nltk-tagging-from-scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c136c80f",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import nltk\n",
    "import tagutils; reload(tagutils)\n",
    "from tagutils import *\n",
    "from IPython.core.display import HTML\n",
    "from nltk.corpus import brown\n",
    "import random as pyrand\n",
    "from collections import Counter,defaultdict\n",
    "from tagutils import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f123614",
   "metadata": {},
   "source": [
    "# Training Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91c129e7",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sents = list(brown.tagged_sents())\n",
    "pyrand.shuffle(sents)\n",
    "training_set = sents[:-1000]\n",
    "test_set = sents[-1000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec3e3c5d",
   "metadata": {},
   "source": [
    "# Posteriors and Conditionals"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7e9b8ad",
   "metadata": {},
   "source": [
    "Let's start by defining some useful little functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "a146ffd8",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 0.20000000000000001, 2: 0.20000000000000001, 3: 0.59999999999999998}\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "c = Counter([1,2,3,3,3])\n",
    "def posterior(c):\n",
    "    \"\"\"Given a `Counter`, compute an equivalent posterior (represented\n",
    "    as a dictionary. This basically just normalizes.\"\"\"\n",
    "    n = sum(c.values())\n",
    "    return {k:v*1.0/n for k,v in c.items()}\n",
    "def pmax(c,default=None):\n",
    "    \"\"\"Given a dictionary, returns the key corresponding to the\n",
    "    maximum value. Useful for finding $\\arg\\max_c P(c|x)$.\"\"\"\n",
    "    if c is None: return default\n",
    "    if len(c)==0: return default\n",
    "    return max([(v,k) for k,v in c.items()])[1]\n",
    "print posterior(c)\n",
    "print pmax(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "ad6efd47",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Conditional:\n",
    "    \"\"\"Given a set of pairs (u,v), compute\n",
    "    estimates of $P(v|u)$, returning a posterior\n",
    "    distribution given $u$.\"\"\"\n",
    "    def train(self,pairs):\n",
    "        counts = defaultdict(Counter)\n",
    "        for k,v in pairs:\n",
    "            counts[k].update([v])\n",
    "        posteriors = {}\n",
    "        for k,v in counts.items():\n",
    "            posteriors[k] = posterior(v)\n",
    "        self.posteriors = posteriors\n",
    "    def __getitem__(self,k):\n",
    "        return self.posteriors.get(k,None)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13072a7d",
   "metadata": {},
   "source": [
    "With these definitions, we can trivially compute a unigram model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "1463ed74",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cs = Conditional()\n",
    "cs.train(brown.tagged_words()[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "17f218c7",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'IN': 0.2857142857142857, 'TO': 0.7142857142857143}"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cs[\"to\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68519f20",
   "metadata": {},
   "source": [
    "# A Simple \"Greedy Bigram Tagger\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7596e2f",
   "metadata": {},
   "source": [
    "The simplest \"bigram\" tagger uses a probabilistic model (this actually isn't usually\n",
    "called a \"bigram tagger\"; see below).\n",
    "\n",
    "$P(T_n|W_n,W_{n-1})$\n",
    "\n",
    "What we actually want to find is the most likely tag sequence $T_1 ...T_N$ given a\n",
    "sequence of input words $W_1 ... W_N$.  Assuming that $W_i = \\epsilon$ \n",
    "(some special, \"empty\" symbol), we can write under a Markov assumption:\n",
    "\n",
    "$P(T_1 ... T_N | W_1 ... W_N) = \\prod_i P(T_i|W_i,W_{i-1})$\n",
    "\n",
    "The best tag sequence is the one that maximizes the posterior probability of\n",
    "the entire sequence.\n",
    "\n",
    "However, there is another question we can ask, namely what the most likely\n",
    "tag is at each position. Due to the Markov property, this is really very easy \n",
    "to answer for this models since it is just given by:\n",
    "\n",
    "$T_i = \\arg\\max_{T_i} P(T_i|W_i,W_{i-1})$\n",
    "\n",
    "Note that this local tagging may not even result in a tag sequence with non-zero\n",
    "probability.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "a3adff3b",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def words(tagged):\n",
    "    return [w for w,t in tagged]\n",
    "def tags(tagged):\n",
    "    return [t for w,t in tagged]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "935bf138",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def bigrams(sent):\n",
    "    sent = ['']+sent\n",
    "    return zip(sent,sent[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "19b604f2",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sentences_bigrams(sentences):    \n",
    "    for sent in sentences:\n",
    "        for b in zip(bigrams(words(sent)),tags(sent)):\n",
    "            yield b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "8af5772d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('', 'The'), 'AT'),\n",
       " (('The', 'Fulton'), 'NP-TL'),\n",
       " (('Fulton', 'County'), 'NN-TL'),\n",
       " (('County', 'Grand'), 'JJ-TL'),\n",
       " (('Grand', 'Jury'), 'NN-TL'),\n",
       " (('Jury', 'said'), 'VBD'),\n",
       " (('said', 'Friday'), 'NR'),\n",
       " (('Friday', 'an'), 'AT'),\n",
       " (('an', 'investigation'), 'NN'),\n",
       " (('investigation', 'of'), 'IN')]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(sentences_bigrams(brown.tagged_sents()[:2]))[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "31f58f6a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bgs = Conditional()\n",
    "bgs.train(sentences_bigrams(brown.tagged_sents()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "e36240a9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('', 'The'), ('The', 'man'), ('man', 'said'), ('said', 'something'), ('something', '.')]\n",
      "['AT', 'NN', 'VBD', 'PN', '.']\n"
     ]
    }
   ],
   "source": [
    "sent = \"The man said something .\".split()\n",
    "bs = bigrams(sent)\n",
    "print bs\n",
    "ts = [pmax(bgs[b]) for b in bs]\n",
    "print ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "5b8a57fe",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def tagger1(sent):\n",
    "    bs = bigrams(sent)\n",
    "    ts = [pmax(bgs[b]) for b in bs]\n",
    "    return zip(sent,ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8d1b171a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<font size=-2>The</font> <font color='blue' size=+1>man</font> <font color='red' size=+2>said</font> something ."
      ],
      "text/plain": [
       "<IPython.core.display.HTML at 0x11244e10>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(stags(tagger1(\"The man said something .\".split())))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4881dfd",
   "metadata": {},
   "source": [
    "# Recursive \"Greedy\" Decoding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40256ea9",
   "metadata": {},
   "source": [
    "Instead of modeling the probability distribution of a tag given previous words,\n",
    "we can also model the probability distribution of a tag given the current word\n",
    "and previous tags.\n",
    "\n",
    "$P(T_i|W_i,T_{i-1})$\n",
    "\n",
    "Let us estimate this probability distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "297d0fa2",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def tbigrams(tagged):\n",
    "    ws = words(tagged)\n",
    "    ts = tags(tagged)\n",
    "    return zip([None]+ts,ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "ca1aeda9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(None, 'The'),\n",
       " ('AT', 'Fulton'),\n",
       " ('NP-TL', 'County'),\n",
       " ('NN-TL', 'Grand'),\n",
       " ('JJ-TL', 'Jury'),\n",
       " ('NN-TL', 'said'),\n",
       " ('VBD', 'Friday'),\n",
       " ('NR', 'an'),\n",
       " ('AT', 'investigation'),\n",
       " ('NN', 'of'),\n",
       " ('IN', \"Atlanta's\"),\n",
       " ('NP$', 'recent'),\n",
       " ('JJ', 'primary'),\n",
       " ('NN', 'election'),\n",
       " ('NN', 'produced'),\n",
       " ('VBD', '``'),\n",
       " ('``', 'no'),\n",
       " ('AT', 'evidence'),\n",
       " ('NN', \"''\"),\n",
       " (\"''\", 'that'),\n",
       " ('CS', 'any'),\n",
       " ('DTI', 'irregularities'),\n",
       " ('NNS', 'took'),\n",
       " ('VBD', 'place'),\n",
       " ('NN', '.')]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = brown.tagged_sents()[0]\n",
    "tbigrams(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "022438e8",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[((None, 'The'), 'AT'), (('AT', 'Fulton'), 'NP-TL'), (('NP-TL', 'County'), 'NN-TL'), (('NN-TL', 'Grand'), 'JJ-TL'), (('JJ-TL', 'Jury'), 'NN-TL')]\n"
     ]
    }
   ],
   "source": [
    "bgs2 = Conditional()\n",
    "bs = [(b,t) for s in brown.tagged_sents() for (b,(w,t)) in zip(tbigrams(s),s)]\n",
    "print bs[:5]\n",
    "bgs2.train(bs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "abe256fc",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'DTI': 1.0}"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bgs2[('VBD','some')]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44a6654f",
   "metadata": {},
   "source": [
    "Given this distribution, we can now attempt to \"decode\" an input string.\n",
    "\n",
    "A simple attempt is the following:\n",
    "\n",
    "We start off with an emtpy tag (`None`) for $T_{-1}$ and then update\n",
    "our estimate for the current tag using $\\arg\\max_{T_i} P(T_i|W_i,T_{i-1})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "e3984584",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def greedy_decode(words):\n",
    "    tag = None\n",
    "    result = []\n",
    "    for w in words:\n",
    "        ntag = pmax(bgs2[(tag,w)])\n",
    "        result.append(ntag)\n",
    "        tag = ntag\n",
    "    return zip(words,result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "82601d46",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('The', 'AT'),\n",
       " ('man', 'NN'),\n",
       " ('said', 'VBD'),\n",
       " ('something', 'PN'),\n",
       " ('.', '.')]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "greedy_decode(\"The man said something .\".split())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21c59cca",
   "metadata": {},
   "source": [
    "However, this kind of \"greedy decoding\" isn't really a good way of doing things.\n",
    "\n",
    "What we really want to know is one of the following:\n",
    "\n",
    "- what is the tag sequence that maximizes $P(T_1 ... T_n|W_1 ... W_n)$\n",
    "- if we average over all possible tag sequences $T_1 ... T_n$ weighted by their conditional\n",
    "  probabilities $P(T_1 ... T_n|W_1 ... W_n)$, what is the marginal distribution of\n",
    "  each $T_i$?\n",
    "\n",
    "These are different questions. The correspond to \n",
    "\n",
    "- Viterbi decoding \n",
    "- the forward-backward algorithm\n",
    "\n",
    "respectively.\n",
    "\n",
