ML-MER.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predict topics of Math Questions on the UBC Math Education Resources\n",
    "\n",
    "**URL**: http://www.math-education-resources.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use simple machine learning algorithms and [scikit-learn](http://scikit-learn.org/stable/) to **predict the topics of Math Questions** from the [Math Education Resources](http://www.math-education-resources.com). For demonstration we will only consider two topics here, but the production Flask app is trained on a larger set and handles more topics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data inspection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The questions live in a MongoDB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import helpers\n",
    "from pymongo import MongoClient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of questions: 1928.\n",
      "(u'ID', u'UBC+MATH100+December_2013+01_(a)')\n",
      "(u'_id', ObjectId('55870669ceac4768093a511e'))\n",
      "(u'answer_html', u'<p><span class=\"math\">\\\\(\\\\lim_{x \\\\to -5} \\\\frac{x^2 + 2x - 15}{2x+10}={\\\\color{blue}-4}\\\\)</span></p>')\n",
      "(u'answer_latex', u' $\\\\lim_{x \\\\to -5} \\\\frac{x^2 + 2x - 15}{2x+10}={\\\\color{blue}-4}$ ')\n",
      "(u'contributors', [u'Konradbe', u'CarmenBruni'])\n",
      "(u'course', u'MATH100')\n",
      "(u'flags', [u'QGQ', u'QGH', u'QGS', u'QGT'])\n",
      "(u'hints_html', [u'<p>Try factoring the numerator, i.e., <span class=\"math\">\\\\(x^2 + 2x - 15\\\\)</span>.</p>'])\n",
      "(u'hints_latex', [u'Try factoring the numerator, i.e., $x^2 + 2x - 15$.'])\n",
      "(u'hints_raw', [u'Try factoring the numerator, i.e., &lt;math>x^2 + 2x - 15&lt;/math>.'])\n",
      "(u'is_multiple_choice', False)\n",
      "(u'num_votes', 10)\n",
      "(u'number', u'01_(a)')\n",
      "(u'number_human', u'1 (a)')\n",
      "(u'question', u'1 (a)')\n",
      "(u'rating', 5.0)\n",
      "(u'sols_html', [u'<p><span class=\"math\">\\\\[\\\\begin{aligned}\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2 + 2x - 15}{2x+10} &amp;= \\\\lim_{x \\\\to -5} \\\\frac{(x-3)(x+5)}{2(x+5)}\\n\\\\\\\\ &amp;= \\\\lim_{x \\\\to -5} \\\\frac{x-3}{2}\\n\\\\\\\\ &amp;= \\\\frac{(-5)-3}{2}\\n\\\\\\\\ &amp;= {\\\\color{blue}-4}\\\\end{aligned}\\\\]</span></p>'])\n",
      "(u'sols_latex', [u'\\\\begin{align*}\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2 + 2x - 15}{2x+10} &= \\\\lim_{x \\\\to -5} \\\\frac{(x-3)(x+5)}{2(x+5)}\\n\\\\\\\\ &= \\\\lim_{x \\\\to -5} \\\\frac{x-3}{2}\\n\\\\\\\\ &= \\\\frac{(-5)-3}{2}\\n\\\\\\\\ &= {\\\\color{blue}-4}\\n\\\\end{align*}'])\n",
      "(u'sols_raw', [u'&lt;math>\\n\\\\begin{align}\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2 + 2x - 15}{2x+10} &amp;= \\\\lim_{x \\\\to -5} \\\\frac{(x-3)(x+5)}{2(x+5)}\\n\\\\\\\\ &amp;= \\\\lim_{x \\\\to -5} \\\\frac{x-3}{2}\\n\\\\\\\\ &amp;= \\\\frac{(-5)-3}{2}\\n\\\\\\\\ &amp;= {\\\\color{blue}-4}\\n\\\\end{align}\\n&lt;/math>'])\n",
      "(u'solvers', [u'NicholasHu'])\n",
      "(u'statement_html', u'<p><strong>Short-Answer Question. Simplify your answer as much as possible and show your work.</strong></p>\\n<p>Evaluate the limit</p>\\n<p><span class=\"math\">\\\\[\\\\begin{aligned}\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2+2x-15}{2x+10}\\\\end{aligned}\\\\]</span></p>')\n",
      "(u'statement_latex', u'\\\\textbf{Short-Answer Question. Simplify your answer as much as possible\\nand show your work.}\\n\\nEvaluate the limit\\n\\n\\\\begin{align*}\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2+2x-15}{2x+10}\\n\\\\end{align*}')\n",
      "(u'statement_raw', u\"'''Short-Answer Question. Simplify your answer as much as possible and show your work.'''\\n\\nEvaluate the limit\\n\\n:&lt;math>\\n\\\\lim_{x \\\\to -5} \\\\frac{x^2+2x-15}{2x+10}\\n&lt;/math>\")\n",
      "(u'term', u'December')\n",
      "(u'term_year', u'December_2013')\n",
      "(u'topics', [u'Limit_of_a_rational_function'])\n",
      "(u'url', u'http://wiki.ubc.ca/Science:Math_Exam_Resources/Courses/MATH100/December_2013/Question_01_(a)')\n",
      "(u'year', 2013)\n"
     ]
    }
   ],
   "source": [
    "client = MongoClient()\n",
    "questions_collection = client['merdb'].questions\n",
    "print(\"Total number of questions: %d.\" %questions_collection.count())\n",
    "select = {\"course\": \"MATH100\", \"year\": 2013, \"term\": \"December\", \"number\": \"01_(a)\"}\n",
    "for q in questions_collection.find(select):\n",
    "    for key in sorted(q.keys()):\n",
    "        print(key, q[key])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### For our analysis we focus on two topics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOTAL:\n",
      "## - Topic\n",
      "==========\n",
      "48 - Eigenvalues and eigenvectors\n",
      "41 - Probability density function\n"
     ]
    }
   ],
   "source": [
    "TOPIC0 = \"Probability_density_function\"\n",
    "TOPIC1 = \"Eigenvalues_and_eigenvectors\"\n",
    "topic_tags = [TOPIC0, TOPIC1]\n",
    "questions = helpers.get_questions_with_topics(topic_tags)\n",
    "topic_tags2 = []\n",
    "print('TOTAL:\\n## - Topic\\n==========')\n",
    "for topic, count in helpers.count_topics_in_questions(questions).iteritems():\n",
    "    if count > 10:\n",
    "        topic_tags2.append(topic)\n",
    "        print('%2d - %s' %(count, topic.replace('_', ' ')))\n",
    "topic_tags = topic_tags2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Being in the *IPython Notebook* we can acutally even display them nicely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import HTML, Javascript, display\n",
    "def display_MER_question(q, right=True):\n",
    "    ''' A helper function to display questions in the notebook. '''\n",
    "    def base_html(title, body):\n",
    "        top = \"<div style='background: #AAFFAA; width: 40%;\"\n",
    "        left = \"position:absolute; left: 50%;\"\n",
    "        middle = \"</div><div style='display: inline-block; width: 40%;\"\n",
    "        end = \"</div>\"\n",
    "        if right:\n",
    "            return top + \"'>\" + title + middle + \"'>\" + body + end\n",
    "        else:\n",
    "            return top + left + \"'>\" + title + middle + left + \"'>\" + body  + end\n",
    "    topic = base_html('Topic', q['topics'][0])\n",
    "    statement = base_html('Statement', q['statement_html'])\n",
    "    hint = base_html('Hint', q['hints_html'][0])\n",
    "    sol = base_html('Solution', q['sols_html'][0])\n",
    "    display(HTML(data = base_html(q['topics'][0], (\"<h3>STATEMENT</h3>\" + q['statement_html'] +\n",
    "                                                   \"<h3>HINT</h3>\" + q['hints_html'][0] +\n",
    "                                                   \"<h3>SOLUTION</h3>\" + q['sols_html'][0]))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style='background: #AAFFAA; width: 40%;position:absolute; left: 50%;'>Eigenvalues_and_eigenvectors</div><div style='display: inline-block; width: 40%;position:absolute; left: 50%;'><h3>STATEMENT</h3><p>Suppose that <em>A</em> is a symmetric 4x4 matrix with eigenvalues 0, 1, 4, 5. Define a sequence of vectors <span class=\"math\">\\(\\mathbf{x}_n \\in \\mathbb{R}^4\\)</span> by choosing <strong>x</strong><sub>0</sub> at random, and then settings</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "\\mathbf{y}_n &amp;= (A-3I)^{-1}\\mathbf{x}_{n-1} \\\\\n",
       "\\mathbf{x}_n &amp;= \\mathbf{y}_n/\\|\\mathbf{y}_{n}\\|\\end{aligned}\\]</span></p>\n",
       "<p>for <em>n = 1, 2, ...</em>. You then observe that <strong>x</strong><sub>n</sub> converges to</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "\\mathbf{x}_\\infty = [1/2, 1/2, 1/2, 1/2]^T\\end{aligned}\\]</span></p>\n",
       "<p>as <span class=\"math\">\\(n \\to \\infty\\)</span>.</p>\n",
       "<p><strong>(b)</strong> What is the value of the inner (dot) product <span class=\"math\">\\(\\langle \\mathbf{x}_\\infty, A\\mathbf{x}_\\infty\\rangle\\)</span>?</p><h3>HINT</h3><p>Recall that from <span>part (a)</span> that <span class=\"math\">\\(\\displaystyle A\\mathbf x_{\\infty} = 4\\mathbf x_{\\infty}\\)</span>.</p><h3>SOLUTION</h3><p>From part (a), we recall that <span class=\"math\">\\(\\displaystyle \\lambda = 4\\)</span> was the eigenvalue associated to the eigenvector <span class=\"math\">\\(\\displaystyle x_{\\infty}\\)</span>. We can use these to find the solution:</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "Ax_{\\infty} &amp;= \\lambda x_{\\infty}\\\\\n",
       "Ax_{\\infty}\\cdot x_{\\infty} &amp;= \\lambda x_{\\infty}\\cdot x_{\\infty}\\\\\n",
       "Ax_{\\infty}\\cdot x_{\\infty} &amp;= 4(1)\\\\\n",
       "\\langle \\mathbf{x}_\\infty, A\\mathbf{x}_\\infty\\rangle &amp;= 4\\end{aligned}\\]</span></p></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style='background: #AAFFAA; width: 40%;'>Probability_density_function</div><div style='display: inline-block; width: 40%;'><h3>STATEMENT</h3><p>Seeds are dispersed from a tree in all directions uniformly. The density of seeds that lands on the ground at a distance <em>r</em> away is approximately described by the function</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "s(r) = 50 \\sin\\left(\\frac{\\pi r}{10}\\right) \\text{ seeds/m}^2, \\quad 0 \\leq r \\leq 10 \\text{ m}\\end{aligned}\\]</span></p>\n",
       "<p>At what distance from the tree are the seeds most densely distributed?</p><h3>HINT</h3><p>The seeds are most densely distributed at the point where the function that describes the density has a maximum.</p><h3>SOLUTION</h3><p>Since we look for the maximum of <em>s</em>, we set its derivative to zero.</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "0 = \\frac{d}{dr}50\\sin\\left(\\frac{\\pi r}{10}\\right) = 50\\frac{\\pi}{10}\\cos\\left(\\frac{\\pi r}{10}\\right),\\end{aligned}\\]</span></p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "\\cos\\left(\\frac{\\pi r}{10}\\right)=0,\\end{aligned}\\]</span></p>\n",
       "<p>Due to the restriction on <em>r</em> the only possible zero is when</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "\\frac{\\pi r}{10} = \\frac{\\pi}{2}\\end{aligned}\\]</span></p>\n",
       "<p>which is attained at</p>\n",
       "<p><span class=\"math\">\\[\\begin{aligned}\n",
       "\\displaystyle r=5\\end{aligned}\\]</span></p>\n",
       "<p>Note that <span class=\"math\">\\(\\sin(\\pi(5)/10) = \\sin(\\pi/2) = 1\\)</span> gives indeed the maximum value for sine and hence for <em>s</em>.</p></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_MER_question(questions[2], right=False)\n",
    "display_MER_question(questions[51])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare for machine learning algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Split into train and test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAIN/TEST:\n",
      "##/## - Topic\n",
      "=============\n",
      "35/13 - Eigenvalues and eigenvectors\n",
      "34/ 7 - Probability density function\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(23)  # for reproducibility we set the seed of the random number generator\n",
    "m = 20\n",
    "test_indices = np.random.choice(range(len(questions)), m, replace=False)\n",
    "questions_train = [q for i, q in enumerate(questions) if not i in test_indices]\n",
    "questions_test = [q for i, q in enumerate(questions) if i in test_indices]\n",
    "print('TRAIN/TEST:\\n##/## - Topic\\n=============')\n",
    "for t in topic_tags:\n",
    "    print('%2d/%2d - %s' % (sum([1 for q in questions_train if t in q['topics']]),\n",
    "                          sum([1 for q in questions_test if t in q['topics']]),\n",
    "                          t.replace('_', ' ')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming text data to vectors\n",
    "\n",
    "To apply machine learning we have to transform the questions and topics (labels) into a vector representation.\n",
    "\n",
    "#### Identifying class labels\n",
    "\n",
    "Turning the topics into a vector is the easy part:\n",
    "\n",
    "**0 = Probability density function**\n",
    "\n",
    "**1 = Eigenvalues and eigenvectors**\n",
    "\n",
    "In the case of more than two classes use scikit-learns [label binarizer](http://scikit-learn.org/stable/modules/multiclass.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def questions_to_y(qs):\n",
    "    '''Return array or Booleans indicating whether the corresponding question is of TOPIC1'''\n",
    "    def topic_from_question(q):\n",
    "        return TOPIC1 in q['topics']\n",
    "    y = np.zeros(shape=(len(qs)))\n",
    "    for i, q in enumerate(qs):\n",
    "        y[i] = topic_from_question(q)\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train = questions_to_y(questions_train)\n",
    "y_test = questions_to_y(questions_test)\n",
    "assert y_train.shape[0] == len(questions_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Manufactoring the feature vector\n",
    "\n",
    "Transforming the text of the question to a vector is more tricky. Our strategy is the following:\n",
    "\n",
    "1. Extract all words from a question (bag of words).\n",
    "2. Collapse plurals, tense, etc.\n",
    "3. Remove stopwords (they don't contain useful information).\n",
    "4. This leaves $n$ words in our corpus, each question will be a vector in $\\mathbb{R}^n$.\n",
    "5. Question vector is calculated by TF-IDF (leads to sparse vectors)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Helpers from Natural Language Toolkit\n",
    "\n",
