsicA28lkYp/+0938FUCxmLRZA4oCdieudJt7GU15y1suombaUUswG+LCWSlVjeGC2RdqTtH3kXfM4F/y/6QY/PJnAKk5RW/rnT922c0YyouzuPcFULNL9941Hu2MIzqNrM1nSf12F6nf7ipwPPTBa0j73wFcKdkYgsxFjOK9vM+02M/zgu9Hb+4r/zMr/vs5/zOTHy9CiKqvb99+WPwtJCQmsGnzJq7roc2wSU5OZuOmjUB+L5sLHT16lPsfGE1CYv7OlAEBAfj5+aGgYLfbSU1LLTD7ozzlLZuxWq1YrdZLnp+dXXbLjSuav3/+w7GcnOwiz8vK0o5ZLCV7mAbaLJU333oTo9HIhPETK/RhS959ZRdzTwDZ2d7fl54sufdV3NcqOyv/WEAZ3tcNvW+gU6dObNu2jb9X/S2FGlGpSCYtKozBzwfLdY2wLj+Gdfmx/KVQq06AU8WnYQi+LWsWui7h3bW4krIwtwinxkOd8G1bq8B2ylnbo4l75k8qajPgvO0Oa4zpSkjuFs7VlbFAP5NMaBbm8TxHQm7/khLOHAJQAkwo/j6oWY5iZ0Plj+15B6XSMIZrPVxc6Tm4chxF9qnJW7bmzX2BtoQt8t2bsK48jnX5MXfTXlPjGgTf1hq/jnVJ+UYr3vjUCyntbRSS9/VyJhSdhOd9nuDdZ5r3GTgTiv5auXIcuDJsBc4XQoiqzN/fn759+7Jw0UIWLVroLtQs+WsJDoeDJk2aEBVVOBd45dWXSUhMoE2bNjw99mk6dryGgID8/mEbN23kgQfv93oL5dJyqdos35deHMeokaMq5D31cmGvk/Pnz9OiRUuP5+Ut74qIKLrny8VmzJxOTEw0w+4YRqOGjQoVvVzO3NnUTqf7mMViKZOCTt59FTcLKzs7m7S0NAAiapb8vvQUERnJwUMHOX++6OV2Fy7FiyjhTK+Sat+uA9u2bePM2bNlOq4Ql0sKNaJCBfRvqhVq1p0i3OZEMRuxrtC6vQf2K7zkxxGXge1gPBgVIt+5EZ+Iwk1SnUneP/XJW3al2oqZeWD1vFbVWMMfx+lU9zbMZcm68jiJU0u39WBAnyaEP9m9TOMxhvpjCPHDlZqN7USye/vli+Xt8FPUDkqeKIqCqWEotn8SsJ0ouoN//thltwbcvTuRqu1U5duicIHQmZKNKzm74PleUAwKgf2beWwmnXM4wb00zjeq7BKOvDhtp1O1rWA9LCN0755VzI5XxY3tTMrCmZrtceenC3d6Ks1nJoQQldHgwUNYuGghy1cs57WJr2M2m1mU27Nm8M2DC50fHR3Nnr17MBqNfDbtc49bDicmJBR67VKMPlranpNTdC+N9HTPuUl4eDgnTpwgJqbsd5la/OdiJk16p1TXDho0iJfHvVKm8YSFhVGjRg2Sk5M5evQoPS/YNv1CebsiNWta9G5DF8vbpevnX37m519+LvK8BQsXsGDhAgCWL11OvXqe8ydvNGum5RMJCfEkpyR77I1z4U5PzYrZRakyad6sGWvWrOZoMbtU5d1X3tdWiCuBNBMWFcq/c30MIb6oGTYyN53BcT6DnNwmwJ6WPTnitacRxhA/j0UagOzcZVPeMARqy02c8UXPPMg55DmJyvvFOmuL9+97Ka4cB66krNL9Yy27prQX8svdcSt7m+fkzhFvde9i5H+tdx3z88f2/Fm6chzuJtHejl0cU6NQDGH+xb53Vt7rJgN+7Qon2Zcjr6G2uXkY5jIsaOR9nmqGDdshz0/csrZq9+XbOsKrpU9+7Wq7myRnb/f8vZA3trGmxasikBBCVGbX9biO0NBQ0tPTWbV6FTExMezYsR3A4+5IcXGxANSoEeaxSAO4l015I6/xbt74nuzbt9fj61d30HasWrdundfveyk52dkkJCaU6p/09PQyjwega+6OWxs2bvB4PC4ujqNHtV/+u3frVi4xlLVrr7kWk4/2c3vjRs/fP+s3rAe02Td5hZ3KLm93tKNHjxbZxHr9eu2+unUt+6/Vnr27Aahfv16Zjy3E5ZAZNaJCKT4GAno3If2PQ1iXH8NxLg1UMLesial+4SUghoDcgkpyFs7kLIw1Ci7VsB1LIsPDLlKXYm6qVeOd8Znk/JNQaMlV9u5YdwHpYoEDmpP24x7sp1JI/+MQQf9qVeT7ONNzMAb5ljiuoEEtCBrUosTnV4SA/k3JXHWCrG3nsB1NxNw8vMDxtJ/2gaotdfHzsI16sWP3a0ra3L3YT6eSueE0lh4NCxzPWPgPaoYNxdeI5fpGl30veRSDQkDfpqT/sp+03w4SdFubAkUL1aWS9vM+ACw9Grq/D8uC7Wgi6bm7PoXc26HMxgUwN66BqXkY9qNJpM7dS+Qb/QocdyRY3UWigBu9e9JmCDTj360+WetOk/rTPiw3NCkwY8eVZSf9j4Pa2P2aSpNkIUS1YTKZGDBgIPPmzWXx4kWcOXMGVVVpG9WWxo0aFzo/MLegkpiYQGJiIuHhBX9uHj78DwtzGxF7o0ULLT+Ii4tj//59hZZcbdu+rchdpG79163MmDmdY8ePMe+nudw5/K4i3yc1NZWQkJIvy73ttn9z223/LvH5FWHw4CEs+WsJ6zes59ChQ7RqVTBXm/3NLFRVJSIiwuM26kWZ9M67xW4nPnL0CLZu3Vou244HBQXRq1cvVqxcwTffzGbggIEFmlhnZmYyd948QJvpVVV+Dnfv1p3w8HASExOZPXsWLzz/YoHjhw4dyu8HNeQWr8ZW1eI3bVi7di3btm0DoHevG7wLXIhyJjNqRIXLmzmTtfEMGX8eKfDaxUyNQjFGBIAK8a/9jf2stu5WdbiwrjlJ7HNLStW01Kd2EObW2trdhElrsB1Lyh/37xOcf3V5kU1ezY1rEJzbmybx4w0kf7UVx/n8mTmuTBtZW88S/9Yq4ieu9Dq2ysbSsxHmNhHgUjn/6gqy92tPO1Sbk9R5e0n7ZT8Aofd3RDEV3hb6zJ3zONl7BvGT1hQ65tuiJpY+TQBIeHcNmZvOaGM7XWQsOULyl1sBCB7WtlCRDiB+0hpO9p7BmTvneX1fIfe0Rwkw4Yyzcn78Chy5S9mcKVna98ShBDAZCL3/mkLX2mPSOdl7Bid7zyD9z8OFjmftiCZ13l7sZ9NQc9eruzJspP9xiNin/0S1ObH0aVLkDl/FfWaXUuOhTgBkrj5J0udbcGVqU+RtJ5M5P24ZaqYdn7pBBA0pvGY//c/D7vuyxxR+ylnj/mvAx4DtYDwJk9bgTNGWhjniMjg/fgXOOCuGQDMh97T3Om4hhKjM8hoGr1q9ivnzfwU8z6YBaNa0GbVr10ZVVZ559mlOnToFgN1uZ+mypTz4nwdL1ei1Xt16tG+n/fd13CvjOHz4H/e4S/5awpgnHick2HOBpXnz5u7eNG+8+QYfffwhsbH5M3Os1gzWr1/HCy8+z1PPPOV1bJVNv779aN++Ay6XiyfGjmHXbq0vnM1mY9bsmXw751tA2xHIbC6c7/W7sS+to1ox7uWXyjy2kaNH0DqqFSNHj/D62jGPP4HJx8SevXsY98o4kpO1Gc3R0dE8OfYJYmKiCQ4O5j8PPlTo2i1bNtM6qhWto1qxZcvmQsddLhfJycnuf9Iz8pfRpaSkFDjmSd7Y0z6d6tU9mc1mHn9sDADffPsNs2bPdG+VvXPXTp4YOwaXy8U1Ha9xb2t/oWmfTnW/98W+nv4Vr7z6Mus3rMdqzb+fpKQkps+YzpNPaTtCNWnShNv/fbtXcQtR3mRGjahwvu1rYawVgDPOiv1UChgUAjz0pwFt5kPYk92In7iS7F0xnLv3ZxSLCdXuBLsLY60AajzahYS3V3sdR/iT3Yh9ajH2E8lEPzAfxd+E6tDG9etSD9+WNUmds9vjtTUe6Yya4yD990Okfr+H1O/3oASYQFG03ja5vQH9rvZuhkllpCgKka/3I/bJRThi0ol9bIH2Wdkc7i3Sg/7ViqBbip5ZVJyaz/ckNjod2z8JnH9xKYqfD6pLhdz+Qf7dG3gsllwun3ALka/34/yry8neeo6zw+ehBJrzv35GhZovXI+5ifdroR1xGSR/toXkz7aAUcFgMWlNdnO/LwL6NaXmy73L9oZyWbo1IPTBa0iZsYO0uXtJ+3mf9pnmLo0zhPgR+XZ/FHPhotqlmJuHU/P5niT8dy3WpUexLjuKEmBGzW0grPj7EPFmP4yhZdf4WQghKoNrr7mWOnXqEhMTzbHjxzAYDNx8s+ctqQ0GAy+Pe4Wnnh7Llq1bGHjzAAICArDZbNjtdurUqcvzY1/gxZde8DqOl19+hdH3j+LIkSPcetutWCwW7HY7drudntf1JCqqLV9+9YXHa5979nmys3OYO+9Hvp7+NV9P/5rAwEAURSEjI8Pd2LhL5y5ex1XZKIrClI+nMGLUfZw9e5a777kLi8WCzWZzb0F+5513MXzYcJ0j9U6rVq144/U3GD9xPH/88TsLFvxBYGCgewmZxd/ClI8/ISzM8+YPxYmJiab/Tf09Hruhb8Gc5eD+Q94HX4y777qbgwcP8PMvP/Pf9//Lxx9/jMlsIjNT28CgQYMGfPzRx16Pa7PZ+HX+r/w6/1cURXF/v+c1XAZtptpn0z7zWLATQk9SqBEVTlG0ZSdpP2rrqP2uro1PMTvEBPRqjPHjQaTM2UXOgXhwuPCpFYilZyNC7u3gng3jLd82kdSeNoSUWTvJ2ROLanNiqh9C4MCrCB4WRcpFWyoXuAejgfBnriPgxuak/36Q7L1x7qbGxlqBmJuF4d+5XpEzJqoan8gA6s4YSuoPe8hccxJHbAYGiwlz83CCbm1NQO6smNIwBJip8+kQ0n7eR8aK4zjOpaGYDJibhxE4qAWBt7Qsctpq3m5RnnYLKwn/zvW0+/puN1nbonGmaMvrfDvUJuTu9qUe169dbYKHRZG9OxZHXAauTDvGmgH4RkUSNLhFkU2ZQZvV5UrVZqr4tird+4eO7Ihvm0jSftlPzoF4XFnaLBr/7g0Ive9qjGGlL6QEDrwKU+NQUufuJWd3rLa8LzIA/071CLm3A6b6waUeWwghKitFUbh50M3MmDkd0IoZkcXsPnNj/xuZNXM2X371Bbt378bhcFC3bl369e3HQ//5P/dsGG91aN+B7+Z8z6efTmP7ju3k5OTQuHFjht46lFEjR/P5F58Vea3RaGTihIncMuQW5v40l+3bt5GQ29S4Tp06tGrZih49riuyAFXV1K5dm/n/+43pM75m2fJlnDt3jgBLAK1ateKuu+5m4ICBusSVt1V6u7btSnX90KG30bx5c2bMmsm2bdtITU2hTu06dO/Rg//7z//RqFHZLRUvqQt7y7Qt5X298fqbdO/eg3nz5nLo0CGyc7Jp2rQpN/a/iYf+8x8CAgK9HnPAgIE4HE527drJ6TNnSE1Jwe6wExERQatWrRlw0wBuGXKLFGlEpaRU1LaAolrrf9AW/ctTSd+V3T7Dotxl7Ywh7qnFGGsH0mDenXqH4zXV4eL0kO9Qs+3UnXEb5iK2Dq9qsvefJ/axBRgjLNT/YXipZr5UdjFjF5GzK5bwl66/ZE+mXn4tGRN8418hBos+GbUQojrqpKrqctWJ5C1VzJYtmxl1/yjq1q3LimVVb3l5fHw8vW64Hn9/f5b9tbxQ/6KqatHiRTz3/LNERUXxy0//0zucctHvxr5ER0fzzaxviu9rpIBi4HtFUe6ruOhEdSQ9aoQQVZLtcAJqlh3L9Y2rTZEGIGd3DAAhd7evlkUaIYQQ4kq1dZvWe+/O4XdWmyIN5N/X448+rnMkQlQfsvRJiCucMzaDk71nAOB7dW3qTBmsc0Qlk71ba4IYMvJqnSMpW9m7YzGGWwj00Oy3Kkucuon03MbTQgghxOWIjo52N4/t3Lkz386eo3NEJbNt2zb8/Px44P4H9Q6lTG3bto3WrdvQp09fvUMpU2OeeJwVK1foHYa4QkmhRogrlGIyYLioV4k3W4nrLeTu9oTcXf12F6r13gC9QygXBoup0PebwVd+BAkhhCg5k8lEzfCC/dtCQkJ1isZ7E8ZPYML4CXqHUeYW/uH9dvNVQXBwcKHvN5PJpFM04kojPWpEWZAeNUKIciE9aoQQ5UB61Aghyof0qBFlRHrUCCGEEEIIIYQQQlQSUqgRQgghhBBCCCGEqCSkUCNEJZQ8awcne88gftIavUMRQgghhBBCCFGBpFAjhKi2YsYukoKXEEIIUYamfTqV1lGtGPfyS3qHIirQz7/8TOuoVtz/4P16hyLEFUG23BBCCCGEEEKICjRy9Ai2bt1a4DVFUQgICKBB/QZ0796d++4dQZ06dXSKUAihJ5lRI4QQQgghhBA68PX1pWZ4TWqG1yQ0NBSr1crBQweZOWsm/xp6C9u3b9c7RCGEDqRQI4QQQgghhBA6GDRwEGvXrGPtmnVsWLeRndt38cH7HxIaGkpGRgbPv/AcNptN7zCFEBVMlj4JUUFsJ1NI+99+sndE44y3gsmIT0QAfh3rEDjwKnxb1izROI7zVqwrj5O1/RyOc+k4E6xgNGCqG4T/dY0IHhaFMcjX47X2mHTSfthD1o5onOetoIAh1A+fOkH4d65P0JCWGEP93OerLpWMv45gXXIU2/EkXFYbhkBfjDX88G0dgaVPUyxd65fJ51PRnCnZWP8+TtbWc9jPpOKMzwRVxadWIP5d6hF8Vzt8agYUuu5k7xklGr/W5Jvx71iH5Fk7SJ2985Ln+15dmzpTBnt9H0IIIYSoPnx9fRl882BUl4vnX3yemNgYNm/ezPXXX693aEKICiSFGiEqQNr/9pP06WZwqgAo/j4ogP1EMvYTydiOJ5X4l/SkaZvIXH1S+4vJgMHfhCvDhu1oErajSViXH6X25MH4RBYsMuQcTiB27GLUTLv2go8Bg58PzjgrzjgrObtiMV8VXqDwkvD2aqzLj7n/rgSacWXacKVmYz+Zgu1USpUt1KT+sJu0efu0vxgVDAFmXFYb9lMp2E+lkLHsGLU/GoS5WViB6wxh/kUP6nDhSsspeL6/qdhrXOk5YHeV+j6EEEKIy3Xs2DHmfPctmzZvIi4uDpPJRO3atenapStDbx1KVFTbEo0TGxvL4j8XsXHjRk6fOcP583EYjUYaNmhInz59GDVyNMHBwR6vPXv2LNNnTmfTpo3ExsaiKAo1aoRRv349el7Xk2F3DKdGjRru810uF7///hu//f4b/xz+B6vVSlBQEGFh4XRo356BAwZV6eLGddf1dP/52LGjRd7L+fjzzJgxgzVrVxMTE4PJZKJpk6YMGnQz99x9D2azucj3SE5O5ts537J6zWrOnDmN0+kkMjKSqDZRDL55CGAKMasAACAASURBVH379i1xvPPn/8r4ieNRVZWJ4ycyfPidJb9ZIUQhUqgRopxZ/z5B0iebALD0bkzoA9dibhwKgDMth6zNZ7AdTizxeKZGoYQ92Q3/rvXxqRuMYlBQHS5y9sWR9PkWbIcSSPxwHbXeG1DguuTPtqBm2jG3iSD86R74ttBm8LiyHdhPJmNdfgxDgMl9fvbuGK1IY1So8WgXgga3wGAxo6oqzqQssreew3Y86XI/Ht34RAYS+lAnLN0bYGoUiuJjQHW6sB1NInn6NrK3nCP+zb+pO+vfKIrivq7h/HuKHDP+9b+xrjyOMSIAcxMtmQy5qx0hd7XzeH7O4QRixyxEhSpb8BJCCFG1fff9HN59712cTicAFn8LiqJw5MgRjhw5wj+H/+Hb2XNKNNakd99h6bKlAJhMJiwWC+np6Rw8dJCDhw6ycOFCvpn9LbVr1y5w3f4D+xk1eiRWq1W71seEv8WfmJhoYmKi2bp1K61btSlQrHjxpRdYuGih++9BQUFkZGSQnJzMsWNHOXrsWJUu1Kiq6v6z0+X5gc6u3bt45JGHSU1LBSAgIACbzcaevXvYs3cPCxb+wddfTicsLKzQtVu2bObJsU+6r837ep05c4ZTp07x19K/2Ldnf4li/XbOt7z73iSMRiPvTXqPwYOHeHu7QoiLSKFGiHKkOlwkfaoVaQL6NSViQp8Cx43BvgTe2BxubF7iMWs8eG2h1xQfA35X16HW+wM5N+IXsjafxR6TjqlOkPucnAPnAQh/opu7SANg8PPBt1UEvq0iCoyZsz8eAP9r6xEyLP9JmqIo+IRbCBx4VYljzpO1M4a4pxZ7fR2U/dKg4DuiCr2mGA34tqxJrbdvJPqh37CfSCFndyx+V196x4WU73djXXkcxddI5Nv9Cywh88SZnMX5V5ej5jix9GlCyD0dSn0vQgghRGks+WsJb7/zNgADbhrAE2OepFmzZgCkpKSwdt1aDhwo2S/rAE2bNuOVl1+hZ8/radigIQaDAbvdzs5dO/ngg/fZu28vE1+fyJeff1nguvff/y9Wq5X27TswccJE2rRuA0BWVhbHjh1lwcKFBAYFus/fum0rCxctxGg08vxzL3DH7bcTEBCIqqrEJ8SzYf16Dh85fLkfj67Wb1jv/nOD+oUf5iSnJPPEE2NITUulVctWvPXmW0RFtcXpdLJ02VImvjaBAwcO8NK4F/nqy68LXHvi5AkeG/MYVquVNm3a8OLzL9KpU2cMBgPZ2dls27aVX/73S4ni/PSzaUz7dBq+vr58/NFk+tzQ59IXCSEuSQo1QpSjrO3RWu+T3Fkp5c0Y7Itv20iy1p0mZ9/5AoUaJcCMmpOFIzETzx1sClJyZ9c4U7JQXSqKQbnEFSUY02QofulQMYrqu1MeFLMRv071sJ9MIXtv3CULNZkbT5MyXduVIfyF6y/Zb0h1uDg/fgXOOCvmq8Kp+VKvMotdCCGEKAm73c67700CYPDNg/ng/Q8LHA8NDeWWIbdwy5BbSjzm2CfHFnrNZDLRpXMXvvryawbfcjNr167h3Lmz1KuXX3zYvWc3AC+Pe9ldpAHw9/enbdt2tG1bcGbq7t3a+T2692DUyFHu1xVFITIikqFDbytxzHm2bNnMqPtHXfpEDzp37lziWUeXkpOTw/IVy3lnklZACw0N5frrC+cJ3303h4TEBEJCQpj+9QzCw8MBMBqNDBo4CIvFwiOPPszadWvZum0rnTt1dl/70ccfYbVaada0Gd/OnkNAQP5yeT8/P3r2vJ6ePYufjaSqKu++9y7fzvkGi8XC559+TpcuXcviIxBCIIUaIcpV3iwWc7MwfCIKN6Yt9bgH40n//SDZ+8/jjLeiZjkKneNMzCzwd0vX+mT8eYSEd9aQMzQeS89G+LasieLjefM3/2vrgsmA7XAisWMXEXRLK/yuqeOxwW5J+bWtVezSoYpmO5VC+vwDZO+OxRGbgZplB7XgORd/jp7GiH9zFbhUQu5tT2D/Zpd838TJG8jZG4ehhh+Rb/fH4Cf/KRZCCFGxNm3S+tHkzUopb6GhoXS8uiMrVq5g586dBQo1gQGBZGdnEx8fX6KxAgO12TWJSYm4XC4MhsvfyNZkMlEzvGQbO1wsJCS01O/755I/WbduHQAu1UVycrJ72ZOvry/vv/c+/v6FH3L9tVRbYjZ82HB3keZCvXv1pl3bduzdt5clS/50F2rS09NZuXIFAE8+8WSBIk1JOZ1OJkwcz6/zfyUkJISvvvia9u3bez2OEKJo8tuBEOXIlZQFaP1Qykrq3L0kf7Elv6BgVDAEmcFkBEDNsKHanKjZ9gLX1Xi0C/YzqeTsO0/aD3tI+2EPitmIb1QklhuaEDjoKgy++f9JMNUPIfzp60iasoGcPXHk7InT7qV2IP5d6hN4S8sCS6iqmowVx0h4Zw04ctd9G7SGwphzP8csO2qWw2MRLI8zPYfzryxHtdrx796A0P90uuT7ps0/QMaCf8BkIPKNfvjUKrvvDSGEEKKkdu/ZBUDLli2pVatWmY27Z88e5v00l527dhIXG0dmVuEHHufjzxf4e69evfh1/q+8NO5F7r7rHvr160dUmyhMJlOhawG6deuGyWTiwIEDjBw9kuHDhtOta1ciI0t/Hx07XsPaNetKfX1p5eTkkJOTU+j1evXqMXP6LBo2bFjoWHZ2NsePa5s9dC1mFkvXrt3Yu28vBw4ecL+2d99ed3HrwobFJWW323nm2adZumwpNWtGMGP6DFpc1cLrcYQQxZNCjRBViO1EMslfbgUVgm5rQ9DQVpgahKAY858kxb+1CuuyY6gXzQwxhvhRe9oQsrdHk7nhNDl74rAdSyJ7ZwzZO2NIm7eX2lMK7hYVNLgFlu4NsK48RtbOGHL2xuGIzSD9j0OkLzhE6IPXEjri6oq6/TLjTMki8f314HBh6duEkLvaY24WVmB2UfKM7aR+u+viCTZuqksl4Y1VOM6kYmoUSsT4Gy65PCx7VwxJ0zYDEP5UD/za1y72fCGEEKK8JCRqGxnUqVO3zMacOWsGH3z4gXtGiNFoJCQ4xF1wSc9IJycnh6ysrALXPffc85w4cYKdu3YyfcbXTJ/xNb6+vlzd4WoGDBjIbUNvw88vv/db40aNmTjhNd56+022b9/G9u3bAK240bPn9QwfNrzAEqrKbOitQ5n0zruA1pPn0D+HmDJlMpu3bGbiaxP48ouvCu3clJKS4v6MI4spstXOPZaUlOx+LTH36x4SElKq2TR5nzXAJ5OnSJFGiHIihRohylFePxZHXEaZjJe5+iS4VPy61CP8qe4ez3EmZ3l8HbS12/6d6uHfqZ52bnoOmX+fIPnrbTii00matonIN/oVuMYY5k/wHW0JvqMtqqpiO5RA6ve7yVx7ipSZO7D0aFhoC+uiZO+L4/z4FSW72Yv4RUUS+Vb/Ul17saxNZ1Gz7JgahxIxvo/HAoszqejPESD5y61kbTmLIchM5Ds3arNxiuGITef8hJXgcGlFtiEtL+sehBBCiMrkyNEjfPjRh6iqyr333Mtdd95NkyZNMBqN7nNeeOkFFiz4o8CORgA1Qmvw/Xc/sHHTRlat+ptt27fzzz+H2LxlM5u3bGbW7Jl8O3tOgd2ibv/37fTu1ZvFfy5my5bNbN+xnXPnzjFv3lx++mkeY58cy8P/90iF3X9Z8Pf3p+PVHfnyi68YftcwNm3exJRPpvD8c88XeY3Nw2yc8tS6VWtybDkcP36c1994ndmzviE0tPRLv4QQnkmhRohy5NsmEgDb8SQc8dbL7lPjiNe2rfS9qvBaZABXlp2cAyVb3w1ag96gf7UCIPHD9WTvji32fEVR8G0dQcTrfTl75084461k74ktcaFGtbvcy8G85Uwvu0Qk73M0Nw3zWKRRVZXsndFFXp+x7Chpc/eCUSFiYh9M9YOLfT9XtoO4V5bjSs3Gr2MdwsZIsz0hhBD6qpnb1yQ6uuifd95YunQpLpeLntf15NVXxns8JzExocjrFUWhR/ce9OjeA4DU1FT++msJH03+iDNnzvDue5OY/PGUgvdQsyYjR4xk5IiRqKrKvn37+Gr6VyxfvoxPpn7CDb370LJlyR6M7Ny5gyfHPlnCuy3o6o4dmTplaqmu9cTX15dxL77M/Q+OZs6cbxk+bDiNGjVyHw8NDUVRFFRVJTomhqioth7HiY3Tlq2HhdVwv5bXzyY1NRWr1er1rJqQ0FDem/QuI0aN5J/D//DgQw8wa8ZsgoOLz4WEEN6RQo0Q5cj/2roYIyw44zNJ/nxLoe25vWUI1GZt2I4nezyeOmc3aqa90OuqSwWXWmTjYCWvL4vdmX+N3YliMno+32hwj6XaXSWO379jHRqvfrDE55cX9+d4QmvYpygFizUZC/7BcS7d47U5h+JJ/K+2hr3GI13w71x4y8yLJUxag/1oEj51g4h4vW+RXwchhBCionRory1dPnz4H+Li4i67T01cnPawp3Xr1h6PZ2ZmundrKomQkBCGD78TFZXXXn+Nrdu2Fnu+oii0a9eOyR9Npv9N/YiNjWX7ju0lLtTY7XYSiikkFSc1NaVU1xWnW7dudLy6Izt37eTTz6bx3/fedx/z8/OjadNmHDt2lC1bNnNj/xs9jrF58yaAAsvA2rVth9FoxOl0sm7dWgYMGOh1bJGRtZg9czYjR4/gwIEDPPTwQ8ycPoOAAOm7J0RZkd8WhChHio+BsMe02RPWFcc5P3EltlP5P8ydaTmkLzhE4pSNJRrPv5O2jjxr4xlSvtuNK1trdOtMySLp8y2kfr8bQ0jhbaxdVhtn7/2ZlDm7sB1LQnVqxRXVpZK1PZrk3K2lLyw6JH+9jfMTVmBdexJnWv5sFmdSFolTNuKISQclP6aqxP/auqCA/UQySVM2uWfruKw2Un/cQ+LkDR4/R2dKNudfXYFqcxI48CpChnt+gnWhlO93k7nqBIq/ici3+2MM8bvkNUIIIUR569atG7Vq1cLpdPL+B/+97PGCgoIAOHzksMfjX371BVartdDrLpcLh6Poxv2+vtrPTZvN5n7twj9fzGg04uPjc8nzLtalS1cO7j9Uqn/Kamvuiz3wgPZwa/Gfizl9+nSBYwNuugmAX3/9lYSEwgWm1WtWs3ffXgAGDhzkfj0oKIg+ffoCMHXaVI9fk5KoU6cOs2fOpk6duuzZs5uHH3mYzMzid8oUQpSczKgRopwF9G2KI95K8hdbyVx1wv1Lu2JUcGVoCYTv1SVrKuvfuT6WXo3JXHOSlK+3kTJ9G4ZAszaOCoGDW6A6VaxLjhS61hmbQcr07aRM3w4+BgwWEy6rDZzaOnGfukGEPZ6/JEd1qmSuPqn1xQGUABOoFJixE/rgtZiblmzZk54uXtxkahhK8B1RpP28n/T5B0