asl_recognizer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Artificial Intelligence Engineer Nanodegree - Probabilistic Models\n",
    "## Project: Sign Language Recognition System\n",
    "- [Introduction](#intro)\n",
    "- [Part 1 Feature Selection](#part1_tutorial)\n",
    "    - [Tutorial](#part1_tutorial)\n",
    "    - [Features Submission](#part1_submission)\n",
    "    - [Features Unittest](#part1_test)\n",
    "- [Part 2 Train the models](#part2_tutorial)\n",
    "    - [Tutorial](#part2_tutorial)\n",
    "    - [Model Selection Score Submission](#part2_submission)\n",
    "    - [Model Score Unittest](#part2_test)\n",
    "- [Part 3 Build a Recognizer](#part3_tutorial)\n",
    "    - [Tutorial](#part3_tutorial)\n",
    "    - [Recognizer Submission](#part3_submission)\n",
    "    - [Recognizer Unittest](#part3_test)\n",
    "- [Part 4 (OPTIONAL) Improve the WER with Language Models](#part4_info)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='intro'></a>\n",
    "## Introduction\n",
    "* **Goal** - build a word recognizer for American Sign Language (ASL) video sequences, demonstrating the power of probabalistic models.  \n",
    "* **Approach** - [Hidden Markov models (HMM's)](https://en.wikipedia.org/wiki/Hidden_Markov_model) to analyze a series of measurements taken from ASL videos collected for research (see the [RWTH-BOSTON-104 Database](http://www-i6.informatik.rwth-aachen.de/~dreuw/database-rwth-boston-104.php)).  In the video shown, the right-hand x and y locations are plotted as the speaker produces sign language (signs) the sentence.\n",
    "[![ASLR demo](http://www-i6.informatik.rwth-aachen.de/~dreuw/images/demosample.png)](https://drive.google.com/open?id=0B_5qGuFe-wbhUXRuVnNZVnMtam8)\n",
    "\n",
    "* **Inputs Pre-defined**: raw data, train, and test sets\n",
    "* **Part 1**: Derive variety of feature sets. \n",
    "* **Part 2**: Implement 3x different model selection criterion to determine the optimal number of hidden states for each word model. \n",
    "* **Part 3**: Implement recognizer. Compare effects of the different combinations of feature sets and model selection criteria.  \n",
    "* **Outputs**: At the end of each Part, complete the submission cells with implementations, answer all questions, pass all unit tests, then submit completed notebook for review."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1_tutorial'></a>\n",
    "## PART 1: Data\n",
    "\n",
    "### Features Tutorial\n",
    "##### Load the initial database\n",
    "* **Inputs** - In **asl_data.py** (module) a **Data Handler** designed for this database is in the `AslDb` class.  It creates the initial [pandas](http://pandas.pydata.org/pandas-docs/stable/) dataframe from data included in the `data` directory as well as dictionaries suitable for extracting data in a format friendly to the [hmmlearn](https://hmmlearn.readthedocs.io/en/latest/) library, which are used to create models in Part 2.\n",
    "\n",
    "First set up initial database. Select an example set of features for the training set.  At the end of Part 1, you will create additional feature sets for experimentation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker\n",
       "video frame                                                           \n",
       "98    0         149     181      170      175     161      62  woman-1\n",
       "      1         149     181      170      175     161      62  woman-1\n",
       "      2         149     181      170      175     161      62  woman-1\n",
       "      3         149     181      170      175     161      62  woman-1\n",
       "      4         149     181      170      175     161      62  woman-1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###_DEBUG_IDE\n",
    "\n",
    "# # Auto-reload all changed modules every time before executing a new line\n",
    "# %load_ext autoreload \n",
    "# %autoreload 2\n",
    "\n",
    "def test():\n",
    "    print(\"Called .ipynb file from .py file using notebook_importing.py\")\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from asl_data import AslDb\n",
    "\n",
    "# Initializes the database\n",
    "asl = AslDb()\n",
    "\n",
    "# Display first five rows (pandas data frame) of the ASL database, \n",
    "# indexed by video and frame\n",
    "\n",
    "# print(asl.df.__dict__)\n",
    "\"\"\"\n",
    "{  'is_copy': None, '_data': \n",
    "    BlockManager Items: \n",
    "        Index(['left-x', 'left-y', 'right-x', 'right-y', 'nose-x', 'nose-y', 'speaker'], \n",
    "          dtype='object')\n",
    "    Axis 1: MultiIndex(levels=[[1, 2, 3, .., 200, 201], \n",
    "                               [0, 1, 2, ..., 160, 161]],\n",
    "                       labels=[[97, 97, ..., 124, 124], \n",
    "                               [0, 1, 2,  56]], \n",
    "                       names=['video', 'frame'])\n",
    "    IntBlock: slice(0, 6, 1), 6 x 15746, dtype: int64\n",
    "    ObjectBlock: slice(6, 7, 1), 1 x 15746, dtype: object, '_item_cache': {}\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "left-x         149\n",
       "left-y         181\n",
       "right-x        170\n",
       "right-y        175\n",
       "nose-x         161\n",
       "nose-y          62\n",
       "speaker    woman-1\n",
       "Name: (98, 1), dtype: object"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display data available for an individual frame\n",
    "# Reference: `asl_utils.py`\n",
    "\n",
    "asl.df.ix[98,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame represented by video 98, frame 1 is shown here:\n",
    "![Video 98](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/098-start.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Frame represented by video 150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "left-x         155\n",
       "left-y         182\n",
       "right-x        169\n",
       "right-y        141\n",
       "nose-x         166\n",
       "nose-y          54\n",
       "speaker    woman-1\n",
       "Name: (150, 1), dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display data available for an individual frame\n",
    "# Reference: `asl_utils.py`\n",
    "\n",
    "asl.df.ix[150,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame represented by video 150, frame 1 is shown here:\n",
    "![Video 150](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/150-start.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Feature selection for training the model\n",
    "* About: Feature Selection when training a model\n",
    "* Objectives: \n",
    "    * Choose most relevant variables.\n",
    "    * Keeping model as simple as possible to reduce training time.  \n",
    "* Inputs: \n",
    "    * Raw features (already provided)\n",
    "    * Custom derivation of our own. Add columns to pandas dataframe `asl.df` for selection.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  \n",
       "video frame           \n",
       "98    0          113  \n",
       "      1          113  \n",
       "      2          113  \n",
       "      3          113  \n",
       "      4          113  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the feature named 'grnd-ry' (\"ground\" right y value), which is \n",
    "# the difference b/w right-hand y value and nose y value. \n",
    "# Add it to the `asl.df` frames dictionary\n",
    "# (append result as column label/values to the right of Table) data frame \n",
    "\n",
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Run\n",
    "\n",
    "* Click the code snippet cell below and select \"Run All\"\n",
    "\n",
    "### Task DONE\n",
    "\n",
    "* Add df columns for 'grnd-rx', 'grnd-ly', 'grnd-lx' representing differences between hand and nose locations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  \n",
       "video frame                                      \n",
       "98    0          113        9      119      -12  \n",
       "      1          113        9      119      -12  \n",
       "      2          113        9      119      -12  \n",
       "      3          113        9      119      -12  \n",
       "      4          113        9      119      -12  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_utils import test_features_tryit\n",
    "\n",
    "# DONE \n",
    "# Add df columns for 'grnd-rx', 'grnd-ly', 'grnd-lx' representing \n",
    "# differences between hand and nose locations\n",
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-rx'] = asl.df['right-x'] - asl.df['nose-x']\n",
    "asl.df['grnd-ly'] = asl.df['left-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-lx'] = asl.df['left-x'] - asl.df['nose-x']\n",
    "\n",
    "asl.df.head()\n",
    "\n",
    "# Test the code\n",
    "# Expected: [9, 113, -12, 119]\n",
    "# test_features_tryit(asl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 113, -12, 119]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Collect the features into a list\n",
    "features_ground = ['grnd-rx','grnd-ry','grnd-lx','grnd-ly']\n",
    "\n",
    "# Show a single set of features for a given (video, frame) tuple\n",
    "[asl.df.ix[98,1][v] for v in features_ground]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Build the training set\n",
    "\n",
    "* Collect the feature for all the Words in the training set by passing the defined feature list `features_ground` to the `AslDb.build_training` method of `asl_data.py`. Each WordData object (see `WordsData` class in `asl_data.py` in the training set has multiple examples from various videos suitable for the hmmlearn library. \n",
    "* WordData object is dictionary of lists of feature list sequence lists for each word `{'FRANK': [[[87, 225], [87, 225], ...], [[88, 219], [88, 219], ...]]]}`.\n",
    "* Shown below are unique words that have been loaded into the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training words - num_items: 112\n",
      "Training words - words: ['JOHN', 'WRITE', 'HOMEWORK', 'IX-1P', 'SEE', 'YESTERDAY', 'IX', 'LOVE', 'MARY', 'CAN', 'GO', 'GO1', 'FUTURE', 'GO2', 'PARTY', 'FUTURE1', 'HIT', 'BLAME', 'FRED', 'FISH', 'WONT', 'EAT', 'BUT', 'CHICKEN', 'VEGETABLE', 'CHINA', 'PEOPLE', 'PREFER', 'BROCCOLI', 'LIKE', 'LEAVE', 'SAY', 'BUY', 'HOUSE', 'KNOW', 'CORN', 'CORN1', 'THINK', 'NOT', 'PAST', 'LIVE', 'CHICAGO', 'CAR', 'SHOULD', 'DECIDE', 'VISIT', 'MOVIE', 'WANT', 'SELL', 'TOMORROW', 'NEXT-WEEK', 'NEW-YORK', 'LAST-WEEK', 'WILL', 'FINISH', 'ANN', 'READ', 'BOOK', 'CHOCOLATE', 'FIND', 'SOMETHING-ONE', 'POSS', 'BROTHER', 'ARRIVE', 'HERE', 'GIVE', 'MAN', 'NEW', 'COAT', 'WOMAN', 'GIVE1', 'HAVE', 'FRANK', 'BREAK-DOWN', 'SEARCH-FOR', 'WHO', 'WHAT', 'LEG', 'FRIEND', 'CANDY', 'BLUE', 'SUE', 'BUY1', 'STOLEN', 'OLD', 'STUDENT', 'VIDEOTAPE', 'BORROW', 'MOTHER', 'POTATO', 'TELL', 'BILL', 'THROW', 'APPLE', 'NAME', 'SHOOT', 'SAY-1P', 'SELF', 'GROUP', 'JANA', 'TOY1', 'MANY', 'TOY', 'ALL', 'BOY', 'TEACHER', 'GIRL', 'BOX', 'GIVE2', 'GIVE3', 'GET', 'PUTASIDE']\n"
     ]
    }
   ],
   "source": [
    "training = asl.build_training(features_ground)\n",
    "\n",
    "print(\"Training words - num_items: {}\".format(training.num_items))\n",
    "print(\"Training words - words: {}\".format(training.words))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Training data object `training` is an instance of class `WordsData` built by calling the `build_training` method of class `AslDb` defined in the `asl_data.py` module. Access data using:\n",
    "    * `WordsData` instance properties:\n",
    "        * `words` - get list of keys\n",
    "    * `WordsData` instance methods:\n",
    "        * `get_all_sequences` - getter for entire db of words as series of sequences of feature lists for each frame\n",
    "        * `get_all_Xlengths` - getter for entire db of words as (X, lengths) tuple for use training multiple sequences with the `hmmlearn` library. where X is a numpy array of feature lists and lengths is list of lengths of sequences within X. i.e. `{'FRANK': (array([[ 87, 225],[ 87, 225], ... [ 87, 225,  62, 127], [ 87, 225,  65, 128]]), [14, 18]), }`\n",
    "        * `get_word_sequences` - getter for single word series of sequences of feature lists for each frame\n",
    "        * `get_word_Xlengths` - getter for single word (X, lengths) tuple for use with hmmlearn library, where X is a numpy array of feature lists and lengths is a list of lengths of sequences within X\n",
    "\n",
    "* The following example outputs two nested lists:\n",
    "    * First list is a concatenation of all the sequences(the X portion)\n",
    "    * Second is a list of the sequence lengths(the Lengths portion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-11,  48,   7, 120],\n",
       "        [-11,  48,   8, 109],\n",
       "        [ -8,  49,  11,  98],\n",
       "        [ -7,  50,   7,  87],\n",
       "        [ -4,  54,   7,  77],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [-10,  59,   7,  71],\n",
       "        [-15,  64,   9,  77],\n",
       "        [-17,  75,  13,  81],\n",
       "        [ -4,  48,  -4, 113],\n",
       "        [ -2,  53,  -4, 113],\n",
       "        [ -4,  55,   2,  98],\n",
       "        [ -4,  58,   2,  98],\n",
       "        [ -1,  59,   2,  89],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -2,  73,   5,  90],\n",
       "        [ -3,  79,  -4,  96],\n",
       "        [-15,  98,  13, 135],\n",
       "        [ -6,  93,  12, 128],\n",
       "        [ -2,  89,  14, 118],\n",
       "        [  5,  90,  10, 108],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,  13, 100],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  7,  85,  17, 111]]), [17, 20, 12])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.get_word_Xlengths('CHOCOLATE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### More feature sets\n",
    "* `asl.df` is still a Simple \"feature set\", but is enough to started modeling.\n",
    "* Improve results fom `asl.df` by manipulating the raw values. Below we setup other options for later experimentation. \n",
    "    * Option 1: **Grouped Statistics** to normalize each speaker's range of motion using [Pandas stats](http://pandas.pydata.org/pandas-docs/stable/api.html#api-dataframe-stats) functions and [pandas groupby](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.groupby.html). See below example for finding the Means of all speaker subgroups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>man-1</th>\n",
       "      <td>206.248203</td>\n",
       "      <td>218.679449</td>\n",
       "      <td>155.464350</td>\n",
       "      <td>150.371031</td>\n",
       "      <td>175.031756</td>\n",
       "      <td>61.642600</td>\n",
       "      <td>88.728430</td>\n",
       "      <td>-19.567406</td>\n",
       "      <td>157.036848</td>\n",
       "      <td>31.216447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-1</th>\n",
       "      <td>164.661438</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>162.655120</td>\n",
       "      <td>57.245098</td>\n",
       "      <td>60.087364</td>\n",
       "      <td>-11.637255</td>\n",
       "      <td>104.026144</td>\n",
       "      <td>2.006318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>183.214509</td>\n",
       "      <td>176.527232</td>\n",
       "      <td>156.866295</td>\n",
       "      <td>119.835714</td>\n",
       "      <td>170.318973</td>\n",
       "      <td>58.022098</td>\n",
       "      <td>61.813616</td>\n",
       "      <td>-13.452679</td>\n",
       "      <td>118.505134</td>\n",
       "      <td>12.895536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x      left-y     right-x     right-y      nose-x  \\\n",
       "speaker                                                               \n",
       "man-1    206.248203  218.679449  155.464350  150.371031  175.031756   \n",
       "woman-1  164.661438  161.271242  151.017865  117.332462  162.655120   \n",
       "woman-2  183.214509  176.527232  156.866295  119.835714  170.318973   \n",
       "\n",
       "            nose-y    grnd-ry    grnd-rx     grnd-ly    grnd-lx  \n",
       "speaker                                                          \n",
       "man-1    61.642600  88.728430 -19.567406  157.036848  31.216447  \n",
       "woman-1  57.245098  60.087364 -11.637255  104.026144   2.006318  \n",
       "woman-2  58.022098  61.813616 -13.452679  118.505134  12.895536  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_means = asl.df.groupby('speaker', 0, None, True, True, True, False).mean()\n",
    "df_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To select a mean that matches by speaker, use the pandas [map](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.map.html) method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  \n",
       "video frame                                      \n",
       "98    0          113        9      119      -12  \n",
       "      1          113        9      119      -12  \n",
       "      2          113        9      119      -12  \n",
       "      3          113        9      119      -12  \n",
       "      4          113        9      119      -12  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# asl.df['left-x-mean']= asl.df['speaker'].map(df_means['left-x'], na_action=None)\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Run\n",
    "\n",
    "* Click the code snippet cell below and select \"Run All\"\n",
    "\n",
    "### Task DONE\n",
    "\n",
    "* Create a dataframe named `df_std` with standard deviations grouped by speaker (i.e. mean and std should be relative to the speaker)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "      <th>left-x-mean</th>\n",
       "      <th>left-x-std</th>\n",
       "      <th>left-y-mean</th>\n",
       "      <th>left-y-std</th>\n",
       "      <th>right-x-mean</th>\n",
       "      <th>right-x-std</th>\n",
       "      <th>right-y-mean</th>\n",
       "      <th>right-y-std</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>164.661438</td>\n",
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       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
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       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "      <td>17.573442</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "      <td>17.573442</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "      <td>17.573442</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "      <td>17.573442</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  left-x-mean  left-x-std  \\\n",
       "video frame                                                                \n",
       "98    0          113        9      119      -12   164.661438   17.573442   \n",
       "      1          113        9      119      -12   164.661438   17.573442   \n",
       "      2          113        9      119      -12   164.661438   17.573442   \n",
       "      3          113        9      119      -12   164.661438   17.573442   \n",
       "      4          113        9      119      -12   164.661438   17.573442   \n",
       "\n",
       "             left-y-mean  left-y-std  right-x-mean  right-x-std  right-y-mean  \\\n",
       "video frame                                                                     \n",
       "98    0       161.271242   26.594521    151.017865    16.459943    117.332462   \n",
       "      1       161.271242   26.594521    151.017865    16.459943    117.332462   \n",
       "      2       161.271242   26.594521    151.017865    16.459943    117.332462   \n",
       "      3       161.271242   26.594521    151.017865    16.459943    117.332462   \n",
       "      4       161.271242   26.594521    151.017865    16.459943    117.332462   \n",
       "\n",
       "             right-y-std  \n",
       "video frame               \n",
       "98    0        34.667787  \n",
       "      1        34.667787  \n",
       "      2        34.667787  \n",
       "      3        34.667787  \n",
       "      4        34.667787  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_utils import test_std_tryit\n",
    "# DONE Create a dataframe named `df_std` with standard deviations grouped by speaker\n",
    "\n",
    "df_std = asl.df.groupby('speaker', 0, None, True, True, True, False).std()\n",
    "\n",
    "asl.df['left-x-mean'] = asl.df['speaker'].map(df_means['left-x'], na_action=None)\n",
    "asl.df['left-x-std'] = asl.df['speaker'].map(df_std['left-x'], na_action=None)\n",
    "asl.df['left-y-mean'] = asl.df['speaker'].map(df_means['left-y'], na_action=None)\n",
    "asl.df['left-y-std'] = asl.df['speaker'].map(df_std['left-y'], na_action=None)\n",
    "\n",
    "asl.df['right-x-mean'] = asl.df['speaker'].map(df_means['right-x'], na_action=None)\n",
    "asl.df['right-x-std'] = asl.df['speaker'].map(df_std['right-x'], na_action=None)\n",
    "asl.df['right-y-mean'] = asl.df['speaker'].map(df_means['right-y'], na_action=None)\n",
    "asl.df['right-y-std'] = asl.df['speaker'].map(df_std['right-y'], na_action=None)\n",
    "\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df_std\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>man-1</th>\n",
       "      <td>15.154425</td>\n",
       "      <td>36.328485</td>\n",
       "      <td>18.901917</td>\n",
       "      <td>54.902340</td>\n",
       "      <td>6.654573</td>\n",
       "      <td>5.520045</td>\n",
       "      <td>53.487999</td>\n",
       "      <td>20.269032</td>\n",
       "      <td>36.572749</td>\n",
       "      <td>15.080360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-1</th>\n",
       "      <td>17.573442</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>3.549392</td>\n",
       "      <td>3.538330</td>\n",
       "      <td>33.972660</td>\n",
       "      <td>16.764706</td>\n",
       "      <td>27.117393</td>\n",
       "      <td>17.328941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>15.388711</td>\n",
       "      <td>28.825025</td>\n",
       "      <td>14.890288</td>\n",
       "      <td>39.649111</td>\n",
       "      <td>4.099760</td>\n",
       "      <td>3.416167</td>\n",
       "      <td>39.128572</td>\n",
       "      <td>16.191324</td>\n",
       "      <td>29.320655</td>\n",
       "      <td>15.050938</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            left-x     left-y    right-x    right-y    nose-x    nose-y  \\\n",
       "speaker                                                                   \n",
       "man-1    15.154425  36.328485  18.901917  54.902340  6.654573  5.520045   \n",
       "woman-1  17.573442  26.594521  16.459943  34.667787  3.549392  3.538330   \n",
       "woman-2  15.388711  28.825025  14.890288  39.649111  4.099760  3.416167   \n",
       "\n",
       "           grnd-ry    grnd-rx    grnd-ly    grnd-lx  \n",
       "speaker                                              \n",
       "man-1    53.487999  20.269032  36.572749  15.080360  \n",
       "woman-1  33.972660  16.764706  27.117393  17.328941  \n",
       "woman-2  39.128572  16.191324  29.320655  15.050938  "
      ]
     },
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "<font color=green>Correct!</font><br/>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test the code\n",
    "test_std_tryit(df_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1_submission'></a>\n",
    "### Features Implementation Submission\n",
    "Implement four feature sets and answer the question that follows.\n",
    "- normalized Cartesian coordinates\n",
    "    - use *mean* and *standard deviation* statistics and the [standard score](https://en.wikipedia.org/wiki/Standard_score) equation to account for speakers with different heights and arm length\n",
    "    \n",
    "```\n",
    "Standard Score (of a raw score x)\n",
    "\n",
    "z = x - m / std\n",
    "\n",
    "where m is the mean\n",
    "where std is the standard deviation\n",
    "```\n",
    "\n",
    "- polar coordinates\n",
    "    - calculate polar coordinates with [Cartesian to polar equations](https://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates)\n",
    "    - use the [np.arctan2](https://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.arctan2.html) function and *swap the x and y axes* to move the $0$ to $2\\pi$ discontinuity to 12 o'clock instead of 3 o'clock;  in other words, the normal break in radians value from $0$ to $2\\pi$ occurs directly to the left of the speaker's nose, which may be in the signing area and interfere with results.  By swapping the x and y axes, that discontinuity move to directly above the speaker's head, an area not generally used in signing.\n",
    "\n",
    "- delta difference\n",
    "    - as described in Thad's lecture, use the difference in values between one frame and the next frames as features. Videos number 12 and 13 briefly mention using delta-y as a feature. The idea of using delta y as a feature is that the direction (i.e. positive or negative y) and the speed of movement between successive frames could be more useful than where the hand is exactly. delta values for the first frame of each video should be zero.\n",
    "    - pandas [diff method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.diff.html) and [fillna method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.fillna.html) will be helpful for this one\n",
    "\n",
    "- custom features\n",
    "    - These are your own design; combine techniques used above or come up with something else entirely. We look forward to seeing what you come up with! \n",
    "    Some ideas to get you started:\n",
    "        - normalize using a [feature scaling equation](https://en.wikipedia.org/wiki/Feature_scaling)\n",
    "        - normalize the polar coordinates\n",
    "        - adding additional deltas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>...</th>\n",
       "      <th>left-y-mean</th>\n",
       "      <th>left-y-std</th>\n",
       "      <th>right-x-mean</th>\n",
       "      <th>right-x-std</th>\n",
       "      <th>right-y-mean</th>\n",
       "      <th>right-y-std</th>\n",
       "      <th>norm-rx</th>\n",
       "      <th>norm-ry</th>\n",
       "      <th>norm-lx</th>\n",
       "      <th>norm-ly</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>...</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
       "      <td>0.741835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>...</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
       "      <td>0.741835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>...</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
       "      <td>0.741835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>...</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
       "      <td>0.741835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>...</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