    "Python provides a [natural language toolkit](http://www.nltk.org/) with many useful functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import helpers\n",
    "from nltk import PorterStemmer\n",
    "from nltk.corpus import stopwords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['sensat', 'sensat', 'season', 'fli', 'fli', 'fli']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[PorterStemmer().stem_word(w) for w in ['sensation', 'sensational', 'seasonal', 'flying', 'flies', 'fly']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['i', 'me', 'my', 'myself', 'we', 'our', 'ours', 'ourselves', 'you', 'your']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stopwords.words('english')[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using these techniques, the question above reads:\n",
      "seed dispers tree direct uniformli densiti seed land ground distanc away approxim describ function distanc tree seed dens distribut seed dens distribut point function describ densiti ha maximum sinc look maximum set deriv zero due restrict onli possibl zero attain note give inde maximum valu sine henc fraction sine cosin pi greater_than\n"
     ]
    }
   ],
   "source": [
    "print(\"Using these techniques, the question above reads:\\n%s\" %helpers.question_to_BOW(questions[51]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TF-IDF (term frequency inverse document frequency) counts the total frequency of each word (term) in the corpus, and then calculates the relative frequency of each word in each document. This way ubiquitos words get a smaller weight than rare words. TF-IDF does not account for *where* the words appear.\n",
    "\n",
    "Using the helper functions above we could write our own vectoriser, but again, scikit-learn has us covered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 434)\t0.163989609452\n",
      "  (0, 409)\t0.0684264934708\n",
      "  (0, 405)\t0.131991372399\n",
      "  (0, 398)\t0.282444594921\n",
      "  (0, 346)\t0.237962228498\n",
      "  (0, 345)\t0.0673386860857\n",
      "  (0, 336)\t0.105970856098\n",
      "  (0, 333)\t0.564889189843\n",
      "  (0, 317)\t0.131991372399\n",
      "  (0, 285)\t0.105970856098\n",
      "  (0, 282)\t0.114034843661\n",
      "  (0, 278)\t0.0967399310369\n",
      "  (0, 264)\t0.0744987478251\n",
      "  (0, 254)\t0.0875090059757\n",
      "  (0, 224)\t0.102590127448\n",
      "  (0, 202)\t0.141222297461\n",
      "  (0, 178)\t0.141222297461\n",
      "  (0, 166)\t0.0642804450217\n",
      "  (0, 160)\t0.0684264934708\n",
      "  (0, 159)\t0.141222297461\n",
      "  (0, 158)\t0.0320872447232\n",
      "  (0, 153)\t0.0895798692975\n",
      "  (0, 149)\t0.11784027945\n",
      "  (0, 144)\t0.0557871902578\n",
      "  (0, 107)\t0.141222297461\n",
      "  (0, 100)\t0.183587320898\n",
      "  (0, 98)\t0.282444594921\n",
      "  (0, 97)\t0.141222297461\n",
      "  (0, 95)\t0.109750189188\n",
      "  (0, 88)\t0.263982744799\n",
      "  (0, 87)\t0.105970856098\n",
      "  (0, 86)\t0.119507243028\n",
      "  (0, 71)\t0.118981114249\n",
      "  (0, 28)\t0.12483131066\n",
      "  (0, 17)\t0.141222297461\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<1x435 sparse matrix of type '<type 'numpy.float64'>'\n",
       "\twith 35 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "\n",
    "vectorizer = TfidfVectorizer(min_df=2)\n",
    "vectorizer.fit(helpers.questions_to_BOW(questions))\n",
    "print(vectorizer.transform([helpers.question_to_BOW(questions[51])]))\n",
    "vectorizer.transform([helpers.question_to_BOW(questions[51])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest is easy: Extract the text from each question and apply the vectorizer to obtain the feature vector of each question. Then concatenate these vectors to a matrix X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = helpers.questions_to_X(questions_train)\n",
    "X_test = helpers.questions_to_X(questions_test)\n",
    "assert X_train.shape[0] == len(questions_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The classifier\n",
    "\n",
    "Scikit-learn has many classifiers to choose from, so we'll just take one off the shelf for now. We use a Support Vector Classifier because this performs best at the full dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import svm\n",
    "\n",
    "classifier =svm.SVC(kernel='linear', probability = True, random_state=np.random.RandomState(0))\n",
    "trained_classifier = classifier.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it, the classifier is trained and can be used to predict the topic of a new question from the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  7.34326245e-07   9.99999266e-01]\n",
      " [  2.57611375e-02   9.74238863e-01]\n",
      " [  4.83091746e-03   9.95169083e-01]\n",
      " [  4.10751854e-03   9.95892481e-01]\n",
      " [  8.94500612e-03   9.91054994e-01]\n",
      " [  5.57600593e-03   9.94423994e-01]\n",
      " [  3.35646796e-06   9.99996644e-01]\n",
      " [  4.10778820e-03   9.95892212e-01]\n",
      " [  1.39688570e-01   8.60311430e-01]\n",
      " [  9.86724050e-01   1.32759505e-02]\n",
      " [  9.88683208e-01   1.13167924e-02]\n",
      " [  9.87196084e-01   1.28039157e-02]\n",
      " [  9.92788110e-01   7.21189047e-03]\n",
      " [  9.57833590e-01   4.21664098e-02]\n",
      " [  9.85230569e-01   1.47694308e-02]\n",
      " [  9.31794975e-01   6.82050245e-02]\n",
      " [  5.13109520e-02   9.48689048e-01]\n",
      " [  2.50226207e-07   9.99999750e-01]\n",
      " [  1.83022756e-05   9.99981698e-01]\n",
      " [  9.36550252e-03   9.90634497e-01]]\n"
     ]
    }
   ],
   "source": [
    "preds = trained_classifier.predict_proba(X_test)\n",
    "print(preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row is a question, and the probability that the classifier assigns this question to be in either of the classes. The left column is the confidence that this question is `TOPIC0`, the right column is that it is in `TOPIC1`. We see that the classifier is very confident in its predictions. So, how well did it do?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score: 1.000000\n"
     ]
    }
   ],
   "source": [
    "print(\"Classifier score: %f\" %classifier.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is...surprisingly high! Let's explore this result a bit, by visualizing the features that this machine learning algorithm picked up on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Most important words:\n",
      " 1.332, eigenvalu\n",
      " 1.330, matrix\n",
      "-1.063, probabl\n",
      " 0.928, eigenvector\n",
      "-0.835, function\n",
      "-0.769, integr\n",
      " 0.666, dimens\n",
      "-0.637, median\n",
      "-0.608, indic\n",
      "Least important words:\n",
      " 0.000, typic\n",
      " 0.000, good\n",
      " 0.000, via\n",
      " 0.000, wait\n",
      " 0.000, real\n",
      " 0.000, perpendicular\n",
      " 0.000, calculu\n",
      " 0.000, invers\n",
      " 0.000, quick\n",
      " 0.000, trivial\n"
     ]
    }
   ],
   "source": [
    "coef_vec = trained_classifier.coef_.toarray()[0, :]\n",
    "most_important_features = np.abs(coef_vec).argsort()[-1:-10:-1]\n",
    "least_important_features = np.abs(coef_vec).argsort()[:10]\n",
    "print('Most important words:')\n",
    "for ind in most_important_features:\n",
    "    print('%6.3f, %s' % (coef_vec[ind], vectorizer.get_feature_names()[ind]))\n",
    "print('Least important words:')\n",
    "for ind in least_important_features:\n",
    "    print('%6.3f, %s' % (coef_vec[ind], vectorizer.get_feature_names()[ind]))    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty sweet: The classifier learned that **matrix**, **eigenvalu** and **eigenvector** are really good indicators for an **Eigenvalues and eigenvectors** questions. On the other hand, **probabl**, **function** and **integr** indicate a question on **Probability density function**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good job on the features, but how is it possible to separate the classes with a linear classifier so perfectly? A useful way to visualize high-dimensional data is using [Principal Component Analysis](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) to project the data down to 3D. Of course, scikit-learn has you covered here as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first 3 principal components explain 0.19 of the variance in the dataset.\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from sklearn.decomposition import PCA\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "pca = PCA(n_components=3)\n",
    "pca.fit(X_train.toarray())\n",
    "pca_X_train = pca.transform(X_train.toarray())\n",
    "pca_X_test = pca.transform(X_test.toarray())\n",
    "print('The first 3 principal components explain %.2f of the variance in the dataset.' % sum(pca.explained_variance_ratio_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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gcWF71hMOzUIk+DcG7+5qE5oFSqHFVD5w4FmDwkZY3Ulhm3MYLTFtxsSk2p8JlNKsM5tk\nWV4Ri8Umuq47zDCMCxRFeZnn+UZ4NzGbAEwAcIiu649qmrYxm3Mw9m2YiCkiu3btOnbbtm3HwQsm\njcKzTrjwSuDH4VVozTcq2i7GVobmZoDJ1pPdaGk9sdCaAfCye8LWyTasMTFhdCeFkW4hYhL35xjY\nm8uNCZFleW4sFjvKNM0ZkiS9IknSOnjz3QLP2ny7ruvPA3hb07Qw3AQxughMxBQRnucbdV130TqT\nJ5vg2CBOpj3rSQwt04eDALt1aNkMMNsLXFhjS8IsYsJm1Qgj3U7EIM91YjpyPCEkrqrqklgsttG2\n7WmO46xSFOVtP1amBt516HwAo3Rdn6NpWk0O52PsQ+zzIoYQcgaAh+D9UB+nlN6f5nVj4VlQfkQp\nfTGbc/E8bxiGkWrBj6G5uV+qOJlUj0W0FidBUbZE60mhmwFmm53U2YRVfDERUxy6jYihlLa5PwNy\nCQpucbwoipt4np9pWdYUwzAu9xtJ7kGzW/pAeEG/szRN+yqHczL2EcK4+OQNQggP4O8AToXn2llK\nCFlAKV2d4nX3A3gdWS4ghBBy6qmnOrZtV8ybN+/42tranldccUU9PEEyFF58xrHwBIyF1s0At6Cl\nWOkqgXBhFTFhtcSENSYmbHQLEeOHxHAAaEIfpbyM3QFaxNRwHGeqqjo3Go2OsSzrUlEU35Yk6Qt/\nflXw4vN+pev6GwDma5pm53BuRjcnjItPPhkHYB2ldBMAEEKeBzAVwOqk110LYB6AsZkOTAgpA/D/\n4MWMDAAwYPHixcKAAQPEVatWDerdu7d12WWXreQ4bg+8gm4ugCXwap6EySccVotGWOcdxpiYMImB\ngLCJmHQuHw45ipBcAnt9Wlly/EaSy3ie35zQSPJVjuMseNdAA97N5Ug/6HdrDudndGP2dRETBKUG\nbIVXRn8vhJAB8ITNd+GJmEwvbCaAt+BZeLYD2Hbuueee3tTUdPusWbPmJ732WHiZSvUdfgedD7PE\nFBfmTioOYRMxbbmTcg3Mzdqd5Luy0sbUCIKwi+f5xyzLOs0wjBmyLL8oiuIW//WVAHpHo9Fnamtr\n/yoIwiuapuViEWJ0Q8J4Ec8nmVykHgJwE/V+jYk1WtoemNIYpfRpSuliSulqSmmDqqpNlmW1FxMT\nNsJq0WAipriEbc7dRsQg98DcXKv9un59mJT4Qb8LJUl63bbtcy3LOolSGnxfdsdiscMAXALgWl3X\ny7OcB6ObEsaLeD7ZBq96ZMAgeNaYRI4B8DwhZCOA6QAeIYRMyeZkkUhEtywrldUizCImrJYYJr4Y\nbdEtRIxfJyavMS0doSOuKEmSvlVVdZbjOEMNw/iJ4zhlCWNUAjgcwF26rh+azVwY3ZN9/WK4DMAI\nQsgQQogE4FwACxJfQCkdRikdSikdCi8u5ipK6YIUY7WLpmm6bdupFvywCgGAiYFiE1ZLTNjoFiIG\nyK2DtU/RWhbwPK9HIpGneZ5fZ5rmldFo9BD//HF4N51xADfpuj5d13UpyzkxuhFhXTjzAqU0Tgi5\nBsAb8H5scyilqwkhM/z9s/J5vn79+jXYtt3d3ElhFWBhFV9MxBSHMIiYxD5lEQAHAxjhPy8DUGZZ\nVp0kSe8it5iYolb79RtJfuDXlJkOoMSPrQG87MwmAJPhNZKcqWladTZzY3QPwrj45BVK6SIAi5K2\npRQvlNJLcjnXyJEj9Wg0mkqshF3EKJ09iSwIqyUmjCnWXV0MpKMz582hdU+15L9SNLcmKYFX+bYa\nXjn/BgA6x3FDbNs+HzkG9uZwfNbHiqK4jef5WYZh/J9lWRcqivJvQRB2+ONthtdf7i5d158E8CFr\nJLlvss+LmGIycuRIy3GcVAtQmEVMWC0aYZ13GFOsw0ghLTEi0guTYHsEnsWhIemvKuGxDu8mAgCu\nAvAevGrce5FluTIWi5mxWGyaaZqn+VVyO2RVoZRyxXInJcNxnA2AiqL4oWVZFwuC8J4sy5/6NWV2\nwruBmgHPKvOMpmmN2Z6LEU6YiCku6arnhtUlA4R37mG1xITVnRS2OWcrYhSkFybBn4iWwkSH1+R1\nY8K2jrYCSdvFmuf5nbFYrIZS2tswjEsURZnH83xHyjlknd1EKc212i8A8JIkfSkIwibLsqabpjlc\nUZRXOI4z4BUG3QhgDIARfk2ZdTmejxEiwrj4hJlYmqqZzBJTfJiIYbRFsogJ2oGkEybBtqA3WlBd\nuwFenahvErYVotp2WhEDr/ljXFXV52zbPs40zSskSVogSdKaDMfuFHcSAPip1gSAy/N8TSQSecKy\nrFMMw/iZLMsviaK4Ed7/01Z4tbZu1XV9PoBFmqbF2xia0U1gIqa4BBeZ5AtkmEVMWC0xYRZfTMTk\nFx4t+5KVwbOoTIbX4T0QKEE7kMS/jUnPo0Wee0A6EcP5wbWuHzD7YSwW2+JXyR2sKMriDNxLWXfA\nzkO1XwFAPLj5I4Q4qqq+HY1GN9i2PS0ej3+lKMoSf3518Kr9ngPgcF3XH9c0bVcO52aEgDAuPqGl\nf//+1HXdIKYh8YcdZhETZjEQVktMGOfdWYho372jwlv8Et07FMAaALsStnXldiBtVeVtIXBEUdzi\nN2GclqF7qTMtMSmPlyRpgyAIsyzLmmoYxqWKoszneb4W3k3VRgAHwGsk+RiAz1jQb/eFiZgi47qu\ni9Y/7LBaM4Dwzj2s4ou5k5oJrCRtZfDwaO3e2Q1gQ8L2RrSOfzkCXg+1rtJotT06VOzOb8KYqXup\naHVikqGUCmgOXm4Bx3FNqqr+y7bt8aZpXi6K4uuyLH/t794BLzj6FwCW6Lr+vKZpZrbzYHRdwrj4\nhB03Ho9zgtDio4/D+7GHoTZFMmEVMWG1xITRndTR7zSBlz6cLu4keOygtXtnK1oKlmwXrrD9FtuM\niUEKIdEB91JR68Qk0ebxhBAoivJJPB7fbNv2dMdxDlQU5TWO46LwBOimaDR6EaV0GoBfaJq2KYe5\nMLogYVx8Qo0oinZDQ4NSUVFhJe0KXEqd5VPPlrBaNMIqYsLuTgriT9oSJ6XwxEeie6cBwPqkbYX8\nrXQbERPExKQ70HcvzfLdSz/13UsNQMvA2iznlVN2UluWmEQEQajmeX62aZpn+EG/80RR3A7AdRxH\nIIT0AfA7XdefB/C2pmld2TXI6ABMxBQZnuft+vp6qaKiInlXYNEIm4gJqyUmrOKrK7uTJKQWJYPh\nmfaPhBcwq6OltaQeXjf5hoR9nb3IdBcRwyGDwFyO4wzfNXO8aZpXSpL0iiRJa/3jnTRZlZmQsyUm\nUxFECIlFIpH/RKPRw2zbvsBxnA9lWf4Q3vVJh1dj53x4Qb9PaJpWm8O8GF2EMC4+oUYURStNz4+w\nBveGVQwwS0zHiKD9Am1B/Eni30541xkOwFvw6p+EQRx0FxHT3r69+O6l//nupemO43wtSdIHmRyb\njkK7k1IhSdIqnue3WZZ1tmEYwwgh9YSQOng3iBsBHAQv6HeWpmnLc5gbowvAREyREQTBampqklPs\nCquIYZaY4hIEhueLIP6kLfeOBu//OblA25akbcku0oDj/XOEqZpqh0TME088Meyh2Q+dYRqmOnzY\n8MrHHn7sP4MGDUr3eRSCVEKFJgT2ZiwERFGs5Hl+lmma0yzLurAjx6agYIG9bZ6U5+sjkchTtm2f\nGI/HTyCEJBYarYL3fbxB1/XXAczXNM3Odo6MziWMi0+o4XnebGxsZJaYzmdfsMQIaC1GksVKCbwA\nyOQMnh1J29JVm+6uZOw/ef/993vd9/f7znLPcgm/H++s/e/aIZf9/LIpby5484VCTjAJDq1FlwuA\nby8mJuVgHGdEIpF/WZb1Hcdx9o9GowdKkpRNJdyiW2ICCCGuoijvNTU1DXIc5wjTNKEoylt+R+xG\neN/77wEY6Vf63ZrDPBmdBBMxRYbnedMwjFQiJqwWjbDOO6ziK4iJkdF25dgy/zWJ9U8a4BUES7Sg\n6MjBXdCBOYeNjC0x77333kB6ECXCAYIDAMJ3hdj6v6wf7LouOK4oOjkQMMnzpQn7O/x/TAihkiR9\nZprmmGg0+gPHcZYnFJbLiFzbDmRriUmEEGLzPP+m67ojDMO4XJbleYIg7Ib3mWwG0BvAHbqu/xPA\nfzVNK/TvgZFHwrj4hBqe5w3DMLQUu8JqiQnSw8NGcIHvirEPEaQXJn3hBceORWv3zg4AaxO2Geh6\n7y0sZPy9KC8vt7AHoC4F4Qjc3S4nK7JdJAEDtC9Ssk6RhvfbjkYikcdM0zzbMIyf+IXlGjpwfFEC\ne9tA4DjOlGX539Fo9GjLsi4RRXGxJEmf+wHLu+EJ/kvhNZJ8StO0TN8fo5NhIqbI8DzfZJpmq9Qk\nhFfEOAjv9yhwKRUrE4ZDy/iTdFaUKFq7dyr9f4fCu+C+VqQ554uM3DPPPffcAQteX3CYqqjRq6+4\n+vMxY8bUFXpiachYxFx66aXr5r82v2rb3G39aW9KyLeEzvjJjDcLPL9E0omUvZaYbIUApZQD4Pru\npWdt257gZy+9nKF7KR8xMTn