    "We will cover these algorithms in more detail in the next lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b7977b7",
   "metadata": {},
   "source": [
    "# The TnT Tagger"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "408bcf35",
   "metadata": {},
   "source": [
    "The TnT Tagger is a widely used Hidden Markov Model Tagger developed by Thorsten Brants.\n",
    "\n",
    "It uses a Hidden Markov Model composed of four components, connected via smoothing.\n",
    "\n",
    "The formula for the probability estimation is roughly as follows:\n",
    "\n",
    "$P(T_n|\\hbox{context}) = \\lambda_1 \\hat{P}(T_n) + \\lambda_2 \\hat{P}(T_n|T_{n-1}) + \\lambda_3 \\hat{P}(T_n|T_{n-1},T_{n-2} + \\lambda_4 \\hat{P}(T_n|W_n)$\n",
    "\n",
    "The linear combination of the posterior probabilities is a more general way of handling\n",
    "missing data than backoff.\n",
    "\n",
    "There are some details missing from the above formula related to normalization (these are\n",
    "very important details to make things work).\n",
    "\n",
    "The TnT tagger finds the maximum likelihood label sequence via Viterbi decoding\n",
    "(dynamic programming similar to the edit distance algorithm)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54f6c28f",
   "metadata": {},
   "source": [
    "# Equivalence to Hidden Markov Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "626e2ba6",
   "metadata": {},
   "source": [
    "In a Hidden Markov Model, we think of hidden states giving rise to \n",
    "an observable label sequence.\n",
    "\n",
    "In the case of tagging, the hidden states in question are parts of speech tags (in context),\n",
    "and the observable labels are words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "1070de81",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1816ccd0>"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5aWlpuH//Ptzc3HD9+nUAgJWVFXbt2oX4+Hh07NhR5jq+RV1dHY0aNcLly5dl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\nedzhgDO1tL0AAAAASUVORK5CYII=\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "open(\"hmm1.dot\",\"w\").write(\"\"\"\n",
    "digraph hmm1 {\n",
    "rankdir = \"LR\";\n",
    "subgraph cluster_labels {\n",
    "AT -> NN -> VBD -> PP -> AT2 -> NN2;\n",
    "}\n",
    "subgraph cluster_text {\n",
    "The -> fox -> jumps -> over -> a -> dog;\n",
    "}\n",
    "AT -> The; NN -> fox; VBD -> jumps; PP -> over; AT2 -> a; NN2 -> dog;\n",
    "}\n",
    "\"\"\")\n",
    "!dot -Tpng hmm1.dot -o hmm1.png\n",
    "figsize(12,5)\n",
    "imshow(imread(\"hmm1.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "433769e4",
   "metadata": {},
   "source": [
    "If we use the tags as identities for the hidden states, we obtain this\n",
    "Hidden Markov Model corresponding to a bigram tagger."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "cbb3fff2",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x18a25dd0>"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LkZaWBqFQiIsXL+Lll19GcHAwurq68M033+DcuXMICQkZnCGRx+Nh8uTJEAgE+NOf/oQ/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\n9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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "open(\"hmm2.dot\",\"w\").write(\"\"\"\n",
    "digraph hmm2 {\n",
    "rankdir = \"LR\";\n",
    "subgraph cluster_states {\n",
    "AT -> NN -> VBD -> PP -> NN;\n",
    "PP -> AT;\n",
    "}\n",
    "AT -> the;\n",
    "NN -> fox;\n",
    "NN -> dog;\n",
    "VBD -> jumps;\n",
    "PP -> over;\n",
    "the [shape=record];\n",
    "fox [shape=record];\n",
    "dog [shape=record];\n",
    "jumps [shape=record];\n",
    "over [shape=record];\n",
    "}\n",
    "\"\"\")\n",
    "!dot -Tpng hmm2.dot -o hmm2.png\n",
    "figsize(12,5)\n",
    "imshow(imread(\"hmm2.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afbd27ef",
   "metadata": {},
   "source": [
    "So, in this equivalence between n-gram taggers and Hidden Markov Models, we view...\n",
    "\n",
    "- each tag becomes a hidden state\n",
    "- words are the symbols emitted from each state\n",
    "\n",
    "Note that this is an odd kind of model, because the \"hidden\" state isn't really hidden\n",
    "at all, it's the label sequence we want to infer based on the word sequence."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63afed5e",
   "metadata": {},
   "source": [
    "For a trigram tagger, the hidden states become pairs of tags, representing the two previous tags, and state transitions are constrained so that \"(U,V)\" can only transition to \"(V,X)\"."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "077802c7",
   "metadata": {},
   "source": [
    "Of course, these n-gram hidden states are really just a finite state\n",
    "approximation to a natural language grammar expressed using the tags\n",
    "as non-terminal symbols, and using a simple probabilistic model\n",
    "for the non-terminal to terminal mappings."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c986bb38",
   "metadata": {},
   "source": [
    "# Weighted Finite State Transducers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb20634",
   "metadata": {},
   "source": [
    "A more general model in which the \"hidden states\" actually deserve their name is a\n",
    "*transducer*. In a transducer, each hidden state has both a distribution of\n",
    "input symbols and a distribution of output symbols.\n",
    "\n",
    "This might make a big differnce, since the statistics of tags and words may depend on the position in a sentence. That is, there might be multiple \"AT\" nodes for different positions\n",
    "in the sentence.\n",
    "\n",
    "The usual way of representing this is as *weighted finite state transducers*.\n",
    "In a weighted finite state transducer, we put input and output symbols on the\n",
    "edges, not the states.\n",
    "\n",
    "Here is a simple illustration of this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "5888fa74",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16d308d0>"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9/SESiZCbm4ucnBzcvn0bV65cwa+//gp9fX34+voiODgYXl5eLXZR9JVr6SYA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\neIAyxlhAPEAZYywgHqCMMRbQJyre+PrCrwy2AAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "open(\"hmm3.dot\",\"w\").write(\"\"\"\n",
    "digraph hmm3 {\n",
    "rankdir = \"LR\";\n",
    "state -> state [label=\"AT -> The\"];\n",
    "state -> state [label=\"AT -> a\"];\n",
    "state -> state [label=\"NN -> fox\"];\n",
    "state -> state [label=\"NN -> dog\"];\n",
    "state -> state [label=\"VBD -> jumps\"];\n",
    "state -> state [label=\"PP -> over\"];\n",
    "}\n",
    "\"\"\")\n",
    "!dot -Tpng hmm3.dot -o hmm3.png\n",
    "figsize(12,5)\n",
    "imshow(imread(\"hmm3.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f221ba1f",
   "metadata": {},
   "source": [
    "We can now introduce more complicated state structures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "636c4f11",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1b2fe210>"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YiouLIx0dHVq6dCm5uLjUO9KbPXs275WWllbjPJvNpps3b5KZmRlvBPfnn3/W\n2Z+joyP179+fiIjS0tJIQUGBoqOjeeezs7NJVVWVli1bRkREv/76K1laWtKQIUNEPmL+l/z8fHJ0\ndKSwsLBGXf/48WOaNm2akFW1DpriI8xITwyUlJTg2bNn+OGHHxp8bUBAAHR1dWFlZSUCZXWzbt06\n5OfnY+fOnXW2MTQ0hIODA65evYqEhIR6+7t16xbv9e+ztOrqauTn5+PKlSv45ptv4OrqisTERIwY\nMQL37t3D2rVrBdJKRGCz2XxrFpWUlCAlJcWbdTY3N0deXh7ev38PU1NTgfptKqqqqlixYgW2bdvW\nqEmNbt26IS4uDoWFhSJQ9/XCmJ4YyM/Ph7y8PLp06dKg69LS0rBx40bMnz9fRMrqplOnThg7dix2\n795dZxsWi4V169ahpKTki1l/c3JyeK8+ffoAADZu3AgzMzMsWrQI3bp1w+HDhxEREYFbt27B1tZW\n4FluRUVFdO/eHcuXL0dqaipKS0tx4sQJlJSUYODAgUhJScG6devw559/Yu3atVi5ciVflm9RYmlp\nCQCNqm2rrq6OPn36wNvbW9iyvm6EN+AUDAmElDj+/v60cuXKBl3D5XJpwYIF9PPPP4tIVU3+e3tL\nRBQeHk4sFqvO29t/+e233whAgycy5s6dS0ePHm1Uvd3/3t5yuVzasWMHSUlJ8W6NWSwWDRs2jEpK\nSni3tfn5+ZSTk0P9+/cnW1tbvvckSlJSUkhfX79RVdauXr1KQ4YMEWoKq9ZAU3yE2YYmBnx9feHo\n6NigaxISEvDmzRuxrkGbOHEi3zKOgQMHYvv27SgoKOBbF7hmzRq+W8l58+ZBWloa7du3b1C8xox+\n/mXSpEkoLS0F8HnEuXz5cpiZmSE8PBzl5eUwMjLC2LFjkZWVBScnJwwaNIi31OfPP//E8+fPkZ2d\nDV1d3UZrEBRdXV38+OOPOHfuHH777bcGXWtvb48NGzYgMTGRSRsmJFj/55riC/h/a6q+Fqqrq9G7\nd29cv34dRkZGAl/n7u6O3r17Y/bs2SJUxyAuMjMzMW7cOFy7dq3Bs8ZLlizB8OHD4erqKiJ1LY+m\n+AjzTE/EhISEoH379ujevbvA17x+/Rr379+Hg4ODCJUxiBMtLS1MnDgRS5cuRUVFRYOudXV1RUhI\niIiUfX0wpidibt++DRcXF7Rp00ag9lwuF5s3b8aECROYEpqtCBaLhYULFyIlJQXh4eENurZXr16I\njo7+qu44Z0hVAAAgAElEQVSQRAnzTE+ElJaW4vnz5zhw4IDA18TExCA1NRWenp6N3qPbnKioqMCn\nT59QWFiIwsJClJeXo6KiAhUVFXx/xHJycpCRkYGioiKUlJSgrKyM9u3bo127dk3OMN1ckJeXx4YN\nG+Dt7Q1ra2uBr+vUqRNUVVURFBSE4cOHi1Dh1wFjeiIkOzsbcnJyDXqW5+Pjg1mzZkFRUVGEykRH\nQUEBwsLCEB4ejhcvXvCWkHTo0AHq6upQVVVF+/btoaKiwpc5urS0FBUVFcjLy8PHjx+RlZUFNpsN\nBQUF9OrVC2ZmZrCwsICFhUWL/dkAn/cs//3333j37p3A6f3btGkDa2trHD9+nDE9IcCYnghJS0uD\nkZGRwGnhc3Nzce/ePZw/f17EyoRDSUkJ0tPTkZSUhIcPH+LFixfIzc1Fhw4dYGpqiokTJ8LExAT6\n+vqNGq3l5uYiMTERr1+/RmxsLLZt24bc3FxoamrC2NgY1tbW0NPTQ+fOnaGkpCSCdyh8VFRU4Orq\niiVLlsDX11fgxx6Ojo7YtWsXCgoKRJpw4muAMT0REhwcjKFDhwrcfuvWrRgyZEiDFzGLm+joaFy4\ncAGPHj2CkpISzMzMMHToUEyZMgUaGhro1KmTUFJfqampQU1NDYMHDwbwOe1VXl4esrOzkZycjDt3\n7uDly5eorKzEsGHDMH78eJiYmDS59oiomTx5Mv755x88evQIdnZ2Al1jYGCALl26IDY2tkG/Uww1\nYZasiAgiwsiRI7F161aBtj2lpqZixIgR8Pf3F8vasYZQVlaGrKws3L17FxcvXkRubi5GjBiBqVOn\nol+/fhI3mRcvXuDs2bPw9/eHmpoaxo4dC0dHR+jq6kJBQUGi2urizp07uHTpEjw9PQW+Zvv27VBS\nUsKiRYtEqKxl0BQfYUxPRKSkpMDV1RV3795Fhw4dvtj++PHjiIuLE2od1aby6dMn+Pj44Pr162Cz\n2bC1tcXQoUNhZGTU4IXI4qCkpASxsbF4+vQp7ty5Aw6Hg/Hjx8PNzQ1t27aVtDw+KioqMHnyZOzZ\nswd6enoCXfP69Wvs2LEDXl5eohXXAmiSjzRlK0hjkEBIieDh4UGTJk0SqC2Hw6Fvv/2W3rx5I2JV\nX4bNZlNWVhbt3r2bDA0NadiwYfTgwQPicrmSltYguFwuPXz4kEaOHEk9evSgbdu2UWpqKlVWVkpa\nGo8jR47QyJEjicPhCNQ+Pz+fnJ2dmS1pxGRZaXYQEe7cuYMRI0YI1D44OBgAmlQhrakQEV68eIGf\nf/4Z06ZNQ3FxMU6dOoWgoCDY2Ni0uOUzLBYLQ4cOxfXr13HlyhXIyclh6dKlmDt3Lu7duydpeQA+\nLzqOjo4WOMNy27Zt0bFjRzx69EjEylo5QrNeAZFASLHz8eNHMjY2pszMzC+2ZbPZZGFhQadPnxaD\nstrjZ2Zm0tSpU0lNTY327dtH5eXlEtEiDh4+fEimpqY0aNAgCgsLk/jIz8vLi5YuXSrwaO/gwYM0\ndepUEatq/jTFRxjTEwHR0dHk6OgoUNvQ0FDq27cvFRcXi1gVPxwOhyIiIuiHH34gOzs72rt3r0Am\n3RooLy+nW7du0bRp02jUqFF07tw5qq6ulogWNptNzs7OVFBQIFD7mJgY6tChg8DtWytN8RHm9lYE\npKenC5yo8u7du1i4cKFYH7RzuVysXLkSjo6OGDRoEG7duoWffvoJWlpaYtMgSeTl5eHs7IyTJ0/i\n4MGDOHbsGPr06YOoqCixa5GWlsaAAQMEXpvZu3dvqKur48WLFyJW1nphTE8EREREYNiwYV9sR0QI\nCwsTW/aM3NxcbN++Hba2tmjXrh0SEhIwZ84cgRfItjakpKSgq6uLgIAAHDhwADt37sTkyZNx586d\nRtW1aCzjxo3Dtm3b8PHjxy+2ZbFYmDVrFp4+fSoGZa0TxvREQGxsrEBZVYKDg9GuXTuBlrQ0BSLC\n1atXYWxsjJSUFPj4+GDt2rXo1KmTSOO2FKSlpeHg4AAvLy8sXrwYq1evhpubG96/fy+W+KampjAx\nMcHFixcFaj9t2jS8ePFC4JKZDPwwpidkCgsLkZWVxZdkszbYbDb++OMPODs7i2xDPZfLRWRkJGbN\nmoVz587Bx8cHBw8ehJqamsQXFDdH2rRpAysrK9y7dw/ffPMNZs+ejZ07d4o8tbyUlBS2bt0KPz8/\ngercduzYESUlJYzpNRLmN1/I3Lt3D9ra2l8cvcXExCAmJgYuLi4i0VFaWoply5Zh8eLFmDlzJk6c\nOIGhQ4e2uKUnkqB9+/b4+eefcebMGQDAqFGjcPbsWZHGNDIygoqKChITE7/YVlZWFu3bt/9iXRKG\n2mFMT8jcunULQ4cO/eJIys/PD0uXLkW7du2EGr+8vBw3b97Et99+Cw6Hg+vXr8PW1rbFbMhvTmho\naGDFihU4c+YMLl68iEmTJuHJkyeNqmwmCGPGjMGePXu+uNNAWloaJiYmPFNmaCDCmkIWFAmEFBsl\nJSXUu3dvioqKqrdddXU1jR07lj58+CDU+BkZGeTm5kZ2dnb0+PFjZuW+ECkpKaHr16/T4MGDacGC\nBfTx40ehx8jIyKBu3boJtDPnwYMH1LVrV4HX97U2muIjzEhPiKSkpEBaWhrGxsb1tktKSkKbNm2E\nliKovLwc/v7+mDBhAvr16wd/f39YWloKJdMJw2eUlJQwevRo3L59G1JSUpgyZQoePXrU4NTv9aGt\nrQ0XFxecOnXqi6M9U1NT5OXlfbHeMENNmNRSQiQpKQlDhgz54q3t+vXrYWdnBxmZpv/4S0pK8Msv\nvyArKwv79++HiYkJY3YiRFVVFXv37kV4eDg2bdqEbt26Yffu3ZCXlxdK/+7u7pg6dSry8vLqnV1v\n3749hg8fjoiICBgYGAgl9tcCM9ITIq9fv4atrW29bTIyMnDt2jWhFP2Jjo7G8OHDoaioCG9vbwwY\nMIAxPDEgIyMDKysrXL9+HW3btsXAgQMREREhlOxBXbp0QY8ePfDmzZsvtp05cyYiIyOZWdwGwpie\nEImPj//iToxbt27BycmpSTnzqqurcejQIfzyyy9Ys2YNduzY0aJTqLdUZGVlsXnzZuzcuRPr16/H\nli1bUFlZ2eR+x40bh2PHjn2xnbOzM1JSUoQS82uCMT0hQUTIycmpN89cdXU1goKCsGbNmkYvHamq\nqsKmTZtw8OBBeHp6Yty4cUK5TWZoHLKysnBycsLx48dx48YNzJ8/H58+fWpSnwMHDsSTJ0+QnJxc\nbztFRUXIysqirKysSfG+NhjTExKpqakAAGVl5TrbFBcXo7i4GObm5o2K8f79e3z//ffIysrCw4cP\nG1RLl0G0aGho4P79++jSpQsmTpyIZ8+eNbovTU1NODs74+DBg1+8Ze7WrVuTYn2NMKYnJAICAtCz\nZ896bzOfPHnSoMpo/6WkpARTp06Fjo4OPDw8RL51jaHhKCgoYOPGjZg7dy7c3NwQFxfXqH5YLBaW\nL1+Ou3fvIjc3t962pqam8PHxaVScrxXG9ISEn58f+vfvX+d5IsK+fftgY2PT4L5fvXqFMWPGwNXV\nFdu2bWN2VTRzJkyYgAMHDmDu3Lnw9vZuVPKCzp07o1+/foiJiam3Xe/evXHv3j3muV5DEM5SQcGR\nQEiRU1xcTBoaGvTq1as628TExJC6unqD86BlZGSQiYkJXb58+atdiNoS4XK5lJaWRn379qXz5883\nqo+bN2/SsmXL6m1TXl5OGhoaFBkZ2agYLZWm+Agz0hMCiYmJUFBQqHO9FBHB19cXbm5uDSqoEx0d\njYkTJ2LVqlVwdXVlkgS0IFgsFrp06QIfHx94eHhgz549KC8vb1Afffr0QUREBAoLC+tsIy8vDwcH\nB4SFhTVV8lcD81ckBN69e4ehQ4fWmS2ltLQUISEhcHd3F7jPlJQUzJ49GytWrICbm5uwpNaKq6sr\njIyMEBoayjuWnZ1dY6Kke/fu+Oabb/jWhbm5uWHChAki1VcfS5YsESh3oaQwNDTEhQsXcPPmTRw+\nfLhB13bp0gVdunSBt7d3ve1cXV3x9OlTke0Jbm0wpicE4uPj611s/OHDBygrK6Nr164C9ZeUlIQ5\nc+Zg2bJl+Pbbb0W+4DgrKwvx8fHYuXMnb7aQzWbXWDKRnJyMR48e8f0RZmVlISsrS6T66iM3N1fk\nqZ+airq6Ok6fPg0/Pz/s27dP4K1r0tLSmDFjBk6dOlXvKNHBwQGZmZkCpaViYExPKLx58wbW1tZ1\nng8ODsbgwYMF6is7OxuzZ8/G+PHjMXnyZGFJ/CLy8vK4e/fuFyuF6erqwsvLC0VFRY2OtWrVKty6\ndQtVVVWN7qOloa2tjZMnT+L69esCLTz+F3t7ewCodya4bdu2UFFRadJn8jXBmJ4QKCoqqjNFFBHh\n0qVLAq3NKykpwa+//gonJycsXLhQZMlFa8PAwACmpqZYt25dvSOGXbt2ITIysknpypOTkzF9+nQY\nGRlh3bp1ePLkCT5+/PjFNWlcLhd3796FsbExlJWV8cMPPyA/P593vrq6GgcPHoS+vj7k5eXRrVs3\n7Ny5E+Xl5eByuQgMDORdO2fOHIwcOVKsZTe1tLRw4cIFXLlyBefPnxfodlROTg5ubm5fLPuoq6uL\npKQkYUlt1TCm10QKCgoAoM4N54mJiXj79i369OlTbz+VlZX4+eefIScnh59++knoOr9E+/btsWDB\nArx8+RIPHz6ss52lpSXs7e3h7u7e6DoSHh4e8Pf3x5w5c3Dp0iU4OzvDyckJK1aswIsXL+o0v+Tk\nZCxcuBDy8vLw9PSEmpoaX83YM2fOYM2aNRg9ejROnz6NiRMnYuPGjTh69ChSU1OxePFitGnTBp6e\nntDS0pLIw/9OnTrhwIED2LJlC65duybQNU5OTrh//369bfr374/AwEBhSGz9CGcCWXAkEFKkXLx4\nkZYuXUpcLrfW8zt37qSZM2d+sR9PT09ycnKSSM3ZwYMHk7W1NXG5XDI3N6fRo0dTampqjc8KAGVm\nZpK/vz8pKSnRiRMnyMrKiqysrGrtl8vl0vPnz3mv2mrMVlVV0ZUrV8jExIQAkJSUFB04cKDW/m7f\nvk1t2rTh5SssKioiGxsb0tPTIyIifX19mjJlCt9nsXDhQurevTvduXOH2rRpQ8+fPyeiz8uM7O3t\nSUdHp+E/MCGQnJxM33zzDb1+/fqLbYuLi8nBwYFiYmLqbBMaGkrDhg2r8/ewtdEUH2FGek3k1q1b\nMDIyqnXBcHl5Oe7cuYMff/yx3j78/Pxw7tw5eHh4CC1FUWNgsVj466+/EBwcXO+owcrKCiYmJvDw\n8OC7vfxfqqurMWDAAN4rOzubd47L5SI6OhobN27Enj17kJ6eDkNDQ6xZs6bOSaHy8nJUVVWhZ8+e\nAD7vPf1vTsL09HTo6enxfRa9evVCZmYmKioqUF1dDX19fQCfd09IcleLrq4u1qxZAycnJ0RHR9fb\ntm3btrC3t8fOnTvrbNOjRw+kp6c3+0mdZoEQzVcgJBBSZHA4HNLW1qbg4OBaz797945sbW3r7eP1\n69fUtWtXun//vigkCsS/Iz0iok+fPpGNjQ21b9++zpEeEVFgYCDJy8uTjIxMnSO9urh69SpZWlqS\nvLw8qamp0ejRoykwMPCLmZ4DAwNJUVGR/Pz8iM1mU2ZmJllYWPBGehYWFjRq1CgqKioiDodDJSUl\nNHHiRBowYADdv3+flJSUeNdmZ2eTpaWlxEZ6/3LhwgUaNWoUFRYW1tsuISGBdHR0KDs7u842jo6O\ndObMGWFLbJY0xUcY02sCaWlpJCsrS7m5ubWe9/X1pTVr1tR5PZvNpgkTJtDp06dFJVEg/mt6REQn\nTpwgAPWaHpfLJRcXFwLQYNOzt7enGTNm0JkzZyghIUHgtPbZ2dlkZmZGXbt2pZkzZ5KLiwupqanx\nTC84OJjU1NTI1taWZs+eTfb29tShQwe6fv065eTkkLm5Oe/a0aNHk7q6OnXp0qVB2kXB+vXracaM\nGVRWVlZnGy6XS6NHj6br16/X2Wbfvn00b968r+IWtyk+wtzeNoG3b9+ie/fudWa4vXXrVp1JRblc\nLjZs2ABFRUWRLz7+EoqKinyJEqZPn44+ffrUyBijrKzMu3X8d1O8mppag3P5BQYG4uTJk5g6dSp6\n9uwp8DpEDQ0N3LhxA4aGhrh37x6srKzg5OTEK3o0bNgwXLp0CRUVFbh58yaKiopw7tw5uLi4QF1d\nHb6+vjAwMMC9e/cwYMAAWFhYoGPHjg3SLgpWrlyJ+Ph47N+/v85JHBaLhXnz5iE4OLjOfpydnREf\nH4/S0lJRSW0dCM97BUMCIUXGwYMH69wb+enTJzI3N6eUlJRaz1+7do1MTU0pNTVVlBIZ/oO/vz9l\nZmZSSUkJ3bp1izp37lzvSFyc5OTk0JgxYygoKKjONh8+fKCRI0fWO5Kzt7en5ORkEShsXjTFR5iR\nXiMhIiQkJMDJyanW8wEBAejYsSO6dOlS41x1dTW2bduGGzduCLxLg6HpbNy4Ebq6ulBVVcWYMWMg\nIyODdevWSVoWgM+7Nn7++WfMmDEDOTk5tbZp164dlJWV+bYL/i+6urrIy8sTlcxWQb2ml56ejuHD\nh6NPnz7o27cv/v77bwBAfn4+HBwc0KtXLzg6OvJlit2yZQv09fVhaGiIO3fuiFa9BOFwOHj//j0s\nLS1rnONyubh8+TK+++67GkkCKisrMX/+fIwcORLa2trikssA4OzZs9i1axeWL1+Obdu24f79+2jT\npo2kZfEYNmwYFi5ciJ9++gnFxcU1zsvJycHBwQGbNm2q8zbYxMTki7PBXzssquunh89borKzs2Fq\naoqSkhKYmZnB19cXx48fR6dOnbBy5Ups27YNBQUF2Lp1K+Li4jBlyhQ8ffoUGRkZsLe3x9u3b/n+\n8FksllAKqEiaiooKTJkyBRcvXqyRrj07OxsODg4IDg6usSzi9OnT2LZtG8LDw1t9AW4iQnx8PF6/\nfo309HSkpKTwfqdyc3PBZrMhLS2Ntm3bgsVioW3bttDU1ISmpiZ69eqFfv36oW/fvvVmo25tcDgc\nzJ07F3Z2dpg2bVqN89nZ2dDX10d0dHStmbPv3buHixcvwsPDQxxyJUZTfKTe4gr//gICn9cKGRkZ\nISMjA9evX+c9UJ05cyZsbGywdetWXLt2DZMnT4asrCz09PTQs2dPRERECLzvtCVRUlICOTm5WtM9\npaSkwMDAoIbhffjwAefOncONGzdajeFxuVxkZmbi/fv3eP/+Pd68eYOEhATk5+ejqKgIKioqUFNT\ng6amJnr27AkzMzOoqKhASUkJ0tLS4HK5vM30ZWVl+PTpEwoKChATE4O7d+8iLy8PMjIyaNu2LTp0\n6IDevXtDX18fnTt3RpcuXdChQ4dWlVRVWloav/76K6ZOnYo+ffrUSEyrqakJJycnPH78uFbT09HR\nQUxMDLhcLpOKrA4EriiTkpKCqKgoDBo0CDk5OdDQ0ADweUbt32cQmZmZfAbXuXNnZGRk1Ohr/fr1\nvK9tbGwalU1Y0jx+/Bi6urq1/sFFRkbW+qzv999/h4ODA7p16yYOiSIlNTUVV69exdWrV5GRkYGe\nPXuif//+GDRoENzc3KCkpARFRUXIy8s3esE1m81GeXk5KioqUFFRgYKCAkRERODKlSuIjIxEaWkp\nDA0N4ebmhtGjR7eaFPq9evXC6tWrsXTpUvj6+taYYV6xYgW8vLwwbdq0Gr9/2traKCsrQ2JiIm8h\ndmsgKCgIQUFBQulLINMrKSnB+PHjsW/fvhq3GiwWq97/tLWd+6/ptVQCAwNhampa6/t7/PgxVq9e\nzfueiHD79m2EhYVh06ZN4pQpFDgcDjIzMxEbG4uQkBC8evUKhYWF6NevH1asWAEbGxuR3ILKyMhA\nWVmZ13eXLl1gbGyMuXPnAvi8rzkoKAi3b9+Gh4cHunTpAktLS5ibm0NfXx9qamotchTIYrEwfvx4\n3L9/H2fPnsXSpUv5zpuYmCAzMxNsNrtGUgoVFRUYGBggJCSkVZne/w6ONmzY0Oi+vmh61dXVGD9+\nPKZPn46xY8cC+Dy6y87OhqamJrKysqCurg7g89D6v9tg3r9/Dx0dnUaLa84EBgbWmjyzoKAAaWlp\n0NLS4h0rLCzEvn374OXlBTU1NXHKbBJVVVW4d+8eTp06hZiYGFhZWWHs2LGYNWsWNDU1oaKiIlF9\nPXr0QI8ePTB79mx8/PgRmZmZePbsGQ4cOIC3b99i4MCBmDlzJiwsLFpkEfRVq1bBzc0NgwYNwqBB\ng3jH5eTkoKGhgWfPntX66MjGxgZBQUGYM2eOOOW2HOpbz8Llcmn69Ok11qK5u7vT1q1biYhoy5Yt\ntGrVKiIiio2NJRMTE6qsrKSkpCTq3r17jTVFXwjZIvjw4QMpKChQenp6jXPHjh2j6dOn873v48eP\n008//SROiY2mpKSEXrx4QevXr6chQ4aQlZUVHTx4kIqLiyUtrUGkpaXR1q1bydLSkhwcHGjPnj0U\nHR3d4t6Ht7c3DRkyhPLz8/mOHz16lNzc3Gq9Ji4ujszNzVvce20ITfGReq98+PAhsVgsMjExIVNT\nUzI1NSU/Pz/Ky8sjOzs70tfXJwcHB75iN5s3b6YePXqQgYEB+fv7C1VscyE4OJi6du1aY/sUh8Mh\ne3t7vkIw7969oz59+lBcXJy4ZTaIoqIi8vDwIHt7e3JxcSEvLy969epVrZlRWhKlpaUUHR1NXl5e\n5ObmRg4ODnTo0CH69OmTpKUJBJvNpvnz55Onpyff8YSEBFJSUqKsrKwa13A4HLKysqK3b9+KS6bY\nEZnpiYLWYHqenp40derUGsdTU1OpR48evP/KVVVVNHXqVPrzzz/FLVEgKisr6c2bN7R69Wrq0aMH\nffvttxQeHt6q926+fv2apk+fTj179iR3d3d6+/YtlZaWSlpWvaSmppKlpSV9/PiR7/jgwYPpwoUL\ntV4zd+7cOhNhtAaa4iPMnHYDISK8ffu21hnnN2/ewNzcnJfuKCoqCvn5+Vi+fLmYVX6ZBw8eYPbs\n2Vi0aBE6deqES5cuwcfHBxYWFi3y4b+gGBoa4uTJk7h9+zYMDQ3x22+/Ydq0aTh9+nStC4KbAzo6\nOhgzZgzmzZvHV9/W3d0dISEhtWZgNjMzQ3x8vDhlthyE572CIYGQQqWyspK+++47SkpKqnFu69at\nvIwpHA6HpkyZQr6+vuKWWCdlZWUUEhJClpaWZGhoSN7e3q16VCcocXFxNGLECDIwMCAPDw8qKCho\ndjWGKysrqX///nTz5k2+4yNHjqz12V1YWBgtWLBAXPLETlN8hBnpNZB/14zp6enVOPfq1StYWFgA\nAO7evYvU1NRmUZ6wsrISJ0+exJgxY3Do0CGsWrUK4eHhmDhxYqse1QmKkZERbt++jTNnziApKQlu\nbm749ddf8fLlS75yl5JETk4Ohw8fxpEjR/g0qaurIy0trUb7Dh061Khmx/AZxvQaSEVFBRQUFGqY\nxb97cTt16oSysjL88ccf+OWXX/gy+4obLpeLoKAgGBgY4Pjx4zhy5AjOnz+PMWPGSHy5SXODxWLB\n3NwcW7du5S0ItrOzw6JFi1BQUNAstk4OGDAAHTt2xJEjR3jHBg8ejDNnztRo26lTJ+Tn5/NquDD8\nfxjTayB5eXm1rvy/fv069PT0oKKigocPH0JbWxvffvutBBR+Li5+7tw5uLq64syZMzh69CgCAwNr\nHZ0y1ERRURGrVq1CbGwsevfujRkzZmDRokUICgqSaNlKGRkZLFmyBJs2beKN4szNzXH58uUatXRV\nVFTQpUsXoe1iaE0wptdAIiIieDUa/svp06dhZWUFGRkZHDlyBD///LPY9z4SEQICAmBubo5Lly5h\n7969OHz4MOzt7cVaTrK1oK6ujiVLlsDHxwdjx47F0qVLMXr0aIneNpqYmGDmzJk4deoUAMDY2BgV\nFRV8VeGAz3t4zczM8ODBA0nIbNYwptdAwsPDoaury3csPz8fT548gbW1NW7fvo2SkhIYGxuLTROH\nw0FERAQWLlwIT09P/PXXXzh//jz09PRqZIBhaDjy8vJwdHTEkydP8N1332Hx4sVYsWIFnj17JlDt\nWmHCYrGwatUqhIWFITc3F3Jycpg5cybu3LlT4xZ80KBBCA0NRXV1tVg1NnuENZsiKBIIKVTMzc0p\nNDSU71hQUBCZmZlRUVERDRgwQKwztmVlZTRv3jwyMTEhPz+/Zr/mrDVQVFREN27coH79+tGMGTPE\nvvOBy+XS1q1b6fvvvyciooyMDHJycqqho7i4mLp161brzqGWTlN8hBnpNYCCggKkp6fXyIYcHR0N\nV1dXPH78GOrq6hg9erTItbDZbPj4+MDJyQmKiooIDAzEiBEjGlyvgqHhKCsrw8XFBY8ePULXrl1h\na2sLLy8vlJSUiCU+i8XC9OnT4efnh7CwMGhra0NBQaFGOc62bdtCX1+fKQv5PzCm1wBiY2PRvn17\nXo7Bf3n+/DnGjx+Py5cvY9WqVSJ/lpeVlYUJEybg4sWLOHToELZv396iEhm0FlRUVLB+/Xp4e3vj\n2bNnsLW1RUhIiFhmerW1tbF//34cPXoUbDYbpqamePr0aY125ubmjOn9D4zpNYC4uDiYm5vzZewg\nIuTl5aGyshLJyckwMTERWfyqqio8evQIM2fOhL6+Pk6cOIG+ffsyz+0kiLS0NLp3746///4bS5Ys\nwapVq/D333/XWwRdWIwfPx7Z2dlIT0/HwIEDcfny5RptLC0tERcXJ3ItLQnG9BpAbGwshgwZwncs\nMTERCgoKWL9+PRwdHdG+fXuRxK6ursbmzZuxYsUK/Pbbb9i6dWuryb7cGpCWlsb06dPh7e2N169f\nY8qUKXj37p3I444aNQqbNm1C37598fTpU+Tm5vKd79WrF5KSkkSuoyXBmJ6AVFdXIzU1lbfj4l/O\nnjen+a4AACAASURBVD0LaWlpREREYObMmSLZ4ZCTk4OpU6ciKSkJT548wbBhw5hU4M0UXV1dHD58\nGNOnT8eYMWNw8eJFka7tGzt2LAICApCTk4Pu3bsjICCA77yKigpyc3ObxeLq5gLzlyMgJSUlKC4u\nRr9+/XjHuFwuzp07h4KCAsyfP5+XQl+YvH79GtOnT8fAgQOxf/9+xuxaCJMnT8bZs2fh4+ODtWvX\n8iUKECZaWlpYvXo1PDw8MGHCBAQEBPAto/m3QHtqaqpI4rdEmL8gASkpKYGysjJfvYeUlBSkpqai\nqqoK8+bNE2o8LpeLR48eYdSoUfjxxx/h7u4usltnBuEjJSWF/v3749ixY8jIyICrq2ut9WKEwcKF\nC5GcnIwhQ4YgMTGRr+6toqIidHV1mZ0Z/4ExPQEpLS2tsf3sxYsX6NmzJ7p27Sp0Q/L19cWGDRtw\n/PhxjB8/Xqh9M4gPFRUVeHl5YeTIkZg7d269hbobC4vFwujRo3H16lXo6ekhKyuL77yxsTHu378v\n9LgtFcb0BOR/1+cREaKiolBQUICRI0cKbZsXl8vF6dOnsXLlShw4cADW1tZMJpQWjry8PBYvXoxl\ny5Zh/PjxIhl1OTk54dixY+jXrx/CwsL4zhkbG+Phw4di3z3SXGFMT0CioqL4qktxOBzExMSgurq6\n1nKPjeXvv//G5cuX4e/vDwMDA6H1yyB5nJyc4Ovri82bN+PEiRNgs9lC69vAwADW1tZ4/Pgx7t69\ny3eub9++KC8vZ9br/R/MAi8BiYuLg5mZGe97NpuNqKgoLF++XGi3tvv27eMVAxfFpAiD5LGwsICn\npye++eYblJaWYtGiRULpV0pKCps2bYK9vT1KS0uRn5/PexzTrl076OvrIzU1lcm0A2akJzDx8fG8\nUpf/fl9SUoIFCxYIpX9PT08EBATg3LlzjOG1crp164bw8HAEBgZi7969NdJCNZbOnTvD2toaUlJS\n8PX15TtnaWnJJBX9PxjTE4D8/Hzk5eXxmZ6npyfs7e2FUuTay8sLp06dwpEjR2pNW8XQ+tDR0cHR\no0dx9uxZ7NixQ2gZmidMmICOHTvi2rVrfGvzhg0bJpbF0i0BxvQE4NWrV1BVVUXHjh0BfH6ed+HC\nBQwdOrTJ6+Z8fX1x8OBB7N+/XyiF0Tdt2gRtbe1atx5t2rQJhoaGKC4uxrFjx8BiscBisSAlJQVt\nbW3MmzePb+Zv6dKlvDaysrLQ1NSEra0tDh06hE+fPjVZq6B4eHi0ysmcTp064f79+4iOjsbhw4eF\nkgLK1NQULBYLKSkpfJ+lqakpUlJSmtx/a4AxPQGIiYlBnz59eHtcnz59irKyMtjZ2TW5323btuHM\nmTPo37+/MKTihx9+QEFBQY2lEUVFRdixYwfs7Oz4tq/Fxsbi5cuX+PPPP3HlyhWsW7eO7zp5eXnE\nxsYiKioKJ06cQK9evbBixQrMnj1bbKv83dzcEBsbK5ZY4kZZWRmHDh3C+fPnsXv37ibPsHbq1Amu\nrq7Izc3lW5CsqKiI0tLSpsptFTCmJwCxsbEYMGAA7/uAgACoqanByMio0X2+evUKrq6uWLVqVZP6\n+V80NDQwadIknD17ls+UAgMDUVxcDBcXF77Rae/evdG3b19Mnz4dxsbGiImJ4etPSkqK12bEiBE4\nfPgwDh48CH9/f9y4cUNgXadPn8bkyZNx6dIlvHv3rkEzl0VFRUhMTOR9f+PGDb49pmVlZXxabt68\niZiYGMTExCAgIABv3rwBl8tFfHw8/P39ERUVxWtbUVGBGzduoLq6Go8fP4afnx+SkpJ4P7uMjAwE\nBwfj9u3bePDgQa1FeJqKuro6bt++jYcPH8Lb27vJt7o//PADysrK+N6nvLw82Gy22NJfNWuEkM+v\nQUggZJOorq4mR0dHXuHkiooKcnV1pbVr1za6z8rKSnJ0dKRLly6JpNTg48ePSVlZmaKjo4mIiM1m\n05w5c0hLS4vKysqIiOjo0aO8z4LD4dDTp0+pe/futHr1al4/S5YsIUVFxRr95+TkULdu3RpUYvDZ\ns2c0atQoUlRUJD09PXJxcSEfn//H3nmHRXVtffg3wzD0jiMovSPVQrEQRUTFitiwxRaMeqMp6rV7\nLQmxX3uJJrFFY4kFFSwYEY0giCIooFKl9zK0gZlZ3x9ezicKShmKyvs88+icfc7e6wxn1uy99ipn\nqaqq6oPXHjhwoNZzA4CuX7/OvE9KSqrVzuFwyNHRkfT09IjD4ZCuri798ccfZGZmRhwOh3g8Ht27\nd4+IiNLS0ggALVmyhJSVlUlKSoqsrKwoOTmZoqOjqVevXqSgoEBsNpvk5OTIxMSkwffcWJ4/f052\ndnZ07NixZvc1f/58GjJkCPNeJBLR119/TdeuXWt23+2B5uiRjpneBygpKUFRURGT/r2wsBChoaFN\nDjsrLS3FrFmz4OTkhDFjxrRILK2ZmRnMzc0ZA3lpaSn+/vtvrF69GnJycrXOZbFYkJKSgpOTEywt\nLfH9999/sH8NDQ3IysoiOzu7wTL16NEDV65cQUxMDL788kukp6fj66+/hq6uLpYvX44nT540+j7f\nR2FhIfz8/HD//n1UVFRg9erV2L9/P549ewY1NTXs3r271vmRkZF4+vQpHj58CIFAgBUrVjDL+vXr\n1yM+Ph5xcXGYM2eOROV8EzMzM5w7dw6HDh3C/fv3m9XX5MmTERISwixp2Ww2TE1N3/Hh+xzpUHof\noKSkBAoKCowv3v379yEnJ/dO9uSGIBKJsG3bNpSVlWHx4sUtljxAXV0drq6uTO3dy5cvo6qqCl9+\n+eU75168eBEXL17EoUOHwGKxMHPmTGRlZb23/4qKCgiFwnqzNHt6ejKvkydP1mrT19fHunXrcOTI\nEbi4uCA7OxsbN26UeOyyu7s7bGxs0KNHD6irq8Pc3BwuLi4wMTGBgYHBOzuZBw4cgK6uLuzt7eHt\n7Q1/f3/Y29vD0tISW7duxejRo/Hdd9812477IUxMTLBhwwb88MMPtZanjcXCwgKmpqZMASHgtQPz\nrVu3JCHmR02H0vsAxcXF6NKlC4DXoWc7duyAs7Nzk/oKCwvDnTt3cO7cuRatO8tmszF16lQUFRUh\nKCgIGzZswODBg+tUUqNHj8bo0aMxa9Ys/Pbbb7h58yYePHjw3v6fPn2KgoIC9OrVq87258+fM6+8\nvDwAr1NzZWVlISAgACNGjICDgwNCQkLQv39/nD59ulEzGykpqVo2wbp2kuXl5cFmsyElJQUWiwUZ\nGRlIS0szx95O9/TmDFhaWhpCoRDm5uaIjIzEyZMnMXLkSERFRWHu3LkNlrOp9O/fHwsXLsTcuXOb\nnB1FQ0MDdnZ2tWy7FhYWiI2NRXFxsSTF/ejoiMj4AAUFBYwrSXx8PEJDQ+Hp6dnofqKiouDj44N9\n+/bVyrzcUtjY2MDFxQU///wzkpOTsWHDhve6fRQWFuLs2bOMi8rbiMVi5OXl4Z9//sGmTZugoqIC\nb2/vOvuKjY1951hAQAAWL16M3NxcuLm54eDBg3B0dIS5uXmjPw8jIyOcPXsWffr0QWFh4Ts7zk1h\nyZIl2LZtG4qKinDhwgUMGjQIT58+RVZWFpycnODg4AA5OTn4+vo2e6yGMGnSJOTn52PZsmU4cuQI\nZGRkGt3H7NmzMWHCBCQkJMDExAT6+vpQUFBAUlIS7O3tW0Dqj4MOpfcBXr58CTMzMwDAtWvXwOPx\nGr3bWlpaipUrV2Lx4sX44osvWkLMd2CxWFi+fDkGDRoEFRWVepdlNQqOxWKBy+WiZ8+e6Nu3L9Ne\nXl5ey5+Py+XCxMQE/v7+jYocEYlEmD17Nnx8fOoslt4Y5s+fj6VLl+Lo0aOQkZHBpEmTmtUf8Pr+\ndXV1IRQKwePxcPbsWTx69AgzZ85EZWUliAhcLrdVij7VyDNnzhw8ePAA3333HXbt2tXopBZ9+vRh\nwiVNTEwgLS3NpJ/qUHod1MuLFy/g4eEBgUCAoKAgiESiWokHGsLOnTthamqKGTNmtIyQ9eDo6Ii9\ne/dCQ0ODcayuwcnJCVu3bmXey8jIQE9PDwMGDGCW3p6enkyNXykpKSgpKUFPTw8ODg6NjjceM2ZM\nk++jurq6Vh0QHx8f6OnpIS0tDWZmZujduzesrKyY9s2bN9dyMVq6dGktRfvVV1+Bz+fXGuPw4cMY\nNmwYcnNz0bdvXxgbG6Nr164ICAhAbGwshEIhdHR0MGDAgCbfR2ORkZHBrl278PXXX+Pw4cNNCnn8\n8ssvcefOHYwfPx4A4OrqWsv957NEUlvIDaUNhmwW48ePp0ePHlF6ejo5OzuTiYkJCYXCBl//999/\nk56eHr169aoFpfx0KSkpIU9PTzIzM2uR/mtcVtozr169IisrK4qNjW30tU+ePCF1dXUSi8VERPTo\n0SP6+uuvW8RVqjVpzt+sYyPjPRARUlNToaqqiqSkJGRmZmLIkCENtkGlp6dj3bp1OHToUJN2ezsA\nDAwMEB0d3Wq2tPaIjo4ONmzYAG9v70YX+amZ5dc4b1tYWCA/P19isb4fIx1K7z1kZ2dDIBBAVVUV\nFy9eRE5OTqNsOv/9738xbNgwDB48uAWl/LRJSkpiiqm3BNra2q0aR9wUWCwWPD098dVXX+Gnn35q\n1LUaGhowNzdnfjSkpKRARJ91QtEOm957ePr0KdTV1SErK4urV69CR0cHLi4uDbr24sWLCAkJqbMW\n6acKEaG0tBS5ubnIy8tDYWEhysrKUFZWhtLSUhQVFaG0tBREhOrq6loB9goKCuByuZCVlYWcnBxU\nVFSgpKQEFRUVKCsrQ1lZGZ06dYKqqqpE/RvZbDZUVFQk1l9LwWKxMGvWLMyePRs7d+7EggULGvQ5\nyMrKokePHti3bx/i4+NhaGgIaWlp8Pn8Ju0Ifwp0KL338PTpU5iamiIyMhIZGRlwdXWt1yH3TdLS\n0vCf//wHBw8ehJaWVitI2jZUVVUhKioK9+7dQ0REBJ49e4a8vDxUV1dDT08PhoaG0NTUhKamJjp1\n6gQzMzNoaGiAzWZDRkam1peuuLgY5eXl4PP54PP5SE1NRUZGBvPKzMwEEUFNTQ1WVlaws7ODvb09\nnJycmr0b/LEgLy+PjRs3onfv3rC1tYWrq2uDrnN1dcXmzZsRGhoKY2Nj6OrqIjw8HB4eHi0scfuk\nQ+m9h2fPnsHGxgYBAQGwtrZu8K7tgQMHMHHixCY7Mbc3ioqKkJ6ejtTUVMTFxeHly5fIyspCfn4+\nlJSUYGhoCGdnZ0yePBlGRkYwMDCQ+CxCLBYjNTUV8fHxzOu3335jip5raWnB0NAQlpaW0NHRgY6O\nDrS1tVvFJ7I10dfXx7lz57Bx40Y4Ojo2qOC7o6MjZGRkcO/ePUydOhUGBgYIDg7uUHod1KYmK8eo\nUaNw6dIl6OnpNSj90507d3D37l2cO3euFaRsORITE+Hv74+///4bz58/h7KyMnr16oV+/frBzc0N\nSkpKzIvL5ba4PGw2G/r6+tDX12d8DkUiEUpLS1FSUgI+n4+0tDQ8fPgQp0+fxvPnz6GgoIC+ffvC\nzc0Nffr0+SiWsQ3B2dkZ3bt3x7x583D06NEP5hqUl5fHiBEjmIpohoaG+PPPP1tD1HYJ63/bv603\nIIv1UVRbLyoqgouLC/bv349ly5ZBTk4O69evR+/eveu9Jj8/Hx4eHliyZAnjF9XeISIUFxcjIyMD\niYmJCA4OxqNHj1BcXAxLS0t88cUXGDBgwEeX0bm8vBwRERG4d+8e7t+/j9zcXOjq6qJHjx5wcnKC\nrq4utLW1oaio2NaiNom8vDwMGDAAa9aswfjx4z+o+C5fvgwvLy/cvHkTPB4PTk5OyMvL+2jtes3R\nIx0zvXooKCgAh8OBWCyGoaEhwsLCoKen995rTp48iV69ejXLEbe1KC8vx927d3Hp0iU8evQI6urq\nsLOzw4ABAzB9+nR06dIFqqqqH23GYnl5ebi4uMDFxYUJocvMzER8fDyuXr2K6OholJeXw87ODiNG\njICbm1urzFglhaamJvz8/DBv3jwMGTLkg7PYXr16wcjICDt37sQff/wBsViM5OTkz7LiXofSq4fC\nwkLo6uoiJCQE0tLS0NTUhLa2dr3n5+bm4tSpUzhz5kyt6IH2Qnl5OXJychAXF4crV64w2WK8vLyw\nYsUK6OjotLWILQabzQaPxwOPx4OdnR3Gjh0LIsLLly9x+fJlbN68Gd9//z369u2LYcOGwdbWFpqa\nmlBRUWmxTDiSwMjICO7u7li+fDl27dr13udOSUkJBgYGuHHjBsrLy9GtWze8fPmyQ+l18P8UFBTA\nwMAA4eHh4PP5TJWpuhAKhZg/fz6GDx/+XsXY2ojFYkRHR+Py5cu4f/8+2Gw2bG1tMXToUHz77bcw\nNDRslwq6NWCxWDAzM8OiRYuwcOFCpKWl4eXLl4iIiMDZs2eRlZUFc3NzuLu7Y+DAge12h3jmzJkY\nPnw4zp07V28CCOB1Fhl9fX2kpKQgNDT0sy4U9Hk+8Q0gOzsb2tra+Pvvv8Fms9+bRy0oKAjR0dH4\n/fff23S3UCwWo6ysDHl5ebh8+TJOnTqFnJwcjBgxAps2bYKNjU2bydaekZaWhqGhIQwNDRlHcj6f\nj9OnT2Pnzp1YtGgR+vTpg4kTJ8LR0REqKiqQl5dvF0t/DQ0NnDp1CrNmzYKbmxs6depU53lSUlLo\n3r07oqKiEBISAhcXFwQGBoKI2sV9tCYdGxn1sHbtWpSWluLWrVvgcDgICgqq1z1gypQp8PHxadVg\n9DcRCAQICQmBv78/nj59ClVVVTg4OMDBwQE2NjafzK5lW0BESElJQVRUFCIiIhAbG4vy8nL06NED\ngwcPhoODQ7vYDNi4cSMqKyuxdu3aes+JiIiAq6sr3N3dsWfPHvzrX//CqVOn2oX8jaVjI6MFyMjI\nwPPnz2FhYQGBQFCvwrt16xaEQiH69OnTqvLVpIG/dOkSNm3ahJKSEixcuBB//vlniyYo/dxgsVgw\nMDCAgYEBRo0aBeC16WPv3r2YMGEClJSU8NVXX2H69OlQV1dvM3PBzJkz0bdvXwwZMqReDwM7Ozuw\nWCykpaVBRUUFIpEIAoHgo1R6zaFD6dVDjdHfzc2t3gr0OTk58PHxwe+//96qO38PHjzAn3/+iYSE\nBFhZWWHnzp3o06fPO/UvOmgZ1NXVsXr1avz73/9GWFgYgoODMWfOHMjLy2Po0KEYPnz4O6m8WprO\nnTtj27Zt+Omnn3DixIk6U39xOBx4eXnh77//hr+/P+Tk5CAQCFpVzvZA+92aamMSExMhJycHsVgM\nJyenOs85deoUnJ2dWy0x6MuXLzF06FDGtvTXX3/B19cXbm5uHQqvDZCRkYGLiwtWrlyJv/76CytX\nrsS5c+egr6+PH3/8EeXl5a0qz+jRo6Grq4tr167Ve87kyZMhIyOD33//HUpKSp9l6vgOpVcH+fn5\nSElJQZ8+fRATE1OnO0dZWRlu3ryJHTt2tKghuLq6GoGBgZgxYwZWrVqFiRMn4vHjx5g0aRKkpaU/\nOyN0e0VKSgpWVla4dOkSHjx4gMrKSowbNw5LlizBP//802pZTRYuXIidO3ciKSmpzvY+ffpAW1sb\nt2/fhqqqKsLCwlpFrvZEx/K2DmJiYsDn89GrVy8cP34cPB7vnXN+//13WFhY1LtbJgkSExOxYMEC\nlJSUYMeOHbCysoKsrGyLjddB82GxWLCyssL69etRWlqKgIAA+Pj4QFdXF3v27Gl01u3GYmFhgeHD\nh2Pp0qU4efLkOzZGLpcLNTU16OrqIiMjA0KhEJMnT25RmdobHTO9OoiJiYGamhrYbDaUlJTeUWyp\nqanw9fXFl19+KfGZllgsxtOnT7F48WJ8/fXXmDBhAq5fv46ePXt2KLyPCDabDWVlZUycOBERERHw\n9vbG3LlzMX36dNy9e7fFkniyWCwsXrwYJSUldVaY43A4MDAwQJ8+fZCeno6IiIgWkaM906H06iAm\nJgZdunTBixcvYG1tXUvZEBEOHTqE8ePHw9raWqLj0v9KTE6aNAlWVlY4ffo0pk+f3qB0Vh20X+Tk\n5DBjxgycPXsWXl5eWLx4McaNG9fk8o4fQlZWFkuWLMGePXveaWOxWLCzs0NZWRkqKirw9OlTVFRU\ntIgc7ZUOpVcHz549g6KiImJiYt7Z/s/Ly0NISAh+/PFHiYUoiUQi3Lp1C+7u7oiKisK1a9cwc+bM\ndhsF0EHjYbFYUFdXx+jRo3Hr1i24uLhg8uTJ2LRpE1JTUyXuu+rk5ITy8nKcPXv2nTY7Ozvcvn0b\n6urqEAqFePnypUTHbu90KL23EAgESElJgby8PPLy8t5ReqdPn4azszOUlJQkMl5WVhZmzJgBX19f\nrFy5EgcOHGDq7HbwaaKoqIjvvvsOJ0+ehFAoxIQJE/Drr79KdLNDUVERK1aswPr165GdnV2rrVu3\nbiAiVFZWQkdHp846xZ8yHUrvLQoKClBZWQl1dXXIy8vD2NiYacvPz8eOHTskUq+hoqICd+/exeTJ\nk6GlpYVLly7B1dW1w273mcBisaCvr4+VK1fil19+wdmzZzFlyhSEh4dLzHeuT58+cHV1xaVLlwC8\nNp+kp6ejuLgYI0aMQE5ODhQUFHDz5k0cP34cV69e/Tx2c5tcR62JtMGQjSI6Opp4PB59++23NH36\ndOa4WCwmX19fmjZtWqNKQNZFWVkZzZs3jwYMGED37t1rdn8dfPxUVVXRlStXqH///uTj40PZ2dkS\n6TchIYEGDRpEGRkZtGbNGurWrRu5uLiQvb09ycrKEpfLJQDEYrGIzWbT6NGjJTJuS9McPdLhsvIW\nmZmZKCsrg5qaGgwMDJjjhYWFuHHjBo4ePdrkpAJisRgPHjzAnDlzMGTIEAQGBn5y6cw7aBrS0tIY\nPnw4hg4dijVr1sDd3R1btmxB//79mxwmRkSQlZWFkpISjIyMIBAI6rUd1hx/s0j6p0qH0nuL3Nxc\ncDgcFBYW1sqsEhoaCmtr6w8mEq2PiooKbN26FWFhYdi1axf69evXofA6eAcpKSmsW7cOHh4e2L17\nN06dOoXVq1fDyMiIOYeIEBUVBRsbm3o30woKCrBv3z6cOXMGMTExDbYXfg5Kr8Om9xbFxcUwMzND\namoqOnfuDOD1DG3Pnj0YO3Zso/sjImRkZGDKlCm4d+8efv/9d7i6ukJaWlrSonfwicDhcNCvXz8c\nP34cJiYmcHNzQ0BAAFMyMzc3FyNHjsT58+frnbllZ2fj6NGjiI6ObrDCU1RUbFf5IFuKDqX3FklJ\nSfjiiy+Qm5vLBG0HBQWhoKCg0b+CIpEI58+fx5gxYzB48GD4+/tDU1OzJcTu4BOEy+Uycb2//vor\n5s6di7CwMHh6eiItLQ2zZs1CeHh4nddaWlri3Llz6NWr1zttHA6nzhli586dPw83qfcZ/CoqKsjR\n0ZHs7OzI0tKSli1bRkRE+fn5NGjQIDI1NSV3d3cqLCxkrvH19SUTExMyNzen69evS9QA2RoMHjyY\nNm/eTMOHD6fq6moSCoXk6elJR44caVQ/YrGYDh48SKamphQfH99C0nbwObF161ZSVlYmNptNAAgA\nDR8+nCoqKuq9Jjs7m+zt7ZnzAZCsrCwpKyvXOgaAHB0dqaCgoBXvqOk0R4+8d6YnKyuL27dvIzIy\nElFRUbh9+zbu3buHjRs3wt3dHS9evICbmxs2btwI4HUkw+nTpxETE4Nr165h/vz5LRZu01IkJSUh\nOjoaNjY24HA4iI+PB5/Pf28q7rdJS0vD3LlzERISguvXr9dye+mgg6ZiamoKNptd6zt148YN/PLL\nL/Vew+PxcOrUqVoJbisrK3Ho0KF30k/xeLzPIhfjB5e3NSFQVVVVEIlEUFNTg5+fH6ZPnw4AmD59\nOi5evAgAuHTpEpP9w8DAACYmJh+d309ZWRnu3buHnj17AgCuX78OLy+vBu+gZWVlYfTo0TAzM8Mv\nv/wCQ0PDlhS3g8+E+Ph4eHt7o6ioqNbx6upqLFq06L3fMwsLC5w/fx79+/dnYsW5XC7mzp1bK3bc\n3Nz8s9hc++DurVgsRo8ePZCQkIB58+bBysoK2dnZjJG/c+fOjMd3RkYGnJ2dmWt1dHSQnp7+Tp9v\nprQeMGBAq6VZF4lEKCsrQ3l5OcrLyyEQCCAUChlDb41TaHZ2NrS0tJCamorz589j3759Derf398f\nmzdvxnfffYdJkyZ9tkV3OpAsIpEIFy5cAI/HQ2pqKthsNoRCYa32VatW4dy5c/XO1NTU1HDs2DFM\nnz4dwcHBCA8Px8iRI3HixAmkpaUBeJ0cNTIykrmm5odeRkYGcnJyzKstMi0HBQUhKChIIn01uEZG\ncXExhgwZgp9//hleXl4oLCxk2tTV1VFQUIAFCxbA2dkZU6ZMAQB89dVXGDZsWK0IhtaqkSEWixEV\nFYXQ0FA8e/YMsbGxSEpKQnV1NfPAyMvLQ1pamvkjVlZWIjk5GUQEVVVVsNlsFBQUwNTUFJaWlrC0\ntIStrS369esHLS0tZiwiwvbt23H+/HkcPnwYFhYWHXnuOpAoFRUVKC4uRlxcHE6ePInTp09DIBCg\nqqoKRAQOh4ONGzdi0aJFta6JiopCZGQkXr58iYSEBERGRiI5ORmKiopQUlJCfn4+qqurQUQwMzOr\nlYy2tLSUKTYlJSXFvJSVlWFsbAxjY2OYmprC3t4etra2rZrItlVqZKioqGD48OGIiIhA586dkZWV\nBS0tLWRmZjL55rp27YrU1FTmmrS0tBaPIyUi5OXlISEhAYmJiYiIiEB6ejqysrKgoKAAfX19GBgY\nwMXFBfr6+tDU1ISamhpUVFTeO5WvrKxEYWEhMjMzUVhYiOTkZCQnJ+PChQvYv38/ZGRk0LlzZ1ha\nWiIrKwvXrl3DmTNnYGlp2aL328HnSc0sS0tLCwMGDICvry9u3rwJf39/PHz4EElJSVixYgVy/CEK\nSQAAIABJREFUc3ORl5eHnJwc8Pl8KCsro2vXrtDR0YGNjQ3+9a9/gcPh4OTJk9i0aRNUVVVx4cIF\nBAYGYvfu3XV+J4gIRUVFKCkpQUlJCbKzs5Geno60tDQ8efIE/v7+KC4uhrKyMng8HgwMDNCtWzd0\n6dIF+vr64PF47WrZ/N6ZXl5eHjgcDlRVVVFRUYEhQ4bgP//5D65fvw4NDQ0sXboUGzduRFFRETZu\n3IiYmBhMnjwZYWFhSE9Px6BBgxAfH19r1iOpmZ5IJMLdu3dx7NgxhIaGQltbG1988QUGDRoEbW1t\nKCkpQVlZWeJTcSJCaWkp+Hw+iouLER0dDX9/f9y7dw88Hg8jR47E5MmToa+vL9FxW4o3XRpUVFTg\n7u6OefPmMRXU3myXl5dHr169sHjxYnTp0qXVZe3g/0lLS4Ofnx/8/Pzw+PFj6OvrQ0tLC2KxGMuX\nL4e+vj4UFRWhoKBQp09oWVkZU+xKLBajsrKyySnMqqurUVZWxnwvEhMT8c8//yAiIgJJSUkwNTXF\nsGHDMHr0aIkVlW+OHnmv0ouOjsb06dMhFoshFosxbdo0LFmyBAUFBZgwYQJevXoFAwMDnDlzhtkJ\n8vX1xW+//QYOh4OdO3diyJAhEhO2qqoKcXFxuHHjBgICAgAAQ4YMgaenJ8zMzJrUp6SoSQ91/vx5\nPH78GCYmJhg/fjwcHR3btYJgsVhwcHCAsrIyKioq8OzZM3h7e+PAgQNMu5GRERPGFBcXB3Nzc1y+\nfLnO4jMdtAxlZWWIj49HSEgIbt26hdTUVFhaWmLw4MFwd3dn/D+pndWxzcvLw82bN3Hz5k3ExMRA\nV1cXbm5u6N27N0xMTOqtMvghmjV5arKzSxNp6pAPHz6k8ePHk4uLC+3Zs4eioqKorKxMwtJJhuzs\nbAoKCqJvvvmGnJ2dae3atZSbm9vWYtUJAAoJCSGi14kQ9u3bR6qqqrXa161bR0RElZWVFBgYSHJy\nchQXF9fgMRYuXNiRWKGJlJWV0aFDh2jQoEE0cOBA2rFjB4WFhbXb5+l95ObmUlhYGO3YsYMGDhxI\nbm5udPDgwSZ9j5ujutq10hOLxRQXF0cLFiygnj170m+//fbRfXGSkpJo/vz55OzsTKdOnaL8/Py2\nFqkWbyq9yspKOnr0KCkpKdVqX79+PRG9zgTy4MEDkpGRaZTSs7a2JgUFBbK2tqbdu3dTXFwc8fn8\nD15X8/cfM2YMKSgokJqaGs2cOZNSUlKIiMjBwYG++uor5nyBQEAeHh40YMAAIiJ69eoV+fj4kLq6\nOikqKpKnpyfFxsaSWCymqKgoAkAPHjwge3t7UlBQaPD9tDQikYgyMzPpxIkT5ODgQIMHD6aAgIC2\nFkviXLt2jYYMGUK9evWi48ePU2ZmJolEogZd2xyl1+DdW0nR0Gkpn8/H9u3bce/ePUybNg0eHh4t\nWoSnJRGLxXj27BmOHj2KmJgYLFu2rNXKRn4IFouFQYMGQUNDA2VlZQgJCcGoUaPw22+/Me02Njaw\nsrJCRUUFHj58CF1dXVy9erXBIUuZmZl48uQJbty4gQsXLqC8vBy2trZwc3PD2LFjYWJiUueS7MWL\nFxg8eDDU1NQwe/ZslJeXY/fu3TA2NsbZs2dx48YNfP/990hKSoKCggIyMzPRrVs3XLt2Ddra2hg+\nfDjk5eXx5ZdfgsPh4MiRI6iursalS5dQUFAAW1tbODo6wtvbGzo6Ohg/frxEP9umUFVVhf379+Py\n5cvo06cPRo0aBXt7+0/W/UkoFCIyMhJ+fn74559/MGrUKMybN++DdaQ/qeWtWCym3NxcGjVqFI0e\nPZry8vJaSbKWRywWU0BAAHXt2pW2b99OAoGgrUUiAKSlpUUGBgZkZ2dHK1eurBVWCIBUVVVJX1+f\nunXrRrNnz6ZXr17V2VdVVRUlJyczr7qoqKigY8eOkYWFBQEgaWlpunz5cp3nHjp0iKSkpCg8PJw5\ndu3aNVJQUKB//vmHkpKSSE9Pjw4ePEhEROvWrSM7OzsSCoV07Ngx4nA4dPv2bUaeBw8ekKysLN2+\nfZuZ6d26daupH51EEYvFFB4eTj179qTRo0dTRkZGW4vU6mRlZZGnpyd1796dwsLCSCwW13tuc1RX\nu1N6gYGB5ODgQIcOHWoXSqElSEtLo1mzZtHMmTMpJyenTWXBG8vb+tprbHofIiYmplYs55sIhUJ6\n/PgxbdiwgQYNGkQaGhrUrVs3+ve//01JSUl19rdlyxZisVi1lsIFBQXEZrMpMDCQKisracyYMdSj\nRw/Kzc2lzp0709KlS0ksFtOOHTuIxWLVeuF/yTL9/f0ZpdcenjE+n0/r1q2joUOH0qVLl9qFTG2F\nQCAgPz8/Gjp0KK1du7ZeM8gno/SSk5PJ3t7+swjQr66uppkzZ5K3t3ebbsg0ROnV2PSayl9//UUO\nDg7E4XBIQUGBPDw8KCgo6IP2m99//52kpKTozp07JBaLSSQS0dmzZ0lZWZlCQ0OJiOjo0aOkqqpK\nq1atIi6XSzdv3iQioj/++IOkpaUpNjaWGUckEpFAICChUMgovbamurqa5s+fTwMHDqSioqK2Fqfd\nUFRURK6urjR37lyqqqp6p705f7t2Y9OLjIyEt7c3duzYgSFDhrSrbfeWQiwWY8mSJaiqqsL27dvb\nJMcei8VCSEhIrfDBt9vXrVuHNWvWNHkMY2NjODk5YeDAgRgwYACMjIwaVEkuNTUVQ4cORVVVFTw8\nPCAQCHDx4kU4ODjgxIkTUFVVRVFREczNzSEUCqGmpobIyEgoKioiNzcXU6ZMQVJSEtzc3KCqqoqy\nsjJER0djzZo16NSpE2xtbVslOqg+CgsLMW/ePGhra8PX17dVIxokSV5eHu7evYu4uDgIhUKYmJhg\nxIgRzS6eVVlZiRUrViAzMxP79u2Dmpoa0/bR2/TKy8tp+PDhzK+0pAkMDCQul9uoay5cuNDoa5pC\neXk5OTk50c6dO1t8rLqABJe39VFVVdXgXbm3KS0tpZkzZ5KSkhJ16tSJFi9e/E4qpWXLlhEA2rFj\nR63jQqGQdu7cScbGxsTlcsnY2Jh8fX2pqKiozWd6QqGQfvjhB/L09GxRjwQul0t//PFHo6+5dOlS\ng893cHCole6KzWaTvb29RDwVhEIheXl50XfffVfrc2rO365dKL0LFy7Q3LlzW2zMGzduNPpD+uuv\nv1rtS5GUlETu7u6UmZnZKuN10Pbcu3ePxowZ0+L2OwB07NixRl9z4cKFBp9/7NgxevDgAZWWllJR\nURFt376duFwunT59urHi1olAICAvLy8KDg6uJWNTaXOlV1VVRaampnTv3r1m9/348WPy9PQkU1NT\nsra2pg0bNhCfzyc1NTVml1JLS4ucnJyIiOju3bs0YsQI0tHRIRcXF7p27RrTl6qqaq1rBg4cSESv\nZ2ZLly4lU1NTsrKyorVr1743iWND2bBhA/3666/N7qeDtmXLli0