       "      <td>0.741835</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 23 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly    ...     left-y-mean  left-y-std  \\\n",
       "video frame                               ...                               \n",
       "98    0          113        9      119    ...      161.271242   26.594521   \n",
       "      1          113        9      119    ...      161.271242   26.594521   \n",
       "      2          113        9      119    ...      161.271242   26.594521   \n",
       "      3          113        9      119    ...      161.271242   26.594521   \n",
       "      4          113        9      119    ...      161.271242   26.594521   \n",
       "\n",
       "             right-x-mean  right-x-std  right-y-mean  right-y-std   norm-rx  \\\n",
       "video frame                                                                   \n",
       "98    0        151.017865    16.459943    117.332462    34.667787  1.153232   \n",
       "      1        151.017865    16.459943    117.332462    34.667787  1.153232   \n",
       "      2        151.017865    16.459943    117.332462    34.667787  1.153232   \n",
       "      3        151.017865    16.459943    117.332462    34.667787  1.153232   \n",
       "      4        151.017865    16.459943    117.332462    34.667787  1.153232   \n",
       "\n",
       "              norm-ry   norm-lx   norm-ly  \n",
       "video frame                                \n",
       "98    0      1.663433 -0.891199  0.741835  \n",
       "      1      1.663433 -0.891199  0.741835  \n",
       "      2      1.663433 -0.891199  0.741835  \n",
       "      3      1.663433 -0.891199  0.741835  \n",
       "      4      1.663433 -0.891199  0.741835  \n",
       "\n",
       "[5 rows x 23 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DONE add features for normalized by speaker values of left, right, x, y\n",
    "# Name these 'norm-rx', 'norm-ry', 'norm-lx', and 'norm-ly'\n",
    "# using Z-score scaling (X-Xmean)/Xstd \n",
    "\n",
    "# Standard Score equation to normalise Cartesian coordinates x and y\n",
    "def standard_score(x, m, std):\n",
    "    return (x - m) / std\n",
    "\n",
    "features_r_l = ['right-x', 'right-y', 'left-x', 'left-y']\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly']\n",
    "\n",
    "for f_index, f_val in enumerate(features_norm):\n",
    "    f_mean = asl.df['speaker'].map(df_means[features_r_l[f_index]], na_action=None)\n",
    "    f_std  = asl.df['speaker'].map(df_std[features_r_l[f_index]], na_action=None)\n",
    "    asl.df[f_val] = standard_score(asl.df[features_r_l[f_index]], f_mean, f_std)\n",
    "\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "<p>5 rows × 27 columns</p>\n",
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      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly      ...       right-y-mean  \\\n",
       "video frame                                 ...                      \n",
       "98    0          113        9      119      ...         117.332462   \n",
       "      1          113        9      119      ...         117.332462   \n",
       "      2          113        9      119      ...         117.332462   \n",
       "      3          113        9      119      ...         117.332462   \n",
       "      4          113        9      119      ...         117.332462   \n",
       "\n",
       "             right-y-std   norm-rx   norm-ry   norm-lx   norm-ly   polar-rr  \\\n",
       "video frame                                                                   \n",
       "98    0        34.667787  1.153232  1.663433 -0.891199  0.741835  113.35784   \n",
       "      1        34.667787  1.153232  1.663433 -0.891199  0.741835  113.35784   \n",
       "      2        34.667787  1.153232  1.663433 -0.891199  0.741835  113.35784   \n",
       "      3        34.667787  1.153232  1.663433 -0.891199  0.741835  113.35784   \n",
       "      4        34.667787  1.153232  1.663433 -0.891199  0.741835  113.35784   \n",
       "\n",
       "             polar-rtheta    polar-lr  polar-ltheta  \n",
       "video frame                                          \n",
       "98    0          0.079478  119.603512     -0.100501  \n",
       "      1          0.079478  119.603512     -0.100501  \n",
       "      2          0.079478  119.603512     -0.100501  \n",
       "      3          0.079478  119.603512     -0.100501  \n",
       "      4          0.079478  119.603512     -0.100501  \n",
       "\n",
       "[5 rows x 27 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DONE add features for polar coordinate values where the nose is the origin\n",
    "# Name these 'polar-rr', 'polar-rtheta', 'polar-lr', and 'polar-ltheta'\n",
    "# Note that 'polar-rr' and 'polar-rtheta' refer to the radius and angle\n",
    "\n",
    "# Convert Cartesian coordinates x and y to polar coords with r ≥ 0 and ϕ (phi) in the interval (−pi, pi] by:\n",
    "#\n",
    "# radius = sqrt(x^2 + y^2)\n",
    "\n",
    "# Use the np.arctan2 function for tan-1 ( y / x ) and swap the x and y axes to move the 0 to 2pi discontinuity to 12 o'clock \n",
    "# instead of 3 o'clock (i.e. the normal break in radians value from 0 to 2pi occurs directly to the left \n",
    "# of the speaker's nose, which may be in the signing area and interfere with results, but by swapping \n",
    "# the x and y axes, that discontinuity moves to directly above the speaker's head area that's not generally\n",
    "# used in signing.\n",
    "#\n",
    "# angle = np.arctan2(y, x)   \n",
    "\n",
    "# Convert Cartesian coordinates x and y to radius (Euclidean Norm) in Polar Coordinates \n",
    "def radius(x, y):\n",
    "    return np.sqrt(x**2 + y**2)\n",
    "\n",
    "# Convert Cartesian coordinates x and y to angle (theta) in Polar Coordinates \n",
    "def angle(x, y):\n",
    "    # Swap the x and y axes in the calculation\n",
    "    # (i.e. instead of `np.arctan2(y, x)`)\n",
    "    return np.arctan2(x, y)\n",
    "\n",
    "# Differences between hand and nose locations (see previous task where calculated)\n",
    "features_ground = ['grnd-rx', 'grnd-ry', 'grnd-lx', 'grnd-ly']\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
    "\n",
    "for f_index, f_val in enumerate(features_polar):\n",
    "    if f_index % 2 == 0: # even indexes (i.e. 0, 2)\n",
    "        asl.df[f_val] = radius(asl.df[features_ground[f_index]], \n",
    "                               asl.df[features_ground[f_index + 1]])\n",
    "    else: # odd indexes\n",
    "        asl.df[f_val] = angle(asl.df[features_ground[f_index - 1]], \n",
    "                              asl.df[features_ground[f_index]])\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.0</td>\n",
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       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
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      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly    ...      norm-lx   norm-ly  \\\n",
       "video frame                               ...                          \n",
       "98    0          113        9      119    ...    -0.891199  0.741835   \n",
       "      1          113        9      119    ...    -0.891199  0.741835   \n",
       "      2          113        9      119    ...    -0.891199  0.741835   \n",
       "      3          113        9      119    ...    -0.891199  0.741835   \n",
       "      4          113        9      119    ...    -0.891199  0.741835   \n",
       "\n",
       "              polar-rr  polar-rtheta    polar-lr  polar-ltheta  delta-rx  \\\n",
       "video frame                                                                \n",
       "98    0      113.35784      0.079478  119.603512     -0.100501       0.0   \n",
       "      1      113.35784      0.079478  119.603512     -0.100501       0.0   \n",
       "      2      113.35784      0.079478  119.603512     -0.100501       0.0   \n",
       "      3      113.35784      0.079478  119.603512     -0.100501       0.0   \n",
       "      4      113.35784      0.079478  119.603512     -0.100501       0.0   \n",
       "\n",
       "             delta-ry  delta-lx  delta-ly  \n",
       "video frame                                \n",
       "98    0           0.0       0.0       0.0  \n",
       "      1           0.0       0.0       0.0  \n",
       "      2           0.0       0.0       0.0  \n",
       "      3           0.0       0.0       0.0  \n",
       "      4           0.0       0.0       0.0  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DONE add features for left, right, x, y differences by one time step, i.e. the \"delta\" values discussed in the lecture\n",
    "# Name these 'delta-rx', 'delta-ry', 'delta-lx', and 'delta-ly'\n",
    "\n",
    "# Replace any NaN values with 0 after taking the results of the difference\n",
    "def frame_difference(f):\n",
    "    return f.diff().fillna(0, None, 0, False, None, None)\n",
    "\n",
    "features_r_l = ['right-x', 'right-y', 'left-x', 'left-y']\n",
    "\n",
    "# Features representing the difference in values between one frame and the next frames \n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
    "\n",
    "for f_index, f_val in enumerate(features_delta):\n",
    "    asl.df[f_val] = frame_difference(asl.df[features_r_l[f_index]])\n",
    "\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
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       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
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       "      <th>nose-x</th>\n",
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       "      <th>...</th>\n",
       "      <th>right-x-rescaled</th>\n",
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       "      <th>right-y-rescaled</th>\n",
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       "      <th>left-x-min</th>\n",
       "      <th>left-x-rescaled</th>\n",
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       "      <th>left-y-min</th>\n",
       "      <th>left-y-rescaled</th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
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       "      <td>0.683761</td>\n",
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       "      <td>119</td>\n",
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       "      <td>-17</td>\n",
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       "      <td>9</td>\n",
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       "<p>5 rows × 43 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly       ...         right-x-rescaled  \\\n",
       "video frame                                  ...                            \n",
       "98    0          113        9      119       ...                 0.683761   \n",
       "      1          113        9      119       ...                 0.683761   \n",
       "      2          113        9      119       ...                 0.683761   \n",
       "      3          113        9      119       ...                 0.683761   \n",
       "      4          113        9      119       ...                 0.683761   \n",
       "\n",
       "             right-y-max  right-y-min  right-y-rescaled  left-x-max  \\\n",
       "video frame                                                           \n",
       "98    0              124          -17          0.921986          70   \n",
       "      1              124          -17          0.921986          70   \n",
       "      2              124          -17          0.921986          70   \n",
       "      3              124          -17          0.921986          70   \n",
       "      4              124          -17          0.921986          70   \n",
       "\n",
       "             left-x-min  left-x-rescaled  left-y-max  left-y-min  \\\n",
       "video frame                                                        \n",
       "98    0             -27         0.154639         137          31   \n",
       "      1             -27         0.154639         137          31   \n",
       "      2             -27         0.154639         137          31   \n",
       "      3             -27         0.154639         137          31   \n",
       "      4             -27         0.154639         137          31   \n",
       "\n",
       "             left-y-rescaled  \n",
       "video frame                   \n",
       "98    0             0.830189  \n",
       "      1             0.830189  \n",
       "      2             0.830189  \n",
       "      3             0.830189  \n",
       "      4             0.830189  \n",
       "\n",
       "[5 rows x 43 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DONE add features of your own design, which may be a combination of the above or something else\n",
    "# Name these whatever you would like, such as:\n",
    "#   - normalize using a Feature Scaling equation\n",
    "\n",
    "# Rescaling the range of features to scale to the range in [0, 1] or [-1, 1]\n",
    "# using the Feature Scaling equation to normalise:\n",
    "#\n",
    "#   normalised = orig - min(orig) / max(orig) - min(orig)\n",
    "#\n",
    "def rescale(orig, min, max):\n",
    "    return (orig - min) / (max - min)\n",
    "\n",
    "df_max = asl.df.groupby('speaker').max()\n",
    "df_min = asl.df.groupby('speaker').min()\n",
    "\n",
    "# Differences between hand and nose locations (see previous task where calculated)\n",
    "features_ground = ['grnd-rx', 'grnd-ry', 'grnd-lx', 'grnd-ly']\n",
    "\n",
    "# Features representing the Max and Min \n",
    "features_max = ['right-x-max', 'right-y-max', 'left-x-max', 'left-y-max']\n",
    "features_min = ['right-x-min', 'right-y-min', 'left-x-min', 'left-y-min']\n",
    "\n",
    "features_rescaled = ['right-x-rescaled', 'right-y-rescaled', 'left-x-rescaled', 'left-y-rescaled']\n",
    "\n",
    "for f_index, f_val in enumerate(features_ground):\n",
    "\n",
    "    # Map the Max and Min onto the data\n",
    "    asl.df[features_max[f_index]] = asl.df['speaker'].map(df_max[f_val], na_action=None)\n",
    "    asl.df[features_min[f_index]] = asl.df['speaker'].map(df_min[f_val], na_action=None)\n",
    "    \n",
    "    # Normalise by rescaling using the Feature Scaling equation\n",
    "    asl.df[features_rescaled[f_index]] = rescale(asl.df[f_val],\n",
    "                                               asl.df[features_min[f_index]],\n",
    "                                               asl.df[features_max[f_index]])\n",
    "\n",
    "# DONE define list named 'features_custom' for building the training set\n",
    "features_custom = ['right-x-rescaling', 'right-y-rescaling',  'left-x-rescaling', 'left-y-rescaling']\n",
    "\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1:**  What custom features did you choose for the features_custom set and why?\n",
    "\n",
    "**Answer 1:** The custom feature chosen for the features_custom was to rescale the features into a lower range between 0 and 1 for the Cartesian coordinates x and y use the Feature Scaling equation to achieve the normalisation. \n",
    "\n",
    "The benefits of rescaling are that interpretation and analysis of plotted data becomes easier. In stochastic environments such as the one we are using, rescaling is known to improve the convergence speed of gradient-descent. We are using similar gradient-based optimisation methods such as the iterative Baum-Welch algorithm (aka Expectation-Maximization (EM) algorithm) to solve the third fundamental problem of HMMs by estimating the model parameters given just the observed data. Rescaling is therefore important since HMMs already have a large vocabulary of signs and use a lot of memory.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1_test'></a>\n",
    "### Features Unit Testing\n",
    "Run the following unit tests as a sanity check on the defined \"ground\", \"norm\", \"polar\", and 'delta\"\n",
    "feature sets.  The test simply looks for some valid values but is not exhaustive.  However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9, 113, -12, 119]\n",
      "[1.1532321114002382, 1.6634329223668574, -0.89119923044101379, 0.74183544610811614]\n",
      "[113.35784048754634, 0.079478244608206572, 119.60351165413162, -0.10050059905462982]\n",
      "[0.0, 0.0, 0.0, 0.0]\n"
     ]
    }
   ],
   "source": [
    "# Verify values of features before tests\n",
    "\n",
    "# Collect the features into a list\n",
    "features_ground = ['grnd-rx','grnd-ry','grnd-lx','grnd-ly']\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly']\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
    "\n",
    "# Show a single set of features for a given (video, frame) tuple\n",
    "print([asl.df.ix[98,1][v] for v in features_ground])\n",
    "print([asl.df.ix[98,1][v] for v in features_norm])\n",
    "print([asl.df.ix[98,1][v] for v in features_polar])\n",
    "print([asl.df.ix[98,1][v] for v in features_delta])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 0.015s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import unittest\n",
    "# import numpy as np\n",
    "\n",
    "class TestFeatures(unittest.TestCase):\n",
    "\n",
    "    def test_features_ground(self):\n",
    "        sample = (asl.df.ix[98, 1][features_ground]).tolist()\n",
    "        self.assertEqual(sample, [9, 113, -12, 119])\n",
    "\n",
    "    def test_features_norm(self):\n",
    "        sample = (asl.df.ix[98, 1][features_norm]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [ 1.153,  1.663, -0.891,  0.742], 3)\n",
    "\n",
    "    def test_features_polar(self):\n",
    "        sample = (asl.df.ix[98,1][features_polar]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [113.3578, 0.0794, 119.603, -0.1005], 3)\n",
    "\n",
    "    def test_features_delta(self):\n",
    "        sample = (asl.df.ix[98, 0][features_delta]).tolist()\n",
    "        self.assertEqual(sample, [0, 0, 0, 0])\n",
    "        sample = (asl.df.ix[98, 18][features_delta]).tolist()\n",
    "        self.assertTrue(sample in [[-16, -5, -2, 4], [-14, -9, 0, 0]], \"Sample value found was {}\".format(sample))\n",
    "                         \n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestFeatures())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='part2_tutorial'></a>\n",
    "## PART 2: Model Selection\n",
    "### Model Selection Tutorial\n",
    "* Objective: Model Selection should tune the number of states for each word HMM prior to testing on unseen data. 3x tuning methods include: \n",
    "    * Log likelihood using Cross-Validation folds (CV)\n",
    "    * Bayesian Information Criterion (BIC)\n",
    "    * Discriminative Information Criterion (DIC) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Train a single word\n",
    "* \"train\" models for each word using the training set we built with sequence data. \n",
    "* e.g. Train a single word using Gaussian hidden Markov models (HMM) using the `fit` method during training. [Baum-Welch Expectation-Maximization](https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm) (EM) algorithm is invoked iteratively to find the best estimate for the model (for the number of hidden states specified) from a group of sample sequences. \n",
    "    * Assume the correct number of hidden states is 3 (a guess). The \"best\" number of states for training is determined by some model selection technique that chooses the \"best\" parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Built instance of a Hidden Markov Model (HMM) with Gaussian emissions using hmmlearn\n",
      "Number of states trained in model for BOOK is 3\n",
      "logL = -2331.1138127433196\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "from hmmlearn.hmm import GaussianHMM\n",
    "\n",
    "def train_a_word(word, num_hidden_states, features):\n",
    "    \n",
    "    warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "    \n",
    "    # Build training set\n",
    "    training = asl.build_training(features)\n",
    "    \n",
    "    # Call getter for single word (X, lengths) tuple for use with hmmlearn library,\n",
    "    # where \"X\" is a numpy array of feature lists\n",
    "    # where \"lengths\" is a list of lengths of sequences within X\n",
    "    X, lengths = training.get_word_Xlengths(word)\n",
    "    \n",
    "    # Build instance of Hidden Markov Model (HMM) with Gaussian emissions\n",
    "    # - \"fit\" method trains the HMM using the input matrix of concatenated sequences\n",
    "    #   of observations (aka samples), and the lengths of each seqence.\n",
    "    # - \"n_components\" attribute is the number of hidden States in the HMM\n",
    "    # - \"n_iter\" is number of Baum-Welch (EM algorithm) iterations\n",
    "    #\n",
    "    # Reference: \n",
    "    # - http://hmmlearn.readthedocs.io/en/latest/tutorial.html\n",
    "    # - http://hmmlearn.readthedocs.io/en/latest/api.html\n",
    "    model = GaussianHMM(n_components=num_hidden_states, n_iter=1000).fit(X, lengths)\n",
    "    \n",
    "    # \"score\" method calculates the log likelihood score of the HMM sample(s). \n",
    "    # Since the Baum-Welch algorithm\n",
    "    # (aka Expectation-Maximization (EM) algorithm) is a gradient-based optimisation method\n",
    "    # we try to avoid it getting stuck in local optima but running the \"fit\" method with\n",
    "    # different initialisations, and then selecting the highest scored model.\n",
    "    logL = model.score(X, lengths)\n",
    "    return model, logL\n",
    "\n",
    "demoword = 'BOOK'\n",
    "model, logL = train_a_word(demoword, 3, features_ground)\n",
    "print(\"Built instance of a Hidden Markov Model (HMM) with Gaussian emissions using hmmlearn\")\n",
    "print(\"Number of states trained in model for {} is {}\".format(demoword, model.n_components))\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The HMM model has been trained and information can be pulled from the model, including means and variances for each feature and hidden state.  The [log likelihood](http://math.stackexchange.com/questions/892832/why-we-consider-log-likelihood-instead-of-likelihood-in-gaussian-distribution) for any individual sample or group of samples can also be calculated with the `score` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for word BOOK is 3\n",
      "\n",
      "\t - Hidden state #0\n",
      "\t - Mean =  [ -3.46504869  50.66686933  14.02391587  52.04731066]\n",
      "\t - Variance =  [ 49.12346305  43.04799144  39.35109609  47.24195772]\n",
      "\n",
      "\t - Hidden state #1\n",
      "\t - Mean =  [ -11.45300909   94.109178     19.03512475  102.2030162 ]\n",
      "\t - Variance =  [  77.403668    203.35441965   26.68898447  156.12444034]\n",
      "\n",
      "\t - Hidden state #2\n",
      "\t - Mean =  [ -1.12415027  69.44164191  17.02866283  77.7231196 ]\n",
      "\t - Variance =  [ 19.70434594  16.83041492  30.51552305  11.03678246]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def show_model_stats(word, model):\n",
    "    print(\"Number of states trained in model for word {} is {}\\n\".format(word, model.n_components))    \n",
    "    variance = np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])    \n",
    "    for i in range(model.n_components):  # for each hidden state\n",
    "        print(\"\\t - Hidden state #{}\".format(i))\n",
    "        print(\"\\t - Mean = \", model.means_[i])\n",
    "        print(\"\\t - Variance = \", variance[i])\n",
    "        print()\n",
    "    \n",
    "show_model_stats(demoword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Try it!\n",
    "Experiment by changing the feature set, word, and/or num_hidden_states values in the next cell to see changes in values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for word CHOCOLATE is 12\n",
      "\n",
      "\t - Hidden state #0\n",
      "\t - Mean =  [ -7.          63.           2.11111111  83.22222222]\n",
      "\t - Variance =  [  1.11111111e-03   1.11111111e-03   2.76654321e+00   1.73950617e-01]\n",
      "\n",
      "\t - Hidden state #1\n",
      "\t - Mean =  [   5.14285714   87.28571428   12.28571429  104.14285713]\n",
      "\t - Variance =  [  1.2667347    3.34836733  15.91979596  16.40959184]\n",
      "\n",
      "\t - Hidden state #2\n",
      "\t - Mean =  [  -9.99999574   48.3333357     8.6666643   108.99996876]\n",
      "\t - Variance =  [  2.00334327   0.22555918   2.89222206  80.67057272]\n",
      "\n",
      "\t - Hidden state #3\n",
      "\t - Mean =  [ -8.4  52.6   6.1  69.2]\n",
      "\t - Variance =  [ 8.441       5.84099999  0.091       0.361     ]\n",
      "\n",
      "\t - Hidden state #4\n",
      "\t - Mean =  [ -15.   98.   13.  135.]\n",
      "\t - Variance =  [ 0.01  0.01  0.01  0.01]\n",
      "\n",
      "\t - Hidden state #5\n",
      "\t - Mean =  [ -1.00000000e+00   5.90000000e+01  -2.34436366e-07   8.56666663e+01]\n",
      "\t - Variance =  [  3.33333372e-03   3.33333372e-03   2.00333310e+00   5.55888824e+00]\n",
      "\n",
      "\t - Hidden state #6\n",
      "\t - Mean =  [  -3.49999978   53.50000048   -0.99999974  105.49999855]\n",
      "\t - Variance =  [  0.75250048  13.25250149   9.0025      56.25251899]\n",
      "\n",
      "\t - Hidden state #7\n",
      "\t - Mean =  [ -3.  82.  14.  96.]\n",
      "\t - Variance =  [ 0.005  0.005  0.005  0.005]\n",
      "\n",
      "\t - Hidden state #8\n",
      "\t - Mean =  [-15.99999999  69.49999999  11.          78.99999999]\n",
      "\t - Variance =  [  1.00500004  30.25500009   4.00500001   4.00500007]\n",
      "\n",
      "\t - Hidden state #9\n",
      "\t - Mean =  [ -3.25  73.     1.75  88.  ]\n",
      "\t - Variance =  [  0.69    13.5025  11.69    29.5025]\n",
      "\n",
      "\t - Hidden state #10\n",
      "\t - Mean =  [ -5.49999681  52.00000426   7.          81.99998935]\n",
      "\t - Variance =  [  2.25500001e+00   4.00500001e+00   5.00001065e-03   2.50050000e+01]\n",
      "\n",
      "\t - Hidden state #11\n",
      "\t - Mean =  [  -3.99999989   90.99999999   12.99999996  122.99999981]\n",
      "\t - Variance =  [  4.00500097   4.00499996   1.0050001   25.00500253]\n",
      "\n",
      "logL = -252.5939226435246\n"
     ]
    }
   ],
   "source": [
    "# Replace with any word key contained in `training.words`\n",
    "# (i.e. CHOCOLATE, BOOK, etc)\n",
    "my_testword = 'CHOCOLATE'\n",
    "\n",
    "# Experiment here with different parameters\n",
    "# (i.e. Number of States: 3, 5, 7, 12)\n",
    "# (i.e. Feature Set: features_ground, features_norm, \n",
    "#  features_polar, features_delta)\n",
    "model, logL = train_a_word(my_testword, 12, features_ground)\n",