iff0D7HDPt7h5Avi1rkjqn4JM/24lknLnLpjI3nub0bT8U+Z6Rb/bDr20tsracBUB1uoh9dkmR55dlDx4hhBDiUkwmEy88/yLPPvcMixYvwul08sSYJ2natCmgNaxdumwpR44c5pWXX73keD2692DmrJmsXr2ar77+khH3jcTf35+kpCRmzJzOzFkzCQ0NJSWl4OyTjIwMbrt9KMPuGE7fPn1o1qw5RqMRl8vF5i2bmfLJZAB6XrBD0eQpH3Pu3DluueVfdLq2k7tHSkJCAl9+9QVnz57VllL16FFWH5cu+vbpS+PGjTl58iRfTf+Kt954y33svvtG8NNPP5GQmMD/PfwQb775FlFtonA6nSxbvowJE7XlZ9f3vN69NXeeZ556mg3r13Ps+DFGjh7Biy+8RKdrO2EwGMjOzmbjxg3M+3keX3z2ZbHx1atXn9kzZzNi1H1s37Gdxx5/lC8+/7JA42chROlIoUaIChByZzv8O9Uj7ed9ZO+MwZGUheJjxNQsDL+OdQgc0LzEY0VM7EPaT3vJWHIUe3QaqODbthZBQ1oSOPAq4ietKXSNIcBM5Ls3kr09mux953HGW3GmZKP4+WBqEIKlZyOCb2+DwZLfEDdkWBSmukFk7YjGfioVZ2Imqt2JMTIA37aRBA9tg1+HSr5rUe6yLMW38BKusDHdMDUKJf33Q9hOpaC6VMxXhRN4UzOCbmtDyre7ih3alVp8z5xCS8JszmL785RlDx4hhBCiJG4edDPn4+J4/8P3WfLXEpb8tQSLxYKPjw9paWkAdO7c+RKjaK67ric39r+RZcuX8fHkj5k8ZTLBQcGkpaehqiq3334HToeD337/rdC10dHRTPlkMlM+mYzJx4QlwEJGRgZOp7Yku0GDBrz4wkvu8x0OJ0uXLWXpsqUABAYGoqpqgdkhY58cW+V3JDIYDNw/+gEmvjaBP37/ncceeYy6dbWZzDVCa/DJJ1N55NGHOXjoIHcMu52AgADsdrt7JlHr1m14d9J7hcZt0qQp06Z9ytinnuTAgQOMGj0Ss9mMv78/6enpuFyuAk2gi9OwYcPcZVCj2LxlM2OeeJzPPv280E5VQgjvSKFGiApibhZGzZd6lejcGvdfQ437r/F4TPExEHJPB0Lu6eDxeMS4XkSMK/g+ikHB0r0hlu4NSxyvT+0ggm+PIvj2qBJfU9nk7YBlKGK5UdAtrQi6pZXHY56+BqXpsVNnymCvzhdCCCEq0ujR99O9ew++nfMNm7dsJj4+HpOPiZYtWtKlS1eGDh1a4rE++vBjZs2exe+//8bpM6dRUbmm4zXccccwht46lHEvv1TomsDAQD7/7As2btzIrl07iY2LJTkpGX9/f5o0bkK/fv247977CvQ/GTVqFA0bNmDTpk0cO36M+Ph4bDYbdWrX4eqOHbnn7nvodG2nMvl89Db01qFMnTaVhIR4ps+YzoTxE9zHOl7dkQW/L2D6jBmsWbuamJgYfHx8aHFVCwbfPJh77rm3yIJJ927dWbRgMd98+w2r16wm+tw57DY7DRs2pF3bdtx8c8nzlyZNmjJrxixG3T+S9RvW8+RTT/DJ5KlSrBHiMigXb48nRCn0P2iL/uWppO9C9A5EiDyOeCtnh80FFSLe6EtA7yZ6hyRKoZdfS8YE3/hXiMHifbdDIYTwrJOqqstVJ5K3CCHKlgKKge8VRblP71BE1SYzaoQQ1Y4jNl1bAqZqvXX8u1x6ZyYhhBBCCCGEqAykUCOEqDasK4+T8OF61NwmzShaLxqDv0nfwIQQQgghhBCihKRQI8rExbvqCKEHV44D1WrDEOyLb6sIgodHFdhyXFQ9ivY/WaMrhBBCiKpC8hZx2aRQI8pChsXgq3cMQhA0qAVBg6r2Dg+iIItixoCScukzhRCixDIAg95BCCGqrWS9AxBVn/yQEmUhuqYh0Ncg82qEEGWsjjHU4av4nNA7DiFEtRILyBMmIUSZUxRyFEU5pXccouqTQo0oC6ddqDFRJlliIoQoW339o7JNis9veschhKhWUoD98nxJCFHmFFzAAr3DEFWfFGpEmfBTTLP6+bfJ0TsOIUT10dQnkkDFNxvYqncsQohqZ4aikKl3EEKIakQr/sYAh/UNRFQHUqgRZcJHMc7q498m80a/ttI8Swhx2cINgbxR49+ZBkV5A2nKJ4QoY4qizEUhAwWn3rEIIaoHxUAmMEHvOET1oKiq5L+izLTKVu0b5lu3hSzL2mc455Q+WkII7/grZrr6NuOhoBsygwx+b/kqpkl6xySEqLYaq6q6GZUw1SUbbAghSklxF2meVRTlC73DEdWDFGpEWWuW6bK9ZFCUYUnODMNJRwLpriwflzwQr3AKiglARbXrHUvVoBgMKGYXrmy9I7nSKCj4KSZXTWOQs4Wptm+Oat8aZPCfAvyid2xCiGqvgaqqLwJ3A2ZUVMAI0sFGB6bcf0veUjIGwAxI3qIPZ24/Gl9gnaIoHwOLdI5JVCNSqBHlxQh0BRoDIUjCU9FCgFeBt4BUnWOpSh4ETgHL9Q7kCpQFJAJrkW0thRAVzwB0Bpqi/QyV9gAVS/KW0pG8RT+ZQAKwBkjTORZRDUmhRojqaRqQAzyrdyBVTBvgb6A5kK5zLEIIIcSVQvKW0pG8RYhqSgo1QlQ/DYGdQGvgvM6xVEXfAYfQnuoJIYQQonxJ3nJ5JG8RohqSQo0Q1c9XaFMxX9Y7kCrqKmBj7r9lCY4QQghRviRvuTyStwhRDUmhRojqpRmwGWgBJOkcS1U2A4gGxusdiBBCCFGNSd5SNiRvEaKakUKNENXLN8Bx4HW9A6niGgPbgFZoT/mEEEIIUfYkbykbjZG8RYhqRQo1QlQfrdB2zGmO7JhQFj4DMoAX9A5ECCGEqIYkbylbkrcIUY1IoUaI6mMusAt4V+9Aqol6wB4gCojVORYhhBCiupG8pWxJ3iJENSKFGiGqh/bAUrSnUhk6x1KdfAwYgLF6ByKEEEJUI5K3lA/JW4SoJqRQI0T1MB9t+vBHegdSzdQCDgAdgLM6xyKEEEJUF5K3lA/JW4SoJqRQI0TVdy3wB9pTqSydY6mO3gVCgEf1DkQIIYSoBiRvKV+StwhRDUihRoiqbzGwCPhU70CqqXDgH6AzcELnWIQQQoiqTvKW8iV5ixDVgBRqhKjauqM142sB5OgcS3X2BlAfeEDvQIQQQogqTPKWiiF5ixBVnBRqhKjalqMlPNP1DqSaCwWOANcBh3WORQghhKiqJG+pGJK3CFHFGfQOQAhRajcAjYFv9A3jipACTAYm6h2IEEIIUUXdgOQtFUXyFiGqOJlRI0TVpABrgK+AOTrHcqUIAo4CfYH9OscihBBCVCWSt1Q8yVuEqMJkRo0QVdNNQE3gB70DuYKkA+8Dr+sdiBBCCFHFSN5S8SRvEaIKkxk1QlQ9CrAZ+BCYp3MsVxoL2tOpm4FdOscihBBCVAWSt+hH8hYhqiiZUSNE1TME8AN+1juQK1AmMAltNwUhhBBCXJrkLfqRvEWIKkpm1AhRtRiAHcBrwG/6hnLF8kPbQWEY2hNCIYQQQngmeYv+JG8RogqSGTVCVC3/BhzA73oHcgXLBt5Cnk4JIYQQlyJ5i/4kbxGiCpIZNUJUHUZgL/As8KfOsVzpTMA/wChgrc6xCCGEEJWR5C2Vh+QtQlQxMqNGiKrjLiAFWKJ3IAI72pOpN9GaJAohhBCiIMlbKg/JW4SoYmRGjRBVgw9wEHgYWKlzLELjA+wHHgNW6ByLEEIIUZlI3lL5SN4iRBUiM2qEqBpGAmeRZKcycaA1R3wLeTolhBBCXEjylspH8hYhqhAp1AhR+ZmBCcB4vQMRhcwDgoBBegcihBBCVBKSt1RekrcIUUVIoUaIyu9B4BCwTu9ARCEutGRU1nwLIYQQGslbKi/JW4SoIqRQI0Tl5ge8gvZDVVRO89GSnaF6ByKEEELoTPKWyk/yFiGqACnUCFG5PQxsB7boHYgokoo2vfsN5L+pQgghrmySt1R+krcIUQXIrk9CVF4BwFFgILBb51hE8RRgIzAZmKtzLEIIIYQeJG+pOiRvEaKSkyqqEJXX42jruyXZqfzynk69hrb9pRBCCHGlkbyl6pC8RYhKTmbUCFE5BaM9lboBOKBvKKKEFGAVMBP4Rt9QhBBCiAoleUvVI3mLEJWYFGqEqJzGAy2B+/QORHilFzALaAXYdY5FCCGEqCiSt1RNkrcIUUlJoUaIyqcGcATonvtvUbUsBX4GvtY7ECGEEKICSN5StUneIkQlJIUaISqft4A6wIN6ByJKpStawnMVkKNzLEIIIUR5k7ylapO8RYhKSAo1QlQuNYF/gGuBk/qGIi7DQmAJME3vQIQQQohyJHlL9SB5ixCVjBRqhKhc/gsEAo/pHYi4LNegJT3NgUydYxFCCCHKi+Qt1YPkLUJUMlKoEaLyqI22U0I74JzOsYjL9z9gA/Ch3oEIIYQQ5UDylupF8hYhKhEp1AhReUwBXMDTegciykRbYDna06kMnWMRQgghyprkLdWL5C1CVCJSqBGicmgA7AZaA3E6xyLKzg/APuAdvQMRQgghypDkLdWT5C1CVBJSqBGicvgCSAVe1DsQUaZaAuvQdlJI0TkWIYQQoqxI3lI9Sd4iRCUhhRoh9NcE2Aa0ABJ1jkWUvVnAaWCi3oEIIYQQZUDylupN8hYhKgEp1Aihv1nAGWCC3oGIctEE2Ir2lEoSWiGEEFWd5C3Vm+QtQlQCUqgRQl8tgPXIFNPq7gsgGRindyBCCCHEZZC85cogeYsQOpNCjRD6+gHYD7ytdyCiXDUAdgFtkKaLQgghqi7JW64MkrcIoTMp1Aihn7bACrRtENN1jkWUv08AB/CM3oEIIYQQpSB5y5VF8hYhdCSFGiH08wuwCfhA70BEhaiD9hSyHXBO51iEEEIIb0necmWRvEUIHUmhRgh9dAQWoT2VytQ5FlFx3gcswON6ByKEEEJ4QfKWK5PkLULoRAo1QuhjAbAMbVqpuHJEAIeAa4BTOscihBBClJTkLVcmyVuE0IkUaoSoeN2An9F2TMjWORZR8d4CagP/0TsQIYQQogQkb7mySd4ihA6kUCNExVsK/A/4Uu9AhC5qAEfQEt+jOscihBBCXIrkLVc2yVuE0IFB7wCEuML0QlvfPUvvQIRukoEpwES9AxFCCCEuQfIWIXmLEDqQGTVCVBwFWIWW7MzWNRKht2C0p1K9gYM6xyKEEEJ4InmLyCN5ixAVTGbUCFFx+qGt8f1O70CE7tKAD4HXdI5DCCGEKIrkLSKP5C1CVDCZUSNExVCADWi7JfyocyyicghAezo1ENitcyxCCCHEhSRvEReTvEWICiQzaoSoGDcDQcA8vQMRlYYVeA94Xe9AhBBCiItI3iIuJnmLEBVIZtQIUf4UYDva9oa/6hyLqFz80J5O3QZs1TkWIYQQAiRvEUWTvEWICiIzaoQof7fl/nu+rlGIyigbeBt4Q+9AhBBCiFySt4iiSN4iRAWRGTVClC8D2jreccBCnWMRlZMZOAzcC6zXORYhhBBX6mZjVAAAIABJREFUNslbxKVI3iJEBZAZNUKUr+Foa3oX6R2IqLRsaE+m3tQ7ECGEEFc8yVvEpUjeIkQFkBk1QpQfH2A/MAZYpnMsonLzAQ4CDwMrdY5FCCHElUnyFlFSkrcIUc5kRo0Q5edeIBZYrncgotJzAK+hPZ1S9A1FCCHEFUryFlFSkrcIUc6kUCNE+TABE4HxgExbEyUxFwgFBugdiBBCiCuO5C3CW5K3CFGOpFAjRPm4HzgGrNE7EFFlOJGnU0IIIfQheYvwluQtQpQjKdQIUfb8gFfRnkoJ4Y3/oT3V/JfegQghhLhiSN4iSkvylv9n776j4yivxo9/Z7YXdduSbbn3XnADGzC911AcOiGQBAgpEAiQ0F94IfAm5EcogdBDB1NsOjYY927Llm3ZlmTLVrO6tpeZ3x9ryxYqllYrrcr9nMPBuzPz7F0dafbunWfuI0Q7kUKNELF3I7AZWBnvQESXowH3EVlNQc7PQgghOoLkLSJakrcI0U7kD0qI2LIDdxP50BIiGp8BfuCSeAcihBCi25O8RbSV5C1CtAMp1AgRWzcDK4D18Q5EdFk6kennDwCG+IYihBCim5O8RbSV5C1CtANF16WxuxAxkgDsAk4BtsQ5FtG1KcCPwPPAm3GORQghRPckeYuIFclbhIgxKdQIETv3AOOBK+IdiOgW5gIvAWOAYHxDEUII0Q1J3iJiaS6StwgRM1KoESI2koGdwBxgR5xjEd3Hd8BbwH/iHYgQQohuRfIW0R4kbxEiRqRQI0RsPAgMAq6LcxyiezkOeBsYSaRRnxBCCBELkreI9iB5ixAxIoUaIdouDcgBpgO5cY5FdD+fAwuAZ+MdiBBCiG5B8hbRniRvESIGpFAjRNv9L5AC/CregYhuaRrwMTAC8MY5FiGEEF2f5C2iPUneIkQMSKFGiLZJB7KByUBBnGMR3dd8YAnw93gHIoQQokuTvEV0BMlbhGgjKdQI0TZ/BwzAbfEORHRrE4GvgeGAK86xCCGE6LokbxEdQfIWIdpICjVCRK8/kAWMA4riHIvo/t4FNhCZsi6EEEK0luQtoiNJ3iJEG0ihRojo/QvwAH+KdyCiRxgD/EDk6lRNnGMRQgjR9UjeIjqS5C1CtIEUaoSIziBgPTAaOBDnWETP8TqwC3go3oEIIYToUiRvEfEgeYsQUZJCjRDReQkoBv4S70BEjzIMWAWMBCriHIsQQoiuQ/IWEQ+StwgRJSnUCNF6w4GVRJYdrIxzLKLneREoBe6NdyBCCCG6BMlbRDxJ3iJEFKRQI0TrvQHsRKZxiviQ6etCCCFaQ/IWEU+StwgRBSnUCNE6Y4HvkcZoIr6eAXzAHfEORAghRKcmeYvoDCRvEaKVpFAjROu8B6wDHo93IKJH6wdsQZZYFUII0TzJW0RnIHmLEK0khRohWm4S8CWRq1LuOMcixFOAGfhtvAMRQgjRKUneIjoTyVuEaAUp1AjRcp8Ai4F/xDsQIYA+wDZgCrA3zrEIIYTofCRvEZ2J5C1CtIIUaoRomenAfCJXpXxxjkWIQx4D0oCb4h2IEEKITkXyFtEZSd4iRAtJoUaIlvkC+BR4Lt6BCHGEVCAHmAHkxjkWIYQQnYfkLaIzkrxFiBZS4x2AEF3AbGAM8J94ByLET1QQWUnhvngHIoQQotOQvEV0VpK3CNFCMqNGiKNbBPwXSXhE55QE7AKOB7bHORYhhBDxJ3mL6MwkbxGiBWRGjRDNOxkYALwe70CEaEI18H/A/fEORAghRNxJ3iI6O8lbhGgBmVEjRNMUYCmR+7vfjHMsQjTHSeTq1GlAVpxjEUIIER+St4iuQvIWIY5CZtQI0bQzgBTg7XgHIsRRuIAngAfjHYgQQoi4kbxFdBWStwhxFDKjRojGKcBqIh8i78c5FiFawkbk6tT5wLo4xyKEEKJjSd4iuhrJW4RohsyoEaJx5wNm4MN4ByJEC3mBx4CH4h2IEEKIDid5i+hqJG8Rohkyo0aIhlRgA/BX4NM4xyJEa1iAHGAesCLOsQghhOgYkreIrkryFiGaIDNqhGjoEsAPfBbvQIRoJT/wCPBwvAMRQgjRYSRvEV2V5C1CNEFm1AhRnwHYAvwe+CrOsQgRDROwHfgF8EOcYxFCCNG+JG8RXZ3kLUI0QmbUCFHfFUA58HW8AxEiSkEiqyg8TKS5pBBCiO5L8hbR1UneIkQjZEaNEIeZgG3AjcDiOMciRFsYgK3AbUjyLoQQ3ZXkLaK7kLxFiJ+QGTVCHHYNsAdJdkTXFwbuR65OCSFEdyZ5i+guJG8R4iekUCNEhAW4j8iKCUJ0B+8DNuCceAcihBAi5iRvEd2N5C1CHEEKNUJE3EBkyuXyeAciRIxoRJL4h5FzvRBCdDeSt4juRvIWIY4gfwRCRKr39xL5cBCiO/mEyHTii+IdiBBCiJiRvEV0V5K3CHGQFGqEgF8Da4C18Q5EiBjTiSTyDxFp1CeEEKLrk7xFdFeStwhxkKz6JHo6J7ALOB3YHOdYhGgPCrAMeAZ4K86xCCGEaBvJW0R3J3mLEMiMGiFuBX5Akh3RfelEmk0+ABjjG4oQQog2krxFdHeStwiBzKgRPVsSsBM4EdgW51iEaE8KkeVbXwNeiXMsQgghoiN5i+gpJG8RPZ4UakRPdj8wDLgm3oEI0QGOB14HRgGBOMcihBCi9SRvET2J5C2iR5NCjeipUoEcYBaRe72F6Am+AuYDz8c7ECGEEK0ieYvoiSRvET2WFGpET/U/QB/gxngHIkQHmgF8CIwAfHGORQghRMtJ3iJ6IslbRI8lhRrRE/UGtgNTgT1xjkWIjvYp8C3wz3gHIoQQokUkbxE9meQtokeSQo3oiZ4EbMAt8Q5EiDiYDHxBpM+BJ86xCCGEODrJW0RPJnmL6JGkUCN6mr7AVmA8UBjnWISIl/eB1cDf4h2IEEKIZkneIoTkLaIHkkKN6Gn+HxAE/hjvQISIo3FElr0cBtTGORYhhBBNk7xFCMlbRA8khRrRkwwENgBjgNI4xyJEvL1JpOfBI/EORAghRKMkbxHiMMlbRI8ihRrRk/wbKAfujncgQnQCI4DlwEigMs6xCCGEaEjyFiEOk7xF9ChSqBE9xVBgDZGTe3mcYxGis3gZ2A/8Nd6BCCGEqEfyFiEakrxF9BhSqBE9xatAPvBAXKMQonMZDKwDRgFl8Q1FCCHEEV5F8hYhfmowkreIHkIKNaInGA38CAwHquMcixCdzXNEGvPdGe9AhBBCAJK3CNEcyVtEjyCFGtETvA1sBh6LdyBCdEKZwCYiKyoUxzkWIYQQkrcI0RzJW0SPoMY7ACFi6Hwg7SfPTQBOIrK8pRCioX3AG8CfG9l2BWDp2HCEEKLHkLxFiNaTvEX0CDKjRnQni4GHDv7/kI+AZcBTcYlIiK4hA8gGJhJJgA7ZCZx98P9CCCFiS/IWIaIjeYvo9mRGjehODIB2xONjgJlE7mUVQjStGHgRuPcnz2tE/q6EEELEnuQtQkRH8hbR7UmhRnQnBiB8xOOHiNzf7YlPOEJ0KX8DLgOGHPFcGEl4hBCivUjeIkT0JG8R3ZoUakR3onI44TmWyH3eLx6xXQESOjooITopE2A74nEZ8Czw1yOeCyOfE0II0V4kbxGi5SRvET2K/CKL7uTIK1MPH/zPf/BxCvAh8EIc4hKiM5oD5AAnHvHcU8B5wMiDj2UKsRBCtB/JW4RoOclbRI8ihRrRnRy61/tEItMgXz34/GxgA7AXuD4ukQnR+SwGfklkGdgHACNQBTwN3H9wH5lCLIQQ7UfyFiFaTvIW0aNIoUZ0J4euTD0MPEgk+bmHyAoKtwG/5/CVKiEEfEWkeeUc4Dsgk0jCcyowDkl4hBCiPUneIkTrSN4iegxjvAMQIoZUYAbQh8jJ+2siv+PHUH/pPiHEYUXA6cBdwFrgJuBJDn9pkIK+EEK0D8lbhGg9yVtEjyC/yKI7MQC3APOJnLiXACcjyY4QR6MRWWnkYuCfwGAiU+8tyJUpIYRoL5K3CBEdyVtEtyczakR3kkhkdYSrgHnAD/ENR4guZzkwBXiJyPTh4UjCI4QQ7UXyFiHaRvIW0W3JjBrRnaQAO4mcsCXZESI6lcAlwOOAA0iPbzhCCNFtSd4iRNtJ3iK6JUXX9XjHIESsjCKybJ/8UgsRGyOA3USmGAshhIgtyVuEiC3JW0S3IYUaIYQQQgghhBBCiE6iNT1qFGACcAKQGtY1S/uEJIToDhSUsKooNUSmdX8NeJvZfTiRpRV7abpu64j4hBBdkwIhRVGqgC3A90Cwmd3rzi26ptvk0pQQoimK0qpzyxjgJCBN18LWDghPCNFVKUpYUdQqYDvwLRBoyWEtKdQY/XroLyE9fGNQDyWv8O9SDmguS0APSn8bIUSTVFQSVWtgnCnTN8zUxxzQQ185VeudRKZ5AyhhXbslhPY7BTILQhWaS/NZQ4Tl3CKEaJKKglUxBTIMyb4E1apq6PPNivFOoPjgLooW1m8JB/kdCpmlu4Oat1qzhoO6KoUaIURTVFXBbFMCaYOMPnuSqmoa800W5chzi6qHg3fo4dAt6FqvQMFmNHelVQ8FJG8RQjRJUVQUqzNgSh/uMyT1NepaaIFqtt0J7Gn2uKPc+mT0aP53d4dKz3ym5lv7tmBhTIMWQvQMKaqDc2yT9Gucc6qsquk4YEdQDz/l0f03LfPtdJSEq+QGfSFEqzkVC+PMmaGRpr6FJsUwEygJBfSnfC7tpqwvvY7ygpB0/xBCtJotSWXINEto4CRzodGszARK9aDvpXBN6eWuFW/bQyW7kZOLEKK1VHsK1jEnarZxp5YpJstMIL+pfZst1Lg038u7Q6WX317+tj1AqB1CFUL0JGfaJuh/TDqryoj6rFv3/36BZ4PDr8u5RQjRNpPNg4ITzAMK1ZD6krdG+/OyN12OoFe+RAkh2mbEbEtw2Exroar4P9JqSm+qXvg3hx70xTssIUQXZx17ctgx7eIDiskyAnA1tk9zU/USzIrxinsq3pcijRAiJr70ZimrfLstOvxhkTdbijRCiJjYGNhjqtW8KbrOnes+dkuRRggREzuX+U2eKi1FUdSba775lxRphBAx4cteZAiW5TuA85rap7lCzblbA/sDtbqckIQQsZMd3G/360FrpeaOdyhCiG6kKFSVEPBpttoDsiqrECJ2KveHEsI1pQbNXRHvUIQQ3Yh/5/IEze++vqntTRZqajXfJd/5tia0T1hCiJ4qQbGSGyyVxntCiNjSUYqyg61ZzVIIIY7KYAgr/t2r5NwihIipwJ6NKCbrXCKrazfQ5JelMFr/4nB1e8UlhOihUgwOZKaeECLWjJoRd5XMphFCxJbJHCbsKo93GEKIbkYPeEDXABqdHNNkoUYBh08LtldcQogeyq6YCenheIchhOhmjLqBcFB60wghYstg0iHoj3cYQohuSA8Fg4CzsW3N3n6gy7JznYLrlY2UzH2d6seWxXTcit99Rcnc1/F+sSum4wohuoalL3zK49NuYuEDr8R03LduepLHp91E1mfLYzquEKJr+GrDi9z+ykze/vGhmI777Be/4fZXZrJ654KYjivE0cg3os7hP0vzmf3EEh75fEdMx7317U3MfmIJC7OKYzquEG0h91uKLiO0rwb3W1sIrC1Eq/ShJlowTUzHMW8cplFpbRo7XO7F/VYWgRX7CB/woDrNGEf3wn7JGCzH9I3ROxBCdEYVe0tY+eqX5K/KxlNRiy3JQeaUEcy85gwyxgyKasysz5bz+YOvNruPyWbhjz/+v6jGF0J0fgeq97Io63VyCldT663AYUliaMZk5o6/igG9xkQ15uqdC3h36cPN7mM22njs6u+jGl8I0fkVVHh5c9Ve1uRXUeEJkGg1MXlAElfMyGR0RnQtZrcV1fLjrnK2F9eyr9JLlSdIIKyRZDMxOiOBcyakc8KIXjF+J6I5UqjpAtQkK4YBiahptpiOa0h3oA1IRHGaYzpue/CvLaTqL9+DL7Kcs+IwoVV48S/Ox79kD4l3zcZ2+tCoxg7urqTyD1+j1/gPj13tJ7BiH4GV+3D+cgqOKyfE6q0I0WnYkp2kDkrH2SsppuMmZqSSOigdizO256z2kLcym/l3PEvQFwDA4rThKq9h+zdryVm0nrPvv45xZ8+KenzVaMCW5Gh0m8na+c+9QkTDYUmmd9IgEm1tu4jyU8mOdHonDcJmbnSWeKeyY/8qXl10J4FQpCeb1eyk1lvOxrxv2Zy/mHnH/5Vjhp0V9fgG1YjdktjoNrOx8597hYhGkt3EwFQbaY7Yfn6mJ1oYmGrDaen8X41X51dy9/yt+IKRnmxOi4EKd4Dvth/g+5wy7j1rJGeMS2/1uJ9tLuaTTUV1j20mA4qiUOYKsHRXOUt3lTN3ZC8ePG80RoOsCdIRFF1vfDJftebJuqfi/fFZwX0dHJIQ9YXLvZRf8zG6O4h5Wl8S7zgWQ4YTrdJL7b/W4vs2D0wqaf8+F+OQ5FaNrftDlF3zCVqJG+OIVJLumYNxSDKaO4D7tc143ssGBZKfOBXL9H7t9A57lgeTL0JFYXeoNN6hiB7OVVbNiz/7KwG3j8Ezx3DmX64hqW8a7ooaFv39fbK/WIXBZOTaN/9C72Gt+/s/NKNmwNSRXPHvO9rpHYgjnaiOpWaRnf1bpb+eiK8aTzmPf3QpvqCbkf1mcOnse0h19qXWW8Gnq59mfe6XGFQTfzz/dTJSWneR6dCMmmEZU7n5rOfa6R2II826VMW0+zWCBZvjHYro4cpdAX7+0hrcgTDTByfz5zNGkpFkpdId4J+Lc/k6uxSTQeHla6cytFfjF4ma8vmWYmp9ISZnJjEg1Y7dbACgpMbHB+sLeWt1pCbwyzmDuP646GYbi4ZSr3rao1rsI4DCn26Tcpjo9DxvbUF3B1H72El6aC6GjMiVNDXFRuLdszGOTIOghuuVja0f+9MctBI3is1I8qMn1xV6VIeZhJunYZkzAHRwvbg+lm9JCNEJrHztSwJuHwnpKVz0t9+Q1Ddy9d+Rmsg5D1xPxphBhIMhlj7/SZwjFUJ0JYuyXsMXdJPsSOe6kx8n1Rm5hTrBlsrPj7+PzLTRhLUgX254Ic6RCiG6kjdWFeAOhElPsPDohePISLICkOIw85ezRzEq3UkwrPPS0j2tHvvs8RlcPi2TURkJdUUagPREK7fMHcoZY/sA8PmWkti8GXFUnX9+VzeihzU8H23H98UuQvtqUWxGTGN64bhyAuYJfSiZ+zoAvd6+GEPfw9N6Xa9sxP3aZqxnDCPp7tn1xjzyGFRwv74Z/6pCtGofapod6wkDcVw7EbWRKYIVv/uK4KYSEu86DttZw9vxnUdP13R8i/IAsF8wCtVuqrddMajYLxtDzSNL8a/Yh+YONPpem+L7NjK29dQhGHrbG2y3zxuHf2kBoZwKQnurMQ6M7S0iQsSCFtZY9+4isj5dRmVBKSabhX7jhzDrurPInDycx6fdBMCvP32UpH6H7y9e+sKnLHtxAePPPZZzHri+3phHHqOoCsteWkju8i14K104eycx8uSpzP7luY3e3vTWTU9SsD6Hs++/jgnnHdeO7zx6uqax/es1AEy5ZC5mu7XedtWgMv3KU/nsL/9h99Is/C5vl7iVS4hY0rQwS7e9x+qdCzhQU4DFaGNg73GcMvFahqRP4vZXZgJw7yXzSU04POvsqw0v8vXGl5g2/Bx+fvx99cY88hhFUflm08ts37ccl6+KJHsvJgw6idMn34C1kdubnv3iN+wuXs/lc/7KjBHntuM7j56ma2zM+waA40ZfjMVUP7dQVQMnjruC/y65j+yCZfgCrkbfqxDdWVjT+WD9fhZmlVBQ6cVuMjC2bwJXzxrAxMwkZj+xBIAPfjWDvkmHP5//szSfl5fv5azx6fzl7FH1xjzyGEWBV5fvZWVuBVXeIL2cZuaO7M31xw3E0cjtTbe+vYkNBdXcc9ZIzpmQ0Y7vPHqarvPd9shs9Aun9K1XTAEwqArzpmfy4ILtLN9djtsfavS9RmtM3wS+yi6lzBWI2ZiieVKo6SB6SKPq3sUEVu2PPGFQIKwTWLmfwJpCku47oU3jB3dXUPPEcvSaAIrdBJqOVuzC8142gU0lpP7rLBRj15tAFc6vQquM3N9tbuLWI8u0g88HNYJZpVhmZbZobM0TJJRT3uzYprG9URwmdHeQwPoiKdSITiccCvHRH58ld/kWIFJg0MIau5dmkbdiK+c/emObxi/N2cfnD7+Gr9qN2WFF1zSqC8tZ8+Y3FKzP4aqX78Jg7HofJWW5RbjLawAYcuzYRvcZPCvyfDgYYt/GXQybI72qRM8R1kK8/O0dbN+/AgBVMaDpYbbtW8aO/Su5eu4jbRq/sGIn7y57BI+/BovJjq5rVLiK+GHrW+SWbOC357yEQe1655aSqjxqvRUAjOrXeH+rkf0jxaqwFiSvZBNjBsxudD8huqNQWOOu+VtZmVsJRAoMYU1neW4Fq/IrefC80W0af1epi0e/yKHGF8JuNqDpUFTt5+01+9hQUMULV07ukj1W8ss8VLgjt/bOHJzS6D4zDj4fDOts2lfDccNSY/b6WfsjOVO/JOtR9hSx0vU+Abso9xubI0UaVSHh5mnYzhuBYjESLnZR8/Rqav62ok3j1/zvckwjU0m4dTrGoSnogTC+b3Op+fsqQjvK8S7IwX5h20588RDaUx35hwLGQY33n1GTragpVrRKH6H86hYXasJ7quvWWzQObnxsRVUwDEwitK2MUH51q+MXor0t/8/n5C7fgmJQOfn3lzLpouMxWc1UF5XzzRNv88Ujb7Rp/IUPvkrG6IGccvvl9B7en1AgSPYXq/j68bcozt7DpvlLmXrp3Ni8mQ5UlnewYZ6i0GtI44Vae3IC9tQEPBW1lOUVRVWoKcst5KXL7qd6fxmqQSUxI43BM8dwzLxTSO4vqyeIzuubTS+zff8KVMXAedNv49hRF2IyWqlwFTF/5ZO8t+zRNo3/ztKH6Z82igtn/pG+KcMIhQOs2/0lH638GwVl21i542Nmj7kkRu+m45RURWbqKiikJw9pdB+nNRmnNQWXr5LiqryoCjXFlbk8MX8e5bWFGBQDKc4MRvabwZyxl5OWID31ROf16oq9rMytxKDArScN44JJGVhMBoqrffzft7t4/MudbRr/fz7PYWS6k9+fMoyhvR0EQhpfZ5fy1Dc72V7s4tPNxVw8pev9jeSVewBQgMFN9J9JtptIsZuo9ATJL3e3uVDjCYQprPLyyaYivtt+AICfTe16P7uuSgo1HUDzBPG8mw2A8xeTsV9yeElGQ4aT5IfnUvGrhYTaMJVM7WUn+X9PQTk4DU4xG7CdPYLgzgq883fg+2FvzAo1gQ3FVP7h66iONU1KJ/XpM1q8v1buBUBJMKNYDE3up6bZ0Cp9aBXeFo8dPnjCg8jPrymGNBshaNXYQnQEv9vHmjcjU+yP/9X5TPv5KXXbkvqmcdHffs3r1zxKaa2nqSGOKqF3Mpc8/VuM5shth0aziYkXzKFkRwHr31vMju/WxaxQs3ftDt7+9VNRHdvapr3uskjh1Zpox2gxNbmfs1cynorauv1by1vlwlvtxppoJ+DyUpZbSFluIRs/WsJZf72GsWfOjGpcIdqTL+jmhy1vAXDGlJs4Ydy8um2pzr5cd/Lj/OOz6/BW1Eb9Gkn23tx42t8xGiK3KxsNZmaOPJ/9FTks2/Y+m/MXxaxQs6toHc99eXNUx7a2aW+NpwwAmyUBk9HS5H6J9t64fJXUesujisvtr8Ljr8ZmScAXcFNclUtxVS4rdsznstn3MnVYy3MtITqK2x/inTWRprQ3zBnMZdP6123LSLLy6IVjueGNDdSWhqJ+jV4JZp68ZDzmg3cSmI0q507MIKfUxYfrC1m840DMCjXr91bx23eiazI9ZUASz/x8Uov3Lz/4PTHBasTSzF0SvZxmKj3Buv1bq7TWz0XPrWrwvNmocu2sAV2yyNVVSaGmAwTWFKL7QmA2YLu4YbFEMarYLxtLzWPLon4Nx2Vj6oo0R7LMGYh3/g5CeVVRj92ASUVNiW7am5rYdNLSGP3Qctzm5n9VFWtku+5t+Wofh8aOjN90ESiasYXoCPkrtxL0+jFaTBwz7+QG2w1GI9OvOI2FD7wS9WtMv/LUuiLNkUbMncz69xZTtrtBk/qoqSYjjrTGl5s9mqaWwG5K0OsHaLZIA4eX0A54fK0a39k7iTm/Op+RJ08ldWAfDCYjoUCQPau3s/ifH1CeW8TC+18hoU8KA6aObNXYQrS3nP2rCIS8GA0Wjh97WYPtBtXIieOu4O0fH4z6NU4Y9/O6Is2Rxg88kWXb3qe4KjfqsX/KoJpIsEV3Zdlubt056dBy3CZD8/mO2RjJo/zB1hXSk+y9OGPKjUwcdDK9EgdgNJgIhQPsLFzDZ2v/HyVVebz944MkOfowLGNKq8YWor2tzq/EG9QwG1UuPaZ/g+1Gg8q8aZk88vmOqF9j3rTMuiLNkU4YkcaH6wvJLYv+4tVPmQwKqY7m84imJFhb9zXcGwwDNFukAbCaDPX2by1Voe491fpCBMM6BlXh6pkDuFhm03QoKdR0gNDOyL3KpuEpDZrhHmKe2KdNr2Ec3fgUesPBmSJ6rb9N4x/JPL4Pvec3TNyEEB2rZEcBAH1GDmjQDPeQzCkj2vQafccNbvT5hD6R2wV9Ne42jX+kzEnDuPWrJ2M2XjwNmTWOIbPG1XvOaDYxbM4EMicP47WrH6WyoJTvn/mIq1/+c5yiFKJx+8tzAOifOqJBM9xDhqRPbtNrDOzVeG+oJHtvADz+mjaNf6Qh6RN5YN4XMRsvnkb1n8Wo/vV73xgNZsYMmM3g9En849NrKavdx8K1/+K2c1+KU5RCNG5nqQuAEX0cDZrhHjIpM7oLNoeM6ZvQ6PO9nZHiaa0v+tk6PzWhfxISJh2QAAAgAElEQVSf3XJszMbrDHo5LXXvSdN19lV6+e+qAv6zbA8Lsop58pLxrV76W0Sn63VS6oK06kiRRE1r+vaa5ra1hGprvABUN1MkrLdp/Hipm80SaP6kWjfzpomfQ3NjR8ZvuuoczdhCdARvVSThcfZqusm1s3fbGmA3VQA6NMtGC2ttGj9eTLZIwhbyNz9TLuiLTB1u6ucQDYvTzqzrzwKgMCsPT1X0t48I0R7c/sgs3ERb032Ukuxt67HUVAHIdHCWjaZHdzU43g7NlAmGm79AdmjmTVM/h2jYzE5OmXQdAHsPbMHli+FsaiFioMoTyanTmlmhtZezdbPvf6qpAtChWTZhrWt+J7IdnCnjDzWfd/kOzqQ5tH9bqIrCwFQ7d581innT+lNS4+fhBTvQ9K75M+xqpFAjOjW1V2Q5XL02gO5vOmk71MtGTW358rmGI/rSaM1MgwxHMbYQonM7VMDy1XiaLda4yiJfdBzNFMOi0W/8wSajuk71/uh6VAghOp9DM4K8/lqCoaaLNTWeSGPOBFtaTF9/YO/ITD4dnYra2N2aKoSIr17OSHGr1hdqtlhzaPnsNGfTxbBoXHLwVrWcUhc5Ja6Yji0aJ7c+dQA1KVIZ1sqbLgYcKjR0BYEtpVT/9fuojjWN70Pyw3NbvH/dSk86hPZUYRrZMKHRqnx1S3gbB7f8y5RhYFKkdboOofyqRpfe1jWd8N7qVo8tREewJTsBcDXT6DbaJrjxsG/Tbj6+s+VNO4/Uf+IwLvrbb1q8f9qhlZ50nbK8QjJGD2qwj6eqFs/BZqm9hvSNKi4huiKHJfLZW+Mta3KfQ01zu4K8ks28tviuqI4d3Hsi153yeIv3P7TSk45OSVUemb0a9iZ0+apw+SJLE2c0sTKUEN1Rsj3y1bPc3XSj2+a2dTZZ+6u55+PsqI4d3y+Rxy4ad/QdDxp8qJ0FkF/mZlRGw1u8qjxBKj2Ri0+D02J7e1LvIwo/+6t8jG7k9UVsSaGmAxhHRBrYBXdVonmCjfapCWSVdHRY0QtqdYWR1tJqWtcrxzAoqW7p7cDaokYLNf51B5fZNamYJrS8149qN2EclUZoezmBtUVYT2j4RS24rQzdHTnhmafKFzXRuaSPGgBAaU4BAY+v0dtzCja0bZnLjqQFQ7jLo+tL4a1uXa+cXkMycKQl4i6vIX/ltkYLNfkrtwFgMBnJnDw8qriaUrglr+7fSf1ie0VdiLbqnxZpcL2/Yif+oKfR23NySzZ2dFhRC2tBar0VUR3rCbTunNQneTAJtlRqvRXkFK5utFCTUxhZUcWgmhiS3vJVX1pi74Gtdf9OTZC8RXQuI/pELjDtLHXjCYQbvU1p076uc4EpGNapcEe32Ehre+UMTrOT6jBR4Q6yZk9Vo4WaNfmRArDJoLS5189PFVYf/u4Xi9uqxNFJoaYDmKf3Q7Ea0X0hvB/vwHHF+Hrb9ZCG5/1tcYqu9cxTMkj//poOeS1FVbCePATPh9vwfLID+0Wj6vWK0TUdz/uRSrbl2EzUZu55bYz1lCG4tpfj+zYPx7UTMfykV5Dn3UjCYxyZ1uiMGyHiafCscZhsFoJeP+vf+55Z151Zb7sWCrP2rW/jFF3rDZw2irvW/rtDXktRVUafPp11b3/Hhg++Z+rlJ2G2Hb4vXte0up/dsOMnYnG2/NZHXddRFKXJ7X6Xl1WvfglEmjXbU+SqlOhcRvafidloIxDysmzbB5w8sf5nflgLsWTrO3GKrvWG9z2Gp65vuNxse1AVlclDTuPH7HdZvv1DZo+5FIvp8PlD07W6n924AXOwmp0tHvto5xZfwMWiza8DMLDXOJzWlCjfhRDtY8bgFGwmFW9Q46MNhVw1c0C97SFN5901++MUXetNHZjMsjtP6JDXUhWFU0b34f11+/loQyE/m9IP2xGFLk3XeXdt5Gc3e1gaDkvLv+aHNR1Vodnzy1urI8uqG1SF8f0lb+kI0qOmA6h2E/ZLxwDg+s8GPB9tQ/dHqqjhEhfV9/9AuEju9WuK/YrxKA4TWombqvu+J3zwvkitykfN/y4jtL0cTCrO6xuuQBEuclEy93VK5r6O94tdDcc+fyRqugPdE6Tq7kWE8iP9KDRPkNrn1+FfshcA542yxKXofCwOK9OuOBWAH5/7mHXvLKprfltTXM7Hdz1PVaH0P2nKrGvPxOywUlNcwfw/PUdNceRn5amsZeEDr1KUnY/BZGTOr85vcGx1YRmPT7uJx6fdRNZny+ttqykq5/XrHmPTx0vrxgQIB0PkLt/Cmzc8TsXeEhRV4cRbL27fNylEFKwmByeMmwfAF+uf58fs9wgebH5b6SrmtcV3U+GS/idNOXnCtVhNDirdxby66C4qXcUAuHyVvPPjQxSUZWNQTZwx5aYGx1bUFnL7KzO5/ZWZrN65oN62SlcRTy/4BatyPq0bEyAUDrJ93wr+38KbOFCzF0VROfuYm9v3TQoRBYfFyGXTMgH494/5vL9uP/6DzW+La3z85eNsiqqjm7XfE1w9cwAOs4GSGj/3fJxNcc3B87InwP98voNtxbWYDAo3zGk4S7io2sfsJ5Yw+4klLMwqrrettNbPDa9vYMHmYkqPWClY03VySlw88Nk2PtscOeaSqf1ItMoCKx1BZtR0EMc1EwluLyOwpojaf66h9l9rUWwmdFcAjCpJ959wuO+LWepnRzKk2Uh68ESq/vI9gTVFlF3+EYrDhO4JRm7UNCgk/uk4jEOSWz22YjGS/D8nUfnHbwjlVFB+3aeRsb0h0HRQwPnLKVim94v9GxMiBmb/8hyKtuaRvzKbb598h0V/fw+T3Yq/1oNqNHDBYzcx/0+Rvi8Gs5zyj+TslcSFj/+a+Xc8S/7KbJ47924sTht+tw90HdWgctZfr6H3sNb//RdtyaPo4O1NRosJk9WM3+1DC0USUpPVzOl3X8mg6Q1vixCiMzht0g3sPZBNTuEqPl71FJ+u/gcWkx1voBaDauTquf/Dq4sifV+Mhtg2rezqEu1pXHPSY7y66E5yClfxyPsXYDU78Qfc6OioioHL59xLRsrQVo+998DWutubjAYLZqMVf9BNWItcADQbrfzs2LsY0W9aTN+TELFy/XED2VZUy+r8Sv7x3W7+3+Jc7CYDtf4QRlXhofPH1PV9MRmanuHRE6U5zTxy4Vjunr+V1fmV/Oz51TgtBtz+cOQrkapw95kjo1o+e0eJi8e+zAEiK2TZTQY8gRCBI1YOPnt8OjfPbf15S0RHsvYOopgMJD92Cp6PtuP7YhehfTVgUDAfl4njygn1bqtRY9yluzuwTOtH2kvn4v5vFoG1RWhVPtQUG6ZJfXDMG49pVPQ9HkzDU0l75Xzcb2URWLGP8AEPSqIF0+g07JeOxXKM3OMtOi+Dycil//gta99ZRNZny6gsKEU1qAw/fiKzfnE2aYMz6va1OGO3DGx3MWTWWK5766+sfOUL8ldvw1NRiyM1gQFTRzLzmjPIGNPwqtTR2FMTOfWOeezbtIvSnAI8VS78Li8mm4WUgX0YNH0MUy45kaS+0ptGdF5Gg4lfnvZ/LM1+j9U7F1BWW4CqGBg74HhOnXgtfZIG1+1ra8XtOz3FqP4z+eP5b/Bd1mvk7F+Ny1eJ05bK0PQpnDThKgb0GtPqMRNsqVw483bySjZRWLkTt68SX8CF2WSjX+IAhvedznGjLybVKXmL6LxMBpW/XTKeD9btZ2FWMfsqvRhUhdnDUrnm2IEMSj2cqyS04vadnmLG4BRevfYY3li1lzX5lVR6gqQ6zEzKTOLKmZlRNfnt5TTz0PljWLenkuyiWsrdAaq9IcwGlcHJFsb3S+ScCelMzJQ2EB1J0ZtYB71a82TdU/H++Kzgvg4OqWfyryui6vZvUNMd9H73Z/EOR4h282DyRago7A6VxjuUHiF/9TbevfnvJPZN4zefPRbvcIRoNyeqY6lZZGf/1ugaO4rWySlcwwtf3UqKsy9/ufTjeIcjRLuZdamKafdrBAs2xzuUHmHtnkp+924WGYkWPvz1zHiHI0S7Sr3qaY9qsY8AGtxPLPfYdBKedyLTWC3T5CqIECJ2Vr/xNQCDZ7b+6q0QQjTl+y1vAjCy34w4RyKE6E4ONa2dPliaYYueTQo1HUQPa1Td9z3+VfvRXIG650N5VVTd9z2BNYVgVLH9TL5MCSFaTgtrzL/zeXKXb8Hv8tQ9f2B3IfPvfJ68FVtRjQamzTs5jlEKIboaTQvz2qI/s33fCryBwwseFFfm8tqiP7Nj/0oMqpHjx1wWxyiFEF1NWNO59+NsVuZW4PIfXqI6t8zNvR9nsyqvEqOqcOkx/eMYpRDxJzf+dRQd/Ev21q0ipDhM6GEdfAdPUKpCwu9mYBoq1WMhRCvoOjmL1pOzaD0AZocVPazVrf6kqAqn3flzeg/PjGeUQoguRkdn857FbN6zGIisBKXpYQIHV39SFJWLZt1B39Th8QxTCNHF6MD3OWV8n1MGgMNsIKzr+IIaAKoCfzx1OMN6t74hrhDdiRRqOopBIeEPMwmsLiSUV4lW6YOwhpruwDwpHfslYzCNlMaSQojWUQwqp//5CvJWbOXArv14KmvRNI3EvmkMmDKCaVecQsbo1jfEFUL0bKpi4GfH3sn2/SsprtyNy1uJpmukOPsyNH0yJ4ydR2YvWbVMCNE6BgXuOG04q/Iq2V3mptIdRNN0MhItTB6QxGXH9GdUFA1xhehupFDTQRRFwX7BKOwXjIp3KEKIbkRRFKZcMpcpl8yNdyhCiG5EURSOG/0zjhstCxwIIWJHURQumtKPi6b0i3coQnRq0qNGCCGEEEIIIYQQopOQQo0QQgghhBBCCCFEJyGFGiGEEEIIIYQQQohOQgo1XVDJ3Ncpmfs64SLX0XcWQogYeXzaTTw+7SaqC8viHYoQogu5/ZWZ3P7KTCpqC+MdihCiG5n9xBJmP7GEompfvEMRIuakmbDoFkJ7qvH/uJfAxmJCeVVo1X4UiwHDgEQsswdgv3A0aoK5xePpYY2K33xBKKccAMe1E3FePznq+Hw/7sW7cCehnAq0ah+K2YChXwLmGf2wXzoWQ6qtyePcb2QRyq9CsRqwTO+H81fHYOjT+JKFuj9M+fWfoAfCpL1+IardFHXMQoij27N2O3nLt1KUnU91UTmeilq0cBhHWhL9Jwxl8sUnMHBadE3k2zK2FtZY9dqXbP50GbUllTjSEhlzxgzm/Oo8jObGzwsHdhfy6pUPM/TYcfzs77dGFbMQInpV7hKe+Gge/pAHgN+c+SzD+x7TYD+Xr5Ks/MXkFK1hf/kOqj0HUBWVZEcGI/pO44Rx8+iVOCCqGELhALuK11NwIJuCsmwKyrZR440U52887R+Mzjy22eN3F2/gy/UvUFCWjUE1MjRjKudMu5mM5KGN7q/rOs98fhOFFTu586J3SXGmRxW3ECJiT7mH73PK2FBQRe4BD9XeIBajysBUO8ePSOPiKf1IsDZfAliRW8H8DYVkF9Xi8odIspmYnJnEvOmZjOkb3Ypct769iQ0F1S3a94bZg/jF7Porlm4sqOLFH/ewrbgWo6oweUASvzlxCEN6NfGdSNe5+a1N7Cx18d8bppGeaI0q7niSQo3o8gJZpVT+9svDTyigOMzoniCh7eWEtpfj/TSHlMdPwTg0pUVjej7aXlekaQtd06l5dCm+b/MOh2c3oftChHZXEtpdiXfhTlKeOBXT6F71jvV+m0vNI0sjDywGdFcQ33f5BLJKSXvxXNSkhicc93+zCBe6SLr/BCnSCNEBVr32FXkrttY9NjusEIKaonJqisrZ9vUajpl3MqfeMa9Dx/76f//Lpvk/AmCyWagprmDVa19yYNc+Ln36tkZf75vH/4tqUDn1T62PVQjRdh+tfLKuSNOcB985B00P1z22GO2EtCCl1fmUVuezaudnXD7nXqYOPaPVMZRU5fPi179r9XEQKdK88NWthLUQRoOZQMhHdsGP5JZs4PfnvkLvpIENjlm98zPySzdzzrRbpUgjRBtt3lfNb97aVPdYAZwWI+5AiG3FtWwrruXjjYU8dckEhvZuvMDx1Dc7+WhDEQCqAg6LkQp3gG+3H2DxjgP84dThUa3YlWA1kupo+rtJIKTh8kfOayPTnfW2bSyo4nfvZhHSdMwGBV9IZ9nuCjbtq+alq6cyoJEL3guzSti8v4abTxzSJYs0IIUa0R2ENDCqWE4YiO30oZgmpqPaTej+EL4f91L7zFq0Ax4q715Er9cvQLE0/2sfLnXjfnkjaroDAmG0yuinU3oX7Kwr0tgvGYPjyvGoKTb0kEZgfRE1T61EK3FT/dCPpL15IYqqAJECj+v59QAk3D4L2zkj0F0Bqh/4gcD6Yjzvb8P5yyn1fwz7anC/vQXzMX2xnjQ46piFEC03ZNZYRpw4mcwpI0jJ7I3RYkLXdSr3lrLilc/ZsmAF695ZRMaYQYw/p/kr0bEauzy/mE0fL8WSYOfSp39L/4nDOLC7kPdve5rcZVvIX5XN4Jlj673WlgUrKFi/k+N/cwFJ/Xr9NBQhRDvbsucHtu5dwsDe49h7YGuz+2p6mKHpU5g58nxG9ptJoj0NTQuz58AWPlr5JIUVOby95EEykofSL3VEq2OxmRPITBvNgF5jGNBrLK8t/nOLjlu49l+EtRCnTrye06f8krAW4v1lj7E+90u+3vgfrjzxwXr7e/zVLFz7L9KTBnPiuJ+3Ok4hRH0hTceoKswd2YszxqUzeUASdrMBfzDMDzvLeXrRbkprA/zpwy28dcM0LCZDvePfX7e/rkhz7bEDuGLGAJwWI9XeIC8tzeejDUX837e7GNrbwaTMpFbF9thF45rd/o/vdvH+ukJS7CZmDU2tt+25H/IJaTrXHjuAX8weTCis8fhXO/k6u5SXl+/h/nNH19u/xhvkuR/yGJxm5/Jp/VsVZ2ciPWpEl2fITCTt9QtIvu8ELLMy62aSKBYjtlOHknz/CQBoJW58i/ccdbzaf65G94ZIuG0GmA1H3b85vu8iRRrz1AwSbp2OmhKp+CpGFcuM/iT9eTYA4cJaQrsr644LF1SjlXkwjk7Dft5IFFVBTbTgvHU6AIH1RQ3jfnoVAAm/n9mmmIUQLTf9ytOYcsmJ9B7WD6Pl4LlHUUgdlM45D1xP5pTIl6QtC1Z02Nh7124HXWfShXPoP3EYAL2H9WPm1ZGr63vWbK+3v6/Ww+J/fkDqwHRmXtP6K/BCiLbxBz3MX/UUFqOd86cffTbLzWc9zy1nP8+04WeTaE8DQFUNDEmfxK/O+CdOawqaHmbJ1rdbHUvf1OE8fMU3/PrMZzhn2i1MHHxSC9+Dl71lW0mwpXHGlBsxqEbMRisXH/snFEVlZ9GaBscsXPsv3P4qLj72TgyqXDsWoq0GpNh465fTePD8MRw3LBX7we8xFpOB08f24eHzxwBQXOPnux0H6h0b0nReXb4XgNPG9Oam44fgPHhxO8lm4vbTRjB1YBKaDs/9kEcshcIa32RH4jl9bB+MBy9cA3gDYbKLakhzmLlh9mCMqoLVZOD204ajKrBuT1WD8Z77IY8qb5DbTxuO0dB1yx1d6qyoB8N4P8nBtzifUH4Vui+EmmhBTbVhmtAH62lDMY/rXe+YwKYSfEv2EMwuQyt1R3qXOM2YRqRiO2cE1rmDGn2t6seW4ftqN45rJ+K4agLut7fi+zaPcIkLNcmCZc5AnNdPQk2wABDcUY77zSyCW0rR3EGMQ5JxXDUB6/ENp3l6v9hFzePLMU1KJ/XpM/B+uRvvJzsI7akGBUyj0rBfPg7LzOgqgJoniPej7fh+3Et4Xw16IIyhjwPzzP445o1rtL+Jrun4vtqN96vdhHIr0d1BFKcZNcWKaUwvrHMHRx1PezP0tje73TwlAzXDiVbsIphTju3MYU3u61tWgH9pAeZjM7HOHkDtP1e3KTatwguAcXhqo9uNo9Lq/q37QoePq/YDYPjJfaDG/gn1ttfFvTifwJoiHFdNwDggsU0xi4bCwRAbPviBbd+soTy3iKDXjzXJgSMticzJwxl31sy6L8SHFKzPYcei9RRm5VJbUomnyoU1wU766IFMvGAOo09t2HcAYOEDr7BlwQpm33gux/7ibFa99hVbv1xFTVE5tmQnI+dOYc6vzsOaGPk7Lt62hxUvf87+zbvxu7z0GtaPY39xNiPnTmkwdtZny/n8wVcZMHUkV/z7DrIWLGfDBz9Qnhcp/PUdO5gZV5/O0OPGR/VzCnh8rHtnETnfb6BiTwnhYIjE9FSGHjeeGVefTmJGw78DXdPYsnAlWxYsp3TXfgIuL5YEO/bUBPqNG8Lo06ZFHU9nkDFmEPs27KT2QMNEor3G9la5AUjuX//zMHlA5LGnqn4j+iX/mo+nopZzH7oBg6lLpQWdXigcZPn2D9mY9y0l1XkEgl7slkQSbGkMSZ/EMcPOYnCfCfWO2V28gaz8Rew5sJUqdwlufxU2cwL900Yxc+T5TBp8SqOv9faPD7F210JOn/xLTpl4HYuz3mB97ldUuopwWJMZP/BEzphyI3ZL5DOioGwb3216lfwDm/EG3PRNGcopE69nwqATG4y9eucC3l36MMMypnLzWc+xZudClu/4kJKqPBQUMnuN4aTxVx21f0lT/EEPP2a/x5a933Ogei8hLUiyvQ+jM49j7virGr0lRtM11u76nLW7FlJUuQtfwI3NnIDTlsLA3uOYPPjUqOPpaF+uf4EqdwnnTb+NJHvvo+4/LKPh+f0QpzWFMZnHsWbXQvaV72h1LKoS3Zcab6AGXddIcWagqocvctnMThyWJNy++uepPQe2sCrnU6YOPbPRPjyiecGwxvwNRXy3/QD55W68QY1Eq5E0h5mJmYmcMTad8f3r54MbC6r4PqeMrYW1lNT4qfYGcVqNjEp3ct7EDE4a1fjv3iOf7+CLLSX84riBXHPsQP67qoCvs0sprvGTbDNx/Ig