9PgNrDiEEsix/zvN8pV8X50BFURZwHGcBsOEF/Y6CF/T7qKZpq3M5\nL6M4hHXxCS0cx+mmaXanmJiwupOAZpdSPkSMgLYrx2poGX+S+LcDLS0qbcWf9EY4vyft8sijj4z4\ny5y/THHGOzwM4OMZHx/x7OPPPnnUUUd1pONyvshYxJSUlDivzX9t7uzZsw+qqalRJ1w0YdsZZ5yx\no8DzS6RNEZNNTEwCey0hfvbSBwnZS18qivJuO+6lfMTE5NrIkffjYAAAgiDs5nn+ccuyTvVryrwo\nimIlvM9rG7zf6026ri8AsEDTtH0tHixUhHXxCS0cxzWZpplqEQqrGHDgXUS7olumPTIN7g3iT9rK\n4JHQ0nKiA6iF53MPtjUi9/iTrlwnJieeeuGpE+kkCmmYFAUAy7Hkx554bNQjDz/yfidNKePvc0lJ\niXP99dd31p17u5aYNPszHbuFCBFFcXOQveS7l+bxPK+nOtiPiclFhOTjJqOVNcfv6v16NBpdb9v2\nD+Px+GeKovzXF2QN8EoB/ABeTZlZmqZV5zgHRoEI46IZagRBaDIMI1UMSVgtMUCzRSPXO6Zi48AT\nIj3RtouHorV7pwrAtwnbixV/Esa2AxkRd+ICkZvfGpUpotFoZ1yjwvb5puublLOISWfF4TiuyXcv\nnZDgXlqfYggenqsmKyilQo4iCADSjiFJ0tqkasXz/WaYDoBN8GLQ7tJ1/R8APmKNJLseTMQUGVEU\nmyzLYiKm8HDwBElb7p0IvGC+erR072xCS8HSlWpIhL3tQFq+e/x3v3zpzZdOik+M89SgRPxcjJ91\nx1nfdMJUwmZVzMQSk/cGjr576f1YLFbZhnup01KsE2gzw4nn+cZIJPKM3wzzSkmSXpMkaZW/eycA\n1bKsRwRBeFHX9Qc1TQtTvaNuDxMxRUYUxSbTNLubiAlcYcVa7EW0338nAs8knJzBU5Xw/KcAnoAn\nYsJCGN1JGQmCe/9w71Lh94K75L0loyRRis741Yz3J0+eXFXoyaWgYCLmvffe671mzZoehx56aO0J\nJ5ywJ0/DtmdpySUmpl0rToJ76WzDMC72rRmBeylXEZJzinUm1pyEZpibbNs+Jx6PH6iq6iK/SJ7p\nOE4fQRCOgZeK/aimadnUzGEUACZiiowkSU2maab63OPw4irCSD5rrihIL0yCPxGtmwPugZddEGzL\nJP4kjLViwihiMkIQBHrvH+5dBmBZJ0+lICLm1jtuPfrFt148kfQnLn2SknO/f+57v7v1d1/lYej2\nAnvb7Z2UjkzbBvjupWds2z4x0b1EKeU5juvSlphERFHczvP8TMuyJhmGMcOvKVPtj7Hdn8+tuq7P\nA/C6pmldyfq8T8JETJGRZbmxpqYmnSWmpNjzyROZBCUTeO+vvQJtQfxJ4t92NMefBPVP8kEYq/aG\nNSYmTHPOSsRs2bJFefChB4+q0+sip5xwyvqLL754U7Dvm2++KZ2/aP6Jwk+EGK/x1GlwuLlPz/3O\nhedduHb48OG5fp8zcSdlu9h2pAEjVRTlv7576WzHcb7ItXdSHgKDgaTspPbgOC4aiURetm37CMuy\nLhIE4X0jWYl1AAAgAElEQVRKqQjvGl0Hz8J7DryaMo9pmrY7x/kxcoCJmCKjqqpu23aqzz3s7qQe\naBYpqawopfDcTcnunY1Jz4sZfxJWS0zYhFfY6LCIqa6ulqf+eOpP6gfWl9EKSj545IMjK7dWvnXr\nLbcuB4DNmzeXcOWcy2s8BQC+jHddzXW3bNkSyZOISSUU8hET0+GgYFEUNwXuJUppP0rplizPDXhr\nVK49qIRs6uTIsvy1IAhbLcuaDkDzhQzgXas3ATgAXk2ZxwF8xoJ+OwcmYoqMpmnpRExXTbEW0b57\npwTA2fBSihMDYrehWZzo6FqBv0A4LTHd1p3UxejQgvSPf/zjIL2PXip9X4oBgDPE4Z6b99zJgYgZ\nPXp0Ha/zTnRjVJSGSrHo+qgoGmJs5MiR+agMW7CYmGwtKYF7qamp6ep4PD4xGo3WSJK0IYsp5GrJ\nAXKIq+F5vjYSiTzR1NR0s23bF1JKE7OwdsCLvfsFgHd0XZ+raZqZ7VwZ2dEVF81uTc+ePbuSJUZF\n+wXaBLQUJg3wynQnWlB+BOBNeD15wkQYLTFhdSeFiQ5bYkzTFGmE7v1/ISWExmPxvb/zfv362Xf9\n5q6Xf3f/76bYrq0ovGLddfNdr/Tp0yeah/mmS7Fuc38Hxs62ASPlOK6WELI8Go2e5TjOF372Usaf\nLaVU4Dgu1zozbkfOmYwfT0QlSVoQjUanOo7ztaIo7/jWHQOeVeYkAIf6Qb+bcpgvo4MwEVNkDj74\n4IYiiJjE+JO2MngctHbvbAOwOmFbJncWYRQDQHgtMWGcc9Zs2rRJfeSRR46wLEucMmXK2lNPPXVn\nviaWhg6LmEmTJm2ce/VcJzYwJnC9ONd93+XGjh67IvE1U6dO3X7mmWfOqqqqkvv3728LgpAv90Mm\nbQdy6Z2UdYFGSikvCMI2SZK+sCwrMXsp0zTlfLQtyDW7CQBEURTXCYIw07KsqYZhXOYH/dbA+3wq\nAVQA+J2u688BWKxpWrHamezTMBHjQwg5A8BD8H40j1NK70/afwGAG+Fd4HQAV1FKl3f0PIceeqjh\nOE6qRShTEcOjteUk+XkpPPGRXKBtPVoKlnzcBQJd1xXWHmEVMfuMJWbt2rUlk6dPvtIaZKluiUsW\nXLPgxLtvu/u5Cy64YHMBT9thEXPsscfW3nfbfS/8+dE/T2wymtQjRx657m9/+tu7ya8TBIEOGjQo\n1xiPZNrNTkIB6sRkejwhxPFrsfzTtu2TTNOc4Zf635jB8bmKkJxFDBKsOYQQQ1XV52zbHmtZ1mWi\nKL4pSdJXvtWrBl5W5AXwgn6f0DStNsdzM9ohjAtP3iGE8AD+DuBUeJaIpYSQBZTSxDLiGwCcRCmt\n9wXPbADHdvRcPXr0SNeHIw5PxPRG2xk8KrwfSnIGz1Y0CxYdxWtqCITXEhPGeYdVxGQ15wf+/MAY\nY7gRIZMICAjiA+LCg488ePoFF1wwO98TTCCr7KRp06ZtmzZt2tMFmA8AYOvWrcqiRYsGuq6L733v\ne9uHDRsWBAQXMiYm6+aRCedO7L30XkL20meyLL/Xjqsnpy7WfkxPznVmEscghEBRlKXxeHxzQiPJ\nVzmOs+HdGG4EcBC8oN+ZmqZ9ncv5GW3DRIzHOADrKKWbAIAQ8jyAqfDcKgAASulHCa//BMDATAcn\nnkyvADAwEokMPvjgg7Xf/va3P929e7d26aWXGuPHj5cBlMOrE3MeWlpLdqGlBaUJXa+aKLPEFI99\nKiamobEhQntQjsBzh5CehJqWqRT4tF2uYu/atWtLrr756sl6Pz0CDpj7xlzrod8/9NqoUaMaUNje\nSTm5k5BChIiiuJHjuFmWZU3PwL3U6e4keNe2VjefgiDs5Hn+McuyTvMbSc4XRXGrv7sKnkX8/3Rd\nXwTgRU3TulLl725D2C7ghWIAWgalbvW3peMyAAszGZgQMhte8Nc6AM8YhnF1Q0ODAACHHnrolvLy\n8qUA5gF4El52z8MAngLwEoC3AXwK4Bt4tVIa0cUurj5hFTEdtsRs3bpVufnqq0+8esqUs2655poT\nqqur5QLNLR1hjInJmtO+e9q3wlIhTrdRQuspuHc496hRRxW6FUGXEzGzn5w9snF4o1oxsaKh4pSK\nButwS5r51MzR/u6UQoM0R/bmKmLyXqzOdy89zfP8ZtM0Z8RisaGpDs6DCMkqvTppDmK6ORBCYqqq\nviZJ0hu2bf/YsqwTKd0b4N0IrwHsafAK5LW1pjCyJIwLTyHI+IJFCDkFXr+dCRke8lsA11NKm4IN\nBx100Pa77777n2j549YQ3joxYXTLAB20xFiWxf3+6qvPOL2qqtcJihJdUlXV6/arrur597lzX5Uk\nqViLXljdSVlx6aWXbti6bevCZ/79zEQn5gjHHH3Mitl/n724wKftciKm3qhXhf2EvdcLsYcYr99Z\nr/pPMwnsLVqdmBYTaCNF23cvvRuLxTb77qVlsiz/N8m9lKs7qShtCyRJ+obn+e1+8PIwRVFe9Fsv\nOPCETJ94PP732trafwmCMF/TtFy72TN89pk7unbYBmBQwvNB8KwxLSCEjALwGIAplNKMArYopbsS\nBYy/LdXiGVZrBhDeuXdIxHz55ZflZTt2VMwoL288QlGi15SXN8rbt++3cuXKsgLOMZl9SsQAwO23\n3f7VmuVrHly/ev0fX3j2hYUlJSWFjvfqciLm2NHHVsa+jonRuqgQa4jx9he2NP6I8UFwcyF7J+Uk\nIjI5XhTFjaqqznIcZ4hhGBe5rptYubwrBPZmNAbP8w2RSOQpnuc3mqY5IxqNHpywe1c0Gj3Qdd3r\nAFyt63oxrxndGiZiPJYBGEEIGUIIkQCcC2BB4gsIIQcAeBHAhZTSnJp/UUqp67rJloswV+wNqyWm\nQ/OWJMm1Kd2bq+oAsCmFoijFDKIOYxxPlxIEGdDlRMxPL/7pxnPGnfOx+x+Xi70UEyaPnPzZNVdd\n862/OxAxGrxYvcMAHOs4zhmO45T62UlZB/aiCF2oA/cSx3GVhmHMiMViQ4JdXcASE7QcaJeg9YIs\ny3Oj0egZpmlO8ucAeJ9FFYDR8IJ+D8llXgyPMN495x1KaZwQcg2AN+B90eZQSlcTQmb4+2cBuB1A\nTwCP+q7mGKV0XDbn43k+quu6VF5enphqGffP3eUuoBmwT1hiRo0a1SAccsjm361aNfQ4QYi/H48L\n2ujR6w4++OBMa17kg33OEtMJdLXfIOE4rvSGX95Qf8Mvb/gSXqZiP3gZMGXwMhoVeGXwgwSAegDx\nxsbGKymluiiKucTE5BKQ2qHeS6qqvhuNRitt257uOM6yPMXEFMUSk4goilt4np9lWdZkwzCukGV5\nPpoDhLfB+3+7Wdf1BQAWaJqWkUhitCaMC09BoJQuArAoadushMeXA7g8H+cSRdGur6+XysvLk3cF\n1ph81W8pFvuEJUYQBHrfrFnvzH7kkUP+s2FDRb8DD9xz91VXfctxRTWMhFXEhGnOxRQxyYUpy1M8\nLoXXPygQJ4mNURvgJSH0h2cpBgDE43Ey49oZYz/94lNOkZX9J540ceID9zywSVXVjoqZggT2toUk\nSRt4np/t9ywqp5RKOZ6/4DExqeA4zlJVdV40Gj3SsqyfwKvdFYiVoJHtDwCM1HV9tqZp1bnMc1+F\niZhOQBAEq7GxMVVWS2DRCJuIicO7EwwbHXbNqKrqXvfrX68q0HwyYZ9Kse4k8vX5Eni9dZLFSeJz\nDZ6lI1GcNACoTnrelhDolbz//gfuP+KDDR8cq1yiGHJElt969a1+f/nbXy6/6f9uepLjuI5cX3J2\nJ2XjDuJ5Xo9EIk83NTX9xrbt8wDMF0VxU0fH8S05ubp7s7YGEUIgy/KXPM9vsSxrRiwWO1kQhGqO\n40x/zE3wrGp36br+BICPWSPJjsFETCcgCIKl63qqu4uwxsWE1Z0URgvSPpVi3UlkaolJJVCSxUoU\nLQVKPYCdCY/z0Ri1VczLshXLhuAoUK6Eo7zEI3ZErOnDzz+MmKZ5uSzLcwVB2JPJwJRSnuO4nOrE\nIPveSy4ARxTFRb57aaksy+93sA9SUWNi0k7C+7xrCCF1fk2ZlxJE2U54RUyvAjBK1/VnNE1rSjcW\noyVhXHhCD8/zVlNTUypLTFhFTBjFAJDCErNr1y4pFouRfv362UV2E2VKWN1JYSL4fPshvTgpg/d7\nTbSW1KO5MGUgXIrRub2ViOlV1quB7mxuSOnscAjncmsEQai2LOtSSZJelSRpdauRWpO1CAnqpeTS\nfBEAL4riekEQZvvF8Qarqvoix3EZLfLZuoKSyEeGEwCIkiS977ruCtu2p8fj8aAhpgvP1bQRXuHV\ng/xGkjklkOwrMBHTCQiCYDQ1NaWyxITVohHWee8VMdFolMx64IEj9nz66VAOgHLIIduvuvXWz7tg\nE7cwipiuZh5XkN56EjzmAUxDS0GyES2tKjndncfjcTLniTnDV65Zud+gfoPqfzbjZ99k+X1rJWJu\nvuHmT7/46RdDzHqz3CgxSMmWEuv3s37/gSzLDRzHVdu2/SPHcQYqirK4neaQnVkoD/ADczmOsyOR\nyNOWZX3HMIwZfnXcTPpnFaVOTIaIhJCYJEnrBEGYaZrmWYZhXOJXLK6D9zvZAqAHvOJ48wC8rmla\nMYRwaAnjwhN6eJ43TNNUU+xilpjisnfeL8+bN6js44+H3di3b71ACH1m1aoBc+fM0S//5S8LXR22\no7CYmLZR0LY4KYP3GSYHyW5OeC4BOAvAo4Wc6P/d8n/HLtmwZDR3IEfd5S75+OqPhz4357nXsiic\n2EpoDB8+3Fg4b+Gjr7766uh+/fpNHj9+/MtDhgxpAABRFLfzPD/bNM2zDcO4SFXVeW1YNnKxxOTa\nMoAgISaHEOKqqvpONBoNehZ9KsvyB+1YeopWJyYDREJIDAA4jmuKRCL/sm17vGmaV4iiuEiW5aDr\neR289jI/BHC4ruuPa5q2Ow/n75YwEdMJ8DzfZBhGq9QkhFfEhNkSIwDAznXrek6U5ZjMcRQAjtU0\n88n163t16uxSE9aYmHwILxntCxSgtUCpREu3T3spw31RYOvRjh07pPc+e2+U9hOtiVM4So+k2Dh3\n4/5LlizZ7/TTT9/RweFSBt8OHDjQvu6669Y0NjbGVVU1WxzAcUYkEnnWt2xcKcvyPFEUtySPgdyq\n/eZqieHgdY9usVGSpPV+9tI5vnvppXQijFLK58GKknNMjE8Li45fU+bjeDy+2bKs6Y7jDFcUZZEf\neB2DZ/kbAq+mzGMAPmdBv60J48ITegghTaZpdqfA3jBbYmQAKBswQF+9dKk4nlJwhGC1YcglI0du\n7+T5pSKM7qRMkNC2OCmH976Ts3i2AliFZuGSjyZ7BU+xtiyLBw8QybMiEI6AyITatp3N76g9l0/K\n/X5dliXRaHSbbds/dhznPVmWP00SDbl0wC5Y80Y/e+mpDNxLArz09Kzx3Uk5ZYz6VqWU70cQhKpI\nJDLbsqzvG4YxQ1GUeYIgVPm7q+EFkF8HYLGu6y9ommYmj7Evw0RMJ8BxXKNpmqnESlgtGmGd996Y\nmOk//vHmv65cud8f1q/vKwLY0bdv3VWXX/5t24d3CmF0J/Hw3DzDkF6g8GidxbMNXif5YHtOi1EH\nKLiIGTRokDmkz5DtG97dMEAdqVr2FlvSdM047rjjsnEbpBMpbe4PkCRpDc/zj1uWda5pmoNUVV0Q\nuD1yFCIFrTGT4F6qbMO9lC93kpGHMeLpXF8cx0Ujkcgrtm2PtCzrQkEQPpBl+WP/9Qa8VOyTARym\n6/ojmqZlEg+0TxDGhSf0CILQZJpmqjuusFpigmrDYWOviCkpKXFuuO++T1auXFkWj8fJ4Ycf3pBF\nYbBi0NXcSSJS1z9JfCzB+26XolmgVAH4Fs0CpSvdXRZcxHAch0cffPSN2/5w23Hr31nff0jFkOpb\n/3jr//r06ZPNHX97tVzardXC83xtJBJ53DTNyYZhXC7L8gt+WnDW7qRCWmISkSRpHc/zjyVlLwWi\nIy/ZSYGoy5ZM34ssyysFQdjmv5fhiqK8zPN8I7xrVSWltLdlWW8CuAbAYtZIkomYTkEUxcZuJmIc\nhPO71MINJkkSPeqoo+o7cT6ZUEx3koD0KcaJAiXRetIAYAeANQnbRwLYD8BrRZp3rhSlYm/fvn2j\nsx+e/V4ehuLQdsxGRhlGhJC4qqovR6PRY/w07P+gk5tHIkMRFDRftCzrlAT3UmUeeycVrdYMz/N1\nkUjkH5ZlnWya5gxJkl6RJGmdP47uOM5gABcBOELX9X9ompZRM+LuShgXntAjiqLRzURM6N1JISJf\nIoZH+0GyMrxibIlunl0A1iU8z6ReR9iCEbta76T2SCdSSDv7Wx/gVZj9jOO4Ktu2fwSAp5R2Sop1\nR1ObfffSYj976UeO43ycDxGDTiiY57+XJbFYbINt22c7jrNKUZS3/RYMMQAbABwNry7RK7nMLeyE\nceEJPZIkNZqmmeqzD6sYCHNgb9jmnUlMDA+vnH1blWQVAI1oKVB2w7s4BlYVA+FazPNJmN53uzEx\n7dSCaUWQhm0YxnWxWOz7giD8K9MCcwG5upOQpQjy3UuzLcs6h1JaAc8qmAv5cEmJ2bikRFHczPP8\nTMuyphiGcbkoim+hWQxFkZ9A9lATxgUz9Miy3NjQ0JDOEpNLs7POIqziK4yWGALv4n4A0ltSVHgW\nlMQsnj3wUjYDgdKE4i7UYQpGDpslpj2XT1b9j/y4knpCSJWfhv1vURS3dnBeuVhisj7edy892dTU\ndE0sFjud47g6URQrs5xH0H06a3KxCHEcZ6qqOjcajR4TjUZ/CCBKKQXxVGqxgt27LGFceEKPoii6\nZVmpPvsYvI62YSOMFg2g682bg2dBacvNE4G3yH4PzYKkFi2LtTUiXItwVyNsIqaVJcY0TW7jxo0l\ngwYNEgRByKnqriRJH7muu8a27fPSpGGnJA+WmJzcOIQQlxBSz/P8et+99JEsyx9m0QZB7OxaM4Gb\nD4Adi8WmmKZ5jqIoX3awmWe3hImYTiASiTSmETFxsJiYYlJMSwxB+wKlBJ6FJDFIth5eKfLguQvg\nZwDmFGne+yKhFjFLly7tcf+s+0/QoXMRRLjfX/t7OmHChKzHJoS4fhr2HMuyfmSa5kBVVf+TgXtE\nyCWwNw8iCAAEnuc3i6K43LKsc0zTHKIoyksJ2UsZjYE8xMTkmuEEeJV+AWzza41NUVV1Zq5jhp0w\nLjyhp2fPnrpt2+ksMWH8Pwl9inWOEHjpw20FyZbCizFJria7NeGxjvbvmANLDKNwhFbEWJbF3T/7\n/gnOOIf0OaBPvVvvls6ePxsDBgxQhwwZkk0a+14hwfN8TSQSmZOQhj1XEISaTI7NknylR8cD95Jl\nWd/1s5fSVSgu2DyQh9YFlFKR47ioqqqLHMep5DiuMdcxw04YF8zQM3To0IZoNNqdspO6RYp1Ggg8\nC0mZ4zjlu3fv7qVpWiQSiSQGyWrw6pwkF2vbjpYCJR/NJLtanZhMCJMgAEIsYnbt2iUZMJTeB/Ru\ncOEi0isSd0tdd8OGDSVZipgWdWIIITFVVV+KRqNjLMu6TJKkBZIkpSwK2VmBvUnsFQ9+xs/bfnG8\nczN1L3U0s6hQY/jjBNlJ4Hk+5yak3YEwLjyhZ+zYsY2xWCydJSasIoZDF734u66L2tpasWfPnjGO\na7H+B72T9kd6N08pAHvnzp36o3feKduVlVwTpbGTL7rom7N/9KOl8MRKWoHiui4qKyvVWCymDB8+\nvCnp/NnQXdsOdCW65Pe4DfaKmN69e0fFuBgzdhmS0keJxppiotAgYMCAAdkWE2wVNOzHZywL0rD9\nbthLUmRAFaXYXTtjtOqd5LvGHvPdS4N991Jbn0+nZSelGgfNwoXCy1Dap2EiphMoLy+PU5ryGhnW\n2BKg2arRldrGlyxfvnzAE3fffRytr9f48nL85JZb9owePVpGs1gBgB+gdbG24LkOIH7vL395xvRt\n23pN7dGjcUc8zv/m4Yf79x0w4PMJEybUpTu5ZVncHddfP6Fu+fJhAgBh2LDtv3v44SU9evTI5TMK\nY9uBsBFaEaOqqnvN+dd8/PBzDx/fWNpYrkQV5dILLo0p/RQn7saJwAkUADbUbVCH9RiWibBJK0RE\nUdzG8/ws0zTPMQzjQlVV5yelYXcVS0yrMXier/cLyk1MKI6Xzr2Us4jJU72aILYmUbgwS0xnT2Af\nJYbUC1FYLTFAswArloiJoJ1ibbFYLPrCX/9Kfu66zrgBA6xVdXXufbfdVnbrnDnv9OnTZw88N9D3\nADze1olc10XNli19JvXo0QAAfUXRGUsIXbNmTY8JEyakjQmYM3PmQX2//PLAv/foUc8Tgr+tWzfg\nkT/+8chb7rlnWQ7vO4zuJCBcwiu0IsZ1XQiCQM8cf+YKSZIazzzzTGe//fYbdOP/bjyKEEL/eupf\nP3l13av9/rbsb8c9NfmphYPKBrWXottm2wG/G/Y//ViTK2VZfkEUxW3AXitIp4uYdALEdy+95RfH\nO9dxnA9lWf4ohXspH9e1fHXCTh6HiZjOnsA+SiyNHzbMIiaf6coq2i51XwbvopIcJLsx8fm6detk\ne+3as47t0aMRu3bhcAD96upKV6xYUXfKKafUwCv41q4g4DgOJRUVDV81NipjSksty3XJatflju3X\nr80Mhx1r1vQ+WxBiku9C+q6i2A+uX98ni88jEeZOKjyhFTH3/fm+I97+5u3DuT6c61Q5riALay46\n/yLn3u/cu3TG6zNOPmPuGWfF3Th/y/G3vNeegPGtxe22HfC7YS+ORqNbbds+33XdJZIkLUORK/am\noV0BksK99HLgXvI/g5xTrPOVnZQ0DgETMUzEdAb9+/en1Pt1JNdvCLOIydQVpqDtLJ4yeJ9JskDZ\nhJbF29r1Bfft2xe1hKAqGuX7S5JT7zjcNkpJv379AjN6xsLrvBtu+OD+O+449ZC6utLtlHJlEyas\nPv3006vbOqbnAQfULfviC/EU33X4qW1LZQMG5NrnhImYwhNKEbN69erSxV8vHllxVkUDL/M02hR1\n5y6ce8S0KdPcfv36xaeOmPrtQ0sfOqlCrdC/O/i7mXTL5gDQTOuqSJL0Lcdxc3yrxiBCyG50AXdS\nJgLEdy89meBemucX9uMBuB2teJwCEflpciqiZasPJmI6ewL7Kq7rUrS+ywlzTEwcngVFRttNAyla\nZ/FsTnqel2C1ioqK2EkXX/zhr5966vjDDYN867rk4ClTPjv00EODtMSMU6xPPPHEPUOffPKVFStW\nlB9fUREdM2ZMbXtBupddffU3t61Ysf+VGzb0Fwmhe/r1q7nthhu+yPFtsZiYwtOuiNm0aZP6wMMP\nHFNdU93j4MEHV930q5u+Kisr66x4MA6Au2fPHpmUEMrLvGc+KBXdqBwlhmHQl9e83H/2l7PH33zc\nzUueX/38Yde9fd34v57610+CGJm2xu3IRARBqOF5/nHTNCc7jjOO47jVObyvnNw4lFIO8NxGmbye\nEOKoqvqm7176seM4/xNF8fNc5pBAvlztEoDEODwW2NvZE9hXoZS6rutySQthV7bESEhvPSkH0BPA\nZfB+YImCZAtaWlWK2uvj4ssu23Dk2LG7165dW3bUoEFN48aNS7SEdMgFNnDgQGvgwIEZl/kuKyuL\nP/DEE2999tlnPR3HIcccc0ytqqq53tGF0RITJqsG0I6IqaurE66+8epJtcNqy+Sj5Oji1Yv3q76p\nuvzxvz/+Th6yz7KBA+AcdthhDWqTajdsaFC1wZpZ901daT+hn9mrVy/t6xVf97r5uJv/e9rQ03ad\nMviUXbf+99Zjdho7pf1L90/7e8w2RTpIwzYM4wLXdY+MRqPr06Vht0WeYmo6LBwkSfqW5/lqy7J+\n6DjOcOQnNVrkOC7f47TXvXyfgImYToLjuJhhGGJpaWniRaSzRIyE9jsa82hZRbYBwDYAq/3n0wD8\nB15tlC7FqFGjGkaNGtWQYlfBK/ZKkkSPO+64tgqCZUvYXB5hok2R+NFHH/WuVWu1HuN66ACg9Ffs\nVU+vGrxr1y6pb9++7d4Z79q1S7rnz/ccvXn75j5DBwzddcsNt3zWq1evXBYjDoBbUVERu/3a2999\nYNYDx+95f09Z/179d97z23s2CoJw2m0TblsRvLhcLo8//L2HP8lw3KxEBCEEHMftoJTWRqPRSY7j\nDPDTsDvynRXgFYjMilwygoLsJdM0J1FKh8VisYEd7BuVDAvsLRBMxHQSoihGdV2XS0tLEysuBpVv\n87lAiWhfoAhoaT1pAFAF4JuE7e35c8NYtber9U7KlMClFCYREybrUZufrSAILuIgfhM+UIcSUEAQ\n0rtm4m6cAIAbd3H5Ly7/fmVZZT9ppBTbtH7T/ht/sbHPC0+98Gpbx7fDXrfP2LFj614Y+8JC13VR\nWlpqO44zLBqNZmX98y0xuVgOeY7jahVFmZ2Uhp2pMMlHnZmsjyeEOJIkfWRZ1ojAveRnL2UzXD6C\nlAEvyDgK3wqjaVqYrgEFgYmYTkIQBKuhoUHq379/8q4gLiYThS2gbXFSDk/EJAfJVsNrTx88z/pu\nJ8W8w0QYu1gDzWnWubqmGKlpU8SccMIJuwc+M3Bn5TuVfYX+Qjy+Ni5MOHzCqrasKXd9cteRm+o3\n9bqy/MrPtzRt6ddwaoPWO9K7RhusNW5+dnO/5cuXlx199NH1Wc631XfBd2uRVPs6QF7qvHAc15SU\nhv3vIA27wOfPRxyKQAgxFEV5PiF76ZV2iuO1Io8Ve4PsJB5Fds13VcK26BQcQsgZAB6C9yV5nFJ6\nf4rX/A3A9+Et/j+llHY4WFMQBFvXdTnFrsClRNEyKDaVQJHgFWNLFCg7AKxFs3DJh0DJhE63aixd\nurTH8zNnHhVrbFRGnnTSuiuuumptqhgF13Xx6quv7l+5eXOfY8aMEcaOHUtyuAvuDMIYFxMm2hQx\nqnHOu+0AACAASURBVKq6j/31sTf+38z/d+j23dvLDzv2sB0zrpixrq0Bf3HkL1Zc+PqFU+/dcu/J\ntU5tD5VTDYVXbLgAKEiWd/cB6YRKriIma3cS4FlyOI5zgBYl/1ukYbf1vimlAsdxuQT25qtIXYzn\n+Tq/ON6pfvZSpkIsIN8VezkwEQOAiZgWEEJ4AH8HcCq8eI+lhJAFlNLVCa+ZBOBASukIQsh4AI8C\nOLaD55HHjBmDL7/88vBly5Yd1r9/f2Hq1KlxeOJEBnANmgVKoptnF4D1aBYtBrqOS6FTLTErV67U\nHrj22mlXRKNiP553H//228EP6br8q5tuWpH82ofuuWdUzcKFR03gOPL5O++Irw0cePydf/3r/zop\nKDMbmIgpLO266nr06BH/7U2//TrTAXupvWJ/Ofkvr5/1ylmXuSUuJ38gR42hhhLfEBcO6n1Q5RFH\nHJEqZitTUgoVXyBkLUT8wNqc3EnJ55Yk6RuO43YF7QpUVX2tjcW9K1hiRDT3XnJUVX3Dz14633Gc\n92VZ/jhDAZovESMxS0xLmIhpyTgA6yilmwCAEPI8gKnwglcDpgB4CgAopZ8QQnoQQvpSSnekG5QQ\ncgyAWwEMAjAQQMWKFSvcWCzG9+3bt+n444/fBWAdvGJt/QC8CC+rp6sIlEzoVEvMq//5z+ApliWf\nV17eCACDolHh6oULj0SSiKmurpZXvf76kU/26NFYLgjU6t8fV3/++fDPPvts5dixY9O2EOhihC3N\nOkzfY6AA8UY7jB3StUuuPXNc/3Grdpy9o4f5iSkNqhy0a9jgYbtv/NWNX+VoCUxrickxrqUgbQME\