    "show_model_stats(my_testword, model)\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Visualize the hidden states\n",
    "\n",
    "* Plot the Means and Variances for each State and Feature.  \n",
    "* Experiment by varying the Number of States Trained for the HMM model and examine the variances. \n",
    "\n",
    "1) Are some models are \"better\" than others?  \n",
    "\n",
    "2) How can you tell?  \n",
    "\n",
    "3) Write what you think in the classroom online."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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rVlMhN1b7XXkM+4oysEy5i9rn1rOIO46iLBPuTrs54Q4X61OAMKWUj/5U4dZE\nPHFHeENHKbXTnUetqsKwr2IY9lUMw76Kcb3a51ET7vQy6/U60OtcXtadMjAwMDC4cpTamQ2glOoF\nvIc2WmmWiLyulPonWo/5CqVUAPA50Aa4gDZqKV4vOwEYDhQAY0SfS+GsTn19fbRoshHAL2ixokp8\nAWdIoV49DPsqhmFf2RCB9DTIzISc7Mth3r29ISAAQs0Q5Dnmelz7FaW8UqhuOYqyopTqAbyP5gQ+\nFZG3iqQ/BzyO5jySgOEickJPswC/6VlPikgfSqG8o548EcO+imHYVzE8yb7TJ4X337YSfxRq14VW\ntyrw3kfdOs05sA9+/UVIToK77lU8+qQiOLiCguZXAE9qP2dU5qinMmEnStQdbdTSDqXUChGxD3Lz\nCxAnIllKqaeAt4EBelq2iLTGwMDghkREWL1C+HymEBAIL7zsxe2dNCewYcMFunb14q57IT9fWPSF\nsHShsHe38H//8KJ5q6p3FtcjlaGZXarQkYisF5HCKapb0TqtDQzKTWUp3Hki17PCncUizPhAmPmR\n0KI1vPvRZSdRFF9fxeBHvXjz314EBMK/Jlj5aX05xiwblEplOApn8y6czoXQGQGstvsdoJTaqZTa\nqpS6vxLs83gMhTvPUbi7WhgKdwXk5QlT37Dy/bfCAwMU417zIjyiuJMoqnDX8BbFm//2onFTeG+y\nsPJr952FK4W73NxcRowYQd26dQkJCaF169asXr26hJqub6p0HoVSaigQB3SxW11XRM7ondr/U0r9\nJiLHnJQ1FO6KYCjcXXmFu/JgKNy5T2Fwxe/X/MR3y1ty5mQYne8+Rs2bz+IsnFZJCndd/qTIzW3C\n7BlR/Lo3gY5dE3ASc9BGSQp32dnZWCwWJk+eTLVq1di2bRsPPvggs2bNcoiY68w+T76+VJrCXVkX\noAOwxu73OGCck3z3oIUYr1ZCXbOB/qVt83qJ9WQo3F3GUxTu/vznP4tIyXGNDIW7iivc+foEi7d3\nsPz3g00VVrirdVNL6XzbOnn/bYvk5zu3R8R9hbtCWrRoIYsXLy4xjydfX0TKH+upMhyFDxCPFgSw\nMOBfsyJ52qAFBWxUZH044K9/jwKOUCQAobPlenEUq1evFi8vrxIvju44iurVq8usWbOK5fnf//4n\nXl5ekpWVJWPHjpU777zT5XYOHDgggMTHxzusX79+vbzyyivSvn17ESndUdx1113yj3/8QxITE8Xb\n21t27tyB4IKuAAAgAElEQVTp1j6VxVGIFA8K+N5778ntt98up06dkpycHHniiSdk4MCBtvwzZ86U\n9PR0ycnJkdGjR0urVq2K1WVPaY7C29tbXnjhBcnJyZGsrCzZvXu3REdHy9atW6WgoEBmz54tdevW\nlTVr1hSz/euvv5YmTZo4rBs1apQ888wzLvc1IiJCtm3bJvn5+TJ48GAZMGCAU1sHDBggDz30kGRk\nZMhvv/0mN910k+14JSUliclkkkWLFkleXp68++674uXlZXMUy5YtkwYNGsj+/fslPz9f/vWvf0mH\nDh0cttO7d2+5ePGinDhxQqKiomT16tVObW7fvr3MnTtXRLSgjFu2bBERkc2b4gWQgX1yZM8u7aJ+\n5MgR+f777yUnJ0fOnz8vnTt3ltGjR9vaum7dug5BE0+fPi0RERGyatUqsVgssmbNGjGZIqR3tz/k\nn+MLJCvL0VnMmjVLzGazBAYGir+/v5jNZvH29haTySRms7nYOS8ikpiYKP7+/nLgwAGn+1eIJ19f\nRCpXCrWsTyjuCB29A5iARUqpPUqpwgl8TYGdSqm9aBPv3hLH0VLXNYbCXXGqUuGuLBgKd2VXuNu9\nQ5gySetPeG2ylzb8lYor3N1777107BhHbJvV/PoLvPy8lbNnLk8DKKvCXX5+PkOGDGHYsGE0adLE\npR3XM5XRmY2ULnR0j4hUF5HW+tJHX79ZRFqISCv9c2Zl2OepGAp3xalKhbuyYCjcua9wFxd3G6NH\nreD1l62Ydb9Uv+HlzoQrpXAXEX2OFyd6kXQe/vGMlR//Zy2zwp3VauWRRx7Bz8+PadOmubTheqdS\nHIVB+TAU7q4cV0Lhzp6goCAH0SFD4a5sFCrcbfzfOWpE/oNp0x/m7h5ZjJtYvNP/SirctW2nmPpf\nL25uAO+/LcyZEcahgxfdUrgTEUaMGMG5c+dYsmQJvr6+Zd7v64VKcRSVoYh3I2Ao3F05roTCnT2t\nW7dm/vz5WCwWvvvOULgrCyLCm298zvN/S+SVFyA/z4yPDzz2pA81a1ardIW7qGjFa5O9GDBUse1n\n4W8jrMycsZOGDdoArhXunnrqKQ4cOMDKlSsJDAws835fV7jTkVGWhUpQxCttm9dLZ7aIoXBXSFUr\n3BWOVurb11HhzmQyydChhsJd0e3Y22W1WiUt1So7t1llxjSLjPxLgdSuMVgC/KMlICBYmjatOoW7\n5CSrfPKhRapFdpWu7bfIMyPOSfVq9eXQAatDp3dCQoIA4u/v73D+zZs3z+VxKbTPk6k0hbuyUhmK\neCKypaRtljfW0+4dQnLSlY91VREOHz5M48aNq9oMlxj2VQyPt+/QZfsK/xmiu3/RF6uApQDy87Ul\nNwcyMyAjQ7h4Af44DYVdFf7+0KI13NZe0fkuhb9/xUJsXKlYSslJwo8/CDu3CYcPXg42GBkFMTdB\naCiYQhTBJvD1Az9f8PEFL2/wUuDlBei7opTtq3Z8b7m6x7fTnYpgk3vtWt5YT5XhKPoDPUTkcf33\nI8DtIvKMXZ59ep7T+u9jaAp3E4GtIjJPXz8TWC0ii51sx37CXdsFCxa4ZV9GRgYmkwmAFYuaceJY\nRCklDAwMSsLH14J/QAEBAQUEBuURHpFNWEQ2EdFZ3FQrDR+fK3eNsf//XimyMn05ezqU1AuBXEwJ\nIi01gJxsX3JzfMjJ8cFq8eyu3CF/3UlEZLZbeYu2X7du3aomKODVQgyFu6rCsK9iGPZVDMO+Iny9\npkzZK03hrqxUliKeS8RQuLtqGPZVDMO+imHYVzHKa19lOIodQEulVDya/HwwWrgOezKAVUqp02gj\nr7aKiOgT7/YppQYCvmjebnsl2GhgYGBg4CaV0UfhjRYxNgfNUQQBd6ONbipUxLsXGAm0RHNW+0Tk\nz3r5XL28gyJeSRgKd1cPT7KvwAqpOUJ6DuRbRO9oFfx9vAjxB5O/IsjDhr57Uvs5w7CvYlxr9rmr\ncFcZTxTtgF+LjHrqKyKvFGYQke+B7/X0NoD9lMd8EWlQlg3Wq1cPQ+Hu6uAJ9h08b+WdjXlsSrDi\nK3BHNUXjKC8CfOB84lnSfGuw56yVfIHICMULXX25q4G304l0VxtPaL+SMOyrGNeafUopt/p2q2TU\nU5H804BEEZmk/y4A9qA9UbwlIk6nKV+JUU+eiGGfazILvFl+uhYbzlcj2KeArtXO0y4yhRqBOcXs\ny8j34dc0M9+evYlzOYE0DklnQJ2T1AkuPuHtamIc34ph2FcxyjvqqTIm3PVH08ku/P0IMM1F3qFo\nCnf+dutq6p/1gQSgQWnbvN4m3HkyVWXf/44WyO0fZErjtzNl4ve5crFIRNDExETp3LmzBAYGynPP\nPWdbn1dglc935clt/8mUJu9kykdb8qTA4jr0dGVzJdrPWXRbe4KDg+XYsWNO00qL9tuqVSuHCXee\nhvH/qBgeEz0WN0cuKaXuASYAfUQkt3C9iJzRP+OBDWghyW8oDIU7R4U7/0ATd8ea2fl8NZ4IXc6r\n3f0IC3R8jeRK4c7XWzH0Vl/W/jWQ7o28mfpjPo8syOVMmmsVNEPh7uphr3DnLkUV7iqCK4U70EKD\n1KhRg9DQUBo3blylErFVTWU4ih1AI6XUzUopP7RO7BX2GfR+iY/RnMR5u/XhSil//XsU0Am4YcKM\ngxa4b8yYMYwfP55z585x8uRJnn76aVucInc4duwYnTp1okWLFhw/fpyzZ8/Sr18/7r33XrZsuTzJ\nvX///qxYsYL58+eTlpbG3r17adu2LT/88AMAixcvZvDgwYwZM4bk5GR+//13fH19ueOOO7h48aJb\ntmRmZrJkyRLMZjPz5s2zrZ8+fToZGRlkZGQwfvx4BgwYYPttLznZ9f0/qPPaeV779gKZGZf4+5OD\nnG7nxIkTxMbGuuyHMAco3u/jx+Refuw/Z6XP7By+P+z+xakslOWiV8igQYNo06YNKSkpvP766/Tv\n35+kpKRKsM6gkPz8fE6cOEGjRo3YtWtXMUcxbtw4EhISSE9PZ8WKFbz00kvs2rWriqytYtx57Cjr\nAvQCDqPFapqgr/snmmMAWAecQ+uL2AOs0Nd3BH5Di/f0GzDCne1dL6+eDIW7y9v+7+ojAkjcv9Pk\nhyMFLusXKbvC3YmLFrnptn7ibaom/kGh0ukOQ+GuqhXuCmMpbd68ucIKdy1btnTrf14WhbuDBw9K\nTEyMfPXVVyXW6cnXFxEPUririuV6cRSGwp1Ieo5V/r4yR+qO3S+AnLqQ67Jue8qqcPfxJ5/KKyuT\npcHrF6R+91HSpJmhcFcVCnfOlAwrqnD3/fffS0REhJw/f96pLWVRuHvqqackMDBQAGnTpo1cunTJ\naZ2FePL1RcSz+igMysmNrnD3v6MWes7MYeUBC4/GaW3Q/OZqlaJw98TjI3jtz5F8/HAIYfeM5+Dv\ne3lvXTIF1vKNAjQU7squcOeKiircde/enbi4OJe6J2VRuPvvf//LpUuX+Omnn3jggQfw9/d3acf1\njOEoPIgbVeEuM0/YfcbCk1/nEhoAi4b682icNlOushXu+t0awdE3YgF4b20iA+blkpJVdmdhKNy5\nr3B322238c0337jctyulcOfs3C2rwh1ouh533HEHp0+f5qOPPnJpx/WM4Sg8iBtN4e5itjB5Qx5z\ndhVwJk14pqMPS/8SQMsaxVXPykpZFO5O6KO8xnX1IfGSsDHeyupDBcSnXB4ZZSjcXRmFu/PnzzN2\n7Fj69+9PZmam08EHV1LhrigRERGkpqa6pXBXlIKCAo4dO1bmfb8eMByFB3GjKNx9MGMOr63No9vH\n2czcXkDDSMVdDb0ZfYcf/j5XZvZ0eRTu7m7kw9q/BnB70xjij8XTY2YOjy/OYd2RAloZCnflVrgD\n7fVQUlISXl5etlelXl5eREdHV7rCnTPsRzk5U7g7f/48CxYsICMjA4vFwpo1a/jyyy/dukG6HjGk\nUD2Mhx9+mHfffZdJkyYRHR1N7dq1mTZtGvfff7/bdTRq1IhNmzaxd+9e6tWrR40aNViyZAlr1qyh\nU6dOtnyLFy+mV69eDBgwALPZTPPmzdm5cyf33KPFcBwwYACff/45//73v4mMjCQ2Npa8vDx+/vln\nIiMjbfVs3ryZwMBAh2XmzJn07duXFi1aEBxenUNZ0cw7FMHxm5/khzWr+HLree5q4M2q4QHc29iH\nYD/nDiIsLMw2v8JkMvHuu++61QajR4+mT58+3HvvvYSEhNC+fXu2bdsGwF/+8hfq1q1LzZo1iY2N\ndXhfHuSn+O8rT1Cz4DCn/nUTS//1EE8tzSOj02Q+/XIFptAwZs75otTjERcXxyeffMIzzzxDeHg4\nDRs2ZPbs2S7zL1iwgJ07dxIeHs6LL77I4sWLiY52OyiyS6ZNm0ZGRgYxMTE8+uijPPbYY7a0qKgo\nFi1axIsvvkhkZCRHjhyhefPmtvR+/foxduxYBg4cSGhoKM2bN3cYulwWvvvuO5o1a4bJZGL06NEs\nWLCAwMBAgoKCmDBhAp06dSIsLIytW7fy6quvsnv3bsxmM7179+aBBx5wqGvcuHFMmjSJsLAwpkyZ\nQu3atVm+fDlvvPGG7T/zzjvvYLW6nitT6ChSUlLw9vYmPDzcIV0pxUcffUStWrUIDw/n+eef5733\n3qNPnz7l2v9rncoKCngY6I4W3G8HMEhE9tvleRpoKSIj9Uix/URkgFIqFvgSLV7UTWjDaBuLiKWk\nbZZX4S7fIlzZva84P278kTu73Fkl2y56Kojouqb6p1Xgp5820b7jHRRYocAq5BVAVj7kFGjB+S5m\nCxeyhMRLQsJFKwkXhZOpglXAxwta3+RF31gfejXxJjTgysdeutKxdvItwoZ4Cyv2W9hywkKaHi0k\nMggaRnpRP9KLmBBFVJAiMhhMfopgP0WgL/j7gK+XNunP20tTRvt500/c2bmzTRXN/i2KB4SiqtLz\nzx0M+4rj61X8dZwryqtwV1lBAY+KNrMapdQCoC+OE+f6oqnZASwGpiltT/sCC0SbqX1cKXVUr69E\nKdTy8tTSXDbGu77rqBpug53uqVVVDW1hd+n2BfpC3XBFk2pe3NdUEVfbmzY3eRHo6wFXwzLg663o\n3siH7o18sFiF/eesbD9l5WiKlWMpwrcHC2zOwz3iYJcnH19PP/8M+4ry3YgAGkRW7v+qMhxFTeCU\n3e/TaDKnTvOISIFSKg2I1NdvLVK2prON2AcFBDKUUofctM9QyKoYbtv3WyUb4oLrpv2qCMO+inHV\n7Ws4tkzZPUbh7qogdlKoZeF6VaC6Whj2VQzDvoph2FcxymtfVQUFtOW5ElKoBgYGBgaVR2V0Zvug\ndWbfjXaR3wEMFpHf7fKMAlrYdWY/ICIPK6WaAfO53Jn9A9CotM5sQ+Hu6nGt2pcnkGsV8q1CvoCl\nsKNeT/dW4A34KPD3Uvh5KSqjO+VabT9PwbCvYniMwp3e5/AMsAbtvzdLRH5XSv0TXQoVmAl8rndW\nX0CLMIuebyFax3cBMKo0JwGGwt3VxNPtW79hAw3ad+bntDy2pOWzNyOfg1kWMiyON0RegK8CPy+F\nRYRLTsY0BHspWof40NrkS1yoD53NftTwr9hkQE9vP8O+inGt2eeuwl2l9FGIyLfAt0XWvQLaHAvg\nfTQn8qmIvFWk+E/Ag2h62p7rmg08hgyLlY0X8/j+Qh4raMD5bVpfXai3orXJh0diAogN8qF+oA81\n/L2I8fMi1Fs5DCksEOFSgZCUbyUhx0JCtoXD2QX8cqmAWX9k8aH+ArRJkDfdwv3oEeHPnWF++Hld\nW6O4DAzKw1XtzNbnWHyI3RwLpdQK+zkWwEngUeD5q2mbwbVFWoGVb1NyWZaUy9oLueQKmLwVLchl\nbMNIOpp9aRbsg7eb48t9lCLcVxHu60XjIMe/RYEIv2UUsDE1jw0X85jzRzYfnckmxFtxb4Qf/aID\n+FOEP0HehtMwuD652iE8bHMsRCQPKJxjYUNEEkTkV8DTJjgYVDHZFuHrpBwG7kul3uYkHj+Yzu5L\n+Qy/KZC5Mbk0Ht+fzb1acuTdl2lp8nXbSZSGj1K0CfFlTO1glrUM52THaixuHkb/agH8mJrP0P1p\n1NucxKMH0lidkkt+OSPQuktpCnwmk8khxIU9pSkSjhkz5oZWcjNwztUeHuvOHAu3sJ9HUb16dTZs\n2OBWuYyMDLfzVgUZGRm89NJLLFq0iJMnTxIUFETDhg0ZOnQoLVq0YPbs2Zw5c4YJEyY4lOvWrRvz\n5s2jZk1t2klCQgKffPIJe/fuxWq1cssttzBixAiHEA35+fl88cUXrFu3zhbivE2bNgwbNswWFXTL\nli3MnTuXhIQE/Pz8aNOmDaNGjbKFl/juu+9YtWoVH3zwgct9euutt1i7di0LFy60hf549913Wbt2\nLaAFWxMRfH21iLEtW7bk2WefZdCgQQQEBGBFYUFhAfxeeJfobn+mJ+ncSRqNc3PwOq0FIFTAV199\nRUhISIWO8VtvvUV0dDQjRoxwmScQTRy+H7CPIH60hLLmXAiLzucQKgV0Jp1upNOEbOzdlavzLzEx\nkcmTJ3PgwAGqVavG6NGji8Ufss9rsVhc7uM333zDyZMnHQIAFnLw4EHS0tJclrVYLBw6dOiq/UcS\nExMZNGgQ69atw9u79P6fwnAk//jHP1y2T1l46qmnGD9+PN7e3kycOJEZM4qPuD99+jTDhw+nS5cu\nxf53zuzz9OtLuexzR7TiSi1o/61P7X4/AkxzkXc20N+deq8X4SIRTSglOjpalixZIhkZGZKXlycr\nVqyQ559/XkTcEy46evSohIWFyfjx4yUlJUXS09Pl/ffftymIFXLfffdJmzZtZPv27ZKfny+pqaky\nbdo0+fTTT0VEZNGiRRISEiJffPGFZGVlyR9//CE9evSQunXryoULF0SkdOGijIwMMZlMEhERIW+/\n/bbTPM726bt9hwWQhj+dlaANiVL9p3Py5MFUWX8hVwqcqKiNGDHCQbioIjgTLnKHPItVvk3OkaF7\nkyTix0QJ2pAoLbYlyevHL8mxLE2Yx5V97du3l2effVaysrJk8eLFYjabXQrvlNc+kdKPV6tWrRwU\n7iobZ8JFJeFMuKi85OXlSbVq1cRqtcrChQtlxIgRTvN1795d7rjjDqf/O2f2eTLXhMId0AFYY/d7\nHDDORd4bzlHc6FKoCdkFMuVEhrTbkSwBX24XQO7ffV4WnsuWzALnEpsiZZdCFRHp37+/VK9eXUJD\nQ6Vz5ysvhZqWb5Fn5y6WkMbNheBQ8WoWJ20X/CjPrt8jf+Q6SrsaUqieK4X65ZdfykMPPeTyf1cU\nT76+iFw7jsIHiAduBvzQtLGbuch7wzmKG1EK9UR2gfR4dpxU79lfgjZod+Fdd6XIpC37y3SnWVYp\n1JkzZ0p6errk5OTI6NGjpVWrypNCTcjIlUFTPxa/GrUl8PsTYtqQKD32pMiMM5mSmFtgSKF6qBRq\nWlqaNGrUSE6dOnXDO4qr2pktIgVA4RyLA8BC0edYKKX6ACilblNKnQYeAj5WSv3uusbrixtBCnXO\nnDn8cimfNxMyuGNXCk23JbPuQh4FAq/dbOL3dlGsvzWCITGBgBYKuzKkUIcPH05ISIgtbe/evaSl\npblVtzNKkkKtG+zH/OeeoF5IIKN/X8nYusEk5loZc+QSDbYkM2FfIlmBIRzMLCi8STKkUD1ACvXl\nl19mxIgR1KpVy+W2bxSuunCRiHwrIo1FpIGIvK6ve0W0iXiIyA4RqSUiwSISKSIVk/m6hrhepVCj\nm7ZgXmI2Od368eHn8+m0/Ryvn8jERyn+dbOJp2oG0SPSn+frBFMv0LFDs7KlUENDQymc1e+O83OF\nu1KoPimJvFTPxO7bItnWNoIJdYOxBgZz6kIqbXem0GRbMs8cTueXcxfwDjK53J4hhXqZypBC3bNn\nD+vWrXMQ6LqRMRTuPIjrQQo1xyrsSs9nxpks3v50NgeOxVOrRg0eia3LprcmYE1N4clTm4nvEM2G\nWyN4rk4wEb5X/jQsixRqgi6FWng37yy2/5WWQlVK0dzky7h6Jlb0aY9f4knergG3hviy5HwOa3bs\n4fOAOrTZnsyoQ+nMOpvF3oz8Mg29NaRQyy+FumHDBhISEqhTpw4xMTFMmTKFJUuW2FTxbjSuuqOo\niPrd9c61JIX6+N9G82tGPrsu5XM6p4BH9pyj7c9niF53ks5bz/J/y9eTfuo4Pb9cx6R1W/lhxy5O\nHdCkUE+u/IpqfpV76pVHCrWQolKbAK2vghTq8Rnv8FmDAP5zbhNBJw7w8l8epn6gNyuSc/jbkUt0\n3HWB6pvOsyoll2+Sc5l6MpPlSTkczy5wKsBlSKGWXwr1iSee4NixYzYZ35EjR9K7d2/WrFlTrv2/\n5nGnI+NKLWhhO44B9bncmR1bJM/TwHT9+0Dgq9LqvV46s0U0++bNmydt27aVoKAgqV69uvTq1Ut+\n/vlnEXGvM1tE5LfffpPevXtLSEiIBAcHS5cuXeSnn35yKJObmyuvvPKKNGjQQIKCgqRm7Try4LDH\nZPm+I7ImJUcWJGbJE59+JTe1uFV8AoPENzRMzHfdJzFLdts6nv3GvlcYW89hGfDocHnggQeK2blt\n2zbx8/NzGIHkbJ8KOzkLR8MULlOnTnXabkU7sy0Wi0ydOlUaN24sJpNJ6tevL+PGjRMRrTO1T58+\nYjKZpE6dOjJnzhyH9jt8+LC0atVKzGaz9O3bV0REduzYIbGxsWIymWTo0KEycODAYqOeirJ69WqJ\ni4sTs9ksMTEx0r9/f1m1apVT+48fPy5dunSRgIAAady4sUNnrdVqlWNZ+bLwXLaMO5outfsMkvBh\nz9qOgf+/l4iKqiF1fj4nHXcmCyBDv98t/4y/JG/vTZBb7+khQaYQib01Tp4aO15u69BRLhVYxGK1\nyurVq6VRo0YuRz3NnTtXmjdvLiEhIVKrVi157LHHbGlFz7mShu0OGTJEoqOjJTg4WGJjY2Xp0qW2\ntJdfflmioqLEbDbLli1bZN++fXLrrbdKcHCwtGrVSqZMmWJr3/Xr18uyZcukdu3aYjab5Z133hER\nka1bt8qdd94p4eHhEhUVJb169ZITJ044tUVEpFu3brJ9+3ZJTk6W+vXru8xXyI3emX3Fo8eWhFKq\nAzBRRP6k/x4HICJv2uVZo+fZokeiTQSipQRDyyuF+u7JTH7NLLk/oLJwtTvnz593eE9sH+FUxPFq\nbLX91qRGrfo6i4AFQQQKBPJFKBAtgmq+Vci1CjlW9E8ht5RTwAuI9vOihp8Xvpcu0rpmNeoGeFM3\nwJv6Ad40CvIh2EPCV1xrQdkqQlqBlfhsC0ezLRzPLuB0rpVTuRbO5Fo5n2clOd9aqtSvv4Igby1a\nboAXWLKzCTUF46u0oIk+SuGjwFspvJV2LhR+anKuyu673aKfDvZnhTtnSGmSnufPnaNa9epu1FQ1\nVIV9b9Y3uR2ssrxSqFfbUfQHeojI4/rvR4DbReQZuzz79Dyn9d/H9DzJReqyn5nddsGCBW7ZkJGR\ngcmkdRL+hxh+I6jC+1VenP0lrGLFWxV/LaPsPpX+9/eyW+fF5SFsXgjeej5vwBvBG8EXwUf/9EXw\nQ/DFSgBCAFYCsBKEFRMWgrASioVQLJiw2Oq2bz9PxLDvMhYgHW8y8OaS/pmFF9l4kYUXuXiRiyIH\nL/JR5KPILrCCjw8WFAX6jHgr2D5FP/u0kM6F6+xuZmxnJy6dVFnXO+QRcVsfuiqoCvv+ySlqkO9W\n3qLnX7du3apMM/uqIHYKd0qppG7durkVLhdDSrGiGPZVDMO+imHYV4TBZct+TUihlkX97nQR9TuX\niBvCG4Vcr1KFVwvDvoph2FcxDPsqhidJoZbEDqCRUupmpZQfWmf1iiJ5VgCfKaXOA8eB/5XUP2Fg\nYGBgULlc1T4KAKVUL+A9LqvfvW6vfqeUCgBWAw2BSKC5iDiPmaxjSKFePY7lZRPk7UMNb9+qNsUp\nnt5+hn0Vw7CvYpRXCvWqDo8tywLUA/a5k/d6Gx7rqRzKy5aOiful3/nDVW2KSzy5/UQM+yqKYV/F\nuCaGx5YFfaLdNyLS3EV6hUc9eSKebN+6qGDWR2u2jT2SRGiB52lLeXL7gWFfRTHsqxjlHfVU5U8O\nrhaMJwqPY2jyMbnn9D7pmLhf1menVbU5DiQmJkrnzp0lMDBQnnvuuao2xyVXQy8jODhYjh075jTN\n0/Qoyoon/z9Erj378MTosQbuMX/+fOLi4jCZTNSoUYOePXuyadMmACZOnMjQoUOLlVFKcfToUdvv\n/fv306dPH8xmMyEhIXTr1o3Nmzc7lMnLy2PixIk0atSI4OBg6tWrx/Dhw22xj0BTS2vXrh1BwcEs\naHQr5574O9az59iXnw2ULq0JmnSnj4+PQ5C2kSNHYjKZMJlM+Pn54evra/vds2dPEhISUErZ1hUu\nX331ldNtzJgxg6ioKFatWsXUqVNLbuBSKE1qtDJISEigW7duBAUF0aRJE9atW1fuujIyMqhfv/4V\ntK7yKDzOpQXCtKdevXoVah972rVrx+HDh4mPjy8Wx6lr164EBATYzr1bbrnlimzzWsRwFB7GwoUL\nGTNmDOPHj+fcuXOcPHmSp59+2hanyB2OHTtGp06daNGiBcePH+fs2bP069ePe++9ly1bttjy9e/f\nnxUrVjB//nzS0tLYu3cvbdu25YcffgBg8eLFDB48mDFjxvDhiUO03riCaLzY13cou5MSXW3egczM\nTJYsWYLZbGbevHm29dOnTycjI4OMjAzGjx/PgAEDbL9Xr15ty5eammpbn5GRwYABA5xu58SJE8TG\nxnrEZKyyXPQKGTRoEG3atCElJYXXX3+d/v37k5SUVAnWGRSSn5/PiRMnaNSokUPsJ3umTZtmO/cO\nHTpUBVZ6CO48dlztBfgS+APIR9PVHlFS/uvl1ZMnK9w9kXJcHk0+Jj/88IPENL1F6j77lORZrVdU\n4dXFeecAACAASURBVM6eskhkeqLCnYjIypUrbTGjOnToIHv37nV6/hkKd56pcNelS5cyv4bz5OuL\nyDWicFdZy/XiKDxV4e58QZ50TNwvn11KkvXr18sj48eKqW0r2Z+XVWGFO1f7VFYtZU9WuCsoKJDZ\ns2dL3bp1Zc2aNcVsNxTuPFPhrkuXLhIVFSWRkZHSsWNHt64dnnx9ETH6KK4LPFXhblOuJkZzZ0AI\nAM1r1qbgwkVbP4UrnCnczZ07t8QyRbkeFO68vb0ZNmwY/v7+7N+/v1jZjIwMzGazwzpD4a7qFe4m\nT55MfHw8Z86c4YknnuC+++7j2LFjLu24njEchQfhqQp3G3MvUdvbj5u9/QDIPHeewIgIfi/FURQq\n3LVu3RqAIUOGMH/+fPLz3QtgBtefwl1KSvFoNCaTifT0dId16enphISEuNyeoXB3mcpQuAO4/fbb\nbTcTw4YNo1OnTi6dz/WO4Sg8CE9UuHvny3nsyMuke0AoSimbwl3Trp1LdRRz584lPj6emJgYYmJi\neO6550hOTr4qfzZPV7izp1mzZsTHxzs8Qezdu5dmzSqmAmwo3JVf4c4ZSikHO24kPNJRlKaCd73i\naQp3r7z9Fp+8ORmvZWvo7x3soHA37P/+xllLPhlWCyJCTk6Ow7JlyxaOHTvG9u3bbSph+/ZpCndl\nff1UHq5FhbvXXnuNnJwcli5dyq+//sqDDz5YkSYwFO4qoHCXmprKmjVryMnJoaCggC+++IIff/yR\nHj16lGv/r3U8zlEopbyBD4GeQCwwSCkVW7VWXT0efvhh3n33XSZNmkR0dDS1a9dm2rRp3H///W7X\n0ahRIzZt2sTevXupV68eNWrUYMmSJaxZs4ZOnTrZ8i1evJhevXoxYMAAzGYzzZs3Z+fOndxzzz1Y\nRdjX4w6aTptM+ifzuCkqmtjYWPLy8vj5559pH1MTgLOWfDZv3kxgYKDDMnPmTPr27UuLFi1sTxQx\nMTGMHj2ab775xuGCVBJhYWEO8yjeffddt8qNHj2aPn36cO+99xISEkL79u3Ztm0bAH/5y1+oW7cu\nNWvWJDY2ttj78hEjRrB//37CwsJs7f7++++zcuVKwsLC+OKLL0o9HnFxcXzyySc888wzhIeH07Bh\nQ2bPnu0y/4IFC9i5cyfh4eG8+OKLLF68mOhot4Miu6RweGdMTAyPPvoojz32mC0tKiqKRYsW8eKL\nLxIZGcmRI0do3vxyIIR+/foxduxYBg4cSGhoKM2bN3cYulwWvvvuO5o1a4bJZGL06NEsWLCAwMBA\ngoKCmDBhAp06dSIsLIytW7fy6quvsnv3bsxmM7179+aBBx5wqGvcuHFMmjSJsLAwpkyZQu3atVm+\nfDlvvPGG7T/zzjvvYLW6jhxQ6ChSUlLw9vYmPDzcIT0/P5+XXnqJ6OhooqKi+OCDD1i2bBmNGzcu\n1/5f63hcCA93VPCKUl6Fu0P52aRaLRU1+Yry66+/0rJly6o2g515mczPusCLoTW4L/ByZ3lh++WK\nlXvPH+LugFD+FGAuoaari6e0nysM+yqGYV9xWvoFEehE7MwZ14TCnTu4o4Knr69wrKc5tcM4bPK/\ngtZfX7RIz2HAmTQHJT779ptRN5wTQX5VY5yBgQEAY44lE53n3g1veWM9XbOOokiZJMBQuLs6GPZV\nDMO+imHYVzGKKdyJG2HGPVEK1R0VPAfc2dH/b++8w6Oo9sf9nmz6pkAKvRdBELhIES7NKBZAURCl\niBev+FMUvBQLChZUvDawfEXBDoJcQEFFUWkCNoqIgvQepEMIhE1I2d3P74/ZLJtks1myyWaTnPd5\n5snuzJmZz85O5uzMOefz5lJRDVT+QsfnGzo+39Dx+UZ5Mdx5gzcWPI1Go9H4iYB79ATuLXieymvD\nnf/Q8flGWcVnR0ghk6qEEezh96E+fr5R3uIr14Y74CDwF/AnXuQiqSi5nkR0fL6i43PPH/ZT8oB1\njXxnS/ZYTh8/3yhv8XlzfRWRgGyjyCVJRAK5UUijKTfsFyNFyAFJK6KkRlOQQGyj0GgumRMnTtC9\ne3d69+7Nww8/XNbhlCpFiZWioqIKjCw/6Kggvp41z6NoasyYMXzwwQclE6imwhCodxQCLFNKCfCu\niLyXv0C+cRSsXr3aqw1bLBavy5YFFouFJ598ks8++4xDhw4RGRlJkyZNGDp0KK1atWLmzJkcOXKE\niRMn5lkvKSmJOXPmULu2MWL64MGDvP/++2zevBm73U6zZs0YPnx4npG3OTk5fPrpp6xYscKZubZt\n27YMGzbMmext7dq1fPLJJxw8eJDQ0FDatm3LyJEjnaOGv//+e5YsWcJbb71V6Gd66aWXWL58OQsW\nLCA+Ph6A1157jeXLlwOG6EdECAkJAaB169aMHTuWwYMH50m0B/Doo49yzTXXFNhHblqQ+fPnEx0d\n7dN3/NJLL5GYmMjw4cOLvY3CKOz8O378OC+//DI7duygWrVqjB49ukBaCdeyNput0M/4zTffcOjQ\nIWdeJ7uCA50VoXbIxMaZ8+cKXddms7Fr1y6//Y8cP36cwYMHs2LFCkwmU5Hlc0eZP/roo4Uen0vh\ngQceYMKECZhMJiZNmsR77+W91Pzwww/MmjWLkydPEhcXx/jx4z0OqCsP15dixefN8yl/T0Btx99q\nwGagu6fyFamN4oEHHpDExERZuHChWCwWyc7OlsWLF8sjjzwiIt75KPbu3StVqlSRCRMmSEpKiqSl\npcmbb77pFMPkcvPNN0vbtm1lw4YNkpOTI2fPnpVp06bJBx98ICIin332mURHR8unn34qGRkZcuzY\nMbnxxhulfv36cubMGREp2sFssVgkKipK4uLi5JVXXnFbpiR8FMOHD8/jo/CFopzUReEp5sLi69Sp\nk4wdO1YyMjLk888/l9jY2EJ9CpcaX7I9TR6wrpEvbfsl6cPHpXWXjoWW9bcz+1K/Z3c+iuKSnZ0t\n1apVE7vdLgsWLJDhw4fnWb5s2TKpV6+erF27Vmw2mxw+fFgOHz5cZHyBTIUVFwGTgEc8lakoFUUg\nG+5yWblypbRs2VKeeuopESm6otCGu7I33P3zpuskJDpS2nZoJx0nDJNmXS7+v2jD3dUi4t5w17lz\nZ+ePJm8J5OuLSAWqKAAzEO3y+leMkdoVvqIIVMOdK6tWrZKnn35aOnXqJCJFVxTacFf2hrv2A26U\nced+kC1btkhsrUSp/0/js2rDXeGGO6vVKiEhIfLiiy9K48aNpXbt2jJy5EjJyMhwu81cAvn6IlKx\nDHfVgZ+VUpuBDcASEfm+jGPyC4FquHO3HW8kP9pwFxiGuw6T/k0zc3VatWpFz38NIBs72WLThjsP\nhrsTJ06Qk5PD559/zk8//cSff/7JH3/8weTJkwuNoyITcBWFiOwXkTaOqaUUMdiuIhGohjt328ld\n7gltuAsMw11O3VgaKmNbLeo3RoBkzmvDnQfDXUREBAAPPfQQNWvWJCEhgXHjxmnDnabsCUTDXf7t\n5Bru3Jna8qMNd4FhuLP8fZKGKgaAC4dOAXBAzmvDnQfDXdWqValTp06efbmLtbKgK4oAItAMd1Om\nTGHy5MnMnTuXzMzMPIa7sWPHOvcnog13+QkUw91V/W5g43MzScgIYvv27fzvkzmEoDggadpw58Fw\nB8YjqrfeeouTJ0+SmprK66+/zk033VSsz1/eCciKorKqUCFwDHcAAwcOZPbs2bz++uvEx8fnMdzl\njocAtOHODYFiuLvh/x7GZMmmXs3aTsNduArmAOeJj4/XhrtCDHcATz31FB06dOCyyy7j8ssvp23b\ntgXGL1UavGnx9ueEkQhwH9AICMUYR9HC0zoVpdeTiI7PV3R8F7Ha7TLa+pPMs+3JM3+17Yg8YF0j\np+0XCqyjj59vlLf4KMe5njoCe0VkP4BSah5wC1Cwu4iPzLTvZJecLbqgH8nqqFhqW1fWYRSKjs83\n/BmfHSEbO42IyTO/oYoGgZfsmwpkktXHzzfKIr6xQW2opiJKdR+BWFHUBv52eX8YuCp/oZJI4ZFT\nC+IjA6uBKicnB0cmi4BEx+cb/o6vhh3OJm9nte3i7ywBWtRXZIYU7H2mj59vlEV8vyevJ8LLjoTF\nTeERiBWFV4iR/+k9MFSoSUlJWoXqH3R8vqHj8w0dn28UUKF6s1IgVhRaharjKzY6Pt/Q8flGRY0v\nEHs9aRWqRqPRBBBahRpg6Ph8o7zHl0U250lHyPt/GUE4UUSWdnjl/viVNeUtvnKtQr3USXeP9R86\nPt8oLD673S4bbFvkHev/ZKF1maTYz0q6PUMy7Jnyi22TvGP9nyyyLheL3XNSutKKL1DQ8flGRUoK\nqNFUKkSEH2Q9G2UbzVQD+gZdQ5yKJVJFEKHC+GdQW65T/+Q0qSy0L8MiBUd3azSlSalUFEWNrFZK\njVNKbVdKbVFKrVRK1XdZZlNK/emYdNuExivKswr1d9nGbjlIe3UFSeoqglVB01uToHrcGnQt2eRw\n09238sTECW62ZOBOhZrLzJkztQpVc8mUeEWhlDIBbwO9gBbAYKVUi3zF/gDai0hr4HPgFZdlF0Tk\nH46pb0nHVx6YO3cu7du3Jyoqipo1a9KrVy9+/vlnACZNmsTQoUMLrKOUYu/evc7327dvp2/fvsTG\nxhIdHU1SUhK//vprnnWys7OZNGkSTZs2xWw206BBA+655x5nkjwwtJodO3bEbDYTHx/P5MmT8+TQ\nKerCA4bjOTg4OE82zxEjRjjTcoSGhhISEuJ836tXLw4ePIhSKk/6jqioKObPn+92H++99x4JCQks\nWbKEqVOneoynKIpyUpck++RvfpOtxCSH8di1D2E2m2nevDkrVqwoUDZRxXFtUGeyyCKZo3kS5bli\nsVho1KhRaYdeIuR+z0VlTHalQYMGbo9PcejYsSO7d+9m//79ztxPueQ/90wmEw899FCJ7Le8URp3\nFM6R1SKSDeSOrHYiIqtEnPfP6zC6wGowMryOGTOGCRMmcOLECQ4dOsSDDz7oTGjnDfv27aNLly60\natWKAwcOcPToUfr168f111/P2rVrneUGDBjA4sWLmTt3LufOnWPz5s20a9eOlStXAkYuqCFDhjBm\nzBhOnz7Ntm3bCAkJoWvXrqSmpnoVS3p6OgsXLiQ2NpY5c+Y458+YMQOLxYLFYmHChAkMHDjQ+d41\nn9DZs2ed8y0WCwMHDnS7n+TkZFq0aBEQGT69veidklR+sK+jOvG8defLtG3blpSUFF544QUGDBjA\nqVOnCqzTUNUmkThS5RwbZVtJh16pyMnJITk5maZNm+ZJEpiL63l3/PhxIiIiuP3228so2rKlNMZR\neDWy2oXhgGumsXCl1EbACrwkIm5zbpfEyOxAw2Kx8PHHHzN+/Hji4uL47bffAIiOjqZPnz6sXr2a\ngwcPcuLECbefYf369Rw+fJj//ve/NGvWjOuuu44tW7YA0Lp1a6699lpGjBjBm2++ye+//87SpUuZ\nPXs26enpzjuW3NTWq1atYtSoUQwePJhatWo5E+o98MADjB49mtGjR3PPPfewc+dOzp07V+gxXbp0\nKREREdxxxx288847dOjQoUAZd58pN433mjVrMJkKPopx5aWXXmLFihUopZg6dSqTJ0+mbdu2zJs3\njyVLlmCxWGjbti3jxo0jJsZIZzFp0iS2bNlCdnY2jRs3ZsyYMTRs2JCvv/6aOXPmOLfVtm1b/vvf\n/5KUlMScOXOoXbu2c5+JiYkMHz6cP//8kxdeeIH+/fvz2Wef0b59eyZMmMDatWv58MMPOX78OA0a\nNGDs2LHOczUn1MbBf6SAQNrio2z6fRNPP/U069evJz4+nnr16vHiiy/St2/Bm+rsExewKcW/b7qL\nfWt20aBefZ588klnbK6xnjt3jldeeYU///yTevXq0aFDhzzf18aNG51ZY6+77jqsViu7du1yLv/2\n22+ZP38+Z86coXnz5jz88MNOB0VSUhJjx45lwYIFnD17lp49ezJ69Gi3lfWOHTt44403OHz4MGFh\nYVx77bWMHDnSWfHnujemTJlClSpVmDp1Kvv27QOgQ4cOjBkzhqioKJ599lkOHTpEnz59CAoK4l//\n+heDBw9m+/btvPPOOxw8eJDq1avz0EMPOT0ohbFnzx5q1arFmjVrWLRokcfryPfff09MTAw2m83j\n9SOQry/gQ3zetHhfygQMAD5weX8XMK2QskMx7ijCXObVdvxtBBwEGhe1z4rS60mrUC9SkVWoF+yZ\n8j/rEvnA+rmctqcWW4X66q9vy9uZn8qtQ/p5VKHefvvtYrFY5K+//pJatWo5vy+tQi1chZqfpKQk\neeaZZ9xuz5VAvr6IBFavJ69GViulegITgb4ikpU7X0SOOP7uB1YDbUshxoBEq1ALUtFUqNt2budb\n+4+kYaFXUDfiVZViq1D/0+n/kRAcR71Bzfn9z98LlMlVoT733HOYzWauuOIKhg0b5lyuVaiFq1Bd\nSU5OZs2aNXmOXWWjNCqKIkdWK6XaAu9iVBInXeZXVUqFOV4nAF0ohayxgYpWoRakoqlQd4clc4IU\nrg3qTC1laEeLq0INVSH0CeqBOdJMiuUMxyVv/LkqVFfdaf36F1P7aBVq4SpUV2bPnk3Xrl0LVCCV\niRKvKETECowClgI7gAUisk0p9ZxSKveB66tAFPBZvm6wlwMblVKbgVUYbRSVpqLQKtSSI9BUqLtT\n9/Pe+fm0Hn4VPVQHGquLF2hfVKhmFUHnoH8Aiq/sK9ls3+VclqtCddWdHjp0yPlaq1ALV6G68skn\nn1TquwkovVxPdoxsxgLYAETkaRHJrRD6YDxWigKygP84yvwKzAXMGNKiwl2GFRCtQi05AkWF+vO6\nX9hk286889/wx5LfSPw1nBZBjfOU9VWFGq3MRBJOPWrxq/wBwDk5j8lkon///kyaNImMjAy2b9/O\nrFmznOtpFapnFSoY9sYjR45U2t5OuZTVOIrhQKqINAFeB152rNsC41FVS+BG4B3H9ioNWoWal/Ko\nQs2SbGq2q8uodx9m6EPD6BrfgUnNxnJg9jYiLaFu1ykJFeqNQV3ppNoA8I19DV/ZfmDs/z3GWcs5\natSo4VSh5pKQkKBVqB5UqACzZs2if//+Hh8DVgZKPCmgUqozMElEbnC8fwJARF50KbPUUWatUioY\nOA4kAo+7lnUt52mf7du3l40bN3oV3+rVq7n66qsB2Gk/wFnSPK/gZw4lH6Je/XplHUahVPb4cpP1\nCYIdwY6dHKxkSw7ZZHOW82SQCUAwwTRR9bhcNaI68Sil8px/pUWGZLJT9rNd9nGedABCCKYqMYQT\nRqgKIZQQTAShCEKhUIBCcejQIerVq7zfr6+URXxtVDMiVHjRBaHA+aeU+l28SDteVuMonGVExKqU\nOgfEO+avy7dubXc7KYlxFH+3SMVSNcvzCv6mDqTYvOvZUyZU4vicT8YFlBjvlECQLYggqyLIpgjN\nNJGYEUVYRjCR50JRtgx2spWdjlX92c++NlFciA4jy2wlK9JKeqSFtOA07CbBFiyIElA4/wJI7cr7\n/ZYIZRDfuU2nCLvg3aVcG+604c5f6Ph8Q8fnGzo+3wgYw5034yhyyxx2PHqKBVK8XLcAog13fkPH\n5xs6Pt/Q8flGIBnuvDHULQZy+5sNAH5wjBJcDAxSSoUppRoCTYENpRCjRqPRaLykVAx37gx1Sqnn\nMIaLL1ZKhQOzMUZdnwEGOUZio5SaCNyDketpjIgU2c1CG+78h47PN3yJL8eeTo79ApHBRQ92LC4V\n+fj5g/IWnzbcFUJ5y8USaOj4fMOX+P5KmSc/H39F0nNOl1xA+ajIx88flLf4CETDnVKqrlJqlUNa\ntE0pNdpNmauVUudc5EVP+zNGjSYQEbFz3mqkpDifc7SMo9FUNvytQrUCD4tIC6ATMNLNYDyAn+Si\nvOg5/4aoKY+UZ8OdN2RYT2MXI0fWA/eO8yhW0oY7TUnj14pCRI6JyCbH6/MYuaDcjpOozGjDXeUx\n3OVy8OBBkpKSiIyMdGu4S3PcRYSbqmK1X/C4LW248x5PhruDBw/Su3dvqlatSo0aNRg1atQlxVmR\nKLNxFEqpBhiN2evdLO7sSAx4FHhEpKDKqyKKi8DIibNw4ULGjh3L888/T0hICBs2bGDatGlYrVav\nxEVHjhxhxIgR3HLLLcyePZvg4GC+++47rr32WqZMmeJMNjdx4kROnTrFww8/TNOmTblw4QLLly/n\n7bffpk+fPqxZs4ZXXnnFGUt6ejrTp0+nffv2vP/++0RHRxcpLrpw4QILFizAbDbz7LPPMmjQIAAG\nDRrkfD1z5kyOHDnCxIkTneutW2eMu/zqq68KiIvc7WvdunXExcWRnp7u8/d7/PjxIgU1nrDZbIXK\nlgo7/0aOHEmLFi344osvWLduHbfeeitz5sxx5kUy1dyPigom/VQEOfZMkg8dKFZ8RX1fNpstj7io\ntLkUQRUYxy8zM5PNmzcXmY6/KKxWK3v37uXIkSOsWbOGmjVr5vncuSnU58+fj8Vi4ZFHHkEp5TEH\nV6BfXwJGXOTNhJEM8Hegv5tlMUCU43VvYE9R26sojdlnz56V8PBwWbBgQaFlvBEXDR06VHr16lWg\nzIgRI6Rbt24iIrJ8+XIJDw+XQ4cOud2P3W6XevXqycsvv5xn/sqVK6Vly5by1FNPiUjR4qJZs2ZJ\nnTp15I033pCWLVt6/ZkuRVw0bNgwCQ4OlpCQEAkPD5fly5eLzWaTF198URo1aiRxcXFy++23S0pK\ninOdAQMGSPXq1SUmJka6desmW7duFRGRd99917kts9ksN910k4gULS6qXbu2vPTSS1K9enUZOnSo\niIh8/fXX0qZNG4mNjZXOnTvL5s2b3Z5/u3btktDQUElLS3PO69q1q0yfPt35fuOp92V76iI5k7lf\net3RTobff5f07t1boqKipGPHjrJ3715nWddYT58+LTfffLNER0dLhw4d5Mknn8zzfS1btkyaNWsm\nMTExMnLkSGndurVTXCRiCJ6aN28uVapUkeuvv14OHjyYZz/Tp0+XJk2aSGxsrDz44INit9vdfkfr\n16+Xdu3aSXR0tFSrVk3Gjh0rIiJ169YVQMxms5jNZvn1119l7969kpSUJHFxcRIfHy9DhgyR1NRU\nERG57rrrRCkl4eHhYjabnefn2rVrpXPnzhIbGyutW7f26v9806ZNcvXVV4uIyGOPPSZvv/12nuXN\nmzeXJUuWON8/8sgjct9993ncZiBfX0SK35hdFpVECEYK8nFelj8IJHgqU1EqCm24u0hFNtzlpyjD\nXbYtQ34+/or8bVknObYL0uuOdlKlaoysX79ecnJyZMiQIdpwVwqGuxkzZshdd90l6enpcvjwYWnZ\nsqUsWrTI7TZzCeTri0j56fWkgA+BHSLiNg2oUqqGoxxKqY4Y7Sgp/ouy7NCGu4JUNMPd9u0F9SpF\nGe7O5xhtO9EhNQkOCsekwri2Twc6duxIcHAwd955p1uznDbc+Wa46969O9u2bSMmJoY6derQvn37\nS8riXJHwd6+nLhgO7Wtcur/2VkqNUEqNcJQZAGx1tFH8H8ZgvJIfFRiAaMNdQSqa4S4lpeBvnqIM\nd0Z3WEVUiGGTCwmKJDohOPeOu1CznDbcFd9wZ7fbufHGG+nfvz/p6emcPn2a1NRUxo8fX2gcFRl/\n93r6WUSUiLSWi91fvxWRGSIyw1Fmmoi0FJE2ItJJDJlRpUAb7kqOQDPcnT17loyMDLfHrSjD3fmc\no5iDEzEpw2UREhSBnRwybWcLbMsVbbgrvuHuzJkzHDp0iFGjRjklV//+97/9cu4GIv6+o0ApdaNS\napdSaq9SqsA36cjzNN+xfL2jd1SlQBvuSo5AMdytX78eESE9PZ0lS5bkqWxy8WS4E7FjyTlGdEgt\nZ/mQoEjjc+R4zpepDXfFN9wlJCTQsGFDpk+fjtVq5ezZs8yaNYvWrVsX6/OXd/zdRlFs+11lQRvu\n8lIeDXeAswvxqFGjqFq1Kk2aNGHmzJmFli/McJdhS8Em2USHXGwrCg4KIwiTs+3CE9OmTcNisWjD\nXT68MdwtWrSI77//nsTERJo0aUJISAivv/56sT5/eadUkgIWujMf7Hee2imKa7jLsp13jnYNFNZv\n2MBVHTuWdRiFouPzjUuNLyVrD8mWH7ky/l4igi9ezLamLiDHnk7z2FvKND5/o+MrSJgpliAvjdGB\nZLjzhC/2uxKXgexLW0ZqtvtUB2VFSGPYlPJXWYdRKDo+3yhOfCEqknBT3p5tMSG1+Tv9VzalfFiS\n4VXI4+dPyiK+tvH3EBkcX3RBHyi3hjvXkdmARSm1y8tVy5uBKtDQ8flGMeMbVeKBFEIFPX5+owzi\n8779kgAy3HnCF/tdHsRFhXopVFQDlb/Q8fmGjs83dHy+EUiGO0/4Yr/TaDQaTRng18Zs8M1+Vxja\ncOcjYkesF8CWCUEhqOBICHJ/s6mPn2/o+HxDx+cbxTXc+b2iKA2K2+spEPFnfPYLJ8na/T/sZ3cD\nAsGRYDX6+QdF1yOkQV+C4/L2XtbHzzd0fL6h4/ON8tLrSRMg2FJ3krn9A0ARUu9GTAltCIqqi2Sm\nYD39B9Zjv5D119tI4wEE177a7QhajUZTOSiVNgovRl+Pc+hQtyilViql6rsss7nkgcrffqEpAXKO\nrCZzyzRUaCwRV44ntOHNmKLroZQiKCKB0LrXEdHucUzxrcje9xnZe+YhdltZh63RaMqIEq8ovBx9\n/QfQXkRaA58Dr7gsu+CSB6pvScdX2clO/pbsvQswxV9BRNtHCYpwn9xPmcIJa3kfIXWvw3rsJ7K2\nvx/QlUVFV6G6UpSBT6tQNSVNadxRdAT2ish+EckG5gF5ho+KyCoRyU16sw6jm6zGQWmpUH/84g1y\nDn5DcPVOhLW8jxx7kEcVqlJBLNsewtWjVxHf4SES4mK1CrWUKEqFeiloFar3eFKh7tixg2uuOx1/\nawAAIABJREFUuYbY2FiaNGnCF198USL7LI+URhuFN6OvXRkOuCaQCVdKbQSswEsi4jaVqlahri6w\nricV6s/ffULvIY8ye8q9VJU6cPzHS1Khvv9yNWLSN/HYe39pFWoRlIYKtaTi0yrUi3hSodpsNu6+\n+25uvvlmJk6cyObNmxkyZAjvvfdentTs7uIL5OtLwKhQMcY+fODy/i5gWiFlh2LcUYS5zKvt+NsI\nw27XuKh9VhTDXWmpULMPrxbL6gfk/93RXbp16yoixVOhZh1cImk/jJAWTWvLk08+KSJahSriHxVq\n/s/74IMPahVqKapQ//rrLzGbzXk+z3XXXec87wsjkK8vIgGkQgU6A0td3j8BPOGmXE9gB1DNw7Zm\nAgOK2mdFqShKQ4WalfydWFY/IBf+mi4rVyzzSYVqt9tl16q35PFh7aRjm0Zit+VoFaqUvgrV3WeN\ni4vTKlQHpaFCdVdR9OzZU2699Va328wlkK8vIoGlQi1y9LVSqi3wLtBXRE66zK+qlApzvE7AMOIV\ndEdWUEpShVqjRg2y939JzoHFmKp1IKzF/6NW7bo+qVCVUhzlCupc1oWU0ylkbZ2B2AvPvqtVqCWj\nQnVHv379tArVQWmoUJs1a0a1atV49dVXycnJYdmyZaxZs8atT6QyUOIVhYhYMTKYLcW4Y1ggItuU\nUs8ppXJ7Mb0KRAGf5esGezmw0aFBXYXRRlFpKoqSU6HG8/fG/5Hz9zKCa3YjrPkwVJCpxFSoJ7Oq\nkFCjDrbUHeQcWgq2bLfb0CrUklGhusMbBalWoRZfhRoSEsKXX37JkiVLqFGjBlOnTuWOO+6gTp3K\n2e+mVMZRiKE3vUxEGovIC455T4vIYsfrniJSXfJ1gxWRX0WklRga1FYiUrI5lAOcklChWk9t4uo2\n8Sxc8iOhjW8jtOkglDK+5pJUofa88VbCrhiB5GRgTz9MdvJ3iOTtPqtVqCWjQi0uWoVafBUqQOvW\nrVmzZg0pKSksXbqU/fv30zGAXRilSVkNuCtUd6qUesIxf5dS6obSiC9QKa4KNffxT+a2D8ja/gET\nH+jN+p2pTJr+A6mpqaWmQg2Ob0Voo76IKZLzu74g9ednOL/nOy6cP61VqCWkQvUFrUItvgoVYMuW\nLWRmZpKRkcGUKVM4duwYd999d7E+f3mnrAbcudWdOsoNAloCNwLvOLZXaShKhSpiQ2xZ2M7uJufv\nFWRu/4iMtcaFTqwZhDYewBV9X+bnn3/xiwpVmcJZ9+c+Em54n/juLxBzWW8iYxJ579VHuPm6q7i8\nFlSLDaZ6YhWqV6+uVaiFUJgK1Ve0CtU93qhQZ8+eTc2aNalWrRorV65k+fLlhIWFFevzl3dKPCmg\nL7pT4HHXsq7lPO2z2CrUfQuxpwWA4U4uvkhLSyMmJhpEALsxGlqsYM9BrJlGhlcXVFgcQbGNCKnR\nhaAql5V6Tqaikp7Z04+Sc+wXbKnbkYyTuHw4l8y0IRAUjFLBoJQxOX+zqDx/LpW0c2nExMYUb2U/\noOPzDR1fQcIuv4egcO8Md4GUFNAX3WltjHEVruvWdreTkhhwV5ujmAmsXgxWWxBn0rIAhWBcQO1E\nYCcKO8HkEEYOYWQTSQZVsWaGQyZw4hhQeON0SeHdgJ1EoAdB5BDJOcJJI5gsQmxZmGw5BGFDYXdM\nAo5PmqdSKSY2myL1XGB9p67o+HxDx1eQg+vWkY13qc2LO+DO79ljlVI3Ak2Bn5RS74rIS/mKdFNK\nvc5F0102Rj6oPIiL4U4pdSopKSk5f5lC0CpF39Dx+YaOzzd0fL4RMCrUQnWnLu0X64GJwDSl1BIu\n6k6PAFcC80VklOPRU5Etn+KFeCOXiqoq9Bc6Pt/Q8fmGjs83AkmF6mnAXUdgLzAfuBMjYeAELupO\nF2M8pgpSSjXEuPPYUAoxajQajcZLSsVw50F3Gopx6zMKQ3fa3bFKZ3HoTpVSnwO3YiQF/A0YIiJ/\n59tFnjaKiIiIdp4Sdblit9sJCvK3Ktx7dHy+UZHiC81JJyzHAiKIUlhN4ViDw7GaSq/nTUU6fmVB\neYtv9+7dXqlQSzzXk6cJLxIGYjRqhzle349xt1Epcj2J6Ph8pULEd3SnyIf3i7x8g8jnT4ts+0Hk\nm1dF/u92Y95m9/mU/BZfGaLj843i5nryd2N2oe0XuYiIa46DD8grNdJoKjYpf8OCCRAaCf2egaad\njfktksCaDV88B9+/CcFhxjyNxg/4+x7Jm4SBrpnq+mLki9Jo8pBrtIuOjq44RruMc7DwaTCFwJAp\nzkrCKVIKDoVbn4K6rWDJq7DbkFn5YrS7+uqrtdFOUyR+rSjEu4SB/1FKbXMkBvwPcLc/YywLXI12\nt912W4kZ7X799dc862RnZ3s02gF88803dOzYEbPZTHx8PHfeeWeeVAjff/99QBnt0tLSKobRbul3\n8OVzcP409H8GYqu7XzEkDPpPgprNYPFLcGS7NtpdAp6MdtOmTaN9+/aEhYW5TdWxcuVKmjdvTmRk\nJElJSXmy6FZ0/N7qIkUnDHxCRFqKkRgwSUR2+jtGf/Laa68xZswYJkyYwIkTJ5g/fz4PPvigMy+R\nN+zbt48uXbrQqlUrDhw4wNGjR+nXrx/XX389a9deHNQ+YMAAFi9ezNy5czl37hybN2+mXbt2rFy5\nEjBSegwZMoQxY8Zw+vRptm3bRlhYGF27diU1NdWrWNLT01m4cCGxsbHMmTPHOX/GjBlYLBYsFgsT\nJkxg4MCBzveuaSHOnj3rnG+xWBg4cKDb/SQnJ9OiRYtSH4nuDZdy0ctl8ODBtG3blpSUFF6YPJkB\nt/Xn1M4/oPcjUKuIDLlhkXDbcxCTCF9OhvMFM9JqCpKTk0NycjJNmzbNk+spl1q1avHkk09yzz33\nFFj39OnT9O/fn+eff54zZ87Qvn37Qs/NCok3DRmBPpXXxuyzZ8+K2WzOY7TLH19xjHa5jBgxQrp1\n6yYixTPaiYjYbDZp2bKlPPXUUyIiMn78+IAy2pnN5jxGu1q1agWU0S4/q1atKmi0WztPujaoItMf\n+Xehn9et0e7kfpHXbjFi3bFNRC7daNe9e/c8RrtHH300oIx2Q4cOzWO0u++++4xDVsJGO1cmTpwo\nw4YNyzPv3XffzSNtslgsEh4eLjt27MhTLpCuL+4IJHGRxkvWrl1LZmYm/fr182k7y5cv5/bbby8w\n/4477uCXX37hwoULrFixgo4dOxbq+921axeHDh0qsJ2goCBuu+02li9f7lUss2bNYvDgwQwaNIid\nO3fy+++/X/oHKoKZM2dy55138thjj2GxWOjZsydvvfUWX375JW+88QZHjx6latWqjBw50rlOr169\n2LNnDydPnuTKK6/kzjvvBOC+++7Ls62vv/7aqxiOHz/OmTNnSE5O5r333uOPP/7gnnvu4d133yUl\nJYX777+fvn37kpWVVWDdbdu20ahRI8M3sfsX+PFj2rRozrYLkYXub968eTzzzDOkpqbSpEkTwy+e\n2BB6jTMK/DoXRBg5ciTh4eEcO3aMjz76iI8++si5jdxfxZMnT+b06dM0btyYX375xbn8q6++4tNP\nP2XRokWcOnWKbt26MXjw4DxxfPPNN/z2229s2bKFBQsWsHTpUrfxjh49mtGjR5OWlsa+ffu44447\nAPjxxx+Bi3eOnTt3RkR44oknOHr0KDt27ODvv/9m0qRJgJGYr169enz99ddYLBYGDx7MkSNH6NOn\nD08++SRnzpxhypQp3HbbbZw6dcptLB9//DFVqlShS5curF27lipVqjB16lTGjx9PlSpVOHDgQKHH\nPZdt27bRpk0b53uz2Uzjxo2dmXUrOrqiKENSUlJISEgoEaOdO1tdzZo1fTLauW7HG6lPIBjtEhMT\nA8pot27dugLrOo12J/bCklegZnNiW3XnfCHSH/BgtGvuGIq0cw22VR9estHOVTw0Y8YMhgwZUimN\ndkVRHAthRUJXFGVIfHw8p0+fLgGjXYJbm1dJGe2OHTvmXO6JQDDa3XTTTQFltDt69GiBdaOiokg7\ncwo+mwjhMdDvadLSM3wz2l1+DadWfWoY7VwsbEUZ7VzfJycnM23atEpptCuK4lgIKxK6oihDOnfu\nTFhYmE9GOzAkRO6EMiVptHNnZstPIBjtvvnmm4Ay2uV/dAPQMjSN/QcOct4eCnf8F6LifDfadR1K\nYtfbCA5S/P3ZFLAbtsGijHau7+vWrcu4ceMqrdHOEy1btmTz5s3O9+np6ezbt89nC2F5we8VhS/2\nu4pGbGwszz33XB6jndVqLdJol59nnnmGX3/9lYkTJ3LmzJkSNdrde++9TqNdLiJCZmZmnilQjHa5\nF/RAMdrleTSRcY7Gh1Zy2bb/8Y8G1Xl2fxUyzYklY7RTCtP1I+nf7UomvfEuGe/dz/YVi4o02rlW\ngCNGjGDu3LmV1mhntVrJzMzEZrM5t5t7t9+vXz+2bt3KwoULyczM5LnnnqN169Y0b968WMen3OFN\ni3dJTRi5n/YBjTDyPm0GWuQr8yAww/F6EEYm2QrZ6ymXOXPmSLt27SQyMlKqVq0qvXv3ll9++UVE\nvOv1JCLy119/SZ8+fSQ6OlrMZrP06NFDfvrppzzrZGVlydNPPy2NGzeWyMhIqVevngwfPlySk5Od\nZb788ktp3769M5ZBgwbl6Sk1fvx4QyCRbxo+fLj079+/QJzr16+X0NDQPD2QPPV6yu0NkztNnTrV\n7TFz7YUkYvTOmjp1qtStW1eioqKkUaNG8sQTT4iIyPnz56Vv374SFRUl9erVk1mzZuU5frt373b2\nVrrllltEROS3336TFi1aSFRUlAwdOlQGDRpUoNdTfr777jtp3769xMbGSo0aNWTAgAGSdjZV5Phe\nke/fFJl6s5GC4/s35MDe3dKjRw8JDw+Xyy67TJYvX+72c7r7rPn37/pZTp44IX16dJbo8BDpUCdG\nnhzQXbpc2Uok/awzxqZNmxba6+mJJ56QK664QqKjo6VOnTry73//2+1+3MXlyp133imJiYliNpul\nRYsW8sUXXziXPfXUU5KQkCCxsbGydu1a2bp1q1x55ZViNpulTZs2MmXKlDyf78svv5S6detKbGys\njBgxQkRE1q1bJ927d5eqVatKQkKC9O7dO895nJ+kpCTZsGGDnD59Who1auS2zDPPPFPgvH7mmWec\ny5cvXy7NmjWT8PBw6dGjhxw4cKDANgLx+uJKcXs9lUpSwMLwxX4nHgItruGO/RvhvPueEmXFrl27\naNasWVmHUSiVKr5CTznJYyVE7MajHpsVsjMgKx0yLUY6jpRkI/WGKQRa9mSD1KZjrwElE58ncrJg\n4yJY/5kRE0BCA2Mgn7kqmKtAcLgRlykYgoIAxa49e2h2mZfHrwzGsFSq889bmnWD8CivihbXcOfv\nimIAcKOI3Ot4fxdwlYiMcimz1VHmsOP9PkeZ0/m25Wq4azdv3jyvYrBYLERFGQe11a7PiD+3z+fP\npdHkIoDNFIbVFEZGeBzpkdWwRCZyJrYROSHmPOefP1B2G9EZx6mSlkzs+cOEZZ8n1JpBSE6Gwy6o\nKe9saPX/yIjwToWa//xLSkoqMxWqXxBtuCsrdHy+oePzDR1fAdyPZSmEgDHc5epO38Rok/hALupO\njwB1lVLjgHuBqkC6Uqq+iORe6FsCPyilMjC82rn2u0IRbbjzGzo+39Dx+YaOzzcCxnDnojvtBbQA\nBiulWjgW/4ZhrTsGdAZOAnPJm0o8G8NB8Q/gUy7a7zQajUZTBpR4G0VRDdb57XfAt8BXwCgRWayU\nsgDfAW2BM8AgcdjvCiMhIUFyB1EVRXp6OmazuRifzD/o+HyjTOPLugAZ6ZCZYUyC0UgcZIKISIiK\nId0mmP3YRnGp6O/XN8pbfL///rtXhrvSePRUG+ORUS6HMTzYgJE9FqNyAEApNQ14TxzZY4FwoCHG\nc7SXiqokwEhDXKxeTwGIjs83/B6fCPy2BuZNh+2bgBCo2QpaXAmhYZBhgbRU2PY7ZGeRZY4lrP8w\n6H8PRATeBUV/v75R3uJTSnnVtlsadxRF9mxyKTsUw0/RQ0SyHPNqi8gRpVQj4AfgWhEp0DWpJHo9\nBSI6Pt/wZ3wxR/bRdNlcok8cIjMmjr87Xs+p5u3IjqpSoKwpO5P4vVuI3/IL1Q9uJ8scy8FufTne\nugsSZPJLvN6gv1/fKG/xedvrqTQG1XUGlrq8fwJ4wk25nhjyomoetjUTGFDUPsv7gDtXdHzecfz4\ncenWrZtERUXJuHHjnPP9El/6eZG3nxW5sanI0G4i3y8Qyc7yatVVq1aJbNskMvYOkRuaiIy8ReTA\nLo/reBrYJiJiNptl3759bpd9/PHHHtPC9+jRI8+Au0D5fgtDx+cbgZRm3BvdaVvgXaCviJx0mV9V\nKRXmeJ0AdAG2l0KMAYU23JUjw92mX+D+3vD1HOh7F7z7LdxwO4SEer/DFm05+NBLJJ2IIHLG1zS/\nohUrJo42BuwVA224857iGu6ys7MZMGAADRo0QCnF6tWrSySe8kKJVxTine70VSAK+Ewp9adSKrci\nuRzY6NCgrsJoo6jQFYU23JUTw112Frz7Aky4G8Ij4LX58MBTEBlVPMPdkCG0TepJyt/JvHDzNQx4\nZRqnHugHRw6WeOgaA18MdwBdu3Zlzpw5eTLoVhq8ue0I9Km8PnrShruLBLThbs9WGXZZbZnYqKrI\n28/KqqVLS9ZwZ7dL11YtZHrbuiJ9W4ks+Z+IizmuUMOdA9dYteGucHwx3LlSu3btQvcXSNcXdxT3\n0VOZX+RLYiqvFcV3330nJpMpz8WxOBVF9erV5aOPPipQ5ocffpCgoCDJyMiQ8ePHS/fu3QuNZceO\nHQLI/v37Cyx7+umnpVOnTiJSdEVxzTXXyKOPPirHjx8Xk8kkGzduLFDG14pCpOBz+zfeeEOuuuoq\nWbBggWRmZsp9990ngwYNci7/8MMPJS0tTTIzM2X06NHSpk2bQrcl4ji+27eJfPKGSO/mMqxhoky8\n5y4RMb4jk8kkjz32mGRmZkpGRoZs2rRJEhMTZd26dWK1WmXmzJlSv359yczMzLPdVatWyaJFi6R5\n8+Z55o8cOVJGDf+3yPh/GW0XTw4XOXHEGV9cXJysX79ecnJyZMiQITJw4MC8sTrOhYEDB8rtt98u\nFotF/vrrL6lVq5bz+zp16pRERUXJZ599JtnZ2fLaa6+JyWRyVhRffvml1KpVS7Zv3y45OTny/PPP\n59F/AtKnTx9JTU2V5ORkSUhIkO+++87t99OpUyf55JNPRMRIyrh27VoRcf8979mzR5YtWyaZmZly\n8uRJ6datm4wePdq5vH79+s6kiatWrZLDhw9LXFycLFmyRGw2myxbtkzi4uLk5MmTbmP56KOPJDY2\nViIiIiQsLExiY2PFZDJJVFSUxMbGFjjndUXhnzYKjZdow11BAspw9/wo+HQaXH0TdO4JNes5F5WI\n4c6F2NhYzlvt8N+PYcRE2LLBaAv56hMQKdxw54LNZtOGOzeUhOGusqMrijJEG+4KUuaGu1PH4OWH\njdfnz8KkGfDoqwUaq3023BVmSwsKglvvhneXGGMxpj8PG1ZTg4vnSGFmuVOnThmGOxdrnTbclYzh\nrrKjK4oyRBvuSg6fDXeWNHjvRbj3evj5eyJDQ8l4ajp0Mj53iRruWrZk//79eaRGBQx3NerC5A9h\n/FTIzoRVi+HxYcagPnE/9ikxMZHg4OA81jptuCsZw11lR1cUZYg23JUcxTLc5WTDxp+ovm8L+xfM\nhC9nQZcb4INl/KN9e+Yu+qJkDXcOLrvsMv7xj3/w7LPPkpmZWbjhTilI6gtdrocru8CBnTBuILwx\nwUgRYsl7V2Iymejfvz+TJk0iIyOD7du3a8OdA18NdwBZWVlkZmYCRnfZzMzMPBVahcabhoxLnYAb\ngV3AXuBxN8vDgPmO5euBBi7LnnDM3wXc4M3+ymtjdi7acOdHw13tWjLrkVHG8bu+hcgNTWT39ZdL\nm7o1JTYmpuQNd7k9mxzknn8HDhy4dMNdhkXkm09l1S3/lNphJpE+l4s8eqfxWZYuFsm8ICdPnnSe\nB+56PWnDXfENd/Xr1y+wPL/lLhCvL64EjOHOkT12N3AdRp6n34DB4jIeQin1INBaREYopQYB/URk\noCPL7P+AjkAtYAVwmYjYPO2z2IY7m9WDxaxsWLNmDT169CjrMAqlROMr7Njnny/imOf4a7cbf21W\nsFodZrksyM5k09pfubJZU6N9Ie0spJyAE0fgxGFI3gsX0o1txlSFTtfAP6+Dtl0gLLxAGKVBieUC\n2rMV1iyBP36BfY4G/6AgqFkf6jeBxJoQXw3iqoE5BsxREBll5J8KDTPaXEzBYDIZSQuVAqX48eef\n6d7d8f3mf0zkacyKn8azVKr/D28xBXt9/ItruCuNpIAdgb3iSOanlJoH3ELeEda3AJMcrz8Hpinj\nQeQtwDwx8j4dUErtdWxvLaXBpBFGQrcAogcYwxEDlECP78r8M4JDoFotqF4bevaDy1oZU51GxkWy\nvNL0CmMCSD0NW3+Dg3vg4C74ex/8udZISHiJdAfwbaB7qRLo51+ZxPf+91C3canuwu/ZY/OXERGr\nUuocEO+Yvy7furXd7cQ1KSBgUUrt8jI+bcjyjXIYn3ddbP1EOTx+AYWOLz/1mlxK6cAx3HnCYb9r\nCvyklHpXLtrvcumllJoAWDE+1G/utiMuKtRL3H+FNFD5Cx2fb+j4fEPH5xsBY7jDoTt1eV/HMc/V\nfrce+BeG/a4VF3WnR4AMoL2ItAbOAgNKIUaNRqPReElpNGYHYzRmX4tx4f8NGCJGYsDOGG0Ti4FW\nQDLQGjCJyB1KqZYYatTcxuyfgGQR6eJpn9pw5z90fL6RJ77sbMjMhKws47WIw4gXBKGhEBkJ4f5p\nZHcbXwCi4/ONgDHcOdoccrPHmoCPHJXEc0AoRtvEh8BsoJ9jtc6OdbcppRZgNHxbgU3ABnf7yScu\nYsqUKV7FV97EIoGGjs8HbDYifvqJOps3U/X334l0HfwWFIQ9NBSTo59+LlazmXNXXMHJq6/mdNeu\n2Er5swX08UPH5ytuxEVeGe78mrwP4zHSBy7v7wKmFVJ2KEbDdlhR2y3v4yhc0fH5RkDGl5ws8vTT\nInXqGB19IyNFevUSef11kZ9+Ejl0SCQ3SZ7NJpKWJrJ5s8gHH4jcf79I/frGemFhIgMGGOsUkrXV\nVwLy+Lmg4/ON4o6j8HdjdqHtF64opXoCE3FRpGo05Y4dO+DFF2HuXGPsx/XXs/Xee7ni8cchLMz9\nOkFBEB0NrVsb0/DhxiOp9eth3jyYPRs+/xw6doSHH4YBA4x1NJpSxN9nWLHtdxpNuWHbNrj9dmjZ\nEhYuhP/8B/bvh++/53SPHoVXEoWhFHTqBG+8AYcOwTvvQGoqDBxoVCaff25URBpNKeHXikJ8s99p\nNIHN3r0wdCi0agVLl8KECZCcDK+9Bl52tigSsxkeeMC4W5k3D2w2o1Jq2xa+/jrgMg1oKgZ+v2cV\nkW9F5DIRaSwiLzjmPS0iix2ve4pIdRH5h2Pq63mLGk0Zc/gw3H8/XH45LFoEjz4KBw7A5MngRXr2\nYmEyGXcUW7fCnDmQng59+0KXLlDJfM6a0kc/3NRoisvx4zBuHDRpAh9/bFQW+/bByy9DfLx/YjCZ\n4M47jTuMGTOMO5ikJLj2WvjlF//EoKnw6IpCo7lUDh822h0aNoQ334TBg2H3bpg2DTxYBEuVkBCj\notq7F6ZONe40unaF66+HVav0IymNT+iKQqPxlo0b4V//gkaNYPp0GDIEdu407iZKqg3CVyIijLuc\n/fvh1Vfhzz/hmmuMXlLz58Ml2AY1mlx0RaHReOLsWfjwQ/jnP6FDB/jiC+OX+549xvymTcs6QveY\nzfDII8ajqBkz4Nw5GDQI6taFxx837jw0Gi/RFYVGk5/Tp+HTT40xCjVqwL33QkqK0T318GF4663A\nuYMoiogIo2LbsQMWL4arroIpU4wKrkMHY5zHzp1lHaUmwCmr7LFvYqT3+EDyZY9VSoUBnwDtMBIF\nDhSRg/6OU1OJOHzYGNC2fj2sWQO//WY8069WzbjIDh0K7dv7Tc5TKphMcPPNxnT0qNFTauFCowvv\nhAlQrx50707NGjUgLg6aNzfyTWk0+LmicMke67TfKaUWi4v9DhgOpIpIE4f97mVgoD/j1FQgsrLg\nzBljOn7cqBQOHzae4e/cCbt2GXcLYFwY27eHZ5+FG2+Edu0q5qjnWrXgsceM6fBh405j1SpYupRm\np04ZdxwhIUZ33+bNjUb7hg2hTh2j8qxWzejVZTaX78pT4zX+vqMotv3OkZekZMlt7AsgLj9xAt5/\nv6zDKJRixefNV+daJvd1rgI1d7LbjclmM/5arRen7GzIyqLDmTPGxctiMaZ8SfacVKtmXAhvu80Y\nQd2pE7Rpc+mjpss7derAgw8akwgbZs+mY0gIbN5sTJs2Ge0y7hrBg4IgJgaiooxHXBERRrbb0FCj\nogkJMe5kcieljHUc2tU8Uy6FvXZQIf8/fOXVV43KvxQp8TTjHnem1ADgRhG51/H+LuAqERnlUmar\no8xhx/t9jjKn823LNXtsu3nz5nkVg2v2xMumTKFKgFUUYrejAvhXbLHj8+aXp5sy4nIxyX0tjouO\nmEzG5Mi8ag8NJVspgsxmbBER2MLDsUZFYY2JIScmhpwqVchMTCQ7IQF7GVUI5S27KAA2G2EpKYSe\nPk3o2bOEpqYSfP48powMgi0WTBcuEJSdjSkri6DsbJTVirJaCbJawW5H2e0om0N7L4LKTTcigvLW\nm54722armP8fPrDl5ZfJrO1WBFoAN9ljy8yZ7RfExXCnlDrldbpcrVL0FR2fb+j4fEPHl5+hQy+l\ndLlQoXqTPTa3zGGHBCnXflco4oV4I5eKqir0Fzo+39Dx+YaOzzcCSYXqiSKzxzreD3MVLMYMAAAE\nA0lEQVS8HgD8UCrtExqNRqPxCr/eUYhn+91GR2LAD4HZSqm9wBmMykSj0Wg0ZYTf2yhE5Fvg23zz\nnnZ5nQncXoohvFeK2y4JdHy+oePzDR2fb1TI+Pza60mj0Wg05Y/A7Wem0Wg0moBAVxQajUaj8Uil\nqCiUUq8qpXYqpbYopb5QSlVxzG+glLrgUK7+qZSaEUjxOZY9oZTaq5TapZS6oYziu10ptU0pZVdK\ntXeZHyjHz218jmVlfvzyxTNJKXXE5Zj1LuuYwMjB5jhGe5VSj5d1PPlRSh1USv3lOGYbyzoeAKXU\nR0qpk45Bwrnz4pRSy5VSexx/qwZYfMU7/0Skwk/A9UCw4/XLwMuO1w2ArQEcXwtgMxAGNAT2AaYy\niO9yoBmwGmjvMj9Qjl9h8QXE8csX6yTgkbI+ZvliMjmOTSMg1HHMWpR1XPliPAgklHUc+WLqDlzp\n+j8AvAI87nj9eO7/cgDFV6zzr1LcUYjIMhGxOt6uwxjoFzB4iO8WYJ6IZInIAWAvRr4sf8e3Q0R2\n+Xu/3uIhvoA4fuUAZw42EckGcnOwaTwgIj9idOF35RZgluP1LOBWvwblQiHxFYtKUVHk4x7gO5f3\nDZVSfyil1iilupVVUC64xlcb+Ntl2WHHvEAi0I6fK4F6/EY5HjN+VJaPJlwI1OPkigDLlFK/O/K8\nBSrVReSY4/VxoHpZBlMIl3z+ldtcT/lRSq0AarhZNFFEvnKUmQhYgU8dy44B9UQkRSnVDvhSKdVS\nRNICJD6/4U18bgio4xcoeIoVmA48j3Hhex6YivHjQOOZriJyRClVDViulNrp+MUcsIiIKKUCbfxB\nsc6/ClNRiEhPT8uVUncDNwHXiuNhnYhkAVmO1787MtVeBpR4Y1lx4sO73Fh+ia+QdQLm+BWC346f\nK97GqpR6H/imlMPxhjI5TpeCiBxx/D2plPoC43FZIFYUJ5RSNUXkmFKqJnCyrANyRURO5L6+lPOv\nUjx6UoZV7zGgr4hkuMxPVIZMCaVUI6ApsD9Q4sPIezVIKRWmlGroiG+Dv+MrjEA5fh4IuOPnuHjk\n0g/YWlhZP+JNDrYyQyllVkpF577G6PwRCMfNHa656oYBgXa3W7zzr6x7Dvip9X8vxjPYPx3TDMf8\n24BtjnmbgJsDKT7HsokYPVJ2Ab3KKL5+GM+ts4ATwNIAO35u4wuU45cv1tnAX8AWjItKzbKOyRFX\nb2C341hNLOt48sXWCKMn1mbH+RYQ8QH/w3j8muM4/4YD8cBKYA+wAogLsPiKdf7pFB4ajUaj8Uil\nePSk0Wg0muKjKwqNRqPReERXFBqNRqPxiK4oNBqNRuMRXVFoNBqNxiO6otBoNBqNR3RFodFoNBqP\n/H8DFjxGCJbKrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed3e6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gEJEcYBSwAfgDiBGRw0qpN5RSvU3R3gH8gJVKqf1KqWrV40l3uCtbh7vKwNEc\n7r5dLSTEw1PPu+DhYf389BmgqBsGx/4QsrMda2xVeVKUw52vry9r167lypUrLF68mLFjxxZ62ao2\n2ONu5OiL7nCnO9zZcrhr2LChBAUFSd++fSUxMdG8T3VxuDt1MlUi6j0h3l7FO9x17x4l9UKjpMc/\nJ5nDdYe76zz44IPy7rvvFpuuNaq6w12lP+TLYnGWgmLdunXi6upa5MPRnoKiVq1asmjRokJx/vvf\n/4qLi4usX79eJk6cKJ06dbJ5nD/++EMAOXXqVKGw1157Tdq3by8ixRcU9957r0yYMEEuXLggrq6u\nsnfvXrs0laSgELn+4M67du+//760a9dOzp49KxkZGfL0009L//79zfE/++wzuXr1qmRkZMjYsWOl\nRYsWhdKypLiCwtXVVV566SXJyMiQtLQ0+fXXX6VmzZryyy+/SE5OjkRHR0t4eLhkZGQUqcPegsLT\n01O+//57ycnJkZdfflnatWtnjpdXUBiNRul45wSpGXyXHP/zksTFxUnTpk3NBUVmZqbUr19fZs+e\nLVlZWbJy5UpxdXGTWxq+Ivt2G4vVEB4eLm3atJFz585JYmKi/OMf/5BPPvnEat779+8v06ZNk9zc\nXElPT5eff/4537ldunSpef3SpUuyatUqSU1NlatXr0qfPn3koYceMod37txZFixYYF5PSUmRevXq\nyaJFiyQ7O1t+/fVXCQ4OlsOHD1vNy6ZNmyQgIEB8fX3F3d1dAgICxN3dXXx8fCQgIEC2bNlSaJ+0\ntDQJDQ2VdevWWU2zOKp6QeFws8dWZ3SHu8LcqMNdvXr1zC52q1atMlcLVQeHux9/EPb9tornn51E\n4ybB9jnctW1DQADMnW1kzpz5usOdiZEjR9KiRQv++c9/2syHM6MXFA6E7nBXmBt1uMsrYG69VXO4\nu3jxIrm5zu9wd/K4sHCukJWVwCN965u3F+dwFxERTpsOipQU2P6z7nAHMGHCBA4dOkRMTIxDtIFV\nBnpB4UDoDndlR1hYGOvWrctXyGRkZFC3bl2WLVvGt986r8Ndbi6sXGakXn2oW682CQnXr7E9DneG\nQMWAJxSZ6WE89vAkLl++XG0d7qZMmcK6dev48ccfqVGjRol1OwsVXlAU516nlPJUSq0whe9SSkVU\ndB4rC93hruwYOXIkkydPJjZWG3ia53AHmoOap6dzOtzFnxWuXAY3N3jldRf69Sudw92Djyp6dB/B\n6v/M58X+v61yAAAgAElEQVQxv5CWZqx2DndvvfUWy5YtY9OmTfmMuqol9jRklNWCNmPsSaAh4AEc\nACILxHkOmGf63R9YUVy6ztKYncfSpUulVatW4uPjI7Vq1ZKePXvK9u3bRcS+xmwRkd9//1169eol\n/v7+4uvrK507dzY3IObpy8zMlNdee00aNWokPj4+Ur9+fRkxYoTExsaa0/nmm2+kdevW4uPjI4GB\ngdK/f/98PaU+//xzAQotI0aMkEcffbRQPnft2iUeHh75eiAV1Zjt6+ubb5k1a5bVc1awMTs3N1dm\nzZolN998s/j5+UnDhg3llVdeERGRa9euSe/evcXPz0/q168vixcvznf+/vzzT3NPn7xG1D179khk\nZKT4+fnJoEGDpH///oV6PRVk3bp10rp1awkICJDQ0FDp06ePXL161Wb+C57Dzz//PF8cy8Zsy/OV\nd67em5EpfXrkiK9PuHz+2Y8iIpKamiqDBw+WgIAAq72e9uzZI7fffrv4+flJVFSUREVFmXXl5Bjl\nlQnfS2CN1uLhESAhwaHy6KPXNVj2rrJ1HfOYMGGC1KlTR3x9faVhw4Yyf/58c9gnn3wiQUFBEhAQ\nICtWrJBz585J586dxdfXV5o0aSLz5s3L17Fhx44d0qRJEzEYDDJ69GgRETl69Kj07NlTQkJCJCgo\nSLp06SK//fab1byIiAwbNkxiYmLEaDTKTTfdJFlZWYXiAOLh4ZHv/ps+fbrNNIuisp8ptsDOxmyH\nmxRQKbXBFGenUsoNba6nmlJERkvrcPfrHuHS34WT/fPPP7n55ptLnF5VwZn1OaU20UqOP48dp1Hj\nJuRkQ3Y2pKbA+QTh/Dk4d1b7iuj+oOLhvooAQ9nVpf9+QHh/hpHky+DuDjf/A+o3UPj4gI8veHiA\nUqBcTH8td7YzG0553SwoT313dVL4+pXuetvrcFfRBUWxpkRKqUOmOPGm9ZOmOJcKpGU5KWCr5cuX\nlzg/a1Y2JfZkUGnl6OhUKi6uRgIMGRgC0wm5KZXbWp7Hzz+rXI6VlenKubgA4uMCSDgbwJXLXmRl\nuSFSPRt3HYmBT+0lKDi9VPt26dKlylqh2oVYTAqolPrb3lkQ7cRR3ajKCmfWp2urmjizNihHfV9v\nuKHd7XLbruiCwp5JAfPixJuqngKAxKISFd3hrkQ4sz5dW9XEmbVB1dfncJMCmtaHmH73Af5bVPuE\njo6Ojk75UqFtFJDPvc4VWCQi05VSb6C1vq9RSnkBS4CWQBLQX0RO2U5Rd7grKeWh768UIdsIdWtU\nbp21M187XVvVxVH12etwV+EFRXlQ2l5PtqjqJiPFUR767pmXzl8pwt4x3vjYmKG0InDma6drq7o4\nqj57ez054oC7oUqpv01TjO9XSj1Z0XnUKRkXrhk5d1X7otgTb6zs7Ojo6JQxFVpQKKVcgblADyAS\nGKCUirQSdYWI3G5aysahRKfc+C3heuGw/UzJRxOXBbrD3XWsOdzlsWXLFurVq2dzX93hTscaFf1F\n0RY4ISKnRCQLWA48VMF5cHiqmsPds3064+kGbcNc2GaloNAd7oqnPB3uHB1Hdbh76aWXCAsLo0aN\nGoSHh/Pmm2+WyTGrIhVdUNQFzlqsx5u2FeQxpdRBpdQqpVSYlXCnpSo63KVkCs1CXbinoSvHLwkX\nr13/wtAd7uyjPB3udGxTlMPdiBEjOHr0KFevXmXHjh18+eWXfP3115WU08rFEQfcrQW+EpFMpdQz\nwGLg3oKRCozMtvmpXRpSUlLKNL2SHHfy5MlMnDiRoKAg9uzZA4C/vz+9evViy5YtnDlzhosXL1rN\n365du4iPj+fNN9/klltu4f777+fgwYMANG/enPvuu4+RI0cyffp0Zs2axYYNG1iyZAmpqanmL5am\nTZsCsHnzZkaNGsWAAQOoU6cOu3btAmDQoEFs3ryZsWPHMnz4cA4fOUpathCSG4/npSTgNj5bf4Q7\na2pjizZs2IC3tzdRUVF8/PHHtGnTplC+rWnKm51169atuLq6FnneZsyYwaZNm1BKMWvWLKZNm0bL\nli1Zvnw533//PSkpKbRs2ZLx48ebZwCdOnUqBw8eJCsri0aNGjFu3DgaNGjA2rVrWbp0qTmtli1b\n8uabb9KlSxeWLl1K3bp1zcesWbMmI0aMYP/+/UyfPp1HH32UlStX0rp1ayZNmsTOnTv57LPPuHDh\nAhEREbzwwgs0atTIqoa86b/T0tI4c+aM1eubd1+eOXOG+Ph4unXrxrZt27jpppt45ZVXuOWWWwDo\n378/EyZMoFWrVmRmZvLee++xfft2goOD6d69O5mZmeb0jx8/zjvvvEN8fDzt2rVDKUVubq45vCgN\n/fv355FHHuHHH3/k4sWLtGnThldeeQUPD49CeT937hwzZ87k5MmTuLq6cscddzBlyhTGjh0LaA/l\nJ598kgkTJtCmTRvefPNN/vjjD3Jzc7ntttsYP348NWvWZOHChfz888/s2LGD0aNH0717d8aOHUtc\nXBwffvghf/75JwaDgWHDhtGlS5ci75tr166Rnp7OwYMH+fbbbwkJCSl03vO+gv/++2/S09PZsGED\nQUEln82hsp4pZYY9E0KV1QJ0ADZYrL8CvFJEfFfgSnHpOsukgFXR4W7KrM/EK6KDbPozW3KNRmn3\nUaqMX3vdxU13uKs8hzsRkYkTJ8rdd98tiYmJdjncubm5mXXpDncib731lvj6+gogDRo0MFuylpSq\nPimgww24U0pZWqr1BuyzNHMCqqLDXexlrXv17XVdcVGKO8Nd2X4mF6OI7nBXyQ53oN0rkydPJigo\nyD6HO4svPns0OLvD3csvv8y1a9f49ddfGTx4MAEBATbz4cxUaEEhIjnAKGADWgEQIyKHlVJvKKV6\nm6KNUUodVkodAMYAQysyj5VJVXS4i0024ukKwT5a28BdEa4kpsGxv0V3uKtEh7s8EhISCAu73sxX\nnMOdZbg9GqqDw51SipYtW+Lt7c2UKVNs5tuZqfBxFCLyg4jcLCKNRGS6adtrIrLG9PsVEWkqIi1E\npIuIHK3oPFYWVc3hTkSIvWzEz/N6+F0R2i21/Uyu7nBXSQ53ltSuXZuzZ6/3H7HH4S6PstRQVR3u\nLMnJyeHkyZMl1u4M6FaoDkRVc7iLSxZSssDXHbOzncE9iwY1MlmxbrvucFcJDncFiYoqncNdaTQU\nRVVzuDMajcyfP5/Lly8jIuzevZu5c+faZQHsjDjiyOxqa4UK8OKLLzJ79mymTZtGzZo1CQsLY86c\nOTz88MN2p9GkSRO2bdvGgQMHiIiIoHbt2qxevZoNGzZw1113meOtWrWKnj170q9fPwICArjtttvY\nu3cvXbt2BaBfv34sWbKE9957j+DgYCIjI0lPTzf3oMkbaPfngZ14e3ubl43PBrH7+2jC2zxIo1tu\nM39RhIaGMnbsWL777juSkpLs0mIwGPKNoyjqjc+SsWPH0rt3b7p164a/vz/t27c399x64oknCA8P\np27dukRGRtK+fft8+44YMYIjR45gMBjM5/2DDz5g7dq15mqN4q5H69atWbBgAaNGjSIwMJDGjRsT\nHR1tM/5TTz2Ft7c3X331FdOnT8fb25slS5bYpbUopkyZQnh4OA0aNKBbt24MHjzYHObh4cHXX39N\ndHQ0QUFBrFixgkcffbTUGopiz549tGvXDj8/P3r37s0HH3xAw4YNAa0H2owZMzAYDMTExDBu3DjS\n09MJCQmhffv2dO/ePV9aY8eOZdWqVQQGBjJmzBj8/f358ccfWb58OXXq1CE0NJSJEyeSmZlpMz95\nBYWIcPToUXNvP0v+85//0KhRI/z9/Rk0aBCjR49m9OjRpdJf1alo4yJX4E/gfrQxFHuAASJyxCLO\nc0BzERmplOoPPCIi1jvPmyjtXE/ZuYI19f/b+j86de5U4vSqCjeiTwSuZcLFFOHjndnsOJPL3jHe\nuLooizjC53tzmLE5m8hairkPe1KzlA5cJcWZr52urepSnvrcXaxXl9qDozrcOZQV6pOrMth6Sp+b\n6Ea4t5Er8x/ztBr23xO5jF+bSar9bdc6OjolZP0ILxoFl65yyN6CoqIH3Fkbmd3OVhwRyVFKXQGC\nKeAOZTngDkhRSh0rw3zqblt2cgKTzaDj4MzXTtdWdSk3fY0n3tDuDulwV2aIhRVqWVPV3aiKw5n1\n6dqqJs6sDaq+vopuzC6JFSr2WqHq6Ojo6JQfFd1G4YbWmH0fWoGwB3hcRA5bxHkeaGbRmP2oiEQV\nla7ucFcyHEFfSq6QkisEuik8XcquodsRtJUXuraqi6Pqs9fhrkKrnkxtDnkjs/OsUA9bWqECnwFL\nlFInMFmhFpduREQEusOd/VSWPhFhQ1IW78Sl8sdVrYX7MtAtyIPR9Xy4N9B6o3hJcOZrp2urujiq\nPqVUrD3xKryNQkR+AH4osO01i98ZQN+KzpdO+SIijD1+jc/OpxPm6cJ7jf35Z7AnX15IZ0FCOg8e\nTObdxv48W9ensrOqo6NTgCrbmK1TtZgRm8pn59MZU8+HNxr44W6qbpoU4ceL9X0ZcuQKE05cI8Td\nhb43eRWTmo6OTkXiiCOzOymlflVK5Sil+lR0/nTKnujzaUyLTWVgLS/ebHi9kMjD00URHRnAXQHu\nPHX0Cj8l2R5RawvdCvU6uhWqTlnjiJ7ZcWgzxi6ryLw5ElXNCrWoKaPXJ2by1LBhpN9Xl3/7p5pH\nkBa0QvX39GD73fW51r0RPXr25IdDx3Ur1FKiW6HaT1FWqHkkJSVRs2bNIu9zZ8fhPLNF5IyIHASq\n5ZDpqmiFaosjqTk88WsCxp+/xxAQwIplX5rDbFmhxl++QsT7yxl1/CqgW6HqlC9FWaHmMXHiRLun\nt3dWHHFktl3oVqiF81cZVqhHjx7lypUrhfJzFVdeIILs/64h0NeX/lF97bZCnYAXL2Zq7zCbtm7F\nS7dCBXQr1MqwQj106BA7duzggQce4Icffij1c0G3Qi2ZFWofYKHF+mBgjo240UAfe9LVrVArzwr1\n888/l7vuuitfeFauUXrsTxLD1gvSutM9pbJCnbPnqADy7OFEMRqNNvOZh26FqluhlrUVak5OjrRs\n2VL27t1r9T4vCboVasmwZ2R2taUqWqEWJEeE5/68ytbkLKb4XGHfz1tLZYXaK0QbU/FJ2wZ4BwTq\nVqgF0K1Qr1NeVqgffvgh7dq1o1WrVjaPXV1wOM/s6kxVtEK1JC1X6H8omWUXM3g1wpfUDStv2Ar1\nmV2ncF17jKF74ki8fFm3QjWhW6FepzysUBMSEvjwww+ZPn26zXxWJxzOM1sp1UYpFY826G6+Uuqw\n7RSdi6pmhWpJYraRBw5eZn1SFh808eflcL8ysUL96OYavBDmw4KEdIb/cYUMo31TzuhWqBq6FWph\n7LFC3b17N+fPnycyMtJsuLV7925CQ0PLxHmwqlEZVqhGQExLLuT3zAYOAtuB82izWFebbiBVzQoV\nINMonMvIpeW2eH67dI3PG3oyKMiFnTt3lokVqlKKaQ39mdbQj1V/Z9Ji9yWiz6eRU8wcZboVqoZu\nhWqd4qxQe/TowZkzZ8z37htvvEHLli3Zv38/rsV0rnBGHHEcxQjgsog0Bt4D3q7IPFY2VcEK9T+b\n/8dO8eXVU9eYdPIaZ/b9wtl7w0nuFkFU/UC8vb357LPPeOihh2jWrFmZWKG+emstjL0akRMzn+f/\nvEarPYlMO5PCxqRMknMK96TWrVA1dCtU6xRnherp6Znvvg0ICMDd3d3mWAtnp1o73M2OS+VgauF6\n3b8uXuSmWrVKnF5VwZa+vFMsgFEgRyBbhGyBaznC5RwjSdlGEnO0eG4Kuhg8eCXcl3YBhbtElgci\nwrrELGbGpbLvWjZGQAHB7ooQdxdcU69RO8iAuwIPF4Wr0sKtja5whDEXJcGZ70tn1gblq++thn7U\n9izdV061crgr7TiKbYTyO4UnoRPx5PjF0veAcXSK0qcsFlcEV9NfH3IJxUgTcqlDFreQTiPJwDNJ\nSE+CLRWXfXyAqUAaLvyJF0fx5lKWO1ezXEnOhbNJV8hBkQPkWhQRlm8aFfd6VHY4833pzNqgfPVt\nuXiI2pSv33CVnRRQLBzulFJ/d+nSxa7pcu1Et2WsuujaqibOrA3KUd/jN7a7Q1qhngNuN/lbu6I1\nVhdsFRTgd4t50m+iGIc7scN4oyRUddvC4nBmfbq2qokza4Oqr6+iC4p9QAs0h7t9aCXs3AJxfkNr\nO7ndwuGuKtYU6Ojo6DgFldGYPQfw5/oXxRbAG5PDnVLqKWCiaZckoL+InLKSnBndCrVkOLM+XZtj\nc01yScjJpqGbJ+4WnQmcQVtROKo+h7RCRWuo/k1EngRQSg0G2onIKIs42YAv8DfalONWW2kKNma/\n++67ZZbJlJQU/Pz8yiw9R8OZ9enaHJs1tfzZFeTDYwlXuONKhnm7M2grCkfVZ2/briM2Zq8FvhKR\nTKXUM8Bi4N6CkSwbs1u3bi1lOf++o/rblhXOrE/X5th8kXgacjLIaRTOPTWuzyPmDNqKoqrrc7hJ\nAUUkUUTyRsosBPQZuXSKRXe4u46jOtxliJETOdpXxOHs9HI5hk754HCTAiqlLKcr7Y02J1S1wpkc\n7kB7+Li5ueWbYLCgw527u7t5PW/6BN3hrnQ4qsPd0ewMcoFb3Lw4lZNJqlGbosRRHe6GDh2Kh4dH\nvvuvOs7zBA44KSAwRil1WCl1ABiDZotabXAmhzvQGvFWr15NQEAAS5cuNW+35XCXkpLCunXrzPF0\nhzvn4VC2NqliP58gjMDRnIyid6gAinO4e+mll/Ldf9VxniegYo2LymtxFuOi5ORk8fX1lZiYGJtx\n7DEuGjRokPTo0aNQnJEjR0rHjh1l8+bNsnHjRvHy8pK4uDirxzEajVK/fn15++23823Pzc2Vpk2b\nyquvvioi1o2LLFm8eLHUq1dP3n//fWnatKndmk6fPi1AkSZOeQwZMkTc3NzE3d1dvLy8ZOPGjZKb\nmytvvfWWNGzYUIKCgqRv376SmJho3qdPnz5Sq1YtqVGjhnTs2FEOHTokIiLz5883p+Xr6ysPPPCA\niBRvXFS3bl2ZMWOG1KpVSwYNGiQiImvXrpUWLVpIQECAdOjQQQ4cOFCsFnuNi/r27SuDBw8WPz8/\niYyMlD179pjjWRoXpaWlyZAhQ8RgMMitt94qM2fONBsXiWjmRC1bthQ/Pz+JioqSfv365TNtKkpD\neHi4vPPOO9KsWTOpUaOGREVFSXp6utW8Hz9+XMLubCfu/n4SFBwswb27S/S1v6Vjx44CiJeXl/j6\n+sry5cslKSlJevXqJSEhIWIwGKRXr15y9uxZERGZNGmSuLi4iKenp/j6+srzzz8vIprRVteuXSUw\nMFBuvvlmWbFiRbHnOikpSRo0aCAiIh9//LFMmDAhX7g1A6vSohsX6ZQZO3fuJCMjg0ceeeSG0tm4\ncSN9+/YttD0qKort27eTmZnJpk2baNu2bT6vAkuOHTtGXFxcoXRcXFx47LHH2Lhxo115Wbx4MQMG\nDKB///4cPXqUffv2lVxQMURHRzNw4EBeeukl1q1bR9euXfnoo4/45ptv2Lp1KwkJCQQGBvL888+b\n9+nRowfHjx/nr7/+4o477mDgwIEAPP300+a0UlJSWLt2rV15uHDhAklJScTGxvLpp5/y22+/MXz4\ncObPn09iYiLPPPMMvXv3LnKiupKwZs0a+vfvT3JyMr1792bUqFFW473++uucPHmSkydPsmHDBhYv\nXmwOy8rK4uGHH2bw4MEkJSXRt29fVq9ebQ63R0NMTAzr16/n9OnTHDx40Oakga+++io+nTswOfYP\nzsXH0/KpoRzOTjdPIb5w4ULzF6PRaGTYsGHExsYSFxeHt7e3Wd/06dPp2LEjc+bMISUlhTlz5pCa\nmsr999/P448/zl9//cXy5ct57rnnOHLkiNW8/PTTTxgMBsLCwoiPj8dgMDB27Fjmzp2LwWDINzPw\nxx9/TFBQEK1atcp3bqobekHhQDiDw50lcXFxbN68uVQOd3mEhITk06k73GlUNYe7HDdXks+eo86l\nZLy8vOjSsSOHs9PzeWHk4SgOd2PGjDG/TPzf//0fQ4cOZfv27Tbz4czoBYUDUdUd7gqyZMmSG3a4\ny/vnzVt0hzuNquZw1+eN1xARJne+n6ZNm3J+2WqSJZdzuYXvBUdwuAO44447CA4Oxs3NjZ49ezJw\n4EC+/vprq2k6O3pB4UBUZYc7a5SFw11p0R3uNBzF4e58cA2azf4/Es5pDnefvjCB9NOxHLLSTdYR\nHO6soZSy+gVUHajwgkIp1V0pdUwpdUIp9bKVcE+l1ApT+C6lVERF57GyqIoOd6D9A2dkZORbysrh\nrrToDncajuJwt3bVaupdTMZNKQIDA3FRCm8XNw5npzukwx1ovf5SUlIwGo38+OOPLF26lN69exeK\nVx3QHe4cjKrgcLd9+3aCg4PN6ezYsQNvb+98S1k73OUtRb3xWaI73Gk4gsNdphj5c9+vfPPPR/I5\n3LVu0oTD2ekO6XAH2jWvW7cuBoOBCRMmsGDBAoccn1IRVGuHu2PZ6SQbC7+1HTx4kObNm5c4vaqC\nM+vTtTke8blZzL52kRkB9ejo5W/e/mnKXyxNTWSGIYzDVVSbvZTntWvu4YO3Kt07v+5wZweLwwz8\n6edZOKB+ICSfLbzdWXBmfbo2h8RFhCt7fmVL7vX3PRcfD3LDA5mQfLZKa7OLctQ37uQlamaV74hx\nR5wU0C5Ed7i7EZxZn67NQdlWdHCV1mYH5aZvR/FRisJhHe6KnBTQIk68qeopAN3hrkxxZn26tqqJ\nM2uDqq/P4SYFNK0PMf3uA/y3qPYJHR0dHZ3ypUIbswGUUj2B99Ec7haJyHSl1Btcd7jzApYALdEd\n7soFZ9OXRAbeuOGNm9Nps0TXVnVxVH32OtzZNeke0B04hmZd+rKVcE9ghSl8FxBhEfaKafsx4J/F\npQlEA6eB/abl9uLy5yyTAlYUzqTvsjFDns3ZKp/kaJP6OZO2gujaqi6Oqg87JwUsto3CYuzD/Wi9\nlPYopdaIiOWMW+axD0qp/mhjH/qZxkj0B5oCdYBNSqmbTfsUleYEEVlVbCmnU+05zVXzX9FrKHV0\nygV72ijaAidE5JSIZAHLgYcKxHkIzbIUYBVwn9LG2T8ELBeRTBE5jfb10NbONHV0iuW0aKOEL168\nyJ2dO+oOdziuw51O1cWeXk83MvahLvBLgX3rmn4XleZ0pdRrwE9o1VKFhliWxTgKW6SkpJRpeiVl\n06ZNrFy5kri4OHx8fGjcuDGDBg2iWbNmREdHc+7cOSZPnpxvny5durB06VLq1tVO75kzZ1iwYAEH\nDhzAaDRyyy23MGLECG677TazvuzsbL788ks2bdpEYmIiAQEBtGzZkiFDhpgne9u5cydffPEFZ86c\nwcPDgzZt2vDMM89Qs6ZWrbl+/Xq+//77fFNDFGTGjBls3LiRmJgY84ju2bNnm6cqz8nJQURwd3cH\noHnz5rzwwgsMGDAg30R7ABMmTODee69bqO9vrvDwgb0L1mL0cGHFihX4+/vf0PWbMWMGNWvWZMSI\nEaVOo6QsWrSIbdu2ERsby+DBgxk6dGihOHnX7cyZM1y8eNGmxrlz5wJYDd+/fz+ZmZk2971w4QK5\nubkVev936dKF+fPn2x1/3Lhx3H///WVi8jR16lR69epFixYt6N+/f6FJ//bt28f8+fM5e/Ysfn5+\nPPfcc3Tp0qXEx6nsZ8oNU1zdFFrPo4UW64OBOQXiHALqWayfROs3PAcYZLH9M1N6NtMEagMKrd1j\nMfBacXl0pjaKWbNmSc2aNWX16tWSkpIiWVlZsmbNGvnXv/4lIvYZF504cUIMBoNMmjRJEhMT5erV\nq/LBBx+Ir6+v7Nixw6zvwQcflJYtW8ru3bslOztbkpOTZc6cObJw4UIREVm5cqX4+/vLl19+KWlp\naXL+/HkZNmyYhIeHS1JSkogUb1yUkpIifn5+EhQUJDNnzrQap7TGRdnGXBmT87OsyD0uTYf3kkcm\nPVsm1+5GDWvsMVsqSHR0tPzwww/Su3dvu4yLrN0D9pBnsmSLsjTrsRdAli5danf8zp07y4IFC8rk\n2A0bNpTExETZvXu33HffffnCDh8+LDVr1pQffvhBsrOz5dKlS3LixIlSHaeqt1HYU/VUkrEPFBj7\nYGtfm2mKyHmThkzgc7RqqmrBlStXeO2115g7dy6PPvoovr6+uLu78+CDD/LOO+/Ync7UqVPp0KED\n06dPJygoCH9/f8aMGcPgwYOZOHEioH21bNy4kW+//ZY2bdrg5uZGQEAAzz//PCNGjEBEePHFF/n3\nv//N448/jre3N6GhoSxcuBA/Pz/ee+89u/KyevVqDAYDr732Wj7TnLIgnlSyMbJk2L/544sNrHln\nAT169GDTpk0YjUZmzJhBo0aNCA4OJioqKt/8Un379iU0NJSAgAA6derE4cOHAc2D4csvv2TmzJn4\n+fnx4IMPAoU9yS2raPKqc95++21CQ0MZNmwYoPkk3H777RgMBu68804OHjxoU8uQIUPo0aMH/v7+\nNuNYkpWVxRNPPIG/vz9NmzbFcgqbiIgINm3aBEB6ejpDhw4lMDCQyMhI9uzZky+d3377jTvuuAN/\nf3/69etHRkZ+e9KiNERERPDuu+/SvHlzAgICrO6fx4kTJ+jcuTMBAQGEhISYLW07deoEwJNPPmn2\nRL98+TIPPPAANWvWJDAwkAceeMA8y/HkyZP5+eefGTVqFH5+fmZDo6NHj3L//fcTFBTELbfcQkxM\nTLHn8PLly4gIQUFB7N271zxJYB7Tpk3jmWeeoUePHri5uREcHEyjRo2KTdcZsaeguJGxD2uA/qYZ\nYRsATYDdRaWplKpt+quAh9G+VqoFusNdyTgtWkP24uhoOj/+ELf/awBrN+gOd5Y4ksNdt27dzLPY\njqus/IIAACAASURBVB49GsChHe7yDJqaNWtG7dq1GTRokN2TWTobxRYUIpIDjAI2AH8AMSJyWCn1\nhlIqb87dz4BgpdQJYDzwsmnfw0AMcARYDzwvIrm20jSl9aVS6nfgd7Tqq2llI9Xx0R3uClOUw91p\nrmLAgyDlhb9yR4DLflqY7nCn4SgOd+7u7sTGxpKQkICXlxd33323TW2O4nAXHx/PkiVLWL16NceP\nHyc9Pd1cwFU37BqZLSI/iMjNItJIRKabtr0mImtMvzNEpK+INBaRtmIxQE5Eppv2u0VE1hWVpmn7\nvSLSTERuE5FBImLdMssJ0R3uClOUw91puUoDagDgh9YQnmiqudEd7jQcxeFu5syZiAht27aladOm\nLFq0yKY2R3G48/b2ZtiwYdx88834+fkxadKkCjHdckR0hzsHQne4s58rkkUimTRQWkHhjgs+uJFY\nQ3vo6Q53Go7icBcaGsqCBQtISNAc7p577rl8bT6WOIrDXfPmzfMdy9p9UV3QCwoHQne4s5+8gXYN\n1PXGX4PyINFfy4/ucKfhKA53K1euNL+UBAYGopTCxUV7/Diqw92wYcP4/PPPOXXqFGlpacyYMYMH\nHnigxNqdAbsKihuxL1VKvWLafkwp9c/i0jQ1cO8ybV9hauyuNugOd/mx5XB3Rq7hiiIMv+tx8STD\nU3GZTN3hzoQjONwB7Nmzh3bt2uVzuGvYsCGAwzrcDR8+nCeeeIJ27doRHh6Op6cnH374Yan0V3mK\n6z+LNnnfSaAh4AEcACILxHkOmGf63R9YYfodaYrvCTQwpeNaVJpojd/9Tb/nAc8Wl0dnGkdRETiD\nvlk5+2VGzq/5tsUar8qzOVtlT+7FSspV+eIM180WzqxNxHH1Yec4imJnj70R+1Ku9356yzKeabdC\naQIzgL+BUNFGeOc7ti1Ka4UabTzKMUkutD0zMxNPTyvOd06CM+i7ShadVR2iXBqbt+WKkXHZP+Pu\n6oYnrpWYu/LBGa6bLZxZG5SvvhdcWnCT8i7VvmVphVqRU3gEA8midZ8tGD8fZTGFR3YdCPYp3ECV\nnZ2NaTYJp8QZ9IUAXufi2ZKevzE+0pBJaogXUHTPsaqIM1w3WzizNihffftid+Ftf0fCUqFboVpH\nt2WsuujaqibOrA0cV1+ZWaHeiH2ptX3rAS8ANZVSJ0RkhkWaiUCIUupXoDnwmpVjFUJ0K9QS4cz6\ndG1VE2fWBlVfX2VM4TEa6IrWjjFEKdUiL03TPtvRph1fBtwDfHsD+nR0dHR0bhC7rFBvxL5UKTUZ\nGI5WaTwP6C4i/zSluRitsJotptHZSqmGaAXFP9DmeeoiVqYZt0S3Qi0Zla0vh1zSSCeTrEJhLrjg\ngTs+eOFaigbpytZWnujaqi6Oqs9eK9QK9cxWSvVBKyieNK0PBtqJSKEZzZRS0cB3YofTXWl7Pdli\ny5Yt3HPPPWWWnqNRWfpSJJVf5CDHJRZ33GiqGnOTCqIG/njiToL8xVkuECsJ5GKkpbqVO9StuCn7\nm9Kc+drp2qoujqqvLHs9OSTObFxU3lSGvpTATBJuScboIgQn+BIU70tmTjJnyd892R2IcA/kYsNr\n7LvpMAfTjlL3WADe1+wbd+nM107XVnWp8vrsGWxRVgvQAdhgsf4K8IqNuNFAH3vS1QfclYyK1Jdr\nzJVfcg/IxzlfyYqcdXLZeMXufc8aL8iSnDUyL2eFHMkt2jDmwoUL0rFjR/H29pbx48ffaLYdEnuN\niyIjI21eY0c0LhLR/+cqC8rQuKgssadhvNqzbNkyWrdujZ+fH7Vr16ZHjx5s27YNsO2XXNBY58iR\nI/Tu3ZuAgAD8/f3p0qULO3bsyLdPVlYWU6dOpUmTJvj6+hIREcHw4cPNk+SBNoVz27Zt8fX1JTg4\nmIEDB+abSDA6OtrmlNGZksX3xq2MGzaaUZ6D6HCxKQbTJH4jR440T8vh4eGBu7u7eb1Hjx6cOXOG\nMJdQRgYMYFzAEFrWaIqPnw9fLf//9s48vqkqfdzPSbrRtHQDi+w7yr4qyL6IIA58VSggMFVwFEUH\ncAYVEGV+MzqKIjjjAogIisrqKIisAg4KIgMCgqy1pexLC7Tp3uT9/XHT0LRpm+5Jeh8/1yb3ntx7\n3pyQk3vPue/zhdNjLVq0iBo1arBhwwbmzp3r2htdAJXhjZ41axZt2rTBx8eH2bNnl2pfR48edcvL\nHAWhlOL8+SInN9rp06cPixcvLpNjR0VFsWXLFjIyMhwy4YLmHs+dPsbHx8cusqpqVGhHIS64LZRS\nXZRS54ARwEKl1NGC9+h9vP3220yZMoUZM2Zw+fJl4uPjefrpp+0J7VwhJiaG7t2706ZNG2JjY7lw\n4QIPPvggAwcOZM+ePfZyw4cPZ926dXz++efcvHmTQ4cO0alTJ7777jtAywX1yCOPMGXKFK5du8bR\no0fx9/enR48eXL9+vdA63JBk1lq3EptylsNf7ic0JIQVn62wb1+wYAFmsxmz2cyMGTMYOXKk/fnG\njRtv7efGDVKSU9ie9BNzby4hcMRtpDmZ23DmzBlatmzpFhk+i0oT74ymTZsyZ86cMvFA67jO/v37\n6dy5M4cPH6Z169YO244ePWr/TCYnJ1OvXj2nQrAqgSunHe6+eMulpxs3bojJZJJVq1YVWMYVZ/bY\nsWNl8ODB+cpMnDhRevbsKTt27JCtW7dKQECAxMfHOz2O1WqV+vXryxtvvOGw3mKxSKtWrWTWrFki\n4tyZfdZ6UT7KXitLstfK/KX/lrp168r8+fOlVatWLsfkzJl9whIrC7NXyqfZ6+Sa9bp9fXR0tPj4\n+Iivr68EBATI1q1bxWKxyD//+U9p3LixhIeHy4gRIyQhIcH+muHDh0tkZKRUr15devbsKUeOHBER\nkYULF9r3ZTKZ5IEHHsj3/uYcM+cSTc7lnNdff10iIyNl7NixIiKyfv16adeunYSEhEi3bt3k0KFD\nTuPPzZgxY1xyZo8YMULGjRsnQUFB0rJlS9m3b5+9XIMGDWTr1q0iIpKamirR0dESGhoqd955p8yZ\nM8fh0tOBAwekQ4cOEhQUJFFRUTJy5EiHS0+FxdCgQQN58803pU2bNlK9enWJioqStLQ0p3U/deqU\n9OrVS6pXry4RERESFRUlIiI9e/YUQAICAsRkMsmKFSskMTFRhgwZIjVq1JDQ0FAZMmSInD17VkRE\nZsyYIQaDQfz9/cVkMsmkSZNEROTYsWMyYMAACQsLk+bNm8vKlSuLfK8TExOlUaNGIiLy/vvvy7Rp\n0wosu3PnTgkKChKz2Vzkfp2hX3rSKTM8XYVqFSv/sx5hvXUngVTjYcNA1n3ynzJToTY3NGSYoT8W\nLPzHuo3TVs2dsHTpUru+dONGXYWaG12Fmh9XVai5WbZsGQ8//LBbTnGtCLymoxg/fjy33XZbvtPH\nkjJo0CBCQ0Pz5Z+PjY3l7rvvpmnTpowcOZLMzPz3ApQUT1ahpkk631r/yz45QnPVkIcN93LjbGKZ\nq1ATj1/hYcNAwglhq+xmu3UvmZI/0Y2uQtXQVaj5cVWFmkNqaipr1qzh0UcfLbAO3o7XdBSPPvoo\nmzZtKrP9TZs2zakP4IUXXmDq1KmcPn2asLAwPvroozI7pieqUK1iJZV0vrB+ywWu0Ft1oZ+6G1/l\nU24q1CAVyDBDfzqpVpyUOFZbN5FCmsPrdBWqhq5CzY+rKtQcvvzyS8LDw/N1IFUJr+koevXqRXh4\nuMO6mJgYBg0aRKdOnejZsyfHjx93eX/9+/cnODjYYZ2IsH37doYPHw5AdHR0qbWlufEkFWq/fv24\nIFfYL7+RJGbCCWG44T5aGprYv3jKU4VqVAbuMrRhmKEfApyTS5yyniHdpHVCugpVQ1eh5sdVFWoO\ny5Yt449//KNbTJSoLCq8oyiNLa+4PPHEE/z73/9m//79vPXWWzz99NOlqToJCQmEhobaLw3VrVu3\nWNP6isITVKjjJ4wnISmRxpPb8bV1OxlkUp0g7su8h8AM/wpToeZwu6rJKMNgahJOCmnEdkxgg+V7\nHn4yihkzZ+gqVF2F6hRXVKigdSo7duwgOjra6faqQoV2FEopI/AeMBjNfjdaKdUyT7EJwHURaQrM\nA94oybHMZjO7d+9mxIgRtG/fnieffNJ+GeXLL7+kdevW+Zb77ivUj1QhuJMKdXjUCBZ8sog35s0h\nLCKMZi2bczTtFM/8dybVI6rTW3Whm2rHL7v3ExgYWKEq1Nz4KB/CVQitVTNqnDGRyE3qPHsnkQ80\npPvAnpiCTXTu2oUffvoBEdFVqDZ0FWrhKlSATz/9lG7dutGkSZMSxe0tVHSupxLb8qSQiubkeoqL\ni+OBBx7gyJEjJCUl0aJFi0Kvwx+3xnKDpHzr48/EU79BfQ7s3Mdncz9h7nrtV5iIMDiyL99c2IaP\njw+/7jnER39bwPxNzk9x3Q1BEODs2Xjq1quLIFgRLFixYMEiFjLIIoNMMsjATJrtFaBQ1CSMOiqS\nhqoOkUS45an4zp076d27Nxe5yik5wwW5wg1u/QI2YMBENaoRgB8++OGLj/LBiMH+n0KhwPb/W38r\nm5zPpTfizbFB+cbXTrWgmgoouqAT3DXXU2lseQ4jjc5yPV26dImUlBR7TpWIiAhmz55Nnz59EBFi\nYmJo2vSWOvNsy+uYw5z86qgLCZZjnLLGk4SZXyy3TmEb927Bx6uW0XnkPXy+7BMa/uEOh+3uhsNX\nXE5XWwtuZJ0C0bYrq0JZFQarwpCtMGYbMGYrwjMC8Us34pfmg3+KD0aLgXSuc5zruD7aU7GYzWaH\ny0K3Y+I2YzXSgrPIrJZNtr+VLH8LKb7JJBsFi1GwGq2gQAyC2N4w7a/grI+ouJ9WebB9Lr0Sb44N\nyjW+mweu4p9Wvl/lbpc9Vil1xFbmnO15jK1MgVNSlFJX0S6jBaN1ftnABSAJzeDki/ZPPhEo+BTj\nFjXQOqcAtNTq2UCcbX9+QBPb+lQglkr87igh7mrbKgv02DwTb44N3De+BuJCmvGKPqMojS2vQFwJ\ntDjYbFQNy3Kf7oSn27YKQ4/NM/Hm2MDz43PHpIAF2fJ0dHR0dCqBCr30BKWz5RWEbrgrHt4cX1WJ\nLduaRobVjMmnBk4HUjwMb243cN/43NJwV17ohrvi4c3xVZXYjt/4moSMk7QJG011v7qVW7EywJvb\nDdw3PldnPXnNndk6OlWJ5KwLDn91dMoTt+wolFJLlFJXbDOgdHSK5PLly/Tq1Yv777+fv/zlL5Vd\nnXLlpZen89JTHwKQnJV/El+rVq0K1G7u3LmTunULPgOpDGmTjvvjlh0FmgZ1UFGFvBVvMdzl8Oij\nj+Lj4+Nw86MrhjullMNd2UFBQaxcudLpMaqS4S7Tqt1AGGAMIznrAnkvH+uGO9cpzHCXmJjIyJEj\niYiIoEaNGowZM4akpPw36FYF3LKjEJH/og1kVzm8xXCXQ0pKCmvXriUkJITly5fb1xfHcJezPsdX\n4IyqZLjLsCQDilrV2pFpNds7Dp3iU5jh7qWXXuL69evExsYSExPD5cuXS62p9VQq+j6KMsPZndll\nhdlsLtP9Fee4M2fO5IUXXiA8PJx9+/YBEBwczJAhQ9i5cydxcXFcvnzZaf327t3LuXPneO2112jR\nogX33nsvhw8fBqBt27b079+fiRMn8uqrrzJ37lw2b97Mp59+SkpKiv2MJSfnzY4dO3jmmWcYPXo0\ntWvXZu/evQCMHTuWHTt2MHnyZMaPH8/x48e5efNmge/X5s2bqVatGlFRUbz//vsOvoMcnMWUk531\n+++/x2g0Fvq+vf7662zbtg2lFHPnzuUf//gHHTp0YMWKFWzYsAGz2UyHDh147rnnqF5dc3bPnj2b\nw4cPk5mZSZMmTZgyZQqNGjVi/fr1LF++3L6vDh068Nprr9G3b1+WL19OnTp17MesWbMmEyZM4ODB\ng7z66qs89NBDrF69ms6dOzNjxgz27NnDRx99xKVLl2jYsCFTp04tMGdQTnrv1NRU4uLinL6fOZ/L\npNRrZKXB+OEvsGvXj0RG/osXn3+JFi1aADBq1CimTZtGp06dyMjIYN68efz4449EREQwaNAgMjIy\n7Ps/deoUb775JufOnePuu+9GKYXFYrFvLyyGUaNG8eCDD7JlyxYuX75Mly5dmD59On5+fvnqfv78\neebMmUNMTAxGo5GOHTvyyiuvMHnyZEDLr/X4448zbdo0unTpwmuvvcaxY8ewWCy0bt2a5557jpo1\na7J48WJ27drF7t27efbZZxk0aBCTJ08mPj6ef/3rX5w8eZLQ0FAee+wx+vbtW+jnJjk5mbS0NA4f\nPszXX39NjRo1HN73/fv3061bNw4cOABo/zZ27dpVou+GyvpOKTNc0eBVxgI0BI64UtZbVKgbN24U\no9HooP/Miysq1MjISFmyZEm+Mtu3bxeDwSCbNm2SF154QXr16lXgcY4dOyaA/P777/m2vfzyy9K1\na1cRca5CzU2/fv1k2rRpcunSJTEajfK///3PpZicqVALI0dNmtN28+fPl7vvvlvOnj0r6enp8sQT\nT8ioUaPs5T/66CNJSkqS9PR0mTx5srRr1y7fvnJDESpUo9Eozz//vKSnp0tqaqocOHBAatasKT/9\n9JNkZ2fL0qVLpUGDBpKenl5oHEWpUC3WLBn/l4Hi5+8r679ZJ7vOvyUTnxstd999t71cbhXqCy+8\nID169JCEhASJj4+XVq1a2VWoGRkZUr9+fXn77bclMzNTVq9eLT4+Pva4ioqhQYMG0qVLFzl//rwk\nJCTIHXfcIR988IHTuo8aNUr+8Y9/iMVikbS0NNm1a5fDe7t8+XL782vXrsmaNWskJSVFkpKSZPjw\n4TJs2DD79t69e8uHH35of242m6Vu3bqyZMkSycrKkgMHDkhERIQcPXrUaV22bdsmISEhYjKZxNfX\nV0JCQsTX11cCAwMlJCREdu7cKSKaBnbw4MGSmJgoiYmJ0rdvX5k3b57zhisCXYWqU2Z4suHOGfHx\n8WVuuCssdXRuvNVwl5J9BcFK13s688CQPxAScDsDH26nG+7KwXDXsWNHMjMziYiIICIiAqPRWGpV\ngaeidxRuhCca7gqjvAx3ruCthrvkTO31tW/XMpEG+dbG6pusG+7KwXAXFRVF8+bNSU5OJikpiSZN\nmjidSFIVcMuOQin1BbAHaKGUOqeUmlDZdaoIPMlw179//yLrUZ6Gu6LwVsNdctZFjMofo9LOOqv7\n1kYoWHCkG+7y46rh7uDBgzz55JOYTCaCgoKYOHFihXx23RG37CiAZWiZWs8A74pI2Ymp3RhPMNw9\n/vjjJCUlMXXqVPvxRMRutqtow11BTJw4kZkzZ3qd4S456wL+xluK3iDf2oXWQzfcOccVw12XLl1Y\nvHgxaWlppKWlsWjRItq2bVvs2L0Bt+soXLTgeS3uZLgbOXIkn376KfPmzSMiIoKWLVuSlpZmn0GT\nw+7dux3sdhVtuHPG5MmTGTp0KAMHDiQ4OJiuXbvaZ255rOHOJ5MMaxJ+hlsdhb8xCD9DUIH71Q13\nznHFcLdkyRLi4uKoW7cuderU4ffff2fZsmUlit/TcbtcT65Y8PJS0lxPGZZkrJL/evnen3/m7rvu\nKvb+PAVvjs+bY9t3ZBvG28/QNmwMwX63ziRO3FhPUtZ5WodFVWLtSoc3txuUb3z+xhAMqvAp5AXh\nroY7V3DFglcmxCRt4Xpm/sS0vk3gQMKv5XFIt8Cb4/Pm2Iy3gwEfTL63OawP9qvDtYzjHEjw3Cu0\n3txuUL7xdYgYT6BPRNEFS4E7dhQukfuGO8CslDpRhrt3VxtVWeHN8VWB2J4rsqAH4s3tBuUan+vj\nl05oUHQR9+woXLHgISKLgEXlUQFPt1EVhTfHp8fmmXhzbOD58bndYDauWfB0dHR0dCoItxvMBucW\nvMLK64a74uHN8ZVLbGJFLBlgzQbJ1v4qBcoAGMDohzL6QwkHFF1FbzfPxV3j0w13pcBdbVRlhTfH\nV1axWdMTyb6yD0vCEaxJvwO2fyfGaij/ULBmI5Y0yE4FsQKgAiLwqdEBn1rdMJgKTo9SUvR281zc\nNb5KnfWklBoEvIN2RrBYRF7Ps90f+AToBCQAI0UkTinVEDgG5AxM/yQiE8ujjjo6eRERrEkxZJ3f\nieXqQcCKIagevg0GYwxriSGwFso30PE11mys5nNYk2KwXD9B1vntZJ3bhiG4Ib51+2Gs2RGl3PEK\nr46O65R5R5Hrhrl70aa27lNKrROR33IVmwBcF5GmSqlRwBtAjmggRkTal3W9dHQKw3LjJJmx67Em\nxYBPNXzr9sOnTm8MAYVPO1QGH4zVG2Ks3hDfuv2RzCSyL+8j69IPZBxbgor7Bt/6g/C5rQvKUL6X\npnR0yovy+KlzF3BaRH4XkUxgBTAsT5lhaGk6ANYA/ZU7GGd0PJaSqlAtSXGkHXqH9EPzkfRr+DUd\nSWDX1/Br8lCRnYQzlF91fOv1p1rnWfi3/BPK6EfmiU9I+9/fyb52MJ+NriQUZDnMQVeh6pQ15XHp\nyZUb5uxlRCRbKXUTyPlX2Ugp9QtarqeXRGSXs4N4o7goh23btrF69Wri4+MJDAykadOmjB07ljZt\n2rB06VLOnz/PzJkzHV6TV6wTFxfHhx9+yKFDh7BarbRo0YIJEybQunVre3xZWVl89tlnbNu2jYSE\nBEJCQujQoQPR0dH2rKB79uzhk08+IS4uDj8/P7p06cKTTz5JzZra+NemTZvYsGGDQw6hvLz++uts\n3bqVVatW2VN/vP3222zduhXQjHAigq+vL6BJlqZOncro0aMdMrICTJs2jX79+uU7Rk7+qJUrVxIc\nHFxk+/lhpi6/EqHOkiX+XKQdVzKaIKeE1ycMs0uJSk83QrlA3dRfkaOLMEsEZ2mHGcfsu0uWLOGH\nH37gzJkzjBs3jkcffTTfnnLarTB5FcB7770H4HT7wYMHHcRFebl06ZKDuKgi6Nu3LwsXLnS5/JQp\nU7j33ntdsgEWxezZsxkyZAjt2rVj1KhRfPnll/ZtV69eZf78+fz666/4+/szbtw4hg4dWqLjVPZ3\nSqlxRVpRnAUYjjYukfN8HFpiv9xljgB1cz2PQbshxR+IsK3rhNaZVC/qmN4iLhIRmTt3rtSsWVPW\nrl0rZrNZMjMzZd26dfLXv/5VRFwTF50+fVpCQ0NlxowZkpCQIElJSfLOO++IyWSS3bt32+P7wx/+\nIB06dJCff/5ZsrKy5MaNG/Luu+/K4sWLRURk9erVEhwcLJ999pmkpqbKxYsX5bHHHpMGDRpIYmKi\niBQtLjKbzRIUFCTh4eEyZ84cp2XKQlw0YcIEB3FRQVgzkyX99Boxf/+smP/7Z8n4fZ1Ys9IcyjgT\nFxUHZ3W2WrMl88IPkrL7RTHvfErSjiwUS8pl+/alS5fKt99+K0OHDi1UXCRS8GfAFXbs2GEXFzmj\ntLGXBPKIi4oir7ioNDRu3FgSEhLk559/lv79+zts69Onj0yePFkyMzPl4MGDEhYWJtu3by/RcTxd\nXFQeHUU3YHOu59OB6XnKbAa62R77oN2xqJzsayfQuahjektHcePGDTGZTLJq1aoCy7jSUYwdO1YG\nDx6cr8zEiROlZ8+esmPHDtm6dasEBARIfHy80+NYrVapX7++vPHGGw7rLRaLtGrVSmbNmiUiRXcU\ny5Ytk7p168r8+fOlVatWLsdUnI4iOjpafHx8xNfXVwICAmTr1q1isVjkn//8pzRu3FjCw8NlxPCH\n5eKh1WLe9ZyYdz4tD93XRSIjb5Pq1atLz5495ciRIyIisnDhQvu+TCaTPPDAAyJStOGuTp068vrr\nr0tkZKSMHTtWRDRDWrt27SQkJES6desmhw4dEmt2umTEbRDzrili/n6SpJ/8Qizp1+37Lcpwl/N+\njRgxQsaNGydBQUHSsmVL2bdvn71cbsNdamqqREdHS2hoqNx5550yZ84ch47iwIED0qFDBwkKCpKo\nqCgZOXKkQ0fhLIbcx3nzzTelTZs2Ur16dYmKipK0NMdON4dTp05Jr169pHr16hIRESFRUVEiItKz\nZ08BJCAgQEwmk6xYsUISExNlyJAhUqNGDQkNDZUhQ4bI2bNnRURkxowZYjAYxN/fX0wmk0yaNElE\nNCPjgAEDJCwsTJo3by4rV650Wo/cJCYmSqNGjURE5P3335dp06bZtyUnJwsgV65csa/705/+ZG/b\n4qJ3FPm/3H2A34FGgB9wCGiVp8wkYIHt8Shgle1xTcBoe9wY7Y7s8KKO6S0dha5CvUVZqVDj42Ik\n+fRGGT+svQzv11TSDr8nFvP5SlehWjNuSvrJz8X8/STtzOb0WrFmJLncUfj7+8uGDRskOztbXnzx\nRV2FWsYq1KSkJAHk8uVbZ32PP/64tG/f3uk+i8LTO4oyH8wWkWzgGdtZwzFbJ3BUKfX/lFI5F/g+\nAiKUUqfREte8aFvfCzislDqINsg9UURcy0ftBegq1PyUWIX6wfvM/vODRJxfhDq3jpmT/o+v/huH\nz51PYDDVrnQVqvKrjn+z0VTrMhufmp3IOvcdqXtfwpIch2SlFHm8Hj16cP/992M0Ghk3bpyuQi1j\nFWpwcDDdu3fn73//O+np6Rw4cIC1a9c6yKuqEuUywVtEvhWR5iLSRGx3VYvIyyKyzvY4XURGiEhT\nEblLRH63rV8rIq1EpL2IdBSR9eVRP3dFV6HmpzgqVBEhkEQyTiznTNzvRP1pFrXve4c6Q5fTccQ8\nt1ShGqrVwP+OP1Ktyyx8buuCpF0j6/xO0o8sIPvaIcTq3F6XV0Gqq1DLXoX62WefERsbS7169Xjq\nqacYO3ZsoTPGvBn9TiA3QlehFh8RKxbzOazms2Rf/C+t1Dayr/yPurfXZMNXK7mRnMaNm0lur0I1\nBNbCv8VYjBHtMIY0wZoUR8bRhaT+NJ2M06uwJB5DFaI8LQhdhZofV1WoDRo04JtvvuHq1avsY4SC\n4QAAHPJJREFU3buXa9eucZcXOzMKo1w6CqXUIKXUCaXUaaXUi062+yulVtq277XdkZ2zbbpt/Qml\n1H3lUT93RVehFo1Ys7AknyHrwi7Sf1tC6p4XSd//GlbzeTBWI1Y6E9j1NZ768zRmvfqOx6lQRRmR\n4KaoDrPwufMJjCFNyb74I+m//psOfE36kQVYbp5GMpMQS3qR75euQnWOKyrUY8eOkZycTGZmJsuX\nL2fLli0OZxxVClcGMoqzoKXtiEEbjM4ZzG6Zp8zTOA5mr7Q9bmkr7482GB6DbXC7sMVbBrNzWL58\nuXTq1EkCAwMlMjJS7r//fvnxxx9FxLXBbBGRX3/9VYYMGSLBwcFiMpmkd+/e9gHEnPgyMjLk5Zdf\nliZNmkhgYKDUr19fJkyYIGfOnLHv56uvvpLOnTtLYGCghIWFyahRoxxmSn388ceClgjJYZkwYYI8\n9NBD+eq5d+9e8fPzk4SEBPs6LaZHxJqVKpa0BLGYz8vpg9sEEFNggJgC/cVUzV9M1fzkn093F/PO\np8S88ylJ2f2CpP32sWRe3C3R4x5xGMy2WCwyd+5cad68uQQFBUnjxo1l+vTpIqLNaBk6dKgEBQVJ\n/fr1ZdmyZQ7v38mTJ+0zfXIGUfft2yctW7aUoKAgGTt2rIwaNSrfrKe8bNy4UTp37iwhISFSq1Yt\nGT58uCQlJTlt8+jo6Hzv4ccffywiItbsDMm6dlh+3/GWpOx9RaZHd5aRA5pp78GemXLs25cFkJSY\nDZJ56SdpUK+2bPr6M7GkXhXzzasybuxYCQkJcTrrad++fdK+fXv7rKeoqCiHgfzCYsg9aH6rHZ1P\n2502bZrUrl1bTCaTNG7cWBYuXGjf9sEHH0h4eLiEhITIypUr5fz589K7d28xmUzSrFkzWbBggcPE\nht27d0uzZs0kNDRUnn32WREROX78uNx///1So0YNCQ8Pl759+8ovv/zitC4iIo899pisWrVKrFar\n3HbbbZKZmZmvzLx586RGjRoSGBgo3bt3d5hZVlwq+zulIHBxMLvMkwK6ojJVSm22ldmjlPIBLqHN\neHoxd9nc5Qo7ZolVqDFrbQnfHEm6mUT1kOrF3p+nUGbx5fvoSK6/AjmfLREEq/ZcrCAW+yKWLLBm\naVlZC8Lgj6oWgSGgBgZTbQxB9TAE1UUF1Mh3GcJdk6+VBTmxSZYZS9IZrOZ4rKmXkbRLWNOuQnZa\nwS9WRjD4gcFHSyWifLTst7ZFYdAy4qJAof0l7yU4VejT0qD/mys5/neOL1EWAajcpICluTO7DvBT\nntfWcXaQsrgzuw4XMJF/FoPForh+03tnN5RvfCpX/6F9k4jtS0ebZOeDoLBiQDAgGLFiwIoRC772\nJRt/svAnmwCyLX5gVmDG5gi7aVvy4/F3wBZC/tiqAQ1tCxjIxpc0fEnHh0yMZOJDJgYsGCUbg9WC\nworCggErWsuIrcVsGXDtJzR5+4HyzTKt/5srOXE//UQm5ZvC3B0Ndy4huQx3Sqmrffv2PVOGu9e1\njJ6LHptn4s2xgfvGV2kq1EJVprYU5I2An5RS7wJvASFo6cbPAz2VUs8BbdFSfSwu6oDignijOHi6\ntrAovDk+PTbPxJtjA8+Przw6CrvKFO2LfxTwCDikIH8DrQMZDWQB20VElFLrgNVo+aFmAt2Bn/Md\nQUdHR0enwigXw50zlalS6v8BycAAtDTjnwL9gFSgt9huulNKzQTGo52qvSsiM50cwgFdhVo8vDm+\nSo0tMxXSkiHDDFar4zajL5hCoVp1m0K1+Ojt5rm4a3xuqUJVSg0HBonI47bn44C7ReQZJ2WXAt+I\nyJoC9pV7MLvTihUryqyeZrOZoKCgMtufu+HN8VVGbH6ZZprHbabGjVNkG/y4FtaMq+F3kO0TgNGS\ngV9WCrWu/kqo+RzZRn/O1L6Hs7Xuss0ych293TwXd42vb9++ladCrQhyD2Z37txZynJKpDdPsQTv\njq9CYxOBI1th+1KwZELvCfh0GkYtHz9qOSt/8QQ+uz+nScwOmqjrMOSvEFx0KpQc9HbzXDw9vopO\n4VHoQLeOjqvkGO2Cg4OLZbQrM7IzYeNc2Pg21GwAj74Pd48AH7+CX3N7C3hoNgyaChePwcdPwem9\nRR5KN9rpVDYV3VHYB7qVUn5oA93rKrgObsfnn39O586dCQoK4vbbb2fw4MH88MMPQMFfEkoph1w5\nv/32G0OHDiUkJITg4GD69u3L7t27HV6TmZlp35/JZKJhw4aMHz/enusItEycd911FyaTiYiICMaM\nGeOQD2rp0qWFZv4E7cvHx8fHIaHgxIkTCQoKIigoCD8/P3x9fe3PBw8eTFxcHEop+7qcZeXKlU6P\nsWjRImrUqEFSUhJz584ttD5FUewvy+QE+GIaHNkG94yB0W9CuIvJ4pSCtvcx63xD2ry5HZ8W3Zj9\n+PBbNyeWgKNHj3rUr9W8n92i6NOnD4sXFzn50SWioqLYsmULGRkZDgkNQcuFds899xAYGOj0/Tx4\n8CCdOnUiMDCQTp06FZgp1xup0I5CXEhBrpTqopQ6B4wAFiqljlZkHSuat99+mylTpjBjxgwuX75M\nfHw8Tz/9tD0vkSvExMTQvXt32rRpQ2xsLBcuXODBBx9k4MCB7Nlz66b24cOHs27dOl566SVu3rzJ\noUOH6NSpE9999x0Aa9as4ZFHHmHKlClcu3aNo0eP4u/vT48ePbh+/bpLdUlJSWHt2rWEhISwfPly\n+/oFCxZgNpsxm83MmDGDkSNH2p9v3LjRXi4noVvOMnLkSKfHOXPmDC1btnSawK9cuXAMPnkWrp2B\n/5sFPcaRbbEW/bo8NG3TkTnvf8yQznfAmYOwYY52lqJTruzfv5/OnTtz+PBhWrdu7bAtPDycKVOm\n8OKL+dLTkZmZybBhwxg7dizXr18nOjqaYcOGkZlZRdrMlTwf7r54aq6nijLaiYiD0c5ZfJ5qtDOZ\nTA5Gu9q1a2tGuxEjHPJJDR8+XCIjI0tntPvTaJG3HpAdU++TOrfXcsloVxRjxoyRV8Y/JPLGfSLL\nnhW5eSVfmRyj3b333us1RrvAwEAHo13Xrl0r1WiXmw8//FB69+7tsG7z5s1Su3ZtsVqt9nX16tWT\njRs3FnlcEc/P9aSnGa9E9uzZQ3p6Og8++GCp9rN161ZGjBiRb31UVBQ//vgjaWlpbNu2jbvuusvB\nTZCbEydOEB8fn28/BoOBhx9+mK1bt7pUl2XLljF69GhGjRrF8ePH2b9/f/EDKoKlS5cyZswYnn/+\necxmMwMGDODf//43X331FfPnz+fChQuEhYUxadIk+2sGDx7MqVOnuHLlCh07dmTMmDEAPPHEEw77\nWr/eiQLFkg0XjkPMXqjbGu77M5euXCUxMZEzZ86waNEifvnlF8aPH8/ChQtJSEjgySefZOjQoWRk\nZBQdUL028ODLkHgOlj0DZ37JV2TdunX069ePGzduMHToUJ55Jt9EQQD+9re/ERMTQ0xMDJs3b2bZ\nsmX2bZmZmfzf//0f48aNIzExkREjRrB27Vr7dldiWLVqFZs2bSI2NpbDhw+zdOlSp/WYNWsWAwcO\ntGetffbZZwHsKcMPHTpkP2O0Wq0MGjSIM2fOEB8fT7Vq1ezxvfrqq/Ts2ZN3330Xs9nMu+++S0pK\nCvfeey+PPPIIV65cYcWKFTz99NP89ttvTuvy3XffERoaSr169Th37hyhoaFMnjyZ9957j9DQ0CIz\nAYN2ea9t27YOZ7Bt27bl6FGvvuBhR+8oKpGKMtolJiZ6v9FuwQJeffVVatasabfWrVmzxi7zKbHR\nLiEelk+FxLPaYPSIf4B/YLGNdkXS7B4Y9w4EhsCqmbD7c62DstGjRw+6du3qtUa73r17V6rRrijM\nZjMhISEO60JCQkqUct0T0TuKSqSijHZhYWFeabTLzZkzZ3jwwQd54IEHCA0N5c477yy90e7XLbB0\nEiRdgfptoWFHMBiBkhvtCiWintZZtOgJP3wCn/4ZLp4EvN9oN3fu3Eo32hVGUFAQSUlJDuuSkpII\nDg526fWejt5RVCIVZbQLDAz0GqNdQdSrV4+NGzfyzTff2DuZEhntxAonfiDQz4fU/34GjTrB+AVc\nSnWclVRao12B+FWDodO1gfKUG7B8Cvy+D7KKlhSB5xrtzp49W+lGu8Jo1aoVhw8fdnjvDh8+TKtW\nrVx6vadT4R1Faex33kZlGe1OnDjhMUY7V5k4cSIzZ860/6osttHu1Ak4vEkbI/j6H7SvF87n5oZY\nhr7Epl17y81oZ7Vayc7OJj093fEXdPPuMGERtBusnVWc2sOdMevh4olCp9J6itEut6Eup30q22hn\nsVjsZ2pWq5X09HT72XCfPn0wGo3861//IiMjg3fffReAfv36Ffu98UhcGfEuq4VS2O8KWzx11lMO\n5W20yyHHaFe7dm03MNo5n/VkMpkclrlz5zp9z6Kjox1m6+QY7erVq+e60W7n1yJ7V8vJdyZKu9uD\nJSTAR4a1ry9yZJvs2/tTpRnt8vLKi3+VMf3vkqw3/yDyxn0S+7c/aDPEDm0VuRrrMOspJSVFxo0b\n5/ZGu1q1ajkY7dq1a1fpRjtnn+3o6Gj79gMHDkjHjh0lICBAOnToIAcOHCjweHnx9FlPFZ3rqcT2\nOymkoiU13PH7/yD5ar7VJ06coEWLFsXfn4fglvEV+3MoNpdOLpueCKdOnaRZ48aaNc9igewMyEzT\nlrSbYE4EcwKk5hrnCa0NLXpoYwORTYudg6mi+GHbJnrUMmqf29j9WvJB0JIMhtSCoDCoFqItfgHg\n6w8+/mDwAYNBG1/JSUioDNjVRHajXTEpw/fJLT+TZUi5xteiJwSULI+Uq4Y7t0sKqJQ6YitzzvY8\nxlbmWp59lTopYJsTq4m4GVPScHQ8AKsyYjH4YjH6keVTjQy/IDJ9g0n3DyHZVAtzYCRZvoGVXU2X\nyJ1YTokVU+pVAtOuYUpPoFp6Ir5Zqfhlp+KblYrBmo3RmuXgG9TxTn5u8ydSq5VMhepqUsDK6Cge\nRxMXGYH9wNU8HcVFtHTk6cBVoCnQKW9HkWe/VwHdcOc63hyfHptn4s2xgfvG10BcSDNe0dljLwK9\ngNZoPuwzQN5TgXPANBHZqZSaBLyNZr8rEFcCLQ6ebqMqCm+OT4/NM/Hm2MDz46voWU85FzULO41Z\nijaIDRAMJBc2PqGjo6OjU75U1qWnxmiXng4Al4FEtNH3dUqpADT7XQe0jmK5iOTLI517jKJatWqd\nCkpNURKsVqt9Kp83Ulnx+aYm42/OGURWWI1G0kNvw2o0ltkxvLnt9Ng8F3eN7+TJkx5vuBuLlmm2\nt4gUmjCnxLOeCsDTJSNFUSnx/fQd/O0paNUJGt0B2Vnw/Qa4vT7M/QICymZA2ZvbTo/Nc3HX+Fyd\n9VTRYxQuiYuUUgOAmbjQSeh4AL8fhzf+Ak1bwT+WQEA1bX23AfDKE/DWCzDjHW0Kp46OjtvhduIi\npVQHYCEwVESuVHD9dMqa69dg9pMQGASvfHCrkwC4qw9MeB5+2ASfv1es3Va64a4C0Q13OpWN24mL\ngDeBIGC1UuqgUsrrDXhea7i7cAHeeh5uJjLRWpughk3zG+4encLgOAtxH871HMNdGTBr1izatGmD\nj48Ps2fPLtW+dMOd65TGcPfEE0/QokULDAZDgenVvZUKP9cXkW9FpLmINBGRV23rXhaRdbbHA0Qk\nUkTa25ahhe/Rs/Fqw90rL8L+XTB+Ggu+WFWw4e7QbxCpXZG8cfG8exvunFBU9l9nNG3alDlz5jBk\nyJByqJFOQZTUcAfQrl073n//fXvOqCqFK3k+3H3x1FxPXm24e/Xv0qp6gMjUkSIWS5ExxW76Wsvv\n8+9XCtx3DpVmuMuT66nMDHevFB6zbrirfMNdbrp3715gXq6C8PRcT/roYSXitYa7UaMYdeM0x5PT\n2d9/tGuD1C3aan/XfwZHC7fiVbjhzgmXLl0qO8OdC+iGu8o13FV19I6iEvFaw12L+kQe/pH+bVry\nyZbtRb4uNzV2xBLasav7GO4KoMwNd0WgG+5uURmGu6qO3lFUIl5puGvciPbrF8Ed7Rgz9a/FN9z9\n8B03+jXixp9HcOPa1co13BVCuRjuCkE33N2iMgx3VR29o6hEvM5w99Fifo+NpdbWk9T6YhfP/XVa\n8Q13HbvDM3+Dn3fC3BfAanXpZWVmuLMRGBhIamqq/XneL6FyM9yVEt1wl5+yMNxVdfSOohLxKsPd\n+v8QExfHz4PacXDvTxw8dKjkhrsho+Gxv8KO9fD+31xyVZTacJfLoAbQvn17Pv/8cywWC5s2bap4\nw10J0Q13zimt4Q60MZ709HRExKH9qgSujHiX5QIMAk4Ap4EXnWz3B1batu8FGha1T0+d9ZSDVxju\n6ofJQ7VDRWJPOhyzVIY7fz+Z2yJC5NmHRH76TsRqtZcvE8Od7f07efKkfabPsGHDREQzwbmN4c72\nfuV8LnPeqxwDnG64qxjDXe/evfNtd/W7wtNnPVV0ricjcBK4Fy2d+D5gtIj8lqvM00BbEZmolBoF\nPCgizifT2yhxridLttNfq99//71XD3AVGF/u9yLnsdUKCGRlQnoaZKTDlfMQfxriTmn5mtJToc8D\nMG4y1G6Qf78lRQS2rIEv3odL57QUIJ17Qb0mUK8xVA/VTG7+AWDU7G3f79rlGJsb3GdRVnjz59Kb\nY4Nyjs/oU+LPubsa7txLhTrrcdinT40rMcGh2pjCI5OgQbPyO052Fmz/Gv6zDM6cAmvpL9Ho6HgN\nH27SfjyVAHftKMrMcJc7zTjQAu1yVlnhrjaqssKb49Nj80y8OTZw3/gaiBsa7gzAPUB7tEtPp4Fd\necqkA/eLyGml1FNouZ/yISKLgEXlUUlPt1EVhTfHp8fmmXhzbOD58VX0rKcQIFNEfheRTOA3IK8V\n/CSQ08PtQxvcLlSFqqOjo6NTflT0pacoYDHQDs1DcRr4QUQeyVVmEtDGNpi9GagtIm0K22+NGjUk\n5yaqsiAlJQWTyVRm+3M3vDk+PbYyJDkZUlK0CQ1WK4SEQHBwuRzKm9sN3De+/fv3u63hzlUVak+0\ndOOdReS4k33ZxygiIyM7rVixoszqaTabCQoKKrP9uRveHJ8eW9kQtn8/bZ9/HmW1IkohRiMoxaG3\n3uJm27Zlfjxvbjdw3/j69u3r0mB2Rd9D0Q3YnOv5dGC6k3ID0HwVt7myX0+/j6Ki8eb49NjKgFOn\nRMLCRFq1Erl2Tbt/JSFBpHlzkYgIbXsZ483tJuK+8eGm2WN1w52OjjuTlATDhmnz8tetg4gI7XF4\nOGzYoN3bMmQIuOgn0fEOdMOdjo6Ohgj88Y9w4gSsXg2NGztub9oUvvoK4uJg9GiXUqvoeAcVPT0W\nEfkW+DbPupdzPR5Q0XXS0dEBli6Fr7+Gt9+Gfv2cl+nZE+bNg0mTYMkSmDChQquoUznoSQF1dHTg\nwgWYOlXrCCZPLrzsxInQqxf85S/a63S8Hr2j0NGp6ohoX/4ZGfDRR0UbCQ0GrVxmJjz1lH4Jqgqg\ndxQ6OlWdL76A9evh1VehmYs5u5o2hb//XRvwXrmyfOunU+noHYWOTlXm+HF45hno2rXoS055mTIF\n7roLnnwSClCz6ngHekeho1NViY2FAQPAzw8+/VRL1V4cjEZtdlT16jBoEOSRP+l4D3pHoaNTFblw\nQeskUlNhyxbtUlJJqF8fNm/Wxjfuuw+u6Lc+eSMV3lEopQYppU4opU4rpV50st1fKbXStn2vUqph\nRddRR8drEYGtW6F/f+1LfeNGKG1KjpYttZvxLlzQZkN9840+wO1lVGhHYTPcvQcMBloCo5VSLfMU\nmwBcF5GmwDzgjYqso46O1yECly7Bf/4D3brBwIFawr9vvoG77y6bY3Trpg2IZ2XBH/6gPf/Pf+Dc\nOb3T8AKqtuHuzTfh4MF8qy9fvkxkZGTx9+cheHN8VSq2vOpakVuZXtPStCU5GU6dgps3tXING8L0\n6RAdDf7+ZV/JrCztxr2//x3OntXWhYRol7aCgyEwEAJs6lqDQUsPotSt2LxIXZubcv1cvvkm1K5d\nope6arir6Duz6wBncz0/B+T9SWMvIyLZSqmbaM6KAg13kZGR7Ny5s9iVaf7994Q66SiCrFZSj+dL\nWOs1eHN8VS623F+sSiG2L16rvz8Wf3+sAQGk9elDav36pDZowI127RAfH9izp/wq2qwZavFiQn77\njcDYWExxcVS7eBFDYiLGCxcwZGSACCqncwNMViupJ8pSUulelOfn8vCOHaTXqVMu+86hwlN4lBWS\ny3CnlLrat2/fM2W4e3fVFpYV3hyfHptn4s2xQXnGN3ZsaV7dwJVCFd1RnAfq5Xpe17bOWZlztktP\nIRRhuBMXxBvFwdO1hUXhzfHpsXkm3hwbeH58bpdm3PY82vZ4OLC9sPEJHR0dHZ3ypULPKGxjDjlp\nxo3Akpw049gMd8BHwKdKqdNo5rtRFVlHHR0dHR1H3DHNeDowoqLrlYdFlXz88sab49Nj80y8OTbw\n8PgqdHqsjo6Ojo7noafw0NHR0dEpFL2j0NHR0dEplCrfUSil6imldiilflNKHVVKTbatD1dKbVVK\nnbL9DavsupYUpZRRKfWLUuob2/NGtjxap215tfwqu44lQSkVqpRao5Q6rpQ6ppTq5i3tppSaavs8\nHlFKfaGUCvDkdlNKLVFKXVFKHcm1zmlbKY1/2eI8rJTqWHk1L5oCYnvT9rk8rJT6j1IqNNe26bbY\nTiil7qucWhePKt9RANnAX0SkJdAVmGTLP/Ui8J2INAO+sz33VCYDx3I9fwOYZ8undR0tv5Yn8g6w\nSUTuANqhxejx7aaUqgP8GegsIq3RZgiOwrPbbSkwKM+6gtpqMNDMtjwBfFBBdSwpS8kf21agtYi0\nBU4C0wFs3y2jgFa217xvy4Hn1lT5jkJELorIAdvjZLQvmzrAMGCZrdgy4P8qp4alQylVFxgCLLY9\nV0A/YI2tiEfGppQKAXqhTadGRDJF5AZe0m5oMxKr2W46DQQu4sHtJiL/RZvunpuC2moY8Ilo/ASE\nKqVur5iaFh9nsYnIFhHJtj39Ce3mYtBiWyEiGSISC5wG7qqwypaQKt9R5MaW0rwDsBeIFJGLtk2X\nAE/NNDcfeB6w2p5HADdyfYjPoXWMnkYj4Crwse2y2mKllAkvaDcROQ+8BcSjdRA3gf14R7vlpqC2\ncpYTzpNjHQ9stD32yNj0jsKGUioIWAtMEZGk3Ntsd4Z73DxipdQDwBUR2V/ZdSkHfICOwAci0gFI\nIc9lJg9utzC0X56NgNqAifyXNrwKT22rolBKzUS7vP1ZZdelNOgdBaCU8kXrJD4TkS9tqy/nnO7a\n/nqiuqs7MFQpFQesQLt08Q7aqXzOzZbO8m15AueAcyKy1/Z8DVrH4Q3tNgCIFZGrIpIFfInWlt7Q\nbrkpqK1cyQnn9iilHgUeAMbkSkPkkbFV+Y7Cds3+I+CYiLyda1PunFPRwNcVXbfSIiLTRaSuiDRE\nG0DbLiJjgB1oebTAc2O7BJxVSrWwreoP/IYXtBvaJaeuSqlA2+czJzaPb7c8FNRW64A/2mY/dQVu\n5rpE5REopQahXfIdKiKpuTatA0YpzeTZCG3A/ufKqGOxEJEqvQA90E55DwMHbcv9aNfyvwNOAduA\n8Mquaynj7AN8Y3vcGO3DeRpYDfhXdv1KGFN74H+2tvsKCPOWdgP+BhwHjgCfAv6e3G7AF2jjLVlo\nZ4MTCmorQKGZMGOAX9Fmf1V6DMWM7TTaWETOd8qCXOVn2mI7AQyu7Pq7sugpPHR0dHR0CqXKX3rS\n0dHR0SkcvaPQ0dHR0SkUvaPQ0dHR0SkUvaPQ0dHR0SkUvaPQ0dHR0SkUvaPQ0dHR0SkUvaPQ0dHR\n0SmU/w9YFHes4GxSjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc81048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4cS3lHsurzoNqoq7bQM7mYKjk/0K5QisrpfqhKdk3QeviedIhSwPgeaXUQrRu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\ndHRCCL3S19HR0Qkh9EpfR0dHJ4T4f0VAYEsUqhC7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f74dd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LwPLFQp27hHsaFt/KLwODksJdfuo4ezZiYFAkLl68SKtWrQgKCuKFF14o1baI\nCN+trcNfx+CFidnOQ0MpxYjRikpV4J0ZFi4n3vjMwJQpU+jfv7/T9Hr16jld1p6QkECVKs4VpAcN\nGsTLL798w20yuLVxCwciIlnASGADcBhYISIHlVJTlVJdAZRSTZVSZ4CewByl1MHSa3HpsHTpUpo0\naUJgYCAVK1bk4Ycf5scffwSc3zyUUrliCx06dIiuXbsSEhJCUFAQbdu2Zdu2bbnKZGRkMGXKFGrV\nqkVAQACxsbEMGTKEEydOWPOsW7eO++67j4CAAMLDw+nXr1+u+FkLFy7MN7IqaDclLy+vXIEZR4wY\nQWBgIIGBgfj4+ODt7W3df/jhhzlx4gRKKeux7G358uUOzzF37lwiIiJITk5m5syZ+banIIp6E/0x\nQTh+NIIBQxVNmuUdYfj5KV6c5IEpTXMiZrPQtm1bIiMjCQ4OpkGDBjckIGbPwYMH3WqapCDsr92C\naNOmDfPmzSuWc/fq1YuNGzeSnp6eKzAkwIsvvkitWrUICgrizjvvvCkheNwVt3Ag4FKo910iUkVE\nAkQkXETqlW6Lby6GImHJKhKWNFeThHmzM4mqlEznR523pWqM4qlnFYd+g/i1YigSlhL5KRIGBASw\ndu1arl69yqJFixg9enSeH2G3Da7EOymr260SC8tQJMyhpBQJs+nRo4dERUVJcHDxKhIGBUZJTOV+\nsmrFjgIVCS0Wi0z/d5b06Zol587maLkbioTupUiYzSOPPCL/+c9/Cqw3P8pqLKxSv8mX5HarOBBD\nkTCHklAk7NOnjzV9/vz5kpycLCZT8SkSPtl/rHRrf10Wz09xWZHw0t8W6f94lkx6IUs6dTIUCUXc\nT5FQRHPE0dHREh8f77BOVymrDsRtprAMnGMoEualOBUJV61aZRVdGjJkCEFBQda04lAkVBlxxFbz\npfcAf5cVCcMjFIOHKw4fgGef/tpQJMQ9FQlHjBhBgwYNeOih20ZdIheGAykDGIqEeSlORUJPT08u\nXryI2awpEtaoUYPg4GBiY2Ot5yoMqamCj3ckFnM5nn/JA29vdUOKhG3bKxo1hc/mCQf2exmKhG6m\nSDh27FgOHDjAihUrSv0ZW2lhOJAygKFIWHw4UiQ0mUxUrlyZpUs1RcJNmzZx9epV66ozbUR/Y4qE\n6enC0k8tWCyK8XEe3BGrlb0RRUKlFKNe9KDKHfDGKxb27BRDkdBNFAnj4uKIj49n48aNBAcH33C/\nbxXcxoEVoWVCAAAgAElEQVQURanwVsdQJCw+7BUJ//77b+tKtmxFwvDwcFJTU5k4sXCKhKmpwlvT\nLJw+CYFBUO+enBvbjSoS/rTtW8bFpVOpSibPDl/Mli2GImFpKxK+/vrrLF26lE2bNhEeHn7Dfb6V\ncAsHYhON92E05cEnlFJ17bINBa6ISE3gHeCNm9vK0uWFF17g7bffZtq0aURGRlK1alU++OADHn30\nUZfrqFWrFj/++CP79+8nNjaWihUr8uWXX7Jhwwbuv/9+a75Vq1bRqVMnevfuTUhICHfffTe7d+/m\nwQcfBKB3794sXryYd955h/DwcOrWrUtaWho//fRTrn+obdu24efnx0MPPYSfnx9+fn7Mnz+fbt26\ncc8991hHINHR0YwePZp169Zx+bJrmgihoaG53gNxVbN69OjRdO3alQ4dOhAUFETz5s3ZsWMHAE8+\n+SQxMTFUrlyZunXr0rx581xlhw4dyqFDhwgNDbXafdasWaxdu5bQ0FA+/fRz6t/djW/XCr/tg86P\nKXx8cp+/Tp06fPLJJ4wcOZLy5ctTs2ZNFi5c6LCtIsKUKVOoUSOKBV9Ec/Lc+zS++wvWrWrArp8F\ns7nwYYji4uKIiYmhWrVqdOjQgQEDBljTfHx8WL16NQsXLiQsLIzly5fz+OOPW9ObNGnich8KYteu\nXTRr1ozAwEC6du3KrFmzqF69OqC92zRw4EBCQ0NZsWIFY8aMIS0tjYiICJo3b07Hjh1z1TV69GhW\nrVpF+fLlGTVqFEFBQWzcuJFly5ZRqVIloqOjGT9+POnp6U7bk+1ARITff/+devXyvi0wceJETp06\nRc2aNa3X32uvvVao/pd13CUWVqGVCiWfDhQ2FtaJ48KR34tmlyNHjlC7du0i1XGrcEvYQnTtUgtY\nLJCRoW1pqXD+rHD6FPxPn1pv86CiZz9Fhai8U15FiXmUliqs/0rYuF5IvASh5aFqDERWUIRHgq8v\neHlpm/LQVBQVFIuSYklwS1wXxURJ2OKueoqqMYX78l2NheUuDqTAYIpKqQN6njP6/jE9zyW7umwV\nCRsvW7bshtuzd0dlftpcvbDdMbiN8PS0EBxqIjziOmERqdSu+zflw9Oc5k9JSSEwMLBI57RY4PjR\ncI79EUHy1XJcu+rL9RTfItVpcOvR5qGj3NPI8YKBgmjbtm2ZCqZYbIihSOiOGLbIwbBFDoYtcih2\nW6zeUKTibqlI6AxXovFm5zmjT2FlKxU6RQxFQrfAsEUOhi1yMGyRQ1m1hVs8RMe1aLxfAwP1z7ZK\nhQYGBgYGpYBbPAMBp0qFU9Feqf9aVypcDDRCk7y1KhU6IyIiQrJfBrvZXL9+nYCAgFI5t7th2CKH\n/GyRlgnX0oWUDDBl6U/tAU8PCPRRBPpCoK/C000fit8oxnWRg7vZYs+ePWVHkbCkMBQJ3QPDFjnY\n28IiwoYjZmb9mMmxREEB9St6UL+ih9VRXEwRfjphJjkdfDyhXyMvhjfzJjygbHsS47rIwd1sUdYU\nCQ0Mbjt+PmnmjYQMDl4UqocpZjzsQ5sanoT753UMWRbh1/MWlu/PYtGeLJbvz2JQEy9GNPfGz7ts\nOxKDsou7PAMxMCgR3EmRMJtr6cLL36bz5PJ0rprgjU4+fDOkHN3v8XLoPAC8PBT3VvbkjU6+xA8p\nR9sansz+OYtHPjWx87QWC8pQJDS42ZSIAylsWBKlVHul1B6l1G/63wdsyiTode7Ttwol0XZ3xlAk\nLNuKhAAHkkLotMDEyt/MDLvPi/gh5Xj8bi88PRw7DkeKhNXDPXi3qy+Le/tiFuj3RTpTN2WQWcCb\n6YYioevkp0g4btw4qlatSnBwMDExMbftW+hQAg6kiGFJLgGPiMg9aCuuFtuV6yciDfXtf8XddnfG\nUCQs24qEaZlC3IZUZh2pQ6APrOjvy7g2PpQrYPopP0XC5jGerB9cjicbe7F4bxbL9meRlHbrPtO8\nmeSnSDh06FB+//13kpOT2bZtG59//jmrV68upZaWMq6IhtzIBrQANtjsvwS8ZJdnA9BC/+yF5jiU\nXR6FttrKV99PAJrcSFtuFUEpQ5Ewh7KoSPivSa+LT3AFCWrUR0YsPCar13ydryKhM/JTJNx2Ikuq\ndpooQfUfl/s69jMUCW+SIuGZM2fk7rvvzvP/cKOUVUGpkniIXhk4bbN/BmjmLI+IZCmlrgLh5H4T\nszuwV0RsI599qpQyA18C0/SO5sIulInTOd+SJiUlpdjOvXPnTtLS0ggLC3Na54kTJ7h48aLD9B07\ndnDmzBnWr1/PsGHD8uSpXbs2c+fOZcOGDSxatIjatWtz7Ngxh2HDT506xalTp6hatWqeeho3bsyX\nX37JAw88wO+//87Vq1dJSEhwaIt3332X+++/n6pVq3L48GHmzJlDnTp1CuxTdrj0LVu24Onp6dAW\n2QwaNIgLFy4QGRnJ0KFDAU3o6Pvvv2fGjBmEhITw/vvv07NnT/79738DUK1aNasA0dy5c+nWrRvz\n5s2jdu3atGvXLldd2e3Ktm92+8xmMwkJCezeu49z5y+w6KeL3P3yrwyIOYY6v5YhY6Ywffp06tSp\nw3fffUeHDh347LPP8LGPvKjz0ksvsWfPHjIzM2natKnTa6tl+DmWb1zP6cZLaf7aW/htncCTTz7J\n7NmzATCZTOzfv9/atwMHDrBo0SJMJpM1yGBCQgKZmZkMGDCA7t278+abb/LTTz/x6quv8sQTT5CQ\nkMDRo0cZN26c0z6YTCbmz5/Pq6++io+PD8899xwTJ06ka9euudqbkpLC8OHDqVWrFnFxcWRlZfHH\nH3+QkJDA1KlTadu2LXPnzqVy5coA/PDDDzRt2pSRI0disVh488036dOnD9OmTaN9+/asX7+e9u3b\n07lzZwDi4+MZOHAggwcPZsKECRw/fpxhw4aRmpqKo+X9e/bsIS4uDrPZTFZWFoGBgaSnp+Pl5cXs\n2bOZNm2aVcNm6dKlLF68GJPJRMWKFalWrVqR/t+L835xU3HFy9zIhvaS3zyb/QHAB3Z5DgBVbPaP\nARE2+/X0YzVsjlXW/wYBG4EnC2rLrTICWbJkiURFReWbJy4uzirDabth8wvZ09PTofRmtkztmTNn\n5KmnnpLevXs7Pc/WrVsFcPiL8qOPPpKaNWuKSP4jkJMnT4pSSn755RcREenQoYOMGjXKYZ+cjUDs\n+3no0CGH7bWXob3zzjtl06ZN1v1z586Jl5eXwxHNlStXBJCkpCSHdYk4H4H8cjZLmr74reDpLf9a\nnSRXUjVt865du8rLL7+cq47atWs7lEu1JSMjQ7755huZOXOm0zxxcXHSrl07WXsoU5q+d12qv7hb\nvH3KSXqWdm7bEUi1atVyXQtz5syxjkC2bNkiFStWFIslR4+9RYsW1r6PGDEi3z7ExMTI4sWLrWlj\nx46V4cOH52nv5s2bZcCAATJs2DDrSMIWe9va88svv0hoaKh1317SdtmyZdKyZctcZZ5++mmZMmWK\n0zpFRPr16ydr1qyRlJQUqVWrlqSmpjrMZ7FYZO/evTJ58mRJTk7Ot86CKKsjkJJ4iH4jYUmwD0ui\nlKoC/Fd3ENafwCJyVv97DVgK3FcCbXdLDEXCvLirImFqhrDpaBY9l6STlgUREZG8/VgIoX7as44b\nUSS0xdvb22VFwi53eRE/1I/WtQPJzDDx0NwU4n/Pfe0YioR5uVFFQqUUjRo1ws/Pj7i4OKftvpUp\nCQdS6LAkSqlQYD0wQUR+ys6slPJSSkXon72BLmijmNsCQ5Gw+CgpRcJzyRZmbM7gm73nOHZZGN7M\nizce9sHXK3eZG1EkdISrioTh/orJ7bUIveW8YNTXGfx9Xdh/zoxFxFAkdMCNKBLaUlwqkWWRYncg\nIpIFjER7UH4YWCEiB5VSU5VS2ZOg84FwpdSfwPNA9lLfkUBNYLLdcl1fYINS6ldgH9oI5pPibru7\nYigSFh/FqUiYaRaq39WAQVMW0+aj63zw+Tek//Uj/Rp68WJrH/x98jqcG1UkjI+PJy0tjczMTJYs\nWcIPP9y4IuGageV4raMPZgu8vTWT9p+YuPOf3Zk6zVAktKcgRUKLxcKcOXO4cuUKIsLOnTv58MMP\nXfrhdCtSUi8SWtD1dwAzgIhMFpHskYjoeXJ9FpFpwDQgEPADxovI/0TkOjAJzZH4AudFxPG49RbF\nUCTMTWkoEg4aPIR9vx0iIDiUGs270uyDNJL+8SaHf17PqVcq0SxlFT0ef5RAX+dLcwujSFihQgUi\nIyOZNWsWy5cvt97gXMXTQ9GzvhfRQYpnmntTIVBxpPYEDqRVJqpKNZr+sz2tu/TLDr1lKBIWoEj4\n3//+lxo1ahAUFET//v157rnneO655wrV/7JOscfC0t8DOQK0R1uBtQt4QkQO2eR5BqgvIiOUUn2A\nx0Skt/6+yBdozzcqAZuAbJmufOt0RGFjYZktQhHUQgH4YcsPtGrdqmiV3CLcTFs4upwlW01QwKJ/\ntghkWcBs0UYS6VmQbgZTppCcDldNQlKacP6acD5ZOHNVOHLJQpr+mCYiANpU96RNDU/aVPfMM1Xl\nDHeJeXTkbwub/jTz/Z9mfj1vsTqPO0IV1cMUFYM9qBSsiAhQBPtCSDlFgI/C1wt8vbSYXF4eCk8P\n8NJ/hnroCojK5q8t9vvG/0gOJWELT4XTF1QLojRjYd0H/Cl6pFyl1DKgG2B7s+8GTNE/rwI+UNoE\nZjdgmWhLd//Sp7iyH5YXVGexsWBXFm9ucf2BrmOawm7nynS3F2XXFt6eUDFIUSlY0au+F3WjPKhb\nwYPakQqPUn45sSjUjvSgdqQHz7TwJjFVOHDBwqGLFg5etHAqycL+81lcKfGvrOxeF8VP8dvilfbe\n9G3kXax12uNu74FUBrbbla2sfy6oTiD3eyBAilLqj0L0oTgw1NZyKNO2cD5jXijKtC2KGcMWORS7\nLfqNh36FL16mFAmLDbGRtC1NyqrCWElg2CIHwxY5GLbIoazaoiQcSGHlaZsAvdFiZ1URkRl2ZZsp\npf7W9ysAP2NgYGBgUGqUxEN0L7QH3u3Qbva7gL4ictAmz7PAPTYP0bsD9wLPAG/p2V4A5gC10J7J\nnQPigWGO6nSEoUjoHpS0La5mCd4K/MuAVJ9xXeRg2CIHd7OFq4qExR7KRHdIndCcyDFgkn5sKtBV\n/1wOWAn8CexEcyAb9LRJaG+l/w08bFPn28AV2zoL2m6VUCZlnZK0hdlikYpbL0qnfZdL7BzFiXFd\n5GDYIgd3swUuhjJxC0lbpVQPoKOIPKXvDwCaichImzyDgNfRHMsR4F8ictpBXbbBFBsvW7as5Dvg\ngJSUFAIDA0vl3O5GSdriJD48o2rgJ2aWc4T8wyuWPsZ1kYNhixzczRZt27a95SRt1wJfiEi6Umo4\nsAh4wD6T2DxEb9KkiZTWmnt3We/vDpSkLRadT4MjyaQpTyo0vp97Akt22WJRMa6LHAxb5FBWbeEu\nkrYFPngXkUTJCe0+D2h8k9pm4MbsSM4gO2LIzuS87+64o6RtSWFI2hrcbNzFgRQYgFEpVdFmtyvF\nvjzf/TEkbfNK2s5pVIlrHWvgt+UrdjhwIO4maXujOJK0LSyGpK3r5Cdpm83ly5eJjIws8Dq/lXEL\nByKuBWAcpZQ6qJTaD4wCBpVOa0sHQ9I2r6Tt2aRk/OKPM+3wBdo+3tPhCMRdJG2BAsPxOyI/SVuD\nkiM/Sdtsxo8f77KMwC2LK0/ay+p2q6zCMiRtc7CVtN2UaBL/hAuyKdEkb55MEf+EC3Ipw2zN6y6S\ntjNmzJCoqCjp37+/bN68OV852PzIT9I22149e/aUAQMGGJK2JSxp+9NPP0nz5s1lwYIF1uu8KJTV\nVVilfpMvye1WcSDx8fHi6emZrw64Kw4kKipKFixYkCfP999/Lx4eHpKamirjx4+XVq1aOT1Ptnrh\n8ePH86RNnjxZmjdvLiIFO5AHHnhAxo4dKxcuXBBPT0/ZvXu3S32ydSCv/XVNAhIuyNVMs2y5ki7+\nCRck/pIpV357FcF3331XmjVrJqdPnxaTySRPP/209OnTx5o+f/58SU5OFpPJJKNHj5YGDRo4rUuk\nYAfi6ekp48aNE5PJJKmpqTJ37lyJjIyU7du3S1ZWlixcuFBiYmLEZMrdbls6d+4svr6+AshDDz0k\nZrPZYb64uDjx9fWV9evXS1ZWlkyYMEGaNWtmTbd1IOPHj5eWLVtKYmKinDp1SurVq2d1IOnp6XLH\nHXfI22+/LRkZGbJy5Urx8vKy9mvv3r359iEmJkaaNm0qZ8+elcTERLnzzjvlo48+ytPezZs3S58+\nfWTatGliNpslLS1Ntm7d6tS2ly5dklWrVsn169clOTlZevToId26dbOm2ysSpqSkSJUqVWTBggWS\nmZkpe/fulfDwcDl48KBD+23atElCQkIkICDAqu7p7e0t/v7+EhISYlVczMrKkkaNGsnu3btzXedF\noaw6ELeYwjLIn8TERCIiIvDyyn/R3IoVK3Kpr4WGhuZKv3TpEhUrVsxTrmLFilgsFi5fvkxiYqLD\nPLZ1ZJdxVI8r6n2nTp1i8+bN9O3bl6ioKNq1a3fDWiARERFMrl8ZU5fa3BERRsCZP/EEh89BbPn4\n44+ZPn06VapUwdfXlylTprBq1Srr9NKQIUMICgqypu3fv5+rV6/eUNts8fDw4JVXXsHX1xc/Pz/W\nrVvH8OHDadasGZ6engwcOBBfX1+2b9/utI5169Zx7do1vvnmGzp06GDVy3BEy5Yt6dSpE56engwY\nMID9+/c7zLdixQomTZpEWFgYVatWZdSoUda07du3k5mZyZgxY/D29qZHjx40bdrUmj537twC+zBq\n1CgqVapEWFgYjzzyCPv27XPYDm9vb06ePMm5c+coV65cvs8TwsPD6d69O/7+/gQFBTFp0iS2bNmS\nr91iY2OtGveNGjWie/fuDkXVANq1a0dSUhKPPvooK1eu5OzZs8TGxlrVL7N1WN577z2aNWtG48bG\nOh7DgZQBDEnbvPzv77+Jij/K8N2nSUpKovHddbk70KtAB1LSkrb2REZGUq5cOev+zZC0zcbf3x+T\nyeTwujEkbfPiiqTtuXPneO+995g+fbrTdt5OGA6kDGBI2ublaJqZK1nCfcE57300C/Zmz7VMzOL8\n5diSkrTNxv7mZF/mZknaFoQhaZsXVyRtd+7cyfnz56lbt65VCG3nzp1ER0c7dWS3Mm7jQJRSHZVS\nfyil/lRKTXCQ7quUWq6n71BKxd78VpYOhqRtXnbpIw1bB3JfsDcpZuHgdecjteKUtAVo2LAhS5cu\nxWw28+233+Y7pQKlI2nriF69evH664akrT0FSdpmLyXPvnanTp1Ko0aN2LdvH56e7h4HofhxCwei\nqxh+CDwM1EWLyFvXLttQ4IqI1ATeAd64ua0sXQxJ29w8XaciaQ9Xp2lUqFXStpnuTBwt582mKJK2\nQ4cO5dChQ4SGhlrtPmvWLNauXWudHino+ygNSVtHxMXFERMTQ7Vq1ejQoQMDBgywphmSts4lbX19\nfXNdtyEhIXh7ezt9V+RWx11iYbUApojIQ/r+SwAi8rpNng16np/1iL8XgEjJpwOFlbSNT0xn+f9M\nN1zOlv9dvEiFqKgi1XGrUBK2SLiSQf1AL76uX956TESI/flv/D0U9QK8KOeh8FSOp55KC+O6yMGw\nRQ4lYYsno8vxQHnfQpUtTUnbwlAUFcNcTzjtgik6Dd2QHz8Qyk+E3XA5W0R8OXqx8Kt3biVKwhY+\nwL2XL5GQkHuV0aOE8RNBHDEpMvHgxl/dK1mM6yIHwxY5lIQtYi8ew4PkYq3THncZgbgSjfeAnueM\nvn9Mz+N0iYwuQHWyRBvvHEOuMwfDFjkYtsjBsEUO7maLGHFBD8RdRiCFVTFMzK9SVwxQUpRVicqS\nwLBFDoYtcjBskUNZtYVbPETHhWCK+v5A/XMP4Pv8nn8YGBgYGJQsbjGFBaCU6gS8C3gCC0RkulJq\nKtor9V8rpcoBi4FGwGWgj4gcd16jIWnrLhi2yKGs2uKcOYMsgTu8fIqtzrJqi5LA3WzhqqSt2ziQ\nkqCwq7CKg7IqEFMSGLbIoSzaQkTo9PdRUsTMxgp18FPFM3FRFm1RUribLVxdheUuU1gGBgZuymlz\nBslixgIczkwr7eYYuBGGAzG4pTEUCXMorCLhwcw0jo6ayKkZszhoOBADG4rkQIoSfkQp9ZJ+/A+l\nVPYLhFWVUpuVUod08ajRNvmnKKXOKqX26VunorS9LGIoEuZVJMzeli9f7vAchiJhDoVVJDyQmYaX\ngiDlwYGb6EDcVZFw0KBB+Pj45Lr+bsc4WFAEB1KU8CN6vj5APaAjMFuvLwt4QUTqAs2BZ+3qfEdE\nGuqb65H3bgEMRcK8ioTZx1NSUujdu7fD8xiKhEXnQGYaoR5eVPD05kBGGrfyc9NsClIkHDduXK7r\n73aMgwVFG4HcB/wpIsdFJANYBnSzy9MNWKR/XgW0U9p/cjdgmYiki8hfwJ/AfSJyXkT2AojINTR5\n28pFaOMtwdWrV5k8eTIffvghjz/+OAEBAXh7e/PII4/w1ltvuVzPlClTaNGiBdOnTycsLIygoCBG\njRrFgAEDGD9+PACbNm3iu+++46uvvqJp06Z4eXkREhLCs88+y9ChQxERXnjhBV5++WX69u2Ln58f\n0dHRzJs3j8DAQN555x2X2vLll18SGhrK5MmTWbRoUcEFCsGgQYNYtGgRb775JoGBgWzatAmLxcKM\nGTOoUaMG4eHh9OrVK1f8rZ49e1pjHLVq1YqDBw8C2kjm888/t9b1yCOPAHl/JduOUrKnhd544w2i\no6MZPHgwoI3eGjZsSGhoKP/4xz/49ddfnfahfv36Vh0YpRSZmZm5oujak5GRwZNPPklQUBD16tXD\ndhFJbGwsmzZtAiAtLY1BgwZRvnx56taty65du3LV88svv3DvvfcSFBTEN0OeJSAji0gPb5LEzDlz\nZr59iI2N5T//+Q/169cnJCSE3r17YzI5Dg30559/0rp1a0JCQoiIiLD+EGjVqhUADRo0sI4wr1y5\nQpcuXYiMjKR8+fJ06dLFOuqdNGkSW7duZeTIkQQGBjJypPYO8u+//0779u0JCwujTp06rFixwqnt\nsrly5QoiQlhYGLt37y6W2GO3KkV5kbAo4UcqA9vtyuZyFPp0VyNgh83hkUqpJ4HdaCOVPD93iyOU\nSXGQkpJSbOfeuXMnaWlphIWFOa3zxIkTXLx40WH6jh07OHPmDOvXr2fYsGF58tSuXZu5c+eyYcMG\nFi1aRO3atTl27JjDsOGnTp3i1KlTVK1aNU89jRs35ssvv+SBBx7g999/5+rVqyQkJDi0xbvvvsv9\n999P1apVOXz4MHPmzKFOnToF9ik7XPqWLVsK/NU3aNAgLly4QGRkJEOHDgU0oaPvv/+eGTNmEBIS\nwvvvv0/Pnj3597//DUC1atWsAkRz586lW7duzJs3j9q1a9OuXbtcdWW3K9u+2e0zm80kJCSwb98+\nzp8/z759+/jss88QEfbv38+UKVOYPn06derU4bvvvqNDhw589tln+Pg4XiL70ksvsWfPHjIzM2na\ntKnTa+vEiROsWbOGqVOnMnDgQBYsWMCTTz7J7NmzATCZTOzfv9/atwMHDrBo0SJMJpM1yGBCQgKZ\nmZkMGDCA7t27M+KDd5h56Bf2jniRKv37AfDOii+Y/+wYp30wmUzMnz+fV199FR8fH5577jkmTpxI\n165dc7U3JSWF4cOHU6tWLeLi4sjKyuKPP/4gISGBqVOn0rZtW+bOnUvlytqt4YcffqBp06aMHDkS\ni8XCm2++SZ8+fZg2bRrt27dn/fr1tG/fns6dOwMQHx/PwIEDGTx4MBMmTOD48eMMGzaM1NRUHC3v\n37NnD3FxcZjNZrKysggMDCQ9PR0vLy9mz57NtGnTaNiwIRcuXGD16tW89957REdH069fvyJHSC7O\n+8VNxRXZQkcb2st882z2BwAf2OU5AFSx2T+G9sr+B0B/m+PzgR42+4HAHuBxm2NRaO+IeADT0d4V\nuS0kbZcsWSJRUVH55omLi7PKcNpu2MiCenp6Snx8fJ6y2TK1Z86ckaeeekp69+7t9Dxbt24VwKHG\n9UcffSQ1a9YUkfwlbU+ePClKKfnll19ERKRDhw4yatQoh31yJmlr389Dhw45bK+9DO2dd94pmzZt\nsu6fO3dOvLy8HMoFX7lyRQBJSkpyWJdIwZK23t7euWzVtWtXefnll3PVUbt2batcqjMyMjLkm2++\nkZkzZzrNExcXJ+3atbPuHzx4UMqVK2fdt5W0rVatWq5rYc6cOVZJ2y1btkjFihXFYrHIopS/5R8X\nDsl9LZrLSxMnSruLh6XFkCfz7UNMTIwsXrzYmjZ27FgZPnx4nvZu3rxZBgwYIMOGDbNqm9tib1t7\nfvnlFwkNDbXu20vaLlu2TFq2bJmrzNNPPy1TpkxxWqeISL9+/WTNmjWSkpIitWrVktTU1Fzpe/bs\nkUuXLklmZqasX79eAgMD5ccff8y3zoK4HSVtbyT8CHbhR5yWVUp5A18Cn4vI6uwMInJRRMwiYgE+\nQZtCuy0wFAnzki0zmr3dddddLpUzFAk1XFUkPJCRRlVPH6rHxOKhFHd5+XHq1O2rSAhw7733Eh4e\njpeXF506daJfv36sXr3aYZ23OkVxIEUJP/I10EdfpVUNqAXs1J+PzAcOi8jbthUppWxFuB9DG93c\nFhiKhMWHoUio4YoiocVi4WBmGnd7+1nT63n7Ya5YgfETJ96WioSOUErdFgsLHFFoByIiWcCnwB/A\ndeCCiBxUSk1VSmVPdi4GOiulMoB5wPt62YNoeh4pevn5ImIG7kebChuhlEpXSp2zWa77oVIqVSmV\nDrwIuC7FV8YxFAmLD0ORUMMVRcJX332Hyxkmrn2zyapIeLePHxX69eSjObenIiFoqxBTUlKwWCxs\n3ObFRNkAACAASURBVLiRJUuW5Hm+c7tQ1GW8g4A7gQAgWilVV0Qmi0j2SKQ/sF5EfICngJF62bpA\nNNqzjjrAEL2+n4HjaMuCg4C/gRN6XVnAEBHxBdYCnQvb9rKIoUiYm9DQ0Fzr8PP7hWiLoUio4Yoi\n4eJFi9h5Zwt+W/21VZGwnrcfgQ3v5sn3374tFQlB+84rV65MaGgoY8eO5ZNPPnGrMCQ3k0LHwiqK\niiAwwTZvdj69WJ46gRloziRatNVcuc7tjMLGwjpvzuBUVsYNl7Pl119/pX79+kWq41bBsEUOZckW\nX6clsSMjhQ2RdfC0mR7qdelPKnh4MyAgPJ/SBVOWbFHSlIQtYr18ifL0LlTZm6FIWFLLeB3VGQ4k\n6dNm9vlzURzLeLeG+fNtVNANl8vFHeUhyfl6/dsKwxY5lDFb1EpJZ+uh3NNy0RWD2RPqxy9JqU5K\nuUgZs0WJUgK26Ho+mWZJJRs5wF0EpYoNEZkLzAVNkbBt27aGImHpY9gihzJli23kvAlcApQpW5Qw\nxW6LbQVnyY+YgrMUzYEURUUwv7KOjicCoUopL30U4uhceRBDkdAtMGyRg2GLHAxb5FBWbeFWy3id\n1amX2azXgV5n4aPKGRgYGBgUmSIJShVFRVApNQkYgra6aoyIxDurUz9eHS3eVhjwC9qb7M6XU2Ao\nEroLZdEWmVi4QjrB+FCO4guUVxZtUVIYtsjB3WxhKBJiKBK6C2XRFp9Z/mC7XASghYqiu6qOvyrc\nihZbyqItSgrDFjm4my1uxiosA4NbklTJZI/8TXMVRQg+fCenOShXGOfRkDBVruAKDAxuE9xGkdAF\ncapWSqm9SqkspVQPR3UYGNhTGEXCHfI/MrHQVlWmm0c1xno04hoZbJWbq8Nxo5SUIiGUjpiWgfvj\nFg7ERXGqU2hvvi+9ua1zHwxFwpJXJBQRfpTzxBJEVRUIQIwKoi5hvDx4JBMnTSqwjuLEHRQJSwt3\nVSQETTfn3nvvJSAggCpVqrikM3Ir4hYOBBfEqUTkhIj8ClhKo4GljaFIeHMUCY+RzHlSaZkrdif8\nwyOaTCxcwrEwkiuUVUXC25H8FAkPHTpE3759mT59eq7/j9sRd3kG4spb7S5xKwpKpaSkMGnSJMaP\nH09YWJhVPS4oKIjOnTuTkJDgkqDUa6+9Rp06dWjfvr1VQa5+/fq0a9eOESNGMGvWLPbs2cOGDRtY\nvHgx169ft45wsmMCbd68mZEjR/LEE09QqVIlaxyp/v37s3nzZkaPHs2QIUMKFJTasGEDfn5+9OrV\ni9mzZ9O0adM87S6qoNSMGTPYtGkTSilmzpzJtGnTaNSoEcuWLWP9+vWkpKTQqFEjnn/+eYKDgwF4\nbuYUju/6lUUpGdSsUYMxY8ZQrVo1vlq3lqNLv+NPtYnFb8+mUaNGvPbaa7Rt25YlS5ZYRY9mzJhh\nFZ3at28f06dP5/HHH2flypU0adKEUaNG8frrrzN//nwuXLhAbGws//rXv6hRo4bTfmR/B4cPHyY9\nPZ01a9Y4DF9/4sQJzpw5Q4cOHfjxxx+pUKECL730klWoq0+fPowdO5bGjRuTnp7OO++8Y41f1rFj\nR6ugFMDRo0d56623OHPmDM2aNUMpZRXKAvj555+d9qFPnz489thjbNy4kYsXL9K0aVNeeumlPIJZ\nKSkpVpXHY8eO4enpyb333ktcXByjR48G4J577gFg7NixNG3alNdee43Dhw9jNpu5++67ef7554mM\njGTevHls3bqVbdu28dxzz9GxY0dGjx7NqVOneO+99zhy5AihoaEMHjyYtm3b5nvdXLt2jbS0NH79\n9Ve++uorIiIicl2Dr776Kh07dsTPz8/63QD5KkUWxG0nKFWcGy6IU9mkLcRGfCq/7VYRlIqPjxdP\nT0+HokfZOBJfEsktyhP1/9s78/Amq/Rh3ydpSZeUli4UoewDjCCbgLgBIoIoOAzKUpVFxBn5iQou\nyOaC4wKiCPq5IIrKgAgIjgguCE5hcAFRhCog+y5UoEL3LXm+P5ImaZu0oUuatOe+rlxN3+Wc8z59\n29O855znjo+Xd999t8Qx//3vf8VgMEhWVpZMnjxZevbs6bGeQvnUoUOHSux78skn5corrxSR0oVS\nIiLXX3+9TJo0SU6fPi1Go1F+/PFHr66pUChVWixcKS6BmjdvnnTv3l2OHz8uOTk58s9//lMSExNF\nRCTdmid93p4s753/WXJycmTChAnSsWNHx7nXjbpVukwdKWnWXMc2yhBKGY1GeeyxxyQnJ0eysrJk\nwYIFEhcXJ1u2bJGCggJ5//33pWnTppKTk+PxGgYMGCAmk0kAufHGG8Visbg97qmnnhKTySSfffaZ\nFBQUyJQpU6R79+6O/a5CqcmTJ8u1114r586dk2PHjkm7du0cQqnc3Fxp0qSJvPzyy5KXlycfffSR\nBAUFOa5r+/btpV5D06ZNpVu3bnLy5Ek5d+6c/PWvf5U333yzRHuTkpIkMTFRnn32WbFYLJKdnS2b\nN2/2GNuzZ8/KypUrJTMzU9LS0mTIkCEyaNAgx/7iQqmMjAxJSEiQd999V/Lz82X79u0SExMju3bt\nchu/DRs2SGRkpISHhzvkbMHBwRIWFiaRkZEOYVbz5s3l8ccfl8suu0waNGggd955p5w7d87jz88b\naqNQqjLxZlV7reXcuXPExsY63NieWLFiRRF5TlRUVJH9Z8+e5ZJLLilx3iWXXILVaiU1NZVz5865\nPca1jMJz3JXjjXzp2LFjJCUlcccddxAfH0+fPn0uOpV7bGxskessLUW3K/Pnz+e5554jISEBk8nE\njBkzWLlyJQUFBWyUk7QeczN967Zy7Nu5cycXLlwAoL4KRbANsnuLwWDg6aefxmQyERoaytq1a7n3\n3nvp3r07RqOR0aNHYzKZ2LJli8cy1q5dS3p6Op9//jn9+vVzpDt3x7XXXsvNN9+M0Whk5MiR7Ny5\n0+1xK1asYPr06URHR9O4cWMefPBBx74tW7aQn5/PxIkTCQ4OZsiQIUU+IS5YsKDMa3jwwQdp2LAh\n0dHR3HLLLezYscNtO4KDgzl69Ci///47ISEhpY6bxcTEcNtttxEWFkZERATTp08vNX3+2rVradas\nmUNR3LlzZ2677Ta3ThyAPn36cP78ef7+97/z0UcfcfLkSZo1a+aQlxWm0T9x4gSLFy9m1apV7N+/\nn+zsbB544AGP7ajJ+EsH4s2q9lqLNhKWpLKNhHtOH2FdwVGOTFtMz790cGskDCWIKEx8L6e9FggF\nupHQ3f6jR2u3kTA0NJQxY8bQunVrzGYz06ZN84kMzR/xiw5EbPmt7gfWAXuAFVJMTqWU6qaUOgEM\nBd5SSu2qvhb7Fm0krDw8GQm/uySXfR+u58Cnm0s1EiaocE6RxW5skwVqspHQtZN03d+4ceMKXYMr\ngWgk7NChQ5G6vJ2gURPxiw4EQEQ+F5HWItJS7OlLxEVOJSLbRCRBRMJFJEZESppeaijaSFh5uDMS\nvvbJEnZyjlYZIYSZQko1EuYcTuESwlho3cNJyazRRsJXX32V/Px8Pv74Y4eREOAf//iH19dQFoFo\nJBwzZgzvvfcehw4dIisri1mzZjFw4MCLvvaagN90IF4sJDQppZbb929VSjXzfSurD20kLEplGgmX\nb/ma+oTyzKgHyzQS7t29h5dibmDtrdN4zfoL/5o3u8YaCd9//32io6NZvny5w0gI0LVrV6+voSwC\n0Uh49913M2rUKLp3707Tpk0xmUy8+uqr5br+QMcvcmHZFxLuA/pim8K7DbhdRHa7HHMf0EFEximl\nEoHBIuJ+8r8dnQvLP/DHWJyTHLbLGX6UMxwng/GGy2inor0+/6RkMse6g3qYGGxoQQNCiSYEQxmP\nM/wxFtWFjoUTf4uFt7mw/KUDKbceV0q5gPJ2IJusv/OlHCv7wFLIzc3FZDJVqIyagr/EwopQgGDB\nSp59PWoTzFyjGtDD0PCiy9sr53nD+iv59rKCMWDCiAIUCnddib/Ewh/QsXBSFbEYpJpzpSG+XOcG\nWjLFiuhxi8wbrYyFhKejICa2YgNj+fn5BFc8eWuNwJ9iYbSCQSAkT2h0Dsw5aVhIYyP7ylXegCC4\nEAbpoZAeJhQYLKDA0381/hSL6kbHwklVxOLYmT3kXPBuent58ZcOpNIQrbT1R3QsnOhYONGxcOJv\nsahypW25UEr1B17BJox6R0Rm4bKQUCllAiYBjZRS3YDhInIEm9b2oFKqsEttaN/mEdFKW79Ax8KJ\njoUTHQsngRoLn3YgLll3HYPlSqlPcVlICAzE1jn0BNoDLwDDgQ1AexHpZB9Ev7W08Q+NRqPRVC0+\nHUQvbbDcRWWbAPzbPtvqGWACEAm0xuZNP0MxPa4ntNLWP9CxcFIYCwtWMskmjzyk2IiJQlGHYMIJ\nxViJOl1/Q98XTvwtFt4qbX39CMvjYLmIfA58rpT6FXjWvu0JpdQd2AbLc7G1Nx3ItpdVogMpPoj+\n0ksvVdnFlEZGRgZms7la6vY3dCycpOWkk/NXSG2UCQKRf4QSkh5MaEYwSiA7Ip/siHzS4nKwGoR6\np8KIO2bGWOA3S7YqDX1fOPG3WHg7dhxIg+ingCYick4p1QX4RCnVTkTSXA9yHUTv2rWrVNfcan+b\n112d6FjYSJFzfJr9NQUmK21UM65QHTAnhLk9Nkty2Ca/sKfRIbIbWehnuJpGqnxTMv0VfV84CdRY\n+PrfGm+y7roOqAdhe3x1TkRyReQcgIj8BBzE9lhLo/FIeZS2lY2IsMt6gE+sX6OsilsNfbnecCVm\n5b7zAAhTIfQydGOIoR8hmFhj3cgO62+lJnHUSluNr/F1B+JN1t1PgdH290OA/4qIKKXi7IPwKKVa\nAK1w8wirJqOVtlWvtC2rvRf7R7RALCTJD/xPfiSBeJrviCFexZR9op2h19/Kgw1G80i9uxnY+Uae\n/uQF8uXizYaglbYXQ2lK23bt2hW594KCgrjlllsqpd5Aw6cdiDdZd4GFQIxS6gDwMFCYF6snkKyU\n2gGsBMaJiHeJk2oAWmnrG6VtZZIlOXxq/S975TBdVTv6Wa++6LGMQqVtxoUMnp//ArNGPc17J1eQ\nIZlV1GoNlK603bVrl+O+S09Pp3HjxgwdOrSaWlrNeGOdCtRXTTESnj9/XsLDw2XFihUej/HGSDhi\nxAi56aabShwzbtw46dGjh4iIrF+/XkJCQuTYsWNu67FardKkSRN54YUXimy3WCzSrl07eeKJJ0Sk\nbCPhokWLJCEhQebNmyft2rXz+pouxkg4evRoCQoKkuDgYAkPD5f169eLxWKRmTNnSosWLSQ6OlqG\nDh1axCY3ZMgQiY+Pl7p160qPHj3k119/FRGRt956q0hZAwcOFBHPRsIz1lSZuuFZiWoULZNmTpH4\n+HgZMWKEJCUlyZo1a6Rjx44SGRkpV111lezcubPMaxER2bp1q9QxmWTadzPlvYL/yCnrmRLxGjp0\nqIwcOVLMZrO0bdtWtm3b5tjvaiTMysqS0aNHS1RUlFx66aUye/Zsh5FQxGYd7Ny5s5jNZhk2bJgM\nHz68iNmxtGto2rSpvPjii9K+fXupW7euDBs2TLKzs0tcT1JSkuzfv1969uwpdevWlZiYGBk2bJiI\niPTo0UMACQsLk/DwcFm2bJmkpqbKgAEDJDY2VqKiomTAgAFy/PhxERGZNm2aGAwGMZlMEh4eLuPH\njxcRm0HzhhtukHr16knr1q1l+fLlZcY5NTVVmjdvLiIib7zxhkyaNMnjsRs3bhSz2SwZGRllllsa\ngWokrPY/8lX5qikdiFbaOqlKpa2IyMKFCyUtLc2t0rZ4WSLuO5B7p90nCwpWyJQNz1SJ0vZsQaos\nKVgj8wuWS7Jlr1itVke8tNK26pW2rowZM0ZGjx7t8WfnLYHagdS8uYE1EK20LUlVKG3Blqo7IiLC\nrdK2LPIkn9/lD47K78QTSy9DtypR2sYY63GboS+NacA3sp0vrd+QI7YU5VppWzRuVaG0LSQrK4uV\nK1dy1113eWxDTUd3IAGAVtqWpLKVtikpKVgsFqZMmULLli3dKm09ISIclhN8ZP2SdDJpqOoz0NCL\nEGWqMqVtiDJxk6EH16jOHOMUK6xfkioXtNLWhapS2hby8ccfEx0dXSmCr0BFdyABgFbaVh6elLaN\nGjVi6dKlrF69ulSlbXHCwsL4ImMjX1q/wYiRkBQjl6g4DMrg9pzKVNoqpehgaMOthhswUYeDcpzj\ncpoUKTVFHKCVtu7wVmlbyKJFixg1apRW2vqSipgHlVJT7dv3KqVu9GW7qxOttK083CltC2eypaen\nYzKZSlXaHjp0iHwpYK/1MKstX9OgYwJffvg5V1s7EfEVbNn0fYk6XakKpW2cimao4UaaqYbkkc/H\n1vX8x7KB/VbPi4m10tY93ihtwdbZJCUlMXr0aLf7aws+7UBckineBLQFbldKtS122FjgTxH5CzAX\nWzJF7MclAu2A/sAbhetCagNaaVuUylTabt26FYBRo0a5VdpmShYn5DRXjOnBlt0/EFkvkmGDh5FJ\nNjPm/Ysjn+3l2uhuLFv6YbUpbQ3KQJyKprlqxJWqIznksVWSAVhr2cgP1l+wYCFLcrCKVSttPeCN\n0hZsj2GvuuoqWrZsWa7rrin4TTJFl2PcmgexrwcpPNb1OE/1lddI+Lv8wTHxPA7gDceOHqNJ0yYV\nKqOm4E+xKExcKPZ3gmDFigUrVqwUiIU88sgjn2xyySQLq0uyw2giuUTF8RfVhEuIu+jHF75KWSEi\npHCO/XKUU3KGVC44rt2AIpwwQjBRh2DqEEywMmLAiBEDBgwuVkXn9bl3LJYff7ovqpuqiEVzlXBR\ni1Zd8VcjYUXMg42ALcXObVS8gsowEp5rlMkfzS7+43gREuCcpWptYAFDNceixJ89sW1V9n5BCSir\nQolCWcFYYMBQoDAWGKiXG0ZwjpHgHCOhGcEYCwxYyWAfu8vlMMzIyCjXPVkR6hNCjLEOOeZ88kIt\n5Jss5IdYyArKICNIsBgFMbi8wGZVVOBwKxYLYqX826l/R5xUQSxOHTxJvdOe0+VUBl51IB4kUK77\nTcC/gS7YJE+FEqjCTxljAQuwoliZs4FQpdQJlzKDgTVKqQjgJ5dqGgLPKKXex/Yoyy2ijYT+iI6F\nEx0LJzoWTvwtFpVjJPQkgRKR3S6HOcYt7LKnF4DhxcYtGgKbgV0uZS4G0rCNhRSWGQksEZFnlFJv\nAfHYOqX92D6Z1LPX6S4RYxFEGwn9Ah0LJzoWTnQsnARqLLwZRL8COCAih0QkD1gGDCp2zCBgkf39\nSqCPsj0cHgQsE1sm3cPAbuAy+/aDwI3AfwrLtJ9jxtY5gK3DyrCvjPw3cJ19e31syRSdU0M0Go1G\n41PKHERXSg0B+ovIPfbvRwLdReR+l2N+tR9zwv79QWxjGzOALSKyxL59IbZB8THYOooXROQ5pdR/\nsD26ugvYCmwHOgMZQKiItLGfPx2YjE0qdY+IOLPrOdviGAMJDQ3t4rpYypdYrVbHdMTaTm2MhTJl\ngyUIKQgusr02xsITOhZO/C0W+/bt80sjIcDP9ld/EXnOvu1jnIPpIiJDAZRSjQFHJ2HvbFoBa911\nHvZjigilyjMLqzIIVEFMVVDbYpFVcI6fz71LZJ0mXFavaJbg2haL0tCxcOJvsVBKeTV27E2XV24J\nVCnnetp+Doiyl+GpLo3Gr0nP/93+9RQi1mpujUZTdXjTgZRbAmXfnmhfXd4c57iF2zLt5yTZy8Be\npvfCC42mGNVhJCzsQKyST1ZB2WlFKgttJNT4mjI7EKmABEpEdmGbursb+BIYLyIWT2Xay5oMPGwv\nK8ZeNkqpbkqpE8BQ4C2lVOHxtQZtJAwMI2F6/u+EGOs53leE3r17ExcXR926denYseNFCcSKo42E\n3lOakTA1NZXhw4cTExNDbGwsd955J2lpaZVSb6Dh1aiNiHwuIq1FpGXhuIWIPCkin9rf54jIUBH5\ni4hcISKHXM59zn5eG9dxC3dl2rcfspfxF3uZufbt20QkQUTCRSRGRNznGKihaCNhYBgJC6y5ZBWc\nJS6kLUEqtEgHUlY2ZXcUGgnT0tJYsGABI0aMKDVbsqZyKM1I+Pjjj/Pnn39y+PBhDh48SEpKCjNm\nzKiehlYz/jPsr/HIhQsXePLJJ3n99de59dZbCQ8PJzg4mFtuuYUXX3zR63JmzJjBVVddxXPPPUd0\ndDQRERE8+OCDjBw5ksmTJwOwYcMG1q9fz+rVq+nWrRtBQUFERkYyfvx4xo4di4jwyCOP8Pjjj3PH\nHXcQGhpKgwYNeOeddzCbzcydO9ertqxatYqoqCiefPJJFi1aVPYJ5eCuu+5i0aJFzJ49G7PZzIYN\nG7BarcyaNYuWLVsSExPDsGHDiuTfGjp0KA0aNCAyMpKePXuya5ftg+6CBQv44IMPHGUVOrCL/5c8\navSdLJj1JXWDG7JnayrXXnonL7zwAg0aNGDMmDGA7dNbp06diIqK4uqrryY5OdnjNXTo0MHhgVFK\nkZ+fXySLbnHy8vIYNWoUERERtGvXDtdJJM2aNWPDhg0AZGdnc9ddd1GvXj3atm3Ltm3bipTz888/\nc/nllxMREcHw4cPJyckpsr+0a2jWrBkvvfQSHTp0IDIy0u35hRw4cIBevXoRGRlJbGys4x+Bnj17\nAtCxY0fHJ8w///yTgQMHEhcXR7169Rg4cKDjU+/06dPZvHkz999/P2azmfvvt00S/e233+jbty/R\n0dG0adOGFStWuG2HK3/++SciQnR0ND/++GOJ3GOHDx/m73//O3Xr1iUyMpLBgwc77pNahzfWqUB9\naSOhNhL62kg45I6bZNTE6yXfkiPLP39djEaDPDLp4Uo1ElosFrfHaSOhb4yEa9askZtuuklSU1Ml\nNTVVevfuLXPnzvX48/MGbSTUVBnaSFgSfzQSAuRLNsEqjCCDibCgGJRB8cj0f1SqkbC09QLaSFg0\nblVhJLz88svJy8sjJiaGmJgYjEYj9913n8d21GR0BxIAaCNhSfzJSFiIiJBvzaKO0QxAqDGaqJhw\n8o3O8yvLSOgJbSR0UlVGwmHDhtG6dWvS09NJS0ujZcuWpc5+q8noDiQA0EbCyqMqjIRZWVkA5Fj+\n5Owf5zEZIgAwGoIxKCPp+c7OtjKNhBVBGwlL4q2RcMeOHdx7772Eh4djNpsZN26cT+5df8SrDqQq\nLIKeyrSvDdlq377cvk6k1DpqOtpIWHlUhpHQlU6dOrF06VIsFgurP1vBju8POT6BACh7B1L4R64q\njITlQRsJ3eONkbBbt2688847ZGdnk52dzYIFC+jQocNFX3tNoMwOpCosgmWU+QIw117Wn/ayPdZR\nW9BGwqL40khYyNixY9m9ezdRUVGOuL/yyiusWbOGqKgoln24kl79OxCkQh3nGDBgkVyyLbYFhVVl\nJLxYtJHQPd4YCd99912OHDlCQkICjRo14tChQ1U2k9Df8SaZYqVbBO2nlSgTmAWcARqITSblqNtT\nHVLKBZQ3F1a+NZsCa/ZFn+fK1h9+oPsVV1SojJpCbYnFbxdWU8dgpl29oY5t2QWpbD+3kKbmnsSY\nWtWaWHiDjoWTqohFsCGMIENIuc6tTCNhVVkE3ZUZA5wX20r14sd7qqPSJSwp2b9wNMPz7A5vCG4J\n28/9UkktCmxqUyxiwlsX+T7EWI9gFcbRjP9xNON/tSoWZaFj4aQqYtEioi+XhHWq1DKLUx3ZeKsU\n13TuQIZSam81NcXfDGPViY6FEx0LJzoWTvwtFpVjJOTisvGe8DIbLx62O7Lx2j+FuB7vqY4iiEs6\n9+okUA1jVYGOhRMdCyc6Fk4CNRaBlI3XUx0ajUajqQbKHEQHUErdDMwDjMC7YhM7/QvbcvdPlVIh\n2PzmnYFUIFHsCRXtFsG7gQJgotgTKror0769BTbFbTQ28dQIEcktrQ5PxMbGSuFiMF+TmZlJeHh4\ntdTtb/hdLCy5SEEmKigcjCafVu13sahGdCyc+FssfvrpJ6+MhF51IIGKNhL6B/4Wi+ydr2A9bxsa\nU6H1CW58A8GXlJ56vrLwt1hUJzoWTvwtFt7OwtIr0TW1CsnPwnp+P0GNrqNOm1GooBDy9i3Fmv1H\ndTdNowk4dAeiqVVYUn8BrATV70Zwgysxtf0HAAVn3Scd1Gg0nvGbDsSLdCk9lVLblVIFSqkh7srQ\naIpTXGlbcDYZVScSQ4RtlqIhJAaDuTGWM+6zxQYSWmmr8TV+0YF4mS7lGHAXsNS3rfMftNK2Ykrb\nl2bPxJK6G2NMB5Ry3vrG2E5Y0w9jzT3vtgzX9vr6j6hW2vqf0vbkyZMMGjSI6OhoEhISmD9/fqXU\nGYj4RQcCXAEcEJvONg/bLKxBrgeIyBERSQas1dHA6kYrbSuutLWc3wvWXIyxHYscExRrW61rqeLH\nWFppGziUprQdMWIEzZs3JyUlhc8++4xp06aRlJRUTS2tXvxlJbo36VK8wnUlenx8vMeP7FVNRkZG\npdWdkZHB9OnTmTx5MtHR0Q79aEREBAMGDGDjxo0cOXKElJQUt3Vu3bqVEydO8Pzzz9OmTRv69u3r\nUJB26NCBPn36MG7cOF555RV++ukn1q1bx+LFi8nMzHR8wilMKpeUlMT999/P7bffTsOGDR2JCEeM\nGEFSUhITJkzg7rvv5rfffuPChQts3LjRbSzWrVtHaGgow4YN44033igiLCrE3TUVuhw2bdqE0Wgs\nNW6zZs1iw4YNKKWYM2cObz87kgGdQ3hoyst89tkXZGRk0LlzZx5++GGurhvBhf1J3HHnUyQnJ5OX\nl0fLli2ZOHEizZs3Z82aNSxZssRRVufOnXn++efp3bs3S5YsoVGjRo464+LiGDt2LDt27OC5557j\n1ltv5aOPPqJr1648+OCDzJw5k4ULF3L69GmaNWvGQw89RMuWLT1eR+HPYM+ePeTm5vLJJ5+4xYh3\nwAAAH4pJREFU9Z8cOXKEEydO0K9fP7755hvq16/P1KlTadOmDQCJiYlMmjSJLl26kJuby9y5cx0J\nMPv3709ubq4j1vv37+fFF1/kxIkTdO/e3dYBWyyO/d9//73Ha0hMTGTw4MF89dVXpKSk0K1bN6ZO\nnUqdOnWKtDcjI8OhCT548CBGo5HLL7+cp556igkTJgDQvn17ACZNmkS3bt14/vnn2bNnDxaLhcsu\nu4yHH36YuLg43nnnHTZv3sx3333HAw88QP/+/ZkwYQLHjh3j1VdfZd++fURFRTFmzBh69+5d6n2T\nnp5OdnY2ycnJrF69mtjYWMd1Z2dns3HjRiZMmMC3334LwNVXX83MmTPdpvv3lsr8e+FTvNEWVvUL\n28LAd1y+Hwm85uHY94Eh3pSrlbZaaVuoobVaLZLx7SR5cUqiW6Vt7qFPJGPjeHlnwesVUtq6HpOU\nlCRGo1Eee+wxrbStIUrbtLQ0ASQlJcVx3j333COdOnXy8NPzDq20rRjepEuptWilbUkuVmlrTTsE\n+RksXLXFrdJWotoDVkbd0rlCStviGAwGnn76aa20rSFK24iICK655hqeeeYZcnJy2L59O6tWrXJI\nxWob/tKBeJMupdailbYluVilbcHpraCMHD2R4lZpeyazDtagKKZOn1Fupa074uLiCAlxptTWStui\nBKLS9oMPPuDw4cM0btyY//u//2PEiBGlzmCryfhFByK2xIn3A+uAPcAKEdmllPqXUupvAEqpbkqp\nE8BQ4C2l1K7qa7Fv0UrbimHN/J2C098S1LCHR6VtQkICH32fzpoN2/jq06XlUtoCJf44FT9HK22L\nEohK26ZNm7J27VrOnDnD1q1bOXv2LFfUUq+JX3QgdqyA2F8WABF5UkQK/91KBr4FTgEHgAHV0cjq\nQCtty4/kZ1Bw7lcMka2o0+K2UpW22UGNMZmCCTv5Aekpey9aafvll1+W+kgFtNK2OIGotN2zZw/p\n6enk5eWxZMkSvvrqqyKfUGoTftGBVESbW1vQStuieKO0teb+ieX8PpSxDiFt70EZjKUqbUffcx/N\nWnem9eC3uKzTFVzRoUWR8spS2n7wwQdl/jy00rYogai0XbduHS1atKBevXrMnz+fL7/8kri4MvMO\n1kj8IpliRbS5UsoFlDeZYkHKD+T/XjEjYdqFNOpG1q1QGTWFKo+FFP1GLNlI7gWw5IChDiGdH8Vo\n9v4ZtTUnlZzkV5HsMxBsRgWFoYJCoQLTNAvR94UTHQsnVRGL4MZ9HWucLpbKVNr6gopoc4uMcFbG\nOpB6HCeOis2qsFgUf16onTMziuPrWFgIJp/G5BFCmqUBWT8ewPbU03uCuJL6HCA4L4egvHyMZFdO\n2/R94UDHwklVxCLlwm4uUHp2hYriLx1IpSEuRkKl1JnevXsfraam+JuisjrRsXCiY+FEx8KJv8Wi\n0pS2vqAi2lyPiBdClKoiUBWVVYGOhRMdCyc6Fk4CNRZ+MYhOxbS5Go1Go6kG/GIQHSqmzfWEVtr6\nBwEdi/xcSEuxfS1EKYiIhbAoz+d5IKBjUcnoWDjxt1hopS1aaesvBGQsCvJg8yL48T+2juK6sWAK\nh7Q/4MAWOLIdOtwEfe8DY7DXxQZkLKoIHQsn/hYLv52FpZTqD7yC7ZPGOyIyq9h+E/BvoAu2MY7h\nInJEKdUM2yr1vfZDt4jIOF+1W1OLsFpgzSzY/x10vAl6jYUQs3N/54Gw+d+wZRmcOwqDn4KwyOpr\nr0ZTTfh0DKQSFgweFJFO9pfuPDQlKG4gvGhE4Kv/Z+s8+oyDGycU7TwAlAF63gW3TIWUA/DxU0Uf\ncfkIbSDUVDe+HkQvUxxl/36R/f1KoI+qSKL9AEYbCCtmIJwzZ06p7XHL5kWQ/CVclchd/++T0v+I\nXtoLBj4Gv++FtS/YPrlUEG0g9D8D4YoVK7j66qsJCwtzG88dO3bQpUsXwsLC6NKli8fMwzURXz/C\nqsiCQYDmSqmfgTTgcRHZXLyCmiKUWrFiBR9++CEPPfQQzzzzDMHBwfzwww+89tprFBQUeCWQOnny\nJOPGjWPQoEEsXryYoKAgvvjiC/r06cNLL73kSNMwffp0zpw5wyOPPEKrVq3Izs5m/fr1vP766wwY\nMIBNmzYxe/ZsR1syMzN5++23HSktIiIiigik3MXiiy++YMWKFYSHh/P000+TmJgI2ORDhe/ff/99\nTp48yfTp0x3nFqYIX716dQmBlLu6tmzZQnR0dJk5qdzR6PSPtDq2gd/jOrKvoCmnT58uIlHyeF6T\n62m1/2uOL36Kg01vcGy3WCwl2lzWfTFixAiaNWuG0Whk9+7d3H777SxevLhIiphCSrsHymLHjh1F\nBFLF8fbaK4K7WBTeu95w/vx59u7dWylt/PbbbxkxYgTvvfcejRo1KlLm8ePH6du3L23atOHnn38u\nsi8/P5+RI0dy2223MXPmTNasWUP//v1ZvHgxwcHej41poVQliaOAX4EEl+8PYltkYwJi7Nu6YOtk\n6pZWX6AKpc6fPy/h4eGyYsUKj8d4I5AaMWKE3HTTTSWOGTdunPTo0UNERNavXy8hISFy7Ngxt/VY\nrVZp0qSJvPDCC0W2WywWadeunTzxxBMiUlQgVZykpCRZtGiRJCQkyLx586Rdu3ZeX9PFCKRGjx4t\nQUFBEhwcLOHh4bJ+/XqxWCwyc+ZMadGihURHR8vQoUPl3LlzjnOGDBki8fHxUtccLj2a15Nf540X\nsRTIW2+9VaSsgQMHikgpAqkN8yXpn92kUVy0zJo1S+Lj42XEiBEiIrJmzRrp2LGjREZGSrt27WTn\nzp1lXouIyNatW8VkMsnWrVs9xmvo0KEycuRIMZvN0rZtW9m2bZtjv6tAKisrS0aPHi1RUVFy6aWX\nyuzZsx0CKRGbJKpz585iNptl2LBhMnz48CLyLNdruOqqq4pcQ9OmTeXFF1+U9u3bS926dWXYsGGS\nnZ3tts379++Xnj17St26dR3Hioj06NFDAAkLC5Pw8HBZtmyZpKamyoABAyQ2NlaioqJkwIABcvz4\ncRERmTZtmhgMBjGZTBIeHi7jx48XEZvw7IYbbpB69epJ69atZfny5WXGOTU1VZo3by4iIm+88YZM\nmjTJ7XFvv/229OrVq8i2devWScOGDcVqtTq2NW7cWL744osy63UlUIVSvu5ArgLWuXw/FZha7Jh1\nwFX290HYVmcqN2VtBLqWVl+gdiCBbiAsTlJSks8NhIXMmzfPrYGwkIULF0rar99KzqybZMKNnaVj\nhw4eyxIppQOxFEjSM2PFaFDy2F23OQyExe19kydPrrUGQhEpYiBct26d3xsIXXHXgbz88svSv3//\nItsGDBggL730kts6PRGoHYivx0DKvWBQKRVnH4RHKdUCaAWUug4kUKlpBsKUlBSfGwgLmT9/vlsD\nYaFk6e6bexCx/iVMsQnMeG81O5OTy2cgNBjhqkQMSvH0X9IwHfiG0NDQEva+/v37awOh3UBYp04d\nvzcQlkVGRgaRkUVn4EVGRpYrtX0g4tMORLwQRwELgRil1AHgYWCKfXtPIFkptQPb4Po4EfEu93eA\nUdMMhOvXr/e5gbCQo0ePujUQpqSkYNmziSl33kzL59ZT96EPaXZpe0dd5cIYRFx8A0JadobP58Cv\n60vY+wYOHKgNhHYD4V133RUQBsLSMJvNpKWlFdmWlpZGRESEV+cHOj5PZSIin4tIaxFpKSLP2bc5\nxFEikiMiQ0XkLyJyhdhXm4vIKhFpJ7YpvJeLyBpft91X1DQD4VdffeVTA6Erbg2E2dk0OvY/lj79\nAKv3nGND0v+4cCGt8gyEt86AhMvg8zk0llSmT3nMUffatWu1gdBuIHzkkUcCwkBYGu3atSM5OblI\n7JKTk916RGoiPu9AlFL9lVJ7lVIHlFJT3Ow3KaWW2/dvtS8gLNw31b59r1LqRl+225cEuoHQ9fX9\n999z8uRJnxkIi1PEQCjCmZ+TWP3orbB5Een1WmCKa0xMk5ZkZWVVnoGwTigMnwlX38k/WhmZP+8l\ntn7yb8RqJTs7WxsI7f+smM3mgDAQWiwWxyc7q9VKTk6O49Pzddddh9Fo5NVXXyU3N5fXXnsNgOuv\nv/6iYxOQeDNQUlkvbKvPDwItgDrATqBtsWPuA+bb3ycCy+3v29qPNwHN7eUYS6svUAfRC1myZIl0\n6dJFwsLCJD4+Xm6++Wb59ttvRcS7QXQRkV9++UUGDBggEREREh4eLr169SoycCliG0R98sknpWXL\nlhIWFiZNmjSRsWPHytGjRx3HfPLJJ9K1a1cJCwuTevXqSWJiYpGZW++9916hjrjIa+zYsY4ZX65s\n3bpV6tSpU2RGVGmD6OHh4UVec+bMcRuz4gPfloICmfPMk9K6WYKYQ4KlRXSoTO13qchPqyU9LU3+\n9re/idlsliZNmsiiRYuKxG/fvn2OmUeFg7fbtm2Ttm3bitlslhEjRkhiYqKjvqSkpCIzm0RE5OhO\n+WJ8b+maUFciQ+tIXFSEDBk0UNIunC/R9t27d8sVV1whZrNZIiMjpWvXrvLxxx+7vU538So+4cB1\nED0zM1NGjhwpkZGRbmdhbdu2TTp16uSYhTVs2LAicfziiy+ka9euEhkZKQ0aNJAhQ4ZIWlpaiXrc\ntcuVSZMmScOGDSU8PFwaNmwob731lmPfm2++KQ0aNJDIyEhZvny5nDx5Unr16iXh4eHSqlUrmT9/\nfpHr++6776RVq1YSFRUlDzzwgIiI/Pbbb3LzzTdLbGysREdHS+/eveXnn3/2GMMxY8bIihUrxGq1\nSv369SUvL6/EMe7u7dGjRzv2b9++XS6//HIJCQmRzp07y/bt2z3W54lAHUT3aS6sipgHsY+FFB7r\nepyn+sqdC+uPQ3Bqb9nHlcLevXtp06ZNhcqoKVx0LDzek1LsrYBYbcdbC8CSDwX5kJsJWech87wt\n1Ujmn7ZzImKh+zBofyMEm8p5NeUgPxf2bYYdn8PJ3bZtwaEQ1xQiL4GQcNtq9+BQMASB0WgblEfZ\nXgr7+zIIsPW2+nfESZXEolFbiPVK61ECf82FVZGFhI2ALcXObVS8gspYSNj41FZaHk+66PNcaQNw\n5MsKlVFT8HUsCgx1yA8OIy84nOyQhlyIu4I0cwKZobGQpuBbj/9zVCFB0OhvENKJSyyphGefwZz+\nB6ZzPxNUkEOQJReF7/6Z8wf074iTqojFvmY38nv9zpVaZnH8RShVaYg2EvojOhZOdCyc6Fg4qYJY\nrKvIyX5pJKyIedCbc4sg2kjoF+hYONGxcKJj4SRQYxEwCwnt2xPts7SaY1tI+AMajUajqRZ8LpSq\niHlQKTUduBsoACaKyBel1aWNhP6BX8dCBDLTIDsLcrLBUgCxDcBct0qq8+tY+BgdCyf+FgttJEQb\nCf0Fv41FVgY88Q/Y9SPUMUGr9rZth3+DXgNg/FNQt16lVum3sagGdCyc+Fss/HUWlkbjH2SmwxP3\nwG874dEXodfNEFzHNg14xQJY+jok/wCzF0PjltXdWo3GLwmYlehKqWZKqWyl1A77a76v267xf7wy\nEmamw/S7YW8yTJsHN/zd1nkABAXDHePh1VW2NSZP3Qvp592XU81oI6GmutFKWz9GGwmrwEhoKYBn\n74f9v8K0V+Da/u4b2+JS7sqJ4/HNO+DZB2yfTHyANhIGnpHwn//8J23atMFgMPD+++9XSnsCBa20\n9VNefvllJk6cyLRp00hJSeHYsWPcd999F/UH5eDBg1xzzTW0b9+ew4cP8/vvvzN48GD69evH9987\nF9MNGTKETz/9lKVLl3LhwgV27txJly5d+PrrrwFYuXIld9xxBxMnTuTs2bPs2rULk8nEtddey59/\n/ulVWzIzM1m1ahWRkZEsWbLEsX3+/PlkZGSQkZHBtGnTGD58uOP7L75wzpEoTIxX+Bo+fLjbeo4e\nPUrbtm3dJkIE4N2X4Ofv4MF/wTX9Sm90VAxc0Rt2boHXny5lhbx7ysqm7I5XXnmFU6dOkZaWxoIF\nCxgxYkSp2ZI1lcNPP/1E165dSU5O5rLLLiuyLzo6mokTJzJlSokHJgB07NiRN95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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f6fe9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from matplotlib import (cm, pyplot as plt, mlab)\n",
    "\n",
    "def visualize(word, model):\n",
    "    \"\"\" visualize the input model for a particular word \"\"\"\n",
    "    \n",
    "    # Variance of Hidden States\n",
    "    variance = np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])\n",
    " \n",
    "    figures = []\n",
    "    for parm_idx in range(len(model.means_[0])):\n",
    "        \n",
    "        # print(\"parma_idx: {} means: {} variance: {}\".format(parm_idx, model.means_[:,parm_idx], variance[:,parm_idx]))\n",
    "        \n",
    "        # xmin = int(min(model.means_[:,parm_idx]) - max(variance[:,parm_idx]))\n",
    "        # xmax = int(max(model.means_[:,parm_idx]) + max(variance[:,parm_idx]))\n",
    "        \n",
    "        xmin = int((min(model.means_[:,parm_idx]) - max(variance[:,parm_idx]))*100)/100\n",
    "        xmax = int((max(model.means_[:,parm_idx]) + max(variance[:,parm_idx]))*100)/100\n",
    "        \n",
    "        fig, axs = plt.subplots(model.n_components, sharex=True, sharey=False)\n",
    "        colours = cm.rainbow(np.linspace(0, 1, model.n_components))\n",
    "        for i, (ax, colour) in enumerate(zip(axs, colours)):\n",
    "            x = np.linspace(xmin, xmax, 100)\n",
    "            mu = model.means_[i, parm_idx]\n",
    "            sigma = math.sqrt(np.diag(model.covars_[i])[parm_idx])\n",
    "            \n",
    "            # print(\"parma_idx: {} i: {} mu: {} sigma: {} xmin: {} xmax: {}\".format(parm_idx, i, mu, sigma, xmin, xmax))\n",
    "            \n",
    "            ax.plot(x, mlab.normpdf(x, mu, sigma), c=colour)\n",
    "            ax.set_title(\"{} feature {} hidden state #{}\".format(word, parm_idx, i))\n",
    "            ax.grid(True)\n",
    "        figures.append(plt)\n",
    "    for p in figures:\n",
    "        p.show()\n",
    "        \n",
    "visualize(my_testword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  ModelSelector class\n",
    "* Review `SelectorModel` class in `my_model_selectors.py` module.  \n",
    "* `SelectorModel` is designed as a Strategy Pattern for choosing different Model Selectors.  \n",
    "* Subclass the `SelectorModel` to implement the following model selectors classes/functions in the `my_model_selectors.py` module. Run them from this notebook:\n",
    "\n",
    "    *`SelectorCV `:  Log likelihood with CV\n",
    "    * `SelectorBIC`: BIC \n",
    "    * `SelectorDIC`: DIC\n",
    "\n",
    "* Train each word in the training set with a range of values for the number of Hidden States, then Score these alternatives with the Model Selector, and choose the \"best\" according to each strategy. \n",
    "* e.g. the simple case of training with a constant value for `n_components` can be called using the provided `SelectorConstant` subclass as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for VEGETABLE is 3\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "# Experiment here with different feature sets defined in Part 1\n",
    "# i.e. Feature Set: features_ground, features_norm, features_polar, \n",
    "#                   features_delta\n",
    "training = asl.build_training(features_ground)\n",
    "\n",
    "# Experiment here with different words contained in `training.words`\n",
    "# (i.e. VEGETABLE, CHOCOLATE, BOOK, etc)\n",
    "word = 'VEGETABLE'\n",
    "model = SelectorConstant(training.get_all_sequences(), \n",
    "                         training.get_all_Xlengths(), \n",
    "                         word, n_constant=3).select()\n",
    "print(\"Number of states trained in model for {} is {}\"\n",
    "      .format(word, model.n_components))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Cross-Validation (CV) folds\n",
    "* Scoring the model simply using Log Likelihood calculated from feature sequences it trained on, we expect more complex models to have higher likelihoods, but doesn't inform us which would have a \"better\" likelihood score on unseen data.  The model will likely overfit as complexity is added.  \n",
    "* Estimate the \"better\" Topology model using only training data by comparing scores using Cross-Validation (CV).  \n",
    "* CV techniques include:\n",
    "    * Break-down the training set into \"folds\", rotate which fold is \"left out\" of training.  The \"left out\" fold is scored. Use this as a proxy method of finding the \"best\"  model to use on \"unseen data\". \n",
    "        * e.g. Given a set of word sequences broken-down into three folds using [scikit-learn Kfold](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) class object. Implement `SelectorCV` to use this technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'TRAIN' fold indices: [1 2] 'TEST' fold indices: [0]\n",
      "'TRAIN' fold indices: [0 2] 'TEST' fold indices: [1]\n",
      "'TRAIN' fold indices: [0 1] 'TEST' fold indices: [2]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "# Experiment here with different feature sets\n",
    "training = asl.build_training(features_ground) \n",
    "\n",
    "# Experiment here with different words\n",
    "word = 'CHOCOLATE' \n",
    "word_sequences = training.get_word_sequences(word)\n",
    "split_method = KFold()\n",
    "for cv_train_idx, cv_test_idx in split_method.split(word_sequences):\n",
    "\n",
    "    # View indices of the folds\n",
    "    print(\"'TRAIN' fold indices: {} 'TEST' fold indices: {}\".format(cv_train_idx, cv_test_idx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tip:** To run `hmmlearn` training using X,lengths tuples on new folds, subsets must be combined based on the indices given for the folds.\n",
    "* Helper utility is in `asl_utils` module named `combine_sequences` for this purpose."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Scoring models with other criterion (i.e. BIC and DIC)\n",
    "\n",
    "* **BIC** when used to scoring model topologies will balance fit and complexity within the training set for each word.\n",
    "    * **BIC equation** has a **penalty term** that penalizes \"complexity\" to avoid \"overfitting\". This avoids using **CV** in the selection process.  Refer to these [slides](http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf) about this criterion and try to use formula mentioned the SelectorBIC implementation.\n",
    "\n",