0bpgziERr5ILC9uJaXluxly2FNbj8YYb2snPtsQM5YUTD2ZoLs4p59IscpgxI4pmfT+LzLcXM31BEfrkHBRidkcAVMzIbzLBoKU8gzPvr9rNkZxkFFV6CYY0+CRZmDU3lihmZjd4So+k6X2wp4YstJew+4MYdCJNgMZJsNzGuXwInj+oddTztrffB76VNmTowmb5JFoqq/ewodnH2EenV9uJaqrxBAC5rYhbKvGmZrN9bTdb+GvZVeslMabzHZmutyK2oe+2zx9c/39f6Q2g6pCdaMBxRwHFajCTZTHXHHbK1sIbPNhdz+tg+TB2YHJP44qXLZGR6SKPyjm8JbiqJPHGwD4lW7Uer9BHaXYlW7a9XqNE8QSp/91XdY8VuQrEY0Kt8BNYURv47bwSJtzf9Qa6HNCpv/4bg5tK62RVaqQfvR9sJbj1A6j/PxL9mP9UPLoGQhmI3QSBMaEc51fd9D/ed0OxtKLXPrMHzwTZQlUjvEneAwPpiAuuLcf76GBzzmp8m9lOhPVVU3vkdWkkkUcegoJgMhPfXRoo33+SS/OjJmCf0qXdcgz4qDhO6J0i42k84v5pwfnWnLdS0hJpoQSt2gaY3uY/uDUZmpVgMJN42Iyava8hwEi6oIbSrotHtoR0H++CYVIyDD08hVJMiJ9pwUW29/cP7I4/VxMMnYs0TpPZfa1EznDiurp/wi7bTQmHeveUfFKzPiTyhKFicNrzVbjwVtRzYuQ9vlateoSbg8fHWTU/WPTY7rBgtJjyVteSt2Ereiq3kX3Q8Z957dZOvGw6Feefmv7Nvw8662RS1JZWse3cR+7N2c+WLd5K3Yiuf3PNvwsEwFoeVkD9IcfYe5v/pec5/9EbGnDatyfG/e+pd1r79HYqqYHbY8Lu87FmznT1rtjP3d5cw8+rTW/VzKssr4v3b/klNUeR3WjWoGMwmKgtKWffuIrZ+sZKf/d+tZE4eXu+4Bfe9TPaXhwuiFqeNgNuHt8pFeW4RZXlFXbZQo+s6hVtyAUiO8e1EzY1tS44U8ar2179aVrUv8tiWdPje76LsfDZ+tITRp01jyKz6t0OJtglrIf799W3sLo7cxqqgYDU78fhrcPkqKarchcdfXa9Q4w96ePaLX9c9tpjsmAwWXL5KduxfyY79K5k18kIunX13M68b5IWvbiW3ZCNGQ+SzospdwtJt77HnQBa3nPUCO/av5I0f/kI4HMRidhAK+yko28Zri+7iqrmPMHnIqU2O/8mqv7Mk+x0URcVqcuALuNhVtJZdRWs5d9pvOWnCVa36OZVU5fHiN3+g0nWoJ4IBo8FMWe0+lm57j3W7v+SGU59kSPqkese9teQBNuQezvGsZie+oBu3v4qSqjxKqvK6RKFmX/kOlm57n4zkYRw/9nKq3aVtHtNuieQTR/axaW82cyKKolLpKkbTwnXFGm/AhdtfjdN6+AuTpoX5cPkTWEx2zpveeM8s0bSQpvOH97LqGrMe6kNS4w1S6Qmy64Cbam+oXqHGEwhzy9ub6x7bzQYsRpUqT5BVeZWsyqvkgkmV3HnGyCZfN6jp/O7dzWzaV4PZGCnoldT6+WB9IVsKa3j2ismszqvgvk+3EQzrOCwGAiGN7cUu7pmfzYPnj+GU0U0XIp/+bjfvrdsf6YtiNuLyh1i3t4p1e6u4Ze4QrpjRugbZ+eUebn8/i+Kagxc/VQWzQWFflY8P1hfyVXYpT1w8jok/uYXnoQXb+Wbb4c9Pp8WAOxCiyhskv9xDXpmn0xZqWiLRaqKo2o+m1/9OVHzEylkDUxu/CD4o7fDza/IrY1ao+XxL5Pv9iD4Ohvep358mwWJEVaCkxk9Y0+uKNS5/iGpvkOQjenKGNZ0nv96F3Wzg1rmNNzDvSrpMocb3XV6kSGM1kvjHWVhPHBQpuoQ1tDIP/uX70D31K2qKqmA5cRDWU4dgnpRe9+VWqw3g+zYX17/X4/1sZ6Snx9zBjb6u9+MdKO61/70AACAASURBVBYjyY+djHlmf9B1/Cv2UfPoMkI7ynG9uhHvpzlYTxuK84YpGNJsaFU+av62Av+yAmqfWYPl+IEoxoZXKEK7KghuKsH+83E4rpyA6jQTLvfgem4dvm/zcL2wDtPYXpgntqy5muYKUHnXIrQSN5a5g3BcPRHj4CQUg0qosBb3yxvxfZtH9X3fR1YEOrgKUmBTSaRIoyo4f3MMtnNGRHq86DpahZfAmiJCuZVHefXOS6vxE8qLxG8c0nRl1fXyRrRSD45fTMbQ19nkfq1hO3dEpCC4vpjaZ9Y02qMGwHnt4dlZAIYBSai9bIS2l+P5LCfSo8YdoPbZtf+fvfMOq+JK//hnbufSi3RUUMResXeNLZoYY4rpdbOpm002v/RN35RN2+ymF42J6THRJMZeYscCCApIkSq9c3ub3x8XLiAXBCSWZD7Pc58HZs6cOdPOzHnP+35fAFRjwlxl9SuScVQa8P3XzNPq70h0nbQNByhMzESpUTHv8euJmz0GhVqJw+5AV1FD9s4UzPrWOkaCTCBu9mgGLxhP1KgBePg6B86mBgNp6xP47e0fOPLjLvqOH8TAi9wbU5K+24FCreSK/9xLzKShiCLk7Erhl6eXU5qWz+4PfyZ59W8Mnj+eaXdfhleQL4aaBja88BlZvx1h2+vfEDdzFDJF2/C9suMFFCZmMv6m+Uy8ZT5qLy26ylq2v7WatPUJ7PjvaiKGRRM5snPaBmadge/vdxpp4i4aw6TbFhIUE45MLqO2qIJd768lbcMB1jzyPrd//xwab+eLvjAxk7QNBxDkMmbefwXDF09B7alBFEX0VXXk7k+jIvtkVy7XeYFZZ6Aqr4wDqzZRnOI0poy+qnPhAz1Rd1MmqCNrdjNg1mgihsVQmVtCwmfOQW2fsc5YbtHhYNPLX6D0UDPrgSt7pH0SzSSd2EROaSIqhYYrJj3K8D6zUCrUOBx26gwVHCvchdmqb7WNIMgY3ncWo2Pm0y90pGvAbTQ3cPjEBn499C77M9cwIHwcI6Lde9bsyViNUq7mtoteZ2DkJBBF0gp38+WuZyisTGdj8sfsO/4Do2PmsWD0XfhoA9GZavh2z4scK9jJ2oQ3GdZnhttQlJNVx8kpTWTmsBuZPfwmPFRe1Bsq+fng/0g8sYF1h96mT/BQYkI6lyXRaNHxcaORZkTf2Vw04hZC/WKQyeRUNZxkfeIHJJ3YyMrtj/LIkm/xUDu9SnNKk0g6sRGZIOeSsfcxbsClaJSeiKJIg7GK4ycTKKnJ7srlOic4RAff730JUXSwdOL/9Vj4z4myJABC/dr3IO5p1EoPegcNJr/iKBuTP2LuyNtxOGz8uP81RNFB/7CxrrJ7Mr7nZPVxLhv/oCt0S6LzbE4rJ6mwDo1SxsNzY5kR1wu1QobdIVKhM7Mnuxq9xdZqG5kAM+OCmDs4mJGRvvh4NE4AmWxsSivnvd9yWXuklPg+/sxqx5jyY1IxaoWcV5cOYUJMAKIIe3OqeG7dcTJKdSzfk8+a5GLmDg7mjqnRBHqpqDFYeGVDFruyq3hraw7TBwS1CmtpIrNMR1JhHdePj+KGCU5dlEqdmXd25LIprZx3d+QyJNyn07ooOrONh753GmlmxQVx08TeRAd5IpcJnKw18tGuPDanV/DE2jS+vG2sKwtScmEtm9MrkAtwz8wYFg0LxVOtQBRFqvQWDuTVcKLi9ILf5yv1Riu5lc73Tswp2ZIEofm6ONqZ2La3WJ5b1TPnoc5oZd8J54T2gqFtx7weKjmDwrw5VtzAJ3vyuXVyH+x2B29uycYhwpgWXjM/JBWTWa7j77P7EejV+Wy/5ysXzKjO2hi35jE3Bo+5zRYyQS5DHuKFdsnANtsIGgV+z7Z14ZV5q9AuGYjgqaT+xT0Y1hxv11Aj6q34/WsmqpGhTbWimdIb27Ja9MuTMXx1DOWoUHwfntRcv58G3yenULH0exxVRqzHKlCNaHvjiXorHgv74/3XZpdPeaAWnyemYK8yYk0qRf/pEVRvdG5m2/D1MRylOjSz++L7z2mt1inCvfF9ciqOejOWA8UY12W5vHWazq0qPgzPK5tnVAVBQB6o7TBUqD0sSaXUPLCpy9sBrpCwnkL/WQpYnd5OmunuQ92sWVUYVmcgj/LB85queTF1hGZ6H+y3j0K3PBnD9+kYvk93ZX3CISLv64fPI5PwWNDay0CQCXjdMZr6F/fQ8Pp+Gt4+CFYHOERkQVq0VzhjTK0najD8kIFqkjNUS6LnafJaGLJwIkMunuBaLpPL8AkNdDsAV2rUXPbKnW2Wa7y1jL5qJipPDeueXkHSdzvaNdSYdUYuf/1ueo9xDroFIHbGSMbdMJfd7/9EwsoN9I6P4+KnbnJto/X3ZtELt/PO/P9DV1nHyZQcoka3nR2z6E0Mv2wKM+673LXMK8iPRc/diq6iloJDx9n94c8se/fBTp2jhM82UVdcxaB547j0X7e3WucX2YtLXrgdY72e3L3HOLJmt8tbpzjVeW77jh/E2GubZ/AFQcAryI9hiybRVQoOHeerO1/v8naAKySsOxQlZ/HF7a+2Wa7y1DDrgavoN6X73m5drTuwbxjDF08hZe1uVt3yMkoPNVajc0YxetIQ+o539h9Jq3dSmpbPzL9fiXdw5zLiSXSe/IqjAIzpdzFj+i1wLZfJ5Ph7hTJlUFvjmEqh4aaZL7VZ7qH2ZsqgK9EoPflq17Psyfi+XUONyaLj1gWv0i90tHOBAEP7TGdmzfVsSPqQ7amf0T90DFdPedK1jZfGn+umPcez31xMvbGSvPJUt+E1Jque8QMWsyj+HtcyH20Q1057hnpDBdmlh9mU9DF3zn+7U+doR+oqqnUljIqZy/XTn2+1LtA7guunP4fRXE/GyX3sz1zr8tZpOrcDwscxrYUIrSAI+GiDGBu7sFP7b0l2yWHe23B3l7cDXCFhXWVP+ncUVqYT338hMR2EM3WFo/m/UViZDsC42EU9UmdnuXjMXXyw8W9sObKCHUe/wOGw4xDtqJVa5o10vhvqDVVsSPyA8IABTB54xVlt3x+FY8X1AMwfEsK8Ic3jC7lMINRHw9LRbTPyaJRyXljc1mvSW6Ng6ehwPNVynl93nB+Sits11OjMdl5eMoRRTQNjAabGBnHtOD0f785nVUIho3v78tiCONc2/loVTy8ayKXv7qdKb+HoyTpGRrWdNNVb7FwyPJS7pke7lgV5qXlqYRyVOjOJBXUs35PPW1cP79Q5+vJAISV1ZuYM6sUzlwxqtS7Cz4NnLhlEg8nG/twafk4pcXnrHCt2eq6P7evP1fGRrm0EQSDIS83FQ0PpKokFtdz3dcrpC7qhKSSsp1ixtwCLXUSrkjMjrrU3bmgLb/3cKoNbo1hL40yVztIjbdqUVo7V7hRBnjs42G2Zv06N5oHvUlm5r4CvDhRiF51GI61K7krjXaWz8NGuPGKDPbm8G1mpzkcuGHUdodGtyVFl7LE61ROdD6U1rRLR7nBbRjmkVwsjTTMtPRo8r2vrli94KFEOdj4ATd4c7vC8vu3HuyAIrjotSaU46s1tyrjDuDEHAO1V7RsaNBc5O0DL4eLm/TWd21oTYgehQV1CKUPmr+nez6fj+MquYD5wEsMPTuFMz1tGIPNrG4sqOkSnZ4tDxPv+cQjKMxMQPhXtdUPxeXQyQqO1XjRYXSFYosmGo87s9rx7zO2H7zPTUQwIAIeI4KlEPbMvAW/PR+bn9DpoeGM/KGT43OcM1bJmVlHz4CbK5n9J+SVfU/fibuzVPffM/BlReTrdOvWVPacx0n+a86VbfDQXRzt9T/jwGJeRpiV9xzV/cEy4eUGb9SoPNeFDnc95RU5xm/VNTLzl4jbLBEFw1Zl/8DjGOn2bMu44us4pZjvu+jntlhk8z3mP5iWkNbe18dwaqhsQHe7PQ1eRKRV4Bvp069fk+dSt/Sqa9ys0CtcpNSqm3X0Zg+ePPc3WPV/3vMevZ+qdi/GNCMJuteEd4s+4G+ay5N93IQgC+up6dr67hqB+4cQvmwVA2sYDLF/2LK9Nupt3Fz7CrvfX4rCdvdCJPxpqpfN+qjdW9lidQ6KmApBfcQyHw/216dNrWLORpgWx4c0hvbOG39RmvVrpQZ9ezm+P0pqcdtswe/jNbZYJguCqM7vkEAZzXfsH0YKD2esAmD7k2nbLjIpxGnYzi5tDJDWN51ZnqsYh9kzfIZcp8fYI6NZPq+q6Nlydvpz1ie/jofLhkrH39cgx1OnL+W6v09A3JGrqWQ/96h8Wz1/n/ZfokBEICCgVagZFTuK+iz9ypeb+6eB/MFsNLJ34MDKZnMr6IlZsfZjHV83k8c9nsnzLQ1TWF53Vdl9oeDZ6T/fUQBlgcj+nZ9OxkoZWXhMtGRru02ykacHYPs2G/hsmtNXm9FDJGRLu9IY7Udm+F8aNE9pOOAqC4KrzcH4t9afokbTH+sZQmmVjI9stM6fRKHAwr/n7rkl8t8ZgbRMa1F2UcoEAT2W3fk2ePj1BQm413yc6vZRvm9wHf21rj5O4EC/8Gj2tvjzQ9hkURZEvEgpd/xssPfN90HStJsQEtGlTE2P6+PHmlcMYHumDIAioFTImxgTw/nUjXWFa/9ueg8Fi56E5schlAkU1Rh778Rhz/rOHi97cwyM/HKOo5sIaE10wHjXq8REYvjqGeU8hNY9vw2N+P2c4k2/HedFFmwPTxhxMO/KdOjYNZqdnQkssdsQGC4KbQbwixn2oTMsBf3vhNE0ZfhwN7jtSWYhnG7HYJlTDgp1+ig4RW3Y1qtFhbss1YS/X42h0xat9dGu75USbo7F8c0epGhMGShm2zGpq/r4Rj0UDUI0ORR7UsUhvR6iGBtPrx6u6vX1PYMurpe6FXeAQUU2MdHmhnIpxTQa2jCrUM/ugju9ZC6zDYKXuuZ1Y9p9ENTESrxuHI+/ji1hvxnygGN3HiejeP4w1swq/p6a12V4zo0+7gtem9dlYj1a4QrVs+bXU3L8R0eZAPaU3Yp0J06YTWDOrCfxgIYK6Zw1QfxZiJg0hYeUGsn47wuoH3mboJZPoPXoAHn4dh8c5bHZSf9nH8a2HKc8sxFRvwG5t7YpsM1sxNejR+rXtB3r1c68JpQ1oLturv/v71TPAOWgw1bs3tPiEBuAX4V4zJXJkfwS5DNHuoDyz0BUm0x71pdU0lDmN0d/d/99WrrMtaTr2prIAfcYNRK5UUJZRwJd/fZ2RS6bSe+xAvHt1X/wtckQ/7t342ukL9jDhQ6Nd+3XY7FTkFLP7g5/Y8urXHFmzmyvfuq/bXivdqVsmlzHp9oVMut29Z8H2/3yPWWdk6Rv3IFPIObpuH+ueXoFnoA+D5oylJD2PvR+vQ1dRx4J/3titdv/ZGRQ5ke2pn3GsYCefbHmIsf0X0i90NJ6ajl337Q4bh7J/5UjeVoqrszCY67E7Wg9ObHYzBktDK92PJsL83XvBemn8T1vG28Opu2C0NLhd7+8ZSqC3+34nJmQEMkGOQ7RzsiqL2PD2NbIAanRl1Bmceiwfb36g3b7DZnf2HXX6Mtey2LB45DIlRVXHeW/9XUyIu4z+YfGdEuJtj+iQ4TyzbH23t+8qPya87jJYtLw23cVsNbBi28PoTDX4e4VxVQuPqbNJ/7B47g1zf+2zig+RdGIT42IvpW/wMBqM1bz96x3ojNUMjpoCgkBawS4KKtN46LIveuS8/BGZEO3PqoRCdmVX8fDqo1w8LJRRUb74eig73M7mEFl/tJTtxyvJLtdTb7Jitbc2RlhsDhpMtla6H030ayd5R8uyMe2MHQIaB+ANJpvb9SE+asL93OudjIjwQS6AXYSsch1j+nR8X5TVmyhvHHs99P1R2ulaXMde3tA8IR7fxx+lXOB4mY57vzrC4hFhjO7td1qR3o4YFuHLz/ecW72s3Eo9z/ycgUOEyf0C3KasVshlXD8+ird3nGB3dhX/3pjJdeOjCPFWc7LWxMe780kraUAhE7A5RNxEsHWZE5V6jpc5Exy4C3tqyZg+fozp4z6s9nB+DZvTK1g0LJShET7U6C3c/eURqvUWJvcPRAB2Z1eRXtLAyltGt2sQOt+4YAw1qpGheN46Ev3KI1j2FmHZ67T0yXv7op4QgcelA1BEtp7RcBis1D68BevRFoKKajmCn8b10DpqnNoSYjsdhyzAfachtLg75YHtGDSaytjcz/Z0ZAgR1AoEbxVinRlHrandck209DRqOqaOaHm8ikgffB4YT/1bB7CmlDuFkwFZqBfqceF4XBKLMvbCiiG2lzRQ89AWxHoLyiG98HtqqtuPQHulAd0nyQhaJd73nNmstzt07xx0GmnGhOH/0qzmFVol2ksHoOjtQ80DmzBvy8M8r1+nBZsd9WYaPkhsFaql+yQZ0WjD9+lmAeu6f+/F9Gs2xnWZaC93b6iS6JjeY+KYcuel7P3oF7J3pZC9y+m+GtA3lH5ThjHy8mkE9G79crEYTHx771ucTGmelVaolWj9vV19h77K6bpsNVrAjV3CK8j9YE4mk7Uo496g0eR10Z43hFdw+4YQpUaFxluLsVaHocb9YK0lusrmmXND9enLW03NhuuA3iHMffRaNv/7K4qSsihKygLANzyQ6IlDGblkKiED287One/IFHJC4qJY+sY9/Pjw+2RuS2TTy1+y9I17Tr/xWai7MDGTY7/uZ+iiiUSNisVus7Hjv6tRqJXcsOJRfMODsJosfH7zS6Ss3U38NbPo1b/9WUkJ9/QLHc38UXewKfkT0gp3kVa4C4Bg374MipzExLglLi+DJsxWAx9uup+88mY3eaVcjYfG3/UOazA6Y/ktNiPuOg8frXsjbMtsPu2VEQSnQd/ucP9N5NOBIUSp0OCh8kZvrkVnOr2uXUMLT6POlLfYmwdTvXx7s3Tiw/y4/zVOlCVzoiwZgACvMOIiJjIh7jIiA9t6JJ4vpBXuJjV/B1FBg5gQt+SM67PazCzf+n8UVqbjpfHnjrlvuTXinUtsdis/7H8VrdqXRfH3ArA99XMajFUsjL+XWcOc4vqbk5ezIekDtqV8xqXjTp+q/M/IqN5+3D6lDyv2FrAnp5o9Oc4+oU+AB5P6BbJ4RBhRp4xfDBY7D36XSurJetcytUKGn1bhGq5U650GYZPVDrQ11AR6uh/ctszEE+Tl3qAhayxja8eLuFc724EztbS3xpndp8Zweo+aKn3zd0ZnyjuP10lUgAcPzYnljS3ZHCmq50iR83yF+aoZHx3A4hFhDAjpGR3Ls0VxrZEHvk2l3mRjaLgPz14yqF3D+LKxEeRVGfgltZS1R5y/llwyPJTscj3ppQ2u1N1nQpM3ja+Hgsn9uifQbLU7eH1zNr4eCu6e4fQoX5VQSJXewt3To7luvNNT69O9+Xy0O59V+wu5b9bZ0+86Ey4YQw2A143D8ZgTjWlbHpbkMqxpFdgL6jAU1GFYnY7Pw5PwmNd84vWfp2A9WoHgq8b77njU48JdXi6Ac8Z49qrGf8720fQsLUNnev28zCUU3Fk8Lo5FNSES87Y8LEmlWFLLcZTqMP6UifHnTLxuG+U2TOt8xF6up+bBzTgqDSj6++P38myEdmYZdB8lIuqteN46EkGrxNFOhy7aHK51MjezDO5w6C0Y1zeGo7XjzaMaGYoiNhBbZhXm3YWdNtToPkxErDPj/c+pCEqnqLb5QDEyfw3qFh442isGYfo1G/O+k5Kh5gyYfPsihiyYQMbmgxQczuRkSg7VeaVU55Vy+KutLPjnTQxd1DxbsvfjdZxMycHDz4tZf7+S6ElDXF4uAA67g1fHN2rY9JBr7blCbNH++7f/xyUU3FmGL55CvynDSd90kIJDGRQlZ1NXXEXy6t9I/mEn0+5azMRb24ZpXSiMuWommdsSyd55BGOt7rSeWL933XabjU0vf4naW8uMvy0FoDQtH31VPXEXjcG3MYOUUqNixGVT2fLa1+TsTpUMNd1kzsjbGN1vAcm5m8kpTSS/PJXyujzK6/LYlfYNV095kvj+zff35uTl5JWn4Kn249Jx9xMXMcHl5QLObDn/t7JRu+mC7zuaB2wvXLvFJRTcWcYPuJTBUZNJOrGZ7NLD5JYdoVpXwr7jP7D/+I/MH30nF424uYdb3TP8sO9VBAQWxd+L1dZ6cs1ib/7fajdjthqQCTKUCvce5Da7lZXbHyO75BAeKm/umPtfgn3de+KeS3Yc/YLyujyunPSYy6ssrXA3giBj8sClrnJTB1/FxqQPSSvaIxlqOuCWSX2YNziYrRkVJBXWcfRkPfnVRvKri/j28Ekemz+glYfCp3vzST1Zj5+HkntnxjAh2h//FoYXu0Nk2mtOY/KF3bO0TvC64W+Tuhw+tGh4KJP6BbAlvYLEglpSTtZRUmdmTXIJa5NL+MvUvtw08cKYRCpvMHP/N6lU6CzEBnvy2hVD8VC172EvCAKPLRjAjLgg1qWWklOhx2p3EOnvwaJhoVw0KJil7ycAnHHGJ7tDZOMxp3PARYOCUcq7p8jy5YEi8quNPDIv1uVVtienGpkAS1po1Vw5JoKPd+ez90S1ZKj5vZCHeeN53TA8rxuGaHdgTSlH9+kRrEfKaHgzoZUxxrwjHwCfv41DMzu6TV2d8Tz5PbF3EKcpmp3hWIBbXZVTkQc0l7GX67tsqHHW4YH2ikForxiEKIrYjleh/+Io5l0F6JYno5oYibJf59xQLUfLqfvnji63AUA5NBi/52d0a1t7lZGaf2zGXqJD3tsX/9fmdHgu7KXO0BD98mT0y5PbLWf44iiGL5zihSE7OhcGYC9qcL0tOsoiJQ/3wpZZhb1U16l6rWkVGNdloZ7RHKrlqDWDyYYs2q+VlVwR4fzwtZd1TmtEon38IoKYcPMCJty8AIfdQVFSFrs//InCxCw2vfJlK2NMxtbDAFz0f8tc2iwt0VfXt1l2NtFVtK8f4QzHcvZNWv/TD5xaGqDqS6u7bKgB8Az0If6a2cRfMxtRFClNy2f/p+vJ3J7ErvfX0m/qcIJjO2coKDqSw5qHuy7qCRAxvB9LXr2rW9u2R0vvpZqiih411HSn7kNfbKHyRDFzHrnWde3qGlOqn5rm2y+qV+P66p5q8p+SQO9wZg+/idnDb8LhsHOiLJmNSR9xoiyJ1fv+3coYcyTPGbq8ZMI/XNosLWkwndtr0ZHejtVmdoVMdSZkxcuj2VO3Rl/aZUMNgLdHINOGLGPakGWIokhhZTrbUlaSWrCDDUkfMDhqMuEBnctel1uWwsrtj3S5DQB9ew3n5tmvdLp8jd45S/3eho494T7e/ADQvlix3WFj1W9Pkl60B7VCy+1z3iQisP30yueK6oZitqasoHevIYwfsNi1vEZfiqfaF7Wy+b2hUXnhqfGjRlfqriqJFoT7eXDDhN7cMME56D1SVMcnu/NJLqrj9c1ZrYwx2487n90HLurHRYPaCrZW63tO76Y7VOra1+M02xw0mJyTpf6dmCwNaFGmrN6Et6br790ATxVXxUdwVXwEoiiSUarjs/0F7Myq4uPdeUzuF9AmjXR7pJ6s4/E1aacv6Iah4T68tKR7SU6qdBb+9nUKxXUm+gR48OZVwzpttJoYE8BENynI64xWV7rzlunfu8OBvBqX99OCIZ3LcHwqJXUmPttfwOAwby4Z3qwpW1ZvwtdD6dIcAqe2k59W6Wr/hcAFIybsDkEuQzUqFL+XZoFChmiyYT1e5Vpvb9RsUcS6d6WyHC45K+1sD0eZHnuJ+8G5JbXMOcgXQNH/9K5g8jBvZP5OY40l4czT2QqCgHJgEL7PTEPWSwsOEWtq2ek3bMLqwFFj6t6vmw+Qo9bkNNIU1iMP98L/jTmdMnL9brR4ujoylDStEzrx8hHtDurfTEDQKNyHap0i7CWaJSHQ3wOZXEbv+DiWvnkfMoUcq9FMaVq+a32TDktInPsZl/yE9LPSzvaoL6mirtj9gKsoOcspri4IBA84fSYxv4ggPAOdL+sTe46ecdsEQSBsSF8Wv/xXvEP8ER0iRcmdT7PrsNrQV9V369dZ8eSu0PI8q7Q9J5TenbrrS6vZ8/E6Qgf1YdTStppYNsspOijmzok2SnQemUxO/7Ax3DbndeQyBRabkaLK5v6gSbMlop2wnazig2elne1RoyuhusG9SHlu+REcoh0BgYjA0xtHAr3DXQaqjKJ9Z9w2QRDo3WswN858EV9tMKLoILfsSKe3tzusNBiru/UzWM6+8d0hOvhq13Ok5u9AKVdz60Wv0jf4/PR8/jHhDWx2K0snPtIm5MJmb2sgsNovnIHU+YJcJjC6tx//XjoEhUzAaHWQ3mICsEmHJbYd48Kh/J5LmNAdSuvNlNS5n0BPKarDLjZmv+yEcSTcz4MAT+c39f4OErp0FkEQGBTmzQuLBxPsrcIhQsrJzj/zVrtItd7arV97mj6no9Zg5f5vUyisMRLup+Gtq4f3iC7LlnSnnIi/VsnYPmcWXtkU9hQdpGVQO5qtp+PNLdlYbQ7+b25sm77F4kZ6xNyOHMn5ygXjUSNa7e1m4xEUMpcejNhCKFjwVCLWmbGdqEXRu7Xeg8NgRb8q9fdrcCfRf5mKzz9aC0yJoojhS+eARzU6rNNZkDTz+2H46hj6b46hmRODvB3RL1EUEXVWl6dJh+dWLnOeX1qf29OhGhXaac+TnsChs1Dz8BbsebXIgrX4vzG3U2LIp0sDXnH1ahxlejxvGo7XLe4FrNpDEeULShlYHU4PGDdhTdbMKmyZTuOicpB7zYCWGNccx5ZVjdddY1pdX5mfGjQKbEX1OPQWZI0zKNYM50BOHtr9bDZ/duxWG3Kl+65SrpQjk8tw2OythILVXh4Ya3VUZJ8ksG/rrHEWg4l9y3/9XdvcGfatWM/8J25otUwURfav3ABAn7EDO50FaeiiSSSs3MCBVZsYcvH4dkVzRVHErDO6vG46OrcyuQyZolEvw9J5uPJFYwAAIABJREFUg0Hv+DgeOfRhp8ufCQ6b3dVGd4gOBwe/2AI4vZNOvRfOdt1bX/8Gm9nC3EevQ2ihdeQb5vRsKE3Pb1W+NC2v1XqJrmGzW1HI3RvgFTJlox6MDVsLoWCN0gu9uZaSmuw24Stmq4EtR1b8nk3uFFtTVnLl5MdaLRNFkW0pnwHQP3wsWnXHgslNxPdfxPbUz9hx9AvG9JuPr6f71KyiKGKy6FxeNx2dW5lMjlzm7Fdsjs73Hf3DxvD6LQmdLn8mdLSf6oZi/vW9U7fmrvnv0j9sTJsyoijy3Z6XSDqxEblMyc2zXqF/OwK+55qjBTtJK9zF5EFXttEN8vcMpaK+gMr6QoJ8nBMD5XX5mK0Ggn37noPWXhhY7Y52w0SUcplTD8YhYm2hB+OlVlBrtHKiUk+fU7Q1DRY7K/cV/K5t7gyf7y/g4XmtPcJEUWRVY6ahMX388DmNYHITFw8NZVVCIV8dKGLe4OB2xYBFUURntrs8TTo6t3KZgKLx3enOCNAeo3v7sefhtpMjvxc6s40Hv0slt9JAiLea/109/IzEkJsobzCzYq/zO+GasZEouhmq1NTGXdnO8U93vWl2ZVWxJ6eapaPD2+gGhfhoKKwxUlRjdIVo5VcZMFjs9GlHf/Z85ILxqKl7cQ91L+/BfOBkKx0Re4mOupf2OD0J1HJntqRG1PHOTEkN7x7Eklzq0lKwZlRS84/NOOrOrcVe8FRi/DmLho8ScTSm2LNXGal/aQ+WxFIQwPOm4Z2uz/PaYcjDvRDrzFTfux7T9jxEc/Pg0V6mw/BzJtV/+QXz7uYOWfdRErVP7cC0q6CVN4u92kj9fw84vX4EUI/pOPPUuUI0Wql9dCu2zGpkgR5OI03o2RP6KpvxGWUzPkO3onXolKBR4DHfGQNp3llA/at7sZc7Z+xFsx3T7gJqn9wOdmfq7aay7WGvMqJbnowi2g/t0tZ6M4Jc5rzfzXZ07x1GtNhx1BjRfZwEgHpC57RvJNryy1PLWffsp5zYdwyzvnm2p664knVPr8BmtqJQK4kc1d+1ru/4wQBse/NbCg4fd/U9Jcfy+PquNzDWdS7M7fdC5anhyI+7+O2dHzHrnJ6Huso61j29gvwDGSAITLljUafrm3DzfPwigjDW6lh16yukbz7USjS4vrSK5B928ul1L5C1o/k5+e2dH52CuDuSWnmz6Kvq2fLq19SdrARBcJ3P842i5Gy+uvN10jcdbBXO5rDZKTqSw3f3/4/cfccAmHjbxa2MIwAFh47zSvwdvBJ/BwWHjvdo3aeSsyeVzO1JjLhsKmFD+rZaFzq4D9oAb04eySH1572IokhJWh5Jq3cC0G/K0K6dGAkAvtr1DF/veo6Mk/sxWZvv7+qGYr7a9Sw2uxmlXE10SPMkwIAIZ6jkTwfeIqc00dV3FFSk8f6Ge9F3Mu3174VG6cn+zDX8evhdjBZnP1ZvqOKrXc+SVXIQAYG5I2/rdH2zh91IoHcEenMt/1v3F5Jzt7TSbKnRlbLv+I+88dONpBb85lr+6+F3WbntUVLzf2uVCrzBWMWP+1+nWleMgMCA8Lahp38E1h54kwNZPyET5Nw4419dTsP9jxXj+ceK8WxM+sjteoO5Hp2p1vVrwmTVt1renuh0E1abibUJb+DtEcCC0Xe2WT8o0qm3tCbhDUxWPWargbUJb7ZaJ9GW59cd51+/Hichtxp9i+/8kjoTL/x6HIvNgVohY0Rks8F0bF+n98P/tp0gqaDW1beklzRw/zcp1JvOrQelp0rO2iOlvL8zF13jMVXpLLzw63EO5dciALdO7rz20vXjowj301BrtPLXL5LZmlGBuYVocGm9ibXJJdyyMpGdWc3eqR/szOOJNWnszKpslQq8Wm/hzS3ZFNeZEIBxfc/PjGRGi53/+/4ox8t0BHqq+O+y4YSeJkNyS3Iq9Czfk8+JSr1L+NlktbMlvZw7VyVTY7AyLMKHq9tJe770/QQm/3snL/x63O36JramV2CxOZALMG+IewN9R5itdt7alk2Ap5I7pvZts74pbOs/W3PQm20YLHb+uy2n1boLgQvGowaLHdP2PEwbckAAwVPlTDXd5BImE/D5x4RWoS6et43CfKgER7mBmr9vApUcQSY4Mx6p5fi9MJPa/9tyjg7IGdKkjA1w6p98dczpAaSzuFS8vP46BtXwzlsZZd4q/P59EbVPbMeeX0fdsztBJiB4qZwGm5ZhMC3dw+wi5p0FmHc6jTeCpxJEEFsYxLxuG4Ui5vzslEw7C1yZvUS9lZr7NrRb9kz0b7qD113x2PLqsKaWY1yXjXFdNoJGgWixu/RrBK0S32emnzZMS/fuQUS9Fe8Hxru8nFrtq/F+N/6ShXFjjjOPoUNE3tcPj4XnX8z6hYLdYiVj8yGO/rwXBAG1lwcOq81liBDkMuY9fn2rFNvT7lpMXkIaDWU1fPXX11GolQgyGVajGYVayeWv38239751rg6JkLjehMRFsX/FehI+24jaU4OpwegSJ53xt6VEjuycrgOAxlvLVW//ndUPvkNVbgk/PfYhglyGxssDq8nSOoSmRdfjsDvI3JZI5rZEwGlAArC0MIhNu2sxvfqfv4bGgkPHXUYWpYcahVqJWWd0ZdwSZAITbppP/LLZ56xum9nKln9/hdbfm+n3ts0wI1comH7v5ax/biW/Pvspm17+wnXNhi+eIgkJdxOr3UJy7hYOZq9DQECj8sLusGJpNETIBDlXTHq0VXaeBaPvJPPkAWr1Zby7/i4UcjUyQYbFZkQpV3PL7H/z4aZzJ7AaERhHRMAAtqasZHvqKtRKT0yWBsTGD5eF8fcSE9J571MPtTd3zH2L5Vseoqwuj893PIFMkKNReWG1mVqFwAgtOg+HaCclfzsp+dsBpwFJRMRsbdb+mz/6znbTkF/I1OhK2ZX2DeAMyfh+38t8v+/ldst3J+X4Gz/dSI2urTzA5zueaPV/ex4/TWw+spxqXQnXTnsGD1XbCbRZw28k8cRG0ov28s8v5gDOa+vjEcSs4WfPK/tCw2JzsDWjgl+PliHg9JaxOhyYGj3f5QI8PC+2Vdrsv0zty8G8WsoazNz7dQoqhQy5AEar06jz0pLBPPjdmYcvd5cBIV7EBnvx+f5CvkwoRKtWoDPZXMLGd8+IbmV4Oh3eGgVvXjmMR344Rl6Vgad+SkcugJdGgcnqaBUC03JIZHOI7MisZEem03jjqZIj4vQ6auIvU/sS0+v89FTfkVnpCssyWGzc9WX7+pvu9G/qjFY+2ZPPJ3vykQlOXRe92eYSaB7T24+XlgxGcYa5udcfc4Y9jY32bzdTWEes2FdASZ2ZpxbGuc0+dcOEKDanl7PvRDUL/ucMrbU7RAI9VVw/4fRh/ecLF4yhxuuO0SiH9cKSWIq9qAF7tRHsDuTh3ihHBKO9YnAboVtFuDeB71+MbvkRLIeKcTRYEHzUqKdE4XndMBTR5z51ofe9Y1H088fwUyb2/DoEDyWKuEA8lw3pdAagligifQj8aBHG9dmYduRjO1GDqLMgqBXI+/mgHByEenIUqrHNKtjaKwchj/DCcrgUW0EdjiojotWOLFiLckgw2iVxXTIYnXVayLuLJlu7qdaBbuvfdBeZVon/f+Zi2nQC07ZcrFk1iA1mBJUceZgXqvgwtEsHndYDyJJYgmlrHpp5Me1eC0W0HwH/mUvD+4explciqBWoJ0biffcYBHX7IRQSHTP9vsuJGNGf/EMZ1BSUo6+sw+Fw4BfZi6hRscRfe1EboVu/yF7cuPJxdr+/ltyENEz1BrS+nsTOGMmEmxfQq194O3s7e8z+x9UED4gi6fsdVOWVotKqCR3Uh/E3ziNmUtc9KPyjgrn5iydJ/WkPGVsOU5F9EnODAYVGRa/eIYQPjSZ2+kiiJzZ/FIy99iL8I3qRfzCdqtxSdFV12C02vEP8iRjej9FXzSRqVOcNRmebkEF9WPjMLeQfzKA0w5k5ydxgQOmhxjc8iKhRsQy/bEqnhZB/r7r3rfiV2pOVLHjqJjQ+7j8uh186GblSwf5P11NTUI53iD/DLpnE5Ns771kl0ZqFY+4hOng42SWHqagvpMFYiUN0EOgdSUzoSKYNXtZG6DbQO4L7L1nBxqQPOH4yAaOlAQ+1D0N7T2f28JsI9Y85R0fTzOLxDxAWEMu+jB8oq8tFpfQgKnAQM4fd0GXPDoAgnygeXPw5B7J+5kjuVkpqcjBaGlAq1IT59KdPr6EM7T2NuIgJrm2mDbmGQO9IskoOUl6bR72xEpvdip9nCH2DhzF54BXEhI7qycM+b2iZLcvusLnStZ9vlNXmsePol/QLHc2YfgvclvH2COTeiz/kp4P/JafEKcLfP2wMl477e6cEqf+s3DU9mmERPiQW1FJYY6RKb8HhEInw0zAyyperxkS0EbqN8PPgoxtG8vHufA7k1dBgsuGrVTI11o8bJkQRE3TuDQ/3z+5H/2BP1iSXkFdlwEMlZ2CoF9eNi2JCN7wgIv09WHHTaNallrLteAUnKgw0mG2oFTL69/JkSLg3U/oHMT66+V5bFh9BhJ+Gw/m15FUZqNJbsNodhHirGRrhw+WjwhkZ1XmD0dnG0SIboNHqwNiBbIU7/Zu+gVpumBBFYkEtxbUmdGYb/loVcSFezBsS7FaIuqsUVhtdaeK7E/aUX2Xg64NFjIryZV472wd4qnjv2pH8b3sOiQVOr8sxMX7cNzOmR7R6zhaC2E56xzqHIfXx6u+GplqLznKT/vgY12dT/8pelCNCTquRIiHxR+NZvyXIEMixlZ/rpvzpSP15L78++ylRowdw7YcPnevmSEj0KNNlg6nfpuXkMUkEuac5kPUL3+x+vt3sQxISf2QmXClDmbMSa2HKuW7KH451qaW8uD6TUVG+vH3NiHPdHAmJs07A9W8ZZGptLNBGqf+C0aiRkJCQkJCQkJCQkJCQkJCQ+KMjGWokJCQkJCQkJCQkJCQkJCQkzhMkQ42EhISEhISEhISEhISEhITEeYJkqJGQkJCQkJCQkJCQkJCQkJA4T7hgsj79kfBY0B+PBf3PdTMkJCT+ZAy7ZBLDLpl0rpshISFxgTEudhHjYqUMYBISEj3LwmGhLBwWeq6bISFxXiJ51EhISEhISEhISEhISEhISEicJ0iGGgkJCQkJCQkJCQkJCQkJCYnzBMlQIyEhISEhISEhISEhISEhIXGeIBlqJCQkJCQkJCQkJCQkJCQkJM4TLkgx4er7N2I9UobPI5MkUd5TsCSVUvPAplbLlCNCCHhr3jlqkcQfmYb/HcSwOr3Vsgv5ufzyjtcoTMzk4qdvlkR3T6Hg0HG+uvP1VsuiRg/g2g8fOkctkvgjs+La5yjPLGq17M6fXsQ3POgctejMeHf9XeSUJnL1lH9KorynkF1ymPc23N1qWb/Q0dy94L1z1CKJPzKvr72e4uqsVsueuOJHArzDz1GLzox7vzpCUmEdjy8YIInynkJiQS33fZ3SatmoKF/evmbEOWqRxB+ZR384xq7sqlbL/rdsOKN7+3W7zgvSUCPRCWQCMl+1808fdbvFHHoLhq+OYdpZgL1Mh6CWo+wfgMelcWhm9DmjJohWO4bv0zFtycV+sgHkAoo+vmgW9MdjUSyCIJxR/e5w1JqwJJdiPV6FNaMKW2YVot4KQPDG6xDU8jPeh73KiP7LVCz7irBXGJB5qVAMDEJ7xSDUY8LOuP6OMB8qxrA6A2t6JaLegryXFtXESDyvG4Y8wOOM6rZmVKL/Jg1rShmOejMyfw2q+HA8rx2KItLH7TaCpxKZvwYAR4MFbI4zaoPE+Y8gE9D6ewPg4evZbjmzzkjCZxs5vi2R+pIqFBoVIQOiGLl0OgMvGtOtfTeU15C24QAlx3KpPFGCoboes86I2suDoH7hxM0aw4jLp6JQKbtVf2coScvjwOebKErKwlivR+vvTfSEIUy4eT7+UcFnXv+xPJJW/0bB4ePoK+tQqJV4hwQQObI/Iy6bSkhcVA8cRWtEh4Mja3aT+vNeqnJLEB0O/CKDGTx/HPHXzEau7N6nQnlWESeP5FCSlkdpWh6VuSWIdgcD58Sz+KU7OtzWw88Lz0Bnv6Ovqu/W/iUuLARBhpfG+UGrVbl/5wCYLDq2p64iJX87NboSlAo14QEDmDTwckb0nd2tfZssOo4W7CSzOIGCynRqdaWIgK82iJiQkUwZfDWRgXHdqruzFFams+PoKk6UJmOw1OOl8WdA+HhmD7+RIJ/uPfc6Uy05JYcprEynsDKNoqoMTFY9AC/fsBOlov3vw57iSO5W9masprgmC6vNjL9XGMP7zGTm8BvQKNt/h7THgaxf+Gb3850qG+AVxhNXrmm1zFPth7dHAAANxuou71/iwkMmgJ/W+V3grWn/faY32/jiQCE7jldSWm9GrZARG+zFklFhzIzrdUZtOJxfy4/JxRwrrqfGYEUuEwj10TCmjx9XjYkg0v/MvuE7Ir2kga8OFpFcWEeDyYq/VsXYvv7cMCHqjPdbWG1kVUIBB/NqqTZY8NEoGRnly7XjIhkY6t1DR+CebRkV/JhcTHa5HrPNQaiPmhlxQVw3LgpPdfe+WwqrjRwpqiOjtIH00gZyKvRY7SKDw7z56IZRHW7rrVEQ4Om8z2oNVhxit5rQCslQ8wdF1ktLr2+WdljGXq6n5v6N2Et0AAgeCkS9FUtiqfO3eAA+D0zo1v4degs1D2zGltloWdQowGLHmlaJNa0S894i/J6fgaDo2eg74+YT6N451KN1tsSaU0PNA5sQ682A01DhqDNj2VeEZX8RXrePwvO6Yb/LvnWfp6D/JNn5j0xA8FBgL9ZhXJ2BaWseAW/MQRHj3626jRtyqH91L9hFEEDQKnGUGzD9mo15Wx5+L85ENbqtEcrr1pF43ToSaPZ0k/hj4x0SwF0/v9RhmfqyGr6841XqTlYCoNKqseiM5B/MIP9gBgVXTGfuo9d1ed+FSVns+O9q1/9ylQKFRoWxTk9hYhaFiVkkrf6Nq9/5O97B3XsWOiL1l71seP4zHHYHCAJqTw0NZTWkrN1N+qaDLH3jHvqMHdjt+nf87wcOfL4RsfHtrvbywGq0UJFVREVWEV6Bvj1uqLHbbPzwj3c5secoAHKlAkEmUJ5ZSHlmIce3HGbZ+w+i0mq6XPe6p5e38YrpLMvefdD19yvxHRt1JP4Y+HmG8OQpg+pTqdWX8c6vd1KtKwZArdBisujJLjlEdskhJg1cytKJD3d532/+dBOVDc33qkqhAVGkquEkVQ0nOZyzgYXx9zBjaNf7rc5wMGsd3+75Fw7RjoCAWuVJrb6MA1k/kZy7mVtnv0ZseHyX603MWc/aA//5HVrcOb7b8yL7M9cCIBPkKOVqyuvy2JKygqTcTdxz8Qf4ars2AFbK1S5DS3s0GWAi3BjX7pz/tuvvf6wY36V9S1yYBHurWX1nx9e6vMHMPV8eobjOBICHUo7eYudwQS2HC2pZMrKWh+bGdmv/7/2Wy6qEQtf/HkoZVrtIXpWBvCoDP6eU8q/Fg5jUL7Bb9XfEr0dLeXlDFnaHiAB4quWUNZj5JbWUrRnlvHL5EMb06d730oG8Gh778Rgmq3OS1kstp1pvYWtGBTsyK3liwQDmDQnpwaNp5pUNmfyUUgqAXCagksvIrzaycl8hm9MrePeaEfTy7roh+p0dJ9p4xXSWJy5u7m+Wvp9AaeNY8UyQDDV/UkRRpO7p37CX6JCFeuH75BRUQ4MRzXYMP6aj+zAJ49pMFLEBaBcN6HL99a/tw5ZZheCjwvfRKagmRoBDxLQ5l/o39mPZV4T+0yN43d6xdbKrCIKArJcW5cAglHGBIIDuo6QeqVs026h9fBtivRlFbAC+j09BEe2HQ29BvzIFw7dp6D5OQjEgEPXYnnWhNe8vchlptFcNxvPmEci0Smy5tdT9axe27Bpqn9xO4KeLEVRd8xqy5tRQ/9o+sItoLorG+96xyPw02Et11L+2D8uhEmqf+o2gVZch8+v6YE3iz4Uoiqx55H3qTlbiGx7IoudvJ3JEP2xmK4e/2cZvb/9A0ve/ERzXm5FLpnapbp/QQCb/ZRFRYwYQHBvl8ugx64ykbz7E9je/pSq3hHVPr2DZew+eprauUZ5VxIYXPsdhdzB4wXhmP3gVWn9v6kqq2PDCZ+QlpPPjw+9zxw/PuzyOusJv7/xIwsoNKNRKJv/lEoZdOgnPAB9Eh4OG8hpydh91eZj0JLveXcuJPUdRqJXMfew6hiyYgCATyNmdyrpnVlCSlsfGF1dxyQu3d7lumUJO8IAoQgf3IWxwXzK3J5G771iPH4PEnwNRFFm5/TGqdcUEeIVx7bTniA4ZjtVmZnf6t6w7/C57M1YTETCACXGXdaluu2gnIiCO8QMuZVDUZAK8wnCIDkprclib8CbZpYf5+eB/CfHty6CoyT16XMXVWXy390Ucop3RMfNZPP7veGn8qdaV8N2eF8ksPsDK7Y/y6NLv8NJ0dUAl4KsNpnfQYCKDBiEI8OvhsxNStjdjNfsz1yIIMhaOuYepg69CIVeRW5bCFzufoqrhJJ9tf5z7Fn7UpXpHxcxhVMycdtcXVR3nzZ9uBGBsfynMUOL0iKLIE2vSKK4zEear5ulFAxkW4YvZ5uD7wyd5f2cuPyaXMCDEi0tHdM1zPiG32mWkmTOoF3+dFk2YrwaHKJJW3MCrm7LIrtDz3C/H+f7OcXh10xPEHdnlOl5pNNLMHRzM32bF4K9VUVpn4uWNmRzMq+WJNel89Zd4/LWqLtVdpbPw5Jo0TFYHY/v68ei8AYT6aqjRW/jv9hNsSivnpQ2ZxIZ4ERPUdc+5jvgxqZifUkqRCXDX9GiuGB2BSiEj9WQdz/ycQXGtiad+Sue960Z2uW6ZTKBvoJaBoV4MDPUmo7SBDcfKe7T9XWrPOduzxDnFvLsQa3olyAT8np+BaqjTZV9Qy/FcNhTt5c5ZYf3yI4hWe5fqtmZVYd6eD4DPI5NRT4pEEAQEuQyP+f3wvmO0s+7v0nDUGHvwqMBjSRy9vrsCv+dn4Hn9MJSDz8xVsSWGnzJxlOkRPBT4vTgLRbTTRVvmqcL77njUU6JABN1HiT22zyaajE3qqb3xvjseWaMLpyLaD78XZzV71/yS2eW69cuTweZAEReIz2OTXcYYeagXvs/NQBasRdRZ0H95tMeOR+KPS9ZvyZQczUWQCSx59W4iR/QDQKFWMv7GeYy5ehYAu99fi91q61LdkSP6MeWvl9InfmCrsCu1lwcjl0xl1oNXA5B/MIP60p51ad/9/locNjuhg/uw8JlbXMYY37BAlrx6F94h/pgbDOz/dEOX6y4+eoKElRtAEFjy2t1MuHk+ngFOo4wgk+ETGsioK6YzYGbPGrZ1lXUc+norANPvu5xhiyYhk8sQBIH+U4dz8T9vAiBt40HKs7ruGXPDise45ct/suDJGxl5+bTfxdAk8efhaMFOCiqOIQgybp71b6JDhgOgVKiZOewGpg66CoANSR9is1u7VPe1U5/mwcWfMXnQFQR4OQdiMkFGeEAst895gxDfvgBsP7qq5w6okQ1JH2J32IgKGsQ1U59yGWMCvMK4edYr+HmGYLQ0sC3lsy7XPWXQlTx19c/cPPsVLhpxM316/T4ev6dis1vYmOQ0wEwdfDUzh12PQu4cCEaHDOfmWa8gIJBXnsKxgl09uu9D2esA8NL4MzByYo/WLfHHZFd2FWklDcgEePGyIQyL8AVArZBx3fgorhgdAcDHu/Ox2rsW4r8pzTnIj/L34J8LBxLm6/zGlgkCQyN8eGnJYAAazDYSC2p76pBc7bU5RAaGevHkxXEuY0yor4YXLxtCiLeaBrONVfsLT1NTWz5PKERvsRPirebFy4YQ2nhc/p4qnrw4jrgQL6x2kY935/foMVlsDj7Z46zzyjERXDsuClVjdMawCF9eWjIEAUg5Wc/ubnjGPH/pIL64LZ5/LhzIlWMiCPc9txPU3Tbb2cv1VF69GkQIXH5JuyEXotlOxeXfIuqt+L4wA82U3s7lFjvmvYWY9xZhy6nBXmFANFqRBXigGhaM9srBTo+ILmBcn039K3s7FM/VrUhGvzIFzbx++D7mflbEvLcQ47osrGmVOBosCF4qlIOC0C6JQz0uokttOl8xbckFQDUmFGVsWxdS7dVDMKxOx1FtxJJYinp854+7qW55lA+ayW3d9D0uiUW3IhlRb8W0swDt4p6L+xbkv5/tsem4NBdFI++lbbNeu2wI5t2F2DKrsRXUoejt2yP7teXWYsupce3jVOTBnmhmR2P8JQvT5ly0lw/qdN2OBgvmhJPOuq8a3Ob8ybRKtJfGofs4CdPWXLzuGvO7aAu1pL6shvcWPQqiyK1fP02v/u7vPZvZytvzHsKsM3L5a3cTO8NpObdZrGTvPEL2zhTKs4rQlddgMZrxDPAhcmR/xl43h9BBXdNfSv15L78++2mH4rm7P/iJPR/9wtBFE1n4zC1uy2TvPMKRNbspOZaLsU6PxltL2NBoRl81k5iJba/thUja+gQA+owb5DZMZ9wNczn09Tb0VfXkH8wgZtLQHtt32JC+rr91lbX4hHbsHt9ZTA0GchpDg8ZeOwfZKc+JSqth1NLp7Hx3DekbDzDz71d06TnZ/+kGRIfIwDnxZ/U+yNyWiN1iazR0TWuzPnbGSAJ6h1BdUEbahgMEx0Z2qf5Tz9O5plZfxgvfLkZE5KHLviTMv5/bclabmWe+uRiTRccts/7N0D7TAefg81jBLo4V7qK4Oos6QwUWmxFvTQB9Q0Ywfcg1RAV1vv+FZr2NjsRzNyZ9xKbkj4nvv5Brpj7ltsyxgl0kZK6loPIYBnM9HipvevcawuRBVzIwonshzOcbiSecRtDYsLFEBLb19J0x9Dp2pX1Dg7GK7JJDXRqkx4S2bwRVKjSMiJ7DpuSPKKrK6HrDO8A654cNAAAgAElEQVRobiCjaC8A04Zcg0zW2iNWrdQyMe5y1ie+R9KJTVwy9m9d6ltOre9skVl8AJ2pBgGBGUOubbM+MjCO2PCxZBYfIPHEBob07pp3ZXvYHTaSTjgTaozuNx+57OwEDpQ3mLn8vQRE4PNbxhDTy70Hgdnm4NJ39qEz23l5yWCmxjrF0S02B7uzq9iTU0V2uZ4KnRmjxY6/p4rhET4sG9t1vY91qaW8uD6zQ/HcT3bnsXxvAQuGhvDkxe6/xXdnV/FzSilpJfXUG214aRQMCfNm6ehwxkf3zDv2XNNkTInv48+AEK82668dF8l3h09SpbdwOL+WCTGdP+4ag9No3K+XJ3JZ22c33M8DH42CepMNo6VrE+Md0WCyse+Ec8JqWXxkm31rVXIWjwzjw115bE6v4N6ZMZ3uWxyiyNYM5zm7bFQY2lM8+eUygWVjI3n2lwz25lShN9u6rRlzKofya6gxWBGAa8a2/SYZEOJFfF8/DubVsimtnCn9u2ZLcHeNziXd/oqSB3uiHO6MOzNuzW23nDmhCFFvRfBWtRrsWw6VUPfMTkybTmA7UQOiCIKAo0yPaUsu1Xf/inFTTneb1y1Em4O6F3ZR+/h2zHuKcNSYENRyxFoTln1F1D68lYYPDp/VNv1eWJKccX2qse4HwfJeWhR9/VqV7XzdZY11uw//EdQK173T1brPFQ6D1aW3095xKQf3QmgUkbIklvTYvpvOkeCpRDnIfcaTpjZZMypxGDo/k2hNLXcJAKvj3btzNtXtqDJiz6/rdN3dxSfEn6hRzqxRaRsPtFsuZ08qZp0RjY+WmMnNg/28hHTWPvohx37dT0X2SURRRBAE6kurSdtwgM9vfomj6/b97sfRErvNxs///ITVD75D9s4j6KvqUaiVGGoayNmVwnf3vdVKe+VCpuDQcQCiJ7g3OHgH+xMU47zX8g/27KDn5JHmd4ZvWM9lBypKzsZhc35ARU8Y7LZMdKOBRVdZR1Vu559/s85Izi5nVorB88adYUu7Rn7jtYoaFYtC7V6AuW/j8Rb08LU6F/h5hhAd4jToJp3Y2G659KK9mCw6PFQ+DIxszv6WWXyAz3Y8zuGc9ZTW5CCKIvw/e+cdHkd19eF3thf1LtmWJblIci9yo7kbm24MoSSEVCBAQgJ8IZACIYQEAiSUUJKA6TYQwBTj3nuVbVmSLavZqqu+kra374/RrrTWrqyV1pZF9n0ePY925s6de6ffc8/5HQSaDbXklq7jpa9/zMHib853N7xwOO18sO1x3tr0MPkVO2gzNSGXKmk3N1NQsZN/r3+Arw+8cu6KBgHFNeL3lz/DU6Q2gcSoDABO1QRXq06rFCdeXK7gCuaX1R3F4RQ9CzNTfPcrc4iordFqakCn9/+9fTHhPldJ0SOI1PoWWc/sOI/ussGgsHI37WZxYmvayKuCVu+5SAhXMnGoeI2sL/QfJrGntIl2i4NwlcxrsH+gvJnff1nI2vw6SuoNogipIKBrtbChsJ673j/C2vwLqwFodzj549cneOSzfHYWN9JksKGUSWgx2thV0sSDnxzn1a2lF7RN5wu3J8uMdN9OB/HhStLjxAnaQwF6vSRFiB4ZJfUGHD7UZatbTLSaxWeALyNRXzlWqcfesb/pfvrl7m+jwUp5o7HXdZc3GGnqSNQyI8133dM7ltscLo5WBi8hwOEz4jgkI17rV4NmRpp4bwV6ri5G+mXeUs1Px3ZUh2VzOeE/neKzjHlTuVj2ilQEeafFTVDLUC/LQjV7OPLRsQgdKtwOXTvGTwox/reQ1uf2opiYiDSIF25PtL9+CPPGMqRDwgn76WSUM4YgqOU4jTbMG0ppf+MwxhX5yEbGoJ6ffkHadD5wNps8YriyNP9eH9K0SNGbo7z3F7rL5cLRcRO5DT2+kKVFYt1Tib38/A/8g4HjtB46nq/++iVIBKSpkdgLG4LaL/tp8fjLhkci+LH0es6jCxxn9EiyejdIddctiVEj8ePe1/UasZfrezyvwWLMldOpOHyKwvUHmH3fUp9lCjuMOKPnTfHKSqNQK5l66zwy508lKTsVuUp8kLfWNnLgg40cXLGJdU+/T+rU0UQkBV+4zRdbX/yUgjX7iB6WwBX33UDGpeNRqJVYDGYK1uxl68ufse/ddSSMHsaYxRd2sB5MDE2tmPRiRpG4Ef51muIyUmgoqQ7IoOEPh81OW10LRVty2fm6KFqZuWBqUMNsGktF4VJtbATqKN/vo9j0TkNnQ2kNcRm906mqKSgXxYmBxKxhlOzKY/9766ktPI3L6SJ6WDyj500h57YFKLXBdcF1H/+ez5XYr8byGo/RczAzJWMRpbpccks3cNXUe32WyS0TZ+QnpM1FJu00YClkai7P/g4T0uYxNC5bFJwFmttr2Z6/gu0FK/lk918ZkTSF6LALkyb36wMvc7h0LXHhQ7lq6r1kDb0EpVyN2WbgcMlavj74CluOv0dK7CimZPj2NB4MtJmaMFrE92pidIbfcolR6dS2lKBrCa5Bo0QnhjQnRfn2wuortR3tDFfHolX5/h5Liur83tS1lJEU5b//Fwvu458Y5f9b2b2u3dxMu7nFk/GrP7jDnlJiRpESE7i+Yn9YOCaeI5V6NhXWc88Vvvu9scOIM2d0HPIuHodqhZSbp6YwZ3Q8WUlhqDrGS7WtZj46UMXHh6p4Zt0pJg2L9Az8zzf/3FrG+oI6hkapuPuKdGZlxKBWSDFY7KwvqOPVbWV8sL+SUQlhLBzT/4yHA0WzwYreJBpK3MYYX6TFailtMFLe0HuDBsC1E5L48mgNFc0m/rT6hE+NGoDrJiSRHkQtF7fhJVarIFLteyImPVbjVb63+y/rqFsA0vxsE6WRE62R02y0Ud5o4JIRwfG+KmsUvzG7tv1s0jrOY4vRRovR5sn4NRjpn6FmznDaXtqPo6Yda349irHeeiBOow3LXjGuXbXA+8WimJyEYnL3DxlpYhjh908TjSPfFGNaU0LYD85/vnt7ZSvGTwsRolRE/30R0oTOC0+ikaO5PhNJmAL9n3ZgeC8vIEONOySrL/QUotVXHI2dujCSHh5K0o6bwNnUex0Zl8GGq8MyLI3zn/Kts+7AHngDhaOLpbnnY6bGTmDH7Fw4O85XT/uVdHlgBbLvzrr9nytBKUMIU+Bqt16w85W5IIcNf1uJvqqBqmMlDJng/XFsMZgp2ZkH0M2wkZqTSWpOdxfeiKRY5j90CxaDmbwvd3Hsy91cdte1568THTSd0XFw5WY00eHc+tqDXuE4Sq2KyTfNQRmu4avf/oc9b30TkKHGHZLVF3oK0eorhoZOA2V4vH8jcFicuK69oe8GzTdu+C0tlfXeCwWBzAVTueoPd/a5Xl+42xkW738gIVcpUIZrsLQZvY7DuWg+0zn7enz1Xna8JhqblGFqHA47dUWV1BVVUrB2P7e+9iDhPbQhUDz9ivNfp3ud1WjBarQE3Vh0oZmYPp/P9z1PU3s15XV5pCV4a3aYbQYKK3YBolGnKyOTpzIyuXtq+eiwJK6f8SvMNgP7T33F/lNfc+XkwMWXA6Vef4YdBR8RpormnsWvEh3WmV1DJddySdYy1Ipw3t/2ezYdfTsgQ00gKZDPpqcQrb7SZmrw/B+p9j8REamJ61a+v1Q2nOD46W0ATBsVXHHaNqPYTne7fSGXqVArwjFZ22g19i0byYWm1SS2s6eMTl373GZs6LehxmDWU9Bx704beXW/6uoL8zLj+fvGEqr1Zo5XtTJuiPdkgcFiZ3eJGIqyMNvbsDElNYopqd37nxSh4oH5IzBa7Xydp+ObPB0/ujSw0O2+UNFk4pNDVURp5Lx06wQSuxiHtEoZSyenEK6S8fhXJ3hn75mADDXukKy+0FOIVl9pMFg9/8eF+c8SFBcm6rs0dinfG7KTw3l0yWie21DMhsJ6NhTWo5ZLsDtd2BwuUiJV3D8ng1v9RDj0lYZ2q1e7faGUSwlXymiz2D3le0NjR9lwlQxlD9l748IUNBttnvLBoLEX/eq6rtFgHdSGmn4FkEsilJ6wCLOP8CfLzjNgcSCJ0yCfGFh6LuUsMe7MdvzCKC2b15WAC1Rzh3sZabzaNHs4yCU4ylu8Bu7nQlBKkUSr+vQnhAX/4nIbUoAeMwS5vZxcpt4Lfnatm56yD6mkAdc9kAR+zAITMuzNvnuzXwBnH87XuTJFCRf4fKkjtZ5QksJ1B7qtP7U1F7vFRlhCFKlTAps1G3mFKEBZdbS4/w3tBcdX7wWXqD/iTzMla/5UpAoZDaXVtDf03oNNppSjjY3o058yzL9xrq9YTZ0vY5nS/0tUrhLX2Yx9T12oiQ5HGxuBQtP5YZW1YCqz71vap1TSPWEzi/3yFx7kxt0vq6n3/bK0d75Ldr7xJUMmjuDHn/yRX259kV9tf4lr/vRj5GolTeW1rP7DW31ovX9sHe2Uqfz3S6bqPI82kzmo+x8INMpIT8iFW8uiK8dPb8PmsBCpiScjybensD/GDBN1Nsrrjva/ob3gYMk3uHAxMX2Bl5GmKxPS5iGTKqhtKaXV2HvjhTsFcl/+1PLgZvgAsNg6rz25zP9gSt7h5WSxBWeyxGwz8MH2x3G6HAyNFbNCBROrXWynTNpzGll3v6z2wTG55e6XvId+yaWdz2mLvf/nK7d0PQ6nDYkgZfIAeI9FqOWeUJINPsKfdhQ3YrE7iQ9TMDlADcNLO3Q2jlVdGC/0Nfk6XMD8rHgvI01X5mTGo5AKlDUYaWjv/TtPKZMQo5X36S9MGXzNJXOXhCk9GR1UcnGdsQ86MlePT+KvS8d4DAYmmxObQ3TTN9sdtJptnt/Bwt2vnvoEoOzolymAxDGmXtbt9gwLpO5z4U4F7m63z/3KOq+TYOr+DAT9VvZRLUjHuqcSy5ZyXPfleImResRX56X5DNlwtlowrjqJdV8V9go9rnYbnBW/52gIblYgf9jyxZlZ87pSLFt7UKjuuJGcdUaPV8i5UM1LRzVv8IZKhQgxEIy5cjolO45xYuNB5j34HS9hUrd2TfbCaQiS7g9rk97A4U+2ULr7OE2ndVjaTbjOUupvr78wHzzVx0TdlOOr93Byk/9YfLcGSmttc48eDl3JXjSN7EXT+t/IQcgdy3/j+d/Q2MqxL3ayZ/kaircf5eo//pCsBTkD2Lre4+ryzlNoVCx74X5PRiupTMbYJTOwtBnZ8OwKTh84QfXxMlLGhd4n/WFyxiIKKnZytHwj10//pZfgqtt4Myl9IRKh+7PFaNGzq/C/FFbuob71NGarAafL+0MwEINIfyivE70KDxav5lj5Jr/l3BooLQYdET14bnTlXCmQ/xcQ9X/+QJ2+HLUinO/NfuqCidOGCJyDJWLYU9bQSwhXD4zI7cLsBHaVNLH5ZD2/mDfCS5h0Q4dg7fyseCQ+QkhbTTY+za1mb2kzZ5qMGCx2zh67B+L10B+OV4maImuO69hyst5vObcGSl2bpUdvlK4syE5gQfbgDZUKFLvDyd/WF/N1Xi3jUiJ46rpsRiaEYbY5OFqp559bS3l3bwVHK/W8dMsEZBeZCH+IgaX/hppLh9GmkuFsNmPNrUWZ0yE82mLGekiMf1f5CBOyl7fQ/Kv1OJs7Z0kEjRyhw1rqsjtxtVm9PTTOI+5wIJfRhqsXYqwXql3ng67eF64eLI0ebwt17y+TrnXTkxXT7Ai47oHk7GMm+LEidx6z4HlCebx0enGuACR9OF891S3Wf+HP16g5E5GrlZ7sQG4RV2NLG6f3FQLdw54AGkqrWfmzFzA0doqXKbQqZEo5giDgsNkxtxqxmfvuzREI7vASq8GM1XBujwS7+cJ8iJ0PFOpO7wu7xX8/3B4qck3vPuzOhTY2glk/uor4kUP49MF/8s0TbzNkwgjCE3yL3AWK21PGbun53eDul0Ld+351PQZjl8zwSjvuZuKNl7P15c+wmSycPnAiaIYauVqJpc2I3ey/X12vR7l6cIc9uRmXOhuFTE2bqYlTNQc9Yq3t5haKqkUj8OSzwp4AaltKeX3tfbSZOlO/K+Ua5FIlgiBgd9gxWVs93gTnG3fYjMVmxGI7t6eF1T54PaKU8s5rz2b3/+y2dfRRKe+fx6DT5WTljj9RULEThUzFjxY8R3xkar/q9IVCJrbT7uj5feTul0LWuwnCgcbdL1sP/bI5Oq9Hpax/56u2pZSKBvG7YCDCntxcPioWtVxCk8HGoTMtHkHVFqONAx2agL7ChMoaDPzio2MegVYQs/IoZRIEQRRkbTPbvbw/zifu8B6j1dErDxK3l8NgRNVFP9Vi998Pdx/PznB0Lj7YX8nXebWkxWp45bYJHm2icJWMBdkJjE4M4863D3O0spWvjtWydHLv9O3OhbtfPfUJwNLRL7W89/1S97Ju9/UaSN3nwu3ZZOnhmjPbO69ZdYDn62Kj36MuQSVDedkwzBvLMG8s8xhqzNtOg8OFdFiEzzTb+md242w2IxsdQ9hPJiMfl4CkSwyZ5VANLQ9tELNBXQg6rMJh9+Wgvdl3Vo9vC9IuWifOBiP4Sa3uDu+SxPT+BSpo5QgqGS6zvUdvqM66B8dHx9nHTOLHbdVt8AvkmJ0LtzaNswcBM2dXDZ0A9u3WpnH2cK5cFjuujlmcC3m+5Colo2ZPpGDtfgrW7fcYak5uPITT4SRmeKLPNNvf/PFtDI2tJGalcsV9Sxk6cYRXKEz5/kI+uvfvF+zR4nKKL5N5D36HabcvuDA7HSC6ari01euJH+k7nXOnNkpwUti7GXnFRCKSY2mtaaRw/QGmf6/7YLsvuPvVXu8/LM1mtmJpE+9DbQD96uo9FTPctwCtVCYjakgc9cVVtOmafJbpC2HxkVjajD2G27nXKTTKQa9P40YhUzE29QpyS9eRW7rOY6g5Vr4Jp8tBfORwn2m2P9rxFG2mJobGZrJk6r2kJ0xAKe98JhZVH+CNdfdzgR4tODv2dP30X3LF2Nsu0F4HhoguWid6UwPJjPRZTt9hvArvQcfmXLhcLj7d/QyHS9cilcj5wbxnyOjIFhZs3B5O+h68sGx2MyZrW0f5CyOA318iNXFUNxWhN/r3xuja5/Beenr54+ApMduaRhnBmGGX9auu/qCSS7lsZKyoRVJQ5zHUbDlZj8PpIjVG7TPN9tNrimgy2MhMDOPuK9IYPyTSyyBw8HQzD3yUdwGHROKOfjEvg1tyfL/Hvy101TNpaLcwwk9qdbc3U6zWf1i3Lz4+VAXAjZNTvASk3aTGaLgkI4atRQ3sKG4MmqHG3a+evLAsNgdtFrtX+UDqbjPbsdidfkOgPMcsgLrPvW8lp+oMPfar67pAz9fFRlCmx1Xz0zFvLMOy4wyuB2ciKKQezRpf3jQOXTv2wgaQCET9eR7S+O6DP2dzH2ak3DdAT54HBt8zh5IYNY6KVpx1hsD3ew7Mm8toe7m7zkZvUM5LI+Lnwc0CI4lSIUQqcekt2Mv1KKf7FrBylJ87e9PZCIKAdHgk9pONPWaLsnvqDu5A7XwhTY0U5c1dojeYzIehxuXsmvEqeP2SDRfrsp/W43K6fIYRerJMCZ3le1e3eG6dTSacerPPzE9dM1hd6PM1ZvF0Ctbu59SWXOyPfheZQk5Bh2ZNto9Uxq21jdTklyNIJSx74T6fHhXGpsDTBLrDruxW/54HlnbfzyxtbARNp3W01gZvgO2mcP0BNj3/UZ+2zVqYw4KHbw1qezTR4aijwjC1tNNQUk3GLN8puhs6sih1zZQULMLjo2itaewuNNwP3JmPDI2tmFrafWZ+6prByl2+N8SPDPCjLIhZl+LSk2ksraGhpNpvmYZSsV+xacE/VwPJlIxF5JauI+/MNm5yWJFJFZ6wp8np3Q18ze21nGnIRyJI+dH853ymHG43BX6PSzvCrnryPDBb230uD1fFUK8/TbMh+Gl7c0s38MX+F/q07aS0Bdww86GgtidMFY1WGYXB0oKuudRviu7eZBs6F1/se4G9RauQCFLumPOUR9PofOBuZ5upEYNZ7zPzU22XDFb96deFJDEqncLK3T1m33KvC1NF90tI2Ol0cKh0LSDeu10ztQ0Ei8YksKGwnu2nGvg/+ygUMolHs+ZsEWEQMzsV1LQhFeCZG8f6TDnc5Gfs0hOyjm/Fnrwe2i2+x0sxGgVnmkzoWoPvebyxsI4XN5f0adv5WfH8cr5vI21fidYoiFLLaTHZKGswMiPdd9hceUe2obQeEnucjd4kZh0CSPaTWRUgJUpcV6MPntejO4NVo8GK3mTzmfmprMskb1ov5Tyg8xi4gPIGA5k+jI8tRhvNHX1Piw2ebllarIY9pU1ebT8bd2auKI18UAsJQz/FhN0opqUgRChxGcQsT446A7Y88aGkWuDDUFPf4U0RpfJppAE8YVOBIOmw2Lnr94XthO9ZC/kY0Zpv2e//g7WvuCwOnM3mPv252oMnStsVd8Yt60Hf/XXUGz2GFsWUwNKMdtbt+xy6LA5sx3QddQ+Oj3+JRo6swzPMX79shQ0eQ2Aw++U+ni6DDbuf69d9HuXZcQGFXcnHJ0CHJdzfPeeuWxKnRhqAESgYpM0cgzpSi6XdRMnOPFprm6g8IooA+wp7atWJ16wmKsxv2Et5R9hUICjDxedUW12z3zI1BeU+l6eMFzNWle3JD3i/58JusWFobO3Tnz/DUn9xZ9wq31/gc31bXbNn8D98enevhf6irxGzjcgDCD86F0MnjUTSIU5Xvt/39VO2V+xvWHxUQAaomOFJhCeK12rT6VqfZRx2Oy1VHdlhkoM3o56akwVAxZFiv2Fd5fvEfg2fnhW0/V4MZA6ZiUYZidnaTkHFLprbdZTpRBHgs7M9AbQYxG8arSrKp5EGoKhmf8DtUCvED1y9wX/ihDMNvu+l4R0Zq05W7gl4v+fC5rDQZmrq05/JFvwJL8CTccsdnnY2ekMdupZSAEal9E276+uD/2RH4ccIgoTbLn+c8cPn9Kme3pKeOMmje+OvX0XV+wDRqygxcnAYakYmieeqJxHrk1Viv0Ym909PrKh6P60dnjvBzsrVF6anRROpltFucbC7tAldq5ljleIEkS9DTX2baAyJ0ih8GmlA9KgJlDClzKt+X5yobfO53J2xal9Z4Ps9Fxa7kyaDrU9//gxL/WVKx+TrgXLf/a1vs1DWMfjPGR7I5HXn/7pW/0aYWr14jgINq+qJCUMjPcY6f/3a37E8LkwRmKEmVkOMVhxruEP6zsa9T7lUYOLQCJ9l+oI7O1pZg8GviLW7Xzk+MqkNNoLiUSPIJKjmDMf0ZRHmTeU4qtvABbLMWGQ+To6kww3J2WzC2WxCEu0dqmErbfYIEQeCLKPDO6DBiO1kY7eQK+sxHbbjvmdZ1VeOwLgyH8dpPcYvi9Bc5z+TjLPNgsTPw9Rn3UtGol4SXAtwf1HNT8ey9TTWgzXYipuQj/S2IBs/KQAXSGLVPtOo91x3mngsz+ix7K5EeYm326RpdZFo0FBKUV0+rN99uVCo5qfTfqIR88YytHdO6CYmbfxIHIjLRsf69LjpK7K0KGQjorGXNGNYmU/Uk3O81jsajJg3lYttXJARUN2SMAXKGUOw7KrA8Ekhyjnewt8ukw3jl2IaRdW8dIQgzub3BqlMRuaCHI58uo3CdftFLwmXi6Qxw4lJ7Z7lxJ3JyNDUhqGpFW2M9/OnvrjSI0QcCPEjRa+z9roWagtPdwu5qsg9RdVR3zNE466eyb5319FYVsORT7cxadlsv/sxtxpQRfR+5mH8tZcw/tpLel3+QjBm8XRObjxE+d4C6ooqSBjtfY8f+GAjuFyExUUy3Eca9Z5w2h0eg4kv8tfs84QnDZs8KvDG+0EZpmHEpeM4te0oBz7YQNaCqV4i1laThSOfiul7s6+cFtB9IggCY6+ayd7la8hfs4/L7rm+m07N0c92eDI0ZVwyLgg9Ehk9dzKb//4xljYjR1ftYOot87zWF28/StNpHQiCTw+2wYxUImNi2nz2nPyM3LL1NLZV4sLFsLhsn1okaoXoRdXeYYw4W6y0pqnYZxapc5EULRpy9cZ6KhoKu4VcldbmUl53zOe2OSOXsDXvPXT6cvac+IxZWTf63Y/R0opG2fuP5emjrmH6RTDo7crkjCs5Wr6Jk9X7qG4qIiXG+zttW/4KXLiIUMd5DAWBsOHIm2zJexcBgZsveZQpI85/5iC1IoysoZeQf2Y72/NXMDF9vpeItcVmYs+JzwGYnL7wgr+D+8qolGmEqaJpNzez9fgHXDf9Aa/11U1FnKoRvWOnjljcr30dKBZFhBOj0n2GLF5oZFIJczPjWXWkho2FdVQ1m3ABWUlhDPMRmq7tMKg0Gaw0G6xEnxWqUVJv8AgRB4I7hKe+3cqJ2rZuIVdHKvQcq/LtYbx4bAIf7KugvNHIqiPV3DDJv+dnq9lGRA+ZA8/m6vFJXD0+sHHF+WbhmAQ2n2xgf3kzp+raGZXg7TW78kAlLsQwGl9p1P0RoZKTGKFE12phdZ6O6yYmewlMgyjEvK9M9MYckxw8g0aYUsasjBh2FDfy0cEq5p0lYm2yOlh1RJw0W5idENCzRSIIzM9K4JNDVXyWW82yySleWjBOl4uPDoohX5eOiPVc48EgZ3gU0Ro5zUYbKw9Ucf9c73HPqbp2j2FzUQBp4y9WgiYt7facseypxLSmxGvZ2UiHRyKJ14ALWv64HXuHpdlld2LefpqWhzb0SYxVmhSGLFv0jGn96y5spc2d9W4tp+V3WxDCfceqydKi0HRo07T9Yx9t/zqMo0sYlNNow3KgGv1TO9A/vi3gtl1sKC8bhjw7Dpwu9L/firUj65XL6sDwUT7G/4qzxtofTkTwIQJVf8un6Oa8i/4vu7qtk4+KRTlXHMjq/7oLy95KsW6HE9O6EtreOCzWffOYbkY6AP1fdqGb8y71t3wacL9cThfOFnPnn6EzTtHZavFadzaOmnZ0c4X+Sc0AACAASURBVN5FN+ddTGu6p27WXDcaSaIWl9FGy6ObPR5HTqONttcPYdl+BoCwn0722baejtm5cNdp2X6GttcP4exwJ7SXt9Dy2GZcRhvSlDDU13QfnJrWFHv65ajp7kKv/eFEkEmwFzbQ+tddnmPj0LXT8oetOHUGhDAF2tuDN0AMBLfnTMnOPPK+2i0u8zNojEvv8E5wufjy0X/RXCF+3Djsdk5uPsxH9/0jIKFXN5HJsSSPTQNg9RPLqS+u9NR7YuNBPnv4VVQRvmcj4jJSPNo065/5kG2vfEarrnN2w2IwU7Y3n69+/yarfvNGwG272Bg1exLJ49JxOV189n+vUZUnznDbrTb2v7+egys2AnDp3dchlXd/eb927aM8k3MXq59Y3m3dB3f9jb1vr6GhtBpnlyxerbWN7PzXV6x58h0AkrKHM+Ky8d22//Cu53gm5y4+vOu5gPt12d3XIZFJqckvZ/UTb2NsafPs+/P/e43W2iaU4Rpm3tl90HHm4EmeybmLZ3Lu4szBk93Wz/j+lWhiwrG0m/jsoX/S0BFG5bDbKVi7j22vfAaI4Wpuo6EbfXWDp273/dFbwuIiybl1PgBbX/qU46v3eI5ryc48vvnj2wCMuXIaCaO66xSsfmI5z+TcxWvXPuqzfpvZgrGlzfPnsIqx8E67w2u51TgwIrduz5mCil0cOPU1gN+0vglRaURqEnDh4r2tv6WhtQIQMwMdK9/CG+t/7hFQDYSYsGRS48QQwZU7/kRNU7Gn3qNlm1i++deoFb4/3pOiMjzaNJ/u/RurD/6Tli5hUGabgZNVe/lg2+O8u+WxgNt2sTEu9QpS48ficjlZvukRTndkvbI7rGw9/gHbC1YCcOXkn/oMf3nqkxt4aPkMVux4stu67fkrWJv7LwBumPlQwGm4X13zMx5aPoNX1/ws0G6xePJPkUpknGnIZ+WOJ2k3i98Wze21vL35EZoNtagV4cyb8P1u2xbXHOKh5TN4aPkMimu6ZxV0upy0m1s8f13D6IwWvdc6X7jrXpf774D6JJMquHLyTwHYXrCSrcc/wO4Qv8fK6/JYvukRXC4naQkTfGrKrMv9t2ffPWGytnP8zHYAcgZQRPhs3J4zu0qa+Oa4zmvZ2aTFakgIV+ACfv9lIZUd0g92h5OtRQ388uNjfRJETYpUMSZZNM78+ZuTlNQbPPVuPlHPo5/nE67yPYBOj9NyS474rnl+QzGvbSujrotnjsFiZ19ZE3/8+gS//yJwL+WLjctHxjImORynCx77vIDj1eK41Gp3smJ/pUdn5ieXDfepM7Ps9X1c+ux2nvqm+/v9hkmih21hbRuPrSrgdKMRl8uF3eHk8JkWHvwkD4PVgVQicOPk7t649684yqXPbuf+FUcD7tePLxuOTCJQUNPGn7856QnDqm0189iqAnStFsKVMr47o/v7/fCZFi59djuXPrudw2e6Px/umDEMrUKKrtXCY6sKqO3wGGo2WvnzNycprG1DLhX48WXdtSQBT91v7iwPqE8KmYQfXyrW+dHBSlbsr8TaEd53vKqVxz4vwOmCCUMiPGntu/LmznLPvn1htTtpMdo8f+aOuh1Ol9fydsuFSSoUNBOXfHwCkkQtTp0Bx2k9SARU89J8lhUkAuG/mI7+8W3Yjuho/N4qBI0cl80BNieSRC3hP55M69M7A25HxM+n0fSr9djLWmj60VcIahkuuxNsThTTUpBnxmJ4P8/ntmF3T8FlsWP6ogjjh8cxfngcocO1y2W04VYIlE/qPpM/2BAEgcg/zqb5gXU4atppvm+NeKysDk8KcvV1o9Fc49+zqCciHp5Fc1U79qJGWn6zGVQycIjnAUAxayjaH0wMWn/cOHUGGm77zOe6hpv/6/U7cWv3j56eEJQyov48l+YHN2AvaqLxB18iaOW4THZRjFqAsJ9MRjktOEJgXVHOHIr2R5MwvHUE48p8jB8XiOerI9RKiFQS9dRchD68zOUjY4h4eBatf9uNeX0p5g2l4v3orlslI+rJ2UiiBkZIdOikkUQkxdBa20RjWQ2CRCD7St9u7YJEwoKHb2XVI69z5lAR/1r6OxRaFQ6rHYfNTkRSDHMfuImv//BWwO1Y8H+3suLu52koqeatW59EoVHisDlw2OykzxpLUvZw9rz1jc9t5/xiGXaLldz/bmPv22vZ+/ZaFFoVgiBgMZg9oumpU/t2v11MCILADc/cw4d3/Q19VQPv//CvKDRK7BabxwgwadlsJi29POC62+v1bHvlc7a98jkSmRSlVoXdavd4mwAkj0njxhfu85m2vT8kjB7G4t/dwdo/vUv+N3vJX7MPpVblCSGTq5UsffYeNNHdY7XPhSpcw7IX7ueTX7xI5ZFi3rz5cZThGuwWq8e4MXTSSBb/9o6g9gng8nuvp76kitJdx1n9+HLW/vk9JBKJJ4NV8pg0Fj36vT7Vve+ddez699fdlhdtyaVoS67n97hrZnH1Ez/sWwf6QXriJKK1STQbatHpyxEECZPTfaeklggSls58iHe2PEpJ7WH+8ulNKOUa7A4bDqeNaG0S1067hw+3PxFwO26Y+SCvrbmX2pYSnvviuyhlGuxOsd7MITMZFpvNxmPdDZcA1+Tcj81hYfeJT9mc9y6b895FJdeCIGCxGnB1fLiMSJoScLsuNgRB4M65f+Gf39xDU3s1L63+CUqZBpvD4kmRPivzRmZm3hBw3V/uf7FjHxI2Hn2LjUf9vyMeuOZtosOC9x2YEjOamy95jI93/ZlDJWs4XLIWpULrMaooZGrunPtXwlSBZ7Fraa/lz/9d6nPdkx9f6/X7+R/uC7zxPXBJ1jKqGk+yt+gLvjrwEt8cehWZRIHFLoaQxIYP4ftzn+7XPo6WbcTusCARpOSMWBKMZgeFiUMjPJ4U5Y1GJAIsyI73WVYiCPxy/kh+90UBuRV6bvn3ATQKKTaHE5vDRWKEkvvnpPHk6u5GgHPxy/kj+PnKY5Q2GPn+8kOo5VLsTrHeGenRZCWF8c6eCp/b3jsnA4vdyedHanh/XwXv76tAq5AiCGCwODyi6ZOHDQ6tyZ4QBIE/3zCG+z48SrXezN3vH0Etl2J1OHF0JJu5YVIy100MXNbg9unDKNK1s+VkAzuLG9lZ3IhSJsHudHnqlkkEHlk8ivS44Gm5AIxKCOORxaP469pTrM2vY11+HVql1BNCppZL+PMN2URrAhfcjQ1T8NQNY3j083z2lzez7PX9hCmlnmtDKhF4dPFoMoLcJ4Clk1Mo0rXz5bFaXtlayuvby5BLJZg6skylRKl48rq+eddtKKzj6TVF3Zaf1LVz9SudYcaTh0Xyym3BH8eeTdAMNYIgGmaMK8TwD8WkxG6hIV1RXZ6K5IWFGN7Pw1bQgMvuRJqoRXnpMLTfHY+9pG9xkfIx8cS8vJj2t49iO1aHy+pANjQC1ZUj0NycjeFd3y7EAIJUQsSvZqJakIHpyyKsx3Q4mzqy+CRokY+MRpGT4tcANdiQJmiJ+c81GFfkY95+BkdtO4JGjmxkDJrrR6Oak9bnuiVaBTH/XIzxk0LMm8pwVLWBQopsVAyqJSNRXzPKr5uds0l8icuz+pcF4HwgHxlD7PLrMHyYh3VPJY56I0KEEnlWLJqbx6Cc6vsh7rI7cXXEoMqz+qYxEfb9CcjHxGH8b6Goh9PhRaOYNRTtd8cj7UemKfXiEcjSIjF8lI/taJ0Y3pegQZGTgvb2cT5DGC8UgiCQvWga+95dB0Dq1EyvTDlnM3ruZG597UH2vPUN1cfLcNodRCTHMGr2JGb+YAn1pyr71I6UcRl8981fs+uNr6g4UozDaiM6NYFx11zCtNsXsPs/3QekbiRSCYt+813GLJ7BkU+3UXGkGEOjKNIckRRDwqihpM8cQ/aivukqXGxEJEbzww9+z7531nJySy6tNY0otCoSRg9j8k2zyVrQN02Cqx//AaV78qnILaJN14yxuU00OqfEkpiZSuaCqWQtyPGIP5+NoSPblNs7KlDGX3MJcRkp7H9vPRWHizC3GglPjCZtxhhm/XAJ0cP67mabMi6dH330BPveWUvJzjza6pqRymUkZQ9n7JIZTLjhMqSy7q9sdwYtBIGk7MDTB0tlMm76+/0c/XwHeV/voaG0GpfTRcLoYYy5cho5ty/w6fn0bUAQBCalL2TL8fcA0ZgR0UP2mfHD5/Czxf9k49HlnK4/jsPpIDosiXGpVzB/wp1UN3X3xOwNw+PHcf9V/2Ldkf9QpjuCzWElPiKVnJFXMXvsbWzowWggkUhZNuvXTMm4kj0nP6NUd5Q2k6jTFBWWREr0SEYPmeFTIHkwEqVN5KHr32Nz3nvknd5KU3sNSrmWITGjuCRrGRPT5/epXrdBy+VyeqVf91nW1V0nw63D0tfQm2mjriYpOoMtee9TqsvFaGklSpvI6JTpzJ9wJ3ERFz5MvKu2TF/7dfOljzEqZTp7TnxGVdMpbA4LCZFpTBg+l7kT7hCNiv3AHfY0OmV6j/fuhUYQBBZkxfPBfvF7Y/KwKOLC/Hvzzh4dx0u3TOCdvWfIr27D7nSRFKHispGxfH/mMIrr+6b7NDYlgtdun8ibu05zrLIVi8PJsGg1S8YlckvOUN7efdrvtlKJwMOLRrFoTAKrjtRwtFJPU4eXemKEkpEJYUxPi/ZrgBpsJIQrefsHU3h/XwXbihqoabWgUUgZlaBl6aQU5mX1rZ8yicBT149ha1EDa47rKKxpQ2+yIZMIpESqmJIayU1Th/g1aLgzGPnKFtYbrhqXRHqslg/3V3K0Uk+r2UZiuJJpaVHcMTOVoT4iG3rL9LRo3r5zKu/tO8OB8maajTZitAomDo3kuzOG+m1zV22Z7OS+9euRxaPJSYtm1ZFqTtUZsNidDI9RMyczju9OHxbUcKuBRHD5yfWmdxrzHmv6ZFyerW+DmhADgzW3luZfrUeSqCX+o2UD3ZyAcdmd1F+7EpfZTsyb1yL3kzp8sGHNr6f5vjVI4jTEfbi0T54vFztND6zDdlRHxCOX9KjJ9MeopUgQKLEHHnMdYuA4c/AkK+55nojkWH721V8GujkB096g55+L/w+5SsHdXz7dTb9osLL37TVse+VzRs+bwtJn7xno5pwXnsm5C4B7vnyayBT/g7HZkjG0btZQlX9+RPhDnB+Kaw7x2tp7iQ5L5nc3rxro5gRMq7GRP350FQqZisdu+rybftFgJbd0Pe9v+z1DY7P41XXvDHRzzgvu0Krf3vQ5MeH+vaFn3ixBXvIOtgr/k70hLj4On2nh5yuPkRSh5NN7eg6juxhpbLdy3at7Uckl/Peu6d30iwYrGwvrePyrE2QmhvHWnYPf29MXy17fR22rhZdvnXBOXaOY771olCg1o4BuGX6C6xseIkQ/sRc14jLZUV6e+q0x0gDYjooxytrbx34rjTQhQlzsVBwWXVknLZv9rTHSAJw5XASCwKU/vbiEX0OE+F+hpFbU3ZuVeeO3xkgDUFIrhicumvSTAW5JiBD/m+RWiNowN0xM/tYYaQByK0RP4B9d6lu/JkQn3w6/oBDdcOoM6Oa8C4B8YiIxL57/7AXBwNqRtlt7x4QBbklwsR7TIYlVo7568GuQdKXt5QMYPx38QnIhek9rTaPHw2HYlNHc/q+HB7hFvaMi9xQypZzpd3w7QkAAnA4nVUdLGDV7ok+x38HM8tufpK4o5NH7v0Rze43Hw2FE0hTuXfLaALeod5TqcpFLlcwZ1zctp4uVUl0uQ2IyGZsauJ7YxczzX3yP6qZTA92MEBeQ2laLRzz2QmmLBIOjlXqUMgm3Tx88GXJ7w5EKPaMTwrjMh9jvYOY3n+Wzo7gxqHWGDDXfNuQSJNHeoq+SiMCz3AwU2lvHob11YLILnU+i/9q3uPmLHUEr73a9CcqQx9C3EYlchjbW2xPl7DTSFzOLHrmdRY/cPtDNCCoSqYRfbXtpoJtxXlBHhXW73oItEB3i4kAqkXfzRNH4yXR1MbJs1q9ZNuvXA92MoPPrpSsHugnnBa0yqtv1Jgih75ZvI3KpQIzWOwOcv0xXFyMPLRzFQwu7Z3Md7Hzw477pFF7shKtk3a43ubT3ac99EdKoCREixAUlpFETIkSI80FIoyZEiBDng5BGTYgQIc4XIY2aECFChAgRIkSIECFChAgRIkSIQUDIUBMiRIgQIUKECBEiRIgQIUKECHGREDLUXEDalx9BN+dd9H/ZNdBNCREixLeInW98yTM5d7H6ieUD3ZQQIUIMQtbl/puHls9gxY4nB7opIS4ge4u+4KHlM3h97f0D3ZQQFxFv7izn0me389Q3Jwe6KSGA+1cc5dJnt7M6r3agmxLiAjN4FJVChOig6YF12I7qUF05gshHLx3o5oQIEeJbwod3PUfF4SLGXTOLq5/44UA3J0SIEIOMV9f8zJOu242AgFKuISZ8CKNTpnFZ9i1EhyUOUAtDhAhxobh/xVFyK/QsGZfI767KDFrZC0WN3sxNb+wH4OVbJzAlNSooZUP0npChJkSIECFChAgRIkSIICGTKlErxKx4TqcTo0VPdVMR1U1F7D25ih8vfIGMxEkD3MoQIUIMBhIjlKTGqAlThobt/2uEzniIECFChAgRIkSIEEFiUvoCbrv8D57fNruF42e28dne5zBa9Hyw7Q88uuy/yKSKAWxliBAhBgO/vzproJsQYoAIadSECBEiRIgQIUKECHGekMuUTM5YxNIZDwHQYtBRXHNogFsVIkSIECEuZkIeNf3EfroF439PYM2twVFvRJBJkCZokU9OQn3lCOSZsb2qx1FnwLy5HOuhGhzVbTgajAhSCdKUMJSXDkNz0xgk4b5nXhw1bRhW5GM9XIOjzggCSKJUSJPCUE5PQX31KCRRKk95l9OFeV0JpnUl2EubcRlsCGEKJNEq5NlxqOakoZwxJCjH50LjbDFj3lqO9UA19jOtOBuMuFwgTdSinJ6C5paxSOM03bbTzXm3V/VH/30RislJtC8/guGdY+csL5+YSMyLVwbcjxAhGspqOLRiE6cPnqBN14xULiM8MZrhOVmMu2YWSdnDe1VPq66ZwvUHOL2/kJbKetrqmpHIpEQNiWfk7IlMu30BqvDu9wRAS1UD+95dx+kDhbTpmgHQRIcTmRJH+qyxTFx6GZqocE95l9PJ8dV7Of71buqKq7C2m1CGa9DEhJMyNp2shTlkXDKu/wdnADC2tHFiwyHK9uTTdLqW9voWXE4XEcmxpM8ay/Q7FhEe3z0m+5mcu3pV/22vP0RqTiY73/iSXf/++pzlh00Zze3/ejjgfoT430HXUsaOgo84VXMQvaEOqVROlCaRkclTyRl5FcPisntVT4tBR27pBk7VHKCxtRK9sR6JREps+FDGpl7O7DG3oVaG+9y2sa2aLXnvcarmAC2GOgQgTBVNTHgKmUNmMGP0DYSpOu8bp8vJweJvOFi8mprmYsxWA2pFOGHqaFLjxzIpbQFZQ2cF4/AMCKOHzPD8r2sp89uXVmMDW/Leo7ByN80GHTKJjITINCZlLOTSrGU9euK0m1vYUbCSwordNLZV4nQ5iNDEMzQ2i8kZixiXekWv27v/1Nd8sutpXLhYNuvXzMpc2vvOhrioKG808vHBKg6faaGuzYJcKpAQrmRKahRLxiWSleT7Hj6bujYLGwvrOHi6hapmE/XtVqQSgSFRKi4bGcstOUMJV/keXla3mPhgfyWHTrega7MgAFEaOSmRKqanR3PdhGSiNHJPeafLxZrjOtYc11FSb8BgdRCulBGlkTM2JZx5mfHMzIgJxuG5qHHr1zy2ZDRXj0/yLD98poWfrzxGUoSST++Zwc7iRlYeqKS4zoDd6SQjXstNU4awaEzCALa+E4PFzsoDlWw/1UhViwmAlCg1V4yK5dZpQ32Gdr25s5y3dp9hybhEHlsymo8PVrHmuI7KFhMKqYTxQyL4wSWpjEmOuNDduSCEDDX9wPhZIW2vHASnCwBBJQNBwF7WIv6VNPd6kN72ygEs28+IP+QSBLUMV7sNe3Ez9uJmzBvKiP7HIqQJWq/tbEWNNP9yPS6jTVwgkyCoZDh1Bpw6A7ajOmQjY7wML61P78S8sczzW9DKcRltOPQWHOV6HOX6QWuoMXx4HOPHBeIPqYCglUO7DcdpPcbTekwbyoh+fiHyEdFe20miVT5qE3E5nLharV7LBLW8x22c7VawOfvekRD/0xxauZlNf/8Yl0O8huRqJQgCDSXVNJRUU3eqsteD9E3Pf0TRZlHcUiqXIdcosbQZqSuqoK6ogoI1+7jtjYeJSPS+J2pPnGbF3c9jNZgBkMikyNVKWmubaK1touJwEYmZw7wML1//4S0K1u73/FaGqbEazJha2mksraGhrGbQGmr2vr2WA+9vAEAilaAIU2NpN9FYVkNjWQ0Fa/Zxy6u/ImHUUK/ttLH+Px4cdgdmvcFrmVyj6nEbc6sRh83ej56E+F9gR8HHfLn/HzhdDgAUMjUCArUtJdS2lFDTXMy9S17rVV1f7Ps7x05vAUAqkaOUqzFZ2z2aK4dL1nHvkleJ0noL5FY2nODVtT/DYjN2bCtDLlPTbKil2VBLSe1hhsRkehkrPtz+BLml6zy/VYowzDYDBksLupayHo0bgwOX5z/3uTmb03V5/HvDg5isrQAo5RrsThtnGvI505DP4ZI1/HTRi4SporttW1xziLc3/8azrft8NbZV0dBawbHyzfztB7t71dLt+Sv5cv8/EAQJt1/xBFMyQpNOg5VPDlXx8uYSHB2Xn1ouQUCgtMFIaYORknoDr9w2sVd1vbiphK1FDQDIpQJquZR2i51TdQZO1RlYX1DHK7dNJCFc6bXdydo27l95DKNVvO5lEnFbXasFXauF3Ao9oxPCvAwvT359gg2F9Z7fYUopBqudFpON8kYjZQ3G/wlDTW/46GAlL20uFY3hShkWu5P86jbyq0+QV9XKQwtHDmj7KptNPPDRMWpbLQCo5GJQT0m9gZJ6A98c1/HidyYwLEbtc3uXy8VvVxWw/VQjUomAWi6h1WxnV0kTe0ub+MM1WSzIvjgMUsEkZKjpI+at5bS9dAAA5ezhhP1oIrLh4qyQs9WCZV8V9lNNva5PNjwSxS+moZg+BGlKOIJEwGV3YjteR9vrh7CfaKT1hb1E/3W+13Ztrx3CZbQhz44j/MEZyEeJHjwusx17eQvmjWUIYZ0zL9ajOtFIIxEI+9lU0dtGI8flcuFsMmE9UIO9tLm/h2fAkCZqCfvpZBSzhiJLjUSQSXA5nNiLm2n/Ty7WA9Xo/7SD2OXXIgiCZ7v4z7/jt86WJ7dj2VyOJF6DLF08x9pbx6K9dazP8rZTjTTdvxZg0Bq8QgwcJzYeZONzKwHInD+Fy+65nrj0ZABMegOlu4+jO3Gm1/XFpiez4OFbSb9kLNFD4xEkEhx2O1VHS9j64qfUFJSz7un3uPnFX3htt+Uf/8VqMJM8Lp0rf/NdErNSAbCZLTSUioYJZVjnC7XicBEFa/cjSCXMfeAmJlx/GUqtCpfLhaFRT9neAuqLq/p7eAaMiKQYrrhvKSMvH09sWjISmRSnw0ldUQXbX11F2Z58vvrtf/jRR497PVvuX/ec3zq/fOzfFK4/QHhiNHEjUwCYccciZtyxyGd53YkzvP/jZwAGrcErxPnnaNkmVu17HoAJafNYPPkuEqPSATBa9BRW7qGqsfdpdxOi0rgh6SGyhswkNmIoEkGCw2mnvO4YXx14mYqGAv67+6/8ZOHfvbb76sBLWGxGUuPHsmzWIwyNFTOZWO1mdC1lHC5Zi0oR5ilfUptLbuk6JIKUa6f9nOmjr0Ml1+JyuWgzNXKyah81zcX9PTwDysmqfZ7/Y8O7fx8YzHqWb/41JmsrKTGj+M6lv2VYXDZOp4Njp7fwye6/UNl4khXb/8hPF/3Da9t6/Rne2vQwFpuRobGZXDvtATKSJiMRJNjsZkp0R9hX9EWv2rku9z+sP/JvZFIld859mjHDLutfx0MMGJtP1POPTSUAzM2M4yeXpZEWK3rRtpps7CltokjX3uv6hsdq+OX8EcxMj2FItAqJIGB3OMmrauWfW8sorG3j2XWneO4m73fUK1tLMVodjEkO5/8WjWJ0onjvm20OyhqMrC+o8/KoOFLRwobCeqQC3Dc3g2vGJ6FVynC5XDQarOwvb6a03tjfw/OtoMVk49WtZSwem8B9czKI0SpoNdt4d08FKw5U8lluNeOHRAyYZ43N4eS3qwqobbWQGK7kN0tGM61jzHzoTAtPrylC12rh0VX5vPX9KShk3ZVZdhY3YrI6+PncDJZOSkYpl1LZbOK5Dac4UC7WkZUUztBo34aewUrIUNMHXHan6EkDqOanEfl7bzdSSYQS9cIMWJjR6zrDfjy52zJBJkExKYnoZxfQ8P0vsO6rwlHTjjS588PGViBamsN/Ps1jpAHRu0eeFYc8K86rTnd5RU4y2pvHdJYXBKSxGtSLR/S6zW6subU0/2p9wNtB8EODNMu6u3ILUgnyzFii/jyXxru+xlHegu2oDsWkJB81eGP4IA/L5nJQSol6aq5XCJkvnM0mWn63FSwOlHOHo709NJgK0XscdjubXvgYgOwrp3Pdn3/itV4dqWXskhmMXTLD1+Y+ueJn13dbJpXJSJ2ayc0vP8B/bvoDpbvz0Vc3EJnS+byozisFYMHDt3iMNABylZLkMWkkj0nzqtNdPm1GNtNuX+BZLggCYXFRjL/mkl632c2ZgydZcc/zAW8HwQ8Nyrl1frdlEqmEpOzh3Pj8vbz9vadoKK2m4nARqVPPnVpz79trKFx/AJlSzo3P3esVQuYLQ1Mrnz38KnaLjayFOcz8weI+9yXEtxeH084X+0WDyeSMRXxv9p+81muUkUwdsZipI3p//SyZck+3ZVKJjBFJU7hr0T945rNbOFG5h6a2amLCUzxlTtcfB+CGGQ96c1R09QAAIABJREFUjDQACpmKYXHZ3UKv3OVHp0znirG3eZYLgkCEJo5po67udZvdFNcc4rW19wa8HcCIpCm99jo6F24x4VX7XgDE85A1tPszcUfhR7SZmtAoI7hr0UuEq0VvAYlEyqT0BShlav6z8UFOVO2hpDaXEUmd346rD/4Ti81IYmQa9y55HaW8M6RVLlORNWQmWUNm9thOl8vFl/v/wfaClShlGn604DlGJk8NxiEIMQDYHU5e2iwaaRZmx/PEtd73XIRazpVjE7lybO/Txd91eVq3ZTKphMmpUbxw8zhue/Mge0ubqNGbSY7s/GbOr24D4JfzR3iMNAAquZTs5HCyk73fge7y09KiuSWn01NVEATiwpRcNe7c3/Bn4w4V6guTh0X22uvobDadqGdfWc+T962mvnvKmm1OpqVF8burMj0TRREqOffPzaDFZGPNcR1v7ixnYXa810RSIDy2qgC51P+2zh6CCDadqKe43oBMIvDcTePIiO+MDskZHs1zN43jh28f9hjsrpnQ/dy2WxzcdXkat07rvBaGRqt55sZx/ODtQ5xpMvHe3goeXTK6T/27WAkZavqA9VANzgaj6JVyT855358kQolibDyWXRVY8+tQdzHUSDRynBYHjkYT8h7qcCN0xH46W8y4nC4ESd9uWC/kkh7DgHpCEqE8d6EgISikKKemYCzXYztef05DjWVPJe1vHgEg4teXnFNvyGV30vKHbTh1BmSjYoh85NKgtT3E/wan95+gva6lwytl2XnfnzpSy5AJGZzadpSqYyVehhplmBq7xUZ7g75XdSm04iyGsakNl9OJIOm/Vr1ELusxDKgn1JHacxcKEjKFnLQZY2gsraHqaMk5DTUlO4+x/dVVACz5/Z3n1Bty2O2s+vXrtNY2kZg5jKsevzNobQ/x7eJU9QFRQ0aQcm3Oz8/7/jTKSIYnjCf/zHbK6/K8DDUqhRabyUKrsbFXdank4j3bbm7C6XIiEfr/DJFK5B5jR6BoFH3XPDhStpGTVXsA0fhhMLfg6gh7kkmVfHf2kyhk3b+bjpVvBmDm6Bt8tjt72KUMixtDRUMBR8s2egw1Jms7xyu2A7B4yt1eRpre4nQ6+Hj30xw49TUaZQQ/XfgPUuN9ew6HGBwcPN0iasgIcN+c3k8e95UItZzxKRHsKG4kr6rVy1CjVUqx2J00Gqw91NCJRiEFoNlow+lyIemjgaErcqlAjLY3o6Xu+NPd6Q1Wu5Mm+/mVQ7hjRqpPI8ydM1M7NF3MnKozeBnJAqHN3HdD0paTYqjc5aNivYw0bjLitMzNjGNDYT2bT9b7NNSo5BK+M7W7F6JSJuG2aUN5Zt0pthU18JvFo/psjLoYCRlq+oDbK0U2MhppfOAvQ7/1FjZg/PIktuP1OOuNuHzcFM4Gk9dvxcwhmNeU0PqXXdgK6lFeloo8MxbBh9sYgGJqMsgl2IuaaP7lOtTXjEYxJcmnwG5vUYxL6DF06EJjP63H+PkJbMd0OGoNuEy2rmHhADgaenaXtJ/Wo39qBzhdaG4fh3p++jn32/biPmx5dUiiVUQ9NUfULAoRIgDcXikJo4YSntBdf6DP9R4v48in26g6VkJbXQs2k6VbmbZ6b4NMxiXjyPtqN6sfX071TWWMmjOJpOxUpDLf1/Xw6VlI5TJ0J87w4d3PM2np5aROy/IpsNtbhk4c0WPo0IWmsbyGwx9toSL3FPqaRqxGC7i8Hy7t9S3nrOPL3/4Hl9PFzB8sZszi6efc74ZnVlB5pBhNTDg3Pn8vctWFM3CHGFy4vVJSYkYSqQ2em/uZ+nx2n/yM8ro89IY6rHZTtzJ6Y73X76yhl3Dg1Nes2PEEp+tvYnzqFQyNy0Yq8f0MGZWcg1Qip7LxJK+t+RkzM29gZHIOkZr4Prc7PXECT9y6ps/b9xW7w0Kbj+dsTFgyd1/5CnERQ7uts9nN1LWUA/ToxTIyOYeKhgIqu4SvVTQU4HI5EQQJmefwmvGFw2njva2/5djpLYSrY7n7ypdJjg7cwzrExUV+tahVNDIhjPjw4L03CmpaWXWkhryqVurbLJh8aDI2tHtf/7MyYlidp+NPq09y4+Q2Lh8VS1ZiGDKp7/FKzvBo5FKBk7p27l9xlOsnJjMlNapf/Rg/JJKv7rvwGldLxiXyu6t6nsBxCwb3BZlEYMJQ34blYTFqYrUKGg1WinTtfTbUvHzrBKak+v+eq9GbuemN/T7XFelE76ietp+SGsWGwnpO+gnDy0oMR91hvDubScMiAWiz2KnWmxkS9e0JfwqNJPuAs1kU1zxb2Lc/GFbm0/7GoU6DgkRACFd4DC5Ogw2sjm7Gm/B7puKoaMV2vB7jinyMK/JBIUU+Nh7VnOGoF49A6BLzKRsaQcSvZtD64n5sx+qwHasTd+fOEHXtKK8QqsGGeVMZ+r/sArflWiIgaBUIHaJVLpMdl9nu0wjmxtlmpeV3W3AZbChmDSXsJ93D0s7GuOoEpq9OgVxC5B9nI+3jgzDE/zaGJvFlFpEUPHG8fe+tZ+tLn3oMCoJUgipCg1QuPhcs7SbsFls3483cB26i6bSOqmMl7HtnLfveWYtMKSdlfAZZC6Yy7ppLkKs69a9iUhNZ9Jvb2fDsCipzT1GZewqAyJRY0meNY9LSy71CqAYbBev2s/rx5TjtohCiIBFQhqmRKcTjaDVasJksWM3+ZwvNbUY+e/BVrAYzIy6fwBX33nDO/R7+ZCtHP9+BVC5j6bP3EJE0eJ/PIc4/bSbRvT5KG3hYgD+25L3P6oOveDxCJIIUtSICmVS89k1WA3aHBavd7LXdtTm/oF5/hvK6Y2zJe5ctee8ikypJix/HxPT5TBt5NfIuXiXxkaksm/VrPt/7HKW6I5TqRI/WmLBkMofMYmbmDV4hVBczOSOv5rbL/wCImjzVTadYc+g1imsP8cnuv/DThf9AJvWe2TdY9J5jHKnxb2SL6lhnMHfqCbrP+/+3d+fxUdX3/sffZ9YsZCEQloQlyCargiCLgoIb0Cri1mr9tba2t6jttcut9dHett5Wa3u9ttUWF+qutWoXtFWpsgpVEAj7IktCCIEESMgkmcxktnN+f0wSCJmBgIEc8PV8PPJ48MhZODOZnJzzPp/v55vmyTylapqm91qSvjLlV4Q054jDjRONdG/H6vVXV+3VE0t3N9+uOI14tUnTsBh/KKZw1FTDMeHNPZefp9LDQW3aV6tXPt6rVz7eK4/LoeGNszfNGN5dXveRG/HeOan6r6sG6jcLd2lDWa02lMVDp55ZXo3rl6OZF/Q85dDhXJOV6pY7SeAlSbkZ8aDGF4w0f+/aOSsSrnvv1P7t3pTX1/g5zO2UfLa6pubTtcGILMtqVRWTm2Tm4/h+j3y+fYEIQQ3aV3S3T/65ayVLSp01WGkzB8vZO1PGUb90NQ/9Ww0Lils9vXVkpajz76cpXFiu0IoyRTYeVLSoWpF1FYqsq1Dg9S3q/LtrWoRKqTMGyjO+l0KLSxReV6HwpoMyK/wK/mOHgv/coU53jlL67SPO2OtvL6avQbX/t0KKmvJOKVD6F4fJ1b9zi+oi/7PrVP/yplYVNk0s01LNL5YptrdWzr5ZyvrvS084PCy8vqK5Z1HGvePkGdn2sb7A6XSoaL8++H08pBl9yxSNuuky5fTtIcdR55a3f/Kstsz/uNW5JTW7k7707H3as2qbdi3fqLJ1O3VwZ5lK12xX6ZrtWvXy+7p17g9azBY1cual6n/pSG17f7VK13yisvW7VLO/Suv/9oHW/32ZJt81UxO+NuOMvf72Eqiu03sPvSwzGtP5V43RuC9fo9yB+S2qi5Y9+ZZWPPtOq/exiWWa+seP/6jDpQfUpV9PXfuLO084PKy0cLsWPfq6JOmqH96qXhcObL8XBbRBRXWx3imcI0uWLhlysyaef4O6ZfaVw3HkhurVZT9TYdG/dOwf1vSULH1rxlztLF+traXLVXxgg/ZX79SuikLtqijU0s1/0t3Tn2wxW9S4QddpaO9LtK54gXZVFGr3gQ067C/Xiu1/18rt8zRt9GxdecEdZ+jVtw+PK0UF3Ubo61f9Vo+9/TXtKl+j+Wuf0rVjkw9Ni8RaV+OcTnk5gxSNhXWwpkR/W/Fr3T39CaV5s87oMcD+iivr9eQH8ZDmxtF5mnVhT/XJSZPzqOvkn7/9id7belDWMX8Ls1LdevK2C7Rmj08fFlVpw95a7Trk19rSGq0trdGrq8s055jZoj4/socm9s/Rwm2HtLbUp437alReE9Kb68v11vpyfWNSgb4y4ex9ANSRDtdHEn4/dBqHaJ3OfZ+rCGpOQVM/ltiB+hOs2TYNy/ZIpiXP2Dxl3pu4SahZ3brMuIlhGPKOyZN3THxsuFkXUsPSPfL/ca1i+/2qm7NG2f9zWYttnDmpSrtpiNJuGiLLshTdXqX6P21WaHmp/M+tl2dCr1ZTWCcT3nxQNT9Z2rYXewz38G7K/sXlp7TtsUIf75MVjMpZkKWsn0xKGLA0VUMl43+6UOFV+2VkeJT90BQ50pMnuJIUq/DL97MPpKgZD9k+z40UTl16TryZXm1523o6nMiOxWtlmZb6TRimq+67NeE69Ydrk25vGIYKxg1Vwbh44/GG2np9srBQH8yZJ9++Si3+zeu6/tctG42md8nUmFuv0Jhbr5BlWarYukcrX5ivHUvWaflTb6n/pJGtprBOpmxDkd6879SaeeaP7K9Zj9x1Stseq/jDzQoHQupyXk9d99DXEwYsgeO8j5K09Pd/1+6PtiglM003/uaeFjNmJVJTXqU3f/i0zGhMo2+Zoguun/SpXgM+G5r6mlT7K9plfxv3LJZlmRqcP143jE/cnLupmiMRwzA0KO9iDcqLD/ELhGq1oWSR3i18QlV1+/TWqt/pK1MePuY1dNHkYV/U5GFflGVZ2lu5TYs3vqhNpUv1r3VPa2jvS5SX07a/tbsPbNSLS37YxlfbUkHuSN1xxa9PadtE3C6vZl78XT313j1avvU1TRh8vbpm9m5enu7NkiFDliz56g+0arbcxBeIV0KnHzU9d9PPPRCuVSgSOOmqmnRvlm6d/DM98e5slVfv0tPvfVuzr5mjVO/xm5zD3nIa+1JW1LRP8Ld0e6VMSxrXr7