nQdjjp2H/wDCMyxRFmcvzfKr6STlZUvLUe6nVHCRJ+ibIXjJNc4hfHK+9woH5bDsQiJh9voM1wERM\nMgPgiYeArQDGZ/CagfDcOOnYAeBZ/7gtAHaMHTt27g9/+EPpnHPO+TzptSfDy/0P24W/02NiaJrH\niei6LpQA0DjOBaUQeJ5UcBxtaGgQAc/V9OC99x7x5RtvjAaAoydN+vKXN964ootZacLaeiAsdFjE\nrFy5UnvkqUdG1+g1pQcfcHD1r37+qxWJdWNmLZ912NDyoTtmTpz5bq1VK14sXzzlvNHnfT152OSq\nPMw3nVDh4LUNyMWdlJMlJl2KtJ+G/aJt2+NM07xckqRXJElak3w8chdRBan467uXnrAs63sJxfHa\nci/l253EA8i43EN3hl0IW5LphSv5Lri9Vu5bKaXzKKWfUEq3U0odQohhGIaU4uVduVZMW3SqiJky\ndeqm/6iq/ayul7xjGMrvLEsZc+aZrWKVBg8ebMT79q15vrZW2x2L8e/v3o0NJSXWkUceWQcAsx95\n5KCdL7543CxKySxKyfYXXjh+zqxZI4r/jtpkrzuprq5OePfdd3svW7ash+uyON880SERU11dLd/2\n4G3f2dx/c5/4CXHuo8aPRtxx/x1jEl9z6/hbv5w5cea7HOHQS+0Ve2XqKy/mScAA3nW8DMBQAEfC\nuxH6gW3bR/sF33LJTipYxV1CCBRF+VSW5eej0eiZpmmeQinde23N9fy5Zif5Y6QNyPXdS69LkvSG\nbdvnW5Z1bJrGvkAeRYyfncQjPxWAQw+zxLRkGzyXT8AgeJaWtl4z0N/WIXiebzRNc0CKXWEVMZ3m\nTrIsi1v64Yf7jTj66LVPbdrUp6K01Bp9yilrL7vyylbBlpIk0TvPOGP1/R99NHheZWWfw4YOpTef\nfPLyILPkm//9b9iVohgbLIpxAPiJKMb+8b//DcVVV60t9vtqAxcAWb58edmfrr9+0oDGxkgtpaTH\nmDFr/vC3v33QRYOUw+T+6pCI+eKLL3oaFYbU55A+OgDIx8v1K59fObCpqYkvKSlxAIAjLe8X26mU\nmzyXUniB/EFgf3nSXwRenaY6ePFy9QCqHcc5Hl5cXbaxEzkH9mZyvCiKW3ieD9KwL1BV9UU/DTvX\nwNxi9V5KdC8F2UvJVpJ8uLaA5j5OLCbGh4mYliwDMIIQMgRe0bZzAZyX9JoF8AJvnyeEHAugrq14\nmHRwHNdommYqsdLpbpks6ZR5u66Lh26/fczAr78edKEsx750XW7DwIE1l1155bpULiCi6/xBr712\n+KyhQ3c2vPTSPO1Pf7qF++yzA+pc91twHCRNs7bF43vF2HbH4SVN62pmWwqAzLrrrhNnNDWpU8vK\nmmzXxfVLlx48d+7cygsuuGBzZ08w5HRIxEiS5FCLckHdmLgZ5zhwVBTFTCwgCtKLkzJ4ndYtNIuT\n4K8y4fFVAB5Dy546VFXVr0zT/AmltJ/jOKU8z3c0hiLnOjGZVtxNSMOeGHTDRn7qxOQ9JiYVKdxL\n/xZFcbs/BpAfS0xiHycOzJ0EIJyLZcGglMYJIdcAeAPeF2YOpXQ1IWSGv38WpXQhIWQSIWQdvIvG\nJdmcSxCEJtM0U33+zBLTATZu3BiJrVw58Kr99qsTOA7jKcVvvvlmwJo1a0oPOeSQVhdtqmlO9d/+\n9vqC6dMvXHvkkSdUHHIITrj77i8P8wXPBT//+ef3/fznB2yvr9cogDcjEfOWn/88135H+YYC4Bp2\n7Oh5vKpaACBzHMYCWFVZWda5U+sWdEjETJgwYc+whcOq17+zvj/Xi3PdTS539klnfyFJUuDmSSVO\ngsdAsxgJshDXJ2zTkWIh3mPuEXupe+vScDVWDV+hVCS+hHIcF+V5/tN4PH6saZpXyrL8Qkeqzhba\nnZSMn4b9lp+GfQG8a2FOlpgcj+/QGIF7yc9eusBxnP/KsvyJP4bTwWrFrUhybbGYGB8mYpKglC4C\nsChp26yk59fkeh5BEAzDMFIt+mEVMZ1iiXEch/jRiwC81Uf0t6c75nf33juuf01NxSXxOL+uuprc\nc/31k+775z/nDhw40Bo9enTDnf/4x/zXXnvtAEIIPSUSiT10yy0T3XicHzdp0tc/u+aa5ODDzoAC\nID0HDtz95rp1+19QXt7U6LrkAwBjDjwwLBlWXZ32FhwCoARAORFJj3t+fw9d+vFSWq/Xlw86bZA8\n7qhxU+E1RE0skVCPlpWw65HFQuRSFzd9cNOEEwecuOniwy7e9Gn1p/ys5bOOfXTio29JvBTMmwIA\nIYTjOK5aEIRvbNs+z3Xdt2VZzlSUc3noXdTh4yVJWs1x3E7Lsq6KxWInCYIwP0u3UD7cSR0uUidJ\n0upE95IkSW8gP5lJUsJcOBSvBliXhomYTkIUxSbTNLuTiHHQCfMeNmyYER86dOc/N2zoO7akxPqs\nqUluGjx494gRI1KazqP19XzV22+Pe1iWLXngwJojGhuHr6iu7vX2W2/1/+kll2wEgBEjRjT98pe/\nXL1o0aJ+j//mN2ffDCBCCP3jzJmnUUpx1bXXFl3IiMuW9VBfeunAhrvvXgbAVZ999oBbjzmm8je1\ntSX/qakp1yklB06c+NX06dO3tDtY8emKMTptQfy//ZDaklIOz81jA6h/etXT5N0t70qPfe+xz7fX\nbt9w4csXHnt95PrXzj303G9QgPfOEQ43jrlx6R0f3zHhk+pPBvVSevG/PubXSxMEDBLOy/nl87/l\nOO4flmX92HXd/oqivJ5B1lLR3EnJCIKwB0ADpZTz07BfSJOGnRbfkpQPd1KHO0XzPF8biUTmWJZ1\nmmVZlyDHAGN/LsmWGBbYCyZiOg1Jkhpt2071+bOYmA4gCAK97g9/+Pj+228f+/iSJUcZrsuN6NVL\n13VdSFUGnpNlNybLdlNFRZ3M8258xAjHXLUqXiKKrRabt1588ZAZrst9v6TEBADBtqV7Xn11dDoR\n47ouGhoahEgk4kiSlNfFi5aWxpVFi44hui5b06bxZffcc+oBd97570dfeumlNWvWlJaXl8cGDx7M\nLmqZwcMTIencPBXw7nQPQEtXz8ak53EAuOjQi7iFGxdOPu6W40bteWNPb17g43fPufuU/e7bbzch\nhD74+IMn1DfWlw7df2jVHb+548N8/D+N6DmiaVy/cZWLKxcfMnHQRHJYr8OSi+VRoGX/I0EQdkci\nkccsy5puGMbFqqr+m+O4puSx9w5QZHdSquNlWV4Yj8cPMU3zMj8NuyMB9jlnJyGHJpS+e2mRZVl7\n4vH4GZZljZNl+dMcqjOLSYKqw+KqOxLGxbJbIElSY01NTXeyxHRaA8ht27apX7333pF3UModKorx\n2z/55PAfTZw4fMShh26actFFX06aNKk6eK2gKPSwadM+vHHhwjHTed7ZzPNYPmjQnj9NmtQqw4zj\neddOSJm0KCWE51NeFLdv3y7PvPPO8fbmzX1iguAcd/75n/3wvPPyZhWJH3JIY82//vVs79NP/4Wy\ncKFY/9BD/7YmT96qwOvSna/zFJBiZScReNk66WJQgmyexHYd9fBqOa3xHx/oH7MIGaAIinu+ev7n\n1y2+7kicB5T0K7EaVzSW/OLGX/ywz+A+teREQsv2L2ta/+X6/jfdddPJzz3+3Ou5vsl/r/n3oE+q\nPhn8s1E/+/jT6k9HN8WaDrjosIs2JrxkryUGCdYUjuNsVVWfsyzrFMMwrlAUZa4gCOlSvXOqE+NX\n/M1JxBBCHEVRPonFYttt2/6h4zifK4ryXobxJfnqnZRTQK4gCJvj8XiN4zhH+sXxXuE4rsOZRUmW\nGArWwRoAEzGdhizLjZZlpQvsTVU/pqvjoJO+T4sXLx4w0XH4MxXF/sC2xa2GUTKjqam0h2UpDy1f\nPsJxnHk/+MEP9l6ob7rjjs/nDBzYMG/ZsoGHjx/f457Jk5dUVFS0uiBMu+iiFfd/8slhXGOjGuE4\nPArQaRddtCzVHJ744x+P/m5lZe+pffrU74nF+Huefnrc0gMP1PNZBVj66KP9AACUQvrvfwdYkyev\nytfYIUJC2+nGZfDcPIlxKPXwyiAE23QkuHmampr4559/fohpmsLUqVPrBw0aFEcH3EDr69ZH7lx8\n51RpoBSlfShnxs2Ierhq6At1rax3WWPvIb0bAKDn2J6NW57a0qempkZM9X3LFJe6+GrXV/vdMv6W\nD0f2Gtk4tt9Y/PmzP/eOOtFNyTExSCFECCFUVdV3otFotWVZF4qi+Losy6laKHS2JWZvTIsoils4\njpttWdY5hmEM/P/sXXd4FNX6/s6ZvumBkIRu6NKrgYjCRZoCigiIIihg73oVlWu5Xn9XLFdQUa+A\nqCjSlSaCFFGaIL0KSG8JKSTZMjNb5vz+2Nkw2WzfSZncfZ/Hx92dPWcO2dk5737f+72f2g07YEQr\n0lSQ1xxlbQeimINGCMlq9dIAm832MM/ziwOQx0Br0ZKYWCQGYiSm2mAymcwB0klxVb0eHVBtaTBB\nEJwXCUEKIbDIZot7BgA6YKxkCYJEiSK3cO7cLkOHDv3R836MMTz48MN/wcMP/wUAbcDPjTYnJ6do\n8owZi5Z8+WUHxeGgx9xxx9Hhw4f79AQqOnUqfWBqqhkjBGks6+oGACdOnEjSi8Twq1ZlJrz77tDi\nDz6Ya8/JuaPOsGEtE197rbD0zTe9HZ+NDE81T6CKHhoqlhufhfJpHoeiKGC32zHP8wEjCfn5+Wz/\n2/pPLCbFycADmTZjmmvF0hW727ZtGzKJWXpiaVbbRm1P7v5ld1vkQIrMyLzjkoOhMe1EFgTERQBR\nCBylDooBxhUfHx/VpogRhrdy3tqtPqXqCnWVt298+w+vt2lJjM/rm2XZIxjjAo1OZr2XTqZahL3a\n8drzUxRlMZlMc9Uy7IfVaqtLAcZHnArymkMXcbAnvWS3289KkjSWpulNHMf9EUZ6SVumHYvEqIiR\nmGpCcnJyqR8S4wBjfi7VZnY3evToMxO++67g+by8tBNOJ92NEJQaH28BAGARAsXlCuRM7fFc8Imc\nnJyinJycTcHWwCcnW46ZzULnxETRqShwihDUPDVVtxJIuW/fK8Wffvqd3LdvPgC4iubP/wk5HAV6\nzV9F8E7zeEdT4sDdD0ZLSDx9xTyvBdWTLFmypOGsxbN6SnaJbdaw2eW3Xn5ra/369X2G76e8OqVX\nYXJhqmuEiwYEgLYh8vwrz7dds3zNsVD/US92f/EQdIdDEw5MsG+es7kzn8ZL5DJBLzzzwvL9x/Zn\n7lu5LwvVQQTOAzxw+wNbdNZL+SQpmo0xoDiXpukrJpNplsZoboknwhFl3yUANwmJiACo3ioVCISm\nDPuiLMv3KoqygeM4f0Rer3RStJGYchVOLMse8eq9tCKU9JJXdRJAjMQAgDE3y1qBhg0b+ovEGFkT\nUy3XU2JiovPzJUuW/Pezz9rI+/Y1mrF/f+t6GCsuWWbfRwjuHjlyf4DhIZEv05dfZuHiYs7y7LNH\nwelESS+/3EMcNuwve+/ehQAAdzzxxO7P/v3v3m0LChLzFAUpnTufueWWW67o9W8kcXEulcAAABBX\ns2YS1KwGcAz4Jydp4CYoLaG8DqUE3KaSntfMEN2mCbt27UqesXTGTaZBJik1NbX05I6Tma+/83rP\nWR/O2uTr/RfzLqa6mrgJDAAAaUJQ3p95AkRQVTTn8zkb161bd+jcuXMJ3bt3z+/QoUOp0+k8tXLl\nytOFhYV8m+Ftrubk5BRF8+/zAX+6FY+wN2jvJIyxaDKZ5nmM5nieX0DTdB7oHEkJExgAiD/tixpF\nuiLL8mi1G/Zqb7JBCKEwxlGngiB6slCBCFEUVeSpXgojveRd7h0jMRAjMdWGbt26Wex2e20iMdXa\nxbpOnTqOKf/4xwEAOPD1118fmT5/fleEMRl5zz27x4wZcy7A0ICRGA/sPXteSXruuYFACKLOnk2m\n8vKSHO3bl3iO9+jR42r9GTN+Pnz4cFKLxETHDTfcUFSJTSOruos1hmvVPP5SPQxU1KGcU1/LAIB0\ncHdnr1QcOnQoBRoC4uvyDgCAlG4p5r++/au+oijg6/Po3K7z2YNrDrZ2tnMywAJQf1DO9m3bF0OE\npdH9+/e/AgBl5JWmaeIvBRkOFKIARhjWrFmT/vaMt28pthQnNE1renHOf+dsqlOnTiCSgiGEaIQn\nwiHLcq4kSeNYlv0Romw7AFGQoFDcdmmaLsAYz5IkaZjNZpuglmFr07d6VCcxekdiPEAIOQVBWC3L\ncttQ0kuaDtYexEgMxEhMtSEzM9Pup1lYrMQ6SowfP/70+PHjT/s7rigKFBcXM8nJyQ6McUgkxtm6\ntaXkP/9ZmzJx4l0AAAWrV39LkpPL3dwaNmwoNWzYsCpcNPXuYm2CwDqUeHC7U2sJSiEAnNI8D6Q9\niAd3NKbSkZqaKitXFUQUAggjkPIlNsGUYPNHKN94/Y09R08czdzxnx2dAQNp2KThpQ/f//AUVOO1\nLDklzNPXtDwlcgn17K/P3tyf7v/Xv6b+6w7z9eYEpY6CivYXpd56560ZWzdsVWi6wnI948MiIhzH\nHaQoqkCSpNEIoWKEUKAfAH6hNnKMpropJAKEMbYLgrBEluVstRv2MpZlPT3TqqR3UggIaJjHcdxh\niqIuy7Ls6b200k96iYHyYt6YsBdqyKbzPwqHH8Zt1EhMtZVYh4Nff/217vuTJw+1lZQkMoIgvfHp\np67s7GwKAADn5bH0qVPx9p49iwAA2N9/T3E2bWpTMjJkcDpR3H//20FJSrIgh4OO+/LLFpZnnz1a\nTf+Msi7WIYCBigTF+7kTKlrf52peCznNU1RUxKxduzYTAGDgwIGXNVU4VRI5GjRo0OU1v645e3jF\n4cYoCRHqEqU8c/8zm/29n6ZpsnTB0lX5+fk/S5KEGzVqJAFAb6gmgz7JKeE7V945/JEOj2wf1mzY\npQXHFjT+7s/vukxoO2Hnu5++2780vTQROgJhadYBdYDkzc+re/ToUUf79u39TRm2roWm6csmk2mm\nzWZ7iBASryjKNh8NDYMBg9tqP8xhboTjUaN2w/5dLcO+S1GUPRzH/Qo1RxMTtEybpukiiqK+kCRp\noJrSW0zTdK72PV6RGASxSAwAxEhMdcIBvm/sRiUx1VZiHSpEUcTv/P3vd7xutZqGCoL0u93OvPj8\n86kfLV7M169fH4SlS5vGT58+5OqsWXMBY5IyadJ4y5NP/mh94olj8R9/3JrKy0sqmj9/GZWbyyc9\n99xAR+vWV+XBg3ODn9k37HY7mvnxx20uHD6ckZCeXvrAk08e9CdA9YKHxCDwpHkUJQkwvkZOCEkC\nhJLAXZLsrUO5AACHNa/p8ovuzJkzwtP33jsqq6QkAQBgwYwZ5g/nzVvUtGlTPaYPCSzLko/e+WjL\nunXr0ktKSthOnToV+eqh5Y20tDTt3yCs3kl6gqd55cH2D/4+9Y+pA367+NvR7Ze2t34t+7U1A5sO\nzPuK/arorP1sExrTdgSIKJKCEEbE4XAEWmtE0RCMsQ1jfIgQ0lj1k5lP03TIQnIdjPLCJiAMw5xT\ny7BHiqLYQFEUPcqjw2474GtpoaxDTS/9KMtyO0mS7mMY5heWZXdpiCAD5dtUxEgM1PBNpzYjMzNT\nIe58kvdNxqgkpsakk/zh+PHj8XE2mzCU52UAgGyWdTR3ueDIkSNJ9evXB+tjjx3HhYUb6owZ8zgA\ngOXhh5dbn3jiGACAddKk49YHHjhBkpOdzuRky9XZs1cpGRlhG1Zp8dbkydnx27a1GceyjiNHjzZ5\n/dChRv+ZN29lYmKi54YngO/ISRq4O6wL4E7jlCQ/9FC83K9frjhmzGn6wIGClMcf71q4ePEsJSMj\nYn1HuJj+1ls33FFUlDzZZBIBAN4pKkqe/tZbN0yfPTssu/hoQdM0GRwFuQQvEqMQBaZsndL97lZ3\nH+uY1rH0vPk8P33P9E5v5by1U6CFqITIvjC8+fCLmy9uPrbh3IbOdzS74/eBTQfmrTmzJt3VwYX5\nX3hR2iTxpC5xkSME6lH1iq+//voK3zuNIDaosNcf1L5LfyKEbJIkPcCy7AqWZUOt2oq2A3VE49Uy\n7K8lSeoPAN0JIUlBBwWGLtVJ4RjmcRx3iKKoS7Isj3K5XE016SU2FompiBq96dR2KIri0WNobzI1\nngz4QbUKe0NBRkaGVAwA510u3IiilGJFQWddLsjIyCi7Gch9+lyI/+yzssee10lCQrkbqhJaxMQv\nLBYLd/6PP9otzMy08yzL5dA0c7G4OOvYsWPju3fvzoObrChQXodSCgAnAKAuAGwFgKOg3ujFkSPT\nk5955m52+/bz/IYNXWwjR25RMjKqlDyU5uamdNU4GnehKNeWvLxkAKjSdeiAchFSjDC0Tm1d8Oq2\nV//2eMfHt88+NLtb9/TuZyuDwAAALDi2oPGOyztaDs0aunPt2bWd2tVtl7/i5Io2k2+evCWpfdLG\nR1585I7c07n1Wme0PjVj5oxdPM/f7m8uQkg04lwMAC6O4/ZhjPNlWR6lKEoGx3G/BXPM1SMSEyl5\nUEXKay0WSyuHwzEAACCMppe6rUMDBsKsJFTTS7MlSRrkSS95RYUQxDQxAGDMzbI2wZeoNBaJqSSk\np6fbB9933y+jv/mm7w1OJ9lHCO59771F7dq1EwEA2M2b66RMmjTe8vDDywFjkvLgg+Ouzpo1137z\nzeH6sSBwi1nL6VAcDkfSxg0b6l3NzY1Pb9KETkhJUSA5WSaK4gCXy6HY7XJpaekhcAtmS8HtPOsL\nncEttC3bJOSBA/Msjz66NuH990c4mzc/ZX7jjUhv2hGjcbt25xeePNkoRxWsL3K5cKN27S6AMRtA\nliMo468ff3rnLzsbPDnvyXsFlyC27NAyV2wnYkHQl8hITgnPOzqvqyeF1Lle57y5R+Z2nX/r/JU8\nzRNoALD1p63f2F12pLrz1vNeqwrPa9F4vZSNZRjmoloJNEoUxQye53/AGAfaRKslEqMFQsjBMMxa\nh8Nxi1qG/VMEhEQXXU0kc6jppVWe9BJCqAQAjsG167NSSLTRUKM3ndoOhJBLFEVGEATtzcCoJKbG\nR2IAAJ576aVD3XNyLh88eLDO/dddVzp48OCeoK4bl5SwtnHj1punTDkAAAAURXBpqa/PwhMp8Vdy\nHA9uU7YyHYrL5Sqe+tJLCcm7dtk7E5L7q8NBLplMtv+7ciV+CMfZjzgczKHU1JIHunbdDcFveBVK\nrNnt21PjP/+8v9y79y52z57W8dOmtalq4fHk11/f8+z583Wy9+5tBQDQrEuXY9Nee20PALSrynXo\ngAqamKVrlzZYv3F9dyqHctp5O7tu37qO1AeU8uaUN3UlizzNKz8M+2EZjWkC4E4tDc0aesnz3ANN\ne4FgmpeIK4RUnxVvx9yvJUkaLIriJI7jFtA07dP3pjo0MT7WQGOMCwRBmCVJ0u1+yrADjQfQqcQa\nYxxx6kdNL12WJOkhp9PZg2GYMxhje0JCgtF+HFQKYiSmGkFRlFxaWsoKgqDtJGtUElPjIzEe9O7d\nu7C3alIHmmiYNGTIZWnIkHxwdzFONL/yCgKAFgDQDcoTFoCK1vcnoXzap9wN/I8//kgx//57q/eT\nk/NphKC/oqB7i4vjbQMG7J155kzduHr1zG8888y+ZK+ybT+oUJ2U8Oabf7ONHLnF/MYbe7m1a/cl\nvfTScNuYMaei1e2EA0EQlP/Om7c2Pz//FwCfYlmjoIImZsYvM27iW/JS02ZNL1+Vr8bnNcurs2Hj\nhnb169U339jzxrx27dqZ9Tq5N2Hxfu6FSiMx4KM8W7XOXyXLcldJkiayLPuDpqRZi6ibP3qfOwLQ\nCCGnWoa9WJblnmoZ9g8sy54McQ1KpJoiDaIWB9M0XQgAuQghSRTFiRzHRd1EtLbAEJtObQXDMHJp\naSmXnp6ufdlTqlxtFRIRwggl1gjczrHaqEl9cJuxeYgKD9c6HHsIyWUA+FPzWtjEQJIkKgEhQquV\nBjxCxIQQGTVu3PEWLVqE+2u+gk9M4Q8/fA9qnyB54MC8KzffPBOC9A2qLHiRFyOi3HcPIwwD6w88\nsPLkym4AAPH2ePHK7itQUr8k8afin9r+/OnPbV4c9+KW7OzskLQ/R48ejT9x4kRCamqq3K1bzxpE\naQAAIABJREFUt+Jg/Z2CwCdJ0VS0RNP/yG8qiuO43apOZqSiKDs4jtviVU5d7ekk0OhZ1DLs7WoZ\n9ghFUXZxHLc5kLYnFMO9cNcRDRBCNMMwvymKkqFWXsUAMRJTraBpWrJarb46VnuiGkZSn3siGtVJ\nvjgInOZJAHeJorbkWAaAAgDYrb5mgUpYf5cuXYq/S042LyouTugmCPJ6q5UnjRtfue666yJpUFfR\nJ8Z7I6wmAlNLUOEafvDeB4/veGZH1pX1V1KsRVZB4RXcpn+bMyn1UqzFScWmhasXtsrOzv492MRT\n/jOly7Lly3KstDVOKVJwvCne/OxDz6568P4H/ZozBkGwSEtUmphABEgtaZ4lSdJoURQzBEFY7qme\nqU5hr3YO8CIhDMOcVdc8UhTFhjzPfx/AA0eXe7BOZdoAanUSx3HHIPrGlrUGMRJTjaBpWrJYLJyP\nQ56UkpFIDEDlki8Kgnc4xlAxzeMRyXqIi/eNcaD6etTW8AAAcTNmtEIOB7Y8++xRUBRIevrpG8VR\no44m9u5dOPnDD9fOmjq1x/eXL6ektGp1Yco//rGLpgOmCvyhqtsO/K+hAompU6eOY/b02WuWL1/e\n6LftvzXNa5qXklIvxQoAQAu0S3bIQX8Znzx50rRk5ZKbLDdZ4ul02oUkpJQsL0n+ZP4nA27ocsP8\nDh06lEaw1qC9k/wcD3XugESEoqhSk8n0pSiKQ2w220Se5xeompOaEInx2YCSoiizyWT6SpKk/mrf\nooXexnLqGqL2mVERVom1P2hKtSko7xfzP40YialGUBRls1gs/iIxRgwXesS94X5hEQTvcGyC8mme\nEgDIA4DjmueRfLFDajsQKhwdOxYkP/XUSAAA5uDBTOrUqUzzlCl/AAA0a9bMNnWW70aEYULvtgPV\nhp25O1My4zLFRgmNJACANWfWpPdp2Cdfa7tfDfAZTaxTp45jwoQJp66//vqrb899+ybzBTNPsZRS\nuqfUNLjH4D+DTXrq1Kl4PpGXbSZbnJNzMsABUAmUAyUiOHToUEplkJgAx0NBSFEctYpmmSzLN6iC\n36XqoWoT9qptD/wSIU8ZtizLF1RjuXUcx+3zmkOXNBDoRGI087AQQUq7tiJGYqoRFEWJNpvNF4lx\ngDE/G3/iXhYC294ngvtL6W19f0HzWqWkeUBnEmPv3buw+KOPFqdMmHA/AED+5s0z9BDXFhcX0xcv\nXhSaNm1qi4uLC6ftQE2A38/tx9M/Nv398u8tZvefvWLd2XX15xye0zszLvOHjmkdI9nQ9ULAlGh2\ndvbVJ8xPbP9+/fetHS4HNbLryL33jr73bLBJW7ZsacalWEHFiEASACkigGyIIAqR+vXrW4ON94Og\nwt5INTERWP/vcDgcebIs34Ux/pMQUp3CXgpCaHug9i26IsvyaEVRGvI8v0ZDXHTTxOg0jyc6z0Ms\nElMGI26UtQYURVltNlsdH4eMVKGEoXw6JxsqalMoqGh9f0bzWilUX+pM39JwRYG4L7/sCCzrAELA\nNH9+VrSlzt99+22T5TNm9EtyubCZ5+VXPv2UtG/f3kgkxi9ez3597+TNk9lhy4fdjxAiH/b5cEk1\nExiAEHRd/fv3v6J2rA4ZTZo0EfuN6rd30TeLbsG/YRdxEIQSEPRq3+twnz59wvUi8sCfsNdzfUSj\niQnb7Vct/50tiuJ4AMCRRjMIIVFVN4UjyqVpOl/Vydxus9keUMuwS9Q59EwDRTMHwLVIDAVuC4cY\nIEZiqhUURVlFUczwcagmkZg4CKxDiQN3lKQE3F8uAdzNA/+Ca4SlJn/hFNDxe5D42mtdqVOnMvM3\nbPicPnEiPvmpp0Y6mzcvloYOvRzJfCdOnIj78aOPbvmcZR3NTSbndpuN+88//pH64aJFmON8yalq\nLHySLowwtEltk7/+3HoghKCmiU0jjUjojUoRp/fs3/NSn5v6zCGnCSouLmYPs4frPXHbEwejmLKy\n00mRWP8XMwyz0eFw3KJ6syygKCpcYhptOims8RhjWRCERbIs9xJF8UGWZX9QCVxNSSfRAOBUq6li\nmhgNYiSmGoExtoii6IusVJXnCguBOxwngptQeVvfX4LyaR7PTfJRANgBAGH9Qq1muMAdOdIFliee\nOARPPHFIyciQ7RkZctE338xzhtCA0B+OHj2a1AoAmrOsEwCgp8kk8xYLlZubyzdp0kSvZVcb5hya\nkzXn8JzeH/X9aPGKkyuaT1o3adjs/rNXNEpoJB0/fjxu9erVjWmaVu68884zITbH1AOVVmE3osUI\ndyuLa/Z/QdNQQRBMfBtx76QQ5g4IhNBZiqJyRVF8kOO4xQzDnAtjeJWb5akpsW0Oh+OimhI7Fe4c\neq3FG14VThhiJKYMMRJTjVAjMb5IjB6RGAyeDsf+S45pqKhDOef1Wji/IGp8J2stcnNzuePHj8fT\nNB3XrFkzNj09PWp/E2/9izNKE7SmTZtavicE5TudOI2mleN2O22Oi1PS0tL0uLlWOziKc71949ur\nejfoXZhTP6fw/V3vWylEkZ07d6Y8/vLjI+TGMgtOgAWrFljmfjp3SVZWVlWUlgYlMatOrcokQGBo\nljvC9sm+T1r2a9zvUuvUyAlrhAjF7C5in5goCBCFEHLxPL/NbrfnqX2XNnl1ZQ6EKo3EaKGWYc8U\nRXEcAPCKovAByrCDrQNAh0gMIYSFa/fiWDpJA8NsONUBhFAqACwEgCbg1nCMIoQUe72nEQDMBXcP\nEwIAMwkhH4UyP03TVpvN5ktUGgqJ8VTz+Ev1xIM7SqLVoRSA21nW85reG4JhXHvPnj0rfP3GG716\nU1R9hWH4zyWp9/g33tjWpEmTGnVz6NChQ2nnu+7afv+SJT2vQ4icQIg8OHnyJZPJZCQjRL+4t801\nQSxGGF7s/uIhAIBnPnmmn72bnY3vHG8DACj5tSTh488+7jjtvWnbq2BZQUkMR3Gu93a91wcANv9Z\n9Gfqbxd+azn4usEXvN9XJBUxiWyi0+O6m2fLY9NN0ZNlDSqQGEVR4IsvvsgqKChokJOTw910001V\nmk7yjPVoWliWPUlR1BxJku52uVyZgiCsDqZ3UTUx0fydfJZXhzyYosw0TW92Op03qQ0YF/kqww5l\nKgAg0br+eulqEMQiMWUwxIZTjXgJANYRQt5FCE1Wn7/k9R4HADxLCNmHEIoHgN0IoXWEkKBiToZh\nrJIk+foMnACQAgBZ4D/V44SKnii5msdmqPoGYYbonwQAsHbx4ututdnYvm3a2IDjqLi9e7mflyxp\n+uDzz1dpv6FQ8PTkyYcPDB58/ty5c3H3tWlT0qxZs1vAWCXWYROuUmupia5Dl21COBUrVwuvmkId\nb7abqaHLh979bu93V/fI6HH1+xPfN5h9aHb2qjtWLcUo6J8uuLC3Sf8rALDpn7//cxAAwNxBc5dk\nJVWMEs05NKdlqb2Uey37tb0HCw4mTtszrccbPd/Y6uu9EaIciVEUBZ547onem09uboObYHrF7hXx\nN6+7ucMH73ywMdyJo+mA7V3ZRFFUkSAIsyVJGm6z2e5XxbOBopQ0RPEjS43ERNtAksYYn6Mo6pRa\nhv0zx3H7I1iHLuXVmnkIxDpYlyFGYgJjGADcrD7+GgA2gReJIYTkgps8ACHEghA6Cm4re5+bIUKI\nBoBMAGjUrFmztm3atGn+1FNPPWKxWIQ5c+bY4Jr1vQhuHxRPWuc8lE/z1MSL2DCRGIfZzKWxrFON\n96I0jnPazeYaq5Tt0KFDqcZHxGgl1uVgNpspmqZJoA7QXdt2Pb1i54p0ug7tJA6CyH6Ce93eK2T9\nSAKb4OqV2evYuDXjxk9oO2H9zIMzBz/f9fllIRAYgBA1Mfvy96V5Hh8uPJzki5g83unxo69vf73b\noxse7SM6Rebe1vce0JHAAHiRmP379ydtO7ytnTBWMHMCRyVBUsqPs35s8+iJR39v0aJFuOeNKp0E\nXiRC7WG0SJbl3qpOZhHDMBWiV/7GhwldGkgihJxqA8YrkiSN0pRhh7Q2vQzz1Hm8GwXHAAbZcKoR\n6YSQPPVxHgCkB3ozQqgpAHQGt7jV1/E/wR1dyQeAc3l5eaRRo0Z0s2bNitLT0wsVRTmCMS4FgBvB\nTVSqInSuJwwTiWncqVPezwcPNqwvigAIUeusVrZply55wUfWCBiRxCCz2UxNefzxvqf3729JAEiH\nvn33vfn++7/7ci1+9eVX95a+Uspvnbu1HcZYufNvd26dNHGSr0aDfvHvG/+963Dh4QbT904fcV+b\n+356tOOjJ0JdKwQhMZ/t/6zFbxd+azl30NwlJ4tPxr+3670+yVzyht4NyhqLAgCAQAvKnc3vPPH+\n7vdzaES7+jfpr/c1Vo7EXL16laMSKMTyLA0AhOIphARECgoKuEhIDESRTvI1FiFEeJ7/zW6358qy\nPEZRlPUcx1XoHebdQTtc6NT3qGwOmqavmEymWZIk3aGWYS+mKKokhDl0cV73EvYSPeasLfifJzEI\noXXgbgDojSnaJ4QQEqhZmJpKWgIATxNC/In7bgGAK4QQOwDAhAkTBp0/f/6DyZMnL/J6X00qsQ4H\nhonEDB0+/NJCi4WZsWtXT56mcerw4QdvGzYsojLoaoAh2w6898Yb3Rrs29fyq/h4q0wIemrjxs6f\nfvzx1aeefbaC2y3P88rHH3y8FQC2Rnq+70983+Bw4eGWrVNbH19+cnmvES1GnOiR0SOUJo1BSczg\npoMvDGw68GJWUpYtKynLlsAmrOuY1rHCprb3yt6kT/d/2m1cm3F7tlza0vDN39/s/Fr2a3uDdKYO\nBBrcaeVkcEdtW6mPxwNAUnZ2dmLjOY2h5GRJHaopVVK8rxglQZK1ffv2EbkB6xmJ0YJl2eMY4y8l\nSbpbUZRMNbqhPVe0JEQPt91yBEQtw16oKcP+nmXZU4Em0MMjxrMWr3liJEaFITacygQhpL+/Ywih\nPIRQBiEkFyGUCX5KhxFCDAAsBYBvCSHLApyrXOjUZDJZZFn29Rl4rKWNBiN0si7D6PvuOwv33RcH\n7oLXaEtdqxIRtR1wOp1o69atdWw2G33DDTcUpqamVumN8OKRI41eY1kHhxBwCJERGCsL9+1rCO4O\n4brCbDdTr257dcTzXZ9f9mjHR0+8suWVbk/98tTwbXdvm6OHJqZpUtNyAvDsTN8drPdc2VN3TKsx\nBwdfNzi3f5P+ue/ver/9BfMF3nu8BgJc070l+3jMwzVhfrG61hJwk70Sk8lU+srTr8S/9s5r/Rw7\nHa2ub349evaDZ9fFx8dHEtWIOBKjCnMDXl80TReo0Y0RNpttnCAIizHGHp+gaHsv6ZVOKpe215Rh\ne7ph71Q7ePu8XvTqhO1VnRTTxGjwP09igmAFuH/hvKP+vwJBUZ0xvwCAI4SQ6eFMnpiYWOqHxDjB\nXX1kNBiqxFqFrm0Hqghhp5MkScJP33//APno0axUhJRZcXHi659++kPHjlXnjmuqW7f00KVLad04\nzq4QAgcUBSdmZIQSkg8bCWyCa9PITf9NM6XZAdyppXxb/gE9NTGhYGK7iSc9jwVagFezXz0DAGng\nn6i4oLxYvxjczUk9j61ea8sB972irAt29+7dizes2DCHYZg6Vqv1ZYTQEJfL9R1FUeGWf0fcsgDc\n94GgFTRqdGO+JEl9bTbbg2ozxssQfSSFAn3SST5TcKozsbYb9g9+yrD1auTrPU8sEqPCaBtOVWMq\nACxCCE0EtcQaAAAhVB8AZhFCbgP3TWQsABxACHlyuy8TQtYEmzw9PT1QJMao6STDRGJUGJHEhJ1O\nmjlzZsu6hw83+yQuzsYgBPMsFtPHr7/ed/ayZcsraY0V8MhLL21/7aGHMvdYrYIIAKfr1Suc9uyz\nByrrfB4C4+95AERKYhjwH0FJArftgQ3cZETbxPSY5nm4hn5+fWJUEqBgjE+Iovggz/MLVIIQKqJp\nWRBO3yUiCMJGu92eK0nSWIZh1urQxTrq6iRwEym/ZEHt4P2VJEkDVAK2iKbpcponLy1LxPCRloqR\nGBUxEhMAhJAicOtYvF+/BAC3qY+3QISbYNu2bc21jMQYMRJjGDGyBmFHYvLOn0/qBQCMajR2I8s6\nZl25klIJa/MFAuC+3j9ZunTB+vXrMymKUl667bZLiYmJNdG0zx+JiYPAqR4GykdQSsDty+R5bobo\nN1ZvBDO7o3ie/9XhcORKkjSWZdlVLMsGtRFQTdqiNcoLayzLskcwxgWSJN0NOqSTotXEhFJZhBBy\nCYLwkyzL7SVJGscwzFqO47TEXLdO2HAthYQgRmLKYLQNp1ahbdu2ktoy3htOMCaJMYywVwMjRmLC\n1sRc16pVwc9r1sAIRUFxCJEVksTWycq6WEnr84uMjAx57NixZ6r6vCGAgms+TMkA0BoAmkF5nyY7\nVEz1nNU8j6rv0zffftNk9S+rWwus4Jg4duK+nJycohCG+WsA6SEiCAAUlmWPYoyLVSFtGsdxvwVx\nzsUAoITorlsBkUZSPFVANpvtKYfD0Y+m6csY40gMKHWtTgoGjuMOUhSVJ0nSaEVRGnnKsCsxEhPT\nxKgw2oZT2+Dv4naAMT8bI0Y1jLjmsCMxEyZMOPnS3r37B2/e3MGEECgZGYVvv/POpspZnk9UdzWV\np7O6v1SPCdwO18XgTvuUgFuLchiukRTH+vXr681dPLejw+nAdw668+LIkSPP67G4mbNmNp+xeMYA\n1AMRIhK0/9X9zT+b+tniHj2CVlNh8L/RYnC7xQIAAE3TlwVBmCVJ0t2iKKYJgrA8QJQgmlSSZ3xE\nkRSVtBQhhApUt9wF3mmaEKALiQkniqISsJmqod8DPM8vAn01MVp9TiwSo8KIG2VtgsNPJMao6SQj\nCpKNGIkJWxODMYZ3P/lky9mzZ3ebzWa6ZcuWFpZla0XrAnD/LeIhcKoHw7UUj+f/xzTPtY1MRwPA\nIfAyrNy0aVPdF99+cbiruwtjBitvzXorS5Kl1feNvS/qyrZFqxd1pfvRLq4JZwcAMNvNcQuXLmzZ\no0cPn55TGvhLJyFfxyiKsphMpq9EURymbrQLfDnn6qBJiWo8QohmWXaby+X6S5KkcSzL/siy7JFQ\nx+uUTgrbbVdThp0jiuKDGOOjepRYE0JYjLG2AWSMxKiIkZhqRGZmpguu/arWbihGJTFGjGq4wHgk\nJqISawCAmtYbKkTQULE/mJaoJIK7EkYrmPX0CfM8D+ff7VMTs+D7Bde7OrtwfCd3PyeRFbnFqxd3\n1oPEEEIQYM05KQBFUUL5jP2SGH9tAxBCTkEQvledcyf5EfwG09oEQ9iaGC08JEpN0xRIkjTa5XJl\n8jy/MZBfl/b8EH1/ISYSIqQa+m1Ru2HfjRC6TAiBSFNznrVArDrJJ2IkpppBCPFEArRfeCNqSwCM\nuW4FjEe8IiYxNRQebxQtMQnkjVICbi2K53Ep6ODFoYFPEqMQBZWLf6EyAWzUGNZv2N4vfvziFiVH\nwUQkmDnAOEa8OeJ4CEP9amIgQEpI9TvZbLfbC1TBb7lIR3VHYkCTyqFp+rLJZJopiuJIURTv4Xl+\naQhdpXWpToIoriuGYU47nc49LperrSiKd6tl2OFWn5VNp0Z0MAA4EhISaksUNWoYbcOpdSDuu6D3\nF96okZhYiXXVIGziVVRUxMyePbtVydWrfHavXheHDh1aVe7EGNwkxQQA7cF3qkfrjeIhJoG8USob\nPknMqNtHHf3j7T9aW1mrgBhElO0KHnHPiLAaAvrDk48/eYxlWGXtlrVtOIZzTHp50u4bb7yxMPjI\ngBGToNEUVfB7VSP4/VUlQNFUJulOgjDGNpPJ9I2mnHkBTdP5Ac5PY4yrVBPjBwpFUTsBIFHV9yyk\nadqnaWogaATCFIRfhl+rESMx1QxCiGK32ymWLWfQa1QSEyuxrhqEJewtLS2lHxox4q5OeXlp7QlB\nc1euVM6fPv3zY089dUyHtTDgP4Li8UbxVFK0hGvd1qPxRqls+CQxt9xyy5W3nW8v+3rx152cLic9\n7L5hh/RIJQG4NUuPPvLoiUcfCbm/U9lQCJxOCpoSomk6V+0wXSb4VUlItaWT1PHlCARCSBEEYY0s\ny7mSJN3PsuwKlmX9XcO6OPZC9GkbGiHk4Hl+tSzLHSRJGs8wzBqO4w6GOQ+jugfHSIwXjLbh1Dow\nDCOXlpZydevW1ebsjUpijJpOMlokJqx00rfffpvV+sqVutMFQcQIQX+Hg7rv669vDpHEeLxR/BEV\nf94o2lRPa3C3dlga6pqrGX7N7gYNGpQ3aNCgtb6O7d27N2nbtm3pcXFxjhEjRpxLSEjQ2xPGF4IJ\ne0Nag5fg936GYdZFS0JCPbcf+E0HcRy3D2OcL8vyKEVRMtRyce/PS4/qpIg0MVoQQhiPIJfjuANe\nZdhrw/gba9NJMRKjgdE2nFoHmqZls9nM1q1bV/uyEckAgDGjGkZcc1iRGIvFwjYAAKwKCxtQlGKX\nZRbKe6P4IirBvFGKwY8tu8ERtmPv6tWrM96c8eZgV5aLImaCfvj5hyvf/PebH6vAzM+feBcgzDJp\njeD3RrvdfhdEJ4zVIxLjdzzDMBdV2/9Roihm+tCb6JEK0r2JJE3TeWoZ9h02m+1+tRt2KK0/PL2T\nKHBX0sWgwogbZa0CTdOS2WzmvF72kBjderhUEYxIvowYiQm1xJoDgOTbbruNeXXxYrYvQnwWx6HP\nJIntO3SoCwBehmveKB6SUsEbpVL+BTUbfr93paWl9AcffNC+sLAwrlevXufGjBlzDgDg468+zkF9\nkZJ4XaJICIGLP12s9+2332Y99thjoYhzo0HAdFK4XahVwe8WURRdLpfrFlmW23IcdziCdUXTPDKk\nKJIaPfpakqTBoihO4jhuAU3TheocevVO0oMIlfsOYYwlbRk2x3FLGYY5E2gSjdkdhvAq7Wo9jLbh\n1DpQFCVZLBbvjtUErhECI20iRoxqGJHEeNJJCRA41YMAoKRt27Ylz02bdn7q22+nW4qLcVbXrn+9\n9MILmwDgKhiLJFcVfJIYq9VK3XLbLeOvMFfSXOkueuW/VzqP/Hnk53/98197rKLVxNZhnQCqW24y\ngZLSEu8fJxFjy5YtddZvX98YIUQG3zT4rMYELyphrz/QNH3B5XLlOxyO/oqipPE8/2uIpc0AELWw\nlwIAVyglyart/ypZlrtKkjSBZdllLMueADd5iEaYDKBTOgl8ECFPGbbdbr8ky/JdLpdrO8dxWwP8\nmz0khofoS8drFWIkpppB07RotVp93ew8rQeMRGKMGImpqcTL2xtFS1Tqgbvi53oon+rReqMUg+Zm\nd+ONN8KNP/5Yhcs3NHySmFmzZrXMh/y6yhgFY4QVpaOCv53z7YB/vv7PPW2btz278/edrRJuSrA4\nS500PoFJj9t65OqxmK1bt6bOWD6ju9BesBOFoGmLpqU/j5/f0a1bt2LQSRPjAxghJAmC8I0oih7B\n77IwjNsiTiepgtqwyAPHcbtVncxIRVF2RDKHFyhwt12IRtwMcI18+ATLsqcoipqppsUa8jy/zE8Z\ntmeeOIhpYsrBaBtOrQNFUTabzeZLxGvE1gOxEuvQ4csbRfvY442iTfV4vFEagzsKs6rKVx0ZjBjt\nqbDmkpISjiQTVPZrORnA6XBSdrsdv/3629teePUFfOCbA1kcy9kfG/HYhn79+vktAQ4H67evbyy0\nExwpTVJEAIACR0H8ph2b6gciMQghUBQl4gojT3USxthqMpm+FkVxqMbhNxQNR9SRmHAHMQxzTtXJ\njAaA1AjPDQCRESl/y4IgP0TVbthfSpI0yFcZtppe80TlMcQiMeVgtE2y1kElMYk+DhmxQilWYu1G\nKKmeaLxRUtX5Y6gc+IzEDBgw4NxXC74irhMuhDIRQb8iaNKsyTme5xWe55VZH8/aBACb9F4Mxlgh\nrmvtSYhCEIUoz/r8RWJwgGMhnRZUIqEKfn9QNRyTOI5byDBMsOah0URiIiZAHkJgtVr/LsvyHRjj\nbymKKo5gKr1S+SGJg9W02I+yLHf0UYZNA4BDI9aOaWI0MNqGU+tAUZTFZrPV9XHIiCTGiOkkz2YQ\njoiaBf+pHo83ihXKp3r8eqMcPnw4Yc2aNY0oiiLDhw8vDKE1gBEde6u7AWQ48Hkt9OzZs+hfU/61\ncOr0qUNsVpvpuuuuOzfniznLK3sxg28afG7agmmZ+c78eKIQhE4gMmDCgAvqYX/RFp+9k8IApU2l\nqILfrXa7vUCW5XsURfmJ47hDgcZD5JGYqKIgKmmQKIo6pJKupQzDnA5nDn9alnDho/t0QHAct5+i\nqFy1DLshz/M/e3XCjgl7vWC0DafWAWNsFUXRF1nxaGKMhJqqLwkGT/8kz03XlzeK9rHHG0Wb6vH2\nRglp89i6dWvq9Oeeu+M2SWJFhNDflyyx/vvLL5e2aNHCGmBY2F2sYwgLfgnt2LFjz4wdO3ZGuBOu\nW7eu3heLvuhqlaxc9+u7n37hmRcOCoIQ0jXSrVu34heZF7dv3LqxAcZYGTBpwMU2bdp4ymyDCXt1\nTemwLHsMYzxXkqQxquB3kx/Bb1SRmCjLswEAaJZldymKckYVzm7hOO73UPsX6dFAUkXYukZNGfZw\nm802nmXZtZo5YpEYL8RITDWDoih/JMaompiavmatN4q2imes+noilPdGKYZK9EaZP2NGj6ccDubO\nxEQrAECq2Rz35SefdPj39OnbAwxTfvnll/jZ77xzFxCC+o0evXvChAmn9FpTDPpaG+zZsyfp/2b+\nX3+qF6UwiYxz7Y61nZz/ceI3//Hm3lDn6NixY2nHjh19aVH8aWJQNK67/ppHApRtsrNEURytCn5/\n0EYb1MqeaovEqKAQQk6GYc5gjGdLkjRaFMVMQRBWhkhO9NLERESG1DLsBbIs3yjL8j1QngjZ/Y37\nX0RN33BqPWiatoqi6Ct6YcR0Uk2IxHDgP4KSBO4ePt7eKAoA7ASAfKhibxTZbDY1oqiSnDclAAAg\nAElEQVSym1xjjJU/zGY+0Ji1a9emTP/735tMEUU7jRC8PnVqY0LIsokTJ56s/BX/T0BXErN129YM\nR5aDSspKsgIAoBuRZefqnc0BIGQSEwABq5OiqK4JSIC8BL8TeJ6frxH8YgAg4ZRka6FD3yUATYk1\nRVHFJpNpjupGPIHn+YUURZUEWYNempiw0klaqGXYmyVJkpxO5yBJknpxHHch0vlqK2IkpprBMIyl\nFpGYyo7EIACIdzgcyYqiJHMc5x1RKfNGgfLpnlzNYzNU3KC6AsA5cOtYqhQts7NPzlyypFcDmnaJ\nhKBvFIW6IScnYD+eVfPmNX3R5cIjWNYBAIAcDvrDhQu71mASY7TqpIhIzIULF/hDhw4lxcXFOXv2\n7FlE0zQBABB4walNALisLopnePv58+f5Kf+a0vtc7rm0hmkNC96c8uaWrKyscKN8lSXsDUokVDHq\nMlmWe3kJfvVoORBxFESNBJWbAyHkEARhqWatSxiGCfQ9i1oTo0azEERJyCiKuuJ0Oi+p3bBb8Dw/\nM5r5ahtiJKaaQdO0zQ+JMUJqxhueG2akv2S13igVqnoIIQkH9+yRz+/YYSdOp5TYsmVBr1tuOU/T\ntE9vlDDXXS1C2WdfeunAWxYLe8+mTe0QxqTnPff8dt/99wdLDSnau6KLEESMRxRqMsK+fvfs2ZM0\nddbUG+W6Mq1YFdxmfZuLb0156w+WZcntt99+fuWmlSUFmwqSUTwi6BgiD9z5wPYJT0y4PTczty7b\nl7Xv/2t/ysQnJ9ZdtWjVwri4uHA2vcr0iQk6VhX8btMIftcwDHMiivPq1QFb8Y4EadaaJ8vySJfL\n9SvHcX/40snooYnxCHJD1eEEmgchJJlMpgV2u70PQqjKf2zVZBhtk6x1YFnWbLPZfH0ORozEAFwr\ns/YV8hQgcKrHlzfKGc/jnTt24KsLF7YY3qBBCYUQ+fnnn5M2Op3nBgwZEq2pWLWlwWiaJm9MnfoH\nAPwR6pg7xo8/9d6+fY2IzcbQAPB/GCv3jxsX8vhqgpGEyGGTmM/nf96RdCZQ77p6pYQQOLL+SIO1\na9eeHzp06OW0tDT7zP/M/GnR4kXXWWwWtudjPS/HxcU5r8hX6sTdFGdDCAGTzjiLzhQl7dq1K+Xm\nm28uCOPUfqMtUWpiwhrLsuxxjPHXquC3PkRJQqJ02w0YyWFZ9iRFUXPUrt2ZgiD86ON8urQc0GEO\nADUlhRBycRx3DIxlgFrpiJGYagbHcZaioqLakE7yeKMoANAB3NoTb6LiyxvlguZxIG8UyD91qnFH\nk8nOUm6PjPZJSeK6U6eSwJ0uigaGaj3Qr1+/wriZMy98PnXqVUVR0MQxY/Z6evjEoAvCJjHFluK4\nuHpxMoD7Fz9KQeRq8dUyJ+709HT7k088WdY1/MCBA4nEQa5RfgUAHIA4jgt38/ZFYjyOfLr4xIQK\nmqavqILfewCAVRSFxRhHIkKNdvMPOp6iqCJBEGZrGjEuoijK7DmuhybGqzQ6mnk8zR89iJEYDWIk\nppphMpnMsiwbIRITyBslGdzeKBZwX1PNAaAQAnijRAIhJUW+JEl0G/X5JauV5Zo3vxpwUGgwFIkB\nAJKdnS1nL1u2oroXUksRNolp2ahl3r6D+xqn90gvsVvsFFwAaNm3pV/xaLt27Uo7NO3w1/7l+1ui\nLKSQMwS1SW9zWnXhDQc+SQzo4BMTyViMsY3juGWSJD0oiqJH8BtQROuNaNNJoTZ/xBjbBUFYLMty\nb7UR4yKGYTz+O3poYiIW9XrBe54YidEgRmKqGfHx8VZJknx9DlWtiYkD/+6y4XijPAMAa9XXdUWv\nPn3yfzh+PKXo/PkkGgAu161rHTJ48GUdpq4JVVXhINQu1jFEhrBJzLOPPHvw7Q/fpo8tOlafRrRz\n7MCxu7Kzs/0SbIwxzPlszrrpH02/+NeZv+pmdcsqfPrJp494xMBhIKBPTBRpmWh1KaUURe3XCH4v\nBB9ShmiFvTSEuHa1Aug3u92eK8vyGEVRNnAct0cnnxhd0kk+IjqxEmsNYiSmmpGWllYaIBIj6HQa\nX94o2seBvFE8JCXUqolKIwSCICh3PfrosVOnTsURQuDGpk1toRqGBYHhIjEQIzGVibBJTGpqquO9\nf763UxRFzDAMCYWMsCxLXvz7i4cBABRFgcLCQpbjODvGYV2K/iIx0WpioiJACCEXz/PbVcHvGEVR\n1nIcdyCc8RGeGyACbxZV0/OlLMt3K4qSAe57ni7C3mjmUKGdB+k0Z61BjMQEAUIoFQAWAkATcItM\nRxFCfEYZEEIUAOwCgAuEkKGhzN+2bdtSu90ebTqJh8CpHgHcpcVaG/wLAHBY81yvL0alRpBYliWt\nW7e2BH9nWDBaJMZobQeMVjkVsU9MJKR66dKlDd945407RFnk403xlvfefO/7/v37Xwk+EgACkBg/\nx0IFBRHeE7TpIJZlT2CMv5Ik6R7V4XdjMP+YaJsvRjqepukCtYHkCEVRWmKMj0S6BnUdemliGISQ\nNhUfIzEaxEhMcLwEAOsIIe8ihCarz1/y896nAeAIhNGcr3PnzqLL5fK1IXnaDiBw600CpXo83ija\nVE8wb5TKQqyTdeUjFompXOhqdhcIZ8+eFV6d+uqdztucNHsda7cetcY994/nRm69YevniYmJoWzE\nvgS4iuZYpfnEhDqWpul8jcPvKJ7nfwgi+K02nxmMsSwIwnybzfaAoiidnU7nQZqmI01Z69m6wPPD\nLRaJ8UKMxATHMAC4WX38Nbi71FYgMQihhgBwKwD8HwA8F+rk7777LhUXF8csXrw459KlS2nDhw8X\nGzduLABAfXATlbbg7pWhTfUUgFuPEo03SmXBqJ2sjURijKiJMdJ6q2ytu3fvTlWSFUxfRzsBAJg2\njMO+xc4ePHgwMScnpyiEKbyJCg0ACYQQG0TpExPF2AokBGNsM5lMc0VRvC0EwW+0wt5oG0gSjPFF\nQkiRJEljGYYJJxWmXYdu1UkYY206KaaJ0cBom011IJ0Qkqc+zgOAdD/vmwYAL4BbX+IXCKH7AOB2\ncKenGgNAUkpKCjNv3rwb69WrZ/vb3/72F7jTVoUAkAUA80Afr4GqglEjMUZas990ktlspnbs2FEn\nNTVV7tKlS1hVITGUocoiMY0bN7YqVxUMNiDYhIlSoiBiJahhw4b+mvyxcC0KmwzuX+m3g/u+kwzu\n1LLVZrOZMcZnIAoiEmnLAn/VRarD7wpZlrMDCX51ENVSeohyMcYXWZbdJknS3YqiZPI8vy7Mv4ne\nmhgE7nuVHjrAWoMYiQEAhNA6AMjwcWiK9gkhxGc/EITQEAC4QgjZixDqE+R05wBgEbhFs+eGDBmS\nd+LEiYvLli2bCeVvnNeBm8QYicAAGDMSUyvSSXv27El6cvz4+xJsNqFIUXDrLl0Of7V48aowhaIx\nVCGJ6datW/HA3gN3rJ279gZSnxC4AHjCPRN2NWnSpDG4SYnnPy1p8QjvPST1TwAoUp9bAECkKGqQ\n0+m8gaKosCMIAFGXOfsV5qquub/b7fbCAIJfCqKzYwi5OskfCCEMxtih8b4ZYbPZxgqCsBhjHFIX\n6UoosaYAwJ6QkGA0jVmlwmibTaWAENLf3zGEUB5CKIMQkosQygQAX4K7XgAwDCF0K7h/CSUihOYS\nQsb5ONev3q+1atXK88ta+8XzaGKMBiO2SzCisLcCiXn96aeHPVZamvA8xoqZELh1796206ZNO/X8\n889HJVCsqbA6rJRACy6M3CTNbDdTCWxCtI0DASqXxGhNIJMBIPnjaR8n79u3z37x4sXEZs2aQevW\nra8HdzrZky4+D+UNIbXoAgAHtetVicImq9Wa6XK5Otvt9mMsy4bb5bxS9TQawe8YRVHq8Ty/QfMD\nsVqEvV4omwNjLJpMpu8kSepns9ke4nl+AU3TeUHGl5sjGmjSUhii9NqqjTDaZlMdWAEA4wHgHfX/\ny7zfQAh5BQBeAQBACN0MAH/3RWD8QVEUTyRA+8V3gDE/H6MRAgDjRWJ8amLy8vLSRqnh7gSEYIjD\nQf9+7Fg9cIvNqxOVQgh+v/x7qtVhZYZkDbl0yXqJX3tmbYPhzYefS+VTo/31Gw2JiQcvkuL13AXl\nIylXAeB0p06dijt16lQCACH9ytes09daFQAAjHEBIaTUbrffSQjZyHHcnjDmjjgSE2oURxX8zhZF\ncZQoiqN5nv9eFfxGXWINOpAYbUoKIaQIgrBOluXLkiSNYxhmNcdxh4PMoVs6CSFkB/dnUpP0jzUC\nRtwkqxpTAWARQmgiqCXWAAAIofoAMIsQcpuPMWHdAAkhRFEUSiPeAqh5jr2hIhaJqXz41MSkpaUV\nLrtwof6TCClWQmANwzg7N28eTh8eQ+HmhjcXrDy1sv7cI3OvcypOfFPDm3J1IDAA/kkMAnfloT+S\nkgRu0aWWpOQDwAnNcz1/SfuLlnjWTmGMC1mW/VKSpHsVRUkJpcTZM3dVGOWpgt9vRFG8VRTFiTzP\nf6eDY68ezRt9th3gOO4QRVEFqk4mI9Df09O4MZp1qNCmk2LNH71gtM2mykEIKQKAW3y8fgkAKhAY\nNV1UIWUUCDRNy2azmU1KStJe8EYmMUYiBADGi8T4TidNm7biqfvvv+8bWeYKCcFN2rU79txzzwX7\ntVhV0L3ih8Y06VKvS9GqU6saYYRJ8+Tm0d7gMbgFshQAXA/lG5Ymq8dEuEZIigHgMgAc1bxWleWv\nwVI+GAAUmqYL1YjH3aIo3iUIwg8hbPIRG+VBmFEcVfC70iP4RQhdgUrunRQCGH9/I5qmc00m00xR\nFEfabLZ7BEFYijH2RVb0Sid5eidhiEViKiBGYmoAaJqWS0pKuKSkJO3LRoxoAMSEvVUBn+mkHj16\nXF29Zctn27Ztq5ucnGzv1atXYW0W9V6wXODXn1tf/2+N/nbpz6t/Jq06tar+kKwhlzwaGR+goLzP\nknckJR7cv3RZcFcPFoJbj3IQrlkc1CShfVAS46mm0ZQ4326z2cYLgrAAY+yX9EUTDSGEhJ0O0gh+\nC+x2+92KohSA++8eCULqnRQEAQmIJ4IkSdIAm832oKqTyde+xyMOjnIdAOUjMTFNjBeMttnUSngi\nMV4vxyIxYSAvL4/Nzc3l4+Pjnc2aNQu1RYIHNT6dlJ+fz6796af6sixTOb17k9atW/uMbKSmpjqG\nDBmiRz+pGo8L5gtC7wa9c1umtLS2SGlh3Xh+Y6bFbklP5BI95pDeJMUEbuNHbSTlNJTv/+UCgMkA\nsArC06dUB3ySGE96gxBSTmeHEHIKgrBUkqS+NpttEs/z82ia9pdurJa+SyzL/uVwOC64XK7rRVF0\n8jy/PsT0VxnUdFK0Au+gKSlVJ7NGluVcSZLuZ1l2Jcuyf2reoqcmxrMfxCIxXoiRmBoAmqYls9nM\neb3sicRUWbmnTqjySMzhw4cTDs2f36IJIeicouAT3btfGnTnnRfDmKJGR2Ly8vLYac8917dHYWFi\nfYSUBWvWsPe8/TbTsmXL6l5aVcPTST0ZAJKzM7PLCAqN6eQBTQbwUN65uhjK61HMEHqKxAjfuaCa\nGO/jCCEQBOEXWZaLJEm6n+O4pQzDnPYxR5Wlk3zAxTDMaqfT2UMUxbt5nl8axOHXGzREudn708T4\nAsdx+zDG+bIsj1IUJYPjuF9V4lUZJdY1nVhXOWIkpgaAoijRZrN5R2IIXCMyRrKZrvI02N4ffrhu\nRGKiVDcuzulSFFj8xx+Zpzp1upqVlRVW08qioiKmtLSUTktLs8fFxelRqqsLVq9a1TCnsDBhXHr6\nVQCALFlOXb90Kd/y5Zere2l6w9MDzF9lj8cjRduk9LLmNQvoQz6M8sMhJE2MrwMcx+3HGJfIsnyX\n2rl5r9dbdGs7EAFoNV3zrSRJg1XB73yKonz2rPM1HipRE+PzzQxzUe27NEoUxQye53/Qo9RbjaZh\nuBbhjkVivBAjMTUANE3brFarN4kBMCaJcQGAd1Sp0mC32xGIIlM3JUUCAKAwhroYE4vFEs61rRzc\nty/+0IIFHZMRgs087+w1duzxCNJSlQK7zcbUwbhsU63DMA671WokG3/P2it4pHg9R1CRpJzXPK+q\nygyjk5iQGkAyDHMGIeRpzpjC8/wvmtRNxOmkSDQxXqAAwKV2wl4ly/INoihO5DhuMcMw50IYr0fP\norDnoCjKYjKZvlaJ1yRCiBxtJMYTEUIIAcSEvT4RIzE1ABhj0WazmXwc8uRBjRRCrNJIDMuyhGvQ\noHR/Xl58x3r1rFesVuYsRSn9MjND/rIXFhbCxY0b69yTlnbRxDDKhdJSduWCBc2bTZkSkdup3ujY\nvfuVn376CbIsFi6ZYVyLLBZT89Gja0ykSAN/Hin1wF3Z8ySUJylXwa1J8TyvKde50UlM2fFgZIKm\n6QK1cmmMKIqpgiAsUzfvaNNJ0fT3KSNBquB3h91uL5BlebSiKOs4jtsXaLDeZnfhQK20WiXLcleH\nw3Gry+XKYBjmTBTr0OpqYukkH4iRmBoAmqatNpstycchI4p7q1wk2+/uu89sWLCg6faLFxNRXJy9\n65gxJ9LS0kK+iZrNZlQPY2TCWAEAaJiYaMeXLiVYrVaqJqSVsrOzrxY/+eSWGfPnd1DsdrrFrbce\n6zd4cN0qXoa2m7qvKIrWI8VDSjweKUkA0BoAvqniNUeK2kJiQiIiaurma1EU71Arl+aDzg0gw0QF\nAsGy7EmM8Zcah991AQS/UVUnEUIAoozmcBy32+Fw5Didzt6SJNEcx21RoynhrsVTXg3gvi5jJMYL\nMRJTA4AxtkiS5C+dZDQSU+WamNTUVMfIxx47YbfbEcuyYW8+SUlJjqMAuESWqSSOc52+epUnycli\nTSAwHgwaPDhv0ODB69SnSQBwo86nwOA2cvNHUnx5pOSCu2+P57m/0HkLMFbTOkOTGK/qpJD+7t6V\nS6Apz44A0ZrV+UxHaaJGI0VRHKMKfn2VHEdbnUQBAIni318GjuMW2u32gaIoZvI8vzxMgbKv/ktG\nkhZUCWIkpgYAY2wRRdEXWTFi64FqM7uLhMAAAKSkpNizBg4smf/NN3w8IcgaF2e/acyYk3qvT0f4\nNLsLAgqudTpOVhQled++femlpaXJnTp1EpKTk+PBLYzV6lEuAMBhuEZcapJHSmXC0CQmjOPlgBAi\ngiBslGW5yOFwDHM6nZkURRWFuyhCCIUxrpS2AWofI2/B71Wv89eE3ksAAAzG+KrJZPpSFMUh6noX\neK83yFq06SQCMRJTAUbbIGslKIqy2Ww2Xxu/UdNJRruulFZt2jgaTpmyz2w206mpqfZICVEVwVfb\nARoCi2bjwO2DUqIoSvFDY8fW37dtW2pDjJW/AJT3Pvnki8GDB1+qun9CjYbRSUxU4lyO4/Y5HI4B\nDofjNgCgOY7bH+YU0aaTAgqDEUIKz/M/yrLcQyP4Pat5S7TCXr1IDI0QcqpRrmWe9bIs+30YDTlj\nJCYIjLbZ1EowDGMRRbG2kBgjOg27AICKi4tz1aQUkhe0Hinp4K4AuwuukRSPR4o2kvKX5nmZR8r0\n6dOvv7B1a5sTDgdlAqC+AYBXX3hhxODBgz+upLUbgRBoYSQS4+t69UTpohHnAsdx38myPEJRlFS1\ncinUobprYryhCn53qoLfkV5l4tFGYvQ2qStbr8PhuKL+TbdxHLc92N9UTSd5UlAxEuMDRttsaiUY\nhrGKoujrszCiJqbGu996wG7aVNfZsqVZqV9fAbud4jZsyJD79r0CPF8d+g0O/EdRvD1SLOoYrR4l\nZI+U06dPp97idNKecrghAPBwSYkvYXkMNRv+NDEBj4cIiqKofE3PpVRBEJaHGOGIusQ61PEsy55S\nBb/3qILfnyHKSIxODSQR+BAYMwxzBmM8W5Kku0VRzBQEYUWQc3kTqmiqvmolYiSmBoBlWYskSf4i\nMUb7jAwTiVEyMiT+p58aSrfeStN//hkPLOuqRALjaSboj6T48ki5AL49UgQAaAUAhyJZSNu2bfO+\nXbHC9YrDgesAwJcIkYZpaflBB0YHo/jaGCUKAxBaOinS6xkjhFwIIVmtXBpus9nGqT2XgvknRdN3\nKezxmgaXI0VRvEeNpFRrOskTzfEVaaEoqsRkMs0RRXGYzWabwPP8QoqiSvzMo61OAohFYirAEJtN\nbQfHceaSkhJfn4UR00mGicQ4W7e2IFnG3KZNzV0NG2K5d+9oNvI4CExSXFCeoBQDwFnN43BKJyMR\n9pbhkUceObFn27Y/mvzyyw3JGLtcPC99+umniyKdr5ahNpAY7fFoyqQVgLLKpSWSJP3NZrNN5Hn+\nO5qmC/0NjKZ5pOe84fZL0gh+BwFAFiEkHtwl/mEjnJYDARCQCCGEHIIgLJVluZcoipM4jlvipevx\nrCVWnRQEMRJTA8DzvDVAJMZoJMYwkRgQRUwfOZJMBMGBLBYaX7rEKfXr+yrZDNUjRUtSCgDgpOa5\nnt1noyIxAAAz585dd+LEiW15eXl8165drwqCYKQS6MpEbSIxEWli1FQI0o5VK5c2qD2XHvAhpi13\n3mjcfiFCAqQ2ZFxtsVjay7J8FwAsCrDGQIg2khOSrkbVyWyz2+15siyPdLlcv3Ic94dX9EY7Dwo2\n5/8ijLHZ1HLEx8ebZVn2p4kx2mdUbSXW4YL/+ecMpV49Ue7XLw9fvtyQ27y5i3jHHSKwbFkpMpT3\nSNGSlFwAOAbXUkBVmatWQIf0TIsWLawtWrSoKit/o6DWkBhCSKTpJAzuaEiFAxzH7UUIlajNDtdy\nHOfL1TqaSIwelUGEYZhVquB3I8dxe8IarI8mJmRxMMuyJymK+kKjk/lRQwJjmpggMNoGWStRp04d\nfyTGiJGYmlhiXc4jBdQoijRwYDLwfDIAJCiZmYo4bBgNLGsEjxRfJdYx6AMjkRifkZZohb3BoiGq\nmNbTcymV5/lNXoQnGk1MtJVNAAA0wzAnKYrSOvz+HAah06VtQThEiKKoq4IgfCFJ0h02m+0BVSdj\nVtNJnlRzLBLjAzVts/mfRPPmzUsDkBihqtcTJaojEuPtkeKtRzGBu3pHq0c5AzzviaykA0AX4Pnv\nqnjdkSLqdFIVwyikAMBYf9fK0sQEHUfTdL5Xz6XlmuhBNI65uhEIreDXZrPdIwjCYj8Ov+WghyYm\nkjJtjLFdEIRFsiz3FkXxQY7jFoH7R2yp+pYYifGBGImpAejQoYPV4XD42viNWmKt93Wl9UjxRVJ4\ncH/RtSRFq0cp80jxg1QwSApMhS7ppBh8wkiRmKCamAjTSaH2XLL6qFwSoRojMWqrBQB1/RhjyWQy\nzZMkaaAoipNUh99gLsRVoonxBVUns1nVyYxBCBXSNJ2reUuMxHghRmJqAJKSkvxdmP8rJdaheKR4\nV/Yc0zwO2SPFDxQwVnrGaJEYgAjW++eff8bvPbo3laEYV69uvQrq+xZd643aRGIqJZ2khVpls1iS\npH42m20Sz/Pz/PU+ChFRe8wAgFOb3lIFvz/JstxNFMUJaiXQGX8T6KGJAXc0KGLCwbLscdX/5kGn\n09mWZdmDCCFHQkKCUa7NKoPRNsjaCp9+AmBcTYx3VEPrkeLLGp+C8gSlGAAuah5XtvjUMGXhXgh7\nw71w4QK/b9++lObNm5tbt25tCT6ienDo0KGE7379riXXmHO6HC585PsjaQ/d9dDRjIyMyiYyhicx\n6NrNJFKzu7DSUGrl0nq1cmkCuP+GkUZi9Oh75PPcHMftwhgXyrJ8l6Iov3Act9vPNHr5xEQ1B03T\nBQihcwBgUiNdP0czX21FjMTUDPi72I1CYrQeKUngvondo3mugH4eKZUBo0ViAK5FY0LecOfNm9fk\nvddeG9UAAC66XNTQUaM2/uvdd3dW2gqjwOZ9mzPim8fbk9KTZACAy67LCXsO7Em+NePWvEo+teFJ\njPZ4JFENNRITNvnhOG4PQqjYbrff53A4WlIUtSvcOSD6DtgBCQjDMKcRQnNkWfY4/K71kXLTwydG\nr9YFFE3TGwghWQ6Ho7EO89U6xEhMDUBmZiZRFMVTcaL9QtUETYy3R4qvSIoDyhMUFwDsA4BCcJMX\nqcpXHR6MGIkJSxcjSRJ+7/XXRy6w25k+GJNzhEDO4sV9+91666k+ffoUVOI6I4N3wgxVGbGoTSQm\n0t5JEZEfAHflkt1utzudzt6SJMVxHPdrGD2X9OggHXQ8TdNFGOPZoijepQp+l2CMy+5RXv2KIoIP\nk7pIwWCM7QzDbIOYHsYnYiSmhoC4/ba9bzpVoYnBAJAA/klKIrhJiJak5EFgj5TOAHAaqj/CEiqM\nGokJOex/5swZE+V00n0wJgAAjRGCbhiTQ4cO1akCEhM2Kchun523cOvCVopTQU6nE1O5FOmQ3cGn\nNbvOqBUkRrXvR/6OB0FUjSMBAAuC8KUkSSPVyqUVYZCiqDQxoepZVMHvd5IkDVAdc7+jadoj+KUB\nIFhrhWDQqxO2hwxR4C5QiMELMRJTQ0AIURRFwRiX20v1SCdpPVK8CUoyuKMsNqioR4nGI8Uwhncq\njEpiQv6J26RJE5uLoly/2u3MzRiT84TAbkXBo9u182sfX53o3KlzKUMzf+4+srsOQzFKztCc/IYN\nG1ZFRM/wJEaNfGAAIOFEQTzQwauFwhiXmkymr0RRvNNms90nCMJCtXIp6Ngozx0yeVAFv2tkWe4q\nSdIEjuOWMgxzOpw5AkCXdJKmdxKG/2fvzePcqM6s4fPce0uq6m7ZbbOaLWbfmYRAyEAIkIWEJUAI\n2MYLYJzMlslMkvmS8M5MMkOWSSbfN9+b+TLvOzMvMWAMZgfbYUkgIRAWk0AStrDYLMZgm63dXlqq\nUte99Xx/1C13tVrq1tbdUqPz+/XPVksqVXVJuqee5zzntH5Fe1LQITFVgohmArgJwPsArAcwh5m3\nlnlcL4CfADgS8ZfhZcz82Fjbl1KGhUIh09PTkxYuVkNi0h4p5Vo93RjpkfIagAzN2ukAACAASURB\nVKfs/7ejcXOpUrSi4d1omPLtJM/zoq99+9s3z/3Wt+buA/AbxsizL7jg/glsJdW8mh511FE7jjrq\nqMm4+mxrEoP4b91IgnXdmUvpyAJLEm4OguAThUJhied5K8Yab26CsHdEcvRYyGazv0sJfh9gZkcI\n0bBPTKMtKYukEuOgQ2LKop0WmsnG5QDuY+YfEtE37O3Lyzzu3wHczcwXEJFCTCLGhFKquG3btkxP\nT0/614kmZjdUJikeGvNIGQ+0W1zClK/EAMCCBQte++hHP/r//eEPf5h54IEH7jjyyCM75emRaLdK\nDAOYgfj7YAaA3jAM80KIp9CE8Mc6n2uSCpCdXLqvWCz22/HmmxzHeX2s59f52kD8vVPz8x3HWS+E\nuCoIgouYWQghXm5gH5L9aLQlBQyRGBfNzV+bMminhWaycQ6AU+z/lwF4ACUkhoimAziZmS8BAGbW\niNsxFWGfM/uoo47quuaaa87q6+vLnnTSSdHnPvc5ifiLyQMwF0OkZBua65EyHmi3yka77S9QZ/TA\nvvvuG+y7776bxmF/pgpajcQkmrWEqKR/9kRsBHkEUhcxzDw7CIJDUScRaaSdVOm52Wz2CSLqLxaL\n86IouiebzT5bYRPNGLGu6/lSyi2e5/2kUCh8yRhzUhRF69KC3xrRNGGv3U6nnVQBHRJTPfZg5mS8\n8y3EVvWl2B/AO0R0NYA/AfA7AH/LzMMYORH9KYD/BDAb8TlY/+abb/Zu3LjRzJo1692ZM2duQCyM\nzQP4IoD/GI8DGkd0KjHjj3Y0vGsHTDSJIQwX1ic/CWnJIf4eGB6ZEf97GOKF7YH0BjOZzEAYhouY\n+X3GmB4pZa1+QHVPJ2GUSkomk3lZCLEsCIL5zDwzm83+ulSz06BRHlBjZlEpbCzBmwBCa953g1Kq\nZt1YvY69JdsQGPLckWhOZWfKoZ0WmnEHEd2H+OqmFP+QvsHMTETlvugUgGMB/DUzP05EP0JcrflW\nyeNeALAE8ZfRFmbmE0444Vdz5szZfOqpp65N7xLa8xx1hL3jj070wPhgPEhM2qIgTVCSlrCPIYLS\njzh89FkMVV4rLeoHlLuPiDiTyfwiCILDfN9f4rru9UqpWrRPdbeTxqriKKXe9jzvJ0EQzLeTSz8t\nIS2TVolJQEROJpN5KIqiXYIgWJzJZG7PZDKv1LiZhisxlggNWqIn0anElEU7LpDjBmb+ZKX7iOgt\nItqTmd8kolkA3i7zsDcAvMHMj9vbt6KMboaZ+xFXaXZCSunn8/ls6UMxJJJtpRTlsdAR9o4/2inJ\nupXaM2OhHhLThfIEJfkZxBBB2QpgM4Dn7e1GEtIT8W4PEU0DMJ2IclEUvSilBADfcZwHgyC4NJvN\n3uw4zoYattv0SszOB0g50NXVdbXv+58rFAoL7eRSUO3zx0BTAiQB6Gw2+3shxBYr+H3Qdd3Hx3xm\nE/cjNZkExOekXSwrJhTttNBMNlYDuATAv9p/V5Y+wBKc14noEGZeC+ATiEeVx4RSqlAoFDJl7kqU\n6e1EYjqVmPFHp500PihHYlyUJyjJbYMhgrIVwDsA1qKyj1Kt6LLauRyAaUTkAfCY+QBm7pJS7kVE\nBcSLnA/gYKvHi7LZ7JNEtKNYLM5l5jszmczzY73YeGhiSmEzl24KguCTNpjxeillfxPaSbJJuUca\n2Cn4XWorR7u5rvuzakI1m2R2V9qSasa005RDh8RUjx8AuJmIkjbQHAAgor0AXMnMZ9nHfQnA9USU\nQTwltLiajQsh8r7v95S5KyEx7cTCO5WY8Ue7kZhW3tcMhgjJ3ogrK/MwRFYIw0lKP4BXUrcbnRpx\nEVdRpgHIEVE3gCwRdSEmMBHiz39CVHYQ0SZmfkZr/SljDCmlHmXmHDP3RlE0k5kPICIJQFotyvIg\nCOZHUTTNdd3fjLE/DU0nVUtC7OTSvUEQJJNLNyP+3qi7bTJadlKN29hJHqSU/bYFdoGtHN1cheC3\nGZqYNBHiRrc3VdFOC82kgpm3IK6slP5+E4CzUrefAnB8rduXUuZ93y/nCdMK0QO1ot2EvcmVd6tN\npoyGjiamejioLJztRfxeTQhJgHgRfCr1u0YvIBwAvSUkxbMVlS6reUiTlAEi2oy4irMdMUnqjqKo\nl5l7Acxg5n3s/3MA9tNaHwrgTSLaAmArET0lpQQzH05Ea5VSb3qetzQIgoW+7093Xfe+Cro+YJzb\nSaVwXffxwcHB/mKxOI+INkopX63ztYEmGdWVVnOEEEXP81YEQXB6oVD4guu6K8YQ/DachF0iDmZ0\nKjFl0U4LzZQGEQ34vl+pndRu56kdKxvJPrdL266dNDHjjbThYzlNShZDAaRJRWVT6nZ66mN3xJOH\nY7ZdSl/fkpRpqQqKh5isJJ4hBcQkqUBE72DI3ykA4DLzDGbutT97IiYryTFoxOSk3/77lhDiRXt7\nmzHmNGY+WEr5CyHETlsHrfU+UsrDhRDrpJTbPM+7yvf9eb7vf87zvJXlFlrb0pnQ8exMJvOSEOLa\nIAguM8ZEzLymHrdhNEkTU+7vYitHPy8Wi2+PJfhtxnQSRlZzOpWYMmi3xXHKQimVLxQK5Rb+dkmy\nTqPdKjFA++li2q2d1AjS0RnldCmJ4WO65fNi6nYe1VfYylXjBIaTlB4AriUrHhElbqpJJaVARBvt\nPm2zr59JEZQZzLw/gF5mTo6HAPQT0VbEJGULEb1CRFvtz6gtKyHEvVrrHVrry5RSK4QQbwEAM79h\njAkBHCqEeEUIsa2rq2u5jQNY6HnejWVaI42Ia+t+rlLqLSJay8z7+r5/rud5d9aqj7HZSY1WLEYl\nQtls9g9W8HthFEW/zmazvy1DuJoynZQ6lk47qQLabaGZslBK5X3fn0okpt0qMe1GYtqpnTQWgahk\n6Jbc7kbsPJ32Snkp9f8dVbzGaCDE5GQ6M+8LoJuIThVCJO2eLIaTFJ+I3sIQSdkBQKVISq/dTm+q\nkpLB8ErKVjsEkBAXv87Kw04opdZYInOxlPIWKeV6AGDmt7TWoZTyACnl60T0rud5twRB8Cnf9y+z\notq0KWcjsQMNTRcREUspH4yi6LBCobCgSv1JGg055drgzDFbQY7jvGYFvxcFQbCb67r3lFSvVJNG\nrDuVmDHQITEtAsdxBiqQmHbUxLSbsBdovxZYu1ViJID9UF6TUmro1o9YPP8khvK9Go3OyCUTPkSU\nw5AmJfm3CMBn5qIxBgBmEdEjRJToUoiZp6cqKXsCOCxVSfFgW1aWoPQD2CyE2CqE6AeQb5SkVAOl\n1LPGmAFjzIXMfLdSKpmO3GIrMgcKIRwi2ux53s+CIPiwJTIrlFKJmeeECHtHef6g53k3WpK1xJKs\nETl1lZ6PxtpJEnFw5pjHbwW/S4MgSEbFb0mFXI7Q1dSB9Ig10NHElEW7LTRTFo7j5IMgKHc+2lET\n06nEjD9aTROTNnQrp0thAJ/EEEl5HcAzGNvQrVp0URy+Og2xb4qXtHsQE5UQQyPIBSuA3YEh8WzE\nzNMA9AohtkVRdLLW+lz7mF57fAOwLR9bPXlZCJHc3jGKUHZCIaVcT0TXaq3na61zSqkkgHaHMeYF\nZj5USukQ0QbXdR8rFos7giC4OJPJ3GY1Ho22kxoiEURkrP7kZ0EQfMj3/SU2c+mNsZ7MzEoIUfd7\nqVazPCv4vSEIgk8mDr9Syj40xyemtCXVqcSUQbstjlMW2Ww239fXV4nEdCox449OJWZ0JIZu5QjK\nWIZuvQBOBnBNA6+fjCEn1ZSEnCS6lAjDxbPbiegNDLV8NDP3JJUUxK2e2alKyjT73KSS8jQzHwKA\npJTLLVmZ6CDVuiGEeEspdZXWemEYhtOUUsk0UhBF0XMADpFSHkREL2ez2T8KIQaKxeKFzHwvM4t6\nWyGNtpNKSYTrur+1k0sXMfNdmUzmuTE20Sh5qPn5yah4sVh8xwp+VwPQTSC16XYSoUNiyqLdFpop\nC9d1dxSLxalCYjTiRaed0G6VmGZrYlyUJyjVGLptxehfsLkqXj+DkRM+iXg2GUNOG7rl7RhyQlIG\nAXRFUdQLq0VJjSEPI1opXcpmIcRzlrRsKy3/M/MDWuvPGmPOEkLciDYr5wshtjmOc1UYhvO01ucr\npVbaVk8YRdHzzHywUuowIlrrOM5rRLQsCIIFRLRVCLGuzpdt1HF3RDsqk8mssz43F0VRNCObzT4y\nSmuuodHmRqaKrOC3r1gszok3xWikhdipxFSHDolpEXR3d+8oFotTSRPTTlUNoP1ITK3tpLShW7m2\nT6mh2xY019CNAOySIilpr5TRxpC32Z8AQDalSell5oMxfAw5gq2kIG77vCOEWGfFs9tqnVohIqOU\nuk1rfVYYhpc4jnM9xc64bQMi8h3HWa61Pj8Mw4WO49xoJ50iZl6rtd7fjmCvVUq943neUt/3/yKK\nImHHnGutPo1LbEDK5+Yi3/d3sZNL5fat4eylRkiQjXa4sVgsLg6C4GzXde9uoILnYEik3KnEVECH\nxLQIZsyYMVolpt3OUzuOWI878Vq3bl33+vXru3t6evTxxx/fr5RqpNxc2k4qNXQrJSxpQ7eErGxI\n/a5RQ7dkDDlp9/QgJicuM8+MomhvKeXHiGg7hutSEq+UAgCnZMJnNoYmfGYgPj/pMeStRLQ+NYbc\n9IA8ImKl1J1a64+HYbhYKbVcCLG92a8zniAirZS6RWt9hj2G64UQOxBXC14xxuwLIPGS2SGEeD6K\notm+78/1PO/WGltLDQt7UYEESSm3e5539WjOuU0IgGxGgKQPYBsz5wqFwiK7n/V8vhwMVf8E2qwS\nOFFot4VmymLWrFlTrZ3UqcSk8PBDD+3y7LJlxxzNjE1RRNeuWbP50i9/+Xkhqn7JUkO3aQBOQ1xh\nqWTotjF1u9EKws4xZAwnKYkmpXQMuWDbPTsQf6EfaYw5QUr5BABhScreAI5KVVJcu79bU6PHG4UQ\n/UKIrXabDR5G7SAiOI7zS621b31YlgshRnNrbTlYMna3MeYkrfUSpdR1Qoh3AYCZX9daF5VShwoh\nXgFASqnHoijat1AoXOJ53gohRFXvn0Y1MRijHSSEGLRC2k8nU1Ulk0uNtpOGRQ7UCUVxNtSNQRB8\nIuXwW0uSOJg5I4QIEX/2DBqf0JuS6JCYFsEHP/jBHYODg5VIjDfR+9MgOsLeEvz2ppsO/6ve3vzu\nnqcjZix99tlZTz755KZjjz028edIDN0q6VJKDd0ixBM+61C7oVslJGPI01IkJfFKcRG3lBKSEth2\nT3rCh5h5Wonr7GGpSkq3MWYRgI1E9I4lKS8KIZJKykCrTPiUg1LqUUtkLrXVjDcne59qARFBKfWI\n9ZK5VEp5s5QySbZ+O/GSQXy+ted5dwRB8LFCobDE87zrpJT9VbxMo8LeMZ9vhbT3BEFwgp1cutFx\nnI3NeH00IWw30dXY/bwvJfi9I5PJvFTjvoSIj2kwl8u17GdjMtFuC82UxV577VWpVNiOrZlOJSYF\nrTWhWMzsssceiLLZ6chkuvZlnuG67m4Ymvqp1dDtEsReKmOOnabQnSIpiVeKiyGL/BDDSUrS7knE\ns2wnfBIdyi7MfFCqkrLT7yUlnn01PYZsjDkmiqKPSSl/KoR4u9a/5WRDKfUHY0ygtV4kpbwpRQLa\nBkqpp40xeWPMXGb+FRH1J1qjMAx3ZebZUsqNRATP8+4vFovbbUBjmixUQtOFvZXguu5v7OTS/FRC\nd8OVmCb4uwwTB2ez2ScTwW8URY9ks9nHqqwoJsJegQZCMac62m1xnMqoVMJsx3bSe7ESQ4gX8RG6\nFKVU7zFnnjntN88/H75/xoz8O/39wctSFs/YffeXAbyL+gzdyo1YuymvlFyq1ZNUUzSGBw1uI6LX\nkRpDxsigwfelKinT7fMS8exWInpdCPFMasJn1AVIKfWkjrGoHasZACClfB5A0RgzF8BKKWW9kzzj\nCmYmm2w9I3U+01EHbhRFZwLYQkSv2XP6rBDit0KIHDO/j4hey2azTxDRdksWVmUymbWjvGajmpia\nNCmZTGatEOK6IAjmRVE0oxU0MWWmiuA4zuuJw6/v+7t5nnf3WH+n1HYkGhfWT1m020IzlaGZuRw9\nb0cSM1UrMaMZuu1c4DHU8tlp6Hbcaafl73j11QPu/d3vdstMmxacvGDBC7vuumutAtFkDHk6M/cQ\n0dFEdGCqmgIMH0PeQUSbYEkKEQ0yc2nQ4N4Ybo9fLmjwhRRJaXhCwrrKGq31QinlDVLKsa7uWw5S\nylcArDDGXMTMP1dKPTPR+2At8rss6Uy8b2akSErynuxPnc/1QognreZoBzNP11ovBFCQUj6UVAiY\n2THGJF4yr2QymbVEtKJYLM5j5gey2ezvKuxWowtuzSRIKbXZTi7NR/wZrVs70ixNDMoQISnlVruf\n56cEv6NpjdLtpHyD+zRl0SExLYJZs2ZFGBqbTX8I23XEut3eWxFi3cleKD+KPB2jG7ollYyy6O3t\nxeKvfvV5jJ6OnKQhJy2fpJKS/Jt8mflRFG2JouhgKeW9FOf4bCOigJlLgwb3wOhBg31E9DJVGTTY\nLNhqhjbGzAfQlm0Z23JZprVeqLX2lFK/bfZrpM7nsCpK6nxGGDqf/SWkc+tYrREi6nccZ2kYhvO1\n1ucppVbbkeDES+YgpdShRLTOcZyNQoirfd9fGEXRdNd17y/TFhlXYW8l2MmlqwqFwteLxeK5Qogb\nhBD1vJebpokpd58VJt8UBMHHE4dfpdQ7lfaFYluATjtpFLTbQjOlwcxJNSBNYjoj1s3DaIZuuyLO\n9ulDfYZu1UBiaMIn7ZXiItarKAxv9/hE1Iehdk8BNmiQiHqJiLXWn0Zc8emxx+FgZNDgBhqyym84\naLBZsG2Y22xb5lYp5auTvU+1QgjxjlLqaq31Iq21J6V8sJa/LzNLm8lUiaQk5zMhKemx8v5mkE4i\nKjiOs0xrfUEYhvMdx7nZLp4RM6/TWs9OvGSklFu6urqW+r4/3/f9aZ7n/bSkctKwJqbe5wshBgEY\nIupLZS5tG/OJKTRLEzNaxdIKfn9hBb+XZjKZlZlMZkRLkpkznXbS2GjFheY9C0tiSrNH2rGdNFlm\nd1lUdpwdy9DtNABPAxjL1nw0lBtDTiZ7StOQC4gJRdp1dgDx+HE6aHBvAEdyhaBBAJsAzBJC/FRK\nuQkTFDTYLNi2zM3GmDloYX3JaBBCbLXOuIuY2VNK/TyZskrpUkpbPjsnthCLthOC0o94Yqt/IoMj\niShUSt1kjf0utcZ++fgQ+FVjzN6wXjJCiHxXV9c1vu9fUCgU5tu2SLLI1q2Jse10QmOjxNJ13bsH\nBwePT00ubarh+c3QxFS1jWw2+5QQYosV/D6azWbXlJzrpKKTfG90UAYdEtNCICLj+77yPC/NutuR\nxIxXJWY8Dd2SK57RQIjDBUvHkJN2T+kYsk9Eb2No6mgHAKTHkAHswcyHlixqpUGDL6XGkEcEDWqt\nT46i6HQp5TXtRGASSClfA3CDMWYegDullC9M9j5Vi5QuZboQ4rEoik4Jw/AgxESzVJeSVFNes7qU\nrUS0nVokk4mIIqXUT40xp4RhmHjJbAEAZt6otQ6VUocIIV4loq22LXKm7/uXWr+WHQ36xCjEmUN1\nPdmSIElExnXdx+zk0gJm/mkmk6n2PdUMTUzV0QVW8PuTlOD3rhQJTCo6XWjcjHLKokNiWghKqeK2\nbduynuelRVztqImpV9hbauhWSlgyiBeHdDWlWYZuSSuv3Bhy2islPYbsUzyGvB5D1ZSIhwcNzmTm\nA7hC0CCGFrWnbHug5kVNKfWQ1pqsNf4yewXdVpBSvkFE12utFzCzUko9O9n7lKBKXUrS3nmBmQ8A\nkJVS3iyE6GtCe2LCQLGXzIPWS2axlPLGlPA68ZLZXwjxOhG967runcVi8WTbvrkODbSDmmCUJxG3\nkwAAmUzmRTu5lGQulVY6yu1DokOpG+Wmk0bdaSm3eZ53lRX8Xux53k0Ux1ukp5M6lZgK6JCYFoJS\nKtixY0dmzz33TP+6HTUxlYS9lQzd0q2StKHbVgAvpm43w9DNS0gKUmnItm2zr5TyEKTye1B+DHln\n0KAd69