    "* **DIC** when used as a scoring model topology has **advantages** over BIC, shown by Alain Biem here: [reference](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf) (and also found [here](https://pdfs.semanticscholar.org/ed3d/7c4a5f607201f3848d4c02dd9ba17c791fc2.pdf)).  \n",
    "    * **DIC** scores the ability of a training set to discriminate one word against competing words. It provides a **penalty** if model likelihoods for non-matching words are too similar to model likelihoods for the correct word in the word set (rather than using a penalty term for complexity like in BIC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part2_submission'></a>\n",
    "### Model Selection Implementation Submission\n",
    "\n",
    "Implement the following classes in the `my_model_selectors.py` module:\n",
    "    * `SelectorCV`\n",
    "    * `SelectorBIC`\n",
    "    * `SelectorDIC`\n",
    "\n",
    "Run the selectors on the following 5x five words ('FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN'), then answer given questions about your results.\n",
    "\n",
    "**Tip:** The `hmmlearn` library may not be able to train or score all models.\n",
    "    * Implement `try/except` contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "words_to_train = ['FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.6087903659790754 seconds\n",
      "Training complete for BOOK with 2 states with time 5.771827931981534 seconds\n",
      "Training complete for VEGETABLE with 2 states with time 1.9629898630082607 seconds\n",
      "Training complete for FUTURE with 2 states with time 4.7354352889815345 seconds\n",
      "Training complete for JOHN with 3 states with time 51.43302696500905 seconds\n"
     ]
    }
   ],
   "source": [
    "from importlib import reload\n",
    "import my_model_selectors\n",
    "reload(my_model_selectors)\n",
    "\n",
    "# DONE: Implement SelectorCV in my_model_selector.py\n",
    "from my_model_selectors import SelectorCV\n",
    "\n",
    "# Experiment here with different feature sets defined in Part 1\n",
    "training = asl.build_training(features_ground)\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorCV(sequences, \n",
    "                       Xlengths, \n",
    "                       word,\n",
    "                       min_n_components=2, \n",
    "                       max_n_components=15, \n",
    "                       random_state = 14).select()\n",
    "    end = timeit.default_timer() - start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.46016899397363886 seconds\n",
      "Training complete for BOOK with 12 states with time 2.9711857740185224 seconds\n",
      "Training complete for VEGETABLE with 15 states with time 1.0915613939869218 seconds\n",
      "Training complete for FUTURE with 15 states with time 3.1830719559802674 seconds\n",
      "Training complete for JOHN with 15 states with time 26.19039085903205 seconds\n"
     ]
    }
   ],
   "source": [
    "# DONE: Implement SelectorBIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "# Experiment here with different feature sets defined in Part 1\n",
    "training = asl.build_training(features_ground)\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorBIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# DONE: Implement SelectorDIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorDIC\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorDIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "**Question 2:**  Compare and contrast the possible advantages and disadvantages of the various model selectors implemented.\n",
    "\n",
    "**Answer 2:**\n",
    "\n",
    "The coloured Bar Graph are shown below that contrast the word times and states results for each of the CV, BIC, and DIC model selectors.\n",
    "\n",
    "Occam's Razor Principle selects models that the \"best\" fix with data that are simple enough for efficient computation (smooths noisy characteristics of the source distribution) and complex enough to capture data specifics (without allowing it to be so complex that it over-fits the data, by such means as applying a penalty against large models in BIC).\n",
    "\n",
    "BIC adopts Occam's Razor Principle and is a classical Bayesian-based model selection criteria focused on estimating models using within-class statistics, whereas DIC adopts the Discriminative Principle that has regard for competing classification categories (scores ability of training set to discriminate one word against other competing words).\n",
    "\n",
    "CV selects the \"best\" fit of model with data based only on the training data by using its technique of folding to break-down the training set into \"training\" samples and a \"test\" sample that is used for validation.\n",
    "\n",
    "CV ADVANTAGES\n",
    "==============\n",
    "* CV avoids limit over-validation\n",
    "\n",
    "CV DISADVANTAGES\n",
    "==============\n",
    "* CV takes twice as long as BIC and DIC for the word \"JOHN\"\n",
    "* CV estimates the \"best\" fit of model with data by scoring models by simply using likelihood calculated from samples of each features (i.e. a word) that it trained on, such that we expect more complex models to have higher likelihoods, but CV does not inform us which would have a \"better\" likelihood score on unseen data, so the model will likely overfit as complexity is added.\n",
    "\n",
    "BIC ADVANTAGES \n",
    "==============\n",
    "* BIC is faster than CV and DIC\n",
    "* BIC finds more states than CV and DIC\n",
    "* BIC system size is less than DIC\n",
    "* BIC avoids using CV by using a penalty term that increases with higher complexity (number of free parameters) to avoid over-fitting\n",
    "\n",
    "DIC ADVANTAGES \n",
    "==============\n",
    "* DIC performance of resulting models is usually higher than BIC (surprisingly slower in our results though), \n",
    "since DIC is a model selection criterion focused more on goal of classification than BIC,\n",
    "* DIC determines discriminant models and therefore replaces Occam's Razor Principle with the Discriminative Principle, where the goal is to select the model less likely to have generated data belonging to competing classification categories\n",
    "(i.e. other words)\n",
    "* DIC is known to decreases error rates by >18% compared to BIC\n",
    "DIC expected to have higher number of parameters than BIC\n",
    "DIC more oriented to goal of classification than BIC\n",
    "\n",
    "Reference [0] - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "# data to plot\n",
    "objects = ('CV', 'BIC', 'DIC')\n",
    "n_groups = len(objects)\n",
    "times_0 = (0.4674927319865674, 0.48493634100304917, 0.9151478260173462)\n",
    "times_1 = (5.107056170003489, 2.6952258159872144, 5.55813252000371)\n",
    "times_2 = (2.002914613985922, 1.0019054600270465, 4.528326347004622) \n",
    "times_3 = (4.821659260021988, 3.1833312090020627, 5.543100375973154) \n",
    "times_4 = (49.81151062599383, 27.996902102022432, 29.335177061031573)\n",
    "\n",
    "# create plot\n",
    "fig, ax = plt.subplots()\n",
    "index = np.arange(n_groups)\n",
    "bar_width = 0.15\n",
    "opacity = 0.8\n",
    " \n",
    "rects1 = plt.bar(index, \n",
    "                 times_0, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='b',\n",
    "                 label='FISH')\n",
    " \n",
    "rects2 = plt.bar(index + bar_width, \n",
    "                 times_1, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='g',\n",
    "                 label='BOOK')\n",
    "\n",
    "rects3 = plt.bar(index + (2 * bar_width), \n",
    "                 times_2, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='y',\n",
    "                 label='VEGETABLE')\n",
    "\n",
    "rects4 = plt.bar(index + (3 * bar_width), \n",
    "                 times_3, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='c',\n",
    "                 label='FUTURE')\n",
    "\n",
    "rects5 = plt.bar(index + (4 * bar_width), \n",
    "                 times_4, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='r',\n",
    "                 label='JOHN')\n",
    "\n",
    "plt.xlabel('Technique')\n",
    "plt.ylabel('Time (s)')\n",
    "plt.title('Word Times by Technique')\n",
    "plt.xticks(index + bar_width, objects)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lX7F6UDcBlwCb6qsgaZikCkkVy5YtK1xkZmaWCgVPUJL6AUsjYmZD9SJiYkSU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\niAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fd52a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "# data to plot\n",
    "objects = ('CV', 'BIC', 'DIC')\n",
    "n_groups = len(objects)\n",
    "states_0 = (5, 5, 3)\n",
    "states_1 = (2, 12, 15)\n",
    "states_2 = (2, 15, 15) \n",
    "states_3 = (2, 15, 15) \n",
    "states_4 = (3, 15, 15)\n",
    "\n",
    "# create plot\n",
    "fig, ax = plt.subplots()\n",
    "index = np.arange(n_groups)\n",
    "bar_width = 0.15\n",
    "opacity = 0.8\n",
    " \n",
    "rects1 = plt.bar(index, \n",
    "                 states_0, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='b',\n",
    "                 label='FISH')\n",
    " \n",
    "rects2 = plt.bar(index + bar_width, \n",
    "                 states_1, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='g',\n",
    "                 label='BOOK')\n",
    "\n",
    "rects3 = plt.bar(index + (2 * bar_width), \n",
    "                 states_2, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='y',\n",
    "                 label='VEGETABLE')\n",
    "\n",
    "rects4 = plt.bar(index + (3 * bar_width), \n",
    "                 states_3, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='c',\n",
    "                 label='FUTURE')\n",
    "\n",
    "rects5 = plt.bar(index + (4 * bar_width), \n",
    "                 states_4, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='r',\n",
    "                 label='JOHN')\n",
    "\n",
    "plt.xlabel('Technique')\n",
    "plt.ylabel('States')\n",
    "plt.title('Word States by Technique')\n",
    "plt.xticks(index + bar_width, objects)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part2_test'></a>\n",
    "### Model Selector Unit Testing\n",
    "Run the following unit tests as a sanity check on the implemented model selectors.  The test simply looks for valid interfaces  but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 65.680s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_model_selectors import TestSelectors\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestSelectors())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_tutorial'></a>\n",
    "## PART 3: Recognizer\n",
    "The objective of this section is to \"put it all together\".  Using the four feature sets created and the three model selectors, you will experiment with the models and present your results.  Instead of training only five specific words as in the previous section, train the entire set with a feature set and model selector strategy.  \n",
    "### Recognizer Tutorial\n",
    "##### Train the full training set\n",
    "The following example trains the entire set with the example `features_ground` and `SelectorConstant` features and model selector.  Use this pattern for you experimentation and final submission cells.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "# autoreload for automatically reloading changes made in my_model_selectors and my_recognizer\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "def train_all_words(features, model_selector):\n",
    "    training = asl.build_training(features)  # Experiment here with different feature sets defined in part 1\n",
    "    sequences = training.get_all_sequences()\n",
    "    Xlengths = training.get_all_Xlengths()\n",
    "    model_dict = {}\n",
    "    for word in training.words:\n",
    "        model = model_selector(sequences, Xlengths, word, \n",
    "                        n_constant=3).select()\n",
    "        model_dict[word]=model\n",
    "    return model_dict\n",
    "\n",
    "models = train_all_words(features_ground, SelectorConstant)\n",
    "print(\"Number of word models returned = {}\".format(len(models)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Load the test set\n",
    "The `build_test` method in `ASLdb` is similar to the `build_training` method already presented, but there are a few differences:\n",
    "- the object is type `SinglesData` \n",
    "- the internal dictionary keys are the index of the test word rather than the word itself\n",
    "- the getter methods are `get_all_sequences`, `get_all_Xlengths`, `get_item_sequences` and `get_item_Xlengths`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of test set items: 178\n",
      "Number of test set sentences: 40\n"
     ]
    }
   ],
   "source": [
    "test_set = asl.build_test(features_ground)\n",
    "print(\"Number of test set items: {}\".format(test_set.num_items))\n",
    "print(\"Number of test set sentences: {}\".format(len(test_set.sentences_index)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_submission'></a>\n",
    "### Recognizer Implementation Submission\n",
    "For the final project submission, students must implement a recognizer following guidance in the `my_recognizer.py` module.  Experiment with the four feature sets and the three model selection methods (that's 12 possible combinations). You can add and remove cells for experimentation or run the recognizers locally in some other way during your experiments, but retain the results for your discussion.  For submission, you will provide code cells of **only three** interesting combinations for your discussion (see questions below). At least one of these should produce a word error rate of less than 60%, i.e. WER < 0.60 . \n",
    "\n",
    "**Tip:** The hmmlearn library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# DONE implement the recognize method in my_recognizer\n",
    "from my_recognizer import recognize\n",
    "from asl_utils import show_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features_ground\n",
      "\n",
      "**** WER = 0.6573033707865169\n",
      "Total correct: 61 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *WHO *BOOK *NEW                                               JOHN WRITE HOMEWORK\n",
      "    7: JOHN *WHAT GO *HAVE                                           JOHN CAN GO CAN\n",
      "   12: JOHN *TEACHER *WHAT CAN                                       JOHN CAN GO CAN\n",
      "   21: JOHN *VIDEOTAPE *NEW *MARY *CAR *TEACHER *CHICAGO *EAT        JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *FRANK *IX *LOVE IX IX                                        JOHN LIKE IX IX IX\n",
      "   28: *IX *TELL IX IX *LOVE                                         JOHN LIKE IX IX IX\n",
      "   30: *IX LIKE *MARY *MARY IX                                       JOHN LIKE IX IX IX\n",
      "   36: MARY VEGETABLE *YESTERDAY *GO *IX *JOHN                       MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GIVE *JOHN MARY *IX                                     JOHN IX THINK MARY LOVE\n",
      "   43: *FRANK *SHOULD BUY HOUSE                                      JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *SEE BUY CAR SHOULD                                    FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *MARY BUY HOUSE                                   JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *MARY *GO *IX                                             JOHN DECIDE VISIT MARY\n",
      "   67: *IX *POSS NOT *ARRIVE HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   74: *IX *IX *GO *LOVE                                             JOHN NOT VISIT MARY\n",
      "   77: *IX *GIVE1 *LOVE                                              ANN BLAME MARY\n",
      "   84: *LOVE *ARRIVE *GO BOOK                                        IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *GIVE *IX *IX IX *BUY *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *MARY *GIVE1 *SOMETHING-ONE SOMETHING-ONE WOMAN *ARRIVE       JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: *IX-1P GIVE IX *IX WOMAN BOOK                                 JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *SOMETHING-ONE NEW CAR *BOOK                                  POSS NEW CAR BREAK-DOWN\n",
      "  105: *FRANK *IX-1P                                                 JOHN LEG\n",
      "  107: *LIKE *SUE *WHAT *GO *WHO                                     JOHN POSS FRIEND HAVE CANDY\n",
      "  108: WOMAN *LOVE                                                   WOMAN ARRIVE\n",
      "  113: *HAVE CAR *SUE SUE *HAVE                                      IX CAR BLUE SUE BUY\n",
      "  119: *VEGETABLE *BUY1 *HAVE *WHAT *SUE                             SUE BUY IX CAR BLUE\n",
      "  122: JOHN *BOOK BOOK                                               JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *BLAME *ARRIVE                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *FRANK *NEW YESTERDAY *TEACHER BOOK                           JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *VISIT WHO                                               LOVE JOHN WHO\n",
      "  167: JOHN *SUE *MARY *WOMAN *LOVE                                  JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *SUE BLAME                                              JOHN MARY BLAME\n",
      "  174: *WHAT *NEW-YORK *NEW-YORK *GO *WHAT                           PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *BOX                                                     JOHN ARRIVE\n",
      "  184: *TOY1 BOY *NEW-YORK TEACHER APPLE                             ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *JOHN *JOHN BOX                                          JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *GO BOX                                           JOHN GIVE GIRL BOX\n",
      "  199: *LOVE CHOCOLATE *TELL                                         LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *WOMAN *LIKE *BOOK HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n",
      "features_norm\n",
      "\n",
      "**** WER = 0.6460674157303371\n",
      "Total correct: 63 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *MARY WRITE *ARRIVE                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN *NEW *MARY CAN                                           JOHN CAN GO CAN\n",
      "   12: *GO *CAR *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: *LIKE *NEW *HAVE *IX-1P *GIVE1 *CAR *FUTURE *HAVE             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *GO *LIKE *GO                                       JOHN LIKE IX IX IX\n",
      "   28: *ANN LIKE *LIKE *LIKE *GO                                     JOHN LIKE IX IX IX\n",
      "   30: *SHOOT LIKE *MARY *LIKE *MARY                                 JOHN LIKE IX IX IX\n",
      "   36: MARY *FUTURE *GIVE3 *WOMAN *MARY *LIKE                        MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *MARY *WILL *WHO *MARY                                   JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *POSS *FRANK *HAVE *HAVE *SOMETHING-ONE                       FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *MAN *CHOCOLATE HOUSE                             JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *SEE VISIT MARY                                           JOHN DECIDE VISIT MARY\n",
      "   67: *LIKE FUTURE *JOHN *ARRIVE *CAN                               JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE *BLAME MARY                                      JOHN WILL VISIT MARY\n",
      "   74: JOHN *BILL *MARY MARY                                         JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME *GO                                                 ANN BLAME MARY\n",
      "   84: *JOHN *HAVE *POSS *NEW                                        IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *FUTURE *THROW GIVE *GO IX NEW *BREAK-DOWN                    JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SELF *GIVE1 IX *GIVE1 WOMAN *VIDEOTAPE                       JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *GIVE1 IX *IX WOMAN BOOK                                 JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *IX *GIVE1 *LIKE *TOY1                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *SOMETHING-ONE *HOMEWORK                                      WOMAN ARRIVE\n",
      "  113: IX *NEW *IX *JOHN *BOX                                        IX CAR BLUE SUE BUY\n",
      "  119: *WHO *BUY1 *SOMETHING-ONE *PEOPLE *SUE                        SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *VIDEOTAPE YESTERDAY *NEW                          JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *ARRIVE YESTERDAY WHAT BOOK                              JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *GO WHO                                                  LOVE JOHN WHO\n",
      "  167: JOHN *JOHN *SAY-1P LOVE *IX                                   JOHN IX SAY LOVE MARY\n",
      "  171: *LIKE *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *NEW *GIVE1 GIVE1 *VISIT *BLAME                               PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *VISIT *BOX                                                   JOHN ARRIVE\n",
      "  184: *IX BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *VISIT *GIVE3 *PREFER *ARRIVE                                 JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SEE *PREFER BOX                                         JOHN GIVE GIRL BOX\n",
      "  199: *JOHN CHOCOLATE *MARY                                         LIKE CHOCOLATE WHO\n",
      "  201: JOHN *THINK MARY *LIKE *GIVE1 HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n",
      "features_polar\n",
      "\n",
      "**** WER = 0.6910112359550562\n",
      "Total correct: 55 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *MARY *BROTHER *ARRIVE                                        JOHN WRITE HOMEWORK\n",
      "    7: JOHN *HAVE GO CAN                                             JOHN CAN GO CAN\n",
      "   12: JOHN *TEACHER *WHAT CAN                                       JOHN CAN GO CAN\n",
      "   21: *SHOULD *NEW WONT *MARY *CAR *CAR *VISIT *FUTURE              JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *FRANK *MARY *LOVE *TELL *LOVE                                JOHN LIKE IX IX IX\n",
      "   28: *FRANK *TELL *LOVE *TELL *LOVE                                JOHN LIKE IX IX IX\n",
      "   30: *SHOULD LIKE *MARY *MARY *MARY                                JOHN LIKE IX IX IX\n",
      "   36: *SOMETHING-ONE *PREFER *GIRL *GIVE *MARY *JOHN                MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GIVE *CORN MARY *MARY                                   JOHN IX THINK MARY LOVE\n",
      "   43: *FRANK *POSS BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *SEE BUY CAR *WHAT                                     FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *MARY *GIVE MARY                                        JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD *YESTERDAY NOT BUY HOUSE                              JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GO MARY                                         JOHN WILL VISIT MARY\n",
      "   74: *GO *WHO *GIVE *GO                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *LOVE *ARRIVE *POSS *COAT                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *GIVE *WOMAN *WOMAN *WOMAN *BOOK *BREAK-DOWN            JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SEE *GIVE1 *WOMAN *WOMAN WOMAN *CHOCOLATE                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *WOMAN *WOMAN *WOMAN WOMAN BOOK                          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: *FRANK *FRANK                                                 JOHN LEG\n",
      "  107: *LIKE *SOMETHING-ONE *HAVE *GO *WHO                           JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *GIVE *BOOK                                                   WOMAN ARRIVE\n",
      "  113: *JOHN *HAVE BLUE *JOHN *BOX                                   IX CAR BLUE SUE BUY\n",
      "  119: *VEGETABLE *LOVE *GO *HAVE *GO                                SUE BUY IX CAR BLUE\n",
      "  122: JOHN *BLAME BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *BOX YESTERDAY *CHOCOLATE                          JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *FRANK BUY YESTERDAY *TEACHER BOOK                            JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY *TELL                                              LOVE JOHN WHO\n",
      "  167: JOHN *JOHN *MARY LOVE *LOVE                                   JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *SUE BLAME                                               JOHN MARY BLAME\n",
      "  174: *HAVE *GIVE1 GIVE1 *GIRL *WHAT                                PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *BOX                                                     JOHN ARRIVE\n",
      "  184: *SOMETHING-ONE BOY *BLAME TEACHER *GIRL                       ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *SOMETHING-ONE *YESTERDAY BOX                            JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  199: *LOVE *HOMEWORK *FRANK                                        LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *WOMAN *LIKE BUY HOUSE                             JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features_delta\n",
      "\n",
      "**** WER = 0.6460674157303371\n",
      "Total correct: 63 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *LOVE *GO1                                               JOHN WRITE HOMEWORK\n",
      "    7: JOHN *FINISH GO *TEACHER                                      JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *IX *LOVE *MARY *BUY *VIDEOTAPE *FUTURE *MARY            JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   28: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   30: JOHN *IX *WHO *JOHN IX                                        JOHN LIKE IX IX IX\n",
      "   36: *IX *IX *IX IX *MARY *IX                                      MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY IX *JOHN *IX *IX                                        JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *WOMAN *VISIT HOUSE                                      JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *NOT BUY CAR *FUTURE                                    FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *IX BUY *BOOK                                      JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *WHO *FUTURE *IX *IX                                          JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *WHO *IX *FINISH *LOVE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *MARY VISIT *VIDEOTAPE                                   JOHN WILL VISIT MARY\n",