UEBDw3pltdXU1mZmZ0ZUrVyQy\nplAopP/85z9kb29PRkZGNHHiRIqMjKSpU6cSAFJRUWGeY6LXG2nffvstmZubk7m5Oa1atYpKS0uJ\niMjT05PZsX/zGiKiM2fOUL9+/UhPT48mTJhAqampdcpTWlpKUlJSjVa278Pf358sLCyourqaiFow\niWhrcOfOHcjKysLBwaFZ/YjFYowdOxYJCQno2bMnbGxs4Ofnh6SkJCZ+dMiQIRgyZAhcXFwAAFOm\nTIGUlBRcXV0hJyeHkSNH4sqVKwAAe3v7Wtf06dMHWVlZcHFxgZ+fH3r06AFzc3Ps3bsXCxcuRFVV\nVbPkd3Nzw5kzZ9rUxtRB8/nnn3/g4eEBU1NT/Pvf/8bly5fx6tWrWufcunULXC4XgwYNksiYEyZM\nwO7du6Gvr4/evXujqKgI69atY8ob2NjYMM8x8LpgfXR0NHr16gVbW1ucPHkSy5YtAwDme9i9e3fm\nGpFIhPXr12PmzJlQUVGBi4sLEhIS4OTkhOfPn9eSRSQS4ejRo1BSUoK5ublE7g8AXF1dISMjg8DA\nwOZ3JiFF3GDeHnLdunW0evXqZvcrFApJXV2dhg8fznj95+XlkUAgqHd5e+LECRoxYgRZW1uTvr4+\nsdlsWrBgARHVvbzduHEjaWhoUFRUFAmFQqqqqqK7d+8Sj8drtj9hdnY2mZqatrkLSwfNY8yYMYx7\nDACSk5MjPT098vb2Znacly5dKlEbrqOjI+np6dHKlSvp5s2bVFBQQFlZWURU9/L26dOnNHPmTHJw\ncCAzMzNSUVF5JwrnzeVtYWEhGRgY0J9//knl5eUkEokoOTmZtLS0aPny5bX6vnHjBmlqatLy5cuZ\nWZmk2LNnD3377beMjE2lzd28MzIymJlXc5CSksK2bdvw+++/Y8eOHVi0aBGmTp2KHTt21Hn+1atX\nMX36dNja2kJPTw8sFgsZGRmoqKiod4y4uDjk5+fD3t6emZEREdhsNlOpqqmoqqqCy+UiICCg1i5V\nBx8XfD6/1vuKigq8evUKqampOH36NCwtLSEUCrFkyRIIhUKJRFqcOHECy5cvx6VLl3DgwAF06tQJ\nf/zxB5Po902EQiEWLFiAhIQEmJubo3PnzpCTk8OTJ0/q7b+6uhppaWmYPHkygNfPfM3zn5KSAuB1\nJMm5c+fwr3/9C9OmTcNPP/0kcQ8MZ2dnBAUFNfu71uZKTywWS8xVY8aMGRg7dizy8vIQHR2NKVOm\n4Icffqg1Vo2rRGBgIOTl5XH58mVoa2sjIyMDVlZWzLk1f7A3r+nUqRPU1dVx5MiRdxRTc6tIsVgs\nsFgsJCUlMQ9SBx8flZWVdR4nIkhJSSEhIQFycnKQkpKSmFIwNTXFyZMnkZ+fj7S0NEybNg1btmzB\nqVOnwGKxatXUEAqFCAkJwZ07d2Bvbw8ul4tVq1bVUnpvXyMlJQUVFRVs3LgRFhYWtcauCQ3dv38/\n1qxZg+nTp8PX17dFXM6kpaUlYv5pc6XXuXNnvHz5stn9iMVieHt7w9vbG6qqqggODoZYLAYRQUFB\nAfLy8tixYwccHR0hLy+PLl26QCAQ4PTp07C2tsaRI0dQVlbG9KeoqAhZWVns3r0bPXv2hJKSEiZN\nmoTjx4/j0KFDmDFjBtTV1ZGdnY3z589j7969zSrvWFJSgqqqKvj4+LTrVFQdvJ/Hjx8z/2exWGCz\n2ejSpQsMDQ0xadIkTJkyBWvWrIFIJJJYYs2BAwfC09MTtra2SEpKQnFxMVMCQV9fH35+fjAwMIC0\ntDR69uwJHo+HXbt2Ydq0aXjy5AkTZ12Drq4uzp49Cw0NDUhLS6NXr14YPnw4li9fjtWrV8Pa2hoC\ngQAhISGorKyEuro6li9fjv79+8Pb2xtRUVEAAAMDA4k+y5GRkejUqVPzZ8fNXmg3kreHvHTpEjk4\nODTbV0ksFtO8efNIW1ubZGVlydTUlLZu3UplZWVUWFhI8+bNI3V1dWKxWGRkZERZWVk0depUUlFR\noc6dO9O2bdtIRUWFydqRl5dHs2fPJjU1NWKxWGRnZ0dERA8ePCBvb29SV1cnaWlp0tXVpW+++abZ\nURUPHz6k/v37N9mfrYP2gaenJ8nIyJC0tDSTOunZs2dUWVnJnHP27FlydnaWmH/enj17qGfPnsTl\nconH49GUKVPoxYsXRER0/vx5srCwICkpKQJAYrGYDh8+TDo6OqSkpEReXl60fv36Wt/LP//8k0xN\nTZlriIgyMjJo3bp1ZG5uThwOh1RVVcnDw4P8/f2pe/fu75STBEDbtm2TyP0RvbbZ9+3bl86cOUNE\nH3lEBp/Ph7W1Nfz8/GBnZ9eaorQr9u7di4qKCixevLitRemgGSxYsAAyMjL4+uuvYWpqWuc5fD4f\n3bp1w5kzZ9C7d+9WlvDjJDQ0FN7e3oiOjoaSklLLZU5uCeoS9vDhw4iLi8PWrVtbU5R2Q1FREcaN\nG4dff/31o0kz30HdCASCBpUo8PPzw5kzZ3DixIlWkOrj58svv8TYsWMxevRoAM0LQ2tzPz0AmDhx\nIsLDw9+7g/SpUlVVhRkzZsDBwQG6urrN7o/P5yM/P5+x6bxJZWUl8vLyQESorKxETk4O88rPz3/H\nCM/n85n23Nxc5Ofng8/n19l3S1JRUYGcnJxWHbOpNLQmy9ChQyESibBt27ZW/zw/JoRCIXx9fSEQ\nCDB06FDJdNrMpXajqW/IwMBAMjExoYcPH7ayRG3Ltm3baMyYMRLLsLFjxw7i8Xj0+PHjd9q+//57\nsrOzIz6fT4cPH2ZsLywWi9TV1cnDw4OxBRERLViwgDlHSkqKVFVVydbWlhYtWtSqIXMHDhxoFxlR\nJE1ycjI5OzvT9u3bP7qM4K2BUCikzZs3k5OT0zv5GZvzPLQbpUdEdPv2berevTuVlJS0okRtg1gs\npqNHj5KzszMVFxdLrF8+n0+ysrK0Z8+eWsfz8/OJw+HQDz/8wBiza/4WIpGIbt68SVpaWuTl5cVc\ns2DBApKXlyei1w9gfHw8rV69mmRkZMjBwaFRmy41qaE6qI1IJKL+/fvT6tWrOz6fNxCJRLRy5Ur6\n4osvJJ5aql0sb2vo378/vvvuO7i6uuLatWu1fIU+JaqqqrB69WqcPHkSv/32W71V6ZuCoqIi5syZ\ng2PHjtWyefj7+0MkEmHkyJHv+FCx2Wx88cUX6NatG7Kzs+vsV0pKCsbGxli/fj1OnDiB2NhYnD59\nusFyHTlyBO7u7vj5558REhLSqLC9x48fw9fXl3nv6+uLpKQk5n1xcXGt9o0bN+LmzZu4ceMG/vvf\n/yI4OBgikQh37tzB9u3b4efnx5zL5/OZ5dPx48exdetWhIWFMe5OMTExOHz4MLZs2YKDBw8iMjKy\nwXI3BDabjRMnTiArKwuTJ0/+LE08bxMVFYWpU6ciOzsbf/zxh+RTrjVdFzeNDw0pEono5cuXZGlp\nSVu2bHlvyuiPkeTkZOrevTvNmjWLysvLW2SMx48fk6KiIt2/f5+IXge4T5kyhfT19Zll1NszvaCg\nIOratSv99NNPTD9vzvTepKCggIyNjWnWrFkNlunFixc0depUkpGRIVlZWTIzM6P9+/fXcuWoj7eX\ntwDo+vXrzPukpKRa7RwOhywtLUlJSYlYLBbJyMjQzp07SUNDg1gsFklLSzOFdtLS0ggATZo0iTgc\nDrFYLNLU1KQXL17QgwcPqEuXLiQlJUUsFovYbDbJyck1+J4bg1AoJD8/P9LS0pJYEouPjYqKClq3\nbh3xeDy6dOnSe5f8zVFd7WqmB7z+5TMxMcGVK1cQExODCRMm4Nq1axAIBG0tWrNIS0vD7t27MWfO\nHPj4+GDv3r0tljRSX18ftra22LRpE0QiEYqLi3H79m1s3LjxHYdYFosFKSkpDBw4EKamppg0adIH\n+1dWVgaXy0VRUVGDZTI1NcXx48eRnJyMPXv2wN7eHps2bUKXLl0wbdo0/PXXX42+z/chJyeHiIgI\nREdHQ01NDfv374e/vz+SkpJgYWGBX375pdb5XC4X6enpeP78OfT09LB48WKkpKQgJycHq1atQnh4\nOJKSknD48GGJylmDlJQURo4cibCwMBQXF8PT0xMHDhx4J1nBp0hqair2798PT09PFBUV4eHDhxg1\napTEnLffocnqsok0ZkiBQEB3794lZ2dncnNzoydPnrSgZC2DQCAgT09P0tbWJk1NTerduzdNnTqV\n5s2bR0uXLqW1a9fSpk2b6MCBA3TixAl69uxZs8cUi8W0du1a6tSpE8XGxtKePXvI0NCwVu62mple\nYmIiJSYm0v3798nb25vs7e0Zo3F9M73i4mIyMTGh6dOn1zm+oaEh86rPQfXJkyc0evRoZqOkJt1X\nXTRlprdw4ULGjmhmZkYjRowgoVBIYrGYPDw8yN7enoj+f6ZXE6BPRLR+/XpSUFCg1NRUcnBwIAUF\nBdLQ0CBra2u6c+dOvXJKiurqakpOTqaFCxeSoaEh+fj4fJK5FnNycmjFihVkaGhICxYsoOTk5AYn\nKWiO6mrzMLT3weVy0a9fPwQHB+PYsWNYtmwZU9qve/fu0NPTa7lfg2ZQUVGBp0+fIiwsDP7+/lBW\nVoajoyMuX76MkJAQhISEgM1mM2FKABj7ZXh4eLPHZ7FYmDx5MjZv3ozr169j+/btGDFiRJ22EUND\nQ+ZfExMTdO3aFY8ePXqvv+CDBw+Ql5eHfv361dn+Zpqwrl27AgDKysoQExODkJAQnDlzBo8fP4aZ\nmRnmzJmDCRMmwNXVtcH3x+Vya7nXZGRk1HlOTTwzi8UCh8NhnhUWi/WOm0hpaSkToC8QCMDlcqGj\no4PQ0FBERkbiwYMHOHPmDL755hsmzKolICKkpKQgNjYWUlJSMDIyQnZ2NqZMmQJTU1MMGjQI3bp1\ng7GxcYPdY9oLAoEAiYmJePbsGQIDA/HixQvY2Njg4sWLsLGxab0SEU1Wl02kOUPy+XwKDQ2lOXPm\nkJmZGc2ePZuCg4MlnsKmqeTl5dGvv/5KAwYMIEdHR9q+fTslJiaSUCik0tJS2r17N8nKytYZssNi\nscjd3V1iNkyxWEzjxo2jTp06EZfLJT8/v1rtb9r0iF6ntlq9ejXJysoyyS3fnOmJRCJKTU2lffv2\nkb6+PllbWzeoYHcNx48fJ01NTdLQ0KBvvvmG7t+/T9nZ2Q3asXx7pmdlZUWjRo2inJwcevr0KTk4\nOLwz01u8eDHz3tzcnDw9PZn3w4YNIxsbGyL6/5meq6srpaSkUEREBBkaGtLUqVMpJCSETp06RQUF\nBVRcXExLly4lWVnZBt9zY7ly5QqNGTOGrKysaP78+XT79m3KzMyk6upqys3NpeDgYJo7dy6ZmZnR\noEGDaN++fZSUlNTu7d5JSUm0b98+cnd3J3Nzc5o7dy7duXOHcnJymrxj3Rw90q5nem+jqKgIJycn\nODk5ITs7G0eOHMGaNWtAROjevTv69OkDY2NjdO7cGRoaGpCVlW3SOPS/1Dl1Fa8Ri8VITEyEsrIy\nSkpKkJ2djcePHyMkJATx8fEwNDTEwoULMWzYsFq/xAoKCpg/fz44HA5WrVqFgoKCWrurLBYLI0aM\nQFlZGRQVFZsk95uwWCz88MMP8PPzQ6dOneotLl7z68rhcKCurg4vLy/07duXaS8vL2dmpDIyMlBX\nV0evXr2wc+fORsnZtWtXbNmyBV5eXs3erV6yZAkWLVoEbW1t8Hg8zJw5s9kzZGdnZ9ja2qK0tBRW\nVlb46aef8OzZMyxbtgwzZsyASCSCmpoavv7662aNU4NYLEZGRgZSUlIQGBiIO3fugIgwcuRI7N69\nm5kh16CpqQkXFxe4uLigqqoKV69exZUrV3Ds2DGoqanB2toaPXr0gKGhITQ1NaGmpgZlZeVWKxJe\nYzsuLCxEXl4ekpKS8OjRI0RHR6OoqAjdunXDvHnz3vletAXtIgytOQgEAqSmpiI1NRUhISF49OgR\nUlJSIC8vD3Nzc/To0QOmpqYwMjL64HL4zp07UFdXR1RUFBQUFODp6QngtVtDYmIiEhIS8OzZM5w/\nfx5EBHl5eVhZWaF3796wtraGnp4eeDzeeyt9iUQi3L9/HzNnzkRCQgJzvEuXLjAxMQGLxcKwYcMw\nadKkZkdoCAQChIaGQkFBgckeXUN6ejqePXvGvOdwONDQ0ICZmRmzwRIXF8cY0tlsNmRlZaGurg4D\nAwPIy8s3S7bGsHv3bixatIhxcxEIBHj27BkKCwvRuXNnGBsb4+7duxg8eDAA4ObNm9DX14eZmRmA\n19mMFRQUmGzYjx49gkAgQO/evZGeng4dHR1UV1fj0aNH4PP5MDExgZ6eHqqrq5GcnIzMzEyIxWKo\nqanB3Ny8WRtQfD4ffn5+OH/+PNLS0mBubo6hQ4fCzs4OBgYGUFBQaFR/xcXFyMzMRHp6Op48eYKn\nT58iPj4e5eXlUFVVhZWVFbp16wZ9fX3o6elBV1e32VXK+Hw+UlNT8erVK6SkpCAmJgbPnz9HXl4e\n5OXlYWxsDBsbG9jZ2aFr167Q1taGiopKs8Z8m48+9lbS1HwpwsPD8ejRI8TGxiIvLw9CoRAqKipQ\nVVWFqqoqFBQUIC0tDS6XC+D1l6WsrAylpaUQi8WwtLREZWUlKisrIS8vDz09PVhbW0NFRQUrVqwA\nl8vFDz/8gFmzZsHQ0LBBZQ1riIyMxPjx4xnFN2PGDBw6dAjh4eHYv38/wsPDYWtri9GjR6NXr17g\n8XhQVlb+LEpjvkl4eDiWLVuGkpISidg736ZG6bXEMykWi5mZz+PHj+Hv74+QkBAYGBhg4sSJ8PLy\nanYexrrIysrCtGnTYGNjAwMDA8TExCA+Ph7Z2dmorKwEl8uFsrIyZGVlweFwmJk3EaFz587Mc1xW\nVgYiQnl5OYqLi1FSUoLS0lIIBALIysqCx+PB1NQU3bp1g62tLWxsbKChoSHx+6mLDqX3AYgIfD4f\nhYWFKC8vR0VFBSorK1FVVQWRSASRSITS0lLMmDEDpaWljIyjRo3Cli1boKioCHV1dWZaLhKJ4OHh\ngVu3boGIoKOjg7Fjx2Lx4sXvLEveR1JSEhYuXIiAgAAEBATA3d2dacvMzERMTAzCwsLw8OFDFBQU\noHv37nBzc0Pfvn2hqqoq8c+pPaKpqQldXV3s2rVLIhm230bSSo+IkJSUhL///hvBwcF49eoVNDU1\nYWtri549e8LMzIzJbdcSJCUlYebMmRg9ejTmzZtXy8RTWVmJoqIiRnEFBATg5s2bYLPZeP78OZSV\nlfHjjz8yk4A3/5WVlYWMjAxkZGSgqKgIVVXVJpuPJMFHX/e2PRAREUHKysrvbDD4+fnVaSh+8uQJ\ncTicWrU+O3XqRMeOHaPCwsIGG5dLSkoY94r3kZ2dTVu3bqWePXuSvr4+TZgwgU6ePEkpKSmUn5//\nWTqztjWVlZVUVFREGRkZFBQURCtWrKA+ffpQ165dycvLi/78889WDaksLCykQYMG0a7ePB9cAAAg\nAElEQVRduxp0/rJly+jixYs0cuRI0tbWrrXZ095pjh75LGZ6DeH48eOYPXv2O/n3zc3Nce3aNRgY\nGNQ6XlVVBXd3dwQHBzPHapaejo6O+Oabb+Dt7d0gQzIRNXjZSv9zaYiJiUFUVBRevHiB4uJiAGBs\nKRYWFjA3N5doeFsHr2ff8fHxePnyJWJjY5GcnAyhUAhFRUXo6urCysoKxsbGMDc3b/U6J4mJiZgz\nZw4GDBiARYsWNcju6Onpia1bt2L69OlITk7GhAkT8N///rcVpG0+zdEjH9XubUsSGxtbZ8GR58+f\nY+/evdi8eXMtxcTlcjF8+HDcvXu3VpEg4LUd6siRIxg/fnyDlF5j7HQsFgsGBgYwMDDAsGHDmOPZ\n2dm4du0arl69imXLloHP58PU1BQuLi7o168fevfuDVVVVcZfTZI1Gj4FiIgxdYhEIgiFQkRFRSE0\nNBShoaF48OABioqK0LVrV/Tt2xeurq74/vvv20Vq/+LiYkyaNAk+Pj746quvGnTNy5cvwWaz8eTJ\nE+Z5sLa2bmFJ2wcdM73/MXz4cPj7+9fZJiUlhePHj78TohUfHw9bW9t3Kqh988032LBhQ5vZ3cRi\nMfLy8pCYmIhXr14hLi4OL1++RFFREbPrbGZmBnNzcxgZGTFuPp+TEhQIBEhLS2N2IOPj45GQkICS\nkhJmp1pPTw9mZma1dj4VFRXb1ef0+PFjzJkzBzNnzoSPj0+DbYWzZ89mampkZGQgKCgI58+fr9fh\nvL3RsZEhAXg8HnJzc+tt19fXR1BQ0DvL3GnTpuHUqVMQiURgsVjo1KkT4uLi2l0Zx5qsIWKxGCkp\nKbh9+zZu376N4OBg5OTkQFVVlfGB7N27NxwcHD6Z5bFIJMKzZ88QFhaGsLAwhIeHIzY2FiKRCPr6\n+ujbty/69euHL774gtmFr4mYaU8K7m2Ki4vRt29fbN68GR4eHg2WNTc3F/r6+njy5AnGjBmDQYMG\n4ZdffkFKSgpT3ay906H0msnTp09ha2v7XrlYLBZ8fHxw8ODBWsdTUlJgZWUFoVCIdevWgcViITAw\nEAcPHmRCvNozYrEYWVlZSExMRHJyMpKTk5GamoqsrCwQEWRkZBj3BB0dHWhpaYHH40FDQ4N5tabP\n3psIBALk5+ejoKAAeXl5zL8ZGRlIS0sDn8+HQCBAdXU1NDQ00KVLF+jp6TEzNz09PYn7j7UGRISg\noCDMnz8f69evx9ixYxvlLnXmzBn8+uuvOHLkCOzt7bFs2TL89NNPyMvLa0GpJUuHTa+ZnD59Gmw2\n+71pu4kIR48exaJFixinV+D1DHDMmDGYOHEi82urpqaGSZMm4fr16+3+S1VTorBLly7M0kYsFqOq\nqgrV1dWorq5GZWUlEhMTERkZieDgYLx48QIJCQng8/mMU7OJiQl0dHSgra0NLS0taGtrQ1tbG8rK\nylBXV4eysnKj3DTKyspqKbScnBykpKQwy9Hk5GTk5+dDKBRCRkYGxsbGMDQ0hKmpKWxtbTF16lSm\ngLq0tDSkpaVbLTqhpQkJCcHChQvx559/wsbGplEKTywW4/bt21i+fDmSk5Oho6MDALC0tGwpcdsd\nn/1MTywWw8LCos7auxwOB2KxGIMHD4anpyfGjRtXp/NlWVkZ5OTkmIevqqoKmzdvxp07d3DgwAEY\nGxu3+H20BcXFxUhPT0dGRgYyMzNRUFCAwsJCFBYWori4GGVlZaiqqkJlZSWqq6vBZrPB4XDqXYaJ\nRCJmGc5isRjfMDk5OSgoKIDH40FTUxM8Hg+dOnVC586d0aVLl1ZziG1rqqurceTIERw4cAC7du2q\nFS7YUCorKzFu3DicP38e586dQ0hICIDXIZ4///yzpEVuMTpmes2gsrIS3t7ejP3myZMnyMjIQGVl\nJXbv3o2FCxdiypQpmDp1ar19vB06xOVysWzZMujr62Py5Mk4c+bMJ1nlTEVFBSoqKujWrds7bUQE\noVAIsVjM/FuzM1rTXvPg1ijBmr8Bm81mdhRrdpsbM5v5FBGLxVi6dClSUlJw9epVaGlpNamfwMBA\nGBkZQVpaGi9evICrqyt27dqF77//XsISt2Oa7OHXRNpgyEaxefNmOnXqFI0bN47i4uJo7969NGrU\nqCb1JRQKaf/+/dS9e/fPruBRB5IjPz+f5s2bR15eXrXy/jWW6upqcnZ2pkuXLhER0bRp0yg1NZV0\ndXUpOjpaUuK2Cs3RI5/3z2cddO7cGQkJCejSpQsKCgrQs2dPhISENKlMn5SUFHx8fLB27VosXLiw\nRfOwdfBp8urVK3h7e4PH4+Ho0aNMzr+m8OjRIyQkJDC5C0tLSyEvL8/E0n4udCi9t1BXV8erV69g\naWmJp0+fwsDAANra2vX68H2ImjTg3333HSZNmoSrV69KWOIOPkXEYjGCg4Mxbdo0eHh4YNWqVc1K\nOUZEuHr1Kr755hsoKSmBz+ejuroa2dnZ0NTUlEg6s4+FDqX3FmpqakhJSYGhoSGio6PB4/FgYWHx\njqtKY2CxWBg/fjxOnDiBnTt3Yvfu3Z9spbcOmo9AIMCmTZuwbt06bNq0Cd9//32zd57LysoQERGB\nBQsWAABu374NPT09xsbX3vxKW5IOpfcWqqqqjJPm8+fPwWKx4OXlxeQLaw7du3fHL7/8gkOHDmHT\npk2NKoPYUry5eaCmpobJkyfXyvP3Zsp1RUVFuLm5ITQ0tENptxDFxcVYuXIl7ty5g7Nnz8LZ2Vki\n/cbGxoLH4zHKLSAgAJaWlggKCoKmpmabJ/ZsTTqU3luoqamhtLQUMjIySE9PR1lZGcaMGYOioiJE\nREQ0u38DAwMEBgYiPj4e8+bNQ05OjgSkbh6rVq3C4cOHsXTpUoSGhjKzgRo8PT3x22+/4ccff0RB\nQQFmz57dLuT+1Hjw4AHGjRsHKSkpnDx5UqK59nx9fZlYbbFYjBs3bsDKygrPnz8Hj8eT2DgfBZLb\nT2kYbTBkoygvLycjIyMKDw+nnj17UlhYGBERjRkzhrZs2SKxcaqrq2nJkiXUp08fSk5ObrM6BwAo\nJCSEeX/jxg3icrm12tetW8e8z8jIIA6HQzExMQ0e4//YO++oqK7v7T8DQ5ciIlUUpYpUwYoiimAD\nFQsi9i4axdj1G42BIBjURGPB2JUEGxYERMSGETsoIjakSJMqvc/s9w9f5iehDTBD0fmsNUs495Q9\ngHvOPXfvZ5uZmdGxY8coKyurRkU2bikoKKDMzEzKysqqUZcjOzu7Vp2OvLw8ysnJ4XxfVFREWVlZ\nlJmZSQUFBZyfc2VlJadGR25uLmVmZjbZLl5RWlpKhw8fJl1dXQoPD+f5/C9fviQVFRXOe0xJSSFx\ncXFKSkoiFRUVOnr0KM/X5Dct8SOCnd5/kJCQgKKiIjIzM9G7d2/O7s7FxQUnT57k2TpMJhO//fYb\nVqxYgWnTpsHPzw9VVVU8m7+pEBFycnJw7dq1WsG+1XF0hYWF8Pf3h6SkZJOyK/r3749t27bByMgI\nzs7O2L9/P+Li4hoNLmWz2fjrr79gYWGBbt26oUePHrC2tsbly5dBRFi4cCFmzJjB6V9eXo4xY8Zg\n3bp1AAB/f3+MHDkSPXr0gLq6OgYPHoxTp06BzWbj9evXUFJSwr59+2BgYFArp7q1SEhIwIIFC/Dg\nwQNcunSJ5wn/bDYbp0+fxrx58zh5ta9fv4aenh4KCgpQWlqK/v3783TNdg+vPC+3tMGSTWbWrFnk\