yvZAx5EMPFs5tGCxpsBpRSv253IiOE2KyUutbqS6RS6qmJeN2ULmVYqyd1TjMYrjPqp3gk\nOamWlVrfC631ecaYM4QQN6DB9sRkQCn1e2PMgBVer5JSJmPV/caYEMBBQogsEW10XfehYrG4PQiC\nSyk2MayXxDSce1T6/PTkUhAEM13XvWeMi4Qkw6sRJNq2qpES/H6sUCh8IZvN3gSA7b52hL2joN0W\nxykNx3GKO3bsyJT8up3aSQIxOdgd8Rf/qRhOWGo1dKsHWQylIeeseNZNVVOA4UGDA0S02QoYz42i\n6DUp5VMlV96zMI5Bg82CUurBMAwpDMOLLZFpq7BCABBCvK2UWmaJjFJKVRrlrRqN6FJoyEm46tez\nbZk7bFbRJSl9SVvBEpcVxph5zPwrpdTv7V0DxpjnmflQKaVDROuz2exTRLRjcHBwvjFmI+rTljXq\n9ltptHmb53lX+b5/odXw3DLK5FLDmhjUOeFkBb+/LBaL7xSLxUWpbUg0TqymLDokpoUgpfQHBgay\nJb9uJRJT0dANwx1bt2HovfUqhkhKrYZu5eAA6E2RlFJDN4HhXikFikeQtyMmHkVmTgcNzmDmA+3+\nD0ZR9Okoik4H0JeqpPTTOAcNNgtKqQdKKjJt9+UnhHhXKXWN1voSS2R+M9rjrS7Fi6JomFcKlzfp\nS6opDbXwxgLZrCKt9Wmp4MiaJmVaAXaM/Bqt9QKtdS41fVWMoug5AIdIKQ8hopcymcwrg4ODG40x\nHwiCYMB13cdqea3xNKoTQhS7urpWBEFwRipzacT5YGZl84rqBjM7jWwjm80+DaAYhuHcIAhOzGaz\nG1v5O2ey0SExLQQppZ/P50srMRM9rly3oRti8mIQk51vAXigjtdPxpB7MVRJSZOU0jHkAhG9i6EM\nnwKA0rHV/TC8krIzLJFKggYBCGPMXCnlg1LKRiaVJgVW0/ArS2SSikzbiQKFEP12dPlirbUjpfxN\nWpNSpuWzU5eCIZO+F1Mtnwlv6VAcHPmrkuDImkIAWwFCiD7rJbOAmacppe6ypE9HUfSC9ZI5jIjW\nEpFRSt2jtT7F9/3pruveWypEHwUNuf1aTU3F80xEkeu6dxWLxT+1Gp4blFKbSx7WsE8MahD2VoKU\n8t0wDLcZY44JgmB2Npu9psF9mrLokJgWglKq4Pt+KYlhDGlMmvFFnGT1jGboltakVG3oVrLP5Yz7\nYH+XBA1OT7V7uhCTFAcj05D7MZThk4whT+PhY8hpoWUXhiov6fZAVUGDVmC6EEDYjiO/lsjcnyIy\n17Y6kamkS0FcHftYFEWnIbbHT/ulbKikS2klKKUes0TmEutQXMvIb0uAiPKO41wThuEcrfVcpdSt\nVnQ6zEsGgCOE2O553lLf9y/yff8Cz/PuqJJENsMob6zwSLiuu2ZwcLA/CIKFmUxmdSaTebFkG41+\nzzbLa6boed5Vg4ODZ6Kxv8uURofE1AAimgngJgDvQzyRMoeZt5Z53P8AsBDxAv4MgMXMPKZZkZQy\nXygUdi1zV9JSquaDUc7QLX3bYDhJabahW9JyMgCOEkJ4GE5SEs+DpN2TjCEnJCUZQ04HDe6eGkNO\nt63SlZRXhRC/p6Ex5LrbA0KIN6WUNxpjLgJwi5Ryfb3bmixYIvPLViEyVpfSU1pFSRHPHli9VOqc\nJsSzqLX+HBGtU0r9ohZ9SqtAKfWUMSYwxixA+76nBh3HWaG1PicMw0uUUisQVz1nMPO0MAz3Y+bd\nAGSEEEFXV9dy3/c/ay32bxRCjPr+Gw9hbyVkMpkXKM6Dmmcnlx4joqbEDvAojr21bkMIMei67u8Q\nX7x1UAYdElMbLgdwHzP/kIi+YW9fnn4AEc0G8AUAhzNzkYhuAjAPwLKxNi6EKFeJAYbGrH2MNHQr\nJSyjGbptRXOcH0cbQ/YADGqti0T0fiHEWorHkF9FXMnZgZjcdacyX5Ix5HIahuTKu6agwUYhpXwD\nwC3GmAsB3GBvtxUskfmFJTKLLJEZl4pFBV1KmqRMR0xe0y2fDUKIp6vRpdgqwCKt9aeVUj9rRyIj\npXwRQ++p1fZ2S4OZsymNUXJOuwHM1Fp/DXHFdIs9p/1CiEeEENMQ69a2ep53axAEp1sdynVjOOg2\nXIlBDSTIcZxNNpQxmVz6GeIKyLg69laDEiLEiCvkHZRBh8TUhnMAnGL/vwyx5uPyksdsR/zm67IL\nbRdiL5MxIYQYyOfz3qOPPnpIsViccdppp0WIF/Us4spOD8obur2W+l0zrrZLx5BLM3w0hotnt1I8\nhrzN/hgp5a7GmEuMMe8QETHzvqg+aHBSNAylsFfLK40x84jounZMXLZE5j6t9empikxdRCYliB4m\nnE2RT8ZwU7d3LIlNzmndX+xE5DuOc20Yhgu01mdbXUajk2wTDinleiK6Tms9n5ndiRojrwQeHnuQ\nPqczEJ9TiaEAyX4i6hNCvERE9xpjDmTmE5VSdwshdmpLjDG9APYXQrxBRO94nvfzIAi2WR3KCqVU\n2c/RRFZiEqQnl3zfv8iSh1ZpJ6U/Lw0Hr05VdEhMbdiDmd+y/38LwB6lD2DmLUT0b4idYn0AP2fm\nX5Q+juIwv88D2B/AbAD7SymPevjhh7v22muvD33oQx8aOO2009YhJiYFAA8BeBnNGbVLxpATe/wu\nDG/5RBgSzwYYnoa8lYhCHmkANgsjgwZ3MPMHAbxERK/SJAQNNgqriblba71AKbWsHYWZlsjcq7X+\nlK3ILC9HZJhZ8Og5PlmMzPFJcpn6x1uXQkSB4zjLbVjhuamwwraC9cNJB0fWNMVTC5g53ZotTbou\nHS9PCOjzqdiDQqWqlxDiHWPMVptGfruU8mV711ZjzFoABwshHCLaZB10mgcI5wAAIABJREFUtwdB\nsCiTydyWyWReKbPJhoS9qJM8pCaXzgQwm5lLJ0RrQhPbSenqS4fEVECHxJSAiO4DsGeZu/4hfYOZ\nudyVIBEdCODLiInJNgC3ENECZr6+5KERgGMQZ9+sBrD+wx/+8BmHHXbYJ7/zne/8rOSxh6M2R9rS\nMeRS8Sxh5Bjym7CGbhSPIavUGHIvxy6kSSWl6qBBY8zexpj5QoiH27ElAwBSyueYOaO1XqSUuloI\nMUIH1eogIkgp79Vanx2G4RIhxBoAw7xTEFf60pEH/QDWWb+UfiLKT3b1w+oyrg/DcJ7W+nyl1O1t\nSmTeTYIjwzD0lFK/qrdFZls+5SpkyXlNzBeTz+rr1bbxxoKNiCgYY+Yw832pylLeeskcIqXMEtH6\nTCbzHBENFIvFOcx8XzabHVaFarQSg5G5c1WD4smlO/P5/OGDg4OfFUKsKDO5VC0abich9tnqVGKq\nQIfElICZP1npPiJ6i4j2ZOY3iWgWgLfLPOw4AI8yc599zu0ATgQwjMRwLCL4Yvp355577geKxWK5\nc1IaPSAxkqSMNYb8DoZcZ30MBQ2mx5DTC1o6aDC5QtsshNhaSzCdtSy/w7ZklgkhKsXOtzSUUk9q\nrTNa64stkdkx2ftUikSXUlIhSy9m0xFrojiKok8Q0R9SC1qiNWp5QkBEoeM4N2itL9Raz1FK3TLe\nGqnxgBBim+M4V9sWmaeUuqccSSypkJVr+TgYTlL6iegVGprcGlc9hZRyAxEtS3nJPExDXjLPAzhY\nSnkwEb3kOM4GIloWBMECZp6WzWYfSn2PNMPsru7n2/0wSqkH7OTSqkwms3as55VBUzQxnXZSdeiQ\nmNqwGsAlAP7V/ruyzGNeAPBNSygCAJ8A8NtqNp7NZvNBEChY51vb7pnGzN1EdJwQ4nDEZCWDymPI\n2xBP7hAPDxrci5mPSFVSag4arBdSypeY+V6t9UKl1FIhxPZmbHeioZT6bUJkHMe5mibBSK5El1Ku\n5QMMVcjK6lKYGVrrM5l5P6XUr9ultZcGEWml1M1a68+FYTjPcZybmqBDmHAQUd62lhaEYbhACPE0\ngOk8vOVTrkJWt6PweEAI8Y5SaqnNvpqWImQ6iqIXOeUlo5R6x0YBLAiCYLrrundb8jyhwt5K28hk\nMi9IKd+yk0sPu647qtniOO1HuiVF6Ah7K6JDYmrDDwDcTERLYEesAYCI9gJwJTOfxcxPEdG1AJ5A\n3DL6PYD/U83Ge3t7D1mzZs1BSqm5iN+0BQB+FEUboyg6iIhW0lAqMvPwkdXdmPng1GLW9KDBRqCU\nelpr3a21XuQ4zlXU4r4llaCUejgMw4zVlixrtg6kSl3KNqQWNCJ6PVUt88da0CjWyNyttT4rDMOF\nViPTdl+SFBur3aq1Pi8MwwWO49zQqsdhyeeMkvOarpJpABRF0R5E9AwRbRRCPJv6rLZ8pUkIscNW\nluZprS+0rT6N2EtmrfWSOUII8aKUcofneVf7vj/H9/25nufdyswNCWIbfb6FAqAdx9mYTC75vj/T\ndd2fV/N9aauhza7EEDqVmIog+0fvoAWwYsWK3I9+9KP7Tj75ZPONb3zjvg0bNuzi+/6MQw89NGOM\nOQ7AbogFxUlroDRocGdVhcYpaLBRhGH4SWbez07JtOUH01YyPs3Me1kCUPVx8JBfSqUcn3JX3elz\nO6pRX43HQbYis4fjONe1KgEYC/Y4PsPMu9qcogmvLFnyOW0UkpKIotPnsz91XoscB0eey8y9lpC1\nrIHfaGBmqbU+j5mnOY5zY/qChYj2llLuJoR4CcAAMwvf989h5l2FEGsBdHmeV6oJrApBEJzIzD2e\n591b534jn89/q7u7+7sJYYmiyPV9/0IiMq7r3iqEGPUzwswqn89f3tPT89169iGB7/unE9GA67qP\nIvYl+/NcLteWn8/xRofETDKsnuWTGJpQOiibzX6CiDJSSsydOzf/7W9/ewOArcz8PgBaSnmXLSW3\nHQmwC865ALqUUje2gwajHOxxnMPM0x3HWZEQxlF0KWkPnCLKL2gTrkuxx3EWM+9mCUBbflHa4ziD\nmfe2hKyplT57XrtsavlOTUpJ5TOP4eQzfV6rIp/2OD7FzLMtQW674Ehg53F8kpkPVkpdV5IbtatS\naj8hxKsA+pkZQRCcZow5XgjxXFdX1531vGYQBB9lZuV53v117rPM5/N/39PT852S3wvf989m5lk2\nc6miHi6KIrdQKHy5p6fnB/XsQwLf988SQryVzWafQExiLsvlcp3Fugw6JGaSQUR7ArgSsRncegCv\nHnPMMUVjzNJvf/vbvzzllFNeSh7LzDIMw4uJ6A3Hce6bpF1uGPaK8yIAA0qpVZPdz68ViS4liqIZ\nURSditgl+S0MGQ8CI0lK+t+WIp92wTk7VcloVyIDrfXpzHyArfTVpFnikcGgSTUlnc+U9sFJk5St\nzWr5MDOMMadEUXSMzVtqu2m4BFrrD0dR9KdKqRVCiLdSd/VKKfcXQmy0LXIUCoWLoiianc1mr3Uc\npypvrTR83/8YEWnXdX9dz75GUZQtFApf7enp+X7pfcyMYrF4ktb6QzZzqazXjTEm5/v+n/X09Pxb\nPfuQoFAofFZK+Uo2m30GwB65XO7PG9neVEZHEzPJYOY3AXym9Pdf+tKXzvva1762+rrrrtt+yCGH\nvA3EGgDHcW4Mw/DzWustSqnfTfgONwFEFCmlbg7D8BKt9ccdx/nlZO9TGildSqWwQRfWXJCINtkK\nWbeUcrWd3BpTl9JKoDhx+U6t9WfCMJxviUxLEa1qQEN+OKeFYXipUupaIcROu3bbyivX8knOq4eh\n85oQlAnzwSk5jgdt3tJiW8lo16m+x7TWO7TWF0sp03ELpV4yGyk2vPSLxeJ8Zi7NNKoGEo05klcU\n5FKcufSIzVxaNMrkUsMeMcl27GdQoiPqHRUdEtOi+PGPf/ybbdu2fWnJkiX/vnr16utmzJiRB2Ln\nUqXU9Vrry4wx26SUL421rVYExWOy14dheJnWOj+ehl+lqEGXkh4vX2cnt/pLWwPMrMIwXBBF0XFC\niJ+2E4FJYInMT20uznzbImsrIpO08oQQL0ZRNFNr/ZdE9BIzJ8ns0zEkdk/aPS+nzmvTJvKaATsN\nlw6OrLk60QpQSv3RGJM3xlzIzHcrpf5o70p7yWQAKCHE247jPF4sFucxc862U6p+KTTu+Dvqe956\n3WwvFotzoyh6yHXdYZOnVlzcFBJj96VRYjbl0WkntTguuOCCf9y4cePnV65cuVwptbNcbYzZ1xgz\nz15tvjXaNloZURRN11pfJoT4hVLqmWZtl5ndcpoUHoo9KKdLSf6teRqEmTNhGC4ioo3tmu0DDGmW\nUlqfliIyPNyEsVzLB7AtH2b2AOwuhLjXWuC3RJxFrTDGHGyMOU9KeZuUspzTbVsgiqLdtdYLhBBr\nSi5aFBEdrLX+IBG95LruY8aYmb7vL5BS/tF13fur+TwVCoXPSCk3ZbPZuirUWutdgyCY19PT8x9j\nPdYY0xsEwQIhxMt2cokBIAzDvQcHB8/s7u6+sp59SJDP5y/NZDIPOI7zNoAwl8v9w5hPeo+iQ2Ja\nHH19fXTRRRdd09PT88Err7zyNsT5NAAArfWRURSdrpT6SSuar1UL++V2sZTyjpR1+agoo18obfkQ\nhusXSgW0TV+cmdkNw/ASIlrrOM6vmr39iUKKyEyzUzITRmRslSztJDzM4A1xFlnahHGnyVu5Vp7W\n+vgoij5iyX7fRB1Hs2GM2c8YM1dKeaeU8vnJ3p96wMwZY8y+URR9BvH5ezs5x4irZGEmk3k8k8k8\nDCCMoqjL9/35RNTned7qsS4sUjqSuvKotNZ7FovF87q7u/+rmsfbyaU5RBS6rnubEGIwDMPZg4OD\np3Z3d19Tzz4kyOfzX8hkMnc7jrMdwNZcLvedMZ/0HkWHxLQBVq1aJb/3ve/df+KJJ6pvfvObwwS9\nWuuPRFF0pDVfa9veaVJZklJeL6XcNMrIajldyrBx5MnUpTBzVxiGi4UQTyqlHpnwHWgSLJE5j5l7\nLJFpWgXDVsnSNvnp89qLoVDR0gmfpEpW05eW1voDURSdZkWybaktAYAoiva0lYz7lVJ/mOz9KUWJ\n5ihdJRvmLIzYlHMPAANCiAeFEH1JlYyIZkspp9lx64CZHd/3L7BTRzcLISq2VgqFwoVSyuey2ewf\nKz1mNIRhuM/g4OCnuru7l9ZwzNL3/bOSySVjzJ5hGH6ou7u7NGamJuTz+b/KZrO3KKVCABtzudz/\n3cj2pjI6mpg2wLnnnmvefffdM//t3/7td7Nnzz5+0aJFjyf3SSkfZuYZWusL2mlkmYcH0yUL2JvG\nmMuMMXnEjsKlI6sVdSmtAiIqKKWu1VpfprUeVEo9PvazWg9WI7NSa/3ZMAwvqoXI8Mhk5LRh3wzE\njtSlrsLrxqtKppT6g45xsVLq+nZMIwcAIcSbSd6SjSl4dKL3IdWmLUdAp2PoM5tUyNamwiR3RpUw\ns9Janx9F0YellDfSkEXBemPMXgAOs2nZA57n3RQEwRm+7y92Xff6UUacGzW7qznBmoiM53mri8Xi\nR3zf/7xSak0zCD8zZ+znQCB2Z++gAjokpk2wZMmS/IYNG07/8Y9//Oi+++677dRTT10L7JxkuMsm\n+56hlLqrVfQYVehS0mZ9/UKI55j5LWY+Ukr5YynltlFfoEUhhNhhreQXWyJTV3l7slFCZOZZ4zLN\nI5ORh1XLMDIZuR9x7taYycjjBaXUM8YYbROX21YkK4TYUhIc+ctm/i15ZE5TaTVFYCinqd9OFL1g\nz3PVBpsUx0bcorU+IwzDxZZc7rD7sElrPSilPFhKuZ6I+l3XvcsShSWu616vlBpRUWPmhrOX6iEg\ndnLp4WKx2B+G4TlEtKnefUghmU7qQkfYOyo6JKaNcMUVV2zYsmXLZ7/+9a/fuXz58m2HHnroW0A8\nsuw4zi1hGF5mjPlTpdSaidiflMiynEV+OV1KHxG9REO+GmXbX1rrgjHmIiHENRM11tpsCCG2KqWW\na60vMcYMtpuOgVPJyAA2A/hgGIZfQTzdU5qM3E9NTEYeL9hzYIwx8wHcJKXcMNn7VA+EENtLgiPv\nqrYqmUxwWdO+tOYo+czmMOQYnZzf58eDgFqSfLcx5iSt9RJLZBJy8q4xJgRwgB3BftsShe1BEFyS\nzWZvcRzntZJNNlqJaWi6KZvN/jGKolnGmBOCIDjedd1GqrDJdJJA3F7toAI6JKbN8OMf//jxbdu2\nffGyyy77j9WrV1+3yy67DAAAERWVUiu01kuMMVubsWhW0KWUS7pOt3w2pr7w6tKl2BZZj736v64d\nJ0oAQAjxrh2HX4TYaXndZO9TgjJX3KXJyArDWz6PM/MRACIb4tmW5FJKuRbAbcaYuQBulVK+Otn7\nVA+IqOA4zjKbU3SBzSkyQMV2XvrcAsCW1LndJIR4LlVNmbCcJltJfsR6yVwipbw5RS63GWNeBHCI\nECJDRG9ks9mniWigWCzOiaLo7hL9y7iPWI8FItohhPijMeYEm7l0b61tbx6evyTRITGjoiPsbVNc\neOGF/2PDhg1/sXLlyuWZTGbnBzeKolm2ZL5irJJ5OV1Kmqwgvior1aWkhbTj5qthhaWfAyCVUje3\nov6lWhhj9jHGXFRi9jWusJ/r7pIr7nSVLJ3R1J8+t6X6hdQ2hT0njlLqpolc7JoNY8z7jDFz7ERc\nW3ktlZzbXaIoOgmx0H0L4s9tD2LxbNpVOP3TkgTUGHOgMeb8MhNYGSHEoVLKPBG9CoC11nsEQTBf\nKbXGdd3HACCfz/9FNptdWclNdywUi8VjjTH7dHV1ra73GIIg+Agzu9ls9mHf9+cSUdHzvNtq0Xnx\n8PylfQHckcvl6opieC+gQ2LaFH19fTR//vylnuedsHTp0luRGr02xhxijPmMUmopEQWjtHyStsBo\nOT6TtlBxHLMwn4j6lVJ3torWpx4YY/Y3xlxQDbmsFsycKZnySVdTkmTkdMsnfX7rymiyROYCDJHL\ndiYyCblcLaWs1R12XFHSqi1XTRl2bjl2jXallLcLId5uxXZeNbAXYRcJIR4qEcVLIcQhUkpDRC8B\niIwx01NeLfcWCoUvZrPZG5VS79bz2kEQfIiZd/U87+5699/3/dOIKHJd90E7uXQ2M+9hM5cGxt4C\nEEWRVygU/qanp+dfEecmXZfL5VrK1byV0CExbYxVq1bJ7373u/cfc8wxM44++uh3N27cuPtHPvIR\nc8IJJzjMvDfiSkqI0XN8Wnosm2MTuUsp9l55YLL3pxFYcnmOHfUd06CwpJ1XruWTwfCWTykJHRdB\noCUyFwIgpdQt7Uxk7KK5QAhxT8pJdtxRQRydPreJH06lakqxdHs2N+pA+/6qasFsRURRNENrvZCI\nnisRLhMRHaSUyhDRWsReMq7v+/OIKB9F0d6e510jpawra6rRFGxgRPp0krl0stb6g67rrlBKvT3W\nNowx033fv6ynp+d/IiYxV+VyuYfq3aepjo4mps1ARKcC+DyA/e3PzBdffFE+88wzvPfee2879thj\nXyWitUKIh40xHwCwq9WVtOVCQ0SDJfEEbTmyDMR6DGa+R2u9UCl1DRH1YSgZOR1/kBZZpkdWk/iD\n5HZ+MtpsFGdf3aq1vlBrfWE7ExkhxGYrwF6otVbNnCTjIUPGStWUIoYL318TQjyZEkdXfW6ttuRe\nY8xHtNaXWSLT36xjmUgIIfodx1lqJy7PU0qttpUlZuZ1Wuv3SSkPF0KsFUIEXV1dy33f/yyAniiK\nlJSy3pduWBODEl0OxZNLDxWLxf4gCC7JZDJ3ZDKZUduXzJzOX+Im7NOURqcS0yQQ0UwANyFmzusB\nzGHmEVcERNQL4CcAjkT8Br2MmavODSKiYwB8AHHq9asANv3TP/3TrOXLlz/2/e9//6GPf/zjO8vi\nVlcyF0BRKXVHO7djoijq1VpfJqX8mZTyucnen2pRspAl/84GsDvicVCDobbAMBfayW7njQVmlrYi\nw5bItGULAwCiKNpVa32xEOLBaoNVechduNSQMSEpLkaa9qUrZeNSBdVaHxdF0UdtcOSYV/6tCmZ2\ntNYXMLN0HOfm9N+LiGZJKfcQQrwMYAczUz6f/3sA2zzPu66eaozv+x8nokHXdeuuehQKhXOllBuy\n2ewIM8IwDPctFotzHcd5YLRMKK31rGKxeE53d/d/I9bE/K9cLvf7evdpqqNTiWkeLgdwHzP/kIi+\nYW9fXuZx/w7gbma+gIgUYk+NqsHMTwN4uuTXb2zZsuW8yy+//K5ly5ZtP+KIIzYDO0cYbwvD8FJj\nzClKqQdrP6zWgB1ZXmEnfQoTJZAdC1w5GTk9wTUs+kAI8esoivZm5iPtpE9blv6JyFivjzl2QubW\ndiUydpLsGq31xVprqZT6LbBTdzTM3A1D53c6YiOytO7olVSlbFIMGZVST9jgyIullDdJKV+f6H1o\nBogoVErdpLU+y6aSr0g+K8y8WWsdSikPklK+RkRbAEAp9Xvf9y+zrZtaBb4KsYVAI6iYYu04zutC\niKt8358fRdFM13XvK/f+KKnEoNL2OojRqcQ0CUT0AoBTmPktItoTwAPMfFjJY6YD+AMzHzAe+3Dp\npZee/9hjj/3vlStXXrfbbrvtXBijKOrRWi8RQvxKKVVKgNoKxpjZxpgLbbl83J1XeaSvRrrlk05G\nTrd80lfcFRcyrfXJURQd7TjONUTU6JfnpMFWZOYCCJVSt7UTkeGRVvl7MvP7EY+1Ooh1R2mSUlpN\nadkFxhhzkDHms+04gZUGM8MYc0oURe+31aV0BtY0KeWBRLSxUCj8ZXd397fDMDx8cHDwrEwmc3sm\nk6kqiw0AfN8/i2I/mrpb1oVCYZ5S6slMJvNCpcdEUeTZySXf87zbS99Dg4ODB4ZheGJ3d/dyAPsA\n+H9yuVzF7b3X0SExTQIR9duFDRT3bbYkt1OPeT+A/wbwHIA/AfA7AH/LzE1bwObMmfP19evX//Wq\nVauuLRm93k1rfelEjvmOF4wxhxtjzlRKXdWMvj+XN+1LExVg9JZP3d4UYRh+nJkPdBxn2XgJcScC\nKSIzaD1LWobIcGzcV2qVnw4eTJPQfmb2mflEIvqjlPI+IcTkHkADsJlkcydauDwe0FofG0XRaVLK\nG5MJP7t+7Qbg6DAMP9LT0/NtAAjDcL9isTjHcZxfZLPZJ6vZvm0FvVbt48shn88vchzn0bHIk51c\nOoeZd3Vd94b05NLg4OBhWuv3d3V13YiYxHw/l8tVTcbea+iQmBpARPcB2LPMXf8AYFmatBDRFmae\nWfL84wCsAXAiMz9ORD8CsJ2Zv9Wsfezr66MFCxZcmclkTrz66qtvwfDR6/2NMZ9TSl0jhKhrDLFV\nYPv+JzqOs5SI8qM9dgztQi+GT4KUkpStGMcwSTtVcgYzz3IcZ3krX9mPBWZWYRjOJaLAarAmhMiU\nmeIq1aZIjKympCf0RpBQZu4Ow/BiIlrbbGv/iUYURXvYCayq9T6tBI7N+3qZeWYURYfYStlbiCtl\nM2AnMIUQvud5j9KQl8yuQRAsUEr9IZvN/nqsc1goFC6QUr6QzWafrXdf8/n8ZZlM5heO44zpBm0n\nl07RWn8gPblULBaPNsYc3NXVdTtiEnNFLpdry5bgRKBDYpoE2046lZnfJKJZAH5Vpp20J4A1zLy/\nvf0RAJcz89nN3Je+vj5x1lln/eK4447ruuKKK36Wvk9r/f4oik5xHOcnYy3+rQ6t9alRFB3qOM41\niN/LafFsmqQkycjl2j1ba50EaTasAPscZp7W7MToiYYlMvOIyG8WkSnT0qvGKr+fhoz76rLK5ziR\nfCERbVBK/azNicwMrfUiIcTvpZQPt9Kx2PPbVXJ+Z6bObzdS4+YADDP/CRH9xgYuJhXMxEsmothL\nxhhjeoIgWEBEmzzPu2u092M1raCxkM/n/yyTydzpOE7V+UnFYvHoMAw/nbS/isXiB40xe3V1df0U\nMYn5x1wu15ahpROBDolpEojohwD6mPlfiehyxNqJEcJeIvo1gM8z81oi+mcAHjN/o9n7c/3113v/\n8i//8sTixYs3LF68+Dfp+8IwPM22MK5plwUzdTVWSlLeh3gKJDH/KkdSWlq7AOwkMmkTuZZpx9QK\nS2QuIqK8JTJjfslwdVb5lbQp4zbFxcxuGIYLiOitWjKKWhFRFOWs/8rLSql7J5LI8FDMxcwy53cm\ngAhD53dLyfkdkcUVRdEutrr0lJTyQRruJXOgUipLQ14yGd/35xBR5HneLZW+C/L5/ELHcdbUoqMp\ns40vZrPZm8sFVI6GVPvrfism7/U872eIp5O+nsvl+sbaxnsVHRLTJFA8Yn0zgP2QGrEmor0AXMnM\nZ9nH/QniEesMgJcBLGbmcUlrvuKKK/Zavnz5b773ve898olPfGLn1YVtYZwPQNnR2El/E9iWT09p\nu4etwRviq7HtSGlSYEmLMeajAELHcW5rhWOpFyldSdHqStr5WBIiM6CUWom4rVl6tZ0mKT0YmXyd\nrqaMW0uvimPJWOforUqpVW1+Xjx7LO9YF+ymkWUeSq1PftLVlBzKnF8hREJYao5CsC2/BUS02RLM\nncdCRPtJKWcIIdYC8JlZ+L7/GWbe3fO8FUKIEVXofD5/aSaT+VWZYMmqMTAw8OV6Dfe01jNt1WiA\niDZ0dXX9EjGJ+Uoul9te7z5NdXRIzBTH3/zN3xx755133nP11VevPOqoozYnv+fY0v9iInrDcZz7\nJmJfOJWMnG73pNo+RYz01UhIS8VkZLtgLrRXy/e0Uqm8VthjWUBEW5RSP22nY+FYIJ2upuzCzEcj\nTuIVGNsTp2WrT8zspNpkLSVcrhX2WOZSPMJ8W7XVWB6a5KpUTRGoXE0Zl2qZJZhzKB73vzVdZSGi\nPaWUs4QQLyH2kkEQBKcZY452Xfc6pdSW9Lby+fwXMpnM3Y7j1B0LMjAw8LWurq7/XY4kVQMbOfDn\nRDTY1dV1pZUm/FUul2vJvKtWQIfEvAewePHic9esWfPfd9xxx4rdd999J6O3V2VLhBCPKaUqmi9V\nCx6ZjJwmKUky8mgtn7rNv5g5G4bhYiHEH5VSbW3Rbb+YLyai15VSP28VIsPlrfLT53eYdsEuZtuj\nKPpTAFscx2n76pLWeg6AZMFsWSPCsWCrfuczs+c4zo3JZ49H+uKkqynTMdxBOrnY2NKI9qgJxyKs\npmxXx3FW0HC7gl2klO+zE5lbgDjoMQzDj2Wz2Rsdx3kjeWA+n//LbDZ7u1JqzEiQShgYGPgfXV1d\n/68Qou5Jw0Kh8Glm3g9A5Hnew0KIBblcrm3fa+ONDol5j2DOnDl/98orr/ztqlWrlruuu/NqxQr+\nLpNSrhrLSyK1iPVWWMSSlsCIlk+lZORmIuWH85BSqq0dLq0W41IiemEiM6N4dKv8XsSTIJW0KWUF\n0vbKP2nHrG5zIiNLkrzbQlOWINW2ncnMM6IoOgExOelHfH4TX5wtKO+L05LHa1vkH+PYQPK6EuuF\naVLKA4QQm4noLQAYHBw8eHBw8LxMJrM6k8m8CAADAwNfcl33+tIKTS37kM/nv9Xd3f3dRip1vu+f\nTUSbEbfgZriu+/5cLte2n5nxRofEvEfQ19dHCxcu/C8p5UeXLVt2M4aPXu9rjJmnlLqWYp+M0Vo+\n6UDJ0pbPpLcEoiiaqbVeLKW8s9WSiWuF7fkvFkL8Xin1aJO2mSxilbQpHipb5ffXWy2zRCbdJmvb\nLx575f9ZZu6202QtJRq3bb1h1RQMJ6LDXIaZeRaA3aWUN9uFfjJ3vyForY+PouhkpdQNQojNqbs8\nO7m0hYheB4AwDPcqFosXOY7zYDabfWJgYOCrnuf9REpZl/6EmWU+n//7np6e7zRyDIVC4Xwp5UvZ\nbPY5Zt5l2rRpf9nI9qY6OiTmPYS+vj5x5pln3nfkkUfuetxxx71MyC18AAAgAElEQVT5+uuv7/GB\nD3wAH/3oRyUz74V4ETOoTFLqXsQmEsaYvYwxC6zl+ph+Da2MKIqmaa0XCyEeqbblZ1sCo1VTkuDB\nckRlx3gRDNsmW0BE71pRadt++fDQWPxM28KYMKPCCm29tDYlTURLtSn95UiX1vrEKIqOt07YdVUi\nWgXGmMOMMZ+RUt4upUxPGmUskfGJ6BUAbIyZ4fv+Qinlc8aYD3Z1df2HEKIu89EoirKFQuGrPT09\n329k/wuFwlyl1NN2SsrL5XJfaWR7Ux2d7KRJAlUZGGkfKwE8AeANZv5Mja9zMoCLARyAOPV672ef\nfVY++eSTR+yzzz7bDz744A1EtE4I8dsoig5i5kMdx7mqHchKJUgpNwG4zRgzh4iubecQPCHEdqXU\ntVrrS7XWg0qpp3n0vKYZALIYTlK2ENHLKTI6KZUDGkokX6C1PqudR5YpziVbrbU+MwzDRTYpvmni\nSx6yFBimS0md49K23mtCiD/US0SVUo9qrQOt9WKl1PUTEekxXpBSvgCgYIyZw8z3pZLJB6Moeh7A\nwVLKQ4joJSllf1dX11Lf9y8CkGXmuivJPDLzqNHtSMQXHB2Mgk4lZpJAsa/MuzwUGDmDy/jK2Md+\nFcAHAeSY+ZwaX+c4AMcBeAVx6vVr3/ve93a56qqrfnPFFVes+fSnP/188ljbVz6bmafbMnnbTmAA\ngNb6qCiKPmnjCcZljH28wCOt8mcx8+GITfs8lFjlY3hFJd/K5MBWZJJpsrvauX1hPzOfYubZ1nG5\nqqt4Lm/wtrP1gyFLgYSEllZTxmVxs5EeZ0+RKuZu1kvmiRKDPyKiA5RSLg15yTiFQuHviehVz/Nu\nqkeYa6s6F/f09Px7I/udz+cXZzKZ+x3H6QOQz+Vy/9TI9qY6OpWYycM5AE6x/18G4AGUSb0mon0A\nnAngewC+WuuLMPMTiKs4aWx+8803z/nmN7/587333nvb0Ucfvcm+FpRSd4dhOF9rfUa7LzBKqWe1\n1t1a60W2utQyIYs8tlV+MsmVEJTXiej1KIpOEULcopRqW71PqiKzUGt9plLq7nZ9n9nPzM+11h+z\nScvXppKW09N65aopgG33ID7HG4UQz6RE0hN+ESGlfB5A0RgzF8BKKeW6id6HZkEI8Y5SaqnWegEz\nT7P2CwyAmfllrfV+UsrDhRDrbOU5EkL0+b6/2HXd66WUO2p5PWZWTapyJpUYgVi/1MEo6FRiJglU\nRWCkve8WAP8CYBqA/6vWdtJoWLx48WceffTRK1euXFk6ep0Nw/AyIcRTzRKUTiZsyOL+juNcO5Ft\nMh5p/pVewKah/Lhq/2iTXIkIW0p5s5SyblOuVoB9ny2k2KysLYlM+hwbY44FsDeAtxGf3yQOYUu5\nc0xE/iTu+qgwxuxtjLlICPFzpdQzk70/jcC+z9IePzsnrMh6yQB4vVAofKG7u/v7xWLxJK318XZS\nqWrn3TAM9xocHDy7u7v7/zSyvynXXw1gfS6X+5+NbG+qo0NixhHUeGDk2QDOYOYvEtGpAP6umSQG\nAObMmfPlV1555e9WrVp1bcno9TSt9RIp5c/s1Vnbwpb8k2yiFc26wuUhq/xeLl9NERi60h4RLEl1\n+ozYIM8LpJTXW/1P28IuMIuIaGMrGhWW6I/KVVOGhUsinuTbR0p5uxDi9XrPcSvAtmMWWlH5byd7\nfxoBx6Px59nvgBvTBJKZdyGiowYHB0/o6en5IQAUi8VjwjA8PZvN3uo4zvpqXiMMw/cNDg5+rLu7\n++pG9nVgYOArnuddJaVUAJ7L5XL/2cj2pjo6JGaSQNUFRv4LgEWIc4FcxFd3tzHzxc3clzPPPPO/\nmPm0a6+99kYhxM43RBRFe2qtF0kpb5BSvjHaNlodHI/FzgUQKKVWVqMZGUW3MOlW+caYQ4wx59j2\nRdsKl4GdnjiLKDb3m/CgRR5p8JbWpkxHrD8qV03ZgjIGb3bM9yR7btp60ieKol6t9cVlMoraCsws\noyjqNcZ8HMC+VgvTbc9zL4BQCLHF87w7yXrJhGG4f7FYvMBxnHuqSbYeHBw8KAzDD3d3d1/XyL4O\nDAx83U5J9QB4PJfLNUSKpjo6JGaSQFUGRqYefwqa3E5K0NfXJ84555x7jjnmmBnf/e53707fZ4w5\n2C6WV5UYSLUdOPYqWURx1MK99nfpKZBy1ZR0MF254MFJEz9b4fLpSqllQoi2DohLEZkNzXYp5uHe\nOOWqKeWmuRoyeNNafyCKotPsyHJNYYCtBmsiuZCI1ttz05KLhhXDz0yfZx4aO++BFUoj1pzsJoR4\nUAjxKg1ZRyReMv1EtAEAtNZ7BEEwXyn1WDabXTPa+3JwcPAwrfX7u7q6bmzkOAYGBv6hu7v7h0S0\nK4AHcrncDY1sb6qjQ2ImCVRlYGTq8acgbifVNJ1ULVatWpX9x3/8xyfmz5+/6c/+7M/WpO+zV5Yn\nOI6ztJX7+OVg39/dSTWFmXdn5uMQT/lIDJ8CKffT0sI6u1ieopS6ut0msEphiczFdrGsKWWZRxq8\nzQCQEJa0N045J9od41Fh0FofY6fjrhNC1G1l3wqw52Y+EfXbEMwJJ+9c4jZcco5nIhbDp4XSCRnd\nUnrBobU+MoqiM6WUt0opX029jCOEOLTES2ZaEAQLhRCvuK5bkcQVi8WjjTGHdHV13dbIMVrX32/b\nteCuXC63st7tvRfQITEd7MQPfvCDPX7yk588/s///M9rzjjjjGE6mDAMT2fmvewYaUv1+e0CNlo1\nRWO4bsFn5hOJ6BGl1G8ms5rSDGitT4ii6EOWyAxM9v40ghSReVUpdV9CLkrI6E4H2tQ57sJIk8Z0\nRWVSvHGMMUcYY86UUq6YAvolx2ZHRUqpW+qpUFXxGklltBxRmYGYjKZbe1tSrb2aYk2MMbONMRcK\nIe5RSqXbRVIIcbCUEkS0DoCJosj1fX8eERU8z7u93LEXi8VjjTH7dHV1rW7g+J18Pv/1np6e7yG+\nwL0pl8v9vN7tvRfQITEdDMNXvvKVo1etWnXf0qVLf3rMMcfsTHPl2KF0DoBBpdQdE9kb59Gt8nth\nFzCUr6ZspTKeGlEU7aq1vtRmRrXtGGkCrfXJURQd7TjONdRCo+S1IFnAoijaI4qiTyGe7NmBePFK\nyOgWKt/aK5vb1Aqw+qVzpZQ3Silfn+z9aQQpgWzOeknV7KfCw6f2drZ/MKQzK/XHSZPRpk4XRlG0\nu/WSeUwpla5AE8VeMp7Vzwwys/R9/zxmnu553g1CiGFV6SAIPsTMu3qedzfqRBRFXYVC4a+twHg2\ngKtzudyD9W7vvYAOielgBJYsWXLWQw89dNUdd9xx/Z577pkevXbCMLxECPGSUuqBZr4mx8GDI0aR\ny7QDmmaVb4zZxxhz0RQRLkNr/QlmPsBxnGX1LC7jDftd441STUkvYNuZ+UAAb0gpf21HklvumKqF\nMeZAY8z5UspbbKJy28Je0JzBzPtYp+JC6f3MnCsVSaeISrrtU0pUJlxnFkXRdK31AiJ62bYxd36X\nENG+UsqZQoh1AArMTEEQfCKKokNd171OSrnTZT0IgpOYucvzvPvq3RdjTK/v+5f29PT8CLGb+5W5\nXK7tbS7GEx0S00FZzJ0792/WrVv39dWrV1/red7Oqx+OQwk/L4R4IGXnPSbKfLGVE1dWCh7c2uwr\nsARWuHyuUuoaIcS74/EaEwVLZM5k5j3s4jLhLRQebvBWrh0AlK+mbKESgzdm7rKtpbVKqfsnsvo3\nHkjaF2UyfdoOURRJrfWnABxKRL9H7CKdEJXkomMnQYGtrExEmn09YGbPesnssJXmnS1zItpDSrmX\nEOJlxCQbQRCcoLU+yXXdG5RSm+3vTmVmeJ73QL37obXerVgszunu7v5fiNtJ/5nL5R5v7OimNjok\npoOKOOuss35sjDl9+fLlpaPXu2mtL7GiuPXJ7+10wDBtSmrx6kUspq1klT8wWe0ArfWf2EmSq4QQ\ndSXYtgrsVfK5tty/Yjz0SzwUiTCzzHmehrgN1F+ygNU1dm6JzCVE9IJS6lettvjVipRZ4epWT1lP\n2j5RFO2spKREtIkgPgKQI6LHhRBvpCoqLZXsXQ2YWWmtz2dmz3rJpCt/M6WUs20Uw7sAMDg4ePjg\n4ODZmUzm9kwm87Lv+58kooLruo/Uuw8lhnn7APiPXC73ZGNHNrXRITEdVERfX58499xz7z7iiCNm\nfv/737/b9325cePG3ffff383iqKD7ZTPevz/7Z15fFTl2fd/133OIZNJZkIIm+y4oHWru1jr0ket\nWCuLioqAoNRafWyrrbXaPrV9X/vY2te2ahfFpVbFBRRUsK2tUtEWV7QakLAlBNmXJEYIIcw553r/\nOPckZ04mZEJmDdf38+EjcU4y93Ayc37nvq7f7/J6UsrhWRfjAiVZuFvefrDpKb7HWZb1GBWYAysI\ne5k4lwIg3YDZpe15Tgx4S7abEnSB+HdTGtMtnHxCpsqyrEXp/Nm5QE9Zv9IwjL8ahrE8V+sI7I72\nCZznPvDCGhN2UpLtmumbgHNN03xaKbU5V68nHfhKZcO1q8w/eiBiGMYhSqktRLQFAGKx2NCWlpbL\nLct6zXXdg4ioPhQKvbu/zx8IzBsC4DeRSCRnvyOFgIgYIQEiKgJwFLyp1wcbhnFoKBSa1KdPn5Kt\nW7fS8ccf77zwwgsbyBubUARguGEYLyqlNiEPt4lTRZdivqrr/E/ms+BKBd2AeQWAZr09zoHHewVd\nIIFdM/+AyeBuStbPsy5jTlNKfWKaZsE3OrquO0Cn4b5qmmZlpp6HE517QaHSG95snlaBgkS3T7sg\nv45wHOdwx3HG9pCeHziOc7rruifrid7+nJ94lsxnRLQOAGzb7rtnz57J8N5rS0Kh0If7+9yBwLwh\nAO6ORCIFbzzIJCJiCgTycmVmw2v2qoXOlQkcMxTAEwD6A2AADzHz/V18noMBzIM39boGQM2AAQPq\nRo4cef+111771rhx4xL6YGKx2NnMfKhuJi30Cz/Ztj0eQMg0zdnZbjBMJ/ouu0w7ylr0B65/NyUY\n8ObfTdmvgLdMo4XMdKXUsh4iZPrZtj1V95ft94WPmUOu6yYIFE6cht2Ijt0+aXvP+np+8r5Ulgo6\n5+erek6Zf6K3pYVMCxFVw8uSKW1ubv5vItoSDoef3N/Pjr17937Btu1jw+HwbHgi5ueRSKQ2DS+n\nxyIipkAgL+F3BzP/ioh+CK9GfVvgmIEABjLzR0RUCuADAOOZuduzj77//e8f/cILL7z20EMPvXz8\n8ce3Onn0DsYEAJYuXRT0LxQzq1gsNkk3+M3P550l3122P1PDv6PSAs96Xg6gXim1JB96kLqDTo+d\nppRaaprmm7leT3dxXbePjvVfbJpm0gZOX9knQaD4hIp/RldQqGR1GrYulU1SSr3Wlcb/fMXnKns5\nMENO6SwZIp0l09TUNAlAlIh2hkKh55VSXTYjtLS0HOs4ziHhcPgFeCLmp5FIZGNn33cgIyKmQCBv\n1tJZzLxVi5VFHJi1lOR7XgTwO2ZemI41XHvttWMWLVr0+Ny5c58ePHhwazosMxs6Mn5TPM6/kGHm\nXvHANcuy0vJvt5/rAHxpw0hsrmwNeEN7N1d8N2Wv/jkhvYOxIt3W+Fyghcx0PWX9X7leT3eJzyci\noiql1LokQqUMXtkn6PbpctknG+gMpqlKqbdN03wn1+vpLq7rHmTb9iSl1L8CQpOIaKRhGGGl1Kqm\npqbLTNN813GcI5m5f3Fx8dNKqaauPFdLS8tJrusOLC4ufhmeiPlRJBIp6NlomUZETIGge1DK9d8J\nQH386w6OHwHgDQBHMXPaUlwvv/zy/161atXtCxYsCFqvi2Ox2Ayl1Lsd3VEWErqZ9Bql1Pumae53\no14KzxOfhN3RboqDtrJPfUCspBzwpksxVyulPgiEehUkPiHzkWma/871elKBmYMZOf4m2jAAgtcQ\nXx0o+RSc20dnr0wlok96gqvMdd1yPT9quWmaC/2vh4iGGIZR0dzcfFKvXr1eM01zXUtLy9m2bR8b\nCoWeMk0z5blme/bsOY2Zo8XFxX8HMBTA9yORyGedfd+BjIiYPIKIXgUwMMlDPwbwuF+0EFG9/jBM\n9nNKASwC8HNmTvvcjQsvvPD+WCw25qmnnnomYL0ut237Gl0TL/hmNP1BfI1uvux0im0yODHgLdlu\nij/gLdluStpmN7muG7Vt+2ql1L9N0/wgXT83V7iuG9Glpf+YprnfttZ0EXB1BZtoy+GJlGRunwYi\namTmEr0js6In5OJo4TyFvOnkfyvE8qUffWNzJRHtMAzjrwD8Nx+DmfnwUCj0nGmaqwGgpaXl+Fgs\ndk5RUdGzlmWlFKa5Z8+eM5nZLC4u/ie8nJhvRyKRLu3mHGiIiCkQdDnpbGbeQkQHAXg9WTmJiCwA\nLwP4GzPfm4m11NXVqfHjxy84/PDD+999991/8T8WT8HV03u3ZOL5s4mOJb9KB5TVJDuGvYC3aJLd\nlHjPAtDxbkpWE0q10Lxa9yxkzBWTLbSQma53mDKebMqJgyaTuX3irq6EQYTa1dVp2UdfKKdS28To\nTL+kjMLMRb4esxcKqVmeE3Ny4u/tCgCD4A2PbSCiOrSd772WZcE0zfVoy5I5bO/eveN79eq1oFev\nXis6e87m5uZziGhvKBT6FzwTx3WRSCQjQZ89BRExBYJu7K1j5ruJ6DYAvZM09hKAx/VxN2dyPS+9\n9FLRT37yk3cnTpy444YbbkjYztdD7843TfPRQg+PAwDHcYY5jnO5UuoVIrIDF7BkAW/Bi1eXAt4y\njXbFXGUYxl8Mw+j0gzXf0TtM05RSS7pbKvPtnAXdPv6yz2dJBGl856zbZR/dwzSFiDabpvnXHrCD\nYdq2PRFtuUV5URpjZnDiVOxWsQLvXMeFSj0S+5E+cxznywAO0tk4/nJ9PEtmKxFtBrwAu5aWlkmm\nab4ZCoX2WWpvbm4eQ0SfhUKhd+CJmGsikUhBn/9MIyKmQCDPYj0H3hZjLbTFmrxx7Q8z84VE9GUA\nbwKohGexBoDbmfmVTKzpV7/6Vb+HH354yY9//OP3L7roooRyiw6PO1aHx+X9zJskDhB/b0ofeEF+\nCkAtEW0N7KZ8Rnk22bszdLPilJ4QgQ+0CpnpSqn3Omsm9ZV9gm6f+LkGEsP8giFvGf/Q1DsYVxJR\nvXbJFfQHNXsBjOOYubceHJm2Mmlnz5vkXPuFSgyJQiWlqdjsZcmc5brucToUz9/3ElJKHW4YRgMR\nfQoAjuOUNzc3TzYMY0UoFFrY0fncvXv3RYZhbCoqKvoIQP9IJHJdGv85eiQiYoRuccsttxw1b968\nhTNnzvzLCSec0Dqhlz3r9deZuUx/aOV8G5kTh0z2CQiVYMBbcDelyXGcE1zXPUPvMKWtWTpX+CLw\nZwdyMAoS3cM0TSn1rmEYH/jPc0CoxM91ve9c+y9eebFzxt7A1UlE1FRopZhksJfDNIaZh+tAybT0\nenBi1ECCWIHn7GpCovXc//du3WDZtn2C67pf0RPK/VbodlkyruuGm5ubJxFRQ3Fx8UvJbnx27959\niWEYq4qKilYAiEYikW93Z30HAiJihG5z7bXXnr9o0aIn5s6d+8zgwYNbO+m5LXOl0TTNlzN9YdDb\nw8mGTMZ7U/xDJoO9KSmVAmzbPsN13aMKZYepMxzHOdhxnEsMw3jKMIxNuV5PqujPrXCSidj94PUs\nMNr3IfnPed6F+SVDl2IuA+CYpvl8oe34BfHtYByr++ZSct6wN6+rj0+YBuc4NcK3k+ITKxkPbnQc\nZ5TjOOMMw3jJMIxVvocUER1mmqYiolUAHGa2mpubL2bmUHFx8bNKqYTPkN27d19hmuZHvXr1qgVg\nRiKRWzK59p6AiBghLUyaNOn6qqqq/5k/f/4TJSUlrW9M9jJXrlFKVaaj8ZKTx6gHA96CSbTxD7Zu\nB7zpHaYLuG1SdEFcDPeFjoy/yDTNJ5RSeZNJocs+ZUnOdVyUJhUqABzHcS5WSr3VQ+z+hp6FZZim\nOacn/M7Ztn2K67qn61LMdm7LREoQKL5zHZ/LllD28ZX4crpL5TjOYMdxrlBKvR5IXybysmRKlFIr\nAexlZtqzZ88FrusOD4VCTxmG0do32NTUNNWyrLd69eq1GcDeSCTyP1l/MQWGiBghbVx00UW/bW5u\n/vozzzzzjFKq9UNF9yvMMAzj750NvOPkAW/+C1cY7WPU/X8y3smvt8UvAaB6QkoxANi2fbTrul81\nTfPPuqSSFQIlvmB2SrwUEJzhVK+UaqB9DOrUAXLT95WEW0jonpIJzBzWE5bzojm2KwR6kfq4rjsK\nwCHw3s+l8DKR/MnDfqGyKx9KfPvCdd0K27YnK6U+NgzjDUrMkhlqGEYfpdRqALuZGS0tLafbtn2K\nzpLZBgBNTU3X9OrV6zXLshoANEQikZ/n6OUUDCJihLRRV1dH48ePn3/ooYcOuueeexb4H3Ndd6Bt\n21MNw3hGKbW5gzvsZAFvwd2UrDRWdgZ7KcWTdeNlxktl2UDX9880TfMxpVRj59/ROb6yT8JOik+o\nFMMr8SWblNytUoC2k0/TuThL0vF6cokWz2OZuY9lWU9lQ7B3FfbCG/2C1J887O9Fqic9RJaZT1RK\nvWiaZsHPW2IvG2cyec6yvwR2iPqbpjlYKVUDT7ihpaXlmFgsNqaoqOg5y7Jqm5qarisqKppvmmYz\ngI2RSOT/5eSFFBAiYoS0Mnv27F533XXXuxdeeOGuI488cnttbe1BRx99tBo9erTJzIPhDad0AexE\nx7spWXEudBftIInH+Rf8QEIAsG17tJ7e+1iqzctJHCD+7JQ+8M53spC3eiLamUlR6hMy/+oJAX9a\nyHyNmQdqIZP19wp7E9ATmmh9O6WlSNwpDfYjtROljuMMdxznsiTziQoSXUK/jIjifUz+XbNywzBG\nKKXWE9EOAIjFYiNbWloutSzrb7FY7OxQKPSsaZougNWRSOR3uXkVhYOImB4GEY0BcC+8jINHmPnu\nJMfcD+ACeHdF05n5P918znMAnAfgYHjbw4dYlhU9+OCD3cGDB+++9NJLN1x88cU1RFTvuu4QZj7W\nsqxH91UOKBT0ndcM3X9R8Hf7AGDb9pm6efnP8XOUzNnlu3D5yz4JgwiVUvW5FqVayExXSr3RnWnR\n+YLuyzrf5/JJ6/sosHvmD3qLO37i/Sn+sk9cpOxXeKPeqZ2slPqnaZrd+jzKB3T5bywz97Us62ki\n2u17uNQwjEOVUtuIaBMA2Lbdf8+ePZMBFIVCoT+aplkE4KNIJPJwTl5AASEipgdBRAaAlQDOBbAR\nwPsAJrFvijURfQ3Ajcz8NSI6FcB9zDy6m897CYAjANQAqAZQc9NNN/V78cUXX585c+ZfTzzxxAT7\nbiwW+yozD9IfwAXttgDaUnANw/hbod5JBnuRXNc9GUAFgHp4ZYAQ2ju74v/NuAOku+hp0dOUUot6\nyEUStm2fw8yjLMt6grpoV+b2IxL8ZZ/47ll9YPcsfr53ZqJ8qntKpuqsn4ynL2cafY7+i5mP0g3M\nDb6HQ9qC3UhE6wDAcZxoc3PzTUqpD4uLi5cQ0eJIJPJkjpZfMIiI6UEQ0WkAfsrMY/TXtwEAM//S\nd8yD8EYWzNZft07HTvd6rr322vNef/31WXPnzn1myJAhfus16QTPmM6/SPdTZx1fz89zhmHU5no9\nydBln3gvUnBScjnaLlwN8AaMDgVQrB0xDfnQi9QdfELmddM0P8r1eroLe3blM7Vd+XGl1M7A4wa3\n5acEg97KkTgiIeWm6UyiTQBTyZsftbAnfDbYtn2y7jV7Wim12feQqYVMjLwsGXfXrl3/Q0QbiIhD\nodCPy8rKns7VugsFM9cLENLKYADrfV9vAHBqCscMAZB2EfPwww+/euWVV94xderUO15++eVW6zUR\nsWma82Kx2HTbts+2LGtRup872yilthiG8bzjOBOJKGdzo3xlH3+/Qrw3JYpA8BeATYZhxL/eE/hZ\nZNv2ONu2v2ZZ1jPwGq4LFqVUvWmaT9i2Pc22bTZN8+Ncr6k7EBEMw3iHmUO2bX+TiD4CUOzbTYkP\nF/XvnK319Z7lncNJKfW5ZVmPxWKxybZtF+vm2IIWz6Zpvu84zs4kCdm267ormPlQ0zQPB7AGgFFc\nXPxkS0vLxa7rFuVw2QWDiJieRapv9uDtTcY+JJ5++umZY8eOHTV9+vSJs2fPfjpuvSYi27KsZ2Kx\n2Dds2/6sJ9wZG4axFsBfbNu+UjfGNnT6TV0kUPZp3UnxCZV4oF/8znq7UmrV/pR9tNicb9v2pbZt\nX6rt5AWdGquUqtNC5irbtpHvQobbh/oF+1OKADTAs+2eTERvG4ZR5TvfBXe+iGi3ZVmPx2KxK/Tv\n3bxCLzvrGWVNjuNczsyv+n7vXGZebdv2CKXU0QBiSimnuLj4PQAFn6KdDaSc1IMgotEAfuYrJ90O\n701yt++YBwEsYuZn9dcZKyfFqauro4svvviFkSNHDvv1r3893/+Y67p9bduebhjGXC0CCh69fTza\nsqw/dbVXAWhX9glOSvZb0INun3i/Qlrf1NpOfgUR7TZN88VCvzMGWn/vrsqHad7cfm5XcL4P0Naf\nEkykbQ1w1Bb5s3Vo4Y5cvZ50wV5a8SXMbFmWNTsfd466iv69m0JEHyul1gT6kQ4CUFJaWvoHAH0B\n/CkSifwrtyvOf0TE9CCIyITX2HsOgE0A3sO+G3tHA7i3u429qbB48WLrhhtueGfcuHGN3/3ud9/0\nP+Y4zgjHcS7Vdf3tmV5LNojFYl9h5sO0w6ddnoe2qXbk9vFPxW4dRKidPjmxoLM3x2cyEW3XW/zZ\nXkLaiU/zVkr9wzTNpZl8Li1ME+b7oC2RtjeAPUgs8+3XLCfbto91Xfc83UiasRuTbKFdPhf5XD4F\n4WjUwrTUd77jwtTv8NpNRDVIHDzJlmX1U0rtBXBPJBJ5N4IcbBEAACAASURBVJevoxAQEdPDIKIL\n0GaxfpSZf0FE1wEAM8/Ux/wewBh4/RFXM3NWbKf33HNPxUMPPbTk1ltv/c+ECRMS7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4290eb7350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels_train = [TOPIC1 if _ else TOPIC0 for _ in y_train]\n",
    "labels_test = [TOPIC1 if _ else TOPIC0 for _ in y_test]\n",
    "fig = plt.figure(1, figsize=(8, 6))\n",
    "plt.clf()\n",
    "ax = Axes3D(fig, rect=[0, 0, .95, 1], elev=25, azim=70)\n",
    "for c, i, label in zip('rgb', [0, 1], labels_train):\n",
    "    ax.scatter(pca_X_train[y_train == i, 0],\n",
    "               pca_X_train[y_train == i, 1],\n",
    "               pca_X_train[y_train == i, 2],\n",
    "               c=c, label=label)\n",
    "for c, i, label in zip('rgb', [0, 1], [l + ' (test)' for l in labels_test]):\n",
    "    ax.scatter(pca_X_test[y_test == i, 0],\n",
    "               pca_X_test[y_test == i, 1],\n",
    "               pca_X_test[y_test == i, 2],\n",
    "               c=c, label=label, marker='x')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a clear separation between the two classes (red and green) in the training as well as in the test set (dots and crosses)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When restricting to two topics we were able to predict the correct topic for each question in the test set. This approach can now be generalized to all topics on the Math Education Resources, and machine learning can therefore be used to predict the topic of any question on the website.\n",
    "\n",
    "This serves two purposes:\n",
    "\n",
    "1. Help contributors label questions by suggesting sensible topics or label automatically.\n",
    "2. Help learners find similar questions on related topics, even if the topic label is missing.\n",
    "\n",
    "In the future we plan to incorporate other data to build a full question-recommendation algorithm that takes the course and difficulty into account."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}