O+d2Xi6Z4PB5JXlRqGobEFnTW2IP7ZrW2IaMknlXpq2W7t9zXo8cVFenDm0Bbb5KR7dMuYfN0yJl+WZemTCr9eWlmqZTur9My/S3RJ/xwN6Na2yppN+2r0oze3tvHVtjQ8L1MPz7Jnz6aaYESRmJm0qqbSH/+ZZKceqeL78L7JCdc9HbLT3DpYF9aB2uSfw4N18WWZqe6EPWaaXkMiRy/LTju1HkR29ek7tX0GuYfGx0tHi6oVa4ep4czGfbgGJh7uYAUjimytbPP+HBlepV07SJ2+PlpSfEru4zEMQ+7zuyrrgcly5KZJpqXIpuNv00LElFndcGpfx/mlPVnN7+N5nROGNJZlKbw2+cVrcEGxAq9vlRyGsn46Wa4k4z2b99cQle/HS2TVhOQe1UMZ94z9dC8An3l5I+LN/g7u2qe6g9UnWPvEmvbRfXDvhMvDwZD2b97d5v2lZKbrwhsm67LGITt71+487vqGYajnsALN/NU3ldG9syzTUtn6tk+va0aiqq+qPaWvYE37BOnSkfex24BeCUMay7K0Z/UnSbffMv9jrXr5fRlOh6775TfUuffxy4ojDSH9/ftzFPT51WfMYF3xPfv0AIO99c2NzzRYXr1LNfUHP/X+mvaRn5N4Jo1QJNjcF6ct0ryZmjB4lmaMjoeoxRXrjru+YRjqkztUX57yS2WldZNlmdp9YEOb/7+YGVFd8PApfQXCxw9fT8XAvDEq6DZSMTOq99Y902KZ25WibtkFkuKzVSWzqzxewXv0MLDeXYfKYThlWaY+2Zd4SMOJZKXlava0J5TTKU9lVds1d8G9aoi033kUZ96wvPh1bNEhvw7Vffrr7aZ9DEwSjATDsebZmtoiM8WtmRf21DcnF0jSCXu0GIahIT0z9ODMoeqW4ZFpSRv3tf33NBKzdLg+ckpfn6aZ7ukWNS1tTvI+lFUHm4OMjhoqNqh7PPBduzd5D7+1pfFlg5Mc4ycVdWqIxBIuW9e43wyvS3lZpza5jV1RUXMKPBf1lKNrmszKgPxPrWk1PffJMho7kEeLE9+Y+V/ZJCvQukTNMi3JtJI2Dja8jaXJR32wrUhMhjtxMybD6Wjel5WgMVgynlE91H3pl9u8/unS9D7GdvsSjm8Mvr1TsSR/QCKfVKr2kfjFTae7LpJ3bF7C9Y5W86sPFS2qljOvk7IfmJz05wC0Vd+Lz1enbtnyH/RpyWN/azU998lqqto4tGtfwuUrnntX4frWVWaWacoyLTlcic8VLm+80iwaPnJeikWizX1vjuVwOpr3FQsnLrdNpM+YwfrhmrltXv90aX4fi/YlPLdsmLdcvrJDiTZV+dYS/evBlyRJU/7zRvUbf+Incu888IIO7ihTdn5XXf+rbyb9OQDHGpg3VllpuaoJHNI/1/y+1fTcJyvFE79oLq8uSrh80cbnFYq0fmBlWqYsy0zaOLipN000duRJaDQWadW3pYnD4WzeV9Rs+zlkQM+L9OhXP27z+mfC5cNv1wuL79P63Qt0zahvtGgsPLJgqhasf1ardv5TV15whzJSW/ak2rb3Q+2tjFcEXNDvyubvp3o6aVjvSdpUulTvrZ2r8/MnnFKvms6duuuuaXP0xPy7VHpoi55Z8F1946rH5HWfOz0fPkvG9M1WbiePDvnDmrO0uNX03CcrvbHnZfGhxAHeiytLFQi3vpk2LUumFW96m4i38W9c5KihMcerEHE6DLkaH5qET2I4zeg+2We0kuRMevnjvbqwd1ar65OXV5ZKknp3Tu2woGbK4K76964qrSyuTtjQuLiyvnlmqKmDEzePD0ZMvVG4T18e33KoWzhq6vU18Wvcywd3PadmfJKoqDklhsuhjLvjHfkbFpXI98AHiu45kgKbtSEF3t6h2scTd78+lqdxyFJ45T7V/2lTc6Nb09eguifXKPCnzTISNAKz6iOq/NI8+V/eqEhxtaxY/GRlmZZCheXyPxN/UuU5KnTw/3GdfD9dqoblpS2qWWKHg6p9fJVi5X7JkLwX9TyZt8QWPBf1lIx4z5+6x1fJrItfAJr1YdW/tll1v/s44fto+hrk+8lSKRxTyrT+Sr95aKt1jlX/p00KLd0jI9Wl7AenyHGOJbjoGE6XS1O/c7Mkadt7q/Tm/U+rqqS8eXmwpl7r5y3Xwkdea9P+CsbFL8qK/r1JK56fr0hD/Hc+UF2nJY/9VSufn59wGutQfYOenvXf+ujZd3RoV5nM5nOLqZJV27TsyfjU0v0mHAkdPpgzT/Pue0o7lq5rUc1SX1WrhY+8ppp9lVLjUKqzTd+Lh0iGocqi/Vr4yGtqqIvfmIb8QX380nta8OtXE76PAV+d5v3gSUVDEQ2/dqLGfumqE/5fK1+Yr+0LC+VJ8+qGR+9RajbNEtF2TodL1469V5K0rvh9vbTkRzrQOJOQJAVCNVq5/U3NW/lom/bXNGRpW9mHWrTxheaGwf6Gav1z9eNatPHFhL1MQuF6Pfy3m7Rww/MqP7xLphm/eTMtUzv2r9a7hfEhjUfPUPRu4RN6cfH92rTnAwVCR66p6oJVmrfyUR3275cho/mYzlbD+kxSbmYfmVZMiza+2GLZpCFfUEZqjsLRoOa+/x2VVcYr9Uwzpg27F+mVZfEGxefnT2iemrvJjDF3y+NK1YGaEj0xf7aKKtbKtOLn7ki0QVtKl+uZBd874fHlZORp9rQ5ykzL1e4DG/Tcwu8rEj3+sHHYk8vp0LemxCt1F2w7pJ+8tVV7qo4Eq7XBiP6xoVy/Xdi2StexBfFZez4qPqyXVpY2VzhUB8L6w5Jivbxyr7JSW4ez9aGYvjB3lV5cUaqiQ/WKmfH+NaZlac2eas1dHq/sHdfvyHC+p5eV6MdvbtWynZWqPaoJ7uH6sH67cJf21zTIkHRxQfvNkHm2SnE7tGaPTw//a4eqG6c/r2uI6omlxXq7cYTE1y7p22HHd8X5uRrQOC33/fO2aHVJdXMPozV7qvVff92sqGmpX9c0XT00ccVxJ69Tzywv0Rtr9inU+Lnb5wvq/nlbVFIVkMfl0O3jElePn82oqDlFKVP7KVYZlP+pQoWW7mm+aZfTIauxxMx9QduaynrH5sk7uY9Cy0rl/+M6+Z9ZJ6OTJ74fS0qZMUCKWWp4r/UTLfNAveqfXa/6Z9dLLoeMNJcsf0RqPAk68zop4+4xRzaIWQotK1VoWTxhNdLdkqUWFTud7hwl13lnwYnvmNDU1SdLaTcNUeAv2xSct13Bedvj72Mg0twDyD24i+pf2dRiu+huX/OwqdBHZTo0642k/2XWLy6XZ3g3hVbtlyRZUVPV31+QdP327MGDz4YhV49V3UGflj7+V21fWNh80244nQo1BgS9RycehnCsfuOHadCUUdqxZJ2WzZmnZU+8qZSMVDXUBSXL0siZl8qMxbT57dal8rXlVVr+5Fta/uRbcric8qSnKOQPNgfC2fldNfW7R4bkmDFTOxav1Y7FayVJnvR4eHl0xc7ku2Yqd0D+qb0xZ9IxT2S6FPTQmFuv0JpXF2rtG0u09o0l8makKVwfbO4B1GNIX6147t0W21Xu2q+6A/FKyaJlG/SHaxL3+JCk6//3LvW6oL+KP9oiSYpFY3r9nt8mXb89e/Dg3DLqvKtU21hRs6FkkTaULJLXlSaHw6lgOF5V2r/H6Dbta3D+eI3oe7k27Vmqdwuf1PzCp5TiyVBDuE6WLF088DqZVkxrdr3Tattqf7nmr31K89c+JafDJa87TQ3heplW/CK7S0a+rrv43ub1TSumjXuWaOOeJZKkFHe6LFktKnamjZ591s9I5DAcunz4l/SXjx5WYdG7uvrCO9W5U3yWrvSULN0x9X/1zILvav/hHfrtP78irztNMTPaXH2UnzNYt07+Wav9dsvqq69e8YheXHK/yqq264n5d8nl9MjjSlEw7JdlmXIYbavO65rZq7myZldFoZ5bdJ/uvPL/5HIev28f7OfKId1U2VhRs3h7pRZvr1Sq2ymXw1BdKP5geFTvtjWOHtcvR5cN6qoPdlTq6WUlmrusRJ1SXPI3RGVJ+vyIHopZluZvbt0+oaI2pLnLSzR3eYlcDkNpHqfqQ1HFGnsO52Wn6NtTj/xuR01LS3dUaumOeKVFuscpS2pRsfONSQU6L7f9ZuA9W2WnunXLmHw9vrhY7246oE4pLtWHok23grphVF7SAORMcDsdeuj6obr39Y2qqA3pO29sUkrjbLxNs4N1z/Tql9cPlSfJ6IRLB3RRIBzTY4uLNGdpsVLdzubPr9OQfjx9kHp1Pvcq/whqPoX0W4bKc1FPBf66VeF1B2RWBWS4HHL17yzPhT2UMu28Nu8r66eTFXhjq4LvFcWH51jxm/zUzw9U6jX941NOH8NIdyv74akKF5YrvOWQzEP1Mn0hGakuOXtnKuXSPkq94Xw5jmqslHbzEDnzOylcWKFoaY3MqqCsSEyObmlyD+umtFmD7T9rUWOZY/PQrqNk3DNWzr5ZCr61Q9ESn2Racg3IUerV5yl11mDVv7TxuLu2akPJJoSKO3ZIWGN/nmTaswcPPjsuvv0qFYwbojWvLlRp4Xb5K2vkdjmVO7CX+owZrBGfm9Dmfc18+D+06pUF2vzOCvnKDsmypF4X9NcF10/S8M9P0DsPPN9qG296im763bdU8vE27dtYpLqDPgWq6+RO8ahL3x4aePmFGv2FqfKmH6kkG3vbleqcn6s9q7epaneF/FU1ioWjyujeWfkj+2v0LVPUe5S9m23HovE/+m5v6+EXV3zvFnXp11Pr/7pUlbvLZZmmug/uo2Ezxmv0LVP00TNvH3ffJ+qZY0Zajn+PheP9eU51f/hsu2z4bRqYN1bLtr6movJC1Qar5JBLPTsP0ICeF2nMgM+1eV//7/KH9MHmV7Vm1zuqrNsnyVJB95EaP+h6jRkwQ39e/vNW23g96brzyke1c/9qlRzcJF/goOobquVxpSg3q6+G97lMlw69WSnuIzdZk4fdqi4ZvbSzfLUO+kpUG6xUNBZRdnp3FXQboUvOv0nnHVNFcrYaM2CG/rVuruqCVVq86SXdOOG+5mUF3UboB7P+rCWbXta2so/kqz8gp+FSz679Narf1bpkyE1JA5NBeWP1w1lvaNmWP2tb2Yc67C9XNBZR14xe6t11qEadd+Kqvibdsvpq9rQ/6Mn5d2vH/o/1wuL7dcfUXycdngb7+uLYXhrTN1tvFO7T2lKfqvxhuZxODchN16g+2ZoxvO3X/T+/boheW12m+ZsPaJ8vKFnSiF6Zum5kT00f3l0Pvru91TbpXqceuXGYVpf4tHl/rQ7WheQLRJTidqpPTpomDeyim0bnNQ+tkqQvjslXfnaKCvf4VFIVUFV9WJGYqe4ZXg3Pz9QNo/J0YRsDps+CL4zppfzsVL22ukw7D/rlcTnUPzddN47K0zXDOv6+rlfnVL341Yv02uoyfbCjUvtr4vdO53VN0+SBXXXrxb3UyZs8ljAMQw/OHKq/FO7T/M0HVOYLKiPFpZH5mbpjYh8N7Xn8vqJnK+PY6dOa1JiBTT86/JfhmyJlZ/iQgOOrvO3viu33K/3LI9Xpaxd29OHgJP1P9iw5ZKgo+ukbXQLt6emZP5JvX6Umfv1zmjR7ZkcfDk7SZY6hql2cpn1b2t7DBABOZPzNDrmLXlRk7/Ef9gFn0tpSn7792kb1yPTqb7MTzxp8tnv23yV67qNSTR/eXf89Y/CJNzgL5dz+WMDhTRsoaf+xy+hRg7NK7FAg3kdHkquN04cDwInUHayWb398WvS2Th8OAAAAnA4MfcJZI1bhjw8Bs+LDvrwXn3gbE8E7AAAHGElEQVRmJgA4kZryKr3zs+cly5InPUX9Jg7v6EMCAADAZxhBDWyvYfFu1T66UlZ9Yzm7IWV8a6yMVMZJAzh1295frfd++YpC/mD8G4ahK77/BXlSW88OBwAAAJwpxwtqLMc5Nhc5zk5WKCYrEJGR6ZH7/K5Ku3movGOppjlbWbJkMOoSNhANRRSqb1BKVrp6DivQ2NuuVL/xw068IeyLyxYAp4HBPRGA0yF+cknYNDhpUGNJdWkGTxXR8VKnD1Dq9AEdfRhoJ34zpFxnRkcfBqAR107UiGsndvRhoJ1EjKjcHm6mALSvaNiQ151y4hWBM2h0n2x9eN/kjj6M0+rOSwt056UFHX0Yp5XhdLslJZzmM+ljbbecO/u4uhx3pmIAOFmHzXp1dqSfeEUAOAkxZ0wZ3ZwdfRgAzjHhsFPObCq5AbQvR3pnybJCkgIJlyfbMN3hfW1a6si603ZkAD6TQlZU/dy5ZkcfB4Bzi8MwYj3Pd0c7+jgAnGMMZ8w7YHykow8DwLnFU3CRZZnRfyjJ0KfjNYpY1MuV4+zlZApkAO1nYsoAvyGjKs+Z3dGHAuAcYchQb1eXoGEYh7r2ZZ4EAO3DcEi5Be6gw5secHXt29GHA+CcYShl8CS/w5P6UrI1jhfURCTrp491uT2Q66CfBIBP797Mq0P9Xd1K3XL+55TUYcFsR1pHHxKAs5whQ1ekDg16DNdql0ffvmhWejCjKw3LAXw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      "text/plain": [
       "<Figure size 1440x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Q10: YOUR CODE GOES HERE\n",
    "# (...)\n",
    "\n",
    "\n",
    "# Q10: Sample answer.\n",
    "\n",
    "# train a decision tree on it with small depth, e.g., k=2\n",
    "genre_tree = DecisionTreeClassifier(random_state=31337, max_depth=2)\n",
    "genre_tree.fit(train_features, train_labels)\n",
    "\n",
    "# predict labels on test data\n",
    "pred_labels_tree = genre_tree.predict(test_features)\n",
    "\n",
    "# plot tree using sklearn's plot_tree. you can also try using more\n",
    "# advanced tree visualizations, e.g., https://explained.ai/decision-tree-viz/\n",
    "feature_names = list(df_numerical.columns)\n",
    "plt.figure(figsize=(20,15))\n",
    "tree.plot_tree(genre_tree.fit(train_features, train_labels),\n",
    "               feature_names=feature_names,\n",
    "               class_names=genre_tree.classes_,\n",
    "               filled=True,\n",
    "               proportion=True,\n",
    "               precision=1,\n",
    "               rounded=True,\n",
    "               rotate=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) popularity prediction\n",
    "\n",
    "Let's use what we learned above to try out another prediction task: song popularity. First, we'll do some feature engineering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make sure we start with a clean slate\n",
    "df = pd.read_csv('data/spotify_songs.csv')\n",
    "\n",
    "# hot-encode \"mode\" categorical column\n",
    "df.loc[df['mode'] == 'Major', 'mode'] = 1\n",
    "df.loc[df['mode'] == 'Minor', 'mode'] = 0\n",
    "\n",
    "# hot-encode \"key\" categorical columns, i.e.,\n",
    "# A -> 0, A# -> 1, etc.\n",
    "keys = df['key'].unique()\n",
    "for i in range(len(keys)):\n",
    "    df.loc[df['key'] == keys[i], 'key'] = i\n",
    "\n",
    "# ditto for time signatures\n",
    "signatures = df['time_signature'].unique()\n",
    "for i in range(len(signatures)):\n",
    "    df.loc[df['time_signature'] == signatures[i], 'time_signature'] = i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll pose our popularity prediction task as a binary decision between \"popular\" and \"unpopular\". Our data is exponentially distributed in terms of popularity (**how can we check that?**), so we'll choose a cutoff at the 75th percentile to split our songs at:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert popularity from [1, 100] to \"popular\" or \"not popular\" by splitting below and above the 75th %\n",
    "pop_75th = np.percentile(df['popularity'], 75)\n",
    "df.loc[df['popularity'] < pop_75th, 'popularity'] = 0 \n",
    "df.loc[df['popularity'] >= pop_75th, 'popularity'] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And as we've done before, split into train and test datasets. We'll use these to train a [`RandomForestClassifier`](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# select only numerical features\n",
    "df_numerical = df.select_dtypes(exclude=[np.object])\n",
    "\n",
    "# remove our label from features\n",
    "df_features = df_numerical.drop(['popularity'], axis=1)\n",
    "\n",
    "# standard scale\n",
    "X = np.array(df_features)\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X)\n",
    "X = scaler.transform(X)\n",
    "\n",
    "# features and label\n",
    "features = X\n",
    "labels = df['popularity']\n",
    "\n",
    "# split our data into training and test, reserving 20% of rows for test set\n",
    "train_features, test_features, train_labels, test_labels = train_test_split(features,\n",
    "                                                                            labels, test_size=0.2, random_state=31337)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's train a few other ML algos (some more powerful) on these:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RFC Accuracy: 0.9356811009817672\n",
      "RFC AUC: 0.8917930261499624\n"
     ]
    }
   ],
   "source": [
    "# train RFC\n",
    "rfc = RandomForestClassifier(random_state=31337)\n",
    "rfc.fit(train_features, train_labels)\n",
    "\n",
    "# predict labels on test data\n",
    "pred_labels_rfc = rfc.predict(test_features)\n",
    "accuracy_rfc = accuracy_score(test_labels, pred_labels_rfc)\n",
    "print('RFC Accuracy: ' + str(accuracy_rfc))\n",
    "\n",
    "auc_rfc = roc_auc_score(test_labels, pred_labels_rfc)\n",
    "print('RFC AUC: ' + str(auc_rfc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad!\n",
    "\n",
    "Now go forth and **try out for yourself with other models, and compare their performance**. In particular, we recommend you try out `xgboost`'s [`XGBClassifier`](https://xgboost.readthedocs.io/en/latest/python/index.html), [KNeighborsClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html), and [LinearSVC](https://scikit-learn.org/stable/modules/generated/sklearn.svm.LinearSVC.html) and see how those do on the same task. Do they beat the RFC above?\n",
    "\n",
    "You can also try out regression on the `popularity` ranks, instead of the binary decision classification problem we formulated above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBC Accuracy: 0.7487508765778401\n",
      "XGBC AUC: 0.5\n"
     ]
    }
   ],
   "source": [
    "# Q11: YOUR CODE GOES HERE\n",
    "# Try out xgboost's XGBClassifier as well as try and formulate the problem as a regression on popularity ranks.\n",
    "\n",
    "# Q11: Sample answer.\n",
    "\n",
    "# XGBClassifier on binary decision classification problem\n",
    "xgbc = XGBClassifier(objective = \"binary:logistic\", n_estimators=15, seed = 31337)\n",
    "xgbc.fit(train_features, train_labels)\n",
    "pred_labels_xgbc = xgbc.predict(test_features)\n",
    "accuracy_xgbc = accuracy_score(test_labels, pred_labels_xgbc)\n",
    "print(\"XGBC Accuracy: \" + str(accuracy_xgbc))\n",
    "\n",
    "auc_xgbc = roc_auc_score(test_labels, pred_labels_xgbc) \n",
    "print(\"XGBC AUC: \" + str(auc_xgbc))"
   ]
  }
 ],
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