n4+NDe/bsoUWLFhERUVxcHCkpKVFMTAzP10tOTiY9PT3y9vZudnWo5oL/iKYKCwvTtm3b6r3OYDDI\nzs6OiouLm7RORUUF+fv7U9++fUlYWJiYTCaNHj2a7t27V+97fvDgAUlISNC4ceMoMTGRXrx4QYaG\nhqSlpUUJCQl069YtEhER4ezsPnz4QKKiopSenk4vXrwgaWlpmjJlCn38+JHS09PJycmJ1NXV6fXr\n1xQdHU0AyNDQkN6+fdv8H2AzYbPZFBYWRuLi4rRz506+/d6zsrLIwsKCioqKOG179+6lzZs308WL\nF0lMTKxZu++2piV+5LvPyKgLbW1tJCcnY+zYsbhw4QIqKiqgpKQEQ0NDuLm54cyZMzxV3+jWrRtC\nQkKwfft2TJ06Ff/73//Qt29fns3fGHPmzIGamhokJCRgaGhYQ7YeACwtLTFkyBCIioqiV69esLOz\nq1NkICcnp8ZT7s2bN3O+FhERwaRJkzB27FicP38e27dvR0hICG7evImLFy/Czs6u1nzVBXz++OMP\nTkbLyZMnMXjwYHz8+BF6enrQ1tbG77//Dnd3d3h4eGDw4MFQVFREYGAgSkpK0KNHD/z9998gImho\naMDf3x+pqamcc6y///67Ri51a/D+/XscOHAA8fHxuHbtGoYNG8Y3NZeIiAj069ePkzXEZrPx5s0b\nzJw5E8+ePYO8vDxHFv67gXe+lzvaYMkm4+fnRzNnzqSysjIyNDTkVJdftWoVKSoqUlJSEl/Wrays\npCtXrlC3bt3o8OHDrXLOh/+c6dV13c3Njau5YmNja+wKv6aiooKuXLlCQ4YMIUlJSRIVFSVra2sK\nDQ2lioqKOufz9vYmBoNR49wuNzeXhISEKCwsjFgsFs2ZM4d69OhB8fHxxGQyycvLi4iI/vjjD2Iw\nGHXWGA4KCuLs9Fr7LDU4OJg0NDTI09Ozybvl5jB8+HC6desW5/vKykqaNGkSlZSU0IoVK2jChAl8\nt4EftMSPCM706kBbWxs5OTlgMBhQVVVFTk4OAMDGxgYlJSW4f/8+X9ZlMpkYP348rl69ipCQECxZ\nsgRRUVFtHh5CXCZ29+7dm1Mz+Osxq1evhq6uLhYtWgRZWVm4ubkhOjoaoaGhsLGxqfd8UFNTE0wm\nEydPnkRRURFyc3Oxe/duKCgoQEFBAUJCQpg+fTpycnKwZcsWMJlMjBw5EsAXmX8xMTGcOnUKubm5\nqKqqQkFBAZ4+fQozMzPOGq2ll/fkyRPMnz8fhw4dgp+fHzZu3Mh3Sa7q6n5fv9+qqioQEZhMJqKj\no5slWtDh4Y3f5Z42WLLJ5Ofnk4WFBeXl5XGqsRMRFRcXk5SUFM2YMYPvNhQXF9Px48epR48e9Ntv\nv/FtHfBwp1cfJiYmdODAAfr48WOTdjfFxcU0fPhwkpSUJHV1dVJTUyNRUVFasmQJ5xyqsrKSevXq\nRSIiImRmZkZVVVVERFReXk7Lly8nSUlJUlNTIw0NDVJXV6fOnTvTtWvXODs9flNQUEDr1q0jPT09\nunz5cqvs7oi+vP/x48eTn59fjfbY2FiaP38+sVgskpWVpbCwsFaxh9e05HcnONOrg2rtt5KSEvTu\n3RuJiYmwtLSEpKQkpk6diuvXryMzM5Ov8U2SkpKYO3cuhg0bhp9++gmjR4/GunXrYGVl1WDB8qbi\n6OjYoDSTo6NjnSoqTSEqKqpZ4yQlJREaGoqjR48iIiICoqKisLKygpOTE+dnwGQy8euvv+Ly5cuY\nN28ep11UVBT79u2Dvb09goKCkJOTgy5dumDkyJEYNmwYsrKy4Ojo2KL31RAZGRkICgqCn58f+vTp\ng9u3bzdbGaU5vHv3DiUlJZgyZUqN9qCgIOjp6SE6OhqlpaWtfp7ZLuCh8+WKNliyWUycOJE+fPhA\nN2/epHXr1nHab9++TQoKCrRq1apWs6W4uJhu375NlpaWNGrUKIqOjm61tQU0jZKSEjpw4ACZmJjQ\nihUr6P3791RZWdnqdmzatIlOnjxZq33YsGEUEBBAbm5upKWlRVlZWa1uGy9oiR8RnOnVg6ysLEpL\nS6GgoICkpCROe58+faCvr4/jx48jPT29VWyRlJSElZUVgoKCYGNjg8WLF2Pz5s148+ZNm5/3CfhC\nWloa/P39MXHiRISGhsLHxwd79uyBlpZWqys2JycnIyQkBFZWVjXaCwsL8eTJE+jo6CAgIABqamrf\n35NbCNLQ6kVOTg7FxcUc1ZVq5yItLY0uXbpg0KBBra6Y0qlTJ6xZswYXLlyAhoYGFi1ahCVLliA2\nNrZV7RDwfyQnJ2Pjxo1wdHTEv//+Cw8PD5w7dw4DBgxok6JCRITt27dj3LhxHCn4al6+fAk5OTmI\ni4sjJiYGsrKyAqcn4P9QVVVFWloa5OXlISIigjdv3gAAxMXFYWpqih49eiAkJKRZOnstRU1NDYsX\nL8aVK1egrKwMR0dHLF26FE+fPuUU/hbAH+j/Z648fPgQP/zwA+zt7VFaWgo/Pz/8/vvvMDc3b1K2\nCq95//49Hj16hNWrV9dSm37+/DnGjh2L169fQ1VVFUpKSt+l0xM8yKgHdXV1xMfHQ0JCApqamrh/\n/z7nQH/YsGFwdnaGubk54uPjoa2t3SY2ysvLw93dHYsXL8a///4Lb29v5OTkwNLSEs7OztDS0moT\nu75FiAgPHjzA+fPnERkZCU1NTdjb22PDhg1QV1dva/M4BAYGYvr06bWkolgsFl6+fIlJkyYhOjoa\nPXv2RLdu3b5LGf7v7x1ziby8PFJSUsBgMNC3b98asXkDBw5ERUUF1NTUsHHjxjY/V1NXV8f06dNx\n9uxZnDhxAiUlJbCxscGYMWMQEhLCqRomoGkUFxcjOTkZO3bsgLGxMRYtWgRNTU0EBgbi2LFjcHBw\naFcOr7CwEOfPn6/1xBb4kpecnJyMESNGICYmBmw2+5us28INXDk9FosFU1NT2NvbAwByc3NhY2MD\nHR0d2NraIi8vj9PX09MT2tra0NPTQ2hoKH+sbgVkZWWRlpYGADA3N0d0dDTKy8sBfAmHcHZ2hoKC\nAu7cuYOXL1+2pak16NatGzw9PfHo0SMsW7YMly9fhoODA1auXInQ0FCUlJS0tYntnpcvX8Lb2xuO\njo5wcXEBEeHIkSN4+vQpR3m4vUFE2Lp1KwYNGoTu3bvXul5aWgpxcXEwGAzk5+fj9evXbSay0OZw\n84h3165d5OzsTPb29kREtG7dOtqxYwcREXl5edGGDRuIiOjVq1dkbGxMFRUVlJCQQJqamrUSqblc\nss15/fo1WVhYENEX6R9NTc0a6WexsbE0d+5c+u2332jVqlWtLhTQFCorK+nAgQPUvXt36tmzJ/36\n66+UkpJCZWVlbSZp1V5gs9lUXl5OBQUFdPz4cTI1NaWuXbvS0qVL6fXr121tHte8evWKevbsWW8I\nyqtXr2jx4sWUnZ1No0ePJhEREUpMTGxlK3lHS/xIozu9lJQUBAcHY+HChZzUooCAAMyZMwfAl2T1\ny5cvAwCuXLmC6dOnQ0REBBoaGtDS0sLjx4/55rD5iaysLHJzc1FSUgJxcXFoa2vXCFHp2bMncnNz\nsWzZMrx58wa5ubltaG3DMJlMuLi4IDExERcvXoSEhASWL1+O8ePHw93dHf/++y/Kysra2sxWpbS0\nFPfu3YOnpyccHR0xffp0JCYm4vfff0d8fDwOHjwIPT29tjaTa86dO4cff/wRCgoKdV6/du0aDA0N\ncfnyZYiLi0NaWhpqamqtbGX7oNEHGT/++CO8vb1RUFDAacvIyOBUZVJSUkJGRgaAL7FKX8tbd+vW\nDampqbXm3LZtG+drKyurWvFE7YHqR/vx8fEwMDCAoaEh53YX+KIaIicnh48fP8LCwgKnTp3C6tWr\n29DixmEwGDAxMYGJiQlcXV1RVFSEgwcPYtq0aWCxWFiwYAGWLVv2Tf9niIuLw759+3Dq1CnIyclh\n3rx52L9/P5SVlSEkJNQmYSYtpbi4GNevX+dsPuoiLCwMP/74I3799VdoaWnBxMSk1eMHW8KdO3dw\n584dnszV4LsODAyEoqIiTE1N612wun5CfdR17Wun116pFhONi4uDgYEBBgwYgLdv33KuCwsLY+DA\ngThw4AAWLlyIyZMnw9nZuVVTjVqCsLAwZGVlsXHjRqxZswZPnz7F7du3sXLlShARdHR00L9/f+jr\n66NXr14dMrShqKgIsbGxePXqFaKiopCcnAwxMTH0798fN27cgKGhYYd8X19TVVWFFStWYPTo0RyR\n0P+Sn5+PFy9eQFJSEs+ePcPgwYOhoqLSypa2jP9ujn755Zdmz9Wg04uIiEBAQACCg4NRVlaGgoIC\nzJo1C0pKSvj06ROUlZWRnp7OyUFVU1NDcnIyZ3xKSkqH3jVoa2sjLi4OAKCnp1erDOSAAQOwceNG\n7NixA4MGDcLhw4exZcuWtjC1RYiIiGDQoEEYNGgQysvLUVxcjAcPHuCff/6Bi4sLunTpAjs7O0yd\nOhVmZmbtOsyhtLQUt2/fhp+fH8LCwqCgoAA7OzvMnDkT2trakJKS6vCO7msiIiJw69YtvHjxot7f\ny/PnzyEtLY3U1FSYmJiAiHhWcKgjwiDiTjfo7t272LlzJ65evYr169ejS5cu2LBhA7y8vJCXlwcv\nLy/ExsbC2dkZjx8/RmpqKkaOHIm4uLgauz0Gg8G1VFFb8+effyImJgaHDh1CSkoKli5disDAQM71\n8vJyaGtrw9fXF3p6enB2doavr2+H2e1xQ1lZGR48eIDw8HBERkaiuLgYysrK0NHRgb6+PkeKvWvX\nrjwVQmgIIkJBQQEyMjKQnJyMxMRExMTEIC0tDfn5+VBUVISFhQWGDh0KPT29du2kW8rs2bPh6OhY\npwhrNTt27EBqaipERUWhq6uLu3fvwtvbu8Pt9r6mJX6kSTf11c6rOu3m6NGj0NDQwLlz5wAA+vr6\nHFUOJpOJAwcOdMgzkmqqcxSJCDIyMigtLeWodQCAmJgYFi1ahFu3bsHS0hJWVlY4e/YsXF1d29hy\n3iEuLo7hw4dj+PDhKCsrQ35+PifkISIiAgcPHkRCQgLk5eXRp08fmJiYwNjYGCYmJjyr5lVYWIgP\nHz7g+fPnePbsGZ4/f4709HRISkrCxMQEAwcOxKxZs6CoqAhpaWlIS0t/046umjt37qC4uJijIVgX\nVVVViIyMxJw5c+Dj44MtW7YgJCSEp5XWOhpc7/R4tmAH2uklJiZi6tSpuHXrFqSkpDBv3jyMHz8e\nkydP5vTJzMzEkiVL8M8//yA+Ph6Ojo4ICwvr0J+iTSU/Px8xMTGIjY1FbGws3r9/j9zcXAgLC0NG\nRobzkpaWhpycHIAvHxjV6VpEhKKiIpSVlaG8vBzl5eUoKCjA58+fkZeXh4qKCnTq1AlqamowMDDg\nPFj6b27p90ROTg5MTU3h4+PDKe1YX79p06bhxIkTWL16NU6fPg1nZ2ecOXOmTdPlWkqr7fS+N9TV\n1cFisVBQUABpaWkYGxsjLCyshtNTVFQEg8FAcXEx9PT0YG1tjZ07d8Lb2/u72G0AX8J7LCwsOCq8\nLBYLhYWFKC4u5jiy0tJSzrkw8OW2ubKyEsCXP2BpaWmIi4tDVFQUTCYT4uLikJCQgKSkJOdfcXHx\nNnuP7QkiwokTJ9C/f/9a9Uz+S35+Prp27YrIyEjo6OiguLgYIiIi383fZl0InF4DCAsLQ0FBAYWF\nhQAAU1NTHD16FCwWq8b5VZ8+fXDz5k1MmzYNv/zyC+zs7PDu3bsOFefFS4SFhSEnJ8fZ1QngLZ8+\nfUJQUBAuXrzY6G7tzZs30NbWxvnz5+Hg4IDIyEioqqp+107v+33nXKKsrMzZnZiamiI3N7dGvB4A\nDB48GH/99RcAoHPnzpg7dy58fHxa3VYB3z5VVVVwcXHBxIkTufpQuXnzJlRUVHDnzh2YmZnh4cOH\nUFdX79Bn7S1F4PQaQVVVlZNbLCcnBy0tLSQmJtboY2ZmhlevXiE+Ph4AMH78eISHh+Phw4etba6A\nbxgiwrlz5/D+/XvMnz+/0f5sNhsRERF4//49+vTpgx49euDhw4ffrdBANQKn1wja2to1nJyFhQUS\nEhJq9FFUVIS1tTUnjk9JSQmbN2/Gli1bamSyCBDQEvLy8nDixAmcPXsWnTp1arR/fHw8MjMzERcX\nh2XLloHNZuPp06ftShmmLRA4vUbo1asXPnz4wPl++PDhNTIzqlm8eDHu3r2LiooKAMCUKVPQqVMn\n3Lt3r9VsFfDtQkQ4dOgQ+vXrBwMDA67GhIeHQ1lZGSUlJbCzs0NGRgby8/PrVGH5nhA4vUaQk5PD\np0+fON/36dOnRs2MaoYOHYqSkhJkZ2dz2v73v/9hz5497VqMQEDHICgoCOfPn8eSJUu46k9ECA8P\nh5GREXR1dSEkJIR3795BSUmp3nS17wWB02sEaWlpjqACAEhJSdV5yyokJAQ9Pb0a9SrMzMygr6+P\nH3/8scPEJgpof2RmZsLd3R0nT57kepeWn5/PuSMZNmwYAODDhw+wsLD4rp/cAgKn1yjS0tLIzc3l\nCIhKSkpCRESkRo5xNcOHD4evry/newaDgS1btiAuLg53795tNZsFfDsQEXbv3g17e3uub2uBL45S\nSkoKjx8/5oyLi4vD0KFD+WVqh0Hg9BpBRkYG4uLinHM9MTExaGlp1VkJzdDQEOHh4TWUpLt06QIv\nLy/s2bOn1WwW8O1QLfixdOnSJo2rlnQTFhaGjo4OKisrkZSUxNn1fc8InF4jiIuLQ0lJCa9eveK0\nGRkZISAgoFZfdXV1GBsb4/z58zXazc3NISsri127drV5PQ0BHYfExETs3LkT+/fvr1cctD7Cw8Px\n8uVLLFu2DEwmExUVFSgoKICuri6frO04CJxeIzAYDGhra9dwesbGxrh//36tehNCQkJYtGgRrl69\nykmxAr5o83l6euLAgQM1CgwJENAQGzZswOzZs5t1S3rnzh1ISUlh+vTpAL4oAomJiX3353mAwOlx\nhY6ODmJiYjjf6+rqQlxcHO/evavV19bWFoWFhbWyNlRUVHDs2DHs3buXcz4oQEBdVFRU4NdffwWD\nweA4raaQkZGBiIgIODg4QExMDMAXdWUpKSlem9ohETg9LtDR0cGHDx84ZRRFREQwfPhwTgHwr2Ey\nmejbt2+d1ywsLKCuro7Nmzfz3WYBHZe7d+/i+vXr2LdvH1dByP8lLCwMnTp1wq53mbIAACAASURB\nVJgxYzhtr1+/7tCCvrxE4PS4QFtbG0VFRfj8+TOnbdy4cXU6NgAYO3YsR2Pwa5hMJtasWYMrV67g\n+vXrfLNXQMfl06dP2LFjB3bv3t3kczzgy9Pe4OBgjgxXNY8ePUKvXr14aWqHReD0uEBBQQFSUlLI\nycnhtNnY2CAuLq7OBxN6enqIioqqEd9XjZqaGi5duoTdu3cLUtQE1ODz58+YPXs27OzsYGpq2qw5\n8vLyEBMTg8GDB3OKdwFAZGSkYKf3/xE4PS5gMBjQ1NREVlYWp01OTg5lZWV1Oj01NTXo6+vjzJkz\ndc5nYGAAe3t7zJw5E0VFRXyzW0DHoaqqCrt27YKmpiZcXV2bXaksISEBnz59wpIlSzhKKiwWC1FR\nUd99zm01AqfHJdra2jVSzJhMJoSFhTlae/9l3rx5uHTpUq0nvMAXJzp//nx07doVXl5enLNCAd8n\nbDYbHh4eSEpKgre3d4tknxITE9GlSxcYGxtz2pKTk1FaWirY6f1/BE6PS/T19WtkYQgLC0NLSwuh\noaF19re2tgabzeZUU/svkpKSOHz4MB49eoSHDx8K0tS+Y86fP48zZ85g165dzXpw8TX//PMP1q5d\nWyM0pfohRufOnVtq6jeBwOlxSe/evTl6ecCX3Zq+vj4uXrxY75jx48c3qKknJCQET09PuLq64tat\nWzy1V0DH4NGjR/D19UVAQACnlGpzKSgoQEREBPr27Vuj/dWrVxgyZEiL5v6WEDg9LuncuXONMz3g\nS9pZYGAgR07qv4wcORI3btxocF5zc3Ps378f69evR0pKCs/sFdD+iY2NhY2NDVxdXaGtrd3i+Q4e\nPAh1dfUaogREhFevXgnSz75CUCODSyQlJWuErABf4vckJCQQExNT69MVADQ0NJCVlYXY2Fjo6+vX\nO/fAgQOxfPlyuLi44ODBg21a5Wv//v0oLy/H6tWrAQCVlZVwc3NrcIy7uztfbWqsgLq7uzsCAgIQ\nHR2Nn376ia+28Io3b95gw4YN8PX1bbCEI7fk5ubi5MmTGDBgQI3b2JKSEqSnp3OKNgkAQK1MGyzJ\nE/Ly8sjS0pJKSkpqtE+bNo2OHDlS77itW7fSkiVLGp2fxWKRq6srjR07lgoLC1tsb3P4+PEjMRgM\nYjAY9O7dOyIiKi4uJgANvvgNN+u7uLiQjIwM323hBSkpKaSmpka+vr48mzMoKIg6d+5Mfn5+Ndo/\nffpEY8aM4dk67YWW/N0Jbm+5RFJSEgoKCnj+/HmN9qlTpyI6OrpeIYFZs2bh9u3bSE9Pb3B+ISEh\neHt7Q09PDxs2bEB+fj7PbOcGIsLhw4fRqVMnKCsrw83NDUQESUlJEBHnpaKigtmzZ9do45aLFy/i\n7du3TRZd+Hotc3NzWFtbN2v99sC7d+/g4uKCrVu3wsnJiWfzXrx4EaWlpRg+fHiN9qKiIk5xegFf\nEDg9LhEREYG6ujqePXtWo33cuHGIj4+vN59WU1MTpqamtcbVt4a7uzsKCwuxaNEilJaW8sR2bvj8\n+TNCQkIwYsQITJ8+HdevX69VAKmlrFu3DgMHDsTo0aMREhLCl1Cdf//9F/3794eBgQGOHz9e49rt\n27cxatQo9OzZE7a2tnj8+DHP12+IlJQUODg4YNq0aVi0aFGNMqItISMjA9euXcOwYcNqBCQDQFpa\nGlRVVXmyzreCwOk1AW1t7VrOS1xcHCIiIigrK6tzDIPBwNy5cxEWFsbVGpKSkvjrr78gJyeHX375\npd55ec3r16/x7t07rF69GjNnzkRBQQHCw8N5ukZAQADWrFkDNpuNWbNmQV9fH+vXr0dISEid2StN\npaSkBG5ubtDS0oKcnBwWLlzIkQA7c+YMHB0dQUQYPHgwKisrMWHCBDx58qTF63LD8+fPsWDBAri6\numL69Ok8K8HIYrGwadMmiIuLY8KECbWuP3nyBL179+bJWt8MLbmvbg5tsCTPuH79OhkZGdVqX7hw\nIcXExNQ77tOnT2RlZUUVFRVcr5Wfn0+zZs2i6dOnt8oZn6urK/Xv359YLBaxWCwaMWIETZkypVY/\nFRUVmj17drPXYbPZVFBQQG/fvqVdu3aRtrY2SUlJUa9evejq1auNjjc3Nydra+ta7S4uLiQhIUFP\nnjwhFotFycnJJCcnRytXriQiIlNTU3Jzc6OioiJisViUnZ1Ntra2NHr06Ga/F2558OABGRgYUEBA\nALHZbJ7OHR0dTWpqauTg4ECvX7+udX3WrFl048YNnq7ZHmiJHxHs9JqAtrY2MjMzaygjA1/SykJC\nQuodp6CgAC0tLZw4cYLrtWRkZHDo0CHIyMhg7dq1NYoT8Zq8vDycPn0aurq6CAoKQlBQEPr27YvQ\n0NAaWSjckpGRAQaDwXn9N9WupKQEqampyMjIQGVlJSQkJKCqqtriwFwRERGYmppCSEgI3bp1g4iI\nCGft2NhYbNu2DTIyMmAymejatStCQ0Nr1DThNSwWC/7+/li7di08PDxgb2/P8yLbly5dwg8//ICS\nkpJaZ3dsNhsxMTFQUVHh6ZodHUHIShPo3r07REREkJ6eXqO6fO/eveHp6Yk1a9bUOU5YWBgTJ07E\n+vXrMWvWLIiLi3O1noSEBP744w/s2LED48ePh5+fHzQ1NXnyXr7m5MmTyM3NxenTp3H69Oka13bu\n3AkvL68mzScvL1+j9KWEhAQA4OnTpzh27BjCw8Px8eNHaGhoYMWKFbC2toaGhgZkZWVb/F7qOydT\nVFTEjBkzMG7cuBrt1XpzvKa8vBzbt2/H7du3sX///hppYbyCzWbj/v37WLRoEaKiomr8TQJfzvMK\nCwsFTu8/CHZ6TUBYWBgGBga1BEL19fXx8uVLZGZm1jvW1tYWQkJCePToUZPWFBcXx88//4xp06bB\nxcUF796946nkfFFREf7++2/Y2NigrKyM80SUxWJhxYoVOHjwYJNLWIqIiGDIkCGcV7UjmjlzJm7e\nvAlzc3MEBgYiMjISq1evhrGxMU8cXkMsXrwYR44cQXh4OEpKSlBeXo6IiAhs3LiR52tlZ2dj06ZN\nePToEc6ePcsXhwcAe/fuhb6+PoKDgzFgwACIiIjUuB4ZGQlVVVVB+tl/EDi9JmJiYlIrc0JVVRWa\nmpp48OBBveNERESwefPmBm+DG2LVqlVYsGAB7O3t4evryzPHFxMTg7i4OMydO7fGrkdISAjjx49H\ncXEx1w9hGuP48eO4desWjh07BktLy2YriTSHlStXYtu2bTh//jwmTJiA8ePHIzAwEM7OzjxdJyoq\nChMnTkSnTp1w5swZvu2ykpKS4O7uDicnJ4SFhdUpKf/8+XMMHDiQ57fUHR6enSxySRssyVMuXrxI\nbm5utdo9PT1p/fr1DR5U5+bm0pgxY6iqqqrZ6yclJdHAgQPJ09OTPn/+3Ox5BPCWkpISCg4OJlNT\nU/L39+frWmw2mzw9PWnZsmX06NEj6tmzZ62/KTabTZMnT6ZLly7x1Za2oiV+RLDTayJGRkZISkqq\n1T516lTExMQ0GFsnLS0NVVXVOstHckv37t1x8eJFJCYmYtasWTyPpRPQdLKzs7Fy5UocPnwYJ0+e\nhIODA1/XKysrQ3h4ONzc3PDs2TM4OTnVOsssKChAeno6BgwYwFdbOiICp9dEZGRk6lQ8rn7A0FAm\nBZPJhL29PTZt2gQWi9VsG1RUVODj4wMbGxsMGTIE165dE2jytQGVlZUIDg6GgYEBunfvjvPnz8PQ\n0JDvt5PHjx9Hnz59IC8vjydPnmDmzJm1+nz+/Bni4uKChxh1IHB6TURMTAwlJSV1pj9169at0dAS\nGxsbziF6S/nhhx9w9uxZnD59GqtWraqzOpsA3kNEiIyMxMKFC/H333/j4sWL+N///sezDIuGePfu\nHTw9PbFgwQIwGAxkZWXVKVCRk5ODHj168N2ejojA6TURMTExiImJ1ZlLa2Zmhjt37jQ4XlJSEhs2\nbEBwcHCL80aFhIRgYWGBU6dOQUtLC0OHDsWFCxcEBcX5CIvFwr59+2BnZwdbW1v4+vpi8ODBrVJP\nls1mw8fHBwsWLICenh5iYmIgLS3NCQn6mvj4eEEmRj0InF4TERUVRbdu3epM0dLR0WnU6QGAs7Mz\nXr58ybMUMyaTiVWrVuHGjRu4efMmpk2bBn9//xbdQguoSW5uLnx8fDBlyhR8/PgR4eHhmDFjRqs+\nGU1KSsK7d+84YTYHDhyoM1QFAJ49e1ajGpqA/0Pg9JpIdZGgf//9t9Y1TU1NREdHN6qQIikpCV1d\nXU5eKK8wMjLCvn374OHhgd9//x2Wlpb1ytUL4J7r16/DzMwM//77L/bt24cdO3ZAS0ur1e346aef\n4OjoCHFxcZSVleH06dP16uS9fv1acJ5XH7x6hMwtbbAkzwkODiZjY+Na7VVVVWRpaUmXL19udI47\nd+6Qnp4e3/JqS0tL6dixY2Rra0u//PILJSQk8GWdb5Wqqiq6fv06OTg40MSJEyk8PLxN7bl06RL1\n79+fcnNziYjo/v37pKamRmVlZbX6FhUVkYmJCaWmpra2ma1GS/yIYKfXDLS0tBAXF1erEpqwsDAm\nTJjAVSFvCwsLSEpKNjtYuTHExcUxd+5c/PPPP5CQkMC4ceOwZ8+eeiWwBPwfz58/h7W1NbZs2QJX\nV1f4+vrWGfzbWnz+/Bl79+7FX3/9xcmuePDgAWbPnl1nGl1UVBQ6deqErl27trapHQKB02sGGhoa\nEBUVrTNez8HBAa9evWq0kDeTyYSXlxeuXLlSb42NlsJgMNClSxesW7cO586dQ3R0NJycnODr64uU\nlJQOJ8DJT8rLyxEWFoYFCxZg/fr1cHJywq1btzBs2DBISUm1qW2BgYEwMDDgpLNVVVUhKioK8+bN\nq7N/REQETE1N6zzrEyBwes1CREQERkZG+PjxY61rPXv2hIyMDFeqKNbW1igoKGgwZ5dX9OnTB0eO\nHIG3tzdiYmJgb2+Pffv2obKyku9rt2fYbDaCg4NhZWWFnTt3YsaMGTh37hyWLl3a5s4O+PIU1tvb\nGy4uLpy2yspKFBYWomfPnnWOefDgAQYOHNhaJnY4BE6vmQwdOhQJCQl1XjM0NKz32tcICQlhxIgR\nOHz4MK/NqxMGgwEtLS14eXnhyJEjuHnzJuzs7HDu3DmkpKR8V6Eu2dnZCA4OhpOTEzw8PLBgwQJc\nvnwZI0aMqKVW0laUlpbip59+wowZM2qEn7x69QpKSkp1xgXm5+cjMTERgwYNak1TOxQCp9dMRowY\ngbi4uDpvEQcPHsx1kv7YsWNx6tSpOm+V+YmZmRnOnj2LX3/9FTExMXB0dISrqys+fPjQqna0NhkZ\nGfj5559hb2+PgIAAuLi4ICAgAAsXLuRa8qu1uHfvHsrLy+Hq6lqjfd++fRg8eHCd4TIZGRmQlJQU\nBCY3BM8ep3BJGyzJFwoKCmjq1KnEYrFqXYuNjSVLS0uuhQVWrlxJmzZtqnOu1iI1NZWWLVtGenp6\ntGHDBnr9+nWbVWXjNYWFhRQbG0vu7u7Up08fcnJyoufPn7e1WQ2Sm5tLQ4cOpYcPH9Zo//z5M8nK\nytKbN2/qHHf37l2aN29ea5jYprTEjwhERJuJqKgo2Gw22Gx2rWj87t27o6ysDDExMVxpqW3duhWO\njo7IyMhos9gqVVVV7N+/H/Hx8QgLC8OaNWvAYrFga2sLR0fHNq3F21wyMjLg5+eH4OBgiImJwdbW\nFmfPnoWurm6rylo1lbKyMri6umLYsGG16infvn0burq69cYJJiQkwMjIqDXM7LAIbm+bSfV5Sl0P\nAqSkpDBw4EBcvXqVq7m6dOmCQYMGcRXqwm969eqFxYsXIzAwEL/++isePHiAIUOGYPHixYiMjERe\nXl67zfSoqqpCbm4uXr16hSVLlsDU1BT379+Hl5cXrl69ihUrVqBPnz7t2uEBwI0bN5CWloZt27bV\neALLZrNx69YtLFu2rN483xcvXqBfv36tZWqHpH3/9tsxwsLCUFFRQWRkZJ1R8ePHj4eHhwfWr18P\nUVHRRudzcHDAsmXLMHnyZEhLS/PD5CbBYDBgbm6Oc+fOISEhAREREdi3bx9SUlKgpaWFESNGwMLC\nAsrKym0uUvn+/XvcunUL9+7dw+fPn6GsrAwrKyts3LgRGhoabW5fU8jOzsb+/fvh6elZy7EVFRUh\nPj6+Qfn+pKQkQZ3bxuDhbTZXtMGSfOOPP/6grVu31nmtsrKSTExMKD4+nqu52Gw2TZgwgX7//Xde\nmshzqqqqyM/PjwYNGkQyMjJkbW1NR48epbS0NCotLaXKykqeV/yqhsViUUVFBZWUlNC7d+9o586d\nZG5uTrKysuTk5ET37t1r03PRllJWVkYjR44kDw+POq8nJCTQ9OnTGxw/cOBAyszM5JeJ7YaW+BHB\nTq8FaGpqwt/fH7/88kuta0wmEwMGDMCHDx/qjaf6GgaDATc3N/zwww9wdnaGoqIiP0xuMcLCwnBy\ncoKTkxNSU1MRFRWFFy9eYMOGDSgtLeUURe/Vqxe6d+8ONTU1KCsrQ15evkm3lSwWCxkZGfj06ROS\nkpLw8eNHxMfHIykpCWw2G3JycjA0NMT27dthZmYGeXl5Pr7r1uH48ePo2rUrVq1aVed1f3//BuPv\n7t69C2VlZUFNjEYQOL0WoKmpicePH6O8vLzOdKBx48bh3r17GDlyJFfzGRkZwdzcHKGhoXUKQ7Y3\n1NTUoKamBjs7O85Dnfz8fNy5cwdhYWE4cuQI3rx5g/LycoiKikJDQwNqampQVVWFoqJiDSf4+fNn\nFBYWIi0tDWlpaUhMTASLxYKYmBj69euHAQMGYPTo0Rg6dCjExcUhJCTUKnJOrUVKSgqOHj2KwMBA\nSEpK1tnn9OnTOHjwYL1zXL9+Haampu3+zLKtEfx0WkB1Otr79+/rlPHR0dGBj49Pk+acO3cuXF1d\nMW7cuA71iV3thLp06YLJkydj8uTJAL486MnKykJmZiYyMzORn5+PgoICFBYW1giGVldXh5iYGGRk\nZCArKwsFBQWoqKhAUVGxQ53JNYeEhARMnToVGzZsqHeH/+TJE5SWltYrF1VZWYl79+5h+/bt/DT1\nm0Dg9FqAhIQE+vbti7dv39b5x6iqqoqioiK8ffsWurq6XM1pYGAALS0t7N69G+7u7rw2udURERGB\nqqoqVFVV29qUdsvPP/+M5cuXY/LkyfU6+ICAAEycOLHeh1yfPn1CRkaGIP2MC76d+4M2YuTIkXj7\n9m2d16SlpdGvXz+cOXOG6/mEhISwZcsWBAcHIz4+nldmCmiHVFVVwcvLC6KiopgxY0a9t+tFRUV4\n8uQJ5s6dW+9ciYmJ6N27Nzp16sQna78dBE6vhYwcORIfPnyoN3ZtwoQJuHjxYpNUkrt3744ZM2bg\n4sWLvDJTQDvEz88Px48fh4eHR4NhTenp6ZCUlISenl69fRISEjB48GB+mPnNIXB6LcTMzAxZWVn1\n6tQNGjQIDAYD79+/b9K8U6dORXBwcJ1KLgI6Pg8ePICvry/u3LkDJSWlBvvevn0bFhYWDZ5txsTE\nwNLSktdmfpMInF4LERERgYiISL1Oj8lkwtbWFq9evWrSvGpqapgyZQqWLFnCs1oaAtoHT58+xaxZ\ns7B161au0g7Pnj1bryx8NUlJSVyFRgkQOD2eICsri9zc3HqvOzg4NLnko5CQEBYtWoTKykrcuHGj\npSbyhKqqKgwfPhxycnKIiYnhtDMYjAZfRUVFbWh1+yI5ORk//fQTvLy8GnVkABAZGYmcnJwGK5tV\nVFTg8+fP7SKTpyMgcHo8QE9Pr87qaNVoaGg0+fYW+LKL9Pb2xuHDh9tFvmtMTAwiIyNRVFQEX19f\nTvvly5c5r2o9uq/b2ptkU1uRkpKCefPmYcqUKZgyZQpXY3x9fWFvbw9ZWdl6+zx58gTy8vICp8cl\njTo9DQ0NGBkZwdTUFP379wfwpRyejY0NdHR0YGtri7y8PE5/T09PaGtrQ09PD6GhofyzvB2hqamJ\n27dv13tdXl4ekpKSdVZQawxDQ0N0794dO3bsaHORz9u3b6OiogIuLi7w8fHh1AiZMGEC59W9e3eI\niYnVaOM2WPann37Cpk2bEB0djby8vCbJ2VdUVCAtLQ3v37/H+/fvkZWV1a7k8LOzs7F48WJYWVlh\nwYIFXI3Jzc3FgwcPsHDhwgb7BQYGQl9fXyAPzy2N5alpaGhQTk5OjbZ169bRjh07iIjIy8uLNmzY\nQEREr169ImNjY6qoqKCEhATS1NSslQvJxZIdjsjISOrVq1eD+nn79++nyZMnN2v++Ph40tHRoSdP\nnjTXRJ4wbNgwmj9/Pj169Ijk5eXp0KFDtfrMnTuXlJSUmjW/n58f9e3bl2RlZWnw4MG0bt06un//\nPle6hPv27aNevXqRqKgoiYmJkZGREd27d69ZdvCaz58/k7OzM7m7u3OtsUhE9PjxY3J0dGywD4vF\nImNjYwoKCmqpmR2KlvgRrpxednZ2jTZdXV369OkTERGlp6eTrq4uERFt376dvLy8OP1GjRpFDx48\n4Jmx7ZW8vDxSVFSkd+/e1dsnKSmJunbtSmlpac1a4/r16zRt2rQm/afhJR8+fCBxcXF6+/YtlZeX\nk7m5OY0YMYJKSkpq9GuJ0yP6Irzw9OlTmjZtGsnLy5OIiAj17t2bjh49Snl5efWO++uvv+jy5cuU\nlJREL168oFGjRpGhoWGz7eAVWVlZNGbMGHJxcaGKioomjfX09KRTp0412Cc1NZXk5eU5/x+/F1ri\nRxq972AwGBg5ciSEhYWxZMkSLFq0CBkZGZzH7EpKSsjIyAAApKWl1YgI79atG1JTU2vNuW3bNs7X\nVlZWsLKyasFete2RlZVFnz59EBUVBW1t7Tr7dO/eHYMGDcKjR48wceLEJq8xfPhwnD9/Hjt37sT6\n9etbPTVr3bp16N+/P9TU1CAqKooVK1Zg/fr1SEhIgL6+fpPnW7t2Lefr2bNnc4QvGQwGzMzMcObM\nGdy9exdbt25FeHg4FixYgIiICBw5cqTWXBUVFcjJyYGnpydSU1M51eXq05xrLdLT07Fy5UoMHToU\n69ata7Lgwo0bN7B3794G+7158wa6urrtVqCCV9y5cwd37tzhzWSNecXqnUlmZiYZGxtTeHg4ycnJ\n1ejTuXNnIiL64YcfyNfXl9O+YMEC8vf355mHbs94enrSxo0bG+wTFBREa9eubfYaHz9+JAkJCbp5\n82az52gOHz58IBEREQJQ6/XHH3/U6MvtTo/JZHJeFy9eJKIvu7zKykq6f/8+jRo1ioSFhUlYWJiM\njY3pwoUL9cpGpaSkUOfOnWnVqlWUkZFBREQeHh5t+reWmppKRkZGtGXLlmbJXd29e5eGDh1KpaWl\nDfbbu3dvvVJU3zIt+d02+tFTHUfUtWtXODg44PHjx1BSUsKnT5+grKyM9PR0zqeMmpoakpOTOWNT\nUlKgpqbGG+/czhk1ahTc3d1RUVFRb3T9wIEDmyxA8DXq6uoIDQ3Fjh07YGJi0mpySteuXQOLxcKP\nP/4ICQkJTnt0dDQOHjwIFxcXroRSv6Yuxeljx47h999/R3p6Ovr374/t27fDxsYGRkZGDe7a2Gw2\nysrKMG7cOMjIyODNmzcIDAxskj285PHjx3Bzc8PixYvh4uLSZDUYFouFw4cPw8HBodEn3y9fvsQP\nP/zQEnO/PxryiMXFxVRQUEBEREVFRTR48GC6fv06rVu3jnN25+npWetBRnl5OcXHx1OvXr1qCUo2\nsmSHhc1mk7W1da3zz68pLy+nqVOn0qtXr1q01o4dO8ja2poqKytbNA83VFZWkp2dHVlaWtb6Xd6/\nf5/k5OToypUrnLaWnOlt2bKFPDw8KDU1lcrLy7kWI83Ly6P+/fuTuLg4ycjIkKSkJJmamrbJ39rN\nmzdJSUmJgoODmy1ompCQQHp6epSfn99o34kTJ9Lnz5+btU5HpiW/2wZ3ehkZGXBwcADwJTB1xowZ\nsLW1hbm5ORwdHXH06FFoaGjg3LlzAAB9fX04OjpCX18fTCYTBw4c+OZlgaphMBjo0qULCgsL65Xr\nFhUVxZAhQ/Dbb7/hxIkTzV5r2bJlePHiBTZu3AgPD486tfx4BRFBX18fDg4OtX6X+vr6cHV1rRGy\nZGVlha5duzZrLTc3t2aNk5WVxYkTJ+Dn54fS0lIMGzYMoqKiuHTpUrPmaw7FxcXw8/PDhQsXcOXK\nFQwYMKDZcz19+hS2traQkZFpsF91QLwgDrKJ8M73ckcbLNlqrF69mu7fv99gn9evX5OUlFSDO0Ju\nKCkpoUmTJtHu3btbNI+AlsNisWjhwoVkY2NDKSkpLZbLnz9/fq2oh7o4fvw4rVu3jm/y/O2ZlvgR\nQUYGDzEwMMD9+/cb7KOrqwt9fX3cu3evRWtJSEhg586d8Pf3x969e+vN/RXAP4gIkZGRGD16NOTk\n5BAUFAQ1NbUW3d1kZWXhw4cP0NTUbLSvn58fTE1Nv5u7KV4hcHo8pGfPno06PQaDgS1btiAsLKzF\nGRY9e/aEv78/bt++DU9PzxbNJaBpEBH++usvLFmyBGvWrMGvv/7Kk4yI/fv3w8zMrNGKZnl5ebh3\n7x7MzMxavOb3hsDp8ZCePXsiJiam0QT70aNHIzExkSfqKUpKSvDx8UFUVBRmz56NlJSUFs8poGHi\n4uIwZ84cXL58GWfPnsWoUaN4cq6ak5MDX19fzJkzp9Envi9fvkTXrl3rLfotoH4ETo+HqKmpQU5O\nDo8ePWqwH5PJhIaGBs+CLZWUlHDy5EkYGBjAyckJQUFB7Srv9FuhoqIChw8fxrRp0zBw4ECcP38e\nvXr14tn8Dx48gLGxMQwNDRvt+/z5c0yePPmbKo7UWgh+YjyEyWRi+PDhjZ7XMRgMWFtbY8eOHTxT\nT5GTk8P69evh5eWFn3/+GevXr0daWprA+fGAqqoqvHnzBjNmzMClS5dwsISkZwAAIABJREFU4cIF\nLFu2jOfS7NevX8eKFSsaPaNjs9mIiYmBk5MTT9f/XhA4PR4zevRoPHv2rM7g26+xsrLC69ev8fLl\nS56uP2TIEFy7dg1KSkqYNGkSTp8+zdP5vzeKi4uxZcsWLF++HFOnTsXZs2f5ItZZXFyM9+/fc9Lx\nGqKyshKZmZkwMTHhuR3fAwKnx2MsLS2RnZ3doKgoAHTu3Blz5sxBYGAgz3djXbt2xdq1a+Hr64tD\nhw7B0dGxzhxoAfVTVVWFiIgIDB48GGlpafD394ejoyPfNOsOHTqE3r17Q05OrtG+ZWVlYDKZgvq2\nzUTg9HiMiIgI1NXVkZ2d3WjfNWvW4NGjRyguLuaLLVpaWrh06RIGDRqE+fPnY8+ePSgoKODLWt8S\nMTExcHFxgbe3Nzw8PHDkyBGunFFzyc7Oxh9//IHZs2dzdUZ379499OzZUxCq0kwETo8P6OnpISkp\nqdF+ysrKkJSURFZWFt9sUVRUxI8//oiTJ08iJCQEQ4cOxcuXL1FVVcW3NTsqhYWF2Lp1K8aNG4eR\nI0fi0qVLsLOz47s4561bt2BoaAhTU1Ou+vv5+cHY2Fjg9JqJwOnxgX79+jUoH/81I0aMwF9//cVn\ni7442GvXrmHHjh3YvHkzFixY0OhT5u+F3Nxc7Nu3D87OzhAWFsbdu3cxbdq0Vlv/2rVr+Pnnn7nq\nW1BQgNDQUK4dpIA64E1SCPe0wZKtzvPnz2nUqFFc9X379i0pKyvXUqfmJ1VVVXT06FGSkZGhLVu2\n1BIC/Z548uQJGRgY0KhRoyg5ObnVU7qKiopo9OjRXP8Obt26Rerq6s0WM/hWaIkfEez0+ICqqirS\n09M54qoNoaWlhaFDh+LUqVOtYNkXhIWFMX/+fDx79gwlJSWYNGkS9uzZg7S0tFazoS0pKCjA+fPn\n4ezsDG9vb/z2228ICQlBt27dWv2Wcc2aNbC2tuZaNOD+/fuYMWOGID6vJfDQ+XJFGyzZ6rDZbBoz\nZgydO3eOq/5xcXFkbW3NkfFqTaqqqigzM5M2btxIGhoa5OnpSYWFha1uR2tx/fp1MjAwoLFjx9KL\nFy+ovLy8zWx58+YNiYqKUmpqKlf9y8rKaNKkSfTmzRs+W9b+aYkfEXxc8AEGg4Hhw4fj1q1bXPXX\n1NSEgoIC4uLi+GxZbYSFhdG1a1ds374dV69eRXJyMiZMmIDt27fj+fPnHT64mc1mIyEhASdOnMCU\nKVNw6NAh7Ny5E0FBQTAyMmqy+CmvICKcPXsWrq6uUFVV5WpMUVERysrKoKury2frvm0ETo9PjBw5\nEpGRkVyHo0yYMAFHjx7ls1X1w2AwYGBggL179+L48eMQExPDrFmzMG7cODx8+LDN7GoJcXFxWLp0\nKaytrfHixQts27YNvr6+GDVqVFubhpKSEjx48ABbt27lekxGRsY3XwujNRBEN/IJY2NjCAkJISUl\nhatPZgsLC7i7uyMhIYEvEf/cIiwsjO7du2PNmjWYO3cuTp8+jc2bN0NKSgoODg4YMGAANDU126Vw\nJZvNxocPHxAdHQ1/f38kJCTAxsYG4eHh6NatW1ubV4MbN26gV69eTUplu3z5Mvr168dHq74PGNTK\n9y8MBqPD3zJxy/LlyzFx4kTY2Ng02peIsGnTJpSUlGDPnj3tKgaroKAACQkJCAgIQGBgIDp16oRJ\nkyZh0qRJnBoqbUlhYSFH8SQ7OxtDhgzBpEmToKen12p1RJpCQUEB+vbti2PHjsHS0pKrMUQEc3Nz\n7N27FxYWFny2sP3TEj8icHp85Ny5c4iLi8PmzZu56p+dnY1x48bhwoULUFdX57N1zYOIcO3aNZw8\neRJv3ryBlpYWbG1t0b9/fygrK0NeXp6v8vXl5eXIzc1FVlYWoqKiEBYWhufPn0NbWxuTJk3ChAkT\n+JYqxguICIcOHcKlS5dw7do1rp/CxsbGYuzYsYiKikLnzp35bGX7pyV+RHB7y0d69+6N8+fPc91f\nQUEB1tbWCAsLw7x58/hoWfNhMBgYO3YsxowZg/T0dMTFxSEqKgq///47kpKSICEhAX19fZiZmcHQ\n0BA6OjotuhWuqqrC69evERMTg+fPnyM6OhqlpaXQ0NCAmZkZFi9ejJ49e0JFRaXN69xyQ0FBAa5c\nuYI///yzSWEnoaGhGDZsmMDh8QCB0+MjioqKSE5ORnFxMaSkpLgaM3XqVKxatQrOzs583TG1FAaD\nAVVVVaiqqnJu0aqqqvD8+XOEhobC19cXHz58ABFBWVkZampqUFFRQZcuXaCgoAB5eflaTqqoqAif\nPn1CRkYGUlNT8fHjR6SkpEBSUhJ6enoYOnQoPD09YWRk1GHj1CIjI6GqqgodHR2ux1RWViI8PBwu\nLi58tOz7QeD0+EiXLl2gpqaGkJAQTJ48masxvXv3hqKiIo4fP46lS5fy2ULewmQyYW5uDnNzcwBf\n1ECysrKQk5ODz58/Iy8vDyUlJSgqKsLHjx9ryeWLi4tDVVUV2trakJWVRefOndG5c2coKipy/aHR\nnikqKsL//vc/eHh4NGlcTk4OCgsLuT7/E9AwAqfHR5hMJqysrODv78+10xMXF8eaNWuwdOlSODo6\ntsuDeG4RFxeHurp6uz2fbE2ICKdOnYK0tHSTnVdmZia6d+/ernf+HYmOeY/QgRg9ejSePHmCnJwc\nrscMGDAA/fr1Q0hICB8tE9CaZGVl4dKlS9i7d2+Tzx5DQkIET2x5iMDp8RltbW0oKyvj/fv3XI9h\nMBhwdXXF8ePHv5sn3d86N2/eRN++fZuVTREYGAhjY2M+WPV9InB6rcCoUaMQGxvbpDFaWlpQVFSE\nj48Pn6wS0FokJyfjzz//xJw5c5o89sWLF8jPz4e2tjYfLPs+ETi9VsDOzq7J2nXVZ3teXl7fjfrJ\ntwibzcbWrVsxYsQI9O7du8njL168CGtra8jIyPDBuu8TgdNrBZSUlJCcnNzk4t59+/bFjBkzWq24\nT3BwMA4fPoyEhAROW1VVFXx8fGpUbfPx8YGvr2+NW++QkBCcPXu2VewEvjiT8PBwHDt2DH///Xer\nrdtUHj58iLS0NGzevLnJWTYlJSUIDw/H9OnT+WTdd0qz9VmaSRss2eaUlZXRxIkT6fHjx00em5KS\nQhYWFq0iOzVmzBhiMBi0cuVKTltxcTEBoLKyMk4bAGIymRQeHs5pGz9+PPXu3ZvvNlZz/vx5kpaW\nJiEhIdLQ0Gi1dZvKlClTKDg4uFlj37x5QyNHjvzuBUProiV+RLDTawXExMQwYMAAnDhxosljVVRU\nMHr0aCxZsgTl5eW8N+4/CAkJ4e+//0Z8fHyD/cTFxbFr1y6UlpY2e60nT54gPj6+WbV/L1y4ABUV\nFXz69KnGzrS9wGaz4ePjAzabjaFDhzZrjtjYWAwcOLDDBmK3VwQ/zVbC1tYWAQEBKCwsbNI4ISEh\nrFy5Eu/evUNQUBCfrPs/lJSUoKGhgZUrVzZ4O758+XLcvXsXr169avZaW7ZswYgRI+Do6Ihr166h\noqKCq3Hm5ua4du0aUlJSMGbMGNjb24PFYuHo0aMYO3YsLCwssHnzZhQXF+PJkyewtLSEt7c3Z7yn\npyesrKwQFRXVbNsbIzY2Fj4+Pti9e3ezi4IHBQXB2tqax5YJEDi9VsLExASysrLNchIyMjI4efIk\njh07hrKyMj5Y938oKChg2rRpCA8Px/379+vtN3PmTGhpaWHXrl1NPqusZvfu3XBycsLHjx8xY8YM\n9OnTB7/88gsePnzYYFxj586dISIiAmFhYXTu3BlSUlLYuHEjli1bhqysLDCZTBw/fhwDBw6EiooK\nlJSUcOzYMSQnJyMhIQHHjx9Hjx49YGBg0Cy7G4PFYmHfvn3YsGEDevTo0aw58vPz8eLFC2hpafHY\nOgGCM71WZNu2bbR///5mja2qqqK1a9fS2rVreWzV/zFmzBgyMjKi3NxcUlNTo0WLFtV7phcTE0Pn\nzp2jTp060e3bt5t9psdmsyknJ4cePnxI7u7upK2tTbKystS3b1/6+++/6x1na2tLpqamRET06dMn\nUldXp61bt9Lnz5+pvLycAgICSFJSknbv3k2ZmZmkp6dH3t7e5OnpSaampnwtxLR3716aMmVKi2T3\njx07Ro6OjlRVVcVDy74dWuJHBDu9VsTR0RFPnz5t1lhhYWGsWbMG58+fx9WrV/katNy5c2d4enri\n7NmzSE5OrrffsGHDoKWlBXd3d5SUlDQ4J4PB4LxevHhRo11ERARycnKQlZWFiIgIqqqqkJ+f3+ic\n1ZSVlSEtLQ0rV66EnJwcREVFYW1tDQkJCbx9+xZdu3bFli1bsGvXLuzZswdubm58S++LiIjAn3/+\nie3btzf7traqqgpnzpzB5MmTO4RyTEdDkHvbiqipqeHTp09gsVjN+mNWVlZGYGAgVq9eDUtLS8jK\nyvLByi/Y29tjz549mD9/fr19FBUVsWTJEmzYsAFMJhNKSkr19vXz8+N8XX3L9+7dO/j7++PmzZt4\n+fIlJCUlMWnSJNjY2MDY2BjKyspc2SosLAwpKSlER0dj+PDhAL7kq1ZVVUFOTg4A8PjxY9jY2CAn\nJwf379+HnZ0dV3M3hfLycnh4eODPP/9sUTBxYmIisrOzMXbsWB5aJ4AD7zac3NEGS7YbqqqqaP78\n+RQaGtqieby9vWnq1KlUWlrKI8u+UH17W82OHTsIQL23t0RELBaLdHV1CUCTb29tbGyoS5cuNGLE\nCLp48WKNNRrj69vbgoICGjFiBCkqKtKlS5coKiqKJk+eTOLi4nTr1i0KCgqiLl26UHR0NEVERJCs\nrCyFhobytMZtaWkpOTg40OrVq6mysrJFcwUEBNAPP/zAI8u+TVriRwS3t62IsLAwLC0tsXPnzhbN\ns2jRIoiJicHNzY3rJ57NYfbs2VBQUGiwj5CQENzc3JpVVWzTpk0IDw/H9evX4eDg0GwVEWlpafz2\n228YMGAA5s6di/79+yMxMRFHjx6FkpISli9fjnHjxkFHRwcmJiawtbXF8uXLeVZ9juj/tXffUVFe\n+f/A3wzFqKCESBOw0ERAAcUW4AtYEBVExbCCQYOxRw3qimxyLLgaQMUVVz1u1qBYsazGRlGaYEMU\nCSp2BxcBEel1BmY+vz/8Zn7ytTMzPMDc1zk5Jwzz3PvhCp+593luIYSGhkJDQwOrVq2Ciop0A6jz\n589jypQpMomNeRvbLr6V5efnw8zMDE+ePIGBgUGLyyEijBw5EkFBQXB3d29TZ2ooErFYjAsXLmDj\nxo2IjY2VevunxsZGuLq64tixY23i/JG2Spo8wnp6rczIyAjOzs5IT0+XqhwlJSVERkYiJCQEBw4c\naNEEX0Y6IpEIUVFRWLduHbZt2yaT/e6io6Nhbm4ObW1tGUTIvAtLehxYtGgRLl++3OL5bX8aOHAg\nTp06hfDwcFy9elVG0TGfKiUlBbt370ZSUhKsrKykLk8kEmHnzp3w8vKSeojMvB9Lehxwc3PD06dP\n0djYKHVZurq62LdvH0JCQrB9+/ZPPlycabnq6mqEhIRgy5Yt+O2332R2BnBOTg6amprg5uYmk/KY\nd2NJjwOqqqrQ1tbGvXv3ZFLeoEGDcOTIEZw+fRpBQUFsqCtH5eXl+Mtf/oJnz57h+PHjMunh/en6\n9evw9vZG586dZVYm8zaW9DjA4/Hg7OyM8PBwmZWppaWFQ4cOgcfjYcKECUhJSZFZ2czrCdBHjhzB\ntGnTMHToUGzduhVdunSRaR1JSUnw8/OTaZnMO8hk0sxn4KDKNunJkyekoaFBhYWFMi1XKBRSamoq\nDR48mFasWEF1dXUyLV8RFRYWkpeXF7m4uNAff/wh0/l9f3r06BFNmDCBampqZF52RyRNHmE9PY4Y\nGxtj+PDhSEhIkGm5qqqqcHZ2xn/+8x/k5eVhzpw5yMnJkfqhiSKqr69HbGws/Pz8YGNjg7i4OAwc\nOFAu04M2btwIFxeXDnHUZZsnw+T7STioss26dOkS+fr6kkAgkEv59fX1FBUVRcbGxvTbb7/JpY6O\nqrq6mubNm0fOzs6UkZEh9SqLD8nPzydtbW16+vSp3OroaKTJI6ynxyEHBwdUVVWhvLxcLuV/8cUX\nCAgIQEJCAo4cOQJ/f3/cvXuX9fo+oKamRnIuRZcuXXD27FkMHTpUrlNILl68CFdXV/Tt21dudTD/\nH0t6HLOzs0NycrJc6zA1NcWxY8cwadIkLF26FGvWrEFVVZVc62yPMjIyMHnyZJw+fRq//vorNm/e\n3OKdUj5HYmIigoKC5F4P8xpLehxzdXXFjh075D7NpFu3bvD29sb+/fvx4MEDjBs3DpmZmTKZK9ie\nERHKysqwYcMGzJkzB/Pnz8fevXthY2PTKtu0V1dXo6SkBJaWlnKvi3mNJT2O2dvb4+XLl7h+/Xqr\n1Kerq4vDhw8jODgYq1atwuLFi2W28L69aWhowJ49e+Dn54e6ujqcPHkS3t7erRrD+vXr4eDgILMJ\nzszHsQ0H2oDw8HAUFBQgMjKyVTcOICJs3rwZkZGRWLJkCebMmQNNTc0Ov3mBQCDAvXv3sGjRIsn6\n2ZacSSutkpISGBoaIjs7m5P62zNp8ghLem1AVVUVvL29ceDAgQ9uxCkPRIT79+9j//79uHHjBkaP\nHo2ZM2e2ehytQSwWIz4+HtHR0WhqasK3334LT09Pzta57ty5E2lpaTh8+HCH/6CRNanyiLSPjj8X\nB1W2C4GBgS0+H1VWSktLyd/fn/T09OjXX3/9rE092zKRSETZ2dk0bNgw6tu3L6WmpnIdEjU0NNDE\niROpuLiY61DaJWnyCOvptRFJSUmIjIzE77//zuk5pyKRCDdu3MCRI0fw8OFDDBkyBJ6enrCzs2t3\nvZH8/HzEx8cjISEBqqqq8PLygoeHR6s8kf2YnJwchIeH4+DBg1yH0i6xnl4HUF1dTVZWVnT58mWu\nQyGi172jiooK2rp1K/Xu3Zv+53/+h65cuSKXJViy9urVK1q4cCF169aNAgICKC8vj4RCIddhNePh\n4UEHDhzgOox2S5o8wnp6bci2bdtw8+ZN/Pvf/27R9uvyUlZWhpMnTyIuLg4NDQ1wcnKCo6MjBgwY\ngG7dunEdHpqampCbm4vMzEwkJSXh5cuXcHZ2hp+fH0xMTLgO7y3Xrl2Dn58fMjIy2GahLcQeZHQQ\nAoEAo0aNQlRUFMzNzbkO5y0NDQ0oKyvDiRMnsGfPHlRXV8PLywvTp0/HwIEDW31YXlhYiKNHj2L/\n/v1oaGjAxIkTMX36dPTu3Rvq6uptcjje1NSEBQsWwN7eHvPmzeM6nHaLJb0OJCIiAjweD0uXLuU6\nlA8iImRlZeHMmTPIyMhAU1MTjI2NMWTIEJibm8PAwADa2trQ0NCQOvn8OYG3uLgYeXl5uHnzJh4/\nfozq6mpYW1vDzc0Nrq6uMt/qSR7y8/Mxe/ZsxMbGsjNtpcCSXgeSm5uLgIAAXLx4sd1MWK2vr0dJ\nSQmKiopw7do13LhxA7m5uRAIBDAwMICFhQVMTU1hbGwMbW1t9OjRA1paWujatStUVVUBvE5sdXV1\nKCoqQlFREfLy8nDv3j3cv38fhYWFUFZWhoWFBezt7eHg4AB9fX306NGjzfbo3mf9+vVQU1Njy86k\nxJJeByISiTBjxgwMGjQIy5Yta1d/0G8Si8Xg8/nIzs7G48eP8fTpU+Tn56O2thZCoRBCoRAikUiy\n+YGKigqUlZXxxRdfQF1dHfr6+jA3N4epqSkGDBgAMzMzTp9qy8KTJ0/g5uaG+Ph4qQ4DZ+Sc9Coq\nKjB79mzcvXsXSkpK2LNnD8zMzCRbZvfp0wdHjx6VnCQfGhqKqKgoKCsrY9u2bW/t98+S3sfduXMH\nM2bMwNmzZ9GzZ0+uw5GpxsZGCASC9ya9zp07Q01Nrd0m+/cRiURYsmQJvvrqK6xdu7bdJ3CuyXXK\nyowZMyR7sTU2NlJFRQWtWLGCwsPDiYgoLCyMVq5cSUREd+/eJRsbGxIKhcTn88nExIREIlGz8j6h\nSoaIFi9eTNHR0VyHwcjIgwcPyMnJierr67kOpUOQJo988OOmsrIS6enpmDVrFoDXn8bdu3fH6dOn\nMXPmTADAzJkz8fvvvwMATp06BV9fX6iqqqJPnz4wNTVttYX0Hc3s2bNx6NAhdshPBxEdHQ0fH592\nc5+2I/vgokM+nw9tbW0EBATgjz/+wODBg7F161YUFxdL1mbq6uqiuLgYwOspBMOHD5dcb2hoiIKC\ngrfKXbt2reT/XVxc4OLiIoMfpWPp378/NDU1ERUVhTlz5nAdDiOF3NxcyTxHpmVSU1ORmpoqk7I+\nmPSampqQlZWF7du3Y8iQIQgMDERYWFiz9ygpKX3w/su7vvdm0mPeTVVVFStWrMDMmTPh7u4OIyMj\nrkNiWqC2thY//fQTlixZgl69enEdTrv1fztHISEhLS7rg8NbQ0NDGBoaYsiQIQCAqVOnIisrC3p6\nenjx4gUAoKioCDo6OgAAAwMD5OfnS65//vw5DAwMWhycohs8eDC8vLwQExMj13rq6upQXV3dbChN\nRKiurm72vurq6rcOE6+rq0NdXZ1c4/uQ+vr6Nn3A+dWrVyEUCjF//vwO93Cmvfpg0tPT04ORkREe\nPnwI4PW21lZWVvD09ER0dDSA1/cqJk2aBACYOHEiYmJiIBQKwefz8ejRIwwdOlTOP0LH9sMPPyAh\nIUFyC0EeRo0aBS0tLfzrX/+SvFZQUPDWErNu3brBwMAAT58+lbw2duzYt57Qt6aAgABYW1tzVv+H\nCAQCbN26FStXruQ6FOYNH31u/s9//hPTp0+HjY0NcnJy8PPPPyM4OBgXLlyAubk5kpOTERwcDACw\ntLSEj48PLC0tMW7cOOzcuZN9uklJX18fTk5O+OGHH+RaT1NTE9avX4+mpqYPvq+yshI7duxg044+\nQUREBJSVlTFixAiuQ2HewCYntwMlJSUYPXo0wsLCMG7cOJmXP2LECOTl5UFFRQUBAQEICQlBQUEB\njIyMmv1bKSkpwdfXF5mZmUhOToaRkRGcnJxARLh06dIn1zd69Gjo6upi9OjRcHBwgImJyScvyaqp\nqUFsbCxKS0sxaNAgREREIDMzE3w+H8DrZV5paWkoKyuDpqYmHB0dJaeMvXmtnZ0dysrKUFBQIJcH\nRVlZWZg7dy4OHz7MJiLLAdtaSgHcvn2bxowZI5eyhw8fTo6OjvTdd99Rr1696PHjx5Sfn//WvxUA\nevLkCenr69Pf//53IiJydHQkBweHz6rvzJkz5ODgQGpqavTll1+Su7s7nT9/npqamj54nUAgoG++\n+YbU1NSIx+ORgYEB9e3bl/r06UNEROXl5TRgwABSVVUlJSUlUlFRIQsLC3r27BkJBALy8fGRXKuv\nr08mJiZkYGDwWbF/Kh8fH4qLi5NL2Qw791YhWFhYwMrKCqtXr5bLubXKysoICgpCZWWlZN7lu3Tu\n3BkLFy5ERESEpHf1uTw8PJCWlobMzEwEBgZCIBDA19cXVlZWCA4Oxr1799553a1bt5CUlIRly5ah\ntLQU+/fvb3aa27Jly1BfX48LFy6gsrISFy9ehJKSEoKDg5GTk4OkpCQEBgbi1atXiImJ+ehQviWI\nCLt27QKPx4OTk5PMy2dkQHa599NwUGWHUVBQQDo6OpSSkiLTcocPH07Ozs5ERBQUFESGhob0+PHj\nd/b0CgsLKTc3l/T09GjevHn09ddfv7enJxQKydLSUvJfYWHhO99z8uRJsrW1JQDE4/Fo+/bt7yzv\nxIkTpKysTK9evZJc6+npKenpaWho0F//+tdmG52Gh4eThoYGnTlz5q1rp0yZIvOe3rVr18jU1JQe\nP34s03KZ5qTJI9yciMK0SM+ePXH06FFs2bIF1tbW6NGjh8zrmDdvHg4ePIg1a9a89z0WFhaYPHky\nzp07B6FQ+N6NOpWUlJp9788DeEpLS3H//n0kJSUhJiYGL168gLm5OYKCguDn54eBAwe+s7w/16sK\nhUIArzc1eHOajaqq6lvn+AoEAqiqqoLH40FJSQkCgQDA6x6ZrFe7VFVVYfPmzdi+fXub3LyU+V+y\ny72fhoMqO5ywsDCaMmWKzLZAf7On19jYSLNnzyYVFZX39vSIiEpKSkhbW5uUlJQ++57e5MmTSVNT\nk0xMTGjdunWUmZlJpaWlH92KPjMzk3r06EFz586lkpISOnPmDOno6Eh6eosXL6aePXvSuXPnqKKi\ngs6fP0+9evWi77//nrKyskhHR4fmzp1Lr169ori4ONLT05NZT08gENDUqVNp9erV1NjYKJMymfeT\nJo+wpNcOVVVVkZOTE0VERHz05v+neDPpERHdunWLOnXq9MGkR0QUEhJCPB7vs5PeTz/9RLGxsSQQ\nCD7rOqFQKDn7QkVFhfr3708WFhaSpFdVVUUjR46krl27Eo/Hoy5dupCjoyM9f/5ccq2GhgapqKiQ\nubk59evXj4yNjT8rhncRi8W0c+dOcnFxodraWqnLYz5OmjzCpqy0U0VFRZg1axYWLVqECRMmSFVW\neno6eDweHBwcALwe+iUmJqKurg5eXl6S9506dQpjx46VLJovKSlBRkYGunfv3mo37RsaGnDjxg1U\nVVXBxMQEVVVVqKiowJgxYwAAr169wp07d1BTU4OuXbvC0tJSsk68vr4eN2/eRFVVFXr06IHly5dD\nXV1d6jWxJ06cQHR0NHbt2gV9fX2pf0bm49gmogoqOzsbU6ZMwe7du+Hq6somgn/EkiVL4OLiAj09\nPcTExGD37t04cOAApkyZ0qLyiAinT5/G/PnzkZKSAgsLCxlHzLyPNHmEPchox2xtbbF3716sXr0a\n6urqbMnfR5iYmCA4OBj//e9/oaenh1WrVkmWULZEeno6du7ciYSEBJbw2hHW0+sAUlJSMGfOHOzd\nuxdff/0125VXzsRiMRISEhAQEIDjx4/D0dGR65AUDhveKjgiwuUwUsQLAAAIvklEQVTLl7Fhwwb4\n+fnB39+f65A6LKFQiO3btyMtLQ0///yzZAcipnWxpMcAeL0zioeHB5ycnLBx40a2S6+MlZeXIyAg\nAJWVlTh+/Di++uorrkNSWNLkETYO6kAMDAyQkpICTU1NzJgxA1evXmUfMDIgFApx7NgxTJs2DW5u\nbrhw4QJLeO0Y6+l1QGKxGOfPn8esWbMQEREBX19frkNq15YuXYq0tDQcO3YMffv2ZU/J2wDW02Oa\n4fF4cHd3x8WLF3H06FEsX74chYWFXIfV7mRmZmL8+PEQCoVISEiAsbExS3gdAEt6HZiZmRn27duH\nL7/8EpMmTcKDBw+4DqldaGpqwj/+8Q/MmDEDCxcuxJYtW+SyzpnhBhveKgAiwrlz57B69Wp4eXlh\n0aJF7J7UO4jFYuTk5GDTpk0QCoUIDQ2Fqakp12Ex78CGt8wHKSkpwcPDA3FxcaipqcGoUaOQmJjI\nPnzeIBaLsX79evj4+MDT0xP79u1jCa+DYj09BZSamoo1a9bA3t4eixcvRq9evRR2QrNQKERaWhpW\nr14Na2trbNq0Cd27d+c6LOYj2Dw95rMVFxfj0KFDkqkYCxculOx3pyhu376NtWvXQiQSYfny5bC3\nt0fnzp25Dov5BCzpMS3G5/MRGBiI+vp6rFq1CoMGDULXrl25DktuxGIxCgsLsX//fsTExOC7777D\nggUL2ETudoYlPUYqQqEQFy9exN69e1FZWYnFixdj7NixXIclcy9fvsSOHTuQkpKC8ePHw8fHB8bG\nxlyHxbQAS3qMzMTHxyMoKAi9e/fG2rVrYWVl1a57QSKRCGVlZYiJiUFkZCQcHR2xceNG6OjocB0a\nIwWW9BiZKi8vR2JiIk6cOIH6+np4e3vjm2++aVfJTywW48aNGzh48CAePHgABwcHTJ48GVZWVmyC\ncQfAkh4jN9nZ2fjxxx9x//59rFmzBt9++y26dOnSJh96EBEEAgHu3buH1atXIyMjAyEhIfj++++h\npqbGdXiMDLGkx8hVY2MjMjIykJiYiNu3b0s2LHV2dkb//v2hrKzMaXxlZWVISUnBtWvX8OTJE+jp\n6cHV1RXu7u7Q0NDgNDZGPljSY1oFEUEsFuPWrVsICwtDXFwcRowYgQULFmD8+PGtPt3j5s2b2LVr\nF2JiYmBiYoIff/wRU6dOhbq6OhvCdnAs6TGcKC4uRnJyMi5dugQ+n4/OnTvD1NQU1tbWMDU1Ra9e\nvaCnpyd1T7CyshLPnj1DXl4ecnNzcefOHZSWlkJLSwvDhg2Ds7MzrKys2uSQm5EPlvTaudTUVLi4\nuHAdRouJxWLU1dWhuroa169fR2xsLK5evYqCggJoaWmhf//+6N+/P8zMzNC7d28YGhpCV1e3WTKs\nqqpCbW0tnj9/jqSkJKipqeHBgwe4f/8+CgsLoaWlhSFDhmDkyJEYOXIkNDU10aVLF6iqqnL4k7eO\n9v77IWupqalwdXVlBwO1Z+39l5rH40FdXR3q6urw8vKSHBtZUVGBhw8fgs/n49mzZ8jJyUFKSgpq\na2tRX1/f7JdWTU0NKioq6Nq1Kx49eoQJEybA3d0d8+fPh6mpKQwMDBR2yNrefz9kLTU1VarrWdJj\n5EZTUxNDhw5tdkqbWCxGY2Mjmpqamr2Xx+OBx+NBVVUV69atw5o1a1o7XEZBsKTHtCoej4dOnTqh\nU6dOXIfCKChO7ukxDMNIq93c02MPMRiG4ZJibqLGMIzCYkmPYRiFwpIewzAKpVWTXnx8PCwsLGBm\nZobw8PDWrJozs2bNgq6uLgYMGCB5raysDGPGjIG5uTnc3NxQUVEh+V5oaCjMzMxgYWGB8+fPcxGy\nXOXn58PV1RVWVlawtrbGtm3bAChumzQ0NGDYsGGwtbWFpaUl/va3vwFQ3Pb4k0gkgp2dHTw9PQHI\nuD2olTQ1NZGJiQnx+XwSCoVkY2NDubm5rVU9Z9LS0igrK4usra0lr61YsYLCw8OJiCgsLIxWrlxJ\nRER3794lGxsbEgqFxOfzycTEhEQiESdxy0tRURHdunWLiIiqq6vJ3NyccnNzFbpNamtriYiosbGR\nhg0bRunp6QrdHkREERER5OfnR56enkQk27+ZVkt6V65cobFjx0q+Dg0NpdDQ0NaqnlN8Pr9Z0uvX\nrx+9ePGCiF4ngX79+hER0S+//EJhYWGS940dO5auXr3ausG2Mi8vL7pw4QJrE3qd/Ozt7enOnTsK\n3R75+fk0atQoSk5OJg8PDyKS7d9Mqw1vCwoKYGRkJPna0NAQBQUFrVV9m1JcXAxdXV0AgK6uLoqL\niwEAhYWFMDQ0lLyvo7dRXl4ebt26hWHDhil0m4jFYtja2kJXV1cy9Ffk9li6dCk2bdrU7IQ+WbZH\nqyU9Nin53ZSUlD7YNh213WpqauDt7Y3IyMi39rxTtDbh8XjIzs7G8+fPkZaWhpSUlGbfV6T2OHv2\nLHR0dGBnZ/feOb3StkerJT0DAwPk5+dLvs7Pz2+WoRWJrq4uXrx4AQAoKiqSnNfwf9vo+fPnMDAw\n4CRGeWpsbIS3tzf8/f0xadIkAKxNAKB79+6YMGECbt68qbDtceXKFZw+fRp9+/aFr68vkpOT4e/v\nL9v2kM+o/G2NjY1kbGxMfD6fBAKBwjzIIHr7nt6KFSsk9yFCQ0PfuikrEAjo6dOnZGxsTGKxmJOY\n5UUsFpO/vz8FBgY2e11R26SkpITKy8uJiKiuro6cnJwoMTFRYdvjTampqZJ7erJsj1ZLekREsbGx\nZG5uTiYmJvTLL7+0ZtWcmTZtGunr65OqqioZGhpSVFQUlZaW0qhRo8jMzIzGjBkj+aUnItqwYQOZ\nmJhQv379KD4+nsPI5SM9PZ2UlJTIxsaGbG1tydbWluLi4hS2TXJycsjOzo5sbGxowIABtHHjRiIi\nhW2PN6Wmpkqe3sqyPVp9wwGGYRgusRUZDMMoFJb0GIZRKCzpMQyjUFjSYxhGobCkxzCMQmFJj2EY\nhfL/AIbqez0P4zalAAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "open(\"hmm3.dot\",\"w\").write(\"\"\"\n",
    "digraph hmm3 {\n",
    "rankdir = \"LR\";\n",
    "state -> state2 [label=\"AT -> The\"];\n",
    "state -> state2 [label=\"AT -> a\"];\n",
    "state -> state2 [label=\"NN -> fox\"];\n",
    "state -> state2 [label=\"NN -> dog\"];\n",
    "state -> state2 [label=\"VBD -> jumps\"];\n",
    "state -> state2 [label=\"PP -> over\"];\n",
    "state2 -> state [label=\"AT -> The\"];\n",
    "state2 -> state [label=\"AT -> a\"];\n",
    "state2 -> state [label=\"NN -> fox\"];\n",
    "state2 -> state [label=\"NN -> dog\"];\n",
    "state2 -> state [label=\"VBD -> jumps\"];\n",
    "state2 -> state [label=\"PP -> over\"];\n",
    "}\n",
    "\"\"\")\n",
    "!dot -Tpng hmm3.dot -o hmm3.png\n",
    "figsize(12,8)\n",
    "imshow(imread(\"hmm3.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dffb811",
   "metadata": {},
   "source": [
    "For the simple n-gram taggers, the \"hidden\" state sequence was trivially given by the tag sequence.\n",
    "\n",
    "Weighted finite state transducers offer a lot more power. How are we going to use this power?\n",
    "\n",
    "One way we may be able to use this power is to do the following:\n",
    "\n",
    "- write down a full natural language grammar\n",
    "- approximate this grammar using finite state models\n",
    "- translate into a finite state transducer representing the non-terminals (labels) and terminals (words)"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}