      "   74: JOHN *WHO *IX MARY                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *IX                                               ANN BLAME MARY\n",
      "   84: *JOHN *CAR *IX BOOK                                           IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *WHO IX *IX *IX IX *CAR *CAN                                  JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *IX *IX *JOHN *IX WOMAN *IX                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX WOMAN *VISIT                                  JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *JOHN *CAR CAR *HOUSE                                         POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *IX                                                      JOHN LEG\n",
      "  107: JOHN *JOHN *VISIT HAVE *MARY                                  JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *FUTURE *VISIT                                                WOMAN ARRIVE\n",
      "  113: *JOHN CAR *MARY *MARY *BUY1                                   IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 *GIVE1 CAR *FUTURE                                SUE BUY IX CAR BLUE\n",
      "  122: JOHN *PEOPLE BOOK                                             JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *IX *ARRIVE                                   JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY *IX *IX *VISIT                                       JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *GIVE1 *GIVE1 *JOHN                                           LOVE JOHN WHO\n",
      "  167: JOHN IX *IX *VISIT *VISIT                                     JOHN IX SAY LOVE MARY\n",
      "  171: *IX *JOHN BLAME                                               JOHN MARY BLAME\n",
      "  174: *CAR *IX GIVE1 *IX *VISIT                                     PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *GIVE1                                                   JOHN ARRIVE\n",
      "  184: *IX *JOHN *GIVE1 TEACHER *IX                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *JOHN BOX                                            JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX *LIKE BOX                                            JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *VISIT *MARY                                            LIKE CHOCOLATE WHO\n",
      "  201: JOHN *IX *IX *LIKE BUY HOUSE                                  JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "'right-x-rescaling'",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/Users/Ls/miniconda3/envs/aind/lib/python3.6/site-packages/pandas/indexes/base.py\u001b[0m in \u001b[0;36mget_value\u001b[0;34m(self, series, key)\u001b[0m\n\u001b[1;32m   2174\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2175\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mtslib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_value_box\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2176\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mpandas/tslib.pyx\u001b[0m in \u001b[0;36mpandas.tslib.get_value_box (pandas/tslib.c:19053)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/tslib.pyx\u001b[0m in \u001b[0;36mpandas.tslib.get_value_box (pandas/tslib.c:18687)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'str' object cannot be interpreted as an integer",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-40-92d8211ab8c3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfeatures_names\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfeatures\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mall_features\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;31m# TODO Recognize the test set and display the result with the show_errors method\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mmodels\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_all_words\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel_selector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     \u001b[0mtest_set\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_test\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0mprobabilities\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguesses\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrecognize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodels\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtest_set\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-33-3098eb261b6d>\u001b[0m in \u001b[0;36mtrain_all_words\u001b[0;34m(features, model_selector)\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtrain_all_words\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel_selector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0mtraining\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_training\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfeatures\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# Experiment here with different feature sets defined in part 1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     \u001b[0msequences\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtraining\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_all_sequences\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0mXlengths\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtraining\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_all_Xlengths\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/code/aind-projects/AIND-Recognizer/asl_data.py\u001b[0m in \u001b[0;36mbuild_training\u001b[0;34m(self, feature_list, csvfilename)\u001b[0m\n\u001b[1;32m     59\u001b[0m                 {'FRANK': [[[87, 225], [87, 225], ...], [[88, 219], [88, 219], ...]]]}\n\u001b[1;32m     60\u001b[0m         \"\"\"\n\u001b[0;32m---> 61\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mWordsData\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcsvfilename\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeature_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mbuild_test\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeature_method\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcsvfile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'data'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'test_words.csv'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/code/aind-projects/AIND-Recognizer/asl_data.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, asl, csvfile, feature_list)\u001b[0m\n\u001b[1;32m     87\u001b[0m         \u001b[0;34m:\u001b[0m\u001b[0mparam\u001b[0m \u001b[0mfeature_list\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlist\u001b[0m \u001b[0mof\u001b[0m \u001b[0mstr\u001b[0m \u001b[0mfeature\u001b[0m \u001b[0mlabels\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     88\u001b[0m         \"\"\"\n\u001b[0;32m---> 89\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_load_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0masl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcsvfile\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeature_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     90\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_hmm_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcreate_hmmlearn_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     91\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum_items\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/code/aind-projects/AIND-Recognizer/asl_data.py\u001b[0m in \u001b[0;36m_load_data\u001b[0;34m(self, asl, fn, feature_list)\u001b[0m\n\u001b[1;32m    124\u001b[0m                     \u001b[0;31m# logging.info(\"Data of individual frames: \", asl.df.__dict__)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    125\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 126\u001b[0;31m                     \u001b[0msample\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0masl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvid_frame\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    127\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    128\u001b[0m                 \u001b[0;31m# print(\"Sample: \", sample)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/miniconda3/envs/aind/lib/python3.6/site-packages/pandas/core/series.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m    601\u001b[0m         \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_apply_if_callable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    602\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 603\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    604\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    605\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mis_scalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/miniconda3/envs/aind/lib/python3.6/site-packages/pandas/indexes/base.py\u001b[0m in \u001b[0;36mget_value\u001b[0;34m(self, series, key)\u001b[0m\n\u001b[1;32m   2181\u001b[0m                     \u001b[0;32mraise\u001b[0m \u001b[0mInvalidIndexError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2182\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2183\u001b[0;31m                     \u001b[0;32mraise\u001b[0m \u001b[0me1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2184\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# pragma: no cover\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2185\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0me1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/Ls/miniconda3/envs/aind/lib/python3.6/site-packages/pandas/indexes/base.py\u001b[0m in \u001b[0;36mget_value\u001b[0;34m(self, series, key)\u001b[0m\n\u001b[1;32m   2167\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2168\u001b[0m             return self._engine.get_value(s, k,\n\u001b[0;32m-> 2169\u001b[0;31m                                           tz=getattr(series.dtype, 'tz', None))\n\u001b[0m\u001b[1;32m   2170\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2171\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minferred_type\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m'integer'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'boolean'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mpandas/index.pyx\u001b[0m in \u001b[0;36mpandas.index.IndexEngine.get_value (pandas/index.c:3557)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/index.pyx\u001b[0m in \u001b[0;36mpandas.index.IndexEngine.get_value (pandas/index.c:3240)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/index.pyx\u001b[0m in \u001b[0;36mpandas.index.IndexEngine.get_loc (pandas/index.c:4279)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/src/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas.hashtable.PyObjectHashTable.get_item (pandas/hashtable.c:13742)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/src/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas.hashtable.PyObjectHashTable.get_item (pandas/hashtable.c:13696)\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'right-x-rescaling'"
     ],
     "output_type": "error"
    }
   ],
   "source": [
    "# Features All using BIC\n",
    "\n",
    "features_all = {\n",
    "    'features_ground': features_ground, \n",
    "    'features_norm': features_norm,\n",
    "    'features_polar': features_polar, \n",
    "    'features_delta': features_delta,\n",
    "    'features_rescaled': features_rescaled\n",
    "}\n",
    "\n",
    "# DONE Choose a feature set and model selector\n",
    "model_selector = SelectorBIC # change as needed\n",
    "\n",
    "print(\"\\nLoading WER results for Model Selector: SelectorBIC ...\")\n",
    "\n",
    "# DONE Recognize the test set and display the result with the show_errors method\n",
    "for features_name, features in features_all.items():\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    print(\"\\nWER results for Feature Set: %r\" % features_name)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Loading WER results for Model Selector: SelectorDIC ...\n",
      "\n",
      "WER results for Feature Set: 'features_ground'\n",
      "\n",
      "**** WER = 0.5730337078651685\n",
      "Total correct: 76 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "    7: *SOMETHING-ONE *CAR *ARRIVE *ARRIVE                           JOHN CAN GO CAN\n",
      "   12: *IX *WHAT *WHAT *CAR                                          JOHN CAN GO CAN\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *CAR *CAR *FUTURE *MARY             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   28: JOHN *WHO IX IX *LOVE                                         JOHN LIKE IX IX IX\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "   36: *VISIT *VISIT *GIVE *GO *MARY *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY *GO *GIVE MARY *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *FUTURE *GIVE1 CAR *JOHN                                FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *MARY BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *GO *MARY MARY                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *JOHN *GIVE1 *VISIT BOOK                                      IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY IX *IX *IX IX *ARRIVE *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *SOMETHING-ONE IX *IX *VISIT *ARRIVE                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX *IX BOOK                                      JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *IX NEW CAR *ARRIVE                                           POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *IX *HAVE *ARRIVE *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *IX ARRIVE                                                    WOMAN ARRIVE\n",
      "  113: IX CAR *IX *MARY *BOX                                         IX CAR BLUE SUE BUY\n",
      "  119: *VISIT *BUY1 IX *BOX *IX                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *BUY BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *MARY BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "  167: JOHN *MARY *GO LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "  174: *CAR *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *SOMETHING-ONE *VISIT BOX                                JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SOMETHING-ONE *VISIT BOX                                JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE *GO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *LOVE *JOHN *GIVE1 HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# Features All without Delta using DIC\n",
    "\n",
    "features_all_without_delta = {\n",
    "    'features_ground': features_ground, \n",
    "    'features_norm': features_norm,\n",
    "    'features_polar': features_polar, \n",
    "    'features_rescaled': features_rescaled\n",
    "}\n",
    "\n",
    "# DONE Choose a feature set and model selector\n",
    "model_selector = SelectorDIC # change as needed\n",
    "\n",
    "print(\"\\nLoading WER results for Model Selector: SelectorDIC ...\")\n",
    "\n",
    "# DONE Recognize the test set and display the result with the show_errors method\n",
    "for features_name, features in features_all_without_delta.items():\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    print(\"\\nWER results for Feature Set: %r\" % features_name)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Features All without Rescaled using CV\n",
    "\n",
    "features_all_without_rescaled = {\n",
    "    'features_ground': features_ground, \n",
    "    'features_norm': features_norm,\n",
    "    'features_polar': features_polar, \n",
    "    'features_delta': features_delta\n",
    "}\n",
    "\n",
    "# DONE Choose a feature set and model selector\n",
    "model_selector = SelectorCV # change as needed\n",
    "\n",
    "print(\"\\nLoading WER results for Model Selector: SelectorCV ...\")\n",
    "\n",
    "# DONE Recognize the test set and display the result with the show_errors method\n",
    "for features_name, features in features_all_without_rescaled.items():\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    print(\"\\nWER results for Feature Set: %r\" % features_name)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3:**  Summarize the error results from three combinations of features and model selectors.  What was the \"best\" combination and why?  What additional information might we use to improve our WER?  For more insight on improving WER, take a look at the introduction to Part 4.\n",
    "\n",
    "**Answer 3:**\n",
    "\n",
    "The coloured Bar Graph shown below contrasts the Word Error Rate (WER) percentage results depending on the combination of Feature Sets (ground, norm, polar, rescaled) and Model Selectors (Constant, CV, BIC, DIC) strategy chosen for the recogniser implementation that was trained with the entire set of words. The results were obtained using a custom IDE debugging configuration that was setup and then by running `python3 main.py`.\n",
    "\n",
    "The following Table summarises the error results from only the three most interesting combinations. All of these combinations achieved a WER < 60% (i.e. WER < 0.60):\n",
    "\n",
    "| Features Set   | Model Selector    | WER      | Avg. Timeframe | Avg. States |      \n",
    "| -------------- | :---------------: | :------: | :------------: | ----------: |\n",
    "| `features_all` | SelectorConstant  | 0.5618   | 0.0526         | 3.0         |\n",
    "| `features_all` | SelectorCV        | 0.5618   | 1.1034         | 4.7         |\n",
    "| `features_all` | SelectorBIC       | 0.4831   | 0.6824         | 8.1         |\n",
    "| `features_all` | SelectorDIC       | 0.4944   | 2.0946         | 7.2         |\n",
    "\n",
    "\n",
    "| Features Set                  | Model Selector   | WER     | Avg. Timeframe | Avg. States |\n",
    "| ----------------------------- | :--------------: | :-----: | :------------: | ----------: |\n",
    "| `features_all_without_delta`  | SelectorConstant | 0.5674  | 0.0447         | 3.0         |\n",
    "| `features_all_without_delta`  | SelectorCV       | 0.5056  | 1.0275         | 4.7         |\n",
    "| `features_all_without_delta`  | SelectorBIC      | 0.5169  | 0.5856         | 8.3         |\n",
    "| `features_all_without_delta`  | SelectorDIC      | 0.4888  | 2.1126         | 7.6         |\n",
    "\n",
    "\n",
    "| Features Set                    | Model Selector   | WER     | Avg. Timeframe | Avg. States |   \n",
    "| ------------------------------- | :-------------:  | :-----: | :------------: | ----------: |\n",
    "| `features_all_without_rescaled` | SelectorConstant | 0.5955  | 0.0510         | 3.0          |\n",
    "| `features_all_without_rescaled` | SelectorCV       | 0.5618  | 1.1714         | 4.6          |\n",
    "| `features_all_without_rescaled` | SelectorBIC      | 0.4831  | 0.6565         | 8.1          |\n",
    "| `features_all_without_rescaled` | SelectorDIC      | 0.5112  | 2.1671         | 7.2          |\n",
    "\n",
    "The combination of `features_all_without_rescaled` with BIC was the \"best\" combination in terms of WER, with the lowest WER of 48.31%. With `features_all_without_rescaled` and DIC, the WER result was comparable at 51.12%, however it was 3x slower than BIC.\n",
    "\n",
    "The combination `features_all` (all the features sets), which includes rescaling, did not perform faster than `features_all_without_rescaled` that excluded rescaling. In the answer to Question 1 in Part 1, the benefits of using rescaling when using large vocabularies to improve speed were discussed, however these results prove otherwise, and is especially obvious in the Bar Graph for CV where removing just the rescale feature reduced the WER by 5%. \n",
    "\n",
    "The combination of `features_all` with BIC or DIC achieved a 3% better WER than the result when removed the `norm` and `polar` feature sets were removed, which was as expected since `norm` and `polar` apply fixes that should reduce errors. The `norm` feature set was meant to fix results to account for different height and arm lengths, whilst the `polar` feature was meant to fix the results to account for discontinuity in the signing area to prevent interference.  \n",
    "\n",
    "The recogniser currently implemented in Part 3 is equivalent to a \"0-gram\" Statistical Language Models (SLM). The additional information that we may obtain to make better choices and improve our WER is through applying SLM on our data using \"1-gram\", \"2-gram\", and \"3-gram\" statistics, and by converting the probabilities data already calculated into a pandas DataFrame, as highlighted in Part 4, since each word has a probability of occurrence within the set, and also some probability of being adjacent to specific other words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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+fgxs93DdlFJK5WFptqCMMWNF5EbgDbHGWL4GFAcKG2O2ZkcFlfIknVJKqZzL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\nd1BmZtaS3EGZmVlL+h91wI6Y5jGQgQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1205ae3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "# data to plot\n",
    "objects = ('CONSTANT', 'CV', 'BIC', 'DIC')\n",
    "n_groups = len(objects)\n",
    "times_0 = (66.85, 65.73, 58.99, 57.30) # only ground feature\n",
    "times_1 = (62.35, 64.61, 60.67, 59.55) # only norm feature\n",
    "times_2 = (61.80, 69.10, 55.01, 54.49) # only polar feature\n",
    "times_3 = (64.04, 64.61, 62.36, 62.92) # only delta feature\n",
    "times_4 = (56.18, 56.18, 48.31, 49.44) # all features\n",
    "times_5 = (58.99, 55.62, 51.69, 52.81) # all features except norm and polar\n",
    "times_6 = (59.55, 56.18, 48.31, 51.12) # all features except rescaled\n",
    "times_7 = (56.74, 50.56, 51.69, 48.88) # all features except delta\n",
    "\n",
    "# create plot\n",
    "fig, ax = plt.subplots()\n",
    "index = np.arange(n_groups)\n",
    "bar_width = 0.10\n",
    "opacity = 0.8\n",
    " \n",
    "rects1 = plt.bar(index, \n",
    "                 times_0, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#ff4000',\n",
    "                 label='Only Ground Feature')\n",
    " \n",
    "rects2 = plt.bar(index + bar_width, \n",
    "                 times_1, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#ff8000',\n",
    "                 label='Only Norm Feature')\n",
    "\n",
    "rects3 = plt.bar(index + (2 * bar_width), \n",
    "                 times_2, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#ffbf00',\n",
    "                 label='Only Polar Feature')\n",
    "\n",
    "rects4 = plt.bar(index + (3 * bar_width), \n",
    "                 times_3, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#ffff00',\n",
    "                 label='Only Delta Feature')\n",
    "\n",
    "rects5 = plt.bar(index + (4 * bar_width), \n",
    "                 times_4, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#40ff00',\n",
    "                 label='All Features')\n",
    "\n",
    "rects6 = plt.bar(index + (5 * bar_width), \n",
    "                 times_5, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#00dd22',\n",
    "                 label='All Features, No Norm or Polar')\n",
    "\n",
    "rects7 = plt.bar(index + (6 * bar_width), \n",
    "                 times_6, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#00bfff',\n",
    "                 label='All Features, No Delta')\n",
    "\n",
    "rects8 = plt.bar(index + (7 * bar_width), \n",
    "                 times_7, \n",
    "                 bar_width,\n",
    "                 alpha=opacity,\n",
    "                 color='#0000ff',\n",
    "                 label='All Features, No Rescaled')\n",
    "\n",
    "plt.xlabel('Technique')\n",
    "plt.ylabel('Word Error Rate (WER) %')\n",
    "plt.title('Word Error Rate (WER) by Technique')\n",
    "plt.xticks(index + bar_width, objects)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_test'></a>\n",
    "### Recognizer Unit Tests\n",
    "Run the following unit tests as a sanity check on the defined recognizer.  The test simply looks for some valid values but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "..\n",
      "----------------------------------------------------------------------\n",
      "Ran 2 tests in 40.233s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=2 errors=0 failures=0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_recognizer import TestRecognize\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestRecognize())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part4_info'></a>\n",
    "## PART 4: (OPTIONAL)  Improve the WER with Language Models\n",
    "We've squeezed just about as much as we can out of the model and still only get about 50% of the words right! Surely we can do better than that.  Probability to the rescue again in the form of [statistical language models (SLM)](https://en.wikipedia.org/wiki/Language_model).  The basic idea is that each word has some probability of occurrence within the set, and some probability that it is adjacent to specific other words. We can use that additional information to make better choices.\n",
    "\n",
    "##### Additional reading and resources\n",
    "- [Introduction to N-grams (Stanford Jurafsky slides)](https://web.stanford.edu/class/cs124/lec/languagemodeling.pdf)\n",
    "- [Speech Recognition Techniques for a Sign Language Recognition System, Philippe Dreuw et al](https://www-i6.informatik.rwth-aachen.de/publications/download/154/Dreuw--2007.pdf) see the improved results of applying LM on *this* data!\n",
    "- [SLM data for *this* ASL dataset](ftp://wasserstoff.informatik.rwth-aachen.de/pub/rwth-boston-104/lm/)\n",
    "\n",
    "##### Optional challenge\n",
    "The recognizer you implemented in Part 3 is equivalent to a \"0-gram\" SLM.  Improve the WER with the SLM data provided with the data set in the link above using \"1-gram\", \"2-gram\", and/or \"3-gram\" statistics. The `probabilities` data you've already calculated will be useful and can be turned into a pandas DataFrame if desired (see next cell).  \n",
    "Good luck!  Share your results with the class!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a DataFrame of log likelihoods for the test word items\n",
    "df_probs = pd.DataFrame(data=probabilities)\n",
    "df_probs.head()"
   ]
  }
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